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lfunc_lfunctions • Show schema
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{'Lhash': '642179815575787395732004294320', 'a10': [-0.6633186959675602, -1.1489016830261471], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.2882074516546105, -2.2312407569546138], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.6633186959675602, 1.1489016830261471], 'a6': [2.576414903309221, 4.8119746770474995e-61], 'a7': [-1.4615700597194903, 2.205405395960472], 'a8': [1.0, 0.0], 'a9': [-1.8189568769969318, 3.1505257277354985], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [1.4615700597194903, -2.205405395960472]]], [23, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 7, 23], 'central_character': '322.93', 'coefficient_field': 'CDF', 'conductor': 322, 'conductor_radical': 322, 'conjugate': '1977944110911110746403126938801', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], 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[[1.0, 0], [-4.442782966381821, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-322-7.2-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/322/2/e/a/93/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5467824269210116, 0.4374472113935641, 0.31483006051822, 0.17388593390217896, 0.009414266104108006, -0.1829944695442771, -0.40615159437853915, -0.6606298288459849, -0.9442816867464153, -1.2519127019143288, -1.5751261902189853, -1.9023743754756197, -2.2192574520434714, -2.509105748693197, -2.753861871802027, -2.9352518435890573, -3.0361996432508027, -3.0424016438074926, -2.9439403732708462, -2.736785620409466, -2.4240102979620985, -2.0165436350597603, -1.5332993063144913, -1.0005535245122168, -0.4505081132006117, 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'7.72533496705778790704969292417020', '9.007285304215757508335261545169690', '9.751315994298724444603332212340444', '10.44115013585907181165281289202501', '11.22040153916537187092892718282656'], 'prelabel': '2-322-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': -0.2502717513737644, 'root_number': '-0.0017074634091758564 - 0.9999985422832907*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.250271751374', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50659055062977806152411770583', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10531674061861146930969354187', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36768867488444447139865524111', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'bad_primes': [2, 7, 23], 'central_character': '7.2', 'conductor': 322, 'conductor_radical': 322, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/322/2/e/a/93/1'], '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': '2-322-7.2-c1-0-1', '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': '2-322-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': -0.2502717513737644, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50659055062977806152411770583', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '642179815575787395732004294320', 'Lhash_array': ['642179815575787395732004294320'], 'factors': ['2-322-7.2-c1-0-1'], 'label': '2-322-7.2-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/322/2/e/a/93/1'}