-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1318834677428072595937165638220', 'a10': [3.0776835371752536, 0.0], 'a2': [-1.902113032590307, 0.0], 'a3': [0.0, 0.0], 'a4': [1.618033988749895, 0.0], 'a5': [-1.618033988749895, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.618033988749895, 0.0], 'a8': [0.7265425280053609, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.94339561671401, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 19], 'central_character': '3249.1', 'coefficient_field': 'CDF', 'conductor': 3249, 'conductor_radical': 57, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.902113032590307, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.618033988749895, 0], [5.0, 0]], [[1.0, 0], [1.618033988749895, 0], [7.0, 0]], [[1.0, 0], [-0.2360679774997897, 0], [11.0, 0]], [[1.0, 0], [4.97979656976556, 0], [13.0, 0]], [[1.0, 0], [0.2360679774997897, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-8.23606797749979, 0], [23.0, 0]], [[1.0, 0], [-8.5065080835204, 0], [29.0, 0]], [[1.0, 0], [-7.330937578935453, 0], [31.0, 0]], [[1.0, 0], [-5.257311121191336, 0], [37.0, 0]], [[1.0, 0], [3.526711513754839, 0], [41.0, 0]], [[1.0, 0], [8.23606797749979, 0], [43.0, 0]], [[1.0, 0], [8.381966011250105, 0], [47.0, 0]], [[1.0, 0], [-12.139220723547204, 0], [53.0, 0]], [[1.0, 0], [13.208790101860185, 0], [59.0, 0]], [[1.0, 0], [2.76393202250021, 0], [61.0, 0]], [[1.0, 0], [-8.955536060099984, 0], [67.0, 0]], [[1.0, 0], [-8.784022634946174, 0], [71.0, 0]], [[1.0, 0], [-0.7082039324993691, 0], [73.0, 0]], [[1.0, 0], [0.17151342515380985, 0], [79.0, 0]], [[1.0, 0], [-9.94427190999916, 0], [83.0, 0]], [[1.0, 0], [-0.8980559531591708, 0], [89.0, 0]], [[1.0, 0], [-12.310734148701014, 0], [97.0, 0]], [[1.0, 0], [13.652475842498529, 0], [101.0, 0]], [[1.0, 0], [-5.15130999491937, 0], [103.0, 0]], [[1.0, 0], [-1.6245984811645315, 0], [107.0, 0]], [[1.0, 0], [15.388417685876266, 0], [109.0, 0]], [[1.0, 0], [12.759762125280599, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 58, 'label': '2-57e2-1.1-c1-0-58', '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/3249/2/a/ba/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1060437310261014e-61, 0.07321203600824495, 0.14559264124236548, 0.21628450507242084, 0.2843807859438359, 0.34890574545135555, 0.40880140432887385, 0.4629215344817842, 0.5100338277691434, 0.5488306073853948, 0.5779480093216759, 0.5959931820460028, 0.6015787398549883, 0.5933634555976709, 0.5700979814527929, 0.5306742300721817, 0.4741769221375062, 0.3999357031491525, 0.3075761491294964, 0.19706791876561136, 0.06876827223552835, -0.07654082957044651, -0.23762380069663097, -0.41277236049755883, -0.5997978727658266, -0.7960364666877824, -0.9983680738203203, -1.203250217846456, -1.4067670397072087, -1.6046936342451914, -1.792575322801607, -1.965820998963939, -2.1198091740273117, -2.2500048291236427, -2.35208466873731, -2.4220678833280136, -2.4564490858926615, -2.4523297078074218, -2.4075438422428355, -2.3207743269221384, -2.191654778366434, -2.0208533409373843, -1.8101341066274563, -1.5623925024214973, -1.2816614333850422, -0.9730856085957076, -0.6428622553681346, -0.29814733103668056, 0.05307264869744711, 0.40214195519615575, 0.7399278149500156, 1.057039891323544, 1.3440724349409912, 1.5918633838749163, 1.7917637250724043, 1.9359096043986062, 2.0174890341763176, 2.0309946307135687, 1.9724536516615598, 1.8396267192521536, 1.632167027691056, 1.3517325491647236, 1.0020447707342597, 0.5888888005367553, 0.12005125154817589, -0.39480589127007454, -0.9443352361037164, -1.5157554945996397, -2.0951600885030057, -2.6678762549840815, -3.218865993763311, -3.7331583079422654, -4.196300545055811, -4.594815319266006, -4.916648557005706, -5.151593714134174, -5.291677207545483, -5.331490617768627, -5.268456263730921, -5.103014319966713, -4.83872171375366, -4.482255558479608, -4.043316783956436, -3.5344328301393335, -2.970661677406886, -2.3692029806206705, -1.7489255324077355, -1.1298235748750398, -0.5324174789077392, 0.022883108802180523, 0.5164335045816186, 0.9300040558934162, 1.247403790418155, 1.4550554832727738, 1.5425008742411814, 1.5028164731443048, 1.3329228804153683, 1.0337737610680284, 0.610414452239595, 0.07190453737127724, -0.5688965613984305, -1.295677002792085, -2.089144050887021, -2.927606030575134, -3.7876466334985825, -4.644869631470264, -5.474688905116536, -6.253136406742307, -6.95765936665309, -7.567877804875915, -8.066274269091721, -8.438789685092956, -8.675302233723281, -8.769970168696274, -8.721424330739975, -8.532801624071396, -8.21161669700982, -7.769475279588131, -7.221638830398412, -6.58645607867983, -5.884682465473579, -5.138713153609249, -4.371758979480082, -3.606997284117151, -2.866730854813191, -2.1715881501609413, -1.5397965455334588, -0.9865575562341308, -0.5235489643812309, -0.1585736424325102, 0.10463116774061848, 0.2664170506776289, 0.33108008316255694, 0.30655610212299805, 0.20396960293769856, 0.037056643167825094, -0.1785123670280347, -0.425879699625185, -0.6877837871710103, -0.9473441425566012, -1.1888126634960925, -1.3982578015353107, -1.564151153403706, -1.677830530264854, -1.733819287464872, -1.7299884020022869, -1.6675551646582438, -1.5509200685167166, -1.3873511633419768, -1.18653243863092, -0.9599993422032931, -0.7204900109278217, -0.48124490701801065, -0.25529009976560085, -0.0547402642472255, 0.10984347703325463, 0.2300084420809493, 0.29984991894800594, 0.3163130336695647, 0.2793416117080728, 0.1918664841791445, 0.05963394000946331, -0.10911668540630286, -0.30410938933163206, -0.5135978439857889, -0.7250117635426887, -0.9256489238421197, -1.1033757834458764, -1.247298896918851, -1.3483705455437844, -1.399895204566728, -1.3979084833000603, -1.3414067797654003, -1.232413760860789, -1.075878514143316, -0.8794093654487565, -0.6528564330561595, -0.4077645024699818, -0.15672528398242766, 0.08733586900464288, 0.3118995070888378, 0.5055765150963459, 0.6587761821041127, 0.7642790958702221, 0.8176806805716907, 0.81767783184801, 0.7661794185235362, 0.6682309948809397, 0.5317543995401813, 0.3671134504520502, 0.18652709795269815, 0.0033605924645882163, -0.16866707897141575, -0.316315503354662, -0.42764752780154397, -0.4927981574749432, -0.5046414221323597, -0.4593135681760716, -0.35655802952646165, -0.19986689447255565, 0.003595443552363191, 0.2432886557769775, 0.5058024801155473, 0.7755495874709295, 1.0356110861726924, 1.2686905795806342, 1.4581250413043847, 1.5888958333921919, 1.6485813311043043, 1.6281940369896684, 1.5228497912995127, 1.3322245533889214, 1.0607648945896004, 0.717631292356301, 0.3163678874948673, -0.1256922133048041, -0.5882615862434016, -1.0491340406711194, -1.4853692039436628, -1.874563971025886, -2.1961415282056325, -2.432585231404515, -2.5705451999333104, -2.6017501767572373, -2.5236658775266596, -2.339853344205617, -2.0599961596371617, -1.699583000054435, -1.2792509825595109, -0.8238145762879356, -0.36102340966279195, 0.07989095037870678, 0.46980525172245324, 0.7813476279587046, 0.9905034471335956, 1.0780929375038268, 1.0310337003186192, 0.8433103314373737, 0.5165871306816491, 0.060417651688072956, -0.5079742384617709, -1.1643441390193852, -1.8784862634839048, -2.615657134560947, -3.3382974471571347, -4.007967212892135, -4.587394965186739, -5.042532562097934, -5.3445036332073235, -5.4713363300786675, -5.409379776405987, -5.154318149531234, -4.711716000604615, -4.097052271525847, -3.3352272691470533, -2.4595551910299576, -1.5102831217240817], 'positive_zeros': ['1.04037711747277045353466480018289', '2.42983823881104555334837911185698', '3.26221579717063236169472769160944', '4.51733432225526173868594556666110', '5.03344743239140268126007866551778', '6.57893654462552042188781147992947', '6.86495192252138223027151690134694', '7.83588750615818787591865198518038', '8.194860808665771438721497916036356'], 'prelabel': '2-57e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0934659728630765, 'root_angle': 0.5, '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': '1.04037711747277045353466480018', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42983823881104555334837911186', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26221579717063236169472769161', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 25.94339561671401, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 3249, 'conductor_radical': 57, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3249/2/a/ba/1/1'], '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': '2-57e2-1.1-c1-0-58', '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': '2-57e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0934659728630765, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04037711747277045353466480018', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1318834677428072595937165638220', 'Lhash_array': ['1318834677428072595937165638220'], 'factors': ['2-57e2-1.1-c1-0-58'], 'label': '2-57e2-1.1-c1-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3249/2/a/ba/1/1'}