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lfunc_lfunctions • Show schema
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{'Lhash': '2628187956902576129372959426246,4009831878462805702084707191039', 'a10': -3, 'a2': 1, 'a3': -2, 'a4': -2, 'a5': -3, 'a6': -2, 'a7': 1, 'a8': -3, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.414177379069041, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [1, -2, 1]], [31, [1, -2, 1]]], 'bad_primes': [11, 31], 'central_character': '341.1', 'coefficient_field': '1.1.1.1', 'conductor': 116281, 'conductor_radical': 341, 'degree': 4, 'euler_factors': [[1, -1, 3, -2, 4], [1, 2, 7, 6, 9], [1, 3, 11, 15, 25], [1, -1, 3, -7, 49], [1, -2, 1], [1, 2, 7, 26, 169], [1, 4, 33, 68, 289], [1, 10, 58, 190, 361], [1, 2, 42, 46, 529], [1, 0, 58, 0, 841], [1, -2, 1], [1, 4, 73, 148, 1369], [1, -9, 71, -369, 1681], [1, 17, 157, 731, 1849], [1, 9, 83, 423, 2209], [1, -3, 77, -159, 2809], [1, 0, 113, 0, 3481], [1, 11, 121, 671, 3721], [1, 14, 183, 938, 4489], [1, 11, 141, 781, 5041], [1, -8, 117, -584, 5329], [1, 10, 183, 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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 451869065517845945, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07327473077312776756495047181', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16319960542823909784227014131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83340761680378082441701435865', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.414177379069041, 'bad_primes': [11, 31], 'central_character': '1.1', 'conductor': 116281, 'conductor_radical': 341, 'degree': 4, 'dirichlet_coefficients': [1, 1, -2, -2, -3, -2, 1, -3, -3, -3, 2, 4, -2, 1, 6, 1, -4, -3, -10, 6, -2, 2, -2, 6, -2, -2, 14, -2, 0, 6, 2, 2, -4, -4, -3, 6, -4, -10, 4, 9, 9, -2, -17, -4, 9, -2, -9, -2, -2, -2, 8, 4, 3, 14, -6, -3, 20, 0, 0, -12, -11, 2, -3, 1, 6, -4, -14, 8, 4, -3, -11, 9, 8, -4, 4, 20, 2, 4, -10, -3, -4, 9, 23, 4, 12, -17, 0, -6, -5, 9, -2, 4, -4, -9, 30, -4, 16, -2, -6, 4], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, 2, 7, 26, 169], 'euler17': [1, 4, 33, 68, 289], 'euler19': [1, 10, 58, 190, 361], 'euler2': [1, -1, 3, -2, 4], 'euler23': [1, 2, 42, 46, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 2, 7, 6, 9], 'euler31': [1, -2, 1, 0, 0], 'euler37': [1, 4, 73, 148, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, 17, 157, 731, 1849], 'euler47': [1, 9, 83, 423, 2209], 'euler5': [1, 3, 11, 15, 25], 'euler53': [1, -3, 77, -159, 2809], 'euler59': [1, 0, 113, 0, 3481], 'euler61': [1, 11, 121, 671, 3721], 'euler67': [1, 14, 183, 938, 4489], 'euler7': [1, -1, 3, -7, 49], 'euler71': [1, 11, 141, 781, 5041], 'euler73': [1, -8, 117, -584, 5329], 'euler79': [1, 10, 183, 790, 6241], 'euler83': [1, -23, 297, -1909, 6889], 'euler89': [1, 5, 123, 445, 7921], 'euler97': [1, -16, 178, -1552, 9409], 'euler_factors': [[1, -1, 3, -2, 4], [1, 2, 7, 6, 9], [1, 3, 11, 15, 25], [1, -1, 3, -7, 49], [1, -2, 1, 0, 0], [1, 2, 7, 26, 169], [1, 4, 33, 68, 289], [1, 10, 58, 190, 361], [1, 2, 42, 46, 529], [1, 0, 58, 0, 841], [1, -2, 1, 0, 0], [1, 4, 73, 148, 1369], [1, -9, 71, -369, 1681], [1, 17, 157, 731, 1849], [1, 9, 83, 423, 2209], [1, -3, 77, -159, 2809], [1, 0, 113, 0, 3481], [1, 11, 121, 671, 3721], [1, 14, 183, 938, 4489], [1, 11, 141, 781, 5041], [1, -8, 117, -584, 5329], [1, 10, 183, 790, 6241], [1, -23, 297, -1909, 6889], [1, 5, 123, 445, 7921], [1, -16, 178, -1552, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/341/2/a/a'], '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': '4-341e2-1.1-c1e2-0-1', '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': '4-341e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.650120816463347, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 451869065517845945, 'z1': {'__RealLiteral__': 0, 'data': '2.07327473077312776756495047181', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2628187956902576129372959426246,4009831878462805702084707191039', 'Lhash_array': ['2628187956902576129372959426246', '4009831878462805702084707191039'], 'label': '4-341e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/341/2/a/a'}