Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.37341.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 57x - 148 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.13924\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(5\) | −8.27848 | −0.740450 | −0.370225 | − | 0.928942i | \(-0.620719\pi\) | ||||
−0.370225 | + | 0.928942i | \(0.620719\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −72.0744 | −1.97557 | −0.987784 | − | 0.155830i | \(-0.950195\pi\) | ||||
−0.987784 | + | 0.155830i | \(0.950195\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −89.4668 | −1.90874 | −0.954370 | − | 0.298627i | \(-0.903471\pi\) | ||||
−0.954370 | + | 0.298627i | \(0.903471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.8354 | 0.427499 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −38.0744 | −0.543200 | −0.271600 | − | 0.962410i | \(-0.587553\pi\) | ||||
−0.271600 | + | 0.962410i | \(0.587553\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 46.9098 | 0.566413 | 0.283207 | − | 0.959059i | \(-0.408602\pi\) | ||||
0.283207 | + | 0.959059i | \(0.408602\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −65.1883 | −0.590987 | −0.295493 | − | 0.955345i | \(-0.595484\pi\) | ||||
−0.295493 | + | 0.955345i | \(0.595484\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −56.4668 | −0.451734 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 118.274 | 0.757341 | 0.378671 | − | 0.925532i | \(-0.376381\pi\) | ||||
0.378671 | + | 0.925532i | \(0.376381\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −175.616 | −1.01747 | −0.508734 | − | 0.860924i | \(-0.669886\pi\) | ||||
−0.508734 | + | 0.860924i | \(0.669886\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 216.223 | 1.14059 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −57.9494 | −0.279864 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −157.467 | −0.699659 | −0.349829 | − | 0.936813i | \(-0.613760\pi\) | ||||
−0.349829 | + | 0.936813i | \(0.613760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 268.400 | 1.10201 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 293.666 | 1.11861 | 0.559304 | − | 0.828962i | \(-0.311068\pi\) | ||||
0.559304 | + | 0.828962i | \(0.311068\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −230.934 | −0.819001 | −0.409500 | − | 0.912310i | \(-0.634297\pi\) | ||||
−0.409500 | + | 0.912310i | \(0.634297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −74.5063 | −0.246817 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −139.240 | −0.432134 | −0.216067 | − | 0.976379i | \(-0.569323\pi\) | ||||
−0.216067 | + | 0.976379i | \(0.569323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 114.223 | 0.313616 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 128.400 | 0.332776 | 0.166388 | − | 0.986060i | \(-0.446790\pi\) | ||||
0.166388 | + | 0.986060i | \(0.446790\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 596.666 | 1.46281 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −140.729 | −0.327019 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 58.5822 | 0.129267 | 0.0646335 | − | 0.997909i | \(-0.479412\pi\) | ||||
0.0646335 | + | 0.997909i | \(0.479412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −514.116 | −1.07911 | −0.539555 | − | 0.841950i | \(-0.681408\pi\) | ||||
−0.539555 | + | 0.841950i | \(0.681408\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 740.649 | 1.41333 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −129.876 | −0.236820 | −0.118410 | − | 0.992965i | \(-0.537780\pi\) | ||||
−0.118410 | + | 0.992965i | \(0.537780\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 195.565 | 0.341206 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −221.495 | −0.370234 | −0.185117 | − | 0.982716i | \(-0.559266\pi\) | ||||
−0.185117 | + | 0.982716i | \(0.559266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −700.658 | −1.12337 | −0.561684 | − | 0.827352i | \(-0.689846\pi\) | ||||
−0.561684 | + | 0.827352i | \(0.689846\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 169.400 | 0.260809 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −504.521 | −0.746694 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −791.582 | −1.12734 | −0.563671 | − | 0.826000i | \(-0.690611\pi\) | ||||
−0.563671 | + | 0.826000i | \(0.690611\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 854.668 | 1.13026 | 0.565132 | − | 0.825000i | \(-0.308825\pi\) | ||||
0.565132 | + | 0.825000i | \(0.308825\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 315.198 | 0.402212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −354.821 | −0.437251 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 921.574 | 1.09760 | 0.548802 | − | 0.835953i | \(-0.315084\pi\) | ||||
0.548802 | + | 0.835953i | \(0.315084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −626.267 | −0.721436 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 526.847 | 0.587435 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −388.342 | −0.419401 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1561.47 | 1.63447 | 0.817236 | − | 0.576303i | \(-0.195505\pi\) | ||||
0.817236 | + | 0.576303i | \(0.195505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −648.669 | −0.658523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1599.03 | −1.57534 | −0.787671 | − | 0.616096i | \(-0.788713\pi\) | ||||
−0.787671 | + | 0.616096i | \(0.788713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1213.55 | −1.16092 | −0.580459 | − | 0.814290i | \(-0.697127\pi\) | ||||
−0.580459 | + | 0.814290i | \(0.697127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 173.848 | 0.161579 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1370.27 | −1.23803 | −0.619014 | − | 0.785380i | \(-0.712468\pi\) | ||||
−0.619014 | + | 0.785380i | \(0.712468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −371.867 | −0.326774 | −0.163387 | − | 0.986562i | \(-0.552242\pi\) | ||||
−0.163387 | + | 0.986562i | \(0.552242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 472.400 | 0.403948 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 731.585 | 0.609042 | 0.304521 | − | 0.952506i | \(-0.401504\pi\) | ||||
0.304521 | + | 0.952506i | \(0.401504\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 539.660 | 0.437596 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −805.201 | −0.636247 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −266.521 | −0.205310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3863.72 | 2.90287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −880.999 | −0.645829 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1502.27 | 1.07494 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2386.05 | −1.66715 | −0.833575 | − | 0.552406i | \(-0.813710\pi\) | ||||
−0.833575 | + | 0.552406i | \(0.813710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 692.801 | 0.472850 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 65.1831 | 0.0434739 | 0.0217369 | − | 0.999764i | \(-0.493080\pi\) | ||||
0.0217369 | + | 0.999764i | \(0.493080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 328.369 | 0.214084 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 223.519 | 0.142500 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1515.27 | 0.944950 | 0.472475 | − | 0.881344i | \(-0.343361\pi\) | ||||
0.472475 | + | 0.881344i | \(0.343361\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2173.33 | 1.32618 | 0.663092 | − | 0.748538i | \(-0.269244\pi\) | ||||
0.663092 | + | 0.748538i | \(0.269244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 417.721 | 0.249493 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6448.26 | 3.77085 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −979.127 | −0.560773 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3098.15 | 1.70343 | 0.851714 | − | 0.524007i | \(-0.175564\pi\) | ||||
0.851714 | + | 0.524007i | \(0.175564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −793.085 | −0.427420 | −0.213710 | − | 0.976897i | \(-0.568555\pi\) | ||||
−0.213710 | + | 0.976897i | \(0.568555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −342.669 | −0.181067 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1453.83 | 0.753383 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1586.47 | 0.806459 | 0.403230 | − | 0.915099i | \(-0.367888\pi\) | ||||
0.403230 | + | 0.915099i | \(0.367888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −385.201 | −0.192128 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −456.318 | −0.223372 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −945.643 | −0.454408 | −0.227204 | − | 0.973847i | \(-0.572958\pi\) | ||||
−0.227204 | + | 0.973847i | \(0.572958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1790.00 | −0.844553 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −878.013 | −0.406843 | −0.203421 | − | 0.979091i | \(-0.565206\pi\) | ||||
−0.203421 | + | 0.979091i | \(0.565206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5807.30 | 2.64329 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 422.188 | 0.188804 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1704.42 | 0.749046 | 0.374523 | − | 0.927218i | \(-0.377806\pi\) | ||||
0.374523 | + | 0.927218i | \(0.377806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −395.267 | −0.170739 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −175.747 | −0.0746323 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2742.78 | 1.14528 | 0.572639 | − | 0.819807i | \(-0.305920\pi\) | ||||
0.572639 | + | 0.819807i | \(0.305920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3462.15 | 1.42177 | 0.710883 | − | 0.703310i | \(-0.248296\pi\) | ||||
0.710883 | + | 0.703310i | \(0.248296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1542.35 | 0.623025 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1303.59 | 0.518062 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2744.19 | 1.07313 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4674.18 | 1.77074 | 0.885372 | − | 0.464884i | \(-0.153904\pi\) | ||||
0.885372 | + | 0.464884i | \(0.153904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3094.15 | −1.15400 | −0.576999 | − | 0.816745i | \(-0.695777\pi\) | ||||
−0.576999 | + | 0.816745i | \(0.695777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2221.95 | −0.815984 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4366.68 | −1.57925 | −0.789626 | − | 0.613588i | \(-0.789726\pi\) | ||||
−0.789626 | + | 0.613588i | \(0.789726\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1313.07 | −0.467744 | −0.233872 | − | 0.972267i | \(-0.575140\pi\) | ||||
−0.233872 | + | 0.972267i | \(0.575140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 389.629 | 0.136728 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 827.917 | 0.286248 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2431.11 | −0.828273 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −586.695 | −0.196996 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3381.00 | −1.11899 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1938.29 | −0.632403 | −0.316202 | − | 0.948692i | \(-0.602408\pi\) | ||||
−0.316202 | + | 0.948692i | \(0.602408\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 664.486 | 0.213755 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1911.78 | 0.606429 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1229.31 | −0.384566 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2101.98 | 0.648577 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3406.39 | 1.03683 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2810.59 | 0.843995 | 0.421997 | − | 0.906597i | \(-0.361329\pi\) | ||||
0.421997 | + | 0.906597i | \(0.361329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −508.201 | −0.150578 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5677.70 | −1.66010 | −0.830049 | − | 0.557690i | \(-0.811688\pi\) | ||||
−0.830049 | + | 0.557690i | \(0.811688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2754.87 | 0.794965 | 0.397482 | − | 0.917610i | \(-0.369884\pi\) | ||||
0.397482 | + | 0.917610i | \(0.369884\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1513.56 | 0.431104 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1908.29 | −0.536550 | −0.268275 | − | 0.963342i | \(-0.586454\pi\) | ||||
−0.268275 | + | 0.963342i | \(0.586454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1152.70 | 0.319974 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2374.75 | 0.650871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1120.91 | −0.303371 | −0.151685 | − | 0.988429i | \(-0.548470\pi\) | ||||
−0.151685 | + | 0.988429i | \(0.548470\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −593.838 | −0.158724 | −0.0793620 | − | 0.996846i | \(-0.525288\pi\) | ||||
−0.0793620 | + | 0.996846i | \(0.525288\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −405.645 | −0.105779 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4196.87 | −1.08114 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2564.00 | −0.652559 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7256.88 | −1.82490 | −0.912450 | − | 0.409188i | \(-0.865812\pi\) | ||||
−0.912450 | + | 0.409188i | \(0.865812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4698.41 | 1.16753 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −945.594 | −0.232217 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3120.96 | 0.757511 | 0.378755 | − | 0.925497i | \(-0.376352\pi\) | ||||
0.378755 | + | 0.925497i | \(0.376352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1102.27 | −0.264446 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1064.46 | 0.252447 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3114.51 | −0.730224 | −0.365112 | − | 0.930964i | \(-0.618969\pi\) | ||||
−0.365112 | + | 0.930964i | \(0.618969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1062.96 | −0.246404 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2764.72 | −0.633701 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 803.254 | 0.182064 | 0.0910321 | − | 0.995848i | \(-0.470983\pi\) | ||||
0.0910321 | + | 0.995848i | \(0.470983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5221.42 | −1.17040 | −0.585201 | − | 0.810889i | \(-0.698984\pi\) | ||||
−0.585201 | + | 0.810889i | \(0.698984\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1878.80 | 0.416521 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4069.81 | 0.892432 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3276.37 | 0.710678 | 0.355339 | − | 0.934737i | \(-0.384365\pi\) | ||||
0.355339 | + | 0.934737i | \(0.384365\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1580.54 | −0.339156 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3207.50 | 0.680937 | 0.340469 | − | 0.940256i | \(-0.389414\pi\) | ||||
0.340469 | + | 0.940256i | \(0.389414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9161.80 | 1.92443 | 0.962213 | − | 0.272299i | \(-0.0877839\pi\) | ||||
0.962213 | + | 0.272299i | \(0.0877839\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1165.03 | 0.242141 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2055.66 | 0.422794 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3463.34 | −0.704934 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4684.42 | −0.943663 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3277.09 | 0.653412 | 0.326706 | − | 0.945126i | \(-0.394061\pi\) | ||||
0.326706 | + | 0.945126i | \(0.394061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −484.972 | −0.0957157 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1946.01 | 0.380198 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5832.19 | 1.12804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1616.53 | −0.309553 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4797.10 | 0.909525 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4256.10 | 0.799027 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2748.81 | 0.511020 | 0.255510 | − | 0.966806i | \(-0.417757\pi\) | ||||
0.255510 | + | 0.966806i | \(0.417757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3640.65 | 0.670256 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1800.80 | −0.328341 | −0.164170 | − | 0.986432i | \(-0.552495\pi\) | ||||
−0.164170 | + | 0.986432i | \(0.552495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4904.55 | 0.885692 | 0.442846 | − | 0.896598i | \(-0.353969\pi\) | ||||
0.442846 | + | 0.896598i | \(0.353969\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −521.544 | −0.0932879 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5017.04 | −0.888912 | −0.444456 | − | 0.895801i | \(-0.646603\pi\) | ||||
−0.444456 | + | 0.895801i | \(0.646603\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8524.51 | −1.49618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4110.81 | 0.714776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1786.06 | −0.307675 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5051.90 | 0.862243 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1115.60 | 0.188663 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −974.683 | −0.163331 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10026.8 | 1.66502 | 0.832508 | − | 0.554013i | \(-0.186904\pi\) | ||||
0.832508 | + | 0.554013i | \(0.186904\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1417.20 | −0.233220 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1075.18 | 0.175353 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10196.6 | −1.64820 | −0.824100 | − | 0.566444i | \(-0.808319\pi\) | ||||
−0.824100 | + | 0.566444i | \(0.808319\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2194.76 | −0.351631 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12657.4 | 2.01008 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1618.98 | −0.252646 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −732.813 | −0.113370 | −0.0566851 | − | 0.998392i | \(-0.518053\pi\) | ||||
−0.0566851 | + | 0.998392i | \(0.518053\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4097.74 | −0.628502 | −0.314251 | − | 0.949340i | \(-0.601753\pi\) | ||||
−0.314251 | + | 0.949340i | \(0.601753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2415.60 | 0.367337 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7741.61 | −1.16727 | −0.583633 | − | 0.812018i | \(-0.698369\pi\) | ||||
−0.583633 | + | 0.812018i | \(0.698369\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1833.64 | 0.274140 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 799.562 | 0.118536 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2204.34 | 0.324068 | 0.162034 | − | 0.986785i | \(-0.448195\pi\) | ||||
0.162034 | + | 0.986785i | \(0.448195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4658.47 | −0.679176 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11591.2 | −1.67597 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5800.39 | 0.831798 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3272.01 | 0.465388 | 0.232694 | − | 0.972550i | \(-0.425246\pi\) | ||||
0.232694 | + | 0.972550i | \(0.425246\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2643.00 | 0.372870 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 898.802 | 0.125778 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2004.07 | 0.278195 | 0.139097 | − | 0.990279i | \(-0.455580\pi\) | ||||
0.139097 | + | 0.990279i | \(0.455580\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4506.81 | −0.620615 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10581.6 | −1.44557 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14014.4 | −1.89940 | −0.949699 | − | 0.313164i | \(-0.898611\pi\) | ||||
−0.949699 | + | 0.313164i | \(0.898611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7158.16 | 0.962529 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10252.1 | 1.36778 | 0.683889 | − | 0.729587i | \(-0.260287\pi\) | ||||
0.683889 | + | 0.729587i | \(0.260287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4176.66 | 0.552890 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2078.40 | −0.273000 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10263.6 | 1.33776 | 0.668878 | − | 0.743372i | \(-0.266775\pi\) | ||||
0.668878 | + | 0.743372i | \(0.266775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2482.00 | 0.321024 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −195.549 | −0.0250997 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6553.10 | 0.834740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10292.5 | −1.30117 | −0.650585 | − | 0.759433i | \(-0.725476\pi\) | ||||
−0.650585 | + | 0.759433i | \(0.725476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −985.106 | −0.123602 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 561.891 | 0.0699738 | 0.0349869 | − | 0.999388i | \(-0.488861\pi\) | ||||
0.0349869 | + | 0.999388i | \(0.488861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15711.8 | 1.94208 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −670.557 | −0.0822722 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11349.3 | 1.38222 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2653.32 | 0.320778 | 0.160389 | − | 0.987054i | \(-0.448725\pi\) | ||||
0.160389 | + | 0.987054i | \(0.448725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4545.81 | −0.545567 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 410.075 | 0.0488583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7075.35 | −0.836904 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6520.00 | −0.765673 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4597.68 | −0.536065 | −0.268033 | − | 0.963410i | \(-0.586374\pi\) | ||||
−0.268033 | + | 0.963410i | \(0.586374\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2681.37 | 0.310408 | 0.155204 | − | 0.987882i | \(-0.450396\pi\) | ||||
0.155204 | + | 0.987882i | \(0.450396\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1253.16 | −0.144045 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2149.94 | 0.245382 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3598.81 | −0.407866 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19344.8 | −2.17710 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13557.6 | −1.51519 | −0.757594 | − | 0.652726i | \(-0.773625\pi\) | ||||
−0.757594 | + | 0.652726i | \(0.773625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2024.50 | 0.224691 | 0.112346 | − | 0.993669i | \(-0.464164\pi\) | ||||
0.112346 | + | 0.993669i | \(0.464164\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2937.38 | 0.323762 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3057.97 | −0.334743 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1179.52 | −0.128235 | −0.0641177 | − | 0.997942i | \(-0.520423\pi\) | ||||
−0.0641177 | + | 0.997942i | \(0.520423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15506.8 | 1.66309 | 0.831547 | − | 0.555454i | \(-0.187456\pi\) | ||||
0.831547 | + | 0.555454i | \(0.187456\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7629.23 | −0.812720 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9294.46 | −0.983474 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7666.24 | −0.805774 | −0.402887 | − | 0.915250i | \(-0.631993\pi\) | ||||
−0.402887 | + | 0.915250i | \(0.631993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21165.8 | −2.20989 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2379.26 | 0.246771 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5184.54 | 0.534187 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11940.9 | −1.22226 | −0.611128 | − | 0.791532i | \(-0.709284\pi\) | ||||
−0.611128 | + | 0.791532i | \(0.709284\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1028.01 | 0.104539 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13964.4 | −1.41082 | −0.705411 | − | 0.708799i | \(-0.749237\pi\) | ||||
−0.705411 | + | 0.708799i | \(0.749237\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14419.6 | −1.44738 | −0.723691 | − | 0.690124i | \(-0.757556\pi\) | ||||
−0.723691 | + | 0.690124i | \(0.757556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4361.49 | −0.434966 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8781.18 | 0.870117 | 0.435058 | − | 0.900402i | \(-0.356728\pi\) | ||||
0.435058 | + | 0.900402i | \(0.356728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −909.135 | −0.0895095 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4759.41 | −0.465609 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16644.4 | 1.61799 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2648.85 | −0.255868 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1155.60 | 0.110925 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10270.5 | 0.979686 | 0.489843 | − | 0.871811i | \(-0.337054\pi\) | ||||
0.489843 | + | 0.871811i | \(0.337054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14088.0 | 1.33547 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1368.95 | 0.128964 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12926.6 | −1.21024 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12516.1 | −1.16459 | −0.582297 | − | 0.812976i | \(-0.697846\pi\) | ||||
−0.582297 | + | 0.812976i | \(0.697846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2836.93 | 0.262352 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12534.1 | −1.15205 | −0.576024 | − | 0.817433i | \(-0.695397\pi\) | ||||
−0.576024 | + | 0.817433i | \(0.695397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4503.20 | −0.411387 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5370.00 | 0.487603 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1550.47 | −0.139935 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14357.3 | −1.28801 | −0.644007 | − | 0.765019i | \(-0.722729\pi\) | ||||
−0.644007 | + | 0.765019i | \(0.722729\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2634.04 | 0.234891 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16412.8 | 1.45489 | 0.727446 | − | 0.686165i | \(-0.240707\pi\) | ||||
0.727446 | + | 0.686165i | \(0.240707\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13237.6 | 1.16646 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17421.9 | −1.52610 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3581.31 | 0.311864 | 0.155932 | − | 0.987768i | \(-0.450162\pi\) | ||||
0.155932 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4904.61 | −0.424593 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1266.57 | −0.109006 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10046.3 | 0.859601 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10035.7 | 0.853710 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5113.27 | −0.432462 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6838.64 | 0.575060 | 0.287530 | − | 0.957772i | \(-0.407166\pi\) | ||||
0.287530 | + | 0.957772i | \(0.407166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −330.872 | −0.0276635 | −0.0138318 | − | 0.999904i | \(-0.504403\pi\) | ||||
−0.0138318 | + | 0.999904i | \(0.504403\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1185.80 | 0.0985765 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6686.45 | 0.552688 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7917.49 | −0.650734 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 527.240 | 0.0430890 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26273.4 | −2.13513 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11343.8 | 0.916698 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8228.33 | −0.661227 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3531.64 | −0.282224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10233.6 | 0.813265 | 0.406633 | − | 0.913592i | \(-0.366703\pi\) | ||||
0.406633 | + | 0.913592i | \(0.366703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10386.5 | −0.820857 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3078.49 | 0.241960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5374.48 | 0.420103 | 0.210052 | − | 0.977690i | \(-0.432637\pi\) | ||||
0.210052 | + | 0.977690i | \(0.432637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4627.04 | −0.359704 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5548.20 | 0.428968 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5541.08 | −0.426095 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3910.76 | −0.299103 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23749.7 | −1.80665 | −0.903327 | − | 0.428952i | \(-0.858883\pi\) | ||||
−0.903327 | + | 0.428952i | \(0.858883\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20660.9 | 1.56326 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8232.56 | −0.619571 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4551.40 | −0.340708 | −0.170354 | − | 0.985383i | \(-0.554491\pi\) | ||||
−0.170354 | + | 0.985383i | \(0.554491\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6056.41 | −0.450965 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13864.8 | −1.02152 | −0.510758 | − | 0.859725i | \(-0.670635\pi\) | ||||
−0.510758 | + | 0.859725i | \(0.670635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26668.4 | 1.95453 | 0.977267 | − | 0.212011i | \(-0.0680014\pi\) | ||||
0.977267 | + | 0.212011i | \(0.0680014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14022.5 | −1.02234 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3680.97 | 0.266969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 723.611 | 0.0522085 | 0.0261043 | − | 0.999659i | \(-0.491690\pi\) | ||||
0.0261043 | + | 0.999659i | \(0.491690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9282.45 | 0.666262 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5982.67 | 0.427200 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9254.38 | −0.657422 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6665.84 | 0.471109 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5753.39 | 0.404545 | 0.202273 | − | 0.979329i | \(-0.435167\pi\) | ||||
0.202273 | + | 0.979329i | \(0.435167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8238.09 | −0.576307 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13100.0 | 0.911782 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9298.15 | −0.643894 | −0.321947 | − | 0.946758i | \(-0.604337\pi\) | ||||
−0.321947 | + | 0.946758i | \(0.604337\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2206.39 | 0.152022 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3939.21 | 0.270052 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7480.54 | 0.510261 | 0.255131 | − | 0.966907i | \(-0.417882\pi\) | ||||
0.255131 | + | 0.966907i | \(0.417882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8449.27 | 0.573466 | 0.286733 | − | 0.958011i | \(-0.407431\pi\) | ||||
0.286733 | + | 0.958011i | \(0.407431\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1168.89 | −0.0789400 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31985.7 | −2.14943 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12385.4 | −0.828182 | −0.414091 | − | 0.910236i | \(-0.635900\pi\) | ||||
−0.414091 | + | 0.910236i | \(0.635900\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2483.75 | −0.165265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12457.4 | 0.824832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28991.8 | −1.91023 | −0.955113 | − | 0.296240i | \(-0.904267\pi\) | ||||
−0.955113 | + | 0.296240i | \(0.904267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7293.33 | 0.478204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28726.3 | 1.87435 | 0.937177 | − | 0.348853i | \(-0.113429\pi\) | ||||
0.937177 | + | 0.348853i | \(0.113429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7766.73 | −0.504316 | −0.252158 | − | 0.967686i | \(-0.581140\pi\) | ||||
−0.252158 | + | 0.967686i | \(0.581140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1760.08 | 0.113735 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6451.02 | 0.414855 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5378.15 | −0.344202 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10143.0 | 0.646048 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5995.45 | 0.380055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17284.6 | −1.09047 | −0.545236 | − | 0.838283i | \(-0.683560\pi\) | ||||
−0.545236 | + | 0.838283i | \(0.683560\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5814.86 | 0.365118 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19752.9 | 1.23444 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4383.87 | −0.272677 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1993.46 | −0.123411 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31764.4 | −1.95729 | −0.978643 | − | 0.205568i | \(-0.934096\pi\) | ||||
−0.978643 | + | 0.205568i | \(0.934096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20740.6 | 1.27205 | 0.636026 | − | 0.771668i | \(-0.280577\pi\) | ||||
0.636026 | + | 0.771668i | \(0.280577\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5735.34 | −0.350122 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23613.3 | −1.43483 | −0.717415 | − | 0.696646i | \(-0.754675\pi\) | ||||
−0.717415 | + | 0.696646i | \(0.754675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4222.28 | −0.255376 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3687.93 | 0.222030 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1400.83 | 0.0839489 | 0.0419745 | − | 0.999119i | \(-0.486635\pi\) | ||||
0.0419745 | + | 0.999119i | \(0.486635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −539.617 | −0.0321902 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6305.93 | −0.374456 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19793.0 | −1.16999 | −0.584997 | − | 0.811036i | \(-0.698904\pi\) | ||||
−0.584997 | + | 0.811036i | \(0.698904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29180.8 | −1.71710 | −0.858549 | − | 0.512731i | \(-0.828634\pi\) | ||||
−0.858549 | + | 0.512731i | \(0.828634\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10219.2 | −0.598612 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2718.39 | −0.158518 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7710.07 | −0.447579 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8431.76 | −0.487281 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37054.6 | 2.13186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9691.22 | −0.555081 | −0.277540 | − | 0.960714i | \(-0.589519\pi\) | ||||
−0.277540 | + | 0.960714i | \(0.589519\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1524.60 | 0.0869363 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24254.8 | 1.37694 | 0.688469 | − | 0.725266i | \(-0.258283\pi\) | ||||
0.688469 | + | 0.725266i | \(0.258283\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10930.3 | 0.617772 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17033.1 | 0.958459 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27067.1 | 1.51639 | 0.758193 | − | 0.652030i | \(-0.226082\pi\) | ||||
0.758193 | + | 0.652030i | \(0.226082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12544.1 | −0.699688 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8264.61 | −0.458973 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11487.6 | −0.635183 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6908.11 | −0.380314 | −0.190157 | − | 0.981754i | \(-0.560900\pi\) | ||||
−0.190157 | + | 0.981754i | \(0.560900\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4540.69 | −0.248898 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17991.9 | −0.981973 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11181.2 | −0.607628 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5724.86 | 0.309777 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14121.5 | 0.760856 | 0.380428 | − | 0.924811i | \(-0.375777\pi\) | ||||
0.380428 | + | 0.924811i | \(0.375777\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7386.74 | −0.396296 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3458.10 | −0.184737 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11193.2 | −0.595424 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27122.6 | 1.43669 | 0.718343 | − | 0.695690i | \(-0.244901\pi\) | ||||
0.718343 | + | 0.695690i | \(0.244901\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7124.24 | −0.375781 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11448.1 | 0.601310 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −53381.8 | −2.79212 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3362.73 | 0.175151 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29577.0 | −1.53413 | −0.767064 | − | 0.641571i | \(-0.778283\pi\) | ||||
−0.767064 | + | 0.641571i | \(0.778283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8494.84 | −0.438786 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1781.51 | 0.0916393 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6678.54 | −0.342117 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34389.1 | 1.75436 | 0.877181 | − | 0.480160i | \(-0.159421\pi\) | ||||
0.877181 | + | 0.480160i | \(0.159421\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8792.65 | 0.444881 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21859.4 | −1.10150 | −0.550748 | − | 0.834672i | \(-0.685657\pi\) | ||||
−0.550748 | + | 0.834672i | \(0.685657\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1216.94 | 0.0610713 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9360.77 | 0.467854 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16828.4 | −0.837677 | −0.418838 | − | 0.908061i | \(-0.637563\pi\) | ||||
−0.418838 | + | 0.908061i | \(0.637563\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12590.6 | 0.624194 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15612.2 | 0.770871 | 0.385436 | − | 0.922735i | \(-0.374051\pi\) | ||||
0.385436 | + | 0.922735i | \(0.374051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25648.0 | −1.26130 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7692.01 | 0.376755 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9591.90 | −0.467931 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5405.70 | 0.262659 | 0.131330 | − | 0.991339i | \(-0.458075\pi\) | ||||
0.131330 | + | 0.991339i | \(0.458075\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21770.6 | 1.05361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6565.54 | 0.316483 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7432.52 | −0.356855 | −0.178428 | − | 0.983953i | \(-0.557101\pi\) | ||||
−0.178428 | + | 0.983953i | \(0.557101\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14095.2 | −0.674077 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10851.9 | −0.516927 | −0.258463 | − | 0.966021i | \(-0.583216\pi\) | ||||
−0.258463 | + | 0.966021i | \(0.583216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2603.07 | −0.123509 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2836.78 | 0.134071 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5241.16 | −0.246737 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24016.7 | 1.12622 | 0.563112 | − | 0.826381i | \(-0.309604\pi\) | ||||
0.563112 | + | 0.826381i | \(0.309604\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9362.89 | −0.437349 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26716.0 | 1.24309 | 0.621544 | − | 0.783379i | \(-0.286506\pi\) | ||||
0.621544 | + | 0.783379i | \(0.286506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9916.45 | 0.459625 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3306.80 | 0.152678 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13775.8 | 0.633595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15964.1 | 0.731423 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3193.39 | −0.145750 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13133.6 | −0.597142 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35503.3 | −1.60808 | −0.804038 | − | 0.594578i | \(-0.797319\pi\) | ||||
−0.804038 | + | 0.594578i | \(0.797319\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9343.53 | 0.421595 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5121.10 | 0.230196 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45996.3 | 2.05974 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3188.88 | 0.142261 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9626.24 | −0.427828 | −0.213914 | − | 0.976852i | \(-0.568621\pi\) | ||||
−0.213914 | + | 0.976852i | \(0.568621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5301.49 | 0.234735 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8294.17 | 0.365868 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50499.5 | 2.21929 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3777.62 | 0.165396 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2409.76 | −0.105115 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14915.6 | 0.648215 | 0.324107 | − | 0.946020i | \(-0.394936\pi\) | ||||
0.324107 | + | 0.946020i | \(0.394936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39232.2 | −1.69868 | −0.849340 | − | 0.527845i | \(-0.823000\pi\) | ||||
−0.849340 | + | 0.527845i | \(0.823000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15664.3 | 0.675731 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7828.48 | 0.336466 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10833.1 | −0.463893 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5636.41 | −0.240479 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1312.17 | −0.0557797 | −0.0278898 | − | 0.999611i | \(-0.508879\pi\) | ||||
−0.0278898 | + | 0.999611i | \(0.508879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32578.1 | −1.37983 | −0.689916 | − | 0.723890i | \(-0.742352\pi\) | ||||
−0.689916 | + | 0.723890i | \(0.742352\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12209.4 | −0.515246 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15486.0 | 0.651149 | 0.325574 | − | 0.945516i | \(-0.394442\pi\) | ||||
0.325574 | + | 0.945516i | \(0.394442\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4875.60 | 0.204266 | 0.102133 | − | 0.994771i | \(-0.467433\pi\) | ||||
0.102133 | + | 0.994771i | \(0.467433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9829.11 | −0.410310 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1865.64 | −0.0776000 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7268.61 | 0.301246 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4741.62 | 0.195812 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11091.5 | 0.456403 | 0.228201 | − | 0.973614i | \(-0.426716\pi\) | ||||
0.228201 | + | 0.973614i | \(0.426716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10400.3 | −0.426434 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9622.50 | −0.393139 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −48075.7 | −1.95722 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27046.0 | 1.09718 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27485.4 | −1.11107 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10265.0 | 0.413489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1127.04 | −0.0452393 | −0.0226197 | − | 0.999744i | \(-0.507201\pi\) | ||||
−0.0226197 | + | 0.999744i | \(0.507201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3495.08 | −0.139800 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31542.5 | 1.25726 | 0.628630 | − | 0.777705i | \(-0.283616\pi\) | ||||
0.628630 | + | 0.777705i | \(0.283616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21430.0 | 0.851201 | 0.425600 | − | 0.904911i | \(-0.360063\pi\) | ||||
0.425600 | + | 0.904911i | \(0.360063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6166.99 | −0.244100 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29408.3 | 1.15999 | 0.579994 | − | 0.814621i | \(-0.303055\pi\) | ||||
0.579994 | + | 0.814621i | \(0.303055\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14110.0 | −0.554631 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10390.0 | 0.406994 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57052.8 | 2.22714 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11619.6 | 0.452028 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14053.3 | 0.544824 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10515.9 | 0.406288 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3247.51 | 0.125041 | 0.0625203 | − | 0.998044i | \(-0.480086\pi\) | ||||
0.0625203 | + | 0.998044i | \(0.480086\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9831.27 | −0.377248 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17925.3 | 0.685492 | 0.342746 | − | 0.939428i | \(-0.388643\pi\) | ||||
0.342746 | + | 0.939428i | \(0.388643\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −649.227 | −0.0247432 | −0.0123716 | − | 0.999923i | \(-0.503938\pi\) | ||||
−0.0123716 | + | 0.999923i | \(0.503938\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1454.91 | 0.0552615 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −281.201 | −0.0106446 | −0.00532232 | − | 0.999986i | \(-0.501694\pi\) | ||||
−0.00532232 | + | 0.999986i | \(0.501694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16702.4 | −0.630123 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5838.03 | −0.219508 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6531.75 | −0.244767 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22706.0 | −0.848021 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17496.6 | −0.651275 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20770.7 | −0.770570 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4888.76 | −0.180764 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4849.60 | 0.178721 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28661.3 | −1.05275 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22119.6 | −0.809780 | −0.404890 | − | 0.914365i | \(-0.632690\pi\) | ||||
−0.404890 | + | 0.914365i | \(0.632690\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14391.3 | −0.525114 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23370.6 | −0.849948 | −0.424974 | − | 0.905206i | \(-0.639717\pi\) | ||||
−0.424974 | + | 0.905206i | \(0.639717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −61599.7 | −2.23291 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12768.3 | −0.461319 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 456.282 | 0.0164316 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44334.6 | 1.59136 | 0.795682 | − | 0.605715i | \(-0.207113\pi\) | ||||
0.795682 | + | 0.605715i | \(0.207113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8246.44 | −0.295037 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19816.5 | 0.706681 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8891.64 | 0.316060 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10921.9 | −0.386973 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31674.4 | −1.11862 | −0.559312 | − | 0.828957i | \(-0.688935\pi\) | ||||
−0.559312 | + | 0.828957i | \(0.688935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2298.58 | 0.0809162 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5402.39 | 0.189567 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22717.7 | −0.794597 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5825.76 | 0.203116 | 0.101558 | − | 0.994830i | \(-0.467617\pi\) | ||||
0.101558 | + | 0.994830i | \(0.467617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14713.7 | −0.511355 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −698.816 | −0.0242091 | −0.0121045 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121045 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19143.6 | −0.661083 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1564.63 | 0.0538598 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10938.8 | 0.375357 | 0.187679 | − | 0.982230i | \(-0.439904\pi\) | ||||
0.187679 | + | 0.982230i | \(0.439904\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62685.7 | 2.14422 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15051.1 | 0.513214 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34467.3 | −1.17157 | −0.585784 | − | 0.810467i | \(-0.699213\pi\) | ||||
−0.585784 | + | 0.810467i | \(0.699213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38695.1 | −1.31115 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25573.5 | 0.863819 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10606.9 | 0.357158 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1049.82 | 0.0352396 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12332.4 | −0.412676 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25614.9 | 0.854478 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24386.7 | 0.810985 | 0.405493 | − | 0.914098i | \(-0.367100\pi\) | ||||
0.405493 | + | 0.914098i | \(0.367100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5358.19 | 0.177637 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33108.9 | −1.09425 | −0.547124 | − | 0.837052i | \(-0.684277\pi\) | ||||
−0.547124 | + | 0.837052i | \(0.684277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15213.3 | 0.501251 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15155.7 | −0.497816 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8633.92 | −0.282726 | −0.141363 | − | 0.989958i | \(-0.545149\pi\) | ||||
−0.141363 | + | 0.989958i | \(0.545149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −66421.9 | −2.16839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3346.80 | −0.108925 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22005.7 | 0.714011 | 0.357006 | − | 0.934102i | \(-0.383798\pi\) | ||||
0.357006 | + | 0.934102i | \(0.383798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36149.4 | 1.16936 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2924.05 | 0.0942994 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15054.2 | 0.484019 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15185.7 | −0.486772 | −0.243386 | − | 0.969930i | \(-0.578258\pi\) | ||||
−0.243386 | + | 0.969930i | \(0.578258\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30080.3 | −0.961298 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10870.2 | 0.346341 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41110.7 | 1.30591 | 0.652953 | − | 0.757398i | \(-0.273530\pi\) | ||||
0.652953 | + | 0.757398i | \(0.273530\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4251.60 | 0.134649 |
(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 | 1344.4.a.bs.1.2 | 3 | ||
4.3 | odd | 2 | 1344.4.a.bu.1.2 | 3 | |||
8.3 | odd | 2 | 672.4.a.p.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 672.4.a.r.1.2 | yes | 3 | ||
24.5 | odd | 2 | 2016.4.a.v.1.2 | 3 | |||
24.11 | even | 2 | 2016.4.a.u.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.p.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
672.4.a.r.1.2 | yes | 3 | 8.5 | even | 2 | ||
1344.4.a.bs.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1344.4.a.bu.1.2 | 3 | 4.3 | odd | 2 | |||
2016.4.a.u.1.2 | 3 | 24.11 | even | 2 | |||
2016.4.a.v.1.2 | 3 | 24.5 | odd | 2 |