Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.5498 | −0.943606 | −0.471803 | − | 0.881704i | \(-0.656397\pi\) | ||||
−0.471803 | + | 0.881704i | \(0.656397\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −34.7492 | −0.952479 | −0.476240 | − | 0.879316i | \(-0.658000\pi\) | ||||
−0.476240 | + | 0.879316i | \(0.658000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.2990 | 0.795760 | 0.397880 | − | 0.917437i | \(-0.369746\pi\) | ||||
0.397880 | + | 0.917437i | \(0.369746\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.6495 | −0.544791 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.5498 | 0.150512 | 0.0752562 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752562 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −58.5980 | −0.707542 | −0.353771 | − | 0.935332i | \(-0.615101\pi\) | ||||
−0.353771 | + | 0.935332i | \(0.615101\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 125.347 | 1.13638 | 0.568189 | − | 0.822898i | \(-0.307644\pi\) | ||||
0.568189 | + | 0.822898i | \(0.307644\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.7010 | −0.109608 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −35.4020 | −0.226689 | −0.113345 | − | 0.993556i | \(-0.536156\pi\) | ||||
−0.113345 | + | 0.993556i | \(0.536156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 291.794 | 1.69057 | 0.845286 | − | 0.534313i | \(-0.179430\pi\) | ||||
0.845286 | + | 0.534313i | \(0.179430\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −104.248 | −0.549914 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −259.897 | −1.15478 | −0.577389 | − | 0.816469i | \(-0.695928\pi\) | ||||
−0.577389 | + | 0.816469i | \(0.695928\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 111.897 | 0.459432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 338.248 | 1.28842 | 0.644212 | − | 0.764847i | \(-0.277185\pi\) | ||||
0.644212 | + | 0.764847i | \(0.277185\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.80397 | −0.0241301 | −0.0120651 | − | 0.999927i | \(-0.503841\pi\) | ||||
−0.0120651 | + | 0.999927i | \(0.503841\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −94.9485 | −0.314535 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 250.694 | 0.778033 | 0.389016 | − | 0.921231i | \(-0.372815\pi\) | ||||
0.389016 | + | 0.921231i | \(0.372815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 31.6495 | 0.0868984 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −536.900 | −1.39149 | −0.695745 | − | 0.718289i | \(-0.744925\pi\) | ||||
−0.695745 | + | 0.718289i | \(0.744925\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 366.598 | 0.898765 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −175.794 | −0.408500 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −35.8904 | −0.0791955 | −0.0395977 | − | 0.999216i | \(-0.512608\pi\) | ||||
−0.0395977 | + | 0.999216i | \(0.512608\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −57.7940 | −0.121308 | −0.0606538 | − | 0.998159i | \(-0.519319\pi\) | ||||
−0.0606538 | + | 0.998159i | \(0.519319\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −393.498 | −0.750884 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −481.691 | −0.878327 | −0.439164 | − | 0.898407i | \(-0.644725\pi\) | ||||
−0.439164 | + | 0.898407i | \(0.644725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 376.042 | 0.656088 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −363.752 | −0.608021 | −0.304010 | − | 0.952669i | \(-0.598326\pi\) | ||||
−0.304010 | + | 0.952669i | \(0.598326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −581.299 | −0.931999 | −0.465999 | − | 0.884785i | \(-0.654305\pi\) | ||||
−0.465999 | + | 0.884785i | \(0.654305\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −41.1030 | −0.0632822 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 693.691 | 0.987928 | 0.493964 | − | 0.869482i | \(-0.335547\pi\) | ||||
0.493964 | + | 0.869482i | \(0.335547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1334.39 | 1.76468 | 0.882341 | − | 0.470611i | \(-0.155967\pi\) | ||||
0.882341 | + | 0.470611i | \(0.155967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −111.299 | −0.142024 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −106.206 | −0.130879 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 353.038 | 0.420472 | 0.210236 | − | 0.977651i | \(-0.432577\pi\) | ||||
0.210236 | + | 0.977651i | \(0.432577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 875.382 | 0.976053 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 618.199 | 0.667641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1445.88 | −1.51347 | −0.756735 | − | 0.653722i | \(-0.773207\pi\) | ||||
−0.756735 | + | 0.653722i | \(0.773207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −312.743 | −0.317493 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −474.852 | −0.467817 | −0.233909 | − | 0.972259i | \(-0.575152\pi\) | ||||
−0.233909 | + | 0.972259i | \(0.575152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1999.59 | −1.91287 | −0.956433 | − | 0.291951i | \(-0.905696\pi\) | ||||
−0.956433 | + | 0.291951i | \(0.905696\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1166.74 | −1.05414 | −0.527068 | − | 0.849823i | \(-0.676709\pi\) | ||||
−0.527068 | + | 0.849823i | \(0.676709\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1337.18 | −1.17503 | −0.587515 | − | 0.809213i | \(-0.699894\pi\) | ||||
−0.587515 | + | 0.809213i | \(0.699894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −779.691 | −0.666712 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 906.578 | 0.754723 | 0.377361 | − | 0.926066i | \(-0.376831\pi\) | ||||
0.377361 | + | 0.926066i | \(0.376831\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1322.39 | −1.07229 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 335.691 | 0.265253 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −123.495 | −0.0927836 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1014.74 | 0.743872 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1463.27 | 1.04703 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1714.89 | 1.19820 | 0.599101 | − | 0.800674i | \(-0.295525\pi\) | ||||
0.599101 | + | 0.800674i | \(0.295525\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.4119 | −0.0139315 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 470.611 | 0.313874 | 0.156937 | − | 0.987609i | \(-0.449838\pi\) | ||||
0.156937 | + | 0.987609i | \(0.449838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −284.846 | −0.181597 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −443.910 | −0.276831 | −0.138415 | − | 0.990374i | \(-0.544201\pi\) | ||||
−0.138415 | + | 0.990374i | \(0.544201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1669.98 | 1.01904 | 0.509518 | − | 0.860460i | \(-0.329824\pi\) | ||||
0.509518 | + | 0.860460i | \(0.329824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 752.083 | 0.449197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1296.11 | −0.757945 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 373.485 | 0.213905 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 743.871 | 0.408995 | 0.204497 | − | 0.978867i | \(-0.434444\pi\) | ||||
0.204497 | + | 0.978867i | \(0.434444\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −606.764 | −0.327005 | −0.163503 | − | 0.986543i | \(-0.552279\pi\) | ||||
−0.163503 | + | 0.986543i | \(0.552279\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 94.9485 | 0.0501708 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3078.38 | −1.59523 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3114.78 | −1.58336 | −0.791678 | − | 0.610939i | \(-0.790792\pi\) | ||||
−0.791678 | + | 0.610939i | \(0.790792\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1610.70 | −0.803377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2413.07 | −1.15955 | −0.579774 | − | 0.814777i | \(-0.696859\pi\) | ||||
−0.579774 | + | 0.814777i | \(0.696859\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1099.79 | 0.518902 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −610.475 | −0.282874 | −0.141437 | − | 0.989947i | \(-0.545172\pi\) | ||||
−0.141437 | + | 0.989947i | \(0.545172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −805.784 | −0.366766 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −527.382 | −0.235847 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3793.81 | −1.66727 | −0.833636 | − | 0.552315i | \(-0.813745\pi\) | ||||
−0.833636 | + | 0.552315i | \(0.813745\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −107.671 | −0.0457235 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2804.68 | 1.17112 | 0.585562 | − | 0.810627i | \(-0.300874\pi\) | ||||
0.585562 | + | 0.810627i | \(0.300874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3106.04 | −1.27553 | −0.637763 | − | 0.770232i | \(-0.720140\pi\) | ||||
−0.637763 | + | 0.770232i | \(0.720140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −173.382 | −0.0700370 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2741.87 | 1.08966 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −366.598 | −0.143360 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −261.952 | −0.0992365 | −0.0496182 | − | 0.998768i | \(-0.515800\pi\) | ||||
−0.0496182 | + | 0.998768i | \(0.515800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4051.07 | 1.51089 | 0.755447 | − | 0.655210i | \(-0.227420\pi\) | ||||
0.755447 | + | 0.655210i | \(0.227420\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1180.50 | −0.433523 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2874.83 | −1.03971 | −0.519855 | − | 0.854254i | \(-0.674014\pi\) | ||||
−0.519855 | + | 0.854254i | \(0.674014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3066.97 | −1.09252 | −0.546261 | − | 0.837615i | \(-0.683949\pi\) | ||||
−0.546261 | + | 0.837615i | \(0.683949\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1445.07 | −0.507103 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3568.46 | −1.21576 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1128.12 | 0.378793 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2036.23 | 0.673919 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −595.422 | −0.194268 | −0.0971340 | − | 0.995271i | \(-0.530968\pi\) | ||||
−0.0971340 | + | 0.995271i | \(0.530968\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1091.26 | −0.351041 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 71.7808 | 0.0227693 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1743.90 | −0.538090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 393.498 | 0.119772 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3779.79 | −1.13504 | −0.567520 | − | 0.823360i | \(-0.692097\pi\) | ||||
−0.567520 | + | 0.823360i | \(0.692097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −123.309 | −0.0365360 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1827.62 | 0.534376 | 0.267188 | − | 0.963644i | \(-0.413906\pi\) | ||||
0.267188 | + | 0.963644i | \(0.413906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 850.249 | 0.245354 | 0.122677 | − | 0.992447i | \(-0.460852\pi\) | ||||
0.122677 | + | 0.992447i | \(0.460852\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6591.10 | −1.85321 | −0.926604 | − | 0.376039i | \(-0.877286\pi\) | ||||
−0.926604 | + | 0.376039i | \(0.877286\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2644.78 | −0.734156 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2081.07 | 0.570381 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 182.556 | 0.0494083 | 0.0247042 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247042 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1523.90 | −0.407315 | −0.203657 | − | 0.979042i | \(-0.565283\pi\) | ||||
−0.203657 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2185.65 | −0.563034 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4003.18 | 1.01884 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2357.73 | 0.592903 | 0.296451 | − | 0.955048i | \(-0.404197\pi\) | ||||
0.296451 | + | 0.955048i | \(0.404197\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4355.71 | −1.08238 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −333.897 | −0.0819978 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2782.55 | −0.675372 | −0.337686 | − | 0.941259i | \(-0.609644\pi\) | ||||
−0.337686 | + | 0.941259i | \(0.609644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −318.618 | −0.0755630 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2043.78 | −0.479183 | −0.239591 | − | 0.970874i | \(-0.577013\pi\) | ||||
−0.239591 | + | 0.970874i | \(0.577013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5664.21 | 1.31302 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1059.11 | 0.242759 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3452.84 | −0.782614 | −0.391307 | − | 0.920260i | \(-0.627977\pi\) | ||||
−0.391307 | + | 0.920260i | \(0.627977\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2644.29 | 0.592728 | 0.296364 | − | 0.955075i | \(-0.404226\pi\) | ||||
0.296364 | + | 0.955075i | \(0.404226\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 476.098 | 0.104399 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2679.49 | 0.581208 | 0.290604 | − | 0.956843i | \(-0.406144\pi\) | ||||
0.290604 | + | 0.956843i | \(0.406144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2626.15 | 0.563524 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1019.69 | −0.216476 | −0.108238 | − | 0.994125i | \(-0.534521\pi\) | ||||
−0.108238 | + | 0.994125i | \(0.534521\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 432.206 | 0.0907844 | 0.0453922 | − | 0.998969i | \(-0.485546\pi\) | ||||
0.0453922 | + | 0.998969i | \(0.485546\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1854.60 | 0.385463 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4801.70 | −0.977346 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4337.63 | −0.873802 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2245.92 | 0.447809 | 0.223904 | − | 0.974611i | \(-0.428120\pi\) | ||||
0.223904 | + | 0.974611i | \(0.428120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 378.638 | 0.0747293 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −938.228 | −0.183305 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4675.33 | 0.904284 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1424.56 | −0.270094 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 609.718 | 0.114467 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3197.08 | −0.594354 | −0.297177 | − | 0.954822i | \(-0.596045\pi\) | ||||
−0.297177 | + | 0.954822i | \(0.596045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5998.76 | −1.10439 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3355.60 | −0.611829 | −0.305915 | − | 0.952059i | \(-0.598962\pi\) | ||||
−0.305915 | + | 0.952059i | \(0.598962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2256.39 | 0.407472 | 0.203736 | − | 0.979026i | \(-0.434692\pi\) | ||||
0.203736 | + | 0.979026i | \(0.434692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6139.19 | −1.08773 | −0.543866 | − | 0.839172i | \(-0.683040\pi\) | ||||
−0.543866 | + | 0.839172i | \(0.683040\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1230.19 | 0.215917 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3500.21 | −0.608606 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −618.199 | −0.106494 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −511.033 | −0.0872216 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4011.53 | −0.678404 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7029.81 | −1.16735 | −0.583676 | − | 0.811987i | \(-0.698386\pi\) | ||||
−0.583676 | + | 0.811987i | \(0.698386\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2339.07 | −0.384926 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5081.76 | 0.828795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10328.4 | 1.66951 | 0.834757 | − | 0.550619i | \(-0.185608\pi\) | ||||
0.834757 | + | 0.550619i | \(0.185608\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2719.73 | 0.435740 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10139.6 | −1.61024 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3967.18 | −0.619089 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1967.54 | −0.304389 | −0.152194 | − | 0.988351i | \(-0.548634\pi\) | ||||
−0.152194 | + | 0.988351i | \(0.548634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4365.46 | 0.669564 | 0.334782 | − | 0.942296i | \(-0.391337\pi\) | ||||
0.334782 | + | 0.942296i | \(0.391337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1007.07 | 0.153144 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6071.59 | 0.915462 | 0.457731 | − | 0.889091i | \(-0.348662\pi\) | ||||
0.457731 | + | 0.889091i | \(0.348662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3837.53 | 0.573732 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9638.04 | −1.41693 | −0.708463 | − | 0.705748i | \(-0.750611\pi\) | ||||
−0.708463 | + | 0.705748i | \(0.750611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3425.27 | −0.499384 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −370.485 | −0.0535687 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6132.61 | 0.879439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 522.725 | 0.0743488 | 0.0371744 | − | 0.999309i | \(-0.488164\pi\) | ||||
0.0371744 | + | 0.999309i | \(0.488164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3044.23 | 0.429475 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3229.84 | 0.448351 | 0.224175 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224175 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4389.82 | 0.604505 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1320.46 | −0.180390 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6639.71 | −0.899892 | −0.449946 | − | 0.893056i | \(-0.648557\pi\) | ||||
−0.449946 | + | 0.893056i | \(0.648557\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5144.66 | 0.691782 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14224.4 | −1.89774 | −0.948871 | − | 0.315664i | \(-0.897773\pi\) | ||||
−0.948871 | + | 0.315664i | \(0.897773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −61.2358 | −0.00804338 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2921.82 | 0.380828 | 0.190414 | − | 0.981704i | \(-0.439017\pi\) | ||||
0.190414 | + | 0.981704i | \(0.439017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1322.39 | 0.171039 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1411.83 | 0.181215 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7318.33 | −0.932215 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −811.940 | −0.102645 | −0.0513226 | − | 0.998682i | \(-0.516344\pi\) | ||||
−0.0513226 | + | 0.998682i | \(0.516344\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2338.63 | 0.291237 | 0.145618 | − | 0.989341i | \(-0.453483\pi\) | ||||
0.145618 | + | 0.989341i | \(0.453483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10883.6 | 1.34529 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −854.537 | −0.104845 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9031.21 | 1.09990 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2727.57 | 0.329755 | 0.164877 | − | 0.986314i | \(-0.447277\pi\) | ||||
0.164877 | + | 0.986314i | \(0.447277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1331.73 | −0.159828 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14077.6 | −1.66516 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5009.94 | 0.588340 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13306.3 | 1.55144 | 0.775721 | − | 0.631076i | \(-0.217386\pi\) | ||||
0.775721 | + | 0.631076i | \(0.217386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11007.5 | −1.27428 | −0.637138 | − | 0.770750i | \(-0.719882\pi\) | ||||
−0.637138 | + | 0.770750i | \(0.719882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2256.25 | 0.259344 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −144.543 | −0.0164974 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3888.33 | −0.437600 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6525.62 | 0.729300 | 0.364650 | − | 0.931145i | \(-0.381189\pi\) | ||||
0.364650 | + | 0.931145i | \(0.381189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11716.3 | 1.30034 | 0.650171 | − | 0.759788i | \(-0.274697\pi\) | ||||
0.650171 | + | 0.759788i | \(0.274697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1120.46 | 0.123498 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7345.10 | −0.804036 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14611.4 | −1.58853 | −0.794264 | − | 0.607573i | \(-0.792143\pi\) | ||||
−0.794264 | + | 0.607573i | \(0.792143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15239.8 | 1.63446 | 0.817228 | − | 0.576314i | \(-0.195510\pi\) | ||||
0.817228 | + | 0.576314i | \(0.195510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3724.50 | −0.396760 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2231.61 | 0.236133 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10678.8 | 1.12241 | 0.561206 | − | 0.827676i | \(-0.310338\pi\) | ||||
0.561206 | + | 0.827676i | \(0.310338\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11753.8 | −1.22720 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1820.29 | −0.188796 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4228.23 | 0.432797 | 0.216399 | − | 0.976305i | \(-0.430569\pi\) | ||||
0.216399 | + | 0.976305i | \(0.430569\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 284.846 | 0.0289661 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −910.121 | −0.0919492 | −0.0459746 | − | 0.998943i | \(-0.514639\pi\) | ||||
−0.0459746 | + | 0.998943i | \(0.514639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4456.16 | −0.447290 | −0.223645 | − | 0.974671i | \(-0.571796\pi\) | ||||
−0.223645 | + | 0.974671i | \(0.571796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9235.14 | −0.921009 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4429.42 | −0.438907 | −0.219453 | − | 0.975623i | \(-0.570427\pi\) | ||||
−0.219453 | + | 0.975623i | \(0.570427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9344.35 | −0.914151 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 236.432 | 0.0229835 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 802.851 | 0.0775523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4832.10 | −0.463830 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2752.85 | 0.262591 | 0.131296 | − | 0.991343i | \(-0.458086\pi\) | ||||
0.131296 | + | 0.991343i | \(0.458086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9693.90 | −0.918927 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15253.8 | 1.42812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 670.598 | 0.0623977 | 0.0311989 | − | 0.999513i | \(-0.490067\pi\) | ||||
0.0311989 | + | 0.999513i | \(0.490067\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7239.22 | −0.669466 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8244.70 | 0.757797 | 0.378898 | − | 0.925438i | \(-0.376303\pi\) | ||||
0.378898 | + | 0.925438i | \(0.376303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −373.485 | −0.0341195 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3299.38 | 0.299588 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8164.91 | −0.732488 | −0.366244 | − | 0.930519i | \(-0.619356\pi\) | ||||
−0.366244 | + | 0.930519i | \(0.619356\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1831.43 | −0.163317 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8175.59 | 0.724715 | 0.362357 | − | 0.932039i | \(-0.381972\pi\) | ||||
0.362357 | + | 0.932039i | \(0.381972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5009.61 | 0.441435 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2417.35 | −0.211752 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 878.448 | 0.0764961 | 0.0382480 | − | 0.999268i | \(-0.487822\pi\) | ||||
0.0382480 | + | 0.999268i | \(0.487822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1582.15 | −0.136167 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21095.3 | 1.80499 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8711.42 | −0.741060 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11381.4 | −0.962600 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11712.6 | −0.984910 | −0.492455 | − | 0.870338i | \(-0.663900\pi\) | ||||
−0.492455 | + | 0.870338i | \(0.663900\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7341.82 | −0.613834 | −0.306917 | − | 0.951736i | \(-0.599297\pi\) | ||||
−0.306917 | + | 0.951736i | \(0.599297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3078.38 | 0.254452 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3544.92 | 0.291355 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −323.014 | −0.0263985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12616.3 | 1.02528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12308.9 | 0.994690 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8414.03 | 0.676149 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15868.7 | −1.26109 | −0.630545 | − | 0.776153i | \(-0.717169\pi\) | ||||
−0.630545 | + | 0.776153i | \(0.717169\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9318.13 | −0.736426 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14107.0 | 1.10877 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2315.26 | −0.180975 | −0.0904875 | − | 0.995898i | \(-0.528843\pi\) | ||||
−0.0904875 | + | 0.995898i | \(0.528843\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −520.146 | −0.0404359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2074.49 | 0.160392 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8225.61 | 0.629113 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4819.05 | −0.366588 | −0.183294 | − | 0.983058i | \(-0.558676\pi\) | ||||
−0.183294 | + | 0.983058i | \(0.558676\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −253.781 | −0.0192018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1099.79 | −0.0827689 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2540.86 | 0.190203 | 0.0951017 | − | 0.995468i | \(-0.469682\pi\) | ||||
0.0951017 | + | 0.995468i | \(0.469682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9564.25 | −0.712161 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24220.0 | −1.78445 | −0.892227 | − | 0.451587i | \(-0.850858\pi\) | ||||
−0.892227 | + | 0.451587i | \(0.850858\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11772.1 | 0.862778 | 0.431389 | − | 0.902166i | \(-0.358024\pi\) | ||||
0.431389 | + | 0.902166i | \(0.358024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −785.855 | −0.0572942 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1717.38 | −0.124556 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10584.3 | −0.763655 | −0.381827 | − | 0.924234i | \(-0.624705\pi\) | ||||
−0.381827 | + | 0.924234i | \(0.624705\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12153.2 | 0.872315 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18656.8 | 1.32536 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3541.49 | −0.250295 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8712.63 | −0.612621 | −0.306311 | − | 0.951932i | \(-0.599095\pi\) | ||||
−0.306311 | + | 0.951932i | \(0.599095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17098.6 | −1.19615 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8624.48 | −0.600277 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15362.9 | 1.06387 | 0.531937 | − | 0.846784i | \(-0.321464\pi\) | ||||
0.531937 | + | 0.846784i | \(0.321464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9200.91 | −0.630768 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26003.8 | −1.77377 | −0.886883 | − | 0.461994i | \(-0.847134\pi\) | ||||
−0.886883 | + | 0.461994i | \(0.847134\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20567.7 | −1.39596 | −0.697982 | − | 0.716115i | \(-0.745918\pi\) | ||||
−0.697982 | + | 0.716115i | \(0.745918\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4335.22 | −0.292776 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1302.85 | 0.0875512 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19642.1 | 1.31342 | 0.656711 | − | 0.754142i | \(-0.271947\pi\) | ||||
0.656711 | + | 0.754142i | \(0.271947\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9350.65 | 0.619127 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8454.59 | 0.557060 | 0.278530 | − | 0.960428i | \(-0.410153\pi\) | ||||
0.278530 | + | 0.960428i | \(0.410153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10705.4 | −0.701922 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24168.4 | −1.57696 | −0.788479 | − | 0.615061i | \(-0.789131\pi\) | ||||
−0.788479 | + | 0.615061i | \(0.789131\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2037.56 | −0.132305 | −0.0661523 | − | 0.997810i | \(-0.521072\pi\) | ||||
−0.0661523 | + | 0.997810i | \(0.521072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3384.37 | 0.218696 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13724.7 | −0.878378 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6108.70 | 0.389088 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2741.87 | −0.173808 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12339.5 | −0.778489 | −0.389244 | − | 0.921135i | \(-0.627264\pi\) | ||||
−0.389244 | + | 0.921135i | \(0.627264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1786.27 | −0.112161 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18091.8 | −1.13063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3273.77 | −0.202674 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10222.6 | −0.629906 | −0.314953 | − | 0.949107i | \(-0.601989\pi\) | ||||
−0.314953 | + | 0.949107i | \(0.601989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1211.75 | −0.0743187 | −0.0371594 | − | 0.999309i | \(-0.511831\pi\) | ||||
−0.0371594 | + | 0.999309i | \(0.511831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 215.342 | 0.0131459 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2817.22 | −0.171184 | −0.0855922 | − | 0.996330i | \(-0.527278\pi\) | ||||
−0.0855922 | + | 0.996330i | \(0.527278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1247.16 | 0.0754320 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20986.2 | 1.25766 | 0.628831 | − | 0.777542i | \(-0.283534\pi\) | ||||
0.628831 | + | 0.777542i | \(0.283534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4964.87 | −0.296173 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5231.69 | −0.310666 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2384.09 | 0.140927 | 0.0704635 | − | 0.997514i | \(-0.477552\pi\) | ||||
0.0704635 | + | 0.997514i | \(0.477552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7577.10 | 0.445862 | 0.222931 | − | 0.974834i | \(-0.428438\pi\) | ||||
0.222931 | + | 0.974834i | \(0.428438\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1180.50 | 0.0691503 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4437.54 | −0.257605 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11339.4 | −0.655315 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2008.30 | 0.115543 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11724.6 | 0.671547 | 0.335774 | − | 0.941943i | \(-0.391002\pi\) | ||||
0.335774 | + | 0.941943i | \(0.391002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −369.927 | −0.0210941 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32304.3 | −1.83390 | −0.916952 | − | 0.398997i | \(-0.869358\pi\) | ||||
−0.916952 | + | 0.398997i | \(0.869358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5482.85 | 0.308522 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33367.1 | −1.86934 | −0.934669 | − | 0.355519i | \(-0.884304\pi\) | ||||
−0.934669 | + | 0.355519i | \(0.884304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4683.18 | 0.261219 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2550.75 | 0.141655 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20025.8 | −1.10729 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1043.67 | −0.0574577 | −0.0287288 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287288 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17618.0 | −0.961567 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3568.46 | 0.193924 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19773.3 | −1.06995 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11305.7 | −0.609143 | −0.304572 | − | 0.952489i | \(-0.598513\pi\) | ||||
−0.304572 | + | 0.952489i | \(0.598513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15229.4 | 0.817055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7934.35 | −0.423865 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13306.8 | −0.704860 | −0.352430 | − | 0.935838i | \(-0.614645\pi\) | ||||
−0.352430 | + | 0.935838i | \(0.614645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6243.22 | 0.329309 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36575.6 | 1.92113 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13673.7 | 0.715201 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 547.669 | 0.0285259 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10701.2 | 0.555062 | 0.277531 | − | 0.960717i | \(-0.410484\pi\) | ||||
0.277531 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4571.69 | −0.235163 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 485.042 | 0.0248469 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2121.14 | −0.108210 | −0.0541051 | − | 0.998535i | \(-0.517231\pi\) | ||||
−0.0541051 | + | 0.998535i | \(0.517231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −71.7808 | −0.00363189 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21584.0 | 1.08762 | 0.543809 | − | 0.839209i | \(-0.316981\pi\) | ||||
0.543809 | + | 0.839209i | \(0.316981\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16738.4 | 0.836588 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9945.21 | 0.495048 | 0.247524 | − | 0.968882i | \(-0.420383\pi\) | ||||
0.247524 | + | 0.968882i | \(0.420383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6556.94 | −0.325068 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2867.01 | −0.141562 | −0.0707808 | − | 0.997492i | \(-0.522549\pi\) | ||||
−0.0707808 | + | 0.997492i | \(0.522549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7847.71 | −0.385930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12009.5 | 0.588227 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10824.1 | 0.525934 | 0.262967 | − | 0.964805i | \(-0.415299\pi\) | ||||
0.262967 | + | 0.964805i | \(0.415299\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7073.19 | 0.342313 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6401.26 | 0.308564 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14512.0 | −0.696761 | −0.348381 | − | 0.937353i | \(-0.613268\pi\) | ||||
−0.348381 | + | 0.937353i | \(0.613268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13067.1 | −0.624910 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33075.8 | 1.57556 | 0.787778 | − | 0.615959i | \(-0.211231\pi\) | ||||
0.787778 | + | 0.615959i | \(0.211231\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1001.69 | −0.0473415 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1338.68 | −0.0630206 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6728.44 | −0.315518 | −0.157759 | − | 0.987478i | \(-0.550427\pi\) | ||||
−0.157759 | + | 0.987478i | \(0.550427\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8347.65 | −0.389926 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24233.3 | 1.12757 | 0.563784 | − | 0.825922i | \(-0.309345\pi\) | ||||
0.563784 | + | 0.825922i | \(0.309345\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3997.87 | −0.185300 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19820.6 | −0.911615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12640.1 | 0.579127 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −955.854 | −0.0436263 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32860.5 | 1.49406 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17200.4 | −0.779069 | −0.389535 | − | 0.921012i | \(-0.627364\pi\) | ||||
−0.389535 | + | 0.921012i | \(0.627364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6131.35 | −0.276656 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2155.66 | −0.0965318 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16992.6 | 0.758071 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4208.87 | 0.187059 | 0.0935295 | − | 0.995617i | \(-0.470185\pi\) | ||||
0.0935295 | + | 0.995617i | \(0.470185\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2644.78 | 0.117104 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3177.34 | 0.140157 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20199.7 | 0.887709 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10358.5 | −0.451842 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23632.1 | −1.02702 | −0.513511 | − | 0.858083i | \(-0.671656\pi\) | ||||
−0.513511 | + | 0.858083i | \(0.671656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28425.1 | 1.23075 | 0.615377 | − | 0.788233i | \(-0.289004\pi\) | ||||
0.615377 | + | 0.788233i | \(0.289004\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7932.88 | 0.342212 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25457.5 | 1.09416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 398.699 | 0.0170731 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39409.6 | 1.67528 | 0.837640 | − | 0.546223i | \(-0.183935\pi\) | ||||
0.837640 | + | 0.546223i | \(0.183935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16346.6 | −0.692352 | −0.346176 | − | 0.938170i | \(-0.612520\pi\) | ||||
−0.346176 | + | 0.938170i | \(0.612520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1428.29 | 0.0602749 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3738.87 | 0.157211 | 0.0786054 | − | 0.996906i | \(-0.474953\pi\) | ||||
0.0786054 | + | 0.996906i | \(0.474953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45196.2 | 1.89352 | 0.946761 | − | 0.321937i | \(-0.104334\pi\) | ||||
0.946761 | + | 0.321937i | \(0.104334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8038.46 | 0.335561 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6440.41 | 0.266922 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7878.44 | 0.325351 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15899.7 | 0.654254 | 0.327127 | − | 0.944980i | \(-0.393920\pi\) | ||||
0.327127 | + | 0.944980i | \(0.393920\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23135.7 | −0.948612 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3059.07 | −0.124982 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8500.89 | 0.346082 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1296.62 | 0.0524144 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32577.4 | −1.31227 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33926.7 | −1.36182 | −0.680908 | − | 0.732369i | \(-0.738415\pi\) | ||||
−0.680908 | + | 0.732369i | \(0.738415\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5563.79 | 0.222547 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35432.4 | 1.41231 | 0.706154 | − | 0.708058i | \(-0.250428\pi\) | ||||
0.706154 | + | 0.708058i | \(0.250428\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6780.17 | −0.269309 | −0.134655 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134655 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30675.1 | 1.20995 | 0.604977 | − | 0.796243i | \(-0.293182\pi\) | ||||
0.604977 | + | 0.796243i | \(0.293182\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40024.1 | 1.57325 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14405.1 | −0.564271 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24105.2 | −0.940981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17966.6 | −0.698938 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13012.9 | −0.504490 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40861.3 | 1.57330 | 0.786652 | − | 0.617397i | \(-0.211813\pi\) | ||||
0.786652 | + | 0.617397i | \(0.211813\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6737.76 | 0.258543 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43839.0 | 1.67647 | 0.838236 | − | 0.545308i | \(-0.183587\pi\) | ||||
0.838236 | + | 0.545308i | \(0.183587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44625.1 | −1.70074 | −0.850371 | − | 0.526183i | \(-0.823623\pi\) | ||||
−0.850371 | + | 0.526183i | \(0.823623\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1135.91 | 0.0431450 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43967.5 | −1.66436 | −0.832178 | − | 0.554509i | \(-0.812906\pi\) | ||||
−0.832178 | + | 0.554509i | \(0.812906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2814.68 | −0.105831 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14690.2 | −0.550491 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29588.9 | −1.10508 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14026.0 | 0.522089 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10330.1 | −0.383234 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5664.21 | −0.209436 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32768.2 | 1.20359 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13584.3 | 0.497309 | 0.248654 | − | 0.968592i | \(-0.420012\pi\) | ||||
0.248654 | + | 0.968592i | \(0.420012\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4273.67 | −0.155939 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16421.6 | 0.597226 | 0.298613 | − | 0.954374i | \(-0.403476\pi\) | ||||
0.298613 | + | 0.954374i | \(0.403476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46369.0 | −1.68082 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1829.15 | 0.0660873 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29487.3 | 1.05843 | 0.529214 | − | 0.848488i | \(-0.322487\pi\) | ||||
0.529214 | + | 0.848488i | \(0.322487\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9591.23 | −0.343151 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13567.6 | −0.483839 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3560.85 | 0.126573 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17996.3 | −0.637622 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3441.85 | −0.121554 | −0.0607769 | − | 0.998151i | \(-0.519358\pi\) | ||||
−0.0607769 | + | 0.998151i | \(0.519358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10066.8 | −0.353240 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3867.55 | 0.135275 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5646.60 | −0.196869 | −0.0984346 | − | 0.995144i | \(-0.531384\pi\) | ||||
−0.0984346 | + | 0.995144i | \(0.531384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6769.18 | 0.235254 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44680.1 | 1.54785 | 0.773927 | − | 0.633275i | \(-0.218290\pi\) | ||||
0.773927 | + | 0.633275i | \(0.218290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42398.4 | 1.46414 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48924.6 | 1.67881 | 0.839406 | − | 0.543505i | \(-0.182903\pi\) | ||||
0.839406 | + | 0.543505i | \(0.182903\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21681.9 | −0.741647 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18417.6 | −0.628002 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52014.3 | 1.76801 | 0.884003 | − | 0.467482i | \(-0.154839\pi\) | ||||
0.884003 | + | 0.467482i | \(0.154839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2763.55 | 0.0936401 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3690.57 | 0.124660 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55352.8 | 1.85804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10500.6 | −0.351379 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42738.2 | −1.42569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47117.7 | 1.56691 | 0.783456 | − | 0.621448i | \(-0.213455\pi\) | ||||
0.783456 | + | 0.621448i | \(0.213455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1854.60 | −0.0614843 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8195.04 | −0.270846 | −0.135423 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135423 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1533.10 | −0.0503574 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4643.51 | 0.152056 | 0.0760282 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760282 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12267.8 | −0.400490 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12034.6 | −0.391677 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43986.5 | 1.42721 | 0.713607 | − | 0.700546i | \(-0.247060\pi\) | ||||
0.713607 | + | 0.700546i | \(0.247060\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30329.0 | 0.981077 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −852.859 | −0.0274210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1595.21 | −0.0511337 | −0.0255668 | − | 0.999673i | \(-0.508139\pi\) | ||||
−0.0255668 | + | 0.999673i | \(0.508139\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21089.4 | −0.673971 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32356.0 | 1.03091 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21501.2 | −0.682998 | −0.341499 | − | 0.939882i | \(-0.610935\pi\) | ||||
−0.341499 | + | 0.939882i | \(0.610935\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7017.22 | −0.222237 |
(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 | 2352.4.a.bz.1.1 | 2 | ||
4.3 | odd | 2 | 147.4.a.i.1.1 | 2 | |||
7.6 | odd | 2 | 336.4.a.m.1.2 | 2 | |||
12.11 | even | 2 | 441.4.a.r.1.2 | 2 | |||
21.20 | even | 2 | 1008.4.a.ba.1.1 | 2 | |||
28.3 | even | 6 | 147.4.e.l.79.2 | 4 | |||
28.11 | odd | 6 | 147.4.e.m.79.2 | 4 | |||
28.19 | even | 6 | 147.4.e.l.67.2 | 4 | |||
28.23 | odd | 6 | 147.4.e.m.67.2 | 4 | |||
28.27 | even | 2 | 21.4.a.c.1.1 | ✓ | 2 | ||
56.13 | odd | 2 | 1344.4.a.bo.1.1 | 2 | |||
56.27 | even | 2 | 1344.4.a.bg.1.1 | 2 | |||
84.11 | even | 6 | 441.4.e.p.226.1 | 4 | |||
84.23 | even | 6 | 441.4.e.p.361.1 | 4 | |||
84.47 | odd | 6 | 441.4.e.q.361.1 | 4 | |||
84.59 | odd | 6 | 441.4.e.q.226.1 | 4 | |||
84.83 | odd | 2 | 63.4.a.e.1.2 | 2 | |||
140.27 | odd | 4 | 525.4.d.g.274.1 | 4 | |||
140.83 | odd | 4 | 525.4.d.g.274.4 | 4 | |||
140.139 | even | 2 | 525.4.a.n.1.2 | 2 | |||
420.419 | odd | 2 | 1575.4.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.c.1.1 | ✓ | 2 | 28.27 | even | 2 | ||
63.4.a.e.1.2 | 2 | 84.83 | odd | 2 | |||
147.4.a.i.1.1 | 2 | 4.3 | odd | 2 | |||
147.4.e.l.67.2 | 4 | 28.19 | even | 6 | |||
147.4.e.l.79.2 | 4 | 28.3 | even | 6 | |||
147.4.e.m.67.2 | 4 | 28.23 | odd | 6 | |||
147.4.e.m.79.2 | 4 | 28.11 | odd | 6 | |||
336.4.a.m.1.2 | 2 | 7.6 | odd | 2 | |||
441.4.a.r.1.2 | 2 | 12.11 | even | 2 | |||
441.4.e.p.226.1 | 4 | 84.11 | even | 6 | |||
441.4.e.p.361.1 | 4 | 84.23 | even | 6 | |||
441.4.e.q.226.1 | 4 | 84.59 | odd | 6 | |||
441.4.e.q.361.1 | 4 | 84.47 | odd | 6 | |||
525.4.a.n.1.2 | 2 | 140.139 | even | 2 | |||
525.4.d.g.274.1 | 4 | 140.27 | odd | 4 | |||
525.4.d.g.274.4 | 4 | 140.83 | odd | 4 | |||
1008.4.a.ba.1.1 | 2 | 21.20 | even | 2 | |||
1344.4.a.bg.1.1 | 2 | 56.27 | even | 2 | |||
1344.4.a.bo.1.1 | 2 | 56.13 | odd | 2 | |||
1575.4.a.p.1.1 | 2 | 420.419 | odd | 2 | |||
2352.4.a.bz.1.1 | 2 | 1.1 | even | 1 | trivial |