Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 34x^{4} + 241x^{2} - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(4.91092\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.91092 | 1.73627 | 0.868136 | − | 0.496326i | \(-0.165318\pi\) | ||||
0.868136 | + | 0.496326i | \(0.165318\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.1171 | 2.01464 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 39.8626 | 1.76170 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 24.5546 | 0.776485 | ||||||||
\(11\) | 12.0023 | 0.328984 | 0.164492 | − | 0.986378i | \(-0.447402\pi\) | ||||
0.164492 | + | 0.986378i | \(0.447402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.9540 | 1.00175 | 0.500873 | − | 0.865521i | \(-0.333012\pi\) | ||||
0.500873 | + | 0.865521i | \(0.333012\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 66.8251 | 1.04414 | ||||||||
\(17\) | 44.7080 | 0.637840 | 0.318920 | − | 0.947782i | \(-0.396680\pi\) | ||||
0.318920 | + | 0.947782i | \(0.396680\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31.7414 | −0.383262 | −0.191631 | − | 0.981467i | \(-0.561378\pi\) | ||||
−0.191631 | + | 0.981467i | \(0.561378\pi\) | |||||||
\(20\) | 80.5857 | 0.900976 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 58.9423 | 0.571206 | ||||||||
\(23\) | −39.4080 | −0.357267 | −0.178634 | − | 0.983916i | \(-0.557168\pi\) | ||||
−0.178634 | + | 0.983916i | \(0.557168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 230.587 | 1.73930 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 87.2713 | 0.558823 | 0.279412 | − | 0.960171i | \(-0.409861\pi\) | ||||
0.279412 | + | 0.960171i | \(0.409861\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 304.718 | 1.76545 | 0.882726 | − | 0.469887i | \(-0.155705\pi\) | ||||
0.882726 | + | 0.469887i | \(0.155705\pi\) | |||||||
\(32\) | 9.27181 | 0.0512200 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 219.557 | 1.10746 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −151.061 | −0.671197 | −0.335599 | − | 0.942005i | \(-0.608939\pi\) | ||||
−0.335599 | + | 0.942005i | \(0.608939\pi\) | |||||||
\(38\) | −155.879 | −0.665447 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 199.313 | 0.787855 | ||||||||
\(41\) | 282.927 | 1.07770 | 0.538851 | − | 0.842401i | \(-0.318859\pi\) | ||||
0.538851 | + | 0.842401i | \(0.318859\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −143.177 | −0.507773 | −0.253886 | − | 0.967234i | \(-0.581709\pi\) | ||||
−0.253886 | + | 0.967234i | \(0.581709\pi\) | |||||||
\(44\) | 193.443 | 0.662786 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −193.530 | −0.620313 | ||||||||
\(47\) | 88.8029 | 0.275601 | 0.137800 | − | 0.990460i | \(-0.455997\pi\) | ||||
0.137800 | + | 0.990460i | \(0.455997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 122.773 | 0.347255 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 756.764 | 2.01816 | ||||||||
\(53\) | 149.940 | 0.388601 | 0.194301 | − | 0.980942i | \(-0.437756\pi\) | ||||
0.194301 | + | 0.980942i | \(0.437756\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 60.0114 | 0.147126 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 428.582 | 0.970269 | ||||||||
\(59\) | −712.934 | −1.57315 | −0.786577 | − | 0.617493i | \(-0.788149\pi\) | ||||
−0.786577 | + | 0.617493i | \(0.788149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 65.0347 | 0.136506 | 0.0682528 | − | 0.997668i | \(-0.478258\pi\) | ||||
0.0682528 | + | 0.997668i | \(0.478258\pi\) | |||||||
\(62\) | 1496.45 | 3.06531 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −489.068 | −0.955211 | ||||||||
\(65\) | 234.770 | 0.447994 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 698.725 | 1.27407 | 0.637036 | − | 0.770834i | \(-0.280160\pi\) | ||||
0.637036 | + | 0.770834i | \(0.280160\pi\) | |||||||
\(68\) | 720.565 | 1.28502 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −291.400 | −0.487082 | −0.243541 | − | 0.969891i | \(-0.578309\pi\) | ||||
−0.243541 | + | 0.969891i | \(0.578309\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 476.241 | 0.763560 | 0.381780 | − | 0.924253i | \(-0.375311\pi\) | ||||
0.381780 | + | 0.924253i | \(0.375311\pi\) | |||||||
\(74\) | −741.849 | −1.16538 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −511.580 | −0.772135 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 256.947 | 0.365935 | 0.182967 | − | 0.983119i | \(-0.441430\pi\) | ||||
0.182967 | + | 0.983119i | \(0.441430\pi\) | |||||||
\(80\) | 334.126 | 0.466955 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1389.43 | 1.87118 | ||||||||
\(83\) | 1177.61 | 1.55735 | 0.778673 | − | 0.627430i | \(-0.215893\pi\) | ||||
0.778673 | + | 0.627430i | \(0.215893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 223.540 | 0.285251 | ||||||||
\(86\) | −703.129 | −0.881632 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 478.443 | 0.579570 | ||||||||
\(89\) | 1009.96 | 1.20287 | 0.601433 | − | 0.798923i | \(-0.294597\pi\) | ||||
0.601433 | + | 0.798923i | \(0.294597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −635.145 | −0.719765 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 436.104 | 0.478518 | ||||||||
\(95\) | −158.707 | −0.171400 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1149.16 | −1.20288 | −0.601441 | − | 0.798917i | \(-0.705407\pi\) | ||||
−0.601441 | + | 0.798917i | \(0.705407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 402.929 | 0.402929 | ||||||||
\(101\) | 288.883 | 0.284604 | 0.142302 | − | 0.989823i | \(-0.454550\pi\) | ||||
0.142302 | + | 0.989823i | \(0.454550\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1113.21 | 1.06493 | 0.532464 | − | 0.846453i | \(-0.321266\pi\) | ||||
0.532464 | + | 0.846453i | \(0.321266\pi\) | |||||||
\(104\) | 1871.71 | 1.76477 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 736.345 | 0.674718 | ||||||||
\(107\) | 263.840 | 0.238377 | 0.119189 | − | 0.992872i | \(-0.461971\pi\) | ||||
0.119189 | + | 0.992872i | \(0.461971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1246.96 | −1.09575 | −0.547877 | − | 0.836559i | \(-0.684564\pi\) | ||||
−0.547877 | + | 0.836559i | \(0.684564\pi\) | |||||||
\(110\) | 294.711 | 0.255451 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2034.45 | −1.69367 | −0.846835 | − | 0.531855i | \(-0.821495\pi\) | ||||
−0.846835 | + | 0.531855i | \(0.821495\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −197.040 | −0.159775 | ||||||||
\(116\) | 1406.56 | 1.12583 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3501.16 | −2.73142 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1186.95 | −0.891769 | ||||||||
\(122\) | 319.380 | 0.237011 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4911.19 | 3.55676 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1143.07 | 0.798670 | 0.399335 | − | 0.916805i | \(-0.369241\pi\) | ||||
0.399335 | + | 0.916805i | \(0.369241\pi\) | |||||||
\(128\) | −2475.95 | −1.70973 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1152.94 | 0.777841 | ||||||||
\(131\) | 1544.70 | 1.03024 | 0.515118 | − | 0.857119i | \(-0.327748\pi\) | ||||
0.515118 | + | 0.857119i | \(0.327748\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3431.38 | 2.21214 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1782.18 | 1.12368 | ||||||||
\(137\) | 243.730 | 0.151995 | 0.0759974 | − | 0.997108i | \(-0.475786\pi\) | ||||
0.0759974 | + | 0.997108i | \(0.475786\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −624.857 | −0.381293 | −0.190646 | − | 0.981659i | \(-0.561058\pi\) | ||||
−0.190646 | + | 0.981659i | \(0.561058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1431.04 | −0.845707 | ||||||||
\(143\) | 563.555 | 0.329559 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 436.356 | 0.249913 | ||||||||
\(146\) | 2338.78 | 1.32575 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2434.67 | −1.35222 | ||||||||
\(149\) | 3082.32 | 1.69472 | 0.847359 | − | 0.531020i | \(-0.178191\pi\) | ||||
0.847359 | + | 0.531020i | \(0.178191\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1840.16 | −0.991720 | −0.495860 | − | 0.868402i | \(-0.665147\pi\) | ||||
−0.495860 | + | 0.868402i | \(0.665147\pi\) | |||||||
\(152\) | −1265.30 | −0.675191 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1523.59 | 0.789535 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 129.576 | 0.0658679 | 0.0329339 | − | 0.999458i | \(-0.489515\pi\) | ||||
0.0329339 | + | 0.999458i | \(0.489515\pi\) | |||||||
\(158\) | 1261.85 | 0.635362 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 46.3591 | 0.0229063 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3575.75 | 1.71825 | 0.859124 | − | 0.511768i | \(-0.171009\pi\) | ||||
0.859124 | + | 0.511768i | \(0.171009\pi\) | |||||||
\(164\) | 4559.97 | 2.17118 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5783.16 | 2.70398 | ||||||||
\(167\) | −2054.63 | −0.952049 | −0.476025 | − | 0.879432i | \(-0.657923\pi\) | ||||
−0.476025 | + | 0.879432i | \(0.657923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.67889 | 0.00349517 | ||||||||
\(170\) | 1097.79 | 0.495273 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2307.60 | −1.02298 | ||||||||
\(173\) | −3279.38 | −1.44120 | −0.720598 | − | 0.693353i | \(-0.756133\pi\) | ||||
−0.720598 | + | 0.693353i | \(0.756133\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 802.054 | 0.343506 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4959.81 | 2.08850 | ||||||||
\(179\) | −3287.59 | −1.37277 | −0.686385 | − | 0.727239i | \(-0.740803\pi\) | ||||
−0.686385 | + | 0.727239i | \(0.740803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2709.27 | −1.11259 | −0.556293 | − | 0.830986i | \(-0.687777\pi\) | ||||
−0.556293 | + | 0.830986i | \(0.687777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1570.91 | −0.629396 | ||||||||
\(185\) | −755.306 | −0.300169 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 536.598 | 0.209839 | ||||||||
\(188\) | 1431.25 | 0.555237 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −779.397 | −0.297597 | ||||||||
\(191\) | −2106.69 | −0.798087 | −0.399044 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399044 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3956.67 | 1.47569 | 0.737844 | − | 0.674972i | \(-0.235844\pi\) | ||||
0.737844 | + | 0.674972i | \(0.235844\pi\) | |||||||
\(194\) | −5643.44 | −2.08853 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1892.16 | −0.684319 | −0.342160 | − | 0.939642i | \(-0.611158\pi\) | ||||
−0.342160 | + | 0.939642i | \(0.611158\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4422.23 | 1.57529 | 0.787646 | − | 0.616128i | \(-0.211299\pi\) | ||||
0.787646 | + | 0.616128i | \(0.211299\pi\) | |||||||
\(200\) | 996.566 | 0.352339 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1418.68 | 0.494150 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1414.63 | 0.481963 | ||||||||
\(206\) | 5466.87 | 1.84901 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3137.71 | 1.04597 | ||||||||
\(209\) | −380.969 | −0.126087 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1402.47 | 0.457584 | 0.228792 | − | 0.973475i | \(-0.426522\pi\) | ||||
0.228792 | + | 0.973475i | \(0.426522\pi\) | |||||||
\(212\) | 2416.61 | 0.782893 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1295.70 | 0.413888 | ||||||||
\(215\) | −715.883 | −0.227083 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6123.73 | −1.90253 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 967.213 | 0.296407 | ||||||||
\(221\) | 2099.22 | 0.638954 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1111.09 | 0.333651 | 0.166826 | − | 0.985986i | \(-0.446648\pi\) | ||||
0.166826 | + | 0.985986i | \(0.446648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9991.01 | −2.94067 | ||||||||
\(227\) | 1715.41 | 0.501567 | 0.250784 | − | 0.968043i | \(-0.419312\pi\) | ||||
0.250784 | + | 0.968043i | \(0.419312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 934.139 | 0.269562 | 0.134781 | − | 0.990875i | \(-0.456967\pi\) | ||||
0.134781 | + | 0.990875i | \(0.456967\pi\) | |||||||
\(230\) | −967.648 | −0.277412 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3478.86 | 0.984477 | ||||||||
\(233\) | −3585.12 | −1.00802 | −0.504010 | − | 0.863698i | \(-0.668143\pi\) | ||||
−0.504010 | + | 0.863698i | \(0.668143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 444.014 | 0.123252 | ||||||||
\(236\) | −11490.5 | −3.16934 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5944.92 | 1.60897 | 0.804487 | − | 0.593970i | \(-0.202440\pi\) | ||||
0.804487 | + | 0.593970i | \(0.202440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5606.87 | 1.49863 | 0.749316 | − | 0.662212i | \(-0.230382\pi\) | ||||
0.749316 | + | 0.662212i | \(0.230382\pi\) | |||||||
\(242\) | −5828.99 | −1.54835 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1048.17 | 0.275010 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1490.39 | −0.383931 | ||||||||
\(248\) | 12146.9 | 3.11019 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 613.865 | 0.155297 | ||||||||
\(251\) | −5182.08 | −1.30315 | −0.651574 | − | 0.758585i | \(-0.725891\pi\) | ||||
−0.651574 | + | 0.758585i | \(0.725891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −472.986 | −0.117535 | ||||||||
\(254\) | 5613.52 | 1.38671 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8246.64 | −2.01334 | ||||||||
\(257\) | 37.7581 | 0.00916453 | 0.00458226 | − | 0.999990i | \(-0.498541\pi\) | ||||
0.00458226 | + | 0.999990i | \(0.498541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3783.82 | 0.902549 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7585.90 | 1.78877 | ||||||||
\(263\) | 1147.11 | 0.268950 | 0.134475 | − | 0.990917i | \(-0.457065\pi\) | ||||
0.134475 | + | 0.990917i | \(0.457065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 749.701 | 0.173788 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11261.5 | 2.56680 | ||||||||
\(269\) | 5417.07 | 1.22782 | 0.613912 | − | 0.789374i | \(-0.289595\pi\) | ||||
0.613912 | + | 0.789374i | \(0.289595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6108.76 | −1.36930 | −0.684651 | − | 0.728871i | \(-0.740045\pi\) | ||||
−0.684651 | + | 0.728871i | \(0.740045\pi\) | |||||||
\(272\) | 2987.62 | 0.665996 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1196.94 | 0.263904 | ||||||||
\(275\) | 300.057 | 0.0657968 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7247.04 | −1.57196 | −0.785979 | − | 0.618253i | \(-0.787841\pi\) | ||||
−0.785979 | + | 0.618253i | \(0.787841\pi\) | |||||||
\(278\) | −3068.62 | −0.662028 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −563.644 | −0.119659 | −0.0598295 | − | 0.998209i | \(-0.519056\pi\) | ||||
−0.0598295 | + | 0.998209i | \(0.519056\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −49.6198 | −0.0104226 | −0.00521129 | − | 0.999986i | \(-0.501659\pi\) | ||||
−0.00521129 | + | 0.999986i | \(0.501659\pi\) | |||||||
\(284\) | −4696.54 | −0.981296 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2767.58 | 0.572204 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2914.20 | −0.593160 | ||||||||
\(290\) | 2142.91 | 0.433918 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7675.65 | 1.53830 | ||||||||
\(293\) | −5681.57 | −1.13284 | −0.566418 | − | 0.824118i | \(-0.691671\pi\) | ||||
−0.566418 | + | 0.824118i | \(0.691671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3564.67 | −0.703536 | ||||||||
\(296\) | −6021.70 | −1.18245 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15137.0 | 2.94249 | ||||||||
\(299\) | −1850.36 | −0.357891 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9036.86 | −1.72190 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2121.12 | −0.400180 | ||||||||
\(305\) | 325.173 | 0.0610471 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9112.83 | −1.69413 | −0.847063 | − | 0.531493i | \(-0.821631\pi\) | ||||
−0.847063 | + | 0.531493i | \(0.821631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7482.24 | 1.37085 | ||||||||
\(311\) | 2520.08 | 0.459487 | 0.229743 | − | 0.973251i | \(-0.426211\pi\) | ||||
0.229743 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1041.28 | −0.188040 | −0.0940200 | − | 0.995570i | \(-0.529972\pi\) | ||||
−0.0940200 | + | 0.995570i | \(0.529972\pi\) | |||||||
\(314\) | 636.335 | 0.114365 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4141.26 | 0.737228 | ||||||||
\(317\) | −1294.04 | −0.229277 | −0.114638 | − | 0.993407i | \(-0.536571\pi\) | ||||
−0.114638 | + | 0.993407i | \(0.536571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1047.45 | 0.183844 | ||||||||
\(320\) | −2445.34 | −0.427183 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1419.09 | −0.244460 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1173.85 | 0.200349 | ||||||||
\(326\) | 17560.2 | 2.98335 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11278.2 | 1.89858 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7053.87 | −1.17135 | −0.585674 | − | 0.810547i | \(-0.699170\pi\) | ||||
−0.585674 | + | 0.810547i | \(0.699170\pi\) | |||||||
\(332\) | 18979.7 | 3.13750 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10090.1 | −1.65302 | ||||||||
\(335\) | 3493.63 | 0.569783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1616.01 | −0.261216 | −0.130608 | − | 0.991434i | \(-0.541693\pi\) | ||||
−0.130608 | + | 0.991434i | \(0.541693\pi\) | |||||||
\(338\) | 37.7104 | 0.00606857 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3602.83 | 0.574678 | ||||||||
\(341\) | 3657.32 | 0.580806 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5707.40 | −0.894541 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16104.8 | −2.50231 | ||||||||
\(347\) | −2320.46 | −0.358987 | −0.179494 | − | 0.983759i | \(-0.557446\pi\) | ||||
−0.179494 | + | 0.983759i | \(0.557446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8883.26 | −1.36249 | −0.681247 | − | 0.732054i | \(-0.738562\pi\) | ||||
−0.681247 | + | 0.732054i | \(0.738562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 111.283 | 0.0168506 | ||||||||
\(353\) | −7213.82 | −1.08769 | −0.543843 | − | 0.839187i | \(-0.683031\pi\) | ||||
−0.543843 | + | 0.839187i | \(0.683031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1457.00 | −0.217830 | ||||||||
\(356\) | 16277.6 | 2.42334 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16145.1 | −2.38350 | ||||||||
\(359\) | 571.681 | 0.0840451 | 0.0420225 | − | 0.999117i | \(-0.486620\pi\) | ||||
0.0420225 | + | 0.999117i | \(0.486620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5851.48 | −0.853110 | ||||||||
\(362\) | −13305.0 | −1.93175 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2381.21 | 0.341474 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7595.02 | −1.08026 | −0.540132 | − | 0.841580i | \(-0.681626\pi\) | ||||
−0.540132 | + | 0.841580i | \(0.681626\pi\) | |||||||
\(368\) | −2633.45 | −0.373038 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3709.25 | −0.521174 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12739.0 | 1.76837 | 0.884184 | − | 0.467139i | \(-0.154715\pi\) | ||||
0.884184 | + | 0.467139i | \(0.154715\pi\) | |||||||
\(374\) | 2635.19 | 0.364338 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3539.92 | 0.485525 | ||||||||
\(377\) | 4097.74 | 0.559799 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2726.44 | 0.369519 | 0.184759 | − | 0.982784i | \(-0.440849\pi\) | ||||
0.184759 | + | 0.982784i | \(0.440849\pi\) | |||||||
\(380\) | −2557.90 | −0.345309 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10345.8 | −1.38570 | ||||||||
\(383\) | −44.4732 | −0.00593336 | −0.00296668 | − | 0.999996i | \(-0.500944\pi\) | ||||
−0.00296668 | + | 0.999996i | \(0.500944\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19430.9 | 2.56220 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18521.2 | −2.42338 | ||||||||
\(389\) | −2160.33 | −0.281576 | −0.140788 | − | 0.990040i | \(-0.544964\pi\) | ||||
−0.140788 | + | 0.990040i | \(0.544964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1761.85 | −0.227879 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9292.25 | −1.18816 | ||||||||
\(395\) | 1284.74 | 0.163651 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10915.6 | −1.37994 | −0.689970 | − | 0.723838i | \(-0.742376\pi\) | ||||
−0.689970 | + | 0.723838i | \(0.742376\pi\) | |||||||
\(398\) | 21717.2 | 2.73514 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1670.63 | 0.208829 | ||||||||
\(401\) | −7119.55 | −0.886617 | −0.443308 | − | 0.896369i | \(-0.646195\pi\) | ||||
−0.443308 | + | 0.896369i | \(0.646195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14307.8 | 1.76854 | ||||||||
\(404\) | 4655.97 | 0.573375 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1813.08 | −0.220813 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10435.9 | −1.26166 | −0.630832 | − | 0.775920i | \(-0.717286\pi\) | ||||
−0.630832 | + | 0.775920i | \(0.717286\pi\) | |||||||
\(410\) | 6947.16 | 0.836819 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17941.7 | 2.14545 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5888.06 | 0.696467 | ||||||||
\(416\) | 435.349 | 0.0513094 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1870.91 | −0.218921 | ||||||||
\(419\) | 6763.41 | 0.788579 | 0.394289 | − | 0.918986i | \(-0.370991\pi\) | ||||
0.394289 | + | 0.918986i | \(0.370991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12708.5 | 1.47119 | 0.735597 | − | 0.677419i | \(-0.236902\pi\) | ||||
0.735597 | + | 0.677419i | \(0.236902\pi\) | |||||||
\(422\) | 6887.44 | 0.794491 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5977.01 | 0.684598 | ||||||||
\(425\) | 1117.70 | 0.127568 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4252.34 | 0.480245 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3515.64 | −0.394278 | ||||||||
\(431\) | 8478.80 | 0.947585 | 0.473793 | − | 0.880636i | \(-0.342885\pi\) | ||||
0.473793 | + | 0.880636i | \(0.342885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13442.6 | −1.49194 | −0.745968 | − | 0.665982i | \(-0.768013\pi\) | ||||
−0.745968 | + | 0.665982i | \(0.768013\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20097.4 | −2.20755 | ||||||||
\(437\) | 1250.87 | 0.136927 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11890.4 | −1.29270 | −0.646352 | − | 0.763040i | \(-0.723706\pi\) | ||||
−0.646352 | + | 0.763040i | \(0.723706\pi\) | |||||||
\(440\) | 2392.21 | 0.259192 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10309.1 | 1.10940 | ||||||||
\(443\) | 11118.4 | 1.19245 | 0.596223 | − | 0.802819i | \(-0.296667\pi\) | ||||
0.596223 | + | 0.802819i | \(0.296667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5049.78 | 0.537938 | ||||||||
\(446\) | 5456.48 | 0.579309 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14077.5 | −1.47964 | −0.739818 | − | 0.672807i | \(-0.765088\pi\) | ||||
−0.739818 | + | 0.672807i | \(0.765088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3395.77 | 0.354547 | ||||||||
\(452\) | −32789.5 | −3.41214 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8424.24 | 0.870858 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6557.10 | −0.671178 | −0.335589 | − | 0.942009i | \(-0.608935\pi\) | ||||
−0.335589 | + | 0.942009i | \(0.608935\pi\) | |||||||
\(458\) | 4587.48 | 0.468033 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3175.72 | −0.321889 | ||||||||
\(461\) | 5157.65 | 0.521075 | 0.260538 | − | 0.965464i | \(-0.416100\pi\) | ||||
0.260538 | + | 0.965464i | \(0.416100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6069.13 | −0.609193 | −0.304596 | − | 0.952482i | \(-0.598522\pi\) | ||||
−0.304596 | + | 0.952482i | \(0.598522\pi\) | |||||||
\(464\) | 5831.91 | 0.583491 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17606.2 | −1.75020 | ||||||||
\(467\) | 16351.0 | 1.62020 | 0.810101 | − | 0.586290i | \(-0.199412\pi\) | ||||
0.810101 | + | 0.586290i | \(0.199412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2180.52 | 0.214000 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −28419.4 | −2.77142 | ||||||||
\(473\) | −1718.45 | −0.167049 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −793.535 | −0.0766523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 29195.0 | 2.79362 | ||||||||
\(479\) | −9345.33 | −0.891439 | −0.445719 | − | 0.895173i | \(-0.647052\pi\) | ||||
−0.445719 | + | 0.895173i | \(0.647052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7092.93 | −0.672369 | ||||||||
\(482\) | 27534.9 | 2.60204 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19130.2 | −1.79660 | ||||||||
\(485\) | −5745.81 | −0.537946 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −648.574 | −0.0603485 | −0.0301742 | − | 0.999545i | \(-0.509606\pi\) | ||||
−0.0301742 | + | 0.999545i | \(0.509606\pi\) | |||||||
\(488\) | 2592.45 | 0.240481 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16109.9 | 1.48071 | 0.740354 | − | 0.672217i | \(-0.234658\pi\) | ||||
0.740354 | + | 0.672217i | \(0.234658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3901.72 | 0.356440 | ||||||||
\(494\) | −7319.16 | −0.666609 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20362.8 | 1.84338 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6357.21 | 0.570316 | 0.285158 | − | 0.958481i | \(-0.407954\pi\) | ||||
0.285158 | + | 0.958481i | \(0.407954\pi\) | |||||||
\(500\) | 2014.64 | 0.180195 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25448.8 | −2.26262 | ||||||||
\(503\) | 3100.43 | 0.274833 | 0.137417 | − | 0.990513i | \(-0.456120\pi\) | ||||
0.137417 | + | 0.990513i | \(0.456120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1444.42 | 0.127279 | ||||||||
\(506\) | −2322.80 | −0.204073 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18423.0 | 1.60903 | ||||||||
\(509\) | 16682.7 | 1.45275 | 0.726374 | − | 0.687300i | \(-0.241204\pi\) | ||||
0.726374 | + | 0.687300i | \(0.241204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20691.0 | −1.78598 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 185.427 | 0.0159121 | ||||||||
\(515\) | 5566.04 | 0.476250 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1065.84 | 0.0906682 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9358.55 | 0.789230 | ||||||||
\(521\) | 11268.9 | 0.947597 | 0.473798 | − | 0.880633i | \(-0.342883\pi\) | ||||
0.473798 | + | 0.880633i | \(0.342883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21181.0 | −1.77090 | −0.885448 | − | 0.464738i | \(-0.846148\pi\) | ||||
−0.885448 | + | 0.464738i | \(0.846148\pi\) | |||||||
\(524\) | 24896.1 | 2.07556 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5633.37 | 0.466970 | ||||||||
\(527\) | 13623.3 | 1.12608 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10614.0 | −0.872360 | ||||||||
\(530\) | 3681.72 | 0.301743 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13284.5 | 1.07958 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1319.20 | 0.106606 | ||||||||
\(536\) | 27853.0 | 2.24453 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26602.8 | 2.13184 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13392.8 | −1.06433 | −0.532163 | − | 0.846642i | \(-0.678621\pi\) | ||||
−0.532163 | + | 0.846642i | \(0.678621\pi\) | |||||||
\(542\) | −29999.7 | −2.37748 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 414.524 | 0.0326702 | ||||||||
\(545\) | −6234.81 | −0.490036 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14270.9 | 1.11550 | 0.557752 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(548\) | 3928.23 | 0.306215 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1473.56 | 0.114241 | ||||||||
\(551\) | −2770.11 | −0.214175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −35589.6 | −2.72935 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10070.9 | −0.768169 | ||||||||
\(557\) | −12713.6 | −0.967130 | −0.483565 | − | 0.875309i | \(-0.660658\pi\) | ||||
−0.483565 | + | 0.875309i | \(0.660658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6722.71 | −0.508659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2768.01 | −0.207761 | ||||||||
\(563\) | 16455.5 | 1.23183 | 0.615913 | − | 0.787814i | \(-0.288787\pi\) | ||||
0.615913 | + | 0.787814i | \(0.288787\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10172.2 | −0.757433 | ||||||||
\(566\) | −243.679 | −0.0180964 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11616.0 | −0.858091 | ||||||||
\(569\) | −22665.7 | −1.66994 | −0.834968 | − | 0.550298i | \(-0.814514\pi\) | ||||
−0.834968 | + | 0.550298i | \(0.814514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12436.3 | −0.911460 | −0.455730 | − | 0.890118i | \(-0.650622\pi\) | ||||
−0.455730 | + | 0.890118i | \(0.650622\pi\) | |||||||
\(572\) | 9082.90 | 0.663943 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −985.201 | −0.0714534 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15784.4 | 1.13884 | 0.569421 | − | 0.822046i | \(-0.307168\pi\) | ||||
0.569421 | + | 0.822046i | \(0.307168\pi\) | |||||||
\(578\) | −14311.4 | −1.02989 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7032.82 | 0.503486 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1799.63 | 0.127844 | ||||||||
\(584\) | 18984.2 | 1.34516 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27901.7 | −1.96691 | ||||||||
\(587\) | −5373.31 | −0.377820 | −0.188910 | − | 0.981994i | \(-0.560495\pi\) | ||||
−0.188910 | + | 0.981994i | \(0.560495\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9672.18 | −0.676631 | ||||||||
\(590\) | −17505.8 | −1.22153 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10094.7 | −0.700826 | ||||||||
\(593\) | 19885.4 | 1.37706 | 0.688530 | − | 0.725208i | \(-0.258256\pi\) | ||||
0.688530 | + | 0.725208i | \(0.258256\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 49678.1 | 3.41425 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9086.99 | −0.621396 | ||||||||
\(599\) | 5568.32 | 0.379825 | 0.189913 | − | 0.981801i | \(-0.439180\pi\) | ||||
0.189913 | + | 0.981801i | \(0.439180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5796.37 | 0.393409 | 0.196704 | − | 0.980463i | \(-0.436976\pi\) | ||||
0.196704 | + | 0.980463i | \(0.436976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −29658.0 | −1.99796 | ||||||||
\(605\) | −5934.73 | −0.398811 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9808.47 | −0.655871 | −0.327935 | − | 0.944700i | \(-0.606353\pi\) | ||||
−0.327935 | + | 0.944700i | \(0.606353\pi\) | |||||||
\(608\) | −294.300 | −0.0196307 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1596.90 | 0.105994 | ||||||||
\(611\) | 4169.65 | 0.276082 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2745.09 | 0.180870 | 0.0904350 | − | 0.995902i | \(-0.471174\pi\) | ||||
0.0904350 | + | 0.995902i | \(0.471174\pi\) | |||||||
\(614\) | −44752.4 | −2.94146 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15727.9 | −1.02623 | −0.513114 | − | 0.858321i | \(-0.671508\pi\) | ||||
−0.513114 | + | 0.858321i | \(0.671508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13005.2 | 0.844462 | 0.422231 | − | 0.906488i | \(-0.361247\pi\) | ||||
0.422231 | + | 0.906488i | \(0.361247\pi\) | |||||||
\(620\) | 24555.9 | 1.59063 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12375.9 | 0.797794 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −5113.64 | −0.326489 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2088.39 | 0.132700 | ||||||||
\(629\) | −6753.64 | −0.428116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10019.2 | −0.632102 | −0.316051 | − | 0.948742i | \(-0.602357\pi\) | ||||
−0.316051 | + | 0.948742i | \(0.602357\pi\) | |||||||
\(632\) | 10242.6 | 0.644666 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6354.95 | −0.398087 | ||||||||
\(635\) | 5715.35 | 0.357176 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5143.97 | 0.319203 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12379.7 | −0.764613 | ||||||||
\(641\) | 28621.9 | 1.76365 | 0.881824 | − | 0.471579i | \(-0.156316\pi\) | ||||
0.881824 | + | 0.471579i | \(0.156316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21100.2 | −1.29411 | −0.647054 | − | 0.762444i | \(-0.723999\pi\) | ||||
−0.647054 | + | 0.762444i | \(0.723999\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6969.06 | −0.424449 | ||||||||
\(647\) | 3060.93 | 0.185993 | 0.0929965 | − | 0.995666i | \(-0.470355\pi\) | ||||
0.0929965 | + | 0.995666i | \(0.470355\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8556.83 | −0.517543 | ||||||||
\(650\) | 5764.69 | 0.347861 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 57630.9 | 3.46165 | ||||||||
\(653\) | 23083.9 | 1.38337 | 0.691687 | − | 0.722197i | \(-0.256868\pi\) | ||||
0.691687 | + | 0.722197i | \(0.256868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7723.50 | 0.460736 | ||||||||
\(656\) | 18906.6 | 1.12527 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19482.0 | −1.15161 | −0.575806 | − | 0.817586i | \(-0.695312\pi\) | ||||
−0.575806 | + | 0.817586i | \(0.695312\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2297.05 | 0.135166 | 0.0675831 | − | 0.997714i | \(-0.478471\pi\) | ||||
0.0675831 | + | 0.997714i | \(0.478471\pi\) | |||||||
\(662\) | −34641.0 | −2.03378 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 46942.7 | 2.74357 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3439.19 | −0.199649 | ||||||||
\(668\) | −33114.8 | −1.91804 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17156.9 | 0.989298 | ||||||||
\(671\) | 780.565 | 0.0449081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17610.4 | −1.00866 | −0.504332 | − | 0.863510i | \(-0.668261\pi\) | ||||
−0.504332 | + | 0.863510i | \(0.668261\pi\) | |||||||
\(674\) | −7936.10 | −0.453542 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 123.762 | 0.00704152 | ||||||||
\(677\) | −25472.5 | −1.44607 | −0.723033 | − | 0.690814i | \(-0.757252\pi\) | ||||
−0.723033 | + | 0.690814i | \(0.757252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8910.89 | 0.502525 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17960.8 | 1.00844 | ||||||||
\(683\) | −6821.30 | −0.382152 | −0.191076 | − | 0.981575i | \(-0.561198\pi\) | ||||
−0.191076 | + | 0.981575i | \(0.561198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1218.65 | 0.0679741 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9567.79 | −0.530187 | ||||||||
\(689\) | 7040.29 | 0.389280 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16765.6 | −0.923003 | −0.461502 | − | 0.887139i | \(-0.652689\pi\) | ||||
−0.461502 | + | 0.887139i | \(0.652689\pi\) | |||||||
\(692\) | −52854.3 | −2.90350 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11395.6 | −0.623300 | ||||||||
\(695\) | −3124.29 | −0.170519 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12649.1 | 0.687401 | ||||||||
\(698\) | −43625.0 | −2.36566 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14137.8 | 0.761736 | 0.380868 | − | 0.924629i | \(-0.375625\pi\) | ||||
0.380868 | + | 0.924629i | \(0.375625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4794.89 | 0.257244 | ||||||||
\(704\) | −5869.93 | −0.314249 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35426.5 | −1.88852 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2483.11 | 0.131531 | 0.0657654 | − | 0.997835i | \(-0.479051\pi\) | ||||
0.0657654 | + | 0.997835i | \(0.479051\pi\) | |||||||
\(710\) | −7155.21 | −0.378212 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 40259.5 | 2.11908 | ||||||||
\(713\) | −12008.4 | −0.630738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2817.78 | 0.147383 | ||||||||
\(716\) | −52986.5 | −2.76564 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2807.48 | 0.145925 | ||||||||
\(719\) | 9074.07 | 0.470662 | 0.235331 | − | 0.971915i | \(-0.424383\pi\) | ||||
0.235331 | + | 0.971915i | \(0.424383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −28736.2 | −1.48123 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −43665.6 | −2.24146 | ||||||||
\(725\) | 2181.78 | 0.111765 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27924.6 | −1.42457 | −0.712286 | − | 0.701889i | \(-0.752340\pi\) | ||||
−0.712286 | + | 0.701889i | \(0.752340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11693.9 | 0.592892 | ||||||||
\(731\) | −6401.14 | −0.323878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11177.6 | −0.563238 | −0.281619 | − | 0.959526i | \(-0.590871\pi\) | ||||
−0.281619 | + | 0.959526i | \(0.590871\pi\) | |||||||
\(734\) | −37298.5 | −1.87563 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −365.384 | −0.0182992 | ||||||||
\(737\) | 8386.30 | 0.419150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12147.5 | 0.604671 | 0.302335 | − | 0.953202i | \(-0.402234\pi\) | ||||
0.302335 | + | 0.953202i | \(0.402234\pi\) | |||||||
\(740\) | −12173.4 | −0.604732 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8190.00 | 0.404390 | 0.202195 | − | 0.979345i | \(-0.435192\pi\) | ||||
0.202195 | + | 0.979345i | \(0.435192\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15411.6 | 0.757901 | ||||||||
\(746\) | 62560.3 | 3.07037 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8648.43 | 0.422751 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11143.0 | −0.541432 | −0.270716 | − | 0.962659i | \(-0.587260\pi\) | ||||
−0.270716 | + | 0.962659i | \(0.587260\pi\) | |||||||
\(752\) | 5934.26 | 0.287766 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20123.7 | 0.971963 | ||||||||
\(755\) | −9200.78 | −0.443511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20072.7 | −0.963746 | −0.481873 | − | 0.876241i | \(-0.660043\pi\) | ||||
−0.481873 | + | 0.876241i | \(0.660043\pi\) | |||||||
\(758\) | 13389.3 | 0.641585 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6326.48 | −0.301955 | ||||||||
\(761\) | −5593.19 | −0.266430 | −0.133215 | − | 0.991087i | \(-0.542530\pi\) | ||||
−0.133215 | + | 0.991087i | \(0.542530\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −33953.8 | −1.60786 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −218.405 | −0.0103019 | ||||||||
\(767\) | −33475.1 | −1.57590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35021.4 | −1.64227 | −0.821133 | − | 0.570737i | \(-0.806658\pi\) | ||||
−0.821133 | + | 0.570737i | \(0.806658\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 63770.3 | 2.97298 | ||||||||
\(773\) | 36389.0 | 1.69317 | 0.846585 | − | 0.532254i | \(-0.178655\pi\) | ||||
0.846585 | + | 0.532254i | \(0.178655\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7617.96 | 0.353091 | ||||||||
\(776\) | −45808.6 | −2.11911 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10609.2 | −0.488893 | ||||||||
\(779\) | −8980.49 | −0.413042 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3497.47 | −0.160242 | ||||||||
\(782\) | −8652.32 | −0.395660 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 647.878 | 0.0294570 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23542.2 | −1.06632 | −0.533158 | − | 0.846016i | \(-0.678995\pi\) | ||||
−0.533158 | + | 0.846016i | \(0.678995\pi\) | |||||||
\(788\) | −30496.2 | −1.37866 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6309.24 | 0.284143 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3053.64 | 0.136744 | ||||||||
\(794\) | −53605.4 | −2.39595 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 71273.6 | 3.17365 | ||||||||
\(797\) | −9662.12 | −0.429423 | −0.214711 | − | 0.976678i | \(-0.568881\pi\) | ||||
−0.214711 | + | 0.976678i | \(0.568881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3970.20 | 0.175789 | ||||||||
\(800\) | 231.795 | 0.0102440 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −34963.5 | −1.53941 | ||||||||
\(803\) | 5715.99 | 0.251199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 70264.2 | 3.07066 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11515.7 | 0.501385 | ||||||||
\(809\) | −24010.3 | −1.04346 | −0.521728 | − | 0.853112i | \(-0.674713\pi\) | ||||
−0.521728 | + | 0.853112i | \(0.674713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13412.7 | −0.580746 | −0.290373 | − | 0.956913i | \(-0.593779\pi\) | ||||
−0.290373 | + | 0.956913i | \(0.593779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8903.89 | −0.383392 | ||||||||
\(815\) | 17878.7 | 0.768423 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4544.62 | 0.194610 | ||||||||
\(818\) | −51249.7 | −2.19059 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22799.9 | 0.970983 | ||||||||
\(821\) | 17462.1 | 0.742304 | 0.371152 | − | 0.928572i | \(-0.378963\pi\) | ||||
0.371152 | + | 0.928572i | \(0.378963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14905.4 | −0.631311 | −0.315655 | − | 0.948874i | \(-0.602224\pi\) | ||||
−0.315655 | + | 0.948874i | \(0.602224\pi\) | |||||||
\(824\) | 44375.4 | 1.87608 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29123.5 | −1.22458 | −0.612288 | − | 0.790635i | \(-0.709751\pi\) | ||||
−0.612288 | + | 0.790635i | \(0.709751\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9272.75 | −0.388487 | −0.194244 | − | 0.980953i | \(-0.562225\pi\) | ||||
−0.194244 | + | 0.980953i | \(0.562225\pi\) | |||||||
\(830\) | 28915.8 | 1.20926 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22963.7 | −0.956879 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10273.2 | −0.425769 | ||||||||
\(836\) | −6140.13 | −0.254020 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33214.6 | 1.36919 | ||||||||
\(839\) | −20794.4 | −0.855664 | −0.427832 | − | 0.903858i | \(-0.640723\pi\) | ||||
−0.427832 | + | 0.903858i | \(0.640723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16772.7 | −0.687717 | ||||||||
\(842\) | 62410.3 | 2.55439 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22603.9 | 0.921869 | ||||||||
\(845\) | 38.3944 | 0.00156309 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10019.8 | 0.405755 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5488.94 | 0.221493 | ||||||||
\(851\) | 5953.02 | 0.239797 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31567.2 | −1.26711 | −0.633553 | − | 0.773699i | \(-0.718404\pi\) | ||||
−0.633553 | + | 0.773699i | \(0.718404\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10517.4 | 0.419948 | ||||||||
\(857\) | 21907.7 | 0.873223 | 0.436612 | − | 0.899650i | \(-0.356178\pi\) | ||||
0.436612 | + | 0.899650i | \(0.356178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12141.1 | 0.482247 | 0.241124 | − | 0.970494i | \(-0.422484\pi\) | ||||
0.241124 | + | 0.970494i | \(0.422484\pi\) | |||||||
\(860\) | −11538.0 | −0.457491 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 41638.7 | 1.64527 | ||||||||
\(863\) | 7598.88 | 0.299732 | 0.149866 | − | 0.988706i | \(-0.452116\pi\) | ||||
0.149866 | + | 0.988706i | \(0.452116\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16396.9 | −0.644523 | ||||||||
\(866\) | −66015.4 | −2.59041 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3083.96 | 0.120387 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32807.9 | 1.27630 | ||||||||
\(872\) | −49707.2 | −1.93039 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6142.90 | 0.237742 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5560.67 | 0.214105 | 0.107053 | − | 0.994253i | \(-0.465859\pi\) | ||||
0.107053 | + | 0.994253i | \(0.465859\pi\) | |||||||
\(878\) | −58392.7 | −2.24449 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4010.27 | 0.153621 | ||||||||
\(881\) | −37010.1 | −1.41532 | −0.707662 | − | 0.706551i | \(-0.750250\pi\) | ||||
−0.707662 | + | 0.706551i | \(0.750250\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38430.3 | 1.46465 | 0.732323 | − | 0.680958i | \(-0.238436\pi\) | ||||
0.732323 | + | 0.680958i | \(0.238436\pi\) | |||||||
\(884\) | 33833.4 | 1.28726 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 54601.8 | 2.07041 | ||||||||
\(887\) | 21019.9 | 0.795694 | 0.397847 | − | 0.917452i | \(-0.369758\pi\) | ||||
0.397847 | + | 0.917452i | \(0.369758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24799.1 | 0.934007 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17907.6 | 0.672188 | ||||||||
\(893\) | −2818.73 | −0.105627 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16437.9 | −0.613921 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −69133.3 | −2.56905 | ||||||||
\(899\) | 26593.2 | 0.986576 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6703.53 | 0.247866 | ||||||||
\(902\) | 16676.4 | 0.615590 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −81098.5 | −2.98373 | ||||||||
\(905\) | −13546.3 | −0.497564 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14566.9 | −0.533281 | −0.266641 | − | 0.963796i | \(-0.585914\pi\) | ||||
−0.266641 | + | 0.963796i | \(0.585914\pi\) | |||||||
\(908\) | 27647.5 | 1.01048 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 329.028 | 0.0119662 | 0.00598309 | − | 0.999982i | \(-0.498096\pi\) | ||||
0.00598309 | + | 0.999982i | \(0.498096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14134.0 | 0.512342 | ||||||||
\(914\) | −32201.4 | −1.16535 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15055.6 | 0.543070 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26414.9 | −0.948147 | −0.474073 | − | 0.880485i | \(-0.657217\pi\) | ||||
−0.474073 | + | 0.880485i | \(0.657217\pi\) | |||||||
\(920\) | −7854.54 | −0.281474 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25328.8 | 0.904729 | ||||||||
\(923\) | −13682.4 | −0.487932 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3776.53 | −0.134239 | ||||||||
\(926\) | −29805.0 | −1.05772 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 809.163 | 0.0286229 | ||||||||
\(929\) | −18244.8 | −0.644342 | −0.322171 | − | 0.946682i | \(-0.604413\pi\) | ||||
−0.322171 | + | 0.946682i | \(0.604413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −57781.8 | −2.03080 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 80298.5 | 2.81311 | ||||||||
\(935\) | 2682.99 | 0.0938430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 140.951 | 0.00491427 | 0.00245713 | − | 0.999997i | \(-0.499218\pi\) | ||||
0.00245713 | + | 0.999997i | \(0.499218\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7156.24 | 0.248309 | ||||||||
\(941\) | −21674.8 | −0.750879 | −0.375440 | − | 0.926847i | \(-0.622508\pi\) | ||||
−0.375440 | + | 0.926847i | \(0.622508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11149.6 | −0.385027 | ||||||||
\(944\) | −47641.9 | −1.64260 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8439.15 | −0.290043 | ||||||||
\(947\) | −22150.2 | −0.760069 | −0.380035 | − | 0.924972i | \(-0.624088\pi\) | ||||
−0.380035 | + | 0.924972i | \(0.624088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22361.4 | 0.764893 | ||||||||
\(950\) | −3896.99 | −0.133089 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15980.9 | −0.543203 | −0.271602 | − | 0.962410i | \(-0.587553\pi\) | ||||
−0.271602 | + | 0.962410i | \(0.587553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10533.4 | −0.356916 | ||||||||
\(956\) | 95815.1 | 3.24151 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −45894.2 | −1.54778 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63062.3 | 2.11682 | ||||||||
\(962\) | −34832.8 | −1.16742 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 90366.8 | 3.01921 | ||||||||
\(965\) | 19783.4 | 0.659947 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13804.2 | −0.459064 | −0.229532 | − | 0.973301i | \(-0.573720\pi\) | ||||
−0.229532 | + | 0.973301i | \(0.573720\pi\) | |||||||
\(968\) | −47314.8 | −1.57103 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28217.2 | −0.934020 | ||||||||
\(971\) | 24806.1 | 0.819841 | 0.409921 | − | 0.912121i | \(-0.365556\pi\) | ||||
0.409921 | + | 0.912121i | \(0.365556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3185.10 | −0.104781 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4345.95 | 0.142531 | ||||||||
\(977\) | 2069.03 | 0.0677524 | 0.0338762 | − | 0.999426i | \(-0.489215\pi\) | ||||
0.0338762 | + | 0.999426i | \(0.489215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12121.8 | 0.395724 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 79114.2 | 2.57091 | ||||||||
\(983\) | −22474.1 | −0.729210 | −0.364605 | − | 0.931162i | \(-0.618796\pi\) | ||||
−0.364605 | + | 0.931162i | \(0.618796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9460.80 | −0.306037 | ||||||||
\(986\) | 19161.1 | 0.618877 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24020.7 | −0.773484 | ||||||||
\(989\) | 5642.31 | 0.181410 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40924.6 | 1.31182 | 0.655910 | − | 0.754839i | \(-0.272285\pi\) | ||||
0.655910 | + | 0.754839i | \(0.272285\pi\) | |||||||
\(992\) | 2825.29 | 0.0904265 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22111.1 | 0.704492 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60402.8 | 1.91873 | 0.959366 | − | 0.282164i | \(-0.0910522\pi\) | ||||
0.959366 | + | 0.282164i | \(0.0910522\pi\) | |||||||
\(998\) | 31219.7 | 0.990224 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2205.4.a.by.1.6 | yes | 6 | |
3.2 | odd | 2 | 2205.4.a.bx.1.1 | ✓ | 6 | ||
7.6 | odd | 2 | 2205.4.a.bx.1.6 | yes | 6 | ||
21.20 | even | 2 | inner | 2205.4.a.by.1.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2205.4.a.bx.1.1 | ✓ | 6 | 3.2 | odd | 2 | ||
2205.4.a.bx.1.6 | yes | 6 | 7.6 | odd | 2 | ||
2205.4.a.by.1.1 | yes | 6 | 21.20 | even | 2 | inner | |
2205.4.a.by.1.6 | yes | 6 | 1.1 | even | 1 | trivial |