Lfunction data - 20-325e10-1.1-c1e10-0-2

Formats: - HTML - YAML - JSON - 2026-03-03T07:24:10.324974

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '460215761046573453227963515903,868057171432521837666236805706,1549702762963501151664881270813,1771242786600646103207168524486,1851200314314834922806773114167,2147067966341954634656209661024,2477564547336026351160644447876,2594772275505568175994564332854,3622109061484083202855840883417,4194090470825440020631973559470', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 2, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 2, 'a9': 10, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13854.940974815514, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [13, [1, -10, 60, -263, 1076, -3957, 13988, -44447, 131820, -285610, 371293]]], 'bad_primes': [5, 13], 'central_character': '325.1', 'coefficient_field': '1.1.1.1', 'conductor': 13147210297489166259765625, 'conductor_radical': 65, 'degree': 20, 'euler_factors': [[1, 0, -2, -2, 0, 9, 9, -20, -23, 20, 45, 40, -92, -160, 144, 288, 0, -256, -512, 0, 1024], [1, 3, -1, -20, -26, 41, 130, 19, -274, -129, 409, -387, -2466, 513, 10530, 9963, -18954, -43740, -6561, 59049, 59049], [1], [1, -2, -12, -8, 97, 281, -260, -1954, -835, 2855, 19063, 19985, -40915, -670222, -624260, 4722767, 11411953, -6588344, -69177612, -80707214, 282475249], [1, 3, -29, -38, 576, -3, -7311, 6832, 74554, -49384, -752787, -543224, 9021034, 9093392, -107040351, -483153, 1020419136, -740512498, -6216407549, 7073843073, 25937424601], [1, -10, 60, -263, 1076, -3957, 13988, -44447, 131820, -285610, 371293], [1, 4, -33, -158, 411, 2612, -4681, -45867, 1590, 464191, 1440069, 7891247, 459510, -225344571, -390961801, 3708666484, 9920540859, -64833510334, -230199995553, 474351505988, 2015993900449], [1, -4, -71, 194, 3329, -5754, -110903, 98987, 2917208, -788473, -61357653, -14980987, 1053112088, 678951833, -14452989863, -14247473646, 156615737849, 173411117366, -1205832975911, -1290750791116, 6131066257801], [1, 15, 82, 51, -1455, -4488, 18491, 99225, -338668, -4764405, -26762865, -109581315, -179155372, 1207270575, 5174539931, -28886307384, -215392218495, 173646097797, 6421500793042, 27017289921945, 41426511213649], [1, -1, -79, -146, 3192, 11779, -67556, -384403, 890654, 4091745, -7513779, 118660605, 749040014, -9375204767, -47781075236, 241600824071, 1898676040632, -2518481941114, -39519466623919, -14507145975869, 420707233300201], [1, 0, 196, -58, 19212, -8830, 1240273, -642678, 58197790, -29213300, 2064436353, -905612300, 55928076190, -19146020298, 1145418161233, -252795403330, 17050720719372, -1595731618438, 167166643338436, 0, 819628286980801], [1, 17, 51, -502, -372, 37861, 106407, -1104416, -5601148, 10960902, 176313507, 405553374, -7667971612, -55941983648, 199423849527, 2625431555977, -954450224148, -47655802320766, 179136452149971, 2209349576516309, 4808584372417849], [1, 6, -95, -384, 6327, 16770, -184789, -272397, 682286, 2994381, 158651253, 122769621, 1146922766, -18773873637, -522169549429, 1942908490770, 30053909532807, -74785641170304, -758567896766495, 1964291606363766, 13422659310152401], [1, 12, -17, -1046, -4829, 18006, 201631, 424281, -166530, -8309917, -106017329, -357326431, -307913970, 33733309467, 689336264431, 2647034024658, -30525862163621, -284322267217922, -198699404719217, 6031111343242116, 21611482313284249], [1, 24, 574, 9050, 131625, 1564668, 17091801, 162432260, 1426688920, 11144731054, 80789503263, 523802359538, 3151555824280, 16864204529980, 83402536595481, 358848793412676, 1418814217679625, 4584939240190150, 13667678543850814, 26859131354466408, 52599132235830049], [1, -16, 360, -5202, 70840, -827910, 8873881, -85670898, 767302102, -6234367896, 47765603005, -330421498488, 2155351604518, -12754426281546, 70019189426761, -346228230609630, 1570123342378360, -6110847349432074, 22413488548089960, -52796217468834128, 174887470365513049], [1, -12, -64, 738, 5664, -9081, -336339, -2403693, 23185887, 87777036, -1346009523, 5178845124, 80710072647, -493668064647, -4075541081379, -6492227559219, 238910542542624, 1836624795796422, -9397148006676544, -103955949823859268, 511116753300641401], [1, 5, -233, -770, 32534, 66025, -3312205, -3580430, 267548612, 86879620, -17862005833, 5299656820, 995548385252, -812689581830, -45860263789405, 55764470773525, 1676163859460774, -2419911983736170, -44667803928366473, 58470730464170705, 713342911662882601], [1, -16, 52, 292, -5179, 79117, -447406, -998192, 21597155, -259219709, 2885084279, -17367720503, 96949628795, -300219220496, -9015732442126, 106817848090519, -468483961253251, 1769727788754316, 21115519232945332, -435304550340719152, 1822837804551761449], [1, 19, 13, -1414, -468, 62551, -611944, -7048209, 20077850, 215658713, -492609879, 15311768623, 101212441850, -2522631531399, -15550525717864, 112856350134401, -59950932875028, -12860499903964874, 8394795906194893, 871121513650531589, 3255243551009881201], [1, 16, 556, 6628, 138310, 1355050, 21700050, 182641092, 2434430397, 17870802926, 204427402421, 1304568613598, 12973079585613, 71050489686564, 616243249612050, 2809115662094650, 20931036838031590, 73222157384574916, 448391811093109036, 941945387332286608, 4297625829703557649], [1, 28, 796, 14548, 260362, 3680098, 50574318, 587393268, 6622303989, 64844383118, 616222982693, 5122706266322, 41329799195349, 289607789461452, 1969873782619758, 11323869099847102, 63290736094358602, 279378467930641132, 1207618612685622556, 3355844687513312932, 9468276082626847201], [1, 14, 365, 5938, 99060, 1242880, 17268661, 193270322, 2158927097, 21045178074, 209861984865, 1746749780142, 14872848771233, 110509457605414, 819541656978181, 4895754834371840, 32386713385933140, 161133870776405126, 822086664730749965, 2617163573745565642, 15516041187205853449], [1, -10, -306, 2112, 65305, -271977, -10058402, 21214470, 1225818667, -762210039, -120541083185, -67836693471, 9709709661307, 14955543701430, -631086682358882, -1518735736760673, 32455363206208105, 93416579299357248, -1204596174544836786, -3503564037074852090, 31181719929966183601], [1, 37, 516, 4163, 40703, 282376, -2037243, -34573291, -28158538, -544608903, -24070563673, -52827063591, -264943684042, -31554109216843, -180355658012283, 2424858792410632, 33904459516625087, 336363258282384419, 4044115734698511876, 28128549170218913029, 73742412689492826049], [1, 16, -212, -2956, 44937, 300739, -8876434, -33361416, 1202430095, 2074882817, -123397240149, 209563164517, 12265989399095, -34372300266216, -923685281490034, 3160797114570239, 47701531007557137, -316923210082832156, -2295656215931529812, 17498964362949774416, 110462212541120451001], [1, -46, 1485, -36612, 753240, -13444130, 211701086, -2992715688, 38268483312, -445019410726, 4728280756025, -45836999304778, 405990339457008, -3270221235601176, 23827143737956766, -155854313605188590, 899407951837503960, -4502814196093534044, 18811535708606099085, -60019566456145250818, 134391637934412192049], [1, 39, 502, 2567, 43221, 942582, 7741629, 83129873, 1638415990, 13185533701, 57580805199, 1410852106007, 18758224669510, 101837669009539, 1014769640410029, 13220200154266674, 64863066537265629, 412204105012012981, 8625294622756238902, 71699909284386025773, 196715135728956532249], [1, 22, 961, 16982, 426932, 6256952, 115514033, 1428630242, 21099024689, 221564754542, 2720100956393, 24150558245078, 250677512330009, 1850117593667018, 16305748467973313, 96270962318594648, 716007704521569812, 3104376034970902958, 19148526986642746081, 47781652147730806558, 236736367459211723401], [1, 13, -241, -2890, 35874, 242561, -5486405, -4965266, 839793236, -459254064, -110741787261, -51895709232, 10723319830484, -7164367415602, -894543856627205, 4469029195261873, 74687937173095266, -679902983849521130, -6406850504904501361, 39052545193795487549, 339456738992222314849]], 'euler_factors_factorization': [[[[1, 0, -2, -2, 0, 9, 9, -20, -23, 20, 45, 40, -92, -160, 144, 288, 0, -256, -512, 0, 1024], 1]], [[[1, 3, -1, -20, -26, 41, 130, 19, -274, -129, 409, -387, -2466, 513, 10530, 9963, -18954, -43740, -6561, 59049, 59049], 1]], [1], [[[1, -2, -12, -8, 97, 281, -260, -1954, -835, 2855, 19063, 19985, -40915, -670222, -624260, 4722767, 11411953, -6588344, -69177612, -80707214, 282475249], 1]], [[[1, 3, -29, -38, 576, -3, -7311, 6832, 74554, -49384, -752787, -543224, 9021034, 9093392, -107040351, -483153, 1020419136, -740512498, -6216407549, 7073843073, 25937424601], 1]], [[[1, -10, 60, -263, 1076, -3957, 13988, -44447, 131820, -285610, 371293], 1]], [[[1, 4, -33, -158, 411, 2612, -4681, -45867, 1590, 464191, 1440069, 7891247, 459510, -225344571, -390961801, 3708666484, 9920540859, -64833510334, -230199995553, 474351505988, 2015993900449], 1]], [[[1, -4, -71, 194, 3329, -5754, -110903, 98987, 2917208, -788473, -61357653, -14980987, 1053112088, 678951833, -14452989863, -14247473646, 156615737849, 173411117366, -1205832975911, -1290750791116, 6131066257801], 1]], [[[1, 15, 82, 51, -1455, -4488, 18491, 99225, -338668, -4764405, -26762865, -109581315, -179155372, 1207270575, 5174539931, -28886307384, -215392218495, 173646097797, 6421500793042, 27017289921945, 41426511213649], 1]], [[[1, -1, -79, -146, 3192, 11779, -67556, -384403, 890654, 4091745, -7513779, 118660605, 749040014, -9375204767, -47781075236, 241600824071, 1898676040632, -2518481941114, -39519466623919, -14507145975869, 420707233300201], 1]], [[[1, 0, 98, -29, 4804, -1573, 148924, -27869, 2919518, 0, 28629151], 2]], [[[1, 17, 51, -502, -372, 37861, 106407, -1104416, -5601148, 10960902, 176313507, 405553374, -7667971612, -55941983648, 199423849527, 2625431555977, -954450224148, -47655802320766, 179136452149971, 2209349576516309, 4808584372417849], 1]], [[[1, 6, -95, -384, 6327, 16770, -184789, -272397, 682286, 2994381, 158651253, 122769621, 1146922766, -18773873637, -522169549429, 1942908490770, 30053909532807, -74785641170304, -758567896766495, 1964291606363766, 13422659310152401], 1]], [[[1, 12, -17, -1046, -4829, 18006, 201631, 424281, -166530, -8309917, -106017329, -357326431, -307913970, 33733309467, 689336264431, 2647034024658, -30525862163621, -284322267217922, -198699404719217, 6031111343242116, 21611482313284249], 1]], [[[1, 12, 215, 1945, 19360, 131839, 909920, 4296505, 22321945, 58556172, 229345007], 2]], [[[1, -8, 148, -1417, 13132, -99183, 695996, -3980353, 22033796, -63123848, 418195493], 2]], [[[1, -12, -64, 738, 5664, -9081, -336339, -2403693, 23185887, 87777036, -1346009523, 5178845124, 80710072647, -493668064647, -4075541081379, -6492227559219, 238910542542624, 1836624795796422, -9397148006676544, -103955949823859268, 511116753300641401], 1]], [[[1, 5, -233, -770, 32534, 66025, -3312205, -3580430, 267548612, 86879620, -17862005833, 5299656820, 995548385252, -812689581830, -45860263789405, 55764470773525, 1676163859460774, -2419911983736170, -44667803928366473, 58470730464170705, 713342911662882601], 1]], [[[1, -16, 52, 292, -5179, 79117, -447406, -998192, 21597155, -259219709, 2885084279, -17367720503, 96949628795, -300219220496, -9015732442126, 106817848090519, -468483961253251, 1769727788754316, 21115519232945332, -435304550340719152, 1822837804551761449], 1]], [[[1, 19, 13, -1414, -468, 62551, -611944, -7048209, 20077850, 215658713, -492609879, 15311768623, 101212441850, -2522631531399, -15550525717864, 112856350134401, -59950932875028, -12860499903964874, 8394795906194893, 871121513650531589, 3255243551009881201], 1]], [[[1, 8, 246, 1346, 28129, 121377, 2053417, 7172834, 95698182, 227185928, 2073071593], 2]], [[[1, 14, 300, 3074, 42145, 327819, 3329455, 19184834, 147911700, 545301134, 3077056399], 2]], [[[1, 7, 158, 1863, 24007, 159037, 1992581, 12834207, 90342346, 332208247, 3939040643], 2]], [[[1, -10, -306, 2112, 65305, -271977, -10058402, 21214470, 1225818667, -762210039, -120541083185, -67836693471, 9709709661307, 14955543701430, -631086682358882, -1518735736760673, 32455363206208105, 93416579299357248, -1204596174544836786, -3503564037074852090, 31181719929966183601], 1]], [[[1, 37, 516, 4163, 40703, 282376, -2037243, -34573291, -28158538, -544608903, -24070563673, 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'2.60844358081501628651745976562123', '2.85734023305156338157693619844431', '2.88896443726096609350629779134483', '2.92536223700126030693975628001961', '3.21827616564514736408726341937716', '3.30855400539417621871621452515785', '3.38437080392205097488660864211489', '3.69305772236395202280858204778185', '3.79963793488928692050183580793002', '3.87922728683128571548391341224870', '4.03809302786921102858973721705039', '4.08601168261360109043459507196873', '4.28453488737234209050662763348390', '4.35070330811764194893977131323095', '4.38253418394432217872515640317017', '4.72953985306795719842202753117153', '4.74270486523912597336563670747018', '4.74487096456355678535994273630256', '4.80500425596141091670361190294354', '5.26664192557304588251133803399624', '5.28812691428062560802281212936625', '5.43033595061470435161501801932327', '5.43099376035393462081097303927383', '5.51855229939170861720174097408983', '5.57294638996977729968995568144390', '5.73346457528027922362011124061313', '5.86466793178073916631668934924574', '5.92451738963955669441373586871855', '6.00036447364893754614782741170522', '6.16150951970931447231171605922508', '6.40189669876616271690706526687841', '6.41851429454254822571980352270444', '6.56307941116428957628199777906000', '6.70530347622290615359581660162734', '6.79219310570615819398789212896904', '6.79989487753336400016596300787653', '6.90152285643176020934443795974482', '6.90295212320603869747901248281667', '7.19787450661979239667536816647441', '7.27091852862963447703090957958147', '7.34813149348629776899471103335787', '7.35418158910286248817041685080648', '7.36557956553132273570047350687250', '7.41402754332503463661616998991626', '7.905039637636977287126122576952182', '7.947163007507300041065290417533779', '7.993182538743470859570876449408716', '8.112937238503238129273530333861452', '8.263751788719906557301423808476320', '8.279338929102326372649353522858200', '8.299491136673246386180770680911006', '8.332251895272422288299479030130461', '8.452495138087032218167312116640885', '8.570257900094381620791207790329250', '8.749411600118394582405919990252904', '8.766788680741436015635418004467790', '8.955996774465326121344576338919281', '9.063571873980550877160900555026475', '9.066455423612529080995609951808746', '9.104981724032977739274748725061867', '9.522083296482535727136917589320194', '9.605578193179933896889976380920677', '9.626837214053619447650977371762591', '9.719759307060589489025321259123493', '9.797872046256043466421593337303947', '9.910805192698529750209032177340229', '9.970862927052501390850645376729035', '10.07364353006304148892501918696838', '10.11432295727373514992142123192689', '10.29418563620992583162003737330609', '10.31818802703695770858273103855298', '10.38488350607772644113915774778065', '10.46607022218642748003500768550843', '10.54401821650306555100958009299593', '10.77476095567489547286607423999347', '10.83902534086140765608428048896164', '10.84437353824291152942444453613049', '10.85277327539404454988032916167853', '10.97329393291252472831394739534739', '11.04567892093531445218506641854741', '11.07301302754863353634735324716315', '11.22287276814048962237666425118314', '11.43021679818646908695468425357074', '11.51177974386928753529330213078814', '11.52890752365409593688302245703128', '11.87551986927591335156548354754818', '11.91300881827255369169898783041216', '11.97326256028608982065232159853651', '12.04839362172914562853234572542992', '12.28382721173562070288969122285610'], 'prelabel': '20-325e10-1.1-c1e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6109432223674471, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e10-0', 'trace_hash': 1479534185626611579, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36304622185617679769022233344', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.68477636603985020595255067532', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.22249992441489060596500792987', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 13854.940974815514, 'bad_primes': [5, 13], 'central_character': '1.1', 'conductor': 13147210297489166259765625, 'conductor_radical': 65, 'degree': 20, 'dirichlet_coefficients': [1, 0, -3, 2, 0, 0, 2, 2, 10, 0, -3, -6, 10, 0, 0, 4, -4, 0, 4, 0, -6, 0, -15, -6, 0, 0, -13, 4, 1, 0, 0, -1, 9, 0, 0, 20, -17, 0, -30, 0, -6, 0, -12, -6, 0, 0, -24, -12, 16, 0, 12, 20, 16, 0, 0, 4, -12, 0, 12, 0, -5, 0, 20, 3, 0, 0, 16, -8, 45, 0, -19, 20, -16, 0, 0, 8, -6, 0, -28, 0, 15, 0, -14, -12, 0, 0, -3, -6, 10, 0, 20, -30, 0, 0, 0, 3, -37, 0, -30, 0], 'euler11': [1, 3, -29, -38, 576, -3, -7311, 6832, 74554, -49384, -752787, -543224, 9021034, 9093392, -107040351, -483153, 1020419136, -740512498, -6216407549, 7073843073, 25937424601], 'euler13': [1, -10, 60, -263, 1076, -3957, 13988, -44447, 131820, -285610, 371293, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, 4, -33, -158, 411, 2612, -4681, -45867, 1590, 464191, 1440069, 7891247, 459510, -225344571, -390961801, 3708666484, 9920540859, -64833510334, -230199995553, 474351505988, 2015993900449], 'euler19': [1, -4, -71, 194, 3329, -5754, -110903, 98987, 2917208, -788473, -61357653, -14980987, 1053112088, 678951833, -14452989863, -14247473646, 156615737849, 173411117366, -1205832975911, -1290750791116, 6131066257801], 'euler2': [1, 0, -2, -2, 0, 9, 9, -20, -23, 20, 45, 40, -92, -160, 144, 288, 0, -256, -512, 0, 1024], 'euler23': [1, 15, 82, 51, -1455, -4488, 18491, 99225, -338668, -4764405, -26762865, -109581315, -179155372, 1207270575, 5174539931, -28886307384, -215392218495, 173646097797, 6421500793042, 27017289921945, 41426511213649], 'euler29': [1, -1, -79, -146, 3192, 11779, -67556, -384403, 890654, 4091745, -7513779, 118660605, 749040014, -9375204767, -47781075236, 241600824071, 1898676040632, -2518481941114, -39519466623919, -14507145975869, 420707233300201], 'euler3': [1, 3, -1, -20, -26, 41, 130, 19, -274, -129, 409, -387, -2466, 513, 10530, 9963, -18954, -43740, -6561, 59049, 59049], 'euler31': [1, 0, 196, -58, 19212, -8830, 1240273, -642678, 58197790, -29213300, 2064436353, -905612300, 55928076190, -19146020298, 1145418161233, -252795403330, 17050720719372, -1595731618438, 167166643338436, 0, 819628286980801], 'euler37': [1, 17, 51, -502, -372, 37861, 106407, -1104416, -5601148, 10960902, 176313507, 405553374, -7667971612, -55941983648, 199423849527, 2625431555977, -954450224148, -47655802320766, 179136452149971, 2209349576516309, 4808584372417849], 'euler41': [1, 6, -95, -384, 6327, 16770, -184789, -272397, 682286, 2994381, 158651253, 122769621, 1146922766, -18773873637, -522169549429, 1942908490770, 30053909532807, -74785641170304, -758567896766495, 1964291606363766, 13422659310152401], 'euler43': [1, 12, -17, -1046, -4829, 18006, 201631, 424281, -166530, -8309917, -106017329, -357326431, -307913970, 33733309467, 689336264431, 2647034024658, -30525862163621, -284322267217922, -198699404719217, 6031111343242116, 21611482313284249], 'euler47': [1, 24, 574, 9050, 131625, 1564668, 17091801, 162432260, 1426688920, 11144731054, 80789503263, 523802359538, 3151555824280, 16864204529980, 83402536595481, 358848793412676, 1418814217679625, 4584939240190150, 13667678543850814, 26859131354466408, 52599132235830049], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, -16, 360, -5202, 70840, -827910, 8873881, -85670898, 767302102, -6234367896, 47765603005, -330421498488, 2155351604518, -12754426281546, 70019189426761, -346228230609630, 1570123342378360, -6110847349432074, 22413488548089960, -52796217468834128, 174887470365513049], 'euler59': [1, -12, -64, 738, 5664, -9081, -336339, -2403693, 23185887, 87777036, -1346009523, 5178845124, 80710072647, -493668064647, -4075541081379, -6492227559219, 238910542542624, 1836624795796422, -9397148006676544, -103955949823859268, 511116753300641401], 'euler61': [1, 5, -233, -770, 32534, 66025, -3312205, -3580430, 267548612, 86879620, -17862005833, 5299656820, 995548385252, -812689581830, -45860263789405, 55764470773525, 1676163859460774, -2419911983736170, -44667803928366473, 58470730464170705, 713342911662882601], 'euler67': [1, -16, 52, 292, -5179, 79117, -447406, -998192, 21597155, -259219709, 2885084279, -17367720503, 96949628795, -300219220496, -9015732442126, 106817848090519, -468483961253251, 1769727788754316, 21115519232945332, -435304550340719152, 1822837804551761449], 'euler7': [1, -2, -12, -8, 97, 281, -260, -1954, -835, 2855, 19063, 19985, -40915, -670222, -624260, 4722767, 11411953, -6588344, -69177612, -80707214, 282475249], 'euler71': [1, 19, 13, -1414, -468, 62551, -611944, -7048209, 20077850, 215658713, -492609879, 15311768623, 101212441850, -2522631531399, -15550525717864, 112856350134401, -59950932875028, -12860499903964874, 8394795906194893, 871121513650531589, 3255243551009881201], 'euler73': [1, 16, 556, 6628, 138310, 1355050, 21700050, 182641092, 2434430397, 17870802926, 204427402421, 1304568613598, 12973079585613, 71050489686564, 616243249612050, 2809115662094650, 20931036838031590, 73222157384574916, 448391811093109036, 941945387332286608, 4297625829703557649], 'euler79': [1, 28, 796, 14548, 260362, 3680098, 50574318, 587393268, 6622303989, 64844383118, 616222982693, 5122706266322, 41329799195349, 289607789461452, 1969873782619758, 11323869099847102, 63290736094358602, 279378467930641132, 1207618612685622556, 3355844687513312932, 9468276082626847201], 'euler83': [1, 14, 365, 5938, 99060, 1242880, 17268661, 193270322, 2158927097, 21045178074, 209861984865, 1746749780142, 14872848771233, 110509457605414, 819541656978181, 4895754834371840, 32386713385933140, 161133870776405126, 822086664730749965, 2617163573745565642, 15516041187205853449], 'euler89': [1, -10, -306, 2112, 65305, -271977, -10058402, 21214470, 1225818667, -762210039, -120541083185, -67836693471, 9709709661307, 14955543701430, -631086682358882, -1518735736760673, 32455363206208105, 93416579299357248, -1204596174544836786, -3503564037074852090, 31181719929966183601], 'euler97': [1, 37, 516, 4163, 40703, 282376, -2037243, -34573291, -28158538, -544608903, -24070563673, -52827063591, -264943684042, -31554109216843, -180355658012283, 2424858792410632, 33904459516625087, 336363258282384419, 4044115734698511876, 28128549170218913029, 73742412689492826049], 'euler_factors': [[1, 0, -2, -2, 0, 9, 9, -20, -23, 20, 45, 40, -92, -160, 144, 288, 0, -256, -512, 0, 1024], [1, 3, -1, -20, -26, 41, 130, 19, -274, -129, 409, -387, -2466, 513, 10530, 9963, -18954, -43740, -6561, 59049, 59049], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -12, -8, 97, 281, -260, -1954, -835, 2855, 19063, 19985, -40915, -670222, -624260, 4722767, 11411953, -6588344, -69177612, -80707214, 282475249], [1, 3, -29, -38, 576, -3, -7311, 6832, 74554, -49384, -752787, -543224, 9021034, 9093392, -107040351, -483153, 1020419136, -740512498, -6216407549, 7073843073, 25937424601], [1, -10, 60, -263, 1076, -3957, 13988, -44447, 131820, -285610, 371293, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, -33, -158, 411, 2612, -4681, -45867, 1590, 464191, 1440069, 7891247, 459510, -225344571, -390961801, 3708666484, 9920540859, -64833510334, -230199995553, 474351505988, 2015993900449], [1, -4, -71, 194, 3329, -5754, -110903, 98987, 2917208, -788473, -61357653, -14980987, 1053112088, 678951833, -14452989863, -14247473646, 156615737849, 173411117366, -1205832975911, -1290750791116, 6131066257801], [1, 15, 82, 51, -1455, -4488, 18491, 99225, -338668, -4764405, -26762865, -109581315, -179155372, 1207270575, 5174539931, -28886307384, -215392218495, 173646097797, 6421500793042, 27017289921945, 41426511213649], [1, -1, -79, -146, 3192, 11779, -67556, -384403, 890654, 4091745, -7513779, 118660605, 749040014, -9375204767, -47781075236, 241600824071, 1898676040632, -2518481941114, -39519466623919, -14507145975869, 420707233300201], [1, 0, 196, -58, 19212, -8830, 1240273, -642678, 58197790, -29213300, 2064436353, -905612300, 55928076190, -19146020298, 1145418161233, -252795403330, 17050720719372, -1595731618438, 167166643338436, 0, 819628286980801], [1, 17, 51, -502, -372, 37861, 106407, -1104416, -5601148, 10960902, 176313507, 405553374, -7667971612, -55941983648, 199423849527, 2625431555977, -954450224148, -47655802320766, 179136452149971, 2209349576516309, 4808584372417849], [1, 6, -95, -384, 6327, 16770, -184789, -272397, 682286, 2994381, 158651253, 122769621, 1146922766, -18773873637, -522169549429, 1942908490770, 30053909532807, -74785641170304, -758567896766495, 1964291606363766, 13422659310152401], [1, 12, -17, -1046, -4829, 18006, 201631, 424281, -166530, -8309917, -106017329, -357326431, -307913970, 33733309467, 689336264431, 2647034024658, -30525862163621, -284322267217922, -198699404719217, 6031111343242116, 21611482313284249], [1, 24, 574, 9050, 131625, 1564668, 17091801, 162432260, 1426688920, 11144731054, 80789503263, 523802359538, 3151555824280, 16864204529980, 83402536595481, 358848793412676, 1418814217679625, 4584939240190150, 13667678543850814, 26859131354466408, 52599132235830049], [1, -16, 360, -5202, 70840, -827910, 8873881, -85670898, 767302102, -6234367896, 47765603005, -330421498488, 2155351604518, -12754426281546, 70019189426761, -346228230609630, 1570123342378360, -6110847349432074, 22413488548089960, -52796217468834128, 174887470365513049], [1, -12, -64, 738, 5664, -9081, -336339, -2403693, 23185887, 87777036, -1346009523, 5178845124, 80710072647, -493668064647, -4075541081379, -6492227559219, 238910542542624, 1836624795796422, -9397148006676544, -103955949823859268, 511116753300641401], [1, 5, -233, -770, 32534, 66025, -3312205, -3580430, 267548612, 86879620, -17862005833, 5299656820, 995548385252, -812689581830, -45860263789405, 55764470773525, 1676163859460774, -2419911983736170, -44667803928366473, 58470730464170705, 713342911662882601], [1, -16, 52, 292, -5179, 79117, -447406, -998192, 21597155, -259219709, 2885084279, -17367720503, 96949628795, -300219220496, -9015732442126, 106817848090519, -468483961253251, 1769727788754316, 21115519232945332, -435304550340719152, 1822837804551761449], [1, 19, 13, -1414, -468, 62551, -611944, -7048209, 20077850, 215658713, -492609879, 15311768623, 101212441850, -2522631531399, -15550525717864, 112856350134401, -59950932875028, -12860499903964874, 8394795906194893, 871121513650531589, 3255243551009881201], [1, 16, 556, 6628, 138310, 1355050, 21700050, 182641092, 2434430397, 17870802926, 204427402421, 1304568613598, 12973079585613, 71050489686564, 616243249612050, 2809115662094650, 20931036838031590, 73222157384574916, 448391811093109036, 941945387332286608, 4297625829703557649], [1, 28, 796, 14548, 260362, 3680098, 50574318, 587393268, 6622303989, 64844383118, 616222982693, 5122706266322, 41329799195349, 289607789461452, 1969873782619758, 11323869099847102, 63290736094358602, 279378467930641132, 1207618612685622556, 3355844687513312932, 9468276082626847201], [1, 14, 365, 5938, 99060, 1242880, 17268661, 193270322, 2158927097, 21045178074, 209861984865, 1746749780142, 14872848771233, 110509457605414, 819541656978181, 4895754834371840, 32386713385933140, 161133870776405126, 822086664730749965, 2617163573745565642, 15516041187205853449], [1, -10, -306, 2112, 65305, -271977, -10058402, 21214470, 1225818667, -762210039, -120541083185, -67836693471, 9709709661307, 14955543701430, -631086682358882, -1518735736760673, 32455363206208105, 93416579299357248, -1204596174544836786, -3503564037074852090, 31181719929966183601], [1, 37, 516, 4163, 40703, 282376, -2037243, -34573291, -28158538, -544608903, -24070563673, -52827063591, -264943684042, -31554109216843, -180355658012283, 2424858792410632, 33904459516625087, 336363258282384419, 4044115734698511876, 28128549170218913029, 73742412689492826049]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/2/e/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '20-325e10-1.1-c1e10-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '20-325e10-1.1-c1e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6109432223674471, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e10-0', 'trace_hash': 1479534185626611579, 'z1': {'__RealLiteral__': 0, 'data': '0.36304622185617679769022233344', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '460215761046573453227963515903,868057171432521837666236805706,1549702762963501151664881270813,1771242786600646103207168524486,1851200314314834922806773114167,2147067966341954634656209661024,2477564547336026351160644447876,2594772275505568175994564332854,3622109061484083202855840883417,4194090470825440020631973559470', 'Lhash_array': ['460215761046573453227963515903', '868057171432521837666236805706', '1549702762963501151664881270813', '1771242786600646103207168524486', '1851200314314834922806773114167', '2147067966341954634656209661024', '2477564547336026351160644447876', '2594772275505568175994564332854', '3622109061484083202855840883417', '4194090470825440020631973559470'], 'factors': ['2-325-13.9-c1-0-0', '2-325-13.9-c1-0-3', '2-325-13.9-c1-0-8', '2-325-13.3-c1-0-4', '2-325-13.9-c1-0-10', '2-325-13.3-c1-0-8', '2-325-13.3-c1-0-10', '2-325-13.3-c1-0-14', '2-325-13.9-c1-0-17', '2-325-13.3-c1-0-19'], 'label': '20-325e10-1.1-c1e10-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/2/e/c'}