-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1513077143640783723394973075588', 'a10': [-2.5080520346751687, -0.7161708565330718], 'a2': [0.3883060903315708, -1.3598596913694478], 'a3': [0, 0], 'a4': [-1.6984367604228199, -1.0560836003103335], 'a5': [0, -1.84434618556083], 'a6': [0, 0], 'a7': [0, 2.179589798446278], 'a8': [-2.0956388568935496, 1.8995519949393058], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.923534996511162, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.3883060903315708, 1.3598596913694478]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [3.473711505874756, -2.6331214126874847]]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.379', 'coefficient_field': 'CDF', 'conductor': 1368, 'conductor_radical': 114, 'conjugate': '1216247179846952535797226239875', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3883060903315708, 1.3598596913694478]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.84434618556083], [-5.0, 0]], [[1.0, 0], [0, -2.179589798446278], [-7.0, 0]], [[1.0, 0], [-4.965194664416731, 0], [11.0, 0]], [[1.0, 0], [-3.691494737032921, 0], [13.0, 0]], [[1.0, 0], [-2.8556988132438432, 0], [17.0, 0]], [[1.0, 0], [3.473711505874756, -2.6331214126874847]], [[1.0, 0], [0, 7.1658335852681025], [-23.0, 0]], [[1.0, 0], [-9.321128386916065, 0], [29.0, 0]], [[1.0, 0], [4.765788215284413, 0], [31.0, 0]], [[1.0, 0], [2.3652819754458743, 0], [37.0, 0]], [[1.0, 0], [0, 0.6133113791827856], [-41.0, 0]], [[1.0, 0], [1.9358024055178862, 0], [43.0, 0]], [[1.0, 0], [0, 7.160145990020725], [-47.0, 0]], [[1.0, 0], [11.414256724074201, 0], [53.0, 0]], [[1.0, 0], [0, -4.6496250229851155], [-59.0, 0]], [[1.0, 0], [0, 1.2605526988805107], [-61.0, 0]], [[1.0, 0], [0, 3.300409990992827], [-67.0, 0]], [[1.0, 0], [11.834335475046412, 0], [71.0, 0]], [[1.0, 0], [-15.763935605584132, 0], [73.0, 0]], [[1.0, 0], [5.397841247651786, 0], [79.0, 0]], [[1.0, 0], [-10.957053637802263, 0], [83.0, 0]], [[1.0, 0], [0, 3.2344640791333426], [-89.0, 0]], [[1.0, 0], [0, -4.470993928867218], [-97.0, 0]], [[1.0, 0], [0, 16.561689496927304], [-101.0, 0]], [[1.0, 0], [-7.106981453165523, 0], [103.0, 0]], [[1.0, 0], [0, -20.486704332303045], [-107.0, 0]], [[1.0, 0], [-0.20376093647095295, 0], [109.0, 0]], [[1.0, 0], [0, 10.013563925251354], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 60, 'label': '2-1368-152.75-c1-0-60', 'leading_term': '1.958225619214936634346289570912301834292692519040366681', '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/1368/2/e/g/379/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9582256192149365, 2.025338320257806, 2.08547434792317, 2.137852045767341, 2.18137900356556, 2.214653618422159, 2.2359845191946444, 2.2434263158763863, 2.2348294424818747, 2.207901542180382, 2.160277824410129, 2.0895979925814383, 1.9935875834047498, 1.8701417855358915, 1.7174099626088455, 1.533879174516905, 1.3184549775491623, 1.0705377110266967, 0.7900923748443354, 0.47771009918454777, 0.1346591322808513, -0.23707675238965986, -0.6347744836846048, -1.0549644830855713, -1.4934417294766116, -1.945296500640776, -2.404965791626722, -2.8663059205683705, -3.3226862645503834, -3.7671034346607963, -4.1923145171081035, -4.590987296251509, -4.955864658639706, -5.279939680163403, -5.556637248448504, -5.779997497831599, -5.9448558628240855, -6.047014214956574, -6.083397362147892, -6.052189180712354, -5.952942834692193, -5.7866599265986505, -5.555834022423696, -5.264454799015773, -4.917970062573817, -4.523204063647397, -4.088231858719434, -3.6222109051286857, -3.135172581235516, -2.637777847409874, -2.141042750698115, -1.6560408687458983, -1.1935910273826635, -0.7639396529903413, -0.3764478807370405, -0.039293984401868313, 0.24079821711859536, 0.45879461648469994, 0.6115400729192161, 0.6978930976007947, 0.7187988853479763, 0.6772954479836837, 0.5784497519886442, 0.42922315419672685, 0.23826798611727587, 0.015659769519849185, -0.22742784660775883, -0.4790958602928964, -0.7271285946860899, -0.9594245748420257, -1.1644344392266313, -1.3315897874360247, -1.4517065236478115, -1.5173465536711084, -1.5231226556358897, -1.4659329670445873, -1.3451137823123547, -1.1625021743304682, -0.9224032521658914, -0.6314605299502675, -0.29843177200119286, 0.06612335882489728, 0.45023365561327, 0.8409709309469532, 1.2249518327827076, 1.588867389192451, 1.920018929460467, 2.2068380532841414, 2.4393682805678014, 2.609686956479596, 2.7122479125245595, 2.7441282518257193, 2.705166347504559, 2.597982584976158, 2.427879369952582, 2.2026222576400953, 1.9321095024761599, 1.6279426327325899, 1.3029155659290568, 0.9704440513127996, 0.6439606256015269, 0.3363025996867376, 0.05912170124948251, -0.17765622247604124, -0.36629463011730523, -0.5016089712894285, -0.5812089682886888, -0.605606143797493, -0.5781784471155464, -0.504990654044001, -0.3944763435308333, -0.2569943438524951, -0.10427923521840823, 0.051188559058514965, 0.19686269541988752, 0.32082695521885707, 0.41247163090743016, 0.4631143491598924, 0.46653114888724573, 0.41936718532361167, 0.32140170651055905, 0.17564874187501056, -0.01171703778912907, -0.23161095290906036, -0.4724578009824166, -0.7207632986390894, -0.9618118613146047, -1.1804574005811745, -1.3619675893280638, -1.4928776795928922, -1.561807767795655, -1.5601975956930645, -1.482915642246369, -1.3287043625439967, -1.1004307929078712, -0.8051210646716407, -0.45376823192229393, -0.06091469793584455, 0.35597717978881377, 0.7773406648801422, 1.182469595166145, 1.550586293942444, 1.861958536746537, 2.0990068191267905, 2.247341325305982, 2.296669384284997, 2.2415188768351015, 2.0817309033957136, 1.8226857387436144, 1.4752392130393754, 1.0553615468288526, 0.5834865819494595, 0.08359545536245779, -0.41792582201462325, -0.893601572833525, -1.3162896874718593, -1.6606397965612398, -1.904508669872345, -2.030254609287508, -2.0258363721373485, -1.8856501713140295, -1.6110502638855042, -1.2105140414283073, -0.6994306415308884, -0.09951200007475441, 0.5621540875817655, 1.2543690576742152, 1.9433482354608875, 2.5944303508676567, 3.1738846988182803, 3.6507206645648904, 3.998401306985901, 4.196365038760349, 4.231267202383439, 4.097866249683212, 3.7994967226909613, 3.3480924588923555, 2.7637473174663265, 2.073825973131953, 1.3116625606666452, 0.5149087445667637, -0.27638625664470584, -1.0218643125417732, -1.6830046362552182, -2.225210902935218, -2.619723239585481, -2.845246428127566, -2.8891993131446037, -2.7485097396342018, -2.429903385987027, -1.9496623265493984, -1.3328585484676818, -0.6120973025637602, 0.17416662306820857, 0.9836515204129708, 1.772501616738096, 2.4976469586888372, 3.1191394297899278, 3.602333760789973, 3.919789731301976, 4.052786379348979, 3.9923601886750304, 3.7398057643508453, 3.306607944868111, 2.71380688366215, 1.9908304564750474, 1.1738594594234981, 0.30381857526219574, -0.5758916893373264, -1.4217913496283587, -2.192706972635297, -2.8520091796923746, -3.3695720925393067, -3.7233417143586562, -3.9004236509264243, -3.8976295013860276, -3.7214539426343527, -3.3874890018101294, -2.9193161320011254, -2.346948351788517, -1.7049218896870664, -1.0301577635775703, -0.3597271736262423, 0.2713403860846639, 0.8320711373921841, 1.2972602979513308, 1.6487818894132047, 1.8764189713531365, 1.9781696629235561, 1.9600185731873554, 1.8351980868626525, 1.622997064552677, 1.3472037326248567, 1.0342929179833018, 0.711483761922602, 0.4048015429940611, 0.13727572996584606, -0.07260404717732151, -0.21207109462735887, -0.27482647652662767, -0.26129915123980213, -0.1784091083852839, -0.038856116114093404, 0.14000997136535206, 0.33765195796209035, 0.5320322464734832, 0.701399296033247, 0.8260418868599567, 0.8898817972599424, 0.8817870539254404, 0.796507960884957, 0.6351652845682093, 0.4052523928871094, 0.12014854236081125, -0.20182363112168258, -0.5387296082343246, -0.8666474659700861], 'positive_zeros': ['1.19360740520169155418989909669452', '3.23018233833255353604152291323815', '3.81249068196591353141953577710272', '4.73575165548763415381262303109532', '5.99021945450458731357014187035496', '6.60162257199304483927780240392738', '7.14507906698043755174570574451590', '8.036055131928566223479231304577404', '8.915944383993592074203614377305859', '9.618479883756977969369211848121242'], 'prelabel': '2-1368-152.75-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.305077154396121, 'root_angle': 0.5591512915522601, 'root_number': '-0.1847615828418016810108734959274854458853468640615345743 + 0.9827833726237904024461856539451238228168581688245802530*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.27957564577613003', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19360740520169155418989909669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23018233833255353604152291324', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81249068196591353141953577710', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.923534996511162, 'bad_primes': [2, 3, 19], 'central_character': '152.75', 'conductor': 1368, 'conductor_radical': 114, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/2/e/g/379/23'], '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': '2-1368-152.75-c1-0-60', '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': '2-1368-152.75-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.305077154396121, 'root_angle': 0.27957564577613003, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19360740520169155418989909669', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1513077143640783723394973075588', 'Lhash_array': ['1513077143640783723394973075588'], 'label': '2-1368-152.75-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/2/e/g/379/23'}