-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2775351568618162912265014935476', 'a10': [0, -24.97168245627909], 'a2': [3.2974215362099017, 0], 'a3': [1.7320508075688772, 0], 'a4': [6.872988787460868, 0], 'a5': [0, -7.573093758883451], 'a6': [5.711301634687368, 0], 'a7': [0, 2.6457513110645907], 'a8': [9.47345510106304, 0], 'a9': [3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.160796768602342, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7320508075688772, 0]]], [7, [[1.0, 0], [0, -2.6457513110645907]]], [23, [[1.0, 0], [-15.387948826975055, 17.094181199998935]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.22', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '1815896926626215595303106662024', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.2974215362099017, 0], [4.0, 0]], [[1.0, 0], [-1.7320508075688772, 0]], [[1.0, 0], [0, 7.573093758883451], [-25.0, 0]], [[1.0, 0], [0, -2.6457513110645907]], [[1.0, 0], [0, 5.869479302329113], [-121.0, 0]], [[1.0, 0], [-8.024257697636067, 0], [169.0, 0]], [[1.0, 0], [0, -15.470444855904008], [-289.0, 0]], [[1.0, 0], [0, -2.9588161358057175], [-361.0, 0]], [[1.0, 0], [-15.387948826975055, 17.094181199998935]], [[1.0, 0], [45.98694802405539, 0], [841.0, 0]], [[1.0, 0], [-57.09207180008808, 0], [961.0, 0]], [[1.0, 0], [0, -39.01496922159152], [-1369.0, 0]], [[1.0, 0], [-19.909110397125424, 0], [1681.0, 0]], [[1.0, 0], [0, -65.55838528077939], [-1849.0, 0]], [[1.0, 0], [82.35496462526629, 0], [2209.0, 0]], [[1.0, 0], [0, 26.904917230327094], [-2809.0, 0]], [[1.0, 0], [-44.49978883503449, 0], [3481.0, 0]], [[1.0, 0], [0, -93.31723293222701], [-3721.0, 0]], [[1.0, 0], [0, 3.331859394200947], [-4489.0, 0]], [[1.0, 0], [62.73631087095075, 0], [5041.0, 0]], [[1.0, 0], [-49.44308311688223, 0], [5329.0, 0]], [[1.0, 0], [0, -3.586009926243265], [-6241.0, 0]], [[1.0, 0], [0, -122.35452463987725], [-6889.0, 0]], [[1.0, 0], [0, -27.068539806533636], [-7921.0, 0]], [[1.0, 0], [0, -44.36489943212866], [-9409.0, 0]], [[1.0, 0], [24.68520450075201, 0], [10201.0, 0]], [[1.0, 0], [0, 116.85464726983682], [-10609.0, 0]], [[1.0, 0], [0, 131.50816113740814], [-11449.0, 0]], [[1.0, 0], [0, 142.93669983116234], [-11881.0, 0]], [[1.0, 0], [0, 67.53707110598823], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-483-23.22-c2-0-44', 'leading_term': '5.335217266199454953121300205738178106497850286337707188', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/483/3/f/a/22/42', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [5.335217266199455, 5.447233400003948, 5.544450079260568, 5.626350263750069, 5.692166907222186, 5.740898446880794, 5.771339849043322, 5.782127757534949, 5.771797745836894, 5.738851285297615, 5.6818298020124605, 5.599393079750818, 5.490399243306378, 5.3539835943357055, 5.189633645448831, 4.997257793296363, 4.77724518323509, 4.530514451073754, 4.258549191554872, 3.963418211676562, 3.647778892885521, 3.314862320621181, 2.9684392498895527, 2.612766463799184, 2.252513645058545, 1.892671509289406, 1.5384426289336273, 1.195117087458528, 0.8679358206883214, 0.5619451966638161, 0.28184702581373783, 0.031848746085178015, -0.18448104056740844, -0.3643462256082798, -0.5058404950035447, -0.6080428356860237, -0.6710861470016025, -0.6961944309506218, -0.6856848466984221, -0.6429319545745651, -0.5722927220092895, -0.47899228640351804, -0.36897202425755027, -0.2487031078423825, -0.12497037688125989, -0.004632942421672877, 0.1056306021256349, 0.19958323905812783, 0.27168676548216747, 0.31734451514394346, 0.33311866885727975, 0.3169115247871872, 0.2681008562661393, 0.18762074183048533, 0.07798099658217161, -0.056779471776060714, -0.2112074773868882, -0.3786177545246058, -0.551338680420568, -0.7210145284863831, -0.8789542041539592, -1.016513595445757, -1.125496238315136, -1.1985551018551552, -1.2295770763367104, -1.214031311833201, -1.149262991726654, -1.034715482157185, -0.8720660818766851, -0.6652637672131547, -0.4204612959113044, -0.14583866550133207, 0.1486799645219179, 0.45180840272192685, 0.7513667403159285, 1.0348178632141545, 1.2898496004522773, 1.5049761952557066, 1.6701301082233608, 1.7772137799133745, 1.820581060234967, 1.79741965833101, 1.7080092081715246, 1.5558343286116816, 1.3475382428333194, 1.0927098860719697, 0.8035056674827216, 0.4941157873082836, 0.18009381478042527, -0.12242335956249213, -0.39757054903389283, -0.6306434301085949, -0.8089765629404637, -0.9227626970564257, -0.9657658802608561, -0.9358835386326978, -0.8355179307262919, -0.6717250892233048, -0.4561192938430573, -0.2045228757385987, 0.06363578657252672, 0.326159486465604, 0.5591243333029329, 0.7380836246939968, 0.8393788947647347, 0.8414945045286578, 0.7263859746762756, 0.4807095310412411, 0.09688139830699617, -0.4260995931385537, -1.082123573057065, -1.8577802545392466, -2.7325377361096193, -3.679300377657385, -4.6653368331223835, -5.653548944485399, -6.60403236555721, -7.475861629945895, -8.229017011519971, -8.826358954029294, -9.235548911629023, -9.430813763921039, -9.394454897157019, -9.118012621160165, -8.60301153872649, -7.8612321956050835, -6.914477904142066, -5.7938318751374736, -4.538427323347217, -3.1937805078451245, -1.8097621516405937, -0.4383048169808193, 0.8690388118265692, 2.0635603493236863, 3.1017518234873513, 3.9474251743327105, 4.573476937721878, 4.963197085510414, 5.111044434436208, 5.022839555481964, 4.715358171667158, 4.215341818142264, 3.557976082770194, 2.784918029165802, 1.9419814850227988, 1.0766100147793038, 0.23528116242267913, -0.5390090601211529, -1.2090359641592894, -1.7452771412795034, -2.127372106954573, -2.3450259345395157, -2.3983055103973134, -2.2973139155443465, -2.06126659301937, -1.7170299920829433, -1.2972169102086146, -0.8379605792522172, -0.3765097883890915, 0.05120141136022569, 0.41285446716023455, 0.6817712425329376, 0.8385350391735232, 0.8721064221136252, 0.7803661120367803, 0.5700554020902066, 0.2561248495569651, -0.1394583277336551, -0.5893573667911319, -1.0628502990303912, -1.5280117263912623, -1.9539393778675735, -2.312870528193467, -2.5820419453204377, -2.7451659400786848, -2.793423052017144, -2.7259069858410854, -2.549497140153385, -2.278175601778995, -1.9318458030456198, -1.534746192720144, -1.1135815583728328, -0.6955148358209224, -0.30617177410275725, 0.03219110634387216, 0.30221816497201526, 0.4925726353231559, 0.5985602850700525, 0.6222169845969742, 0.5718607234437476, 0.4611510257165646, 0.30773791823394503, 0.1316154690289878, -0.0466812475606778, -0.2078841119805424, -0.3356526395975317, -0.41794707492578254, -0.44799719581642755, -0.4247837010311375, -0.35299004119067706, -0.24242771891813442, -0.10698377927212166, 0.036818350388585025, 0.1715179516403013, 0.28052379020121454, 0.349863250891227, 0.36970934161090746, 0.33553617116405027, 0.24878204068143037, 0.11693929342286408, -0.046961450944729345, -0.22545190199214146, -0.39823728880465503, -0.5441945991886069, -0.6435936050452066, -0.6803480496215288, -0.6440913104279968, -0.5318748679646345, -0.34930943487481536, -0.11100662338819105, 0.1597688735239492, 0.43226413829620747, 0.6701793444034222, 0.8342765671571529, 0.8854841404673179, 0.7882724946071631, 0.5140409825771994, 0.04423821246812568, -0.6270568228374023, -1.491338334227915, -2.524859087045125, -3.688927725124908, -4.931367617578893, -6.189098130413797, -7.391709328078624, -8.465817081573933, -9.339914340544466, -9.949382112711197, -10.241295407957772, -10.178658251485917, -9.74372901617537, -8.94015172616423, -7.793687395786664, -6.351436624004347, -4.679553630360937, -2.8595645923283404, -0.9835108664733757, 0.8517680938043161, 2.5508243084324507, 4.025830024128163, 5.202398662604697, 6.024570992478198, 6.458592556409668, 6.495191031363726, 6.150168724179318, 5.463248019042897, 4.495237064897996], 'positive_zeros': ['2.18936635072667905523938834236435', '3.16686631852434159514662134713617', '3.83897029525734023543799539418450', '5.02743617622963070133223415312722', '6.22879392601262405007590676289109', '7.01465694197560048673597964475988', '7.60829757767592823258393827358208', '9.233998561428698243070875424455425', '10.28619822375202508819276947167638', '11.17077189473896364215846203262509'], 'prelabel': '2-483-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6277812459687175, 'root_angle': 0.23329506298979288, 'root_number': '0.74322526956517104604052987305862857099142063139050370059 + 0.66904125334674156640635698979121773485675671547501389781*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11664753149489644', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18936635072667905523938834236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16686631852434159514662134714', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83897029525734023543799539418', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.160796768602342, 'bad_primes': [3, 7, 23], 'central_character': '23.22', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/3/f/a/22/42'], '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': '2-483-23.22-c2-0-44', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-483-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6277812459687175, 'root_angle': 0.11664753149489644, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18936635072667905523938834236', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2775351568618162912265014935476', 'Lhash_array': ['2775351568618162912265014935476'], 'label': '2-483-23.22-c2-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/3/f/a/22/42'}