Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 6x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.48008\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86205 | 1.31667 | 0.658334 | − | 0.752726i | \(-0.271262\pi\) | ||||
0.658334 | + | 0.752726i | \(0.271262\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.46722 | 0.733612 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.86205 | −0.760178 | ||||||||
\(7\) | 2.63089 | 0.994384 | 0.497192 | − | 0.867641i | \(-0.334365\pi\) | ||||
0.497192 | + | 0.867641i | \(0.334365\pi\) | |||||||
\(8\) | −0.992053 | −0.350744 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.86205 | −0.588831 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.46722 | −0.423551 | ||||||||
\(13\) | −6.48008 | −1.79725 | −0.898626 | − | 0.438716i | \(-0.855433\pi\) | ||||
−0.898626 | + | 0.438716i | \(0.855433\pi\) | |||||||
\(14\) | 4.89885 | 1.30927 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.78170 | −1.19543 | ||||||||
\(17\) | −4.72410 | −1.14576 | −0.572881 | − | 0.819639i | \(-0.694174\pi\) | ||||
−0.572881 | + | 0.819639i | \(0.694174\pi\) | |||||||
\(18\) | 1.86205 | 0.438889 | ||||||||
\(19\) | 0.532775 | 0.122227 | 0.0611135 | − | 0.998131i | \(-0.480535\pi\) | ||||
0.0611135 | + | 0.998131i | \(0.480535\pi\) | |||||||
\(20\) | −1.46722 | −0.328081 | ||||||||
\(21\) | −2.63089 | −0.574108 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.54563 | −0.947830 | −0.473915 | − | 0.880571i | \(-0.657160\pi\) | ||||
−0.473915 | + | 0.880571i | \(0.657160\pi\) | |||||||
\(24\) | 0.992053 | 0.202502 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −12.0662 | −2.36638 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.86011 | 0.729492 | ||||||||
\(29\) | 10.6229 | 1.97263 | 0.986316 | − | 0.164868i | \(-0.0527197\pi\) | ||||
0.986316 | + | 0.164868i | \(0.0527197\pi\) | |||||||
\(30\) | 1.86205 | 0.339962 | ||||||||
\(31\) | 0.190644 | 0.0342407 | 0.0171204 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171204 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(32\) | −6.91965 | −1.22323 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.79650 | −1.50859 | ||||||||
\(35\) | −2.63089 | −0.444702 | ||||||||
\(36\) | 1.46722 | 0.244537 | ||||||||
\(37\) | −4.22812 | −0.695099 | −0.347549 | − | 0.937662i | \(-0.612986\pi\) | ||||
−0.347549 | + | 0.937662i | \(0.612986\pi\) | |||||||
\(38\) | 0.992053 | 0.160932 | ||||||||
\(39\) | 6.48008 | 1.03764 | ||||||||
\(40\) | 0.992053 | 0.156857 | ||||||||
\(41\) | −0.605176 | −0.0945126 | −0.0472563 | − | 0.998883i | \(-0.515048\pi\) | ||||
−0.0472563 | + | 0.998883i | \(0.515048\pi\) | |||||||
\(42\) | −4.89885 | −0.755909 | ||||||||
\(43\) | −9.24893 | −1.41045 | −0.705224 | − | 0.708985i | \(-0.749154\pi\) | ||||
−0.705224 | + | 0.708985i | \(0.749154\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −8.46419 | −1.24798 | ||||||||
\(47\) | −8.82712 | −1.28757 | −0.643784 | − | 0.765207i | \(-0.722637\pi\) | ||||
−0.643784 | + | 0.765207i | \(0.722637\pi\) | |||||||
\(48\) | 4.78170 | 0.690179 | ||||||||
\(49\) | −0.0784084 | −0.0112012 | ||||||||
\(50\) | 1.86205 | 0.263333 | ||||||||
\(51\) | 4.72410 | 0.661506 | ||||||||
\(52\) | −9.50774 | −1.31849 | ||||||||
\(53\) | 6.69644 | 0.919827 | 0.459914 | − | 0.887964i | \(-0.347880\pi\) | ||||
0.459914 | + | 0.887964i | \(0.347880\pi\) | |||||||
\(54\) | −1.86205 | −0.253393 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.60999 | −0.348774 | ||||||||
\(57\) | −0.532775 | −0.0705678 | ||||||||
\(58\) | 19.7804 | 2.59730 | ||||||||
\(59\) | −5.92760 | −0.771708 | −0.385854 | − | 0.922560i | \(-0.626093\pi\) | ||||
−0.385854 | + | 0.922560i | \(0.626093\pi\) | |||||||
\(60\) | 1.46722 | 0.189418 | ||||||||
\(61\) | −3.21636 | −0.411813 | −0.205906 | − | 0.978572i | \(-0.566014\pi\) | ||||
−0.205906 | + | 0.978572i | \(0.566014\pi\) | |||||||
\(62\) | 0.354989 | 0.0450836 | ||||||||
\(63\) | 2.63089 | 0.331461 | ||||||||
\(64\) | −3.32133 | −0.415166 | ||||||||
\(65\) | 6.48008 | 0.803755 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.22812 | 0.638717 | 0.319358 | − | 0.947634i | \(-0.396533\pi\) | ||||
0.319358 | + | 0.947634i | \(0.396533\pi\) | |||||||
\(68\) | −6.93131 | −0.840545 | ||||||||
\(69\) | 4.54563 | 0.547230 | ||||||||
\(70\) | −4.89885 | −0.585524 | ||||||||
\(71\) | −2.74381 | −0.325630 | −0.162815 | − | 0.986657i | \(-0.552057\pi\) | ||||
−0.162815 | + | 0.986657i | \(0.552057\pi\) | |||||||
\(72\) | −0.992053 | −0.116915 | ||||||||
\(73\) | −15.6756 | −1.83469 | −0.917347 | − | 0.398088i | \(-0.869674\pi\) | ||||
−0.917347 | + | 0.398088i | \(0.869674\pi\) | |||||||
\(74\) | −7.87297 | −0.915214 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0.781701 | 0.0896673 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.0662 | 1.36623 | ||||||||
\(79\) | 1.21103 | 0.136252 | 0.0681258 | − | 0.997677i | \(-0.478298\pi\) | ||||
0.0681258 | + | 0.997677i | \(0.478298\pi\) | |||||||
\(80\) | 4.78170 | 0.534610 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.12687 | −0.124442 | ||||||||
\(83\) | 4.66278 | 0.511807 | 0.255903 | − | 0.966702i | \(-0.417627\pi\) | ||||
0.255903 | + | 0.966702i | \(0.417627\pi\) | |||||||
\(84\) | −3.86011 | −0.421172 | ||||||||
\(85\) | 4.72410 | 0.512400 | ||||||||
\(86\) | −17.2219 | −1.85709 | ||||||||
\(87\) | −10.6229 | −1.13890 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.40768 | 0.679213 | 0.339606 | − | 0.940568i | \(-0.389706\pi\) | ||||
0.339606 | + | 0.940568i | \(0.389706\pi\) | |||||||
\(90\) | −1.86205 | −0.196277 | ||||||||
\(91\) | −17.0484 | −1.78716 | ||||||||
\(92\) | −6.66947 | −0.695340 | ||||||||
\(93\) | −0.190644 | −0.0197689 | ||||||||
\(94\) | −16.4365 | −1.69530 | ||||||||
\(95\) | −0.532775 | −0.0546616 | ||||||||
\(96\) | 6.91965 | 0.706234 | ||||||||
\(97\) | −7.32927 | −0.744175 | −0.372087 | − | 0.928198i | \(-0.621358\pi\) | ||||
−0.372087 | + | 0.928198i | \(0.621358\pi\) | |||||||
\(98\) | −0.146000 | −0.0147482 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.46722 | 0.146722 | ||||||||
\(101\) | 11.3599 | 1.13035 | 0.565176 | − | 0.824970i | \(-0.308808\pi\) | ||||
0.565176 | + | 0.824970i | \(0.308808\pi\) | |||||||
\(102\) | 8.79650 | 0.870983 | ||||||||
\(103\) | −2.06064 | −0.203041 | −0.101520 | − | 0.994833i | \(-0.532371\pi\) | ||||
−0.101520 | + | 0.994833i | \(0.532371\pi\) | |||||||
\(104\) | 6.42859 | 0.630375 | ||||||||
\(105\) | 2.63089 | 0.256749 | ||||||||
\(106\) | 12.4691 | 1.21111 | ||||||||
\(107\) | 1.14971 | 0.111147 | 0.0555735 | − | 0.998455i | \(-0.482301\pi\) | ||||
0.0555735 | + | 0.998455i | \(0.482301\pi\) | |||||||
\(108\) | −1.46722 | −0.141184 | ||||||||
\(109\) | −13.3402 | −1.27776 | −0.638879 | − | 0.769307i | \(-0.720602\pi\) | ||||
−0.638879 | + | 0.769307i | \(0.720602\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.22812 | 0.401316 | ||||||||
\(112\) | −12.5801 | −1.18871 | ||||||||
\(113\) | 6.29738 | 0.592408 | 0.296204 | − | 0.955125i | \(-0.404279\pi\) | ||||
0.296204 | + | 0.955125i | \(0.404279\pi\) | |||||||
\(114\) | −0.992053 | −0.0929143 | ||||||||
\(115\) | 4.54563 | 0.423882 | ||||||||
\(116\) | 15.5862 | 1.44715 | ||||||||
\(117\) | −6.48008 | −0.599084 | ||||||||
\(118\) | −11.0375 | −1.01608 | ||||||||
\(119\) | −12.4286 | −1.13933 | ||||||||
\(120\) | −0.992053 | −0.0905617 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −5.98902 | −0.542220 | ||||||||
\(123\) | 0.605176 | 0.0545669 | ||||||||
\(124\) | 0.279718 | 0.0251194 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.89885 | 0.436424 | ||||||||
\(127\) | −10.0943 | −0.895724 | −0.447862 | − | 0.894103i | \(-0.647814\pi\) | ||||
−0.447862 | + | 0.894103i | \(0.647814\pi\) | |||||||
\(128\) | 7.65483 | 0.676598 | ||||||||
\(129\) | 9.24893 | 0.814323 | ||||||||
\(130\) | 12.0662 | 1.05828 | ||||||||
\(131\) | −4.64756 | −0.406060 | −0.203030 | − | 0.979173i | \(-0.565079\pi\) | ||||
−0.203030 | + | 0.979173i | \(0.565079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.40167 | 0.121541 | ||||||||
\(134\) | 9.73502 | 0.840977 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 4.68656 | 0.401869 | ||||||||
\(137\) | 15.7676 | 1.34712 | 0.673558 | − | 0.739135i | \(-0.264765\pi\) | ||||
0.673558 | + | 0.739135i | \(0.264765\pi\) | |||||||
\(138\) | 8.46419 | 0.720520 | ||||||||
\(139\) | 10.0386 | 0.851461 | 0.425730 | − | 0.904850i | \(-0.360017\pi\) | ||||
0.425730 | + | 0.904850i | \(0.360017\pi\) | |||||||
\(140\) | −3.86011 | −0.326239 | ||||||||
\(141\) | 8.82712 | 0.743378 | ||||||||
\(142\) | −5.10910 | −0.428746 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.78170 | −0.398475 | ||||||||
\(145\) | −10.6229 | −0.882188 | ||||||||
\(146\) | −29.1888 | −2.41568 | ||||||||
\(147\) | 0.0784084 | 0.00646701 | ||||||||
\(148\) | −6.20360 | −0.509933 | ||||||||
\(149\) | −10.4653 | −0.857350 | −0.428675 | − | 0.903459i | \(-0.641019\pi\) | ||||
−0.428675 | + | 0.903459i | \(0.641019\pi\) | |||||||
\(150\) | −1.86205 | −0.152036 | ||||||||
\(151\) | −15.6433 | −1.27304 | −0.636518 | − | 0.771262i | \(-0.719626\pi\) | ||||
−0.636518 | + | 0.771262i | \(0.719626\pi\) | |||||||
\(152\) | −0.528542 | −0.0428704 | ||||||||
\(153\) | −4.72410 | −0.381921 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.190644 | −0.0153129 | ||||||||
\(156\) | 9.50774 | 0.761228 | ||||||||
\(157\) | 8.98970 | 0.717456 | 0.358728 | − | 0.933442i | \(-0.383211\pi\) | ||||
0.358728 | + | 0.933442i | \(0.383211\pi\) | |||||||
\(158\) | 2.25500 | 0.179398 | ||||||||
\(159\) | −6.69644 | −0.531062 | ||||||||
\(160\) | 6.91965 | 0.547047 | ||||||||
\(161\) | −11.9591 | −0.942507 | ||||||||
\(162\) | 1.86205 | 0.146296 | ||||||||
\(163\) | 19.8400 | 1.55399 | 0.776994 | − | 0.629508i | \(-0.216744\pi\) | ||||
0.776994 | + | 0.629508i | \(0.216744\pi\) | |||||||
\(164\) | −0.887929 | −0.0693356 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.68232 | 0.673879 | ||||||||
\(167\) | 11.5133 | 0.890928 | 0.445464 | − | 0.895300i | \(-0.353039\pi\) | ||||
0.445464 | + | 0.895300i | \(0.353039\pi\) | |||||||
\(168\) | 2.60999 | 0.201365 | ||||||||
\(169\) | 28.9915 | 2.23011 | ||||||||
\(170\) | 8.79650 | 0.674661 | ||||||||
\(171\) | 0.532775 | 0.0407423 | ||||||||
\(172\) | −13.5703 | −1.03472 | ||||||||
\(173\) | −7.50512 | −0.570604 | −0.285302 | − | 0.958438i | \(-0.592094\pi\) | ||||
−0.285302 | + | 0.958438i | \(0.592094\pi\) | |||||||
\(174\) | −19.7804 | −1.49955 | ||||||||
\(175\) | 2.63089 | 0.198877 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.92760 | 0.445546 | ||||||||
\(178\) | 11.9314 | 0.894297 | ||||||||
\(179\) | 6.54867 | 0.489470 | 0.244735 | − | 0.969590i | \(-0.421299\pi\) | ||||
0.244735 | + | 0.969590i | \(0.421299\pi\) | |||||||
\(180\) | −1.46722 | −0.109360 | ||||||||
\(181\) | −8.04433 | −0.597930 | −0.298965 | − | 0.954264i | \(-0.596641\pi\) | ||||
−0.298965 | + | 0.954264i | \(0.596641\pi\) | |||||||
\(182\) | −31.7449 | −2.35309 | ||||||||
\(183\) | 3.21636 | 0.237760 | ||||||||
\(184\) | 4.50951 | 0.332446 | ||||||||
\(185\) | 4.22812 | 0.310858 | ||||||||
\(186\) | −0.354989 | −0.0260290 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.9514 | −0.944576 | ||||||||
\(189\) | −2.63089 | −0.191369 | ||||||||
\(190\) | −0.992053 | −0.0719711 | ||||||||
\(191\) | −8.72833 | −0.631560 | −0.315780 | − | 0.948832i | \(-0.602266\pi\) | ||||
−0.315780 | + | 0.948832i | \(0.602266\pi\) | |||||||
\(192\) | 3.32133 | 0.239696 | ||||||||
\(193\) | 15.0613 | 1.08413 | 0.542066 | − | 0.840336i | \(-0.317642\pi\) | ||||
0.542066 | + | 0.840336i | \(0.317642\pi\) | |||||||
\(194\) | −13.6475 | −0.979831 | ||||||||
\(195\) | −6.48008 | −0.464048 | ||||||||
\(196\) | −0.115043 | −0.00821734 | ||||||||
\(197\) | 13.0882 | 0.932498 | 0.466249 | − | 0.884654i | \(-0.345605\pi\) | ||||
0.466249 | + | 0.884654i | \(0.345605\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.16738 | 0.508082 | 0.254041 | − | 0.967193i | \(-0.418240\pi\) | ||||
0.254041 | + | 0.967193i | \(0.418240\pi\) | |||||||
\(200\) | −0.992053 | −0.0701488 | ||||||||
\(201\) | −5.22812 | −0.368763 | ||||||||
\(202\) | 21.1527 | 1.48830 | ||||||||
\(203\) | 27.9478 | 1.96155 | ||||||||
\(204\) | 6.93131 | 0.485289 | ||||||||
\(205\) | 0.605176 | 0.0422673 | ||||||||
\(206\) | −3.83701 | −0.267337 | ||||||||
\(207\) | −4.54563 | −0.315943 | ||||||||
\(208\) | 30.9858 | 2.14848 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.89885 | 0.338053 | ||||||||
\(211\) | 5.98824 | 0.412247 | 0.206124 | − | 0.978526i | \(-0.433915\pi\) | ||||
0.206124 | + | 0.978526i | \(0.433915\pi\) | |||||||
\(212\) | 9.82519 | 0.674797 | ||||||||
\(213\) | 2.74381 | 0.188002 | ||||||||
\(214\) | 2.14082 | 0.146344 | ||||||||
\(215\) | 9.24893 | 0.630772 | ||||||||
\(216\) | 0.992053 | 0.0675007 | ||||||||
\(217\) | 0.501564 | 0.0340484 | ||||||||
\(218\) | −24.8401 | −1.68238 | ||||||||
\(219\) | 15.6756 | 1.05926 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.6125 | 2.05922 | ||||||||
\(222\) | 7.87297 | 0.528399 | ||||||||
\(223\) | −0.300522 | −0.0201245 | −0.0100622 | − | 0.999949i | \(-0.503203\pi\) | ||||
−0.0100622 | + | 0.999949i | \(0.503203\pi\) | |||||||
\(224\) | −18.2049 | −1.21636 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 11.7260 | 0.780004 | ||||||||
\(227\) | −22.8179 | −1.51448 | −0.757239 | − | 0.653138i | \(-0.773452\pi\) | ||||
−0.757239 | + | 0.653138i | \(0.773452\pi\) | |||||||
\(228\) | −0.781701 | −0.0517694 | ||||||||
\(229\) | 28.2109 | 1.86423 | 0.932113 | − | 0.362167i | \(-0.117963\pi\) | ||||
0.932113 | + | 0.362167i | \(0.117963\pi\) | |||||||
\(230\) | 8.46419 | 0.558112 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.5385 | −0.691888 | ||||||||
\(233\) | −19.3845 | −1.26992 | −0.634961 | − | 0.772544i | \(-0.718984\pi\) | ||||
−0.634961 | + | 0.772544i | \(0.718984\pi\) | |||||||
\(234\) | −12.0662 | −0.788794 | ||||||||
\(235\) | 8.82712 | 0.575818 | ||||||||
\(236\) | −8.69712 | −0.566134 | ||||||||
\(237\) | −1.21103 | −0.0786648 | ||||||||
\(238\) | −23.1426 | −1.50011 | ||||||||
\(239\) | −15.2735 | −0.987964 | −0.493982 | − | 0.869472i | \(-0.664459\pi\) | ||||
−0.493982 | + | 0.869472i | \(0.664459\pi\) | |||||||
\(240\) | −4.78170 | −0.308657 | ||||||||
\(241\) | −7.21213 | −0.464574 | −0.232287 | − | 0.972647i | \(-0.574621\pi\) | ||||
−0.232287 | + | 0.972647i | \(0.574621\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.71912 | −0.302111 | ||||||||
\(245\) | 0.0784084 | 0.00500933 | ||||||||
\(246\) | 1.12687 | 0.0718464 | ||||||||
\(247\) | −3.45243 | −0.219673 | ||||||||
\(248\) | −0.189129 | −0.0120097 | ||||||||
\(249\) | −4.66278 | −0.295492 | ||||||||
\(250\) | −1.86205 | −0.117766 | ||||||||
\(251\) | 19.0750 | 1.20400 | 0.602000 | − | 0.798496i | \(-0.294371\pi\) | ||||
0.602000 | + | 0.798496i | \(0.294371\pi\) | |||||||
\(252\) | 3.86011 | 0.243164 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −18.7961 | −1.17937 | ||||||||
\(255\) | −4.72410 | −0.295834 | ||||||||
\(256\) | 20.8963 | 1.30602 | ||||||||
\(257\) | 26.1060 | 1.62845 | 0.814224 | − | 0.580551i | \(-0.197163\pi\) | ||||
0.814224 | + | 0.580551i | \(0.197163\pi\) | |||||||
\(258\) | 17.2219 | 1.07219 | ||||||||
\(259\) | −11.1237 | −0.691195 | ||||||||
\(260\) | 9.50774 | 0.589645 | ||||||||
\(261\) | 10.6229 | 0.657544 | ||||||||
\(262\) | −8.65399 | −0.534645 | ||||||||
\(263\) | 27.0086 | 1.66542 | 0.832710 | − | 0.553710i | \(-0.186788\pi\) | ||||
0.832710 | + | 0.553710i | \(0.186788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.69644 | −0.411359 | ||||||||
\(266\) | 2.60999 | 0.160028 | ||||||||
\(267\) | −6.40768 | −0.392144 | ||||||||
\(268\) | 7.67083 | 0.468570 | ||||||||
\(269\) | −10.0527 | −0.612923 | −0.306462 | − | 0.951883i | \(-0.599145\pi\) | ||||
−0.306462 | + | 0.951883i | \(0.599145\pi\) | |||||||
\(270\) | 1.86205 | 0.113321 | ||||||||
\(271\) | 29.2643 | 1.77768 | 0.888841 | − | 0.458216i | \(-0.151511\pi\) | ||||
0.888841 | + | 0.458216i | \(0.151511\pi\) | |||||||
\(272\) | 22.5892 | 1.36967 | ||||||||
\(273\) | 17.0484 | 1.03182 | ||||||||
\(274\) | 29.3600 | 1.77370 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.66947 | 0.401455 | ||||||||
\(277\) | −0.694566 | −0.0417325 | −0.0208662 | − | 0.999782i | \(-0.506642\pi\) | ||||
−0.0208662 | + | 0.999782i | \(0.506642\pi\) | |||||||
\(278\) | 18.6923 | 1.12109 | ||||||||
\(279\) | 0.190644 | 0.0114136 | ||||||||
\(280\) | 2.60999 | 0.155976 | ||||||||
\(281\) | −10.6688 | −0.636447 | −0.318223 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318223 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(282\) | 16.4365 | 0.978781 | ||||||||
\(283\) | −21.6221 | −1.28530 | −0.642650 | − | 0.766160i | \(-0.722165\pi\) | ||||
−0.642650 | + | 0.766160i | \(0.722165\pi\) | |||||||
\(284\) | −4.02578 | −0.238886 | ||||||||
\(285\) | 0.532775 | 0.0315589 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.59215 | −0.0939818 | ||||||||
\(288\) | −6.91965 | −0.407744 | ||||||||
\(289\) | 5.31709 | 0.312770 | ||||||||
\(290\) | −19.7804 | −1.16155 | ||||||||
\(291\) | 7.32927 | 0.429650 | ||||||||
\(292\) | −22.9997 | −1.34595 | ||||||||
\(293\) | −5.75860 | −0.336421 | −0.168211 | − | 0.985751i | \(-0.553799\pi\) | ||||
−0.168211 | + | 0.985751i | \(0.553799\pi\) | |||||||
\(294\) | 0.146000 | 0.00851491 | ||||||||
\(295\) | 5.92760 | 0.345118 | ||||||||
\(296\) | 4.19452 | 0.243802 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.4869 | −1.12884 | ||||||||
\(299\) | 29.4561 | 1.70349 | ||||||||
\(300\) | −1.46722 | −0.0847103 | ||||||||
\(301\) | −24.3329 | −1.40253 | ||||||||
\(302\) | −29.1286 | −1.67616 | ||||||||
\(303\) | −11.3599 | −0.652609 | ||||||||
\(304\) | −2.54757 | −0.146113 | ||||||||
\(305\) | 3.21636 | 0.184168 | ||||||||
\(306\) | −8.79650 | −0.502862 | ||||||||
\(307\) | −18.4941 | −1.05552 | −0.527758 | − | 0.849395i | \(-0.676967\pi\) | ||||
−0.527758 | + | 0.849395i | \(0.676967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.06064 | 0.117226 | ||||||||
\(310\) | −0.354989 | −0.0201620 | ||||||||
\(311\) | −11.3134 | −0.641523 | −0.320761 | − | 0.947160i | \(-0.603939\pi\) | ||||
−0.320761 | + | 0.947160i | \(0.603939\pi\) | |||||||
\(312\) | −6.42859 | −0.363947 | ||||||||
\(313\) | −18.5401 | −1.04795 | −0.523975 | − | 0.851733i | \(-0.675552\pi\) | ||||
−0.523975 | + | 0.851733i | \(0.675552\pi\) | |||||||
\(314\) | 16.7392 | 0.944651 | ||||||||
\(315\) | −2.63089 | −0.148234 | ||||||||
\(316\) | 1.77685 | 0.0999558 | ||||||||
\(317\) | −0.821434 | −0.0461363 | −0.0230682 | − | 0.999734i | \(-0.507343\pi\) | ||||
−0.0230682 | + | 0.999734i | \(0.507343\pi\) | |||||||
\(318\) | −12.4691 | −0.699232 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.32133 | 0.185668 | ||||||||
\(321\) | −1.14971 | −0.0641707 | ||||||||
\(322\) | −22.2684 | −1.24097 | ||||||||
\(323\) | −2.51688 | −0.140043 | ||||||||
\(324\) | 1.46722 | 0.0815125 | ||||||||
\(325\) | −6.48008 | −0.359450 | ||||||||
\(326\) | 36.9430 | 2.04608 | ||||||||
\(327\) | 13.3402 | 0.737714 | ||||||||
\(328\) | 0.600367 | 0.0331497 | ||||||||
\(329\) | −23.2232 | −1.28034 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.98217 | 0.438740 | 0.219370 | − | 0.975642i | \(-0.429600\pi\) | ||||
0.219370 | + | 0.975642i | \(0.429600\pi\) | |||||||
\(332\) | 6.84135 | 0.375468 | ||||||||
\(333\) | −4.22812 | −0.231700 | ||||||||
\(334\) | 21.4384 | 1.17306 | ||||||||
\(335\) | −5.22812 | −0.285643 | ||||||||
\(336\) | 12.5801 | 0.686303 | ||||||||
\(337\) | −12.4690 | −0.679230 | −0.339615 | − | 0.940565i | \(-0.610297\pi\) | ||||
−0.339615 | + | 0.940565i | \(0.610297\pi\) | |||||||
\(338\) | 53.9835 | 2.93632 | ||||||||
\(339\) | −6.29738 | −0.342027 | ||||||||
\(340\) | 6.93131 | 0.375903 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.992053 | 0.0536441 | ||||||||
\(343\) | −18.6225 | −1.00552 | ||||||||
\(344\) | 9.17543 | 0.494706 | ||||||||
\(345\) | −4.54563 | −0.244729 | ||||||||
\(346\) | −13.9749 | −0.751295 | ||||||||
\(347\) | 20.9124 | 1.12264 | 0.561318 | − | 0.827600i | \(-0.310295\pi\) | ||||
0.561318 | + | 0.827600i | \(0.310295\pi\) | |||||||
\(348\) | −15.5862 | −0.835511 | ||||||||
\(349\) | −7.67825 | −0.411008 | −0.205504 | − | 0.978656i | \(-0.565883\pi\) | ||||
−0.205504 | + | 0.978656i | \(0.565883\pi\) | |||||||
\(350\) | 4.89885 | 0.261854 | ||||||||
\(351\) | 6.48008 | 0.345881 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7984 | −0.734413 | −0.367207 | − | 0.930139i | \(-0.619686\pi\) | ||||
−0.367207 | + | 0.930139i | \(0.619686\pi\) | |||||||
\(354\) | 11.0375 | 0.586635 | ||||||||
\(355\) | 2.74381 | 0.145626 | ||||||||
\(356\) | 9.40151 | 0.498279 | ||||||||
\(357\) | 12.4286 | 0.657791 | ||||||||
\(358\) | 12.1939 | 0.644470 | ||||||||
\(359\) | −17.9162 | −0.945581 | −0.472790 | − | 0.881175i | \(-0.656753\pi\) | ||||
−0.472790 | + | 0.881175i | \(0.656753\pi\) | |||||||
\(360\) | 0.992053 | 0.0522858 | ||||||||
\(361\) | −18.7162 | −0.985061 | ||||||||
\(362\) | −14.9789 | −0.787275 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −25.0138 | −1.31108 | ||||||||
\(365\) | 15.6756 | 0.820500 | ||||||||
\(366\) | 5.98902 | 0.313051 | ||||||||
\(367\) | 9.46842 | 0.494248 | 0.247124 | − | 0.968984i | \(-0.420515\pi\) | ||||
0.247124 | + | 0.968984i | \(0.420515\pi\) | |||||||
\(368\) | 21.7359 | 1.13306 | ||||||||
\(369\) | −0.605176 | −0.0315042 | ||||||||
\(370\) | 7.87297 | 0.409296 | ||||||||
\(371\) | 17.6176 | 0.914661 | ||||||||
\(372\) | −0.279718 | −0.0145027 | ||||||||
\(373\) | 11.6402 | 0.602706 | 0.301353 | − | 0.953513i | \(-0.402562\pi\) | ||||
0.301353 | + | 0.953513i | \(0.402562\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 8.75698 | 0.451607 | ||||||||
\(377\) | −68.8376 | −3.54531 | ||||||||
\(378\) | −4.89885 | −0.251970 | ||||||||
\(379\) | −6.60408 | −0.339229 | −0.169614 | − | 0.985511i | \(-0.554252\pi\) | ||||
−0.169614 | + | 0.985511i | \(0.554252\pi\) | |||||||
\(380\) | −0.781701 | −0.0401004 | ||||||||
\(381\) | 10.0943 | 0.517147 | ||||||||
\(382\) | −16.2526 | −0.831554 | ||||||||
\(383\) | 19.7376 | 1.00855 | 0.504273 | − | 0.863544i | \(-0.331761\pi\) | ||||
0.504273 | + | 0.863544i | \(0.331761\pi\) | |||||||
\(384\) | −7.65483 | −0.390634 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 28.0448 | 1.42744 | ||||||||
\(387\) | −9.24893 | −0.470149 | ||||||||
\(388\) | −10.7537 | −0.545936 | ||||||||
\(389\) | 25.3648 | 1.28605 | 0.643023 | − | 0.765846i | \(-0.277680\pi\) | ||||
0.643023 | + | 0.765846i | \(0.277680\pi\) | |||||||
\(390\) | −12.0662 | −0.610997 | ||||||||
\(391\) | 21.4740 | 1.08599 | ||||||||
\(392\) | 0.0777853 | 0.00392875 | ||||||||
\(393\) | 4.64756 | 0.234439 | ||||||||
\(394\) | 24.3709 | 1.22779 | ||||||||
\(395\) | −1.21103 | −0.0609335 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.2400 | −1.96940 | −0.984699 | − | 0.174264i | \(-0.944245\pi\) | ||||
−0.984699 | + | 0.174264i | \(0.944245\pi\) | |||||||
\(398\) | 13.3460 | 0.668975 | ||||||||
\(399\) | −1.40167 | −0.0701715 | ||||||||
\(400\) | −4.78170 | −0.239085 | ||||||||
\(401\) | 11.1227 | 0.555443 | 0.277721 | − | 0.960662i | \(-0.410421\pi\) | ||||
0.277721 | + | 0.960662i | \(0.410421\pi\) | |||||||
\(402\) | −9.73502 | −0.485538 | ||||||||
\(403\) | −1.23539 | −0.0615392 | ||||||||
\(404\) | 16.6675 | 0.829240 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 52.0402 | 2.58271 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.68656 | −0.232019 | ||||||||
\(409\) | −11.6111 | −0.574131 | −0.287066 | − | 0.957911i | \(-0.592680\pi\) | ||||
−0.287066 | + | 0.957911i | \(0.592680\pi\) | |||||||
\(410\) | 1.12687 | 0.0556520 | ||||||||
\(411\) | −15.7676 | −0.777757 | ||||||||
\(412\) | −3.02342 | −0.148953 | ||||||||
\(413\) | −15.5949 | −0.767373 | ||||||||
\(414\) | −8.46419 | −0.415992 | ||||||||
\(415\) | −4.66278 | −0.228887 | ||||||||
\(416\) | 44.8399 | 2.19846 | ||||||||
\(417\) | −10.0386 | −0.491591 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.5499 | 0.906220 | 0.453110 | − | 0.891455i | \(-0.350314\pi\) | ||||
0.453110 | + | 0.891455i | \(0.350314\pi\) | |||||||
\(420\) | 3.86011 | 0.188354 | ||||||||
\(421\) | −19.9755 | −0.973545 | −0.486773 | − | 0.873529i | \(-0.661826\pi\) | ||||
−0.486773 | + | 0.873529i | \(0.661826\pi\) | |||||||
\(422\) | 11.1504 | 0.542793 | ||||||||
\(423\) | −8.82712 | −0.429189 | ||||||||
\(424\) | −6.64323 | −0.322624 | ||||||||
\(425\) | −4.72410 | −0.229152 | ||||||||
\(426\) | 5.10910 | 0.247537 | ||||||||
\(427\) | −8.46189 | −0.409500 | ||||||||
\(428\) | 1.68689 | 0.0815388 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.2219 | 0.830516 | ||||||||
\(431\) | −25.9565 | −1.25028 | −0.625141 | − | 0.780512i | \(-0.714959\pi\) | ||||
−0.625141 | + | 0.780512i | \(0.714959\pi\) | |||||||
\(432\) | 4.78170 | 0.230060 | ||||||||
\(433\) | −33.5788 | −1.61369 | −0.806847 | − | 0.590760i | \(-0.798828\pi\) | ||||
−0.806847 | + | 0.590760i | \(0.798828\pi\) | |||||||
\(434\) | 0.933937 | 0.0448304 | ||||||||
\(435\) | 10.6229 | 0.509331 | ||||||||
\(436\) | −19.5731 | −0.937380 | ||||||||
\(437\) | −2.42180 | −0.115850 | ||||||||
\(438\) | 29.1888 | 1.39469 | ||||||||
\(439\) | −17.0280 | −0.812703 | −0.406351 | − | 0.913717i | \(-0.633199\pi\) | ||||
−0.406351 | + | 0.913717i | \(0.633199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0784084 | −0.00373373 | ||||||||
\(442\) | 57.0020 | 2.71131 | ||||||||
\(443\) | 25.2148 | 1.19799 | 0.598995 | − | 0.800753i | \(-0.295567\pi\) | ||||
0.598995 | + | 0.800753i | \(0.295567\pi\) | |||||||
\(444\) | 6.20360 | 0.294410 | ||||||||
\(445\) | −6.40768 | −0.303753 | ||||||||
\(446\) | −0.559587 | −0.0264972 | ||||||||
\(447\) | 10.4653 | 0.494991 | ||||||||
\(448\) | −8.73805 | −0.412834 | ||||||||
\(449\) | −26.6596 | −1.25814 | −0.629072 | − | 0.777347i | \(-0.716565\pi\) | ||||
−0.629072 | + | 0.777347i | \(0.716565\pi\) | |||||||
\(450\) | 1.86205 | 0.0877778 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.23968 | 0.434598 | ||||||||
\(453\) | 15.6433 | 0.734988 | ||||||||
\(454\) | −42.4881 | −1.99406 | ||||||||
\(455\) | 17.0484 | 0.799241 | ||||||||
\(456\) | 0.528542 | 0.0247512 | ||||||||
\(457\) | −21.9481 | −1.02669 | −0.513344 | − | 0.858183i | \(-0.671594\pi\) | ||||
−0.513344 | + | 0.858183i | \(0.671594\pi\) | |||||||
\(458\) | 52.5300 | 2.45457 | ||||||||
\(459\) | 4.72410 | 0.220502 | ||||||||
\(460\) | 6.66947 | 0.310965 | ||||||||
\(461\) | −4.32624 | −0.201493 | −0.100746 | − | 0.994912i | \(-0.532123\pi\) | ||||
−0.100746 | + | 0.994912i | \(0.532123\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4573 | 0.532468 | 0.266234 | − | 0.963908i | \(-0.414221\pi\) | ||||
0.266234 | + | 0.963908i | \(0.414221\pi\) | |||||||
\(464\) | −50.7957 | −2.35813 | ||||||||
\(465\) | 0.190644 | 0.00884092 | ||||||||
\(466\) | −36.0949 | −1.67206 | ||||||||
\(467\) | −15.5544 | −0.719770 | −0.359885 | − | 0.932997i | \(-0.617184\pi\) | ||||
−0.359885 | + | 0.932997i | \(0.617184\pi\) | |||||||
\(468\) | −9.50774 | −0.439495 | ||||||||
\(469\) | 13.7546 | 0.635129 | ||||||||
\(470\) | 16.4365 | 0.758161 | ||||||||
\(471\) | −8.98970 | −0.414223 | ||||||||
\(472\) | 5.88050 | 0.270672 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.25500 | −0.103575 | ||||||||
\(475\) | 0.532775 | 0.0244454 | ||||||||
\(476\) | −18.2355 | −0.835824 | ||||||||
\(477\) | 6.69644 | 0.306609 | ||||||||
\(478\) | −28.4401 | −1.30082 | ||||||||
\(479\) | 9.99686 | 0.456768 | 0.228384 | − | 0.973571i | \(-0.426656\pi\) | ||||
0.228384 | + | 0.973571i | \(0.426656\pi\) | |||||||
\(480\) | −6.91965 | −0.315837 | ||||||||
\(481\) | 27.3986 | 1.24927 | ||||||||
\(482\) | −13.4293 | −0.611689 | ||||||||
\(483\) | 11.9591 | 0.544156 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.32927 | 0.332805 | ||||||||
\(486\) | −1.86205 | −0.0844642 | ||||||||
\(487\) | 39.5800 | 1.79354 | 0.896770 | − | 0.442497i | \(-0.145907\pi\) | ||||
0.896770 | + | 0.442497i | \(0.145907\pi\) | |||||||
\(488\) | 3.19080 | 0.144441 | ||||||||
\(489\) | −19.8400 | −0.897195 | ||||||||
\(490\) | 0.146000 | 0.00659562 | ||||||||
\(491\) | −9.29053 | −0.419276 | −0.209638 | − | 0.977779i | \(-0.567229\pi\) | ||||
−0.209638 | + | 0.977779i | \(0.567229\pi\) | |||||||
\(492\) | 0.887929 | 0.0400310 | ||||||||
\(493\) | −50.1838 | −2.26017 | ||||||||
\(494\) | −6.42859 | −0.289236 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.911604 | −0.0409322 | ||||||||
\(497\) | −7.21865 | −0.323801 | ||||||||
\(498\) | −8.68232 | −0.389064 | ||||||||
\(499\) | −23.3475 | −1.04518 | −0.522588 | − | 0.852585i | \(-0.675033\pi\) | ||||
−0.522588 | + | 0.852585i | \(0.675033\pi\) | |||||||
\(500\) | −1.46722 | −0.0656163 | ||||||||
\(501\) | −11.5133 | −0.514377 | ||||||||
\(502\) | 35.5185 | 1.58527 | ||||||||
\(503\) | 12.0518 | 0.537365 | 0.268683 | − | 0.963229i | \(-0.413412\pi\) | ||||
0.268683 | + | 0.963229i | \(0.413412\pi\) | |||||||
\(504\) | −2.60999 | −0.116258 | ||||||||
\(505\) | −11.3599 | −0.505509 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.9915 | −1.28756 | ||||||||
\(508\) | −14.8106 | −0.657114 | ||||||||
\(509\) | −1.65102 | −0.0731801 | −0.0365901 | − | 0.999330i | \(-0.511650\pi\) | ||||
−0.0365901 | + | 0.999330i | \(0.511650\pi\) | |||||||
\(510\) | −8.79650 | −0.389515 | ||||||||
\(511\) | −41.2409 | −1.82439 | ||||||||
\(512\) | 23.6003 | 1.04300 | ||||||||
\(513\) | −0.532775 | −0.0235226 | ||||||||
\(514\) | 48.6106 | 2.14412 | ||||||||
\(515\) | 2.06064 | 0.0908026 | ||||||||
\(516\) | 13.5703 | 0.597397 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −20.7129 | −0.910074 | ||||||||
\(519\) | 7.50512 | 0.329438 | ||||||||
\(520\) | −6.42859 | −0.281912 | ||||||||
\(521\) | 21.3715 | 0.936302 | 0.468151 | − | 0.883648i | \(-0.344920\pi\) | ||||
0.468151 | + | 0.883648i | \(0.344920\pi\) | |||||||
\(522\) | 19.7804 | 0.865766 | ||||||||
\(523\) | −12.1593 | −0.531688 | −0.265844 | − | 0.964016i | \(-0.585651\pi\) | ||||
−0.265844 | + | 0.964016i | \(0.585651\pi\) | |||||||
\(524\) | −6.81902 | −0.297890 | ||||||||
\(525\) | −2.63089 | −0.114822 | ||||||||
\(526\) | 50.2913 | 2.19280 | ||||||||
\(527\) | −0.900622 | −0.0392317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.33722 | −0.101618 | ||||||||
\(530\) | −12.4691 | −0.541623 | ||||||||
\(531\) | −5.92760 | −0.257236 | ||||||||
\(532\) | 2.05657 | 0.0891637 | ||||||||
\(533\) | 3.92159 | 0.169863 | ||||||||
\(534\) | −11.9314 | −0.516323 | ||||||||
\(535\) | −1.14971 | −0.0497064 | ||||||||
\(536\) | −5.18658 | −0.224026 | ||||||||
\(537\) | −6.54867 | −0.282596 | ||||||||
\(538\) | −18.7186 | −0.807016 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.46722 | 0.0631393 | ||||||||
\(541\) | 20.5396 | 0.883065 | 0.441532 | − | 0.897245i | \(-0.354435\pi\) | ||||
0.441532 | + | 0.897245i | \(0.354435\pi\) | |||||||
\(542\) | 54.4916 | 2.34062 | ||||||||
\(543\) | 8.04433 | 0.345215 | ||||||||
\(544\) | 32.6891 | 1.40153 | ||||||||
\(545\) | 13.3402 | 0.571431 | ||||||||
\(546\) | 31.7449 | 1.35856 | ||||||||
\(547\) | 19.1832 | 0.820215 | 0.410107 | − | 0.912037i | \(-0.365491\pi\) | ||||
0.410107 | + | 0.912037i | \(0.365491\pi\) | |||||||
\(548\) | 23.1346 | 0.988261 | ||||||||
\(549\) | −3.21636 | −0.137271 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.65964 | 0.241109 | ||||||||
\(552\) | −4.50951 | −0.191938 | ||||||||
\(553\) | 3.18609 | 0.135486 | ||||||||
\(554\) | −1.29332 | −0.0549477 | ||||||||
\(555\) | −4.22812 | −0.179474 | ||||||||
\(556\) | 14.7288 | 0.624642 | ||||||||
\(557\) | −22.1368 | −0.937966 | −0.468983 | − | 0.883207i | \(-0.655379\pi\) | ||||
−0.468983 | + | 0.883207i | \(0.655379\pi\) | |||||||
\(558\) | 0.354989 | 0.0150279 | ||||||||
\(559\) | 59.9338 | 2.53493 | ||||||||
\(560\) | 12.5801 | 0.531608 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.8658 | −0.837988 | ||||||||
\(563\) | 25.1244 | 1.05887 | 0.529435 | − | 0.848351i | \(-0.322404\pi\) | ||||
0.529435 | + | 0.848351i | \(0.322404\pi\) | |||||||
\(564\) | 12.9514 | 0.545351 | ||||||||
\(565\) | −6.29738 | −0.264933 | ||||||||
\(566\) | −40.2614 | −1.69231 | ||||||||
\(567\) | 2.63089 | 0.110487 | ||||||||
\(568\) | 2.72200 | 0.114213 | ||||||||
\(569\) | −25.6815 | −1.07663 | −0.538313 | − | 0.842745i | \(-0.680938\pi\) | ||||
−0.538313 | + | 0.842745i | \(0.680938\pi\) | |||||||
\(570\) | 0.992053 | 0.0415525 | ||||||||
\(571\) | 13.3087 | 0.556953 | 0.278476 | − | 0.960443i | \(-0.410171\pi\) | ||||
0.278476 | + | 0.960443i | \(0.410171\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.72833 | 0.364631 | ||||||||
\(574\) | −2.96467 | −0.123743 | ||||||||
\(575\) | −4.54563 | −0.189566 | ||||||||
\(576\) | −3.32133 | −0.138389 | ||||||||
\(577\) | −13.1005 | −0.545380 | −0.272690 | − | 0.962102i | \(-0.587913\pi\) | ||||
−0.272690 | + | 0.962102i | \(0.587913\pi\) | |||||||
\(578\) | 9.90069 | 0.411814 | ||||||||
\(579\) | −15.0613 | −0.625924 | ||||||||
\(580\) | −15.5862 | −0.647184 | ||||||||
\(581\) | 12.2673 | 0.508932 | ||||||||
\(582\) | 13.6475 | 0.565706 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 15.5511 | 0.643508 | ||||||||
\(585\) | 6.48008 | 0.267918 | ||||||||
\(586\) | −10.7228 | −0.442955 | ||||||||
\(587\) | −0.287665 | −0.0118732 | −0.00593659 | − | 0.999982i | \(-0.501890\pi\) | ||||
−0.00593659 | + | 0.999982i | \(0.501890\pi\) | |||||||
\(588\) | 0.115043 | 0.00474428 | ||||||||
\(589\) | 0.101571 | 0.00418514 | ||||||||
\(590\) | 11.0375 | 0.454406 | ||||||||
\(591\) | −13.0882 | −0.538378 | ||||||||
\(592\) | 20.2176 | 0.830939 | ||||||||
\(593\) | −31.8957 | −1.30980 | −0.654900 | − | 0.755716i | \(-0.727289\pi\) | ||||
−0.654900 | + | 0.755716i | \(0.727289\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4286 | 0.509522 | ||||||||
\(596\) | −15.3549 | −0.628962 | ||||||||
\(597\) | −7.16738 | −0.293341 | ||||||||
\(598\) | 54.8486 | 2.24293 | ||||||||
\(599\) | −33.5486 | −1.37076 | −0.685379 | − | 0.728186i | \(-0.740364\pi\) | ||||
−0.685379 | + | 0.728186i | \(0.740364\pi\) | |||||||
\(600\) | 0.992053 | 0.0405004 | ||||||||
\(601\) | −32.8320 | −1.33925 | −0.669623 | − | 0.742701i | \(-0.733544\pi\) | ||||
−0.669623 | + | 0.742701i | \(0.733544\pi\) | |||||||
\(602\) | −45.3091 | −1.84666 | ||||||||
\(603\) | 5.22812 | 0.212906 | ||||||||
\(604\) | −22.9523 | −0.933915 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −21.1527 | −0.859269 | ||||||||
\(607\) | −45.1195 | −1.83135 | −0.915673 | − | 0.401925i | \(-0.868341\pi\) | ||||
−0.915673 | + | 0.401925i | \(0.868341\pi\) | |||||||
\(608\) | −3.68662 | −0.149512 | ||||||||
\(609\) | −27.9478 | −1.13250 | ||||||||
\(610\) | 5.98902 | 0.242488 | ||||||||
\(611\) | 57.2005 | 2.31408 | ||||||||
\(612\) | −6.93131 | −0.280182 | ||||||||
\(613\) | −46.5727 | −1.88105 | −0.940527 | − | 0.339719i | \(-0.889668\pi\) | ||||
−0.940527 | + | 0.339719i | \(0.889668\pi\) | |||||||
\(614\) | −34.4370 | −1.38976 | ||||||||
\(615\) | −0.605176 | −0.0244031 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9597 | −1.24639 | −0.623195 | − | 0.782067i | \(-0.714166\pi\) | ||||
−0.623195 | + | 0.782067i | \(0.714166\pi\) | |||||||
\(618\) | 3.83701 | 0.154347 | ||||||||
\(619\) | −14.6825 | −0.590139 | −0.295070 | − | 0.955476i | \(-0.595343\pi\) | ||||
−0.295070 | + | 0.955476i | \(0.595343\pi\) | |||||||
\(620\) | −0.279718 | −0.0112337 | ||||||||
\(621\) | 4.54563 | 0.182410 | ||||||||
\(622\) | −21.0661 | −0.844672 | ||||||||
\(623\) | 16.8579 | 0.675398 | ||||||||
\(624\) | −30.9858 | −1.24043 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −34.5226 | −1.37980 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.1899 | 0.526334 | ||||||||
\(629\) | 19.9741 | 0.796418 | ||||||||
\(630\) | −4.89885 | −0.195175 | ||||||||
\(631\) | −12.7589 | −0.507922 | −0.253961 | − | 0.967214i | \(-0.581733\pi\) | ||||
−0.253961 | + | 0.967214i | \(0.581733\pi\) | |||||||
\(632\) | −1.20141 | −0.0477894 | ||||||||
\(633\) | −5.98824 | −0.238011 | ||||||||
\(634\) | −1.52955 | −0.0607462 | ||||||||
\(635\) | 10.0943 | 0.400580 | ||||||||
\(636\) | −9.82519 | −0.389594 | ||||||||
\(637\) | 0.508093 | 0.0201314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.74381 | −0.108543 | ||||||||
\(640\) | −7.65483 | −0.302584 | ||||||||
\(641\) | 16.3406 | 0.645415 | 0.322708 | − | 0.946499i | \(-0.395407\pi\) | ||||
0.322708 | + | 0.946499i | \(0.395407\pi\) | |||||||
\(642\) | −2.14082 | −0.0844915 | ||||||||
\(643\) | 5.93513 | 0.234059 | 0.117029 | − | 0.993128i | \(-0.462663\pi\) | ||||
0.117029 | + | 0.993128i | \(0.462663\pi\) | |||||||
\(644\) | −17.5466 | −0.691435 | ||||||||
\(645\) | −9.24893 | −0.364176 | ||||||||
\(646\) | −4.68656 | −0.184390 | ||||||||
\(647\) | −8.09795 | −0.318363 | −0.159182 | − | 0.987249i | \(-0.550886\pi\) | ||||
−0.159182 | + | 0.987249i | \(0.550886\pi\) | |||||||
\(648\) | −0.992053 | −0.0389715 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.0662 | −0.473276 | ||||||||
\(651\) | −0.501564 | −0.0196579 | ||||||||
\(652\) | 29.1097 | 1.14002 | ||||||||
\(653\) | 28.4218 | 1.11223 | 0.556116 | − | 0.831105i | \(-0.312291\pi\) | ||||
0.556116 | + | 0.831105i | \(0.312291\pi\) | |||||||
\(654\) | 24.8401 | 0.971324 | ||||||||
\(655\) | 4.64756 | 0.181595 | ||||||||
\(656\) | 2.89377 | 0.112983 | ||||||||
\(657\) | −15.6756 | −0.611565 | ||||||||
\(658\) | −43.2427 | −1.68578 | ||||||||
\(659\) | 7.38736 | 0.287771 | 0.143885 | − | 0.989594i | \(-0.454040\pi\) | ||||
0.143885 | + | 0.989594i | \(0.454040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.4264 | −1.22235 | −0.611174 | − | 0.791497i | \(-0.709302\pi\) | ||||
−0.611174 | + | 0.791497i | \(0.709302\pi\) | |||||||
\(662\) | 14.8632 | 0.577674 | ||||||||
\(663\) | −30.6125 | −1.18889 | ||||||||
\(664\) | −4.62573 | −0.179513 | ||||||||
\(665\) | −1.40167 | −0.0543546 | ||||||||
\(666\) | −7.87297 | −0.305071 | ||||||||
\(667\) | −48.2880 | −1.86972 | ||||||||
\(668\) | 16.8926 | 0.653596 | ||||||||
\(669\) | 0.300522 | 0.0116189 | ||||||||
\(670\) | −9.73502 | −0.376096 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 18.2049 | 0.702268 | ||||||||
\(673\) | −15.5966 | −0.601203 | −0.300601 | − | 0.953750i | \(-0.597187\pi\) | ||||
−0.300601 | + | 0.953750i | \(0.597187\pi\) | |||||||
\(674\) | −23.2179 | −0.894319 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 42.5370 | 1.63604 | ||||||||
\(677\) | −3.86670 | −0.148609 | −0.0743047 | − | 0.997236i | \(-0.523674\pi\) | ||||
−0.0743047 | + | 0.997236i | \(0.523674\pi\) | |||||||
\(678\) | −11.7260 | −0.450336 | ||||||||
\(679\) | −19.2825 | −0.739995 | ||||||||
\(680\) | −4.68656 | −0.179721 | ||||||||
\(681\) | 22.8179 | 0.874384 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.2736 | 1.31144 | 0.655722 | − | 0.755002i | \(-0.272364\pi\) | ||||
0.655722 | + | 0.755002i | \(0.272364\pi\) | |||||||
\(684\) | 0.781701 | 0.0298891 | ||||||||
\(685\) | −15.7676 | −0.602448 | ||||||||
\(686\) | −34.6760 | −1.32394 | ||||||||
\(687\) | −28.2109 | −1.07631 | ||||||||
\(688\) | 44.2256 | 1.68609 | ||||||||
\(689\) | −43.3935 | −1.65316 | ||||||||
\(690\) | −8.46419 | −0.322226 | ||||||||
\(691\) | −44.7295 | −1.70159 | −0.850796 | − | 0.525497i | \(-0.823879\pi\) | ||||
−0.850796 | + | 0.525497i | \(0.823879\pi\) | |||||||
\(692\) | −11.0117 | −0.418602 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.9399 | 1.47814 | ||||||||
\(695\) | −10.0386 | −0.380785 | ||||||||
\(696\) | 10.5385 | 0.399462 | ||||||||
\(697\) | 2.85891 | 0.108289 | ||||||||
\(698\) | −14.2973 | −0.541160 | ||||||||
\(699\) | 19.3845 | 0.733190 | ||||||||
\(700\) | 3.86011 | 0.145898 | ||||||||
\(701\) | 11.1637 | 0.421646 | 0.210823 | − | 0.977524i | \(-0.432386\pi\) | ||||
0.210823 | + | 0.977524i | \(0.432386\pi\) | |||||||
\(702\) | 12.0662 | 0.455410 | ||||||||
\(703\) | −2.25264 | −0.0849599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.82712 | −0.332449 | ||||||||
\(706\) | −25.6932 | −0.966978 | ||||||||
\(707\) | 29.8867 | 1.12400 | ||||||||
\(708\) | 8.69712 | 0.326858 | ||||||||
\(709\) | 41.7860 | 1.56931 | 0.784654 | − | 0.619934i | \(-0.212841\pi\) | ||||
0.784654 | + | 0.619934i | \(0.212841\pi\) | |||||||
\(710\) | 5.10910 | 0.191741 | ||||||||
\(711\) | 1.21103 | 0.0454172 | ||||||||
\(712\) | −6.35676 | −0.238230 | ||||||||
\(713\) | −0.866599 | −0.0324544 | ||||||||
\(714\) | 23.1426 | 0.866091 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.60837 | 0.359082 | ||||||||
\(717\) | 15.2735 | 0.570401 | ||||||||
\(718\) | −33.3608 | −1.24502 | ||||||||
\(719\) | −17.9903 | −0.670924 | −0.335462 | − | 0.942054i | \(-0.608892\pi\) | ||||
−0.335462 | + | 0.942054i | \(0.608892\pi\) | |||||||
\(720\) | 4.78170 | 0.178203 | ||||||||
\(721\) | −5.42132 | −0.201900 | ||||||||
\(722\) | −34.8504 | −1.29700 | ||||||||
\(723\) | 7.21213 | 0.268222 | ||||||||
\(724\) | −11.8028 | −0.438649 | ||||||||
\(725\) | 10.6229 | 0.394526 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.9340 | 0.887664 | 0.443832 | − | 0.896110i | \(-0.353619\pi\) | ||||
0.443832 | + | 0.896110i | \(0.353619\pi\) | |||||||
\(728\) | 16.9129 | 0.626835 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 29.1888 | 1.08033 | ||||||||
\(731\) | 43.6928 | 1.61604 | ||||||||
\(732\) | 4.71912 | 0.174424 | ||||||||
\(733\) | −7.40496 | −0.273509 | −0.136754 | − | 0.990605i | \(-0.543667\pi\) | ||||
−0.136754 | + | 0.990605i | \(0.543667\pi\) | |||||||
\(734\) | 17.6307 | 0.650760 | ||||||||
\(735\) | −0.0784084 | −0.00289214 | ||||||||
\(736\) | 31.4542 | 1.15942 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.12687 | −0.0414806 | ||||||||
\(739\) | 30.9698 | 1.13924 | 0.569622 | − | 0.821907i | \(-0.307090\pi\) | ||||
0.569622 | + | 0.821907i | \(0.307090\pi\) | |||||||
\(740\) | 6.20360 | 0.228049 | ||||||||
\(741\) | 3.45243 | 0.126828 | ||||||||
\(742\) | 32.8049 | 1.20430 | ||||||||
\(743\) | −49.7620 | −1.82559 | −0.912796 | − | 0.408416i | \(-0.866081\pi\) | ||||
−0.912796 | + | 0.408416i | \(0.866081\pi\) | |||||||
\(744\) | 0.189129 | 0.00693382 | ||||||||
\(745\) | 10.4653 | 0.383418 | ||||||||
\(746\) | 21.6746 | 0.793564 | ||||||||
\(747\) | 4.66278 | 0.170602 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.02477 | 0.110523 | ||||||||
\(750\) | 1.86205 | 0.0679924 | ||||||||
\(751\) | 34.4375 | 1.25664 | 0.628320 | − | 0.777955i | \(-0.283743\pi\) | ||||
0.628320 | + | 0.777955i | \(0.283743\pi\) | |||||||
\(752\) | 42.2087 | 1.53919 | ||||||||
\(753\) | −19.0750 | −0.695130 | ||||||||
\(754\) | −128.179 | −4.66800 | ||||||||
\(755\) | 15.6433 | 0.569319 | ||||||||
\(756\) | −3.86011 | −0.140391 | ||||||||
\(757\) | −18.4833 | −0.671787 | −0.335894 | − | 0.941900i | \(-0.609038\pi\) | ||||
−0.335894 | + | 0.941900i | \(0.609038\pi\) | |||||||
\(758\) | −12.2971 | −0.446651 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.528542 | 0.0191722 | ||||||||
\(761\) | −7.05014 | −0.255567 | −0.127784 | − | 0.991802i | \(-0.540786\pi\) | ||||
−0.127784 | + | 0.991802i | \(0.540786\pi\) | |||||||
\(762\) | 18.7961 | 0.680910 | ||||||||
\(763\) | −35.0966 | −1.27058 | ||||||||
\(764\) | −12.8064 | −0.463320 | ||||||||
\(765\) | 4.72410 | 0.170800 | ||||||||
\(766\) | 36.7524 | 1.32792 | ||||||||
\(767\) | 38.4113 | 1.38695 | ||||||||
\(768\) | −20.8963 | −0.754031 | ||||||||
\(769\) | −15.9027 | −0.573465 | −0.286732 | − | 0.958011i | \(-0.592569\pi\) | ||||
−0.286732 | + | 0.958011i | \(0.592569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.1060 | −0.940185 | ||||||||
\(772\) | 22.0982 | 0.795333 | ||||||||
\(773\) | 17.1271 | 0.616020 | 0.308010 | − | 0.951383i | \(-0.400337\pi\) | ||||
0.308010 | + | 0.951383i | \(0.400337\pi\) | |||||||
\(774\) | −17.2219 | −0.619030 | ||||||||
\(775\) | 0.190644 | 0.00684814 | ||||||||
\(776\) | 7.27103 | 0.261015 | ||||||||
\(777\) | 11.1237 | 0.399062 | ||||||||
\(778\) | 47.2305 | 1.69330 | ||||||||
\(779\) | −0.322423 | −0.0115520 | ||||||||
\(780\) | −9.50774 | −0.340432 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 39.9857 | 1.42988 | ||||||||
\(783\) | −10.6229 | −0.379633 | ||||||||
\(784\) | 0.374925 | 0.0133902 | ||||||||
\(785\) | −8.98970 | −0.320856 | ||||||||
\(786\) | 8.65399 | 0.308678 | ||||||||
\(787\) | 46.2646 | 1.64915 | 0.824577 | − | 0.565749i | \(-0.191413\pi\) | ||||
0.824577 | + | 0.565749i | \(0.191413\pi\) | |||||||
\(788\) | 19.2034 | 0.684092 | ||||||||
\(789\) | −27.0086 | −0.961530 | ||||||||
\(790\) | −2.25500 | −0.0802292 | ||||||||
\(791\) | 16.5677 | 0.589081 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.8423 | 0.740131 | ||||||||
\(794\) | −73.0667 | −2.59304 | ||||||||
\(795\) | 6.69644 | 0.237498 | ||||||||
\(796\) | 10.5162 | 0.372735 | ||||||||
\(797\) | −3.91542 | −0.138691 | −0.0693456 | − | 0.997593i | \(-0.522091\pi\) | ||||
−0.0693456 | + | 0.997593i | \(0.522091\pi\) | |||||||
\(798\) | −2.60999 | −0.0923925 | ||||||||
\(799\) | 41.7002 | 1.47525 | ||||||||
\(800\) | −6.91965 | −0.244647 | ||||||||
\(801\) | 6.40768 | 0.226404 | ||||||||
\(802\) | 20.7111 | 0.731333 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −7.67083 | −0.270529 | ||||||||
\(805\) | 11.9591 | 0.421502 | ||||||||
\(806\) | −2.30036 | −0.0810266 | ||||||||
\(807\) | 10.0527 | 0.353872 | ||||||||
\(808\) | −11.2696 | −0.396464 | ||||||||
\(809\) | 6.75253 | 0.237406 | 0.118703 | − | 0.992930i | \(-0.462126\pi\) | ||||
0.118703 | + | 0.992930i | \(0.462126\pi\) | |||||||
\(810\) | −1.86205 | −0.0654257 | ||||||||
\(811\) | −43.4268 | −1.52492 | −0.762461 | − | 0.647035i | \(-0.776009\pi\) | ||||
−0.762461 | + | 0.647035i | \(0.776009\pi\) | |||||||
\(812\) | 41.0057 | 1.43902 | ||||||||
\(813\) | −29.2643 | −1.02635 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.8400 | −0.694964 | ||||||||
\(816\) | −22.5892 | −0.790781 | ||||||||
\(817\) | −4.92760 | −0.172395 | ||||||||
\(818\) | −21.6204 | −0.755939 | ||||||||
\(819\) | −17.0484 | −0.595719 | ||||||||
\(820\) | 0.887929 | 0.0310078 | ||||||||
\(821\) | −7.15064 | −0.249559 | −0.124780 | − | 0.992184i | \(-0.539822\pi\) | ||||
−0.124780 | + | 0.992184i | \(0.539822\pi\) | |||||||
\(822\) | −29.3600 | −1.02405 | ||||||||
\(823\) | −9.57872 | −0.333893 | −0.166947 | − | 0.985966i | \(-0.553391\pi\) | ||||
−0.166947 | + | 0.985966i | \(0.553391\pi\) | |||||||
\(824\) | 2.04426 | 0.0712153 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.0384 | −1.01038 | ||||||||
\(827\) | 6.11637 | 0.212687 | 0.106343 | − | 0.994329i | \(-0.466086\pi\) | ||||
0.106343 | + | 0.994329i | \(0.466086\pi\) | |||||||
\(828\) | −6.66947 | −0.231780 | ||||||||
\(829\) | 34.4276 | 1.19572 | 0.597861 | − | 0.801600i | \(-0.296018\pi\) | ||||
0.597861 | + | 0.801600i | \(0.296018\pi\) | |||||||
\(830\) | −8.68232 | −0.301368 | ||||||||
\(831\) | 0.694566 | 0.0240942 | ||||||||
\(832\) | 21.5225 | 0.746157 | ||||||||
\(833\) | 0.370409 | 0.0128339 | ||||||||
\(834\) | −18.6923 | −0.647262 | ||||||||
\(835\) | −11.5133 | −0.398435 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.190644 | −0.00658963 | ||||||||
\(838\) | 34.5408 | 1.19319 | ||||||||
\(839\) | 9.40836 | 0.324813 | 0.162406 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162406 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(840\) | −2.60999 | −0.0900530 | ||||||||
\(841\) | 83.8470 | 2.89127 | ||||||||
\(842\) | −37.1953 | −1.28183 | ||||||||
\(843\) | 10.6688 | 0.367453 | ||||||||
\(844\) | 8.78609 | 0.302430 | ||||||||
\(845\) | −28.9915 | −0.997337 | ||||||||
\(846\) | −16.4365 | −0.565100 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −32.0204 | −1.09958 | ||||||||
\(849\) | 21.6221 | 0.742069 | ||||||||
\(850\) | −8.79650 | −0.301717 | ||||||||
\(851\) | 19.2195 | 0.658836 | ||||||||
\(852\) | 4.02578 | 0.137921 | ||||||||
\(853\) | −35.0942 | −1.20160 | −0.600802 | − | 0.799398i | \(-0.705152\pi\) | ||||
−0.600802 | + | 0.799398i | \(0.705152\pi\) | |||||||
\(854\) | −15.7565 | −0.539175 | ||||||||
\(855\) | −0.532775 | −0.0182205 | ||||||||
\(856\) | −1.14058 | −0.0389841 | ||||||||
\(857\) | 21.3605 | 0.729661 | 0.364831 | − | 0.931074i | \(-0.381127\pi\) | ||||
0.364831 | + | 0.931074i | \(0.381127\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.21468 | 0.177923 | 0.0889613 | − | 0.996035i | \(-0.471645\pi\) | ||||
0.0889613 | + | 0.996035i | \(0.471645\pi\) | |||||||
\(860\) | 13.5703 | 0.462742 | ||||||||
\(861\) | 1.59215 | 0.0542604 | ||||||||
\(862\) | −48.3323 | −1.64621 | ||||||||
\(863\) | 4.35787 | 0.148344 | 0.0741718 | − | 0.997245i | \(-0.476369\pi\) | ||||
0.0741718 | + | 0.997245i | \(0.476369\pi\) | |||||||
\(864\) | 6.91965 | 0.235411 | ||||||||
\(865\) | 7.50512 | 0.255182 | ||||||||
\(866\) | −62.5254 | −2.12470 | ||||||||
\(867\) | −5.31709 | −0.180578 | ||||||||
\(868\) | 0.735908 | 0.0249783 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 19.7804 | 0.670620 | ||||||||
\(871\) | −33.8787 | −1.14793 | ||||||||
\(872\) | 13.2342 | 0.448166 | ||||||||
\(873\) | −7.32927 | −0.248058 | ||||||||
\(874\) | −4.50951 | −0.152536 | ||||||||
\(875\) | −2.63089 | −0.0889404 | ||||||||
\(876\) | 22.9997 | 0.777087 | ||||||||
\(877\) | −13.8710 | −0.468391 | −0.234196 | − | 0.972189i | \(-0.575246\pi\) | ||||
−0.234196 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(878\) | −31.7070 | −1.07006 | ||||||||
\(879\) | 5.75860 | 0.194233 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.9512 | 1.37968 | 0.689841 | − | 0.723961i | \(-0.257681\pi\) | ||||
0.689841 | + | 0.723961i | \(0.257681\pi\) | |||||||
\(882\) | −0.146000 | −0.00491608 | ||||||||
\(883\) | −35.5876 | −1.19762 | −0.598809 | − | 0.800892i | \(-0.704359\pi\) | ||||
−0.598809 | + | 0.800892i | \(0.704359\pi\) | |||||||
\(884\) | 44.9155 | 1.51067 | ||||||||
\(885\) | −5.92760 | −0.199254 | ||||||||
\(886\) | 46.9511 | 1.57735 | ||||||||
\(887\) | 32.2626 | 1.08327 | 0.541635 | − | 0.840614i | \(-0.317805\pi\) | ||||
0.541635 | + | 0.840614i | \(0.317805\pi\) | |||||||
\(888\) | −4.19452 | −0.140759 | ||||||||
\(889\) | −26.5570 | −0.890694 | ||||||||
\(890\) | −11.9314 | −0.399942 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.440934 | −0.0147636 | ||||||||
\(893\) | −4.70287 | −0.157376 | ||||||||
\(894\) | 19.4869 | 0.651738 | ||||||||
\(895\) | −6.54867 | −0.218898 | ||||||||
\(896\) | 20.1390 | 0.672798 | ||||||||
\(897\) | −29.4561 | −0.983510 | ||||||||
\(898\) | −49.6414 | −1.65656 | ||||||||
\(899\) | 2.02520 | 0.0675443 | ||||||||
\(900\) | 1.46722 | 0.0489075 | ||||||||
\(901\) | −31.6346 | −1.05390 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.3329 | 0.809749 | ||||||||
\(904\) | −6.24734 | −0.207784 | ||||||||
\(905\) | 8.04433 | 0.267402 | ||||||||
\(906\) | 29.1286 | 0.967734 | ||||||||
\(907\) | 14.5809 | 0.484149 | 0.242075 | − | 0.970258i | \(-0.422172\pi\) | ||||
0.242075 | + | 0.970258i | \(0.422172\pi\) | |||||||
\(908\) | −33.4790 | −1.11104 | ||||||||
\(909\) | 11.3599 | 0.376784 | ||||||||
\(910\) | 31.7449 | 1.05233 | ||||||||
\(911\) | −33.5719 | −1.11229 | −0.556144 | − | 0.831086i | \(-0.687720\pi\) | ||||
−0.556144 | + | 0.831086i | \(0.687720\pi\) | |||||||
\(912\) | 2.54757 | 0.0843585 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.8684 | −1.35181 | ||||||||
\(915\) | −3.21636 | −0.106330 | ||||||||
\(916\) | 41.3917 | 1.36762 | ||||||||
\(917\) | −12.2272 | −0.403779 | ||||||||
\(918\) | 8.79650 | 0.290328 | ||||||||
\(919\) | 36.2522 | 1.19585 | 0.597924 | − | 0.801553i | \(-0.295992\pi\) | ||||
0.597924 | + | 0.801553i | \(0.295992\pi\) | |||||||
\(920\) | −4.50951 | −0.148674 | ||||||||
\(921\) | 18.4941 | 0.609403 | ||||||||
\(922\) | −8.05566 | −0.265299 | ||||||||
\(923\) | 17.7801 | 0.585239 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.22812 | −0.139020 | ||||||||
\(926\) | 21.3341 | 0.701083 | ||||||||
\(927\) | −2.06064 | −0.0676803 | ||||||||
\(928\) | −73.5071 | −2.41299 | ||||||||
\(929\) | 24.1790 | 0.793286 | 0.396643 | − | 0.917973i | \(-0.370175\pi\) | ||||
0.396643 | + | 0.917973i | \(0.370175\pi\) | |||||||
\(930\) | 0.354989 | 0.0116405 | ||||||||
\(931\) | −0.0417740 | −0.00136909 | ||||||||
\(932\) | −28.4414 | −0.931631 | ||||||||
\(933\) | 11.3134 | 0.370383 | ||||||||
\(934\) | −28.9630 | −0.947697 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.42859 | 0.210125 | ||||||||
\(937\) | −16.4072 | −0.535999 | −0.267999 | − | 0.963419i | \(-0.586362\pi\) | ||||
−0.267999 | + | 0.963419i | \(0.586362\pi\) | |||||||
\(938\) | 25.6118 | 0.836254 | ||||||||
\(939\) | 18.5401 | 0.605035 | ||||||||
\(940\) | 12.9514 | 0.422427 | ||||||||
\(941\) | 8.02749 | 0.261689 | 0.130844 | − | 0.991403i | \(-0.458231\pi\) | ||||
0.130844 | + | 0.991403i | \(0.458231\pi\) | |||||||
\(942\) | −16.7392 | −0.545394 | ||||||||
\(943\) | 2.75091 | 0.0895819 | ||||||||
\(944\) | 28.3440 | 0.922519 | ||||||||
\(945\) | 2.63089 | 0.0855829 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.0500 | 1.17147 | 0.585733 | − | 0.810504i | \(-0.300807\pi\) | ||||
0.585733 | + | 0.810504i | \(0.300807\pi\) | |||||||
\(948\) | −1.77685 | −0.0577095 | ||||||||
\(949\) | 101.579 | 3.29741 | ||||||||
\(950\) | 0.992053 | 0.0321865 | ||||||||
\(951\) | 0.821434 | 0.0266368 | ||||||||
\(952\) | 12.3298 | 0.399612 | ||||||||
\(953\) | 6.99518 | 0.226596 | 0.113298 | − | 0.993561i | \(-0.463858\pi\) | ||||
0.113298 | + | 0.993561i | \(0.463858\pi\) | |||||||
\(954\) | 12.4691 | 0.403702 | ||||||||
\(955\) | 8.72833 | 0.282442 | ||||||||
\(956\) | −22.4097 | −0.724782 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.6146 | 0.601412 | ||||||||
\(959\) | 41.4828 | 1.33955 | ||||||||
\(960\) | −3.32133 | −0.107195 | ||||||||
\(961\) | −30.9637 | −0.998828 | ||||||||
\(962\) | 51.0175 | 1.64487 | ||||||||
\(963\) | 1.14971 | 0.0370490 | ||||||||
\(964\) | −10.5818 | −0.340817 | ||||||||
\(965\) | −15.0613 | −0.484839 | ||||||||
\(966\) | 22.2684 | 0.716473 | ||||||||
\(967\) | 13.1569 | 0.423098 | 0.211549 | − | 0.977367i | \(-0.432149\pi\) | ||||
0.211549 | + | 0.977367i | \(0.432149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.51688 | 0.0808539 | ||||||||
\(970\) | 13.6475 | 0.438194 | ||||||||
\(971\) | −22.7163 | −0.728999 | −0.364500 | − | 0.931204i | \(-0.618760\pi\) | ||||
−0.364500 | + | 0.931204i | \(0.618760\pi\) | |||||||
\(972\) | −1.46722 | −0.0470613 | ||||||||
\(973\) | 26.4104 | 0.846679 | ||||||||
\(974\) | 73.6998 | 2.36149 | ||||||||
\(975\) | 6.48008 | 0.207529 | ||||||||
\(976\) | 15.3797 | 0.492291 | ||||||||
\(977\) | −5.69712 | −0.182267 | −0.0911335 | − | 0.995839i | \(-0.529049\pi\) | ||||
−0.0911335 | + | 0.995839i | \(0.529049\pi\) | |||||||
\(978\) | −36.9430 | −1.18131 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.115043 | 0.00367490 | ||||||||
\(981\) | −13.3402 | −0.425920 | ||||||||
\(982\) | −17.2994 | −0.552047 | ||||||||
\(983\) | 16.9445 | 0.540446 | 0.270223 | − | 0.962798i | \(-0.412903\pi\) | ||||
0.270223 | + | 0.962798i | \(0.412903\pi\) | |||||||
\(984\) | −0.600367 | −0.0191390 | ||||||||
\(985\) | −13.0882 | −0.417026 | ||||||||
\(986\) | −93.4447 | −2.97589 | ||||||||
\(987\) | 23.2232 | 0.739203 | ||||||||
\(988\) | −5.06549 | −0.161155 | ||||||||
\(989\) | 42.0422 | 1.33686 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0516 | 1.14522 | 0.572609 | − | 0.819829i | \(-0.305931\pi\) | ||||
0.572609 | + | 0.819829i | \(0.305931\pi\) | |||||||
\(992\) | −1.31919 | −0.0418844 | ||||||||
\(993\) | −7.98217 | −0.253306 | ||||||||
\(994\) | −13.4415 | −0.426338 | ||||||||
\(995\) | −7.16738 | −0.227221 | ||||||||
\(996\) | −6.84135 | −0.216776 | ||||||||
\(997\) | 18.6585 | 0.590922 | 0.295461 | − | 0.955355i | \(-0.404527\pi\) | ||||
0.295461 | + | 0.955355i | \(0.404527\pi\) | |||||||
\(998\) | −43.4741 | −1.37615 | ||||||||
\(999\) | 4.22812 | 0.133772 |
(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 | 1815.2.a.v.1.3 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bk.1.2 | 4 | |||
5.4 | even | 2 | 9075.2.a.cq.1.2 | 4 | |||
11.5 | even | 5 | 165.2.m.b.91.1 | ✓ | 8 | ||
11.9 | even | 5 | 165.2.m.b.136.1 | yes | 8 | ||
11.10 | odd | 2 | 1815.2.a.r.1.2 | 4 | |||
33.5 | odd | 10 | 495.2.n.b.91.2 | 8 | |||
33.20 | odd | 10 | 495.2.n.b.136.2 | 8 | |||
33.32 | even | 2 | 5445.2.a.br.1.3 | 4 | |||
55.9 | even | 10 | 825.2.n.i.301.2 | 8 | |||
55.27 | odd | 20 | 825.2.bx.g.124.2 | 16 | |||
55.38 | odd | 20 | 825.2.bx.g.124.3 | 16 | |||
55.42 | odd | 20 | 825.2.bx.g.499.3 | 16 | |||
55.49 | even | 10 | 825.2.n.i.751.2 | 8 | |||
55.53 | odd | 20 | 825.2.bx.g.499.2 | 16 | |||
55.54 | odd | 2 | 9075.2.a.dg.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.b.91.1 | ✓ | 8 | 11.5 | even | 5 | ||
165.2.m.b.136.1 | yes | 8 | 11.9 | even | 5 | ||
495.2.n.b.91.2 | 8 | 33.5 | odd | 10 | |||
495.2.n.b.136.2 | 8 | 33.20 | odd | 10 | |||
825.2.n.i.301.2 | 8 | 55.9 | even | 10 | |||
825.2.n.i.751.2 | 8 | 55.49 | even | 10 | |||
825.2.bx.g.124.2 | 16 | 55.27 | odd | 20 | |||
825.2.bx.g.124.3 | 16 | 55.38 | odd | 20 | |||
825.2.bx.g.499.2 | 16 | 55.53 | odd | 20 | |||
825.2.bx.g.499.3 | 16 | 55.42 | odd | 20 | |||
1815.2.a.r.1.2 | 4 | 11.10 | odd | 2 | |||
1815.2.a.v.1.3 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.bk.1.2 | 4 | 3.2 | odd | 2 | |||
5445.2.a.br.1.3 | 4 | 33.32 | even | 2 | |||
9075.2.a.cq.1.2 | 4 | 5.4 | even | 2 | |||
9075.2.a.dg.1.3 | 4 | 55.54 | odd | 2 |