-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_25.12', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9510565162951535, 0.30901699437494745], 'a3': [0.5877852522924731, 0.8090169943749475], 'a4': [0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8090169943749475, -0.5877852522924731], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [-0.5877852522924731, 0.8090169943749475], 'a9': [-0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 2.6866231198656254, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]]], 'bad_primes': [5], 'central_character': '25.12', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 25, 'conductor_radical': 5, 'conjugate': 'dirichlet_L_25.23', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^3', 'a^18', 0, 'a^12', 'a^5', 'a^7', 'a^6', 0, 'a^4', 'a^1', 'a^11', 'a^14', 0, 'a^16', 'a^17', 'a^15', 'a^2', 0, 'a^8', 'a^13', 'a^19', 'a^10', 0, 'a^0', 'a^9', 'a^3', 'a^18', 0, 'a^12', 'a^5', 'a^7', 'a^6', 0, 'a^4', 'a^1', 'a^11', 'a^14', 0, 'a^16', 'a^17', 'a^15', 'a^2', 0, 'a^8', 'a^13', 'a^19', 'a^10', 0, 'a^0', 'a^9', 'a^3', 'a^18', 0, 'a^12', 'a^5', 'a^7', 'a^6', 0, 'a^4', 'a^1', 'a^11', 'a^14', 0, 'a^16', 'a^17', 'a^15', 'a^2', 0, 'a^8', 'a^13', 'a^19', 'a^10', 0, 'a^0', 'a^9', 'a^3', 'a^18', 0, 'a^12', 'a^5', 'a^7', 'a^6', 0, 'a^4', 'a^1', 'a^11', 'a^14', 0, 'a^16', 'a^17', 'a^15', 'a^2', 0, 'a^8', 'a^13', 'a^19', 'a^10', 0], 'euler_factors': [[1, 'a^9'], [1, 'a^3'], [0], [1, 'a^5'], [1, 'a^4'], [1, 'a^11'], [1, 'a^17'], [1, 'a^2'], [1, 'a^19'], [1, 'a^18'], [1, 'a^12'], [1, 'a^1'], [1, 'a^16'], [1, 'a^15'], [1, 'a^13'], [1, 'a^3'], [1, 'a^6'], [1, 'a^4'], [1, 'a^17'], [1, 'a^8'], [1, 'a^19'], [1, 'a^18'], [1, 'a^7'], [1, 'a^14'], [1, 'a^13'], [1, 'a^0']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-5e2-25.12-r1-0-0', 'leading_term': '0.644730020182879814210777881800+0.779344716476498023783424980295*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/25/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0114618065082093, 1.2348990748320934, 1.4358140104105623, 1.5874400282922856, 1.6439999614563099, 1.5532760962000438, 1.2717418031498455, 0.7793692330783575, 0.09194250273009483, -0.7318042929992498, -1.5911178571020506, -2.3542801511735196, -2.879869088868107, -3.0455557273917897, -2.7789217312821406, -2.082735299035451, -1.0467669850797783, 0.1598508099844664, 1.3175075205213764, 2.2022767352313224, 2.6395539522700315, 2.5512973247997053, 1.9824208913074985, 1.0957555731069961, 0.13296280153742812, -0.6509627965742464, -1.0624318769895122, -1.0306268190450525, -0.6341418417215606, -0.0802520728657103, 0.3614418110971038, 0.45330981835821194, 0.08219535250111933, -0.6828246870688375, -1.5922218089311295, -2.283898641879449, -2.400643992727199, -1.720572908454689, -0.2548412827269002, 1.726373186671179, 3.7565922849284443, 5.310520322263336, 5.97332636804923, 5.58300723285898, 4.29217509177082, 2.521697747791715, 0.8175829190894115, -0.33984372757725073, -0.7041887351655096, -0.34353163673040626, 0.40030714974687326, 1.060199302241432, 1.2419104345046816, 0.7912997105630554, -0.140410847394438, -1.1636564301978947, -1.8243279525351013, -1.8110003958913317, -1.1040505346509772, 0.003322824096517963, 1.0278161162704862, 1.5132958278799469, 1.2469785737058376, 0.3733848148844937, -0.6540590522491913, -1.2720494132831535, -1.073897252630426, -0.022734269172693965, 1.492916817286822, 2.7989997047900665, 3.220112032416482, 2.386140439542796, 0.421453126176876, -2.076603092317026, -4.270131903398033, -5.426493648678383, -5.223765951106622, -3.8764197760459504, -2.022708262573137, -0.4263921552239573, 0.3661802432269342, 0.2509496583083364, -0.4320057142358247, -1.1141223868297547, -1.3168615689560734, -0.9062264066038335, -0.14952025150634443, 0.4557213135852476, 0.48850147279957723, -0.12193020305767754, -1.0125464924970529, -1.5526658518027774, -1.184103082536087, 0.24164978829574885, 2.316979523735711, 4.219334105130339, 5.087739432954642, 4.452236465837682, 2.4941333479992185, -0.007976680095588091, -2.033146515143342, -2.802276655522454, -2.1465312112931922, -0.5693184840605444, 1.0314337579632773, 1.8353274248545992, 1.5166426639711896, 0.38645777653416885, -0.8115989373551243, -1.3344814228337833, -0.859174898748168, 0.3449352899161861, 1.5841441618137106, 2.1488981846079707, 1.7252393695118724, 0.5701829822920068, -0.6507816781456581, -1.2672831356351746, -1.0073751669136473, -0.1554312053465645, 0.6372328148087396, 0.7816049416436621, 0.1608396695449641, -0.7390687974535939, -1.0798432158048317, -0.1765056884291469, 2.0326811923479333, 4.841003851288124, 7.0668270635665635, 7.647364328137938, 6.210864778593789, 3.302788319529593, 0.12803830198026997, -2.0566905567486016, -2.566397579640533, -1.5838913893679434, 0.02497084989360228, 1.252155769392041, 1.5174829981555347, 0.9352817956482689, 0.13873524993220643, -0.20296087947684885, 0.14637351414247546, 0.838301645719973, 1.199514783051622, 0.7269330012793451, -0.5158218188855691, -1.8768585692963085, -2.5046250411026567, -1.9091664577572998, -0.33076448229353084, 1.3429609235770648, 2.089280828961696, 1.3887448976335928, -0.4122300859419386, -2.26121336589614, -3.008167716109438, -2.1014123545457988, 0.05885317102969181, 2.338767323463563, 3.5388532377261406, 3.1070410270831452, 1.458130586376606, -0.2972078628839208, -1.0430722877145313, -0.33619637521901435, 1.3495660438784638, 2.9542214522426784, 3.5134434199470395, 2.7480998856842698, 1.1889570611263087, -0.2242703180023575, -0.7839730023654272, -0.4588823124550659, 0.15163233894013495, 0.3049958240925116, -0.3104684695560198, -1.3311438051593922, -1.989659010068372, -1.7210389485412412, -0.6704648898631865, 0.28537837302562635, 0.06852623154059743, -1.8416435902127126, -4.931524163551054, -7.814201470709488, -8.97757651442081, -7.674461071112784, -4.3937213038003735, -0.6023925700597008, 2.090406950745087, 2.8272572509843985, 1.9007823492262026, 0.43128614493183304, -0.4311585056114216, -0.2361717647430846, 0.5792076414051176, 1.1311426982430064, 0.81078297358305, -0.24160620606488709, -1.2459927545715939, -1.3834488143500554, -0.4388983455919763, 0.9958568326672927, 1.921989386647871, 1.6571934070721115, 0.35662465153514644, -1.0628445352667635, -1.5639624656443598, -0.7479065218527772, 0.822429220680984, 1.9930878457313406, 1.8472144786654219, 0.4100878133724636, -1.2887011630645135, -1.8779197764928868, -0.5996119264632461, 2.102972321765047, 4.791799485912827, 5.922715470880932, 4.829968805740589, 2.1454851549768175, -0.6258228047520138, -2.078060227117492, -1.760594566506724, -0.35309941148661983, 0.9181654266694489, 1.172568523757348, 0.43303655152524184, -0.5202209337862732, -0.8400145045133307, -0.2920528259312079, 0.5995454352353757, 1.0382289979886228, 0.6718318621168927, -0.04876092805941025, -0.1875238971720839, 0.8949068889826903, 2.8965895378049336, 4.6063532051370215, 4.666408304444031, 2.559622927312602, -0.8962941215946134, -3.9519403119614527, -5.000845312479334, -3.605752283462583, -0.7662245893945064, 1.7626152383333753, 2.626757844834258, 1.7030518953603722, 0.04464088858864988, -0.9751629488808782, -0.6702352442840415, 0.5324951613123103, 1.5261911747639694, 1.4469374436812528, 0.3633176546112618, -0.7906218768600697, -0.9692681824493332, 0.14342748137125902, 1.8662446237488473, 3.035033522324948, 2.894274950683209, 1.6639562746162457, 0.3335357076274429, -0.15468225810506542, 0.3203893359865053, 0.9603226096009203, 0.7301397753456067, -0.7033786563626466, -2.5407251862005533, -3.3268819157046634, -2.0369130574315, 1.033860577221053, 4.283644562273248, 5.783607590888622, 4.561205187044884, 1.2738292468008126, -2.218368236664415, -4.0801735311102805, -3.6567135486394253, -1.7563868547695496, 0.08150379838970963, 0.7362113047316495, 0.20669783006733938, -0.6071794036857259, -0.7832791612350474, -0.16184685268874624, 0.5951234371442486, 0.6777669527034256, -0.06944675791320111, -0.9261380023908776, -0.8745045453406, 0.48663706375757965, 2.4707941433505507, 3.7256050877481517, 3.2738880432548667, 1.3624384844621513, -0.5945002947712921, -1.0049519004571168, 0.6953931962073948, 3.5495483877995895, 5.71072471421325, 5.75566054807145, 3.701164888264003, 0.9575890532952958, -0.7404042044613552, -0.6062106055330905, 0.688422682711578, 1.6297302793372312, 1.094489782341381, -0.7750137404634753, -2.7216471838331917, -3.395119514974956, -2.409405653013386, -0.5993049003960438, 0.6948947384325992, 0.7009017873809597, -0.23536520649480785, -1.0466404286986122, -0.9160962792086054, 0.01999714137368188, 0.839235855638736, 0.7161102872006041, -0.2619609178212246, -1.0942731288244594, -0.7434297559425801, 0.825340958416894, 2.360241142363063, 2.1411344433673682, -0.6602617385464522, -5.141373708946729, -9.075350220372087, -10.34335315064496, -8.361160050409703, -4.442760809390715, -0.8398625491529129, 0.8049190151149425, 0.4359443337310545, -0.6780509477442508, -1.1339546882966114, -0.5056861303659838, 0.48906125071611645, 0.8052331684866078, 0.09421997348297702, -0.9702943460090327, -1.3279122665355083, -0.5404975028956265, 0.7428398030718161, 1.3074373609278125, 0.4531790532085861, -1.3097015040302151, -2.5933787415875957, -2.263579810879271, -0.42912060313596034, 1.5750498782718523, 2.2514501672528326, 1.1954685187239906, -0.515357569913132, -1.1688577872811003, 0.1540424530792971, 2.74071897805572, 4.718963192420504, 4.500713663380728, 2.051854487992948, -1.0377961290499749, -2.75081700643526, -2.1538570125852976, -0.031039758318588323, 1.8285568706388367, 2.067875420303427, 0.7475999904135272, -0.8726936292169077, -1.4893307656118628, -0.8233778804164342, 0.2816009381359363, 0.7379412047434565, 0.22739100101672247, -0.5714056800186731, -0.7220588959584506, -0.021926591733805595, 0.7144917644772871, 0.40560964129191646, -1.1524021911134863, -2.813723063934833, -2.8291026693841164, -0.2962330296428616, 3.883909675927224, 7.426227344006458, 8.23770588233674, 5.953449051266393, 2.2131089669913484, -0.5581722724071103, -0.9084291733507508, 0.7149812645439657, 2.542756016238718, 3.007733885603713, 1.9287826114202702, 0.4269594693054396, -0.2404991144337595, 0.15927333655671996, 0.6978545491537189, 0.2415928482843641, -1.407411021673797, -3.2406170185533263, -3.898545709474817, -2.884160257003826, -1.0342224514943346, 0.19123255826132635, -0.023275730741492313, -1.161820571164524, -1.90038024826182, -1.3786021221886597, -0.05989472973382421, 0.6423069560927818, -0.30745807853651674, -2.460349610589396, -4.047870464861335, -3.386160036286339, -0.37614762023571985, 3.2046109272903687, 4.951883668804601, 3.6631076302192183, 0.26635454496376604, -2.9055972485553694, -3.894849777019831, -2.505869727857736, -0.22775783100500552, 1.1325797252034393, 0.8859710017557616, -0.2165058135062896, -0.9154759422943353, -0.6765036872639066, -0.08418616155989087, -0.10308909072097107, -0.9882042012817704, -1.9407155423816538, -1.8740559128011856, -0.566874805979154, 0.9415782292734705, 1.192258966129967, -0.30459766522405074, -2.4111176049335024, -3.1425727702174977, -1.3253742132634945, 2.273760853540239, 5.382289005427736, 5.943381705328773, 3.723663953157394, 0.46515452853211847, -1.5433689831886943, -1.2678890597953854, 0.39755298340574674, 1.5914342860379376, 1.1773056898279441, -0.32374919438326644, -1.3285151151534305, -0.7107523940105926, 1.15344045651454, 2.737691624363913, 2.7529354926582092, 1.2847834864507155, -0.3417677661481811, -0.806465185482445, 0.026525916321481102, 1.0762473623754747, 1.1508938551385341, 0.11405626444179505, -1.0125403817647654, -1.1098417751835976, -0.1515714965481308, 0.6756891920573798, 0.12894612844716316, -1.7001634048595475, -3.126557068518534, -2.152913726671483, 1.7189595533621351, 6.742209669941369, 10.010926753725759, 9.583399889744054, 5.921798581915417, 1.470356262884747, -1.249684670841758, -1.4329216987656732, -0.24539660686429138, 0.5078923612519822, 0.013725311321931966, -1.047217299041155, -1.4275058978014141, -0.6549567356821777, 0.5257982562242816, 0.9842684394307584, 0.4232962598487266, -0.26575699477813874, 0.0977747196268673, 1.6960740918115298, 3.33418125574434, 3.4338108780838077, 1.5321427842060427, -1.1381219627687713, -2.621555356299278, -1.9585536350735941, -0.09042258889126412, 0.9309208696887695, -0.2197649949937392, -2.89485957883627, -4.971930456070347, -4.694846213671446, -2.2330103104222547, 0.43680104796065955, 1.2297087382182594, -0.2735150814351937, -2.5384333744349217, -3.4902965062052322, -2.3297089445895045, -0.13628772173019998, 1.2111280264642013, 0.7420758448308691, -0.8367314945281918, -1.9403227670794367, -1.629493329715061, -0.39608376498853504, 0.47447074610561313, 0.2502964680120629, -0.5630971736214009, -0.8731751562142567, -0.29139830608168804, 0.3062118836153462, -0.3799023490827422, -2.582997896675633, -4.838999460285076, -5.013527133225279, -2.217085291721359, 2.1178164349503477, 5.104680166749513, 4.618952880181035, 1.0109167875655993, -3.1651295057871236, -5.184475469070079, -4.211508994906649, -1.6764467145769877, 0.21361341561397207, 0.3910335485316544, -0.42602351057619026, -0.7772774019562371, -0.03980503148326223, 1.0138904993956905, 1.1470922030847817, 0.06267708671327388, -1.1762162234493931, -1.1566687600591392, 0.44074340618846264, 2.421307658833557, 3.144289740188427, 2.072181901399506, 0.28528803601613345, -0.5736359473928311, 0.07775417351343542, 1.1670558560173938, 1.0335229148126737, -0.836862233383413, -3.1128031271965293, -3.7291708103862957, -1.8485012029518662, 1.1738054869533325, 2.817693117863326, 1.5803166055520705, -1.6422486705323867, -4.251459508218029, -4.130927020200643, -1.3887361524585708, 1.8512366934326594, 3.339372272542401, 2.5238419463345534, 0.7266008962309224, -0.31516711805389963, -0.047761204233591474, 0.647575025658158, 0.6288731288992231, -0.21766386403300317, -0.9057626736258014, -0.5103856063382265, 0.7181069681425866, 1.5259141259123221, 1.0076361438009642, -0.25529874993903234, -0.5540860690118352, 1.2715184430766977, 4.422571653945815, 6.482622093406588, 5.401502356638545, 1.396235960401495, -3.0112973189364283, -4.9644428719095135, -3.557795835375429, -0.43493808396472067, 1.7805104238302127, 1.7483492594530952, 0.3343169967029267, -0.5236669087063556, 0.2035287453705404, 1.7258135810687518, 2.38115460753299, 1.4011532840487995, -0.2905337786589761, -1.0126009024100744, -0.01957627962024722, 1.7534495932327, 2.6276226660519253, 1.841794558076194, 0.2684622583585408, -0.5188968279919972, 0.1384172427363482, 1.3389763328209523, 1.6068058818405229, 0.4878658976533953, -0.9247731002831089, -1.1567799329349202, -0.07342991240005521, 0.6555206521460573, -0.9955858624785393, -5.302083310651933, -10.07115377950299, -12.174342115885075, -10.09393637442873, -5.226741807240034, -0.7565549068497422, 0.9077739463056279, -0.13031711228864476, -1.7752845970283078, -2.053019393510026, -0.7798265192981944, 0.6545739439192076, 0.9359448288455554, 0.140270520145395, -0.5499663921659765, -0.2760101696657061, 0.5268863250205562, 0.6684847225497021, -0.3482499770734655, -1.5783680928786876], 'positive_zeros': ['2.53697086841699069617471037383', '5.271666807742885535512824955853', '7.546235426316997947360196195419', '9.10948746674385242248092493874', '10.04127195440645353175684419329', '11.918653617674503527194083085845', '14.57262733679717144719959217015', '15.465058561758441375706318282157', '16.83308497875659815585739629775', '18.43659889685501390907522205087', '19.79751353288739774116964077882', '20.94263438758535628752522516288', '22.554738471618482718543933796679', '24.81110471234110254220674287560', '25.44479545347519047315252707127', '26.937370590951947319496327143508', '27.76592015262657287458855724947', '29.020891228401326118514567875090', '30.93647437606106020903457044129', '32.290098339412004849073389491877', '33.53029009449851364147581123610', '34.60708824148501390198007573854', '36.07410042646804915281895378680', '37.23956141102694371665256472252', '38.18032658172820478651300422064', '39.09525480081067716060088301292', '41.26411348306455394772890018342', '42.49502833319671315349974307526', '43.822973862734365723352663661364', '44.2941273764080429102353474697', '45.50991931679339646618139861647', '46.932076847664354538198028234834', '48.0611878252549736743511441833', '49.36746060445183087078478939101', '50.87550858001472352838356819827', '51.63472690792848857327189699096', '53.37616340398336450846293846285', '54.288251226033894052561093665791', '54.88335402078418443166491863190', '56.44159334680065073744925517635', '56.89426689698612697877540590324', '59.11852007807877315008209707833', '60.42727528327599412550675891934', '61.038592229726976852688044843445', '62.12373228752408183164949109978', '63.22224266550044278462318201450', '64.44667128258382113064638834184', '65.46683307388468069626178985535', '66.63290041724153511364802449659', '67.579765174876420680285665876879', '69.29528704824002764685889979897', '70.38546102370092492846116362087', '71.38197447448722583462696057154', '72.289032853197095421155110583366', '73.41263312689518576861488093221', '73.84320533694915658752110117984', '75.54735338543844250116989167475', '76.9571283051942977326491795689', '78.134126942936291472484336817196', '78.93521872770552549402987029555', '80.08659597460648023007628286687', '80.908919283401510261182367942858', '82.6285733692903487234601936334', '82.971360293275027998361197895652', '83.93496848165137307235063310724', '85.21847474449847038716896384621', '86.669034867123111815701774586513', '88.10662562923833513943119297331', '88.8233993875813121737574562783', '89.74696280943238993961032400551', '90.602654556890486966497859179958', '91.476179760761454887689088597467', '93.013125738691966695023197994748', '93.65721629837101195847660421143', '95.45035277062048332945553562390', '96.09726189498251760206345606571', '97.07303005553341630385908888237', '98.552531137139966822609992820656', '99.30636664588396578212266117362', '100.30660196708523876231043655711', '101.17681559155409771216871281169', '102.04241050295808665828454736615', '103.07028668531781870055537958457', '105.10967842091563573112356652475', '105.74716130722349228556244862908', '106.71365027386661870277283576430', '107.52721401200747710863156519104', '108.56722938259557980826174325527', '109.46247918538933286155408694481', '110.685700167240919440255254073293', '111.77432549907652936775974286410', '112.47769573258436638966553166043', '113.95117597493521925714082478728', '115.004217213678911900580014884238', '116.07140878643943507912019638685', '117.10051310546152819063540335772', '117.895682870391553274944490251641', '118.75747983696846423654176045427', '119.477917199573716352562268180817', '120.649818894081782285405428169136', '122.41294324351634285611478016321', '123.01214519695306829821069829136', '124.50644347836065374099937648439', '124.92366403127631960363625713429', '125.68517365058942687729719789696', '127.41866106533707037212494821371', '127.80397460075305941820041889684', '129.07748817838790911973041738473', '129.628730167473007175023733059295', '130.96898607439938004721033742459', '132.21003230750110608609550371727', '133.47307408385042302506233891356', '134.31470580259830622844180495208', '135.394579870454895010215460430101', '135.53707963142045391985943638610', '136.98095768614364775755271566922', '137.766133341195981346051662891161', '138.874223617894296144831893117552', '140.36369225531668540347181634540', '141.18010975928346751379568332694', '142.12325594246867434186269646135', '142.94455943792870890143679802023', '144.2954981401542770892391996492', '144.992950710114830613297954568424', '145.964702409436739311973195569597', '146.91671504621583961355459296374', '147.5283923988957970452932688919', '148.63327366422682159763314801712', '150.44582125340939414068596777905', '151.31587891680028687451940963807', '151.87932855387254886112839040722', '152.97844810610037428949083787386', '153.91094804598371767593415851454', '154.34475448798045868246527559989', '155.8002752810467725160761657510', '156.89100325035822800644067660782', '157.4673213397850170257693832943', '158.99975268849302290861684048665', '159.64856370840611787538391308650', '160.95851966814444903607591242788', '161.71778564635405204247327158410', '162.918468073687338160330616294152', '163.53808049927379953154494672115', '164.48917250489794964215784676145', '164.90872755705889490499948184', '166.41130739651281366378250194806', '167.5709361502387756469607163124', '169.00765043756157756301589133614', '169.53573802369397849527909605558', '170.323611880114023728896815218341', '171.26375675565219282411811599926', '172.11929895589817974460164828082', '173.49921109330118048416762606342', '174.04116116922462078560272669875', '174.88559182806809595805778317632', '176.12625063144487686269022622046', '177.03798618156569478314542172902', '178.25042900482678672744707297942', '179.5424450899406897008697093445', '180.02081053450200863520201946872', '180.8683383760149311456430445781', '181.70233521219751068146057869494', '182.74487155525401326429127706059', '183.26554577871899744259028267514', '184.77921413762727958345441934051', '185.983094594866564731719430095407', '186.95273133089990179997974195134', '187.451547147183744083338169328702', '188.691445910124140141165702090108', '189.3786825150150773410087690867', '190.68877113415316342755845140459', '191.212134653689785019972004701883', '192.284956640162638502698439264519', '193.14295698654752429909906372627', '193.62918850847557604209391989235', '195.7074286921010104143951370917', '196.22652513346310669190288108517', '197.33900211008942622508694847646', '198.17113642850978610002271955315', '198.85814783529810815156401935930', '199.60563304441091930264362863330'], 'prelabel': '1-5e2-25.12-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6866231198656254, 'root_angle': 0.56, 'root_number': '-0.187381314585724630542550734447+0.982287250728688681085641742865*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.28', 'prec': 14}, 'spectral_label': 'r1-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.742258162169778768367207722570+0.444958682568329178807577593192*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.53697086842', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.27166680774', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.54623542632', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.6866231198656254, 'bad_primes': [5], 'central_character': '25.12', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/12'], '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': '1-5e2-25.12-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': '1-5e2-25.12-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6866231198656254, 'root_angle': 0.28, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.53697086842', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_25.12', 'Lhash_array': ['dirichlet_L_25.12'], 'label': '1-5e2-25.12-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/25/12'}