Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 60 \) |
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 | 1.1 | ||
Root | \(8.26209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2621 | −0.554101 | −0.277050 | − | 0.960855i | \(-0.589357\pi\) | ||||
−0.277050 | + | 0.960855i | \(0.589357\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.26209 | 0.144234 | 0.0721172 | − | 0.997396i | \(-0.477024\pi\) | ||||
0.0721172 | + | 0.997396i | \(0.477024\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.5725 | 0.737592 | 0.368796 | − | 0.929510i | \(-0.379770\pi\) | ||||
0.368796 | + | 0.929510i | \(0.379770\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −74.8346 | −1.06765 | −0.533825 | − | 0.845595i | \(-0.679246\pi\) | ||||
−0.533825 | + | 0.845595i | \(0.679246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.8830 | −0.614387 | −0.307193 | − | 0.951647i | \(-0.599390\pi\) | ||||
−0.307193 | + | 0.951647i | \(0.599390\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 81.4555 | 0.738463 | 0.369231 | − | 0.929338i | \(-0.379621\pi\) | ||||
0.369231 | + | 0.929338i | \(0.379621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −152.407 | −0.975907 | −0.487953 | − | 0.872870i | \(-0.662256\pi\) | ||||
−0.487953 | + | 0.872870i | \(0.662256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 93.9797 | 0.544492 | 0.272246 | − | 0.962228i | \(-0.412234\pi\) | ||||
0.272246 | + | 0.962228i | \(0.412234\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −51.3104 | −0.247801 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −167.310 | −0.743396 | −0.371698 | − | 0.928354i | \(-0.621224\pi\) | ||||
−0.371698 | + | 0.928354i | \(0.621224\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.6209 | −0.0709291 | −0.0354645 | − | 0.999371i | \(-0.511291\pi\) | ||||
−0.0354645 | + | 0.999371i | \(0.511291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 133.552 | 0.473640 | 0.236820 | − | 0.971554i | \(-0.423895\pi\) | ||||
0.236820 | + | 0.971554i | \(0.423895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −46.8346 | −0.145352 | −0.0726759 | − | 0.997356i | \(-0.523154\pi\) | ||||
−0.0726759 | + | 0.997356i | \(0.523154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −237.690 | −0.692972 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 105.104 | 0.272400 | 0.136200 | − | 0.990681i | \(-0.456511\pi\) | ||||
0.136200 | + | 0.990681i | \(0.456511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.3104 | 0.0645036 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 77.7099 | 0.171474 | 0.0857370 | − | 0.996318i | \(-0.472676\pi\) | ||||
0.0857370 | + | 0.996318i | \(0.472676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.6896 | −0.102198 | −0.0510989 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510989 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 172.863 | 0.329861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −667.132 | −1.21647 | −0.608233 | − | 0.793759i | \(-0.708121\pi\) | ||||
−0.608233 | + | 0.793759i | \(0.708121\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 344.056 | 0.575098 | 0.287549 | − | 0.957766i | \(-0.407160\pi\) | ||||
0.287549 | + | 0.957766i | \(0.407160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1074.70 | −1.72308 | −0.861539 | − | 0.507691i | \(-0.830499\pi\) | ||||
−0.861539 | + | 0.507691i | \(0.830499\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −54.0000 | −0.0799204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −420.863 | −0.599377 | −0.299688 | − | 0.954037i | \(-0.596883\pi\) | ||||
−0.299688 | + | 0.954037i | \(0.596883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 296.565 | 0.392195 | 0.196098 | − | 0.980584i | \(-0.437173\pi\) | ||||
0.196098 | + | 0.980584i | \(0.437173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −374.173 | −0.477468 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −950.596 | −1.13217 | −0.566084 | − | 0.824348i | \(-0.691542\pi\) | ||||
−0.566084 | + | 0.824348i | \(0.691542\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −354.786 | −0.408700 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −254.415 | −0.274762 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −135.916 | −0.142270 | −0.0711349 | − | 0.997467i | \(-0.522662\pi\) | ||||
−0.0711349 | + | 0.997467i | \(0.522662\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 392.463 | 0.386649 | 0.193324 | − | 0.981135i | \(-0.438073\pi\) | ||||
0.193324 | + | 0.981135i | \(0.438073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −799.117 | −0.764460 | −0.382230 | − | 0.924067i | \(-0.624844\pi\) | ||||
−0.382230 | + | 0.924067i | \(0.624844\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −374.000 | −0.337906 | −0.168953 | − | 0.985624i | \(-0.554039\pi\) | ||||
−0.168953 | + | 0.985624i | \(0.554039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 428.361 | 0.376418 | 0.188209 | − | 0.982129i | \(-0.439732\pi\) | ||||
0.188209 | + | 0.982129i | \(0.439732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −125.649 | −0.104602 | −0.0523011 | − | 0.998631i | \(-0.516656\pi\) | ||||
−0.0523011 | + | 0.998631i | \(0.516656\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 407.277 | 0.330251 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 767.959 | 0.591586 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1303.31 | −0.979196 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 358.830 | 0.250716 | 0.125358 | − | 0.992112i | \(-0.459992\pi\) | ||||
0.125358 | + | 0.992112i | \(0.459992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2084.15 | 1.39002 | 0.695011 | − | 0.718999i | \(-0.255400\pi\) | ||||
0.695011 | + | 0.718999i | \(0.255400\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 522.165 | 0.340432 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −575.517 | −0.358903 | −0.179451 | − | 0.983767i | \(-0.557432\pi\) | ||||
−0.179451 | + | 0.983767i | \(0.557432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −890.287 | −0.543260 | −0.271630 | − | 0.962402i | \(-0.587563\pi\) | ||||
−0.271630 | + | 0.962402i | \(0.587563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 181.924 | 0.106386 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −762.036 | −0.436439 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1361.89 | 0.748794 | 0.374397 | − | 0.927269i | \(-0.377850\pi\) | ||||
0.374397 | + | 0.927269i | \(0.377850\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3154.72 | −1.70018 | −0.850090 | − | 0.526638i | \(-0.823452\pi\) | ||||
−0.850090 | + | 0.526638i | \(0.823452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 469.898 | 0.243504 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1876.99 | −0.954139 | −0.477070 | − | 0.878865i | \(-0.658301\pi\) | ||||
−0.477070 | + | 0.878865i | \(0.658301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −835.903 | −0.409183 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1058.19 | −0.508488 | −0.254244 | − | 0.967140i | \(-0.581827\pi\) | ||||
−0.254244 | + | 0.967140i | \(0.581827\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2391.59 | −1.10819 | −0.554093 | − | 0.832455i | \(-0.686935\pi\) | ||||
−0.554093 | + | 0.832455i | \(0.686935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1001.74 | −0.455958 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3957.46 | −1.73919 | −0.869595 | − | 0.493766i | \(-0.835620\pi\) | ||||
−0.869595 | + | 0.493766i | \(0.835620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −256.552 | −0.110820 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1236.91 | 0.516486 | 0.258243 | − | 0.966080i | \(-0.416856\pi\) | ||||
0.258243 | + | 0.966080i | \(0.416856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −361.061 | −0.148273 | −0.0741366 | − | 0.997248i | \(-0.523620\pi\) | ||||
−0.0741366 | + | 0.997248i | \(0.523620\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −836.552 | −0.332457 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −393.786 | −0.153992 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −575.135 | −0.217881 | −0.108941 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108941 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1755.28 | −0.654652 | −0.327326 | − | 0.944912i | \(-0.606147\pi\) | ||||
−0.327326 | + | 0.944912i | \(0.606147\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2182.56 | −0.789347 | −0.394673 | − | 0.918821i | \(-0.629142\pi\) | ||||
−0.394673 | + | 0.918821i | \(0.629142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2946.07 | −1.04945 | −0.524727 | − | 0.851271i | \(-0.675833\pi\) | ||||
−0.524727 | + | 0.851271i | \(0.675833\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1564.02 | 0.540751 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −93.1044 | −0.0317204 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −267.751 | −0.0886158 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2081.63 | −0.679171 | −0.339585 | − | 0.940575i | \(-0.610287\pi\) | ||||
−0.339585 | + | 0.940575i | \(0.610287\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 667.761 | 0.211818 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −964.427 | −0.301703 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2587.22 | −0.787490 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 591.288 | 0.177559 | 0.0887793 | − | 0.996051i | \(-0.471703\pi\) | ||||
0.0887793 | + | 0.996051i | \(0.471703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4369.86 | 1.27770 | 0.638849 | − | 0.769332i | \(-0.279411\pi\) | ||||
0.638849 | + | 0.769332i | \(0.279411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3580.09 | −1.03310 | −0.516548 | − | 0.856258i | \(-0.672783\pi\) | ||||
−0.516548 | + | 0.856258i | \(0.672783\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3853.73 | 1.08355 | 0.541773 | − | 0.840525i | \(-0.317753\pi\) | ||||
0.541773 | + | 0.840525i | \(0.317753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −234.173 | −0.0650033 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2519.71 | 0.681952 | 0.340976 | − | 0.940072i | \(-0.389243\pi\) | ||||
0.340976 | + | 0.940072i | \(0.389243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3498.30 | 0.935044 | 0.467522 | − | 0.883982i | \(-0.345147\pi\) | ||||
0.467522 | + | 0.883982i | \(0.345147\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1188.45 | −0.309907 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1759.15 | −0.453167 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1298.83 | −0.326619 | −0.163310 | − | 0.986575i | \(-0.552217\pi\) | ||||
−0.163310 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 428.626 | 0.106512 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4682.87 | −1.13661 | −0.568306 | − | 0.822818i | \(-0.692401\pi\) | ||||
−0.568306 | + | 0.822818i | \(0.692401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1716.95 | 0.411916 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4137.19 | 0.970000 | 0.485000 | − | 0.874514i | \(-0.338820\pi\) | ||||
0.485000 | + | 0.874514i | \(0.338820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 525.522 | 0.121821 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 851.771 | 0.193061 | 0.0965305 | − | 0.995330i | \(-0.469225\pi\) | ||||
0.0965305 | + | 0.995330i | \(0.469225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3045.15 | 0.682581 | 0.341291 | − | 0.939958i | \(-0.389136\pi\) | ||||
0.341291 | + | 0.939958i | \(0.389136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 131.552 | 0.0288469 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1512.69 | −0.328118 | −0.164059 | − | 0.986451i | \(-0.552459\pi\) | ||||
−0.164059 | + | 0.986451i | \(0.552459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1158.06 | −0.245850 | −0.122925 | − | 0.992416i | \(-0.539227\pi\) | ||||
−0.122925 | + | 0.992416i | \(0.539227\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8650.56 | −1.81704 | −0.908520 | − | 0.417842i | \(-0.862787\pi\) | ||||
−0.908520 | + | 0.417842i | \(0.862787\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 191.089 | 0.0393018 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 687.219 | 0.139878 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5920.13 | −1.18040 | −0.590201 | − | 0.807257i | \(-0.700951\pi\) | ||||
−0.590201 | + | 0.807257i | \(0.700951\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 388.550 | 0.0766855 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2816.12 | 0.544684 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1370.52 | −0.262444 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −243.448 | −0.0457042 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1906.71 | 0.354469 | 0.177234 | − | 0.984169i | \(-0.443285\pi\) | ||||
0.177234 | + | 0.984169i | \(0.443285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6750.08 | 1.23075 | 0.615373 | − | 0.788236i | \(-0.289006\pi\) | ||||
0.615373 | + | 0.788236i | \(0.289006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2225.44 | 0.401883 | 0.200942 | − | 0.979603i | \(-0.435600\pi\) | ||||
0.200942 | + | 0.979603i | \(0.435600\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7761.66 | −1.37520 | −0.687600 | − | 0.726090i | \(-0.741336\pi\) | ||||
−0.687600 | + | 0.726090i | \(0.741336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −801.980 | −0.140759 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3807.81 | 0.655951 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 864.313 | 0.147518 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 480.621 | 0.0805395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6513.99 | 1.08170 | 0.540848 | − | 0.841121i | \(-0.318104\pi\) | ||||
0.540848 | + | 0.841121i | \(0.318104\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3335.66 | −0.544020 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3625.89 | −0.586097 | −0.293049 | − | 0.956098i | \(-0.594670\pi\) | ||||
−0.293049 | + | 0.956098i | \(0.594670\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 494.529 | 0.0785345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5959.09 | 0.938077 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4830.55 | 0.747313 | 0.373656 | − | 0.927567i | \(-0.378104\pi\) | ||||
0.373656 | + | 0.927567i | \(0.378104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9300.98 | 1.42656 | 0.713281 | − | 0.700878i | \(-0.247208\pi\) | ||||
0.713281 | + | 0.700878i | \(0.247208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7446.44 | 1.12276 | 0.561380 | − | 0.827558i | \(-0.310271\pi\) | ||||
0.561380 | + | 0.827558i | \(0.310271\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1720.28 | 0.257192 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5872.73 | 0.863373 | 0.431686 | − | 0.902024i | \(-0.357919\pi\) | ||||
0.431686 | + | 0.902024i | \(0.357919\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4269.92 | −0.622529 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5373.52 | −0.770584 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8708.80 | 1.23868 | 0.619340 | − | 0.785123i | \(-0.287400\pi\) | ||||
0.619340 | + | 0.785123i | \(0.287400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1078.59 | −0.150937 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4355.98 | 0.604676 | 0.302338 | − | 0.953201i | \(-0.402233\pi\) | ||||
0.302338 | + | 0.953201i | \(0.402233\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5269.10 | −0.719821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5116.37 | 0.693431 | 0.346716 | − | 0.937970i | \(-0.387297\pi\) | ||||
0.346716 | + | 0.937970i | \(0.387297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2906.74 | 0.387801 | 0.193900 | − | 0.981021i | \(-0.437886\pi\) | ||||
0.193900 | + | 0.981021i | \(0.437886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −270.000 | −0.0357415 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1446.15 | −0.188491 | −0.0942453 | − | 0.995549i | \(-0.530044\pi\) | ||||
−0.0942453 | + | 0.995549i | \(0.530044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6095.69 | −0.788420 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2104.31 | −0.268049 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1377.59 | 0.174154 | 0.0870770 | − | 0.996202i | \(-0.472247\pi\) | ||||
0.0870770 | + | 0.996202i | \(0.472247\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6094.96 | −0.759022 | −0.379511 | − | 0.925187i | \(-0.623908\pi\) | ||||
−0.379511 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3249.11 | 0.401613 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −880.402 | −0.107223 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10329.4 | −1.24879 | −0.624394 | − | 0.781109i | \(-0.714654\pi\) | ||||
−0.624394 | + | 0.781109i | \(0.714654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −797.466 | −0.0950139 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1482.82 | 0.175395 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7525.80 | 0.877468 | 0.438734 | − | 0.898617i | \(-0.355427\pi\) | ||||
0.438734 | + | 0.898617i | \(0.355427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9532.73 | 1.10356 | 0.551778 | − | 0.833991i | \(-0.313950\pi\) | ||||
0.551778 | + | 0.833991i | \(0.313950\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1870.87 | −0.213530 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 499.657 | 0.0566278 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1909.54 | −0.213409 | −0.106705 | − | 0.994291i | \(-0.534030\pi\) | ||||
−0.106705 | + | 0.994291i | \(0.534030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7780.10 | 0.863482 | 0.431741 | − | 0.901998i | \(-0.357899\pi\) | ||||
0.431741 | + | 0.901998i | \(0.357899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4144.70 | −0.453702 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11480.5 | 1.24815 | 0.624074 | − | 0.781365i | \(-0.285476\pi\) | ||||
0.624074 | + | 0.781365i | \(0.285476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1562.80 | −0.167609 | −0.0838046 | − | 0.996482i | \(-0.526707\pi\) | ||||
−0.0838046 | + | 0.996482i | \(0.526707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4752.98 | −0.506321 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7086.91 | 0.744882 | 0.372441 | − | 0.928056i | \(-0.378521\pi\) | ||||
0.372441 | + | 0.928056i | \(0.378521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −97.9847 | −0.0102304 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1773.93 | −0.182776 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14548.5 | 1.48917 | 0.744587 | − | 0.667526i | \(-0.232647\pi\) | ||||
0.744587 | + | 0.667526i | \(0.232647\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2272.13 | −0.229553 | −0.114776 | − | 0.993391i | \(-0.536615\pi\) | ||||
−0.114776 | + | 0.993391i | \(0.536615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2757.88 | −0.276824 | −0.138412 | − | 0.990375i | \(-0.544200\pi\) | ||||
−0.138412 | + | 0.990375i | \(0.544200\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17714.6 | −1.75532 | −0.877661 | − | 0.479282i | \(-0.840897\pi\) | ||||
−0.877661 | + | 0.479282i | \(0.840897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6846.17 | 0.674044 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 702.763 | 0.0683152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1272.07 | −0.122877 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9413.68 | 0.897959 | 0.448979 | − | 0.893542i | \(-0.351788\pi\) | ||||
0.448979 | + | 0.893542i | \(0.351788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5784.34 | −0.548323 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −679.580 | −0.0636250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4065.97 | −0.378330 | −0.189165 | − | 0.981945i | \(-0.560578\pi\) | ||||
−0.189165 | + | 0.981945i | \(0.560578\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8984.27 | 0.825773 | 0.412886 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412886 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11405.3 | 1.04193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3530.73 | −0.318662 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4151.04 | 0.372397 | 0.186199 | − | 0.982512i | \(-0.440383\pi\) | ||||
0.186199 | + | 0.982512i | \(0.440383\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2721.08 | 0.241207 | 0.120603 | − | 0.992701i | \(-0.461517\pi\) | ||||
0.120603 | + | 0.992701i | \(0.461517\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1962.32 | 0.172915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6571.92 | −0.572289 | −0.286145 | − | 0.958186i | \(-0.592374\pi\) | ||||
−0.286145 | + | 0.958186i | \(0.592374\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11028.7 | 0.954759 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3995.59 | −0.341877 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −246.448 | −0.0209647 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4049.20 | 0.340496 | 0.170248 | − | 0.985401i | \(-0.445543\pi\) | ||||
0.170248 | + | 0.985401i | \(0.445543\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3872.83 | −0.323799 | −0.161900 | − | 0.986807i | \(-0.551762\pi\) | ||||
−0.161900 | + | 0.986807i | \(0.551762\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7032.93 | −0.581327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5532.00 | −0.454673 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −643.771 | −0.0523167 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1870.00 | −0.151116 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1250.74 | −0.0999505 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5476.29 | 0.435202 | 0.217601 | − | 0.976038i | \(-0.430177\pi\) | ||||
0.217601 | + | 0.976038i | \(0.430177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2141.81 | 0.168339 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15867.7 | 1.24032 | 0.620158 | − | 0.784477i | \(-0.287068\pi\) | ||||
0.620158 | + | 0.784477i | \(0.287068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7754.93 | 0.599584 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4318.93 | 0.332115 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6121.57 | −0.465672 | −0.232836 | − | 0.972516i | \(-0.574800\pi\) | ||||
−0.232836 | + | 0.972516i | \(0.574800\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4617.24 | 0.349353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7405.33 | 0.554347 | 0.277174 | − | 0.960820i | \(-0.410602\pi\) | ||||
0.277174 | + | 0.960820i | \(0.410602\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −628.244 | −0.0467795 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20196.3 | 1.48800 | 0.744000 | − | 0.668180i | \(-0.232926\pi\) | ||||
0.744000 | + | 0.668180i | \(0.232926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5341.83 | 0.391504 | 0.195752 | − | 0.980653i | \(-0.437285\pi\) | ||||
0.195752 | + | 0.980653i | \(0.437285\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2036.39 | 0.147693 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21443.1 | 1.54712 | 0.773561 | − | 0.633722i | \(-0.218474\pi\) | ||||
0.773561 | + | 0.633722i | \(0.218474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3043.37 | −0.217316 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 553.068 | 0.0392895 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18441.6 | −1.29670 | −0.648352 | − | 0.761341i | \(-0.724541\pi\) | ||||
−0.648352 | + | 0.761341i | \(0.724541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4781.96 | −0.334529 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6213.39 | 0.430276 | 0.215138 | − | 0.976584i | \(-0.430980\pi\) | ||||
0.215138 | + | 0.976584i | \(0.430980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3839.80 | 0.264565 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22782.0 | 1.55400 | 0.777000 | − | 0.629501i | \(-0.216741\pi\) | ||||
0.777000 | + | 0.629501i | \(0.216741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14788.6 | 1.00373 | 0.501865 | − | 0.864946i | \(-0.332648\pi\) | ||||
0.501865 | + | 0.864946i | \(0.332648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6516.55 | −0.437910 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18559.8 | −1.24105 | −0.620525 | − | 0.784186i | \(-0.713081\pi\) | ||||
−0.620525 | + | 0.784186i | \(0.713081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1619.19 | −0.107210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2519.83 | 0.166028 | 0.0830138 | − | 0.996548i | \(-0.473545\pi\) | ||||
0.0830138 | + | 0.996548i | \(0.473545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11012.6 | −0.718561 | −0.359281 | − | 0.933230i | \(-0.616978\pi\) | ||||
−0.359281 | + | 0.933230i | \(0.616978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19538.6 | 1.26870 | 0.634349 | − | 0.773047i | \(-0.281268\pi\) | ||||
0.634349 | + | 0.773047i | \(0.281268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9755.09 | 0.627335 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12520.6 | 0.793688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8676.78 | 0.547412 | 0.273706 | − | 0.961813i | \(-0.411750\pi\) | ||||
0.273706 | + | 0.961813i | \(0.411750\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1794.15 | 0.112124 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8217.53 | −0.511131 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7988.18 | −0.492222 | −0.246111 | − | 0.969242i | \(-0.579153\pi\) | ||||
−0.246111 | + | 0.969242i | \(0.579153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2200.43 | −0.134956 | −0.0674779 | − | 0.997721i | \(-0.521495\pi\) | ||||
−0.0674779 | + | 0.997721i | \(0.521495\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31423.1 | −1.90938 | −0.954691 | − | 0.297597i | \(-0.903815\pi\) | ||||
−0.954691 | + | 0.297597i | \(0.903815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 408.916 | 0.0247325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8769.09 | −0.525515 | −0.262757 | − | 0.964862i | \(-0.584632\pi\) | ||||
−0.262757 | + | 0.964862i | \(0.584632\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10420.7 | 0.621637 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28986.3 | 1.71342 | 0.856712 | − | 0.515795i | \(-0.172503\pi\) | ||||
0.856712 | + | 0.515795i | \(0.172503\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3755.04 | 0.220959 | 0.110480 | − | 0.993878i | \(-0.464761\pi\) | ||||
0.110480 | + | 0.993878i | \(0.464761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2610.83 | 0.152246 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12414.4 | −0.720671 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −256.209 | −0.0147404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3404.61 | 0.195004 | 0.0975022 | − | 0.995235i | \(-0.468915\pi\) | ||||
0.0975022 | + | 0.995235i | \(0.468915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21691.9 | −1.23144 | −0.615721 | − | 0.787964i | \(-0.711135\pi\) | ||||
−0.615721 | + | 0.787964i | \(0.711135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1394.78 | 0.0788318 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6003.49 | 0.336335 | 0.168168 | − | 0.985758i | \(-0.446215\pi\) | ||||
0.168168 | + | 0.985758i | \(0.446215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2877.58 | −0.160506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3633.72 | 0.200920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22090.1 | −1.21613 | −0.608065 | − | 0.793887i | \(-0.708054\pi\) | ||||
−0.608065 | + | 0.793887i | \(0.708054\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4451.44 | −0.242953 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1393.49 | 0.0757275 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24940.0 | 1.34375 | 0.671876 | − | 0.740663i | \(-0.265489\pi\) | ||||
0.671876 | + | 0.740663i | \(0.265489\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8513.25 | 0.456733 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4027.49 | −0.214242 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20007.0 | −1.05977 | −0.529886 | − | 0.848069i | \(-0.677765\pi\) | ||||
−0.529886 | + | 0.848069i | \(0.677765\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7655.16 | 0.402087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 909.618 | 0.0475773 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16188.8 | −0.839692 | −0.419846 | − | 0.907595i | \(-0.637916\pi\) | ||||
−0.419846 | + | 0.907595i | \(0.637916\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8200.61 | 0.423588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3810.18 | −0.195181 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7264.04 | −0.370575 | −0.185288 | − | 0.982684i | \(-0.559322\pi\) | ||||
−0.185288 | + | 0.982684i | \(0.559322\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9994.33 | −0.505682 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27522.4 | −1.38685 | −0.693426 | − | 0.720528i | \(-0.743900\pi\) | ||||
−0.693426 | + | 0.720528i | \(0.743900\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3510.51 | −0.175456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2936.48 | −0.146171 | −0.0730853 | − | 0.997326i | \(-0.523285\pi\) | ||||
−0.0730853 | + | 0.997326i | \(0.523285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8395.29 | 0.414527 | 0.207263 | − | 0.978285i | \(-0.433544\pi\) | ||||
0.207263 | + | 0.978285i | \(0.433544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6809.44 | 0.334871 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3838.02 | 0.187234 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35222.9 | −1.71145 | −0.855727 | − | 0.517428i | \(-0.826890\pi\) | ||||
−0.855727 | + | 0.517428i | \(0.826890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15773.6 | −0.760343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1328.71 | −0.0637952 | −0.0318976 | − | 0.999491i | \(-0.510155\pi\) | ||||
−0.0318976 | + | 0.999491i | \(0.510155\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39056.4 | 1.86044 | 0.930220 | − | 0.367003i | \(-0.119616\pi\) | ||||
0.930220 | + | 0.367003i | \(0.119616\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4395.88 | −0.208574 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2686.63 | 0.126478 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10509.2 | −0.492813 | −0.246406 | − | 0.969167i | \(-0.579250\pi\) | ||||
−0.246406 | + | 0.969167i | \(0.579250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20180.8 | 0.939009 | 0.469505 | − | 0.882930i | \(-0.344433\pi\) | ||||
0.469505 | + | 0.882930i | \(0.344433\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2349.49 | 0.108898 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 947.485 | 0.0435779 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1810.45 | 0.0829489 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9384.94 | −0.426704 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19486.2 | −0.882604 | −0.441302 | − | 0.897359i | \(-0.645483\pi\) | ||||
−0.441302 | + | 0.897359i | \(0.645483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1289.42 | 0.0579602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1683.32 | −0.0753802 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38955.5 | −1.73134 | −0.865668 | − | 0.500619i | \(-0.833106\pi\) | ||||
−0.865668 | + | 0.500619i | \(0.833106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3504.85 | 0.155185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5655.19 | −0.248527 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4179.52 | −0.182992 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41073.8 | 1.78501 | 0.892507 | − | 0.451033i | \(-0.148944\pi\) | ||||
0.892507 | + | 0.451033i | \(0.148944\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7397.33 | 0.320290 | 0.160145 | − | 0.987093i | \(-0.448804\pi\) | ||||
0.160145 | + | 0.987093i | \(0.448804\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5290.93 | −0.227403 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6795.53 | −0.290998 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20477.0 | −0.870465 | −0.435233 | − | 0.900318i | \(-0.643334\pi\) | ||||
−0.435233 | + | 0.900318i | \(0.643334\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12109.6 | −0.512896 | −0.256448 | − | 0.966558i | \(-0.582552\pi\) | ||||
−0.256448 | + | 0.966558i | \(0.582552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34564.6 | −1.45336 | −0.726680 | − | 0.686976i | \(-0.758938\pi\) | ||||
−0.726680 | + | 0.686976i | \(0.758938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34571.8 | −1.44841 | −0.724203 | − | 0.689587i | \(-0.757792\pi\) | ||||
−0.724203 | + | 0.689587i | \(0.757792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17787.4 | 0.739852 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11958.0 | −0.495596 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13192.9 | −0.542870 | −0.271435 | − | 0.962457i | \(-0.587498\pi\) | ||||
−0.271435 | + | 0.962457i | \(0.587498\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1161.07 | −0.0476061 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5008.70 | −0.203911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13374.7 | 0.542573 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13628.4 | −0.548971 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25796.2 | 1.03546 | 0.517729 | − | 0.855545i | \(-0.326778\pi\) | ||||
0.517729 | + | 0.855545i | \(0.326778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26349.2 | 1.05026 | 0.525130 | − | 0.851022i | \(-0.324017\pi\) | ||||
0.525130 | + | 0.851022i | \(0.324017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13466.3 | 0.534884 | 0.267442 | − | 0.963574i | \(-0.413822\pi\) | ||||
0.267442 | + | 0.963574i | \(0.413822\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44430.9 | −1.75254 | −0.876272 | − | 0.481816i | \(-0.839977\pi\) | ||||
−0.876272 | + | 0.481816i | \(0.839977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19787.3 | −0.777789 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2214.62 | −0.0864507 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23064.5 | −0.897255 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1282.76 | −0.0495603 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13993.4 | 0.538797 | 0.269398 | − | 0.963029i | \(-0.413175\pi\) | ||||
0.269398 | + | 0.963029i | \(0.413175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49227.2 | 1.88253 | 0.941264 | − | 0.337672i | \(-0.109639\pi\) | ||||
0.941264 | + | 0.337672i | \(0.109639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44724.5 | −1.70453 | −0.852264 | − | 0.523112i | \(-0.824771\pi\) | ||||
−0.852264 | + | 0.523112i | \(0.824771\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20387.9 | −0.771769 | −0.385885 | − | 0.922547i | \(-0.626104\pi\) | ||||
−0.385885 | + | 0.922547i | \(0.626104\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3682.34 | −0.138922 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2383.08 | 0.0893022 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6184.55 | 0.230980 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14323.2 | −0.531373 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7865.44 | −0.290828 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1805.31 | −0.0663098 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19788.7 | 0.724446 | 0.362223 | − | 0.932091i | \(-0.382018\pi\) | ||||
0.362223 | + | 0.932091i | \(0.382018\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11895.2 | −0.432607 | −0.216304 | − | 0.976326i | \(-0.569400\pi\) | ||||
−0.216304 | + | 0.976326i | \(0.569400\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1560.55 | 0.0565681 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21387.7 | −0.770212 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21020.2 | 0.754507 | 0.377253 | − | 0.926110i | \(-0.376869\pi\) | ||||
0.377253 | + | 0.926110i | \(0.376869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11894.9 | 0.424187 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4182.76 | −0.148679 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50942.1 | 1.79909 | 0.899546 | − | 0.436827i | \(-0.143898\pi\) | ||||
0.899546 | + | 0.436827i | \(0.143898\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12094.3 | 0.425753 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1968.93 | −0.0688673 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29785.2 | −1.03846 | −0.519232 | − | 0.854633i | \(-0.673782\pi\) | ||||
−0.519232 | + | 0.854633i | \(0.673782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32940.7 | −1.14116 | −0.570582 | − | 0.821240i | \(-0.693282\pi\) | ||||
−0.570582 | + | 0.821240i | \(0.693282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1516.77 | −0.0523785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14141.4 | −0.485253 | −0.242626 | − | 0.970120i | \(-0.578009\pi\) | ||||
−0.242626 | + | 0.970120i | \(0.578009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37155.3 | −1.27093 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35528.4 | 1.20764 | 0.603819 | − | 0.797122i | \(-0.293645\pi\) | ||||
0.603819 | + | 0.797122i | \(0.293645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2875.68 | −0.0974394 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5906.00 | 0.198868 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20958.8 | −0.703529 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8776.40 | −0.292769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2325.32 | 0.0773290 | 0.0386645 | − | 0.999252i | \(-0.487690\pi\) | ||||
0.0386645 | + | 0.999252i | \(0.487690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35146.5 | 1.16159 | 0.580796 | − | 0.814049i | \(-0.302741\pi\) | ||||
0.580796 | + | 0.814049i | \(0.302741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9136.21 | 0.301021 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35451.4 | −1.16089 | −0.580445 | − | 0.814299i | \(-0.697122\pi\) | ||||
−0.580445 | + | 0.814299i | \(0.697122\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5002.12 | −0.163298 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29728.4 | 0.964586 | 0.482293 | − | 0.876010i | \(-0.339804\pi\) | ||||
0.482293 | + | 0.876010i | \(0.339804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10912.8 | −0.353007 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10878.6 | 0.349765 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37667.8 | −1.20742 | −0.603712 | − | 0.797202i | \(-0.706312\pi\) | ||||
−0.603712 | + | 0.797202i | \(0.706312\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14730.3 | −0.469330 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37460.1 | −1.18994 | −0.594972 | − | 0.803746i | \(-0.702837\pi\) | ||||
−0.594972 | + | 0.803746i | \(0.702837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1080.4.a.b.1.1 | yes | 2 | |
3.2 | odd | 2 | 1080.4.a.a.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 2160.4.a.bd.1.2 | 2 | |||
12.11 | even | 2 | 2160.4.a.y.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.a.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
1080.4.a.b.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
2160.4.a.y.1.2 | 2 | 12.11 | even | 2 | |||
2160.4.a.bd.1.2 | 2 | 4.3 | odd | 2 |