-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2016.221', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 216.64928838596404, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '2016.221', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 2016, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_2016.821', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^21', 0, 0, 0, 0, 0, 'a^33', 0, 'a^31', 0, 0, 0, 'a^16', 0, 'a^23', 0, 0, 0, 'a^18', 0, 'a^18', 0, 0, 0, 'a^23', 0, 'a^8', 0, 0, 0, 0, 0, 'a^17', 0, 0, 0, 'a^10', 0, 'a^29', 0, 0, 0, 'a^16', 0, 0, 0, 0, 0, 'a^25', 0, 'a^6', 0, 0, 0, 'a^29', 0, 'a^19', 0, 0, 0, 'a^4', 0, 'a^11', 0, 0, 0, 'a^30', 0, 'a^22', 0, 0, 0, 0, 0, 'a^28', 0, 0, 0, 'a^35', 0, 'a^37', 0, 0, 0, 'a^38', 0, 0, 0, 0, 0, 'a^20', 0, 'a^8', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^21'], [0], [1, 'a^33'], [1, 'a^31'], [1, 'a^16'], [1, 'a^23'], [1, 'a^18'], [1, 'a^23'], [1, 'a^8'], [1, 'a^17'], [1, 'a^10'], [1, 'a^29'], [1, 'a^16'], [1, 'a^25'], [1, 'a^29'], [1, 'a^19'], [1, 'a^11'], [1, 'a^30'], [1, 'a^22'], [1, 'a^28'], [1, 'a^35'], [1, 'a^38'], [1, 'a^8'], [1, 'a^21']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-2016-2016.221-r1-0-0', 'leading_term': '0.0535153247703337222865873928611-0.604460565356701757589850538533*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/2016/221', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6068249047761785, -1.1104520758972578, -1.949670193439707, -1.357681898045776, 0.2251863448630605, 1.495799023511007, 1.322306950648088, -0.07143707455127349, -1.0694873105677676, -0.1546934164055389, 2.3865722167821373, 4.4419977667782895, 4.078869086437505, 1.6145701195682403, -0.6132983742833508, -0.7589815998118445, 0.48343056772949006, 0.7743605333787072, -0.93402640886538, -2.9536629150592573, -2.8671428733101196, -0.6717610586213207, 0.955392963803652, -0.11314491996661649, -2.66938204709782, -3.5191224434432034, -1.4707185106467153, 1.1282167185637284, 1.409901551092062, -0.3409804863158052, -1.2782648346699248, -0.07629526440364982, 1.1489758484267052, -0.10310421910435985, -2.860796813429274, -3.612699304717834, -1.0523737264096102, 1.9251650005693077, 1.9820515834131727, -0.2308492127402973, -1.1852576775034773, 0.4523594380202322, 2.086011047032504, 1.2676628695398142, -0.5153474510442153, -0.10987120987610663, 2.27358070333947, 2.96470909436206, 0.16712840787441094, -3.1167832973872307, -3.1542925974434883, -0.7178182466607876, 0.27243135582343764, -1.3503999950111794, -2.471835609240216, -0.7618626010511874, 1.6212542037352202, 1.5237987555717485, -0.026843556989751598, 0.6758989026026948, 3.9396536192276383, 5.644107249524294, 3.2715821699251713, -0.17778201447292463, -0.5636016722707841, 1.4202842719766147, 1.874412685395625, 0.094099632798651, -0.589211464270805, 1.2730309085644802, 2.4727563641090597, 0.3475247841760365, -2.4638336504863076, -1.818747233997939, 1.3383207830449892, 2.2607537961020485, -0.27907586559042963, -2.302526102712882, -1.1646674195328828, 0.4316317600438372, -0.6225266295212994, -2.4288161033994813, -1.3833740804470058, 1.4177667204053561, 1.7385582434125055, -0.5941440345718181, -1.0429018910970953, 2.2136898671062264, 4.970878245242472, 3.4833548957712157, 0.19062359540674145, -0.5923332682757254, 0.4861875636124636, -0.09969738369301318, -1.8218261866790668, -0.7444376430401852, 3.1554159782356526, 4.938402536589743, 2.4125273629080883, -0.24958423637998442, 0.6637377038143811, 2.5069797171623853, 1.1785119932594568, -1.7418730773462727, -1.852340065434122, 0.4207066207317913, 0.8059779431093433, -1.107287910979315, -1.2721139098711018, 1.136234294225497, 1.6028331867150467, -1.9627431146675427, -4.979350315974981, -3.2951061004600417, 0.2176012471632782, 0.7258537101823037, -0.8137041292514, -0.4654409649629314, 1.017643998103182, -0.24476542189643513, -3.4433782249131184, -3.661654650791113, -0.4349538266368074, 1.020461519465668, -1.380229313337854, -3.0693994062963084, -0.866785770031615, 1.5876000518307691, 0.4646816402132641, -1.6131333541627257, -0.6824561570505318, 1.3364243222129397, 0.5455386015068493, -1.3196171023112808, 0.01248742423381179, 2.951187089475927, 2.0903482345775033, -2.279289317738444, -4.187273723850401, -1.819556292912527, 0.08478831787625582, -0.9552850570310031, -1.3741994830653868, 0.8184704476554162, 1.8257529663429657, -0.619566263878891, -2.3051441641169452, 0.13440663211686804, 2.7711957043318454, 1.060222121224532, -2.1160980359472235, -1.6434279863892745, 0.8309398625311762, 0.3534435678513814, -2.1761395554751255, -2.0767466856857153, 0.16632139472444346, 0.1623705119958505, -1.4834191677631847, 0.01509351190942594, 4.124847355681326, 4.89536927796906, 1.2790598846552679, -0.885447489918312, 0.9565607879547029, 2.2157936087677066, 0.1687683160022455, -1.3440188148057344, 0.10520237338256713, 0.7299675204054946, -1.7203874626283635, -2.8596142044350126, 0.29083023438103656, 3.0942245421131864, 1.2389436057352552, -1.506675210374058, -0.1939305265469389, 2.5177504778408153, 1.7846586560014284, -0.488218824633194, 0.017383074355439645, 1.4256618080738515, -0.29420509177841264, -2.7044364353455452, -1.0378201240012048, 2.379973820208723, 1.868185760079058, -1.1601444193322517, -0.7832474828971019, 2.476667924213037, 2.835060218114919, -0.007755216044050155, -0.9410091812224222, 0.562240844598201, 0.27238937503940996, -1.3207603673840715, 0.6380046186696606, 5.178659532680603, 5.708869398986513, 1.4383676885049645, -1.251615243446666, -0.20779427222533828, -0.31792847692522275, -3.14367506767626, -3.8709177970497723, -1.11144241955585, 0.1662013275033, -1.6119088694279942, -1.7061671100863744, 1.0252139082524834, 1.2039127218264578, -2.538477328110678, -4.019055241253315, -0.5339861257832291, 2.2719506544381587, 0.8573446503914496, -0.5065408200642998, 1.036979884152285, 1.6438432500653009, -0.5099571788898691, -0.8520334250654776, 2.17981276187525, 2.9193656872772102, -1.0604103476190823, -3.7586514141606147, -1.4426443935137567, 0.9562876923556434, -0.3391633047426174, -1.3271852503575419, 0.8384326733096666, 1.8721467813307542, -0.7396986461664677, -2.286608280682092, -0.14915523988457116, 0.9224996162458798, -1.3939344358994394, -1.7088499248811346, 2.5948698118894797, 5.451606568534774, 2.8314428035313517, -0.3317924531866345, 0.12547647655812746, 0.75085613431273, -0.8817112430683487, -0.8078962112354608, 2.2367957000959913, 2.5866548808422767, -1.71285760087269, -4.246608141833019, -1.6974172444751725, 0.45861058549496286, -1.059193492544142, -1.4718243555012227, 1.7047295174736683, 3.3727099146999144, 1.0672054666455524, -0.36557185649565943, 1.0707884760140425, 0.7428605892935815, -2.0952080652352483, -1.5362482246799367, 3.2343669927685816, 5.131367419621393, 1.8455688072208245, -0.4036946487552047, 1.0085484079780973, 1.2160106731711888, -1.1523434846494283, -1.2787257402294618, 1.181033673087076, 0.9500027182541753, -1.627878454396139, -0.5617766345170327, 3.5055339757599633, 3.6064622220829547, -0.4211340182959205, -1.8175153036813436, 0.15892897974511938, -0.05365949843385569, -2.38343903357302, -1.710843639380097, 0.9200427657580801, 0.3000922187044245, -1.8686397404259387, -0.3582967859866224, 2.245098638563208, 0.11622531609543588, -3.7913647032243287, -2.7963717782985493, 0.9708538928165088, 1.2473489066592274, -0.4748824982367893, 0.46498354184655, 1.6237221504342942, -0.8023446031938333, -2.9453874008218572, -0.8531013351232586, 0.7747440706833023, -2.2756590096332836, -4.717966800730651, -1.712679277638633, 1.7907201466065648, 0.8599681399924942, -0.5551815416455511, 1.0537387516820604, 1.552396472891858, -1.1868345651923653, -1.9936297828635026, 0.7678693643785275, 1.2162445991292867, -1.9333934511124875, -2.1402097479158053, 1.8748882071970578, 3.255039294123361, 0.42020579043289463, -0.3771229175161873, 2.032941465863851, 2.098107392606259, -0.4252676780822414, -0.5895809397857041, 0.36234367435997816, -2.463525521309357, -5.971010096832519, -3.7986714555894507, 0.8936607365536219, 0.8919282770319847, -1.7633835206526045, -0.9896733301485761, 1.1856619859792499, 0.23537537749242304, -0.6983308025265209, 1.9897461604455526, 3.719840912733432, 0.9088005425492668, -1.1981908897552023, 0.7847257606173509, 1.2818522074710088, -2.430379925527219, -3.9070391111176552, -0.23348772001236884, 2.191315034787278, 0.3375628759057116, -0.6409541800764517, 0.8051429723225443, 0.1953909635243254, -1.5689934516854527, 0.9886246463123964, 5.399230780594495, 4.3145963941857275, -0.38734109072288647, -1.159613275099367, 0.9920699774568, 0.20212387604883808, -1.6040505953710384, 0.3038870405164452, 2.564668639924568, 0.727618789981765, -1.1558305838312672, 0.6073283138589645, 1.0831837151359274, -2.60577670501243, -4.232496965250767, -0.8921131282903323, 0.684479019965353, -2.502741110074608, -4.07735779932208, -1.4098098133456327, 0.2194827664205381, -0.20114942020340001, 1.8807780142053705, 4.777650479594597, 2.7715041672180467, -1.188106663883392, -0.17392291919364603, 2.9733543207715885, 1.4036007199973368, -2.1214516905590397, -1.5755252938325852, 0.18844739889158862, -1.252880933558904, -2.061546802566798, 0.8342173976763181, 2.1733362339747835, -0.5866763515255868, -1.5434347606945569, 0.9689803797187574, 0.45841321627939935, -3.703716453815553, -3.968677784139329, 0.4245079504888013, 2.124185677226877, 0.15322121199431651, -0.09982898229130843, 0.5375164668221413, -1.9969233732246303, -3.9741926510227548, -0.7011116346082662, 2.629333382241139, 0.5415615855751368, -1.7996743162381899, 0.5430426586899342, 2.304517429934216, -0.45637748158293256, -2.274554882307704, -0.2745471057601636, 0.2585586422471095, -1.8726632113192114, -1.3884571179958378, 0.7877514755340899, -1.376786302854227, -5.352702777138479, -3.880414709352426, 0.4622690148346878, 0.5575996656811344, -1.1597327276420901, 0.8681591430326534, 3.1256320433055116, 1.107739316470962, -0.8457102984424346, 0.6077287267509237, 0.7268319916912889, -1.6772296436289975, -0.2664598042005121, 4.849149473493579, 5.374667207479739, 0.7018817274583133, -1.291626329016369, 0.17146797457648427, -0.6457634439446187, -2.428902101171593, -0.3915757575756885, 2.049908320223971, 0.35360082014325556, -0.8937547833853262, 1.968233178146602, 2.9390470967008246, -1.1132235796938479, -3.2221886401552853, -0.4629822626071469, 0.42621396970400577, -2.443950573011804, -2.7840632400804477, -0.1451545512948524, -0.2067576935192896, -1.7455873032489464, -0.007018958991696375, 1.3721143399352733, -2.222402890930509, -5.019969152936814, -1.6149909517987555, 1.8668222184866774, 0.026166090302906224, -1.8549697907730889, -0.16341347965243566, 0.15902414403933746, -1.9863071113723174, -1.1970649196422938, 1.386855821912662, -0.4175640862984862, -3.92640169516348, -2.380247692074832, 0.8969372698815985, -0.30091246306823527, -1.8840537319896502, 1.2068094598873247, 3.682896979980282, 1.0884406766707673, -1.156300376270349, 0.19442840022529143, 0.5373143998046853, -0.2275318577121932, 3.154771038276265, 7.648087579939359, 5.483525100726834, -0.20525376172151646, -1.0049665642998975, 1.0440921483259247, -0.04712270028394553, -1.2275219805777384, 1.1852581037134315, 2.2567043892105008, -0.39046609999858933, -0.6937187859020082, 2.390681622903762, 2.2068809825362816, -0.7762334890249087, 0.39604975648494206, 3.6911943802663303, 1.8486645739499665, -2.220642039350436, -1.5579277313126272, 0.8698765937157338, 0.062294501476947046, -0.27270224005163174, 2.2690793327219754, 2.28225146375112, -0.6519974179897619, 0.6130880075964515, 5.3038372533117215, 5.0143459675762925, 0.5893999489021758, -0.10498199714690927, 1.84247077725092, 0.7908181216730165, -0.3154768384459906, 2.4068749451271136, 3.8600774401243045, 1.0509330304330238, -0.023107803152096547, 2.0122513540947997, 0.42340781626282564, -4.197722660841071, -3.8789022023764717, 0.18689117621606668, 0.23782297880806108, -2.1495044762559243, -1.0328829596277957, 0.5869880018168511, -1.3399101769845452, -2.176469221977447, 0.278894364677168, -0.12657186380066918, -3.757773057974056, -2.8578420614946327, 1.9952674471810397, 2.352342836642972, -1.0449200892242796, -1.014733447301802, 0.7456773465333254, -0.7586625651809302, -1.789993254208243, 0.9346663934239772, 1.780864257929704, -1.180076575689586, -1.2061772695637314, 2.012312989924836, 0.9518118788535743, -3.217550269728908, -2.5169290802892235, 1.2659300509966105, 1.1847640762586111, -0.2444852050437876, 1.5912088351628109, 2.392855198759665, -0.4737552494359225, -1.0810625159531435, 1.4808966461513036, 0.2969675318115377, -3.6312338703936873, -2.453973204510217, 1.701763390308462, 0.9610674612393085, -2.0927199131201544, -1.0829839354344595, 0.7833425106576998, -0.20985257096130586, 0.5066034770433694, 3.7689304039679934, 2.856273848671237, -1.4518515067679534, -1.1339506672107094, 2.2824613729675405, 1.1603881238893088, -1.9562144812655926, -0.8394309756480466, 0.514293759604658, -2.4222044035242623, -4.1283930177403585, -1.3631824967575188, 0.2243288224166194, -0.253427521699242, 2.50584895105774, 5.562198763573642, 2.0821190581540794, -3.0884808899214504, -1.857646520089567, 1.5080373580080573, 0.5425606544857092, -0.8153678209798984, 0.4913460927857389, -0.48228041744170597, -3.594410912743591, -2.3504038548869475, 1.194950921980315, 0.04815195601234728, -2.400368494369169, -0.02332407320081817, 2.091629402096748, -1.1586850891024516, -3.467794913419118, -0.8185833280566156, 0.5895314414497996, -1.0450231555250604, 0.010978422951660665, 2.6314590267303752, 1.3409927555494463, -0.18572003204240836, 2.7636628368832983, 3.9024890759225728, -1.1185754058775952, -4.387519736047204, -1.4933329482729012, 0.5707989870668446, -0.7652096105848467, -0.14816286652774155, 1.385325746844012, -0.8699135264202774, -2.4907825258330925, 1.1904426610482823, 3.695712467079926, 0.664545747667032, -1.0772252554964907, 0.9393255783533737, -0.26883233620330865, -4.495357738403738, -3.966276044627972, -0.09044503088572502, 0.18338167682140316, -1.0386710510003951, 0.032710981387977324, -1.1079759574429864, -5.249936727861279, -4.422161777748167, 1.462813063159571, 3.0205696785455527, 0.055957080275679194, 0.29882711825998876, 2.2432569471052872, 0.24157085378018112, -1.8022426455042722, 0.12564646959944636, 0.7047388380899791, -1.7177572745020986, -0.7147216826515161, 2.723745668520176, 1.1091036558080476, -2.7224870749828836, -1.192178618740167, 1.6993150068426683, -0.3987436398780969, -2.5561259094661635], 'positive_zeros': ['0.10387994974313026249477106247', '1.20843076179790228630714856184', '2.172943329568731296538825048375', '2.836256601287064672083756686904', '4.2627152851909225555063509395', '4.882961748919941137866812654557', '5.489251413192940215154761338641', '6.65328902144072906215659677829', '7.17183457471489461073629891420', '8.28327410008013803954704364922', '9.00657241443538755665504778191', '9.70101207869521624387954745934', '10.29947491981491532722873034529', '11.34441024472224303866311883394', '12.15507488625748925155572511308', '12.74896248417713761205559060736', '13.63929853526277002432772561203', '14.08048063590374192926507929271', '15.01359843545348301778770519067', '16.05490399972852208862779804187', '16.33761556140797407979462952980', '17.27370908572716422596341393003', '18.1164170091101026159993575216', '18.32011599277202410646399023486', '19.664737814207052014649019415902', '20.100528260843814060042017045822', '20.9536292571741316323107540594', '21.38293149300492281233599564554', '22.22008299521314217027961217382', '22.99287634110719792245779135548', '23.72213234293876894418054768', '24.55799676582863582596040691106', '24.89832033883837923644793918371', '25.77341308214809607431474516446', '26.48556465328615383745652664144', '27.004769426075840745788055280437', '28.15048626328747481386126431027', '28.60377059238066268604821421326', '29.044086799618699323729478746407', '29.755844208756988682285248737011', '30.8805882262922375476262322322', '31.14488976874229103963007349490', '31.992457697102989348377807315450', '32.751260332123235519690117116286', '33.267978786455150028307330134175', '33.925938877410409688141231199141', '34.54375958010414701888626844562', '35.59893204212396052085070244047', '36.08086268982994457599404506569', '36.64753782044365511528919180924', '37.160603579118499424125574862015', '38.16860981517872638560595274920', '38.60702901296592000631694224182', '39.45773160244254973952627890745', '40.05671499522503442026473356101', '40.71401161264640528378875132245', '41.32548547589317242007671177240', '41.87371046399577079431015153371', '42.656142126581103050189299469236', '43.69940796973110548961589285984', '43.843042193713671815754809359042', '44.58807614485823172594610879990', '45.250461474954230257220261187152', '45.92597092330251526597490455979', '46.653277530610056992081000880143', '47.37798145217736028180002109601', '47.85765564540370180885894372524', '48.721092668279301046377307413671', '49.09307305668959515082316357095', '49.68619539022672392495636557684', '50.739435424055959968006696149596', '51.13217147932824669226540437756', '51.89491873676329730697393495719', '52.483062693865812237013190270814', '52.93548057134245359298425919588', '53.72820185474848219066816856383', '54.48616498217132403439916267496', '55.019575080134227566203796938302', '55.84701684328494807001309322415', '56.24700930874689357205435602489', '56.84431513978405063270446898320', '57.585147491664929139747688272104', '58.30578682434870394600659773343', '58.82989119179232010834729659280', '59.6865874150351009315112073997', '60.197283243304325359513065410105', '60.67207353018704874162679050316', '61.19900800489558547863029964827', '62.29748856097377987287369372451', '62.86513484282194647544946623397', '63.061986504071841910588693268507', '64.21626588244946447216781323406', '64.426237618219164489909569336366', '65.19895492731199081372733784607', '65.74342367945328108801072592279', '66.601365481166379950942826930160', '67.30932396348523592094085451867', '67.64826768392742048560768982034', '68.36980929988993992573690030707', '68.85679026540992394971599968740', '69.61756244616531194589627666258', '70.4491110166356481684107997430', '70.88857524171463422681586760086', '71.46533136335763633225785643182', '72.11561973222149926107024085202', '72.830394119017694866596620638316', '73.27635699888985554650909434949', '73.8986812298415747746133192515', '74.9411424138369830549631132935', '75.28554385528324445321260587324', '75.790772490895656390940241882567', '76.34644995977881309495777268973', '77.07852361409396440571212776930', '77.99019149045204457843548490468', '78.277022240080505404907187043822', '78.91657622962667438115045788712', '79.82699512607314313769566221535', '80.11336706515070484586427382129', '80.712181651959823709779419327716', '81.36283734881831018797338275833', '82.37151174850614436802997054777', '82.64206804498373509222117484445', '83.29187798634865081477288520327', '83.911886647204368126390185288284', '84.48546897456189313445202205054', '85.04572724587560865711031260574', '85.9036669279755308594786997486', '86.534895702702791451210757915192', '86.86677566844554253682552893094', '87.6844917040945891434441358594', '88.1622049226278475169164683134', '88.783765111227362017538427405305', '89.38331483104702798742627074734', '90.21818193128812128812764703519', '90.82241096259767953915116522233', '91.1746316689686416454231885590', '91.80122781891360048129962216609', '92.59011850341330985778046066986', '92.93819639102667064262868018434', '93.86873942994009999198020063567', '94.49747855845162399036014702290', '94.842738355389224301287352028558', '95.50437183154090269949741483307', '96.16894102091289257388568462382', '96.69548046232462838452479259304', '97.3641602835014204867442186304', '98.17491834840209674023398649928', '98.50038590330794985799900680860', '99.314973906201322307862341582875', '99.812292721999907336872361343690', '100.090106507089260116004831320212', '101.173728165134710948241313936188', '101.65917741163183462668714372419', '102.303444020206734334936792065995', '102.84930141653310086366649092783', '103.245538255408962622690187798842', '104.1432268992748674901457036257', '104.594301204616983930623991166', '105.13031258317030546101467944590', '105.95441349077031111077201821756', '106.60837491997776241213434196249', '107.02338599918762997363634017126', '107.52776736493090847213636641312', '108.055889399553042412010092488052', '109.030878733348930163099457955456', '109.53188262187070522619037614936', '110.0261711367712765732596562137', '110.595611279471069435097665590024', '111.32651308381508659849869210867', '111.797000114481125295365869985581', '112.30346200232274188869397344283', '113.20550466061954702618989157385', '113.53585824074367046684424660561', '114.567626000168708522765407500256', '114.83024251171568045632799798369', '115.084452213184520256901442963905', '116.13040352162726691666527673869', '116.5778542785096539451642524156', '117.295077884822471545331601696069', '118.04625730898909204363565019889', '118.238218599799295561948828942709', '118.987014585730891960480056999580', '119.62995889003172314436712046704', '120.19640376966196506321364892613', '120.665073691561552504153319438182', '121.53188210248813879034421313314', '122.216083945347866120418558386934', '122.527785680755489189105679307403', '122.92409595894155517306765334523', '123.79569042070826069591998495355', '124.4209754273533790047074519375', '124.95087146415538280554461216645', '125.5853913236860357997611222466', '126.29010207228867467407535023136', '126.60945718049908685492994988893', '127.35313261025999132533701356134', '127.70034430131836906864388321737', '128.70496936159740877732033007678', '129.13990271618757947984190582334', '129.60397205717895300134679338220', '130.42938492560109990863003418038', '130.84054586437577019684328847682', '131.34787990400009463161609503859', '131.8934286131899741586395609648', '132.8650925666749346553974486436', '133.39327733375457588699246925347', '133.64798679623577521002389706352', '134.410103664600207217042532714433', '135.04081911985744064179105718616', '135.44440301624921933004787020957', '136.17623440352176486329294727386', '136.92549231340359458871424032545', '137.24945930574603621495458013756', '138.14974107342154395300843857814', '138.3989424620233416001792040850', '139.06326871201709007363295170854', '139.53616894344006673602235939214', '140.415738583752240988914665677172', '140.94004268383796875265214394730', '141.58899478652322719076362924198', '141.90320120445974383261281950369', '142.622374535561005723228185960343', '143.09158506210514813202067827785', '143.94300073032710116113041776248', '144.34103913610730157229220161725', '144.910412627950702831326029732838', '145.72275686578712402941174489751', '146.21577120592366830800632098141', '146.69771001008933085817919397179', '146.93210138605382588381805074466', '148.10968963316824824115436355581', '148.57138159830913420658418551396', '149.056083091273598071833930508088', '149.56545008947401959330654741494', '150.26871065783791280770009184252', '150.70449598611004843535929696094', '151.4625747261786695900414309603', '151.838979546073498248753763719166', '152.62331773295455500473773303160', '153.29078613082884636049163229872', '153.76187347450476494279758851227', '154.109025054838621635029415109306', '154.917132027319697194084807017191', '155.26331606336257563569112450270', '156.312375394655104940109872253446', '156.58008121944492686439141214479', '157.30593228035781080301371856279', '157.56734697425216906970852802710', '158.57472429460151605095983114189', '158.75538491735740912464761441832', '159.404338907197288958612559849717', '160.29341431740165320069089393087', '160.65433910415441905713047824436', '161.38190690600249584321620304388', '161.70876308460861976474587715515', '162.4624957617398169600132405966', '162.79921747756429091220672860363', '163.61531609785757394245583033015', '164.26914105321402720865318626526', '164.828519993913594667824522850519', '165.21406462461282297207544689380', '165.84699359770903981584577625323', '166.4446413791455449646200934880', '166.990469925673363092455948468059', '167.568803086871558815590357124471', '168.31677158783246483980358534042', '168.94213340820476055534982011671', '169.155922873748720009460898967258', '169.95164561366993758755476416213', '170.4451260934742047415004665664', '170.96077699186084762061255198437', '171.72875117275399328612147517441', '172.271891203077509333456605154834', '172.943553858587110040195117345164', '173.38695558294272632640892837673', '173.68487931745581387726735941440', '174.57027865066298318900787950187', '175.09585048047182930095070416391', '175.721837509116302814566411740329', '176.355136522142320168146110517774', '176.65522592587721246756201880305', '177.6757061306115002987753027864', '177.92357584601160394923680167089', '178.19755653973416736908894881019', '179.16622661073246797457948579063', '179.82979664135575791878028180434', '180.38517720569069797164448267554', '180.83115486201356135997701480621', '181.19529473549344742294307054271', '182.056601004295648599811633862721', '182.50454200153495985527919565695', '183.126899090831299493814475255752', '183.66743112777870605092205962000', '184.46238667687424560492534544956', '184.81231709129449691595294506641', '185.31133412275214155984520718163', '186.111310452569654031832302657798', '186.29595977699907092275684456557', '187.129789140339768082400089517309', '187.95492163601731848557534505208', '188.28313782833062349536344033193', '188.771511474165472780220861421954', '189.29365276195744974867682431284', '189.92236212460526404846456196905', '190.68232976610330714925744903642', '191.1135964471575986171071078942', '191.54028119247737565197727734010', '192.51082308260807104604037134298', '192.84681919563163423562968196775', '193.42791493937350915519866999658', '193.61358343353038777111212103389', '194.60678338365009557197829609918', '195.320458558426368496165339647855', '195.58193259663566912588156307676', '196.2726018789266388568231940904', '196.85924748996992453220016452480', '197.28654562259875421527944375254', '197.87187888063956739233793452603', '198.51387783441995853841982727703', '199.15789776774261726924199780915', '199.65277328404508403150077684231'], 'prelabel': '1-2016-2016.221-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 216.64928838596404, 'root_angle': -0.9437840641650573, 'root_number': '-0.984445375420199302270189071683-0.175690929799414674926499648416*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.471892032083', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.00560613069272282562950608592-0.140618937919934977784043699292*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.103879949743', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.2084307618', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.17294332957', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 216.64928838596404, 'bad_primes': [2, 3, 7], 'central_character': '2016.221', 'conductor': 2016, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2016/221'], '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': '1-2016-2016.221-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2016-2016.221-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 216.64928838596404, 'root_angle': -0.47189203208252867, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.103879949743', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2016.221', 'Lhash_array': ['dirichlet_L_2016.221'], 'label': '1-2016-2016.221-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2016/221'}