-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2879538507171592694822705214559', 'a10': [1.1847925309040954, 0.0], 'a2': [1.3472963553338606, 0.0], 'a3': [2.879385241571817, 0.0], 'a4': [-0.18479253090409536, 0.0], 'a5': [0.8793852415718167, 0.0], 'a6': [3.879385241571817, 0.0], 'a7': [0.3472963553338607, 0.0], 'a8': [-2.943563014047729, 0.0], 'a9': [5.2908593693815895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8825995129682234, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [0, 0]]]], 'bad_primes': [19], 'central_character': '361.1', 'coefficient_field': 'CDF', 'conductor': 361, 'conductor_radical': 19, 'conjugate': '2879538507171592694822705214559', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3472963553338606, 0], [2.0, 0]], [[1.0, 0], [-2.879385241571817, 0], [3.0, 0]], [[1.0, 0], [-0.8793852415718167, 0], [5.0, 0]], [[1.0, 0], [-0.3472963553338607, 0], [7.0, 0]], [[1.0, 0], [2.2266815969056775, 0], [11.0, 0]], [[1.0, 0], [2.573977952239538, 0], [13.0, 0]], [[1.0, 0], [-0.4679111137620439, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.694592710667721, 0], [23.0, 0]], [[1.0, 0], [-6.879385241571817, 0], [29.0, 0]], [[1.0, 0], [-7.106066838477494, 0], [31.0, 0]], [[1.0, 0], [4.9435630140477285, 0], [37.0, 0]], [[1.0, 0], [2.475651900285685, 0], [41.0, 0]], [[1.0, 0], [-3.9016739480461466, 0], [43.0, 0]], [[1.0, 0], [7.2908593693815895, 0], [47.0, 0]], [[1.0, 0], [-2.8374961755702346, 0], [53.0, 0]], [[1.0, 0], [-6.305407289332279, 0], [59.0, 0]], [[1.0, 0], [-9.128355544951825, 0], [61.0, 0]], [[1.0, 0], [7.674992351140469, 0], [67.0, 0]], [[1.0, 0], [-9.305407289332278, 0], [71.0, 0]], [[1.0, 0], [-1.3891854213354429, 0], [73.0, 0]], [[1.0, 0], [-11.845236962093876, 0], [79.0, 0]], [[1.0, 0], [14.830689042143186, 0], [83.0, 0]], [[1.0, 0], [-10.29085936938159, 0], [89.0, 0]], [[1.0, 0], [9.453363193811356, 0], [97.0, 0]], [[1.0, 0], [9.248970303380007, 0], [101.0, 0]], [[1.0, 0], [-5.5098001797636265, 0], [103.0, 0]], [[1.0, 0], [10.234422383429319, 0], [107.0, 0]], [[1.0, 0], [-1.8229482556195458, 0], [109.0, 0]], [[1.0, 0], [-17.687785577240675, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-19e2-1.1-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/361/2/a/h/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.0755324460928546, 3.086615780175558, 3.117503225586518, 3.1614835708204443, 3.2084880691267075, 3.2463840961726906, 3.262284413718056, 3.2437262442456096, 3.179700218477447, 3.061560457794707, 2.883836892719199, 2.6449348815785894, 2.347671565815249, 1.9995755200837109, 1.6128698774832562, 1.2040693328724934, 0.7931469795725732, 0.40226567843482, 0.05411739419594755, -0.23003185638224702, -0.43244000184801984, -0.5409320167878104, -0.5506587890946902, -0.46533298795594463, -0.29772156724436555, -0.06922402009454227, 0.1915542134129397, 0.4512172257501308, 0.6748432802242822, 0.8298311487216785, 0.8899453997201895, 0.8390928744845558, 0.6743248266379369, 0.40758216114117757, 0.06579222420961214, -0.31091638400363875, -0.6729003119205654, -0.9663590552174285, -1.1398779739469316, -1.1514449392230004, -0.9750687973599862, -0.6060668442509366, -0.06415004557346098, 0.6063722312367958, 1.3396310165113168, 2.0544348223928695, 2.6632057429533287, 3.0826766586502923, 3.245055736660184, 3.108155247182375, 2.6629692833770533, 1.9373954273651166, 0.9952235517593595, -0.06987919050416116, -1.1449475290801006, -2.1117048783382844, -2.862189445912959, -3.3138520269244935, -3.4218566786077, -3.1865592325019536, -2.65472302243094, -1.913895594504905, -1.0804011342843411, -0.282448015818077, 0.35926154593206805, 0.7504637725001942, 0.838724658797064, 0.6225828568967725, 0.15259411059091382, -0.4763380966612651, -1.1405291912798359, -1.7087625249541116, -2.06588592162482, -2.134797060844671, -1.8928795604497057, -1.3796628888461429, -0.6938079323491183, 0.02072387868475742, 0.5975587341869643, 0.8763808228706347, 0.7323012287591598, 0.10099366797958455, -1.005089676526227, -2.4927938542438586, -4.197999887693412, -5.90803760959866, -7.393475754488892, -8.44416604185997, -8.903437401431507, -8.694427606581279, -7.833737602588114, -6.429724824781842, -4.665454192813553, -2.7691098676070283, -0.9770092150529225, 0.5042117181785, 1.529459819203624, 2.0353930658340325, 2.045471162239782, 1.6592492269086123, 1.0283633081191628, 0.32423608504121704, -0.295892634192191, -0.7177752879900331, -0.8881551210564193, -0.8186751247184446, -0.575489014663313, -0.25748143128905626, 0.03151683177339705, 0.20985228573756526, 0.2380731095395143, 0.12713456839594858, -0.06708650706792685, -0.26149478309825563, -0.37115307983455315, -0.335733265699156, -0.1399359408307789, 0.17799104697474877, 0.5327414856913018, 0.8128525637430302, 0.9116378409163096, 0.7608191567994315, 0.35819053526297123, -0.2186315211935156, -0.81756639818166, -1.2374700313844211, -1.2696581599970223, -0.7473139724314181, 0.4081625029174461, 2.1551258743742783, 4.3229191483471565, 6.630701891565038, 8.732227067085658, 10.278879298848352, 10.98858757792307, 10.706046864080767, 9.440686129967345, 7.372959821599794, 4.826034721233722, 2.207422539272231, -0.06810073515579934, -1.6584347590538586, -2.359994602555877, -2.145174067061683, -1.1631380919255634, 0.29634986661702445, 1.8681370506790334, 3.191456944299443, 3.986498141320025, 4.110759357041091, 3.5828975622153085, 2.569372112751962, 1.3378872994834305, 0.18936598383550055, -0.6149188657873322, -0.9135670379933711, -0.6785319704956538, -0.014576037331597961, 0.8740391721580905, 1.7402284176228031, 2.359042165769895, 2.584040057217442, 2.380768148786347, 1.8292698068579167, 1.0958546480495208, 0.38252299225802594, -0.1316665285659642, -0.34096716715241104, -0.24112295776473824, 0.07237916073149751, 0.435374379063748, 0.6665557133368575, 0.6247710950917548, 0.25553880492235787, -0.3869886857355295, -1.1496846658009234, -1.8199663299791766, -2.18484868022787, -2.093338745018127, -1.5045019605102976, -0.5069930154100205, 0.6965958777346906, 1.8375608702994484, 2.6489783667192732, 2.9355817263078205, 2.6264618000180557, 1.7956843741652784, 0.6444560316248559, -0.5509950968847526, -1.5120418180576658, -2.0310423887890345, -2.0252170360678123, -1.5559272480649724, -0.8078191997823498, -0.03359016826600275, 0.5200105889396993, 0.6837873341991901, 0.41460240125629483, -0.19347106605171602, -0.9388741038870833, -1.5747226802771104, -1.8852244382204983, -1.7535838219332551, -1.20068398137585, -0.38211629674302866, 0.45663268370214105, 1.0543485073262682, 1.2157725461636855, 0.875859226621875, 0.1259682569759229, -0.807928502971497, -1.6307602511786452, -2.069771541886529, -1.965179568243135, -1.3321461906996084, -0.3731651023415412, 0.566406403313384, 1.0904361595513024, 0.8678429092666656, -0.26012738671011987, -2.212879016524447, -4.665610505964779, -7.11198772136149, -8.98090436793911, -9.778143747498685, -9.215673914534184, -7.29342254573448, -4.310360298919582, -0.8004080824263572, 2.591072427605834, 5.258322865969063, 6.774458356667866, 6.983058666224726, 6.019456171637651, 4.258471489012304, 2.2052898340947777, 0.36101960209908945, -0.899909944676224, -1.4083811749364024, -1.2170691442184527, -0.5551541846199157, 0.26075300043119, 0.9300263785668185, 1.2541913305786716, 1.1817212330704832, 0.8017504786311547, 0.2936035073800452, -0.14743707942323747, -0.3814401421603472, -0.36827871762044495, -0.17184071144113686, 0.07476912109453561, 0.22812655556701747, 0.19447064592944324, -0.03206671236136029, -0.3674879575823298, -0.6731456495539757], 'positive_zeros': ['2.27155535338614360775181545454711', '3.15907241361875228465613894041798', '4.27223811406285223842955492809310', '5.26288813311469045183077624962262', '6.61698226712208514730901470996344', '7.925179242709707989742441980581965', '8.532441758409032066690774716174609', '9.621167918096850934933523719003793', '10.13895912933182563538853339236021', '11.82847035227092728952560802421508'], 'prelabel': '2-19e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.697821990954359, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27155535338614360775181545455', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15907241361875228465613894042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27223811406285223842955492809', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.8825995129682234, 'bad_primes': [19], 'central_character': '1.1', 'conductor': 361, 'conductor_radical': 19, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/361/2/a/h/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': '2-19e2-1.1-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': '2-19e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.697821990954359, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27155535338614360775181545455', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2879538507171592694822705214559', 'Lhash_array': ['2879538507171592694822705214559'], 'label': '2-19e2-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/361/2/a/h/1/2'}