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lfunc_lfunctions • Show schema
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{'Lhash': '1809620898798775625920189230820,2698204922502748250251331975815', 'a10': -2, 'a2': -1, 'a3': -2, 'a4': 1, 'a5': 2, 'a6': 2, 'a7': -2, 'a8': -3, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 85.05859063916354, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [5, [1, -2, 1]], [7, [1, 2, 1]], [11, [1, -2, 1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '1155.1', 'coefficient_field': '1.1.1.1', 'conductor': 1334025, 'conductor_radical': 1155, 'degree': 4, 'euler_factors': [[1, 1, 0, 2, 4], [1, 2, 1], [1, -2, 1], [1, 2, 1], [1, -2, 1], [1, 6, 18, 78, 169], [1, 3, 32, 51, 289], [1, 1, 34, 19, 361], [1, 7, 54, 161, 529], [1, 9, 40, 261, 841], [1, 2, 46, 62, 961], [1, 6, 66, 222, 1369], [1, -4, 86, -164, 1681], [1, -1, 82, -43, 1849], [1, 2, 78, 94, 2209], [1, 15, 124, 795, 2809], [1, -17, 186, -1003, 3481], [1, 11, 148, 671, 3721], [1, -22, 238, -1474, 4489], [1, -2, 126, -142, 5041], [1, 14, 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'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': 2218209635562301615, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42753918033326313510965428364', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12850837763730799097357776973', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.45959341744008594917124935014', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 85.05859063916354, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 1334025, 'conductor_radical': 1155, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, 1, 2, 2, -2, -3, 3, -2, 2, -2, -6, 2, -4, 1, -3, -3, -1, 2, 4, -2, -7, 6, 3, 6, -4, -2, -9, 4, -2, 1, -4, 3, -4, 3, -6, 1, 12, -6, 4, -4, 1, 2, 6, 7, -2, -2, 3, -3, 6, -6, -15, 4, 4, 6, 2, 9, 17, -4, -11, 2, -6, 1, -12, 4, 22, -3, 14, 4, 2, -9, -14, 6, -6, -1, -4, -12, -4, 2, 5, -4, -15, 4, -6, -1, 18, -6, -17, -6, 12, -7, 4, 2, -2, -2, -15, -3, 6, 3], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, 6, 18, 78, 169], 'euler17': [1, 3, 32, 51, 289], 'euler19': [1, 1, 34, 19, 361], 'euler2': [1, 1, 0, 2, 4], 'euler23': [1, 7, 54, 161, 529], 'euler29': [1, 9, 40, 261, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 2, 46, 62, 961], 'euler37': [1, 6, 66, 222, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, -1, 82, -43, 1849], 'euler47': [1, 2, 78, 94, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 15, 124, 795, 2809], 'euler59': [1, -17, 186, -1003, 3481], 'euler61': [1, 11, 148, 671, 3721], 'euler67': [1, -22, 238, -1474, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -2, 126, -142, 5041], 'euler73': [1, 14, 178, 1022, 5329], 'euler79': [1, 4, 94, 316, 6241], 'euler83': [1, 15, 218, 1245, 6889], 'euler89': [1, 17, 212, 1513, 7921], 'euler97': [1, 15, 144, 1455, 9409], 'euler_factors': [[1, 1, 0, 2, 4], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 6, 18, 78, 169], [1, 3, 32, 51, 289], [1, 1, 34, 19, 361], [1, 7, 54, 161, 529], [1, 9, 40, 261, 841], [1, 2, 46, 62, 961], [1, 6, 66, 222, 1369], [1, -4, 86, -164, 1681], [1, -1, 82, -43, 1849], [1, 2, 78, 94, 2209], [1, 15, 124, 795, 2809], [1, -17, 186, -1003, 3481], [1, 11, 148, 671, 3721], [1, -22, 238, -1474, 4489], [1, -2, 126, -142, 5041], [1, 14, 178, 1022, 5329], [1, 4, 94, 316, 6241], [1, 15, 218, 1245, 6889], [1, 17, 212, 1513, 7921], [1, 15, 144, 1455, 9409]], 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1155/2/a/o'], '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': '4-1155e2-1.1-c1e2-0-32', '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': '4-1155e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2218209635562301615, 'z1': {'__RealLiteral__': 0, 'data': '1.42753918033326313510965428364', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1809620898798775625920189230820,2698204922502748250251331975815', 'Lhash_array': ['1809620898798775625920189230820', '2698204922502748250251331975815'], 'factors': ['2-1155-1.1-c1-0-23', '2-1155-1.1-c1-0-38'], 'label': '4-1155e2-1.1-c1e2-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/a/o'}