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lfunc_lfunctions • Show schema
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{'Lhash': '1221314683948427156015034619019,1480431297207349904838692648550,2228087350327276954918598701656', '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, 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432, 2523, 6728, 24389], 1]], [[[1, -8, 101, -480, 3131, -7688, 29791], 1]], [[[1, -4, 95, -264, 3515, -5476, 50653], 1]], [[[1, 8, 123, 624, 5043, 13448, 68921], 1]], [[[1, -8, 145, -692, 6235, -14792, 79507], 1]], [[[1, -8, 125, -592, 5875, -17672, 103823], 1]], [[[1, 8, 127, 576, 6731, 22472, 148877], 1]], [[[1, 8, 113, 1024, 6667, 27848, 205379], 1]], [[[1, -2, 131, -204, 7991, -7442, 226981], 1]], [[[1, -12, 185, -1288, 12395, -53868, 300763], 1]], [[[1, 12, 245, 1688, 17395, 60492, 357911], 1]], [[[1, -18, 279, -2536, 20367, -95922, 389017], 1]], [[[1, 6, 233, 940, 18407, 37446, 493039], 1]], [[[1, 2, 245, 328, 20335, 13778, 571787], 1]], [[[1, -2, 255, -348, 22695, -15842, 704969], 1]], [[[1, 8, 259, 1424, 25123, 75272, 912673], 1]], [[[1, 40, 815, 10160, 82315, 408040, 1030301], 1]], [[[1, -28, 533, -6312, 54899, -297052, 1092727], 1]], [[[1, -14, 237, -1704, 25359, -160286, 1225043], 1]], [[[1, 6, 83, -220, 9047, 71286, 1295029], 1]], [[[1, 32, 619, 7632, 69947, 408608, 1442897], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 3, 'label': '6-825e3-1.1-c1e3-0-3', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/825/2/a/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0416666666667', 'prec': 50}, 'plot_values': [8.544148764964472, 8.511707772104598, 8.463564434133072, 8.384142329845211, 8.260908713009801, 8.0925505869879, 7.880848091914817, 7.62700062374987, 7.328821095186057, 6.98404798137934, 6.5917406371891785, 6.152998653951665, 5.670538047619012, 5.148748349531161, 4.594074376926147, 4.014731097937733, 3.4208588526039727, 2.8250548412418275, 2.2411931738990436, 1.6841130423159607, 1.1697262447139447, 0.7134188102392994, 0.329401788050646, 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'5.81889204724798485412087037557505', '6.38739929905039578222873250660652', '6.47542481197842590998376621368345', '6.96569658306558056074072397097006', '7.34550030273298068337234858901460', '7.47731373788340706321215657623105', '7.978377094133140898193965544622628', '8.042429170907351404348630653449677', '8.511226800400000433009649511040874', '8.535774714872927885589435672187534', '9.168836514074333158517830630843236', '9.438473589711820249722211533544533', '9.743114596036594428248933507773941', '10.39880474317943414924290156145232', '10.45481668105131590752179542421931', '10.77539098589023463741862450922136'], 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 196704137727893065, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.963447407139270182895892958408', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.16785437323250681236653867749', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.75765100409066135275359600174', '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': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/a/n'], '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-c1e3-0-3', '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': 0, 'prelabel': '6-825e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5666433657124306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 196704137727893065, 'z1': {'__RealLiteral__': 0, 'data': '0.963447407139270182895892958408', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1221314683948427156015034619019,1480431297207349904838692648550,2228087350327276954918598701656', 'Lhash_array': ['1221314683948427156015034619019', '1480431297207349904838692648550', '2228087350327276954918598701656'], 'label': '6-825e3-1.1-c1e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/a/n'}