Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(1,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("349.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.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: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.358260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 349.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.358260 | −0.253328 | −0.126664 | − | 0.991946i | \(-0.540427\pi\) | ||||
−0.126664 | + | 0.991946i | \(0.540427\pi\) | |||||||
\(3\) | −1.20564 | −0.696078 | −0.348039 | − | 0.937480i | \(-0.613152\pi\) | ||||
−0.348039 | + | 0.937480i | \(0.613152\pi\) | |||||||
\(4\) | −1.87165 | −0.935825 | ||||||||
\(5\) | −1.57855 | −0.705949 | −0.352975 | − | 0.935633i | \(-0.614830\pi\) | ||||
−0.352975 | + | 0.935633i | \(0.614830\pi\) | |||||||
\(6\) | 0.431934 | 0.176336 | ||||||||
\(7\) | 1.55949 | 0.589433 | 0.294716 | − | 0.955585i | \(-0.404775\pi\) | ||||
0.294716 | + | 0.955585i | \(0.404775\pi\) | |||||||
\(8\) | 1.38706 | 0.490399 | ||||||||
\(9\) | −1.54642 | −0.515475 | ||||||||
\(10\) | 0.565531 | 0.178837 | ||||||||
\(11\) | 0.789060 | 0.237910 | 0.118955 | − | 0.992900i | \(-0.462046\pi\) | ||||
0.118955 | + | 0.992900i | \(0.462046\pi\) | |||||||
\(12\) | 2.25654 | 0.651408 | ||||||||
\(13\) | 2.87707 | 0.797956 | 0.398978 | − | 0.916960i | \(-0.369365\pi\) | ||||
0.398978 | + | 0.916960i | \(0.369365\pi\) | |||||||
\(14\) | −0.558704 | −0.149320 | ||||||||
\(15\) | 1.90317 | 0.491396 | ||||||||
\(16\) | 3.24637 | 0.811593 | ||||||||
\(17\) | 4.64739 | 1.12716 | 0.563579 | − | 0.826062i | \(-0.309424\pi\) | ||||
0.563579 | + | 0.826062i | \(0.309424\pi\) | |||||||
\(18\) | 0.554022 | 0.130584 | ||||||||
\(19\) | −2.65313 | −0.608670 | −0.304335 | − | 0.952565i | \(-0.598434\pi\) | ||||
−0.304335 | + | 0.952565i | \(0.598434\pi\) | |||||||
\(20\) | 2.95449 | 0.660645 | ||||||||
\(21\) | −1.88019 | −0.410291 | ||||||||
\(22\) | −0.282688 | −0.0602694 | ||||||||
\(23\) | 6.97009 | 1.45337 | 0.726683 | − | 0.686973i | \(-0.241061\pi\) | ||||
0.726683 | + | 0.686973i | \(0.241061\pi\) | |||||||
\(24\) | −1.67230 | −0.341356 | ||||||||
\(25\) | −2.50818 | −0.501636 | ||||||||
\(26\) | −1.03074 | −0.202145 | ||||||||
\(27\) | 5.48137 | 1.05489 | ||||||||
\(28\) | −2.91882 | −0.551606 | ||||||||
\(29\) | 9.67743 | 1.79705 | 0.898527 | − | 0.438919i | \(-0.144638\pi\) | ||||
0.898527 | + | 0.438919i | \(0.144638\pi\) | |||||||
\(30\) | −0.681829 | −0.124484 | ||||||||
\(31\) | −1.20813 | −0.216986 | −0.108493 | − | 0.994097i | \(-0.534603\pi\) | ||||
−0.108493 | + | 0.994097i | \(0.534603\pi\) | |||||||
\(32\) | −3.93716 | −0.695998 | ||||||||
\(33\) | −0.951324 | −0.165604 | ||||||||
\(34\) | −1.66497 | −0.285541 | ||||||||
\(35\) | −2.46174 | −0.416109 | ||||||||
\(36\) | 2.89437 | 0.482394 | ||||||||
\(37\) | 7.25596 | 1.19287 | 0.596436 | − | 0.802661i | \(-0.296583\pi\) | ||||
0.596436 | + | 0.802661i | \(0.296583\pi\) | |||||||
\(38\) | 0.950510 | 0.154193 | ||||||||
\(39\) | −3.46872 | −0.555440 | ||||||||
\(40\) | −2.18954 | −0.346197 | ||||||||
\(41\) | −6.83210 | −1.06699 | −0.533497 | − | 0.845802i | \(-0.679123\pi\) | ||||
−0.533497 | + | 0.845802i | \(0.679123\pi\) | |||||||
\(42\) | 0.673597 | 0.103938 | ||||||||
\(43\) | −5.06871 | −0.772971 | −0.386485 | − | 0.922295i | \(-0.626311\pi\) | ||||
−0.386485 | + | 0.922295i | \(0.626311\pi\) | |||||||
\(44\) | −1.47684 | −0.222642 | ||||||||
\(45\) | 2.44111 | 0.363899 | ||||||||
\(46\) | −2.49711 | −0.368178 | ||||||||
\(47\) | 3.70134 | 0.539896 | 0.269948 | − | 0.962875i | \(-0.412993\pi\) | ||||
0.269948 | + | 0.962875i | \(0.412993\pi\) | |||||||
\(48\) | −3.91397 | −0.564932 | ||||||||
\(49\) | −4.56798 | −0.652569 | ||||||||
\(50\) | 0.898580 | 0.127078 | ||||||||
\(51\) | −5.60309 | −0.784590 | ||||||||
\(52\) | −5.38487 | −0.746747 | ||||||||
\(53\) | −10.8348 | −1.48828 | −0.744138 | − | 0.668026i | \(-0.767139\pi\) | ||||
−0.744138 | + | 0.668026i | \(0.767139\pi\) | |||||||
\(54\) | −1.96375 | −0.267233 | ||||||||
\(55\) | −1.24557 | −0.167953 | ||||||||
\(56\) | 2.16310 | 0.289057 | ||||||||
\(57\) | 3.19873 | 0.423682 | ||||||||
\(58\) | −3.46704 | −0.455244 | ||||||||
\(59\) | 3.23659 | 0.421368 | 0.210684 | − | 0.977554i | \(-0.432431\pi\) | ||||
0.210684 | + | 0.977554i | \(0.432431\pi\) | |||||||
\(60\) | −3.56206 | −0.459861 | ||||||||
\(61\) | 14.5741 | 1.86603 | 0.933014 | − | 0.359840i | \(-0.117169\pi\) | ||||
0.933014 | + | 0.359840i | \(0.117169\pi\) | |||||||
\(62\) | 0.432824 | 0.0549686 | ||||||||
\(63\) | −2.41164 | −0.303838 | ||||||||
\(64\) | −5.08222 | −0.635277 | ||||||||
\(65\) | −4.54160 | −0.563316 | ||||||||
\(66\) | 0.340821 | 0.0419522 | ||||||||
\(67\) | 9.43650 | 1.15285 | 0.576426 | − | 0.817149i | \(-0.304447\pi\) | ||||
0.576426 | + | 0.817149i | \(0.304447\pi\) | |||||||
\(68\) | −8.69829 | −1.05482 | ||||||||
\(69\) | −8.40345 | −1.01166 | ||||||||
\(70\) | 0.881942 | 0.105412 | ||||||||
\(71\) | 13.6644 | 1.62167 | 0.810834 | − | 0.585276i | \(-0.199014\pi\) | ||||
0.810834 | + | 0.585276i | \(0.199014\pi\) | |||||||
\(72\) | −2.14498 | −0.252788 | ||||||||
\(73\) | −6.93119 | −0.811235 | −0.405617 | − | 0.914043i | \(-0.632943\pi\) | ||||
−0.405617 | + | 0.914043i | \(0.632943\pi\) | |||||||
\(74\) | −2.59952 | −0.302188 | ||||||||
\(75\) | 3.02397 | 0.349178 | ||||||||
\(76\) | 4.96573 | 0.569608 | ||||||||
\(77\) | 1.23053 | 0.140232 | ||||||||
\(78\) | 1.24270 | 0.140709 | ||||||||
\(79\) | −0.331026 | −0.0372433 | −0.0186216 | − | 0.999827i | \(-0.505928\pi\) | ||||
−0.0186216 | + | 0.999827i | \(0.505928\pi\) | |||||||
\(80\) | −5.12456 | −0.572944 | ||||||||
\(81\) | −1.96930 | −0.218811 | ||||||||
\(82\) | 2.44767 | 0.270300 | ||||||||
\(83\) | 8.48465 | 0.931311 | 0.465656 | − | 0.884966i | \(-0.345819\pi\) | ||||
0.465656 | + | 0.884966i | \(0.345819\pi\) | |||||||
\(84\) | 3.51906 | 0.383961 | ||||||||
\(85\) | −7.33614 | −0.795716 | ||||||||
\(86\) | 1.81592 | 0.195815 | ||||||||
\(87\) | −11.6675 | −1.25089 | ||||||||
\(88\) | 1.09447 | 0.116671 | ||||||||
\(89\) | −1.23323 | −0.130722 | −0.0653609 | − | 0.997862i | \(-0.520820\pi\) | ||||
−0.0653609 | + | 0.997862i | \(0.520820\pi\) | |||||||
\(90\) | −0.874552 | −0.0921858 | ||||||||
\(91\) | 4.48677 | 0.470341 | ||||||||
\(92\) | −13.0456 | −1.36010 | ||||||||
\(93\) | 1.45657 | 0.151039 | ||||||||
\(94\) | −1.32604 | −0.136771 | ||||||||
\(95\) | 4.18810 | 0.429690 | ||||||||
\(96\) | 4.74681 | 0.484469 | ||||||||
\(97\) | −3.08231 | −0.312961 | −0.156481 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156481 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(98\) | 1.63653 | 0.165314 | ||||||||
\(99\) | −1.22022 | −0.122637 | ||||||||
\(100\) | 4.69443 | 0.469443 | ||||||||
\(101\) | 1.86510 | 0.185585 | 0.0927923 | − | 0.995685i | \(-0.470421\pi\) | ||||
0.0927923 | + | 0.995685i | \(0.470421\pi\) | |||||||
\(102\) | 2.00736 | 0.198759 | ||||||||
\(103\) | −14.2911 | −1.40815 | −0.704074 | − | 0.710127i | \(-0.748638\pi\) | ||||
−0.704074 | + | 0.710127i | \(0.748638\pi\) | |||||||
\(104\) | 3.99066 | 0.391317 | ||||||||
\(105\) | 2.96798 | 0.289645 | ||||||||
\(106\) | 3.88168 | 0.377022 | ||||||||
\(107\) | 7.90169 | 0.763885 | 0.381943 | − | 0.924186i | \(-0.375255\pi\) | ||||
0.381943 | + | 0.924186i | \(0.375255\pi\) | |||||||
\(108\) | −10.2592 | −0.987192 | ||||||||
\(109\) | −9.71011 | −0.930060 | −0.465030 | − | 0.885295i | \(-0.653956\pi\) | ||||
−0.465030 | + | 0.885295i | \(0.653956\pi\) | |||||||
\(110\) | 0.446238 | 0.0425471 | ||||||||
\(111\) | −8.74809 | −0.830332 | ||||||||
\(112\) | 5.06269 | 0.478380 | ||||||||
\(113\) | 11.1633 | 1.05015 | 0.525076 | − | 0.851055i | \(-0.324037\pi\) | ||||
0.525076 | + | 0.851055i | \(0.324037\pi\) | |||||||
\(114\) | −1.14598 | −0.107331 | ||||||||
\(115\) | −11.0026 | −1.02600 | ||||||||
\(116\) | −18.1128 | −1.68173 | ||||||||
\(117\) | −4.44917 | −0.411326 | ||||||||
\(118\) | −1.15954 | −0.106744 | ||||||||
\(119\) | 7.24757 | 0.664383 | ||||||||
\(120\) | 2.63980 | 0.240980 | ||||||||
\(121\) | −10.3774 | −0.943399 | ||||||||
\(122\) | −5.22133 | −0.472717 | ||||||||
\(123\) | 8.23708 | 0.742712 | ||||||||
\(124\) | 2.26119 | 0.203061 | ||||||||
\(125\) | 11.8520 | 1.06008 | ||||||||
\(126\) | 0.863993 | 0.0769706 | ||||||||
\(127\) | −11.4985 | −1.02032 | −0.510162 | − | 0.860078i | \(-0.670415\pi\) | ||||
−0.510162 | + | 0.860078i | \(0.670415\pi\) | |||||||
\(128\) | 9.69507 | 0.856932 | ||||||||
\(129\) | 6.11106 | 0.538048 | ||||||||
\(130\) | 1.62707 | 0.142704 | ||||||||
\(131\) | 15.0200 | 1.31231 | 0.656154 | − | 0.754627i | \(-0.272182\pi\) | ||||
0.656154 | + | 0.754627i | \(0.272182\pi\) | |||||||
\(132\) | 1.78055 | 0.154977 | ||||||||
\(133\) | −4.13754 | −0.358770 | ||||||||
\(134\) | −3.38072 | −0.292050 | ||||||||
\(135\) | −8.65261 | −0.744698 | ||||||||
\(136\) | 6.44619 | 0.552757 | ||||||||
\(137\) | 5.18646 | 0.443110 | 0.221555 | − | 0.975148i | \(-0.428887\pi\) | ||||
0.221555 | + | 0.975148i | \(0.428887\pi\) | |||||||
\(138\) | 3.01062 | 0.256281 | ||||||||
\(139\) | 16.8266 | 1.42721 | 0.713605 | − | 0.700548i | \(-0.247061\pi\) | ||||
0.713605 | + | 0.700548i | \(0.247061\pi\) | |||||||
\(140\) | 4.60751 | 0.389406 | ||||||||
\(141\) | −4.46250 | −0.375810 | ||||||||
\(142\) | −4.89542 | −0.410814 | ||||||||
\(143\) | 2.27018 | 0.189842 | ||||||||
\(144\) | −5.02027 | −0.418356 | ||||||||
\(145\) | −15.2763 | −1.26863 | ||||||||
\(146\) | 2.48317 | 0.205508 | ||||||||
\(147\) | 5.50736 | 0.454239 | ||||||||
\(148\) | −13.5806 | −1.11632 | ||||||||
\(149\) | 6.55102 | 0.536681 | 0.268340 | − | 0.963324i | \(-0.413525\pi\) | ||||
0.268340 | + | 0.963324i | \(0.413525\pi\) | |||||||
\(150\) | −1.08337 | −0.0884565 | ||||||||
\(151\) | 20.9181 | 1.70229 | 0.851144 | − | 0.524932i | \(-0.175909\pi\) | ||||
0.851144 | + | 0.524932i | \(0.175909\pi\) | |||||||
\(152\) | −3.68004 | −0.298491 | ||||||||
\(153\) | −7.18684 | −0.581021 | ||||||||
\(154\) | −0.440850 | −0.0355247 | ||||||||
\(155\) | 1.90709 | 0.153181 | ||||||||
\(156\) | 6.49223 | 0.519795 | ||||||||
\(157\) | −2.27007 | −0.181172 | −0.0905858 | − | 0.995889i | \(-0.528874\pi\) | ||||
−0.0905858 | + | 0.995889i | \(0.528874\pi\) | |||||||
\(158\) | 0.118593 | 0.00943477 | ||||||||
\(159\) | 13.0629 | 1.03596 | ||||||||
\(160\) | 6.21500 | 0.491339 | ||||||||
\(161\) | 10.8698 | 0.856661 | ||||||||
\(162\) | 0.705521 | 0.0554309 | ||||||||
\(163\) | 9.57334 | 0.749842 | 0.374921 | − | 0.927057i | \(-0.377670\pi\) | ||||
0.374921 | + | 0.927057i | \(0.377670\pi\) | |||||||
\(164\) | 12.7873 | 0.998520 | ||||||||
\(165\) | 1.50171 | 0.116908 | ||||||||
\(166\) | −3.03971 | −0.235927 | ||||||||
\(167\) | 18.4356 | 1.42659 | 0.713297 | − | 0.700862i | \(-0.247201\pi\) | ||||
0.713297 | + | 0.700862i | \(0.247201\pi\) | |||||||
\(168\) | −2.60793 | −0.201206 | ||||||||
\(169\) | −4.72246 | −0.363266 | ||||||||
\(170\) | 2.62824 | 0.201577 | ||||||||
\(171\) | 4.10287 | 0.313754 | ||||||||
\(172\) | 9.48685 | 0.723366 | ||||||||
\(173\) | −7.03539 | −0.534890 | −0.267445 | − | 0.963573i | \(-0.586179\pi\) | ||||
−0.267445 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(174\) | 4.18001 | 0.316886 | ||||||||
\(175\) | −3.91149 | −0.295680 | ||||||||
\(176\) | 2.56158 | 0.193086 | ||||||||
\(177\) | −3.90217 | −0.293305 | ||||||||
\(178\) | 0.441816 | 0.0331155 | ||||||||
\(179\) | −18.8686 | −1.41031 | −0.705153 | − | 0.709055i | \(-0.749122\pi\) | ||||
−0.705153 | + | 0.709055i | \(0.749122\pi\) | |||||||
\(180\) | −4.56890 | −0.340546 | ||||||||
\(181\) | −2.10777 | −0.156669 | −0.0783345 | − | 0.996927i | \(-0.524960\pi\) | ||||
−0.0783345 | + | 0.996927i | \(0.524960\pi\) | |||||||
\(182\) | −1.60743 | −0.119151 | ||||||||
\(183\) | −17.5712 | −1.29890 | ||||||||
\(184\) | 9.66792 | 0.712728 | ||||||||
\(185\) | −11.4539 | −0.842107 | ||||||||
\(186\) | −0.521831 | −0.0382625 | ||||||||
\(187\) | 3.66707 | 0.268162 | ||||||||
\(188\) | −6.92761 | −0.505248 | ||||||||
\(189\) | 8.54815 | 0.621786 | ||||||||
\(190\) | −1.50043 | −0.108853 | ||||||||
\(191\) | −6.25482 | −0.452583 | −0.226292 | − | 0.974060i | \(-0.572660\pi\) | ||||
−0.226292 | + | 0.974060i | \(0.572660\pi\) | |||||||
\(192\) | 6.12734 | 0.442203 | ||||||||
\(193\) | −12.1063 | −0.871431 | −0.435716 | − | 0.900084i | \(-0.643505\pi\) | ||||
−0.435716 | + | 0.900084i | \(0.643505\pi\) | |||||||
\(194\) | 1.10427 | 0.0792819 | ||||||||
\(195\) | 5.47555 | 0.392112 | ||||||||
\(196\) | 8.54967 | 0.610690 | ||||||||
\(197\) | −12.3250 | −0.878121 | −0.439061 | − | 0.898457i | \(-0.644689\pi\) | ||||
−0.439061 | + | 0.898457i | \(0.644689\pi\) | |||||||
\(198\) | 0.437156 | 0.0310673 | ||||||||
\(199\) | 0.0989600 | 0.00701509 | 0.00350754 | − | 0.999994i | \(-0.498884\pi\) | ||||
0.00350754 | + | 0.999994i | \(0.498884\pi\) | |||||||
\(200\) | −3.47899 | −0.246002 | ||||||||
\(201\) | −11.3771 | −0.802476 | ||||||||
\(202\) | −0.668191 | −0.0470138 | ||||||||
\(203\) | 15.0919 | 1.05924 | ||||||||
\(204\) | 10.4870 | 0.734239 | ||||||||
\(205\) | 10.7848 | 0.753244 | ||||||||
\(206\) | 5.11994 | 0.356723 | ||||||||
\(207\) | −10.7787 | −0.749173 | ||||||||
\(208\) | 9.34005 | 0.647616 | ||||||||
\(209\) | −2.09348 | −0.144809 | ||||||||
\(210\) | −1.06331 | −0.0733752 | ||||||||
\(211\) | 22.9635 | 1.58087 | 0.790437 | − | 0.612543i | \(-0.209854\pi\) | ||||
0.790437 | + | 0.612543i | \(0.209854\pi\) | |||||||
\(212\) | 20.2790 | 1.39277 | ||||||||
\(213\) | −16.4744 | −1.12881 | ||||||||
\(214\) | −2.83086 | −0.193514 | ||||||||
\(215\) | 8.00121 | 0.545678 | ||||||||
\(216\) | 7.60297 | 0.517316 | ||||||||
\(217\) | −1.88406 | −0.127899 | ||||||||
\(218\) | 3.47874 | 0.235610 | ||||||||
\(219\) | 8.35654 | 0.564683 | ||||||||
\(220\) | 2.33127 | 0.157174 | ||||||||
\(221\) | 13.3709 | 0.899422 | ||||||||
\(222\) | 3.13409 | 0.210346 | ||||||||
\(223\) | 11.5656 | 0.774488 | 0.387244 | − | 0.921977i | \(-0.373427\pi\) | ||||
0.387244 | + | 0.921977i | \(0.373427\pi\) | |||||||
\(224\) | −6.13997 | −0.410244 | ||||||||
\(225\) | 3.87871 | 0.258581 | ||||||||
\(226\) | −3.99935 | −0.266033 | ||||||||
\(227\) | −16.5148 | −1.09612 | −0.548062 | − | 0.836438i | \(-0.684634\pi\) | ||||
−0.548062 | + | 0.836438i | \(0.684634\pi\) | |||||||
\(228\) | −5.98690 | −0.396492 | ||||||||
\(229\) | −24.0669 | −1.59039 | −0.795194 | − | 0.606355i | \(-0.792631\pi\) | ||||
−0.795194 | + | 0.606355i | \(0.792631\pi\) | |||||||
\(230\) | 3.94181 | 0.259915 | ||||||||
\(231\) | −1.48358 | −0.0976126 | ||||||||
\(232\) | 13.4231 | 0.881273 | ||||||||
\(233\) | −0.181911 | −0.0119174 | −0.00595868 | − | 0.999982i | \(-0.501897\pi\) | ||||
−0.00595868 | + | 0.999982i | \(0.501897\pi\) | |||||||
\(234\) | 1.59396 | 0.104200 | ||||||||
\(235\) | −5.84275 | −0.381139 | ||||||||
\(236\) | −6.05776 | −0.394327 | ||||||||
\(237\) | 0.399099 | 0.0259243 | ||||||||
\(238\) | −2.59651 | −0.168307 | ||||||||
\(239\) | 18.2061 | 1.17766 | 0.588828 | − | 0.808258i | \(-0.299590\pi\) | ||||
0.588828 | + | 0.808258i | \(0.299590\pi\) | |||||||
\(240\) | 6.17839 | 0.398814 | ||||||||
\(241\) | −11.2575 | −0.725162 | −0.362581 | − | 0.931952i | \(-0.618104\pi\) | ||||
−0.362581 | + | 0.931952i | \(0.618104\pi\) | |||||||
\(242\) | 3.71780 | 0.238989 | ||||||||
\(243\) | −14.0698 | −0.902580 | ||||||||
\(244\) | −27.2777 | −1.74628 | ||||||||
\(245\) | 7.21079 | 0.460681 | ||||||||
\(246\) | −2.95101 | −0.188150 | ||||||||
\(247\) | −7.63325 | −0.485692 | ||||||||
\(248\) | −1.67574 | −0.106410 | ||||||||
\(249\) | −10.2295 | −0.648266 | ||||||||
\(250\) | −4.24611 | −0.268548 | ||||||||
\(251\) | 9.20365 | 0.580929 | 0.290465 | − | 0.956886i | \(-0.406190\pi\) | ||||
0.290465 | + | 0.956886i | \(0.406190\pi\) | |||||||
\(252\) | 4.51374 | 0.284339 | ||||||||
\(253\) | 5.49982 | 0.345771 | ||||||||
\(254\) | 4.11944 | 0.258477 | ||||||||
\(255\) | 8.84476 | 0.553881 | ||||||||
\(256\) | 6.69108 | 0.418193 | ||||||||
\(257\) | −29.8651 | −1.86293 | −0.931466 | − | 0.363827i | \(-0.881470\pi\) | ||||
−0.931466 | + | 0.363827i | \(0.881470\pi\) | |||||||
\(258\) | −2.18935 | −0.136303 | ||||||||
\(259\) | 11.3156 | 0.703118 | ||||||||
\(260\) | 8.50029 | 0.527166 | ||||||||
\(261\) | −14.9654 | −0.926336 | ||||||||
\(262\) | −5.38108 | −0.332444 | ||||||||
\(263\) | 7.09679 | 0.437607 | 0.218803 | − | 0.975769i | \(-0.429785\pi\) | ||||
0.218803 | + | 0.975769i | \(0.429785\pi\) | |||||||
\(264\) | −1.31954 | −0.0812121 | ||||||||
\(265\) | 17.1033 | 1.05065 | ||||||||
\(266\) | 1.48231 | 0.0908865 | ||||||||
\(267\) | 1.48683 | 0.0909926 | ||||||||
\(268\) | −17.6618 | −1.07887 | ||||||||
\(269\) | 0.833960 | 0.0508474 | 0.0254237 | − | 0.999677i | \(-0.491907\pi\) | ||||
0.0254237 | + | 0.999677i | \(0.491907\pi\) | |||||||
\(270\) | 3.09988 | 0.188653 | ||||||||
\(271\) | −21.9704 | −1.33461 | −0.667304 | − | 0.744786i | \(-0.732552\pi\) | ||||
−0.667304 | + | 0.744786i | \(0.732552\pi\) | |||||||
\(272\) | 15.0872 | 0.914793 | ||||||||
\(273\) | −5.40944 | −0.327394 | ||||||||
\(274\) | −1.85810 | −0.112252 | ||||||||
\(275\) | −1.97910 | −0.119344 | ||||||||
\(276\) | 15.7283 | 0.946733 | ||||||||
\(277\) | 9.95992 | 0.598434 | 0.299217 | − | 0.954185i | \(-0.403275\pi\) | ||||
0.299217 | + | 0.954185i | \(0.403275\pi\) | |||||||
\(278\) | −6.02828 | −0.361552 | ||||||||
\(279\) | 1.86828 | 0.111851 | ||||||||
\(280\) | −3.41457 | −0.204060 | ||||||||
\(281\) | 13.2894 | 0.792781 | 0.396391 | − | 0.918082i | \(-0.370263\pi\) | ||||
0.396391 | + | 0.918082i | \(0.370263\pi\) | |||||||
\(282\) | 1.59873 | 0.0952032 | ||||||||
\(283\) | −16.2832 | −0.967937 | −0.483969 | − | 0.875085i | \(-0.660805\pi\) | ||||
−0.483969 | + | 0.875085i | \(0.660805\pi\) | |||||||
\(284\) | −25.5750 | −1.51760 | ||||||||
\(285\) | −5.04935 | −0.299098 | ||||||||
\(286\) | −0.813315 | −0.0480923 | ||||||||
\(287\) | −10.6546 | −0.628922 | ||||||||
\(288\) | 6.08852 | 0.358769 | ||||||||
\(289\) | 4.59823 | 0.270484 | ||||||||
\(290\) | 5.47289 | 0.321379 | ||||||||
\(291\) | 3.71617 | 0.217846 | ||||||||
\(292\) | 12.9728 | 0.759173 | ||||||||
\(293\) | −23.1953 | −1.35508 | −0.677542 | − | 0.735484i | \(-0.736955\pi\) | ||||
−0.677542 | + | 0.735484i | \(0.736955\pi\) | |||||||
\(294\) | −1.97307 | −0.115072 | ||||||||
\(295\) | −5.10912 | −0.297464 | ||||||||
\(296\) | 10.0644 | 0.584983 | ||||||||
\(297\) | 4.32512 | 0.250969 | ||||||||
\(298\) | −2.34697 | −0.135956 | ||||||||
\(299\) | 20.0535 | 1.15972 | ||||||||
\(300\) | −5.65981 | −0.326769 | ||||||||
\(301\) | −7.90461 | −0.455614 | ||||||||
\(302\) | −7.49411 | −0.431237 | ||||||||
\(303\) | −2.24865 | −0.129181 | ||||||||
\(304\) | −8.61305 | −0.493992 | ||||||||
\(305\) | −23.0060 | −1.31732 | ||||||||
\(306\) | 2.57476 | 0.147189 | ||||||||
\(307\) | −12.3670 | −0.705825 | −0.352912 | − | 0.935656i | \(-0.614809\pi\) | ||||
−0.352912 | + | 0.935656i | \(0.614809\pi\) | |||||||
\(308\) | −2.30313 | −0.131233 | ||||||||
\(309\) | 17.2300 | 0.980181 | ||||||||
\(310\) | −0.683234 | −0.0388051 | ||||||||
\(311\) | −19.4193 | −1.10117 | −0.550583 | − | 0.834781i | \(-0.685594\pi\) | ||||
−0.550583 | + | 0.834781i | \(0.685594\pi\) | |||||||
\(312\) | −4.81131 | −0.272387 | ||||||||
\(313\) | 11.2697 | 0.636999 | 0.318499 | − | 0.947923i | \(-0.396821\pi\) | ||||
0.318499 | + | 0.947923i | \(0.396821\pi\) | |||||||
\(314\) | 0.813276 | 0.0458958 | ||||||||
\(315\) | 3.80689 | 0.214494 | ||||||||
\(316\) | 0.619564 | 0.0348532 | ||||||||
\(317\) | 9.30611 | 0.522683 | 0.261342 | − | 0.965246i | \(-0.415835\pi\) | ||||
0.261342 | + | 0.965246i | \(0.415835\pi\) | |||||||
\(318\) | −4.67992 | −0.262437 | ||||||||
\(319\) | 7.63607 | 0.427538 | ||||||||
\(320\) | 8.02254 | 0.448474 | ||||||||
\(321\) | −9.52662 | −0.531724 | ||||||||
\(322\) | −3.89422 | −0.217016 | ||||||||
\(323\) | −12.3301 | −0.686067 | ||||||||
\(324\) | 3.68584 | 0.204769 | ||||||||
\(325\) | −7.21621 | −0.400283 | ||||||||
\(326\) | −3.42974 | −0.189956 | ||||||||
\(327\) | 11.7069 | 0.647394 | ||||||||
\(328\) | −9.47651 | −0.523253 | ||||||||
\(329\) | 5.77221 | 0.318232 | ||||||||
\(330\) | −0.538004 | −0.0296161 | ||||||||
\(331\) | −4.26779 | −0.234579 | −0.117290 | − | 0.993098i | \(-0.537421\pi\) | ||||
−0.117290 | + | 0.993098i | \(0.537421\pi\) | |||||||
\(332\) | −15.8803 | −0.871544 | ||||||||
\(333\) | −11.2208 | −0.614895 | ||||||||
\(334\) | −6.60475 | −0.361396 | ||||||||
\(335\) | −14.8960 | −0.813855 | ||||||||
\(336\) | −6.10380 | −0.332990 | ||||||||
\(337\) | 25.2589 | 1.37594 | 0.687971 | − | 0.725738i | \(-0.258502\pi\) | ||||
0.687971 | + | 0.725738i | \(0.258502\pi\) | |||||||
\(338\) | 1.69187 | 0.0920255 | ||||||||
\(339\) | −13.4589 | −0.730988 | ||||||||
\(340\) | 13.7307 | 0.744651 | ||||||||
\(341\) | −0.953284 | −0.0516232 | ||||||||
\(342\) | −1.46989 | −0.0794827 | ||||||||
\(343\) | −18.0402 | −0.974078 | ||||||||
\(344\) | −7.03059 | −0.379064 | ||||||||
\(345\) | 13.2653 | 0.714178 | ||||||||
\(346\) | 2.52050 | 0.135503 | ||||||||
\(347\) | 0.724410 | 0.0388884 | 0.0194442 | − | 0.999811i | \(-0.493810\pi\) | ||||
0.0194442 | + | 0.999811i | \(0.493810\pi\) | |||||||
\(348\) | 21.8375 | 1.17061 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | 1.40133 | 0.0749042 | ||||||||
\(351\) | 15.7703 | 0.841755 | ||||||||
\(352\) | −3.10665 | −0.165585 | ||||||||
\(353\) | −21.4860 | −1.14359 | −0.571793 | − | 0.820398i | \(-0.693752\pi\) | ||||
−0.571793 | + | 0.820398i | \(0.693752\pi\) | |||||||
\(354\) | 1.39799 | 0.0743024 | ||||||||
\(355\) | −21.5700 | −1.14482 | ||||||||
\(356\) | 2.30817 | 0.122333 | ||||||||
\(357\) | −8.73798 | −0.462463 | ||||||||
\(358\) | 6.75987 | 0.357270 | ||||||||
\(359\) | −12.4632 | −0.657780 | −0.328890 | − | 0.944368i | \(-0.606675\pi\) | ||||
−0.328890 | + | 0.944368i | \(0.606675\pi\) | |||||||
\(360\) | 3.38596 | 0.178456 | ||||||||
\(361\) | −11.9609 | −0.629521 | ||||||||
\(362\) | 0.755128 | 0.0396886 | ||||||||
\(363\) | 12.5114 | 0.656679 | ||||||||
\(364\) | −8.39766 | −0.440157 | ||||||||
\(365\) | 10.9412 | 0.572690 | ||||||||
\(366\) | 6.29506 | 0.329048 | ||||||||
\(367\) | −27.7310 | −1.44755 | −0.723773 | − | 0.690038i | \(-0.757594\pi\) | ||||
−0.723773 | + | 0.690038i | \(0.757594\pi\) | |||||||
\(368\) | 22.6275 | 1.17954 | ||||||||
\(369\) | 10.5653 | 0.550009 | ||||||||
\(370\) | 4.10347 | 0.213329 | ||||||||
\(371\) | −16.8968 | −0.877238 | ||||||||
\(372\) | −2.72619 | −0.141346 | ||||||||
\(373\) | 19.0340 | 0.985542 | 0.492771 | − | 0.870159i | \(-0.335984\pi\) | ||||
0.492771 | + | 0.870159i | \(0.335984\pi\) | |||||||
\(374\) | −1.31376 | −0.0679331 | ||||||||
\(375\) | −14.2893 | −0.737898 | ||||||||
\(376\) | 5.13397 | 0.264764 | ||||||||
\(377\) | 27.8427 | 1.43397 | ||||||||
\(378\) | −3.06246 | −0.157516 | ||||||||
\(379\) | −18.0869 | −0.929062 | −0.464531 | − | 0.885557i | \(-0.653777\pi\) | ||||
−0.464531 | + | 0.885557i | \(0.653777\pi\) | |||||||
\(380\) | −7.83866 | −0.402115 | ||||||||
\(381\) | 13.8631 | 0.710226 | ||||||||
\(382\) | 2.24085 | 0.114652 | ||||||||
\(383\) | −24.1015 | −1.23153 | −0.615765 | − | 0.787930i | \(-0.711153\pi\) | ||||
−0.615765 | + | 0.787930i | \(0.711153\pi\) | |||||||
\(384\) | −11.6888 | −0.596492 | ||||||||
\(385\) | −1.94246 | −0.0989968 | ||||||||
\(386\) | 4.33721 | 0.220758 | ||||||||
\(387\) | 7.83838 | 0.398447 | ||||||||
\(388\) | 5.76901 | 0.292877 | ||||||||
\(389\) | 8.92229 | 0.452378 | 0.226189 | − | 0.974083i | \(-0.427373\pi\) | ||||
0.226189 | + | 0.974083i | \(0.427373\pi\) | |||||||
\(390\) | −1.96167 | −0.0993331 | ||||||||
\(391\) | 32.3927 | 1.63817 | ||||||||
\(392\) | −6.33605 | −0.320019 | ||||||||
\(393\) | −18.1088 | −0.913469 | ||||||||
\(394\) | 4.41556 | 0.222453 | ||||||||
\(395\) | 0.522541 | 0.0262919 | ||||||||
\(396\) | 2.28383 | 0.114767 | ||||||||
\(397\) | −32.1747 | −1.61480 | −0.807401 | − | 0.590004i | \(-0.799126\pi\) | ||||
−0.807401 | + | 0.590004i | \(0.799126\pi\) | |||||||
\(398\) | −0.0354534 | −0.00177712 | ||||||||
\(399\) | 4.98839 | 0.249732 | ||||||||
\(400\) | −8.14248 | −0.407124 | ||||||||
\(401\) | 11.1234 | 0.555474 | 0.277737 | − | 0.960657i | \(-0.410416\pi\) | ||||
0.277737 | + | 0.960657i | \(0.410416\pi\) | |||||||
\(402\) | 4.07594 | 0.203290 | ||||||||
\(403\) | −3.47587 | −0.173145 | ||||||||
\(404\) | −3.49082 | −0.173675 | ||||||||
\(405\) | 3.10864 | 0.154469 | ||||||||
\(406\) | −5.40681 | −0.268336 | ||||||||
\(407\) | 5.72538 | 0.283797 | ||||||||
\(408\) | −7.77181 | −0.384762 | ||||||||
\(409\) | 26.0533 | 1.28825 | 0.644126 | − | 0.764920i | \(-0.277221\pi\) | ||||
0.644126 | + | 0.764920i | \(0.277221\pi\) | |||||||
\(410\) | −3.86377 | −0.190818 | ||||||||
\(411\) | −6.25303 | −0.308439 | ||||||||
\(412\) | 26.7480 | 1.31778 | ||||||||
\(413\) | 5.04743 | 0.248368 | ||||||||
\(414\) | 3.86159 | 0.189787 | ||||||||
\(415\) | −13.3934 | −0.657458 | ||||||||
\(416\) | −11.3275 | −0.555376 | ||||||||
\(417\) | −20.2868 | −0.993450 | ||||||||
\(418\) | 0.750009 | 0.0366842 | ||||||||
\(419\) | 4.22720 | 0.206512 | 0.103256 | − | 0.994655i | \(-0.467074\pi\) | ||||
0.103256 | + | 0.994655i | \(0.467074\pi\) | |||||||
\(420\) | −5.55501 | −0.271057 | ||||||||
\(421\) | 36.0653 | 1.75772 | 0.878859 | − | 0.477082i | \(-0.158306\pi\) | ||||
0.878859 | + | 0.477082i | \(0.158306\pi\) | |||||||
\(422\) | −8.22691 | −0.400480 | ||||||||
\(423\) | −5.72384 | −0.278303 | ||||||||
\(424\) | −15.0285 | −0.729848 | ||||||||
\(425\) | −11.6565 | −0.565422 | ||||||||
\(426\) | 5.90213 | 0.285959 | ||||||||
\(427\) | 22.7283 | 1.09990 | ||||||||
\(428\) | −14.7892 | −0.714863 | ||||||||
\(429\) | −2.73703 | −0.132145 | ||||||||
\(430\) | −2.86651 | −0.138236 | ||||||||
\(431\) | 11.3277 | 0.545635 | 0.272818 | − | 0.962066i | \(-0.412044\pi\) | ||||
0.272818 | + | 0.962066i | \(0.412044\pi\) | |||||||
\(432\) | 17.7946 | 0.856141 | ||||||||
\(433\) | −12.8261 | −0.616382 | −0.308191 | − | 0.951325i | \(-0.599724\pi\) | ||||
−0.308191 | + | 0.951325i | \(0.599724\pi\) | |||||||
\(434\) | 0.674985 | 0.0324003 | ||||||||
\(435\) | 18.4178 | 0.883065 | ||||||||
\(436\) | 18.1739 | 0.870373 | ||||||||
\(437\) | −18.4926 | −0.884620 | ||||||||
\(438\) | −2.99381 | −0.143050 | ||||||||
\(439\) | 11.5063 | 0.549166 | 0.274583 | − | 0.961563i | \(-0.411460\pi\) | ||||
0.274583 | + | 0.961563i | \(0.411460\pi\) | |||||||
\(440\) | −1.72768 | −0.0823638 | ||||||||
\(441\) | 7.06404 | 0.336383 | ||||||||
\(442\) | −4.79025 | −0.227849 | ||||||||
\(443\) | 11.3816 | 0.540755 | 0.270378 | − | 0.962754i | \(-0.412851\pi\) | ||||
0.270378 | + | 0.962754i | \(0.412851\pi\) | |||||||
\(444\) | 16.3734 | 0.777046 | ||||||||
\(445\) | 1.94671 | 0.0922829 | ||||||||
\(446\) | −4.14348 | −0.196200 | ||||||||
\(447\) | −7.89819 | −0.373572 | ||||||||
\(448\) | −7.92568 | −0.374453 | ||||||||
\(449\) | −18.6872 | −0.881904 | −0.440952 | − | 0.897531i | \(-0.645359\pi\) | ||||
−0.440952 | + | 0.897531i | \(0.645359\pi\) | |||||||
\(450\) | −1.38959 | −0.0655057 | ||||||||
\(451\) | −5.39093 | −0.253849 | ||||||||
\(452\) | −20.8937 | −0.982758 | ||||||||
\(453\) | −25.2197 | −1.18493 | ||||||||
\(454\) | 5.91658 | 0.277679 | ||||||||
\(455\) | −7.08259 | −0.332037 | ||||||||
\(456\) | 4.43682 | 0.207773 | ||||||||
\(457\) | −11.2023 | −0.524023 | −0.262012 | − | 0.965065i | \(-0.584386\pi\) | ||||
−0.262012 | + | 0.965065i | \(0.584386\pi\) | |||||||
\(458\) | 8.62222 | 0.402890 | ||||||||
\(459\) | 25.4740 | 1.18903 | ||||||||
\(460\) | 20.5931 | 0.960158 | ||||||||
\(461\) | −9.04204 | −0.421130 | −0.210565 | − | 0.977580i | \(-0.567530\pi\) | ||||
−0.210565 | + | 0.977580i | \(0.567530\pi\) | |||||||
\(462\) | 0.531508 | 0.0247280 | ||||||||
\(463\) | −0.803861 | −0.0373586 | −0.0186793 | − | 0.999826i | \(-0.505946\pi\) | ||||
−0.0186793 | + | 0.999826i | \(0.505946\pi\) | |||||||
\(464\) | 31.4165 | 1.45848 | ||||||||
\(465\) | −2.29927 | −0.106626 | ||||||||
\(466\) | 0.0651713 | 0.00301900 | ||||||||
\(467\) | 8.77838 | 0.406215 | 0.203108 | − | 0.979156i | \(-0.434896\pi\) | ||||
0.203108 | + | 0.979156i | \(0.434896\pi\) | |||||||
\(468\) | 8.32729 | 0.384929 | ||||||||
\(469\) | 14.7162 | 0.679529 | ||||||||
\(470\) | 2.09322 | 0.0965532 | ||||||||
\(471\) | 2.73690 | 0.126110 | ||||||||
\(472\) | 4.48933 | 0.206638 | ||||||||
\(473\) | −3.99951 | −0.183898 | ||||||||
\(474\) | −0.142981 | −0.00656734 | ||||||||
\(475\) | 6.65453 | 0.305331 | ||||||||
\(476\) | −13.5649 | −0.621747 | ||||||||
\(477\) | 16.7552 | 0.767169 | ||||||||
\(478\) | −6.52252 | −0.298333 | ||||||||
\(479\) | 32.9704 | 1.50645 | 0.753227 | − | 0.657761i | \(-0.228496\pi\) | ||||
0.753227 | + | 0.657761i | \(0.228496\pi\) | |||||||
\(480\) | −7.49308 | −0.342011 | ||||||||
\(481\) | 20.8759 | 0.951859 | ||||||||
\(482\) | 4.03313 | 0.183704 | ||||||||
\(483\) | −13.1051 | −0.596303 | ||||||||
\(484\) | 19.4228 | 0.882856 | ||||||||
\(485\) | 4.86559 | 0.220935 | ||||||||
\(486\) | 5.04066 | 0.228649 | ||||||||
\(487\) | −10.6257 | −0.481496 | −0.240748 | − | 0.970588i | \(-0.577393\pi\) | ||||
−0.240748 | + | 0.970588i | \(0.577393\pi\) | |||||||
\(488\) | 20.2152 | 0.915098 | ||||||||
\(489\) | −11.5420 | −0.521949 | ||||||||
\(490\) | −2.58334 | −0.116703 | ||||||||
\(491\) | −21.9301 | −0.989692 | −0.494846 | − | 0.868981i | \(-0.664776\pi\) | ||||
−0.494846 | + | 0.868981i | \(0.664776\pi\) | |||||||
\(492\) | −15.4169 | −0.695049 | ||||||||
\(493\) | 44.9748 | 2.02556 | ||||||||
\(494\) | 2.73469 | 0.123039 | ||||||||
\(495\) | 1.92618 | 0.0865754 | ||||||||
\(496\) | −3.92203 | −0.176104 | ||||||||
\(497\) | 21.3096 | 0.955865 | ||||||||
\(498\) | 3.66481 | 0.164224 | ||||||||
\(499\) | 43.5451 | 1.94935 | 0.974673 | − | 0.223635i | \(-0.0717922\pi\) | ||||
0.974673 | + | 0.223635i | \(0.0717922\pi\) | |||||||
\(500\) | −22.1829 | −0.992048 | ||||||||
\(501\) | −22.2268 | −0.993021 | ||||||||
\(502\) | −3.29730 | −0.147166 | ||||||||
\(503\) | 8.73420 | 0.389439 | 0.194719 | − | 0.980859i | \(-0.437620\pi\) | ||||
0.194719 | + | 0.980859i | \(0.437620\pi\) | |||||||
\(504\) | −3.34508 | −0.149002 | ||||||||
\(505\) | −2.94416 | −0.131013 | ||||||||
\(506\) | −1.97037 | −0.0875934 | ||||||||
\(507\) | 5.69360 | 0.252862 | ||||||||
\(508\) | 21.5211 | 0.954845 | ||||||||
\(509\) | −15.6844 | −0.695200 | −0.347600 | − | 0.937643i | \(-0.613003\pi\) | ||||
−0.347600 | + | 0.937643i | \(0.613003\pi\) | |||||||
\(510\) | −3.16872 | −0.140313 | ||||||||
\(511\) | −10.8091 | −0.478168 | ||||||||
\(512\) | −21.7873 | −0.962871 | ||||||||
\(513\) | −14.5428 | −0.642079 | ||||||||
\(514\) | 10.6995 | 0.471933 | ||||||||
\(515\) | 22.5593 | 0.994081 | ||||||||
\(516\) | −11.4378 | −0.503519 | ||||||||
\(517\) | 2.92058 | 0.128447 | ||||||||
\(518\) | −4.05393 | −0.178119 | ||||||||
\(519\) | 8.48217 | 0.372326 | ||||||||
\(520\) | −6.29946 | −0.276250 | ||||||||
\(521\) | −24.9842 | −1.09458 | −0.547288 | − | 0.836944i | \(-0.684340\pi\) | ||||
−0.547288 | + | 0.836944i | \(0.684340\pi\) | |||||||
\(522\) | 5.36151 | 0.234667 | ||||||||
\(523\) | 9.50069 | 0.415436 | 0.207718 | − | 0.978189i | \(-0.433396\pi\) | ||||
0.207718 | + | 0.978189i | \(0.433396\pi\) | |||||||
\(524\) | −28.1123 | −1.22809 | ||||||||
\(525\) | 4.71586 | 0.205817 | ||||||||
\(526\) | −2.54249 | −0.110858 | ||||||||
\(527\) | −5.61464 | −0.244577 | ||||||||
\(528\) | −3.08835 | −0.134403 | ||||||||
\(529\) | 25.5822 | 1.11227 | ||||||||
\(530\) | −6.12743 | −0.266158 | ||||||||
\(531\) | −5.00514 | −0.217205 | ||||||||
\(532\) | 7.74402 | 0.335746 | ||||||||
\(533\) | −19.6564 | −0.851415 | ||||||||
\(534\) | −0.532672 | −0.0230510 | ||||||||
\(535\) | −12.4732 | −0.539264 | ||||||||
\(536\) | 13.0890 | 0.565357 | ||||||||
\(537\) | 22.7488 | 0.981683 | ||||||||
\(538\) | −0.298774 | −0.0128811 | ||||||||
\(539\) | −3.60441 | −0.155253 | ||||||||
\(540\) | 16.1947 | 0.696907 | ||||||||
\(541\) | 15.3139 | 0.658395 | 0.329197 | − | 0.944261i | \(-0.393222\pi\) | ||||
0.329197 | + | 0.944261i | \(0.393222\pi\) | |||||||
\(542\) | 7.87112 | 0.338093 | ||||||||
\(543\) | 2.54121 | 0.109054 | ||||||||
\(544\) | −18.2975 | −0.784499 | ||||||||
\(545\) | 15.3279 | 0.656575 | ||||||||
\(546\) | 1.93799 | 0.0829382 | ||||||||
\(547\) | 27.4217 | 1.17247 | 0.586235 | − | 0.810141i | \(-0.300610\pi\) | ||||
0.586235 | + | 0.810141i | \(0.300610\pi\) | |||||||
\(548\) | −9.70725 | −0.414673 | ||||||||
\(549\) | −22.5378 | −0.961891 | ||||||||
\(550\) | 0.709033 | 0.0302333 | ||||||||
\(551\) | −25.6755 | −1.09381 | ||||||||
\(552\) | −11.6561 | −0.496115 | ||||||||
\(553\) | −0.516232 | −0.0219524 | ||||||||
\(554\) | −3.56824 | −0.151600 | ||||||||
\(555\) | 13.8093 | 0.586172 | ||||||||
\(556\) | −31.4934 | −1.33562 | ||||||||
\(557\) | 1.30097 | 0.0551239 | 0.0275619 | − | 0.999620i | \(-0.491226\pi\) | ||||
0.0275619 | + | 0.999620i | \(0.491226\pi\) | |||||||
\(558\) | −0.669329 | −0.0283350 | ||||||||
\(559\) | −14.5830 | −0.616797 | ||||||||
\(560\) | −7.99172 | −0.337712 | ||||||||
\(561\) | −4.42117 | −0.186662 | ||||||||
\(562\) | −4.76107 | −0.200834 | ||||||||
\(563\) | 42.9705 | 1.81099 | 0.905494 | − | 0.424358i | \(-0.139500\pi\) | ||||
0.905494 | + | 0.424358i | \(0.139500\pi\) | |||||||
\(564\) | 8.35223 | 0.351692 | ||||||||
\(565\) | −17.6218 | −0.741354 | ||||||||
\(566\) | 5.83363 | 0.245206 | ||||||||
\(567\) | −3.07110 | −0.128974 | ||||||||
\(568\) | 18.9533 | 0.795264 | ||||||||
\(569\) | −4.22327 | −0.177049 | −0.0885243 | − | 0.996074i | \(-0.528215\pi\) | ||||
−0.0885243 | + | 0.996074i | \(0.528215\pi\) | |||||||
\(570\) | 1.80898 | 0.0757699 | ||||||||
\(571\) | −4.12901 | −0.172794 | −0.0863968 | − | 0.996261i | \(-0.527535\pi\) | ||||
−0.0863968 | + | 0.996261i | \(0.527535\pi\) | |||||||
\(572\) | −4.24898 | −0.177659 | ||||||||
\(573\) | 7.54109 | 0.315033 | ||||||||
\(574\) | 3.81712 | 0.159323 | ||||||||
\(575\) | −17.4822 | −0.729060 | ||||||||
\(576\) | 7.85927 | 0.327469 | ||||||||
\(577\) | 35.5668 | 1.48067 | 0.740333 | − | 0.672241i | \(-0.234668\pi\) | ||||
0.740333 | + | 0.672241i | \(0.234668\pi\) | |||||||
\(578\) | −1.64736 | −0.0685212 | ||||||||
\(579\) | 14.5959 | 0.606584 | ||||||||
\(580\) | 28.5919 | 1.18721 | ||||||||
\(581\) | 13.2317 | 0.548945 | ||||||||
\(582\) | −1.33135 | −0.0551864 | ||||||||
\(583\) | −8.54931 | −0.354076 | ||||||||
\(584\) | −9.61396 | −0.397828 | ||||||||
\(585\) | 7.02324 | 0.290375 | ||||||||
\(586\) | 8.30994 | 0.343281 | ||||||||
\(587\) | −17.3760 | −0.717185 | −0.358592 | − | 0.933494i | \(-0.616743\pi\) | ||||
−0.358592 | + | 0.933494i | \(0.616743\pi\) | |||||||
\(588\) | −10.3078 | −0.425088 | ||||||||
\(589\) | 3.20532 | 0.132073 | ||||||||
\(590\) | 1.83039 | 0.0753561 | ||||||||
\(591\) | 14.8596 | 0.611241 | ||||||||
\(592\) | 23.5555 | 0.968127 | ||||||||
\(593\) | 19.0958 | 0.784172 | 0.392086 | − | 0.919929i | \(-0.371754\pi\) | ||||
0.392086 | + | 0.919929i | \(0.371754\pi\) | |||||||
\(594\) | −1.54952 | −0.0635775 | ||||||||
\(595\) | −11.4406 | −0.469021 | ||||||||
\(596\) | −12.2612 | −0.502239 | ||||||||
\(597\) | −0.119310 | −0.00488305 | ||||||||
\(598\) | −7.18435 | −0.293790 | ||||||||
\(599\) | −9.20830 | −0.376241 | −0.188120 | − | 0.982146i | \(-0.560240\pi\) | ||||
−0.188120 | + | 0.982146i | \(0.560240\pi\) | |||||||
\(600\) | 4.19442 | 0.171236 | ||||||||
\(601\) | −8.39228 | −0.342328 | −0.171164 | − | 0.985243i | \(-0.554753\pi\) | ||||
−0.171164 | + | 0.985243i | \(0.554753\pi\) | |||||||
\(602\) | 2.83191 | 0.115420 | ||||||||
\(603\) | −14.5928 | −0.594266 | ||||||||
\(604\) | −39.1513 | −1.59304 | ||||||||
\(605\) | 16.3812 | 0.665991 | ||||||||
\(606\) | 0.805600 | 0.0327253 | ||||||||
\(607\) | −23.7898 | −0.965599 | −0.482800 | − | 0.875731i | \(-0.660380\pi\) | ||||
−0.482800 | + | 0.875731i | \(0.660380\pi\) | |||||||
\(608\) | 10.4458 | 0.423633 | ||||||||
\(609\) | −18.1954 | −0.737316 | ||||||||
\(610\) | 8.24214 | 0.333714 | ||||||||
\(611\) | 10.6490 | 0.430813 | ||||||||
\(612\) | 13.4512 | 0.543734 | ||||||||
\(613\) | 15.9458 | 0.644043 | 0.322021 | − | 0.946732i | \(-0.395638\pi\) | ||||
0.322021 | + | 0.946732i | \(0.395638\pi\) | |||||||
\(614\) | 4.43062 | 0.178805 | ||||||||
\(615\) | −13.0026 | −0.524317 | ||||||||
\(616\) | 1.70682 | 0.0687697 | ||||||||
\(617\) | −14.0750 | −0.566638 | −0.283319 | − | 0.959026i | \(-0.591436\pi\) | ||||
−0.283319 | + | 0.959026i | \(0.591436\pi\) | |||||||
\(618\) | −6.17282 | −0.248307 | ||||||||
\(619\) | 6.01473 | 0.241752 | 0.120876 | − | 0.992668i | \(-0.461430\pi\) | ||||
0.120876 | + | 0.992668i | \(0.461430\pi\) | |||||||
\(620\) | −3.56940 | −0.143351 | ||||||||
\(621\) | 38.2056 | 1.53314 | ||||||||
\(622\) | 6.95714 | 0.278956 | ||||||||
\(623\) | −1.92321 | −0.0770517 | ||||||||
\(624\) | −11.2608 | −0.450791 | ||||||||
\(625\) | −6.16815 | −0.246726 | ||||||||
\(626\) | −4.03747 | −0.161370 | ||||||||
\(627\) | 2.52399 | 0.100798 | ||||||||
\(628\) | 4.24878 | 0.169545 | ||||||||
\(629\) | 33.7213 | 1.34455 | ||||||||
\(630\) | −1.36386 | −0.0543373 | ||||||||
\(631\) | −2.12252 | −0.0844960 | −0.0422480 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422480 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(632\) | −0.459152 | −0.0182641 | ||||||||
\(633\) | −27.6858 | −1.10041 | ||||||||
\(634\) | −3.33401 | −0.132410 | ||||||||
\(635\) | 18.1509 | 0.720298 | ||||||||
\(636\) | −24.4492 | −0.969474 | ||||||||
\(637\) | −13.1424 | −0.520721 | ||||||||
\(638\) | −2.73570 | −0.108307 | ||||||||
\(639\) | −21.1310 | −0.835929 | ||||||||
\(640\) | −15.3042 | −0.604950 | ||||||||
\(641\) | 6.77267 | 0.267504 | 0.133752 | − | 0.991015i | \(-0.457297\pi\) | ||||
0.133752 | + | 0.991015i | \(0.457297\pi\) | |||||||
\(642\) | 3.41301 | 0.134701 | ||||||||
\(643\) | −11.2524 | −0.443751 | −0.221875 | − | 0.975075i | \(-0.571218\pi\) | ||||
−0.221875 | + | 0.975075i | \(0.571218\pi\) | |||||||
\(644\) | −20.3445 | −0.801685 | ||||||||
\(645\) | −9.64661 | −0.379835 | ||||||||
\(646\) | 4.41739 | 0.173800 | ||||||||
\(647\) | 34.2906 | 1.34810 | 0.674051 | − | 0.738685i | \(-0.264553\pi\) | ||||
0.674051 | + | 0.738685i | \(0.264553\pi\) | |||||||
\(648\) | −2.73153 | −0.107305 | ||||||||
\(649\) | 2.55386 | 0.100248 | ||||||||
\(650\) | 2.58528 | 0.101403 | ||||||||
\(651\) | 2.27151 | 0.0890275 | ||||||||
\(652\) | −17.9179 | −0.701721 | ||||||||
\(653\) | 25.1564 | 0.984447 | 0.492224 | − | 0.870469i | \(-0.336184\pi\) | ||||
0.492224 | + | 0.870469i | \(0.336184\pi\) | |||||||
\(654\) | −4.19412 | −0.164003 | ||||||||
\(655\) | −23.7099 | −0.926422 | ||||||||
\(656\) | −22.1795 | −0.865966 | ||||||||
\(657\) | 10.7186 | 0.418171 | ||||||||
\(658\) | −2.06795 | −0.0806172 | ||||||||
\(659\) | −5.93357 | −0.231139 | −0.115570 | − | 0.993299i | \(-0.536869\pi\) | ||||
−0.115570 | + | 0.993299i | \(0.536869\pi\) | |||||||
\(660\) | −2.81068 | −0.109406 | ||||||||
\(661\) | 23.0235 | 0.895511 | 0.447756 | − | 0.894156i | \(-0.352223\pi\) | ||||
0.447756 | + | 0.894156i | \(0.352223\pi\) | |||||||
\(662\) | 1.52898 | 0.0594255 | ||||||||
\(663\) | −16.1205 | −0.626068 | ||||||||
\(664\) | 11.7687 | 0.456714 | ||||||||
\(665\) | 6.53131 | 0.253273 | ||||||||
\(666\) | 4.01996 | 0.155770 | ||||||||
\(667\) | 67.4526 | 2.61178 | ||||||||
\(668\) | −34.5051 | −1.33504 | ||||||||
\(669\) | −13.9440 | −0.539105 | ||||||||
\(670\) | 5.33664 | 0.206172 | ||||||||
\(671\) | 11.4999 | 0.443948 | ||||||||
\(672\) | 7.40261 | 0.285562 | ||||||||
\(673\) | −33.7956 | −1.30272 | −0.651362 | − | 0.758767i | \(-0.725802\pi\) | ||||
−0.651362 | + | 0.758767i | \(0.725802\pi\) | |||||||
\(674\) | −9.04927 | −0.348565 | ||||||||
\(675\) | −13.7482 | −0.529170 | ||||||||
\(676\) | 8.83879 | 0.339954 | ||||||||
\(677\) | −10.0119 | −0.384788 | −0.192394 | − | 0.981318i | \(-0.561625\pi\) | ||||
−0.192394 | + | 0.981318i | \(0.561625\pi\) | |||||||
\(678\) | 4.82179 | 0.185180 | ||||||||
\(679\) | −4.80684 | −0.184470 | ||||||||
\(680\) | −10.1756 | −0.390218 | ||||||||
\(681\) | 19.9109 | 0.762989 | ||||||||
\(682\) | 0.341524 | 0.0130776 | ||||||||
\(683\) | 28.5554 | 1.09264 | 0.546321 | − | 0.837576i | \(-0.316028\pi\) | ||||
0.546321 | + | 0.837576i | \(0.316028\pi\) | |||||||
\(684\) | −7.67913 | −0.293619 | ||||||||
\(685\) | −8.18710 | −0.312813 | ||||||||
\(686\) | 6.46307 | 0.246761 | ||||||||
\(687\) | 29.0161 | 1.10704 | ||||||||
\(688\) | −16.4549 | −0.627338 | ||||||||
\(689\) | −31.1725 | −1.18758 | ||||||||
\(690\) | −4.75241 | −0.180921 | ||||||||
\(691\) | −28.4025 | −1.08048 | −0.540240 | − | 0.841511i | \(-0.681667\pi\) | ||||
−0.540240 | + | 0.841511i | \(0.681667\pi\) | |||||||
\(692\) | 13.1678 | 0.500564 | ||||||||
\(693\) | −1.90293 | −0.0722861 | ||||||||
\(694\) | −0.259527 | −0.00985152 | ||||||||
\(695\) | −26.5616 | −1.00754 | ||||||||
\(696\) | −16.1835 | −0.613435 | ||||||||
\(697\) | −31.7514 | −1.20267 | ||||||||
\(698\) | −0.358260 | −0.0135603 | ||||||||
\(699\) | 0.219319 | 0.00829541 | ||||||||
\(700\) | 7.32093 | 0.276705 | ||||||||
\(701\) | 10.9741 | 0.414488 | 0.207244 | − | 0.978289i | \(-0.433551\pi\) | ||||
0.207244 | + | 0.978289i | \(0.433551\pi\) | |||||||
\(702\) | −5.64986 | −0.213240 | ||||||||
\(703\) | −19.2510 | −0.726065 | ||||||||
\(704\) | −4.01017 | −0.151139 | ||||||||
\(705\) | 7.04428 | 0.265303 | ||||||||
\(706\) | 7.69758 | 0.289702 | ||||||||
\(707\) | 2.90861 | 0.109390 | ||||||||
\(708\) | 7.30350 | 0.274482 | ||||||||
\(709\) | 50.6627 | 1.90268 | 0.951338 | − | 0.308150i | \(-0.0997097\pi\) | ||||
0.951338 | + | 0.308150i | \(0.0997097\pi\) | |||||||
\(710\) | 7.72766 | 0.290014 | ||||||||
\(711\) | 0.511906 | 0.0191980 | ||||||||
\(712\) | −1.71056 | −0.0641058 | ||||||||
\(713\) | −8.42076 | −0.315360 | ||||||||
\(714\) | 3.13047 | 0.117155 | ||||||||
\(715\) | −3.58359 | −0.134019 | ||||||||
\(716\) | 35.3154 | 1.31980 | ||||||||
\(717\) | −21.9501 | −0.819741 | ||||||||
\(718\) | 4.46505 | 0.166634 | ||||||||
\(719\) | −25.5125 | −0.951456 | −0.475728 | − | 0.879592i | \(-0.657815\pi\) | ||||
−0.475728 | + | 0.879592i | \(0.657815\pi\) | |||||||
\(720\) | 7.92475 | 0.295338 | ||||||||
\(721\) | −22.2869 | −0.830008 | ||||||||
\(722\) | 4.28511 | 0.159475 | ||||||||
\(723\) | 13.5726 | 0.504770 | ||||||||
\(724\) | 3.94500 | 0.146615 | ||||||||
\(725\) | −24.2727 | −0.901466 | ||||||||
\(726\) | −4.48234 | −0.166355 | ||||||||
\(727\) | −9.11030 | −0.337882 | −0.168941 | − | 0.985626i | \(-0.554035\pi\) | ||||
−0.168941 | + | 0.985626i | \(0.554035\pi\) | |||||||
\(728\) | 6.22341 | 0.230655 | ||||||||
\(729\) | 22.8711 | 0.847077 | ||||||||
\(730\) | −3.91981 | −0.145079 | ||||||||
\(731\) | −23.5563 | −0.871260 | ||||||||
\(732\) | 32.8872 | 1.21554 | ||||||||
\(733\) | 4.30094 | 0.158859 | 0.0794294 | − | 0.996840i | \(-0.474690\pi\) | ||||
0.0794294 | + | 0.996840i | \(0.474690\pi\) | |||||||
\(734\) | 9.93491 | 0.366704 | ||||||||
\(735\) | −8.69364 | −0.320670 | ||||||||
\(736\) | −27.4424 | −1.01154 | ||||||||
\(737\) | 7.44596 | 0.274276 | ||||||||
\(738\) | −3.78513 | −0.139333 | ||||||||
\(739\) | 9.26480 | 0.340811 | 0.170406 | − | 0.985374i | \(-0.445492\pi\) | ||||
0.170406 | + | 0.985374i | \(0.445492\pi\) | |||||||
\(740\) | 21.4377 | 0.788065 | ||||||||
\(741\) | 9.20297 | 0.338080 | ||||||||
\(742\) | 6.05345 | 0.222229 | ||||||||
\(743\) | −44.1214 | −1.61866 | −0.809328 | − | 0.587357i | \(-0.800169\pi\) | ||||
−0.809328 | + | 0.587357i | \(0.800169\pi\) | |||||||
\(744\) | 2.02035 | 0.0740695 | ||||||||
\(745\) | −10.3411 | −0.378869 | ||||||||
\(746\) | −6.81912 | −0.249666 | ||||||||
\(747\) | −13.1209 | −0.480067 | ||||||||
\(748\) | −6.86347 | −0.250953 | ||||||||
\(749\) | 12.3226 | 0.450259 | ||||||||
\(750\) | 5.11929 | 0.186930 | ||||||||
\(751\) | −23.6421 | −0.862711 | −0.431355 | − | 0.902182i | \(-0.641964\pi\) | ||||
−0.431355 | + | 0.902182i | \(0.641964\pi\) | |||||||
\(752\) | 12.0159 | 0.438176 | ||||||||
\(753\) | −11.0963 | −0.404372 | ||||||||
\(754\) | −9.97491 | −0.363265 | ||||||||
\(755\) | −33.0202 | −1.20173 | ||||||||
\(756\) | −15.9991 | −0.581883 | ||||||||
\(757\) | −51.5916 | −1.87513 | −0.937565 | − | 0.347810i | \(-0.886925\pi\) | ||||
−0.937565 | + | 0.347810i | \(0.886925\pi\) | |||||||
\(758\) | 6.47981 | 0.235357 | ||||||||
\(759\) | −6.63082 | −0.240684 | ||||||||
\(760\) | 5.80913 | 0.210719 | ||||||||
\(761\) | −31.7407 | −1.15060 | −0.575300 | − | 0.817942i | \(-0.695115\pi\) | ||||
−0.575300 | + | 0.817942i | \(0.695115\pi\) | |||||||
\(762\) | −4.96658 | −0.179920 | ||||||||
\(763\) | −15.1428 | −0.548207 | ||||||||
\(764\) | 11.7068 | 0.423539 | ||||||||
\(765\) | 11.3448 | 0.410172 | ||||||||
\(766\) | 8.63460 | 0.311981 | ||||||||
\(767\) | 9.31190 | 0.336233 | ||||||||
\(768\) | −8.06706 | −0.291095 | ||||||||
\(769\) | 48.7532 | 1.75808 | 0.879042 | − | 0.476744i | \(-0.158183\pi\) | ||||
0.879042 | + | 0.476744i | \(0.158183\pi\) | |||||||
\(770\) | 0.695905 | 0.0250787 | ||||||||
\(771\) | 36.0066 | 1.29675 | ||||||||
\(772\) | 22.6588 | 0.815507 | ||||||||
\(773\) | −15.4314 | −0.555028 | −0.277514 | − | 0.960722i | \(-0.589510\pi\) | ||||
−0.277514 | + | 0.960722i | \(0.589510\pi\) | |||||||
\(774\) | −2.80818 | −0.100938 | ||||||||
\(775\) | 3.03020 | 0.108848 | ||||||||
\(776\) | −4.27534 | −0.153476 | ||||||||
\(777\) | −13.6426 | −0.489425 | ||||||||
\(778\) | −3.19650 | −0.114600 | ||||||||
\(779\) | 18.1265 | 0.649448 | ||||||||
\(780\) | −10.2483 | −0.366949 | ||||||||
\(781\) | 10.7820 | 0.385812 | ||||||||
\(782\) | −11.6050 | −0.414995 | ||||||||
\(783\) | 53.0455 | 1.89569 | ||||||||
\(784\) | −14.8294 | −0.529621 | ||||||||
\(785\) | 3.58342 | 0.127898 | ||||||||
\(786\) | 6.48766 | 0.231407 | ||||||||
\(787\) | 29.7489 | 1.06043 | 0.530216 | − | 0.847862i | \(-0.322111\pi\) | ||||
0.530216 | + | 0.847862i | \(0.322111\pi\) | |||||||
\(788\) | 23.0681 | 0.821768 | ||||||||
\(789\) | −8.55619 | −0.304609 | ||||||||
\(790\) | −0.187205 | −0.00666047 | ||||||||
\(791\) | 17.4090 | 0.618994 | ||||||||
\(792\) | −1.69252 | −0.0601409 | ||||||||
\(793\) | 41.9309 | 1.48901 | ||||||||
\(794\) | 11.5269 | 0.409074 | ||||||||
\(795\) | −20.6205 | −0.731333 | ||||||||
\(796\) | −0.185218 | −0.00656489 | ||||||||
\(797\) | 5.55839 | 0.196888 | 0.0984442 | − | 0.995143i | \(-0.468613\pi\) | ||||
0.0984442 | + | 0.995143i | \(0.468613\pi\) | |||||||
\(798\) | −1.78714 | −0.0632641 | ||||||||
\(799\) | 17.2016 | 0.608548 | ||||||||
\(800\) | 9.87510 | 0.349137 | ||||||||
\(801\) | 1.90709 | 0.0673838 | ||||||||
\(802\) | −3.98506 | −0.140717 | ||||||||
\(803\) | −5.46912 | −0.193001 | ||||||||
\(804\) | 21.2939 | 0.750977 | ||||||||
\(805\) | −17.1585 | −0.604759 | ||||||||
\(806\) | 1.24526 | 0.0438626 | ||||||||
\(807\) | −1.00546 | −0.0353938 | ||||||||
\(808\) | 2.58700 | 0.0910104 | ||||||||
\(809\) | 8.22890 | 0.289313 | 0.144656 | − | 0.989482i | \(-0.453792\pi\) | ||||
0.144656 | + | 0.989482i | \(0.453792\pi\) | |||||||
\(810\) | −1.11370 | −0.0391314 | ||||||||
\(811\) | −4.19373 | −0.147262 | −0.0736310 | − | 0.997286i | \(-0.523459\pi\) | ||||
−0.0736310 | + | 0.997286i | \(0.523459\pi\) | |||||||
\(812\) | −28.2467 | −0.991265 | ||||||||
\(813\) | 26.4885 | 0.928991 | ||||||||
\(814\) | −2.05117 | −0.0718936 | ||||||||
\(815\) | −15.1120 | −0.529350 | ||||||||
\(816\) | −18.1897 | −0.636768 | ||||||||
\(817\) | 13.4479 | 0.470484 | ||||||||
\(818\) | −9.33384 | −0.326350 | ||||||||
\(819\) | −6.93845 | −0.242449 | ||||||||
\(820\) | −20.1854 | −0.704905 | ||||||||
\(821\) | −12.6670 | −0.442081 | −0.221041 | − | 0.975265i | \(-0.570945\pi\) | ||||
−0.221041 | + | 0.975265i | \(0.570945\pi\) | |||||||
\(822\) | 2.24021 | 0.0781363 | ||||||||
\(823\) | −24.6674 | −0.859853 | −0.429926 | − | 0.902864i | \(-0.641460\pi\) | ||||
−0.429926 | + | 0.902864i | \(0.641460\pi\) | |||||||
\(824\) | −19.8226 | −0.690554 | ||||||||
\(825\) | 2.38609 | 0.0830730 | ||||||||
\(826\) | −1.80829 | −0.0629186 | ||||||||
\(827\) | −39.0120 | −1.35658 | −0.678290 | − | 0.734795i | \(-0.737278\pi\) | ||||
−0.678290 | + | 0.734795i | \(0.737278\pi\) | |||||||
\(828\) | 20.1740 | 0.701095 | ||||||||
\(829\) | −54.1581 | −1.88099 | −0.940494 | − | 0.339811i | \(-0.889637\pi\) | ||||
−0.940494 | + | 0.339811i | \(0.889637\pi\) | |||||||
\(830\) | 4.79833 | 0.166553 | ||||||||
\(831\) | −12.0081 | −0.416557 | ||||||||
\(832\) | −14.6219 | −0.506923 | ||||||||
\(833\) | −21.2292 | −0.735548 | ||||||||
\(834\) | 7.26796 | 0.251669 | ||||||||
\(835\) | −29.1016 | −1.00710 | ||||||||
\(836\) | 3.91826 | 0.135516 | ||||||||
\(837\) | −6.62219 | −0.228896 | ||||||||
\(838\) | −1.51444 | −0.0523154 | ||||||||
\(839\) | −34.3418 | −1.18561 | −0.592804 | − | 0.805346i | \(-0.701979\pi\) | ||||
−0.592804 | + | 0.805346i | \(0.701979\pi\) | |||||||
\(840\) | 4.11675 | 0.142041 | ||||||||
\(841\) | 64.6526 | 2.22940 | ||||||||
\(842\) | −12.9208 | −0.445279 | ||||||||
\(843\) | −16.0223 | −0.551838 | ||||||||
\(844\) | −42.9797 | −1.47942 | ||||||||
\(845\) | 7.45464 | 0.256447 | ||||||||
\(846\) | 2.05062 | 0.0705019 | ||||||||
\(847\) | −16.1835 | −0.556070 | ||||||||
\(848\) | −35.1738 | −1.20787 | ||||||||
\(849\) | 19.6318 | 0.673760 | ||||||||
\(850\) | 4.17605 | 0.143237 | ||||||||
\(851\) | 50.5747 | 1.73368 | ||||||||
\(852\) | 30.8343 | 1.05637 | ||||||||
\(853\) | 16.9647 | 0.580862 | 0.290431 | − | 0.956896i | \(-0.406201\pi\) | ||||
0.290431 | + | 0.956896i | \(0.406201\pi\) | |||||||
\(854\) | −8.14263 | −0.278635 | ||||||||
\(855\) | −6.47658 | −0.221494 | ||||||||
\(856\) | 10.9601 | 0.374608 | ||||||||
\(857\) | −35.7135 | −1.21995 | −0.609974 | − | 0.792421i | \(-0.708820\pi\) | ||||
−0.609974 | + | 0.792421i | \(0.708820\pi\) | |||||||
\(858\) | 0.980567 | 0.0334760 | ||||||||
\(859\) | −41.2222 | −1.40648 | −0.703241 | − | 0.710951i | \(-0.748265\pi\) | ||||
−0.703241 | + | 0.710951i | \(0.748265\pi\) | |||||||
\(860\) | −14.9755 | −0.510659 | ||||||||
\(861\) | 12.8457 | 0.437779 | ||||||||
\(862\) | −4.05826 | −0.138225 | ||||||||
\(863\) | 25.7153 | 0.875359 | 0.437680 | − | 0.899131i | \(-0.355800\pi\) | ||||
0.437680 | + | 0.899131i | \(0.355800\pi\) | |||||||
\(864\) | −21.5810 | −0.734201 | ||||||||
\(865\) | 11.1057 | 0.377606 | ||||||||
\(866\) | 4.59507 | 0.156147 | ||||||||
\(867\) | −5.54382 | −0.188278 | ||||||||
\(868\) | 3.52631 | 0.119691 | ||||||||
\(869\) | −0.261199 | −0.00886057 | ||||||||
\(870\) | −6.59835 | −0.223705 | ||||||||
\(871\) | 27.1495 | 0.919926 | ||||||||
\(872\) | −13.4685 | −0.456100 | ||||||||
\(873\) | 4.76656 | 0.161324 | ||||||||
\(874\) | 6.62515 | 0.224099 | ||||||||
\(875\) | 18.4832 | 0.624845 | ||||||||
\(876\) | −15.6405 | −0.528444 | ||||||||
\(877\) | −33.6362 | −1.13581 | −0.567907 | − | 0.823093i | \(-0.692247\pi\) | ||||
−0.567907 | + | 0.823093i | \(0.692247\pi\) | |||||||
\(878\) | −4.12225 | −0.139119 | ||||||||
\(879\) | 27.9652 | 0.943244 | ||||||||
\(880\) | −4.04359 | −0.136309 | ||||||||
\(881\) | 17.0869 | 0.575671 | 0.287835 | − | 0.957680i | \(-0.407064\pi\) | ||||
0.287835 | + | 0.957680i | \(0.407064\pi\) | |||||||
\(882\) | −2.53076 | −0.0852152 | ||||||||
\(883\) | −27.7133 | −0.932628 | −0.466314 | − | 0.884619i | \(-0.654418\pi\) | ||||
−0.466314 | + | 0.884619i | \(0.654418\pi\) | |||||||
\(884\) | −25.0256 | −0.841702 | ||||||||
\(885\) | 6.15977 | 0.207059 | ||||||||
\(886\) | −4.07757 | −0.136988 | ||||||||
\(887\) | 50.1913 | 1.68526 | 0.842630 | − | 0.538493i | \(-0.181006\pi\) | ||||
0.842630 | + | 0.538493i | \(0.181006\pi\) | |||||||
\(888\) | −12.1341 | −0.407194 | ||||||||
\(889\) | −17.9318 | −0.601413 | ||||||||
\(890\) | −0.697428 | −0.0233778 | ||||||||
\(891\) | −1.55389 | −0.0520574 | ||||||||
\(892\) | −21.6467 | −0.724785 | ||||||||
\(893\) | −9.82014 | −0.328618 | ||||||||
\(894\) | 2.82961 | 0.0946362 | ||||||||
\(895\) | 29.7850 | 0.995604 | ||||||||
\(896\) | 15.1194 | 0.505103 | ||||||||
\(897\) | −24.1773 | −0.807257 | ||||||||
\(898\) | 6.69488 | 0.223411 | ||||||||
\(899\) | −11.6916 | −0.389936 | ||||||||
\(900\) | −7.25959 | −0.241986 | ||||||||
\(901\) | −50.3536 | −1.67752 | ||||||||
\(902\) | 1.93136 | 0.0643071 | ||||||||
\(903\) | 9.53014 | 0.317143 | ||||||||
\(904\) | 15.4841 | 0.514993 | ||||||||
\(905\) | 3.32721 | 0.110600 | ||||||||
\(906\) | 9.03522 | 0.300175 | ||||||||
\(907\) | 42.8683 | 1.42342 | 0.711709 | − | 0.702475i | \(-0.247922\pi\) | ||||
0.711709 | + | 0.702475i | \(0.247922\pi\) | |||||||
\(908\) | 30.9099 | 1.02578 | ||||||||
\(909\) | −2.88424 | −0.0956642 | ||||||||
\(910\) | 2.53741 | 0.0841143 | ||||||||
\(911\) | −46.7726 | −1.54964 | −0.774822 | − | 0.632179i | \(-0.782161\pi\) | ||||
−0.774822 | + | 0.632179i | \(0.782161\pi\) | |||||||
\(912\) | 10.3843 | 0.343857 | ||||||||
\(913\) | 6.69489 | 0.221569 | ||||||||
\(914\) | 4.01335 | 0.132750 | ||||||||
\(915\) | 27.7371 | 0.916959 | ||||||||
\(916\) | 45.0449 | 1.48833 | ||||||||
\(917\) | 23.4236 | 0.773517 | ||||||||
\(918\) | −9.12633 | −0.301214 | ||||||||
\(919\) | 10.6493 | 0.351288 | 0.175644 | − | 0.984454i | \(-0.443799\pi\) | ||||
0.175644 | + | 0.984454i | \(0.443799\pi\) | |||||||
\(920\) | −15.2613 | −0.503150 | ||||||||
\(921\) | 14.9102 | 0.491309 | ||||||||
\(922\) | 3.23940 | 0.106684 | ||||||||
\(923\) | 39.3135 | 1.29402 | ||||||||
\(924\) | 2.77675 | 0.0913483 | ||||||||
\(925\) | −18.1992 | −0.598387 | ||||||||
\(926\) | 0.287991 | 0.00946397 | ||||||||
\(927\) | 22.1002 | 0.725865 | ||||||||
\(928\) | −38.1016 | −1.25075 | ||||||||
\(929\) | 59.9077 | 1.96551 | 0.982754 | − | 0.184918i | \(-0.0592019\pi\) | ||||
0.982754 | + | 0.184918i | \(0.0592019\pi\) | |||||||
\(930\) | 0.823736 | 0.0270114 | ||||||||
\(931\) | 12.1195 | 0.397199 | ||||||||
\(932\) | 0.340473 | 0.0111526 | ||||||||
\(933\) | 23.4127 | 0.766497 | ||||||||
\(934\) | −3.14494 | −0.102906 | ||||||||
\(935\) | −5.78865 | −0.189309 | ||||||||
\(936\) | −6.17126 | −0.201714 | ||||||||
\(937\) | −48.4932 | −1.58420 | −0.792101 | − | 0.610390i | \(-0.791013\pi\) | ||||
−0.792101 | + | 0.610390i | \(0.791013\pi\) | |||||||
\(938\) | −5.27221 | −0.172144 | ||||||||
\(939\) | −13.5872 | −0.443401 | ||||||||
\(940\) | 10.9356 | 0.356680 | ||||||||
\(941\) | −31.7973 | −1.03656 | −0.518282 | − | 0.855210i | \(-0.673428\pi\) | ||||
−0.518282 | + | 0.855210i | \(0.673428\pi\) | |||||||
\(942\) | −0.980521 | −0.0319471 | ||||||||
\(943\) | −47.6204 | −1.55073 | ||||||||
\(944\) | 10.5072 | 0.341979 | ||||||||
\(945\) | −13.4937 | −0.438949 | ||||||||
\(946\) | 1.43287 | 0.0465865 | ||||||||
\(947\) | −31.0555 | −1.00917 | −0.504583 | − | 0.863363i | \(-0.668354\pi\) | ||||
−0.504583 | + | 0.863363i | \(0.668354\pi\) | |||||||
\(948\) | −0.746973 | −0.0242606 | ||||||||
\(949\) | −19.9415 | −0.647329 | ||||||||
\(950\) | −2.38405 | −0.0773488 | ||||||||
\(951\) | −11.2199 | −0.363829 | ||||||||
\(952\) | 10.0528 | 0.325813 | ||||||||
\(953\) | −8.61722 | −0.279139 | −0.139570 | − | 0.990212i | \(-0.544572\pi\) | ||||
−0.139570 | + | 0.990212i | \(0.544572\pi\) | |||||||
\(954\) | −6.00272 | −0.194345 | ||||||||
\(955\) | 9.87355 | 0.319501 | ||||||||
\(956\) | −34.0755 | −1.10208 | ||||||||
\(957\) | −9.20637 | −0.297600 | ||||||||
\(958\) | −11.8120 | −0.381627 | ||||||||
\(959\) | 8.08825 | 0.261183 | ||||||||
\(960\) | −9.67232 | −0.312173 | ||||||||
\(961\) | −29.5404 | −0.952917 | ||||||||
\(962\) | −7.47900 | −0.241133 | ||||||||
\(963\) | −12.2194 | −0.393764 | ||||||||
\(964\) | 21.0702 | 0.678625 | ||||||||
\(965\) | 19.1104 | 0.615186 | ||||||||
\(966\) | 4.69504 | 0.151060 | ||||||||
\(967\) | 44.5830 | 1.43369 | 0.716846 | − | 0.697232i | \(-0.245585\pi\) | ||||
0.716846 | + | 0.697232i | \(0.245585\pi\) | |||||||
\(968\) | −14.3940 | −0.462641 | ||||||||
\(969\) | 14.8657 | 0.477556 | ||||||||
\(970\) | −1.74314 | −0.0559690 | ||||||||
\(971\) | −10.0866 | −0.323695 | −0.161848 | − | 0.986816i | \(-0.551745\pi\) | ||||
−0.161848 | + | 0.986816i | \(0.551745\pi\) | |||||||
\(972\) | 26.3338 | 0.844657 | ||||||||
\(973\) | 26.2409 | 0.841244 | ||||||||
\(974\) | 3.80676 | 0.121976 | ||||||||
\(975\) | 8.70017 | 0.278629 | ||||||||
\(976\) | 47.3131 | 1.51446 | ||||||||
\(977\) | −42.6221 | −1.36360 | −0.681801 | − | 0.731538i | \(-0.738803\pi\) | ||||
−0.681801 | + | 0.731538i | \(0.738803\pi\) | |||||||
\(978\) | 4.13505 | 0.132224 | ||||||||
\(979\) | −0.973089 | −0.0311001 | ||||||||
\(980\) | −13.4961 | −0.431116 | ||||||||
\(981\) | 15.0159 | 0.479422 | ||||||||
\(982\) | 7.85668 | 0.250717 | ||||||||
\(983\) | 8.80618 | 0.280874 | 0.140437 | − | 0.990090i | \(-0.455149\pi\) | ||||
0.140437 | + | 0.990090i | \(0.455149\pi\) | |||||||
\(984\) | 11.4253 | 0.364225 | ||||||||
\(985\) | 19.4557 | 0.619909 | ||||||||
\(986\) | −16.1127 | −0.513132 | ||||||||
\(987\) | −6.95923 | −0.221515 | ||||||||
\(988\) | 14.2868 | 0.454522 | ||||||||
\(989\) | −35.3294 | −1.12341 | ||||||||
\(990\) | −0.690073 | −0.0219320 | ||||||||
\(991\) | 60.1419 | 1.91047 | 0.955236 | − | 0.295846i | \(-0.0956017\pi\) | ||||
0.955236 | + | 0.295846i | \(0.0956017\pi\) | |||||||
\(992\) | 4.75659 | 0.151022 | ||||||||
\(993\) | 5.14543 | 0.163285 | ||||||||
\(994\) | −7.63436 | −0.242147 | ||||||||
\(995\) | −0.156213 | −0.00495229 | ||||||||
\(996\) | 19.1460 | 0.606663 | ||||||||
\(997\) | 18.0567 | 0.571861 | 0.285930 | − | 0.958250i | \(-0.407697\pi\) | ||||
0.285930 | + | 0.958250i | \(0.407697\pi\) | |||||||
\(998\) | −15.6005 | −0.493824 | ||||||||
\(999\) | 39.7725 | 1.25835 |
(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 | 349.2.a.b.1.6 | ✓ | 17 | |
3.2 | odd | 2 | 3141.2.a.e.1.12 | 17 | |||
4.3 | odd | 2 | 5584.2.a.m.1.12 | 17 | |||
5.4 | even | 2 | 8725.2.a.m.1.12 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.a.b.1.6 | ✓ | 17 | 1.1 | even | 1 | trivial | |
3141.2.a.e.1.12 | 17 | 3.2 | odd | 2 | |||
5584.2.a.m.1.12 | 17 | 4.3 | odd | 2 | |||
8725.2.a.m.1.12 | 17 | 5.4 | even | 2 |