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lfunc_lfunctions • Show schema
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{'Lhash': '2116128507863567672955778756110', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-16.848857801796104, 0.0], 'a6': [0.0, 0.0], 'a7': [7.69771560359221, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.15300848303106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [11, [[1.0, 0], [-11.0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '528.1', 'coefficient_field': 'CDF', 'conductor': 528, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [16.848857801796104, 0], [125.0, 0]], [[1.0, 0], [-7.69771560359221, 0], [343.0, 0]], [[1.0, 0], [-11.0, 0]], [[1.0, 0], [-24.848857801796104, 0], [2197.0, 0]], [[1.0, 0], [15.942004612572733, 0], [4913.0, 0]], [[1.0, 0], [15.151142198203896, 0], [6859.0, 0]], [[1.0, 0], [17.755710991019477, 0], 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'6.55561076875186715878678075720316', '7.49956260017542225733054480130588', '8.204999707146142173908727035681081', '8.848569820353239873905411581597060', '9.959088829180883620329534705200328'], 'prelabel': '2-528-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.581488016920852, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66933105027724299302279399416', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31715648920465848974587737425', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99360765766063151571840891145', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.15300848303106, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 528, 'conductor_radical': 66, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/528/4/a/p/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': '2-528-1.1-c3-0-22', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-528-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.581488016920852, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66933105027724299302279399416', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2116128507863567672955778756110', 'Lhash_array': ['2116128507863567672955778756110'], 'label': '2-528-1.1-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/528/4/a/p/1/1'}