Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(1025,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2441150464.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 77x^{4} - 188x^{2} + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.4 | ||
Root | \(-2.27249 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1025 |
Dual form | 1728.3.e.v.1025.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 1.88259i | − 0.376519i | −0.982119 | − | 0.188259i | \(-0.939715\pi\) | ||||
0.982119 | − | 0.188259i | \(-0.0602845\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.9726 | 1.56751 | 0.783754 | − | 0.621071i | \(-0.213302\pi\) | ||||
0.783754 | + | 0.621071i | \(0.213302\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.171573i | − 0.0155975i | −0.999970 | − | 0.00779877i | \(-0.997518\pi\) | ||||
0.999970 | − | 0.00779877i | \(-0.00248245\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.48528 | −0.498868 | −0.249434 | − | 0.968392i | \(-0.580245\pi\) | ||||
−0.249434 | + | 0.968392i | \(0.580245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 27.2699i | − 1.60411i | −0.597249 | − | 0.802056i | \(-0.703740\pi\) | ||||
0.597249 | − | 0.802056i | \(-0.296260\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.32478 | −0.280251 | −0.140126 | − | 0.990134i | \(-0.544751\pi\) | ||||
−0.140126 | + | 0.990134i | \(0.544751\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.51472i | − 0.152814i | −0.997077 | − | 0.0764069i | \(-0.975655\pi\) | ||||
0.997077 | − | 0.0764069i | \(-0.0243448\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.4558 | 0.858234 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 34.8003i | − 1.20001i | −0.799997 | − | 0.600004i | \(-0.795165\pi\) | ||||
0.799997 | − | 0.600004i | \(-0.204835\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.9469 | −0.869254 | −0.434627 | − | 0.900610i | \(-0.643120\pi\) | ||||
−0.434627 | + | 0.900610i | \(0.643120\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 20.6569i | − 0.590196i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −46.4264 | −1.25477 | −0.627384 | − | 0.778710i | \(-0.715874\pi\) | ||||
−0.627384 | + | 0.778710i | \(0.715874\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 23.5047i | 0.573285i | 0.958038 | + | 0.286643i | \(0.0925393\pi\) | ||||
−0.958038 | + | 0.286643i | \(0.907461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 55.1858 | 1.28339 | 0.641695 | − | 0.766960i | \(-0.278231\pi\) | ||||
0.641695 | + | 0.766960i | \(0.278231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 57.5980i | − 1.22549i | −0.790281 | − | 0.612744i | \(-0.790065\pi\) | ||||
0.790281 | − | 0.612744i | \(-0.209935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 71.3970 | 1.45708 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 51.7436i | 0.976294i | 0.872761 | + | 0.488147i | \(0.162327\pi\) | ||||
−0.872761 | + | 0.488147i | \(0.837673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.323002 | −0.00587276 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 82.2843i | − 1.39465i | −0.716756 | − | 0.697324i | \(-0.754374\pi\) | ||||
0.716756 | − | 0.697324i | \(-0.245626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −79.8823 | −1.30955 | −0.654773 | − | 0.755826i | \(-0.727236\pi\) | ||||
−0.654773 | + | 0.755826i | \(0.727236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.2091i | 0.187833i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44.5362 | −0.664720 | −0.332360 | − | 0.943153i | \(-0.607845\pi\) | ||||
−0.332360 | + | 0.943153i | \(0.607845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 41.2304i | − 0.580711i | −0.956919 | − | 0.290355i | \(-0.906227\pi\) | ||||
0.956919 | − | 0.290355i | \(-0.0937735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66.3381 | 0.908741 | 0.454371 | − | 0.890813i | \(-0.349864\pi\) | ||||
0.454371 | + | 0.890813i | \(0.349864\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.88259i | − 0.0244493i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 115.050 | 1.45633 | 0.728167 | − | 0.685400i | \(-0.240373\pi\) | ||||
0.728167 | + | 0.685400i | \(0.240373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 36.3381i | 0.437808i | 0.975746 | + | 0.218904i | \(0.0702482\pi\) | ||||
−0.975746 | + | 0.218904i | \(0.929752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −51.3381 | −0.603978 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 158.027i | 1.77558i | 0.460245 | + | 0.887792i | \(0.347762\pi\) | ||||
−0.460245 | + | 0.887792i | \(0.652238\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −71.1601 | −0.781979 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.0244i | 0.105520i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 62.8823 | 0.648271 | 0.324135 | − | 0.946011i | \(-0.394927\pi\) | ||||
0.324135 | + | 0.946011i | \(0.394927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 130.702i | 1.29408i | 0.762458 | + | 0.647038i | \(0.223992\pi\) | ||||
−0.762458 | + | 0.647038i | \(0.776008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −72.4521 | −0.703419 | −0.351709 | − | 0.936109i | \(-0.614399\pi\) | ||||
−0.351709 | + | 0.936109i | \(0.614399\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 168.255i | − 1.57248i | −0.617924 | − | 0.786238i | \(-0.712026\pi\) | ||||
0.617924 | − | 0.786238i | \(-0.287974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −103.397 | −0.948596 | −0.474298 | − | 0.880364i | \(-0.657298\pi\) | ||||
−0.474298 | + | 0.880364i | \(0.657298\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 140.115i | − 1.23995i | −0.784621 | − | 0.619976i | \(-0.787142\pi\) | ||||
0.784621 | − | 0.619976i | \(-0.212858\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.61678 | −0.0575373 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 299.220i | − 2.51446i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.971 | 0.999757 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 87.4574i | − 0.699660i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −120.052 | −0.945292 | −0.472646 | − | 0.881252i | \(-0.656701\pi\) | ||||
−0.472646 | + | 0.881252i | \(0.656701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 198.421i | − 1.51467i | −0.653028 | − | 0.757333i | \(-0.726502\pi\) | ||||
0.653028 | − | 0.757333i | \(-0.273498\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −58.4264 | −0.439296 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 120.375i | − 0.878650i | −0.898328 | − | 0.439325i | \(-0.855218\pi\) | ||||
0.898328 | − | 0.439325i | \(-0.144782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9416 | 0.0859105 | 0.0429553 | − | 0.999077i | \(-0.486323\pi\) | ||||
0.0429553 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.11270i | 0.00778111i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −65.5147 | −0.451826 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 55.5088i | − 0.372542i | −0.982498 | − | 0.186271i | \(-0.940360\pi\) | ||||
0.982498 | − | 0.186271i | \(-0.0596403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −203.154 | −1.34539 | −0.672695 | − | 0.739920i | \(-0.734863\pi\) | ||||
−0.672695 | + | 0.739920i | \(0.734863\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 50.7300i | 0.327290i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 164.971 | 1.05077 | 0.525384 | − | 0.850865i | \(-0.323922\pi\) | ||||
0.525384 | + | 0.850865i | \(0.323922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 38.5654i | − 0.239537i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 178.948 | 1.09784 | 0.548919 | − | 0.835875i | \(-0.315039\pi\) | ||||
0.548919 | + | 0.835875i | \(0.315039\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 43.8924i | − 0.262828i | −0.991328 | − | 0.131414i | \(-0.958048\pi\) | ||||
0.991328 | − | 0.131414i | \(-0.0419518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −126.941 | −0.751131 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 191.858i | − 1.10901i | −0.832181 | − | 0.554504i | \(-0.812908\pi\) | ||||
0.832181 | − | 0.554504i | \(-0.187092\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 235.425 | 1.34529 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 144.765i | − 0.808740i | −0.914595 | − | 0.404370i | \(-0.867491\pi\) | ||||
0.914595 | − | 0.404370i | \(-0.132509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.735065 | 0.00406113 | 0.00203057 | − | 0.999998i | \(-0.499354\pi\) | ||||
0.00203057 | + | 0.999998i | \(0.499354\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 87.4020i | 0.472443i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.67877 | −0.0250202 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 290.132i | − 1.51902i | −0.650498 | − | 0.759508i | \(-0.725440\pi\) | ||||
0.650498 | − | 0.759508i | \(-0.274560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 63.6030 | 0.329549 | 0.164775 | − | 0.986331i | \(-0.447310\pi\) | ||||
0.164775 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 88.3710i | − 0.448584i | −0.974522 | − | 0.224292i | \(-0.927993\pi\) | ||||
0.974522 | − | 0.224292i | \(-0.0720069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 318.204 | 1.59902 | 0.799508 | − | 0.600656i | \(-0.205094\pi\) | ||||
0.799508 | + | 0.600656i | \(0.205094\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 381.848i | − 1.88102i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 44.2498 | 0.215853 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.913587i | 0.00437123i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −46.6310 | −0.221000 | −0.110500 | − | 0.993876i | \(-0.535245\pi\) | ||||
−0.110500 | + | 0.993876i | \(0.535245\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 103.892i | − 0.483220i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −295.676 | −1.36256 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 176.853i | 0.800239i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −47.2770 | −0.212004 | −0.106002 | − | 0.994366i | \(-0.533805\pi\) | ||||
−0.106002 | + | 0.994366i | \(0.533805\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 342.500i | 1.50881i | 0.656410 | + | 0.754404i | \(0.272074\pi\) | ||||
−0.656410 | + | 0.754404i | \(0.727926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 381.647 | 1.66658 | 0.833290 | − | 0.552836i | \(-0.186455\pi\) | ||||
0.833290 | + | 0.552836i | \(0.186455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 383.716i | − 1.64685i | −0.567424 | − | 0.823426i | \(-0.692060\pi\) | ||||
0.567424 | − | 0.823426i | \(-0.307940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −108.434 | −0.461419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 315.161i | 1.31867i | 0.751850 | + | 0.659334i | \(0.229162\pi\) | ||||
−0.751850 | + | 0.659334i | \(0.770838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −256.558 | −1.06456 | −0.532279 | − | 0.846569i | \(-0.678664\pi\) | ||||
−0.532279 | + | 0.846569i | \(0.678664\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 134.411i | − 0.548618i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.5327 | 0.139808 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 246.000i | − 0.980080i | −0.871700 | − | 0.490040i | \(-0.836982\pi\) | ||||
0.871700 | − | 0.490040i | \(-0.163018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.603030 | −0.00238352 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 443.046i | 1.72391i | 0.506982 | + | 0.861957i | \(0.330761\pi\) | ||||
−0.506982 | + | 0.861957i | \(0.669239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −509.416 | −1.96686 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 479.897i | − 1.82470i | −0.409409 | − | 0.912351i | \(-0.634265\pi\) | ||||
0.409409 | − | 0.912351i | \(-0.365735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 97.4121 | 0.367593 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 418.406i | 1.55541i | 0.628628 | + | 0.777706i | \(0.283617\pi\) | ||||
−0.628628 | + | 0.777706i | \(0.716383\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −278.347 | −1.02711 | −0.513555 | − | 0.858057i | \(-0.671672\pi\) | ||||
−0.513555 | + | 0.858057i | \(0.671672\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3.68124i | − 0.0133863i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 192.617 | 0.695369 | 0.347685 | − | 0.937612i | \(-0.386968\pi\) | ||||
0.347685 | + | 0.937612i | \(0.386968\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 435.515i | 1.54988i | 0.632037 | + | 0.774939i | \(0.282219\pi\) | ||||
−0.632037 | + | 0.774939i | \(0.717781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 518.774 | 1.83312 | 0.916562 | − | 0.399894i | \(-0.130953\pi\) | ||||
0.916562 | + | 0.399894i | \(0.130953\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 257.907i | 0.898629i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −454.647 | −1.57317 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 117.634i | − 0.401482i | −0.979644 | − | 0.200741i | \(-0.935665\pi\) | ||||
0.979644 | − | 0.200741i | \(-0.0643350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −154.908 | −0.525111 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.7939i | 0.0762339i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 605.529 | 2.01172 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 150.386i | 0.493068i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 371.618 | 1.21048 | 0.605241 | − | 0.796042i | \(-0.293077\pi\) | ||||
0.605241 | + | 0.796042i | \(0.293077\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 27.8680i | − 0.0896076i | −0.998996 | − | 0.0448038i | \(-0.985734\pi\) | ||||
0.998996 | − | 0.0448038i | \(-0.0142663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −279.368 | −0.892548 | −0.446274 | − | 0.894896i | \(-0.647249\pi\) | ||||
−0.446274 | + | 0.894896i | \(0.647249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 546.367i | 1.72355i | 0.507287 | + | 0.861777i | \(0.330648\pi\) | ||||
−0.507287 | + | 0.861777i | \(0.669352\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.97078 | −0.0187172 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 145.206i | 0.449554i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −139.147 | −0.428145 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 631.997i | − 1.92096i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 305.294 | 0.922337 | 0.461168 | − | 0.887313i | \(-0.347430\pi\) | ||||
0.461168 | + | 0.887313i | \(0.347430\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 83.8436i | 0.250279i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 159.206 | 0.472422 | 0.236211 | − | 0.971702i | \(-0.424094\pi\) | ||||
0.236211 | + | 0.971702i | \(0.424094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.62335i | 0.0135582i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 245.752 | 0.716478 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 296.387i | − 0.854141i | −0.904218 | − | 0.427070i | \(-0.859546\pi\) | ||||
0.904218 | − | 0.427070i | \(-0.140454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −108.839 | −0.311858 | −0.155929 | − | 0.987768i | \(-0.549837\pi\) | ||||
−0.155929 | + | 0.987768i | \(0.549837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.3200i | 0.0349008i | 0.999848 | + | 0.0174504i | \(0.00555492\pi\) | ||||
−0.999848 | + | 0.0174504i | \(0.994445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −77.6201 | −0.218648 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 92.2254i | − 0.256895i | −0.991716 | − | 0.128448i | \(-0.959001\pi\) | ||||
0.991716 | − | 0.128448i | \(-0.0409994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −332.647 | −0.921459 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 124.888i | − 0.342158i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0673 | 0.0356058 | 0.0178029 | − | 0.999842i | \(-0.494333\pi\) | ||||
0.0178029 | + | 0.999842i | \(0.494333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 567.759i | 1.53035i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 233.632 | 0.626361 | 0.313180 | − | 0.949694i | \(-0.398606\pi\) | ||||
0.313180 | + | 0.949694i | \(0.398606\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 225.689i | 0.598646i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −683.528 | −1.80351 | −0.901753 | − | 0.432253i | \(-0.857719\pi\) | ||||
−0.901753 | + | 0.432253i | \(0.857719\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 279.858i | 0.730699i | 0.930870 | + | 0.365350i | \(0.119051\pi\) | ||||
−0.930870 | + | 0.365350i | \(0.880949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.54416 | −0.00920560 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 260.434i | − 0.669497i | −0.942308 | − | 0.334748i | \(-0.891349\pi\) | ||||
0.942308 | − | 0.334748i | \(-0.108651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −95.8460 | −0.245130 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 216.593i | − 0.548337i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −167.809 | −0.422693 | −0.211346 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211346 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 60.2430i | 0.150232i | 0.997175 | + | 0.0751159i | \(0.0239327\pi\) | ||||
−0.997175 | + | 0.0751159i | \(0.976067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 174.758 | 0.433643 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.96551i | 0.0195713i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 532.765 | 1.30260 | 0.651301 | − | 0.758819i | \(-0.274223\pi\) | ||||
0.651301 | + | 0.758819i | \(0.274223\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 902.869i | − 2.18612i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 68.4098 | 0.164843 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 483.255i | 1.15335i | 0.816973 | + | 0.576676i | \(0.195651\pi\) | ||||
−0.816973 | + | 0.576676i | \(0.804349\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.2061 | 0.0693731 | 0.0346865 | − | 0.999398i | \(-0.488957\pi\) | ||||
0.0346865 | + | 0.999398i | \(0.488957\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 585.098i | − 1.37670i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −876.512 | −2.05272 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 634.971i | 1.47325i | 0.676302 | + | 0.736625i | \(0.263582\pi\) | ||||
−0.676302 | + | 0.736625i | \(0.736418\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.5004 | −0.0658209 | −0.0329104 | − | 0.999458i | \(-0.510478\pi\) | ||||
−0.0329104 | + | 0.999458i | \(0.510478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.7151i | 0.0428263i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 287.547 | 0.655006 | 0.327503 | − | 0.944850i | \(-0.393793\pi\) | ||||
0.327503 | + | 0.944850i | \(0.393793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 0.176624i | 0 0.000398699i | −1.00000 | 0.000199349i | \(-0.999937\pi\) | |||||
1.00000 | 0.000199349i | \(-6.34549e-5\pi\) | ||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 297.500 | 0.668540 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.5166i | 0.0813287i | 0.999173 | + | 0.0406644i | \(0.0129474\pi\) | ||||
−0.999173 | + | 0.0406644i | \(0.987053\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.03277 | 0.00894184 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 133.966i | 0.294430i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −243.235 | −0.532244 | −0.266122 | − | 0.963939i | \(-0.585742\pi\) | ||||
−0.266122 | + | 0.963939i | \(0.585742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 155.231i | 0.336726i | 0.985725 | + | 0.168363i | \(0.0538481\pi\) | ||||
−0.985725 | + | 0.168363i | \(0.946152\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −444.550 | −0.960151 | −0.480076 | − | 0.877227i | \(-0.659391\pi\) | ||||
−0.480076 | + | 0.877227i | \(0.659391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 853.357i | 1.82732i | 0.406482 | + | 0.913659i | \(0.366755\pi\) | ||||
−0.406482 | + | 0.913659i | \(0.633245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −488.676 | −1.04195 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.46838i | − 0.0200177i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −114.248 | −0.240521 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 445.882i | 0.930861i | 0.885085 | + | 0.465430i | \(0.154100\pi\) | ||||
−0.885085 | + | 0.465430i | \(0.845900\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 301.088 | 0.625963 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 118.382i | − 0.244086i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −438.413 | −0.900232 | −0.450116 | − | 0.892970i | \(-0.648617\pi\) | ||||
−0.450116 | + | 0.892970i | \(0.648617\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 186.754i | 0.380355i | 0.981750 | + | 0.190178i | \(0.0609064\pi\) | ||||
−0.981750 | + | 0.190178i | \(0.939094\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −948.999 | −1.92495 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 452.403i | − 0.910268i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 432.775 | 0.867284 | 0.433642 | − | 0.901085i | \(-0.357228\pi\) | ||||
0.433642 | + | 0.901085i | \(0.357228\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 45.6913i | − 0.0908377i | −0.998968 | − | 0.0454188i | \(-0.985538\pi\) | ||||
0.998968 | − | 0.0454188i | \(-0.0144622\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 246.058 | 0.487244 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 267.051i | 0.524658i | 0.964978 | + | 0.262329i | \(0.0844906\pi\) | ||||
−0.964978 | + | 0.262329i | \(0.915509\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 727.898 | 1.42446 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 136.398i | 0.264850i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.88225 | −0.0191146 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 144.101i | 0.276586i | 0.990391 | + | 0.138293i | \(0.0441616\pi\) | ||||
−0.990391 | + | 0.138293i | \(0.955838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 631.083 | 1.20666 | 0.603330 | − | 0.797491i | \(-0.293840\pi\) | ||||
0.603330 | + | 0.797491i | \(0.293840\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 734.839i | 1.39438i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 516.647 | 0.976648 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 152.435i | − 0.285994i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −316.755 | −0.592066 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 12.2498i | − 0.0227269i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −235.765 | −0.435794 | −0.217897 | − | 0.975972i | \(-0.569920\pi\) | ||||
−0.217897 | + | 0.975972i | \(0.569920\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 194.654i | 0.357164i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 813.418 | 1.48705 | 0.743526 | − | 0.668707i | \(-0.233152\pi\) | ||||
0.743526 | + | 0.668707i | \(0.233152\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 185.304i | 0.336304i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1262.40 | 2.28281 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 175.773i | 0.315571i | 0.987473 | + | 0.157786i | \(0.0504355\pi\) | ||||
−0.987473 | + | 0.157786i | \(0.949565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −357.895 | −0.640242 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 572.927i | 1.01763i | 0.860875 | + | 0.508816i | \(0.169917\pi\) | ||||
−0.860875 | + | 0.508816i | \(0.830083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −263.779 | −0.466865 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 814.664i | 1.43175i | 0.698230 | + | 0.715873i | \(0.253971\pi\) | ||||
−0.698230 | + | 0.715873i | \(0.746029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 128.284 | 0.224665 | 0.112333 | − | 0.993671i | \(-0.464168\pi\) | ||||
0.112333 | + | 0.993671i | \(0.464168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 75.4113i | − 0.131150i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.4996 | 0.0528589 | 0.0264294 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264294 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 398.722i | 0.686268i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.87780 | 0.0152278 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 193.794i | − 0.330143i | −0.986282 | − | 0.165071i | \(-0.947215\pi\) | ||||
0.986282 | − | 0.165071i | \(-0.0527855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 143.486 | 0.243610 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 684.488i | − 1.15428i | −0.816645 | − | 0.577140i | \(-0.804169\pi\) | ||||
0.816645 | − | 0.577140i | \(-0.195831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −563.310 | −0.946740 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 814.244i | − 1.35934i | −0.733519 | − | 0.679669i | \(-0.762123\pi\) | ||||
0.733519 | − | 0.679669i | \(-0.237877\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −531.368 | −0.884139 | −0.442069 | − | 0.896981i | \(-0.645756\pi\) | ||||
−0.442069 | + | 0.896981i | \(0.645756\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 227.738i | − 0.376427i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 464.880 | 0.765865 | 0.382933 | − | 0.923776i | \(-0.374914\pi\) | ||||
0.382933 | + | 0.923776i | \(0.374914\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 373.539i | 0.611357i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1120.59 | −1.82804 | −0.914019 | − | 0.405672i | \(-0.867038\pi\) | ||||
−0.914019 | + | 0.405672i | \(0.867038\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 561.372i | 0.909841i | 0.890532 | + | 0.454921i | \(0.150332\pi\) | ||||
−0.890532 | + | 0.454921i | \(0.849668\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 471.340 | 0.761454 | 0.380727 | − | 0.924687i | \(-0.375674\pi\) | ||||
0.380727 | + | 0.924687i | \(0.375674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1733.96i | 2.78324i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 371.749 | 0.594799 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1266.04i | 2.01279i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 431.160 | 0.683296 | 0.341648 | − | 0.939828i | \(-0.389015\pi\) | ||||
0.341648 | + | 0.939828i | \(0.389015\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 226.009i | 0.355920i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −463.029 | −0.726891 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 399.580i | 0.623370i | 0.950186 | + | 0.311685i | \(0.100893\pi\) | ||||
−0.950186 | + | 0.311685i | \(0.899107\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1013.66 | −1.57646 | −0.788231 | − | 0.615380i | \(-0.789003\pi\) | ||||
−0.788231 | + | 0.615380i | \(0.789003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.4710i | 0.0440046i | 0.999758 | + | 0.0220023i | \(0.00700412\pi\) | ||||
−0.999758 | + | 0.0220023i | \(0.992996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.1177 | −0.0217531 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 274.692i | − 0.420662i | −0.977630 | − | 0.210331i | \(-0.932546\pi\) | ||||
0.977630 | − | 0.210331i | \(-0.0674542\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −373.547 | −0.570300 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 87.7065i | 0.133090i | 0.997783 | + | 0.0665451i | \(0.0211976\pi\) | ||||
−0.997783 | + | 0.0665451i | \(0.978802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 212.368 | 0.321282 | 0.160641 | − | 0.987013i | \(-0.448644\pi\) | ||||
0.160641 | + | 0.987013i | \(0.448644\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 109.993i | 0.165403i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −122.313 | −0.183378 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.7056i | 0.0204257i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1099.17 | 1.63325 | 0.816623 | − | 0.577171i | \(-0.195843\pi\) | ||||
0.816623 | + | 0.577171i | \(0.195843\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 715.745i | 1.05723i | 0.848862 | + | 0.528615i | \(0.177288\pi\) | ||||
−0.848862 | + | 0.528615i | \(0.822712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 689.979 | 1.01617 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 588.823i | 0.862112i | 0.902325 | + | 0.431056i | \(0.141859\pi\) | ||||
−0.902325 | + | 0.431056i | \(0.858141\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −226.617 | −0.330828 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 335.572i | − 0.487042i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −466.975 | −0.675796 | −0.337898 | − | 0.941183i | \(-0.609716\pi\) | ||||
−0.337898 | + | 0.941183i | \(0.609716\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 22.4811i | − 0.0323469i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 640.971 | 0.919613 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 374.525i | 0.534273i | 0.963659 | + | 0.267136i | \(0.0860774\pi\) | ||||
−0.963659 | + | 0.267136i | \(0.913923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 247.210 | 0.351650 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1434.13i | 2.02847i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 259.647 | 0.366215 | 0.183108 | − | 0.983093i | \(-0.441384\pi\) | ||||
0.183108 | + | 0.983093i | \(0.441384\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 94.7107i | 0.132834i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.09476 | 0.00292973 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1124.90i | 1.56454i | 0.622942 | + | 0.782268i | \(0.285937\pi\) | ||||
−0.622942 | + | 0.782268i | \(0.714063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −794.985 | −1.10261 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 746.669i | − 1.02989i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 185.241 | 0.254803 | 0.127401 | − | 0.991851i | \(-0.459336\pi\) | ||||
0.127401 | + | 0.991851i | \(0.459336\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1504.91i | − 2.05870i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −62.0732 | −0.0846837 | −0.0423419 | − | 0.999103i | \(-0.513482\pi\) | ||||
−0.0423419 | + | 0.999103i | \(0.513482\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.64121i | 0.0103680i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 156.357 | 0.211579 | 0.105789 | − | 0.994389i | \(-0.466263\pi\) | ||||
0.105789 | + | 0.994389i | \(0.466263\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 371.220i | − 0.499624i | −0.968294 | − | 0.249812i | \(-0.919631\pi\) | ||||
0.968294 | − | 0.249812i | \(-0.0803688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −104.500 | −0.140269 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1846.19i | − 2.46487i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −380.653 | −0.506861 | −0.253431 | − | 0.967354i | \(-0.581559\pi\) | ||||
−0.253431 | + | 0.967354i | \(0.581559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 382.456i | 0.506564i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −351.088 | −0.463789 | −0.231895 | − | 0.972741i | \(-0.574492\pi\) | ||||
−0.231895 | + | 0.972741i | \(0.574492\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 300.772i | 0.395232i | 0.980280 | + | 0.197616i | \(0.0633199\pi\) | ||||
−0.980280 | + | 0.197616i | \(0.936680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1134.53 | −1.48693 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 533.637i | 0.695745i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −378.955 | −0.492790 | −0.246395 | − | 0.969170i | \(-0.579246\pi\) | ||||
−0.246395 | + | 0.969170i | \(0.579246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 249.305i | − 0.322516i | −0.986912 | − | 0.161258i | \(-0.948445\pi\) | ||||
0.986912 | − | 0.161258i | \(-0.0515552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −578.168 | −0.746023 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 125.157i | − 0.160664i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.07403 | −0.00905765 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 310.572i | − 0.395634i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1126.62 | 1.43154 | 0.715769 | − | 0.698337i | \(-0.246076\pi\) | ||||
0.715769 | + | 0.698337i | \(0.246076\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1537.42i | − 1.94364i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 518.059 | 0.653290 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 451.324i | − 0.566278i | −0.959079 | − | 0.283139i | \(-0.908624\pi\) | ||||
0.959079 | − | 0.283139i | \(-0.0913758\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1570.69 | −1.96582 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11.3818i | − 0.0141741i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −72.6030 | −0.0901901 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 684.710i | 0.846365i | 0.906044 | + | 0.423183i | \(0.139087\pi\) | ||||
−0.906044 | + | 0.423183i | \(0.860913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1324.62 | 1.63331 | 0.816656 | − | 0.577125i | \(-0.195826\pi\) | ||||
0.816656 | + | 0.577125i | \(0.195826\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 336.886i | − 0.413357i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −293.852 | −0.359672 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 837.836i | 1.02051i | 0.860024 | + | 0.510253i | \(0.170448\pi\) | ||||
−0.860024 | + | 0.510253i | \(0.829552\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 217.033 | 0.263710 | 0.131855 | − | 0.991269i | \(-0.457907\pi\) | ||||
0.131855 | + | 0.991269i | \(0.457907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 458.215i | − 0.554069i | −0.960860 | − | 0.277035i | \(-0.910648\pi\) | ||||
0.960860 | − | 0.277035i | \(-0.0893517\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 335.706 | 0.404953 | 0.202476 | − | 0.979287i | \(-0.435101\pi\) | ||||
0.202476 | + | 0.979287i | \(0.435101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1946.99i | − 2.33732i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −82.6314 | −0.0989598 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1202.59i | 1.43336i | 0.697401 | + | 0.716681i | \(0.254340\pi\) | ||||
−0.697401 | + | 0.716681i | \(0.745660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −370.058 | −0.440021 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 238.978i | 0.282815i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1327.36 | 1.56713 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 163.176i | 0.191746i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 730.471 | 0.856355 | 0.428178 | − | 0.903695i | \(-0.359156\pi\) | ||||
0.428178 | + | 0.903695i | \(0.359156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1244.03i | − 1.45161i | −0.687899 | − | 0.725807i | \(-0.741467\pi\) | ||||
0.687899 | − | 0.725807i | \(-0.258533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1584.24 | 1.84428 | 0.922141 | − | 0.386855i | \(-0.126439\pi\) | ||||
0.922141 | + | 0.386855i | \(0.126439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 746.392i | − 0.864881i | −0.901663 | − | 0.432440i | \(-0.857653\pi\) | ||||
0.901663 | − | 0.432440i | \(-0.142347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −361.191 | −0.417562 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 19.7395i | − 0.0227152i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 288.830 | 0.331607 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 959.632i | − 1.09672i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1351.97 | 1.54158 | 0.770792 | − | 0.637087i | \(-0.219861\pi\) | ||||
0.770792 | + | 0.637087i | \(0.219861\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 649.799i | 0.737569i | 0.929515 | + | 0.368785i | \(0.120226\pi\) | ||||
−0.929515 | + | 0.368785i | \(0.879774\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −829.881 | −0.939843 | −0.469922 | − | 0.882708i | \(-0.655718\pi\) | ||||
−0.469922 | + | 0.882708i | \(0.655718\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 296.662i | − 0.334455i | −0.985918 | − | 0.167228i | \(-0.946519\pi\) | ||||
0.985918 | − | 0.167228i | \(-0.0534815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1317.28 | −1.48175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 306.696i | 0.343445i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −272.533 | −0.304506 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 937.759i | 1.04311i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1411.04 | 1.56608 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1.38383i | − 0.00152909i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −964.450 | −1.06334 | −0.531670 | − | 0.846952i | \(-0.678435\pi\) | ||||
−0.531670 | + | 0.846952i | \(0.678435\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 399.941i | 0.439013i | 0.975611 | + | 0.219507i | \(0.0704448\pi\) | ||||
−0.975611 | + | 0.219507i | \(0.929555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.23463 | 0.00682873 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2177.19i | − 2.37425i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1363.99 | −1.48421 | −0.742107 | − | 0.670281i | \(-0.766174\pi\) | ||||
−0.742107 | + | 0.670281i | \(0.766174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 267.391i | 0.289698i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −996.118 | −1.07688 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 78.7364i | − 0.0847539i | −0.999102 | − | 0.0423770i | \(-0.986507\pi\) | ||||
0.999102 | − | 0.0423770i | \(-0.0134930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −380.173 | −0.408349 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.80822i | 0.00942056i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −861.705 | −0.919642 | −0.459821 | − | 0.888012i | \(-0.652086\pi\) | ||||
−0.459821 | + | 0.888012i | \(0.652086\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 641.991i | 0.682243i | 0.940019 | + | 0.341122i | \(0.110807\pi\) | ||||
−0.940019 | + | 0.341122i | \(0.889193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 82.6124 | 0.0876060 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1259.50i | − 1.32999i | −0.746849 | − | 0.664994i | \(-0.768434\pi\) | ||||
0.746849 | − | 0.664994i | \(-0.231566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −430.221 | −0.453342 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 867.155i | − 0.909921i | −0.890512 | − | 0.454961i | \(-0.849653\pi\) | ||||
0.890512 | − | 0.454961i | \(-0.150347\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −546.200 | −0.571938 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1320.82i | − 1.37729i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −234.865 | −0.244397 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 119.739i | − 0.124081i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −157.972 | −0.163363 | −0.0816813 | − | 0.996659i | \(-0.526029\pi\) | ||||
−0.0816813 | + | 0.996659i | \(0.526029\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 826.466i | − 0.851149i | −0.904923 | − | 0.425575i | \(-0.860072\pi\) | ||||
0.904923 | − | 0.425575i | \(-0.139928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 131.029 | 0.134665 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1777.33i | 1.81917i | 0.415514 | + | 0.909587i | \(0.363602\pi\) | ||||
−0.415514 | + | 0.909587i | \(0.636398\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.1131 | 0.0276947 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 587.324i | − 0.597481i | −0.954334 | − | 0.298740i | \(-0.903434\pi\) | ||||
0.954334 | − | 0.298740i | \(-0.0965665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −166.367 | −0.168900 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 193.962i | − 0.196120i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1132.76 | 1.14304 | 0.571522 | − | 0.820587i | \(-0.306353\pi\) | ||||
0.571522 | + | 0.820587i | \(0.306353\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 599.049i | − 0.602059i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1296.22 | 1.30012 | 0.650060 | − | 0.759883i | \(-0.274744\pi\) | ||||
0.650060 | + | 0.759883i | \(0.274744\pi\) | |||||||
\(998\) | 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 | 1728.3.e.v.1025.4 | 8 | ||
3.2 | odd | 2 | inner | 1728.3.e.v.1025.6 | 8 | ||
4.3 | odd | 2 | inner | 1728.3.e.v.1025.3 | 8 | ||
8.3 | odd | 2 | 864.3.e.e.161.5 | yes | 8 | ||
8.5 | even | 2 | 864.3.e.e.161.6 | yes | 8 | ||
12.11 | even | 2 | inner | 1728.3.e.v.1025.5 | 8 | ||
24.5 | odd | 2 | 864.3.e.e.161.4 | yes | 8 | ||
24.11 | even | 2 | 864.3.e.e.161.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.e.e.161.3 | ✓ | 8 | 24.11 | even | 2 | ||
864.3.e.e.161.4 | yes | 8 | 24.5 | odd | 2 | ||
864.3.e.e.161.5 | yes | 8 | 8.3 | odd | 2 | ||
864.3.e.e.161.6 | yes | 8 | 8.5 | even | 2 | ||
1728.3.e.v.1025.3 | 8 | 4.3 | odd | 2 | inner | ||
1728.3.e.v.1025.4 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.e.v.1025.5 | 8 | 12.11 | even | 2 | inner | ||
1728.3.e.v.1025.6 | 8 | 3.2 | odd | 2 | inner |