Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(251,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bc (of order \(4\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(64\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Character | \(\chi\) | \(=\) | 560.251 |
Dual form | 560.2.bc.a.531.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40740 | + | 0.138663i | −0.995182 | + | 0.0980492i | ||||
\(3\) | −0.176544 | + | 0.176544i | −0.101928 | + | 0.101928i | −0.756232 | − | 0.654304i | \(-0.772962\pi\) |
0.654304 | + | 0.756232i | \(0.272962\pi\) | |||||||
\(4\) | 1.96155 | − | 0.390307i | 0.980773 | − | 0.195154i | ||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0.223988 | − | 0.272948i | 0.0914428 | − | 0.111431i | ||||
\(7\) | −2.53089 | + | 0.771085i | −0.956588 | + | 0.291443i | ||||
\(8\) | −2.70656 | + | 0.821311i | −0.956912 | + | 0.290377i | ||||
\(9\) | 2.93766i | 0.979221i | ||||||||
\(10\) | 0.897132 | − | 1.09323i | 0.283698 | − | 0.345710i | ||||
\(11\) | 0.978755 | − | 0.978755i | 0.295106 | − | 0.295106i | −0.543988 | − | 0.839093i | \(-0.683086\pi\) |
0.839093 | + | 0.543988i | \(0.183086\pi\) | |||||||
\(12\) | −0.277393 | + | 0.415206i | −0.0800765 | + | 0.119860i | ||||
\(13\) | −2.57707 | − | 2.57707i | −0.714752 | − | 0.714752i | 0.252774 | − | 0.967525i | \(-0.418657\pi\) |
−0.967525 | + | 0.252774i | \(0.918657\pi\) | |||||||
\(14\) | 3.45506 | − | 1.43617i | 0.923403 | − | 0.383831i | ||||
\(15\) | − | 0.249671i | − | 0.0644649i | ||||||
\(16\) | 3.69532 | − | 1.53121i | 0.923830 | − | 0.382802i | ||||
\(17\) | − | 7.40385i | − | 1.79570i | −0.440304 | − | 0.897849i | \(-0.645129\pi\) | ||
0.440304 | − | 0.897849i | \(-0.354871\pi\) | |||||||
\(18\) | −0.407344 | − | 4.13447i | −0.0960119 | − | 0.974503i | ||||
\(19\) | −1.84697 | + | 1.84697i | −0.423723 | + | 0.423723i | −0.886483 | − | 0.462760i | \(-0.846859\pi\) |
0.462760 | + | 0.886483i | \(0.346859\pi\) | |||||||
\(20\) | −1.11103 | + | 1.66301i | −0.248435 | + | 0.371861i | ||||
\(21\) | 0.310684 | − | 0.582946i | 0.0677969 | − | 0.127209i | ||||
\(22\) | −1.24178 | + | 1.51322i | −0.264749 | + | 0.322619i | ||||
\(23\) | 3.59564 | 0.749744 | 0.374872 | − | 0.927077i | \(-0.377687\pi\) | ||||
0.374872 | + | 0.927077i | \(0.377687\pi\) | |||||||
\(24\) | 0.332830 | − | 0.622825i | 0.0679385 | − | 0.127134i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 3.98432 | + | 3.26963i | 0.781389 | + | 0.641227i | ||||
\(27\) | −1.04826 | − | 1.04826i | −0.201738 | − | 0.201738i | ||||
\(28\) | −4.66350 | + | 2.50034i | −0.881320 | + | 0.472521i | ||||
\(29\) | 3.00471 | − | 3.00471i | 0.557960 | − | 0.557960i | −0.370766 | − | 0.928726i | \(-0.620905\pi\) |
0.928726 | + | 0.370766i | \(0.120905\pi\) | |||||||
\(30\) | 0.0346201 | + | 0.351387i | 0.00632073 | + | 0.0641543i | ||||
\(31\) | −10.5897 | −1.90197 | −0.950985 | − | 0.309237i | \(-0.899926\pi\) | ||||
−0.950985 | + | 0.309237i | \(0.899926\pi\) | |||||||
\(32\) | −4.98847 | + | 2.66743i | −0.881845 | + | 0.471539i | ||||
\(33\) | 0.345587i | 0.0601590i | ||||||||
\(34\) | 1.02664 | + | 10.4202i | 0.176067 | + | 1.78705i | ||||
\(35\) | 1.24437 | − | 2.33485i | 0.210337 | − | 0.394662i | ||||
\(36\) | 1.14659 | + | 5.76236i | 0.191098 | + | 0.960394i | ||||
\(37\) | −6.74670 | − | 6.74670i | −1.10915 | − | 1.10915i | −0.993262 | − | 0.115888i | \(-0.963029\pi\) |
−0.115888 | − | 0.993262i | \(-0.536971\pi\) | |||||||
\(38\) | 2.34331 | − | 2.85552i | 0.380136 | − | 0.463227i | ||||
\(39\) | 0.909936 | 0.145706 | ||||||||
\(40\) | 1.33307 | − | 2.49458i | 0.210777 | − | 0.394428i | ||||
\(41\) | 6.05682 | 0.945917 | 0.472958 | − | 0.881085i | \(-0.343186\pi\) | ||||
0.472958 | + | 0.881085i | \(0.343186\pi\) | |||||||
\(42\) | −0.356424 | + | 0.863518i | −0.0549974 | + | 0.133244i | ||||
\(43\) | 1.28129 | − | 1.28129i | 0.195395 | − | 0.195395i | −0.602628 | − | 0.798022i | \(-0.705880\pi\) |
0.798022 | + | 0.602628i | \(0.205880\pi\) | |||||||
\(44\) | 1.53786 | − | 2.30189i | 0.231841 | − | 0.347023i | ||||
\(45\) | −2.07724 | − | 2.07724i | −0.309657 | − | 0.309657i | ||||
\(46\) | −5.06051 | + | 0.498581i | −0.746131 | + | 0.0735118i | ||||
\(47\) | −3.23567 | −0.471971 | −0.235986 | − | 0.971757i | \(-0.575832\pi\) | ||||
−0.235986 | + | 0.971757i | \(0.575832\pi\) | |||||||
\(48\) | −0.382062 | + | 0.922714i | −0.0551458 | + | 0.133182i | ||||
\(49\) | 5.81085 | − | 3.90307i | 0.830122 | − | 0.557582i | ||||
\(50\) | 0.138663 | + | 1.40740i | 0.0196098 | + | 0.199036i | ||||
\(51\) | 1.30711 | + | 1.30711i | 0.183032 | + | 0.183032i | ||||
\(52\) | −6.06090 | − | 4.04920i | −0.840495 | − | 0.561523i | ||||
\(53\) | 6.09045 | + | 6.09045i | 0.836588 | + | 0.836588i | 0.988408 | − | 0.151820i | \(-0.0485135\pi\) |
−0.151820 | + | 0.988408i | \(0.548514\pi\) | |||||||
\(54\) | 1.62068 | + | 1.32997i | 0.220546 | + | 0.180986i | ||||
\(55\) | 1.38417i | 0.186641i | ||||||||
\(56\) | 6.21671 | − | 4.16564i | 0.830743 | − | 0.556657i | ||||
\(57\) | − | 0.652143i | − | 0.0863784i | ||||||
\(58\) | −3.81218 | + | 4.64546i | −0.500564 | + | 0.609979i | ||||
\(59\) | −9.72909 | − | 9.72909i | −1.26662 | − | 1.26662i | −0.947823 | − | 0.318797i | \(-0.896721\pi\) |
−0.318797 | − | 0.947823i | \(-0.603279\pi\) | |||||||
\(60\) | −0.0974485 | − | 0.489742i | −0.0125805 | − | 0.0632254i | ||||
\(61\) | −8.74709 | − | 8.74709i | −1.11995 | − | 1.11995i | −0.991748 | − | 0.128202i | \(-0.959079\pi\) |
−0.128202 | − | 0.991748i | \(-0.540921\pi\) | |||||||
\(62\) | 14.9040 | − | 1.46840i | 1.89281 | − | 0.186487i | ||||
\(63\) | −2.26519 | − | 7.43492i | −0.285387 | − | 0.936712i | ||||
\(64\) | 6.65090 | − | 4.44585i | 0.831362 | − | 0.555731i | ||||
\(65\) | 3.64453 | 0.452049 | ||||||||
\(66\) | −0.0479200 | − | 0.486379i | −0.00589854 | − | 0.0598692i | ||||
\(67\) | −2.29246 | − | 2.29246i | −0.280069 | − | 0.280069i | 0.553068 | − | 0.833136i | \(-0.313457\pi\) |
−0.833136 | + | 0.553068i | \(0.813457\pi\) | |||||||
\(68\) | −2.88978 | − | 14.5230i | −0.350437 | − | 1.76117i | ||||
\(69\) | −0.634791 | + | 0.634791i | −0.0764198 | + | 0.0764198i | ||||
\(70\) | −1.42757 | + | 3.45862i | −0.170628 | + | 0.413384i | ||||
\(71\) | −10.7355 | −1.27407 | −0.637034 | − | 0.770835i | \(-0.719839\pi\) | ||||
−0.637034 | + | 0.770835i | \(0.719839\pi\) | |||||||
\(72\) | −2.41273 | − | 7.95095i | −0.284344 | − | 0.937029i | ||||
\(73\) | −4.00333 | −0.468554 | −0.234277 | − | 0.972170i | \(-0.575272\pi\) | ||||
−0.234277 | + | 0.972170i | \(0.575272\pi\) | |||||||
\(74\) | 10.4308 | + | 8.55978i | 1.21256 | + | 0.995055i | ||||
\(75\) | 0.176544 | + | 0.176544i | 0.0203856 | + | 0.0203856i | ||||
\(76\) | −2.90202 | + | 4.34379i | −0.332885 | + | 0.498267i | ||||
\(77\) | −1.72242 | + | 3.23183i | −0.196288 | + | 0.368301i | ||||
\(78\) | −1.28064 | + | 0.126174i | −0.145004 | + | 0.0142864i | ||||
\(79\) | 1.12435i | 0.126499i | 0.997998 | + | 0.0632494i | \(0.0201464\pi\) | ||||
−0.997998 | + | 0.0632494i | \(0.979854\pi\) | |||||||
\(80\) | −1.53026 | + | 3.69572i | −0.171088 | + | 0.413194i | ||||
\(81\) | −8.44286 | −0.938096 | ||||||||
\(82\) | −8.52437 | + | 0.839854i | −0.941359 | + | 0.0927464i | ||||
\(83\) | 1.73594 | − | 1.73594i | 0.190544 | − | 0.190544i | −0.605387 | − | 0.795931i | \(-0.706982\pi\) |
0.795931 | + | 0.605387i | \(0.206982\pi\) | |||||||
\(84\) | 0.381894 | − | 1.26474i | 0.0416680 | − | 0.137994i | ||||
\(85\) | 5.23531 | + | 5.23531i | 0.567849 | + | 0.567849i | ||||
\(86\) | −1.62562 | + | 1.98095i | −0.175295 | + | 0.213611i | ||||
\(87\) | 1.06093i | 0.113743i | ||||||||
\(88\) | −1.84519 | + | 3.45292i | −0.196698 | + | 0.368082i | ||||
\(89\) | 7.69624 | 0.815800 | 0.407900 | − | 0.913027i | \(-0.366261\pi\) | ||||
0.407900 | + | 0.913027i | \(0.366261\pi\) | |||||||
\(90\) | 3.21154 | + | 2.63547i | 0.338527 | + | 0.277803i | ||||
\(91\) | 8.50945 | + | 4.53516i | 0.892033 | + | 0.475414i | ||||
\(92\) | 7.05302 | − | 1.40341i | 0.735328 | − | 0.146315i | ||||
\(93\) | 1.86956 | − | 1.86956i | 0.193864 | − | 0.193864i | ||||
\(94\) | 4.55388 | − | 0.448667i | 0.469697 | − | 0.0462764i | ||||
\(95\) | − | 2.61200i | − | 0.267986i | ||||||
\(96\) | 0.409767 | − | 1.35161i | 0.0418217 | − | 0.137948i | ||||
\(97\) | 10.9023i | 1.10696i | 0.832864 | + | 0.553478i | \(0.186700\pi\) | ||||
−0.832864 | + | 0.553478i | \(0.813300\pi\) | |||||||
\(98\) | −7.63698 | + | 6.29893i | −0.771452 | + | 0.636288i | ||||
\(99\) | 2.87525 | + | 2.87525i | 0.288974 | + | 0.288974i | ||||
\(100\) | −0.390307 | − | 1.96155i | −0.0390307 | − | 0.196155i | ||||
\(101\) | 7.36104 | − | 7.36104i | 0.732451 | − | 0.732451i | −0.238654 | − | 0.971105i | \(-0.576706\pi\) |
0.971105 | + | 0.238654i | \(0.0767061\pi\) | |||||||
\(102\) | −2.02087 | − | 1.65838i | −0.200096 | − | 0.164204i | ||||
\(103\) | 12.6931i | 1.25069i | 0.780349 | + | 0.625344i | \(0.215041\pi\) | ||||
−0.780349 | + | 0.625344i | \(0.784959\pi\) | |||||||
\(104\) | 9.09158 | + | 4.85842i | 0.891502 | + | 0.476407i | ||||
\(105\) | 0.192518 | + | 0.631892i | 0.0187878 | + | 0.0616663i | ||||
\(106\) | −9.41621 | − | 7.72718i | −0.914583 | − | 0.750530i | ||||
\(107\) | −5.21896 | + | 5.21896i | −0.504536 | + | 0.504536i | −0.912844 | − | 0.408308i | \(-0.866119\pi\) |
0.408308 | + | 0.912844i | \(0.366119\pi\) | |||||||
\(108\) | −2.46536 | − | 1.64707i | −0.237229 | − | 0.158489i | ||||
\(109\) | 9.35887 | − | 9.35887i | 0.896417 | − | 0.896417i | −0.0987000 | − | 0.995117i | \(-0.531468\pi\) |
0.995117 | + | 0.0987000i | \(0.0314684\pi\) | |||||||
\(110\) | −0.191932 | − | 1.94808i | −0.0183000 | − | 0.185742i | ||||
\(111\) | 2.38218 | 0.226107 | ||||||||
\(112\) | −8.17177 | + | 6.72474i | −0.772160 | + | 0.635428i | ||||
\(113\) | −9.83245 | −0.924959 | −0.462480 | − | 0.886630i | \(-0.653040\pi\) | ||||
−0.462480 | + | 0.886630i | \(0.653040\pi\) | |||||||
\(114\) | 0.0904278 | + | 0.917825i | 0.00846933 | + | 0.0859622i | ||||
\(115\) | −2.54250 | + | 2.54250i | −0.237090 | + | 0.237090i | ||||
\(116\) | 4.72111 | − | 7.06662i | 0.438344 | − | 0.656119i | ||||
\(117\) | 7.57058 | − | 7.57058i | 0.699900 | − | 0.699900i | ||||
\(118\) | 15.0418 | + | 12.3437i | 1.38471 | + | 1.13633i | ||||
\(119\) | 5.70900 | + | 18.7384i | 0.523343 | + | 1.71774i | ||||
\(120\) | 0.205058 | + | 0.675750i | 0.0187191 | + | 0.0616872i | ||||
\(121\) | 9.08408i | 0.825825i | ||||||||
\(122\) | 13.5235 | + | 11.0978i | 1.22436 | + | 1.00474i | ||||
\(123\) | −1.06930 | + | 1.06930i | −0.0964153 | + | 0.0964153i | ||||
\(124\) | −20.7722 | + | 4.13324i | −1.86540 | + | 0.371176i | ||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 4.21897 | + | 10.1498i | 0.375856 | + | 0.904216i | ||||
\(127\) | 12.0507i | 1.06933i | 0.845065 | + | 0.534664i | \(0.179562\pi\) | ||||
−0.845065 | + | 0.534664i | \(0.820438\pi\) | |||||||
\(128\) | −8.74400 | + | 7.17931i | −0.772867 | + | 0.634568i | ||||
\(129\) | 0.452408i | 0.0398323i | ||||||||
\(130\) | −5.12931 | + | 0.505360i | −0.449871 | + | 0.0443230i | ||||
\(131\) | 6.27543 | − | 6.27543i | 0.548287 | − | 0.548287i | −0.377658 | − | 0.925945i | \(-0.623271\pi\) |
0.925945 | + | 0.377658i | \(0.123271\pi\) | |||||||
\(132\) | 0.134885 | + | 0.677885i | 0.0117402 | + | 0.0590023i | ||||
\(133\) | 3.25031 | − | 6.09864i | 0.281837 | − | 0.528820i | ||||
\(134\) | 3.54429 | + | 2.90853i | 0.306180 | + | 0.251259i | ||||
\(135\) | 1.48246 | 0.127590 | ||||||||
\(136\) | 6.08086 | + | 20.0389i | 0.521430 | + | 1.71833i | ||||
\(137\) | 2.07590i | 0.177356i | 0.996060 | + | 0.0886781i | \(0.0282642\pi\) | ||||
−0.996060 | + | 0.0886781i | \(0.971736\pi\) | |||||||
\(138\) | 0.805382 | − | 0.981426i | 0.0685587 | − | 0.0835445i | ||||
\(139\) | 12.2922 | + | 12.2922i | 1.04261 | + | 1.04261i | 0.999051 | + | 0.0435635i | \(0.0138711\pi\) |
0.0435635 | + | 0.999051i | \(0.486129\pi\) | |||||||
\(140\) | 1.52959 | − | 5.06561i | 0.129274 | − | 0.428122i | ||||
\(141\) | 0.571240 | − | 0.571240i | 0.0481071 | − | 0.0481071i | ||||
\(142\) | 15.1091 | − | 1.48861i | 1.26793 | − | 0.124921i | ||||
\(143\) | −5.04465 | −0.421855 | ||||||||
\(144\) | 4.49818 | + | 10.8556i | 0.374848 | + | 0.904634i | ||||
\(145\) | 4.24929i | 0.352885i | ||||||||
\(146\) | 5.63428 | − | 0.555112i | 0.466297 | − | 0.0459414i | ||||
\(147\) | −0.336808 | + | 1.71494i | −0.0277795 | + | 0.141446i | ||||
\(148\) | −15.8672 | − | 10.6007i | −1.30428 | − | 0.871370i | ||||
\(149\) | 4.08134 | + | 4.08134i | 0.334356 | + | 0.334356i | 0.854238 | − | 0.519882i | \(-0.174024\pi\) |
−0.519882 | + | 0.854238i | \(0.674024\pi\) | |||||||
\(150\) | −0.272948 | − | 0.223988i | −0.0222861 | − | 0.0182886i | ||||
\(151\) | −20.7250 | −1.68657 | −0.843286 | − | 0.537465i | \(-0.819382\pi\) | ||||
−0.843286 | + | 0.537465i | \(0.819382\pi\) | |||||||
\(152\) | 3.48199 | − | 6.51585i | 0.282426 | − | 0.528505i | ||||
\(153\) | 21.7500 | 1.75839 | ||||||||
\(154\) | 1.97600 | − | 4.78731i | 0.159231 | − | 0.385772i | ||||
\(155\) | 7.48806 | − | 7.48806i | 0.601456 | − | 0.601456i | ||||
\(156\) | 1.78488 | − | 0.355154i | 0.142905 | − | 0.0284351i | ||||
\(157\) | −9.66337 | − | 9.66337i | −0.771221 | − | 0.771221i | 0.207099 | − | 0.978320i | \(-0.433598\pi\) |
−0.978320 | + | 0.207099i | \(0.933598\pi\) | |||||||
\(158\) | −0.155905 | − | 1.58240i | −0.0124031 | − | 0.125889i | ||||
\(159\) | −2.15047 | −0.170543 | ||||||||
\(160\) | 1.64123 | − | 5.41354i | 0.129750 | − | 0.427978i | ||||
\(161\) | −9.10020 | + | 2.77255i | −0.717196 | + | 0.218507i | ||||
\(162\) | 11.8825 | − | 1.17071i | 0.933576 | − | 0.0919796i | ||||
\(163\) | −1.58658 | − | 1.58658i | −0.124270 | − | 0.124270i | 0.642236 | − | 0.766507i | \(-0.278007\pi\) |
−0.766507 | + | 0.642236i | \(0.778007\pi\) | |||||||
\(164\) | 11.8807 | − | 2.36402i | 0.927730 | − | 0.184599i | ||||
\(165\) | −0.244367 | − | 0.244367i | −0.0190240 | − | 0.0190240i | ||||
\(166\) | −2.20245 | + | 2.68386i | −0.170943 | + | 0.208308i | ||||
\(167\) | 13.4079i | 1.03754i | 0.854914 | + | 0.518769i | \(0.173609\pi\) | ||||
−0.854914 | + | 0.518769i | \(0.826391\pi\) | |||||||
\(168\) | −0.362105 | + | 1.83294i | −0.0279370 | + | 0.141415i | ||||
\(169\) | 0.282627i | 0.0217405i | ||||||||
\(170\) | −8.09412 | − | 6.64223i | −0.620791 | − | 0.509436i | ||||
\(171\) | −5.42577 | − | 5.42577i | −0.414919 | − | 0.414919i | ||||
\(172\) | 2.01321 | − | 3.01340i | 0.153506 | − | 0.229770i | ||||
\(173\) | −2.90615 | − | 2.90615i | −0.220951 | − | 0.220951i | 0.587948 | − | 0.808899i | \(-0.299936\pi\) |
−0.808899 | + | 0.587948i | \(0.799936\pi\) | |||||||
\(174\) | −0.147111 | − | 1.49315i | −0.0111524 | − | 0.113195i | ||||
\(175\) | 0.771085 | + | 2.53089i | 0.0582886 | + | 0.191318i | ||||
\(176\) | 2.11813 | − | 5.11549i | 0.159660 | − | 0.385595i | ||||
\(177\) | 3.43523 | 0.258208 | ||||||||
\(178\) | −10.8317 | + | 1.06718i | −0.811869 | + | 0.0799885i | ||||
\(179\) | 3.28164 | + | 3.28164i | 0.245281 | + | 0.245281i | 0.819031 | − | 0.573750i | \(-0.194512\pi\) |
−0.573750 | + | 0.819031i | \(0.694512\pi\) | |||||||
\(180\) | −4.88537 | − | 3.26384i | −0.364134 | − | 0.243272i | ||||
\(181\) | −12.9371 | + | 12.9371i | −0.961607 | + | 0.961607i | −0.999290 | − | 0.0376831i | \(-0.988002\pi\) |
0.0376831 | + | 0.999290i | \(0.488002\pi\) | |||||||
\(182\) | −12.6050 | − | 5.20284i | −0.934348 | − | 0.385660i | ||||
\(183\) | 3.08850 | 0.228308 | ||||||||
\(184\) | −9.73182 | + | 2.95314i | −0.717439 | + | 0.217708i | ||||
\(185\) | 9.54127 | 0.701488 | ||||||||
\(186\) | −2.37197 | + | 2.89045i | −0.173922 | + | 0.211938i | ||||
\(187\) | −7.24656 | − | 7.24656i | −0.529921 | − | 0.529921i | ||||
\(188\) | −6.34692 | + | 1.26291i | −0.462897 | + | 0.0921069i | ||||
\(189\) | 3.46134 | + | 1.84474i | 0.251775 | + | 0.134185i | ||||
\(190\) | 0.362187 | + | 3.67613i | 0.0262758 | + | 0.266695i | ||||
\(191\) | − | 17.0926i | − | 1.23677i | −0.785874 | − | 0.618387i | \(-0.787786\pi\) | ||
0.785874 | − | 0.618387i | \(-0.212214\pi\) | |||||||
\(192\) | −0.389289 | + | 1.95907i | −0.0280945 | + | 0.141384i | ||||
\(193\) | 18.8951 | 1.36010 | 0.680050 | − | 0.733166i | \(-0.261958\pi\) | ||||
0.680050 | + | 0.733166i | \(0.261958\pi\) | |||||||
\(194\) | −1.51173 | − | 15.3438i | −0.108536 | − | 1.10162i | ||||
\(195\) | −0.643422 | + | 0.643422i | −0.0460764 | + | 0.0460764i | ||||
\(196\) | 9.87486 | − | 9.92407i | 0.705347 | − | 0.708862i | ||||
\(197\) | −2.93046 | − | 2.93046i | −0.208786 | − | 0.208786i | 0.594965 | − | 0.803751i | \(-0.297166\pi\) |
−0.803751 | + | 0.594965i | \(0.797166\pi\) | |||||||
\(198\) | −4.44532 | − | 3.64794i | −0.315915 | − | 0.259248i | ||||
\(199\) | 17.4475i | 1.23682i | 0.785857 | + | 0.618408i | \(0.212222\pi\) | ||||
−0.785857 | + | 0.618408i | \(0.787778\pi\) | |||||||
\(200\) | 0.821311 | + | 2.70656i | 0.0580754 | + | 0.191382i | ||||
\(201\) | 0.809443 | 0.0570937 | ||||||||
\(202\) | −9.33922 | + | 11.3806i | −0.657105 | + | 0.800738i | ||||
\(203\) | −5.28771 | + | 9.92148i | −0.371124 | + | 0.696351i | ||||
\(204\) | 3.07413 | + | 2.05378i | 0.215232 | + | 0.143793i | ||||
\(205\) | −4.28282 | + | 4.28282i | −0.299125 | + | 0.299125i | ||||
\(206\) | −1.76006 | − | 17.8642i | −0.122629 | − | 1.24466i | ||||
\(207\) | 10.5628i | 0.734165i | ||||||||
\(208\) | −13.4692 | − | 5.57708i | −0.933918 | − | 0.386701i | ||||
\(209\) | 3.61545i | 0.250086i | ||||||||
\(210\) | −0.358569 | − | 0.862629i | −0.0247436 | − | 0.0595271i | ||||
\(211\) | −13.1176 | − | 13.1176i | −0.903055 | − | 0.903055i | 0.0926446 | − | 0.995699i | \(-0.470468\pi\) |
−0.995699 | + | 0.0926446i | \(0.970468\pi\) | |||||||
\(212\) | 14.3238 | + | 9.56955i | 0.983765 | + | 0.657239i | ||||
\(213\) | 1.89529 | − | 1.89529i | 0.129863 | − | 0.129863i | ||||
\(214\) | 6.62149 | − | 8.06884i | 0.452636 | − | 0.551574i | ||||
\(215\) | 1.81201i | 0.123578i | ||||||||
\(216\) | 3.69813 | + | 1.97623i | 0.251626 | + | 0.134465i | ||||
\(217\) | 26.8015 | − | 8.16558i | 1.81940 | − | 0.554316i | ||||
\(218\) | −11.8739 | + | 14.4694i | −0.804205 | + | 0.979991i | ||||
\(219\) | 0.706765 | − | 0.706765i | 0.0477588 | − | 0.0477588i | ||||
\(220\) | 0.540251 | + | 2.71511i | 0.0364237 | + | 0.183053i | ||||
\(221\) | −19.0803 | + | 19.0803i | −1.28348 | + | 1.28348i | ||||
\(222\) | −3.35268 | + | 0.330319i | −0.225017 | + | 0.0221696i | ||||
\(223\) | −3.49894 | −0.234307 | −0.117153 | − | 0.993114i | \(-0.537377\pi\) | ||||
−0.117153 | + | 0.993114i | \(0.537377\pi\) | |||||||
\(224\) | 10.5685 | − | 10.5975i | 0.706136 | − | 0.708076i | ||||
\(225\) | 2.93766 | 0.195844 | ||||||||
\(226\) | 13.8382 | − | 1.36339i | 0.920502 | − | 0.0906915i | ||||
\(227\) | 3.37074 | − | 3.37074i | 0.223724 | − | 0.223724i | −0.586341 | − | 0.810065i | \(-0.699432\pi\) |
0.810065 | + | 0.586341i | \(0.199432\pi\) | |||||||
\(228\) | −0.254536 | − | 1.27921i | −0.0168571 | − | 0.0847176i | ||||
\(229\) | 4.60318 | − | 4.60318i | 0.304186 | − | 0.304186i | −0.538463 | − | 0.842649i | \(-0.680995\pi\) |
0.842649 | + | 0.538463i | \(0.180995\pi\) | |||||||
\(230\) | 3.22577 | − | 3.93087i | 0.212701 | − | 0.259194i | ||||
\(231\) | −0.266477 | − | 0.874645i | −0.0175329 | − | 0.0575474i | ||||
\(232\) | −5.66461 | + | 10.6002i | −0.371900 | + | 0.695937i | ||||
\(233\) | − | 1.89297i | − | 0.124012i | −0.998076 | − | 0.0620062i | \(-0.980250\pi\) | ||
0.998076 | − | 0.0620062i | \(-0.0197499\pi\) | |||||||
\(234\) | −9.60507 | + | 11.7046i | −0.627903 | + | 0.765153i | ||||
\(235\) | 2.28797 | − | 2.28797i | 0.149250 | − | 0.149250i | ||||
\(236\) | −22.8814 | − | 15.2867i | −1.48945 | − | 0.995081i | ||||
\(237\) | −0.198497 | − | 0.198497i | −0.0128938 | − | 0.0128938i | ||||
\(238\) | −10.6332 | − | 25.5807i | −0.689245 | − | 1.65815i | ||||
\(239\) | − | 11.1410i | − | 0.720651i | −0.932827 | − | 0.360325i | \(-0.882666\pi\) | ||
0.932827 | − | 0.360325i | \(-0.117334\pi\) | |||||||
\(240\) | −0.382299 | − | 0.922616i | −0.0246773 | − | 0.0595546i | ||||
\(241\) | − | 15.5869i | − | 1.00404i | −0.864856 | − | 0.502020i | \(-0.832590\pi\) | ||
0.864856 | − | 0.502020i | \(-0.167410\pi\) | |||||||
\(242\) | −1.25962 | − | 12.7849i | −0.0809715 | − | 0.821846i | ||||
\(243\) | 4.63532 | − | 4.63532i | 0.297356 | − | 0.297356i | ||||
\(244\) | −20.5719 | − | 13.7438i | −1.31698 | − | 0.879854i | ||||
\(245\) | −1.34901 | + | 6.86878i | −0.0861849 | + | 0.438830i | ||||
\(246\) | 1.35666 | − | 1.65320i | 0.0864973 | − | 0.105404i | ||||
\(247\) | 9.51954 | 0.605714 | ||||||||
\(248\) | 28.6617 | − | 8.69745i | 1.82002 | − | 0.552289i | ||||
\(249\) | 0.612939i | 0.0388435i | ||||||||
\(250\) | −1.09323 | − | 0.897132i | −0.0691420 | − | 0.0567396i | ||||
\(251\) | −2.76100 | − | 2.76100i | −0.174273 | − | 0.174273i | 0.614581 | − | 0.788854i | \(-0.289325\pi\) |
−0.788854 | + | 0.614581i | \(0.789325\pi\) | |||||||
\(252\) | −7.34517 | − | 13.6998i | −0.462702 | − | 0.863007i | ||||
\(253\) | 3.51926 | − | 3.51926i | 0.221254 | − | 0.221254i | ||||
\(254\) | −1.67098 | − | 16.9602i | −0.104847 | − | 1.06418i | ||||
\(255\) | −1.84853 | −0.115759 | ||||||||
\(256\) | 11.3108 | − | 11.3166i | 0.706925 | − | 0.707289i | ||||
\(257\) | 16.3721i | 1.02126i | 0.859800 | + | 0.510631i | \(0.170588\pi\) | ||||
−0.859800 | + | 0.510631i | \(0.829412\pi\) | |||||||
\(258\) | −0.0627320 | − | 0.636719i | −0.00390553 | − | 0.0396404i | ||||
\(259\) | 22.2775 | + | 11.8729i | 1.38425 | + | 0.737746i | ||||
\(260\) | 7.14892 | − | 1.42249i | 0.443357 | − | 0.0882189i | ||||
\(261\) | 8.82681 | + | 8.82681i | 0.546366 | + | 0.546366i | ||||
\(262\) | −7.96187 | + | 9.70220i | −0.491886 | + | 0.599404i | ||||
\(263\) | 10.3460 | 0.637965 | 0.318982 | − | 0.947761i | \(-0.396659\pi\) | ||||
0.318982 | + | 0.947761i | \(0.396659\pi\) | |||||||
\(264\) | −0.283834 | − | 0.935352i | −0.0174688 | − | 0.0575669i | ||||
\(265\) | −8.61320 | −0.529105 | ||||||||
\(266\) | −3.72883 | + | 9.03392i | −0.228629 | + | 0.553905i | ||||
\(267\) | −1.35873 | + | 1.35873i | −0.0831528 | + | 0.0831528i | ||||
\(268\) | −5.39153 | − | 3.60201i | −0.329340 | − | 0.220027i | ||||
\(269\) | −9.06161 | − | 9.06161i | −0.552496 | − | 0.552496i | 0.374664 | − | 0.927160i | \(-0.377758\pi\) |
−0.927160 | + | 0.374664i | \(0.877758\pi\) | |||||||
\(270\) | −2.08642 | + | 0.205562i | −0.126975 | + | 0.0125101i | ||||
\(271\) | 22.1493 | 1.34548 | 0.672738 | − | 0.739881i | \(-0.265118\pi\) | ||||
0.672738 | + | 0.739881i | \(0.265118\pi\) | |||||||
\(272\) | −11.3369 | − | 27.3596i | −0.687398 | − | 1.65892i | ||||
\(273\) | −2.30295 | + | 0.701638i | −0.139381 | + | 0.0424651i | ||||
\(274\) | −0.287850 | − | 2.92162i | −0.0173896 | − | 0.176502i | ||||
\(275\) | −0.978755 | − | 0.978755i | −0.0590211 | − | 0.0590211i | ||||
\(276\) | −0.997408 | + | 1.49293i | −0.0600369 | + | 0.0898641i | ||||
\(277\) | −18.1242 | − | 18.1242i | −1.08898 | − | 1.08898i | −0.995634 | − | 0.0933421i | \(-0.970245\pi\) |
−0.0933421 | − | 0.995634i | \(-0.529755\pi\) | |||||||
\(278\) | −19.0046 | − | 15.5956i | −1.13982 | − | 0.935363i | ||||
\(279\) | − | 31.1090i | − | 1.86245i | ||||||
\(280\) | −1.45033 | + | 7.34143i | −0.0866736 | + | 0.438734i | ||||
\(281\) | 9.63776i | 0.574940i | 0.957790 | + | 0.287470i | \(0.0928142\pi\) | ||||
−0.957790 | + | 0.287470i | \(0.907186\pi\) | |||||||
\(282\) | −0.724753 | + | 0.883172i | −0.0431584 | + | 0.0525921i | ||||
\(283\) | −1.09319 | − | 1.09319i | −0.0649833 | − | 0.0649833i | 0.673868 | − | 0.738852i | \(-0.264632\pi\) |
−0.738852 | + | 0.673868i | \(0.764632\pi\) | |||||||
\(284\) | −21.0582 | + | 4.19014i | −1.24957 | + | 0.248639i | ||||
\(285\) | 0.461135 | + | 0.461135i | 0.0273153 | + | 0.0273153i | ||||
\(286\) | 7.09984 | − | 0.699504i | 0.419822 | − | 0.0413625i | ||||
\(287\) | −15.3292 | + | 4.67033i | −0.904853 | + | 0.275681i | ||||
\(288\) | −7.83600 | − | 14.6545i | −0.461741 | − | 0.863522i | ||||
\(289\) | −37.8170 | −2.22453 | ||||||||
\(290\) | −0.589218 | − | 5.98045i | −0.0346001 | − | 0.351184i | ||||
\(291\) | −1.92473 | − | 1.92473i | −0.112830 | − | 0.112830i | ||||
\(292\) | −7.85271 | + | 1.56253i | −0.459545 | + | 0.0914400i | ||||
\(293\) | −23.1027 | + | 23.1027i | −1.34967 | + | 1.34967i | −0.463658 | + | 0.886014i | \(0.653463\pi\) |
−0.886014 | + | 0.463658i | \(0.846537\pi\) | |||||||
\(294\) | 0.236226 | − | 2.46031i | 0.0137770 | − | 0.143488i | ||||
\(295\) | 13.7590 | 0.801081 | ||||||||
\(296\) | 23.8015 | + | 12.7192i | 1.38343 | + | 0.739288i | ||||
\(297\) | −2.05198 | −0.119068 | ||||||||
\(298\) | −6.31000 | − | 5.17815i | −0.365529 | − | 0.299962i | ||||
\(299\) | −9.26624 | − | 9.26624i | −0.535881 | − | 0.535881i | ||||
\(300\) | 0.415206 | + | 0.277393i | 0.0239719 | + | 0.0160153i | ||||
\(301\) | −2.25482 | + | 4.23079i | −0.129966 | + | 0.243858i | ||||
\(302\) | 29.1683 | − | 2.87377i | 1.67845 | − | 0.165367i | ||||
\(303\) | 2.59910i | 0.149314i | ||||||||
\(304\) | −3.99704 | + | 9.65322i | −0.229246 | + | 0.553650i | ||||
\(305\) | 12.3703 | 0.708319 | ||||||||
\(306\) | −30.6110 | + | 3.01591i | −1.74991 | + | 0.172408i | ||||
\(307\) | 23.0642 | − | 23.0642i | 1.31634 | − | 1.31634i | 0.399697 | − | 0.916647i | \(-0.369115\pi\) |
0.916647 | − | 0.399697i | \(-0.130885\pi\) | |||||||
\(308\) | −2.11720 | + | 7.01165i | −0.120639 | + | 0.399526i | ||||
\(309\) | −2.24089 | − | 2.24089i | −0.127480 | − | 0.127480i | ||||
\(310\) | −9.50038 | + | 11.5770i | −0.539585 | + | 0.657530i | ||||
\(311\) | 14.9822i | 0.849565i | 0.905295 | + | 0.424782i | \(0.139649\pi\) | ||||
−0.905295 | + | 0.424782i | \(0.860351\pi\) | |||||||
\(312\) | −2.46279 | + | 0.747340i | −0.139428 | + | 0.0423098i | ||||
\(313\) | −2.43405 | −0.137581 | −0.0687904 | − | 0.997631i | \(-0.521914\pi\) | ||||
−0.0687904 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(314\) | 14.9402 | + | 12.2603i | 0.843122 | + | 0.691887i | ||||
\(315\) | 6.85901 | + | 3.65555i | 0.386462 | + | 0.205967i | ||||
\(316\) | 0.438840 | + | 2.20546i | 0.0246867 | + | 0.124067i | ||||
\(317\) | 7.09234 | − | 7.09234i | 0.398345 | − | 0.398345i | −0.479304 | − | 0.877649i | \(-0.659111\pi\) |
0.877649 | + | 0.479304i | \(0.159111\pi\) | |||||||
\(318\) | 3.02657 | − | 0.298189i | 0.169722 | − | 0.0167216i | ||||
\(319\) | − | 5.88174i | − | 0.329314i | ||||||
\(320\) | −1.55921 | + | 7.84658i | −0.0871623 | + | 0.438637i | ||||
\(321\) | − | 1.84276i | − | 0.102853i | ||||||
\(322\) | 12.4232 | − | 5.16394i | 0.692316 | − | 0.287775i | ||||
\(323\) | 13.6747 | + | 13.6747i | 0.760879 | + | 0.760879i | ||||
\(324\) | −16.5611 | + | 3.29531i | −0.920059 | + | 0.183073i | ||||
\(325\) | −2.57707 | + | 2.57707i | −0.142950 | + | 0.142950i | ||||
\(326\) | 2.45295 | + | 2.01295i | 0.135856 | + | 0.111487i | ||||
\(327\) | 3.30451i | 0.182740i | ||||||||
\(328\) | −16.3931 | + | 4.97453i | −0.905160 | + | 0.274673i | ||||
\(329\) | 8.18915 | − | 2.49498i | 0.451482 | − | 0.137553i | ||||
\(330\) | 0.377807 | + | 0.310038i | 0.0207976 | + | 0.0170670i | ||||
\(331\) | 3.73150 | − | 3.73150i | 0.205102 | − | 0.205102i | −0.597080 | − | 0.802182i | \(-0.703673\pi\) |
0.802182 | + | 0.597080i | \(0.203673\pi\) | |||||||
\(332\) | 2.72757 | − | 4.08267i | 0.149695 | − | 0.224065i | ||||
\(333\) | 19.8195 | − | 19.8195i | 1.08610 | − | 1.08610i | ||||
\(334\) | −1.85918 | − | 18.8703i | −0.101730 | − | 1.03254i | ||||
\(335\) | 3.24203 | 0.177131 | ||||||||
\(336\) | 0.255466 | − | 2.62989i | 0.0139368 | − | 0.143473i | ||||
\(337\) | 11.1971 | 0.609945 | 0.304973 | − | 0.952361i | \(-0.401353\pi\) | ||||
0.304973 | + | 0.952361i | \(0.401353\pi\) | |||||||
\(338\) | −0.0391897 | − | 0.397769i | −0.00213164 | − | 0.0216358i | ||||
\(339\) | 1.73586 | − | 1.73586i | 0.0942792 | − | 0.0942792i | ||||
\(340\) | 12.3127 | + | 8.22593i | 0.667749 | + | 0.446113i | ||||
\(341\) | −10.3647 | + | 10.3647i | −0.561282 | + | 0.561282i | ||||
\(342\) | 8.38857 | + | 6.88387i | 0.453602 | + | 0.372237i | ||||
\(343\) | −11.6971 | + | 14.3589i | −0.631582 | + | 0.775309i | ||||
\(344\) | −2.41554 | + | 4.52021i | −0.130237 | + | 0.243714i | ||||
\(345\) | − | 0.897730i | − | 0.0483321i | ||||||
\(346\) | 4.49309 | + | 3.68714i | 0.241550 | + | 0.198222i | ||||
\(347\) | −1.69866 | + | 1.69866i | −0.0911889 | + | 0.0911889i | −0.751230 | − | 0.660041i | \(-0.770539\pi\) |
0.660041 | + | 0.751230i | \(0.270539\pi\) | |||||||
\(348\) | 0.414087 | + | 2.08106i | 0.0221974 | + | 0.111556i | ||||
\(349\) | −8.68835 | − | 8.68835i | −0.465077 | − | 0.465077i | 0.435238 | − | 0.900315i | \(-0.356664\pi\) |
−0.900315 | + | 0.435238i | \(0.856664\pi\) | |||||||
\(350\) | −1.43617 | − | 3.45506i | −0.0767663 | − | 0.184681i | ||||
\(351\) | 5.40289i | 0.288385i | ||||||||
\(352\) | −2.27173 | + | 7.49325i | −0.121084 | + | 0.399391i | ||||
\(353\) | 0.340882i | 0.0181433i | 0.999959 | + | 0.00907166i | \(0.00288764\pi\) | ||||
−0.999959 | + | 0.00907166i | \(0.997112\pi\) | |||||||
\(354\) | −4.83474 | + | 0.476338i | −0.256964 | + | 0.0253171i | ||||
\(355\) | 7.59114 | − | 7.59114i | 0.402896 | − | 0.402896i | ||||
\(356\) | 15.0965 | − | 3.00390i | 0.800114 | − | 0.159206i | ||||
\(357\) | −4.31604 | − | 2.30026i | −0.228429 | − | 0.121743i | ||||
\(358\) | −5.07361 | − | 4.16353i | −0.268149 | − | 0.220050i | ||||
\(359\) | −25.6134 | −1.35182 | −0.675912 | − | 0.736982i | \(-0.736250\pi\) | ||||
−0.675912 | + | 0.736982i | \(0.736250\pi\) | |||||||
\(360\) | 7.32824 | + | 3.91611i | 0.386232 | + | 0.206397i | ||||
\(361\) | 12.1774i | 0.640918i | ||||||||
\(362\) | 16.4138 | − | 20.0015i | 0.862688 | − | 1.05126i | ||||
\(363\) | −1.60374 | − | 1.60374i | −0.0841746 | − | 0.0841746i | ||||
\(364\) | 18.4618 | + | 5.57462i | 0.967660 | + | 0.292190i | ||||
\(365\) | 2.83078 | − | 2.83078i | 0.148170 | − | 0.148170i | ||||
\(366\) | −4.34675 | + | 0.428259i | −0.227208 | + | 0.0223855i | ||||
\(367\) | −16.4093 | −0.856557 | −0.428278 | − | 0.903647i | \(-0.640880\pi\) | ||||
−0.428278 | + | 0.903647i | \(0.640880\pi\) | |||||||
\(368\) | 13.2871 | − | 5.50569i | 0.692636 | − | 0.287004i | ||||
\(369\) | 17.7929i | 0.926262i | ||||||||
\(370\) | −13.4284 | + | 1.32302i | −0.698108 | + | 0.0687804i | ||||
\(371\) | −20.1105 | − | 10.7180i | −1.04409 | − | 0.556452i | ||||
\(372\) | 2.93752 | − | 4.39692i | 0.152303 | − | 0.227970i | ||||
\(373\) | 0.461478 | + | 0.461478i | 0.0238944 | + | 0.0238944i | 0.718953 | − | 0.695059i | \(-0.244622\pi\) |
−0.695059 | + | 0.718953i | \(0.744622\pi\) | |||||||
\(374\) | 11.2036 | + | 9.19397i | 0.579326 | + | 0.475409i | ||||
\(375\) | −0.249671 | −0.0128930 | ||||||||
\(376\) | 8.75753 | − | 2.65749i | 0.451635 | − | 0.137050i | ||||
\(377\) | −15.4867 | −0.797606 | ||||||||
\(378\) | −5.12728 | − | 2.11633i | −0.263719 | − | 0.108852i | ||||
\(379\) | −21.8512 | + | 21.8512i | −1.12242 | + | 1.12242i | −0.131044 | + | 0.991377i | \(0.541833\pi\) |
−0.991377 | + | 0.131044i | \(0.958167\pi\) | |||||||
\(380\) | −1.01948 | − | 5.12357i | −0.0522984 | − | 0.262833i | ||||
\(381\) | −2.12748 | − | 2.12748i | −0.108994 | − | 0.108994i | ||||
\(382\) | 2.37010 | + | 24.0561i | 0.121265 | + | 1.23082i | ||||
\(383\) | 16.2481 | 0.830241 | 0.415120 | − | 0.909766i | \(-0.363739\pi\) | ||||
0.415120 | + | 0.909766i | \(0.363739\pi\) | |||||||
\(384\) | 0.276236 | − | 2.81117i | 0.0140966 | − | 0.143457i | ||||
\(385\) | −1.06731 | − | 3.50318i | −0.0543953 | − | 0.178539i | ||||
\(386\) | −26.5930 | + | 2.62004i | −1.35355 | + | 0.133357i | ||||
\(387\) | 3.76399 | + | 3.76399i | 0.191335 | + | 0.191335i | ||||
\(388\) | 4.25523 | + | 21.3853i | 0.216026 | + | 1.08567i | ||||
\(389\) | −12.7387 | − | 12.7387i | −0.645878 | − | 0.645878i | 0.306117 | − | 0.951994i | \(-0.400970\pi\) |
−0.951994 | + | 0.306117i | \(0.900970\pi\) | |||||||
\(390\) | 0.816333 | − | 0.994770i | 0.0413366 | − | 0.0503721i | ||||
\(391\) | − | 26.6216i | − | 1.34631i | ||||||
\(392\) | −12.5218 | + | 15.3364i | −0.632445 | + | 0.774605i | ||||
\(393\) | 2.21578i | 0.111771i | ||||||||
\(394\) | 4.53066 | + | 3.71798i | 0.228252 | + | 0.187309i | ||||
\(395\) | −0.795033 | − | 0.795033i | −0.0400025 | − | 0.0400025i | ||||
\(396\) | 6.76217 | + | 4.51771i | 0.339812 | + | 0.227023i | ||||
\(397\) | −1.55444 | − | 1.55444i | −0.0780150 | − | 0.0780150i | 0.667023 | − | 0.745038i | \(-0.267568\pi\) |
−0.745038 | + | 0.667023i | \(0.767568\pi\) | |||||||
\(398\) | −2.41931 | − | 24.5555i | −0.121269 | − | 1.23086i | ||||
\(399\) | 0.502858 | + | 1.65050i | 0.0251744 | + | 0.0826286i | ||||
\(400\) | −1.53121 | − | 3.69532i | −0.0765605 | − | 0.184766i | ||||
\(401\) | 15.4547 | 0.771769 | 0.385885 | − | 0.922547i | \(-0.373896\pi\) | ||||
0.385885 | + | 0.922547i | \(0.373896\pi\) | |||||||
\(402\) | −1.13921 | + | 0.112239i | −0.0568186 | + | 0.00559799i | ||||
\(403\) | 27.2905 | + | 27.2905i | 1.35944 | + | 1.35944i | ||||
\(404\) | 11.5659 | − | 17.3121i | 0.575427 | − | 0.861308i | ||||
\(405\) | 5.97001 | − | 5.97001i | 0.296652 | − | 0.296652i | ||||
\(406\) | 6.06618 | − | 14.6967i | 0.301059 | − | 0.729384i | ||||
\(407\) | −13.2067 | −0.654633 | ||||||||
\(408\) | −4.61130 | − | 2.46422i | −0.228294 | − | 0.121997i | ||||
\(409\) | −10.5094 | −0.519656 | −0.259828 | − | 0.965655i | \(-0.583666\pi\) | ||||
−0.259828 | + | 0.965655i | \(0.583666\pi\) | |||||||
\(410\) | 5.43377 | − | 6.62151i | 0.268355 | − | 0.327013i | ||||
\(411\) | −0.366488 | − | 0.366488i | −0.0180775 | − | 0.0180775i | ||||
\(412\) | 4.95420 | + | 24.8981i | 0.244076 | + | 1.22664i | ||||
\(413\) | 32.1253 | + | 17.1213i | 1.58078 | + | 0.842486i | ||||
\(414\) | −1.46466 | − | 14.8661i | −0.0719843 | − | 0.730628i | ||||
\(415\) | 2.45498i | 0.120510i | ||||||||
\(416\) | 19.7298 | + | 5.98150i | 0.967334 | + | 0.293267i | ||||
\(417\) | −4.34025 | −0.212543 | ||||||||
\(418\) | −0.501328 | − | 5.08839i | −0.0245208 | − | 0.248881i | ||||
\(419\) | 0.488822 | − | 0.488822i | 0.0238805 | − | 0.0238805i | −0.695066 | − | 0.718946i | \(-0.744625\pi\) |
0.718946 | + | 0.695066i | \(0.244625\pi\) | |||||||
\(420\) | 0.624265 | + | 1.16434i | 0.0304610 | + | 0.0568142i | ||||
\(421\) | 14.5806 | + | 14.5806i | 0.710613 | + | 0.710613i | 0.966663 | − | 0.256051i | \(-0.0824214\pi\) |
−0.256051 | + | 0.966663i | \(0.582421\pi\) | |||||||
\(422\) | 20.2807 | + | 16.6428i | 0.987247 | + | 0.810160i | ||||
\(423\) | − | 9.50532i | − | 0.462165i | ||||||
\(424\) | −21.4863 | − | 11.4820i | −1.04347 | − | 0.557615i | ||||
\(425\) | −7.40385 | −0.359140 | ||||||||
\(426\) | −2.40462 | + | 2.93024i | −0.116504 | + | 0.141970i | ||||
\(427\) | 28.8827 | + | 15.3932i | 1.39773 | + | 0.744930i | ||||
\(428\) | −8.20023 | + | 12.2742i | −0.396373 | + | 0.593297i | ||||
\(429\) | 0.890604 | − | 0.890604i | 0.0429988 | − | 0.0429988i | ||||
\(430\) | −0.251258 | − | 2.55023i | −0.0121168 | − | 0.122983i | ||||
\(431\) | − | 35.7322i | − | 1.72116i | −0.509316 | − | 0.860580i | \(-0.670101\pi\) | ||
0.509316 | − | 0.860580i | \(-0.329899\pi\) | |||||||
\(432\) | −5.47877 | − | 2.26855i | −0.263597 | − | 0.109146i | ||||
\(433\) | 3.38964i | 0.162896i | 0.996678 | + | 0.0814479i | \(0.0259544\pi\) | ||||
−0.996678 | + | 0.0814479i | \(0.974046\pi\) | |||||||
\(434\) | −36.5881 | + | 15.2086i | −1.75629 | + | 0.730035i | ||||
\(435\) | −0.750189 | − | 0.750189i | −0.0359688 | − | 0.0359688i | ||||
\(436\) | 14.7050 | − | 22.0107i | 0.704243 | − | 1.05412i | ||||
\(437\) | −6.64103 | + | 6.64103i | −0.317684 | + | 0.317684i | ||||
\(438\) | −0.896699 | + | 1.09270i | −0.0428459 | + | 0.0522114i | ||||
\(439\) | − | 7.38471i | − | 0.352453i | −0.984350 | − | 0.176227i | \(-0.943611\pi\) | ||
0.984350 | − | 0.176227i | \(-0.0563891\pi\) | |||||||
\(440\) | −1.13683 | − | 3.74633i | −0.0541964 | − | 0.178599i | ||||
\(441\) | 11.4659 | + | 17.0703i | 0.545996 | + | 0.812873i | ||||
\(442\) | 24.2078 | − | 29.4993i | 1.15145 | − | 1.40314i | ||||
\(443\) | 18.4426 | − | 18.4426i | 0.876234 | − | 0.876234i | −0.116908 | − | 0.993143i | \(-0.537298\pi\) |
0.993143 | + | 0.116908i | \(0.0372984\pi\) | |||||||
\(444\) | 4.67276 | − | 0.929783i | 0.221759 | − | 0.0441255i | ||||
\(445\) | −5.44207 | + | 5.44207i | −0.257979 | + | 0.257979i | ||||
\(446\) | 4.92441 | − | 0.485172i | 0.233178 | − | 0.0229736i | ||||
\(447\) | −1.44107 | −0.0681605 | ||||||||
\(448\) | −13.4046 | + | 16.3804i | −0.633308 | + | 0.773900i | ||||
\(449\) | −18.9231 | −0.893035 | −0.446517 | − | 0.894775i | \(-0.647336\pi\) | ||||
−0.446517 | + | 0.894775i | \(0.647336\pi\) | |||||||
\(450\) | −4.13447 | + | 0.407344i | −0.194901 | + | 0.0192024i | ||||
\(451\) | 5.92815 | − | 5.92815i | 0.279145 | − | 0.279145i | ||||
\(452\) | −19.2868 | + | 3.83767i | −0.907175 | + | 0.180509i | ||||
\(453\) | 3.65887 | − | 3.65887i | 0.171909 | − | 0.171909i | ||||
\(454\) | −4.27658 | + | 5.21137i | −0.200710 | + | 0.244582i | ||||
\(455\) | −9.22393 | + | 2.81025i | −0.432425 | + | 0.131746i | ||||
\(456\) | 0.535612 | + | 1.76506i | 0.0250823 | + | 0.0826566i | ||||
\(457\) | − | 31.9731i | − | 1.49564i | −0.663903 | − | 0.747819i | \(-0.731101\pi\) | ||
0.663903 | − | 0.747819i | \(-0.268899\pi\) | |||||||
\(458\) | −5.84022 | + | 7.11679i | −0.272895 | + | 0.332546i | ||||
\(459\) | −7.76117 | + | 7.76117i | −0.362260 | + | 0.362260i | ||||
\(460\) | −3.99488 | + | 5.97960i | −0.186262 | + | 0.278800i | ||||
\(461\) | 0.872708 | + | 0.872708i | 0.0406461 | + | 0.0406461i | 0.727138 | − | 0.686492i | \(-0.240850\pi\) |
−0.686492 | + | 0.727138i | \(0.740850\pi\) | |||||||
\(462\) | 0.496320 | + | 1.19402i | 0.0230909 | + | 0.0555510i | ||||
\(463\) | − | 3.59688i | − | 0.167161i | −0.996501 | − | 0.0835805i | \(-0.973364\pi\) | ||
0.996501 | − | 0.0835805i | \(-0.0266356\pi\) | |||||||
\(464\) | 6.50252 | − | 15.7042i | 0.301872 | − | 0.729048i | ||||
\(465\) | 2.64395i | 0.122610i | ||||||||
\(466\) | 0.262484 | + | 2.66416i | 0.0121593 | + | 0.123415i | ||||
\(467\) | −4.76343 | + | 4.76343i | −0.220425 | + | 0.220425i | −0.808677 | − | 0.588252i | \(-0.799816\pi\) |
0.588252 | + | 0.808677i | \(0.299816\pi\) | |||||||
\(468\) | 11.8952 | − | 17.8049i | 0.549855 | − | 0.823031i | ||||
\(469\) | 7.56967 | + | 4.03430i | 0.349535 | + | 0.186287i | ||||
\(470\) | −2.90283 | + | 3.53734i | −0.133897 | + | 0.163165i | ||||
\(471\) | 3.41203 | 0.157218 | ||||||||
\(472\) | 34.3229 | + | 18.3417i | 1.57984 | + | 0.844247i | ||||
\(473\) | − | 2.50813i | − | 0.115324i | ||||||
\(474\) | 0.306889 | + | 0.251840i | 0.0140959 | + | 0.0115674i | ||||
\(475\) | 1.84697 | + | 1.84697i | 0.0847446 | + | 0.0847446i | ||||
\(476\) | 18.5122 | + | 34.5279i | 0.848504 | + | 1.58258i | ||||
\(477\) | −17.8917 | + | 17.8917i | −0.819205 | + | 0.819205i | ||||
\(478\) | 1.54484 | + | 15.6798i | 0.0706592 | + | 0.717178i | ||||
\(479\) | −2.53429 | −0.115795 | −0.0578974 | − | 0.998323i | \(-0.518440\pi\) | ||||
−0.0578974 | + | 0.998323i | \(0.518440\pi\) | |||||||
\(480\) | 0.665980 | + | 1.24548i | 0.0303977 | + | 0.0568481i | ||||
\(481\) | 34.7735i | 1.58553i | ||||||||
\(482\) | 2.16132 | + | 21.9370i | 0.0984454 | + | 0.999203i | ||||
\(483\) | 1.11711 | − | 2.09607i | 0.0508303 | − | 0.0953743i | ||||
\(484\) | 3.54558 | + | 17.8188i | 0.161163 | + | 0.809947i | ||||
\(485\) | −7.70906 | − | 7.70906i | −0.350050 | − | 0.350050i | ||||
\(486\) | −5.88100 | + | 7.16650i | −0.266768 | + | 0.325079i | ||||
\(487\) | 17.4209 | 0.789414 | 0.394707 | − | 0.918807i | \(-0.370846\pi\) | ||||
0.394707 | + | 0.918807i | \(0.370846\pi\) | |||||||
\(488\) | 30.8586 | + | 16.4904i | 1.39690 | + | 0.746486i | ||||
\(489\) | 0.560202 | 0.0253332 | ||||||||
\(490\) | 0.946148 | − | 9.85418i | 0.0427426 | − | 0.445166i | ||||
\(491\) | 10.2394 | − | 10.2394i | 0.462098 | − | 0.462098i | −0.437245 | − | 0.899343i | \(-0.644046\pi\) |
0.899343 | + | 0.437245i | \(0.144046\pi\) | |||||||
\(492\) | −1.68012 | + | 2.51483i | −0.0757457 | + | 0.113377i | ||||
\(493\) | −22.2464 | − | 22.2464i | −1.00193 | − | 1.00193i | ||||
\(494\) | −13.3978 | + | 1.32000i | −0.602795 | + | 0.0593897i | ||||
\(495\) | −4.06622 | −0.182763 | ||||||||
\(496\) | −39.1324 | + | 16.2151i | −1.75710 | + | 0.728079i | ||||
\(497\) | 27.1704 | − | 8.27798i | 1.21876 | − | 0.371318i | ||||
\(498\) | −0.0849917 | − | 0.862651i | −0.00380857 | − | 0.0386563i | ||||
\(499\) | −2.70543 | − | 2.70543i | −0.121112 | − | 0.121112i | 0.643953 | − | 0.765065i | \(-0.277293\pi\) |
−0.765065 | + | 0.643953i | \(0.777293\pi\) | |||||||
\(500\) | 1.66301 | + | 1.11103i | 0.0743721 | + | 0.0496869i | ||||
\(501\) | −2.36710 | − | 2.36710i | −0.105754 | − | 0.105754i | ||||
\(502\) | 4.26868 | + | 3.50299i | 0.190521 | + | 0.156346i | ||||
\(503\) | − | 19.8860i | − | 0.886671i | −0.896356 | − | 0.443336i | \(-0.853795\pi\) | ||
0.896356 | − | 0.443336i | \(-0.146205\pi\) | |||||||
\(504\) | 12.2372 | + | 18.2626i | 0.545090 | + | 0.813481i | ||||
\(505\) | 10.4101i | 0.463243i | ||||||||
\(506\) | −4.46501 | + | 5.44099i | −0.198494 | + | 0.241881i | ||||
\(507\) | −0.0498962 | − | 0.0498962i | −0.00221597 | − | 0.00221597i | ||||
\(508\) | 4.70348 | + | 23.6380i | 0.208683 | + | 1.04877i | ||||
\(509\) | 19.1507 | + | 19.1507i | 0.848840 | + | 0.848840i | 0.989988 | − | 0.141148i | \(-0.0450794\pi\) |
−0.141148 | + | 0.989988i | \(0.545079\pi\) | |||||||
\(510\) | 2.60162 | − | 0.256322i | 0.115202 | − | 0.0113501i | ||||
\(511\) | 10.1320 | − | 3.08691i | 0.448214 | − | 0.136557i | ||||
\(512\) | −14.3496 | + | 17.4954i | −0.634169 | + | 0.773194i | ||||
\(513\) | 3.87220 | 0.170962 | ||||||||
\(514\) | −2.27019 | − | 23.0421i | −0.100134 | − | 1.01634i | ||||
\(515\) | −8.97537 | − | 8.97537i | −0.395502 | − | 0.395502i | ||||
\(516\) | 0.176578 | + | 0.887419i | 0.00777342 | + | 0.0390664i | ||||
\(517\) | −3.16693 | + | 3.16693i | −0.139281 | + | 0.139281i | ||||
\(518\) | −32.9996 | − | 13.6209i | −1.44992 | − | 0.598466i | ||||
\(519\) | 1.02613 | 0.0450421 | ||||||||
\(520\) | −9.86414 | + | 2.99329i | −0.432571 | + | 0.131265i | ||||
\(521\) | −17.7051 | −0.775674 | −0.387837 | − | 0.921728i | \(-0.626778\pi\) | ||||
−0.387837 | + | 0.921728i | \(0.626778\pi\) | |||||||
\(522\) | −13.6468 | − | 11.1989i | −0.597304 | − | 0.490163i | ||||
\(523\) | −7.11421 | − | 7.11421i | −0.311083 | − | 0.311083i | 0.534246 | − | 0.845329i | \(-0.320595\pi\) |
−0.845329 | + | 0.534246i | \(0.820595\pi\) | |||||||
\(524\) | 9.86020 | − | 14.7589i | 0.430745 | − | 0.644745i | ||||
\(525\) | −0.582946 | − | 0.310684i | −0.0254418 | − | 0.0135594i | ||||
\(526\) | −14.5610 | + | 1.43461i | −0.634891 | + | 0.0625519i | ||||
\(527\) | 78.4047i | 3.41536i | ||||||||
\(528\) | 0.529167 | + | 1.27706i | 0.0230290 | + | 0.0555767i | ||||
\(529\) | −10.0713 | −0.437884 | ||||||||
\(530\) | 12.1222 | − | 1.19433i | 0.526555 | − | 0.0518783i | ||||
\(531\) | 28.5808 | − | 28.5808i | 1.24030 | − | 1.24030i | ||||
\(532\) | 3.99528 | − | 13.2314i | 0.173217 | − | 0.573653i | ||||
\(533\) | −15.6089 | − | 15.6089i | −0.676096 | − | 0.676096i | ||||
\(534\) | 1.72387 | − | 2.10068i | 0.0745991 | − | 0.0909052i | ||||
\(535\) | − | 7.38073i | − | 0.319097i | ||||||
\(536\) | 8.08750 | + | 4.32186i | 0.349327 | + | 0.186676i | ||||
\(537\) | −1.15871 | −0.0500020 | ||||||||
\(538\) | 14.0098 | + | 11.4968i | 0.604006 | + | 0.495662i | ||||
\(539\) | 1.86725 | − | 9.50755i | 0.0804283 | − | 0.409519i | ||||
\(540\) | 2.90792 | − | 0.578616i | 0.125137 | − | 0.0248997i | ||||
\(541\) | −3.16209 | + | 3.16209i | −0.135949 | + | 0.135949i | −0.771806 | − | 0.635857i | \(-0.780647\pi\) |
0.635857 | + | 0.771806i | \(0.280647\pi\) | |||||||
\(542\) | −31.1730 | + | 3.07128i | −1.33899 | + | 0.131923i | ||||
\(543\) | − | 4.56794i | − | 0.196029i | ||||||
\(544\) | 19.7492 | + | 36.9339i | 0.846741 | + | 1.58353i | ||||
\(545\) | 13.2354i | 0.566944i | ||||||||
\(546\) | 3.14388 | − | 1.30682i | 0.134546 | − | 0.0559267i | ||||
\(547\) | −25.4712 | − | 25.4712i | −1.08907 | − | 1.08907i | −0.995624 | − | 0.0934460i | \(-0.970212\pi\) |
−0.0934460 | − | 0.995624i | \(-0.529788\pi\) | |||||||
\(548\) | 0.810239 | + | 4.07197i | 0.0346117 | + | 0.173946i | ||||
\(549\) | 25.6960 | − | 25.6960i | 1.09668 | − | 1.09668i | ||||
\(550\) | 1.51322 | + | 1.24178i | 0.0645237 | + | 0.0529498i | ||||
\(551\) | 11.0992i | 0.472841i | ||||||||
\(552\) | 1.19674 | − | 2.23946i | 0.0509365 | − | 0.0953176i | ||||
\(553\) | −0.866967 | − | 2.84560i | −0.0368672 | − | 0.121007i | ||||
\(554\) | 28.0211 | + | 22.9948i | 1.19050 | + | 0.976956i | ||||
\(555\) | −1.68446 | + | 1.68446i | −0.0715012 | + | 0.0715012i | ||||
\(556\) | 28.9095 | + | 19.3140i | 1.22604 | + | 0.819098i | ||||
\(557\) | −14.5968 | + | 14.5968i | −0.618485 | + | 0.618485i | −0.945143 | − | 0.326658i | \(-0.894078\pi\) |
0.326658 | + | 0.945143i | \(0.394078\pi\) | |||||||
\(558\) | 4.31366 | + | 43.7828i | 0.182612 | + | 1.85348i | ||||
\(559\) | −6.60395 | −0.279317 | ||||||||
\(560\) | 1.02321 | − | 10.5334i | 0.0432385 | − | 0.445118i | ||||
\(561\) | 2.55868 | 0.108027 | ||||||||
\(562\) | −1.33640 | − | 13.5642i | −0.0563724 | − | 0.572170i | ||||
\(563\) | −25.5265 | + | 25.5265i | −1.07581 | + | 1.07581i | −0.0789337 | + | 0.996880i | \(0.525152\pi\) |
−0.996880 | + | 0.0789337i | \(0.974848\pi\) | |||||||
\(564\) | 0.897554 | − | 1.34347i | 0.0377938 | − | 0.0565704i | ||||
\(565\) | 6.95259 | − | 6.95259i | 0.292498 | − | 0.292498i | ||||
\(566\) | 1.69014 | + | 1.38697i | 0.0710417 | + | 0.0582986i | ||||
\(567\) | 21.3680 | − | 6.51017i | 0.897372 | − | 0.273401i | ||||
\(568\) | 29.0562 | − | 8.81717i | 1.21917 | − | 0.369960i | ||||
\(569\) | − | 12.4537i | − | 0.522084i | −0.965327 | − | 0.261042i | \(-0.915934\pi\) | ||
0.965327 | − | 0.261042i | \(-0.0840662\pi\) | |||||||
\(570\) | −0.712943 | − | 0.585058i | −0.0298619 | − | 0.0245054i | ||||
\(571\) | −15.2950 | + | 15.2950i | −0.640077 | + | 0.640077i | −0.950574 | − | 0.310497i | \(-0.899504\pi\) |
0.310497 | + | 0.950574i | \(0.399504\pi\) | |||||||
\(572\) | −9.89531 | + | 1.96896i | −0.413744 | + | 0.0823264i | ||||
\(573\) | 3.01760 | + | 3.01760i | 0.126062 | + | 0.126062i | ||||
\(574\) | 20.9267 | − | 8.69860i | 0.873463 | − | 0.363073i | ||||
\(575\) | − | 3.59564i | − | 0.149949i | ||||||
\(576\) | 13.0604 | + | 19.5381i | 0.544184 | + | 0.814088i | ||||
\(577\) | 6.33648i | 0.263791i | 0.991264 | + | 0.131896i | \(0.0421064\pi\) | ||||
−0.991264 | + | 0.131896i | \(0.957894\pi\) | |||||||
\(578\) | 53.2236 | − | 5.24380i | 2.21381 | − | 0.218113i | ||||
\(579\) | −3.33582 | + | 3.33582i | −0.138632 | + | 0.138632i | ||||
\(580\) | 1.65853 | + | 8.33518i | 0.0688667 | + | 0.346100i | ||||
\(581\) | −3.05492 | + | 5.73203i | −0.126739 | + | 0.237805i | ||||
\(582\) | 2.97575 | + | 2.44198i | 0.123349 | + | 0.101223i | ||||
\(583\) | 11.9221 | 0.493764 | ||||||||
\(584\) | 10.8352 | − | 3.28798i | 0.448365 | − | 0.136057i | ||||
\(585\) | 10.7064i | 0.442656i | ||||||||
\(586\) | 29.3112 | − | 35.7182i | 1.21083 | − | 1.47550i | ||||
\(587\) | −26.0843 | − | 26.0843i | −1.07662 | − | 1.07662i | −0.996811 | − | 0.0798046i | \(-0.974570\pi\) |
−0.0798046 | − | 0.996811i | \(-0.525430\pi\) | |||||||
\(588\) | 0.00868764 | + | 3.49539i | 0.000358272 | + | 0.144147i | ||||
\(589\) | 19.5589 | − | 19.5589i | 0.805908 | − | 0.805908i | ||||
\(590\) | −19.3644 | + | 1.90786i | −0.797221 | + | 0.0785453i | ||||
\(591\) | 1.03471 | 0.0425623 | ||||||||
\(592\) | −35.2618 | − | 14.6006i | −1.44925 | − | 0.600081i | ||||
\(593\) | 11.6626i | 0.478925i | 0.970906 | + | 0.239462i | \(0.0769711\pi\) | ||||
−0.970906 | + | 0.239462i | \(0.923029\pi\) | |||||||
\(594\) | 2.88796 | − | 0.284533i | 0.118494 | − | 0.0116745i | ||||
\(595\) | −17.2869 | − | 9.21315i | −0.708694 | − | 0.377702i | ||||
\(596\) | 9.59871 | + | 6.41276i | 0.393178 | + | 0.262677i | ||||
\(597\) | −3.08025 | − | 3.08025i | −0.126066 | − | 0.126066i | ||||
\(598\) | 14.3262 | + | 11.7564i | 0.585841 | + | 0.480756i | ||||
\(599\) | −4.35971 | −0.178133 | −0.0890664 | − | 0.996026i | \(-0.528388\pi\) | ||||
−0.0890664 | + | 0.996026i | \(0.528388\pi\) | |||||||
\(600\) | −0.622825 | − | 0.332830i | −0.0254267 | − | 0.0135877i | ||||
\(601\) | −39.9253 | −1.62859 | −0.814293 | − | 0.580454i | \(-0.802875\pi\) | ||||
−0.814293 | + | 0.580454i | \(0.802875\pi\) | |||||||
\(602\) | 2.58678 | − | 6.26706i | 0.105429 | − | 0.255426i | ||||
\(603\) | 6.73449 | − | 6.73449i | 0.274249 | − | 0.274249i | ||||
\(604\) | −40.6529 | + | 8.08909i | −1.65414 | + | 0.329141i | ||||
\(605\) | −6.42341 | − | 6.42341i | −0.261149 | − | 0.261149i | ||||
\(606\) | −0.360398 | − | 3.65797i | −0.0146402 | − | 0.148595i | ||||
\(607\) | 31.4255 | 1.27552 | 0.637761 | − | 0.770234i | \(-0.279861\pi\) | ||||
0.637761 | + | 0.770234i | \(0.279861\pi\) | |||||||
\(608\) | 4.28689 | − | 14.1402i | 0.173856 | − | 0.573460i | ||||
\(609\) | −0.818065 | − | 2.68510i | −0.0331497 | − | 0.108806i | ||||
\(610\) | −17.4099 | + | 1.71529i | −0.704906 | + | 0.0694501i | ||||
\(611\) | 8.33857 | + | 8.33857i | 0.337343 | + | 0.337343i | ||||
\(612\) | 42.6637 | − | 8.48919i | 1.72458 | − | 0.343155i | ||||
\(613\) | 27.5057 | + | 27.5057i | 1.11094 | + | 1.11094i | 0.993023 | + | 0.117921i | \(0.0376231\pi\) |
0.117921 | + | 0.993023i | \(0.462377\pi\) | |||||||
\(614\) | −29.2624 | + | 35.6587i | −1.18094 | + | 1.43907i | ||||
\(615\) | − | 1.51222i | − | 0.0609784i | ||||||
\(616\) | 2.00750 | − | 10.1618i | 0.0808844 | − | 0.409429i | ||||
\(617\) | − | 13.9785i | − | 0.562751i | −0.959598 | − | 0.281376i | \(-0.909209\pi\) | ||
0.959598 | − | 0.281376i | \(-0.0907907\pi\) | |||||||
\(618\) | 3.46456 | + | 2.84310i | 0.139365 | + | 0.114366i | ||||
\(619\) | −7.34739 | − | 7.34739i | −0.295316 | − | 0.295316i | 0.543860 | − | 0.839176i | \(-0.316962\pi\) |
−0.839176 | + | 0.543860i | \(0.816962\pi\) | |||||||
\(620\) | 11.7655 | − | 17.6108i | 0.472515 | − | 0.707267i | ||||
\(621\) | −3.76917 | − | 3.76917i | −0.151252 | − | 0.151252i | ||||
\(622\) | −2.07747 | − | 21.0860i | −0.0832992 | − | 0.845471i | ||||
\(623\) | −19.4784 | + | 5.93446i | −0.780385 | + | 0.237759i | ||||
\(624\) | 3.36250 | − | 1.39330i | 0.134608 | − | 0.0557767i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 3.42569 | − | 0.337512i | 0.136918 | − | 0.0134897i | ||||
\(627\) | −0.638288 | − | 0.638288i | −0.0254908 | − | 0.0254908i | ||||
\(628\) | −22.7268 | − | 15.1835i | −0.906899 | − | 0.605886i | ||||
\(629\) | −49.9516 | + | 49.9516i | −1.99170 | + | 1.99170i | ||||
\(630\) | −10.1603 | − | 4.19373i | −0.404794 | − | 0.167082i | ||||
\(631\) | 30.8802 | 1.22932 | 0.614660 | − | 0.788792i | \(-0.289293\pi\) | ||||
0.614660 | + | 0.788792i | \(0.289293\pi\) | |||||||
\(632\) | −0.923438 | − | 3.04311i | −0.0367324 | − | 0.121048i | ||||
\(633\) | 4.63169 | 0.184093 | ||||||||
\(634\) | −8.99831 | + | 10.9652i | −0.357368 | + | 0.435483i | ||||
\(635\) | −8.52114 | − | 8.52114i | −0.338151 | − | 0.338151i | ||||
\(636\) | −4.21824 | + | 0.839343i | −0.167264 | + | 0.0332821i | ||||
\(637\) | −25.0335 | − | 4.91650i | −0.991864 | − | 0.194799i | ||||
\(638\) | 0.815577 | + | 8.27796i | 0.0322890 | + | 0.327727i | ||||
\(639\) | − | 31.5373i | − | 1.24760i | ||||||
\(640\) | 1.10640 | − | 11.2595i | 0.0437342 | − | 0.445070i | ||||
\(641\) | −24.9879 | −0.986962 | −0.493481 | − | 0.869756i | \(-0.664276\pi\) | ||||
−0.493481 | + | 0.869756i | \(0.664276\pi\) | |||||||
\(642\) | 0.255521 | + | 2.59349i | 0.0100846 | + | 0.102357i | ||||
\(643\) | 12.5054 | − | 12.5054i | 0.493166 | − | 0.493166i | −0.416136 | − | 0.909302i | \(-0.636616\pi\) |
0.909302 | + | 0.416136i | \(0.136616\pi\) | |||||||
\(644\) | −16.7683 | + | 8.99035i | −0.660764 | + | 0.354269i | ||||
\(645\) | −0.319901 | − | 0.319901i | −0.0125961 | − | 0.0125961i | ||||
\(646\) | −21.1419 | − | 17.3495i | −0.831816 | − | 0.682609i | ||||
\(647\) | − | 23.7903i | − | 0.935293i | −0.883916 | − | 0.467647i | \(-0.845102\pi\) | ||
0.883916 | − | 0.467647i | \(-0.154898\pi\) | |||||||
\(648\) | 22.8511 | − | 6.93421i | 0.897676 | − | 0.272402i | ||||
\(649\) | −19.0448 | −0.747573 | ||||||||
\(650\) | 3.26963 | − | 3.98432i | 0.128245 | − | 0.156278i | ||||
\(651\) | −3.29006 | + | 6.17323i | −0.128948 | + | 0.241948i | ||||
\(652\) | −3.73139 | − | 2.49289i | −0.146133 | − | 0.0976291i | ||||
\(653\) | −2.86761 | + | 2.86761i | −0.112218 | + | 0.112218i | −0.760986 | − | 0.648768i | \(-0.775285\pi\) |
0.648768 | + | 0.760986i | \(0.275285\pi\) | |||||||
\(654\) | −0.458212 | − | 4.65077i | −0.0179175 | − | 0.181859i | ||||
\(655\) | 8.87480i | 0.346767i | ||||||||
\(656\) | 22.3819 | − | 9.27427i | 0.873867 | − | 0.362099i | ||||
\(657\) | − | 11.7604i | − | 0.458818i | ||||||
\(658\) | −11.1794 | + | 4.64696i | −0.435820 | + | 0.181157i | ||||
\(659\) | 26.6806 | + | 26.6806i | 1.03933 | + | 1.03933i | 0.999194 | + | 0.0401351i | \(0.0127788\pi\) |
0.0401351 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(660\) | −0.574715 | − | 0.383959i | −0.0223708 | − | 0.0149456i | ||||
\(661\) | −2.65709 | + | 2.65709i | −0.103349 | + | 0.103349i | −0.756890 | − | 0.653542i | \(-0.773282\pi\) |
0.653542 | + | 0.756890i | \(0.273282\pi\) | |||||||
\(662\) | −4.73429 | + | 5.76912i | −0.184003 | + | 0.224223i | ||||
\(663\) | − | 6.73703i | − | 0.261645i | ||||||
\(664\) | −3.27267 | + | 6.12415i | −0.127004 | + | 0.237663i | ||||
\(665\) | 2.01408 | + | 6.61071i | 0.0781026 | + | 0.256352i | ||||
\(666\) | −25.1458 | + | 30.6422i | −0.974379 | + | 1.18736i | ||||
\(667\) | 10.8039 | − | 10.8039i | 0.418327 | − | 0.418327i | ||||
\(668\) | 5.23321 | + | 26.3003i | 0.202479 | + | 1.01759i | ||||
\(669\) | 0.617719 | − | 0.617719i | 0.0238824 | − | 0.0238824i | ||||
\(670\) | −4.56283 | + | 0.449548i | −0.176278 | + | 0.0173676i | ||||
\(671\) | −17.1225 | −0.661007 | ||||||||
\(672\) | 0.00512522 | + | 3.73674i | 0.000197710 | + | 0.144148i | ||||
\(673\) | −3.09585 | −0.119336 | −0.0596681 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596681 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(674\) | −15.7588 | + | 1.55262i | −0.607006 | + | 0.0598046i | ||||
\(675\) | −1.04826 | + | 1.04826i | −0.0403476 | + | 0.0403476i | ||||
\(676\) | 0.110311 | + | 0.554385i | 0.00424274 | + | 0.0213225i | ||||
\(677\) | 9.01828 | − | 9.01828i | 0.346601 | − | 0.346601i | −0.512241 | − | 0.858842i | \(-0.671185\pi\) |
0.858842 | + | 0.512241i | \(0.171185\pi\) | |||||||
\(678\) | −2.20235 | + | 2.68375i | −0.0845809 | + | 0.103069i | ||||
\(679\) | −8.40657 | − | 27.5925i | −0.322614 | − | 1.05890i | ||||
\(680\) | −18.4695 | − | 9.86985i | −0.708273 | − | 0.378492i | ||||
\(681\) | 1.19017i | 0.0456074i | ||||||||
\(682\) | 13.1501 | − | 16.0245i | 0.503544 | − | 0.613611i | ||||
\(683\) | 29.3053 | − | 29.3053i | 1.12134 | − | 1.12134i | 0.129797 | − | 0.991541i | \(-0.458568\pi\) |
0.991541 | − | 0.129797i | \(-0.0414324\pi\) | |||||||
\(684\) | −12.7606 | − | 8.52517i | −0.487914 | − | 0.325968i | ||||
\(685\) | −1.46788 | − | 1.46788i | −0.0560849 | − | 0.0560849i | ||||
\(686\) | 14.4714 | − | 21.8307i | 0.552520 | − | 0.833500i | ||||
\(687\) | 1.62533i | 0.0620102i | ||||||||
\(688\) | 2.77285 | − | 6.69669i | 0.105714 | − | 0.255309i | ||||
\(689\) | − | 31.3911i | − | 1.19591i | ||||||
\(690\) | 0.124481 | + | 1.26346i | 0.00473893 | + | 0.0480993i | ||||
\(691\) | −10.1726 | + | 10.1726i | −0.386983 | + | 0.386983i | −0.873610 | − | 0.486627i | \(-0.838227\pi\) |
0.486627 | + | 0.873610i | \(0.338227\pi\) | |||||||
\(692\) | −6.83484 | − | 4.56626i | −0.259822 | − | 0.173583i | ||||
\(693\) | −9.49403 | − | 5.05990i | −0.360648 | − | 0.192210i | ||||
\(694\) | 2.15515 | − | 2.62624i | 0.0818086 | − | 0.0996906i | ||||
\(695\) | −17.3839 | −0.659407 | ||||||||
\(696\) | −0.871351 | − | 2.87146i | −0.0330285 | − | 0.108842i | ||||
\(697\) | − | 44.8438i | − | 1.69858i | ||||||
\(698\) | 13.4327 | + | 11.0232i | 0.508436 | + | 0.417235i | ||||
\(699\) | 0.334193 | + | 0.334193i | 0.0126403 | + | 0.0126403i | ||||
\(700\) | 2.50034 | + | 4.66350i | 0.0945041 | + | 0.176264i | ||||
\(701\) | 20.9837 | − | 20.9837i | 0.792543 | − | 0.792543i | −0.189364 | − | 0.981907i | \(-0.560643\pi\) |
0.981907 | + | 0.189364i | \(0.0606426\pi\) | |||||||
\(702\) | −0.749179 | − | 7.60403i | −0.0282759 | − | 0.286996i | ||||
\(703\) | 24.9218 | 0.939945 | ||||||||
\(704\) | 2.15820 | − | 10.8610i | 0.0813404 | − | 0.409339i | ||||
\(705\) | 0.807855i | 0.0304256i | ||||||||
\(706\) | −0.0472675 | − | 0.479757i | −0.00177894 | − | 0.0180559i | ||||
\(707\) | −12.9540 | + | 24.3060i | −0.487186 | + | 0.914121i | ||||
\(708\) | 6.73836 | − | 1.34080i | 0.253243 | − | 0.0503902i | ||||
\(709\) | 17.1087 | + | 17.1087i | 0.642531 | + | 0.642531i | 0.951177 | − | 0.308646i | \(-0.0998758\pi\) |
−0.308646 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(710\) | −9.63116 | + | 11.7364i | −0.361451 | + | 0.440458i | ||||
\(711\) | −3.30295 | −0.123870 | ||||||||
\(712\) | −20.8303 | + | 6.32101i | −0.780649 | + | 0.236890i | ||||
\(713\) | −38.0769 | −1.42599 | ||||||||
\(714\) | 6.39336 | + | 2.63891i | 0.239265 | + | 0.0987588i | ||||
\(715\) | 3.56711 | − | 3.56711i | 0.133402 | − | 0.133402i | ||||
\(716\) | 7.71792 | + | 5.15623i | 0.288432 | + | 0.192697i | ||||
\(717\) | 1.96688 | + | 1.96688i | 0.0734544 | + | 0.0734544i | ||||
\(718\) | 36.0483 | − | 3.55162i | 1.34531 | − | 0.132545i | ||||
\(719\) | 53.3287 | 1.98883 | 0.994413 | − | 0.105559i | \(-0.0336632\pi\) | ||||
0.994413 | + | 0.105559i | \(0.0336632\pi\) | |||||||
\(720\) | −10.8568 | − | 4.49538i | −0.404608 | − | 0.167533i | ||||
\(721\) | −9.78746 | − | 32.1249i | −0.364504 | − | 1.19639i | ||||
\(722\) | −1.68855 | − | 17.1385i | −0.0628414 | − | 0.637829i | ||||
\(723\) | 2.75178 | + | 2.75178i | 0.102340 | + | 0.102340i | ||||
\(724\) | −20.3273 | + | 30.4261i | −0.755457 | + | 1.13078i | ||||
\(725\) | −3.00471 | − | 3.00471i | −0.111592 | − | 0.111592i | ||||
\(726\) | 2.47948 | + | 2.03473i | 0.0920223 | + | 0.0755158i | ||||
\(727\) | − | 21.9423i | − | 0.813793i | −0.913474 | − | 0.406897i | \(-0.866611\pi\) | ||
0.913474 | − | 0.406897i | \(-0.133389\pi\) | |||||||
\(728\) | −26.7561 | − | 5.28577i | −0.991646 | − | 0.195904i | ||||
\(729\) | − | 23.6919i | − | 0.877478i | ||||||
\(730\) | −3.59152 | + | 4.37656i | −0.132928 | + | 0.161984i | ||||
\(731\) | −9.48646 | − | 9.48646i | −0.350869 | − | 0.350869i | ||||
\(732\) | 6.05823 | − | 1.20546i | 0.223919 | − | 0.0445552i | ||||
\(733\) | 23.7073 | + | 23.7073i | 0.875648 | + | 0.875648i | 0.993081 | − | 0.117433i | \(-0.0374665\pi\) |
−0.117433 | + | 0.993081i | \(0.537467\pi\) | |||||||
\(734\) | 23.0944 | − | 2.27535i | 0.852430 | − | 0.0839847i | ||||
\(735\) | −0.974485 | − | 1.45080i | −0.0359444 | − | 0.0535137i | ||||
\(736\) | −17.9368 | + | 9.59112i | −0.661158 | + | 0.353533i | ||||
\(737\) | −4.48752 | −0.165300 | ||||||||
\(738\) | −2.46721 | − | 25.0417i | −0.0908193 | − | 0.921799i | ||||
\(739\) | 4.51925 | + | 4.51925i | 0.166243 | + | 0.166243i | 0.785326 | − | 0.619083i | \(-0.212495\pi\) |
−0.619083 | + | 0.785326i | \(0.712495\pi\) | |||||||
\(740\) | 18.7156 | − | 3.72403i | 0.688001 | − | 0.136898i | ||||
\(741\) | −1.68062 | + | 1.68062i | −0.0617391 | + | 0.0617391i | ||||
\(742\) | 29.7898 | + | 12.2960i | 1.09362 | + | 0.451399i | ||||
\(743\) | −1.02788 | −0.0377093 | −0.0188546 | − | 0.999822i | \(-0.506002\pi\) | ||||
−0.0188546 | + | 0.999822i | \(0.506002\pi\) | |||||||
\(744\) | −3.52457 | + | 6.59554i | −0.129217 | + | 0.241804i | ||||
\(745\) | −5.77189 | −0.211466 | ||||||||
\(746\) | −0.713474 | − | 0.585494i | −0.0261221 | − | 0.0214365i | ||||
\(747\) | 5.09960 | + | 5.09960i | 0.186585 | + | 0.186585i | ||||
\(748\) | −17.0428 | − | 11.3861i | −0.623148 | − | 0.416316i | ||||
\(749\) | 9.18438 | − | 17.2329i | 0.335590 | − | 0.629677i | ||||
\(750\) | 0.351387 | − | 0.0346201i | 0.0128309 | − | 0.00126415i | ||||
\(751\) | − | 39.5491i | − | 1.44317i | −0.692328 | − | 0.721583i | \(-0.743415\pi\) | ||
0.692328 | − | 0.721583i | \(-0.256585\pi\) | |||||||
\(752\) | −11.9569 | + | 4.95450i | −0.436022 | + | 0.180672i | ||||
\(753\) | 0.974879 | 0.0355266 | ||||||||
\(754\) | 21.7960 | − | 2.14742i | 0.793762 | − | 0.0782046i | ||||
\(755\) | 14.6548 | − | 14.6548i | 0.533341 | − | 0.533341i | ||||
\(756\) | 7.50958 | + | 2.26756i | 0.273121 | + | 0.0824702i | ||||
\(757\) | −32.2655 | − | 32.2655i | −1.17271 | − | 1.17271i | −0.981562 | − | 0.191146i | \(-0.938779\pi\) |
−0.191146 | − | 0.981562i | \(-0.561221\pi\) | |||||||
\(758\) | 27.7234 | − | 33.7833i | 1.00696 | − | 1.22706i | ||||
\(759\) | 1.24261i | 0.0451039i | ||||||||
\(760\) | 2.14527 | + | 7.06954i | 0.0778170 | + | 0.256439i | ||||
\(761\) | 3.78659 | 0.137264 | 0.0686320 | − | 0.997642i | \(-0.478137\pi\) | ||||
0.0686320 | + | 0.997642i | \(0.478137\pi\) | |||||||
\(762\) | 3.28922 | + | 2.69922i | 0.119156 | + | 0.0977823i | ||||
\(763\) | −16.4698 | + | 30.9028i | −0.596248 | + | 1.11876i | ||||
\(764\) | −6.67135 | − | 33.5278i | −0.241361 | − | 1.21299i | ||||
\(765\) | −15.3796 | + | 15.3796i | −0.556050 | + | 0.556050i | ||||
\(766\) | −22.8676 | + | 2.25301i | −0.826240 | + | 0.0814044i | ||||
\(767\) | 50.1452i | 1.81064i | ||||||||
\(768\) | 0.00102944 | + | 3.99474i | 3.71467e−5 | + | 0.144148i | ||||
\(769\) | − | 35.7569i | − | 1.28943i | −0.764424 | − | 0.644714i | \(-0.776976\pi\) | ||
0.764424 | − | 0.644714i | \(-0.223024\pi\) | |||||||
\(770\) | 1.98789 | + | 4.78238i | 0.0716387 | + | 0.172345i | ||||
\(771\) | −2.89040 | − | 2.89040i | −0.104095 | − | 0.104095i | ||||
\(772\) | 37.0636 | − | 7.37489i | 1.33395 | − | 0.265428i | ||||
\(773\) | 16.9413 | − | 16.9413i | 0.609337 | − | 0.609337i | −0.333436 | − | 0.942773i | \(-0.608208\pi\) |
0.942773 | + | 0.333436i | \(0.108208\pi\) | |||||||
\(774\) | −5.81937 | − | 4.77552i | −0.209173 | − | 0.171652i | ||||
\(775\) | 10.5897i | 0.380394i | ||||||||
\(776\) | −8.95414 | − | 29.5076i | −0.321435 | − | 1.05926i | ||||
\(777\) | −6.02905 | + | 1.83687i | −0.216291 | + | 0.0658972i | ||||
\(778\) | 19.6948 | + | 16.1621i | 0.706093 | + | 0.579438i | ||||
\(779\) | −11.1867 | + | 11.1867i | −0.400807 | + | 0.400807i | ||||
\(780\) | −1.01097 | + | 1.51323i | −0.0361985 | + | 0.0541824i | ||||
\(781\) | −10.5074 | + | 10.5074i | −0.375985 | + | 0.375985i | ||||
\(782\) | 3.69142 | + | 37.4672i | 0.132005 | + | 1.33983i | ||||
\(783\) | −6.29943 | −0.225123 | ||||||||
\(784\) | 15.4966 | − | 23.3207i | 0.553448 | − | 0.832884i | ||||
\(785\) | 13.6661 | 0.487763 | ||||||||
\(786\) | −0.307246 | − | 3.11849i | −0.0109591 | − | 0.111233i | ||||
\(787\) | −27.4719 | + | 27.4719i | −0.979267 | + | 0.979267i | −0.999789 | − | 0.0205228i | \(-0.993467\pi\) |
0.0205228 | + | 0.999789i | \(0.493467\pi\) | |||||||
\(788\) | −6.89200 | − | 4.60444i | −0.245517 | − | 0.164027i | ||||
\(789\) | −1.82654 | + | 1.82654i | −0.0650264 | + | 0.0650264i | ||||
\(790\) | 1.22917 | + | 1.00869i | 0.0437319 | + | 0.0358875i | ||||
\(791\) | 24.8849 | − | 7.58166i | 0.884805 | − | 0.269573i | ||||
\(792\) | −10.1435 | − | 5.42056i | −0.360434 | − | 0.192611i | ||||
\(793\) | 45.0838i | 1.60097i | ||||||||
\(794\) | 2.40326 | + | 1.97217i | 0.0852884 | + | 0.0699898i | ||||
\(795\) | 1.52061 | − | 1.52061i | 0.0539305 | − | 0.0539305i | ||||
\(796\) | 6.80986 | + | 34.2240i | 0.241369 | + | 1.21304i | ||||
\(797\) | 28.5576 | + | 28.5576i | 1.01156 | + | 1.01156i | 0.999932 | + | 0.0116300i | \(0.00370202\pi\) |
0.0116300 | + | 0.999932i | \(0.496298\pi\) | |||||||
\(798\) | −0.936585 | − | 2.25319i | −0.0331547 | − | 0.0797621i | ||||
\(799\) | 23.9564i | 0.847518i | ||||||||
\(800\) | 2.66743 | + | 4.98847i | 0.0943078 | + | 0.176369i | ||||
\(801\) | 22.6090i | 0.798849i | ||||||||
\(802\) | −21.7509 | + | 2.14298i | −0.768051 | + | 0.0756714i | ||||
\(803\) | −3.91828 | + | 3.91828i | −0.138273 | + | 0.138273i | ||||
\(804\) | 1.58776 | − | 0.315931i | 0.0559959 | − | 0.0111420i | ||||
\(805\) | 4.47432 | − | 8.39530i | 0.157699 | − | 0.295895i | ||||
\(806\) | −42.1928 | − | 34.6245i | −1.48618 | − | 1.21959i | ||||
\(807\) | 3.19955 | 0.112630 | ||||||||
\(808\) | −13.8774 | + | 25.9688i | −0.488204 | + | 0.913578i | ||||
\(809\) | 33.8337i | 1.18953i | 0.803900 | + | 0.594764i | \(0.202755\pi\) | ||||
−0.803900 | + | 0.594764i | \(0.797245\pi\) | |||||||
\(810\) | −7.57437 | + | 9.23000i | −0.266136 | + | 0.324309i | ||||
\(811\) | 22.8205 | + | 22.8205i | 0.801336 | + | 0.801336i | 0.983304 | − | 0.181968i | \(-0.0582469\pi\) |
−0.181968 | + | 0.983304i | \(0.558247\pi\) | |||||||
\(812\) | −6.49966 | + | 21.5253i | −0.228093 | + | 0.755388i | ||||
\(813\) | −3.91034 | + | 3.91034i | −0.137142 | + | 0.137142i | ||||
\(814\) | 18.5871 | − | 1.83128i | 0.651479 | − | 0.0641863i | ||||
\(815\) | 2.24376 | 0.0785954 | ||||||||
\(816\) | 6.83164 | + | 2.82873i | 0.239155 | + | 0.0990252i | ||||
\(817\) | 4.73299i | 0.165586i | ||||||||
\(818\) | 14.7909 | − | 1.45726i | 0.517152 | − | 0.0509519i | ||||
\(819\) | −13.3228 | + | 24.9979i | −0.465535 | + | 0.873497i | ||||
\(820\) | −6.72933 | + | 10.0726i | −0.234999 | + | 0.351749i | ||||
\(821\) | 9.05164 | + | 9.05164i | 0.315904 | + | 0.315904i | 0.847192 | − | 0.531287i | \(-0.178292\pi\) |
−0.531287 | + | 0.847192i | \(0.678292\pi\) | |||||||
\(822\) | 0.566614 | + | 0.464977i | 0.0197629 | + | 0.0162180i | ||||
\(823\) | −10.9205 | −0.380663 | −0.190332 | − | 0.981720i | \(-0.560956\pi\) | ||||
−0.190332 | + | 0.981720i | \(0.560956\pi\) | |||||||
\(824\) | −10.4250 | − | 34.3546i | −0.363171 | − | 1.19680i | ||||
\(825\) | 0.345587 | 0.0120318 | ||||||||
\(826\) | −47.5872 | − | 19.6420i | −1.65577 | − | 0.683433i | ||||
\(827\) | −13.4654 | + | 13.4654i | −0.468237 | + | 0.468237i | −0.901343 | − | 0.433106i | \(-0.857418\pi\) |
0.433106 | + | 0.901343i | \(0.357418\pi\) | |||||||
\(828\) | 4.12273 | + | 20.7194i | 0.143275 | + | 0.720049i | ||||
\(829\) | 28.8777 | + | 28.8777i | 1.00296 | + | 1.00296i | 0.999996 | + | 0.00296878i | \(0.000944995\pi\) |
0.00296878 | + | 0.999996i | \(0.499055\pi\) | |||||||
\(830\) | −0.340414 | − | 3.45514i | −0.0118160 | − | 0.119930i | ||||
\(831\) | 6.39944 | 0.221994 | ||||||||
\(832\) | −28.5971 | − | 5.68258i | −0.991427 | − | 0.197008i | ||||
\(833\) | −28.8978 | − | 43.0227i | −1.00125 | − | 1.49065i | ||||
\(834\) | 6.10847 | − | 0.601830i | 0.211519 | − | 0.0208397i | ||||
\(835\) | −9.48085 | − | 9.48085i | −0.328098 | − | 0.328098i | ||||
\(836\) | 1.41114 | + | 7.09188i | 0.0488052 | + | 0.245278i | ||||
\(837\) | 11.1008 | + | 11.1008i | 0.383699 | + | 0.383699i | ||||
\(838\) | −0.620187 | + | 0.755749i | −0.0214240 | + | 0.0261069i | ||||
\(839\) | − | 2.25826i | − | 0.0779639i | −0.999240 | − | 0.0389820i | \(-0.987589\pi\) | ||
0.999240 | − | 0.0389820i | \(-0.0124115\pi\) | |||||||
\(840\) | −1.04004 | − | 1.55213i | −0.0358848 | − | 0.0535537i | ||||
\(841\) | 10.9435i | 0.377362i | ||||||||
\(842\) | −22.5424 | − | 18.4989i | −0.776864 | − | 0.637514i | ||||
\(843\) | −1.70149 | − | 1.70149i | −0.0586025 | − | 0.0586025i | ||||
\(844\) | −30.8507 | − | 20.6109i | −1.06193 | − | 0.709457i | ||||
\(845\) | −0.199847 | − | 0.199847i | −0.00687496 | − | 0.00687496i | ||||
\(846\) | 1.31803 | + | 13.3778i | 0.0453149 | + | 0.459938i | ||||
\(847\) | −7.00460 | − | 22.9908i | −0.240681 | − | 0.789975i | ||||
\(848\) | 31.8319 | + | 13.1804i | 1.09311 | + | 0.452617i | ||||
\(849\) | 0.385992 | 0.0132472 | ||||||||
\(850\) | 10.4202 | − | 1.02664i | 0.357409 | − | 0.0352133i | ||||
\(851\) | −24.2587 | − | 24.2587i | −0.831579 | − | 0.831579i | ||||
\(852\) | 2.97795 | − | 4.45744i | 0.102023 | − | 0.152709i | ||||
\(853\) | −13.3778 | + | 13.3778i | −0.458047 | + | 0.458047i | −0.898014 | − | 0.439967i | \(-0.854990\pi\) |
0.439967 | + | 0.898014i | \(0.354990\pi\) | |||||||
\(854\) | −42.7840 | − | 17.6594i | −1.46404 | − | 0.604294i | ||||
\(855\) | 7.67319 | 0.262418 | ||||||||
\(856\) | 9.83903 | − | 18.4118i | 0.336291 | − | 0.629302i | ||||
\(857\) | 46.6899 | 1.59490 | 0.797448 | − | 0.603388i | \(-0.206183\pi\) | ||||
0.797448 | + | 0.603388i | \(0.206183\pi\) | |||||||
\(858\) | −1.12994 | + | 1.37693i | −0.0385756 | + | 0.0470076i | ||||
\(859\) | −2.79689 | − | 2.79689i | −0.0954288 | − | 0.0954288i | 0.657781 | − | 0.753210i | \(-0.271495\pi\) |
−0.753210 | + | 0.657781i | \(0.771495\pi\) | |||||||
\(860\) | 0.707242 | + | 3.55435i | 0.0241167 | + | 0.121202i | ||||
\(861\) | 1.88176 | − | 3.53080i | 0.0641302 | − | 0.120329i | ||||
\(862\) | 4.95472 | + | 50.2895i | 0.168758 | + | 1.71287i | ||||
\(863\) | − | 31.6740i | − | 1.07820i | −0.842243 | − | 0.539099i | \(-0.818765\pi\) | ||
0.842243 | − | 0.539099i | \(-0.181235\pi\) | |||||||
\(864\) | 8.02538 | + | 2.43306i | 0.273029 | + | 0.0827744i | ||||
\(865\) | 4.10992 | 0.139742 | ||||||||
\(866\) | −0.470016 | − | 4.77058i | −0.0159718 | − | 0.162111i | ||||
\(867\) | 6.67638 | − | 6.67638i | 0.226742 | − | 0.226742i | ||||
\(868\) | 49.3852 | − | 26.4780i | 1.67624 | − | 0.898720i | ||||
\(869\) | 1.10046 | + | 1.10046i | 0.0373305 | + | 0.0373305i | ||||
\(870\) | 1.15984 | + | 0.951792i | 0.0393222 | + | 0.0322688i | ||||
\(871\) | 11.8157i | 0.400360i | ||||||||
\(872\) | −17.6438 | + | 33.0169i | −0.597494 | + | 1.11809i | ||||
\(873\) | −32.0272 | −1.08396 | ||||||||
\(874\) | 8.42572 | − | 10.2674i | 0.285004 | − | 0.347302i | ||||
\(875\) | −2.33485 | − | 1.24437i | −0.0789324 | − | 0.0420675i | ||||
\(876\) | 1.11050 | − | 1.66221i | 0.0375202 | − | 0.0561608i | ||||
\(877\) | 8.47123 | − | 8.47123i | 0.286053 | − | 0.286053i | −0.549464 | − | 0.835517i | \(-0.685168\pi\) |
0.835517 | + | 0.549464i | \(0.185168\pi\) | |||||||
\(878\) | 1.02398 | + | 10.3932i | 0.0345577 | + | 0.350755i | ||||
\(879\) | − | 8.15729i | − | 0.275139i | ||||||
\(880\) | 2.11945 | + | 5.11495i | 0.0714467 | + | 0.172425i | ||||
\(881\) | − | 6.46468i | − | 0.217801i | −0.994053 | − | 0.108900i | \(-0.965267\pi\) | ||
0.994053 | − | 0.108900i | \(-0.0347329\pi\) | |||||||
\(882\) | −18.5041 | − | 22.4349i | −0.623067 | − | 0.755422i | ||||
\(883\) | −1.58594 | − | 1.58594i | −0.0533710 | − | 0.0533710i | 0.679918 | − | 0.733289i | \(-0.262016\pi\) |
−0.733289 | + | 0.679918i | \(0.762016\pi\) | |||||||
\(884\) | −29.9797 | + | 44.8740i | −1.00833 | + | 1.50928i | ||||
\(885\) | −2.42908 | + | 2.42908i | −0.0816525 | + | 0.0816525i | ||||
\(886\) | −23.3988 | + | 28.5134i | −0.786098 | + | 0.957926i | ||||
\(887\) | 19.1490i | 0.642960i | 0.946916 | + | 0.321480i | \(0.104180\pi\) | ||||
−0.946916 | + | 0.321480i | \(0.895820\pi\) | |||||||
\(888\) | −6.44751 | + | 1.95651i | −0.216364 | + | 0.0656562i | ||||
\(889\) | −9.29212 | − | 30.4991i | −0.311648 | − | 1.02291i | ||||
\(890\) | 6.90455 | − | 8.41377i | 0.231441 | − | 0.282030i | ||||
\(891\) | −8.26349 | + | 8.26349i | −0.276837 | + | 0.276837i | ||||
\(892\) | −6.86334 | + | 1.36566i | −0.229802 | + | 0.0457258i | ||||
\(893\) | 5.97618 | − | 5.97618i | 0.199985 | − | 0.199985i | ||||
\(894\) | 2.02817 | − | 0.199823i | 0.0678321 | − | 0.00668308i | ||||
\(895\) | −4.64093 | −0.155129 | ||||||||
\(896\) | 16.5943 | − | 24.9125i | 0.554376 | − | 0.832267i | ||||
\(897\) | 3.27181 | 0.109242 | ||||||||
\(898\) | 26.6323 | − | 2.62392i | 0.888732 | − | 0.0875613i | ||||
\(899\) | −31.8190 | + | 31.8190i | −1.06122 | + | 1.06122i | ||||
\(900\) | 5.76236 | − | 1.14659i | 0.192079 | − | 0.0382197i | ||||
\(901\) | 45.0928 | − | 45.0928i | 1.50226 | − | 1.50226i | ||||
\(902\) | −7.52126 | + | 9.16528i | −0.250430 | + | 0.305170i | ||||
\(903\) | −0.348845 | − | 1.14500i | −0.0116088 | − | 0.0381031i | ||||
\(904\) | 26.6121 | − | 8.07550i | 0.885105 | − | 0.268587i | ||||
\(905\) | − | 18.2958i | − | 0.608173i | ||||||
\(906\) | −4.64215 | + | 5.65684i | −0.154225 | + | 0.187936i | ||||
\(907\) | 31.5859 | − | 31.5859i | 1.04879 | − | 1.04879i | 0.0500460 | − | 0.998747i | \(-0.484063\pi\) |
0.998747 | − | 0.0500460i | \(-0.0159368\pi\) | |||||||
\(908\) | 5.29624 | − | 7.92749i | 0.175762 | − | 0.263083i | ||||
\(909\) | 21.6243 | + | 21.6243i | 0.717231 | + | 0.717231i | ||||
\(910\) | 12.5921 | − | 5.23415i | 0.417423 | − | 0.173510i | ||||
\(911\) | − | 11.2057i | − | 0.371263i | −0.982619 | − | 0.185631i | \(-0.940567\pi\) | ||
0.982619 | − | 0.185631i | \(-0.0594330\pi\) | |||||||
\(912\) | −0.998567 | − | 2.40988i | −0.0330659 | − | 0.0797990i | ||||
\(913\) | − | 3.39811i | − | 0.112461i | ||||||
\(914\) | 4.43347 | + | 44.9989i | 0.146646 | + | 1.48843i | ||||
\(915\) | −2.18390 | + | 2.18390i | −0.0721974 | + | 0.0721974i | ||||
\(916\) | 7.23269 | − | 10.8260i | 0.238975 | − | 0.357701i | ||||
\(917\) | −11.0436 | + | 20.7213i | −0.364691 | + | 0.684279i | ||||
\(918\) | 9.84688 | − | 11.9992i | 0.324995 | − | 0.396034i | ||||
\(919\) | −2.37775 | −0.0784347 | −0.0392174 | − | 0.999231i | \(-0.512486\pi\) | ||||
−0.0392174 | + | 0.999231i | \(0.512486\pi\) | |||||||
\(920\) | 4.79325 | − | 8.96962i | 0.158029 | − | 0.295720i | ||||
\(921\) | 8.14371i | 0.268345i | ||||||||
\(922\) | −1.34926 | − | 1.10724i | −0.0444355 | − | 0.0364649i | ||||
\(923\) | 27.6662 | + | 27.6662i | 0.910643 | + | 0.910643i | ||||
\(924\) | −0.864087 | − | 1.61165i | −0.0284264 | − | 0.0530193i | ||||
\(925\) | −6.74670 | + | 6.74670i | −0.221830 | + | 0.221830i | ||||
\(926\) | 0.498752 | + | 5.06224i | 0.0163900 | + | 0.166356i | ||||
\(927\) | −37.2880 | −1.22470 | ||||||||
\(928\) | −6.97405 | + | 23.0037i | −0.228935 | + | 0.755134i | ||||
\(929\) | 12.3153i | 0.404051i | 0.979380 | + | 0.202026i | \(0.0647524\pi\) | ||||
−0.979380 | + | 0.202026i | \(0.935248\pi\) | |||||||
\(930\) | −0.366617 | − | 3.72109i | −0.0120218 | − | 0.122019i | ||||
\(931\) | −3.52361 | + | 17.9413i | −0.115482 | + | 0.588002i | ||||
\(932\) | −0.738838 | − | 3.71314i | −0.0242015 | − | 0.121628i | ||||
\(933\) | −2.64503 | − | 2.64503i | −0.0865944 | − | 0.0865944i | ||||
\(934\) | 6.04354 | − | 7.36455i | 0.197751 | − | 0.240976i | ||||
\(935\) | 10.2482 | 0.335151 | ||||||||
\(936\) | −14.2724 | + | 26.7080i | −0.466508 | + | 0.872978i | ||||
\(937\) | 3.38760 | 0.110668 | 0.0553340 | − | 0.998468i | \(-0.482378\pi\) | ||||
0.0553340 | + | 0.998468i | \(0.482378\pi\) | |||||||
\(938\) | −11.2129 | − | 4.62824i | −0.366116 | − | 0.151117i | ||||
\(939\) | 0.429719 | − | 0.429719i | 0.0140233 | − | 0.0140233i | ||||
\(940\) | 3.59494 | − | 5.38096i | 0.117254 | − | 0.175508i | ||||
\(941\) | 3.59002 | + | 3.59002i | 0.117031 | + | 0.117031i | 0.763197 | − | 0.646166i | \(-0.223629\pi\) |
−0.646166 | + | 0.763197i | \(0.723629\pi\) | |||||||
\(942\) | −4.80208 | + | 0.473120i | −0.156460 | + | 0.0154151i | ||||
\(943\) | 21.7782 | 0.709195 | ||||||||
\(944\) | −50.8494 | − | 21.0548i | −1.65501 | − | 0.685276i | ||||
\(945\) | −3.75196 | + | 1.14311i | −0.122051 | + | 0.0371853i | ||||
\(946\) | 0.347784 | + | 3.52994i | 0.0113074 | + | 0.114768i | ||||
\(947\) | −24.0700 | − | 24.0700i | −0.782171 | − | 0.782171i | 0.198026 | − | 0.980197i | \(-0.436547\pi\) |
−0.980197 | + | 0.198026i | \(0.936547\pi\) | |||||||
\(948\) | −0.466836 | − | 0.311886i | −0.0151621 | − | 0.0101296i | ||||
\(949\) | 10.3169 | + | 10.3169i | 0.334900 | + | 0.334900i | ||||
\(950\) | −2.85552 | − | 2.34331i | −0.0926454 | − | 0.0760271i | ||||
\(951\) | 2.50422i | 0.0812050i | ||||||||
\(952\) | −30.8418 | − | 46.0276i | −0.999587 | − | 1.49176i | ||||
\(953\) | 1.16774i | 0.0378269i | 0.999821 | + | 0.0189134i | \(0.00602069\pi\) | ||||
−0.999821 | + | 0.0189134i | \(0.993979\pi\) | |||||||
\(954\) | 22.6999 | − | 27.6617i | 0.734935 | − | 0.895580i | ||||
\(955\) | 12.0863 | + | 12.0863i | 0.391102 | + | 0.391102i | ||||
\(956\) | −4.34841 | − | 21.8536i | −0.140637 | − | 0.706794i | ||||
\(957\) | 1.03839 | + | 1.03839i | 0.0335663 | + | 0.0335663i | ||||
\(958\) | 3.56676 | − | 0.351411i | 0.115237 | − | 0.0113536i | ||||
\(959\) | −1.60070 | − | 5.25389i | −0.0516892 | − | 0.169657i | ||||
\(960\) | −1.11000 | − | 1.66054i | −0.0358251 | − | 0.0535937i | ||||
\(961\) | 81.1422 | 2.61749 | ||||||||
\(962\) | −4.82178 | − | 48.9402i | −0.155460 | − | 1.57789i | ||||
\(963\) | −15.3316 | − | 15.3316i | −0.494052 | − | 0.494052i | ||||
\(964\) | −6.08368 | − | 30.5744i | −0.195942 | − | 0.984736i | ||||
\(965\) | −13.3609 | + | 13.3609i | −0.430101 | + | 0.430101i | ||||
\(966\) | −1.28157 | + | 3.10490i | −0.0412340 | + | 0.0998986i | ||||
\(967\) | −30.7287 | −0.988168 | −0.494084 | − | 0.869414i | \(-0.664497\pi\) | ||||
−0.494084 | + | 0.869414i | \(0.664497\pi\) | |||||||
\(968\) | −7.46085 | − | 24.5866i | −0.239801 | − | 0.790242i | ||||
\(969\) | −4.82837 | −0.155110 | ||||||||
\(970\) | 11.9187 | + | 9.78076i | 0.382686 | + | 0.314041i | ||||
\(971\) | −12.6093 | − | 12.6093i | −0.404652 | − | 0.404652i | 0.475217 | − | 0.879869i | \(-0.342370\pi\) |
−0.879869 | + | 0.475217i | \(0.842370\pi\) | |||||||
\(972\) | 7.28320 | − | 10.9016i | 0.233609 | − | 0.349669i | ||||
\(973\) | −40.5887 | − | 21.6320i | −1.30121 | − | 0.693490i | ||||
\(974\) | −24.5181 | + | 2.41562i | −0.785611 | + | 0.0774014i | ||||
\(975\) | − | 0.909936i | − | 0.0291413i | ||||||
\(976\) | −45.7169 | − | 18.9297i | −1.46336 | − | 0.605924i | ||||
\(977\) | 52.9758 | 1.69485 | 0.847423 | − | 0.530918i | \(-0.178153\pi\) | ||||
0.847423 | + | 0.530918i | \(0.178153\pi\) | |||||||
\(978\) | −0.788428 | + | 0.0776790i | −0.0252111 | + | 0.00248390i | ||||
\(979\) | 7.53274 | − | 7.53274i | 0.240747 | − | 0.240747i | ||||
\(980\) | 0.0347963 | + | 14.0000i | 0.00111153 | + | 0.447212i | ||||
\(981\) | 27.4932 | + | 27.4932i | 0.877791 | + | 0.877791i | ||||
\(982\) | −12.9911 | + | 15.8308i | −0.414563 | + | 0.505180i | ||||
\(983\) | − | 3.97679i | − | 0.126840i | −0.997987 | − | 0.0634199i | \(-0.979799\pi\) | ||
0.997987 | − | 0.0634199i | \(-0.0202007\pi\) | |||||||
\(984\) | 2.01589 | − | 3.77234i | 0.0642642 | − | 0.120258i | ||||
\(985\) | 4.14429 | 0.132048 | ||||||||
\(986\) | 34.3943 | + | 28.2248i | 1.09534 | + | 0.898861i | ||||
\(987\) | −1.00527 | + | 1.88622i | −0.0319982 | + | 0.0600391i | ||||
\(988\) | 18.6730 | − | 3.71554i | 0.594067 | − | 0.118207i | ||||
\(989\) | 4.60706 | − | 4.60706i | 0.146496 | − | 0.146496i | ||||
\(990\) | 5.72280 | − | 0.563833i | 0.181882 | − | 0.0179198i | ||||
\(991\) | 28.1763i | 0.895049i | 0.894272 | + | 0.447524i | \(0.147694\pi\) | ||||
−0.894272 | + | 0.447524i | \(0.852306\pi\) | |||||||
\(992\) | 52.8265 | − | 28.2473i | 1.67724 | − | 0.896853i | ||||
\(993\) | 1.31755i | 0.0418111i | ||||||||
\(994\) | −37.0918 | + | 15.4179i | −1.17648 | + | 0.489027i | ||||
\(995\) | −12.3372 | − | 12.3372i | −0.391116 | − | 0.391116i | ||||
\(996\) | 0.239235 | + | 1.20231i | 0.00758044 | + | 0.0380966i | ||||
\(997\) | 41.7859 | − | 41.7859i | 1.32337 | − | 1.32337i | 0.412348 | − | 0.911027i | \(-0.364709\pi\) |
0.911027 | − | 0.412348i | \(-0.135291\pi\) | |||||||
\(998\) | 4.18277 | + | 3.43248i | 0.132403 | + | 0.108653i | ||||
\(999\) | 14.1446i | 0.447515i |
(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 | 560.2.bc.a.251.1 | ✓ | 128 | |
7.6 | odd | 2 | inner | 560.2.bc.a.251.2 | yes | 128 | |
16.3 | odd | 4 | inner | 560.2.bc.a.531.2 | yes | 128 | |
112.83 | even | 4 | inner | 560.2.bc.a.531.1 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bc.a.251.1 | ✓ | 128 | 1.1 | even | 1 | trivial | |
560.2.bc.a.251.2 | yes | 128 | 7.6 | odd | 2 | inner | |
560.2.bc.a.531.1 | yes | 128 | 112.83 | even | 4 | inner | |
560.2.bc.a.531.2 | yes | 128 | 16.3 | odd | 4 | inner |