Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(26,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.s (of order \(6\), 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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 458.6 | ||
Root | \(-0.617942 - 0.356769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.458 |
Dual form | 567.2.s.f.26.6 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.15715 | + | 1.24543i | 1.52534 | + | 0.880653i | 0.999549 | + | 0.0300373i | \(0.00956260\pi\) |
0.525787 | + | 0.850616i | \(0.323771\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.10220 | + | 3.64112i | 1.05110 | + | 1.82056i | ||||
\(5\) | 1.23588 | 0.552704 | 0.276352 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276352 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63409 | + | 0.248083i | 0.995594 | + | 0.0937667i | ||||
\(8\) | 5.49086i | 1.94131i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.66599 | + | 1.53921i | 0.843060 | + | 0.486741i | ||||
\(11\) | − | 5.49086i | − | 1.65556i | −0.561055 | − | 0.827779i | \(-0.689604\pi\) | ||
0.561055 | − | 0.827779i | \(-0.310396\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.57031 | − | 1.48397i | −0.712875 | − | 0.411578i | 0.0992497 | − | 0.995063i | \(-0.468356\pi\) |
−0.812125 | + | 0.583484i | \(0.801689\pi\) | |||||||
\(14\) | 5.37317 | + | 3.81574i | 1.43604 | + | 1.01980i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.63409 | + | 4.56239i | −0.658524 | + | 1.14060i | ||||
\(17\) | −2.15715 | + | 3.73630i | −0.523186 | + | 0.906185i | 0.476450 | + | 0.879202i | \(0.341923\pi\) |
−0.999636 | + | 0.0269831i | \(0.991410\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.80660 | + | 2.77509i | −1.10271 | + | 0.636650i | −0.936932 | − | 0.349513i | \(-0.886347\pi\) |
−0.165779 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(20\) | 2.59808 | + | 4.50000i | 0.580948 | + | 1.00623i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.83850 | − | 11.8446i | 1.45797 | − | 2.52528i | ||||
\(23\) | − | 1.63148i | − | 0.340187i | −0.985428 | − | 0.170093i | \(-0.945593\pi\) | ||
0.985428 | − | 0.170093i | \(-0.0544069\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47259 | −0.694518 | ||||||||
\(26\) | −3.69636 | − | 6.40228i | −0.724916 | − | 1.25559i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.63409 | + | 10.1126i | 0.875762 | + | 1.91110i | ||||
\(29\) | 0.440925 | − | 0.254568i | 0.0818777 | − | 0.0472721i | −0.458502 | − | 0.888693i | \(-0.651614\pi\) |
0.540380 | + | 0.841421i | \(0.318281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.04290 | + | 4.06622i | −1.26494 | + | 0.730314i | −0.974026 | − | 0.226434i | \(-0.927293\pi\) |
−0.290915 | + | 0.956749i | \(0.593960\pi\) | |||||||
\(32\) | −1.85383 | + | 1.07031i | −0.327713 | + | 0.189205i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.30660 | + | 5.37317i | −1.59607 | + | 0.921491i | ||||
\(35\) | 3.25544 | + | 0.306602i | 0.550269 | + | 0.0518253i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.53189 | + | 2.65332i | 0.251842 | + | 0.436203i | 0.964033 | − | 0.265783i | \(-0.0856304\pi\) |
−0.712191 | + | 0.701986i | \(0.752297\pi\) | |||||||
\(38\) | −13.8248 | −2.24267 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.78607i | 1.07297i | ||||||||
\(41\) | −0.177017 | + | 0.306602i | −0.0276454 | + | 0.0478832i | −0.879517 | − | 0.475867i | \(-0.842134\pi\) |
0.851872 | + | 0.523751i | \(0.175468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0318939 | + | 0.0552418i | 0.00486377 | + | 0.00842430i | 0.868447 | − | 0.495782i | \(-0.165118\pi\) |
−0.863583 | + | 0.504206i | \(0.831785\pi\) | |||||||
\(44\) | 19.9929 | − | 11.5429i | 3.01404 | − | 1.74016i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.03189 | − | 3.51934i | 0.299586 | − | 0.518899i | ||||
\(47\) | 4.93224 | − | 8.54290i | 0.719442 | − | 1.24611i | −0.241779 | − | 0.970331i | \(-0.577731\pi\) |
0.961221 | − | 0.275778i | \(-0.0889356\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.87691 | + | 1.30695i | 0.982416 | + | 0.186707i | ||||
\(50\) | −7.49090 | − | 4.32488i | −1.05937 | − | 0.611630i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 12.4784i | − | 1.73044i | ||||||
\(53\) | −3.57005 | − | 2.06117i | −0.490384 | − | 0.283124i | 0.234350 | − | 0.972152i | \(-0.424704\pi\) |
−0.724734 | + | 0.689029i | \(0.758037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.78607i | − | 0.915034i | ||||||
\(56\) | −1.36219 | + | 14.4635i | −0.182031 | + | 1.93276i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.26819 | 0.166521 | ||||||||
\(59\) | 1.53921 | + | 2.66599i | 0.200388 | + | 0.347082i | 0.948653 | − | 0.316317i | \(-0.102446\pi\) |
−0.748266 | + | 0.663399i | \(0.769113\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.97259 | + | 3.44828i | 0.764712 | + | 0.441507i | 0.830985 | − | 0.556295i | \(-0.187778\pi\) |
−0.0662730 | + | 0.997802i | \(0.521111\pi\) | |||||||
\(62\) | −20.2568 | −2.57262 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.20440 | 0.650550 | ||||||||
\(65\) | −3.17660 | − | 1.83401i | −0.394009 | − | 0.227481i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.16599 | + | 10.6798i | 0.753295 | + | 1.30475i | 0.946217 | + | 0.323532i | \(0.104870\pi\) |
−0.192922 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(68\) | −18.1391 | −2.19968 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.64061 | + | 4.71581i | 0.793705 | + | 0.563647i | ||||
\(71\) | − | 4.63148i | − | 0.549655i | −0.961494 | − | 0.274828i | \(-0.911379\pi\) | ||
0.961494 | − | 0.274828i | \(-0.0886208\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.09568 | − | 3.51934i | −0.713446 | − | 0.411908i | 0.0988899 | − | 0.995098i | \(-0.468471\pi\) |
−0.812336 | + | 0.583190i | \(0.801804\pi\) | |||||||
\(74\) | 7.63148i | 0.887141i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.2089 | − | 11.6676i | −2.31812 | − | 1.33837i | ||||
\(77\) | 1.36219 | − | 14.4635i | 0.155236 | − | 1.64826i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.165989 | − | 0.287501i | 0.0186752 | − | 0.0323463i | −0.856537 | − | 0.516086i | \(-0.827388\pi\) |
0.875212 | + | 0.483740i | \(0.160722\pi\) | |||||||
\(80\) | −3.25544 | + | 5.63858i | −0.363969 | + | 0.630412i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.763705 | + | 0.440925i | −0.0843371 | + | 0.0486920i | ||||
\(83\) | −3.69636 | − | 6.40228i | −0.405728 | − | 0.702742i | 0.588678 | − | 0.808368i | \(-0.299649\pi\) |
−0.994406 | + | 0.105626i | \(0.966315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.66599 | + | 4.61763i | −0.289167 | + | 0.500852i | ||||
\(86\) | 0.158887i | 0.0171332i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 30.1496 | 3.21396 | ||||||||
\(89\) | −1.71623 | − | 2.97259i | −0.181920 | − | 0.315094i | 0.760615 | − | 0.649204i | \(-0.224898\pi\) |
−0.942534 | + | 0.334110i | \(0.891564\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.40228 | − | 4.54656i | −0.671142 | − | 0.476609i | ||||
\(92\) | 5.94040 | − | 3.42969i | 0.619330 | − | 0.357570i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 21.2792 | − | 12.2855i | 2.19478 | − | 1.26716i | ||||
\(95\) | −5.94040 | + | 3.42969i | −0.609472 | + | 0.351879i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.85939 | + | 2.22822i | −0.391861 | + | 0.226241i | −0.682966 | − | 0.730450i | \(-0.739310\pi\) |
0.291105 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(98\) | 13.2068 | + | 11.3840i | 1.33409 | + | 1.14996i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.30008 | − | 12.6441i | −0.730008 | − | 1.26441i | ||||
\(101\) | 9.15642 | 0.911098 | 0.455549 | − | 0.890211i | \(-0.349443\pi\) | ||||
0.455549 | + | 0.890211i | \(0.349443\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.20382i | − | 0.414215i | −0.978318 | − | 0.207107i | \(-0.933595\pi\) | ||
0.978318 | − | 0.207107i | \(-0.0664049\pi\) | |||||||
\(104\) | 8.14826 | − | 14.1132i | 0.799003 | − | 1.38391i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.13409 | − | 8.89251i | −0.498667 | − | 0.863717i | ||||
\(107\) | 8.93193 | − | 5.15685i | 0.863482 | − | 0.498532i | −0.00169460 | − | 0.999999i | \(-0.500539\pi\) |
0.865177 | + | 0.501467i | \(0.167206\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0637877 | + | 0.110484i | −0.00610976 | + | 0.0105824i | −0.869064 | − | 0.494699i | \(-0.835278\pi\) |
0.862954 | + | 0.505282i | \(0.168611\pi\) | |||||||
\(110\) | 8.45159 | − | 14.6386i | 0.805827 | − | 1.39573i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.07031 | + | 11.3643i | −0.762572 | + | 1.07382i | ||||
\(113\) | 1.99143 | + | 1.14975i | 0.187338 | + | 0.108159i | 0.590736 | − | 0.806865i | \(-0.298838\pi\) |
−0.403398 | + | 0.915025i | \(0.632171\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.01632i | − | 0.188023i | ||||||
\(116\) | 1.85383 | + | 1.07031i | 0.172123 | + | 0.0993755i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.66792i | 0.705889i | ||||||||
\(119\) | −6.60905 | + | 9.30660i | −0.605851 | + | 0.853135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.1496 | −1.74087 | ||||||||
\(122\) | 8.58919 | + | 14.8769i | 0.777629 | + | 1.34689i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −29.6112 | − | 17.0960i | −2.65916 | − | 1.53527i | ||||
\(125\) | −10.4711 | −0.936567 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.386795 | −0.0343225 | −0.0171613 | − | 0.999853i | \(-0.505463\pi\) | ||||
−0.0171613 | + | 0.999853i | \(0.505463\pi\) | |||||||
\(128\) | 14.9343 | + | 8.62234i | 1.32002 | + | 0.762114i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.56827 | − | 7.91248i | −0.400664 | − | 0.693970i | ||||
\(131\) | 20.8634 | 1.82285 | 0.911424 | − | 0.411469i | \(-0.134984\pi\) | ||||
0.911424 | + | 0.411469i | \(0.134984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.3495 | + | 6.11742i | −1.15755 | + | 0.530448i | ||||
\(134\) | 30.7173i | 2.65357i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.5155 | − | 11.8446i | −1.75919 | − | 1.01567i | ||||
\(137\) | 0.700500i | 0.0598477i | 0.999552 | + | 0.0299239i | \(0.00952648\pi\) | ||||
−0.999552 | + | 0.0299239i | \(0.990474\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0429 | + | 5.79827i | 0.851827 | + | 0.491803i | 0.861267 | − | 0.508153i | \(-0.169671\pi\) |
−0.00943957 | + | 0.999955i | \(0.503005\pi\) | |||||||
\(140\) | 5.72720 | + | 12.4980i | 0.484037 | + | 1.05627i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.76819 | − | 9.99080i | 0.484056 | − | 0.838409i | ||||
\(143\) | −8.14826 | + | 14.1132i | −0.681392 | + | 1.18021i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.544932 | − | 0.314617i | 0.0452542 | − | 0.0261275i | ||||
\(146\) | −8.76620 | − | 15.1835i | −0.725496 | − | 1.25660i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.44070 | + | 11.1556i | −0.529422 | + | 0.916986i | ||||
\(149\) | − | 0.350250i | − | 0.0286936i | −0.999897 | − | 0.0143468i | \(-0.995433\pi\) | ||
0.999897 | − | 0.0143468i | \(-0.00456688\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.65498 | 0.378817 | 0.189409 | − | 0.981898i | \(-0.439343\pi\) | ||||
0.189409 | + | 0.981898i | \(0.439343\pi\) | |||||||
\(152\) | −15.2377 | − | 26.3924i | −1.23594 | − | 2.14071i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.9517 | − | 29.5033i | 1.68834 | − | 2.37745i | ||||
\(155\) | −8.70420 | + | 5.02537i | −0.699139 | + | 0.403648i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.07031 | − | 0.617942i | 0.0854198 | − | 0.0493171i | −0.456682 | − | 0.889630i | \(-0.650962\pi\) |
0.542101 | + | 0.840313i | \(0.317629\pi\) | |||||||
\(158\) | 0.716125 | − | 0.413455i | 0.0569718 | − | 0.0328927i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.29111 | + | 1.32278i | −0.181128 | + | 0.104575i | ||||
\(161\) | 0.404743 | − | 4.29747i | 0.0318982 | − | 0.338688i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.80660 | + | 16.9855i | 0.768112 | + | 1.33041i | 0.938585 | + | 0.345047i | \(0.112137\pi\) |
−0.170473 | + | 0.985362i | \(0.554530\pi\) | |||||||
\(164\) | −1.48850 | −0.116232 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 18.4143i | − | 1.42922i | ||||||
\(167\) | −11.8446 | + | 20.5155i | −0.916564 | + | 1.58754i | −0.111970 | + | 0.993712i | \(0.535716\pi\) |
−0.804595 | + | 0.593825i | \(0.797617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.09568 | − | 3.62983i | −0.161206 | − | 0.279217i | ||||
\(170\) | −11.5019 | + | 6.64061i | −0.882154 | + | 0.509312i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.134095 | + | 0.232259i | −0.0102246 | + | 0.0177096i | ||||
\(173\) | −5.99111 | + | 10.3769i | −0.455496 | + | 0.788942i | −0.998717 | − | 0.0506481i | \(-0.983871\pi\) |
0.543221 | + | 0.839590i | \(0.317205\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.14713 | − | 0.861492i | −0.691458 | − | 0.0651227i | ||||
\(176\) | 25.0514 | + | 14.4635i | 1.88832 | + | 1.09022i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 8.54977i | − | 0.640832i | ||||||
\(179\) | 19.3862 | + | 11.1926i | 1.44900 | + | 0.836578i | 0.998422 | − | 0.0561615i | \(-0.0178862\pi\) |
0.450574 | + | 0.892739i | \(0.351220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.90380i | 0.661815i | 0.943663 | + | 0.330907i | \(0.107355\pi\) | ||||
−0.943663 | + | 0.330907i | \(0.892645\pi\) | |||||||
\(182\) | −8.14826 | − | 17.7812i | −0.603989 | − | 1.31803i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.95822 | 0.660409 | ||||||||
\(185\) | 1.89324 | + | 3.27919i | 0.139194 | + | 0.241091i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.5155 | + | 11.8446i | 1.50024 | + | 0.866165i | ||||
\(188\) | 41.4743 | 3.02482 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.0858 | −1.23953 | ||||||||
\(191\) | 9.95138 | + | 5.74543i | 0.720057 | + | 0.415725i | 0.814774 | − | 0.579779i | \(-0.196861\pi\) |
−0.0947169 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.51100 | − | 9.54534i | −0.396691 | − | 0.687089i | 0.596625 | − | 0.802520i | \(-0.296508\pi\) |
−0.993315 | + | 0.115432i | \(0.963175\pi\) | |||||||
\(194\) | −11.1004 | −0.796960 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.69788 | + | 27.7871i | 0.692706 | + | 1.98479i | ||||
\(197\) | − | 19.8228i | − | 1.41232i | −0.708053 | − | 0.706159i | \(-0.750426\pi\) | ||
0.708053 | − | 0.706159i | \(-0.249574\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.50000 | − | 4.33013i | −0.531661 | − | 0.306955i | 0.210032 | − | 0.977695i | \(-0.432643\pi\) |
−0.741693 | + | 0.670740i | \(0.765977\pi\) | |||||||
\(200\) | − | 19.0675i | − | 1.34828i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.7518 | + | 11.4037i | 1.38973 | + | 0.802361i | ||||
\(203\) | 1.22459 | − | 0.561171i | 0.0859495 | − | 0.0393864i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.218772 | + | 0.378925i | −0.0152797 | + | 0.0264653i | ||||
\(206\) | 5.23557 | − | 9.06827i | 0.364779 | − | 0.631816i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.5409 | − | 7.81782i | 0.938890 | − | 0.542068i | ||||
\(209\) | 15.2377 | + | 26.3924i | 1.05401 | + | 1.82560i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0813 | + | 19.1934i | −0.762869 | + | 1.32133i | 0.178497 | + | 0.983940i | \(0.442877\pi\) |
−0.941366 | + | 0.337387i | \(0.890457\pi\) | |||||||
\(212\) | − | 17.3320i | − | 1.19037i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.6900 | 1.75613 | ||||||||
\(215\) | 0.0394171 | + | 0.0682725i | 0.00268823 | + | 0.00465614i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.5604 | + | 8.96358i | −1.32785 | + | 0.608487i | ||||
\(218\) | −0.275200 | + | 0.158887i | −0.0186389 | + | 0.0107612i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 24.7089 | − | 14.2657i | 1.66587 | − | 0.961792i | ||||
\(221\) | 11.0891 | − | 6.40228i | 0.745932 | − | 0.430664i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2343 | − | 9.37285i | 1.08713 | − | 0.627653i | 0.154317 | − | 0.988021i | \(-0.450682\pi\) |
0.932810 | + | 0.360369i | \(0.117349\pi\) | |||||||
\(224\) | −5.14868 | + | 2.35939i | −0.344011 | + | 0.157643i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.86387 | + | 4.96037i | 0.190502 | + | 0.329959i | ||||
\(227\) | −14.1788 | −0.941079 | −0.470540 | − | 0.882379i | \(-0.655941\pi\) | ||||
−0.470540 | + | 0.882379i | \(0.655941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.07075i | − | 0.269003i | −0.990913 | − | 0.134501i | \(-0.957057\pi\) | ||
0.990913 | − | 0.134501i | \(-0.0429433\pi\) | |||||||
\(230\) | 2.51119 | − | 4.34950i | 0.165583 | − | 0.286798i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.39780 | + | 2.42106i | 0.0917700 | + | 0.158950i | ||||
\(233\) | −6.03053 | + | 3.48173i | −0.395073 | + | 0.228096i | −0.684356 | − | 0.729148i | \(-0.739917\pi\) |
0.289283 | + | 0.957244i | \(0.406583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.09568 | − | 10.5580i | 0.397638 | − | 0.688730i | ||||
\(236\) | −6.47145 | + | 11.2089i | −0.421256 | + | 0.729636i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −25.8475 | + | 11.8446i | −1.67544 | + | 0.767773i | ||||
\(239\) | −22.9844 | − | 13.2701i | −1.48674 | − | 0.858369i | −0.486852 | − | 0.873484i | \(-0.661855\pi\) |
−0.999886 | + | 0.0151157i | \(0.995188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 13.6038i | − | 0.876297i | −0.898903 | − | 0.438149i | \(-0.855634\pi\) | ||
0.898903 | − | 0.438149i | \(-0.144366\pi\) | |||||||
\(242\) | −41.3085 | − | 23.8495i | −2.65541 | − | 1.53310i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.9959i | 1.85627i | ||||||||
\(245\) | 8.49906 | + | 1.61524i | 0.542985 | + | 0.103194i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4726 | 1.04813 | ||||||||
\(248\) | −22.3271 | − | 38.6716i | −1.41777 | − | 2.45565i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −22.5878 | − | 13.0411i | −1.42858 | − | 0.824791i | ||||
\(251\) | −2.55060 | −0.160993 | −0.0804963 | − | 0.996755i | \(-0.525651\pi\) | ||||
−0.0804963 | + | 0.996755i | \(0.525651\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.95822 | −0.563198 | ||||||||
\(254\) | −0.834376 | − | 0.481727i | −0.0523534 | − | 0.0302263i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.2727 | + | 28.1851i | 1.01704 | + | 1.76157i | ||||
\(257\) | −18.0602 | −1.12657 | −0.563283 | − | 0.826264i | \(-0.690462\pi\) | ||||
−0.563283 | + | 0.826264i | \(0.690462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.37691 | + | 7.36913i | 0.209831 | + | 0.457895i | ||||
\(260\) | − | 15.4218i | − | 0.956422i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 45.0056 | + | 25.9840i | 2.78046 | + | 1.60530i | ||||
\(263\) | − | 8.06902i | − | 0.497557i | −0.968560 | − | 0.248779i | \(-0.919971\pi\) | ||
0.968560 | − | 0.248779i | \(-0.0800292\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.41217 | − | 2.54737i | −0.271037 | − | 0.156484i | ||||
\(266\) | −36.4157 | − | 3.42969i | −2.23279 | − | 0.210288i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.9243 | + | 44.9022i | −1.58358 | + | 2.74284i | ||||
\(269\) | −1.04758 | + | 1.81445i | −0.0638718 | + | 0.110629i | −0.896193 | − | 0.443664i | \(-0.853678\pi\) |
0.832321 | + | 0.554294i | \(0.187012\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3066 | − | 12.3014i | 1.29428 | − | 0.747255i | 0.314873 | − | 0.949134i | \(-0.398038\pi\) |
0.979411 | + | 0.201879i | \(0.0647046\pi\) | |||||||
\(272\) | −11.3643 | − | 19.6835i | −0.689061 | − | 1.19349i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.872425 | + | 1.51108i | −0.0527051 | + | 0.0912879i | ||||
\(275\) | 19.0675i | 1.14981i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.6990 | −1.30377 | −0.651883 | − | 0.758319i | \(-0.726021\pi\) | ||||
−0.651883 | + | 0.758319i | \(0.726021\pi\) | |||||||
\(278\) | 14.4427 | + | 25.0155i | 0.866216 | + | 1.50033i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.68351 | + | 17.8752i | −0.100609 | + | 1.06824i | ||||
\(281\) | −19.5994 | + | 11.3157i | −1.16920 | + | 0.675040i | −0.953493 | − | 0.301417i | \(-0.902540\pi\) |
−0.215712 | + | 0.976457i | \(0.569207\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.26370 | − | 4.77105i | 0.491226 | − | 0.283610i | −0.233857 | − | 0.972271i | \(-0.575135\pi\) |
0.725083 | + | 0.688661i | \(0.241801\pi\) | |||||||
\(284\) | 16.8638 | − | 9.73630i | 1.00068 | − | 0.577743i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −35.1541 | + | 20.2962i | −2.07870 | + | 1.20014i | ||||
\(287\) | −0.542342 | + | 0.763705i | −0.0320135 | + | 0.0450801i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.806602 | − | 1.39708i | −0.0474472 | − | 0.0821810i | ||||
\(290\) | 1.56733 | 0.0920371 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 29.5935i | − | 1.73183i | ||||||
\(293\) | −13.1674 | + | 22.8066i | −0.769248 | + | 1.33238i | 0.168724 | + | 0.985663i | \(0.446035\pi\) |
−0.937971 | + | 0.346713i | \(0.887298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.90228 | + | 3.29485i | 0.110755 | + | 0.191834i | ||||
\(296\) | −14.5690 | + | 8.41142i | −0.846806 | + | 0.488904i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.436212 | − | 0.755542i | 0.0252691 | − | 0.0437674i | ||||
\(299\) | −2.42106 | + | 4.19340i | −0.140013 | + | 0.242510i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0703069 | + | 0.153424i | 0.00405242 | + | 0.00884324i | ||||
\(302\) | 10.0415 | + | 5.79747i | 0.577824 | + | 0.333607i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 29.2394i | − | 1.67700i | ||||||
\(305\) | 7.38143 | + | 4.26167i | 0.422659 | + | 0.244023i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.81772i | − | 0.389108i | −0.980892 | − | 0.194554i | \(-0.937674\pi\) | ||
0.980892 | − | 0.194554i | \(-0.0623259\pi\) | |||||||
\(308\) | 55.5268 | − | 25.4452i | 3.16393 | − | 1.44987i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −25.0350 | −1.42190 | ||||||||
\(311\) | −13.4707 | − | 23.3320i | −0.763855 | − | 1.32304i | −0.940850 | − | 0.338823i | \(-0.889971\pi\) |
0.176995 | − | 0.984212i | \(-0.443362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.0584 | − | 11.5807i | −1.13377 | − | 0.654581i | −0.188887 | − | 0.981999i | \(-0.560488\pi\) |
−0.944880 | + | 0.327418i | \(0.893821\pi\) | |||||||
\(314\) | 3.07842 | 0.173725 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.39576 | 0.0785179 | ||||||||
\(317\) | −21.7091 | − | 12.5338i | −1.21931 | − | 0.703966i | −0.254536 | − | 0.967063i | \(-0.581923\pi\) |
−0.964769 | + | 0.263097i | \(0.915256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.39780 | − | 2.42106i | −0.0782617 | − | 0.135553i | ||||
\(320\) | 6.43204 | 0.359562 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.22529 | − | 8.76620i | 0.346922 | − | 0.488521i | ||||
\(323\) | − | 23.9452i | − | 1.33235i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.92562 | + | 5.15321i | 0.495105 | + | 0.285849i | ||||
\(326\) | 48.8538i | 2.70576i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.68351 | − | 0.971976i | −0.0929564 | − | 0.0536684i | ||||
\(329\) | 15.1113 | − | 21.2792i | 0.833116 | − | 1.17316i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.19788 | − | 7.27095i | 0.230736 | − | 0.399647i | −0.727289 | − | 0.686332i | \(-0.759220\pi\) |
0.958025 | + | 0.286684i | \(0.0925531\pi\) | |||||||
\(332\) | 15.5410 | − | 26.9178i | 0.852922 | − | 1.47730i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −51.1013 | + | 29.5033i | −2.79614 | + | 1.61435i | ||||
\(335\) | 7.62045 | + | 13.1990i | 0.416349 | + | 0.721138i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.1451 | − | 24.5000i | 0.770533 | − | 1.33460i | −0.166739 | − | 0.986001i | \(-0.553324\pi\) |
0.937271 | − | 0.348601i | \(-0.113343\pi\) | |||||||
\(338\) | − | 10.4401i | − | 0.567867i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.4178 | −1.21577 | ||||||||
\(341\) | 22.3271 | + | 38.6716i | 1.20908 | + | 2.09418i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7902 | + | 5.14868i | 0.960580 | + | 0.278003i | ||||
\(344\) | −0.303325 | + | 0.175125i | −0.0163542 | + | 0.00944210i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.8475 | + | 14.9230i | −1.38957 | + | 0.802268i | ||||
\(347\) | −8.62860 | + | 4.98173i | −0.463208 | + | 0.267433i | −0.713392 | − | 0.700765i | \(-0.752842\pi\) |
0.250184 | + | 0.968198i | \(0.419509\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.4530 | + | 11.2312i | −1.04130 | + | 0.601193i | −0.920200 | − | 0.391448i | \(-0.871974\pi\) |
−0.121097 | + | 0.992641i | \(0.538641\pi\) | |||||||
\(350\) | −18.6588 | − | 13.2505i | −0.997356 | − | 0.708269i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.87691 | + | 10.1791i | 0.313240 | + | 0.542548i | ||||
\(353\) | 32.0652 | 1.70666 | 0.853330 | − | 0.521371i | \(-0.174579\pi\) | ||||
0.853330 | + | 0.521371i | \(0.174579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.72397i | − | 0.303797i | ||||||
\(356\) | 7.21570 | − | 12.4980i | 0.382432 | − | 0.662391i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.8794 | + | 48.2885i | 1.47347 | + | 2.55212i | ||||
\(359\) | −10.2828 | + | 5.93680i | −0.542707 | + | 0.313332i | −0.746175 | − | 0.665749i | \(-0.768112\pi\) |
0.203468 | + | 0.979082i | \(0.434779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.90228 | − | 10.2231i | 0.310647 | − | 0.538056i | ||||
\(362\) | −11.0891 | + | 19.2069i | −0.582829 | + | 1.00949i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.09568 | − | 32.8693i | 0.162258 | − | 1.72282i | ||||
\(365\) | −7.53356 | − | 4.34950i | −0.394324 | − | 0.227663i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5721i | 0.708460i | 0.935158 | + | 0.354230i | \(0.115257\pi\) | ||||
−0.935158 | + | 0.354230i | \(0.884743\pi\) | |||||||
\(368\) | 7.44343 | + | 4.29747i | 0.388016 | + | 0.224021i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.43162i | 0.490327i | ||||||||
\(371\) | −8.89251 | − | 6.31499i | −0.461676 | − | 0.327858i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1716 | 1.56223 | 0.781113 | − | 0.624390i | \(-0.214652\pi\) | ||||
0.781113 | + | 0.624390i | \(0.214652\pi\) | |||||||
\(374\) | 29.5033 | + | 51.1013i | 1.52558 | + | 2.64238i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 46.9079 | + | 27.0823i | 2.41909 | + | 1.39666i | ||||
\(377\) | −1.51108 | −0.0778248 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6770 | −0.651173 | −0.325587 | − | 0.945512i | \(-0.605562\pi\) | ||||
−0.325587 | + | 0.945512i | \(0.605562\pi\) | |||||||
\(380\) | −24.9758 | − | 14.4198i | −1.28123 | − | 0.739720i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.3111 | + | 24.7875i | 0.732219 | + | 1.26824i | ||||
\(383\) | 31.9864 | 1.63443 | 0.817214 | − | 0.576334i | \(-0.195517\pi\) | ||||
0.817214 | + | 0.576334i | \(0.195517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.68351 | − | 17.8752i | 0.0857997 | − | 0.911002i | ||||
\(386\) | − | 27.4543i | − | 1.39739i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.2264 | − | 9.36832i | −0.823771 | − | 0.475604i | ||||
\(389\) | − | 7.57666i | − | 0.384152i | −0.981380 | − | 0.192076i | \(-0.938478\pi\) | ||
0.981380 | − | 0.192076i | \(-0.0615220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.09568 | + | 3.51934i | 0.308272 | + | 0.177981i | ||||
\(392\) | −7.17629 | + | 37.7602i | −0.362457 | + | 1.90718i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.6880 | − | 42.7609i | 1.24376 | − | 2.15426i | ||||
\(395\) | 0.205143 | − | 0.355317i | 0.0103218 | − | 0.0178780i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.824125 | + | 0.475809i | −0.0413617 | + | 0.0238802i | −0.520538 | − | 0.853838i | \(-0.674269\pi\) |
0.479177 | + | 0.877719i | \(0.340935\pi\) | |||||||
\(398\) | −10.7858 | − | 18.6815i | −0.540641 | − | 0.936418i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.14713 | − | 15.8433i | 0.457357 | − | 0.792165i | ||||
\(401\) | 21.0325i | 1.05031i | 0.851006 | + | 0.525156i | \(0.175993\pi\) | ||||
−0.851006 | + | 0.525156i | \(0.824007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.1365 | 1.20233 | ||||||||
\(404\) | 19.2486 | + | 33.3396i | 0.957655 | + | 1.65871i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.34053 | + | 0.314617i | 0.165788 | + | 0.0156142i | ||||
\(407\) | 14.5690 | − | 8.41142i | 0.722159 | − | 0.416939i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4472 | + | 10.0732i | −0.862709 | + | 0.498085i | −0.864919 | − | 0.501912i | \(-0.832630\pi\) |
0.00220932 | + | 0.999998i | \(0.499297\pi\) | |||||||
\(410\) | −0.943850 | + | 0.544932i | −0.0466134 | + | 0.0269123i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.3066 | − | 8.83727i | 0.754102 | − | 0.435381i | ||||
\(413\) | 3.39304 | + | 7.40432i | 0.166960 | + | 0.364343i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.56827 | − | 7.91248i | −0.224248 | − | 0.388408i | ||||
\(416\) | 6.35320 | 0.311491 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 75.9099i | 3.71287i | ||||||||
\(419\) | −4.79464 | + | 8.30457i | −0.234234 | + | 0.405705i | −0.959050 | − | 0.283238i | \(-0.908591\pi\) |
0.724816 | + | 0.688943i | \(0.241925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.30660 | − | 7.45925i | −0.209891 | − | 0.363542i | 0.741789 | − | 0.670633i | \(-0.233978\pi\) |
−0.951680 | + | 0.307092i | \(0.900644\pi\) | |||||||
\(422\) | −47.8081 | + | 27.6020i | −2.32726 | + | 1.34365i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.3176 | − | 19.6027i | 0.549632 | − | 0.951990i | ||||
\(425\) | 7.49090 | − | 12.9746i | 0.363362 | − | 0.629362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.8769 | + | 10.5648i | 0.719944 | + | 0.511266i | ||||
\(428\) | 37.5534 | + | 21.6815i | 1.81521 | + | 1.04801i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.196365i | 0.00946958i | ||||||||
\(431\) | 9.99885 | + | 5.77284i | 0.481628 | + | 0.278068i | 0.721095 | − | 0.692837i | \(-0.243639\pi\) |
−0.239467 | + | 0.970905i | \(0.576973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.8707i | − | 1.09910i | −0.835462 | − | 0.549548i | \(-0.814800\pi\) | ||
0.835462 | − | 0.549548i | \(-0.185200\pi\) | |||||||
\(434\) | −53.3583 | − | 5.02537i | −2.56128 | − | 0.241226i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.536379 | −0.0256879 | ||||||||
\(437\) | 4.52750 | + | 7.84186i | 0.216580 | + | 0.375127i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.218772 | − | 0.126308i | −0.0104414 | − | 0.00602837i | 0.494770 | − | 0.869024i | \(-0.335252\pi\) |
−0.505212 | + | 0.862995i | \(0.668586\pi\) | |||||||
\(440\) | 37.2614 | 1.77637 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.8944 | 1.51706 | ||||||||
\(443\) | 18.8552 | + | 10.8860i | 0.895837 | + | 0.517212i | 0.875847 | − | 0.482589i | \(-0.160303\pi\) |
0.0199896 | + | 0.999800i | \(0.493637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.12106 | − | 3.67378i | −0.100548 | − | 0.174154i | ||||
\(446\) | 46.6930 | 2.21098 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.7089 | + | 1.29113i | 0.647684 | + | 0.0610000i | ||||
\(449\) | 10.7904i | 0.509229i | 0.967043 | + | 0.254614i | \(0.0819485\pi\) | ||||
−0.967043 | + | 0.254614i | \(0.918051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.68351 | + | 0.971976i | 0.0792735 | + | 0.0457686i | ||||
\(452\) | 9.66802i | 0.454746i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.5858 | − | 17.6587i | −1.43546 | − | 0.828765i | ||||
\(455\) | −7.91248 | − | 5.61902i | −0.370943 | − | 0.263424i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.5110 | + | 30.3299i | −0.819130 | + | 1.41878i | 0.0871937 | + | 0.996191i | \(0.472210\pi\) |
−0.906324 | + | 0.422584i | \(0.861123\pi\) | |||||||
\(458\) | 5.06984 | − | 8.78123i | 0.236898 | − | 0.410320i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.34165 | − | 4.23870i | 0.342306 | − | 0.197631i | ||||
\(461\) | −16.4735 | − | 28.5330i | −0.767249 | − | 1.32891i | −0.939049 | − | 0.343783i | \(-0.888292\pi\) |
0.171800 | − | 0.985132i | \(-0.445042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.61320 | − | 4.52620i | 0.121446 | − | 0.210351i | −0.798892 | − | 0.601474i | \(-0.794580\pi\) |
0.920338 | + | 0.391124i | \(0.127914\pi\) | |||||||
\(464\) | 2.68223i | 0.124519i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.3450 | −0.803492 | ||||||||
\(467\) | −10.8332 | − | 18.7637i | −0.501302 | − | 0.868281i | −0.999999 | − | 0.00150418i | \(-0.999521\pi\) |
0.498697 | − | 0.866777i | \(-0.333812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5923 | + | 29.6613i | 0.627635 | + | 1.36963i | ||||
\(470\) | 26.2986 | − | 15.1835i | 1.21306 | − | 0.700363i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.6386 | + | 8.45159i | −0.673795 | + | 0.389016i | ||||
\(473\) | 0.303325 | − | 0.175125i | 0.0139469 | − | 0.00805225i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.6914 | − | 9.63676i | 0.765852 | − | 0.442165i | ||||
\(476\) | −47.7800 | − | 4.50000i | −2.18999 | − | 0.206257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −33.0539 | − | 57.2510i | −1.51185 | − | 2.61860i | ||||
\(479\) | 22.4308 | 1.02489 | 0.512444 | − | 0.858721i | \(-0.328740\pi\) | ||||
0.512444 | + | 0.858721i | \(0.328740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 9.09312i | − | 0.414611i | ||||||
\(482\) | 16.9426 | − | 29.3454i | 0.771714 | − | 1.33665i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −40.2563 | − | 69.7259i | −1.82983 | − | 3.16936i | ||||
\(485\) | −4.76975 | + | 2.75382i | −0.216583 | + | 0.125044i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0813 | + | 19.1934i | −0.502142 | + | 0.869736i | 0.497855 | + | 0.867260i | \(0.334121\pi\) |
−0.999997 | + | 0.00247528i | \(0.999212\pi\) | |||||||
\(488\) | −18.9340 | + | 32.7947i | −0.857103 | + | 1.48455i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.3221 | + | 14.0693i | 0.737357 | + | 0.635587i | ||||
\(491\) | −13.3838 | − | 7.72716i | −0.604004 | − | 0.348722i | 0.166611 | − | 0.986023i | \(-0.446718\pi\) |
−0.770615 | + | 0.637301i | \(0.780051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.19657i | 0.0989285i | ||||||||
\(494\) | 35.5339 | + | 20.5155i | 1.59874 | + | 0.923035i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 42.8432i | − | 1.92372i | ||||||
\(497\) | 1.14899 | − | 12.1997i | 0.0515394 | − | 0.547234i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.34502 | −0.0602112 | −0.0301056 | − | 0.999547i | \(-0.509584\pi\) | ||||
−0.0301056 | + | 0.999547i | \(0.509584\pi\) | |||||||
\(500\) | −22.0124 | − | 38.1267i | −0.984426 | − | 1.70508i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.50203 | − | 3.17660i | −0.245568 | − | 0.141779i | ||||
\(503\) | −18.1391 | −0.808781 | −0.404390 | − | 0.914586i | \(-0.632516\pi\) | ||||
−0.404390 | + | 0.914586i | \(0.632516\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.3163 | 0.503568 | ||||||||
\(506\) | −19.3242 | − | 11.1569i | −0.859067 | − | 0.495983i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.813121 | − | 1.40837i | −0.0360764 | − | 0.0624862i | ||||
\(509\) | 28.1838 | 1.24922 | 0.624612 | − | 0.780935i | \(-0.285257\pi\) | ||||
0.624612 | + | 0.780935i | \(0.285257\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.1835 | − | 10.7825i | −0.671679 | − | 0.476991i | ||||
\(512\) | 46.5767i | 2.05842i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −38.9586 | − | 22.4928i | −1.71839 | − | 0.992114i | ||||
\(515\) | − | 5.19543i | − | 0.228938i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.9079 | − | 27.0823i | −2.06301 | − | 1.19108i | ||||
\(518\) | −1.89324 | + | 20.1020i | −0.0831843 | + | 0.883233i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.0703 | − | 17.4423i | 0.441612 | − | 0.764895i | ||||
\(521\) | 17.0915 | − | 29.6033i | 0.748792 | − | 1.29694i | −0.199611 | − | 0.979875i | \(-0.563968\pi\) |
0.948402 | − | 0.317070i | \(-0.102699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.9157 | − | 18.4266i | 1.39558 | − | 0.805737i | 0.401652 | − | 0.915792i | \(-0.368436\pi\) |
0.993925 | + | 0.110055i | \(0.0351027\pi\) | |||||||
\(524\) | 43.8591 | + | 75.9663i | 1.91600 | + | 3.31860i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0494 | − | 17.4061i | 0.438175 | − | 0.758942i | ||||
\(527\) | − | 35.0858i | − | 1.52836i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.3383 | 0.884273 | ||||||||
\(530\) | −6.34515 | − | 10.9901i | −0.275615 | − | 0.477380i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −50.3376 | − | 35.7471i | −2.18241 | − | 1.54983i | ||||
\(533\) | 0.909976 | − | 0.525375i | 0.0394154 | − | 0.0227565i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0388 | − | 6.37327i | 0.477250 | − | 0.275541i | ||||
\(536\) | −58.6414 | + | 33.8566i | −2.53292 | + | 1.46238i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.51956 | + | 2.60937i | −0.194852 | + | 0.112498i | ||||
\(539\) | 7.17629 | − | 37.7602i | 0.309105 | − | 1.62645i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.2089 | + | 33.2708i | 0.825855 | + | 1.43042i | 0.901264 | + | 0.433269i | \(0.142640\pi\) |
−0.0754099 | + | 0.997153i | \(0.524027\pi\) | |||||||
\(542\) | 61.2821 | 2.63229 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 9.23526i | − | 0.395958i | ||||||
\(545\) | −0.0788343 | + | 0.136545i | −0.00337689 | + | 0.00584894i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.99797 | − | 10.3888i | −0.256454 | − | 0.444192i | 0.708835 | − | 0.705374i | \(-0.249221\pi\) |
−0.965290 | + | 0.261182i | \(0.915888\pi\) | |||||||
\(548\) | −2.55060 | + | 1.47259i | −0.108956 | + | 0.0629060i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.7473 | + | 41.1315i | −1.01259 | + | 1.75385i | ||||
\(551\) | −1.41290 | + | 2.44722i | −0.0601916 | + | 0.104255i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.508554 | − | 0.716125i | 0.0216259 | − | 0.0304527i | ||||
\(554\) | −46.8080 | − | 27.0246i | −1.98868 | − | 1.14817i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 48.7565i | 2.06774i | ||||||||
\(557\) | −7.53838 | − | 4.35228i | −0.319411 | − | 0.184412i | 0.331719 | − | 0.943378i | \(-0.392371\pi\) |
−0.651130 | + | 0.758966i | \(0.725705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.189318i | − | 0.00800729i | ||||||
\(560\) | −9.97396 | + | 14.0449i | −0.421477 | + | 0.593507i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −56.3719 | −2.37791 | ||||||||
\(563\) | 11.7183 | + | 20.2967i | 0.493868 | + | 0.855405i | 0.999975 | − | 0.00706612i | \(-0.00224924\pi\) |
−0.506107 | + | 0.862471i | \(0.668916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.46117 | + | 1.42096i | 0.103542 | + | 0.0597801i | ||||
\(566\) | 23.7681 | 0.999047 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.4308 | 1.06705 | ||||||||
\(569\) | −29.7165 | − | 17.1569i | −1.24578 | − | 0.719253i | −0.275517 | − | 0.961296i | \(-0.588849\pi\) |
−0.970265 | + | 0.242044i | \(0.922182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7363 | − | 18.5958i | −0.449300 | − | 0.778210i | 0.549041 | − | 0.835796i | \(-0.314993\pi\) |
−0.998341 | + | 0.0575853i | \(0.981660\pi\) | |||||||
\(572\) | −68.5171 | −2.86485 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.12106 | + | 0.971976i | −0.0885312 | + | 0.0405695i | ||||
\(575\) | 5.66545i | 0.236266i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7850 | − | 14.3096i | −1.03181 | − | 0.595718i | −0.114310 | − | 0.993445i | \(-0.536466\pi\) |
−0.917504 | + | 0.397727i | \(0.869799\pi\) | |||||||
\(578\) | − | 4.01827i | − | 0.167138i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.29111 | + | 1.32278i | 0.0951333 | + | 0.0549252i | ||||
\(581\) | −8.14826 | − | 17.7812i | −0.338047 | − | 0.737690i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3176 | + | 19.6027i | −0.468727 | + | 0.811860i | ||||
\(584\) | 19.3242 | − | 33.4706i | 0.799643 | − | 1.38502i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −56.8081 | + | 32.7982i | −2.34672 | + | 1.35488i | ||||
\(587\) | −9.25784 | − | 16.0350i | −0.382112 | − | 0.661837i | 0.609252 | − | 0.792977i | \(-0.291470\pi\) |
−0.991364 | + | 0.131139i | \(0.958136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.5683 | − | 39.0894i | 0.929909 | − | 1.61065i | ||||
\(590\) | 9.47666i | 0.390148i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.1406 | −0.663375 | ||||||||
\(593\) | 9.37285 | + | 16.2343i | 0.384897 | + | 0.666661i | 0.991755 | − | 0.128149i | \(-0.0409036\pi\) |
−0.606858 | + | 0.794810i | \(0.707570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.16802 | + | 11.5019i | −0.334856 | + | 0.471531i | ||||
\(596\) | 1.27530 | − | 0.736295i | 0.0522384 | − | 0.0301598i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.4452 | + | 6.03053i | −0.427135 | + | 0.246607i | ||||
\(599\) | 22.4059 | − | 12.9360i | 0.915480 | − | 0.528552i | 0.0332896 | − | 0.999446i | \(-0.489402\pi\) |
0.882190 | + | 0.470893i | \(0.156068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6211 | − | 7.28677i | 0.514824 | − | 0.297234i | −0.219991 | − | 0.975502i | \(-0.570603\pi\) |
0.734814 | + | 0.678268i | \(0.237269\pi\) | |||||||
\(602\) | −0.0394171 | + | 0.418522i | −0.00160652 | + | 0.0170577i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.78571 | + | 16.9494i | 0.398175 | + | 0.689659i | ||||
\(605\) | −23.6667 | −0.962187 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.2796i | 0.904300i | 0.891942 | + | 0.452150i | \(0.149343\pi\) | ||||
−0.891942 | + | 0.452150i | \(0.850657\pi\) | |||||||
\(608\) | 5.94040 | − | 10.2891i | 0.240915 | − | 0.417277i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.6152 | + | 18.3861i | 0.429798 | + | 0.744433i | ||||
\(611\) | −25.3548 | + | 14.6386i | −1.02574 | + | 0.592214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.6112 | + | 21.8432i | −0.509360 | + | 0.882238i | 0.490581 | + | 0.871396i | \(0.336785\pi\) |
−0.999941 | + | 0.0108424i | \(0.996549\pi\) | |||||||
\(614\) | 8.49100 | − | 14.7069i | 0.342669 | − | 0.593520i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 79.4169 | + | 7.47961i | 3.19980 | + | 0.301362i | ||||
\(617\) | −1.76370 | − | 1.01827i | −0.0710039 | − | 0.0409941i | 0.464078 | − | 0.885794i | \(-0.346386\pi\) |
−0.535082 | + | 0.844800i | \(0.679719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 38.0011i | − | 1.52739i | −0.645575 | − | 0.763697i | \(-0.723382\pi\) | ||
0.645575 | − | 0.763697i | \(-0.276618\pi\) | |||||||
\(620\) | −36.5960 | − | 21.1287i | −1.46973 | − | 0.848549i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 67.1075i | − | 2.69076i | ||||||
\(623\) | −3.78325 | − | 8.25585i | −0.151573 | − | 0.330764i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.42184 | 0.176874 | ||||||||
\(626\) | −28.8460 | − | 49.9627i | −1.15292 | − | 1.99691i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.50000 | + | 2.59808i | 0.179570 | + | 0.103675i | ||||
\(629\) | −13.2181 | −0.527040 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.80457 | 0.111648 | 0.0558240 | − | 0.998441i | \(-0.482221\pi\) | ||||
0.0558240 | + | 0.998441i | \(0.482221\pi\) | |||||||
\(632\) | 1.57863 | + | 0.911420i | 0.0627944 | + | 0.0362544i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −31.2199 | − | 54.0744i | −1.23990 | − | 2.14757i | ||||
\(635\) | −0.478034 | −0.0189702 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7363 | − | 13.5644i | −0.623495 | − | 0.537440i | ||||
\(638\) | − | 6.96345i | − | 0.275686i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.4571 | + | 10.6562i | 0.729581 | + | 0.421224i | ||||
\(641\) | − | 1.87766i | − | 0.0741631i | −0.999312 | − | 0.0370815i | \(-0.988194\pi\) | ||
0.999312 | − | 0.0370815i | \(-0.0118061\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.6211 | + | 7.28677i | 0.497726 | + | 0.287362i | 0.727774 | − | 0.685817i | \(-0.240555\pi\) |
−0.230048 | + | 0.973179i | \(0.573888\pi\) | |||||||
\(644\) | 16.4984 | − | 7.56042i | 0.650129 | − | 0.297922i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.8221 | − | 51.6534i | 1.17333 | − | 2.03227i | ||||
\(647\) | −18.2292 | + | 31.5739i | −0.716663 | + | 1.24130i | 0.245651 | + | 0.969358i | \(0.420998\pi\) |
−0.962315 | + | 0.271939i | \(0.912335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.6386 | − | 8.45159i | 0.574615 | − | 0.331754i | ||||
\(650\) | 12.8359 | + | 22.2325i | 0.503467 | + | 0.872031i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −41.2309 | + | 71.4140i | −1.61473 | + | 2.79679i | ||||
\(653\) | 15.0716i | 0.589797i | 0.955529 | + | 0.294898i | \(0.0952858\pi\) | ||||
−0.955529 | + | 0.294898i | \(0.904714\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.7848 | 1.00750 | ||||||||
\(656\) | −0.932559 | − | 1.61524i | −0.0364103 | − | 0.0630645i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 59.0992 | − | 27.0823i | 2.30393 | − | 1.05578i | ||||
\(659\) | −27.2512 | + | 15.7335i | −1.06156 | + | 0.612891i | −0.925863 | − | 0.377860i | \(-0.876660\pi\) |
−0.135695 | + | 0.990751i | \(0.543327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.9099 | − | 6.87620i | 0.463242 | − | 0.267453i | −0.250164 | − | 0.968203i | \(-0.580485\pi\) |
0.713407 | + | 0.700750i | \(0.247151\pi\) | |||||||
\(662\) | 18.1109 | − | 10.4564i | 0.703901 | − | 0.406398i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 35.1541 | − | 20.2962i | 1.36424 | − | 0.787646i | ||||
\(665\) | −16.4984 | + | 7.56042i | −0.639782 | + | 0.293181i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.415322 | − | 0.719359i | −0.0160813 | − | 0.0278537i | ||||
\(668\) | −99.5991 | −3.85360 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 37.9630i | 1.46664i | ||||||||
\(671\) | 18.9340 | − | 32.7947i | 0.730940 | − | 1.26602i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.87242 | − | 10.1713i | −0.226365 | − | 0.392076i | 0.730363 | − | 0.683059i | \(-0.239351\pi\) |
−0.956728 | + | 0.290983i | \(0.906018\pi\) | |||||||
\(674\) | 61.0262 | − | 35.2335i | 2.35064 | − | 1.35714i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.81109 | − | 15.2613i | 0.338888 | − | 0.586971i | ||||
\(677\) | 10.8726 | − | 18.8320i | 0.417870 | − | 0.723772i | −0.577855 | − | 0.816139i | \(-0.696110\pi\) |
0.995725 | + | 0.0923676i | \(0.0294435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7188 | + | 4.91189i | −0.411349 | + | 0.188501i | ||||
\(680\) | −25.3548 | − | 14.6386i | −0.972311 | − | 0.561364i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 111.227i | 4.25911i | ||||||||
\(683\) | −11.1647 | − | 6.44593i | −0.427205 | − | 0.246647i | 0.270950 | − | 0.962593i | \(-0.412662\pi\) |
−0.698155 | + | 0.715947i | \(0.745995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.865736i | 0.0330781i | ||||||||
\(686\) | 31.9638 | + | 33.2630i | 1.22038 | + | 1.26999i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.336046 | −0.0128116 | ||||||||
\(689\) | 6.11742 | + | 10.5957i | 0.233055 | + | 0.403663i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.95303 | + | 5.16904i | 0.340589 | + | 0.196639i | 0.660533 | − | 0.750797i | \(-0.270331\pi\) |
−0.319943 | + | 0.947437i | \(0.603664\pi\) | |||||||
\(692\) | −50.3781 | −1.91509 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.8176 | −0.942063 | ||||||||
\(695\) | 12.4119 | + | 7.16599i | 0.470809 | + | 0.271821i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.763705 | − | 1.32278i | −0.0289274 | − | 0.0501037i | ||||
\(698\) | −55.9508 | −2.11777 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −16.0923 | − | 35.1168i | −0.608232 | − | 1.32729i | ||||
\(701\) | − | 41.2056i | − | 1.55631i | −0.628071 | − | 0.778156i | \(-0.716155\pi\) | ||
0.628071 | − | 0.778156i | \(-0.283845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.7264 | − | 8.50230i | −0.555417 | − | 0.320670i | ||||
\(704\) | − | 28.5767i | − | 1.07702i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 69.1696 | + | 39.9351i | 2.60323 | + | 1.50298i | ||||
\(707\) | 24.1189 | + | 2.27156i | 0.907084 | + | 0.0854307i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.3001 | + | 24.7685i | −0.537051 | + | 0.930199i | 0.462010 | + | 0.886875i | \(0.347128\pi\) |
−0.999061 | + | 0.0433248i | \(0.986205\pi\) | |||||||
\(710\) | 7.12881 | − | 12.3475i | 0.267540 | − | 0.463392i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.3221 | − | 9.42356i | 0.611696 | − | 0.353163i | ||||
\(713\) | 6.63394 | + | 11.4903i | 0.248443 | + | 0.430316i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0703 | + | 17.4423i | −0.376608 | + | 0.652304i | ||||
\(716\) | 94.1168i | 3.51731i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.5755 | −1.10375 | ||||||||
\(719\) | 0.881850 | + | 1.52741i | 0.0328875 | + | 0.0569627i | 0.882001 | − | 0.471248i | \(-0.156196\pi\) |
−0.849113 | + | 0.528211i | \(0.822863\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.04290 | − | 11.0733i | 0.0388395 | − | 0.412390i | ||||
\(722\) | 25.4642 | − | 14.7018i | 0.947681 | − | 0.547144i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −32.4198 | + | 18.7176i | −1.20487 | + | 0.695634i | ||||
\(725\) | −1.53115 | + | 0.884011i | −0.0568656 | + | 0.0328314i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3515 | − | 10.0179i | 0.643533 | − | 0.371544i | −0.142441 | − | 0.989803i | \(-0.545495\pi\) |
0.785974 | + | 0.618259i | \(0.212162\pi\) | |||||||
\(728\) | 24.9645 | − | 35.1541i | 0.925248 | − | 1.30290i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.8340 | − | 18.7651i | −0.400985 | − | 0.694526i | ||||
\(731\) | −0.275200 | −0.0101786 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.4237i | 0.569689i | 0.958574 | + | 0.284844i | \(0.0919419\pi\) | ||||
−0.958574 | + | 0.284844i | \(0.908058\pi\) | |||||||
\(734\) | −16.9032 | + | 29.2772i | −0.623908 | + | 1.08064i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.74618 | + | 3.02448i | 0.0643651 | + | 0.111484i | ||||
\(737\) | 58.6414 | − | 33.8566i | 2.16008 | − | 1.24712i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.2284 | − | 28.1085i | 0.596973 | − | 1.03399i | −0.396292 | − | 0.918124i | \(-0.629703\pi\) |
0.993265 | − | 0.115863i | \(-0.0369634\pi\) | |||||||
\(740\) | −7.95995 | + | 13.7870i | −0.292614 | + | 0.506822i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.3176 | − | 24.6974i | −0.415482 | − | 0.906670i | ||||
\(743\) | 6.51411 | + | 3.76092i | 0.238979 | + | 0.137975i | 0.614708 | − | 0.788755i | \(-0.289274\pi\) |
−0.375728 | + | 0.926730i | \(0.622607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.432868i | − | 0.0158591i | ||||||
\(746\) | 65.0847 | + | 37.5767i | 2.38292 | + | 1.37578i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 99.5991i | 3.64170i | ||||||||
\(749\) | 24.8069 | − | 11.3678i | 0.906424 | − | 0.415369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.8463 | 0.943147 | 0.471573 | − | 0.881827i | \(-0.343686\pi\) | ||||
0.471573 | + | 0.881827i | \(0.343686\pi\) | |||||||
\(752\) | 25.9840 | + | 45.0056i | 0.947539 | + | 1.64119i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.25964 | − | 1.88195i | −0.118709 | − | 0.0685366i | ||||
\(755\) | 5.75302 | 0.209374 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5103 | 1.21795 | 0.608976 | − | 0.793188i | \(-0.291580\pi\) | ||||
0.608976 | + | 0.793188i | \(0.291580\pi\) | |||||||
\(758\) | −27.3462 | − | 15.7883i | −0.993258 | − | 0.573458i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.8320 | − | 32.6179i | −0.683108 | − | 1.18318i | ||||
\(761\) | −8.73002 | −0.316463 | −0.158232 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158232 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.195432 | + | 0.275200i | −0.00707512 | + | 0.00996290i | ||||
\(764\) | 48.3122i | 1.74787i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 68.9995 | + | 39.8369i | 2.49305 | + | 1.43936i | ||||
\(767\) | − | 9.13654i | − | 0.329902i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.36906 | + | 2.52248i | 0.157552 | + | 0.0909628i | 0.576703 | − | 0.816954i | \(-0.304339\pi\) |
−0.419151 | + | 0.907917i | \(0.637672\pi\) | |||||||
\(770\) | 25.8939 | − | 36.4627i | 0.933150 | − | 1.31402i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.1705 | − | 40.1324i | 0.833924 | − | 1.44440i | ||||
\(773\) | −2.90140 | + | 5.02537i | −0.104356 | + | 0.180750i | −0.913475 | − | 0.406895i | \(-0.866612\pi\) |
0.809119 | + | 0.587645i | \(0.199945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.4571 | − | 14.1203i | 0.878525 | − | 0.507217i | ||||
\(776\) | −12.2348 | − | 21.1914i | −0.439205 | − | 0.760726i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.43621 | − | 16.3440i | 0.338305 | − | 0.585961i | ||||
\(779\) | − | 1.96495i | − | 0.0704018i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.4308 | −0.909986 | ||||||||
\(782\) | 8.76620 | + | 15.1835i | 0.313479 | + | 0.542961i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.0772 | + | 27.9325i | −0.859901 | + | 0.997589i | ||||
\(785\) | 1.32278 | − | 0.763705i | 0.0472119 | − | 0.0272578i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.3944 | − | 12.3521i | 0.762629 | − | 0.440304i | −0.0676098 | − | 0.997712i | \(-0.521537\pi\) |
0.830239 | + | 0.557408i | \(0.188204\pi\) | |||||||
\(788\) | 72.1773 | − | 41.6716i | 2.57121 | − | 1.48449i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.885047 | − | 0.510982i | 0.0314886 | − | 0.0181799i | ||||
\(791\) | 4.96037 | + | 3.52259i | 0.176370 | + | 0.125249i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2343 | − | 17.7263i | −0.363429 | − | 0.629478i | ||||
\(794\) | −2.37035 | −0.0841206 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 36.4112i | − | 1.29056i | ||||||
\(797\) | −2.19657 | + | 3.80457i | −0.0778064 | + | 0.134765i | −0.902303 | − | 0.431102i | \(-0.858125\pi\) |
0.824497 | + | 0.565867i | \(0.191458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.2792 | + | 36.8566i | 0.752804 | + | 1.30389i | ||||
\(800\) | 6.43758 | − | 3.71674i | 0.227603 | − | 0.131407i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.1945 | + | 45.3702i | −0.924960 | + | 1.60208i | ||||
\(803\) | −19.3242 | + | 33.4706i | −0.681937 | + | 1.18115i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.500215 | − | 5.31117i | 0.0176303 | − | 0.187194i | ||||
\(806\) | 52.0662 | + | 30.0604i | 1.83395 | + | 1.05883i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 50.2767i | 1.76873i | ||||||||
\(809\) | −43.9347 | − | 25.3657i | −1.54466 | − | 0.891812i | −0.998535 | − | 0.0541105i | \(-0.982768\pi\) |
−0.546129 | − | 0.837701i | \(-0.683899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.8126i | 1.11709i | 0.829474 | + | 0.558546i | \(0.188641\pi\) | ||||
−0.829474 | + | 0.558546i | \(0.811359\pi\) | |||||||
\(812\) | 4.61763 | + | 3.27919i | 0.162047 | + | 0.115077i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 41.9034 | 1.46871 | ||||||||
\(815\) | 12.1198 | + | 20.9921i | 0.424539 | + | 0.735323i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.306602 | − | 0.177017i | −0.0107267 | − | 0.00619304i | ||||
\(818\) | −50.1817 | −1.75456 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.83961 | −0.0642421 | ||||||||
\(821\) | 22.4679 | + | 12.9718i | 0.784135 | + | 0.452720i | 0.837894 | − | 0.545834i | \(-0.183787\pi\) |
−0.0537589 | + | 0.998554i | \(0.517120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0703069 | + | 0.121775i | 0.00245074 | + | 0.00424481i | 0.867248 | − | 0.497876i | \(-0.165887\pi\) |
−0.864797 | + | 0.502121i | \(0.832553\pi\) | |||||||
\(824\) | 23.0826 | 0.804120 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.90228 | + | 20.1980i | −0.0661889 | + | 0.702779i | ||||
\(827\) | 16.1772i | 0.562535i | 0.959629 | + | 0.281267i | \(0.0907548\pi\) | ||||
−0.959629 | + | 0.281267i | \(0.909245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.8592 | − | 16.6619i | −1.00232 | − | 0.578690i | −0.0933864 | − | 0.995630i | \(-0.529769\pi\) |
−0.908934 | + | 0.416940i | \(0.863103\pi\) | |||||||
\(830\) | − | 22.7579i | − | 0.789938i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.3769 | − | 7.72316i | −0.463761 | − | 0.267752i | ||||
\(833\) | −19.7177 | + | 22.8749i | −0.683177 | + | 0.792567i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6386 | + | 25.3548i | −0.506589 | + | 0.877438i | ||||
\(836\) | −64.0652 | + | 110.964i | −2.21574 | + | 3.83778i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.6855 | + | 11.9428i | −0.714570 | + | 0.412557i | ||||
\(839\) | 10.7350 | + | 18.5936i | 0.370615 | + | 0.641924i | 0.989660 | − | 0.143431i | \(-0.0458136\pi\) |
−0.619045 | + | 0.785355i | \(0.712480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3704 | + | 24.8902i | −0.495531 | + | 0.858284i | ||||
\(842\) | − | 21.4543i | − | 0.739365i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −93.1806 | −3.20741 | ||||||||
\(845\) | −2.59002 | − | 4.48605i | −0.0890994 | − | 0.154325i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.4418 | − | 4.75069i | −1.73320 | − | 0.163236i | ||||
\(848\) | 18.8077 | − | 10.8586i | 0.645859 | − | 0.372887i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.3180 | − | 18.6588i | 1.10850 | − | 0.639992i | ||||
\(851\) | 4.32883 | − | 2.49925i | 0.148390 | − | 0.0856732i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.8102 | + | 12.5921i | −0.746766 | + | 0.431146i | −0.824524 | − | 0.565827i | \(-0.808557\pi\) |
0.0777582 | + | 0.996972i | \(0.475224\pi\) | |||||||
\(854\) | 18.9340 | + | 41.3180i | 0.647909 | + | 1.41387i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.3156 | + | 49.0440i | 0.967806 | + | 1.67629i | ||||
\(857\) | −29.0366 | −0.991871 | −0.495936 | − | 0.868359i | \(-0.665175\pi\) | ||||
−0.495936 | + | 0.868359i | \(0.665175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.8314i | − | 0.813116i | −0.913625 | − | 0.406558i | \(-0.866729\pi\) | ||
0.913625 | − | 0.406558i | \(-0.133271\pi\) | |||||||
\(860\) | −0.165725 | + | 0.287045i | −0.00565119 | + | 0.00978815i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.3794 | + | 24.9058i | 0.489763 | + | 0.848294i | ||||
\(863\) | −27.6069 | + | 15.9388i | −0.939749 | + | 0.542564i | −0.889881 | − | 0.456192i | \(-0.849213\pi\) |
−0.0498671 | + | 0.998756i | \(0.515880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.40432 | + | 12.8247i | −0.251754 | + | 0.436051i | ||||
\(866\) | 28.4839 | − | 49.3355i | 0.967922 | − | 1.67649i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −73.7574 | − | 52.3786i | −2.50349 | − | 1.77784i | ||||
\(869\) | −1.57863 | − | 0.911420i | −0.0535512 | − | 0.0309178i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 36.6005i | − | 1.24016i | ||||||
\(872\) | −0.606650 | − | 0.350250i | −0.0205438 | − | 0.0118610i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.5548i | 0.762927i | ||||||||
\(875\) | −27.5820 | − | 2.59772i | −0.932441 | − | 0.0878188i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.28123 | −0.0770316 | −0.0385158 | − | 0.999258i | \(-0.512263\pi\) | ||||
−0.0385158 | + | 0.999258i | \(0.512263\pi\) | |||||||
\(878\) | −0.314617 | − | 0.544932i | −0.0106178 | − | 0.0183906i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 30.9607 | + | 17.8752i | 1.04368 | + | 0.602571i | ||||
\(881\) | 11.8808 | 0.400275 | 0.200137 | − | 0.979768i | \(-0.435861\pi\) | ||||
0.200137 | + | 0.979768i | \(0.435861\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.7120 | −1.67294 | −0.836472 | − | 0.548010i | \(-0.815385\pi\) | ||||
−0.836472 | + | 0.548010i | \(0.815385\pi\) | |||||||
\(884\) | 46.6229 | + | 26.9178i | 1.56810 | + | 0.905343i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.1157 | + | 46.9657i | 0.910968 | + | 1.57784i | ||||
\(887\) | 12.3588 | 0.414969 | 0.207485 | − | 0.978238i | \(-0.433472\pi\) | ||||
0.207485 | + | 0.978238i | \(0.433472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.01886 | − | 0.0959575i | −0.0341713 | − | 0.00321831i | ||||
\(890\) | − | 10.5665i | − | 0.354191i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 68.2554 | + | 39.4072i | 2.28536 | + | 1.31945i | ||||
\(893\) | 54.7497i | 1.83213i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.9591 | + | 13.8328i | 0.800866 | + | 0.462380i | ||||
\(896\) | 37.1994 | + | 26.4170i | 1.24274 | + | 0.882531i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.4387 | + | 23.2764i | −0.448454 | + | 0.776745i | ||||
\(899\) | −2.07026 | + | 3.58580i | −0.0690470 | + | 0.119593i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4023 | − | 8.89251i | 0.513124 | − | 0.296253i | ||||
\(902\) | 2.42106 | + | 4.19340i | 0.0806125 | + | 0.139625i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.31312 | + | 10.9346i | −0.209971 | + | 0.363681i | ||||
\(905\) | 11.0041i | 0.365788i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.7628 | −1.18748 | −0.593742 | − | 0.804656i | \(-0.702350\pi\) | ||||
−0.593742 | + | 0.804656i | \(0.702350\pi\) | |||||||
\(908\) | −29.8067 | − | 51.6267i | −0.989169 | − | 1.71329i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.0703 | − | 21.9755i | −0.333827 | − | 0.728482i | ||||
\(911\) | 41.5024 | − | 23.9614i | 1.37504 | − | 0.793877i | 0.383479 | − | 0.923550i | \(-0.374726\pi\) |
0.991557 | + | 0.129672i | \(0.0413926\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.1541 | + | 20.2962i | −1.16343 | + | 0.671707i | ||||
\(914\) | −75.5478 | + | 43.6175i | −2.49890 | + | 1.44274i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.8221 | − | 8.55754i | 0.489736 | − | 0.282749i | ||||
\(917\) | 54.9563 | + | 5.17587i | 1.81482 | + | 0.170922i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.2408 | + | 29.8619i | 0.568721 | + | 0.985053i | 0.996693 | + | 0.0812614i | \(0.0258949\pi\) |
−0.427972 | + | 0.903792i | \(0.640772\pi\) | |||||||
\(920\) | 11.0713 | 0.365011 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 82.0667i | − | 2.70272i | ||||||
\(923\) | −6.87296 | + | 11.9043i | −0.226226 | + | 0.391835i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.31964 | − | 9.21389i | −0.174909 | − | 0.302951i | ||||
\(926\) | 11.2742 | − | 6.50914i | 0.370492 | − | 0.213903i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.544932 | + | 0.943850i | −0.0178883 | + | 0.0309834i | ||||
\(929\) | 29.1774 | − | 50.5368i | 0.957280 | − | 1.65806i | 0.228219 | − | 0.973610i | \(-0.426710\pi\) |
0.729061 | − | 0.684449i | \(-0.239957\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.6815 | + | 12.8021i | −1.20219 | + | 0.419571i | ||||
\(932\) | −25.3548 | − | 14.6386i | −0.830523 | − | 0.479503i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 53.9682i | − | 1.76589i | ||||||
\(935\) | 25.3548 | + | 14.6386i | 0.829189 | + | 0.478733i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29.8596i | − | 0.975471i | −0.872992 | − | 0.487735i | \(-0.837823\pi\) | ||
0.872992 | − | 0.487735i | \(-0.162177\pi\) | |||||||
\(938\) | −7.62045 | + | 80.9122i | −0.248816 | + | 2.64188i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 51.2574 | 1.67183 | ||||||||
\(941\) | −8.10885 | − | 14.0449i | −0.264341 | − | 0.457852i | 0.703050 | − | 0.711141i | \(-0.251821\pi\) |
−0.967391 | + | 0.253289i | \(0.918488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.500215 | + | 0.288799i | 0.0162892 | + | 0.00940459i | ||||
\(944\) | −16.2177 | −0.527841 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.872425 | 0.0283650 | ||||||||
\(947\) | 24.4167 | + | 14.0970i | 0.793435 | + | 0.458090i | 0.841170 | − | 0.540770i | \(-0.181867\pi\) |
−0.0477355 | + | 0.998860i | \(0.515200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4452 | + | 18.0916i | 0.339065 | + | 0.587278i | ||||
\(950\) | 48.0077 | 1.55758 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −51.1013 | − | 36.2894i | −1.65620 | − | 1.17615i | ||||
\(953\) | 56.3488i | 1.82532i | 0.408725 | + | 0.912658i | \(0.365973\pi\) | ||||
−0.408725 | + | 0.912658i | \(0.634027\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.2988 | + | 7.10069i | 0.397978 | + | 0.229773i | ||||
\(956\) | − | 111.585i | − | 3.60893i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 48.3866 | + | 27.9360i | 1.56330 | + | 0.902571i | ||||
\(959\) | −0.173782 | + | 1.84518i | −0.00561172 | + | 0.0595840i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.5683 | − | 30.4291i | 0.566718 | − | 0.981585i | ||||
\(962\) | 11.3249 | − | 19.6152i | 0.365128 | − | 0.632421i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 49.5330 | − | 28.5979i | 1.59535 | − | 0.921076i | ||||
\(965\) | −6.81096 | − | 11.7969i | −0.219253 | − | 0.379757i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.0155 | + | 29.4717i | −0.547181 | + | 0.947746i | 0.451285 | + | 0.892380i | \(0.350966\pi\) |
−0.998466 | + | 0.0553658i | \(0.982368\pi\) | |||||||
\(968\) | − | 105.148i | − | 3.37958i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.7188 | −0.440483 | ||||||||
\(971\) | −16.3472 | − | 28.3142i | −0.524608 | − | 0.908647i | −0.999589 | − | 0.0286515i | \(-0.990879\pi\) |
0.474982 | − | 0.879996i | \(-0.342455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.0155 | + | 17.7647i | 0.801960 | + | 0.569509i | ||||
\(974\) | −47.8081 | + | 27.6020i | −1.53187 | + | 0.884426i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.4647 | + | 18.1662i | −1.00716 | + | 0.581485i | ||||
\(977\) | −21.3583 | + | 12.3312i | −0.683313 | + | 0.394511i | −0.801102 | − | 0.598528i | \(-0.795753\pi\) |
0.117789 | + | 0.993039i | \(0.462419\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.3221 | + | 9.42356i | −0.521656 | + | 0.301178i | ||||
\(980\) | 11.9855 | + | 34.3416i | 0.382861 | + | 1.09700i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.2473 | − | 33.3373i | −0.614206 | − | 1.06384i | ||||
\(983\) | −17.7915 | −0.567461 | −0.283730 | − | 0.958904i | \(-0.591572\pi\) | ||||
−0.283730 | + | 0.958904i | \(0.591572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 24.4987i | − | 0.780594i | ||||||
\(986\) | −2.73568 | + | 4.73833i | −0.0871217 | + | 0.150899i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 34.6287 | + | 59.9787i | 1.10169 | + | 1.90818i | ||||
\(989\) | 0.0901258 | − | 0.0520341i | 0.00286583 | − | 0.00165459i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.9517 | − | 27.6292i | 0.506722 | − | 0.877669i | −0.493247 | − | 0.869889i | \(-0.664190\pi\) |
0.999970 | − | 0.00777992i | \(-0.00247645\pi\) | |||||||
\(992\) | 8.70420 | − | 15.0761i | 0.276359 | − | 0.478667i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.6725 | − | 24.8857i | 0.560538 | − | 0.789327i | ||||
\(995\) | −9.26913 | − | 5.35153i | −0.293851 | − | 0.169655i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.9553i | 1.23373i | 0.787070 | + | 0.616864i | \(0.211597\pi\) | ||||
−0.787070 | + | 0.616864i | \(0.788403\pi\) | |||||||
\(998\) | −2.90140 | − | 1.67512i | −0.0918423 | − | 0.0530252i | ||||
\(999\) | 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 | 567.2.s.f.458.6 | 12 | ||
3.2 | odd | 2 | inner | 567.2.s.f.458.1 | 12 | ||
7.5 | odd | 6 | 567.2.i.f.215.1 | 12 | |||
9.2 | odd | 6 | 567.2.i.f.269.6 | 12 | |||
9.4 | even | 3 | 189.2.p.d.80.1 | yes | 12 | ||
9.5 | odd | 6 | 189.2.p.d.80.6 | yes | 12 | ||
9.7 | even | 3 | 567.2.i.f.269.1 | 12 | |||
21.5 | even | 6 | 567.2.i.f.215.6 | 12 | |||
63.4 | even | 3 | 1323.2.c.d.1322.2 | 12 | |||
63.5 | even | 6 | 189.2.p.d.26.1 | ✓ | 12 | ||
63.31 | odd | 6 | 1323.2.c.d.1322.1 | 12 | |||
63.32 | odd | 6 | 1323.2.c.d.1322.11 | 12 | |||
63.40 | odd | 6 | 189.2.p.d.26.6 | yes | 12 | ||
63.47 | even | 6 | inner | 567.2.s.f.26.6 | 12 | ||
63.59 | even | 6 | 1323.2.c.d.1322.12 | 12 | |||
63.61 | odd | 6 | inner | 567.2.s.f.26.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.1 | ✓ | 12 | 63.5 | even | 6 | ||
189.2.p.d.26.6 | yes | 12 | 63.40 | odd | 6 | ||
189.2.p.d.80.1 | yes | 12 | 9.4 | even | 3 | ||
189.2.p.d.80.6 | yes | 12 | 9.5 | odd | 6 | ||
567.2.i.f.215.1 | 12 | 7.5 | odd | 6 | |||
567.2.i.f.215.6 | 12 | 21.5 | even | 6 | |||
567.2.i.f.269.1 | 12 | 9.7 | even | 3 | |||
567.2.i.f.269.6 | 12 | 9.2 | odd | 6 | |||
567.2.s.f.26.1 | 12 | 63.61 | odd | 6 | inner | ||
567.2.s.f.26.6 | 12 | 63.47 | even | 6 | inner | ||
567.2.s.f.458.1 | 12 | 3.2 | odd | 2 | inner | ||
567.2.s.f.458.6 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.c.d.1322.1 | 12 | 63.31 | odd | 6 | |||
1323.2.c.d.1322.2 | 12 | 63.4 | even | 3 | |||
1323.2.c.d.1322.11 | 12 | 63.32 | odd | 6 | |||
1323.2.c.d.1322.12 | 12 | 63.59 | even | 6 |