-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '842692406723434280315932937605,1553110097429069877242293588914', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -243, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 948.2515534652371, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 243]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, 243], [1, 0, -6250, 0, 9765625], [1, 0, -22082, 0, 282475249], [1, 0, 322102, 0, 25937424601], [1, -2404, 2187390, -892588372, 137858491849], [1, 0, -2839714, 0, 2015993900449], [1, 0, 2901574, 0, 6131066257801], [1, 0, 12872686, 0, 41426511213649], [1, 0, -41022298, 0, 420707233300201], [1, 0, -49326674, 0, 819628286980801], [1, 33100, 412590414, 2295284976700, 4808584372417849], [1, 0, -231712402, 0, 13422659310152401], [1, 0, 282780982, 0, 21611482313284249], [1, 0, 458690014, 0, 52599132235830049], [1, 0, -836390986, 0, 174887470365513049], [1, 0, 1429848598, 0, 511116753300641401], [1, -77252, 3181160478, -65246753444852, 713342911662882601], [1, 0, 1437442918, 0, 1822837804551761449], [1, 0, 3608458702, 0, 3255243551009881201], [1, -2900, 4148245686, -6011907619700, 4297625829703557649], [1, 0, -3959005298, 0, 9468276082626847201], [1, 0, 7878081286, 0, 15516041187205853449], [1, 0, -11168118898, 0, 31181719929966183601], [1, -268772, 35234277510, -2308036615554404, 73742412689492826049], [1, 0, -21020201002, 0, 110462212541120451001], [1, 0, 3332671486, 0, 134391637934412192049], [1, 0, 28051034614, 0, 196715135728956532249], [1, -228964, 43878607422, -3522894952097236, 236736367459211723401], [1, 0, -36848703586, 0, 339456738992222314849]], 'euler_factors_factorization': [[1], [[[1, 0, 243], 1]], [[[1, 0, -3125], 2]], [[[1, -236, 16807], 1], [[1, 236, 16807], 1]], [[[1, 0, 161051], 2]], [[[1, -1202, 371293], 2]], [[[1, 0, -1419857], 2]], [[[1, -1432, 2476099], 1], [[1, 1432, 2476099], 1]], [[[1, 0, 6436343], 2]], [[[1, 0, -20511149], 2]], [[[1, -10324, 28629151], 1], [[1, 10324, 28629151], 1]], [[[1, 16550, 69343957], 2]], [[[1, 0, -115856201], 2]], [[[1, -3352, 147008443], 1], [[1, 3352, 147008443], 1]], [[[1, 0, 229345007], 2]], [[[1, 0, -418195493], 2]], [[[1, 0, 714924299], 2]], [[[1, -38626, 844596301], 2]], [[[1, -35536, 1350125107], 1], [[1, 35536, 1350125107], 1]], [[[1, 0, 1804229351], 2]], [[[1, -1450, 2073071593], 2]], [[[1, -100564, 3077056399], 1], [[1, 100564, 3077056399], 1]], [[[1, 0, 3939040643], 2]], [[[1, 0, -5584059449], 2]], [[[1, -134386, 8587340257], 2]], [[[1, 0, -10510100501], 2]], [[[1, -140900, 11592740743], 1], [[1, 140900, 11592740743], 1]], [[[1, 0, 14025517307], 2]], [[[1, -114482, 15386239549], 2]], [[[1, 0, -18424351793], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 2, 'label': '4-192e2-1.1-c5e2-0-2', 'leading_term': '3.48661655583752503867227664919047838078958710961046743729048662138368408297780514704632589', '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/192/6/c/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03515625', 'prec': 34}, 'plot_values': [3.4866165558375246, 3.467884921381167, 3.4271376275287286, 3.354552093869175, 3.251920299586316, 3.1233768292453106, 2.9704594046648545, 2.794523871196834, 2.598040838441982, 2.3838759386030612, 2.154955335304525, 1.9143696155616132, 1.6654416008360087, 1.4116140083915651, 1.1564021451608086, 0.903339452952669, 0.6559466312984304, 0.4176682275363168, 0.19182801965996252, -0.01842289633943422, -0.21015427272886056, -0.38069888971974636, -0.5277032143354372, -0.6491564770785486, -0.743440150835374, -0.8093423835564861, -0.8461028790808219, -0.8534114907936329, -0.8314448837122068, -0.7808489801687772, -0.70276390879632, -0.5987909139936827, -0.471002428289691, -0.321895078626374, -0.15438230399316014, 0.02826386757300419, 0.2224393947289638, 0.4242740065387267, 0.6296776329711055, 0.8344092131188772, 1.0341423667190714, 1.2245320344091428, 1.401297368538169, 1.5602806504741236, 1.6975439265396608, 1.8094146513054288, 1.8925912060159154, 1.9441701419512625, 1.961754515970023, 1.943458483179243, 1.88801149322142, 1.7947373021958934, 1.6636466129760519, 1.4953892994107523, 1.291328143372661, 1.0534651050812067, 0.7844894749706612, 0.4876812570417934, 0.16692833628395015, -0.17338769427604486, -0.528408883170929, -0.8929252131666012, -1.2614276430069071, -1.628233337355606, -1.9875728812826579, -2.3337060780029137, -2.6610389930901217, -2.964219498241685, -3.2382770991366345, -3.478687818203692, -3.6815274494115173, -3.843496724033352, -3.9620769868420687, -4.035508865953581, -4.06293861619237, -4.044346616919131, -3.9806729572811133, -3.87369582098201, -3.7261263838760166, -3.5414412315653396, -3.3239392809094483, -3.0785364644635487, -2.8107810287167023, -2.5266224143189087, -2.232385654818327, -1.9345292805953604, -1.6395842594979864, -1.3539174857847847, -1.0836452998730286, -0.8344193988849122, -0.6113289336884149, -0.4187243212433428, -0.2601247375073782, -0.13809230344471585, -0.054163032115710136, -0.00877935503605247, -0.0012619252373184877, -0.029802784162300217, -0.09149273073509254, -0.1823711021224012, -0.2975187680633661, -0.43115414188003476, -0.576795558733955, -0.7273874496298934, -0.8755284465767019, -1.013607346282034, -1.1340854787069758, -1.2296197819950465, -1.2933806240910786, -1.319139465645872, -1.3015973269209207, -1.2364173528025717, -1.1205352954542647, -0.9521227450525986, -0.7308500081064461, -0.4577734415568931, -0.13552333293424756, 0.2318820204816913, 0.638945341988879, 1.0789371272065587, 1.543915111532927, 2.025010189158189, 2.5125592929395415, 2.996401290753468, 3.4661146099641957, 3.9112891880795173, 4.321848747493176, 4.688263781633223, 5.001928575954841, 5.255283229082407, 5.442208644889361, 5.558032730632482, 5.599903717485618, 5.566666437882419, 5.459176113276565, 5.280043979816586, 5.033860213321085, 4.726822709998697, 4.366848592154167, 3.963113942300854, 3.5260472445738853, 3.066819516013593, 2.597228480793018, 2.129186186666972, 1.6745177440976617, 1.2444958820015863, 0.8495906782260988, 0.499096903411917, 0.20087946505499552, -0.03887015201859919, -0.21584541845728866, -0.32771756328235524, -0.3742606215330945, -0.35729000266107935, -0.2806677556363692, -0.15010296940160542, 0.026980576865759526, 0.24174772750509363, 0.48422082803598077, 0.7436376164362758, 1.0088356483235947, 1.2686068705035185, 1.5121585527326094, 1.7294053677998895, 1.9114543138829825, 2.050781936219754, 2.1416841239387137, 2.180300520902445, 2.164971805944847, 2.0960937468790157, 1.9763349501899028, 1.8103268335498077, 1.6047129231062784, 1.3677050093414482, 1.1089587139525434, 0.8390467651093391, 0.5691815893208997, 0.3106707690263621, 0.0745320754321981, -0.12899870953943487, -0.2908954533197767, -0.4037164659699927, -0.46199907956774855, -0.46246727974977614, -0.40431734165322436, -0.2892320995025664, -0.12149329170694204, 0.09219496484152229, 0.342809287130467, 0.6193419766535273, 0.909131559094584, 1.1982975397479936, 1.4722762023425344, 1.7162781945446448, 1.9159743058596823, 2.057891839410449, 2.1301681481522343, 2.122807799558883, 2.028405404489636, 1.842204625249069, 1.5626894280095391, 1.1914158147599963, 0.7333832419196221, 0.1966464897753094, -0.40759449923024427, -1.0655573990233, -1.761093953546525, -2.4763491240798197, -3.1922662207256867, -3.889241450291345, -4.547858854052093, -5.149431305725088, -5.676872712678126, -6.115025465000888, -6.4515568920720305, -6.6769986650651685, -6.785550987078931, -6.774798398418126, -6.646319762690662, -6.40509182760009, -6.059833965789623, -5.622158585818826, -5.106622220258165, -4.529722796186762, -3.909676297203126, -3.26538802088248, -2.616018812752755, -1.9800656946138055, -1.374815879977974, -0.815659352520201, -0.3155463336207314, 0.11537827667727289, 0.47020112503086786, 0.74524213819642, 0.9402747839071115, 1.0581778869840757, 1.1049003346499398, 1.0888316552454862, 1.0205118152766044, 0.9118337006007995, 0.7755502134281133, 0.6244481335358626, 0.4707480840241057, 0.3253924891856542, 0.19746063200920774, 0.09369243508812848, 0.018044899237803388, -0.028468688995025738, -0.047975199678757005, -0.04556370835673338, -0.029171832635487123, -0.009106402661568085, 0.0023850260375894777, -0.008196634842407707, -0.05491779817231418, -0.15164213035111093, -0.31120749580723855, -0.5447173131935411, -0.8607360610181101, -1.2647702623928025, -1.75865458445738, -2.340310851107875, -3.0034810781693086, -3.7377940722394145, -4.52895666803047, -5.359090176800294, -6.2074230280248575, -7.050796299601702, -7.86482089099912, -8.6244051472194, -9.305261371091872, -9.884289126249328, -10.3412534697033, -10.658870260183548, -10.824443848813656, -10.829545116267445, -10.671396810071542, -10.352104465277803, -9.879614268267549, -9.266539684434811, -8.530584150360836, -7.693087148910081, -6.778890771344055, -5.814792669083048, -4.828926189056736, -3.849341076988734, -2.903044869837491, -2.0149275041178973, -1.2066622717041977, -0.4961465495468107, 0.10352596359365251, 0.5840129654739222, 0.9424950628305002, 1.1810132328612384, 1.3068612502603776, 1.3314135962539855, 1.2701016727079173, 1.1409165033548652, 0.9640241274993615, 0.760179195063403, 0.5501157369089987, 0.35311709084333365, 0.18637069576347753, 0.06390401882672425, -0.0038952047764511098, -0.0108422435610625, 0.04490132281207798, 0.16079976769191884, 0.3302390607021669, 0.5429627913932101, 0.7858169969185219, 1.0434865573077472, 1.2996003533987985, 1.5375463448404818, 1.7417650995354172, 1.8984085494023923, 1.9966002256013426, 2.0287380166912237, 1.9914953980301138, 1.885645785946377, 1.7166235707357733, 1.4938514393614566, 1.2307658452920534, 0.9437376209146731, 0.6515772915030882, 0.3742304223954776, 0.13189151576228933, -0.05629104394907408, -0.17327185059953581, -0.20515582173925345, -0.14215518217958917, 0.020799942135181233, 0.2834704836318646, 0.6402312577162944, 1.080051194140423, 1.586929220481722, 2.140544365881286, 2.71706733678111, 3.290446713163741, 3.8333674765077816, 4.3190081016453385, 4.72187262616946, 5.019750483479607, 5.194162518178767, 5.232203467906199, 5.12641419188041, 4.876198411258378, 4.487050252429184, 3.971311804183299, 3.346823481464796, 2.636913347699566, 1.8686687039849794, 1.0721972214117776, 0.27881289678382276, -0.480247882868637, -1.175396290277291, -1.7802301742591455, -2.2725620037402767, -2.635876126409805, -2.8596128307772166, -2.940230212537494, -2.8806844642339104, -2.6908729957708633, -2.3864100970871975, -1.9883662655458094, -1.5215808740796963, -1.0137696409017494, -0.49371077031990096, 0.010065977427356015, 0.4708577159944024, 0.8652096196204068, 1.1739470179292055, 1.3833723987536657, 1.4855584982544676, 1.4790354187177515, 1.3683131156083372, 1.163886571517092, 0.8811255993937762, 0.5395795085315507, 0.16151304574291916, -0.22934931937715852, -0.6092817336977736, -0.9561056302568218, -1.2502809215362234, -1.4764144594108892, -1.623701181164145, -1.6870716140833697, -1.6668423326864803, -1.5692711272880828, -1.4054507262996245, -1.1911872820494507, -0.9453388834073715, -0.689104313196857, -0.4441299376808828, -0.23145109944313233, -0.06973880376242496, 0.02576208229962571, 0.04451337313453989, -0.018617505808735724, -0.16276583364119349, -0.3810332683748552, -0.6606322035853811, -0.9836694973114631, -1.327892407363702, -1.6682622995208476, -1.9780165534986092, -2.2308119493520837, -2.4017333583798295, -2.469638337954827, -2.4177493275834974, -2.2357613474929625, -1.9197508947262438, -1.4736368301444691, -0.9083055604871002, -0.24213817189006231, 0.5005503501656883, 1.2900123186326833, 2.0930334537574007, 2.874337694962664, 3.5985553896542113, 4.232210780394888, 4.745258705669705, 5.113206598591225, 5.317859056235659, 5.3490987848793505, 5.20464108682051, 4.891078601053923, 4.422664743379726, 3.8213979828861775, 3.1150748906822243, 2.3364119179337637, 1.5207825989270574, 0.7045962838081092, -0.07678234530627555, -0.7910101377536406, -1.4101943480377803, -1.9127638356377892, -2.2839142789263125, -2.5169513170208475, -2.6126355760725697, -2.57971820037838, -2.433313420644211, -2.1945593936982406, -1.8883615867244923, -1.5423418470736845, -1.18443111768553, -0.8414598109456016, -0.5371002845637644, -0.29055334522827075, -0.11524352856245947, -0.01804247395036949, 0.0010735112037772174, -0.05104864886849614, -0.16132550838361315, -0.3114560332254403, -0.4791725941223386, -0.6400582971390092, -0.7690346991232049, -0.8426114188642102, -0.8401310960017124, -0.7459523114109732, -0.5500457238954165, -0.24959929261121191, 0.15125864692850668, 0.6408276921051705, 1.2009641831961917, 1.8076021171032148, 2.4324657035111485, 3.0446556014391013, 3.6124924550085042, 4.105831093557866, 4.497509507156797, 4.765883222746734, 4.895415387520345, 4.878877437174082, 4.716799505586885, 4.418875862341893, 4.002257429345451, 3.4919104737837268, 2.918009811469916, 2.315275605191413, 1.7199466816080335, 1.1683936187635997, 0.6942587596519183, 0.3268439699405332, 0.08896726571951923, -0.004302135490639377, 0.05330479452520667, 0.2588386330120559, 0.6002764306985725, 1.0572448915501498, 1.6021655171610734, 2.202128291840601, 2.820587193932587, 3.420099048579335, 3.963978223106976, 4.419388128366771, 4.758372851128599, 4.9606901447475416, 5.01379635647158, 4.9148596385253045, 4.669551268284431, 4.292905971667623, 3.807047369483441, 3.2407259755059106, 2.6265805812797614, 2.0000276621169646, 1.3959068018307348, 0.8456134762239375, 0.37687774557875564, 0.015327667141394812, -0.2243263809954826], 'positive_zeros': ['0.66476709479072142129475142476483', '1.22518783736578990330557901000752', '2.05652942633563333049894265028440', '3.35949394079718829127442004073126', '3.36950289415907175661937133932428', '4.09157782044275270518137119568047', '5.23191296068089890820530308937755', '5.47950722604040903197899933399489', '6.26996523397665687498222192206826', '6.55987681479371000024761533393432', '7.14856256120258757932112919023531', '8.111066823814208726958604509033338', '8.659706740944889884598262326530432', '8.846486679487611342418607639076897', '8.879290033560392649422035915079430', '10.18872131841901903748712317135195', '10.68415613373045265184274991948215', '10.73373892615096661357399166337055', '11.48423878379929271081370102813491', '11.63320948851240841647611729683375'], 'prelabel': '4-192e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.549206556264805, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e2-0', 'trace_hash': 2068665332431656894, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66476709479072142129475142476', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.22518783736578990330557901001', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.05652942633563333049894265028', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 948.2515534652371, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -243, 0, 0, 0, 2404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6250, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2900, 0, 0, 0, 0, 0, 0, 0, 59049, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 268772, 0, 0, 0], 'euler11': [1, 0, 322102, 0, 25937424601], 'euler13': [1, -2404, 2187390, -892588372, 137858491849], 'euler17': [1, 0, -2839714, 0, 2015993900449], 'euler19': [1, 0, 2901574, 0, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 12872686, 0, 41426511213649], 'euler29': [1, 0, -41022298, 0, 420707233300201], 'euler3': [1, 0, 243, 0, 0], 'euler31': [1, 0, -49326674, 0, 819628286980801], 'euler37': [1, 33100, 412590414, 2295284976700, 4808584372417849], 'euler41': [1, 0, -231712402, 0, 13422659310152401], 'euler43': [1, 0, 282780982, 0, 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, -77252, 3181160478, -65246753444852, 713342911662882601], 'euler67': [1, 0, 1437442918, 0, 1822837804551761449], 'euler7': [1, 0, -22082, 0, 282475249], 'euler71': [1, 0, 3608458702, 0, 3255243551009881201], 'euler73': [1, -2900, 4148245686, -6011907619700, 4297625829703557649], 'euler79': [1, 0, -3959005298, 0, 9468276082626847201], 'euler83': [1, 0, 7878081286, 0, 15516041187205853449], 'euler89': [1, 0, -11168118898, 0, 31181719929966183601], 'euler97': [1, -268772, 35234277510, -2308036615554404, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 243, 0, 0], [1, 0, -6250, 0, 9765625], [1, 0, -22082, 0, 282475249], [1, 0, 322102, 0, 25937424601], [1, -2404, 2187390, -892588372, 137858491849], [1, 0, -2839714, 0, 2015993900449], [1, 0, 2901574, 0, 6131066257801], [1, 0, 12872686, 0, 41426511213649], [1, 0, -41022298, 0, 420707233300201], [1, 0, -49326674, 0, 819628286980801], [1, 33100, 412590414, 2295284976700, 4808584372417849], [1, 0, -231712402, 0, 13422659310152401], [1, 0, 282780982, 0, 21611482313284249], [1, 0, 458690014, 0, 52599132235830049], [1, 0, -836390986, 0, 174887470365513049], [1, 0, 1429848598, 0, 511116753300641401], [1, -77252, 3181160478, -65246753444852, 713342911662882601], [1, 0, 1437442918, 0, 1822837804551761449], [1, 0, 3608458702, 0, 3255243551009881201], [1, -2900, 4148245686, -6011907619700, 4297625829703557649], [1, 0, -3959005298, 0, 9468276082626847201], [1, 0, 7878081286, 0, 15516041187205853449], [1, 0, -11168118898, 0, 31181719929966183601], [1, -268772, 35234277510, -2308036615554404, 73742412689492826049]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/6/c/b'], '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': '4-192e2-1.1-c5e2-0-2', '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': '4-192e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.549206556264805, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 2068665332431656894, 'z1': {'__RealLiteral__': 0, 'data': '0.66476709479072142129475142476', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '842692406723434280315932937605,1553110097429069877242293588914', 'Lhash_array': ['842692406723434280315932937605', '1553110097429069877242293588914'], 'label': '4-192e2-1.1-c5e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/6/c/b'}