crystalline_obstruction

This package computes an approximation the crystalline obstruction map on its space of Tate classes. In practice, this gives rigorous upper bounds on the:

• middle geometric Picard number of a given projective hypersurface;
• the geometric Picard number of a Jacobian; or
• the dimension of the geometric endomorphism algebra of a Jacobian.

See examples below.

For more details see:

• "Effective obstruction to lifting Tate classes from positive characteristic" by Edgar Costa and Emre Can Sertoz. (arXiv:2003.11037)

To compute a p-adic approximation for the Frobenius matrix we rely on the libraries controlledreduction, and (hypellfrob). At the moment we support:

• Jacobians hyperelliptic curves with a Weierstrass point over Qp (hypellfrob)

• Jacobians of quartic curves (controlledreduction)

• quartic and quintic surfaces (controlledreduction)

Installing

sage -pip install --upgrade git+https://github.com/edgarcosta/crystalline_obstruction.git@master#egg=crystalline_obstruction

If you don't have permissions to install it system wide, please add the flag --user to install it just for you.

sage -pip install --user --upgrade git+https://github.com/edgarcosta/crystalline_obstruction.git@master#egg=crystalline_obstruction

Examples

Jacobians of hyperelliptic curves with a Weierstrass point over Qp

Example 5.1

sage: from crystalline_obstruction import crystalline_obstruction
sage: f = ZZ['x,y']('x^5 - 2*x^4 + 2*x^3 - 4*x^2 + 3*x - 1 -y^2')
sage: crystalline_obstruction(f=f, p=31, precision=3) # bounding dim Pic
(1,
 {'dim Li': [1],
  'dim Ti': [2],
  'factors': [(t - 1, 2)],
  'p': 31,
  'precision': 3,
  'rank T(X_Fpbar)': 2})

Bounding the geometric dimension of Endomorphism algebra

sage: from crystalline_obstruction import crystalline_obstruction
sage: f = ZZ['x,y']('x^5 - 2*x^4 + 2*x^3 - 4*x^2 + 3*x - 1 -y^2')
sage: crystalline_obstruction(f=f, p=31, precision=3, tensor=True) # bounding dim End
(1,
 {'dim Li': [1],
  'dim Ti': [4],
  'factors': [(t - 1, 4)],
  'p': 31,
  'precision': 3,
  'rank T(X_Fpbar)': 4})

Example 5.2

With prec = 100 takes about 3 minutes

sage: f = ZZ['x,y']('x^5 - 2*x^4 + 7*x^3 - 5*x^2 + 8*x + 3 -y^2')
sage: crystalline_obstruction(f=f, p=4999, precision=20) # bounding dim Pic
(2,
 {'dim Li': [2],
  'dim Ti': [2],
  'factors': [(t - 1, 2)],
  'p': 4999,
  'precision': 20,
  'rank T(X_Fpbar)': 2})

Hyperelliptic curve given in a non-Weierstrass format

sage: f = ZZ['x,y']('(2*x^6+3*x^5+5*x^4+6*x^3+4*x^2+x) -y*(x^4+x^3+x) -y^2')
sage: crystalline_obstruction(f=f, p=59, precision=3)
(3,
 {'dim Li': [1, 2],
  'dim Ti': [3, 6],
  'factors': [(t - 1, 3), (t^2 + t + 1, 3)],
  'p': 31,
  'precision': 3,
  'rank T(X_Fpbar)': 9})

Jacobians of quartic plane curves

Example 5.3

sage: f = ZZ['x,y,z']('x*y^3 + x^3*z - x*y^2*z + x^2*z^2 + y^2*z^2 - y*z^3')
sage: crystalline_obstruction(f, p=31, precision=3) # bounding dim Pic
(1,
 {'dim Li': [1],
  'dim Ti': [3],
  'factors': [(t - 1, 3)],
  'p': 31,
  'precision': 3,
  'rank T(X_Fpbar)': 3})

Example 5.4

sage: f=ZZ['x,y,z']('x^3*z+2*x^2*z^2-x*z^3-y^4')
sage: crystalline_obstruction(f,p=43,precision=4,tensor=True)
(9,
 {'precision': 4,
  'p': 43,
  'rank T(X_Fpbar)': 18,
  'factors': [(t + 1, 4), (t - 1, 6), (t^2 + 1, 4)],
  'dim Ti': [4, 6, 8],
  'dim Li': [2, 3, 4]})
sage: crystalline_obstruction(f,p=43,precision=4,tensor=False)
(5,
 {'precision': 4,
  'p': 43,
  'rank T(X_Fpbar)': 7,
  'factors': [(t + 1, 2), (t - 1, 3), (t^2 + 1, 1)],
  'dim Ti': [2, 3, 2],
  'dim Li': [1, 2, 2]})

Product of 3 elliptic curves over x^3 - 3*x - 1

sage: f=ZZ['x,y,z']('x^3*z + x^2*y*z + x^2*z^2 - x*y^3 - x*y*z^2 - x*z^3 + y^2*z^2')
sage: crystalline_obstruction(f=f, p=31, precision=3) # bounding dim Pic
(3,
 {'dim Li': [1, 2],
  'dim Ti': [3, 6],
  'factors': [(t - 1, 3), (t^2 + t + 1, 3)],
  'p': 31,
  'precision': 3,
  'rank T(X_Fpbar)': 9})

Another gennus 3 plane quartic

sage: f = ZZ['x,y,z']('x^4+x^2*y^2+2*x^2*y*z-x^2*z^2-6*y^4+16*y^3*z-12*y^2*z^2-16*y*z^3-6*z^4')
sage: crystalline_obstruction(f=f, p=5003, precision=3) # bounding dim Pic
(6,
 {'dim Li': [2, 2, 2],
  'dim Ti': [2, 3, 4],
  'factors': [(t + 1, 2), (t - 1, 3), (t^2 + 1, 2)],
  'p': 5003,
  'precision': 3,
  'rank T(X_Fpbar)': 9})
sage: crystalline_obstruction(f=f, p=5003, precision=3, tensor=True) # bounding dim End
(9,
 {'dim Li': [2, 3, 4],
  'dim Ti': [4, 6, 8],
  'factors': [(t + 1, 4), (t - 1, 6), (t^2 + 1, 4)],
  'p': 5003,
  'precision': 3,
  'rank T(X_Fpbar)': 18})

Quartic surfaces

Example 5.6

sage: f = ZZ['x,y,z,w']("x^4 + y^4 + z^4 + w^4 + 101^3*x*y*z*w")
sage: crystalline_obstruction(f, p=101, precision=3)
(20,
 {'dim Li': [1, 7, 12],
  'dim Ti': [1, 7, 12],
  'factors': [(t - 1, 1), (t - 1, 7), (t + 1, 12)],
  'p': 101,
  'precision': 3,
  'rank T(X_Fpbar)': 20})
sage: crystalline_obstruction(f=f, p=101, precision=4)
(19,
 {'dim Li': [1, 6, 12],
  'dim Ti': [1, 7, 12],
  'factors': [(t - 1, 1), (t - 1, 7), (t + 1, 12)],
  'p': 101,
  'precision': 4,
  'rank T(X_Fpbar)': 20})

Example 5.7

sage: f = ZZ['x,y,z,w']("y^4 - x^3*z + y*z^3 + z*w^3 + w^4")
sage: crystalline_obstruction(f=f, p=89, precision=3)
(4,
 {'dim Li': [1, 0, 3, 0],
  'dim Ti': [1, 1, 4, 4],
  'factors': [(t - 1, 1), (t + 1, 1), (t - 1, 4), (t^4 + 1, 1)],
  'p': 89,
  'precision': 3,
  'rank T(X_Fpbar)': 10})

Example 5.8

sage: f = ZZ['x,y,z,w']("x^4 + 2*y^4 + 2*y*z^3 + 3*z^4 - 2*x^3*w- 2*y*w^3")
sage: crystalline_obstruction(f=f, p=67, precision=3)
(3,
 {'dim Li': [1, 2],
  'dim Ti': [1, 3],
  'factors': [(t - 1, 1), (t + 1, 3)],
  'p': 67,
  'precision': 3,
  'rank T(X_Fpbar)': 4})

Quintic surfaces

It takes about 1 day of CPU time to compute the zeta function of a quintic surface. We may still demonstrate the functionality of crystalline_obstruction by providing the characteristic polynomial and an approximation of the Frobenius matrix.

Example 5.10

sage: # f doesn't play a role
sage: f =  ZZ['x,y,z,w']('10*x^4*y + 3*x^4*w - 10*x*w^4 + 3*y^4*w - 3*z^5 - 23*x^3*y*z')
sage: p, prec, cp, frob_matrix = [23, 6, [1, 0, 0, 0, -85169, 0, 0, 0, -48851843370, 0, 0, 0, 603386141590105, 0, 0, 0, 3460669831806921011036, 0, 0, 0, 39592132843636527277692216, 0, 0, 0, -116969749152102735961006849109758, 0, 0, 0, 32732931572473581734064117661723788478, 0, 0, 0, -867646721730951228138863823200631295521336, 0, 0, 0, -5939048712179129622337175952133368350994228438236, 0, 0, 0, -81091389047171959500149106085257035712245669586120505, 0, 0, 0, 514141964489056211156037329282607472395213736740030063102570, 0, 0, 0, 70195024966720298936256907286265573899667849017556809742662099729, 0, 0, 0, -64542751082767918430897798773372060387158551764172664212787858136578721], [[43145601836, 35420286327, 27049816172, 20137969355, 2878219241, 11345072, 1555741252, 193785856, 2949727069, 965882079, 2037967003, 583118034, 2617496370, 658203581, 1366351294, 494709990, 1861415346, 2179594195, 919758109, 986893200, 1625552186, 2663839001, 1823113699, 2592775464, 2517487149, 1703787744, 1691432420, 1578490644, 2272546119, 2586889603, 2305183947, 1279774096, 1644135450, 2195528963, 148322262, 145807327, 1127363653, 413106703, 166922569, 340504788, 1870742237, 492979907, 943523687, 604499524, 20213918, 2038789828, 424238082, 513674962, 22472441, 54796591, 87871245, 27553740], [76351266693, 1653383152, 48979429706, 30551797230, 2636662270, 1914377860, 29116505, 181840553, 3219683244, 1951847206, 2161625514, 291127261, 2291446668, 755413587, 38054259, 434794875, 1225215129, 2944381248, 833134244, 3113042134, 323142939, 2660911193, 124099007, 1717189729, 5609125, 1402127081, 1545409583, 498455609, 2530088228, 3085028755, 1016328945, 887194111, 12243774, 1465801983, 1004836374, 1119255923, 2886081492, 24995549, 1141201120, 1886194810, 382762665, 1289586425, 3372476936, 213972473, 419694064, 399097380, 3121904126, 2489215595, 134715794, 109018138, 48155237, 141777182], [64957489594, 14744045718, 25852998108, 23745728724, 928551262, 2119591818, 833133002, 2597680053, 3144649631, 1739765931, 2861686956, 3271970478, 2476173123, 312642036, 151268378, 1700741716, 442552982, 1232672419, 782790717, 955956360, 1457689561, 3255048343, 1096779518, 670769700, 2875290559, 3012001133, 1949365782, 484734522, 183394916, 1937948168, 1757310124, 3342437878, 1426436241, 2154195870, 2057816808, 1406984566, 1301411116, 1658399590, 2256316836, 3026127020, 1357059639, 2432209106, 2126293604, 845754758, 1621494940, 2426584755, 2583759441, 75874355, 96373936, 12502618, 84684835, 79999103], [76939530034, 65245824747, 43832676029, 67810880151, 2335073137, 195753943, 2427015269, 3107385744, 1228381401, 1748677695, 508431491, 3226892364, 1325045249, 2343760697, 142545720, 2449986128, 1743282723, 1547980822, 1841846187, 613774918, 1274850877, 2797907542, 2415674015, 739347972, 1692546770, 58500684, 763010556, 2957306742, 2748952433, 115257554, 2778897789, 3086519293, 2943013254, 2741293088, 1519886575, 2560541470, 2621715536, 125521580, 3029973218, 1415617179, 3370806009, 2002478578, 1748434539, 956679664, 529020010, 2854357247, 86807198, 3066548669, 94520432, 31193870, 95605391, 58612354], [53105791051, 24076203488, 46505406209, 53244168458, 2583523622, 3144995896, 1182030145, 436692766, 1182976388, 956286663, 2564597221, 1799216676, 1699444424, 3130929993, 2911434806, 458322242, 2530153962, 2752381595, 2887021663, 690154882, 363981670, 2822543624, 3040579875, 258869991, 1975750324, 2578555553, 3342858364, 2018853405, 3124487509, 1420980043, 937696890, 2201760882, 2621837344, 2213450402, 1084670409, 2368721792, 34076869, 1698495628, 600955477, 997708007, 424868397, 2555080603, 2524548885, 1855741062, 1125757586, 525548988, 1351402927, 1344973369, 110164245, 72444915, 127864098, 38561519], [73116281986, 34596178387, 44219376616, 67215120880, 1424905522, 2044453049, 1389802646, 2895937429, 323472184, 1570197465, 3341285946, 3245268145, 2123043014, 2943437374, 2394530299, 1939293461, 1631163657, 2452635015, 1812651459, 3127706221, 679033692, 2876922777, 2965502102, 319388327, 1867262866, 2300658122, 2087304073, 1049447036, 157861742, 595560919, 2109811160, 1807585157, 1057946778, 74660530, 2505579267, 293647762, 2042485905, 2711731970, 1416122535, 2762143485, 2805277524, 1442502224, 410663689, 1136024602, 449972920, 2071799129, 3006445184, 557154070, 121564134, 110515084, 147767506, 61160560], [57888016647, 68548901805, 37281031131, 48912683660, 1452094167, 1811347957, 1242004186, 3192343213, 2974267724, 3075404244, 2670991610, 2369541788, 3404535141, 1186237282, 96965585, 1334745246, 2283126625, 536564976, 2538009566, 1856539967, 355747049, 1209052822, 474999565, 1901824230, 589784952, 10648678, 1436496211, 1340840844, 3150491171, 2067453946, 2950978522, 1692599210, 754101782, 3281361815, 1160314212, 1212925516, 1486435766, 2750992809, 2903904169, 890518140, 1377750301, 974405166, 2346248469, 1678059760, 3336730037, 3071567062, 961731982, 712060979, 19378646, 7970338, 42973401, 31378617], [20717392048, 63960583804, 16206189551, 70835291118, 890179787, 246369882, 2039339275, 1188532544, 3029210078, 840577113, 1348038326, 1256893650, 970216797, 976423968, 1900928196, 3138635246, 3066272370, 788699854, 2349683657, 1103540046, 3322743737, 3325096522, 909995575, 1683898494, 472054208, 1487587146, 1727077222, 1017381034, 2613949080, 3187769893, 1621446042, 1428755860, 1130699780, 789568035, 2587463315, 2799514460, 260450229, 1393730517, 944443871, 2667736167, 214685082, 515011078, 3186846259, 1403515591, 3833617, 305321044, 2548041913, 487299206, 57269297, 88516079, 86712302, 87305688], [35075027071, 31521865792, 55167271782, 58612187494, 1248360765, 985926303, 3182491692, 626025684, 3321887424, 554719911, 2641618218, 1558876612, 2991831490, 2333342065, 1474437080, 2562146387, 1255130010, 587532493, 2736526292, 2884975606, 2653150280, 426805204, 1138235868, 2629132806, 2834211501, 1072821752, 2506099757, 1008464900, 1339909505, 846034599, 1820232581, 3391486229, 1782743984, 2362858356, 1882488981, 241108724, 900599385, 1860824637, 1906209065, 2948893411, 2974734233, 2964874064, 3307688834, 2901920603, 2262363145, 965947445, 3222508794, 3034953822, 128500822, 8377444, 119699238, 42880020], [12179982718, 69259063145, 9011722897, 45667839451, 2393330021, 1724353654, 1650735576, 3010162513, 3235663529, 1851237041, 2985071629, 2925568904, 762733912, 494438245, 1727395427, 2799533297, 2224849685, 2013221234, 2172566108, 1536963293, 3044227491, 2163876846, 3096098494, 2189538406, 1257086252, 478001847, 1129789072, 186142933, 181073388, 724940772, 2410126438, 2938292895, 174411300, 3317716213, 1479159900, 3219607459, 2363722512, 2935695620, 1791012162, 2599629602, 2492614190, 760430209, 1369613844, 2108400064, 173124151, 1623779323, 1236277163, 785100952, 45800614, 104499655, 108755733, 5199384], [53278722209, 23310891782, 71068225159, 20445874863, 2173798724, 2172262761, 2023609736, 1627220376, 2812933557, 3281603752, 2834278385, 2316630541, 80917128, 677442391, 1926789741, 1083632534, 663335548, 508890065, 364562926, 275257261, 895061445, 2397962957, 1198035201, 1988769865, 948822565, 3403151231, 3105887685, 3274670931, 2888660896, 2726974392, 589886083, 622912887, 90433907, 1849297405, 779251316, 2857385726, 602764381, 420693920, 1379585172, 106086120, 2099829758, 1103681013, 2692724678, 1618481779, 2898690874, 784420129, 2016255279, 2385211297, 116972459, 77335372, 90287523, 142330198], [64871454621, 57326935971, 61823488871, 15658121746, 932282322, 1013928228, 2273343874, 1511453648, 1113270150, 3324083602, 2398943056, 531689505, 962939390, 1279003021, 1039158515, 1577746962, 3256722858, 3092492416, 2388047059, 1286945220, 1766272879, 2294918219, 1440110247, 1376015181, 1535446972, 3131523416, 2964546107, 3297413791, 956611377, 2738720331, 2739052060, 1573461648, 2171911850, 601236284, 1637009245, 2545193708, 1307635468, 2724228560, 856386761, 3351777419, 3328800465, 2531954356, 77859853, 1530723117, 1440033381, 2247702347, 3215229294, 2370841426, 66530325, 27998380, 99675288, 20986277], [49736139872, 72237041666, 71146475368, 62242323563, 1807199654, 200124495, 1861750180, 1907715611, 1743601319, 1287067994, 2943193229, 2820562335, 3178385111, 1840005014, 132372981, 2273796951, 318936423, 489636052, 2329646724, 2123574590, 2504866681, 62474348, 17128399, 2842504496, 2341222555, 1510167603, 1923177131, 3394786798, 341649866, 3338723953, 2891399667, 1616953245, 2675788191, 2854996026, 3284664201, 100489829, 446689808, 1325050815, 434867739, 1402852869, 490515802, 920045517, 84683677, 36877234, 2127362414, 1955956156, 614917098, 617872069, 6078916, 12266003, 37972796, 35779620], [7399384855, 77298324284, 74774063773, 78046242999, 1562270101, 2176398230, 3230893398, 1026577607, 2864188666, 1821012994, 2447450539, 948410566, 3123856481, 273531548, 1104025829, 1882728549, 2830241701, 3167543946, 2730965559, 671863902, 3326534551, 133010817, 3053187302, 451705878, 851526884, 2781203838, 1765917552, 2044844532, 2176970769, 3218528506, 1958342659, 1570821317, 518029161, 278279231, 424468956, 3191718464, 2753760744, 3249370540, 3139489926, 1994988789, 1430176271, 1698296609, 3257103140, 2832371754, 619036076, 2058080664, 2347002639, 2791873791, 25167521, 143882096, 40343003, 49993338], [1156822490, 50304973043, 65364284775, 39321505272, 1207160175, 1494871959, 1783328138, 100876298, 319092501, 861246868, 1418314021, 2402613994, 2059945389, 569955433, 3198830524, 2770357291, 291045220, 1794915239, 225402783, 1962995260, 2537373754, 164391235, 784336685, 1511535137, 2616889561, 1805956642, 1469023225, 1481058274, 2078282231, 1909209829, 1082848096, 2419955304, 610894099, 2900797628, 2422895624, 1044241354, 893826759, 87530502, 2187425718, 1921854792, 1182613862, 2395799462, 975009008, 3077205903, 1049577722, 1088501864, 620844727, 367900341, 31981472, 37463578, 110991774, 106975139], [11340704645, 61765606220, 14659972277, 5265987103, 170900764, 965053596, 2749316224, 2699033486, 1879695861, 1409000493, 1322977480, 2325591755, 1138724181, 366912997, 2798094785, 747281293, 1099828927, 2647907085, 1180890840, 187094857, 1166711133, 2019934796, 1462228128, 2961017263, 1673053120, 3127667765, 936570833, 3071950403, 871613865, 2043468120, 1239087579, 1505257770, 1358230891, 2340307937, 1259432229, 1551717310, 121069976, 1297742064, 1695016096, 3000204203, 1248789462, 2404536150, 682084780, 2037997961, 2291956371, 2592839151, 1909510278, 343122464, 106154307, 20891786, 209747, 117475848], [56038936293, 77129975324, 19156667478, 4439095036, 1679565524, 737053055, 2329579357, 2367483978, 2757591118, 1639634166, 1949101029, 2311063069, 2944698441, 1056673245, 174760762, 3257880425, 3111876931, 2503841295, 514531390, 1695083417, 1240643437, 2329102613, 2509740864, 1690862480, 588584720, 2075017289, 24819438, 1456410991, 680079939, 1508484417, 2693635800, 1137307956, 1434607129, 2463954672, 1423709292, 2612385448, 2450704993, 3008477418, 782677810, 937368634, 2076117379, 2664519272, 336489678, 1391947971, 382952599, 854737247, 2307337414, 548677466, 91973551, 45706999, 51056114, 103430910], [4848756339, 19942216079, 41538047541, 77029607625, 3106126471, 1294988251, 725499856, 1788055420, 568258010, 1806096298, 1339883722, 1781810506, 1667148215, 2728324308, 2097589167, 2511849504, 2271558568, 2227281567, 2051761000, 110565370, 809449764, 2370447873, 979193191, 2603867743, 2592030057, 719624322, 2862249651, 2677950766, 1950703347, 2345887691, 1091165011, 3078447650, 3086292490, 2126535610, 643152174, 1551681568, 390505569, 1021925558, 717677188, 285534397, 2758076533, 1262054919, 2968473932, 3326869845, 133056863, 1702307211, 2995939934, 3123923043, 87106868, 46313370, 106335820, 112006390], [69078548243, 29599861201, 73295242686, 49177787249, 2374990350, 1868879582, 2952885199, 2033897268, 3376722736, 969724896, 756550224, 1700635410, 2232734936, 2033175344, 1681870285, 3284979876, 1577811454, 1072098954, 2397821116, 2796105469, 2065300088, 2944813395, 494031697, 2931941238, 671576839, 2764402016, 2597371416, 3316415448, 1309408492, 2706004993, 1414166546, 2113607241, 2221355985, 710708809, 1476764266, 3033377264, 1758362765, 89903941, 497267130, 3371365944, 2449928605, 2405739694, 1530487436, 3362852862, 3103783553, 2848296080, 2561353646, 2766902737, 138092678, 53213035, 147661440, 86825136], [17147101220, 30872918745, 33997649272, 22787226218, 1087039156, 2379878908, 1863388332, 2494556747, 1813010558, 488692523, 1550924063, 1044545276, 178707079, 342255824, 2231497881, 2122272054, 1426263925, 1245164869, 2811930389, 2595087516, 470378911, 628026132, 1155186845, 2264714596, 2575345029, 1325271431, 240558748, 3156699860, 1490462859, 1103919178, 582078664, 2693946001, 2322096928, 2773318081, 1368088967, 1098096935, 1400882896, 1564394243, 2823443867, 367876030, 166097651, 974851504, 957602815, 1485488258, 714590979, 239202760, 348108220, 1302412858, 39576329, 16875057, 48189401, 132893304], [33488504229, 58843198620, 26836508031, 21477550765, 1501713608, 3072525886, 2887433432, 3144026699, 1564031464, 2531925790, 37772026, 1322309514, 1857181713, 2073908321, 434755223, 445228411, 1507305207, 1008224573, 492992373, 1012253460, 1705816252, 1362779555, 1637293778, 525893551, 2599557175, 2518778691, 2379311107, 2741277563, 3224598252, 1421309426, 2440606199, 2001690759, 1262888738, 2714350727, 636066748, 3300308824, 2140938279, 969622247, 2368956300, 3402639067, 1313286614, 15979434, 1186172882, 2731378616, 2339527823, 2504629137, 722604662, 2874733016, 59106472, 75813226, 57803672, 2424013], [3283639482, 67109613946, 56788599650, 77196472211, 2290630812, 2826802833, 339913343, 2599898150, 2627648294, 2752591378, 2399321889, 2693813820, 2775081675, 134071071, 905329036, 2738494011, 2299965776, 2663151807, 661561834, 1609387648, 193283605, 320258256, 2080271524, 2619528052, 3278691538, 2394211427, 266074856, 2225726330, 1973928954, 3325176516, 643005319, 2979437204, 1434647264, 2085284167, 282077957, 2179024255, 1036469401, 1297727183, 672103240, 761535543, 1916607595, 2825538891, 335914103, 2131816778, 1599094067, 2136288875, 2852689080, 3352468546, 28510263, 124276552, 117848836, 84681089], [24043817050, 76897070378, 5595288545, 74209700123, 2983229536, 3023837163, 2752546804, 2004449931, 313905334, 1228161015, 2983854308, 1537259326, 2534130179, 745093993, 2341767793, 670685543, 2325521030, 2273032247, 2224233032, 662548442, 1146230921, 1623372131, 1080491746, 2326529051, 54376531, 2308213553, 3265226602, 416279116, 3248832386, 2991745286, 107046577, 901348104, 1678587150, 2249581217, 2931603713, 74033044, 275827707, 1203814710, 3242242127, 1325731270, 230572309, 3229478599, 183572821, 980946504, 2899644201, 3329369784, 2378137923, 1244333649, 28075175, 21182948, 108458818, 97368205], [74573614564, 63960128864, 38651883847, 9697318535, 2666087044, 2790577235, 3074727170, 3193449605, 1079295125, 2888114508, 1309320034, 2478029568, 1152112113, 1079051072, 2680435387, 1471643569, 209583774, 3251355164, 1368783360, 1080090718, 433143705, 3398084722, 982360981, 3136856081, 1410200725, 2789431053, 66095537, 1216498612, 564514461, 1474467992, 457081277, 175607001, 2906951048, 644398544, 434129784, 1674263978, 3345399680, 1277712284, 2842618944, 198642513, 1065802796, 760398285, 621163645, 1105251384, 2537055089, 2725410921, 1866473966, 1097325722, 141074351, 75723905, 74246996, 67899452], [13603014407, 21189610246, 17989181935, 25944717186, 3126461323, 949287671, 2545314205, 2186172517, 80820873, 3401843106, 3326137985, 265708420, 3270635052, 534475127, 860954239, 2978646303, 917638383, 1985178415, 3005867056, 3021654440, 2187814717, 2023502372, 196095171, 405387466, 1614193498, 2854664481, 2719515469, 2535177714, 2592328275, 2182609955, 1362136222, 2799009955, 2277600691, 43220634, 1877596973, 2087524160, 889413979, 2181739313, 3203399152, 3052462273, 2746808948, 1097446932, 441361720, 2601097508, 1548998641, 1756765277, 2155038061, 236752593, 24266806, 142007861, 274567, 35906520], [72252922246, 64206792571, 65305348885, 25374413924, 1356957358, 2405896922, 1199450828, 2306520891, 1040738822, 381354053, 2953570162, 3329775481, 1296697519, 1233804939, 161512992, 1527042519, 3364903680, 3106708785, 2014721892, 3352972545, 1510053799, 3123734857, 2664977777, 2792517768, 266477448, 1380512325, 2544758318, 2922272935, 3250621119, 3062585493, 306247070, 2097725327, 1981342613, 2931697438, 1751829684, 1117493065, 250702461, 261369378, 1476393828, 858557846, 1943060194, 2332839009, 874756033, 3332205063, 2166353900, 126660057, 2435481799, 758947192, 110989284, 89212879, 19224581, 125541830], [65019865042, 50358305236, 29103815256, 69348346707, 423570461, 198331760, 3279709426, 578562562, 1999254438, 825289358, 965890106, 3390287607, 884712894, 2527527293, 143603076, 280856427, 119034039, 1008927476, 1803695926, 905072057, 433930443, 1247414200, 2285796649, 2687703410, 3379939033, 1137983374, 960683274, 1407699567, 2091410700, 1491231358, 2516798230, 2362423035, 300811273, 1343642566, 1274312815, 3038686216, 1473691305, 2782499980, 1973002353, 951424578, 219266153, 2362722541, 2522680664, 675071137, 3204720594, 1576349965, 505449265, 773011140, 104904671, 57532646, 99474277, 136422076], [16920143821, 77039583507, 38847886811, 14777970488, 1322961771, 1950891832, 1021375950, 306626915, 2129482646, 2989657990, 433668887, 1143882, 1084559572, 60949701, 417500301, 210501037, 752992377, 1675084986, 1069780117, 2380964922, 3258111920, 2727510246, 13858972, 719366952, 107450411, 558901932, 2271205978, 2048017543, 3186566717, 295644139, 3300873681, 3399066753, 3191183070, 1760917743, 1830748112, 2778451750, 2013906266, 2278273441, 2697572687, 1796917458, 50762196, 1864905665, 3380656242, 2130710915, 381315689, 1180137153, 2665341131, 1332893332, 103701576, 84459918, 141156810, 15112346], [22581017786, 35295055099, 31487098854, 70817634685, 2037517169, 573094956, 112108739, 2449788282, 2572128341, 1118287301, 3162270736, 939710494, 760647053, 3399174416, 843158518, 3074670383, 2590823523, 2355962059, 9983173, 1473483086, 1289588380, 2176658015, 937182587, 665231162, 3243907557, 2426711715, 1123127375, 2585762879, 2417532415, 16037923, 641266427, 2341731246, 2727286778, 672434164, 378734905, 3076625429, 1062901691, 1517272004, 534580053, 877689016, 2949205107, 1993417820, 2109256262, 2525996275, 1667665209, 1680202279, 191091153, 2831596217, 15705361, 78210071, 60957360, 66322826], [3292569002, 19192063397, 65951271639, 22325817606, 1006213568, 1544356321, 1586178463, 3315699688, 3002102025, 903820282, 684091323, 1287722344, 1590744308, 808872326, 2173062586, 2288816572, 1065796540, 2149233781, 433138668, 1970944635, 2275675246, 383852980, 2334937621, 510118173, 1073447858, 1100784232, 2863821517, 1315126062, 804661003, 614031345, 1105653194, 1453992403, 13754874, 868469880, 1960613357, 1796250757, 1073494686, 422561865, 2981714618, 1240283441, 26313219, 375071327, 3307691410, 3046727959, 2741083696, 3234512678, 1683450822, 907159307, 85886965, 43833766, 35487152, 29764061], [11981511440, 43512463336, 78089874390, 65104361154, 3315758269, 389638009, 2169164661, 2473522488, 1940505170, 2641293458, 1279035198, 1268901559, 2045559878, 2403881823, 3019078716, 408128767, 2391528339, 1518578542, 318315584, 981127261, 2995330871, 506732044, 121402050, 2511339341, 853704639, 1456189800, 2809909632, 3219385854, 2596801039, 2844177263, 1338361283, 1610214774, 3275514157, 492861273, 2118742796, 3240492862, 2224680106, 3342591518, 2412062693, 3146739986, 2201311830, 1029189901, 942800751, 1785374425, 1577607996, 1017582974, 2123732025, 225878239, 108028515, 129610779, 36408171, 75620749], [71619232617, 30416202892, 47556254129, 3594688308, 1021602385, 2588732156, 2618275702, 584102917, 2100421479, 1000513524, 1113584307, 139976321, 2762305865, 2603715989, 2707104255, 1433895670, 2457280463, 1322036665, 3277406068, 5807270, 647258709, 729745955, 625771327, 2309877327, 3360634742, 2328147653, 2335747796, 1714330737, 1231162009, 2702799989, 1010347979, 2015177821, 1797552925, 2082145656, 1421626320, 3196872166, 539562382, 1575823334, 2303896844, 1580065132, 639524775, 1231331312, 2994066469, 844563726, 2618132596, 208767573, 2136713777, 1386684398, 15898336, 87768306, 111905142, 30273508], [64120613181, 12160676334, 36303514778, 72882572431, 1657154968, 339325141, 3285058743, 322647473, 3370518808, 970287016, 1039947898, 1924970096, 2025268220, 495314269, 2845122080, 1252869846, 1598090462, 2466106161, 1185794555, 1524721359, 799491063, 59849473, 1127178342, 2381856195, 3018936231, 1739057370, 3261969365, 2633919198, 2737706698, 3133912288, 1535674833, 1186678054, 962536062, 422974462, 156039935, 2653307853, 626602409, 69361813, 835351122, 2759583033, 773147139, 954830004, 2584439574, 1727940780, 460514947, 2708484692, 1189334531, 3209916271, 91594197, 117616844, 85189551, 75482647], [76397996966, 21332767697, 16063664255, 63711219552, 1821476789, 85189263, 1203550394, 2246547425, 1420967439, 1496705657, 289655192, 2784373399, 37793393, 3160969534, 1137180398, 1208476672, 2251918270, 3106719572, 413524659, 247783945, 2518717925, 474718022, 1438739631, 1086033780, 2310787552, 1815338825, 1728678919, 1063940900, 525983642, 1187433029, 743494320, 1771975177, 2203761652, 1784415233, 1443989036, 836167392, 972842937, 1850241325, 2880807983, 3056168171, 2584794556, 163780378, 3049067703, 402743294, 939537672, 1099809860, 1334545307, 638739210, 50873188, 145487569, 141425604, 89827494], [39510712702, 52855993019, 35076132681, 46170305869, 218079491, 1062293318, 94537521, 624647202, 1055234135, 1454509328, 3176723154, 1559320420, 2914309783, 1194861178, 897985182, 2996647506, 75841051, 161252724, 1812369479, 847475480, 848782915, 328265706, 1064672806, 1977086279, 2247801868, 330605381, 1265334420, 2118573654, 1505953313, 3320869306, 1068969436, 1137550031, 2292460347, 2163553006, 1500912012, 3320488311, 2564581489, 2008170595, 3238750313, 2435366362, 1871966642, 2058037999, 1338717323, 2097732342, 3379414564, 494483509, 1573215249, 1756329818, 106634053, 74335428, 103333612, 142447717], [78190574301, 70797517873, 26188343375, 47330299714, 1911649462, 1189264933, 1357495834, 65076798, 1537702375, 2564916967, 3184463942, 2819003050, 582686531, 1142972074, 1904215908, 3032777723, 943178181, 2559257127, 3393577044, 2246521113, 480642178, 204652988, 134474146, 1329335324, 1288448937, 913753936, 1602009800, 2071607815, 168394178, 1301481680, 3341007623, 447480617, 1189045697, 971696479, 2087532118, 2214428178, 3384479762, 2128284300, 1101659060, 1134635862, 1752909235, 2622807001, 103874118, 3152715202, 1889128920, 373170768, 2165233156, 898398791, 28641222, 74283280, 91416283, 22273782], [13531972352, 4104701969, 10213273924, 71344573701, 3156683323, 1856276180, 3055450985, 613105733, 538477656, 1652608144, 2391209881, 3173702265, 230057523, 2918007332, 497886589, 820175032, 2404704234, 2171531085, 1687292788, 1644621854, 2139131675, 942244703, 446866034, 3019077497, 3254664059, 2563819062, 1859707918, 802313163, 1103082231, 3148989915, 2556412234, 2766322493, 969990638, 2555377395, 935925384, 1951900658, 1396263852, 162265161, 1055056138, 1669151699, 742235070, 625673439, 379531579, 910212258, 1112459055, 3394923901, 1931586092, 1025653996, 18218763, 114767449, 59169999, 56529349], [9774101298, 42439635995, 66138455644, 19956888423, 1622814289, 1581853313, 1358206074, 2903249635, 92506115, 2139581624, 1947724341, 1156343055, 1263368748, 1616809702, 1103801441, 2160068690, 2156323784, 1489609904, 1637663641, 1948075137, 137699252, 2097790739, 2674789301, 3273844265, 2393179946, 56087501, 1715555441, 512199305, 1983390625, 1351041482, 3051339344, 2792083114, 349208977, 441836992, 2107781594, 1215513729, 1406472632, 2963622335, 1200102556, 2824292728, 919897926, 1188854751, 3283915022, 2894092185, 330487023, 2949133002, 1165221285, 2699317674, 111797211, 70190666, 26435488, 9307148], [34879166408, 22733035987, 59253552384, 63773482323, 1311539350, 42394980, 366549988, 1848822708, 1945206853, 2579398572, 3047381895, 3092111973, 3063121554, 3336442054, 3232497441, 1197267369, 2122237715, 2985682923, 1050458001, 1279976174, 881450850, 2982500137, 1896408788, 2241586555, 2540927300, 873097020, 1381961946, 2433020201, 1596361989, 2870522452, 3211220716, 1832258476, 1383486524, 2165166939, 3309940879, 2081175240, 1425057851, 2638498015, 2284431507, 1404977195, 2376084736, 1332985079, 156338130, 861281621, 3296882629, 838539244, 754728601, 1688314609, 129420927, 52591836, 51880570, 26922312], [40600852097, 3266499882, 26251430328, 56820560243, 2316516921, 242404475, 866541445, 793766294, 1234847989, 1602637010, 1344249398, 1389181692, 461241816, 53373202, 195793963, 181793288, 1048528232, 3207484044, 1353270895, 1685769843, 2606864091, 3377308983, 3391848134, 1436464678, 2941823556, 769895767, 1948970389, 3012246934, 2523184249, 2493585250, 1674169770, 1451728329, 1617608653, 354904260, 3333864582, 3032139588, 1476410526, 1893177035, 196565705, 3271280133, 384764953, 1017641716, 2023297994, 1346155983, 2977802111, 30307215, 942302755, 1962246495, 11248938, 103613542, 44867717, 5908595], [45978734867, 36000943706, 26000055876, 9831343330, 2490605370, 147081251, 3311527143, 2632959753, 2133495157, 1712313683, 1570153742, 1394085522, 263697599, 1286256853, 628433393, 2286682333, 2881050564, 261220292, 3374672815, 906398536, 2517457088, 1311829196, 3221128771, 3179904192, 3134873274, 534775415, 2131411472, 3020728299, 2768566856, 3223611989, 2993572774, 323084174, 689152266, 1693088121, 729618512, 349130639, 755620771, 2044379127, 2661372136, 3203369344, 5148205, 248167424, 1145198796, 803583315, 2111935072, 787324592, 2499881845, 3153836544, 19932017, 34303045, 101205469, 127932224], [13282363702, 11135695456, 61778437644, 62168918994, 1165684551, 1732184349, 159867664, 422250606, 83621767, 1940506228, 2223370624, 2739435493, 531198317, 1295033630, 1252768462, 2270904448, 488691695, 2667010793, 2234943166, 839993120, 3011459414, 982426508, 1092641956, 1850494670, 2660312917, 3256949316, 2886569414, 3009902314, 2492776547, 2651970495, 2804811613, 1028096803, 1246067596, 2461935272, 854568220, 2614043587, 2885489518, 1660031509, 2560519528, 1165664288, 1781419253, 2972213226, 954272185, 415693513, 3206240595, 628962278, 1045526571, 607638472, 136076450, 119027243, 126444938, 89151046], [70794188876, 56917916874, 24626534884, 30272337110, 261860290, 1035168498, 1481477978, 2877890364, 1918961139, 1448570291, 875691788, 3169396527, 1130144813, 657192639, 3041666211, 1157564194, 851153939, 969285205, 460704490, 930542096, 2806525504, 2337013187, 1466678398, 2511197477, 3331799435, 831048742, 667884327, 1333912738, 2832159349, 3060419445, 2143898931, 1100299967, 3230139504, 1533264387, 3298741696, 2046597063, 1619672029, 2719426758, 921767964, 1033752825, 1606429434, 108746530, 670703000, 635125887, 1640367475, 2744783706, 1429894843, 962789453, 133819996, 88156887, 81961544, 125563324], [76788915799, 64995158097, 39392099264, 43184894898, 1254832965, 950964578, 2717198242, 2466802900, 3353513574, 580433543, 778000070, 3334530685, 3238770921, 1306806134, 1651461847, 2388365862, 1239663936, 1097331909, 1446319994, 2610841711, 1008879797, 848292026, 1240586121, 1985107184, 656079623, 2019161306, 428034393, 2645505448, 2201461100, 2385139606, 2475897606, 1693359728, 1351987242, 1932670818, 39096458, 1456064404, 1702100464, 3332644087, 755033167, 1784321048, 2185159344, 1518518834, 820339988, 1097470599, 2072829023, 255190750, 1274718512, 2429789184, 89849937, 37293331, 125748081, 49035574], [17897484017, 77598174709, 1066628519, 78236315344, 1103731636, 2683870184, 1186766213, 1453186414, 737245657, 1488373976, 2747631980, 3283659561, 2007067515, 262697053, 263695437, 678155621, 1854732144, 3259170472, 6174120, 2973475397, 1128880687, 387164543, 1232928225, 2196260248, 1681245398, 1198898552, 982162974, 2586721818, 1961460493, 2430890010, 3188101024, 275335254, 1887164053, 1981686440, 2491310504, 276314571, 9061563, 1193079805, 1646045991, 573010891, 1299773516, 1897238996, 488238779, 3154430289, 1500477979, 2599066010, 923288540, 1542548084, 74438040, 94098730, 87830656, 81047525], [39978686733, 35185884311, 24247113866, 60811935600, 688094266, 526776038, 3167190229, 1834094083, 2687642276, 732943645, 1017424688, 1227056555, 3073071929, 1579719764, 2026139368, 1989644210, 542111725, 2399570726, 2638342075, 3069725751, 1085841017, 1496325329, 2424861296, 1098290066, 348120709, 2392060559, 1582254456, 1692933630, 3236035370, 2902707686, 2987140226, 2583939784, 2450973311, 2359543113, 1364999538, 1546954930, 2214388618, 2190690982, 2828969088, 3305816266, 2950364514, 2424424802, 3115138101, 2732357887, 1914850648, 3039993605, 1654618114, 2731158943, 75541291, 80067391, 26906169, 13571600], [1269409031, 29005176858, 36081847379, 76288066534, 104366249, 2481506547, 3313418295, 785833709, 1108535485, 109603602, 2839325528, 2345999586, 403079554, 479210497, 1093637304, 436357909, 1429331274, 632358389, 421890978, 1121403157, 126552417, 2684023916, 1536501982, 1177836325, 1100801781, 3092856276, 946281502, 2940230760, 538440695, 1812472036, 2563916582, 1648801736, 1248653187, 335426158, 1515950424, 3039612403, 965082737, 2255317095, 1159019726, 2657287175, 765130765, 969260641, 2925080568, 1999532554, 1319441322, 2144920407, 1827634487, 2781162921, 75406158, 56427149, 78827984, 39695386], [29682091077, 8592119039, 45584334685, 69834798179, 1824058286, 2970701367, 336275065, 650569881, 1395574243, 3337823664, 3145572069, 395560141, 428159283, 976740034, 2721610194, 3200770321, 993309280, 1691802467, 669307889, 783612829, 3272472545, 970597861, 1082214860, 3092830102, 1010084445, 2742835744, 2382672971, 366241857, 180909582, 3059231449, 2370042038, 1111784695, 1934604520, 1280547678, 1776190088, 122342658, 1824602949, 3224426741, 2859641152, 848956680, 991157170, 2214979120, 1250488495, 1430347161, 50747223, 2272308092, 1154183861, 3349387949, 98119460, 28800808, 82675308, 41752351], [24378140818, 31136158667, 41034811957, 16448544553, 2194168536, 3339224778, 1271919481, 123460941, 2023266254, 2068050382, 146449947, 2477745955, 3306140014, 1789922491, 674006973, 2465329520, 3360625519, 996489513, 2941252121, 2208356914, 3175522577, 410745408, 170710462, 996954090, 427079180, 1210505686, 1933231144, 2298384457, 2177171881, 506552000, 1132767066, 2365538408, 3189658354, 188994404, 3279280591, 1098952581, 1647100081, 1201746435, 2124177397, 274828449, 1193864312, 794269097, 3116700560, 1371947723, 1095810574, 1336871665, 200882437, 1170776866, 28631297, 43726749, 89315762, 29414102], [37402184827, 50409273328, 69367993767, 4357308462, 1309386458, 1382176858, 3102550293, 703630812, 854799370, 2003378108, 1143783077, 2623868129, 1323279953, 1487205875, 2424612137, 531408790, 334162722, 1055413581, 1709290816, 688647738, 1150753457, 1390238174, 2362086246, 628094419, 2480759622, 150608738, 695909321, 1289102758, 838420196, 2918007102, 2994587511, 3224654142, 2594426887, 2733981020, 540420834, 2066973246, 2490173959, 2344325554, 2087133459, 1318283686, 2234213491, 2830555743, 3146903378, 1522002345, 327529430, 2223573001, 556803481, 1264894568, 74989499, 102218923, 100113825, 104382464], [12544689601, 49210145121, 14715495059, 72207555735, 1525784787, 1148920955, 2639887560, 1691595030, 326332372, 764307733, 1242622058, 2400248697, 1223944080, 1247454266, 2479902021, 1007199992, 3184880426, 300045948, 45547015, 935721213, 2934525219, 1555154821, 734350831, 2630308428, 2214627496, 1882853531, 1919646815, 2691733539, 1869968931, 1058671002, 1886022701, 1552854292, 1241417502, 1844222524, 3340509972, 582498874, 3303930404, 1834755586, 2097105753, 2059229192, 1485597577, 156571143, 2143536382, 3385729099, 1346515335, 3263083163, 1347623682, 1641595123, 67016319, 111968416, 4216429, 34616012], [16696504310, 58174313563, 54039350149, 20063422675, 954805923, 2389350929, 2868915695, 1756726269, 3112027765, 482627124, 2340547620, 1461663041, 3208533258, 1718444218, 1826028466, 953754616, 1935590990, 2568220250, 2650881054, 1452777704, 3389691263, 2046023167, 1470339699, 939433988, 2077816849, 2215781820, 463565184, 929073224, 2313598175, 1196381133, 1166299226, 3189527622, 757615630, 2222972816, 1842762576, 1505236035, 1218313496, 3073572340, 1686281041, 299561246, 736997671, 3248443686, 1927454372, 2324192389, 3093128159, 1647208135, 3204787777, 3257328333, 96676705, 87896731, 15551358, 63208485]]]
sage: crystalline_obstruction(None, p, prec, cp=ZZ['T'](cp), frob_matrix=matrix(frob_matrix), shift=1)
(1,
 {'precision': 6,
  'p': 23,
  'rank T(X_Fpbar)': 5,
  'factors': [(t - 1, 1), (t - 1, 1), (t + 1, 1), (t^2 + 1, 1)],
  'dim Ti': [1, 1, 1, 2],
  'dim Li': [1, 0, 0, 0]})

Example 5.10

sage: # f doesn't play a role
sage: f = ZZ['x,y,z,w']('3*x^4*z + 9*x*y^4 + 9*y^2*z^3 + z^5 + 5*w^5')
sage: p, prec, cp, frob_matrix = [31, 6, [1, -50, 1452, -78116, 2321986, -40307502, 1906053166, -11171982492, -230889485210, -46463852390356, 1022477903317523, -49641284766618410, 2911562749301475837, -31630618937964180114, 1120399902799562715761, -20083673210179063376992, -2115596073582206419866076, 54740915682760522743399988, -1121590321854386635690836935, 70848900184596578675160353810, 6872693654267406372651488488, 4849628113451439548007546839660, -1301384083974162208410945269944517, 3268802689260334562010701613725640, -1704339289519299940348514141687753010, 95392689820377535587415105215080269670, -1648118163971196864446307190441090159924, 91672374917382811699505916111692139152870, -1573993124996153400210600128645615347548210, 2901074419181246091076020443574145624080840, -1109938821489928668170426767342450900639660997, 3974892383122137044267325691380592570645367660, 5413365015846166068173386436794750287506651368, 53628645311793937109461707184255025635872452773010, -815870733244748194617159391892361411291869179745735, 38266835270096239552058525066271147853504496689357108, -1421237405039364562023237580343205232021196116643187676, -12965832610082491520272303206906341202281203416259388512, 695110285041395279318564258259398495205858314435516084081, -18858699041220700504796517862291225880088579208184329814034, 1668220991586525252720170152539903538634478318472771909000317, -27333410766265432700922015376550666602104614598787148463402410, 541038454672851524169165213002721966047700900469015482515766803, -23627229803324070371704332604903825996040464394726192674223665876, -112830141677901665752197721953714192901947046995168296826877882010, -5246559616888568632410536919581193848905619557698946655009299535772, 860206586798100164968002237461960092955845352143879520297981444344366, -17481432806887543949976999223811177021113136918628928243723134680379822, 967774390739217006844241355155973280576184016956324151876974366866051906, -31288007937606976680344158900651775007624986641817120761085072083150492196, 558892035074946518823354878559069442827841835992186484595176394116568546732, -18495015348038002912852756139644136864929614476187713901376188524312065200050, 355474194989290415985029973003960310543947190232327861184450343437277893144961], [[791205227773, 315606997590, 565469833501, 578557400357, 10092875530, 1538779860, 3915753189, 13342654448, 18520623105, 271807163, 25186898104, 3669759137, 26911843318, 23877977943, 25135788838, 6237155391, 7130481740, 9872243291, 25707080708, 23139261645, 6307963049, 37954757, 10917007957, 19265913387, 3228193711, 24740328937, 17587989314, 20845291901, 26152411983, 25037118442, 23452832194, 20983311434, 3144769022, 23952960929, 5743303412, 2975338894, 14928854047, 8433924790, 12673637527, 5302123843, 24686658420, 5737347909, 19949226578, 980205306, 10957471668, 16497243774, 20160680957, 5889034505, 300904776, 780250744, 823662214, 623656], [163895925509, 651002798587, 538030790667, 469569894481, 871473550, 12453236238, 10069275416, 26413821126, 9421971608, 25836860193, 2590045598, 12217662309, 23360520115, 17312511379, 26756067698, 23675978192, 8333112759, 12173863215, 22073139746, 15519388237, 12151361369, 4532761565, 23080371162, 25388872001, 21622642476, 26428637235, 8174017225, 10487265373, 3539035733, 11036612591, 12957481091, 24474554808, 4723926010, 24930446915, 9141151660, 2871784572, 2337958713, 19015330405, 10354073129, 23120992601, 27313811762, 2489311718, 26878657663, 11193128429, 7340818228, 2047778997, 10393503176, 6086803655, 866741939, 169002225, 60555161, 730986215], [806743801104, 156136358878, 685196531675, 625959191442, 9521154465, 11813178029, 1129906321, 13572019914, 10503652221, 1936230271, 24226757734, 25838055956, 1322702823, 14683597144, 7653078128, 22827749527, 940385589, 18243487383, 20673678629, 10699424692, 26458849773, 20584279124, 13369970997, 7023702364, 10090011254, 24471958527, 8491946529, 25789829225, 1431282958, 5511180744, 7564720595, 17711897492, 21389216134, 1996963115, 16753431959, 15467425045, 3003000225, 11411281102, 12677226769, 9583813339, 10965941395, 26608313235, 21283442150, 15079163995, 22170684749, 13935496650, 6680757114, 1878924849, 317664199, 406152879, 494900725, 698483620], [178296194340, 695592077100, 118406855969, 598931423934, 11110296181, 23774743262, 23568960147, 15181141161, 11973335530, 19926814663, 2071041490, 11939146312, 17496974368, 20917139454, 19122192830, 94882630, 5281150173, 9865580120, 9542163134, 26159312893, 1407952079, 13307551443, 68696775, 1084162659, 11045764008, 20669542857, 24472526819, 10656379735, 6055246275, 4621498724, 16615349713, 10087804364, 26804199135, 19328444541, 21384196459, 3226428385, 11178460965, 6586149981, 13657252616, 19885077441, 8252464244, 21372754793, 4829672063, 17511744969, 10150837067, 19703677841, 1830608745, 20535587579, 564235843, 557888044, 39145010, 50517784], [693607077784, 402422422942, 69341846808, 764204578724, 25412244730, 19533756394, 4524198683, 20285140935, 16795289554, 10236074822, 22091676878, 3726042117, 5415910273, 4916607750, 787934967, 17453668856, 261787343, 23403457657, 21269912789, 3864649596, 24856481628, 25606636368, 6645798910, 3087924663, 25037777378, 1594752282, 11921948287, 25684438804, 11797570924, 10079143398, 12927748619, 24766835177, 4071288404, 12987941877, 3878266811, 12037104731, 26731800805, 23102565705, 15589451244, 26304278565, 249349740, 11770607496, 23502971997, 25642013940, 19873357395, 22663999095, 15168302945, 21406185751, 242214291, 560942446, 628640707, 368957802], [368673883675, 670069935200, 400303518847, 81125867136, 10745439914, 5780032181, 1767879470, 42162697, 10246327514, 10390260514, 8446329905, 23824877299, 10670204774, 17619338777, 6788197286, 13015624040, 21418212046, 19397199441, 24963226935, 9950178903, 19730050006, 27399557328, 10225677980, 5148128553, 20646100068, 27379544689, 26921074343, 530606168, 24882158525, 26942088530, 21484899618, 6556733647, 2202836688, 9850314480, 13862294893, 11976654297, 15045879543, 12840607309, 11555662207, 7246343682, 1564923834, 480539277, 10574908201, 1768193965, 10251206821, 1205460203, 20957651370, 19610763711, 243350809, 414852066, 521697079, 873837196], [671510222418, 125190633771, 813362902907, 333370418539, 11908392111, 26683034798, 18944207942, 7776015324, 1878871529, 9455578584, 15401073761, 10581728294, 8009287720, 3444414123, 18584766011, 13445722442, 20204826848, 7886250332, 18358307942, 12403744366, 21503358320, 18291571855, 22960635522, 23843373015, 13178049160, 3858383039, 7005297478, 26331831148, 14050590970, 12311852213, 9224015094, 17226895889, 16366207766, 10656881811, 17948843481, 9537592804, 23080321376, 9000239362, 6968132322, 16076729921, 25249424701, 2855114167, 15092662077, 25125206709, 9864646586, 25174574209, 11651271353, 5132738324, 164725465, 365366414, 122938822, 380440573], [373323478443, 384301104451, 145220512677, 336204900532, 4052674671, 24843684983, 18885168287, 24225676733, 26181232373, 12296557278, 24752565598, 10380385805, 23982413099, 19756752414, 10969055810, 13198028319, 390039520, 17603198100, 23843554148, 24848689530, 16914489576, 17316534528, 6167264620, 15331181502, 16067991083, 4451623157, 1719208323, 6829665831, 4681019561, 25263537017, 17815087192, 4842446047, 15774164868, 19973117782, 1105351562, 15448551501, 10273192052, 20789398188, 15544214153, 24530656717, 14030707136, 18593536438, 8840116240, 26605433676, 8059651343, 16641146921, 23722504077, 19542138453, 691200696, 668540204, 36483819, 147189896], [774014642587, 336933985285, 800807986638, 823742777305, 17771088489, 24982956079, 24042454953, 7913613474, 16909832353, 4854813497, 13489664942, 17804346188, 15703511683, 19265176176, 22776043852, 8489084702, 25451300049, 14895812511, 8001839319, 9723370658, 6187079045, 7111819864, 25389407154, 9806309205, 9263139047, 27418386015, 18253714717, 23135324769, 6250487406, 11009631214, 11199447934, 5214166489, 23475601973, 22933124107, 17776714369, 26114672366, 8583716542, 24898092308, 22735407874, 18208478153, 17461181427, 21545701096, 13050900614, 9527447775, 19907151053, 3769839537, 9219735482, 22625061669, 718461975, 154987717, 415301024, 128389746], [416261089139, 822930715007, 589012936207, 458367437718, 22542210480, 12392986467, 25421592873, 14047586946, 17237053876, 19320274491, 25026749345, 17592818339, 15344339297, 7641355106, 15893944497, 20545827778, 10347616046, 8962959971, 13548933873, 6354561753, 3055000710, 8985611950, 940932243, 6537855577, 22569696754, 9083975105, 17799227623, 4129067382, 6444914384, 4933242040, 16833860777, 3690282935, 11057788133, 13288363156, 15413079441, 9442002661, 5522371465, 12534264348, 10669725297, 24004706222, 9540500077, 10393797273, 15159838457, 4740472477, 417625583, 21694178572, 27082266593, 13735890564, 647719800, 543736300, 312282009, 717365730], [164690618693, 847471799876, 310874457951, 795033245382, 26539974634, 7093319033, 26625157736, 18402618350, 21430138676, 10894312454, 3241533631, 1596097310, 4245866361, 26444937314, 14012531526, 1614606728, 6428359981, 9943314139, 19909188528, 11817650182, 16121465339, 13831190144, 12223783321, 9448443562, 22554040886, 8050819722, 6822967382, 10736307314, 9003583642, 11126133585, 16353138848, 4388490727, 12562314915, 13629811757, 23477821170, 14270372290, 11740469668, 12896313348, 5497979146, 6766151698, 12569526414, 1703687243, 16009759319, 22803487873, 10134091394, 22594407908, 1429100465, 7447176531, 599456370, 517432499, 883396568, 330329024], [466370788907, 659536241220, 418376653759, 363758004456, 7240895587, 7400114656, 4059672487, 14823541529, 3124607397, 8884249452, 6633365585, 25988792743, 27075578684, 3178274256, 2077871968, 1742841607, 4161626558, 8503208767, 18727170339, 3401056159, 11967302, 4196888407, 12778834756, 16130784714, 21324723393, 16210404277, 12943467076, 13634388163, 26439581258, 4605203016, 6527163181, 22142211156, 7206255257, 3313968944, 25541406168, 12754734519, 14941106766, 12547830258, 25518770464, 12069136535, 12943598113, 4092607042, 11912505625, 1692328657, 21317613326, 21971222658, 23670783894, 18278553064, 846438427, 573108883, 239543900, 492676329], [130118419780, 5497120849, 261819346129, 652734746422, 26503886635, 9671178531, 9855809726, 20223173020, 211849846, 4207429492, 1759975555, 20438509746, 5598166403, 3249938444, 10674465073, 9967954799, 20273377861, 25453990012, 15600895235, 22702554477, 10237780442, 894312118, 13569665092, 7805597229, 10311736274, 22680099782, 1113377524, 18539715571, 14980372854, 11180798241, 17215418635, 19378358137, 23921951350, 20045913501, 16554372930, 5722193931, 25857066241, 6885187513, 20333772743, 25609005357, 21925813083, 16223206316, 18515353508, 1696861446, 14577877441, 12518361534, 12822293594, 23905455444, 119588669, 859910197, 154897049, 169041472], [226079394793, 817945237285, 101956629027, 735938931740, 14151812015, 5503074802, 12295643336, 3124133252, 3886249094, 20648066522, 12908303714, 18959867530, 2283241388, 17035423831, 23121152995, 67949830, 11233895878, 21699366515, 19890635989, 2753587865, 26347249370, 4571552237, 461011261, 8996919107, 1624500502, 15845470634, 24357178051, 12618987937, 17325833040, 22050444615, 23570580393, 17317976121, 24806988702, 2932363191, 6080820717, 13205489833, 2242970621, 5812422996, 27009127983, 11446285961, 4976900735, 16993685245, 9134213891, 23510074531, 4391880360, 21464920521, 24498409215, 8596175814, 58404356, 609181562, 90373195, 58176668], [424799159948, 407184572913, 271088467897, 384021717726, 1233509995, 15508561177, 23518478352, 10375983309, 3711964118, 14480971007, 15307126680, 21564029722, 3859719697, 16205079593, 2414535223, 15431809455, 2671359683, 18111089638, 24613998481, 14236492266, 11290830881, 13929561576, 25895210687, 16633660607, 17928871545, 9054590918, 16299509561, 12479999313, 8993157908, 12764380417, 17032087146, 20745634093, 18475020586, 7500084231, 23595540415, 16508370263, 575406686, 15378335695, 17135593914, 4467660945, 6934289777, 24004736075, 24324988767, 11839949877, 15237842672, 15015354215, 21673087908, 26746013995, 597570280, 513025906, 325068670, 123920113], [82243957962, 496187934834, 213072099306, 742791826584, 25051681312, 27269285005, 14486138676, 25323927838, 14535004441, 5657845464, 19261896500, 2283655858, 6726173447, 5318286654, 15013398115, 4953599027, 3824605036, 26969715730, 21463771072, 19855711203, 23118862777, 20194703054, 2452932009, 13931517025, 20409676150, 6384200140, 15743147787, 12405156571, 2387259780, 5345950341, 5505337709, 15313266044, 2772994268, 39626060, 5512755482, 10993011060, 4245149703, 9909986907, 19026149188, 13310054352, 23756896314, 15060240603, 23813899641, 12210474463, 6766002309, 5453969469, 7594244778, 21230710809, 125289289, 177660484, 39297487, 351714532], [704462852836, 509311197074, 664893415483, 71335609483, 25617400095, 18746953423, 24988461834, 24380777235, 4093764086, 21251606669, 2255382587, 22827763322, 19219478177, 22671829571, 6787352846, 26898926889, 10522084759, 27193271486, 19479538138, 2851597806, 13929012318, 26526937739, 19721481792, 24712083070, 24199129325, 19928829694, 2715838700, 19279350337, 8801119294, 24626295468, 6194503266, 25750141103, 7352544939, 1021653298, 23013508533, 10993612429, 7038043801, 6486309924, 1635605415, 16359481200, 7580718269, 2062674776, 24604675820, 25879499980, 25563985607, 2719003335, 321303933, 23152947463, 685885029, 739197105, 318193230, 844632835], [482130966916, 395858668012, 236121476730, 351234652232, 3910309279, 10426539597, 22349948666, 12960682151, 7325868912, 17097720129, 4757596288, 4513626195, 6171847443, 26731363023, 16272181232, 20240946839, 18418916135, 11323518924, 26002810137, 11978102524, 19542576700, 15479466096, 20682355157, 14119423184, 1152708712, 686187387, 16959652763, 9751251035, 26890316918, 1169985260, 19595894809, 22458722117, 10197315646, 3976051444, 8848170040, 10134299652, 13372157644, 11586221976, 9754468649, 1977236668, 2396330597, 1472615227, 18460815890, 22583297384, 19130968031, 19837269241, 8407330386, 18927527927, 390157109, 212183959, 830798780, 211069488], [429572190361, 589397232419, 716349328257, 354308020566, 19078700915, 7842977246, 2357968314, 21749418092, 23977243880, 6104165453, 21589062160, 26854360483, 25032751255, 25596459130, 676605659, 21919208905, 24232317615, 8196639413, 20395787034, 8555430158, 26502834929, 12366954, 14687015483, 20674269520, 1875737243, 17497096570, 11384527017, 10556510941, 7379429813, 9952370975, 38743273, 2866195985, 14415904394, 232529791, 24926164110, 10146018861, 6491742147, 16210556580, 4911838276, 6033351099, 181792339, 2180982928, 10796695841, 7539751707, 23413666546, 3185757594, 14115682631, 20108377633, 217301837, 295965592, 734307042, 93036827], [755101401475, 581954254745, 3750866607, 102234715519, 25770464827, 13363909288, 4514983964, 8376814730, 16233694422, 17168424061, 11686849619, 23728229994, 9063961133, 13043728361, 23049713495, 1128685479, 13897187749, 9320002099, 27284846323, 11768006286, 12276931178, 4827421649, 16255996876, 17207304013, 16429311211, 5894861544, 9751898501, 20543954572, 430035472, 23808642103, 16988400892, 10866585279, 13288620642, 19924454943, 5595696075, 24508577339, 18017837732, 11733830863, 6259158199, 21863591495, 11763742329, 9969195977, 9823314534, 12326021600, 16493503655, 11457177935, 19621429044, 23432417640, 744161450, 64132540, 865040175, 537656872], [7954273880, 151352767075, 303394503880, 437932779846, 16154632611, 4703272229, 22613365741, 14572318335, 17291069268, 23094903745, 19816828337, 7916264966, 24299706686, 12780217263, 11288941059, 11364810211, 5304272949, 2058299777, 25500462763, 807769325, 17243769809, 2458511761, 18920959027, 12700368269, 21903611007, 27018995593, 10276954522, 6308868218, 19991900310, 6612042576, 19681342682, 21841885016, 1538452097, 23667866949, 13777423031, 19449209257, 12804982233, 9464990215, 14435739031, 27191726012, 22161445726, 25400659441, 13146335261, 1071743346, 2121610488, 26150084565, 4962454921, 7287772857, 84190476, 298493869, 12685608, 333605846], [745634634681, 349949202295, 139297249832, 768112148874, 24751568390, 1619421772, 21282356809, 16142876915, 18984562967, 22583429568, 13751629295, 6291511783, 6044601092, 12853771800, 16634127901, 11083951358, 17581803512, 16889107861, 25560193687, 1719358208, 23833140070, 11100113332, 10754917389, 12089032273, 13695860233, 7628319203, 11983790745, 10839034277, 20897484431, 3521086888, 13059887204, 3171270209, 8020230286, 27272665028, 12027795462, 16819741331, 12851196940, 26008481990, 12339332907, 10539849836, 26945151578, 13842101803, 22809010151, 17339778235, 4341542436, 3355438450, 24603595811, 23189374881, 306319701, 667629771, 167939873, 730764677], [154656508251, 799965482743, 151332117107, 646806099094, 11685593530, 7998774473, 7735189564, 4329145877, 14327423295, 10529992859, 21570520564, 17861656725, 551938756, 25275780932, 8047917998, 11766717554, 4533242840, 26042519525, 21499482018, 25707695314, 1769743066, 25721694449, 9882474004, 4789212692, 397397339, 26780053080, 6307201875, 13433910419, 24457489990, 6866178623, 7197987061, 124568664, 14864233772, 26356189460, 20019164035, 22814324264, 16774144423, 543678682, 19400102467, 19281065784, 17765158096, 21045818315, 23848205264, 21515504337, 21469567545, 6394487366, 17943519479, 7259598321, 475757215, 117849262, 476306684, 773398117], [139404364814, 706836046180, 651025969258, 603965458103, 6910853188, 25167896716, 8959927365, 14827888938, 16582054318, 8140301563, 11003490951, 4352236878, 20362548152, 19791928331, 15725796498, 24351477027, 21833877716, 11670838150, 14291492683, 21017433351, 17223012705, 9568479189, 22567435769, 4809173251, 18124005664, 2891526302, 23998747898, 23349773128, 18715250715, 15097798839, 19044902576, 24115442283, 21813890590, 20254480540, 21984667296, 24235762211, 12762965825, 14714090697, 4654133230, 2746567419, 5653981469, 12262438182, 12372375962, 17656923673, 18924382419, 16508175707, 18456630766, 548599312, 148146438, 799641560, 343338828, 792374871], [24023365339, 432359428633, 145395872113, 709918515184, 26934342715, 884956752, 7748792116, 25169175621, 17779468502, 20247620953, 5197857079, 7343204329, 21858720713, 15157537389, 3998545757, 16182951917, 26181665226, 22070233372, 18861755258, 26899886866, 19345735349, 25084402370, 14049623274, 18483392818, 26723703512, 2824538402, 20266694323, 3683016721, 21553837852, 19077165578, 14425565823, 3881680500, 16805826609, 19656731255, 4624019055, 19950016954, 3711801678, 22548016036, 2967115772, 13440866478, 13843031152, 15881538886, 24329893029, 26661571483, 13754658274, 27327910717, 20166967850, 10033868456, 67182921, 45629931, 820709930, 795137071], [209190594359, 509856632805, 442501517035, 829035941280, 13998759869, 17774521212, 20039649083, 4873416256, 5465579186, 21803829013, 5562035686, 12309597707, 8582470187, 11187837070, 11180974662, 6851224688, 26132985368, 5328999076, 17292222251, 17964576291, 23236910994, 451746508, 4270506711, 6302922387, 21818965414, 4791539676, 23253300756, 8933904260, 20156816404, 2983930358, 8194393060, 11774070475, 10401627563, 20550395318, 17030647072, 16669151546, 20188818634, 27051458235, 26687415687, 3261595312, 24697114937, 15586463836, 10437377569, 6156265882, 15034673012, 8322976131, 14032777781, 20532332269, 526136118, 49988266, 572044439, 361896050], [770905790289, 398883314607, 361611521583, 579024225327, 8187616181, 17282081066, 14610918760, 15420443367, 7283355729, 11525875237, 25110778224, 13287331941, 23921320717, 2805254759, 19146316410, 18875603454, 2177127582, 16434897969, 11393498882, 5073727654, 1884253718, 20792921617, 23443358067, 8774874136, 945808760, 7508797029, 8901492706, 21487482011, 15560270603, 26695704808, 24488821597, 25509083491, 26500891105, 17805333755, 1404046420, 21511327862, 23796017756, 6378768227, 4428595551, 2358040823, 16444076325, 24049733815, 4081455071, 23572209133, 9755930113, 20491755718, 20898121605, 18189657247, 725079614, 618860607, 557874716, 264906041], [574356931822, 215259036435, 411254809611, 661387698054, 2874930421, 1344582375, 24017145592, 1273456657, 25223112180, 12817900863, 15872252650, 2141121981, 20571926182, 12945467847, 4830374461, 23830905993, 22724271775, 6149330128, 24852538397, 7570981696, 5511897929, 19354883976, 24994454382, 186026319, 23290577667, 15834916343, 19124247851, 14855653313, 25396307506, 3002207028, 6763205334, 21334524849, 25904507866, 25982395366, 18984018855, 14178495513, 22617002909, 17096035837, 1972205802, 7804840178, 13647433986, 20631285168, 21357992810, 3012403858, 16806908354, 24322935606, 8397896590, 22850449432, 59757177, 360486442, 123291098, 430970873], [372315196282, 663628939371, 113107130286, 12991838763, 27236425129, 13167610313, 21678320739, 10928733707, 18543149751, 12787391345, 7584466851, 22151547860, 22000228614, 7802413777, 843149284, 19236089248, 9117344962, 7612756025, 18431714950, 17335099250, 25129030466, 17966595662, 25135709354, 11434393741, 22891891317, 4118382612, 6532256977, 24697022712, 6078485518, 7781187922, 16305710429, 26033596578, 24012142471, 24776871365, 24932277155, 12657506429, 826632949, 2610979836, 20725164514, 24763807841, 13027596364, 27101587684, 3046115087, 13263385557, 8393067906, 11490121573, 8004624421, 24053614984, 96737817, 428030164, 681527410, 81646531], [226842649823, 99191777250, 106132864986, 28266816521, 4530195912, 12379311902, 21538983210, 226664033, 8060379657, 23563569309, 828787604, 16959568164, 22295966723, 24618773566, 15117700622, 11364232216, 24823812743, 13830129262, 15517396704, 591137233, 9672687766, 26955998695, 19698975110, 3327003607, 5680782643, 4565924621, 18133954587, 21043532127, 25128620398, 25989906015, 15397673030, 18807796844, 9013686449, 24417213643, 19772457603, 336231580, 23178591066, 7160605370, 9990815470, 19217456698, 20290208908, 17892897688, 20182766442, 23304150614, 7568493202, 13415880416, 17926821670, 24606017779, 344684292, 847941011, 412899859, 691229299], [634919107616, 211255287483, 464971700720, 699839372282, 9014401774, 7430780476, 20682598631, 26266433486, 12576808438, 22330127018, 21229661056, 23298035895, 23191016765, 8991063548, 4188689248, 20753537078, 13674249389, 16758201030, 23943058599, 7815920756, 17578199452, 22453648843, 16278856679, 2223725325, 23536309986, 8343299390, 16401502568, 3718744841, 18606141565, 2852044206, 108831545, 8783018208, 12383119942, 13402324984, 6933046429, 3989056130, 11119491618, 18583607851, 25423593179, 11285320662, 9563070588, 10202777691, 14510653600, 22771095384, 18231760672, 16005374524, 13417774640, 12693601155, 524800796, 166276601, 137262014, 236643720], [190427239456, 19049062125, 364194282119, 520974792570, 23160694828, 26726356647, 20167391806, 586461193, 4832319773, 15291088055, 14343936034, 1427640582, 6699520205, 26475933222, 21935902715, 19194003059, 6354029142, 4554799465, 20179336602, 26951041268, 11206318960, 6547053215, 8988079023, 18869615370, 5528774453, 9983993300, 2194507360, 8037403604, 1761081728, 18495586730, 5861161351, 24421135515, 482289041, 16729582450, 14623608517, 2683511032, 7665192308, 15535267894, 8615768589, 10041486861, 20336462303, 9400868141, 25569366866, 25504087748, 16838590044, 9601915293, 1261370253, 1159464635, 575762372, 715009733, 683387144, 84516365], [214962335373, 532004105002, 534156393276, 706629824229, 21897558536, 22019667629, 9935341559, 5855029334, 15873882692, 3881858843, 18076313280, 18091262844, 2003208127, 1174813138, 16168160112, 19610841335, 16336904520, 5952217558, 19976766575, 18048253568, 3711486718, 13816771610, 13214341046, 4601398076, 8858199129, 6056357036, 2240814974, 18400057068, 9935687395, 21616328427, 16250920378, 7299014201, 5565266754, 7726962567, 27177698946, 13436207147, 16796734247, 11398639643, 20044420045, 18784223049, 8001443790, 22511368983, 748565680, 17074117783, 23096023434, 1316667681, 20867805341, 8631386823, 473625019, 862998866, 271270871, 354280656], [830290136614, 427763233752, 277239167729, 134398571552, 5646817741, 15449657674, 22081189144, 16464808102, 3683747143, 11968795425, 16297283172, 27423865327, 10017276760, 22366143097, 4329403952, 5770371372, 9768126536, 9010768357, 19335746064, 5160364718, 24885053801, 5328550537, 20506936976, 19217181263, 1309554452, 14241634267, 7031907258, 16788120711, 17340462963, 27204166870, 3871615575, 18283552837, 6776084067, 10718239987, 8462177322, 21325804084, 23747997609, 13481185884, 19138165177, 2115840334, 7026576002, 3700943866, 17761614641, 3539929959, 20881600682, 18022329415, 17812681251, 17755779976, 87954792, 121311317, 471356578, 426114715], [93848370273, 255589592515, 140806113049, 714434624169, 2013054998, 13234783593, 740454871, 13999691853, 9541322848, 21488571785, 13724585546, 4120450808, 19970624235, 8364953324, 20022986955, 9927544346, 17618324643, 24577121749, 4390890902, 17221396706, 8328510065, 17852891196, 19954395270, 18426827273, 1727930111, 9739465548, 360799328, 17906803668, 2726665760, 8789486854, 9829105644, 7593607139, 19947222862, 3824868257, 17896546171, 8051584740, 13304536166, 19507398210, 5154562541, 20767014204, 16794280597, 4033923608, 11193299177, 21065647527, 11614646186, 17754828338, 22842796121, 6450320753, 747632708, 267047299, 329451350, 117550919], [468255811549, 26856115610, 30733716014, 604890137108, 10608582261, 16749900966, 2489687624, 21026852267, 1258818054, 14636619279, 8674470220, 25571053328, 9509697206, 2064058895, 26203674854, 25643272106, 9260191722, 9752978944, 24625722216, 6717435570, 12994260607, 26296240420, 21091128938, 4477346554, 8440817578, 22043116308, 1374478341, 22751794846, 8618305846, 26912841239, 8894067400, 16314598129, 19042448213, 14379881278, 14551947956, 13744136037, 12954494799, 5359069169, 4501734223, 10154725490, 4924736105, 12571322678, 5959432653, 8147617191, 14687728452, 12725680792, 11299882695, 8175814295, 144886805, 168531855, 426401908, 533183207], [698959588314, 193645910990, 546697462496, 255652452486, 24318102737, 9396334019, 19141404088, 13594162098, 3356010400, 27068274402, 4052420936, 786110741, 22490919771, 13290818325, 24626964448, 12528960434, 26444317562, 9297574064, 20321584690, 18894055646, 1932306570, 23909226904, 22662036516, 22883253291, 14812941637, 6165508718, 21594856928, 6365797610, 27180054171, 23073597414, 11344869864, 16125823350, 7720081094, 6830634550, 26235519635, 15475560716, 17666379572, 20774618318, 11349579167, 10242840510, 7338091096, 9697028346, 16108847471, 7378077066, 20648883434, 24766713874, 23387672829, 23833341229, 66785328, 278315729, 104745340, 862169763], [546923131243, 180260090096, 64866896492, 96444783736, 20513863368, 1205674382, 26282283321, 17605878329, 10388233889, 6792667238, 1107679166, 17536575969, 9434977534, 25526609248, 20660858548, 4686113295, 6336957814, 583065391, 23910257344, 23259986588, 26126966067, 10532372171, 21757768097, 17503206143, 11650715957, 24158589199, 2727155560, 11509373999, 23660355928, 4967826198, 17722533902, 8638392203, 24836937926, 10776373078, 22624475428, 7382643056, 25427087189, 20389312064, 16638323224, 23712911468, 20437574414, 23744302130, 14608443379, 24325867989, 23152453757, 24323631649, 21327359881, 4198598522, 864449876, 666317216, 823553933, 855411470], [644072358731, 110502036110, 502744560105, 355449375280, 13758179130, 20554921845, 9341791658, 2051760885, 8680057133, 20171158213, 17797287736, 4173148235, 25505685674, 25230542601, 5730582128, 8722345349, 14030038497, 5227768080, 406348651, 26297020969, 23504890711, 13018456882, 22854517252, 27426506589, 26766046102, 1711970505, 24882723872, 8227055621, 1707914527, 22628314220, 1745349848, 15792815367, 10645474493, 23499761172, 20200692316, 2391464744, 2365573792, 926002457, 27374905508, 20036512007, 22165099820, 25689246718, 25965594203, 2962838516, 2872451475, 16205548778, 10331590038, 4159069492, 105907996, 522922667, 706717650, 772650814], [203640275433, 597851216689, 844976971801, 231810458599, 21116352615, 13899757835, 21979561906, 23381721170, 10042882109, 20444902783, 6773273917, 20478114540, 26114686378, 12392090195, 1741192717, 19336367087, 16552452077, 1850078326, 12582470898, 3018575400, 104060955, 5447374653, 13219725963, 10630960107, 20575910054, 7355567439, 22001121662, 8986055250, 17704924073, 10528528140, 10737627728, 22852138839, 19304049494, 301089298, 4079884952, 22640575805, 24141135331, 26500659659, 11451984443, 10572933439, 23495175776, 5559307159, 10213912767, 14454380323, 11809700046, 27196890302, 24057484125, 22011154874, 42684556, 822387944, 731009439, 578123778], [721347289369, 29799048375, 421821568718, 117833037103, 17524202195, 24254304365, 10214047152, 19516142628, 26289970391, 18119104812, 21370903876, 6185000712, 7119976925, 14828737780, 112158744, 1951595390, 16983708391, 17022529939, 20858470218, 13746448234, 6607345394, 24048792128, 1427483350, 1084076045, 9828389792, 17973658144, 25048695113, 662125094, 13716015038, 2985049830, 23431601007, 24800220441, 7714138146, 23576074337, 13490508142, 16074866263, 13133906958, 5761521182, 13623091267, 22641998829, 26248722535, 9665486652, 2058562533, 15594320073, 13653592074, 10766917892, 25965751621, 11652890235, 19608427, 667613577, 702697720, 730185214], [428948278409, 623454198870, 163261688573, 458061469733, 26084750856, 6048290588, 12418792107, 17618286575, 19555075683, 6263653602, 26525473795, 22704959395, 4476077817, 20958425254, 21927587771, 8995042522, 9485406846, 6528038373, 9840266884, 1717780246, 9964205659, 23104553983, 17691702201, 8742187302, 26759094538, 4029221714, 12200150068, 12706427901, 5076653434, 10009584451, 15483666286, 25885080290, 13540032998, 11972697674, 3117813158, 26727313524, 27062040333, 19814379616, 2704468737, 24922004933, 2419255965, 14505122704, 10444535252, 20977894897, 157942303, 9656333995, 24149827917, 8635380491, 475478702, 536998725, 40782326, 320960640], [81137156964, 59283249125, 27561028330, 842982172207, 3379466798, 13432175039, 7816959597, 5549017081, 7852988076, 4719253225, 12702922917, 14656848205, 22468728328, 25912836977, 16701941300, 12619565188, 20025016990, 1628390816, 16695778562, 10055690131, 3705156580, 18927719631, 453887120, 10961772174, 11798946456, 3301666625, 16074142227, 1510292534, 7002172926, 15782416789, 24776522181, 23181694910, 15542800925, 9425829558, 24733592544, 23295937970, 27068895363, 27216012745, 17064627164, 24293553992, 17023791329, 8692752005, 22282503950, 19908293062, 10524714737, 23066890564, 13227293807, 11834313767, 395232621, 181515164, 274226525, 302620631], [229815515816, 177556911455, 59173031074, 34929570788, 18366669665, 6669573182, 9426107287, 3125515077, 15623316016, 10349776002, 10556991658, 18516700892, 22953644836, 5531199924, 11534181904, 1017299162, 21383427845, 3455445907, 925353720, 14067954132, 24775726628, 25273725384, 1481899541, 22673582497, 4520888968, 662993745, 10885341209, 5470420487, 339364843, 24529803132, 23531532328, 11369623736, 3349977645, 25966064349, 24253790230, 19849776501, 14180735542, 3778374426, 26603086697, 19262096884, 23459829421, 1168125353, 5162432666, 16829823027, 24167158281, 15011181739, 8650487101, 25319699810, 884604178, 217700771, 825922552, 310991266], [574194720788, 540732676763, 472277366870, 441657367908, 1035392188, 981425745, 10080801061, 376602787, 22264754001, 21469675239, 15155418973, 1306681806, 21642236367, 3979044959, 5835229479, 5866848425, 8246360747, 5098239571, 26600488277, 8922354280, 3812013518, 9445114720, 20101061013, 18113417769, 10189820466, 19025633968, 16952750830, 9902817103, 1611182375, 19416525554, 2593837673, 15930766793, 21162156882, 1900616696, 1033800803, 25106598153, 25842537874, 7213071382, 5518830769, 27164345820, 19978985121, 27482245271, 13935923024, 11988590568, 368201632, 13359598645, 3914539911, 10061608279, 173895874, 230320229, 169994946, 677771980], [639113556447, 521605171091, 627508089919, 111686090937, 7972645472, 10178315715, 11465262890, 23469720808, 12502923751, 21553105012, 4649879286, 11428820592, 323569878, 8716994594, 15526326347, 8160469171, 183422226, 20975664478, 19203904583, 23338086624, 14607858285, 3123585885, 9936111227, 6460638576, 18690440795, 8964840524, 7552826360, 20556749419, 16316925578, 16163179125, 4968834256, 19564436939, 23475696554, 2266345241, 3969119968, 15789643323, 16573853237, 14405785839, 3859343884, 2467161164, 21210779669, 3857296985, 4327984431, 20917199222, 17997330271, 12657499578, 21821260809, 4631800954, 656655644, 765005579, 883476884, 871150147], [76976636238, 730584282985, 619323509506, 616468205526, 813887640, 15313401638, 17862762991, 25032653698, 20415953805, 1012322732, 22369860710, 17125734643, 24783058655, 26931283263, 10159257287, 13860908697, 3132688446, 10241633153, 11291422826, 16968287162, 2428811746, 14066487336, 12625580273, 4097961920, 27512049973, 13834897093, 13975444118, 27437179982, 27428936865, 12665957277, 26241094830, 13162023245, 212846496, 7813260956, 21042942073, 12944802556, 11213261565, 3536284545, 21740149650, 15796718515, 22117864252, 26292063480, 5688931055, 1531836108, 16194017832, 8904151731, 3434340456, 27181115797, 49835833, 752349300, 605271357, 682414062], [667681180383, 502354773700, 395445762830, 521671616553, 25800223897, 23912998116, 12548918048, 9412017973, 26269152961, 2357866386, 2232256494, 16744113359, 22539361177, 3071386163, 8794516046, 15475665372, 21360312819, 7879368828, 5641542998, 21233916767, 22720726367, 2324254202, 10865697160, 7132020952, 20687017247, 15250371849, 17800026803, 1419132446, 10919692371, 10587649728, 11331597028, 1445118475, 14382383536, 26834424073, 20133055679, 20000894030, 8372029353, 14274273392, 1865517504, 22048195286, 25161393660, 3269402414, 11096983386, 26368845272, 14586529293, 15236070402, 23548295082, 25096809531, 314913071, 700435701, 315900699, 156060809], [174838225157, 72775301842, 223650927612, 39050161964, 9546287560, 7281111360, 9117044324, 21131608676, 1633937894, 10167608687, 15279488134, 11994309913, 523357996, 26760745443, 19422742046, 18812086531, 16899979468, 11773066912, 9125731516, 24436902797, 13190203299, 13833838288, 937939844, 24415085183, 954336085, 1268717160, 14047737017, 4506281179, 14916185401, 21302503585, 21416824641, 14924442871, 23831397064, 20163393426, 26902778453, 1233565702, 19077539965, 6094423486, 4192007860, 7129362237, 1271114669, 15095398261, 10382373990, 17968021538, 18904291908, 20069610614, 24863811919, 26248706508, 663938686, 116734693, 345083960, 555031247], [683377834370, 46150191412, 96737901229, 333701384056, 2823437406, 21329035927, 27224603558, 9099999005, 19109467485, 22262258408, 15336074511, 22461275339, 22486576175, 7051352876, 7570920130, 22135470888, 10294108558, 22172682265, 4201416887, 4469413499, 19634603889, 9093183097, 26947223432, 7825539591, 21843218171, 27202796856, 4802776246, 24449274804, 297057438, 10974855631, 14294350232, 2979556630, 12563993689, 3615910804, 6821632770, 19898628378, 563012545, 3129574899, 4307872189, 3465552217, 10862723950, 3401777219, 18849774471, 11323589294, 25325414753, 25153490644, 332829237, 10227392962, 864091788, 311000026, 58864712, 796048537], [214775890802, 588414940503, 246726023318, 258263571171, 4362883239, 17775373371, 11030543442, 16375777838, 20915537715, 10796204181, 21067144796, 13585133813, 3474643215, 22666031734, 13274685336, 520298792, 8754686378, 6201968159, 12731723281, 24720464819, 21434360039, 13634711648, 2918310612, 64347444, 842600181, 9352424813, 5359746922, 3865383459, 22682305804, 18571832315, 4805606701, 16275851136, 18453735893, 7263352018, 24726876859, 16966732233, 7072252828, 25617944114, 10626496231, 23668067705, 19818104204, 5476057682, 9327026203, 8345020975, 10345541092, 24290759125, 13131115501, 23187663154, 54641953, 879240519, 758206263, 17912017], [430439285285, 775678217194, 234300971784, 489902031912, 12462432264, 3311777182, 6148472482, 24615918838, 9786803075, 11026620175, 8945986758, 2029326278, 20193450158, 1391527938, 19931366920, 24404663603, 1921785728, 20674823490, 2261869151, 23835099208, 20077771333, 9208788483, 4987272498, 9384565303, 16270960390, 1375849285, 22250384447, 10275020680, 7249888346, 66859963, 25440366597, 8920210010, 22756163149, 285680190, 2182372379, 7946365284, 7495650332, 3630255248, 19455950176, 18035741038, 21765410124, 19856184511, 9729259976, 25970026707, 3750994203, 11633419941, 11831316098, 9533887405, 822352463, 574388259, 362331780, 829042492]]]
sage: crystalline_obstruction(None, p, prec, cp=ZZ['T'](cp), frob_matrix=matrix(frob_matrix), shift=1)
(1,
 {'precision': 6,
  'p': 31,
  'rank T(X_Fpbar)': 1,
  'factors': [(t - 1, 1)],
  'dim Ti': [1],
  'dim Li': [1]})
sage: p, prec, cp, frob_matrix = [29, 20, [1, 0, -2842, 0, 6013150, 0, -10071827774, 0, 15254991663062, 0, -20413558347816132, 0, 25183725078986957040, 0, -28930070889860844230928, 0, 31354850260650911077304990, 0, -32210910187460313693800838218, 0, 31469749051369186051984935167815, 0, -29487887771743951016409382448309010, 0, 26375254206671919727420037524201218102, 0, -22687771924747537276536393100397652851152, 0, 18654716170549122056729371560154561740400662, 0, -14751210083611446627308483619671774252597078610, 0, 11134462438140703573965162950721453584523122115415, 0, -8060666688446319677418837207062523136249075778277578, 0, 5549638432165421174581815213181323814007419569332900990, 0, -3621608054910425904455783818875359831667388368853669213968, 0, 2229789730011501301782431770242470466232536768280068005971440, 0, -1278364339274865965744914151333054799649434908505466913889814212, 0, 675678187351849649046322496707080304502427854168152833458887250102, 0, -315520954290489659668386035103197938982314585966240185540378144606974, 0, 133233655948586273480174419013776063687939548595971624731289307998865150, 0, -44537719192048520439577824156929296908244118848853271558880931945855044762, 0, 11083984014029299642865954626156618594848630761272269796423949481912843741841], [[0, 0, 0, 0, 0, 0, 0, 3880086648207125467844153773537, 0, 0, 0, 2007794337450675149529651759986, 0, 0, 0, 1680322661544885578488878698816, 0, 0, 0, 0, 4646365873726544835475487633967, 0, 0, 0, 0, 756334969447717728992507348368, 0, 0, 0, 0, 2252683283703118881092969413016, 0, 0, 0, 0, 0, 0, 0, 460179053005128304490889809726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 122904640100824771629818441892], [0, 0, 0, 0, 394884588970833494392904529193, 0, 81469574480799658468275923157, 0, 0, 0, 1789470719067966560105270253344, 0, 0, 0, 4388653721447379814758802789936, 0, 0, 0, 0, 2670093532022402087208018674771, 0, 0, 0, 0, 0, 0, 0, 0, 0, 345002662846512604418289985775, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27815734699993536474300213539, 0, 135227290593429690631658334990, 0], [0, 0, 0, 0, 0, 3167008960711884447483681907275, 0, 0, 3535994462548388927879656688244, 0, 0, 0, 4538587039876107716540629837073, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3107110602950945681900904015899, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42757424166942121058533455353, 0, 0], [0, 0, 0, 0, 1713549514509064576330738694813, 0, 1841059576208004181290536362514, 0, 0, 0, 5093828738173820155364346728790, 0, 0, 0, 1050893405093303682658455885691, 0, 0, 0, 0, 229524883144614362510686135535, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2544830079530741321051308539235, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 136658233897562160233928741033, 0, 122714888091705448645765877970, 0], [0, 137201174146729755220481579259710, 0, 22314338383105980227455299840511, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 655978878896362620602641812003, 0, 0, 0, 0, 0, 0, 0, 0, 4340404559101892612967351296059, 0, 0, 0, 462090322595428603919189723142, 0, 0, 1495396501850961494323678357839, 0, 2532267893886708122077927441206, 0, 1319165409728310984893881593589, 0, 0, 0, 0], [0, 0, 28064285698257836748400133102425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3547183911767781911776573230968, 0, 0, 4157793287046480688297675297916, 0, 0, 0, 0, 2073422713766636015292129654287, 0, 0, 0, 5010540621742938092891070360627, 0, 0, 0, 0, 0], [0, 94644438986727315523092900961657, 0, 29099090138035590711947385611624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3289415569664483390744280560601, 0, 0, 0, 0, 0, 0, 0, 0, 1037188895708099745509425319006, 0, 0, 0, 298803490408942497968898141236, 0, 0, 1424039091560427978027861499797, 0, 1922234421766966232151679185559, 0, 3481943509194258637062868128285, 0, 0, 0, 0], [112518232954717354814891370736304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4178861363187678250844907977675, 0, 0, 0, 0, 2485844378231900836095047929174, 0, 0, 0, 0, 3046439490466320746724232580119, 0, 0, 0, 0, 1621367678694631569442313445800, 0, 0, 0, 2679082048923359473702879474407, 0, 0, 0, 1161922550001404142082073648411, 0, 0, 0, 0, 5002856789056863172984671211575, 0, 0, 0, 0, 0, 0, 0], [0, 0, 79036556482631564729641217487661, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1620241562511733483480075356017, 0, 0, 4108135390194377504034107928704, 0, 0, 0, 0, 2586120798138529860888793442913, 0, 0, 0, 2043599174083338197029459168889, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 174425405833355218571320882169, 0, 0, 0, 0, 0, 3858342419865001323246452383181, 0, 0, 0, 3593212375845154015095587426961, 0, 0, 0, 0, 1338576832185159284806614741486, 0, 0, 0, 0, 0, 0, 0, 378153322582516935234909872820, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 124027610169886697136652534789783, 0, 64784316166143073935997146939310, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1468635811587369974480516422787, 0, 0, 0, 0, 0, 0, 0, 0, 3532415310080844143430734375379, 0, 0, 0, 4433541302339863133564513399027, 0, 0, 1433784431064776861935742102693, 0, 951218707135241207583575985251, 0, 2022050627564484924442059345246, 0, 0, 0, 0], [60564379450736573105173090719333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1190920717323609800079984583208, 0, 0, 0, 0, 595229067463226182224546444264, 0, 0, 0, 0, 5118092759859294756396968630091, 0, 0, 0, 0, 134809898056075908301057396513, 0, 0, 0, 4720315478173615672712058127744, 0, 0, 0, 2421013819106300035595894950384, 0, 0, 0, 0, 2348551927961156667698115982640, 0, 0, 0, 0, 0, 0, 0], [0, 0, 90338588941751961815629322904136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4713245124066363810049618246319, 0, 0, 1283928208404253822882345001036, 0, 0, 0, 0, 605364802826588883286603936360, 0, 0, 0, 3833441121186005358943159921808, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2301507736355253963931289818992, 0, 0, 0, 0, 0, 660458320901044783645067335609, 0, 0, 0, 2061488484784456025204142952533, 0, 0, 0, 0, 739517474195048101577870673743, 0, 0, 0, 0, 0, 0, 0, 620634650064558077860577538786, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 85015534272312125553055210854188, 0, 33214528601040198948438520292577, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1598407863456430714558014273733, 0, 0, 0, 0, 0, 0, 0, 0, 3615571436273970038041334804377, 0, 0, 0, 838972215237324987659322550980, 0, 0, 2249617271831306799034952878142, 0, 2139731417324202765291487636015, 0, 3918185930217885729744242724616, 0, 0, 0, 0], [83982981829404577311463721338448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3686205045133942282904952090120, 0, 0, 0, 0, 3073054025664861702186476243735, 0, 0, 0, 0, 751071230524173728101129567545, 0, 0, 0, 0, 2417163913238830800870171014431, 0, 0, 0, 2868368039957648707207291985331, 0, 0, 0, 4475881055837529420192341822010, 0, 0, 0, 0, 421682447199008159948176156700, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4710333283196506568684578692853, 0, 0, 0, 3266898077612885202741699506897, 0, 0, 0, 1447647928579197340946852814299, 0, 0, 0, 0, 2748119451392470435892200555171, 0, 0, 0, 0, 3723993309973679599364421446264, 0, 0, 0, 0, 4938039271472444233527691352287, 0, 0, 0, 0, 0, 0, 0, 1913294974210151499400095787938, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 150343968742576699061304080999], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250900305976959188906168791587, 0, 0, 0, 0, 0, 1692399256088877370156884520904, 0, 0, 0, 4040701229080932513240866600509, 0, 0, 0, 0, 2305179764255064875004302053839, 0, 0, 0, 0, 0, 0, 0, 630657352381520097459438870135, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4848298741732124024145019139522, 0, 0, 0, 1030234417562440156043425698855, 0, 0, 0, 1604129345014354745432974493604, 0, 0, 0, 0, 0, 851579580855179153871297547654, 0, 0, 0, 0, 0, 0, 0, 0, 125319416258435402764461327882, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 7451483880433089659959765198185, 0, 21517903080110104740598072065905, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1495322256575197962423567995996, 0, 0, 0, 0, 0, 0, 0, 0, 1127106932925445545251188265100, 0, 0, 0, 1808381317776834756583102184405, 0, 0, 5034671324822009356052483515103, 0, 1444453106516505335409693961409, 0, 137565210123447548474950372851, 0, 0, 0, 0], [94525504420957615386051139119851, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2281130944173145944765737920272, 0, 0, 0, 0, 913105582689943105749605898465, 0, 0, 0, 0, 4009351096243288042575239554028, 0, 0, 0, 0, 759465578254945147273657800120, 0, 0, 0, 1842201915399801603231584973749, 0, 0, 0, 107169084236901922230809372673, 0, 0, 0, 0, 2782151064979968275553376360871, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2843207439951998582788482192882, 0, 0, 0, 2538004091569584800276220327786, 0, 0, 0, 2856344193095350991173589030697, 0, 0, 0, 0, 3010746730173202103391621127162, 0, 0, 0, 0, 4968820933384191622809250665334, 0, 0, 0, 0, 1833944724139356148237315132349, 0, 0, 0, 0, 0, 0, 0, 4211243927394159765385280290870, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63490518807233666558846953738], [0, 0, 38805347967212648984964669180489, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1850257119562724812710866025713, 0, 0, 3938792002635554357854317084954, 0, 0, 0, 0, 659999430131834355049648655364, 0, 0, 0, 2440184304309193900229928520153, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3314173450557979842369005218016, 0, 0, 0, 0, 0, 185827021115173033564862751487, 0, 0, 0, 2079945839581418603790096777380, 0, 0, 0, 0, 964301840597843581616908852886, 0, 0, 0, 0, 0, 0, 0, 5027074720770300808739229816477, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4681214533561590845231872064251, 0, 0, 0, 1651307650794393012780161943423, 0, 0, 0, 374340109326916451786631954553, 0, 0, 0, 0, 0, 1920587156508017288824595483491, 0, 0, 0, 0, 0, 0, 0, 0, 2981575364271092595573091392397, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [27533331404216658011496164669635, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 598468002059645622390915135494, 0, 0, 0, 0, 3164315171476205512307256281963, 0, 0, 0, 0, 1002929863099379832399478827689, 0, 0, 0, 0, 3939972028433299351699100478897, 0, 0, 0, 4129382218398650008025285211293, 0, 0, 0, 3801183632545493811993478163296, 0, 0, 0, 0, 1035458778499104000114590140135, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 887671061384078760421285535278, 0, 0, 0, 2431908808277754573868144341014, 0, 0, 0, 1394868941216021936986531174512, 0, 0, 0, 0, 3625157782785170605394015251053, 0, 0, 0, 0, 687778445956086762874740801856, 0, 0, 0, 0, 2401597526251251105244881044038, 0, 0, 0, 0, 0, 0, 0, 651217655776647066497619611820, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 172144457660057362354898434691], [0, 0, 0, 0, 2871746543416432370664235831584, 0, 96947166411809657716636051980, 0, 0, 0, 2554619459887884610272917338971, 0, 0, 0, 3507256420209070978853557822991, 0, 0, 0, 0, 3651277188788907613361054641536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2308700533347438030840755521591, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173517429639059981945826049124, 0, 16373903083425667276933275069, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 665983842530199668776820910194, 0, 0, 0, 861281001415238079233424761813, 0, 0, 0, 4279476692648693438974230313044, 0, 0, 0, 0, 0, 1987289232187410467828963159988, 0, 0, 0, 0, 0, 0, 0, 0, 3234370608622285164197515796757, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 24556151170080979720669278885507, 0, 60797904609921636350382479332553, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3479539026859257838580180734045, 0, 0, 0, 0, 0, 0, 0, 0, 3494872668471424056289853406129, 0, 0, 0, 4255451936617578305721815004600, 0, 0, 223838479079402170475464243195, 0, 3230087396095724053626823146329, 0, 1550674516003122297263229409577, 0, 0, 0, 0], [38600513743116842569893897904967, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3804281812839498158247784890174, 0, 0, 0, 0, 337937983408395214433944974041, 0, 0, 0, 0, 4761428900934884068346496710253, 0, 0, 0, 0, 2699649630778645072479811459054, 0, 0, 0, 973412565144324052554698807199, 0, 0, 0, 3529532916287459866993045744199, 0, 0, 0, 0, 1295178854459580997028594375746, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1417763850973707774590667705964, 0, 0, 0, 4276325555355066745567639133264, 0, 0, 0, 4481080315747327767288357579451, 0, 0, 0, 0, 3276983615719821050577142303276, 0, 0, 0, 0, 745256594189502026822073884097, 0, 0, 0, 0, 1896904579763588077845179233338, 0, 0, 0, 0, 0, 0, 0, 421008137566062294252800510491, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131679017464478723450371932255], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4496666692033053371683677676122, 0, 0, 0, 0, 0, 3325275272122516054663536988114, 0, 0, 0, 4954357384577254179828740092563, 0, 0, 0, 0, 2018404202328438459316237186390, 0, 0, 0, 0, 0, 0, 0, 4191338531765181625182967624010, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5127951428021666901444713277340, 0, 0, 0, 4759287567979972081332526942148, 0, 0, 0, 2794413620268268530166441721142, 0, 0, 0, 0, 0, 3918265416099533020325357588983, 0, 0, 0, 0, 0, 0, 0, 0, 106575453315837592516099326169, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2628673287156008799482903286237, 0, 0, 2237750010019951997929209497800, 0, 0, 0, 3853602763323021937635284221647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2622354648773488401959038603555, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 142634738500519560916766446516, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2664425372355573178958232007552, 0, 0, 0, 1258294688305001870061243085276, 0, 0, 0, 4174624701747791659709389828720, 0, 0, 0, 0, 4956461299785447965166779680115, 0, 0, 0, 0, 1893446411679917971740008587844, 0, 0, 0, 0, 4318405615033645335167958073976, 0, 0, 0, 0, 0, 0, 0, 152602138898378071359332220620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47940404018928165868537944081], [0, 0, 0, 0, 3302754956619941027839791979160, 0, 1204389973280532344378534044704, 0, 0, 0, 1159718196977414979135334337140, 0, 0, 0, 1332754012528666271017851417682, 0, 0, 0, 0, 4073559697797659093278342333517, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2868052881392046619459642889458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19252460003371514767530028163, 0, 127111186492682023232043783724, 0], [0, 0, 0, 0, 0, 3606318713780418005677416543580, 0, 0, 1501193250501774443090831825773, 0, 0, 0, 4412575903544391945490882998469, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2549723199193794441289999375541, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36360496130922404670380150832, 0, 0], [134166688700699714676772119276674, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3272209625587567939220177515418, 0, 0, 0, 0, 1145863168921720436638272351220, 0, 0, 0, 0, 3347327922093095694755342364702, 0, 0, 0, 0, 4480304437519946765993664273490, 0, 0, 0, 3774836072878788354591051085099, 0, 0, 0, 4925107837256144222990826981639, 0, 0, 0, 0, 2198576355870355269263974907545, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 796421124971417533199185077789, 0, 0, 0, 586821565786558506507604701553, 0, 0, 0, 111891876187941448682125145856, 0, 0, 0, 0, 230691217866115351559510448160, 0, 0, 0, 0, 4106333819429663339290164161376, 0, 0, 0, 0, 3248899483715735370492692433341, 0, 0, 0, 0, 0, 0, 0, 4851365489477980503813676025627, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82687474010093001767417815055], [0, 0, 0, 0, 1936529801183720236614405866472, 0, 1601926503009025457317528463983, 0, 0, 0, 1450305437240930786780796507341, 0, 0, 0, 3197093243185596034797384221332, 0, 0, 0, 0, 1776446207088298762549678876434, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2587663878106371606103642176958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1480812054321964857194647914, 0, 68233378429112831872572208773, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 4702997065441819535573706606539, 0, 0, 0, 4348575367134942904465835586656, 0, 0, 0, 1851635037369756268284551457549, 0, 0, 0, 0, 0, 525928935229075990202370612229, 0, 0, 0, 0, 0, 0, 0, 0, 324048348328590109893058362206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3087119938123736061476104633311, 0, 0, 2405398986744398811415835416010, 0, 0, 0, 3098238248204360686757579968278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3127902909194849885264070388165, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89544324253158410275726412025, 0, 0], [0, 0, 0, 0, 2490614278135151409749709820508, 0, 4345762588505471075372035870262, 0, 0, 0, 600012019423694607538465032179, 0, 0, 0, 4517970135323294134905934217835, 0, 0, 0, 0, 3360510618022310376496248441699, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4737701517037544409388611569498, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129333783305581764460965767214, 0, 84421574604147724833479671513, 0], [0, 0, 0, 0, 0, 0, 0, 3823116457561426820514824233013, 0, 0, 0, 110852469258048889070492993833, 0, 0, 0, 1043330041828239032309182244706, 0, 0, 0, 0, 3094292030330524170090113065363, 0, 0, 0, 0, 2054184714136858378716734477387, 0, 0, 0, 0, 3621534663106655080218452359825, 0, 0, 0, 0, 0, 0, 0, 3311582515109485752650072311940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109088299966305072008918048651], [0, 0, 0, 0, 3976222298529524953170353523109, 0, 4570937235166155665307885536678, 0, 0, 0, 4249613549334918704113464053836, 0, 0, 0, 1825890080991933068819281353878, 0, 0, 0, 0, 956732870055873078963356988045, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3129903679411584696280757728121, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65466028462250081331253997484, 0, 95229650307656804320313801665, 0], [0, 0, 0, 0, 0, 1051467779681478069038040009061, 0, 0, 809445147715660044274382208413, 0, 0, 0, 4147569160476357461513134431014, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4635435342615717058181432804841, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137716483640186196548582034289, 0, 0], [0, 0, 0, 0, 3415704646610032911097543508907, 0, 1425677262241812486164065239552, 0, 0, 0, 1138687491399167711336028587972, 0, 0, 0, 422271182863746017724919492950, 0, 0, 0, 0, 4299632889771751649799768716824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2755215061915831365082877470992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132138464556930215349361976638, 0, 107368019179726435336718499917, 0], [0, 136634738020037521765034351405628, 0, 25571428282958466425842653890358, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1676342140542332187126300369075, 0, 0, 0, 0, 0, 0, 0, 0, 313537150786471628357674085682, 0, 0, 0, 3880165139137952074394574080239, 0, 0, 610196082971456300968805414176, 0, 3611994166379264985422314697469, 0, 1545908704483794506703430923439, 0, 0, 0, 0], [0, 0, 73040033153747459144380762451585, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321400942486421298009844295764, 0, 0, 5036153196699288111713289058465, 0, 0, 0, 0, 1127562540086423726510319385440, 0, 0, 0, 3605301625913398218722894359625, 0, 0, 0, 0, 0], [0, 93520130554352000591974599528581, 0, 41725325344488393661417289339357, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1078036639699674740366677845620, 0, 0, 0, 0, 0, 0, 0, 0, 1319150654428540745386273961869, 0, 0, 0, 3870294371768580704462786987682, 0, 0, 933229052062223968237829920778, 0, 177439944192238088749720098718, 0, 4022524796393811403925612467089, 0, 0, 0, 0], [41622883577924942890614137426268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3798888112686654065486045433234, 0, 0, 0, 0, 168637644578743154476409431072, 0, 0, 0, 0, 618567175420183860883139409278, 0, 0, 0, 0, 2426008005456074028427560275655, 0, 0, 0, 4202456894808309211428532295429, 0, 0, 0, 4877645016271832820762521476898, 0, 0, 0, 0, 3434335130899944044301193955730, 0, 0, 0, 0, 0, 0, 0]]]
sage: crystalline_obstruction(None, p, prec, cp=ZZ['T'](cp), frob_matrix=matrix(frob_matrix), shift=1)
(3,
 {'precision': 20,
  'p': 29,
  'rank T(X_Fpbar)': 5,
  'factors': [[(29*T - 1, 1)], (29*T - 1, 2), (29*T + 1, 2)],
  'dim Ti': [[1], [2], [2]],
  'dim Ki': [[1], [1], [1]]})
sage: p, prec, cp, frob_matrix = [23, 16, [1, 0, 0, 0, -1329377, 0, 0, 0, 944707116511, 0, 0, 0, -475048924246822985, 0, 0, 0, 186554727206404860527516, 0, 0, 0, -61591830166121444161069480130, 0, 0, 0, 18295662732925011468096778914628840, 0, 0, 0, -5119876554844468134243670708248649214440, 0, 0, 0, 1349761826171331226472102726373233629065721730, 0, 0, 0, -320156982958304705872194217790579355890918360850716, 0, 0, 0, 63843655790670841419910707994522381723827254660386815785, 0, 0, 0, -9942584337524400988781250471688178784684095736164873856654271, 0, 0, 0, 1095652781002286405135488248511710479564380773795778030331117121857, 0, 0, 0, -64542751082767918430897798773372060387158551764172664212787858136578721], [[0, 0, 0, 0, 2931369991417881028711, 0, 45671654465898100062831, 0, 0, 0, 34599003473583763402644, 0, 0, 0, 18038971750047685691957, 0, 0, 0, 0, 97394571556004121963191, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125909835698288480587686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2889351926141760776314, 0, 1557913577977663634821, 0], [988690341229872304598303, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31889220854363508864731, 0, 0, 0, 0, 101310937172568974349095, 0, 0, 0, 0, 35159863735028368535871, 0, 0, 0, 0, 140196130576558792613089, 0, 0, 0, 68618493289167247120803, 0, 0, 0, 133181343361526516923061, 0, 0, 0, 0, 117039860847733057594002, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74345062445735573766794, 0, 0, 0, 0, 0, 112466402473414311460315, 0, 0, 0, 56462416352283509033831, 0, 0, 0, 0, 138729532203713297973886, 0, 0, 0, 0, 0, 0, 0, 131308319391729164341609, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1277472372531445046502083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127089526242018945579007, 0, 0, 0, 0, 40004117214783818916518, 0, 0, 0, 0, 119935042830373929034200, 0, 0, 0, 0, 87358901183308728967458, 0, 0, 0, 122572265597495175401578, 0, 0, 0, 61849183637199991786941, 0, 0, 0, 0, 98458827630017329965068, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 13167805260599617184780, 0, 0, 0, 59419604458112566792025, 0, 0, 0, 97685502903229405440545, 0, 0, 0, 0, 43621521690873488349674, 0, 0, 0, 0, 22450673443926746400377, 0, 0, 0, 0, 79893014996434360010930, 0, 0, 0, 0, 0, 0, 0, 106194426070617342411353, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2453491762812787668471], [0, 0, 0, 0, 0, 0, 0, 0, 0, 82327572575086676635251, 0, 0, 0, 61431924975063853855566, 0, 0, 0, 68461442159155781698704, 0, 0, 0, 0, 0, 95748608831725621191799, 0, 0, 0, 0, 0, 0, 0, 0, 38621506059291018491909, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 91274985542000605488515, 0, 0, 0, 103297757140511599482635, 0, 0, 0, 97513996990455092531070, 0, 0, 0, 0, 117747596717055054294178, 0, 0, 0, 0, 53201137038991280326742, 0, 0, 0, 0, 50986003179547818666128, 0, 0, 0, 0, 0, 0, 0, 133813390539079752546505, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5619851597618389045745], [0, 1505173621854881578233880, 0, 1862582105921534652037553, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99902143629142829258326, 0, 0, 0, 0, 0, 0, 0, 0, 78078785927481076508853, 0, 0, 0, 10702797325483163856538, 0, 0, 13704836744316457670710, 0, 96742935329237667668222, 0, 97199263842606774886941, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 25212508619200065936704, 0, 0, 0, 10319151139657619444060, 0, 0, 0, 64530731280776347513835, 0, 0, 0, 0, 0, 128611782911788878233721, 0, 0, 0, 0, 0, 0, 0, 0, 38386194702661744376408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1273705179437824984640586, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83529017383701245171605, 0, 0, 111208437982563670618825, 0, 0, 0, 0, 106259312732233626499650, 0, 0, 0, 94316422907182894431339, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 13583010972897300761808, 0, 0, 0, 32644998505635790246873, 0, 0, 0, 132178785232340361024600, 0, 0, 0, 0, 33586101360178191189419, 0, 0, 0, 0, 78847851118917283839084, 0, 0, 0, 0, 118768676141240528384341, 0, 0, 0, 0, 0, 0, 0, 128027679280419860336649, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2962908147177291585478], [0, 67073482144250261166023, 0, 1426328301320205715265203, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4963866047770936209907, 0, 0, 0, 0, 0, 0, 0, 0, 37174672008175085009952, 0, 0, 0, 67120512973451463775501, 0, 0, 90699454842735758253152, 0, 27632033995538324830497, 0, 66163887383270755310939, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 76840144499279799791586, 0, 0, 0, 89063155654921315842441, 0, 0, 0, 2088302193744098811617, 0, 0, 0, 0, 0, 11028928647364379995759, 0, 0, 0, 0, 0, 0, 0, 0, 83312704962415848092064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 306182053819705738192065, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99508634399474299587479, 0, 0, 11009756797362302336300, 0, 0, 0, 0, 55472872935109770889568, 0, 0, 0, 49906221239579222166429, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 10801599408312295657166, 0, 0, 0, 129307121785310040643991, 0, 0, 0, 19603820239860455515370, 0, 0, 0, 0, 57762035119142773298758, 0, 0, 0, 0, 21889246468166675978818, 0, 0, 0, 0, 80894687672987744725082, 0, 0, 0, 0, 0, 0, 0, 68899460198193942484427, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2768326825571736786959], [0, 445707875541185258074445, 0, 2643347876588639829183313, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71641870407820519849021, 0, 0, 0, 0, 0, 0, 0, 0, 128747342771549784256926, 0, 0, 0, 44067345782379939973633, 0, 0, 36285179395444536072207, 0, 36050515357844583586793, 0, 5321974998046793567391, 0, 0, 0, 0], [0, 0, 0, 0, 100419646405552344604797, 0, 48345162898028037700433, 0, 0, 0, 112312491808143090781415, 0, 0, 0, 78464681258384296165041, 0, 0, 0, 0, 82581676542171012466361, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100623700107525344284323, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2300588748586574069674, 0, 2319859626994039819870, 0], [0, 0, 2123467184663709895301378, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67941613721304210828540, 0, 0, 94279404298466519098057, 0, 0, 0, 0, 71912096944910318780984, 0, 0, 0, 69924770311378815488243, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 72637612369098173523477, 0, 0, 77335330975403764417402, 0, 0, 0, 39325817930969216237055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59699269056315467423192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 239335218600684152767, 0, 0], [0, 0, 0, 0, 0, 0, 0, 111036120402557343933156, 0, 0, 0, 59994064208156316718026, 0, 0, 0, 31267413117905352177247, 0, 0, 0, 0, 24242970404643600418442, 0, 0, 0, 0, 17478352392830220747536, 0, 0, 0, 0, 55510837964042987471267, 0, 0, 0, 0, 0, 0, 0, 124939929438710285814673, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4433376867216656480353], [0, 1962073084040872413058959, 0, 1729177455851823528795184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86892942434036651655674, 0, 0, 0, 0, 0, 0, 0, 0, 136183440576255768897430, 0, 0, 0, 107708921859881114734984, 0, 0, 129096393906779859203462, 0, 102484955841469621484398, 0, 110075247114914703615868, 0, 0, 0, 0], [0, 0, 0, 0, 69383169052924839415004, 0, 112703686205334609153606, 0, 0, 0, 84515095856368506879967, 0, 0, 0, 60871566230191732488976, 0, 0, 0, 0, 23730731060809452058147, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36780784637932053399466, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3827771861179033544223, 0, 3157134179154981486688, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 127502695374233020688680, 0, 0, 0, 139815377606471461582854, 0, 0, 0, 33420868241695187526966, 0, 0, 0, 0, 0, 127537556404334632585642, 0, 0, 0, 0, 0, 0, 0, 0, 53887980215235726777940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3150072395057440250706519, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126989031120572120988135, 0, 0, 26666248433258078282696, 0, 0, 0, 0, 66247905155289144097889, 0, 0, 0, 48678049180657325608916, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 67617239928950718038486, 0, 0, 74413992150107491883805, 0, 0, 0, 110942422174022713127367, 0, 0, 0, 0, 0, 0, 0, 0, 0, 134915922681279925288257, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3465082216197095806263, 0, 0], [0, 3216223897354642703124205, 0, 3066900907550216430800691, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31246110211660497271873, 0, 0, 0, 0, 0, 0, 0, 0, 9753986935091538668617, 0, 0, 0, 139649234881533013497031, 0, 0, 107524753069555115710081, 0, 140428264510102778127756, 0, 106980884048375240943604, 0, 0, 0, 0], [0, 0, 0, 0, 58797205610545144399939, 0, 70893639084243195820840, 0, 0, 0, 101655285108393792445041, 0, 0, 0, 125604696282494588898379, 0, 0, 0, 0, 125993095787075478094116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54655674357731332762788, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2113208451783115974560, 0, 1969245500434053698428, 0], [1170676759745587913374985, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26440074078182025414712, 0, 0, 0, 0, 123554360349531075804470, 0, 0, 0, 0, 43590843713598019210055, 0, 0, 0, 0, 43707146165796608209012, 0, 0, 0, 40042127956837304345398, 0, 0, 0, 72890526308024044158402, 0, 0, 0, 0, 82950208561624950245814, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 55412095909418500230430, 0, 0, 119524733991637137157012, 0, 0, 0, 120835372042522533706564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10304196967429776601527, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4764834378290740005569, 0, 0], [0, 0, 0, 0, 0, 0, 0, 75046209495853686765952, 0, 0, 0, 63095713139416155109340, 0, 0, 0, 131087204894271564472596, 0, 0, 0, 0, 5737265145803407277543, 0, 0, 0, 0, 101657644013331917125023, 0, 0, 0, 0, 38234306301142399862055, 0, 0, 0, 0, 0, 0, 0, 7043680580872686964164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 846121212768007214306], [0, 2725150658259554307310217, 0, 76950561774421656408836, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73776201088617566485289, 0, 0, 0, 0, 0, 0, 0, 0, 39083401124613900409367, 0, 0, 0, 100770451770752149025098, 0, 0, 56833058115381896709305, 0, 30350423876225173391001, 0, 140487728241624883312993, 0, 0, 0, 0], [0, 0, 0, 0, 93348389817880247482299, 0, 82079690248335532539347, 0, 0, 0, 32431545749148364421846, 0, 0, 0, 46710228572618294319291, 0, 0, 0, 0, 96817513910110195566644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 114505105499117712464286, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 914555105737903832548, 0, 3208036679349886299582, 0], [0, 0, 1906945304282129987831197, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32759257868978498693069, 0, 0, 29514249534087453525993, 0, 0, 0, 0, 39767469787237180447975, 0, 0, 0, 134090713677451472735656, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 138668727238714788094820, 0, 0, 57502686989113087027718, 0, 0, 0, 114637197488326942332101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 93049119121736325751260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13733813967760042261, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56791663515484689347659, 0, 0, 0, 0, 0, 87581703081504401489387, 0, 0, 0, 138170860417795599803833, 0, 0, 0, 0, 18612313905647867102665, 0, 0, 0, 0, 0, 0, 0, 106159925406020599636233, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 100836619453585721449283, 0, 116531019197871569614873, 0, 0, 0, 37123595049802046454921, 0, 0, 0, 132971664784583106220013, 0, 0, 0, 0, 112103056280464668110962, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72330350078507819489515, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1611327970392109788434, 0, 4993348735843961080232, 0], [998837083312008765538242, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117913814442638756074137, 0, 0, 0, 0, 97367533965375155786118, 0, 0, 0, 0, 84210383276767067010846, 0, 0, 0, 0, 76246562367208992648240, 0, 0, 0, 73709824443323926826974, 0, 0, 0, 51967740811368227134702, 0, 0, 0, 0, 61121567826519515075608, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42714143461776925260155, 0, 0, 0, 0, 0, 44290044433715200061178, 0, 0, 0, 109934889841239070488880, 0, 0, 0, 0, 62291625524380891893811, 0, 0, 0, 0, 0, 0, 0, 41459635890116245158931, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1025117116309861734985762, 0, 1473358252706763058224300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47529361826902771459491, 0, 0, 0, 0, 0, 0, 0, 0, 69786874505081299851404, 0, 0, 0, 42387220767315623594642, 0, 0, 122923398645912869144138, 0, 78819276917095575369055, 0, 105805103253173808385743, 0, 0, 0, 0], [0, 0, 0, 0, 76058309653930236213202, 0, 34525478694296394894812, 0, 0, 0, 66050149030451521124290, 0, 0, 0, 79512090534558410154101, 0, 0, 0, 0, 59113805758893799846985, 0, 0, 0, 0, 0, 0, 0, 0, 0, 61902631686986362168837, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4506079040085036602286, 0, 1364892267470951037933, 0], [1460006995078783431133598, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1819597338735568727952, 0, 0, 0, 0, 106083815287717470349296, 0, 0, 0, 0, 60332749887529850175074, 0, 0, 0, 0, 93889827399264637498359, 0, 0, 0, 72413530355980945471452, 0, 0, 0, 68090717299230055859553, 0, 0, 0, 0, 78375389587050597199478, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 132818605458888981979254, 0, 0, 115352028133253947635075, 0, 0, 0, 72853226700889431266571, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15060668231958594161602, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4607275495445928795448, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14209271997649433804913, 0, 0, 0, 0, 0, 79783113310381019881050, 0, 0, 0, 124663924261627419864131, 0, 0, 0, 0, 108219784750452503988421, 0, 0, 0, 0, 0, 0, 0, 127310408463211141613327, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2626914112533920382266728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 136288416425559205872291, 0, 0, 0, 0, 127809036132552291447843, 0, 0, 0, 0, 89366177838201849847787, 0, 0, 0, 0, 41022869022906258112595, 0, 0, 0, 104472722022047833840146, 0, 0, 0, 88426685696152605050927, 0, 0, 0, 0, 8635352464731714882841, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 124096615464782286087265, 0, 29804788746858702650725, 0, 0, 0, 10125408743981972880136, 0, 0, 0, 22435533669652015042417, 0, 0, 0, 0, 73671325374573195386608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90147246720718463257037, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5466146729912070222598, 0, 1784867750730090546006, 0], [3174605500935935158931956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 109534680979064297128008, 0, 0, 0, 0, 119044642405198270878243, 0, 0, 0, 0, 28471241332882920340289, 0, 0, 0, 0, 11939426592033784235331, 0, 0, 0, 79980055201511624131601, 0, 0, 0, 15366229020559995714920, 0, 0, 0, 0, 5304034795267861455538, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88152232074584367464253, 0, 0, 0, 0, 0, 88323369254588817396143, 0, 0, 0, 15771009745425002564986, 0, 0, 0, 0, 8943340666078867285205, 0, 0, 0, 0, 0, 0, 0, 37766569879971189384303, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [269242847942975256376861, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108715452006751264753084, 0, 0, 0, 0, 133471337268450149638533, 0, 0, 0, 0, 51327460004436983181118, 0, 0, 0, 0, 137948264180544556617093, 0, 0, 0, 90041924985481247796864, 0, 0, 0, 37238224931552335722345, 0, 0, 0, 0, 111598818606730655624110, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 126116982511412273395105, 0, 0, 0, 75465507188057102019908, 0, 0, 0, 117735854894290496110659, 0, 0, 0, 0, 53817171655727394323514, 0, 0, 0, 0, 22699644159482516163511, 0, 0, 0, 0, 74163282108041782311183, 0, 0, 0, 0, 0, 0, 0, 76464378345011347810406, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4896627104180737648191], [0, 0, 0, 0, 0, 0, 0, 0, 0, 14815982601150739603346, 0, 0, 0, 50122519500770887322061, 0, 0, 0, 102015191921924623590893, 0, 0, 0, 0, 0, 29341109507858706952320, 0, 0, 0, 0, 0, 0, 0, 0, 130622396794784657094577, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 31276459427421025936027, 0, 0, 0, 95070071327249977636595, 0, 0, 0, 133630781295807020223296, 0, 0, 0, 0, 93598524657297575503681, 0, 0, 0, 0, 135040681231086406307578, 0, 0, 0, 0, 40464770227824528970354, 0, 0, 0, 0, 0, 0, 0, 110143359963712227690756, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5682142063162957529256], [0, 1927835858913635414717302, 0, 2161453922045590847346982, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80665275622899688030265, 0, 0, 0, 0, 0, 0, 0, 0, 13437287991303995933558, 0, 0, 0, 129554978619334542933263, 0, 0, 30191500209075417599019, 0, 15134128508829006895427, 0, 56772720539298114761963, 0, 0, 0, 0]]]
sage: crystalline_obstruction(None, p, prec, cp=ZZ['T'](cp), frob_matrix=matrix(frob_matrix), shift=1)
(1,
 {'precision': 16,
  'p': 23,
  'rank T(X_Fpbar)': 5,
  'factors': [(t - 1, 1), (t - 1, 1), (t + 1, 1), (t^2 + 1, 1)],
  'dim Ti': [1, 1, 1, 2],
  'dim Li': [1, 0, 0, 0]})

Citing this code

Please cite the following preprint if this code has been helpful in your research:

• "Effective obstruction to lifting Tate classes from positive characteristic" by Edgar Costa and Emre Can Sertoz. (arXiv:2003.11037)