-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_111.77', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.17364817766693036, 0.984807753012208], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.766044443118978, 0.6427876096865394], 'a8': [-0.5, -0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 11.928606652203378, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [37, [1]]], 'bad_primes': [3, 37], 'central_character': '111.77', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 111, 'conductor_radical': 111, 'conjugate': 'dirichlet_L_111.62', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^8', 'a^2', 0, 'a^2', 'a^12', 0, 'a^6', 'a^3', 0, 'a^17', 'a^6', 0, 'a^16', 'a^10', 0, 'a^5', 'a^10', 0, 'a^7', 'a^6', 0, 'a^4', 'a^3', 0, 'a^10', 'a^12', 0, 'a^9', 'a^2', 0, 'a^14', 'a^4', 0, 0, 'a^9', 0, 'a^14', 'a^17', 0, 'a^9', 'a^11', 0, 'a^10', 'a^15', 0, 'a^4', 'a^8', 0, 'a^7', 'a^7', 0, 'a^5', 'a^14', 0, 'a^16', 'a^16', 0, 'a^17', 'a^13', 0, 'a^6', 'a^1', 0, 'a^2', 'a^0', 0, 'a^8', 'a^5', 0, 'a^0', 0, 0, 'a^13', 'a^5', 0, 'a^11', 'a^0', 0, 'a^3', 'a^1', 0, 'a^12', 'a^13', 0, 'a^15', 'a^16', 0, 'a^1', 'a^14', 0, 'a^1', 'a^7', 0, 'a^15', 'a^8', 0, 'a^12'], 'euler_factors': [[1, 'a^4'], [0], [1, 'a^2'], [1, 'a^2'], [1, 'a^3'], [1, 'a^17'], [1, 'a^10'], [1, 'a^5'], [1, 'a^6'], [1, 'a^12'], [1, 'a^9'], [0], [1, 'a^17'], [1, 'a^9'], [1, 'a^15'], [1, 'a^7'], [1, 'a^16'], [1, 'a^17'], [1, 'a^2'], [1, 'a^5'], [1, 'a^0'], [1, 'a^11'], [1, 'a^1'], [1, 'a^16'], [1, 'a^15'], [1, 'a^15']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-111-111.77-r1-0-0', 'leading_term': '0.545601147211484902456042768292+1.91935465505296674962677404294*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/111/77', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.995395425401186, 2.6290625626523894, 3.056436560508473, 3.1290021803211148, 2.7011796347748214, 1.7156797588475594, 0.27876560526265665, -1.3199303503114745, -2.66690058105177, -3.355932793237957, -3.1481443257686, -2.093530030807921, -0.5489300691710274, 0.936530926039966, 1.8373993455309312, 1.8806506659704962, 1.1761633046749038, 0.1708243256873609, -0.5699432425353791, -0.6553619996548179, -0.08487364697478174, 0.7419728367255518, 1.2468787168790878, 1.0181373041305684, 0.08500569690896166, -1.0553428455039464, -1.7046213421762462, -1.3926077742956449, -0.21693959600969814, 1.1359306363587112, 1.7460256525704783, 1.0158245865525457, -0.9006125641177568, -3.0841867767647555, -4.312078495421515, -3.757570197897956, -1.515765482975227, 1.3861031647773536, 3.5369884680642873, 3.9412407368987963, 2.583820701949381, 0.40405635117862915, -1.3110745182572963, -1.725933277032951, -0.9279383387827662, 0.23148208316476687, 0.8011921997844528, 0.42427203735036284, -0.43420066602845037, -0.885090279291245, -0.33797009075984374, 1.001359460015105, 2.2508459612282428, 2.5175476117441478, 1.6055316063722014, 0.20202115753172967, -0.6428855222717439, -0.37461476421213147, 0.5400676514046668, 0.8826604160563034, -0.3847106607655979, -3.2004194382915414, -6.230996086425035, -7.662670738565165, -6.445285264041188, -3.0894732798652567, 0.6024517353322959, 2.7208384679007733, 2.5065798880899726, 0.7683392492003723, -0.831589014470866, -1.0597254788188, 0.023336414727467687, 1.2549014725346435, 1.4147469296523092, 0.24748286645716472, -1.3668886372070879, -2.201140841560966, -1.7324370451366924, -0.5516424646898125, 0.2126986049507329, -0.06258883697534239, -0.9213215030474191, -1.256411070855864, -0.38083758828030345, 1.226173682954366, 2.227592239931953, 1.6039641272930942, -0.3068310688168915, -1.879779240863813, -1.449283423716216, 1.2444378567874272, 4.648686197804988, 6.468639359860691, 5.418035084932489, 2.2351447341465587, -0.8902231269015443, -2.0292757034955846, -0.9660262109408387, 0.788767840880972, 1.3794005709668726, 0.1700643966690698, -1.8317879437720885, -2.985094362954211, -2.4929901893630775, -1.018308798336007, 0.05944918249247285, -0.015520838550739394, -0.7220479059825353, -0.8932356174729872, 0.015933452024161257, 1.295180063662792, 1.6436439883639815, 0.5203059637109249, -1.156022815766034, -1.730864634432869, -0.37103077072575624, 2.0150406141136603, 3.464412863660892, 2.7418107449820557, 0.6035245271013112, -0.7056985520665936, 0.6039836832031126, 4.177009749140767, 7.6303975258664405, 8.455760899299845, 6.071700814679811, 2.237699546230292, -0.4959286915310718, -0.8800419324883219, 0.24801570755833152, 1.0676252974027665, 0.599431032922981, -0.5013161974621672, -0.8422474561702522, 0.13088330938883094, 1.5107060904904963, 1.8684773604613818, 0.7597357085734454, -0.7812100514777495, -1.293778867735151, -0.4175666872144361, 0.7088774650845924, 0.6485757239126543, -0.7364893683874655, -1.9902396995827845, -1.5067600841133548, 0.6599099128162026, 2.50897753491661, 1.815528756913491, -1.6648613303453097, -5.658092322586416, -7.166948683805477, -5.043795540173346, -0.978001879708962, 2.0202744246974773, 2.2194209107467833, 0.44789331175980085, -1.0244236057194906, -0.7776131621997263, 0.558305604251842, 1.2498816974631346, 0.4244404833065766, -1.0237905001582166, -1.4627250648874628, -0.3141209637529686, 1.3253417543218726, 1.8738976355909165, 0.9536511897545035, -0.2616462153591742, -0.4159969586251344, 0.45916358052308304, 0.9578980678908989, -0.026973476780026928, -1.7766229460222827, -2.165860666732913, 0.1792907909823092, 4.149929574416793, 6.785677808684032, 5.884103170474512, 2.1097140929282148, -1.5300141426291365, -2.4263107797916765, -0.6979730801789807, 1.1366128823615416, 0.7542491071863899, -1.7253734656191333, -4.021097413880126, -4.076155894352544, -2.0421721648901014, 0.09405728391376021, 0.6746133726893383, -0.04407090564127382, -0.4837449170566005, 0.3076336429230514, 1.5928895763734965, 1.9179747298806065, 0.9326639857306359, -0.09181382106464592, 0.2929312668708267, 1.9306047661838102, 3.0483761482311147, 2.182817435638513, -0.04265645703796092, -1.3795466256243194, -0.353718020555036, 1.935248301786779, 2.7054417719066923, 0.3544329780258175, -3.6462294797140804, -5.923981050811047, -4.407021962453547, -0.3504407377023958, 2.877657732231207, 3.0115426666788787, 0.854752929649981, -0.8766437884293915, -0.44728674598907936, 1.3355915700736585, 2.3527112403728516, 1.6127256489355555, 0.16327557962160347, -0.37733207714117883, 0.1942419931037588, 0.5080987767572945, -0.5809980555799813, -2.4272648700743122, -3.182386668820041, -1.9197860634311739, 0.1916299198233145, 1.1246356564516138, 0.2948544623589089, -0.7680372521314446, -0.29522801330305976, 1.367145646042164, 1.7469472524291407, -1.1071071349889667, -6.0913416430212655, -9.550703017846187, -8.601528278884823, -3.952206043111869, 0.7237955154750083, 2.2531547156558993, 0.7204073882972362, -1.1858891636341093, -1.2780392380059924, 0.01506548625808574, 0.6314767738373243, -0.4519651347320413, -2.012901373141728, -2.1175163638517143, -0.45774161613877595, 1.284226893498096, 1.4092587377443375, 0.11675468330260481, -0.9015978749051836, -0.6307794749211063, 0.023254605842915926, -0.527028996082696, -2.3325754308339444, -3.526763025762513, -2.473359648770891, 0.002955513486653527, 1.1218313774085056, -0.8441583039521188, -4.344361213328856, -5.8099250470863195, -3.306522349148846, 1.3075057925673788, 4.143492007828638, 3.1636855728205036, 0.063532875813973, -1.7639053214881424, -0.834621415899859, 1.1760619346539007, 1.6822097295691416, 0.175017304654793, -1.424630654664943, -1.214457349752061, 0.4715561680699252, 1.6288133441709864, 1.0649549180154474, -0.28304068882335, -0.7147890915890722, 0.011281304590317936, 0.4422533369170817, -0.5135182714439118, -1.8839953903459108, -1.5980840882111345, 0.8809679998545336, 3.510428518927305, 3.7632124400114515, 1.6103678646195754, -0.19051358600310492, 0.8796594165407795, 4.087230077667584, 6.0029975172804715, 4.225257086600438, 0.16863615498524476, -2.274732714751834, -0.8052976447701116, 2.941490861534487, 5.2745035647290655, 4.325309769020962, 1.6319879098871959, -0.04088875259596637, 0.17392272219329136, 0.7754577009096095, 0.25701222863016093, -0.87227524994641, -0.8977587397726737, 0.6521822597403816, 2.160561615575933, 1.831122085193555, -0.04535841048791021, -1.3867717638543093, -0.8874703636554914, 0.36567372550225696, 0.3560813742647884, -1.0803155397088469, -1.750721093079656, 0.20413644747570203, 3.582313432596286, 4.909948187970887, 2.247051970720504, -2.280063702816225, -4.362848828140761, -1.9669098244925947, 2.538916431532299, 4.943046516278342, 3.543448139049112, 0.4962693926053747, -1.044011756130192, -0.4222386151759598, 0.35428352094892174, -0.44418349583555866, -2.068103976815567, -2.4383693086667404, -0.9554950959501229, 0.6943089285994817, 0.7080436038489313, -0.5426191895883388, -1.0550305035987908, 0.15449000903695942, 1.7539628732095176, 1.8633717106814638, 0.5819175137123708, -0.1238794732037143, 0.8023773295428627, 1.6611026543448575, -0.20401834436165178, -4.817313094048227, -8.657475665148194, -8.013433178255564, -3.055052130244229, 2.1077461122420695, 3.6351247699763256, 1.7553304530750908, -0.05100325153535007, 0.6866227779898058, 2.7708795990686435, 3.193644542711117, 0.9748651968532619, -1.708469433079139, -2.2518680245295837, -0.6579113272979926, 0.7915138226856692, 0.530967902344108, -0.5445621864034607, -0.6450226445983824, 0.341050908914085, 0.7557333437592508, -0.37098176116524506, -1.7274593750695184, -1.3112617796888897, 0.7664668620933313, 2.0716833232092218, 0.8228226456345997, -1.6323699874580804, -2.22063630108686, 0.003612813964329901, 2.3335155712209565, 1.4189057898407802, -2.5748365648186518, -5.735718830124965, -4.644367400537217, -0.22980721162348894, 3.26887078498919, 2.9899968694377104, 0.3115872137726339, -1.2350035054020476, -0.188282340968981, 1.5646714492297493, 1.6028115379116317, 0.019929196290370117, -1.0513088387832978, -0.4548315608505895, 0.5637102325022312, 0.28902510956720384, -0.9596179548174214, -1.2329283584432789, 0.2605931023570689, 1.8219798530524003, 1.357668061748193, -0.7652320698008852, -1.988540398833239, -0.8218791890908046, 1.1336231033407658, 1.2592368194325938, -0.3810587937398419, -0.6219047958431629, 2.944382287783969, 8.402330888869072, 10.897072710643826, 7.768226900184779, 1.5428881423934897, -2.7378005622689976, -2.733720051358196, -0.5941090616573197, 0.32321109220271294, -0.5723656278099016, -1.157314274930263, -0.01448612012299064, 1.5352895736305892, 1.3263424173416412, -0.6075622583832605, -1.9989401914777363, -1.3203167905423017, 0.2671609821628171, 0.5732755620029191, -0.6652815421302893, -1.5653441306298022, -0.8707387438312687, 0.18787739787922697, -0.3169435302005315, -1.9073349850720998, -1.7417692477439193, 1.7332995557202797, 6.112124799214442, 7.20234723840027, 3.872801485497482, -0.3248462248272639, -1.0353227282781845, 1.979170192275774, 4.742335136190746, 3.837151484601222, 0.23684344401455926, -2.2621408183817775, -1.7282447498310503, -0.02078480859875906, 0.08941213515827584, -1.4548942948539503, -2.2612134481874877, -0.9343950862053962, 1.0570136474211895, 1.4568488832626785, 0.22962045302784542, -0.5988604207758308, 0.11493781703660076, 1.107133337457635, 0.7367463695414314, -0.358396742147547, 0.07697592982718392, 2.592577354875769, 4.674656989095876, 3.657983320703078, 0.38960825452908815, -1.3536607519919293, 0.5742836710466903, 3.7929636745223254, 4.073276126528956, 0.512660259773128, -3.221418821590218, -3.239602974262375, -0.05056518645018456, 2.198717348411269, 0.7811472989189994, -2.5629791114467158, -4.10696567063256, -2.670519100828155, -0.519063692640791, -0.006707354315700781, -0.740421913899355, -0.823216239851633, 0.029558143378619863, 0.0645821405331446, -1.724566847150248, -3.7194357125533175, -3.5742859263543676, -1.38491985139924, 0.3344236514943316, 0.003588976849998582, -0.9207061535969818, -0.12522650498161225, 1.9997985381504277, 2.5186811740781763, 0.03669424173936434, -2.6892732557432164, -1.5821742309449907, 3.579194906938446, 8.22965983189528, 7.921455863699986, 3.2999731981231912, -0.8511872479477673, -1.1957450958650715, 0.808438038895599, 1.5280729456429119, -0.10102531972334398, -1.768288575800585, -1.3942701543543434, 0.07433176931408822, 0.30908368746058823, -0.9596329414787206, -1.6234704732777372, -0.32644903227881905, 1.491915249997482, 1.562734696642241, -0.0322509999192696, -1.0036312221848225, -0.14736907727076798, 0.9249005313016485, 0.20380294352379888, -1.536439021620883, -1.5593521719142551, 0.7374939950229559, 2.136972376778882, -0.7255407811378703, -6.632026434251924, -10.317331963181706, -8.194396389134566, -2.432032162808793, 1.6396244764083565, 1.5521339421889941, -0.21397380031202642, -0.19529310551944054, 1.5583848403029348, 2.1483863389130553, 0.2256383276350104, -2.0455989580978975, -1.936726889553855, 0.23973766523575263, 1.7425800936281675, 1.119682783806983, -0.2030320288355842, -0.40966622777721584, 0.0004810310710093584, -0.7519820960400483, -2.600791775846992, -3.244178481978285, -1.3883698213888673, 0.9770152215269767, 0.9042919814767123, -1.416043258759385, -2.5542686809620445, -0.36389121591798335, 2.7661288087854263, 2.6084914966633246, -1.396294792459821, -5.020969399446275, -4.271024993927892, -0.28205848494618163, 2.140076997146457, 0.42548516402926917, -2.916710102659464, -3.8386140647356077, -1.7541633571757074, 0.3631647526756858, 0.3054133969446229, -0.7434171595005237, -0.4971403700027224, 0.9431413003230601, 1.4071832385228378, 0.0384646376880959, -1.368329916030285, -1.0339796836627644, 0.12301054719757927, -0.14653264494244167, -1.8958432077616603, -2.5448027417919725, -0.48406238062037665, 2.317022867364802, 2.6953982711819204, 0.6581895118703786, -0.46293861584345175, 1.2913661917581574, 3.2610470020270164, 1.215923122380842, -4.850157598928548, -9.830840544027877, -9.112827767294657, -3.8226909971827716, 0.766288955211939, 1.4216007036027865, -0.08257526285614454, -0.35519723829197747, 1.0264570392600472, 1.7524270464824234, 0.7405556468484336, -0.19450384017660655, 0.8081546198974983, 2.707182623966432, 2.924644983537565, 1.045013924499941, -0.5480123520702578, -0.030206843496313272, 1.3889368273702987, 1.4504302995286456, 0.2947733530957331, 0.1447220985829801, 1.5372705766811217, 1.8112937696754114, -1.3179901685993516, -5.762973057514598, -6.6853375623015685, -2.4072817186068702, 2.995482743105269, 4.223723178773661, 0.9367632191908384, -2.2218533935297806, -1.627644832372111, 1.1284480810939614, 1.975340515926431, -0.0963612312507285, -2.1106633049964563, -1.5251852344481407, 0.43466972626591893, 0.9130707637943173, -0.42410747609851124, -1.1795586232043156, 0.059169638667357194, 1.6710366425066505, 1.5034896040686752, 0.050220003313238254, -0.4417279511896559, 0.48968295724973043, 0.7807298354514841, -0.8321475799303886, -2.434974918848191, -1.4627278217280606, 1.1766003162910137, 1.6085711810058168], 'positive_zeros': ['1.92968763949086467834074663928', '3.85785762330755023242120404130', '5.36967192071794529042085605623', '6.282982972287919539150920193725', '7.52295606774409013843532541453', '8.79751194302037289932349180878', '9.86933403806298517575999899205', '11.41245496654935982668355967981', '12.87284297592872490895675452522', '13.99398589426781151129329513322', '14.84424847147796771066142277902', '15.71576872345548240955743405660', '17.23874540385486348220917121881', '17.94627583337036141763866157155', '18.69003916621496390194569339232', '20.56803081485282559015564231293', '21.691028162630939663300111614698', '22.49477768632714784392595393707', '23.484794710734514766208408624772', '24.86658820818458413688075528754', '25.28447058849175479006041240968', '26.32869024667799349744035532615', '27.45407082645259629389611159581', '28.3166916929756092395004572533', '29.89585602043379156774479048109', '30.78905957404996275310585218785', '31.590272438447769850926230905118', '33.09327439584588443650409831370', '33.42887063958451107829106823782', '34.37117437871323313940593464183', '35.40649584074154558415155096622', '36.301589968521699757660910289755', '37.5961708453621681479827565541', '38.04579635590153808494073246105', '39.91895044333993264399899660579', '40.56482355204745998784936309775', '41.41669434952909234042920643430', '42.15828886024458837797272814427', '43.27006089319857151185196700672', '44.16361441127699494345764782919', '44.85604796839340891600131169178', '45.85328395403493309318326194981', '46.746750585129063402612381962040', '48.20492510429891320562772937974', '49.13474277062982657751800750860', '49.87438988875529661607040644485', '50.71438765663996230755005412334', '51.61960646503690267194380067385', '52.72888942079762371066419915020', '53.29335936512178135513107667908', '54.05739288115575826016106782951', '54.984068463261526093771148523234', '56.41156950017300252192020421260', '57.284435528458701496213262150726', '57.926464150542414934864361651517', '59.356007811968391103531324529992', '59.98406536996964214976938258389', '60.544478736261465006532814293440', '61.8261092536096842909611596661', '62.094678036221861457258589502096', '63.43141990267251256202107591002', '64.113547803504880061657719510100', '65.02950506243263776290871567324', '66.27620885776105463048471004181', '67.30663445134163282107125365923', '67.899361949593460625593340991462', '69.10834849684387016329260024595', '69.60588701344507529291517291218', '70.19397436651406875905426758385', '71.53049901905336182432618863597', '72.25707902785094879318974162736', '72.874660972506273140731470910675', '73.664243459536144411581880128705', '75.251803814277684944534575342457', '76.03825763488576684242740356249', '76.8713842926956057886091636437', '77.409646068285011658853868996052', '78.50694040258804630807678898126', '79.40028977790626874775178388235', '80.288307283168964685066199723859', '80.43978852385241445132894199301', '81.87459671088106375918819489441', '82.411366232253592102658073571263', '83.66056107786915795044214105830', '84.694209369080619058826368893262', '85.43715180921155225884516865536', '86.27766145893249997797686482007', '87.10685382119399954524974616687', '88.05240922117186941430214383456', '88.74599331804197472789768080891', '89.25599289901023766650252890439', '90.21988346146221805065391450860', '91.49618164943181379015485561902', '91.734577176983721460322559956050', '93.13863086106635894310315300', '93.82326228022118892932831564975', '95.29404813133772182247182076071', '95.54591530533637894943223328734', '96.319668680340627209567820877011', '97.07818432161878356845088343424', '98.11789302421965617920806698715', '98.957572146587859193426801331810', '99.470242451738000667288991851024', '100.29191309222533942420084541691', '101.40276235984453707800863002779', '102.32399216507195569990389780460', '103.49954465243340307449534301294', '104.18432322326838858379138240777', '104.58434659497043591769699927877', '105.78220816992101889556146087944', '106.435005094245322969980779139550', '107.15990583704841605581669583182', '108.29546821634478440406594732554', '108.52803850182466726125598488268', '109.35672198412768580292538018359', '110.79255839243699568442310332935', '111.85383476615378085887127408299', '112.03544892666902790195477861423', '113.22644408882875072766996659266', '114.173265461370551923848245949364', '114.83537039504730349480733135929', '115.52651253210734409882790384660', '116.17575352700751316148979765634', '117.08107340974688436789640893569', '117.915075797337307766250067325263', '118.74961631635483790272403884640', '119.50184802822084297190727179300', '120.64031806343669560101509284424', '121.60053091895957181339614404447', '122.21804349430964749607244154011', '123.128660888097391724155462697681', '123.86910897829551629111290836186', '124.45350622129126960289556360274', '125.27059687579289566846764195443', '126.14354624576706694792715025210', '126.99510165950597405433317843635', '127.74261200772310067659439783133', '128.21429321097574968695118808576', '129.77264887544215865955626943187', '130.74012927926789198524301795778', '131.09342490435541446453598593033', '131.87757690880499069434124318603', '132.723960350748563280468718395311', '133.68858647588663410177737250989', '134.23139696190741866783693416331', '135.22853423687956420489174960301', '135.54290991388381404844642102584', '136.4365019213918733738921392867', '137.78022283657592450959168878902', '138.26139564386718793971498268024', '139.39538251960679076205503144322', '140.31789782150998661284065133390', '140.65090342954821886033150855010', '141.69754123686721593864315971395', '142.55331596310315584904987390819', '143.09481299192869666438351200378', '143.94358251078691729527576119132', '144.36008174650837196295360010409', '145.66488117089774985169167231623', '146.19287078147204814853369584249', '147.22325542066789404155853212857', '148.12955668776170357737330055564', '148.82588975383717278144696900626', '150.164363477089738141739084020816', '150.30723220658327682994447678697', '151.23851273188658350291934500539', '151.58280131376841452997293796329', '153.0272029230290834051122029927', '153.43853897462880774923894213707', '154.08326045213084914423292825952', '155.00341574639380987072401071', '155.73904354367223007409821061411', '157.098936840128495754801642317715', '157.69156461379647460029848975570', '158.42291546290062178471791149479', '159.355664707364237811710937056854', '159.78543707776441224037745185057', '160.675315985308530244045290718131', '161.556582743306577566415591076', '162.22015830684783198496327124841', '162.84986503793073367542762669049', '163.66302626529332243706724990985', '164.327619190208522203934625137434', '165.77422476699589414532277969384', '166.51465255952183156381624708498', '166.91891225714830885333842714869', '167.83886906982842799492478679222', '168.71813059238053936297879060164', '169.62651226321441349107199062888', '170.310218619885485355409116599341', '170.34192728736839325819445552627', '171.72533470019156433578479016770', '172.324203523350954774023156607681', '173.157951056862896172165380968849', '173.96969295308124474708981978492', '175.02230415503540605408945511919', '175.664410650634180370933452472589', '176.795602708723083816813336537832', '177.27426454051513801919575380342', '177.92847307216321843066122565531', '178.75661254480996821406422592761', '179.64216098467093913517227766852', '179.96118725413461576324978475827', '180.9867573787517812054023920511', '181.97995643558668143962419488209', '182.323479104958591588958395914437', '183.19962560198958217576395736740', '184.61360926105844202861438797128', '185.29336294950452159421554279992', '185.72614628120815706243353135064', '186.750987156412205081866531281218', '187.014436697291857080377188251498', '188.288244702651355765910538429877', '188.75673081403415155080059165264', '189.81715380964179878506484766196', '189.92515372042135001011676827123', '190.83966681629761545197376603569', '192.0016872382541227583836558415', '192.88445781279939050512289647332', '193.62035171662239224888239323646', '194.363802427042621761229221353764', '195.23603583696224947764037782117', '195.85257332798056478030614186976', '196.55263024176330564156557741501', '197.512232166866955021819866945839', '197.985672239213693462276535429705', '198.62219461399337835858433297007', '199.54539431096726303334862644646'], 'prelabel': '1-111-111.77-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.928606652203378, 'root_angle': 0.823683561132639, 'root_number': '-0.850471973706385539559586267179+0.526020362666660522735393130566*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.411841780566', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.928566586116929673606694806588+0.934437359165398234165108660468*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.92968763949', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.85785762331', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.36967192072', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.928606652203378, 'bad_primes': [3, 37], 'central_character': '111.77', 'conductor': 111, 'conductor_radical': 111, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/111/77'], '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': '1-111-111.77-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': '1-111-111.77-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.928606652203378, 'root_angle': 0.4118417805663195, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92968763949', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_111.77', 'Lhash_array': ['dirichlet_L_111.77'], 'label': '1-111-111.77-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/111/77'}