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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 3, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '771490579057544097', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 775.3793437874414, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1, -1]], [17, [1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '97104.1', 'coefficient_field': '1.1.1.1', 'conductor': 97104, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -3, 5], [1, -1], [1, -3, 11], [1, -5, 13], [1], [1, 2, 19], [1, -6, 23], [1, -6, 29], [1, 4, 31], [1, 11, 37], [1, -12, 41], [1, -1, 43], [1, 12, 47], [1, 9, 53], [1, -12, 59], [1, -10, 61], [1, 5, 67], [1, 0, 71], [1, -7, 73], [1, 1, 79], [1, -15, 83], [1, -9, 89], [1, -19, 97]], 'gamma_factors': [[], [0]], 'index': 48, 'label': '2-97104-1.1-c1-0-48', 'leading_term': '6.82319564129', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/97104/cz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [6.823195641291555, 5.933856488278648, 3.597385902394477, 0.8919006315189033, -0.7025153509382303, -0.481907736316522, 0.6151783076937593, 0.8700101949980389, -0.1614553146496281, -0.9032154942910245, 0.258018399881238, 2.490629078784099, 3.174455523302216, 1.472223145477756, -0.05617242490269005, 1.201817774361519, 3.827954449203594, 3.908694900342437, 0.7785760027643295, -1.524364942933238, -0.0311029712951545, 2.562632773036026, 1.963172830054461, -1.009136757229654, -1.913069038365408, -0.09464443218219055, 0.5074315859309666, -1.260966185378927, -1.232918308669081, 2.562856018899056, 5.305744131989002, 2.723920188397055, -1.652655904519318, -2.145768202385666, 0.1520800043455515, 0.559712667632483, -0.594353987040888, 0.04068044608455553, 1.179756127621903, -0.5816278232261609, -3.024662990202915, -1.802979510676208, 0.7145048118425245, -0.4711681491475234, -2.785385674369038, -0.6316137671095123, 2.725791434537798, -0.01446214101677509, -6.016755244214299, -6.145686556456369, -0.8139657264016315, 1.588467255192245, -0.172577330102059, -0.3083646622719706, 1.477294745832865, 0.9842988193321173, -0.5555938924400419, 0.1732015962884007, 0.7066706149809662, -0.8258139848667768, 0.2924371052590759, 5.175638925468949, 6.389063965289599, 1.91077394281806, 0.02822617739572445, 3.07696381552688, 2.871340917377623, -2.187462931329122, -3.795911348733072, -0.6000510035165785, 0.5600812490784629, -0.2110387558960749, 1.80438176261646, 3.213498172609283, -0.1968345086911486, -2.60659229888394, 0.08234564810272765, 1.320521150821329, -1.408650839612513, -0.7687540023470624, 3.842126426343195, 4.149440394119013, 0.1529498620631718, -1.027460453523641, -0.004706980044650525, -0.3455626497187379, 0.9910988305823724, 4.007921463432925, 2.537817376121449, -1.100292790943838, 0.8661662221774465, 3.909212115602092, 0.2546738076623438, -2.839939285672121, 2.07481009826621, 5.858156167086746, 1.744981041999927, -1.293509307916635, 1.395024825380134, 2.417844089596542, 0.3208432125600462, 0.1337105510884151, 0.1479674621792161, -1.507017751153746, -0.6469482072032866, 0.9383829359959235, -2.20365712443133, -4.465624150079674, -0.1574707385001138, 2.453833244824263, -1.006706251567708, -1.530251046097882, 1.680281475155105, -0.1933855524690194, -3.47573214152164, 0.01654918667959147, 3.568362529569418, 0.978462550389689, -0.4080818379063258, 1.567962384112717, 0.5452793658122413], 'positive_zeros': ['0.8568929578056549', '1.360264922384071', '1.968146009834587', '2.467590308267863', '3.471255576107863', '3.575292710494813', '4.557124368270858', '5.002676099315589', '5.663589445378642', '6.262662433897969', '6.589178674496443', '7.101193120940400', '7.892099905506796', '8.480857927015711', '8.862000669389117', '9.243549424911817', '9.699366756703184', '10.40341240843145', '10.70691082970742', '11.28707720528303', '11.74938864367057', '12.54313074300515', '12.97708228622411', '13.29489376800835', '13.88166597028988', '14.21956182784155', '14.62500136495540', '14.97943838403589', '15.89776282591519', '15.99490642146477', '16.64668929174237', '17.30394944031635', '17.63230344429042', '17.81423530957371', '18.48892635407662', '18.99398083083720', '19.38053808933947', '19.79603644223070'], 'prelabel': '2-97104-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.845634196179503, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 771490579057544097, 'z1': {'__RealLiteral__': 0, 'data': '0.8568929578056549', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.360264922384071', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.968146009834587', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 775.3793437874414, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 97104, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 5, 0, 3, 0, 0, 0, -2, 0, 1, 0, 6, 0, 4, 0, 1, 0, 6, 0, -4, 0, 3, 0, 3, 0, -11, 0, 5, 0, 12, 0, 1, 0, 3, 0, -12, 0, 1, 0, 0, 0, -9, 0, 9, 0, -2, 0, 12, 0, 10, 0, 1, 0, 15, 0, -5, 0, 6, 0, 0, 0, 7, 0, 4, 0, 3, 0, -1, 0, 1, 0, 15, 0, 0, 0, 6, 0, 9, 0, 5, 0, -4, 0, -6, 0, 19, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, -5, 13], 'euler17': [1, 0, 0], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 11, 37], 'euler41': [1, -12, 41], 'euler43': [1, -1, 43], 'euler47': [1, 12, 47], 'euler5': [1, -3, 5], 'euler53': [1, 9, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -7, 73], 'euler79': [1, 1, 79], 'euler83': [1, -15, 83], 'euler89': [1, -9, 89], 'euler97': [1, -19, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -3, 5], [1, -1, 0], [1, -3, 11], [1, -5, 13], [1, 0, 0], [1, 2, 19], [1, -6, 23], [1, -6, 29], [1, 4, 31], [1, 11, 37], [1, -12, 41], [1, -1, 43], [1, 12, 47], [1, 9, 53], [1, -12, 59], [1, -10, 61], [1, 5, 67], [1, 0, 71], [1, -7, 73], [1, 1, 79], [1, -15, 83], [1, -9, 89], [1, -19, 97]], 'index': 48, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/97104/cz'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-97104-1.1-c1-0-48', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-97104-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.845634196179503, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 771490579057544097, 'z1': {'__RealLiteral__': 0, 'data': '0.8568929578056549', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '771490579057544097', 'Lhash_array': ['771490579057544097'], 'label': '2-97104-1.1-c1-0-48', 'type': 'ECQ', 'url': 'EllipticCurve/Q/97104/cz'}