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lfunc_lfunctions • Show schema
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{'Lhash': '1015513049870931492964734557076', 'a10': [822.37870704476, -7023.08288874618], 'a2': [-8.0, 8.0], 'a3': [52.94933459514875, 52.94933459514875], 'a4': [0.0, -128.0], 'a5': [-490.34134973693375, 387.54401135633873], 'a6': [-847.18935352238, 0.0], 'a7': [-2624.0107411137765, 2624.0107411137765], 'a8': [1024.0, 1024.0], 'a9': [0.0, -953.7359318619675], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.073786100611273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [8.0, -8.0]]], [5, [[1.0, 0], [490.34134973693375, -387.54401135633873]]]], 'bad_primes': [2, 5], 'central_character': '10.3', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'conjugate': '4353068897012773345238565783083', 'degree': 2, 'euler_factors': [[[1.0, 0], [8.0, -8.0]], [[1.0, 0], [-52.94933459514875, -52.94933459514875], [0, 6561.0]], [[1.0, 0], [490.34134973693375, -387.54401135633873]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.018362232259431, 'root_angle': -0.3933438959786185, 'root_number': '-0.7837346793504365 - 0.6210957674815282*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.393343895979', 'prec': 50}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.801098543784933523304306953121', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.52661646363352644481874717553', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.31654700935727973072703631691', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.073786100611273, 'bad_primes': [2, 5], 'central_character': '5.3', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/9/c/a/3/2'], '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': '2-10-5.3-c8-0-0', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-10-5.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.018362232259431, 'root_angle': -0.3933438959786185, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.801098543784933523304306953121', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1015513049870931492964734557076', 'Lhash_array': ['1015513049870931492964734557076'], 'factors': ['2-10-5.3-c8-0-0'], 'label': '2-10-5.3-c8-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/9/c/a/3/2'}