-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '777315534292912285246254340658,2360921445786251147084481909900', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 64, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -243, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 555.8476513354576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 243]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.1', 'coefficient_field': '1.1.1.1', 'conductor': 21609, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, 0, -64, 0, 1024], [1, 0, 243], [1, 0, 6250, 0, 9765625], [1], [1, 0, -322102, 0, 25937424601], [1, 0, 560257, 0, 137858491849], [1, 0, 2839714, 0, 2015993900449], [1, 0, -4926251, 0, 6131066257801], [1, 0, -12872686, 0, 41426511213649], [1, 0, -41022298, 0, 420707233300201], [1, 0, 49843573, 0, 819628286980801], [1, -13322, 183056835, -923800195154, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, 44950, 799142511, 6608029512850, 21611482313284249], [1, 0, 458690014, 0, 52599132235830049], [1, 0, -836390986, 0, 174887470365513049], [1, 0, 1429848598, 0, 511116753300641401], [1, 0, 197224726, 0, 713342911662882601], [1, 75878, 4139617935, 102444792868946, 1822837804551761449], [1, 0, -3608458702, 0, 3255243551009881201], [1, 0, -1957684943, 0, 4297625829703557649], [1, -181714, 14409107247, -559144226487886, 9468276082626847201], [1, 0, 7878081286, 0, 15516041187205853449], [1, 0, 11168118898, 0, 31181719929966183601], [1, 0, -884916482, 0, 73742412689492826049], [1, 0, 21020201002, 0, 110462212541120451001], [1, 0, -21537040043, 0, 134391637934412192049], [1, 0, -28051034614, 0, 196715135728956532249], [1, -495686, 92198631747, -7626743537085614, 236736367459211723401], [1, 0, -36848703586, 0, 339456738992222314849]], 'euler_factors_factorization': [[[[1, 0, -32], 2]], [[[1, 0, 243], 1]], [[[1, 0, 3125], 2]], [1], [[[1, 0, -161051], 2]], [[[1, -427, 371293], 1], [[1, 427, 371293], 1]], [[[1, 0, 1419857], 2]], [[[1, -3143, 2476099], 1], [[1, 3143, 2476099], 1]], [[[1, 0, -6436343], 2]], [[[1, 0, -20511149], 2]], [[[1, -2723, 28629151], 1], [[1, 2723, 28629151], 1]], [[[1, -6661, 69343957], 2]], [[[1, 0, 115856201], 2]], [[[1, 22475, 147008443], 2]], [[[1, 0, 229345007], 2]], [[[1, 0, -418195493], 2]], [[[1, 0, 714924299], 2]], [[[1, -38626, 844596301], 1], [[1, 38626, 844596301], 1]], [[[1, 37939, 1350125107], 2]], [[[1, 0, -1804229351], 2]], [[[1, -78127, 2073071593], 1], [[1, 78127, 2073071593], 1]], [[[1, -90857, 3077056399], 2]], [[[1, 0, 3939040643], 2]], [[[1, 0, 5584059449], 2]], [[[1, -134386, 8587340257], 1], [[1, 134386, 8587340257], 1]], [[[1, 0, 10510100501], 2]], [[[1, -211477, 11592740743], 1], [[1, 211477, 11592740743], 1]], [[[1, 0, -14025517307], 2]], [[[1, -247843, 15386239549], 2]], [[[1, 0, -18424351793], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 4, 'label': '4-147e2-1.1-c5e2-0-4', 'leading_term': '3.79059081963801108847024390255363406619936123514156595595115551599463917312535724868024576', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/147/6/c/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.037109375', 'prec': 37}, 'plot_values': [3.790590819638011, 3.7705580092897875, 3.719242360954133, 3.6311024442774924, 3.5078721553168557, 3.3524126631540034, 3.1661486194270774, 2.950748992869819, 2.7086651287316355, 2.4426277164560286, 2.155524633727389, 1.850480056621584, 1.5308459600283684, 1.2001240079544835, 0.8619338154521963, 0.5199690305055475, 0.17796366580755804, -0.16036466107697214, -0.4913480701473103, -0.8114249751224585, -1.1171726742366206, -1.4053631474216235, -1.672993929262975, -1.9173379102173513, -2.135973389770984, -2.326822458636651, -2.488181223246468, -2.6187412409555657, -2.7176207872391984, -2.78436473510134, -2.8189769144007113, -2.821895573852461, -2.794025635940614, -2.7366893147192077, -2.6516555953664143, -2.5410683939652956, -2.4074692494215015, -2.2537081732337434, -2.0829547635990915, -1.8985990059211468, -1.7042464617626858, -1.5036168489179886, -1.3005213383766967, -1.0987655289270297, -0.9021103508994422, -0.7141842281145744, -0.5384324382515562, -0.37804155202560663, -0.2358846461339628, -0.11445989345673716, -0.015840320599221216, 0.05837212192722757, 0.10708373994080028, 0.12973813154825115, 0.12633335883116734, 0.09743225787076505, 0.044155230534421844, -0.031830209015986134, -0.12834255734287867, -0.24271877590636468, -0.37187265908146905, -0.512348218547604, -0.6604013879947498, -0.8120698258901552, -0.9632753939307863, -1.109902166137129, -1.2479164921112078, -1.3734420290547684, -1.4828930664633357, -1.573034062627077, -1.6411199121899165, -1.6849283885302484, -1.7028981650407229, -1.6941258906282177, -1.6584894776485208, -1.596606707454928, -1.5099288141339084, -1.4006627652838852, -1.2718207163535873, -1.1271115336453228, -0.9709358648410427, -0.8082540913090471, -0.6445237018684129, -0.4855511976644332, -0.3373769197321215, -0.20611812904114798, -0.09781488339562117, -0.01827132415600707, 0.027116989532947874, 0.03351604420248785, -0.0031796881265053227, -0.08620896912020898, -0.2178070727200205, -0.3990929319491379, -0.6299840211495321, -0.9091205389782574, -1.2338483990827824, -1.6001899391643684, -2.0029066920639043, -2.435520160079284, -2.890461741377673, -3.3591381790946917, -3.8321717802243183, -4.299495148555979, -4.750679788213852, -5.175036063429315, -5.562021583521677, -5.901317338285415, -6.183298539132112, -6.399058212055174, -6.540912935362939, -6.6023511228751754, -6.578536367937574, -6.466167149729121, -6.263935296396131, -5.972293443362841, -5.593828161729764, -5.132939611736135, -4.596098260499893, -3.9914475886456056, -3.328928410889234, -2.6198207425135154, -1.8767375891058524, -1.113127177432649, -0.34315504127139806, 0.4188062981194745, 1.1583755071619635, 1.861651344075032, 2.5154536902459785, 3.1077502795101277, 3.6279039300007887, 4.066992885372762, 4.418032139760291, 4.6761476061536325, 4.838744313774783, 4.905508691638241, 4.8785008168891615, 4.761980968108561, 4.562407922167916, 4.28811133872508, 3.9491850724167548, 3.5570503423111917, 3.1242438527887937, 2.6639325693646323, 2.18961184919792, 1.71463698418108, 1.2518653992184818, 0.8132619401171174, 0.40953739929829963, 0.049867813701189596, -0.2584088773967529, -0.5099373799360566, -0.7015328842188067, -0.8321832010905599, -0.9030819072255095, -0.9174947317146309, -0.8806267230037416, -0.7993702295621041, -0.6820259807111289, -0.5379599399494707, -0.3772253259623177, -0.2101659228522289, -0.04700297842309533, 0.10256710187659751, 0.2297536484399407, 0.3270237847091455, 0.38839301344367627, 0.409670507103139, 0.3886177576561897, 0.3250429599058808, 0.22080352276625292, 0.07973156022750481, -0.09252768328007321, -0.28874279711824913, -0.5004139198584221, -0.7181018510216971, -0.9318769118719614, -1.1316757375752513, -1.307837489772772, -1.4514061901432393, -1.5546915896763551, -1.6114459305235238, -1.6173722336407326, -1.5701304515437733, -1.4697130736549053, -1.3182671123665632, -1.1202739211345376, -0.882200492662561, -0.6124566339763297, -0.3209093742616837, -0.018637115015610377, 0.2826443154329092, 0.5709664103035557, 0.8347105876450766, 1.0630370819199255, 1.2464476700198055, 1.3771554098925498, 1.4495335499654098, 1.4603381126899886, 1.408971214637252, 1.2975019318878214, 1.1306884349084274, 0.9157818836299527, 0.6622885292813874, 0.38157368102223554, 0.086399604454317, -0.20963158984791308, -0.49267066184353275, -0.7492853599310875, -0.9670472314221121, -1.1352361584136554, -1.2452710053372844, -1.2913762354820217, -1.2707285430637791, -1.1839979466792472, -1.0351380019810248, -0.8317125874496956, -0.5843328110024802, -0.30669555310515, -0.014745077896841218, 0.27361075863284506, 0.5394866275997776, 0.7635905373162257, 0.927218282850326, 1.012996943194918, 1.0057627926286388, 0.8933027467496086, 0.6670197645624473, 0.3224752151940342, -0.14021940337876979, -0.7162324316020275, -1.395919041234433, -2.165132006333721, -3.0054151453036457, -3.8948143645397133, -4.808304366952449, -5.719029898067491, -6.598866356374946, -7.41995353757679, -8.155244386755776, -8.780158685224494, -9.272943841279465, -9.616270463473697, -9.797233088265902, -9.80872547082164, -9.648956393776645, -9.32247342180283, -8.839154505474148, -8.214791796653312, -7.4696256762790565, -6.6284544535424965, -5.718877575949009, -4.770961856867673, -3.8154285232798424, -2.882977637899482, -2.002670576145523, -1.201081527496009, -0.5010888059734064, 0.07893214874526724, 0.5257727475467054, 0.8319422510877431, 0.9957416885368631, 1.0213985029067711, 0.918591420587816, 0.7021045861236989, 0.39091733733595657, 0.007426266832079373, -0.42373080143491665, -0.8767378185916473, -1.3258374470624892, -1.746473332213962, -2.11637023239312, -2.416543815697535, -2.6320218375193116, -2.7525513092537035, -2.7728123878004616, -2.6927203719662383, -2.5170788202783996, -2.255447649796198, -1.921299980412286, -1.5314984119079489, -1.105131048730202, -0.6626997858294895, -0.2248844844022031, 0.1884050454832174, 0.5590730423661565, 0.8717424490191058, 1.1143923802557585, 1.27903945844098, 1.3618528215671737, 1.3634671325261274, 1.2885790548941962, 1.1458201073579317, 0.9469457424342617, 0.7062990267197536, 0.4397742452462705, 0.16400815293205112, -0.10467146962279293, -0.3511152687387798, -0.5622185470969652, -0.7276205506494119, -0.8402271405930922, -0.8965531195079325, -0.8968093067890227, -0.8447958425789602, -0.7475448415151892, -0.614789985397217, -0.45824660987054383, -0.290789177802749, -0.12553497197694571, 0.02507177529152217, 0.15014774020451435, 0.2411641356071408, 0.2925731255834751, 0.30229001228893526, 0.27188222426213354, 0.20660985696976805, 0.11511345084104982, 0.008966487682422038, -0.09806563234876028, -0.19090759692919476, -0.2541519493029598, -0.27321916231650695, -0.23531249533339324, -0.13061426419737732, 0.04704010769246813, 0.29921256660317336, 0.6226634660949696, 1.0089018230241111, 1.4445568430819031, 1.9115703062177156, 2.3881268203382158, 2.8494622284376447, 3.2692403442547455, 3.6207741995628684, 3.8786507773544536, 4.020032709981038, 4.026266721939972, 3.8838956511403726, 3.58595137520551, 3.132374701877515, 2.5307064376814656, 1.7957629858586979, 0.9495196014477111, 0.02006893666666519, -0.959349142974739, -1.9519349709198082, -2.9189707768207187, -3.821711240006383, -4.623287929900974, -5.2906447519344635, -5.796160830577182, -6.119386010440684, -6.247851678785202, -6.178390373573478, -5.916774306529345, -5.478447161977307, -4.88691320312548, -4.173778669183475, -3.376128473457456, -2.535880679212285, -1.6966389504755284, -0.9025067003201268, -0.19501486586332803, 0.38829534775477464, 0.8163316004855982, 1.0656549554888182, 1.121982354324264, 0.9807109446282795, 0.6473537892683422, 0.1370463725550574, -0.5259825524487171, -1.31000904744336, -2.177044916552185, -3.0853340988433735, -3.9909206925635656, -4.850595771461636, -5.623394001704481, -6.273428645528095, -6.770920116801805, -7.09440177894854, -7.230955421550208, -7.177448106488506, -6.939795186327528, -6.533124728164729, -5.980106430963168, -5.310163940953895, -4.557147735526322, -3.7578889439652343, -2.949681092209574, -2.1685727910857966, -1.447192461820725, -0.8132053282388391, -0.28793721163658875, 0.11462627886454838, 0.38816703854934753, 0.5342347662552895, 0.5615468439709641, 0.48531095569506283, 0.32577018442549505, 0.10678846903652599, -0.14592935570262208, -0.4066435491128269, -0.6512226740407168, -0.8588696012060336, -1.0132446970923519, -1.1036463875409939, -1.1253832576838472, -1.08009036594231, -0.9753033636249696, -0.8238385317259994, -0.6427012185746938, -0.45172830199500524, -0.2721077209395764, -0.12469234297933247, -0.02849288478291228, 0.0008402678939337709, -0.04781794852100523, -0.1801602399418015, -0.3959061574475937, -0.6887860609547357, -1.0467284372039702, -1.4528002738762174, -1.8859953730708818, -2.322983666241576, -2.7391622383194094, -3.11089365265088, -3.4163658326393147, -3.6378958190680373, -3.7621717334927633, -3.782182757223025, -3.6965848715495317, -3.5108986889377953, -3.2359995102643055, -2.888394762338592, -2.4881042286995476, -2.0580608480411806, -1.6218315828673326, -1.2024270978425309, -0.8203667845030981, -0.4923535818417428, -0.23011069523791391, -0.03941107161380483, 0.08006457007241072, 0.13497430626129825, 0.13742529940028808, 0.10436201575237271, 0.05588632420727742, 0.01392490834578189, 0.00021221488344466032, 0.03459699353332027, 0.133258944050719, 0.3071244266155022, 0.5608655659648378, 0.891874219715437, 1.2904089762166222, 1.7394439496411929, 2.216014122015361, 2.6920469175295407, 3.1365954516649053, 3.5175166630007433, 3.8039907156537636, 3.968674976790351, 3.9897885068367986, 3.8531974242474183, 3.553444534870182, 3.0951617302604344, 2.4927185801190572, 1.7704561363788975, 0.9610160262180528, 0.10415571658935212, -0.7558217082857852, -1.5725004260931232, -2.3002176036770154, -2.8971845956425644, -3.3278828949460757, -3.565995086413936, -3.5961059234347887, -3.415547441494132, -3.033837564638451, -2.473601633074389, -1.7707277301707611, -0.9703396982153439, -0.1229138495442532, 0.7100791059421244, 1.475344190170726], 'positive_zeros': ['0.61319383602466123003363729960704', '1.86243862887864202761484032071924', '2.10094004331203923642477091920865', '3.24023912076418603559457399213821', '3.33781404314844089602731556852174', '4.61818483850676143900332679746313', '5.53488486678782408201045875137341', '6.02292028923262869382215871362706', '6.36362963533110108365532922463432', '7.05305830452699616447645318448149', '7.61818635230342723819810588003441', '8.128821895189613885053504448727957', '8.487735949416690918645448220058455', '9.568641317143513811998128737776818', '9.871762248068828598134417346377257', '10.52176348900673877468694182112004', '11.00677069816009224198216718914180', '11.49734065026930261320698469912410', '11.80383264807515841549356492127561', '12.05209667589065974776508992130437'], 'prelabel': '4-147e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e2-0', 'trace_hash': 1645336253694917396, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61319383602466123003363729961', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86243862887864202761484032072', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.10094004331203923642477091921', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 555.8476513354576, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 21609, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 64, 0, 0, 0, 0, -243, 0, 0, 0, 0, 0, 0, 3072, 0, 0, 0, 0, 0, 0, 0, 0, -6250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15552, 13322, 0, 0, 0, 0, 0, -44950, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131072, 0, 0, -75878, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 181714, 0, 59049, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -400000], 'euler11': [1, 0, -322102, 0, 25937424601], 'euler13': [1, 0, 560257, 0, 137858491849], 'euler17': [1, 0, 2839714, 0, 2015993900449], 'euler19': [1, 0, -4926251, 0, 6131066257801], 'euler2': [1, 0, -64, 0, 1024], 'euler23': [1, 0, -12872686, 0, 41426511213649], 'euler29': [1, 0, -41022298, 0, 420707233300201], 'euler3': [1, 0, 243, 0, 0], 'euler31': [1, 0, 49843573, 0, 819628286980801], 'euler37': [1, -13322, 183056835, -923800195154, 4808584372417849], 'euler41': [1, 0, 231712402, 0, 13422659310152401], 'euler43': [1, 44950, 799142511, 6608029512850, 21611482313284249], 'euler47': [1, 0, 458690014, 0, 52599132235830049], 'euler5': [1, 0, 6250, 0, 9765625], 'euler53': [1, 0, -836390986, 0, 174887470365513049], 'euler59': [1, 0, 1429848598, 0, 511116753300641401], 'euler61': [1, 0, 197224726, 0, 713342911662882601], 'euler67': [1, 75878, 4139617935, 102444792868946, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -3608458702, 0, 3255243551009881201], 'euler73': [1, 0, -1957684943, 0, 4297625829703557649], 'euler79': [1, -181714, 14409107247, -559144226487886, 9468276082626847201], 'euler83': [1, 0, 7878081286, 0, 15516041187205853449], 'euler89': [1, 0, 11168118898, 0, 31181719929966183601], 'euler97': [1, 0, -884916482, 0, 73742412689492826049], 'euler_factors': [[1, 0, -64, 0, 1024], [1, 0, 243, 0, 0], [1, 0, 6250, 0, 9765625], [1, 0, 0, 0, 0], [1, 0, -322102, 0, 25937424601], [1, 0, 560257, 0, 137858491849], [1, 0, 2839714, 0, 2015993900449], [1, 0, -4926251, 0, 6131066257801], [1, 0, -12872686, 0, 41426511213649], [1, 0, -41022298, 0, 420707233300201], [1, 0, 49843573, 0, 819628286980801], [1, -13322, 183056835, -923800195154, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, 44950, 799142511, 6608029512850, 21611482313284249], [1, 0, 458690014, 0, 52599132235830049], [1, 0, -836390986, 0, 174887470365513049], [1, 0, 1429848598, 0, 511116753300641401], [1, 0, 197224726, 0, 713342911662882601], [1, 75878, 4139617935, 102444792868946, 1822837804551761449], [1, 0, -3608458702, 0, 3255243551009881201], [1, 0, -1957684943, 0, 4297625829703557649], [1, -181714, 14409107247, -559144226487886, 9468276082626847201], [1, 0, 7878081286, 0, 15516041187205853449], [1, 0, 11168118898, 0, 31181719929966183601], [1, 0, -884916482, 0, 73742412689492826049]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/c/a'], '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': '4-147e2-1.1-c5e2-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-147e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 1645336253694917396, 'z1': {'__RealLiteral__': 0, 'data': '0.61319383602466123003363729961', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '777315534292912285246254340658,2360921445786251147084481909900', 'Lhash_array': ['777315534292912285246254340658', '2360921445786251147084481909900'], 'label': '4-147e2-1.1-c5e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/c/a'}