Formats: - HTML - YAML - JSON - 2026-08-09T10:24:36.849905
  • lfunc_lfunctions • Show schema
    {'Lhash': '1807805985909976822631066661319', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-574250.685175344, 0], 'a4': [0, 0], 'a5': [84139153.81810646, 0], 'a6': [0, 0], 'a7': [-5957377838.630525, 0], 'a8': [0, 0], 'a9': [235620670597.35202, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.816322987608302, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '11.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '8.1', 'coefficient_field': 'CDF', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [574250.685175344, 0], [94143178827.0, 0]], [[1.0, 0], [-84139153.81810646, 0], [11920928955078124, 0]], [[1.0, 0], [5957377838.630525, 0], [27368747340080914000, 0]], [[1.0, 0], [-1243256411309.5957, 0], [895430243255237400000000, 0]], [[1.0, 0], [-7214793069972.663, 0], [41753905413413120000000000, 0]], [[1.0, 0], [65093560057173.61, 0], [19967568900859523000000000000, 0]], [[1.0, 0], [556138696371464.1, 0], [257829627945307720000000000000, 0]], [[1.0, 0], [3081257119920496.0, 0], [20880467999847910000000000000000, 0]], [[1.0, 0], [46993534951159384, 0], [4316720717749415700000000000000000, 0]], [[1.0, 0], [-240562513269829730, 0], [20013311644049280000000000000000000, 0]], [[1.0, 0], [528192705182580500, 0], [1171223165167387700000000000000000000, 0]], [[1.0, 0], [-1598369240539904500, 0], [12417343769139487000000000000000000000, 0]], [[1.0, 0], [-7359940984338115000, 0], [37134234731477574000000000000000000000, 0]], [[1.0, 0], [16399669173781789000, 0], [287243845682065600000000000000000000000, 0]], [[1.0, 0], [26408883842419147000, 0], [4553496434179608000000000000000000000000, 0]], [[1.0, 0], [324946544750691900000, 0], [53653278865596930000000000000000000000000, 0]], [[1.0, 0], [322520414057991500000, 0], [115501122579584380000000000000000000000000, 0]], [[1.0, 0], [1098962191597867500000, 0], [999356547346805200000000000000000000000000, 0]], [[1.0, 0], [230177166820549750000, 0], [3792643488006830000000000000000000000000000, 0]], [[1.0, 0], [-833705872252890000000, 0], [7184983626352716000000000000000000000000000, 0]], [[1.0, 0], [-2599918226814564000000, 0], [44200084506410990000000000000000000000000000, 0]], [[1.0, 0], [10580747448102288000000, 0], [137656310293626940000000000000000000000000000, 0]], [[1.0, 0], [-40743388587193440000000, 0], [685441117453157960000000000000000000000000000, 0]], [[1.0, 0], [94002871993922780000000, 0], [4963064143419832000000000000000000000000000000, 0]], [[1.0, 0], [131017712187383830000000, 0], [12571630183484300000000000000000000000000000000, 0]], [[1.0, 0], [59118445464552890000000, 0], [19735865111266046000000000000000000000000000000, 0]], [[1.0, 0], [77825696641344160000000, 0], [47405298629774560000000000000000000000000000000, 0]], [[1.0, 0], [68162626128121470000000, 0], [72578744721851540000000000000000000000000000000, 0]], [[1.0, 0], [427400293264515600000000, 0], [166266287664560630000000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-2e3-1.1-c23-0-3', 'leading_term': '2.176747147642017576555257960281227758410775', 'load_key': 'CMFs-workshop', 'motivic_weight': 23, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [23], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/8/24/a/a/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.09375', 'prec': 14}, 'plot_values': [-6.915811900591777e-61, 0.20289874481988712, 0.3988037640815821, 0.5808908815739304, 0.7426711603680664, 0.8781489573753599, 0.981968731787663, 1.0495472403576287, 1.0771880697617415, 1.0621758407789519, 1.0028478629497866, 0.8986415127462203, 0.7501161429897585, 0.5589488953114878, 0.327904369160747, 0.060778688062839537, -0.23768091592876267, -0.5618793177893667, -0.9054973040537051, -1.2616332694030292, -1.6229596768986114, -1.9818907864315836, -2.3307578623250613, -2.661987858313192, -2.968281452307198, -3.2427862686913556, -3.4792611847670547, -3.672227770820251, -3.817105158546881, -3.910324966607884, -3.9494233292469034, -3.933107566565354, -3.8612955937175646, -3.7351267797448333, -3.556943622255602, -3.3302442876143816, -3.059606762615636, -2.75058605693813, -2.4095865697336145, -2.0437123721735513, -1.6605987446405182, -1.2682288271780064, -0.874739680545746, -0.48822239995543704, -0.11652116327652608, 0.23296377866606005, 0.5534641565632468, 0.8390178872624942, 1.0846247774203706, 1.28637944116467, 1.441577630329383, 1.5487927683852216, 1.6079201692849896, 1.6201871957352125, 1.5881284509014895, 1.5155259839276929, 1.4073154016257547, 1.2694596935154336, 1.1087934713417684, 0.932841173163641, 0.7496135622088063, 0.5673875389155347, 0.3944748594344006, 0.23898579601499212, 0.10859406760430064, 0.010309499449488516, -0.04973517078331284, -0.06647714088992818, -0.036090241646604876, 0.0438797527099085, 0.1744157069783731, 0.35496922707443807, 0.5834428996250001, 0.8562161726603429, 1.1682151886670866, 1.5130256420315122, 1.8830464804743638, 2.2696810399687566, 2.6635610312032516, 3.054797719084463, 3.433253689995545, 3.7888278171174914, 4.1117454412267715, 4.392845407685288, 4.623855459093456, 4.7976475902768385, 4.9084653339566, 4.95211556017723, 4.926118231111469, 4.8298086381446375, 4.664387935360535, 4.432919240608481, 4.140268163484251, 3.792988294329822, 3.3991539006734155, 2.968143775064213, 2.5103818069431805, 2.037041356891416, 1.5597218418336636, 1.0901070455148374, 0.6396155059825892, 0.21905386395161378, -0.1617157457340801, -0.4940833315628444, -0.770963298525943, -0.9870217754175086, -1.1388506875260243, -1.225081772317026, -1.2464355361667303, -1.2057021745502468, -1.107653666425317, -0.9588885379479818, -0.7676130970984436, -0.5433651914739426, -0.29668865733926897, -0.038768531358730214, 0.21896128618223204, 0.46522496289111853, 0.6893124510239308, 0.8814737782557582, 1.033285784011076, 1.1379777547360435, 1.1907034897727733, 1.1887488837246167, 1.1316661029767063, 1.021327807634548, 0.8618975537898206, 0.6597154188068836, 0.42310092673655364, 0.16207840598499837, -0.11196712398206952, -0.3866926778600965, -0.6492453316787444, -0.8867402039773961, -1.0867515081953565, -1.237798836631725, -1.3298105134553202, -1.3545461995788861, -1.3059619559669753, -1.180502658910651, -0.9773089698436509, -0.6983289268387488, -0.3483275545400269, 0.06520842791088154, 0.5322698151998089, 1.0406230684446092, 1.576198525751213, 2.123556096640693, 2.6664125567104358, 3.188211769815976, 3.6727170233801263, 4.104603273993774, 4.470026544924536, 4.7571480436965405, 4.956591792075965, 5.06181666246971, 5.0693866375413865, 4.9791267620045, 4.794156512280763, 4.52079701704517, 4.168353541692645, 3.7487797070152826, 3.2762348413808464, 2.7665504591019636, 2.236625914898749, 1.7037766202741744, 1.1850606610131262, 0.6966110962846326, 0.25300155772126626, -0.13332804618313346, -0.45256087914223175, -0.6978858046003824, -0.8657555870458462, -0.9560078924973808, -0.9718419168724237, -0.9196495257034062, -0.8087060459763303, -0.6507320447101405, -0.4593432872055061, -0.2494113243214707, -0.036361564068547673, 0.1645609809665796, 0.3390259912779404, 0.4743191944160173, 0.5599785266783789, 0.5883350532419916, 0.5549322000337064, 0.4588017354366468, 0.30258092405377435, 0.09246211951356144, -0.16202651682279806, -0.4484028103574323, -0.7517609347313934, -1.0554292471895812, -1.3417281370549, -1.5927951535835656, -1.791440776138677, -1.9219958758515996, -1.9711113466003585, -1.9284716305164578, -1.7873869228624604, -1.545233621246895, -1.2037189091722595, -0.7689529799222592, -0.251320990969968, 0.3348439871884815, 0.9717764187714222, 1.6389624605252417, 2.3139647726031494, 2.973352680539188, 3.59369664381534, 4.152582061941132, 4.629595579194571, 5.0072373783072575, 5.2717155227342305, 5.413583149967193, 5.428186059635034, 5.315896701875048, 5.082120383130202, 4.737070220581719, 4.29531848814285, 3.775142967830071, 3.1976972040233744, 2.5860426275388666, 1.9640878908540182, 1.3554860265710038, 0.7825428944827036, 0.2651906182828907, -0.17992274185227036, -0.5401811180142706, -0.8075473164089753, -0.9788798227832128, -1.0560017813196572, -1.0455167964750103, -0.9583791145838384, -0.8092385024984768, -0.6155920900174836, -0.3967859422728617, -0.17291759763039863, 0.036303242697701084, 0.21267562432760684, 0.34054965130547066, 0.4077332363757598, 0.4062126445178747, 0.3326453210454387, 0.18859502931445457, -0.019507306634154297, -0.2806791255594462, -0.5799652456356867, -0.8992529409869785, -1.218282262551016, -1.5157993338541809, -1.7707914925183414, -1.9637374243660297, -2.077803233836346, -2.0999169149107653, -2.0216589353981287], 'positive_zeros': ['1.42610746650890802960986163752964', '4.15551091387888452174319835525798', '6.10621489963350830003614920011600', '6.42466379102561216966283980141294', '9.521333393595047162042737082394020', '10.79524661974056312355186155720394', '12.14946864444288184488189567579572', '13.39229671775951288574836396720456', '15.80962119748965286284403023802592'], 'prelabel': '2-2e3-1.1-c23-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.178447932306388, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c23-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42610746650890802960986163753', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.15551091387888452174319835526', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.10621489963350830003614920012', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 26.816322987608302, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8/24/a/a/1/1'], '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': '2-2e3-1.1-c23-0-3', 'motivic_weight': 23, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [23], 'order_of_vanishing': 1, 'prelabel': '2-2e3-1.1-c23-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.178447932306388, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c23-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42610746650890802960986163753', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1807805985909976822631066661319', 'Lhash_array': ['1807805985909976822631066661319'], 'factors': ['2-2e3-1.1-c23-0-3'], 'label': '2-2e3-1.1-c23-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/24/a/a/1/1'}