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lfunc_lfunctions • Show schema
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{'Lhash': '3363183349198991715076811215971', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.224744871391589, 1.224744871391589], 'a4': [0.0, -2.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.224744871391589, 1.224744871391589], 'a8': [0.0, 0.0], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.224744871391589, -1.224744871391589]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.68', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '3433663919734359997734400655821', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 2.0]], [[1.0, 0], [-1.224744871391589, -1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.224744871391589, -1.224744871391589], [0, -7.0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [3.6742346141747673, 3.6742346141747673], [0, 13.0]], [[1.0, 0], 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'14.23187670196270868084606180817341'], 'prelabel': '2-75-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475517, 'root_angle': -0.041744700400729175, 'root_number': '0.9914128330590283 - 0.13076924120706412*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0208723502004', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.65308386127335085338012855862', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17428157854659057736214700116', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.68718685796925635333848569441', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5988780151596031, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/2/e/b/68/2'], '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': '2-75-15.8-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': '2-75-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475517, 'root_angle': -0.020872350200364587, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.65308386127335085338012855862', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3363183349198991715076811215971', 'Lhash_array': ['3363183349198991715076811215971'], 'label': '2-75-15.8-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/2/e/b/68/2'}