-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_151.128', 'a10': [-0.9781476007338057, -0.20791169081775934], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.6691306063588582, -0.7431448254773942], 'a6': [-0.10452846326765347, 0.9945218953682733], 'a7': [0.6691306063588582, -0.7431448254773942], 'a8': [1.0, 0.0], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.701241051920901, 'analytic_normalization': 0, 'bad_lfactors': [[151, [1]]], 'bad_primes': [151], 'central_character': '151.128', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 151, 'conductor_radical': 151, 'conjugate': 'dirichlet_L_151.105', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^9', 'a^5', 'a^13', 'a^4', 'a^13', 'a^0', 'a^3', 'a^8', 'a^1', 'a^14', 'a^14', 'a^8', 'a^7', 'a^10', 'a^7', 'a^13', 'a^0', 'a^3', 'a^7', 'a^11', 'a^10', 'a^9', 'a^11', 'a^9', 'a^12', 'a^3', 'a^6', 'a^2', 'a^7', 'a^5', 'a^10', 'a^2', 'a^11', 'a^8', 'a^4', 'a^10', 'a^8', 'a^13', 'a^9', 'a^2', 'a^2', 'a^6', 'a^1', 'a^5', 'a^14', 'a^4', 'a^11', 'a^6', 'a^1', 'a^4', 'a^6', 'a^7', 'a^14', 'a^13', 'a^9', 'a^1', 'a^0', 'a^12', 'a^11', 'a^2', 'a^1', 'a^0', 'a^12', 'a^5', 'a^12', 'a^12', 'a^4', 'a^6', 'a^8', 'a^3', 'a^3', 'a^14', 'a^5', 'a^5', 'a^14', 'a^3', 'a^3', 'a^8', 'a^6', 'a^4', 'a^12', 'a^12', 'a^5', 'a^12', 'a^0', 'a^1', 'a^2', 'a^11', 'a^12', 'a^0', 'a^1', 'a^9', 'a^13', 'a^14', 'a^7', 'a^6', 'a^4', 'a^1'], 'euler_factors': [[1, 'a^10'], [1, 'a^9'], [1, 'a^13'], [1, 'a^13'], [1, 'a^1'], [1, 'a^14'], [1, 'a^7'], [1, 'a^0'], [1, 'a^10'], [1, 'a^6'], [1, 'a^7'], [1, 'a^4'], [1, 'a^9'], [1, 'a^2'], [1, 'a^14'], [1, 'a^6'], [1, 'a^0'], [1, 'a^11'], [1, 'a^12'], [1, 'a^8'], [1, 'a^3'], [1, 'a^3'], [1, 'a^12'], [1, 'a^2'], [1, 'a^7'], [1, 'a^6']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-151-151.128-r0-0-0', 'leading_term': '0.369018501006174911262391281273-0.706025228911515224575917003287*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/151/128', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.7966468966514598, 0.6645657653705171, 0.4830289400966449, 0.15321840548019056, -0.19291805329549344, -0.3147115393100543, 0.0018953109373309703, 0.8125913769869435, 1.9316834113625818, 2.9535713111138655, 3.3999540872153164, 2.949124124729502, 1.6421889868021688, -0.05628319814381941, -1.413994799366642, -1.76508190267302, -0.8711197670102631, 0.8914770355236713, 2.6559139453410223, 3.4801476018135533, 2.854520351124717, 1.017567093710209, -1.128276068684675, -2.4919379687138967, -2.4094826529075806, -1.0373463377948398, 0.7329689493888163, 1.8112993987714847, 1.5771689915448552, 0.25595451013505244, -1.2500974089803238, -1.9743884372142344, -1.5337237133516677, -0.36421169001095377, 0.624827135470003, 0.7343097546794172, -0.005502769699175727, -0.8776403376844334, -1.066461482882206, -0.34550082129235477, 0.6917744957652523, 1.0918036674323008, 0.38171122614251646, -0.8692817633809443, -1.2833681612064352, 0.3613120889397269, 4.097364508554306, 8.469441995156762, 11.29646473896437, 11.041097795926664, 7.835192350529804, 3.405880017681241, -0.06950257778013287, -1.358078325299424, -0.808594683051241, 0.18996720418946528, 0.43823755365636274, -0.16005254900462373, -0.7068946302723389, -0.27734057506051485, 1.1372807353108734, 2.5529010224731348, 2.8542699876838773, 1.8234992519441184, 0.39285413735487557, -0.14784216557107063, 0.6867334591234601, 2.0963623606571877, 2.6789604589024187, 1.7186850630247967, -0.07624512085673935, -1.1116813725083246, -0.3206841869202244, 1.786346434010865, 3.431754640916546, 3.065844592473878, 0.7779135590337357, -1.6580550827234215, -2.234502727029997, -0.4535817023761805, 2.165119638921543, 3.3094655136533504, 1.8159283781012225, -1.3427364269376012, -3.8775276606544313, -4.085138126667132, -2.1716953586050414, 0.10964762011359419, 1.0862445502727585, 0.5358314617367911, -0.39739540386770195, -0.5203861947265791, 0.22278249907906109, 0.8486523869173934, 0.5304497564892423, -0.41819287967605817, -0.8600427098296543, -0.17116197403338532, 0.8211126214815301, 0.42427847534796115, -2.204750083231545, -5.8747104030873185, -8.03557762130955, -6.916852601936182, -3.225120902292327, 0.2609523747129543, 0.9793768104008349, -1.2484640592061733, -4.138821611440521, -5.022610480171011, -3.160624705319233, -0.19763381588759202, 1.5473990304118495, 1.2233774689037216, -0.01879384749667621, -0.46646883547255646, 0.3305577385918182, 1.2306251131232553, 0.9196628871549016, -0.5035645843612802, -1.509322828972342, -0.7377167924297895, 1.474264034885165, 3.29418736617579, 3.1729585784012677, 1.3664991138149067, -0.3957127376627517, -0.7414048690297165, -0.020654459632813427, 0.2829766842103476, -0.5354960683981642, -1.314780746333406, -0.12999231177808615, 3.410842419273106, 7.1351375712583875, 7.89652455376114, 4.474226527961422, -1.0392554011694504, -4.863545255154577, -4.745814509063126, -1.7501667057379753, 1.009641101290522, 1.3408362773956704, -0.2744992491771275, -1.6723508216818281, -1.4463625686883674, -0.21602813285417224, 0.42510259636716424, -0.12772142494238228, -0.8859189074719802, -0.6064292098889195, 0.6032217110154009, 1.3654969609267953, 0.7417080389498741, -0.4690963207356701, -0.5082867167720068, 1.2145385043756114, 3.088914905093335, 2.782630748627395, -0.14545294479171028, -3.3546925923765545, -3.7734783210379095, -0.6656436211564202, 3.4680605412901935, 5.205632434547261, 3.439222612482546, 0.2407232325811004, -1.451606196187051, -0.8090642482739143, 0.37110936869184774, -0.0068392014687787914, -1.854161837265613, -3.01040560503003, -1.7505823964363112, 1.171723251792497, 3.230847514804169, 2.7678577750079696, 0.6221069807532893, -0.9736598388727264, -0.8600086383512425, 0.03993136717432296, 0.17673098313601085, -0.5961676198432162, -0.9062557818419651, 0.23832856878130015, 1.9376424992274455, 2.2787059793114257, 0.6898360443087437, -1.1112742111796545, -0.9903651632508852, 0.8646202264624903, 1.6223629841336624, -1.312482172269727, -7.134426206780722, -11.763999659545895, -11.480553956513573, -6.455986263529824, -0.5531586882863053, 2.3599461469533027, 1.73962137733679, 0.08915898758271365, -0.18236417913493694, 0.876880343376678, 1.5298824218931568, 0.8594152939639188, -0.1712535281523378, -0.22320660586149982, 0.4800989714528227, 0.37373429082875614, -1.2909409850133087, -3.130911577074862, -3.0146196805395875, -0.6464681555146748, 1.8116889847528423, 2.0451185243887107, 0.23057609320248162, -1.150698281401034, -0.24087496200407077, 1.940261689920374, 2.6736624622319614, 0.8803668255351691, -1.3357448668170946, -0.9404661839749707, 2.4388389566913804, 5.766382850682274, 5.727804896363523, 2.302286461392192, -1.2348510042896772, -1.8550050481613598, 0.14946170205691245, 1.9159646946017095, 1.4837314834100874, -0.12832434589848382, -0.4855682020200952, 1.17561913367842, 3.090970911892558, 3.1985735896204517, 1.565514949124636, 0.07517553714865262, -0.019286872134861605, 0.5389800972626356, 0.38029751866249495, -0.379688863600705, -0.27829348320116953, 1.1337998276844647, 1.9265784933081287, -0.2850993738301783, -5.026182229968697, -8.420546128597106, -6.745521601348496, -0.5008806031747605, 5.645433349968489, 7.283603898739391, 4.386218685448314, 0.758583502952566, -0.3087963546022505, 0.8024326557067489, 1.3419748662612196, -0.09032477068513449, -2.0046634865127495, -2.219594164081168, -0.7121519909443429, 0.5113083864521336, 0.16639633546018914, -0.6293459925900804, 0.05974661934167427, 2.2492278374089527, 3.7823458910178704, 2.988812516168414, 0.8585174277843882, -0.13098223180472895, 0.887464786442439, 2.1142435088854197, 1.4851380625093331, -0.5316505164005694, -1.4399724042398012, -0.024815255074835608, 1.7842338839221408, 1.1285262791707098, -2.0334901096275324, -4.426845221207148, -3.1978769930150044, 0.44549460856290485, 2.2312737696342193, -0.42917112470549484, -5.4016601480893405, -8.058893941170139, -6.19537577657574, -2.0301680238758633, 0.6726345906657443, 0.6370468542113978, -0.36567059795048035, -0.43955946642878996, 0.13608574804214016, -0.04741474611586001, -1.069255725393543, -1.4366265403783058, -0.3708544012287584, 0.7339369398001532, -0.005040449267853336, -2.2269987507264157, -3.398820387531953, -1.998960338258832, 0.2221414887504241, 0.16667060739918046, -2.5519192279245475, -4.577102970762299, -2.545127908201457, 2.6643049881001026, 6.421066134426733, 5.289116704623502, 0.7170333702162168, -2.7841726175746917, -2.6527937553758063, -0.529476129732096, 0.5241496726374796, -0.07376263037754119, -0.29033162652601563, 1.171748489210722, 2.775538789910094, 2.129515264326165, -0.6701994183283648, -2.8680443394126853, -2.3609848804860367, -0.20326244606126453, 0.9010226323319388, 0.04758203661229533, -0.9975593924067712, -0.4673943529157102, 0.9683523711440882, 1.308961356371341, 0.201174609783092, -0.5479095267136173, 0.1590397039903262, 0.4905755966685789, -2.2943245444411904, -7.6915055422917025, -11.227776558807246, -8.928103478922791, -2.0633573251201827, 3.6769794517982852, 4.006481478789839, 0.24863431411943476, -2.7663271806281378, -2.2869157535332323, -0.05017132553900086, 0.7788130946851994, -0.3018123339688202, -1.1048246752027977, -0.1736354899624395, 1.2778850640259378, 1.3195820781482561, 0.09093765855989057, -0.5511912771160041, 0.15086965860783524, 0.784734520445455, 0.09838785532514377, -0.6555728553074248, 0.930084362128043, 4.807399450792026, 7.6138333827339295, 6.3157722489829435, 2.011886750076517, -1.131513354282835, -0.7642615423845641, 1.046204002307774, 0.8181025078382356, -1.635568614602115, -2.9407985728565182, -0.7029534999360267, 3.102744052480931, 4.395349725137521, 2.0441103778308922, -0.7876384496340559, -0.6828977618262809, 1.8597485855362925, 3.3741509855084804, 1.986385321262168, -0.42967601250760373, -1.029681887677366, 0.30731412335747427, 1.244807488930125, 0.45990637637565024, -0.6645142666970635, -0.3030814579684532, 1.0674080038610487, 1.440748697910289, 0.3620407966924969, -0.31791089614400503, 0.7086956376041622, 1.9144600067364506, 0.939720693848459, -1.4995541559997096, -1.5189596873209343, 3.1647435190801723, 9.42980174267179, 11.341317242492336, 6.694761755018117, -0.28900296585437596, -3.528371205550207, -1.4993749724479124, 1.9683411283467331, 2.828677114051256, 1.145177437718789, -0.27713872948990526, -0.14862830058131524, 0.1280556305268462, -0.67298851703347, -1.4257329044005624, -0.4624186441630066, 1.4542478291975591, 1.663697393936612, -0.7654590193290156, -3.40783258220366, -3.39634379893808, -1.0666481062002102, 0.6573024147579477, 0.2762151025817105, -0.49315229951152584, 0.349939105864661, 1.69917214348504, 0.5995529486416279, -3.2823909712736983, -6.309264862599027, -5.0812899014878194, -0.9305463890630277, 1.45078036196746, -0.18924252867575841, -2.8976687088588147, -2.444664724466424, 1.1615799804352842, 3.7383676275463396, 2.353039096963621, -1.0551049075918293, -2.3847202812813144, -0.535926360609647, 1.7113374914162127, 1.7230337673471332, 0.16486063383639665, -0.6420045936482355, -0.18663482216235136, 0.013681445165757334, -0.7190259113702432, -1.0022959761689922, 0.20933432661686385, 1.4406194212108736, 0.5432431719260402, -1.7434331302752217, -2.049384010503405, 1.0455821527074198, 4.196101595964642, 2.783764452337297, -3.1338756323938597, -8.192482580478599, -7.724489943820354, -3.0570656405927292, 0.4838417318568031, 0.09584840177369996, -1.8116996792123048, -1.6868314487335736, 0.31188892006588476, 1.0920911036227896, -0.6399239151422242, -2.566593264676153, -2.173339790154581, -0.24012596689040294, 0.5455041086848043, -0.3931095911562108, -0.8183872814130837, 0.7589944466363535, 2.58998243987475, 2.03796988753194, -0.5728304504548718, -2.2337490470543266, -1.346924200548864, 0.225491929954018, 0.07872713283640129, -1.1793854920136742, -1.0201044486693809, 0.890477289236615, 1.9046211535182804, 0.5991894817045602, -0.047390401316850524, 4.130304090500595, 12.368697878939539, 18.297672670088556, 16.522044504820364, 8.668196574396863, 1.41104605677182, -0.9188684804035636, -0.01083174705344236, 0.19814479996145182, -1.151851348303563, -1.8511618754870947, -0.7757873823035722, 0.35847655976717263, -0.15906480734474884, -1.3608625294899044, -1.225575618428117, 0.07127876347615239, 0.44186690165751114, -0.6675086909443686, -1.1148812064863842, 0.6624940709316325, 2.737084257939766, 1.9502106098144651, -1.390784695422344, -3.276636459558648, -1.2432387578366575, 1.9149836342506272, 1.4755776776331007, -2.916893452009442, -6.487226495354407, -5.32697443558488, -1.2243018658449119, 0.9846394369566327, -0.30936864148008336, -2.076801082343437, -1.5004975309112767, 0.1256450992879405, -0.1887602469972578, -2.301377299405272, -2.886787703449062, -0.22736632629546924, 3.126508317423537, 3.6578939471446814, 1.4307147992762295, -0.4099896970001981, -0.09218335496090431, 0.8780501113352919, 0.6474524076582701, -0.13048415338233388, 0.13979694924924346, 0.8418962690973089, -0.1599107138070466, -2.684187153127626, -3.4620438865562875, -0.5788969682638532, 2.923731138173275, 2.211130378977817, -2.8299611776816547, -6.643625201066639, -4.646701018332242, 0.9195786662860178, 3.6990151795853077, 1.032429940197269, -3.22632737707021, -4.085814103940675, -1.4244219173607744, 0.956688609756513, 0.8800614744423556, -0.060174841965643364, 0.12120437677403949, 0.7518960134131178, 0.2383659390571758, -0.7763401581962972, -0.2303291769158258, 1.755857816908224, 2.43085025951303, 0.374076731590315, -1.9587705868293925, -1.344306307332022, 1.5871687476596374, 3.0237152325625125, 1.249473763116009, -1.0344856404614582, -0.7965062461923109, 0.7902060989775272, 0.16909991091141618, -2.9237919530252063, -4.3941724422507376, -1.3721414438148816, 3.3316141873927805, 4.521235790047376, 1.4246163244935803, -1.3626339977577357, -0.10913193432536022, 3.2450313925688965, 4.097464856679173, 1.4472632726077626, -1.2482811708878452, -1.1843312811649207, 0.3646863259389313, 0.7464617065232819, 0.04569909449233539, 0.41853631593034957, 2.19278545052319, 3.098124740382042, 1.7798520641381175, -0.06718177236033222, -0.3634443438318892, 0.1965292925942035, -0.2729909912510693, -0.9506579810661759, 1.1677347827989073, 6.067121145372513, 8.593886447246216, 3.9731136204904933, -5.483202906046045, -11.864494745419359, -10.337815084049982, -4.20254490911517, -0.13538539838536093, -0.2928610141552821, -1.3641820675634375, -0.4939504273726602, 0.9813219353292375, 0.6346373312923468, -0.7900860719571429, -0.6230708266991271, 1.2844360950155151, 2.1014437313961505, 0.35262122884527647, -1.6746348338756878, -1.2437220842295644, 0.8097269489703331, 1.4750232161971126, 0.20469465708838305, -0.35801930448783753, 1.325478031411326, 3.072499883733244, 2.229493785932431, -0.15782307392108105, -0.8550730647708975, 0.4745669086547739, 0.5637667948532289, -2.218503552982303, -4.501646295886727, -2.142031206521896, 3.4731962324717336, 6.380710190563008, 3.6525183334010967, -0.6661070969104015, -0.8697878799239921, 3.04796304648118, 5.874711378752848, 4.329748034539801, 0.8444737117091021, -0.5537766887290789, 0.3903445804770362, 0.9268333428183394], 'positive_zeros': ['1.066154196336515001377192419683', '1.873965014104157665525650462214', '4.05192557081429061437203666588', '5.1652305910587271449454547573', '6.7062581552468036929130833031', '7.991211683061812807334345555584', '9.11235332045108017015952252931', '10.4080135449243615152843201406', '11.248206568559308188052712405756', '12.2881148437445716755196554765', '13.22107899298374593719321539059', '14.020111850582577359364263178183', '16.24127540010145996467173917244', '17.11657501285431096210569578793', '17.74670920152286220776898404659', '18.51327277128282140468470576994', '20.13142875941149328539245068740', '20.42025659870746020091484372725', '21.86102927291501823331854634616', '22.5557847737298016860650862187', '23.838903149505910567937164276556', '24.74098840019080193516062206585', '25.81086419111003581977142281205', '27.16902488135564858677250295885', '27.97675619377650051942962556171', '28.67143375716434067916923294809', '29.55286901746233290083727825085', '30.36019514267833834028247880049', '31.01070852511345917673334643142', '32.78024985190002868117353255815', '33.29845094765497622190266048885', '34.71106847377708870915984631556', '35.61955594362136479135944592634', '36.15376532816553482125273637100', '37.086542840459383536762336517084', '37.9292487593978652895777510206', '39.28498591713437321911895438541', '40.00855759433171230001068292438', '40.46267466926264564372338623770', '41.26571510383309111755831841662', '42.75267118959299363838919362280', '43.9228080749222228975188773120', '44.64226729865084298735008751384', '45.68649358880085084699513572381', '46.20494626286926131266413114666', '47.04237664087400298340235328502', '47.992751449456858431906346713685', '48.559715386159605755855925869006', '49.67494578803432975592746385660', '50.67333509710316762832791988944', '51.902295640794443821094745050', '52.68782020243346482230705044831', '53.12342176680062260915757016765', '54.25471847618627993367682060365', '55.40506225536701168538916973180', '56.23295731998174046923152571814', '56.654228435046074724882393456302', '57.455538157926516913393848404108', '58.53959520712922421633014041027', '59.240916040884083321714106310662', '59.905423778300675884939832615271', '61.59980429786731956350779718645', '62.52482984493646940542999659400', '62.88555266893167216558477538148', '63.99479666515867928291930871895', '64.48170875943307539655518335241', '65.09698244349272942152297894931', '66.320076764048264019866426099122', '67.2227940506379508615638629010', '67.8494620841672284724805240678', '68.85662803297900898758726069530', '69.48396438987360084657484073421', '70.807521133048343884172731534', '71.543190143942963298181100614063', '72.47138159865816586883020804192', '72.93901076456122614091874196562', '74.40620760962640978682692423636', '74.699445738823941372300592210644', '75.46604525721550224038473422517', '76.01829306075923492800936629104', '76.85148403363187151597896270784', '78.14695752346154483091941018007', '79.490269954625199333078723664613', '79.80843586322461699347444191152', '80.61145740575697679693828195930', '81.70291887755025444335369787722', '82.24164204023628029411218066545', '82.80112188350411435588330444120', '84.25237918298051044076243558139', '84.467068159614596125368323001609', '85.54282633518069162854419897651', '86.25360801929957193663365906574', '87.00286773279747533072069142300', '88.08604238722760053648766406552', '88.719570112455786296638433843703', '90.1961033517254814238657678280', '90.8101820010703815338234277229', '91.47616088678485407744207869722', '91.85490481107782135942842111309', '92.89256947929525548535267752287', '93.43662075900200930405250570302', '94.64556297552488386625365992131', '95.02850843761694986663627639664', '96.09885910885733057461731643352', '97.235467602487182993365238525416', '98.21979086667134559157112935936', '98.72225533461386047972518624673', '99.15909338951989506157095950586', '100.24458015728694832313708543955', '101.28236236216299956278236277350', '101.88586928276675161228653215364', '102.601766869465164559940520768821', '103.487786252050936303882173825826', '104.01510908182827643946875995803', '104.47658131639008932070680556199', '106.0285772405700777806522178976', '106.89366228463575379295310782201', '107.82072629848261391946243721996', '108.36959506206269861483840657508', '109.09648758363292539041167826291', '110.02327474850636731204353134932', '110.57798271180994507331641286488', '111.27684197278186949539887760667', '111.761313464865241137929837970808', '113.28592935601399164941262967089', '113.87360316697568473912981377540', '114.494779490689410555200781671295', '115.369792193681548465923301147603', '116.451596003357044806736024095894', '116.973693318224457885033194418599', '118.0590956406200601048177076805', '118.68985917482025024020382128682', '119.48063471189682525359075736900', '120.073617756891624928079205448178', '121.035119925038292123753251849976', '121.40283923787006159468738311014', '122.30730661299532871771977233040', '122.94885216163267737311104455866', '124.35995475760909618504805152466', '125.12456963372672893941109067548', '126.151524351604662212479748933781', '126.64910891911491997870140858632', '126.96624481640751083296179907411', '127.88712195908460369459152183073', '128.67181846215338899959684356387', '129.83623636004112344379603691856', '130.393982114629117500735664403', '130.86243545403298372731656752702', '131.62256261810489543534819757232', '132.89016297053623776504028579218', '133.41745629107442060940267262396', '134.28400112060259815605165840273', '135.21129085884981513981750150996', '136.0000021871146867301935576403', '136.910612962716111796053854780970', '137.61385140106452827729844538138', '137.82388891576281678877236671837', '138.71012397395013089192298327233', '139.45159830002477048835113651953', '140.22893611097343216855198117233', '141.10017362141057756726062838026', '142.42746096483209453216956668091', '142.82829579778410490337837472707', '143.70144132037832010164342888221', '144.288984477233467831636090143090', '145.35833246023421630744222921856', '145.83370379525809027544181671262', '146.448790232830950220741982528111', '147.43507724149208699518597982034', '148.37449967144408764168186263639', '148.771652542633807225365687294788', '149.55453391809756183695190597723', '150.432939996935484574251079068392', '150.6355354028000683742406659440', '152.609817529250393869374259393057', '153.128166843041122388440319862059', '153.50109848977766835369696701707', '154.54715706007280995866192079533', '154.95757027245877243023694645569', '155.91898912948024592298381969673', '156.400794072092324934590006148389', '157.101571578813245695058074873147', '158.002688287240822740830974661', '158.85901479978768052831191610354', '159.499666336160503997139230243890', '160.738360197694274235578665938461', '161.20571729061810049788365854658', '162.15285821760436360727906742550', '162.46001310031509468930129204486', '163.456585627779557185117296706557', '164.57897165180743975978682516933', '165.026281249289268253607563554061', '165.86284609875041438781506456403', '166.192510653453582774564208195579', '166.85068982858115118620894604398', '167.856494485381159177322728961421', '168.59161797488223143048788205348', '169.63434667113847698172641089250', '170.38259427416326789090206008404', '171.402060286462983970869412691059', '172.15540909291112759963670876824', '172.44295368684612250825261481833', '173.189533751206562984970765865337', '173.79238906667577619663681079976', '174.72828188313330832464137135930', '175.463644557917902714884420953703', '176.39550737234302282185463952592', '177.0201365664381737420087640943', '177.52218081117740684921221922878', '178.52395741988055451972781330176', '179.49634540003832161053803248167', '180.01095184955426008681883266332', '181.07699827304017388103251596237', '181.79503066631628429121537902918', '182.53436691780015789468252650858', '182.65844250748416242219853525594', '184.04607801824987821684320049802', '184.55449670414738975220271001727', '184.9070067995805166528029315092', '185.51703483788290639785905863362', '186.699518399520614326355632226202', '188.1529420398235257007737093156', '188.36195394965009121813002923008', '189.15164970111797293831340513727', '189.81989684412678853307957306363', '190.42815711799360294878784967683', '191.29408461683609716591032235284', '192.063261827842317097385572173435', '192.85934875220620779803160942081', '193.23065634992985095230513233376', '194.35108897028477574396346294028', '194.9001968537980656493461936319', '195.40194406200830742895829720098', '196.37420036607426469557447977248', '197.43760920037301505714665412263', '197.90087084104250738476022556146', '199.171822622555356499738905141080', '199.589514729275326060141039271846'], 'prelabel': '1-151-151.128-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': -0.6933918075288783, 'root_number': '-0.570864404890517927108394652450-0.821044353996174077452376507348*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.346695903764', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.594893119206136876525146180674-0.518918419007910003230457063563*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06615419634', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.8739650141', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.05192557081', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.701241051920901, 'bad_primes': [151], 'central_character': '151.128', 'conductor': 151, 'conductor_radical': 151, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/151/128'], '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': '1-151-151.128-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': '1-151-151.128-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': -0.34669590376443915, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06615419634', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_151.128', 'Lhash_array': ['dirichlet_L_151.128'], 'label': '1-151-151.128-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/151/128'}