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lfunc_lfunctions • Show schema
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{'Lhash': '1316894791648829303423598423337', 'a10': [0.0, 0.0], 'a2': [-4.84167313632514, 0.0], 'a3': [0.0, 0.0], 'a4': [15.441798759012512, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [7.0, 0.0], 'a8': [-36.03075713744864, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 92.9280082590415, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-7.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1', 'coefficient_field': 'CDF', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.84167313632514, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.0, 0]], [[1.0, 0], [62.19621022878107, 0], [1331.0, 0]], [[1.0, 0], [-14.093355594510696, 0], [2197.0, 0]], [[1.0, 0], [63.51043926156736, 0], [4913.0, 0]], [[1.0, 0], [-48.70943428006838, 0], [6859.0, 0]], [[1.0, 0], [-99.37842433248088, 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'5.52931423230877525085196812831905', '6.59778730484775323996138150156663', '7.44380724064143645443749456587682', '7.950255032770666764527606914869437', '8.708952584152947494571799003310581'], 'prelabel': '2-1575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.639917440468125, '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': '1.03884681742093122192886934427', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20340493222719642801705499646', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97175482012530223609525338787', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.9280082590415, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 1575, 'conductor_radical': 105, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/4/a/bg/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': '2-1575-1.1-c3-0-80', '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': '2-1575-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.639917440468125, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03884681742093122192886934427', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1316894791648829303423598423337', 'Lhash_array': ['1316894791648829303423598423337'], 'factors': ['2-1575-1.1-c3-0-80'], 'label': '2-1575-1.1-c3-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/4/a/bg/1/1'}