Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.02162\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02162 | −1.42950 | −0.714750 | − | 0.699380i | \(-0.753460\pi\) | ||||
−0.714750 | + | 0.699380i | \(0.753460\pi\) | |||||||
\(3\) | −1.90055 | −1.09728 | −0.548640 | − | 0.836058i | \(-0.684854\pi\) | ||||
−0.548640 | + | 0.836058i | \(0.684854\pi\) | |||||||
\(4\) | 2.08694 | 1.04347 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.84218 | 1.56856 | ||||||||
\(7\) | −3.09218 | −1.16873 | −0.584366 | − | 0.811490i | \(-0.698657\pi\) | ||||
−0.584366 | + | 0.811490i | \(0.698657\pi\) | |||||||
\(8\) | −0.175759 | −0.0621403 | ||||||||
\(9\) | 0.612075 | 0.204025 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.963188 | 0.290412 | 0.145206 | − | 0.989401i | \(-0.453615\pi\) | ||||
0.145206 | + | 0.989401i | \(0.453615\pi\) | |||||||
\(12\) | −3.96633 | −1.14498 | ||||||||
\(13\) | −2.95920 | −0.820733 | −0.410367 | − | 0.911921i | \(-0.634599\pi\) | ||||
−0.410367 | + | 0.911921i | \(0.634599\pi\) | |||||||
\(14\) | 6.25120 | 1.67070 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.81856 | −0.954640 | ||||||||
\(17\) | −0.0389621 | −0.00944969 | −0.00472484 | − | 0.999989i | \(-0.501504\pi\) | ||||
−0.00472484 | + | 0.999989i | \(0.501504\pi\) | |||||||
\(18\) | −1.23738 | −0.291654 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.87682 | 1.28243 | ||||||||
\(22\) | −1.94720 | −0.415144 | ||||||||
\(23\) | −3.88160 | −0.809370 | −0.404685 | − | 0.914456i | \(-0.632619\pi\) | ||||
−0.404685 | + | 0.914456i | \(0.632619\pi\) | |||||||
\(24\) | 0.334039 | 0.0681853 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.98236 | 1.17324 | ||||||||
\(27\) | 4.53836 | 0.873408 | ||||||||
\(28\) | −6.45319 | −1.21954 | ||||||||
\(29\) | 9.32783 | 1.73213 | 0.866067 | − | 0.499928i | \(-0.166640\pi\) | ||||
0.866067 | + | 0.499928i | \(0.166640\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.37788 | 1.68432 | 0.842158 | − | 0.539231i | \(-0.181285\pi\) | ||||
0.842158 | + | 0.539231i | \(0.181285\pi\) | |||||||
\(32\) | 8.07119 | 1.42680 | ||||||||
\(33\) | −1.83058 | −0.318664 | ||||||||
\(34\) | 0.0787664 | 0.0135083 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.27736 | 0.212894 | ||||||||
\(37\) | −1.11739 | −0.183698 | −0.0918491 | − | 0.995773i | \(-0.529278\pi\) | ||||
−0.0918491 | + | 0.995773i | \(0.529278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.62409 | 0.900575 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0747 | −1.88575 | −0.942873 | − | 0.333152i | \(-0.891888\pi\) | ||||
−0.942873 | + | 0.333152i | \(0.891888\pi\) | |||||||
\(42\) | −11.8807 | −1.83323 | ||||||||
\(43\) | 4.95348 | 0.755399 | 0.377699 | − | 0.925928i | \(-0.376715\pi\) | ||||
0.377699 | + | 0.925928i | \(0.376715\pi\) | |||||||
\(44\) | 2.01012 | 0.303036 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.84711 | 1.15699 | ||||||||
\(47\) | −8.01557 | −1.16919 | −0.584595 | − | 0.811325i | \(-0.698747\pi\) | ||||
−0.584595 | + | 0.811325i | \(0.698747\pi\) | |||||||
\(48\) | 7.25735 | 1.04751 | ||||||||
\(49\) | 2.56155 | 0.365936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0740492 | 0.0103690 | ||||||||
\(52\) | −6.17566 | −0.856410 | ||||||||
\(53\) | 6.05981 | 0.832379 | 0.416189 | − | 0.909278i | \(-0.363365\pi\) | ||||
0.416189 | + | 0.909278i | \(0.363365\pi\) | |||||||
\(54\) | −9.17483 | −1.24854 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.543479 | 0.0726254 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18.8573 | −2.47609 | ||||||||
\(59\) | −2.77465 | −0.361229 | −0.180615 | − | 0.983554i | \(-0.557809\pi\) | ||||
−0.180615 | + | 0.983554i | \(0.557809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0302 | −1.28424 | −0.642119 | − | 0.766605i | \(-0.721945\pi\) | ||||
−0.642119 | + | 0.766605i | \(0.721945\pi\) | |||||||
\(62\) | −18.9585 | −2.40773 | ||||||||
\(63\) | −1.89264 | −0.238451 | ||||||||
\(64\) | −8.67975 | −1.08497 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.70074 | 0.455530 | ||||||||
\(67\) | 9.34881 | 1.14214 | 0.571070 | − | 0.820902i | \(-0.306529\pi\) | ||||
0.571070 | + | 0.820902i | \(0.306529\pi\) | |||||||
\(68\) | −0.0813115 | −0.00986047 | ||||||||
\(69\) | 7.37716 | 0.888106 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.5894 | −1.49409 | −0.747043 | − | 0.664775i | \(-0.768527\pi\) | ||||
−0.747043 | + | 0.664775i | \(0.768527\pi\) | |||||||
\(72\) | −0.107578 | −0.0126782 | ||||||||
\(73\) | −0.897116 | −0.104999 | −0.0524997 | − | 0.998621i | \(-0.516719\pi\) | ||||
−0.0524997 | + | 0.998621i | \(0.516719\pi\) | |||||||
\(74\) | 2.25894 | 0.262597 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.97835 | −0.339414 | ||||||||
\(78\) | −11.3698 | −1.28737 | ||||||||
\(79\) | −8.89241 | −1.00047 | −0.500237 | − | 0.865888i | \(-0.666754\pi\) | ||||
−0.500237 | + | 0.865888i | \(0.666754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4616 | −1.16240 | ||||||||
\(82\) | 24.4104 | 2.69567 | ||||||||
\(83\) | 9.60447 | 1.05423 | 0.527114 | − | 0.849795i | \(-0.323274\pi\) | ||||
0.527114 | + | 0.849795i | \(0.323274\pi\) | |||||||
\(84\) | 12.2646 | 1.33817 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.0140 | −1.07984 | ||||||||
\(87\) | −17.7280 | −1.90064 | ||||||||
\(88\) | −0.169289 | −0.0180463 | ||||||||
\(89\) | 8.74675 | 0.927153 | 0.463577 | − | 0.886057i | \(-0.346566\pi\) | ||||
0.463577 | + | 0.886057i | \(0.346566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.15035 | 0.959218 | ||||||||
\(92\) | −8.10067 | −0.844553 | ||||||||
\(93\) | −17.8231 | −1.84817 | ||||||||
\(94\) | 16.2044 | 1.67136 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.3397 | −1.56560 | ||||||||
\(97\) | 7.78824 | 0.790776 | 0.395388 | − | 0.918514i | \(-0.370610\pi\) | ||||
0.395388 | + | 0.918514i | \(0.370610\pi\) | |||||||
\(98\) | −5.17848 | −0.523105 | ||||||||
\(99\) | 0.589543 | 0.0592513 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.04363 | −0.302852 | −0.151426 | − | 0.988469i | \(-0.548387\pi\) | ||||
−0.151426 | + | 0.988469i | \(0.548387\pi\) | |||||||
\(102\) | −0.149699 | −0.0148224 | ||||||||
\(103\) | −0.328573 | −0.0323753 | −0.0161876 | − | 0.999869i | \(-0.505153\pi\) | ||||
−0.0161876 | + | 0.999869i | \(0.505153\pi\) | |||||||
\(104\) | 0.520106 | 0.0510006 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.2506 | −1.18989 | ||||||||
\(107\) | −12.7873 | −1.23620 | −0.618099 | − | 0.786101i | \(-0.712097\pi\) | ||||
−0.618099 | + | 0.786101i | \(0.712097\pi\) | |||||||
\(108\) | 9.47129 | 0.911375 | ||||||||
\(109\) | 15.2412 | 1.45984 | 0.729919 | − | 0.683534i | \(-0.239558\pi\) | ||||
0.729919 | + | 0.683534i | \(0.239558\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.12366 | 0.201569 | ||||||||
\(112\) | 11.8077 | 1.11572 | ||||||||
\(113\) | 2.56380 | 0.241182 | 0.120591 | − | 0.992702i | \(-0.461521\pi\) | ||||
0.120591 | + | 0.992702i | \(0.461521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 19.4666 | 1.80743 | ||||||||
\(117\) | −1.81125 | −0.167450 | ||||||||
\(118\) | 5.60929 | 0.516377 | ||||||||
\(119\) | 0.120478 | 0.0110442 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0723 | −0.915661 | ||||||||
\(122\) | 20.2773 | 1.83582 | ||||||||
\(123\) | 22.9485 | 2.06919 | ||||||||
\(124\) | 19.5711 | 1.75753 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.82620 | 0.340865 | ||||||||
\(127\) | −15.4761 | −1.37328 | −0.686641 | − | 0.726997i | \(-0.740916\pi\) | ||||
−0.686641 | + | 0.726997i | \(0.740916\pi\) | |||||||
\(128\) | 1.40475 | 0.124163 | ||||||||
\(129\) | −9.41432 | −0.828884 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.842204 | 0.0735837 | 0.0367919 | − | 0.999323i | \(-0.488286\pi\) | ||||
0.0367919 | + | 0.999323i | \(0.488286\pi\) | |||||||
\(132\) | −3.82032 | −0.332516 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −18.8997 | −1.63269 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.00684795 | 0.000587206 0 | ||||||||
\(137\) | 5.07379 | 0.433483 | 0.216742 | − | 0.976229i | \(-0.430457\pi\) | ||||
0.216742 | + | 0.976229i | \(0.430457\pi\) | |||||||
\(138\) | −14.9138 | −1.26955 | ||||||||
\(139\) | 2.73039 | 0.231589 | 0.115794 | − | 0.993273i | \(-0.463059\pi\) | ||||
0.115794 | + | 0.993273i | \(0.463059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.2340 | 1.28293 | ||||||||
\(142\) | 25.4510 | 2.13580 | ||||||||
\(143\) | −2.85026 | −0.238351 | ||||||||
\(144\) | −2.33725 | −0.194770 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.81363 | 0.150097 | ||||||||
\(147\) | −4.86835 | −0.401534 | ||||||||
\(148\) | −2.33193 | −0.191684 | ||||||||
\(149\) | −6.64567 | −0.544435 | −0.272217 | − | 0.962236i | \(-0.587757\pi\) | ||||
−0.272217 | + | 0.962236i | \(0.587757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.19059 | 0.422404 | 0.211202 | − | 0.977442i | \(-0.432262\pi\) | ||||
0.211202 | + | 0.977442i | \(0.432262\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0238477 | −0.00192797 | ||||||||
\(154\) | 6.02108 | 0.485192 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.7371 | 0.939723 | ||||||||
\(157\) | −11.6478 | −0.929598 | −0.464799 | − | 0.885416i | \(-0.653873\pi\) | ||||
−0.464799 | + | 0.885416i | \(0.653873\pi\) | |||||||
\(158\) | 17.9771 | 1.43018 | ||||||||
\(159\) | −11.5169 | −0.913353 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0026 | 0.945937 | ||||||||
\(162\) | 21.1493 | 1.66165 | ||||||||
\(163\) | 0.556796 | 0.0436116 | 0.0218058 | − | 0.999762i | \(-0.493058\pi\) | ||||
0.0218058 | + | 0.999762i | \(0.493058\pi\) | |||||||
\(164\) | −25.1991 | −1.96772 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.4166 | −1.50702 | ||||||||
\(167\) | 22.1563 | 1.71451 | 0.857254 | − | 0.514894i | \(-0.172169\pi\) | ||||
0.857254 | + | 0.514894i | \(0.172169\pi\) | |||||||
\(168\) | −1.03291 | −0.0796904 | ||||||||
\(169\) | −4.24316 | −0.326397 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.3376 | 0.788236 | ||||||||
\(173\) | −11.4561 | −0.870994 | −0.435497 | − | 0.900190i | \(-0.643427\pi\) | ||||
−0.435497 | + | 0.900190i | \(0.643427\pi\) | |||||||
\(174\) | 35.8392 | 2.71696 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.67799 | −0.277239 | ||||||||
\(177\) | 5.27336 | 0.396370 | ||||||||
\(178\) | −17.6826 | −1.32537 | ||||||||
\(179\) | −5.96612 | −0.445928 | −0.222964 | − | 0.974827i | \(-0.571573\pi\) | ||||
−0.222964 | + | 0.974827i | \(0.571573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.17784 | 0.459195 | 0.229597 | − | 0.973286i | \(-0.426259\pi\) | ||||
0.229597 | + | 0.973286i | \(0.426259\pi\) | |||||||
\(182\) | −18.4985 | −1.37120 | ||||||||
\(183\) | 19.0629 | 1.40917 | ||||||||
\(184\) | 0.682227 | 0.0502945 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 36.0315 | 2.64196 | ||||||||
\(187\) | −0.0375278 | −0.00274430 | ||||||||
\(188\) | −16.7280 | −1.22002 | ||||||||
\(189\) | −14.0334 | −1.02078 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.6639 | −1.35047 | −0.675235 | − | 0.737602i | \(-0.735958\pi\) | ||||
−0.675235 | + | 0.737602i | \(0.735958\pi\) | |||||||
\(192\) | 16.4963 | 1.19051 | ||||||||
\(193\) | −23.9067 | −1.72084 | −0.860421 | − | 0.509583i | \(-0.829800\pi\) | ||||
−0.860421 | + | 0.509583i | \(0.829800\pi\) | |||||||
\(194\) | −15.7449 | −1.13041 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.34580 | 0.381843 | ||||||||
\(197\) | 6.70152 | 0.477463 | 0.238732 | − | 0.971086i | \(-0.423268\pi\) | ||||
0.238732 | + | 0.971086i | \(0.423268\pi\) | |||||||
\(198\) | −1.19183 | −0.0846997 | ||||||||
\(199\) | 3.15886 | 0.223926 | 0.111963 | − | 0.993712i | \(-0.464286\pi\) | ||||
0.111963 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.7678 | −1.25325 | ||||||||
\(202\) | 6.15306 | 0.432928 | ||||||||
\(203\) | −28.8433 | −2.02440 | ||||||||
\(204\) | 0.154536 | 0.0108197 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.664250 | 0.0462805 | ||||||||
\(207\) | −2.37583 | −0.165132 | ||||||||
\(208\) | 11.2999 | 0.783505 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4580 | 0.788801 | 0.394401 | − | 0.918939i | \(-0.370952\pi\) | ||||
0.394401 | + | 0.918939i | \(0.370952\pi\) | |||||||
\(212\) | 12.6465 | 0.868562 | ||||||||
\(213\) | 23.9267 | 1.63943 | ||||||||
\(214\) | 25.8511 | 1.76714 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.797659 | −0.0542738 | ||||||||
\(217\) | −28.9980 | −1.96852 | ||||||||
\(218\) | −30.8118 | −2.08684 | ||||||||
\(219\) | 1.70501 | 0.115214 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.115296 | 0.00775567 | ||||||||
\(222\) | −4.29322 | −0.288142 | ||||||||
\(223\) | −7.51422 | −0.503189 | −0.251595 | − | 0.967833i | \(-0.580955\pi\) | ||||
−0.251595 | + | 0.967833i | \(0.580955\pi\) | |||||||
\(224\) | −24.9575 | −1.66755 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.18302 | −0.344769 | ||||||||
\(227\) | −4.20184 | −0.278886 | −0.139443 | − | 0.990230i | \(-0.544531\pi\) | ||||
−0.139443 | + | 0.990230i | \(0.544531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.5758 | 1.49185 | 0.745927 | − | 0.666028i | \(-0.232007\pi\) | ||||
0.745927 | + | 0.666028i | \(0.232007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.66048 | 0.372433 | ||||||||
\(232\) | −1.63945 | −0.107635 | ||||||||
\(233\) | 10.9789 | 0.719251 | 0.359626 | − | 0.933097i | \(-0.382904\pi\) | ||||
0.359626 | + | 0.933097i | \(0.382904\pi\) | |||||||
\(234\) | 3.66165 | 0.239370 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.79054 | −0.376932 | ||||||||
\(237\) | 16.9004 | 1.09780 | ||||||||
\(238\) | −0.243560 | −0.0157876 | ||||||||
\(239\) | −2.72559 | −0.176304 | −0.0881520 | − | 0.996107i | \(-0.528096\pi\) | ||||
−0.0881520 | + | 0.996107i | \(0.528096\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.1540 | −0.718493 | −0.359246 | − | 0.933243i | \(-0.616966\pi\) | ||||
−0.359246 | + | 0.933243i | \(0.616966\pi\) | |||||||
\(242\) | 20.3623 | 1.30894 | ||||||||
\(243\) | 6.26765 | 0.402070 | ||||||||
\(244\) | −20.9325 | −1.34006 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −46.3930 | −2.95791 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.64825 | −0.104664 | ||||||||
\(249\) | −18.2537 | −1.15678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.3683 | −1.72747 | −0.863737 | − | 0.503944i | \(-0.831882\pi\) | ||||
−0.863737 | + | 0.503944i | \(0.831882\pi\) | |||||||
\(252\) | −3.94983 | −0.248816 | ||||||||
\(253\) | −3.73871 | −0.235051 | ||||||||
\(254\) | 31.2868 | 1.96311 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.5196 | 0.907477 | ||||||||
\(257\) | −20.2628 | −1.26396 | −0.631980 | − | 0.774985i | \(-0.717757\pi\) | ||||
−0.631980 | + | 0.774985i | \(0.717757\pi\) | |||||||
\(258\) | 19.0322 | 1.18489 | ||||||||
\(259\) | 3.45517 | 0.214694 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.70933 | 0.353399 | ||||||||
\(262\) | −1.70261 | −0.105188 | ||||||||
\(263\) | −9.56235 | −0.589640 | −0.294820 | − | 0.955553i | \(-0.595260\pi\) | ||||
−0.294820 | + | 0.955553i | \(0.595260\pi\) | |||||||
\(264\) | 0.321742 | 0.0198019 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.6236 | −1.01735 | ||||||||
\(268\) | 19.5104 | 1.19179 | ||||||||
\(269\) | −4.57455 | −0.278915 | −0.139458 | − | 0.990228i | \(-0.544536\pi\) | ||||
−0.139458 | + | 0.990228i | \(0.544536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.1359 | −1.34466 | −0.672330 | − | 0.740252i | \(-0.734706\pi\) | ||||
−0.672330 | + | 0.740252i | \(0.734706\pi\) | |||||||
\(272\) | 0.148779 | 0.00902105 | ||||||||
\(273\) | −17.3907 | −1.05253 | ||||||||
\(274\) | −10.2573 | −0.619665 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.3957 | 0.926712 | ||||||||
\(277\) | −23.5542 | −1.41523 | −0.707617 | − | 0.706597i | \(-0.750230\pi\) | ||||
−0.707617 | + | 0.706597i | \(0.750230\pi\) | |||||||
\(278\) | −5.51981 | −0.331056 | ||||||||
\(279\) | 5.73996 | 0.343643 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3229 | −0.615815 | −0.307907 | − | 0.951416i | \(-0.599629\pi\) | ||||
−0.307907 | + | 0.951416i | \(0.599629\pi\) | |||||||
\(282\) | −30.7972 | −1.83395 | ||||||||
\(283\) | 30.8729 | 1.83520 | 0.917602 | − | 0.397501i | \(-0.130123\pi\) | ||||
0.917602 | + | 0.397501i | \(0.130123\pi\) | |||||||
\(284\) | −26.2733 | −1.55903 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.76214 | 0.340722 | ||||||||
\(287\) | 37.3370 | 2.20393 | ||||||||
\(288\) | 4.94017 | 0.291103 | ||||||||
\(289\) | −16.9985 | −0.999911 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8019 | −0.867703 | ||||||||
\(292\) | −1.87223 | −0.109564 | ||||||||
\(293\) | 6.36103 | 0.371616 | 0.185808 | − | 0.982586i | \(-0.440510\pi\) | ||||
0.185808 | + | 0.982586i | \(0.440510\pi\) | |||||||
\(294\) | 9.84194 | 0.573993 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.196392 | 0.0114151 | ||||||||
\(297\) | 4.37130 | 0.253648 | ||||||||
\(298\) | 13.4350 | 0.778270 | ||||||||
\(299\) | 11.4864 | 0.664276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.3170 | −0.882859 | ||||||||
\(302\) | −10.4934 | −0.603826 | ||||||||
\(303\) | 5.78456 | 0.332314 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.0482109 | 0.00275604 | ||||||||
\(307\) | −5.88645 | −0.335958 | −0.167979 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167979 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(308\) | −6.21563 | −0.354168 | ||||||||
\(309\) | 0.624469 | 0.0355248 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.3885 | −1.43965 | −0.719825 | − | 0.694156i | \(-0.755778\pi\) | ||||
−0.719825 | + | 0.694156i | \(0.755778\pi\) | |||||||
\(312\) | −0.988486 | −0.0559620 | ||||||||
\(313\) | −6.03850 | −0.341316 | −0.170658 | − | 0.985330i | \(-0.554589\pi\) | ||||
−0.170658 | + | 0.985330i | \(0.554589\pi\) | |||||||
\(314\) | 23.5475 | 1.32886 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.5579 | −1.04396 | ||||||||
\(317\) | 15.8757 | 0.891670 | 0.445835 | − | 0.895115i | \(-0.352907\pi\) | ||||
0.445835 | + | 0.895115i | \(0.352907\pi\) | |||||||
\(318\) | 23.2829 | 1.30564 | ||||||||
\(319\) | 8.98445 | 0.503033 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.3029 | 1.35646 | ||||||||
\(322\) | −24.2647 | −1.35222 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −21.8327 | −1.21293 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.12563 | −0.0623428 | ||||||||
\(327\) | −28.9665 | −1.60185 | ||||||||
\(328\) | 2.12224 | 0.117181 | ||||||||
\(329\) | 24.7855 | 1.36647 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1696 | 0.778829 | 0.389414 | − | 0.921063i | \(-0.372677\pi\) | ||||
0.389414 | + | 0.921063i | \(0.372677\pi\) | |||||||
\(332\) | 20.0440 | 1.10005 | ||||||||
\(333\) | −0.683928 | −0.0374790 | ||||||||
\(334\) | −44.7916 | −2.45089 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −22.4410 | −1.22426 | ||||||||
\(337\) | −2.14993 | −0.117114 | −0.0585571 | − | 0.998284i | \(-0.518650\pi\) | ||||
−0.0585571 | + | 0.998284i | \(0.518650\pi\) | |||||||
\(338\) | 8.57806 | 0.466585 | ||||||||
\(339\) | −4.87261 | −0.264644 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.03266 | 0.489146 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.7245 | 0.741051 | ||||||||
\(344\) | −0.870620 | −0.0469407 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.1599 | 1.24509 | ||||||||
\(347\) | 11.0525 | 0.593329 | 0.296664 | − | 0.954982i | \(-0.404126\pi\) | ||||
0.296664 | + | 0.954982i | \(0.404126\pi\) | |||||||
\(348\) | −36.9972 | −1.98326 | ||||||||
\(349\) | 35.3451 | 1.89198 | 0.945989 | − | 0.324199i | \(-0.105095\pi\) | ||||
0.945989 | + | 0.324199i | \(0.105095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.4299 | −0.716835 | ||||||||
\(352\) | 7.77407 | 0.414360 | ||||||||
\(353\) | −22.1904 | −1.18108 | −0.590538 | − | 0.807010i | \(-0.701084\pi\) | ||||
−0.590538 | + | 0.807010i | \(0.701084\pi\) | |||||||
\(354\) | −10.6607 | −0.566611 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.2539 | 0.967457 | ||||||||
\(357\) | −0.228973 | −0.0121185 | ||||||||
\(358\) | 12.0612 | 0.637455 | ||||||||
\(359\) | −9.50861 | −0.501845 | −0.250923 | − | 0.968007i | \(-0.580734\pi\) | ||||
−0.250923 | + | 0.968007i | \(0.580734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −12.4892 | −0.656419 | ||||||||
\(363\) | 19.1428 | 1.00474 | ||||||||
\(364\) | 19.0962 | 1.00091 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −38.5379 | −2.01441 | ||||||||
\(367\) | 2.18321 | 0.113963 | 0.0569813 | − | 0.998375i | \(-0.481852\pi\) | ||||
0.0569813 | + | 0.998375i | \(0.481852\pi\) | |||||||
\(368\) | 14.8221 | 0.772657 | ||||||||
\(369\) | −7.39060 | −0.384739 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.7380 | −0.972828 | ||||||||
\(372\) | −37.1957 | −1.92851 | ||||||||
\(373\) | −12.3407 | −0.638977 | −0.319488 | − | 0.947590i | \(-0.603511\pi\) | ||||
−0.319488 | + | 0.947590i | \(0.603511\pi\) | |||||||
\(374\) | 0.0758669 | 0.00392298 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.40881 | 0.0726538 | ||||||||
\(377\) | −27.6029 | −1.42162 | ||||||||
\(378\) | 28.3702 | 1.45921 | ||||||||
\(379\) | 18.5014 | 0.950352 | 0.475176 | − | 0.879891i | \(-0.342384\pi\) | ||||
0.475176 | + | 0.879891i | \(0.342384\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.4130 | 1.50688 | ||||||||
\(382\) | 37.7312 | 1.93050 | ||||||||
\(383\) | −11.4322 | −0.584156 | −0.292078 | − | 0.956394i | \(-0.594347\pi\) | ||||
−0.292078 | + | 0.956394i | \(0.594347\pi\) | |||||||
\(384\) | −2.66978 | −0.136242 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 48.3302 | 2.45994 | ||||||||
\(387\) | 3.03190 | 0.154120 | ||||||||
\(388\) | 16.2536 | 0.825151 | ||||||||
\(389\) | 12.5237 | 0.634978 | 0.317489 | − | 0.948262i | \(-0.397160\pi\) | ||||
0.317489 | + | 0.948262i | \(0.397160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.151235 | 0.00764829 | ||||||||
\(392\) | −0.450216 | −0.0227394 | ||||||||
\(393\) | −1.60065 | −0.0807420 | ||||||||
\(394\) | −13.5479 | −0.682534 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.23034 | 0.0618270 | ||||||||
\(397\) | −11.7504 | −0.589734 | −0.294867 | − | 0.955538i | \(-0.595275\pi\) | ||||
−0.294867 | + | 0.955538i | \(0.595275\pi\) | |||||||
\(398\) | −6.38602 | −0.320102 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.6418 | 0.731178 | 0.365589 | − | 0.930776i | \(-0.380868\pi\) | ||||
0.365589 | + | 0.930776i | \(0.380868\pi\) | |||||||
\(402\) | 35.9198 | 1.79152 | ||||||||
\(403\) | −27.7510 | −1.38237 | ||||||||
\(404\) | −6.35187 | −0.316017 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 58.3101 | 2.89388 | ||||||||
\(407\) | −1.07626 | −0.0533482 | ||||||||
\(408\) | −0.0130148 | −0.000644330 0 | ||||||||
\(409\) | −12.7478 | −0.630338 | −0.315169 | − | 0.949035i | \(-0.602061\pi\) | ||||
−0.315169 | + | 0.949035i | \(0.602061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.64298 | −0.475653 | ||||||||
\(412\) | −0.685713 | −0.0337827 | ||||||||
\(413\) | 8.57972 | 0.422180 | ||||||||
\(414\) | 4.80302 | 0.236056 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −23.8842 | −1.17102 | ||||||||
\(417\) | −5.18923 | −0.254118 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.84601 | 0.139037 | 0.0695184 | − | 0.997581i | \(-0.477854\pi\) | ||||
0.0695184 | + | 0.997581i | \(0.477854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.1505 | −0.543442 | −0.271721 | − | 0.962376i | \(-0.587593\pi\) | ||||
−0.271721 | + | 0.962376i | \(0.587593\pi\) | |||||||
\(422\) | −23.1637 | −1.12759 | ||||||||
\(423\) | −4.90613 | −0.238544 | ||||||||
\(424\) | −1.06507 | −0.0517242 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −48.3707 | −2.34357 | ||||||||
\(427\) | 31.0152 | 1.50093 | ||||||||
\(428\) | −26.6864 | −1.28993 | ||||||||
\(429\) | 5.41705 | 0.261538 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9363 | 0.719455 | 0.359727 | − | 0.933057i | \(-0.382870\pi\) | ||||
0.359727 | + | 0.933057i | \(0.382870\pi\) | |||||||
\(432\) | −17.3300 | −0.833791 | ||||||||
\(433\) | −38.7567 | −1.86253 | −0.931265 | − | 0.364343i | \(-0.881294\pi\) | ||||
−0.931265 | + | 0.364343i | \(0.881294\pi\) | |||||||
\(434\) | 58.6230 | 2.81399 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31.8074 | 1.52330 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.44688 | −0.164698 | ||||||||
\(439\) | 31.4285 | 1.50000 | 0.749999 | − | 0.661438i | \(-0.230054\pi\) | ||||
0.749999 | + | 0.661438i | \(0.230054\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.56786 | 0.0746600 | ||||||||
\(442\) | −0.233085 | −0.0110867 | ||||||||
\(443\) | −10.6508 | −0.506036 | −0.253018 | − | 0.967462i | \(-0.581423\pi\) | ||||
−0.253018 | + | 0.967462i | \(0.581423\pi\) | |||||||
\(444\) | 4.43194 | 0.210331 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.1909 | 0.719309 | ||||||||
\(447\) | 12.6304 | 0.597398 | ||||||||
\(448\) | 26.8393 | 1.26804 | ||||||||
\(449\) | −4.10400 | −0.193680 | −0.0968399 | − | 0.995300i | \(-0.530873\pi\) | ||||
−0.0968399 | + | 0.995300i | \(0.530873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.6302 | −0.547644 | ||||||||
\(452\) | 5.35049 | 0.251666 | ||||||||
\(453\) | −9.86495 | −0.463496 | ||||||||
\(454\) | 8.49452 | 0.398668 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.25947 | −0.433140 | −0.216570 | − | 0.976267i | \(-0.569487\pi\) | ||||
−0.216570 | + | 0.976267i | \(0.569487\pi\) | |||||||
\(458\) | −45.6397 | −2.13260 | ||||||||
\(459\) | −0.176824 | −0.00825343 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.64611 | 0.309540 | 0.154770 | − | 0.987951i | \(-0.450536\pi\) | ||||
0.154770 | + | 0.987951i | \(0.450536\pi\) | |||||||
\(462\) | −11.4433 | −0.532392 | ||||||||
\(463\) | −22.2948 | −1.03613 | −0.518064 | − | 0.855342i | \(-0.673347\pi\) | ||||
−0.518064 | + | 0.855342i | \(0.673347\pi\) | |||||||
\(464\) | −35.6189 | −1.65357 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.1951 | −1.02817 | ||||||||
\(467\) | 15.4739 | 0.716048 | 0.358024 | − | 0.933712i | \(-0.383451\pi\) | ||||
0.358024 | + | 0.933712i | \(0.383451\pi\) | |||||||
\(468\) | −3.77997 | −0.174729 | ||||||||
\(469\) | −28.9082 | −1.33486 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.1372 | 1.02003 | ||||||||
\(472\) | 0.487671 | 0.0224469 | ||||||||
\(473\) | 4.77113 | 0.219377 | ||||||||
\(474\) | −34.1662 | −1.56931 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.251429 | 0.0115242 | ||||||||
\(477\) | 3.70906 | 0.169826 | ||||||||
\(478\) | 5.51011 | 0.252026 | ||||||||
\(479\) | 32.2057 | 1.47152 | 0.735758 | − | 0.677245i | \(-0.236826\pi\) | ||||
0.735758 | + | 0.677245i | \(0.236826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.30658 | 0.150767 | ||||||||
\(482\) | 22.5491 | 1.02709 | ||||||||
\(483\) | −22.8115 | −1.03796 | ||||||||
\(484\) | −21.0202 | −0.955465 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −12.6708 | −0.574759 | ||||||||
\(487\) | −3.65139 | −0.165460 | −0.0827301 | − | 0.996572i | \(-0.526364\pi\) | ||||
−0.0827301 | + | 0.996572i | \(0.526364\pi\) | |||||||
\(488\) | 1.76291 | 0.0798030 | ||||||||
\(489\) | −1.05822 | −0.0478542 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.54862 | 0.205276 | 0.102638 | − | 0.994719i | \(-0.467272\pi\) | ||||
0.102638 | + | 0.994719i | \(0.467272\pi\) | |||||||
\(492\) | 47.8921 | 2.15914 | ||||||||
\(493\) | −0.363431 | −0.0163681 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −35.8100 | −1.60792 | ||||||||
\(497\) | 38.9286 | 1.74619 | ||||||||
\(498\) | 36.9021 | 1.65362 | ||||||||
\(499\) | −21.8234 | −0.976950 | −0.488475 | − | 0.872578i | \(-0.662447\pi\) | ||||
−0.488475 | + | 0.872578i | \(0.662447\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.1091 | −1.88130 | ||||||||
\(502\) | 55.3283 | 2.46942 | ||||||||
\(503\) | 24.7388 | 1.10305 | 0.551524 | − | 0.834159i | \(-0.314046\pi\) | ||||
0.551524 | + | 0.834159i | \(0.314046\pi\) | |||||||
\(504\) | 0.332650 | 0.0148174 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.55825 | 0.336005 | ||||||||
\(507\) | 8.06433 | 0.358149 | ||||||||
\(508\) | −32.2977 | −1.43298 | ||||||||
\(509\) | 17.3491 | 0.768987 | 0.384494 | − | 0.923128i | \(-0.374376\pi\) | ||||
0.384494 | + | 0.923128i | \(0.374376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.77404 | 0.122716 | ||||||||
\(512\) | −32.1626 | −1.42140 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 40.9637 | 1.80683 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −19.6471 | −0.864916 | ||||||||
\(517\) | −7.72050 | −0.339547 | ||||||||
\(518\) | −6.98504 | −0.306905 | ||||||||
\(519\) | 21.7729 | 0.955725 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.456675 | −0.0200073 | −0.0100036 | − | 0.999950i | \(-0.503184\pi\) | ||||
−0.0100036 | + | 0.999950i | \(0.503184\pi\) | |||||||
\(522\) | −11.5421 | −0.505183 | ||||||||
\(523\) | −37.7965 | −1.65273 | −0.826363 | − | 0.563138i | \(-0.809594\pi\) | ||||
−0.826363 | + | 0.563138i | \(0.809594\pi\) | |||||||
\(524\) | 1.75763 | 0.0767824 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.3314 | 0.842890 | ||||||||
\(527\) | −0.365381 | −0.0159163 | ||||||||
\(528\) | 6.99019 | 0.304209 | ||||||||
\(529\) | −7.93318 | −0.344921 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.69830 | −0.0736998 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.7313 | 1.54769 | ||||||||
\(534\) | 33.6066 | 1.45430 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.64314 | −0.0709729 | ||||||||
\(537\) | 11.3389 | 0.489309 | ||||||||
\(538\) | 9.24800 | 0.398710 | ||||||||
\(539\) | 2.46726 | 0.106272 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.1299 | −0.908444 | −0.454222 | − | 0.890889i | \(-0.650083\pi\) | ||||
−0.454222 | + | 0.890889i | \(0.650083\pi\) | |||||||
\(542\) | 44.7503 | 1.92219 | ||||||||
\(543\) | −11.7413 | −0.503866 | ||||||||
\(544\) | −0.314470 | −0.0134828 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 35.1573 | 1.50459 | ||||||||
\(547\) | −12.5424 | −0.536276 | −0.268138 | − | 0.963381i | \(-0.586408\pi\) | ||||
−0.268138 | + | 0.963381i | \(0.586408\pi\) | |||||||
\(548\) | 10.5887 | 0.452327 | ||||||||
\(549\) | −6.13925 | −0.262017 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.29660 | −0.0551872 | ||||||||
\(553\) | 27.4969 | 1.16929 | ||||||||
\(554\) | 47.6175 | 2.02308 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.69816 | 0.241656 | ||||||||
\(557\) | 32.0252 | 1.35695 | 0.678475 | − | 0.734623i | \(-0.262641\pi\) | ||||
0.678475 | + | 0.734623i | \(0.262641\pi\) | |||||||
\(558\) | −11.6040 | −0.491237 | ||||||||
\(559\) | −14.6583 | −0.619981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0713233 | 0.00301127 | ||||||||
\(562\) | 20.8690 | 0.880307 | ||||||||
\(563\) | 19.5807 | 0.825228 | 0.412614 | − | 0.910906i | \(-0.364616\pi\) | ||||
0.412614 | + | 0.910906i | \(0.364616\pi\) | |||||||
\(564\) | 31.7923 | 1.33870 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −62.4132 | −2.62342 | ||||||||
\(567\) | 32.3491 | 1.35853 | ||||||||
\(568\) | 2.21270 | 0.0928430 | ||||||||
\(569\) | 18.6525 | 0.781953 | 0.390977 | − | 0.920401i | \(-0.372137\pi\) | ||||
0.390977 | + | 0.920401i | \(0.372137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.460181 | −0.0192580 | −0.00962899 | − | 0.999954i | \(-0.503065\pi\) | ||||
−0.00962899 | + | 0.999954i | \(0.503065\pi\) | |||||||
\(572\) | −5.94832 | −0.248712 | ||||||||
\(573\) | 35.4716 | 1.48185 | ||||||||
\(574\) | −75.4812 | −3.15052 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.31265 | −0.221361 | ||||||||
\(577\) | −11.7478 | −0.489069 | −0.244534 | − | 0.969641i | \(-0.578635\pi\) | ||||
−0.244534 | + | 0.969641i | \(0.578635\pi\) | |||||||
\(578\) | 34.3644 | 1.42937 | ||||||||
\(579\) | 45.4358 | 1.88825 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.6987 | −1.23211 | ||||||||
\(582\) | 29.9238 | 1.24038 | ||||||||
\(583\) | 5.83673 | 0.241733 | ||||||||
\(584\) | 0.157676 | 0.00652470 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.8596 | −0.531224 | ||||||||
\(587\) | 4.90039 | 0.202261 | 0.101130 | − | 0.994873i | \(-0.467754\pi\) | ||||
0.101130 | + | 0.994873i | \(0.467754\pi\) | |||||||
\(588\) | −10.1599 | −0.418989 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7365 | −0.523911 | ||||||||
\(592\) | 4.26683 | 0.175366 | ||||||||
\(593\) | 18.4976 | 0.759606 | 0.379803 | − | 0.925067i | \(-0.375992\pi\) | ||||
0.379803 | + | 0.925067i | \(0.375992\pi\) | |||||||
\(594\) | −8.83709 | −0.362590 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.8691 | −0.568101 | ||||||||
\(597\) | −6.00357 | −0.245710 | ||||||||
\(598\) | −23.2211 | −0.949583 | ||||||||
\(599\) | 21.4258 | 0.875433 | 0.437717 | − | 0.899113i | \(-0.355787\pi\) | ||||
0.437717 | + | 0.899113i | \(0.355787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0390 | −1.22532 | −0.612659 | − | 0.790348i | \(-0.709900\pi\) | ||||
−0.612659 | + | 0.790348i | \(0.709900\pi\) | |||||||
\(602\) | 30.9652 | 1.26205 | ||||||||
\(603\) | 5.72217 | 0.233025 | ||||||||
\(604\) | 10.8324 | 0.440766 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.6942 | −0.475043 | ||||||||
\(607\) | 29.3882 | 1.19283 | 0.596415 | − | 0.802676i | \(-0.296591\pi\) | ||||
0.596415 | + | 0.802676i | \(0.296591\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 54.8180 | 2.22134 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.7196 | 0.959593 | ||||||||
\(612\) | −0.0497687 | −0.00201178 | ||||||||
\(613\) | 5.51121 | 0.222596 | 0.111298 | − | 0.993787i | \(-0.464499\pi\) | ||||
0.111298 | + | 0.993787i | \(0.464499\pi\) | |||||||
\(614\) | 11.9002 | 0.480251 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.523472 | 0.0210913 | ||||||||
\(617\) | −45.9066 | −1.84813 | −0.924065 | − | 0.382234i | \(-0.875155\pi\) | ||||
−0.924065 | + | 0.382234i | \(0.875155\pi\) | |||||||
\(618\) | −1.26244 | −0.0507827 | ||||||||
\(619\) | −0.478605 | −0.0192368 | −0.00961839 | − | 0.999954i | \(-0.503062\pi\) | ||||
−0.00961839 | + | 0.999954i | \(0.503062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.6161 | −0.706910 | ||||||||
\(622\) | 51.3258 | 2.05798 | ||||||||
\(623\) | −27.0465 | −1.08359 | ||||||||
\(624\) | −21.4759 | −0.859725 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.2075 | 0.487912 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −24.3083 | −0.970008 | ||||||||
\(629\) | 0.0435359 | 0.00173589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8542 | 0.670954 | 0.335477 | − | 0.942048i | \(-0.391103\pi\) | ||||
0.335477 | + | 0.942048i | \(0.391103\pi\) | |||||||
\(632\) | 1.56292 | 0.0621698 | ||||||||
\(633\) | −21.7765 | −0.865536 | ||||||||
\(634\) | −32.0947 | −1.27464 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.0352 | −0.953056 | ||||||||
\(637\) | −7.58013 | −0.300336 | ||||||||
\(638\) | −18.1631 | −0.719085 | ||||||||
\(639\) | −7.70566 | −0.304831 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9012 | −0.904542 | −0.452271 | − | 0.891880i | \(-0.649386\pi\) | ||||
−0.452271 | + | 0.891880i | \(0.649386\pi\) | |||||||
\(642\) | −49.1312 | −1.93905 | ||||||||
\(643\) | 8.58168 | 0.338429 | 0.169214 | − | 0.985579i | \(-0.445877\pi\) | ||||
0.169214 | + | 0.985579i | \(0.445877\pi\) | |||||||
\(644\) | 25.0487 | 0.987057 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.2647 | 1.07188 | 0.535942 | − | 0.844255i | \(-0.319957\pi\) | ||||
0.535942 | + | 0.844255i | \(0.319957\pi\) | |||||||
\(648\) | 1.83872 | 0.0722318 | ||||||||
\(649\) | −2.67251 | −0.104905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 55.1121 | 2.16001 | ||||||||
\(652\) | 1.16200 | 0.0455074 | ||||||||
\(653\) | 26.2598 | 1.02763 | 0.513813 | − | 0.857902i | \(-0.328233\pi\) | ||||
0.513813 | + | 0.857902i | \(0.328233\pi\) | |||||||
\(654\) | 58.5592 | 2.28985 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 46.1079 | 1.80021 | ||||||||
\(657\) | −0.549102 | −0.0214225 | ||||||||
\(658\) | −50.1069 | −1.95337 | ||||||||
\(659\) | 23.0115 | 0.896399 | 0.448200 | − | 0.893934i | \(-0.352065\pi\) | ||||
0.448200 | + | 0.893934i | \(0.352065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.5998 | −1.19019 | −0.595097 | − | 0.803654i | \(-0.702886\pi\) | ||||
−0.595097 | + | 0.803654i | \(0.702886\pi\) | |||||||
\(662\) | −28.6454 | −1.11334 | ||||||||
\(663\) | −0.219126 | −0.00851015 | ||||||||
\(664\) | −1.68807 | −0.0655100 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.38264 | 0.0535763 | ||||||||
\(667\) | −36.2069 | −1.40194 | ||||||||
\(668\) | 46.2389 | 1.78904 | ||||||||
\(669\) | 14.2811 | 0.552140 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.66099 | −0.372959 | ||||||||
\(672\) | 47.4330 | 1.82977 | ||||||||
\(673\) | −37.8667 | −1.45966 | −0.729828 | − | 0.683631i | \(-0.760400\pi\) | ||||
−0.729828 | + | 0.683631i | \(0.760400\pi\) | |||||||
\(674\) | 4.34634 | 0.167415 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.85523 | −0.340586 | ||||||||
\(677\) | −43.6943 | −1.67931 | −0.839654 | − | 0.543122i | \(-0.817242\pi\) | ||||
−0.839654 | + | 0.543122i | \(0.817242\pi\) | |||||||
\(678\) | 9.85056 | 0.378309 | ||||||||
\(679\) | −24.0826 | −0.924206 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.98579 | 0.306016 | ||||||||
\(682\) | −18.2606 | −0.699234 | ||||||||
\(683\) | 15.0878 | 0.577320 | 0.288660 | − | 0.957432i | \(-0.406790\pi\) | ||||
0.288660 | + | 0.957432i | \(0.406790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −27.7456 | −1.05933 | ||||||||
\(687\) | −42.9064 | −1.63698 | ||||||||
\(688\) | −18.9152 | −0.721134 | ||||||||
\(689\) | −17.9322 | −0.683161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.7207 | 0.407834 | 0.203917 | − | 0.978988i | \(-0.434633\pi\) | ||||
0.203917 | + | 0.978988i | \(0.434633\pi\) | |||||||
\(692\) | −23.9083 | −0.908856 | ||||||||
\(693\) | −1.82297 | −0.0692489 | ||||||||
\(694\) | −22.3439 | −0.848164 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.11585 | 0.118106 | ||||||||
\(697\) | 0.470454 | 0.0178197 | ||||||||
\(698\) | −71.4542 | −2.70458 | ||||||||
\(699\) | −20.8659 | −0.789220 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.5411 | 0.926904 | 0.463452 | − | 0.886122i | \(-0.346611\pi\) | ||||
0.463452 | + | 0.886122i | \(0.346611\pi\) | |||||||
\(702\) | 27.1501 | 1.02472 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −8.36023 | −0.315088 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 44.8605 | 1.68835 | ||||||||
\(707\) | 9.41144 | 0.353954 | ||||||||
\(708\) | 11.0052 | 0.413600 | ||||||||
\(709\) | −42.8046 | −1.60756 | −0.803781 | − | 0.594925i | \(-0.797182\pi\) | ||||
−0.803781 | + | 0.594925i | \(0.797182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.44282 | −0.204122 | ||||||||
\(712\) | −1.53732 | −0.0576136 | ||||||||
\(713\) | −36.4012 | −1.36323 | ||||||||
\(714\) | 0.462896 | 0.0173235 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.4509 | −0.465313 | ||||||||
\(717\) | 5.18011 | 0.193455 | ||||||||
\(718\) | 19.2228 | 0.717388 | ||||||||
\(719\) | 21.2712 | 0.793283 | 0.396641 | − | 0.917974i | \(-0.370176\pi\) | ||||
0.396641 | + | 0.917974i | \(0.370176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.01601 | 0.0378381 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.1987 | 0.788388 | ||||||||
\(724\) | 12.8928 | 0.479156 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −38.6995 | −1.43627 | ||||||||
\(727\) | 10.5343 | 0.390696 | 0.195348 | − | 0.980734i | \(-0.437416\pi\) | ||||
0.195348 | + | 0.980734i | \(0.437416\pi\) | |||||||
\(728\) | −1.60826 | −0.0596061 | ||||||||
\(729\) | 19.4728 | 0.721215 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.192998 | −0.00713828 | ||||||||
\(732\) | 39.7831 | 1.47043 | ||||||||
\(733\) | 25.0892 | 0.926692 | 0.463346 | − | 0.886178i | \(-0.346649\pi\) | ||||
0.463346 | + | 0.886178i | \(0.346649\pi\) | |||||||
\(734\) | −4.41362 | −0.162910 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.3291 | −1.15481 | ||||||||
\(737\) | 9.00466 | 0.331691 | ||||||||
\(738\) | 14.9410 | 0.549985 | ||||||||
\(739\) | 28.4679 | 1.04721 | 0.523604 | − | 0.851962i | \(-0.324587\pi\) | ||||
0.523604 | + | 0.851962i | \(0.324587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 37.8811 | 1.39066 | ||||||||
\(743\) | −10.1611 | −0.372774 | −0.186387 | − | 0.982476i | \(-0.559678\pi\) | ||||
−0.186387 | + | 0.982476i | \(0.559678\pi\) | |||||||
\(744\) | 3.13257 | 0.114846 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.9482 | 0.913417 | ||||||||
\(747\) | 5.87865 | 0.215089 | ||||||||
\(748\) | −0.0783182 | −0.00286360 | ||||||||
\(749\) | 39.5407 | 1.44478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.6900 | 0.937440 | 0.468720 | − | 0.883347i | \(-0.344715\pi\) | ||||
0.468720 | + | 0.883347i | \(0.344715\pi\) | |||||||
\(752\) | 30.6079 | 1.11616 | ||||||||
\(753\) | 52.0148 | 1.89552 | ||||||||
\(754\) | 55.8024 | 2.03221 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −29.2869 | −1.06515 | ||||||||
\(757\) | 31.5781 | 1.14773 | 0.573863 | − | 0.818952i | \(-0.305444\pi\) | ||||
0.573863 | + | 0.818952i | \(0.305444\pi\) | |||||||
\(758\) | −37.4027 | −1.35853 | ||||||||
\(759\) | 7.10559 | 0.257917 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.42183 | −0.124041 | −0.0620207 | − | 0.998075i | \(-0.519754\pi\) | ||||
−0.0620207 | + | 0.998075i | \(0.519754\pi\) | |||||||
\(762\) | −59.4619 | −2.15408 | ||||||||
\(763\) | −47.1283 | −1.70616 | ||||||||
\(764\) | −38.9504 | −1.40918 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.1115 | 0.835052 | ||||||||
\(767\) | 8.21074 | 0.296473 | ||||||||
\(768\) | −27.5952 | −0.995757 | ||||||||
\(769\) | −28.5086 | −1.02805 | −0.514024 | − | 0.857776i | \(-0.671846\pi\) | ||||
−0.514024 | + | 0.857776i | \(0.671846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.5104 | 1.38692 | ||||||||
\(772\) | −49.8919 | −1.79565 | ||||||||
\(773\) | 1.42585 | 0.0512844 | 0.0256422 | − | 0.999671i | \(-0.491837\pi\) | ||||
0.0256422 | + | 0.999671i | \(0.491837\pi\) | |||||||
\(774\) | −6.12934 | −0.220315 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.36886 | −0.0491391 | ||||||||
\(777\) | −6.56672 | −0.235580 | ||||||||
\(778\) | −25.3182 | −0.907701 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1260 | −0.433901 | ||||||||
\(782\) | −0.305740 | −0.0109332 | ||||||||
\(783\) | 42.3331 | 1.51286 | ||||||||
\(784\) | −9.78144 | −0.349337 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.23590 | 0.115421 | ||||||||
\(787\) | 24.3199 | 0.866912 | 0.433456 | − | 0.901175i | \(-0.357294\pi\) | ||||
0.433456 | + | 0.901175i | \(0.357294\pi\) | |||||||
\(788\) | 13.9857 | 0.498219 | ||||||||
\(789\) | 18.1737 | 0.647001 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.92771 | −0.281877 | ||||||||
\(792\) | −0.103618 | −0.00368189 | ||||||||
\(793\) | 29.6814 | 1.05402 | ||||||||
\(794\) | 23.7547 | 0.843024 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.59236 | 0.233660 | ||||||||
\(797\) | 33.5714 | 1.18916 | 0.594580 | − | 0.804037i | \(-0.297319\pi\) | ||||
0.594580 | + | 0.804037i | \(0.297319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.312303 | 0.0110485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.35366 | 0.189162 | ||||||||
\(802\) | −29.6002 | −1.04522 | ||||||||
\(803\) | −0.864091 | −0.0304931 | ||||||||
\(804\) | −37.0804 | −1.30773 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 56.1019 | 1.97610 | ||||||||
\(807\) | 8.69415 | 0.306049 | ||||||||
\(808\) | 0.534946 | 0.0188193 | ||||||||
\(809\) | 18.2407 | 0.641311 | 0.320655 | − | 0.947196i | \(-0.396097\pi\) | ||||
0.320655 | + | 0.947196i | \(0.396097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5439 | 1.28323 | 0.641615 | − | 0.767027i | \(-0.278265\pi\) | ||||
0.641615 | + | 0.767027i | \(0.278265\pi\) | |||||||
\(812\) | −60.1942 | −2.11240 | ||||||||
\(813\) | 42.0703 | 1.47547 | ||||||||
\(814\) | 2.17578 | 0.0762612 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.282761 | −0.00989863 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 25.7712 | 0.901069 | ||||||||
\(819\) | 5.60070 | 0.195704 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.6240 | 0.370781 | 0.185390 | − | 0.982665i | \(-0.440645\pi\) | ||||
0.185390 | + | 0.982665i | \(0.440645\pi\) | |||||||
\(822\) | 19.4944 | 0.679946 | ||||||||
\(823\) | 37.0620 | 1.29190 | 0.645950 | − | 0.763380i | \(-0.276462\pi\) | ||||
0.645950 | + | 0.763380i | \(0.276462\pi\) | |||||||
\(824\) | 0.0577498 | 0.00201181 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.3449 | −0.603507 | ||||||||
\(827\) | 27.8197 | 0.967385 | 0.483693 | − | 0.875238i | \(-0.339295\pi\) | ||||
0.483693 | + | 0.875238i | \(0.339295\pi\) | |||||||
\(828\) | −4.95821 | −0.172310 | ||||||||
\(829\) | 13.8198 | 0.479982 | 0.239991 | − | 0.970775i | \(-0.422855\pi\) | ||||
0.239991 | + | 0.970775i | \(0.422855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44.7658 | 1.55291 | ||||||||
\(832\) | 25.6851 | 0.890469 | ||||||||
\(833\) | −0.0998033 | −0.00345798 | ||||||||
\(834\) | 10.4906 | 0.363261 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.5602 | 1.47110 | ||||||||
\(838\) | −5.75355 | −0.198753 | ||||||||
\(839\) | 6.42771 | 0.221909 | 0.110955 | − | 0.993825i | \(-0.464609\pi\) | ||||
0.110955 | + | 0.993825i | \(0.464609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.0084 | 2.00029 | ||||||||
\(842\) | 22.5421 | 0.776850 | ||||||||
\(843\) | 19.6192 | 0.675721 | ||||||||
\(844\) | 23.9122 | 0.823090 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.91831 | 0.340999 | ||||||||
\(847\) | 31.1452 | 1.07016 | ||||||||
\(848\) | −23.1397 | −0.794622 | ||||||||
\(849\) | −58.6754 | −2.01373 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.33727 | 0.148680 | ||||||||
\(852\) | 49.9337 | 1.71070 | ||||||||
\(853\) | −26.3952 | −0.903753 | −0.451876 | − | 0.892081i | \(-0.649245\pi\) | ||||
−0.451876 | + | 0.892081i | \(0.649245\pi\) | |||||||
\(854\) | −62.7009 | −2.14558 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.24749 | 0.0768177 | ||||||||
\(857\) | 17.0307 | 0.581757 | 0.290878 | − | 0.956760i | \(-0.406053\pi\) | ||||
0.290878 | + | 0.956760i | \(0.406053\pi\) | |||||||
\(858\) | −10.9512 | −0.373868 | ||||||||
\(859\) | 24.7212 | 0.843476 | 0.421738 | − | 0.906718i | \(-0.361420\pi\) | ||||
0.421738 | + | 0.906718i | \(0.361420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −70.9607 | −2.41833 | ||||||||
\(862\) | −30.1954 | −1.02846 | ||||||||
\(863\) | −1.03890 | −0.0353646 | −0.0176823 | − | 0.999844i | \(-0.505629\pi\) | ||||
−0.0176823 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(864\) | 36.6300 | 1.24618 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 78.3513 | 2.66249 | ||||||||
\(867\) | 32.3064 | 1.09718 | ||||||||
\(868\) | −60.5172 | −2.05409 | ||||||||
\(869\) | −8.56506 | −0.290550 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.6650 | −0.937391 | ||||||||
\(872\) | −2.67877 | −0.0907147 | ||||||||
\(873\) | 4.76699 | 0.161338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.55825 | 0.120222 | ||||||||
\(877\) | 21.2022 | 0.715948 | 0.357974 | − | 0.933732i | \(-0.383468\pi\) | ||||
0.357974 | + | 0.933732i | \(0.383468\pi\) | |||||||
\(878\) | −63.5364 | −2.14425 | ||||||||
\(879\) | −12.0894 | −0.407767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.6819 | 0.528338 | 0.264169 | − | 0.964476i | \(-0.414902\pi\) | ||||
0.264169 | + | 0.964476i | \(0.414902\pi\) | |||||||
\(882\) | −3.16962 | −0.106727 | ||||||||
\(883\) | −19.6406 | −0.660960 | −0.330480 | − | 0.943813i | \(-0.607211\pi\) | ||||
−0.330480 | + | 0.943813i | \(0.607211\pi\) | |||||||
\(884\) | 0.240617 | 0.00809281 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.5319 | 0.723378 | ||||||||
\(887\) | 24.7805 | 0.832049 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(888\) | −0.373252 | −0.0125255 | ||||||||
\(889\) | 47.8548 | 1.60500 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.0765 | −0.337575 | ||||||||
\(892\) | −15.6817 | −0.525063 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −25.5339 | −0.853980 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.34372 | −0.145114 | ||||||||
\(897\) | −21.8305 | −0.728898 | ||||||||
\(898\) | 8.29672 | 0.276865 | ||||||||
\(899\) | 87.4752 | 2.91746 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.236103 | −0.00786572 | ||||||||
\(902\) | 23.5118 | 0.782856 | ||||||||
\(903\) | 29.1107 | 0.968744 | ||||||||
\(904\) | −0.450611 | −0.0149871 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 19.9432 | 0.662567 | ||||||||
\(907\) | −21.3228 | −0.708010 | −0.354005 | − | 0.935243i | \(-0.615181\pi\) | ||||
−0.354005 | + | 0.935243i | \(0.615181\pi\) | |||||||
\(908\) | −8.76899 | −0.291009 | ||||||||
\(909\) | −1.86293 | −0.0617895 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0175 | 1.12705 | 0.563524 | − | 0.826100i | \(-0.309445\pi\) | ||||
0.563524 | + | 0.826100i | \(0.309445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.25091 | 0.306160 | ||||||||
\(914\) | 18.7191 | 0.619174 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 47.1144 | 1.55670 | ||||||||
\(917\) | −2.60424 | −0.0859997 | ||||||||
\(918\) | 0.357470 | 0.0117983 | ||||||||
\(919\) | −41.7419 | −1.37694 | −0.688470 | − | 0.725265i | \(-0.741717\pi\) | ||||
−0.688470 | + | 0.725265i | \(0.741717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.1875 | 0.368640 | ||||||||
\(922\) | −13.4359 | −0.442487 | ||||||||
\(923\) | 37.2545 | 1.22625 | ||||||||
\(924\) | 11.8131 | 0.388622 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 45.0716 | 1.48114 | ||||||||
\(927\) | −0.201112 | −0.00660537 | ||||||||
\(928\) | 75.2867 | 2.47141 | ||||||||
\(929\) | −22.9048 | −0.751481 | −0.375741 | − | 0.926725i | \(-0.622612\pi\) | ||||
−0.375741 | + | 0.926725i | \(0.622612\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.9123 | 0.750517 | ||||||||
\(933\) | 48.2520 | 1.57970 | ||||||||
\(934\) | −31.2824 | −1.02359 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.318344 | 0.0104054 | ||||||||
\(937\) | −11.6675 | −0.381160 | −0.190580 | − | 0.981672i | \(-0.561037\pi\) | ||||
−0.190580 | + | 0.981672i | \(0.561037\pi\) | |||||||
\(938\) | 58.4413 | 1.90818 | ||||||||
\(939\) | 11.4765 | 0.374520 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.4401 | −1.80730 | −0.903648 | − | 0.428276i | \(-0.859121\pi\) | ||||
−0.903648 | + | 0.428276i | \(0.859121\pi\) | |||||||
\(942\) | −44.7530 | −1.45813 | ||||||||
\(943\) | 46.8690 | 1.52627 | ||||||||
\(944\) | 10.5952 | 0.344844 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.64541 | −0.313599 | ||||||||
\(947\) | 9.30476 | 0.302364 | 0.151182 | − | 0.988506i | \(-0.451692\pi\) | ||||
0.151182 | + | 0.988506i | \(0.451692\pi\) | |||||||
\(948\) | 35.2702 | 1.14552 | ||||||||
\(949\) | 2.65474 | 0.0861765 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.1726 | −0.978413 | ||||||||
\(952\) | −0.0211751 | −0.000686287 0 | ||||||||
\(953\) | −17.2460 | −0.558652 | −0.279326 | − | 0.960196i | \(-0.590111\pi\) | ||||
−0.279326 | + | 0.960196i | \(0.590111\pi\) | |||||||
\(954\) | −7.49829 | −0.242766 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.68815 | −0.183968 | ||||||||
\(957\) | −17.0754 | −0.551968 | ||||||||
\(958\) | −65.1076 | −2.10353 | ||||||||
\(959\) | −15.6891 | −0.506626 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.9445 | 1.83692 | ||||||||
\(962\) | −6.68465 | −0.215522 | ||||||||
\(963\) | −7.82680 | −0.252215 | ||||||||
\(964\) | −23.2777 | −0.749726 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 46.1161 | 1.48376 | ||||||||
\(967\) | −3.68636 | −0.118545 | −0.0592727 | − | 0.998242i | \(-0.518878\pi\) | ||||
−0.0592727 | + | 0.998242i | \(0.518878\pi\) | |||||||
\(968\) | 1.77029 | 0.0568994 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.7457 | 0.729944 | 0.364972 | − | 0.931019i | \(-0.381079\pi\) | ||||
0.364972 | + | 0.931019i | \(0.381079\pi\) | |||||||
\(972\) | 13.0802 | 0.419548 | ||||||||
\(973\) | −8.44285 | −0.270665 | ||||||||
\(974\) | 7.38171 | 0.236525 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 38.3010 | 1.22599 | ||||||||
\(977\) | −45.0177 | −1.44024 | −0.720122 | − | 0.693848i | \(-0.755914\pi\) | ||||
−0.720122 | + | 0.693848i | \(0.755914\pi\) | |||||||
\(978\) | 2.13931 | 0.0684075 | ||||||||
\(979\) | 8.42476 | 0.269257 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.32873 | 0.297843 | ||||||||
\(982\) | −9.19557 | −0.293442 | ||||||||
\(983\) | 42.3156 | 1.34966 | 0.674830 | − | 0.737974i | \(-0.264217\pi\) | ||||
0.674830 | + | 0.737974i | \(0.264217\pi\) | |||||||
\(984\) | −4.03341 | −0.128580 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.734720 | 0.0233982 | ||||||||
\(987\) | −47.1061 | −1.49940 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.2274 | −0.611397 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.1589 | −0.989796 | −0.494898 | − | 0.868951i | \(-0.664795\pi\) | ||||
−0.494898 | + | 0.868951i | \(0.664795\pi\) | |||||||
\(992\) | 75.6906 | 2.40318 | ||||||||
\(993\) | −26.9299 | −0.854594 | ||||||||
\(994\) | −78.6988 | −2.49618 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −38.0945 | −1.20707 | ||||||||
\(997\) | −38.8905 | −1.23167 | −0.615837 | − | 0.787873i | \(-0.711182\pi\) | ||||
−0.615837 | + | 0.787873i | \(0.711182\pi\) | |||||||
\(998\) | 44.1186 | 1.39655 | ||||||||
\(999\) | −5.07113 | −0.160444 |
(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 | 9025.2.a.cd.1.1 | 9 | ||
5.4 | even | 2 | 1805.2.a.u.1.9 | 9 | |||
19.2 | odd | 18 | 475.2.l.b.251.1 | 18 | |||
19.10 | odd | 18 | 475.2.l.b.176.1 | 18 | |||
19.18 | odd | 2 | 9025.2.a.ce.1.9 | 9 | |||
95.2 | even | 36 | 475.2.u.c.99.6 | 36 | |||
95.29 | odd | 18 | 95.2.k.b.81.3 | yes | 18 | ||
95.48 | even | 36 | 475.2.u.c.24.6 | 36 | |||
95.59 | odd | 18 | 95.2.k.b.61.3 | ✓ | 18 | ||
95.67 | even | 36 | 475.2.u.c.24.1 | 36 | |||
95.78 | even | 36 | 475.2.u.c.99.1 | 36 | |||
95.94 | odd | 2 | 1805.2.a.t.1.1 | 9 | |||
285.29 | even | 18 | 855.2.bs.b.271.1 | 18 | |||
285.59 | even | 18 | 855.2.bs.b.631.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.61.3 | ✓ | 18 | 95.59 | odd | 18 | ||
95.2.k.b.81.3 | yes | 18 | 95.29 | odd | 18 | ||
475.2.l.b.176.1 | 18 | 19.10 | odd | 18 | |||
475.2.l.b.251.1 | 18 | 19.2 | odd | 18 | |||
475.2.u.c.24.1 | 36 | 95.67 | even | 36 | |||
475.2.u.c.24.6 | 36 | 95.48 | even | 36 | |||
475.2.u.c.99.1 | 36 | 95.78 | even | 36 | |||
475.2.u.c.99.6 | 36 | 95.2 | even | 36 | |||
855.2.bs.b.271.1 | 18 | 285.29 | even | 18 | |||
855.2.bs.b.631.1 | 18 | 285.59 | even | 18 | |||
1805.2.a.t.1.1 | 9 | 95.94 | odd | 2 | |||
1805.2.a.u.1.9 | 9 | 5.4 | even | 2 | |||
9025.2.a.cd.1.1 | 9 | 1.1 | even | 1 | trivial | ||
9025.2.a.ce.1.9 | 9 | 19.18 | odd | 2 |