-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2438413275186523634569656592849', 'a10': [-3.42213890983277, 1.493394271501461], 'a2': [-1.6606586744832494, -0.17454226001887388], 'a3': [-1.6580809652275124, -0.500766924576894], 'a4': [0.7710270311363558, 0.1638868546929889], 'a5': [1.9447108081460298, -1.1036756193193793], 'a6': [2.6661015471422758, 1.121008136158004], 'a7': [-0.9072531881831386, 0.5238028724206812], 'a8': [1.924352297855634, 0.6252599640643479], 'a9': [2.4984649744995986, 1.6606242113129386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6580809652275124, 0.500766924576894]]], [5, [[1.0, 0], [-1.9447108081460298, 1.1036756193193793]]]], 'bad_primes': [3, 5], 'central_character': '225.184', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '520661350309627302274247256334', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.6606586744832494, 0.17454226001887388], [1.9562952014676114, 0.4158233816355187]], [[1.0, 0], [1.6580809652275124, 0.500766924576894]], [[1.0, 0], [-1.9447108081460298, 1.1036756193193793]], [[1.0, 0], [0.9072531881831386, -0.5238028724206812], [3.5, -6.06217782649107]], [[1.0, 0], [-0.5242787015647825, 4.988178642273937], [-10.759623608071863, -2.2870285989953527]], [[1.0, 0], [5.175295824974062, -0.5439455099575469], [12.715918809539474, -2.7028519806308715]], [[1.0, 0], [2.4576225877352083, 0.798529984662053], [13.753288904374106, 9.992349288972044]], [[1.0, 0], [0.4206082762979399, -1.29449916756183], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [2.886548090786142, 6.483293161548681], [-15.390003946253739, 17.092330985980066]], [[1.0, 0], [2.865684160819664, -3.182664692554112], [-3.0313254347619507, -28.841134965679927]], [[1.0, 0], [4.453698364574343, 4.946333140970575], [-3.2403823612972578, 30.830178756416473]], [[1.0, 0], [-1.7462743408511079, -2.4035404309301804], [-11.433628791873055, 35.189091102920685]], [[1.0, 0], [-0.29531356392565195, -2.809720875464012], [-40.10405163008603, 8.524379323528132]], [[1.0, 0], [-0.43474441152563514, 0.2509998030230109], [21.5, -37.239092362730865]], [[1.0, 0], [4.177287672020774, 3.7612467140830135], [4.912837773579713, 46.74252908230885]], [[1.0, 0], [-13.134505600237146, 4.26765956979846], [42.877900701872214, -31.152618371501077]], [[1.0, 0], [-0.19299020032277617, -1.8361791019643177], [-57.710708443294536, 12.266789758247802]], [[1.0, 0], [-1.1340275970436613, 10.789551859419664], [-59.66700364476215, -12.682613139883319]], [[1.0, 0], [-0.8998740591998848, 0.8102502422622901], [7.0034070389327825, -66.63296698967432]], [[1.0, 0], [3.6224343072913534, 11.148706432049442], [-57.440206600621266, 41.73275291276559]], [[1.0, 0], [-0.855883084320731, 1.178022003296159], [-22.558240589371163, -69.42712568954622]], [[1.0, 0], [2.691587201565939, -2.989310430813217], [-8.257748598144625, -78.56722973409359]], [[1.0, 0], [-0.15978309295310428, -0.751720350092769], [-75.82427298433588, 33.75914137529142]], [[1.0, 0], [13.869382961427148, 10.07669655866976], [27.502512499370322, 84.64402995026867]], [[1.0, 0], [-11.030733207290472, -9.932116791414824], [10.139260936962387, 96.46862385072251]], [[1.0, 0], [-2.5055492404534943, -4.3397385853310615], [-50.5, 87.4685657822283]], [[1.0, 0], [1.1899326841964706, -5.598193134323233], [-94.09518213718789, -41.89387423680742]], [[1.0, 0], [0, -3.877230837666954], [-107.0, 0]], [[1.0, 0], [-7.067380587332494, 5.134752558296562], [33.68285238686927, -103.66516027617173]], [[1.0, 0], [-0.7317611565112458, 0.07691119675224148], [110.53067888292004, -23.494021062406805]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-15e2-225.184-c1-0-17', '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/225/2/u/a/184/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.30984569585891714, 0.4008467665844995, 0.49444763166298733, 0.5914966264343573, 0.6911982784725057, 0.7909068664569694, 0.8860884218398363, 0.9704069705566372, 1.0359111716975773, 1.0733224113812063, 1.072439598235552, 1.0226767468117817, 0.9137400868700671, 0.736435755579287, 0.4835800693030807, 0.15096414352545973, -0.2616947908736847, -0.7498995776102511, -1.3037124958068689, -1.9073875714325887, -2.5393903331826873, -3.1728832770781232, -3.7767274303017415, -4.317011330622433, -4.759070280025428, -5.069904185972627, -5.220846387993253, -5.19028446511725, -4.966193721747784, -4.548221499892975, -3.9490615583059427, -3.194886759012415, -2.324666990328497, -1.388286220214914, -0.4434827675401545, 0.44823843599718655, 1.226445657284689, 1.836981035963787, 2.2370428405750964, 2.399623637684083, 2.316785640880071, 2.0013216018651625, 1.4864772206486085, 0.8235919911409318, 0.07773467492169128, -0.6783547862732131, -1.3714802872779415, -1.935640260961744, -2.319276483470321, -2.4912580822779957, -2.4448171328016395, -2.198837470728731, -1.7961768490163021, -1.2990475415885163, -0.7818530148553781, -0.3222312630273095, 0.008660742038836558, 0.1554175840782598, 0.08598594729121796, -0.20348602528193874, -0.687328574563942, -1.3129037351710582, -2.0068632865806326, -2.68441634438711, -3.2604487466495558, -3.6610093747330583, -3.8335466497897768, -3.7543765645819844, -3.4321945513815986, -2.906974399787017, -2.2442615571888127, -1.5255721472327342, -0.8362454566099774, -0.25256081953887727, 0.16986676450648436, 0.4045058636956164, 0.45766044359583535, 0.36676570424600585, 0.19330725360223971, 0.011353007727343198, -0.10651054351934502, -0.10349554548514155, 0.04934473787086971, 0.34563845335199483, 0.7424198884852903, 1.1657067807137727, 1.5224064073598742, 1.7168563450472794, 1.6693457218741703, 1.3333993568316975, 0.7085720030713274, -0.153958313006967, -1.1546401452294228, -2.157836474659812, -3.0117471443016055, -3.573087130416868, -3.7325629649048375, -3.436731165005952, -2.7021145223788396, -1.6184993187387062, -0.3400077810029615, 0.9354184236551659, 1.9954155316770268, 2.647033952977241, 2.7495101335540717, 2.240316137745389, 1.149666535291578, -0.39959847941606536, -2.207453871029332, -4.025525257734963, -5.594973635572655, -6.687328510904652, -7.14142426357541, -6.890042362124498, -5.971471175756416, -4.523717546996889, -2.7621108495477893, -0.9439934856095201, 0.6734566259956714, 1.8749307044855668, 2.5209106771455456, 2.5678792891463345, 2.0713901797876453, 1.1717316334774208, 0.06514672351926411, -1.0337545048865855, -1.931165130886882, -2.487423425330285, -2.6383848447084928, -2.401158501188665, -1.8637334836604127, -1.1612774435920497, -0.44454204254947377, 0.15269698797273992, 0.540220866947454, 0.6864934272183445, 0.6194963497570768, 0.4136836071750883, 0.16660130979062743, -0.02895259477455482, -0.11036779441321634, -0.06199752917528125, 0.08091934987834834, 0.24228413961397824, 0.32678426366288194, 0.24788094891368134, -0.044906815880630224, -0.5465875955632254, -1.1906967630799652, -1.8592044298364296, -2.4070113956560077, -2.6960076371611166, -2.6309666274783177, -2.188552005336808, -1.4317546676177846, -0.5050274060554566, 0.3903485509086813, 1.0364787012785674, 1.2465050684313401, 0.9092473692019218, 0.020396040828412135, -1.307748557997794, -2.86156539942357, -4.364500635534267, -5.531269588790057, -6.126634537418266, -6.015952688301679, -5.1959844423403405, -3.79844095933365, -2.064625598057749, -0.2960031044641354, 1.208865380005823, 2.2171892659589436, 2.610471268549929, 2.407486873457444, 1.756150393790701, 0.8957769287219864, 0.09816295988355192, -0.3989758755080024, -0.4506120321775062, -0.04103081483150529, 0.7106280138447202, 1.577810484154652, 2.281048478230072, 2.557008834119857, 2.2258296375818807, 1.240534160832872, -0.29375673276294423, -2.136143174951821, -3.958764090523738, -5.417294424060581, -6.226974325705367, -6.226482036521915, -5.414637940589925, -3.9512288330491057, -2.121683961328422, -0.27388886910812693, 1.257991037390822, 2.224805432979172, 2.5122931620748026, 2.1583391298245105, 1.3344507756354145, 0.2970168932270965, -0.6788454395319968, -1.366094543716821, -1.6367606102107344, -1.4851249409574383, -1.0184876881697724, -0.41937491474310973, 0.10968947655216905, 0.40350372655841854, 0.37817263831168146, 0.05035639327105491, -0.47259553205942856, -1.0279111293930343, -1.447392122077699, -1.607549045528377, -1.4654740462167855, -1.0702899932645613, -0.5471193194384624, -0.05849031537385904, 0.2453183624337382, 0.2721985059115809, 0.016584116284266846, -0.43849437988383866, -0.9467173984832061, -1.343976465883713, -1.5005906825405255, -1.364271244490675, -0.9800594213444661, -0.479877583475015, -0.04325481916277105, 0.16029907700609203, 0.030524404612798622, -0.4211458289530455, -1.0606004381144747, -1.6578714551682046, -1.947343063856801, -1.7066799283610639, -0.8330662564547769, 0.6057296707748057, 2.362695480656712, 4.052047375157833, 5.232437678275017, 5.514249502242231, 4.664398923657668, 2.680873405056263, -0.18453359167175276, -3.4645000927575316, -6.56928802242301, -8.91407627847511, -10.050307112367436, -9.768809159915822, -8.148759315717838, -5.539716737837442, -2.4806684553430003, 0.42408600901624127], 'positive_zeros': ['1.92356890356657319845940828488453', '4.31070147335546335465694067095893', '5.51272200313389578681075583710397', '6.99566177630040469075483100254965', '7.29804447822907667483583226651425', '9.193096281391135780152615906624379', '9.883939388669206011200790719621754', '10.22082766698625935005819284635513', '11.35451916193452297414136846584294', '12.53245340746900870178380830602759'], 'prelabel': '2-15e2-225.184-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.8092119989603255, 'root_number': '-0.8256865599203066 + 0.564129156104318*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.40460599948', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92356890356657319845940828488', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.31070147335546335465694067096', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.51272200313389578681075583710', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.184', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/u/a/184/8'], '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': '2-15e2-225.184-c1-0-17', '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': '2-15e2-225.184-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.40460599948016274, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92356890356657319845940828488', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2438413275186523634569656592849', 'Lhash_array': ['2438413275186523634569656592849'], 'label': '2-15e2-225.184-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/u/a/184/8'}