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lfunc_lfunctions • Show schema
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{'Lhash': '1738624455983782731517071705365', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.1603272351954362, 0.0], 'a4': [0.0, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.2626653816092523, 0.0], 'a8': [0.0, 0.0], 'a9': [-26.974295177654586, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.28175720528139, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '920.1', 'coefficient_field': 'CDF', 'conductor': 920, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.1603272351954362, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [2.2626653816092523, 0], [343.0, 0]], [[1.0, 0], [8.804263823119678, 0], [1331.0, 0]], [[1.0, 0], [-37.44041616880041, 0], [2197.0, 0]], [[1.0, 0], [-71.0912017337676, 0], [4913.0, 0]], [[1.0, 0], [-106.59853959792095, 0], 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'4.97465378152495280524072713397316', '5.73175702462688106949581519797739', '6.68370327282760759655966522842777', '7.79591186889932104941632434728065', '8.304174480293233280090974729570864', '9.253939854279693732115502055502034'], 'prelabel': '2-920-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.367615435490738, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37153286218675604085788943349', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99590893938077346615988920897', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57032158720735069435598753201', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 54.28175720528139, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 920, 'conductor_radical': 230, 'degree': 2, 'index': 48, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/920/4/a/b/1/3'], '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': '2-920-1.1-c3-0-48', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-920-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.367615435490738, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37153286218675604085788943349', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1738624455983782731517071705365', 'Lhash_array': ['1738624455983782731517071705365'], 'factors': ['2-920-1.1-c3-0-48'], 'label': '2-920-1.1-c3-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/920/4/a/b/1/3'}