Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(657,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.657");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.x (of order \(4\), degree \(2\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 993.13 | ||
Character | \(\chi\) | \(=\) | 1400.993 |
Dual form | 1400.2.x.c.657.13 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.26512 | − | 1.26512i | 0.730419 | − | 0.730419i | −0.240283 | − | 0.970703i | \(-0.577240\pi\) |
0.970703 | + | 0.240283i | \(0.0772404\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.98283 | + | 1.75168i | −0.749439 | + | 0.662074i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 0.201074i | − | 0.0670248i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.28140 | 1.29089 | 0.645445 | − | 0.763807i | \(-0.276672\pi\) | ||||
0.645445 | + | 0.763807i | \(0.276672\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.40575 | + | 4.40575i | −1.22194 | + | 1.22194i | −0.254994 | + | 0.966943i | \(0.582073\pi\) |
−0.966943 | + | 0.254994i | \(0.917927\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.77213 | + | 3.77213i | 0.914876 | + | 0.914876i | 0.996651 | − | 0.0817746i | \(-0.0260588\pi\) |
−0.0817746 | + | 0.996651i | \(0.526059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.01983 | −1.83988 | −0.919938 | − | 0.392064i | \(-0.871761\pi\) | ||||
−0.919938 | + | 0.392064i | \(0.871761\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.292427 | + | 4.72462i | −0.0638128 | + | 1.03100i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.07403 | + | 2.07403i | 0.432466 | + | 0.432466i | 0.889466 | − | 0.457001i | \(-0.151076\pi\) |
−0.457001 | + | 0.889466i | \(0.651076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.54099 | + | 3.54099i | 0.681463 | + | 0.681463i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.383780i | − | 0.0712661i | −0.999365 | − | 0.0356331i | \(-0.988655\pi\) | ||
0.999365 | − | 0.0356331i | \(-0.0113448\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.01573i | 0.182430i | 0.995831 | + | 0.0912151i | \(0.0290751\pi\) | ||||
−0.995831 | + | 0.0912151i | \(0.970925\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.41649 | − | 5.41649i | 0.942891 | − | 0.942891i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.30041 | + | 5.30041i | −0.871383 | + | 0.871383i | −0.992623 | − | 0.121240i | \(-0.961313\pi\) |
0.121240 | + | 0.992623i | \(0.461313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.1476i | 1.78505i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.42580i | − | 0.535019i | −0.963555 | − | 0.267510i | \(-0.913799\pi\) | ||
0.963555 | − | 0.267510i | \(-0.0862007\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.67869 | + | 4.67869i | 0.713494 | + | 0.713494i | 0.967264 | − | 0.253771i | \(-0.0816708\pi\) |
−0.253771 | + | 0.967264i | \(0.581671\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.51241 | − | 6.51241i | −0.949932 | − | 0.949932i | 0.0488727 | − | 0.998805i | \(-0.484437\pi\) |
−0.998805 | + | 0.0488727i | \(0.984437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.863214 | − | 6.94657i | 0.123316 | − | 0.992367i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.54442 | 1.33649 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.18400 | + | 6.18400i | 0.849438 | + | 0.849438i | 0.990063 | − | 0.140625i | \(-0.0449112\pi\) |
−0.140625 | + | 0.990063i | \(0.544911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.1461 | + | 10.1461i | −1.34388 | + | 1.34388i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.39231 | 1.22277 | 0.611387 | − | 0.791331i | \(-0.290612\pi\) | ||||
0.611387 | + | 0.791331i | \(0.290612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.99639i | − | 0.255612i | −0.991799 | − | 0.127806i | \(-0.959207\pi\) | ||
0.991799 | − | 0.127806i | \(-0.0407935\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.352218 | + | 0.398696i | 0.0443753 | + | 0.0502309i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.224086 | + | 0.224086i | −0.0273764 | + | 0.0273764i | −0.720662 | − | 0.693286i | \(-0.756162\pi\) |
0.693286 | + | 0.720662i | \(0.256162\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.24781 | 0.631763 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.88462 | 0.935732 | 0.467866 | − | 0.883799i | \(-0.345023\pi\) | ||||
0.467866 | + | 0.883799i | \(0.345023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.62980 | + | 9.62980i | −1.12708 | + | 1.12708i | −0.136434 | + | 0.990649i | \(0.543564\pi\) |
−0.990649 | + | 0.136434i | \(0.956436\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.48927 | + | 7.49965i | −0.967442 | + | 0.854664i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.59338i | 0.966831i | 0.875391 | + | 0.483415i | \(0.160604\pi\) | ||||
−0.875391 | + | 0.483415i | \(0.839396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.56279 | 1.06253 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.32562 | − | 6.32562i | 0.694327 | − | 0.694327i | −0.268854 | − | 0.963181i | \(-0.586645\pi\) |
0.963181 | + | 0.268854i | \(0.0866450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.485529 | − | 0.485529i | −0.0520542 | − | 0.0520542i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.04559 | −0.110832 | −0.0554162 | − | 0.998463i | \(-0.517649\pi\) | ||||
−0.0554162 | + | 0.998463i | \(0.517649\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.01837 | − | 16.4533i | 0.106754 | − | 1.72478i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.28502 | + | 1.28502i | 0.133250 | + | 0.133250i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.17461 | − | 4.17461i | −0.423867 | − | 0.423867i | 0.462666 | − | 0.886533i | \(-0.346893\pi\) |
−0.886533 | + | 0.462666i | \(0.846893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.860879i | − | 0.0865216i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.776429i | − | 0.0772576i | −0.999254 | − | 0.0386288i | \(-0.987701\pi\) | ||
0.999254 | − | 0.0386288i | \(-0.0122990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.01402 | − | 5.01402i | 0.494046 | − | 0.494046i | −0.415533 | − | 0.909578i | \(-0.636405\pi\) |
0.909578 | + | 0.415533i | \(0.136405\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.54274 | − | 9.54274i | 0.922531 | − | 0.922531i | −0.0746766 | − | 0.997208i | \(-0.523792\pi\) |
0.997208 | + | 0.0746766i | \(0.0237925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.7639i | − | 1.41412i | −0.707153 | − | 0.707061i | \(-0.750021\pi\) | ||
0.707153 | − | 0.707061i | \(-0.249979\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.4114i | 1.27295i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.24428 | − | 6.24428i | −0.587412 | − | 0.587412i | 0.349518 | − | 0.936930i | \(-0.386345\pi\) |
−0.936930 | + | 0.349518i | \(0.886345\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.885884 | + | 0.885884i | 0.0819000 | + | 0.0819000i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.0871 | − | 0.871910i | −1.29136 | − | 0.0799278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.33035 | 0.666396 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.33405 | − | 4.33405i | −0.390788 | − | 0.390788i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.29780 | + | 2.29780i | −0.203897 | + | 0.203897i | −0.801667 | − | 0.597770i | \(-0.796053\pi\) |
0.597770 | + | 0.801667i | \(0.296053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.8382 | 1.04230 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.47139i | − | 0.390667i | −0.980737 | − | 0.195333i | \(-0.937421\pi\) | ||
0.980737 | − | 0.195333i | \(-0.0625789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.9019 | − | 14.0482i | 1.37887 | − | 1.21813i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.36069 | + | 5.36069i | −0.457995 | + | 0.457995i | −0.897997 | − | 0.440002i | \(-0.854978\pi\) |
0.440002 | + | 0.897997i | \(0.354978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1143 | 1.11234 | 0.556171 | − | 0.831068i | \(-0.312270\pi\) | ||||
0.556171 | + | 0.831068i | \(0.312270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.4780 | −1.38770 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.8628 | + | 18.8628i | −1.57738 | + | 1.57738i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.69620 | − | 9.88034i | −0.634772 | − | 0.814917i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.0575i | 1.64317i | 0.570084 | + | 0.821586i | \(0.306911\pi\) | ||||
−0.570084 | + | 0.821586i | \(0.693089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.84788 | 0.150378 | 0.0751892 | − | 0.997169i | \(-0.476044\pi\) | ||||
0.0751892 | + | 0.997169i | \(0.476044\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.758479 | − | 0.758479i | 0.0613194 | − | 0.0613194i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.72270 | − | 2.72270i | −0.217295 | − | 0.217295i | 0.590063 | − | 0.807357i | \(-0.299103\pi\) |
−0.807357 | + | 0.590063i | \(0.799103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.6470 | 1.24089 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.74550 | − | 0.479403i | −0.610431 | − | 0.0377822i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4404 | + | 12.4404i | 0.974407 | + | 0.974407i | 0.999681 | − | 0.0252734i | \(-0.00804564\pi\) |
−0.0252734 | + | 0.999681i | \(0.508046\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.73815 | − | 2.73815i | −0.211885 | − | 0.211885i | 0.593183 | − | 0.805068i | \(-0.297871\pi\) |
−0.805068 | + | 0.593183i | \(0.797871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 25.8213i | − | 1.98626i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.61258i | 0.123317i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.36706 | + | 4.36706i | −0.332021 | + | 0.332021i | −0.853354 | − | 0.521332i | \(-0.825435\pi\) |
0.521332 | + | 0.853354i | \(0.325435\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.8824 | − | 11.8824i | 0.893138 | − | 0.893138i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.1423i | 1.13179i | 0.824478 | + | 0.565893i | \(0.191469\pi\) | ||||
−0.824478 | + | 0.565893i | \(0.808531\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.26686i | − | 0.688800i | −0.938823 | − | 0.344400i | \(-0.888082\pi\) | ||
0.938823 | − | 0.344400i | \(-0.111918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.52568 | − | 2.52568i | −0.186704 | − | 0.186704i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.1500 | + | 16.1500i | 1.18100 | + | 1.18100i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.2239 | − | 0.818482i | −0.961894 | − | 0.0595358i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.2586 | 0.886998 | 0.443499 | − | 0.896275i | \(-0.353737\pi\) | ||||
0.443499 | + | 0.896275i | \(0.353737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.67292 | + | 1.67292i | 0.120419 | + | 0.120419i | 0.764748 | − | 0.644329i | \(-0.222863\pi\) |
−0.644329 | + | 0.764748i | \(0.722863\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.41191 | + | 7.41191i | −0.528077 | + | 0.528077i | −0.919998 | − | 0.391922i | \(-0.871810\pi\) |
0.391922 | + | 0.919998i | \(0.371810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.36448 | −0.0967252 | −0.0483626 | − | 0.998830i | \(-0.515400\pi\) | ||||
−0.0483626 | + | 0.998830i | \(0.515400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.566992i | 0.0399925i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.672261 | + | 0.760970i | 0.0471835 | + | 0.0534096i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.417035 | − | 0.417035i | 0.0289859 | − | 0.0289859i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −34.3361 | −2.37508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7141 | −1.01296 | −0.506481 | − | 0.862251i | \(-0.669054\pi\) | ||||
−0.506481 | + | 0.862251i | \(0.669054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.97502 | − | 9.97502i | 0.683477 | − | 0.683477i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.77923 | − | 2.01401i | −0.120782 | − | 0.136720i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.3658i | 1.64649i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.2382 | −2.23584 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.72778 | + | 3.72778i | −0.249630 | + | 0.249630i | −0.820819 | − | 0.571189i | \(-0.806483\pi\) |
0.571189 | + | 0.820819i | \(0.306483\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.1068 | + | 20.1068i | 1.33453 | + | 1.33453i | 0.901264 | + | 0.433270i | \(0.142640\pi\) |
0.433270 | + | 0.901264i | \(0.357360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.4574 | −1.55011 | −0.775056 | − | 0.631893i | \(-0.782278\pi\) | ||||
−0.775056 | + | 0.631893i | \(0.782278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.25200 | + | 20.2280i | −0.0823753 | + | 1.33090i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0820 | − | 18.0820i | −1.18459 | − | 1.18459i | −0.978542 | − | 0.206047i | \(-0.933940\pi\) |
−0.206047 | − | 0.978542i | \(-0.566060\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8717 | + | 10.8717i | 0.706192 | + | 0.706192i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.6607i | − | 0.689584i | −0.938679 | − | 0.344792i | \(-0.887950\pi\) | ||
0.938679 | − | 0.344792i | \(-0.112050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.7323i | 1.85081i | 0.378978 | + | 0.925406i | \(0.376276\pi\) | ||||
−0.378978 | + | 0.925406i | \(0.623724\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.47515 | − | 1.47515i | 0.0946311 | − | 0.0946311i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.3334 | − | 35.3334i | 2.24821 | − | 2.24821i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 16.0054i | − | 1.01430i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.17077i | 0.137018i | 0.997651 | + | 0.0685088i | \(0.0218241\pi\) | ||||
−0.997651 | + | 0.0685088i | \(0.978176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.87976 | + | 8.87976i | 0.558265 | + | 0.558265i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.7794 | − | 16.7794i | −1.04667 | − | 1.04667i | −0.998856 | − | 0.0478117i | \(-0.984775\pi\) |
−0.0478117 | − | 0.998856i | \(-0.515225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.22516 | − | 19.7945i | 0.0761280 | − | 1.22997i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0771683 | −0.00477660 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0795 | − | 11.0795i | −0.683191 | − | 0.683191i | 0.277527 | − | 0.960718i | \(-0.410485\pi\) |
−0.960718 | + | 0.277527i | \(0.910485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.32280 | + | 1.32280i | −0.0809541 | + | 0.0809541i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.9736 | 1.52267 | 0.761335 | − | 0.648359i | \(-0.224544\pi\) | ||||
0.761335 | + | 0.648359i | \(0.224544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.40205i | 0.388897i | 0.980913 | + | 0.194448i | \(0.0622917\pi\) | ||||
−0.980913 | + | 0.194448i | \(0.937708\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.5271 | − | 22.1039i | −1.18184 | − | 1.33779i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.0777 | − | 21.0777i | 1.26644 | − | 1.26644i | 0.318519 | − | 0.947916i | \(-0.396815\pi\) |
0.947916 | − | 0.318519i | \(-0.103185\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.204237 | 0.0122273 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.76219 | −0.105123 | −0.0525617 | − | 0.998618i | \(-0.516739\pi\) | ||||
−0.0525617 | + | 0.998618i | \(0.516739\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.33848 | + | 7.33848i | −0.436227 | + | 0.436227i | −0.890740 | − | 0.454513i | \(-0.849813\pi\) |
0.454513 | + | 0.890740i | \(0.349813\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00091 | + | 6.79276i | 0.354222 | + | 0.400964i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4580i | 0.673997i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.5628 | −0.619202 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.8548 | + | 15.8548i | −0.926246 | + | 0.926246i | −0.997461 | − | 0.0712146i | \(-0.977312\pi\) |
0.0712146 | + | 0.997461i | \(0.477312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.1604 | + | 15.1604i | 0.879694 | + | 0.879694i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.2754 | −1.05689 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.4726 | − | 1.08146i | −1.00711 | − | 0.0623341i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.982278 | − | 0.982278i | −0.0564304 | − | 0.0564304i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.09271 | − | 8.09271i | −0.461875 | − | 0.461875i | 0.437394 | − | 0.899270i | \(-0.355901\pi\) |
−0.899270 | + | 0.437394i | \(0.855901\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 12.6867i | − | 0.721721i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.2529i | − | 1.82889i | −0.404705 | − | 0.914447i | \(-0.632626\pi\) | ||
0.404705 | − | 0.914447i | \(-0.367374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.45483 | + | 3.45483i | −0.195278 | + | 0.195278i | −0.797972 | − | 0.602694i | \(-0.794094\pi\) |
0.602694 | + | 0.797972i | \(0.294094\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9389 | − | 11.9389i | 0.670556 | − | 0.670556i | −0.287288 | − | 0.957844i | \(-0.592754\pi\) |
0.957844 | + | 0.287288i | \(0.0927537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.64311i | − | 0.0919967i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 24.1455i | − | 1.34767i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.2519 | − | 30.2519i | −1.68326 | − | 1.68326i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.6781 | − | 18.6781i | −1.03290 | − | 1.03290i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.3207 | + | 1.50531i | 1.34084 | + | 0.0829905i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.08402 | 0.114548 | 0.0572739 | − | 0.998359i | \(-0.481759\pi\) | ||||
0.0572739 | + | 0.998359i | \(0.481759\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.06578 | + | 1.06578i | 0.0584042 | + | 0.0584042i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.7691 | − | 11.7691i | 0.641103 | − | 0.641103i | −0.309723 | − | 0.950827i | \(-0.600236\pi\) |
0.950827 | + | 0.309723i | \(0.100236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.7996 | −0.858114 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.34873i | 0.235497i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4566 | + | 15.2859i | 0.564603 | + | 0.825363i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.49402 | − | 6.49402i | 0.348617 | − | 0.348617i | −0.510977 | − | 0.859594i | \(-0.670716\pi\) |
0.859594 | + | 0.510977i | \(0.170716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.2983 | 0.818899 | 0.409450 | − | 0.912333i | \(-0.365721\pi\) | ||||
0.409450 | + | 0.912333i | \(0.365721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.2014 | −1.66541 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2674 | − | 19.2674i | 1.02550 | − | 1.02550i | 0.0258329 | − | 0.999666i | \(-0.491776\pi\) |
0.999666 | − | 0.0258329i | \(-0.00822380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.9250 | + | 16.7188i | −1.00161 | + | 0.884853i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 3.44336i | − | 0.181733i | −0.995863 | − | 0.0908667i | \(-0.971036\pi\) | ||
0.995863 | − | 0.0908667i | \(-0.0289637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.3177 | 2.38514 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.27380 | − | 9.27380i | 0.486748 | − | 0.486748i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.2373 | − | 20.2373i | −1.05638 | − | 1.05638i | −0.998313 | − | 0.0580658i | \(-0.981507\pi\) |
−0.0580658 | − | 0.998313i | \(-0.518493\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.688839 | −0.0358595 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.0942 | − | 1.42940i | −1.19899 | − | 0.0742108i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.7529 | + | 19.7529i | 1.02277 | + | 1.02277i | 0.999735 | + | 0.0230311i | \(0.00733166\pi\) |
0.0230311 | + | 0.999735i | \(0.492668\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.69084 | + | 1.69084i | 0.0870827 | + | 0.0870827i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.77071i | − | 0.450521i | −0.974299 | − | 0.225261i | \(-0.927677\pi\) | ||
0.974299 | − | 0.225261i | \(-0.0723234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.81400i | 0.297860i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.4151 | − | 17.4151i | 0.889871 | − | 0.889871i | −0.104640 | − | 0.994510i | \(-0.533369\pi\) |
0.994510 | + | 0.104640i | \(0.0333689\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.940765 | − | 0.940765i | 0.0478218 | − | 0.0478218i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.5372i | 1.49759i | 0.662800 | + | 0.748797i | \(0.269368\pi\) | ||||
−0.662800 | + | 0.748797i | \(0.730632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.6470i | 0.791305i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | − | 5.65685i | −0.285351 | − | 0.285351i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.02864 | + | 4.02864i | 0.202192 | + | 0.202192i | 0.800938 | − | 0.598747i | \(-0.204334\pi\) |
−0.598747 | + | 0.800938i | \(0.704334\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.34522 | − | 37.8906i | 0.117408 | − | 1.89690i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.06117 | 0.0529925 | 0.0264963 | − | 0.999649i | \(-0.491565\pi\) | ||||
0.0264963 | + | 0.999649i | \(0.491565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.47505 | − | 4.47505i | −0.222918 | − | 0.222918i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.6932 | + | 22.6932i | −1.12486 | + | 1.12486i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0914 | −0.795668 | −0.397834 | − | 0.917457i | \(-0.630238\pi\) | ||||
−0.397834 | + | 0.917457i | \(0.630238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5639i | 0.669056i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.6233 | + | 16.4524i | −0.916395 | + | 0.809567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.5912 | − | 16.5912i | 0.812477 | − | 0.812477i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.0871 | 1.61641 | 0.808204 | − | 0.588902i | \(-0.200440\pi\) | ||||
0.808204 | + | 0.588902i | \(0.200440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.8527 | −1.06504 | −0.532518 | − | 0.846419i | \(-0.678754\pi\) | ||||
−0.532518 | + | 0.846419i | \(0.678754\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.30948 | + | 1.30948i | −0.0636690 | + | 0.0636690i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.49705 | + | 3.95851i | 0.169234 | + | 0.191566i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 47.7275i | 2.30430i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.1827 | −0.490484 | −0.245242 | − | 0.969462i | \(-0.578867\pi\) | ||||
−0.245242 | + | 0.969462i | \(0.578867\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0245 | + | 11.0245i | −0.529801 | + | 0.529801i | −0.920513 | − | 0.390712i | \(-0.872229\pi\) |
0.390712 | + | 0.920513i | \(0.372229\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.6334 | − | 16.6334i | −0.795683 | − | 0.795683i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.4238 | 0.545227 | 0.272613 | − | 0.962124i | \(-0.412112\pi\) | ||||
0.272613 | + | 0.962124i | \(0.412112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.39678 | − | 0.173570i | −0.0665132 | − | 0.00826525i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.12567 | − | 2.12567i | −0.100994 | − | 0.100994i | 0.654805 | − | 0.755798i | \(-0.272751\pi\) |
−0.755798 | + | 0.654805i | \(0.772751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.3752 | + | 25.3752i | 1.20021 | + | 1.20021i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.8564i | − | 1.07866i | −0.842094 | − | 0.539330i | \(-0.818677\pi\) | ||
0.842094 | − | 0.539330i | \(-0.181323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 14.6672i | − | 0.690651i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.33780 | − | 2.33780i | 0.109839 | − | 0.109839i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9220 | − | 18.9220i | 0.885133 | − | 0.885133i | −0.108918 | − | 0.994051i | \(-0.534739\pi\) |
0.994051 | + | 0.108918i | \(0.0347385\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.7141i | 1.24691i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.1123i | 0.983298i | 0.870794 | + | 0.491649i | \(0.163606\pi\) | ||||
−0.870794 | + | 0.491649i | \(0.836394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.34112 | + | 8.34112i | 0.387645 | + | 0.387645i | 0.873847 | − | 0.486202i | \(-0.161618\pi\) |
−0.486202 | + | 0.873847i | \(0.661618\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.82644 | − | 2.82644i | −0.130792 | − | 0.130792i | 0.638680 | − | 0.769472i | \(-0.279481\pi\) |
−0.769472 | + | 0.638680i | \(0.779481\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0517963 | − | 0.836850i | 0.00239173 | − | 0.0386422i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.88909 | −0.317433 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0313 | + | 20.0313i | 0.921042 | + | 0.921042i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.24344 | − | 1.24344i | 0.0569334 | − | 0.0569334i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.4149 | −0.704327 | −0.352163 | − | 0.935939i | \(-0.614554\pi\) | ||||
−0.352163 | + | 0.935939i | \(0.614554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 46.7046i | − | 2.12955i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.4055 | + | 9.19251i | −0.473467 | + | 0.418274i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.43657 | − | 5.43657i | 0.246354 | − | 0.246354i | −0.573118 | − | 0.819473i | \(-0.694266\pi\) |
0.819473 | + | 0.573118i | \(0.194266\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.4773 | 1.42345 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.86088 | −0.129110 | −0.0645548 | − | 0.997914i | \(-0.520563\pi\) | ||||
−0.0645548 | + | 0.997914i | \(0.520563\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.44767 | − | 1.44767i | 0.0651997 | − | 0.0651997i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.6338 | + | 13.8114i | −0.701274 | + | 0.619524i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 25.4666i | − | 1.14004i | −0.821631 | − | 0.570020i | \(-0.806935\pi\) | ||
0.821631 | − | 0.570020i | \(-0.193065\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.92820 | −0.309529 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.1711 | − | 16.1711i | 0.721034 | − | 0.721034i | −0.247782 | − | 0.968816i | \(-0.579702\pi\) |
0.968816 | + | 0.247782i | \(0.0797016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.6672 | − | 32.6672i | −1.45080 | − | 1.45080i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7310 | 1.14051 | 0.570253 | − | 0.821469i | \(-0.306845\pi\) | ||||
0.570253 | + | 0.821469i | \(0.306845\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.22588 | − | 35.9626i | 0.0984672 | − | 1.59089i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.3981 | − | 28.3981i | −1.25381 | − | 1.25381i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.8822 | − | 27.8822i | −1.22626 | − | 1.22626i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0497i | 0.485030i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.37847i | − | 0.235635i | −0.993035 | − | 0.117817i | \(-0.962410\pi\) | ||
0.993035 | − | 0.117817i | \(-0.0375898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.09945 | − | 1.09945i | 0.0480755 | − | 0.0480755i | −0.682660 | − | 0.730736i | \(-0.739177\pi\) |
0.730736 | + | 0.682660i | \(0.239177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.83146 | + | 3.83146i | −0.166901 | + | 0.166901i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 14.3968i | − | 0.625947i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.88855i | − | 0.0819562i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0932 | + | 15.0932i | 0.653760 | + | 0.653760i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.1568 | + | 19.1568i | 0.826679 | + | 0.826679i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.69576 | − | 29.7410i | 0.159188 | − | 1.28104i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1072 | 0.735497 | 0.367748 | − | 0.929925i | \(-0.380129\pi\) | ||||
0.367748 | + | 0.929925i | \(0.380129\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.7237 | − | 11.7237i | −0.503113 | − | 0.503113i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.3185 | + | 21.3185i | −0.911512 | + | 0.911512i | −0.996391 | − | 0.0848791i | \(-0.972950\pi\) |
0.0848791 | + | 0.996391i | \(0.472950\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.401423 | −0.0171323 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.07785i | 0.131121i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0529 | − | 17.0392i | −0.640113 | − | 0.724580i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.9932 | − | 12.9932i | 0.550540 | − | 0.550540i | −0.376057 | − | 0.926597i | \(-0.622720\pi\) |
0.926597 | + | 0.376057i | \(0.122720\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.2263 | −1.74369 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.8635 | 1.72526 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.52351 | − | 9.52351i | 0.401368 | − | 0.401368i | −0.477347 | − | 0.878715i | \(-0.658401\pi\) |
0.878715 | + | 0.477347i | \(0.158401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.9614 | + | 16.7510i | −0.796303 | + | 0.703475i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.0170i | 1.63568i | 0.575446 | + | 0.817840i | \(0.304829\pi\) | ||||
−0.575446 | + | 0.817840i | \(0.695171\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.7540 | 0.784831 | 0.392416 | − | 0.919788i | \(-0.371639\pi\) | ||||
0.392416 | + | 0.919788i | \(0.371639\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.5086 | − | 15.5086i | 0.647880 | − | 0.647880i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.95452 | + | 7.95452i | 0.331151 | + | 0.331151i | 0.853024 | − | 0.521872i | \(-0.174766\pi\) |
−0.521872 | + | 0.853024i | \(0.674766\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.23289 | 0.175913 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.46214 | + | 23.6231i | −0.0606596 | + | 0.980051i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.4762 | + | 26.4762i | 1.09653 | + | 1.09653i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5572 | − | 15.5572i | −0.642114 | − | 0.642114i | 0.308961 | − | 0.951075i | \(-0.400019\pi\) |
−0.951075 | + | 0.308961i | \(0.900019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.14597i | − | 0.335649i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.7540i | 0.771435i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.2956 | + | 13.2956i | −0.545987 | + | 0.545987i | −0.925277 | − | 0.379291i | \(-0.876168\pi\) |
0.379291 | + | 0.925277i | \(0.376168\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.72623 | + | 1.72623i | −0.0706500 | + | 0.0706500i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.8479i | 0.892680i | 0.894863 | + | 0.446340i | \(0.147273\pi\) | ||||
−0.894863 | + | 0.446340i | \(0.852727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.9050i | 1.13827i | 0.822245 | + | 0.569134i | \(0.192721\pi\) | ||||
−0.822245 | + | 0.569134i | \(0.807279\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0450579 | + | 0.0450579i | 0.00183490 | + | 0.00183490i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.0865 | + | 22.0865i | 0.896462 | + | 0.896462i | 0.995121 | − | 0.0986594i | \(-0.0314554\pi\) |
−0.0986594 | + | 0.995121i | \(0.531455\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.81321 | + | 0.112228i | 0.0734751 | + | 0.00454769i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.3841 | 2.32151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.3711 | + | 26.3711i | 1.06512 | + | 1.06512i | 0.997726 | + | 0.0673938i | \(0.0214684\pi\) |
0.0673938 | + | 0.997726i | \(0.478532\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.34199 | + | 5.34199i | −0.215060 | + | 0.215060i | −0.806413 | − | 0.591353i | \(-0.798594\pi\) |
0.591353 | + | 0.806413i | \(0.298594\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.8879 | −0.799364 | −0.399682 | − | 0.916654i | \(-0.630879\pi\) | ||||
−0.399682 | + | 0.916654i | \(0.630879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.6882i | 0.589419i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.07323 | − | 1.83154i | 0.0830620 | − | 0.0733792i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −43.4394 | + | 43.4394i | −1.73480 | + | 1.73480i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39.9877 | −1.59441 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9106 | 0.633392 | 0.316696 | − | 0.948527i | \(-0.397427\pi\) | ||||
0.316696 | + | 0.948527i | \(0.397427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.6152 | + | 18.6152i | −0.739887 | + | 0.739887i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.8018 | + | 34.4080i | 1.06193 | + | 1.36329i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1.58539i | − | 0.0627172i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.1569 | 1.03314 | 0.516569 | − | 0.856246i | \(-0.327209\pi\) | ||||
0.516569 | + | 0.856246i | \(0.327209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.86867 | − | 2.86867i | 0.113129 | − | 0.113129i | −0.648276 | − | 0.761405i | \(-0.724510\pi\) |
0.761405 | + | 0.648276i | \(0.224510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.0219 | + | 23.0219i | 0.905086 | + | 0.905086i | 0.995871 | − | 0.0907850i | \(-0.0289376\pi\) |
−0.0907850 | + | 0.995871i | \(0.528938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.2122 | 1.57847 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.79893 | − | 0.297026i | −0.188085 | − | 0.0116414i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.4970 | + | 10.4970i | 0.410778 | + | 0.410778i | 0.882010 | − | 0.471231i | \(-0.156190\pi\) |
−0.471231 | + | 0.882010i | \(0.656190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.93631 | + | 1.93631i | 0.0755425 | + | 0.0755425i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 34.3398i | − | 1.33769i | −0.743403 | − | 0.668844i | \(-0.766789\pi\) | ||
0.743403 | − | 0.668844i | \(-0.233211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.6084i | − | 0.684887i | −0.939539 | − | 0.342443i | \(-0.888746\pi\) | ||
0.939539 | − | 0.342443i | \(-0.111254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −42.0504 | + | 42.0504i | −1.63310 | + | 1.63310i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.795972 | − | 0.795972i | 0.0308202 | − | 0.0308202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.43220i | 0.364670i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.54735i | − | 0.329967i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.66679 | + | 6.66679i | 0.256986 | + | 0.256986i | 0.823827 | − | 0.566841i | \(-0.191835\pi\) |
−0.566841 | + | 0.823827i | \(0.691835\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.5877 | + | 32.5877i | 1.25245 | + | 1.25245i | 0.954620 | + | 0.297826i | \(0.0962615\pi\) |
0.297826 | + | 0.954620i | \(0.403739\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.5901 | + | 0.964941i | 0.598294 | + | 0.0370310i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 50.8751 | 1.94954 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.1883 | − | 17.1883i | −0.657693 | − | 0.657693i | 0.297141 | − | 0.954834i | \(-0.403967\pi\) |
−0.954834 | + | 0.297141i | \(0.903967\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.6766 | + | 29.6766i | −1.13223 | + | 1.13223i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.4904 | −2.07592 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.3621i | 0.850695i | 0.905030 | + | 0.425348i | \(0.139848\pi\) | ||||
−0.905030 | + | 0.425348i | \(0.860152\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.50799 | + | 1.70697i | 0.0572837 | + | 0.0648426i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.9226 | − | 12.9226i | 0.489476 | − | 0.489476i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −45.7518 | −1.73049 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.2586 | −0.689616 | −0.344808 | − | 0.938673i | \(-0.612056\pi\) | ||||
−0.344808 | + | 0.938673i | \(0.612056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.5084 | − | 42.5084i | 1.60324 | − | 1.60324i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.36006 | + | 1.53953i | 0.0511502 | + | 0.0578998i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.3565i | 1.29028i | 0.764063 | + | 0.645142i | \(0.223202\pi\) | ||||
−0.764063 | + | 0.645142i | \(0.776798\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.72791 | 0.0648016 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.10665 | + | 2.10665i | −0.0788948 | + | 0.0788948i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.4871 | − | 13.4871i | −0.503685 | − | 0.503685i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.87614 | 0.144556 | 0.0722778 | − | 0.997385i | \(-0.476973\pi\) | ||||
0.0722778 | + | 0.997385i | \(0.476973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.15897 | + | 18.7249i | −0.0431621 | + | 0.697352i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.3499 | + | 36.3499i | 1.35187 | + | 1.35187i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.82189 | + | 7.82189i | 0.290098 | + | 0.290098i | 0.837119 | − | 0.547021i | \(-0.184238\pi\) |
−0.547021 | + | 0.837119i | \(0.684238\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.9559i | 0.924292i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.2973i | 1.30552i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.96432 | + | 7.96432i | −0.294169 | + | 0.294169i | −0.838725 | − | 0.544556i | \(-0.816698\pi\) |
0.544556 | + | 0.838725i | \(0.316698\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.959400 | + | 0.959400i | −0.0353399 | + | 0.0353399i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.6579i | − | 0.759913i | −0.925004 | − | 0.379957i | \(-0.875939\pi\) | ||
0.925004 | − | 0.379957i | \(-0.124061\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 89.4023i | − | 3.28427i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.9614 | − | 11.9614i | −0.438821 | − | 0.438821i | 0.452794 | − | 0.891615i | \(-0.350427\pi\) |
−0.891615 | + | 0.452794i | \(0.850427\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.27192 | − | 1.27192i | −0.0465371 | − | 0.0465371i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.20576 | + | 35.6375i | −0.0805966 | + | 1.30216i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.8083 | −1.37965 | −0.689823 | − | 0.723978i | \(-0.742312\pi\) | ||||
−0.689823 | + | 0.723978i | \(0.742312\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.74629 | + | 2.74629i | 0.100080 | + | 0.100080i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6665 | + | 15.6665i | −0.569407 | + | 0.569407i | −0.931962 | − | 0.362555i | \(-0.881904\pi\) |
0.362555 | + | 0.931962i | \(0.381904\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.4680 | 0.815536 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3166i | 1.46148i | 0.682658 | + | 0.730738i | \(0.260824\pi\) | ||||
−0.682658 | + | 0.730738i | \(0.739176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.8616 | + | 29.2742i | 0.936253 | + | 1.05980i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.3802 | + | 41.3802i | −1.49415 | + | 1.49415i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6390 | −0.708202 | −0.354101 | − | 0.935207i | \(-0.615213\pi\) | ||||
−0.354101 | + | 0.935207i | \(0.615213\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.4559 | −1.52901 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.8633 | − | 24.8633i | 0.894271 | − | 0.894271i | −0.100651 | − | 0.994922i | \(-0.532092\pi\) |
0.994922 | + | 0.100651i | \(0.0320924\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.4924 | − | 26.5924i | −0.842787 | − | 0.953997i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.4743i | 0.984369i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.7572 | 1.20793 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.35896 | − | 1.35896i | 0.0485652 | − | 0.0485652i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2824 | + | 10.2824i | 0.366529 | + | 0.366529i | 0.866210 | − | 0.499681i | \(-0.166549\pi\) |
−0.499681 | + | 0.866210i | \(0.666549\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.0339 | −0.998032 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.3193 | + | 1.44333i | 0.829140 | + | 0.0513191i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.79562 | + | 8.79562i | 0.312342 | + | 0.312342i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.97178 | − | 4.97178i | −0.176110 | − | 0.176110i | 0.613548 | − | 0.789658i | \(-0.289742\pi\) |
−0.789658 | + | 0.613548i | \(0.789742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49.1313i | − | 1.73814i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.210241i | 0.00742851i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.2290 | + | 41.2290i | −1.45494 | + | 1.45494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.5947 | − | 31.5947i | 1.11219 | − | 1.11219i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.9963i | − | 1.12493i | −0.826821 | − | 0.562465i | \(-0.809853\pi\) | ||
0.826821 | − | 0.562465i | \(-0.190147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5246i | 0.404682i | 0.979315 | + | 0.202341i | \(0.0648549\pi\) | ||||
−0.979315 | + | 0.202341i | \(0.935145\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.09938 | + | 8.09938i | 0.284058 | + | 0.284058i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.5223 | − | 37.5223i | −1.31274 | − | 1.31274i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.30834 | − | 0.204768i | −0.115603 | − | 0.00715517i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.1844 | −0.529939 | −0.264969 | − | 0.964257i | \(-0.585362\pi\) | ||||
−0.264969 | + | 0.964257i | \(0.585362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.8465 | − | 16.8465i | −0.587233 | − | 0.587233i | 0.349648 | − | 0.936881i | \(-0.386301\pi\) |
−0.936881 | + | 0.349648i | \(0.886301\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.9187 | − | 13.9187i | 0.484000 | − | 0.484000i | −0.422406 | − | 0.906407i | \(-0.638814\pi\) |
0.906407 | + | 0.422406i | \(0.138814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.4450 | 0.883742 | 0.441871 | − | 0.897078i | \(-0.354315\pi\) | ||||
0.441871 | + | 0.897078i | \(0.354315\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 53.3317i | − | 1.85006i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.4595 | − | 22.9472i | 1.02071 | − | 0.795074i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.59668 | + | 3.59668i | −0.124319 | + | 0.124319i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.9718 | 1.62165 | 0.810823 | − | 0.585291i | \(-0.199020\pi\) | ||||
0.810823 | + | 0.585291i | \(0.199020\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8527 | 0.994921 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.22939 | + | 2.22939i | −0.0767841 | + | 0.0767841i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.5348 | + | 12.8405i | −0.499423 | + | 0.441203i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.5682i | 0.637258i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.9865 | −0.753686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.4660 | − | 18.4660i | 0.632262 | − | 0.632262i | −0.316373 | − | 0.948635i | \(-0.602465\pi\) |
0.948635 | + | 0.316373i | \(0.102465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.59503 | − | 6.59503i | −0.225282 | − | 0.225282i | 0.585436 | − | 0.810718i | \(-0.300923\pi\) |
−0.810718 | + | 0.585436i | \(0.800923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.8668 | 1.66731 | 0.833656 | − | 0.552284i | \(-0.186244\pi\) | ||||
0.833656 | + | 0.552284i | \(0.186244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.1856 | + | 1.00180i | 0.551603 | + | 0.0341411i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.6363 | − | 24.6363i | −0.838628 | − | 0.838628i | 0.150050 | − | 0.988678i | \(-0.452057\pi\) |
−0.988678 | + | 0.150050i | \(0.952057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.4957 | + | 14.4957i | 0.492301 | + | 0.492301i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.7917i | 1.24807i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.97453i | − | 0.0669045i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.839407 | + | 0.839407i | −0.0284096 | + | 0.0284096i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.7489 | + | 14.7489i | −0.498035 | + | 0.498035i | −0.910826 | − | 0.412791i | \(-0.864554\pi\) |
0.412791 | + | 0.910826i | \(0.364554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 40.1165i | 1.35310i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.7980i | 0.464865i | 0.972612 | + | 0.232433i | \(0.0746685\pi\) | ||||
−0.972612 | + | 0.232433i | \(0.925331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.6467 | + | 16.6467i | 0.560205 | + | 0.560205i | 0.929366 | − | 0.369160i | \(-0.120355\pi\) |
−0.369160 | + | 0.929366i | \(0.620355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.7822 | + | 21.7822i | 0.731374 | + | 0.731374i | 0.970892 | − | 0.239518i | \(-0.0769895\pi\) |
−0.239518 | + | 0.970892i | \(0.576989\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.531125 | − | 8.58116i | 0.0178134 | − | 0.287803i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.9421 | 1.37161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.2284 | + | 52.2284i | 1.74776 | + | 1.74776i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.1206 | + | 23.1206i | −0.771974 | + | 0.771974i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.389816 | 0.0130011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.6537i | 1.55426i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.4732 | + | 20.7369i | −0.781139 | + | 0.690079i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.71913 | + | 5.71913i | −0.189901 | + | 0.189901i | −0.795653 | − | 0.605753i | \(-0.792872\pi\) |
0.605753 | + | 0.795653i | \(0.292872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.156120 | −0.00517817 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.6578 | 1.44645 | 0.723224 | − | 0.690614i | \(-0.242660\pi\) | ||||
0.723224 | + | 0.690614i | \(0.242660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.0825 | − | 27.0825i | 0.896299 | − | 0.896299i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.83245 | + | 8.86599i | 0.258650 | + | 0.292781i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.83476i | − | 0.192471i | −0.995359 | − | 0.0962355i | \(-0.969320\pi\) | ||
0.995359 | − | 0.0962355i | \(-0.0306802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.4766 | −0.674726 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.7377 | + | 34.7377i | −1.14341 | + | 1.14341i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00819 | − | 1.00819i | −0.0331133 | − | 0.0331133i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.3688 | 0.865131 | 0.432566 | − | 0.901602i | \(-0.357608\pi\) | ||||
0.432566 | + | 0.901602i | \(0.357608\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.92283 | + | 55.7103i | −0.226887 | + | 1.82583i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.8039 | − | 40.8039i | −1.33586 | − | 1.33586i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.8652 | + | 21.8652i | 0.714306 | + | 0.714306i | 0.967433 | − | 0.253127i | \(-0.0814592\pi\) |
−0.253127 | + | 0.967433i | \(0.581459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.74157i | 0.285270i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 57.2544i | − | 1.86644i | −0.359306 | − | 0.933220i | \(-0.616986\pi\) | ||
0.359306 | − | 0.933220i | \(-0.383014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.10521 | − | 7.10521i | 0.231378 | − | 0.231378i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.6937 | + | 10.6937i | −0.347497 | + | 0.347497i | −0.859177 | − | 0.511679i | \(-0.829024\pi\) |
0.511679 | + | 0.859177i | \(0.329024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 84.8531i | − | 2.75445i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 30.2084i | − | 0.979574i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.6129 | − | 18.6129i | −0.602931 | − | 0.602931i | 0.338158 | − | 0.941089i | \(-0.390196\pi\) |
−0.941089 | + | 0.338158i | \(0.890196\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.07874 | − | 2.07874i | −0.0671962 | − | 0.0671962i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.23910 | − | 20.0196i | 0.0400125 | − | 0.646465i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.9683 | 0.966719 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.91880 | − | 1.91880i | −0.0618324 | − | 0.0618324i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.723258 | − | 0.723258i | 0.0232584 | − | 0.0232584i | −0.695382 | − | 0.718640i | \(-0.744765\pi\) |
0.718640 | + | 0.695382i | \(0.244765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −76.5447 | −2.45897 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.6768i | − | 0.663549i | −0.943359 | − | 0.331775i | \(-0.892353\pi\) | ||
0.943359 | − | 0.331775i | \(-0.107647\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.0035 | + | 22.9721i | −0.833633 | + | 0.736453i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.12309 | + | 6.12309i | −0.195895 | + | 0.195895i | −0.798238 | − | 0.602343i | \(-0.794234\pi\) |
0.602343 | + | 0.798238i | \(0.294234\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.47659 | −0.143072 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.96863 | −0.0947812 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.4070 | − | 26.4070i | 0.842254 | − | 0.842254i | −0.146898 | − | 0.989152i | \(-0.546929\pi\) |
0.989152 | + | 0.146898i | \(0.0469288\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.6730 | − | 28.8642i | 1.03999 | − | 0.918758i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.4075i | 0.617123i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.1187 | −0.766157 | −0.383078 | − | 0.923716i | \(-0.625136\pi\) | ||||
−0.383078 | + | 0.923716i | \(0.625136\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.63654 | − | 2.63654i | 0.0836680 | − | 0.0836680i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0465 | − | 12.0465i | −0.381517 | − | 0.381517i | 0.490132 | − | 0.871648i | \(-0.336949\pi\) |
−0.871648 | + | 0.490132i | \(0.836949\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.5374 | −1.18763 |
(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 | 1400.2.x.c.993.13 | yes | 32 | |
5.2 | odd | 4 | inner | 1400.2.x.c.657.3 | ✓ | 32 | |
5.3 | odd | 4 | inner | 1400.2.x.c.657.14 | yes | 32 | |
5.4 | even | 2 | inner | 1400.2.x.c.993.4 | yes | 32 | |
7.6 | odd | 2 | inner | 1400.2.x.c.993.3 | yes | 32 | |
35.13 | even | 4 | inner | 1400.2.x.c.657.4 | yes | 32 | |
35.27 | even | 4 | inner | 1400.2.x.c.657.13 | yes | 32 | |
35.34 | odd | 2 | inner | 1400.2.x.c.993.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.x.c.657.3 | ✓ | 32 | 5.2 | odd | 4 | inner | |
1400.2.x.c.657.4 | yes | 32 | 35.13 | even | 4 | inner | |
1400.2.x.c.657.13 | yes | 32 | 35.27 | even | 4 | inner | |
1400.2.x.c.657.14 | yes | 32 | 5.3 | odd | 4 | inner | |
1400.2.x.c.993.3 | yes | 32 | 7.6 | odd | 2 | inner | |
1400.2.x.c.993.4 | yes | 32 | 5.4 | even | 2 | inner | |
1400.2.x.c.993.13 | yes | 32 | 1.1 | even | 1 | trivial | |
1400.2.x.c.993.14 | yes | 32 | 35.34 | odd | 2 | inner |