-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1714308626736295389252175080202', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7320508075688773, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.4641016151377544, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.549044428938494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '6080.1', 'coefficient_field': 'CDF', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7320508075688773, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [7.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [11.0, 0]], [[1.0, 0], [0.7320508075688773, 0], [13.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [23.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [29.0, 0]], [[1.0, 0], [-5.464101615137754, 0], [31.0, 0]], [[1.0, 0], [3.267949192431123, 0], [37.0, 0]], [[1.0, 0], [6.0, 0], [41.0, 0]], [[1.0, 0], [8.928203230275509, 0], [43.0, 0]], [[1.0, 0], [0.9282032302755092, 0], [47.0, 0]], [[1.0, 0], [-7.267949192431122, 0], [53.0, 0]], [[1.0, 0], [-6.928203230275509, 0], [59.0, 0]], [[1.0, 0], [-8.392304845413264, 0], [61.0, 0]], [[1.0, 0], [3.267949192431123, 0], [67.0, 0]], [[1.0, 0], [9.464101615137755, 0], [71.0, 0]], [[1.0, 0], [7.464101615137754, 0], [73.0, 0]], [[1.0, 0], [10.928203230275509, 0], [79.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [83.0, 0]], [[1.0, 0], [8.535898384862245, 0], [89.0, 0]], [[1.0, 0], [-14.588457268119896, 0], [97.0, 0]], [[1.0, 0], [4.392304845413264, 0], [101.0, 0]], [[1.0, 0], [3.6602540378443864, 0], [103.0, 0]], [[1.0, 0], [11.660254037844387, 0], [107.0, 0]], [[1.0, 0], [6.392304845413264, 0], [109.0, 0]], [[1.0, 0], [18.588457268119896, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 109, 'label': '2-6080-1.1-c1-0-109', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6080/2/a/z/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-7.827386404184717e-61, 0.19797910714566444, 0.3948851055813069, 0.5896045883100475, 0.7809464500969461, 0.9676100777097911, 1.1481614356978647, 1.3210188335874746, 1.484449565830961, 1.6365780040080207, 1.7754051401825846, 1.8988390647757953, 2.004735429560596, 2.090946600136894, 2.155377936292738, 2.1960494414747473, 2.2111608814210264, 2.199158375761863, 2.1588004072555336, 2.089221167250272, 1.9899891623461048, 1.8611590481221207, 1.703314734907399, 1.5176019322777474, 1.3057484673845525, 1.070070930508062, 0.8134664709526402, 0.5393888871647912, 0.25180852411022503, -0.04484409653078041, -0.3457505393201191, -0.6457917624483549, -0.939649131754901, -1.221917313808941, -1.487226745148466, -1.7303729300741477, -1.9464494220283974, -2.1309810102224485, -2.2800533798242335, -2.390435355429405, -2.4596897865377296, -2.4862692006469453, -2.4695925415449262, -2.4100996309898353, -2.309280440720545, -2.1696768337620065, -1.9948551198417357, -1.7893485553662998, -1.558569785287928, -1.3086941495985063, -1.0465157346784673, -0.7792790097818257, -0.5144898197654117, -0.2597103736619449, -0.022343641502747532, 0.19058678350677064, 0.372654814038513, 0.5182411444413705, 0.6227267352876081, 0.6826636992188942, 0.6959171450799551, 0.6617721378775067, 0.5810007628207434, 0.4558853281104113, 0.2901949801787578, 0.08911440534032078, -0.1408751858575268, -0.39216099687879824, -0.6562060884083487, -0.9237943171107029, -1.185306257795477, -1.4310182413821844, -1.651415489200727, -1.837509428193035, -1.9811486775057106, -2.075312942419822, -2.114379163895578, -2.0943497666171655, -2.0130337274692796, -1.8701724379185913, -1.6675039313833238, -1.4087609495986233, -1.0996004758666824, -0.7474647012494893, -0.36137583508808974, 0.04833036151013207, 0.47032504188325097, 0.892651224844826, 1.3031217304440113, 1.6897369537153362, 2.0411080992010606, 2.3468707502804786, 2.598073430614825, 2.787526162590112, 2.910094951577506, 2.9629296154764293, 2.9456144042648775, 2.860233359761412, 2.7113452758564556, 2.5058663391490454, 2.252861947814812, 1.9632526983968706, 1.6494429633485923, 1.3248837203054935, 1.0035842027114126, 0.6995893933057431, 0.42644226254232404, 0.19665086663397854, 0.021180890634044703, -0.091006096510054, -0.13334953316606554, -0.10200467827713125, 0.003939214520017402, 0.18234859363085426, 0.42805052206832883, 0.7329558430121372, 1.086299065293877, 1.4749887785653513, 1.8840578494970657, 2.2971983793229307, 2.697362603162273, 3.0674077538489284, 3.390760548113031, 3.652075503996832, 3.8378608546649193, 3.9370464357751946, 3.9414695993516116, 3.8462579103191676, 3.6500910317457196, 3.35532867797238, 2.967996648901832, 2.497628558129854, 1.956966710642277, 1.3615314333100093, 0.7290737665435738, 0.07893154408553646, -0.5686867106833121, -1.1934621661569702, -1.7757400555277492, -2.2972866026365386, -2.741997217938082, -3.0965261730743188, -3.350810757675767, -3.4984669318245007, -3.537038567007613, -3.468088321129616, -3.2971247790636, -3.0333674346171398, -2.6893580947610656, -2.280434044102872, -1.824084511568207, -1.3392173437745336, -0.8453670529064297, -0.36187835647150807, 0.09289919824560071, 0.5023700282374232, 0.8523709260929496, 1.1317385380100218, 1.3327400469015438, 1.4513471404731415, 1.4873402901076802, 1.4442380164486266, 1.329053831603681, 1.1518915608789104, 0.9253973854661792, 0.6640938470295532, 0.38362687750359376, 0.09996136748756569, -0.17143637261107345, -0.4163898391654474, -0.6227386256294676, -0.7809638075519834, -0.8846808775692456, -0.9309747019712603, -0.9205583211066547, -0.8577457729966451, -0.750238099084785, -0.6087308701809356, -0.446360507169161, -0.2780149244683118, -0.1195411773517954, 0.013111525911286252, 0.1047711888660611, 0.14190062464716122, 0.11338940371995722, 0.011238708877786885, -0.16889779990169318, -0.4273475378926619, -0.7602492769187469, -1.1595930738309972, -1.6134725331920439, -2.1065415132949408, -2.620656980134937, -3.135680006070666, -3.630398399022595, -4.083527585992068, -4.4747415408632705, -4.785683027038047, -5.000902396693156, -5.108676705130332, -5.101665888474743, -4.977370017041127, -4.738360856796921, -4.392271723209689, -3.9515413840895177, -3.4329199865580873, -2.856757038556763, -2.2461027530390107, -1.6256639752952027, -1.020663929971602, -0.4556606991391933, 0.04661765848118115, 0.4663633189622978, 0.7876490308525023, 0.9992090515331734, 1.0949994474644869, 1.0745070555195204, 0.9427886741232648, 0.7102354645716337, 0.3920714246247683, 0.0076084408351020935, -0.4207068755945789, -0.8684082853236182, -1.310231806806571, -1.7213831072142762, -2.0787860540395333, -2.362248314611089, -2.555483454879901, -2.6469357527288606, -2.630363601326107, -2.5051494735224007, -2.2763183513462697, -1.9542615902089788, -1.5541786083597104, -1.0952637591641603, -0.5996794579938612, -0.09136835111565775, 0.40523362089304615, 0.8665155193285267, 1.2709709561826004, 1.6003701371809407, 1.8407606802056569, 1.9832420038676026, 2.0244696612626716, 1.9668600618706067, 1.8184818577253958, 1.5926370392101712, 1.3071515982414925, 0.9834115630630047, 0.6451944131121484, 0.31735754938265587, 0.024453956234913893, -0.21065005983678003, -0.36807943997254355, -0.43210502273417045, -0.39208341692175264, -0.24312824760221896], 'positive_zeros': ['1.35235105511538362174068784131644', '2.53590389288630047714337459903814', '3.06566300237167678146767588062389', '3.97894299381630711573307858105401', '5.06957600138719121341195212249043', '5.24869759704150111834635173248225', '6.33379901165874026266606079896929', '7.20883961411822483944228841816566', '7.84501182151761096713105601714245'], 'prelabel': '2-6080-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35235105511538362174068784132', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53590389288630047714337459904', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06566300237167678146767588062', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 48.549044428938494, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'index': 109, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6080/2/a/z/1/2'], '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': '2-6080-1.1-c1-0-109', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6080-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35235105511538362174068784132', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1714308626736295389252175080202', 'Lhash_array': ['1714308626736295389252175080202'], 'label': '2-6080-1.1-c1-0-109', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/z/1/2'}