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lfunc_lfunctions • Show schema
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{'Lhash': '1243082469486226171909815265428', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.3826834323650898, 0.9238795325112867], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.3065629648763766, 1.3065629648763766], 'a8': [0.0, 0.0], 'a9': [-0.7071067811865476, 0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5331277188085835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.3826834323650898, -0.9238795325112867]]]], 'bad_primes': [2, 3], 'central_character': '3072.2945', 'coefficient_field': 'CDF', 'conductor': 3072, 'conductor_radical': 6, 'conjugate': '2282855848311268501469619576339', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.3065629648763766, -1.3065629648763766], [0, 1.0]], [[1.0, 0], [0, 0], 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'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.980619162143275163864283279250', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.79215098797286723014965572334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96690950421897460765673965633', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5331277188085835, 'bad_primes': [2, 3], 'central_character': '96.5', 'conductor': 3072, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3072/1/p/b/2945/2'], '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': '2-3072-96.5-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3072-96.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2381953475960825, 'root_angle': -0.28125, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.980619162143275163864283279250', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1243082469486226171909815265428', 'Lhash_array': ['1243082469486226171909815265428'], 'label': '2-3072-96.5-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3072/1/p/b/2945/2'}