Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(919,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.919");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.t (of order \(6\), degree \(2\), 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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 919.5 | ||
Root | \(-0.147520 - 0.550552i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.919 |
Dual form | 1710.2.t.b.1189.5 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.445186 | − | 2.19130i | 0.199093 | − | 0.979981i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.67513i | 1.76703i | 0.468400 | + | 0.883517i | \(0.344831\pi\) | ||||
−0.468400 | + | 0.883517i | \(0.655169\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.710109 | − | 2.12032i | −0.224556 | − | 0.670503i | ||||
\(11\) | 3.96239 | 1.19471 | 0.597353 | − | 0.801979i | \(-0.296219\pi\) | ||||
0.597353 | + | 0.801979i | \(0.296219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.698071 | + | 0.403032i | 0.193610 | + | 0.111781i | 0.593672 | − | 0.804707i | \(-0.297678\pi\) |
−0.400061 | + | 0.916488i | \(0.631011\pi\) | |||||||
\(14\) | 2.33757 | + | 4.04878i | 0.624741 | + | 1.08208i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.01621 | + | 2.31876i | −0.974074 | + | 0.562382i | −0.900476 | − | 0.434906i | \(-0.856782\pi\) |
−0.0735981 | + | 0.997288i | \(0.523448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.01270 | + | 3.15018i | 0.691160 | + | 0.722702i | ||||
\(20\) | −1.67513 | − | 1.48119i | −0.374571 | − | 0.331205i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.43153 | − | 1.98119i | 0.731604 | − | 0.422392i | ||||
\(23\) | 5.52574 | + | 3.19029i | 1.15220 | + | 0.665221i | 0.949422 | − | 0.314004i | \(-0.101671\pi\) |
0.202775 | + | 0.979225i | \(0.435004\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.60362 | − | 1.95108i | −0.920724 | − | 0.390215i | ||||
\(26\) | 0.806063 | 0.158082 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.04878 | + | 2.33757i | 0.765148 | + | 0.441758i | ||||
\(29\) | 2.03150 | − | 3.51866i | 0.377240 | − | 0.653400i | −0.613419 | − | 0.789757i | \(-0.710206\pi\) |
0.990660 | + | 0.136358i | \(0.0435397\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.35026 | 0.601725 | 0.300862 | − | 0.953668i | \(-0.402726\pi\) | ||||
0.300862 | + | 0.953668i | \(0.402726\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.31876 | + | 4.01621i | −0.397664 | + | 0.688774i | ||||
\(35\) | 10.2446 | + | 2.08130i | 1.73166 | + | 0.351805i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.19394i | − | 0.360681i | −0.983604 | − | 0.180340i | \(-0.942280\pi\) | ||
0.983604 | − | 0.180340i | \(-0.0577200\pi\) | |||||||
\(38\) | 4.18416 | + | 1.22179i | 0.678761 | + | 0.198201i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.19130 | − | 0.445186i | −0.346475 | − | 0.0703902i | ||||
\(41\) | 2.02785 | + | 3.51235i | 0.316698 | + | 0.548537i | 0.979797 | − | 0.199995i | \(-0.0640926\pi\) |
−0.663099 | + | 0.748532i | \(0.730759\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.36551 | + | 3.67513i | −0.970732 | + | 0.560452i | −0.899459 | − | 0.437005i | \(-0.856039\pi\) |
−0.0712725 | + | 0.997457i | \(0.522706\pi\) | |||||||
\(44\) | 1.98119 | − | 3.43153i | 0.298676 | − | 0.517322i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.38058 | 0.940765 | ||||||||
\(47\) | 8.12382 | + | 4.69029i | 1.18498 | + | 0.684149i | 0.957162 | − | 0.289554i | \(-0.0935071\pi\) |
0.227819 | + | 0.973703i | \(0.426840\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.8568 | −2.12241 | ||||||||
\(50\) | −4.96239 | + | 0.612127i | −0.701788 | + | 0.0865678i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.698071 | − | 0.403032i | 0.0968051 | − | 0.0558904i | ||||
\(53\) | 1.34790 | + | 0.778209i | 0.185148 | + | 0.106895i | 0.589709 | − | 0.807616i | \(-0.299242\pi\) |
−0.404561 | + | 0.914511i | \(0.632576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.76400 | − | 8.68279i | 0.237858 | − | 1.17079i | ||||
\(56\) | 4.67513 | 0.624741 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 4.06300i | − | 0.533499i | ||||||
\(59\) | −3.94723 | − | 6.83680i | −0.513886 | − | 0.890076i | −0.999870 | − | 0.0161086i | \(-0.994872\pi\) |
0.485985 | − | 0.873967i | \(-0.338461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.20299 | − | 3.81568i | 0.282063 | − | 0.488548i | −0.689829 | − | 0.723972i | \(-0.742314\pi\) |
0.971893 | + | 0.235424i | \(0.0756478\pi\) | |||||||
\(62\) | 2.90141 | − | 1.67513i | 0.368480 | − | 0.212742i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.19394 | − | 1.35026i | 0.148090 | − | 0.167479i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.42008 | + | 3.70663i | 0.784337 | + | 0.452837i | 0.837965 | − | 0.545724i | \(-0.183745\pi\) |
−0.0536280 | + | 0.998561i | \(0.517079\pi\) | |||||||
\(68\) | 4.63752i | 0.562382i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.91276 | − | 3.31985i | 1.18480 | − | 0.396798i | ||||
\(71\) | −1.08427 | − | 1.87801i | −0.128679 | − | 0.222879i | 0.794486 | − | 0.607283i | \(-0.207740\pi\) |
−0.923165 | + | 0.384403i | \(0.874407\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2463 | − | 5.91573i | 1.19924 | − | 0.692384i | 0.238857 | − | 0.971055i | \(-0.423227\pi\) |
0.960387 | + | 0.278671i | \(0.0898940\pi\) | |||||||
\(74\) | −1.09697 | − | 1.90000i | −0.127520 | − | 0.220871i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.23449 | − | 1.03398i | 0.485729 | − | 0.118606i | ||||
\(77\) | 18.5247i | 2.11108i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.67513 | − | 8.09756i | −0.525993 | − | 0.911047i | −0.999541 | − | 0.0302792i | \(-0.990360\pi\) |
0.473548 | − | 0.880768i | \(-0.342973\pi\) | |||||||
\(80\) | −2.12032 | + | 0.710109i | −0.237059 | + | 0.0793926i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.51235 | + | 2.02785i | 0.387874 | + | 0.223939i | ||||
\(83\) | − | 9.92478i | − | 1.08939i | −0.838636 | − | 0.544693i | \(-0.816646\pi\) | ||
0.838636 | − | 0.544693i | \(-0.183354\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.29314 | + | 9.83301i | 0.357192 | + | 1.06654i | ||||
\(86\) | −3.67513 | + | 6.36551i | −0.396300 | + | 0.686411i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 3.96239i | − | 0.422392i | ||||||
\(89\) | 9.13141 | − | 15.8161i | 0.967928 | − | 1.67650i | 0.266393 | − | 0.963865i | \(-0.414168\pi\) |
0.701535 | − | 0.712635i | \(-0.252498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.88423 | + | 3.26358i | −0.197521 | + | 0.342116i | ||||
\(92\) | 5.52574 | − | 3.19029i | 0.576099 | − | 0.332611i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.38058 | 0.967533 | ||||||||
\(95\) | 8.24422 | − | 5.19931i | 0.845839 | − | 0.533438i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7439 | + | 6.20299i | −1.09088 | + | 0.629818i | −0.933810 | − | 0.357770i | \(-0.883537\pi\) |
−0.157067 | + | 0.987588i | \(0.550204\pi\) | |||||||
\(98\) | −12.8664 | + | 7.42842i | −1.29970 | + | 0.750384i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.99149 | + | 3.01131i | −0.399149 | + | 0.301131i | ||||
\(101\) | −5.21933 | + | 9.04014i | −0.519343 | + | 0.899528i | 0.480405 | + | 0.877047i | \(0.340490\pi\) |
−0.999747 | + | 0.0224809i | \(0.992844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.13093i | − | 0.209967i | −0.994474 | − | 0.104984i | \(-0.966521\pi\) | ||
0.994474 | − | 0.104984i | \(-0.0334790\pi\) | |||||||
\(104\) | 0.403032 | − | 0.698071i | 0.0395205 | − | 0.0684515i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.55642 | 0.151173 | ||||||||
\(107\) | 7.95746i | 0.769277i | 0.923067 | + | 0.384639i | \(0.125674\pi\) | ||||
−0.923067 | + | 0.384639i | \(0.874326\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.20299 | + | 9.01184i | 0.498356 | + | 0.863177i | 0.999998 | − | 0.00189769i | \(-0.000604054\pi\) |
−0.501643 | + | 0.865075i | \(0.667271\pi\) | |||||||
\(110\) | −2.81373 | − | 8.40152i | −0.268278 | − | 0.801054i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.04878 | − | 2.33757i | 0.382574 | − | 0.220879i | ||||
\(113\) | − | 12.3004i | − | 1.15713i | −0.815637 | − | 0.578564i | \(-0.803613\pi\) | ||
0.815637 | − | 0.578564i | \(-0.196387\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.45088 | − | 10.6883i | 0.881299 | − | 0.996690i | ||||
\(116\) | −2.03150 | − | 3.51866i | −0.188620 | − | 0.326700i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.83680 | − | 3.94723i | −0.629379 | − | 0.363372i | ||||
\(119\) | −10.8405 | − | 18.7763i | −0.993747 | − | 1.72122i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.70052 | 0.427320 | ||||||||
\(122\) | − | 4.40597i | − | 0.398898i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.67513 | − | 2.90141i | 0.150431 | − | 0.260554i | ||||
\(125\) | −6.32487 | + | 9.21933i | −0.565713 | + | 0.824602i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3754 | + | 5.99024i | 0.920668 | + | 0.531548i | 0.883848 | − | 0.467774i | \(-0.154944\pi\) |
0.0368202 | + | 0.999322i | \(0.488277\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.358849 | − | 1.76633i | 0.0314731 | − | 0.154917i | ||||
\(131\) | −6.30606 | − | 10.9224i | −0.550963 | − | 0.954296i | −0.998205 | − | 0.0598835i | \(-0.980927\pi\) |
0.447242 | − | 0.894413i | \(-0.352406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.7275 | + | 14.0847i | −1.27704 | + | 1.22130i | ||||
\(134\) | 7.41327 | 0.640409 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.31876 | + | 4.01621i | 0.198832 | + | 0.344387i | ||||
\(137\) | −5.53206 | − | 3.19394i | −0.472636 | − | 0.272876i | 0.244707 | − | 0.969597i | \(-0.421308\pi\) |
−0.717342 | + | 0.696721i | \(0.754642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.63752 | + | 11.4965i | −0.562987 | + | 0.975122i | 0.434247 | + | 0.900794i | \(0.357015\pi\) |
−0.997234 | + | 0.0743282i | \(0.976319\pi\) | |||||||
\(140\) | 6.92478 | − | 7.83146i | 0.585250 | − | 0.661879i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.87801 | − | 1.08427i | −0.157599 | − | 0.0909901i | ||||
\(143\) | 2.76603 | + | 1.59697i | 0.231307 | + | 0.133545i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.80606 | − | 6.01810i | −0.565213 | − | 0.499776i | ||||
\(146\) | 5.91573 | − | 10.2463i | 0.489589 | − | 0.847993i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.90000 | − | 1.09697i | −0.156179 | − | 0.0901702i | ||||
\(149\) | −0.449692 | − | 0.778890i | −0.0368402 | − | 0.0638091i | 0.847017 | − | 0.531565i | \(-0.178396\pi\) |
−0.883858 | + | 0.467756i | \(0.845063\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3757 | −0.844359 | −0.422179 | − | 0.906512i | \(-0.638735\pi\) | ||||
−0.422179 | + | 0.906512i | \(0.638735\pi\) | |||||||
\(152\) | 3.15018 | − | 3.01270i | 0.255514 | − | 0.244362i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.26234 | + | 16.0428i | 0.746381 | + | 1.29277i | ||||
\(155\) | 1.49149 | − | 7.34144i | 0.119799 | − | 0.589679i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2534 | − | 7.07452i | 0.977929 | − | 0.564608i | 0.0762850 | − | 0.997086i | \(-0.475694\pi\) |
0.901644 | + | 0.432478i | \(0.142361\pi\) | |||||||
\(158\) | −8.09756 | − | 4.67513i | −0.644208 | − | 0.371933i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.48119 | + | 1.67513i | −0.117099 | + | 0.132431i | ||||
\(161\) | −14.9150 | + | 25.8336i | −1.17547 | + | 2.03597i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.4617i | 1.36770i | 0.729621 | + | 0.683852i | \(0.239697\pi\) | ||||
−0.729621 | + | 0.683852i | \(0.760303\pi\) | |||||||
\(164\) | 4.05571 | 0.316698 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.96239 | − | 8.59511i | −0.385156 | − | 0.667110i | ||||
\(167\) | −20.0979 | − | 11.6036i | −1.55523 | − | 0.897910i | −0.997702 | − | 0.0677489i | \(-0.978418\pi\) |
−0.557523 | − | 0.830161i | \(-0.688248\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.17513 | − | 10.6956i | −0.475010 | − | 0.822742i | ||||
\(170\) | 7.76845 | + | 6.86907i | 0.595813 | + | 0.526833i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.35026i | 0.560452i | ||||||||
\(173\) | −16.6055 | + | 9.58721i | −1.26250 | + | 0.728902i | −0.973557 | − | 0.228445i | \(-0.926636\pi\) |
−0.288939 | + | 0.957348i | \(0.593302\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.12154 | − | 21.5225i | 0.689524 | − | 1.62695i | ||||
\(176\) | −1.98119 | − | 3.43153i | −0.149338 | − | 0.258661i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 18.2628i | − | 1.36886i | ||||||
\(179\) | 18.3707 | 1.37309 | 0.686546 | − | 0.727086i | \(-0.259126\pi\) | ||||
0.686546 | + | 0.727086i | \(0.259126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.10966 | − | 5.38610i | 0.231140 | − | 0.400345i | −0.727004 | − | 0.686633i | \(-0.759088\pi\) |
0.958144 | + | 0.286288i | \(0.0924213\pi\) | |||||||
\(182\) | 3.76845i | 0.279336i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.19029 | − | 5.52574i | 0.235191 | − | 0.407363i | ||||
\(185\) | −4.80758 | − | 0.976711i | −0.353460 | − | 0.0718092i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.9138 | + | 9.18783i | −1.16373 | + | 0.671880i | ||||
\(188\) | 8.12382 | − | 4.69029i | 0.592490 | − | 0.342075i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.54005 | − | 8.62485i | 0.329370 | − | 0.625712i | ||||
\(191\) | −3.47627 | −0.251534 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.57171 | − | 4.37153i | 0.545024 | − | 0.314670i | −0.202089 | − | 0.979367i | \(-0.564773\pi\) |
0.747112 | + | 0.664698i | \(0.231440\pi\) | |||||||
\(194\) | −6.20299 | + | 10.7439i | −0.445348 | + | 0.771366i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.42842 | + | 12.8664i | −0.530602 | + | 0.919029i | ||||
\(197\) | 12.6448i | 0.900906i | 0.892800 | + | 0.450453i | \(0.148737\pi\) | ||||
−0.892800 | + | 0.450453i | \(0.851263\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.18783 | + | 3.78943i | −0.155091 | + | 0.268625i | −0.933092 | − | 0.359637i | \(-0.882900\pi\) |
0.778001 | + | 0.628263i | \(0.216234\pi\) | |||||||
\(200\) | −1.95108 | + | 4.60362i | −0.137962 | + | 0.325525i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.4387i | 0.734461i | ||||||||
\(203\) | 16.4502 | + | 9.49754i | 1.15458 | + | 0.666596i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.59939 | − | 2.87999i | 0.600608 | − | 0.201148i | ||||
\(206\) | −1.06547 | − | 1.84544i | −0.0742346 | − | 0.128578i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 0.806063i | − | 0.0558904i | ||||||
\(209\) | 11.9375 | + | 12.4823i | 0.825732 | + | 0.863416i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.65022 | + | 11.5185i | 0.457820 | + | 0.792967i | 0.998845 | − | 0.0480390i | \(-0.0152972\pi\) |
−0.541026 | + | 0.841006i | \(0.681964\pi\) | |||||||
\(212\) | 1.34790 | − | 0.778209i | 0.0925739 | − | 0.0534476i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.97873 | + | 6.89137i | 0.271981 | + | 0.471084i | ||||
\(215\) | 5.21949 | + | 15.5849i | 0.355966 | + | 1.06288i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.6629i | 1.06327i | ||||||||
\(218\) | 9.01184 | + | 5.20299i | 0.610359 | + | 0.352391i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.63752 | − | 5.86907i | −0.447501 | − | 0.395692i | ||||
\(221\) | −3.73813 | −0.251454 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.57468 | + | 0.909141i | −0.105448 | + | 0.0608806i | −0.551797 | − | 0.833979i | \(-0.686058\pi\) |
0.446348 | + | 0.894859i | \(0.352724\pi\) | |||||||
\(224\) | 2.33757 | − | 4.04878i | 0.156185 | − | 0.270521i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.15022 | − | 10.6525i | −0.409106 | − | 0.708593i | ||||
\(227\) | − | 12.8691i | − | 0.854150i | −0.904216 | − | 0.427075i | \(-0.859544\pi\) | ||
0.904216 | − | 0.427075i | \(-0.140456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1114 | −1.06467 | −0.532336 | − | 0.846533i | \(-0.678686\pi\) | ||||
−0.532336 | + | 0.846533i | \(0.678686\pi\) | |||||||
\(230\) | 2.84055 | − | 13.9818i | 0.187300 | − | 0.921931i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.51866 | − | 2.03150i | −0.231012 | − | 0.133375i | ||||
\(233\) | 1.90632 | − | 1.10062i | 0.124887 | − | 0.0721037i | −0.436255 | − | 0.899823i | \(-0.643695\pi\) |
0.561142 | + | 0.827719i | \(0.310362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8945 | − | 15.7137i | 0.906375 | − | 1.02505i | ||||
\(236\) | −7.89446 | −0.513886 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.7763 | − | 10.8405i | −1.21709 | − | 0.702686i | ||||
\(239\) | 4.70052 | 0.304052 | 0.152026 | − | 0.988377i | \(-0.451420\pi\) | ||||
0.152026 | + | 0.988377i | \(0.451420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.6405 | + | 21.8939i | −0.814244 | + | 1.41031i | 0.0956262 | + | 0.995417i | \(0.469515\pi\) |
−0.909870 | + | 0.414894i | \(0.863819\pi\) | |||||||
\(242\) | 4.07077 | − | 2.35026i | 0.261679 | − | 0.151081i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.20299 | − | 3.81568i | −0.141032 | − | 0.244274i | ||||
\(245\) | −6.61407 | + | 32.5559i | −0.422557 | + | 2.07992i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.833453 | + | 3.41327i | 0.0530313 | + | 0.217181i | ||||
\(248\) | − | 3.35026i | − | 0.212742i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.867833 | + | 11.1466i | −0.0548866 | + | 0.704973i | ||||
\(251\) | −6.21933 | + | 10.7722i | −0.392561 | + | 0.679935i | −0.992787 | − | 0.119896i | \(-0.961744\pi\) |
0.600226 | + | 0.799831i | \(0.295077\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.8951 | + | 12.6412i | 1.37654 | + | 0.794743i | ||||
\(254\) | 11.9805 | 0.751723 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 22.7011 | + | 13.1065i | 1.41606 | + | 0.817561i | 0.995950 | − | 0.0899138i | \(-0.0286592\pi\) |
0.420107 | + | 0.907475i | \(0.361992\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.2569 | 0.637335 | ||||||||
\(260\) | −0.572393 | − | 1.70911i | −0.0354983 | − | 0.105995i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.9224 | − | 6.30606i | −0.674790 | − | 0.389590i | ||||
\(263\) | 5.03329 | − | 2.90597i | 0.310366 | − | 0.179190i | −0.336724 | − | 0.941603i | \(-0.609319\pi\) |
0.647090 | + | 0.762413i | \(0.275986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.30536 | − | 2.60720i | 0.141617 | − | 0.160159i | ||||
\(266\) | −5.71203 | + | 19.5615i | −0.350227 | + | 1.19939i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.42008 | − | 3.70663i | 0.392169 | − | 0.226419i | ||||
\(269\) | −11.7501 | − | 20.3518i | −0.716418 | − | 1.24087i | −0.962410 | − | 0.271600i | \(-0.912447\pi\) |
0.245992 | − | 0.969272i | \(-0.420886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3430 | − | 28.3069i | −0.992765 | − | 1.71952i | −0.600372 | − | 0.799721i | \(-0.704981\pi\) |
−0.392393 | − | 0.919798i | \(-0.628353\pi\) | |||||||
\(272\) | 4.01621 | + | 2.31876i | 0.243518 | + | 0.140595i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.38787 | −0.385906 | ||||||||
\(275\) | −18.2413 | − | 7.73092i | −1.09999 | − | 0.466192i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.6688i | 1.18178i | 0.806751 | + | 0.590892i | \(0.201224\pi\) | ||||
−0.806751 | + | 0.590892i | \(0.798776\pi\) | |||||||
\(278\) | 13.2750i | 0.796184i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.08130 | − | 10.2446i | 0.124382 | − | 0.612234i | ||||
\(281\) | −5.79631 | + | 10.0395i | −0.345779 | + | 0.598906i | −0.985495 | − | 0.169705i | \(-0.945719\pi\) |
0.639716 | + | 0.768611i | \(0.279052\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.4621 | + | 14.7005i | −1.51356 | + | 0.873855i | −0.513688 | + | 0.857977i | \(0.671721\pi\) |
−0.999874 | + | 0.0158784i | \(0.994946\pi\) | |||||||
\(284\) | −2.16854 | −0.128679 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.19394 | 0.188861 | ||||||||
\(287\) | −16.4207 | + | 9.48049i | −0.969282 | + | 0.559615i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.25329 | − | 3.90282i | 0.132547 | − | 0.229578i | ||||
\(290\) | −8.90327 | − | 1.80879i | −0.522818 | − | 0.106216i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 11.8315i | − | 0.692384i | ||||||
\(293\) | − | 22.2628i | − | 1.30061i | −0.759674 | − | 0.650304i | \(-0.774642\pi\) | ||
0.759674 | − | 0.650304i | \(-0.225358\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.7388 | + | 5.60593i | −0.974568 | + | 0.326390i | ||||
\(296\) | −2.19394 | −0.127520 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.778890 | − | 0.449692i | −0.0451199 | − | 0.0260500i | ||||
\(299\) | 2.57158 | + | 4.45410i | 0.148718 | + | 0.257587i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.1817 | − | 29.7596i | −0.990338 | − | 1.71532i | ||||
\(302\) | −8.98558 | + | 5.18783i | −0.517062 | + | 0.298526i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.22179 | − | 4.18416i | 0.0700745 | − | 0.239978i | ||||
\(305\) | −7.38058 | − | 6.52610i | −0.422611 | − | 0.373683i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.0744 | + | 15.6314i | −1.54522 | + | 0.892132i | −0.546721 | + | 0.837315i | \(0.684124\pi\) |
−0.998496 | + | 0.0548168i | \(0.982543\pi\) | |||||||
\(308\) | 16.0428 | + | 9.26234i | 0.914126 | + | 0.527771i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.37905 | − | 7.10362i | −0.135121 | − | 0.403458i | ||||
\(311\) | 17.7889 | 1.00872 | 0.504359 | − | 0.863494i | \(-0.331729\pi\) | ||||
0.504359 | + | 0.863494i | \(0.331729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.40177 | + | 3.11871i | 0.305326 | + | 0.176280i | 0.644833 | − | 0.764323i | \(-0.276927\pi\) |
−0.339507 | + | 0.940604i | \(0.610260\pi\) | |||||||
\(314\) | 7.07452 | − | 12.2534i | 0.399238 | − | 0.691501i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.35026 | −0.525993 | ||||||||
\(317\) | −11.9018 | − | 6.87153i | −0.668474 | − | 0.385944i | 0.127024 | − | 0.991900i | \(-0.459457\pi\) |
−0.795498 | + | 0.605956i | \(0.792791\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.04960 | − | 13.9423i | 0.450691 | − | 0.780620i | ||||
\(320\) | −0.445186 | + | 2.19130i | −0.0248867 | + | 0.122498i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 29.8300i | 1.66236i | ||||||||
\(323\) | −19.4041 | − | 5.66608i | −1.07968 | − | 0.315269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.42731 | − | 3.21740i | −0.134643 | − | 0.178469i | ||||
\(326\) | 8.73084 | + | 15.1223i | 0.483557 | + | 0.837544i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.51235 | − | 2.02785i | 0.193937 | − | 0.111970i | ||||
\(329\) | −21.9277 | + | 37.9799i | −1.20891 | + | 2.09390i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.56230 | −0.0858716 | −0.0429358 | − | 0.999078i | \(-0.513671\pi\) | ||||
−0.0429358 | + | 0.999078i | \(0.513671\pi\) | |||||||
\(332\) | −8.59511 | − | 4.96239i | −0.471718 | − | 0.272346i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.2071 | −1.26984 | ||||||||
\(335\) | 10.9805 | − | 12.4182i | 0.599928 | − | 0.678478i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.2909 | − | 6.51881i | 0.615055 | − | 0.355102i | −0.159886 | − | 0.987135i | \(-0.551113\pi\) |
0.774941 | + | 0.632033i | \(0.217779\pi\) | |||||||
\(338\) | −10.6956 | − | 6.17513i | −0.581766 | − | 0.335883i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.1622 | + | 2.06456i | 0.551123 | + | 0.111967i | ||||
\(341\) | 13.2750 | 0.718884 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 36.7318i | − | 1.98333i | ||||||
\(344\) | 3.67513 | + | 6.36551i | 0.198150 | + | 0.343205i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.58721 | + | 16.6055i | −0.515412 | + | 0.892719i | ||||
\(347\) | 21.2610 | − | 12.2750i | 1.14135 | − | 0.658959i | 0.194585 | − | 0.980886i | \(-0.437664\pi\) |
0.946764 | + | 0.321927i | \(0.104331\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.86907 | −0.367693 | −0.183846 | − | 0.982955i | \(-0.558855\pi\) | ||||
−0.183846 | + | 0.982955i | \(0.558855\pi\) | |||||||
\(350\) | −2.86177 | − | 23.1998i | −0.152968 | − | 1.24008i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.43153 | − | 1.98119i | −0.182901 | − | 0.105598i | ||||
\(353\) | − | 29.1368i | − | 1.55080i | −0.631473 | − | 0.775398i | \(-0.717549\pi\) | ||
0.631473 | − | 0.775398i | \(-0.282451\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.59800 | + | 1.53990i | −0.244037 | + | 0.0817295i | ||||
\(356\) | −9.13141 | − | 15.8161i | −0.483964 | − | 0.838250i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.9095 | − | 9.18536i | 0.840844 | − | 0.485462i | ||||
\(359\) | −10.4223 | − | 18.0520i | −0.550069 | − | 0.952747i | −0.998269 | − | 0.0588138i | \(-0.981268\pi\) |
0.448200 | − | 0.893933i | \(-0.352065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.847322 | + | 18.9811i | −0.0445959 | + | 0.999005i | ||||
\(362\) | − | 6.21933i | − | 0.326881i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.88423 | + | 3.26358i | 0.0987603 | + | 0.171058i | ||||
\(365\) | −8.40162 | − | 25.0864i | −0.439761 | − | 1.31308i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1758 | − | 13.3806i | −1.20977 | − | 0.698461i | −0.247060 | − | 0.969000i | \(-0.579465\pi\) |
−0.962709 | + | 0.270540i | \(0.912798\pi\) | |||||||
\(368\) | − | 6.38058i | − | 0.332611i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.65184 | + | 1.55793i | −0.241838 | + | 0.0809931i | ||||
\(371\) | −3.63823 | + | 6.30159i | −0.188887 | + | 0.327162i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 27.6312i | − | 1.43069i | −0.698772 | − | 0.715344i | \(-0.746270\pi\) | ||
0.698772 | − | 0.715344i | \(-0.253730\pi\) | |||||||
\(374\) | −9.18783 | + | 15.9138i | −0.475091 | + | 0.822882i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.69029 | − | 8.12382i | 0.241883 | − | 0.418954i | ||||
\(377\) | 2.83627 | − | 1.63752i | 0.146075 | − | 0.0843365i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.4387 | 1.46080 | 0.730398 | − | 0.683022i | \(-0.239335\pi\) | ||||
0.730398 | + | 0.683022i | \(0.239335\pi\) | |||||||
\(380\) | −0.380626 | − | 9.73936i | −0.0195257 | − | 0.499619i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.01054 | + | 1.73813i | −0.154033 | + | 0.0889307i | ||||
\(383\) | −14.7601 | + | 8.52175i | −0.754206 | + | 0.435441i | −0.827212 | − | 0.561891i | \(-0.810074\pi\) |
0.0730058 | + | 0.997332i | \(0.476741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 40.5932 | + | 8.24694i | 2.06882 | + | 0.420303i | ||||
\(386\) | 4.37153 | − | 7.57171i | 0.222505 | − | 0.385390i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.4060i | 0.629818i | ||||||||
\(389\) | −1.28115 | + | 2.21901i | −0.0649568 | + | 0.112508i | −0.896675 | − | 0.442690i | \(-0.854024\pi\) |
0.831718 | + | 0.555198i | \(0.187358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.5901 | −1.49643 | ||||||||
\(392\) | 14.8568i | 0.750384i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.32241 | + | 10.9507i | 0.318518 | + | 0.551690i | ||||
\(395\) | −19.8255 | + | 6.63970i | −0.997530 | + | 0.334080i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.6367 | + | 10.7599i | −0.935347 | + | 0.540023i | −0.888499 | − | 0.458879i | \(-0.848251\pi\) |
−0.0468484 | + | 0.998902i | \(0.514918\pi\) | |||||||
\(398\) | 4.37565i | 0.219332i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.612127 | + | 4.96239i | 0.0306063 | + | 0.248119i | ||||
\(401\) | −13.9502 | − | 24.1624i | −0.696638 | − | 1.20661i | −0.969625 | − | 0.244595i | \(-0.921345\pi\) |
0.272987 | − | 0.962018i | \(-0.411988\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.33872 | + | 1.35026i | 0.116500 | + | 0.0672613i | ||||
\(404\) | 5.21933 | + | 9.04014i | 0.259671 | + | 0.449764i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.9951 | 0.942710 | ||||||||
\(407\) | − | 8.69323i | − | 0.430907i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.6543 | − | 32.3103i | 0.922398 | − | 1.59764i | 0.126704 | − | 0.991941i | \(-0.459560\pi\) |
0.795694 | − | 0.605699i | \(-0.207107\pi\) | |||||||
\(410\) | 6.00729 | − | 6.79384i | 0.296679 | − | 0.335524i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.84544 | − | 1.06547i | −0.0909184 | − | 0.0524918i | ||||
\(413\) | 31.9629 | − | 18.4538i | 1.57279 | − | 0.908053i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.7482 | − | 4.41838i | −1.06758 | − | 0.216890i | ||||
\(416\) | −0.403032 | − | 0.698071i | −0.0197603 | − | 0.0342258i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.5793 | + | 4.84121i | 0.810919 | + | 0.236791i | ||||
\(419\) | −16.5271 | −0.807399 | −0.403700 | − | 0.914892i | \(-0.632276\pi\) | ||||
−0.403700 | + | 0.914892i | \(0.632276\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4902 | + | 18.1696i | 0.511263 | + | 0.885534i | 0.999915 | + | 0.0130548i | \(0.00415559\pi\) |
−0.488652 | + | 0.872479i | \(0.662511\pi\) | |||||||
\(422\) | 11.5185 | + | 6.65022i | 0.560712 | + | 0.323727i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.778209 | − | 1.34790i | 0.0377931 | − | 0.0654597i | ||||
\(425\) | 23.0132 | − | 2.83875i | 1.11630 | − | 0.137700i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.8388 | + | 10.2992i | 0.863281 | + | 0.498415i | ||||
\(428\) | 6.89137 | + | 3.97873i | 0.333107 | + | 0.192319i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.3127 | + | 10.8872i | 0.593769 | + | 0.525026i | ||||
\(431\) | −8.69640 | + | 15.0626i | −0.418891 | + | 0.725540i | −0.995828 | − | 0.0912482i | \(-0.970914\pi\) |
0.576937 | + | 0.816788i | \(0.304248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.124800 | + | 0.0720532i | 0.00599750 | + | 0.00346266i | 0.502996 | − | 0.864289i | \(-0.332231\pi\) |
−0.496998 | + | 0.867752i | \(0.665564\pi\) | |||||||
\(434\) | 7.83146 | + | 13.5645i | 0.375922 | + | 0.651116i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.4060 | 0.498356 | ||||||||
\(437\) | 6.59739 | + | 27.0185i | 0.315596 | + | 1.29247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5381 | + | 26.9128i | 0.741593 | + | 1.28448i | 0.951770 | + | 0.306813i | \(0.0992625\pi\) |
−0.210177 | + | 0.977663i | \(0.567404\pi\) | |||||||
\(440\) | −8.68279 | − | 1.76400i | −0.413936 | − | 0.0840955i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.23732 | + | 1.86907i | −0.153984 | + | 0.0889025i | ||||
\(443\) | −26.7774 | − | 15.4599i | −1.27223 | − | 0.734523i | −0.296824 | − | 0.954932i | \(-0.595927\pi\) |
−0.975408 | + | 0.220409i | \(0.929261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.5926 | − | 27.0508i | −1.45023 | − | 1.28233i | ||||
\(446\) | −0.909141 | + | 1.57468i | −0.0430491 | + | 0.0745632i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 4.67513i | − | 0.220879i | ||||||
\(449\) | −3.40009 | −0.160460 | −0.0802301 | − | 0.996776i | \(-0.525566\pi\) | ||||
−0.0802301 | + | 0.996776i | \(0.525566\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.03515 | + | 13.9173i | 0.378360 | + | 0.655339i | ||||
\(452\) | −10.6525 | − | 6.15022i | −0.501051 | − | 0.289282i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.43453 | − | 11.1449i | −0.301988 | − | 0.523058i | ||||
\(455\) | 6.31265 | + | 5.58181i | 0.295942 | + | 0.261679i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.11634i | 0.426445i | 0.977004 | + | 0.213222i | \(0.0683959\pi\) | ||||
−0.977004 | + | 0.213222i | \(0.931604\pi\) | |||||||
\(458\) | −13.9529 | + | 8.05571i | −0.651976 | + | 0.376419i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.53090 | − | 13.5289i | −0.211255 | − | 0.630786i | ||||
\(461\) | 2.13823 | + | 3.70352i | 0.0995871 | + | 0.172490i | 0.911514 | − | 0.411269i | \(-0.134914\pi\) |
−0.811927 | + | 0.583759i | \(0.801581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.4871i | − | 1.37038i | −0.728364 | − | 0.685190i | \(-0.759719\pi\) | ||
0.728364 | − | 0.685190i | \(-0.240281\pi\) | |||||||
\(464\) | −4.06300 | −0.188620 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.10062 | − | 1.90632i | 0.0509850 | − | 0.0883087i | ||||
\(467\) | 15.9575i | 0.738423i | 0.929345 | + | 0.369212i | \(0.120372\pi\) | ||||
−0.929345 | + | 0.369212i | \(0.879628\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.3290 | + | 30.0147i | −0.800179 | + | 1.38595i | ||||
\(470\) | 4.17611 | − | 20.5557i | 0.192629 | − | 0.948163i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.83680 | + | 3.94723i | −0.314689 | + | 0.181686i | ||||
\(473\) | −25.2226 | + | 14.5623i | −1.15974 | + | 0.669575i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.72305 | − | 20.3802i | −0.354358 | − | 0.935110i | ||||
\(476\) | −21.6810 | −0.993747 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.07077 | − | 2.35026i | 0.186193 | − | 0.107498i | ||||
\(479\) | −10.5410 | + | 18.2576i | −0.481632 | + | 0.834211i | −0.999778 | − | 0.0210814i | \(-0.993289\pi\) |
0.518146 | + | 0.855292i | \(0.326622\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.884226 | − | 1.53152i | 0.0403172 | − | 0.0698315i | ||||
\(482\) | 25.2809i | 1.15151i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.35026 | − | 4.07077i | 0.106830 | − | 0.185035i | ||||
\(485\) | 8.80959 | + | 26.3046i | 0.400023 | + | 1.19443i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.2365i | − | 0.463859i | −0.972733 | − | 0.231929i | \(-0.925496\pi\) | ||
0.972733 | − | 0.231929i | \(-0.0745038\pi\) | |||||||
\(488\) | −3.81568 | − | 2.20299i | −0.172728 | − | 0.0997245i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.5500 | + | 31.5012i | 0.476599 | + | 1.42308i | ||||
\(491\) | 3.68901 | + | 6.38956i | 0.166483 | + | 0.288357i | 0.937181 | − | 0.348844i | \(-0.113426\pi\) |
−0.770698 | + | 0.637200i | \(0.780092\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.8423i | 0.848613i | ||||||||
\(494\) | 2.42842 | + | 2.53925i | 0.109260 | + | 0.114246i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.67513 | − | 2.90141i | −0.0752156 | − | 0.130277i | ||||
\(497\) | 8.77996 | − | 5.06911i | 0.393835 | − | 0.227381i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.1944 | − | 22.8534i | −0.590663 | − | 1.02306i | −0.994143 | − | 0.108070i | \(-0.965533\pi\) |
0.403480 | − | 0.914988i | \(-0.367800\pi\) | |||||||
\(500\) | 4.82174 | + | 10.0872i | 0.215635 | + | 0.451112i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.4387i | 0.555164i | ||||||||
\(503\) | −27.0701 | − | 15.6289i | −1.20700 | − | 0.696860i | −0.244895 | − | 0.969550i | \(-0.578754\pi\) |
−0.962102 | + | 0.272689i | \(0.912087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.4861 | + | 15.4617i | 0.778122 | + | 0.688036i | ||||
\(506\) | 25.2823 | 1.12394 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.3754 | − | 5.99024i | 0.460334 | − | 0.265774i | ||||
\(509\) | −1.79384 | + | 3.10703i | −0.0795108 | + | 0.137717i | −0.903039 | − | 0.429559i | \(-0.858669\pi\) |
0.823528 | + | 0.567275i | \(0.192002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.6568 | + | 47.9030i | 1.22346 | + | 2.11910i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.2130 | 1.15621 | ||||||||
\(515\) | −4.66952 | − | 0.948662i | −0.205764 | − | 0.0418031i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.1897 | + | 18.5847i | 1.41570 | + | 0.817356i | ||||
\(518\) | 8.88277 | − | 5.12847i | 0.390287 | − | 0.225332i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.35026 | − | 1.19394i | −0.0592129 | − | 0.0523576i | ||||
\(521\) | −1.56134 | −0.0684036 | −0.0342018 | − | 0.999415i | \(-0.510889\pi\) | ||||
−0.0342018 | + | 0.999415i | \(0.510889\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2025 | − | 6.46779i | −0.489853 | − | 0.282817i | 0.234660 | − | 0.972077i | \(-0.424602\pi\) |
−0.724513 | + | 0.689261i | \(0.757935\pi\) | |||||||
\(524\) | −12.6121 | −0.550963 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.90597 | − | 5.03329i | 0.126706 | − | 0.219462i | ||||
\(527\) | −13.4554 | + | 7.76845i | −0.586124 | + | 0.338399i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.85589 | + | 15.3389i | 0.385039 | + | 0.666907i | ||||
\(530\) | 0.692896 | − | 3.41058i | 0.0300975 | − | 0.148146i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.83399 | + | 19.7968i | 0.209580 | + | 0.858299i | ||||
\(533\) | 3.26916i | 0.141603i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.4372 | + | 3.54256i | 0.753877 | + | 0.153158i | ||||
\(536\) | 3.70663 | − | 6.42008i | 0.160102 | − | 0.277305i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.3518 | − | 11.7501i | −0.877429 | − | 0.506584i | ||||
\(539\) | −58.8686 | −2.53565 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3004 | + | 28.2332i | −0.700810 | + | 1.21384i | 0.267372 | + | 0.963593i | \(0.413845\pi\) |
−0.968182 | + | 0.250246i | \(0.919489\pi\) | |||||||
\(542\) | −28.3069 | − | 16.3430i | −1.21588 | − | 0.701991i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.63752 | 0.198832 | ||||||||
\(545\) | 22.0640 | − | 7.38937i | 0.945116 | − | 0.316526i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.6599 | + | 14.2374i | 1.05438 | + | 0.608748i | 0.923873 | − | 0.382699i | \(-0.125005\pi\) |
0.130510 | + | 0.991447i | \(0.458339\pi\) | |||||||
\(548\) | −5.53206 | + | 3.19394i | −0.236318 | + | 0.136438i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −19.6629 | + | 2.42548i | −0.838429 | + | 0.103423i | ||||
\(551\) | 17.2047 | − | 4.20106i | 0.732947 | − | 0.178971i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.8572 | − | 21.8568i | 1.60985 | − | 0.929448i | ||||
\(554\) | 9.83440 | + | 17.0337i | 0.417823 | + | 0.723691i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.63752 | + | 11.4965i | 0.281494 | + | 0.487561i | ||||
\(557\) | 24.3934 | + | 14.0836i | 1.03358 | + | 0.596740i | 0.918009 | − | 0.396559i | \(-0.129796\pi\) |
0.115574 | + | 0.993299i | \(0.463129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.92478 | −0.250591 | ||||||||
\(560\) | −3.31985 | − | 9.91276i | −0.140289 | − | 0.418891i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.5926i | 0.489005i | ||||||||
\(563\) | 7.02776i | 0.296185i | 0.988974 | + | 0.148092i | \(0.0473133\pi\) | ||||
−0.988974 | + | 0.148092i | \(0.952687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.9540 | − | 5.47599i | −1.13396 | − | 0.230376i | ||||
\(566\) | −14.7005 | + | 25.4621i | −0.617909 | + | 1.07025i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.87801 | + | 1.08427i | −0.0787997 | + | 0.0454950i | ||||
\(569\) | 21.5320 | 0.902668 | 0.451334 | − | 0.892355i | \(-0.350948\pi\) | ||||
0.451334 | + | 0.892355i | \(0.350948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1417 | 0.591813 | 0.295907 | − | 0.955217i | \(-0.404378\pi\) | ||||
0.295907 | + | 0.955217i | \(0.404378\pi\) | |||||||
\(572\) | 2.76603 | − | 1.59697i | 0.115654 | − | 0.0667726i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.48049 | + | 16.4207i | −0.395708 | + | 0.685386i | ||||
\(575\) | −19.2139 | − | 25.4680i | −0.801276 | − | 1.06209i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.22918i | − | 0.176063i | −0.996118 | − | 0.0880315i | \(-0.971942\pi\) | ||
0.996118 | − | 0.0880315i | \(-0.0280576\pi\) | |||||||
\(578\) | − | 4.50659i | − | 0.187449i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.61486 | + | 2.88517i | −0.357713 | + | 0.119800i | ||||
\(581\) | 46.3996 | 1.92498 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.34089 | + | 3.08356i | 0.221197 | + | 0.127708i | ||||
\(584\) | −5.91573 | − | 10.2463i | −0.244795 | − | 0.423997i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.1314 | − | 19.2802i | −0.459834 | − | 0.796456i | ||||
\(587\) | −2.11194 | + | 1.21933i | −0.0871691 | + | 0.0503271i | −0.542951 | − | 0.839764i | \(-0.682693\pi\) |
0.455782 | + | 0.890092i | \(0.349360\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0933 | + | 10.5539i | 0.415888 | + | 0.434868i | ||||
\(590\) | −11.6932 | + | 13.2243i | −0.481403 | + | 0.544434i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.90000 | + | 1.09697i | −0.0780897 | + | 0.0450851i | ||||
\(593\) | −2.19785 | − | 1.26893i | −0.0902549 | − | 0.0521087i | 0.454193 | − | 0.890903i | \(-0.349928\pi\) |
−0.544448 | + | 0.838794i | \(0.683261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45.9706 | + | 15.3959i | −1.88461 | + | 0.631169i | ||||
\(596\) | −0.899385 | −0.0368402 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.45410 | + | 2.57158i | 0.182142 | + | 0.105160i | ||||
\(599\) | 14.1776 | − | 24.5563i | 0.579281 | − | 1.00334i | −0.416281 | − | 0.909236i | \(-0.636667\pi\) |
0.995562 | − | 0.0941078i | \(-0.0299998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.5705 | 0.961463 | 0.480731 | − | 0.876868i | \(-0.340371\pi\) | ||||
0.480731 | + | 0.876868i | \(0.340371\pi\) | |||||||
\(602\) | −29.7596 | − | 17.1817i | −1.21291 | − | 0.700275i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.18783 | + | 8.98558i | −0.211090 | + | 0.365618i | ||||
\(605\) | 2.09261 | − | 10.3003i | 0.0850767 | − | 0.418766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 20.5042i | − | 0.832241i | −0.909310 | − | 0.416120i | \(-0.863390\pi\) | ||
0.909310 | − | 0.416120i | \(-0.136610\pi\) | |||||||
\(608\) | −1.03398 | − | 4.23449i | −0.0419334 | − | 0.171731i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.65482 | − | 1.96148i | −0.390912 | − | 0.0794180i | ||||
\(611\) | 3.78067 | + | 6.54831i | 0.152950 | + | 0.264916i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.211935 | − | 0.122361i | 0.00855999 | − | 0.00494211i | −0.495714 | − | 0.868486i | \(-0.665094\pi\) |
0.504274 | + | 0.863544i | \(0.331760\pi\) | |||||||
\(614\) | −15.6314 | + | 27.0744i | −0.630832 | + | 1.09263i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.5247 | 0.746381 | ||||||||
\(617\) | 0.401053 | + | 0.231548i | 0.0161458 | + | 0.00932177i | 0.508051 | − | 0.861327i | \(-0.330366\pi\) |
−0.491905 | + | 0.870649i | \(0.663699\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1685 | 0.448902 | 0.224451 | − | 0.974485i | \(-0.427941\pi\) | ||||
0.224451 | + | 0.974485i | \(0.427941\pi\) | |||||||
\(620\) | −5.61213 | − | 4.96239i | −0.225388 | − | 0.199294i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.4057 | − | 8.89446i | 0.617711 | − | 0.356635i | ||||
\(623\) | 73.9422 | + | 42.6905i | 2.96243 | + | 1.71036i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.3866 | + | 17.9640i | 0.695464 | + | 0.718561i | ||||
\(626\) | 6.23743 | 0.249298 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 14.1490i | − | 0.564608i | ||||||
\(629\) | 5.08721 | + | 8.81131i | 0.202840 | + | 0.351330i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.9695 | − | 36.3202i | 0.834781 | − | 1.44588i | −0.0594281 | − | 0.998233i | \(-0.518928\pi\) |
0.894209 | − | 0.447650i | \(-0.147739\pi\) | |||||||
\(632\) | −8.09756 | + | 4.67513i | −0.322104 | + | 0.185967i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.7431 | −0.545807 | ||||||||
\(635\) | 17.7454 | − | 20.0689i | 0.704206 | − | 0.796409i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.3711 | − | 5.98778i | −0.410920 | − | 0.237245i | ||||
\(638\) | − | 16.0992i | − | 0.637373i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.710109 | + | 2.12032i | 0.0280695 | + | 0.0838129i | ||||
\(641\) | −12.5999 | − | 21.8237i | −0.497666 | − | 0.861984i | 0.502330 | − | 0.864676i | \(-0.332476\pi\) |
−0.999996 | + | 0.00269246i | \(0.999143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.4581 | + | 10.6568i | −0.727917 | + | 0.420263i | −0.817660 | − | 0.575702i | \(-0.804729\pi\) |
0.0897424 | + | 0.995965i | \(0.471396\pi\) | |||||||
\(644\) | 14.9150 | + | 25.8336i | 0.587734 | + | 1.01799i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.6375 | + | 4.79510i | −0.772628 | + | 0.188661i | ||||
\(647\) | − | 22.0132i | − | 0.865427i | −0.901531 | − | 0.432714i | \(-0.857556\pi\) | ||
0.901531 | − | 0.432714i | \(-0.142444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.6405 | − | 27.0901i | −0.613942 | − | 1.06338i | ||||
\(650\) | −3.71081 | − | 1.57269i | −0.145550 | − | 0.0616860i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.1223 | + | 8.73084i | 0.592233 | + | 0.341926i | ||||
\(653\) | − | 33.6785i | − | 1.31794i | −0.752169 | − | 0.658970i | \(-0.770992\pi\) | ||
0.752169 | − | 0.658970i | \(-0.229008\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.7417 | + | 8.95598i | −1.04489 | + | 0.349939i | ||||
\(656\) | 2.02785 | − | 3.51235i | 0.0791744 | − | 0.137134i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 43.8554i | 1.70966i | ||||||||
\(659\) | 22.9538 | − | 39.7572i | 0.894154 | − | 1.54872i | 0.0593053 | − | 0.998240i | \(-0.481111\pi\) |
0.834848 | − | 0.550480i | \(-0.185555\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.24472 | + | 12.5482i | −0.281787 | + | 0.488069i | −0.971825 | − | 0.235704i | \(-0.924260\pi\) |
0.690038 | + | 0.723773i | \(0.257594\pi\) | |||||||
\(662\) | −1.35299 | + | 0.781148i | −0.0525854 | + | 0.0303602i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.92478 | −0.385156 | ||||||||
\(665\) | 24.3075 | + | 38.5428i | 0.942603 | + | 1.49463i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.4511 | − | 12.9622i | 0.869311 | − | 0.501897i | ||||
\(668\) | −20.0979 | + | 11.6036i | −0.777613 | + | 0.448955i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.30029 | − | 16.2447i | 0.127501 | − | 0.627588i | ||||
\(671\) | 8.72909 | − | 15.1192i | 0.336983 | − | 0.583671i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.8397i | − | 0.764764i | −0.924004 | − | 0.382382i | \(-0.875104\pi\) | ||
0.924004 | − | 0.382382i | \(-0.124896\pi\) | |||||||
\(674\) | 6.51881 | − | 11.2909i | 0.251095 | − | 0.434909i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3503 | −0.475010 | ||||||||
\(677\) | 10.3479i | 0.397702i | 0.980030 | + | 0.198851i | \(0.0637209\pi\) | ||||
−0.980030 | + | 0.198851i | \(0.936279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.9998 | − | 50.2291i | −1.11291 | − | 1.92761i | ||||
\(680\) | 9.83301 | − | 3.29314i | 0.377079 | − | 0.126286i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.4965 | − | 6.63752i | 0.440225 | − | 0.254164i | ||||
\(683\) | 40.3307i | 1.54321i | 0.636100 | + | 0.771607i | \(0.280547\pi\) | ||||
−0.636100 | + | 0.771607i | \(0.719453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.46168 | + | 10.7005i | −0.361512 | + | 0.408846i | ||||
\(686\) | −18.3659 | − | 31.8107i | −0.701213 | − | 1.21454i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.36551 | + | 3.67513i | 0.242683 | + | 0.140113i | ||||
\(689\) | 0.627285 | + | 1.08649i | 0.0238977 | + | 0.0413920i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.8202 | 1.74308 | 0.871541 | − | 0.490322i | \(-0.163121\pi\) | ||||
0.871541 | + | 0.490322i | \(0.163121\pi\) | |||||||
\(692\) | 19.1744i | 0.728902i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.2750 | − | 21.2610i | 0.465954 | − | 0.807056i | ||||
\(695\) | 22.2374 | + | 19.6629i | 0.843514 | + | 0.745857i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.2886 | − | 9.40422i | −0.616974 | − | 0.356210i | ||||
\(698\) | −5.94879 | + | 3.43453i | −0.225165 | + | 0.129999i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.0783 | − | 18.6607i | −0.532109 | − | 0.705310i | ||||
\(701\) | −18.6375 | − | 32.2811i | −0.703929 | − | 1.21924i | −0.967077 | − | 0.254486i | \(-0.918094\pi\) |
0.263147 | − | 0.964756i | \(-0.415240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.91130 | − | 6.60966i | 0.260665 | − | 0.249288i | ||||
\(704\) | −3.96239 | −0.149338 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.5684 | − | 25.2332i | −0.548289 | − | 0.949665i | ||||
\(707\) | −42.2639 | − | 24.4010i | −1.58950 | − | 0.917696i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8356 | − | 39.5524i | 0.857608 | − | 1.48542i | −0.0165958 | − | 0.999862i | \(-0.505283\pi\) |
0.874204 | − | 0.485559i | \(-0.161384\pi\) | |||||||
\(710\) | −3.21203 | + | 3.63259i | −0.120546 | + | 0.136329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.8161 | − | 9.13141i | −0.592732 | − | 0.342214i | ||||
\(713\) | 18.5127 | + | 10.6883i | 0.693306 | + | 0.400280i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.73084 | − | 5.35026i | 0.176923 | − | 0.200088i | ||||
\(716\) | 9.18536 | − | 15.9095i | 0.343273 | − | 0.594567i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.0520 | − | 10.4223i | −0.673694 | − | 0.388957i | ||||
\(719\) | 14.5188 | + | 25.1473i | 0.541460 | + | 0.937836i | 0.998821 | + | 0.0485550i | \(0.0154616\pi\) |
−0.457360 | + | 0.889281i | \(0.651205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.96239 | 0.371019 | ||||||||
\(722\) | 8.75675 | + | 16.8618i | 0.325892 | + | 0.627530i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.10966 | − | 5.38610i | −0.115570 | − | 0.200173i | ||||
\(725\) | −16.2174 | + | 12.2350i | −0.602301 | + | 0.454395i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6107 | − | 6.70346i | 0.430618 | − | 0.248618i | −0.268992 | − | 0.963143i | \(-0.586690\pi\) |
0.699610 | + | 0.714525i | \(0.253357\pi\) | |||||||
\(728\) | 3.26358 | + | 1.88423i | 0.120956 | + | 0.0698341i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.8192 | − | 17.5247i | −0.733543 | − | 0.648618i | ||||
\(731\) | 17.0435 | − | 29.5202i | 0.630376 | − | 1.09184i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.72829i | 0.322387i | 0.986923 | + | 0.161193i | \(0.0515343\pi\) | ||||
−0.986923 | + | 0.161193i | \(0.948466\pi\) | |||||||
\(734\) | −26.7612 | −0.987772 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.19029 | − | 5.52574i | −0.117596 | − | 0.203682i | ||||
\(737\) | 25.4388 | + | 14.6871i | 0.937052 | + | 0.541007i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.1661 | − | 28.0005i | −0.594679 | − | 1.03001i | −0.993592 | − | 0.113025i | \(-0.963946\pi\) |
0.398913 | − | 0.916989i | \(-0.369387\pi\) | |||||||
\(740\) | −3.24965 | + | 3.67513i | −0.119459 | + | 0.135100i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.27645i | 0.267127i | ||||||||
\(743\) | −40.5255 | + | 23.3974i | −1.48674 | + | 0.858367i | −0.999886 | − | 0.0151182i | \(-0.995188\pi\) |
−0.486850 | + | 0.873486i | \(0.661854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.90698 | + | 0.638661i | −0.0698664 | + | 0.0233987i | ||||
\(746\) | −13.8156 | − | 23.9293i | −0.505825 | − | 0.876114i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.3757i | 0.671880i | ||||||||
\(749\) | −37.2022 | −1.35934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.6180 | − | 33.9794i | 0.715871 | − | 1.23993i | −0.246751 | − | 0.969079i | \(-0.579363\pi\) |
0.962623 | − | 0.270846i | \(-0.0873036\pi\) | |||||||
\(752\) | − | 9.38058i | − | 0.342075i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.63752 | − | 2.83627i | 0.0596349 | − | 0.103291i | ||||
\(755\) | −4.61910 | + | 22.7362i | −0.168106 | + | 0.827455i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.30977 | + | 1.91090i | −0.120296 | + | 0.0694527i | −0.558940 | − | 0.829208i | \(-0.688792\pi\) |
0.438645 | + | 0.898661i | \(0.355459\pi\) | |||||||
\(758\) | 24.6286 | − | 14.2193i | 0.894551 | − | 0.516469i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.19931 | − | 8.24422i | −0.188599 | − | 0.299049i | ||||
\(761\) | 28.3928 | 1.02924 | 0.514619 | − | 0.857419i | \(-0.327933\pi\) | ||||
0.514619 | + | 0.857419i | \(0.327933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.1315 | + | 24.3246i | −1.52526 | + | 0.880611i | ||||
\(764\) | −1.73813 | + | 3.01054i | −0.0628835 | + | 0.108917i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.52175 | + | 14.7601i | −0.307903 | + | 0.533304i | ||||
\(767\) | − | 6.36344i | − | 0.229770i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.11577 | − | 5.39668i | 0.112358 | − | 0.194609i | −0.804363 | − | 0.594139i | \(-0.797493\pi\) |
0.916720 | + | 0.399529i | \(0.130826\pi\) | |||||||
\(770\) | 39.2782 | − | 13.1545i | 1.41549 | − | 0.474057i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 8.74306i | − | 0.314670i | ||||||
\(773\) | −21.6189 | − | 12.4817i | −0.777577 | − | 0.448935i | 0.0579936 | − | 0.998317i | \(-0.481530\pi\) |
−0.835571 | + | 0.549382i | \(0.814863\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.4233 | − | 6.53662i | −0.554022 | − | 0.234802i | ||||
\(776\) | 6.20299 | + | 10.7439i | 0.222674 | + | 0.385683i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.56230i | 0.0918628i | ||||||||
\(779\) | −4.95523 | + | 16.9698i | −0.177540 | + | 0.608005i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.29631 | − | 7.44142i | −0.153734 | − | 0.266275i | ||||
\(782\) | −25.6257 | + | 14.7950i | −0.916375 | + | 0.529069i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.42842 | + | 12.8664i | 0.265301 | + | 0.459515i | ||||
\(785\) | −10.0474 | − | 30.0004i | −0.358605 | − | 1.07076i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.1744i | 1.50336i | 0.659530 | + | 0.751678i | \(0.270755\pi\) | ||||
−0.659530 | + | 0.751678i | \(0.729245\pi\) | |||||||
\(788\) | 10.9507 | + | 6.32241i | 0.390104 | + | 0.225226i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.8496 | + | 15.6629i | −0.492745 | + | 0.557261i | ||||
\(791\) | 57.5061 | 2.04468 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.07568 | − | 1.77575i | 0.109221 | − | 0.0630586i | ||||
\(794\) | −10.7599 | + | 18.6367i | −0.381854 | + | 0.661390i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.18783 | + | 3.78943i | 0.0775455 | + | 0.134313i | ||||
\(797\) | − | 11.1481i | − | 0.394885i | −0.980314 | − | 0.197443i | \(-0.936736\pi\) | ||
0.980314 | − | 0.197443i | \(-0.0632636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.5026 | −1.53901 | ||||||||
\(800\) | 3.01131 | + | 3.99149i | 0.106466 | + | 0.141121i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.1624 | − | 13.9502i | −0.853204 | − | 0.492598i | ||||
\(803\) | 40.6000 | − | 23.4404i | 1.43274 | − | 0.827194i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 49.9692 | + | 44.1841i | 1.76118 | + | 1.55728i | ||||
\(806\) | 2.70052 | 0.0951219 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.04014 | + | 5.21933i | 0.318031 | + | 0.183615i | ||||
\(809\) | 13.3561 | 0.469577 | 0.234788 | − | 0.972046i | \(-0.424560\pi\) | ||||
0.234788 | + | 0.972046i | \(0.424560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3781 | − | 42.2241i | 0.856031 | − | 1.48269i | −0.0196534 | − | 0.999807i | \(-0.506256\pi\) |
0.875685 | − | 0.482883i | \(-0.160410\pi\) | |||||||
\(812\) | 16.4502 | − | 9.49754i | 0.577289 | − | 0.333298i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.34661 | − | 7.52856i | −0.152349 | − | 0.263876i | ||||
\(815\) | 38.2638 | + | 7.77370i | 1.34032 | + | 0.272301i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.7547 | − | 8.98049i | −1.07597 | − | 0.314187i | ||||
\(818\) | − | 37.3087i | − | 1.30447i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.80555 | − | 8.88729i | 0.0630524 | − | 0.310358i | ||||
\(821\) | 11.6448 | − | 20.1694i | 0.406407 | − | 0.703917i | −0.588077 | − | 0.808805i | \(-0.700115\pi\) |
0.994484 | + | 0.104888i | \(0.0334483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2481 | + | 14.5770i | 0.880092 | + | 0.508122i | 0.870689 | − | 0.491834i | \(-0.163673\pi\) |
0.00940343 | + | 0.999956i | \(0.497007\pi\) | |||||||
\(824\) | −2.13093 | −0.0742346 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.4538 | − | 31.9629i | 0.642090 | − | 1.11213i | ||||
\(827\) | 21.7954 | + | 12.5836i | 0.757899 | + | 0.437573i | 0.828541 | − | 0.559928i | \(-0.189171\pi\) |
−0.0706416 | + | 0.997502i | \(0.522505\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.7513 | 0.581797 | 0.290898 | − | 0.956754i | \(-0.406046\pi\) | ||||
0.290898 | + | 0.956754i | \(0.406046\pi\) | |||||||
\(830\) | −21.0437 | + | 7.04767i | −0.730437 | + | 0.244628i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.698071 | − | 0.403032i | −0.0242013 | − | 0.0139726i | ||||
\(833\) | 59.6682 | − | 34.4495i | 2.06738 | − | 1.19360i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.3742 | + | 38.8749i | −1.18957 | + | 1.34532i | ||||
\(836\) | 16.7787 | − | 4.09703i | 0.580303 | − | 0.141699i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.3128 | + | 8.26353i | −0.494429 | + | 0.285459i | ||||
\(839\) | −9.18901 | − | 15.9158i | −0.317240 | − | 0.549476i | 0.662671 | − | 0.748910i | \(-0.269423\pi\) |
−0.979911 | + | 0.199435i | \(0.936089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.24600 | + | 10.8184i | 0.215379 | + | 0.373048i | ||||
\(842\) | 18.1696 | + | 10.4902i | 0.626167 | + | 0.361518i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.3004 | 0.457820 | ||||||||
\(845\) | −26.1865 | + | 8.77003i | −0.900842 | + | 0.301698i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.9756i | 0.755089i | ||||||||
\(848\) | − | 1.55642i | − | 0.0534476i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.5106 | − | 13.9650i | 0.634909 | − | 0.478996i | ||||
\(851\) | 6.99929 | − | 12.1231i | 0.239933 | − | 0.415576i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.9216 | + | 8.03761i | −0.476665 | + | 0.275203i | −0.719026 | − | 0.694984i | \(-0.755412\pi\) |
0.242361 | + | 0.970186i | \(0.422078\pi\) | |||||||
\(854\) | 20.5985 | 0.704866 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.95746 | 0.271981 | ||||||||
\(857\) | −3.85662 | + | 2.22662i | −0.131740 | + | 0.0760600i | −0.564422 | − | 0.825487i | \(-0.690901\pi\) |
0.432682 | + | 0.901547i | \(0.357567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.8926 | − | 41.3831i | 0.815204 | − | 1.41197i | −0.0939775 | − | 0.995574i | \(-0.529958\pi\) |
0.909181 | − | 0.416400i | \(-0.136708\pi\) | |||||||
\(860\) | 16.1067 | + | 3.27224i | 0.549232 | + | 0.111582i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.3928i | 0.592401i | ||||||||
\(863\) | 20.6483i | 0.702877i | 0.936211 | + | 0.351439i | \(0.114307\pi\) | ||||
−0.936211 | + | 0.351439i | \(0.885693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.6159 | + | 40.6559i | 0.462955 | + | 1.38234i | ||||
\(866\) | 0.144106 | 0.00489693 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.5645 | + | 7.83146i | 0.460408 | + | 0.265817i | ||||
\(869\) | −18.5247 | − | 32.0857i | −0.628407 | − | 1.08843i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.98778 | + | 5.17499i | 0.101237 | + | 0.175348i | ||||
\(872\) | 9.01184 | − | 5.20299i | 0.305179 | − | 0.176195i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.2227 | + | 20.1000i | 0.650219 | + | 0.679893i | ||||
\(875\) | −43.1016 | − | 29.5696i | −1.45710 | − | 0.999635i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.2740 | + | 8.24107i | −0.481997 | + | 0.278281i | −0.721248 | − | 0.692676i | \(-0.756431\pi\) |
0.239251 | + | 0.970958i | \(0.423098\pi\) | |||||||
\(878\) | 26.9128 | + | 15.5381i | 0.908262 | + | 0.524385i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.40152 | + | 2.81373i | −0.283215 | + | 0.0948507i | ||||
\(881\) | −31.1197 | −1.04845 | −0.524224 | − | 0.851580i | \(-0.675645\pi\) | ||||
−0.524224 | + | 0.851580i | \(0.675645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.20102 | − | 4.15751i | −0.242334 | − | 0.139911i | 0.373915 | − | 0.927463i | \(-0.378015\pi\) |
−0.616249 | + | 0.787552i | \(0.711348\pi\) | |||||||
\(884\) | −1.86907 | + | 3.23732i | −0.0628635 | + | 0.108883i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.9199 | −1.03877 | ||||||||
\(887\) | −11.2435 | − | 6.49143i | −0.377519 | − | 0.217961i | 0.299219 | − | 0.954184i | \(-0.403274\pi\) |
−0.676738 | + | 0.736224i | \(0.736607\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.0052 | + | 48.5064i | −0.939263 | + | 1.62685i | ||||
\(890\) | −40.0194 | − | 8.13036i | −1.34145 | − | 0.272530i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.81828i | 0.0608806i | ||||||||
\(893\) | 9.69933 | + | 39.7219i | 0.324576 | + | 1.32924i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.17840 | − | 40.2558i | 0.273374 | − | 1.34560i | ||||
\(896\) | −2.33757 | − | 4.04878i | −0.0780926 | − | 0.135260i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.94457 | + | 1.70005i | −0.0982614 | + | 0.0567313i | ||||
\(899\) | 6.80606 | − | 11.7884i | 0.226995 | − | 0.393167i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.21791 | −0.240464 | ||||||||
\(902\) | 13.9173 | + | 8.03515i | 0.463395 | + | 0.267541i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.3004 | −0.409106 | ||||||||
\(905\) | −10.4182 | − | 9.21203i | −0.346312 | − | 0.306218i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.8857 | − | 20.7186i | 1.19157 | − | 0.687951i | 0.232904 | − | 0.972500i | \(-0.425177\pi\) |
0.958661 | + | 0.284549i | \(0.0918439\pi\) | |||||||
\(908\) | −11.1449 | − | 6.43453i | −0.369858 | − | 0.213538i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.25782 | + | 1.67766i | 0.273744 | + | 0.0556140i | ||||
\(911\) | −12.4993 | −0.414120 | −0.207060 | − | 0.978328i | \(-0.566390\pi\) | ||||
−0.207060 | + | 0.978328i | \(0.566390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 39.3258i | − | 1.30149i | ||||||
\(914\) | 4.55817 | + | 7.89499i | 0.150771 | + | 0.261143i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.05571 | + | 13.9529i | −0.266168 | + | 0.461017i | ||||
\(917\) | 51.0638 | − | 29.4817i | 1.68627 | − | 0.973571i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.08744 | −0.200806 | −0.100403 | − | 0.994947i | \(-0.532013\pi\) | ||||
−0.100403 | + | 0.994947i | \(0.532013\pi\) | |||||||
\(920\) | −10.6883 | − | 9.45088i | −0.352383 | − | 0.311586i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.70352 | + | 2.13823i | 0.121969 | + | 0.0704187i | ||||
\(923\) | − | 1.74798i | − | 0.0575356i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.28054 | + | 10.1000i | −0.140743 | + | 0.332087i | ||||
\(926\) | −14.7435 | − | 25.5366i | −0.484503 | − | 0.839183i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.51866 | + | 2.03150i | −0.115506 | + | 0.0666873i | ||||
\(929\) | 14.6502 | + | 25.3749i | 0.480658 | + | 0.832524i | 0.999754 | − | 0.0221920i | \(-0.00706453\pi\) |
−0.519096 | + | 0.854716i | \(0.673731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.7592 | − | 46.8018i | −1.46692 | − | 1.53387i | ||||
\(932\) | − | 2.20123i | − | 0.0721037i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.97873 | + | 13.8196i | 0.261072 | + | 0.452190i | ||||
\(935\) | 13.0487 | + | 38.9622i | 0.426739 | + | 1.27420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.80715 | − | 2.19806i | −0.124374 | − | 0.0718075i | 0.436522 | − | 0.899694i | \(-0.356210\pi\) |
−0.560896 | + | 0.827886i | \(0.689543\pi\) | |||||||
\(938\) | 34.6580i | 1.13162i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.66123 | − | 19.8898i | −0.217265 | − | 0.648734i | ||||
\(941\) | −28.6436 | + | 49.6122i | −0.933756 | + | 1.61731i | −0.156918 | + | 0.987612i | \(0.550156\pi\) |
−0.776838 | + | 0.629700i | \(0.783178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.8778i | 0.842696i | ||||||||
\(944\) | −3.94723 | + | 6.83680i | −0.128471 | + | 0.222519i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.5623 | + | 25.2226i | −0.473461 | + | 0.820059i | ||||
\(947\) | 6.56809 | − | 3.79209i | 0.213434 | − | 0.123226i | −0.389472 | − | 0.921038i | \(-0.627343\pi\) |
0.602906 | + | 0.797812i | \(0.294009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.53690 | 0.309581 | ||||||||
\(950\) | −16.8785 | − | 13.7883i | −0.547610 | − | 0.447351i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.7763 | + | 10.8405i | −0.608544 | + | 0.351343i | ||||
\(953\) | −15.4370 | + | 8.91256i | −0.500054 | + | 0.288706i | −0.728736 | − | 0.684795i | \(-0.759892\pi\) |
0.228682 | + | 0.973501i | \(0.426558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.54759 | + | 7.61756i | −0.0500788 | + | 0.246498i | ||||
\(956\) | 2.35026 | − | 4.07077i | 0.0760129 | − | 0.131658i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.0821i | 0.681130i | ||||||||
\(959\) | 14.9321 | − | 25.8631i | 0.482182 | − | 0.835163i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.7757 | −0.637927 | ||||||||
\(962\) | − | 1.76845i | − | 0.0570172i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.6405 | + | 21.8939i | 0.407122 | + | 0.705156i | ||||
\(965\) | −6.20852 | − | 18.5381i | −0.199859 | − | 0.596761i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6974 | − | 14.8364i | 0.826372 | − | 0.477106i | −0.0262371 | − | 0.999656i | \(-0.508353\pi\) |
0.852609 | + | 0.522550i | \(0.175019\pi\) | |||||||
\(968\) | − | 4.70052i | − | 0.151081i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.7816 | + | 18.3757i | 0.667258 | + | 0.590007i | ||||
\(971\) | 24.6840 | + | 42.7539i | 0.792146 | + | 1.37204i | 0.924636 | + | 0.380852i | \(0.124369\pi\) |
−0.132490 | + | 0.991184i | \(0.542297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −53.7477 | − | 31.0313i | −1.72307 | − | 0.994817i | ||||
\(974\) | −5.11824 | − | 8.86505i | −0.163999 | − | 0.284054i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.40597 | −0.141032 | ||||||||
\(977\) | 14.5017i | 0.463949i | 0.972722 | + | 0.231975i | \(0.0745186\pi\) | ||||
−0.972722 | + | 0.231975i | \(0.925481\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.1822 | − | 62.6694i | 1.15639 | − | 2.00292i | ||||
\(980\) | 24.8872 | + | 22.0059i | 0.794991 | + | 0.702952i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.38956 | + | 3.68901i | 0.203899 | + | 0.117721i | ||||
\(983\) | −5.97931 | + | 3.45215i | −0.190710 | + | 0.110107i | −0.592315 | − | 0.805706i | \(-0.701786\pi\) |
0.401605 | + | 0.915813i | \(0.368453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.7086 | + | 5.62930i | 0.882870 | + | 0.179364i | ||||
\(986\) | 9.42113 | + | 16.3179i | 0.300030 | + | 0.519667i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.37270 | + | 0.984841i | 0.107300 | + | 0.0313320i | ||||
\(989\) | −46.8989 | −1.49130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.02421 | + | 8.70218i | 0.159599 | + | 0.276434i | 0.934724 | − | 0.355374i | \(-0.115646\pi\) |
−0.775125 | + | 0.631808i | \(0.782313\pi\) | |||||||
\(992\) | −2.90141 | − | 1.67513i | −0.0921199 | − | 0.0531855i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.06911 | − | 8.77996i | 0.160783 | − | 0.278483i | ||||
\(995\) | 7.32979 | + | 6.48119i | 0.232370 | + | 0.205468i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.0709 | − | 15.0521i | −0.825675 | − | 0.476704i | 0.0266946 | − | 0.999644i | \(-0.491502\pi\) |
−0.852369 | + | 0.522940i | \(0.824835\pi\) | |||||||
\(998\) | −22.8534 | − | 13.1944i | −0.723412 | − | 0.417662i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1710.2.t.b.919.5 | 12 | ||
3.2 | odd | 2 | 570.2.q.b.349.2 | yes | 12 | ||
5.4 | even | 2 | inner | 1710.2.t.b.919.1 | 12 | ||
15.14 | odd | 2 | 570.2.q.b.349.6 | yes | 12 | ||
19.11 | even | 3 | inner | 1710.2.t.b.1189.1 | 12 | ||
57.11 | odd | 6 | 570.2.q.b.49.6 | yes | 12 | ||
95.49 | even | 6 | inner | 1710.2.t.b.1189.5 | 12 | ||
285.239 | odd | 6 | 570.2.q.b.49.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.b.49.2 | ✓ | 12 | 285.239 | odd | 6 | ||
570.2.q.b.49.6 | yes | 12 | 57.11 | odd | 6 | ||
570.2.q.b.349.2 | yes | 12 | 3.2 | odd | 2 | ||
570.2.q.b.349.6 | yes | 12 | 15.14 | odd | 2 | ||
1710.2.t.b.919.1 | 12 | 5.4 | even | 2 | inner | ||
1710.2.t.b.919.5 | 12 | 1.1 | even | 1 | trivial | ||
1710.2.t.b.1189.1 | 12 | 19.11 | even | 3 | inner | ||
1710.2.t.b.1189.5 | 12 | 95.49 | even | 6 | inner |