-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1744165162310340685752956502286', 'a10': [0.0, 0.0], 'a2': [-1.2535093220464881, 2.1711418335457355], 'a3': [0.6109380811315954, -1.05817579679856], 'a4': [-2.1425712409148927, -3.711042248100491], 'a5': [0.0, 0.0], 'a6': [1.5316331597832973, 2.6528664513019313], 'a7': [0.22187616226319093, 0.0], 'a8': [5.728894806356167, 0.0], 'a9': [0.7535093220464881, 1.305116429761297], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.3328142433947865, 4.1501332740773496]]]], 'bad_primes': [5, 19], 'central_character': '475.201', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1079396593417556344892843281028', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2535093220464881, -2.1711418335457355], [-1.0, -1.7320508075688772]], [[1.0, 0], [-0.6109380811315954, 1.05817579679856], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.22187616226319093, 0], [7.0, 0]], [[1.0, 0], [0.778123837736809, 0], [11.0, 0]], [[1.0, 0], [2.5, 4.330127018922194], [-6.5, 11.258330249197702]], [[1.0, 0], [-3.5386518038762733, 6.129124714608964], [-8.5, -14.722431864335457]], [[1.0, 0], [-1.3328142433947865, 4.1501332740773496]], [[1.0, 0], [-4.038651803876274, -6.995150118393402], [-11.5, 19.91858428704209]], [[1.0, 0], [0.11093808113159546, 0.19215039301412157], [-14.5, 25.11473670974872]], [[1.0, 0], [-2.5070186440929763, 0], [31.0, 0]], [[1.0, 0], [-1.9046564768699978, 0], [37.0, 0]], [[1.0, 0], [-3.617956725224572, 6.26648486767447], [-20.5, -35.50704155516198]], [[1.0, 0], [-3.649589885007869, 6.3212751076230855], [-21.5, -37.239092362730865]], [[1.0, 0], [1.3960805629613808, 2.4180824665084724], [-23.5, 40.703193977868615]], [[1.0, 0], [-2.190243002479894, -3.7936121612173825], [-26.5, 45.89934640057525]], [[1.0, 0], [-1.3960805629613808, 2.4180824665084724], [-29.5, -51.09549882328188]], [[1.0, 0], [-6.292161125922761, -10.898342759508015], [-30.5, 52.827549630850754]], [[1.0, 0], [5.285142481829785, 9.154135303769861], [-33.5, 58.023702053557386]], [[1.0, 0], [-4.920695078651701, 8.52289388477888], [-35.5, -61.48780366869514]], [[1.0, 0], [7.038651803876274, -12.191302541100034], [-36.5, -63.21985447626402]], [[1.0, 0], [0.7921611259227617, -1.3720633178791903], [-39.5, -68.41600689897065]], [[1.0, 0], [-9.521055932278928, 0], [83.0, 0]], [[1.0, 0], [1.5702849636595708, 2.7198133394198245], [-44.5, 77.07626093681505]], [[1.0, 0], [3.181223044791166, -5.5100399437872625], [-48.5, -84.00446416709055]], [[1.0, 0], [-3.69726164657287, -6.403845020739976], [-50.5, 87.4685657822283]], [[1.0, 0], [12.203836246885736, 0], [103.0, 0]], [[1.0, 0], [-1.6335512832261652, 0], [107.0, 0]], [[1.0, 0], [-3.8081997277044657, 6.595995413754098], [-54.5, -94.39676901250381]], [[1.0, 0], [12.488978728715521, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-475-19.11-c1-0-12', '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/475/2/e/d/201/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9253677397889601, 0.9562651641337175, 0.9728786531056075, 0.9734140367910478, 0.9540765688039992, 0.9101036057846676, 0.8368869409744509, 0.7310335328082121, 0.5912832243507804, 0.41923627852752643, 0.21984567349256465, 0.0016191730132450264, -0.22352870299170954, -0.44082544815437, -0.6336145833508753, -0.7847375556755265, -0.8782524087357593, -0.901358434754777, -0.8463382178320935, -0.7122816673726707, -0.5063304121530331, -0.24418414374939112, 0.050350150190938636, 0.34690664927938525, 0.6112319103701873, 0.8088592799873714, 0.909507458829371, 0.8917693122643925, 0.7475300468158381, 0.4854789508162482, 0.13307763852733503, -0.26356468014617346, -0.6422769102533978, -0.9299733746185254, -1.0501324050625995, -0.9320177247251509, -0.5207158220683499, 0.2132030421806042, 1.2657340036717675, 2.594506488961334, 4.117968832075046, 5.71938300593462, 7.255764299573354, 8.571242204064246, 9.513644331777874, 9.952512805953722, 9.796351597986634, 9.006758938926122, 7.607276476984283, 5.685298613934632, 3.386192963600363, 0.8997964472409217, -1.559461637022968, -3.7765576490461052, -5.560989554080291, -6.769645700214275, -7.324179977302461, -7.220267740976256, -6.52718122764029, -5.377493884922026, -3.9482003310584326, -2.4358887236058853, -1.029594824343916, 0.11458426634414119, 0.893239495983437, 1.266735062548255, 1.2599867180131858, 0.9529932583473126, 0.46291594317710477, -0.07904120875507459, -0.5517898648660099, -0.8652239147370798, -0.9740876961844527, -0.8824673542208357, -0.6383274523446715, -0.31945457566442664, -0.013871168780872318, 0.20110104239529983, 0.2766634109956295, 0.20341671267956749, 0.012912297615556194, -0.2305033451011854, -0.4457929053518747, -0.555698470061103, -0.5068952538729229, -0.2850499672184551, 0.07901580481809714, 0.5139628660569354, 0.9228443874205109, 1.20530802478913, 1.2821975111450488, 1.1167649269573108, 0.7271019262452205, 0.1860894971822849, -0.3921453132406399, -0.87714051954577, -1.1533645693650527, -1.1508764807739345, -0.8679493583577766, -0.3794604617524335, 0.17235303306948088, 0.6043362303069972, 0.7315474400921436, 0.41118751682868715, -0.41840814785097014, -1.7132033277910983, -3.320350866834817, -4.999285978044634, -6.464499657887864, -7.442344016497745, -7.730428896057296, -7.24667892573004, -6.0564432880151315, -4.370087343380723, -2.50951504169274, -0.848837405033208, 0.25957372637054343, 0.5585386227663836, -0.056789330095584574, -1.5111293714286935, -3.5578311066013177, -5.823686786957581, -7.8813871237416135, -9.334874351513847, -9.899592969759412, -9.46032024487915, -8.093848684027195, -6.051355547814674, -3.704170847921693, -1.4648292831809502, 0.29914248050058434, 1.3396315949674085, 1.574225115827174, 1.0946022551263526, 0.13606519293419594, -0.983762561662573, -1.9420029294913737, -2.4849011673450025, -2.482139816875705, -1.948977864734489, -1.0322360949798226, 0.03488719882596584, 0.9966381762535378, 1.6403900930782285, 1.8475090378903491, 1.6170905970483982, 1.057702108746885, 0.3508071118718661, -0.3030819166447015, -0.740226398322061, -0.8761361829702756, -0.7235228714763896, -0.3817042240734947, -0.0015639690211831276, 0.26299051985279776, 0.30250617751183384, 0.0844381161805405, -0.33872757136691595, -0.8476395036797965, -1.2945892164685489, -1.5502885122540926, -1.5443324300484906, -1.286672739425615, -0.8632526997958732, -0.4070058168814454, -0.05328630535994266, 0.10595849095283887, 0.05406735382647469, -0.14369881711461482, -0.36233882053439176, -0.4623809228251716, -0.344458541157927, 0.0047750399451678815, 0.4920950095690289, 0.9325010587633619, 1.098853652486566, 0.7945361641029407, -0.07136298036209784, -1.4300342284398577, -3.040001392638171, -4.524940945886026, -5.457820880200383, -5.472707885139623, -4.375498463144537, -2.2221371932545666, 0.6610335087923221, 3.726362267065838, 6.316854246306223, 7.816791158230645, 7.804577196175812, 6.168358343366002, 3.152468540135163, -0.6807417485999003, -4.567754468511283, -7.712843841128617, -9.46834945122166, -9.481677277185058, -7.772372392303772, -4.720318777732447, -0.9689454310071532, 2.7308927084125845, 5.695850306494243, 7.459456987149604, 7.859573438251329, 7.045201652655881, 5.406039039302991, 3.4485715196891498, 1.6555274591501437, 0.3677204498300286, -0.28155788567265555, -0.36640864099848414, -0.10910002638562888, 0.21488084155133982, 0.3753246133940163, 0.2586011332432925, -0.10820732295055406, -0.5839391006296172, -0.9777343372375646, -1.1265654560144187, -0.9583001211836467, -0.5189094800433319, 0.04441743369210415, 0.5369709524774204, 0.7871017625965767, 0.7082054116662583, 0.32996666932212726, -0.21227174377038321, -0.7262908779985786, -1.0326275429944158, -1.0301881870615763, -0.7341061617863431, -0.2716476919644422, 0.16327730018922493, 0.38156374324432085, 0.2711101111826481, -0.15652604908316836, -0.7630593498114676, -1.3270590750901283, -1.6205900951366181, -1.4928064821674978, -0.9306182719390383, -0.07323393899349256, 0.8273569927247667, 1.4890243744224865, 1.69830984572192, 1.3910897459089828, 0.685097799204496, -0.1505181515548076, -0.7821201618870804, -0.9281252374685235, -0.46602670397589535, 0.50868880215699, 1.6962977124283685, 2.680372236888087, 3.0647399631942767, 2.6166641071886745, 1.3676125719103087], 'positive_zeros': ['1.37590370879508833567984685783642', '2.72906864628016150800411087153232', '3.79261435691656696779702123729031', '4.59389301000982668979591950169217', '6.41999319106522427040436988798787', '7.86060123988430621937283087616719', '8.606375649925596022542469409065993', '9.506449086445786822578826774308135', '10.00698133303412958156068315148762', '10.72570370520519314144769957306250'], 'prelabel': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.13550657612455358, 'root_number': '0.9107472158164717 - 0.4129642949245674*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0677532880623', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37590370879508833567984685784', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72906864628016150800411087153', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79261435691656696779702123729', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.11', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/d/201/1'], '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': '2-475-19.11-c1-0-12', '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': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.06775328806227679, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37590370879508833567984685784', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1744165162310340685752956502286', 'Lhash_array': ['1744165162310340685752956502286'], 'label': '2-475-19.11-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/d/201/1'}