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lfunc_lfunctions • Show schema
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{'Lhash': '2528337462093676727211905653054', 'a10': [-0.6861406616345072, 0.39614349569663065], 'a2': [-0.5, -0.8660254037844386], 'a3': [-1.1861406616345072, -1.2621688994810694], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, -0.7922869913932613], 'a6': [-0.5, 1.6583123951777], 'a7': [2.5, -0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [-0.18614066163450715, 2.9942197070499468], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [1.1861406616345072, 1.2621688994810694]]], [7, [[1.0, 0], [-2.5, 0.8660254037844386]]], [13, [[1.0, 0], [3.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.335', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '565102555155135881284299642976', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], 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'2-546-273.62-c1-0-29', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/546/2/q/f/335/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6366679077014238, 0.830718154230446, 1.0367570462553415, 1.2552125712153719, 1.4831760841216932, 1.713759449971194, 1.9359428342828622, 2.134855863763099, 2.292446225996176, 2.3885193034953525, 2.40214254469835, 2.3133888936324114, 2.1053509256058, 1.7663025088275466, 1.2918290426390395, 0.6867009233897226, -0.03376272846706649, -0.8430936745376917, -1.7040585513205029, -2.570179578131305, -3.3884407001796757, -4.103095868022285, -4.660347659515359, -5.013516380648673, -5.128192609938755, -4.986781631874025, -4.591826357944502, -3.9675510286265685, -3.1592076048074147, -2.2300254823426524, -1.2558455330663794, -0.3178316388127946, 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'10.95377306254011928489423664215840'], 'prelabel': '2-546-273.62-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.931640676225393, 'root_number': '-0.9770281769534402 - 0.21311016268361568*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.465820338113', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.99450657905141344499325334863', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.92063457148674118812806012423', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03586786604847722971286312233', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.62', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/f/335/1'], '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': '2-546-273.62-c1-0-29', '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': '2-546-273.62-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.4658203381126965, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99450657905141344499325334863', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2528337462093676727211905653054', 'Lhash_array': ['2528337462093676727211905653054'], 'label': '2-546-273.62-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/f/335/1'}