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lfunc_lfunctions • Show schema
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{'Lhash': '243763965142785165852529891835,2900850462534839263461457746666', 'a10': -2, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.99366952191765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1]], [7, [1, -1, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.1', 'coefficient_field': '1.1.1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, -1, 1], [1], [1, 2, -1, 10, 25], [1, -1, 1], [1, 4, 5, 44, 121], [1, 6, 23, 78, 169], [1, 4, 38, 68, 289], [1, 8, 54, 152, 361], [1, -8, 41, -184, 529], [1, 2, -25, 58, 841], [1, 0, -31, 0, 961], [1, 20, 174, 740, 1369], [1, 6, -5, 246, 1681], [1, -4, -27, -172, 1849], [1, 0, -47, 0, 2209], [1, 12, 142, 636, 2809], [1, -4, -43, -236, 3481], [1, 6, -25, 366, 3721], [1, 4, -51, 268, 4489], [1, 16, 206, 1136, 5041], [1, -20, 246, -1460, 5329], [1, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.99366952191765, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, -2, 0, 1, -1, 0, -2, -4, 0, -6, 1, 0, -1, -4, 0, -8, 0, 0, -4, 8, 0, 5, -6, 0, 0, -2, 0, 0, 0, 0, -4, -2, 0, -20, -8, 0, 2, -6, 0, 4, 0, 0, 8, 0, 0, 0, 5, 0, 0, -12, 0, 8, -1, 0, -2, 4, 0, -6, 0, 0, 1, 12, 0, -4, 0, 0, -2, -16, 0, 20, -20, 0, 0, -4, 0, 0, 2, 0, -6, -4, 0, 8, 4, 0, 4, 12, 0, -6, 0, 0, 0, 16, 0, 14, 0, 0, 0], 'euler11': [1, 4, 5, 44, 121], 'euler13': [1, 6, 23, 78, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, -8, 41, -184, 529], 'euler29': [1, 2, -25, 58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -31, 0, 961], 'euler37': [1, 20, 174, 740, 1369], 'euler41': [1, 6, -5, 246, 1681], 'euler43': [1, -4, -27, -172, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 2, -1, 10, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, -4, -43, -236, 3481], 'euler61': [1, 6, -25, 366, 3721], 'euler67': [1, 4, -51, 268, 4489], 'euler7': [1, -1, 1, 0, 0], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 0, -79, 0, 6241], 'euler83': [1, 4, -67, 332, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, -14, 99, -1358, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 2, -1, 10, 25], [1, -1, 1, 0, 0], [1, 4, 5, 44, 121], [1, 6, 23, 78, 169], [1, 4, 38, 68, 289], [1, 8, 54, 152, 361], [1, -8, 41, -184, 529], [1, 2, -25, 58, 841], [1, 0, -31, 0, 961], [1, 20, 174, 740, 1369], [1, 6, -5, 246, 1681], [1, -4, -27, -172, 1849], [1, 0, -47, 0, 2209], [1, 12, 142, 636, 2809], [1, -4, -43, -236, 3481], [1, 6, -25, 366, 3721], [1, 4, -51, 268, 4489], [1, 16, 206, 1136, 5041], [1, -20, 246, -1460, 5329], [1, 0, -79, 0, 6241], [1, 4, -67, 332, 6889], [1, -12, 214, -1068, 7921], [1, -14, 99, -1358, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/f/j'], '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': '4-1134e2-1.1-c1e2-0-2', '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': 0, 'prelabel': '4-1134e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 800913839565739877, 'z1': {'__RealLiteral__': 0, 'data': '0.19229586220280067418553044688', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '243763965142785165852529891835,2900850462534839263461457746666', 'Lhash_array': ['243763965142785165852529891835', '2900850462534839263461457746666'], 'label': '4-1134e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/f/j'}