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lfunc_lfunctions • Show schema
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{'Lhash': '681366476161427657124028177668', 'a10': [-1.5, -2.598076211353316], 'a2': [0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-3.0, 0], 'a6': [0, 0], 'a7': [2.5, -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], [-2.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.541', 'coefficient_field': 'CDF', 'conductor': 1134, 'conductor_radical': 42, 'conjugate': '1913606095554847945574168524468', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0], [5.0, 0]], [[1.0, 0], [-2.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-2.0, -3.4641016151377544], [-6.5, 11.258330249197702]], [[1.0, 0], 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3687159358349428', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53750337517195478273435520502', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08033819687691849851095425972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44831225174260494937688310190', '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': '63.16', 'conductor': 1134, 'conductor_radical': 42, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/h/k/541/1'], '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': '2-1134-63.16-c1-0-7', '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': '2-1134-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.00915861815445, 'root_angle': -0.3687159358349428, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53750337517195478273435520502', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '681366476161427657124028177668', 'Lhash_array': ['681366476161427657124028177668'], 'label': '2-1134-63.16-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/h/k/541/1'}