Lfunction data - 16-31e16-1.1-c1e8-0-6

Formats: - HTML - YAML - JSON - 2025-01-13T22:38:12.703902

• 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
  instance_types	text[]
  instance_urls	text[]
  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': '298756000367416749980077644347,425598273225760778926783250643,445343524740513875617428478244,1190059707022013816001002568252,1492957533731614848310379481260,1505535372836579338479472405497,1599551801615048771698916128562,1599842694345554429929436023221', 'a10': 24, 'a2': -6, 'a3': -6, 'a4': 23, 'a5': -4, 'a6': 36, 'a7': -7, 'a8': -72, 'a9': 13, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12022753.901702773, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '961.1', 'coefficient_field': '1.1.1.1', 'conductor': 727423121747185263828481, 'conductor_radical': 31, 'degree': 16, 'euler_factors': [[1, 6, 13, 12, 6, 6, 20, 96, 209, 192, 80, 48, 96, 384, 832, 768, 256], [1, 6, 23, 58, 108, 148, 141, 94, 43, 282, 1269, 3996, 8748, 14094, 16767, 13122, 6561], [1, 4, -10, -24, 209, 296, -1370, -36, 10516, -180, -34250, 37000, 130625, -75000, -156250, 312500, 390625], [1, 7, 37, 134, 458, 1471, 4694, 14192, 39103, 99344, 230006, 504553, 1099658, 2252138, 4353013, 5764801, 5764801], [1, -2, 11, -58, 116, 164, 429, 4756, -24153, 52316, 51909, 218284, 1698356, -9340958, 19487171, -38974342, 214358881], [1, 6, 33, 38, -12, -1132, 1651, 16194, 133363, 210522, 279019, -2487004, -342732, 14109134, 159284697, 376491102, 815730721], [1, -8, 57, -276, 1508, -6624, 35159, -145358, 660723, -2471086, 10160951, -32543712, 125949668, -391880532, 1375841433, -3282709384, 6975757441], [1, 5, 29, -70, -590, -4435, -2714, 42900, 426339, 815100, -979754, -30419665, -76889390, -173326930, 1364330549, 4469358695, 16983563041], [1, -32, 482, -4756, 36491, -242752, 1483440, -8389808, 42757269, -192965584, 784739760, -2953563584, 10211677931, -30611247308, 71353298498, -108954414304, 78310985281], [1, 0, 22, -180, 1443, -7200, 41144, -176400, 2524805, -5115600, 34602104, -175600800, 1020606483, -3692006820, 13086113062, 0, 500246412961], [1], [1, -8, -108, 464, 12218, -32184, -676016, 215272, 32912163, 7965064, -925465904, -1630216152, 22898499098, 32175596048, -277098452172, -759455017064, 3512479453921], [1, -7, 41, -518, 3626, -15911, 162114, -1177414, 5416137, -48273974, 272513634, -1096602031, 10246209386, -60013512118, 194754273881, -1363279917167, 7984925229121], [1, -4, 43, 328, -2092, 17288, -42379, -635666, 2926363, -27333638, -78358771, 1374517016, -7152131692, 48218769304, 271818611107, -1087274444428, 11688200277601], [1, 16, 98, 1032, 15811, 124176, 665780, 6457216, 60186949, 303489152, 1470708020, 12892324848, 77152636291, 236684047224, 1056363102242, 8105969927408, 23811286661761], [1, -4, -27, 588, -4432, 1608, 100691, -1155796, 6693663, -61257188, 282841019, 239394216, -34970611792, 245898949884, -598437750483, -4698844559348, 62259690411361], [1, -5, 69, 270, -1990, 37635, -145834, -485900, 5823099, -28668100, -507648154, 7729438665, -24113548390, 193029560730, 2910456821229, -12443257424095, 146830437604321], [1, 24, 240, 2760, 45340, 460152, 3320208, 33529320, 329968230, 2045288520, 12354493968, 104445761112, 627770430940, 2331085790760, 12364889846640, 75425828064504, 191707312997281], [1, 32, 372, 3904, 71258, 818016, 5802064, 61883552, 673463043, 4146197984, 26045465296, 246028946208, 1435928580218, 5270888417728, 33650518166868, 193942771370336, 406067677556641], [1, -27, 421, -3318, 6786, 165549, -1786666, 6219816, -615913, 441606936, -9006583306, 59251808139, 172443667266, -5986432986618, 53930219530741, -245568244276557, 645753531245761], [1, 6, 33, -1262, -12972, -61052, 133831, 7999944, 53220103, 583995912, 713185399, -23750265884, -368381982252, -2616216350366, 4994029467537, 66284391114582, 806460091894081], [1, -10, 19, 1570, -21460, 132020, 181241, -13939970, 166725259, -1101257630, 1131125081, 65091008780, -835868738260, 4830978546430, 4618661654899, -192039089861590, 1517108809906561], [1, 26, 483, 5778, 60548, 592908, 6213461, 66709124, 637073703, 5536857292, 42804532829, 339017086596, 2873506419908, 22759776835254, 157912200337227, 705537325730302, 2252292232139041], [1, -20, 242, -4000, 68843, -792820, 7783224, -90672800, 1003585605, -8069879200, 61650917304, -558913522580, 4319364097163, -22336237796000, 120269472412562, -884626697910580, 3936588805702081], [1, 26, 553, 9382, 155996, 2075516, 25882775, 288684676, 3076868599, 28002413572, 243531029975, 1894267414268, 13810213718876, 80566426291174, 460633518725737, 2100755396430938, 7837433594376961], [1, -6, -175, 1710, 20100, -34908, -3282737, -2562300, 524145455, -258792300, -33487200137, -35965747308, 2091614060100, 17972271856710, -185766026355175, -643281211264206, 10828567056280801], [1, -9, 153, -1022, 10518, 65143, 100606, 11245944, -57583577, 1158332232, 1067329054, 71183514961, 1183810166358, -11847781039346, 182690001368937, -1106886478882383, 12667700813876161], [1, -13, 197, -2706, 34378, -233349, 3468374, -23496268, 207915163, -2514100676, 39709413926, -285862559007, 4506254523178, -37953049832742, 295643879314253, -2087515919421959, 17181861798319201], [1, -50, 937, -7270, -1612, 457900, 351959, -151776100, 2534993455, -16543594900, 4181624879, 592993779100, -227546955532, -111857961521230, 1571442803858017, -9140195604083450, 19925626416901921], [1, 11, 173, -462, -9482, -284757, -591454, 7218134, 314874193, 815649142, -7552276126, -410875021029, -1546015077002, -8512050528366, 360177653201357, 2587866028492987, 26584441929064321]], 'euler_factors_factorization': [[[[1, 3, 2, 0, 1, 0, 8, 24, 16], 2]], [[[1, 6, 23, 58, 108, 148, 141, 94, 43, 282, 1269, 3996, 8748, 14094, 16767, 13122, 6561], 1]], [[[1, 1, -4, 5, 25], 4]], [[[1, 7, 37, 134, 458, 1471, 4694, 14192, 39103, 99344, 230006, 504553, 1099658, 2252138, 4353013, 5764801, 5764801], 1]], [[[1, -2, 11, -58, 116, 164, 429, 4756, -24153, 52316, 51909, 218284, 1698356, -9340958, 19487171, -38974342, 214358881], 1]], [[[1, 6, 33, 38, -12, -1132, 1651, 16194, 133363, 210522, 279019, -2487004, -342732, 14109134, 159284697, 376491102, 815730721], 1]], [[[1, -8, 57, -276, 1508, -6624, 35159, -145358, 660723, -2471086, 10160951, -32543712, 125949668, -391880532, 1375841433, -3282709384, 6975757441], 1]], [[[1, 5, 29, -70, -590, -4435, -2714, 42900, 426339, 815100, -979754, -30419665, -76889390, -173326930, 1364330549, 4469358695, 16983563041], 1]], [[[1, -16, 113, -570, 2741, -13110, 59777, -194672, 279841], 2]], [[[1, 0, 11, -90, 661, -2610, 9251, 0, 707281], 2]], [1], [[[1, -2, -33, -74, 1369], 4]], [[[1, -7, 41, -518, 3626, -15911, 162114, -1177414, 5416137, -48273974, 272513634, -1096602031, 10246209386, -60013512118, 194754273881, -1363279917167, 7984925229121], 1]], [[[1, -4, 43, 328, -2092, 17288, -42379, -635666, 2926363, -27333638, -78358771, 1374517016, -7152131692, 48218769304, 271818611107, -1087274444428, 11688200277601], 1]], [[[1, 8, 17, 380, 4721, 17860, 37553, 830584, 4879681], 2]], [[[1, -4, -27, 588, -4432, 1608, 100691, -1155796, 6693663, -61257188, 282841019, 239394216, -34970611792, 245898949884, -598437750483, -4698844559348, 62259690411361], 1]], [[[1, -5, 69, 270, -1990, 37635, -145834, -485900, 5823099, -28668100, -507648154, 7729438665, -24113548390, 193029560730, 2910456821229, -12443257424095, 146830437604321], 1]], [[[1, 6, 6, 366, 3721], 4]], [[[1, 8, -3, 536, 4489], 4]], [[[1, -27, 421, -3318, 6786, 165549, -1786666, 6219816, -615913, 441606936, -9006583306, 59251808139, 172443667266, -5986432986618, 53930219530741, -245568244276557, 645753531245761], 1]], [[[1, 6, 33, -1262, -12972, -61052, 133831, 7999944, 53220103, 583995912, 713185399, -23750265884, -368381982252, -2616216350366, 4994029467537, 66284391114582, 806460091894081], 1]], [[[1, -10, 19, 1570, -21460, 132020, 181241, -13939970, 166725259, -1101257630, 1131125081, 65091008780, -835868738260, 4830978546430, 4618661654899, -192039089861590, 1517108809906561], 1]], [[[1, 26, 483, 5778, 60548, 592908, 6213461, 66709124, 637073703, 5536857292, 42804532829, 339017086596, 2873506419908, 22759776835254, 157912200337227, 705537325730302, 2252292232139041], 1]], [[[1, -10, 71, -1290, 19001, -114810, 562391, -7049690, 62742241], 2]], [[[1, 13, 192, 2195, 31031, 212915, 1806528, 11864749, 88529281], 2]], [[[1, -3, -92, 579, 7555, 58479, -938492, -3090903, 104060401], 2]], [[[1, -9, 153, -1022, 10518, 65143, 100606, 11245944, -57583577, 1158332232, 1067329054, 71183514961, 1183810166358, -11847781039346, 182690001368937, -1106886478882383, 12667700813876161], 1]], [[[1, -13, 197, -2706, 34378, -233349, 3468374, -23496268, 207915163, -2514100676, 39709413926, -285862559007, 4506254523178, -37953049832742, 295643879314253, -2087515919421959, 17181861798319201], 1]], [[[1, -25, 156, 265, -6349, 28885, 1853436, -32375725, 141158161], 2]], [[[1, 11, 173, -462, -9482, -284757, -591454, 7218134, 314874193, 815649142, -7552276126, -410875021029, -1546015077002, -8512050528366, 360177653201357, 2587866028492987, 26584441929064321], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 6, 'label': '16-31e16-1.1-c1e8-0-6', 'load_key': 'CMFs-workshop', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/961/2/g/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'plot_values': [0.017235007175243712, 0.0169124547815258, 0.01637004351821331, 0.01560747191615893, 0.01463200474544774, 0.013459362938850942, 0.012114318781802186, 0.010630882406795885, 0.009051960546837599, 0.0074299812712284126, 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7.357932004463592, 2.6688606403092296, -29.89713527469285, -108.1502817802234, -237.65396035076915, -400.04745716203377, -546.1625026434631, -598.2822064534246, -463.68606937460163, -58.27863642717949, 664.5852858050504, 1688.9921503517949, 2928.600331407566, 4233.414873439773, 5411.8236452114215, 6265.87003371262, 6632.261603150712, 6419.897132224339, 5634.6715844294795, 4385.907778077925, 2869.2972047540106, 1318.3778418374256, -45.1069945147478, -1054.0137248018918, -1624.4381133375741, -1764.4269853026954, -1561.7703170106804, -1155.3383282641626, -697.2560731580868, -310.705030464016, -62.85975196668146, 40.35809223896842, 39.86063511869825, -3.205316797466942, -35.746274805576995, -32.74149929487769, -2.5993812083055046, 19.975792460312444, -12.915316630747022, -147.1062835498576, -412.28086789186307, -811.4390600644755], 'positive_zeros': ['0.23567692889004931292023260099107', '0.33573783907737316012342669251197', '0.35131409606111784251594584189748', '0.938791577748437918209742390880943', '1.17773583151605095628262952506152', '1.18765799705811748491905021438643', '1.26182388216994766718607037726719', '1.26205335607265657257296920292321', '1.43357197271161183365410659094277', '2.41733248453880606556833348629206', '2.42978022294154093150363102380788', '2.58152695877098653976313965568011', '2.58292996710064620528850832070719', '2.61222208103411756529330113996863', '2.69134623497512939176059267328096', '3.02483050540509451531363459000987', '3.27615575302814060441686210196253', '3.30716302845353359267805451433292', '3.39701402242738453076934934570610', '3.44524718485351057974136785103015', '3.49471874149431193227568583481423', '3.58996063837341351886563394607414', '3.63527944416769712697640294979719', '4.49483721096350252278023941830658', '4.49684487333086695161552711886463', '4.55066861970383148489962242127487', '4.68184639001601892346686826730921', '4.72815404116699187644120566856895', '4.85195571277571176062779709849005', '5.08364270818420114843095404203230', '5.15977538942328685608051088224139', '5.36238127818924991538182404450189', '5.44729134049164742649384579226246', '5.46652886372924600501066242668842', '5.59708931000269959781845697015792', '5.81348007118471474245349890509816', '6.07736571937361348679674090764345', '6.08700178299702460366128814982936', '6.18985980473671396670847002587859', '6.21294147819629253419544726650246', '6.27260602718360331329765466662466', '6.48415277889825493582452760006268', '6.53733028557399593440204309597517', '6.55748353050949308187048799404083', '6.59486868051703260175091181848399', '6.93115371436448443038222340643347', '7.04262432401231294952646350480813', '7.05574185086875396355502102351418', '7.10492888017794513395171620279392', '7.16741078738246837435151027237704', '7.33228309009776100252781492832735', '7.38097028612823111660516312483167', '7.50978096545018254542313758111158', '7.61395202860187210850919353779558', '7.84733721006105728717279447340551', '7.85648123916705843052285899480668', '7.958564336619433022015108095423834', '7.979673174750219011560261860058658', '8.235751918416963000992752466943190', '8.343262354397487767261807970490343', '8.611165454964057849982726690013294', '8.737560294768368131369023765155511', '8.805843887167785853485525540798726', '8.860907903832274713085315712290175', '8.912476505579886803445758920082512', '8.957731713251618218069548492811010', '8.961684916808060892042133217659016', '9.043100366155654803708437477623138', '9.155715924229156744484176411249723', '9.179097528717666711408984642298518', '9.578315772400596141654861156415125', '9.720557659277721424725403276312560', '9.775398735965225059565316756372610', '9.786434163554116899063474113780440', '9.813995384062814789026081154579478', '9.913737553296989845008047448902475', '9.966546334175008286360619722507709', '10.30108373006669157371349266687046', '10.31218592810817477030784387935265', '10.46975839909492525840701158542523'], 'prelabel': '16-31e16-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.77013061682027, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e8-0', 'trace_hash': 147425760376257188, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23567692889004931292023260099', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.33573783907737316012342669251', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.35131409606111784251594584190', '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': 12022753.901702773, 'bad_primes': [31], 'central_character': '1.1', 'conductor': 727423121747185263828481, 'conductor_radical': 31, 'degree': 16, 'dirichlet_coefficients': [1, -6, -6, 23, -4, 36, -7, -72, 13, 24, 2, -138, -6, 42, 24, 199, 8, -78, -5, -92, 42, -12, 32, 432, 26, 36, 2, -161, 0, -144, 0, -504, -12, -48, 28, 299, 8, 30, 36, 288, 7, -252, 4, 46, -52, -192, -16, -1194, 12, -156, -48, -138, 4, -12, -8, 504, 30, 0, 5, 552, -24, 0, -91, 1179, 24, 72, -32, 184, -192, -168, 27, -936, -6, -48, -156, -115, -14, -216, 10, -796, -71, -42, -26, 966, -32, -24, 0, -144, 20, 312, 42, 736, 0, 96, 20, 3024, -26, -72, 26, 598], 'euler11': [1, -2, 11, -58, 116, 164, 429, 4756, -24153, 52316, 51909, 218284, 1698356, -9340958, 19487171, -38974342, 214358881], 'euler13': [1, 6, 33, 38, -12, -1132, 1651, 16194, 133363, 210522, 279019, -2487004, -342732, 14109134, 159284697, 376491102, 815730721], 'euler17': [1, -8, 57, -276, 1508, -6624, 35159, -145358, 660723, -2471086, 10160951, -32543712, 125949668, -391880532, 1375841433, -3282709384, 6975757441], 'euler19': [1, 5, 29, -70, -590, -4435, -2714, 42900, 426339, 815100, -979754, -30419665, -76889390, -173326930, 1364330549, 4469358695, 16983563041], 'euler2': [1, 6, 13, 12, 6, 6, 20, 96, 209, 192, 80, 48, 96, 384, 832, 768, 256], 'euler23': [1, -32, 482, -4756, 36491, -242752, 1483440, -8389808, 42757269, -192965584, 784739760, -2953563584, 10211677931, -30611247308, 71353298498, -108954414304, 78310985281], 'euler29': [1, 0, 22, -180, 1443, -7200, 41144, -176400, 2524805, -5115600, 34602104, -175600800, 1020606483, -3692006820, 13086113062, 0, 500246412961], 'euler3': [1, 6, 23, 58, 108, 148, 141, 94, 43, 282, 1269, 3996, 8748, 14094, 16767, 13122, 6561], 'euler31': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler37': [1, -8, -108, 464, 12218, -32184, -676016, 215272, 32912163, 7965064, -925465904, -1630216152, 22898499098, 32175596048, -277098452172, -759455017064, 3512479453921], 'euler41': [1, -7, 41, -518, 3626, -15911, 162114, -1177414, 5416137, -48273974, 272513634, -1096602031, 10246209386, -60013512118, 194754273881, -1363279917167, 7984925229121], 'euler43': [1, -4, 43, 328, -2092, 17288, -42379, -635666, 2926363, -27333638, -78358771, 1374517016, -7152131692, 48218769304, 271818611107, -1087274444428, 11688200277601], 'euler47': [1, 16, 98, 1032, 15811, 124176, 665780, 6457216, 60186949, 303489152, 1470708020, 12892324848, 77152636291, 236684047224, 1056363102242, 8105969927408, 23811286661761], 'euler5': [1, 4, -10, -24, 209, 296, -1370, -36, 10516, -180, -34250, 37000, 130625, -75000, -156250, 312500, 390625], 'euler53': [1, -4, -27, 588, -4432, 1608, 100691, -1155796, 6693663, -61257188, 282841019, 239394216, -34970611792, 245898949884, -598437750483, -4698844559348, 62259690411361], 'euler59': [1, -5, 69, 270, -1990, 37635, -145834, -485900, 5823099, -28668100, -507648154, 7729438665, -24113548390, 193029560730, 2910456821229, -12443257424095, 146830437604321], 'euler61': [1, 24, 240, 2760, 45340, 460152, 3320208, 33529320, 329968230, 2045288520, 12354493968, 104445761112, 627770430940, 2331085790760, 12364889846640, 75425828064504, 191707312997281], 'euler67': [1, 32, 372, 3904, 71258, 818016, 5802064, 61883552, 673463043, 4146197984, 26045465296, 246028946208, 1435928580218, 5270888417728, 33650518166868, 193942771370336, 406067677556641], 'euler7': [1, 7, 37, 134, 458, 1471, 4694, 14192, 39103, 99344, 230006, 504553, 1099658, 2252138, 4353013, 5764801, 5764801], 'euler71': [1, -27, 421, -3318, 6786, 165549, -1786666, 6219816, -615913, 441606936, -9006583306, 59251808139, 172443667266, -5986432986618, 53930219530741, -245568244276557, 645753531245761], 'euler73': [1, 6, 33, -1262, -12972, -61052, 133831, 7999944, 53220103, 583995912, 713185399, -23750265884, -368381982252, -2616216350366, 4994029467537, 66284391114582, 806460091894081], 'euler79': [1, -10, 19, 1570, -21460, 132020, 181241, -13939970, 166725259, -1101257630, 1131125081, 65091008780, -835868738260, 4830978546430, 4618661654899, -192039089861590, 1517108809906561], 'euler83': [1, 26, 483, 5778, 60548, 592908, 6213461, 66709124, 637073703, 5536857292, 42804532829, 339017086596, 2873506419908, 22759776835254, 157912200337227, 705537325730302, 2252292232139041], 'euler89': [1, -20, 242, -4000, 68843, -792820, 7783224, -90672800, 1003585605, -8069879200, 61650917304, -558913522580, 4319364097163, -22336237796000, 120269472412562, -884626697910580, 3936588805702081], 'euler97': [1, 26, 553, 9382, 155996, 2075516, 25882775, 288684676, 3076868599, 28002413572, 243531029975, 1894267414268, 13810213718876, 80566426291174, 460633518725737, 2100755396430938, 7837433594376961], 'euler_factors': [[1, 6, 13, 12, 6, 6, 20, 96, 209, 192, 80, 48, 96, 384, 832, 768, 256], [1, 6, 23, 58, 108, 148, 141, 94, 43, 282, 1269, 3996, 8748, 14094, 16767, 13122, 6561], [1, 4, -10, -24, 209, 296, -1370, -36, 10516, -180, -34250, 37000, 130625, -75000, -156250, 312500, 390625], [1, 7, 37, 134, 458, 1471, 4694, 14192, 39103, 99344, 230006, 504553, 1099658, 2252138, 4353013, 5764801, 5764801], [1, -2, 11, -58, 116, 164, 429, 4756, -24153, 52316, 51909, 218284, 1698356, -9340958, 19487171, -38974342, 214358881], [1, 6, 33, 38, -12, -1132, 1651, 16194, 133363, 210522, 279019, -2487004, -342732, 14109134, 159284697, 376491102, 815730721], [1, -8, 57, -276, 1508, -6624, 35159, -145358, 660723, -2471086, 10160951, -32543712, 125949668, -391880532, 1375841433, -3282709384, 6975757441], [1, 5, 29, -70, -590, -4435, -2714, 42900, 426339, 815100, -979754, -30419665, -76889390, -173326930, 1364330549, 4469358695, 16983563041], [1, -32, 482, -4756, 36491, -242752, 1483440, -8389808, 42757269, -192965584, 784739760, -2953563584, 10211677931, -30611247308, 71353298498, -108954414304, 78310985281], [1, 0, 22, -180, 1443, -7200, 41144, -176400, 2524805, -5115600, 34602104, -175600800, 1020606483, -3692006820, 13086113062, 0, 500246412961], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -8, -108, 464, 12218, -32184, -676016, 215272, 32912163, 7965064, -925465904, -1630216152, 22898499098, 32175596048, -277098452172, -759455017064, 3512479453921], [1, -7, 41, -518, 3626, -15911, 162114, -1177414, 5416137, -48273974, 272513634, -1096602031, 10246209386, -60013512118, 194754273881, -1363279917167, 7984925229121], [1, -4, 43, 328, -2092, 17288, -42379, -635666, 2926363, -27333638, -78358771, 1374517016, -7152131692, 48218769304, 271818611107, -1087274444428, 11688200277601], [1, 16, 98, 1032, 15811, 124176, 665780, 6457216, 60186949, 303489152, 1470708020, 12892324848, 77152636291, 236684047224, 1056363102242, 8105969927408, 23811286661761], [1, -4, -27, 588, -4432, 1608, 100691, -1155796, 6693663, -61257188, 282841019, 239394216, -34970611792, 245898949884, -598437750483, -4698844559348, 62259690411361], [1, -5, 69, 270, -1990, 37635, -145834, -485900, 5823099, -28668100, -507648154, 7729438665, -24113548390, 193029560730, 2910456821229, -12443257424095, 146830437604321], [1, 24, 240, 2760, 45340, 460152, 3320208, 33529320, 329968230, 2045288520, 12354493968, 104445761112, 627770430940, 2331085790760, 12364889846640, 75425828064504, 191707312997281], [1, 32, 372, 3904, 71258, 818016, 5802064, 61883552, 673463043, 4146197984, 26045465296, 246028946208, 1435928580218, 5270888417728, 33650518166868, 193942771370336, 406067677556641], [1, -27, 421, -3318, 6786, 165549, -1786666, 6219816, -615913, 441606936, -9006583306, 59251808139, 172443667266, -5986432986618, 53930219530741, -245568244276557, 645753531245761], [1, 6, 33, -1262, -12972, -61052, 133831, 7999944, 53220103, 583995912, 713185399, -23750265884, -368381982252, -2616216350366, 4994029467537, 66284391114582, 806460091894081], [1, -10, 19, 1570, -21460, 132020, 181241, -13939970, 166725259, -1101257630, 1131125081, 65091008780, -835868738260, 4830978546430, 4618661654899, -192039089861590, 1517108809906561], [1, 26, 483, 5778, 60548, 592908, 6213461, 66709124, 637073703, 5536857292, 42804532829, 339017086596, 2873506419908, 22759776835254, 157912200337227, 705537325730302, 2252292232139041], [1, -20, 242, -4000, 68843, -792820, 7783224, -90672800, 1003585605, -8069879200, 61650917304, -558913522580, 4319364097163, -22336237796000, 120269472412562, -884626697910580, 3936588805702081], [1, 26, 553, 9382, 155996, 2075516, 25882775, 288684676, 3076868599, 28002413572, 243531029975, 1894267414268, 13810213718876, 80566426291174, 460633518725737, 2100755396430938, 7837433594376961]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/961/2/g/a'], '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': '16-31e16-1.1-c1e8-0-6', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '16-31e16-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.77013061682027, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 147425760376257188, 'z1': {'__RealLiteral__': 0, 'data': '0.23567692889004931292023260099', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '298756000367416749980077644347,425598273225760778926783250643,445343524740513875617428478244,1190059707022013816001002568252,1492957533731614848310379481260,1505535372836579338479472405497,1599551801615048771698916128562,1599842694345554429929436023221', 'Lhash_array': ['298756000367416749980077644347', '425598273225760778926783250643', '445343524740513875617428478244', '1190059707022013816001002568252', '1492957533731614848310379481260', '1505535372836579338479472405497', '1599551801615048771698916128562', '1599842694345554429929436023221'], 'label': '16-31e16-1.1-c1e8-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/961/2/g/a'}