Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(67.8521965066\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 107x^{3} - 3x^{2} + 2151x - 2916 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(9.27140\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 8.27140 | 1.59183 | 0.795916 | − | 0.605407i | \(-0.206990\pi\) | ||||
0.795916 | + | 0.605407i | \(0.206990\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −16.5428 | −1.12560 | ||||||||
\(7\) | −22.8621 | −1.23444 | −0.617218 | − | 0.786792i | \(-0.711740\pi\) | ||||
−0.617218 | + | 0.786792i | \(0.711740\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 41.4161 | 1.53393 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.987996 | −0.0270811 | −0.0135405 | − | 0.999908i | \(-0.504310\pi\) | ||||
−0.0135405 | + | 0.999908i | \(0.504310\pi\) | |||||||
\(12\) | 33.0856 | 0.795916 | ||||||||
\(13\) | 4.22276 | 0.0900910 | 0.0450455 | − | 0.998985i | \(-0.485657\pi\) | ||||
0.0450455 | + | 0.998985i | \(0.485657\pi\) | |||||||
\(14\) | 45.7241 | 0.872878 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −73.8741 | −1.05395 | −0.526973 | − | 0.849882i | \(-0.676673\pi\) | ||||
−0.526973 | + | 0.849882i | \(0.676673\pi\) | |||||||
\(18\) | −82.8322 | −1.08465 | ||||||||
\(19\) | 71.1586 | 0.859205 | 0.429602 | − | 0.903018i | \(-0.358654\pi\) | ||||
0.429602 | + | 0.903018i | \(0.358654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −189.101 | −1.96501 | ||||||||
\(22\) | 1.97599 | 0.0191492 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −66.1712 | −0.562798 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.44552 | −0.0637039 | ||||||||
\(27\) | 119.241 | 0.849926 | ||||||||
\(28\) | −91.4483 | −0.617218 | ||||||||
\(29\) | 27.8984 | 0.178642 | 0.0893209 | − | 0.996003i | \(-0.471530\pi\) | ||||
0.0893209 | + | 0.996003i | \(0.471530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −136.861 | −0.792935 | −0.396468 | − | 0.918049i | \(-0.629764\pi\) | ||||
−0.396468 | + | 0.918049i | \(0.629764\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −8.17211 | −0.0431085 | ||||||||
\(34\) | 147.748 | 0.745253 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 165.664 | 0.766965 | ||||||||
\(37\) | 201.718 | 0.896278 | 0.448139 | − | 0.893964i | \(-0.352087\pi\) | ||||
0.448139 | + | 0.893964i | \(0.352087\pi\) | |||||||
\(38\) | −142.317 | −0.607550 | ||||||||
\(39\) | 34.9281 | 0.143410 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −204.140 | −0.777592 | −0.388796 | − | 0.921324i | \(-0.627109\pi\) | ||||
−0.388796 | + | 0.921324i | \(0.627109\pi\) | |||||||
\(42\) | 378.203 | 1.38947 | ||||||||
\(43\) | 54.1024 | 0.191873 | 0.0959365 | − | 0.995387i | \(-0.469415\pi\) | ||||
0.0959365 | + | 0.995387i | \(0.469415\pi\) | |||||||
\(44\) | −3.95198 | −0.0135405 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 41.4490 | 0.128638 | 0.0643188 | − | 0.997929i | \(-0.479513\pi\) | ||||
0.0643188 | + | 0.997929i | \(0.479513\pi\) | |||||||
\(48\) | 132.342 | 0.397958 | ||||||||
\(49\) | 179.674 | 0.523831 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −611.042 | −1.67771 | ||||||||
\(52\) | 16.8910 | 0.0450455 | ||||||||
\(53\) | −428.612 | −1.11084 | −0.555418 | − | 0.831571i | \(-0.687442\pi\) | ||||
−0.555418 | + | 0.831571i | \(0.687442\pi\) | |||||||
\(54\) | −238.483 | −0.600988 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 182.897 | 0.436439 | ||||||||
\(57\) | 588.581 | 1.36771 | ||||||||
\(58\) | −55.7969 | −0.126319 | ||||||||
\(59\) | −164.858 | −0.363774 | −0.181887 | − | 0.983319i | \(-0.558221\pi\) | ||||
−0.181887 | + | 0.983319i | \(0.558221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 188.248 | 0.395125 | 0.197563 | − | 0.980290i | \(-0.436697\pi\) | ||||
0.197563 | + | 0.980290i | \(0.436697\pi\) | |||||||
\(62\) | 273.722 | 0.560690 | ||||||||
\(63\) | −946.857 | −1.89354 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 16.3442 | 0.0304823 | ||||||||
\(67\) | −932.167 | −1.69974 | −0.849868 | − | 0.526995i | \(-0.823318\pi\) | ||||
−0.849868 | + | 0.526995i | \(0.823318\pi\) | |||||||
\(68\) | −295.496 | −0.526973 | ||||||||
\(69\) | −190.242 | −0.331920 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −263.336 | −0.440173 | −0.220086 | − | 0.975480i | \(-0.570634\pi\) | ||||
−0.220086 | + | 0.975480i | \(0.570634\pi\) | |||||||
\(72\) | −331.329 | −0.542326 | ||||||||
\(73\) | −900.401 | −1.44362 | −0.721808 | − | 0.692094i | \(-0.756689\pi\) | ||||
−0.721808 | + | 0.692094i | \(0.756689\pi\) | |||||||
\(74\) | −403.437 | −0.633764 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 284.634 | 0.429602 | ||||||||
\(77\) | 22.5876 | 0.0334299 | ||||||||
\(78\) | −69.8563 | −0.101406 | ||||||||
\(79\) | −956.182 | −1.36176 | −0.680879 | − | 0.732396i | \(-0.738402\pi\) | ||||
−0.680879 | + | 0.732396i | \(0.738402\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −131.942 | −0.180990 | ||||||||
\(82\) | 408.279 | 0.549841 | ||||||||
\(83\) | −194.877 | −0.257717 | −0.128858 | − | 0.991663i | \(-0.541131\pi\) | ||||
−0.128858 | + | 0.991663i | \(0.541131\pi\) | |||||||
\(84\) | −756.405 | −0.982507 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −108.205 | −0.135675 | ||||||||
\(87\) | 230.759 | 0.284368 | ||||||||
\(88\) | 7.90397 | 0.00957461 | ||||||||
\(89\) | −213.751 | −0.254580 | −0.127290 | − | 0.991866i | \(-0.540628\pi\) | ||||
−0.127290 | + | 0.991866i | \(0.540628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −96.5410 | −0.111211 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −1132.03 | −1.26222 | ||||||||
\(94\) | −82.8981 | −0.0909605 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −264.685 | −0.281399 | ||||||||
\(97\) | −628.762 | −0.658156 | −0.329078 | − | 0.944303i | \(-0.606738\pi\) | ||||
−0.329078 | + | 0.944303i | \(0.606738\pi\) | |||||||
\(98\) | −359.348 | −0.370404 | ||||||||
\(99\) | −40.9189 | −0.0415405 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −51.1371 | −0.0503796 | −0.0251898 | − | 0.999683i | \(-0.508019\pi\) | ||||
−0.0251898 | + | 0.999683i | \(0.508019\pi\) | |||||||
\(102\) | 1222.08 | 1.18632 | ||||||||
\(103\) | −363.089 | −0.347342 | −0.173671 | − | 0.984804i | \(-0.555563\pi\) | ||||
−0.173671 | + | 0.984804i | \(0.555563\pi\) | |||||||
\(104\) | −33.7821 | −0.0318520 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 857.223 | 0.785480 | ||||||||
\(107\) | −1514.53 | −1.36837 | −0.684184 | − | 0.729310i | \(-0.739841\pi\) | ||||
−0.684184 | + | 0.729310i | \(0.739841\pi\) | |||||||
\(108\) | 476.965 | 0.424963 | ||||||||
\(109\) | 811.356 | 0.712971 | 0.356485 | − | 0.934301i | \(-0.383975\pi\) | ||||
0.356485 | + | 0.934301i | \(0.383975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1668.49 | 1.42672 | ||||||||
\(112\) | −365.793 | −0.308609 | ||||||||
\(113\) | −12.4496 | −0.0103642 | −0.00518211 | − | 0.999987i | \(-0.501650\pi\) | ||||
−0.00518211 | + | 0.999987i | \(0.501650\pi\) | |||||||
\(114\) | −1177.16 | −0.967117 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 111.594 | 0.0893209 | ||||||||
\(117\) | 174.890 | 0.138193 | ||||||||
\(118\) | 329.716 | 0.257227 | ||||||||
\(119\) | 1688.91 | 1.30103 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.02 | −0.999267 | ||||||||
\(122\) | −376.495 | −0.279396 | ||||||||
\(123\) | −1688.52 | −1.23780 | ||||||||
\(124\) | −547.445 | −0.396468 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1893.71 | 1.33893 | ||||||||
\(127\) | 632.599 | 0.442000 | 0.221000 | − | 0.975274i | \(-0.429068\pi\) | ||||
0.221000 | + | 0.975274i | \(0.429068\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 447.503 | 0.305430 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2243.16 | 1.49607 | 0.748036 | − | 0.663658i | \(-0.230997\pi\) | ||||
0.748036 | + | 0.663658i | \(0.230997\pi\) | |||||||
\(132\) | −32.6884 | −0.0215543 | ||||||||
\(133\) | −1626.83 | −1.06063 | ||||||||
\(134\) | 1864.33 | 1.20190 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 590.993 | 0.372626 | ||||||||
\(137\) | −1252.77 | −0.781252 | −0.390626 | − | 0.920550i | \(-0.627741\pi\) | ||||
−0.390626 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(138\) | 380.484 | 0.234703 | ||||||||
\(139\) | 2815.19 | 1.71785 | 0.858925 | − | 0.512101i | \(-0.171133\pi\) | ||||
0.858925 | + | 0.512101i | \(0.171133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 342.842 | 0.204769 | ||||||||
\(142\) | 526.673 | 0.311249 | ||||||||
\(143\) | −4.17207 | −0.00243976 | ||||||||
\(144\) | 662.657 | 0.383482 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1800.80 | 1.02079 | ||||||||
\(147\) | 1486.16 | 0.833851 | ||||||||
\(148\) | 806.873 | 0.448139 | ||||||||
\(149\) | 2406.46 | 1.32312 | 0.661560 | − | 0.749892i | \(-0.269895\pi\) | ||||
0.661560 | + | 0.749892i | \(0.269895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2185.59 | 1.17788 | 0.588942 | − | 0.808175i | \(-0.299545\pi\) | ||||
0.588942 | + | 0.808175i | \(0.299545\pi\) | |||||||
\(152\) | −569.268 | −0.303775 | ||||||||
\(153\) | −3059.58 | −1.61668 | ||||||||
\(154\) | −45.1753 | −0.0236385 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 139.713 | 0.0717048 | ||||||||
\(157\) | −1074.18 | −0.546044 | −0.273022 | − | 0.962008i | \(-0.588023\pi\) | ||||
−0.273022 | + | 0.962008i | \(0.588023\pi\) | |||||||
\(158\) | 1912.36 | 0.962908 | ||||||||
\(159\) | −3545.22 | −1.76827 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 525.828 | 0.257398 | ||||||||
\(162\) | 263.884 | 0.127979 | ||||||||
\(163\) | −2706.30 | −1.30045 | −0.650226 | − | 0.759741i | \(-0.725326\pi\) | ||||
−0.650226 | + | 0.759741i | \(0.725326\pi\) | |||||||
\(164\) | −816.559 | −0.388796 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 389.754 | 0.182233 | ||||||||
\(167\) | −455.547 | −0.211086 | −0.105543 | − | 0.994415i | \(-0.533658\pi\) | ||||
−0.105543 | + | 0.994415i | \(0.533658\pi\) | |||||||
\(168\) | 1512.81 | 0.694737 | ||||||||
\(169\) | −2179.17 | −0.991884 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2947.11 | 1.31796 | ||||||||
\(172\) | 216.410 | 0.0959365 | ||||||||
\(173\) | 1342.64 | 0.590051 | 0.295026 | − | 0.955489i | \(-0.404672\pi\) | ||||
0.295026 | + | 0.955489i | \(0.404672\pi\) | |||||||
\(174\) | −461.518 | −0.201078 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15.8079 | −0.00677027 | ||||||||
\(177\) | −1363.61 | −0.579068 | ||||||||
\(178\) | 427.503 | 0.180015 | ||||||||
\(179\) | −4655.64 | −1.94401 | −0.972007 | − | 0.234951i | \(-0.924507\pi\) | ||||
−0.972007 | + | 0.234951i | \(0.924507\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −176.320 | −0.0724074 | −0.0362037 | − | 0.999344i | \(-0.511527\pi\) | ||||
−0.0362037 | + | 0.999344i | \(0.511527\pi\) | |||||||
\(182\) | 193.082 | 0.0786384 | ||||||||
\(183\) | 1557.07 | 0.628973 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2264.07 | 0.892524 | ||||||||
\(187\) | 72.9873 | 0.0285420 | ||||||||
\(188\) | 165.796 | 0.0643188 | ||||||||
\(189\) | −2726.10 | −1.04918 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1672.03 | 0.633422 | 0.316711 | − | 0.948522i | \(-0.397421\pi\) | ||||
0.316711 | + | 0.948522i | \(0.397421\pi\) | |||||||
\(192\) | 529.370 | 0.198979 | ||||||||
\(193\) | 2954.45 | 1.10189 | 0.550947 | − | 0.834540i | \(-0.314267\pi\) | ||||
0.550947 | + | 0.834540i | \(0.314267\pi\) | |||||||
\(194\) | 1257.52 | 0.465386 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 718.696 | 0.261915 | ||||||||
\(197\) | −1817.35 | −0.657264 | −0.328632 | − | 0.944458i | \(-0.606588\pi\) | ||||
−0.328632 | + | 0.944458i | \(0.606588\pi\) | |||||||
\(198\) | 81.8379 | 0.0293735 | ||||||||
\(199\) | 4780.99 | 1.70309 | 0.851546 | − | 0.524280i | \(-0.175666\pi\) | ||||
0.851546 | + | 0.524280i | \(0.175666\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7710.33 | −2.70569 | ||||||||
\(202\) | 102.274 | 0.0356237 | ||||||||
\(203\) | −637.816 | −0.220522 | ||||||||
\(204\) | −2444.17 | −0.838853 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 726.179 | 0.245608 | ||||||||
\(207\) | −952.570 | −0.319846 | ||||||||
\(208\) | 67.5641 | 0.0225227 | ||||||||
\(209\) | −70.3044 | −0.0232682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3201.72 | 1.04462 | 0.522312 | − | 0.852755i | \(-0.325070\pi\) | ||||
0.522312 | + | 0.852755i | \(0.325070\pi\) | |||||||
\(212\) | −1714.45 | −0.555418 | ||||||||
\(213\) | −2178.16 | −0.700681 | ||||||||
\(214\) | 3029.06 | 0.967582 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −953.930 | −0.300494 | ||||||||
\(217\) | 3128.93 | 0.978828 | ||||||||
\(218\) | −1622.71 | −0.504147 | ||||||||
\(219\) | −7447.58 | −2.29799 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −311.952 | −0.0949511 | ||||||||
\(222\) | −3336.99 | −1.00885 | ||||||||
\(223\) | 1897.23 | 0.569721 | 0.284860 | − | 0.958569i | \(-0.408053\pi\) | ||||
0.284860 | + | 0.958569i | \(0.408053\pi\) | |||||||
\(224\) | 731.586 | 0.218219 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.8991 | 0.00732861 | ||||||||
\(227\) | −4468.42 | −1.30652 | −0.653258 | − | 0.757135i | \(-0.726598\pi\) | ||||
−0.653258 | + | 0.757135i | \(0.726598\pi\) | |||||||
\(228\) | 2354.32 | 0.683855 | ||||||||
\(229\) | −5345.88 | −1.54264 | −0.771322 | − | 0.636445i | \(-0.780404\pi\) | ||||
−0.771322 | + | 0.636445i | \(0.780404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 186.831 | 0.0532147 | ||||||||
\(232\) | −223.187 | −0.0631594 | ||||||||
\(233\) | 4480.46 | 1.25976 | 0.629882 | − | 0.776691i | \(-0.283103\pi\) | ||||
0.629882 | + | 0.776691i | \(0.283103\pi\) | |||||||
\(234\) | −349.780 | −0.0977173 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −659.432 | −0.181887 | ||||||||
\(237\) | −7908.97 | −2.16769 | ||||||||
\(238\) | −3377.83 | −0.919967 | ||||||||
\(239\) | 779.836 | 0.211060 | 0.105530 | − | 0.994416i | \(-0.466346\pi\) | ||||
0.105530 | + | 0.994416i | \(0.466346\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4204.89 | −1.12390 | −0.561952 | − | 0.827170i | \(-0.689950\pi\) | ||||
−0.561952 | + | 0.827170i | \(0.689950\pi\) | |||||||
\(242\) | 2660.05 | 0.706588 | ||||||||
\(243\) | −4310.86 | −1.13803 | ||||||||
\(244\) | 752.991 | 0.197563 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3377.04 | 0.875254 | ||||||||
\(247\) | 300.485 | 0.0774066 | ||||||||
\(248\) | 1094.89 | 0.280345 | ||||||||
\(249\) | −1611.90 | −0.410242 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2761.48 | 0.694433 | 0.347217 | − | 0.937785i | \(-0.387127\pi\) | ||||
0.347217 | + | 0.937785i | \(0.387127\pi\) | |||||||
\(252\) | −3787.43 | −0.946768 | ||||||||
\(253\) | 22.7239 | 0.00564680 | ||||||||
\(254\) | −1265.20 | −0.312542 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 586.469 | 0.142346 | 0.0711730 | − | 0.997464i | \(-0.477326\pi\) | ||||
0.0711730 | + | 0.997464i | \(0.477326\pi\) | |||||||
\(258\) | −895.006 | −0.215971 | ||||||||
\(259\) | −4611.70 | −1.10640 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1155.44 | 0.274024 | ||||||||
\(262\) | −4486.31 | −1.05788 | ||||||||
\(263\) | −5970.38 | −1.39981 | −0.699903 | − | 0.714238i | \(-0.746774\pi\) | ||||
−0.699903 | + | 0.714238i | \(0.746774\pi\) | |||||||
\(264\) | 65.3769 | 0.0152412 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3253.66 | 0.749981 | ||||||||
\(267\) | −1768.02 | −0.405248 | ||||||||
\(268\) | −3728.67 | −0.849868 | ||||||||
\(269\) | 3914.34 | 0.887217 | 0.443608 | − | 0.896221i | \(-0.353698\pi\) | ||||
0.443608 | + | 0.896221i | \(0.353698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 78.0865 | 0.0175034 | 0.00875170 | − | 0.999962i | \(-0.497214\pi\) | ||||
0.00875170 | + | 0.999962i | \(0.497214\pi\) | |||||||
\(272\) | −1181.99 | −0.263487 | ||||||||
\(273\) | −798.529 | −0.177030 | ||||||||
\(274\) | 2505.54 | 0.552428 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −760.969 | −0.165960 | ||||||||
\(277\) | 76.0512 | 0.0164963 | 0.00824815 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824815 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(278\) | −5630.38 | −1.21470 | ||||||||
\(279\) | −5668.26 | −1.21631 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3852.67 | −0.817905 | −0.408952 | − | 0.912556i | \(-0.634106\pi\) | ||||
−0.408952 | + | 0.912556i | \(0.634106\pi\) | |||||||
\(282\) | −685.683 | −0.144794 | ||||||||
\(283\) | 1550.13 | 0.325603 | 0.162802 | − | 0.986659i | \(-0.447947\pi\) | ||||
0.162802 | + | 0.986659i | \(0.447947\pi\) | |||||||
\(284\) | −1053.35 | −0.220086 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.34414 | 0.00172517 | ||||||||
\(287\) | 4667.06 | 0.959887 | ||||||||
\(288\) | −1325.31 | −0.271163 | ||||||||
\(289\) | 544.378 | 0.110804 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5200.74 | −1.04767 | ||||||||
\(292\) | −3601.60 | −0.721808 | ||||||||
\(293\) | −4236.01 | −0.844608 | −0.422304 | − | 0.906454i | \(-0.638779\pi\) | ||||
−0.422304 | + | 0.906454i | \(0.638779\pi\) | |||||||
\(294\) | −2972.31 | −0.589622 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1613.75 | −0.316882 | ||||||||
\(297\) | −117.810 | −0.0230169 | ||||||||
\(298\) | −4812.92 | −0.935587 | ||||||||
\(299\) | −97.1234 | −0.0187853 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1236.89 | −0.236855 | ||||||||
\(302\) | −4371.17 | −0.832890 | ||||||||
\(303\) | −422.976 | −0.0801958 | ||||||||
\(304\) | 1138.54 | 0.214801 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6119.15 | 1.14317 | ||||||||
\(307\) | 10078.1 | 1.87357 | 0.936786 | − | 0.349903i | \(-0.113785\pi\) | ||||
0.936786 | + | 0.349903i | \(0.113785\pi\) | |||||||
\(308\) | 90.3505 | 0.0167149 | ||||||||
\(309\) | −3003.26 | −0.552911 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2652.97 | −0.483717 | −0.241859 | − | 0.970312i | \(-0.577757\pi\) | ||||
−0.241859 | + | 0.970312i | \(0.577757\pi\) | |||||||
\(312\) | −279.425 | −0.0507030 | ||||||||
\(313\) | −6710.68 | −1.21185 | −0.605926 | − | 0.795521i | \(-0.707197\pi\) | ||||
−0.605926 | + | 0.795521i | \(0.707197\pi\) | |||||||
\(314\) | 2148.36 | 0.386111 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3824.73 | −0.680879 | ||||||||
\(317\) | 3677.89 | 0.651642 | 0.325821 | − | 0.945431i | \(-0.394359\pi\) | ||||
0.325821 | + | 0.945431i | \(0.394359\pi\) | |||||||
\(318\) | 7090.44 | 1.25035 | ||||||||
\(319\) | −27.5635 | −0.00483781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12527.3 | −2.17821 | ||||||||
\(322\) | −1051.66 | −0.182008 | ||||||||
\(323\) | −5256.77 | −0.905556 | ||||||||
\(324\) | −527.768 | −0.0904952 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5412.60 | 0.919558 | ||||||||
\(327\) | 6711.05 | 1.13493 | ||||||||
\(328\) | 1633.12 | 0.274920 | ||||||||
\(329\) | −947.611 | −0.158795 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9806.39 | −1.62842 | −0.814212 | − | 0.580568i | \(-0.802831\pi\) | ||||
−0.814212 | + | 0.580568i | \(0.802831\pi\) | |||||||
\(332\) | −779.507 | −0.128858 | ||||||||
\(333\) | 8354.38 | 1.37483 | ||||||||
\(334\) | 911.094 | 0.149260 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3025.62 | −0.491253 | ||||||||
\(337\) | 7143.41 | 1.15468 | 0.577339 | − | 0.816505i | \(-0.304091\pi\) | ||||
0.577339 | + | 0.816505i | \(0.304091\pi\) | |||||||
\(338\) | 4358.34 | 0.701368 | ||||||||
\(339\) | −102.975 | −0.0164981 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 135.218 | 0.0214736 | ||||||||
\(342\) | −5894.22 | −0.931938 | ||||||||
\(343\) | 3733.97 | 0.587800 | ||||||||
\(344\) | −432.819 | −0.0678374 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2685.28 | −0.417229 | ||||||||
\(347\) | 5160.20 | 0.798312 | 0.399156 | − | 0.916883i | \(-0.369303\pi\) | ||||
0.399156 | + | 0.916883i | \(0.369303\pi\) | |||||||
\(348\) | 923.037 | 0.142184 | ||||||||
\(349\) | 8712.04 | 1.33623 | 0.668115 | − | 0.744058i | \(-0.267101\pi\) | ||||
0.668115 | + | 0.744058i | \(0.267101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 503.527 | 0.0765706 | ||||||||
\(352\) | 31.6159 | 0.00478731 | ||||||||
\(353\) | 7117.30 | 1.07313 | 0.536566 | − | 0.843858i | \(-0.319721\pi\) | ||||
0.536566 | + | 0.843858i | \(0.319721\pi\) | |||||||
\(354\) | 2727.21 | 0.409463 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −855.005 | −0.127290 | ||||||||
\(357\) | 13969.7 | 2.07102 | ||||||||
\(358\) | 9311.27 | 1.37463 | ||||||||
\(359\) | 3548.73 | 0.521712 | 0.260856 | − | 0.965378i | \(-0.415995\pi\) | ||||
0.260856 | + | 0.965378i | \(0.415995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1795.46 | −0.261767 | ||||||||
\(362\) | 352.639 | 0.0511998 | ||||||||
\(363\) | −11001.2 | −1.59066 | ||||||||
\(364\) | −386.164 | −0.0556057 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3114.15 | −0.444751 | ||||||||
\(367\) | −80.0110 | −0.0113802 | −0.00569011 | − | 0.999984i | \(-0.501811\pi\) | ||||
−0.00569011 | + | 0.999984i | \(0.501811\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −8454.67 | −1.19277 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9798.95 | 1.37126 | ||||||||
\(372\) | −4528.14 | −0.631110 | ||||||||
\(373\) | −3211.09 | −0.445747 | −0.222874 | − | 0.974847i | \(-0.571544\pi\) | ||||
−0.222874 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(374\) | −145.975 | −0.0201823 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −331.592 | −0.0454802 | ||||||||
\(377\) | 117.808 | 0.0160940 | ||||||||
\(378\) | 5452.20 | 0.741881 | ||||||||
\(379\) | −8177.57 | −1.10832 | −0.554160 | − | 0.832410i | \(-0.686961\pi\) | ||||
−0.554160 | + | 0.832410i | \(0.686961\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5232.48 | 0.703591 | ||||||||
\(382\) | −3344.05 | −0.447897 | ||||||||
\(383\) | −12926.5 | −1.72458 | −0.862291 | − | 0.506413i | \(-0.830971\pi\) | ||||
−0.862291 | + | 0.506413i | \(0.830971\pi\) | |||||||
\(384\) | −1058.74 | −0.140699 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5908.89 | −0.779157 | ||||||||
\(387\) | 2240.71 | 0.294320 | ||||||||
\(388\) | −2515.05 | −0.329078 | ||||||||
\(389\) | 4734.66 | 0.617113 | 0.308556 | − | 0.951206i | \(-0.400154\pi\) | ||||
0.308556 | + | 0.951206i | \(0.400154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1699.10 | 0.219763 | ||||||||
\(392\) | −1437.39 | −0.185202 | ||||||||
\(393\) | 18554.0 | 2.38150 | ||||||||
\(394\) | 3634.71 | 0.464756 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −163.676 | −0.0207702 | ||||||||
\(397\) | 9938.80 | 1.25646 | 0.628229 | − | 0.778028i | \(-0.283780\pi\) | ||||
0.628229 | + | 0.778028i | \(0.283780\pi\) | |||||||
\(398\) | −9561.98 | −1.20427 | ||||||||
\(399\) | −13456.2 | −1.68835 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −335.296 | −0.0417553 | −0.0208777 | − | 0.999782i | \(-0.506646\pi\) | ||||
−0.0208777 | + | 0.999782i | \(0.506646\pi\) | |||||||
\(402\) | 15420.7 | 1.91322 | ||||||||
\(403\) | −577.932 | −0.0714363 | ||||||||
\(404\) | −204.549 | −0.0251898 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1275.63 | 0.155932 | ||||||||
\(407\) | −199.297 | −0.0242722 | ||||||||
\(408\) | 4888.34 | 0.593159 | ||||||||
\(409\) | 6560.85 | 0.793186 | 0.396593 | − | 0.917995i | \(-0.370192\pi\) | ||||
0.396593 | + | 0.917995i | \(0.370192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10362.2 | −1.24362 | ||||||||
\(412\) | −1452.36 | −0.173671 | ||||||||
\(413\) | 3769.00 | 0.449056 | ||||||||
\(414\) | 1905.14 | 0.226166 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −135.128 | −0.0159260 | ||||||||
\(417\) | 23285.6 | 2.73453 | ||||||||
\(418\) | 140.609 | 0.0164531 | ||||||||
\(419\) | 7116.69 | 0.829768 | 0.414884 | − | 0.909874i | \(-0.363822\pi\) | ||||
0.414884 | + | 0.909874i | \(0.363822\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9799.43 | 1.13443 | 0.567215 | − | 0.823570i | \(-0.308021\pi\) | ||||
0.567215 | + | 0.823570i | \(0.308021\pi\) | |||||||
\(422\) | −6403.44 | −0.738660 | ||||||||
\(423\) | 1716.66 | 0.197321 | ||||||||
\(424\) | 3428.89 | 0.392740 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4356.32 | 0.495456 | ||||||||
\(427\) | −4303.73 | −0.487757 | ||||||||
\(428\) | −6058.13 | −0.684184 | ||||||||
\(429\) | −34.5089 | −0.00388369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10523.3 | −1.17608 | −0.588039 | − | 0.808832i | \(-0.700100\pi\) | ||||
−0.588039 | + | 0.808832i | \(0.700100\pi\) | |||||||
\(432\) | 1907.86 | 0.212481 | ||||||||
\(433\) | 4770.97 | 0.529511 | 0.264755 | − | 0.964316i | \(-0.414709\pi\) | ||||
0.264755 | + | 0.964316i | \(0.414709\pi\) | |||||||
\(434\) | −6257.86 | −0.692136 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3245.42 | 0.356485 | ||||||||
\(437\) | −1636.65 | −0.179157 | ||||||||
\(438\) | 14895.2 | 1.62493 | ||||||||
\(439\) | 10231.2 | 1.11232 | 0.556159 | − | 0.831076i | \(-0.312274\pi\) | ||||
0.556159 | + | 0.831076i | \(0.312274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7441.40 | 0.803520 | ||||||||
\(442\) | 623.905 | 0.0671405 | ||||||||
\(443\) | −10508.1 | −1.12699 | −0.563493 | − | 0.826121i | \(-0.690543\pi\) | ||||
−0.563493 | + | 0.826121i | \(0.690543\pi\) | |||||||
\(444\) | 6673.97 | 0.713362 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3794.46 | −0.402854 | ||||||||
\(447\) | 19904.8 | 2.10618 | ||||||||
\(448\) | −1463.17 | −0.154304 | ||||||||
\(449\) | 7230.71 | 0.759996 | 0.379998 | − | 0.924987i | \(-0.375925\pi\) | ||||
0.379998 | + | 0.924987i | \(0.375925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 201.689 | 0.0210580 | ||||||||
\(452\) | −49.7983 | −0.00518211 | ||||||||
\(453\) | 18077.9 | 1.87499 | ||||||||
\(454\) | 8936.83 | 0.923847 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4708.65 | −0.483558 | ||||||||
\(457\) | −2418.74 | −0.247580 | −0.123790 | − | 0.992308i | \(-0.539505\pi\) | ||||
−0.123790 | + | 0.992308i | \(0.539505\pi\) | |||||||
\(458\) | 10691.8 | 1.09081 | ||||||||
\(459\) | −8808.84 | −0.895776 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11342.8 | −1.14596 | −0.572979 | − | 0.819570i | \(-0.694212\pi\) | ||||
−0.572979 | + | 0.819570i | \(0.694212\pi\) | |||||||
\(462\) | −373.663 | −0.0376285 | ||||||||
\(463\) | 11785.9 | 1.18302 | 0.591508 | − | 0.806299i | \(-0.298533\pi\) | ||||
0.591508 | + | 0.806299i | \(0.298533\pi\) | |||||||
\(464\) | 446.375 | 0.0446604 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8960.93 | −0.890787 | ||||||||
\(467\) | −16294.5 | −1.61461 | −0.807303 | − | 0.590137i | \(-0.799074\pi\) | ||||
−0.807303 | + | 0.590137i | \(0.799074\pi\) | |||||||
\(468\) | 699.561 | 0.0690966 | ||||||||
\(469\) | 21311.3 | 2.09821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8884.97 | −0.869210 | ||||||||
\(472\) | 1318.86 | 0.128614 | ||||||||
\(473\) | −53.4530 | −0.00519613 | ||||||||
\(474\) | 15817.9 | 1.53279 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6755.66 | 0.650515 | ||||||||
\(477\) | −17751.4 | −1.70394 | ||||||||
\(478\) | −1559.67 | −0.149242 | ||||||||
\(479\) | −785.274 | −0.0749062 | −0.0374531 | − | 0.999298i | \(-0.511924\pi\) | ||||
−0.0374531 | + | 0.999298i | \(0.511924\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 851.808 | 0.0807466 | ||||||||
\(482\) | 8409.79 | 0.794721 | ||||||||
\(483\) | 4349.33 | 0.409734 | ||||||||
\(484\) | −5320.10 | −0.499633 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8621.72 | 0.804710 | ||||||||
\(487\) | −8714.29 | −0.810846 | −0.405423 | − | 0.914129i | \(-0.632876\pi\) | ||||
−0.405423 | + | 0.914129i | \(0.632876\pi\) | |||||||
\(488\) | −1505.98 | −0.139698 | ||||||||
\(489\) | −22384.9 | −2.07010 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10943.1 | −1.00582 | −0.502909 | − | 0.864339i | \(-0.667737\pi\) | ||||
−0.502909 | + | 0.864339i | \(0.667737\pi\) | |||||||
\(492\) | −6754.09 | −0.618898 | ||||||||
\(493\) | −2060.97 | −0.188279 | ||||||||
\(494\) | −600.971 | −0.0547347 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2189.78 | −0.198234 | ||||||||
\(497\) | 6020.41 | 0.543365 | ||||||||
\(498\) | 3223.81 | 0.290085 | ||||||||
\(499\) | −5601.85 | −0.502552 | −0.251276 | − | 0.967916i | \(-0.580850\pi\) | ||||
−0.251276 | + | 0.967916i | \(0.580850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3768.01 | −0.336013 | ||||||||
\(502\) | −5522.95 | −0.491039 | ||||||||
\(503\) | −21689.8 | −1.92266 | −0.961331 | − | 0.275395i | \(-0.911191\pi\) | ||||
−0.961331 | + | 0.275395i | \(0.911191\pi\) | |||||||
\(504\) | 7574.86 | 0.669466 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −45.4478 | −0.00399289 | ||||||||
\(507\) | −18024.8 | −1.57891 | ||||||||
\(508\) | 2530.39 | 0.221000 | ||||||||
\(509\) | 13826.0 | 1.20399 | 0.601993 | − | 0.798501i | \(-0.294373\pi\) | ||||
0.601993 | + | 0.798501i | \(0.294373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20585.0 | 1.78205 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 8485.04 | 0.730260 | ||||||||
\(514\) | −1172.94 | −0.100654 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1790.01 | 0.152715 | ||||||||
\(517\) | −40.9515 | −0.00348364 | ||||||||
\(518\) | 9223.40 | 0.782341 | ||||||||
\(519\) | 11105.5 | 0.939263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11971.1 | −1.00664 | −0.503322 | − | 0.864099i | \(-0.667889\pi\) | ||||
−0.503322 | + | 0.864099i | \(0.667889\pi\) | |||||||
\(522\) | −2310.89 | −0.193764 | ||||||||
\(523\) | 9668.82 | 0.808390 | 0.404195 | − | 0.914673i | \(-0.367552\pi\) | ||||
0.404195 | + | 0.914673i | \(0.367552\pi\) | |||||||
\(524\) | 8972.62 | 0.748036 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11940.8 | 0.989813 | ||||||||
\(527\) | 10110.5 | 0.835712 | ||||||||
\(528\) | −130.754 | −0.0107771 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6827.78 | −0.558004 | ||||||||
\(532\) | −6507.33 | −0.530317 | ||||||||
\(533\) | −862.033 | −0.0700540 | ||||||||
\(534\) | 3536.05 | 0.286554 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7457.34 | 0.600948 | ||||||||
\(537\) | −38508.6 | −3.09454 | ||||||||
\(538\) | −7828.67 | −0.627357 | ||||||||
\(539\) | −177.517 | −0.0141859 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6793.28 | 0.539863 | 0.269932 | − | 0.962880i | \(-0.412999\pi\) | ||||
0.269932 | + | 0.962880i | \(0.412999\pi\) | |||||||
\(542\) | −156.173 | −0.0123768 | ||||||||
\(543\) | −1458.41 | −0.115260 | ||||||||
\(544\) | 2363.97 | 0.186313 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1597.06 | 0.125179 | ||||||||
\(547\) | 5584.91 | 0.436551 | 0.218276 | − | 0.975887i | \(-0.429957\pi\) | ||||
0.218276 | + | 0.975887i | \(0.429957\pi\) | |||||||
\(548\) | −5011.08 | −0.390626 | ||||||||
\(549\) | 7796.49 | 0.606095 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1985.21 | 0.153490 | ||||||||
\(552\) | 1521.94 | 0.117351 | ||||||||
\(553\) | 21860.3 | 1.68100 | ||||||||
\(554\) | −152.102 | −0.0116646 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11260.8 | 0.858925 | ||||||||
\(557\) | −4172.24 | −0.317385 | −0.158693 | − | 0.987328i | \(-0.550728\pi\) | ||||
−0.158693 | + | 0.987328i | \(0.550728\pi\) | |||||||
\(558\) | 11336.5 | 0.860059 | ||||||||
\(559\) | 228.461 | 0.0172860 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 603.707 | 0.0454341 | ||||||||
\(562\) | 7705.34 | 0.578346 | ||||||||
\(563\) | −7734.17 | −0.578963 | −0.289482 | − | 0.957184i | \(-0.593483\pi\) | ||||
−0.289482 | + | 0.957184i | \(0.593483\pi\) | |||||||
\(564\) | 1371.37 | 0.102385 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3100.26 | −0.230236 | ||||||||
\(567\) | 3016.47 | 0.223421 | ||||||||
\(568\) | 2106.69 | 0.155625 | ||||||||
\(569\) | 1392.55 | 0.102599 | 0.0512995 | − | 0.998683i | \(-0.483664\pi\) | ||||
0.0512995 | + | 0.998683i | \(0.483664\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16996.1 | 1.24565 | 0.622823 | − | 0.782363i | \(-0.285986\pi\) | ||||
0.622823 | + | 0.782363i | \(0.285986\pi\) | |||||||
\(572\) | −16.6883 | −0.00121988 | ||||||||
\(573\) | 13830.0 | 1.00830 | ||||||||
\(574\) | −9334.11 | −0.678743 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2650.63 | 0.191741 | ||||||||
\(577\) | 6849.23 | 0.494172 | 0.247086 | − | 0.968994i | \(-0.420527\pi\) | ||||
0.247086 | + | 0.968994i | \(0.420527\pi\) | |||||||
\(578\) | −1088.76 | −0.0783500 | ||||||||
\(579\) | 24437.4 | 1.75403 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4455.29 | 0.318135 | ||||||||
\(582\) | 10401.5 | 0.740817 | ||||||||
\(583\) | 423.467 | 0.0300827 | ||||||||
\(584\) | 7203.21 | 0.510395 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8472.01 | 0.597228 | ||||||||
\(587\) | −6701.08 | −0.471181 | −0.235590 | − | 0.971852i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971852i | \(0.575702\pi\) | |||||||
\(588\) | 5944.62 | 0.416925 | ||||||||
\(589\) | −9738.85 | −0.681294 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15032.1 | −1.04625 | ||||||||
\(592\) | 3227.49 | 0.224070 | ||||||||
\(593\) | −9898.21 | −0.685448 | −0.342724 | − | 0.939436i | \(-0.611350\pi\) | ||||
−0.342724 | + | 0.939436i | \(0.611350\pi\) | |||||||
\(594\) | 235.620 | 0.0162754 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9625.84 | 0.661560 | ||||||||
\(597\) | 39545.5 | 2.71104 | ||||||||
\(598\) | 194.247 | 0.0132832 | ||||||||
\(599\) | 13149.2 | 0.896934 | 0.448467 | − | 0.893799i | \(-0.351970\pi\) | ||||
0.448467 | + | 0.893799i | \(0.351970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27142.4 | 1.84220 | 0.921100 | − | 0.389326i | \(-0.127292\pi\) | ||||
0.921100 | + | 0.389326i | \(0.127292\pi\) | |||||||
\(602\) | 2473.79 | 0.167482 | ||||||||
\(603\) | −38606.7 | −2.60728 | ||||||||
\(604\) | 8742.34 | 0.588942 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 845.952 | 0.0567070 | ||||||||
\(607\) | 6708.40 | 0.448576 | 0.224288 | − | 0.974523i | \(-0.427994\pi\) | ||||
0.224288 | + | 0.974523i | \(0.427994\pi\) | |||||||
\(608\) | −2277.07 | −0.151887 | ||||||||
\(609\) | −5275.63 | −0.351033 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 175.029 | 0.0115891 | ||||||||
\(612\) | −12238.3 | −0.808340 | ||||||||
\(613\) | 17755.6 | 1.16989 | 0.584943 | − | 0.811074i | \(-0.301117\pi\) | ||||
0.584943 | + | 0.811074i | \(0.301117\pi\) | |||||||
\(614\) | −20156.2 | −1.32482 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −180.701 | −0.0118192 | ||||||||
\(617\) | −14555.4 | −0.949722 | −0.474861 | − | 0.880061i | \(-0.657502\pi\) | ||||
−0.474861 | + | 0.880061i | \(0.657502\pi\) | |||||||
\(618\) | 6006.52 | 0.390967 | ||||||||
\(619\) | 29452.5 | 1.91243 | 0.956215 | − | 0.292665i | \(-0.0945422\pi\) | ||||
0.956215 | + | 0.292665i | \(0.0945422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2742.55 | −0.177222 | ||||||||
\(622\) | 5305.94 | 0.342040 | ||||||||
\(623\) | 4886.80 | 0.314262 | ||||||||
\(624\) | 558.850 | 0.0358524 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13421.4 | 0.856909 | ||||||||
\(627\) | −581.516 | −0.0370391 | ||||||||
\(628\) | −4296.72 | −0.273022 | ||||||||
\(629\) | −14901.8 | −0.944629 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9911.19 | 0.625290 | 0.312645 | − | 0.949870i | \(-0.398785\pi\) | ||||
0.312645 | + | 0.949870i | \(0.398785\pi\) | |||||||
\(632\) | 7649.46 | 0.481454 | ||||||||
\(633\) | 26482.7 | 1.66286 | ||||||||
\(634\) | −7355.77 | −0.460781 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14180.9 | −0.884133 | ||||||||
\(637\) | 758.720 | 0.0471924 | ||||||||
\(638\) | 55.1271 | 0.00342085 | ||||||||
\(639\) | −10906.4 | −0.675194 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13548.5 | −0.834844 | −0.417422 | − | 0.908713i | \(-0.637066\pi\) | ||||
−0.417422 | + | 0.908713i | \(0.637066\pi\) | |||||||
\(642\) | 25054.6 | 1.54023 | ||||||||
\(643\) | −2254.31 | −0.138260 | −0.0691302 | − | 0.997608i | \(-0.522022\pi\) | ||||
−0.0691302 | + | 0.997608i | \(0.522022\pi\) | |||||||
\(644\) | 2103.31 | 0.128699 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10513.5 | 0.640325 | ||||||||
\(647\) | 17967.1 | 1.09175 | 0.545874 | − | 0.837868i | \(-0.316198\pi\) | ||||
0.545874 | + | 0.837868i | \(0.316198\pi\) | |||||||
\(648\) | 1055.54 | 0.0639897 | ||||||||
\(649\) | 162.879 | 0.00985141 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25880.6 | 1.55813 | ||||||||
\(652\) | −10825.2 | −0.650226 | ||||||||
\(653\) | −365.239 | −0.0218881 | −0.0109440 | − | 0.999940i | \(-0.503484\pi\) | ||||
−0.0109440 | + | 0.999940i | \(0.503484\pi\) | |||||||
\(654\) | −13422.1 | −0.802517 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3266.24 | −0.194398 | ||||||||
\(657\) | −37291.1 | −2.21440 | ||||||||
\(658\) | 1895.22 | 0.112285 | ||||||||
\(659\) | 29229.1 | 1.72778 | 0.863889 | − | 0.503683i | \(-0.168022\pi\) | ||||
0.863889 | + | 0.503683i | \(0.168022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23681.1 | −1.39348 | −0.696740 | − | 0.717324i | \(-0.745367\pi\) | ||||
−0.696740 | + | 0.717324i | \(0.745367\pi\) | |||||||
\(662\) | 19612.8 | 1.15147 | ||||||||
\(663\) | −2580.28 | −0.151146 | ||||||||
\(664\) | 1559.01 | 0.0911167 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16708.8 | −0.972150 | ||||||||
\(667\) | −641.664 | −0.0372494 | ||||||||
\(668\) | −1822.19 | −0.105543 | ||||||||
\(669\) | 15692.7 | 0.906900 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −185.988 | −0.0107004 | ||||||||
\(672\) | 6051.24 | 0.347369 | ||||||||
\(673\) | 16016.2 | 0.917351 | 0.458676 | − | 0.888604i | \(-0.348324\pi\) | ||||
0.458676 | + | 0.888604i | \(0.348324\pi\) | |||||||
\(674\) | −14286.8 | −0.816480 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8716.67 | −0.495942 | ||||||||
\(677\) | 24082.5 | 1.36715 | 0.683577 | − | 0.729878i | \(-0.260423\pi\) | ||||
0.683577 | + | 0.729878i | \(0.260423\pi\) | |||||||
\(678\) | 205.951 | 0.0116659 | ||||||||
\(679\) | 14374.8 | 0.812451 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36960.1 | −2.07975 | ||||||||
\(682\) | −270.437 | −0.0151841 | ||||||||
\(683\) | 24224.1 | 1.35711 | 0.678556 | − | 0.734549i | \(-0.262606\pi\) | ||||
0.678556 | + | 0.734549i | \(0.262606\pi\) | |||||||
\(684\) | 11788.4 | 0.658980 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7467.94 | −0.415637 | ||||||||
\(687\) | −44217.9 | −2.45563 | ||||||||
\(688\) | 865.639 | 0.0479683 | ||||||||
\(689\) | −1809.92 | −0.100076 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13948.7 | 0.767919 | 0.383960 | − | 0.923350i | \(-0.374560\pi\) | ||||
0.383960 | + | 0.923350i | \(0.374560\pi\) | |||||||
\(692\) | 5370.55 | 0.295026 | ||||||||
\(693\) | 935.491 | 0.0512790 | ||||||||
\(694\) | −10320.4 | −0.564492 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1846.07 | −0.100539 | ||||||||
\(697\) | 15080.6 | 0.819540 | ||||||||
\(698\) | −17424.1 | −0.944858 | ||||||||
\(699\) | 37059.7 | 2.00533 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33334.1 | −1.79602 | −0.898011 | − | 0.439973i | \(-0.854988\pi\) | ||||
−0.898011 | + | 0.439973i | \(0.854988\pi\) | |||||||
\(702\) | −1007.05 | −0.0541436 | ||||||||
\(703\) | 14354.0 | 0.770087 | ||||||||
\(704\) | −63.2317 | −0.00338514 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14234.6 | −0.758819 | ||||||||
\(707\) | 1169.10 | 0.0621903 | ||||||||
\(708\) | −5454.43 | −0.289534 | ||||||||
\(709\) | −7107.92 | −0.376507 | −0.188253 | − | 0.982120i | \(-0.560283\pi\) | ||||
−0.188253 | + | 0.982120i | \(0.560283\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39601.3 | −2.08884 | ||||||||
\(712\) | 1710.01 | 0.0900075 | ||||||||
\(713\) | 3147.81 | 0.165338 | ||||||||
\(714\) | −27939.4 | −1.46443 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18622.5 | −0.972007 | ||||||||
\(717\) | 6450.34 | 0.335972 | ||||||||
\(718\) | −7097.45 | −0.368906 | ||||||||
\(719\) | −13003.1 | −0.674456 | −0.337228 | − | 0.941423i | \(-0.609489\pi\) | ||||
−0.337228 | + | 0.941423i | \(0.609489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8300.98 | 0.428772 | ||||||||
\(722\) | 3590.92 | 0.185097 | ||||||||
\(723\) | −34780.4 | −1.78907 | ||||||||
\(724\) | −705.279 | −0.0362037 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 22002.3 | 1.12477 | ||||||||
\(727\) | −5524.86 | −0.281851 | −0.140926 | − | 0.990020i | \(-0.545008\pi\) | ||||
−0.140926 | + | 0.990020i | \(0.545008\pi\) | |||||||
\(728\) | 772.328 | 0.0393192 | ||||||||
\(729\) | −32094.4 | −1.63057 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3996.77 | −0.202224 | ||||||||
\(732\) | 6228.29 | 0.314487 | ||||||||
\(733\) | −22106.6 | −1.11395 | −0.556976 | − | 0.830529i | \(-0.688038\pi\) | ||||
−0.556976 | + | 0.830529i | \(0.688038\pi\) | |||||||
\(734\) | 160.022 | 0.00804703 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 920.977 | 0.0460307 | ||||||||
\(738\) | 16909.3 | 0.843416 | ||||||||
\(739\) | −6619.82 | −0.329518 | −0.164759 | − | 0.986334i | \(-0.552685\pi\) | ||||
−0.164759 | + | 0.986334i | \(0.552685\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2485.44 | 0.123218 | ||||||||
\(742\) | −19597.9 | −0.969625 | ||||||||
\(743\) | −18894.1 | −0.932919 | −0.466460 | − | 0.884543i | \(-0.654471\pi\) | ||||
−0.466460 | + | 0.884543i | \(0.654471\pi\) | |||||||
\(744\) | 9056.27 | 0.446262 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6422.17 | 0.315191 | ||||||||
\(747\) | −8071.03 | −0.395320 | ||||||||
\(748\) | 291.949 | 0.0142710 | ||||||||
\(749\) | 34625.3 | 1.68916 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4931.32 | 0.239609 | 0.119805 | − | 0.992797i | \(-0.461773\pi\) | ||||
0.119805 | + | 0.992797i | \(0.461773\pi\) | |||||||
\(752\) | 663.185 | 0.0321594 | ||||||||
\(753\) | 22841.3 | 1.10542 | ||||||||
\(754\) | −235.617 | −0.0113802 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10904.4 | −0.524589 | ||||||||
\(757\) | −6248.31 | −0.299998 | −0.149999 | − | 0.988686i | \(-0.547927\pi\) | ||||
−0.149999 | + | 0.988686i | \(0.547927\pi\) | |||||||
\(758\) | 16355.1 | 0.783701 | ||||||||
\(759\) | 187.959 | 0.00898875 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18867.0 | −0.898723 | −0.449361 | − | 0.893350i | \(-0.648348\pi\) | ||||
−0.449361 | + | 0.893350i | \(0.648348\pi\) | |||||||
\(762\) | −10465.0 | −0.497514 | ||||||||
\(763\) | −18549.3 | −0.880117 | ||||||||
\(764\) | 6688.11 | 0.316711 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25853.1 | 1.21946 | ||||||||
\(767\) | −696.156 | −0.0327728 | ||||||||
\(768\) | 2117.48 | 0.0994895 | ||||||||
\(769\) | −4752.05 | −0.222839 | −0.111420 | − | 0.993773i | \(-0.535540\pi\) | ||||
−0.111420 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4850.92 | 0.226591 | ||||||||
\(772\) | 11817.8 | 0.550947 | ||||||||
\(773\) | −7050.12 | −0.328040 | −0.164020 | − | 0.986457i | \(-0.552446\pi\) | ||||
−0.164020 | + | 0.986457i | \(0.552446\pi\) | |||||||
\(774\) | −4481.42 | −0.208115 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5030.10 | 0.232693 | ||||||||
\(777\) | −38145.2 | −1.76120 | ||||||||
\(778\) | −9469.32 | −0.436364 | ||||||||
\(779\) | −14526.3 | −0.668111 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 260.175 | 0.0119204 | ||||||||
\(782\) | −3398.21 | −0.155396 | ||||||||
\(783\) | 3326.64 | 0.151832 | ||||||||
\(784\) | 2874.78 | 0.130958 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −37108.1 | −1.68397 | ||||||||
\(787\) | −19524.7 | −0.884345 | −0.442173 | − | 0.896930i | \(-0.645792\pi\) | ||||
−0.442173 | + | 0.896930i | \(0.645792\pi\) | |||||||
\(788\) | −7269.41 | −0.328632 | ||||||||
\(789\) | −49383.4 | −2.22826 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 284.623 | 0.0127940 | ||||||||
\(792\) | 327.351 | 0.0146868 | ||||||||
\(793\) | 794.925 | 0.0355972 | ||||||||
\(794\) | −19877.6 | −0.888450 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19124.0 | 0.851546 | ||||||||
\(797\) | 25078.7 | 1.11459 | 0.557297 | − | 0.830313i | \(-0.311838\pi\) | ||||
0.557297 | + | 0.830313i | \(0.311838\pi\) | |||||||
\(798\) | 26912.4 | 1.19384 | ||||||||
\(799\) | −3062.01 | −0.135577 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8852.74 | −0.390507 | ||||||||
\(802\) | 670.592 | 0.0295255 | ||||||||
\(803\) | 889.592 | 0.0390947 | ||||||||
\(804\) | −30841.3 | −1.35285 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1155.86 | 0.0505131 | ||||||||
\(807\) | 32377.0 | 1.41230 | ||||||||
\(808\) | 409.097 | 0.0178119 | ||||||||
\(809\) | 11722.0 | 0.509425 | 0.254712 | − | 0.967017i | \(-0.418019\pi\) | ||||
0.254712 | + | 0.967017i | \(0.418019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3540.61 | −0.153302 | −0.0766509 | − | 0.997058i | \(-0.524423\pi\) | ||||
−0.0766509 | + | 0.997058i | \(0.524423\pi\) | |||||||
\(812\) | −2551.26 | −0.110261 | ||||||||
\(813\) | 645.885 | 0.0278625 | ||||||||
\(814\) | 398.594 | 0.0171630 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9776.67 | −0.419427 | ||||||||
\(817\) | 3849.85 | 0.164858 | ||||||||
\(818\) | −13121.7 | −0.560867 | ||||||||
\(819\) | −3998.35 | −0.170591 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43675.7 | −1.85663 | −0.928315 | − | 0.371794i | \(-0.878743\pi\) | ||||
−0.928315 | + | 0.371794i | \(0.878743\pi\) | |||||||
\(822\) | 20724.3 | 0.879373 | ||||||||
\(823\) | 28732.5 | 1.21695 | 0.608476 | − | 0.793572i | \(-0.291781\pi\) | ||||
0.608476 | + | 0.793572i | \(0.291781\pi\) | |||||||
\(824\) | 2904.72 | 0.122804 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7537.99 | −0.317531 | ||||||||
\(827\) | −33810.2 | −1.42164 | −0.710821 | − | 0.703373i | \(-0.751676\pi\) | ||||
−0.710821 | + | 0.703373i | \(0.751676\pi\) | |||||||
\(828\) | −3810.28 | −0.159923 | ||||||||
\(829\) | −34664.8 | −1.45230 | −0.726150 | − | 0.687536i | \(-0.758692\pi\) | ||||
−0.726150 | + | 0.687536i | \(0.758692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 629.050 | 0.0262593 | ||||||||
\(832\) | 270.257 | 0.0112614 | ||||||||
\(833\) | −13273.3 | −0.552090 | ||||||||
\(834\) | −46571.1 | −1.93360 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −281.217 | −0.0116341 | ||||||||
\(837\) | −16319.5 | −0.673936 | ||||||||
\(838\) | −14233.4 | −0.586735 | ||||||||
\(839\) | 11115.4 | 0.457384 | 0.228692 | − | 0.973499i | \(-0.426555\pi\) | ||||
0.228692 | + | 0.973499i | \(0.426555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23610.7 | −0.968087 | ||||||||
\(842\) | −19598.9 | −0.802163 | ||||||||
\(843\) | −31867.0 | −1.30197 | ||||||||
\(844\) | 12806.9 | 0.522312 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3433.31 | −0.139527 | ||||||||
\(847\) | 30407.1 | 1.23353 | ||||||||
\(848\) | −6857.79 | −0.277709 | ||||||||
\(849\) | 12821.8 | 0.518306 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4639.52 | −0.186887 | ||||||||
\(852\) | −8712.64 | −0.350341 | ||||||||
\(853\) | −23695.9 | −0.951153 | −0.475577 | − | 0.879674i | \(-0.657761\pi\) | ||||
−0.475577 | + | 0.879674i | \(0.657761\pi\) | |||||||
\(854\) | 8607.46 | 0.344896 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12116.3 | 0.483791 | ||||||||
\(857\) | 20605.9 | 0.821336 | 0.410668 | − | 0.911785i | \(-0.365295\pi\) | ||||
0.410668 | + | 0.911785i | \(0.365295\pi\) | |||||||
\(858\) | 69.0177 | 0.00274618 | ||||||||
\(859\) | −43187.1 | −1.71540 | −0.857698 | − | 0.514154i | \(-0.828106\pi\) | ||||
−0.857698 | + | 0.514154i | \(0.828106\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38603.1 | 1.52798 | ||||||||
\(862\) | 21046.6 | 0.831613 | ||||||||
\(863\) | 47551.7 | 1.87564 | 0.937822 | − | 0.347117i | \(-0.112839\pi\) | ||||
0.937822 | + | 0.347117i | \(0.112839\pi\) | |||||||
\(864\) | −3815.72 | −0.150247 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9541.94 | −0.374421 | ||||||||
\(867\) | 4502.77 | 0.176381 | ||||||||
\(868\) | 12515.7 | 0.489414 | ||||||||
\(869\) | 944.704 | 0.0368779 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3936.32 | −0.153131 | ||||||||
\(872\) | −6490.85 | −0.252073 | ||||||||
\(873\) | −26040.9 | −1.00956 | ||||||||
\(874\) | 3273.29 | 0.126683 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −29790.3 | −1.14900 | ||||||||
\(877\) | −8116.63 | −0.312519 | −0.156260 | − | 0.987716i | \(-0.549944\pi\) | ||||
−0.156260 | + | 0.987716i | \(0.549944\pi\) | |||||||
\(878\) | −20462.4 | −0.786528 | ||||||||
\(879\) | −35037.7 | −1.34447 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24256.1 | 0.927594 | 0.463797 | − | 0.885942i | \(-0.346487\pi\) | ||||
0.463797 | + | 0.885942i | \(0.346487\pi\) | |||||||
\(882\) | −14882.8 | −0.568174 | ||||||||
\(883\) | 46859.3 | 1.78589 | 0.892945 | − | 0.450167i | \(-0.148635\pi\) | ||||
0.892945 | + | 0.450167i | \(0.148635\pi\) | |||||||
\(884\) | −1247.81 | −0.0474755 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21016.2 | 0.796899 | ||||||||
\(887\) | 14372.4 | 0.544057 | 0.272028 | − | 0.962289i | \(-0.412306\pi\) | ||||
0.272028 | + | 0.962289i | \(0.412306\pi\) | |||||||
\(888\) | −13347.9 | −0.504423 | ||||||||
\(889\) | −14462.5 | −0.545621 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 130.358 | 0.00490142 | ||||||||
\(892\) | 7588.91 | 0.284860 | ||||||||
\(893\) | 2949.45 | 0.110526 | ||||||||
\(894\) | −39809.6 | −1.48930 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2926.34 | 0.109110 | ||||||||
\(897\) | −803.347 | −0.0299030 | ||||||||
\(898\) | −14461.4 | −0.537398 | ||||||||
\(899\) | −3818.21 | −0.141651 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31663.3 | 1.17076 | ||||||||
\(902\) | −403.378 | −0.0148903 | ||||||||
\(903\) | −10230.8 | −0.377033 | ||||||||
\(904\) | 99.5965 | 0.00366431 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −36155.7 | −1.32582 | ||||||||
\(907\) | 17332.1 | 0.634512 | 0.317256 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317256 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(908\) | −17873.7 | −0.653258 | ||||||||
\(909\) | −2117.90 | −0.0772787 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44304.9 | 1.61129 | 0.805646 | − | 0.592397i | \(-0.201818\pi\) | ||||
0.805646 | + | 0.592397i | \(0.201818\pi\) | |||||||
\(912\) | 9417.30 | 0.341927 | ||||||||
\(913\) | 192.537 | 0.00697926 | ||||||||
\(914\) | 4837.49 | 0.175066 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21383.5 | −0.771322 | ||||||||
\(917\) | −51283.2 | −1.84680 | ||||||||
\(918\) | 17617.7 | 0.633410 | ||||||||
\(919\) | −4764.32 | −0.171013 | −0.0855063 | − | 0.996338i | \(-0.527251\pi\) | ||||
−0.0855063 | + | 0.996338i | \(0.527251\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 83359.9 | 2.98241 | ||||||||
\(922\) | 22685.6 | 0.810315 | ||||||||
\(923\) | −1112.01 | −0.0396556 | ||||||||
\(924\) | 747.325 | 0.0266074 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23571.8 | −0.836519 | ||||||||
\(927\) | −15037.7 | −0.532799 | ||||||||
\(928\) | −892.750 | −0.0315797 | ||||||||
\(929\) | −23226.2 | −0.820267 | −0.410134 | − | 0.912025i | \(-0.634518\pi\) | ||||
−0.410134 | + | 0.912025i | \(0.634518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12785.3 | 0.450078 | ||||||||
\(932\) | 17921.9 | 0.629882 | ||||||||
\(933\) | −21943.8 | −0.769996 | ||||||||
\(934\) | 32589.1 | 1.14170 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1399.12 | −0.0488587 | ||||||||
\(937\) | 23752.5 | 0.828133 | 0.414066 | − | 0.910247i | \(-0.364108\pi\) | ||||
0.414066 | + | 0.910247i | \(0.364108\pi\) | |||||||
\(938\) | −42622.5 | −1.48366 | ||||||||
\(939\) | −55506.7 | −1.92907 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23210.4 | −0.804079 | −0.402040 | − | 0.915622i | \(-0.631699\pi\) | ||||
−0.402040 | + | 0.915622i | \(0.631699\pi\) | |||||||
\(942\) | 17769.9 | 0.614624 | ||||||||
\(943\) | 4695.21 | 0.162139 | ||||||||
\(944\) | −2637.73 | −0.0909436 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 106.906 | 0.00367422 | ||||||||
\(947\) | 7778.59 | 0.266917 | 0.133458 | − | 0.991054i | \(-0.457392\pi\) | ||||
0.133458 | + | 0.991054i | \(0.457392\pi\) | |||||||
\(948\) | −31635.9 | −1.08385 | ||||||||
\(949\) | −3802.18 | −0.130057 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30421.3 | 1.03731 | ||||||||
\(952\) | −13511.3 | −0.459983 | ||||||||
\(953\) | −3979.52 | −0.135267 | −0.0676334 | − | 0.997710i | \(-0.521545\pi\) | ||||
−0.0676334 | + | 0.997710i | \(0.521545\pi\) | |||||||
\(954\) | 35502.8 | 1.20487 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3119.34 | 0.105530 | ||||||||
\(957\) | −227.989 | −0.00770098 | ||||||||
\(958\) | 1570.55 | 0.0529667 | ||||||||
\(959\) | 28640.9 | 0.964405 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11060.0 | −0.371254 | ||||||||
\(962\) | −1703.62 | −0.0570964 | ||||||||
\(963\) | −62726.0 | −2.09898 | ||||||||
\(964\) | −16819.6 | −0.561952 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8698.66 | −0.289726 | ||||||||
\(967\) | −17325.9 | −0.576178 | −0.288089 | − | 0.957604i | \(-0.593020\pi\) | ||||
−0.288089 | + | 0.957604i | \(0.593020\pi\) | |||||||
\(968\) | 10640.2 | 0.353294 | ||||||||
\(969\) | −43480.9 | −1.44149 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20183.0 | 0.667048 | 0.333524 | − | 0.942742i | \(-0.391762\pi\) | ||||
0.333524 | + | 0.942742i | \(0.391762\pi\) | |||||||
\(972\) | −17243.4 | −0.569016 | ||||||||
\(973\) | −64361.0 | −2.12058 | ||||||||
\(974\) | 17428.6 | 0.573355 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3011.96 | 0.0987814 | ||||||||
\(977\) | −47185.7 | −1.54514 | −0.772571 | − | 0.634928i | \(-0.781030\pi\) | ||||
−0.772571 | + | 0.634928i | \(0.781030\pi\) | |||||||
\(978\) | 44769.8 | 1.46378 | ||||||||
\(979\) | 211.185 | 0.00689430 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33603.2 | 1.09365 | ||||||||
\(982\) | 21886.3 | 0.711221 | ||||||||
\(983\) | 7347.90 | 0.238415 | 0.119207 | − | 0.992869i | \(-0.461965\pi\) | ||||
0.119207 | + | 0.992869i | \(0.461965\pi\) | |||||||
\(984\) | 13508.2 | 0.437627 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4121.94 | 0.133133 | ||||||||
\(987\) | −7838.07 | −0.252775 | ||||||||
\(988\) | 1201.94 | 0.0387033 | ||||||||
\(989\) | −1244.36 | −0.0400083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34327.0 | 1.10034 | 0.550168 | − | 0.835054i | \(-0.314564\pi\) | ||||
0.550168 | + | 0.835054i | \(0.314564\pi\) | |||||||
\(992\) | 4379.56 | 0.140172 | ||||||||
\(993\) | −81112.6 | −2.59218 | ||||||||
\(994\) | −12040.8 | −0.384217 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6447.62 | −0.205121 | ||||||||
\(997\) | −37611.0 | −1.19474 | −0.597368 | − | 0.801967i | \(-0.703787\pi\) | ||||
−0.597368 | + | 0.801967i | \(0.703787\pi\) | |||||||
\(998\) | 11203.7 | 0.355358 | ||||||||
\(999\) | 24053.1 | 0.761770 |
(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 | 1150.4.a.q.1.5 | ✓ | 5 | |
5.2 | odd | 4 | 1150.4.b.r.599.1 | 10 | |||
5.3 | odd | 4 | 1150.4.b.r.599.10 | 10 | |||
5.4 | even | 2 | 1150.4.a.v.1.1 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.4.a.q.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1150.4.a.v.1.1 | yes | 5 | 5.4 | even | 2 | ||
1150.4.b.r.599.1 | 10 | 5.2 | odd | 4 | |||
1150.4.b.r.599.10 | 10 | 5.3 | odd | 4 |