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lfunc_lfunctions • Show schema
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{'Lhash': '1562200591771812399075099550489', 'a10': [-6.854101966249685, -1.4109342611737269e-60], 'a2': [-1.3090169943749475, 2.267283942228512], 'a3': [2.618033988749895, 0.0], 'a4': [-2.4270509831248424, -4.203775615332221], 'a5': [1.3090169943749475, 2.267283942228512], 'a6': [-3.4270509831248424, 5.935826422901098], 'a7': [0.0, 0.0], 'a8': [7.47213595499958, 0.0], 'a9': [3.8541019662496847, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-2.5, -2.598076211353316]]]], 'bad_primes': [7, 13], 'central_character': '637.263', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '2188424513791796126000326463271', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3090169943749475, -2.267283942228512], [-1.0, -1.7320508075688772]], [[1.0, 0], [-2.618033988749895, 0], [3.0, 0]], [[1.0, 0], 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'9.216629185926511914001182310231585', '10.00891085542311033615999304552137'], 'prelabel': '2-637-91.81-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.7485596183324155, 'root_number': '-0.7038998290285488 - 0.710299254324246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.374279809166', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23235897296191225582736320914', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04132488132278653363383979846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29760388512439541783887985672', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.81', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/g/c/263/1'], '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': '2-637-91.81-c1-0-17', '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': '2-637-91.81-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.37427980916620773, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23235897296191225582736320914', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1562200591771812399075099550489', 'Lhash_array': ['1562200591771812399075099550489'], 'label': '2-637-91.81-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/g/c/263/1'}