-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3049104528847912771317406762469', 'a10': [-2.0, 1.0], 'a2': [0.0, -1.0], 'a3': [0.0, -1.0], 'a4': [-1.0, 0.0], 'a5': [-1.0, -2.0], 'a6': [-1.0, 0.0], 'a7': [0.0, -1.0], 'a8': [0.0, 1.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [1.0, 2.0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.559', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': '347920090084302904691037302731', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [1.0, 2.0]], [[1.0, 0], [0, 1.0], [-7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [0, 4.0], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [-1.0, 0], [19.0, 0]], [[1.0, 0], [0, -5.0], [-23.0, 0]], [[1.0, 0], [2.0, 0], [29.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 4.0], [-37.0, 0]], [[1.0, 0], [10.0, 0], [41.0, 0]], [[1.0, 0], [0, 5.0], [-43.0, 0]], [[1.0, 0], [0, -8.0], [-47.0, 0]], [[1.0, 0], [0, -5.0], [-53.0, 0]], [[1.0, 0], [-6.0, 0], [59.0, 0]], [[1.0, 0], [2.0, 0], [61.0, 0]], [[1.0, 0], [0, 2.0], [-67.0, 0]], [[1.0, 0], [5.0, 0], [71.0, 0]], [[1.0, 0], [0, 7.0], [-73.0, 0]], [[1.0, 0], [3.0, 0], [79.0, 0]], [[1.0, 0], [0, 2.0], [-83.0, 0]], [[1.0, 0], [1.0, 0], [89.0, 0]], [[1.0, 0], [0, -10.0], [-97.0, 0]], [[1.0, 0], [15.0, 0], [101.0, 0]], [[1.0, 0], [0, 0], [-103.0, 0]], [[1.0, 0], [0, 19.0], [-107.0, 0]], [[1.0, 0], [2.0, 0], [109.0, 0]], [[1.0, 0], [0, 15.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-930-5.4-c1-0-27', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/930/2/d/a/559/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5812033917840791, 0.8917112450746131, 1.2373467012045438, 1.6210280931402787, 2.0415497797776734, 2.4919434175693125, 2.958615757450571, 3.42128829423092, 3.853717488393851, 4.225177602378055, 4.5026793320579435, 4.653849144398421, 4.650309384764226, 4.471295271621981, 4.107144038890901, 3.562216239634824, 2.8567801691292303, 2.027423885560288, 1.1256649125970042, 0.21460531176628442, -0.6362823485346616, -1.357878677002752, -1.8890166499212941, -2.184089694276371, -2.2196568563866226, -1.9990151249548913, -1.5538444893723917, -0.9423264693454295, -0.24357192615228043, 0.4512780737295001, 1.0503649875607568, 1.4734419248756319, 1.6634947180077682, 1.5958383917521355, 1.283065670537983, 0.774710266310891, 0.15122354935332682, -0.4872454259520534, -1.03586559666145, -1.4017624062007497, -1.5196284919109773, -1.363593840381969, -0.9530567553459647, -0.35104594976800396, 0.3451018121289255, 1.0195937972638467, 1.5581235168731675, 1.8685175077042442, 1.8983105709404045, 1.645769959244373, 1.1618828491931312, 0.542384418128806, -0.08922043124078803, -0.6048469558985797, -0.8970052678288368, -0.9010400293243737, -0.6097703689211164, -0.07709972977071808, 0.5907924450630085, 1.2555749022322982, 1.7746530432216394, 2.031388042445155, 1.9613503845926363, 1.5687398405397026, 0.928836134311266, 0.1751075721279387, -0.5271272349686479, -1.0155012545306166, -1.1666761687983103, -0.9257488837943834, -0.32201545260367775, 0.5332612004613745, 1.4676416478178924, 2.2832351303888494, 2.8000918901341656, 2.8977751019839033, 2.5454505156338127, 1.812893280409897, 0.8587866106828946, -0.10222346263718667, -0.8471739115865586, -1.1967259904296281, -1.0593573025571494, -0.45688707391577177, 0.4757726315463829, 1.5179921558192564, 2.4128415930087566, 2.927863236566326, 2.913158896974255, 2.342606722358813, 1.327318347160707, 0.09658506109357766, -1.0507980198438764, -1.8145914508440826, -1.9650859791068276, -1.4018187408540304, -0.18428451306039478, 1.4739413191081692, 3.2477043453386543, 4.770522987499337, 5.716651613223515, 5.875640784693357, 5.201383076502841, 3.8234508282139976, 2.017542775424283, 0.1418691556741486, -1.445204532325907, -2.4661774715040155, -2.7843008195738874, -2.4278796956425506, -1.5736356770617665, -0.49429650937880903, 0.5152390934335409, 1.2134305822601164, 1.469480735239443, 1.2879756891409275, 0.7953613721900201, 0.19345490936014045, -0.30570986678960016, -0.5443896213429017, -0.4642019902923338, -0.11892190634206963, 0.34813100105803485, 0.7545954917533644, 0.9414751265108675, 0.8277348516757624, 0.43959926004429145, -0.09530397938966999, -0.5879612716338636, -0.8503183652717643, -0.76063004289695, -0.31077512493870074, 0.3806945375263061, 1.0959028132331028, 1.579052182345985, 1.6144633987335402, 1.0976749045879233, 0.07692977464356532, -1.249594392764547, -2.5824586559575238, -3.603017432015236, -4.0653485505969025, -3.87032687332228, -3.098291841617878, -1.9884611603094486, -0.8691897333225667, -0.05860612704957763, 0.23475345885341767, -0.019648854940996042, -0.6596313828282807, -1.3762771580350361, -1.8090204441272413, -1.6623581693283687, -0.8086590084076132, 0.6558211510473831, 2.4216327589285527, 4.043722995141304, 5.065478393019603, 5.153607163806452, 4.203463149876339, 2.3818782647566628, 0.09240294623346543, -2.1291244416663657, -3.759511870917264, -4.4316322297851665, -4.034032760800452, -2.7371050731712083, -0.9381045395379768, 0.8581779856713165, 2.1867808836506444, 2.7533076629258284, 2.508879484992286, 1.6478703258051106, 0.5313592082587861, -0.4374888315291587, -0.9451629325045059, -0.8642555855865842, -0.28447582520959663, 0.5299495583847511, 1.2402231566493047, 1.5551778336046986, 1.3336693023598039, 0.6323206632110897, -0.3172307869834821, -1.1930827246352413, -1.6998680676882516, -1.6764749004123563, -1.1565360395679714, -0.35977929726553476, 0.3836529773342429, 0.750249484461613, 0.5409673340585812, -0.24166573585755732, -1.385177364455875, -2.531980348751797, -3.2964369337643404, -3.394672616270995, -2.742638783221483, -1.4883502921978453, 0.0333538819231007, 1.4084752100310824, 2.2772370204314063, 2.4475344923677267, 1.9498460100592594, 1.0156489837265628, -0.011606133409644302, -0.8001456021121849, -1.1433589821573682, -1.0225528017017813, -0.5973784663635924, -0.12925292449684483, 0.13189376857974403, 0.053379079580451384, -0.32345732141658484, -0.7984977574798693, -1.0955146500915507, -0.9811029325365963, -0.3733395044870907, 0.604329600273628, 1.649149340390358, 2.3802915048358377, 2.480869398019098, 1.8283159133507854, 0.5617071112348857, -0.9447781373483785, -2.1995894413582353, -2.7655730235510045, -2.425960802393325, -1.2829617867905765, 0.2518606827494118, 1.5793442631737828, 2.1102549667010146, 1.473070103071746, -0.34048331821394345, -2.9460204026249595, -5.668612393699175, -7.74653215532395, -8.570607404716897, -7.879266763222271, -5.84314613695657, -3.0102083574026532, -0.12992366649081463, 2.083577742257757, 3.1690279495853053, 3.0436423603452956, 1.9974485234052992, 0.5635544691469028, -0.6851625246774633, -1.338116582944683, -1.2760967810061628, -0.6846487534874456, 0.047129500023022526, 0.49900454375415126, 0.3948367192440421, -0.28655496830521476, -1.3055409168435426, -2.2601460211319426], 'positive_zeros': ['2.40531935874045117295226274602562', '3.54288568469892368614829201748176', '4.52910691332778202043452752014960', '5.43887489988290248425580158710056', '6.48148449414858039901327596219843', '7.14030689535698297919481576655823', '8.154227292792793092578435497507155', '8.800218478491754257952755942119448', '9.860805618875227593481910657205507', '10.44008843758896986894137273193505'], 'prelabel': '2-930-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323791808825', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.40531935874045117295226274603', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.54288568469892368614829201748', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.52910691332778202043452752015', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '5.4', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/d/a/559/1'], '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': '2-930-5.4-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-930-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.40531935874045117295226274603', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3049104528847912771317406762469', 'Lhash_array': ['3049104528847912771317406762469'], 'label': '2-930-5.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/d/a/559/1'}