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lfunc_lfunctions • Show schema
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{'Lhash': '3601800891291602842452729183167', 'a10': [-0.16289325076271322, -3.4195501619342923], 'a2': [1.1100908432759002, 0.10600082320479871], 'a3': [-0.8412535328311812, -0.5406408174555976], 'a4': [-0.7427918887205093, -0.1431614022821112], 'a5': [-0.43689979853966654, -3.0387048448004337], 'a6': [-0.8765594719609874, -0.6893339879627067], 'a7': [0.656215263436715, -0.9215253954290032], 'a8': [-2.949329783408048, -0.8660013608207778], 'a9': [0.41541501300188644, 0.9096319953545183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6049930806277366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8412535328311812, 0.5406408174555976]]], [67, [[1.0, 0], [-8.171940343852683, 0.46839194753209895]]]], 'bad_primes': [3, 67], 'central_character': '201.4', 'coefficient_field': 'CDF', 'conductor': 201, 'conductor_radical': 201, 'conjugate': '1251806961865792628358372530293', 'degree': 2, 'euler_factors': [[[1.0, 0], 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1.266883215070646, 'root_angle': 0.496209665911068, 'root_number': '0.01190740432606193 + 0.9999291043480111*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.248104832956', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.84131991153014095491576260211', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.02071396561563831651287556782', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.16036159283608521338732787350', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6049930806277366, 'bad_primes': [3, 67], 'central_character': '67.4', 'conductor': 201, 'conductor_radical': 201, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/201/2/m/a/4/4'], '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': '2-201-67.4-c1-0-10', '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': '2-201-67.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.266883215070646, 'root_angle': 0.248104832955534, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.84131991153014095491576260211', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3601800891291602842452729183167', 'Lhash_array': ['3601800891291602842452729183167'], 'label': '2-201-67.4-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/201/2/m/a/4/4'}