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{'Lhash': '731049215460134734868922540253,1058298681184792623951511381911,1771300905049064449224865386040,2015820416595162881420614793755', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 10, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32385.123305642177, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -4, 6, -4, 1]], [5, [1, 0, 2, 0, 1]], [7, [1, 0, -10, 0, 49]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.1', 'coefficient_field': '1.1.1.1', 'conductor': 7965941760000, 'conductor_radical': 210, 'degree': 8, 'euler_factors': [[1], [1, -4, 6, -4, 1], [1, 0, 2, 0, 1], [1, 0, -10, 0, 49], [1, 0, -32, 0, 498, 0, -3872, 0, 14641], [1, 0, -32, 0, 498, 0, -5408, 0, 28561], [1, 0, -12, 0, 230, 0, -3468, 0, 83521], [1, -8, 88, -440, 2626, -8360, 31768, -54872, 130321], [1, 0, -84, 0, 2822, 0, -44436, 0, 279841], [1, 8, 92, 536, 4054, 15544, 77372, 195112, 707281], [1, 24, 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'trace_hash': 1122899017554003686, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57669614586899238532430541941', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.834850455633638483761216298867', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.39731003537580246177117638474', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32385.123305642177, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 7965941760000, 'conductor_radical': 210, 'degree': 8, 'dirichlet_coefficients': [1, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 20, 0, -8, 0, -24, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 10, 0, 0, 0, 32, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 35, 0, 8, 0, 0, 0, -32, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -32, 0, 498, 0, -3872, 0, 14641], 'euler13': [1, 0, -32, 0, 498, 0, -5408, 0, 28561], 'euler17': [1, 0, -12, 0, 230, 0, -3468, 0, 83521], 'euler19': [1, -8, 88, -440, 2626, -8360, 31768, -54872, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -84, 0, 2822, 0, -44436, 0, 279841], 'euler29': [1, 8, 92, 536, 4054, 15544, 77372, 195112, 707281], 'euler3': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler31': [1, 24, 328, 2952, 19314, 91512, 315208, 714984, 923521], 'euler37': [1, -8, 124, -728, 6838, -26936, 169756, -405224, 1874161], 'euler41': [1, 0, -84, 0, 3590, 0, -141204, 0, 2825761], 'euler43': [1, 0, -44, 0, 4182, 0, -81356, 0, 3418801], 'euler47': [1, -24, 356, -3672, 29190, -172584, 786404, -2491752, 4879681], 'euler5': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler53': [1, -32, 584, -6944, 59650, -368032, 1640456, -4764064, 7890481], 'euler59': [1, 0, 188, 0, 15798, 0, 654428, 0, 12117361], 'euler61': [1, 0, -68, 0, 2454, 0, -253028, 0, 13845841], 'euler67': [1, 0, -4, 0, -4842, 0, -17956, 0, 20151121], 'euler7': [1, 0, -10, 0, 49, 0, 0, 0, 0], 'euler71': [1, 0, -240, 0, 24098, 0, -1209840, 0, 25411681], 'euler73': [1, 0, -176, 0, 17538, 0, -937904, 0, 28398241], 'euler79': [1, 0, -124, 0, 16326, 0, -773884, 0, 38950081], 'euler83': [1, -8, 308, -1832, 37750, -152056, 2121812, -4574296, 47458321], 'euler89': [1, 0, -92, 0, 4134, 0, -728732, 0, 62742241], 'euler97': [1, 0, -80, 0, -1182, 0, -752720, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, -10, 0, 49, 0, 0, 0, 0], [1, 0, -32, 0, 498, 0, -3872, 0, 14641], [1, 0, -32, 0, 498, 0, -5408, 0, 28561], [1, 0, -12, 0, 230, 0, -3468, 0, 83521], [1, -8, 88, -440, 2626, -8360, 31768, -54872, 130321], [1, 0, -84, 0, 2822, 0, -44436, 0, 279841], [1, 8, 92, 536, 4054, 15544, 77372, 195112, 707281], [1, 24, 328, 2952, 19314, 91512, 315208, 714984, 923521], [1, -8, 124, -728, 6838, -26936, 169756, -405224, 1874161], [1, 0, -84, 0, 3590, 0, -141204, 0, 2825761], [1, 0, -44, 0, 4182, 0, -81356, 0, 3418801], [1, -24, 356, -3672, 29190, -172584, 786404, -2491752, 4879681], [1, -32, 584, -6944, 59650, -368032, 1640456, -4764064, 7890481], [1, 0, 188, 0, 15798, 0, 654428, 0, 12117361], [1, 0, -68, 0, 2454, 0, -253028, 0, 13845841], [1, 0, -4, 0, -4842, 0, -17956, 0, 20151121], [1, 0, -240, 0, 24098, 0, -1209840, 0, 25411681], [1, 0, -176, 0, 17538, 0, -937904, 0, 28398241], [1, 0, -124, 0, 16326, 0, -773884, 0, 38950081], [1, -8, 308, -1832, 37750, -152056, 2121812, -4574296, 47458321], [1, 0, -92, 0, 4134, 0, -728732, 0, 62742241], [1, 0, -80, 0, -1182, 0, -752720, 0, 88529281]], 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1680/2/d/b'], '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': '8-1680e4-1.1-c1e4-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1680e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.6626312317205936, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1122899017554003686, 'z1': {'__RealLiteral__': 0, 'data': '0.57669614586899238532430541941', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '731049215460134734868922540253,1058298681184792623951511381911,1771300905049064449224865386040,2015820416595162881420614793755', 'Lhash_array': ['731049215460134734868922540253', '1058298681184792623951511381911', '1771300905049064449224865386040', '2015820416595162881420614793755'], 'label': '8-1680e4-1.1-c1e4-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/d/b'}