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lfunc_lfunctions • Show schema
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{'Lhash': '1488165056121581551784805077497,2553734586560643359257413103499', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 1, 'a7': 0, 'a8': 1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2241.388372887114, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '5929.1', 'coefficient_field': '1.1.1.1', 'conductor': 35153041, 'conductor_radical': 77, 'degree': 4, 'euler_factors': [[1, -1, 1, -2, 4], [1, -1, 3, -3, 9], [1, 0, -3, 0, 25], [1], [1], [1, 6, 22, 78, 169], [1, 9, 51, 153, 289], [1, -6, 47, -114, 361], [1, 9, 63, 207, 529], [1, -13, 97, -377, 841], [1, 2, 63, 62, 961], [1, -4, 26, -148, 1369], [1, 14, 131, 574, 1681], [1, -7, 95, -301, 1849], [1, 7, 77, 329, 2209], [1, 15, 133, 795, 2809], [1, 17, 187, 1003, 3481], [1, -5, 125, -305, 3721], [1, 1, 53, 67, 4489], [1, 5, 145, 355, 5041], [1, -10, 171, -730, 5329], [1, 13, 197, 1027, 6241], [1, 6, 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2.481199611853249, 2.890256158819114, 3.2147368631065794], 'positive_zeros': ['1.17395523329034865877634280035846', '2.01454137764843544928418503701347', '2.02706730455830808668465683112563', '2.79919684210147768572098700245860', '2.90458580459691654215486753119912', '3.34450237365559872646035386773786', '3.95704701578755866902869754944699', '4.39196544169802577884306100993291', '4.69766613703040098006786847397540', '4.91481345673752603231065213656603', '5.10432543421592402421766343064800', '5.78891535535513383998126992434745', '6.26928469160653902768183068484675', '6.36546229577635044538328178786797', '6.88401448939174499490817719171564', '7.19186081668000685798879403949109', '7.53740101524067991837167932917078', '7.953355790671934742512563522499613'], 'prelabel': '4-77e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 776481398623279946, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17395523329034865877634280036', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01454137764843544928418503701', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.02706730455830808668465683113', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2241.388372887114, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 35153041, 'conductor_radical': 77, 'degree': 4, 'dirichlet_coefficients': [1, 1, 1, 0, 0, 1, 0, 1, -2, 0, 0, 0, -6, 0, 0, -1, -9, -2, 6, 0, 0, 0, -9, 1, 3, -6, -2, 0, 13, 0, -2, -6, 0, -9, 0, 0, 4, 6, -6, 0, -14, 0, 7, 0, 0, -9, -7, -1, 0, 3, -9, 0, -15, -2, 0, 0, 6, 13, -17, 0, 5, -2, 0, -3, 0, 0, -1, 0, -9, 0, -5, -2, 10, 4, 3, 0, 0, -6, -13, 0, -2, -14, -6, 0, 0, 7, 13, 0, -3, 0, 0, 0, -2, -7, 0, -6, 0, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 6, 22, 78, 169], 'euler17': [1, 9, 51, 153, 289], 'euler19': [1, -6, 47, -114, 361], 'euler2': [1, -1, 1, -2, 4], 'euler23': [1, 9, 63, 207, 529], 'euler29': [1, -13, 97, -377, 841], 'euler3': [1, -1, 3, -3, 9], 'euler31': [1, 2, 63, 62, 961], 'euler37': [1, -4, 26, -148, 1369], 'euler41': [1, 14, 131, 574, 1681], 'euler43': [1, -7, 95, -301, 1849], 'euler47': [1, 7, 77, 329, 2209], 'euler5': [1, 0, -3, 0, 25], 'euler53': [1, 15, 133, 795, 2809], 'euler59': [1, 17, 187, 1003, 3481], 'euler61': [1, -5, 125, -305, 3721], 'euler67': [1, 1, 53, 67, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 5, 145, 355, 5041], 'euler73': [1, -10, 171, -730, 5329], 'euler79': [1, 13, 197, 1027, 6241], 'euler83': [1, 6, 175, 498, 6889], 'euler89': [1, 3, -83, 267, 7921], 'euler97': [1, 0, 181, 0, 9409], 'euler_factors': [[1, -1, 1, -2, 4], [1, -1, 3, -3, 9], [1, 0, -3, 0, 25], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 6, 22, 78, 169], [1, 9, 51, 153, 289], [1, -6, 47, -114, 361], [1, 9, 63, 207, 529], [1, -13, 97, -377, 841], [1, 2, 63, 62, 961], [1, -4, 26, -148, 1369], [1, 14, 131, 574, 1681], [1, -7, 95, -301, 1849], [1, 7, 77, 329, 2209], [1, 15, 133, 795, 2809], [1, 17, 187, 1003, 3481], [1, -5, 125, -305, 3721], [1, 1, 53, 67, 4489], [1, 5, 145, 355, 5041], [1, -10, 171, -730, 5329], [1, 13, 197, 1027, 6241], [1, 6, 175, 498, 6889], [1, 3, -83, 267, 7921], [1, 0, 181, 0, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5929/2/a/p'], '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': '4-77e4-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-77e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.8806470159729285, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 776481398623279946, 'z1': {'__RealLiteral__': 0, 'data': '1.17395523329034865877634280036', 'prec': 103}}
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{'Lhash': '1488165056121581551784805077497,2553734586560643359257413103499', 'Lhash_array': ['1488165056121581551784805077497', '2553734586560643359257413103499'], 'label': '4-77e4-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5929/2/a/p'}