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lfunc_lfunctions • Show schema
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{'Lhash': '19178248638195707042233446128', 'a10': [74.41280286571202, 33.872781659465986], 'a2': [-3.6405663387540694, -1.6571894077415505], 'a3': [-12.737554429410382, 0], 'a4': [10.507446533738417, 12.066215949527363], 'a5': [-20.439897516378927, 0], 'a6': [46.37191189375923, 21.108540280950354], 'a7': [9.191400184528394, 0], 'a8': [-18.257050893907305, -61.340688720108766], 'a9': [81.24529284219203, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.952673945750476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [3.6405663387540694, 1.6571894077415505]]], [41, [[1.0, 0], [1675.8346484790122, -131.6785136505782]]]], 'bad_primes': [2, 41], 'central_character': '164.163', 'coefficient_field': 'CDF', 'conductor': 164, 'conductor_radical': 82, 'conjugate': '1415857822992373443730735169277', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.6405663387540694, 1.6571894077415505]], [[1.0, 0], [12.737554429410382, 0], 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{'__RealLiteral__': 0, 'data': '-0.3765072997305799', 'prec': 64}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.01512897058128070238061380749', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.45142281224234210743397279817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13160795392988526397872150861', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.952673945750476, 'bad_primes': [2, 41], 'central_character': '164.163', 'conductor': 164, 'conductor_radical': 82, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/164/5/d/f/163/5'], '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': '2-164-164.163-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-164-164.163-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.117362498705996, 'root_angle': -0.3765072997305799, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.01512897058128070238061380749', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '19178248638195707042233446128', 'Lhash_array': ['19178248638195707042233446128'], 'factors': ['2-164-164.163-c4-0-1'], 'label': '2-164-164.163-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/164/5/d/f/163/5'}