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lfunc_lfunctions • Show schema
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{'Lhash': '793630744075633460250857181089', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.1510070650865905, 1.9936027166007122], 'a6': [0, 0], 'a7': [2.4150845077880425, 1.0804475092489165], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.4150845077880425, -1.0804475092489165]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.865', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '1937523614422929590262193706141', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.1510070650865905, -1.9936027166007122], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.4150845077880425, -1.0804475092489165]], [[1.0, 0], [-2.231454574335507, -3.86499269753108], [-5.5, 9.526279441628825]], [[1.0, 0], 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'8.515705828718837711385299280620061'], 'prelabel': '2-2268-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.6237018783264391, 'root_number': '-0.3789125231766794783372178983231616615545795925830292175 - 0.92543249336722683349512056596161803361793795775220533316*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.31185093916321954', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62606426718272936348018197809', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.51021648838913296509927552052', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04291848444461674386414371338', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '63.25', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/i/n/865/2'], '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': '2-2268-63.25-c1-0-9', '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': '2-2268-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.31185093916321954, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62606426718272936348018197809', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '793630744075633460250857181089', 'Lhash_array': ['793630744075633460250857181089'], 'label': '2-2268-63.25-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/i/n/865/2'}