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lfunc_lfunctions • Show schema
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{'Lhash': '802123288791579879052268153771,1236632559557190477236745170533', 'a10': -4, 'a2': -2, 'a3': 0, 'a4': 3, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': -4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3523.703254392535, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1]], [7, [1, 2, 1]], [59, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 59], 'central_character': '7434.1', 'coefficient_field': '1.1.1.1', 'conductor': 55264356, 'conductor_radical': 2478, 'degree': 4, 'euler_factors': [[1, 2, 1], [1], [1, -2, 6, -10, 25], [1, 2, 1], [1, -9, 41, -99, 121], [1, 5, 21, 65, 169], [1, -4, 38, -68, 289], [1, -9, 47, -171, 361], [1, -7, 47, -161, 529], [1, -15, 113, -435, 841], [1, -2, 18, -62, 961], [1, 4, 58, 148, 1369], [1, -4, 86, -164, 1681], [1, -3, -13, -129, 1849], [1, 6, 98, 282, 2209], [1, 1, 5, 53, 2809], [1, 2, 1], [1, 0, 102, 0, 3721], [1, -1, 73, -67, 4489], [1, -20, 222, -1420, 5041], [1, -1, 45, -73, 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824, 10609], 1]], [[[1, 10, 194, 1070, 11449], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 2, 'label': '4-7434e2-1.1-c1e2-0-2', 'leading_term': '2.84244718982871454472628374820524813466321113043980307098282400000000000000000000000000000', 'load_key': 'CMFs-workshop', '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, 'origin': 'ModularForm/GL2/Q/holomorphic/7434/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [2.8424471898287145, 2.8328036665938074, 2.813409395477891, 2.7774409795950934, 2.7262787359391134, 2.6618964290976126, 2.5843627267133105, 2.4939019112153042, 2.391327075428467, 2.2775222633589505, 2.1533825739958092, 2.0199429143130576, 1.8783761259294809, 1.7299685243857668, 1.5761084809358148, 1.4182915326639463, 1.2581023738753443, 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'7.69059718454582682952561272450712', '8.139181243804712772512707268857330'], 'prelabel': '4-7434e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.704595308166411, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1831686401191191985, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63276370369498077598758320683', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.975531080358062073749022312112', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.52208594512164415383041032332', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3523.703254392535, 'bad_primes': [2, 3, 7, 59], 'central_character': '1.1', 'conductor': 55264356, 'conductor_radical': 2478, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 3, 2, 0, -2, -4, 0, -4, 9, 0, -5, 4, 0, 5, 4, 0, 9, 6, 0, -18, 7, 0, -2, 10, 0, -6, 15, 0, 2, -6, 0, -8, -4, 0, -4, -18, 0, -8, 4, 0, 3, 27, 0, -14, -6, 0, 3, 4, 0, -15, -1, 0, 18, 8, 0, -30, -2, 0, 0, -4, 0, 7, -10, 0, 1, 12, 0, 8, 20, 0, 1, 8, 0, 27, -18, 0, -22, 10, 0, -8, -24, 0, 8, -6, 0, -36, -7, 0, 10, 21, 0, 12, 18, 0, -3, -6, 0, -6], 'euler11': [1, -9, 41, -99, 121], 'euler13': [1, 5, 21, 65, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, -9, 47, -171, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, -7, 47, -161, 529], 'euler29': [1, -15, 113, -435, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -2, 18, -62, 961], 'euler37': [1, 4, 58, 148, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, -3, -13, -129, 1849], 'euler47': [1, 6, 98, 282, 2209], 'euler5': [1, -2, 6, -10, 25], 'euler53': [1, 1, 5, 53, 2809], 'euler59': [1, 2, 1, 0, 0], 'euler61': [1, 0, 102, 0, 3721], 'euler67': [1, -1, 73, -67, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -20, 222, -1420, 5041], 'euler73': [1, -1, 45, -73, 5329], 'euler79': [1, 22, 274, 1738, 6241], 'euler83': [1, 24, 290, 1992, 6889], 'euler89': [1, 7, 89, 623, 7921], 'euler97': [1, 3, 185, 291, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, -2, 6, -10, 25], [1, 2, 1, 0, 0], [1, -9, 41, -99, 121], [1, 5, 21, 65, 169], [1, -4, 38, -68, 289], [1, -9, 47, -171, 361], [1, -7, 47, -161, 529], [1, -15, 113, -435, 841], [1, -2, 18, -62, 961], [1, 4, 58, 148, 1369], [1, -4, 86, -164, 1681], [1, -3, -13, -129, 1849], [1, 6, 98, 282, 2209], [1, 1, 5, 53, 2809], [1, 2, 1, 0, 0], [1, 0, 102, 0, 3721], [1, -1, 73, -67, 4489], [1, -20, 222, -1420, 5041], [1, -1, 45, -73, 5329], [1, 22, 274, 1738, 6241], [1, 24, 290, 1992, 6889], [1, 7, 89, 623, 7921], [1, 3, 185, 291, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7434/2/a/l'], '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': '4-7434e2-1.1-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': '4-7434e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.704595308166411, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1831686401191191985, 'z1': {'__RealLiteral__': 0, 'data': '0.63276370369498077598758320683', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '802123288791579879052268153771,1236632559557190477236745170533', 'Lhash_array': ['802123288791579879052268153771', '1236632559557190477236745170533'], 'label': '4-7434e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7434/2/a/l'}