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lfunc_lfunctions • Show schema
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{'Lhash': '1623646616797951017040476588497', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.5, 0.8660254037844386], 'a3': [0.30009784679806384, 0.5197847178962677], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0, 0], 'a6': [-0.30009784679806384, 0.5197847178962677], 'a7': [0.7196868710982038, -1.2465342262823624], 'a8': [-1.0, 0], 'a9': [1.3198825646943315, -2.286103662074898], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.494717941596392, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 13], 'central_character': '1690.991', 'coefficient_field': 'CDF', 'conductor': 1690, 'conductor_radical': 130, 'conjugate': '1002269973256713889559057968695', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.30009784679806384, -0.5197847178962677], [-1.5, 2.598076211353316]], [[1.0, 0], 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'8.559000955006958860780981150500077', '9.265358522828720705907003672386288'], 'prelabel': '2-1690-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6735157467467583, 'root_angle': -0.03243695479078394, 'root_number': '0.97930306285546217230775038866544913905365457959658638988 - 0.2023993850828374076557083208030941141047373252833653144*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.03243695479078394', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28083133988626491157738094987', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16774357755972990975538317326', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48073408357222679634859524547', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.494717941596392, 'bad_primes': [2, 5, 13], 'central_character': '13.3', 'conductor': 1690, 'conductor_radical': 130, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1690/2/e/t/991/3'], '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': '2-1690-13.3-c1-0-34', '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': '2-1690-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6735157467467583, 'root_angle': -0.03243695479078394, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28083133988626491157738094987', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1623646616797951017040476588497', 'Lhash_array': ['1623646616797951017040476588497'], 'factors': ['2-1690-13.3-c1-0-34'], 'label': '2-1690-13.3-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1690/2/e/t/991/3'}