Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4640,2,Mod(1,4640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4640 = 2^{5} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4640.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: | \(37.0505865379\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4640.1 |
$q$-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 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.85410 | 1.45671 | 0.728357 | − | 0.685198i | \(-0.240284\pi\) | ||||
0.728357 | + | 0.685198i | \(0.240284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.23607 | 0.372689 | 0.186344 | − | 0.982485i | \(-0.440336\pi\) | ||||
0.186344 | + | 0.982485i | \(0.440336\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.09017 | 1.68911 | 0.844555 | − | 0.535469i | \(-0.179865\pi\) | ||||
0.844555 | + | 0.535469i | \(0.179865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.61803 | 0.417775 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.38197 | −0.335176 | −0.167588 | − | 0.985857i | \(-0.553598\pi\) | ||||
−0.167588 | + | 0.985857i | \(0.553598\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.23607 | 1.66007 | 0.830034 | − | 0.557713i | \(-0.188321\pi\) | ||||
0.830034 | + | 0.557713i | \(0.188321\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.23607 | −1.36082 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.854102 | −0.178093 | −0.0890463 | − | 0.996027i | \(-0.528382\pi\) | ||||
−0.0890463 | + | 0.996027i | \(0.528382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.618034 | 0.111002 | 0.0555011 | − | 0.998459i | \(-0.482324\pi\) | ||||
0.0555011 | + | 0.998459i | \(0.482324\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | −0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.85410 | −0.651462 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.76393 | 0.783186 | 0.391593 | − | 0.920139i | \(-0.371924\pi\) | ||||
0.391593 | + | 0.920139i | \(0.371924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.85410 | −1.57792 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.70820 | 1.51617 | 0.758083 | − | 0.652158i | \(-0.226136\pi\) | ||||
0.758083 | + | 0.652158i | \(0.226136\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.38197 | −0.820742 | −0.410371 | − | 0.911919i | \(-0.634601\pi\) | ||||
−0.410371 | + | 0.911919i | \(0.634601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.381966 | 0.0569401 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.85410 | 1.12201 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.23607 | 0.313112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.32624 | −0.868976 | −0.434488 | − | 0.900678i | \(-0.643071\pi\) | ||||
−0.434488 | + | 0.900678i | \(0.643071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.23607 | −0.166671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.7082 | −1.55079 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.6180 | −1.51254 | −0.756270 | − | 0.654260i | \(-0.772980\pi\) | ||||
−0.756270 | + | 0.654260i | \(0.772980\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.85410 | 1.13365 | 0.566826 | − | 0.823838i | \(-0.308171\pi\) | ||||
0.566826 | + | 0.823838i | \(0.308171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.47214 | −0.185472 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.09017 | −0.755393 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.47214 | 0.790697 | 0.395349 | − | 0.918531i | \(-0.370624\pi\) | ||||
0.395349 | + | 0.918531i | \(0.370624\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.38197 | 0.166369 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.94427 | −0.586777 | −0.293389 | − | 0.955993i | \(-0.594783\pi\) | ||||
−0.293389 | + | 0.955993i | \(0.594783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0902 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.61803 | −0.186834 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.76393 | 0.542900 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0902 | −1.58527 | −0.792634 | − | 0.609698i | \(-0.791291\pi\) | ||||
−0.792634 | + | 0.609698i | \(0.791291\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.29180 | 0.251557 | 0.125779 | − | 0.992058i | \(-0.459857\pi\) | ||||
0.125779 | + | 0.992058i | \(0.459857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.38197 | 0.149895 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.61803 | −0.173471 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.7082 | 1.24107 | 0.620534 | − | 0.784180i | \(-0.286916\pi\) | ||||
0.620534 | + | 0.784180i | \(0.286916\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.4721 | 2.46055 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.23607 | −0.742405 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7984 | −1.60408 | −0.802041 | − | 0.597269i | \(-0.796252\pi\) | ||||
−0.802041 | + | 0.597269i | \(0.796252\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.472136 | −0.0474514 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.09017 | 0.406987 | 0.203494 | − | 0.979076i | \(-0.434770\pi\) | ||||
0.203494 | + | 0.979076i | \(0.434770\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.94427 | −0.881305 | −0.440653 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440653 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.23607 | 0.608578 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7082 | 1.32522 | 0.662611 | − | 0.748964i | \(-0.269448\pi\) | ||||
0.662611 | + | 0.748964i | \(0.269448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.70820 | −0.163616 | −0.0818081 | − | 0.996648i | \(-0.526069\pi\) | ||||
−0.0818081 | + | 0.996648i | \(0.526069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.70820 | −0.731630 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.7984 | −1.48619 | −0.743093 | − | 0.669188i | \(-0.766642\pi\) | ||||
−0.743093 | + | 0.669188i | \(0.766642\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.854102 | 0.0796454 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.32624 | −0.215061 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.32624 | −0.488255 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.7082 | −1.41636 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9443 | 1.50356 | 0.751780 | − | 0.659413i | \(-0.229195\pi\) | ||||
0.751780 | + | 0.659413i | \(0.229195\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.70820 | 0.766715 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.05573 | −0.0922394 | −0.0461197 | − | 0.998936i | \(-0.514686\pi\) | ||||
−0.0461197 | + | 0.998936i | \(0.514686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.8885 | 2.41824 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.47214 | −0.470966 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.85410 | −0.585585 | −0.292793 | − | 0.956176i | \(-0.594585\pi\) | ||||
−0.292793 | + | 0.956176i | \(0.594585\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.38197 | 0.286855 | 0.143427 | − | 0.989661i | \(-0.454188\pi\) | ||||
0.143427 | + | 0.989661i | \(0.454188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9443 | 1.09010 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.52786 | 0.629512 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.7082 | −1.04815 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.18034 | −0.506313 | −0.253157 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253157 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.23607 | −0.263347 | −0.131674 | − | 0.991293i | \(-0.542035\pi\) | ||||
−0.131674 | + | 0.991293i | \(0.542035\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.527864 | 0.0426753 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.618034 | −0.0496417 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.9443 | 1.83115 | 0.915576 | − | 0.402145i | \(-0.131735\pi\) | ||||
0.915576 | + | 0.402145i | \(0.131735\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.2361 | 0.811773 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.29180 | −0.259430 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.4721 | −1.76015 | −0.880077 | − | 0.474831i | \(-0.842509\pi\) | ||||
−0.880077 | + | 0.474831i | \(0.842509\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.61803 | −0.512119 | −0.256059 | − | 0.966661i | \(-0.582424\pi\) | ||||
−0.256059 | + | 0.966661i | \(0.582424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.0902 | 1.85309 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.76393 | −0.211363 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.7984 | 1.50524 | 0.752621 | − | 0.658454i | \(-0.228789\pi\) | ||||
0.752621 | + | 0.658454i | \(0.228789\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.85410 | 0.291343 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.7984 | 1.41297 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0902 | 0.754175 | 0.377087 | − | 0.926178i | \(-0.376926\pi\) | ||||
0.377087 | + | 0.926178i | \(0.376926\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7082 | 1.01892 | 0.509461 | − | 0.860494i | \(-0.329845\pi\) | ||||
0.509461 | + | 0.860494i | \(0.329845\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.3262 | −1.05903 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.76393 | −0.350251 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.70820 | −0.124916 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.0902 | 1.53408 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.1459 | −1.02356 | −0.511781 | − | 0.859116i | \(-0.671014\pi\) | ||||
−0.511781 | + | 0.859116i | \(0.671014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.85410 | 0.493369 | 0.246685 | − | 0.969096i | \(-0.420659\pi\) | ||||
0.246685 | + | 0.969096i | \(0.420659\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.85410 | 0.705667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1459 | 0.865359 | 0.432680 | − | 0.901548i | \(-0.357568\pi\) | ||||
0.432680 | + | 0.901548i | \(0.357568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2361 | −0.938280 | −0.469140 | − | 0.883124i | \(-0.655436\pi\) | ||||
−0.469140 | + | 0.883124i | \(0.655436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.4721 | −0.738648 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.85410 | 0.270505 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.70820 | −0.678050 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.326238 | 0.0226751 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.94427 | 0.618688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7639 | 0.741020 | 0.370510 | − | 0.928829i | \(-0.379183\pi\) | ||||
0.370510 | + | 0.928829i | \(0.379183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.38197 | 0.367047 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.38197 | 0.161698 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.1803 | −1.43123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.41641 | −0.566149 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.9787 | 1.47180 | 0.735902 | − | 0.677088i | \(-0.236759\pi\) | ||||
0.735902 | + | 0.677088i | \(0.236759\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.381966 | −0.0254644 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.00000 | 0.132745 | 0.0663723 | − | 0.997795i | \(-0.478857\pi\) | ||||
0.0663723 | + | 0.997795i | \(0.478857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.09017 | −0.468532 | −0.234266 | − | 0.972173i | \(-0.575269\pi\) | ||||
−0.234266 | + | 0.972173i | \(0.575269\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.70820 | −0.507163 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.52786 | 0.493167 | 0.246583 | − | 0.969122i | \(-0.420692\pi\) | ||||
0.246583 | + | 0.969122i | \(0.420692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.7984 | 1.48091 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4721 | 1.32423 | 0.662116 | − | 0.749401i | \(-0.269659\pi\) | ||||
0.662116 | + | 0.749401i | \(0.269659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.7984 | −1.66182 | −0.830910 | − | 0.556407i | \(-0.812179\pi\) | ||||
−0.830910 | + | 0.556407i | \(0.812179\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.85410 | −0.501780 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.0689 | 2.80404 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.70820 | −0.234998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.18034 | 0.263861 | 0.131930 | − | 0.991259i | \(-0.457882\pi\) | ||||
0.131930 | + | 0.991259i | \(0.457882\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.05573 | −0.0663731 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.23607 | −0.140028 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30.0689 | 1.87565 | 0.937823 | − | 0.347115i | \(-0.112839\pi\) | ||||
0.937823 | + | 0.347115i | \(0.112839\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.3607 | 1.14088 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.381966 | −0.0236431 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.4721 | −1.63234 | −0.816171 | − | 0.577811i | \(-0.803907\pi\) | ||||
−0.816171 | + | 0.577811i | \(0.803907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.32624 | 0.388618 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.9443 | −1.15937 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.43769 | 0.392513 | 0.196257 | − | 0.980553i | \(-0.437121\pi\) | ||||
0.196257 | + | 0.980553i | \(0.437121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.4164 | 0.693497 | 0.346749 | − | 0.937958i | \(-0.387286\pi\) | ||||
0.346749 | + | 0.937958i | \(0.387286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −37.9787 | −2.29858 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.23607 | 0.0745377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.0000 | 1.80253 | 0.901263 | − | 0.433273i | \(-0.142641\pi\) | ||||
0.901263 | + | 0.433273i | \(0.142641\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.236068 | −0.0141330 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.85410 | 0.110606 | 0.0553032 | − | 0.998470i | \(-0.482387\pi\) | ||||
0.0553032 | + | 0.998470i | \(0.482387\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.180340 | −0.0107201 | −0.00536005 | − | 0.999986i | \(-0.501706\pi\) | ||||
−0.00536005 | + | 0.999986i | \(0.501706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.7082 | 0.693534 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.4164 | 2.20862 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0902 | −0.887657 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.5623 | 1.49849 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.18034 | −0.477901 | −0.238950 | − | 0.971032i | \(-0.576803\pi\) | ||||
−0.238950 | + | 0.971032i | \(0.576803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6180 | 0.676428 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.76393 | 0.392483 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.20163 | −0.300818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.7426 | −1.19559 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.61803 | −0.380196 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.85410 | −0.506984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4721 | −1.05426 | −0.527130 | − | 0.849785i | \(-0.676732\pi\) | ||||
−0.527130 | + | 0.849785i | \(0.676732\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.4721 | 0.823291 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.32624 | −0.528842 | −0.264421 | − | 0.964407i | \(-0.585181\pi\) | ||||
−0.264421 | + | 0.964407i | \(0.585181\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.8885 | 1.80245 | 0.901224 | − | 0.433355i | \(-0.142670\pi\) | ||||
0.901224 | + | 0.433355i | \(0.142670\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.47214 | 0.0829455 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.23607 | −0.518749 | −0.259375 | − | 0.965777i | \(-0.583516\pi\) | ||||
−0.259375 | + | 0.965777i | \(0.583516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23607 | 0.0692065 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.1803 | −1.23799 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0000 | −0.556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.09017 | 0.337822 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.76393 | 0.152846 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.8328 | −1.69987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.7082 | −1.30312 | −0.651560 | − | 0.758597i | \(-0.725885\pi\) | ||||
−0.651560 | + | 0.758597i | \(0.725885\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.81966 | −0.0997168 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.47214 | −0.353611 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8541 | 1.29942 | 0.649708 | − | 0.760184i | \(-0.274891\pi\) | ||||
0.649708 | + | 0.760184i | \(0.274891\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.5623 | 1.38835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.763932 | 0.0413692 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.38197 | −0.0744025 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.2361 | 1.89157 | 0.945786 | − | 0.324792i | \(-0.105294\pi\) | ||||
0.945786 | + | 0.324792i | \(0.105294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.94427 | 0.264661 | 0.132330 | − | 0.991206i | \(-0.457754\pi\) | ||||
0.132330 | + | 0.991206i | \(0.457754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.3262 | 1.77882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.52786 | −0.507117 | −0.253559 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253559 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.94427 | 0.262415 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.61803 | 0.456115 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.0902 | 1.37699 | 0.688493 | − | 0.725243i | \(-0.258272\pi\) | ||||
0.688493 | + | 0.725243i | \(0.258272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.3607 | 1.75583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3262 | 0.804419 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0902 | −0.685171 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.18034 | 0.218212 | 0.109106 | − | 0.994030i | \(-0.465201\pi\) | ||||
0.109106 | + | 0.994030i | \(0.465201\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.70820 | −0.193041 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.3820 | −1.26585 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.27051 | −0.376453 | −0.188226 | − | 0.982126i | \(-0.560274\pi\) | ||||
−0.188226 | + | 0.982126i | \(0.560274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.61803 | 0.0835549 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.09017 | 0.313660 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0689 | −1.03087 | −0.515435 | − | 0.856929i | \(-0.672370\pi\) | ||||
−0.515435 | + | 0.856929i | \(0.672370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.4164 | −1.40459 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.27051 | 0.371506 | 0.185753 | − | 0.982596i | \(-0.440528\pi\) | ||||
0.185753 | + | 0.982596i | \(0.440528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.76393 | −0.242792 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.05573 | 0.104499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18034 | 0.0596924 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.70820 | 0.0861675 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.0902 | 0.708953 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.8541 | 0.594940 | 0.297470 | − | 0.954731i | \(-0.403857\pi\) | ||||
0.297470 | + | 0.954731i | \(0.403857\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −45.1246 | −2.25906 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.32624 | −0.365855 | −0.182927 | − | 0.983126i | \(-0.558557\pi\) | ||||
−0.182927 | + | 0.983126i | \(0.558557\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.76393 | 0.187495 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.70820 | 0.383024 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.88854 | 0.291884 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.4164 | −0.960080 | −0.480040 | − | 0.877247i | \(-0.659378\pi\) | ||||
−0.480040 | + | 0.877247i | \(0.659378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0902 | 0.547038 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −44.7771 | −2.20334 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.29180 | −0.112500 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.47214 | −0.267972 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.0902 | 0.737203 | 0.368602 | − | 0.929587i | \(-0.379837\pi\) | ||||
0.368602 | + | 0.929587i | \(0.379837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4721 | 0.802803 | 0.401401 | − | 0.915902i | \(-0.368523\pi\) | ||||
0.401401 | + | 0.915902i | \(0.368523\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.05573 | 0.148575 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.38197 | −0.0670352 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.1246 | 1.65141 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.1803 | −0.588072 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2918 | 0.495738 | 0.247869 | − | 0.968794i | \(-0.420270\pi\) | ||||
0.247869 | + | 0.968794i | \(0.420270\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.47214 | −0.214917 | −0.107459 | − | 0.994210i | \(-0.534271\pi\) | ||||
−0.107459 | + | 0.994210i | \(0.534271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.61803 | 0.0775788 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.18034 | −0.295646 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.00000 | 0.286364 | 0.143182 | − | 0.989696i | \(-0.454267\pi\) | ||||
0.143182 | + | 0.989696i | \(0.454267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.27051 | −0.392944 | −0.196472 | − | 0.980509i | \(-0.562948\pi\) | ||||
−0.196472 | + | 0.980509i | \(0.562948\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7082 | −0.555022 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.0689 | 1.60781 | 0.803905 | − | 0.594758i | \(-0.202752\pi\) | ||||
0.803905 | + | 0.594758i | \(0.202752\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.23607 | 0.246012 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.4721 | −1.10039 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.56231 | −0.352978 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.67376 | −0.171104 | −0.0855521 | − | 0.996334i | \(-0.527265\pi\) | ||||
−0.0855521 | + | 0.996334i | \(0.527265\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.8328 | 0.689339 | 0.344670 | − | 0.938724i | \(-0.387991\pi\) | ||||
0.344670 | + | 0.938724i | \(0.387991\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.3262 | −1.77353 | −0.886763 | − | 0.462224i | \(-0.847052\pi\) | ||||
−0.886763 | + | 0.462224i | \(0.847052\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.9443 | 1.15182 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −37.1246 | −1.71061 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.65248 | −0.305881 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.23607 | 0.332014 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.41641 | 0.110640 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.3262 | 0.745965 | 0.372982 | − | 0.927838i | \(-0.378335\pi\) | ||||
0.372982 | + | 0.927838i | \(0.378335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.0132 | 1.32289 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.32624 | 0.242352 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.7984 | 0.717367 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.2705 | 0.556030 | 0.278015 | − | 0.960577i | \(-0.410324\pi\) | ||||
0.278015 | + | 0.960577i | \(0.410324\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.3607 | 1.64429 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.3050 | 0.961479 | 0.480740 | − | 0.876863i | \(-0.340368\pi\) | ||||
0.480740 | + | 0.876863i | \(0.340368\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.38197 | −0.0622406 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.472136 | 0.0212209 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.0557 | −0.854766 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3262 | −0.775629 | −0.387814 | − | 0.921737i | \(-0.626770\pi\) | ||||
−0.387814 | + | 0.921737i | \(0.626770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7082 | 0.478407 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0000 | 0.891756 | 0.445878 | − | 0.895094i | \(-0.352892\pi\) | ||||
0.445878 | + | 0.895094i | \(0.352892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.09017 | −0.182010 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.9787 | −1.73111 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.70820 | 0.430309 | 0.215154 | − | 0.976580i | \(-0.430975\pi\) | ||||
0.215154 | + | 0.976580i | \(0.430975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.4508 | 2.23181 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.5967 | 1.74824 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.94427 | 0.394132 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.88854 | −0.434898 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.0344 | −1.40616 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.6738 | −0.861923 | −0.430962 | − | 0.902370i | \(-0.641826\pi\) | ||||
−0.430962 | + | 0.902370i | \(0.641826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1803 | 0.532609 | 0.266305 | − | 0.963889i | \(-0.414197\pi\) | ||||
0.266305 | + | 0.963889i | \(0.414197\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.23607 | −0.272164 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.854102 | −0.0372053 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2705 | −0.968283 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.43769 | 0.192580 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 59.1246 | 2.56097 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.7082 | −0.592657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.3262 | −0.704529 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.70820 | 0.418162 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.0344 | −1.03332 | −0.516661 | − | 0.856190i | \(-0.672825\pi\) | ||||
−0.516661 | + | 0.856190i | \(0.672825\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.1803 | −0.951849 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.70820 | 0.0731714 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.1246 | −0.903223 | −0.451612 | − | 0.892215i | \(-0.649151\pi\) | ||||
−0.451612 | + | 0.892215i | \(0.649151\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.38197 | −0.144339 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.23607 | 0.308267 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54.3050 | −2.30928 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.70820 | 0.327195 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.8541 | 1.30733 | 0.653665 | − | 0.756784i | \(-0.273230\pi\) | ||||
0.653665 | + | 0.756784i | \(0.273230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.7771 | −1.38632 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.76393 | 0.116693 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.3951 | −1.91318 | −0.956588 | − | 0.291443i | \(-0.905865\pi\) | ||||
−0.956588 | + | 0.291443i | \(0.905865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.7984 | 0.664643 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.7082 | −1.24763 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.3607 | −0.518187 | −0.259093 | − | 0.965852i | \(-0.583424\pi\) | ||||
−0.259093 | + | 0.965852i | \(0.583424\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.8541 | −1.12381 | −0.561905 | − | 0.827202i | \(-0.689931\pi\) | ||||
−0.561905 | + | 0.827202i | \(0.689931\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.8885 | 0.956183 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.854102 | −0.0356185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.7426 | −1.23820 | −0.619101 | − | 0.785311i | \(-0.712503\pi\) | ||||
−0.619101 | + | 0.785311i | \(0.712503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.0902 | −0.460892 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.83282 | 0.366447 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.81966 | −0.323857 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.32624 | 0.0961781 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.8328 | 1.85045 | 0.925224 | − | 0.379421i | \(-0.123877\pi\) | ||||
0.925224 | + | 0.379421i | \(0.123877\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.47214 | 0.184271 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.6525 | −0.808395 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.6525 | 1.01236 | 0.506178 | − | 0.862429i | \(-0.331058\pi\) | ||||
0.506178 | + | 0.862429i | \(0.331058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.32624 | 0.218354 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.4164 | 0.876515 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3262 | −0.667072 | −0.333536 | − | 0.942737i | \(-0.608242\pi\) | ||||
−0.333536 | + | 0.942737i | \(0.608242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.5410 | −1.89845 | −0.949224 | − | 0.314601i | \(-0.898129\pi\) | ||||
−0.949224 | + | 0.314601i | \(0.898129\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.47214 | −0.100673 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.47214 | 0.385097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.47214 | 0.262696 | 0.131348 | − | 0.991336i | \(-0.458069\pi\) | ||||
0.131348 | + | 0.991336i | \(0.458069\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.23607 | −0.252698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.7214 | −1.97106 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.74265 | −0.393502 | −0.196751 | − | 0.980454i | \(-0.563039\pi\) | ||||
−0.196751 | + | 0.980454i | \(0.563039\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.7082 | 0.633416 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.20163 | −0.289927 | −0.144963 | − | 0.989437i | \(-0.546306\pi\) | ||||
−0.144963 | + | 0.989437i | \(0.546306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.7771 | −1.19684 | −0.598421 | − | 0.801182i | \(-0.704205\pi\) | ||||
−0.598421 | + | 0.801182i | \(0.704205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.67376 | −0.187552 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.1246 | 1.80788 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.4721 | −0.577961 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.58359 | −0.262505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.36068 | −0.253215 | −0.126607 | − | 0.991953i | \(-0.540409\pi\) | ||||
−0.126607 | + | 0.991953i | \(0.540409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.4164 | −0.692240 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.9443 | −0.672413 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.8328 | 1.89521 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.88854 | 0.0747096 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.2361 | −1.70772 | −0.853861 | − | 0.520501i | \(-0.825745\pi\) | ||||
−0.853861 | + | 0.520501i | \(0.825745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.2918 | −0.484741 | −0.242371 | − | 0.970184i | \(-0.577925\pi\) | ||||
−0.242371 | + | 0.970184i | \(0.577925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.70820 | −0.342885 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.3050 | −0.994840 | −0.497420 | − | 0.867510i | \(-0.665719\pi\) | ||||
−0.497420 | + | 0.867510i | \(0.665719\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.3607 | −0.563706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.85410 | −0.151054 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.59675 | −0.375550 | −0.187775 | − | 0.982212i | \(-0.560128\pi\) | ||||
−0.187775 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.05573 | 0.0412507 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.00000 | −0.195069 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.1803 | −1.48729 | −0.743647 | − | 0.668572i | \(-0.766906\pi\) | ||||
−0.743647 | + | 0.668572i | \(0.766906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5967 | −0.840016 | −0.420008 | − | 0.907520i | \(-0.637973\pi\) | ||||
−0.420008 | + | 0.907520i | \(0.637973\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.6180 | 0.528881 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.8885 | −1.08147 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.854102 | −0.0330710 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.5623 | −1.37492 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.9443 | 0.422499 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2361 | 0.895685 | 0.447842 | − | 0.894113i | \(-0.352193\pi\) | ||||
0.447842 | + | 0.894113i | \(0.352193\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.47214 | 0.210623 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.8885 | 0.841245 | 0.420623 | − | 0.907236i | \(-0.361812\pi\) | ||||
0.420623 | + | 0.907236i | \(0.361812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −60.8885 | −2.33669 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.23607 | −0.124006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.6525 | 1.78511 | 0.892554 | − | 0.450941i | \(-0.148912\pi\) | ||||
0.892554 | + | 0.450941i | \(0.148912\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.85410 | 0.261882 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.4721 | 0.437689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.5279 | −1.46779 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0344 | −0.609979 | −0.304989 | − | 0.952356i | \(-0.598653\pi\) | ||||
−0.304989 | + | 0.952356i | \(0.598653\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.81966 | −0.0691232 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.38197 | −0.128285 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.4164 | −0.508183 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1803 | −0.460703 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.1246 | 1.02448 | 0.512241 | − | 0.858842i | \(-0.328815\pi\) | ||||
0.512241 | + | 0.858842i | \(0.328815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.4721 | 1.30014 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.9443 | −0.487509 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.7639 | 0.592864 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.7082 | −1.19083 | −0.595413 | − | 0.803420i | \(-0.703012\pi\) | ||||
−0.595413 | + | 0.803420i | \(0.703012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.38197 | 0.201839 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.527864 | −0.0197687 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.52786 | −0.281526 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.1246 | −1.23706 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.6525 | −0.397270 | −0.198635 | − | 0.980074i | \(-0.563651\pi\) | ||||
−0.198635 | + | 0.980074i | \(0.563651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.4721 | −1.28381 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 41.7426 | 1.55243 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.2361 | 1.82606 | 0.913032 | − | 0.407887i | \(-0.133734\pi\) | ||||
0.913032 | + | 0.407887i | \(0.133734\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.43769 | 0.275093 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.7771 | −1.32146 | −0.660728 | − | 0.750625i | \(-0.729753\pi\) | ||||
−0.660728 | + | 0.750625i | \(0.729753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.7082 | 0.468749 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | 0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.4164 | 0.861386 | 0.430693 | − | 0.902498i | \(-0.358269\pi\) | ||||
0.430693 | + | 0.902498i | \(0.358269\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −71.3050 | −2.61945 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4164 | 0.712319 | 0.356159 | − | 0.934425i | \(-0.384086\pi\) | ||||
0.356159 | + | 0.934425i | \(0.384086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.18034 | 0.226430 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.875388 | −0.0320288 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 52.8328 | 1.93047 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.76393 | −0.246491 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.23607 | 0.117773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.180340 | −0.00655456 | −0.00327728 | − | 0.999995i | \(-0.501043\pi\) | ||||
−0.00327728 | + | 0.999995i | \(0.501043\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.70820 | 0.0620039 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.03444 | 0.146248 | 0.0731242 | − | 0.997323i | \(-0.476703\pi\) | ||||
0.0731242 | + | 0.997323i | \(0.476703\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.58359 | −0.238342 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.527864 | −0.0190850 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −70.7558 | −2.55484 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3475 | 0.697690 | 0.348845 | − | 0.937181i | \(-0.386574\pi\) | ||||
0.348845 | + | 0.937181i | \(0.386574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −48.6525 | −1.75218 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.832816 | 0.0299543 | 0.0149771 | − | 0.999888i | \(-0.495232\pi\) | ||||
0.0149771 | + | 0.999888i | \(0.495232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.618034 | 0.0222004 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29.7082 | −1.06578 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 70.2492 | 2.51694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.11146 | −0.218685 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.47214 | 0.195558 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.9443 | −0.818916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3475 | −0.475788 | −0.237894 | − | 0.971291i | \(-0.576457\pi\) | ||||
−0.237894 | + | 0.971291i | \(0.576457\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 42.8328 | 1.52489 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.8885 | −2.16495 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.9230 | 1.91486 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.2361 | −0.363036 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.8328 | −0.808780 | −0.404390 | − | 0.914587i | \(-0.632516\pi\) | ||||
−0.404390 | + | 0.914587i | \(0.632516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0557 | 0.391124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.47214 | −0.158015 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.1803 | 0.570992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.29180 | 0.116021 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.4164 | −0.366675 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.4164 | −0.542012 | −0.271006 | − | 0.962578i | \(-0.587356\pi\) | ||||
−0.271006 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.3262 | −0.573292 | −0.286646 | − | 0.958037i | \(-0.592540\pi\) | ||||
−0.286646 | + | 0.958037i | \(0.592540\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.4721 | −0.647846 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.4721 | 0.787165 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.9443 | −1.36249 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.96556 | −0.313282 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.0689 | 0.840010 | 0.420005 | − | 0.907522i | \(-0.362028\pi\) | ||||
0.420005 | + | 0.907522i | \(0.362028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.7771 | 0.898533 | 0.449266 | − | 0.893398i | \(-0.351685\pi\) | ||||
0.449266 | + | 0.893398i | \(0.351685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.0902 | −0.455190 | −0.227595 | − | 0.973756i | \(-0.573086\pi\) | ||||
−0.227595 | + | 0.973756i | \(0.573086\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.2016 | −0.736363 | −0.368181 | − | 0.929754i | \(-0.620019\pi\) | ||||
−0.368181 | + | 0.929754i | \(0.620019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.5410 | −1.68387 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.8541 | −0.376072 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.61803 | 0.229027 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.38197 | 0.116898 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.3607 | 0.564833 | 0.282417 | − | 0.959292i | \(-0.408864\pi\) | ||||
0.282417 | + | 0.959292i | \(0.408864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.00000 | −0.103325 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.0902 | −0.828727 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.5066 | −1.25438 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.291796 | 0.0100144 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.06888 | −0.139480 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.1803 | 0.827919 | 0.413960 | − | 0.910295i | \(-0.364145\pi\) | ||||
0.413960 | + | 0.910295i | \(0.364145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.76393 | 0.0945245 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.2918 | 0.693155 | 0.346577 | − | 0.938021i | \(-0.387344\pi\) | ||||
0.346577 | + | 0.938021i | \(0.387344\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.6525 | 0.499936 | 0.249968 | − | 0.968254i | \(-0.419580\pi\) | ||||
0.249968 | + | 0.968254i | \(0.419580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −60.5410 | −2.06323 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.0344 | −0.852182 | −0.426091 | − | 0.904680i | \(-0.640110\pi\) | ||||
−0.426091 | + | 0.904680i | \(0.640110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.7984 | −0.673165 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.4164 | 0.829225 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.4164 | −0.590811 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.4164 | 1.33557 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.03444 | 0.204235 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.85410 | −0.130292 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.3820 | 1.63374 | 0.816871 | − | 0.576820i | \(-0.195707\pi\) | ||||
0.816871 | + | 0.576820i | \(0.195707\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.2361 | 0.446441 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1803 | −0.410366 | −0.205183 | − | 0.978724i | \(-0.565779\pi\) | ||||
−0.205183 | + | 0.978724i | \(0.565779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.5967 | −0.928705 | −0.464352 | − | 0.885651i | \(-0.653713\pi\) | ||||
−0.464352 | + | 0.885651i | \(0.653713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.7984 | −0.631900 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.58359 | 0.153902 | 0.0769510 | − | 0.997035i | \(-0.475482\pi\) | ||||
0.0769510 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 65.3050 | 2.19026 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.52786 | −0.319195 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −57.8885 | −1.93717 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0902 | −0.337277 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.41641 | 0.281016 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.618034 | 0.0206126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.74265 | 0.291260 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.5623 | 1.11688 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.7082 | −0.455676 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.0902 | −1.23156 | −0.615779 | − | 0.787919i | \(-0.711159\pi\) | ||||
−0.615779 | + | 0.787919i | \(0.711159\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.56231 | −0.0518184 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.72949 | 0.189826 | 0.0949132 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949132 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.83282 | 0.0937525 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.3262 | 0.473611 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.06888 | −0.134366 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.5279 | 0.578191 | 0.289095 | − | 0.957300i | \(-0.406646\pi\) | ||||
0.289095 | + | 0.957300i | \(0.406646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.8885 | 0.984861 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.1115 | −0.991131 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.76393 | 0.156637 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.41641 | 0.112210 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.4508 | 0.375690 | 0.187845 | − | 0.982199i | \(-0.439850\pi\) | ||||
0.187845 | + | 0.982199i | \(0.439850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 56.8328 | 1.86262 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0902 | 0.494030 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.70820 | 0.0558642 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.87539 | 0.0939348 | 0.0469674 | − | 0.998896i | \(-0.485044\pi\) | ||||
0.0469674 | + | 0.998896i | \(0.485044\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −51.5967 | −1.68380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.3607 | −0.402947 | −0.201473 | − | 0.979494i | \(-0.564573\pi\) | ||||
−0.201473 | + | 0.979494i | \(0.564573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.29180 | −0.270018 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −21.0902 | −0.686063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.9098 | 1.42688 | 0.713439 | − | 0.700717i | \(-0.247137\pi\) | ||||
0.713439 | + | 0.700717i | \(0.247137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 79.7214 | 2.58786 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.9443 | 0.484601 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.8328 | −1.32270 | −0.661352 | − | 0.750075i | \(-0.730017\pi\) | ||||
−0.661352 | + | 0.750075i | \(0.730017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.1459 | 0.457751 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.00000 | −0.0646508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.4164 | −0.853030 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6180 | −0.987679 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.23607 | −0.168730 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.85410 | −0.220641 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.5967 | 0.823136 | 0.411568 | − | 0.911379i | \(-0.364981\pi\) | ||||
0.411568 | + | 0.911379i | \(0.364981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.1803 | 0.519787 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.06888 | −0.194760 | −0.0973799 | − | 0.995247i | \(-0.531046\pi\) | ||||
−0.0973799 | + | 0.995247i | \(0.531046\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0344 | 0.417865 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.85410 | −0.315584 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.6525 | −0.660731 | −0.330366 | − | 0.943853i | \(-0.607172\pi\) | ||||
−0.330366 | + | 0.943853i | \(0.607172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.4721 | 0.462531 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.652476 | 0.0208320 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.9443 | −0.986969 | −0.493484 | − | 0.869755i | \(-0.664277\pi\) | ||||
−0.493484 | + | 0.869755i | \(0.664277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1459 | −0.387000 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 49.8885 | 1.58797 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.59675 | 0.146168 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0689 | 1.52696 | 0.763479 | − | 0.645832i | \(-0.223490\pi\) | ||||
0.763479 | + | 0.645832i | \(0.223490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.3607 | 1.21734 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.2361 | 0.419612 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.8197 | 0.691036 | 0.345518 | − | 0.938412i | \(-0.387703\pi\) | ||||
0.345518 | + | 0.938412i | \(0.387703\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.0689 | 0.824783 |
(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 | 4640.2.a.g.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 4640.2.a.i.1.2 | yes | 2 | ||
8.3 | odd | 2 | 9280.2.a.y.1.1 | 2 | |||
8.5 | even | 2 | 9280.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4640.2.a.g.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4640.2.a.i.1.2 | yes | 2 | 4.3 | odd | 2 | ||
9280.2.a.y.1.1 | 2 | 8.3 | odd | 2 | |||
9280.2.a.bd.1.2 | 2 | 8.5 | even | 2 |