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lfunc_lfunctions • Show schema
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{'Lhash': '1442669078530660204367191104836,1939768530429818255008926156316', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 1, 'a5': -2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1143.5654963709767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 2, 1]], [7, [1, 2, 1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.1', 'coefficient_field': '1.1.1.1', 'conductor': 17935225, 'conductor_radical': 385, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, 1, 5, 3, 9], [1, 2, 1], [1, 2, 1], [1], [1, -7, 37, -91, 169], [1, -9, 53, -153, 289], [1, 2, 34, 38, 361], [1, 0, 26, 0, 529], [1, 5, 53, 145, 841], [1, -2, 58, -62, 961], [1, 10, 94, 370, 1369], [1, 4, 66, 164, 1681], [1, 6, 90, 258, 1849], [1, 9, 103, 423, 2209], [1, 12, 122, 636, 2809], [1, 14, 162, 826, 3481], [1, 14, 166, 854, 3721], [1, 6, 18, 402, 4489], [1, -17, 153, -1207, 5041], [1, -15, 201, -1095, 5329], [1, 3, 9, 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'8.108849274358393176865383768812053'], 'prelabel': '4-4235e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.815208100834592, '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': 570512692906384370, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13806523522405957672232335676', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.53020755883409821262301194313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.19808259691164166231137285095', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1143.5654963709767, 'bad_primes': [5, 7, 11], 'central_character': '1.1', 'conductor': 17935225, 'conductor_radical': 385, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 1, -2, 0, -2, 0, -4, 0, 0, -1, 7, 0, 2, -3, 9, 0, -2, -2, 2, 0, 0, 0, 3, 0, 6, -2, -5, 0, 2, 0, 0, 0, 4, -4, -10, 0, -7, 0, -4, 0, -6, 0, 8, 0, -9, 3, 3, 0, -9, 7, -12, 0, 0, 0, 2, 0, -14, 2, -14, 0, 8, -7, -14, 0, -6, 9, 0, 0, 17, 0, 15, 0, -3, -2, 0, 0, -3, 6, 8, 0, -1, 2, -18, 0, 5, 0, 30, 0, -14, 0, -2, 0, 4, 0, -15, 0, 0, 3], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, -7, 37, -91, 169], 'euler17': [1, -9, 53, -153, 289], 'euler19': [1, 2, 34, 38, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, 26, 0, 529], 'euler29': [1, 5, 53, 145, 841], 'euler3': [1, 1, 5, 3, 9], 'euler31': [1, -2, 58, -62, 961], 'euler37': [1, 10, 94, 370, 1369], 'euler41': [1, 4, 66, 164, 1681], 'euler43': [1, 6, 90, 258, 1849], 'euler47': [1, 9, 103, 423, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 12, 122, 636, 2809], 'euler59': [1, 14, 162, 826, 3481], 'euler61': [1, 14, 166, 854, 3721], 'euler67': [1, 6, 18, 402, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -17, 153, -1207, 5041], 'euler73': [1, -15, 201, -1095, 5329], 'euler79': [1, 3, 9, 237, 6241], 'euler83': [1, 1, 65, 83, 6889], 'euler89': [1, -30, 398, -2670, 7921], 'euler97': [1, 15, 189, 1455, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, 1, 5, 3, 9], [1, 2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, -7, 37, -91, 169], [1, -9, 53, -153, 289], [1, 2, 34, 38, 361], [1, 0, 26, 0, 529], [1, 5, 53, 145, 841], [1, -2, 58, -62, 961], [1, 10, 94, 370, 1369], [1, 4, 66, 164, 1681], [1, 6, 90, 258, 1849], [1, 9, 103, 423, 2209], [1, 12, 122, 636, 2809], [1, 14, 162, 826, 3481], [1, 14, 166, 854, 3721], [1, 6, 18, 402, 4489], [1, -17, 153, -1207, 5041], [1, -15, 201, -1095, 5329], [1, 3, 9, 237, 6241], [1, 1, 65, 83, 6889], [1, -30, 398, -2670, 7921], [1, 15, 189, 1455, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4235/2/a/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': '4-4235e2-1.1-c1e2-0-4', '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': '4-4235e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.815208100834592, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 570512692906384370, 'z1': {'__RealLiteral__': 0, 'data': '1.13806523522405957672232335676', 'prec': 103}}
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{'Lhash': '1442669078530660204367191104836,1939768530429818255008926156316', 'Lhash_array': ['1442669078530660204367191104836', '1939768530429818255008926156316'], 'label': '4-4235e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4235/2/a/j'}