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lfunc_lfunctions • Show schema
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{'Lhash': '1098548391062853160661368055558', 'a10': [0, 0], 'a2': [-7.3484692283495345, 7.3484692283495345], 'a3': [-33.0681115275729, -33.0681115275729], 'a4': [0, 148.0], 'a5': [0, 0], 'a6': [486.0, 0], 'a7': [-2872.026723413276, 2872.026723413276], 'a8': [-2968.781568253212, -2968.781568253212], 'a9': [0, 2187.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.553395754584553, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [33.0681115275729, 33.0681115275729]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.43', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '30821318591013314890907125367', 'degree': 2, 'euler_factors': [[[1.0, 0], [7.3484692283495345, -7.3484692283495345], [0, -256.0]], [[1.0, 0], [33.0681115275729, 33.0681115275729]], [[1.0, 0], [0, 0]], [[1.0, 0], [2872.026723413276, -2872.026723413276], [0, -5764801.0]], [[1.0, 0], [234.0, 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'0.3264097326151029 + 0.9452283779352676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19708054137514794', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.866601878202928419442388001279320', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.89585191350432314119044518953633', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.47212726158562086098295036630897', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.553395754584553, 'bad_primes': [3, 5], 'central_character': '5.3', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/9/f/a/43/1'], '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': '2-75-5.3-c8-0-13', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-75-5.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.527512619124859, 'root_angle': 0.19708054137514794, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.866601878202928419442388001279320', 'prec': 117}}
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lfunc_instances • Show schema
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{'Lhash': '1098548391062853160661368055558', 'Lhash_array': ['1098548391062853160661368055558'], 'label': '2-75-5.3-c8-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/9/f/a/43/1'}