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lfunc_lfunctions • Show schema
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{'Lhash': '2075523566941652003518870685709', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -1.4142135623730951], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.38328192970214586, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3], 'central_character': '768.449', 'coefficient_field': 'CDF', 'conductor': 768, 'conductor_radical': 6, 'conjugate': '1295262248379145020176355192126', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], 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'root_analytic_conductor': 0.6190976737980413, 'root_angle': 0.12500000000000003, 'root_number': '0.92387953251128675612818318939698 + 0.38268343236508977172845998403043*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63729939982513489239532469311', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76129092971241327325370869272', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40429449059889297546425732176', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.38328192970214586, 'bad_primes': [2, 3], 'central_character': '48.5', 'conductor': 768, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/1/i/b/449/1'], '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': '2-768-48.5-c0-0-1', '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': '2-768-48.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6190976737980413, 'root_angle': 0.06250000000000001, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63729939982513489239532469311', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2075523566941652003518870685709', 'Lhash_array': ['2075523566941652003518870685709'], 'label': '2-768-48.5-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/1/i/b/449/1'}