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lfunc_lfunctions • Show schema
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{'Lhash': '83305867252875335184950021578', 'a10': [0.0, 0.0], 'a2': [-0.2225209339563144, 1.9749279121818235], 'a3': [-0.7818314824680298, -0.6234898018587335], 'a4': [-2.8758967800842425, -0.6564046730738725], 'a5': [0.0, 0.0], 'a6': [1.4053212843267633, -1.4053212843267633], 'a7': [0.0, 0.0], 'a8': [1.279894474932606, -3.6577282625522725], 'a9': [0.2225209339563144, 0.9749279121818236], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9986290902786379, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.7818314824680298, 0.6234898018587335]]], [23, [[1.0, 0], [0.7818314824680298, 0.6234898018587335]]], [29, [[1.0, 0], [0.9749279121818236, 0.2225209339563144]]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.1655', 'coefficient_field': 'CDF', 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': '2155210757681522314291241781175', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2225209339563144, 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[-0.4338837391175581, -0.9009688679024191]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-2001-2001.1655-c0-0-0', 'leading_term': '0.072542162862715358758926050934802', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2001/1/bf/a/1655/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.07254216286271536, 0.007729093103644491, -0.05546737854101634, -0.11882238136724198, -0.1835762870208596, -0.25036268365677666, -0.3192133419198887, -0.3896141562010179, -0.4605856755512308, -0.5307699904527758, -0.5985148824608283, -0.6619526179719972, -0.7190741352933325, -0.767800515485543, -0.8060535300965604, -0.831826412478837, -0.8432551903709274, -0.8386901318757578, -0.8167661726720276, -0.7764706365258885, -0.7172061409931951, -0.6388462963287633, 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'3.62569044940580168365064957499693', '4.37583685934389915180740728599586', '5.22215500622446814190615074504138', '5.86603154321734295860768053899917', '7.51554069170609761282849952588469', '8.310826685862906139762921665709922', '9.269931707639151176072981675017102'], 'prelabel': '2-2001-2001.1655-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': 0.45859050568134463, 'root_number': '0.12972513090700140525059497583654 + 0.99154999390407004770528679136387*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2292952528406723', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.06571674185132468088912579087', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.52119896990927100255868071971', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.78416199230669708858833641516', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9986290902786379, 'bad_primes': [3, 23, 29], 'central_character': '2001.1655', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2001/1/bf/a/1655/1'], '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': '2-2001-2001.1655-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2001-2001.1655-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9993143100539679, 'root_angle': 0.22929525284067231, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.06571674185132468088912579087', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '83305867252875335184950021578', 'Lhash_array': ['83305867252875335184950021578'], 'label': '2-2001-2001.1655-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2001/1/bf/a/1655/1'}