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lfunc_lfunctions • Show schema
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{'Lhash': '926824121612314093487740788717', 'a10': [0, 0], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.8660254037844386, -0.5], 'a4': [-0.5, 0.8660254037844386], 'a5': [0, 0], 'a6': [-0.8660254037844386, -0.5], 'a7': [0.36602540378443865, -0.6339745962155614], 'a8': [1.0, 0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.8660254037844386, 0.5]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [2.5, -2.598076211353316]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.49', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '1291237758764716940271040556994', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.36602540378443865, 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'7.60984707284275095391136870674338', '8.400347738381861814004683346257742', '9.155440612618433380593529679429449'], 'prelabel': '2-1950-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.10037543095700005, 'root_number': '0.9506913844248081777463318656941127220874106500092640624 + 0.3101385038663235618904515921926751428304648820606384114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05018771547850001', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73113531555575922734967081888', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47011555471893639618725310927', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18451992999944285344997090915', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.49', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/y/b/49/2'], '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': '2-1950-65.49-c1-0-16', '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': '2-1950-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.050187715478500025, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73113531555575922734967081888', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '926824121612314093487740788717', 'Lhash_array': ['926824121612314093487740788717'], 'label': '2-1950-65.49-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/y/b/49/2'}