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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-1.38158\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38158 | 0.976925 | 0.488463 | − | 0.872585i | \(-0.337558\pi\) | ||||
0.488463 | + | 0.872585i | \(0.337558\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0912347 | −0.0456174 | ||||||||
\(5\) | 1.35155 | 0.604432 | 0.302216 | − | 0.953239i | \(-0.402274\pi\) | ||||
0.302216 | + | 0.953239i | \(0.402274\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50510 | −0.568876 | −0.284438 | − | 0.958695i | \(-0.591807\pi\) | ||||
−0.284438 | + | 0.958695i | \(0.591807\pi\) | |||||||
\(8\) | −2.88921 | −1.02149 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.86728 | 0.590485 | ||||||||
\(11\) | 5.20916 | 1.57062 | 0.785311 | − | 0.619102i | \(-0.212503\pi\) | ||||
0.785311 | + | 0.619102i | \(0.212503\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.03908 | −1.67494 | −0.837470 | − | 0.546483i | \(-0.815966\pi\) | ||||
−0.837470 | + | 0.546483i | \(0.815966\pi\) | |||||||
\(14\) | −2.07942 | −0.555749 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.80921 | −0.952302 | ||||||||
\(17\) | −2.23551 | −0.542191 | −0.271096 | − | 0.962552i | \(-0.587386\pi\) | ||||
−0.271096 | + | 0.962552i | \(0.587386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.35678 | −1.22893 | −0.614465 | − | 0.788944i | \(-0.710628\pi\) | ||||
−0.614465 | + | 0.788944i | \(0.710628\pi\) | |||||||
\(20\) | −0.123308 | −0.0275726 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.19688 | 1.53438 | ||||||||
\(23\) | −2.95682 | −0.616541 | −0.308270 | − | 0.951299i | \(-0.599750\pi\) | ||||
−0.308270 | + | 0.951299i | \(0.599750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.17331 | −0.634662 | ||||||||
\(26\) | −8.34348 | −1.63629 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.137318 | 0.0259506 | ||||||||
\(29\) | 0.529336 | 0.0982953 | 0.0491477 | − | 0.998792i | \(-0.484350\pi\) | ||||
0.0491477 | + | 0.998792i | \(0.484350\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.72398 | −0.668846 | −0.334423 | − | 0.942423i | \(-0.608541\pi\) | ||||
−0.334423 | + | 0.942423i | \(0.608541\pi\) | |||||||
\(32\) | 0.515693 | 0.0911624 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.08854 | −0.529680 | ||||||||
\(35\) | −2.03422 | −0.343847 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.79583 | 0.952829 | 0.476415 | − | 0.879221i | \(-0.341936\pi\) | ||||
0.476415 | + | 0.879221i | \(0.341936\pi\) | |||||||
\(38\) | −7.40083 | −1.20057 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.90492 | −0.617422 | ||||||||
\(41\) | 4.00191 | 0.624994 | 0.312497 | − | 0.949919i | \(-0.398835\pi\) | ||||
0.312497 | + | 0.949919i | \(0.398835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50457 | 0.686941 | 0.343470 | − | 0.939163i | \(-0.388397\pi\) | ||||
0.343470 | + | 0.939163i | \(0.388397\pi\) | |||||||
\(44\) | −0.475257 | −0.0716476 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.08509 | −0.602314 | ||||||||
\(47\) | −11.3720 | −1.65878 | −0.829388 | − | 0.558673i | \(-0.811311\pi\) | ||||
−0.829388 | + | 0.558673i | \(0.811311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.73466 | −0.676381 | ||||||||
\(50\) | −4.38418 | −0.620017 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.550974 | 0.0764064 | ||||||||
\(53\) | 8.22971 | 1.13044 | 0.565219 | − | 0.824941i | \(-0.308792\pi\) | ||||
0.565219 | + | 0.824941i | \(0.308792\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.04045 | 0.949335 | ||||||||
\(56\) | 4.34856 | 0.581101 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.731321 | 0.0960272 | ||||||||
\(59\) | −5.35349 | −0.696965 | −0.348482 | − | 0.937315i | \(-0.613303\pi\) | ||||
−0.348482 | + | 0.937315i | \(0.613303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0242 | −1.79562 | −0.897808 | − | 0.440386i | \(-0.854841\pi\) | ||||
−0.897808 | + | 0.440386i | \(0.854841\pi\) | |||||||
\(62\) | −5.14497 | −0.653412 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.33088 | 1.04136 | ||||||||
\(65\) | −8.16213 | −1.01239 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.35409 | −1.14278 | −0.571392 | − | 0.820677i | \(-0.693596\pi\) | ||||
−0.571392 | + | 0.820677i | \(0.693596\pi\) | |||||||
\(68\) | 0.203956 | 0.0247333 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.81045 | −0.335913 | ||||||||
\(71\) | 12.5000 | 1.48347 | 0.741736 | − | 0.670692i | \(-0.234003\pi\) | ||||
0.741736 | + | 0.670692i | \(0.234003\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4873 | 1.22745 | 0.613725 | − | 0.789520i | \(-0.289670\pi\) | ||||
0.613725 | + | 0.789520i | \(0.289670\pi\) | |||||||
\(74\) | 8.00741 | 0.930843 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.488725 | 0.0560606 | ||||||||
\(77\) | −7.84033 | −0.893488 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.72701 | −0.644339 | −0.322169 | − | 0.946682i | \(-0.604412\pi\) | ||||
−0.322169 | + | 0.946682i | \(0.604412\pi\) | |||||||
\(80\) | −5.14834 | −0.575602 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.52897 | 0.610572 | ||||||||
\(83\) | 4.70998 | 0.516987 | 0.258494 | − | 0.966013i | \(-0.416774\pi\) | ||||
0.258494 | + | 0.966013i | \(0.416774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.02141 | −0.327718 | ||||||||
\(86\) | 6.22343 | 0.671090 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.0504 | −1.60437 | ||||||||
\(89\) | −14.4107 | −1.52753 | −0.763766 | − | 0.645493i | \(-0.776652\pi\) | ||||
−0.763766 | + | 0.645493i | \(0.776652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.08944 | 0.952832 | ||||||||
\(92\) | 0.269765 | 0.0281250 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.7113 | −1.62050 | ||||||||
\(95\) | −7.23997 | −0.742805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.2286 | −1.24162 | −0.620812 | − | 0.783959i | \(-0.713197\pi\) | ||||
−0.620812 | + | 0.783959i | \(0.713197\pi\) | |||||||
\(98\) | −6.54132 | −0.660773 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.289516 | 0.0289516 | ||||||||
\(101\) | −13.1550 | −1.30897 | −0.654486 | − | 0.756074i | \(-0.727115\pi\) | ||||
−0.654486 | + | 0.756074i | \(0.727115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.79068 | 0.570572 | 0.285286 | − | 0.958442i | \(-0.407911\pi\) | ||||
0.285286 | + | 0.958442i | \(0.407911\pi\) | |||||||
\(104\) | 17.4482 | 1.71093 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.3700 | 1.10435 | ||||||||
\(107\) | −8.90040 | −0.860434 | −0.430217 | − | 0.902725i | \(-0.641563\pi\) | ||||
−0.430217 | + | 0.902725i | \(0.641563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.44148 | 0.904330 | 0.452165 | − | 0.891934i | \(-0.350652\pi\) | ||||
0.452165 | + | 0.891934i | \(0.350652\pi\) | |||||||
\(110\) | 9.72696 | 0.927429 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.73325 | 0.541741 | ||||||||
\(113\) | −0.0439495 | −0.00413442 | −0.00206721 | − | 0.999998i | \(-0.500658\pi\) | ||||
−0.00206721 | + | 0.999998i | \(0.500658\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.99630 | −0.372657 | ||||||||
\(116\) | −0.0482939 | −0.00448397 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.39628 | −0.680883 | ||||||||
\(119\) | 3.36468 | 0.308439 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.1354 | 1.46685 | ||||||||
\(122\) | −19.3756 | −1.75418 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.339756 | 0.0305110 | ||||||||
\(125\) | −11.0466 | −0.988042 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.52724 | 0.135520 | 0.0677602 | − | 0.997702i | \(-0.478415\pi\) | ||||
0.0677602 | + | 0.997702i | \(0.478415\pi\) | |||||||
\(128\) | 10.4784 | 0.926169 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.2766 | −0.989027 | ||||||||
\(131\) | −2.05574 | −0.179611 | −0.0898055 | − | 0.995959i | \(-0.528625\pi\) | ||||
−0.0898055 | + | 0.995959i | \(0.528625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.06251 | 0.699108 | ||||||||
\(134\) | −12.9234 | −1.11641 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.45886 | 0.553843 | ||||||||
\(137\) | −11.4680 | −0.979774 | −0.489887 | − | 0.871786i | \(-0.662962\pi\) | ||||
−0.489887 | + | 0.871786i | \(0.662962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4276 | −1.39337 | −0.696686 | − | 0.717376i | \(-0.745343\pi\) | ||||
−0.696686 | + | 0.717376i | \(0.745343\pi\) | |||||||
\(140\) | 0.185592 | 0.0156854 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.2697 | 1.44924 | ||||||||
\(143\) | −31.4586 | −2.63070 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.715426 | 0.0594129 | ||||||||
\(146\) | 14.4891 | 1.19913 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.528781 | −0.0434656 | ||||||||
\(149\) | −14.8822 | −1.21919 | −0.609597 | − | 0.792711i | \(-0.708669\pi\) | ||||
−0.609597 | + | 0.792711i | \(0.708669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5748 | 1.18608 | 0.593040 | − | 0.805173i | \(-0.297928\pi\) | ||||
0.593040 | + | 0.805173i | \(0.297928\pi\) | |||||||
\(152\) | 15.4769 | 1.25534 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.8320 | −0.872871 | ||||||||
\(155\) | −5.03315 | −0.404272 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.59395 | 0.286829 | 0.143414 | − | 0.989663i | \(-0.454192\pi\) | ||||
0.143414 | + | 0.989663i | \(0.454192\pi\) | |||||||
\(158\) | −7.91232 | −0.629471 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.696985 | 0.0551015 | ||||||||
\(161\) | 4.45033 | 0.350735 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5991 | 0.830188 | 0.415094 | − | 0.909779i | \(-0.363749\pi\) | ||||
0.415094 | + | 0.909779i | \(0.363749\pi\) | |||||||
\(164\) | −0.365113 | −0.0285106 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.50721 | 0.505058 | ||||||||
\(167\) | 20.8147 | 1.61069 | 0.805344 | − | 0.592808i | \(-0.201981\pi\) | ||||
0.805344 | + | 0.592808i | \(0.201981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.4705 | 1.80542 | ||||||||
\(170\) | −4.17432 | −0.320156 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.410973 | −0.0313364 | ||||||||
\(173\) | 15.4900 | 1.17768 | 0.588841 | − | 0.808249i | \(-0.299584\pi\) | ||||
0.588841 | + | 0.808249i | \(0.299584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.77616 | 0.361043 | ||||||||
\(176\) | −19.8428 | −1.49571 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.9096 | −1.49228 | ||||||||
\(179\) | −5.79634 | −0.433239 | −0.216619 | − | 0.976256i | \(-0.569503\pi\) | ||||
−0.216619 | + | 0.976256i | \(0.569503\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6304 | 1.31046 | 0.655230 | − | 0.755429i | \(-0.272572\pi\) | ||||
0.655230 | + | 0.755429i | \(0.272572\pi\) | |||||||
\(182\) | 12.5578 | 0.930846 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.54289 | 0.629790 | ||||||||
\(185\) | 7.83337 | 0.575921 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6451 | −0.851577 | ||||||||
\(188\) | 1.03752 | 0.0756690 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0026 | −0.725665 | ||||||||
\(191\) | 14.4507 | 1.04562 | 0.522810 | − | 0.852449i | \(-0.324884\pi\) | ||||
0.522810 | + | 0.852449i | \(0.324884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9861 | 1.22268 | 0.611342 | − | 0.791367i | \(-0.290630\pi\) | ||||
0.611342 | + | 0.791367i | \(0.290630\pi\) | |||||||
\(194\) | −16.8948 | −1.21297 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.431966 | 0.0308547 | ||||||||
\(197\) | 16.5500 | 1.17914 | 0.589571 | − | 0.807717i | \(-0.299297\pi\) | ||||
0.589571 | + | 0.807717i | \(0.299297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6857 | −1.53726 | −0.768631 | − | 0.639693i | \(-0.779062\pi\) | ||||
−0.768631 | + | 0.639693i | \(0.779062\pi\) | |||||||
\(200\) | 9.16835 | 0.648300 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.1747 | −1.27877 | ||||||||
\(203\) | −0.796706 | −0.0559178 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.40879 | 0.377767 | ||||||||
\(206\) | 8.00029 | 0.557406 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 23.0041 | 1.59505 | ||||||||
\(209\) | −27.9044 | −1.93018 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.61046 | −0.179711 | −0.0898556 | − | 0.995955i | \(-0.528641\pi\) | ||||
−0.0898556 | + | 0.995955i | \(0.528641\pi\) | |||||||
\(212\) | −0.750835 | −0.0515676 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.2966 | −0.840580 | ||||||||
\(215\) | 6.08816 | 0.415209 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.60497 | 0.380490 | ||||||||
\(218\) | 13.0442 | 0.883462 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.642334 | −0.0433061 | ||||||||
\(221\) | 13.5004 | 0.908138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8225 | 1.19348 | 0.596741 | − | 0.802434i | \(-0.296462\pi\) | ||||
0.596741 | + | 0.802434i | \(0.296462\pi\) | |||||||
\(224\) | −0.776170 | −0.0518601 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.0607198 | −0.00403902 | ||||||||
\(227\) | 4.02849 | 0.267380 | 0.133690 | − | 0.991023i | \(-0.457317\pi\) | ||||
0.133690 | + | 0.991023i | \(0.457317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.30206 | 0.218206 | 0.109103 | − | 0.994030i | \(-0.465202\pi\) | ||||
0.109103 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(230\) | −5.52121 | −0.364058 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.52936 | −0.100408 | ||||||||
\(233\) | 23.4736 | 1.53781 | 0.768904 | − | 0.639365i | \(-0.220803\pi\) | ||||
0.768904 | + | 0.639365i | \(0.220803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.3698 | −1.00262 | ||||||||
\(236\) | 0.488424 | 0.0317937 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.64857 | 0.301322 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.9690 | 1.09307 | 0.546534 | − | 0.837437i | \(-0.315947\pi\) | ||||
0.546534 | + | 0.837437i | \(0.315947\pi\) | |||||||
\(242\) | 22.2923 | 1.43301 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.27950 | 0.0819113 | ||||||||
\(245\) | −6.39914 | −0.408826 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.3501 | 2.05839 | ||||||||
\(248\) | 10.7593 | 0.683219 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.2618 | −0.965243 | ||||||||
\(251\) | −3.02008 | −0.190626 | −0.0953129 | − | 0.995447i | \(-0.530385\pi\) | ||||
−0.0953129 | + | 0.995447i | \(0.530385\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.4026 | −0.968352 | ||||||||
\(254\) | 2.11000 | 0.132393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.18501 | −0.136563 | ||||||||
\(257\) | −13.4671 | −0.840058 | −0.420029 | − | 0.907511i | \(-0.637980\pi\) | ||||
−0.420029 | + | 0.907511i | \(0.637980\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.72333 | −0.542041 | ||||||||
\(260\) | 0.744670 | 0.0461825 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.84017 | −0.175467 | ||||||||
\(263\) | −6.69271 | −0.412690 | −0.206345 | − | 0.978479i | \(-0.566157\pi\) | ||||
−0.206345 | + | 0.978479i | \(0.566157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.1229 | 0.683273 | ||||||||
\(266\) | 11.1390 | 0.682977 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.853418 | 0.0521308 | ||||||||
\(269\) | −23.4572 | −1.43021 | −0.715106 | − | 0.699016i | \(-0.753621\pi\) | ||||
−0.715106 | + | 0.699016i | \(0.753621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.79891 | 0.170022 | 0.0850108 | − | 0.996380i | \(-0.472908\pi\) | ||||
0.0850108 | + | 0.996380i | \(0.472908\pi\) | |||||||
\(272\) | 8.51553 | 0.516330 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.8439 | −0.957166 | ||||||||
\(275\) | −16.5303 | −0.996813 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.33556 | 0.0802459 | 0.0401230 | − | 0.999195i | \(-0.487225\pi\) | ||||
0.0401230 | + | 0.999195i | \(0.487225\pi\) | |||||||
\(278\) | −22.6961 | −1.36122 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.87730 | 0.351236 | ||||||||
\(281\) | −11.5507 | −0.689057 | −0.344529 | − | 0.938776i | \(-0.611961\pi\) | ||||
−0.344529 | + | 0.938776i | \(0.611961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6047 | 1.40315 | 0.701576 | − | 0.712595i | \(-0.252480\pi\) | ||||
0.701576 | + | 0.712595i | \(0.252480\pi\) | |||||||
\(284\) | −1.14043 | −0.0676721 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −43.4625 | −2.56999 | ||||||||
\(287\) | −6.02329 | −0.355544 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0025 | −0.706029 | ||||||||
\(290\) | 0.988418 | 0.0580419 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.956809 | −0.0559930 | ||||||||
\(293\) | −3.75303 | −0.219254 | −0.109627 | − | 0.993973i | \(-0.534966\pi\) | ||||
−0.109627 | + | 0.993973i | \(0.534966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.23552 | −0.421268 | ||||||||
\(296\) | −16.7454 | −0.973305 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.5609 | −1.19106 | ||||||||
\(299\) | 17.8565 | 1.03267 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.77985 | −0.390784 | ||||||||
\(302\) | 20.1362 | 1.15871 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.4051 | 1.17031 | ||||||||
\(305\) | −18.9545 | −1.08533 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.83405 | −0.104675 | −0.0523373 | − | 0.998629i | \(-0.516667\pi\) | ||||
−0.0523373 | + | 0.998629i | \(0.516667\pi\) | |||||||
\(308\) | 0.715310 | 0.0407586 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.95370 | −0.394943 | ||||||||
\(311\) | −23.0474 | −1.30690 | −0.653450 | − | 0.756970i | \(-0.726679\pi\) | ||||
−0.653450 | + | 0.756970i | \(0.726679\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.5384 | −0.708712 | −0.354356 | − | 0.935111i | \(-0.615300\pi\) | ||||
−0.354356 | + | 0.935111i | \(0.615300\pi\) | |||||||
\(314\) | 4.96533 | 0.280210 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.522502 | 0.0293930 | ||||||||
\(317\) | 5.42002 | 0.304419 | 0.152209 | − | 0.988348i | \(-0.451361\pi\) | ||||
0.152209 | + | 0.988348i | \(0.451361\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.75740 | 0.154385 | ||||||||
\(320\) | 11.2596 | 0.629432 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.14848 | 0.342642 | ||||||||
\(323\) | 11.9752 | 0.666315 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.1639 | 1.06302 | ||||||||
\(326\) | 14.6436 | 0.811031 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.5624 | −0.638425 | ||||||||
\(329\) | 17.1160 | 0.943637 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.7273 | −0.754523 | −0.377261 | − | 0.926107i | \(-0.623134\pi\) | ||||
−0.377261 | + | 0.926107i | \(0.623134\pi\) | |||||||
\(332\) | −0.429714 | −0.0235836 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.7572 | 1.57352 | ||||||||
\(335\) | −12.6425 | −0.690736 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7765 | −0.804926 | −0.402463 | − | 0.915436i | \(-0.631846\pi\) | ||||
−0.402463 | + | 0.915436i | \(0.631846\pi\) | |||||||
\(338\) | 32.4264 | 1.76376 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.275658 | 0.0149496 | ||||||||
\(341\) | −19.3988 | −1.05050 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6619 | 0.953652 | ||||||||
\(344\) | −13.0147 | −0.701703 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.4007 | 1.15051 | ||||||||
\(347\) | 9.24009 | 0.496034 | 0.248017 | − | 0.968756i | \(-0.420221\pi\) | ||||
0.248017 | + | 0.968756i | \(0.420221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.5592 | −1.79639 | −0.898193 | − | 0.439602i | \(-0.855119\pi\) | ||||
−0.898193 | + | 0.439602i | \(0.855119\pi\) | |||||||
\(350\) | 6.59864 | 0.352712 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.68633 | 0.143182 | ||||||||
\(353\) | −11.0743 | −0.589423 | −0.294712 | − | 0.955586i | \(-0.595224\pi\) | ||||
−0.294712 | + | 0.955586i | \(0.595224\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.8943 | 0.896658 | ||||||||
\(356\) | 1.31476 | 0.0696820 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.00811 | −0.423242 | ||||||||
\(359\) | 10.6761 | 0.563464 | 0.281732 | − | 0.959493i | \(-0.409091\pi\) | ||||
0.281732 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.69513 | 0.510270 | ||||||||
\(362\) | 24.3579 | 1.28022 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.829273 | −0.0434657 | ||||||||
\(365\) | 14.1742 | 0.741910 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.7721 | 1.08430 | 0.542148 | − | 0.840283i | \(-0.317611\pi\) | ||||
0.542148 | + | 0.840283i | \(0.317611\pi\) | |||||||
\(368\) | 11.2632 | 0.587133 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.8224 | 0.562631 | ||||||||
\(371\) | −12.3866 | −0.643078 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.5360 | −1.94354 | −0.971770 | − | 0.235931i | \(-0.924186\pi\) | ||||
−0.971770 | + | 0.235931i | \(0.924186\pi\) | |||||||
\(374\) | −16.0887 | −0.831927 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.8561 | 1.69442 | ||||||||
\(377\) | −3.19671 | −0.164639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7017 | −0.755174 | −0.377587 | − | 0.925974i | \(-0.623246\pi\) | ||||
−0.377587 | + | 0.925974i | \(0.623246\pi\) | |||||||
\(380\) | 0.660537 | 0.0338848 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.9649 | 1.02149 | ||||||||
\(383\) | 1.17130 | 0.0598507 | 0.0299253 | − | 0.999552i | \(-0.490473\pi\) | ||||
0.0299253 | + | 0.999552i | \(0.490473\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5966 | −0.540053 | ||||||||
\(386\) | 23.4676 | 1.19447 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.11567 | 0.0566396 | ||||||||
\(389\) | 34.5061 | 1.74953 | 0.874766 | − | 0.484546i | \(-0.161015\pi\) | ||||
0.874766 | + | 0.484546i | \(0.161015\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.61002 | 0.334283 | ||||||||
\(392\) | 13.6794 | 0.690916 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.8652 | 1.15193 | ||||||||
\(395\) | −7.74035 | −0.389459 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.05365 | 0.153258 | 0.0766292 | − | 0.997060i | \(-0.475584\pi\) | ||||
0.0766292 | + | 0.997060i | \(0.475584\pi\) | |||||||
\(398\) | −29.9606 | −1.50179 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.0878 | 0.604389 | ||||||||
\(401\) | −21.5513 | −1.07622 | −0.538109 | − | 0.842875i | \(-0.680861\pi\) | ||||
−0.538109 | + | 0.842875i | \(0.680861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.4894 | 1.12028 | ||||||||
\(404\) | 1.20019 | 0.0597118 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.10071 | −0.0546275 | ||||||||
\(407\) | 30.1914 | 1.49653 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.09326 | −0.103505 | −0.0517526 | − | 0.998660i | \(-0.516481\pi\) | ||||
−0.0517526 | + | 0.998660i | \(0.516481\pi\) | |||||||
\(410\) | 7.47268 | 0.369050 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.528311 | −0.0260280 | ||||||||
\(413\) | 8.05755 | 0.396486 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.36578 | 0.312484 | ||||||||
\(416\) | −3.11431 | −0.152692 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −38.5521 | −1.88565 | ||||||||
\(419\) | 4.55800 | 0.222673 | 0.111336 | − | 0.993783i | \(-0.464487\pi\) | ||||
0.111336 | + | 0.993783i | \(0.464487\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.1765 | 1.51945 | 0.759724 | − | 0.650245i | \(-0.225334\pi\) | ||||
0.759724 | + | 0.650245i | \(0.225334\pi\) | |||||||
\(422\) | −3.60656 | −0.175564 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −23.7774 | −1.15473 | ||||||||
\(425\) | 7.09397 | 0.344108 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.1079 | 1.02148 | ||||||||
\(428\) | 0.812026 | 0.0392507 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.41129 | 0.405628 | ||||||||
\(431\) | −6.08401 | −0.293056 | −0.146528 | − | 0.989206i | \(-0.546810\pi\) | ||||
−0.146528 | + | 0.989206i | \(0.546810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.69823 | 0.369953 | 0.184977 | − | 0.982743i | \(-0.440779\pi\) | ||||
0.184977 | + | 0.982743i | \(0.440779\pi\) | |||||||
\(434\) | 7.74371 | 0.371710 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.861391 | −0.0412531 | ||||||||
\(437\) | 15.8391 | 0.757686 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.9627 | −0.570950 | −0.285475 | − | 0.958386i | \(-0.592151\pi\) | ||||
−0.285475 | + | 0.958386i | \(0.592151\pi\) | |||||||
\(440\) | −20.3413 | −0.969736 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.6520 | 0.887183 | ||||||||
\(443\) | 33.6798 | 1.60017 | 0.800087 | − | 0.599884i | \(-0.204787\pi\) | ||||
0.800087 | + | 0.599884i | \(0.204787\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.4768 | −0.923290 | ||||||||
\(446\) | 24.6232 | 1.16594 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.5388 | −0.592405 | ||||||||
\(449\) | −8.14181 | −0.384236 | −0.192118 | − | 0.981372i | \(-0.561536\pi\) | ||||
−0.192118 | + | 0.981372i | \(0.561536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.8466 | 0.981629 | ||||||||
\(452\) | 0.00400972 | 0.000188601 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.56569 | 0.261211 | ||||||||
\(455\) | 12.2849 | 0.575923 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.2011 | −0.851411 | −0.425705 | − | 0.904862i | \(-0.639974\pi\) | ||||
−0.425705 | + | 0.904862i | \(0.639974\pi\) | |||||||
\(458\) | 4.56206 | 0.213171 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.364602 | 0.0169996 | ||||||||
\(461\) | −35.8143 | −1.66804 | −0.834018 | − | 0.551737i | \(-0.813965\pi\) | ||||
−0.834018 | + | 0.551737i | \(0.813965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6283 | 0.819255 | 0.409628 | − | 0.912253i | \(-0.365659\pi\) | ||||
0.409628 | + | 0.912253i | \(0.365659\pi\) | |||||||
\(464\) | −2.01635 | −0.0936068 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.4307 | 1.50232 | ||||||||
\(467\) | 35.8370 | 1.65834 | 0.829169 | − | 0.558999i | \(-0.188814\pi\) | ||||
0.829169 | + | 0.558999i | \(0.188814\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0789 | 0.650102 | ||||||||
\(470\) | −21.2347 | −0.979482 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.4674 | 0.711943 | ||||||||
\(473\) | 23.4651 | 1.07892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9987 | 0.779955 | ||||||||
\(476\) | −0.306975 | −0.0140702 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.38158 | −0.0631920 | ||||||||
\(479\) | 18.6108 | 0.850351 | 0.425176 | − | 0.905111i | \(-0.360212\pi\) | ||||
0.425176 | + | 0.905111i | \(0.360212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.0015 | −1.59593 | ||||||||
\(482\) | 23.4440 | 1.06785 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.47211 | −0.0669139 | ||||||||
\(485\) | −16.5276 | −0.750478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.7084 | 0.621187 | 0.310594 | − | 0.950543i | \(-0.399472\pi\) | ||||
0.310594 | + | 0.950543i | \(0.399472\pi\) | |||||||
\(488\) | 40.5189 | 1.83420 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.84093 | −0.399393 | ||||||||
\(491\) | −26.8768 | −1.21293 | −0.606466 | − | 0.795109i | \(-0.707413\pi\) | ||||
−0.606466 | + | 0.795109i | \(0.707413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.18334 | −0.0532949 | ||||||||
\(494\) | 44.6942 | 2.01089 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.1854 | 0.636943 | ||||||||
\(497\) | −18.8137 | −0.843911 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.7292 | −1.59946 | −0.799729 | − | 0.600361i | \(-0.795024\pi\) | ||||
−0.799729 | + | 0.600361i | \(0.795024\pi\) | |||||||
\(500\) | 1.00784 | 0.0450719 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.17249 | −0.186227 | ||||||||
\(503\) | 26.3328 | 1.17412 | 0.587062 | − | 0.809542i | \(-0.300285\pi\) | ||||
0.587062 | + | 0.809542i | \(0.300285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.7797 | −0.791185 | ||||||||
\(506\) | −21.2799 | −0.946007 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.139337 | −0.00618209 | ||||||||
\(509\) | 42.2347 | 1.87202 | 0.936011 | − | 0.351972i | \(-0.114489\pi\) | ||||
0.936011 | + | 0.351972i | \(0.114489\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.7845 | −0.698266 | ||||||||
\(512\) | −23.9756 | −1.05958 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.6060 | −0.820673 | ||||||||
\(515\) | 7.82640 | 0.344872 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −59.2386 | −2.60531 | ||||||||
\(518\) | −12.0520 | −0.529534 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.5821 | 1.03414 | ||||||||
\(521\) | −13.8354 | −0.606142 | −0.303071 | − | 0.952968i | \(-0.598012\pi\) | ||||
−0.303071 | + | 0.952968i | \(0.598012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.9910 | −1.00533 | −0.502663 | − | 0.864483i | \(-0.667646\pi\) | ||||
−0.502663 | + | 0.864483i | \(0.667646\pi\) | |||||||
\(524\) | 0.187555 | 0.00819338 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.24652 | −0.403167 | ||||||||
\(527\) | 8.32499 | 0.362642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.2572 | −0.619878 | ||||||||
\(530\) | 15.3672 | 0.667507 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.735581 | −0.0318915 | ||||||||
\(533\) | −24.1679 | −1.04683 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0294 | −0.520074 | ||||||||
\(536\) | 27.0259 | 1.16734 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −32.4080 | −1.39721 | ||||||||
\(539\) | −24.6636 | −1.06234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.7557 | −1.79522 | −0.897610 | − | 0.440791i | \(-0.854698\pi\) | ||||
−0.897610 | + | 0.440791i | \(0.854698\pi\) | |||||||
\(542\) | 3.86692 | 0.166098 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.15284 | −0.0494275 | ||||||||
\(545\) | 12.7606 | 0.546606 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.2023 | −1.41963 | −0.709814 | − | 0.704389i | \(-0.751221\pi\) | ||||
−0.709814 | + | 0.704389i | \(0.751221\pi\) | |||||||
\(548\) | 1.04628 | 0.0446947 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.8379 | −0.973812 | ||||||||
\(551\) | −2.83554 | −0.120798 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.61974 | 0.366549 | ||||||||
\(554\) | 1.84518 | 0.0783943 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.49877 | 0.0635620 | ||||||||
\(557\) | −25.6256 | −1.08579 | −0.542895 | − | 0.839800i | \(-0.682672\pi\) | ||||
−0.542895 | + | 0.839800i | \(0.682672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.2035 | −1.15058 | ||||||||
\(560\) | 7.74878 | 0.327446 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.9582 | −0.673157 | ||||||||
\(563\) | −8.59177 | −0.362100 | −0.181050 | − | 0.983474i | \(-0.557950\pi\) | ||||
−0.181050 | + | 0.983474i | \(0.557950\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0594000 | −0.00249898 | ||||||||
\(566\) | 32.6118 | 1.37077 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −36.1150 | −1.51535 | ||||||||
\(569\) | 2.27120 | 0.0952138 | 0.0476069 | − | 0.998866i | \(-0.484841\pi\) | ||||
0.0476069 | + | 0.998866i | \(0.484841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3368 | −1.60434 | −0.802172 | − | 0.597093i | \(-0.796322\pi\) | ||||
−0.802172 | + | 0.597093i | \(0.796322\pi\) | |||||||
\(572\) | 2.87011 | 0.120005 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.32166 | −0.347340 | ||||||||
\(575\) | 9.38291 | 0.391295 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0162 | 0.916547 | 0.458274 | − | 0.888811i | \(-0.348468\pi\) | ||||
0.458274 | + | 0.888811i | \(0.348468\pi\) | |||||||
\(578\) | −16.5824 | −0.689737 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.0652717 | −0.00271026 | ||||||||
\(581\) | −7.08900 | −0.294101 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.8699 | 1.77549 | ||||||||
\(584\) | −30.3001 | −1.25383 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.18511 | −0.214195 | ||||||||
\(587\) | 28.8423 | 1.19045 | 0.595224 | − | 0.803560i | \(-0.297063\pi\) | ||||
0.595224 | + | 0.803560i | \(0.297063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.9485 | 0.821965 | ||||||||
\(590\) | −9.99645 | −0.411547 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.0775 | −0.907381 | ||||||||
\(593\) | −10.5494 | −0.433213 | −0.216607 | − | 0.976259i | \(-0.569499\pi\) | ||||
−0.216607 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.54753 | 0.186431 | ||||||||
\(596\) | 1.35777 | 0.0556164 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.6702 | 1.00884 | ||||||||
\(599\) | 7.21520 | 0.294805 | 0.147403 | − | 0.989077i | \(-0.452909\pi\) | ||||
0.147403 | + | 0.989077i | \(0.452909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0334 | 0.980344 | 0.490172 | − | 0.871626i | \(-0.336934\pi\) | ||||
0.490172 | + | 0.871626i | \(0.336934\pi\) | |||||||
\(602\) | −9.36690 | −0.381767 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.32973 | −0.0541058 | ||||||||
\(605\) | 21.8078 | 0.886613 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.5172 | 0.711001 | 0.355500 | − | 0.934676i | \(-0.384310\pi\) | ||||
0.355500 | + | 0.934676i | \(0.384310\pi\) | |||||||
\(608\) | −2.76245 | −0.112032 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26.1871 | −1.06029 | ||||||||
\(611\) | 68.6764 | 2.77835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5816 | 0.952453 | 0.476226 | − | 0.879323i | \(-0.342004\pi\) | ||||
0.476226 | + | 0.879323i | \(0.342004\pi\) | |||||||
\(614\) | −2.53388 | −0.102259 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.6523 | 0.912689 | ||||||||
\(617\) | −26.2668 | −1.05746 | −0.528731 | − | 0.848789i | \(-0.677332\pi\) | ||||
−0.528731 | + | 0.848789i | \(0.677332\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7447 | −0.472060 | −0.236030 | − | 0.971746i | \(-0.575846\pi\) | ||||
−0.236030 | + | 0.971746i | \(0.575846\pi\) | |||||||
\(620\) | 0.459198 | 0.0184418 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.8419 | −1.27674 | ||||||||
\(623\) | 21.6896 | 0.868975 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.936418 | 0.0374567 | ||||||||
\(626\) | −17.3228 | −0.692359 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.327893 | −0.0130844 | ||||||||
\(629\) | −12.9567 | −0.516616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.30347 | 0.131509 | 0.0657545 | − | 0.997836i | \(-0.479055\pi\) | ||||
0.0657545 | + | 0.997836i | \(0.479055\pi\) | |||||||
\(632\) | 16.5465 | 0.658186 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.48820 | 0.297394 | ||||||||
\(635\) | 2.06414 | 0.0819129 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.5930 | 1.13290 | ||||||||
\(638\) | 3.80957 | 0.150822 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.1621 | 0.559806 | ||||||||
\(641\) | −25.9601 | −1.02536 | −0.512680 | − | 0.858580i | \(-0.671347\pi\) | ||||
−0.512680 | + | 0.858580i | \(0.671347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.7989 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(644\) | −0.406024 | −0.0159996 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.5446 | 0.650940 | ||||||||
\(647\) | 35.1636 | 1.38242 | 0.691211 | − | 0.722653i | \(-0.257077\pi\) | ||||
0.691211 | + | 0.722653i | \(0.257077\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.8872 | −1.09467 | ||||||||
\(650\) | 26.4764 | 1.03849 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.967009 | −0.0378710 | ||||||||
\(653\) | −43.2533 | −1.69263 | −0.846316 | − | 0.532681i | \(-0.821184\pi\) | ||||
−0.846316 | + | 0.532681i | \(0.821184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.77844 | −0.108563 | ||||||||
\(656\) | −15.2441 | −0.595183 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23.6472 | 0.921863 | ||||||||
\(659\) | −20.3893 | −0.794256 | −0.397128 | − | 0.917763i | \(-0.629993\pi\) | ||||
−0.397128 | + | 0.917763i | \(0.629993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.5166 | −1.61481 | −0.807404 | − | 0.589999i | \(-0.799128\pi\) | ||||
−0.807404 | + | 0.589999i | \(0.799128\pi\) | |||||||
\(662\) | −18.9654 | −0.737112 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.6081 | −0.528097 | ||||||||
\(665\) | 10.8969 | 0.422564 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.56516 | −0.0606031 | ||||||||
\(668\) | −1.89902 | −0.0734754 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.4667 | −0.674797 | ||||||||
\(671\) | −73.0544 | −2.82023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.0303 | −1.11903 | −0.559517 | − | 0.828819i | \(-0.689013\pi\) | ||||
−0.559517 | + | 0.828819i | \(0.689013\pi\) | |||||||
\(674\) | −20.4149 | −0.786352 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.14133 | −0.0823587 | ||||||||
\(677\) | 13.5700 | 0.521539 | 0.260769 | − | 0.965401i | \(-0.416024\pi\) | ||||
0.260769 | + | 0.965401i | \(0.416024\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4053 | 0.706330 | ||||||||
\(680\) | 8.72949 | 0.334761 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −26.8010 | −1.02626 | ||||||||
\(683\) | −42.1926 | −1.61446 | −0.807228 | − | 0.590240i | \(-0.799033\pi\) | ||||
−0.807228 | + | 0.590240i | \(0.799033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.4995 | −0.592207 | ||||||||
\(686\) | 24.4013 | 0.931646 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.1588 | −0.654175 | ||||||||
\(689\) | −49.6999 | −1.89342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.0952 | 1.63942 | 0.819709 | − | 0.572781i | \(-0.194135\pi\) | ||||
0.819709 | + | 0.572781i | \(0.194135\pi\) | |||||||
\(692\) | −1.41322 | −0.0537227 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.7659 | 0.484588 | ||||||||
\(695\) | −22.2028 | −0.842199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.94633 | −0.338866 | ||||||||
\(698\) | −46.3648 | −1.75493 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.435751 | −0.0164698 | ||||||||
\(701\) | 47.5830 | 1.79718 | 0.898592 | − | 0.438785i | \(-0.144591\pi\) | ||||
0.898592 | + | 0.438785i | \(0.144591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.0470 | −1.17096 | ||||||||
\(704\) | 43.3969 | 1.63558 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.3000 | −0.575822 | ||||||||
\(707\) | 19.7996 | 0.744642 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00508 | 0.300637 | 0.150319 | − | 0.988638i | \(-0.451970\pi\) | ||||
0.150319 | + | 0.988638i | \(0.451970\pi\) | |||||||
\(710\) | 23.3409 | 0.875968 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 41.6355 | 1.56036 | ||||||||
\(713\) | 11.0111 | 0.412371 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.5179 | −1.59008 | ||||||||
\(716\) | 0.528827 | 0.0197632 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.7499 | 0.550462 | ||||||||
\(719\) | −3.65160 | −0.136182 | −0.0680908 | − | 0.997679i | \(-0.521691\pi\) | ||||
−0.0680908 | + | 0.997679i | \(0.521691\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.71556 | −0.324585 | ||||||||
\(722\) | 13.3946 | 0.498496 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.60851 | −0.0597798 | ||||||||
\(725\) | −1.67975 | −0.0623843 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.3105 | 0.679100 | 0.339550 | − | 0.940588i | \(-0.389725\pi\) | ||||
0.339550 | + | 0.940588i | \(0.389725\pi\) | |||||||
\(728\) | −26.2613 | −0.973309 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.5828 | 0.724791 | ||||||||
\(731\) | −10.0700 | −0.372453 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.3607 | 1.67543 | 0.837717 | − | 0.546104i | \(-0.183890\pi\) | ||||
0.837717 | + | 0.546104i | \(0.183890\pi\) | |||||||
\(734\) | 28.6983 | 1.05928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.52481 | −0.0562053 | ||||||||
\(737\) | −48.7270 | −1.79488 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.4799 | 1.23158 | 0.615790 | − | 0.787911i | \(-0.288837\pi\) | ||||
0.615790 | + | 0.787911i | \(0.288837\pi\) | |||||||
\(740\) | −0.714675 | −0.0262720 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.1130 | −0.628239 | ||||||||
\(743\) | 13.6930 | 0.502348 | 0.251174 | − | 0.967942i | \(-0.419183\pi\) | ||||
0.251174 | + | 0.967942i | \(0.419183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.1140 | −0.736921 | ||||||||
\(746\) | −51.8590 | −1.89869 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.06244 | 0.0388467 | ||||||||
\(749\) | 13.3960 | 0.489480 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.4062 | −1.00007 | −0.500034 | − | 0.866006i | \(-0.666679\pi\) | ||||
−0.500034 | + | 0.866006i | \(0.666679\pi\) | |||||||
\(752\) | 43.3183 | 1.57965 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.41651 | −0.160840 | ||||||||
\(755\) | 19.6986 | 0.716905 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.98983 | −0.363087 | −0.181543 | − | 0.983383i | \(-0.558109\pi\) | ||||
−0.181543 | + | 0.983383i | \(0.558109\pi\) | |||||||
\(758\) | −20.3116 | −0.737749 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.9178 | 0.758768 | ||||||||
\(761\) | −38.8553 | −1.40851 | −0.704253 | − | 0.709949i | \(-0.748718\pi\) | ||||
−0.704253 | + | 0.709949i | \(0.748718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.2104 | −0.514451 | ||||||||
\(764\) | −1.31841 | −0.0476984 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.61825 | 0.0584696 | ||||||||
\(767\) | 32.3302 | 1.16737 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.8198 | 0.714720 | 0.357360 | − | 0.933967i | \(-0.383677\pi\) | ||||
0.357360 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(770\) | −14.6401 | −0.527592 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.54972 | −0.0557756 | ||||||||
\(773\) | −29.0662 | −1.04544 | −0.522720 | − | 0.852505i | \(-0.675083\pi\) | ||||
−0.522720 | + | 0.852505i | \(0.675083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.8173 | 0.424491 | ||||||||
\(776\) | 35.3309 | 1.26831 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 47.6730 | 1.70916 | ||||||||
\(779\) | −21.4374 | −0.768074 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 65.1143 | 2.32997 | ||||||||
\(782\) | 9.13227 | 0.326569 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.0353 | 0.644118 | ||||||||
\(785\) | 4.85741 | 0.173368 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4799 | −1.44295 | −0.721476 | − | 0.692440i | \(-0.756536\pi\) | ||||
−0.721476 | + | 0.692440i | \(0.756536\pi\) | |||||||
\(788\) | −1.50994 | −0.0537893 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.6939 | −0.380472 | ||||||||
\(791\) | 0.0661485 | 0.00235197 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 84.6934 | 3.00755 | ||||||||
\(794\) | 4.21886 | 0.149722 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.97849 | 0.0701258 | ||||||||
\(797\) | −11.4938 | −0.407132 | −0.203566 | − | 0.979061i | \(-0.565253\pi\) | ||||
−0.203566 | + | 0.979061i | \(0.565253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4222 | 0.899374 | ||||||||
\(800\) | −1.63645 | −0.0578573 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29.7748 | −1.05139 | ||||||||
\(803\) | 54.6302 | 1.92786 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.01485 | 0.211995 | ||||||||
\(806\) | 31.0709 | 1.09443 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 38.0076 | 1.33710 | ||||||||
\(809\) | −51.3120 | −1.80403 | −0.902016 | − | 0.431702i | \(-0.857913\pi\) | ||||
−0.902016 | + | 0.431702i | \(0.857913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.5242 | 1.14208 | 0.571040 | − | 0.820922i | \(-0.306540\pi\) | ||||
0.571040 | + | 0.820922i | \(0.306540\pi\) | |||||||
\(812\) | 0.0726873 | 0.00255082 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 41.7119 | 1.46200 | ||||||||
\(815\) | 14.3253 | 0.501792 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.1300 | −0.844203 | ||||||||
\(818\) | −2.89201 | −0.101117 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.493470 | −0.0172327 | ||||||||
\(821\) | −11.2602 | −0.392983 | −0.196492 | − | 0.980506i | \(-0.562955\pi\) | ||||
−0.196492 | + | 0.980506i | \(0.562955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.83791 | −0.133781 | −0.0668906 | − | 0.997760i | \(-0.521308\pi\) | ||||
−0.0668906 | + | 0.997760i | \(0.521308\pi\) | |||||||
\(824\) | −16.7305 | −0.582834 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.1322 | 0.387337 | ||||||||
\(827\) | 22.1887 | 0.771577 | 0.385788 | − | 0.922587i | \(-0.373930\pi\) | ||||
0.385788 | + | 0.922587i | \(0.373930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.6872 | −0.440645 | −0.220323 | − | 0.975427i | \(-0.570711\pi\) | ||||
−0.220323 | + | 0.975427i | \(0.570711\pi\) | |||||||
\(830\) | 8.79484 | 0.305273 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −50.3109 | −1.74422 | ||||||||
\(833\) | 10.5844 | 0.366728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.1321 | 0.973552 | ||||||||
\(836\) | 2.54585 | 0.0880499 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.29725 | 0.217535 | ||||||||
\(839\) | 31.9752 | 1.10391 | 0.551953 | − | 0.833875i | \(-0.313883\pi\) | ||||
0.551953 | + | 0.833875i | \(0.313883\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7198 | −0.990338 | ||||||||
\(842\) | 43.0728 | 1.48439 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.238164 | 0.00819795 | ||||||||
\(845\) | 31.7216 | 1.09126 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.2854 | −0.834457 | ||||||||
\(848\) | −31.3487 | −1.07652 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.80089 | 0.336168 | ||||||||
\(851\) | −17.1373 | −0.587458 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.1065 | −1.06507 | −0.532533 | − | 0.846409i | \(-0.678760\pi\) | ||||
−0.532533 | + | 0.846409i | \(0.678760\pi\) | |||||||
\(854\) | 29.1623 | 0.997912 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.7151 | 0.878925 | ||||||||
\(857\) | 11.3097 | 0.386333 | 0.193166 | − | 0.981166i | \(-0.438124\pi\) | ||||
0.193166 | + | 0.981166i | \(0.438124\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.1279 | 1.09619 | 0.548095 | − | 0.836416i | \(-0.315353\pi\) | ||||
0.548095 | + | 0.836416i | \(0.315353\pi\) | |||||||
\(860\) | −0.555452 | −0.0189408 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.40555 | −0.286294 | ||||||||
\(863\) | 15.1014 | 0.514056 | 0.257028 | − | 0.966404i | \(-0.417257\pi\) | ||||
0.257028 | + | 0.966404i | \(0.417257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.9355 | 0.711829 | ||||||||
\(866\) | 10.6357 | 0.361416 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.511368 | −0.0173569 | ||||||||
\(869\) | −29.8329 | −1.01201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.4901 | 1.91410 | ||||||||
\(872\) | −27.2784 | −0.923764 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21.8830 | 0.740202 | ||||||||
\(875\) | 16.6263 | 0.562073 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.9980 | −1.28310 | −0.641551 | − | 0.767080i | \(-0.721709\pi\) | ||||
−0.641551 | + | 0.767080i | \(0.721709\pi\) | |||||||
\(878\) | −16.5275 | −0.557775 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −26.8185 | −0.904053 | ||||||||
\(881\) | −31.7883 | −1.07097 | −0.535487 | − | 0.844543i | \(-0.679872\pi\) | ||||
−0.535487 | + | 0.844543i | \(0.679872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7099 | −1.06712 | −0.533562 | − | 0.845761i | \(-0.679147\pi\) | ||||
−0.533562 | + | 0.845761i | \(0.679147\pi\) | |||||||
\(884\) | −1.23171 | −0.0414269 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.5313 | 1.56325 | ||||||||
\(887\) | −3.92551 | −0.131806 | −0.0659029 | − | 0.997826i | \(-0.520993\pi\) | ||||
−0.0659029 | + | 0.997826i | \(0.520993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.29865 | −0.0770943 | ||||||||
\(890\) | −26.9088 | −0.901985 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.62603 | −0.0544435 | ||||||||
\(893\) | 60.9173 | 2.03852 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.83405 | −0.261863 | ||||||||
\(896\) | −15.7711 | −0.526875 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.2486 | −0.375370 | ||||||||
\(899\) | −1.97124 | −0.0657444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.3976 | −0.612914 | ||||||||
\(902\) | 28.8013 | 0.958978 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.126979 | 0.00422327 | ||||||||
\(905\) | 23.8285 | 0.792085 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.1647 | 1.23403 | 0.617016 | − | 0.786950i | \(-0.288341\pi\) | ||||
0.617016 | + | 0.786950i | \(0.288341\pi\) | |||||||
\(908\) | −0.367538 | −0.0121972 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.9725 | 0.562633 | ||||||||
\(911\) | −15.0959 | −0.500151 | −0.250075 | − | 0.968226i | \(-0.580455\pi\) | ||||
−0.250075 | + | 0.968226i | \(0.580455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.5350 | 0.811991 | ||||||||
\(914\) | −25.1463 | −0.831765 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.301262 | −0.00995399 | ||||||||
\(917\) | 3.09410 | 0.102176 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.8896 | −0.590123 | −0.295062 | − | 0.955478i | \(-0.595340\pi\) | ||||
−0.295062 | + | 0.955478i | \(0.595340\pi\) | |||||||
\(920\) | 11.5462 | 0.380665 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −49.4803 | −1.62955 | ||||||||
\(923\) | −75.4883 | −2.48473 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.3920 | −0.604724 | ||||||||
\(926\) | 24.3549 | 0.800351 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.272975 | 0.00896084 | ||||||||
\(929\) | −32.0444 | −1.05134 | −0.525671 | − | 0.850688i | \(-0.676186\pi\) | ||||
−0.525671 | + | 0.850688i | \(0.676186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.3626 | 0.831225 | ||||||||
\(932\) | −2.14161 | −0.0701507 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 49.5117 | 1.62007 | ||||||||
\(935\) | −15.7390 | −0.514721 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.6221 | 0.379677 | 0.189839 | − | 0.981815i | \(-0.439204\pi\) | ||||
0.189839 | + | 0.981815i | \(0.439204\pi\) | |||||||
\(938\) | 19.4511 | 0.635101 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.40226 | 0.0457368 | ||||||||
\(941\) | 4.15109 | 0.135322 | 0.0676608 | − | 0.997708i | \(-0.478446\pi\) | ||||
0.0676608 | + | 0.997708i | \(0.478446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.8330 | −0.385334 | ||||||||
\(944\) | 20.3925 | 0.663721 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.4189 | 1.05403 | ||||||||
\(947\) | 7.73026 | 0.251200 | 0.125600 | − | 0.992081i | \(-0.459914\pi\) | ||||
0.125600 | + | 0.992081i | \(0.459914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.3339 | −2.05590 | ||||||||
\(950\) | 23.4851 | 0.761957 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.72126 | −0.315068 | ||||||||
\(953\) | −40.5116 | −1.31230 | −0.656149 | − | 0.754631i | \(-0.727816\pi\) | ||||
−0.656149 | + | 0.754631i | \(0.727816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5309 | 0.632006 | ||||||||
\(956\) | 0.0912347 | 0.00295074 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.7124 | 0.830729 | ||||||||
\(959\) | 17.2605 | 0.557370 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.1320 | −0.552645 | ||||||||
\(962\) | −48.3574 | −1.55911 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.54816 | −0.0498629 | ||||||||
\(965\) | 22.9575 | 0.739030 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0195 | −1.02968 | −0.514839 | − | 0.857287i | \(-0.672148\pi\) | ||||
−0.514839 | + | 0.857287i | \(0.672148\pi\) | |||||||
\(968\) | −46.6185 | −1.49837 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.8342 | −0.733161 | ||||||||
\(971\) | −13.2739 | −0.425980 | −0.212990 | − | 0.977054i | \(-0.568320\pi\) | ||||
−0.212990 | + | 0.977054i | \(0.568320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.7253 | 0.792655 | ||||||||
\(974\) | 18.9393 | 0.606853 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 53.4211 | 1.70997 | ||||||||
\(977\) | 16.6713 | 0.533361 | 0.266680 | − | 0.963785i | \(-0.414073\pi\) | ||||
0.266680 | + | 0.963785i | \(0.414073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −75.0677 | −2.39917 | ||||||||
\(980\) | 0.583824 | 0.0186496 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37.1325 | −1.18494 | ||||||||
\(983\) | −3.93033 | −0.125358 | −0.0626790 | − | 0.998034i | \(-0.519964\pi\) | ||||
−0.0626790 | + | 0.998034i | \(0.519964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3682 | 0.712711 | ||||||||
\(986\) | −1.63488 | −0.0520651 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.95145 | −0.0938981 | ||||||||
\(989\) | −13.3192 | −0.423527 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.9367 | −1.55452 | −0.777262 | − | 0.629177i | \(-0.783392\pi\) | ||||
−0.777262 | + | 0.629177i | \(0.783392\pi\) | |||||||
\(992\) | −1.92043 | −0.0609736 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.9927 | −0.824438 | ||||||||
\(995\) | −29.3094 | −0.929171 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.6435 | −1.19218 | −0.596091 | − | 0.802917i | \(-0.703280\pi\) | ||||
−0.596091 | + | 0.802917i | \(0.703280\pi\) | |||||||
\(998\) | −49.3628 | −1.56255 | ||||||||
\(999\) | 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.j.1.16 | ✓ | 20 | |
3.2 | odd | 2 | 2151.2.a.k.1.5 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.16 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2151.2.a.k.1.5 | yes | 20 | 3.2 | odd | 2 |