Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.21913473024.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.4 | ||
Root | \(1.43998 - 2.49412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.361 |
Dual form | 1960.2.q.y.961.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.43998 | − | 2.49412i | 0.831373 | − | 1.43998i | −0.0655765 | − | 0.997848i | \(-0.520889\pi\) |
0.896950 | − | 0.442133i | \(-0.145778\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.64709 | − | 4.58489i | −0.882362 | − | 1.52830i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.732874 | + | 1.26937i | −0.220970 | + | 0.382731i | −0.955103 | − | 0.296275i | \(-0.904256\pi\) |
0.734133 | + | 0.679006i | \(0.237589\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.22129 | −0.616076 | −0.308038 | − | 0.951374i | \(-0.599672\pi\) | ||||
−0.308038 | + | 0.951374i | \(0.599672\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.87996 | 0.743603 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.63290 | − | 6.29237i | 0.881107 | − | 1.52612i | 0.0309964 | − | 0.999519i | \(-0.490132\pi\) |
0.850111 | − | 0.526603i | \(-0.176535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.74355 | − | 4.75196i | −0.629413 | − | 1.09017i | −0.987670 | − | 0.156552i | \(-0.949962\pi\) |
0.358257 | − | 0.933623i | \(-0.383371\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.25773 | − | 2.17846i | −0.262256 | − | 0.454240i | 0.704585 | − | 0.709619i | \(-0.251133\pi\) |
−0.966841 | + | 0.255379i | \(0.917800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.60713 | −1.27154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.12260 | −1.32263 | −0.661317 | − | 0.750107i | \(-0.730002\pi\) | ||||
−0.661317 | + | 0.750107i | \(0.730002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.25773 | + | 5.64256i | −0.585106 | + | 1.01343i | 0.409756 | + | 0.912195i | \(0.365614\pi\) |
−0.994862 | + | 0.101239i | \(0.967719\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.11065 | + | 3.65575i | 0.367417 | + | 0.636384i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.45065 | − | 5.97671i | −0.567284 | − | 0.982565i | −0.996833 | − | 0.0795211i | \(-0.974661\pi\) |
0.429549 | − | 0.903043i | \(-0.358672\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.19862 | + | 5.54017i | −0.512189 | + | 0.887138i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3199 | 1.76787 | 0.883935 | − | 0.467609i | \(-0.154885\pi\) | ||||
0.883935 | + | 0.467609i | \(0.154885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.31733 | 0.505888 | 0.252944 | − | 0.967481i | \(-0.418601\pi\) | ||||
0.252944 | + | 0.967481i | \(0.418601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.64709 | − | 4.58489i | 0.394604 | − | 0.683475i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.18353 | − | 7.24608i | −0.610230 | − | 1.05695i | −0.991201 | − | 0.132363i | \(-0.957744\pi\) |
0.380971 | − | 0.924587i | \(-0.375590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.4626 | − | 18.1218i | −1.46506 | − | 2.53756i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.50219 | − | 6.06597i | 0.481062 | − | 0.833225i | −0.518701 | − | 0.854955i | \(-0.673584\pi\) |
0.999764 | + | 0.0217309i | \(0.00691771\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.46575 | −0.197641 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.8026 | −2.09311 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.53553 | − | 7.85578i | 0.590476 | − | 1.02273i | −0.403692 | − | 0.914895i | \(-0.632273\pi\) |
0.994168 | − | 0.107840i | \(-0.0343934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.60713 | + | 9.71184i | 0.717920 | + | 1.24347i | 0.961823 | + | 0.273674i | \(0.0882389\pi\) |
−0.243903 | + | 0.969800i | \(0.578428\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.11065 | − | 1.92370i | −0.137759 | − | 0.238605i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.20620 | − | 5.55330i | 0.391700 | − | 0.678444i | −0.600974 | − | 0.799268i | \(-0.705221\pi\) |
0.992674 | + | 0.120825i | \(0.0385539\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.24445 | −0.872130 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.5316 | −1.24987 | −0.624935 | − | 0.780677i | \(-0.714875\pi\) | ||||
−0.624935 | + | 0.780677i | \(0.714875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.26083 | − | 9.11202i | 0.615733 | − | 1.06648i | −0.374522 | − | 0.927218i | \(-0.622193\pi\) |
0.990255 | − | 0.139263i | \(-0.0444735\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43998 | + | 2.49412i | 0.166275 | + | 0.287996i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.09555 | − | 8.82576i | −0.573295 | − | 0.992975i | −0.996225 | − | 0.0868130i | \(-0.972332\pi\) |
0.422930 | − | 0.906162i | \(-0.361002\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.57288 | + | 2.72431i | −0.174764 | + | 0.302701i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.4186 | −1.80217 | −0.901087 | − | 0.433638i | \(-0.857230\pi\) | ||||
−0.901087 | + | 0.433638i | \(0.857230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.26580 | 0.788086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.2564 | + | 17.7646i | −1.09960 | + | 1.90457i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.91512 | + | 8.51324i | 0.521002 | + | 0.902401i | 0.999702 | + | 0.0244228i | \(0.00777479\pi\) |
−0.478700 | + | 0.877978i | \(0.658892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.38215 | + | 16.2504i | 0.972883 | + | 1.68508i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.74355 | − | 4.75196i | 0.281482 | − | 0.487541i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.09423 | 0.212636 | 0.106318 | − | 0.994332i | \(-0.466094\pi\) | ||||
0.106318 | + | 0.994332i | \(0.466094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.75992 | 0.779901 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.83280 | + | 11.8348i | −0.679889 | + | 1.17760i | 0.295125 | + | 0.955459i | \(0.404639\pi\) |
−0.975014 | + | 0.222144i | \(0.928695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.01195 | + | 8.68096i | 0.493843 | + | 0.855360i | 0.999975 | − | 0.00709551i | \(-0.00225859\pi\) |
−0.506132 | + | 0.862456i | \(0.668925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.71020 | + | 8.15831i | 0.455352 | + | 0.788693i | 0.998708 | − | 0.0508091i | \(-0.0161800\pi\) |
−0.543356 | + | 0.839502i | \(0.682847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.49280 | − | 7.78175i | 0.430332 | − | 0.745356i | −0.566570 | − | 0.824014i | \(-0.691730\pi\) |
0.996902 | + | 0.0786572i | \(0.0250632\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.8755 | −1.88650 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9476 | 1.02987 | 0.514933 | − | 0.857231i | \(-0.327817\pi\) | ||||
0.514933 | + | 0.857231i | \(0.327817\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.25773 | − | 2.17846i | 0.117284 | − | 0.203142i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.87996 | + | 10.1844i | 0.543603 | + | 0.941547i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.42579 | + | 7.66570i | 0.402345 | + | 0.696882i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.3004 | − | 28.2332i | 1.46976 | − | 2.54570i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.44696 | −0.483340 | −0.241670 | − | 0.970359i | \(-0.577695\pi\) | ||||
−0.241670 | + | 0.970359i | \(0.577695\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.77689 | − | 8.27382i | 0.420582 | − | 0.728469i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.58707 | + | 7.94503i | 0.400774 | + | 0.694161i | 0.993820 | − | 0.111008i | \(-0.0354079\pi\) |
−0.593046 | + | 0.805169i | \(0.702075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.30357 | − | 5.72194i | −0.284326 | − | 0.492467i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.65685 | + | 9.79796i | −0.483298 | + | 0.837096i | −0.999816 | − | 0.0191800i | \(-0.993894\pi\) |
0.516518 | + | 0.856276i | \(0.327228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.83099 | 0.579397 | 0.289698 | − | 0.957118i | \(-0.406445\pi\) | ||||
0.289698 | + | 0.957118i | \(0.406445\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.0968 | −2.02932 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.62793 | − | 2.81965i | 0.136134 | − | 0.235791i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.56130 | − | 6.16835i | −0.295750 | − | 0.512254i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.981216 | + | 1.69952i | 0.0803844 | + | 0.139230i | 0.903415 | − | 0.428767i | \(-0.141052\pi\) |
−0.823031 | + | 0.567997i | \(0.807719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.66256 | − | 6.34373i | 0.298055 | − | 0.516246i | −0.677636 | − | 0.735397i | \(-0.736996\pi\) |
0.975691 | + | 0.219152i | \(0.0703289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −38.4664 | −3.10982 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.51547 | −0.523335 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.73155 | + | 6.46323i | −0.297810 | + | 0.515822i | −0.975635 | − | 0.219402i | \(-0.929589\pi\) |
0.677825 | + | 0.735223i | \(0.262923\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.0862 | − | 17.4697i | −0.799885 | − | 1.38544i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.13951 | + | 10.6339i | 0.480883 | + | 0.832914i | 0.999759 | − | 0.0219351i | \(-0.00698273\pi\) |
−0.518876 | + | 0.854849i | \(0.673649\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.11065 | + | 3.65575i | −0.164314 | + | 0.284600i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2300 | 1.41068 | 0.705342 | − | 0.708868i | \(-0.250794\pi\) | ||||
0.705342 | + | 0.708868i | \(0.250794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.06585 | −0.620450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.5248 | + | 25.1577i | −1.11074 | + | 1.92386i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.96223 | + | 15.5230i | 0.681386 | + | 1.18020i | 0.974558 | + | 0.224135i | \(0.0719558\pi\) |
−0.293172 | + | 0.956060i | \(0.594711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.0622 | − | 22.6243i | −0.981812 | − | 1.70055i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0187836 | + | 0.0325342i | −0.00140395 | + | 0.00243172i | −0.866727 | − | 0.498784i | \(-0.833780\pi\) |
0.865323 | + | 0.501215i | \(0.167114\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.82105 | 0.507004 | 0.253502 | − | 0.967335i | \(-0.418417\pi\) | ||||
0.253502 | + | 0.967335i | \(0.418417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.2966 | 2.38744 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.45065 | − | 5.97671i | 0.253697 | − | 0.439416i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.32491 | + | 9.22302i | 0.389396 | + | 0.674454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.93101 | + | 5.07666i | 0.212080 | + | 0.367334i | 0.952365 | − | 0.304959i | \(-0.0986428\pi\) |
−0.740285 | + | 0.672293i | \(0.765309\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.38584 | − | 4.13239i | 0.171736 | − | 0.297456i | −0.767291 | − | 0.641300i | \(-0.778396\pi\) |
0.939027 | + | 0.343843i | \(0.111729\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.39724 | −0.458116 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.28714 | −0.661682 | −0.330841 | − | 0.943687i | \(-0.607332\pi\) | ||||
−0.330841 | + | 0.943687i | \(0.607332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.60088 | + | 2.77281i | −0.113483 | + | 0.196559i | −0.917172 | − | 0.398490i | \(-0.869534\pi\) |
0.803689 | + | 0.595049i | \(0.202868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.23373 | − | 15.9933i | −0.651297 | − | 1.12808i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.65995 | + | 9.80332i | 0.395308 | + | 0.684693i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.65867 | + | 11.5331i | −0.462809 | + | 0.801609i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.04269 | 0.556325 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.1055 | −1.79718 | −0.898590 | − | 0.438790i | \(-0.855407\pi\) | ||||
−0.898590 | + | 0.438790i | \(0.855407\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.1653 | + | 26.2671i | −1.03911 | + | 1.79979i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.65867 | + | 2.87289i | 0.113120 | + | 0.195930i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.1510 | − | 26.2423i | −1.02381 | − | 1.77329i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.06974 | + | 13.9772i | −0.542829 | + | 0.940208i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.8214 | 1.59520 | 0.797599 | − | 0.603188i | \(-0.206103\pi\) | ||||
0.797599 | + | 0.603188i | \(0.206103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.29417 | 0.352945 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.71100 | + | 8.15969i | −0.312680 | + | 0.541577i | −0.978942 | − | 0.204141i | \(-0.934560\pi\) |
0.666262 | + | 0.745718i | \(0.267893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.96793 | + | 8.60471i | 0.328290 | + | 0.568616i | 0.982173 | − | 0.187981i | \(-0.0601942\pi\) |
−0.653882 | + | 0.756596i | \(0.726861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.618537 | − | 1.07134i | −0.0405217 | − | 0.0701856i | 0.845053 | − | 0.534682i | \(-0.179569\pi\) |
−0.885575 | + | 0.464497i | \(0.846235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.18353 | − | 7.24608i | 0.272903 | − | 0.472682i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.3500 | −1.90649 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.05710 | 0.0683782 | 0.0341891 | − | 0.999415i | \(-0.489115\pi\) | ||||
0.0341891 | + | 0.999415i | \(0.489115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.26452 | − | 3.92226i | 0.145870 | − | 0.252655i | −0.783827 | − | 0.620979i | \(-0.786735\pi\) |
0.929697 | + | 0.368324i | \(0.120068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.38087 | − | 9.31993i | −0.345183 | − | 0.597874i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.09423 | + | 10.5555i | 0.387766 | + | 0.671631i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.6424 | + | 40.9499i | −1.49828 | + | 2.59510i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.74198 | −0.299311 | −0.149656 | − | 0.988738i | \(-0.547816\pi\) | ||||
−0.149656 | + | 0.988738i | \(0.547816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.68704 | 0.231802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.4626 | − | 18.1218i | 0.655194 | − | 1.13483i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.96484 | + | 13.7955i | 0.496833 | + | 0.860540i | 0.999993 | − | 0.00365291i | \(-0.00116276\pi\) |
−0.503160 | + | 0.864193i | \(0.667829\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.8541 | + | 32.6563i | 1.16704 | + | 2.02138i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.63732 | − | 11.4962i | 0.409275 | − | 0.708885i | −0.585534 | − | 0.810648i | \(-0.699115\pi\) |
0.994809 | + | 0.101763i | \(0.0324484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.00437 | 0.430275 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.3107 | 1.73259 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.4301 | − | 21.5295i | 0.757874 | − | 1.31268i | −0.186059 | − | 0.982539i | \(-0.559571\pi\) |
0.943933 | − | 0.330138i | \(-0.107095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2143 | − | 26.3519i | −0.924201 | − | 1.60076i | −0.792842 | − | 0.609428i | \(-0.791399\pi\) |
−0.131359 | − | 0.991335i | \(-0.541934\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.732874 | − | 1.26937i | −0.0441939 | − | 0.0765462i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8649 | − | 18.8185i | 0.652807 | − | 1.13069i | −0.329632 | − | 0.944109i | \(-0.606925\pi\) |
0.982439 | − | 0.186585i | \(-0.0597419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.4940 | 2.06510 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.285426 | −0.0170271 | −0.00851354 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851354 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.75731 | − | 4.77581i | 0.163905 | − | 0.283892i | −0.772361 | − | 0.635184i | \(-0.780924\pi\) |
0.936266 | + | 0.351292i | \(0.114258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.90131 | − | 13.6855i | −0.468033 | − | 0.810657i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.8959 | − | 30.9966i | −1.05270 | − | 1.82333i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.01564 | − | 5.22325i | 0.176780 | − | 0.306192i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5777 | −1.02690 | −0.513450 | − | 0.858120i | \(-0.671633\pi\) | ||||
−0.513450 | + | 0.858120i | \(0.671633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.07107 | 0.528138 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.84219 | − | 8.38692i | 0.280973 | − | 0.486659i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.79380 | + | 4.83900i | 0.161570 | + | 0.279847i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.6782 | + | 34.0836i | 1.13048 | + | 1.95805i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.60713 | + | 9.71184i | −0.321063 | + | 0.556098i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4771 | 1.45405 | 0.727026 | − | 0.686610i | \(-0.240902\pi\) | ||||
0.727026 | + | 0.686610i | \(0.240902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.8685 | 1.64227 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.7831 | − | 18.6768i | 0.611452 | − | 1.05907i | −0.379544 | − | 0.925174i | \(-0.623919\pi\) |
0.990996 | − | 0.133893i | \(-0.0427477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.48970 | + | 2.58024i | 0.0842030 | + | 0.145844i | 0.905051 | − | 0.425302i | \(-0.139832\pi\) |
−0.820848 | + | 0.571146i | \(0.806499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.99819 | + | 6.92507i | 0.224561 | + | 0.388950i | 0.956188 | − | 0.292755i | \(-0.0945720\pi\) |
−0.731627 | + | 0.681705i | \(0.761239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.21997 | − | 9.04125i | 0.292262 | − | 0.506213i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.1304 | 1.51427 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.8681 | −2.21832 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.11065 | − | 1.92370i | 0.0616076 | − | 0.106708i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.9391 | − | 22.4111i | −0.715532 | − | 1.23934i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1483 | − | 29.7018i | −0.942557 | − | 1.63256i | −0.760570 | − | 0.649256i | \(-0.775081\pi\) |
−0.181987 | − | 0.983301i | \(-0.558253\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.2684 | + | 31.6417i | −1.00110 | + | 1.73396i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.41240 | 0.350347 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8719 | 1.30038 | 0.650192 | − | 0.759770i | \(-0.274689\pi\) | ||||
0.650192 | + | 0.759770i | \(0.274689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.7644 | − | 27.3047i | 0.856203 | − | 1.48299i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.77502 | − | 8.27057i | −0.258582 | − | 0.447876i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.62223 | − | 6.27388i | −0.195014 | − | 0.337774i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.17782 | + | 5.50415i | −0.170595 | + | 0.295478i | −0.938628 | − | 0.344931i | \(-0.887902\pi\) |
0.768033 | + | 0.640410i | \(0.221236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.24821 | 0.495045 | 0.247523 | − | 0.968882i | \(-0.420384\pi\) | ||||
0.247523 | + | 0.968882i | \(0.420384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.6764 | 0.783368 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.98042 | − | 15.5545i | 0.477979 | − | 0.827885i | −0.521702 | − | 0.853128i | \(-0.674703\pi\) |
0.999681 | + | 0.0252431i | \(0.00803599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.26580 | − | 9.12063i | −0.279480 | − | 0.484073i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.1421 | + | 17.5667i | 0.535281 | + | 0.927135i | 0.999150 | + | 0.0412304i | \(0.0131278\pi\) |
−0.463868 | + | 0.885904i | \(0.653539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.55410 | + | 9.61998i | −0.292321 | + | 0.506315i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.4922 | 1.33799 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5217 | 0.550729 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5719 | − | 21.7752i | 0.656249 | − | 1.13666i | −0.325330 | − | 0.945601i | \(-0.605475\pi\) |
0.981579 | − | 0.191056i | \(-0.0611913\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29.9647 | − | 51.9005i | −1.55990 | − | 2.70183i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.368866 | − | 0.638895i | −0.0190992 | − | 0.0330807i | 0.856318 | − | 0.516449i | \(-0.172746\pi\) |
−0.875417 | + | 0.483368i | \(0.839413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.43998 | + | 2.49412i | −0.0743603 | + | 0.128796i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.8214 | 0.814843 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.11120 | −0.365278 | −0.182639 | − | 0.983180i | \(-0.558464\pi\) | ||||
−0.182639 | + | 0.983180i | \(0.558464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.84352 | + | 13.5854i | −0.401836 | + | 0.696000i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.3421 | + | 24.8412i | 0.732846 | + | 1.26933i | 0.955662 | + | 0.294466i | \(0.0951419\pi\) |
−0.222816 | + | 0.974861i | \(0.571525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.78127 | − | 15.2096i | −0.446377 | − | 0.773148i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.75944 | + | 11.7077i | −0.342717 | + | 0.593603i | −0.984936 | − | 0.172918i | \(-0.944681\pi\) |
0.642219 | + | 0.766521i | \(0.278014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.2769 | −0.924302 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.4212 | 1.33277 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.09555 | − | 8.82576i | 0.256385 | − | 0.444072i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.01195 | + | 3.48481i | 0.100977 | + | 0.174897i | 0.912087 | − | 0.409996i | \(-0.134470\pi\) |
−0.811110 | + | 0.584893i | \(0.801136\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.1898 | + | 21.1133i | 0.608729 | + | 1.05435i | 0.991450 | + | 0.130485i | \(0.0416535\pi\) |
−0.382722 | + | 0.923864i | \(0.625013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.23639 | − | 12.5338i | 0.360470 | − | 0.624353i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.14576 | −0.156314 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1156 | 0.501410 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.24761 | − | 7.35708i | 0.210031 | − | 0.363784i | −0.741693 | − | 0.670739i | \(-0.765977\pi\) |
0.951724 | + | 0.306955i | \(0.0993102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.2915 | + | 28.2177i | 0.803601 | + | 1.39188i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.20929 | − | 14.2189i | −0.402978 | − | 0.697979i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.83649 | − | 17.0373i | 0.481695 | − | 0.834320i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.07469 | −0.150209 | −0.0751043 | − | 0.997176i | \(-0.523929\pi\) | ||||
−0.0751043 | + | 0.997176i | \(0.523929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4790 | 1.09556 | 0.547780 | − | 0.836623i | \(-0.315473\pi\) | ||||
0.547780 | + | 0.836623i | \(0.315473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.1483 | + | 38.3620i | −1.07689 | + | 1.86523i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.63290 | + | 6.29237i | 0.176221 | + | 0.305225i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.68837 | − | 8.12049i | −0.226357 | − | 0.392061i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.58627 | − | 4.47955i | 0.124576 | − | 0.215772i | −0.796991 | − | 0.603991i | \(-0.793576\pi\) |
0.921567 | + | 0.388219i | \(0.126910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.78030 | −0.0855557 | −0.0427779 | − | 0.999085i | \(-0.513621\pi\) | ||||
−0.0427779 | + | 0.999085i | \(0.513621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.5128 | −0.983514 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.90131 | + | 11.9534i | −0.330134 | + | 0.571809i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.8932 | − | 22.3318i | −0.615361 | − | 1.06584i | −0.990321 | − | 0.138795i | \(-0.955677\pi\) |
0.374960 | − | 0.927041i | \(-0.377656\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.22129 | + | 10.7756i | 0.295583 | + | 0.511964i | 0.975120 | − | 0.221677i | \(-0.0711529\pi\) |
−0.679538 | + | 0.733641i | \(0.737820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.91512 | + | 8.51324i | −0.232999 | + | 0.403566i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.65173 | 0.267318 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.3574 | −1.19669 | −0.598344 | − | 0.801239i | \(-0.704174\pi\) | ||||
−0.598344 | + | 0.801239i | \(0.704174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.29605 | + | 14.3692i | −0.390646 | + | 0.676618i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.5480 | − | 18.2697i | −0.495589 | − | 0.858386i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3520 | + | 30.0545i | 0.811690 | + | 1.40589i | 0.911680 | + | 0.410901i | \(0.134786\pi\) |
−0.0999897 | + | 0.994988i | \(0.531881\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.0030 | + | 41.5745i | −1.12037 | + | 1.94053i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.8762 | 1.90380 | 0.951898 | − | 0.306414i | \(-0.0991293\pi\) | ||||
0.951898 | + | 0.306414i | \(0.0991293\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1236 | −1.16759 | −0.583796 | − | 0.811901i | \(-0.698433\pi\) | ||||
−0.583796 | + | 0.811901i | \(0.698433\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.38215 | + | 16.2504i | −0.435087 | + | 0.753592i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.5883 | − | 23.5356i | −0.628792 | − | 1.08910i | −0.987795 | − | 0.155763i | \(-0.950217\pi\) |
0.359003 | − | 0.933336i | \(-0.383117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.7467 | + | 18.6138i | 0.495182 | + | 0.857680i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.43119 | + | 4.21094i | −0.111786 | + | 0.193619i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.48709 | 0.251765 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −37.0824 | −1.69789 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.03644 | + | 1.79517i | −0.0473561 | + | 0.0820232i | −0.888732 | − | 0.458427i | \(-0.848413\pi\) |
0.841376 | + | 0.540451i | \(0.181746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.66492 | + | 13.2760i | 0.349490 | + | 0.605335i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.04711 | + | 1.81365i | 0.0475469 | + | 0.0823537i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6745 | + | 28.8811i | −0.755594 | + | 1.30873i | 0.189484 | + | 0.981884i | \(0.439318\pi\) |
−0.945078 | + | 0.326844i | \(0.894015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 35.3631 | 1.59917 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.4487 | 1.64491 | 0.822453 | − | 0.568833i | \(-0.192605\pi\) | ||||
0.822453 | + | 0.568833i | \(0.192605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.8757 | + | 44.8180i | −1.16538 | + | 2.01850i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.87996 | + | 6.72029i | 0.174391 | + | 0.302055i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.74684 | + | 6.48972i | 0.167732 | + | 0.290520i | 0.937622 | − | 0.347657i | \(-0.113022\pi\) |
−0.769890 | + | 0.638176i | \(0.779689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.2509 | − | 45.4679i | 1.17280 | − | 2.03136i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.6381 | 0.697267 | 0.348634 | − | 0.937259i | \(-0.386646\pi\) | ||||
0.348634 | + | 0.937259i | \(0.386646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.6656 | −0.608111 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6147 | + | 20.1172i | −0.515825 | + | 0.893436i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.60525 | + | 6.24448i | 0.159800 | + | 0.276782i | 0.934797 | − | 0.355184i | \(-0.115582\pi\) |
−0.774996 | + | 0.631966i | \(0.782248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.1270 | + | 31.3968i | 0.800326 | + | 1.38620i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.01195 | + | 8.68096i | −0.220853 | + | 0.382529i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2640 | 0.539370 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 51.6218 | 2.26594 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.41181 | − | 12.8376i | 0.324717 | − | 0.562426i | −0.656738 | − | 0.754119i | \(-0.728064\pi\) |
0.981455 | + | 0.191692i | \(0.0613976\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.13641 | − | 3.70038i | −0.0934189 | − | 0.161806i | 0.815529 | − | 0.578717i | \(-0.196446\pi\) |
−0.908948 | + | 0.416910i | \(0.863113\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.6700 | + | 40.9977i | 1.03108 | + | 1.78589i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.33621 | − | 14.4387i | 0.362444 | − | 0.627771i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −48.0238 | −2.08406 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.1448 | −1.08914 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.71020 | + | 8.15831i | −0.203640 | + | 0.352714i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0540961 | + | 0.0936971i | 0.00233442 | + | 0.00404333i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.471449 | + | 0.816574i | 0.0202692 | + | 0.0351073i | 0.875982 | − | 0.482344i | \(-0.160214\pi\) |
−0.855713 | + | 0.517451i | \(0.826881\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.82218 | − | 17.0125i | 0.421510 | − | 0.730077i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.98559 | 0.384900 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1871 | −0.478327 | −0.239164 | − | 0.970979i | \(-0.576873\pi\) | ||||
−0.239164 | + | 0.970979i | \(0.576873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.6851 | − | 51.4162i | 1.26693 | − | 2.19439i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.5412 | + | 33.8463i | 0.832483 | + | 1.44190i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.93775 | − | 17.2127i | −0.421834 | − | 0.730638i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.3652 | + | 24.8813i | −0.608675 | + | 1.05426i | 0.382784 | + | 0.923838i | \(0.374965\pi\) |
−0.991459 | + | 0.130418i | \(0.958368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.36877 | −0.311666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.6711 | 1.29493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.22370 | − | 2.11952i | 0.0515729 | − | 0.0893270i | −0.839086 | − | 0.543998i | \(-0.816910\pi\) |
0.890659 | + | 0.454671i | \(0.150243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.47381 | + | 9.48092i | 0.230285 | + | 0.398865i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.7529 | − | 30.7489i | −0.744240 | − | 1.28906i | −0.950549 | − | 0.310575i | \(-0.899479\pi\) |
0.206309 | − | 0.978487i | \(-0.433855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.89437 | + | 5.01320i | −0.121126 | + | 0.209796i | −0.920212 | − | 0.391421i | \(-0.871984\pi\) |
0.799086 | + | 0.601216i | \(0.205317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.8824 | 0.705272 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.51547 | 0.104902 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.10386 | − | 1.91195i | 0.0459545 | − | 0.0795955i | −0.842133 | − | 0.539270i | \(-0.818700\pi\) |
0.888088 | + | 0.459674i | \(0.152034\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.87112 | − | 11.9011i | −0.285554 | − | 0.494594i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.13332 | + | 8.89117i | 0.212600 | + | 0.368235i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.87996 | + | 10.1844i | −0.243106 | + | 0.421073i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.6719 | −1.63744 | −0.818718 | − | 0.574196i | \(-0.805315\pi\) | ||||
−0.818718 | + | 0.574196i | \(0.805315\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.7510 | 1.47309 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.3733 | + | 23.1632i | −0.550104 | + | 0.952809i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.46654 | − | 7.73628i | −0.183419 | − | 0.317691i | 0.759624 | − | 0.650363i | \(-0.225383\pi\) |
−0.943043 | + | 0.332672i | \(0.892050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.61047 | + | 7.98557i | 0.188694 | + | 0.326828i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.19500 | + | 15.9262i | −0.375697 | + | 0.650727i | −0.990431 | − | 0.138008i | \(-0.955930\pi\) |
0.614734 | + | 0.788735i | \(0.289263\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5063 | −0.714096 | −0.357048 | − | 0.934086i | \(-0.616217\pi\) | ||||
−0.357048 | + | 0.934086i | \(0.616217\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.9484 | −1.38248 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.42579 | + | 7.66570i | −0.179934 | + | 0.311655i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.5719 | − | 39.0957i | −0.916166 | − | 1.58685i | −0.805185 | − | 0.593024i | \(-0.797934\pi\) |
−0.110981 | − | 0.993822i | \(-0.535399\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.29285 | + | 16.0957i | 0.375948 | + | 0.651162i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.92787 | − | 10.2674i | 0.239424 | − | 0.414695i | −0.721125 | − | 0.692805i | \(-0.756375\pi\) |
0.960549 | + | 0.278110i | \(0.0897079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.6009 | 1.31459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.8174 | −0.838078 | −0.419039 | − | 0.907968i | \(-0.637633\pi\) | ||||
−0.419039 | + | 0.907968i | \(0.637633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.39074 | + | 7.60499i | −0.176479 | + | 0.305670i | −0.940672 | − | 0.339317i | \(-0.889804\pi\) |
0.764193 | + | 0.644987i | \(0.223137\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.31002 | + | 14.3934i | 0.333470 | + | 0.577586i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.5813 | − | 20.0594i | 0.462513 | − | 0.801097i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.1435 | −1.99935 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.1004 | 0.879803 | 0.439902 | − | 0.898046i | \(-0.355013\pi\) | ||||
0.439902 | + | 0.898046i | \(0.355013\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.5915 | + | 65.1103i | −1.49413 | + | 2.58790i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.72348 | − | 4.71721i | −0.108078 | − | 0.187197i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.8781 | + | 48.2862i | 1.10284 | + | 1.91017i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.9288 | − | 37.9819i | 0.866137 | − | 1.50019i | 0.000223352 | − | 1.00000i | \(-0.499929\pi\) |
0.865914 | − | 0.500193i | \(-0.166738\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.9895 | −1.49816 | −0.749079 | − | 0.662480i | \(-0.769504\pi\) | ||||
−0.749079 | + | 0.662480i | \(0.769504\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.55379 | 0.376180 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6852 | − | 28.8997i | 0.655964 | − | 1.13616i | −0.325687 | − | 0.945478i | \(-0.605596\pi\) |
0.981651 | − | 0.190686i | \(-0.0610711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.64795 | + | 11.5146i | 0.260955 | + | 0.451987i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.53160 | − | 13.0451i | −0.294734 | − | 0.510495i | 0.680189 | − | 0.733037i | \(-0.261898\pi\) |
−0.974923 | + | 0.222542i | \(0.928564\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.58707 | + | 7.94503i | −0.179232 | + | 0.310438i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −55.7035 | −2.17320 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.153540 | −0.00598106 | −0.00299053 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00299053 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.15279 | − | 10.6569i | 0.239316 | − | 0.414507i | −0.721202 | − | 0.692724i | \(-0.756410\pi\) |
0.960518 | + | 0.278217i | \(0.0897436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2405 | + | 40.2538i | 0.902588 | + | 1.56333i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.95834 | + | 15.5163i | 0.346868 | + | 0.600794i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.3023 | − | 59.4134i | 1.32621 | − | 2.29705i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.4373 | −0.634554 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.82480 | 0.185983 | 0.0929913 | − | 0.995667i | \(-0.470357\pi\) | ||||
0.0929913 | + | 0.995667i | \(0.470357\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.30357 | − | 5.72194i | 0.127154 | − | 0.220238i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.25203 | + | 14.2929i | 0.317151 | + | 0.549322i | 0.979892 | − | 0.199526i | \(-0.0639403\pi\) |
−0.662741 | + | 0.748849i | \(0.730607\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5675 | + | 23.4996i | 0.519907 | + | 0.900506i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.1811 | + | 28.0264i | −0.619152 | + | 1.07240i | 0.370489 | + | 0.928837i | \(0.379190\pi\) |
−0.989641 | + | 0.143565i | \(0.954143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.3137 | −0.432275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.6149 | 1.09173 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.77939 | + | 13.4743i | −0.296371 | + | 0.513330i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.16223 | + | 2.01304i | 0.0442132 | + | 0.0765796i | 0.887285 | − | 0.461221i | \(-0.152589\pi\) |
−0.843072 | + | 0.537801i | \(0.819255\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.41549 | + | 5.91581i | 0.129557 | + | 0.224399i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.1240 | − | 71.2289i | 1.55768 | − | 2.69799i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.56272 | −0.134755 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.77071 | −0.255726 | −0.127863 | − | 0.991792i | \(-0.540812\pi\) | ||||
−0.127863 | + | 0.991792i | \(0.540812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9341 | + | 32.7947i | −0.714111 | + | 1.23688i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.0484 | − | 20.8684i | −0.453769 | − | 0.785951i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.11871 | + | 5.40177i | 0.117126 | + | 0.202868i | 0.918627 | − | 0.395125i | \(-0.129299\pi\) |
−0.801502 | + | 0.597992i | \(0.795965\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.9767 | + | 46.7251i | −1.01171 | + | 1.75233i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.3895 | 0.613790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.25586 | 0.121762 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.52221 | − | 2.63654i | 0.0568478 | − | 0.0984633i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.47466 | + | 4.28623i | 0.0922891 | + | 0.159849i | 0.908474 | − | 0.417941i | \(-0.137248\pi\) |
−0.816185 | + | 0.577791i | \(0.803915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.52172 | − | 11.2960i | −0.242545 | − | 0.420101i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.56130 | − | 6.16835i | 0.132263 | − | 0.229087i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.5847 | 0.689269 | 0.344635 | − | 0.938737i | \(-0.388003\pi\) | ||||
0.344635 | + | 0.938737i | \(0.388003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.4306 | −1.49743 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0515 | − | 20.8739i | 0.445742 | − | 0.772048i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.2848 | − | 21.2779i | −0.453749 | − | 0.785916i | 0.544867 | − | 0.838523i | \(-0.316580\pi\) |
−0.998615 | + | 0.0526068i | \(0.983247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.69948 | + | 8.13974i | 0.173108 | + | 0.299831i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.21475 | − | 7.30016i | 0.155042 | − | 0.268541i | −0.778032 | − | 0.628224i | \(-0.783782\pi\) |
0.933074 | + | 0.359684i | \(0.117115\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.1023 | 1.28951 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.4705 | −0.420811 | −0.210405 | − | 0.977614i | \(-0.567478\pi\) | ||||
−0.210405 | + | 0.977614i | \(0.567478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.981216 | + | 1.69952i | −0.0359490 | + | 0.0622655i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 43.4614 | + | 75.2774i | 1.59017 | + | 2.75426i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.15146 | + | 14.1187i | 0.297451 | + | 0.515200i | 0.975552 | − | 0.219768i | \(-0.0705302\pi\) |
−0.678101 | + | 0.734969i | \(0.737197\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.82836 | + | 11.8271i | −0.248839 | + | 0.431002i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.32511 | 0.266588 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0875 | 0.911821 | 0.455910 | − | 0.890026i | \(-0.349314\pi\) | ||||
0.455910 | + | 0.890026i | \(0.349314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.30927 | − | 9.19592i | 0.192714 | − | 0.333791i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.5425 | + | 42.5088i | 0.889664 | + | 1.54094i | 0.840273 | + | 0.542163i | \(0.182395\pi\) |
0.0493908 | + | 0.998780i | \(0.484272\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.2332 | − | 33.3129i | −0.695378 | − | 1.20443i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.0748 | + | 17.4500i | −0.363778 | + | 0.630083i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0548 | 0.975619 | 0.487810 | − | 0.872950i | \(-0.337796\pi\) | ||||
0.487810 | + | 0.872950i | \(0.337796\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.8769 | 1.65221 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.5414 | + | 35.5787i | −0.738822 | + | 1.27968i | 0.214203 | + | 0.976789i | \(0.431284\pi\) |
−0.953026 | + | 0.302889i | \(0.902049\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.25773 | − | 5.64256i | −0.117021 | − | 0.202687i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.0567 | − | 53.7917i | −1.11272 | − | 1.92729i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.71833 | − | 13.3685i | 0.276184 | − | 0.478364i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 47.0600 | 1.68179 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.46309 | −0.266369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.87373 | + | 17.1018i | −0.351960 | + | 0.609613i | −0.986593 | − | 0.163201i | \(-0.947818\pi\) |
0.634632 | + | 0.772814i | \(0.281151\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.1152 | − | 33.1085i | −0.680520 | − | 1.17870i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.4551 | − | 21.5729i | −0.442293 | − | 0.766075i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.0862 | − | 17.4697i | 0.357719 | − | 0.619588i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.9488 | 1.27337 | 0.636685 | − | 0.771124i | \(-0.280305\pi\) | ||||
0.636685 | + | 0.771124i | \(0.280305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.7933 | −2.15071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.0215 | − | 45.0706i | 0.919424 | − | 1.59249i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.71104 | + | 13.3559i | 0.272117 | + | 0.471320i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.7981 | − | 62.0041i | −1.26015 | − | 2.18265i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.5568 | + | 33.8734i | −0.687582 | + | 1.19093i | 0.285036 | + | 0.958517i | \(0.407994\pi\) |
−0.972618 | + | 0.232410i | \(0.925339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.4017 | −1.52404 | −0.762019 | − | 0.647555i | \(-0.775792\pi\) | ||||
−0.762019 | + | 0.647555i | \(0.775792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −87.6330 | −3.07342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.13951 | + | 10.6339i | −0.215058 | + | 0.372491i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.10126 | − | 15.7638i | −0.318413 | − | 0.551507i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.50676 | − | 11.2700i | −0.227088 | − | 0.393327i | 0.729856 | − | 0.683601i | \(-0.239587\pi\) |
−0.956944 | + | 0.290274i | \(0.906254\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0295033 | − | 0.0511012i | 0.00102842 | − | 0.00178127i | −0.865511 | − | 0.500890i | \(-0.833006\pi\) |
0.866539 | + | 0.499109i | \(0.166339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.22129 | −0.146967 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.519093 | 0.0180506 | 0.00902531 | − | 0.999959i | \(-0.497127\pi\) | ||||
0.00902531 | + | 0.999959i | \(0.497127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0787 | − | 43.4376i | 0.871019 | − | 1.50865i | 0.0100748 | − | 0.999949i | \(-0.496793\pi\) |
0.860944 | − | 0.508700i | \(-0.169874\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.2904 | − | 54.1965i | −1.08545 | − | 1.88006i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.11502 | + | 15.7877i | 0.315438 | + | 0.546355i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.5243 | − | 37.2812i | 0.743988 | − | 1.28863i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.44696 | −0.326145 | −0.163073 | − | 0.986614i | \(-0.552141\pi\) | ||||
−0.163073 | + | 0.986614i | \(0.552141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.7315 | 0.749360 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.411008 | + | 0.711886i | −0.0141559 | + | 0.0245187i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.03292 | − | 6.98523i | −0.138737 | − | 0.240299i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.94095 | − | 13.7541i | −0.272533 | − | 0.472041i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.68001 | + | 15.0342i | −0.297547 | + | 0.515366i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.2482 | −0.727525 | −0.363762 | − | 0.931492i | \(-0.618508\pi\) | ||||
−0.363762 | + | 0.931492i | \(0.618508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.0496 | −0.993476 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.28217 | − | 5.68489i | 0.112117 | − | 0.194192i | −0.804507 | − | 0.593944i | \(-0.797570\pi\) |
0.916624 | + | 0.399751i | \(0.130904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.6253 | + | 18.4036i | 0.362531 | + | 0.627922i | 0.988377 | − | 0.152025i | \(-0.0485793\pi\) |
−0.625845 | + | 0.779947i | \(0.715246\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.717296 | + | 1.24239i | 0.0244170 | + | 0.0422915i | 0.877976 | − | 0.478705i | \(-0.158894\pi\) |
−0.853559 | + | 0.520997i | \(0.825560\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.96223 | + | 15.5230i | −0.304725 | + | 0.527799i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −103.079 | −3.50075 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.9376 | 0.506723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.12192 | + | 12.3355i | −0.241317 | + | 0.417973i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.54360 | − | 9.60179i | −0.187622 | − | 0.324971i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3020 | − | 19.5756i | −0.381640 | − | 0.661020i | 0.609657 | − | 0.792665i | \(-0.291307\pi\) |
−0.991297 | + | 0.131646i | \(0.957974\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.3115 | + | 43.8409i | −0.853737 | + | 1.47872i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.2167 | −0.849572 | −0.424786 | − | 0.905294i | \(-0.639651\pi\) | ||||
−0.424786 | + | 0.905294i | \(0.639651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.0869 | −1.41634 | −0.708168 | − | 0.706044i | \(-0.750478\pi\) | ||||
−0.708168 | + | 0.706044i | \(0.750478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.0622 | − | 22.6243i | 0.439080 | − | 0.760508i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.5361 | + | 19.9810i | 0.387343 | + | 0.670898i | 0.992091 | − | 0.125519i | \(-0.0400595\pi\) |
−0.604748 | + | 0.796417i | \(0.706726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.30544 | − | 3.99315i | −0.0772353 | − | 0.133775i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.9554 | + | 39.7599i | −0.768173 | + | 1.33052i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.0375672 | −0.00125573 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0921 | 0.537298 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.2035 | − | 40.1897i | 0.773882 | − | 1.34040i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.4462 | − | 44.0741i | −0.847735 | − | 1.46832i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.41052 | + | 5.90720i | 0.113370 | + | 0.196362i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.1962 | + | 19.3923i | −0.371763 | + | 0.643912i | −0.989837 | − | 0.142208i | \(-0.954580\pi\) |
0.618074 | + | 0.786120i | \(0.287913\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 72.3481 | 2.39963 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.7584 | −1.81423 | −0.907114 | − | 0.420886i | \(-0.861719\pi\) | ||||
−0.907114 | + | 0.420886i | \(0.861719\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0328 | − | 20.8413i | 0.398226 | − | 0.689748i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.1483 | + | 27.9697i | 0.533847 | + | 0.924650i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0295 | − | 48.5485i | −0.924608 | − | 1.60147i | −0.792190 | − | 0.610275i | \(-0.791059\pi\) |
−0.132419 | − | 0.991194i | \(-0.542274\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.6865 | − | 63.5428i | 1.20886 | − | 2.09381i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.3938 | 0.770016 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.90131 | 0.226914 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.5342 | − | 45.9585i | 0.871496 | − | 1.50948i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.7940 | + | 32.5521i | 0.616610 | + | 1.06800i | 0.990100 | + | 0.140365i | \(0.0448276\pi\) |
−0.373490 | + | 0.927634i | \(0.621839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.0548 | − | 53.7886i | −1.01669 | − | 1.76096i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.32491 | + | 9.22302i | −0.174143 | + | 0.301625i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.4322 | 1.81089 | 0.905446 | − | 0.424461i | \(-0.139536\pi\) | ||||
0.905446 | + | 0.424461i | \(0.139536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.58057 | 0.280016 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.57694 | − | 13.1237i | 0.247001 | − | 0.427819i | −0.715691 | − | 0.698417i | \(-0.753888\pi\) |
0.962692 | + | 0.270598i | \(0.0872215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.2374 | − | 24.6599i | −0.463634 | − | 0.803038i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.84533 | + | 17.0526i | 0.319930 | + | 0.554136i | 0.980473 | − | 0.196653i | \(-0.0630072\pi\) |
−0.660543 | + | 0.750788i | \(0.729674\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.6858 | + | 20.2405i | −0.379339 | + | 0.657034i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.0293 | 0.746775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.8194 | 1.45184 | 0.725921 | − | 0.687778i | \(-0.241414\pi\) | ||||
0.725921 | + | 0.687778i | \(0.241414\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.93101 | + | 5.07666i | −0.0948453 | + | 0.164277i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.0333 | − | 26.0384i | −0.485958 | − | 0.841703i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.72567 | − | 9.91715i | −0.184699 | − | 0.319908i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.9366 | − | 43.1915i | 0.803571 | − | 1.39183i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.77168 | 0.153606 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3195 | 1.03932 | 0.519662 | − | 0.854372i | \(-0.326058\pi\) | ||||
0.519662 | + | 0.854372i | \(0.326058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −57.4093 | + | 99.4358i | −1.84425 | + | 3.19434i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.29033 | + | 10.8952i | 0.201866 | + | 0.349643i | 0.949130 | − | 0.314885i | \(-0.101966\pi\) |
−0.747263 | + | 0.664528i | \(0.768633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.19862 | − | 5.54017i | −0.102438 | − | 0.177428i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0585 | + | 36.4743i | −0.673720 | + | 1.16692i | 0.303121 | + | 0.952952i | \(0.401971\pi\) |
−0.976841 | + | 0.213965i | \(0.931362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4086 | −0.460502 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.5713 | −1.51883 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.3551 | − | 23.1317i | 0.425962 | − | 0.737787i | −0.570548 | − | 0.821264i | \(-0.693269\pi\) |
0.996510 | + | 0.0834771i | \(0.0266026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.64357 | − | 8.04290i | −0.147957 | − | 0.256268i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.17232 | − | 7.22668i | −0.132672 | − | 0.229795i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.72452 | − | 6.45105i | 0.118313 | − | 0.204924i | −0.800786 | − | 0.598950i | \(-0.795585\pi\) |
0.919099 | + | 0.394026i | \(0.128918\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −98.7730 | −3.13447 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.20176 | −0.101503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.9534 | − | 46.6846i | 0.853622 | − | 1.47852i | −0.0242947 | − | 0.999705i | \(-0.507734\pi\) |
0.877917 | − | 0.478813i | \(-0.158933\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.7989 | + | 39.4889i | 0.721326 | + | 1.24937i |
(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 | 1960.2.q.y.361.4 | 8 | ||
7.2 | even | 3 | inner | 1960.2.q.y.961.4 | 8 | ||
7.3 | odd | 6 | 1960.2.a.y.1.4 | yes | 4 | ||
7.4 | even | 3 | 1960.2.a.x.1.1 | ✓ | 4 | ||
7.5 | odd | 6 | 1960.2.q.x.961.1 | 8 | |||
7.6 | odd | 2 | 1960.2.q.x.361.1 | 8 | |||
28.3 | even | 6 | 3920.2.a.cd.1.1 | 4 | |||
28.11 | odd | 6 | 3920.2.a.ce.1.4 | 4 | |||
35.4 | even | 6 | 9800.2.a.cs.1.4 | 4 | |||
35.24 | odd | 6 | 9800.2.a.cl.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.1 | ✓ | 4 | 7.4 | even | 3 | ||
1960.2.a.y.1.4 | yes | 4 | 7.3 | odd | 6 | ||
1960.2.q.x.361.1 | 8 | 7.6 | odd | 2 | |||
1960.2.q.x.961.1 | 8 | 7.5 | odd | 6 | |||
1960.2.q.y.361.4 | 8 | 1.1 | even | 1 | trivial | ||
1960.2.q.y.961.4 | 8 | 7.2 | even | 3 | inner | ||
3920.2.a.cd.1.1 | 4 | 28.3 | even | 6 | |||
3920.2.a.ce.1.4 | 4 | 28.11 | odd | 6 | |||
9800.2.a.cl.1.1 | 4 | 35.24 | odd | 6 | |||
9800.2.a.cs.1.4 | 4 | 35.4 | even | 6 |