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lfunc_lfunctions • Show schema
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{'A10': 3, 'A2': 1, 'A3': -2, 'A4': 1, 'A5': 3, 'A6': -2, 'A7': -2, 'A8': 1, 'A9': 1, 'Lhash': '418085530249370956', 'a10': [0.9486832980505138, 0], 'a2': [0.7071067811865475, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [1.3416407864998738, 0], 'a6': [-0.8164965809277261, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 326.57217418663265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [11, [1]], [13, [1]]], 'bad_primes': [2, 11, 13], 'central_character': '40898.1', 'coefficient_field': '1.1.1.1', 'conductor': 40898, 'conductor_radical': 286, 'degree': 2, 'euler_factors': [[1, -1], [1, 2, 3], [1, -3, 5], [1, 2, 7], [1], [1], [1, -3, 17], [1, 2, 19], [1, -6, 23], [1, 3, 29], [1, 2, 31], [1, -7, 37], [1, 3, 41], [1, -8, 43], [1, 6, 47], [1, 3, 53], [1, 0, 59], [1, 10, 61], [1, -10, 67], [1, 12, 71], [1, 14, 73], [1, -2, 79], [1, 18, 83], [1, -9, 89], [1, 11, 97]], 'gamma_factors': [[], [0]], 'index': 39, 'label': '2-40898-1.1-c1-0-39', 'leading_term': '7.34300414349', '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': 1, 'origin': 'EllipticCurve/Q/40898/bh', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.710756104570426, 2.67651783323364, 2.319084055930792, 0.7276291587837744, -1.01670579046177, -1.41898065178246, 0.1039139155337487, 2.387305392508368, 3.354496818235963, 2.094424753540513, 0.05916463826818842, -0.2866360038788484, 1.730893357953107, 3.938344134036286, 3.622788514532915, 0.761835464640353, -1.817337776767025, -1.776809989606978, 0.04466628228326427, 1.065232441003091, 0.4459512487098199, -0.2587555984579582, 0.07131374670120438, 0.4443594795013546, -0.09198454386225954, -0.3204439609998979, 0.9982018007287696, 1.895382980251401, -0.6480640094905983, -4.893591419701756, -4.456136607651972, 3.211306082829337, 11.37022734393966, 11.2528311400278, 3.493569435973313, -2.620643627423786, -1.608407135063394, 1.93057400653681, 1.702210453606972, -1.043035401548653, -1.276092034416942, 0.8475048182445714, 1.061236003517522, -0.9372214244420018, -1.200071266218768, 0.900383660457526, 1.388077456662549, -1.004120129297153, -2.503877285573743, -1.136996179442984, 0.1523597490630269, -0.3685774620384965, -0.08513196773381626, 1.946829412840063, 2.149356669478657, -0.6678204315343312, -2.033899193381333, 0.09750468861239048, 0.8271242161684755, -2.730402236918056, -5.089841113130078, -1.601245290347069, 2.94801710459675, 2.44649612205367, -0.5086682276903345, -0.6853329544593544, 0.3536869208807214, -0.7680403719045102, -1.693497981043632, -0.2451891992319742, -0.4706452159074357, -4.262520286685235, -5.457409815313926, -1.156467540218271, 1.029571616347493, -3.238839933062282, -5.351821369054357, 1.043735394784205, 7.183275876258421, 3.968433947534462, -2.260601285964631, -1.727559684173118, 2.418218362009304, 2.474052369089451, 0.08450139366626648, 0.119077493964348, 0.8191283778221844, -0.3879555087161191, -0.9882433055965241, 0.1340237117071517, 0.1469505650942637, -0.6846421973080998, 0.3180801933470665, 1.027698129482179, -1.234628239791896, -2.312881782807255, 0.8785046826183323, 2.639385403264904, -0.6145456305013838, -2.696818637273388, -0.4384042086360586, 0.2688450078975752, -1.288953722713481, 1.526469097839459, 5.586276308650217, 0.4931785224454811, -9.025029242749708, -7.726281220411539, 2.689214182249246, 6.442561257581967, 1.684187035262049, 0.02273792756832917, 3.050145243468499, 3.163985821476044, 0.5949611334335323, 0.0514971373698282, 0.1578572787656704, -0.3996715550177244, 0.9910503480991433, 2.194235022178091], 'positive_zeros': ['1.094801582720133', '1.738255377969612', '2.759838716650724', '3.056304258152787', '4.059205521172059', '4.743853447481495', '5.370241463284519', '5.721469874241977', '6.218999319275119', '6.590119907364614', '7.210051495446534', '7.913741763488150', '8.861586630504885', '9.352350021543841', '9.899430427464274', '10.40037802209197', '10.88722189589920', '11.39996492468646', '11.91005352521213', '12.68116405768178', '12.88001721218453', '13.26377326434779', '13.94677994858801', '14.49042309344208', '14.83252489815880', '15.57311302541464', '16.19575913030597', '16.62679477699465', '16.88379830297846', '17.54528350108980', '17.68795495964910', '18.56440431717780', '18.84036722851808', '19.46961472315337'], 'prelabel': '2-40898-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.071308037511635, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 418085530249370956, 'z1': {'__RealLiteral__': 0, 'data': '1.094801582720133', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.738255377969612', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.759838716650724', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 326.57217418663265, 'bad_primes': [2, 11, 13], 'central_character': '1.1', 'conductor': 40898, 'conductor_radical': 286, 'degree': 2, 'dirichlet_coefficients': [1, 1, -2, 1, 3, -2, -2, 1, 1, 3, 0, -2, 0, -2, -6, 1, 3, 1, -2, 3, 4, 0, 6, -2, 4, 0, 4, -2, -3, -6, -2, 1, 0, 3, -6, 1, 7, -2, 0, 3, -3, 4, 8, 0, 3, 6, -6, -2, -3, 4, -6, 0, -3, 4, 0, -2, 4, -3, 0, -6, -10, -2, -2, 1, 0, 0, 10, 3, -12, -6, -12, 1, -14, 7, -8, -2, 0, 0, 2, 3, -11, -3, -18, 4, 9, 8, 6, 0, 9, 3, 0, 6, 4, -6, -6, -2, -11, -3, 0, 4], 'euler11': [1, 0, 0], 'euler13': [1, 0, 0], 'euler17': [1, -3, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 3, 29], 'euler3': [1, 2, 3], 'euler31': [1, 2, 31], 'euler37': [1, -7, 37], 'euler41': [1, 3, 41], 'euler43': [1, -8, 43], 'euler47': [1, 6, 47], 'euler5': [1, -3, 5], 'euler53': [1, 3, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, -10, 67], 'euler7': [1, 2, 7], 'euler71': [1, 12, 71], 'euler73': [1, 14, 73], 'euler79': [1, -2, 79], 'euler83': [1, 18, 83], 'euler89': [1, -9, 89], 'euler97': [1, 11, 97], 'euler_factors': [[1, -1, 0], [1, 2, 3], [1, -3, 5], [1, 2, 7], [1, 0, 0], [1, 0, 0], [1, -3, 17], [1, 2, 19], [1, -6, 23], [1, 3, 29], [1, 2, 31], [1, -7, 37], [1, 3, 41], [1, -8, 43], [1, 6, 47], [1, 3, 53], [1, 0, 59], [1, 10, 61], [1, -10, 67], [1, 12, 71], [1, 14, 73], [1, -2, 79], [1, 18, 83], [1, -9, 89], [1, 11, 97]], 'index': 39, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/40898/bh'], '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': '2-40898-1.1-c1-0-39', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-40898-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.071308037511635, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 418085530249370956, 'z1': {'__RealLiteral__': 0, 'data': '1.094801582720133', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '418085530249370956', 'Lhash_array': ['418085530249370956'], 'factors': ['2-40898-1.1-c1-0-39'], 'label': '2-40898-1.1-c1-0-39', 'type': 'ECQ', 'url': 'EllipticCurve/Q/40898/bh'}