Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(141,560)]
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([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.141");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bd (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: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 141.17 | ||
Character | \(\chi\) | \(=\) | 560.141 |
Dual form | 560.2.bd.a.421.17 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17062 | − | 0.793500i | 0.827755 | − | 0.561089i | ||||
\(3\) | −1.25769 | − | 1.25769i | −0.726125 | − | 0.726125i | 0.243720 | − | 0.969846i | \(-0.421632\pi\) |
−0.969846 | + | 0.243720i | \(0.921632\pi\) | |||||||
\(4\) | 0.740715 | − | 1.85778i | 0.370357 | − | 0.928889i | ||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | −2.47025 | − | 0.474301i | −1.00847 | − | 0.193633i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −0.607051 | − | 2.76252i | −0.214625 | − | 0.976697i | ||||
\(9\) | 0.163545i | 0.0545152i | ||||||||
\(10\) | 0.266666 | − | 1.38884i | 0.0843271 | − | 0.439191i | ||||
\(11\) | −0.651231 | + | 0.651231i | −0.196354 | + | 0.196354i | −0.798435 | − | 0.602081i | \(-0.794338\pi\) |
0.602081 | + | 0.798435i | \(0.294338\pi\) | |||||||
\(12\) | −3.26809 | + | 1.40492i | −0.943416 | + | 0.405564i | ||||
\(13\) | 1.11286 | + | 1.11286i | 0.308652 | + | 0.308652i | 0.844387 | − | 0.535734i | \(-0.179965\pi\) |
−0.535734 | + | 0.844387i | \(0.679965\pi\) | |||||||
\(14\) | −0.793500 | − | 1.17062i | −0.212072 | − | 0.312862i | ||||
\(15\) | −1.77864 | −0.459242 | ||||||||
\(16\) | −2.90268 | − | 2.75217i | −0.725671 | − | 0.688042i | ||||
\(17\) | −0.603016 | −0.146253 | −0.0731265 | − | 0.997323i | \(-0.523298\pi\) | ||||
−0.0731265 | + | 0.997323i | \(0.523298\pi\) | |||||||
\(18\) | 0.129773 | + | 0.191450i | 0.0305879 | + | 0.0451252i | ||||
\(19\) | −0.0481428 | − | 0.0481428i | −0.0110447 | − | 0.0110447i | 0.701563 | − | 0.712608i | \(-0.252486\pi\) |
−0.712608 | + | 0.701563i | \(0.752486\pi\) | |||||||
\(20\) | −0.789884 | − | 1.83741i | −0.176623 | − | 0.410858i | ||||
\(21\) | −1.25769 | + | 1.25769i | −0.274449 | + | 0.274449i | ||||
\(22\) | −0.245594 | + | 1.27910i | −0.0523608 | + | 0.272705i | ||||
\(23\) | − | 3.32354i | − | 0.693005i | −0.938049 | − | 0.346503i | \(-0.887369\pi\) | ||
0.938049 | − | 0.346503i | \(-0.112631\pi\) | |||||||
\(24\) | −2.71090 | + | 4.23785i | −0.553359 | + | 0.865048i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 2.18580 | + | 0.419685i | 0.428670 | + | 0.0823070i | ||||
\(27\) | −3.56737 | + | 3.56737i | −0.686540 | + | 0.686540i | ||||
\(28\) | −1.85778 | − | 0.740715i | −0.351087 | − | 0.139982i | ||||
\(29\) | 4.73058 | + | 4.73058i | 0.878446 | + | 0.878446i | 0.993374 | − | 0.114928i | \(-0.0366636\pi\) |
−0.114928 | + | 0.993374i | \(0.536664\pi\) | |||||||
\(30\) | −2.08211 | + | 1.41135i | −0.380140 | + | 0.257676i | ||||
\(31\) | −6.15445 | −1.10537 | −0.552686 | − | 0.833390i | \(-0.686397\pi\) | ||||
−0.552686 | + | 0.833390i | \(0.686397\pi\) | |||||||
\(32\) | −5.58179 | − | 0.918470i | −0.986731 | − | 0.162364i | ||||
\(33\) | 1.63809 | 0.285155 | ||||||||
\(34\) | −0.705905 | + | 0.478494i | −0.121062 | + | 0.0820610i | ||||
\(35\) | −0.707107 | − | 0.707107i | −0.119523 | − | 0.119523i | ||||
\(36\) | 0.303831 | + | 0.121141i | 0.0506386 | + | 0.0201901i | ||||
\(37\) | 3.26170 | − | 3.26170i | 0.536220 | − | 0.536220i | −0.386196 | − | 0.922417i | \(-0.626211\pi\) |
0.922417 | + | 0.386196i | \(0.126211\pi\) | |||||||
\(38\) | −0.0945583 | − | 0.0181557i | −0.0153394 | − | 0.00294525i | ||||
\(39\) | − | 2.79926i | − | 0.448240i | ||||||
\(40\) | −2.38264 | − | 1.52414i | −0.376729 | − | 0.240988i | ||||
\(41\) | 5.83711i | 0.911604i | 0.890081 | + | 0.455802i | \(0.150647\pi\) | ||||
−0.890081 | + | 0.455802i | \(0.849353\pi\) | |||||||
\(42\) | −0.474301 | + | 2.47025i | −0.0731863 | + | 0.381168i | ||||
\(43\) | 6.87578 | − | 6.87578i | 1.04855 | − | 1.04855i | 0.0497874 | − | 0.998760i | \(-0.484146\pi\) |
0.998760 | − | 0.0497874i | \(-0.0158544\pi\) | |||||||
\(44\) | 0.727467 | + | 1.69222i | 0.109670 | + | 0.255112i | ||||
\(45\) | 0.115644 | + | 0.115644i | 0.0172392 | + | 0.0172392i | ||||
\(46\) | −2.63723 | − | 3.89061i | −0.388838 | − | 0.573639i | ||||
\(47\) | −5.47252 | −0.798249 | −0.399125 | − | 0.916897i | \(-0.630686\pi\) | ||||
−0.399125 | + | 0.916897i | \(0.630686\pi\) | |||||||
\(48\) | 0.189301 | + | 7.11202i | 0.0273233 | + | 1.02653i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.793500 | − | 1.17062i | −0.112218 | − | 0.165551i | ||||
\(51\) | 0.758405 | + | 0.758405i | 0.106198 | + | 0.106198i | ||||
\(52\) | 2.89176 | − | 1.24314i | 0.401015 | − | 0.172392i | ||||
\(53\) | 8.02895 | − | 8.02895i | 1.10286 | − | 1.10286i | 0.108797 | − | 0.994064i | \(-0.465300\pi\) |
0.994064 | − | 0.108797i | \(-0.0346999\pi\) | |||||||
\(54\) | −1.34533 | + | 7.00675i | −0.183077 | + | 0.953498i | ||||
\(55\) | 0.920980i | 0.124185i | ||||||||
\(56\) | −2.76252 | + | 0.607051i | −0.369157 | + | 0.0811205i | ||||
\(57\) | 0.121097i | 0.0160397i | ||||||||
\(58\) | 9.29144 | + | 1.78401i | 1.22003 | + | 0.234252i | ||||
\(59\) | 3.27037 | − | 3.27037i | 0.425766 | − | 0.425766i | −0.461417 | − | 0.887183i | \(-0.652659\pi\) |
0.887183 | + | 0.461417i | \(0.152659\pi\) | |||||||
\(60\) | −1.31746 | + | 3.30431i | −0.170084 | + | 0.426585i | ||||
\(61\) | 8.00019 | + | 8.00019i | 1.02432 | + | 1.02432i | 0.999697 | + | 0.0246228i | \(0.00783847\pi\) |
0.0246228 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(62\) | −7.20453 | + | 4.88355i | −0.914977 | + | 0.620212i | ||||
\(63\) | 0.163545 | 0.0206048 | ||||||||
\(64\) | −7.26298 | + | 3.35397i | −0.907872 | + | 0.419247i | ||||
\(65\) | 1.57382 | 0.195209 | ||||||||
\(66\) | 1.91758 | − | 1.29982i | 0.236038 | − | 0.159997i | ||||
\(67\) | −0.200912 | − | 0.200912i | −0.0245453 | − | 0.0245453i | 0.694728 | − | 0.719273i | \(-0.255525\pi\) |
−0.719273 | + | 0.694728i | \(0.755525\pi\) | |||||||
\(68\) | −0.446663 | + | 1.12027i | −0.0541658 | + | 0.135853i | ||||
\(69\) | −4.17996 | + | 4.17996i | −0.503208 | + | 0.503208i | ||||
\(70\) | −1.38884 | − | 0.266666i | −0.165999 | − | 0.0318727i | ||||
\(71\) | − | 1.91971i | − | 0.227828i | −0.993491 | − | 0.113914i | \(-0.963661\pi\) | ||
0.993491 | − | 0.113914i | \(-0.0363388\pi\) | |||||||
\(72\) | 0.451797 | − | 0.0992804i | 0.0532448 | − | 0.0117003i | ||||
\(73\) | − | 7.86605i | − | 0.920652i | −0.887750 | − | 0.460326i | \(-0.847733\pi\) | ||
0.887750 | − | 0.460326i | \(-0.152267\pi\) | |||||||
\(74\) | 1.23006 | − | 6.40638i | 0.142992 | − | 0.744726i | ||||
\(75\) | −1.25769 | + | 1.25769i | −0.145225 | + | 0.145225i | ||||
\(76\) | −0.125099 | + | 0.0537786i | −0.0143498 | + | 0.00616882i | ||||
\(77\) | 0.651231 | + | 0.651231i | 0.0742147 | + | 0.0742147i | ||||
\(78\) | −2.22121 | − | 3.27688i | −0.251503 | − | 0.371033i | ||||
\(79\) | 1.51045 | 0.169939 | 0.0849696 | − | 0.996384i | \(-0.472921\pi\) | ||||
0.0849696 | + | 0.996384i | \(0.472921\pi\) | |||||||
\(80\) | −3.99858 | + | 0.106431i | −0.447055 | + | 0.0118993i | ||||
\(81\) | 9.46389 | 1.05154 | ||||||||
\(82\) | 4.63175 | + | 6.83306i | 0.511491 | + | 0.754585i | ||||
\(83\) | 11.4075 | + | 11.4075i | 1.25214 | + | 1.25214i | 0.954760 | + | 0.297376i | \(0.0961116\pi\) |
0.297376 | + | 0.954760i | \(0.403888\pi\) | |||||||
\(84\) | 1.40492 | + | 3.26809i | 0.153289 | + | 0.356578i | ||||
\(85\) | −0.426397 | + | 0.426397i | −0.0462492 | + | 0.0462492i | ||||
\(86\) | 2.59301 | − | 13.5049i | 0.279612 | − | 1.45627i | ||||
\(87\) | − | 11.8992i | − | 1.27572i | ||||||
\(88\) | 2.19437 | + | 1.40371i | 0.233920 | + | 0.149636i | ||||
\(89\) | − | 1.79530i | − | 0.190301i | −0.995463 | − | 0.0951507i | \(-0.969667\pi\) | ||
0.995463 | − | 0.0951507i | \(-0.0303333\pi\) | |||||||
\(90\) | 0.227139 | + | 0.0436120i | 0.0239426 | + | 0.00459711i | ||||
\(91\) | 1.11286 | − | 1.11286i | 0.116660 | − | 0.116660i | ||||
\(92\) | −6.17440 | − | 2.46179i | −0.643725 | − | 0.256660i | ||||
\(93\) | 7.74036 | + | 7.74036i | 0.802638 | + | 0.802638i | ||||
\(94\) | −6.40626 | + | 4.34245i | −0.660755 | + | 0.447889i | ||||
\(95\) | −0.0680842 | −0.00698529 | ||||||||
\(96\) | 5.86499 | + | 8.17529i | 0.598593 | + | 0.834387i | ||||
\(97\) | 4.28142 | 0.434712 | 0.217356 | − | 0.976092i | \(-0.430257\pi\) | ||||
0.217356 | + | 0.976092i | \(0.430257\pi\) | |||||||
\(98\) | −1.17062 | + | 0.793500i | −0.118251 | + | 0.0801556i | ||||
\(99\) | −0.106506 | − | 0.106506i | −0.0107043 | − | 0.0107043i | ||||
\(100\) | −1.85778 | − | 0.740715i | −0.185778 | − | 0.0740715i | ||||
\(101\) | 1.91367 | − | 1.91367i | 0.190417 | − | 0.190417i | −0.605459 | − | 0.795876i | \(-0.707011\pi\) |
0.795876 | + | 0.605459i | \(0.207011\pi\) | |||||||
\(102\) | 1.48960 | + | 0.286011i | 0.147492 | + | 0.0283194i | ||||
\(103\) | − | 13.2595i | − | 1.30650i | −0.757143 | − | 0.653249i | \(-0.773406\pi\) | ||
0.757143 | − | 0.653249i | \(-0.226594\pi\) | |||||||
\(104\) | 2.39873 | − | 3.74986i | 0.235215 | − | 0.367704i | ||||
\(105\) | 1.77864i | 0.173577i | ||||||||
\(106\) | 3.02790 | − | 15.7698i | 0.294095 | − | 1.53170i | ||||
\(107\) | 1.20430 | − | 1.20430i | 0.116424 | − | 0.116424i | −0.646495 | − | 0.762918i | \(-0.723766\pi\) |
0.762918 | + | 0.646495i | \(0.223766\pi\) | |||||||
\(108\) | 3.98498 | + | 9.26978i | 0.383455 | + | 0.891985i | ||||
\(109\) | 3.16834 | + | 3.16834i | 0.303472 | + | 0.303472i | 0.842371 | − | 0.538898i | \(-0.181159\pi\) |
−0.538898 | + | 0.842371i | \(0.681159\pi\) | |||||||
\(110\) | 0.730798 | + | 1.07812i | 0.0696789 | + | 0.102795i | ||||
\(111\) | −8.20438 | −0.778726 | ||||||||
\(112\) | −2.75217 | + | 2.90268i | −0.260055 | + | 0.274278i | ||||
\(113\) | 11.7295 | 1.10341 | 0.551707 | − | 0.834038i | \(-0.313977\pi\) | ||||
0.551707 | + | 0.834038i | \(0.313977\pi\) | |||||||
\(114\) | 0.0960905 | + | 0.141759i | 0.00899970 | + | 0.0132769i | ||||
\(115\) | −2.35010 | − | 2.35010i | −0.219147 | − | 0.219147i | ||||
\(116\) | 12.2924 | − | 5.28436i | 1.14132 | − | 0.490640i | ||||
\(117\) | −0.182003 | + | 0.182003i | −0.0168262 | + | 0.0168262i | ||||
\(118\) | 1.23333 | − | 6.42341i | 0.113537 | − | 0.591323i | ||||
\(119\) | 0.603016i | 0.0552784i | ||||||||
\(120\) | 1.07972 | + | 4.91351i | 0.0985647 | + | 0.448540i | ||||
\(121\) | 10.1518i | 0.922890i | ||||||||
\(122\) | 15.7134 | + | 3.01705i | 1.42262 | + | 0.273151i | ||||
\(123\) | 7.34125 | − | 7.34125i | 0.661938 | − | 0.661938i | ||||
\(124\) | −4.55869 | + | 11.4336i | −0.409382 | + | 1.02677i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0.191450 | − | 0.129773i | 0.0170557 | − | 0.0115611i | ||||
\(127\) | −0.429799 | −0.0381385 | −0.0190692 | − | 0.999818i | \(-0.506070\pi\) | ||||
−0.0190692 | + | 0.999818i | \(0.506070\pi\) | |||||||
\(128\) | −5.84083 | + | 9.68941i | −0.516261 | + | 0.856431i | ||||
\(129\) | −17.2951 | −1.52275 | ||||||||
\(130\) | 1.84235 | − | 1.24883i | 0.161585 | − | 0.109530i | ||||
\(131\) | 10.1923 | + | 10.1923i | 0.890502 | + | 0.890502i | 0.994570 | − | 0.104068i | \(-0.0331861\pi\) |
−0.104068 | + | 0.994570i | \(0.533186\pi\) | |||||||
\(132\) | 1.21336 | − | 3.04321i | 0.105609 | − | 0.264877i | ||||
\(133\) | −0.0481428 | + | 0.0481428i | −0.00417451 | + | 0.00417451i | ||||
\(134\) | −0.394616 | − | 0.0757684i | −0.0340896 | − | 0.00654539i | ||||
\(135\) | 5.04502i | 0.434206i | ||||||||
\(136\) | 0.366061 | + | 1.66584i | 0.0313895 | + | 0.142845i | ||||
\(137\) | − | 8.88755i | − | 0.759315i | −0.925127 | − | 0.379657i | \(-0.876042\pi\) | ||
0.925127 | − | 0.379657i | \(-0.123958\pi\) | |||||||
\(138\) | −1.57636 | + | 8.20996i | −0.134188 | + | 0.698878i | ||||
\(139\) | 5.64555 | − | 5.64555i | 0.478849 | − | 0.478849i | −0.425914 | − | 0.904764i | \(-0.640047\pi\) |
0.904764 | + | 0.425914i | \(0.140047\pi\) | |||||||
\(140\) | −1.83741 | + | 0.789884i | −0.155290 | + | 0.0667573i | ||||
\(141\) | 6.88271 | + | 6.88271i | 0.579629 | + | 0.579629i | ||||
\(142\) | −1.52329 | − | 2.24726i | −0.127832 | − | 0.188586i | ||||
\(143\) | −1.44946 | −0.121210 | ||||||||
\(144\) | 0.450105 | − | 0.474721i | 0.0375087 | − | 0.0395601i | ||||
\(145\) | 6.69005 | 0.555578 | ||||||||
\(146\) | −6.24172 | − | 9.20818i | −0.516568 | − | 0.762075i | ||||
\(147\) | 1.25769 | + | 1.25769i | 0.103732 | + | 0.103732i | ||||
\(148\) | −3.64353 | − | 8.47550i | −0.299496 | − | 0.696682i | ||||
\(149\) | −14.7096 | + | 14.7096i | −1.20506 | + | 1.20506i | −0.232454 | + | 0.972607i | \(0.574676\pi\) |
−0.972607 | + | 0.232454i | \(0.925324\pi\) | |||||||
\(150\) | −0.474301 | + | 2.47025i | −0.0387265 | + | 0.201695i | ||||
\(151\) | 8.49500i | 0.691313i | 0.938361 | + | 0.345657i | \(0.112344\pi\) | ||||
−0.938361 | + | 0.345657i | \(0.887656\pi\) | |||||||
\(152\) | −0.103770 | + | 0.162220i | −0.00841686 | + | 0.0131578i | ||||
\(153\) | − | 0.0986206i | − | 0.00797300i | ||||||
\(154\) | 1.27910 | + | 0.245594i | 0.103073 | + | 0.0197905i | ||||
\(155\) | −4.35185 | + | 4.35185i | −0.349549 | + | 0.349549i | ||||
\(156\) | −5.20041 | − | 2.07345i | −0.416366 | − | 0.166009i | ||||
\(157\) | −8.79716 | − | 8.79716i | −0.702090 | − | 0.702090i | 0.262769 | − | 0.964859i | \(-0.415364\pi\) |
−0.964859 | + | 0.262769i | \(0.915364\pi\) | |||||||
\(158\) | 1.76817 | − | 1.19854i | 0.140668 | − | 0.0953510i | ||||
\(159\) | −20.1958 | −1.60163 | ||||||||
\(160\) | −4.59638 | + | 3.29747i | −0.363376 | + | 0.260688i | ||||
\(161\) | −3.32354 | −0.261931 | ||||||||
\(162\) | 11.0786 | − | 7.50960i | 0.870420 | − | 0.590010i | ||||
\(163\) | 3.53993 | + | 3.53993i | 0.277269 | + | 0.277269i | 0.832018 | − | 0.554749i | \(-0.187186\pi\) |
−0.554749 | + | 0.832018i | \(0.687186\pi\) | |||||||
\(164\) | 10.8441 | + | 4.32364i | 0.846779 | + | 0.337619i | ||||
\(165\) | 1.15830 | − | 1.15830i | 0.0901738 | − | 0.0901738i | ||||
\(166\) | 22.4057 | + | 4.30203i | 1.73902 | + | 0.333902i | ||||
\(167\) | 17.1739i | 1.32896i | 0.747307 | + | 0.664479i | \(0.231347\pi\) | ||||
−0.747307 | + | 0.664479i | \(0.768653\pi\) | |||||||
\(168\) | 4.23785 | + | 2.71090i | 0.326958 | + | 0.209150i | ||||
\(169\) | − | 10.5231i | − | 0.809468i | ||||||
\(170\) | −0.160804 | + | 0.837496i | −0.0123331 | + | 0.0642330i | ||||
\(171\) | 0.00787353 | − | 0.00787353i | 0.000602104 | − | 0.000602104i | ||||
\(172\) | −7.68069 | − | 17.8667i | −0.585647 | − | 1.36232i | ||||
\(173\) | −11.0510 | − | 11.0510i | −0.840190 | − | 0.840190i | 0.148694 | − | 0.988883i | \(-0.452493\pi\) |
−0.988883 | + | 0.148694i | \(0.952493\pi\) | |||||||
\(174\) | −9.44199 | − | 13.9294i | −0.715795 | − | 1.05599i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 3.68262 | − | 0.0980206i | 0.277588 | − | 0.00738858i | ||||
\(177\) | −8.22620 | −0.618319 | ||||||||
\(178\) | −1.42457 | − | 2.10162i | −0.106776 | − | 0.157523i | ||||
\(179\) | −1.10235 | − | 1.10235i | −0.0823932 | − | 0.0823932i | 0.664709 | − | 0.747102i | \(-0.268556\pi\) |
−0.747102 | + | 0.664709i | \(0.768556\pi\) | |||||||
\(180\) | 0.300500 | − | 0.129182i | 0.0223980 | − | 0.00962865i | ||||
\(181\) | −3.60640 | + | 3.60640i | −0.268062 | + | 0.268062i | −0.828319 | − | 0.560257i | \(-0.810702\pi\) |
0.560257 | + | 0.828319i | \(0.310702\pi\) | |||||||
\(182\) | 0.419685 | − | 2.18580i | 0.0311091 | − | 0.162022i | ||||
\(183\) | − | 20.1235i | − | 1.48757i | ||||||
\(184\) | −9.18132 | + | 2.01755i | −0.676856 | + | 0.148736i | ||||
\(185\) | − | 4.61274i | − | 0.339135i | ||||||
\(186\) | 15.2030 | + | 2.91906i | 1.11474 | + | 0.214036i | ||||
\(187\) | 0.392703 | − | 0.392703i | 0.0287173 | − | 0.0287173i | ||||
\(188\) | −4.05358 | + | 10.1667i | −0.295638 | + | 0.741485i | ||||
\(189\) | 3.56737 | + | 3.56737i | 0.259488 | + | 0.259488i | ||||
\(190\) | −0.0797009 | + | 0.0540248i | −0.00578211 | + | 0.00391937i | ||||
\(191\) | −17.1989 | −1.24447 | −0.622233 | − | 0.782832i | \(-0.713775\pi\) | ||||
−0.622233 | + | 0.782832i | \(0.713775\pi\) | |||||||
\(192\) | 13.3528 | + | 4.91630i | 0.963654 | + | 0.354803i | ||||
\(193\) | −6.12727 | −0.441051 | −0.220525 | − | 0.975381i | \(-0.570777\pi\) | ||||
−0.220525 | + | 0.975381i | \(0.570777\pi\) | |||||||
\(194\) | 5.01193 | − | 3.39731i | 0.359835 | − | 0.243913i | ||||
\(195\) | −1.97938 | − | 1.97938i | −0.141746 | − | 0.141746i | ||||
\(196\) | −0.740715 | + | 1.85778i | −0.0529082 | + | 0.132698i | ||||
\(197\) | −16.2447 | + | 16.2447i | −1.15739 | + | 1.15739i | −0.172352 | + | 0.985035i | \(0.555137\pi\) |
−0.985035 | + | 0.172352i | \(0.944863\pi\) | |||||||
\(198\) | −0.209191 | − | 0.0401658i | −0.0148665 | − | 0.00285446i | ||||
\(199\) | − | 4.47826i | − | 0.317455i | −0.987322 | − | 0.158728i | \(-0.949261\pi\) | ||
0.987322 | − | 0.158728i | \(-0.0507392\pi\) | |||||||
\(200\) | −2.76252 | + | 0.607051i | −0.195339 | + | 0.0429250i | ||||
\(201\) | 0.505368i | 0.0356459i | ||||||||
\(202\) | 0.721687 | − | 3.75868i | 0.0507777 | − | 0.264460i | ||||
\(203\) | 4.73058 | − | 4.73058i | 0.332022 | − | 0.332022i | ||||
\(204\) | 1.97071 | − | 0.847187i | 0.137977 | − | 0.0593149i | ||||
\(205\) | 4.12746 | + | 4.12746i | 0.288274 | + | 0.288274i | ||||
\(206\) | −10.5214 | − | 15.5219i | −0.733062 | − | 1.08146i | ||||
\(207\) | 0.543549 | 0.0377793 | ||||||||
\(208\) | −0.167503 | − | 6.29307i | −0.0116143 | − | 0.436346i | ||||
\(209\) | 0.0627042 | 0.00433734 | ||||||||
\(210\) | 1.41135 | + | 2.08211i | 0.0973923 | + | 0.143679i | ||||
\(211\) | −6.10477 | − | 6.10477i | −0.420270 | − | 0.420270i | 0.465027 | − | 0.885297i | \(-0.346045\pi\) |
−0.885297 | + | 0.465027i | \(0.846045\pi\) | |||||||
\(212\) | −8.96885 | − | 20.8632i | −0.615983 | − | 1.43289i | ||||
\(213\) | −2.41439 | + | 2.41439i | −0.165431 | + | 0.165431i | ||||
\(214\) | 0.454167 | − | 2.36538i | 0.0310462 | − | 0.161694i | ||||
\(215\) | − | 9.72383i | − | 0.663159i | ||||||
\(216\) | 12.0205 | + | 7.68933i | 0.817890 | + | 0.523193i | ||||
\(217\) | 6.15445i | 0.417791i | ||||||||
\(218\) | 6.22302 | + | 1.19485i | 0.421476 | + | 0.0809257i | ||||
\(219\) | −9.89302 | + | 9.89302i | −0.668508 | + | 0.668508i | ||||
\(220\) | 1.71098 | + | 0.682184i | 0.115354 | + | 0.0459928i | ||||
\(221\) | −0.671074 | − | 0.671074i | −0.0451413 | − | 0.0451413i | ||||
\(222\) | −9.60424 | + | 6.51018i | −0.644594 | + | 0.436935i | ||||
\(223\) | −14.9388 | −1.00038 | −0.500188 | − | 0.865917i | \(-0.666736\pi\) | ||||
−0.500188 | + | 0.865917i | \(0.666736\pi\) | |||||||
\(224\) | −0.918470 | + | 5.58179i | −0.0613678 | + | 0.372949i | ||||
\(225\) | 0.163545 | 0.0109030 | ||||||||
\(226\) | 13.7308 | − | 9.30733i | 0.913357 | − | 0.619114i | ||||
\(227\) | 0.226203 | + | 0.226203i | 0.0150136 | + | 0.0150136i | 0.714574 | − | 0.699560i | \(-0.246621\pi\) |
−0.699560 | + | 0.714574i | \(0.746621\pi\) | |||||||
\(228\) | 0.224971 | + | 0.0896983i | 0.0148991 | + | 0.00594041i | ||||
\(229\) | −17.7070 | + | 17.7070i | −1.17011 | + | 1.17011i | −0.187929 | + | 0.982183i | \(0.560177\pi\) |
−0.982183 | + | 0.187929i | \(0.939823\pi\) | |||||||
\(230\) | −4.61588 | − | 0.886273i | −0.304362 | − | 0.0584391i | ||||
\(231\) | − | 1.63809i | − | 0.107778i | ||||||
\(232\) | 10.1966 | − | 15.9400i | 0.669439 | − | 1.04651i | ||||
\(233\) | 20.3846i | 1.33544i | 0.744412 | + | 0.667720i | \(0.232730\pi\) | ||||
−0.744412 | + | 0.667720i | \(0.767270\pi\) | |||||||
\(234\) | −0.0686376 | + | 0.357477i | −0.00448698 | + | 0.0233690i | ||||
\(235\) | −3.86966 | + | 3.86966i | −0.252429 | + | 0.252429i | ||||
\(236\) | −3.65322 | − | 8.49804i | −0.237804 | − | 0.553175i | ||||
\(237\) | −1.89967 | − | 1.89967i | −0.123397 | − | 0.123397i | ||||
\(238\) | 0.478494 | + | 0.705905i | 0.0310161 | + | 0.0457570i | ||||
\(239\) | 27.5857 | 1.78437 | 0.892184 | − | 0.451673i | \(-0.149172\pi\) | ||||
0.892184 | + | 0.451673i | \(0.149172\pi\) | |||||||
\(240\) | 5.16282 | + | 4.89510i | 0.333258 | + | 0.315978i | ||||
\(241\) | 2.38105 | 0.153377 | 0.0766885 | − | 0.997055i | \(-0.475565\pi\) | ||||
0.0766885 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(242\) | 8.05545 | + | 11.8839i | 0.517824 | + | 0.763927i | ||||
\(243\) | −1.20049 | − | 1.20049i | −0.0770117 | − | 0.0770117i | ||||
\(244\) | 20.7884 | − | 8.93673i | 1.33084 | − | 0.572115i | ||||
\(245\) | −0.707107 | + | 0.707107i | −0.0451754 | + | 0.0451754i | ||||
\(246\) | 2.76855 | − | 14.4191i | 0.176516 | − | 0.919330i | ||||
\(247\) | − | 0.107152i | − | 0.00681795i | ||||||
\(248\) | 3.73606 | + | 17.0017i | 0.237240 | + | 1.07961i | ||||
\(249\) | − | 28.6941i | − | 1.81842i | ||||||
\(250\) | −1.38884 | − | 0.266666i | −0.0878382 | − | 0.0168654i | ||||
\(251\) | −9.49501 | + | 9.49501i | −0.599320 | + | 0.599320i | −0.940132 | − | 0.340812i | \(-0.889298\pi\) |
0.340812 | + | 0.940132i | \(0.389298\pi\) | |||||||
\(252\) | 0.121141 | − | 0.303831i | 0.00763114 | − | 0.0191396i | ||||
\(253\) | 2.16439 | + | 2.16439i | 0.136074 | + | 0.136074i | ||||
\(254\) | −0.503132 | + | 0.341046i | −0.0315693 | + | 0.0213991i | ||||
\(255\) | 1.07255 | 0.0671655 | ||||||||
\(256\) | 0.851144 | + | 15.9773i | 0.0531965 | + | 0.998584i | ||||
\(257\) | 17.5034 | 1.09183 | 0.545915 | − | 0.837841i | \(-0.316182\pi\) | ||||
0.545915 | + | 0.837841i | \(0.316182\pi\) | |||||||
\(258\) | −20.2461 | + | 13.7237i | −1.26047 | + | 0.854400i | ||||
\(259\) | −3.26170 | − | 3.26170i | −0.202672 | − | 0.202672i | ||||
\(260\) | 1.16575 | − | 2.92382i | 0.0722970 | − | 0.181327i | ||||
\(261\) | −0.773665 | + | 0.773665i | −0.0478886 | + | 0.0478886i | ||||
\(262\) | 20.0189 | + | 3.84373i | 1.23677 | + | 0.237466i | ||||
\(263\) | 29.3793i | 1.81160i | 0.423703 | + | 0.905801i | \(0.360730\pi\) | ||||
−0.423703 | + | 0.905801i | \(0.639270\pi\) | |||||||
\(264\) | −0.994403 | − | 4.52524i | −0.0612012 | − | 0.278510i | ||||
\(265\) | − | 11.3547i | − | 0.697511i | ||||||
\(266\) | −0.0181557 | + | 0.0945583i | −0.00111320 | + | 0.00579774i | ||||
\(267\) | −2.25792 | + | 2.25792i | −0.138183 | + | 0.138183i | ||||
\(268\) | −0.522068 | + | 0.224432i | −0.0318904 | + | 0.0137093i | ||||
\(269\) | 10.4537 | + | 10.4537i | 0.637372 | + | 0.637372i | 0.949906 | − | 0.312534i | \(-0.101178\pi\) |
−0.312534 | + | 0.949906i | \(0.601178\pi\) | |||||||
\(270\) | 4.00322 | + | 5.90581i | 0.243628 | + | 0.359416i | ||||
\(271\) | −20.1834 | −1.22605 | −0.613027 | − | 0.790062i | \(-0.710048\pi\) | ||||
−0.613027 | + | 0.790062i | \(0.710048\pi\) | |||||||
\(272\) | 1.75037 | + | 1.65960i | 0.106132 | + | 0.100628i | ||||
\(273\) | −2.79926 | −0.169419 | ||||||||
\(274\) | −7.05227 | − | 10.4040i | −0.426043 | − | 0.628527i | ||||
\(275\) | 0.651231 | + | 0.651231i | 0.0392707 | + | 0.0392707i | ||||
\(276\) | 4.66929 | + | 10.8616i | 0.281058 | + | 0.653792i | ||||
\(277\) | 0.340772 | − | 0.340772i | 0.0204750 | − | 0.0204750i | −0.696795 | − | 0.717270i | \(-0.745391\pi\) |
0.717270 | + | 0.696795i | \(0.245391\pi\) | |||||||
\(278\) | 2.12906 | − | 11.0886i | 0.127693 | − | 0.665047i | ||||
\(279\) | − | 1.00653i | − | 0.0602595i | ||||||
\(280\) | −1.52414 | + | 2.38264i | −0.0910850 | + | 0.142390i | ||||
\(281\) | − | 11.4612i | − | 0.683719i | −0.939751 | − | 0.341860i | \(-0.888943\pi\) | ||
0.939751 | − | 0.341860i | \(-0.111057\pi\) | |||||||
\(282\) | 13.5185 | + | 2.59562i | 0.805015 | + | 0.154567i | ||||
\(283\) | 17.5855 | − | 17.5855i | 1.04535 | − | 1.04535i | 0.0464283 | − | 0.998922i | \(-0.485216\pi\) |
0.998922 | − | 0.0464283i | \(-0.0147839\pi\) | |||||||
\(284\) | −3.56640 | − | 1.42196i | −0.211627 | − | 0.0843776i | ||||
\(285\) | 0.0856285 | + | 0.0856285i | 0.00507219 | + | 0.00507219i | ||||
\(286\) | −1.69677 | + | 1.15015i | −0.100332 | + | 0.0680096i | ||||
\(287\) | 5.83711 | 0.344554 | ||||||||
\(288\) | 0.150212 | − | 0.912877i | 0.00885130 | − | 0.0537918i | ||||
\(289\) | −16.6364 | −0.978610 | ||||||||
\(290\) | 7.83152 | − | 5.30856i | 0.459883 | − | 0.311729i | ||||
\(291\) | −5.38468 | − | 5.38468i | −0.315656 | − | 0.315656i | ||||
\(292\) | −14.6134 | − | 5.82650i | −0.855184 | − | 0.340970i | ||||
\(293\) | −10.0898 | + | 10.0898i | −0.589455 | + | 0.589455i | −0.937484 | − | 0.348029i | \(-0.886851\pi\) |
0.348029 | + | 0.937484i | \(0.386851\pi\) | |||||||
\(294\) | 2.47025 | + | 0.474301i | 0.144068 | + | 0.0276618i | ||||
\(295\) | − | 4.62501i | − | 0.269278i | ||||||
\(296\) | −10.9905 | − | 7.03048i | −0.638810 | − | 0.408638i | ||||
\(297\) | − | 4.64636i | − | 0.269609i | ||||||
\(298\) | −5.54734 | + | 28.8916i | −0.321349 | + | 1.67364i | ||||
\(299\) | 3.69864 | − | 3.69864i | 0.213898 | − | 0.213898i | ||||
\(300\) | 1.40492 | + | 3.26809i | 0.0811128 | + | 0.188683i | ||||
\(301\) | −6.87578 | − | 6.87578i | −0.396314 | − | 0.396314i | ||||
\(302\) | 6.74079 | + | 9.94444i | 0.387889 | + | 0.572238i | ||||
\(303\) | −4.81358 | −0.276533 | ||||||||
\(304\) | 0.00724625 | + | 0.272240i | 0.000415601 | + | 0.0156140i | ||||
\(305\) | 11.3140 | 0.647837 | ||||||||
\(306\) | −0.0782555 | − | 0.115448i | −0.00447357 | − | 0.00659969i | ||||
\(307\) | 18.8661 | + | 18.8661i | 1.07675 | + | 1.07675i | 0.996799 | + | 0.0799466i | \(0.0254750\pi\) |
0.0799466 | + | 0.996799i | \(0.474525\pi\) | |||||||
\(308\) | 1.69222 | − | 0.727467i | 0.0964232 | − | 0.0414513i | ||||
\(309\) | −16.6763 | + | 16.6763i | −0.948680 | + | 0.948680i | ||||
\(310\) | −1.64118 | + | 8.54757i | −0.0932128 | + | 0.485469i | ||||
\(311\) | 0.0904960i | 0.00513156i | 0.999997 | + | 0.00256578i | \(0.000816714\pi\) | ||||
−0.999997 | + | 0.00256578i | \(0.999183\pi\) | |||||||
\(312\) | −7.73300 | + | 1.69929i | −0.437795 | + | 0.0962035i | ||||
\(313\) | − | 26.3979i | − | 1.49210i | −0.665892 | − | 0.746048i | \(-0.731949\pi\) | ||
0.665892 | − | 0.746048i | \(-0.268051\pi\) | |||||||
\(314\) | −17.2787 | − | 3.31761i | −0.975094 | − | 0.187223i | ||||
\(315\) | 0.115644 | − | 0.115644i | 0.00651581 | − | 0.00651581i | ||||
\(316\) | 1.11881 | − | 2.80609i | 0.0629382 | − | 0.157855i | ||||
\(317\) | 2.76566 | + | 2.76566i | 0.155335 | + | 0.155335i | 0.780496 | − | 0.625161i | \(-0.214967\pi\) |
−0.625161 | + | 0.780496i | \(0.714967\pi\) | |||||||
\(318\) | −23.6416 | + | 16.0254i | −1.32576 | + | 0.898658i | ||||
\(319\) | −6.16140 | −0.344972 | ||||||||
\(320\) | −2.76408 | + | 7.50732i | −0.154517 | + | 0.419672i | ||||
\(321\) | −3.02925 | −0.169076 | ||||||||
\(322\) | −3.89061 | + | 2.63723i | −0.216815 | + | 0.146967i | ||||
\(323\) | 0.0290309 | + | 0.0290309i | 0.00161532 | + | 0.00161532i | ||||
\(324\) | 7.01004 | − | 17.5818i | 0.389447 | − | 0.976767i | ||||
\(325\) | 1.11286 | − | 1.11286i | 0.0617305 | − | 0.0617305i | ||||
\(326\) | 6.95287 | + | 1.33499i | 0.385084 | + | 0.0739382i | ||||
\(327\) | − | 7.96956i | − | 0.440718i | ||||||
\(328\) | 16.1251 | − | 3.54342i | 0.890361 | − | 0.195653i | ||||
\(329\) | 5.47252i | 0.301710i | ||||||||
\(330\) | 0.436822 | − | 2.27505i | 0.0240463 | − | 0.125237i | ||||
\(331\) | 7.19158 | − | 7.19158i | 0.395285 | − | 0.395285i | −0.481281 | − | 0.876566i | \(-0.659828\pi\) |
0.876566 | + | 0.481281i | \(0.159828\pi\) | |||||||
\(332\) | 29.6423 | − | 12.7429i | 1.62683 | − | 0.699358i | ||||
\(333\) | 0.533436 | + | 0.533436i | 0.0292321 | + | 0.0292321i | ||||
\(334\) | 13.6275 | + | 20.1042i | 0.745665 | + | 1.10005i | ||||
\(335\) | −0.284132 | −0.0155238 | ||||||||
\(336\) | 7.11202 | − | 0.189301i | 0.387993 | − | 0.0103272i | ||||
\(337\) | −0.126565 | −0.00689444 | −0.00344722 | − | 0.999994i | \(-0.501097\pi\) | ||||
−0.00344722 | + | 0.999994i | \(0.501097\pi\) | |||||||
\(338\) | −8.35007 | − | 12.3186i | −0.454184 | − | 0.670041i | ||||
\(339\) | −14.7520 | − | 14.7520i | −0.801217 | − | 0.801217i | ||||
\(340\) | 0.476313 | + | 1.10799i | 0.0258317 | + | 0.0600892i | ||||
\(341\) | 4.00797 | − | 4.00797i | 0.217044 | − | 0.217044i | ||||
\(342\) | 0.00296929 | − | 0.0154646i | 0.000160561 | − | 0.000836229i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −23.1684 | − | 14.8205i | −1.24916 | − | 0.799068i | ||||
\(345\) | 5.91136i | 0.318257i | ||||||||
\(346\) | −21.7055 | − | 4.16757i | −1.16689 | − | 0.224050i | ||||
\(347\) | −25.0440 | + | 25.0440i | −1.34443 | + | 1.34443i | −0.452846 | + | 0.891589i | \(0.649591\pi\) |
−0.891589 | + | 0.452846i | \(0.850409\pi\) | |||||||
\(348\) | −22.1060 | − | 8.81388i | −1.18501 | − | 0.472474i | ||||
\(349\) | −3.85172 | − | 3.85172i | −0.206178 | − | 0.206178i | 0.596463 | − | 0.802641i | \(-0.296572\pi\) |
−0.802641 | + | 0.596463i | \(0.796572\pi\) | |||||||
\(350\) | −1.17062 | + | 0.793500i | −0.0625724 | + | 0.0424144i | ||||
\(351\) | −7.93997 | −0.423804 | ||||||||
\(352\) | 4.23318 | − | 3.03690i | 0.225629 | − | 0.161867i | ||||
\(353\) | −3.43843 | −0.183009 | −0.0915046 | − | 0.995805i | \(-0.529168\pi\) | ||||
−0.0915046 | + | 0.995805i | \(0.529168\pi\) | |||||||
\(354\) | −9.62978 | + | 6.52749i | −0.511817 | + | 0.346932i | ||||
\(355\) | −1.35744 | − | 1.35744i | −0.0720454 | − | 0.0720454i | ||||
\(356\) | −3.33527 | − | 1.32981i | −0.176769 | − | 0.0704795i | ||||
\(357\) | 0.758405 | − | 0.758405i | 0.0401390 | − | 0.0401390i | ||||
\(358\) | −2.16514 | − | 0.415720i | −0.114431 | − | 0.0219715i | ||||
\(359\) | 31.0991i | 1.64135i | 0.571396 | + | 0.820675i | \(0.306402\pi\) | ||||
−0.571396 | + | 0.820675i | \(0.693598\pi\) | |||||||
\(360\) | 0.249267 | − | 0.389670i | 0.0131375 | − | 0.0205374i | ||||
\(361\) | − | 18.9954i | − | 0.999756i | ||||||
\(362\) | −1.36006 | + | 7.08342i | −0.0714829 | + | 0.372296i | ||||
\(363\) | 12.7678 | − | 12.7678i | 0.670134 | − | 0.670134i | ||||
\(364\) | −1.24314 | − | 2.89176i | −0.0651581 | − | 0.151570i | ||||
\(365\) | −5.56214 | − | 5.56214i | −0.291136 | − | 0.291136i | ||||
\(366\) | −15.9680 | − | 23.5570i | −0.834659 | − | 1.23134i | ||||
\(367\) | 18.1151 | 0.945599 | 0.472799 | − | 0.881170i | \(-0.343244\pi\) | ||||
0.472799 | + | 0.881170i | \(0.343244\pi\) | |||||||
\(368\) | −9.14693 | + | 9.64717i | −0.476817 | + | 0.502894i | ||||
\(369\) | −0.954634 | −0.0496962 | ||||||||
\(370\) | −3.66021 | − | 5.39978i | −0.190285 | − | 0.280721i | ||||
\(371\) | −8.02895 | − | 8.02895i | −0.416842 | − | 0.416842i | ||||
\(372\) | 20.1133 | − | 8.64647i | 1.04282 | − | 0.448299i | ||||
\(373\) | 16.0111 | − | 16.0111i | 0.829022 | − | 0.829022i | −0.158360 | − | 0.987381i | \(-0.550621\pi\) |
0.987381 | + | 0.158360i | \(0.0506206\pi\) | |||||||
\(374\) | 0.148097 | − | 0.771317i | 0.00765792 | − | 0.0398839i | ||||
\(375\) | 1.77864i | 0.0918484i | ||||||||
\(376\) | 3.32210 | + | 15.1179i | 0.171324 | + | 0.779648i | ||||
\(377\) | 10.5290i | 0.542269i | ||||||||
\(378\) | 7.00675 | + | 1.34533i | 0.360388 | + | 0.0691965i | ||||
\(379\) | 15.6288 | − | 15.6288i | 0.802798 | − | 0.802798i | −0.180734 | − | 0.983532i | \(-0.557847\pi\) |
0.983532 | + | 0.180734i | \(0.0578473\pi\) | |||||||
\(380\) | −0.0504309 | + | 0.126485i | −0.00258705 | + | 0.00648856i | ||||
\(381\) | 0.540552 | + | 0.540552i | 0.0276933 | + | 0.0276933i | ||||
\(382\) | −20.1334 | + | 13.6473i | −1.03011 | + | 0.698257i | ||||
\(383\) | −18.0295 | −0.921264 | −0.460632 | − | 0.887591i | \(-0.652377\pi\) | ||||
−0.460632 | + | 0.887591i | \(0.652377\pi\) | |||||||
\(384\) | 19.5322 | − | 4.84031i | 0.996746 | − | 0.247006i | ||||
\(385\) | 0.920980 | 0.0469375 | ||||||||
\(386\) | −7.17272 | + | 4.86199i | −0.365082 | + | 0.247469i | ||||
\(387\) | 1.12450 | + | 1.12450i | 0.0571617 | + | 0.0571617i | ||||
\(388\) | 3.17131 | − | 7.95393i | 0.160999 | − | 0.403800i | ||||
\(389\) | 4.59304 | − | 4.59304i | 0.232876 | − | 0.232876i | −0.581016 | − | 0.813892i | \(-0.697345\pi\) |
0.813892 | + | 0.581016i | \(0.197345\pi\) | |||||||
\(390\) | −3.88774 | − | 0.746467i | −0.196863 | − | 0.0377988i | ||||
\(391\) | 2.00415i | 0.101354i | ||||||||
\(392\) | 0.607051 | + | 2.76252i | 0.0306607 | + | 0.139528i | ||||
\(393\) | − | 25.6373i | − | 1.29323i | ||||||
\(394\) | −6.12624 | + | 31.9066i | −0.308636 | + | 1.60743i | ||||
\(395\) | 1.06805 | − | 1.06805i | 0.0537395 | − | 0.0537395i | ||||
\(396\) | −0.276755 | + | 0.118974i | −0.0139075 | + | 0.00597867i | ||||
\(397\) | −16.6604 | − | 16.6604i | −0.836163 | − | 0.836163i | 0.152189 | − | 0.988351i | \(-0.451368\pi\) |
−0.988351 | + | 0.152189i | \(0.951368\pi\) | |||||||
\(398\) | −3.55350 | − | 5.24235i | −0.178121 | − | 0.262775i | ||||
\(399\) | 0.121097 | 0.00606243 | ||||||||
\(400\) | −2.75217 | + | 2.90268i | −0.137608 | + | 0.145134i | ||||
\(401\) | 23.9835 | 1.19768 | 0.598839 | − | 0.800869i | \(-0.295629\pi\) | ||||
0.598839 | + | 0.800869i | \(0.295629\pi\) | |||||||
\(402\) | 0.401010 | + | 0.591595i | 0.0200005 | + | 0.0295061i | ||||
\(403\) | −6.84905 | − | 6.84905i | −0.341175 | − | 0.341175i | ||||
\(404\) | −2.13769 | − | 4.97265i | −0.106354 | − | 0.247399i | ||||
\(405\) | 6.69198 | − | 6.69198i | 0.332527 | − | 0.332527i | ||||
\(406\) | 1.78401 | − | 9.29144i | 0.0885388 | − | 0.461126i | ||||
\(407\) | 4.24824i | 0.210578i | ||||||||
\(408\) | 1.63471 | − | 2.55550i | 0.0809304 | − | 0.126516i | ||||
\(409\) | − | 19.8597i | − | 0.982000i | −0.871160 | − | 0.491000i | \(-0.836631\pi\) | ||
0.871160 | − | 0.491000i | \(-0.163369\pi\) | |||||||
\(410\) | 8.10684 | + | 1.55656i | 0.400368 | + | 0.0768729i | ||||
\(411\) | −11.1777 | + | 11.1777i | −0.551357 | + | 0.551357i | ||||
\(412\) | −24.6332 | − | 9.82151i | −1.21359 | − | 0.483871i | ||||
\(413\) | −3.27037 | − | 3.27037i | −0.160925 | − | 0.160925i | ||||
\(414\) | 0.636291 | − | 0.431307i | 0.0312720 | − | 0.0211976i | ||||
\(415\) | 16.1327 | 0.791921 | ||||||||
\(416\) | −5.18963 | − | 7.23389i | −0.254443 | − | 0.354671i | ||||
\(417\) | −14.2007 | −0.695409 | ||||||||
\(418\) | 0.0734029 | − | 0.0497558i | 0.00359025 | − | 0.00243363i | ||||
\(419\) | 5.63336 | + | 5.63336i | 0.275208 | + | 0.275208i | 0.831192 | − | 0.555985i | \(-0.187659\pi\) |
−0.555985 | + | 0.831192i | \(0.687659\pi\) | |||||||
\(420\) | 3.30431 | + | 1.31746i | 0.161234 | + | 0.0642855i | ||||
\(421\) | −14.3170 | + | 14.3170i | −0.697768 | + | 0.697768i | −0.963929 | − | 0.266161i | \(-0.914245\pi\) |
0.266161 | + | 0.963929i | \(0.414245\pi\) | |||||||
\(422\) | −11.9905 | − | 2.30225i | −0.583690 | − | 0.112072i | ||||
\(423\) | − | 0.895006i | − | 0.0435167i | ||||||
\(424\) | −27.0541 | − | 17.3061i | −1.31386 | − | 0.840459i | ||||
\(425\) | 0.603016i | 0.0292506i | ||||||||
\(426\) | −0.910521 | + | 4.74216i | −0.0441149 | + | 0.229758i | ||||
\(427\) | 8.00019 | − | 8.00019i | 0.387156 | − | 0.387156i | ||||
\(428\) | −1.34527 | − | 3.12935i | −0.0650263 | − | 0.151263i | ||||
\(429\) | 1.82297 | + | 1.82297i | 0.0880136 | + | 0.0880136i | ||||
\(430\) | −7.71586 | − | 11.3829i | −0.372092 | − | 0.548934i | ||||
\(431\) | −27.8850 | −1.34317 | −0.671585 | − | 0.740927i | \(-0.734386\pi\) | ||||
−0.671585 | + | 0.740927i | \(0.734386\pi\) | |||||||
\(432\) | 20.1729 | − | 0.536945i | 0.970571 | − | 0.0258338i | ||||
\(433\) | −11.7286 | −0.563640 | −0.281820 | − | 0.959467i | \(-0.590938\pi\) | ||||
−0.281820 | + | 0.959467i | \(0.590938\pi\) | |||||||
\(434\) | 4.88355 | + | 7.20453i | 0.234418 | + | 0.345829i | ||||
\(435\) | −8.41398 | − | 8.41398i | −0.403419 | − | 0.403419i | ||||
\(436\) | 8.23292 | − | 3.53924i | 0.394286 | − | 0.169499i | ||||
\(437\) | −0.160004 | + | 0.160004i | −0.00765404 | + | 0.00765404i | ||||
\(438\) | −3.73088 | + | 19.4311i | −0.178268 | + | 0.928454i | ||||
\(439\) | 0.485358i | 0.0231649i | 0.999933 | + | 0.0115824i | \(0.00368688\pi\) | ||||
−0.999933 | + | 0.0115824i | \(0.996313\pi\) | |||||||
\(440\) | 2.54422 | − | 0.559082i | 0.121291 | − | 0.0266532i | ||||
\(441\) | − | 0.163545i | − | 0.00778788i | ||||||
\(442\) | −1.31807 | − | 0.253077i | −0.0626943 | − | 0.0120376i | ||||
\(443\) | −3.09351 | + | 3.09351i | −0.146977 | + | 0.146977i | −0.776766 | − | 0.629789i | \(-0.783141\pi\) |
0.629789 | + | 0.776766i | \(0.283141\pi\) | |||||||
\(444\) | −6.07711 | + | 15.2419i | −0.288407 | + | 0.723350i | ||||
\(445\) | −1.26947 | − | 1.26947i | −0.0601786 | − | 0.0601786i | ||||
\(446\) | −17.4877 | + | 11.8540i | −0.828067 | + | 0.561301i | ||||
\(447\) | 37.0002 | 1.75005 | ||||||||
\(448\) | 3.35397 | + | 7.26298i | 0.158460 | + | 0.343144i | ||||
\(449\) | 20.5596 | 0.970268 | 0.485134 | − | 0.874440i | \(-0.338771\pi\) | ||||
0.485134 | + | 0.874440i | \(0.338771\pi\) | |||||||
\(450\) | 0.191450 | − | 0.129773i | 0.00902504 | − | 0.00611758i | ||||
\(451\) | −3.80131 | − | 3.80131i | −0.178997 | − | 0.178997i | ||||
\(452\) | 8.68818 | − | 21.7907i | 0.408658 | − | 1.02495i | ||||
\(453\) | 10.6840 | − | 10.6840i | 0.501980 | − | 0.501980i | ||||
\(454\) | 0.444291 | + | 0.0853063i | 0.0208516 | + | 0.00400362i | ||||
\(455\) | − | 1.57382i | − | 0.0737820i | ||||||
\(456\) | 0.334532 | − | 0.0735120i | 0.0156659 | − | 0.00344251i | ||||
\(457\) | 31.1867i | 1.45885i | 0.684060 | + | 0.729425i | \(0.260212\pi\) | ||||
−0.684060 | + | 0.729425i | \(0.739788\pi\) | |||||||
\(458\) | −6.67770 | + | 34.7787i | −0.312029 | + | 1.62510i | ||||
\(459\) | 2.15118 | − | 2.15118i | 0.100409 | − | 0.100409i | ||||
\(460\) | −6.10671 | + | 2.62521i | −0.284727 | + | 0.122401i | ||||
\(461\) | −9.42653 | − | 9.42653i | −0.439037 | − | 0.439037i | 0.452651 | − | 0.891688i | \(-0.350478\pi\) |
−0.891688 | + | 0.452651i | \(0.850478\pi\) | |||||||
\(462\) | −1.29982 | − | 1.91758i | −0.0604733 | − | 0.0892141i | ||||
\(463\) | 15.1464 | 0.703914 | 0.351957 | − | 0.936016i | \(-0.385516\pi\) | ||||
0.351957 | + | 0.936016i | \(0.385516\pi\) | |||||||
\(464\) | −0.712027 | − | 26.7507i | −0.0330550 | − | 1.24187i | ||||
\(465\) | 10.9465 | 0.507633 | ||||||||
\(466\) | 16.1752 | + | 23.8627i | 0.749302 | + | 1.10542i | ||||
\(467\) | 22.3279 | + | 22.3279i | 1.03321 | + | 1.03321i | 0.999429 | + | 0.0337836i | \(0.0107557\pi\) |
0.0337836 | + | 0.999429i | \(0.489244\pi\) | |||||||
\(468\) | 0.203310 | + | 0.472935i | 0.00939799 | + | 0.0218614i | ||||
\(469\) | −0.200912 | + | 0.200912i | −0.00927725 | + | 0.00927725i | ||||
\(470\) | −1.45933 | + | 7.60048i | −0.0673141 | + | 0.350584i | ||||
\(471\) | 22.1281i | 1.01961i | ||||||||
\(472\) | −11.0197 | − | 7.04917i | −0.507224 | − | 0.324464i | ||||
\(473\) | 8.95545i | 0.411772i | ||||||||
\(474\) | −3.73119 | − | 0.716409i | −0.171379 | − | 0.0329058i | ||||
\(475\) | −0.0481428 | + | 0.0481428i | −0.00220894 | + | 0.00220894i | ||||
\(476\) | 1.12027 | + | 0.446663i | 0.0513475 | + | 0.0204728i | ||||
\(477\) | 1.31310 | + | 1.31310i | 0.0601227 | + | 0.0601227i | ||||
\(478\) | 32.2924 | − | 21.8892i | 1.47702 | − | 1.00119i | ||||
\(479\) | 21.3820 | 0.976970 | 0.488485 | − | 0.872572i | \(-0.337550\pi\) | ||||
0.488485 | + | 0.872572i | \(0.337550\pi\) | |||||||
\(480\) | 9.92798 | + | 1.63362i | 0.453148 | + | 0.0745644i | ||||
\(481\) | 7.25964 | 0.331011 | ||||||||
\(482\) | 2.78731 | − | 1.88936i | 0.126959 | − | 0.0860582i | ||||
\(483\) | 4.17996 | + | 4.17996i | 0.190195 | + | 0.190195i | ||||
\(484\) | 18.8598 | + | 7.51958i | 0.857263 | + | 0.341799i | ||||
\(485\) | 3.02742 | − | 3.02742i | 0.137468 | − | 0.137468i | ||||
\(486\) | −2.35792 | − | 0.452733i | −0.106957 | − | 0.0205364i | ||||
\(487\) | 10.1750i | 0.461075i | 0.973063 | + | 0.230538i | \(0.0740485\pi\) | ||||
−0.973063 | + | 0.230538i | \(0.925952\pi\) | |||||||
\(488\) | 17.2441 | − | 26.9572i | 0.780605 | − | 1.22029i | ||||
\(489\) | − | 8.90425i | − | 0.402664i | ||||||
\(490\) | −0.266666 | + | 1.38884i | −0.0120467 | + | 0.0627416i | ||||
\(491\) | −11.1601 | + | 11.1601i | −0.503648 | + | 0.503648i | −0.912569 | − | 0.408922i | \(-0.865905\pi\) |
0.408922 | + | 0.912569i | \(0.365905\pi\) | |||||||
\(492\) | −8.20065 | − | 19.0762i | −0.369714 | − | 0.860021i | ||||
\(493\) | −2.85262 | − | 2.85262i | −0.128475 | − | 0.128475i | ||||
\(494\) | −0.0850255 | − | 0.125435i | −0.00382548 | − | 0.00564359i | ||||
\(495\) | −0.150622 | −0.00676996 | ||||||||
\(496\) | 17.8644 | + | 16.9381i | 0.802136 | + | 0.760542i | ||||
\(497\) | −1.91971 | −0.0861108 | ||||||||
\(498\) | −22.7688 | − | 33.5900i | −1.02029 | − | 1.50520i | ||||
\(499\) | 24.2041 | + | 24.2041i | 1.08353 | + | 1.08353i | 0.996178 | + | 0.0873482i | \(0.0278393\pi\) |
0.0873482 | + | 0.996178i | \(0.472161\pi\) | |||||||
\(500\) | −1.83741 | + | 0.789884i | −0.0821716 | + | 0.0353247i | ||||
\(501\) | 21.5994 | − | 21.5994i | 0.964990 | − | 0.964990i | ||||
\(502\) | −3.58078 | + | 18.6494i | −0.159818 | + | 0.832362i | ||||
\(503\) | − | 11.0233i | − | 0.491503i | −0.969333 | − | 0.245751i | \(-0.920965\pi\) | ||
0.969333 | − | 0.245751i | \(-0.0790346\pi\) | |||||||
\(504\) | −0.0992804 | − | 0.451797i | −0.00442230 | − | 0.0201246i | ||||
\(505\) | − | 2.70634i | − | 0.120430i | ||||||
\(506\) | 4.25113 | + | 0.816240i | 0.188986 | + | 0.0362863i | ||||
\(507\) | −13.2347 | + | 13.2347i | −0.587775 | + | 0.587775i | ||||
\(508\) | −0.318358 | + | 0.798472i | −0.0141249 | + | 0.0354264i | ||||
\(509\) | 3.80620 | + | 3.80620i | 0.168707 | + | 0.168707i | 0.786411 | − | 0.617704i | \(-0.211937\pi\) |
−0.617704 | + | 0.786411i | \(0.711937\pi\) | |||||||
\(510\) | 1.25555 | − | 0.851066i | 0.0555966 | − | 0.0376858i | ||||
\(511\) | −7.86605 | −0.347974 | ||||||||
\(512\) | 13.6744 | + | 18.0281i | 0.604329 | + | 0.796735i | ||||
\(513\) | 0.343486 | 0.0151653 | ||||||||
\(514\) | 20.4898 | − | 13.8889i | 0.903767 | − | 0.612614i | ||||
\(515\) | −9.37588 | − | 9.37588i | −0.413151 | − | 0.413151i | ||||
\(516\) | −12.8108 | + | 32.1306i | −0.563963 | + | 1.41447i | ||||
\(517\) | 3.56388 | − | 3.56388i | 0.156739 | − | 0.156739i | ||||
\(518\) | −6.40638 | − | 1.23006i | −0.281480 | − | 0.0540457i | ||||
\(519\) | 27.7973i | 1.22017i | ||||||||
\(520\) | −0.955391 | − | 4.34771i | −0.0418967 | − | 0.190660i | ||||
\(521\) | 8.86849i | 0.388536i | 0.980949 | + | 0.194268i | \(0.0622331\pi\) | ||||
−0.980949 | + | 0.194268i | \(0.937767\pi\) | |||||||
\(522\) | −0.291766 | + | 1.51957i | −0.0127703 | + | 0.0665099i | ||||
\(523\) | 10.6892 | − | 10.6892i | 0.467407 | − | 0.467407i | −0.433666 | − | 0.901074i | \(-0.642780\pi\) |
0.901074 | + | 0.433666i | \(0.142780\pi\) | |||||||
\(524\) | 26.4845 | − | 11.3854i | 1.15698 | − | 0.497374i | ||||
\(525\) | 1.25769 | + | 1.25769i | 0.0548899 | + | 0.0548899i | ||||
\(526\) | 23.3124 | + | 34.3920i | 1.01647 | + | 1.49956i | ||||
\(527\) | 3.71123 | 0.161664 | ||||||||
\(528\) | −4.75485 | − | 4.50829i | −0.206928 | − | 0.196198i | ||||
\(529\) | 11.9541 | 0.519744 | ||||||||
\(530\) | −9.00992 | − | 13.2920i | −0.391366 | − | 0.577368i | ||||
\(531\) | 0.534855 | + | 0.534855i | 0.0232107 | + | 0.0232107i | ||||
\(532\) | 0.0537786 | + | 0.125099i | 0.00233160 | + | 0.00542372i | ||||
\(533\) | −6.49590 | + | 6.49590i | −0.281369 | + | 0.281369i | ||||
\(534\) | −0.851513 | + | 4.43484i | −0.0368486 | + | 0.191914i | ||||
\(535\) | − | 1.70313i | − | 0.0736328i | ||||||
\(536\) | −0.433059 | + | 0.676986i | −0.0187053 | + | 0.0292413i | ||||
\(537\) | 2.77281i | 0.119656i | ||||||||
\(538\) | 20.5323 | + | 3.94232i | 0.885211 | + | 0.169965i | ||||
\(539\) | 0.651231 | − | 0.651231i | 0.0280505 | − | 0.0280505i | ||||
\(540\) | 9.37253 | + | 3.73692i | 0.403329 | + | 0.160811i | ||||
\(541\) | 22.0050 | + | 22.0050i | 0.946069 | + | 0.946069i | 0.998618 | − | 0.0525493i | \(-0.0167347\pi\) |
−0.0525493 | + | 0.998618i | \(0.516735\pi\) | |||||||
\(542\) | −23.6271 | + | 16.0155i | −1.01487 | + | 0.687926i | ||||
\(543\) | 9.07145 | 0.389293 | ||||||||
\(544\) | 3.36591 | + | 0.553852i | 0.144312 | + | 0.0237462i | ||||
\(545\) | 4.48072 | 0.191933 | ||||||||
\(546\) | −3.27688 | + | 2.22121i | −0.140237 | + | 0.0950592i | ||||
\(547\) | −7.10045 | − | 7.10045i | −0.303593 | − | 0.303593i | 0.538825 | − | 0.842418i | \(-0.318869\pi\) |
−0.842418 | + | 0.538825i | \(0.818869\pi\) | |||||||
\(548\) | −16.5111 | − | 6.58314i | −0.705319 | − | 0.281218i | ||||
\(549\) | −1.30840 | + | 1.30840i | −0.0558409 | + | 0.0558409i | ||||
\(550\) | 1.27910 | + | 0.245594i | 0.0545409 | + | 0.0104722i | ||||
\(551\) | − | 0.455486i | − | 0.0194044i | ||||||
\(552\) | 14.0847 | + | 9.00976i | 0.599483 | + | 0.383481i | ||||
\(553\) | − | 1.51045i | − | 0.0642309i | ||||||
\(554\) | 0.128513 | − | 0.669317i | 0.00545998 | − | 0.0284366i | ||||
\(555\) | −5.80138 | + | 5.80138i | −0.246255 | + | 0.246255i | ||||
\(556\) | −6.30644 | − | 14.6699i | −0.267453 | − | 0.622143i | ||||
\(557\) | −30.6211 | − | 30.6211i | −1.29746 | − | 1.29746i | −0.930066 | − | 0.367392i | \(-0.880251\pi\) |
−0.367392 | − | 0.930066i | \(-0.619749\pi\) | |||||||
\(558\) | −0.798683 | − | 1.17827i | −0.0338110 | − | 0.0498801i | ||||
\(559\) | 15.3036 | 0.647273 | ||||||||
\(560\) | 0.106431 | + | 3.99858i | 0.00449752 | + | 0.168971i | ||||
\(561\) | −0.987794 | −0.0417047 | ||||||||
\(562\) | −9.09448 | − | 13.4168i | −0.383628 | − | 0.565952i | ||||
\(563\) | 31.3046 | + | 31.3046i | 1.31933 | + | 1.31933i | 0.914306 | + | 0.405024i | \(0.132737\pi\) |
0.405024 | + | 0.914306i | \(0.367263\pi\) | |||||||
\(564\) | 17.8847 | − | 7.68843i | 0.753081 | − | 0.323741i | ||||
\(565\) | 8.29398 | − | 8.29398i | 0.348930 | − | 0.348930i | ||||
\(566\) | 6.63189 | − | 34.5401i | 0.278759 | − | 1.45183i | ||||
\(567\) | − | 9.46389i | − | 0.397446i | ||||||
\(568\) | −5.30323 | + | 1.16536i | −0.222518 | + | 0.0488975i | ||||
\(569\) | − | 25.3468i | − | 1.06260i | −0.847185 | − | 0.531298i | \(-0.821705\pi\) | ||
0.847185 | − | 0.531298i | \(-0.178295\pi\) | |||||||
\(570\) | 0.168185 | + | 0.0322924i | 0.00704449 | + | 0.00135258i | ||||
\(571\) | −6.57745 | + | 6.57745i | −0.275258 | + | 0.275258i | −0.831213 | − | 0.555955i | \(-0.812353\pi\) |
0.555955 | + | 0.831213i | \(0.312353\pi\) | |||||||
\(572\) | −1.07364 | + | 2.69278i | −0.0448910 | + | 0.112591i | ||||
\(573\) | 21.6308 | + | 21.6308i | 0.903638 | + | 0.903638i | ||||
\(574\) | 6.83306 | − | 4.63175i | 0.285206 | − | 0.193326i | ||||
\(575\) | −3.32354 | −0.138601 | ||||||||
\(576\) | −0.548527 | − | 1.18783i | −0.0228553 | − | 0.0494928i | ||||
\(577\) | −33.7316 | −1.40427 | −0.702133 | − | 0.712046i | \(-0.747769\pi\) | ||||
−0.702133 | + | 0.712046i | \(0.747769\pi\) | |||||||
\(578\) | −19.4749 | + | 13.2010i | −0.810050 | + | 0.549088i | ||||
\(579\) | 7.70618 | + | 7.70618i | 0.320258 | + | 0.320258i | ||||
\(580\) | 4.95542 | − | 12.4286i | 0.205762 | − | 0.516071i | ||||
\(581\) | 11.4075 | − | 11.4075i | 0.473263 | − | 0.473263i | ||||
\(582\) | −10.5762 | − | 2.03068i | −0.438397 | − | 0.0841745i | ||||
\(583\) | 10.4574i | 0.433102i | ||||||||
\(584\) | −21.7301 | + | 4.77509i | −0.899198 | + | 0.197595i | ||||
\(585\) | 0.257392i | 0.0106418i | ||||||||
\(586\) | −3.80510 | + | 19.8177i | −0.157187 | + | 0.818661i | ||||
\(587\) | 11.1272 | − | 11.1272i | 0.459270 | − | 0.459270i | −0.439146 | − | 0.898416i | \(-0.644719\pi\) |
0.898416 | + | 0.439146i | \(0.144719\pi\) | |||||||
\(588\) | 3.26809 | − | 1.40492i | 0.134774 | − | 0.0579377i | ||||
\(589\) | 0.296292 | + | 0.296292i | 0.0122085 | + | 0.0122085i | ||||
\(590\) | −3.66994 | − | 5.41414i | −0.151089 | − | 0.222896i | ||||
\(591\) | 40.8615 | 1.68082 | ||||||||
\(592\) | −18.4444 | + | 0.490937i | −0.758061 | + | 0.0201774i | ||||
\(593\) | −18.3956 | −0.755418 | −0.377709 | − | 0.925924i | \(-0.623288\pi\) | ||||
−0.377709 | + | 0.925924i | \(0.623288\pi\) | |||||||
\(594\) | −3.68689 | − | 5.43914i | −0.151275 | − | 0.223171i | ||||
\(595\) | 0.426397 | + | 0.426397i | 0.0174806 | + | 0.0174806i | ||||
\(596\) | 16.4316 | + | 38.2229i | 0.673065 | + | 1.56567i | ||||
\(597\) | −5.63224 | + | 5.63224i | −0.230512 | + | 0.230512i | ||||
\(598\) | 1.39484 | − | 7.26458i | 0.0570392 | − | 0.297071i | ||||
\(599\) | 3.74093i | 0.152850i | 0.997075 | + | 0.0764250i | \(0.0243506\pi\) | ||||
−0.997075 | + | 0.0764250i | \(0.975649\pi\) | |||||||
\(600\) | 4.23785 | + | 2.71090i | 0.173010 | + | 0.110672i | ||||
\(601\) | 25.1470i | 1.02577i | 0.858458 | + | 0.512883i | \(0.171423\pi\) | ||||
−0.858458 | + | 0.512883i | \(0.828577\pi\) | |||||||
\(602\) | −13.5049 | − | 2.59301i | −0.550418 | − | 0.105683i | ||||
\(603\) | 0.0328582 | − | 0.0328582i | 0.00133809 | − | 0.00133809i | ||||
\(604\) | 15.7818 | + | 6.29237i | 0.642154 | + | 0.256033i | ||||
\(605\) | 7.17840 | + | 7.17840i | 0.291844 | + | 0.291844i | ||||
\(606\) | −5.63489 | + | 3.81958i | −0.228902 | + | 0.155160i | ||||
\(607\) | 20.3554 | 0.826199 | 0.413099 | − | 0.910686i | \(-0.364446\pi\) | ||||
0.413099 | + | 0.910686i | \(0.364446\pi\) | |||||||
\(608\) | 0.224505 | + | 0.312941i | 0.00910489 | + | 0.0126914i | ||||
\(609\) | −11.8992 | −0.482178 | ||||||||
\(610\) | 13.2444 | − | 8.97765i | 0.536250 | − | 0.363494i | ||||
\(611\) | −6.09016 | − | 6.09016i | −0.246382 | − | 0.246382i | ||||
\(612\) | −0.183215 | − | 0.0730497i | −0.00740604 | − | 0.00295286i | ||||
\(613\) | 15.1285 | − | 15.1285i | 0.611033 | − | 0.611033i | −0.332182 | − | 0.943215i | \(-0.607785\pi\) |
0.943215 | + | 0.332182i | \(0.107785\pi\) | |||||||
\(614\) | 37.0554 | + | 7.11483i | 1.49543 | + | 0.287131i | ||||
\(615\) | − | 10.3821i | − | 0.418647i | ||||||
\(616\) | 1.40371 | − | 2.19437i | 0.0565569 | − | 0.0884136i | ||||
\(617\) | 34.6485i | 1.39489i | 0.716636 | + | 0.697447i | \(0.245681\pi\) | ||||
−0.716636 | + | 0.697447i | \(0.754319\pi\) | |||||||
\(618\) | −6.28900 | + | 32.7543i | −0.252981 | + | 1.31757i | ||||
\(619\) | 17.6878 | − | 17.6878i | 0.710932 | − | 0.710932i | −0.255798 | − | 0.966730i | \(-0.582338\pi\) |
0.966730 | + | 0.255798i | \(0.0823383\pi\) | |||||||
\(620\) | 4.86130 | + | 11.3083i | 0.195234 | + | 0.454150i | ||||
\(621\) | 11.8563 | + | 11.8563i | 0.475776 | + | 0.475776i | ||||
\(622\) | 0.0718086 | + | 0.105937i | 0.00287926 | + | 0.00424767i | ||||
\(623\) | −1.79530 | −0.0719272 | ||||||||
\(624\) | −7.70403 | + | 8.12537i | −0.308408 | + | 0.325275i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −20.9467 | − | 30.9019i | −0.837199 | − | 1.23509i | ||||
\(627\) | −0.0788621 | − | 0.0788621i | −0.00314945 | − | 0.00314945i | ||||
\(628\) | −22.8594 | + | 9.82699i | −0.912188 | + | 0.392140i | ||||
\(629\) | −1.96686 | + | 1.96686i | −0.0784238 | + | 0.0784238i | ||||
\(630\) | 0.0436120 | − | 0.227139i | 0.00173754 | − | 0.00904945i | ||||
\(631\) | − | 15.3544i | − | 0.611248i | −0.952152 | − | 0.305624i | \(-0.901135\pi\) | ||
0.952152 | − | 0.305624i | \(-0.0988650\pi\) | |||||||
\(632\) | −0.916921 | − | 4.17265i | −0.0364731 | − | 0.165979i | ||||
\(633\) | 15.3558i | 0.610337i | ||||||||
\(634\) | 5.43209 | + | 1.04299i | 0.215736 | + | 0.0414225i | ||||
\(635\) | −0.303914 | + | 0.303914i | −0.0120605 | + | 0.0120605i | ||||
\(636\) | −14.9593 | + | 37.5193i | −0.593176 | + | 1.48774i | ||||
\(637\) | −1.11286 | − | 1.11286i | −0.0440932 | − | 0.0440932i | ||||
\(638\) | −7.21268 | + | 4.88907i | −0.285553 | + | 0.193560i | ||||
\(639\) | 0.313960 | 0.0124201 | ||||||||
\(640\) | 2.72136 | + | 10.9815i | 0.107571 | + | 0.434083i | ||||
\(641\) | −12.4211 | −0.490602 | −0.245301 | − | 0.969447i | \(-0.578887\pi\) | ||||
−0.245301 | + | 0.969447i | \(0.578887\pi\) | |||||||
\(642\) | −3.54611 | + | 2.40371i | −0.139954 | + | 0.0948669i | ||||
\(643\) | −4.58322 | − | 4.58322i | −0.180744 | − | 0.180744i | 0.610936 | − | 0.791680i | \(-0.290793\pi\) |
−0.791680 | + | 0.610936i | \(0.790793\pi\) | |||||||
\(644\) | −2.46179 | + | 6.17440i | −0.0970082 | + | 0.243305i | ||||
\(645\) | −12.2295 | + | 12.2295i | −0.481537 | + | 0.481537i | ||||
\(646\) | 0.0570202 | + | 0.0109482i | 0.00224343 | + | 0.000430751i | ||||
\(647\) | − | 3.25672i | − | 0.128035i | −0.997949 | − | 0.0640174i | \(-0.979609\pi\) | ||
0.997949 | − | 0.0640174i | \(-0.0203913\pi\) | |||||||
\(648\) | −5.74506 | − | 26.1441i | −0.225687 | − | 1.02704i | ||||
\(649\) | 4.25954i | 0.167202i | ||||||||
\(650\) | 0.419685 | − | 2.18580i | 0.0164614 | − | 0.0857340i | ||||
\(651\) | 7.74036 | − | 7.74036i | 0.303368 | − | 0.303368i | ||||
\(652\) | 9.19850 | − | 3.95433i | 0.360241 | − | 0.154864i | ||||
\(653\) | −12.8699 | − | 12.8699i | −0.503636 | − | 0.503636i | 0.408930 | − | 0.912566i | \(-0.365902\pi\) |
−0.912566 | + | 0.408930i | \(0.865902\pi\) | |||||||
\(654\) | −6.32385 | − | 9.32935i | −0.247282 | − | 0.364806i | ||||
\(655\) | 14.4140 | 0.563203 | ||||||||
\(656\) | 16.0647 | − | 16.9433i | 0.627222 | − | 0.661525i | ||||
\(657\) | 1.28646 | 0.0501895 | ||||||||
\(658\) | 4.34245 | + | 6.40626i | 0.169286 | + | 0.249742i | ||||
\(659\) | 33.4531 | + | 33.4531i | 1.30315 | + | 1.30315i | 0.926259 | + | 0.376887i | \(0.123005\pi\) |
0.376887 | + | 0.926259i | \(0.376995\pi\) | |||||||
\(660\) | −1.29390 | − | 3.00984i | −0.0503650 | − | 0.117158i | ||||
\(661\) | 6.33269 | − | 6.33269i | 0.246313 | − | 0.246313i | −0.573142 | − | 0.819456i | \(-0.694276\pi\) |
0.819456 | + | 0.573142i | \(0.194276\pi\) | |||||||
\(662\) | 2.71211 | − | 14.1251i | 0.105409 | − | 0.548989i | ||||
\(663\) | 1.68800i | 0.0655565i | ||||||||
\(664\) | 24.5885 | − | 38.4383i | 0.954218 | − | 1.49170i | ||||
\(665\) | 0.0680842i | 0.00264019i | ||||||||
\(666\) | 1.04773 | + | 0.201171i | 0.0405989 | + | 0.00779521i | ||||
\(667\) | 15.7222 | − | 15.7222i | 0.608768 | − | 0.608768i | ||||
\(668\) | 31.9054 | + | 12.7210i | 1.23446 | + | 0.492190i | ||||
\(669\) | 18.7883 | + | 18.7883i | 0.726399 | + | 0.726399i | ||||
\(670\) | −0.332612 | + | 0.225459i | −0.0128499 | + | 0.00871025i | ||||
\(671\) | −10.4200 | −0.402258 | ||||||||
\(672\) | 8.17529 | − | 5.86499i | 0.315369 | − | 0.226247i | ||||
\(673\) | −20.3771 | −0.785481 | −0.392740 | − | 0.919649i | \(-0.628473\pi\) | ||||
−0.392740 | + | 0.919649i | \(0.628473\pi\) | |||||||
\(674\) | −0.148160 | + | 0.100429i | −0.00570691 | + | 0.00386840i | ||||
\(675\) | 3.56737 | + | 3.56737i | 0.137308 | + | 0.137308i | ||||
\(676\) | −19.5496 | − | 7.79460i | −0.751906 | − | 0.299792i | ||||
\(677\) | −5.97856 | + | 5.97856i | −0.229775 | + | 0.229775i | −0.812599 | − | 0.582824i | \(-0.801948\pi\) |
0.582824 | + | 0.812599i | \(0.301948\pi\) | |||||||
\(678\) | −28.9747 | − | 5.56330i | −1.11277 | − | 0.213657i | ||||
\(679\) | − | 4.28142i | − | 0.164306i | ||||||
\(680\) | 1.43677 | + | 0.919083i | 0.0550977 | + | 0.0352452i | ||||
\(681\) | − | 0.568985i | − | 0.0218035i | ||||||
\(682\) | 1.51149 | − | 7.87214i | 0.0578781 | − | 0.301440i | ||||
\(683\) | −32.5411 | + | 32.5411i | −1.24515 | + | 1.24515i | −0.287312 | + | 0.957837i | \(0.592762\pi\) |
−0.957837 | + | 0.287312i | \(0.907238\pi\) | |||||||
\(684\) | −0.00879524 | − | 0.0204593i | −0.000336294 | − | 0.000782282i | ||||
\(685\) | −6.28445 | − | 6.28445i | −0.240116 | − | 0.240116i | ||||
\(686\) | 0.793500 | + | 1.17062i | 0.0302960 | + | 0.0446946i | ||||
\(687\) | 44.5397 | 1.69929 | ||||||||
\(688\) | −38.8815 | + | 1.03491i | −1.48234 | + | 0.0394557i | ||||
\(689\) | 17.8702 | 0.680801 | ||||||||
\(690\) | 4.69067 | + | 6.91997i | 0.178571 | + | 0.263439i | ||||
\(691\) | 31.9319 | + | 31.9319i | 1.21475 | + | 1.21475i | 0.969448 | + | 0.245298i | \(0.0788860\pi\) |
0.245298 | + | 0.969448i | \(0.421114\pi\) | |||||||
\(692\) | −28.7159 | + | 12.3446i | −1.09161 | + | 0.469273i | ||||
\(693\) | −0.106506 | + | 0.106506i | −0.00404583 | + | 0.00404583i | ||||
\(694\) | −9.44467 | + | 49.1896i | −0.358515 | + | 1.86721i | ||||
\(695\) | − | 7.98401i | − | 0.302851i | ||||||
\(696\) | −32.8716 | + | 7.22339i | −1.24600 | + | 0.273802i | ||||
\(697\) | − | 3.51987i | − | 0.133325i | ||||||
\(698\) | −7.56526 | − | 1.45257i | −0.286349 | − | 0.0549806i | ||||
\(699\) | 25.6374 | − | 25.6374i | 0.969697 | − | 0.969697i | ||||
\(700\) | −0.740715 | + | 1.85778i | −0.0279964 | + | 0.0702174i | ||||
\(701\) | −1.20601 | − | 1.20601i | −0.0455503 | − | 0.0455503i | 0.683965 | − | 0.729515i | \(-0.260254\pi\) |
−0.729515 | + | 0.683965i | \(0.760254\pi\) | |||||||
\(702\) | −9.29471 | + | 6.30037i | −0.350806 | + | 0.237792i | ||||
\(703\) | −0.314055 | −0.0118448 | ||||||||
\(704\) | 2.54567 | − | 6.91409i | 0.0959435 | − | 0.260585i | ||||
\(705\) | 9.73363 | 0.366590 | ||||||||
\(706\) | −4.02511 | + | 2.72840i | −0.151487 | + | 0.102685i | ||||
\(707\) | −1.91367 | − | 1.91367i | −0.0719709 | − | 0.0719709i | ||||
\(708\) | −6.09327 | + | 15.2825i | −0.228999 | + | 0.574350i | ||||
\(709\) | 33.1834 | − | 33.1834i | 1.24623 | − | 1.24623i | 0.288856 | − | 0.957372i | \(-0.406725\pi\) |
0.957372 | − | 0.288856i | \(-0.0932750\pi\) | |||||||
\(710\) | −2.66618 | − | 0.511921i | −0.100060 | − | 0.0192121i | ||||
\(711\) | 0.247028i | 0.00926426i | ||||||||
\(712\) | −4.95955 | + | 1.08984i | −0.185867 | + | 0.0408434i | ||||
\(713\) | 20.4545i | 0.766028i | ||||||||
\(714\) | 0.286011 | − | 1.48960i | 0.0107037 | − | 0.0557469i | ||||
\(715\) | −1.02492 | + | 1.02492i | −0.0383300 | + | 0.0383300i | ||||
\(716\) | −2.86444 | + | 1.23139i | −0.107049 | + | 0.0460193i | ||||
\(717\) | −34.6941 | − | 34.6941i | −1.29567 | − | 1.29567i | ||||
\(718\) | 24.6772 | + | 36.4053i | 0.920944 | + | 1.35864i | ||||
\(719\) | −34.7079 | −1.29439 | −0.647194 | − | 0.762326i | \(-0.724057\pi\) | ||||
−0.647194 | + | 0.762326i | \(0.724057\pi\) | |||||||
\(720\) | −0.0174063 | − | 0.653950i | −0.000648693 | − | 0.0243713i | ||||
\(721\) | −13.2595 | −0.493810 | ||||||||
\(722\) | −15.0728 | − | 22.2364i | −0.560953 | − | 0.827553i | ||||
\(723\) | −2.99461 | − | 2.99461i | −0.111371 | − | 0.111371i | ||||
\(724\) | 4.02859 | + | 9.37122i | 0.149721 | + | 0.348279i | ||||
\(725\) | 4.73058 | − | 4.73058i | 0.175689 | − | 0.175689i | ||||
\(726\) | 4.81501 | − | 25.0775i | 0.178702 | − | 0.930712i | ||||
\(727\) | − | 22.5592i | − | 0.836673i | −0.908292 | − | 0.418337i | \(-0.862613\pi\) | ||
0.908292 | − | 0.418337i | \(-0.137387\pi\) | |||||||
\(728\) | −3.74986 | − | 2.39873i | −0.138979 | − | 0.0889030i | ||||
\(729\) | − | 25.3720i | − | 0.939703i | ||||||
\(730\) | −10.9247 | − | 2.09761i | −0.404342 | − | 0.0776359i | ||||
\(731\) | −4.14621 | + | 4.14621i | −0.153353 | + | 0.153353i | ||||
\(732\) | −37.3849 | − | 14.9057i | −1.38179 | − | 0.550932i | ||||
\(733\) | −36.3696 | − | 36.3696i | −1.34334 | − | 1.34334i | −0.892709 | − | 0.450633i | \(-0.851198\pi\) |
−0.450633 | − | 0.892709i | \(-0.648802\pi\) | |||||||
\(734\) | 21.2059 | − | 14.3743i | 0.782724 | − | 0.530566i | ||||
\(735\) | 1.77864 | 0.0656060 | ||||||||
\(736\) | −3.05257 | + | 18.5513i | −0.112519 | + | 0.683810i | ||||
\(737\) | 0.261680 | 0.00963912 | ||||||||
\(738\) | −1.11752 | + | 0.757502i | −0.0411363 | + | 0.0278840i | ||||
\(739\) | −28.6280 | − | 28.6280i | −1.05310 | − | 1.05310i | −0.998509 | − | 0.0545872i | \(-0.982616\pi\) |
−0.0545872 | − | 0.998509i | \(-0.517384\pi\) | |||||||
\(740\) | −8.56945 | − | 3.41672i | −0.315019 | − | 0.125601i | ||||
\(741\) | −0.134764 | + | 0.134764i | −0.00495068 | + | 0.00495068i | ||||
\(742\) | −15.7698 | − | 3.02790i | −0.578929 | − | 0.111158i | ||||
\(743\) | 5.92667i | 0.217429i | 0.994073 | + | 0.108714i | \(0.0346734\pi\) | ||||
−0.994073 | + | 0.108714i | \(0.965327\pi\) | |||||||
\(744\) | 16.6841 | − | 26.0816i | 0.611667 | − | 0.956199i | ||||
\(745\) | 20.8026i | 0.762148i | ||||||||
\(746\) | 6.03813 | − | 31.4477i | 0.221072 | − | 1.15138i | ||||
\(747\) | −1.86565 | + | 1.86565i | −0.0682604 | + | 0.0682604i | ||||
\(748\) | −0.438675 | − | 1.02044i | −0.0160395 | − | 0.0373109i | ||||
\(749\) | −1.20430 | − | 1.20430i | −0.0440040 | − | 0.0440040i | ||||
\(750\) | 1.41135 | + | 2.08211i | 0.0515351 | + | 0.0760280i | ||||
\(751\) | −7.28601 | −0.265870 | −0.132935 | − | 0.991125i | \(-0.542440\pi\) | ||||
−0.132935 | + | 0.991125i | \(0.542440\pi\) | |||||||
\(752\) | 15.8850 | + | 15.0613i | 0.579266 | + | 0.549229i | ||||
\(753\) | 23.8835 | 0.870362 | ||||||||
\(754\) | 8.35473 | + | 12.3254i | 0.304261 | + | 0.448866i | ||||
\(755\) | 6.00687 | + | 6.00687i | 0.218613 | + | 0.218613i | ||||
\(756\) | 9.26978 | − | 3.98498i | 0.337139 | − | 0.144932i | ||||
\(757\) | −24.2438 | + | 24.2438i | −0.881155 | + | 0.881155i | −0.993652 | − | 0.112497i | \(-0.964115\pi\) |
0.112497 | + | 0.993652i | \(0.464115\pi\) | |||||||
\(758\) | 5.89397 | − | 30.6969i | 0.214079 | − | 1.11496i | ||||
\(759\) | − | 5.44425i | − | 0.197614i | ||||||
\(760\) | 0.0413305 | + | 0.188084i | 0.00149922 | + | 0.00682251i | ||||
\(761\) | − | 7.13566i | − | 0.258668i | −0.991601 | − | 0.129334i | \(-0.958716\pi\) | ||
0.991601 | − | 0.129334i | \(-0.0412839\pi\) | |||||||
\(762\) | 1.06171 | + | 0.203854i | 0.0384617 | + | 0.00738486i | ||||
\(763\) | 3.16834 | − | 3.16834i | 0.114702 | − | 0.114702i | ||||
\(764\) | −12.7395 | + | 31.9517i | −0.460897 | + | 1.15597i | ||||
\(765\) | −0.0697353 | − | 0.0697353i | −0.00252128 | − | 0.00252128i | ||||
\(766\) | −21.1057 | + | 14.3064i | −0.762581 | + | 0.516912i | ||||
\(767\) | 7.27894 | 0.262827 | ||||||||
\(768\) | 19.0240 | − | 21.1649i | 0.686470 | − | 0.763724i | ||||
\(769\) | −41.9735 | −1.51360 | −0.756802 | − | 0.653645i | \(-0.773239\pi\) | ||||
−0.756802 | + | 0.653645i | \(0.773239\pi\) | |||||||
\(770\) | 1.07812 | − | 0.730798i | 0.0388528 | − | 0.0263361i | ||||
\(771\) | −22.0137 | − | 22.0137i | −0.792805 | − | 0.792805i | ||||
\(772\) | −4.53856 | + | 11.3831i | −0.163346 | + | 0.409687i | ||||
\(773\) | −15.5336 | + | 15.5336i | −0.558705 | + | 0.558705i | −0.928939 | − | 0.370233i | \(-0.879278\pi\) |
0.370233 | + | 0.928939i | \(0.379278\pi\) | |||||||
\(774\) | 2.20866 | + | 0.424075i | 0.0793887 | + | 0.0152431i | ||||
\(775\) | 6.15445i | 0.221074i | ||||||||
\(776\) | −2.59904 | − | 11.8275i | −0.0933001 | − | 0.424582i | ||||
\(777\) | 8.20438i | 0.294331i | ||||||||
\(778\) | 1.73214 | − | 9.02129i | 0.0621002 | − | 0.323429i | ||||
\(779\) | 0.281015 | − | 0.281015i | 0.0100684 | − | 0.0100684i | ||||
\(780\) | −5.14339 | + | 2.21109i | −0.184163 | + | 0.0791697i | ||||
\(781\) | 1.25018 | + | 1.25018i | 0.0447348 | + | 0.0447348i | ||||
\(782\) | 1.59029 | + | 2.34610i | 0.0568687 | + | 0.0838963i | ||||
\(783\) | −33.7514 | −1.20618 | ||||||||
\(784\) | 2.90268 | + | 2.75217i | 0.103667 | + | 0.0982917i | ||||
\(785\) | −12.4411 | −0.444041 | ||||||||
\(786\) | −20.3432 | − | 30.0116i | −0.725618 | − | 1.07048i | ||||
\(787\) | −36.4484 | − | 36.4484i | −1.29924 | − | 1.29924i | −0.928891 | − | 0.370353i | \(-0.879237\pi\) |
−0.370353 | − | 0.928891i | \(-0.620763\pi\) | |||||||
\(788\) | 18.1464 | + | 42.2118i | 0.646438 | + | 1.50373i | ||||
\(789\) | 36.9499 | − | 36.9499i | 1.31545 | − | 1.31545i | ||||
\(790\) | 0.402786 | − | 2.09778i | 0.0143305 | − | 0.0746358i | ||||
\(791\) | − | 11.7295i | − | 0.417052i | ||||||
\(792\) | −0.229570 | + | 0.358879i | −0.00815741 | + | 0.0127522i | ||||
\(793\) | 17.8062i | 0.632317i | ||||||||
\(794\) | −32.7231 | − | 6.28302i | −1.16130 | − | 0.222976i | ||||
\(795\) | −14.2806 | + | 14.2806i | −0.506480 | + | 0.506480i | ||||
\(796\) | −8.31961 | − | 3.31711i | −0.294881 | − | 0.117572i | ||||
\(797\) | −32.7530 | − | 32.7530i | −1.16017 | − | 1.16017i | −0.984438 | − | 0.175732i | \(-0.943771\pi\) |
−0.175732 | − | 0.984438i | \(-0.556229\pi\) | |||||||
\(798\) | 0.141759 | − | 0.0960905i | 0.00501821 | − | 0.00340157i | ||||
\(799\) | 3.30002 | 0.116746 | ||||||||
\(800\) | −0.918470 | + | 5.58179i | −0.0324728 | + | 0.197346i | ||||
\(801\) | 0.293613 | 0.0103743 | ||||||||
\(802\) | 28.0756 | − | 19.0309i | 0.991385 | − | 0.672005i | ||||
\(803\) | 5.12262 | + | 5.12262i | 0.180773 | + | 0.180773i | ||||
\(804\) | 0.938862 | + | 0.374334i | 0.0331111 | + | 0.0132017i | ||||
\(805\) | −2.35010 | + | 2.35010i | −0.0828300 | + | 0.0828300i | ||||
\(806\) | −13.4524 | − | 2.58293i | −0.473839 | − | 0.0909798i | ||||
\(807\) | − | 26.2949i | − | 0.925624i | ||||||
\(808\) | −6.44823 | − | 4.12484i | −0.226848 | − | 0.145111i | ||||
\(809\) | 4.49260i | 0.157951i | 0.996877 | + | 0.0789756i | \(0.0251649\pi\) | ||||
−0.996877 | + | 0.0789756i | \(0.974835\pi\) | |||||||
\(810\) | 2.52370 | − | 13.1439i | 0.0886736 | − | 0.461829i | ||||
\(811\) | 3.24039 | − | 3.24039i | 0.113786 | − | 0.113786i | −0.647922 | − | 0.761707i | \(-0.724362\pi\) |
0.761707 | + | 0.647922i | \(0.224362\pi\) | |||||||
\(812\) | −5.28436 | − | 12.2924i | −0.185445 | − | 0.431378i | ||||
\(813\) | 25.3844 | + | 25.3844i | 0.890268 | + | 0.890268i | ||||
\(814\) | 3.37098 | + | 4.97309i | 0.118153 | + | 0.174307i | ||||
\(815\) | 5.00622 | 0.175360 | ||||||||
\(816\) | −0.114152 | − | 4.28867i | −0.00399612 | − | 0.150133i | ||||
\(817\) | −0.662039 | −0.0231618 | ||||||||
\(818\) | −15.7587 | − | 23.2482i | −0.550990 | − | 0.812856i | ||||
\(819\) | 0.182003 | + | 0.182003i | 0.00635972 | + | 0.00635972i | ||||
\(820\) | 10.7252 | − | 4.61064i | 0.374540 | − | 0.161011i | ||||
\(821\) | 36.5352 | − | 36.5352i | 1.27509 | − | 1.27509i | 0.331706 | − | 0.943383i | \(-0.392376\pi\) |
0.943383 | − | 0.331706i | \(-0.107624\pi\) | |||||||
\(822\) | −4.21538 | + | 21.9545i | −0.147028 | + | 0.765750i | ||||
\(823\) | 24.0637i | 0.838809i | 0.907799 | + | 0.419404i | \(0.137761\pi\) | ||||
−0.907799 | + | 0.419404i | \(0.862239\pi\) | |||||||
\(824\) | −36.6296 | + | 8.04919i | −1.27605 | + | 0.280407i | ||||
\(825\) | − | 1.63809i | − | 0.0570309i | ||||||
\(826\) | −6.42341 | − | 1.23333i | −0.223499 | − | 0.0429131i | ||||
\(827\) | −27.2971 | + | 27.2971i | −0.949213 | + | 0.949213i | −0.998771 | − | 0.0495578i | \(-0.984219\pi\) |
0.0495578 | + | 0.998771i | \(0.484219\pi\) | |||||||
\(828\) | 0.402615 | − | 1.00979i | 0.0139918 | − | 0.0350928i | ||||
\(829\) | 31.3499 | + | 31.3499i | 1.08883 | + | 1.08883i | 0.995649 | + | 0.0931792i | \(0.0297029\pi\) |
0.0931792 | + | 0.995649i | \(0.470297\pi\) | |||||||
\(830\) | 18.8852 | − | 12.8013i | 0.655517 | − | 0.444338i | ||||
\(831\) | −0.857167 | −0.0297348 | ||||||||
\(832\) | −11.8152 | − | 4.35018i | −0.409618 | − | 0.150815i | ||||
\(833\) | 0.603016 | 0.0208933 | ||||||||
\(834\) | −16.6236 | + | 11.2682i | −0.575628 | + | 0.390187i | ||||
\(835\) | 12.1438 | + | 12.1438i | 0.420254 | + | 0.420254i | ||||
\(836\) | 0.0464459 | − | 0.116490i | 0.00160636 | − | 0.00402891i | ||||
\(837\) | 21.9552 | − | 21.9552i | 0.758882 | − | 0.758882i | ||||
\(838\) | 11.0646 | + | 2.12447i | 0.382221 | + | 0.0733885i | ||||
\(839\) | − | 34.6426i | − | 1.19599i | −0.801498 | − | 0.597997i | \(-0.795963\pi\) | ||
0.801498 | − | 0.597997i | \(-0.204037\pi\) | |||||||
\(840\) | 4.91351 | − | 1.07972i | 0.169532 | − | 0.0372539i | ||||
\(841\) | 15.7567i | 0.543336i | ||||||||
\(842\) | −5.39926 | + | 28.1204i | −0.186071 | + | 0.969092i | ||||
\(843\) | −14.4146 | + | 14.4146i | −0.496466 | + | 0.496466i | ||||
\(844\) | −15.8632 | + | 6.81942i | −0.546034 | + | 0.234734i | ||||
\(845\) | −7.44094 | − | 7.44094i | −0.255976 | − | 0.255976i | ||||
\(846\) | −0.710188 | − | 1.04771i | −0.0244168 | − | 0.0360212i | ||||
\(847\) | 10.1518 | 0.348820 | ||||||||
\(848\) | −45.4025 | + | 1.20848i | −1.55913 | + | 0.0414995i | ||||
\(849\) | −44.2341 | −1.51811 | ||||||||
\(850\) | 0.478494 | + | 0.705905i | 0.0164122 | + | 0.0242123i | ||||
\(851\) | −10.8404 | − | 10.8404i | −0.371603 | − | 0.371603i | ||||
\(852\) | 2.69703 | + | 6.27378i | 0.0923987 | + | 0.214936i | ||||
\(853\) | −17.6395 | + | 17.6395i | −0.603963 | + | 0.603963i | −0.941362 | − | 0.337399i | \(-0.890453\pi\) |
0.337399 | + | 0.941362i | \(0.390453\pi\) | |||||||
\(854\) | 3.01705 | − | 15.7134i | 0.103241 | − | 0.537700i | ||||
\(855\) | − | 0.0111349i | − | 0.000380804i | ||||||
\(856\) | −4.05795 | − | 2.59582i | −0.138698 | − | 0.0887231i | ||||
\(857\) | 9.60441i | 0.328080i | 0.986454 | + | 0.164040i | \(0.0524527\pi\) | ||||
−0.986454 | + | 0.164040i | \(0.947547\pi\) | |||||||
\(858\) | 3.58053 | + | 0.687481i | 0.122237 | + | 0.0234702i | ||||
\(859\) | 12.1676 | − | 12.1676i | 0.415155 | − | 0.415155i | −0.468375 | − | 0.883530i | \(-0.655160\pi\) |
0.883530 | + | 0.468375i | \(0.155160\pi\) | |||||||
\(860\) | −18.0647 | − | 7.20258i | −0.616002 | − | 0.245606i | ||||
\(861\) | −7.34125 | − | 7.34125i | −0.250189 | − | 0.250189i | ||||
\(862\) | −32.6428 | + | 22.1267i | −1.11182 | + | 0.753639i | ||||
\(863\) | −31.2901 | −1.06513 | −0.532564 | − | 0.846390i | \(-0.678771\pi\) | ||||
−0.532564 | + | 0.846390i | \(0.678771\pi\) | |||||||
\(864\) | 23.1888 | − | 16.6358i | 0.788900 | − | 0.565961i | ||||
\(865\) | −15.6284 | −0.531383 | ||||||||
\(866\) | −13.7298 | + | 9.30664i | −0.466556 | + | 0.316253i | ||||
\(867\) | 20.9233 | + | 20.9233i | 0.710593 | + | 0.710593i | ||||
\(868\) | 11.4336 | + | 4.55869i | 0.388082 | + | 0.154732i | ||||
\(869\) | −0.983654 | + | 0.983654i | −0.0333682 | + | 0.0333682i | ||||
\(870\) | −16.5261 | − | 3.17310i | −0.560287 | − | 0.107578i | ||||
\(871\) | − | 0.447174i | − | 0.0151519i | ||||||
\(872\) | 6.82925 | − | 10.6759i | 0.231268 | − | 0.361533i | ||||
\(873\) | 0.700207i | 0.0236984i | ||||||||
\(874\) | −0.0603412 | + | 0.314268i | −0.00204107 | + | 0.0106303i | ||||
\(875\) | −0.707107 | + | 0.707107i | −0.0239046 | + | 0.0239046i | ||||
\(876\) | 11.0511 | + | 25.7070i | 0.373383 | + | 0.868557i | ||||
\(877\) | −25.0684 | − | 25.0684i | −0.846501 | − | 0.846501i | 0.143194 | − | 0.989695i | \(-0.454263\pi\) |
−0.989695 | + | 0.143194i | \(0.954263\pi\) | |||||||
\(878\) | 0.385131 | + | 0.568171i | 0.0129976 | + | 0.0191748i | ||||
\(879\) | 25.3797 | 0.856036 | ||||||||
\(880\) | 2.53469 | − | 2.67331i | 0.0854445 | − | 0.0901174i | ||||
\(881\) | 2.08150 | 0.0701277 | 0.0350638 | − | 0.999385i | \(-0.488837\pi\) | ||||
0.0350638 | + | 0.999385i | \(0.488837\pi\) | |||||||
\(882\) | −0.129773 | − | 0.191450i | −0.00436970 | − | 0.00644646i | ||||
\(883\) | −17.8914 | − | 17.8914i | −0.602094 | − | 0.602094i | 0.338774 | − | 0.940868i | \(-0.389988\pi\) |
−0.940868 | + | 0.338774i | \(0.889988\pi\) | |||||||
\(884\) | −1.74378 | + | 0.749632i | −0.0586497 | + | 0.0252129i | ||||
\(885\) | −5.81680 | + | 5.81680i | −0.195530 | + | 0.195530i | ||||
\(886\) | −1.16663 | + | 6.07604i | −0.0391938 | + | 0.204128i | ||||
\(887\) | − | 52.0223i | − | 1.74674i | −0.487060 | − | 0.873368i | \(-0.661931\pi\) | ||
0.487060 | − | 0.873368i | \(-0.338069\pi\) | |||||||
\(888\) | 4.98048 | + | 22.6647i | 0.167134 | + | 0.760579i | ||||
\(889\) | 0.429799i | 0.0144150i | ||||||||
\(890\) | −2.49339 | − | 0.478745i | −0.0835787 | − | 0.0160476i | ||||
\(891\) | −6.16318 | + | 6.16318i | −0.206474 | + | 0.206474i | ||||
\(892\) | −11.0654 | + | 27.7530i | −0.370497 | + | 0.929240i | ||||
\(893\) | 0.263462 | + | 0.263462i | 0.00881643 | + | 0.00881643i | ||||
\(894\) | 43.3133 | − | 29.3597i | 1.44861 | − | 0.981935i | ||||
\(895\) | −1.55895 | −0.0521101 | ||||||||
\(896\) | 9.68941 | + | 5.84083i | 0.323701 | + | 0.195128i | ||||
\(897\) | −9.30344 | −0.310633 | ||||||||
\(898\) | 24.0675 | − | 16.3141i | 0.803144 | − | 0.544407i | ||||
\(899\) | −29.1141 | − | 29.1141i | −0.971009 | − | 0.971009i | ||||
\(900\) | 0.121141 | − | 0.303831i | 0.00403802 | − | 0.0101277i | ||||
\(901\) | −4.84159 | + | 4.84159i | −0.161297 | + | 0.161297i | ||||
\(902\) | −7.46624 | − | 1.43356i | −0.248599 | − | 0.0477323i | ||||
\(903\) | 17.2951i | 0.575546i | ||||||||
\(904\) | −7.12037 | − | 32.4028i | −0.236820 | − | 1.07770i | ||||
\(905\) | 5.10023i | 0.169537i | ||||||||
\(906\) | 4.02919 | − | 20.9848i | 0.133861 | − | 0.697172i | ||||
\(907\) | 15.2655 | − | 15.2655i | 0.506884 | − | 0.506884i | −0.406685 | − | 0.913568i | \(-0.633315\pi\) |
0.913568 | + | 0.406685i | \(0.133315\pi\) | |||||||
\(908\) | 0.587787 | − | 0.252683i | 0.0195064 | − | 0.00838559i | ||||
\(909\) | 0.312972 | + | 0.312972i | 0.0103806 | + | 0.0103806i | ||||
\(910\) | −1.24883 | − | 1.84235i | −0.0413983 | − | 0.0610734i | ||||
\(911\) | 25.0817 | 0.830992 | 0.415496 | − | 0.909595i | \(-0.363608\pi\) | ||||
0.415496 | + | 0.909595i | \(0.363608\pi\) | |||||||
\(912\) | 0.333279 | − | 0.351506i | 0.0110360 | − | 0.0116395i | ||||
\(913\) | −14.8579 | −0.491723 | ||||||||
\(914\) | 24.7466 | + | 36.5078i | 0.818546 | + | 1.20757i | ||||
\(915\) | −14.2294 | − | 14.2294i | −0.470410 | − | 0.470410i | ||||
\(916\) | 19.7799 | + | 46.0115i | 0.653545 | + | 1.52026i | ||||
\(917\) | 10.1923 | − | 10.1923i | 0.336578 | − | 0.336578i | ||||
\(918\) | 0.811258 | − | 4.22518i | 0.0267755 | − | 0.139452i | ||||
\(919\) | 33.4635i | 1.10386i | 0.833891 | + | 0.551929i | \(0.186108\pi\) | ||||
−0.833891 | + | 0.551929i | \(0.813892\pi\) | |||||||
\(920\) | −5.06555 | + | 7.91880i | −0.167006 | + | 0.261075i | ||||
\(921\) | − | 47.4553i | − | 1.56370i | ||||||
\(922\) | −18.5149 | − | 3.55495i | −0.609755 | − | 0.117076i | ||||
\(923\) | 2.13637 | − | 2.13637i | 0.0703195 | − | 0.0703195i | ||||
\(924\) | −3.04321 | − | 1.21336i | −0.100114 | − | 0.0399165i | ||||
\(925\) | −3.26170 | − | 3.26170i | −0.107244 | − | 0.107244i | ||||
\(926\) | 17.7307 | − | 12.0187i | 0.582668 | − | 0.394959i | ||||
\(927\) | 2.16853 | 0.0712239 | ||||||||
\(928\) | −22.0602 | − | 30.7500i | −0.724162 | − | 1.00942i | ||||
\(929\) | 32.1012 | 1.05321 | 0.526604 | − | 0.850111i | \(-0.323465\pi\) | ||||
0.526604 | + | 0.850111i | \(0.323465\pi\) | |||||||
\(930\) | 12.8142 | − | 8.68606i | 0.420196 | − | 0.284827i | ||||
\(931\) | 0.0481428 | + | 0.0481428i | 0.00157782 | + | 0.00157782i | ||||
\(932\) | 37.8701 | + | 15.0992i | 1.24048 | + | 0.494590i | ||||
\(933\) | 0.113815 | − | 0.113815i | 0.00372615 | − | 0.00372615i | ||||
\(934\) | 43.8548 | + | 8.42036i | 1.43497 | + | 0.275522i | ||||
\(935\) | − | 0.555366i | − | 0.0181624i | ||||||
\(936\) | 0.613273 | + | 0.392302i | 0.0200454 | + | 0.0128228i | ||||
\(937\) | 51.7263i | 1.68983i | 0.534904 | + | 0.844913i | \(0.320348\pi\) | ||||
−0.534904 | + | 0.844913i | \(0.679652\pi\) | |||||||
\(938\) | −0.0757684 | + | 0.394616i | −0.00247393 | + | 0.0128847i | ||||
\(939\) | −33.2002 | + | 33.2002i | −1.08345 | + | 1.08345i | ||||
\(940\) | 4.32266 | + | 10.0553i | 0.140989 | + | 0.327967i | ||||
\(941\) | 28.8417 | + | 28.8417i | 0.940213 | + | 0.940213i | 0.998311 | − | 0.0580982i | \(-0.0185036\pi\) |
−0.0580982 | + | 0.998311i | \(0.518504\pi\) | |||||||
\(942\) | 17.5587 | + | 25.9037i | 0.572092 | + | 0.843988i | ||||
\(943\) | 19.3999 | 0.631746 | ||||||||
\(944\) | −18.4935 | + | 0.492243i | −0.601911 | + | 0.0160211i | ||||
\(945\) | 5.04502 | 0.164115 | ||||||||
\(946\) | 7.10615 | + | 10.4835i | 0.231041 | + | 0.340847i | ||||
\(947\) | −32.4926 | − | 32.4926i | −1.05587 | − | 1.05587i | −0.998344 | − | 0.0575247i | \(-0.981679\pi\) |
−0.0575247 | − | 0.998344i | \(-0.518321\pi\) | |||||||
\(948\) | −4.93629 | + | 2.12206i | −0.160323 | + | 0.0689212i | ||||
\(949\) | 8.75383 | − | 8.75383i | 0.284161 | − | 0.284161i | ||||
\(950\) | −0.0181557 | + | 0.0945583i | −0.000589049 | + | 0.00306788i | ||||
\(951\) | − | 6.95666i | − | 0.225585i | ||||||
\(952\) | 1.66584 | − | 0.366061i | 0.0539902 | − | 0.0118641i | ||||
\(953\) | − | 56.0737i | − | 1.81641i | −0.418530 | − | 0.908203i | \(-0.637454\pi\) | ||
0.418530 | − | 0.908203i | \(-0.362546\pi\) | |||||||
\(954\) | 2.57909 | + | 0.495199i | 0.0835010 | + | 0.0160327i | ||||
\(955\) | −12.1614 | + | 12.1614i | −0.393535 | + | 0.393535i | ||||
\(956\) | 20.4331 | − | 51.2480i | 0.660854 | − | 1.65748i | ||||
\(957\) | 7.74911 | + | 7.74911i | 0.250493 | + | 0.250493i | ||||
\(958\) | 25.0303 | − | 16.9666i | 0.808692 | − | 0.548168i | ||||
\(959\) | −8.88755 | −0.286994 | ||||||||
\(960\) | 12.9182 | − | 5.96550i | 0.416933 | − | 0.192536i | ||||
\(961\) | 6.87720 | 0.221845 | ||||||||
\(962\) | 8.49830 | − | 5.76053i | 0.273996 | − | 0.185727i | ||||
\(963\) | 0.196957 | + | 0.196957i | 0.00634685 | + | 0.00634685i | ||||
\(964\) | 1.76368 | − | 4.42346i | 0.0568043 | − | 0.142470i | ||||
\(965\) | −4.33263 | + | 4.33263i | −0.139472 | + | 0.139472i | ||||
\(966\) | 8.20996 | + | 1.57636i | 0.264151 | + | 0.0507185i | ||||
\(967\) | − | 21.7506i | − | 0.699453i | −0.936852 | − | 0.349726i | \(-0.886275\pi\) | ||
0.936852 | − | 0.349726i | \(-0.113725\pi\) | |||||||
\(968\) | 28.0445 | − | 6.16265i | 0.901384 | − | 0.198075i | ||||
\(969\) | − | 0.0730234i | − | 0.00234585i | ||||||
\(970\) | 1.14171 | − | 5.94623i | 0.0366581 | − | 0.190922i | ||||
\(971\) | −9.05037 | + | 9.05037i | −0.290440 | + | 0.290440i | −0.837254 | − | 0.546814i | \(-0.815840\pi\) |
0.546814 | + | 0.837254i | \(0.315840\pi\) | |||||||
\(972\) | −3.11947 | + | 1.34103i | −0.100057 | + | 0.0430135i | ||||
\(973\) | −5.64555 | − | 5.64555i | −0.180988 | − | 0.180988i | ||||
\(974\) | 8.07390 | + | 11.9111i | 0.258704 | + | 0.381657i | ||||
\(975\) | −2.79926 | −0.0896481 | ||||||||
\(976\) | −1.20415 | − | 45.2399i | −0.0385441 | − | 1.44809i | ||||
\(977\) | 38.0834 | 1.21840 | 0.609198 | − | 0.793018i | \(-0.291491\pi\) | ||||
0.609198 | + | 0.793018i | \(0.291491\pi\) | |||||||
\(978\) | −7.06552 | − | 10.4235i | −0.225931 | − | 0.333307i | ||||
\(979\) | 1.16916 | + | 1.16916i | 0.0373664 | + | 0.0373664i | ||||
\(980\) | 0.789884 | + | 1.83741i | 0.0252319 | + | 0.0586940i | ||||
\(981\) | −0.518169 | + | 0.518169i | −0.0165438 | + | 0.0165438i | ||||
\(982\) | −4.20872 | + | 21.9198i | −0.134306 | + | 0.699488i | ||||
\(983\) | 33.0264i | 1.05338i | 0.850058 | + | 0.526690i | \(0.176567\pi\) | ||||
−0.850058 | + | 0.526690i | \(0.823433\pi\) | |||||||
\(984\) | −24.7368 | − | 15.8238i | −0.788581 | − | 0.504445i | ||||
\(985\) | 22.9735i | 0.731996i | ||||||||
\(986\) | −5.60289 | − | 1.07579i | −0.178432 | − | 0.0342600i | ||||
\(987\) | 6.88271 | − | 6.88271i | 0.219079 | − | 0.219079i | ||||
\(988\) | −0.199066 | − | 0.0793694i | −0.00633312 | − | 0.00252508i | ||||
\(989\) | −22.8519 | − | 22.8519i | −0.726649 | − | 0.726649i | ||||
\(990\) | −0.176322 | + | 0.119519i | −0.00560387 | + | 0.00379855i | ||||
\(991\) | −53.6439 | −1.70405 | −0.852027 | − | 0.523498i | \(-0.824627\pi\) | ||||
−0.852027 | + | 0.523498i | \(0.824627\pi\) | |||||||
\(992\) | 34.3528 | + | 5.65267i | 1.09070 | + | 0.179473i | ||||
\(993\) | −18.0895 | −0.574053 | ||||||||
\(994\) | −2.24726 | + | 1.52329i | −0.0712786 | + | 0.0483158i | ||||
\(995\) | −3.16661 | − | 3.16661i | −0.100388 | − | 0.100388i | ||||
\(996\) | −53.3073 | − | 21.2542i | −1.68911 | − | 0.673464i | ||||
\(997\) | −24.9318 | + | 24.9318i | −0.789597 | + | 0.789597i | −0.981428 | − | 0.191831i | \(-0.938557\pi\) |
0.191831 | + | 0.981428i | \(0.438557\pi\) | |||||||
\(998\) | 47.5399 | + | 9.12792i | 1.50485 | + | 0.288939i | ||||
\(999\) | 23.2714i | 0.736273i |
(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.bd.a.141.17 | ✓ | 44 | |
4.3 | odd | 2 | 2240.2.bd.a.1681.17 | 44 | |||
16.5 | even | 4 | inner | 560.2.bd.a.421.17 | yes | 44 | |
16.11 | odd | 4 | 2240.2.bd.a.561.17 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bd.a.141.17 | ✓ | 44 | 1.1 | even | 1 | trivial | |
560.2.bd.a.421.17 | yes | 44 | 16.5 | even | 4 | inner | |
2240.2.bd.a.561.17 | 44 | 16.11 | odd | 4 | |||
2240.2.bd.a.1681.17 | 44 | 4.3 | odd | 2 |