Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.6 | ||
Root | \(0.217953 + 0.377506i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.g.508.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.929081 | − | 1.60921i | 0.656959 | − | 1.13789i | −0.324440 | − | 0.945906i | \(-0.605176\pi\) |
0.981399 | − | 0.191980i | \(-0.0614909\pi\) | |||||||
\(3\) | −1.14703 | − | 1.98672i | −0.662240 | − | 1.14703i | −0.980026 | − | 0.198871i | \(-0.936272\pi\) |
0.317785 | − | 0.948163i | \(-0.397061\pi\) | |||||||
\(4\) | −0.726381 | − | 1.25813i | −0.363191 | − | 0.629065i | ||||
\(5\) | −0.0986811 | + | 0.170921i | −0.0441315 | + | 0.0764381i | −0.887247 | − | 0.461294i | \(-0.847385\pi\) |
0.843116 | + | 0.537732i | \(0.180719\pi\) | |||||||
\(6\) | −4.26275 | −1.74026 | ||||||||
\(7\) | 2.62662 | − | 0.317598i | 0.992769 | − | 0.120041i | ||||
\(8\) | 1.01686 | 0.359513 | ||||||||
\(9\) | −1.13137 | + | 1.95960i | −0.377125 | + | 0.653199i | ||||
\(10\) | 0.183365 | + | 0.317598i | 0.0579852 | + | 0.100433i | ||||
\(11\) | −2.09137 | − | 3.62236i | −0.630571 | − | 1.09218i | −0.987435 | − | 0.158025i | \(-0.949487\pi\) |
0.356864 | − | 0.934156i | \(-0.383846\pi\) | |||||||
\(12\) | −1.66637 | + | 2.88623i | −0.481039 | + | 0.833184i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.92926 | − | 4.52187i | 0.515616 | − | 1.20852i | ||||
\(15\) | 0.452762 | 0.116903 | ||||||||
\(16\) | 2.39750 | − | 4.15260i | 0.599376 | − | 1.03815i | ||||
\(17\) | −0.420653 | − | 0.728592i | −0.102023 | − | 0.176709i | 0.810495 | − | 0.585746i | \(-0.199198\pi\) |
−0.912518 | + | 0.409036i | \(0.865865\pi\) | |||||||
\(18\) | 2.10227 | + | 3.64125i | 0.495511 | + | 0.858250i | ||||
\(19\) | 0.675876 | − | 1.17065i | 0.155057 | − | 0.268566i | −0.778023 | − | 0.628236i | \(-0.783777\pi\) |
0.933080 | + | 0.359670i | \(0.117111\pi\) | |||||||
\(20\) | 0.286720 | 0.0641126 | ||||||||
\(21\) | −3.64380 | − | 4.85406i | −0.795143 | − | 1.05924i | ||||
\(22\) | −7.77220 | −1.65704 | ||||||||
\(23\) | 2.05760 | − | 3.56386i | 0.429038 | − | 0.743116i | −0.567750 | − | 0.823201i | \(-0.692186\pi\) |
0.996788 | + | 0.0800850i | \(0.0255192\pi\) | |||||||
\(24\) | −1.16637 | − | 2.02021i | −0.238084 | − | 0.412373i | ||||
\(25\) | 2.48052 | + | 4.29639i | 0.496105 | + | 0.859279i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.69131 | −0.325492 | ||||||||
\(28\) | −2.30751 | − | 3.07393i | −0.436078 | − | 0.580918i | ||||
\(29\) | −8.23861 | −1.52987 | −0.764936 | − | 0.644106i | \(-0.777230\pi\) | ||||
−0.764936 | + | 0.644106i | \(0.777230\pi\) | |||||||
\(30\) | 0.420653 | − | 0.728592i | 0.0768003 | − | 0.133022i | ||||
\(31\) | −0.640350 | − | 1.10912i | −0.115010 | − | 0.199203i | 0.802774 | − | 0.596284i | \(-0.203357\pi\) |
−0.917784 | + | 0.397080i | \(0.870023\pi\) | |||||||
\(32\) | −3.43809 | − | 5.95495i | −0.607774 | − | 1.05270i | ||||
\(33\) | −4.79774 | + | 8.30993i | −0.835180 | + | 1.44657i | ||||
\(34\) | −1.56328 | −0.268100 | ||||||||
\(35\) | −0.204914 | + | 0.480285i | −0.0346367 | + | 0.0811829i | ||||
\(36\) | 3.28723 | 0.547872 | ||||||||
\(37\) | 1.52242 | − | 2.63692i | 0.250285 | − | 0.433506i | −0.713319 | − | 0.700839i | \(-0.752809\pi\) |
0.963604 | + | 0.267333i | \(0.0861423\pi\) | |||||||
\(38\) | −1.25589 | − | 2.17526i | −0.203732 | − | 0.352874i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.100344 | + | 0.173802i | −0.0158659 | + | 0.0274805i | ||||
\(41\) | −5.39696 | −0.842863 | −0.421431 | − | 0.906860i | \(-0.638472\pi\) | ||||
−0.421431 | + | 0.906860i | \(0.638472\pi\) | |||||||
\(42\) | −11.1966 | + | 1.35384i | −1.72768 | + | 0.208902i | ||||
\(43\) | 5.32778 | 0.812479 | 0.406239 | − | 0.913767i | \(-0.366840\pi\) | ||||
0.406239 | + | 0.913767i | \(0.366840\pi\) | |||||||
\(44\) | −3.03826 | + | 5.26242i | −0.458035 | + | 0.793340i | ||||
\(45\) | −0.223290 | − | 0.386750i | −0.0332862 | − | 0.0576534i | ||||
\(46\) | −3.82334 | − | 6.62223i | −0.563721 | − | 0.976394i | ||||
\(47\) | −5.83204 | + | 10.1014i | −0.850690 | + | 1.47344i | 0.0298969 | + | 0.999553i | \(0.490482\pi\) |
−0.880587 | + | 0.473885i | \(0.842851\pi\) | |||||||
\(48\) | −11.0001 | −1.58772 | ||||||||
\(49\) | 6.79826 | − | 1.66842i | 0.971180 | − | 0.238346i | ||||
\(50\) | 9.21843 | 1.30368 | ||||||||
\(51\) | −0.965006 | + | 1.67144i | −0.135128 | + | 0.234048i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.32398 | − | 4.02525i | −0.319223 | − | 0.552911i | 0.661103 | − | 0.750295i | \(-0.270089\pi\) |
−0.980326 | + | 0.197384i | \(0.936755\pi\) | |||||||
\(54\) | −1.57136 | + | 2.72168i | −0.213835 | + | 0.370373i | ||||
\(55\) | 0.825514 | 0.111312 | ||||||||
\(56\) | 2.67089 | − | 0.322952i | 0.356913 | − | 0.0431562i | ||||
\(57\) | −3.10101 | −0.410739 | ||||||||
\(58\) | −7.65434 | + | 13.2577i | −1.00506 | + | 1.74082i | ||||
\(59\) | 3.02905 | + | 5.24648i | 0.394349 | + | 0.683033i | 0.993018 | − | 0.117964i | \(-0.0376367\pi\) |
−0.598669 | + | 0.800997i | \(0.704303\pi\) | |||||||
\(60\) | −0.328878 | − | 0.569634i | −0.0424580 | − | 0.0735394i | ||||
\(61\) | 5.68285 | − | 9.84298i | 0.727614 | − | 1.26026i | −0.230275 | − | 0.973126i | \(-0.573962\pi\) |
0.957889 | − | 0.287139i | \(-0.0927042\pi\) | |||||||
\(62\) | −2.37975 | −0.302228 | ||||||||
\(63\) | −2.34932 | + | 5.50644i | −0.295987 | + | 0.693746i | ||||
\(64\) | −3.18704 | −0.398380 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.91498 | + | 15.4412i | 1.09736 | + | 1.90068i | ||||
\(67\) | 6.69851 | + | 11.6022i | 0.818354 | + | 1.41743i | 0.906895 | + | 0.421357i | \(0.138446\pi\) |
−0.0885411 | + | 0.996073i | \(0.528220\pi\) | |||||||
\(68\) | −0.611109 | + | 1.05847i | −0.0741078 | + | 0.128358i | ||||
\(69\) | −9.44053 | −1.13651 | ||||||||
\(70\) | 0.582500 | + | 0.775973i | 0.0696221 | + | 0.0927465i | ||||
\(71\) | 5.97040 | 0.708556 | 0.354278 | − | 0.935140i | \(-0.384727\pi\) | ||||
0.354278 | + | 0.935140i | \(0.384727\pi\) | |||||||
\(72\) | −1.15044 | + | 1.99263i | −0.135581 | + | 0.234833i | ||||
\(73\) | 1.94273 | + | 3.36491i | 0.227380 | + | 0.393833i | 0.957031 | − | 0.289986i | \(-0.0936508\pi\) |
−0.729651 | + | 0.683820i | \(0.760317\pi\) | |||||||
\(74\) | −2.82891 | − | 4.89982i | −0.328854 | − | 0.569592i | ||||
\(75\) | 5.69049 | − | 9.85622i | 0.657081 | − | 1.13810i | ||||
\(76\) | −1.96377 | −0.225260 | ||||||||
\(77\) | −6.64368 | − | 8.85034i | −0.757118 | − | 1.00859i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.36669 | − | 9.29537i | 0.603799 | − | 1.04581i | −0.388441 | − | 0.921474i | \(-0.626986\pi\) |
0.992240 | − | 0.124337i | \(-0.0396805\pi\) | |||||||
\(80\) | 0.473177 | + | 0.819566i | 0.0529028 | + | 0.0916303i | ||||
\(81\) | 5.33411 | + | 9.23895i | 0.592679 | + | 1.02655i | ||||
\(82\) | −5.01421 | + | 8.68486i | −0.553726 | + | 0.959082i | ||||
\(83\) | −3.07390 | −0.337404 | −0.168702 | − | 0.985667i | \(-0.553958\pi\) | ||||
−0.168702 | + | 0.985667i | \(0.553958\pi\) | |||||||
\(84\) | −3.46025 | + | 8.11027i | −0.377544 | + | 0.884903i | ||||
\(85\) | 0.166042 | 0.0180098 | ||||||||
\(86\) | 4.94994 | − | 8.57354i | 0.533765 | − | 0.924509i | ||||
\(87\) | 9.44997 | + | 16.3678i | 1.01314 | + | 1.75482i | ||||
\(88\) | −2.12662 | − | 3.68341i | −0.226698 | − | 0.392653i | ||||
\(89\) | −5.99207 | + | 10.3786i | −0.635159 | + | 1.10013i | 0.351323 | + | 0.936254i | \(0.385732\pi\) |
−0.986482 | + | 0.163873i | \(0.947601\pi\) | |||||||
\(90\) | −0.829819 | −0.0874706 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.97840 | −0.623291 | ||||||||
\(93\) | −1.46901 | + | 2.54439i | −0.152329 | + | 0.263841i | ||||
\(94\) | 10.8369 | + | 18.7700i | 1.11774 | + | 1.93598i | ||||
\(95\) | 0.133392 | + | 0.231042i | 0.0136858 | + | 0.0237045i | ||||
\(96\) | −7.88721 | + | 13.6611i | −0.804986 | + | 1.39428i | ||||
\(97\) | −19.4727 | −1.97716 | −0.988578 | − | 0.150709i | \(-0.951844\pi\) | ||||
−0.988578 | + | 0.150709i | \(0.951844\pi\) | |||||||
\(98\) | 3.63129 | − | 12.4900i | 0.366815 | − | 1.26168i | ||||
\(99\) | 9.46448 | 0.951216 | ||||||||
\(100\) | 3.60361 | − | 6.24164i | 0.360361 | − | 0.624164i | ||||
\(101\) | 8.46697 | + | 14.6652i | 0.842495 | + | 1.45924i | 0.887779 | + | 0.460270i | \(0.152247\pi\) |
−0.0452843 | + | 0.998974i | \(0.514419\pi\) | |||||||
\(102\) | 1.79314 | + | 3.10580i | 0.177547 | + | 0.307520i | ||||
\(103\) | 3.61712 | − | 6.26504i | 0.356406 | − | 0.617313i | −0.630952 | − | 0.775822i | \(-0.717335\pi\) |
0.987357 | + | 0.158509i | \(0.0506688\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.18923 | − | 0.143797i | 0.116057 | − | 0.0140331i | ||||
\(106\) | −8.63667 | −0.838867 | ||||||||
\(107\) | 4.92625 | − | 8.53251i | 0.476238 | − | 0.824869i | −0.523391 | − | 0.852093i | \(-0.675333\pi\) |
0.999629 | + | 0.0272237i | \(0.00866664\pi\) | |||||||
\(108\) | 1.22853 | + | 2.12788i | 0.118216 | + | 0.204756i | ||||
\(109\) | −6.90796 | − | 11.9649i | −0.661662 | − | 1.14603i | −0.980179 | − | 0.198115i | \(-0.936518\pi\) |
0.318516 | − | 0.947917i | \(-0.396815\pi\) | |||||||
\(110\) | 0.766969 | − | 1.32843i | 0.0731277 | − | 0.126661i | ||||
\(111\) | −6.98509 | −0.662995 | ||||||||
\(112\) | 4.97847 | − | 11.6687i | 0.470421 | − | 1.10259i | ||||
\(113\) | −4.26864 | −0.401560 | −0.200780 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(114\) | −2.88109 | + | 4.99019i | −0.269839 | + | 0.467374i | ||||
\(115\) | 0.406092 | + | 0.703371i | 0.0378682 | + | 0.0655897i | ||||
\(116\) | 5.98437 | + | 10.3652i | 0.555635 | + | 0.962388i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.2569 | 1.03629 | ||||||||
\(119\) | −1.33629 | − | 1.78014i | −0.122498 | − | 0.163185i | ||||
\(120\) | 0.460394 | 0.0420280 | ||||||||
\(121\) | −3.24765 | + | 5.62509i | −0.295240 | + | 0.511372i | ||||
\(122\) | −10.5596 | − | 18.2898i | −0.956026 | − | 1.65589i | ||||
\(123\) | 6.19049 | + | 10.7222i | 0.558178 | + | 0.966792i | ||||
\(124\) | −0.930276 | + | 1.61129i | −0.0835412 | + | 0.144698i | ||||
\(125\) | −1.96593 | −0.175839 | ||||||||
\(126\) | 6.67833 | + | 8.89649i | 0.594953 | + | 0.792562i | ||||
\(127\) | −2.19024 | −0.194352 | −0.0971761 | − | 0.995267i | \(-0.530981\pi\) | ||||
−0.0971761 | + | 0.995267i | \(0.530981\pi\) | |||||||
\(128\) | 3.91516 | − | 6.78126i | 0.346055 | − | 0.599385i | ||||
\(129\) | −6.11114 | − | 10.5848i | −0.538056 | − | 0.931941i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.13806 | + | 1.97117i | −0.0994326 | + | 0.172222i | −0.911450 | − | 0.411411i | \(-0.865036\pi\) |
0.812017 | + | 0.583633i | \(0.198369\pi\) | |||||||
\(132\) | 13.9400 | 1.21332 | ||||||||
\(133\) | 1.40347 | − | 3.28951i | 0.121696 | − | 0.285237i | ||||
\(134\) | 24.8938 | 2.15050 | ||||||||
\(135\) | 0.166900 | − | 0.289079i | 0.0143645 | − | 0.0248800i | ||||
\(136\) | −0.427743 | − | 0.740873i | −0.0366787 | − | 0.0635293i | ||||
\(137\) | 6.72399 | + | 11.6463i | 0.574469 | + | 0.995010i | 0.996099 | + | 0.0882417i | \(0.0281248\pi\) |
−0.421630 | + | 0.906768i | \(0.638542\pi\) | |||||||
\(138\) | −8.77101 | + | 15.1918i | −0.746638 | + | 1.29321i | ||||
\(139\) | 4.04540 | 0.343126 | 0.171563 | − | 0.985173i | \(-0.445118\pi\) | ||||
0.171563 | + | 0.985173i | \(0.445118\pi\) | |||||||
\(140\) | 0.753106 | − | 0.0910619i | 0.0636490 | − | 0.00769614i | ||||
\(141\) | 26.7582 | 2.25344 | ||||||||
\(142\) | 5.54698 | − | 9.60765i | 0.465492 | − | 0.806256i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.42494 | + | 9.39628i | 0.452079 | + | 0.783023i | ||||
\(145\) | 0.812996 | − | 1.40815i | 0.0675156 | − | 0.116940i | ||||
\(146\) | 7.21982 | 0.597517 | ||||||||
\(147\) | −11.1125 | − | 11.5925i | −0.916545 | − | 0.956135i | ||||
\(148\) | −4.42344 | −0.363605 | ||||||||
\(149\) | 7.67596 | − | 13.2952i | 0.628840 | − | 1.08918i | −0.358945 | − | 0.933359i | \(-0.616864\pi\) |
0.987785 | − | 0.155823i | \(-0.0498031\pi\) | |||||||
\(150\) | −10.5738 | − | 18.3144i | −0.863351 | − | 1.49537i | ||||
\(151\) | 3.06054 | + | 5.30101i | 0.249063 | + | 0.431390i | 0.963266 | − | 0.268548i | \(-0.0865439\pi\) |
−0.714203 | + | 0.699939i | \(0.753211\pi\) | |||||||
\(152\) | 0.687268 | − | 1.19038i | 0.0557448 | − | 0.0965528i | ||||
\(153\) | 1.90366 | 0.153902 | ||||||||
\(154\) | −20.4146 | + | 2.46844i | −1.64506 | + | 0.198912i | ||||
\(155\) | 0.252762 | 0.0203023 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.26834 | − | 3.92888i | −0.181033 | − | 0.313559i | 0.761199 | − | 0.648518i | \(-0.224611\pi\) |
−0.942233 | + | 0.334959i | \(0.891278\pi\) | |||||||
\(158\) | −9.97217 | − | 17.2723i | −0.793343 | − | 1.37411i | ||||
\(159\) | −5.33137 | + | 9.23421i | −0.422805 | + | 0.732320i | ||||
\(160\) | 1.35710 | 0.107288 | ||||||||
\(161\) | 4.27265 | − | 10.0144i | 0.336732 | − | 0.789245i | ||||
\(162\) | 19.8233 | 1.55746 | ||||||||
\(163\) | 0.911271 | − | 1.57837i | 0.0713762 | − | 0.123627i | −0.828128 | − | 0.560538i | \(-0.810594\pi\) |
0.899505 | + | 0.436911i | \(0.143928\pi\) | |||||||
\(164\) | 3.92025 | + | 6.79007i | 0.306120 | + | 0.530215i | ||||
\(165\) | −0.946893 | − | 1.64007i | −0.0737155 | − | 0.127679i | ||||
\(166\) | −2.85590 | + | 4.94656i | −0.221661 | + | 0.383928i | ||||
\(167\) | 10.7079 | 0.828606 | 0.414303 | − | 0.910139i | \(-0.364025\pi\) | ||||
0.414303 | + | 0.910139i | \(0.364025\pi\) | |||||||
\(168\) | −3.70522 | − | 4.93588i | −0.285864 | − | 0.380812i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.154266 | − | 0.267197i | 0.0118317 | − | 0.0204931i | ||||
\(171\) | 1.52934 | + | 2.64889i | 0.116951 | + | 0.202566i | ||||
\(172\) | −3.87000 | − | 6.70303i | −0.295085 | − | 0.511102i | ||||
\(173\) | 6.74634 | − | 11.6850i | 0.512915 | − | 0.888395i | −0.486973 | − | 0.873417i | \(-0.661899\pi\) |
0.999888 | − | 0.0149778i | \(-0.00476775\pi\) | |||||||
\(174\) | 35.1191 | 2.66237 | ||||||||
\(175\) | 7.87992 | + | 10.4972i | 0.595666 | + | 0.793512i | ||||
\(176\) | −20.0563 | −1.51180 | ||||||||
\(177\) | 6.94886 | − | 12.0358i | 0.522308 | − | 0.904664i | ||||
\(178\) | 11.1342 | + | 19.2851i | 0.834547 | + | 1.44548i | ||||
\(179\) | −5.23458 | − | 9.06657i | −0.391251 | − | 0.677667i | 0.601364 | − | 0.798975i | \(-0.294624\pi\) |
−0.992615 | + | 0.121309i | \(0.961291\pi\) | |||||||
\(180\) | −0.324388 | + | 0.561857i | −0.0241785 | + | 0.0418783i | ||||
\(181\) | 12.5209 | 0.930674 | 0.465337 | − | 0.885133i | \(-0.345933\pi\) | ||||
0.465337 | + | 0.885133i | \(0.345933\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.0737 | −1.92742 | ||||||||
\(184\) | 2.09228 | − | 3.62393i | 0.154245 | − | 0.267160i | ||||
\(185\) | 0.300469 | + | 0.520428i | 0.0220909 | + | 0.0382626i | ||||
\(186\) | 2.72965 | + | 4.72789i | 0.200148 | + | 0.346666i | ||||
\(187\) | −1.75948 | + | 3.04751i | −0.128666 | + | 0.222856i | ||||
\(188\) | 16.9451 | 1.23585 | ||||||||
\(189\) | −4.44242 | + | 0.537156i | −0.323139 | + | 0.0390724i | ||||
\(190\) | 0.495729 | 0.0359640 | ||||||||
\(191\) | −6.55685 | + | 11.3568i | −0.474437 | + | 0.821749i | −0.999572 | − | 0.0292704i | \(-0.990682\pi\) |
0.525135 | + | 0.851019i | \(0.324015\pi\) | |||||||
\(192\) | 3.65565 | + | 6.33176i | 0.263823 | + | 0.456956i | ||||
\(193\) | 0.520786 | + | 0.902028i | 0.0374870 | + | 0.0649294i | 0.884160 | − | 0.467184i | \(-0.154731\pi\) |
−0.846673 | + | 0.532113i | \(0.821398\pi\) | |||||||
\(194\) | −18.0917 | + | 31.3358i | −1.29891 | + | 2.24978i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.03722 | − | 7.34118i | −0.502658 | − | 0.524370i | ||||
\(197\) | −1.47833 | −0.105327 | −0.0526635 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526635 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(198\) | 8.79326 | − | 15.2304i | 0.624910 | − | 1.08238i | ||||
\(199\) | −7.04993 | − | 12.2108i | −0.499756 | − | 0.865603i | 0.500244 | − | 0.865885i | \(-0.333244\pi\) |
−1.00000 | 0.000281618i | \(0.999910\pi\) | ||||||||
\(200\) | 2.52233 | + | 4.36881i | 0.178356 | + | 0.308922i | ||||
\(201\) | 15.3668 | − | 26.6162i | 1.08389 | − | 1.87736i | ||||
\(202\) | 31.4660 | 2.21394 | ||||||||
\(203\) | −21.6397 | + | 2.61657i | −1.51881 | + | 0.183647i | ||||
\(204\) | 2.80385 | 0.196309 | ||||||||
\(205\) | 0.532578 | − | 0.922451i | 0.0371968 | − | 0.0644268i | ||||
\(206\) | −6.72120 | − | 11.6415i | −0.468288 | − | 0.811099i | ||||
\(207\) | 4.65582 | + | 8.06412i | 0.323602 | + | 0.560495i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65402 | −0.391097 | ||||||||
\(210\) | 0.873495 | − | 2.04733i | 0.0602769 | − | 0.141279i | ||||
\(211\) | 26.4692 | 1.82222 | 0.911108 | − | 0.412167i | \(-0.135228\pi\) | ||||
0.911108 | + | 0.412167i | \(0.135228\pi\) | |||||||
\(212\) | −3.37619 | + | 5.84774i | −0.231878 | + | 0.401624i | ||||
\(213\) | −6.84825 | − | 11.8615i | −0.469234 | − | 0.812737i | ||||
\(214\) | −9.15376 | − | 15.8548i | −0.625738 | − | 1.08381i | ||||
\(215\) | −0.525751 | + | 0.910628i | −0.0358559 | + | 0.0621043i | ||||
\(216\) | −1.71981 | −0.117019 | ||||||||
\(217\) | −2.03421 | − | 2.70986i | −0.138091 | − | 0.183957i | ||||
\(218\) | −25.6722 | −1.73874 | ||||||||
\(219\) | 4.45676 | − | 7.71934i | 0.301160 | − | 0.521625i | ||||
\(220\) | −0.599638 | − | 1.03860i | −0.0404276 | − | 0.0700227i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.48971 | + | 11.2405i | −0.435561 | + | 0.754414i | ||||
\(223\) | 0.728048 | 0.0487537 | 0.0243769 | − | 0.999703i | \(-0.492240\pi\) | ||||
0.0243769 | + | 0.999703i | \(0.492240\pi\) | |||||||
\(224\) | −10.9218 | − | 14.5495i | −0.729746 | − | 0.972126i | ||||
\(225\) | −11.2256 | −0.748373 | ||||||||
\(226\) | −3.96591 | + | 6.86916i | −0.263808 | + | 0.456929i | ||||
\(227\) | −1.42598 | − | 2.46986i | −0.0946454 | − | 0.163931i | 0.814815 | − | 0.579721i | \(-0.196838\pi\) |
−0.909461 | + | 0.415790i | \(0.863505\pi\) | |||||||
\(228\) | 2.25252 | + | 3.90147i | 0.149177 | + | 0.258381i | ||||
\(229\) | 1.58676 | − | 2.74835i | 0.104856 | − | 0.181616i | −0.808823 | − | 0.588052i | \(-0.799895\pi\) |
0.913679 | + | 0.406436i | \(0.133228\pi\) | |||||||
\(230\) | 1.50917 | 0.0995116 | ||||||||
\(231\) | −9.96262 | + | 23.3508i | −0.655492 | + | 1.53637i | ||||
\(232\) | −8.37748 | −0.550009 | ||||||||
\(233\) | −6.70354 | + | 11.6109i | −0.439163 | + | 0.760653i | −0.997625 | − | 0.0688769i | \(-0.978058\pi\) |
0.558462 | + | 0.829530i | \(0.311392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.15102 | − | 1.99363i | −0.0750845 | − | 0.130050i | ||||
\(236\) | 4.40050 | − | 7.62188i | 0.286448 | − | 0.496142i | ||||
\(237\) | −24.6231 | −1.59944 | ||||||||
\(238\) | −4.10614 | + | 0.496495i | −0.266162 | + | 0.0321830i | ||||
\(239\) | 15.5538 | 1.00609 | 0.503046 | − | 0.864259i | \(-0.332212\pi\) | ||||
0.503046 | + | 0.864259i | \(0.332212\pi\) | |||||||
\(240\) | 1.08550 | − | 1.88014i | 0.0700687 | − | 0.121363i | ||||
\(241\) | −3.78787 | − | 6.56078i | −0.243998 | − | 0.422617i | 0.717851 | − | 0.696196i | \(-0.245126\pi\) |
−0.961849 | + | 0.273579i | \(0.911792\pi\) | |||||||
\(242\) | 6.03465 | + | 10.4523i | 0.387922 | + | 0.671900i | ||||
\(243\) | 9.69985 | − | 16.8006i | 0.622245 | − | 1.07776i | ||||
\(244\) | −16.5117 | −1.05705 | ||||||||
\(245\) | −0.385693 | + | 1.32661i | −0.0246410 | + | 0.0847537i | ||||
\(246\) | 23.0059 | 1.46680 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.651143 | − | 1.12781i | −0.0413476 | − | 0.0716162i | ||||
\(249\) | 3.52587 | + | 6.10698i | 0.223443 | + | 0.387014i | ||||
\(250\) | −1.82651 | + | 3.16361i | −0.115519 | + | 0.200084i | ||||
\(251\) | 1.27476 | 0.0804624 | 0.0402312 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402312 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(252\) | 8.63432 | − | 1.04402i | 0.543911 | − | 0.0657671i | ||||
\(253\) | −17.2128 | −1.08216 | ||||||||
\(254\) | −2.03491 | + | 3.52456i | −0.127682 | + | 0.221151i | ||||
\(255\) | −0.190456 | − | 0.329879i | −0.0119268 | − | 0.0206578i | ||||
\(256\) | −10.4620 | − | 18.1208i | −0.653878 | − | 1.13255i | ||||
\(257\) | 4.24010 | − | 7.34406i | 0.264490 | − | 0.458110i | −0.702940 | − | 0.711249i | \(-0.748130\pi\) |
0.967430 | + | 0.253139i | \(0.0814631\pi\) | |||||||
\(258\) | −22.7110 | −1.41392 | ||||||||
\(259\) | 3.16135 | − | 7.40970i | 0.196437 | − | 0.460416i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.32095 | − | 16.1444i | 0.576952 | − | 0.999311i | ||||
\(262\) | 2.11470 | + | 3.66276i | 0.130646 | + | 0.226286i | ||||
\(263\) | −6.39415 | − | 11.0750i | −0.394280 | − | 0.682913i | 0.598729 | − | 0.800952i | \(-0.295673\pi\) |
−0.993009 | + | 0.118038i | \(0.962339\pi\) | |||||||
\(264\) | −4.87861 | + | 8.45000i | −0.300258 | + | 0.520062i | ||||
\(265\) | 0.917333 | 0.0563513 | ||||||||
\(266\) | −3.98959 | − | 5.31471i | −0.244618 | − | 0.325866i | ||||
\(267\) | 27.4925 | 1.68251 | ||||||||
\(268\) | 9.73135 | − | 16.8552i | 0.594437 | − | 1.02959i | ||||
\(269\) | 2.35586 | + | 4.08047i | 0.143639 | + | 0.248790i | 0.928864 | − | 0.370420i | \(-0.120786\pi\) |
−0.785225 | + | 0.619210i | \(0.787453\pi\) | |||||||
\(270\) | −0.310127 | − | 0.537156i | −0.0188737 | − | 0.0326903i | ||||
\(271\) | −9.00562 | + | 15.5982i | −0.547052 | + | 0.947522i | 0.451422 | + | 0.892310i | \(0.350917\pi\) |
−0.998475 | + | 0.0552119i | \(0.982417\pi\) | |||||||
\(272\) | −4.03407 | −0.244601 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.9885 | 1.50961 | ||||||||
\(275\) | 10.3754 | − | 17.9707i | 0.625659 | − | 1.08367i | ||||
\(276\) | 6.85742 | + | 11.8774i | 0.412768 | + | 0.714936i | ||||
\(277\) | 13.0604 | + | 22.6213i | 0.784725 | + | 1.35918i | 0.929163 | + | 0.369670i | \(0.120529\pi\) |
−0.144438 | + | 0.989514i | \(0.546137\pi\) | |||||||
\(278\) | 3.75850 | − | 6.50991i | 0.225420 | − | 0.390439i | ||||
\(279\) | 2.89790 | 0.173493 | ||||||||
\(280\) | −0.208368 | + | 0.488380i | −0.0124523 | + | 0.0291863i | ||||
\(281\) | 3.66197 | 0.218455 | 0.109227 | − | 0.994017i | \(-0.465162\pi\) | ||||
0.109227 | + | 0.994017i | \(0.465162\pi\) | |||||||
\(282\) | 24.8605 | − | 43.0596i | 1.48042 | − | 2.56416i | ||||
\(283\) | −3.82263 | − | 6.62099i | −0.227232 | − | 0.393577i | 0.729755 | − | 0.683709i | \(-0.239634\pi\) |
−0.956987 | + | 0.290132i | \(0.906301\pi\) | |||||||
\(284\) | −4.33678 | − | 7.51153i | −0.257341 | − | 0.445727i | ||||
\(285\) | 0.306011 | − | 0.530027i | 0.0181265 | − | 0.0313961i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.1757 | + | 1.71406i | −0.836768 | + | 0.101178i | ||||
\(288\) | 15.5591 | 0.916827 | ||||||||
\(289\) | 8.14610 | − | 14.1095i | 0.479183 | − | 0.829968i | ||||
\(290\) | −1.51068 | − | 2.61657i | −0.0887100 | − | 0.153650i | ||||
\(291\) | 22.3359 | + | 38.6869i | 1.30935 | + | 2.26787i | ||||
\(292\) | 2.82233 | − | 4.88842i | 0.165164 | − | 0.286073i | ||||
\(293\) | 17.1534 | 1.00211 | 0.501056 | − | 0.865415i | \(-0.332945\pi\) | ||||
0.501056 | + | 0.865415i | \(0.332945\pi\) | |||||||
\(294\) | −28.9793 | + | 7.11205i | −1.69011 | + | 0.414783i | ||||
\(295\) | −1.19564 | −0.0696130 | ||||||||
\(296\) | 1.54809 | − | 2.68136i | 0.0899807 | − | 0.155851i | ||||
\(297\) | 3.53715 | + | 6.12652i | 0.205246 | + | 0.355497i | ||||
\(298\) | −14.2632 | − | 24.7045i | −0.826244 | − | 1.43110i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −16.5339 | −0.954583 | ||||||||
\(301\) | 13.9940 | − | 1.69209i | 0.806604 | − | 0.0975306i | ||||
\(302\) | 11.3740 | 0.654498 | ||||||||
\(303\) | 19.4238 | − | 33.6430i | 1.11587 | − | 1.93274i | ||||
\(304\) | −3.24083 | − | 5.61328i | −0.185874 | − | 0.321944i | ||||
\(305\) | 1.12158 | + | 1.94263i | 0.0642215 | + | 0.111235i | ||||
\(306\) | 1.76866 | − | 3.06340i | 0.101107 | − | 0.175123i | ||||
\(307\) | 28.0696 | 1.60201 | 0.801007 | − | 0.598655i | \(-0.204298\pi\) | ||||
0.801007 | + | 0.598655i | \(0.204298\pi\) | |||||||
\(308\) | −6.30902 | + | 14.7873i | −0.359490 | + | 0.842586i | ||||
\(309\) | −16.5959 | −0.944105 | ||||||||
\(310\) | 0.234836 | − | 0.406748i | 0.0133378 | − | 0.0231017i | ||||
\(311\) | 11.7670 | + | 20.3811i | 0.667248 | + | 1.15571i | 0.978671 | + | 0.205436i | \(0.0658611\pi\) |
−0.311423 | + | 0.950271i | \(0.600806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.67430 | − | 2.89997i | 0.0946370 | − | 0.163916i | −0.814820 | − | 0.579714i | \(-0.803164\pi\) |
0.909457 | + | 0.415798i | \(0.136498\pi\) | |||||||
\(314\) | −8.42989 | −0.475726 | ||||||||
\(315\) | −0.709330 | − | 0.944930i | −0.0399662 | − | 0.0532408i | ||||
\(316\) | −15.5930 | −0.877177 | ||||||||
\(317\) | −3.63917 | + | 6.30323i | −0.204396 | + | 0.354025i | −0.949940 | − | 0.312432i | \(-0.898856\pi\) |
0.745544 | + | 0.666456i | \(0.232190\pi\) | |||||||
\(318\) | 9.90655 | + | 17.1586i | 0.555532 | + | 0.962209i | ||||
\(319\) | 17.2300 | + | 29.8432i | 0.964694 | + | 1.67090i | ||||
\(320\) | 0.314501 | − | 0.544732i | 0.0175811 | − | 0.0304514i | ||||
\(321\) | −22.6023 | −1.26154 | ||||||||
\(322\) | −12.1457 | − | 16.1798i | −0.676852 | − | 0.901664i | ||||
\(323\) | −1.13724 | −0.0632775 | ||||||||
\(324\) | 7.74919 | − | 13.4220i | 0.430511 | − | 0.745666i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.69329 | − | 2.93286i | −0.0937826 | − | 0.162436i | ||||
\(327\) | −15.8473 | + | 27.4484i | −0.876359 | + | 1.51790i | ||||
\(328\) | −5.48792 | −0.303020 | ||||||||
\(329\) | −12.1104 | + | 28.3847i | −0.667666 | + | 1.56490i | ||||
\(330\) | −3.51896 | −0.193712 | ||||||||
\(331\) | −7.16168 | + | 12.4044i | −0.393642 | + | 0.681807i | −0.992927 | − | 0.118728i | \(-0.962118\pi\) |
0.599285 | + | 0.800536i | \(0.295452\pi\) | |||||||
\(332\) | 2.23282 | + | 3.86736i | 0.122542 | + | 0.212249i | ||||
\(333\) | 3.44486 | + | 5.96668i | 0.188777 | + | 0.326972i | ||||
\(334\) | 9.94855 | − | 17.2314i | 0.544360 | − | 0.942860i | ||||
\(335\) | −2.64407 | −0.144461 | ||||||||
\(336\) | −28.8930 | + | 3.49360i | −1.57624 | + | 0.190592i | ||||
\(337\) | 17.1802 | 0.935868 | 0.467934 | − | 0.883764i | \(-0.344999\pi\) | ||||
0.467934 | + | 0.883764i | \(0.344999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.89627 | + | 8.48060i | 0.265929 | + | 0.460603i | ||||
\(340\) | −0.120610 | − | 0.208902i | −0.00654098 | − | 0.0113293i | ||||
\(341\) | −2.67841 | + | 4.63915i | −0.145044 | + | 0.251224i | ||||
\(342\) | 5.68351 | 0.307329 | ||||||||
\(343\) | 17.3266 | − | 6.54142i | 0.935547 | − | 0.353203i | ||||
\(344\) | 5.41758 | 0.292096 | ||||||||
\(345\) | 0.931602 | − | 1.61358i | 0.0501558 | − | 0.0868723i | ||||
\(346\) | −12.5358 | − | 21.7126i | −0.673928 | − | 1.16728i | ||||
\(347\) | 3.85139 | + | 6.67080i | 0.206753 | + | 0.358107i | 0.950690 | − | 0.310143i | \(-0.100377\pi\) |
−0.743937 | + | 0.668250i | \(0.767044\pi\) | |||||||
\(348\) | 13.7286 | − | 23.7786i | 0.735928 | − | 1.27466i | ||||
\(349\) | −22.3701 | −1.19744 | −0.598721 | − | 0.800958i | \(-0.704324\pi\) | ||||
−0.598721 | + | 0.800958i | \(0.704324\pi\) | |||||||
\(350\) | 24.2133 | − | 2.92776i | 1.29426 | − | 0.156495i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.3806 | + | 24.9080i | −0.766490 | + | 1.32760i | ||||
\(353\) | −11.1311 | − | 19.2797i | −0.592451 | − | 1.02616i | −0.993901 | − | 0.110275i | \(-0.964827\pi\) |
0.401450 | − | 0.915881i | \(-0.368506\pi\) | |||||||
\(354\) | −12.9121 | − | 22.3644i | −0.686270 | − | 1.18865i | ||||
\(355\) | −0.589165 | + | 1.02046i | −0.0312697 | + | 0.0541606i | ||||
\(356\) | 17.4101 | 0.922735 | ||||||||
\(357\) | −2.00386 | + | 4.69672i | −0.106055 | + | 0.248577i | ||||
\(358\) | −19.4534 | −1.02814 | ||||||||
\(359\) | −1.37921 | + | 2.38887i | −0.0727920 | + | 0.126079i | −0.900124 | − | 0.435634i | \(-0.856524\pi\) |
0.827332 | + | 0.561713i | \(0.189858\pi\) | |||||||
\(360\) | −0.227054 | − | 0.393269i | −0.0119668 | − | 0.0207271i | ||||
\(361\) | 8.58638 | + | 14.8721i | 0.451915 | + | 0.782740i | ||||
\(362\) | 11.6330 | − | 20.1489i | 0.611415 | − | 1.05900i | ||||
\(363\) | 14.9006 | 0.782081 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.766844 | −0.0401385 | ||||||||
\(366\) | −24.2246 | + | 41.9582i | −1.26624 | + | 2.19319i | ||||
\(367\) | 7.07485 | + | 12.2540i | 0.369304 | + | 0.639654i | 0.989457 | − | 0.144827i | \(-0.0462626\pi\) |
−0.620153 | + | 0.784481i | \(0.712929\pi\) | |||||||
\(368\) | −9.86618 | − | 17.0887i | −0.514310 | − | 0.890812i | ||||
\(369\) | 6.10597 | − | 10.5759i | 0.317864 | − | 0.550557i | ||||
\(370\) | 1.11664 | 0.0580514 | ||||||||
\(371\) | −7.38263 | − | 9.83472i | −0.383287 | − | 0.510593i | ||||
\(372\) | 4.26823 | 0.221298 | ||||||||
\(373\) | 2.52142 | − | 4.36723i | 0.130554 | − | 0.226127i | −0.793336 | − | 0.608784i | \(-0.791658\pi\) |
0.923890 | + | 0.382657i | \(0.124991\pi\) | |||||||
\(374\) | 3.26940 | + | 5.66276i | 0.169056 | + | 0.292814i | ||||
\(375\) | 2.25499 | + | 3.90576i | 0.116447 | + | 0.201693i | ||||
\(376\) | −5.93034 | + | 10.2716i | −0.305834 | + | 0.529720i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.26297 | + | 7.64787i | −0.167829 | + | 0.393364i | ||||
\(379\) | 6.05964 | 0.311263 | 0.155631 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155631 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(380\) | 0.193787 | − | 0.335650i | 0.00994109 | − | 0.0172185i | ||||
\(381\) | 2.51228 | + | 4.35139i | 0.128708 | + | 0.222929i | ||||
\(382\) | 12.1837 | + | 21.1028i | 0.623371 | + | 1.07971i | ||||
\(383\) | −2.27052 | + | 3.93266i | −0.116018 | + | 0.200950i | −0.918186 | − | 0.396149i | \(-0.870346\pi\) |
0.802168 | + | 0.597098i | \(0.203680\pi\) | |||||||
\(384\) | −17.9633 | −0.916686 | ||||||||
\(385\) | 2.16831 | − | 0.262182i | 0.110507 | − | 0.0133620i | ||||
\(386\) | 1.93541 | 0.0985098 | ||||||||
\(387\) | −6.02771 | + | 10.4403i | −0.306406 | + | 0.530710i | ||||
\(388\) | 14.1446 | + | 24.4992i | 0.718085 | + | 1.24376i | ||||
\(389\) | −2.25383 | − | 3.90374i | −0.114273 | − | 0.197927i | 0.803216 | − | 0.595688i | \(-0.203121\pi\) |
−0.917489 | + | 0.397761i | \(0.869787\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.46213 | −0.175088 | ||||||||
\(392\) | 6.91285 | − | 1.69654i | 0.349152 | − | 0.0856883i | ||||
\(393\) | 5.22157 | 0.263393 | ||||||||
\(394\) | −1.37349 | + | 2.37896i | −0.0691955 | + | 0.119850i | ||||
\(395\) | 1.05918 | + | 1.83456i | 0.0532932 | + | 0.0923065i | ||||
\(396\) | −6.87482 | − | 11.9075i | −0.345473 | − | 0.598376i | ||||
\(397\) | 2.00174 | − | 3.46712i | 0.100465 | − | 0.174010i | −0.811412 | − | 0.584475i | \(-0.801300\pi\) |
0.911876 | + | 0.410465i | \(0.134634\pi\) | |||||||
\(398\) | −26.1998 | −1.31328 | ||||||||
\(399\) | −8.14518 | + | 0.984875i | −0.407769 | + | 0.0493054i | ||||
\(400\) | 23.7883 | 1.18941 | ||||||||
\(401\) | 6.30674 | − | 10.9236i | 0.314944 | − | 0.545498i | −0.664482 | − | 0.747304i | \(-0.731348\pi\) |
0.979426 | + | 0.201806i | \(0.0646810\pi\) | |||||||
\(402\) | −28.5541 | − | 49.4571i | −1.42415 | − | 2.46670i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.3005 | − | 21.3051i | 0.611972 | − | 1.05997i | ||||
\(405\) | −2.10550 | −0.104623 | ||||||||
\(406\) | −15.8944 | + | 37.2539i | −0.788826 | + | 1.84888i | ||||
\(407\) | −12.7358 | −0.631290 | ||||||||
\(408\) | −0.981272 | + | 1.69961i | −0.0485802 | + | 0.0841434i | ||||
\(409\) | 10.3476 | + | 17.9226i | 0.511657 | + | 0.886216i | 0.999909 | + | 0.0135128i | \(0.00430140\pi\) |
−0.488252 | + | 0.872703i | \(0.662365\pi\) | |||||||
\(410\) | −0.989615 | − | 1.71406i | −0.0488736 | − | 0.0846516i | ||||
\(411\) | 15.4253 | − | 26.7174i | 0.760873 | − | 1.31787i | ||||
\(412\) | −10.5096 | −0.517773 | ||||||||
\(413\) | 9.62244 | + | 12.8185i | 0.473490 | + | 0.630756i | ||||
\(414\) | 17.3025 | 0.850373 | ||||||||
\(415\) | 0.303336 | − | 0.525393i | 0.0148902 | − | 0.0257905i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.64021 | − | 8.03708i | −0.227232 | − | 0.393577i | ||||
\(418\) | −5.25304 | + | 9.09854i | −0.256935 | + | 0.445024i | ||||
\(419\) | −21.8175 | −1.06586 | −0.532928 | − | 0.846161i | \(-0.678908\pi\) | ||||
−0.532928 | + | 0.846161i | \(0.678908\pi\) | |||||||
\(420\) | −1.04475 | − | 1.39176i | −0.0509787 | − | 0.0679109i | ||||
\(421\) | −9.42727 | −0.459457 | −0.229728 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229728 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(422\) | 24.5920 | − | 42.5947i | 1.19712 | − | 2.07348i | ||||
\(423\) | −13.1964 | − | 22.8569i | −0.641632 | − | 1.11134i | ||||
\(424\) | −2.36315 | − | 4.09310i | −0.114765 | − | 0.198779i | ||||
\(425\) | 2.08688 | − | 3.61458i | 0.101228 | − | 0.175333i | ||||
\(426\) | −25.4503 | −1.23307 | ||||||||
\(427\) | 11.8006 | − | 27.6586i | 0.571070 | − | 1.33850i | ||||
\(428\) | −14.3133 | −0.691861 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.976930 | + | 1.69209i | 0.0471118 | + | 0.0816000i | ||||
\(431\) | 10.2138 | + | 17.6908i | 0.491980 | + | 0.852134i | 0.999957 | − | 0.00923613i | \(-0.00293999\pi\) |
−0.507977 | + | 0.861370i | \(0.669607\pi\) | |||||||
\(432\) | −4.05491 | + | 7.02332i | −0.195092 | + | 0.337909i | ||||
\(433\) | 26.3486 | 1.26623 | 0.633117 | − | 0.774056i | \(-0.281775\pi\) | ||||
0.633117 | + | 0.774056i | \(0.281775\pi\) | |||||||
\(434\) | −6.25069 | + | 0.755803i | −0.300043 | + | 0.0362797i | ||||
\(435\) | −3.73014 | −0.178846 | ||||||||
\(436\) | −10.0356 | + | 17.3822i | −0.480619 | + | 0.832457i | ||||
\(437\) | −2.78136 | − | 4.81745i | −0.133050 | − | 0.230450i | ||||
\(438\) | −8.28138 | − | 14.3438i | −0.395700 | − | 0.685372i | ||||
\(439\) | −12.5655 | + | 21.7641i | −0.599720 | + | 1.03875i | 0.393142 | + | 0.919478i | \(0.371388\pi\) |
−0.992862 | + | 0.119267i | \(0.961945\pi\) | |||||||
\(440\) | 0.839429 | 0.0400182 | ||||||||
\(441\) | −4.42195 | + | 15.2095i | −0.210569 | + | 0.724260i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.25995 | + | 16.0387i | −0.439953 | + | 0.762022i | −0.997685 | − | 0.0679994i | \(-0.978338\pi\) |
0.557732 | + | 0.830021i | \(0.311672\pi\) | |||||||
\(444\) | 5.07384 | + | 8.78815i | 0.240794 | + | 0.417067i | ||||
\(445\) | −1.18261 | − | 2.04834i | −0.0560611 | − | 0.0971006i | ||||
\(446\) | 0.676415 | − | 1.17159i | 0.0320292 | − | 0.0554762i | ||||
\(447\) | −35.2184 | −1.66577 | ||||||||
\(448\) | −8.37115 | + | 1.01220i | −0.395500 | + | 0.0478219i | ||||
\(449\) | −11.6431 | −0.549471 | −0.274736 | − | 0.961520i | \(-0.588590\pi\) | ||||
−0.274736 | + | 0.961520i | \(0.588590\pi\) | |||||||
\(450\) | −10.4295 | + | 18.0644i | −0.491651 | + | 0.851564i | ||||
\(451\) | 11.2870 | + | 19.5497i | 0.531485 | + | 0.920559i | ||||
\(452\) | 3.10066 | + | 5.37050i | 0.145843 | + | 0.252607i | ||||
\(453\) | 7.02109 | − | 12.1609i | 0.329880 | − | 0.571368i | ||||
\(454\) | −5.29939 | −0.248713 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.15328 | −0.147666 | ||||||||
\(457\) | 10.2592 | − | 17.7695i | 0.479906 | − | 0.831222i | −0.519828 | − | 0.854271i | \(-0.674004\pi\) |
0.999734 | + | 0.0230490i | \(0.00733739\pi\) | |||||||
\(458\) | −2.94845 | − | 5.10687i | −0.137772 | − | 0.238629i | ||||
\(459\) | 0.711453 | + | 1.23227i | 0.0332078 | + | 0.0575176i | ||||
\(460\) | 0.589955 | − | 1.02183i | 0.0275068 | − | 0.0476431i | ||||
\(461\) | −2.04075 | −0.0950473 | −0.0475236 | − | 0.998870i | \(-0.515133\pi\) | ||||
−0.0475236 | + | 0.998870i | \(0.515133\pi\) | |||||||
\(462\) | 28.3203 | + | 37.7268i | 1.31758 | + | 1.75521i | ||||
\(463\) | −3.03155 | −0.140888 | −0.0704441 | − | 0.997516i | \(-0.522442\pi\) | ||||
−0.0704441 | + | 0.997516i | \(0.522442\pi\) | |||||||
\(464\) | −19.7521 | + | 34.2116i | −0.916968 | + | 1.58824i | ||||
\(465\) | −0.289926 | − | 0.502167i | −0.0134450 | − | 0.0232874i | ||||
\(466\) | 12.4563 | + | 21.5749i | 0.577025 | + | 0.999436i | ||||
\(467\) | 6.46371 | − | 11.1955i | 0.299105 | − | 0.518065i | −0.676827 | − | 0.736142i | \(-0.736645\pi\) |
0.975931 | + | 0.218078i | \(0.0699787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.2793 | + | 28.3470i | 0.982585 | + | 1.30894i | ||||
\(470\) | −4.27757 | −0.197310 | ||||||||
\(471\) | −5.20373 | + | 9.01312i | −0.239775 | + | 0.415303i | ||||
\(472\) | 3.08011 | + | 5.33491i | 0.141774 | + | 0.245559i | ||||
\(473\) | −11.1423 | − | 19.2991i | −0.512326 | − | 0.887374i | ||||
\(474\) | −22.8768 | + | 39.6238i | −1.05077 | + | 1.81998i | ||||
\(475\) | 6.70611 | 0.307697 | ||||||||
\(476\) | −1.26898 | + | 2.97429i | −0.0581637 | + | 0.136326i | ||||
\(477\) | 10.5172 | 0.481548 | ||||||||
\(478\) | 14.4507 | − | 25.0294i | 0.660962 | − | 1.14482i | ||||
\(479\) | 18.2911 | + | 31.6810i | 0.835740 | + | 1.44754i | 0.893427 | + | 0.449209i | \(0.148294\pi\) |
−0.0576873 | + | 0.998335i | \(0.518373\pi\) | |||||||
\(480\) | −1.55664 | − | 2.69618i | −0.0710505 | − | 0.123063i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14.0769 | −0.641187 | ||||||||
\(483\) | −24.7967 | + | 2.99830i | −1.12829 | + | 0.136427i | ||||
\(484\) | 9.43611 | 0.428914 | ||||||||
\(485\) | 1.92159 | − | 3.32829i | 0.0872550 | − | 0.151130i | ||||
\(486\) | −18.0239 | − | 31.2183i | −0.817580 | − | 1.41609i | ||||
\(487\) | 18.3748 | + | 31.8261i | 0.832642 | + | 1.44218i | 0.895936 | + | 0.444183i | \(0.146506\pi\) |
−0.0632939 | + | 0.997995i | \(0.520161\pi\) | |||||||
\(488\) | 5.77864 | − | 10.0089i | 0.261587 | − | 0.453081i | ||||
\(489\) | −4.18103 | −0.189073 | ||||||||
\(490\) | 1.77645 | + | 1.85319i | 0.0802520 | + | 0.0837184i | ||||
\(491\) | −8.19797 | −0.369969 | −0.184985 | − | 0.982741i | \(-0.559224\pi\) | ||||
−0.184985 | + | 0.982741i | \(0.559224\pi\) | |||||||
\(492\) | 8.99331 | − | 15.5769i | 0.405450 | − | 0.702260i | ||||
\(493\) | 3.46560 | + | 6.00259i | 0.156083 | + | 0.270343i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.933965 | + | 1.61768i | −0.0419786 | + | 0.0727091i | ||||
\(496\) | −6.14096 | −0.275737 | ||||||||
\(497\) | 15.6820 | − | 1.89619i | 0.703432 | − | 0.0850556i | ||||
\(498\) | 13.1033 | 0.587171 | ||||||||
\(499\) | −21.6266 | + | 37.4584i | −0.968141 | + | 1.67687i | −0.267211 | + | 0.963638i | \(0.586102\pi\) |
−0.700929 | + | 0.713231i | \(0.747231\pi\) | |||||||
\(500\) | 1.42802 | + | 2.47340i | 0.0638629 | + | 0.110614i | ||||
\(501\) | −12.2824 | − | 21.2737i | −0.548736 | − | 0.950439i | ||||
\(502\) | 1.18436 | − | 2.05137i | 0.0528605 | − | 0.0915571i | ||||
\(503\) | 0.0181922 | 0.000811149 | 0.000405575 | − | 1.00000i | \(-0.499871\pi\) | ||||
0.000405575 | 1.00000i | \(0.499871\pi\) | ||||||||
\(504\) | −2.38892 | + | 5.59925i | −0.106411 | + | 0.249411i | ||||
\(505\) | −3.34212 | −0.148722 | ||||||||
\(506\) | −15.9920 | + | 27.6990i | −0.710933 | + | 1.23137i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.59095 | + | 2.75560i | 0.0705869 | + | 0.122260i | ||||
\(509\) | 21.5503 | − | 37.3262i | 0.955200 | − | 1.65446i | 0.221292 | − | 0.975208i | \(-0.428973\pi\) |
0.733909 | − | 0.679248i | \(-0.237694\pi\) | |||||||
\(510\) | −0.707795 | −0.0313417 | ||||||||
\(511\) | 6.17151 | + | 8.22134i | 0.273012 | + | 0.363691i | ||||
\(512\) | −23.2197 | −1.02617 | ||||||||
\(513\) | −1.14311 | + | 1.97993i | −0.0504697 | + | 0.0874161i | ||||
\(514\) | −7.87878 | − | 13.6464i | −0.347518 | − | 0.601919i | ||||
\(515\) | 0.713884 | + | 1.23648i | 0.0314575 | + | 0.0544859i | ||||
\(516\) | −8.87804 | + | 15.3772i | −0.390834 | + | 0.676944i | ||||
\(517\) | 48.7877 | 2.14568 | ||||||||
\(518\) | −8.98664 | − | 11.9715i | −0.394850 | − | 0.525997i | ||||
\(519\) | −30.9531 | −1.35869 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.4770 | − | 18.1467i | −0.459006 | − | 0.795022i | 0.539903 | − | 0.841727i | \(-0.318461\pi\) |
−0.998909 | + | 0.0467056i | \(0.985128\pi\) | |||||||
\(522\) | −17.3198 | − | 29.9988i | −0.758068 | − | 1.31301i | ||||
\(523\) | 17.3701 | − | 30.0860i | 0.759543 | − | 1.31557i | −0.183541 | − | 0.983012i | \(-0.558756\pi\) |
0.943084 | − | 0.332555i | \(-0.107911\pi\) | |||||||
\(524\) | 3.30666 | 0.144452 | ||||||||
\(525\) | 11.8164 | − | 27.6958i | 0.515712 | − | 1.20875i | ||||
\(526\) | −23.7627 | −1.03610 | ||||||||
\(527\) | −0.538730 | + | 0.933107i | −0.0234674 | + | 0.0406468i | ||||
\(528\) | 23.0052 | + | 39.8462i | 1.00117 | + | 1.73408i | ||||
\(529\) | 3.03260 | + | 5.25262i | 0.131852 | + | 0.228375i | ||||
\(530\) | 0.852276 | − | 1.47619i | 0.0370205 | − | 0.0641214i | ||||
\(531\) | −13.7080 | −0.594875 | ||||||||
\(532\) | −5.15809 | + | 0.623691i | −0.223631 | + | 0.0270404i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 25.5427 | − | 44.2413i | 1.10534 | − | 1.91451i | ||||
\(535\) | 0.972255 | + | 1.68400i | 0.0420343 | + | 0.0728055i | ||||
\(536\) | 6.81142 | + | 11.7977i | 0.294209 | + | 0.509584i | ||||
\(537\) | −12.0085 | + | 20.7993i | −0.518205 | + | 0.897557i | ||||
\(538\) | 8.75513 | 0.377460 | ||||||||
\(539\) | −20.2613 | − | 21.1365i | −0.872715 | − | 0.910411i | ||||
\(540\) | −0.484932 | −0.0208682 | ||||||||
\(541\) | −1.64923 | + | 2.85655i | −0.0709059 | + | 0.122813i | −0.899299 | − | 0.437335i | \(-0.855922\pi\) |
0.828393 | + | 0.560148i | \(0.189256\pi\) | |||||||
\(542\) | 16.7339 | + | 28.9839i | 0.718782 | + | 1.24497i | ||||
\(543\) | −14.3619 | − | 24.8756i | −0.616330 | − | 1.06752i | ||||
\(544\) | −2.89249 | + | 5.00993i | −0.124014 | + | 0.214799i | ||||
\(545\) | 2.72674 | 0.116801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9417 | 0.938161 | 0.469080 | − | 0.883155i | \(-0.344585\pi\) | ||||
0.469080 | + | 0.883155i | \(0.344585\pi\) | |||||||
\(548\) | 9.76836 | − | 16.9193i | 0.417284 | − | 0.722756i | ||||
\(549\) | 12.8589 | + | 22.2722i | 0.548803 | + | 0.950554i | ||||
\(550\) | −19.2791 | − | 33.3924i | −0.822065 | − | 1.42386i | ||||
\(551\) | −5.56828 | + | 9.64455i | −0.237217 | + | 0.410871i | ||||
\(552\) | −9.59965 | −0.408588 | ||||||||
\(553\) | 11.1440 | − | 26.1199i | 0.473893 | − | 1.11073i | ||||
\(554\) | 48.5368 | 2.06213 | ||||||||
\(555\) | 0.689297 | − | 1.19390i | 0.0292590 | − | 0.0506781i | ||||
\(556\) | −2.93850 | − | 5.08963i | −0.124620 | − | 0.215848i | ||||
\(557\) | −7.14329 | − | 12.3725i | −0.302671 | − | 0.524241i | 0.674069 | − | 0.738668i | \(-0.264545\pi\) |
−0.976740 | + | 0.214427i | \(0.931212\pi\) | |||||||
\(558\) | 2.69238 | − | 4.66334i | 0.113978 | − | 0.197415i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.50315 | + | 2.00241i | 0.0635196 | + | 0.0846172i | ||||
\(561\) | 8.07273 | 0.340831 | ||||||||
\(562\) | 3.40226 | − | 5.89289i | 0.143516 | − | 0.248577i | ||||
\(563\) | −3.39392 | − | 5.87844i | −0.143037 | − | 0.247747i | 0.785602 | − | 0.618732i | \(-0.212353\pi\) |
−0.928639 | + | 0.370985i | \(0.879020\pi\) | |||||||
\(564\) | −19.4366 | − | 33.6652i | −0.818430 | − | 1.41756i | ||||
\(565\) | 0.421234 | − | 0.729599i | 0.0177215 | − | 0.0306945i | ||||
\(566\) | −14.2061 | −0.597128 | ||||||||
\(567\) | 16.9449 | + | 22.5731i | 0.711621 | + | 0.947981i | ||||
\(568\) | 6.07103 | 0.254735 | ||||||||
\(569\) | 8.66061 | − | 15.0006i | 0.363072 | − | 0.628859i | −0.625393 | − | 0.780310i | \(-0.715061\pi\) |
0.988465 | + | 0.151451i | \(0.0483947\pi\) | |||||||
\(570\) | −0.568618 | − | 0.984875i | −0.0238168 | − | 0.0412519i | ||||
\(571\) | 6.50581 | + | 11.2684i | 0.272260 | + | 0.471568i | 0.969440 | − | 0.245328i | \(-0.0788957\pi\) |
−0.697180 | + | 0.716896i | \(0.745562\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.0837 | 1.25676 | ||||||||
\(574\) | −10.4121 | + | 24.4043i | −0.434593 | + | 1.01862i | ||||
\(575\) | 20.4157 | 0.851392 | ||||||||
\(576\) | 3.60574 | − | 6.24532i | 0.150239 | − | 0.260222i | ||||
\(577\) | −0.365767 | − | 0.633528i | −0.0152271 | − | 0.0263741i | 0.858311 | − | 0.513129i | \(-0.171514\pi\) |
−0.873539 | + | 0.486755i | \(0.838180\pi\) | |||||||
\(578\) | −15.1368 | − | 26.2177i | −0.629607 | − | 1.09051i | ||||
\(579\) | 1.19472 | − | 2.06931i | 0.0496508 | − | 0.0859978i | ||||
\(580\) | −2.36218 | −0.0980842 | ||||||||
\(581\) | −8.07396 | + | 0.976265i | −0.334964 | + | 0.0405023i | ||||
\(582\) | 83.0073 | 3.44076 | ||||||||
\(583\) | −9.72061 | + | 16.8366i | −0.402586 | + | 0.697300i | ||||
\(584\) | 1.97548 | + | 3.42163i | 0.0817459 | + | 0.141588i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.9369 | − | 27.6035i | 0.658347 | − | 1.14029i | ||||
\(587\) | 8.52284 | 0.351775 | 0.175888 | − | 0.984410i | \(-0.443720\pi\) | ||||
0.175888 | + | 0.984410i | \(0.443720\pi\) | |||||||
\(588\) | −6.51296 | + | 22.4016i | −0.268590 | + | 0.923825i | ||||
\(589\) | −1.73119 | −0.0713323 | ||||||||
\(590\) | −1.11085 | + | 1.92404i | −0.0457329 | + | 0.0792117i | ||||
\(591\) | 1.69570 | + | 2.93704i | 0.0697517 | + | 0.120814i | ||||
\(592\) | −7.30004 | − | 12.6440i | −0.300030 | − | 0.519667i | ||||
\(593\) | −15.6547 | + | 27.1147i | −0.642860 | + | 1.11347i | 0.341932 | + | 0.939725i | \(0.388919\pi\) |
−0.984791 | + | 0.173741i | \(0.944415\pi\) | |||||||
\(594\) | 13.1452 | 0.539353 | ||||||||
\(595\) | 0.436129 | − | 0.0527346i | 0.0178795 | − | 0.00216191i | ||||
\(596\) | −22.3027 | −0.913554 | ||||||||
\(597\) | −16.1730 | + | 28.0125i | −0.661917 | + | 1.14647i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.375116 | + | 0.649720i | 0.0153268 | + | 0.0265468i | 0.873587 | − | 0.486668i | \(-0.161788\pi\) |
−0.858260 | + | 0.513215i | \(0.828454\pi\) | |||||||
\(600\) | 5.78641 | − | 10.0224i | 0.236229 | − | 0.409161i | ||||
\(601\) | −9.55305 | −0.389677 | −0.194838 | − | 0.980835i | \(-0.562418\pi\) | ||||
−0.194838 | + | 0.980835i | \(0.562418\pi\) | |||||||
\(602\) | 10.2787 | − | 24.0915i | 0.418927 | − | 0.981897i | ||||
\(603\) | −30.3141 | −1.23449 | ||||||||
\(604\) | 4.44624 | − | 7.70111i | 0.180915 | − | 0.313354i | ||||
\(605\) | −0.640963 | − | 1.11018i | −0.0260588 | − | 0.0451352i | ||||
\(606\) | −36.0925 | − | 62.5141i | −1.46616 | − | 2.53946i | ||||
\(607\) | −11.1197 | + | 19.2599i | −0.451336 | + | 0.781737i | −0.998469 | − | 0.0553087i | \(-0.982386\pi\) |
0.547133 | + | 0.837045i | \(0.315719\pi\) | |||||||
\(608\) | −9.29489 | −0.376958 | ||||||||
\(609\) | 30.0199 | + | 39.9908i | 1.21647 | + | 1.62051i | ||||
\(610\) | 4.16815 | 0.168764 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.38278 | − | 2.39505i | −0.0558957 | − | 0.0968143i | ||||
\(613\) | −4.13993 | − | 7.17057i | −0.167210 | − | 0.289617i | 0.770228 | − | 0.637769i | \(-0.220143\pi\) |
−0.937438 | + | 0.348152i | \(0.886809\pi\) | |||||||
\(614\) | 26.0789 | − | 45.1699i | 1.05246 | − | 1.82291i | ||||
\(615\) | −2.44354 | −0.0985330 | ||||||||
\(616\) | −6.75567 | − | 8.99952i | −0.272194 | − | 0.362601i | ||||
\(617\) | −20.3312 | −0.818503 | −0.409252 | − | 0.912422i | \(-0.634210\pi\) | ||||
−0.409252 | + | 0.912422i | \(0.634210\pi\) | |||||||
\(618\) | −15.4189 | + | 26.7063i | −0.620238 | + | 1.07428i | ||||
\(619\) | 2.67049 | + | 4.62542i | 0.107336 | + | 0.185911i | 0.914690 | − | 0.404156i | \(-0.132435\pi\) |
−0.807354 | + | 0.590067i | \(0.799101\pi\) | |||||||
\(620\) | −0.183601 | − | 0.318007i | −0.00737361 | − | 0.0127715i | ||||
\(621\) | −3.48003 | + | 6.02758i | −0.139649 | + | 0.241879i | ||||
\(622\) | 43.7301 | 1.75342 | ||||||||
\(623\) | −12.4427 | + | 29.1636i | −0.498506 | + | 1.16842i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.2086 | + | 21.1459i | −0.488345 | + | 0.845838i | ||||
\(626\) | −3.11112 | − | 5.38862i | −0.124345 | − | 0.215372i | ||||
\(627\) | 6.48536 | + | 11.2330i | 0.259000 | + | 0.448601i | ||||
\(628\) | −3.29536 | + | 5.70773i | −0.131499 | + | 0.227763i | ||||
\(629\) | −2.56165 | −0.102140 | ||||||||
\(630\) | −2.17962 | + | 0.263549i | −0.0868381 | + | 0.0105001i | ||||
\(631\) | −6.46662 | −0.257432 | −0.128716 | − | 0.991681i | \(-0.541086\pi\) | ||||
−0.128716 | + | 0.991681i | \(0.541086\pi\) | |||||||
\(632\) | 5.45714 | − | 9.45205i | 0.217074 | − | 0.375982i | ||||
\(633\) | −30.3611 | − | 52.5870i | −1.20675 | − | 2.09014i | ||||
\(634\) | 6.76217 | + | 11.7124i | 0.268560 | + | 0.465160i | ||||
\(635\) | 0.216135 | − | 0.374357i | 0.00857707 | − | 0.0148559i | ||||
\(636\) | 15.4904 | 0.614236 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 64.0322 | 2.53506 | ||||||||
\(639\) | −6.75475 | + | 11.6996i | −0.267214 | + | 0.462828i | ||||
\(640\) | 0.772706 | + | 1.33837i | 0.0305439 | + | 0.0529035i | ||||
\(641\) | −11.6644 | − | 20.2034i | −0.460717 | − | 0.797985i | 0.538280 | − | 0.842766i | \(-0.319074\pi\) |
−0.998997 | + | 0.0447808i | \(0.985741\pi\) | |||||||
\(642\) | −20.9993 | + | 36.3719i | −0.828778 | + | 1.43549i | ||||
\(643\) | 3.58878 | 0.141527 | 0.0707637 | − | 0.997493i | \(-0.477456\pi\) | ||||
0.0707637 | + | 0.997493i | \(0.477456\pi\) | |||||||
\(644\) | −15.7030 | + | 1.89873i | −0.618784 | + | 0.0748204i | ||||
\(645\) | 2.41222 | 0.0949810 | ||||||||
\(646\) | −1.05658 | + | 1.83006i | −0.0415707 | + | 0.0720026i | ||||
\(647\) | 19.8262 | + | 34.3400i | 0.779448 | + | 1.35004i | 0.932260 | + | 0.361788i | \(0.117834\pi\) |
−0.152812 | + | 0.988255i | \(0.548833\pi\) | |||||||
\(648\) | 5.42402 | + | 9.39467i | 0.213076 | + | 0.369058i | ||||
\(649\) | 12.6697 | − | 21.9446i | 0.497331 | − | 0.861402i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.05042 | + | 7.14970i | −0.119556 | + | 0.280219i | ||||
\(652\) | −2.64772 | −0.103693 | ||||||||
\(653\) | −9.06777 | + | 15.7058i | −0.354849 | + | 0.614617i | −0.987092 | − | 0.160153i | \(-0.948801\pi\) |
0.632243 | + | 0.774770i | \(0.282135\pi\) | |||||||
\(654\) | 29.4469 | + | 51.0035i | 1.15146 | + | 1.99439i | ||||
\(655\) | −0.224610 | − | 0.389035i | −0.00877623 | − | 0.0152009i | ||||
\(656\) | −12.9392 | + | 22.4114i | −0.505192 | + | 0.875017i | ||||
\(657\) | −8.79183 | −0.343002 | ||||||||
\(658\) | 34.4256 | + | 45.8599i | 1.34205 | + | 1.78780i | ||||
\(659\) | 13.4810 | 0.525147 | 0.262573 | − | 0.964912i | \(-0.415429\pi\) | ||||
0.262573 | + | 0.964912i | \(0.415429\pi\) | |||||||
\(660\) | −1.37561 | + | 2.38263i | −0.0535456 | + | 0.0927437i | ||||
\(661\) | 5.15611 | + | 8.93064i | 0.200549 | + | 0.347362i | 0.948706 | − | 0.316161i | \(-0.102394\pi\) |
−0.748156 | + | 0.663523i | \(0.769061\pi\) | |||||||
\(662\) | 13.3076 | + | 23.0494i | 0.517213 | + | 0.895839i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.12571 | −0.121301 | ||||||||
\(665\) | 0.423750 | + | 0.564495i | 0.0164323 | + | 0.0218902i | ||||
\(666\) | 12.8022 | 0.496076 | ||||||||
\(667\) | −16.9517 | + | 29.3613i | −0.656374 | + | 1.13687i | ||||
\(668\) | −7.77805 | − | 13.4720i | −0.300942 | − | 0.521247i | ||||
\(669\) | −0.835096 | − | 1.44643i | −0.0322867 | − | 0.0559222i | ||||
\(670\) | −2.45655 | + | 4.25487i | −0.0949049 | + | 0.164380i | ||||
\(671\) | −47.5397 | −1.83525 | ||||||||
\(672\) | −16.3780 | + | 38.3874i | −0.631795 | + | 1.48082i | ||||
\(673\) | −9.23056 | −0.355812 | −0.177906 | − | 0.984048i | \(-0.556932\pi\) | ||||
−0.177906 | + | 0.984048i | \(0.556932\pi\) | |||||||
\(674\) | 15.9618 | − | 27.6467i | 0.614827 | − | 1.06491i | ||||
\(675\) | −4.19533 | − | 7.26652i | −0.161478 | − | 0.279689i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.5467 | − | 18.2674i | 0.405343 | − | 0.702075i | −0.589018 | − | 0.808120i | \(-0.700485\pi\) |
0.994361 | + | 0.106045i | \(0.0338187\pi\) | |||||||
\(678\) | 18.1961 | 0.698818 | ||||||||
\(679\) | −51.1475 | + | 6.18450i | −1.96286 | + | 0.237340i | ||||
\(680\) | 0.168841 | 0.00647474 | ||||||||
\(681\) | −3.27129 | + | 5.66604i | −0.125356 | + | 0.217123i | ||||
\(682\) | 4.97693 | + | 8.62029i | 0.190576 | + | 0.330088i | ||||
\(683\) | −19.1106 | − | 33.1005i | −0.731246 | − | 1.26656i | −0.956351 | − | 0.292221i | \(-0.905606\pi\) |
0.225104 | − | 0.974335i | \(-0.427728\pi\) | |||||||
\(684\) | 2.22176 | − | 3.84821i | 0.0849512 | − | 0.147140i | ||||
\(685\) | −2.65412 | −0.101409 | ||||||||
\(686\) | 5.57122 | − | 33.9597i | 0.212710 | − | 1.29659i | ||||
\(687\) | −7.28027 | −0.277760 | ||||||||
\(688\) | 12.7734 | − | 22.1241i | 0.486980 | − | 0.843474i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.73107 | − | 2.99830i | −0.0659006 | − | 0.114143i | ||||
\(691\) | −13.1161 | + | 22.7178i | −0.498960 | + | 0.864224i | −0.999999 | − | 0.00120019i | \(-0.999618\pi\) |
0.501039 | + | 0.865425i | \(0.332951\pi\) | |||||||
\(692\) | −19.6017 | −0.745144 | ||||||||
\(693\) | 24.8596 | − | 3.00590i | 0.944338 | − | 0.114185i | ||||
\(694\) | 14.3130 | 0.543314 | ||||||||
\(695\) | −0.399204 | + | 0.691442i | −0.0151427 | + | 0.0262279i | ||||
\(696\) | 9.60925 | + | 16.6437i | 0.364238 | + | 0.630878i | ||||
\(697\) | 2.27024 | + | 3.93218i | 0.0859916 | + | 0.148942i | ||||
\(698\) | −20.7836 | + | 35.9982i | −0.786670 | + | 1.36255i | ||||
\(699\) | 30.7567 | 1.16333 | ||||||||
\(700\) | 7.48299 | − | 17.5389i | 0.282830 | − | 0.662909i | ||||
\(701\) | −46.7346 | −1.76514 | −0.882570 | − | 0.470180i | \(-0.844189\pi\) | ||||
−0.882570 | + | 0.470180i | \(0.844189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.05794 | − | 3.56446i | −0.0776167 | − | 0.134436i | ||||
\(704\) | 6.66528 | + | 11.5446i | 0.251207 | + | 0.435104i | ||||
\(705\) | −2.64053 | + | 4.57353i | −0.0994480 | + | 0.172249i | ||||
\(706\) | −41.3669 | −1.55687 | ||||||||
\(707\) | 26.8972 | + | 35.8309i | 1.01157 | + | 1.34756i | ||||
\(708\) | −20.1901 | −0.758789 | ||||||||
\(709\) | −23.7232 | + | 41.0898i | −0.890944 | + | 1.54316i | −0.0521988 | + | 0.998637i | \(0.516623\pi\) |
−0.838745 | + | 0.544524i | \(0.816710\pi\) | |||||||
\(710\) | 1.09476 | + | 1.89619i | 0.0410858 | + | 0.0711626i | ||||
\(711\) | 12.1435 | + | 21.0331i | 0.455415 | + | 0.788802i | ||||
\(712\) | −6.09307 | + | 10.5535i | −0.228348 | + | 0.395510i | ||||
\(713\) | −5.27032 | −0.197375 | ||||||||
\(714\) | 5.69629 | + | 7.58827i | 0.213178 | + | 0.283984i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.60461 | + | 13.1716i | −0.284197 | + | 0.492244i | ||||
\(717\) | −17.8408 | − | 30.9011i | −0.666275 | − | 1.15402i | ||||
\(718\) | 2.56280 | + | 4.43890i | 0.0956428 | + | 0.165658i | ||||
\(719\) | 24.6190 | − | 42.6413i | 0.918133 | − | 1.59025i | 0.115884 | − | 0.993263i | \(-0.463030\pi\) |
0.802249 | − | 0.596990i | \(-0.203637\pi\) | |||||||
\(720\) | −2.14136 | −0.0798037 | ||||||||
\(721\) | 7.51104 | − | 17.6047i | 0.279726 | − | 0.655632i | ||||
\(722\) | 31.9098 | 1.18756 | ||||||||
\(723\) | −8.68963 | + | 15.0509i | −0.323171 | + | 0.559748i | ||||
\(724\) | −9.09498 | − | 15.7530i | −0.338012 | − | 0.585454i | ||||
\(725\) | −20.4361 | − | 35.3963i | −0.758977 | − | 1.31459i | ||||
\(726\) | 13.8439 | − | 23.9783i | 0.513795 | − | 0.889919i | ||||
\(727\) | −32.0495 | −1.18865 | −0.594325 | − | 0.804225i | \(-0.702581\pi\) | ||||
−0.594325 | + | 0.804225i | \(0.702581\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.4996 | −0.462947 | ||||||||
\(730\) | −0.712460 | + | 1.23402i | −0.0263693 | + | 0.0456730i | ||||
\(731\) | −2.24114 | − | 3.88178i | −0.0828917 | − | 0.143573i | ||||
\(732\) | 18.9394 | + | 32.8041i | 0.700022 | + | 1.21247i | ||||
\(733\) | 14.1005 | − | 24.4228i | 0.520813 | − | 0.902075i | −0.478894 | − | 0.877873i | \(-0.658962\pi\) |
0.999707 | − | 0.0242025i | \(-0.00770464\pi\) | |||||||
\(734\) | 26.2924 | 0.970472 | ||||||||
\(735\) | 3.07800 | − | 0.755398i | 0.113534 | − | 0.0278633i | ||||
\(736\) | −28.2968 | −1.04303 | ||||||||
\(737\) | 28.0181 | − | 48.5288i | 1.03206 | − | 1.78758i | ||||
\(738\) | −11.3459 | − | 19.6516i | −0.417648 | − | 0.723387i | ||||
\(739\) | −21.2685 | − | 36.8381i | −0.782375 | − | 1.35511i | −0.930555 | − | 0.366153i | \(-0.880675\pi\) |
0.148180 | − | 0.988960i | \(-0.452658\pi\) | |||||||
\(740\) | 0.436510 | − | 0.756058i | 0.0160464 | − | 0.0277932i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.6852 | + | 2.74299i | −0.832801 | + | 0.100698i | ||||
\(743\) | −15.9142 | −0.583836 | −0.291918 | − | 0.956443i | \(-0.594294\pi\) | ||||
−0.291918 | + | 0.956443i | \(0.594294\pi\) | |||||||
\(744\) | −1.49377 | + | 2.58728i | −0.0547641 | + | 0.0948543i | ||||
\(745\) | 1.51495 | + | 2.62396i | 0.0555033 | + | 0.0961346i | ||||
\(746\) | −4.68521 | − | 8.11502i | −0.171538 | − | 0.297112i | ||||
\(747\) | 3.47773 | − | 6.02360i | 0.127243 | − | 0.220392i | ||||
\(748\) | 5.11221 | 0.186921 | ||||||||
\(749\) | 10.2295 | − | 23.9762i | 0.373777 | − | 0.876072i | ||||
\(750\) | 8.38028 | 0.306005 | ||||||||
\(751\) | −9.09981 | + | 15.7613i | −0.332057 | + | 0.575139i | −0.982915 | − | 0.184060i | \(-0.941076\pi\) |
0.650858 | + | 0.759199i | \(0.274409\pi\) | |||||||
\(752\) | 27.9646 | + | 48.4362i | 1.01977 | + | 1.76629i | ||||
\(753\) | −1.46220 | − | 2.53260i | −0.0532855 | − | 0.0922931i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.20807 | −0.0439662 | ||||||||
\(756\) | 3.90270 | + | 5.19896i | 0.141940 | + | 0.189084i | ||||
\(757\) | −44.9004 | −1.63193 | −0.815967 | − | 0.578099i | \(-0.803795\pi\) | ||||
−0.815967 | + | 0.578099i | \(0.803795\pi\) | |||||||
\(758\) | 5.62989 | − | 9.75126i | 0.204487 | − | 0.354182i | ||||
\(759\) | 19.7436 | + | 34.1970i | 0.716648 | + | 1.24127i | ||||
\(760\) | 0.135641 | + | 0.234937i | 0.00492021 | + | 0.00852205i | ||||
\(761\) | −13.2444 | + | 22.9399i | −0.480108 | + | 0.831572i | −0.999740 | − | 0.0228184i | \(-0.992736\pi\) |
0.519631 | + | 0.854391i | \(0.326069\pi\) | |||||||
\(762\) | 9.33644 | 0.338223 | ||||||||
\(763\) | −21.9446 | − | 29.2334i | −0.794449 | − | 1.05832i | ||||
\(764\) | 19.0511 | 0.689244 | ||||||||
\(765\) | −0.187856 | + | 0.325375i | −0.00679193 | + | 0.0117640i | ||||
\(766\) | 4.21900 | + | 7.30752i | 0.152439 | + | 0.264031i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −24.0006 | + | 41.5703i | −0.866049 | + | 1.50004i | ||||
\(769\) | −13.9625 | −0.503502 | −0.251751 | − | 0.967792i | \(-0.581006\pi\) | ||||
−0.251751 | + | 0.967792i | \(0.581006\pi\) | |||||||
\(770\) | 1.59263 | − | 3.73287i | 0.0573944 | − | 0.134523i | ||||
\(771\) | −19.4541 | −0.700623 | ||||||||
\(772\) | 0.756579 | − | 1.31043i | 0.0272299 | − | 0.0471635i | ||||
\(773\) | 6.40564 | + | 11.0949i | 0.230395 | + | 0.399056i | 0.957924 | − | 0.287021i | \(-0.0926648\pi\) |
−0.727529 | + | 0.686077i | \(0.759332\pi\) | |||||||
\(774\) | 11.2005 | + | 19.3998i | 0.402592 | + | 0.697310i | ||||
\(775\) | 3.17681 | − | 5.50239i | 0.114114 | − | 0.197652i | ||||
\(776\) | −19.8010 | −0.710813 | ||||||||
\(777\) | −18.3472 | + | 2.21845i | −0.658201 | + | 0.0795865i | ||||
\(778\) | −8.37594 | −0.300292 | ||||||||
\(779\) | −3.64767 | + | 6.31795i | −0.130691 | + | 0.226364i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4863 | − | 21.6269i | −0.446795 | − | 0.773871i | ||||
\(782\) | −3.21660 | + | 5.57132i | −0.115025 | + | 0.199230i | ||||
\(783\) | 13.9340 | 0.497961 | ||||||||
\(784\) | 9.37058 | − | 32.2305i | 0.334664 | − | 1.15109i | ||||
\(785\) | 0.895370 | 0.0319571 | ||||||||
\(786\) | 4.85125 | − | 8.40262i | 0.173039 | − | 0.299712i | ||||
\(787\) | −13.6599 | − | 23.6597i | −0.486924 | − | 0.843377i | 0.512963 | − | 0.858411i | \(-0.328548\pi\) |
−0.999887 | + | 0.0150334i | \(0.995215\pi\) | |||||||
\(788\) | 1.07383 | + | 1.85993i | 0.0382537 | + | 0.0662574i | ||||
\(789\) | −14.6686 | + | 25.4068i | −0.522217 | + | 0.904506i | ||||
\(790\) | 3.93626 | 0.140046 | ||||||||
\(791\) | −11.2121 | + | 1.35571i | −0.398656 | + | 0.0482036i | ||||
\(792\) | 9.62401 | 0.341974 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.71956 | − | 6.44247i | −0.132002 | − | 0.228635i | ||||
\(795\) | −1.05221 | − | 1.82248i | −0.0373181 | − | 0.0646369i | ||||
\(796\) | −10.2419 | + | 17.7394i | −0.363013 | + | 0.628758i | ||||
\(797\) | −29.4003 | −1.04141 | −0.520707 | − | 0.853736i | \(-0.674332\pi\) | ||||
−0.520707 | + | 0.853736i | \(0.674332\pi\) | |||||||
\(798\) | −5.98265 | + | 14.0224i | −0.211783 | + | 0.496386i | ||||
\(799\) | 9.81305 | 0.347161 | ||||||||
\(800\) | 17.0565 | − | 29.5428i | 0.603040 | − | 1.04450i | ||||
\(801\) | −13.5586 | − | 23.4841i | −0.479068 | − | 0.829770i | ||||
\(802\) | −11.7189 | − | 20.2978i | −0.413810 | − | 0.716740i | ||||
\(803\) | 8.12594 | − | 14.0745i | 0.286758 | − | 0.496680i | ||||
\(804\) | −44.6487 | −1.57464 | ||||||||
\(805\) | 1.29004 | + | 1.71852i | 0.0454679 | + | 0.0605697i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.40450 | − | 9.36087i | 0.190247 | − | 0.329518i | ||||
\(808\) | 8.60968 | + | 14.9124i | 0.302888 | + | 0.524617i | ||||
\(809\) | 3.00617 | + | 5.20683i | 0.105691 | + | 0.183063i | 0.914020 | − | 0.405668i | \(-0.132961\pi\) |
−0.808329 | + | 0.588731i | \(0.799628\pi\) | |||||||
\(810\) | −1.95618 | + | 3.38821i | −0.0687332 | + | 0.119049i | ||||
\(811\) | −8.44807 | −0.296652 | −0.148326 | − | 0.988939i | \(-0.547388\pi\) | ||||
−0.148326 | + | 0.988939i | \(0.547388\pi\) | |||||||
\(812\) | 19.0107 | + | 25.3249i | 0.667143 | + | 0.888730i | ||||
\(813\) | 41.3190 | 1.44912 | ||||||||
\(814\) | −11.8326 | + | 20.4946i | −0.414732 | + | 0.718337i | ||||
\(815\) | 0.179850 | + | 0.311510i | 0.00629989 | + | 0.0109117i | ||||
\(816\) | 4.62721 | + | 8.01456i | 0.161985 | + | 0.280566i | ||||
\(817\) | 3.60092 | − | 6.23697i | 0.125980 | − | 0.218204i | ||||
\(818\) | 38.4551 | 1.34455 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.54742 | −0.0540382 | ||||||||
\(821\) | −17.1318 | + | 29.6731i | −0.597903 | + | 1.03560i | 0.395228 | + | 0.918583i | \(0.370666\pi\) |
−0.993130 | + | 0.117014i | \(0.962668\pi\) | |||||||
\(822\) | −28.6627 | − | 49.6452i | −0.999725 | − | 1.73157i | ||||
\(823\) | 3.11866 | + | 5.40168i | 0.108710 | + | 0.188291i | 0.915248 | − | 0.402891i | \(-0.131995\pi\) |
−0.806538 | + | 0.591182i | \(0.798661\pi\) | |||||||
\(824\) | 3.67809 | − | 6.37064i | 0.128132 | − | 0.221932i | ||||
\(825\) | −47.6037 | −1.65735 | ||||||||
\(826\) | 29.5677 | − | 3.57518i | 1.02879 | − | 0.124397i | ||||
\(827\) | −19.5232 | −0.678889 | −0.339445 | − | 0.940626i | \(-0.610239\pi\) | ||||
−0.339445 | + | 0.940626i | \(0.610239\pi\) | |||||||
\(828\) | 6.76380 | − | 11.7152i | 0.235058 | − | 0.407133i | ||||
\(829\) | −16.3383 | − | 28.2988i | −0.567453 | − | 0.982857i | −0.996817 | − | 0.0797254i | \(-0.974596\pi\) |
0.429364 | − | 0.903131i | \(-0.358738\pi\) | |||||||
\(830\) | −0.563647 | − | 0.976265i | −0.0195645 | − | 0.0338866i | ||||
\(831\) | 29.9615 | − | 51.8949i | 1.03935 | − | 1.80021i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.07530 | − | 4.25133i | −0.141201 | − | 0.147300i | ||||
\(834\) | −17.2445 | −0.597128 | ||||||||
\(835\) | −1.05667 | + | 1.83021i | −0.0365677 | + | 0.0633370i | ||||
\(836\) | 4.10698 | + | 7.11349i | 0.142043 | + | 0.246025i | ||||
\(837\) | 1.08303 | + | 1.87586i | 0.0374349 | + | 0.0648392i | ||||
\(838\) | −20.2702 | + | 35.1091i | −0.700223 | + | 1.21282i | ||||
\(839\) | −24.7427 | −0.854212 | −0.427106 | − | 0.904202i | \(-0.640467\pi\) | ||||
−0.427106 | + | 0.904202i | \(0.640467\pi\) | |||||||
\(840\) | 1.20928 | − | 0.146220i | 0.0417241 | − | 0.00504508i | ||||
\(841\) | 38.8748 | 1.34051 | ||||||||
\(842\) | −8.75869 | + | 15.1705i | −0.301844 | + | 0.522810i | ||||
\(843\) | −4.20040 | − | 7.27531i | −0.144669 | − | 0.250575i | ||||
\(844\) | −19.2267 | − | 33.3017i | −0.661812 | − | 1.14629i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −49.0422 | −1.68610 | ||||||||
\(847\) | −6.74381 | + | 15.8064i | −0.231720 | + | 0.543115i | ||||
\(848\) | −22.2870 | −0.765339 | ||||||||
\(849\) | −8.76938 | + | 15.1890i | −0.300964 | + | 0.521285i | ||||
\(850\) | −3.87776 | − | 6.71647i | −0.133006 | − | 0.230373i | ||||
\(851\) | −6.26507 | − | 10.8514i | −0.214764 | − | 0.371982i | ||||
\(852\) | −9.94888 | + | 17.2320i | −0.340843 | + | 0.590357i | ||||
\(853\) | −18.2245 | −0.623994 | −0.311997 | − | 0.950083i | \(-0.600998\pi\) | ||||
−0.311997 | + | 0.950083i | \(0.600998\pi\) | |||||||
\(854\) | −33.5450 | − | 44.6868i | −1.14789 | − | 1.52915i | ||||
\(855\) | −0.603667 | −0.0206450 | ||||||||
\(856\) | 5.00928 | − | 8.67633i | 0.171214 | − | 0.296551i | ||||
\(857\) | −1.27340 | − | 2.20559i | −0.0434984 | − | 0.0753414i | 0.843457 | − | 0.537197i | \(-0.180517\pi\) |
−0.886955 | + | 0.461856i | \(0.847184\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.0045 | + | 46.7732i | −0.921382 | + | 1.59588i | −0.124104 | + | 0.992269i | \(0.539606\pi\) |
−0.797278 | + | 0.603612i | \(0.793728\pi\) | |||||||
\(860\) | 1.52758 | 0.0520902 | ||||||||
\(861\) | 19.6654 | + | 26.1972i | 0.670196 | + | 0.892797i | ||||
\(862\) | 37.9577 | 1.29284 | ||||||||
\(863\) | 0.621545 | − | 1.07655i | 0.0211576 | − | 0.0366461i | −0.855253 | − | 0.518211i | \(-0.826598\pi\) |
0.876410 | + | 0.481565i | \(0.159931\pi\) | |||||||
\(864\) | 5.81487 | + | 10.0716i | 0.197826 | + | 0.342644i | ||||
\(865\) | 1.33147 | + | 2.30618i | 0.0452715 | + | 0.0784125i | ||||
\(866\) | 24.4800 | − | 42.4006i | 0.831864 | − | 1.44083i | ||||
\(867\) | −37.3754 | −1.26934 | ||||||||
\(868\) | −1.93174 | + | 4.52769i | −0.0655675 | + | 0.153680i | ||||
\(869\) | −44.8949 | −1.52295 | ||||||||
\(870\) | −3.46560 | + | 6.00259i | −0.117495 | + | 0.203507i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −7.02440 | − | 12.1666i | −0.237876 | − | 0.412013i | ||||
\(873\) | 22.0309 | − | 38.1587i | 0.745634 | − | 1.29148i | ||||
\(874\) | −10.3364 | −0.349635 | ||||||||
\(875\) | −5.16376 | + | 0.624377i | −0.174567 | + | 0.0211078i | ||||
\(876\) | −12.9492 | −0.437514 | ||||||||
\(877\) | 0.401330 | − | 0.695125i | 0.0135520 | − | 0.0234727i | −0.859170 | − | 0.511690i | \(-0.829019\pi\) |
0.872722 | + | 0.488218i | \(0.162353\pi\) | |||||||
\(878\) | 23.3488 | + | 40.4412i | 0.787983 | + | 1.36483i | ||||
\(879\) | −19.6755 | − | 34.0790i | −0.663639 | − | 1.14946i | ||||
\(880\) | 1.97917 | − | 3.42803i | 0.0667179 | − | 0.115559i | ||||
\(881\) | −37.0636 | −1.24870 | −0.624352 | − | 0.781143i | \(-0.714637\pi\) | ||||
−0.624352 | + | 0.781143i | \(0.714637\pi\) | |||||||
\(882\) | 20.3669 | + | 21.2467i | 0.685791 | + | 0.715413i | ||||
\(883\) | −22.8671 | −0.769539 | −0.384770 | − | 0.923013i | \(-0.625719\pi\) | ||||
−0.384770 | + | 0.923013i | \(0.625719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.37144 | + | 2.37541i | 0.0461005 | + | 0.0798484i | ||||
\(886\) | 17.2065 | + | 29.8025i | 0.578063 | + | 1.00123i | ||||
\(887\) | 24.6287 | − | 42.6581i | 0.826950 | − | 1.43232i | −0.0734699 | − | 0.997297i | \(-0.523407\pi\) |
0.900420 | − | 0.435022i | \(-0.143259\pi\) | |||||||
\(888\) | −7.10283 | −0.238355 | ||||||||
\(889\) | −5.75292 | + | 0.695616i | −0.192947 | + | 0.0233302i | ||||
\(890\) | −4.39496 | −0.147319 | ||||||||
\(891\) | 22.3112 | − | 38.6441i | 0.747452 | − | 1.29463i | ||||
\(892\) | −0.528840 | − | 0.915978i | −0.0177069 | − | 0.0306692i | ||||
\(893\) | 7.88347 | + | 13.6546i | 0.263810 | + | 0.456932i | ||||
\(894\) | −32.7207 | + | 56.6739i | −1.09434 | + | 1.89546i | ||||
\(895\) | 2.06622 | 0.0690661 | ||||||||
\(896\) | 8.12993 | − | 19.0552i | 0.271602 | − | 0.636591i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.8174 | + | 18.7362i | −0.360980 | + | 0.625236i | ||||
\(899\) | 5.27559 | + | 9.13760i | 0.175951 | + | 0.304756i | ||||
\(900\) | 8.15406 | + | 14.1233i | 0.271802 | + | 0.470775i | ||||
\(901\) | −1.95518 | + | 3.38647i | −0.0651365 | + | 0.112820i | ||||
\(902\) | 41.9462 | 1.39666 | ||||||||
\(903\) | −19.4134 | − | 25.8614i | −0.646036 | − | 0.860613i | ||||
\(904\) | −4.34059 | −0.144366 | ||||||||
\(905\) | −1.23558 | + | 2.14009i | −0.0410721 | + | 0.0711390i | ||||
\(906\) | −13.0463 | − | 22.5969i | −0.433435 | − | 0.750731i | ||||
\(907\) | 2.50228 | + | 4.33407i | 0.0830867 | + | 0.143910i | 0.904574 | − | 0.426316i | \(-0.140189\pi\) |
−0.821488 | + | 0.570226i | \(0.806855\pi\) | |||||||
\(908\) | −2.07161 | + | 3.58813i | −0.0687487 | + | 0.119076i | ||||
\(909\) | −38.3172 | −1.27090 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.0582 | 1.62537 | 0.812685 | − | 0.582703i | \(-0.198005\pi\) | ||||
0.812685 | + | 0.582703i | \(0.198005\pi\) | |||||||
\(912\) | −7.43468 | + | 12.8772i | −0.246187 | + | 0.426408i | ||||
\(913\) | 6.42866 | + | 11.1348i | 0.212757 | + | 0.368507i | ||||
\(914\) | −19.0633 | − | 33.0186i | −0.630557 | − | 1.09216i | ||||
\(915\) | 2.57298 | − | 4.45653i | 0.0850601 | − | 0.147328i | ||||
\(916\) | −4.61037 | −0.152331 | ||||||||
\(917\) | −2.36320 | + | 5.53897i | −0.0780399 | + | 0.182913i | ||||
\(918\) | 2.64399 | 0.0872646 | ||||||||
\(919\) | −14.8028 | + | 25.6392i | −0.488299 | + | 0.845758i | −0.999909 | − | 0.0134590i | \(-0.995716\pi\) |
0.511611 | + | 0.859217i | \(0.329049\pi\) | |||||||
\(920\) | 0.412937 | + | 0.715227i | 0.0136141 | + | 0.0235803i | ||||
\(921\) | −32.1967 | − | 55.7664i | −1.06092 | − | 1.83756i | ||||
\(922\) | −1.89602 | + | 3.28401i | −0.0624422 | + | 0.108153i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 36.6150 | − | 4.42731i | 1.20454 | − | 0.145648i | ||||
\(925\) | 15.1056 | 0.496670 | ||||||||
\(926\) | −2.81656 | + | 4.87842i | −0.0925578 | + | 0.160315i | ||||
\(927\) | 8.18464 | + | 14.1762i | 0.268819 | + | 0.465608i | ||||
\(928\) | 28.3251 | + | 49.0605i | 0.929817 | + | 1.61049i | ||||
\(929\) | 8.41525 | − | 14.5756i | 0.276095 | − | 0.478211i | −0.694316 | − | 0.719671i | \(-0.744293\pi\) |
0.970411 | + | 0.241460i | \(0.0776261\pi\) | |||||||
\(930\) | −1.07746 | −0.0353313 | ||||||||
\(931\) | 2.64164 | − | 9.08604i | 0.0865764 | − | 0.297783i | ||||
\(932\) | 19.4773 | 0.638000 | ||||||||
\(933\) | 26.9944 | − | 46.7557i | 0.883757 | − | 1.53071i | ||||
\(934\) | −12.0106 | − | 20.8030i | −0.392999 | − | 0.680695i | ||||
\(935\) | −0.347255 | − | 0.601463i | −0.0113565 | − | 0.0196699i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0131 | 1.43784 | 0.718922 | − | 0.695091i | \(-0.244636\pi\) | ||||
0.718922 | + | 0.695091i | \(0.244636\pi\) | |||||||
\(938\) | 65.3866 | − | 7.90624i | 2.13495 | − | 0.258148i | ||||
\(939\) | −7.68191 | −0.250690 | ||||||||
\(940\) | −1.67216 | + | 2.89627i | −0.0545400 | + | 0.0944660i | ||||
\(941\) | 26.5338 | + | 45.9578i | 0.864976 | + | 1.49818i | 0.867071 | + | 0.498184i | \(0.166000\pi\) |
−0.00209573 | + | 0.999998i | \(0.500667\pi\) | |||||||
\(942\) | 9.66937 | + | 16.7478i | 0.315045 | + | 0.545674i | ||||
\(943\) | −11.1048 | + | 19.2340i | −0.361620 | + | 0.626345i | ||||
\(944\) | 29.0487 | 0.945453 | ||||||||
\(945\) | 0.346572 | − | 0.812309i | 0.0112740 | − | 0.0264244i | ||||
\(946\) | −41.4086 | −1.34631 | ||||||||
\(947\) | −13.9409 | + | 24.1463i | −0.453017 | + | 0.784649i | −0.998572 | − | 0.0534265i | \(-0.982986\pi\) |
0.545555 | + | 0.838075i | \(0.316319\pi\) | |||||||
\(948\) | 17.8857 | + | 30.9790i | 0.580902 | + | 1.00615i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.23051 | − | 10.7916i | 0.202145 | − | 0.350125i | ||||
\(951\) | 16.6970 | 0.541438 | ||||||||
\(952\) | −1.35882 | − | 1.81014i | −0.0440396 | − | 0.0586670i | ||||
\(953\) | −36.3568 | −1.17771 | −0.588856 | − | 0.808238i | \(-0.700421\pi\) | ||||
−0.588856 | + | 0.808238i | \(0.700421\pi\) | |||||||
\(954\) | 9.77130 | − | 16.9244i | 0.316357 | − | 0.547947i | ||||
\(955\) | −1.29407 | − | 2.24140i | −0.0418753 | − | 0.0725301i | ||||
\(956\) | −11.2980 | − | 19.5687i | −0.365403 | − | 0.632897i | ||||
\(957\) | 39.5267 | − | 68.4623i | 1.27772 | − | 2.21307i | ||||
\(958\) | 67.9754 | 2.19619 | ||||||||
\(959\) | 21.3602 | + | 28.4548i | 0.689757 | + | 0.918855i | ||||
\(960\) | −1.44297 | −0.0465718 | ||||||||
\(961\) | 14.6799 | − | 25.4263i | 0.473545 | − | 0.820205i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.1469 | + | 19.3069i | 0.359202 | + | 0.622157i | ||||
\(964\) | −5.50287 | + | 9.53126i | −0.177236 | + | 0.306981i | ||||
\(965\) | −0.205567 | −0.00661744 | ||||||||
\(966\) | −18.2132 | + | 42.6888i | −0.586000 | + | 1.37349i | ||||
\(967\) | 15.2681 | 0.490988 | 0.245494 | − | 0.969398i | \(-0.421050\pi\) | ||||
0.245494 | + | 0.969398i | \(0.421050\pi\) | |||||||
\(968\) | −3.30239 | + | 5.71990i | −0.106143 | + | 0.183845i | ||||
\(969\) | 1.30445 | + | 2.25937i | 0.0419049 | + | 0.0725815i | ||||
\(970\) | −3.57063 | − | 6.18450i | −0.114646 | − | 0.198572i | ||||
\(971\) | 18.4460 | − | 31.9494i | 0.591961 | − | 1.02531i | −0.402008 | − | 0.915636i | \(-0.631687\pi\) |
0.993968 | − | 0.109669i | \(-0.0349792\pi\) | |||||||
\(972\) | −28.1831 | −0.903975 | ||||||||
\(973\) | 10.6257 | − | 1.28481i | 0.340645 | − | 0.0411891i | ||||
\(974\) | 68.2867 | 2.18805 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.2493 | − | 47.1972i | −0.872229 | − | 1.51074i | ||||
\(977\) | −0.221957 | − | 0.384441i | −0.00710104 | − | 0.0122994i | 0.862453 | − | 0.506137i | \(-0.168927\pi\) |
−0.869554 | + | 0.493838i | \(0.835594\pi\) | |||||||
\(978\) | −3.88452 | + | 6.72818i | −0.124213 | + | 0.215144i | ||||
\(979\) | 50.1265 | 1.60205 | ||||||||
\(980\) | 1.94920 | − | 0.478370i | 0.0622649 | − | 0.0152810i | ||||
\(981\) | 31.2619 | 0.998117 | ||||||||
\(982\) | −7.61658 | + | 13.1923i | −0.243055 | + | 0.420983i | ||||
\(983\) | 22.7802 | + | 39.4564i | 0.726575 | + | 1.25846i | 0.958323 | + | 0.285688i | \(0.0922222\pi\) |
−0.231748 | + | 0.972776i | \(0.574444\pi\) | |||||||
\(984\) | 6.29483 | + | 10.9030i | 0.200672 | + | 0.347574i | ||||
\(985\) | 0.145884 | − | 0.252678i | 0.00464824 | − | 0.00805099i | ||||
\(986\) | 12.8793 | 0.410160 | ||||||||
\(987\) | 70.2835 | − | 8.49835i | 2.23715 | − | 0.270505i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.9624 | − | 18.9875i | 0.348585 | − | 0.603766i | ||||
\(990\) | 1.73546 | + | 3.00590i | 0.0551565 | + | 0.0955338i | ||||
\(991\) | −26.8148 | − | 46.4445i | −0.851799 | − | 1.47536i | −0.879583 | − | 0.475745i | \(-0.842178\pi\) |
0.0277842 | − | 0.999614i | \(-0.491155\pi\) | |||||||
\(992\) | −4.40316 | + | 7.62650i | −0.139801 | + | 0.242142i | ||||
\(993\) | 32.8588 | 1.04274 | ||||||||
\(994\) | 11.5184 | − | 26.9974i | 0.365342 | − | 0.856304i | ||||
\(995\) | 2.78278 | 0.0882200 | ||||||||
\(996\) | 5.12225 | − | 8.87199i | 0.162305 | − | 0.281120i | ||||
\(997\) | −14.5426 | − | 25.1886i | −0.460569 | − | 0.797730i | 0.538420 | − | 0.842677i | \(-0.319021\pi\) |
−0.998989 | + | 0.0449470i | \(0.985688\pi\) | |||||||
\(998\) | 40.1857 | + | 69.6038i | 1.27206 | + | 2.20327i | ||||
\(999\) | −2.57489 | + | 4.45984i | −0.0814658 | + | 0.141103i |
(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 | 1183.2.e.g.170.6 | 12 | ||
7.2 | even | 3 | 8281.2.a.ce.1.1 | 6 | |||
7.4 | even | 3 | inner | 1183.2.e.g.508.6 | 12 | ||
7.5 | odd | 6 | 8281.2.a.cf.1.1 | 6 | |||
13.4 | even | 6 | 91.2.h.b.16.6 | yes | 12 | ||
13.10 | even | 6 | 91.2.g.b.9.1 | ✓ | 12 | ||
13.12 | even | 2 | 1183.2.e.h.170.1 | 12 | |||
39.17 | odd | 6 | 819.2.s.d.289.1 | 12 | |||
39.23 | odd | 6 | 819.2.n.d.100.6 | 12 | |||
91.4 | even | 6 | 91.2.g.b.81.1 | yes | 12 | ||
91.10 | odd | 6 | 637.2.h.l.165.6 | 12 | |||
91.12 | odd | 6 | 8281.2.a.ca.1.6 | 6 | |||
91.17 | odd | 6 | 637.2.g.l.263.1 | 12 | |||
91.23 | even | 6 | 637.2.f.k.295.1 | 12 | |||
91.25 | even | 6 | 1183.2.e.h.508.1 | 12 | |||
91.30 | even | 6 | 637.2.f.k.393.1 | 12 | |||
91.51 | even | 6 | 8281.2.a.bz.1.6 | 6 | |||
91.62 | odd | 6 | 637.2.g.l.373.1 | 12 | |||
91.69 | odd | 6 | 637.2.h.l.471.6 | 12 | |||
91.75 | odd | 6 | 637.2.f.j.295.1 | 12 | |||
91.82 | odd | 6 | 637.2.f.j.393.1 | 12 | |||
91.88 | even | 6 | 91.2.h.b.74.6 | yes | 12 | ||
273.95 | odd | 6 | 819.2.n.d.172.6 | 12 | |||
273.179 | odd | 6 | 819.2.s.d.802.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.1 | ✓ | 12 | 13.10 | even | 6 | ||
91.2.g.b.81.1 | yes | 12 | 91.4 | even | 6 | ||
91.2.h.b.16.6 | yes | 12 | 13.4 | even | 6 | ||
91.2.h.b.74.6 | yes | 12 | 91.88 | even | 6 | ||
637.2.f.j.295.1 | 12 | 91.75 | odd | 6 | |||
637.2.f.j.393.1 | 12 | 91.82 | odd | 6 | |||
637.2.f.k.295.1 | 12 | 91.23 | even | 6 | |||
637.2.f.k.393.1 | 12 | 91.30 | even | 6 | |||
637.2.g.l.263.1 | 12 | 91.17 | odd | 6 | |||
637.2.g.l.373.1 | 12 | 91.62 | odd | 6 | |||
637.2.h.l.165.6 | 12 | 91.10 | odd | 6 | |||
637.2.h.l.471.6 | 12 | 91.69 | odd | 6 | |||
819.2.n.d.100.6 | 12 | 39.23 | odd | 6 | |||
819.2.n.d.172.6 | 12 | 273.95 | odd | 6 | |||
819.2.s.d.289.1 | 12 | 39.17 | odd | 6 | |||
819.2.s.d.802.1 | 12 | 273.179 | odd | 6 | |||
1183.2.e.g.170.6 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.g.508.6 | 12 | 7.4 | even | 3 | inner | ||
1183.2.e.h.170.1 | 12 | 13.12 | even | 2 | |||
1183.2.e.h.508.1 | 12 | 91.25 | even | 6 | |||
8281.2.a.bz.1.6 | 6 | 91.51 | even | 6 | |||
8281.2.a.ca.1.6 | 6 | 91.12 | odd | 6 | |||
8281.2.a.ce.1.1 | 6 | 7.2 | even | 3 | |||
8281.2.a.cf.1.1 | 6 | 7.5 | odd | 6 |