Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,4,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(29.2059454528\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1772.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.32803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.32803 | −1.17664 | −0.588318 | − | 0.808629i | \(-0.700210\pi\) | ||||
−0.588318 | + | 0.808629i | \(0.700210\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.07579 | 0.384474 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.1102 | 0.653890 | 0.326945 | − | 0.945043i | \(-0.393981\pi\) | ||||
0.326945 | + | 0.945043i | \(0.393981\pi\) | |||||||
\(8\) | 16.3879 | 0.724250 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −16.6402 | −0.526208 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −57.2210 | −1.22079 | −0.610395 | − | 0.792098i | \(-0.708989\pi\) | ||||
−0.610395 | + | 0.792098i | \(0.708989\pi\) | |||||||
\(14\) | −40.3032 | −0.769391 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.1458 | −1.23665 | ||||||||
\(17\) | −22.7802 | −0.325000 | −0.162500 | − | 0.986709i | \(-0.551956\pi\) | ||||
−0.162500 | + | 0.986709i | \(0.551956\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −46.2204 | −0.558089 | −0.279045 | − | 0.960278i | \(-0.590018\pi\) | ||||
−0.279045 | + | 0.960278i | \(0.590018\pi\) | |||||||
\(20\) | 15.3790 | 0.171942 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 36.6083 | 0.354769 | ||||||||
\(23\) | 128.447 | 1.16448 | 0.582241 | − | 0.813016i | \(-0.302176\pi\) | ||||
0.582241 | + | 0.813016i | \(0.302176\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 190.433 | 1.43643 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 37.2485 | 0.251404 | ||||||||
\(29\) | 71.6674 | 0.458907 | 0.229454 | − | 0.973320i | \(-0.426306\pi\) | ||||
0.229454 | + | 0.973320i | \(0.426306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −88.7110 | −0.513967 | −0.256983 | − | 0.966416i | \(-0.582729\pi\) | ||||
−0.256983 | + | 0.966416i | \(0.582729\pi\) | |||||||
\(32\) | 132.296 | 0.730842 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 75.8131 | 0.382407 | ||||||||
\(35\) | 60.5511 | 0.292429 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.5848 | −0.135895 | −0.0679475 | − | 0.997689i | \(-0.521645\pi\) | ||||
−0.0679475 | + | 0.997689i | \(0.521645\pi\) | |||||||
\(38\) | 153.823 | 0.656668 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 81.9396 | 0.323895 | ||||||||
\(41\) | 223.209 | 0.850230 | 0.425115 | − | 0.905139i | \(-0.360234\pi\) | ||||
0.425115 | + | 0.905139i | \(0.360234\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −170.565 | −0.604905 | −0.302452 | − | 0.953164i | \(-0.597805\pi\) | ||||
−0.302452 | + | 0.953164i | \(0.597805\pi\) | |||||||
\(44\) | −33.8337 | −0.115923 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −427.477 | −1.37017 | ||||||||
\(47\) | −247.523 | −0.768192 | −0.384096 | − | 0.923293i | \(-0.625487\pi\) | ||||
−0.384096 | + | 0.923293i | \(0.625487\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −196.343 | −0.572428 | ||||||||
\(50\) | −83.2008 | −0.235327 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −176.000 | −0.469362 | ||||||||
\(53\) | 76.4692 | 0.198186 | 0.0990929 | − | 0.995078i | \(-0.468406\pi\) | ||||
0.0990929 | + | 0.995078i | \(0.468406\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 198.461 | 0.473580 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −238.511 | −0.539967 | ||||||||
\(59\) | 258.248 | 0.569849 | 0.284924 | − | 0.958550i | \(-0.408032\pi\) | ||||
0.284924 | + | 0.958550i | \(0.408032\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −97.3761 | −0.204389 | −0.102195 | − | 0.994764i | \(-0.532586\pi\) | ||||
−0.102195 | + | 0.994764i | \(0.532586\pi\) | |||||||
\(62\) | 295.233 | 0.604752 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 192.880 | 0.376718 | ||||||||
\(65\) | −286.105 | −0.545953 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −278.018 | −0.506945 | −0.253472 | − | 0.967343i | \(-0.581573\pi\) | ||||
−0.253472 | + | 0.967343i | \(0.581573\pi\) | |||||||
\(68\) | −70.0671 | −0.124954 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −201.516 | −0.344082 | ||||||||
\(71\) | −292.087 | −0.488231 | −0.244116 | − | 0.969746i | \(-0.578498\pi\) | ||||
−0.244116 | + | 0.969746i | \(0.578498\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −482.377 | −0.773397 | −0.386699 | − | 0.922206i | \(-0.626385\pi\) | ||||
−0.386699 | + | 0.922206i | \(0.626385\pi\) | |||||||
\(74\) | 101.787 | 0.159899 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −142.164 | −0.214571 | ||||||||
\(77\) | −133.212 | −0.197155 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −93.3473 | −0.132942 | −0.0664708 | − | 0.997788i | \(-0.521174\pi\) | ||||
−0.0664708 | + | 0.997788i | \(0.521174\pi\) | |||||||
\(80\) | −395.729 | −0.553048 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −742.847 | −1.00041 | ||||||||
\(83\) | −1011.13 | −1.33718 | −0.668588 | − | 0.743633i | \(-0.733101\pi\) | ||||
−0.668588 | + | 0.743633i | \(0.733101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −113.901 | −0.145345 | ||||||||
\(86\) | 567.646 | 0.711753 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −180.267 | −0.218370 | ||||||||
\(89\) | 60.3336 | 0.0718579 | 0.0359290 | − | 0.999354i | \(-0.488561\pi\) | ||||
0.0359290 | + | 0.999354i | \(0.488561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −692.959 | −0.798262 | ||||||||
\(92\) | 395.077 | 0.447713 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 823.766 | 0.903883 | ||||||||
\(95\) | −231.102 | −0.249585 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 662.927 | 0.693918 | 0.346959 | − | 0.937880i | \(-0.387214\pi\) | ||||
0.346959 | + | 0.937880i | \(0.387214\pi\) | |||||||
\(98\) | 653.435 | 0.673540 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 76.8948 | 0.0768948 | ||||||||
\(101\) | −1585.81 | −1.56231 | −0.781156 | − | 0.624336i | \(-0.785370\pi\) | ||||
−0.781156 | + | 0.624336i | \(0.785370\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2024.01 | −1.93623 | −0.968115 | − | 0.250508i | \(-0.919402\pi\) | ||||
−0.968115 | + | 0.250508i | \(0.919402\pi\) | |||||||
\(104\) | −937.734 | −0.884157 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −254.492 | −0.233193 | ||||||||
\(107\) | −611.358 | −0.552357 | −0.276179 | − | 0.961106i | \(-0.589068\pi\) | ||||
−0.276179 | + | 0.961106i | \(0.589068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1180.33 | 1.03721 | 0.518604 | − | 0.855015i | \(-0.326452\pi\) | ||||
0.518604 | + | 0.855015i | \(0.326452\pi\) | |||||||
\(110\) | 183.042 | 0.158658 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −958.473 | −0.808636 | ||||||||
\(113\) | −1098.57 | −0.914557 | −0.457278 | − | 0.889324i | \(-0.651176\pi\) | ||||
−0.457278 | + | 0.889324i | \(0.651176\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 642.236 | 0.520773 | ||||||||
\(116\) | 220.434 | 0.176438 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −859.459 | −0.670505 | ||||||||
\(119\) | −275.873 | −0.212514 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 324.071 | 0.240492 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −272.857 | −0.197607 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −794.434 | −0.555076 | −0.277538 | − | 0.960715i | \(-0.589518\pi\) | ||||
−0.277538 | + | 0.960715i | \(0.589518\pi\) | |||||||
\(128\) | −1700.28 | −1.17410 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 952.167 | 0.642389 | ||||||||
\(131\) | −364.955 | −0.243406 | −0.121703 | − | 0.992567i | \(-0.538836\pi\) | ||||
−0.121703 | + | 0.992567i | \(0.538836\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −559.739 | −0.364929 | ||||||||
\(134\) | 925.252 | 0.596490 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −373.320 | −0.235382 | ||||||||
\(137\) | −2057.56 | −1.28313 | −0.641567 | − | 0.767067i | \(-0.721715\pi\) | ||||
−0.641567 | + | 0.767067i | \(0.721715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 471.536 | 0.287735 | 0.143867 | − | 0.989597i | \(-0.454046\pi\) | ||||
0.143867 | + | 0.989597i | \(0.454046\pi\) | |||||||
\(140\) | 186.243 | 0.112431 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 972.076 | 0.574471 | ||||||||
\(143\) | 629.431 | 0.368082 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 358.337 | 0.205230 | ||||||||
\(146\) | 1605.37 | 0.910008 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −94.0725 | −0.0522481 | ||||||||
\(149\) | 135.727 | 0.0746255 | 0.0373128 | − | 0.999304i | \(-0.488120\pi\) | ||||
0.0373128 | + | 0.999304i | \(0.488120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1908.95 | −1.02879 | −0.514397 | − | 0.857552i | \(-0.671984\pi\) | ||||
−0.514397 | + | 0.857552i | \(0.671984\pi\) | |||||||
\(152\) | −757.457 | −0.404196 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 443.335 | 0.231980 | ||||||||
\(155\) | −443.555 | −0.229853 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1028.53 | −0.522840 | −0.261420 | − | 0.965225i | \(-0.584191\pi\) | ||||
−0.261420 | + | 0.965225i | \(0.584191\pi\) | |||||||
\(158\) | 310.663 | 0.156424 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 661.482 | 0.326842 | ||||||||
\(161\) | 1555.52 | 0.761444 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 684.628 | 0.328983 | 0.164492 | − | 0.986378i | \(-0.447402\pi\) | ||||
0.164492 | + | 0.986378i | \(0.447402\pi\) | |||||||
\(164\) | 686.545 | 0.326891 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3365.06 | 1.57337 | ||||||||
\(167\) | 799.231 | 0.370337 | 0.185169 | − | 0.982707i | \(-0.440717\pi\) | ||||
0.185169 | + | 0.982707i | \(0.440717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1077.25 | 0.490326 | ||||||||
\(170\) | 379.066 | 0.171018 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −524.622 | −0.232570 | ||||||||
\(173\) | −3670.62 | −1.61313 | −0.806567 | − | 0.591143i | \(-0.798677\pi\) | ||||
−0.806567 | + | 0.591143i | \(0.798677\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 302.755 | 0.130778 | ||||||||
\(176\) | 870.604 | 0.372865 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −200.792 | −0.0845506 | ||||||||
\(179\) | 3971.27 | 1.65825 | 0.829125 | − | 0.559064i | \(-0.188839\pi\) | ||||
0.829125 | + | 0.559064i | \(0.188839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2720.15 | 1.11706 | 0.558529 | − | 0.829485i | \(-0.311366\pi\) | ||||
0.558529 | + | 0.829485i | \(0.311366\pi\) | |||||||
\(182\) | 2306.19 | 0.939264 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2104.98 | 0.843377 | ||||||||
\(185\) | −152.924 | −0.0607741 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 250.582 | 0.0979913 | ||||||||
\(188\) | −761.331 | −0.295350 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 769.115 | 0.293671 | ||||||||
\(191\) | −23.4786 | −0.00889450 | −0.00444725 | − | 0.999990i | \(-0.501416\pi\) | ||||
−0.00444725 | + | 0.999990i | \(0.501416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4974.19 | −1.85518 | −0.927590 | − | 0.373599i | \(-0.878124\pi\) | ||||
−0.927590 | + | 0.373599i | \(0.878124\pi\) | |||||||
\(194\) | −2206.24 | −0.816489 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −603.909 | −0.220084 | ||||||||
\(197\) | 175.739 | 0.0635576 | 0.0317788 | − | 0.999495i | \(-0.489883\pi\) | ||||
0.0317788 | + | 0.999495i | \(0.489883\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5328.65 | 1.89818 | 0.949091 | − | 0.315002i | \(-0.102005\pi\) | ||||
0.949091 | + | 0.315002i | \(0.102005\pi\) | |||||||
\(200\) | 409.698 | 0.144850 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5277.61 | 1.83827 | ||||||||
\(203\) | 867.908 | 0.300075 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1116.05 | 0.380234 | ||||||||
\(206\) | 6735.97 | 2.27824 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4528.81 | 1.50969 | ||||||||
\(209\) | 508.425 | 0.168270 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4931.62 | −1.60904 | −0.804518 | − | 0.593928i | \(-0.797576\pi\) | ||||
−0.804518 | + | 0.593928i | \(0.797576\pi\) | |||||||
\(212\) | 235.203 | 0.0761973 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2034.62 | 0.649924 | ||||||||
\(215\) | −852.825 | −0.270522 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1074.31 | −0.336078 | ||||||||
\(218\) | −3928.19 | −1.22042 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −169.169 | −0.0518425 | ||||||||
\(221\) | 1303.51 | 0.396757 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2070.50 | −0.621754 | −0.310877 | − | 0.950450i | \(-0.600623\pi\) | ||||
−0.310877 | + | 0.950450i | \(0.600623\pi\) | |||||||
\(224\) | 1602.14 | 0.477890 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3656.08 | 1.07610 | ||||||||
\(227\) | 5474.76 | 1.60076 | 0.800380 | − | 0.599494i | \(-0.204631\pi\) | ||||
0.800380 | + | 0.599494i | \(0.204631\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5061.11 | 1.46047 | 0.730234 | − | 0.683197i | \(-0.239411\pi\) | ||||
0.730234 | + | 0.683197i | \(0.239411\pi\) | |||||||
\(230\) | −2137.38 | −0.612760 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1174.48 | 0.332364 | ||||||||
\(233\) | −1740.43 | −0.489354 | −0.244677 | − | 0.969605i | \(-0.578682\pi\) | ||||
−0.244677 | + | 0.969605i | \(0.578682\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1237.62 | −0.343546 | ||||||||
\(236\) | 794.318 | 0.219092 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 918.113 | 0.250052 | ||||||||
\(239\) | −3557.50 | −0.962827 | −0.481413 | − | 0.876494i | \(-0.659876\pi\) | ||||
−0.481413 | + | 0.876494i | \(0.659876\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5027.91 | −1.34388 | −0.671942 | − | 0.740603i | \(-0.734540\pi\) | ||||
−0.671942 | + | 0.740603i | \(0.734540\pi\) | |||||||
\(242\) | −402.692 | −0.106967 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −299.509 | −0.0785823 | ||||||||
\(245\) | −981.714 | −0.255997 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2644.78 | 0.681309 | ||||||||
\(248\) | −1453.79 | −0.372241 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −416.004 | −0.105242 | ||||||||
\(251\) | 1319.91 | 0.331919 | 0.165960 | − | 0.986133i | \(-0.446928\pi\) | ||||
0.165960 | + | 0.986133i | \(0.446928\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1412.92 | −0.351105 | ||||||||
\(254\) | 2643.90 | 0.653123 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4115.55 | 1.00477 | ||||||||
\(257\) | 5827.46 | 1.41443 | 0.707213 | − | 0.707001i | \(-0.249952\pi\) | ||||
0.707213 | + | 0.707001i | \(0.249952\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −370.389 | −0.0888603 | ||||||||
\(260\) | −880.000 | −0.209905 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1214.58 | 0.286401 | ||||||||
\(263\) | −4452.54 | −1.04394 | −0.521968 | − | 0.852965i | \(-0.674802\pi\) | ||||
−0.521968 | + | 0.852965i | \(0.674802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 382.346 | 0.0886314 | ||||||||
\(266\) | 1862.83 | 0.429389 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −855.125 | −0.194907 | ||||||||
\(269\) | 1558.71 | 0.353295 | 0.176647 | − | 0.984274i | \(-0.443475\pi\) | ||||
0.176647 | + | 0.984274i | \(0.443475\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5194.68 | −1.16441 | −0.582203 | − | 0.813043i | \(-0.697809\pi\) | ||||
−0.582203 | + | 0.813043i | \(0.697809\pi\) | |||||||
\(272\) | 1802.96 | 0.401913 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6847.63 | 1.50978 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7425.82 | −1.61074 | −0.805369 | − | 0.592774i | \(-0.798033\pi\) | ||||
−0.805369 | + | 0.592774i | \(0.798033\pi\) | |||||||
\(278\) | −1569.29 | −0.338559 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 992.306 | 0.211791 | ||||||||
\(281\) | 2209.95 | 0.469163 | 0.234581 | − | 0.972096i | \(-0.424628\pi\) | ||||
0.234581 | + | 0.972096i | \(0.424628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3668.07 | 0.770475 | 0.385237 | − | 0.922817i | \(-0.374120\pi\) | ||||
0.385237 | + | 0.922817i | \(0.374120\pi\) | |||||||
\(284\) | −898.400 | −0.187712 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2094.77 | −0.433099 | ||||||||
\(287\) | 2703.11 | 0.555957 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4394.06 | −0.894375 | ||||||||
\(290\) | −1192.56 | −0.241481 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1483.69 | −0.297351 | ||||||||
\(293\) | 1455.91 | 0.290291 | 0.145145 | − | 0.989410i | \(-0.453635\pi\) | ||||
0.145145 | + | 0.989410i | \(0.453635\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1291.24 | 0.254844 | ||||||||
\(296\) | −501.221 | −0.0984220 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −451.704 | −0.0878071 | ||||||||
\(299\) | −7349.89 | −1.42159 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2065.58 | −0.395541 | ||||||||
\(302\) | 6353.04 | 1.21052 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3658.15 | 0.690163 | ||||||||
\(305\) | −486.881 | −0.0914056 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8129.61 | 1.51134 | 0.755670 | − | 0.654953i | \(-0.227311\pi\) | ||||
0.755670 | + | 0.654953i | \(0.227311\pi\) | |||||||
\(308\) | −409.734 | −0.0758011 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1476.16 | 0.270453 | ||||||||
\(311\) | −2030.06 | −0.370142 | −0.185071 | − | 0.982725i | \(-0.559251\pi\) | ||||
−0.185071 | + | 0.982725i | \(0.559251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −513.357 | −0.0927050 | −0.0463525 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463525 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(314\) | 3422.99 | 0.615192 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −287.117 | −0.0511126 | ||||||||
\(317\) | −5230.37 | −0.926710 | −0.463355 | − | 0.886173i | \(-0.653354\pi\) | ||||
−0.463355 | + | 0.886173i | \(0.653354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −788.342 | −0.138366 | ||||||||
\(320\) | 964.399 | 0.168474 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5176.83 | −0.895943 | ||||||||
\(323\) | 1052.91 | 0.181379 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1430.53 | −0.244158 | ||||||||
\(326\) | −2278.46 | −0.387094 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3657.93 | 0.615779 | ||||||||
\(329\) | −2997.56 | −0.502313 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7261.31 | 1.20579 | 0.602897 | − | 0.797819i | \(-0.294013\pi\) | ||||
0.602897 | + | 0.797819i | \(0.294013\pi\) | |||||||
\(332\) | −3110.02 | −0.514110 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2659.87 | −0.435753 | ||||||||
\(335\) | −1390.09 | −0.226713 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1707.70 | 0.276037 | 0.138019 | − | 0.990430i | \(-0.455927\pi\) | ||||
0.138019 | + | 0.990430i | \(0.455927\pi\) | |||||||
\(338\) | −3585.11 | −0.576936 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −350.335 | −0.0558812 | ||||||||
\(341\) | 975.821 | 0.154967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6531.56 | −1.02819 | ||||||||
\(344\) | −2795.20 | −0.438103 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12215.9 | 1.89807 | ||||||||
\(347\) | 3948.37 | 0.610834 | 0.305417 | − | 0.952219i | \(-0.401204\pi\) | ||||
0.305417 | + | 0.952219i | \(0.401204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1623.51 | 0.249010 | 0.124505 | − | 0.992219i | \(-0.460266\pi\) | ||||
0.124505 | + | 0.992219i | \(0.460266\pi\) | |||||||
\(350\) | −1007.58 | −0.153878 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1455.26 | −0.220357 | ||||||||
\(353\) | −5926.17 | −0.893535 | −0.446768 | − | 0.894650i | \(-0.647425\pi\) | ||||
−0.446768 | + | 0.894650i | \(0.647425\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1460.44 | −0.218344 | ||||||||
\(356\) | 185.574 | 0.0276275 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13216.5 | −1.95116 | ||||||||
\(359\) | −3545.16 | −0.521187 | −0.260594 | − | 0.965449i | \(-0.583918\pi\) | ||||
−0.260594 | + | 0.965449i | \(0.583918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4722.67 | −0.688537 | ||||||||
\(362\) | −9052.76 | −1.31437 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2131.40 | −0.306911 | ||||||||
\(365\) | −2411.89 | −0.345874 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3429.59 | 0.487802 | 0.243901 | − | 0.969800i | \(-0.421573\pi\) | ||||
0.243901 | + | 0.969800i | \(0.421573\pi\) | |||||||
\(368\) | −10166.1 | −1.44006 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 508.936 | 0.0715090 | ||||||||
\(371\) | 926.058 | 0.129592 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2462.08 | 0.341773 | 0.170887 | − | 0.985291i | \(-0.445337\pi\) | ||||
0.170887 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(374\) | −833.945 | −0.115300 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4056.39 | −0.556363 | ||||||||
\(377\) | −4100.88 | −0.560229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6713.31 | −0.909867 | −0.454933 | − | 0.890525i | \(-0.650337\pi\) | ||||
−0.454933 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(380\) | −710.822 | −0.0959590 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 78.1374 | 0.0104656 | ||||||||
\(383\) | −3230.45 | −0.430988 | −0.215494 | − | 0.976505i | \(-0.569136\pi\) | ||||
−0.215494 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −666.062 | −0.0881705 | ||||||||
\(386\) | 16554.3 | 2.18287 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2039.03 | 0.266793 | ||||||||
\(389\) | −3075.88 | −0.400908 | −0.200454 | − | 0.979703i | \(-0.564242\pi\) | ||||
−0.200454 | + | 0.979703i | \(0.564242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2926.05 | −0.378457 | ||||||||
\(392\) | −3217.65 | −0.414581 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −584.863 | −0.0747843 | ||||||||
\(395\) | −466.736 | −0.0594533 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4864.47 | 0.614964 | 0.307482 | − | 0.951554i | \(-0.400514\pi\) | ||||
0.307482 | + | 0.951554i | \(0.400514\pi\) | |||||||
\(398\) | −17733.9 | −2.23347 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1978.65 | −0.247331 | ||||||||
\(401\) | 11676.4 | 1.45409 | 0.727044 | − | 0.686591i | \(-0.240893\pi\) | ||||
0.727044 | + | 0.686591i | \(0.240893\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5076.14 | 0.627445 | ||||||||
\(404\) | −4877.61 | −0.600669 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2888.42 | −0.353079 | ||||||||
\(407\) | 336.433 | 0.0409739 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16394.0 | −1.98199 | −0.990993 | − | 0.133917i | \(-0.957244\pi\) | ||||
−0.990993 | + | 0.133917i | \(0.957244\pi\) | |||||||
\(410\) | −3714.24 | −0.447398 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6225.43 | −0.744430 | ||||||||
\(413\) | 3127.44 | 0.372618 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5055.64 | −0.598004 | ||||||||
\(416\) | −7570.14 | −0.892204 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1692.05 | −0.197993 | ||||||||
\(419\) | 8451.89 | 0.985446 | 0.492723 | − | 0.870186i | \(-0.336002\pi\) | ||||
0.492723 | + | 0.870186i | \(0.336002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10486.2 | −1.21393 | −0.606967 | − | 0.794727i | \(-0.707614\pi\) | ||||
−0.606967 | + | 0.794727i | \(0.707614\pi\) | |||||||
\(422\) | 16412.6 | 1.89325 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1253.17 | 0.143536 | ||||||||
\(425\) | −569.504 | −0.0650000 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1179.25 | −0.133648 | ||||||||
\(428\) | −1880.41 | −0.212367 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2838.23 | 0.318306 | ||||||||
\(431\) | 7443.30 | 0.831859 | 0.415929 | − | 0.909397i | \(-0.363456\pi\) | ||||
0.415929 | + | 0.909397i | \(0.363456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3778.56 | −0.419367 | −0.209683 | − | 0.977769i | \(-0.567243\pi\) | ||||
−0.209683 | + | 0.977769i | \(0.567243\pi\) | |||||||
\(434\) | 3575.33 | 0.395441 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3630.46 | 0.398779 | ||||||||
\(437\) | −5936.89 | −0.649885 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5405.03 | −0.587627 | −0.293813 | − | 0.955863i | \(-0.594924\pi\) | ||||
−0.293813 | + | 0.955863i | \(0.594924\pi\) | |||||||
\(440\) | −901.335 | −0.0976579 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4338.11 | −0.466839 | ||||||||
\(443\) | 2183.94 | 0.234226 | 0.117113 | − | 0.993119i | \(-0.462636\pi\) | ||||
0.117113 | + | 0.993119i | \(0.462636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 301.668 | 0.0321358 | ||||||||
\(446\) | 6890.70 | 0.731579 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2335.82 | 0.246332 | ||||||||
\(449\) | 13367.2 | 1.40498 | 0.702492 | − | 0.711692i | \(-0.252071\pi\) | ||||
0.702492 | + | 0.711692i | \(0.252071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2455.30 | −0.256354 | ||||||||
\(452\) | −3378.98 | −0.351623 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18220.2 | −1.88351 | ||||||||
\(455\) | −3464.79 | −0.356994 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13897.3 | −1.42251 | −0.711256 | − | 0.702933i | \(-0.751873\pi\) | ||||
−0.711256 | + | 0.702933i | \(0.751873\pi\) | |||||||
\(458\) | −16843.5 | −1.71844 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1975.39 | 0.200224 | ||||||||
\(461\) | 12543.9 | 1.26730 | 0.633652 | − | 0.773618i | \(-0.281555\pi\) | ||||
0.633652 | + | 0.773618i | \(0.281555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16288.3 | 1.63495 | 0.817475 | − | 0.575965i | \(-0.195373\pi\) | ||||
0.817475 | + | 0.575965i | \(0.195373\pi\) | |||||||
\(464\) | −5672.18 | −0.567509 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5792.21 | 0.575792 | ||||||||
\(467\) | 4689.45 | 0.464672 | 0.232336 | − | 0.972636i | \(-0.425363\pi\) | ||||
0.232336 | + | 0.972636i | \(0.425363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3366.86 | −0.331486 | ||||||||
\(470\) | 4118.83 | 0.404229 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4232.15 | 0.412713 | ||||||||
\(473\) | 1876.21 | 0.182386 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1155.51 | −0.111618 | ||||||||
\(476\) | −848.527 | −0.0817063 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11839.5 | 1.13290 | ||||||||
\(479\) | 15228.0 | 1.45258 | 0.726291 | − | 0.687387i | \(-0.241242\pi\) | ||||
0.726291 | + | 0.687387i | \(0.241242\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1750.09 | 0.165899 | ||||||||
\(482\) | 16733.0 | 1.58126 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 372.171 | 0.0349522 | ||||||||
\(485\) | 3314.63 | 0.310330 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15805.7 | −1.47068 | −0.735342 | − | 0.677697i | \(-0.762978\pi\) | ||||
−0.735342 | + | 0.677697i | \(0.762978\pi\) | |||||||
\(488\) | −1595.79 | −0.148029 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3267.17 | 0.301216 | ||||||||
\(491\) | −9239.13 | −0.849198 | −0.424599 | − | 0.905382i | \(-0.639585\pi\) | ||||
−0.424599 | + | 0.905382i | \(0.639585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1632.60 | −0.149145 | ||||||||
\(494\) | −8801.91 | −0.801653 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7021.11 | 0.635599 | ||||||||
\(497\) | −3537.24 | −0.319249 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 346.738 | 0.0311064 | 0.0155532 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155532 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(500\) | 384.474 | 0.0343884 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4392.69 | −0.390548 | ||||||||
\(503\) | 12519.4 | 1.10977 | 0.554884 | − | 0.831928i | \(-0.312763\pi\) | ||||
0.554884 | + | 0.831928i | \(0.312763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7929.03 | −0.698687 | ||||||||
\(506\) | 4702.24 | 0.413123 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2443.51 | −0.213412 | ||||||||
\(509\) | 9405.03 | 0.818999 | 0.409500 | − | 0.912310i | \(-0.365703\pi\) | ||||
0.409500 | + | 0.912310i | \(0.365703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5841.69 | −0.505717 | ||||||||
\(512\) | −94.4331 | −0.00815116 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19394.0 | −1.66426 | ||||||||
\(515\) | −10120.0 | −0.865908 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2722.76 | 0.231619 | ||||||||
\(518\) | 1232.66 | 0.104556 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4688.67 | −0.395407 | ||||||||
\(521\) | 17884.4 | 1.50390 | 0.751949 | − | 0.659222i | \(-0.229114\pi\) | ||||
0.751949 | + | 0.659222i | \(0.229114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7617.35 | 0.636871 | 0.318435 | − | 0.947945i | \(-0.396843\pi\) | ||||
0.318435 | + | 0.947945i | \(0.396843\pi\) | |||||||
\(524\) | −1122.52 | −0.0935834 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14818.2 | 1.22833 | ||||||||
\(527\) | 2020.85 | 0.167039 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4331.70 | 0.356021 | ||||||||
\(530\) | −1272.46 | −0.104287 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1721.64 | −0.140306 | ||||||||
\(533\) | −12772.3 | −1.03795 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3056.79 | −0.247022 | ||||||||
\(536\) | −4556.13 | −0.367155 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5187.44 | −0.415700 | ||||||||
\(539\) | 2159.77 | 0.172593 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6309.12 | −0.501387 | −0.250694 | − | 0.968066i | \(-0.580659\pi\) | ||||
−0.250694 | + | 0.968066i | \(0.580659\pi\) | |||||||
\(542\) | 17288.0 | 1.37008 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3013.74 | −0.237524 | ||||||||
\(545\) | 5901.67 | 0.463853 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −957.117 | −0.0748142 | −0.0374071 | − | 0.999300i | \(-0.511910\pi\) | ||||
−0.0374071 | + | 0.999300i | \(0.511910\pi\) | |||||||
\(548\) | −6328.63 | −0.493332 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 915.209 | 0.0709539 | ||||||||
\(551\) | −3312.50 | −0.256111 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1130.46 | −0.0869292 | ||||||||
\(554\) | 24713.4 | 1.89525 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1450.35 | 0.110627 | ||||||||
\(557\) | −9284.17 | −0.706253 | −0.353127 | − | 0.935576i | \(-0.614881\pi\) | ||||
−0.353127 | + | 0.935576i | \(0.614881\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9759.90 | 0.738461 | ||||||||
\(560\) | −4792.37 | −0.361633 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7354.79 | −0.552034 | ||||||||
\(563\) | −5842.70 | −0.437372 | −0.218686 | − | 0.975795i | \(-0.570177\pi\) | ||||
−0.218686 | + | 0.975795i | \(0.570177\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5492.86 | −0.409002 | ||||||||
\(566\) | −12207.5 | −0.906569 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4786.71 | −0.353602 | ||||||||
\(569\) | 6805.46 | 0.501405 | 0.250703 | − | 0.968064i | \(-0.419338\pi\) | ||||
0.250703 | + | 0.968064i | \(0.419338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21649.6 | 1.58671 | 0.793353 | − | 0.608762i | \(-0.208334\pi\) | ||||
0.793353 | + | 0.608762i | \(0.208334\pi\) | |||||||
\(572\) | 1936.00 | 0.141518 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8996.04 | −0.654159 | ||||||||
\(575\) | 3211.18 | 0.232897 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23967.4 | 1.72925 | 0.864624 | − | 0.502420i | \(-0.167557\pi\) | ||||
0.864624 | + | 0.502420i | \(0.167557\pi\) | |||||||
\(578\) | 14623.6 | 1.05235 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1102.17 | 0.0789054 | ||||||||
\(581\) | −12245.0 | −0.874367 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −841.161 | −0.0597553 | ||||||||
\(584\) | −7905.16 | −0.560133 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4845.31 | −0.341566 | ||||||||
\(587\) | 7580.37 | 0.533007 | 0.266504 | − | 0.963834i | \(-0.414132\pi\) | ||||
0.266504 | + | 0.963834i | \(0.414132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4100.26 | 0.286839 | ||||||||
\(590\) | −4297.29 | −0.299859 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2420.66 | 0.168055 | ||||||||
\(593\) | −2996.14 | −0.207481 | −0.103741 | − | 0.994604i | \(-0.533081\pi\) | ||||
−0.103741 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1379.36 | −0.0950393 | ||||||||
\(596\) | 417.469 | 0.0286916 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24460.6 | 1.67269 | ||||||||
\(599\) | 21317.9 | 1.45413 | 0.727066 | − | 0.686568i | \(-0.240883\pi\) | ||||
0.727066 | + | 0.686568i | \(0.240883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5703.47 | 0.387104 | 0.193552 | − | 0.981090i | \(-0.437999\pi\) | ||||
0.193552 | + | 0.981090i | \(0.437999\pi\) | |||||||
\(602\) | 6874.31 | 0.465408 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5871.53 | −0.395545 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23658.6 | 1.58200 | 0.790998 | − | 0.611819i | \(-0.209562\pi\) | ||||
0.790998 | + | 0.611819i | \(0.209562\pi\) | |||||||
\(608\) | −6114.80 | −0.407875 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1620.35 | 0.107551 | ||||||||
\(611\) | 14163.5 | 0.937800 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8792.89 | 0.579350 | 0.289675 | − | 0.957125i | \(-0.406453\pi\) | ||||
0.289675 | + | 0.957125i | \(0.406453\pi\) | |||||||
\(614\) | −27055.6 | −1.77830 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2183.07 | −0.142790 | ||||||||
\(617\) | −18080.8 | −1.17975 | −0.589876 | − | 0.807494i | \(-0.700823\pi\) | ||||
−0.589876 | + | 0.807494i | \(0.700823\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9077.15 | −0.589405 | −0.294702 | − | 0.955589i | \(-0.595221\pi\) | ||||
−0.294702 | + | 0.955589i | \(0.595221\pi\) | |||||||
\(620\) | −1364.28 | −0.0883725 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6756.10 | 0.435522 | ||||||||
\(623\) | 730.653 | 0.0469872 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 1708.47 | 0.109080 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3163.55 | −0.201018 | ||||||||
\(629\) | 696.727 | 0.0441659 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10646.4 | −0.671672 | −0.335836 | − | 0.941920i | \(-0.609019\pi\) | ||||
−0.335836 | + | 0.941920i | \(0.609019\pi\) | |||||||
\(632\) | −1529.77 | −0.0962830 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17406.8 | 1.09040 | ||||||||
\(635\) | −3972.17 | −0.248237 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11234.9 | 0.698814 | ||||||||
\(638\) | 2623.63 | 0.162806 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8501.41 | −0.525075 | ||||||||
\(641\) | −14313.4 | −0.881972 | −0.440986 | − | 0.897514i | \(-0.645371\pi\) | ||||
−0.440986 | + | 0.897514i | \(0.645371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20481.6 | 1.25617 | 0.628084 | − | 0.778146i | \(-0.283839\pi\) | ||||
0.628084 | + | 0.778146i | \(0.283839\pi\) | |||||||
\(644\) | 4784.47 | 0.292755 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3504.12 | −0.213417 | ||||||||
\(647\) | −13408.9 | −0.814773 | −0.407387 | − | 0.913256i | \(-0.633560\pi\) | ||||
−0.407387 | + | 0.913256i | \(0.633560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2840.73 | −0.171816 | ||||||||
\(650\) | 4760.83 | 0.287285 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2105.77 | 0.126485 | ||||||||
\(653\) | 27525.1 | 1.64953 | 0.824764 | − | 0.565477i | \(-0.191308\pi\) | ||||
0.824764 | + | 0.565477i | \(0.191308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1824.77 | −0.108855 | ||||||||
\(656\) | −17666.1 | −1.05144 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9975.98 | 0.591040 | ||||||||
\(659\) | −19977.6 | −1.18091 | −0.590453 | − | 0.807072i | \(-0.701051\pi\) | ||||
−0.590453 | + | 0.807072i | \(0.701051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1661.53 | 0.0977698 | 0.0488849 | − | 0.998804i | \(-0.484433\pi\) | ||||
0.0488849 | + | 0.998804i | \(0.484433\pi\) | |||||||
\(662\) | −24165.9 | −1.41878 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16570.3 | −0.968451 | ||||||||
\(665\) | −2798.70 | −0.163201 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9205.49 | 0.534390 | ||||||||
\(668\) | 2458.27 | 0.142385 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4626.26 | 0.266758 | ||||||||
\(671\) | 1071.14 | 0.0616256 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13546.5 | −0.775898 | −0.387949 | − | 0.921681i | \(-0.626816\pi\) | ||||
−0.387949 | + | 0.921681i | \(0.626816\pi\) | |||||||
\(674\) | −5683.29 | −0.324796 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3313.39 | 0.188518 | ||||||||
\(677\) | 9859.39 | 0.559715 | 0.279858 | − | 0.960042i | \(-0.409713\pi\) | ||||
0.279858 | + | 0.960042i | \(0.409713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8028.19 | 0.453746 | ||||||||
\(680\) | −1866.60 | −0.105266 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3247.56 | −0.182340 | ||||||||
\(683\) | 1182.82 | 0.0662654 | 0.0331327 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331327 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10287.8 | −0.573835 | ||||||||
\(686\) | 21737.2 | 1.20981 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13499.5 | 0.748058 | ||||||||
\(689\) | −4375.65 | −0.241943 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4312.15 | −0.237398 | −0.118699 | − | 0.992930i | \(-0.537872\pi\) | ||||
−0.118699 | + | 0.992930i | \(0.537872\pi\) | |||||||
\(692\) | −11290.1 | −0.620208 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13140.3 | −0.718730 | ||||||||
\(695\) | 2357.68 | 0.128679 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5084.75 | −0.276325 | ||||||||
\(698\) | −5403.08 | −0.292994 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 931.213 | 0.0502807 | ||||||||
\(701\) | 23850.3 | 1.28504 | 0.642519 | − | 0.766270i | \(-0.277889\pi\) | ||||
0.642519 | + | 0.766270i | \(0.277889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1413.64 | 0.0758415 | ||||||||
\(704\) | −2121.68 | −0.113585 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19722.5 | 1.05137 | ||||||||
\(707\) | −19204.4 | −1.02158 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28492.0 | −1.50922 | −0.754612 | − | 0.656172i | \(-0.772175\pi\) | ||||
−0.754612 | + | 0.656172i | \(0.772175\pi\) | |||||||
\(710\) | 4860.38 | 0.256911 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 988.743 | 0.0520431 | ||||||||
\(713\) | −11394.7 | −0.598505 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3147.16 | 0.164611 | ||||||||
\(716\) | 12214.8 | 0.637554 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11798.4 | 0.613248 | ||||||||
\(719\) | −14182.8 | −0.735647 | −0.367824 | − | 0.929896i | \(-0.619897\pi\) | ||||
−0.367824 | + | 0.929896i | \(0.619897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24511.2 | −1.26608 | ||||||||
\(722\) | 15717.2 | 0.810157 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8366.63 | 0.429480 | ||||||||
\(725\) | 1791.69 | 0.0917814 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31836.8 | 1.62416 | 0.812078 | − | 0.583549i | \(-0.198336\pi\) | ||||
0.812078 | + | 0.583549i | \(0.198336\pi\) | |||||||
\(728\) | −11356.2 | −0.578142 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8026.83 | 0.406968 | ||||||||
\(731\) | 3885.50 | 0.196594 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10002.6 | 0.504030 | 0.252015 | − | 0.967723i | \(-0.418907\pi\) | ||||
0.252015 | + | 0.967723i | \(0.418907\pi\) | |||||||
\(734\) | −11413.8 | −0.573965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16993.1 | 0.851053 | ||||||||
\(737\) | 3058.20 | 0.152850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18784.8 | 0.935060 | 0.467530 | − | 0.883977i | \(-0.345144\pi\) | ||||
0.467530 | + | 0.883977i | \(0.345144\pi\) | |||||||
\(740\) | −470.363 | −0.0233660 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3081.95 | −0.152482 | ||||||||
\(743\) | −19455.4 | −0.960633 | −0.480317 | − | 0.877095i | \(-0.659478\pi\) | ||||
−0.480317 | + | 0.877095i | \(0.659478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 678.636 | 0.0333735 | ||||||||
\(746\) | −8193.87 | −0.402143 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 770.738 | 0.0376751 | ||||||||
\(749\) | −7403.68 | −0.361181 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19365.5 | 0.940953 | 0.470477 | − | 0.882413i | \(-0.344082\pi\) | ||||
0.470477 | + | 0.882413i | \(0.344082\pi\) | |||||||
\(752\) | 19590.5 | 0.949987 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13647.9 | 0.659186 | ||||||||
\(755\) | −9544.74 | −0.460091 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19298.9 | 0.926595 | 0.463297 | − | 0.886203i | \(-0.346666\pi\) | ||||
0.463297 | + | 0.886203i | \(0.346666\pi\) | |||||||
\(758\) | 22342.1 | 1.07058 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3787.28 | −0.180762 | ||||||||
\(761\) | −30510.0 | −1.45333 | −0.726666 | − | 0.686991i | \(-0.758931\pi\) | ||||
−0.726666 | + | 0.686991i | \(0.758931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14294.1 | 0.678219 | ||||||||
\(764\) | −72.2152 | −0.00341970 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10751.1 | 0.507117 | ||||||||
\(767\) | −14777.2 | −0.695665 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11569.6 | 0.542536 | 0.271268 | − | 0.962504i | \(-0.412557\pi\) | ||||
0.271268 | + | 0.962504i | \(0.412557\pi\) | |||||||
\(770\) | 2216.67 | 0.103745 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15299.6 | −0.713269 | ||||||||
\(773\) | −42711.1 | −1.98734 | −0.993668 | − | 0.112353i | \(-0.964161\pi\) | ||||
−0.993668 | + | 0.112353i | \(0.964161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2217.78 | −0.102793 | ||||||||
\(776\) | 10864.0 | 0.502570 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10236.6 | 0.471723 | ||||||||
\(779\) | −10316.8 | −0.474504 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3212.96 | 0.147207 | ||||||||
\(782\) | 9737.99 | 0.445307 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15539.7 | 0.707895 | ||||||||
\(785\) | −5142.66 | −0.233821 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −403.118 | −0.0182587 | −0.00912936 | − | 0.999958i | \(-0.502906\pi\) | ||||
−0.00912936 | + | 0.999958i | \(0.502906\pi\) | |||||||
\(788\) | 540.535 | 0.0244363 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1553.31 | 0.0699549 | ||||||||
\(791\) | −13303.9 | −0.598019 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5571.96 | 0.249516 | ||||||||
\(794\) | −16189.1 | −0.723589 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16389.8 | 0.729802 | ||||||||
\(797\) | −11413.0 | −0.507237 | −0.253619 | − | 0.967304i | \(-0.581621\pi\) | ||||
−0.253619 | + | 0.967304i | \(0.581621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5638.63 | 0.249662 | ||||||||
\(800\) | 3307.41 | 0.146168 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −38859.3 | −1.71093 | ||||||||
\(803\) | 5306.15 | 0.233188 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7777.62 | 0.340528 | ||||||||
\(806\) | −16893.5 | −0.738275 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −25988.1 | −1.13151 | ||||||||
\(809\) | 21799.0 | 0.947357 | 0.473679 | − | 0.880698i | \(-0.342926\pi\) | ||||
0.473679 | + | 0.880698i | \(0.342926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 404.042 | 0.0174942 | 0.00874711 | − | 0.999962i | \(-0.497216\pi\) | ||||
0.00874711 | + | 0.999962i | \(0.497216\pi\) | |||||||
\(812\) | 2669.50 | 0.115371 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1119.66 | −0.0482113 | ||||||||
\(815\) | 3423.14 | 0.147126 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7883.59 | 0.337591 | ||||||||
\(818\) | 54559.8 | 2.33208 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3432.73 | 0.146190 | ||||||||
\(821\) | 428.289 | 0.0182063 | 0.00910316 | − | 0.999959i | \(-0.497102\pi\) | ||||
0.00910316 | + | 0.999959i | \(0.497102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21469.0 | −0.909309 | −0.454655 | − | 0.890668i | \(-0.650237\pi\) | ||||
−0.454655 | + | 0.890668i | \(0.650237\pi\) | |||||||
\(824\) | −33169.3 | −1.40231 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10408.2 | −0.438437 | ||||||||
\(827\) | −24062.7 | −1.01178 | −0.505889 | − | 0.862599i | \(-0.668835\pi\) | ||||
−0.505889 | + | 0.862599i | \(0.668835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15567.7 | −0.652217 | −0.326108 | − | 0.945332i | \(-0.605737\pi\) | ||||
−0.326108 | + | 0.945332i | \(0.605737\pi\) | |||||||
\(830\) | 16825.3 | 0.703633 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11036.8 | −0.459894 | ||||||||
\(833\) | 4472.72 | 0.186039 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3996.15 | 0.165620 | ||||||||
\(836\) | 1563.81 | 0.0646955 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28128.1 | −1.15951 | ||||||||
\(839\) | 11335.4 | 0.466437 | 0.233218 | − | 0.972424i | \(-0.425074\pi\) | ||||
0.233218 | + | 0.972424i | \(0.425074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19252.8 | −0.789404 | ||||||||
\(842\) | 34898.4 | 1.42836 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15168.6 | −0.618633 | ||||||||
\(845\) | 5386.23 | 0.219280 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1465.34 | 0.0594446 | ||||||||
\(848\) | −6052.22 | −0.245087 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1895.33 | 0.0764814 | ||||||||
\(851\) | −3928.54 | −0.158247 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5152.34 | −0.206814 | −0.103407 | − | 0.994639i | \(-0.532974\pi\) | ||||
−0.103407 | + | 0.994639i | \(0.532974\pi\) | |||||||
\(854\) | 3924.57 | 0.157255 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10018.9 | −0.400045 | ||||||||
\(857\) | 21195.2 | 0.844825 | 0.422413 | − | 0.906404i | \(-0.361183\pi\) | ||||
0.422413 | + | 0.906404i | \(0.361183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33887.6 | 1.34602 | 0.673010 | − | 0.739634i | \(-0.265001\pi\) | ||||
0.673010 | + | 0.739634i | \(0.265001\pi\) | |||||||
\(860\) | −2623.11 | −0.104009 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24771.5 | −0.978795 | ||||||||
\(863\) | 26947.3 | 1.06292 | 0.531458 | − | 0.847085i | \(-0.321644\pi\) | ||||
0.531458 | + | 0.847085i | \(0.321644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18353.1 | −0.721415 | ||||||||
\(866\) | 12575.2 | 0.493442 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3304.35 | −0.129213 | ||||||||
\(869\) | 1026.82 | 0.0400834 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15908.5 | 0.618873 | ||||||||
\(872\) | 19343.2 | 0.751198 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19758.1 | 0.764679 | ||||||||
\(875\) | 1513.78 | 0.0584857 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15854.7 | −0.610462 | −0.305231 | − | 0.952278i | \(-0.598734\pi\) | ||||
−0.305231 | + | 0.952278i | \(0.598734\pi\) | |||||||
\(878\) | 17988.1 | 0.691423 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4353.02 | 0.166750 | ||||||||
\(881\) | 2198.99 | 0.0840930 | 0.0420465 | − | 0.999116i | \(-0.486612\pi\) | ||||
0.0420465 | + | 0.999116i | \(0.486612\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17607.6 | 0.671058 | 0.335529 | − | 0.942030i | \(-0.391085\pi\) | ||||
0.335529 | + | 0.942030i | \(0.391085\pi\) | |||||||
\(884\) | 4009.31 | 0.152543 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7268.21 | −0.275599 | ||||||||
\(887\) | −50391.4 | −1.90753 | −0.953764 | − | 0.300558i | \(-0.902827\pi\) | ||||
−0.953764 | + | 0.300558i | \(0.902827\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9620.77 | −0.362959 | ||||||||
\(890\) | −1003.96 | −0.0378122 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6368.44 | −0.239048 | ||||||||
\(893\) | 11440.6 | 0.428719 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19856.3 | 0.741592 | ||||||||
\(896\) | −20590.8 | −0.767734 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44486.5 | −1.65316 | ||||||||
\(899\) | −6357.69 | −0.235863 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1741.98 | −0.0644105 | ||||||||
\(902\) | 8171.32 | 0.301635 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18003.3 | −0.662368 | ||||||||
\(905\) | 13600.8 | 0.499563 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20022.6 | 0.733009 | 0.366505 | − | 0.930416i | \(-0.380554\pi\) | ||||
0.366505 | + | 0.930416i | \(0.380554\pi\) | |||||||
\(908\) | 16839.2 | 0.615450 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11530.9 | 0.420052 | ||||||||
\(911\) | −14270.0 | −0.518974 | −0.259487 | − | 0.965747i | \(-0.583553\pi\) | ||||
−0.259487 | + | 0.965747i | \(0.583553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11122.4 | 0.403174 | ||||||||
\(914\) | 46250.6 | 1.67378 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15566.9 | 0.561512 | ||||||||
\(917\) | −4419.68 | −0.159161 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36781.2 | 1.32024 | 0.660120 | − | 0.751160i | \(-0.270505\pi\) | ||||
0.660120 | + | 0.751160i | \(0.270505\pi\) | |||||||
\(920\) | 10524.9 | 0.377170 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −41746.4 | −1.49116 | ||||||||
\(923\) | 16713.5 | 0.596027 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −764.620 | −0.0271790 | ||||||||
\(926\) | −54208.0 | −1.92374 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9481.35 | 0.335389 | ||||||||
\(929\) | 35798.6 | 1.26428 | 0.632139 | − | 0.774855i | \(-0.282177\pi\) | ||||
0.632139 | + | 0.774855i | \(0.282177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9075.04 | 0.319466 | ||||||||
\(932\) | −5353.21 | −0.188144 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15606.6 | −0.546750 | ||||||||
\(935\) | 1252.91 | 0.0438230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49934.6 | 1.74097 | 0.870486 | − | 0.492193i | \(-0.163805\pi\) | ||||
0.870486 | + | 0.492193i | \(0.163805\pi\) | |||||||
\(938\) | 11205.0 | 0.390039 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3806.65 | −0.132084 | ||||||||
\(941\) | −28437.4 | −0.985156 | −0.492578 | − | 0.870268i | \(-0.663945\pi\) | ||||
−0.492578 | + | 0.870268i | \(0.663945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28670.6 | 0.990078 | ||||||||
\(944\) | −20439.3 | −0.704706 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6244.10 | −0.214602 | ||||||||
\(947\) | 45305.0 | 1.55461 | 0.777304 | − | 0.629125i | \(-0.216587\pi\) | ||||
0.777304 | + | 0.629125i | \(0.216587\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27602.1 | 0.944155 | ||||||||
\(950\) | 3845.58 | 0.131334 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4520.98 | −0.153914 | ||||||||
\(953\) | 6991.64 | 0.237651 | 0.118825 | − | 0.992915i | \(-0.462087\pi\) | ||||
0.118825 | + | 0.992915i | \(0.462087\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −117.393 | −0.00397774 | ||||||||
\(956\) | −10942.1 | −0.370182 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50679.4 | −1.70916 | ||||||||
\(959\) | −24917.5 | −0.839029 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21921.4 | −0.735838 | ||||||||
\(962\) | −5824.37 | −0.195203 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15464.8 | −0.516689 | ||||||||
\(965\) | −24870.9 | −0.829662 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1119.96 | −0.0372444 | −0.0186222 | − | 0.999827i | \(-0.505928\pi\) | ||||
−0.0186222 | + | 0.999827i | \(0.505928\pi\) | |||||||
\(968\) | 1982.94 | 0.0658410 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11031.2 | −0.365145 | ||||||||
\(971\) | −1998.46 | −0.0660490 | −0.0330245 | − | 0.999455i | \(-0.510514\pi\) | ||||
−0.0330245 | + | 0.999455i | \(0.510514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5710.40 | 0.188147 | ||||||||
\(974\) | 52601.7 | 1.73046 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7706.92 | 0.252759 | ||||||||
\(977\) | −9456.06 | −0.309648 | −0.154824 | − | 0.987942i | \(-0.549481\pi\) | ||||
−0.154824 | + | 0.987942i | \(0.549481\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −663.670 | −0.0216660 | ||||||||
\(980\) | −3019.55 | −0.0984244 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 30748.1 | 0.999197 | ||||||||
\(983\) | 56956.1 | 1.84803 | 0.924016 | − | 0.382353i | \(-0.124886\pi\) | ||||
0.924016 | + | 0.382353i | \(0.124886\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 878.693 | 0.0284238 | ||||||||
\(986\) | 5433.33 | 0.175489 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8134.80 | 0.261946 | ||||||||
\(989\) | −21908.6 | −0.704402 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45020.8 | −1.44312 | −0.721561 | − | 0.692351i | \(-0.756575\pi\) | ||||
−0.721561 | + | 0.692351i | \(0.756575\pi\) | |||||||
\(992\) | −11736.2 | −0.375628 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11772.1 | 0.375641 | ||||||||
\(995\) | 26643.3 | 0.848893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51620.5 | −1.63976 | −0.819878 | − | 0.572538i | \(-0.805959\pi\) | ||||
−0.819878 | + | 0.572538i | \(0.805959\pi\) | |||||||
\(998\) | −1153.95 | −0.0366010 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 495.4.a.j.1.1 | yes | 3 | |
3.2 | odd | 2 | 495.4.a.h.1.3 | ✓ | 3 | ||
5.4 | even | 2 | 2475.4.a.u.1.3 | 3 | |||
15.14 | odd | 2 | 2475.4.a.x.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.4.a.h.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
495.4.a.j.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
2475.4.a.u.1.3 | 3 | 5.4 | even | 2 | |||
2475.4.a.x.1.1 | 3 | 15.14 | odd | 2 |