-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_240.227', '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': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 25.791581950710004, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '240.227', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 240, 'conductor_radical': 30, 'conjugate': 'dirichlet_L_240.203', 'degree': 1, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 'I', 0, 0, 0, '-I', 0, 1, 0, 0, 0, '-I', 0, 'I', 0, 0, 0, 'I', 0, 0, 0, 0, 0, 'I', 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 'I', 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 'I', 0, 'I', 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 'I', 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 'I', 0, 0, 0, 0, 0, 'I', 0, 0, 0], 'euler_factors': [[0], [0], [0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 'I'], [1, 0], [1, 0], [1, 0], [1, '-I'], [1, 0], [1, 1], [1, 0], [1, 0], [1, 0], [1, '-I'], [1, 0], [1, 'I'], [1, 0], [1, 0], [1, 0], [1, 'I'], [1, 0], [1, 0]], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-240-240.227-r1-0-0', 'leading_term': '1.63529901640542711301482238175+0.837139482416913619154083882810*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/240/227', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.8371187729915057, 2.0414205239955168, 1.7182696814375684, 0.8778511133512892, -0.2977317716633462, -1.4304844619443624, -2.058819899283288, -1.861401585836957, -0.87473995202186, 0.44267361849957754, 1.3853573135248523, 1.3648455976821614, 0.2739712759829857, -1.382948166262077, -2.7236200696613886, -2.995474343385181, -2.0640499519529287, -0.550228637779533, 0.5252005572295766, 0.4057477335655799, -0.8577415178670861, -2.385073502374264, -3.035948143648267, -2.2134207565177677, -0.330589886537679, 1.4367553547633733, 1.983121536371542, 1.1016306412515577, -0.33130491961394154, -1.0031771474856948, -0.18909401992223274, 1.639641552555491, 3.1376940792644277, 3.1335181597111124, 1.5879622944227703, -0.3314536178961448, -1.1689793780975135, -0.3728991552984999, 1.230846133302133, 2.118581274052523, 1.36911159295253, -0.5143104821057929, -1.9978073880766185, -1.8327616757714984, -0.17009771948463262, 1.5252909655261426, 1.7311572935699837, 0.21208376160976716, -1.757696487596471, -2.5309238366804405, -1.5863353860864529, -0.02080349415718737, 0.4532679073042564, -0.882470171762115, -3.026378637718142, -4.128770051740678, -3.1905667622394462, -1.005021238290633, 0.5727925527722316, 0.37172570574115815, -0.9884853672684892, -1.7136083587973883, -0.6136852990577807, 1.6712167071023807, 3.222478376477451, 2.6793373269997165, 0.5802571864365773, -1.1320475895291022, -0.9922841299908691, 0.5655831540849154, 1.676344662106858, 0.959837574179237, -1.033985420709504, -2.3374140237706214, -1.5563209579987936, 0.668894473742661, 2.249693165922879, 1.7281008833214062, -0.2622500652336912, -1.6695533716008182, -1.1615511830383416, 0.4831484165880712, 1.2004984852847667, -0.1521895724013781, -2.522540547590108, -3.6989568189146493, -2.607564201191965, -0.4541793199766131, 0.5247795930497096, -0.5920864118481194, -2.4607542818493346, -2.9491470656356786, -1.4710234705155865, 0.3488284151611838, 0.430920934666887, -1.4595655151973572, -3.3823096136886504, -3.2652097743342825, -1.128933955481458, 0.9391512387185336, 1.0566718369893404, -0.4177224560105564, -1.3360099899798232, -0.21582811564713444, 2.029462438164331, 3.0459623333260923, 1.6573284603855538, -0.7686421309327232, -1.766493435120518, -0.4544707414737399, 1.5417138382374178, 1.9685448232777039, 0.5117483833765065, -0.8677087321976149, -0.2318953485315091, 2.0149573602159805, 3.4679045356311304, 2.389294640715715, -0.31699425796930525, -2.0980844277564903, -1.6025440088449183, -0.1284689718178462, -0.001839956506161082, -1.7660989616946177, -3.4677553998437642, -2.908515070001455, -0.26318304956564503, 2.0128923020456337, 1.9312549605271647, 0.19886809935413458, -0.6776017120898087, 0.6277372355102498, 2.697604122481331, 3.079108264439561, 1.2465770872694197, -0.7121348240239089, -0.5418900931904373, 1.4829550071238244, 2.838278065574795, 1.7172868783705528, -0.8253406833145258, -2.116371706367192, -1.021632337894434, 0.762900501449545, 0.8411391377275212, -0.906235461386956, -2.1252854197454223, -0.8555307622933938, 1.9934165212783261, 3.589355809610159, 2.457209118637548, 0.1489292480669065, -0.7130164796966283, 0.37102062075876646, 1.2554464884639263, -0.06115572156531496, -2.7809607847211075, -4.108042003359315, -2.5887027882973666, 0.09106267778526497, 1.0879474348578837, -0.23754261548889805, -1.6977871898830466, -1.1387305369583114, 0.7902589731082119, 1.4310020979247355, -0.49463047082109274, -3.1466655381562596, -3.709856548884721, -1.8026221246742675, 0.08785406578548273, -0.2952144200634039, -2.205298636376355, -2.912233706031118, -1.2195495023347358, 0.9746583759255738, 1.0718934021879427, -0.8936802028779219, -2.231491238850679, -0.9650276010372096, 1.642470994545904, 2.6226732230443606, 0.9831744616290583, -1.117208812814003, -1.1786366933274546, 0.4455094611148725, 1.0716951172712021, -0.7360200546282389, -3.1489451295835016, -3.273006452707937, -0.8059730543094388, 1.5275873179016006, 1.351294696403963, -0.478628082373158, -1.1573298725914742, 0.3126527767394448, 1.7907280872279818, 0.8458822501170299, -1.9182729660038746, -3.4379768405039384, -2.002325887089662, 0.5952951341003034, 1.3613689399278344, -0.11158950555343992, -1.2784724465287516, -0.1341067901510346, 2.0490980627579978, 2.3692404977604062, 0.1854836193764068, -1.8908201666971125, -1.2825214352878578, 1.2426371967774879, 2.572150772099958, 1.2619534668633656, -0.6947484362157867, -0.6417041240207487, 1.132136873491732, 1.7705594513457326, -0.26209178837290525, -2.964321164553902, -3.2666217437247482, -0.9819589896243747, 0.980116782078772, 0.4314786701526757, -1.299352764524883, -1.2889409101823879, 0.9450805462609503, 2.7298869459806454, 1.8287584117157485, -0.48552467468878147, -1.0528550855297243, 0.9689876317782371, 2.938789401893388, 2.197546890561832, -0.4502175100948469, -1.8865503573447715, -0.8817864673758001, 0.342248061579339, -0.701365408876101, -3.179088515638285, -3.8877136869667464, -1.5372682524672996, 1.407975828085215, 1.8643569899427324, 0.05848898567186271, -1.0116543738177408, 0.21097467549022178, 1.734759984682337, 0.8971760742311925, -1.7444669388414877, -2.920739821152331, -0.9697562366903649, 1.882045127417503, 2.4172169725878243, 0.6013100283561424, -0.6099903346278823, 0.504522704570575, 2.0321029816358753, 1.1727757015985016, -1.6793034912283828, -3.22729891693885, -1.6350165555523204, 0.9978980355692701, 1.472748598195023, -0.22932089775219763, -1.0876692900322462, 0.6370921573468156, 2.9204881047817004, 2.787279436933109, 0.4987755074685097, -0.7527302927827224, 0.7295614170356969, 2.746604711204561, 2.213268882895902, -0.5544991247952481, -2.2182252469415036, -0.9397093558286681, 1.2324275935670357, 1.3959352310391662, -0.05971395962223174, -0.06221491061456047, 2.6088416393537157, 5.268723711291032, 4.752607967093512, 1.6366708922681785, -0.5986043241650367, -0.2812843874264261, 0.4407789146795374, -0.9711869310660532, -3.5275227964693707, -3.9388197265489335, -1.3139869207585926, 1.3440441304554303, 1.071783179321637, -1.1283657193558954, -1.8443120283484404, -0.0714711815703167, 1.5040965513365165, 0.5104259249882346, -1.5879003077846163, -1.5301625980433078, 1.0117058503002878, 2.7911354276685394, 1.4419784293199178, -1.2319740378148787, -1.7955108720367898, 0.04391885164883618, 1.1859493934819858, -0.291720034848123, -2.3281390430393634, -1.8795528612067032, 0.592766652767844, 1.6499645896983473, -0.2545720663304655, -2.5125571462902747, -1.986607256870526, 0.6090106125782221, 1.8000613594602208, 0.30905386299214077, -1.2568296109534374, -0.3766084878817115, 1.5598855843541302, 1.1878140271811741, -1.8697077273385783, -4.201991809780244, -3.2314783467745434, -0.6968075643549144, -0.04423350427802533, -1.5265185146163378, -2.073051986032638, -0.035173197296203454, 2.189679666392897, 1.5631523267551626, -1.0752803853006765, -2.007855885734899, 0.17308649614390842, 2.625946690803752, 2.3475042572251197, 0.35864867694009556, -0.0365554824182335, 1.7233836880764877, 2.579237559728383, 0.4499736816176841, -2.4527070213976474, -2.5605962978792087, 0.02473795584060491, 1.6964703284503844, 0.4671733313190047, -1.3804884727933746, -0.8994654904094326, 1.0509505562243464, 1.0977855983198266, -1.4944454401929266, -3.4725013670405693, -2.1579739869581176, 0.6939452516519176, 1.406513639285509, -0.3803565395688036, -1.3836161496287933, 0.329191098513848, 2.4393654113652476, 1.8543519337790872, -0.6226865802873724, -1.4125203397849535, 0.5299963128908584, 2.08449873917869, 0.5025104111723324, -2.5247317423928215, -3.260091582953269, -1.251048380142957, 0.24013041537154103, -0.751706342038865, -1.9772085242441848, -0.5264828505142652, 2.4832442297211905, 3.2030863063618225, 0.5676052945315995, -2.084347077073248, -1.7087179677831363, 0.32418999083355793, 0.6780621491552392, -0.7436562507644773, -0.7099030715213961, 2.1813367167497697, 4.936034189974386, 4.220409714563356, 1.1362785454222464, -0.3731962594494066, 0.8474020112794772, 1.8130510225361225, 0.20653667425475386, -1.9821193181341759, -1.4938110341782933, 1.0965379679826421, 2.0031636781468585, -0.23266787582708007, -2.5645981097673, -1.9324707151801874, 0.2614236934131101, 0.36279345750419495, -2.006102545837099, -3.4321947825662136, -1.9420455693692336, -0.011698381974388012, -0.7597132628663797, -3.091754555141452, -3.222332402382813, -0.37124798394510655, 1.9416855899241747, 1.0024752676133246, -1.228656482860055, -1.2401833986787316, 0.7321647643416467, 1.2843270932779225, -0.6553449452633299, -1.911477867722975, 0.19721346709289606, 3.5944171251965376, 4.205187027953534, 1.7034323088914611, -0.31350353316469176, 0.1475850682918855, 0.7063975110233631, -1.2612828092802761, -4.075309502278728, -3.936398621981769, -0.6491294726888246, 1.8583714271463199, 1.139200041956495, -0.4363846649881539, 0.4243656817259108, 2.8318328229482077, 3.186571262210651, 0.8751869348558258, -0.6614294750032653, 0.7976114789936223, 2.7454700739325824, 1.6908259566547004, -1.4846018581920561, -2.739291075235943, -0.8357262530480758, 1.0119705244648922, 0.2292264086799751, -1.1999468708728684, -0.02279599564458746, 2.938084394852102, 3.76855719555851, 1.3859714265162666, -0.7007350687219306, 0.41518947289878283, 2.779490826904354, 2.7208803375575803, 0.49563279611651395, -0.2608936813296104, 1.66609305219579, 3.1077830445686048, 1.4938960772518743, -0.9643463161771721, -0.49276580737238346, 2.4744594157491413, 3.8510208835380366, 1.9605846670501768, -0.17793850851793125, 0.2600274744605194, 1.5469930038301007, 0.36801624954478646, -2.602292818852562, -3.3727824580343584, -0.6928810693705804, 1.8635140767033112, 1.10934439910401, -1.191812264846135, -1.3391810172595797, 0.5241808393066586, 0.876619770289167, -1.3169875796568877, -2.6857963283956146, -0.6409404199600288, 2.3907983318004153, 2.4079064562407284, -0.24460176996922461, -1.5718000059865889, -0.08665260807654378, 1.1621462044409556, -0.2693896381617217, -2.134716888743676, -0.9921037415731699, 2.1913102057491125, 3.2304311718077745, 1.003780786843729, -0.9166000305338204, 0.17362348116880058, 2.032505989035755, 1.1894083379163223, -1.4685316390063679, -2.06034810646496, 0.1543687381799566, 1.604534496503414, 0.1017285143600963, -1.5933134354253722, -0.05344030719318883, 3.3259652543079574, 4.253610667388178, 1.916457134957468, -0.10649562294507726, 0.34012029381461445, 0.749041854940375, -1.5997529347799948, -4.695923417935861, -4.441136838411844, -0.9313501502370796, 1.4783676569105426, 0.5327062695793839, -0.9776969526149267, -0.09147307211679262, 1.5320450663305336, 0.5246692686828813, -2.3435690391425923, -2.913736169571815, -0.020793938406940663, 2.5447098138998436, 1.7044226228215296, -0.42253271581257057, -0.156877500138958, 1.8691639784318284, 1.9302709691679658, -0.5460734999360406, -1.817597502645496, 0.2816225279894123, 2.7806035078281743, 2.118385392604461, -0.3269995520682103, -0.4825211749097349, 1.962078448130061, 3.116655429197939, 1.0976606009991103, -1.0642257764469671, -0.4183928282660242, 1.1003177456465072, -0.15096267928962165, -3.4195439082700454, -4.393296585827215, -1.8150045985849605, 0.5647844374480662, -0.21774060450074273, -1.9949740110378105, -1.3568976305068332, 0.6590227102467259, 0.32129621606667685, -2.449894223051679, -3.5200565086868454, -0.9050668577134606, 2.0065901474587626, 1.5676269630111417, -0.7305766979205333, -1.0268252490740983, 0.6111401230022735, 0.5437709148880412, -2.116827629542136, -3.6307240009632857, -1.44874219776849, 1.5587502162455313, 1.3675317050473264, -1.115285376887965, -1.7628270888711766, 0.12403543613865144, 0.9268445687171717, -1.1319580350526943, -2.9095384813880893, -1.4300791956920282, 1.1104471722052216, 0.6622733974638186, -2.236247857618704, -3.238680250274664, -0.9847144845500472, 0.9475312685249402, -0.05784327689336629, -1.540492159183587, -0.265191668706041, 2.185101769378075, 1.7815702929907502, -1.3506422775375528, -2.852040260453457, -0.8562474253522917, 1.2210775984312696, 0.2624667500019475, -1.651125047565209, -0.8711283012858866, 1.7072384306416972, 2.0911636303534973, -0.17403117835173582, -1.1044822296703396, 1.272657705821247, 3.562421118855891, 2.282680014423506, -0.6583543085226443, -1.0660857809243383, 0.9635735233584806, 1.6286714006919878, 0.007431162707205124, -0.32726422476673106, 2.5874993117513996, 5.3394494291977495, 4.127003157973312, 0.6427530761122424, -0.5928443190052718, 0.8752454533558587, 1.369139634862339, -0.3593408684209565, -0.9270465912702405, 1.846662995770662, 4.776093279681686, 3.927830456339828, 0.7221465542196359, -0.37402109085516544, 1.1425762774218886, 1.4024113874181496, -1.1726808030433746, -3.180192942795274, -1.914524213314084, 0.0445042863035988, -0.9812679303359148, -3.6260370625706164, -3.5464154883364016, -0.4352235549944555, 1.4506712826338024, 0.112842457744579, -1.1566619365315454, 0.5974895026954465, 3.063130735657186, 2.5492972636984574, 0.19062069201963516, 0.10836569039436511, 2.4943552271068428, 3.09195438962894, 0.0983486226976141, -2.747923008333918, -1.96015003139206, 0.4590848568730722, 0.7471161073143598, -0.3239801438186808], 'positive_zeros': ['1.17435624206612555503805095663', '2.7062878592133200723299586384', '3.80516048151390820815877562248', '5.44054623464780956599534578108', '6.06330952045021560882620802710', '7.55083718207954576487158874209', '8.67287561409507563396018740962', '9.4127945155040995748423764259', '10.87606663623303646444782334960', '11.63879636835045480775313580456', '12.73215287712551204132785147624', '13.776835034792682778489168165731', '14.7196097634218867483583651545', '15.94265373662906456118329303325', '16.40320286901007101012210248880', '17.97467583438726641739159812349', '18.53415738638468113379032928286', '19.46544240469290585812154536853', '20.70832683954966057684908459433', '21.459615721221380374144874072957', '22.3456293114110479096347616038', '23.348265256082797725584061520253', '24.33582004063397806584274799811', '25.220473921467708583247442241134', '25.91551865155845505465711863110', '27.27082621456770270393777264710', '27.70175464187796509204890313772', '28.98571792007549742404619038532', '29.47127003009708656115918524795', '30.77139858220314892302082594918', '31.48301503278293450988428344992', '32.21970154328809911273324888976', '33.33262743108375575224924777136', '34.1290416725353231005485968356', '35.08897469097188930120602887708', '35.66417573866536873673560894685', '36.838569226977251219293204603649', '37.85198383965086727453030698641', '38.12440609819404171714243858039', '39.40317504968920178547758172331', '40.34991726837933003161835715191', '40.83571007850822824883834899031', '42.04745762769478333772570132520', '42.59971691452404691656807287848', '43.647427920856307084247392816440', '44.538012718430898272105603855263', '45.16985012609949550294880767003', '46.03650375138227143947909329270', '47.21250929786243021648196077419', '47.732435259140072206804595102374', '48.429505175949355408644140627752', '49.67489049745214987571108537939', '50.27273026543076648420631563471', '51.12255223928641761587546136488', '51.81796047972337782068122465984', '53.09830208856589134421265833580', '53.36807890674416542247232841027', '54.53019122766986446045436596853', '55.18693950626205254159666683902', '56.05279603278047382051388289850', '57.00285309358685724616156594555', '57.73103662420602720072028212817', '58.34493936254998141616121725519', '59.46186045214395752541122758589', '60.230789768736599453955971128793', '60.88819103924875253888434011175', '61.66608235425378594834567622018', '62.73171737666366440434402510339', '63.41868594183044754664266650954', '64.0817595932698782571504456007', '65.02139589971524346321820513486', '65.790051065508205301572026785585', '66.74331616565519006228088464905', '67.31267261965739254710879097476', '68.09675302303735921485348134739', '69.183515960214260558596675435132', '69.76386647667577539689144571173', '70.51068910239777960226745991252', '71.4903154832666069602280384567', '72.06708121800938006796600577152', '73.07179059101748124850148652873', '73.92836225376019025726365556174', '74.25552959386281944193633294969', '75.45892043947217288129608457889', '76.25935528966733317967522023801', '76.84019330184359014672512354812', '77.61297480192224465280028165238', '78.53488007046861794605101499141', '79.47459905643560973957835368982', '79.91020057987922482935487136011', '80.761892531476492112863402376686', '81.743021190446612982237083157430', '82.46207619792854605744370791116', '83.04412827198050560582000717805', '84.13424273023849316768945206968', '84.58329355783351611875123100018', '85.565416905868149257993092118723', '86.37217287625948386253853532278', '87.17295229723489601953263885288', '87.51254910435098081458145660965', '88.93614109408349203244283527244', '89.454595799015777809549442271920', '89.851852970446807063232409814255', '91.06539937439382160336283058722', '91.71854454527594194154316781877', '92.509822434499436300521158943', '93.1968865918165534525607572670', '93.95256433122928416674863509735', '94.847050160684574328719511790272', '95.6184535098314867684765488865', '96.21057044585842682433376749230', '97.11359705525177294437027956816', '97.78333698801942020537096283605', '98.676997480494720857756903691175', '99.42019811435239987260536579416', '100.05695831995635529630080403332', '100.764740816729674048669931719769', '102.03529857354060020093237199123', '102.16719933056622036211822813962', '103.12895507678902412353675741649', '103.93642467964201042167872362484', '104.669436726232129393280316962322', '105.70599143842204461476432543507', '105.948633216377594997710288150310', '106.91839450594891331824054734875', '107.80972786982668582426538658010', '108.503430342791998204452689479326', '109.203465561938391621456492001283', '109.84229818639098629931061808035', '110.852501455694087984957538074898', '111.505495340459590108603016070717', '112.14667733532273194857632965218', '113.043927724222119573643609054821', '113.682643610854697634473211871356', '114.42626286100035794985171961840', '115.51856311214080673952851713346', '115.78096605256352045066378729416', '116.61818984995852743353512952941', '117.55267562123890422307966064279', '118.38055541173702410305937879638', '118.909129632992945774905800405815', '119.47817684181848975041734356798', '120.77989234624482971470002315000', '121.08833845002414593421532900781', '121.90019191557704017883050801825', '122.68322982341397502330282410341', '123.41330932931545433287510450792', '124.32958523701908147225680891530', '124.75124036811574062871845338426', '125.94194968698778152697861698381', '126.093899000383684795757515861663', '127.22289362704858835363679393657', '127.94178299546401390458400522623', '128.63767758248070186932960912617', '129.28790903629923201723262903665', '129.98203099838019282319744966799', '131.16270390194788855967688505844', '131.52153191648861285817641886780', '132.03826639120263627456880186242', '133.18234846003734996171481775939', '133.942915993678333122876205609451', '134.30746820458345463777824420724', '135.428999645664865287634058930300', '135.82548865116407854663539874562', '136.72996237951392382342886007929', '137.60543459567876831024728555822', '138.164831659109924957520742211567', '138.7526932013000428186119970962', '139.84785029485205313030324931678', '140.255464862577817584042303983502', '141.33565466508486772890137634134', '141.63267682904211378001746640004', '142.66691224449672326739301164477', '143.1861205357443419668417115274', '144.328656611118549448189613432363', '144.62858290367337222682205996067', '145.35411705595591803714263027676', '146.31421036818237035681544630028', '147.016936466426959122770651478478', '147.725453613251069210409535221637', '148.27501763406956988023259662250', '149.121632892880491232354507714178', '149.971881828624574182970533312398', '150.63819495417197132186741099009', '151.21355797202321573631329137963', '151.97539296226328833869333484132', '152.93098112092563494949384010667', '153.41221348582481241727088554538', '154.20151823354236923090141792297', '154.9812491960794545022987264659', '155.638437014616450285064992250823', '156.25528331006713124344407207615', '157.46314771211681930722359082376', '157.708890512204580002596527245297', '158.27030337791565296832737201646', '159.45789682568998737165290132248', '160.0843055333861196346686218945', '160.63988955509162515446679752020', '161.310320542648720444016681138', '162.18932691171020968978185956382', '163.04447352810091191483070384664', '163.46491403790961522112725739371', '164.31210026222782466711371654634', '164.97134224560178418521345215128', '165.88742808334386475654431556060', '166.327846130428728264317844486107', '167.312816170541285751488220445671', '167.88264415616965609479852723170', '168.42067576189140685011809533656', '169.57239466648130594080049863741', '169.96452740644452565479819904999', '170.82068226111501640067185581668', '171.29492969007402844338297758966', '172.26609888265709928115942056735', '173.01707033781998485542392371137', '173.63427350019201768952519494800', '174.1443347651490419447612877646', '175.13051452272862295323639035275', '175.79848896189010930963433653080', '176.54377283587821374226017288763', '177.05114315561809724308198917806', '177.96783300268047255296888018106', '178.51731685052573414361034420848', '179.489917379905176365771707124941', '179.99080990289402417407081553072', '180.65655560823392239608916148963', '181.43536321034830360828248808497', '182.28396627380744540123105844365', '182.84941883822106050475676782936', '183.54327391062050409993175248720', '184.35233521525862030381835266055', '184.86910247122019345704582961783', '185.855857084356762910173810346858', '186.424594663572889474625523846', '187.1888710491936226512147988788', '187.55735262975958620433194294779', '188.82784896187514918819549910856', '189.21787306435029782607810119814', '189.94282939752030195218236473437', '190.45459999411840137835199171826', '191.660686806070896878726458777437', '191.98031634662937466840289648540', '192.69295964369352411788463410837', '193.733778192102824907180710577896', '193.89531684367383996386361371679', '195.04307581560657837384577598647', '195.641839890227326954437867164603', '196.1818867874929824230108215130', '197.22458075854710176639331478941', '197.47813343902283598498136646055', '198.44557916827076420419473685337', '199.303313937451743772060102744549', '199.87872524019399492986983416819'], 'prelabel': '1-240-240.227-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 25.791581950710004, 'root_angle': 0.30120819117478337, 'root_number': '0.584710284663764943254761894084+0.811242185175560853981676916722*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.150604095587', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13233485196940683540507184152+0.183752650304703518811214939754*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17435624207', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.70628785921', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.80516048151', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 25.791581950710004, 'bad_primes': [2, 3, 5], 'central_character': '240.227', 'conductor': 240, 'conductor_radical': 30, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/240/227'], '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': '1-240-240.227-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': '1-240-240.227-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 25.791581950710004, 'root_angle': 0.15060409558739168, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17435624207', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_240.227', 'Lhash_array': ['dirichlet_L_240.227'], 'label': '1-240-240.227-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/240/227'}