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lfunc_lfunctions • Show schema
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{'Lhash': '300919301276728051901951687321', 'a10': [0.0, -3.1622776601683795], 'a2': [-1.4142135623730951, 0.0], 'a3': [-5.41949283394262, 0.0], 'a4': [2.0, 0.0], 'a5': [0.0, 2.23606797749979], 'a6': [7.664320266945453, 0.0], 'a7': [0.0, -8.241985049874389], 'a8': [-2.8284271247461903, 0.0], 'a9': [20.370902577155412, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.267046080286829, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.4142135623730951, 0]]], [5, [[1.0, 0], [0, -2.23606797749979]]], [23, [[1.0, 0], [-22.24448034577889, 5.846631008218037]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.91', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '1470756884983919724995323976170', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4142135623730951, 0]], [[1.0, 0], [5.41949283394262, 0], [9.0, 0]], [[1.0, 0], [0, -2.23606797749979]], [[1.0, 0], [0, 8.241985049874389], 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-2.3200077114609203, -4.848951546114668], 'positive_zeros': ['0.23738347240363406452066612275187', '2.12504045406519273001646631012121', '4.89362661694179991162623717106385', '5.27130891075658291907434332895513', '6.74739336182501520206121853150501', '7.35252435503514435310127118808140', '9.170199438784641790292162797851020', '9.667379533366011273644813280258425', '10.91135040749510304398437959966542', '11.63853423388903362563214539813425'], 'prelabel': '2-230-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5034068946711057, 'root_angle': -0.5818125913513014, 'root_number': '-0.2542013481833929 - 0.9671513193816909*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.290906295676', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23738347240363406452066612275', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12504045406519273001646631012', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89362661694179991162623717106', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.267046080286829, 'bad_primes': [2, 5, 23], 'central_character': '23.22', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/3/d/a/91/2'], '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': '2-230-23.22-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-230-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5034068946711057, 'root_angle': -0.2909062956756507, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.23738347240363406452066612275', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '300919301276728051901951687321', 'Lhash_array': ['300919301276728051901951687321'], 'label': '2-230-23.22-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/3/d/a/91/2'}