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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '2238180232493394014', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1545.903783131989, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1]]], 'bad_primes': [2, 5, 11], 'central_character': '193600.1', 'coefficient_field': '1.1.1.1', 'conductor': 193600, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1], [1, 4, 7], [1], [1, -4, 13], [1, 0, 17], [1, 4, 19], [1, -6, 23], [1, 6, 29], [1, -8, 31], [1, -2, 37], [1, 6, 41], [1, 8, 43], [1, 6, 47], [1, 6, 53], [1, -12, 59], [1, -2, 61], [1, 10, 67], [1, 12, 71], [1, 16, 73], [1, 8, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 227, 'label': '2-440e2-1.1-c1-0-227', 'leading_term': '8.60238870408', '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': 2, 'origin': 'EllipticCurve/Q/193600/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.4947871489229577, -1.487848290838602, -1.792552008237604, -0.6390317193651593, 0.9636046537790546, 0.6172372870376818, -2.694523369355243, -6.461977264085918, -6.761655789943856, -3.102556629783161, 0.3969420576933068, 0.146658256240737, -2.019207263122676, -1.663496562116979, 1.327718041309239, 2.439736334622024, -0.1521818168129696, -2.323627784202672, -0.5706519856636724, 2.285613633040371, 1.970940523436953, -0.2213750236022491, -0.4107096957442514, 0.870777848992408, 0.6426290579456472, -0.265232784464926, 0.2861833072297496, -0.1761892501603156, -4.136384523659141, -6.606559638657936, -1.91255414700738, 4.966929291174789, 5.03967701478008, 0.3820778235664342, -0.09296914836100088, 3.073016641850686, 2.094534219536029, -2.385176257347263, -2.987931154473728, -0.1606111358388157, -0.0718036821336657, -1.712810688563209, -0.3566724060353991, 1.607524720384827, 0.3544666245874173, -0.6864922551953953, 1.034209774337623, 0.9630698338879049, -2.043506820123783, -2.325161766259731, 0.2912311643917277, 0.3683255868690681, -0.6135545215612593, 0.9859871599482821, -0.7592570261327609, -9.373162928961673, -13.70131020556511, -6.705598777608738, 0.1668246571581143, -1.595728788139857, -3.283443369961716, 0.7116696449585396, 2.850622952130619, 0.5499737453504442, -0.1649858614862082, 0.4883777156368279, -0.8968682284967309, -0.9707649193360558, 1.266180003295697, 0.7155776344924298, -0.7259651720287913, 2.425267723165956, 5.029925858303456, 1.793652337314049, -0.6672612507562757, 0.6212872708516803, -0.6726228437895752, -1.990991479593818, 3.510024855213169, 7.719492729121815, 2.810145976565653, -0.8442264605837335, 2.687711551269588, 2.452892769572424, -3.375180658518337, -3.717334209859146, 0.2114729276480947, -0.264229851871614, -1.863038850981832, -0.3184850361590939, 0.04981372168260632, -0.7695970909019169, 0.1642992095959578, -0.1807123550886072, -0.415073470326262, 4.199070033965025, 5.902542868190781, -1.50776896431388, -5.995745025827278, -1.65397579262851, -0.05795704842691723, -2.481393599009684, -0.1975300226199692, 1.616122393163368, -1.851289327996928, -0.9642317630209126, 3.673195061067689, 0.6597047229589481, -4.49956617070626, -1.756751023397774, 1.24579649133556, -0.9582107552050253, -1.435509005512637, -0.02073665744584565, -0.169098636449402, 1.362226140925317, 2.704094261793127, 0.1153857363315915, -0.5809971744049638, 0.6364579735855536], 'positive_zeros': ['1.089719093315937', '1.565354907931775', '2.705091443746502', '3.017944235941877', '3.644499077252739', '4.238640184444889', '4.793301351118019', '5.468512347620169', '5.828975739327986', '6.393253618579301', '6.668629625842749', '6.979661892845273', '7.811717683788045', '8.528535288682617', '8.758785877918308', '9.364687644395076', '10.01990706644874', '10.23930719435830', '10.78312680935439', '11.29276048156940', '11.62260239627363', '12.08748241602646', '12.71666877060232', '13.05944937488740', '13.37248319811772', '13.71409407901104', '14.73421702196719', '14.88455366708235', '15.46259292101668', '16.07017286041105', '16.29455946258933', '16.62092338232670', '17.10778175975546', '17.57779788109812', '17.84956696154765', '18.61988780272206', '18.89191001209601', '19.18853551871162', '19.62337320894243'], 'prelabel': '2-440e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.317982948416734, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2238180232493394014, 'z1': {'__RealLiteral__': 0, 'data': '1.089719093315937', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.565354907931775', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.705091443746502', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1545.903783131989, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 193600, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, -4, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 8, 0, 6, 0, 0, 0, 4, 0, -6, 0, 8, 0, 0, 0, 0, 0, 2, 0, -8, 0, -6, 0, -8, 0, 0, 0, -6, 0, 9, 0, 0, 0, -6, 0, 0, 0, 8, 0, 12, 0, 2, 0, -4, 0, 0, 0, -10, 0, -12, 0, -12, 0, -16, 0, 0, 0, 0, 0, -8, 0, -11, 0, 0, 0, 0, 0, 12, 0, 6, 0, -16, 0, -16, 0, 0, 0, -14, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 2, 3], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 10, 67], 'euler7': [1, 4, 7], 'euler71': [1, 12, 71], 'euler73': [1, 16, 73], 'euler79': [1, 8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 0, 0], [1, 4, 7], [1, 0, 0], [1, -4, 13], [1, 0, 17], [1, 4, 19], [1, -6, 23], [1, 6, 29], [1, -8, 31], [1, -2, 37], [1, 6, 41], [1, 8, 43], [1, 6, 47], [1, 6, 53], [1, -12, 59], [1, -2, 61], [1, 10, 67], [1, 12, 71], [1, 16, 73], [1, 8, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97]], 'index': 227, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/193600/u'], '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': '2-440e2-1.1-c1-0-227', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-440e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.317982948416734, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2238180232493394014, 'z1': {'__RealLiteral__': 0, 'data': '1.089719093315937', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '2238180232493394014', 'Lhash_array': ['2238180232493394014'], 'label': '2-440e2-1.1-c1-0-227', 'type': 'ECQ', 'url': 'EllipticCurve/Q/193600/u'}