Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-3.78432\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.78432 | 0.668979 | 0.334490 | − | 0.942399i | \(-0.391436\pi\) | ||||
0.334490 | + | 0.942399i | \(0.391436\pi\) | |||||||
\(3\) | −8.20788 | −0.526536 | −0.263268 | − | 0.964723i | \(-0.584800\pi\) | ||||
−0.263268 | + | 0.964723i | \(0.584800\pi\) | |||||||
\(4\) | −17.6789 | −0.552467 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −31.0612 | −0.352241 | ||||||||
\(7\) | −88.9969 | −0.686483 | −0.343242 | − | 0.939247i | \(-0.611525\pi\) | ||||
−0.343242 | + | 0.939247i | \(0.611525\pi\) | |||||||
\(8\) | −188.001 | −1.03857 | ||||||||
\(9\) | −175.631 | −0.722760 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −156.575 | −0.390159 | −0.195080 | − | 0.980787i | \(-0.562497\pi\) | ||||
−0.195080 | + | 0.980787i | \(0.562497\pi\) | |||||||
\(12\) | 145.107 | 0.290893 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | −336.793 | −0.459243 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −145.729 | −0.142314 | ||||||||
\(17\) | −447.890 | −0.375880 | −0.187940 | − | 0.982181i | \(-0.560181\pi\) | ||||
−0.187940 | + | 0.982181i | \(0.560181\pi\) | |||||||
\(18\) | −664.642 | −0.483512 | ||||||||
\(19\) | −269.669 | −0.171375 | −0.0856875 | − | 0.996322i | \(-0.527309\pi\) | ||||
−0.0856875 | + | 0.996322i | \(0.527309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 730.476 | 0.361458 | ||||||||
\(22\) | −592.531 | −0.261008 | ||||||||
\(23\) | −1371.05 | −0.540424 | −0.270212 | − | 0.962801i | \(-0.587094\pi\) | ||||
−0.270212 | + | 0.962801i | \(0.587094\pi\) | |||||||
\(24\) | 1543.09 | 0.546843 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −639.550 | −0.185541 | ||||||||
\(27\) | 3436.07 | 0.907095 | ||||||||
\(28\) | 1573.37 | 0.379259 | ||||||||
\(29\) | −3698.11 | −0.816554 | −0.408277 | − | 0.912858i | \(-0.633870\pi\) | ||||
−0.408277 | + | 0.912858i | \(0.633870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 797.974 | 0.149137 | 0.0745684 | − | 0.997216i | \(-0.476242\pi\) | ||||
0.0745684 | + | 0.997216i | \(0.476242\pi\) | |||||||
\(32\) | 5464.54 | 0.943363 | ||||||||
\(33\) | 1285.15 | 0.205433 | ||||||||
\(34\) | −1694.96 | −0.251456 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3104.97 | 0.399301 | ||||||||
\(37\) | 4394.83 | 0.527761 | 0.263881 | − | 0.964555i | \(-0.414997\pi\) | ||||
0.263881 | + | 0.964555i | \(0.414997\pi\) | |||||||
\(38\) | −1020.51 | −0.114646 | ||||||||
\(39\) | 1387.13 | 0.146035 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14320.9 | 1.33048 | 0.665242 | − | 0.746628i | \(-0.268328\pi\) | ||||
0.665242 | + | 0.746628i | \(0.268328\pi\) | |||||||
\(42\) | 2764.35 | 0.241808 | ||||||||
\(43\) | −11337.1 | −0.935037 | −0.467519 | − | 0.883983i | \(-0.654852\pi\) | ||||
−0.467519 | + | 0.883983i | \(0.654852\pi\) | |||||||
\(44\) | 2768.09 | 0.215550 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5188.50 | −0.361532 | ||||||||
\(47\) | 9974.03 | 0.658607 | 0.329303 | − | 0.944224i | \(-0.393186\pi\) | ||||
0.329303 | + | 0.944224i | \(0.393186\pi\) | |||||||
\(48\) | 1196.13 | 0.0749331 | ||||||||
\(49\) | −8886.54 | −0.528741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3676.23 | 0.197914 | ||||||||
\(52\) | 2987.74 | 0.153227 | ||||||||
\(53\) | −11587.1 | −0.566611 | −0.283305 | − | 0.959030i | \(-0.591431\pi\) | ||||
−0.283305 | + | 0.959030i | \(0.591431\pi\) | |||||||
\(54\) | 13003.2 | 0.606827 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16731.5 | 0.712960 | ||||||||
\(57\) | 2213.41 | 0.0902350 | ||||||||
\(58\) | −13994.8 | −0.546258 | ||||||||
\(59\) | 7133.45 | 0.266790 | 0.133395 | − | 0.991063i | \(-0.457412\pi\) | ||||
0.133395 | + | 0.991063i | \(0.457412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16629.8 | 0.572220 | 0.286110 | − | 0.958197i | \(-0.407638\pi\) | ||||
0.286110 | + | 0.958197i | \(0.407638\pi\) | |||||||
\(62\) | 3019.79 | 0.0997694 | ||||||||
\(63\) | 15630.6 | 0.496163 | ||||||||
\(64\) | 25342.9 | 0.773404 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4863.42 | 0.137430 | ||||||||
\(67\) | −4211.88 | −0.114628 | −0.0573138 | − | 0.998356i | \(-0.518254\pi\) | ||||
−0.0573138 | + | 0.998356i | \(0.518254\pi\) | |||||||
\(68\) | 7918.22 | 0.207661 | ||||||||
\(69\) | 11253.4 | 0.284552 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12871.4 | 0.303026 | 0.151513 | − | 0.988455i | \(-0.451585\pi\) | ||||
0.151513 | + | 0.988455i | \(0.451585\pi\) | |||||||
\(72\) | 33018.7 | 0.750636 | ||||||||
\(73\) | 13097.1 | 0.287653 | 0.143826 | − | 0.989603i | \(-0.454059\pi\) | ||||
0.143826 | + | 0.989603i | \(0.454059\pi\) | |||||||
\(74\) | 16631.4 | 0.353061 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4767.46 | 0.0946790 | ||||||||
\(77\) | 13934.7 | 0.267838 | ||||||||
\(78\) | 5249.35 | 0.0976942 | ||||||||
\(79\) | 74729.2 | 1.34717 | 0.673586 | − | 0.739109i | \(-0.264753\pi\) | ||||
0.673586 | + | 0.739109i | \(0.264753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14475.4 | 0.245143 | ||||||||
\(82\) | 54194.7 | 0.890066 | ||||||||
\(83\) | −8547.83 | −0.136195 | −0.0680974 | − | 0.997679i | \(-0.521693\pi\) | ||||
−0.0680974 | + | 0.997679i | \(0.521693\pi\) | |||||||
\(84\) | −12914.0 | −0.199694 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −42903.0 | −0.625521 | ||||||||
\(87\) | 30353.6 | 0.429945 | ||||||||
\(88\) | 29436.3 | 0.405207 | ||||||||
\(89\) | 59586.0 | 0.797387 | 0.398694 | − | 0.917084i | \(-0.369464\pi\) | ||||
0.398694 | + | 0.917084i | \(0.369464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15040.5 | 0.190396 | ||||||||
\(92\) | 24238.8 | 0.298566 | ||||||||
\(93\) | −6549.68 | −0.0785258 | ||||||||
\(94\) | 37744.9 | 0.440594 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −44852.3 | −0.496714 | ||||||||
\(97\) | 17376.2 | 0.187510 | 0.0937552 | − | 0.995595i | \(-0.470113\pi\) | ||||
0.0937552 | + | 0.995595i | \(0.470113\pi\) | |||||||
\(98\) | −33629.5 | −0.353716 | ||||||||
\(99\) | 27499.5 | 0.281992 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 68669.7 | 0.669825 | 0.334913 | − | 0.942249i | \(-0.391293\pi\) | ||||
0.334913 | + | 0.942249i | \(0.391293\pi\) | |||||||
\(102\) | 13912.0 | 0.132400 | ||||||||
\(103\) | −191203. | −1.77584 | −0.887918 | − | 0.460002i | \(-0.847849\pi\) | ||||
−0.887918 | + | 0.460002i | \(0.847849\pi\) | |||||||
\(104\) | 31772.2 | 0.288047 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −43849.2 | −0.379051 | ||||||||
\(107\) | 46117.6 | 0.389410 | 0.194705 | − | 0.980862i | \(-0.437625\pi\) | ||||
0.194705 | + | 0.980862i | \(0.437625\pi\) | |||||||
\(108\) | −60746.1 | −0.501140 | ||||||||
\(109\) | 187271. | 1.50975 | 0.754873 | − | 0.655871i | \(-0.227698\pi\) | ||||
0.754873 | + | 0.655871i | \(0.227698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −36072.2 | −0.277885 | ||||||||
\(112\) | 12969.4 | 0.0976959 | ||||||||
\(113\) | −189262. | −1.39434 | −0.697169 | − | 0.716907i | \(-0.745557\pi\) | ||||
−0.697169 | + | 0.716907i | \(0.745557\pi\) | |||||||
\(114\) | 8376.25 | 0.0603653 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 65378.7 | 0.451119 | ||||||||
\(117\) | 29681.6 | 0.200458 | ||||||||
\(118\) | 26995.2 | 0.178477 | ||||||||
\(119\) | 39860.9 | 0.258035 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −136535. | −0.847776 | ||||||||
\(122\) | 62932.5 | 0.382803 | ||||||||
\(123\) | −117544. | −0.700547 | ||||||||
\(124\) | −14107.3 | −0.0823931 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 59151.2 | 0.331923 | ||||||||
\(127\) | −183029. | −1.00695 | −0.503477 | − | 0.864009i | \(-0.667946\pi\) | ||||
−0.503477 | + | 0.864009i | \(0.667946\pi\) | |||||||
\(128\) | −78959.8 | −0.425972 | ||||||||
\(129\) | 93053.1 | 0.492331 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 221035. | 1.12534 | 0.562668 | − | 0.826683i | \(-0.309775\pi\) | ||||
0.562668 | + | 0.826683i | \(0.309775\pi\) | |||||||
\(132\) | −22720.1 | −0.113495 | ||||||||
\(133\) | 23999.7 | 0.117646 | ||||||||
\(134\) | −15939.1 | −0.0766835 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 84203.7 | 0.390377 | ||||||||
\(137\) | −353821. | −1.61058 | −0.805290 | − | 0.592881i | \(-0.797991\pi\) | ||||
−0.805290 | + | 0.592881i | \(0.797991\pi\) | |||||||
\(138\) | 42586.6 | 0.190360 | ||||||||
\(139\) | 282625. | 1.24072 | 0.620359 | − | 0.784318i | \(-0.286987\pi\) | ||||
0.620359 | + | 0.784318i | \(0.286987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −81865.7 | −0.346780 | ||||||||
\(142\) | 48709.4 | 0.202718 | ||||||||
\(143\) | 26461.2 | 0.108211 | ||||||||
\(144\) | 25594.5 | 0.102859 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 49563.7 | 0.192434 | ||||||||
\(147\) | 72939.7 | 0.278401 | ||||||||
\(148\) | −77695.9 | −0.291571 | ||||||||
\(149\) | −77579.6 | −0.286274 | −0.143137 | − | 0.989703i | \(-0.545719\pi\) | ||||
−0.143137 | + | 0.989703i | \(0.545719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −209693. | −0.748412 | −0.374206 | − | 0.927346i | \(-0.622085\pi\) | ||||
−0.374206 | + | 0.927346i | \(0.622085\pi\) | |||||||
\(152\) | 50698.0 | 0.177985 | ||||||||
\(153\) | 78663.3 | 0.271671 | ||||||||
\(154\) | 52733.5 | 0.179178 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −24523.0 | −0.0806793 | ||||||||
\(157\) | −127745. | −0.413612 | −0.206806 | − | 0.978382i | \(-0.566307\pi\) | ||||
−0.206806 | + | 0.978382i | \(0.566307\pi\) | |||||||
\(158\) | 282799. | 0.901230 | ||||||||
\(159\) | 95105.4 | 0.298341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 122019. | 0.370992 | ||||||||
\(162\) | 54779.6 | 0.163995 | ||||||||
\(163\) | −33444.3 | −0.0985947 | −0.0492973 | − | 0.998784i | \(-0.515698\pi\) | ||||
−0.0492973 | + | 0.998784i | \(0.515698\pi\) | |||||||
\(164\) | −253178. | −0.735048 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −32347.7 | −0.0911115 | ||||||||
\(167\) | 317479. | 0.880893 | 0.440447 | − | 0.897779i | \(-0.354820\pi\) | ||||
0.440447 | + | 0.897779i | \(0.354820\pi\) | |||||||
\(168\) | −137330. | −0.375399 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47362.2 | 0.123863 | ||||||||
\(172\) | 200427. | 0.516577 | ||||||||
\(173\) | −84505.1 | −0.214668 | −0.107334 | − | 0.994223i | \(-0.534231\pi\) | ||||
−0.107334 | + | 0.994223i | \(0.534231\pi\) | |||||||
\(174\) | 114868. | 0.287624 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22817.6 | 0.0555249 | ||||||||
\(177\) | −58550.5 | −0.140474 | ||||||||
\(178\) | 225492. | 0.533435 | ||||||||
\(179\) | −734183. | −1.71266 | −0.856331 | − | 0.516428i | \(-0.827261\pi\) | ||||
−0.856331 | + | 0.516428i | \(0.827261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 363356. | 0.824396 | 0.412198 | − | 0.911094i | \(-0.364761\pi\) | ||||
0.412198 | + | 0.911094i | \(0.364761\pi\) | |||||||
\(182\) | 56918.0 | 0.127371 | ||||||||
\(183\) | −136496. | −0.301294 | ||||||||
\(184\) | 257759. | 0.561267 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −24786.1 | −0.0525321 | ||||||||
\(187\) | 70128.6 | 0.146653 | ||||||||
\(188\) | −176330. | −0.363858 | ||||||||
\(189\) | −305800. | −0.622705 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 54142.3 | 0.107387 | 0.0536937 | − | 0.998557i | \(-0.482901\pi\) | ||||
0.0536937 | + | 0.998557i | \(0.482901\pi\) | |||||||
\(192\) | −208011. | −0.407225 | ||||||||
\(193\) | 208911. | 0.403709 | 0.201855 | − | 0.979416i | \(-0.435303\pi\) | ||||
0.201855 | + | 0.979416i | \(0.435303\pi\) | |||||||
\(194\) | 65757.1 | 0.125441 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 157105. | 0.292112 | ||||||||
\(197\) | −581675. | −1.06786 | −0.533931 | − | 0.845528i | \(-0.679286\pi\) | ||||
−0.533931 | + | 0.845528i | \(0.679286\pi\) | |||||||
\(198\) | 104067. | 0.188646 | ||||||||
\(199\) | −624788. | −1.11841 | −0.559204 | − | 0.829030i | \(-0.688893\pi\) | ||||
−0.559204 | + | 0.829030i | \(0.688893\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34570.6 | 0.0603555 | ||||||||
\(202\) | 259868. | 0.448099 | ||||||||
\(203\) | 329121. | 0.560551 | ||||||||
\(204\) | −64991.8 | −0.109341 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −723575. | −1.18800 | ||||||||
\(207\) | 240799. | 0.390597 | ||||||||
\(208\) | 24628.2 | 0.0394707 | ||||||||
\(209\) | 42223.6 | 0.0668635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 628250. | 0.971464 | 0.485732 | − | 0.874108i | \(-0.338553\pi\) | ||||
0.485732 | + | 0.874108i | \(0.338553\pi\) | |||||||
\(212\) | 204847. | 0.313034 | ||||||||
\(213\) | −105647. | −0.159554 | ||||||||
\(214\) | 174524. | 0.260507 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −645984. | −0.942079 | ||||||||
\(217\) | −71017.3 | −0.102380 | ||||||||
\(218\) | 708693. | 1.00999 | ||||||||
\(219\) | −107500. | −0.151459 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 75693.4 | 0.104250 | ||||||||
\(222\) | −136509. | −0.185899 | ||||||||
\(223\) | 1.09757e6 | 1.47798 | 0.738992 | − | 0.673715i | \(-0.235302\pi\) | ||||
0.738992 | + | 0.673715i | \(0.235302\pi\) | |||||||
\(224\) | −486328. | −0.647603 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −716229. | −0.932783 | ||||||||
\(227\) | −161937. | −0.208584 | −0.104292 | − | 0.994547i | \(-0.533258\pi\) | ||||
−0.104292 | + | 0.994547i | \(0.533258\pi\) | |||||||
\(228\) | −39130.8 | −0.0498518 | ||||||||
\(229\) | −645210. | −0.813040 | −0.406520 | − | 0.913642i | \(-0.633258\pi\) | ||||
−0.406520 | + | 0.913642i | \(0.633258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −114375. | −0.141026 | ||||||||
\(232\) | 695248. | 0.848047 | ||||||||
\(233\) | 839907. | 1.01354 | 0.506770 | − | 0.862081i | \(-0.330839\pi\) | ||||
0.506770 | + | 0.862081i | \(0.330839\pi\) | |||||||
\(234\) | 112325. | 0.134102 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −126112. | −0.147393 | ||||||||
\(237\) | −613369. | −0.709334 | ||||||||
\(238\) | 150846. | 0.172620 | ||||||||
\(239\) | −532168. | −0.602635 | −0.301317 | − | 0.953524i | \(-0.597426\pi\) | ||||
−0.301317 | + | 0.953524i | \(0.597426\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11282.2 | −0.0125127 | −0.00625633 | − | 0.999980i | \(-0.501991\pi\) | ||||
−0.00625633 | + | 0.999980i | \(0.501991\pi\) | |||||||
\(242\) | −516692. | −0.567144 | ||||||||
\(243\) | −953778. | −1.03617 | ||||||||
\(244\) | −293998. | −0.316133 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −444824. | −0.468652 | ||||||||
\(247\) | 45574.1 | 0.0475308 | ||||||||
\(248\) | −150020. | −0.154889 | ||||||||
\(249\) | 70159.5 | 0.0717114 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −592652. | −0.593766 | −0.296883 | − | 0.954914i | \(-0.595947\pi\) | ||||
−0.296883 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(252\) | −276332. | −0.274114 | ||||||||
\(253\) | 214673. | 0.210851 | ||||||||
\(254\) | −692639. | −0.673632 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.10978e6 | −1.05837 | ||||||||
\(257\) | 161530. | 0.152552 | 0.0762762 | − | 0.997087i | \(-0.475697\pi\) | ||||
0.0762762 | + | 0.997087i | \(0.475697\pi\) | |||||||
\(258\) | 352143. | 0.329359 | ||||||||
\(259\) | −391126. | −0.362299 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 649502. | 0.590173 | ||||||||
\(262\) | 836466. | 0.752826 | ||||||||
\(263\) | 377791. | 0.336793 | 0.168396 | − | 0.985719i | \(-0.446141\pi\) | ||||
0.168396 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(264\) | −241610. | −0.213356 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 90822.6 | 0.0787027 | ||||||||
\(267\) | −489075. | −0.419853 | ||||||||
\(268\) | 74461.6 | 0.0633280 | ||||||||
\(269\) | −689.090 | −0.000580624 0 | −0.000290312 | − | 1.00000i | \(-0.500092\pi\) | ||||
−0.000290312 | 1.00000i | \(0.500092\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 625466. | 0.517345 | 0.258673 | − | 0.965965i | \(-0.416715\pi\) | ||||
0.258673 | + | 0.965965i | \(0.416715\pi\) | |||||||
\(272\) | 65270.6 | 0.0534928 | ||||||||
\(273\) | −123450. | −0.100250 | ||||||||
\(274\) | −1.33897e6 | −1.07744 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −198949. | −0.157206 | ||||||||
\(277\) | −744000. | −0.582604 | −0.291302 | − | 0.956631i | \(-0.594088\pi\) | ||||
−0.291302 | + | 0.956631i | \(0.594088\pi\) | |||||||
\(278\) | 1.06954e6 | 0.830015 | ||||||||
\(279\) | −140149. | −0.107790 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.43786e6 | 1.08631 | 0.543153 | − | 0.839634i | \(-0.317230\pi\) | ||||
0.543153 | + | 0.839634i | \(0.317230\pi\) | |||||||
\(282\) | −309806. | −0.231989 | ||||||||
\(283\) | 1.24662e6 | 0.925267 | 0.462634 | − | 0.886550i | \(-0.346905\pi\) | ||||
0.462634 | + | 0.886550i | \(0.346905\pi\) | |||||||
\(284\) | −227553. | −0.167412 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 100138. | 0.0723907 | ||||||||
\(287\) | −1.27451e6 | −0.913355 | ||||||||
\(288\) | −959742. | −0.681825 | ||||||||
\(289\) | −1.21925e6 | −0.858714 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −142622. | −0.0987309 | ||||||||
\(292\) | −231543. | −0.158919 | ||||||||
\(293\) | −1.74658e6 | −1.18855 | −0.594276 | − | 0.804261i | \(-0.702561\pi\) | ||||
−0.594276 | + | 0.804261i | \(0.702561\pi\) | |||||||
\(294\) | 276027. | 0.186244 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −826231. | −0.548116 | ||||||||
\(297\) | −538004. | −0.353911 | ||||||||
\(298\) | −293586. | −0.191511 | ||||||||
\(299\) | 231708. | 0.149887 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00896e6 | 0.641888 | ||||||||
\(302\) | −793543. | −0.500672 | ||||||||
\(303\) | −563632. | −0.352687 | ||||||||
\(304\) | 39298.6 | 0.0243890 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 297687. | 0.181742 | ||||||||
\(307\) | 239330. | 0.144928 | 0.0724638 | − | 0.997371i | \(-0.476914\pi\) | ||||
0.0724638 | + | 0.997371i | \(0.476914\pi\) | |||||||
\(308\) | −246351. | −0.147972 | ||||||||
\(309\) | 1.56937e6 | 0.935041 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.10338e6 | 0.646883 | 0.323441 | − | 0.946248i | \(-0.395160\pi\) | ||||
0.323441 | + | 0.946248i | \(0.395160\pi\) | |||||||
\(312\) | −260782. | −0.151667 | ||||||||
\(313\) | 934831. | 0.539352 | 0.269676 | − | 0.962951i | \(-0.413083\pi\) | ||||
0.269676 | + | 0.962951i | \(0.413083\pi\) | |||||||
\(314\) | −483426. | −0.276698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.32113e6 | −0.744268 | ||||||||
\(317\) | −2.65437e6 | −1.48359 | −0.741794 | − | 0.670628i | \(-0.766025\pi\) | ||||
−0.741794 | + | 0.670628i | \(0.766025\pi\) | |||||||
\(318\) | 359909. | 0.199584 | ||||||||
\(319\) | 579033. | 0.318586 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −378528. | −0.205038 | ||||||||
\(322\) | 461761. | 0.248186 | ||||||||
\(323\) | 120782. | 0.0644164 | ||||||||
\(324\) | −255910. | −0.135433 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −126564. | −0.0659578 | ||||||||
\(327\) | −1.53710e6 | −0.794935 | ||||||||
\(328\) | −2.69234e6 | −1.38180 | ||||||||
\(329\) | −887659. | −0.452123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 648335. | 0.325259 | 0.162630 | − | 0.986687i | \(-0.448002\pi\) | ||||
0.162630 | + | 0.986687i | \(0.448002\pi\) | |||||||
\(332\) | 151117. | 0.0752431 | ||||||||
\(333\) | −771867. | −0.381445 | ||||||||
\(334\) | 1.20144e6 | 0.589299 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −106452. | −0.0514404 | ||||||||
\(337\) | 761016. | 0.365022 | 0.182511 | − | 0.983204i | \(-0.441577\pi\) | ||||
0.182511 | + | 0.983204i | \(0.441577\pi\) | |||||||
\(338\) | 108084. | 0.0514599 | ||||||||
\(339\) | 1.55344e6 | 0.734169 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −124943. | −0.0581871 | ||||||||
\(342\) | 179234. | 0.0828617 | ||||||||
\(343\) | 2.28665e6 | 1.04945 | ||||||||
\(344\) | 2.13138e6 | 0.971100 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −319794. | −0.143609 | ||||||||
\(347\) | 1.06891e6 | 0.476561 | 0.238281 | − | 0.971196i | \(-0.423416\pi\) | ||||
0.238281 | + | 0.971196i | \(0.423416\pi\) | |||||||
\(348\) | −536620. | −0.237530 | ||||||||
\(349\) | 1.57765e6 | 0.693342 | 0.346671 | − | 0.937987i | \(-0.387312\pi\) | ||||
0.346671 | + | 0.937987i | \(0.387312\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −580696. | −0.251583 | ||||||||
\(352\) | −855613. | −0.368062 | ||||||||
\(353\) | −109374. | −0.0467173 | −0.0233587 | − | 0.999727i | \(-0.507436\pi\) | ||||
−0.0233587 | + | 0.999727i | \(0.507436\pi\) | |||||||
\(354\) | −221574. | −0.0939745 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.05342e6 | −0.440530 | ||||||||
\(357\) | −327173. | −0.135865 | ||||||||
\(358\) | −2.77838e6 | −1.14573 | ||||||||
\(359\) | 3.75166e6 | 1.53634 | 0.768169 | − | 0.640247i | \(-0.221168\pi\) | ||||
0.768169 | + | 0.640247i | \(0.221168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.40338e6 | −0.970631 | ||||||||
\(362\) | 1.37506e6 | 0.551504 | ||||||||
\(363\) | 1.12066e6 | 0.446384 | ||||||||
\(364\) | −265900. | −0.105188 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −516543. | −0.201560 | ||||||||
\(367\) | 2.12587e6 | 0.823895 | 0.411947 | − | 0.911208i | \(-0.364849\pi\) | ||||
0.411947 | + | 0.911208i | \(0.364849\pi\) | |||||||
\(368\) | 199802. | 0.0769096 | ||||||||
\(369\) | −2.51518e6 | −0.961621 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.03122e6 | 0.388969 | ||||||||
\(372\) | 115791. | 0.0433829 | ||||||||
\(373\) | 725713. | 0.270080 | 0.135040 | − | 0.990840i | \(-0.456884\pi\) | ||||
0.135040 | + | 0.990840i | \(0.456884\pi\) | |||||||
\(374\) | 265389. | 0.0981078 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.87513e6 | −0.684008 | ||||||||
\(377\) | 624981. | 0.226471 | ||||||||
\(378\) | −1.15724e6 | −0.416577 | ||||||||
\(379\) | 1.40410e6 | 0.502111 | 0.251056 | − | 0.967973i | \(-0.419222\pi\) | ||||
0.251056 | + | 0.967973i | \(0.419222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50228e6 | 0.530197 | ||||||||
\(382\) | 204892. | 0.0718400 | ||||||||
\(383\) | 2.82085e6 | 0.982615 | 0.491307 | − | 0.870986i | \(-0.336519\pi\) | ||||
0.491307 | + | 0.870986i | \(0.336519\pi\) | |||||||
\(384\) | 648093. | 0.224290 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 790587. | 0.270073 | ||||||||
\(387\) | 1.99113e6 | 0.675808 | ||||||||
\(388\) | −307193. | −0.103593 | ||||||||
\(389\) | −1.71293e6 | −0.573940 | −0.286970 | − | 0.957940i | \(-0.592648\pi\) | ||||
−0.286970 | + | 0.957940i | \(0.592648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 614081. | 0.203135 | ||||||||
\(392\) | 1.67068e6 | 0.549133 | ||||||||
\(393\) | −1.81423e6 | −0.592530 | ||||||||
\(394\) | −2.20124e6 | −0.714377 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −486161. | −0.155791 | ||||||||
\(397\) | 3.80080e6 | 1.21032 | 0.605158 | − | 0.796106i | \(-0.293110\pi\) | ||||
0.605158 | + | 0.796106i | \(0.293110\pi\) | |||||||
\(398\) | −2.36440e6 | −0.748191 | ||||||||
\(399\) | −196987. | −0.0619448 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.09440e6 | 0.339871 | 0.169936 | − | 0.985455i | \(-0.445644\pi\) | ||||
0.169936 | + | 0.985455i | \(0.445644\pi\) | |||||||
\(402\) | 130826. | 0.0403766 | ||||||||
\(403\) | −134858. | −0.0413631 | ||||||||
\(404\) | −1.21401e6 | −0.370056 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.24550e6 | 0.374997 | ||||||||
\(407\) | −688122. | −0.205911 | ||||||||
\(408\) | −691134. | −0.205547 | ||||||||
\(409\) | 6.63162e6 | 1.96025 | 0.980125 | − | 0.198380i | \(-0.0635679\pi\) | ||||
0.980125 | + | 0.198380i | \(0.0635679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.90412e6 | 0.848028 | ||||||||
\(412\) | 3.38027e6 | 0.981090 | ||||||||
\(413\) | −634855. | −0.183147 | ||||||||
\(414\) | 911260. | 0.261301 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −923508. | −0.261642 | ||||||||
\(417\) | −2.31975e6 | −0.653283 | ||||||||
\(418\) | 159787. | 0.0447303 | ||||||||
\(419\) | −1.50034e6 | −0.417499 | −0.208749 | − | 0.977969i | \(-0.566939\pi\) | ||||
−0.208749 | + | 0.977969i | \(0.566939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.91392e6 | −0.526282 | −0.263141 | − | 0.964757i | \(-0.584758\pi\) | ||||
−0.263141 | + | 0.964757i | \(0.584758\pi\) | |||||||
\(422\) | 2.37750e6 | 0.649889 | ||||||||
\(423\) | −1.75175e6 | −0.476015 | ||||||||
\(424\) | 2.17838e6 | 0.588464 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −399801. | −0.106738 | ||||||||
\(427\) | −1.48000e6 | −0.392820 | ||||||||
\(428\) | −815311. | −0.215136 | ||||||||
\(429\) | −217191. | −0.0569768 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.04255e6 | 1.56685 | 0.783424 | − | 0.621488i | \(-0.213471\pi\) | ||||
0.783424 | + | 0.621488i | \(0.213471\pi\) | |||||||
\(432\) | −500735. | −0.129092 | ||||||||
\(433\) | 1.81284e6 | 0.464666 | 0.232333 | − | 0.972636i | \(-0.425364\pi\) | ||||
0.232333 | + | 0.972636i | \(0.425364\pi\) | |||||||
\(434\) | −268752. | −0.0684900 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.31075e6 | −0.834085 | ||||||||
\(437\) | 369731. | 0.0926151 | ||||||||
\(438\) | −406813. | −0.101323 | ||||||||
\(439\) | 3.45414e6 | 0.855418 | 0.427709 | − | 0.903916i | \(-0.359321\pi\) | ||||
0.427709 | + | 0.903916i | \(0.359321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.56075e6 | 0.382153 | ||||||||
\(442\) | 286448. | 0.0697413 | ||||||||
\(443\) | 1.64299e6 | 0.397764 | 0.198882 | − | 0.980023i | \(-0.436269\pi\) | ||||
0.198882 | + | 0.980023i | \(0.436269\pi\) | |||||||
\(444\) | 637718. | 0.153522 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.15355e6 | 0.988740 | ||||||||
\(447\) | 636764. | 0.150733 | ||||||||
\(448\) | −2.25544e6 | −0.530929 | ||||||||
\(449\) | 3.90173e6 | 0.913359 | 0.456680 | − | 0.889631i | \(-0.349039\pi\) | ||||
0.456680 | + | 0.889631i | \(0.349039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.24230e6 | −0.519101 | ||||||||
\(452\) | 3.34596e6 | 0.770325 | ||||||||
\(453\) | 1.72113e6 | 0.394066 | ||||||||
\(454\) | −612821. | −0.139539 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −416123. | −0.0937152 | ||||||||
\(457\) | 6.09815e6 | 1.36586 | 0.682932 | − | 0.730482i | \(-0.260704\pi\) | ||||
0.682932 | + | 0.730482i | \(0.260704\pi\) | |||||||
\(458\) | −2.44168e6 | −0.543907 | ||||||||
\(459\) | −1.53898e6 | −0.340959 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.52589e6 | 1.86848 | 0.934238 | − | 0.356651i | \(-0.116081\pi\) | ||||
0.934238 | + | 0.356651i | \(0.116081\pi\) | |||||||
\(462\) | −432830. | −0.0943436 | ||||||||
\(463\) | 2.70655e6 | 0.586765 | 0.293382 | − | 0.955995i | \(-0.405219\pi\) | ||||
0.293382 | + | 0.955995i | \(0.405219\pi\) | |||||||
\(464\) | 538922. | 0.116207 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.17847e6 | 0.678038 | ||||||||
\(467\) | 350172. | 0.0743001 | 0.0371501 | − | 0.999310i | \(-0.488172\pi\) | ||||
0.0371501 | + | 0.999310i | \(0.488172\pi\) | |||||||
\(468\) | −524739. | −0.110746 | ||||||||
\(469\) | 374845. | 0.0786900 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.04851e6 | 0.217782 | ||||||||
\(472\) | −1.34110e6 | −0.277080 | ||||||||
\(473\) | 1.77510e6 | 0.364813 | ||||||||
\(474\) | −2.32118e6 | −0.474529 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −704698. | −0.142556 | ||||||||
\(477\) | 2.03505e6 | 0.409524 | ||||||||
\(478\) | −2.01389e6 | −0.403150 | ||||||||
\(479\) | 8.49125e6 | 1.69096 | 0.845479 | − | 0.534009i | \(-0.179315\pi\) | ||||
0.845479 | + | 0.534009i | \(0.179315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −742726. | −0.146375 | ||||||||
\(482\) | −42695.3 | −0.00837071 | ||||||||
\(483\) | −1.00152e6 | −0.195341 | ||||||||
\(484\) | 2.41380e6 | 0.468368 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.60940e6 | −0.693177 | ||||||||
\(487\) | −3034.65 | −0.000579811 0 | −0.000289905 | − | 1.00000i | \(-0.500092\pi\) | ||||
−0.000289905 | 1.00000i | \(0.500092\pi\) | ||||||||
\(488\) | −3.12642e6 | −0.594289 | ||||||||
\(489\) | 274507. | 0.0519136 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.43114e6 | −0.642295 | −0.321147 | − | 0.947029i | \(-0.604068\pi\) | ||||
−0.321147 | + | 0.947029i | \(0.604068\pi\) | |||||||
\(492\) | 2.07805e6 | 0.387029 | ||||||||
\(493\) | 1.65635e6 | 0.306926 | ||||||||
\(494\) | 172467. | 0.0317971 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −116288. | −0.0212242 | ||||||||
\(497\) | −1.14551e6 | −0.208022 | ||||||||
\(498\) | 265506. | 0.0479735 | ||||||||
\(499\) | −1.11566e6 | −0.200577 | −0.100289 | − | 0.994958i | \(-0.531977\pi\) | ||||
−0.100289 | + | 0.994958i | \(0.531977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.60583e6 | −0.463822 | ||||||||
\(502\) | −2.24278e6 | −0.397217 | ||||||||
\(503\) | −4.99165e6 | −0.879679 | −0.439840 | − | 0.898076i | \(-0.644965\pi\) | ||||
−0.439840 | + | 0.898076i | \(0.644965\pi\) | |||||||
\(504\) | −2.93857e6 | −0.515299 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 812391. | 0.141055 | ||||||||
\(507\) | −234425. | −0.0405027 | ||||||||
\(508\) | 3.23575e6 | 0.556309 | ||||||||
\(509\) | −398811. | −0.0682296 | −0.0341148 | − | 0.999418i | \(-0.510861\pi\) | ||||
−0.0341148 | + | 0.999418i | \(0.510861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.16560e6 | −0.197469 | ||||||||
\(512\) | −1.67305e6 | −0.282056 | ||||||||
\(513\) | −926602. | −0.155453 | ||||||||
\(514\) | 611279. | 0.102054 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.64508e6 | −0.271996 | ||||||||
\(517\) | −1.56169e6 | −0.256962 | ||||||||
\(518\) | −1.48015e6 | −0.242371 | ||||||||
\(519\) | 693607. | 0.113030 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.33110e6 | 1.50605 | 0.753023 | − | 0.657994i | \(-0.228595\pi\) | ||||
0.753023 | + | 0.657994i | \(0.228595\pi\) | |||||||
\(522\) | 2.45792e6 | 0.394813 | ||||||||
\(523\) | 4.93297e6 | 0.788596 | 0.394298 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394298 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(524\) | −3.90766e6 | −0.621711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.42968e6 | 0.225307 | ||||||||
\(527\) | −357405. | −0.0560575 | ||||||||
\(528\) | −187284. | −0.0292359 | ||||||||
\(529\) | −4.55656e6 | −0.707942 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.25285e6 | −0.192825 | ||||||||
\(532\) | −424290. | −0.0649955 | ||||||||
\(533\) | −2.42023e6 | −0.369010 | ||||||||
\(534\) | −1.85081e6 | −0.280873 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 791838. | 0.119049 | ||||||||
\(537\) | 6.02608e6 | 0.901777 | ||||||||
\(538\) | −2607.73 | −0.000388425 0 | ||||||||
\(539\) | 1.39141e6 | 0.206293 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.72340e6 | 0.400054 | 0.200027 | − | 0.979790i | \(-0.435897\pi\) | ||||
0.200027 | + | 0.979790i | \(0.435897\pi\) | |||||||
\(542\) | 2.36696e6 | 0.346093 | ||||||||
\(543\) | −2.98238e6 | −0.434074 | ||||||||
\(544\) | −2.44751e6 | −0.354591 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −467176. | −0.0670654 | ||||||||
\(547\) | −1.28669e7 | −1.83867 | −0.919337 | − | 0.393472i | \(-0.871274\pi\) | ||||
−0.919337 | + | 0.393472i | \(0.871274\pi\) | |||||||
\(548\) | 6.25518e6 | 0.889792 | ||||||||
\(549\) | −2.92071e6 | −0.413578 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 997266. | 0.139937 | ||||||||
\(552\) | −2.11566e6 | −0.295527 | ||||||||
\(553\) | −6.65067e6 | −0.924811 | ||||||||
\(554\) | −2.81553e6 | −0.389750 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.99651e6 | −0.685456 | ||||||||
\(557\) | −1.03791e7 | −1.41750 | −0.708751 | − | 0.705459i | \(-0.750741\pi\) | ||||
−0.708751 | + | 0.705459i | \(0.750741\pi\) | |||||||
\(558\) | −530368. | −0.0721094 | ||||||||
\(559\) | 1.91596e6 | 0.259333 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −575607. | −0.0772180 | ||||||||
\(562\) | 5.44133e6 | 0.726716 | ||||||||
\(563\) | 3.37237e6 | 0.448399 | 0.224199 | − | 0.974543i | \(-0.428023\pi\) | ||||
0.224199 | + | 0.974543i | \(0.428023\pi\) | |||||||
\(564\) | 1.44730e6 | 0.191584 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.71760e6 | 0.618984 | ||||||||
\(567\) | −1.28827e6 | −0.168286 | ||||||||
\(568\) | −2.41983e6 | −0.314713 | ||||||||
\(569\) | −9.65718e6 | −1.25046 | −0.625230 | − | 0.780441i | \(-0.714995\pi\) | ||||
−0.625230 | + | 0.780441i | \(0.714995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.19460e6 | −0.410040 | −0.205020 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205020 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(572\) | −467807. | −0.0597828 | ||||||||
\(573\) | −444394. | −0.0565433 | ||||||||
\(574\) | −4.82316e6 | −0.611016 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.45099e6 | −0.558986 | ||||||||
\(577\) | −1.01384e7 | −1.26774 | −0.633872 | − | 0.773438i | \(-0.718535\pi\) | ||||
−0.633872 | + | 0.773438i | \(0.718535\pi\) | |||||||
\(578\) | −4.61403e6 | −0.574462 | ||||||||
\(579\) | −1.71472e6 | −0.212567 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 760731. | 0.0934955 | ||||||||
\(582\) | −539726. | −0.0660489 | ||||||||
\(583\) | 1.81425e6 | 0.221068 | ||||||||
\(584\) | −2.46227e6 | −0.298747 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.60960e6 | −0.795117 | ||||||||
\(587\) | −777799. | −0.0931691 | −0.0465846 | − | 0.998914i | \(-0.514834\pi\) | ||||
−0.0465846 | + | 0.998914i | \(0.514834\pi\) | |||||||
\(588\) | −1.28950e6 | −0.153807 | ||||||||
\(589\) | −215189. | −0.0255583 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.77432e6 | 0.562267 | ||||||||
\(592\) | −640454. | −0.0751076 | ||||||||
\(593\) | 8.28738e6 | 0.967789 | 0.483894 | − | 0.875126i | \(-0.339222\pi\) | ||||
0.483894 | + | 0.875126i | \(0.339222\pi\) | |||||||
\(594\) | −2.03598e6 | −0.236759 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.37153e6 | 0.158157 | ||||||||
\(597\) | 5.12818e6 | 0.588881 | ||||||||
\(598\) | 876856. | 0.100271 | ||||||||
\(599\) | 1.39700e7 | 1.59085 | 0.795423 | − | 0.606054i | \(-0.207249\pi\) | ||||
0.795423 | + | 0.606054i | \(0.207249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.27397e7 | −1.43871 | −0.719355 | − | 0.694643i | \(-0.755562\pi\) | ||||
−0.719355 | + | 0.694643i | \(0.755562\pi\) | |||||||
\(602\) | 3.81824e6 | 0.429409 | ||||||||
\(603\) | 739736. | 0.0828483 | ||||||||
\(604\) | 3.70714e6 | 0.413473 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.13296e6 | −0.235940 | ||||||||
\(607\) | 6.25976e6 | 0.689583 | 0.344791 | − | 0.938679i | \(-0.387950\pi\) | ||||
0.344791 | + | 0.938679i | \(0.387950\pi\) | |||||||
\(608\) | −1.47362e6 | −0.161669 | ||||||||
\(609\) | −2.70138e6 | −0.295150 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.68561e6 | −0.182665 | ||||||||
\(612\) | −1.39068e6 | −0.150089 | ||||||||
\(613\) | 1.17405e7 | 1.26193 | 0.630964 | − | 0.775812i | \(-0.282660\pi\) | ||||
0.630964 | + | 0.775812i | \(0.282660\pi\) | |||||||
\(614\) | 905700. | 0.0969535 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.61974e6 | −0.278168 | ||||||||
\(617\) | −1.57982e7 | −1.67069 | −0.835343 | − | 0.549729i | \(-0.814731\pi\) | ||||
−0.835343 | + | 0.549729i | \(0.814731\pi\) | |||||||
\(618\) | 5.93901e6 | 0.625523 | ||||||||
\(619\) | 3.16596e6 | 0.332108 | 0.166054 | − | 0.986117i | \(-0.446897\pi\) | ||||
0.166054 | + | 0.986117i | \(0.446897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.71103e6 | −0.490216 | ||||||||
\(622\) | 4.17556e6 | 0.432751 | ||||||||
\(623\) | −5.30297e6 | −0.547393 | ||||||||
\(624\) | −202145. | −0.0207827 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.53770e6 | 0.360815 | ||||||||
\(627\) | −346566. | −0.0352060 | ||||||||
\(628\) | 2.25839e6 | 0.228507 | ||||||||
\(629\) | −1.96840e6 | −0.198375 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.95795e7 | −1.95762 | −0.978811 | − | 0.204764i | \(-0.934357\pi\) | ||||
−0.978811 | + | 0.204764i | \(0.934357\pi\) | |||||||
\(632\) | −1.40492e7 | −1.39913 | ||||||||
\(633\) | −5.15660e6 | −0.511510 | ||||||||
\(634\) | −1.00450e7 | −0.992489 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.68136e6 | −0.164823 | ||||||||
\(637\) | 1.50183e6 | 0.146646 | ||||||||
\(638\) | 2.19125e6 | 0.213127 | ||||||||
\(639\) | −2.26061e6 | −0.219015 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.23060e6 | −0.695072 | −0.347536 | − | 0.937667i | \(-0.612981\pi\) | ||||
−0.347536 | + | 0.937667i | \(0.612981\pi\) | |||||||
\(642\) | −1.43247e6 | −0.137166 | ||||||||
\(643\) | 1.17438e7 | 1.12016 | 0.560081 | − | 0.828438i | \(-0.310770\pi\) | ||||
0.560081 | + | 0.828438i | \(0.310770\pi\) | |||||||
\(644\) | −2.15718e6 | −0.204961 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 457078. | 0.0430932 | ||||||||
\(647\) | −9.24080e6 | −0.867858 | −0.433929 | − | 0.900947i | \(-0.642873\pi\) | ||||
−0.433929 | + | 0.900947i | \(0.642873\pi\) | |||||||
\(648\) | −2.72139e6 | −0.254597 | ||||||||
\(649\) | −1.11692e6 | −0.104091 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 582901. | 0.0539067 | ||||||||
\(652\) | 591260. | 0.0544703 | ||||||||
\(653\) | 1.11349e7 | 1.02188 | 0.510942 | − | 0.859615i | \(-0.329297\pi\) | ||||
0.510942 | + | 0.859615i | \(0.329297\pi\) | |||||||
\(654\) | −5.81686e6 | −0.531795 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.08697e6 | −0.189346 | ||||||||
\(657\) | −2.30026e6 | −0.207904 | ||||||||
\(658\) | −3.35918e6 | −0.302461 | ||||||||
\(659\) | 8.65776e6 | 0.776590 | 0.388295 | − | 0.921535i | \(-0.373064\pi\) | ||||
0.388295 | + | 0.921535i | \(0.373064\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.23594e7 | −1.10025 | −0.550127 | − | 0.835081i | \(-0.685421\pi\) | ||||
−0.550127 | + | 0.835081i | \(0.685421\pi\) | |||||||
\(662\) | 2.45351e6 | 0.217592 | ||||||||
\(663\) | −621282. | −0.0548915 | ||||||||
\(664\) | 1.60700e6 | 0.141448 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.92099e6 | −0.255179 | ||||||||
\(667\) | 5.07030e6 | 0.441285 | ||||||||
\(668\) | −5.61268e6 | −0.486664 | ||||||||
\(669\) | −9.00871e6 | −0.778211 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.60382e6 | −0.223257 | ||||||||
\(672\) | 3.99172e6 | 0.340986 | ||||||||
\(673\) | 6.11057e6 | 0.520048 | 0.260024 | − | 0.965602i | \(-0.416269\pi\) | ||||
0.260024 | + | 0.965602i | \(0.416269\pi\) | |||||||
\(674\) | 2.87993e6 | 0.244192 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −504928. | −0.0424974 | ||||||||
\(677\) | −1.48518e7 | −1.24540 | −0.622698 | − | 0.782462i | \(-0.713964\pi\) | ||||
−0.622698 | + | 0.782462i | \(0.713964\pi\) | |||||||
\(678\) | 5.87872e6 | 0.491144 | ||||||||
\(679\) | −1.54643e6 | −0.128723 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.32916e6 | 0.109827 | ||||||||
\(682\) | −472825. | −0.0389260 | ||||||||
\(683\) | 6.13145e6 | 0.502934 | 0.251467 | − | 0.967866i | \(-0.419087\pi\) | ||||
0.251467 | + | 0.967866i | \(0.419087\pi\) | |||||||
\(684\) | −837313. | −0.0684302 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.65340e6 | 0.702064 | ||||||||
\(687\) | 5.29580e6 | 0.428095 | ||||||||
\(688\) | 1.65214e6 | 0.133068 | ||||||||
\(689\) | 1.95822e6 | 0.157150 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.33358e7 | 1.85920 | 0.929602 | − | 0.368566i | \(-0.120151\pi\) | ||||
0.929602 | + | 0.368566i | \(0.120151\pi\) | |||||||
\(692\) | 1.49396e6 | 0.118597 | ||||||||
\(693\) | −2.44737e6 | −0.193582 | ||||||||
\(694\) | 4.04511e6 | 0.318809 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.70651e6 | −0.446527 | ||||||||
\(697\) | −6.41417e6 | −0.500102 | ||||||||
\(698\) | 5.97033e6 | 0.463831 | ||||||||
\(699\) | −6.89385e6 | −0.533665 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.53633e7 | 1.94944 | 0.974721 | − | 0.223426i | \(-0.0717242\pi\) | ||||
0.974721 | + | 0.223426i | \(0.0717242\pi\) | |||||||
\(702\) | −2.19754e6 | −0.168304 | ||||||||
\(703\) | −1.18515e6 | −0.0904450 | ||||||||
\(704\) | −3.96807e6 | −0.301751 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −413907. | −0.0312529 | ||||||||
\(707\) | −6.11139e6 | −0.459824 | ||||||||
\(708\) | 1.03511e6 | 0.0776075 | ||||||||
\(709\) | −1.64964e7 | −1.23246 | −0.616232 | − | 0.787565i | \(-0.711342\pi\) | ||||
−0.616232 | + | 0.787565i | \(0.711342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.31248e7 | −0.973682 | ||||||||
\(712\) | −1.12022e7 | −0.828141 | ||||||||
\(713\) | −1.09407e6 | −0.0805971 | ||||||||
\(714\) | −1.23813e6 | −0.0908907 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.29796e7 | 0.946189 | ||||||||
\(717\) | 4.36797e6 | 0.317309 | ||||||||
\(718\) | 1.41975e7 | 1.02778 | ||||||||
\(719\) | −9.96268e6 | −0.718710 | −0.359355 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359355 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.70165e7 | 1.21908 | ||||||||
\(722\) | −9.09514e6 | −0.649332 | ||||||||
\(723\) | 92602.6 | 0.00658836 | ||||||||
\(724\) | −6.42375e6 | −0.455452 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.24095e6 | 0.298622 | ||||||||
\(727\) | 2.53565e7 | 1.77932 | 0.889658 | − | 0.456627i | \(-0.150943\pi\) | ||||
0.889658 | + | 0.456627i | \(0.150943\pi\) | |||||||
\(728\) | −2.82762e6 | −0.197739 | ||||||||
\(729\) | 4.31096e6 | 0.300438 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.07775e6 | 0.351462 | ||||||||
\(732\) | 2.41310e6 | 0.166455 | ||||||||
\(733\) | −1.70653e7 | −1.17315 | −0.586576 | − | 0.809894i | \(-0.699524\pi\) | ||||
−0.586576 | + | 0.809894i | \(0.699524\pi\) | |||||||
\(734\) | 8.04497e6 | 0.551168 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.49218e6 | −0.509816 | ||||||||
\(737\) | 659478. | 0.0447230 | ||||||||
\(738\) | −9.51826e6 | −0.643304 | ||||||||
\(739\) | −1.40560e7 | −0.946781 | −0.473391 | − | 0.880853i | \(-0.656970\pi\) | ||||
−0.473391 | + | 0.880853i | \(0.656970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −374067. | −0.0250267 | ||||||||
\(742\) | 3.90245e6 | 0.260212 | ||||||||
\(743\) | 1.55718e7 | 1.03483 | 0.517413 | − | 0.855736i | \(-0.326895\pi\) | ||||
0.517413 | + | 0.855736i | \(0.326895\pi\) | |||||||
\(744\) | 1.23135e6 | 0.0815544 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.74633e6 | 0.180678 | ||||||||
\(747\) | 1.50126e6 | 0.0984362 | ||||||||
\(748\) | −1.23980e6 | −0.0810209 | ||||||||
\(749\) | −4.10433e6 | −0.267324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.89761e6 | −0.381572 | −0.190786 | − | 0.981632i | \(-0.561104\pi\) | ||||
−0.190786 | + | 0.981632i | \(0.561104\pi\) | |||||||
\(752\) | −1.45351e6 | −0.0937287 | ||||||||
\(753\) | 4.86441e6 | 0.312639 | ||||||||
\(754\) | 2.36513e6 | 0.151505 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.40622e6 | 0.344024 | ||||||||
\(757\) | 2.57205e6 | 0.163132 | 0.0815660 | − | 0.996668i | \(-0.474008\pi\) | ||||
0.0815660 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(758\) | 5.31356e6 | 0.335902 | ||||||||
\(759\) | −1.76201e6 | −0.111021 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.56012e7 | −1.60250 | −0.801252 | − | 0.598328i | \(-0.795832\pi\) | ||||
−0.801252 | + | 0.598328i | \(0.795832\pi\) | |||||||
\(762\) | 5.68509e6 | 0.354691 | ||||||||
\(763\) | −1.66665e7 | −1.03642 | ||||||||
\(764\) | −957179. | −0.0593280 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.06750e7 | 0.657349 | ||||||||
\(767\) | −1.20555e6 | −0.0739942 | ||||||||
\(768\) | 9.10895e6 | 0.557270 | ||||||||
\(769\) | −1.15095e7 | −0.701842 | −0.350921 | − | 0.936405i | \(-0.614131\pi\) | ||||
−0.350921 | + | 0.936405i | \(0.614131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.32582e6 | −0.0803243 | ||||||||
\(772\) | −3.69333e6 | −0.223036 | ||||||||
\(773\) | 5.18479e6 | 0.312092 | 0.156046 | − | 0.987750i | \(-0.450125\pi\) | ||||
0.156046 | + | 0.987750i | \(0.450125\pi\) | |||||||
\(774\) | 7.53509e6 | 0.452101 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.26674e6 | −0.194742 | ||||||||
\(777\) | 3.21032e6 | 0.190764 | ||||||||
\(778\) | −6.48229e6 | −0.383954 | ||||||||
\(779\) | −3.86190e6 | −0.228012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.01534e6 | −0.118228 | ||||||||
\(782\) | 2.32388e6 | 0.135893 | ||||||||
\(783\) | −1.27070e7 | −0.740692 | ||||||||
\(784\) | 1.29503e6 | 0.0752469 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.86561e6 | −0.396390 | ||||||||
\(787\) | 1.28463e7 | 0.739333 | 0.369667 | − | 0.929165i | \(-0.379472\pi\) | ||||
0.369667 | + | 0.929165i | \(0.379472\pi\) | |||||||
\(788\) | 1.02834e7 | 0.589958 | ||||||||
\(789\) | −3.10087e6 | −0.177333 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.68438e7 | 0.957190 | ||||||||
\(792\) | −5.16992e6 | −0.292867 | ||||||||
\(793\) | −2.81044e6 | −0.158705 | ||||||||
\(794\) | 1.43834e7 | 0.809676 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.10456e7 | 0.617883 | ||||||||
\(797\) | 2.11768e7 | 1.18090 | 0.590452 | − | 0.807073i | \(-0.298950\pi\) | ||||
0.590452 | + | 0.807073i | \(0.298950\pi\) | |||||||
\(798\) | −745461. | −0.0414398 | ||||||||
\(799\) | −4.46727e6 | −0.247557 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.04651e7 | −0.576320 | ||||||||
\(802\) | 4.14155e6 | 0.227367 | ||||||||
\(803\) | −2.05069e6 | −0.112230 | ||||||||
\(804\) | −611172. | −0.0333444 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −510344. | −0.0276711 | ||||||||
\(807\) | 5655.97 | 0.000305719 0 | ||||||||
\(808\) | −1.29100e7 | −0.695659 | ||||||||
\(809\) | 1.58537e6 | 0.0851648 | 0.0425824 | − | 0.999093i | \(-0.486442\pi\) | ||||
0.0425824 | + | 0.999093i | \(0.486442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.18155e7 | −1.16470 | −0.582350 | − | 0.812938i | \(-0.697867\pi\) | ||||
−0.582350 | + | 0.812938i | \(0.697867\pi\) | |||||||
\(812\) | −5.81850e6 | −0.309686 | ||||||||
\(813\) | −5.13375e6 | −0.272401 | ||||||||
\(814\) | −2.60407e6 | −0.137750 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −535733. | −0.0281659 | ||||||||
\(817\) | 3.05725e6 | 0.160242 | ||||||||
\(818\) | 2.50962e7 | 1.31137 | ||||||||
\(819\) | −2.64157e6 | −0.137611 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.09541e7 | 1.60273 | 0.801365 | − | 0.598176i | \(-0.204108\pi\) | ||||
0.801365 | + | 0.598176i | \(0.204108\pi\) | |||||||
\(822\) | 1.09901e7 | 0.567313 | ||||||||
\(823\) | −2.68746e7 | −1.38307 | −0.691533 | − | 0.722345i | \(-0.743064\pi\) | ||||
−0.691533 | + | 0.722345i | \(0.743064\pi\) | |||||||
\(824\) | 3.59464e7 | 1.84433 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.40249e6 | −0.122521 | ||||||||
\(827\) | −9.94152e6 | −0.505462 | −0.252731 | − | 0.967537i | \(-0.581329\pi\) | ||||
−0.252731 | + | 0.967537i | \(0.581329\pi\) | |||||||
\(828\) | −4.25707e6 | −0.215792 | ||||||||
\(829\) | 7.20887e6 | 0.364318 | 0.182159 | − | 0.983269i | \(-0.441691\pi\) | ||||
0.182159 | + | 0.983269i | \(0.441691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.10666e6 | 0.306762 | ||||||||
\(832\) | −4.28295e6 | −0.214504 | ||||||||
\(833\) | 3.98020e6 | 0.198743 | ||||||||
\(834\) | −8.77867e6 | −0.437032 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −746468. | −0.0369399 | ||||||||
\(837\) | 2.74190e6 | 0.135281 | ||||||||
\(838\) | −5.67777e6 | −0.279298 | ||||||||
\(839\) | 1.96670e7 | 0.964569 | 0.482285 | − | 0.876015i | \(-0.339807\pi\) | ||||
0.482285 | + | 0.876015i | \(0.339807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.83513e6 | −0.333240 | ||||||||
\(842\) | −7.24288e6 | −0.352072 | ||||||||
\(843\) | −1.18018e7 | −0.571979 | ||||||||
\(844\) | −1.11068e7 | −0.536702 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.62917e6 | −0.318444 | ||||||||
\(847\) | 1.21512e7 | 0.581984 | ||||||||
\(848\) | 1.68858e6 | 0.0806364 | ||||||||
\(849\) | −1.02321e7 | −0.487186 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.02554e6 | −0.285215 | ||||||||
\(852\) | 1.86772e6 | 0.0881482 | ||||||||
\(853\) | −2.60044e7 | −1.22370 | −0.611848 | − | 0.790975i | \(-0.709574\pi\) | ||||
−0.611848 | + | 0.790975i | \(0.709574\pi\) | |||||||
\(854\) | −5.60080e6 | −0.262788 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.67015e6 | −0.404429 | ||||||||
\(857\) | 2.74925e7 | 1.27868 | 0.639341 | − | 0.768923i | \(-0.279207\pi\) | ||||
0.639341 | + | 0.768923i | \(0.279207\pi\) | |||||||
\(858\) | −821919. | −0.0381163 | ||||||||
\(859\) | 3.86634e7 | 1.78779 | 0.893896 | − | 0.448274i | \(-0.147961\pi\) | ||||
0.893896 | + | 0.448274i | \(0.147961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.04611e7 | 0.480914 | ||||||||
\(862\) | 2.28669e7 | 1.04819 | ||||||||
\(863\) | −8.41848e6 | −0.384775 | −0.192387 | − | 0.981319i | \(-0.561623\pi\) | ||||
−0.192387 | + | 0.981319i | \(0.561623\pi\) | |||||||
\(864\) | 1.87766e7 | 0.855720 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.86038e6 | 0.310852 | ||||||||
\(867\) | 1.00075e7 | 0.452144 | ||||||||
\(868\) | 1.25551e6 | 0.0565615 | ||||||||
\(869\) | −1.17008e7 | −0.525611 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 711808. | 0.0317920 | ||||||||
\(872\) | −3.52071e7 | −1.56797 | ||||||||
\(873\) | −3.05179e6 | −0.135525 | ||||||||
\(874\) | 1.39918e6 | 0.0619576 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.90048e6 | 0.0836763 | ||||||||
\(877\) | −1.24226e7 | −0.545399 | −0.272699 | − | 0.962099i | \(-0.587916\pi\) | ||||
−0.272699 | + | 0.962099i | \(0.587916\pi\) | |||||||
\(878\) | 1.30716e7 | 0.572257 | ||||||||
\(879\) | 1.43357e7 | 0.625815 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.24684e6 | 0.314564 | 0.157282 | − | 0.987554i | \(-0.449727\pi\) | ||||
0.157282 | + | 0.987554i | \(0.449727\pi\) | |||||||
\(882\) | 5.90637e6 | 0.255652 | ||||||||
\(883\) | −1.58232e7 | −0.682958 | −0.341479 | − | 0.939889i | \(-0.610928\pi\) | ||||
−0.341479 | + | 0.939889i | \(0.610928\pi\) | |||||||
\(884\) | −1.33818e6 | −0.0575949 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.21760e6 | 0.266096 | ||||||||
\(887\) | 1.85905e7 | 0.793382 | 0.396691 | − | 0.917952i | \(-0.370158\pi\) | ||||
0.396691 | + | 0.917952i | \(0.370158\pi\) | |||||||
\(888\) | 6.78161e6 | 0.288603 | ||||||||
\(889\) | 1.62890e7 | 0.691257 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.26650e6 | −0.0956446 | ||||||||
\(892\) | −1.94038e7 | −0.816537 | ||||||||
\(893\) | −2.68969e6 | −0.112869 | ||||||||
\(894\) | 2.40972e6 | 0.100838 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.02718e6 | 0.292423 | ||||||||
\(897\) | −1.90183e6 | −0.0789206 | ||||||||
\(898\) | 1.47654e7 | 0.611018 | ||||||||
\(899\) | −2.95100e6 | −0.121778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.18974e6 | 0.212978 | ||||||||
\(902\) | −8.48556e6 | −0.347267 | ||||||||
\(903\) | −8.28144e6 | −0.337977 | ||||||||
\(904\) | 3.55815e7 | 1.44811 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.51331e6 | 0.263622 | ||||||||
\(907\) | 4.30877e7 | 1.73914 | 0.869571 | − | 0.493808i | \(-0.164395\pi\) | ||||
0.869571 | + | 0.493808i | \(0.164395\pi\) | |||||||
\(908\) | 2.86288e6 | 0.115236 | ||||||||
\(909\) | −1.20605e7 | −0.484123 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 870987. | 0.0347709 | 0.0173854 | − | 0.999849i | \(-0.494466\pi\) | ||||
0.0173854 | + | 0.999849i | \(0.494466\pi\) | |||||||
\(912\) | −322558. | −0.0128417 | ||||||||
\(913\) | 1.33838e6 | 0.0531377 | ||||||||
\(914\) | 2.30773e7 | 0.913735 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.14066e7 | 0.449178 | ||||||||
\(917\) | −1.96714e7 | −0.772524 | ||||||||
\(918\) | −5.82400e6 | −0.228094 | ||||||||
\(919\) | −7.81477e6 | −0.305230 | −0.152615 | − | 0.988286i | \(-0.548769\pi\) | ||||
−0.152615 | + | 0.988286i | \(0.548769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.96439e6 | −0.0763095 | ||||||||
\(922\) | 3.22647e7 | 1.24997 | ||||||||
\(923\) | −2.17526e6 | −0.0840442 | ||||||||
\(924\) | 2.02202e6 | 0.0779123 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.02425e7 | 0.392533 | ||||||||
\(927\) | 3.35812e7 | 1.28350 | ||||||||
\(928\) | −2.02085e7 | −0.770307 | ||||||||
\(929\) | 6.93323e6 | 0.263570 | 0.131785 | − | 0.991278i | \(-0.457929\pi\) | ||||
0.131785 | + | 0.991278i | \(0.457929\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.39643e6 | 0.0906129 | ||||||||
\(932\) | −1.48487e7 | −0.559948 | ||||||||
\(933\) | −9.05644e6 | −0.340607 | ||||||||
\(934\) | 1.32516e6 | 0.0497052 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.58017e6 | −0.208189 | ||||||||
\(937\) | −3.31684e7 | −1.23417 | −0.617085 | − | 0.786896i | \(-0.711687\pi\) | ||||
−0.617085 | + | 0.786896i | \(0.711687\pi\) | |||||||
\(938\) | 1.41853e6 | 0.0526420 | ||||||||
\(939\) | −7.67298e6 | −0.283988 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.00778e6 | −0.184362 | −0.0921809 | − | 0.995742i | \(-0.529384\pi\) | ||||
−0.0921809 | + | 0.995742i | \(0.529384\pi\) | |||||||
\(942\) | 3.96790e6 | 0.145691 | ||||||||
\(943\) | −1.96347e7 | −0.719025 | ||||||||
\(944\) | −1.03955e6 | −0.0379678 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.71756e6 | 0.244053 | ||||||||
\(947\) | −7.37028e6 | −0.267060 | −0.133530 | − | 0.991045i | \(-0.542631\pi\) | ||||
−0.133530 | + | 0.991045i | \(0.542631\pi\) | |||||||
\(948\) | 1.08437e7 | 0.391883 | ||||||||
\(949\) | −2.21341e6 | −0.0797805 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.17867e7 | 0.781162 | ||||||||
\(952\) | −7.49388e6 | −0.267987 | ||||||||
\(953\) | 7.45227e6 | 0.265801 | 0.132900 | − | 0.991129i | \(-0.457571\pi\) | ||||
0.132900 | + | 0.991129i | \(0.457571\pi\) | |||||||
\(954\) | 7.70127e6 | 0.273963 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.40817e6 | 0.332936 | ||||||||
\(957\) | −4.75263e6 | −0.167747 | ||||||||
\(958\) | 3.21336e7 | 1.13122 | ||||||||
\(959\) | 3.14890e7 | 1.10564 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.79924e7 | −0.977758 | ||||||||
\(962\) | −2.81071e6 | −0.0979216 | ||||||||
\(963\) | −8.09967e6 | −0.281450 | ||||||||
\(964\) | 199457. | 0.00691283 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.79007e6 | −0.130679 | ||||||||
\(967\) | −4.78544e7 | −1.64572 | −0.822860 | − | 0.568244i | \(-0.807623\pi\) | ||||
−0.822860 | + | 0.568244i | \(0.807623\pi\) | |||||||
\(968\) | 2.56687e7 | 0.880473 | ||||||||
\(969\) | −991365. | −0.0339175 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.54187e7 | −0.865177 | −0.432588 | − | 0.901592i | \(-0.642400\pi\) | ||||
−0.432588 | + | 0.901592i | \(0.642400\pi\) | |||||||
\(972\) | 1.68618e7 | 0.572450 | ||||||||
\(973\) | −2.51527e7 | −0.851733 | ||||||||
\(974\) | −11484.1 | −0.000387881 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.42345e6 | −0.0814347 | ||||||||
\(977\) | 3.10699e7 | 1.04137 | 0.520683 | − | 0.853750i | \(-0.325677\pi\) | ||||
0.520683 | + | 0.853750i | \(0.325677\pi\) | |||||||
\(978\) | 1.03882e6 | 0.0347291 | ||||||||
\(979\) | −9.32970e6 | −0.311108 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.28905e7 | −1.09118 | ||||||||
\(982\) | −1.29845e7 | −0.429682 | ||||||||
\(983\) | 1.28575e6 | 0.0424398 | 0.0212199 | − | 0.999775i | \(-0.493245\pi\) | ||||
0.0212199 | + | 0.999775i | \(0.493245\pi\) | |||||||
\(984\) | 2.20984e7 | 0.727566 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.26814e6 | 0.205327 | ||||||||
\(987\) | 7.28579e6 | 0.238059 | ||||||||
\(988\) | −805701. | −0.0262592 | ||||||||
\(989\) | 1.55437e7 | 0.505317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.43766e6 | −0.143539 | −0.0717695 | − | 0.997421i | \(-0.522865\pi\) | ||||
−0.0717695 | + | 0.997421i | \(0.522865\pi\) | |||||||
\(992\) | 4.36057e6 | 0.140690 | ||||||||
\(993\) | −5.32146e6 | −0.171261 | ||||||||
\(994\) | −4.33499e6 | −0.139162 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.24035e6 | −0.0396182 | ||||||||
\(997\) | −2.72549e7 | −0.868375 | −0.434187 | − | 0.900823i | \(-0.642964\pi\) | ||||
−0.434187 | + | 0.900823i | \(0.642964\pi\) | |||||||
\(998\) | −4.22202e6 | −0.134182 | ||||||||
\(999\) | 1.51009e7 | 0.478729 |
(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 | 325.6.a.j.1.8 | ✓ | 11 | |
5.2 | odd | 4 | 325.6.b.i.274.15 | 22 | |||
5.3 | odd | 4 | 325.6.b.i.274.8 | 22 | |||
5.4 | even | 2 | 325.6.a.k.1.4 | yes | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.j.1.8 | ✓ | 11 | 1.1 | even | 1 | trivial | |
325.6.a.k.1.4 | yes | 11 | 5.4 | even | 2 | ||
325.6.b.i.274.8 | 22 | 5.3 | odd | 4 | |||
325.6.b.i.274.15 | 22 | 5.2 | odd | 4 |