Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,3,Mod(19,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 7, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.u (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.84743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Character | \(\chi\) | \(=\) | 288.19 |
Dual form | 288.3.u.a.91.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.345994 | + | 1.96984i | −0.172997 | + | 0.984922i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.76058 | − | 1.36311i | −0.940144 | − | 0.340777i | ||||
\(5\) | −7.20074 | + | 2.98264i | −1.44015 | + | 0.596529i | −0.959834 | − | 0.280568i | \(-0.909477\pi\) |
−0.480314 | + | 0.877097i | \(0.659477\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.26150 | + | 4.26150i | 0.608786 | + | 0.608786i | 0.942629 | − | 0.333843i | \(-0.108346\pi\) |
−0.333843 | + | 0.942629i | \(0.608346\pi\) | |||||||
\(8\) | 3.98625 | − | 6.93612i | 0.498281 | − | 0.867015i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.38393 | − | 15.2163i | −0.338393 | − | 1.52163i | ||||
\(11\) | −6.19818 | + | 2.56737i | −0.563471 | + | 0.233397i | −0.646191 | − | 0.763175i | \(-0.723639\pi\) |
0.0827202 | + | 0.996573i | \(0.473639\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.05345 | − | 3.33585i | −0.619496 | − | 0.256604i | 0.0507868 | − | 0.998710i | \(-0.483827\pi\) |
−0.670283 | + | 0.742106i | \(0.733827\pi\) | |||||||
\(14\) | −9.86895 | + | 6.92004i | −0.704925 | + | 0.494288i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2839 | + | 10.2522i | 0.767742 | + | 0.640760i | ||||
\(17\) | − | 24.5802i | − | 1.44589i | −0.690904 | − | 0.722947i | \(-0.742787\pi\) | ||
0.690904 | − | 0.722947i | \(-0.257213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.96459 | − | 11.9856i | 0.261294 | − | 0.630820i | −0.737725 | − | 0.675101i | \(-0.764100\pi\) |
0.999019 | + | 0.0442815i | \(0.0140998\pi\) | |||||||
\(20\) | 31.1446 | − | 1.40106i | 1.55723 | − | 0.0700532i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.91279 | − | 13.0978i | −0.132399 | − | 0.595353i | ||||
\(23\) | 9.72199 | − | 9.72199i | 0.422695 | − | 0.422695i | −0.463435 | − | 0.886131i | \(-0.653383\pi\) |
0.886131 | + | 0.463435i | \(0.153383\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.2768 | − | 25.2768i | 1.01107 | − | 1.01107i | ||||
\(26\) | 9.35754 | − | 14.7099i | 0.359906 | − | 0.565764i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.2168 | − | 21.8346i | −0.364886 | − | 0.779807i | ||||
\(29\) | 5.86371 | − | 14.1563i | 0.202197 | − | 0.488147i | −0.789958 | − | 0.613161i | \(-0.789898\pi\) |
0.992155 | + | 0.125014i | \(0.0398977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 17.5320i | − | 0.565550i | −0.959186 | − | 0.282775i | \(-0.908745\pi\) | ||
0.959186 | − | 0.282775i | \(-0.0912549\pi\) | |||||||
\(32\) | −24.4453 | + | 20.6501i | −0.763915 | + | 0.645316i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 48.4192 | + | 8.50460i | 1.42409 | + | 0.250135i | ||||
\(35\) | −43.3965 | − | 17.9754i | −1.23990 | − | 0.513583i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −36.0346 | + | 14.9260i | −0.973909 | + | 0.403406i | −0.812166 | − | 0.583427i | \(-0.801712\pi\) |
−0.161743 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(38\) | 21.8920 | + | 13.9264i | 0.576106 | + | 0.366485i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.01597 | + | 61.8348i | −0.200399 | + | 1.54587i | ||||
\(41\) | −10.9784 | − | 10.9784i | −0.267765 | − | 0.267765i | 0.560434 | − | 0.828199i | \(-0.310634\pi\) |
−0.828199 | + | 0.560434i | \(0.810634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.4024 | + | 9.27937i | −0.520985 | + | 0.215799i | −0.627650 | − | 0.778496i | \(-0.715983\pi\) |
0.106664 | + | 0.994295i | \(0.465983\pi\) | |||||||
\(44\) | 26.8084 | − | 1.20599i | 0.609281 | − | 0.0274090i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.7871 | + | 22.5146i | 0.343197 | + | 0.489447i | ||||
\(47\) | −27.0104 | −0.574690 | −0.287345 | − | 0.957827i | \(-0.592773\pi\) | ||||
−0.287345 | + | 0.957827i | \(0.592773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 12.6792i | − | 0.258760i | ||||||
\(50\) | 41.0458 | + | 58.5371i | 0.820916 | + | 1.17074i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 25.7385 | + | 23.5224i | 0.494971 | + | 0.452354i | ||||
\(53\) | 34.0172 | + | 82.1247i | 0.641833 | + | 1.54952i | 0.824204 | + | 0.566293i | \(0.191623\pi\) |
−0.182371 | + | 0.983230i | \(0.558377\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 36.9740 | − | 36.9740i | 0.672254 | − | 0.672254i | ||||
\(56\) | 46.5457 | − | 12.5709i | 0.831173 | − | 0.224480i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 25.8568 | + | 16.4486i | 0.445807 | + | 0.283596i | ||||
\(59\) | −27.8391 | − | 67.2095i | −0.471849 | − | 1.13914i | −0.963345 | − | 0.268264i | \(-0.913550\pi\) |
0.491497 | − | 0.870879i | \(-0.336450\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.37082 | + | 15.3805i | −0.104440 | + | 0.252140i | −0.967457 | − | 0.253034i | \(-0.918572\pi\) |
0.863018 | + | 0.505174i | \(0.168572\pi\) | |||||||
\(62\) | 34.5354 | + | 6.06598i | 0.557022 | + | 0.0978384i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32.2196 | − | 55.2983i | −0.503431 | − | 0.864035i | ||||
\(65\) | 67.9404 | 1.04524 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −99.2165 | − | 41.0968i | −1.48084 | − | 0.613386i | −0.511542 | − | 0.859258i | \(-0.670925\pi\) |
−0.969302 | + | 0.245873i | \(0.920925\pi\) | |||||||
\(68\) | −33.5055 | + | 92.4357i | −0.492728 | + | 1.35935i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 50.4237 | − | 79.2650i | 0.720339 | − | 1.13236i | ||||
\(71\) | 2.55754 | + | 2.55754i | 0.0360217 | + | 0.0360217i | 0.724888 | − | 0.688867i | \(-0.241891\pi\) |
−0.688867 | + | 0.724888i | \(0.741891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.7498 | + | 30.7498i | 0.421230 | + | 0.421230i | 0.885627 | − | 0.464397i | \(-0.153729\pi\) |
−0.464397 | + | 0.885627i | \(0.653729\pi\) | |||||||
\(74\) | −16.9342 | − | 76.1469i | −0.228840 | − | 1.02901i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −35.0074 | + | 38.3054i | −0.460623 | + | 0.504019i | ||||
\(77\) | −37.3544 | − | 15.4727i | −0.485122 | − | 0.200944i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −90.6600 | −1.14759 | −0.573797 | − | 0.818997i | \(-0.694530\pi\) | ||||
−0.573797 | + | 0.818997i | \(0.694530\pi\) | |||||||
\(80\) | −119.031 | − | 37.1847i | −1.48789 | − | 0.464809i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 25.4241 | − | 17.8272i | 0.310051 | − | 0.217405i | ||||
\(83\) | 39.3191 | − | 94.9247i | 0.473724 | − | 1.14367i | −0.488781 | − | 0.872407i | \(-0.662558\pi\) |
0.962505 | − | 0.271264i | \(-0.0874417\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 73.3140 | + | 176.996i | 0.862517 | + | 2.08230i | ||||
\(86\) | −10.5278 | − | 47.3398i | −0.122417 | − | 0.550463i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.89991 | + | 53.2256i | −0.0784081 | + | 0.604836i | ||||
\(89\) | −109.290 | + | 109.290i | −1.22798 | + | 1.22798i | −0.263248 | + | 0.964728i | \(0.584794\pi\) |
−0.964728 | + | 0.263248i | \(0.915206\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.1040 | − | 48.5355i | −0.220924 | − | 0.533357i | ||||
\(92\) | −49.8124 | + | 23.3081i | −0.541439 | + | 0.253349i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.34545 | − | 53.2063i | 0.0994196 | − | 0.566025i | ||||
\(95\) | 101.113i | 1.06434i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 63.7161 | 0.656867 | 0.328433 | − | 0.944527i | \(-0.393479\pi\) | ||||
0.328433 | + | 0.944527i | \(0.393479\pi\) | |||||||
\(98\) | 24.9761 | + | 4.38694i | 0.254859 | + | 0.0447647i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −129.511 | + | 60.6004i | −1.29511 | + | 0.606004i | ||||
\(101\) | 14.4312 | − | 5.97761i | 0.142883 | − | 0.0591842i | −0.310096 | − | 0.950705i | \(-0.600361\pi\) |
0.452979 | + | 0.891521i | \(0.350361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.69681 | − | 9.69681i | −0.0941438 | − | 0.0941438i | 0.658466 | − | 0.752610i | \(-0.271205\pi\) |
−0.752610 | + | 0.658466i | \(0.771205\pi\) | |||||||
\(104\) | −55.2409 | + | 42.5622i | −0.531163 | + | 0.409252i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −173.543 | + | 38.5939i | −1.63719 | + | 0.364093i | ||||
\(107\) | −138.127 | + | 57.2140i | −1.29091 | + | 0.534710i | −0.919255 | − | 0.393662i | \(-0.871208\pi\) |
−0.371650 | + | 0.928373i | \(0.621208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −32.0941 | − | 13.2938i | −0.294442 | − | 0.121962i | 0.230573 | − | 0.973055i | \(-0.425940\pi\) |
−0.525014 | + | 0.851093i | \(0.675940\pi\) | |||||||
\(110\) | 60.0402 | + | 85.6257i | 0.545820 | + | 0.778416i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.65814 | + | 96.0372i | 0.0773048 | + | 0.857475i | ||||
\(113\) | − | 125.923i | − | 1.11436i | −0.830392 | − | 0.557180i | \(-0.811883\pi\) | ||
0.830392 | − | 0.557180i | \(-0.188117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −41.0083 | + | 99.0028i | −0.356594 | + | 0.860894i | ||||
\(116\) | −41.3475 | + | 45.2428i | −0.356444 | + | 0.390024i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 142.024 | − | 31.5846i | 1.20360 | − | 0.267666i | ||||
\(119\) | 104.748 | − | 104.748i | 0.880239 | − | 0.880239i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.7338 | + | 53.7338i | −0.444081 | + | 0.444081i | ||||
\(122\) | −28.0930 | − | 17.8711i | −0.230270 | − | 0.146484i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −23.8981 | + | 65.9306i | −0.192727 | + | 0.531698i | ||||
\(125\) | −32.0540 | + | 77.3852i | −0.256432 | + | 0.619081i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 79.4160i | − | 0.625322i | −0.949865 | − | 0.312661i | \(-0.898780\pi\) | ||
0.949865 | − | 0.312661i | \(-0.101220\pi\) | |||||||
\(128\) | 120.077 | − | 44.3347i | 0.938100 | − | 0.346365i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −23.5070 | + | 133.832i | −0.180823 | + | 1.02948i | ||||
\(131\) | −53.2656 | − | 22.0633i | −0.406608 | − | 0.168422i | 0.169999 | − | 0.985444i | \(-0.445624\pi\) |
−0.576607 | + | 0.817022i | \(0.695624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 72.2331 | − | 29.9199i | 0.543106 | − | 0.224962i | ||||
\(134\) | 115.283 | − | 181.222i | 0.860319 | − | 1.35240i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −170.491 | − | 97.9828i | −1.25361 | − | 0.720462i | ||||
\(137\) | −50.7359 | − | 50.7359i | −0.370335 | − | 0.370335i | 0.497264 | − | 0.867599i | \(-0.334338\pi\) |
−0.867599 | + | 0.497264i | \(0.834338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 133.213 | − | 55.1786i | 0.958366 | − | 0.396968i | 0.151997 | − | 0.988381i | \(-0.451430\pi\) |
0.806369 | + | 0.591413i | \(0.201430\pi\) | |||||||
\(140\) | 138.693 | + | 126.752i | 0.990667 | + | 0.905372i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.92286 | + | 4.15307i | −0.0417102 | + | 0.0292469i | ||||
\(143\) | 58.4811 | 0.408959 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 119.425i | 0.823620i | ||||||||
\(146\) | −71.2116 | + | 49.9331i | −0.487751 | + | 0.342007i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 155.857 | − | 7.01134i | 1.05309 | − | 0.0473739i | ||||
\(149\) | −5.00779 | − | 12.0899i | −0.0336093 | − | 0.0811401i | 0.906184 | − | 0.422884i | \(-0.138982\pi\) |
−0.939793 | + | 0.341744i | \(0.888982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.6867 | + | 17.6867i | −0.117130 | + | 0.117130i | −0.763243 | − | 0.646112i | \(-0.776394\pi\) |
0.646112 | + | 0.763243i | \(0.276394\pi\) | |||||||
\(152\) | −63.3434 | − | 82.2125i | −0.416733 | − | 0.540872i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 43.4032 | − | 68.2289i | 0.281839 | − | 0.443045i | ||||
\(155\) | 52.2918 | + | 126.244i | 0.337367 | + | 0.814475i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 73.8536 | − | 178.298i | 0.470405 | − | 1.13566i | −0.493580 | − | 0.869701i | \(-0.664312\pi\) |
0.963985 | − | 0.265958i | \(-0.0856882\pi\) | |||||||
\(158\) | 31.3678 | − | 178.586i | 0.198531 | − | 1.13029i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 114.432 | − | 221.608i | 0.715202 | − | 1.38505i | ||||
\(161\) | 82.8605 | 0.514662 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −132.246 | − | 54.7779i | −0.811322 | − | 0.336061i | −0.0618408 | − | 0.998086i | \(-0.519697\pi\) |
−0.749481 | + | 0.662025i | \(0.769697\pi\) | |||||||
\(164\) | 26.3203 | + | 56.2497i | 0.160490 | + | 0.342986i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 173.383 | + | 110.296i | 1.04447 | + | 0.664433i | ||||
\(167\) | 109.750 | + | 109.750i | 0.657187 | + | 0.657187i | 0.954714 | − | 0.297526i | \(-0.0961616\pi\) |
−0.297526 | + | 0.954714i | \(0.596162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −65.7709 | − | 65.7709i | −0.389177 | − | 0.389177i | ||||
\(170\) | −374.020 | + | 83.1777i | −2.20012 | + | 0.489281i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 96.8946 | − | 4.35888i | 0.563341 | − | 0.0253423i | ||||
\(173\) | 287.188 | + | 118.957i | 1.66005 | + | 0.687613i | 0.998081 | − | 0.0619221i | \(-0.0197230\pi\) |
0.661964 | + | 0.749535i | \(0.269723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 215.434 | 1.23105 | ||||||||
\(176\) | −102.459 | − | 32.0075i | −0.582152 | − | 0.181861i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −177.470 | − | 253.098i | −0.997025 | − | 1.42190i | ||||
\(179\) | −48.9443 | + | 118.162i | −0.273432 | + | 0.660122i | −0.999625 | − | 0.0273677i | \(-0.991288\pi\) |
0.726194 | + | 0.687490i | \(0.241288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 38.9220 | + | 93.9660i | 0.215039 | + | 0.519149i | 0.994184 | − | 0.107694i | \(-0.0343466\pi\) |
−0.779145 | + | 0.626843i | \(0.784347\pi\) | |||||||
\(182\) | 102.563 | − | 22.8089i | 0.563534 | − | 0.125323i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −28.6786 | − | 106.187i | −0.155862 | − | 0.577104i | ||||
\(185\) | 214.957 | − | 214.957i | 1.16193 | − | 1.16193i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 63.1065 | + | 152.353i | 0.337468 | + | 0.814719i | ||||
\(188\) | 101.575 | + | 36.8182i | 0.540291 | + | 0.195841i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −199.176 | − | 34.9844i | −1.04830 | − | 0.184128i | ||||
\(191\) | 66.5635i | 0.348500i | 0.984701 | + | 0.174250i | \(0.0557500\pi\) | ||||
−0.984701 | + | 0.174250i | \(0.944250\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 275.880 | 1.42943 | 0.714714 | − | 0.699417i | \(-0.246557\pi\) | ||||
0.714714 | + | 0.699417i | \(0.246557\pi\) | |||||||
\(194\) | −22.0454 | + | 125.511i | −0.113636 | + | 0.646962i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17.2832 | + | 47.6813i | −0.0881796 | + | 0.243272i | ||||
\(197\) | −167.300 | + | 69.2980i | −0.849240 | + | 0.351767i | −0.764490 | − | 0.644636i | \(-0.777009\pi\) |
−0.0847497 | + | 0.996402i | \(0.527009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −233.526 | − | 233.526i | −1.17350 | − | 1.17350i | −0.981370 | − | 0.192125i | \(-0.938462\pi\) |
−0.192125 | − | 0.981370i | \(-0.561538\pi\) | |||||||
\(200\) | −74.5634 | − | 276.083i | −0.372817 | − | 1.38041i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.78184 | + | 30.4955i | 0.0335735 | + | 0.150968i | ||||
\(203\) | 85.3151 | − | 35.3387i | 0.420271 | − | 0.174082i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 111.797 | + | 46.3078i | 0.545351 | + | 0.225892i | ||||
\(206\) | 22.4562 | − | 15.7462i | 0.109011 | − | 0.0764377i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −64.7278 | − | 123.542i | −0.311192 | − | 0.593953i | ||||
\(209\) | 87.0348i | 0.416434i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 32.7097 | − | 78.9682i | 0.155022 | − | 0.374257i | −0.827219 | − | 0.561880i | \(-0.810078\pi\) |
0.982241 | + | 0.187623i | \(0.0600783\pi\) | |||||||
\(212\) | −15.9792 | − | 355.205i | −0.0753735 | − | 1.67550i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −64.9117 | − | 291.884i | −0.303325 | − | 1.36394i | ||||
\(215\) | 133.637 | − | 133.637i | 0.621566 | − | 0.621566i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 74.7128 | − | 74.7128i | 0.344298 | − | 0.344298i | ||||
\(218\) | 37.2912 | − | 58.6209i | 0.171060 | − | 0.268903i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −189.443 | + | 88.6438i | −0.861104 | + | 0.402927i | ||||
\(221\) | −81.9957 | + | 197.955i | −0.371021 | + | 0.895725i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 373.446i | 1.67465i | 0.546708 | + | 0.837323i | \(0.315881\pi\) | ||||
−0.546708 | + | 0.837323i | \(0.684119\pi\) | |||||||
\(224\) | −192.174 | − | 16.1731i | −0.857920 | − | 0.0722015i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 248.048 | + | 43.5685i | 1.09756 | + | 0.192781i | ||||
\(227\) | −7.71962 | − | 3.19757i | −0.0340071 | − | 0.0140862i | 0.365615 | − | 0.930766i | \(-0.380859\pi\) |
−0.399622 | + | 0.916680i | \(0.630859\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −165.203 | + | 68.4293i | −0.721410 | + | 0.298818i | −0.713017 | − | 0.701147i | \(-0.752672\pi\) |
−0.00839310 | + | 0.999965i | \(0.502672\pi\) | |||||||
\(230\) | −180.831 | − | 115.034i | −0.786224 | − | 0.500149i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −74.8153 | − | 97.1018i | −0.322480 | − | 0.418542i | ||||
\(233\) | −14.0197 | − | 14.0197i | −0.0601703 | − | 0.0601703i | 0.676381 | − | 0.736552i | \(-0.263547\pi\) |
−0.736552 | + | 0.676381i | \(0.763547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 194.495 | − | 80.5625i | 0.827638 | − | 0.342819i | ||||
\(236\) | 13.0771 | + | 290.694i | 0.0554114 | + | 1.23175i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 170.096 | + | 242.581i | 0.714688 | + | 1.01925i | ||||
\(239\) | 230.951 | 0.966321 | 0.483161 | − | 0.875532i | \(-0.339489\pi\) | ||||
0.483161 | + | 0.875532i | \(0.339489\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 111.407i | 0.462269i | 0.972922 | + | 0.231135i | \(0.0742438\pi\) | ||||
−0.972922 | + | 0.231135i | \(0.925756\pi\) | |||||||
\(242\) | −87.2557 | − | 124.439i | −0.360561 | − | 0.514210i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 44.9233 | − | 49.1555i | 0.184112 | − | 0.201457i | ||||
\(245\) | 37.8177 | + | 91.3000i | 0.154358 | + | 0.372653i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −79.9641 | + | 79.9641i | −0.323741 | + | 0.323741i | ||||
\(248\) | −121.604 | − | 69.8871i | −0.490340 | − | 0.281803i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −141.346 | − | 89.9162i | −0.565385 | − | 0.359665i | ||||
\(251\) | −93.4234 | − | 225.544i | −0.372205 | − | 0.898581i | −0.993376 | − | 0.114907i | \(-0.963343\pi\) |
0.621172 | − | 0.783675i | \(-0.286657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.2987 | + | 85.2186i | −0.139521 | + | 0.336833i | ||||
\(254\) | 156.437 | + | 27.4775i | 0.615894 | + | 0.108179i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 45.7867 | + | 251.872i | 0.178854 | + | 0.983876i | ||||
\(257\) | 278.684 | 1.08437 | 0.542187 | − | 0.840258i | \(-0.317597\pi\) | ||||
0.542187 | + | 0.840258i | \(0.317597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −217.169 | − | 89.9543i | −0.838490 | − | 0.347314i | ||||
\(260\) | −255.495 | − | 92.6102i | −0.982674 | − | 0.356193i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 61.8909 | − | 97.2912i | 0.236225 | − | 0.371340i | ||||
\(263\) | −271.210 | − | 271.210i | −1.03122 | − | 1.03122i | −0.999497 | − | 0.0317197i | \(-0.989902\pi\) |
−0.0317197 | − | 0.999497i | \(-0.510098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −489.898 | − | 489.898i | −1.84867 | − | 1.84867i | ||||
\(266\) | 33.9454 | + | 152.640i | 0.127614 | + | 0.573835i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 317.092 | + | 289.791i | 1.18318 | + | 1.08131i | ||||
\(269\) | −54.9518 | − | 22.7618i | −0.204282 | − | 0.0846163i | 0.278197 | − | 0.960524i | \(-0.410263\pi\) |
−0.482478 | + | 0.875908i | \(0.660263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 443.976 | 1.63829 | 0.819143 | − | 0.573589i | \(-0.194449\pi\) | ||||
0.819143 | + | 0.573589i | \(0.194449\pi\) | |||||||
\(272\) | 252.000 | − | 301.940i | 0.926470 | − | 1.11007i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 117.496 | − | 82.3875i | 0.428818 | − | 0.300684i | ||||
\(275\) | −91.7754 | + | 221.565i | −0.333729 | + | 0.805693i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.1329 | + | 55.8478i | 0.0835124 | + | 0.201617i | 0.960119 | − | 0.279590i | \(-0.0901986\pi\) |
−0.876607 | + | 0.481207i | \(0.840199\pi\) | |||||||
\(278\) | 62.6023 | + | 281.500i | 0.225188 | + | 1.01259i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −297.669 | + | 229.349i | −1.06310 | + | 0.819103i | ||||
\(281\) | 159.772 | − | 159.772i | 0.568582 | − | 0.568582i | −0.363149 | − | 0.931731i | \(-0.618298\pi\) |
0.931731 | + | 0.363149i | \(0.118298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −185.468 | − | 447.761i | −0.655366 | − | 1.58219i | −0.804883 | − | 0.593434i | \(-0.797772\pi\) |
0.149517 | − | 0.988759i | \(-0.452228\pi\) | |||||||
\(284\) | −6.13162 | − | 13.1040i | −0.0215902 | − | 0.0461410i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.2341 | + | 115.199i | −0.0707487 | + | 0.402793i | ||||
\(287\) | − | 93.5687i | − | 0.326023i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −315.186 | −1.09061 | ||||||||
\(290\) | −235.249 | − | 41.3203i | −0.811202 | − | 0.142484i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −73.7216 | − | 157.552i | −0.252471 | − | 0.539563i | ||||
\(293\) | −476.574 | + | 197.403i | −1.62653 | + | 0.673732i | −0.994837 | − | 0.101485i | \(-0.967641\pi\) |
−0.631696 | + | 0.775216i | \(0.717641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 400.924 | + | 400.924i | 1.35906 | + | 1.35906i | ||||
\(296\) | −40.1143 | + | 309.439i | −0.135521 | + | 1.04540i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.5479 | − | 5.68155i | 0.0857310 | − | 0.0190656i | ||||
\(299\) | −110.727 | + | 45.8645i | −0.370323 | + | 0.153393i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −135.012 | − | 55.9237i | −0.448544 | − | 0.185793i | ||||
\(302\) | −28.7206 | − | 40.9595i | −0.0951012 | − | 0.135628i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 183.862 | − | 96.3315i | 0.604810 | − | 0.316880i | ||||
\(305\) | − | 129.753i | − | 0.425420i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −196.212 | + | 473.698i | −0.639127 | + | 1.54299i | 0.188716 | + | 0.982032i | \(0.439567\pi\) |
−0.827844 | + | 0.560959i | \(0.810433\pi\) | |||||||
\(308\) | 119.383 | + | 109.104i | 0.387608 | + | 0.354235i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −266.773 | + | 59.3272i | −0.860558 | + | 0.191378i | ||||
\(311\) | −386.346 | + | 386.346i | −1.24227 | + | 1.24227i | −0.283215 | + | 0.959057i | \(0.591401\pi\) |
−0.959057 | + | 0.283215i | \(0.908599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 127.090 | − | 127.090i | 0.406038 | − | 0.406038i | −0.474316 | − | 0.880354i | \(-0.657305\pi\) |
0.880354 | + | 0.474316i | \(0.157305\pi\) | |||||||
\(314\) | 325.667 | + | 207.170i | 1.03716 | + | 0.659778i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 340.934 | + | 123.579i | 1.07890 | + | 0.391074i | ||||
\(317\) | 24.4377 | − | 58.9979i | 0.0770906 | − | 0.186113i | −0.880636 | − | 0.473794i | \(-0.842884\pi\) |
0.957726 | + | 0.287681i | \(0.0928842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 102.797i | 0.322249i | ||||||||
\(320\) | 396.940 | + | 302.089i | 1.24044 | + | 0.944027i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.6693 | + | 163.222i | −0.0890349 | + | 0.506902i | ||||
\(323\) | −294.608 | − | 122.031i | −0.912099 | − | 0.377804i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −287.885 | + | 119.246i | −0.885801 | + | 0.366911i | ||||
\(326\) | 153.660 | − | 241.550i | 0.471350 | − | 0.740952i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −119.910 | + | 32.3848i | −0.365579 | + | 0.0987341i | ||||
\(329\) | −115.105 | − | 115.105i | −0.349863 | − | 0.349863i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 53.7512 | − | 22.2645i | 0.162390 | − | 0.0672643i | −0.300007 | − | 0.953937i | \(-0.596989\pi\) |
0.462398 | + | 0.886673i | \(0.346989\pi\) | |||||||
\(332\) | −277.255 | + | 303.375i | −0.835106 | + | 0.913781i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −254.164 | + | 178.218i | −0.760970 | + | 0.533587i | ||||
\(335\) | 837.010 | 2.49854 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 368.803i | − | 1.09437i | −0.837012 | − | 0.547185i | \(-0.815700\pi\) | ||
0.837012 | − | 0.547185i | \(-0.184300\pi\) | |||||||
\(338\) | 152.315 | − | 106.802i | 0.450636 | − | 0.315983i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −34.4384 | − | 765.540i | −0.101289 | − | 2.25159i | ||||
\(341\) | 45.0113 | + | 108.667i | 0.131998 | + | 0.318671i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 262.846 | − | 262.846i | 0.766315 | − | 0.766315i | ||||
\(344\) | −24.9387 | + | 192.376i | −0.0724961 | + | 0.559231i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −333.692 | + | 524.557i | −0.964429 | + | 1.51606i | ||||
\(347\) | −166.265 | − | 401.400i | −0.479151 | − | 1.15677i | −0.960008 | − | 0.279973i | \(-0.909675\pi\) |
0.480857 | − | 0.876799i | \(-0.340325\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.6685 | + | 59.5550i | −0.0706833 | + | 0.170645i | −0.955273 | − | 0.295726i | \(-0.904439\pi\) |
0.884590 | + | 0.466370i | \(0.154439\pi\) | |||||||
\(350\) | −74.5390 | + | 424.372i | −0.212969 | + | 1.21249i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 98.4999 | − | 190.753i | 0.279829 | − | 0.541913i | ||||
\(353\) | −245.534 | −0.695563 | −0.347782 | − | 0.937576i | \(-0.613065\pi\) | ||||
−0.347782 | + | 0.937576i | \(0.613065\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.0444 | − | 10.7880i | −0.0733646 | − | 0.0303886i | ||||
\(356\) | 559.967 | − | 262.019i | 1.57294 | − | 0.736008i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −215.826 | − | 137.296i | −0.602866 | − | 0.383508i | ||||
\(359\) | −61.7019 | − | 61.7019i | −0.171872 | − | 0.171872i | 0.615930 | − | 0.787801i | \(-0.288781\pi\) |
−0.787801 | + | 0.615930i | \(0.788781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 136.259 | + | 136.259i | 0.377448 | + | 0.377448i | ||||
\(362\) | −198.565 | + | 44.1586i | −0.548523 | + | 0.121985i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.44365 | + | 209.925i | 0.0259441 | + | 0.576718i | ||||
\(365\) | −313.137 | − | 129.706i | −0.857910 | − | 0.355358i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 123.349 | 0.336102 | 0.168051 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168051 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(368\) | 219.095 | − | 19.7523i | 0.595367 | − | 0.0536747i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 349.058 | + | 497.806i | 0.943400 | + | 1.34542i | ||||
\(371\) | −205.010 | + | 494.939i | −0.552588 | + | 1.33407i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5942 | − | 27.9909i | −0.0310836 | − | 0.0750425i | 0.907575 | − | 0.419889i | \(-0.137931\pi\) |
−0.938659 | + | 0.344846i | \(0.887931\pi\) | |||||||
\(374\) | −321.945 | + | 71.5969i | −0.860816 | + | 0.191436i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −107.670 | + | 187.348i | −0.286357 | + | 0.498265i | ||||
\(377\) | −94.4462 | + | 94.4462i | −0.250520 | + | 0.250520i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 205.083 | + | 495.114i | 0.541115 | + | 1.30637i | 0.923937 | + | 0.382546i | \(0.124953\pi\) |
−0.382821 | + | 0.923823i | \(0.625047\pi\) | |||||||
\(380\) | 137.828 | − | 380.242i | 0.362704 | − | 1.00064i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −131.120 | − | 23.0306i | −0.343245 | − | 0.0602894i | ||||
\(383\) | 605.809i | 1.58175i | 0.611979 | + | 0.790874i | \(0.290374\pi\) | ||||
−0.611979 | + | 0.790874i | \(0.709626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 315.129 | 0.818517 | ||||||||
\(386\) | −95.4528 | + | 543.440i | −0.247287 | + | 1.40788i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −239.609 | − | 86.8519i | −0.617549 | − | 0.223845i | ||||
\(389\) | 426.567 | − | 176.690i | 1.09657 | − | 0.454215i | 0.240279 | − | 0.970704i | \(-0.422761\pi\) |
0.856294 | + | 0.516489i | \(0.172761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −238.968 | − | 238.968i | −0.611172 | − | 0.611172i | ||||
\(392\) | −87.9448 | − | 50.5427i | −0.224349 | − | 0.128935i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −78.6214 | − | 353.532i | −0.199547 | − | 0.897290i | ||||
\(395\) | 652.819 | − | 270.407i | 1.65271 | − | 0.684573i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 294.458 | + | 121.969i | 0.741708 | + | 0.307226i | 0.721353 | − | 0.692567i | \(-0.243520\pi\) |
0.0203548 | + | 0.999793i | \(0.493520\pi\) | |||||||
\(398\) | 540.808 | − | 379.211i | 1.35881 | − | 0.952791i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 569.639 | − | 51.3552i | 1.42410 | − | 0.128388i | ||||
\(401\) | 48.4544i | 0.120834i | 0.998173 | + | 0.0604169i | \(0.0192430\pi\) | ||||
−0.998173 | + | 0.0604169i | \(0.980757\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −58.4842 | + | 141.193i | −0.145122 | + | 0.350356i | ||||
\(404\) | −62.4178 | + | 2.80791i | −0.154500 | + | 0.00695028i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40.0932 | + | 180.284i | 0.0987516 | + | 0.444050i | ||||
\(407\) | 185.029 | − | 185.029i | 0.454616 | − | 0.454616i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −242.037 | + | 242.037i | −0.591778 | + | 0.591778i | −0.938111 | − | 0.346334i | \(-0.887427\pi\) |
0.346334 | + | 0.938111i | \(0.387427\pi\) | |||||||
\(410\) | −129.900 | + | 204.201i | −0.316830 | + | 0.498050i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 23.2478 | + | 49.6834i | 0.0564266 | + | 0.120591i | ||||
\(413\) | 167.777 | − | 405.049i | 0.406239 | − | 0.980749i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 800.803i | 1.92965i | ||||||||
\(416\) | 265.755 | − | 84.7589i | 0.638833 | − | 0.203747i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −171.445 | − | 30.1135i | −0.410155 | − | 0.0720419i | ||||
\(419\) | −163.261 | − | 67.6248i | −0.389644 | − | 0.161396i | 0.179256 | − | 0.983802i | \(-0.442631\pi\) |
−0.568900 | + | 0.822407i | \(0.692631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −624.400 | + | 258.635i | −1.48314 | + | 0.614335i | −0.969810 | − | 0.243860i | \(-0.921586\pi\) |
−0.513325 | + | 0.858195i | \(0.671586\pi\) | |||||||
\(422\) | 144.238 | + | 91.7555i | 0.341795 | + | 0.217430i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 705.228 | + | 91.4225i | 1.66327 | + | 0.215619i | ||||
\(425\) | −621.309 | − | 621.309i | −1.46190 | − | 1.46190i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −92.6933 | + | 38.3948i | −0.217080 | + | 0.0899176i | ||||
\(428\) | 597.426 | − | 26.8757i | 1.39585 | − | 0.0627936i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 217.006 | + | 309.481i | 0.504665 | + | 0.719723i | ||||
\(431\) | −606.510 | −1.40722 | −0.703608 | − | 0.710588i | \(-0.748429\pi\) | ||||
−0.703608 | + | 0.710588i | \(0.748429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.82972i | − | 0.00884462i | −0.999990 | − | 0.00442231i | \(-0.998592\pi\) | ||
0.999990 | − | 0.00442231i | \(-0.00140767\pi\) | |||||||
\(434\) | 121.322 | + | 173.023i | 0.279545 | + | 0.398670i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 102.572 | + | 93.7403i | 0.235256 | + | 0.215001i | ||||
\(437\) | −68.2580 | − | 164.789i | −0.156197 | − | 0.377092i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.3389 | + | 36.3389i | −0.0827765 | + | 0.0827765i | −0.747283 | − | 0.664506i | \(-0.768642\pi\) |
0.664506 | + | 0.747283i | \(0.268642\pi\) | |||||||
\(440\) | −109.068 | − | 403.843i | −0.247883 | − | 0.917826i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −361.571 | − | 230.010i | −0.818034 | − | 0.520385i | ||||
\(443\) | 208.435 | + | 503.207i | 0.470508 | + | 1.13591i | 0.963939 | + | 0.266122i | \(0.0857425\pi\) |
−0.493431 | + | 0.869785i | \(0.664258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 460.995 | − | 1112.94i | 1.03594 | − | 2.50099i | ||||
\(446\) | −735.631 | − | 129.210i | −1.64940 | − | 0.289709i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 98.3497 | − | 372.957i | 0.219530 | − | 0.832494i | ||||
\(449\) | −431.670 | −0.961402 | −0.480701 | − | 0.876884i | \(-0.659618\pi\) | ||||
−0.480701 | + | 0.876884i | \(0.659618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 96.2316 | + | 39.8604i | 0.213374 | + | 0.0883823i | ||||
\(452\) | −171.646 | + | 473.542i | −0.379749 | + | 1.04766i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.96966 | − | 14.1001i | 0.0197570 | − | 0.0310575i | ||||
\(455\) | 289.528 | + | 289.528i | 0.636325 | + | 0.636325i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −187.054 | − | 187.054i | −0.409309 | − | 0.409309i | 0.472189 | − | 0.881497i | \(-0.343464\pi\) |
−0.881497 | + | 0.472189i | \(0.843464\pi\) | |||||||
\(458\) | −77.6358 | − | 349.100i | −0.169510 | − | 0.762227i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 289.166 | − | 316.409i | 0.628623 | − | 0.687845i | ||||
\(461\) | −253.784 | − | 105.121i | −0.550508 | − | 0.228028i | 0.0900508 | − | 0.995937i | \(-0.471297\pi\) |
−0.640558 | + | 0.767909i | \(0.721297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −765.246 | −1.65280 | −0.826400 | − | 0.563084i | \(-0.809615\pi\) | ||||
−0.826400 | + | 0.563084i | \(0.809615\pi\) | |||||||
\(464\) | 217.161 | − | 113.778i | 0.468020 | − | 0.245211i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.4673 | − | 22.7659i | 0.0696723 | − | 0.0488538i | ||||
\(467\) | 110.687 | − | 267.223i | 0.237018 | − | 0.572211i | −0.759954 | − | 0.649977i | \(-0.774779\pi\) |
0.996972 | + | 0.0777657i | \(0.0247786\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −247.677 | − | 597.945i | −0.528096 | − | 1.27494i | ||||
\(470\) | 91.4014 | + | 410.999i | 0.194471 | + | 0.874466i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −577.147 | − | 74.8186i | −1.22277 | − | 0.158514i | ||||
\(473\) | 115.030 | − | 115.030i | 0.243193 | − | 0.243193i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −177.468 | − | 428.447i | −0.373618 | − | 0.901993i | ||||
\(476\) | −536.698 | + | 251.131i | −1.12752 | + | 0.527586i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −79.9076 | + | 454.937i | −0.167171 | + | 0.951751i | ||||
\(479\) | − | 158.059i | − | 0.329977i | −0.986296 | − | 0.164988i | \(-0.947241\pi\) | ||
0.986296 | − | 0.164988i | \(-0.0527586\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 339.994 | 0.706848 | ||||||||
\(482\) | −219.454 | − | 38.5461i | −0.455299 | − | 0.0799712i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 275.315 | − | 128.825i | 0.568833 | − | 0.266168i | ||||
\(485\) | −458.803 | + | 190.042i | −0.945985 | + | 0.391840i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −675.116 | − | 675.116i | −1.38628 | − | 1.38628i | −0.832996 | − | 0.553280i | \(-0.813376\pi\) |
−0.553280 | − | 0.832996i | \(-0.686624\pi\) | |||||||
\(488\) | 81.2855 | + | 105.499i | 0.166569 | + | 0.216187i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −192.931 | + | 42.9057i | −0.393738 | + | 0.0875627i | ||||
\(491\) | −87.1226 | + | 36.0874i | −0.177439 | + | 0.0734977i | −0.469634 | − | 0.882861i | \(-0.655614\pi\) |
0.292195 | + | 0.956359i | \(0.405614\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −347.963 | − | 144.131i | −0.705808 | − | 0.292355i | ||||
\(494\) | −129.850 | − | 185.184i | −0.262854 | − | 0.374866i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 179.741 | − | 215.361i | 0.362381 | − | 0.434196i | ||||
\(497\) | 21.7979i | 0.0438590i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 164.812 | − | 397.892i | 0.330285 | − | 0.797378i | −0.668284 | − | 0.743906i | \(-0.732971\pi\) |
0.998569 | − | 0.0534724i | \(-0.0170289\pi\) | |||||||
\(500\) | 226.026 | − | 247.320i | 0.452052 | − | 0.494640i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 476.610 | − | 105.993i | 0.949423 | − | 0.211141i | ||||
\(503\) | 270.905 | − | 270.905i | 0.538578 | − | 0.538578i | −0.384533 | − | 0.923111i | \(-0.625638\pi\) |
0.923111 | + | 0.384533i | \(0.125638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −86.0864 | + | 86.0864i | −0.170468 | + | 0.170468i | ||||
\(506\) | −155.654 | − | 99.0181i | −0.307617 | − | 0.195688i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −108.253 | + | 298.650i | −0.213096 | + | 0.587893i | ||||
\(509\) | 194.137 | − | 468.689i | 0.381409 | − | 0.920803i | −0.610285 | − | 0.792182i | \(-0.708945\pi\) |
0.991694 | − | 0.128621i | \(-0.0410551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 262.081i | 0.512878i | ||||||||
\(512\) | −511.991 | + | 3.04640i | −0.999982 | + | 0.00595000i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −96.4230 | + | 548.964i | −0.187593 | + | 1.06802i | ||||
\(515\) | 98.7463 | + | 40.9021i | 0.191740 | + | 0.0794215i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 167.416 | − | 69.3458i | 0.323821 | − | 0.134131i | ||||
\(518\) | 252.335 | − | 396.665i | 0.487133 | − | 0.765763i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 270.828 | − | 471.243i | 0.520822 | − | 0.906237i | ||||
\(521\) | 240.434 | + | 240.434i | 0.461486 | + | 0.461486i | 0.899142 | − | 0.437656i | \(-0.144191\pi\) |
−0.437656 | + | 0.899142i | \(0.644191\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 846.467 | − | 350.618i | 1.61848 | − | 0.670398i | 0.624611 | − | 0.780936i | \(-0.285257\pi\) |
0.993872 | + | 0.110538i | \(0.0352574\pi\) | |||||||
\(524\) | 170.235 | + | 155.578i | 0.324875 | + | 0.296904i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 628.078 | − | 440.404i | 1.19407 | − | 0.837271i | ||||
\(527\) | −430.941 | −0.817725 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 339.966i | 0.642657i | ||||||||
\(530\) | 1134.52 | − | 795.521i | 2.14061 | − | 1.50098i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −312.422 | + | 14.0546i | −0.587260 | + | 0.0264183i | ||||
\(533\) | 51.7916 | + | 125.036i | 0.0971699 | + | 0.234589i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 823.967 | − | 823.967i | 1.54012 | − | 1.54012i | ||||
\(536\) | −680.555 | + | 524.356i | −1.26969 | + | 0.978276i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 63.8502 | − | 100.371i | 0.118681 | − | 0.186563i | ||||
\(539\) | 32.5523 | + | 78.5883i | 0.0603939 | + | 0.145804i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.87337 | + | 16.5938i | −0.0127049 | + | 0.0306724i | −0.930105 | − | 0.367294i | \(-0.880284\pi\) |
0.917400 | + | 0.397967i | \(0.130284\pi\) | |||||||
\(542\) | −153.613 | + | 874.563i | −0.283419 | + | 1.61358i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 507.584 | + | 600.870i | 0.933059 | + | 1.10454i | ||||
\(545\) | 270.752 | 0.496793 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 354.417 | + | 146.804i | 0.647929 | + | 0.268381i | 0.682349 | − | 0.731026i | \(-0.260958\pi\) |
−0.0344200 | + | 0.999407i | \(0.510958\pi\) | |||||||
\(548\) | 121.638 | + | 259.955i | 0.221967 | + | 0.474370i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −404.696 | − | 257.444i | −0.735811 | − | 0.468079i | ||||
\(551\) | −140.560 | − | 140.560i | −0.255100 | − | 0.255100i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −386.348 | − | 386.348i | −0.698639 | − | 0.698639i | ||||
\(554\) | −118.015 | + | 26.2452i | −0.213024 | + | 0.0473741i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −576.171 | + | 25.9195i | −1.03628 | + | 0.0466178i | ||||
\(557\) | 549.588 | + | 227.647i | 0.986692 | + | 0.408701i | 0.816900 | − | 0.576779i | \(-0.195690\pi\) |
0.169792 | + | 0.985480i | \(0.445690\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 211.371 | 0.378123 | ||||||||
\(560\) | −348.790 | − | 665.715i | −0.622839 | − | 1.18878i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 259.445 | + | 370.005i | 0.461646 | + | 0.658372i | ||||
\(563\) | 150.445 | − | 363.205i | 0.267219 | − | 0.645125i | −0.732131 | − | 0.681164i | \(-0.761474\pi\) |
0.999350 | + | 0.0360391i | \(0.0114741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 375.583 | + | 906.737i | 0.664748 | + | 1.60484i | ||||
\(566\) | 946.190 | − | 210.422i | 1.67171 | − | 0.371770i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.9344 | − | 7.54442i | 0.0491803 | − | 0.0132824i | ||||
\(569\) | −510.987 | + | 510.987i | −0.898045 | + | 0.898045i | −0.995263 | − | 0.0972186i | \(-0.969005\pi\) |
0.0972186 | + | 0.995263i | \(0.469005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 328.247 | + | 792.459i | 0.574864 | + | 1.38784i | 0.897371 | + | 0.441277i | \(0.145474\pi\) |
−0.322507 | + | 0.946567i | \(0.604526\pi\) | |||||||
\(572\) | −219.923 | − | 79.7161i | −0.384480 | − | 0.139364i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 184.316 | + | 32.3742i | 0.321108 | + | 0.0564011i | ||||
\(575\) | − | 491.482i | − | 0.854752i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 305.039 | 0.528663 | 0.264332 | − | 0.964432i | \(-0.414849\pi\) | ||||
0.264332 | + | 0.964432i | \(0.414849\pi\) | |||||||
\(578\) | 109.052 | − | 620.867i | 0.188672 | − | 1.07416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 162.789 | − | 449.106i | 0.280671 | − | 0.774322i | ||||
\(581\) | 572.080 | − | 236.963i | 0.984647 | − | 0.407854i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −421.689 | − | 421.689i | −0.723309 | − | 0.723309i | ||||
\(584\) | 335.861 | − | 90.7080i | 0.575104 | − | 0.155322i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −223.962 | − | 1007.08i | −0.382188 | − | 1.71856i | ||||
\(587\) | 388.900 | − | 161.088i | 0.662521 | − | 0.274425i | −0.0259780 | − | 0.999663i | \(-0.508270\pi\) |
0.688499 | + | 0.725237i | \(0.258270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −210.132 | − | 87.0394i | −0.356760 | − | 0.147775i | ||||
\(590\) | −928.475 | + | 651.040i | −1.57369 | + | 1.10346i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −595.668 | − | 186.083i | −1.00620 | − | 0.314330i | ||||
\(593\) | 1039.64i | 1.75319i | 0.481228 | + | 0.876595i | \(0.340191\pi\) | ||||
−0.481228 | + | 0.876595i | \(0.659809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −441.839 | + | 1066.69i | −0.742587 | + | 1.79276i | ||||
\(596\) | 2.35235 | + | 52.2911i | 0.00394690 | + | 0.0877367i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −52.0351 | − | 233.983i | −0.0870152 | − | 0.391276i | ||||
\(599\) | −22.4929 | + | 22.4929i | −0.0375507 | + | 0.0375507i | −0.725633 | − | 0.688082i | \(-0.758453\pi\) |
0.688082 | + | 0.725633i | \(0.258453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −640.653 | + | 640.653i | −1.06598 | + | 1.06598i | −0.0683147 | + | 0.997664i | \(0.521762\pi\) |
−0.997664 | + | 0.0683147i | \(0.978238\pi\) | |||||||
\(602\) | 156.874 | − | 246.603i | 0.260588 | − | 0.409639i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 90.6211 | − | 42.4033i | 0.150035 | − | 0.0702041i | ||||
\(605\) | 226.654 | − | 547.192i | 0.374636 | − | 0.904450i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 860.149i | − | 1.41705i | −0.705686 | − | 0.708524i | \(-0.749361\pi\) | ||
0.705686 | − | 0.708524i | \(-0.250639\pi\) | |||||||
\(608\) | 126.143 | + | 395.510i | 0.207472 | + | 0.650511i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 255.593 | + | 44.8938i | 0.419005 | + | 0.0735964i | ||||
\(611\) | 217.527 | + | 90.1026i | 0.356018 | + | 0.147467i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 724.830 | − | 300.235i | 1.18243 | − | 0.489779i | 0.297148 | − | 0.954831i | \(-0.403965\pi\) |
0.885283 | + | 0.465052i | \(0.153965\pi\) | |||||||
\(614\) | −865.223 | − | 550.404i | −1.40916 | − | 0.896424i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −256.225 | + | 197.417i | −0.415949 | + | 0.320482i | ||||
\(617\) | 704.685 | + | 704.685i | 1.14212 | + | 1.14212i | 0.988063 | + | 0.154052i | \(0.0492324\pi\) |
0.154052 | + | 0.988063i | \(0.450768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.0442 | + | 13.6874i | −0.0533832 | + | 0.0221121i | −0.409215 | − | 0.912438i | \(-0.634198\pi\) |
0.355832 | + | 0.934550i | \(0.384198\pi\) | |||||||
\(620\) | −24.5635 | − | 546.028i | −0.0396186 | − | 0.880691i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −627.369 | − | 894.716i | −1.00863 | − | 1.43845i | ||||
\(623\) | −931.477 | −1.49515 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 240.835i | 0.385335i | ||||||||
\(626\) | 206.375 | + | 294.320i | 0.329673 | + | 0.470159i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −520.772 | + | 569.834i | −0.829255 | + | 0.907379i | ||||
\(629\) | 366.885 | + | 885.738i | 0.583282 | + | 1.40817i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −718.112 | + | 718.112i | −1.13805 | + | 1.13805i | −0.149255 | + | 0.988799i | \(0.547688\pi\) |
−0.988799 | + | 0.149255i | \(0.952312\pi\) | |||||||
\(632\) | −361.393 | + | 628.829i | −0.571825 | + | 0.994982i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 107.761 | + | 68.5514i | 0.169971 | + | 0.108125i | ||||
\(635\) | 236.870 | + | 571.854i | 0.373023 | + | 0.900557i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −42.2960 | + | 102.112i | −0.0663988 | + | 0.160301i | ||||
\(638\) | −202.495 | − | 35.5673i | −0.317390 | − | 0.0557481i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −732.407 | + | 677.389i | −1.14439 | + | 1.05842i | ||||
\(641\) | 338.159 | 0.527549 | 0.263774 | − | 0.964584i | \(-0.415033\pi\) | ||||
0.263774 | + | 0.964584i | \(0.415033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 332.477 | + | 137.716i | 0.517071 | + | 0.214178i | 0.625930 | − | 0.779879i | \(-0.284720\pi\) |
−0.108859 | + | 0.994057i | \(0.534720\pi\) | |||||||
\(644\) | −311.603 | − | 112.948i | −0.483856 | − | 0.175385i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 342.314 | − | 538.110i | 0.529898 | − | 0.832987i | ||||
\(647\) | 31.2745 | + | 31.2745i | 0.0483377 | + | 0.0483377i | 0.730862 | − | 0.682525i | \(-0.239118\pi\) |
−0.682525 | + | 0.730862i | \(0.739118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 345.103 | + | 345.103i | 0.531746 | + | 0.531746i | ||||
\(650\) | −135.289 | − | 608.348i | −0.208138 | − | 0.935919i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 422.651 | + | 386.262i | 0.648238 | + | 0.592426i | ||||
\(653\) | −355.409 | − | 147.215i | −0.544271 | − | 0.225445i | 0.0935696 | − | 0.995613i | \(-0.470172\pi\) |
−0.637841 | + | 0.770168i | \(0.720172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 449.359 | 0.686044 | ||||||||
\(656\) | −22.3049 | − | 247.409i | −0.0340014 | − | 0.377148i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 266.564 | − | 186.913i | 0.405113 | − | 0.284062i | ||||
\(659\) | 116.271 | − | 280.702i | 0.176435 | − | 0.425952i | −0.810779 | − | 0.585352i | \(-0.800956\pi\) |
0.987214 | + | 0.159401i | \(0.0509562\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 179.920 | + | 434.366i | 0.272194 | + | 0.657134i | 0.999577 | − | 0.0290979i | \(-0.00926347\pi\) |
−0.727383 | + | 0.686232i | \(0.759263\pi\) | |||||||
\(662\) | 25.2600 | + | 113.585i | 0.0381571 | + | 0.171579i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −501.673 | − | 651.116i | −0.755532 | − | 0.980596i | ||||
\(665\) | −430.892 | + | 430.892i | −0.647957 | + | 0.647957i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −80.6200 | − | 194.634i | −0.120870 | − | 0.291805i | ||||
\(668\) | −263.123 | − | 562.326i | −0.393896 | − | 0.841805i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −289.600 | + | 1648.78i | −0.432240 | + | 2.46086i | ||||
\(671\) | − | 111.688i | − | 0.166449i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1168.06 | 1.73561 | 0.867803 | − | 0.496908i | \(-0.165531\pi\) | ||||
0.867803 | + | 0.496908i | \(0.165531\pi\) | |||||||
\(674\) | 726.484 | + | 127.604i | 1.07787 | + | 0.189323i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 157.684 | + | 336.990i | 0.233260 | + | 0.498505i | ||||
\(677\) | 604.882 | − | 250.550i | 0.893474 | − | 0.370089i | 0.111767 | − | 0.993734i | \(-0.464349\pi\) |
0.781707 | + | 0.623645i | \(0.214349\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 271.526 | + | 271.526i | 0.399891 | + | 0.399891i | ||||
\(680\) | 1519.91 | + | 197.034i | 2.23516 | + | 0.289756i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −229.630 | + | 51.0671i | −0.336701 | + | 0.0748785i | ||||
\(683\) | 369.863 | − | 153.202i | 0.541527 | − | 0.224308i | −0.0951163 | − | 0.995466i | \(-0.530322\pi\) |
0.636644 | + | 0.771158i | \(0.280322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 516.663 | + | 214.009i | 0.754253 | + | 0.312422i | ||||
\(686\) | 426.823 | + | 608.709i | 0.622191 | + | 0.887331i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −370.321 | − | 115.686i | −0.538258 | − | 0.168148i | ||||
\(689\) | − | 774.863i | − | 1.12462i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 74.8080 | − | 180.602i | 0.108260 | − | 0.261364i | −0.860460 | − | 0.509518i | \(-0.829824\pi\) |
0.968721 | + | 0.248154i | \(0.0798239\pi\) | |||||||
\(692\) | −917.840 | − | 838.816i | −1.32636 | − | 1.21216i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 848.222 | − | 188.635i | 1.22222 | − | 0.271808i | ||||
\(695\) | −794.653 | + | 794.653i | −1.14339 | + | 1.14339i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −269.851 | + | 269.851i | −0.387160 | + | 0.387160i | ||||
\(698\) | −108.779 | − | 69.1987i | −0.155844 | − | 0.0991386i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −810.157 | − | 293.661i | −1.15737 | − | 0.419515i | ||||
\(701\) | −250.206 | + | 604.050i | −0.356927 | + | 0.861698i | 0.638802 | + | 0.769371i | \(0.279430\pi\) |
−0.995729 | + | 0.0923265i | \(0.970570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 505.998i | 0.719769i | ||||||||
\(704\) | 341.674 | + | 260.029i | 0.485333 | + | 0.369359i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 84.9533 | − | 483.663i | 0.120330 | − | 0.685076i | ||||
\(707\) | 86.9722 | + | 36.0251i | 0.123016 | + | 0.0509548i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −771.157 | + | 319.424i | −1.08767 | + | 0.450527i | −0.853193 | − | 0.521595i | \(-0.825337\pi\) |
−0.234476 | + | 0.972122i | \(0.575337\pi\) | |||||||
\(710\) | 30.2618 | − | 47.5709i | 0.0426223 | − | 0.0670013i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 322.391 | + | 1193.70i | 0.452796 | + | 1.67655i | ||||
\(713\) | −170.446 | − | 170.446i | −0.239055 | − | 0.239055i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −421.107 | + | 174.428i | −0.588961 | + | 0.243956i | ||||
\(716\) | 345.126 | − | 377.640i | 0.482020 | − | 0.527431i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 142.892 | − | 100.195i | 0.199013 | − | 0.139547i | ||||
\(719\) | −263.077 | −0.365893 | −0.182947 | − | 0.983123i | \(-0.558564\pi\) | ||||
−0.182947 | + | 0.983123i | \(0.558564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 82.6459i | − | 0.114627i | ||||||
\(722\) | −315.553 | + | 221.264i | −0.437054 | + | 0.306459i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.2832 | − | 406.421i | −0.0252530 | − | 0.561355i | ||||
\(725\) | −209.609 | − | 506.041i | −0.289116 | − | 0.697988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 320.334 | − | 320.334i | 0.440625 | − | 0.440625i | −0.451597 | − | 0.892222i | \(-0.649146\pi\) |
0.892222 | + | 0.451597i | \(0.149146\pi\) | |||||||
\(728\) | −416.788 | − | 54.0304i | −0.572511 | − | 0.0742176i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 363.844 | − | 571.954i | 0.498416 | − | 0.783499i | ||||
\(731\) | 228.089 | + | 550.655i | 0.312023 | + | 0.753289i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 119.193 | − | 287.758i | 0.162610 | − | 0.392575i | −0.821482 | − | 0.570234i | \(-0.806852\pi\) |
0.984092 | + | 0.177659i | \(0.0568524\pi\) | |||||||
\(734\) | −42.6782 | + | 242.979i | −0.0581446 | + | 0.331034i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36.8966 | + | 438.417i | −0.0501313 | + | 0.595676i | ||||
\(737\) | 720.473 | 0.977576 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −760.509 | − | 315.013i | −1.02911 | − | 0.426269i | −0.196716 | − | 0.980461i | \(-0.563028\pi\) |
−0.832389 | + | 0.554191i | \(0.813028\pi\) | |||||||
\(740\) | −1101.37 | + | 515.352i | −1.48834 | + | 0.696422i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −904.020 | − | 575.084i | −1.21836 | − | 0.775046i | ||||
\(743\) | −89.2306 | − | 89.2306i | −0.120095 | − | 0.120095i | 0.644505 | − | 0.764600i | \(-0.277063\pi\) |
−0.764600 | + | 0.644505i | \(0.777063\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 72.1196 | + | 72.1196i | 0.0968049 | + | 0.0968049i | ||||
\(746\) | 59.1492 | − | 13.1541i | 0.0792885 | − | 0.0176328i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.6436 | − | 658.954i | −0.0396304 | − | 0.880955i | ||||
\(749\) | −832.445 | − | 344.810i | −1.11141 | − | 0.460361i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −418.271 | −0.556953 | −0.278476 | − | 0.960443i | \(-0.589829\pi\) | ||||
−0.278476 | + | 0.960443i | \(0.589829\pi\) | |||||||
\(752\) | −331.792 | − | 276.915i | −0.441213 | − | 0.368238i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −153.367 | − | 218.722i | −0.203404 | − | 0.290082i | ||||
\(755\) | 74.6042 | − | 180.110i | 0.0988135 | − | 0.238557i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −212.675 | − | 513.443i | −0.280944 | − | 0.678260i | 0.718914 | − | 0.695099i | \(-0.244640\pi\) |
−0.999858 | + | 0.0168395i | \(0.994640\pi\) | |||||||
\(758\) | −1046.25 | + | 232.675i | −1.38028 | + | 0.306959i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 701.330 | + | 403.060i | 0.922802 | + | 0.530343i | ||||
\(761\) | −60.9342 | + | 60.9342i | −0.0800712 | + | 0.0800712i | −0.746008 | − | 0.665937i | \(-0.768032\pi\) |
0.665937 | + | 0.746008i | \(0.268032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −80.1175 | − | 193.421i | −0.105003 | − | 0.253500i | ||||
\(764\) | 90.7333 | − | 250.317i | 0.118761 | − | 0.327640i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1193.35 | − | 209.607i | −1.55790 | − | 0.273638i | ||||
\(767\) | 634.135i | 0.826773i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 387.688 | 0.504146 | 0.252073 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252073 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(770\) | −109.033 | + | 620.755i | −0.141601 | + | 0.806176i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1037.47 | − | 376.054i | −1.34387 | − | 0.487117i | ||||
\(773\) | −19.2892 | + | 7.98984i | −0.0249537 | + | 0.0103361i | −0.395125 | − | 0.918627i | \(-0.629299\pi\) |
0.370172 | + | 0.928963i | \(0.379299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −443.154 | − | 443.154i | −0.571812 | − | 0.571812i | ||||
\(776\) | 253.988 | − | 441.942i | 0.327304 | − | 0.569513i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 200.462 | + | 901.404i | 0.257663 | + | 1.15862i | ||||
\(779\) | −186.085 | + | 77.0791i | −0.238877 | + | 0.0989462i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.4183 | − | 9.28595i | −0.0287046 | − | 0.0118898i | ||||
\(782\) | 553.412 | − | 388.049i | 0.707688 | − | 0.496226i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 129.990 | − | 155.750i | 0.165803 | − | 0.198661i | ||||
\(785\) | 1504.16i | 1.91613i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 521.707 | − | 1259.51i | 0.662906 | − | 1.60040i | −0.130321 | − | 0.991472i | \(-0.541601\pi\) |
0.793228 | − | 0.608925i | \(-0.208399\pi\) | |||||||
\(788\) | 723.606 | − | 32.5520i | 0.918282 | − | 0.0413096i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 306.787 | + | 1379.51i | 0.388338 | + | 1.74622i | ||||
\(791\) | 536.619 | − | 536.619i | 0.678406 | − | 0.678406i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 102.614 | − | 102.614i | 0.129400 | − | 0.129400i | ||||
\(794\) | −342.140 | + | 537.836i | −0.430907 | + | 0.677376i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 559.870 | + | 1196.51i | 0.703354 | + | 1.50316i | ||||
\(797\) | 397.554 | − | 959.781i | 0.498813 | − | 1.20424i | −0.451310 | − | 0.892367i | \(-0.649043\pi\) |
0.950123 | − | 0.311875i | \(-0.100957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 663.921i | 0.830940i | ||||||||
\(800\) | −95.9300 | + | 1139.87i | −0.119912 | + | 1.42484i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −95.4475 | − | 16.7649i | −0.119012 | − | 0.0209039i | ||||
\(803\) | −269.539 | − | 111.647i | −0.335665 | − | 0.139037i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −596.657 | + | 247.143i | −0.741189 | + | 0.307010i | ||||
\(806\) | −257.894 | − | 164.057i | −0.319967 | − | 0.203544i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.0650 | − | 123.925i | 0.0198825 | − | 0.153372i | ||||
\(809\) | 349.674 | + | 349.674i | 0.432230 | + | 0.432230i | 0.889386 | − | 0.457157i | \(-0.151132\pi\) |
−0.457157 | + | 0.889386i | \(0.651132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 179.312 | − | 74.2736i | 0.221100 | − | 0.0915827i | −0.269384 | − | 0.963033i | \(-0.586820\pi\) |
0.490484 | + | 0.871450i | \(0.336820\pi\) | |||||||
\(812\) | −369.004 | + | 16.5999i | −0.454439 | + | 0.0204433i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 300.459 | + | 428.496i | 0.369114 | + | 0.526408i | ||||
\(815\) | 1115.65 | 1.36889 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 314.574i | 0.385035i | ||||||||
\(818\) | −393.032 | − | 560.519i | −0.480479 | − | 0.685231i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −357.299 | − | 326.536i | −0.435730 | − | 0.398214i | ||||
\(821\) | 41.2552 | + | 99.5988i | 0.0502499 | + | 0.121314i | 0.947011 | − | 0.321201i | \(-0.104086\pi\) |
−0.896761 | + | 0.442515i | \(0.854086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −818.928 | + | 818.928i | −0.995053 | + | 0.995053i | −0.999988 | − | 0.00493500i | \(-0.998429\pi\) |
0.00493500 | + | 0.999988i | \(0.498429\pi\) | |||||||
\(824\) | −105.912 | + | 28.6043i | −0.128534 | + | 0.0347140i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 739.834 | + | 470.639i | 0.895683 | + | 0.569781i | ||||
\(827\) | −30.9529 | − | 74.7270i | −0.0374280 | − | 0.0903591i | 0.904060 | − | 0.427405i | \(-0.140572\pi\) |
−0.941488 | + | 0.337046i | \(0.890572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 87.1070 | − | 210.295i | 0.105075 | − | 0.253673i | −0.862594 | − | 0.505896i | \(-0.831162\pi\) |
0.967669 | + | 0.252223i | \(0.0811618\pi\) | |||||||
\(830\) | −1577.46 | − | 277.073i | −1.90055 | − | 0.333823i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 75.0123 | + | 552.821i | 0.0901591 | + | 0.664449i | ||||
\(833\) | −311.658 | −0.374140 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1117.63 | − | 462.937i | −1.33848 | − | 0.554416i | ||||
\(836\) | 118.638 | − | 327.301i | 0.141911 | − | 0.391508i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 189.698 | − | 298.201i | 0.226370 | − | 0.355848i | ||||
\(839\) | −500.637 | − | 500.637i | −0.596707 | − | 0.596707i | 0.342728 | − | 0.939435i | \(-0.388649\pi\) |
−0.939435 | + | 0.342728i | \(0.888649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 428.660 | + | 428.660i | 0.509703 | + | 0.509703i | ||||
\(842\) | −293.432 | − | 1319.46i | −0.348494 | − | 1.56705i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −230.650 | + | 252.379i | −0.273281 | + | 0.299027i | ||||
\(845\) | 669.771 | + | 277.428i | 0.792628 | + | 0.328317i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −457.973 | −0.540701 | ||||||||
\(848\) | −424.093 | + | 1357.56i | −0.500109 | + | 1.60089i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1438.85 | − | 1008.91i | 1.69277 | − | 1.18696i | ||||
\(851\) | −205.218 | + | 495.439i | −0.241149 | + | 0.582184i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 222.935 | + | 538.212i | 0.261354 | + | 0.630964i | 0.999023 | − | 0.0441988i | \(-0.0140735\pi\) |
−0.737669 | + | 0.675162i | \(0.764074\pi\) | |||||||
\(854\) | −43.5605 | − | 195.876i | −0.0510076 | − | 0.229363i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −153.765 | + | 1186.13i | −0.179632 | + | 1.38567i | ||||
\(857\) | 172.645 | − | 172.645i | 0.201453 | − | 0.201453i | −0.599169 | − | 0.800622i | \(-0.704502\pi\) |
0.800622 | + | 0.599169i | \(0.204502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 66.9122 | + | 161.540i | 0.0778954 | + | 0.188056i | 0.958030 | − | 0.286668i | \(-0.0925477\pi\) |
−0.880135 | + | 0.474724i | \(0.842548\pi\) | |||||||
\(860\) | −684.712 | + | 320.389i | −0.796177 | + | 0.372546i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 209.849 | − | 1194.73i | 0.243444 | − | 1.38600i | ||||
\(863\) | − | 325.900i | − | 0.377636i | −0.982012 | − | 0.188818i | \(-0.939534\pi\) | ||
0.982012 | − | 0.188818i | \(-0.0604656\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2422.77 | −2.80089 | ||||||||
\(866\) | 7.54396 | + | 1.32506i | 0.00871127 | + | 0.00153009i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −382.805 | + | 179.121i | −0.441019 | + | 0.206361i | ||||
\(869\) | 561.927 | − | 232.758i | 0.646637 | − | 0.267846i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 661.942 | + | 661.942i | 0.759980 | + | 0.759980i | ||||
\(872\) | −220.143 | + | 169.616i | −0.252457 | + | 0.194514i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 348.226 | − | 77.4415i | 0.398428 | − | 0.0886058i | ||||
\(875\) | −466.375 | + | 193.179i | −0.533000 | + | 0.220776i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 93.3817 | + | 38.6800i | 0.106479 | + | 0.0441049i | 0.435287 | − | 0.900292i | \(-0.356647\pi\) |
−0.328808 | + | 0.944397i | \(0.606647\pi\) | |||||||
\(878\) | −59.0089 | − | 84.1550i | −0.0672083 | − | 0.0958485i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 833.246 | − | 75.1204i | 0.946870 | − | 0.0853641i | ||||
\(881\) | − | 129.296i | − | 0.146760i | −0.997304 | − | 0.0733801i | \(-0.976621\pi\) | ||
0.997304 | − | 0.0733801i | \(-0.0233786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.1493 | − | 67.9584i | 0.0318792 | − | 0.0769631i | −0.907138 | − | 0.420833i | \(-0.861738\pi\) |
0.939017 | + | 0.343870i | \(0.111738\pi\) | |||||||
\(884\) | 578.186 | − | 632.657i | 0.654056 | − | 0.715675i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1063.36 | + | 236.478i | −1.20018 | + | 0.266905i | ||||
\(887\) | −338.588 | + | 338.588i | −0.381723 | + | 0.381723i | −0.871723 | − | 0.490000i | \(-0.836997\pi\) |
0.490000 | + | 0.871723i | \(0.336997\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 338.431 | − | 338.431i | 0.380687 | − | 0.380687i | ||||
\(890\) | 2032.82 | + | 1293.16i | 2.28407 | + | 1.45299i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 509.048 | − | 1404.37i | 0.570682 | − | 1.57441i | ||||
\(893\) | −134.096 | + | 323.736i | −0.150163 | + | 0.362526i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 996.837i | − | 1.11378i | ||||||
\(896\) | 700.640 | + | 322.775i | 0.781964 | + | 0.360240i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 149.355 | − | 850.322i | 0.166320 | − | 0.946907i | ||||
\(899\) | −248.188 | − | 102.803i | −0.276071 | − | 0.114352i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2018.64 | − | 836.148i | 2.24045 | − | 0.928023i | ||||
\(902\) | −111.814 | + | 175.770i | −0.123963 | + | 0.194867i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −873.415 | − | 501.959i | −0.966167 | − | 0.555265i | ||||
\(905\) | −560.535 | − | 560.535i | −0.619375 | − | 0.619375i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1031.84 | − | 427.401i | 1.13764 | − | 0.471225i | 0.267268 | − | 0.963622i | \(-0.413879\pi\) |
0.870371 | + | 0.492397i | \(0.163879\pi\) | |||||||
\(908\) | 24.6716 | + | 22.5474i | 0.0271713 | + | 0.0248319i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −670.500 | + | 470.150i | −0.736814 | + | 0.516649i | ||||
\(911\) | −857.136 | −0.940873 | −0.470437 | − | 0.882434i | \(-0.655904\pi\) | ||||
−0.470437 | + | 0.882434i | \(0.655904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 689.307i | 0.754992i | ||||||||
\(914\) | 433.187 | − | 303.748i | 0.473947 | − | 0.332328i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 714.534 | − | 32.1439i | 0.780059 | − | 0.0350916i | ||||
\(917\) | −132.968 | − | 321.014i | −0.145004 | − | 0.350070i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 447.382 | − | 447.382i | 0.486814 | − | 0.486814i | −0.420486 | − | 0.907299i | \(-0.638140\pi\) |
0.907299 | + | 0.420486i | \(0.138140\pi\) | |||||||
\(920\) | 523.226 | + | 679.088i | 0.568724 | + | 0.738140i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 294.879 | − | 463.544i | 0.319826 | − | 0.502759i | ||||
\(923\) | −12.0655 | − | 29.1286i | −0.0130720 | − | 0.0315586i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −533.558 | + | 1288.12i | −0.576820 | + | 1.39257i | ||||
\(926\) | 264.771 | − | 1507.42i | 0.285929 | − | 1.62788i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 148.988 | + | 467.140i | 0.160548 | + | 0.503384i | ||||
\(929\) | 357.338 | 0.384648 | 0.192324 | − | 0.981332i | \(-0.438398\pi\) | ||||
0.192324 | + | 0.981332i | \(0.438398\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −151.968 | − | 62.9473i | −0.163231 | − | 0.0676125i | ||||
\(932\) | 33.6117 | + | 71.8324i | 0.0360641 | + | 0.0770734i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 488.090 | + | 310.494i | 0.522580 | + | 0.332435i | ||||
\(935\) | −908.827 | − | 908.827i | −0.972007 | − | 0.972007i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −504.116 | − | 504.116i | −0.538011 | − | 0.538011i | 0.384934 | − | 0.922944i | \(-0.374224\pi\) |
−0.922944 | + | 0.384934i | \(0.874224\pi\) | |||||||
\(938\) | 1263.55 | − | 281.000i | 1.34707 | − | 0.299573i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −841.229 | + | 37.8433i | −0.894924 | + | 0.0402589i | ||||
\(941\) | 503.223 | + | 208.442i | 0.534775 | + | 0.221511i | 0.633693 | − | 0.773585i | \(-0.281538\pi\) |
−0.0989183 | + | 0.995096i | \(0.531538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −213.463 | −0.226366 | ||||||||
\(944\) | 347.070 | − | 1111.00i | 0.367659 | − | 1.17691i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 186.792 | + | 266.392i | 0.197455 | + | 0.281598i | ||||
\(947\) | 137.566 | − | 332.113i | 0.145265 | − | 0.350700i | −0.834454 | − | 0.551077i | \(-0.814217\pi\) |
0.979719 | + | 0.200378i | \(0.0642169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −145.065 | − | 350.219i | −0.152861 | − | 0.369040i | ||||
\(950\) | 905.376 | − | 201.345i | 0.953028 | − | 0.211942i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −308.995 | − | 1144.10i | −0.324574 | − | 1.20179i | ||||
\(953\) | −129.115 | + | 129.115i | −0.135483 | + | 0.135483i | −0.771596 | − | 0.636113i | \(-0.780541\pi\) |
0.636113 | + | 0.771596i | \(0.280541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −198.535 | − | 479.306i | −0.207890 | − | 0.501891i | ||||
\(956\) | −868.508 | − | 314.811i | −0.908481 | − | 0.329300i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 311.351 | + | 54.6874i | 0.325001 | + | 0.0570850i | ||||
\(959\) | − | 432.422i | − | 0.450909i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 653.628 | 0.680154 | ||||||||
\(962\) | −117.636 | + | 669.735i | −0.122283 | + | 0.696190i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 151.860 | − | 418.954i | 0.157531 | − | 0.434600i | ||||
\(965\) | −1986.54 | + | 822.851i | −2.05859 | + | 0.852695i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 657.007 | + | 657.007i | 0.679428 | + | 0.679428i | 0.959871 | − | 0.280443i | \(-0.0904813\pi\) |
−0.280443 | + | 0.959871i | \(0.590481\pi\) | |||||||
\(968\) | 158.508 | + | 586.901i | 0.163748 | + | 0.606303i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −215.611 | − | 969.524i | −0.222279 | − | 0.999509i | ||||
\(971\) | 654.912 | − | 271.274i | 0.674472 | − | 0.279376i | −0.0190418 | − | 0.999819i | \(-0.506062\pi\) |
0.693514 | + | 0.720443i | \(0.256062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 802.830 | + | 332.543i | 0.825108 | + | 0.341771i | ||||
\(974\) | 1563.46 | − | 1096.29i | 1.60519 | − | 1.12555i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −235.942 | + | 123.618i | −0.241744 | + | 0.126657i | ||||
\(977\) | − | 1493.20i | − | 1.52835i | −0.645010 | − | 0.764174i | \(-0.723147\pi\) | ||
0.645010 | − | 0.764174i | \(-0.276853\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 396.811 | − | 957.986i | 0.405323 | − | 0.978536i | ||||
\(980\) | −17.7644 | − | 394.890i | −0.0181270 | − | 0.402949i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −40.9426 | − | 184.104i | −0.0416931 | − | 0.187479i | ||||
\(983\) | 856.189 | − | 856.189i | 0.870996 | − | 0.870996i | −0.121585 | − | 0.992581i | \(-0.538798\pi\) |
0.992581 | + | 0.121585i | \(0.0387976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 997.994 | − | 997.994i | 1.01319 | − | 1.01319i | ||||
\(986\) | 404.309 | − | 635.565i | 0.410050 | − | 0.644590i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 409.711 | − | 191.711i | 0.414687 | − | 0.194040i | ||||
\(989\) | −127.582 | + | 308.010i | −0.129001 | + | 0.311435i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1223.32i | − | 1.23443i | −0.786793 | − | 0.617217i | \(-0.788260\pi\) | ||
0.786793 | − | 0.617217i | \(-0.211740\pi\) | |||||||
\(992\) | 362.039 | + | 428.576i | 0.364958 | + | 0.432032i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −42.9385 | − | 7.54196i | −0.0431977 | − | 0.00758748i | ||||
\(995\) | 2378.08 | + | 985.034i | 2.39003 | + | 0.989984i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 604.001 | − | 250.185i | 0.605819 | − | 0.250938i | −0.0586209 | − | 0.998280i | \(-0.518670\pi\) |
0.664440 | + | 0.747342i | \(0.268670\pi\) | |||||||
\(998\) | 726.761 | + | 462.323i | 0.728217 | + | 0.463249i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 288.3.u.a.19.3 | 28 | ||
3.2 | odd | 2 | 32.3.h.a.19.5 | ✓ | 28 | ||
12.11 | even | 2 | 128.3.h.a.111.6 | 28 | |||
24.5 | odd | 2 | 256.3.h.b.223.6 | 28 | |||
24.11 | even | 2 | 256.3.h.a.223.2 | 28 | |||
32.27 | odd | 8 | inner | 288.3.u.a.91.3 | 28 | ||
96.5 | odd | 8 | 128.3.h.a.15.6 | 28 | |||
96.11 | even | 8 | 256.3.h.b.31.6 | 28 | |||
96.53 | odd | 8 | 256.3.h.a.31.2 | 28 | |||
96.59 | even | 8 | 32.3.h.a.27.5 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.5 | ✓ | 28 | 3.2 | odd | 2 | ||
32.3.h.a.27.5 | yes | 28 | 96.59 | even | 8 | ||
128.3.h.a.15.6 | 28 | 96.5 | odd | 8 | |||
128.3.h.a.111.6 | 28 | 12.11 | even | 2 | |||
256.3.h.a.31.2 | 28 | 96.53 | odd | 8 | |||
256.3.h.a.223.2 | 28 | 24.11 | even | 2 | |||
256.3.h.b.31.6 | 28 | 96.11 | even | 8 | |||
256.3.h.b.223.6 | 28 | 24.5 | odd | 2 | |||
288.3.u.a.19.3 | 28 | 1.1 | even | 1 | trivial | ||
288.3.u.a.91.3 | 28 | 32.27 | odd | 8 | inner |