-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_664.107', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.6062254109666381, -0.7952928712734264], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.33801687840850275, 0.9411400479795615], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.4090686371713399, -0.91250361647655], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.26498150219666167, -0.964253495453141], 'algebraic': True, 'analytic_conductor': 3.083603036261446, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [83, [1]]], 'bad_primes': [2, 83], 'central_character': '664.107', 'coeff_info': ['x^82 - 1', '0.997065801183740 + 0.0765492528364956*I', '\\\\zeta_{82}'], 'conductor': 664, 'conductor_radical': 166, 'conjugate': 'dirichlet_L_664.211', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^70', 0, 'a^98', 0, 'a^67', 0, 'a^58', 0, 'a^78', 0, 'a^76', 0, 'a^86', 0, 'a^18', 0, 'a^81', 0, 'a^55', 0, 'a^113', 0, 'a^32', 0, 'a^46', 0, 'a^121', 0, 'a^103', 0, 'a^66', 0, 'a^1', 0, 'a^65', 0, 'a^64', 0, 'a^48', 0, 'a^77', 0, 'a^74', 0, 'a^44', 0, 'a^52', 0, 'a^6', 0, 'a^120', 0, 'a^94', 0, 'a^69', 0, 'a^8', 0, 'a^71', 0, 'a^43', 0, 'a^10', 0, 'a^13', 0, 'a^101', 0, 'a^56', 0, 'a^9', 0, 'a^20', 0, 'a^63', 0, 'a^68', 0, 'a^34', 0, 0, 0, 'a^116', 0, 'a^109', 0, 'a^63', 0, 'a^61', 0, 'a^91', 0, 'a^97', 0, 'a^19', 0, 'a^54', 0], 'euler_factors': [[0], [1, 'a^70'], [1, 'a^98'], [1, 'a^67'], [1, 'a^78'], [1, 'a^76'], [1, 'a^18'], [1, 'a^81'], [1, 'a^113'], [1, 'a^121'], [1, 'a^103'], [1, 'a^65'], [1, 'a^48'], [1, 'a^77'], [1, 'a^44'], [1, 'a^120'], [1, 'a^8'], [1, 'a^71'], [1, 'a^13'], [1, 'a^56'], [1, 'a^9'], [1, 'a^68'], [0], [1, 'a^63'], [1, 'a^19'], [1, 'a^92']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-664-664.107-r0-0-0', 'leading_term': '1.96150044000444737374493335341-0.805058152768421114201129624274*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/664/107', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.1202836143960893, 2.021173816719571, 1.6886735273449567, 0.8050939937628294, -0.23211071286561835, -0.7127635549708952, -0.2068434473975192, 1.0215829538959054, 2.1061976616485913, 2.2058196193741275, 1.2462505420640264, 0.14301424590477724, 0.18252698339907897, 1.9319601676597897, 4.565107274984257, 6.296068311621431, 5.727801883447476, 3.049783469740843, -0.0023941585304477577, -1.5128105238124783, -0.947546019224438, 0.4956641913539722, 1.1096996734517617, 0.3377975555851254, -0.750370318689493, -0.6730687608444852, 0.7704366998896827, 2.1223299524814543, 1.7205986498754702, -0.44544538827020286, -2.4839745395776727, -2.3979937967511273, -0.17558003299271097, 2.0648833453770847, 2.182337125543682, 0.25215805353227916, -1.4692874955243973, -0.9194451533482125, 1.543836794143992, 3.486553285895326, 2.982090517286104, 0.622661798548853, -1.245846552852149, -1.1575007249100326, 0.0011000097743895042, 0.34580051957139935, -0.5068233363730048, -0.8957157602573855, 0.6890984029222398, 3.295598982810603, 4.083169896433102, 1.4440645669433392, -2.8702649778212237, -5.283362064670914, -4.073625761173828, -1.0736796607693484, 0.5444323009033811, -0.20955169777594249, -1.4091159079439717, -0.9438059460735145, 0.7901512824026075, 1.5754207589423568, 0.4357850468449957, -0.9729522260338744, -0.5392137543088049, 1.35177767720681, 2.060893103796634, 0.07182537327949119, -2.759091262779113, -3.174712575223311, -0.4885645678953718, 2.408222234132793, 2.4242262425752727, -0.07562779741427775, -1.8804961268195723, -1.0013141511707366, 0.98109305040304, 1.1950264039069585, -0.7081941341551897, -2.212964864063329, -1.4032259785269505, 0.49859398771782354, 0.9314544103812143, -0.39727756565065137, -1.1463965471076047, 0.1805835910830545, 1.7559960541792448, 0.6681114830665905, -2.8538066003971694, -5.031556395726384, -2.9522095751470374, 1.6927031429962873, 4.449794581553977, 3.2751884569635052, 0.49809580858531805, -0.6336927332884285, 0.06208547966995066, 0.38757140438852233, -0.38544720523201004, -0.3172196318277431, 1.9906193927040796, 4.609682973789135, 4.369820939472907, 1.2453293405247454, -1.2055059781503088, -0.37671557186531085, 1.9091735198829043, 1.8724820903497401, -1.0372811632348036, -3.337272470613293, -2.2227077880921198, 0.6957649407743408, 1.7349817703571362, 0.17841954936411716, -1.0345806281195222, 0.2680468806188717, 2.4128198321934535, 2.468393712001374, 0.5275033856806486, -0.6554333685167316, -0.021837098184077666, 0.1203029056249018, -2.1590117622953815, -4.791752286474189, -4.005019530405013, 0.2582857717767933, 3.58374907269778, 2.5443094030324405, -0.9465068501666885, -2.379765474180961, -0.6186787608029116, 1.1458228489450657, 0.35418222842310937, -1.4629786912523572, -1.4777586830163019, 0.03476224009927012, 0.4292212337098524, -0.8279910043608684, -1.1723021310643214, 0.7428560526938709, 2.1350012746635336, -0.34807716952214685, -5.345943455739977, -7.756810179059877, -5.1796523706678315, -0.9144052670912384, 0.6880668506537608, -0.17281352229182934, -0.025000965654888224, 2.1303945935727957, 3.372668207970708, 1.6401946113000687, -0.8341117716520273, -0.7664692366230201, 1.289833112578717, 1.9650921041600733, 0.36417299138862264, -0.6593881182523127, 0.7602024148963654, 2.300659710464634, 1.1222153937474761, -1.117042271234466, -0.057006159589690644, 4.81257970575811, 8.586754613975701, 7.165567554781863, 2.5470372291082235, -0.2570500851944043, 0.09685987928590685, 0.6173272080857246, -0.578281565500834, -1.5951555832162436, -0.6246891498478313, 0.5416435719385643, -0.5794593675609174, -2.552654240872407, -1.6764190722857435, 2.0682115527227074, 4.186652336521644, 1.9601891240917553, -1.3823617384843176, -1.164384904043592, 2.0660060457626956, 3.6020393885487065, 1.6092762834389456, -0.5398157246777395, 0.2102720046994867, 2.0933152770804853, 1.8210731586559137, -0.034172581580446254, -0.2799376043262213, 1.3237039100220636, 1.5114064586489393, -0.9667387679869415, -2.858927859295265, -1.383712404829227, 1.1599622104449272, 0.8375816357740142, -1.5637547851031381, -1.488945330414052, 2.2054070661950727, 5.006943071610313, 3.2186519933370348, -0.6289279320130038, -1.6152369486610283, 0.5511399642031007, 1.9333435978311284, 0.82063882237447, -0.2541030593031508, 0.5055162580674994, 1.1035650853395023, -0.2296984027237819, -1.1843763759572739, 1.040203581951837, 4.195739930606573, 3.251984038806047, -1.9943649266031411, -5.75915034576333, -4.027844978668987, 0.15176069043385282, 1.574169508603157, 0.11320808289306929, -0.546025499243566, 0.3967601749836348, -0.026175264566275114, -2.6906337782452168, -4.142448722365061, -2.028840187864224, 0.8605788591253447, 0.8676701439498663, -0.9158203429723052, -1.0163939202598375, 0.11475077391104552, -1.2730764964779686, -5.334023147660684, -7.094949476255644, -3.658099758534229, 1.0092982806356634, 1.6196285031623594, -0.9496846796249254, -1.7178745098402255, 0.49077993340807774, 1.8772808763391748, 0.37072973089274974, -1.2334207759575204, -0.43849314010521045, 0.7999702229162415, -0.019273180584837794, -1.1691253680151286, 0.18527675119519826, 2.1836960712455276, 0.41673474946900446, -4.566944659918149, -6.898320816266131, -3.7816673263650413, 0.26366029883498543, 0.15812613555723598, -2.501009996179943, -2.7512557981196304, -0.15487930421946966, 1.3653924786334446, 0.44084632308714405, -0.13531575235355173, 0.7920005013931789, 0.34694820811763544, -2.8715474343584666, -5.2157620853938775, -3.3317075759053765, 0.15621955369689988, 0.5503340334230935, -1.4589577871726125, -1.1893472003567305, 1.9706498161912294, 3.3540659792983227, 0.8599586480745316, -1.2310337525662045, 0.9719070904645167, 4.654782296594606, 4.737863905424696, 1.6293317513493608, -0.16767041356705945, 0.5293598985650861, 0.7354342473449242, -0.5177675466578913, -0.5624852590926013, 1.1948489418646324, 1.1573482847225165, -2.1560222272627874, -4.176328799745582, -0.7437353795365046, 4.762394882049899, 5.7279855575642085, 1.8748109336841434, -0.8956158707322008, 0.282010027461983, 1.8846613583833232, 0.9356273753979804, -0.27233547949166187, 0.8207489644353807, 2.0028167792803346, 0.3355750484063752, -2.199013952746413, -1.909054105869087, 0.022330653084118385, -0.4860920955422362, -2.9252986878679557, -2.5148563010743654, 1.5232714589795777, 3.866024542842807, 1.3862249649147738, -1.7461471633990933, -0.7852273035768993, 2.17580072017311, 2.2238842033302557, -0.1483022142920686, -0.46021849041751717, 1.786411727181295, 2.567612086681753, 0.6765339754229328, -0.2964812050995744, 1.395203805612884, 2.562272094076188, 1.0660866776713622, -0.22645250928719393, 0.8750264364782779, 0.7914611060768548, -4.141085529722453, -10.111337227487807, -10.036493656838175, -3.9091980641294173, 1.1921888102352933, 1.343378747285822, -0.09828782516150665, 0.25898645817314564, 0.6483872407769595, -0.9396463293242056, -2.0765793283569716, -0.38540773333146167, 1.4712633350169229, 0.25251366609141257, -1.5818987334970185, 0.3380980570485207, 4.324137007230769, 4.680073277294399, 0.989330335130038, -1.156890713861991, 0.5715301844648323, 1.7729714549224196, -0.5991984261351414, -2.8066742313816717, -0.8988856963153776, 2.3513348017369524, 2.1451680577288794, -0.453864756598929, -0.9836527986566603, 0.6406824337696152, 0.8821514058653921, -0.36622234564310563, 0.06569329994063255, 1.6697807163369307, 0.15895541451391038, -4.460288857765729, -6.269819805507154, -2.593287024495076, 1.2172212636847257, 0.09824362198120523, -2.8708046307100563, -2.075168474437567, 1.3776488963278726, 2.1847563122824702, -0.10898691979405187, -1.245714475083688, -0.12267332812861217, 0.20511441125560642, -0.715755377265421, 0.27206114293313255, 3.0730958229681478, 3.1014520260388436, -0.6991073133174905, -2.8493044287905955, 0.04495367893378868, 3.3333852179815575, 1.7470780185340964, -2.0696602989624844, -2.2994253315857462, 0.5080528661967751, 1.3367962517329426, -0.21726825400622435, -0.0015837562168828081, 2.3784930451416546, 2.6093739266964397, -0.28054893558795513, -1.8357548480231787, 0.04739555118158782, 1.687302974081827, 0.5817661156156758, -0.4048409287509434, 0.5813484625097712, -0.158885833003933, -5.0008542473509, -8.754335316332336, -5.650632082666723, 1.1131691059882496, 3.695723205318945, 1.0824763419389218, -0.9079497055421929, 0.23546292020812815, 1.1226501893598393, 0.12210014102277437, 0.07761633831441751, 1.797236947378482, 1.8385153709388244, -0.6204319844484383, -1.229914144038634, 1.7953020783861504, 3.5905920140546246, 0.7154667690693024, -2.4132406447629458, -0.719608845430744, 2.8083735454537315, 2.200145324320826, -1.4297710938413202, -2.2480634936801263, 0.23823311653763968, 1.2194253751742115, -0.32148873978884546, -0.35635192667951654, 2.0263508221039874, 2.792079668613935, 0.7405739996262896, -0.08681709393065035, 1.9071779620040337, 2.7135070115244995, 0.4092011821621228, -0.7381706542972429, 1.8834443706183086, 3.640543532320721, 0.4035684624683454, -3.6579570812939504, -2.5911530387926054, 1.4368201520096908, 2.039828451242013, -0.7624654914427265, -1.5728918502276676, 0.6152358090241484, 1.5738566973369834, 0.10792023855678998, -0.5442872776419464, 0.20224357581045888, -0.5884272777346491, -2.1931284353321794, 0.011335908320711095, 5.521943133672241, 7.187067802033649, 2.097502658147628, -3.2042891103787263, -2.757325957668514, 0.2703257866960096, 0.35451422595321264, -1.2587594398167141, -0.6914604605557334, 0.4429028034202328, -1.5418728557982027, -4.546405509396501, -3.8313416656163737, -0.4776262611506459, 0.7361634648940765, -0.054967701032455525, 1.032049991759148, 3.241596175607556, 2.137884815196138, -1.4166873175522756, -1.713627882973945, 1.5738957258332764, 2.152472253779695, -1.8888915447789834, -4.251587796980003, -0.9567296021543246, 3.1454767119137865, 2.835242426533261, 0.4192419525070686, -0.021185538897783435, 0.11428332682059464, -1.6632480122756796, -2.893216397011321, -0.9322558970170345, 1.0643727249493833, -0.4125824332133926, -2.217852929346491, -0.1733281908638245, 2.3292864347377704, -0.5046618669274265, -6.105243146271961, -6.757850448905058, -1.9532953980310803, 1.388823762210595, 0.5035266071023011, -0.32578608290282535, 1.0522812718976067, 1.4450974954157032, -0.08454881840654214, 0.14046117650563453, 2.6779900393567506, 2.829292462117761, -0.7227139678497984, -2.7982353726944615, -0.7771669889588868, 0.8268210440611505, -0.9311001123579741, -1.7709570232459961, 1.4432292971832976, 3.9307994892065397, 1.106047663017169, -2.8908480367339546, -2.087056318782299, 1.2464893881410142, 1.2058427529554867, -1.461713734753217, -1.79721874287837, 0.10717650378644497, 0.4563847038090081, -0.3743936638964448, 0.5505704194889488, 1.6041102385134267, -0.49572816705911915, -2.5863705906466437, 1.1071716559176443, 8.055558514054205, 9.685448372563135, 4.596915256653045, 0.2045445028550994, 0.3294168598924338, 0.632569029234165, -1.6290153571258164, -2.708322033687266, -0.48167184586212075, 1.177626636468211, 0.06830571152486259, -0.18130611865030566, 2.249758642148726, 3.208997534688338, 0.5044501577215854, -1.5160145137877, -0.25768455971893683, -0.22416759112330986, -4.3392580624792, -7.270294858600405, -4.176631232649636, 0.5382758989247299, 0.6623622866353186, -1.6046064006788718, -0.8555723435967584, 1.3859226044749253, 0.346614915289559, -2.4326399850931573, -2.022481830552094, 0.668220829110154, 1.1223568365990277, -0.15966101048303366, 0.3377382278629232, 1.2683064450860286, -0.705308118173535, -2.679081812055572, 0.45568828595019656, 5.563951275159823, 4.7639319389925525, -1.4543215850687228, -4.638272789114071, -1.9672519150105845, 0.5871185770501219, -0.3938766810433481, -1.224260696924302, 0.23393293395132664, 0.8807445314322225, -0.15995088542784497, 0.637497296671802, 3.2097075989659567, 2.5260192636648267, -1.8633566352361501, -3.7129041330378274, -0.8138389719903302, 1.0686719345535205, -1.2300264946341997, -2.88423434375305, -0.8762275504133156, -0.06000394066535856, -3.7021476628061842, -6.513973287086034, -3.7055484522788618, 0.6476329142744429, 1.1108607698955957, -0.2678934676991823, 0.4589544614419443, 1.388089227340544, -0.26435195587278065, -1.7084015823527587, -0.2864544067374982, 0.45656452308977064, -2.3163983492244418, -3.994638669237093, -0.5362107287151217, 2.9423368917464616, 0.27006358453406637, -4.697673033495118, -4.40279327200114, -0.1473267684047821, 1.2878862039732246, -0.5036125917885678, -0.8476037231126754, 0.2243637310690791, -0.8066115746176703, -2.6540113720460745, -1.5251208993628929, 0.7594868904683024, 0.03131133740725113, -1.5372969574585045, 0.6070536210833669, 3.5128097268714207, 0.9074412657961528, -4.929840846448052, -6.007009597648137, -1.8657757565219837, 0.5937252421630378, -0.4564549452203172, -0.31317856720640064, 1.62579671922074, 0.7015506634877482, -2.937749215161104, -3.5750785707516535, -0.3501679347248397, 1.3482793615764772, -0.10246150007129906, -0.7483223171953324, 0.032352363589895995, -1.2706763050533447, -3.442468787545422, -1.313339854307436, 3.4178598365258015, 2.9217812854463765, -3.299896485660157, -6.520288503814532], 'positive_zeros': ['1.17266630355536783683943875124', '1.93672373197690777255713097570', '3.51814704335360166452997761479', '3.6626001000130160308902195580', '5.62470384257640448062178380667', '6.45156442184562250372592670862', '7.273212676261292434873677436708', '7.98102109250933159484363472576', '9.00695976201425551171618677943', '10.02048344118472805834581886127', '10.97226022613133572489284703781', '11.69398471474007524515785760005', '12.89289635425322695973871381980', '13.749659995186145036613766841912', '14.21785550586131072150737355795', '14.90521493679638774464085157995', '16.04299480736863870320592080125', '17.33445486769165007763314734077', '17.76544350996700563678599988741', '18.61166582301964980226317649583', '19.45428967578692862452178614663', '20.09785777502496012318311050736', '20.94502644227685376999217340495', '21.91922078406409406050437849713', '22.80388729414859386878538687706', '23.58601474751842956990152822687', '24.27585054986424009652669690783', '25.22165775105924514175585494601', '25.85758961149963331224828568357', '26.533933659458135239073606831999', '27.25677557377596771992249077386', '28.324660785643402962728425755669', '29.45072905996344847412526387488', '29.97832048143541089034918192485', '30.488738881337916423687275167527', '31.00430507456676194039023666317', '32.30777904297279376010868523692', '32.86322367310239518183908407493', '33.65351896626044354250076045620', '34.6076646811763012456110729491', '35.340833588185707367495657282591', '35.89958511972523349166110347850', '36.96368012320767455747049638097', '37.507435429842452475191389342512', '37.8442234866989889216738570516', '39.045350953850669267472161331212', '39.912395171565391465360864544934', '40.70594097821826507322241658903', '41.30720562318413923478785316713', '42.1796064569705467431260004805', '42.62955580584452116305936865904', '43.33974245702587089631426176882', '44.0373874612462319193556951704', '45.41340062018127675131133967778', '45.88340592218682416792948428043', '46.25550250952933525728465552313', '47.37314626310518362908056844039', '47.93775348619873131893257994670', '48.812715921148800891514920799211', '49.255836434507110586776755247219', '50.137398574251470607822498779936', '50.63012607290774577488307403525', '52.126634148680035317335194773113', '52.470913710787796972165409023984', '53.00993709213182154737359839232', '53.8735816093925087500236377027', '54.28179927823706970368180697975', '55.15099031668490834702408640873', '56.100033089133728980989436928535', '56.68681437829011241219507230060', '57.695278673044525280482441051097', '58.09009721208049957526686694504', '59.055470119488949646268065251345', '59.44328950495016380011773962639', '60.21006790523007742896298052604', '61.08782353482277809757143447582', '61.67370741802926737217615766421', '62.335529564321505547139735983919', '63.37805063170128650215776268370', '63.99455872900983854633281447317', '64.86555840372482960211373248822', '65.17291169393741507615116616414', '65.89796578795603108088351024151', '66.462529057294331346597753984076', '67.39221964638827556986732789602', '68.42378394421456160944225988583', '69.08482602739846064605034662983', '69.56501483149260832043392104233', '69.995508005974340177478869738365', '71.134076405860826945529006318898', '71.71136608805335827826219302725', '72.4454245938985929980399208551', '72.63071361261664811862688839810', '73.97796865554448225361992116645', '74.57725196889592648857305025659', '75.25371898209020220702603638113', '75.98944118086633711604179991898', '76.6458042852746635504069613323', '77.1837411106292969985158760456', '77.7884053759097904624080175927', '78.467911035964276386743093977698', '79.655750402852728691226460421476', '80.02133095925037589443347327916', '80.95555735070082815677093311602', '81.686794301646684929113547435388', '81.944780717969527999457829356', '82.54712687419585357741145846745', '83.730829985052205657832032262673', '84.15541306351535933544838414080', '84.818676412510071724332063697251', '85.709725736658635725763372611', '86.165927514293989547951987636623', '87.41884834833090844262495739036', '87.64819884088816344742738686237', '88.3162560887501390082408775786', '88.86270761764577140157873349601', '89.50738432957366552358661001314', '90.3526642331026571879174121638', '91.406398800006815738546018613484', '91.83502817324713327599834358242', '92.68441822460754295380185538193', '92.96436669295941666912973883967', '93.7862749135513591472417347429', '94.68185462760837132192197616324', '94.91333047252116736088360146722', '95.83020910611920809620423192987', '96.67384678286454003104805694629', '97.266750877073956433002970783921', '98.102598852080431903059687302339', '98.51727876759079409738251007871', '99.49010430121253279449613342048', '99.77942225582539522468528116883', '100.81470350156565719369359932596', '101.060089103177851993013383614655', '101.641514293120820030316131551974', '103.01949647748815396653269807386', '103.711947911120501617535321407435', '103.97298293912766574468456504892', '104.538815900355496192941503627173', '105.35953268616735556066906646783', '105.96980550677718714378111886211', '106.53427465266480421354048454984', '107.58651402266098227617176520101', '108.052660137309698173083728476235', '108.692755831855475078960847131249', '109.45142011761369822932672775167', '110.25219368175542296571335044343', '110.81835796307059570486595580041', '111.46060199523818804272203650868', '111.8621153605096290624996276223', '112.51299861766167610955450748919', '113.61231309832906235549164696719', '114.07210721692931797244604685271', '114.87139814157926220265707640159', '115.61101358359083460424105690816', '116.282461180397165935764018948047', '116.63694986753913894888093026732', '117.150741425626420912728255275850', '118.07329778718943091900455351872', '118.74676139069194921112694102398', '119.50786298380856649226662224776', '120.25407002819094151523159082822', '120.8908175799887785135264192813', '121.25027101422524472248926365119', '122.15961044606724327871198993730', '122.806793036290323150138673020079', '123.55005594273850710066143643480', '123.91249237835347491264791153515', '124.3577890327454994495026430678', '125.56807790054954854292876582414', '126.36242643900682021989899014858', '126.832787637407168757629352313077', '127.5379253628600463176916766898', '127.790578628437669909160577964543', '128.67482541271753007780518671113', '129.21624515163339566873045766', '130.05309855188179075357402010222', '130.68236165984596971167451262874', '131.436475410055205975903080093634', '132.15870301293047352609253390496', '132.751067038087771653922573887024', '133.184497978308505027911763212639', '134.19355817797189822155234700343', '134.4008679696148914927404911234', '135.36276390224123425412180763567', '135.75197222336644001554675903563', '136.58789419401569948028469204856', '137.38011146073403433508760727045', '138.04242894121226542188735826493', '138.67126204735507815640132036788', '139.39641926656263744593470323813', '139.90265518772698667438748014220', '140.19241967478815270157661515949', '140.936749499062272011021107634806', '141.97457341107406756660120259098', '142.77487643128412590412873934086', '143.18957910193691472649216504085', '143.88250766799589721987245051063', '144.19937313266160376447676688660', '145.369620635607160261037714921773', '145.90078000102792022007126132893', '146.04912419583205369869120176612', '147.056498932598249186157904616412', '147.67111988175199142527430651623', '148.31100527845619660905949027596', '149.12216784747163816034928247839', '150.10437345629554232285026574424', '150.32565127570005375843368126466', '150.66326819249443741752105741718', '151.66673415654364588881325564005', '152.13761229116917042488847049002', '152.82803506058607502977432814696', '153.40785096117762668237773202057', '154.50639915189475066776065030263', '155.09868354225685376134514078051', '155.4197391422941435314876494115', '156.23066911881459541134596969281', '156.53789140642449917571899124771', '157.443130654889597958708798876307', '158.21626648093872170648497508005', '158.627165853277958365108894187', '159.26368338435804804279119731440', '160.071999476815830794433959733018', '160.80735608136118910964017095760', '161.391458151217256957235344784414', '162.1672917380300640362569475305', '162.64465253376774349142174841026', '163.01472712993760953365971775635', '163.70129798774326010244497595672', '164.31972121093011243008308481144', '165.66562135386154635174709435643', '165.845821990859055825685932069942', '166.36413057262924918781096219625', '167.24322356779438899557969178033', '167.82714646398524776916438675195', '168.160886983671640876471590216512', '169.1110790393562032944627239896', '169.7391821445581528079227777910', '169.964914557926804650110790415831', '171.19928826385114443242553129283', '171.64788963807885655771266054149', '172.29049379447470695728856979884', '172.849639133761429382821969678299', '173.66422661041091487070306447642', '174.32098824632732307735746941862', '174.60583522779825967174803010413', '175.2375846818556855128823351088', '175.91094646180960418249130629679', '176.80421083903345187740833461418', '177.6886304219732814002673324343', '178.054370147519447437532163462267', '178.70810499252089476460018833246', '179.31859653975051057259445566855', '179.579941994654192621977037103681', '180.49915911414335424263775722209', '181.32589212900429466090576969513', '181.74908668109132867701104443000', '182.63415201661117234485508861704', '182.80024064706795630289574524339', '183.99965214727902271858018935068', '184.59792509461607738059530849492', '184.900535692725422248160754578267', '185.590064834076274871180059161301', '186.29605485859741516738453044909', '186.64489027537762531424210110882', '187.534005687075944034623402361648', '188.14076024283179669459578253247', '189.075125044603103819675021866184', '189.60495953439464777132982947965', '190.218648294264823520811275710335', '190.482642262390105735269917673949', '191.430589222729775772569627978466', '191.87962370807206864780344430175', '192.44735043487148409061528817847', '193.17400953094446294190471989544', '194.22842508018279198216133137287', '194.58649602068848744033269410688', '195.05331002095030532350694093021', '195.69021838064884473707619390138', '196.59598685129915881732115897253', '197.16930441608719648964463199967', '197.7813883994787948261556381363', '197.88610925465203692003222717208', '198.8330215504133764375684125291', '199.53412757488157272657488484177'], 'prelabel': '1-664-664.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.083603036261446, 'root_angle': -0.12397058794695826, 'root_number': '0.711665515742265852906728169459-0.702518465026574766612556785979*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.123970587947', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(82)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.47741862730759807832530122253-0.356483251573525921330829009775*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17266630356', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.93672373198', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.51814704335', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.083603036261446, 'bad_primes': [2, 83], 'central_character': '664.107', 'conductor': 664, 'conductor_radical': 166, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/664/107'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-664-664.107-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-664-664.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.083603036261446, 'root_angle': -0.12397058794695826, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17266630356', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_664.107', 'Lhash_array': ['dirichlet_L_664.107'], 'factors': ['1-664-664.107-r0-0-0'], 'label': '1-664-664.107-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/664/107'}
Lfunction data - 1-664-664.107-r0-0-0