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lfunc_lfunctions • Show schema
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{'Lhash': '1170632750855417543656455735540', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 3.4641016151377544], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.5, 0.8660254037844386]]], [19, [[1.0, 0], [-4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.113', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '2142684720012302901814312290909', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386]], [[1.0, 0], [0, -3.4641016151377544], [-5.0, 0]], [[1.0, 0], [1.0, 0], [7.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-11.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-13.0, 0]], [[1.0, 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'8.302578397461485617962229000043634', '9.294512334634324008400509642943564', '9.515191572864907516077214823731079'], 'prelabel': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.2967401358131697, 'root_number': '0.5960395606792696 - 0.8029550685469663*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.148370067907', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.923466411521167865382362748965', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.48557632430000821629214565507', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68828982477715838594221815009', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '57.56', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/f/e/113/1'], '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': '2-912-57.56-c1-0-12', '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': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.14837006790658486, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.923466411521167865382362748965', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1170632750855417543656455735540', 'Lhash_array': ['1170632750855417543656455735540'], 'label': '2-912-57.56-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/f/e/113/1'}