-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1125149218119929199068116441906', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-2.3174905768802465, -1.3380038084062313], 'a6': [0.0, 0.0], 'a7': [6.66796126702039, 2.1303268626001586], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.577668441252989, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]], [7, [[1.0, 0], [-6.66796126702039, -2.1303268626001586]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.145', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '2195991304778152630196877473191', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [2.3174905768802465, 1.3380038084062313], [12.5, 21.650635094610966]], [[1.0, 0], [-6.66796126702039, -2.1303268626001586]], [[1.0, 0], [-5.850470690140144, -10.133312483515283], [-60.5, 104.78907385791707]], [[1.0, 0], [0, -20.498258404201753], [-169.0, 0]], [[1.0, 0], [14.229968945982632, -8.215676401523089], [144.5, -250.28134169370276]], [[1.0, 0], [-26.945799421686417, -15.557164549640314], [180.5, 312.63517076618234]], [[1.0, 0], [-2.8284271247461903, 4.898979485566356], [-264.5, -458.12743860196804]], [[1.0, 0], [-21.64929009370141, 0], [841.0, 0]], [[1.0, 0], [4.6016601011764635, -2.6567696981333917], [480.5, -832.2504130368455]], [[1.0, 0], [9.642306093393017, -16.70096405588768], [-684.5, -1185.5887777808964]], [[1.0, 0], [0, 28.033992698051545], [-1681.0, 0]], [[1.0, 0], [-73.01451238627229, 0], [1849.0, 0]], [[1.0, 0], [27.997211492106846, 16.164197591526772], [1104.5, 1913.050116959825]], [[1.0, 0], [47.390536526874115, 82.0828170624947], [-1404.5, 2432.6653592304883]], [[1.0, 0], [97.8171431156991, -56.47475390920902], [1740.5, -3014.634430573631]], [[1.0, 0], [30.0, 17.320508075688775], [1860.5, 3222.4805274818964]], [[1.0, 0], [-3.843657159493818, -6.657409487119165], [-2244.5, 3887.5880375883453]], [[1.0, 0], [-22.984327302762555, 0], [5041.0, 0]], [[1.0, 0], [5.8387440186032356, -3.3710004308698953], [2664.5, -4615.049376767273]], [[1.0, 0], [-23.59511876335789, 40.867944508757596], [-3120.5, -5404.864545018681]], [[1.0, 0], [0, 39.27630276737017], [-6889.0, 0]], [[1.0, 0], [-87.5329048449065, -50.537146175156664], [3960.5, 6859.787223376538]], [[1.0, 0], [0, -30.0955140200124], [-9409.0, 0]], [[1.0, 0], [-65.55704006662857, 37.84937472974309], [5100.5, -8834.325144005059]], [[1.0, 0], [56.74089897199156, 32.75937329554069], [5304.5, 9187.66350874911]], [[1.0, 0], [63.97237941881974, -110.80341143446935], [-5724.5, -9915.124847928038]], [[1.0, 0], [39.54656767602623, 68.49666447983849], [-5940.5, 10289.247822362915]], [[1.0, 0], [-117.99482987687642, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-168-7.5-c2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/168/3/z/a/145/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2194318067357977, 1.1053682686835327, 0.9747811409855763, 0.8263004987054928, 0.6582592369518526, 0.4691191491203, 0.2579125058412124, 0.024666278953227695, -0.229218653084613, -0.5006570241613115, -0.7846593337756999, -1.0742242389385783, -1.360364476034269, -1.6322857178130221, -1.8777331288326253, -2.083512350634779, -2.2361801494865867, -2.322885436834186, -2.3323247417667314, -2.25575881856009, -2.0880206146634945, -1.8284312690080784, -1.4815322330762124, -1.0575400005248745, -0.5724369710638582, -0.04762876510368068, 0.49087486819198545, 1.0137622912578828, 1.4901686166454189, 1.889786234141851, 2.1852048891531104, 2.354306107714928, 2.382504301929402, 2.2646101458677155, 2.0060953196652345, 1.6235645539214671, 1.1442920485406964, 0.6047531738090359, 0.04817439493168998, -0.4787727492050821, -0.9299038497143827, -1.263756798018922, -1.4477358589537925, -1.4617336862187054, -1.3008064262025663, -0.9765314384910709, -0.5167800647694996, 0.03621628823957606, 0.6294513347345618, 1.2041335501409651, 1.7016489749064379, 2.069911491027379, 2.269413012946139, 2.2782554617006707, 2.0954992420586507, 1.7423022350381445, 1.2605413570017736, 0.708886731870883, 0.15660766533921214, -0.32430634488848736, -0.6678671117939384, -0.822633209366356, -0.7589992368576227, -0.4742212513269633, 0.0056192172830995596, 0.6271773077300029, 1.3149753081537314, 1.9796801444909973, 2.5286613411579815, 2.877598537504778, 2.9616812902524243, 2.7448987316401112, 2.226074181452818, 1.4406545944749016, 0.45778256448996896, -0.6272012105722646, -1.7040353516260272, -2.6612328909694365, -3.400416510968005, -3.849330350494914, -3.9716516119707053, -3.772091051794382, -3.295880920931144, -2.6225270048842537, -1.854541739346629, -1.1026542485414066, -0.469587456102714, -0.034799025455991395, 0.15746348862807166, 0.10485641399950195, -0.15281664145564683, -0.5400471726485457, -0.9579356399490697, -1.3005906126487268, -1.4730944822922127, -1.4081567294533464, -1.0786676874217789, -0.5039202780099032, 0.25178167900802595, 1.0881986356833242, 1.8847009400695416, 2.519929159886601, 2.89241201573722, 2.9386797166924388, 2.6456805207216343, 2.0551380199084797, 1.2587627380349375, 0.384756771626805, -0.4224276924458386, -1.025861899419083, -1.3194809497945195, -1.246934597283138, -0.8125091860948725, -0.08193284814484032, 0.8274304889760837, 1.7656386656319143, 2.575431036238374, 3.1194272552697235, 3.304505059767093, 3.098938880005753, 2.5390359593127427, 1.723797945090151, 0.7982612878179955, -0.07174896204754151, -0.7290673688831019, -1.0535587369030912, -0.9841876703834205, -0.5305960950253489, 0.22815196236773924, 1.1576517541867921, 2.092643329345127, 2.8674548085122926, 3.346725880107591, 3.450560300593761, 3.1692087731947964, 2.564313743571585, 1.7563091096662289, 0.900276770074088, 0.15488721871799535, -0.34948142694463524, -0.5370629151282379, -0.40206319737988006, -0.00976541106482528, 0.5170889979550405, 1.0241094914311477, 1.3581539336196435, 1.4006185771521056, 1.0941665103839138, 0.45711592858286126, -0.41787678657676974, -1.3810125647503724, -2.255267195264329, -2.8730987672441493, -3.1123935957123923, -2.924017578076195, -2.344866835659149, -1.4931802774676712, -0.5465262674403097, 0.2934418203322323, 0.8424327554714109, 0.9726047115012875, 0.6409695540272924, -0.09918842845258088, -1.1067556178360967, -2.179828770993087, -3.0960976639210034, -3.6583452410226647, -3.735555895978127, -3.2908519268043896, -2.3901179572617135, -1.1891998771083023, 0.09786374187988303, 1.242989715234827, 2.0512170956004216, 2.400757740321808, 2.2672342413881736, 1.726788618087165, 0.9373538235726693, 0.10221266877215841, -0.5760543764062535, -0.9409219410571101, -0.9163539477221769, -0.5225137817170568, 0.1308275394886604, 0.871658109333694, 1.5075171769045397, 1.8719448149626454, 1.8646303386762173, 1.4756595178005276, 0.7879043653179778, -0.04328026597546281, -0.8284682473783216, -1.3916535297389958, -1.6154071868004312, -1.4725785968625713, -1.0363902576756885, -0.465786448566365, 0.031198230296542014, 0.24787545004465736, 0.03137118585729663, -0.6755196088696143, -1.8135912712158309, -3.2133651520064985, -4.627616485923735, -5.783481600940569, -6.442475060783123, -6.4545509806770305, -5.793411824856574, -4.564425993673525, -2.9828343369672448, -1.3269299550007427, 0.12309250673865647, 1.1463781548485492, 1.628335872882912, 1.5821479624546984, 1.1398112956317656, 0.5149990351254359, -0.05310482689751866, -0.36115823826533744, -0.2930379306432036, 0.1515067612623342, 0.8580636183712997, 1.628329624884704, 2.2327059307957495, 2.471410353578064, 2.2285378028124496, 1.505155044000252, 0.42272777413758766, -0.8043302655288901, -1.9203034274369, -2.691052939118762, -2.9621349245355018, -2.6972120428353503, -1.9867321946853198, -1.0244262965728876, -0.0574918582200547, 0.676770270099642, 1.0114345328174643, 0.8916979203549237, 0.38680237210630114, -0.33121453221040803, -1.0365336295075718, -1.5134573568682952, -1.6181442832368051, -1.3213966078008155, -0.7204819385073864, -0.01604100349368265, 0.5405619047976269, 0.7160011188093822, 0.36173442364307035, -0.5393524723773174, -1.8596059387928972, -3.351249221699159, -4.7037109967991935, -5.61952464539496, -5.88941712213245, -5.446963000393685], 'positive_zeros': ['0.887586230714801006567079825071163', '3.13608882854240365148848919334688', '4.76098316946319380751964944855493', '5.86721238964887469673297242503983', '7.28790785716971607623447259276476', '7.998747817428375022771866100050328', '9.303463320279947567830246463712164', '10.88933880441071401892830462467547', '11.18637138379464793289978314006575', '12.21067047516377159856232789586372'], 'prelabel': '2-168-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1395486536307113, 'root_angle': -0.1806103676490137, 'root_number': '0.42230610923033973 - 0.9064532807082406*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.180610367649', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887586230714801006567079825071', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.13608882854240365148848919335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.76098316946319380751964944855', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.577668441252989, 'bad_primes': [2, 3, 7], 'central_character': '7.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/3/z/a/145/1'], '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': '2-168-7.5-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-168-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1395486536307113, 'root_angle': -0.1806103676490137, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887586230714801006567079825071', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1125149218119929199068116441906', 'Lhash_array': ['1125149218119929199068116441906'], 'factors': ['2-168-7.5-c2-0-0'], 'label': '2-168-7.5-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/3/z/a/145/1'}