Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [736,4,Mod(1,736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(736, 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("736.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 736 = 2^{5} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 736.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: | \(43.4254057642\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 137x^{6} + 344x^{5} + 6175x^{4} - 7924x^{3} - 89643x^{2} + 45072x + 51084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(9.42564\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 736.1 |
$q$-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 | ||||||||
\(3\) | 7.42564 | 1.42906 | 0.714532 | − | 0.699602i | \(-0.246639\pi\) | ||||
0.714532 | + | 0.699602i | \(0.246639\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.36302 | 0.390241 | 0.195120 | − | 0.980779i | \(-0.437490\pi\) | ||||
0.195120 | + | 0.980779i | \(0.437490\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.40153 | −0.507635 | −0.253817 | − | 0.967252i | \(-0.581686\pi\) | ||||
−0.253817 | + | 0.967252i | \(0.581686\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 28.1401 | 1.04223 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −67.5361 | −1.85117 | −0.925586 | − | 0.378538i | \(-0.876427\pi\) | ||||
−0.925586 | + | 0.378538i | \(0.876427\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −33.5730 | −0.716267 | −0.358133 | − | 0.933670i | \(-0.616587\pi\) | ||||
−0.358133 | + | 0.933670i | \(0.616587\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 32.3982 | 0.557679 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.0641 | 0.343317 | 0.171659 | − | 0.985156i | \(-0.445087\pi\) | ||||
0.171659 | + | 0.985156i | \(0.445087\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −71.4057 | −0.862189 | −0.431094 | − | 0.902307i | \(-0.641872\pi\) | ||||
−0.431094 | + | 0.902307i | \(0.641872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −69.8123 | −0.725443 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −105.964 | −0.847712 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.46606 | 0.0603442 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −96.4102 | −0.617342 | −0.308671 | − | 0.951169i | \(-0.599884\pi\) | ||||
−0.308671 | + | 0.951169i | \(0.599884\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −63.1309 | −0.365763 | −0.182881 | − | 0.983135i | \(-0.558542\pi\) | ||||
−0.182881 | + | 0.983135i | \(0.558542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −501.498 | −2.64544 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −41.0191 | −0.198100 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 84.0774 | 0.373574 | 0.186787 | − | 0.982400i | \(-0.440193\pi\) | ||||
0.186787 | + | 0.982400i | \(0.440193\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −249.301 | −1.02359 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −144.498 | −0.550411 | −0.275206 | − | 0.961385i | \(-0.588746\pi\) | ||||
−0.275206 | + | 0.961385i | \(0.588746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 75.4198 | 0.267475 | 0.133737 | − | 0.991017i | \(-0.457302\pi\) | ||||
0.133737 | + | 0.991017i | \(0.457302\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 122.776 | 0.406719 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 215.075 | 0.667486 | 0.333743 | − | 0.942664i | \(-0.391688\pi\) | ||||
0.333743 | + | 0.942664i | \(0.391688\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −254.611 | −0.742307 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 178.691 | 0.490623 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −55.0233 | −0.142604 | −0.0713021 | − | 0.997455i | \(-0.522715\pi\) | ||||
−0.0713021 | + | 0.997455i | \(0.522715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −294.661 | −0.722402 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −530.233 | −1.23212 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −139.853 | −0.308598 | −0.154299 | − | 0.988024i | \(-0.549312\pi\) | ||||
−0.154299 | + | 0.988024i | \(0.549312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 772.119 | 1.62065 | 0.810325 | − | 0.585981i | \(-0.199291\pi\) | ||||
0.810325 | + | 0.585981i | \(0.199291\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −264.560 | −0.529070 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −146.480 | −0.279516 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −871.806 | −1.58967 | −0.794836 | − | 0.606824i | \(-0.792443\pi\) | ||||
−0.794836 | + | 0.606824i | \(0.792443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 170.790 | 0.297981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 148.801 | 0.248725 | 0.124362 | − | 0.992237i | \(-0.460311\pi\) | ||||
0.124362 | + | 0.992237i | \(0.460311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 745.997 | 1.19606 | 0.598030 | − | 0.801474i | \(-0.295950\pi\) | ||||
0.598030 | + | 0.801474i | \(0.295950\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −786.851 | −1.21144 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 634.942 | 0.939719 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −461.010 | −0.656552 | −0.328276 | − | 0.944582i | \(-0.606468\pi\) | ||||
−0.328276 | + | 0.944582i | \(0.606468\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −696.917 | −0.955991 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 345.272 | 0.456609 | 0.228305 | − | 0.973590i | \(-0.426682\pi\) | ||||
0.228305 | + | 0.973590i | \(0.426682\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 104.992 | 0.133976 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −715.907 | −0.882222 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1276.79 | 1.52067 | 0.760337 | − | 0.649529i | \(-0.225034\pi\) | ||||
0.760337 | + | 0.649529i | \(0.225034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 315.637 | 0.363602 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −468.787 | −0.522699 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −311.545 | −0.336461 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1024.86 | −1.07277 | −0.536386 | − | 0.843973i | \(-0.680211\pi\) | ||||
−0.536386 | + | 0.843973i | \(0.680211\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1900.47 | −1.92934 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 126.508 | 0.124634 | 0.0623169 | − | 0.998056i | \(-0.480151\pi\) | ||||
0.0623169 | + | 0.998056i | \(0.480151\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 258.017 | 0.246827 | 0.123413 | − | 0.992355i | \(-0.460616\pi\) | ||||
0.123413 | + | 0.992355i | \(0.460616\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −304.593 | −0.283097 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1017.46 | −0.919265 | −0.459633 | − | 0.888109i | \(-0.652019\pi\) | ||||
−0.459633 | + | 0.888109i | \(0.652019\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1861.29 | 1.63559 | 0.817797 | − | 0.575507i | \(-0.195195\pi\) | ||||
0.817797 | + | 0.575507i | \(0.195195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 624.329 | 0.533862 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −49.7040 | −0.0413784 | −0.0206892 | − | 0.999786i | \(-0.506586\pi\) | ||||
−0.0206892 | + | 0.999786i | \(0.506586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 100.350 | 0.0813708 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −944.748 | −0.746512 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −226.239 | −0.174280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3230.12 | 2.42684 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1072.99 | −0.786573 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1007.70 | −0.721052 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1755.96 | 1.22690 | 0.613449 | − | 0.789734i | \(-0.289782\pi\) | ||||
0.613449 | + | 0.789734i | \(0.289782\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 560.040 | 0.382239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −377.103 | −0.251509 | −0.125754 | − | 0.992061i | \(-0.540135\pi\) | ||||
−0.125754 | + | 0.992061i | \(0.540135\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 671.322 | 0.437677 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 36.9376 | 0.0235488 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 376.686 | 0.234908 | 0.117454 | − | 0.993078i | \(-0.462527\pi\) | ||||
0.117454 | + | 0.993078i | \(0.462527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2297.98 | −1.40224 | −0.701122 | − | 0.713041i | \(-0.747317\pi\) | ||||
−0.701122 | + | 0.713041i | \(0.747317\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1597.07 | 0.953881 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2267.39 | 1.32593 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −420.640 | −0.240912 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1890.65 | −1.06080 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1191.27 | 0.654987 | 0.327493 | − | 0.944853i | \(-0.393796\pi\) | ||||
0.327493 | + | 0.944853i | \(0.393796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2536.35 | −1.36692 | −0.683462 | − | 0.729986i | \(-0.739527\pi\) | ||||
−0.683462 | + | 0.729986i | \(0.739527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 677.166 | 0.357814 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −275.442 | −0.142736 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1112.51 | 0.565529 | 0.282764 | − | 0.959189i | \(-0.408749\pi\) | ||||
0.282764 | + | 0.959189i | \(0.408749\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −408.583 | −0.203791 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −216.235 | −0.105849 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1481.99 | −0.712135 | −0.356068 | − | 0.934460i | \(-0.615883\pi\) | ||||
−0.356068 | + | 0.934460i | \(0.615883\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2188.05 | −1.03236 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3939.40 | −1.82539 | −0.912695 | − | 0.408642i | \(-0.866003\pi\) | ||||
−0.912695 | + | 0.408642i | \(0.866003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1069.85 | −0.486962 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2009.36 | −0.898596 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1332.84 | −0.585744 | −0.292872 | − | 0.956152i | \(-0.594611\pi\) | ||||
−0.292872 | + | 0.956152i | \(0.594611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 996.224 | 0.430328 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1038.50 | −0.441006 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −603.340 | −0.251931 | −0.125966 | − | 0.992035i | \(-0.540203\pi\) | ||||
−0.125966 | + | 0.992035i | \(0.540203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4132.64 | −1.69711 | −0.848554 | − | 0.529109i | \(-0.822526\pi\) | ||||
−0.848554 | + | 0.529109i | \(0.822526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5733.47 | 2.31601 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 366.832 | 0.145784 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1625.19 | −0.635539 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −79.5939 | −0.0306328 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2364.21 | −0.895647 | −0.447823 | − | 0.894122i | \(-0.647801\pi\) | ||||
−0.447823 | + | 0.894122i | \(0.647801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3292.16 | −1.22785 | −0.613925 | − | 0.789365i | \(-0.710410\pi\) | ||||
−0.613925 | + | 0.789365i | \(0.710410\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1087.71 | −0.399447 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3375.84 | −1.22091 | −0.610453 | − | 0.792052i | \(-0.709013\pi\) | ||||
−0.610453 | + | 0.792052i | \(0.709013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4578.09 | 1.63082 | 0.815408 | − | 0.578886i | \(-0.196512\pi\) | ||||
0.815408 | + | 0.578886i | \(0.196512\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6473.71 | −2.27174 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 906.403 | 0.313384 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −630.450 | −0.214793 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 647.223 | 0.217319 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4822.46 | 1.59606 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2634.81 | 0.859659 | 0.429829 | − | 0.902910i | \(-0.358574\pi\) | ||||
0.429829 | + | 0.902910i | \(0.358574\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1104.94 | 0.355444 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 329.058 | 0.104380 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 593.527 | 0.185674 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5539.50 | 1.70925 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −807.902 | −0.245907 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −551.110 | −0.165493 | −0.0827467 | − | 0.996571i | \(-0.526369\pi\) | ||||
−0.0827467 | + | 0.996571i | \(0.526369\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2981.84 | −0.883508 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1519.50 | −0.444286 | −0.222143 | − | 0.975014i | \(-0.571305\pi\) | ||||
−0.222143 | + | 0.975014i | \(0.571305\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3162.04 | 0.912461 | 0.456231 | − | 0.889862i | \(-0.349199\pi\) | ||||
0.456231 | + | 0.889862i | \(0.349199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4714.85 | 1.34292 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4659.33 | 1.31005 | 0.655027 | − | 0.755605i | \(-0.272657\pi\) | ||||
0.655027 | + | 0.755605i | \(0.272657\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 938.376 | 0.260480 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3423.29 | −0.938256 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1993.51 | −0.539536 | −0.269768 | − | 0.962925i | \(-0.586947\pi\) | ||||
−0.269768 | + | 0.962925i | \(0.586947\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1772.18 | 0.473677 | 0.236838 | − | 0.971549i | \(-0.423889\pi\) | ||||
0.236838 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5403.64 | −1.42652 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1110.87 | −0.289678 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2397.30 | 0.617557 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2563.87 | 0.652524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1484.40 | −0.373285 | −0.186643 | − | 0.982428i | \(-0.559761\pi\) | ||||
−0.186643 | + | 0.982428i | \(0.559761\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1553.33 | −0.385996 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 779.633 | 0.191461 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2791.47 | 0.677537 | 0.338769 | − | 0.940870i | \(-0.389990\pi\) | ||||
0.338769 | + | 0.940870i | \(0.389990\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −790.456 | −0.189639 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2712.99 | −0.643410 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6898.74 | 1.61747 | 0.808735 | − | 0.588173i | \(-0.200153\pi\) | ||||
0.808735 | + | 0.588173i | \(0.200153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −240.068 | −0.0556500 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9481.01 | 2.17314 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2861.59 | 0.648604 | 0.324302 | − | 0.945954i | \(-0.394871\pi\) | ||||
0.324302 | + | 0.945954i | \(0.394871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2226.19 | −0.499009 | −0.249504 | − | 0.968374i | \(-0.580268\pi\) | ||||
−0.249504 | + | 0.968374i | \(0.580268\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2343.81 | 0.519611 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7156.39 | 1.56926 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5283.50 | −1.14605 | −0.573023 | − | 0.819539i | \(-0.694230\pi\) | ||||
−0.573023 | + | 0.819539i | \(0.694230\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1776.51 | −0.381208 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7449.27 | 1.58145 | 0.790723 | − | 0.612174i | \(-0.209705\pi\) | ||||
0.790723 | + | 0.612174i | \(0.209705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5206.96 | −1.09372 | −0.546858 | − | 0.837225i | \(-0.684176\pi\) | ||||
−0.546858 | + | 0.837225i | \(0.684176\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2313.42 | −0.480825 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1358.51 | 0.279408 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4333.92 | −0.882133 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7610.24 | −1.53306 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3588.15 | −0.715433 | −0.357717 | − | 0.933830i | \(-0.616445\pi\) | ||||
−0.357717 | + | 0.933830i | \(0.616445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −610.180 | −0.120427 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −571.764 | −0.111708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −772.179 | −0.149352 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −709.062 | −0.135779 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 939.402 | 0.178110 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3368.77 | 0.632443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1222.71 | −0.227309 | −0.113654 | − | 0.993520i | \(-0.536256\pi\) | ||||
−0.113654 | + | 0.993520i | \(0.536256\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1915.94 | 0.352731 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −158.959 | −0.0289831 | −0.0144916 | − | 0.999895i | \(-0.504613\pi\) | ||||
−0.0144916 | + | 0.999895i | \(0.504613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1532.53 | 0.276754 | 0.138377 | − | 0.990380i | \(-0.455811\pi\) | ||||
0.138377 | + | 0.990380i | \(0.455811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1154.28 | −0.206465 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2444.39 | −0.433093 | −0.216546 | − | 0.976272i | \(-0.569479\pi\) | ||||
−0.216546 | + | 0.976272i | \(0.569479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6511.16 | 1.14281 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7555.27 | −1.31369 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1718.31 | −0.296004 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3557.53 | 0.607188 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13821.3 | 2.33737 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2022.03 | −0.338839 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3229.27 | 0.536245 | 0.268122 | − | 0.963385i | \(-0.413597\pi\) | ||||
0.268122 | + | 0.963385i | \(0.413597\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2365.95 | 0.389349 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3803.71 | −0.620354 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2563.42 | 0.414357 | 0.207178 | − | 0.978303i | \(-0.433572\pi\) | ||||
0.207178 | + | 0.978303i | \(0.433572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −369.084 | −0.0591325 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4263.61 | 0.677090 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5618.46 | 0.884456 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 745.159 | 0.116284 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5755.34 | −0.890383 | −0.445192 | − | 0.895435i | \(-0.646864\pi\) | ||||
−0.445192 | + | 0.895435i | \(0.646864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10312.7 | 1.58174 | 0.790868 | − | 0.611987i | \(-0.209630\pi\) | ||||
0.790868 | + | 0.611987i | \(0.209630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −284.231 | −0.0432226 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5515.25 | 0.831578 | 0.415789 | − | 0.909461i | \(-0.363506\pi\) | ||||
0.415789 | + | 0.909461i | \(0.363506\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 649.223 | 0.0970625 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1679.97 | −0.249057 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −563.557 | −0.0828507 | −0.0414254 | − | 0.999142i | \(-0.513190\pi\) | ||||
−0.0414254 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1760.23 | −0.256631 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 23985.7 | 3.46811 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3254.80 | 0.466751 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7705.08 | 1.09592 | 0.547959 | − | 0.836505i | \(-0.315405\pi\) | ||||
0.547959 | + | 0.836505i | \(0.315405\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4066.20 | −0.573653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 517.303 | 0.0723909 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2346.53 | −0.325734 | −0.162867 | − | 0.986648i | \(-0.552074\pi\) | ||||
−0.162867 | + | 0.986648i | \(0.552074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7482.83 | −1.03043 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3236.78 | 0.442182 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3390.67 | −0.459544 | −0.229772 | − | 0.973244i | \(-0.573798\pi\) | ||||
−0.229772 | + | 0.973244i | \(0.573798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13039.1 | 1.75332 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 837.622 | 0.111751 | 0.0558753 | − | 0.998438i | \(-0.482205\pi\) | ||||
0.0558753 | + | 0.998438i | \(0.482205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2770.27 | 0.366717 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2122.32 | 0.278769 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12669.0 | 1.65126 | 0.825632 | − | 0.564209i | \(-0.190819\pi\) | ||||
0.825632 | + | 0.564209i | \(0.190819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 553.474 | 0.0715866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2800.23 | −0.359422 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2011.40 | −0.256213 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8731.37 | 1.10382 | 0.551908 | − | 0.833905i | \(-0.313900\pi\) | ||||
0.551908 | + | 0.833905i | \(0.313900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4985.00 | 0.625469 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8265.25 | −1.02929 | −0.514647 | − | 0.857402i | \(-0.672077\pi\) | ||||
−0.514647 | + | 0.857402i | \(0.672077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2119.49 | 0.261984 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3040.66 | −0.373066 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5678.26 | −0.691550 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15088.7 | 1.82418 | 0.912091 | − | 0.409988i | \(-0.134467\pi\) | ||||
0.912091 | + | 0.409988i | \(0.134467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2797.13 | 0.335699 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1314.83 | 0.156655 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1506.43 | 0.178187 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17064.0 | −2.00390 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6923.33 | −0.807224 | −0.403612 | − | 0.914930i | \(-0.632245\pi\) | ||||
−0.403612 | + | 0.914930i | \(0.632245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3156.36 | −0.365396 | −0.182698 | − | 0.983169i | \(-0.558483\pi\) | ||||
−0.182698 | + | 0.983169i | \(0.558483\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6052.23 | 0.695672 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2549.93 | −0.291034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7259.09 | −0.822698 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16836.8 | 1.89484 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6355.74 | 0.710314 | 0.355157 | − | 0.934807i | \(-0.384427\pi\) | ||||
0.355157 | + | 0.934807i | \(0.384427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5151.76 | −0.571773 | −0.285886 | − | 0.958264i | \(-0.592288\pi\) | ||||
−0.285886 | + | 0.958264i | \(0.592288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3123.52 | −0.344279 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1642.33 | −0.179779 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11082.9 | 1.20492 | 0.602458 | − | 0.798150i | \(-0.294188\pi\) | ||||
0.602458 | + | 0.798150i | \(0.294188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7164.79 | −0.773652 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13618.8 | 1.46060 | 0.730301 | − | 0.683126i | \(-0.239380\pi\) | ||||
0.730301 | + | 0.683126i | \(0.239380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5570.68 | 0.593428 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8845.98 | 0.936019 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13134.4 | −1.38051 | −0.690257 | − | 0.723564i | \(-0.742503\pi\) | ||||
−0.690257 | + | 0.723564i | \(0.742503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9758.85 | 1.01891 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18834.1 | −1.95342 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1377.13 | 0.141892 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12711.1 | 1.30109 | 0.650546 | − | 0.759467i | \(-0.274540\pi\) | ||||
0.650546 | + | 0.759467i | \(0.274540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 203.728 | 0.0207172 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3915.10 | 0.395541 | 0.197771 | − | 0.980248i | \(-0.436630\pi\) | ||||
0.197771 | + | 0.980248i | \(0.436630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16351.0 | −1.64124 | −0.820619 | − | 0.571475i | \(-0.806371\pi\) | ||||
−0.820619 | + | 0.571475i | \(0.806371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2045.33 | −0.203978 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7265.82 | −0.719961 | −0.359981 | − | 0.932960i | \(-0.617217\pi\) | ||||
−0.359981 | + | 0.932960i | \(0.617217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8196.30 | 0.806973 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8261.10 | 0.808177 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5093.56 | −0.495142 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7566.43 | 0.730888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1548.36 | −0.148626 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19081.1 | −1.82012 | −0.910060 | − | 0.414476i | \(-0.863965\pi\) | ||||
−0.910060 | + | 0.414476i | \(0.863965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2822.73 | −0.267579 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1605.68 | −0.151265 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4471.49 | −0.418639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12350.2 | −1.14916 | −0.574580 | − | 0.818448i | \(-0.694835\pi\) | ||||
−0.574580 | + | 0.818448i | \(0.694835\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11004.7 | −1.01769 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11944.1 | −1.09782 | −0.548910 | − | 0.835881i | \(-0.684957\pi\) | ||||
−0.548910 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2320.02 | −0.211944 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8291.80 | −0.752907 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1398.96 | −0.126261 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1772.57 | −0.159020 | −0.0795101 | − | 0.996834i | \(-0.525336\pi\) | ||||
−0.0795101 | + | 0.996834i | \(0.525336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29252.6 | −2.60860 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5517.89 | −0.489126 | −0.244563 | − | 0.969633i | \(-0.578645\pi\) | ||||
−0.244563 | + | 0.969633i | \(0.578645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 551.957 | 0.0486371 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7944.36 | −0.695900 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21201.4 | −1.84624 | −0.923120 | − | 0.384512i | \(-0.874370\pi\) | ||||
−0.923120 | + | 0.384512i | \(0.874370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7013.51 | −0.607161 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −604.525 | −0.0520281 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1125.73 | 0.0963218 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14525.3 | −1.23563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9897.17 | −0.837067 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9203.33 | −0.773906 | −0.386953 | − | 0.922099i | \(-0.626472\pi\) | ||||
−0.386953 | + | 0.922099i | \(0.626472\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21900.1 | 1.83103 | 0.915513 | − | 0.402289i | \(-0.131785\pi\) | ||||
0.915513 | + | 0.402289i | \(0.131785\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7397.60 | 0.614967 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1519.19 | −0.125573 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3935.47 | −0.321629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4851.24 | 0.394241 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4439.19 | −0.358735 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4480.18 | −0.360026 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17195.4 | 1.37414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3490.20 | −0.277367 | −0.138684 | − | 0.990337i | \(-0.544287\pi\) | ||||
−0.138684 | + | 0.990337i | \(0.544287\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30687.5 | −2.42528 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8120.87 | 0.638275 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16506.0 | 1.29021 | 0.645106 | − | 0.764093i | \(-0.276813\pi\) | ||||
0.645106 | + | 0.764093i | \(0.276813\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21727.5 | 1.68908 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6884.23 | 0.532265 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4334.19 | 0.333289 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2723.96 | 0.208335 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10101.1 | −0.768400 | −0.384200 | − | 0.923250i | \(-0.625523\pi\) | ||||
−0.384200 | + | 0.923250i | \(0.625523\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2532.07 | −0.191583 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12068.1 | −0.908227 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1303.81 | −0.0976005 | −0.0488003 | − | 0.998809i | \(-0.515540\pi\) | ||||
−0.0488003 | + | 0.998809i | \(0.515540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −216.860 | −0.0161475 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6552.09 | 0.485294 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1993.03 | 0.146840 | 0.0734201 | − | 0.997301i | \(-0.476609\pi\) | ||||
0.0734201 | + | 0.997301i | \(0.476609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1776.69 | −0.130214 | −0.0651071 | − | 0.997878i | \(-0.520739\pi\) | ||||
−0.0651071 | + | 0.997878i | \(0.520739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17555.8 | −1.27994 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2437.17 | −0.176760 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9542.03 | 0.688457 | 0.344229 | − | 0.938886i | \(-0.388140\pi\) | ||||
0.344229 | + | 0.938886i | \(0.388140\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24446.4 | −1.75468 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3246.09 | −0.231791 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3716.05 | 0.263985 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4121.95 | −0.291319 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8518.89 | −0.598999 | −0.299499 | − | 0.954096i | \(-0.596820\pi\) | ||||
−0.299499 | + | 0.954096i | \(0.596820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4507.91 | 0.315357 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25067.8 | −1.74475 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11295.1 | 0.782181 | 0.391090 | − | 0.920352i | \(-0.372098\pi\) | ||||
0.391090 | + | 0.920352i | \(0.372098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −987.086 | −0.0680110 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33995.3 | 2.33054 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7880.18 | −0.537522 | −0.268761 | − | 0.963207i | \(-0.586614\pi\) | ||||
−0.268761 | + | 0.963207i | \(0.586614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21198.1 | 1.43875 | 0.719375 | − | 0.694622i | \(-0.244428\pi\) | ||||
0.719375 | + | 0.694622i | \(0.244428\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24532.7 | −1.65680 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14093.1 | 0.947050 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13439.0 | 0.898638 | 0.449319 | − | 0.893371i | \(-0.351667\pi\) | ||||
0.449319 | + | 0.893371i | \(0.351667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6730.62 | 0.447846 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7220.70 | −0.478098 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24209.4 | −1.59512 | −0.797561 | − | 0.603238i | \(-0.793877\pi\) | ||||
−0.797561 | + | 0.603238i | \(0.793877\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4681.49 | −0.306953 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21713.2 | −1.41676 | −0.708379 | − | 0.705832i | \(-0.750573\pi\) | ||||
−0.708379 | + | 0.705832i | \(0.750573\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15809.5 | −1.02656 | −0.513279 | − | 0.858222i | \(-0.671569\pi\) | ||||
−0.513279 | + | 0.858222i | \(0.671569\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 194.719 | 0.0125826 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12003.8 | −0.771947 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8848.88 | 0.566328 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35809.8 | 2.28087 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2023.25 | 0.128254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29674.4 | 1.87214 | 0.936068 | − | 0.351818i | \(-0.114436\pi\) | ||||
0.936068 | + | 0.351818i | \(0.114436\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19565.2 | 1.22851 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7661.28 | 0.478785 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8548.06 | 0.531690 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4187.28 | 0.259227 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6257.34 | −0.385569 | −0.192785 | − | 0.981241i | \(-0.561752\pi\) | ||||
−0.192785 | + | 0.981241i | \(0.561752\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1466.42 | −0.0899377 | −0.0449688 | − | 0.998988i | \(-0.514319\pi\) | ||||
−0.0449688 | + | 0.998988i | \(0.514319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2443.47 | 0.149165 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25202.9 | −1.53142 | −0.765711 | − | 0.643185i | \(-0.777613\pi\) | ||||
−0.765711 | + | 0.643185i | \(0.777613\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9445.10 | 0.571267 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4407.32 | 0.265340 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27800.2 | −1.66601 | −0.833006 | − | 0.553263i | \(-0.813382\pi\) | ||||
−0.833006 | + | 0.553263i | \(0.813382\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1645.31 | −0.0981489 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20992.4 | 1.24656 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1065.63 | −0.0629912 | −0.0314956 | − | 0.999504i | \(-0.510027\pi\) | ||||
−0.0314956 | + | 0.999504i | \(0.510027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14149.4 | −0.832599 | −0.416300 | − | 0.909227i | \(-0.636673\pi\) | ||||
−0.416300 | + | 0.909227i | \(0.636673\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5999.19 | −0.351417 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2928.99 | 0.170799 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2217.43 | −0.128725 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4092.34 | −0.236501 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52145.9 | −3.00010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1643.03 | 0.0941073 | 0.0470536 | − | 0.998892i | \(-0.485017\pi\) | ||||
0.0470536 | + | 0.998892i | \(0.485017\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −897.098 | −0.0511545 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30414.5 | 1.72662 | 0.863311 | − | 0.504672i | \(-0.168387\pi\) | ||||
0.863311 | + | 0.504672i | \(0.168387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9635.25 | 0.544576 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11283.3 | −0.634914 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18182.8 | −1.01866 | −0.509331 | − | 0.860571i | \(-0.670107\pi\) | ||||
−0.509331 | + | 0.860571i | \(0.670107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1643.49 | 0.0916708 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23480.2 | 1.30397 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1847.29 | 0.102143 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15330.4 | −0.843989 | −0.421995 | − | 0.906598i | \(-0.638670\pi\) | ||||
−0.421995 | + | 0.906598i | \(0.638670\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17867.3 | 0.979400 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10026.1 | −0.547212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3477.22 | −0.188966 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34598.5 | 1.87215 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1245.98 | −0.0671328 | −0.0335664 | − | 0.999436i | \(-0.510687\pi\) | ||||
−0.0335664 | + | 0.999436i | \(0.510687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6003.61 | −0.322092 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6968.04 | 0.372243 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1189.37 | −0.0632684 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10282.8 | −0.544683 | −0.272341 | − | 0.962201i | \(-0.587798\pi\) | ||||
−0.272341 | + | 0.962201i | \(0.587798\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12972.9 | −0.684276 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1452.01 | −0.0762668 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9892.66 | 0.517433 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14803.1 | −0.771032 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14800.1 | −0.767666 | −0.383833 | − | 0.923403i | \(-0.625396\pi\) | ||||
−0.383833 | + | 0.923403i | \(0.625396\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2425.75 | −0.125298 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13159.6 | 0.676915 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10216.0 | 0.523328 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24168.5 | −1.23296 | −0.616478 | − | 0.787372i | \(-0.711441\pi\) | ||||
−0.616478 | + | 0.787372i | \(0.711441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21308.7 | −1.08259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1814.91 | 0.0918287 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37052.5 | −1.86707 | −0.933537 | − | 0.358481i | \(-0.883295\pi\) | ||||
−0.933537 | + | 0.358481i | \(0.883295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8248.95 | −0.413969 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58878.3 | 2.94276 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2133.67 | 0.106209 | 0.0531045 | − | 0.998589i | \(-0.483088\pi\) | ||||
0.0531045 | + | 0.998589i | \(0.483088\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17801.5 | 0.882529 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26389.0 | −1.30299 | −0.651494 | − | 0.758654i | \(-0.725857\pi\) | ||||
−0.651494 | + | 0.758654i | \(0.725857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5197.56 | 0.255602 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9716.00 | 0.475890 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9565.66 | 0.466651 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10857.9 | 0.527579 | 0.263789 | − | 0.964580i | \(-0.415028\pi\) | ||||
0.263789 | + | 0.964580i | \(0.415028\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11022.6 | −0.533449 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11066.2 | −0.533430 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4597.95 | 0.220760 | 0.110380 | − | 0.993889i | \(-0.464793\pi\) | ||||
0.110380 | + | 0.993889i | \(0.464793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11534.5 | −0.551613 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1093.90 | 0.0521077 | 0.0260538 | − | 0.999661i | \(-0.491706\pi\) | ||||
0.0260538 | + | 0.999661i | \(0.491706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17499.0 | −0.830284 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2954.49 | 0.139634 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4695.27 | 0.221038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32217.7 | 1.51079 | 0.755397 | − | 0.655267i | \(-0.227444\pi\) | ||||
0.755397 | + | 0.655267i | \(0.227444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20728.4 | 0.968244 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2841.25 | −0.132203 | −0.0661014 | − | 0.997813i | \(-0.521056\pi\) | ||||
−0.0661014 | + | 0.997813i | \(0.521056\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6689.61 | 0.310062 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5869.64 | −0.271007 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10318.0 | 0.474558 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10049.4 | −0.460432 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −816.214 | −0.0372530 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4853.91 | 0.220692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14015.7 | −0.634822 | −0.317411 | − | 0.948288i | \(-0.602814\pi\) | ||||
−0.317411 | + | 0.948288i | \(0.602814\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51227.6 | 2.31147 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 467.294 | 0.0210051 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25922.3 | −1.16082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1782.66 | −0.0795274 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33612.0 | −1.49385 | −0.746925 | − | 0.664908i | \(-0.768471\pi\) | ||||
−0.746925 | + | 0.664908i | \(0.768471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5175.57 | 0.229160 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35929.1 | 1.58489 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −50381.7 | −2.21411 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −943.439 | −0.0413066 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21249.2 | 0.926897 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −377.089 | −0.0163878 | −0.00819390 | − | 0.999966i | \(-0.502608\pi\) | ||||
−0.00819390 | + | 0.999966i | \(0.502608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24291.0 | 1.05175 | 0.525877 | − | 0.850561i | \(-0.323737\pi\) | ||||
0.525877 | + | 0.850561i | \(0.323737\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16530.9 | −0.713116 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6465.93 | −0.277904 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5385.40 | −0.230614 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8882.07 | 0.378956 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5538.66 | 0.235445 | 0.117723 | − | 0.993047i | \(-0.462441\pi\) | ||||
0.117723 | + | 0.993047i | \(0.462441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41353.5 | 1.75151 | 0.875756 | − | 0.482755i | \(-0.160364\pi\) | ||||
0.875756 | + | 0.482755i | \(0.160364\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 53140.8 | 2.24258 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3467.59 | −0.145804 | −0.0729019 | − | 0.997339i | \(-0.523226\pi\) | ||||
−0.0729019 | + | 0.997339i | \(0.523226\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5524.89 | −0.231468 | −0.115734 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115734 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39233.4 | −1.63778 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6126.98 | −0.254847 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17187.7 | −0.712341 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −534.470 | −0.0220717 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42684.4 | 1.75641 | 0.878206 | − | 0.478283i | \(-0.158741\pi\) | ||||
0.878206 | + | 0.478283i | \(0.158741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15094.1 | −0.618889 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55315.6 | 2.25999 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4667.80 | −0.190032 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30368.1 | −1.23195 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38665.0 | −1.56299 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1933.78 | 0.0778956 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39711.0 | −1.59400 | −0.796998 | − | 0.603981i | \(-0.793580\pi\) | ||||
−0.796998 | + | 0.603981i | \(0.793580\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8766.90 | −0.350669 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17088.5 | 0.681136 | 0.340568 | − | 0.940220i | \(-0.389381\pi\) | ||||
0.340568 | + | 0.940220i | \(0.389381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34573.9 | 1.37328 | 0.686639 | − | 0.726999i | \(-0.259085\pi\) | ||||
0.686639 | + | 0.726999i | \(0.259085\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10087.8 | 0.399292 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34786.0 | −1.37211 | −0.686054 | − | 0.727551i | \(-0.740658\pi\) | ||||
−0.686054 | + | 0.727551i | \(0.740658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5815.20 | −0.228581 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32182.1 | −1.26063 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31134.8 | 1.21539 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29269.1 | 1.13863 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28839.7 | −1.11807 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9473.93 | 0.366031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10814.7 | −0.416406 | −0.208203 | − | 0.978086i | \(-0.566761\pi\) | ||||
−0.208203 | + | 0.978086i | \(0.566761\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26644.3 | −1.02240 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10411.1 | 0.398135 | 0.199068 | − | 0.979986i | \(-0.436209\pi\) | ||||
0.199068 | + | 0.979986i | \(0.436209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28277.5 | −1.07771 | −0.538853 | − | 0.842400i | \(-0.681142\pi\) | ||||
−0.538853 | + | 0.842400i | \(0.681142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4530.98 | −0.172099 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16488.4 | 0.624154 | 0.312077 | − | 0.950057i | \(-0.398975\pi\) | ||||
0.312077 | + | 0.950057i | \(0.398975\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16508.7 | −0.622816 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47067.0 | 1.76970 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15357.6 | −0.575499 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2632.38 | −0.0983139 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5733.92 | −0.213434 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6086.46 | 0.225801 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1324.08 | −0.0489585 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5265.23 | −0.194038 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18030.8 | −0.662280 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42168.8 | 1.54376 | 0.771880 | − | 0.635768i | \(-0.219316\pi\) | ||||
0.771880 | + | 0.635768i | \(0.219316\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3559.95 | 0.129897 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20373.7 | 0.740954 | 0.370477 | − | 0.928842i | \(-0.379194\pi\) | ||||
0.370477 | + | 0.928842i | \(0.379194\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23318.3 | −0.845262 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25015.3 | 0.903803 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3545.34 | 0.127675 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36823.5 | 1.32176 | 0.660879 | − | 0.750492i | \(-0.270183\pi\) | ||||
0.660879 | + | 0.750492i | \(0.270183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9079.41 | −0.324839 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4995.70 | −0.178153 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8909.19 | −0.316683 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7260.62 | 0.257249 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10251.0 | 0.362028 | 0.181014 | − | 0.983480i | \(-0.442062\pi\) | ||||
0.181014 | + | 0.983480i | \(0.442062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18180.7 | 0.640009 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1180.37 | −0.0414187 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7090.75 | −0.248013 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28272.1 | −0.985708 | −0.492854 | − | 0.870112i | \(-0.664046\pi\) | ||||
−0.492854 | + | 0.870112i | \(0.664046\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11380.0 | 0.395499 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43672.5 | −1.51295 | −0.756473 | − | 0.654025i | \(-0.773079\pi\) | ||||
−0.756473 | + | 0.654025i | \(0.773079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3323.46 | −0.114769 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −347.270 | −0.0119542 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43064.2 | −1.47772 | −0.738858 | − | 0.673861i | \(-0.764635\pi\) | ||||
−0.738858 | + | 0.673861i | \(0.764635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25045.3 | −0.856698 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18151.1 | −0.618918 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11297.0 | −0.383994 | −0.191997 | − | 0.981396i | \(-0.561496\pi\) | ||||
−0.191997 | + | 0.981396i | \(0.561496\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10315.1 | −0.349518 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 48349.5 | 1.63314 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3541.42 | −0.119248 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25805.5 | −0.866218 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28631.4 | −0.958082 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14363.8 | −0.479157 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25167.0 | 0.836937 | 0.418468 | − | 0.908231i | \(-0.362567\pi\) | ||||
0.418468 | + | 0.908231i | \(0.362567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12759.6 | −0.423009 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2387.35 | 0.0789018 | 0.0394509 | − | 0.999222i | \(-0.487439\pi\) | ||||
0.0394509 | + | 0.999222i | \(0.487439\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21604.5 | 0.711828 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26416.9 | 0.867711 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50653.2 | −1.65869 | −0.829345 | − | 0.558736i | \(-0.811286\pi\) | ||||
−0.829345 | + | 0.558736i | \(0.811286\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −86229.7 | −2.81503 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 52377.0 | 1.70466 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3927.47 | 0.127433 | 0.0637166 | − | 0.997968i | \(-0.479705\pi\) | ||||
0.0637166 | + | 0.997968i | \(0.479705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14728.9 | −0.476447 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15014.9 | −0.484223 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1734.66 | 0.0557723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41415.4 | 1.32755 | 0.663776 | − | 0.747931i | \(-0.268953\pi\) | ||||
0.663776 | + | 0.747931i | \(0.268953\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23979.4 | 0.766328 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19974.3 | 0.636411 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54644.4 | 1.73581 | 0.867907 | − | 0.496727i | \(-0.165465\pi\) | ||||
0.867907 | + | 0.496727i | \(0.165465\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 711.805 | 0.0225430 |
(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 | 736.4.a.e.1.8 | ✓ | 8 | |
4.3 | odd | 2 | 736.4.a.f.1.1 | yes | 8 | ||
8.3 | odd | 2 | 1472.4.a.bg.1.8 | 8 | |||
8.5 | even | 2 | 1472.4.a.bh.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
736.4.a.e.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
736.4.a.f.1.1 | yes | 8 | 4.3 | odd | 2 | ||
1472.4.a.bg.1.8 | 8 | 8.3 | odd | 2 | |||
1472.4.a.bh.1.1 | 8 | 8.5 | even | 2 |