Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1767625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.65963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.22058 | 1.57019 | 0.785093 | − | 0.619377i | \(-0.212615\pi\) | ||||
0.785093 | + | 0.619377i | \(0.212615\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.93097 | 1.46549 | ||||||||
\(5\) | 0.0570810 | 0.0255274 | 0.0127637 | − | 0.999919i | \(-0.495937\pi\) | ||||
0.0127637 | + | 0.999919i | \(0.495937\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.64374 | −1.37720 | −0.688602 | − | 0.725139i | \(-0.741775\pi\) | ||||
−0.688602 | + | 0.725139i | \(0.741775\pi\) | |||||||
\(8\) | 2.06730 | 0.730900 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.126753 | 0.0400828 | ||||||||
\(11\) | −3.71735 | −1.12082 | −0.560412 | − | 0.828214i | \(-0.689357\pi\) | ||||
−0.560412 | + | 0.828214i | \(0.689357\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.736497 | −0.204267 | −0.102134 | − | 0.994771i | \(-0.532567\pi\) | ||||
−0.102134 | + | 0.994771i | \(0.532567\pi\) | |||||||
\(14\) | −8.09121 | −2.16247 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.27135 | −0.317836 | ||||||||
\(17\) | −1.72628 | −0.418684 | −0.209342 | − | 0.977842i | \(-0.567132\pi\) | ||||
−0.209342 | + | 0.977842i | \(0.567132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.753715 | −0.172914 | −0.0864571 | − | 0.996256i | \(-0.527555\pi\) | ||||
−0.0864571 | + | 0.996256i | \(0.527555\pi\) | |||||||
\(20\) | 0.167303 | 0.0374101 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.25467 | −1.75990 | ||||||||
\(23\) | −1.29699 | −0.270441 | −0.135221 | − | 0.990816i | \(-0.543174\pi\) | ||||
−0.135221 | + | 0.990816i | \(0.543174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99674 | −0.999348 | ||||||||
\(26\) | −1.63545 | −0.320738 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.6797 | −2.01827 | ||||||||
\(29\) | −2.49193 | −0.462739 | −0.231369 | − | 0.972866i | \(-0.574321\pi\) | ||||
−0.231369 | + | 0.972866i | \(0.574321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.31032 | 1.13337 | 0.566684 | − | 0.823935i | \(-0.308226\pi\) | ||||
0.566684 | + | 0.823935i | \(0.308226\pi\) | |||||||
\(32\) | −6.95772 | −1.22996 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.83334 | −0.657413 | ||||||||
\(35\) | −0.207988 | −0.0351565 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.11169 | −0.182761 | −0.0913803 | − | 0.995816i | \(-0.529128\pi\) | ||||
−0.0913803 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(38\) | −1.67368 | −0.271507 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.118003 | 0.0186580 | ||||||||
\(41\) | 0.457952 | 0.0715201 | 0.0357601 | − | 0.999360i | \(-0.488615\pi\) | ||||
0.0357601 | + | 0.999360i | \(0.488615\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.49470 | −0.532936 | −0.266468 | − | 0.963844i | \(-0.585857\pi\) | ||||
−0.266468 | + | 0.963844i | \(0.585857\pi\) | |||||||
\(44\) | −10.8955 | −1.64255 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.88007 | −0.424643 | ||||||||
\(47\) | 6.66411 | 0.972061 | 0.486030 | − | 0.873942i | \(-0.338444\pi\) | ||||
0.486030 | + | 0.873942i | \(0.338444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.27684 | 0.896691 | ||||||||
\(50\) | −11.0957 | −1.56916 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.15865 | −0.299351 | ||||||||
\(53\) | 0.214663 | 0.0294862 | 0.0147431 | − | 0.999891i | \(-0.495307\pi\) | ||||
0.0147431 | + | 0.999891i | \(0.495307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.212190 | −0.0286117 | ||||||||
\(56\) | −7.53269 | −1.00660 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.53352 | −0.726586 | ||||||||
\(59\) | 7.80818 | 1.01654 | 0.508269 | − | 0.861198i | \(-0.330285\pi\) | ||||
0.508269 | + | 0.861198i | \(0.330285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.44774 | −0.441437 | −0.220719 | − | 0.975338i | \(-0.570840\pi\) | ||||
−0.220719 | + | 0.975338i | \(0.570840\pi\) | |||||||
\(62\) | 14.0126 | 1.77960 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9075 | −1.61343 | ||||||||
\(65\) | −0.0420400 | −0.00521442 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.5114 | −1.40634 | −0.703168 | − | 0.711024i | \(-0.748232\pi\) | ||||
−0.703168 | + | 0.711024i | \(0.748232\pi\) | |||||||
\(68\) | −5.05968 | −0.613576 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.461855 | −0.0552022 | ||||||||
\(71\) | 9.97235 | 1.18350 | 0.591750 | − | 0.806121i | \(-0.298437\pi\) | ||||
0.591750 | + | 0.806121i | \(0.298437\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.09226 | −0.244881 | −0.122440 | − | 0.992476i | \(-0.539072\pi\) | ||||
−0.122440 | + | 0.992476i | \(0.539072\pi\) | |||||||
\(74\) | −2.46859 | −0.286968 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.20912 | −0.253403 | ||||||||
\(77\) | 13.5451 | 1.54360 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2848 | −1.60717 | −0.803583 | − | 0.595193i | \(-0.797076\pi\) | ||||
−0.803583 | + | 0.595193i | \(0.797076\pi\) | |||||||
\(80\) | −0.0725697 | −0.00811354 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.01692 | 0.112300 | ||||||||
\(83\) | 9.92940 | 1.08989 | 0.544947 | − | 0.838471i | \(-0.316550\pi\) | ||||
0.544947 | + | 0.838471i | \(0.316550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0985378 | −0.0106879 | ||||||||
\(86\) | −7.76025 | −0.836810 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.68487 | −0.819210 | ||||||||
\(89\) | −0.440716 | −0.0467158 | −0.0233579 | − | 0.999727i | \(-0.507436\pi\) | ||||
−0.0233579 | + | 0.999727i | \(0.507436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.68360 | 0.281318 | ||||||||
\(92\) | −3.80144 | −0.396328 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.7982 | 1.52632 | ||||||||
\(95\) | −0.0430228 | −0.00441405 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.68409 | −0.780201 | −0.390100 | − | 0.920772i | \(-0.627560\pi\) | ||||
−0.390100 | + | 0.920772i | \(0.627560\pi\) | |||||||
\(98\) | 13.9382 | 1.40797 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.6453 | −1.46453 | ||||||||
\(101\) | −12.8775 | −1.28135 | −0.640677 | − | 0.767810i | \(-0.721346\pi\) | ||||
−0.640677 | + | 0.767810i | \(0.721346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.75094 | −0.468124 | −0.234062 | − | 0.972222i | \(-0.575202\pi\) | ||||
−0.234062 | + | 0.972222i | \(0.575202\pi\) | |||||||
\(104\) | −1.52256 | −0.149299 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.476676 | 0.0462989 | ||||||||
\(107\) | 20.4655 | 1.97847 | 0.989236 | − | 0.146327i | \(-0.0467452\pi\) | ||||
0.989236 | + | 0.146327i | \(0.0467452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6172 | 1.11272 | 0.556361 | − | 0.830940i | \(-0.312197\pi\) | ||||
0.556361 | + | 0.830940i | \(0.312197\pi\) | |||||||
\(110\) | −0.471185 | −0.0449257 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.63245 | 0.437726 | ||||||||
\(113\) | −5.69792 | −0.536015 | −0.268008 | − | 0.963417i | \(-0.586365\pi\) | ||||
−0.268008 | + | 0.963417i | \(0.586365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0740335 | −0.00690366 | ||||||||
\(116\) | −7.30376 | −0.678137 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.3387 | 1.59616 | ||||||||
\(119\) | 6.29011 | 0.576614 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.81870 | 0.256246 | ||||||||
\(122\) | −7.65597 | −0.693139 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.4954 | 1.66093 | ||||||||
\(125\) | −0.570624 | −0.0510382 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.93084 | 0.260070 | 0.130035 | − | 0.991509i | \(-0.458491\pi\) | ||||
0.130035 | + | 0.991509i | \(0.458491\pi\) | |||||||
\(128\) | −14.7466 | −1.30343 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0933531 | −0.00818761 | ||||||||
\(131\) | −4.34492 | −0.379617 | −0.189809 | − | 0.981821i | \(-0.560787\pi\) | ||||
−0.189809 | + | 0.981821i | \(0.560787\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.74634 | 0.238138 | ||||||||
\(134\) | −25.5619 | −2.20821 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.56873 | −0.306016 | ||||||||
\(137\) | 10.8025 | 0.922922 | 0.461461 | − | 0.887160i | \(-0.347325\pi\) | ||||
0.461461 | + | 0.887160i | \(0.347325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.59821 | 0.135558 | 0.0677791 | − | 0.997700i | \(-0.478409\pi\) | ||||
0.0677791 | + | 0.997700i | \(0.478409\pi\) | |||||||
\(140\) | −0.609608 | −0.0515213 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 22.1444 | 1.85832 | ||||||||
\(143\) | 2.73782 | 0.228948 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.142242 | −0.0118125 | ||||||||
\(146\) | −4.64603 | −0.384508 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.25833 | −0.267833 | ||||||||
\(149\) | −8.16766 | −0.669121 | −0.334560 | − | 0.942374i | \(-0.608588\pi\) | ||||
−0.334560 | + | 0.942374i | \(0.608588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.6281 | −0.946280 | −0.473140 | − | 0.880987i | \(-0.656880\pi\) | ||||
−0.473140 | + | 0.880987i | \(0.656880\pi\) | |||||||
\(152\) | −1.55815 | −0.126383 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 30.0779 | 2.42374 | ||||||||
\(155\) | 0.360200 | 0.0289319 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.31612 | 0.583890 | 0.291945 | − | 0.956435i | \(-0.405698\pi\) | ||||
0.291945 | + | 0.956435i | \(0.405698\pi\) | |||||||
\(158\) | −31.7205 | −2.52355 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.397154 | −0.0313978 | ||||||||
\(161\) | 4.72590 | 0.372453 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.5848 | 1.37735 | 0.688675 | − | 0.725070i | \(-0.258193\pi\) | ||||
0.688675 | + | 0.725070i | \(0.258193\pi\) | |||||||
\(164\) | 1.34225 | 0.104812 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.0490 | 1.71134 | ||||||||
\(167\) | 3.05610 | 0.236488 | 0.118244 | − | 0.992985i | \(-0.462274\pi\) | ||||
0.118244 | + | 0.992985i | \(0.462274\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4576 | −0.958275 | ||||||||
\(170\) | −0.218811 | −0.0167820 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.2429 | −0.781011 | ||||||||
\(173\) | −25.2508 | −1.91978 | −0.959890 | − | 0.280377i | \(-0.909541\pi\) | ||||
−0.959890 | + | 0.280377i | \(0.909541\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.2068 | 1.37631 | ||||||||
\(176\) | 4.72604 | 0.356239 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.978645 | −0.0733525 | ||||||||
\(179\) | 2.05516 | 0.153610 | 0.0768050 | − | 0.997046i | \(-0.475528\pi\) | ||||
0.0768050 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.1941 | −1.87266 | −0.936330 | − | 0.351122i | \(-0.885800\pi\) | ||||
−0.936330 | + | 0.351122i | \(0.885800\pi\) | |||||||
\(182\) | 5.95915 | 0.441722 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.68127 | −0.197666 | ||||||||
\(185\) | −0.0634564 | −0.00466540 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.41719 | 0.469271 | ||||||||
\(188\) | 19.5323 | 1.42454 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0955356 | −0.00693088 | ||||||||
\(191\) | −0.594359 | −0.0430063 | −0.0215031 | − | 0.999769i | \(-0.506845\pi\) | ||||
−0.0215031 | + | 0.999769i | \(0.506845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3926 | 1.03600 | 0.518002 | − | 0.855379i | \(-0.326676\pi\) | ||||
0.518002 | + | 0.855379i | \(0.326676\pi\) | |||||||
\(194\) | −17.0631 | −1.22506 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.3972 | 1.31409 | ||||||||
\(197\) | 4.63529 | 0.330251 | 0.165125 | − | 0.986273i | \(-0.447197\pi\) | ||||
0.165125 | + | 0.986273i | \(0.447197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5742 | −0.891363 | −0.445682 | − | 0.895192i | \(-0.647039\pi\) | ||||
−0.445682 | + | 0.895192i | \(0.647039\pi\) | |||||||
\(200\) | −10.3298 | −0.730424 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −28.5954 | −2.01197 | ||||||||
\(203\) | 9.07993 | 0.637286 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0261404 | 0.00182572 | ||||||||
\(206\) | −10.5498 | −0.735042 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.936342 | 0.0649236 | ||||||||
\(209\) | 2.80182 | 0.193806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.38295 | 0.577106 | 0.288553 | − | 0.957464i | \(-0.406826\pi\) | ||||
0.288553 | + | 0.957464i | \(0.406826\pi\) | |||||||
\(212\) | 0.629172 | 0.0432117 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 45.4452 | 3.10657 | ||||||||
\(215\) | −0.199481 | −0.0136045 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.9932 | −1.56088 | ||||||||
\(218\) | 25.7968 | 1.74718 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.621924 | −0.0419301 | ||||||||
\(221\) | 1.27140 | 0.0855236 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.69892 | −0.314663 | −0.157332 | − | 0.987546i | \(-0.550289\pi\) | ||||
−0.157332 | + | 0.987546i | \(0.550289\pi\) | |||||||
\(224\) | 25.3521 | 1.69391 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.6527 | −0.841644 | ||||||||
\(227\) | 11.3000 | 0.750008 | 0.375004 | − | 0.927023i | \(-0.377641\pi\) | ||||
0.375004 | + | 0.927023i | \(0.377641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.45502 | −0.426560 | −0.213280 | − | 0.976991i | \(-0.568415\pi\) | ||||
−0.213280 | + | 0.976991i | \(0.568415\pi\) | |||||||
\(230\) | −0.164397 | −0.0108400 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.15155 | −0.338216 | ||||||||
\(233\) | 17.6315 | 1.15508 | 0.577540 | − | 0.816363i | \(-0.304013\pi\) | ||||
0.577540 | + | 0.816363i | \(0.304013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.380394 | 0.0248142 | ||||||||
\(236\) | 22.8856 | 1.48972 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.9677 | 0.905391 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.36031 | −0.152041 | −0.0760205 | − | 0.997106i | \(-0.524221\pi\) | ||||
−0.0760205 | + | 0.997106i | \(0.524221\pi\) | |||||||
\(242\) | 6.25915 | 0.402354 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.1052 | −0.646920 | ||||||||
\(245\) | 0.358288 | 0.0228902 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.555109 | 0.0353207 | ||||||||
\(248\) | 13.0453 | 0.828379 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.26712 | −0.0801395 | ||||||||
\(251\) | 8.31979 | 0.525140 | 0.262570 | − | 0.964913i | \(-0.415430\pi\) | ||||
0.262570 | + | 0.964913i | \(0.415430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.82137 | 0.303117 | ||||||||
\(254\) | 6.50816 | 0.408358 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.93112 | −0.433195 | ||||||||
\(257\) | −26.9279 | −1.67972 | −0.839858 | − | 0.542806i | \(-0.817362\pi\) | ||||
−0.839858 | + | 0.542806i | \(0.817362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.05071 | 0.251699 | ||||||||
\(260\) | −0.123218 | −0.00764166 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.64824 | −0.596070 | ||||||||
\(263\) | −2.32501 | −0.143366 | −0.0716831 | − | 0.997427i | \(-0.522837\pi\) | ||||
−0.0716831 | + | 0.997427i | \(0.522837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0122532 | 0.000752707 0 | ||||||||
\(266\) | 6.09847 | 0.373921 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −33.7395 | −2.06097 | ||||||||
\(269\) | −13.3580 | −0.814452 | −0.407226 | − | 0.913327i | \(-0.633504\pi\) | ||||
−0.407226 | + | 0.913327i | \(0.633504\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5887 | 1.00769 | 0.503847 | − | 0.863793i | \(-0.331917\pi\) | ||||
0.503847 | + | 0.863793i | \(0.331917\pi\) | |||||||
\(272\) | 2.19470 | 0.133073 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.9879 | 1.44916 | ||||||||
\(275\) | 18.5746 | 1.12009 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.5340 | 1.05352 | 0.526759 | − | 0.850015i | \(-0.323407\pi\) | ||||
0.526759 | + | 0.850015i | \(0.323407\pi\) | |||||||
\(278\) | 3.54895 | 0.212852 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.429974 | −0.0256959 | ||||||||
\(281\) | −11.3858 | −0.679221 | −0.339610 | − | 0.940566i | \(-0.610295\pi\) | ||||
−0.339610 | + | 0.940566i | \(0.610295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7683 | −0.640108 | −0.320054 | − | 0.947399i | \(-0.603701\pi\) | ||||
−0.320054 | + | 0.947399i | \(0.603701\pi\) | |||||||
\(284\) | 29.2287 | 1.73440 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.07954 | 0.359491 | ||||||||
\(287\) | −1.66866 | −0.0984978 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0200 | −0.824703 | ||||||||
\(290\) | −0.315859 | −0.0185479 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.13236 | −0.358869 | ||||||||
\(293\) | −12.8250 | −0.749246 | −0.374623 | − | 0.927177i | \(-0.622228\pi\) | ||||
−0.374623 | + | 0.927177i | \(0.622228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.445699 | 0.0259496 | ||||||||
\(296\) | −2.29819 | −0.133580 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.1369 | −1.05064 | ||||||||
\(299\) | 0.955229 | 0.0552423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.7338 | 0.733962 | ||||||||
\(302\) | −25.8211 | −1.48584 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.958233 | 0.0549584 | ||||||||
\(305\) | −0.196800 | −0.0112688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6775 | −1.12305 | −0.561527 | − | 0.827458i | \(-0.689786\pi\) | ||||
−0.561527 | + | 0.827458i | \(0.689786\pi\) | |||||||
\(308\) | 39.7002 | 2.26213 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.799852 | 0.0454285 | ||||||||
\(311\) | −25.7035 | −1.45751 | −0.728757 | − | 0.684772i | \(-0.759902\pi\) | ||||
−0.728757 | + | 0.684772i | \(0.759902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.41285 | −0.532046 | −0.266023 | − | 0.963967i | \(-0.585710\pi\) | ||||
−0.266023 | + | 0.963967i | \(0.585710\pi\) | |||||||
\(314\) | 16.2460 | 0.916816 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −41.8684 | −2.35528 | ||||||||
\(317\) | 1.87215 | 0.105151 | 0.0525753 | − | 0.998617i | \(-0.483257\pi\) | ||||
0.0525753 | + | 0.998617i | \(0.483257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.26336 | 0.518649 | ||||||||
\(320\) | −0.736772 | −0.0411868 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.4942 | 0.584820 | ||||||||
\(323\) | 1.30112 | 0.0723964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.68008 | 0.204134 | ||||||||
\(326\) | 39.0485 | 2.16270 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.946724 | 0.0522741 | ||||||||
\(329\) | −24.2823 | −1.33873 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8715 | −0.927341 | −0.463670 | − | 0.886008i | \(-0.653468\pi\) | ||||
−0.463670 | + | 0.886008i | \(0.653468\pi\) | |||||||
\(332\) | 29.1028 | 1.59722 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.78631 | 0.371330 | ||||||||
\(335\) | −0.657080 | −0.0359001 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.1903 | −1.04536 | −0.522681 | − | 0.852528i | \(-0.675068\pi\) | ||||
−0.522681 | + | 0.852528i | \(0.675068\pi\) | |||||||
\(338\) | −27.6630 | −1.50467 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.288812 | −0.0156630 | ||||||||
\(341\) | −23.4577 | −1.27031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.63502 | 0.142278 | ||||||||
\(344\) | −7.22458 | −0.389523 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −56.0713 | −3.01441 | ||||||||
\(347\) | 23.8362 | 1.27960 | 0.639798 | − | 0.768543i | \(-0.279018\pi\) | ||||
0.639798 | + | 0.768543i | \(0.279018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.5199 | −0.723703 | −0.361852 | − | 0.932236i | \(-0.617855\pi\) | ||||
−0.361852 | + | 0.932236i | \(0.617855\pi\) | |||||||
\(350\) | 40.4297 | 2.16106 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25.8643 | 1.37857 | ||||||||
\(353\) | 14.3286 | 0.762636 | 0.381318 | − | 0.924444i | \(-0.375470\pi\) | ||||
0.381318 | + | 0.924444i | \(0.375470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.569232 | 0.0302117 | ||||||||
\(356\) | −1.29173 | −0.0684614 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.56365 | 0.241196 | ||||||||
\(359\) | 15.1952 | 0.801974 | 0.400987 | − | 0.916084i | \(-0.368667\pi\) | ||||
0.400987 | + | 0.916084i | \(0.368667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4319 | −0.970101 | ||||||||
\(362\) | −55.9454 | −2.94042 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.86556 | 0.412268 | ||||||||
\(365\) | −0.119428 | −0.00625117 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.2749 | 1.63253 | 0.816267 | − | 0.577675i | \(-0.196040\pi\) | ||||
0.816267 | + | 0.577675i | \(0.196040\pi\) | |||||||
\(368\) | 1.64892 | 0.0859561 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.140910 | −0.00732556 | ||||||||
\(371\) | −0.782176 | −0.0406086 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6383 | 0.706166 | 0.353083 | − | 0.935592i | \(-0.385133\pi\) | ||||
0.353083 | + | 0.935592i | \(0.385133\pi\) | |||||||
\(374\) | 14.2499 | 0.736844 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.7767 | 0.710479 | ||||||||
\(377\) | 1.83529 | 0.0945225 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3666 | −1.14890 | −0.574448 | − | 0.818541i | \(-0.694783\pi\) | ||||
−0.574448 | + | 0.818541i | \(0.694783\pi\) | |||||||
\(380\) | −0.126099 | −0.00646873 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.31982 | −0.0675279 | ||||||||
\(383\) | −12.1215 | −0.619380 | −0.309690 | − | 0.950838i | \(-0.600225\pi\) | ||||
−0.309690 | + | 0.950838i | \(0.600225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.773166 | 0.0394042 | ||||||||
\(386\) | 31.9600 | 1.62672 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.5218 | −1.14337 | ||||||||
\(389\) | 11.4985 | 0.582999 | 0.291500 | − | 0.956571i | \(-0.405846\pi\) | ||||
0.291500 | + | 0.956571i | \(0.405846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.23897 | 0.113230 | ||||||||
\(392\) | 12.9761 | 0.655392 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.2930 | 0.518555 | ||||||||
\(395\) | −0.815391 | −0.0410268 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2172 | −1.26561 | −0.632807 | − | 0.774309i | \(-0.718098\pi\) | ||||
−0.632807 | + | 0.774309i | \(0.718098\pi\) | |||||||
\(398\) | −27.9221 | −1.39961 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.35259 | 0.317629 | ||||||||
\(401\) | 29.3323 | 1.46479 | 0.732393 | − | 0.680883i | \(-0.238404\pi\) | ||||
0.732393 | + | 0.680883i | \(0.238404\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.64753 | −0.231510 | ||||||||
\(404\) | −37.7435 | −1.87781 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.1627 | 1.00066 | ||||||||
\(407\) | 4.13254 | 0.204842 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.7995 | 1.91851 | 0.959256 | − | 0.282539i | \(-0.0911767\pi\) | ||||
0.959256 | + | 0.282539i | \(0.0911767\pi\) | |||||||
\(410\) | 0.0580468 | 0.00286673 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.9249 | −0.686029 | ||||||||
\(413\) | −28.4510 | −1.39998 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.566781 | 0.0278222 | ||||||||
\(416\) | 5.12434 | 0.251241 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.22167 | 0.304312 | ||||||||
\(419\) | 26.0609 | 1.27316 | 0.636578 | − | 0.771212i | \(-0.280349\pi\) | ||||
0.636578 | + | 0.771212i | \(0.280349\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7112 | −0.570767 | −0.285383 | − | 0.958413i | \(-0.592121\pi\) | ||||
−0.285383 | + | 0.958413i | \(0.592121\pi\) | |||||||
\(422\) | 18.6150 | 0.906164 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.443773 | 0.0215515 | ||||||||
\(425\) | 8.62577 | 0.418412 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5626 | 0.607949 | ||||||||
\(428\) | 59.9838 | 2.89942 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.442963 | −0.0213616 | ||||||||
\(431\) | −19.3962 | −0.934284 | −0.467142 | − | 0.884182i | \(-0.654716\pi\) | ||||
−0.467142 | + | 0.884182i | \(0.654716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.56849 | −0.171490 | −0.0857452 | − | 0.996317i | \(-0.527327\pi\) | ||||
−0.0857452 | + | 0.996317i | \(0.527327\pi\) | |||||||
\(434\) | −51.0582 | −2.45087 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 34.0496 | 1.63068 | ||||||||
\(437\) | 0.977561 | 0.0467631 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5488 | 1.50574 | 0.752872 | − | 0.658167i | \(-0.228668\pi\) | ||||
0.752872 | + | 0.658167i | \(0.228668\pi\) | |||||||
\(440\) | −0.438660 | −0.0209123 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.82324 | 0.134288 | ||||||||
\(443\) | −2.17420 | −0.103299 | −0.0516496 | − | 0.998665i | \(-0.516448\pi\) | ||||
−0.0516496 | + | 0.998665i | \(0.516448\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0251565 | −0.00119253 | ||||||||
\(446\) | −10.4343 | −0.494080 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 47.0315 | 2.22203 | ||||||||
\(449\) | −33.2412 | −1.56875 | −0.784375 | − | 0.620287i | \(-0.787016\pi\) | ||||
−0.784375 | + | 0.620287i | \(0.787016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.70237 | −0.0801614 | ||||||||
\(452\) | −16.7005 | −0.785523 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.0926 | 1.17765 | ||||||||
\(455\) | 0.153183 | 0.00718132 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.5058 | −1.23989 | −0.619944 | − | 0.784646i | \(-0.712845\pi\) | ||||
−0.619944 | + | 0.784646i | \(0.712845\pi\) | |||||||
\(458\) | −14.3339 | −0.669779 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.216990 | −0.0101172 | ||||||||
\(461\) | 36.1977 | 1.68590 | 0.842948 | − | 0.537995i | \(-0.180818\pi\) | ||||
0.842948 | + | 0.537995i | \(0.180818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.82777 | 0.317314 | 0.158657 | − | 0.987334i | \(-0.449284\pi\) | ||||
0.158657 | + | 0.987334i | \(0.449284\pi\) | |||||||
\(464\) | 3.16810 | 0.147075 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 39.1522 | 1.81369 | ||||||||
\(467\) | −33.8542 | −1.56659 | −0.783293 | − | 0.621652i | \(-0.786462\pi\) | ||||
−0.783293 | + | 0.621652i | \(0.786462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.9444 | 1.93681 | ||||||||
\(470\) | 0.844696 | 0.0389629 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.1418 | 0.742988 | ||||||||
\(473\) | 12.9910 | 0.597328 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.76612 | 0.172801 | ||||||||
\(476\) | 18.4362 | 0.845020 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.22058 | 0.101567 | ||||||||
\(479\) | −8.14302 | −0.372064 | −0.186032 | − | 0.982544i | \(-0.559563\pi\) | ||||
−0.186032 | + | 0.982544i | \(0.559563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.818755 | 0.0373320 | ||||||||
\(482\) | −5.24126 | −0.238733 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.26154 | 0.375524 | ||||||||
\(485\) | −0.438616 | −0.0199165 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0940 | −0.638661 | −0.319330 | − | 0.947643i | \(-0.603458\pi\) | ||||
−0.319330 | + | 0.947643i | \(0.603458\pi\) | |||||||
\(488\) | −7.12750 | −0.322647 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.795608 | 0.0359419 | ||||||||
\(491\) | 30.5029 | 1.37658 | 0.688289 | − | 0.725437i | \(-0.258362\pi\) | ||||
0.688289 | + | 0.725437i | \(0.258362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.30176 | 0.193742 | ||||||||
\(494\) | 1.23266 | 0.0554601 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.02261 | −0.360226 | ||||||||
\(497\) | −36.3367 | −1.62992 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6252 | −0.699479 | −0.349739 | − | 0.936847i | \(-0.613730\pi\) | ||||
−0.349739 | + | 0.936847i | \(0.613730\pi\) | |||||||
\(500\) | −1.67248 | −0.0747958 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.4747 | 0.824568 | ||||||||
\(503\) | −10.0657 | −0.448807 | −0.224404 | − | 0.974496i | \(-0.572043\pi\) | ||||
−0.224404 | + | 0.974496i | \(0.572043\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.735058 | −0.0327097 | ||||||||
\(506\) | 10.7062 | 0.475950 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.59020 | 0.381129 | ||||||||
\(509\) | 22.5797 | 1.00083 | 0.500414 | − | 0.865786i | \(-0.333181\pi\) | ||||
0.500414 | + | 0.865786i | \(0.333181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.62365 | 0.337250 | ||||||||
\(512\) | 14.1022 | 0.623234 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −59.7955 | −2.63747 | ||||||||
\(515\) | −0.271188 | −0.0119500 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.7728 | −1.08951 | ||||||||
\(518\) | 8.99491 | 0.395214 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0869092 | −0.00381122 | ||||||||
\(521\) | 10.6301 | 0.465715 | 0.232857 | − | 0.972511i | \(-0.425192\pi\) | ||||
0.232857 | + | 0.972511i | \(0.425192\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8900 | 0.563642 | 0.281821 | − | 0.959467i | \(-0.409062\pi\) | ||||
0.281821 | + | 0.959467i | \(0.409062\pi\) | |||||||
\(524\) | −12.7348 | −0.556324 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.16287 | −0.225112 | ||||||||
\(527\) | −10.8934 | −0.474523 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3178 | −0.926862 | ||||||||
\(530\) | 0.0272092 | 0.00118189 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.04945 | 0.348988 | ||||||||
\(533\) | −0.337280 | −0.0146092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.16819 | 0.0505053 | ||||||||
\(536\) | −23.7974 | −1.02789 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.6625 | −1.27884 | ||||||||
\(539\) | −23.3332 | −1.00503 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.1904 | 1.46996 | 0.734980 | − | 0.678089i | \(-0.237191\pi\) | ||||
0.734980 | + | 0.678089i | \(0.237191\pi\) | |||||||
\(542\) | 36.8366 | 1.58227 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.0110 | 0.514966 | ||||||||
\(545\) | 0.663120 | 0.0284049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6930 | −0.542714 | −0.271357 | − | 0.962479i | \(-0.587472\pi\) | ||||
−0.271357 | + | 0.962479i | \(0.587472\pi\) | |||||||
\(548\) | 31.6619 | 1.35253 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 41.2465 | 1.75876 | ||||||||
\(551\) | 1.87820 | 0.0800141 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 52.0501 | 2.21340 | ||||||||
\(554\) | 38.9357 | 1.65422 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.68430 | 0.198659 | ||||||||
\(557\) | 32.3710 | 1.37160 | 0.685801 | − | 0.727789i | \(-0.259452\pi\) | ||||
0.685801 | + | 0.727789i | \(0.259452\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.57383 | 0.108862 | ||||||||
\(560\) | 0.264425 | 0.0111740 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.2831 | −1.06650 | ||||||||
\(563\) | −17.5807 | −0.740938 | −0.370469 | − | 0.928845i | \(-0.620803\pi\) | ||||
−0.370469 | + | 0.928845i | \(0.620803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.325243 | −0.0136831 | ||||||||
\(566\) | −23.9118 | −1.00509 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.6158 | 0.865021 | ||||||||
\(569\) | −44.7549 | −1.87622 | −0.938112 | − | 0.346332i | \(-0.887427\pi\) | ||||
−0.938112 | + | 0.346332i | \(0.887427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.9021 | 0.874727 | 0.437364 | − | 0.899285i | \(-0.355912\pi\) | ||||
0.437364 | + | 0.899285i | \(0.355912\pi\) | |||||||
\(572\) | 8.02447 | 0.335520 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.70539 | −0.154660 | ||||||||
\(575\) | 6.48073 | 0.270265 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.77713 | −0.282135 | −0.141068 | − | 0.990000i | \(-0.545054\pi\) | ||||
−0.141068 | + | 0.990000i | \(0.545054\pi\) | |||||||
\(578\) | −31.1324 | −1.29494 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.416906 | −0.0173111 | ||||||||
\(581\) | −36.1802 | −1.50101 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.797978 | −0.0330489 | ||||||||
\(584\) | −4.32533 | −0.178983 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.4790 | −1.17646 | ||||||||
\(587\) | −26.4488 | −1.09166 | −0.545830 | − | 0.837896i | \(-0.683786\pi\) | ||||
−0.545830 | + | 0.837896i | \(0.683786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.75619 | −0.195975 | ||||||||
\(590\) | 0.989710 | 0.0407457 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.41334 | 0.0580880 | ||||||||
\(593\) | 3.87732 | 0.159222 | 0.0796112 | − | 0.996826i | \(-0.474632\pi\) | ||||
0.0796112 | + | 0.996826i | \(0.474632\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.359046 | 0.0147195 | ||||||||
\(596\) | −23.9392 | −0.980587 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.12116 | 0.0867408 | ||||||||
\(599\) | −25.3189 | −1.03450 | −0.517251 | − | 0.855834i | \(-0.673045\pi\) | ||||
−0.517251 | + | 0.855834i | \(0.673045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.4456 | 0.874782 | 0.437391 | − | 0.899271i | \(-0.355903\pi\) | ||||
0.437391 | + | 0.899271i | \(0.355903\pi\) | |||||||
\(602\) | 28.2763 | 1.15246 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.0816 | −1.38676 | ||||||||
\(605\) | 0.160894 | 0.00654129 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.0058 | 1.78614 | 0.893070 | − | 0.449919i | \(-0.148547\pi\) | ||||
0.893070 | + | 0.449919i | \(0.148547\pi\) | |||||||
\(608\) | 5.24414 | 0.212678 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.437011 | −0.0176940 | ||||||||
\(611\) | −4.90810 | −0.198560 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.11434 | 0.368125 | 0.184062 | − | 0.982915i | \(-0.441075\pi\) | ||||
0.184062 | + | 0.982915i | \(0.441075\pi\) | |||||||
\(614\) | −43.6955 | −1.76341 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.0017 | 1.12822 | ||||||||
\(617\) | −2.06698 | −0.0832133 | −0.0416067 | − | 0.999134i | \(-0.513248\pi\) | ||||
−0.0416067 | + | 0.999134i | \(0.513248\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.7993 | −0.916383 | −0.458191 | − | 0.888854i | \(-0.651503\pi\) | ||||
−0.458191 | + | 0.888854i | \(0.651503\pi\) | |||||||
\(620\) | 1.05574 | 0.0423994 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −57.0768 | −2.28857 | ||||||||
\(623\) | 1.60585 | 0.0643372 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9511 | 0.998045 | ||||||||
\(626\) | −20.9020 | −0.835411 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.4433 | 0.855682 | ||||||||
\(629\) | 1.91909 | 0.0765190 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4481 | −1.25193 | −0.625964 | − | 0.779852i | \(-0.715294\pi\) | ||||
−0.625964 | + | 0.779852i | \(0.715294\pi\) | |||||||
\(632\) | −29.5309 | −1.17468 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.15727 | 0.165106 | ||||||||
\(635\) | 0.167295 | 0.00663891 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.62287 | −0.183165 | ||||||||
\(638\) | 20.5700 | 0.814375 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.841753 | −0.0332732 | ||||||||
\(641\) | −6.51455 | −0.257309 | −0.128655 | − | 0.991689i | \(-0.541066\pi\) | ||||
−0.128655 | + | 0.991689i | \(0.541066\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.08816 | −0.0823491 | −0.0411746 | − | 0.999152i | \(-0.513110\pi\) | ||||
−0.0411746 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(644\) | 13.8515 | 0.545824 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.88925 | 0.113676 | ||||||||
\(647\) | 11.2824 | 0.443555 | 0.221778 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221778 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.0258 | −1.13936 | ||||||||
\(650\) | 8.17192 | 0.320529 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 51.5406 | 2.01849 | ||||||||
\(653\) | 15.7251 | 0.615372 | 0.307686 | − | 0.951488i | \(-0.400445\pi\) | ||||
0.307686 | + | 0.951488i | \(0.400445\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.248013 | −0.00969065 | ||||||||
\(656\) | −0.582216 | −0.0227317 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −53.9207 | −2.10205 | ||||||||
\(659\) | 1.91095 | 0.0744400 | 0.0372200 | − | 0.999307i | \(-0.488150\pi\) | ||||
0.0372200 | + | 0.999307i | \(0.488150\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.7455 | −1.77929 | −0.889647 | − | 0.456648i | \(-0.849050\pi\) | ||||
−0.889647 | + | 0.456648i | \(0.849050\pi\) | |||||||
\(662\) | −37.4645 | −1.45610 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.5270 | 0.796604 | ||||||||
\(665\) | 0.156764 | 0.00607905 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.23200 | 0.125144 | ||||||||
\(668\) | 8.95734 | 0.346570 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.45910 | −0.0563699 | ||||||||
\(671\) | 12.8164 | 0.494773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.5553 | 1.40910 | 0.704552 | − | 0.709653i | \(-0.251148\pi\) | ||||
0.704552 | + | 0.709653i | \(0.251148\pi\) | |||||||
\(674\) | −42.6136 | −1.64141 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −36.5128 | −1.40434 | ||||||||
\(677\) | −26.1615 | −1.00547 | −0.502733 | − | 0.864442i | \(-0.667672\pi\) | ||||
−0.502733 | + | 0.864442i | \(0.667672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.9988 | 1.07450 | ||||||||
\(680\) | −0.203707 | −0.00781181 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −52.0897 | −1.99462 | ||||||||
\(683\) | −32.3175 | −1.23660 | −0.618298 | − | 0.785944i | \(-0.712177\pi\) | ||||
−0.618298 | + | 0.785944i | \(0.712177\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.616619 | 0.0235598 | ||||||||
\(686\) | 5.85126 | 0.223402 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.44297 | 0.169387 | ||||||||
\(689\) | −0.158099 | −0.00602308 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.28734 | −0.125056 | −0.0625282 | − | 0.998043i | \(-0.519916\pi\) | ||||
−0.0625282 | + | 0.998043i | \(0.519916\pi\) | |||||||
\(692\) | −74.0093 | −2.81341 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 52.9303 | 2.00921 | ||||||||
\(695\) | 0.0912273 | 0.00346045 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.790554 | −0.0299444 | ||||||||
\(698\) | −30.0220 | −1.13635 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 53.3637 | 2.01696 | ||||||||
\(701\) | 11.2419 | 0.424602 | 0.212301 | − | 0.977204i | \(-0.431904\pi\) | ||||
0.212301 | + | 0.977204i | \(0.431904\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.837897 | 0.0316019 | ||||||||
\(704\) | 47.9816 | 1.80838 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.8179 | 1.19748 | ||||||||
\(707\) | 46.9221 | 1.76469 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.71294 | 0.176998 | 0.0884990 | − | 0.996076i | \(-0.471793\pi\) | ||||
0.0884990 | + | 0.996076i | \(0.471793\pi\) | |||||||
\(710\) | 1.26402 | 0.0474380 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.911091 | −0.0341446 | ||||||||
\(713\) | −8.18443 | −0.306509 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.156277 | 0.00584444 | ||||||||
\(716\) | 6.02362 | 0.225113 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.7422 | 1.25925 | ||||||||
\(719\) | −25.7339 | −0.959713 | −0.479856 | − | 0.877347i | \(-0.659311\pi\) | ||||
−0.479856 | + | 0.877347i | \(0.659311\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.3112 | 0.644702 | ||||||||
\(722\) | −40.9295 | −1.52324 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −73.8431 | −2.74436 | ||||||||
\(725\) | 12.4515 | 0.462437 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.9895 | −0.407576 | −0.203788 | − | 0.979015i | \(-0.565325\pi\) | ||||
−0.203788 | + | 0.979015i | \(0.565325\pi\) | |||||||
\(728\) | 5.54780 | 0.205615 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.265200 | −0.00981550 | ||||||||
\(731\) | 6.03283 | 0.223132 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.7612 | −1.02538 | −0.512692 | − | 0.858572i | \(-0.671352\pi\) | ||||
−0.512692 | + | 0.858572i | \(0.671352\pi\) | |||||||
\(734\) | 69.4483 | 2.56338 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.02410 | 0.332633 | ||||||||
\(737\) | 42.7918 | 1.57625 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.7282 | −0.946426 | −0.473213 | − | 0.880948i | \(-0.656906\pi\) | ||||
−0.473213 | + | 0.880948i | \(0.656906\pi\) | |||||||
\(740\) | −0.185989 | −0.00683709 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.73688 | −0.0637630 | ||||||||
\(743\) | 38.6081 | 1.41639 | 0.708197 | − | 0.706015i | \(-0.249509\pi\) | ||||
0.708197 | + | 0.706015i | \(0.249509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.466218 | −0.0170809 | ||||||||
\(746\) | 30.2850 | 1.10881 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.8086 | 0.687711 | ||||||||
\(749\) | −74.5709 | −2.72476 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.2572 | −1.14059 | −0.570296 | − | 0.821439i | \(-0.693171\pi\) | ||||
−0.570296 | + | 0.821439i | \(0.693171\pi\) | |||||||
\(752\) | −8.47239 | −0.308956 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.07542 | 0.148418 | ||||||||
\(755\) | −0.663743 | −0.0241561 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.2245 | −0.807764 | −0.403882 | − | 0.914811i | \(-0.632339\pi\) | ||||
−0.403882 | + | 0.914811i | \(0.632339\pi\) | |||||||
\(758\) | −49.6668 | −1.80398 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0889410 | −0.00322623 | ||||||||
\(761\) | −29.5640 | −1.07170 | −0.535848 | − | 0.844314i | \(-0.680008\pi\) | ||||
−0.535848 | + | 0.844314i | \(0.680008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.3299 | −1.53245 | ||||||||
\(764\) | −1.74205 | −0.0630251 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.9168 | −0.972543 | ||||||||
\(767\) | −5.75070 | −0.207646 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.5926 | 1.13926 | 0.569628 | − | 0.821902i | \(-0.307087\pi\) | ||||
0.569628 | + | 0.821902i | \(0.307087\pi\) | |||||||
\(770\) | 1.71688 | 0.0618719 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 42.1844 | 1.51825 | ||||||||
\(773\) | −46.1914 | −1.66139 | −0.830694 | − | 0.556729i | \(-0.812056\pi\) | ||||
−0.830694 | + | 0.556729i | \(0.812056\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.5311 | −1.13263 | ||||||||
\(776\) | −15.8853 | −0.570249 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.5334 | 0.915418 | ||||||||
\(779\) | −0.345166 | −0.0123668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.0707 | −1.32650 | ||||||||
\(782\) | 4.97181 | 0.177791 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.98003 | −0.285001 | ||||||||
\(785\) | 0.417611 | 0.0149052 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.5553 | 0.447549 | 0.223775 | − | 0.974641i | \(-0.428162\pi\) | ||||
0.223775 | + | 0.974641i | \(0.428162\pi\) | |||||||
\(788\) | 13.5859 | 0.483978 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.81064 | −0.0644197 | ||||||||
\(791\) | 20.7617 | 0.738203 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.53925 | 0.0901713 | ||||||||
\(794\) | −55.9968 | −1.98725 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.8547 | −1.30628 | ||||||||
\(797\) | −44.8797 | −1.58972 | −0.794860 | − | 0.606793i | \(-0.792456\pi\) | ||||
−0.794860 | + | 0.606793i | \(0.792456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.5041 | −0.406987 | ||||||||
\(800\) | 34.7659 | 1.22916 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 65.1347 | 2.29999 | ||||||||
\(803\) | 7.77767 | 0.274468 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.269759 | 0.00950775 | ||||||||
\(806\) | −10.3202 | −0.363514 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −26.6215 | −0.936542 | ||||||||
\(809\) | −41.3567 | −1.45402 | −0.727011 | − | 0.686625i | \(-0.759091\pi\) | ||||
−0.727011 | + | 0.686625i | \(0.759091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.3830 | −1.69896 | −0.849479 | − | 0.527623i | \(-0.823083\pi\) | ||||
−0.849479 | + | 0.527623i | \(0.823083\pi\) | |||||||
\(812\) | 26.6130 | 0.933934 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.17663 | 0.321641 | ||||||||
\(815\) | 1.00376 | 0.0351602 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.63401 | 0.0921522 | ||||||||
\(818\) | 86.1574 | 3.01242 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0766167 | 0.00267557 | ||||||||
\(821\) | 36.0285 | 1.25740 | 0.628702 | − | 0.777647i | \(-0.283587\pi\) | ||||
0.628702 | + | 0.777647i | \(0.283587\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.4334 | 1.30484 | 0.652422 | − | 0.757856i | \(-0.273753\pi\) | ||||
0.652422 | + | 0.757856i | \(0.273753\pi\) | |||||||
\(824\) | −9.82161 | −0.342152 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −63.1777 | −2.19823 | ||||||||
\(827\) | −32.3428 | −1.12467 | −0.562335 | − | 0.826909i | \(-0.690097\pi\) | ||||
−0.562335 | + | 0.826909i | \(0.690097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6445 | 0.578087 | 0.289043 | − | 0.957316i | \(-0.406663\pi\) | ||||
0.289043 | + | 0.957316i | \(0.406663\pi\) | |||||||
\(830\) | 1.25858 | 0.0436860 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.50631 | 0.329572 | ||||||||
\(833\) | −10.8356 | −0.375431 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.174445 | 0.00603693 | ||||||||
\(836\) | 8.21207 | 0.284020 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 57.8702 | 1.99909 | ||||||||
\(839\) | 37.2541 | 1.28615 | 0.643077 | − | 0.765802i | \(-0.277658\pi\) | ||||
0.643077 | + | 0.765802i | \(0.277658\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7903 | −0.785873 | ||||||||
\(842\) | −26.0055 | −0.896210 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.5702 | 0.845741 | ||||||||
\(845\) | −0.711091 | −0.0244623 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.2706 | −0.352903 | ||||||||
\(848\) | −0.272911 | −0.00937181 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.1542 | 0.656984 | ||||||||
\(851\) | 1.44185 | 0.0494260 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.4165 | −1.55503 | −0.777515 | − | 0.628864i | \(-0.783520\pi\) | ||||
−0.777515 | + | 0.628864i | \(0.783520\pi\) | |||||||
\(854\) | 27.8964 | 0.954594 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.3082 | 1.44607 | ||||||||
\(857\) | 46.3601 | 1.58363 | 0.791815 | − | 0.610761i | \(-0.209137\pi\) | ||||
0.791815 | + | 0.610761i | \(0.209137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.7731 | −1.25468 | −0.627341 | − | 0.778745i | \(-0.715857\pi\) | ||||
−0.627341 | + | 0.778745i | \(0.715857\pi\) | |||||||
\(860\) | −0.584673 | −0.0199372 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.0709 | −1.46700 | ||||||||
\(863\) | −4.40567 | −0.149971 | −0.0749854 | − | 0.997185i | \(-0.523891\pi\) | ||||
−0.0749854 | + | 0.997185i | \(0.523891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.44134 | −0.0490070 | ||||||||
\(866\) | −7.92411 | −0.269272 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −67.3924 | −2.28745 | ||||||||
\(869\) | 53.1016 | 1.80135 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.47807 | 0.287269 | ||||||||
\(872\) | 24.0161 | 0.813289 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.17075 | 0.0734268 | ||||||||
\(875\) | 2.07921 | 0.0702900 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.8414 | 0.501158 | 0.250579 | − | 0.968096i | \(-0.419379\pi\) | ||||
0.250579 | + | 0.968096i | \(0.419379\pi\) | |||||||
\(878\) | 70.0567 | 2.36430 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.269767 | 0.00909385 | ||||||||
\(881\) | −17.1858 | −0.579003 | −0.289502 | − | 0.957178i | \(-0.593490\pi\) | ||||
−0.289502 | + | 0.957178i | \(0.593490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.2297 | −0.445216 | −0.222608 | − | 0.974908i | \(-0.571457\pi\) | ||||
−0.222608 | + | 0.974908i | \(0.571457\pi\) | |||||||
\(884\) | 3.72644 | 0.125334 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.82797 | −0.162199 | ||||||||
\(887\) | 24.0644 | 0.808002 | 0.404001 | − | 0.914759i | \(-0.367619\pi\) | ||||
0.404001 | + | 0.914759i | \(0.367619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.6792 | −0.358169 | ||||||||
\(890\) | −0.0558620 | −0.00187250 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.7724 | −0.461135 | ||||||||
\(893\) | −5.02284 | −0.168083 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.117311 | 0.00392127 | ||||||||
\(896\) | 53.7329 | 1.79509 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −73.8147 | −2.46323 | ||||||||
\(899\) | −15.7249 | −0.524453 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.370569 | −0.0123454 | ||||||||
\(902\) | −3.78025 | −0.125868 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.7793 | −0.391774 | ||||||||
\(905\) | −1.43810 | −0.0478041 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.6429 | −0.652233 | −0.326117 | − | 0.945330i | \(-0.605740\pi\) | ||||
−0.326117 | + | 0.945330i | \(0.605740\pi\) | |||||||
\(908\) | 33.1200 | 1.09913 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.340154 | 0.0112760 | ||||||||
\(911\) | −4.93178 | −0.163397 | −0.0816986 | − | 0.996657i | \(-0.526034\pi\) | ||||
−0.0816986 | + | 0.996657i | \(0.526034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.9111 | −1.22158 | ||||||||
\(914\) | −58.8582 | −1.94686 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.9195 | −0.625118 | ||||||||
\(917\) | 15.8318 | 0.522811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.26183 | 0.206559 | 0.103279 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103279 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(920\) | −0.153049 | −0.00504589 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 80.3799 | 2.64717 | ||||||||
\(923\) | −7.34460 | −0.241751 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.55482 | 0.182641 | ||||||||
\(926\) | 15.1616 | 0.498242 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 17.3381 | 0.569152 | ||||||||
\(929\) | −19.8755 | −0.652094 | −0.326047 | − | 0.945353i | \(-0.605717\pi\) | ||||
−0.326047 | + | 0.945353i | \(0.605717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.73095 | −0.155051 | ||||||||
\(932\) | 51.6775 | 1.69275 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −75.1760 | −2.45983 | ||||||||
\(935\) | 0.366300 | 0.0119793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.1857 | −0.528764 | −0.264382 | − | 0.964418i | \(-0.585168\pi\) | ||||
−0.264382 | + | 0.964418i | \(0.585168\pi\) | |||||||
\(938\) | 93.1408 | 3.04116 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.11493 | 0.0363649 | ||||||||
\(941\) | 26.8508 | 0.875310 | 0.437655 | − | 0.899143i | \(-0.355809\pi\) | ||||
0.437655 | + | 0.899143i | \(0.355809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.593960 | −0.0193420 | ||||||||
\(944\) | −9.92690 | −0.323093 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.8476 | 0.937916 | ||||||||
\(947\) | −18.3250 | −0.595481 | −0.297741 | − | 0.954647i | \(-0.596233\pi\) | ||||
−0.297741 | + | 0.954647i | \(0.596233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.54094 | 0.0500211 | ||||||||
\(950\) | 8.36297 | 0.271331 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.0035 | 0.421447 | ||||||||
\(953\) | 24.6170 | 0.797423 | 0.398711 | − | 0.917076i | \(-0.369458\pi\) | ||||
0.398711 | + | 0.917076i | \(0.369458\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0339266 | −0.00109784 | ||||||||
\(956\) | 2.93097 | 0.0947944 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.0822 | −0.584210 | ||||||||
\(959\) | −39.3616 | −1.27105 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.82019 | 0.284522 | ||||||||
\(962\) | 1.81811 | 0.0586183 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.91800 | −0.222814 | ||||||||
\(965\) | 0.821547 | 0.0264465 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.4790 | −1.84840 | −0.924200 | − | 0.381908i | \(-0.875267\pi\) | ||||
−0.924200 | + | 0.381908i | \(0.875267\pi\) | |||||||
\(968\) | 5.82710 | 0.187290 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.973981 | −0.0312726 | ||||||||
\(971\) | 10.4481 | 0.335295 | 0.167648 | − | 0.985847i | \(-0.446383\pi\) | ||||
0.167648 | + | 0.985847i | \(0.446383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.82345 | −0.186691 | ||||||||
\(974\) | −31.2969 | −1.00282 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.38326 | 0.140305 | ||||||||
\(977\) | 5.55962 | 0.177868 | 0.0889340 | − | 0.996038i | \(-0.471654\pi\) | ||||
0.0889340 | + | 0.996038i | \(0.471654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.63830 | 0.0523602 | ||||||||
\(980\) | 1.05013 | 0.0335453 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 67.7342 | 2.16148 | ||||||||
\(983\) | 20.8116 | 0.663787 | 0.331894 | − | 0.943317i | \(-0.392312\pi\) | ||||
0.331894 | + | 0.943317i | \(0.392312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.264587 | 0.00843044 | ||||||||
\(986\) | 9.55240 | 0.304210 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.62701 | 0.0517620 | ||||||||
\(989\) | 4.53259 | 0.144128 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.1881 | 1.78487 | 0.892437 | − | 0.451173i | \(-0.148994\pi\) | ||||
0.892437 | + | 0.451173i | \(0.148994\pi\) | |||||||
\(992\) | −43.9055 | −1.39400 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −80.6884 | −2.55928 | ||||||||
\(995\) | −0.717750 | −0.0227542 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.1483 | 1.36652 | 0.683261 | − | 0.730175i | \(-0.260561\pi\) | ||||
0.683261 | + | 0.730175i | \(0.260561\pi\) | |||||||
\(998\) | −34.6969 | −1.09831 | ||||||||
\(999\) | 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 | 2151.2.a.e.1.6 | 6 | ||
3.2 | odd | 2 | 717.2.a.d.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.2.a.d.1.1 | ✓ | 6 | 3.2 | odd | 2 | ||
2151.2.a.e.1.6 | 6 | 1.1 | even | 1 | trivial |