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lfunc_lfunctions • Show schema
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{'Lhash': '3295481192353643635394408622762', 'a10': [-1.771191654569864, -2.619709931038562], 'a2': [1.0426702172100784, -0.9554259877892626], 'a3': [-0.4539904997395468, -0.8910065241883679], 'a4': [0.17432236371382376, -1.992388444432768], 'a5': [0.3280850806964104, -2.2118680294774435], 'a6': [-1.3246531614740942, -0.49527164445048494], 'a7': [3.17505673142212, 3.17505673142212], 'a8': [-1.7218189607440229, -2.2439562086686036], 'a9': [-0.5877852522924731, 0.8090169943749475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0426702172100784, 0.9554259877892626]]], [3, [[1.0, 0], [0.4539904997395468, 0.8910065241883679]]], [5, [[1.0, 0], [-0.3280850806964104, 2.2118680294774435]]]], 'bad_primes': [2, 3, 5], 'central_character': '300.223', 'coefficient_field': 'CDF', 'conductor': 300, 'conductor_radical': 30, 'conjugate': 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'-0.4015414177679525 + 0.9158408648978832*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.315762709361', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.59967627653891464628719793952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.22907234819706105578800759493', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70466642342085347978875890787', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'bad_primes': [2, 3, 5], 'central_character': '100.23', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/2/w/a/223/22'], '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': '2-300-100.23-c1-0-27', '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': '2-300-100.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5477441844951034, 'root_angle': 0.3157627093611605, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.59967627653891464628719793952', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3295481192353643635394408622762', 'Lhash_array': ['3295481192353643635394408622762'], 'label': '2-300-100.23-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/2/w/a/223/22'}