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lfunc_lfunctions • Show schema
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{'Lhash': '1889740106660708532766343352913', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [2.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.9770551619259145, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-5.5, -2.598076211353316]]]], 'bad_primes': [3, 37], 'central_character': '999.406', 'coefficient_field': 'CDF', 'conductor': 999, 'conductor_radical': 111, 'conjugate': '1403387308037540256383685129579', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 5.196152422706632], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [0, 5.196152422706632], [-19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [0, 0], [-29.0, 0]], 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0.14047220025584325, 'root_number': '0.9041944301794651 + 0.4271210980886246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0702361001279', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49074209117281793383131546920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45181260533058921939057205942', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73130298085626340887296770287', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.9770551619259145, 'bad_primes': [3, 37], 'central_character': '37.36', 'conductor': 999, 'conductor_radical': 111, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/999/2/c/e/406/1'], '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': '2-999-37.36-c1-0-33', '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': '2-999-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.824368099580137, 'root_angle': 0.07023610012792163, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49074209117281793383131546920', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1889740106660708532766343352913', 'Lhash_array': ['1889740106660708532766343352913'], 'label': '2-999-37.36-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/999/2/c/e/406/1'}