-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1312430046139412043625110163236', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [19.524174696260022, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-35.048349392520045, 0.0], 'a8': [0.0, 0.0], 'a9': [138.19339757008018, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15352792519226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-19.524174696260022, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [35.048349392520045, 0], [16807.0, 0]], [[1.0, 0], [-426.0076686214605, 0], [161051.0, 0]], [[1.0, 0], [-1103.2570842055213, 0], [371293.0, 0]], [[1.0, 0], [-109.38679514016037, 0], [1419857.0, 0]], [[1.0, 0], [495.9263070793414, 0], [2476099.0, 0]], [[1.0, 0], [2497.369120233482, 0], [6436343.0, 0]], [[1.0, 0], [42.42214495351649, 0], [20511149.0, 0]], [[1.0, 0], [-7999.557842476049, 0], [28629151.0, 0]], [[1.0, 0], [13763.70055298985, 0], [69343957.0, 0]], [[1.0, 0], [-11863.627515699382, 0], [115856201.0, 0]], [[1.0, 0], [-16816.011973175784, 0], [147008443.0, 0]], [[1.0, 0], [-13036.0, 0], [229345007.0, 0]], [[1.0, 0], [-17817.297109346393, 0], [418195493.0, 0]], [[1.0, 0], [-47346.05667364417, 0], [714924299.0, 0]], [[1.0, 0], [22782.93631336456, 0], [844596301.0, 0]], [[1.0, 0], [-39418.308426891985, 0], [1350125107.0, 0]], [[1.0, 0], [-1616.316095513448, 0], [1804229351.0, 0]], [[1.0, 0], [-53293.259421869276, 0], [2073071593.0, 0]], [[1.0, 0], [-6516.977080051807, 0], [3077056399.0, 0]], [[1.0, 0], [46016.35500833475, 0], [3939040643.0, 0]], [[1.0, 0], [-113488.45367401036, 0], [5584059449.0, 0]], [[1.0, 0], [-107417.86384578809, 0], [8587340257.0, 0]], [[1.0, 0], [197554.01311260377, 0], [10510100501.0, 0]], [[1.0, 0], [-81026.02337663757, 0], [11592740743.0, 0]], [[1.0, 0], [-137442.36230618303, 0], [14025517307.0, 0]], [[1.0, 0], [68693.08877241501, 0], [15386239549.0, 0]], [[1.0, 0], [139632.4688394209, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-20e2-1.1-c5-0-20', 'leading_term': '3.80261502095185065125613345299', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/400/6/a/u/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [3.8026150209518508, 3.7832288204061877, 3.7253398900986605, 3.629754259288964, 3.49780535291259, 3.3313390296193237, 3.1326925897971125, 2.904667724846134, 2.650497393541081, 2.373806641640455, 2.0785674290327694, 1.7690475959223726, 1.4497541862490733, 1.125371452171892, 0.8006939865354644, 0.4805555683280264, 0.1697544558572716, -0.12702398052486039, -0.4052862348381928, -0.6608100435351417, -0.8897228109958888, -1.0885775975220982, -1.2544250768242797, -1.3848797911914605, -1.4781789893096624, -1.5332323298606363, -1.5496607786300107, -1.5278231219365217, -1.468828667592071, -1.3745349077144693, -1.247529175320486, -1.0910936367334871, -0.9091533205702765, -0.7062072856013927, -0.4872434663307797, -0.2576381970419342, -0.023041890866500242, 0.21074717286578135, 0.4379185364550966, 0.6527918757117878, 0.8499626947018718, 1.0244478325442192, 1.171826957728526, 1.2883760620992042, 1.371188906634694, 1.4182824252105306, 1.428682268721209, 1.4024849750668718, 1.3408936817024337, 1.246224853737012, 1.1218841746483392, 0.9723105267331587, 0.8028878581481832, 0.6198256721681684, 0.43000985744923925, 0.24082657747725608, 0.05996292200190948, -0.10481103990348717, -0.24587331050237046, -0.355987883907634, -0.42854271187806675, -0.45778047833898367, -0.43901473919872386, -0.3688240036743798, -0.24521659469601884, -0.06775963701675926, 0.16233371766297092, 0.4421637177157157, 0.7671537553418439, 1.131112670953056, 1.5263502809687273, 1.9438450941647871, 2.3734614185867673, 2.804211289308772, 3.224554928037098, 3.6227318419886863, 3.9871132449276847, 4.306565298720847, 4.57081178554258, 4.770784278029851, 4.898947716871678, 4.949589560511176, 4.919061354376674, 4.805962676978997, 4.611258941086565, 4.338326427513419, 3.9929201582411076, 3.5830627108169844, 3.118854759660213, 2.612210912894082, 2.0765271975838475, 1.5262892281884868, 0.9766325671596536, 0.44286894962802115, -0.06000620095287273, -0.5178082788802068, -0.9176426424838363, -1.248350944688909, -1.500907769289803, -1.6687519315342416, -1.7480386809848616, -1.737801522235507, -1.6400153749429947, -1.4595562342528914, -1.2040562494838052, -0.88365707790642, -0.5106683428012079, -0.09914187349553674, 0.3356240297471856, 0.7776329365807112, 1.210771320237516, 1.6194005373683404, 1.9889369866348905, 2.306397544517277, 2.560888169284938, 2.744015285882793, 2.8502021792059065, 2.8768960550617186, 2.8246555632202677, 2.6971132666270266, 2.5008126063589957, 2.244924150868917, 1.940851112253852, 1.6017390364818707, 1.241909006121763, 0.8762374231555464, 0.519508278419809, 0.18576560748647453, -0.11230553504522266, -0.36394184803765983, -0.5607824106759047, -0.6972443195393009, -0.770774650539029, -0.781965180543469, -0.7345221863901193, -0.6350900435333183, -0.4929339986742452, -0.31949409442055343, -0.1278284743714735, 0.06803010614523412, 0.25377607632257443, 0.4155591865584631, 0.5407049251035924, 0.6183925905486688, 0.6402574411326658, 0.6008860012978875, 0.4981778091603015, 0.3335524892496711, 0.11198781479110008, -0.15811789953332933, -0.46525749572132097, -0.7952907590924054, -1.1320660787460641, -1.4581621681772843, -1.7557174335611168, -2.0073093309126806, -2.1968424590039644, -2.3104024224409443, -2.3370328150437447, -2.2693950701508783, -2.1042753542384953, -1.8429089944811794, -1.4911008829543604, -1.0591295542503047, -0.5614327776820398, -0.01608307018655413, 0.5559279851120371, 1.131567856432991, 1.6867660977891918, 2.1974976008634073, 2.64089616992326, 2.996345634709233, 3.246495343461717, 3.378149117583315, 3.38298156670514, 3.258042893046704, 3.0060226649231816, 2.6352541028350105, 2.1594526903764533, 1.5971958124196675, 0.9711630019657993, 0.30716859408455355, -0.36697049507928836, -1.022680111388095, -1.6319289318454133, -2.1685210102254184, -2.609317750838185, -2.9353286323025922, -3.1326154956577907, -3.192963615672442, -3.1142837236464675, -2.900722135051679, -2.5624705274980966, -2.115281995928472, -1.5797150111657692, -0.9801410394198659, -0.34356408598679805, 0.3016893832736959, 0.9273443959864701, 1.506545600720407, 2.015149519580526, 2.4328742244670902, 2.7442466619582766, 2.9392980486230615, 3.0139707329005843, 2.9702150172603177, 2.8157708716614382, 2.563646373553063, 2.231321164743672, 1.8397183117849127, 1.4120008414877145, 0.9722591500879244, 0.5441618566592663, 0.1496450787378508, -0.19228664497202935, -0.46658043918667713, -0.6629185760452694, -0.7762208557695122, -0.8068371620146995, -0.7604190689831047, -0.6474778168093083, -0.48265420663505004, -0.28374294370258907, -0.07052867424185735, 0.13649747050626387, 0.31746431734776076, 0.4544102723758819, 0.5324576661062389, 0.540799381887784, 0.4734357277806594, 0.3296137645677794, 0.11393863310959888, -0.1638541387563691, -0.4894559429480595, -0.844842387705103, -1.2093821653654175, -1.561132854008743, -1.8782463982977462, -2.140398831305134, -2.3301556344988037, -2.434186284320149, -2.444248984987011, -2.3578790028804946, -2.178730755764785, -1.9165439521030492, -1.5867264768917473, -1.209570072506635, -0.8091377697381469, -0.41188308357471176, -0.045078877723942194, 0.26485263979571466, 0.4940090255364733, 0.6225736307177399, 0.6361801174628277, 0.5269868559011357, 0.2943880502019391, -0.054691293257211906], 'positive_zeros': ['1.03532475423679087487587356142637', '2.25612514199185473571426732836097', '3.52189963238889718297822664587637', '4.08242977034811974254808353409185', '5.86727311680305987173083706129845', '6.70196640617827131516589353407886', '7.975404600083867171843554572149005', '8.665656914040454513598236539186064', '9.277151883823512591451170063467020', '10.31428617868854528135934790250169'], 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03532475423679087487587356143', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25612514199185473571426732836', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52189963238889718297822664588', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.15352792519226, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/6/a/u/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': '2-20e2-1.1-c5-0-20', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03532475423679087487587356143', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1312430046139412043625110163236', 'Lhash_array': ['1312430046139412043625110163236'], 'label': '2-20e2-1.1-c5-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/u/1/2'}