Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, 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("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.4281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.55784\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −34.6634 | −1.87165 | −0.935825 | − | 0.352465i | \(-0.885343\pi\) | ||||
−0.935825 | + | 0.352465i | \(0.885343\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23.2350 | −0.636875 | −0.318438 | − | 0.947944i | \(-0.603158\pi\) | ||||
−0.318438 | + | 0.947944i | \(0.603158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 60.0918 | 1.28204 | 0.641018 | − | 0.767526i | \(-0.278512\pi\) | ||||
0.641018 | + | 0.767526i | \(0.278512\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −19.6634 | −0.280534 | −0.140267 | − | 0.990114i | \(-0.544796\pi\) | ||||
−0.140267 | + | 0.990114i | \(0.544796\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.2350 | −0.123583 | −0.0617916 | − | 0.998089i | \(-0.519681\pi\) | ||||
−0.0617916 | + | 0.998089i | \(0.519681\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −79.7553 | −0.723049 | −0.361524 | − | 0.932363i | \(-0.617744\pi\) | ||||
−0.361524 | + | 0.932363i | \(0.617744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −110.847 | −0.709786 | −0.354893 | − | 0.934907i | \(-0.615483\pi\) | ||||
−0.354893 | + | 0.934907i | \(0.615483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.5202 | −0.246350 | −0.123175 | − | 0.992385i | \(-0.539308\pi\) | ||||
−0.123175 | + | 0.992385i | \(0.539308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −173.317 | −0.837027 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 308.451 | 1.37051 | 0.685257 | − | 0.728302i | \(-0.259690\pi\) | ||||
0.685257 | + | 0.728302i | \(0.259690\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 106.950 | 0.407384 | 0.203692 | − | 0.979035i | \(-0.434706\pi\) | ||||
0.203692 | + | 0.979035i | \(0.434706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −467.868 | −1.65928 | −0.829642 | − | 0.558295i | \(-0.811456\pi\) | ||||
−0.829642 | + | 0.558295i | \(0.811456\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −37.7982 | −0.117307 | −0.0586536 | − | 0.998278i | \(-0.518681\pi\) | ||||
−0.0586536 | + | 0.998278i | \(0.518681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 858.554 | 2.50307 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 568.399 | 1.47313 | 0.736563 | − | 0.676369i | \(-0.236448\pi\) | ||||
0.736563 | + | 0.676369i | \(0.236448\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −116.175 | −0.284819 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 666.893 | 1.47156 | 0.735780 | − | 0.677220i | \(-0.236816\pi\) | ||||
0.735780 | + | 0.677220i | \(0.236816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −862.166 | −1.80966 | −0.904828 | − | 0.425777i | \(-0.860001\pi\) | ||||
−0.904828 | + | 0.425777i | \(0.860001\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 300.459 | 0.573344 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 547.085 | 0.997568 | 0.498784 | − | 0.866726i | \(-0.333780\pi\) | ||||
0.498784 | + | 0.866726i | \(0.333780\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 761.113 | 1.27222 | 0.636109 | − | 0.771599i | \(-0.280543\pi\) | ||||
0.636109 | + | 0.771599i | \(0.280543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −216.562 | −0.347214 | −0.173607 | − | 0.984815i | \(-0.555542\pi\) | ||||
−0.173607 | + | 0.984815i | \(0.555542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 805.407 | 1.19201 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 258.600 | 0.368288 | 0.184144 | − | 0.982899i | \(-0.441049\pi\) | ||||
0.184144 | + | 0.982899i | \(0.441049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 903.680 | 1.19508 | 0.597541 | − | 0.801838i | \(-0.296145\pi\) | ||||
0.597541 | + | 0.801838i | \(0.296145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −98.3172 | −0.125459 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1265.95 | 1.50776 | 0.753880 | − | 0.657012i | \(-0.228180\pi\) | ||||
0.753880 | + | 0.657012i | \(0.228180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2082.99 | −2.39952 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −51.1752 | −0.0552681 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 617.305 | 0.646163 | 0.323082 | − | 0.946371i | \(-0.395281\pi\) | ||||
0.323082 | + | 0.946371i | \(0.395281\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −831.717 | −0.819395 | −0.409698 | − | 0.912221i | \(-0.634366\pi\) | ||||
−0.409698 | + | 0.912221i | \(0.634366\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 904.254 | 0.865036 | 0.432518 | − | 0.901625i | \(-0.357625\pi\) | ||||
0.432518 | + | 0.901625i | \(0.357625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −897.290 | −0.810695 | −0.405347 | − | 0.914163i | \(-0.632849\pi\) | ||||
−0.405347 | + | 0.914163i | \(0.632849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −258.932 | −0.227534 | −0.113767 | − | 0.993507i | \(-0.536292\pi\) | ||||
−0.113767 | + | 0.993507i | \(0.536292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −329.028 | −0.273915 | −0.136957 | − | 0.990577i | \(-0.543732\pi\) | ||||
−0.136957 | + | 0.990577i | \(0.543732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −398.776 | −0.323357 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 681.602 | 0.525062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −791.133 | −0.594390 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1602.36 | 1.11958 | 0.559789 | − | 0.828635i | \(-0.310882\pi\) | ||||
0.559789 | + | 0.828635i | \(0.310882\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1373.59 | 0.916116 | 0.458058 | − | 0.888922i | \(-0.348545\pi\) | ||||
0.458058 | + | 0.888922i | \(0.348545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 354.782 | 0.231304 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 690.827 | 0.430813 | 0.215406 | − | 0.976524i | \(-0.430892\pi\) | ||||
0.215406 | + | 0.976524i | \(0.430892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1072.90 | −0.654693 | −0.327346 | − | 0.944904i | \(-0.606154\pi\) | ||||
−0.327346 | + | 0.944904i | \(0.606154\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1396.24 | −0.816498 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −554.236 | −0.317426 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2828.55 | −1.55520 | −0.777598 | − | 0.628762i | \(-0.783562\pi\) | ||||
−0.777598 | + | 0.628762i | \(0.783562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1138.61 | 0.613633 | 0.306817 | − | 0.951769i | \(-0.400736\pi\) | ||||
0.306817 | + | 0.951769i | \(0.400736\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −212.601 | −0.110171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2489.69 | 1.26560 | 0.632799 | − | 0.774316i | \(-0.281906\pi\) | ||||
0.632799 | + | 0.774316i | \(0.281906\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2764.59 | 1.35329 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1174.61 | −0.564431 | −0.282216 | − | 0.959351i | \(-0.591069\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2249.28 | 1.04224 | 0.521121 | − | 0.853483i | \(-0.325514\pi\) | ||||
0.521121 | + | 0.853483i | \(0.325514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1414.03 | 0.643618 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3692.19 | 1.62261 | 0.811305 | − | 0.584623i | \(-0.198757\pi\) | ||||
0.811305 | + | 0.584623i | \(0.198757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −866.586 | −0.374330 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4240.02 | 1.77047 | 0.885234 | − | 0.465145i | \(-0.153998\pi\) | ||||
0.885234 | + | 0.465145i | \(0.153998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −748.267 | −0.307283 | −0.153641 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153641 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1542.25 | 0.612912 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 456.881 | 0.178665 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1134.04 | 0.429612 | 0.214806 | − | 0.976657i | \(-0.431088\pi\) | ||||
0.214806 | + | 0.976657i | \(0.431088\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1134.32 | 0.423059 | 0.211529 | − | 0.977372i | \(-0.432156\pi\) | ||||
0.211529 | + | 0.977372i | \(0.432156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4392.63 | 1.58864 | 0.794320 | − | 0.607499i | \(-0.207827\pi\) | ||||
0.794320 | + | 0.607499i | \(0.207827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1922.75 | −0.684926 | −0.342463 | − | 0.939531i | \(-0.611261\pi\) | ||||
−0.342463 | + | 0.939531i | \(0.611261\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3842.34 | 1.32847 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 534.749 | 0.182188 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 237.812 | 0.0787071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4135.95 | −1.34944 | −0.674718 | − | 0.738076i | \(-0.735735\pi\) | ||||
−0.674718 | + | 0.738076i | \(0.735735\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2339.34 | −0.742055 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1473.90 | 0.461081 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1181.61 | −0.359655 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3060.01 | 0.918893 | 0.459446 | − | 0.888205i | \(-0.348048\pi\) | ||||
0.459446 | + | 0.888205i | \(0.348048\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2670.37 | −0.780787 | −0.390393 | − | 0.920648i | \(-0.627661\pi\) | ||||
−0.390393 | + | 0.920648i | \(0.627661\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −177.855 | −0.0513231 | −0.0256615 | − | 0.999671i | \(-0.508169\pi\) | ||||
−0.0256615 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3014.80 | −0.847667 | −0.423833 | − | 0.905740i | \(-0.639316\pi\) | ||||
−0.423833 | + | 0.905740i | \(0.639316\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −188.991 | −0.0524613 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2997.51 | 0.811268 | 0.405634 | − | 0.914036i | \(-0.367051\pi\) | ||||
0.405634 | + | 0.914036i | \(0.367051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4320.99 | 1.15494 | 0.577468 | − | 0.816413i | \(-0.304041\pi\) | ||||
0.577468 | + | 0.816413i | \(0.304041\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4292.77 | 1.11941 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −615.043 | −0.158438 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4285.02 | 1.07756 | 0.538781 | − | 0.842446i | \(-0.318885\pi\) | ||||
0.538781 | + | 0.842446i | \(0.318885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1853.12 | 0.460492 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7371.27 | 1.78913 | 0.894567 | − | 0.446935i | \(-0.147484\pi\) | ||||
0.894567 | + | 0.446935i | \(0.147484\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10692.0 | −2.56512 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5789.77 | 1.35746 | 0.678731 | − | 0.734387i | \(-0.262530\pi\) | ||||
0.678731 | + | 0.734387i | \(0.262530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2842.00 | 0.658802 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4402.25 | −0.997806 | −0.498903 | − | 0.866658i | \(-0.666264\pi\) | ||||
−0.498903 | + | 0.866658i | \(0.666264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1181.60 | −0.264859 | −0.132430 | − | 0.991192i | \(-0.542278\pi\) | ||||
−0.132430 | + | 0.991192i | \(0.542278\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −580.876 | −0.127375 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4912.20 | 1.06551 | 0.532754 | − | 0.846270i | \(-0.321157\pi\) | ||||
0.532754 | + | 0.846270i | \(0.321157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4588.62 | −0.974143 | −0.487072 | − | 0.873362i | \(-0.661935\pi\) | ||||
−0.487072 | + | 0.873362i | \(0.661935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5277.69 | −1.10857 | −0.554287 | − | 0.832326i | \(-0.687009\pi\) | ||||
−0.554287 | + | 0.832326i | \(0.687009\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3707.25 | −0.762481 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4526.35 | −0.921300 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9083.85 | −1.81121 | −0.905604 | − | 0.424124i | \(-0.860582\pi\) | ||||
−0.905604 | + | 0.424124i | \(0.860582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3334.46 | 0.658102 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4792.64 | −0.926975 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16217.9 | 3.10560 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4310.83 | −0.809303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10311.4 | −1.91694 | −0.958469 | − | 0.285197i | \(-0.907941\pi\) | ||||
−0.958469 | + | 0.285197i | \(0.907941\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1200.72 | −0.218929 | −0.109464 | − | 0.993991i | \(-0.534914\pi\) | ||||
−0.109464 | + | 0.993991i | \(0.534914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6270.23 | −1.13231 | −0.566157 | − | 0.824298i | \(-0.691570\pi\) | ||||
−0.566157 | + | 0.824298i | \(0.691570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2348.12 | 0.416037 | 0.208018 | − | 0.978125i | \(-0.433299\pi\) | ||||
0.208018 | + | 0.978125i | \(0.433299\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2575.54 | 0.452045 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 201.256 | 0.0346693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1502.30 | 0.256407 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1310.22 | 0.219558 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6583.03 | 1.09316 | 0.546580 | − | 0.837407i | \(-0.315929\pi\) | ||||
0.546580 | + | 0.837407i | \(0.315929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2735.43 | 0.446126 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1513.37 | 0.244624 | 0.122312 | − | 0.992492i | \(-0.460969\pi\) | ||||
0.122312 | + | 0.992492i | \(0.460969\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 987.959 | 0.156894 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17870.9 | −2.81323 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10534.4 | −1.62972 | −0.814862 | − | 0.579656i | \(-0.803187\pi\) | ||||
−0.814862 | + | 0.579656i | \(0.803187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7617.91 | 1.16842 | 0.584208 | − | 0.811604i | \(-0.301405\pi\) | ||||
0.584208 | + | 0.811604i | \(0.301405\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4882.40 | 0.736159 | 0.368079 | − | 0.929794i | \(-0.380015\pi\) | ||||
0.368079 | + | 0.929794i | \(0.380015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3805.56 | 0.568953 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3230.35 | 0.474906 | 0.237453 | − | 0.971399i | \(-0.423687\pi\) | ||||
0.237453 | + | 0.971399i | \(0.423687\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6754.24 | −0.984727 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1082.81 | −0.155279 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10910.4 | −1.55182 | −0.775912 | − | 0.630841i | \(-0.782710\pi\) | ||||
−0.775912 | + | 0.630841i | \(0.782710\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19702.7 | −2.75718 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9337.73 | 1.29622 | 0.648109 | − | 0.761548i | \(-0.275560\pi\) | ||||
0.648109 | + | 0.761548i | \(0.275560\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6661.01 | −0.909971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2566.39 | −0.347828 | −0.173914 | − | 0.984761i | \(-0.555641\pi\) | ||||
−0.173914 | + | 0.984761i | \(0.555641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6734.56 | −0.898485 | −0.449243 | − | 0.893410i | \(-0.648306\pi\) | ||||
−0.449243 | + | 0.893410i | \(0.648306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4027.03 | 0.533082 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5015.93 | 0.653773 | 0.326886 | − | 0.945064i | \(-0.394001\pi\) | ||||
0.326886 | + | 0.945064i | \(0.394001\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1568.26 | 0.202840 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1293.00 | 0.164703 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −484.045 | −0.0611927 | −0.0305964 | − | 0.999532i | \(-0.509741\pi\) | ||||
−0.0305964 | + | 0.999532i | \(0.509741\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8235.48 | 1.02559 | 0.512793 | − | 0.858512i | \(-0.328611\pi\) | ||||
0.512793 | + | 0.858512i | \(0.328611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2555.12 | −0.315830 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7166.87 | −0.872846 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7276.15 | −0.879664 | −0.439832 | − | 0.898080i | \(-0.644962\pi\) | ||||
−0.439832 | + | 0.898080i | \(0.644962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23116.8 | −2.75425 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4518.40 | 0.534457 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4852.57 | −0.565784 | −0.282892 | − | 0.959152i | \(-0.591294\pi\) | ||||
−0.282892 | + | 0.959152i | \(0.591294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11401.6 | −1.31990 | −0.659952 | − | 0.751308i | \(-0.729424\pi\) | ||||
−0.659952 | + | 0.751308i | \(0.729424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −491.586 | −0.0561069 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29885.6 | 3.38704 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13132.5 | 1.46768 | 0.733838 | − | 0.679324i | \(-0.237727\pi\) | ||||
0.733838 | + | 0.679324i | \(0.237727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2695.20 | −0.299129 | −0.149564 | − | 0.988752i | \(-0.547787\pi\) | ||||
−0.149564 | + | 0.988752i | \(0.547787\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 816.299 | 0.0893567 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9673.34 | −1.05167 | −0.525835 | − | 0.850587i | \(-0.676247\pi\) | ||||
−0.525835 | + | 0.850587i | \(0.676247\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14747.7 | 1.58168 | 0.790838 | − | 0.612026i | \(-0.209645\pi\) | ||||
0.790838 | + | 0.612026i | \(0.209645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6329.76 | 0.674291 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 872.877 | 0.0917453 | 0.0458726 | − | 0.998947i | \(-0.485393\pi\) | ||||
0.0458726 | + | 0.998947i | \(0.485393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2484.98 | −0.259453 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10414.9 | −1.07310 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7841.08 | 0.802604 | 0.401302 | − | 0.915946i | \(-0.368558\pi\) | ||||
0.401302 | + | 0.915946i | \(0.368558\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4767.81 | 0.481690 | 0.240845 | − | 0.970564i | \(-0.422576\pi\) | ||||
0.240845 | + | 0.970564i | \(0.422576\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5183.54 | 0.520302 | 0.260151 | − | 0.965568i | \(-0.416228\pi\) | ||||
0.260151 | + | 0.965568i | \(0.416228\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19168.9 | 1.89942 | 0.949712 | − | 0.313124i | \(-0.101376\pi\) | ||||
0.949712 | + | 0.313124i | \(0.101376\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18963.9 | −1.86710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10870.9 | 1.05676 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −255.876 | −0.0247166 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13518.8 | −1.28954 | −0.644772 | − | 0.764375i | \(-0.723048\pi\) | ||||
−0.644772 | + | 0.764375i | \(0.723048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18535.4 | 1.75705 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3086.53 | 0.288973 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1435.08 | −0.133531 | −0.0667655 | − | 0.997769i | \(-0.521268\pi\) | ||||
−0.0667655 | + | 0.997769i | \(0.521268\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9967.64 | −0.916158 | −0.458079 | − | 0.888912i | \(-0.651462\pi\) | ||||
−0.458079 | + | 0.888912i | \(0.651462\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2179.64 | 0.199119 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26382.8 | −2.38115 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9711.73 | 0.871256 | 0.435628 | − | 0.900127i | \(-0.356526\pi\) | ||||
0.435628 | + | 0.900127i | \(0.356526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7305.12 | −0.647553 | −0.323777 | − | 0.946134i | \(-0.604953\pi\) | ||||
−0.323777 | + | 0.946134i | \(0.604953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4158.58 | −0.366445 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −145.255 | −0.0126489 | −0.00632447 | − | 0.999980i | \(-0.502013\pi\) | ||||
−0.00632447 | + | 0.999980i | \(0.502013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7506.78 | 0.649864 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4521.27 | 0.386856 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 878.243 | 0.0747100 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13168.5 | −1.10734 | −0.553668 | − | 0.832737i | \(-0.686772\pi\) | ||||
−0.553668 | + | 0.832737i | \(0.686772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −547.489 | −0.0457745 | −0.0228872 | − | 0.999738i | \(-0.507286\pi\) | ||||
−0.0228872 | + | 0.999738i | \(0.507286\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 836.094 | 0.0691097 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5806.10 | −0.477200 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6426.81 | 0.522282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4486.45 | −0.362554 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19948.5 | −1.59415 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9170.89 | 0.728812 | 0.364406 | − | 0.931240i | \(-0.381272\pi\) | ||||
0.364406 | + | 0.931240i | \(0.381272\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1294.66 | −0.101756 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15008.1 | 1.17313 | 0.586563 | − | 0.809903i | \(-0.300481\pi\) | ||||
0.586563 | + | 0.809903i | \(0.300481\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1134.53 | 0.0877176 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8963.96 | −0.689306 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2304.03 | −0.175269 | −0.0876346 | − | 0.996153i | \(-0.527931\pi\) | ||||
−0.0876346 | + | 0.996153i | \(0.527931\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28115.1 | −2.12726 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4631.88 | 0.346733 | 0.173366 | − | 0.984857i | \(-0.444536\pi\) | ||||
0.173366 | + | 0.984857i | \(0.444536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1645.14 | −0.122498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4713.01 | 0.347240 | 0.173620 | − | 0.984813i | \(-0.444454\pi\) | ||||
0.173620 | + | 0.984813i | \(0.444454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24290.9 | −1.78028 | −0.890141 | − | 0.455685i | \(-0.849394\pi\) | ||||
−0.890141 | + | 0.455685i | \(0.849394\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1993.88 | −0.144610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19147.1 | 1.38146 | 0.690730 | − | 0.723113i | \(-0.257289\pi\) | ||||
0.690730 | + | 0.723113i | \(0.257289\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31324.7 | −2.23677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13206.8 | −0.938197 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20112.1 | −1.41417 | −0.707083 | − | 0.707131i | \(-0.749989\pi\) | ||||
−0.707083 | + | 0.707131i | \(0.749989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 435.196 | 0.0304447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16455.1 | −1.13951 | −0.569756 | − | 0.821814i | \(-0.692962\pi\) | ||||
−0.569756 | + | 0.821814i | \(0.692962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3408.01 | 0.234815 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2444.35 | 0.166734 | 0.0833669 | − | 0.996519i | \(-0.473433\pi\) | ||||
0.0833669 | + | 0.996519i | \(0.473433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20881.1 | −1.41724 | −0.708619 | − | 0.705592i | \(-0.750681\pi\) | ||||
−0.708619 | + | 0.705592i | \(0.750681\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3955.66 | −0.265819 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14041.6 | 0.938928 | 0.469464 | − | 0.882952i | \(-0.344447\pi\) | ||||
0.469464 | + | 0.882952i | \(0.344447\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2271.36 | −0.150392 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7303.82 | −0.481237 | −0.240619 | − | 0.970620i | \(-0.577350\pi\) | ||||
−0.240619 | + | 0.970620i | \(0.577350\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22409.4 | −1.46218 | −0.731092 | − | 0.682279i | \(-0.760989\pi\) | ||||
−0.731092 | + | 0.682279i | \(0.760989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6459.28 | −0.419419 | −0.209710 | − | 0.977764i | \(-0.567252\pi\) | ||||
−0.209710 | + | 0.977764i | \(0.567252\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −43882.2 | −2.82200 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6065.20 | −0.384476 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28348.6 | −1.78850 | −0.894248 | − | 0.447571i | \(-0.852289\pi\) | ||||
−0.894248 | + | 0.447571i | \(0.852289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8011.80 | 0.500691 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51592.1 | 3.20903 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1235.34 | 0.0761202 | 0.0380601 | − | 0.999275i | \(-0.487882\pi\) | ||||
0.0380601 | + | 0.999275i | \(0.487882\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7476.80 | 0.458563 | 0.229282 | − | 0.973360i | \(-0.426362\pi\) | ||||
0.229282 | + | 0.973360i | \(0.426362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24330.3 | 1.47840 | 0.739199 | − | 0.673487i | \(-0.235204\pi\) | ||||
0.739199 | + | 0.673487i | \(0.235204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15495.3 | −0.937201 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10165.2 | −0.609180 | −0.304590 | − | 0.952484i | \(-0.598519\pi\) | ||||
−0.304590 | + | 0.952484i | \(0.598519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6867.96 | 0.409700 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17160.8 | −1.01440 | −0.507199 | − | 0.861829i | \(-0.669319\pi\) | ||||
−0.507199 | + | 0.861829i | \(0.669319\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4982.25 | −0.293173 | −0.146586 | − | 0.989198i | \(-0.546829\pi\) | ||||
−0.146586 | + | 0.989198i | \(0.546829\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1773.91 | 0.103442 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8840.64 | 0.513210 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20032.5 | 1.15253 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26651.2 | 1.52649 | 0.763245 | − | 0.646109i | \(-0.223605\pi\) | ||||
0.763245 | + | 0.646109i | \(0.223605\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24313.1 | 1.38025 | 0.690124 | − | 0.723691i | \(-0.257556\pi\) | ||||
0.690124 | + | 0.723691i | \(0.257556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21397.9 | −1.20939 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26112.7 | 1.46292 | 0.731461 | − | 0.681883i | \(-0.238839\pi\) | ||||
0.731461 | + | 0.681883i | \(0.238839\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3454.14 | 0.192665 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34156.2 | 1.88860 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4874.70 | −0.268368 | −0.134184 | − | 0.990956i | \(-0.542841\pi\) | ||||
−0.134184 | + | 0.990956i | \(0.542841\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5364.51 | −0.292788 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2103.00 | −0.114285 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4679.39 | 0.252123 | 0.126062 | − | 0.992022i | \(-0.459766\pi\) | ||||
0.126062 | + | 0.992022i | \(0.459766\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3157.01 | −0.169372 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28830.2 | 1.53362 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16966.1 | 0.898696 | 0.449348 | − | 0.893357i | \(-0.351656\pi\) | ||||
0.449348 | + | 0.893357i | \(0.351656\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3391.21 | 0.178123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6981.18 | −0.365149 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19586.9 | −1.01595 | −0.507974 | − | 0.861372i | \(-0.669605\pi\) | ||||
−0.507974 | + | 0.861372i | \(0.669605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31344.5 | −1.61905 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2771.18 | −0.141957 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32623.5 | 1.66429 | 0.832145 | − | 0.554558i | \(-0.187113\pi\) | ||||
0.832145 | + | 0.554558i | \(0.187113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9199.90 | 0.465486 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7468.57 | −0.376341 | −0.188170 | − | 0.982136i | \(-0.560256\pi\) | ||||
−0.188170 | + | 0.982136i | \(0.560256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12711.5 | −0.635327 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2585.13 | 0.128682 | 0.0643408 | − | 0.997928i | \(-0.479506\pi\) | ||||
0.0643408 | + | 0.997928i | \(0.479506\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9989.29 | 0.493232 | 0.246616 | − | 0.969113i | \(-0.420681\pi\) | ||||
0.246616 | + | 0.969113i | \(0.420681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14142.8 | −0.695505 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31103.2 | 1.51734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1340.53 | −0.0651354 | −0.0325677 | − | 0.999470i | \(-0.510368\pi\) | ||||
−0.0325677 | + | 0.999470i | \(0.510368\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5693.04 | 0.274425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20580.1 | 0.988105 | 0.494053 | − | 0.869432i | \(-0.335515\pi\) | ||||
0.494053 | + | 0.869432i | \(0.335515\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6562.00 | −0.312579 | −0.156289 | − | 0.987711i | \(-0.549953\pi\) | ||||
−0.156289 | + | 0.987711i | \(0.549953\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8975.48 | 0.425864 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40074.8 | 1.88659 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16766.2 | −0.786221 | −0.393110 | − | 0.919491i | \(-0.628601\pi\) | ||||
−0.393110 | + | 0.919491i | \(0.628601\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40296.9 | 1.87500 | 0.937502 | − | 0.347980i | \(-0.113132\pi\) | ||||
0.937502 | + | 0.347980i | \(0.113132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1063.01 | −0.0492701 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1094.64 | −0.0503459 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17684.5 | −0.810244 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12448.4 | 0.565992 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42549.6 | 1.92723 | 0.963615 | − | 0.267292i | \(-0.0861289\pi\) | ||||
0.963615 | + | 0.267292i | \(0.0861289\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11405.2 | 0.512673 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51809.1 | −2.32005 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5850.28 | −0.260010 | −0.130005 | − | 0.991513i | \(-0.541499\pi\) | ||||
−0.130005 | + | 0.991513i | \(0.541499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 743.243 | 0.0329087 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5031.83 | 0.221132 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13823.0 | 0.605212 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30659.8 | 1.33244 | 0.666218 | − | 0.745757i | \(-0.267912\pi\) | ||||
0.666218 | + | 0.745757i | \(0.267912\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27546.6 | 1.19272 | 0.596358 | − | 0.802718i | \(-0.296614\pi\) | ||||
0.596358 | + | 0.802718i | \(0.296614\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5873.03 | −0.252421 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4788.65 | 0.205060 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42270.3 | 1.79688 | 0.898442 | − | 0.439092i | \(-0.144700\pi\) | ||||
0.898442 | + | 0.439092i | \(0.144700\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8766.81 | 0.371314 | 0.185657 | − | 0.982615i | \(-0.440559\pi\) | ||||
0.185657 | + | 0.982615i | \(0.440559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13187.2 | −0.554489 | −0.277244 | − | 0.960799i | \(-0.589421\pi\) | ||||
−0.277244 | + | 0.960799i | \(0.589421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7127.69 | −0.298619 | −0.149309 | − | 0.988791i | \(-0.547705\pi\) | ||||
−0.149309 | + | 0.988791i | \(0.547705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16882.1 | −0.702198 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11246.4 | 0.466105 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38084.2 | −1.56712 | −0.783558 | − | 0.621318i | \(-0.786597\pi\) | ||||
−0.783558 | + | 0.621318i | \(0.786597\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12101.9 | −0.496204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7070.14 | 0.287835 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27423.4 | 1.11249 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24600.6 | −0.990948 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42235.2 | −1.69532 | −0.847659 | − | 0.530542i | \(-0.821988\pi\) | ||||
−0.847659 | + | 0.530542i | \(0.821988\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15377.2 | −0.612923 | −0.306461 | − | 0.951883i | \(-0.599145\pi\) | ||||
−0.306461 | + | 0.951883i | \(0.599145\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19130.3 | 0.759858 | 0.379929 | − | 0.925016i | \(-0.375949\pi\) | ||||
0.379929 | + | 0.925016i | \(0.375949\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6298.68 | −0.248447 | −0.124223 | − | 0.992254i | \(-0.539644\pi\) | ||||
−0.124223 | + | 0.992254i | \(0.539644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18460.9 | 0.725654 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6008.58 | −0.234554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32875.3 | 1.27892 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4332.93 | −0.167405 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18035.4 | 0.694426 | 0.347213 | − | 0.937786i | \(-0.387128\pi\) | ||||
0.347213 | + | 0.937786i | \(0.387128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18819.3 | −0.719680 | −0.359840 | − | 0.933014i | \(-0.617169\pi\) | ||||
−0.359840 | + | 0.933014i | \(0.617169\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9977.04 | −0.380243 | −0.190121 | − | 0.981761i | \(-0.560888\pi\) | ||||
−0.190121 | + | 0.981761i | \(0.560888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42364.0 | 1.60366 | 0.801829 | − | 0.597554i | \(-0.203861\pi\) | ||||
0.801829 | + | 0.597554i | \(0.203861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −55543.3 | −2.09546 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 386.866 | 0.0144972 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21200.1 | 0.791778 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4713.24 | 0.174856 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11176.7 | −0.413262 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3741.33 | −0.137421 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30111.4 | −1.10235 | −0.551176 | − | 0.834389i | \(-0.685821\pi\) | ||||
−0.551176 | + | 0.834389i | \(0.685821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49694.3 | 1.80729 | 0.903647 | − | 0.428279i | \(-0.140880\pi\) | ||||
0.903647 | + | 0.428279i | \(0.140880\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20997.1 | −0.761118 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47613.4 | −1.71465 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25625.8 | 0.919822 | 0.459911 | − | 0.887965i | \(-0.347881\pi\) | ||||
0.459911 | + | 0.887965i | \(0.347881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45736.7 | 1.63103 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7711.27 | 0.274103 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26165.4 | 0.924067 | 0.462033 | − | 0.886862i | \(-0.347120\pi\) | ||||
0.462033 | + | 0.886862i | \(0.347120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8787.34 | −0.309338 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2284.40 | 0.0799016 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45347.5 | −1.58104 | −0.790522 | − | 0.612434i | \(-0.790191\pi\) | ||||
−0.790522 | + | 0.612434i | \(0.790191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28081.8 | −0.972837 | −0.486418 | − | 0.873726i | \(-0.661697\pi\) | ||||
−0.486418 | + | 0.873726i | \(0.661697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8529.82 | −0.294559 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12696.9 | −0.435684 | −0.217842 | − | 0.975984i | \(-0.569902\pi\) | ||||
−0.217842 | + | 0.975984i | \(0.569902\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13013.6 | −0.445142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1592.18 | 0.0541194 | 0.0270597 | − | 0.999634i | \(-0.491386\pi\) | ||||
0.0270597 | + | 0.999634i | \(0.491386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5670.18 | 0.192129 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23946.4 | −0.806331 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27983.0 | −0.939312 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5671.61 | 0.189198 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47529.1 | 1.58059 | 0.790296 | − | 0.612725i | \(-0.209927\pi\) | ||||
0.790296 | + | 0.612725i | \(0.209927\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23045.3 | −0.761647 | −0.380824 | − | 0.924648i | \(-0.624359\pi\) | ||||
−0.380824 | + | 0.924648i | \(0.624359\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37190.5 | 1.22536 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45865.1 | 1.50190 | 0.750950 | − | 0.660359i | \(-0.229596\pi\) | ||||
0.750950 | + | 0.660359i | \(0.229596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29414.4 | −0.960255 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32496.5 | −1.05440 | −0.527202 | − | 0.849740i | \(-0.676759\pi\) | ||||
−0.527202 | + | 0.849740i | \(0.676759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21963.2 | 0.710462 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37315.0 | 1.19974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26439.3 | 0.847500 | 0.423750 | − | 0.905779i | \(-0.360714\pi\) | ||||
0.423750 | + | 0.905779i | \(0.360714\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9613.77 | −0.306308 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1920.47 | −0.0610049 | −0.0305025 | − | 0.999535i | \(-0.509711\pi\) | ||||
−0.0305025 | + | 0.999535i | \(0.509711\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1080.4.a.k.1.1 | yes | 3 | |
3.2 | odd | 2 | 1080.4.a.e.1.1 | ✓ | 3 | ||
4.3 | odd | 2 | 2160.4.a.br.1.3 | 3 | |||
12.11 | even | 2 | 2160.4.a.bj.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.e.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
1080.4.a.k.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
2160.4.a.bj.1.3 | 3 | 12.11 | even | 2 | |||
2160.4.a.br.1.3 | 3 | 4.3 | odd | 2 |