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lfunc_lfunctions • Show schema
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{'Lhash': '2443196485447762240270043619030', 'a10': [0.29678967268364437, 0.514054792249809], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5935793453672887, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.06653723767426262, -2.6449145158213865], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.06653723767426262, 2.6449145158213865]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.289', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '822048902412772951461853550540', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5935793453672887, 0], [5.0, 0]], [[1.0, 0], [0.06653723767426262, 2.6449145158213865]], [[1.0, 0], 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'10.57594986926823079797590206614487', '11.98647974666041346932303693559672'], 'prelabel': '2-378-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.7085498276705868, 'root_number': '-0.6093008771410005 + 0.792939115642057*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.354274913835', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92734219114311631730865400329', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.69721634376078247122664610306', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.06043877812093635130566172818', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/h/c/289/2'], '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': '2-378-63.16-c1-0-6', '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': '2-378-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.3542749138352934, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92734219114311631730865400329', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2443196485447762240270043619030', 'Lhash_array': ['2443196485447762240270043619030'], 'label': '2-378-63.16-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/h/c/289/2'}