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lfunc_lfunctions • Show schema
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{'Lhash': '506313472835969517317490389301', 'a10': [0, 0], 'a2': [0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.5, -0.8660254037844386], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.0550355892132, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.757', 'coefficient_field': 'CDF', 'conductor': 1134, 'conductor_radical': 42, 'conjugate': '2274140255458704419253749836940', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-5.5, 9.526279441628825]], [[1.0, 0], [2.5, -4.330127018922194], [-6.5, -11.258330249197702]], [[1.0, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39941090450697708471924845253', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18334898427611332614545841639', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97517000591496477531489828277', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.0550355892132, 'bad_primes': [2, 3, 7], 'central_character': '9.4', 'conductor': 1134, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/f/k/757/1'], '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': '2-1134-9.4-c1-0-5', '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': '2-1134-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': -0.4444444444444444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39941090450697708471924845253', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '506313472835969517317490389301', 'Lhash_array': ['506313472835969517317490389301'], 'label': '2-1134-9.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/f/k/757/1'}