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  • lfunc_lfunctions • Show schema
    {'Lhash': '1853978713795230826881255191317', 'a10': [-1.7992723401599513, -2.256216151214136], 'a2': [-0.9009688679024191, -0.4338837391175581], 'a3': [-1.5217932741162659, 1.9082684078636643], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [2.600023863308263, 1.2521055008631548], 'a6': [2.199054995405844, -1.059009071149361], 'a7': [-1.8976451738974078, 2.379571783024394], 'a8': [-0.2225209339563144, -0.9749279121818236], 'a9': [-0.6580707454360769, -2.8831963200454878], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9009688679024191, 0.4338837391175581]]], [29, [[1.0, 0], [5.376574670621934, -0.30404738319322644]]]], 'bad_primes': [2, 29], 'central_character': '58.45', 'coefficient_field': 'CDF', 'conductor': 58, 'conductor_radical': 58, 'conjugate': '3954151085678459718219194485786', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.8672410044497006*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1670544229', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46253132642499295750824365909', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.26531205183255138421576235460', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.66206929019848200283755473434', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'bad_primes': [2, 29], 'central_character': '29.16', 'conductor': 58, 'conductor_radical': 58, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/58/2/d/b/45/1'], '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': '2-58-29.16-c1-0-0', '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': '2-58-29.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': -0.16705442290011938, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46253132642499295750824365909', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1853978713795230826881255191317', 'Lhash_array': ['1853978713795230826881255191317'], 'factors': ['2-58-29.16-c1-0-0'], 'label': '2-58-29.16-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/58/2/d/b/45/1'}