-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1654675149291945510831817355838,2381360768428173315577679825368', 'a10': 0, 'a2': 0, 'a3': 16, 'a4': 15, 'a5': 0, 'a6': 0, 'a7': 28, 'a8': 0, 'a9': 138, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 628.7963350437966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [17, [1, 136, 4913]]], 'bad_primes': [5, 17], 'central_character': '425.1', 'coefficient_field': '1.1.1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'euler_factors': [[1, 0, -15, 0, 64], [1, -16, 118, -432, 729], [1], [1, -28, 882, -9604, 117649], [1, 0, -2262, 0, 1771561], [1, 0, -1030, 0, 4826809], [1, 136, 4913], [1, 160, 20118, 1097440, 47045881], [1, -236, 38258, -2871412, 148035889], [1, 0, -32902, 0, 594823321], [1, 0, -54682, 0, 887503681], [1, -268, 119262, -13575004, 2565726409], [1, 0, -127842, 0, 4750104241], [1, 0, -85030, 0, 6321363049], [1, 0, 7650, 0, 10779215329], [1, 0, 114410, 0, 22164361129], [1, -360, 443158, -73936440, 42180533641], [1, 0, -441862, 0, 51520374361], [1, 0, 252250, 0, 90458382169], [1, 0, -707722, 0, 128100283921], [1, -1656, 1463618, -644212152, 151334226289], [1, 0, 793478, 0, 243087455521], [1, 0, -838870, 0, 326940373369], [1, 2980, 3630038, 2100807620, 496981290961], [1, 2752, 3718722, 2511676096, 832972004929], [1, -1284, 2472766, -1322906484, 1061520150601], [1, 0, -627950, 0, 1194052296529], [1, -1128, 2768182, -1381848504, 1500730351849], [1, 0, -1116262, 0, 1677100110841], [1, -2776, 4812338, -4005482072, 2081951752609]], 'euler_factors_factorization': [[[[1, 0, -15, 0, 64], 1]], [[[1, -8, 27], 2]], [1], [[[1, -14, 343], 2]], [[[1, 0, -2262, 0, 1771561], 1]], [[[1, 0, -1030, 0, 4826809], 1]], [[[1, 136, 4913], 1]], [[[1, 80, 6859], 2]], [[[1, -118, 12167], 2]], [[[1, 0, -32902, 0, 594823321], 1]], [[[1, 0, -54682, 0, 887503681], 1]], [[[1, -134, 50653], 2]], [[[1, 0, -127842, 0, 4750104241], 1]], [[[1, 0, -85030, 0, 6321363049], 1]], [[[1, 0, 7650, 0, 10779215329], 1]], [[[1, 0, 114410, 0, 22164361129], 1]], [[[1, -180, 205379], 2]], [[[1, 0, -441862, 0, 51520374361], 1]], [[[1, 0, 252250, 0, 90458382169], 1]], [[[1, 0, -707722, 0, 128100283921], 1]], [[[1, -828, 389017], 2]], [[[1, 0, 793478, 0, 243087455521], 1]], [[[1, 0, -838870, 0, 326940373369], 1]], [[[1, 1490, 704969], 2]], [[[1, 1376, 912673], 2]], [[[1, -642, 1030301], 2]], [[[1, 0, -627950, 0, 1194052296529], 1]], [[[1, -564, 1225043], 2]], [[[1, 0, -1116262, 0, 1677100110841], 1]], [[[1, -1388, 1442897], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 4, 'label': '4-425e2-1.1-c3e2-0-4', 'leading_term': '19.0494136943862642704775497673182192528216978963050289852358633070263751293115700597842722', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/425/4/c/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [19.049413694386267, 19.01804450929556, 18.955399522831296, 18.84038490502901, 18.675124767514706, 18.466098261556922, 18.213875886700464, 17.9181326753492, 17.580405394037268, 17.202706649546396, 16.78683708015967, 16.334699442025087, 15.848519372180162, 15.330701940864362, 14.783814827271085, 14.210558855844276, 13.613812980657515, 12.996568093791538, 12.361954760038719, 11.713180513280495, 11.053559585098572, 10.386444411650908, 9.715251097660142, 9.043389348738774, 8.374284060631114, 7.711304910932681, 7.057782997209597, 6.416942516796882, 5.791912119938204, 5.185661089076216, 4.6010053673335145, 4.040550771500109, 3.506694137436761, 3.0015759900669963, 2.5270777078018707, 2.0847858056326674, 1.6759864565569431, 1.3016430959544898, 0.9623899913034153, 0.6585242636269716, 0.39000042470400986, 0.15643715714032844, -0.042885198229597306, -0.20900361992488806, -0.34327011316341804, -0.4473178718495132, -0.5230526554285554, -0.5726084629061932, -0.5983315778393433, -0.6027289032153051, -0.5884443618440913, -0.5582037091936406, -0.5147837793478828, -0.46095803763259435, -0.39946000977300616, -0.33293399611634505, -0.26389482920796364, -0.19468800176928877, -0.1274485731149821, -0.06407444202209778, -0.006187673395235724, 0.04487621826385768, 0.08810110486376625, 0.12278325531547994, 0.14855513653116048, 0.16536042498234602, 0.17346618790627125, 0.17342113227528827, 0.16605457676542854, 0.1524207010813286, 0.13378404141244243, 0.11155387979249096, 0.08725754378094847, 0.06247015206404277, 0.038778630819748756, 0.017712669054327314, 0.0007039059704188455, -0.010975963711333471, -0.01625511507280129, -0.014310928846410984, -0.0046025180458748385, 0.013096743953532036, 0.038680773216262905, 0.0716975717800811, 0.11135095575280907, 0.1565070153515063, 0.20572076079766033, 0.257260153150876, 0.3091602999407754, 0.35926052463357, 0.4052860265642231, 0.4448912885486284, 0.47576601665229185, 0.49567657297600914, 0.5025898382273386, 0.4947035582132552, 0.47057888953205185, 0.4291507612888579, 0.36985765502094975, 0.2926244123870553, 0.19797662488799142, 0.08699075006195023, -0.03861936580403432, -0.1765868136479934, -0.32404379915466225, -0.47763810252245414, -0.6335316327558076, -0.787542384583656, -0.9351925402553607, -1.0718651809006352, -1.1928996037024453, -1.2937486933286837, -1.3701131471058483, -1.4180833282731087, -1.4342983020068925, -1.4160556046345218, -1.361476118127219, -1.2695667766021537, -1.140369066318191, -0.9749633257135043, -0.7755776723334569, -0.545528064818194, -0.28926615664407374, -0.012256251600272515, 0.27905487593487255, 0.5774152502454368, 0.8748856585264804, 1.1630545760438793, 1.4332443126989711, 1.6767403562768017, 1.8850754629417474, 2.050245482423968, 2.165050369367927, 2.2232666560219827, 2.220014730008155, 2.1518596063043027, 2.017166667095056, 1.8161074886718567, 1.5509627618065758, 1.2260184571565824, 0.8477757277298821, 0.42473399849822935, -0.032526269071481935, -0.511663982256405, -0.9986449644673216, -1.4781430134212334, -1.933765862291522, -2.348502155341711, -2.7050960606064614, -2.9864965553654477, -3.176352099247273, -3.259414235454813, -3.222106085007123, -3.052833432154304, -2.7425665618115507, -2.285019187500655, -1.6771743654046438, -0.9193046050635346, -0.015370830780042975, 1.0271252098354458, 2.196933836896423, 3.479360766541238, 4.856302753781609, 6.306673058256208, 7.806709855769873, 9.33047045305886, 10.850416638397393, 12.337908973046606, 13.764045124955665, 15.100077134790114, 16.31845154244, 17.393072651651384, 18.300470209805678, 19.01984114848405, 19.5342547135837, 19.83042359352219, 19.899850019527157, 19.73830308984337, 19.346813721862933, 18.730865744699212, 17.901162658046562, 16.872572275253887, 15.66461264213211, 14.300219802173807, 12.805931306990226, 11.210570208177927, 9.545138723521086, 7.8415255377254915, 6.132155197040717, 4.448827937983148, 2.822198069678697, 1.2808449453830504, -0.1493276952285693, -1.445713647699562, -2.589584812569123, -3.566362448142947, -4.3660840397469105, -4.983318794539764, -5.417444814164376, -5.6722436420495725, -5.755939221147265, -5.680542603329555, -5.461637857481649, -5.1175760086349, -4.669028350542414, -4.138144510388128, -3.5479255974415063, -2.9214627169086684, -2.281206521724907, -1.6483891515752425, -1.0422795775048628, -0.47986546358615767, 0.024816665229865798, 0.46069925136779455, 0.8202031702148183, 1.0989556894717876, 1.2961086219567162, 1.4137967462593124, 1.4572356850091583, 1.4339944682845278, 1.3538886519537414, 1.2281628068522477, 1.069226024872496, 0.8898478653596651, 0.7028072383167515, 0.5201977415481388, 0.3530731918821248, 0.21093665301871098, 0.10146464595072986, 0.030221955098681138, 0.0005319902727695897, 0.013421771594964663, 0.06768041595836052, 0.16000151653237293, 0.28523949634969453, 0.4366858299862885, 0.6064994252056172, 0.7860336817206622, 0.9663877996997156, 1.1386966041363675, 1.2947297426584934, 1.4270662318497658, 1.5296613640145849, 1.597851242158542, 1.6288141583419034, 1.621382907575899, 1.5763472654052377, 1.496087932375769, 1.3846960467452332, 1.2474758741410816, 1.090890804637158, 0.922006456218753, 0.7483042165022836, 0.5771478339651844, 0.41552937751432173, 0.2696384960729765, 0.14461708543552304, 0.044291783286361075, -0.028989755031719643, -0.07443261998958314, -0.09282173959397837, -0.0864074584902137, -0.0587702565785479, -0.014559083763612457, 0.040796740377644664, 0.1014275162711184, 0.1614200055968023, 0.21515175929300723, 0.25772581359424657, 0.2852164382750374, 0.2950574929131046, 0.2861341126364352, 0.2590441683523153, 0.216001289399021, 0.16090976899482945, 0.09908300000657123, 0.037107255982773604, -0.017581333666473874, -0.057025476175008354, -0.07323649244554158, -0.05865354637866301, -0.006608111091420115, 0.08818291681195456, 0.22926895040064033, 0.4180539435238744, 0.6536346443422385, 0.932582890719877, 1.249003689158499, 1.594599495505939, 1.9589343677423974, 2.3298241259420434, 2.693744559758499, 3.0365351277581625, 3.343849393916861, 3.602101400460067, 3.798833830358319, 3.9237864708705086, 3.969057942357893, 3.930144996535663, 3.8057987808976135, 3.59887942471021, 3.3158547256370468, 2.967339396085495, 2.5672452549225517, 2.132926096312034, 1.6840530716754663, 1.242356606472743, 0.830356313354109, 0.4707687973534896, 0.18525662282592223, -0.006358836985340829, -0.08715854788721591, -0.04391919220538869, 0.13216042126552555, 0.4448666996352551, 0.8926687661437623, 1.468514964267674, 2.159966561109139, 2.9495178448981587, 3.815093434322431, 4.730944854340571, 5.668361598046982, 6.597101579548569, 7.4861117245956015, 8.305357228769859, 9.026327865350142, 9.62405878676034, 10.077219970817495, 10.3700836853061, 10.4920551961415, 10.439347396450216, 10.213902136734825, 9.824581546390739, 9.28553585455891, 8.61680595357974, 7.842296327655919, 6.989789548211514, 6.088762548048844, 5.169921426720576, 4.263139792124318, 3.396710800549158, 2.5956782355377226, 1.8810542829267112, 1.2687567801781796, 0.7690444806861535, 0.38617614711615794, 0.11826764694314926, -0.042332971680645703, -0.10865274651459288, -0.09813194005418212, -0.03169911266277874, 0.06754637322723515, 0.1756665098237672, 0.2692659975329514, 0.3270052134158869, 0.33074703474569817, 0.2669643010796367, 0.12740377851788448, -0.08990229268071374, -0.3806049999528384, -0.7336579556804992, -1.1319400532117103, -1.5526327839325078, -1.9683837703381306, -2.3484286774940766, -2.6600689454901487, -2.8703763393323567, -2.947689234727143, -2.8636105020959346, -2.5942173135082283, -2.121982575881602, -1.4364474867173833, -0.5356808847337663, 0.5737269631895305, 1.8759980020538716, 3.346848655776083, 4.953829575070847, 6.657529841039777, 8.412975026611644, 10.171070967193502, 11.880937200366642, 13.491229686271664, 14.9531297649045, 16.2211748486432, 17.25651406441761, 18.026938485149, 18.509974732059536, 18.69193246956326, 18.570444601995632, 18.15251731805325, 17.456233475647007, 16.507968354587494, 15.34313096801747, 14.002862836449667, 12.533869953717527, 10.985022073945009, 9.406491533710453, 7.846696385636321, 6.3510796698137195, 4.95978504873995, 3.7064590040320806, 2.6169219272620015, 1.708347377091962, 0.989018406436474, 0.45813926716828385, 0.10657918202226248, -0.08257626702568983, -0.13255761025853724, -0.0716798224292032, 0.06847288731415259, 0.25474895566022593, 0.45417854234570443, 0.6358317612868366, 0.7721308335246375, 0.840514782087745, 0.8240574826076913, 0.7126272527870781, 0.50271346740598, 0.19787306013528402, -0.19215903786129868, -0.6517983415481693, -1.1609915740512207, -1.6962247348870358, -2.2320735642906397, -2.742661142221766, -3.203031915354891, -3.5907446094848847, -3.886774129780687, -4.0769090756746955, -4.151998571109587, -4.108876945962778, -3.9499217091655825, -3.6833379822563197, -3.3221461553780007, -2.8838002627636836, -2.388846079125403, -1.8599891979184022, -1.3207303936688741, -0.7941097283017866, -0.30162276800679705, 0.13807682328057164, 0.5097466878565586, 0.8026212458460615, 1.0103527363123324, 1.13164122663081, 1.169574203650693, 1.1317304270492663, 1.029074856115134, 0.8755739911732959, 0.6868925726294244, 0.47967157377282477, 0.2703031856380579, 0.07409522170516826, -0.09563375521583015, -0.22826396923816614, -0.3163066452521713, -0.3557905244437533, -0.3461902066800843, -0.29038161330039053, -0.19415866571698764, -0.06576148344183948, 0.08483064181249748, 0.24668835348186138, 0.40862946438206343, 0.5601414967306334, 0.6918502037273832, 0.7963680435523731, 0.8683846659089072, 0.9052653934872373, 0.9067202294289795, 0.8750537170281871, 0.8144834910325485, 0.7310444294556566, 0.6317211502206374, 0.5241071636720871, 0.41556386177306265, 0.3128021970890923, 0.22127121836427832, 0.1448464322151027, 0.08558644823266695, 0.04367279913768164, 0.017570975622177784, 0.004280675866163479, -0.00017504369785365827, -0.0002393153803109896, -0.00017248419068324023, -0.0034334015811424497, -0.012084387197118861, -0.026279746542542465, -0.04392326048986435, -0.06048251249155787, -0.0690237279218074, -0.060506064175087804, -0.024204601659096627, 0.051482023036746594, 0.1783334792122591, 0.36710412702397727, 0.626760264214369, 0.9631331821046005, 1.3783506244582837, 1.8697178670004049, 2.4295370658765294, 3.0444725174041456, 3.6960305421562167, 4.361160447944933, 5.012629929339674, 5.618986300581646, 6.1479591505101565, 6.57382308314664, 6.8690757461394645, 6.987060057131426, 6.901365421437763], 'positive_zeros': ['1.30530853611715698700040911665871', '1.87856241144005307199043095477435', '2.37652648658096049057168116664673', '2.50963361618824315808548965487472', '3.17824105483652008526927068338675', '3.84509133227563489834215382424060', '4.43533566661621721496821003341311', '4.93799221350388087564441150223430', '5.99660369516687135390217843672688', '6.62336266089388409498454841080385', '7.18998965101606303987653175214353', '7.19726739581177843532159752184786', '8.048677763764230405898927565495155', '8.227462043810885335529392441679276', '8.645453166227106333881918707610545', '8.784020859390785041390781401898577', '9.686093146921244222301113634369137', '9.760474019427137677442984441525943', '10.83332764987046128352844403801923', '10.94826705527549789951457968560598'], 'prelabel': '4-425e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 230134491604175381, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30530853611715698700040911666', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87856241144005307199043095477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.37652648658096049057168116665', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 628.7963350437966, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'dirichlet_coefficients': [1, 0, 16, 15, 0, 0, 28, 0, 138, 0, 0, 240, 0, 0, 0, 161, -136, 0, -160, 0, 448, 0, 236, 0, 0, 0, 752, 420, 0, 0, 0, 0, 0, 0, 0, 2070, 268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2576, -98, 0, -2176, 0, 0, 0, 0, 0, -2560, 0, 360, 0, 0, 0, 3864, 1455, 0, 0, 0, -2040, 3776, 0, 0, 0, 1656, 0, 0, -2400, 0, 0, 0, 0, 1931, 0, 0, 6720, 0, 0, 0, 0, -2980, 0, 0, 3540, 0, 0, 0, 0, -2752, 0, 0, 0], 'euler11': [1, 0, -2262, 0, 1771561], 'euler13': [1, 0, -1030, 0, 4826809], 'euler17': [1, 136, 4913, 0, 0], 'euler19': [1, 160, 20118, 1097440, 47045881], 'euler2': [1, 0, -15, 0, 64], 'euler23': [1, -236, 38258, -2871412, 148035889], 'euler29': [1, 0, -32902, 0, 594823321], 'euler3': [1, -16, 118, -432, 729], 'euler31': [1, 0, -54682, 0, 887503681], 'euler37': [1, -268, 119262, -13575004, 2565726409], 'euler41': [1, 0, -127842, 0, 4750104241], 'euler43': [1, 0, -85030, 0, 6321363049], 'euler47': [1, 0, 7650, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 114410, 0, 22164361129], 'euler59': [1, -360, 443158, -73936440, 42180533641], 'euler61': [1, 0, -441862, 0, 51520374361], 'euler67': [1, 0, 252250, 0, 90458382169], 'euler7': [1, -28, 882, -9604, 117649], 'euler71': [1, 0, -707722, 0, 128100283921], 'euler73': [1, -1656, 1463618, -644212152, 151334226289], 'euler79': [1, 0, 793478, 0, 243087455521], 'euler83': [1, 0, -838870, 0, 326940373369], 'euler89': [1, 2980, 3630038, 2100807620, 496981290961], 'euler97': [1, 2752, 3718722, 2511676096, 832972004929], 'euler_factors': [[1, 0, -15, 0, 64], [1, -16, 118, -432, 729], [1, 0, 0, 0, 0], [1, -28, 882, -9604, 117649], [1, 0, -2262, 0, 1771561], [1, 0, -1030, 0, 4826809], [1, 136, 4913, 0, 0], [1, 160, 20118, 1097440, 47045881], [1, -236, 38258, -2871412, 148035889], [1, 0, -32902, 0, 594823321], [1, 0, -54682, 0, 887503681], [1, -268, 119262, -13575004, 2565726409], [1, 0, -127842, 0, 4750104241], [1, 0, -85030, 0, 6321363049], [1, 0, 7650, 0, 10779215329], [1, 0, 114410, 0, 22164361129], [1, -360, 443158, -73936440, 42180533641], [1, 0, -441862, 0, 51520374361], [1, 0, 252250, 0, 90458382169], [1, 0, -707722, 0, 128100283921], [1, -1656, 1463618, -644212152, 151334226289], [1, 0, 793478, 0, 243087455521], [1, 0, -838870, 0, 326940373369], [1, 2980, 3630038, 2100807620, 496981290961], [1, 2752, 3718722, 2511676096, 832972004929]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/4/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': '4-425e2-1.1-c3e2-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-425e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 230134491604175381, 'z1': {'__RealLiteral__': 0, 'data': '1.30530853611715698700040911666', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1654675149291945510831817355838,2381360768428173315577679825368', 'Lhash_array': ['1654675149291945510831817355838', '2381360768428173315577679825368'], 'factors': ['2-425-85.84-c3-0-52', '2-425-85.84-c3-0-72'], 'label': '4-425e2-1.1-c3e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/4/c/b'}