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lfunc_lfunctions • Show schema
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{'Lhash': '848815585168308796413885537217', 'a10': [247.42159546057482, 0.0], 'a2': [-4.0, 0.0], 'a3': [9.0, 0.0], 'a4': [16.0, 0.0], 'a5': [-61.855398865143705, 0.0], 'a6': [-36.0, 0.0], 'a7': [49.0, 0.0], 'a8': [-64.0, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.09732475359706, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, 0]]], [3, [[1.0, 0], [-9.0, 0]]], [7, [[1.0, 0], [-49.0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.1', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [61.855398865143705, 0], [3125.0, 0]], [[1.0, 0], [-49.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [36.01807375320419, 0], [371293.0, 0]], [[1.0, 0], [76.68416565443127, 0], [1419857.0, 0]], [[1.0, 0], [-2780.9426099013717, 0], [2476099.0, 0]], 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'positive_zeros': ['0.66959743088157491939817927841924', '1.95726275474324577766465642937556', '3.32172409263404671984003832119740', '4.17986115396981440930176490878201', '5.58975766755886693506405401873755', '7.00286940019357639944771677669592', '7.74543509974456797351202558462692', '8.282183204455919535732010967581413', '9.305148615296999931286116060417958', '10.05969236855182593611643137160879'], 'prelabel': '2-462-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.607980294679876, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66959743088157491939817927842', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95726275474324577766465642938', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32172409263404671984003832120', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 74.09732475359706, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/6/a/q/1/1'], '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': '2-462-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-462-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.607980294679876, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66959743088157491939817927842', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '848815585168308796413885537217', 'Lhash_array': ['848815585168308796413885537217'], 'label': '2-462-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/6/a/q/1/1'}