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lfunc_lfunctions • Show schema
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{'Lhash': '2231677113579689174094254244058', 'a10': [-1.0, 0.0], 'a2': [2.356877181916133, 0.0], 'a3': [0.0, 0.0], 'a4': [3.554870050636933, 0.0], 'a5': [-0.42429024629404044, 0.0], 'a6': [0.0, 0.0], 'a7': [0.7924687119043744, 0.0], 'a8': [3.66463774319097, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.26137902105694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '9801.1', 'coefficient_field': 'CDF', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.356877181916133, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.42429024629404044, 0], [5.0, 0]], [[1.0, 0], [-0.7924687119043744, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5273609756415649, 0], [13.0, 0]], [[1.0, 0], [4.513218235779051, 0], [17.0, 0]], [[1.0, 0], [3.3473387625413076, 0], [19.0, 0]], [[1.0, 0], 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'6.39018609133357001852682541847063', '7.18622461035497142736770610831056'], 'prelabel': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76048282797948837946297829012', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30919654660437840926800670632', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36222689908294538894412320213', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.26137902105694, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'index': 408, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9801/2/a/bv/1/8'], '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': '2-99e2-1.1-c1-0-408', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76048282797948837946297829012', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2231677113579689174094254244058', 'Lhash_array': ['2231677113579689174094254244058'], 'label': '2-99e2-1.1-c1-0-408', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9801/2/a/bv/1/8'}