Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 34x^{3} - 9x^{2} + 260x + 60 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 115) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(4.98640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | 7.39409 | 1.42299 | 0.711497 | − | 0.702689i | \(-0.248018\pi\) | ||||
0.711497 | + | 0.702689i | \(0.248018\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.57544 | 0.193056 | 0.0965278 | − | 0.995330i | \(-0.469226\pi\) | ||||
0.0965278 | + | 0.995330i | \(0.469226\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.6726 | 1.02491 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43.8100 | 1.20084 | 0.600419 | − | 0.799686i | \(-0.295000\pi\) | ||||
0.600419 | + | 0.799686i | \(0.295000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −65.2647 | −1.39240 | −0.696199 | − | 0.717848i | \(-0.745127\pi\) | ||||
−0.696199 | + | 0.717848i | \(0.745127\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −36.9705 | −0.636382 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.0257 | 0.357037 | 0.178519 | − | 0.983937i | \(-0.442870\pi\) | ||||
0.178519 | + | 0.983937i | \(0.442870\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −93.1311 | −1.12451 | −0.562256 | − | 0.826963i | \(-0.690066\pi\) | ||||
−0.562256 | + | 0.826963i | \(0.690066\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26.4371 | 0.274717 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.97335 | 0.0354490 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −84.6447 | −0.542004 | −0.271002 | − | 0.962579i | \(-0.587355\pi\) | ||||
−0.271002 | + | 0.962579i | \(0.587355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −275.951 | −1.59879 | −0.799393 | − | 0.600809i | \(-0.794845\pi\) | ||||
−0.799393 | + | 0.600809i | \(0.794845\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 323.935 | 1.70879 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.8772 | −0.0863371 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −270.136 | −1.20027 | −0.600137 | − | 0.799897i | \(-0.704887\pi\) | ||||
−0.600137 | + | 0.799897i | \(0.704887\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −482.574 | −1.98137 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 178.492 | 0.679898 | 0.339949 | − | 0.940444i | \(-0.389590\pi\) | ||||
0.339949 | + | 0.940444i | \(0.389590\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 46.0544 | 0.163331 | 0.0816654 | − | 0.996660i | \(-0.473976\pi\) | ||||
0.0816654 | + | 0.996660i | \(0.473976\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −138.363 | −0.458354 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 390.733 | 1.21265 | 0.606323 | − | 0.795219i | \(-0.292644\pi\) | ||||
0.606323 | + | 0.795219i | \(0.292644\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −330.216 | −0.962730 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 185.043 | 0.508062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −460.760 | −1.19415 | −0.597077 | − | 0.802184i | \(-0.703671\pi\) | ||||
−0.597077 | + | 0.802184i | \(0.703671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −219.050 | −0.537031 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −688.620 | −1.60017 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 171.714 | 0.378902 | 0.189451 | − | 0.981890i | \(-0.439329\pi\) | ||||
0.189451 | + | 0.981890i | \(0.439329\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −432.337 | −0.907460 | −0.453730 | − | 0.891139i | \(-0.649907\pi\) | ||||
−0.453730 | + | 0.891139i | \(0.649907\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 98.9417 | 0.197865 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 326.324 | 0.622700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −234.236 | −0.427112 | −0.213556 | − | 0.976931i | \(-0.568505\pi\) | ||||
−0.213556 | + | 0.976931i | \(0.568505\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −170.064 | −0.296715 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 465.620 | 0.778295 | 0.389147 | − | 0.921176i | \(-0.372770\pi\) | ||||
0.389147 | + | 0.921176i | \(0.372770\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 363.534 | 0.582856 | 0.291428 | − | 0.956593i | \(-0.405870\pi\) | ||||
0.291428 | + | 0.956593i | \(0.405870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 184.852 | 0.284599 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 156.640 | 0.231828 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −430.514 | −0.613122 | −0.306561 | − | 0.951851i | \(-0.599178\pi\) | ||||
−0.306561 | + | 0.951851i | \(0.599178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −710.387 | −0.974468 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −318.020 | −0.420569 | −0.210285 | − | 0.977640i | \(-0.567439\pi\) | ||||
−0.210285 | + | 0.977640i | \(0.567439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −125.129 | −0.159672 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −625.871 | −0.771269 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1453.20 | 1.73077 | 0.865385 | − | 0.501108i | \(-0.167074\pi\) | ||||
0.865385 | + | 0.501108i | \(0.167074\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −233.350 | −0.268810 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2040.41 | −2.27506 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 465.655 | 0.502897 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −919.515 | −0.962501 | −0.481250 | − | 0.876583i | \(-0.659817\pi\) | ||||
−0.481250 | + | 0.876583i | \(0.659817\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1212.34 | 1.23075 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 773.116 | 0.761662 | 0.380831 | − | 0.924645i | \(-0.375638\pi\) | ||||
0.380831 | + | 0.924645i | \(0.375638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2025.62 | 1.93776 | 0.968882 | − | 0.247521i | \(-0.0796160\pi\) | ||||
0.968882 | + | 0.247521i | \(0.0796160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −132.186 | −0.122857 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −456.342 | −0.412302 | −0.206151 | − | 0.978520i | \(-0.566094\pi\) | ||||
−0.206151 | + | 0.978520i | \(0.566094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 287.101 | 0.252287 | 0.126144 | − | 0.992012i | \(-0.459740\pi\) | ||||
0.126144 | + | 0.992012i | \(0.459740\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1997.41 | −1.70798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1519.75 | −1.26519 | −0.632595 | − | 0.774483i | \(-0.718010\pi\) | ||||
−0.632595 | + | 0.774483i | \(0.718010\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1806.05 | −1.42709 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 89.4780 | 0.0689280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 588.318 | 0.442012 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1319.79 | 0.967490 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −130.296 | −0.0910385 | −0.0455193 | − | 0.998963i | \(-0.514494\pi\) | ||||
−0.0455193 | + | 0.998963i | \(0.514494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 340.530 | 0.232419 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1380.44 | 0.920682 | 0.460341 | − | 0.887742i | \(-0.347727\pi\) | ||||
0.460341 | + | 0.887742i | \(0.347727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −332.984 | −0.217093 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24.8668 | −0.0158533 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −975.666 | −0.608444 | −0.304222 | − | 0.952601i | \(-0.598396\pi\) | ||||
−0.304222 | + | 0.952601i | \(0.598396\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2733.61 | −1.66807 | −0.834034 | − | 0.551713i | \(-0.813974\pi\) | ||||
−0.834034 | + | 0.551713i | \(0.813974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2889.12 | 1.72559 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2859.25 | −1.67205 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 423.224 | 0.242392 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2441.65 | −1.36996 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1040.01 | −0.571820 | −0.285910 | − | 0.958256i | \(-0.592296\pi\) | ||||
−0.285910 | + | 0.958256i | \(0.592296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2822.72 | −1.52125 | −0.760627 | − | 0.649189i | \(-0.775108\pi\) | ||||
−0.760627 | + | 0.649189i | \(0.775108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 692.527 | 0.365931 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1379.76 | 0.714999 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3318.49 | −1.68691 | −0.843454 | − | 0.537202i | \(-0.819481\pi\) | ||||
−0.843454 | + | 0.537202i | \(0.819481\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3406.90 | −1.69927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −82.2351 | −0.0402549 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −954.290 | −0.458563 | −0.229282 | − | 0.973360i | \(-0.573638\pi\) | ||||
−0.229282 | + | 0.973360i | \(0.573638\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1619.68 | −0.764192 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1137.20 | −0.526942 | −0.263471 | − | 0.964667i | \(-0.584867\pi\) | ||||
−0.263471 | + | 0.964667i | \(0.584867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2062.49 | 0.938774 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2577.18 | −1.15253 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4348.83 | −1.91119 | −0.955593 | − | 0.294689i | \(-0.904784\pi\) | ||||
−0.955593 | + | 0.294689i | \(0.904784\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 89.3860 | 0.0386111 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1269.67 | 0.539175 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2627.76 | 1.09725 | 0.548625 | − | 0.836069i | \(-0.315152\pi\) | ||||
0.548625 | + | 0.836069i | \(0.315152\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1985.85 | −0.815507 | −0.407754 | − | 0.913092i | \(-0.633688\pi\) | ||||
−0.407754 | + | 0.913092i | \(0.633688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3196.74 | −1.29131 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1350.68 | 0.536779 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1096.38 | 0.428744 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.7819 | 0.00684362 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4129.34 | 1.56434 | 0.782169 | − | 0.623066i | \(-0.214113\pi\) | ||||
0.782169 | + | 0.623066i | \(0.214113\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2623.33 | 0.978401 | 0.489201 | − | 0.872171i | \(-0.337289\pi\) | ||||
0.489201 | + | 0.872171i | \(0.337289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2412.87 | 0.886098 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3297.25 | 1.19248 | 0.596242 | − | 0.802805i | \(-0.296660\pi\) | ||||
0.596242 | + | 0.802805i | \(0.296660\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3608.58 | −1.28545 | −0.642726 | − | 0.766096i | \(-0.722197\pi\) | ||||
−0.642726 | + | 0.766096i | \(0.722197\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1731.97 | −0.607778 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −302.642 | −0.104637 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −892.461 | −0.304059 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −636.470 | −0.213709 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4080.07 | −1.35036 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4486.91 | −1.46394 | −0.731971 | − | 0.681336i | \(-0.761399\pi\) | ||||
−0.731971 | + | 0.681336i | \(0.761399\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3442.84 | 1.10751 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −230.272 | −0.0730438 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −986.648 | −0.308654 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2688.01 | 0.829400 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1633.30 | −0.497138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5279.87 | −1.58550 | −0.792749 | − | 0.609548i | \(-0.791351\pi\) | ||||
−0.792749 | + | 0.609548i | \(0.791351\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 691.815 | 0.204982 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1784.77 | 0.521846 | 0.260923 | − | 0.965360i | \(-0.415973\pi\) | ||||
0.260923 | + | 0.965360i | \(0.415973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3938.09 | 1.13640 | 0.568201 | − | 0.822890i | \(-0.307640\pi\) | ||||
0.568201 | + | 0.822890i | \(0.307640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1158.21 | 0.329890 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −991.889 | −0.278888 | −0.139444 | − | 0.990230i | \(-0.544531\pi\) | ||||
−0.139444 | + | 0.990230i | \(0.544531\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1953.67 | −0.542311 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3183.26 | −0.872469 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4989.81 | −1.35048 | −0.675239 | − | 0.737599i | \(-0.735959\pi\) | ||||
−0.675239 | + | 0.737599i | \(0.735959\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3317.95 | 0.886838 | 0.443419 | − | 0.896314i | \(-0.353765\pi\) | ||||
0.443419 | + | 0.896314i | \(0.353765\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5386.95 | −1.42211 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1651.08 | 0.430546 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6078.18 | 1.56577 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2351.47 | −0.598467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3640.41 | 0.915460 | 0.457730 | − | 0.889091i | \(-0.348663\pi\) | ||||
0.457730 | + | 0.889091i | \(0.348663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1007.63 | −0.250392 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −925.213 | −0.227212 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7166.41 | 1.73941 | 0.869705 | − | 0.493571i | \(-0.164309\pi\) | ||||
0.869705 | + | 0.493571i | \(0.164309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −965.856 | −0.231719 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2342.34 | −0.555507 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8092.80 | 1.89743 | 0.948714 | − | 0.316137i | \(-0.102386\pi\) | ||||
0.948714 | + | 0.316137i | \(0.102386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2303.80 | 0.534042 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10745.1 | 2.46288 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1356.94 | −0.307562 | −0.153781 | − | 0.988105i | \(-0.549145\pi\) | ||||
−0.153781 | + | 0.988105i | \(0.549145\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6907.18 | 1.54827 | 0.774135 | − | 0.633021i | \(-0.218185\pi\) | ||||
0.774135 | + | 0.633021i | \(0.218185\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1725.41 | −0.382515 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1095.25 | 0.240168 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7889.76 | 1.71137 | 0.855685 | − | 0.517497i | \(-0.173136\pi\) | ||||
0.855685 | + | 0.517497i | \(0.173136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7636.30 | −1.63861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7569.89 | −1.60705 | −0.803527 | − | 0.595269i | \(-0.797046\pi\) | ||||
−0.803527 | + | 0.595269i | \(0.797046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2541.02 | −0.533739 | −0.266869 | − | 0.963733i | \(-0.585989\pi\) | ||||
−0.266869 | + | 0.963733i | \(0.585989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3443.10 | 0.715619 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 638.188 | 0.131258 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4286.71 | −0.872525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6798.98 | −1.36963 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1187.01 | −0.236676 | −0.118338 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118338 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −858.569 | −0.169450 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 217.883 | 0.0425684 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1501.09 | 0.290335 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 164.665 | 0.0315319 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5716.49 | 1.08384 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2161.69 | 0.405829 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2865.01 | 0.532621 | 0.266310 | − | 0.963887i | \(-0.414195\pi\) | ||||
0.266310 | + | 0.963887i | \(0.414195\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14977.6 | 2.75743 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 952.727 | 0.173711 | 0.0868556 | − | 0.996221i | \(-0.472318\pi\) | ||||
0.0868556 | + | 0.996221i | \(0.472318\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −708.750 | −0.127990 | −0.0639951 | − | 0.997950i | \(-0.520384\pi\) | ||||
−0.0639951 | + | 0.997950i | \(0.520384\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −494.709 | −0.0884879 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4406.36 | 0.780712 | 0.390356 | − | 0.920664i | \(-0.372352\pi\) | ||||
0.390356 | + | 0.920664i | \(0.372352\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3708.29 | −0.650860 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3374.24 | −0.586703 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2330.67 | −0.401493 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1631.62 | −0.278480 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2122.85 | 0.359003 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1397.04 | 0.234108 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10068.7 | 1.67198 | 0.835990 | − | 0.548744i | \(-0.184894\pi\) | ||||
0.835990 | + | 0.548744i | \(0.184894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7475.37 | −1.23017 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1171.18 | 0.191010 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5782.71 | −0.934732 | −0.467366 | − | 0.884064i | \(-0.654797\pi\) | ||||
−0.467366 | + | 0.884064i | \(0.654797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11237.2 | −1.80036 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12089.4 | −1.91988 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2407.04 | −0.378916 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 850.321 | 0.132695 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2808.27 | 0.434454 | 0.217227 | − | 0.976121i | \(-0.430299\pi\) | ||||
0.217227 | + | 0.976121i | \(0.430299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1990.62 | −0.305316 | −0.152658 | − | 0.988279i | \(-0.548783\pi\) | ||||
−0.152658 | + | 0.988279i | \(0.548783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −324.584 | −0.0493591 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9719.18 | −1.46544 | −0.732719 | − | 0.680531i | \(-0.761749\pi\) | ||||
−0.732719 | + | 0.680531i | \(0.761749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2328.10 | −0.348064 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 661.608 | 0.0980841 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3571.57 | 0.525070 | 0.262535 | − | 0.964922i | \(-0.415441\pi\) | ||||
0.262535 | + | 0.964922i | \(0.415441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1814.39 | 0.264528 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4350.08 | 0.628980 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1817.67 | −0.260661 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6150.13 | −0.874752 | −0.437376 | − | 0.899279i | \(-0.644092\pi\) | ||||
−0.437376 | + | 0.899279i | \(0.644092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4939.35 | 0.696835 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1647.42 | −0.230538 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2039.11 | −0.283059 | −0.141529 | − | 0.989934i | \(-0.545202\pi\) | ||||
−0.141529 | + | 0.989934i | \(0.545202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −924.262 | −0.127276 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5524.32 | 0.754686 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4989.43 | −0.676227 | −0.338113 | − | 0.941105i | \(-0.609789\pi\) | ||||
−0.338113 | + | 0.941105i | \(0.609789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −963.420 | −0.129547 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10033.8 | −1.33865 | −0.669323 | − | 0.742972i | \(-0.733416\pi\) | ||||
−0.669323 | + | 0.742972i | \(0.733416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −783.200 | −0.103677 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1274.44 | 0.167400 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9316.20 | −1.21427 | −0.607134 | − | 0.794599i | \(-0.707681\pi\) | ||||
−0.607134 | + | 0.794599i | \(0.707681\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −575.592 | −0.0744474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10207.1 | 1.31013 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2152.57 | 0.274196 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5744.41 | 0.726205 | 0.363103 | − | 0.931749i | \(-0.381717\pi\) | ||||
0.363103 | + | 0.931749i | \(0.381717\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2462.12 | −0.308922 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9605.68 | 1.19622 | 0.598111 | − | 0.801414i | \(-0.295918\pi\) | ||||
0.598111 | + | 0.801414i | \(0.295918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18009.9 | 2.22615 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3551.94 | 0.435795 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11834.7 | −1.44133 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10013.5 | −1.21060 | −0.605298 | − | 0.795999i | \(-0.706946\pi\) | ||||
−0.605298 | + | 0.795999i | \(0.706946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7214.16 | −0.865811 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 613.952 | 0.0731491 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1590.10 | 0.188084 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20212.5 | −2.37365 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 674.948 | 0.0786954 | 0.0393477 | − | 0.999226i | \(-0.487472\pi\) | ||||
0.0393477 | + | 0.999226i | \(0.487472\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 900.392 | 0.104234 | 0.0521169 | − | 0.998641i | \(-0.483403\pi\) | ||||
0.0521169 | + | 0.998641i | \(0.483403\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10812.6 | 1.24285 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 625.643 | 0.0714074 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1545.79 | −0.175190 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21141.6 | −2.37931 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10830.3 | 1.21039 | 0.605193 | − | 0.796079i | \(-0.293096\pi\) | ||||
0.605193 | + | 0.796079i | \(0.293096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11231.0 | 1.24649 | 0.623243 | − | 0.782029i | \(-0.285815\pi\) | ||||
0.623243 | + | 0.782029i | \(0.285815\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3129.35 | 0.344922 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2142.01 | 0.234477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13988.9 | −1.52085 | −0.760425 | − | 0.649426i | \(-0.775009\pi\) | ||||
−0.760425 | + | 0.649426i | \(0.775009\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9137.95 | −0.986713 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −298.267 | −0.0319890 | −0.0159945 | − | 0.999872i | \(-0.505091\pi\) | ||||
−0.0159945 | + | 0.999872i | \(0.505091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7265.98 | −0.774024 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7689.96 | −0.813697 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13606.7 | −1.43016 | −0.715079 | − | 0.699044i | \(-0.753609\pi\) | ||||
−0.715079 | + | 0.699044i | \(0.753609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7819.75 | 0.816447 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20871.4 | −2.16474 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1166.75 | 0.120216 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4374.49 | 0.447768 | 0.223884 | − | 0.974616i | \(-0.428126\pi\) | ||||
0.223884 | + | 0.974616i | \(0.428126\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 124.462 | 0.0126566 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1026.64 | 0.103721 | 0.0518604 | − | 0.998654i | \(-0.483485\pi\) | ||||
0.0518604 | + | 0.998654i | \(0.483485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10398.6 | −1.04377 | −0.521884 | − | 0.853016i | \(-0.674771\pi\) | ||||
−0.521884 | + | 0.853016i | \(0.674771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10202.1 | 1.01744 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5755.27 | 0.570282 | 0.285141 | − | 0.958486i | \(-0.407959\pi\) | ||||
0.285141 | + | 0.958486i | \(0.407959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −837.498 | −0.0824564 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24537.2 | −2.40046 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2017.64 | 0.196134 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2328.28 | −0.224902 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12750.4 | −1.22390 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7944.26 | 0.757793 | 0.378896 | − | 0.925439i | \(-0.376304\pi\) | ||||
0.378896 | + | 0.925439i | \(0.376304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17630.4 | 1.67126 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −608.054 | −0.0572824 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4597.57 | 0.430443 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13904.3 | 1.29376 | 0.646881 | − | 0.762591i | \(-0.276073\pi\) | ||||
0.646881 | + | 0.762591i | \(0.276073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7056.11 | −0.652532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3935.58 | −0.361731 | −0.180866 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180866 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2118.30 | −0.193516 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6061.69 | −0.550409 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1664.80 | 0.150254 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7865.34 | 0.705613 | 0.352807 | − | 0.935696i | \(-0.385227\pi\) | ||||
0.352807 | + | 0.935696i | \(0.385227\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8408.58 | −0.749835 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2435.58 | −0.215899 | −0.107950 | − | 0.994156i | \(-0.534429\pi\) | ||||
−0.107950 | + | 0.994156i | \(0.534429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3865.58 | −0.340626 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15250.2 | 1.33587 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19061.4 | −1.65988 | −0.829942 | − | 0.557850i | \(-0.811627\pi\) | ||||
−0.829942 | + | 0.557850i | \(0.811627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1299.79 | 0.112524 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −463.173 | −0.0398628 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10128.1 | −0.866595 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17118.0 | 1.45619 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32155.6 | −2.71961 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8446.00 | 0.710222 | 0.355111 | − | 0.934824i | \(-0.384443\pi\) | ||||
0.355111 | + | 0.934824i | \(0.384443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20207.4 | 1.68950 | 0.844749 | − | 0.535162i | \(-0.179749\pi\) | ||||
0.844749 | + | 0.535162i | \(0.179749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 660.928 | 0.0549434 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6905.89 | −0.570826 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4751.77 | 0.388341 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11649.3 | −0.946689 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2281.71 | 0.184387 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19429.9 | 1.56138 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14466.8 | −1.15608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14298.5 | 1.13631 | 0.568153 | − | 0.822923i | \(-0.307658\pi\) | ||||
0.568153 | + | 0.822923i | \(0.307658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14683.5 | −1.16046 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1435.51 | −0.112826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1820.52 | 0.142303 | 0.0711515 | − | 0.997466i | \(-0.477333\pi\) | ||||
0.0711515 | + | 0.997466i | \(0.477333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11963.9 | −0.930067 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7883.05 | 0.609491 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1539.28 | −0.118367 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9987.06 | 0.763833 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19947.4 | 1.51741 | 0.758707 | − | 0.651432i | \(-0.225832\pi\) | ||||
0.758707 | + | 0.651432i | \(0.225832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3005.73 | −0.227422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8106.72 | 0.610100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6202.95 | −0.464339 | −0.232170 | − | 0.972675i | \(-0.574582\pi\) | ||||
−0.232170 | + | 0.972675i | \(0.574582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7598.77 | 0.565810 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2539.95 | −0.188126 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15907.6 | 1.17203 | 0.586013 | − | 0.810302i | \(-0.300697\pi\) | ||||
0.586013 | + | 0.810302i | \(0.300697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4501.17 | 0.329892 | 0.164946 | − | 0.986303i | \(-0.447255\pi\) | ||||
0.164946 | + | 0.986303i | \(0.447255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30532.7 | 2.22604 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8735.09 | 0.630237 | 0.315119 | − | 0.949052i | \(-0.397956\pi\) | ||||
0.315119 | + | 0.949052i | \(0.397956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19397.1 | 1.39226 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1137.06 | −0.0811932 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20185.9 | −1.43399 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9030.23 | 0.638212 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17132.8 | −1.20468 | −0.602340 | − | 0.798240i | \(-0.705765\pi\) | ||||
−0.602340 | + | 0.798240i | \(0.705765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25699.7 | 1.79785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24380.2 | 1.69690 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7756.71 | −0.537150 | −0.268575 | − | 0.963259i | \(-0.586553\pi\) | ||||
−0.268575 | + | 0.963259i | \(0.586553\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −447.390 | −0.0308255 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26682.1 | −1.82919 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11689.1 | −0.797338 | −0.398669 | − | 0.917095i | \(-0.630528\pi\) | ||||
−0.398669 | + | 0.917095i | \(0.630528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5361.70 | −0.363907 | −0.181954 | − | 0.983307i | \(-0.558242\pi\) | ||||
−0.181954 | + | 0.983307i | \(0.558242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6481.93 | −0.437752 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2941.59 | −0.197674 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6585.62 | −0.440366 | −0.220183 | − | 0.975459i | \(-0.570665\pi\) | ||||
−0.220183 | + | 0.975459i | \(0.570665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2237.76 | −0.148898 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25501.1 | −1.68849 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10187.9 | −0.671265 | −0.335633 | − | 0.941993i | \(-0.608950\pi\) | ||||
−0.335633 | + | 0.941993i | \(0.608950\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6598.94 | −0.432675 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14025.9 | −0.915174 | −0.457587 | − | 0.889165i | \(-0.651286\pi\) | ||||
−0.457587 | + | 0.889165i | \(0.651286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23123.6 | 1.50148 | 0.750741 | − | 0.660597i | \(-0.229697\pi\) | ||||
0.750741 | + | 0.660597i | \(0.229697\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −114.387 | −0.00739162 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5195.82 | 0.334135 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30168.4 | −1.92155 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6760.35 | −0.428542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21569.0 | 1.36078 | 0.680389 | − | 0.732852i | \(-0.261811\pi\) | ||||
0.680389 | + | 0.732852i | \(0.261811\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33176.6 | −2.08318 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 651.480 | 0.0407137 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21551.5 | 1.34050 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12884.9 | 0.797683 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14908.3 | −0.918633 | −0.459317 | − | 0.888273i | \(-0.651906\pi\) | ||||
−0.459317 | + | 0.888273i | \(0.651906\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20215.7 | −1.23986 | −0.619930 | − | 0.784657i | \(-0.712839\pi\) | ||||
−0.619930 | + | 0.784657i | \(0.712839\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1702.65 | −0.103941 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2941.45 | 0.178733 | 0.0893666 | − | 0.995999i | \(-0.471516\pi\) | ||||
0.0893666 | + | 0.995999i | \(0.471516\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7522.78 | 0.455000 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7295.36 | −0.439213 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5575.27 | 0.334115 | 0.167058 | − | 0.985947i | \(-0.446573\pi\) | ||||
0.167058 | + | 0.985947i | \(0.446573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6902.19 | −0.411742 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10059.9 | 0.597376 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20945.0 | 1.23809 | 0.619046 | − | 0.785354i | \(-0.287519\pi\) | ||||
0.619046 | + | 0.785354i | \(0.287519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18339.9 | −1.07919 | −0.539593 | − | 0.841926i | \(-0.681422\pi\) | ||||
−0.539593 | + | 0.841926i | \(0.681422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12076.8 | −0.707424 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1664.92 | 0.0970871 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1946.83 | 0.113016 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39039.8 | −2.25615 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18940.7 | −1.08971 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8682.73 | 0.497318 | 0.248659 | − | 0.968591i | \(-0.420010\pi\) | ||||
0.248659 | + | 0.968591i | \(0.420010\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 124.334 | 0.00708979 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24621.6 | −1.39776 | −0.698880 | − | 0.715238i | \(-0.746318\pi\) | ||||
−0.698880 | + | 0.715238i | \(0.746318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3287.67 | −0.185816 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13196.7 | 0.742584 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12701.5 | 0.711582 | 0.355791 | − | 0.934565i | \(-0.384211\pi\) | ||||
0.355791 | + | 0.934565i | \(0.384211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4878.33 | 0.272104 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29118.6 | 1.61709 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30071.4 | 1.66274 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12914.2 | 0.710968 | 0.355484 | − | 0.934682i | \(-0.384316\pi\) | ||||
0.355484 | + | 0.934682i | \(0.384316\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4334.64 | 0.237604 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13668.0 | 0.745983 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4466.90 | 0.242749 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7334.12 | −0.396855 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13188.4 | 0.710581 | 0.355290 | − | 0.934756i | \(-0.384382\pi\) | ||||
0.355290 | + | 0.934756i | \(0.384382\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25158.1 | 1.34972 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14445.6 | −0.771706 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2764.23 | 0.147043 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13435.5 | −0.711680 | −0.355840 | − | 0.934547i | \(-0.615805\pi\) | ||||
−0.355840 | + | 0.934547i | \(0.615805\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11913.5 | −0.628396 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6346.88 | 0.333370 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14296.3 | 0.747761 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −36895.1 | −1.92172 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17486.8 | 0.907020 | 0.453510 | − | 0.891251i | \(-0.350172\pi\) | ||||
0.453510 | + | 0.891251i | \(0.350172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7242.46 | 0.374096 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24533.2 | 1.26197 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2116.12 | −0.108401 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13036.5 | 0.665060 | 0.332530 | − | 0.943093i | \(-0.392098\pi\) | ||||
0.332530 | + | 0.943093i | \(0.392098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20651.1 | −1.04919 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1152.54 | 0.0583152 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35051.0 | −1.76622 | −0.883108 | − | 0.469169i | \(-0.844554\pi\) | ||||
−0.883108 | + | 0.469169i | \(0.844554\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12208.2 | 0.612664 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10261.9 | −0.512893 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25898.2 | −1.28915 | −0.644575 | − | 0.764541i | \(-0.722965\pi\) | ||||
−0.644575 | + | 0.764541i | \(0.722965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 44942.6 | 2.22808 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25133.5 | 1.24100 | 0.620498 | − | 0.784208i | \(-0.286931\pi\) | ||||
0.620498 | + | 0.784208i | \(0.286931\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5200.07 | 0.255726 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8800.45 | −0.431046 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1631.62 | −0.0795971 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20368.0 | −0.989667 | −0.494833 | − | 0.868988i | \(-0.664771\pi\) | ||||
−0.494833 | + | 0.868988i | \(0.664771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26917.5 | 1.30269 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14113.6 | 0.680326 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25262.7 | 1.21293 | 0.606465 | − | 0.795110i | \(-0.292587\pi\) | ||||
0.606465 | + | 0.795110i | \(0.292587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7450.51 | −0.356306 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14926.1 | 0.711001 | 0.355500 | − | 0.934676i | \(-0.384310\pi\) | ||||
0.355500 | + | 0.934676i | \(0.384310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1026.51 | 0.0487055 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3462.64 | −0.163650 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11206.9 | −0.527583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32390.7 | 1.51891 | 0.759453 | − | 0.650562i | \(-0.225467\pi\) | ||||
0.759453 | + | 0.650562i | \(0.225467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52989.1 | 2.47517 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28163.3 | −1.31043 | −0.655215 | − | 0.755443i | \(-0.727422\pi\) | ||||
−0.655215 | + | 0.755443i | \(0.727422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6898.79 | −0.319757 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7141.63 | −0.329735 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16623.2 | −0.764553 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20398.8 | 0.934606 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −420.968 | −0.0192135 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16592.5 | 0.754408 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34922.9 | −1.58179 | −0.790893 | − | 0.611954i | \(-0.790384\pi\) | ||||
−0.790893 | + | 0.611954i | \(0.790384\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 59838.9 | 2.70003 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5433.79 | −0.244252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28216.4 | 1.26355 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17034.5 | 0.759939 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26096.8 | 1.15985 | 0.579923 | − | 0.814671i | \(-0.303083\pi\) | ||||
0.579923 | + | 0.814671i | \(0.303083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9778.39 | 0.432959 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40213.7 | 1.77389 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15926.4 | 0.699915 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 411.176 | 0.0180025 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10033.3 | −0.437658 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −236.848 | −0.0102931 | −0.00514656 | − | 0.999987i | \(-0.501638\pi\) | ||||
−0.00514656 | + | 0.999987i | \(0.501638\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36386.9 | 1.57548 | 0.787742 | − | 0.616005i | \(-0.211250\pi\) | ||||
0.787742 | + | 0.616005i | \(0.211250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51072.3 | 2.20318 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4771.45 | 0.205076 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4289.09 | −0.183668 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6457.41 | −0.275507 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27347.7 | −1.16254 | −0.581268 | − | 0.813712i | \(-0.697443\pi\) | ||||
−0.581268 | + | 0.813712i | \(0.697443\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2368.01 | −0.100296 | −0.0501480 | − | 0.998742i | \(-0.515969\pi\) | ||||
−0.0501480 | + | 0.998742i | \(0.515969\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8098.38 | 0.341757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19465.1 | −0.818463 | −0.409231 | − | 0.912431i | \(-0.634203\pi\) | ||||
−0.409231 | + | 0.912431i | \(0.634203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33035.4 | 1.38404 | 0.692020 | − | 0.721879i | \(-0.256721\pi\) | ||||
0.692020 | + | 0.721879i | \(0.256721\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58337.6 | 2.43527 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8263.90 | −0.343730 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5686.01 | 0.235656 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1372.40 | −0.0566753 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36015.4 | 1.48199 | 0.740995 | − | 0.671511i | \(-0.234354\pi\) | ||||
0.740995 | + | 0.671511i | \(0.234354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17224.3 | −0.706231 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −55972.5 | −2.28683 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10312.4 | −0.419833 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2103.50 | 0.0853329 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18788.6 | −0.759507 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6213.13 | 0.250274 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9941.26 | 0.399041 | 0.199521 | − | 0.979894i | \(-0.436062\pi\) | ||||
0.199521 | + | 0.979894i | \(0.436062\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12885.9 | 0.515425 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11884.7 | −0.473716 | −0.236858 | − | 0.971544i | \(-0.576118\pi\) | ||||
−0.236858 | + | 0.971544i | \(0.576118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24824.3 | −0.986022 | −0.493011 | − | 0.870023i | \(-0.664104\pi\) | ||||
−0.493011 | + | 0.870023i | \(0.664104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4718.82 | 0.186779 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18701.1 | 0.737653 | 0.368826 | − | 0.929498i | \(-0.379760\pi\) | ||||
0.368826 | + | 0.929498i | \(0.379760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21744.1 | 0.854709 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31696.4 | −1.24160 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18860.8 | −0.736260 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15287.4 | 0.594711 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25445.4 | −0.986478 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −446.930 | −0.0172674 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2743.01 | −0.105615 | −0.0528077 | − | 0.998605i | \(-0.516817\pi\) | ||||
−0.0528077 | + | 0.998605i | \(0.516817\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8776.90 | −0.336789 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39165.3 | 1.49774 | 0.748872 | − | 0.662715i | \(-0.230596\pi\) | ||||
0.748872 | + | 0.662715i | \(0.230596\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27421.4 | 1.04508 | 0.522539 | − | 0.852615i | \(-0.324985\pi\) | ||||
0.522539 | + | 0.852615i | \(0.324985\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6348.34 | −0.241127 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22388.7 | 0.847509 | 0.423754 | − | 0.905777i | \(-0.360712\pi\) | ||||
0.423754 | + | 0.905777i | \(0.360712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −465.865 | −0.0175755 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31122.1 | −1.17018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36389.4 | −1.36363 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13138.8 | −0.490705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11099.2 | 0.413145 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23357.8 | 0.866549 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11530.8 | −0.426358 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1217.55 | 0.0448697 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9929.23 | 0.364706 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8406.44 | 0.307752 | 0.153876 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153876 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21394.1 | 0.780636 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23147.0 | 0.841816 | 0.420908 | − | 0.907103i | \(-0.361712\pi\) | ||||
0.420908 | + | 0.907103i | \(0.361712\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13932.5 | −0.505036 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15983.7 | 0.577492 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4935.67 | 0.177743 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8915.09 | 0.320002 | 0.160001 | − | 0.987117i | \(-0.448850\pi\) | ||||
0.160001 | + | 0.987117i | \(0.448850\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21184.1 | 0.757916 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30388.6 | −1.08370 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6753.40 | −0.240055 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 56054.1 | 1.98604 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29110.6 | 1.02808 | 0.514041 | − | 0.857766i | \(-0.328148\pi\) | ||||
0.514041 | + | 0.857766i | \(0.328148\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30753.4 | 1.08260 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7044.55 | 0.247190 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5481.89 | −0.191740 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47055.8 | 1.64061 | 0.820303 | − | 0.571930i | \(-0.193805\pi\) | ||||
0.820303 | + | 0.571930i | \(0.193805\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5240.56 | −0.182129 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36217.3 | 1.25468 | 0.627339 | − | 0.778747i | \(-0.284144\pi\) | ||||
0.627339 | + | 0.778747i | \(0.284144\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4105.32 | −0.141768 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −88.9096 | −0.00306056 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13445.6 | −0.461376 | −0.230688 | − | 0.973028i | \(-0.574098\pi\) | ||||
−0.230688 | + | 0.973028i | \(0.574098\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23726.0 | −0.811568 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32581.0 | 1.11095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25975.6 | 0.882929 | 0.441465 | − | 0.897279i | \(-0.354459\pi\) | ||||
0.441465 | + | 0.897279i | \(0.354459\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20646.7 | −0.699594 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27419.4 | −0.926169 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3488.43 | −0.117463 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46358.2 | 1.55611 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12628.2 | −0.422573 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13116.6 | −0.437554 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7598.70 | 0.252697 | 0.126348 | − | 0.991986i | \(-0.459674\pi\) | ||||
0.126348 | + | 0.991986i | \(0.459674\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17233.2 | −0.571321 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11186.0 | −0.369696 | −0.184848 | − | 0.982767i | \(-0.559179\pi\) | ||||
−0.184848 | + | 0.982767i | \(0.559179\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9773.84 | −0.322030 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12064.3 | −0.396275 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2597.14 | −0.0850460 | −0.0425230 | − | 0.999095i | \(-0.513540\pi\) | ||||
−0.0425230 | + | 0.999095i | \(0.513540\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63664.6 | 2.07837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7944.84 | 0.258572 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33005.1 | 1.07090 | 0.535452 | − | 0.844566i | \(-0.320141\pi\) | ||||
0.535452 | + | 0.844566i | \(0.320141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16486.3 | −0.533295 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10329.9 | 0.333134 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1059.25 | −0.0340568 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4986.74 | −0.159848 | −0.0799239 | − | 0.996801i | \(-0.525468\pi\) | ||||
−0.0799239 | + | 0.996801i | \(0.525468\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 74448.9 | 2.37922 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18042.9 | 0.574872 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58754.2 | −1.86636 | −0.933182 | − | 0.359405i | \(-0.882980\pi\) | ||||
−0.933182 | + | 0.359405i | \(0.882980\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1343.48 | −0.0425484 |
(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 | 1840.4.a.p.1.4 | 5 | ||
4.3 | odd | 2 | 115.4.a.d.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 1035.4.a.m.1.1 | 5 | |||
20.3 | even | 4 | 575.4.b.h.24.3 | 10 | |||
20.7 | even | 4 | 575.4.b.h.24.8 | 10 | |||
20.19 | odd | 2 | 575.4.a.k.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.4.a.d.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
575.4.a.k.1.1 | 5 | 20.19 | odd | 2 | |||
575.4.b.h.24.3 | 10 | 20.3 | even | 4 | |||
575.4.b.h.24.8 | 10 | 20.7 | even | 4 | |||
1035.4.a.m.1.1 | 5 | 12.11 | even | 2 | |||
1840.4.a.p.1.4 | 5 | 1.1 | even | 1 | trivial |