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lfunc_lfunctions • Show schema
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{'Lhash': '2369532560643223315245139777686', 'a10': [3.49465993840233, -3.6156348522088635], 'a2': [-0.3892106989554361, -1.3596010561258847], 'a3': [1.7260754412201715, 0.14374829117798302], 'a4': [-1.6970300636372417, 1.0583425547106093], 'a5': [1.7778309631957978, 3.0792935555242367], 'a6': [-0.4763667004252388, -2.40272236571893], 'a7': [-0.7934555116166296, -2.523970750837892], 'a8': [2.09942591234415, 1.8953656213453731], 'a9': [2.9586728575668197, 0.49624079023936546], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.3892106989554361, 1.3596010561258847]]], [3, [[1.0, 0], [-1.7260754412201715, -0.14374829117798302]]], [7, [[1.0, 0], [0.7934555116166296, 2.523970750837892]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'5.47809644650966945747586255945058', '6.49575245828188247740094723171728', '8.073493860637842233273141642481213', '8.886864707183135871616497147265692', '9.204986424475591669424513156880975', '10.38420355206782137837843212768389', '12.68173813138232664392652514333497', '12.84530246476976521684661615087319'], 'prelabel': '2-168-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.18342260174947378, 'root_number': '0.8385177936725963 + 0.5448742145618943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0917113008747', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86923160073967519579101624938', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20443228483992500885797833568', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47809644650966945747586255945', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.11', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/11/12'], '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': '2-168-168.11-c1-0-13', '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': '2-168-168.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.09171130087473689, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86923160073967519579101624938', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2369532560643223315245139777686', 'Lhash_array': ['2369532560643223315245139777686'], 'label': '2-168-168.11-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/11/12'}