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lfunc_lfunctions • Show schema
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{'Lhash': '2336711533686736509051768591148', 'a10': [-0.13397459621556135, -0.2320508075688773], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.2679491924311227, 0], 'a6': [-0.5, 0.8660254037844386], 'a7': [-0.36602540378443865, 0.6339745962155614], 'a8': [1.0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.096830764957835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.991', 'coefficient_field': 'CDF', 'conductor': 1014, 'conductor_radical': 78, 'conjugate': '166311939461403242036547286406', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.2679491924311227, 0], [5.0, 0]], [[1.0, 0], 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'10.15817769976471034641876823697098'], 'prelabel': '2-1014-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': -0.7725413265368988, 'root_number': '-0.7553668972738207938978595655305537754934331243526820343 - 0.6553021062860404571947137918734385179039317882843436525*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3862706632684495', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84334037570449778381363369033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40568803763984963013532894067', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.67168461357426992200885985600', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.096830764957835, 'bad_primes': [2, 3, 13], 'central_character': '13.3', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1014/2/e/g/991/1'], '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': '2-1014-13.3-c1-0-25', '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': '2-1014-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': -0.3862706632684494, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84334037570449778381363369033', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2336711533686736509051768591148', 'Lhash_array': ['2336711533686736509051768591148'], 'label': '2-1014-13.3-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/e/g/991/1'}