Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3610,2,Mod(1,3610)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3610, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3610.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3610 = 2 \cdot 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3610.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: | \(28.8259951297\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.0361439\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3610.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.0361439 | −0.0208677 | −0.0104338 | − | 0.999946i | \(-0.503321\pi\) | ||||
−0.0104338 | + | 0.999946i | \(0.503321\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.0361439 | −0.0147557 | ||||||||
\(7\) | 1.83741 | 0.694476 | 0.347238 | − | 0.937777i | \(-0.387120\pi\) | ||||
0.347238 | + | 0.937777i | \(0.387120\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.99869 | −0.999565 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.46576 | −0.743453 | −0.371727 | − | 0.928342i | \(-0.621234\pi\) | ||||
−0.371727 | + | 0.928342i | \(0.621234\pi\) | |||||||
\(12\) | −0.0361439 | −0.0104338 | ||||||||
\(13\) | −2.39309 | −0.663724 | −0.331862 | − | 0.943328i | \(-0.607677\pi\) | ||||
−0.331862 | + | 0.943328i | \(0.607677\pi\) | |||||||
\(14\) | 1.83741 | 0.491069 | ||||||||
\(15\) | −0.0361439 | −0.00933232 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.74198 | 1.63517 | 0.817586 | − | 0.575807i | \(-0.195312\pi\) | ||||
0.817586 | + | 0.575807i | \(0.195312\pi\) | |||||||
\(18\) | −2.99869 | −0.706799 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.0664112 | −0.0144921 | ||||||||
\(22\) | −2.46576 | −0.525701 | ||||||||
\(23\) | 1.62092 | 0.337985 | 0.168993 | − | 0.985617i | \(-0.445949\pi\) | ||||
0.168993 | + | 0.985617i | \(0.445949\pi\) | |||||||
\(24\) | −0.0361439 | −0.00737785 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.39309 | −0.469324 | ||||||||
\(27\) | 0.216816 | 0.0417263 | ||||||||
\(28\) | 1.83741 | 0.347238 | ||||||||
\(29\) | −3.30157 | −0.613086 | −0.306543 | − | 0.951857i | \(-0.599172\pi\) | ||||
−0.306543 | + | 0.951857i | \(0.599172\pi\) | |||||||
\(30\) | −0.0361439 | −0.00659895 | ||||||||
\(31\) | 3.50384 | 0.629308 | 0.314654 | − | 0.949206i | \(-0.398111\pi\) | ||||
0.314654 | + | 0.949206i | \(0.398111\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.0891221 | 0.0155142 | ||||||||
\(34\) | 6.74198 | 1.15624 | ||||||||
\(35\) | 1.83741 | 0.310579 | ||||||||
\(36\) | −2.99869 | −0.499782 | ||||||||
\(37\) | 6.00888 | 0.987854 | 0.493927 | − | 0.869503i | \(-0.335561\pi\) | ||||
0.493927 | + | 0.869503i | \(0.335561\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0864957 | 0.0138504 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 7.98063 | 1.24637 | 0.623183 | − | 0.782076i | \(-0.285839\pi\) | ||||
0.623183 | + | 0.782076i | \(0.285839\pi\) | |||||||
\(42\) | −0.0664112 | −0.0102475 | ||||||||
\(43\) | 5.71443 | 0.871443 | 0.435721 | − | 0.900082i | \(-0.356493\pi\) | ||||
0.435721 | + | 0.900082i | \(0.356493\pi\) | |||||||
\(44\) | −2.46576 | −0.371727 | ||||||||
\(45\) | −2.99869 | −0.447019 | ||||||||
\(46\) | 1.62092 | 0.238992 | ||||||||
\(47\) | 12.4926 | 1.82224 | 0.911120 | − | 0.412142i | \(-0.135219\pi\) | ||||
0.911120 | + | 0.412142i | \(0.135219\pi\) | |||||||
\(48\) | −0.0361439 | −0.00521692 | ||||||||
\(49\) | −3.62392 | −0.517703 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −0.243682 | −0.0341223 | ||||||||
\(52\) | −2.39309 | −0.331862 | ||||||||
\(53\) | 1.92136 | 0.263919 | 0.131960 | − | 0.991255i | \(-0.457873\pi\) | ||||
0.131960 | + | 0.991255i | \(0.457873\pi\) | |||||||
\(54\) | 0.216816 | 0.0295050 | ||||||||
\(55\) | −2.46576 | −0.332482 | ||||||||
\(56\) | 1.83741 | 0.245534 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.30157 | −0.433518 | ||||||||
\(59\) | 4.75396 | 0.618912 | 0.309456 | − | 0.950914i | \(-0.399853\pi\) | ||||
0.309456 | + | 0.950914i | \(0.399853\pi\) | |||||||
\(60\) | −0.0361439 | −0.00466616 | ||||||||
\(61\) | 13.6642 | 1.74952 | 0.874760 | − | 0.484556i | \(-0.161019\pi\) | ||||
0.874760 | + | 0.484556i | \(0.161019\pi\) | |||||||
\(62\) | 3.50384 | 0.444988 | ||||||||
\(63\) | −5.50983 | −0.694174 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.39309 | −0.296826 | ||||||||
\(66\) | 0.0891221 | 0.0109702 | ||||||||
\(67\) | 3.71765 | 0.454183 | 0.227091 | − | 0.973873i | \(-0.427078\pi\) | ||||
0.227091 | + | 0.973873i | \(0.427078\pi\) | |||||||
\(68\) | 6.74198 | 0.817586 | ||||||||
\(69\) | −0.0585864 | −0.00705297 | ||||||||
\(70\) | 1.83741 | 0.219613 | ||||||||
\(71\) | −5.83313 | −0.692265 | −0.346133 | − | 0.938186i | \(-0.612505\pi\) | ||||
−0.346133 | + | 0.938186i | \(0.612505\pi\) | |||||||
\(72\) | −2.99869 | −0.353399 | ||||||||
\(73\) | −0.510408 | −0.0597387 | −0.0298694 | − | 0.999554i | \(-0.509509\pi\) | ||||
−0.0298694 | + | 0.999554i | \(0.509509\pi\) | |||||||
\(74\) | 6.00888 | 0.698519 | ||||||||
\(75\) | −0.0361439 | −0.00417354 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.53061 | −0.516311 | ||||||||
\(78\) | 0.0864957 | 0.00979371 | ||||||||
\(79\) | −12.1354 | −1.36534 | −0.682671 | − | 0.730726i | \(-0.739182\pi\) | ||||
−0.682671 | + | 0.730726i | \(0.739182\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.98824 | 0.998694 | ||||||||
\(82\) | 7.98063 | 0.881314 | ||||||||
\(83\) | 6.23256 | 0.684112 | 0.342056 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342056 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(84\) | −0.0664112 | −0.00724606 | ||||||||
\(85\) | 6.74198 | 0.731271 | ||||||||
\(86\) | 5.71443 | 0.616203 | ||||||||
\(87\) | 0.119332 | 0.0127937 | ||||||||
\(88\) | −2.46576 | −0.262850 | ||||||||
\(89\) | −17.0020 | −1.80220 | −0.901102 | − | 0.433607i | \(-0.857241\pi\) | ||||
−0.901102 | + | 0.433607i | \(0.857241\pi\) | |||||||
\(90\) | −2.99869 | −0.316090 | ||||||||
\(91\) | −4.39709 | −0.460941 | ||||||||
\(92\) | 1.62092 | 0.168993 | ||||||||
\(93\) | −0.126642 | −0.0131322 | ||||||||
\(94\) | 12.4926 | 1.28852 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.0361439 | −0.00368892 | ||||||||
\(97\) | 13.6598 | 1.38695 | 0.693473 | − | 0.720483i | \(-0.256080\pi\) | ||||
0.693473 | + | 0.720483i | \(0.256080\pi\) | |||||||
\(98\) | −3.62392 | −0.366071 | ||||||||
\(99\) | 7.39405 | 0.743130 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.6583 | −1.06054 | −0.530270 | − | 0.847829i | \(-0.677909\pi\) | ||||
−0.530270 | + | 0.847829i | \(0.677909\pi\) | |||||||
\(102\) | −0.243682 | −0.0241281 | ||||||||
\(103\) | 9.74930 | 0.960627 | 0.480313 | − | 0.877097i | \(-0.340523\pi\) | ||||
0.480313 | + | 0.877097i | \(0.340523\pi\) | |||||||
\(104\) | −2.39309 | −0.234662 | ||||||||
\(105\) | −0.0664112 | −0.00648107 | ||||||||
\(106\) | 1.92136 | 0.186619 | ||||||||
\(107\) | −13.2857 | −1.28438 | −0.642191 | − | 0.766545i | \(-0.721974\pi\) | ||||
−0.642191 | + | 0.766545i | \(0.721974\pi\) | |||||||
\(108\) | 0.216816 | 0.0208632 | ||||||||
\(109\) | −1.44392 | −0.138303 | −0.0691513 | − | 0.997606i | \(-0.522029\pi\) | ||||
−0.0691513 | + | 0.997606i | \(0.522029\pi\) | |||||||
\(110\) | −2.46576 | −0.235101 | ||||||||
\(111\) | −0.217185 | −0.0206142 | ||||||||
\(112\) | 1.83741 | 0.173619 | ||||||||
\(113\) | 0.841529 | 0.0791644 | 0.0395822 | − | 0.999216i | \(-0.487397\pi\) | ||||
0.0395822 | + | 0.999216i | \(0.487397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.62092 | 0.151151 | ||||||||
\(116\) | −3.30157 | −0.306543 | ||||||||
\(117\) | 7.17615 | 0.663435 | ||||||||
\(118\) | 4.75396 | 0.437637 | ||||||||
\(119\) | 12.3878 | 1.13559 | ||||||||
\(120\) | −0.0361439 | −0.00329947 | ||||||||
\(121\) | −4.92005 | −0.447277 | ||||||||
\(122\) | 13.6642 | 1.23710 | ||||||||
\(123\) | −0.288451 | −0.0260088 | ||||||||
\(124\) | 3.50384 | 0.314654 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.50983 | −0.490855 | ||||||||
\(127\) | −12.9858 | −1.15230 | −0.576152 | − | 0.817343i | \(-0.695446\pi\) | ||||
−0.576152 | + | 0.817343i | \(0.695446\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.206542 | −0.0181850 | ||||||||
\(130\) | −2.39309 | −0.209888 | ||||||||
\(131\) | 8.92899 | 0.780129 | 0.390065 | − | 0.920787i | \(-0.372453\pi\) | ||||
0.390065 | + | 0.920787i | \(0.372453\pi\) | |||||||
\(132\) | 0.0891221 | 0.00775708 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.71765 | 0.321156 | ||||||||
\(135\) | 0.216816 | 0.0186606 | ||||||||
\(136\) | 6.74198 | 0.578120 | ||||||||
\(137\) | 4.45359 | 0.380496 | 0.190248 | − | 0.981736i | \(-0.439071\pi\) | ||||
0.190248 | + | 0.981736i | \(0.439071\pi\) | |||||||
\(138\) | −0.0585864 | −0.00498720 | ||||||||
\(139\) | −1.21147 | −0.102755 | −0.0513777 | − | 0.998679i | \(-0.516361\pi\) | ||||
−0.0513777 | + | 0.998679i | \(0.516361\pi\) | |||||||
\(140\) | 1.83741 | 0.155290 | ||||||||
\(141\) | −0.451533 | −0.0380259 | ||||||||
\(142\) | −5.83313 | −0.489505 | ||||||||
\(143\) | 5.90078 | 0.493448 | ||||||||
\(144\) | −2.99869 | −0.249891 | ||||||||
\(145\) | −3.30157 | −0.274181 | ||||||||
\(146\) | −0.510408 | −0.0422416 | ||||||||
\(147\) | 0.130983 | 0.0108033 | ||||||||
\(148\) | 6.00888 | 0.493927 | ||||||||
\(149\) | 9.28405 | 0.760579 | 0.380289 | − | 0.924868i | \(-0.375824\pi\) | ||||
0.380289 | + | 0.924868i | \(0.375824\pi\) | |||||||
\(150\) | −0.0361439 | −0.00295114 | ||||||||
\(151\) | 3.34570 | 0.272269 | 0.136135 | − | 0.990690i | \(-0.456532\pi\) | ||||
0.136135 | + | 0.990690i | \(0.456532\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.2171 | −1.63446 | ||||||||
\(154\) | −4.53061 | −0.365087 | ||||||||
\(155\) | 3.50384 | 0.281435 | ||||||||
\(156\) | 0.0864957 | 0.00692520 | ||||||||
\(157\) | 7.05317 | 0.562904 | 0.281452 | − | 0.959575i | \(-0.409184\pi\) | ||||
0.281452 | + | 0.959575i | \(0.409184\pi\) | |||||||
\(158\) | −12.1354 | −0.965443 | ||||||||
\(159\) | −0.0694454 | −0.00550738 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.97829 | 0.234723 | ||||||||
\(162\) | 8.98824 | 0.706183 | ||||||||
\(163\) | −15.8559 | −1.24193 | −0.620964 | − | 0.783839i | \(-0.713259\pi\) | ||||
−0.620964 | + | 0.783839i | \(0.713259\pi\) | |||||||
\(164\) | 7.98063 | 0.623183 | ||||||||
\(165\) | 0.0891221 | 0.00693814 | ||||||||
\(166\) | 6.23256 | 0.483740 | ||||||||
\(167\) | 13.6257 | 1.05439 | 0.527196 | − | 0.849744i | \(-0.323243\pi\) | ||||
0.527196 | + | 0.849744i | \(0.323243\pi\) | |||||||
\(168\) | −0.0664112 | −0.00512374 | ||||||||
\(169\) | −7.27311 | −0.559470 | ||||||||
\(170\) | 6.74198 | 0.517086 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.71443 | 0.435721 | ||||||||
\(173\) | −12.0395 | −0.915344 | −0.457672 | − | 0.889121i | \(-0.651317\pi\) | ||||
−0.457672 | + | 0.889121i | \(0.651317\pi\) | |||||||
\(174\) | 0.119332 | 0.00904651 | ||||||||
\(175\) | 1.83741 | 0.138895 | ||||||||
\(176\) | −2.46576 | −0.185863 | ||||||||
\(177\) | −0.171827 | −0.0129153 | ||||||||
\(178\) | −17.0020 | −1.27435 | ||||||||
\(179\) | −16.0730 | −1.20135 | −0.600675 | − | 0.799493i | \(-0.705102\pi\) | ||||
−0.600675 | + | 0.799493i | \(0.705102\pi\) | |||||||
\(180\) | −2.99869 | −0.223509 | ||||||||
\(181\) | −5.75310 | −0.427625 | −0.213812 | − | 0.976875i | \(-0.568588\pi\) | ||||
−0.213812 | + | 0.976875i | \(0.568588\pi\) | |||||||
\(182\) | −4.39709 | −0.325934 | ||||||||
\(183\) | −0.493877 | −0.0365085 | ||||||||
\(184\) | 1.62092 | 0.119496 | ||||||||
\(185\) | 6.00888 | 0.441782 | ||||||||
\(186\) | −0.126642 | −0.00928588 | ||||||||
\(187\) | −16.6241 | −1.21567 | ||||||||
\(188\) | 12.4926 | 0.911120 | ||||||||
\(189\) | 0.398381 | 0.0289779 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.5460 | −1.48666 | −0.743329 | − | 0.668926i | \(-0.766754\pi\) | ||||
−0.743329 | + | 0.668926i | \(0.766754\pi\) | |||||||
\(192\) | −0.0361439 | −0.00260846 | ||||||||
\(193\) | 12.5139 | 0.900774 | 0.450387 | − | 0.892833i | \(-0.351286\pi\) | ||||
0.450387 | + | 0.892833i | \(0.351286\pi\) | |||||||
\(194\) | 13.6598 | 0.980719 | ||||||||
\(195\) | 0.0864957 | 0.00619408 | ||||||||
\(196\) | −3.62392 | −0.258851 | ||||||||
\(197\) | 6.02346 | 0.429154 | 0.214577 | − | 0.976707i | \(-0.431163\pi\) | ||||
0.214577 | + | 0.976707i | \(0.431163\pi\) | |||||||
\(198\) | 7.39405 | 0.525472 | ||||||||
\(199\) | 11.2535 | 0.797742 | 0.398871 | − | 0.917007i | \(-0.369402\pi\) | ||||
0.398871 | + | 0.917007i | \(0.369402\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −0.134370 | −0.00947775 | ||||||||
\(202\) | −10.6583 | −0.749915 | ||||||||
\(203\) | −6.06634 | −0.425774 | ||||||||
\(204\) | −0.243682 | −0.0170611 | ||||||||
\(205\) | 7.98063 | 0.557392 | ||||||||
\(206\) | 9.74930 | 0.679266 | ||||||||
\(207\) | −4.86064 | −0.337838 | ||||||||
\(208\) | −2.39309 | −0.165931 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.0664112 | −0.00458281 | ||||||||
\(211\) | −14.0676 | −0.968454 | −0.484227 | − | 0.874942i | \(-0.660899\pi\) | ||||
−0.484227 | + | 0.874942i | \(0.660899\pi\) | |||||||
\(212\) | 1.92136 | 0.131960 | ||||||||
\(213\) | 0.210832 | 0.0144460 | ||||||||
\(214\) | −13.2857 | −0.908195 | ||||||||
\(215\) | 5.71443 | 0.389721 | ||||||||
\(216\) | 0.216816 | 0.0147525 | ||||||||
\(217\) | 6.43799 | 0.437039 | ||||||||
\(218\) | −1.44392 | −0.0977947 | ||||||||
\(219\) | 0.0184481 | 0.00124661 | ||||||||
\(220\) | −2.46576 | −0.166241 | ||||||||
\(221\) | −16.1342 | −1.08530 | ||||||||
\(222\) | −0.217185 | −0.0145765 | ||||||||
\(223\) | −25.3025 | −1.69438 | −0.847189 | − | 0.531291i | \(-0.821707\pi\) | ||||
−0.847189 | + | 0.531291i | \(0.821707\pi\) | |||||||
\(224\) | 1.83741 | 0.122767 | ||||||||
\(225\) | −2.99869 | −0.199913 | ||||||||
\(226\) | 0.841529 | 0.0559777 | ||||||||
\(227\) | −22.0111 | −1.46093 | −0.730464 | − | 0.682951i | \(-0.760696\pi\) | ||||
−0.730464 | + | 0.682951i | \(0.760696\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.29529 | −0.349923 | −0.174961 | − | 0.984575i | \(-0.555980\pi\) | ||||
−0.174961 | + | 0.984575i | \(0.555980\pi\) | |||||||
\(230\) | 1.62092 | 0.106880 | ||||||||
\(231\) | 0.163754 | 0.0107742 | ||||||||
\(232\) | −3.30157 | −0.216759 | ||||||||
\(233\) | 20.5518 | 1.34639 | 0.673196 | − | 0.739464i | \(-0.264921\pi\) | ||||
0.673196 | + | 0.739464i | \(0.264921\pi\) | |||||||
\(234\) | 7.17615 | 0.469119 | ||||||||
\(235\) | 12.4926 | 0.814930 | ||||||||
\(236\) | 4.75396 | 0.309456 | ||||||||
\(237\) | 0.438622 | 0.0284915 | ||||||||
\(238\) | 12.3878 | 0.802981 | ||||||||
\(239\) | 0.887170 | 0.0573863 | 0.0286931 | − | 0.999588i | \(-0.490865\pi\) | ||||
0.0286931 | + | 0.999588i | \(0.490865\pi\) | |||||||
\(240\) | −0.0361439 | −0.00233308 | ||||||||
\(241\) | 4.00142 | 0.257754 | 0.128877 | − | 0.991661i | \(-0.458863\pi\) | ||||
0.128877 | + | 0.991661i | \(0.458863\pi\) | |||||||
\(242\) | −4.92005 | −0.316273 | ||||||||
\(243\) | −0.975319 | −0.0625667 | ||||||||
\(244\) | 13.6642 | 0.874760 | ||||||||
\(245\) | −3.62392 | −0.231524 | ||||||||
\(246\) | −0.288451 | −0.0183910 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.50384 | 0.222494 | ||||||||
\(249\) | −0.225269 | −0.0142758 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −12.6687 | −0.799642 | −0.399821 | − | 0.916593i | \(-0.630928\pi\) | ||||
−0.399821 | + | 0.916593i | \(0.630928\pi\) | |||||||
\(252\) | −5.50983 | −0.347087 | ||||||||
\(253\) | −3.99679 | −0.251276 | ||||||||
\(254\) | −12.9858 | −0.814801 | ||||||||
\(255\) | −0.243682 | −0.0152599 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.0448 | 0.813712 | 0.406856 | − | 0.913492i | \(-0.366625\pi\) | ||||
0.406856 | + | 0.913492i | \(0.366625\pi\) | |||||||
\(258\) | −0.206542 | −0.0128587 | ||||||||
\(259\) | 11.0408 | 0.686041 | ||||||||
\(260\) | −2.39309 | −0.148413 | ||||||||
\(261\) | 9.90040 | 0.612819 | ||||||||
\(262\) | 8.92899 | 0.551635 | ||||||||
\(263\) | 28.2516 | 1.74207 | 0.871033 | − | 0.491224i | \(-0.163450\pi\) | ||||
0.871033 | + | 0.491224i | \(0.163450\pi\) | |||||||
\(264\) | 0.0891221 | 0.00548508 | ||||||||
\(265\) | 1.92136 | 0.118028 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.614517 | 0.0376079 | ||||||||
\(268\) | 3.71765 | 0.227091 | ||||||||
\(269\) | −29.5432 | −1.80128 | −0.900641 | − | 0.434563i | \(-0.856903\pi\) | ||||
−0.900641 | + | 0.434563i | \(0.856903\pi\) | |||||||
\(270\) | 0.216816 | 0.0131950 | ||||||||
\(271\) | 27.0112 | 1.64081 | 0.820406 | − | 0.571782i | \(-0.193748\pi\) | ||||
0.820406 | + | 0.571782i | \(0.193748\pi\) | |||||||
\(272\) | 6.74198 | 0.408793 | ||||||||
\(273\) | 0.158928 | 0.00961877 | ||||||||
\(274\) | 4.45359 | 0.269051 | ||||||||
\(275\) | −2.46576 | −0.148691 | ||||||||
\(276\) | −0.0585864 | −0.00352648 | ||||||||
\(277\) | −24.1778 | −1.45270 | −0.726352 | − | 0.687323i | \(-0.758786\pi\) | ||||
−0.726352 | + | 0.687323i | \(0.758786\pi\) | |||||||
\(278\) | −1.21147 | −0.0726591 | ||||||||
\(279\) | −10.5069 | −0.629034 | ||||||||
\(280\) | 1.83741 | 0.109806 | ||||||||
\(281\) | −2.40101 | −0.143232 | −0.0716162 | − | 0.997432i | \(-0.522816\pi\) | ||||
−0.0716162 | + | 0.997432i | \(0.522816\pi\) | |||||||
\(282\) | −0.451533 | −0.0268884 | ||||||||
\(283\) | 8.15093 | 0.484523 | 0.242261 | − | 0.970211i | \(-0.422111\pi\) | ||||
0.242261 | + | 0.970211i | \(0.422111\pi\) | |||||||
\(284\) | −5.83313 | −0.346133 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.90078 | 0.348920 | ||||||||
\(287\) | 14.6637 | 0.865571 | ||||||||
\(288\) | −2.99869 | −0.176700 | ||||||||
\(289\) | 28.4543 | 1.67378 | ||||||||
\(290\) | −3.30157 | −0.193875 | ||||||||
\(291\) | −0.493720 | −0.0289424 | ||||||||
\(292\) | −0.510408 | −0.0298694 | ||||||||
\(293\) | −9.19756 | −0.537327 | −0.268664 | − | 0.963234i | \(-0.586582\pi\) | ||||
−0.268664 | + | 0.963234i | \(0.586582\pi\) | |||||||
\(294\) | 0.130983 | 0.00763906 | ||||||||
\(295\) | 4.75396 | 0.276786 | ||||||||
\(296\) | 6.00888 | 0.349259 | ||||||||
\(297\) | −0.534616 | −0.0310216 | ||||||||
\(298\) | 9.28405 | 0.537811 | ||||||||
\(299\) | −3.87901 | −0.224329 | ||||||||
\(300\) | −0.0361439 | −0.00208677 | ||||||||
\(301\) | 10.4998 | 0.605196 | ||||||||
\(302\) | 3.34570 | 0.192523 | ||||||||
\(303\) | 0.385232 | 0.0221310 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.6642 | 0.782409 | ||||||||
\(306\) | −20.2171 | −1.15574 | ||||||||
\(307\) | 28.3472 | 1.61786 | 0.808929 | − | 0.587907i | \(-0.200048\pi\) | ||||
0.808929 | + | 0.587907i | \(0.200048\pi\) | |||||||
\(308\) | −4.53061 | −0.258155 | ||||||||
\(309\) | −0.352378 | −0.0200461 | ||||||||
\(310\) | 3.50384 | 0.199005 | ||||||||
\(311\) | 17.4409 | 0.988980 | 0.494490 | − | 0.869183i | \(-0.335355\pi\) | ||||
0.494490 | + | 0.869183i | \(0.335355\pi\) | |||||||
\(312\) | 0.0864957 | 0.00489685 | ||||||||
\(313\) | −13.1983 | −0.746012 | −0.373006 | − | 0.927829i | \(-0.621673\pi\) | ||||
−0.373006 | + | 0.927829i | \(0.621673\pi\) | |||||||
\(314\) | 7.05317 | 0.398034 | ||||||||
\(315\) | −5.50983 | −0.310444 | ||||||||
\(316\) | −12.1354 | −0.682671 | ||||||||
\(317\) | 12.2864 | 0.690072 | 0.345036 | − | 0.938589i | \(-0.387867\pi\) | ||||
0.345036 | + | 0.938589i | \(0.387867\pi\) | |||||||
\(318\) | −0.0694454 | −0.00389431 | ||||||||
\(319\) | 8.14087 | 0.455801 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0.480199 | 0.0268021 | ||||||||
\(322\) | 2.97829 | 0.165974 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.98824 | 0.499347 | ||||||||
\(325\) | −2.39309 | −0.132745 | ||||||||
\(326\) | −15.8559 | −0.878175 | ||||||||
\(327\) | 0.0521890 | 0.00288606 | ||||||||
\(328\) | 7.98063 | 0.440657 | ||||||||
\(329\) | 22.9541 | 1.26550 | ||||||||
\(330\) | 0.0891221 | 0.00490601 | ||||||||
\(331\) | −0.996594 | −0.0547778 | −0.0273889 | − | 0.999625i | \(-0.508719\pi\) | ||||
−0.0273889 | + | 0.999625i | \(0.508719\pi\) | |||||||
\(332\) | 6.23256 | 0.342056 | ||||||||
\(333\) | −18.0188 | −0.987424 | ||||||||
\(334\) | 13.6257 | 0.745568 | ||||||||
\(335\) | 3.71765 | 0.203117 | ||||||||
\(336\) | −0.0664112 | −0.00362303 | ||||||||
\(337\) | −8.55919 | −0.466249 | −0.233124 | − | 0.972447i | \(-0.574895\pi\) | ||||
−0.233124 | + | 0.972447i | \(0.574895\pi\) | |||||||
\(338\) | −7.27311 | −0.395605 | ||||||||
\(339\) | −0.0304162 | −0.00165198 | ||||||||
\(340\) | 6.74198 | 0.365635 | ||||||||
\(341\) | −8.63961 | −0.467861 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5205 | −1.05401 | ||||||||
\(344\) | 5.71443 | 0.308102 | ||||||||
\(345\) | −0.0585864 | −0.00315418 | ||||||||
\(346\) | −12.0395 | −0.647246 | ||||||||
\(347\) | −6.63773 | −0.356332 | −0.178166 | − | 0.984000i | \(-0.557016\pi\) | ||||
−0.178166 | + | 0.984000i | \(0.557016\pi\) | |||||||
\(348\) | 0.119332 | 0.00639685 | ||||||||
\(349\) | 31.0443 | 1.66176 | 0.830881 | − | 0.556450i | \(-0.187837\pi\) | ||||
0.830881 | + | 0.556450i | \(0.187837\pi\) | |||||||
\(350\) | 1.83741 | 0.0982138 | ||||||||
\(351\) | −0.518861 | −0.0276948 | ||||||||
\(352\) | −2.46576 | −0.131425 | ||||||||
\(353\) | 17.7629 | 0.945424 | 0.472712 | − | 0.881217i | \(-0.343275\pi\) | ||||
0.472712 | + | 0.881217i | \(0.343275\pi\) | |||||||
\(354\) | −0.171827 | −0.00913248 | ||||||||
\(355\) | −5.83313 | −0.309590 | ||||||||
\(356\) | −17.0020 | −0.901102 | ||||||||
\(357\) | −0.447743 | −0.0236971 | ||||||||
\(358\) | −16.0730 | −0.849483 | ||||||||
\(359\) | −5.13615 | −0.271076 | −0.135538 | − | 0.990772i | \(-0.543276\pi\) | ||||
−0.135538 | + | 0.990772i | \(0.543276\pi\) | |||||||
\(360\) | −2.99869 | −0.158045 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −5.75310 | −0.302376 | ||||||||
\(363\) | 0.177830 | 0.00933364 | ||||||||
\(364\) | −4.39709 | −0.230470 | ||||||||
\(365\) | −0.510408 | −0.0267160 | ||||||||
\(366\) | −0.493877 | −0.0258154 | ||||||||
\(367\) | −5.74589 | −0.299933 | −0.149966 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149966 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(368\) | 1.62092 | 0.0844963 | ||||||||
\(369\) | −23.9315 | −1.24582 | ||||||||
\(370\) | 6.00888 | 0.312387 | ||||||||
\(371\) | 3.53033 | 0.183285 | ||||||||
\(372\) | −0.126642 | −0.00656611 | ||||||||
\(373\) | −37.7854 | −1.95645 | −0.978227 | − | 0.207539i | \(-0.933454\pi\) | ||||
−0.978227 | + | 0.207539i | \(0.933454\pi\) | |||||||
\(374\) | −16.6241 | −0.859611 | ||||||||
\(375\) | −0.0361439 | −0.00186646 | ||||||||
\(376\) | 12.4926 | 0.644259 | ||||||||
\(377\) | 7.90096 | 0.406920 | ||||||||
\(378\) | 0.398381 | 0.0204905 | ||||||||
\(379\) | 32.2663 | 1.65741 | 0.828703 | − | 0.559689i | \(-0.189079\pi\) | ||||
0.828703 | + | 0.559689i | \(0.189079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.469358 | 0.0240459 | ||||||||
\(382\) | −20.5460 | −1.05123 | ||||||||
\(383\) | 21.7799 | 1.11290 | 0.556450 | − | 0.830881i | \(-0.312163\pi\) | ||||
0.556450 | + | 0.830881i | \(0.312163\pi\) | |||||||
\(384\) | −0.0361439 | −0.00184446 | ||||||||
\(385\) | −4.53061 | −0.230901 | ||||||||
\(386\) | 12.5139 | 0.636943 | ||||||||
\(387\) | −17.1358 | −0.871063 | ||||||||
\(388\) | 13.6598 | 0.693473 | ||||||||
\(389\) | 9.68485 | 0.491041 | 0.245521 | − | 0.969391i | \(-0.421041\pi\) | ||||
0.245521 | + | 0.969391i | \(0.421041\pi\) | |||||||
\(390\) | 0.0864957 | 0.00437988 | ||||||||
\(391\) | 10.9282 | 0.552663 | ||||||||
\(392\) | −3.62392 | −0.183036 | ||||||||
\(393\) | −0.322729 | −0.0162795 | ||||||||
\(394\) | 6.02346 | 0.303458 | ||||||||
\(395\) | −12.1354 | −0.610600 | ||||||||
\(396\) | 7.39405 | 0.371565 | ||||||||
\(397\) | −18.3952 | −0.923226 | −0.461613 | − | 0.887081i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887081i | \(0.652729\pi\) | |||||||
\(398\) | 11.2535 | 0.564089 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 36.5367 | 1.82455 | 0.912277 | − | 0.409573i | \(-0.134322\pi\) | ||||
0.912277 | + | 0.409573i | \(0.134322\pi\) | |||||||
\(402\) | −0.134370 | −0.00670178 | ||||||||
\(403\) | −8.38501 | −0.417687 | ||||||||
\(404\) | −10.6583 | −0.530270 | ||||||||
\(405\) | 8.98824 | 0.446629 | ||||||||
\(406\) | −6.06634 | −0.301068 | ||||||||
\(407\) | −14.8164 | −0.734424 | ||||||||
\(408\) | −0.243682 | −0.0120640 | ||||||||
\(409\) | −36.3063 | −1.79523 | −0.897616 | − | 0.440779i | \(-0.854702\pi\) | ||||
−0.897616 | + | 0.440779i | \(0.854702\pi\) | |||||||
\(410\) | 7.98063 | 0.394135 | ||||||||
\(411\) | −0.160970 | −0.00794007 | ||||||||
\(412\) | 9.74930 | 0.480313 | ||||||||
\(413\) | 8.73497 | 0.429820 | ||||||||
\(414\) | −4.86064 | −0.238887 | ||||||||
\(415\) | 6.23256 | 0.305944 | ||||||||
\(416\) | −2.39309 | −0.117331 | ||||||||
\(417\) | 0.0437872 | 0.00214427 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.5001 | 1.92970 | 0.964852 | − | 0.262793i | \(-0.0846437\pi\) | ||||
0.964852 | + | 0.262793i | \(0.0846437\pi\) | |||||||
\(420\) | −0.0664112 | −0.00324054 | ||||||||
\(421\) | 14.1005 | 0.687217 | 0.343609 | − | 0.939113i | \(-0.388351\pi\) | ||||
0.343609 | + | 0.939113i | \(0.388351\pi\) | |||||||
\(422\) | −14.0676 | −0.684800 | ||||||||
\(423\) | −37.4616 | −1.82145 | ||||||||
\(424\) | 1.92136 | 0.0933095 | ||||||||
\(425\) | 6.74198 | 0.327034 | ||||||||
\(426\) | 0.210832 | 0.0102149 | ||||||||
\(427\) | 25.1067 | 1.21500 | ||||||||
\(428\) | −13.2857 | −0.642191 | ||||||||
\(429\) | −0.213277 | −0.0102971 | ||||||||
\(430\) | 5.71443 | 0.275574 | ||||||||
\(431\) | −21.0431 | −1.01361 | −0.506806 | − | 0.862060i | \(-0.669174\pi\) | ||||
−0.506806 | + | 0.862060i | \(0.669174\pi\) | |||||||
\(432\) | 0.216816 | 0.0104316 | ||||||||
\(433\) | 5.25769 | 0.252669 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(434\) | 6.43799 | 0.309034 | ||||||||
\(435\) | 0.119332 | 0.00572152 | ||||||||
\(436\) | −1.44392 | −0.0691513 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.0184481 | 0.000881486 0 | ||||||||
\(439\) | −36.4838 | −1.74128 | −0.870639 | − | 0.491923i | \(-0.836294\pi\) | ||||
−0.870639 | + | 0.491923i | \(0.836294\pi\) | |||||||
\(440\) | −2.46576 | −0.117550 | ||||||||
\(441\) | 10.8670 | 0.517478 | ||||||||
\(442\) | −16.1342 | −0.767425 | ||||||||
\(443\) | −9.23069 | −0.438564 | −0.219282 | − | 0.975662i | \(-0.570371\pi\) | ||||
−0.219282 | + | 0.975662i | \(0.570371\pi\) | |||||||
\(444\) | −0.217185 | −0.0103071 | ||||||||
\(445\) | −17.0020 | −0.805970 | ||||||||
\(446\) | −25.3025 | −1.19811 | ||||||||
\(447\) | −0.335562 | −0.0158715 | ||||||||
\(448\) | 1.83741 | 0.0868095 | ||||||||
\(449\) | 22.8297 | 1.07740 | 0.538699 | − | 0.842498i | \(-0.318916\pi\) | ||||
0.538699 | + | 0.842498i | \(0.318916\pi\) | |||||||
\(450\) | −2.99869 | −0.141360 | ||||||||
\(451\) | −19.6783 | −0.926615 | ||||||||
\(452\) | 0.841529 | 0.0395822 | ||||||||
\(453\) | −0.120927 | −0.00568163 | ||||||||
\(454\) | −22.0111 | −1.03303 | ||||||||
\(455\) | −4.39709 | −0.206139 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.82515 | −0.366045 | −0.183022 | − | 0.983109i | \(-0.558588\pi\) | ||||
−0.183022 | + | 0.983109i | \(0.558588\pi\) | |||||||
\(458\) | −5.29529 | −0.247433 | ||||||||
\(459\) | 1.46177 | 0.0682296 | ||||||||
\(460\) | 1.62092 | 0.0755757 | ||||||||
\(461\) | −3.93168 | −0.183117 | −0.0915584 | − | 0.995800i | \(-0.529185\pi\) | ||||
−0.0915584 | + | 0.995800i | \(0.529185\pi\) | |||||||
\(462\) | 0.163754 | 0.00761852 | ||||||||
\(463\) | −17.2964 | −0.803832 | −0.401916 | − | 0.915676i | \(-0.631656\pi\) | ||||
−0.401916 | + | 0.915676i | \(0.631656\pi\) | |||||||
\(464\) | −3.30157 | −0.153272 | ||||||||
\(465\) | −0.126642 | −0.00587290 | ||||||||
\(466\) | 20.5518 | 0.952044 | ||||||||
\(467\) | −21.0267 | −0.973002 | −0.486501 | − | 0.873680i | \(-0.661727\pi\) | ||||
−0.486501 | + | 0.873680i | \(0.661727\pi\) | |||||||
\(468\) | 7.17615 | 0.331718 | ||||||||
\(469\) | 6.83084 | 0.315419 | ||||||||
\(470\) | 12.4926 | 0.576243 | ||||||||
\(471\) | −0.254929 | −0.0117465 | ||||||||
\(472\) | 4.75396 | 0.218819 | ||||||||
\(473\) | −14.0904 | −0.647877 | ||||||||
\(474\) | 0.438622 | 0.0201466 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.3878 | 0.567794 | ||||||||
\(477\) | −5.76157 | −0.263804 | ||||||||
\(478\) | 0.887170 | 0.0405782 | ||||||||
\(479\) | 21.1317 | 0.965531 | 0.482766 | − | 0.875750i | \(-0.339632\pi\) | ||||
0.482766 | + | 0.875750i | \(0.339632\pi\) | |||||||
\(480\) | −0.0361439 | −0.00164974 | ||||||||
\(481\) | −14.3798 | −0.655663 | ||||||||
\(482\) | 4.00142 | 0.182260 | ||||||||
\(483\) | −0.107647 | −0.00489812 | ||||||||
\(484\) | −4.92005 | −0.223639 | ||||||||
\(485\) | 13.6598 | 0.620261 | ||||||||
\(486\) | −0.975319 | −0.0442414 | ||||||||
\(487\) | 17.2003 | 0.779420 | 0.389710 | − | 0.920938i | \(-0.372575\pi\) | ||||
0.389710 | + | 0.920938i | \(0.372575\pi\) | |||||||
\(488\) | 13.6642 | 0.618549 | ||||||||
\(489\) | 0.573093 | 0.0259162 | ||||||||
\(490\) | −3.62392 | −0.163712 | ||||||||
\(491\) | −33.1374 | −1.49547 | −0.747734 | − | 0.663998i | \(-0.768858\pi\) | ||||
−0.747734 | + | 0.663998i | \(0.768858\pi\) | |||||||
\(492\) | −0.288451 | −0.0130044 | ||||||||
\(493\) | −22.2591 | −1.00250 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.39405 | 0.332338 | ||||||||
\(496\) | 3.50384 | 0.157327 | ||||||||
\(497\) | −10.7179 | −0.480762 | ||||||||
\(498\) | −0.225269 | −0.0100945 | ||||||||
\(499\) | −31.9699 | −1.43117 | −0.715584 | − | 0.698527i | \(-0.753839\pi\) | ||||
−0.715584 | + | 0.698527i | \(0.753839\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −0.492488 | −0.0220027 | ||||||||
\(502\) | −12.6687 | −0.565432 | ||||||||
\(503\) | −25.2415 | −1.12546 | −0.562732 | − | 0.826639i | \(-0.690250\pi\) | ||||
−0.562732 | + | 0.826639i | \(0.690250\pi\) | |||||||
\(504\) | −5.50983 | −0.245427 | ||||||||
\(505\) | −10.6583 | −0.474288 | ||||||||
\(506\) | −3.99679 | −0.177679 | ||||||||
\(507\) | 0.262879 | 0.0116749 | ||||||||
\(508\) | −12.9858 | −0.576152 | ||||||||
\(509\) | 17.0508 | 0.755763 | 0.377881 | − | 0.925854i | \(-0.376653\pi\) | ||||
0.377881 | + | 0.925854i | \(0.376653\pi\) | |||||||
\(510\) | −0.243682 | −0.0107904 | ||||||||
\(511\) | −0.937829 | −0.0414871 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.0448 | 0.575381 | ||||||||
\(515\) | 9.74930 | 0.429605 | ||||||||
\(516\) | −0.206542 | −0.00909250 | ||||||||
\(517\) | −30.8038 | −1.35475 | ||||||||
\(518\) | 11.0408 | 0.485104 | ||||||||
\(519\) | 0.435153 | 0.0191011 | ||||||||
\(520\) | −2.39309 | −0.104944 | ||||||||
\(521\) | 6.80513 | 0.298138 | 0.149069 | − | 0.988827i | \(-0.452372\pi\) | ||||
0.149069 | + | 0.988827i | \(0.452372\pi\) | |||||||
\(522\) | 9.90040 | 0.433329 | ||||||||
\(523\) | −5.22078 | −0.228289 | −0.114144 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114144 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(524\) | 8.92899 | 0.390065 | ||||||||
\(525\) | −0.0664112 | −0.00289842 | ||||||||
\(526\) | 28.2516 | 1.23183 | ||||||||
\(527\) | 23.6228 | 1.02903 | ||||||||
\(528\) | 0.0891221 | 0.00387854 | ||||||||
\(529\) | −20.3726 | −0.885766 | ||||||||
\(530\) | 1.92136 | 0.0834585 | ||||||||
\(531\) | −14.2557 | −0.618643 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.0984 | −0.827243 | ||||||||
\(534\) | 0.614517 | 0.0265928 | ||||||||
\(535\) | −13.2857 | −0.574393 | ||||||||
\(536\) | 3.71765 | 0.160578 | ||||||||
\(537\) | 0.580940 | 0.0250694 | ||||||||
\(538\) | −29.5432 | −1.27370 | ||||||||
\(539\) | 8.93570 | 0.384888 | ||||||||
\(540\) | 0.216816 | 0.00933029 | ||||||||
\(541\) | −26.1671 | −1.12501 | −0.562506 | − | 0.826793i | \(-0.690163\pi\) | ||||
−0.562506 | + | 0.826793i | \(0.690163\pi\) | |||||||
\(542\) | 27.0112 | 1.16023 | ||||||||
\(543\) | 0.207940 | 0.00892355 | ||||||||
\(544\) | 6.74198 | 0.289060 | ||||||||
\(545\) | −1.44392 | −0.0618508 | ||||||||
\(546\) | 0.158928 | 0.00680150 | ||||||||
\(547\) | −35.5365 | −1.51943 | −0.759715 | − | 0.650256i | \(-0.774662\pi\) | ||||
−0.759715 | + | 0.650256i | \(0.774662\pi\) | |||||||
\(548\) | 4.45359 | 0.190248 | ||||||||
\(549\) | −40.9747 | −1.74876 | ||||||||
\(550\) | −2.46576 | −0.105140 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.0585864 | −0.00249360 | ||||||||
\(553\) | −22.2978 | −0.948197 | ||||||||
\(554\) | −24.1778 | −1.02722 | ||||||||
\(555\) | −0.217185 | −0.00921897 | ||||||||
\(556\) | −1.21147 | −0.0513777 | ||||||||
\(557\) | 30.6913 | 1.30043 | 0.650216 | − | 0.759749i | \(-0.274678\pi\) | ||||
0.650216 | + | 0.759749i | \(0.274678\pi\) | |||||||
\(558\) | −10.5069 | −0.444794 | ||||||||
\(559\) | −13.6752 | −0.578398 | ||||||||
\(560\) | 1.83741 | 0.0776448 | ||||||||
\(561\) | 0.600859 | 0.0253683 | ||||||||
\(562\) | −2.40101 | −0.101281 | ||||||||
\(563\) | −31.2044 | −1.31511 | −0.657553 | − | 0.753408i | \(-0.728409\pi\) | ||||
−0.657553 | + | 0.753408i | \(0.728409\pi\) | |||||||
\(564\) | −0.451533 | −0.0190130 | ||||||||
\(565\) | 0.841529 | 0.0354034 | ||||||||
\(566\) | 8.15093 | 0.342609 | ||||||||
\(567\) | 16.5151 | 0.693569 | ||||||||
\(568\) | −5.83313 | −0.244753 | ||||||||
\(569\) | 20.6053 | 0.863820 | 0.431910 | − | 0.901917i | \(-0.357840\pi\) | ||||
0.431910 | + | 0.901917i | \(0.357840\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.38785 | 0.183626 | 0.0918129 | − | 0.995776i | \(-0.470734\pi\) | ||||
0.0918129 | + | 0.995776i | \(0.470734\pi\) | |||||||
\(572\) | 5.90078 | 0.246724 | ||||||||
\(573\) | 0.742614 | 0.0310231 | ||||||||
\(574\) | 14.6637 | 0.612051 | ||||||||
\(575\) | 1.62092 | 0.0675970 | ||||||||
\(576\) | −2.99869 | −0.124946 | ||||||||
\(577\) | 29.8821 | 1.24401 | 0.622004 | − | 0.783014i | \(-0.286319\pi\) | ||||
0.622004 | + | 0.783014i | \(0.286319\pi\) | |||||||
\(578\) | 28.4543 | 1.18354 | ||||||||
\(579\) | −0.452303 | −0.0187971 | ||||||||
\(580\) | −3.30157 | −0.137090 | ||||||||
\(581\) | 11.4518 | 0.475100 | ||||||||
\(582\) | −0.493720 | −0.0204653 | ||||||||
\(583\) | −4.73760 | −0.196211 | ||||||||
\(584\) | −0.510408 | −0.0211208 | ||||||||
\(585\) | 7.17615 | 0.296697 | ||||||||
\(586\) | −9.19756 | −0.379948 | ||||||||
\(587\) | 39.3798 | 1.62538 | 0.812689 | − | 0.582698i | \(-0.198003\pi\) | ||||
0.812689 | + | 0.582698i | \(0.198003\pi\) | |||||||
\(588\) | 0.130983 | 0.00540163 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 4.75396 | 0.195717 | ||||||||
\(591\) | −0.217712 | −0.00895546 | ||||||||
\(592\) | 6.00888 | 0.246964 | ||||||||
\(593\) | −40.1118 | −1.64719 | −0.823597 | − | 0.567176i | \(-0.808036\pi\) | ||||
−0.823597 | + | 0.567176i | \(0.808036\pi\) | |||||||
\(594\) | −0.534616 | −0.0219356 | ||||||||
\(595\) | 12.3878 | 0.507850 | ||||||||
\(596\) | 9.28405 | 0.380289 | ||||||||
\(597\) | −0.406747 | −0.0166470 | ||||||||
\(598\) | −3.87901 | −0.158624 | ||||||||
\(599\) | −31.4596 | −1.28540 | −0.642702 | − | 0.766116i | \(-0.722187\pi\) | ||||
−0.642702 | + | 0.766116i | \(0.722187\pi\) | |||||||
\(600\) | −0.0361439 | −0.00147557 | ||||||||
\(601\) | 34.4890 | 1.40684 | 0.703418 | − | 0.710777i | \(-0.251656\pi\) | ||||
0.703418 | + | 0.710777i | \(0.251656\pi\) | |||||||
\(602\) | 10.4998 | 0.427938 | ||||||||
\(603\) | −11.1481 | −0.453985 | ||||||||
\(604\) | 3.34570 | 0.136135 | ||||||||
\(605\) | −4.92005 | −0.200028 | ||||||||
\(606\) | 0.385232 | 0.0156490 | ||||||||
\(607\) | −12.9979 | −0.527568 | −0.263784 | − | 0.964582i | \(-0.584971\pi\) | ||||
−0.263784 | + | 0.964582i | \(0.584971\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.219261 | 0.00888492 | ||||||||
\(610\) | 13.6642 | 0.553247 | ||||||||
\(611\) | −29.8960 | −1.20946 | ||||||||
\(612\) | −20.2171 | −0.817229 | ||||||||
\(613\) | 8.71181 | 0.351867 | 0.175933 | − | 0.984402i | \(-0.443706\pi\) | ||||
0.175933 | + | 0.984402i | \(0.443706\pi\) | |||||||
\(614\) | 28.3472 | 1.14400 | ||||||||
\(615\) | −0.288451 | −0.0116315 | ||||||||
\(616\) | −4.53061 | −0.182543 | ||||||||
\(617\) | −24.3566 | −0.980559 | −0.490279 | − | 0.871565i | \(-0.663105\pi\) | ||||
−0.490279 | + | 0.871565i | \(0.663105\pi\) | |||||||
\(618\) | −0.352378 | −0.0141747 | ||||||||
\(619\) | 1.64497 | 0.0661168 | 0.0330584 | − | 0.999453i | \(-0.489475\pi\) | ||||
0.0330584 | + | 0.999453i | \(0.489475\pi\) | |||||||
\(620\) | 3.50384 | 0.140718 | ||||||||
\(621\) | 0.351442 | 0.0141029 | ||||||||
\(622\) | 17.4409 | 0.699315 | ||||||||
\(623\) | −31.2396 | −1.25159 | ||||||||
\(624\) | 0.0864957 | 0.00346260 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.1983 | −0.527510 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.05317 | 0.281452 | ||||||||
\(629\) | 40.5118 | 1.61531 | ||||||||
\(630\) | −5.50983 | −0.219517 | ||||||||
\(631\) | −43.4987 | −1.73166 | −0.865829 | − | 0.500341i | \(-0.833208\pi\) | ||||
−0.865829 | + | 0.500341i | \(0.833208\pi\) | |||||||
\(632\) | −12.1354 | −0.482721 | ||||||||
\(633\) | 0.508458 | 0.0202094 | ||||||||
\(634\) | 12.2864 | 0.487955 | ||||||||
\(635\) | −12.9858 | −0.515326 | ||||||||
\(636\) | −0.0694454 | −0.00275369 | ||||||||
\(637\) | 8.67237 | 0.343612 | ||||||||
\(638\) | 8.14087 | 0.322300 | ||||||||
\(639\) | 17.4918 | 0.691964 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 36.8215 | 1.45436 | 0.727181 | − | 0.686446i | \(-0.240830\pi\) | ||||
0.727181 | + | 0.686446i | \(0.240830\pi\) | |||||||
\(642\) | 0.480199 | 0.0189519 | ||||||||
\(643\) | −14.7356 | −0.581117 | −0.290558 | − | 0.956857i | \(-0.593841\pi\) | ||||
−0.290558 | + | 0.956857i | \(0.593841\pi\) | |||||||
\(644\) | 2.97829 | 0.117361 | ||||||||
\(645\) | −0.206542 | −0.00813258 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.04813 | −0.237776 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(648\) | 8.98824 | 0.353092 | ||||||||
\(649\) | −11.7221 | −0.460132 | ||||||||
\(650\) | −2.39309 | −0.0938648 | ||||||||
\(651\) | −0.232694 | −0.00912001 | ||||||||
\(652\) | −15.8559 | −0.620964 | ||||||||
\(653\) | −2.88867 | −0.113043 | −0.0565213 | − | 0.998401i | \(-0.518001\pi\) | ||||
−0.0565213 | + | 0.998401i | \(0.518001\pi\) | |||||||
\(654\) | 0.0521890 | 0.00204075 | ||||||||
\(655\) | 8.92899 | 0.348884 | ||||||||
\(656\) | 7.98063 | 0.311591 | ||||||||
\(657\) | 1.53056 | 0.0597127 | ||||||||
\(658\) | 22.9541 | 0.894845 | ||||||||
\(659\) | −16.3211 | −0.635779 | −0.317889 | − | 0.948128i | \(-0.602974\pi\) | ||||
−0.317889 | + | 0.948128i | \(0.602974\pi\) | |||||||
\(660\) | 0.0891221 | 0.00346907 | ||||||||
\(661\) | −28.5414 | −1.11013 | −0.555066 | − | 0.831806i | \(-0.687307\pi\) | ||||
−0.555066 | + | 0.831806i | \(0.687307\pi\) | |||||||
\(662\) | −0.996594 | −0.0387337 | ||||||||
\(663\) | 0.583152 | 0.0226478 | ||||||||
\(664\) | 6.23256 | 0.241870 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.0188 | −0.698214 | ||||||||
\(667\) | −5.35158 | −0.207214 | ||||||||
\(668\) | 13.6257 | 0.527196 | ||||||||
\(669\) | 0.914530 | 0.0353578 | ||||||||
\(670\) | 3.71765 | 0.143625 | ||||||||
\(671\) | −33.6926 | −1.30069 | ||||||||
\(672\) | −0.0664112 | −0.00256187 | ||||||||
\(673\) | −6.23447 | −0.240321 | −0.120161 | − | 0.992754i | \(-0.538341\pi\) | ||||
−0.120161 | + | 0.992754i | \(0.538341\pi\) | |||||||
\(674\) | −8.55919 | −0.329688 | ||||||||
\(675\) | 0.216816 | 0.00834526 | ||||||||
\(676\) | −7.27311 | −0.279735 | ||||||||
\(677\) | 14.6150 | 0.561700 | 0.280850 | − | 0.959752i | \(-0.409384\pi\) | ||||
0.280850 | + | 0.959752i | \(0.409384\pi\) | |||||||
\(678\) | −0.0304162 | −0.00116813 | ||||||||
\(679\) | 25.0987 | 0.963201 | ||||||||
\(680\) | 6.74198 | 0.258543 | ||||||||
\(681\) | 0.795568 | 0.0304862 | ||||||||
\(682\) | −8.63961 | −0.330828 | ||||||||
\(683\) | −47.0671 | −1.80097 | −0.900486 | − | 0.434885i | \(-0.856789\pi\) | ||||
−0.900486 | + | 0.434885i | \(0.856789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.45359 | 0.170163 | ||||||||
\(686\) | −19.5205 | −0.745297 | ||||||||
\(687\) | 0.191392 | 0.00730208 | ||||||||
\(688\) | 5.71443 | 0.217861 | ||||||||
\(689\) | −4.59799 | −0.175169 | ||||||||
\(690\) | −0.0585864 | −0.00223034 | ||||||||
\(691\) | −27.3484 | −1.04038 | −0.520191 | − | 0.854050i | \(-0.674139\pi\) | ||||
−0.520191 | + | 0.854050i | \(0.674139\pi\) | |||||||
\(692\) | −12.0395 | −0.457672 | ||||||||
\(693\) | 13.5859 | 0.516086 | ||||||||
\(694\) | −6.63773 | −0.251965 | ||||||||
\(695\) | −1.21147 | −0.0459536 | ||||||||
\(696\) | 0.119332 | 0.00452326 | ||||||||
\(697\) | 53.8053 | 2.03802 | ||||||||
\(698\) | 31.0443 | 1.17504 | ||||||||
\(699\) | −0.742822 | −0.0280961 | ||||||||
\(700\) | 1.83741 | 0.0694476 | ||||||||
\(701\) | 19.8319 | 0.749040 | 0.374520 | − | 0.927219i | \(-0.377808\pi\) | ||||
0.374520 | + | 0.927219i | \(0.377808\pi\) | |||||||
\(702\) | −0.518861 | −0.0195831 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.46576 | −0.0929317 | ||||||||
\(705\) | −0.451533 | −0.0170057 | ||||||||
\(706\) | 17.7629 | 0.668516 | ||||||||
\(707\) | −19.5837 | −0.736519 | ||||||||
\(708\) | −0.171827 | −0.00645764 | ||||||||
\(709\) | 32.7102 | 1.22846 | 0.614230 | − | 0.789127i | \(-0.289467\pi\) | ||||
0.614230 | + | 0.789127i | \(0.289467\pi\) | |||||||
\(710\) | −5.83313 | −0.218913 | ||||||||
\(711\) | 36.3904 | 1.36475 | ||||||||
\(712\) | −17.0020 | −0.637175 | ||||||||
\(713\) | 5.67944 | 0.212697 | ||||||||
\(714\) | −0.447743 | −0.0167564 | ||||||||
\(715\) | 5.90078 | 0.220677 | ||||||||
\(716\) | −16.0730 | −0.600675 | ||||||||
\(717\) | −0.0320658 | −0.00119752 | ||||||||
\(718\) | −5.13615 | −0.191680 | ||||||||
\(719\) | −3.24776 | −0.121121 | −0.0605606 | − | 0.998165i | \(-0.519289\pi\) | ||||
−0.0605606 | + | 0.998165i | \(0.519289\pi\) | |||||||
\(720\) | −2.99869 | −0.111755 | ||||||||
\(721\) | 17.9135 | 0.667132 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.144627 | −0.00537873 | ||||||||
\(724\) | −5.75310 | −0.213812 | ||||||||
\(725\) | −3.30157 | −0.122617 | ||||||||
\(726\) | 0.177830 | 0.00659988 | ||||||||
\(727\) | 19.4096 | 0.719862 | 0.359931 | − | 0.932979i | \(-0.382800\pi\) | ||||
0.359931 | + | 0.932979i | \(0.382800\pi\) | |||||||
\(728\) | −4.39709 | −0.162967 | ||||||||
\(729\) | −26.9295 | −0.997388 | ||||||||
\(730\) | −0.510408 | −0.0188910 | ||||||||
\(731\) | 38.5266 | 1.42496 | ||||||||
\(732\) | −0.493877 | −0.0182542 | ||||||||
\(733\) | 12.0753 | 0.446010 | 0.223005 | − | 0.974817i | \(-0.428413\pi\) | ||||
0.223005 | + | 0.974817i | \(0.428413\pi\) | |||||||
\(734\) | −5.74589 | −0.212085 | ||||||||
\(735\) | 0.130983 | 0.00483137 | ||||||||
\(736\) | 1.62092 | 0.0597479 | ||||||||
\(737\) | −9.16681 | −0.337664 | ||||||||
\(738\) | −23.9315 | −0.880930 | ||||||||
\(739\) | 3.04613 | 0.112054 | 0.0560268 | − | 0.998429i | \(-0.482157\pi\) | ||||
0.0560268 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(740\) | 6.00888 | 0.220891 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.53033 | 0.129602 | ||||||||
\(743\) | −39.7565 | −1.45853 | −0.729263 | − | 0.684234i | \(-0.760137\pi\) | ||||
−0.729263 | + | 0.684234i | \(0.760137\pi\) | |||||||
\(744\) | −0.126642 | −0.00464294 | ||||||||
\(745\) | 9.28405 | 0.340141 | ||||||||
\(746\) | −37.7854 | −1.38342 | ||||||||
\(747\) | −18.6895 | −0.683814 | ||||||||
\(748\) | −16.6241 | −0.607837 | ||||||||
\(749\) | −24.4114 | −0.891972 | ||||||||
\(750\) | −0.0361439 | −0.00131979 | ||||||||
\(751\) | −35.7867 | −1.30588 | −0.652938 | − | 0.757411i | \(-0.726464\pi\) | ||||
−0.652938 | + | 0.757411i | \(0.726464\pi\) | |||||||
\(752\) | 12.4926 | 0.455560 | ||||||||
\(753\) | 0.457897 | 0.0166867 | ||||||||
\(754\) | 7.90096 | 0.287736 | ||||||||
\(755\) | 3.34570 | 0.121763 | ||||||||
\(756\) | 0.398381 | 0.0144890 | ||||||||
\(757\) | −49.9062 | −1.81387 | −0.906936 | − | 0.421267i | \(-0.861585\pi\) | ||||
−0.906936 | + | 0.421267i | \(0.861585\pi\) | |||||||
\(758\) | 32.2663 | 1.17196 | ||||||||
\(759\) | 0.144460 | 0.00524355 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.2563 | −1.31429 | −0.657145 | − | 0.753764i | \(-0.728236\pi\) | ||||
−0.657145 | + | 0.753764i | \(0.728236\pi\) | |||||||
\(762\) | 0.469358 | 0.0170030 | ||||||||
\(763\) | −2.65308 | −0.0960478 | ||||||||
\(764\) | −20.5460 | −0.743329 | ||||||||
\(765\) | −20.2171 | −0.730952 | ||||||||
\(766\) | 21.7799 | 0.786939 | ||||||||
\(767\) | −11.3767 | −0.410787 | ||||||||
\(768\) | −0.0361439 | −0.00130423 | ||||||||
\(769\) | −5.51540 | −0.198891 | −0.0994453 | − | 0.995043i | \(-0.531707\pi\) | ||||
−0.0994453 | + | 0.995043i | \(0.531707\pi\) | |||||||
\(770\) | −4.53061 | −0.163272 | ||||||||
\(771\) | −0.471490 | −0.0169803 | ||||||||
\(772\) | 12.5139 | 0.450387 | ||||||||
\(773\) | 38.3992 | 1.38112 | 0.690562 | − | 0.723273i | \(-0.257363\pi\) | ||||
0.690562 | + | 0.723273i | \(0.257363\pi\) | |||||||
\(774\) | −17.1358 | −0.615935 | ||||||||
\(775\) | 3.50384 | 0.125862 | ||||||||
\(776\) | 13.6598 | 0.490359 | ||||||||
\(777\) | −0.399057 | −0.0143161 | ||||||||
\(778\) | 9.68485 | 0.347219 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.0864957 | 0.00309704 | ||||||||
\(781\) | 14.3831 | 0.514667 | ||||||||
\(782\) | 10.9282 | 0.390792 | ||||||||
\(783\) | −0.715834 | −0.0255818 | ||||||||
\(784\) | −3.62392 | −0.129426 | ||||||||
\(785\) | 7.05317 | 0.251738 | ||||||||
\(786\) | −0.322729 | −0.0115113 | ||||||||
\(787\) | −3.12058 | −0.111237 | −0.0556184 | − | 0.998452i | \(-0.517713\pi\) | ||||
−0.0556184 | + | 0.998452i | \(0.517713\pi\) | |||||||
\(788\) | 6.02346 | 0.214577 | ||||||||
\(789\) | −1.02112 | −0.0363529 | ||||||||
\(790\) | −12.1354 | −0.431759 | ||||||||
\(791\) | 1.54624 | 0.0549778 | ||||||||
\(792\) | 7.39405 | 0.262736 | ||||||||
\(793\) | −32.6997 | −1.16120 | ||||||||
\(794\) | −18.3952 | −0.652819 | ||||||||
\(795\) | −0.0694454 | −0.00246298 | ||||||||
\(796\) | 11.2535 | 0.398871 | ||||||||
\(797\) | 0.491495 | 0.0174096 | 0.00870482 | − | 0.999962i | \(-0.497229\pi\) | ||||
0.00870482 | + | 0.999962i | \(0.497229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 84.2252 | 2.97967 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 50.9837 | 1.80142 | ||||||||
\(802\) | 36.5367 | 1.29015 | ||||||||
\(803\) | 1.25854 | 0.0444129 | ||||||||
\(804\) | −0.134370 | −0.00473887 | ||||||||
\(805\) | 2.97829 | 0.104971 | ||||||||
\(806\) | −8.38501 | −0.295349 | ||||||||
\(807\) | 1.06781 | 0.0375886 | ||||||||
\(808\) | −10.6583 | −0.374957 | ||||||||
\(809\) | 33.6552 | 1.18326 | 0.591628 | − | 0.806211i | \(-0.298486\pi\) | ||||
0.591628 | + | 0.806211i | \(0.298486\pi\) | |||||||
\(810\) | 8.98824 | 0.315815 | ||||||||
\(811\) | 48.1108 | 1.68940 | 0.844699 | − | 0.535242i | \(-0.179780\pi\) | ||||
0.844699 | + | 0.535242i | \(0.179780\pi\) | |||||||
\(812\) | −6.06634 | −0.212887 | ||||||||
\(813\) | −0.976289 | −0.0342400 | ||||||||
\(814\) | −14.8164 | −0.519316 | ||||||||
\(815\) | −15.8559 | −0.555407 | ||||||||
\(816\) | −0.243682 | −0.00853056 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −36.3063 | −1.26942 | ||||||||
\(819\) | 13.1855 | 0.460740 | ||||||||
\(820\) | 7.98063 | 0.278696 | ||||||||
\(821\) | −1.89435 | −0.0661131 | −0.0330566 | − | 0.999453i | \(-0.510524\pi\) | ||||
−0.0330566 | + | 0.999453i | \(0.510524\pi\) | |||||||
\(822\) | −0.160970 | −0.00561448 | ||||||||
\(823\) | −26.5567 | −0.925707 | −0.462853 | − | 0.886435i | \(-0.653174\pi\) | ||||
−0.462853 | + | 0.886435i | \(0.653174\pi\) | |||||||
\(824\) | 9.74930 | 0.339633 | ||||||||
\(825\) | 0.0891221 | 0.00310283 | ||||||||
\(826\) | 8.73497 | 0.303929 | ||||||||
\(827\) | −25.7977 | −0.897075 | −0.448537 | − | 0.893764i | \(-0.648055\pi\) | ||||
−0.448537 | + | 0.893764i | \(0.648055\pi\) | |||||||
\(828\) | −4.86064 | −0.168919 | ||||||||
\(829\) | 27.9638 | 0.971221 | 0.485611 | − | 0.874175i | \(-0.338597\pi\) | ||||
0.485611 | + | 0.874175i | \(0.338597\pi\) | |||||||
\(830\) | 6.23256 | 0.216335 | ||||||||
\(831\) | 0.873881 | 0.0303146 | ||||||||
\(832\) | −2.39309 | −0.0829655 | ||||||||
\(833\) | −24.4324 | −0.846533 | ||||||||
\(834\) | 0.0437872 | 0.00151623 | ||||||||
\(835\) | 13.6257 | 0.471539 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.759689 | 0.0262587 | ||||||||
\(838\) | 39.5001 | 1.36451 | ||||||||
\(839\) | −49.9183 | −1.72337 | −0.861685 | − | 0.507443i | \(-0.830591\pi\) | ||||
−0.861685 | + | 0.507443i | \(0.830591\pi\) | |||||||
\(840\) | −0.0664112 | −0.00229140 | ||||||||
\(841\) | −18.0996 | −0.624125 | ||||||||
\(842\) | 14.1005 | 0.485936 | ||||||||
\(843\) | 0.0867820 | 0.00298893 | ||||||||
\(844\) | −14.0676 | −0.484227 | ||||||||
\(845\) | −7.27311 | −0.250203 | ||||||||
\(846\) | −37.4616 | −1.28796 | ||||||||
\(847\) | −9.04015 | −0.310623 | ||||||||
\(848\) | 1.92136 | 0.0659798 | ||||||||
\(849\) | −0.294607 | −0.0101109 | ||||||||
\(850\) | 6.74198 | 0.231248 | ||||||||
\(851\) | 9.73991 | 0.333880 | ||||||||
\(852\) | 0.210832 | 0.00722299 | ||||||||
\(853\) | −7.95618 | −0.272415 | −0.136207 | − | 0.990680i | \(-0.543491\pi\) | ||||
−0.136207 | + | 0.990680i | \(0.543491\pi\) | |||||||
\(854\) | 25.1067 | 0.859135 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.2857 | −0.454097 | ||||||||
\(857\) | 25.1550 | 0.859277 | 0.429638 | − | 0.903001i | \(-0.358641\pi\) | ||||
0.429638 | + | 0.903001i | \(0.358641\pi\) | |||||||
\(858\) | −0.213277 | −0.00728116 | ||||||||
\(859\) | 3.46880 | 0.118354 | 0.0591769 | − | 0.998248i | \(-0.481152\pi\) | ||||
0.0591769 | + | 0.998248i | \(0.481152\pi\) | |||||||
\(860\) | 5.71443 | 0.194861 | ||||||||
\(861\) | −0.530004 | −0.0180625 | ||||||||
\(862\) | −21.0431 | −0.716732 | ||||||||
\(863\) | 40.9708 | 1.39466 | 0.697331 | − | 0.716750i | \(-0.254371\pi\) | ||||
0.697331 | + | 0.716750i | \(0.254371\pi\) | |||||||
\(864\) | 0.216816 | 0.00737624 | ||||||||
\(865\) | −12.0395 | −0.409354 | ||||||||
\(866\) | 5.25769 | 0.178664 | ||||||||
\(867\) | −1.02845 | −0.0349280 | ||||||||
\(868\) | 6.43799 | 0.218520 | ||||||||
\(869\) | 29.9230 | 1.01507 | ||||||||
\(870\) | 0.119332 | 0.00404572 | ||||||||
\(871\) | −8.89666 | −0.301452 | ||||||||
\(872\) | −1.44392 | −0.0488973 | ||||||||
\(873\) | −40.9616 | −1.38634 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.83741 | 0.0621158 | ||||||||
\(876\) | 0.0184481 | 0.000623305 0 | ||||||||
\(877\) | 24.8602 | 0.839469 | 0.419735 | − | 0.907647i | \(-0.362123\pi\) | ||||
0.419735 | + | 0.907647i | \(0.362123\pi\) | |||||||
\(878\) | −36.4838 | −1.23127 | ||||||||
\(879\) | 0.332436 | 0.0112128 | ||||||||
\(880\) | −2.46576 | −0.0831206 | ||||||||
\(881\) | −15.7411 | −0.530332 | −0.265166 | − | 0.964203i | \(-0.585427\pi\) | ||||
−0.265166 | + | 0.964203i | \(0.585427\pi\) | |||||||
\(882\) | 10.8670 | 0.365912 | ||||||||
\(883\) | −7.75970 | −0.261135 | −0.130567 | − | 0.991439i | \(-0.541680\pi\) | ||||
−0.130567 | + | 0.991439i | \(0.541680\pi\) | |||||||
\(884\) | −16.1342 | −0.542651 | ||||||||
\(885\) | −0.171827 | −0.00577589 | ||||||||
\(886\) | −9.23069 | −0.310111 | ||||||||
\(887\) | −34.0594 | −1.14360 | −0.571802 | − | 0.820392i | \(-0.693755\pi\) | ||||
−0.571802 | + | 0.820392i | \(0.693755\pi\) | |||||||
\(888\) | −0.217185 | −0.00728824 | ||||||||
\(889\) | −23.8603 | −0.800247 | ||||||||
\(890\) | −17.0020 | −0.569907 | ||||||||
\(891\) | −22.1628 | −0.742482 | ||||||||
\(892\) | −25.3025 | −0.847189 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.335562 | −0.0112229 | ||||||||
\(895\) | −16.0730 | −0.537260 | ||||||||
\(896\) | 1.83741 | 0.0613836 | ||||||||
\(897\) | 0.140203 | 0.00468123 | ||||||||
\(898\) | 22.8297 | 0.761836 | ||||||||
\(899\) | −11.5682 | −0.385820 | ||||||||
\(900\) | −2.99869 | −0.0999565 | ||||||||
\(901\) | 12.9538 | 0.431553 | ||||||||
\(902\) | −19.6783 | −0.655216 | ||||||||
\(903\) | −0.379503 | −0.0126291 | ||||||||
\(904\) | 0.841529 | 0.0279888 | ||||||||
\(905\) | −5.75310 | −0.191240 | ||||||||
\(906\) | −0.120927 | −0.00401752 | ||||||||
\(907\) | −4.80756 | −0.159633 | −0.0798163 | − | 0.996810i | \(-0.525433\pi\) | ||||
−0.0798163 | + | 0.996810i | \(0.525433\pi\) | |||||||
\(908\) | −22.0111 | −0.730464 | ||||||||
\(909\) | 31.9609 | 1.06008 | ||||||||
\(910\) | −4.39709 | −0.145762 | ||||||||
\(911\) | −9.14462 | −0.302975 | −0.151487 | − | 0.988459i | \(-0.548406\pi\) | ||||
−0.151487 | + | 0.988459i | \(0.548406\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.3680 | −0.508606 | ||||||||
\(914\) | −7.82515 | −0.258833 | ||||||||
\(915\) | −0.493877 | −0.0163271 | ||||||||
\(916\) | −5.29529 | −0.174961 | ||||||||
\(917\) | 16.4062 | 0.541781 | ||||||||
\(918\) | 1.46177 | 0.0482456 | ||||||||
\(919\) | −21.0816 | −0.695419 | −0.347709 | − | 0.937602i | \(-0.613040\pi\) | ||||
−0.347709 | + | 0.937602i | \(0.613040\pi\) | |||||||
\(920\) | 1.62092 | 0.0534401 | ||||||||
\(921\) | −1.02458 | −0.0337610 | ||||||||
\(922\) | −3.93168 | −0.129483 | ||||||||
\(923\) | 13.9592 | 0.459473 | ||||||||
\(924\) | 0.163754 | 0.00538711 | ||||||||
\(925\) | 6.00888 | 0.197571 | ||||||||
\(926\) | −17.2964 | −0.568395 | ||||||||
\(927\) | −29.2352 | −0.960209 | ||||||||
\(928\) | −3.30157 | −0.108379 | ||||||||
\(929\) | 18.8119 | 0.617200 | 0.308600 | − | 0.951192i | \(-0.400140\pi\) | ||||
0.308600 | + | 0.951192i | \(0.400140\pi\) | |||||||
\(930\) | −0.126642 | −0.00415277 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.5518 | 0.673196 | ||||||||
\(933\) | −0.630381 | −0.0206377 | ||||||||
\(934\) | −21.0267 | −0.688016 | ||||||||
\(935\) | −16.6241 | −0.543666 | ||||||||
\(936\) | 7.17615 | 0.234560 | ||||||||
\(937\) | −19.2143 | −0.627704 | −0.313852 | − | 0.949472i | \(-0.601620\pi\) | ||||
−0.313852 | + | 0.949472i | \(0.601620\pi\) | |||||||
\(938\) | 6.83084 | 0.223035 | ||||||||
\(939\) | 0.477038 | 0.0155676 | ||||||||
\(940\) | 12.4926 | 0.407465 | ||||||||
\(941\) | −15.5583 | −0.507185 | −0.253593 | − | 0.967311i | \(-0.581612\pi\) | ||||
−0.253593 | + | 0.967311i | \(0.581612\pi\) | |||||||
\(942\) | −0.254929 | −0.00830604 | ||||||||
\(943\) | 12.9360 | 0.421253 | ||||||||
\(944\) | 4.75396 | 0.154728 | ||||||||
\(945\) | 0.398381 | 0.0129593 | ||||||||
\(946\) | −14.0904 | −0.458118 | ||||||||
\(947\) | −22.1758 | −0.720618 | −0.360309 | − | 0.932833i | \(-0.617329\pi\) | ||||
−0.360309 | + | 0.932833i | \(0.617329\pi\) | |||||||
\(948\) | 0.438622 | 0.0142458 | ||||||||
\(949\) | 1.22145 | 0.0396500 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.444078 | −0.0144002 | ||||||||
\(952\) | 12.3878 | 0.401491 | ||||||||
\(953\) | 4.95575 | 0.160532 | 0.0802662 | − | 0.996773i | \(-0.474423\pi\) | ||||
0.0802662 | + | 0.996773i | \(0.474423\pi\) | |||||||
\(954\) | −5.76157 | −0.186538 | ||||||||
\(955\) | −20.5460 | −0.664854 | ||||||||
\(956\) | 0.887170 | 0.0286931 | ||||||||
\(957\) | −0.294243 | −0.00951152 | ||||||||
\(958\) | 21.1317 | 0.682734 | ||||||||
\(959\) | 8.18308 | 0.264245 | ||||||||
\(960\) | −0.0361439 | −0.00116654 | ||||||||
\(961\) | −18.7231 | −0.603971 | ||||||||
\(962\) | −14.3798 | −0.463624 | ||||||||
\(963\) | 39.8399 | 1.28382 | ||||||||
\(964\) | 4.00142 | 0.128877 | ||||||||
\(965\) | 12.5139 | 0.402838 | ||||||||
\(966\) | −0.107647 | −0.00346349 | ||||||||
\(967\) | −17.2293 | −0.554056 | −0.277028 | − | 0.960862i | \(-0.589349\pi\) | ||||
−0.277028 | + | 0.960862i | \(0.589349\pi\) | |||||||
\(968\) | −4.92005 | −0.158136 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.6598 | 0.438591 | ||||||||
\(971\) | 3.80331 | 0.122054 | 0.0610270 | − | 0.998136i | \(-0.480562\pi\) | ||||
0.0610270 | + | 0.998136i | \(0.480562\pi\) | |||||||
\(972\) | −0.975319 | −0.0312834 | ||||||||
\(973\) | −2.22597 | −0.0713612 | ||||||||
\(974\) | 17.2003 | 0.551133 | ||||||||
\(975\) | 0.0864957 | 0.00277008 | ||||||||
\(976\) | 13.6642 | 0.437380 | ||||||||
\(977\) | 61.7916 | 1.97689 | 0.988445 | − | 0.151582i | \(-0.0484366\pi\) | ||||
0.988445 | + | 0.151582i | \(0.0484366\pi\) | |||||||
\(978\) | 0.573093 | 0.0183255 | ||||||||
\(979\) | 41.9227 | 1.33985 | ||||||||
\(980\) | −3.62392 | −0.115762 | ||||||||
\(981\) | 4.32988 | 0.138242 | ||||||||
\(982\) | −33.1374 | −1.05746 | ||||||||
\(983\) | 11.9175 | 0.380109 | 0.190055 | − | 0.981774i | \(-0.439133\pi\) | ||||
0.190055 | + | 0.981774i | \(0.439133\pi\) | |||||||
\(984\) | −0.288451 | −0.00919549 | ||||||||
\(985\) | 6.02346 | 0.191924 | ||||||||
\(986\) | −22.2591 | −0.708875 | ||||||||
\(987\) | −0.829652 | −0.0264081 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.26263 | 0.294535 | ||||||||
\(990\) | 7.39405 | 0.234998 | ||||||||
\(991\) | −16.1454 | −0.512874 | −0.256437 | − | 0.966561i | \(-0.582549\pi\) | ||||
−0.256437 | + | 0.966561i | \(0.582549\pi\) | |||||||
\(992\) | 3.50384 | 0.111247 | ||||||||
\(993\) | 0.0360208 | 0.00114309 | ||||||||
\(994\) | −10.7179 | −0.339950 | ||||||||
\(995\) | 11.2535 | 0.356761 | ||||||||
\(996\) | −0.225269 | −0.00713792 | ||||||||
\(997\) | −42.5330 | −1.34703 | −0.673517 | − | 0.739172i | \(-0.735217\pi\) | ||||
−0.673517 | + | 0.739172i | \(0.735217\pi\) | |||||||
\(998\) | −31.9699 | −1.01199 | ||||||||
\(999\) | 1.30282 | 0.0412195 |
(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 | 3610.2.a.bj.1.5 | 9 | ||
19.2 | odd | 18 | 190.2.k.d.61.2 | ✓ | 18 | ||
19.10 | odd | 18 | 190.2.k.d.81.2 | yes | 18 | ||
19.18 | odd | 2 | 3610.2.a.bi.1.5 | 9 | |||
95.2 | even | 36 | 950.2.u.g.99.2 | 36 | |||
95.29 | odd | 18 | 950.2.l.i.651.2 | 18 | |||
95.48 | even | 36 | 950.2.u.g.499.2 | 36 | |||
95.59 | odd | 18 | 950.2.l.i.251.2 | 18 | |||
95.67 | even | 36 | 950.2.u.g.499.5 | 36 | |||
95.78 | even | 36 | 950.2.u.g.99.5 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.d.61.2 | ✓ | 18 | 19.2 | odd | 18 | ||
190.2.k.d.81.2 | yes | 18 | 19.10 | odd | 18 | ||
950.2.l.i.251.2 | 18 | 95.59 | odd | 18 | |||
950.2.l.i.651.2 | 18 | 95.29 | odd | 18 | |||
950.2.u.g.99.2 | 36 | 95.2 | even | 36 | |||
950.2.u.g.99.5 | 36 | 95.78 | even | 36 | |||
950.2.u.g.499.2 | 36 | 95.48 | even | 36 | |||
950.2.u.g.499.5 | 36 | 95.67 | even | 36 | |||
3610.2.a.bi.1.5 | 9 | 19.18 | odd | 2 | |||
3610.2.a.bj.1.5 | 9 | 1.1 | even | 1 | trivial |