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{'Lhash': '2166840452855910466041448166003,2291970523546137109571125403891,3250053136254697443516635192749', 'a10': 0, 'a2': -3, 'a3': 3, 'a4': 4, 'a5': 0, 'a6': -9, 'a7': -8, 'a8': -4, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 285.8861833044949, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -3, 3, -1]], [5, [1]], [11, [1, 3, 3, 1]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'euler_factors': [[1, 3, 5, 7, 10, 12, 8], [1, -3, 3, -1], [1], [1, 8, 37, 116, 259, 392, 343], [1, 3, 3, 1], [1, 6, 11, 8, 143, 1014, 2197], [1, 4, 23, 20, 391, 1156, 4913], [1, 2, 5, -108, 95, 722, 6859], [1, 12, 117, 616, 2691, 6348, 12167], [1, 8, 87, 432, 2523, 6728, 24389], [1, -8, 101, -480, 3131, -7688, 29791], [1, 4, 95, 264, 3515, 5476, 50653], [1, 8, 123, 624, 5043, 13448, 68921], [1, 8, 145, 692, 6235, 14792, 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'7.48239538220345664434792632423001', '7.58641999983254212492816478410452', '8.052947122976830871173468382929604', '8.162307526514416849187154306414045', '8.492362227673343736911577944408460', '8.827688934420347286038269668204849', '9.060005868768446311906458682110253', '9.153010968813751776226261488951069', '9.642618645744077532626415376066282', '9.694158568140671318089644424845327', '9.989488157531560371503321545021902'], 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 354312421362695254, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70933572110942068536528085561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80804594194448207286975864668', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.56383985908226904712142055731', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 285.8861833044949, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 561515625, 'conductor_radical': 165, 'degree': 6, 'dirichlet_coefficients': [1, -3, 3, 4, 0, -9, -8, -4, 6, 0, -3, 12, -6, 24, 0, 3, -4, -18, -2, 0, -24, 9, -12, -12, 0, 18, 10, -32, -8, 0, 8, 1, -9, 12, 0, 24, -4, 6, -18, 0, -8, 72, -8, -12, 0, 36, -8, 9, 27, 0, -12, -24, 8, -30, 0, 32, -6, 24, -8, 0, 2, -24, -48, -2, 0, 27, -12, -16, -36, 0, -12, -24, -18, 12, 0, -8, 24, 54, -6, 0, 15, 24, 2, -96, 0, 24, -24, 12, 2, 0, 48, -48, 24, 24, 0, 3, 8, -81, -18, 0], 'euler11': [1, 3, 3, 1, 0, 0, 0], 'euler13': [1, 6, 11, 8, 143, 1014, 2197], 'euler17': [1, 4, 23, 20, 391, 1156, 4913], 'euler19': [1, 2, 5, -108, 95, 722, 6859], 'euler2': [1, 3, 5, 7, 10, 12, 8], 'euler23': [1, 12, 117, 616, 2691, 6348, 12167], 'euler29': [1, 8, 87, 432, 2523, 6728, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, -8, 101, -480, 3131, -7688, 29791], 'euler37': [1, 4, 95, 264, 3515, 5476, 50653], 'euler41': [1, 8, 123, 624, 5043, 13448, 68921], 'euler43': [1, 8, 145, 692, 6235, 14792, 79507], 'euler47': [1, 8, 125, 592, 5875, 17672, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -8, 127, -576, 6731, -22472, 148877], 'euler59': [1, 8, 113, 1024, 6667, 27848, 205379], 'euler61': [1, -2, 131, -204, 7991, -7442, 226981], 'euler67': [1, 12, 185, 1288, 12395, 53868, 300763], 'euler7': [1, 8, 37, 116, 259, 392, 343], 'euler71': [1, 12, 245, 1688, 17395, 60492, 357911], 'euler73': [1, 18, 279, 2536, 20367, 95922, 389017], 'euler79': [1, 6, 233, 940, 18407, 37446, 493039], 'euler83': [1, -2, 245, -328, 20335, -13778, 571787], 'euler89': [1, -2, 255, -348, 22695, -15842, 704969], 'euler97': [1, -8, 259, -1424, 25123, -75272, 912673], 'euler_factors': [[1, 3, 5, 7, 10, 12, 8], [1, -3, 3, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 8, 37, 116, 259, 392, 343], [1, 3, 3, 1, 0, 0, 0], [1, 6, 11, 8, 143, 1014, 2197], [1, 4, 23, 20, 391, 1156, 4913], [1, 2, 5, -108, 95, 722, 6859], [1, 12, 117, 616, 2691, 6348, 12167], [1, 8, 87, 432, 2523, 6728, 24389], [1, -8, 101, -480, 3131, -7688, 29791], [1, 4, 95, 264, 3515, 5476, 50653], [1, 8, 123, 624, 5043, 13448, 68921], [1, 8, 145, 692, 6235, 14792, 79507], [1, 8, 125, 592, 5875, 17672, 103823], [1, -8, 127, -576, 6731, -22472, 148877], [1, 8, 113, 1024, 6667, 27848, 205379], [1, -2, 131, -204, 7991, -7442, 226981], [1, 12, 185, 1288, 12395, 53868, 300763], [1, 12, 245, 1688, 17395, 60492, 357911], [1, 18, 279, 2536, 20367, 95922, 389017], [1, 6, 233, 940, 18407, 37446, 493039], [1, -2, 245, -328, 20335, -13778, 571787], [1, -2, 255, -348, 22695, -15842, 704969], [1, -8, 259, -1424, 25123, -75272, 912673]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/a/h'], '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': '6-825e3-1.1-c1e3-0-6', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 354312421362695254, 'z1': {'__RealLiteral__': 0, 'data': '1.70933572110942068536528085561', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2166840452855910466041448166003,2291970523546137109571125403891,3250053136254697443516635192749', 'Lhash_array': ['2166840452855910466041448166003', '2291970523546137109571125403891', '3250053136254697443516635192749'], 'label': '6-825e3-1.1-c1e3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/a/h'}