Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
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: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-2.45160\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45160 | 1.73354 | 0.866772 | − | 0.498705i | \(-0.166191\pi\) | ||||
0.866772 | + | 0.498705i | \(0.166191\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.01034 | 2.00517 | ||||||||
\(5\) | −1.23909 | −0.554137 | −0.277069 | − | 0.960850i | \(-0.589363\pi\) | ||||
−0.277069 | + | 0.960850i | \(0.589363\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 4.92856 | 1.74251 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.03775 | −0.960621 | ||||||||
\(11\) | −2.19586 | −0.662076 | −0.331038 | − | 0.943618i | \(-0.607399\pi\) | ||||
−0.331038 | + | 0.943618i | \(0.607399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.52432 | 0.422771 | 0.211385 | − | 0.977403i | \(-0.432203\pi\) | ||||
0.211385 | + | 0.977403i | \(0.432203\pi\) | |||||||
\(14\) | 2.45160 | 0.655218 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.06217 | 1.01554 | ||||||||
\(17\) | −7.06712 | −1.71403 | −0.857014 | − | 0.515292i | \(-0.827683\pi\) | ||||
−0.857014 | + | 0.515292i | \(0.827683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.45237 | −0.333197 | −0.166599 | − | 0.986025i | \(-0.553278\pi\) | ||||
−0.166599 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(20\) | −4.96917 | −1.11114 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.38336 | −1.14774 | ||||||||
\(23\) | −2.60977 | −0.544175 | −0.272088 | − | 0.962272i | \(-0.587714\pi\) | ||||
−0.272088 | + | 0.962272i | \(0.587714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.46466 | −0.692932 | ||||||||
\(26\) | 3.73703 | 0.732891 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.01034 | 0.757884 | ||||||||
\(29\) | −6.11799 | −1.13608 | −0.568041 | − | 0.823000i | \(-0.692299\pi\) | ||||
−0.568041 | + | 0.823000i | \(0.692299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.83292 | 0.329203 | 0.164601 | − | 0.986360i | \(-0.447366\pi\) | ||||
0.164601 | + | 0.986360i | \(0.447366\pi\) | |||||||
\(32\) | 0.101697 | 0.0179777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17.3258 | −2.97134 | ||||||||
\(35\) | −1.23909 | −0.209444 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.914123 | 0.150281 | 0.0751404 | − | 0.997173i | \(-0.476059\pi\) | ||||
0.0751404 | + | 0.997173i | \(0.476059\pi\) | |||||||
\(38\) | −3.56064 | −0.577611 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.10692 | −0.965589 | ||||||||
\(41\) | 1.13505 | 0.177265 | 0.0886325 | − | 0.996064i | \(-0.471750\pi\) | ||||
0.0886325 | + | 0.996064i | \(0.471750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.48757 | 0.379351 | 0.189675 | − | 0.981847i | \(-0.439256\pi\) | ||||
0.189675 | + | 0.981847i | \(0.439256\pi\) | |||||||
\(44\) | −8.80614 | −1.32758 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.39812 | −0.943352 | ||||||||
\(47\) | −0.620901 | −0.0905677 | −0.0452839 | − | 0.998974i | \(-0.514419\pi\) | ||||
−0.0452839 | + | 0.998974i | \(0.514419\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.49396 | −1.20123 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.11305 | 0.847728 | ||||||||
\(53\) | −6.86259 | −0.942649 | −0.471325 | − | 0.881960i | \(-0.656224\pi\) | ||||
−0.471325 | + | 0.881960i | \(0.656224\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.72086 | 0.366881 | ||||||||
\(56\) | 4.92856 | 0.658606 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.9989 | −1.96945 | ||||||||
\(59\) | −8.13041 | −1.05849 | −0.529245 | − | 0.848469i | \(-0.677525\pi\) | ||||
−0.529245 | + | 0.848469i | \(0.677525\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.09932 | 0.652901 | 0.326451 | − | 0.945214i | \(-0.394147\pi\) | ||||
0.326451 | + | 0.945214i | \(0.394147\pi\) | |||||||
\(62\) | 4.49360 | 0.570687 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.87502 | −0.984377 | ||||||||
\(65\) | −1.88877 | −0.234273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.28798 | −0.646029 | −0.323015 | − | 0.946394i | \(-0.604696\pi\) | ||||
−0.323015 | + | 0.946394i | \(0.604696\pi\) | |||||||
\(68\) | −28.3416 | −3.43692 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.03775 | −0.363081 | ||||||||
\(71\) | −4.94368 | −0.586707 | −0.293353 | − | 0.956004i | \(-0.594771\pi\) | ||||
−0.293353 | + | 0.956004i | \(0.594771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.24571 | 0.379882 | 0.189941 | − | 0.981796i | \(-0.439170\pi\) | ||||
0.189941 | + | 0.981796i | \(0.439170\pi\) | |||||||
\(74\) | 2.24106 | 0.260518 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.82451 | −0.668117 | ||||||||
\(77\) | −2.19586 | −0.250241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.62522 | −0.970413 | −0.485206 | − | 0.874400i | \(-0.661255\pi\) | ||||
−0.485206 | + | 0.874400i | \(0.661255\pi\) | |||||||
\(80\) | −5.03339 | −0.562750 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.78269 | 0.307296 | ||||||||
\(83\) | 14.6973 | 1.61324 | 0.806621 | − | 0.591069i | \(-0.201294\pi\) | ||||
0.806621 | + | 0.591069i | \(0.201294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.75679 | 0.949807 | ||||||||
\(86\) | 6.09853 | 0.657621 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.8224 | −1.15367 | ||||||||
\(89\) | −2.62512 | −0.278262 | −0.139131 | − | 0.990274i | \(-0.544431\pi\) | ||||
−0.139131 | + | 0.990274i | \(0.544431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.52432 | 0.159792 | ||||||||
\(92\) | −10.4661 | −1.09117 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.52220 | −0.157003 | ||||||||
\(95\) | 1.79962 | 0.184637 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.23555 | 0.430055 | 0.215028 | − | 0.976608i | \(-0.431016\pi\) | ||||
0.215028 | + | 0.976608i | \(0.431016\pi\) | |||||||
\(98\) | 2.45160 | 0.247649 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.8945 | −1.38945 | ||||||||
\(101\) | 8.53644 | 0.849407 | 0.424704 | − | 0.905332i | \(-0.360378\pi\) | ||||
0.424704 | + | 0.905332i | \(0.360378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.764721 | −0.0753502 | −0.0376751 | − | 0.999290i | \(-0.511995\pi\) | ||||
−0.0376751 | + | 0.999290i | \(0.511995\pi\) | |||||||
\(104\) | 7.51271 | 0.736681 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.8243 | −1.63412 | ||||||||
\(107\) | −5.26387 | −0.508878 | −0.254439 | − | 0.967089i | \(-0.581891\pi\) | ||||
−0.254439 | + | 0.967089i | \(0.581891\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.88983 | −0.755709 | −0.377854 | − | 0.925865i | \(-0.623338\pi\) | ||||
−0.377854 | + | 0.925865i | \(0.623338\pi\) | |||||||
\(110\) | 6.67046 | 0.636004 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.06217 | 0.383839 | ||||||||
\(113\) | 3.38966 | 0.318872 | 0.159436 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159436 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.23374 | 0.301548 | ||||||||
\(116\) | −24.5352 | −2.27804 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.9325 | −1.83494 | ||||||||
\(119\) | −7.06712 | −0.647842 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.17822 | −0.561656 | ||||||||
\(122\) | 12.5015 | 1.13183 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.35066 | 0.660108 | ||||||||
\(125\) | 10.4885 | 0.938117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −19.5098 | −1.72444 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.63051 | −0.406122 | ||||||||
\(131\) | 15.2901 | 1.33590 | 0.667951 | − | 0.744205i | \(-0.267172\pi\) | ||||
0.667951 | + | 0.744205i | \(0.267172\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.45237 | −0.125937 | ||||||||
\(134\) | −12.9640 | −1.11992 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −34.8307 | −2.98671 | ||||||||
\(137\) | −11.5984 | −0.990920 | −0.495460 | − | 0.868631i | \(-0.665001\pi\) | ||||
−0.495460 | + | 0.868631i | \(0.665001\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.6844 | −1.16069 | −0.580347 | − | 0.814369i | \(-0.697083\pi\) | ||||
−0.580347 | + | 0.814369i | \(0.697083\pi\) | |||||||
\(140\) | −4.96917 | −0.419972 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.1199 | −1.01708 | ||||||||
\(143\) | −3.34719 | −0.279906 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.58073 | 0.629545 | ||||||||
\(146\) | 7.95719 | 0.658541 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.66595 | 0.301339 | ||||||||
\(149\) | 17.3140 | 1.41842 | 0.709210 | − | 0.704997i | \(-0.249052\pi\) | ||||
0.709210 | + | 0.704997i | \(0.249052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.01569 | 0.0826559 | 0.0413280 | − | 0.999146i | \(-0.486841\pi\) | ||||
0.0413280 | + | 0.999146i | \(0.486841\pi\) | |||||||
\(152\) | −7.15810 | −0.580599 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.38336 | −0.433804 | ||||||||
\(155\) | −2.27115 | −0.182424 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.65737 | −0.611125 | −0.305562 | − | 0.952172i | \(-0.598844\pi\) | ||||
−0.305562 | + | 0.952172i | \(0.598844\pi\) | |||||||
\(158\) | −21.1456 | −1.68225 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.126012 | −0.00996212 | ||||||||
\(161\) | −2.60977 | −0.205679 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.5168 | 1.68533 | 0.842664 | − | 0.538439i | \(-0.180986\pi\) | ||||
0.842664 | + | 0.538439i | \(0.180986\pi\) | |||||||
\(164\) | 4.55194 | 0.355447 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36.0320 | 2.79662 | ||||||||
\(167\) | 15.3106 | 1.18477 | 0.592387 | − | 0.805654i | \(-0.298186\pi\) | ||||
0.592387 | + | 0.805654i | \(0.298186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6764 | −0.821265 | ||||||||
\(170\) | 21.4681 | 1.64653 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.97601 | 0.760664 | ||||||||
\(173\) | −25.8227 | −1.96326 | −0.981632 | − | 0.190784i | \(-0.938897\pi\) | ||||
−0.981632 | + | 0.190784i | \(0.938897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46466 | −0.261904 | ||||||||
\(176\) | −8.91994 | −0.672366 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.43573 | −0.482379 | ||||||||
\(179\) | −5.00100 | −0.373792 | −0.186896 | − | 0.982380i | \(-0.559843\pi\) | ||||
−0.186896 | + | 0.982380i | \(0.559843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.03422 | 0.522850 | 0.261425 | − | 0.965224i | \(-0.415808\pi\) | ||||
0.261425 | + | 0.965224i | \(0.415808\pi\) | |||||||
\(182\) | 3.73703 | 0.277007 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.8624 | −0.948231 | ||||||||
\(185\) | −1.13268 | −0.0832762 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.5184 | 1.13482 | ||||||||
\(188\) | −2.49003 | −0.181604 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.41194 | 0.320076 | ||||||||
\(191\) | 9.51278 | 0.688321 | 0.344160 | − | 0.938911i | \(-0.388164\pi\) | ||||
0.344160 | + | 0.938911i | \(0.388164\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.64395 | 0.406261 | 0.203130 | − | 0.979152i | \(-0.434888\pi\) | ||||
0.203130 | + | 0.979152i | \(0.434888\pi\) | |||||||
\(194\) | 10.3839 | 0.745519 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.01034 | 0.286453 | ||||||||
\(197\) | 0.962282 | 0.0685597 | 0.0342799 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342799 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.51386 | −0.603532 | −0.301766 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301766 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(200\) | −17.0758 | −1.20744 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.9279 | 1.47248 | ||||||||
\(203\) | −6.11799 | −0.429399 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.40643 | −0.0982291 | ||||||||
\(206\) | −1.87479 | −0.130623 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.19205 | 0.429341 | ||||||||
\(209\) | 3.18920 | 0.220602 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.62207 | 0.318196 | 0.159098 | − | 0.987263i | \(-0.449141\pi\) | ||||
0.159098 | + | 0.987263i | \(0.449141\pi\) | |||||||
\(212\) | −27.5213 | −1.89017 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.9049 | −0.882161 | ||||||||
\(215\) | −3.08232 | −0.210212 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.83292 | 0.124427 | ||||||||
\(218\) | −19.3427 | −1.31005 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.9116 | 0.735659 | ||||||||
\(221\) | −10.7726 | −0.724641 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.37627 | −0.159127 | −0.0795635 | − | 0.996830i | \(-0.525353\pi\) | ||||
−0.0795635 | + | 0.996830i | \(0.525353\pi\) | |||||||
\(224\) | 0.101697 | 0.00679494 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.31009 | 0.552779 | ||||||||
\(227\) | −23.8414 | −1.58241 | −0.791205 | − | 0.611550i | \(-0.790546\pi\) | ||||
−0.791205 | + | 0.611550i | \(0.790546\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.15914 | 0.0765981 | 0.0382991 | − | 0.999266i | \(-0.487806\pi\) | ||||
0.0382991 | + | 0.999266i | \(0.487806\pi\) | |||||||
\(230\) | 7.92784 | 0.522746 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −30.1529 | −1.97963 | ||||||||
\(233\) | −0.949682 | −0.0622157 | −0.0311079 | − | 0.999516i | \(-0.509904\pi\) | ||||
−0.0311079 | + | 0.999516i | \(0.509904\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.769351 | 0.0501869 | ||||||||
\(236\) | −32.6057 | −2.12245 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17.3258 | −1.12306 | ||||||||
\(239\) | 5.71424 | 0.369623 | 0.184812 | − | 0.982774i | \(-0.440833\pi\) | ||||
0.184812 | + | 0.982774i | \(0.440833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3910 | 1.44233 | 0.721166 | − | 0.692762i | \(-0.243607\pi\) | ||||
0.721166 | + | 0.692762i | \(0.243607\pi\) | |||||||
\(242\) | −15.1465 | −0.973655 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.4500 | 1.30918 | ||||||||
\(245\) | −1.23909 | −0.0791625 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.21388 | −0.140866 | ||||||||
\(248\) | 9.03367 | 0.573639 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 25.7135 | 1.62627 | ||||||||
\(251\) | 1.54081 | 0.0972550 | 0.0486275 | − | 0.998817i | \(-0.484515\pi\) | ||||
0.0486275 | + | 0.998817i | \(0.484515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.73069 | 0.360285 | ||||||||
\(254\) | −2.45160 | −0.153827 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0802 | −2.00501 | ||||||||
\(257\) | 3.86350 | 0.240999 | 0.120499 | − | 0.992713i | \(-0.461550\pi\) | ||||
0.120499 | + | 0.992713i | \(0.461550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.914123 | 0.0568008 | ||||||||
\(260\) | −7.57461 | −0.469757 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 37.4852 | 2.31584 | ||||||||
\(263\) | 3.85898 | 0.237955 | 0.118977 | − | 0.992897i | \(-0.462038\pi\) | ||||
0.118977 | + | 0.992897i | \(0.462038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.50336 | 0.522357 | ||||||||
\(266\) | −3.56064 | −0.218317 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.2066 | −1.29540 | ||||||||
\(269\) | −29.8634 | −1.82080 | −0.910401 | − | 0.413727i | \(-0.864227\pi\) | ||||
−0.910401 | + | 0.413727i | \(0.864227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.4327 | 1.90940 | 0.954700 | − | 0.297571i | \(-0.0961767\pi\) | ||||
0.954700 | + | 0.297571i | \(0.0961767\pi\) | |||||||
\(272\) | −28.7078 | −1.74067 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.4347 | −1.71780 | ||||||||
\(275\) | 7.60789 | 0.458773 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.75055 | 0.405601 | 0.202801 | − | 0.979220i | \(-0.434996\pi\) | ||||
0.202801 | + | 0.979220i | \(0.434996\pi\) | |||||||
\(278\) | −33.5486 | −2.01211 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.10692 | −0.364958 | ||||||||
\(281\) | −7.23858 | −0.431818 | −0.215909 | − | 0.976414i | \(-0.569271\pi\) | ||||
−0.215909 | + | 0.976414i | \(0.569271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0636 | 0.717108 | 0.358554 | − | 0.933509i | \(-0.383270\pi\) | ||||
0.358554 | + | 0.933509i | \(0.383270\pi\) | |||||||
\(284\) | −19.8259 | −1.17645 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.20597 | −0.485229 | ||||||||
\(287\) | 1.13505 | 0.0669998 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.9442 | 1.93790 | ||||||||
\(290\) | 18.5849 | 1.09134 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.0164 | 0.761728 | ||||||||
\(293\) | 1.86633 | 0.109032 | 0.0545162 | − | 0.998513i | \(-0.482638\pi\) | ||||
0.0545162 | + | 0.998513i | \(0.482638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0743 | 0.586548 | ||||||||
\(296\) | 4.50531 | 0.261866 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 42.4471 | 2.45889 | ||||||||
\(299\) | −3.97813 | −0.230061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.48757 | 0.143381 | ||||||||
\(302\) | 2.49007 | 0.143288 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.89978 | −0.338376 | ||||||||
\(305\) | −6.31851 | −0.361797 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.17131 | −0.180996 | −0.0904981 | − | 0.995897i | \(-0.528846\pi\) | ||||
−0.0904981 | + | 0.995897i | \(0.528846\pi\) | |||||||
\(308\) | −8.80614 | −0.501776 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.56796 | −0.316239 | ||||||||
\(311\) | 6.97271 | 0.395386 | 0.197693 | − | 0.980264i | \(-0.436655\pi\) | ||||
0.197693 | + | 0.980264i | \(0.436655\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0961 | −0.570668 | −0.285334 | − | 0.958428i | \(-0.592105\pi\) | ||||
−0.285334 | + | 0.958428i | \(0.592105\pi\) | |||||||
\(314\) | −18.7728 | −1.05941 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −34.5901 | −1.94584 | ||||||||
\(317\) | −32.1544 | −1.80597 | −0.902986 | − | 0.429670i | \(-0.858630\pi\) | ||||
−0.902986 | + | 0.429670i | \(0.858630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.4342 | 0.752172 | ||||||||
\(320\) | 9.75784 | 0.545480 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.39812 | −0.356553 | ||||||||
\(323\) | 10.2641 | 0.571109 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.28125 | −0.292951 | ||||||||
\(326\) | 52.7507 | 2.92159 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.59416 | 0.308886 | ||||||||
\(329\) | −0.620901 | −0.0342314 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.3663 | −1.33930 | −0.669648 | − | 0.742679i | \(-0.733555\pi\) | ||||
−0.669648 | + | 0.742679i | \(0.733555\pi\) | |||||||
\(332\) | 58.9413 | 3.23483 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 37.5356 | 2.05386 | ||||||||
\(335\) | 6.55227 | 0.357989 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.06781 | 0.385008 | 0.192504 | − | 0.981296i | \(-0.438339\pi\) | ||||
0.192504 | + | 0.981296i | \(0.438339\pi\) | |||||||
\(338\) | −26.1744 | −1.42370 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 35.1177 | 1.90453 | ||||||||
\(341\) | −4.02484 | −0.217957 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 12.2601 | 0.661022 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −63.3070 | −3.40340 | ||||||||
\(347\) | −26.8575 | −1.44178 | −0.720892 | − | 0.693047i | \(-0.756268\pi\) | ||||
−0.720892 | + | 0.693047i | \(0.756268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.3862 | −1.35889 | −0.679445 | − | 0.733726i | \(-0.737779\pi\) | ||||
−0.679445 | + | 0.733726i | \(0.737779\pi\) | |||||||
\(350\) | −8.49396 | −0.454021 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.223313 | −0.0119026 | ||||||||
\(353\) | −25.8412 | −1.37539 | −0.687695 | − | 0.726000i | \(-0.741377\pi\) | ||||
−0.687695 | + | 0.726000i | \(0.741377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.12566 | 0.325116 | ||||||||
\(356\) | −10.5276 | −0.557963 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.2604 | −0.647985 | ||||||||
\(359\) | 24.9557 | 1.31711 | 0.658556 | − | 0.752531i | \(-0.271167\pi\) | ||||
0.658556 | + | 0.752531i | \(0.271167\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8906 | −0.888980 | ||||||||
\(362\) | 17.2451 | 0.906383 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.11305 | 0.320411 | ||||||||
\(365\) | −4.02172 | −0.210507 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.8416 | −0.618126 | −0.309063 | − | 0.951042i | \(-0.600015\pi\) | ||||
−0.309063 | + | 0.951042i | \(0.600015\pi\) | |||||||
\(368\) | −10.6013 | −0.552633 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.77688 | −0.144363 | ||||||||
\(371\) | −6.86259 | −0.356288 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.196072 | −0.0101522 | −0.00507611 | − | 0.999987i | \(-0.501616\pi\) | ||||
−0.00507611 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(374\) | 38.0449 | 1.96725 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.06015 | −0.157815 | ||||||||
\(377\) | −9.32578 | −0.480302 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0964 | −1.23775 | −0.618874 | − | 0.785490i | \(-0.712411\pi\) | ||||
−0.618874 | + | 0.785490i | \(0.712411\pi\) | |||||||
\(380\) | 7.21709 | 0.370229 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.3215 | 1.19323 | ||||||||
\(383\) | −20.1432 | −1.02927 | −0.514635 | − | 0.857409i | \(-0.672073\pi\) | ||||
−0.514635 | + | 0.857409i | \(0.672073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.72086 | 0.138668 | ||||||||
\(386\) | 13.8367 | 0.704270 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.9860 | 0.862334 | ||||||||
\(389\) | 21.1063 | 1.07013 | 0.535067 | − | 0.844810i | \(-0.320286\pi\) | ||||
0.535067 | + | 0.844810i | \(0.320286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.4436 | 0.932733 | ||||||||
\(392\) | 4.92856 | 0.248930 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.35913 | 0.118851 | ||||||||
\(395\) | 10.6874 | 0.537742 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3506 | 0.569673 | 0.284836 | − | 0.958576i | \(-0.408061\pi\) | ||||
0.284836 | + | 0.958576i | \(0.408061\pi\) | |||||||
\(398\) | −20.8726 | −1.04625 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.0740 | −0.703702 | ||||||||
\(401\) | −21.6751 | −1.08240 | −0.541200 | − | 0.840894i | \(-0.682030\pi\) | ||||
−0.541200 | + | 0.840894i | \(0.682030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.79396 | 0.139177 | ||||||||
\(404\) | 34.2340 | 1.70321 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.9989 | −0.744381 | ||||||||
\(407\) | −2.00728 | −0.0994973 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7253 | 1.22259 | 0.611294 | − | 0.791404i | \(-0.290649\pi\) | ||||
0.611294 | + | 0.791404i | \(0.290649\pi\) | |||||||
\(410\) | −3.44800 | −0.170284 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.06679 | −0.151090 | ||||||||
\(413\) | −8.13041 | −0.400071 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2113 | −0.893957 | ||||||||
\(416\) | 0.155019 | 0.00760045 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.81864 | 0.382422 | ||||||||
\(419\) | 0.0686235 | 0.00335248 | 0.00167624 | − | 0.999999i | \(-0.499466\pi\) | ||||
0.00167624 | + | 0.999999i | \(0.499466\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2289 | −0.547261 | −0.273630 | − | 0.961835i | \(-0.588224\pi\) | ||||
−0.273630 | + | 0.961835i | \(0.588224\pi\) | |||||||
\(422\) | 11.3315 | 0.551607 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −33.8227 | −1.64257 | ||||||||
\(425\) | 24.4852 | 1.18771 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.09932 | 0.246773 | ||||||||
\(428\) | −21.1099 | −1.02039 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.55661 | −0.364412 | ||||||||
\(431\) | −3.76067 | −0.181145 | −0.0905725 | − | 0.995890i | \(-0.528870\pi\) | ||||
−0.0905725 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.15019 | 0.0552748 | 0.0276374 | − | 0.999618i | \(-0.491202\pi\) | ||||
0.0276374 | + | 0.999618i | \(0.491202\pi\) | |||||||
\(434\) | 4.49360 | 0.215700 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.6409 | −1.51533 | ||||||||
\(437\) | 3.79036 | 0.181318 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1838 | 0.486046 | 0.243023 | − | 0.970021i | \(-0.421861\pi\) | ||||
0.243023 | + | 0.970021i | \(0.421861\pi\) | |||||||
\(440\) | 13.4099 | 0.639293 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −26.4100 | −1.25620 | ||||||||
\(443\) | −3.18877 | −0.151503 | −0.0757514 | − | 0.997127i | \(-0.524136\pi\) | ||||
−0.0757514 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.25275 | 0.154195 | ||||||||
\(446\) | −5.82567 | −0.275854 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.87502 | −0.372060 | ||||||||
\(449\) | −19.2378 | −0.907889 | −0.453945 | − | 0.891030i | \(-0.649984\pi\) | ||||
−0.453945 | + | 0.891030i | \(0.649984\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.49240 | −0.117363 | ||||||||
\(452\) | 13.5937 | 0.639394 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −58.4496 | −2.74318 | ||||||||
\(455\) | −1.88877 | −0.0885468 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.07754 | 0.424629 | 0.212315 | − | 0.977201i | \(-0.431900\pi\) | ||||
0.212315 | + | 0.977201i | \(0.431900\pi\) | |||||||
\(458\) | 2.84175 | 0.132786 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.9684 | 0.604655 | ||||||||
\(461\) | 22.2184 | 1.03481 | 0.517407 | − | 0.855739i | \(-0.326897\pi\) | ||||
0.517407 | + | 0.855739i | \(0.326897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3963 | −0.483156 | −0.241578 | − | 0.970381i | \(-0.577665\pi\) | ||||
−0.241578 | + | 0.970381i | \(0.577665\pi\) | |||||||
\(464\) | −24.8523 | −1.15374 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.32824 | −0.107854 | ||||||||
\(467\) | −10.0389 | −0.464547 | −0.232273 | − | 0.972651i | \(-0.574616\pi\) | ||||
−0.232273 | + | 0.972651i | \(0.574616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.28798 | −0.244176 | ||||||||
\(470\) | 1.88614 | 0.0870012 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −40.0712 | −1.84443 | ||||||||
\(473\) | −5.46235 | −0.251159 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.03198 | 0.230883 | ||||||||
\(476\) | −28.3416 | −1.29903 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.0090 | 0.640758 | ||||||||
\(479\) | 8.89671 | 0.406501 | 0.203251 | − | 0.979127i | \(-0.434849\pi\) | ||||
0.203251 | + | 0.979127i | \(0.434849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.39342 | 0.0635343 | ||||||||
\(482\) | 54.8938 | 2.50034 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24.7768 | −1.12622 | ||||||||
\(485\) | −5.24822 | −0.238310 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.1080 | 1.27369 | 0.636847 | − | 0.770990i | \(-0.280238\pi\) | ||||
0.636847 | + | 0.770990i | \(0.280238\pi\) | |||||||
\(488\) | 25.1323 | 1.13769 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.03775 | −0.137232 | ||||||||
\(491\) | 3.08069 | 0.139030 | 0.0695149 | − | 0.997581i | \(-0.477855\pi\) | ||||
0.0695149 | + | 0.997581i | \(0.477855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.2366 | 1.94728 | ||||||||
\(494\) | −5.42755 | −0.244197 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.44565 | 0.334319 | ||||||||
\(497\) | −4.94368 | −0.221754 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.72255 | −0.166644 | −0.0833221 | − | 0.996523i | \(-0.526553\pi\) | ||||
−0.0833221 | + | 0.996523i | \(0.526553\pi\) | |||||||
\(500\) | 42.0623 | 1.88108 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.77745 | 0.168596 | ||||||||
\(503\) | −4.44735 | −0.198298 | −0.0991488 | − | 0.995073i | \(-0.531612\pi\) | ||||
−0.0991488 | + | 0.995073i | \(0.531612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5774 | −0.470688 | ||||||||
\(506\) | 14.0494 | 0.624570 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.01034 | −0.177930 | ||||||||
\(509\) | −6.22906 | −0.276098 | −0.138049 | − | 0.990425i | \(-0.544083\pi\) | ||||
−0.138049 | + | 0.990425i | \(0.544083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.24571 | 0.143582 | ||||||||
\(512\) | −39.6282 | −1.75133 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.47177 | 0.417782 | ||||||||
\(515\) | 0.947557 | 0.0417544 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36341 | 0.0599627 | ||||||||
\(518\) | 2.24106 | 0.0984667 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.30891 | −0.408223 | ||||||||
\(521\) | −11.1532 | −0.488631 | −0.244316 | − | 0.969696i | \(-0.578563\pi\) | ||||
−0.244316 | + | 0.969696i | \(0.578563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.4772 | 0.458134 | 0.229067 | − | 0.973411i | \(-0.426432\pi\) | ||||
0.229067 | + | 0.973411i | \(0.426432\pi\) | |||||||
\(524\) | 61.3186 | 2.67871 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.46067 | 0.412505 | ||||||||
\(527\) | −12.9535 | −0.564263 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1891 | −0.703873 | ||||||||
\(530\) | 20.8468 | 0.905528 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.82451 | −0.252525 | ||||||||
\(533\) | 1.73018 | 0.0749424 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.52240 | 0.281988 | ||||||||
\(536\) | −26.0621 | −1.12571 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −73.2131 | −3.15644 | ||||||||
\(539\) | −2.19586 | −0.0945822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.36150 | 0.273502 | 0.136751 | − | 0.990605i | \(-0.456334\pi\) | ||||
0.136751 | + | 0.990605i | \(0.456334\pi\) | |||||||
\(542\) | 77.0604 | 3.31003 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.718708 | −0.0308143 | ||||||||
\(545\) | 9.77620 | 0.418766 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.58101 | 0.195870 | 0.0979349 | − | 0.995193i | \(-0.468776\pi\) | ||||
0.0979349 | + | 0.995193i | \(0.468776\pi\) | |||||||
\(548\) | −46.5137 | −1.98697 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.6515 | 0.795303 | ||||||||
\(551\) | 8.88560 | 0.378539 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.62522 | −0.366781 | ||||||||
\(554\) | 16.5497 | 0.703127 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −54.8791 | −2.32739 | ||||||||
\(557\) | −3.52897 | −0.149527 | −0.0747637 | − | 0.997201i | \(-0.523820\pi\) | ||||
−0.0747637 | + | 0.997201i | \(0.523820\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.79185 | 0.160378 | ||||||||
\(560\) | −5.03339 | −0.212699 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.7461 | −0.748575 | ||||||||
\(563\) | 9.67953 | 0.407944 | 0.203972 | − | 0.978977i | \(-0.434615\pi\) | ||||
0.203972 | + | 0.978977i | \(0.434615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.20009 | −0.176699 | ||||||||
\(566\) | 29.5752 | 1.24314 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.3652 | −1.02234 | ||||||||
\(569\) | 26.8002 | 1.12352 | 0.561762 | − | 0.827299i | \(-0.310124\pi\) | ||||
0.561762 | + | 0.827299i | \(0.310124\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.99922 | −0.0836649 | −0.0418325 | − | 0.999125i | \(-0.513320\pi\) | ||||
−0.0418325 | + | 0.999125i | \(0.513320\pi\) | |||||||
\(572\) | −13.4234 | −0.561260 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.78269 | 0.116147 | ||||||||
\(575\) | 9.04198 | 0.377077 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.27902 | −0.261399 | −0.130699 | − | 0.991422i | \(-0.541722\pi\) | ||||
−0.130699 | + | 0.991422i | \(0.541722\pi\) | |||||||
\(578\) | 80.7661 | 3.35943 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.4013 | 1.26235 | ||||||||
\(581\) | 14.6973 | 0.609748 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0693 | 0.624105 | ||||||||
\(584\) | 15.9967 | 0.661947 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.57551 | 0.189012 | ||||||||
\(587\) | 24.0066 | 0.990859 | 0.495429 | − | 0.868648i | \(-0.335011\pi\) | ||||
0.495429 | + | 0.868648i | \(0.335011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.66209 | −0.109689 | ||||||||
\(590\) | 24.6981 | 1.01681 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.71332 | 0.152617 | ||||||||
\(593\) | −12.2147 | −0.501599 | −0.250799 | − | 0.968039i | \(-0.580693\pi\) | ||||
−0.250799 | + | 0.968039i | \(0.580693\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.75679 | 0.358993 | ||||||||
\(596\) | 69.4352 | 2.84418 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.75279 | −0.398821 | ||||||||
\(599\) | 0.687692 | 0.0280983 | 0.0140492 | − | 0.999901i | \(-0.495528\pi\) | ||||
0.0140492 | + | 0.999901i | \(0.495528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.55551 | 0.0634504 | 0.0317252 | − | 0.999497i | \(-0.489900\pi\) | ||||
0.0317252 | + | 0.999497i | \(0.489900\pi\) | |||||||
\(602\) | 6.09853 | 0.248557 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.07328 | 0.165739 | ||||||||
\(605\) | 7.65536 | 0.311234 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4768 | 0.993485 | 0.496742 | − | 0.867898i | \(-0.334529\pi\) | ||||
0.496742 | + | 0.867898i | \(0.334529\pi\) | |||||||
\(608\) | −0.147702 | −0.00599012 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.4905 | −0.627190 | ||||||||
\(611\) | −0.946453 | −0.0382894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.97120 | −0.241174 | −0.120587 | − | 0.992703i | \(-0.538478\pi\) | ||||
−0.120587 | + | 0.992703i | \(0.538478\pi\) | |||||||
\(614\) | −7.77478 | −0.313765 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.8224 | −0.436047 | ||||||||
\(617\) | 46.9374 | 1.88963 | 0.944814 | − | 0.327607i | \(-0.106242\pi\) | ||||
0.944814 | + | 0.327607i | \(0.106242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.9186 | 0.479047 | 0.239524 | − | 0.970891i | \(-0.423009\pi\) | ||||
0.239524 | + | 0.970891i | \(0.423009\pi\) | |||||||
\(620\) | −9.10811 | −0.365791 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.0943 | 0.685419 | ||||||||
\(623\) | −2.62512 | −0.105173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.32717 | 0.173087 | ||||||||
\(626\) | −24.7517 | −0.989278 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.7087 | −1.22541 | ||||||||
\(629\) | −6.46022 | −0.257586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.4351 | −1.21160 | −0.605802 | − | 0.795615i | \(-0.707148\pi\) | ||||
−0.605802 | + | 0.795615i | \(0.707148\pi\) | |||||||
\(632\) | −42.5099 | −1.69095 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −78.8298 | −3.13073 | ||||||||
\(635\) | 1.23909 | 0.0491717 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.52432 | 0.0603958 | ||||||||
\(638\) | 32.9354 | 1.30392 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.1744 | 0.955575 | ||||||||
\(641\) | 40.1834 | 1.58715 | 0.793574 | − | 0.608474i | \(-0.208218\pi\) | ||||
0.793574 | + | 0.608474i | \(0.208218\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.8069 | −0.899415 | −0.449708 | − | 0.893176i | \(-0.648472\pi\) | ||||
−0.449708 | + | 0.893176i | \(0.648472\pi\) | |||||||
\(644\) | −10.4661 | −0.412422 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.1635 | 0.990043 | ||||||||
\(647\) | 8.81515 | 0.346559 | 0.173280 | − | 0.984873i | \(-0.444564\pi\) | ||||
0.173280 | + | 0.984873i | \(0.444564\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.8532 | 0.700800 | ||||||||
\(650\) | −12.9475 | −0.507844 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 86.2899 | 3.37937 | ||||||||
\(653\) | −12.8758 | −0.503871 | −0.251935 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251935 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9458 | −0.740273 | ||||||||
\(656\) | 4.61076 | 0.180020 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.52220 | −0.0593416 | ||||||||
\(659\) | 19.2643 | 0.750430 | 0.375215 | − | 0.926938i | \(-0.377569\pi\) | ||||
0.375215 | + | 0.926938i | \(0.377569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.2257 | 1.17565 | 0.587823 | − | 0.808990i | \(-0.299985\pi\) | ||||
0.587823 | + | 0.808990i | \(0.299985\pi\) | |||||||
\(662\) | −59.7365 | −2.32173 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 72.4366 | 2.81109 | ||||||||
\(665\) | 1.79962 | 0.0697862 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.9666 | 0.618228 | ||||||||
\(668\) | 61.4009 | 2.37567 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.0636 | 0.620589 | ||||||||
\(671\) | −11.1974 | −0.432270 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.8167 | −1.65046 | −0.825232 | − | 0.564794i | \(-0.808956\pi\) | ||||
−0.825232 | + | 0.564794i | \(0.808956\pi\) | |||||||
\(674\) | 17.3274 | 0.667428 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −42.8162 | −1.64678 | ||||||||
\(677\) | 8.01207 | 0.307929 | 0.153964 | − | 0.988076i | \(-0.450796\pi\) | ||||
0.153964 | + | 0.988076i | \(0.450796\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.23555 | 0.162546 | ||||||||
\(680\) | 43.1584 | 1.65505 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.86729 | −0.377838 | ||||||||
\(683\) | −12.8698 | −0.492451 | −0.246225 | − | 0.969213i | \(-0.579190\pi\) | ||||
−0.246225 | + | 0.969213i | \(0.579190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.3715 | 0.549106 | ||||||||
\(686\) | 2.45160 | 0.0936025 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.1049 | 0.385247 | ||||||||
\(689\) | −10.4608 | −0.398524 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.04215 | −0.343980 | −0.171990 | − | 0.985099i | \(-0.555020\pi\) | ||||
−0.171990 | + | 0.985099i | \(0.555020\pi\) | |||||||
\(692\) | −103.558 | −3.93668 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −65.8438 | −2.49940 | ||||||||
\(695\) | 16.9562 | 0.643184 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.02153 | −0.303837 | ||||||||
\(698\) | −62.2367 | −2.35569 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.8945 | −0.525162 | ||||||||
\(701\) | −43.2487 | −1.63348 | −0.816741 | − | 0.577004i | \(-0.804222\pi\) | ||||
−0.816741 | + | 0.577004i | \(0.804222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.32765 | −0.0500731 | ||||||||
\(704\) | 17.2924 | 0.651732 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −63.3523 | −2.38430 | ||||||||
\(707\) | 8.53644 | 0.321046 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.8179 | 0.819388 | 0.409694 | − | 0.912223i | \(-0.365635\pi\) | ||||
0.409694 | + | 0.912223i | \(0.365635\pi\) | |||||||
\(710\) | 15.0177 | 0.563603 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.9380 | −0.484874 | ||||||||
\(713\) | −4.78352 | −0.179144 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.14746 | 0.155106 | ||||||||
\(716\) | −20.0557 | −0.749517 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 61.1815 | 2.28327 | ||||||||
\(719\) | −2.71418 | −0.101222 | −0.0506109 | − | 0.998718i | \(-0.516117\pi\) | ||||
−0.0506109 | + | 0.998718i | \(0.516117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.764721 | −0.0284797 | ||||||||
\(722\) | −41.4090 | −1.54108 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28.2097 | 1.04840 | ||||||||
\(725\) | 21.1968 | 0.787228 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.24994 | −0.120533 | −0.0602667 | − | 0.998182i | \(-0.519195\pi\) | ||||
−0.0602667 | + | 0.998182i | \(0.519195\pi\) | |||||||
\(728\) | 7.51271 | 0.278439 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.85966 | −0.364922 | ||||||||
\(731\) | −17.5800 | −0.650218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.8484 | 0.843925 | 0.421962 | − | 0.906613i | \(-0.361341\pi\) | ||||
0.421962 | + | 0.906613i | \(0.361341\pi\) | |||||||
\(734\) | −29.0308 | −1.07155 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.265407 | −0.00978303 | ||||||||
\(737\) | 11.6116 | 0.427720 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.8282 | 1.39153 | 0.695766 | − | 0.718269i | \(-0.255065\pi\) | ||||
0.695766 | + | 0.718269i | \(0.255065\pi\) | |||||||
\(740\) | −4.54243 | −0.166983 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.8243 | −0.617641 | ||||||||
\(743\) | 22.5284 | 0.826487 | 0.413244 | − | 0.910620i | \(-0.364396\pi\) | ||||
0.413244 | + | 0.910620i | \(0.364396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.4536 | −0.785999 | ||||||||
\(746\) | −0.480690 | −0.0175993 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 62.2341 | 2.27550 | ||||||||
\(749\) | −5.26387 | −0.192338 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.7581 | −1.41430 | −0.707151 | − | 0.707063i | \(-0.750020\pi\) | ||||
−0.707151 | + | 0.707063i | \(0.750020\pi\) | |||||||
\(752\) | −2.52221 | −0.0919754 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22.8631 | −0.832625 | ||||||||
\(755\) | −1.25853 | −0.0458027 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.582273 | 0.0211631 | 0.0105815 | − | 0.999944i | \(-0.496632\pi\) | ||||
0.0105815 | + | 0.999944i | \(0.496632\pi\) | |||||||
\(758\) | −59.0747 | −2.14569 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.86952 | 0.321731 | ||||||||
\(761\) | −33.7263 | −1.22258 | −0.611288 | − | 0.791408i | \(-0.709348\pi\) | ||||
−0.611288 | + | 0.791408i | \(0.709348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.88983 | −0.285631 | ||||||||
\(764\) | 38.1495 | 1.38020 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49.3831 | −1.78428 | ||||||||
\(767\) | −12.3934 | −0.447498 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0918 | 1.12120 | 0.560599 | − | 0.828087i | \(-0.310571\pi\) | ||||
0.560599 | + | 0.828087i | \(0.310571\pi\) | |||||||
\(770\) | 6.67046 | 0.240387 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.6342 | 0.814623 | ||||||||
\(773\) | 46.5433 | 1.67405 | 0.837023 | − | 0.547168i | \(-0.184294\pi\) | ||||
0.837023 | + | 0.547168i | \(0.184294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.35046 | −0.228115 | ||||||||
\(776\) | 20.8752 | 0.749375 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 51.7443 | 1.85512 | ||||||||
\(779\) | −1.64851 | −0.0590641 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8556 | 0.388444 | ||||||||
\(782\) | 45.2163 | 1.61693 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.06217 | 0.145077 | ||||||||
\(785\) | 9.48816 | 0.338647 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.7996 | −1.34741 | −0.673706 | − | 0.739000i | \(-0.735299\pi\) | ||||
−0.673706 | + | 0.739000i | \(0.735299\pi\) | |||||||
\(788\) | 3.85908 | 0.137474 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.2012 | 0.932198 | ||||||||
\(791\) | 3.38966 | 0.120522 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.77300 | 0.276027 | ||||||||
\(794\) | 27.8273 | 0.987552 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.1435 | −1.21018 | ||||||||
\(797\) | −20.3689 | −0.721504 | −0.360752 | − | 0.932662i | \(-0.617480\pi\) | ||||
−0.360752 | + | 0.932662i | \(0.617480\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.38798 | 0.155236 | ||||||||
\(800\) | −0.352347 | −0.0124573 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −53.1386 | −1.87639 | ||||||||
\(803\) | −7.12711 | −0.251510 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.23374 | 0.113974 | ||||||||
\(806\) | 6.84968 | 0.241270 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 42.0723 | 1.48010 | ||||||||
\(809\) | −8.20215 | −0.288372 | −0.144186 | − | 0.989551i | \(-0.546056\pi\) | ||||
−0.144186 | + | 0.989551i | \(0.546056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9018 | 0.944648 | 0.472324 | − | 0.881425i | \(-0.343415\pi\) | ||||
0.472324 | + | 0.881425i | \(0.343415\pi\) | |||||||
\(812\) | −24.5352 | −0.861018 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.92105 | −0.172483 | ||||||||
\(815\) | −26.6613 | −0.933903 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.61288 | −0.126399 | ||||||||
\(818\) | 60.6166 | 2.11941 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.64025 | −0.196966 | ||||||||
\(821\) | 20.6788 | 0.721694 | 0.360847 | − | 0.932625i | \(-0.382488\pi\) | ||||
0.360847 | + | 0.932625i | \(0.382488\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4881 | −0.574740 | −0.287370 | − | 0.957820i | \(-0.592781\pi\) | ||||
−0.287370 | + | 0.957820i | \(0.592781\pi\) | |||||||
\(824\) | −3.76897 | −0.131298 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.9325 | −0.693541 | ||||||||
\(827\) | −45.9300 | −1.59714 | −0.798571 | − | 0.601900i | \(-0.794411\pi\) | ||||
−0.798571 | + | 0.601900i | \(0.794411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.1979 | 1.56979 | 0.784894 | − | 0.619630i | \(-0.212717\pi\) | ||||
0.784894 | + | 0.619630i | \(0.212717\pi\) | |||||||
\(830\) | −44.6468 | −1.54971 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.0041 | −0.416166 | ||||||||
\(833\) | −7.06712 | −0.244861 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.9712 | −0.656527 | ||||||||
\(836\) | 12.7898 | 0.442344 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.168237 | 0.00581167 | ||||||||
\(839\) | 34.0233 | 1.17462 | 0.587308 | − | 0.809363i | \(-0.300188\pi\) | ||||
0.587308 | + | 0.809363i | \(0.300188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.42981 | 0.290683 | ||||||||
\(842\) | −27.5287 | −0.948700 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.5361 | 0.638038 | ||||||||
\(845\) | 13.2291 | 0.455094 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.17822 | −0.212286 | ||||||||
\(848\) | −27.8770 | −0.957300 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 60.0279 | 2.05894 | ||||||||
\(851\) | −2.38565 | −0.0817791 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.0563 | 1.06335 | 0.531674 | − | 0.846949i | \(-0.321563\pi\) | ||||
0.531674 | + | 0.846949i | \(0.321563\pi\) | |||||||
\(854\) | 12.5015 | 0.427792 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.9433 | −0.886724 | ||||||||
\(857\) | −9.85200 | −0.336538 | −0.168269 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168269 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.6137 | −1.18101 | −0.590503 | − | 0.807036i | \(-0.701070\pi\) | ||||
−0.590503 | + | 0.807036i | \(0.701070\pi\) | |||||||
\(860\) | −12.3612 | −0.421512 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.21965 | −0.314023 | ||||||||
\(863\) | 26.6628 | 0.907613 | 0.453806 | − | 0.891100i | \(-0.350066\pi\) | ||||
0.453806 | + | 0.891100i | \(0.350066\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.9966 | 1.08792 | ||||||||
\(866\) | 2.81982 | 0.0958212 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.35066 | 0.249497 | ||||||||
\(869\) | 18.9397 | 0.642486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.06058 | −0.273122 | ||||||||
\(872\) | −38.8855 | −1.31683 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.29246 | 0.314322 | ||||||||
\(875\) | 10.4885 | 0.354575 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.7876 | 0.701948 | 0.350974 | − | 0.936385i | \(-0.385851\pi\) | ||||
0.350974 | + | 0.936385i | \(0.385851\pi\) | |||||||
\(878\) | 24.9666 | 0.842581 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.0526 | 0.372583 | ||||||||
\(881\) | −27.9289 | −0.940949 | −0.470474 | − | 0.882414i | \(-0.655917\pi\) | ||||
−0.470474 | + | 0.882414i | \(0.655917\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.9829 | 1.31188 | 0.655939 | − | 0.754814i | \(-0.272273\pi\) | ||||
0.655939 | + | 0.754814i | \(0.272273\pi\) | |||||||
\(884\) | −43.2017 | −1.45303 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.81758 | −0.262637 | ||||||||
\(887\) | −3.83646 | −0.128816 | −0.0644079 | − | 0.997924i | \(-0.520516\pi\) | ||||
−0.0644079 | + | 0.997924i | \(0.520516\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 7.97444 | 0.267304 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.52967 | −0.319077 | ||||||||
\(893\) | 0.901780 | 0.0301769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.19668 | 0.207132 | ||||||||
\(896\) | −19.5098 | −0.651776 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47.1635 | −1.57387 | ||||||||
\(899\) | −11.2138 | −0.374002 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.4988 | 1.61573 | ||||||||
\(902\) | −6.11038 | −0.203453 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.7061 | 0.555638 | ||||||||
\(905\) | −8.71602 | −0.289730 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.86310 | 0.0618631 | 0.0309315 | − | 0.999522i | \(-0.490153\pi\) | ||||
0.0309315 | + | 0.999522i | \(0.490153\pi\) | |||||||
\(908\) | −95.6123 | −3.17301 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.63051 | −0.153500 | ||||||||
\(911\) | −31.7046 | −1.05042 | −0.525210 | − | 0.850973i | \(-0.676013\pi\) | ||||
−0.525210 | + | 0.850973i | \(0.676013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.2732 | −1.06809 | ||||||||
\(914\) | 22.2545 | 0.736114 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.64855 | 0.153592 | ||||||||
\(917\) | 15.2901 | 0.504924 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.20652 | −0.204734 | −0.102367 | − | 0.994747i | \(-0.532642\pi\) | ||||
−0.102367 | + | 0.994747i | \(0.532642\pi\) | |||||||
\(920\) | 15.9377 | 0.525450 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 54.4707 | 1.79390 | ||||||||
\(923\) | −7.53575 | −0.248042 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.16712 | −0.104134 | ||||||||
\(926\) | −25.4875 | −0.837572 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.622183 | −0.0204242 | ||||||||
\(929\) | −11.9844 | −0.393196 | −0.196598 | − | 0.980484i | \(-0.562989\pi\) | ||||
−0.196598 | + | 0.980484i | \(0.562989\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.45237 | −0.0475996 | ||||||||
\(932\) | −3.80855 | −0.124753 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.6115 | −0.805312 | ||||||||
\(935\) | −19.2287 | −0.628844 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5854 | 0.607159 | 0.303580 | − | 0.952806i | \(-0.401818\pi\) | ||||
0.303580 | + | 0.952806i | \(0.401818\pi\) | |||||||
\(938\) | −12.9640 | −0.423290 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.08536 | 0.100633 | ||||||||
\(941\) | −29.4475 | −0.959962 | −0.479981 | − | 0.877279i | \(-0.659357\pi\) | ||||
−0.479981 | + | 0.877279i | \(0.659357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.96222 | −0.0964632 | ||||||||
\(944\) | −33.0271 | −1.07494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.3915 | −0.435395 | ||||||||
\(947\) | −1.05890 | −0.0344096 | −0.0172048 | − | 0.999852i | \(-0.505477\pi\) | ||||
−0.0172048 | + | 0.999852i | \(0.505477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.94751 | 0.160603 | ||||||||
\(950\) | 12.3364 | 0.400245 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −34.8307 | −1.12887 | ||||||||
\(953\) | 57.6761 | 1.86831 | 0.934156 | − | 0.356864i | \(-0.116154\pi\) | ||||
0.934156 | + | 0.356864i | \(0.116154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.7872 | −0.381424 | ||||||||
\(956\) | 22.9161 | 0.741158 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.8112 | 0.704687 | ||||||||
\(959\) | −11.5984 | −0.374533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6404 | −0.891625 | ||||||||
\(962\) | 3.41610 | 0.110139 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 89.7957 | 2.89212 | ||||||||
\(965\) | −6.99336 | −0.225124 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5642 | 0.564827 | 0.282414 | − | 0.959293i | \(-0.408865\pi\) | ||||
0.282414 | + | 0.959293i | \(0.408865\pi\) | |||||||
\(968\) | −30.4497 | −0.978690 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.8665 | −0.413120 | ||||||||
\(971\) | 43.8415 | 1.40694 | 0.703470 | − | 0.710725i | \(-0.251633\pi\) | ||||
0.703470 | + | 0.710725i | \(0.251633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.6844 | −0.438701 | ||||||||
\(974\) | 68.9095 | 2.20800 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.7143 | 0.663049 | ||||||||
\(977\) | 13.1600 | 0.421027 | 0.210513 | − | 0.977591i | \(-0.432486\pi\) | ||||
0.210513 | + | 0.977591i | \(0.432486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.76438 | 0.184230 | ||||||||
\(980\) | −4.96917 | −0.158734 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.55263 | 0.241014 | ||||||||
\(983\) | 49.4485 | 1.57716 | 0.788581 | − | 0.614931i | \(-0.210816\pi\) | ||||
0.788581 | + | 0.614931i | \(0.210816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.19235 | −0.0379915 | ||||||||
\(986\) | 105.999 | 3.37569 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.87843 | −0.282460 | ||||||||
\(989\) | −6.49199 | −0.206433 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.17880 | −0.0374459 | −0.0187229 | − | 0.999825i | \(-0.505960\pi\) | ||||
−0.0187229 | + | 0.999825i | \(0.505960\pi\) | |||||||
\(992\) | 0.186403 | 0.00591832 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.1199 | −0.384421 | ||||||||
\(995\) | 10.5494 | 0.334439 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.51368 | −0.206290 | −0.103145 | − | 0.994666i | \(-0.532891\pi\) | ||||
−0.103145 | + | 0.994666i | \(0.532891\pi\) | |||||||
\(998\) | −9.12621 | −0.288885 | ||||||||
\(999\) | 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 | 8001.2.a.o.1.13 | 13 | ||
3.2 | odd | 2 | 2667.2.a.l.1.1 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.1 | ✓ | 13 | 3.2 | odd | 2 | ||
8001.2.a.o.1.13 | 13 | 1.1 | even | 1 | trivial |