Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(29,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.c (of order \(2\), degree \(1\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.13 | ||
Character | \(\chi\) | \(=\) | 210.29 |
Dual form | 210.3.c.a.29.14 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −2.88523 | − | 0.821846i | −0.961744 | − | 0.273949i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −4.52398 | + | 2.12923i | −0.904795 | + | 0.425847i | ||||
\(6\) | −4.08034 | − | 1.16227i | −0.680056 | − | 0.193711i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 7.64914 | + | 4.74244i | 0.849904 | + | 0.526937i | ||||
\(10\) | −6.39787 | + | 3.01119i | −0.639787 | + | 0.301119i | ||||
\(11\) | 18.1525i | 1.65023i | 0.564965 | + | 0.825115i | \(0.308890\pi\) | ||||
−0.564965 | + | 0.825115i | \(0.691110\pi\) | |||||||
\(12\) | −5.77047 | − | 1.64369i | −0.480872 | − | 0.136974i | ||||
\(13\) | 22.5480i | 1.73446i | 0.497906 | + | 0.867231i | \(0.334103\pi\) | ||||
−0.497906 | + | 0.867231i | \(0.665897\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 14.8026 | − | 2.42532i | 0.986842 | − | 0.161688i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −0.457150 | −0.0268912 | −0.0134456 | − | 0.999910i | \(-0.504280\pi\) | ||||
−0.0134456 | + | 0.999910i | \(0.504280\pi\) | |||||||
\(18\) | 10.8175 | + | 6.70682i | 0.600973 | + | 0.372601i | ||||
\(19\) | −30.1627 | −1.58751 | −0.793754 | − | 0.608239i | \(-0.791876\pi\) | ||||
−0.793754 | + | 0.608239i | \(0.791876\pi\) | |||||||
\(20\) | −9.04795 | + | 4.25847i | −0.452398 | + | 0.212923i | ||||
\(21\) | −2.17440 | + | 7.63361i | −0.103543 | + | 0.363505i | ||||
\(22\) | 25.6715i | 1.16689i | ||||||||
\(23\) | −12.3975 | −0.539021 | −0.269510 | − | 0.962997i | \(-0.586862\pi\) | ||||
−0.269510 | + | 0.962997i | \(0.586862\pi\) | |||||||
\(24\) | −8.16067 | − | 2.32453i | −0.340028 | − | 0.0968555i | ||||
\(25\) | 15.9327 | − | 19.2652i | 0.637309 | − | 0.770608i | ||||
\(26\) | 31.8877i | 1.22645i | ||||||||
\(27\) | −18.1720 | − | 19.9694i | −0.673037 | − | 0.739609i | ||||
\(28\) | − | 5.29150i | − | 0.188982i | ||||||
\(29\) | − | 4.70721i | − | 0.162318i | −0.996701 | − | 0.0811588i | \(-0.974138\pi\) | ||
0.996701 | − | 0.0811588i | \(-0.0258621\pi\) | |||||||
\(30\) | 20.9341 | − | 3.42992i | 0.697803 | − | 0.114331i | ||||
\(31\) | 45.2664 | 1.46021 | 0.730103 | − | 0.683337i | \(-0.239472\pi\) | ||||
0.730103 | + | 0.683337i | \(0.239472\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 14.9186 | − | 52.3743i | 0.452078 | − | 1.58710i | ||||
\(34\) | −0.646507 | −0.0190149 | ||||||||
\(35\) | 5.63342 | + | 11.9693i | 0.160955 | + | 0.341980i | ||||
\(36\) | 15.2983 | + | 9.48487i | 0.424952 | + | 0.263469i | ||||
\(37\) | 32.9891i | 0.891597i | 0.895133 | + | 0.445798i | \(0.147080\pi\) | ||||
−0.895133 | + | 0.445798i | \(0.852920\pi\) | |||||||
\(38\) | −42.6564 | −1.12254 | ||||||||
\(39\) | 18.5310 | − | 65.0563i | 0.475154 | − | 1.66811i | ||||
\(40\) | −12.7957 | + | 6.02238i | −0.319893 | + | 0.150560i | ||||
\(41\) | 22.9427i | 0.559578i | 0.960062 | + | 0.279789i | \(0.0902644\pi\) | ||||
−0.960062 | + | 0.279789i | \(0.909736\pi\) | |||||||
\(42\) | −3.07507 | + | 10.7956i | −0.0732159 | + | 0.257037i | ||||
\(43\) | − | 20.2697i | − | 0.471389i | −0.971827 | − | 0.235694i | \(-0.924264\pi\) | ||
0.971827 | − | 0.235694i | \(-0.0757365\pi\) | |||||||
\(44\) | 36.3050i | 0.825115i | ||||||||
\(45\) | −44.7023 | − | 5.16787i | −0.993384 | − | 0.114842i | ||||
\(46\) | −17.5327 | −0.381145 | ||||||||
\(47\) | −9.67333 | −0.205816 | −0.102908 | − | 0.994691i | \(-0.532815\pi\) | ||||
−0.102908 | + | 0.994691i | \(0.532815\pi\) | |||||||
\(48\) | −11.5409 | − | 3.28739i | −0.240436 | − | 0.0684872i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 22.5323 | − | 27.2451i | 0.450646 | − | 0.544902i | ||||
\(51\) | 1.31898 | + | 0.375707i | 0.0258624 | + | 0.00736680i | ||||
\(52\) | 45.0960i | 0.867231i | ||||||||
\(53\) | 5.97465 | 0.112729 | 0.0563646 | − | 0.998410i | \(-0.482049\pi\) | ||||
0.0563646 | + | 0.998410i | \(0.482049\pi\) | |||||||
\(54\) | −25.6991 | − | 28.2411i | −0.475909 | − | 0.522983i | ||||
\(55\) | −38.6510 | − | 82.1216i | −0.702745 | − | 1.49312i | ||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | 87.0263 | + | 24.7891i | 1.52678 | + | 0.434896i | ||||
\(58\) | − | 6.65700i | − | 0.114776i | ||||||
\(59\) | − | 112.848i | − | 1.91268i | −0.292259 | − | 0.956339i | \(-0.594407\pi\) | ||
0.292259 | − | 0.956339i | \(-0.405593\pi\) | |||||||
\(60\) | 29.6053 | − | 4.85064i | 0.493421 | − | 0.0808440i | ||||
\(61\) | −56.3832 | −0.924314 | −0.462157 | − | 0.886798i | \(-0.652924\pi\) | ||||
−0.462157 | + | 0.886798i | \(0.652924\pi\) | |||||||
\(62\) | 64.0163 | 1.03252 | ||||||||
\(63\) | 12.5473 | − | 20.2377i | 0.199164 | − | 0.321234i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −48.0100 | − | 102.007i | −0.738615 | − | 1.56933i | ||||
\(66\) | 21.0981 | − | 74.0684i | 0.319668 | − | 1.12225i | ||||
\(67\) | 67.1684i | 1.00251i | 0.865298 | + | 0.501257i | \(0.167129\pi\) | ||||
−0.865298 | + | 0.501257i | \(0.832871\pi\) | |||||||
\(68\) | −0.914300 | −0.0134456 | ||||||||
\(69\) | 35.7696 | + | 10.1888i | 0.518400 | + | 0.147664i | ||||
\(70\) | 7.96686 | + | 16.9272i | 0.113812 | + | 0.241817i | ||||
\(71\) | − | 20.9402i | − | 0.294932i | −0.989067 | − | 0.147466i | \(-0.952888\pi\) | ||
0.989067 | − | 0.147466i | \(-0.0471117\pi\) | |||||||
\(72\) | 21.6350 | + | 13.4136i | 0.300486 | + | 0.186300i | ||||
\(73\) | 97.7885i | 1.33957i | 0.742556 | + | 0.669784i | \(0.233614\pi\) | ||||
−0.742556 | + | 0.669784i | \(0.766386\pi\) | |||||||
\(74\) | 46.6536i | 0.630454i | ||||||||
\(75\) | −61.8027 | + | 42.4903i | −0.824036 | + | 0.566538i | ||||
\(76\) | −60.3253 | −0.793754 | ||||||||
\(77\) | 48.0271 | 0.623728 | ||||||||
\(78\) | 26.2068 | − | 92.0034i | 0.335985 | − | 1.17953i | ||||
\(79\) | −41.4047 | −0.524110 | −0.262055 | − | 0.965053i | \(-0.584400\pi\) | ||||
−0.262055 | + | 0.965053i | \(0.584400\pi\) | |||||||
\(80\) | −18.0959 | + | 8.51693i | −0.226199 | + | 0.106462i | ||||
\(81\) | 36.0186 | + | 72.5511i | 0.444674 | + | 0.895692i | ||||
\(82\) | 32.4459i | 0.395681i | ||||||||
\(83\) | 121.926 | 1.46899 | 0.734496 | − | 0.678613i | \(-0.237419\pi\) | ||||
0.734496 | + | 0.678613i | \(0.237419\pi\) | |||||||
\(84\) | −4.34880 | + | 15.2672i | −0.0517715 | + | 0.181753i | ||||
\(85\) | 2.06814 | − | 0.973379i | 0.0243310 | − | 0.0114515i | ||||
\(86\) | − | 28.6657i | − | 0.333322i | ||||||
\(87\) | −3.86860 | + | 13.5814i | −0.0444667 | + | 0.156108i | ||||
\(88\) | 51.3431i | 0.583444i | ||||||||
\(89\) | − | 26.8148i | − | 0.301289i | −0.988588 | − | 0.150645i | \(-0.951865\pi\) | ||
0.988588 | − | 0.150645i | \(-0.0481349\pi\) | |||||||
\(90\) | −63.2186 | − | 7.30848i | −0.702428 | − | 0.0812053i | ||||
\(91\) | 59.6564 | 0.655565 | ||||||||
\(92\) | −24.7950 | −0.269510 | ||||||||
\(93\) | −130.604 | − | 37.2020i | −1.40434 | − | 0.400022i | ||||
\(94\) | −13.6802 | −0.145534 | ||||||||
\(95\) | 136.455 | − | 64.2233i | 1.43637 | − | 0.676035i | ||||
\(96\) | −16.3213 | − | 4.64907i | −0.170014 | − | 0.0484278i | ||||
\(97\) | 151.512i | 1.56198i | 0.624542 | + | 0.780991i | \(0.285286\pi\) | ||||
−0.624542 | + | 0.780991i | \(0.714714\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | −86.0872 | + | 138.851i | −0.869567 | + | 1.40254i | ||||
\(100\) | 31.8655 | − | 38.5304i | 0.318655 | − | 0.385304i | ||||
\(101\) | 39.3218i | 0.389324i | 0.980870 | + | 0.194662i | \(0.0623611\pi\) | ||||
−0.980870 | + | 0.194662i | \(0.937639\pi\) | |||||||
\(102\) | 1.86532 | + | 0.531330i | 0.0182875 | + | 0.00520912i | ||||
\(103\) | − | 70.2101i | − | 0.681651i | −0.940127 | − | 0.340826i | \(-0.889293\pi\) | ||
0.940127 | − | 0.340826i | \(-0.110707\pi\) | |||||||
\(104\) | 63.7754i | 0.613225i | ||||||||
\(105\) | −6.41679 | − | 39.1641i | −0.0611123 | − | 0.372991i | ||||
\(106\) | 8.44943 | 0.0797116 | ||||||||
\(107\) | −86.0409 | −0.804121 | −0.402060 | − | 0.915613i | \(-0.631706\pi\) | ||||
−0.402060 | + | 0.915613i | \(0.631706\pi\) | |||||||
\(108\) | −36.3440 | − | 39.9389i | −0.336518 | − | 0.369805i | ||||
\(109\) | 46.4448 | 0.426099 | 0.213049 | − | 0.977041i | \(-0.431660\pi\) | ||||
0.213049 | + | 0.977041i | \(0.431660\pi\) | |||||||
\(110\) | −54.6607 | − | 116.137i | −0.496915 | − | 1.05580i | ||||
\(111\) | 27.1120 | − | 95.1812i | 0.244252 | − | 0.857488i | ||||
\(112\) | − | 10.5830i | − | 0.0944911i | ||||||
\(113\) | 60.7659 | 0.537752 | 0.268876 | − | 0.963175i | \(-0.413348\pi\) | ||||
0.268876 | + | 0.963175i | \(0.413348\pi\) | |||||||
\(114\) | 123.074 | + | 35.0570i | 1.07959 | + | 0.307518i | ||||
\(115\) | 56.0859 | − | 26.3971i | 0.487703 | − | 0.229540i | ||||
\(116\) | − | 9.41442i | − | 0.0811588i | ||||||
\(117\) | −106.933 | + | 172.473i | −0.913953 | + | 1.47413i | ||||
\(118\) | − | 159.591i | − | 1.35247i | ||||||
\(119\) | 1.20950i | 0.0101639i | ||||||||
\(120\) | 41.8682 | − | 6.85984i | 0.348901 | − | 0.0571653i | ||||
\(121\) | −208.514 | −1.72326 | ||||||||
\(122\) | −79.7378 | −0.653589 | ||||||||
\(123\) | 18.8554 | − | 66.1950i | 0.153296 | − | 0.538171i | ||||
\(124\) | 90.5328 | 0.730103 | ||||||||
\(125\) | −31.0592 | + | 121.080i | −0.248474 | + | 0.968639i | ||||
\(126\) | 17.7446 | − | 28.6205i | 0.140830 | − | 0.227146i | ||||
\(127\) | − | 145.061i | − | 1.14221i | −0.820876 | − | 0.571107i | \(-0.806514\pi\) | ||
0.820876 | − | 0.571107i | \(-0.193486\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | −16.6586 | + | 58.4829i | −0.129136 | + | 0.453356i | ||||
\(130\) | −67.8964 | − | 144.259i | −0.522280 | − | 1.10969i | ||||
\(131\) | − | 5.97035i | − | 0.0455752i | −0.999740 | − | 0.0227876i | \(-0.992746\pi\) | ||
0.999740 | − | 0.0227876i | \(-0.00725414\pi\) | |||||||
\(132\) | 29.8372 | − | 104.749i | 0.226039 | − | 0.793549i | ||||
\(133\) | 79.8029i | 0.600022i | ||||||||
\(134\) | 94.9905i | 0.708885i | ||||||||
\(135\) | 124.729 | + | 51.6489i | 0.923920 | + | 0.382585i | ||||
\(136\) | −1.29301 | −0.00950746 | ||||||||
\(137\) | 129.294 | 0.943754 | 0.471877 | − | 0.881664i | \(-0.343577\pi\) | ||||
0.471877 | + | 0.881664i | \(0.343577\pi\) | |||||||
\(138\) | 50.5859 | + | 14.4092i | 0.366564 | + | 0.104414i | ||||
\(139\) | 236.460 | 1.70115 | 0.850576 | − | 0.525851i | \(-0.176253\pi\) | ||||
0.850576 | + | 0.525851i | \(0.176253\pi\) | |||||||
\(140\) | 11.2668 | + | 23.9386i | 0.0804775 | + | 0.170990i | ||||
\(141\) | 27.9098 | + | 7.94999i | 0.197942 | + | 0.0563829i | ||||
\(142\) | − | 29.6139i | − | 0.208548i | ||||||
\(143\) | −409.303 | −2.86226 | ||||||||
\(144\) | 30.5965 | + | 18.9697i | 0.212476 | + | 0.131734i | ||||
\(145\) | 10.0227 | + | 21.2953i | 0.0691224 | + | 0.146864i | ||||
\(146\) | 138.294i | 0.947218i | ||||||||
\(147\) | 20.1966 | + | 5.75292i | 0.137392 | + | 0.0391355i | ||||
\(148\) | 65.9782i | 0.445798i | ||||||||
\(149\) | − | 97.1922i | − | 0.652297i | −0.945319 | − | 0.326148i | \(-0.894249\pi\) | ||
0.945319 | − | 0.326148i | \(-0.105751\pi\) | |||||||
\(150\) | −87.4022 | + | 60.0904i | −0.582681 | + | 0.400603i | ||||
\(151\) | 124.132 | 0.822066 | 0.411033 | − | 0.911621i | \(-0.365168\pi\) | ||||
0.411033 | + | 0.911621i | \(0.365168\pi\) | |||||||
\(152\) | −85.3129 | −0.561269 | ||||||||
\(153\) | −3.49680 | − | 2.16800i | −0.0228549 | − | 0.0141700i | ||||
\(154\) | 67.9205 | 0.441042 | ||||||||
\(155\) | −204.784 | + | 96.3827i | −1.32119 | + | 0.621824i | ||||
\(156\) | 37.0620 | − | 130.113i | 0.237577 | − | 0.834055i | ||||
\(157\) | 50.4117i | 0.321093i | 0.987028 | + | 0.160547i | \(0.0513257\pi\) | ||||
−0.987028 | + | 0.160547i | \(0.948674\pi\) | |||||||
\(158\) | −58.5551 | −0.370602 | ||||||||
\(159\) | −17.2383 | − | 4.91025i | −0.108417 | − | 0.0308820i | ||||
\(160\) | −25.5915 | + | 12.0448i | −0.159947 | + | 0.0752798i | ||||
\(161\) | 32.8006i | 0.203731i | ||||||||
\(162\) | 50.9380 | + | 102.603i | 0.314432 | + | 0.633350i | ||||
\(163\) | 131.802i | 0.808599i | 0.914627 | + | 0.404300i | \(0.132485\pi\) | ||||
−0.914627 | + | 0.404300i | \(0.867515\pi\) | |||||||
\(164\) | 45.8854i | 0.279789i | ||||||||
\(165\) | 44.0257 | + | 268.705i | 0.266822 | + | 1.62852i | ||||
\(166\) | 172.430 | 1.03873 | ||||||||
\(167\) | 189.086 | 1.13225 | 0.566125 | − | 0.824320i | \(-0.308442\pi\) | ||||
0.566125 | + | 0.824320i | \(0.308442\pi\) | |||||||
\(168\) | −6.15014 | + | 21.5911i | −0.0366079 | + | 0.128518i | ||||
\(169\) | −339.413 | −2.00836 | ||||||||
\(170\) | 2.92478 | − | 1.37657i | 0.0172046 | − | 0.00809744i | ||||
\(171\) | −230.718 | − | 143.044i | −1.34923 | − | 0.836517i | ||||
\(172\) | − | 40.5394i | − | 0.235694i | ||||||
\(173\) | 292.614 | 1.69141 | 0.845706 | − | 0.533650i | \(-0.179180\pi\) | ||||
0.845706 | + | 0.533650i | \(0.179180\pi\) | |||||||
\(174\) | −5.47103 | + | 19.2070i | −0.0314427 | + | 0.110385i | ||||
\(175\) | −50.9709 | − | 42.1540i | −0.291263 | − | 0.240880i | ||||
\(176\) | 72.6101i | 0.412557i | ||||||||
\(177\) | −92.7437 | + | 325.593i | −0.523976 | + | 1.83951i | ||||
\(178\) | − | 37.9218i | − | 0.213044i | ||||||
\(179\) | 199.436i | 1.11417i | 0.830456 | + | 0.557084i | \(0.188080\pi\) | ||||
−0.830456 | + | 0.557084i | \(0.811920\pi\) | |||||||
\(180\) | −89.4045 | − | 10.3357i | −0.496692 | − | 0.0574208i | ||||
\(181\) | 42.2460 | 0.233403 | 0.116702 | − | 0.993167i | \(-0.462768\pi\) | ||||
0.116702 | + | 0.993167i | \(0.462768\pi\) | |||||||
\(182\) | 84.3669 | 0.463555 | ||||||||
\(183\) | 162.679 | + | 46.3383i | 0.888954 | + | 0.253215i | ||||
\(184\) | −35.0654 | −0.190573 | ||||||||
\(185\) | −70.2415 | − | 149.242i | −0.379684 | − | 0.806713i | ||||
\(186\) | −184.702 | − | 52.6116i | −0.993022 | − | 0.282858i | ||||
\(187\) | − | 8.29842i | − | 0.0443766i | ||||||
\(188\) | −19.3467 | −0.102908 | ||||||||
\(189\) | −52.8342 | + | 48.0786i | −0.279546 | + | 0.254384i | ||||
\(190\) | 192.977 | − | 90.8255i | 1.01567 | − | 0.478029i | ||||
\(191\) | 212.909i | 1.11471i | 0.830276 | + | 0.557353i | \(0.188183\pi\) | ||||
−0.830276 | + | 0.557353i | \(0.811817\pi\) | |||||||
\(192\) | −23.0819 | − | 6.57477i | −0.120218 | − | 0.0342436i | ||||
\(193\) | − | 81.8019i | − | 0.423844i | −0.977287 | − | 0.211922i | \(-0.932028\pi\) | ||
0.977287 | − | 0.211922i | \(-0.0679723\pi\) | |||||||
\(194\) | 214.271i | 1.10449i | ||||||||
\(195\) | 54.6861 | + | 333.770i | 0.280442 | + | 1.71164i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 140.887 | 0.715162 | 0.357581 | − | 0.933882i | \(-0.383602\pi\) | ||||
0.357581 | + | 0.933882i | \(0.383602\pi\) | |||||||
\(198\) | −121.746 | + | 196.365i | −0.614877 | + | 0.991743i | ||||
\(199\) | −119.398 | −0.599989 | −0.299995 | − | 0.953941i | \(-0.596985\pi\) | ||||
−0.299995 | + | 0.953941i | \(0.596985\pi\) | |||||||
\(200\) | 45.0646 | − | 54.4902i | 0.225323 | − | 0.272451i | ||||
\(201\) | 55.2021 | − | 193.797i | 0.274638 | − | 0.964162i | ||||
\(202\) | 55.6094i | 0.275294i | ||||||||
\(203\) | −12.4541 | −0.0613503 | ||||||||
\(204\) | 2.63797 | + | 0.751414i | 0.0129312 | + | 0.00368340i | ||||
\(205\) | −48.8503 | − | 103.792i | −0.238294 | − | 0.506303i | ||||
\(206\) | − | 99.2921i | − | 0.482000i | ||||||
\(207\) | −94.8300 | − | 58.7942i | −0.458116 | − | 0.284030i | ||||
\(208\) | 90.1920i | 0.433616i | ||||||||
\(209\) | − | 547.528i | − | 2.61975i | ||||||
\(210\) | −9.07472 | − | 55.3864i | −0.0432129 | − | 0.263745i | ||||
\(211\) | 16.6761 | 0.0790339 | 0.0395169 | − | 0.999219i | \(-0.487418\pi\) | ||||
0.0395169 | + | 0.999219i | \(0.487418\pi\) | |||||||
\(212\) | 11.9493 | 0.0563646 | ||||||||
\(213\) | −17.2096 | + | 60.4173i | −0.0807962 | + | 0.283649i | ||||
\(214\) | −121.680 | −0.568599 | ||||||||
\(215\) | 43.1590 | + | 91.6998i | 0.200739 | + | 0.426510i | ||||
\(216\) | −51.3981 | − | 56.4821i | −0.237954 | − | 0.261491i | ||||
\(217\) | − | 119.764i | − | 0.551906i | ||||||
\(218\) | 65.6828 | 0.301297 | ||||||||
\(219\) | 80.3671 | − | 282.143i | 0.366973 | − | 1.28832i | ||||
\(220\) | −77.3019 | − | 164.243i | −0.351372 | − | 0.746560i | ||||
\(221\) | − | 10.3078i | − | 0.0466417i | ||||||
\(222\) | 38.3421 | − | 134.607i | 0.172712 | − | 0.606336i | ||||
\(223\) | − | 72.2345i | − | 0.323922i | −0.986797 | − | 0.161961i | \(-0.948218\pi\) | ||
0.986797 | − | 0.161961i | \(-0.0517818\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 213.236 | − | 71.8022i | 0.947714 | − | 0.319121i | ||||
\(226\) | 85.9360 | 0.380248 | ||||||||
\(227\) | −104.070 | −0.458458 | −0.229229 | − | 0.973373i | \(-0.573620\pi\) | ||||
−0.229229 | + | 0.973373i | \(0.573620\pi\) | |||||||
\(228\) | 174.053 | + | 49.5781i | 0.763388 | + | 0.217448i | ||||
\(229\) | 329.701 | 1.43974 | 0.719871 | − | 0.694107i | \(-0.244201\pi\) | ||||
0.719871 | + | 0.694107i | \(0.244201\pi\) | |||||||
\(230\) | 79.3174 | − | 37.3312i | 0.344858 | − | 0.162309i | ||||
\(231\) | −138.569 | − | 39.4709i | −0.599867 | − | 0.170870i | ||||
\(232\) | − | 13.3140i | − | 0.0573879i | ||||||
\(233\) | 72.7668 | 0.312304 | 0.156152 | − | 0.987733i | \(-0.450091\pi\) | ||||
0.156152 | + | 0.987733i | \(0.450091\pi\) | |||||||
\(234\) | −151.225 | + | 243.913i | −0.646262 | + | 1.04237i | ||||
\(235\) | 43.7619 | − | 20.5968i | 0.186221 | − | 0.0876459i | ||||
\(236\) | − | 225.696i | − | 0.956339i | ||||||
\(237\) | 119.462 | + | 34.0283i | 0.504060 | + | 0.143579i | ||||
\(238\) | 1.71050i | 0.00718697i | ||||||||
\(239\) | − | 291.494i | − | 1.21964i | −0.792540 | − | 0.609819i | \(-0.791242\pi\) | ||
0.792540 | − | 0.609819i | \(-0.208758\pi\) | |||||||
\(240\) | 59.2105 | − | 9.70128i | 0.246710 | − | 0.0404220i | ||||
\(241\) | 281.683 | 1.16881 | 0.584404 | − | 0.811463i | \(-0.301328\pi\) | ||||
0.584404 | + | 0.811463i | \(0.301328\pi\) | |||||||
\(242\) | −294.883 | −1.21853 | ||||||||
\(243\) | −44.2962 | − | 238.929i | −0.182289 | − | 0.983245i | ||||
\(244\) | −112.766 | −0.462157 | ||||||||
\(245\) | 31.6678 | − | 14.9046i | 0.129256 | − | 0.0608352i | ||||
\(246\) | 26.6655 | − | 93.6138i | 0.108396 | − | 0.380544i | ||||
\(247\) | − | 680.108i | − | 2.75347i | ||||||
\(248\) | 128.033 | 0.516261 | ||||||||
\(249\) | −351.786 | − | 100.205i | −1.41279 | − | 0.402428i | ||||
\(250\) | −43.9243 | + | 171.233i | −0.175697 | + | 0.684931i | ||||
\(251\) | 209.382i | 0.834193i | 0.908862 | + | 0.417096i | \(0.136952\pi\) | ||||
−0.908862 | + | 0.417096i | \(0.863048\pi\) | |||||||
\(252\) | 25.0946 | − | 40.4754i | 0.0995818 | − | 0.160617i | ||||
\(253\) | − | 225.045i | − | 0.889508i | ||||||
\(254\) | − | 205.147i | − | 0.807667i | ||||||
\(255\) | −6.76702 | + | 1.10873i | −0.0265373 | + | 0.00434798i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −357.735 | −1.39197 | −0.695983 | − | 0.718058i | \(-0.745031\pi\) | ||||
−0.695983 | + | 0.718058i | \(0.745031\pi\) | |||||||
\(258\) | −23.5588 | + | 82.7073i | −0.0913132 | + | 0.320571i | ||||
\(259\) | 87.2809 | 0.336992 | ||||||||
\(260\) | −96.0200 | − | 204.013i | −0.369308 | − | 0.784667i | ||||
\(261\) | 22.3236 | − | 36.0061i | 0.0855312 | − | 0.137954i | ||||
\(262\) | − | 8.44335i | − | 0.0322265i | ||||||
\(263\) | −149.990 | −0.570304 | −0.285152 | − | 0.958482i | \(-0.592044\pi\) | ||||
−0.285152 | + | 0.958482i | \(0.592044\pi\) | |||||||
\(264\) | 42.1961 | − | 148.137i | 0.159834 | − | 0.561124i | ||||
\(265\) | −27.0292 | + | 12.7214i | −0.101997 | + | 0.0480054i | ||||
\(266\) | 112.858i | 0.424279i | ||||||||
\(267\) | −22.0376 | + | 77.3668i | −0.0825379 | + | 0.289763i | ||||
\(268\) | 134.337i | 0.501257i | ||||||||
\(269\) | − | 165.001i | − | 0.613386i | −0.951808 | − | 0.306693i | \(-0.900777\pi\) | ||
0.951808 | − | 0.306693i | \(-0.0992225\pi\) | |||||||
\(270\) | 176.394 | + | 73.0426i | 0.653310 | + | 0.270528i | ||||
\(271\) | −0.273030 | −0.00100749 | −0.000503745 | − | 1.00000i | \(-0.500160\pi\) | ||||
−0.000503745 | 1.00000i | \(0.500160\pi\) | ||||||||
\(272\) | −1.82860 | −0.00672279 | ||||||||
\(273\) | −172.123 | − | 49.0284i | −0.630486 | − | 0.179591i | ||||
\(274\) | 182.850 | 0.667335 | ||||||||
\(275\) | 349.712 | + | 289.219i | 1.27168 | + | 1.05171i | ||||
\(276\) | 71.5392 | + | 20.3776i | 0.259200 | + | 0.0738320i | ||||
\(277\) | 86.4554i | 0.312113i | 0.987748 | + | 0.156057i | \(0.0498782\pi\) | ||||
−0.987748 | + | 0.156057i | \(0.950122\pi\) | |||||||
\(278\) | 334.405 | 1.20290 | ||||||||
\(279\) | 346.249 | + | 214.673i | 1.24104 | + | 0.769437i | ||||
\(280\) | 15.9337 | + | 33.8543i | 0.0569062 | + | 0.120908i | ||||
\(281\) | 301.513i | 1.07300i | 0.843900 | + | 0.536500i | \(0.180254\pi\) | ||||
−0.843900 | + | 0.536500i | \(0.819746\pi\) | |||||||
\(282\) | 39.4704 | + | 11.2430i | 0.139966 | + | 0.0398687i | ||||
\(283\) | 74.3380i | 0.262679i | 0.991337 | + | 0.131339i | \(0.0419277\pi\) | ||||
−0.991337 | + | 0.131339i | \(0.958072\pi\) | |||||||
\(284\) | − | 41.8803i | − | 0.147466i | ||||||
\(285\) | −446.487 | + | 73.1541i | −1.56662 | + | 0.256681i | ||||
\(286\) | −578.842 | −2.02392 | ||||||||
\(287\) | 60.7006 | 0.211500 | ||||||||
\(288\) | 43.2701 | + | 26.8273i | 0.150243 | + | 0.0931502i | ||||
\(289\) | −288.791 | −0.999277 | ||||||||
\(290\) | 14.1743 | + | 30.1161i | 0.0488769 | + | 0.103849i | ||||
\(291\) | 124.520 | − | 437.148i | 0.427903 | − | 1.50223i | ||||
\(292\) | 195.577i | 0.669784i | ||||||||
\(293\) | −354.478 | −1.20982 | −0.604911 | − | 0.796293i | \(-0.706791\pi\) | ||||
−0.604911 | + | 0.796293i | \(0.706791\pi\) | |||||||
\(294\) | 28.5623 | + | 8.13586i | 0.0971508 | + | 0.0276730i | ||||
\(295\) | 240.280 | + | 510.522i | 0.814508 | + | 1.73058i | ||||
\(296\) | 93.3072i | 0.315227i | ||||||||
\(297\) | 362.496 | − | 329.867i | 1.22052 | − | 1.11066i | ||||
\(298\) | − | 137.451i | − | 0.461243i | ||||||
\(299\) | − | 279.538i | − | 0.934911i | ||||||
\(300\) | −123.605 | + | 84.9807i | −0.412018 | + | 0.283269i | ||||
\(301\) | −53.6286 | −0.178168 | ||||||||
\(302\) | 175.549 | 0.581288 | ||||||||
\(303\) | 32.3164 | − | 113.452i | 0.106655 | − | 0.374430i | ||||
\(304\) | −120.651 | −0.396877 | ||||||||
\(305\) | 255.076 | − | 120.053i | 0.836315 | − | 0.393616i | ||||
\(306\) | −4.94522 | − | 3.06602i | −0.0161609 | − | 0.0100197i | ||||
\(307\) | − | 388.852i | − | 1.26662i | −0.773898 | − | 0.633310i | \(-0.781696\pi\) | ||
0.773898 | − | 0.633310i | \(-0.218304\pi\) | |||||||
\(308\) | 96.0541 | 0.311864 | ||||||||
\(309\) | −57.7019 | + | 202.572i | −0.186738 | + | 0.655574i | ||||
\(310\) | −289.608 | + | 136.306i | −0.934221 | + | 0.439696i | ||||
\(311\) | 153.969i | 0.495078i | 0.968878 | + | 0.247539i | \(0.0796219\pi\) | ||||
−0.968878 | + | 0.247539i | \(0.920378\pi\) | |||||||
\(312\) | 52.4136 | − | 184.007i | 0.167992 | − | 0.589766i | ||||
\(313\) | 114.895i | 0.367076i | 0.983013 | + | 0.183538i | \(0.0587550\pi\) | ||||
−0.983013 | + | 0.183538i | \(0.941245\pi\) | |||||||
\(314\) | 71.2929i | 0.227047i | ||||||||
\(315\) | −13.6729 | + | 118.271i | −0.0434061 | + | 0.375464i | ||||
\(316\) | −82.8094 | −0.262055 | ||||||||
\(317\) | −8.21324 | −0.0259093 | −0.0129546 | − | 0.999916i | \(-0.504124\pi\) | ||||
−0.0129546 | + | 0.999916i | \(0.504124\pi\) | |||||||
\(318\) | −24.3786 | − | 6.94414i | −0.0766622 | − | 0.0218369i | ||||
\(319\) | 85.4477 | 0.267861 | ||||||||
\(320\) | −36.1918 | + | 17.0339i | −0.113099 | + | 0.0532308i | ||||
\(321\) | 248.248 | + | 70.7124i | 0.773359 | + | 0.220288i | ||||
\(322\) | 46.3871i | 0.144059i | ||||||||
\(323\) | 13.7889 | 0.0426899 | ||||||||
\(324\) | 72.0372 | + | 145.102i | 0.222337 | + | 0.447846i | ||||
\(325\) | 434.392 | + | 359.251i | 1.33659 | + | 1.10539i | ||||
\(326\) | 186.396i | 0.571766i | ||||||||
\(327\) | −134.004 | − | 38.1705i | −0.409798 | − | 0.116729i | ||||
\(328\) | 64.8917i | 0.197841i | ||||||||
\(329\) | 25.5932i | 0.0777910i | ||||||||
\(330\) | 62.2617 | + | 380.006i | 0.188672 | + | 1.15153i | ||||
\(331\) | −623.239 | −1.88290 | −0.941449 | − | 0.337157i | \(-0.890535\pi\) | ||||
−0.941449 | + | 0.337157i | \(0.890535\pi\) | |||||||
\(332\) | 243.853 | 0.734496 | ||||||||
\(333\) | −156.449 | + | 252.338i | −0.469816 | + | 0.757772i | ||||
\(334\) | 267.407 | 0.800621 | ||||||||
\(335\) | −143.017 | − | 303.868i | −0.426917 | − | 0.907070i | ||||
\(336\) | −8.69760 | + | 30.5344i | −0.0258857 | + | 0.0908763i | ||||
\(337\) | − | 279.891i | − | 0.830538i | −0.909699 | − | 0.415269i | \(-0.863688\pi\) | ||
0.909699 | − | 0.415269i | \(-0.136312\pi\) | |||||||
\(338\) | −480.002 | −1.42012 | ||||||||
\(339\) | −175.324 | − | 49.9403i | −0.517180 | − | 0.147316i | ||||
\(340\) | 4.13627 | − | 1.94676i | 0.0121655 | − | 0.00572576i | ||||
\(341\) | 821.699i | 2.40967i | ||||||||
\(342\) | −326.285 | − | 202.295i | −0.954049 | − | 0.591507i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 57.3314i | − | 0.166661i | ||||||
\(345\) | −183.515 | + | 30.0679i | −0.531928 | + | 0.0871532i | ||||
\(346\) | 413.819 | 1.19601 | ||||||||
\(347\) | −466.444 | −1.34422 | −0.672110 | − | 0.740452i | \(-0.734612\pi\) | ||||
−0.672110 | + | 0.740452i | \(0.734612\pi\) | |||||||
\(348\) | −7.73720 | + | 27.1628i | −0.0222333 | + | 0.0780540i | ||||
\(349\) | −56.3961 | −0.161593 | −0.0807967 | − | 0.996731i | \(-0.525746\pi\) | ||||
−0.0807967 | + | 0.996731i | \(0.525746\pi\) | |||||||
\(350\) | −72.0838 | − | 59.6148i | −0.205954 | − | 0.170328i | ||||
\(351\) | 450.271 | − | 409.742i | 1.28282 | − | 1.16736i | ||||
\(352\) | 102.686i | 0.291722i | ||||||||
\(353\) | 237.617 | 0.673137 | 0.336568 | − | 0.941659i | \(-0.390734\pi\) | ||||
0.336568 | + | 0.941659i | \(0.390734\pi\) | |||||||
\(354\) | −131.159 | + | 460.458i | −0.370507 | + | 1.30073i | ||||
\(355\) | 44.5865 | + | 94.7328i | 0.125596 | + | 0.266853i | ||||
\(356\) | − | 53.6295i | − | 0.150645i | ||||||
\(357\) | 0.994027 | − | 3.48970i | 0.00278439 | − | 0.00977508i | ||||
\(358\) | 282.045i | 0.787836i | ||||||||
\(359\) | 312.908i | 0.871610i | 0.900041 | + | 0.435805i | \(0.143536\pi\) | ||||
−0.900041 | + | 0.435805i | \(0.856464\pi\) | |||||||
\(360\) | −126.437 | − | 14.6170i | −0.351214 | − | 0.0406027i | ||||
\(361\) | 548.785 | 1.52018 | ||||||||
\(362\) | 59.7449 | 0.165041 | ||||||||
\(363\) | 601.612 | + | 171.367i | 1.65733 | + | 0.472084i | ||||
\(364\) | 119.313 | 0.327783 | ||||||||
\(365\) | −208.215 | − | 442.393i | −0.570451 | − | 1.21204i | ||||
\(366\) | 230.062 | + | 65.5322i | 0.628585 | + | 0.179050i | ||||
\(367\) | − | 58.1239i | − | 0.158376i | −0.996860 | − | 0.0791878i | \(-0.974767\pi\) | ||
0.996860 | − | 0.0791878i | \(-0.0252327\pi\) | |||||||
\(368\) | −49.5899 | −0.134755 | ||||||||
\(369\) | −108.804 | + | 175.492i | −0.294862 | + | 0.475587i | ||||
\(370\) | −99.3364 | − | 211.060i | −0.268477 | − | 0.570432i | ||||
\(371\) | − | 15.8074i | − | 0.0426077i | ||||||
\(372\) | −261.208 | − | 74.4040i | −0.702172 | − | 0.200011i | ||||
\(373\) | − | 435.852i | − | 1.16850i | −0.811572 | − | 0.584252i | \(-0.801388\pi\) | ||
0.811572 | − | 0.584252i | \(-0.198612\pi\) | |||||||
\(374\) | − | 11.7357i | − | 0.0313790i | ||||||
\(375\) | 189.122 | − | 323.818i | 0.504325 | − | 0.863514i | ||||
\(376\) | −27.3603 | −0.0727668 | ||||||||
\(377\) | 106.138 | 0.281534 | ||||||||
\(378\) | −74.7188 | + | 67.9934i | −0.197669 | + | 0.179877i | ||||
\(379\) | −639.393 | −1.68705 | −0.843526 | − | 0.537089i | \(-0.819524\pi\) | ||||
−0.843526 | + | 0.537089i | \(0.819524\pi\) | |||||||
\(380\) | 272.910 | − | 128.447i | 0.718185 | − | 0.338017i | ||||
\(381\) | −119.218 | + | 418.535i | −0.312908 | + | 1.09852i | ||||
\(382\) | 301.098i | 0.788216i | ||||||||
\(383\) | 240.793 | 0.628702 | 0.314351 | − | 0.949307i | \(-0.398213\pi\) | ||||
0.314351 | + | 0.949307i | \(0.398213\pi\) | |||||||
\(384\) | −32.6427 | − | 9.29813i | −0.0850070 | − | 0.0242139i | ||||
\(385\) | −217.273 | + | 102.261i | −0.564346 | + | 0.265613i | ||||
\(386\) | − | 115.685i | − | 0.299703i | ||||||
\(387\) | 96.1279 | − | 155.046i | 0.248392 | − | 0.400635i | ||||
\(388\) | 303.025i | 0.780991i | ||||||||
\(389\) | − | 160.718i | − | 0.413157i | −0.978430 | − | 0.206579i | \(-0.933767\pi\) | ||
0.978430 | − | 0.206579i | \(-0.0662329\pi\) | |||||||
\(390\) | 77.3379 | + | 472.022i | 0.198302 | + | 1.21031i | ||||
\(391\) | 5.66750 | 0.0144949 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | −4.90671 | + | 17.2258i | −0.0124853 | + | 0.0438317i | ||||
\(394\) | 199.244 | 0.505696 | ||||||||
\(395\) | 187.314 | − | 88.1603i | 0.474212 | − | 0.223191i | ||||
\(396\) | −172.174 | + | 277.702i | −0.434784 | + | 0.701268i | ||||
\(397\) | − | 212.339i | − | 0.534859i | −0.963577 | − | 0.267430i | \(-0.913826\pi\) | ||
0.963577 | − | 0.267430i | \(-0.0861743\pi\) | |||||||
\(398\) | −168.854 | −0.424256 | ||||||||
\(399\) | 65.5857 | − | 230.250i | 0.164375 | − | 0.577067i | ||||
\(400\) | 63.7309 | − | 77.0608i | 0.159327 | − | 0.192652i | ||||
\(401\) | 194.436i | 0.484879i | 0.970167 | + | 0.242439i | \(0.0779476\pi\) | ||||
−0.970167 | + | 0.242439i | \(0.922052\pi\) | |||||||
\(402\) | 78.0676 | − | 274.070i | 0.194198 | − | 0.681766i | ||||
\(403\) | 1020.67i | 2.53267i | ||||||||
\(404\) | 78.6435i | 0.194662i | ||||||||
\(405\) | −317.425 | − | 251.527i | −0.783767 | − | 0.621055i | ||||
\(406\) | −17.6128 | −0.0433812 | ||||||||
\(407\) | −598.835 | −1.47134 | ||||||||
\(408\) | 3.73065 | + | 1.06266i | 0.00914375 | + | 0.00260456i | ||||
\(409\) | 294.951 | 0.721152 | 0.360576 | − | 0.932730i | \(-0.382580\pi\) | ||||
0.360576 | + | 0.932730i | \(0.382580\pi\) | |||||||
\(410\) | −69.0848 | − | 146.784i | −0.168499 | − | 0.358010i | ||||
\(411\) | −373.044 | − | 106.260i | −0.907650 | − | 0.258540i | ||||
\(412\) | − | 140.420i | − | 0.340826i | ||||||
\(413\) | −298.568 | −0.722925 | ||||||||
\(414\) | −134.110 | − | 83.1476i | −0.323937 | − | 0.200840i | ||||
\(415\) | −551.592 | + | 259.610i | −1.32914 | + | 0.625565i | ||||
\(416\) | 127.551i | 0.306613i | ||||||||
\(417\) | −682.243 | − | 194.334i | −1.63607 | − | 0.466029i | ||||
\(418\) | − | 774.322i | − | 1.85244i | ||||||
\(419\) | 618.346i | 1.47577i | 0.674929 | + | 0.737883i | \(0.264174\pi\) | ||||
−0.674929 | + | 0.737883i | \(0.735826\pi\) | |||||||
\(420\) | −12.8336 | − | 78.3281i | −0.0305562 | − | 0.186496i | ||||
\(421\) | 172.506 | 0.409752 | 0.204876 | − | 0.978788i | \(-0.434321\pi\) | ||||
0.204876 | + | 0.978788i | \(0.434321\pi\) | |||||||
\(422\) | 23.5836 | 0.0558854 | ||||||||
\(423\) | −73.9926 | − | 45.8752i | −0.174923 | − | 0.108452i | ||||
\(424\) | 16.8989 | 0.0398558 | ||||||||
\(425\) | −7.28365 | + | 8.80708i | −0.0171380 | + | 0.0207226i | ||||
\(426\) | −24.3380 | + | 85.4429i | −0.0571316 | + | 0.200570i | ||||
\(427\) | 149.176i | 0.349358i | ||||||||
\(428\) | −172.082 | −0.402060 | ||||||||
\(429\) | 1180.94 | + | 336.384i | 2.75276 | + | 0.784113i | ||||
\(430\) | 61.0360 | + | 129.683i | 0.141944 | + | 0.301588i | ||||
\(431\) | − | 180.443i | − | 0.418662i | −0.977845 | − | 0.209331i | \(-0.932871\pi\) | ||
0.977845 | − | 0.209331i | \(-0.0671287\pi\) | |||||||
\(432\) | −72.6880 | − | 79.8778i | −0.168259 | − | 0.184902i | ||||
\(433\) | 440.096i | 1.01639i | 0.861243 | + | 0.508194i | \(0.169687\pi\) | ||||
−0.861243 | + | 0.508194i | \(0.830313\pi\) | |||||||
\(434\) | − | 169.371i | − | 0.390257i | ||||||
\(435\) | −11.4165 | − | 69.6791i | −0.0262448 | − | 0.160182i | ||||
\(436\) | 92.8896 | 0.213049 | ||||||||
\(437\) | 373.941 | 0.855700 | ||||||||
\(438\) | 113.656 | − | 399.010i | 0.259489 | − | 0.910982i | ||||
\(439\) | 389.346 | 0.886894 | 0.443447 | − | 0.896301i | \(-0.353756\pi\) | ||||
0.443447 | + | 0.896301i | \(0.353756\pi\) | |||||||
\(440\) | −109.321 | − | 232.275i | −0.248458 | − | 0.527898i | ||||
\(441\) | −53.5440 | − | 33.1971i | −0.121415 | − | 0.0752768i | ||||
\(442\) | − | 14.5775i | − | 0.0329807i | ||||||
\(443\) | 521.471 | 1.17714 | 0.588568 | − | 0.808448i | \(-0.299692\pi\) | ||||
0.588568 | + | 0.808448i | \(0.299692\pi\) | |||||||
\(444\) | 54.2239 | − | 190.362i | 0.122126 | − | 0.428744i | ||||
\(445\) | 57.0949 | + | 121.309i | 0.128303 | + | 0.272605i | ||||
\(446\) | − | 102.155i | − | 0.229047i | ||||||
\(447\) | −79.8771 | + | 280.422i | −0.178696 | + | 0.627343i | ||||
\(448\) | − | 21.1660i | − | 0.0472456i | ||||||
\(449\) | 596.122i | 1.32767i | 0.747880 | + | 0.663833i | \(0.231072\pi\) | ||||
−0.747880 | + | 0.663833i | \(0.768928\pi\) | |||||||
\(450\) | 301.561 | − | 101.544i | 0.670135 | − | 0.225653i | ||||
\(451\) | −416.468 | −0.923431 | ||||||||
\(452\) | 121.532 | 0.268876 | ||||||||
\(453\) | −358.149 | − | 102.017i | −0.790617 | − | 0.225204i | ||||
\(454\) | −147.177 | −0.324179 | ||||||||
\(455\) | −269.884 | + | 127.022i | −0.593152 | + | 0.279170i | ||||
\(456\) | 246.147 | + | 70.1141i | 0.539797 | + | 0.153759i | ||||
\(457\) | 320.229i | 0.700721i | 0.936615 | + | 0.350360i | \(0.113941\pi\) | ||||
−0.936615 | + | 0.350360i | \(0.886059\pi\) | |||||||
\(458\) | 466.268 | 1.01805 | ||||||||
\(459\) | 8.30732 | + | 9.12903i | 0.0180987 | + | 0.0198890i | ||||
\(460\) | 112.172 | − | 52.7942i | 0.243852 | − | 0.114770i | ||||
\(461\) | − | 141.935i | − | 0.307885i | −0.988080 | − | 0.153943i | \(-0.950803\pi\) | ||
0.988080 | − | 0.153943i | \(-0.0491971\pi\) | |||||||
\(462\) | −195.967 | − | 55.8202i | −0.424170 | − | 0.120823i | ||||
\(463\) | − | 233.394i | − | 0.504090i | −0.967716 | − | 0.252045i | \(-0.918897\pi\) | ||
0.967716 | − | 0.252045i | \(-0.0811031\pi\) | |||||||
\(464\) | − | 18.8288i | − | 0.0405794i | ||||||
\(465\) | 670.062 | − | 109.785i | 1.44099 | − | 0.236098i | ||||
\(466\) | 102.908 | 0.220832 | ||||||||
\(467\) | 388.847 | 0.832649 | 0.416325 | − | 0.909216i | \(-0.363318\pi\) | ||||
0.416325 | + | 0.909216i | \(0.363318\pi\) | |||||||
\(468\) | −213.865 | + | 344.946i | −0.456977 | + | 0.737063i | ||||
\(469\) | 177.711 | 0.378915 | ||||||||
\(470\) | 61.8887 | − | 29.1282i | 0.131678 | − | 0.0619750i | ||||
\(471\) | 41.4306 | − | 145.449i | 0.0879631 | − | 0.308810i | ||||
\(472\) | − | 319.182i | − | 0.676234i | ||||||
\(473\) | 367.947 | 0.777900 | ||||||||
\(474\) | 168.945 | + | 48.1233i | 0.356424 | + | 0.101526i | ||||
\(475\) | −480.573 | + | 581.090i | −1.01173 | + | 1.22335i | ||||
\(476\) | 2.41901i | 0.00508195i | ||||||||
\(477\) | 45.7009 | + | 28.3344i | 0.0958091 | + | 0.0594013i | ||||
\(478\) | − | 412.234i | − | 0.862415i | ||||||
\(479\) | 891.549i | 1.86127i | 0.365946 | + | 0.930636i | \(0.380745\pi\) | ||||
−0.365946 | + | 0.930636i | \(0.619255\pi\) | |||||||
\(480\) | 83.7363 | − | 13.7197i | 0.174451 | − | 0.0285827i | ||||
\(481\) | −743.838 | −1.54644 | ||||||||
\(482\) | 398.360 | 0.826472 | ||||||||
\(483\) | 26.9571 | − | 94.6375i | 0.0558118 | − | 0.195937i | ||||
\(484\) | −417.028 | −0.861628 | ||||||||
\(485\) | −322.605 | − | 685.438i | −0.665165 | − | 1.41327i | ||||
\(486\) | −62.6443 | − | 337.896i | −0.128898 | − | 0.695259i | ||||
\(487\) | − | 228.917i | − | 0.470056i | −0.971989 | − | 0.235028i | \(-0.924482\pi\) | ||
0.971989 | − | 0.235028i | \(-0.0755182\pi\) | |||||||
\(488\) | −159.476 | −0.326794 | ||||||||
\(489\) | 108.321 | − | 380.278i | 0.221515 | − | 0.777666i | ||||
\(490\) | 44.7851 | − | 21.0783i | 0.0913981 | − | 0.0430170i | ||||
\(491\) | − | 328.951i | − | 0.669960i | −0.942225 | − | 0.334980i | \(-0.891270\pi\) | ||
0.942225 | − | 0.334980i | \(-0.108730\pi\) | |||||||
\(492\) | 37.7107 | − | 132.390i | 0.0766478 | − | 0.269085i | ||||
\(493\) | 2.15190i | 0.00436491i | ||||||||
\(494\) | − | 961.818i | − | 1.94700i | ||||||
\(495\) | 93.8099 | − | 811.459i | 0.189515 | − | 1.63931i | ||||
\(496\) | 181.066 | 0.365052 | ||||||||
\(497\) | −55.4025 | −0.111474 | ||||||||
\(498\) | −497.500 | − | 141.711i | −0.998996 | − | 0.284560i | ||||
\(499\) | 169.653 | 0.339985 | 0.169993 | − | 0.985445i | \(-0.445626\pi\) | ||||
0.169993 | + | 0.985445i | \(0.445626\pi\) | |||||||
\(500\) | −62.1184 | + | 242.160i | −0.124237 | + | 0.484319i | ||||
\(501\) | −545.556 | − | 155.399i | −1.08893 | − | 0.310178i | ||||
\(502\) | 296.111i | 0.589864i | ||||||||
\(503\) | −353.801 | −0.703381 | −0.351691 | − | 0.936116i | \(-0.614393\pi\) | ||||
−0.351691 | + | 0.936116i | \(0.614393\pi\) | |||||||
\(504\) | 35.4891 | − | 57.2409i | 0.0704150 | − | 0.113573i | ||||
\(505\) | −83.7252 | − | 177.891i | −0.165792 | − | 0.352259i | ||||
\(506\) | − | 318.262i | − | 0.628977i | ||||||
\(507\) | 979.285 | + | 278.945i | 1.93153 | + | 0.550188i | ||||
\(508\) | − | 290.122i | − | 0.571107i | ||||||
\(509\) | − | 909.175i | − | 1.78620i | −0.449859 | − | 0.893099i | \(-0.648526\pi\) | ||
0.449859 | − | 0.893099i | \(-0.351474\pi\) | |||||||
\(510\) | −9.57001 | + | 1.56799i | −0.0187647 | + | 0.00307449i | ||||
\(511\) | 258.724 | 0.506309 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 548.115 | + | 602.331i | 1.06845 | + | 1.17414i | ||||
\(514\) | −505.914 | −0.984269 | ||||||||
\(515\) | 149.494 | + | 317.629i | 0.290279 | + | 0.616755i | ||||
\(516\) | −33.3172 | + | 116.966i | −0.0645682 | + | 0.226678i | ||||
\(517\) | − | 175.595i | − | 0.339643i | ||||||
\(518\) | 123.434 | 0.238289 | ||||||||
\(519\) | −844.260 | − | 240.484i | −1.62670 | − | 0.463360i | ||||
\(520\) | −135.793 | − | 288.518i | −0.261140 | − | 0.554843i | ||||
\(521\) | 77.7672i | 0.149265i | 0.997211 | + | 0.0746326i | \(0.0237784\pi\) | ||||
−0.997211 | + | 0.0746326i | \(0.976222\pi\) | |||||||
\(522\) | 31.5704 | − | 50.9203i | 0.0604797 | − | 0.0975484i | ||||
\(523\) | 781.844i | 1.49492i | 0.664305 | + | 0.747461i | \(0.268727\pi\) | ||||
−0.664305 | + | 0.747461i | \(0.731273\pi\) | |||||||
\(524\) | − | 11.9407i | − | 0.0227876i | ||||||
\(525\) | 112.419 | + | 163.515i | 0.214131 | + | 0.311456i | ||||
\(526\) | −212.118 | −0.403266 | ||||||||
\(527\) | −20.6935 | −0.0392666 | ||||||||
\(528\) | 59.6743 | − | 209.497i | 0.113020 | − | 0.396775i | ||||
\(529\) | −375.303 | −0.709457 | ||||||||
\(530\) | −38.2250 | + | 17.9908i | −0.0721227 | + | 0.0339449i | ||||
\(531\) | 535.175 | − | 863.190i | 1.00786 | − | 1.62559i | ||||
\(532\) | 159.606i | 0.300011i | ||||||||
\(533\) | −517.312 | −0.970566 | ||||||||
\(534\) | −31.1659 | + | 109.413i | −0.0583631 | + | 0.204894i | ||||
\(535\) | 389.247 | − | 183.201i | 0.727565 | − | 0.342432i | ||||
\(536\) | 189.981i | 0.354442i | ||||||||
\(537\) | 163.906 | − | 575.420i | 0.305225 | − | 1.07155i | ||||
\(538\) | − | 233.347i | − | 0.433730i | ||||||
\(539\) | − | 127.068i | − | 0.235747i | ||||||
\(540\) | 249.459 | + | 103.298i | 0.461960 | + | 0.191292i | ||||
\(541\) | 355.089 | 0.656356 | 0.328178 | − | 0.944616i | \(-0.393565\pi\) | ||||
0.328178 | + | 0.944616i | \(0.393565\pi\) | |||||||
\(542\) | −0.386122 | −0.000712403 | ||||||||
\(543\) | −121.890 | − | 34.7197i | −0.224474 | − | 0.0639405i | ||||
\(544\) | −2.58603 | −0.00475373 | ||||||||
\(545\) | −210.115 | + | 98.8918i | −0.385532 | + | 0.181453i | ||||
\(546\) | −243.418 | − | 69.3367i | −0.445821 | − | 0.126990i | ||||
\(547\) | 883.402i | 1.61499i | 0.589872 | + | 0.807497i | \(0.299178\pi\) | ||||
−0.589872 | + | 0.807497i | \(0.700822\pi\) | |||||||
\(548\) | 258.589 | 0.471877 | ||||||||
\(549\) | −431.282 | − | 267.394i | −0.785578 | − | 0.487056i | ||||
\(550\) | 494.568 | + | 409.018i | 0.899214 | + | 0.743669i | ||||
\(551\) | 141.982i | 0.257680i | ||||||||
\(552\) | 101.172 | + | 28.8183i | 0.183282 | + | 0.0522071i | ||||
\(553\) | 109.547i | 0.198095i | ||||||||
\(554\) | 122.266i | 0.220697i | ||||||||
\(555\) | 80.0091 | + | 488.325i | 0.144161 | + | 0.879865i | ||||
\(556\) | 472.921 | 0.850576 | ||||||||
\(557\) | −76.6136 | −0.137547 | −0.0687735 | − | 0.997632i | \(-0.521909\pi\) | ||||
−0.0687735 | + | 0.997632i | \(0.521909\pi\) | |||||||
\(558\) | 489.670 | + | 303.593i | 0.877544 | + | 0.544074i | ||||
\(559\) | 457.042 | 0.817606 | ||||||||
\(560\) | 22.5337 | + | 47.8773i | 0.0402387 | + | 0.0854951i | ||||
\(561\) | −6.82003 | + | 23.9429i | −0.0121569 | + | 0.0426789i | ||||
\(562\) | 426.404i | 0.758726i | ||||||||
\(563\) | 361.800 | 0.642629 | 0.321314 | − | 0.946973i | \(-0.395875\pi\) | ||||
0.321314 | + | 0.946973i | \(0.395875\pi\) | |||||||
\(564\) | 55.8196 | + | 15.9000i | 0.0989710 | + | 0.0281915i | ||||
\(565\) | −274.904 | + | 129.385i | −0.486555 | + | 0.229000i | ||||
\(566\) | 105.130i | 0.185742i | ||||||||
\(567\) | 191.952 | − | 95.2963i | 0.338540 | − | 0.168071i | ||||
\(568\) | − | 59.2277i | − | 0.104274i | ||||||
\(569\) | − | 72.2936i | − | 0.127054i | −0.997980 | − | 0.0635269i | \(-0.979765\pi\) | ||
0.997980 | − | 0.0635269i | \(-0.0202349\pi\) | |||||||
\(570\) | −631.427 | + | 103.455i | −1.10777 | + | 0.181501i | ||||
\(571\) | 90.4610 | 0.158426 | 0.0792128 | − | 0.996858i | \(-0.474759\pi\) | ||||
0.0792128 | + | 0.996858i | \(0.474759\pi\) | |||||||
\(572\) | −818.607 | −1.43113 | ||||||||
\(573\) | 174.978 | − | 614.291i | 0.305372 | − | 1.07206i | ||||
\(574\) | 85.8437 | 0.149553 | ||||||||
\(575\) | −197.526 | + | 238.840i | −0.343523 | + | 0.415374i | ||||
\(576\) | 61.1931 | + | 37.9395i | 0.106238 | + | 0.0658672i | ||||
\(577\) | − | 456.970i | − | 0.791976i | −0.918256 | − | 0.395988i | \(-0.870402\pi\) | ||
0.918256 | − | 0.395988i | \(-0.129598\pi\) | |||||||
\(578\) | −408.412 | −0.706595 | ||||||||
\(579\) | −67.2286 | + | 236.018i | −0.116112 | + | 0.407630i | ||||
\(580\) | 20.0455 | + | 42.5906i | 0.0345612 | + | 0.0734321i | ||||
\(581\) | − | 322.587i | − | 0.555227i | ||||||
\(582\) | 176.098 | − | 618.221i | 0.302573 | − | 1.06224i | ||||
\(583\) | 108.455i | 0.186029i | ||||||||
\(584\) | 276.588i | 0.473609i | ||||||||
\(585\) | 116.525 | − | 1007.95i | 0.199189 | − | 1.72299i | ||||
\(586\) | −501.308 | −0.855474 | ||||||||
\(587\) | −245.442 | −0.418130 | −0.209065 | − | 0.977902i | \(-0.567042\pi\) | ||||
−0.209065 | + | 0.977902i | \(0.567042\pi\) | |||||||
\(588\) | 40.3933 | + | 11.5058i | 0.0686960 | + | 0.0195678i | ||||
\(589\) | −1365.35 | −2.31809 | ||||||||
\(590\) | 339.807 | + | 721.987i | 0.575944 | + | 1.22371i | ||||
\(591\) | −406.492 | − | 115.787i | −0.687803 | − | 0.195918i | ||||
\(592\) | 131.956i | 0.222899i | ||||||||
\(593\) | −308.286 | −0.519876 | −0.259938 | − | 0.965625i | \(-0.583702\pi\) | ||||
−0.259938 | + | 0.965625i | \(0.583702\pi\) | |||||||
\(594\) | 512.647 | − | 466.503i | 0.863041 | − | 0.785359i | ||||
\(595\) | −2.57532 | − | 5.47177i | −0.00432827 | − | 0.00919625i | ||||
\(596\) | − | 194.384i | − | 0.326148i | ||||||
\(597\) | 344.491 | + | 98.1267i | 0.577036 | + | 0.164366i | ||||
\(598\) | − | 395.327i | − | 0.661082i | ||||||
\(599\) | 171.484i | 0.286283i | 0.989702 | + | 0.143142i | \(0.0457205\pi\) | ||||
−0.989702 | + | 0.143142i | \(0.954280\pi\) | |||||||
\(600\) | −174.804 | + | 120.181i | −0.291341 | + | 0.200301i | ||||
\(601\) | −507.061 | −0.843695 | −0.421848 | − | 0.906667i | \(-0.638618\pi\) | ||||
−0.421848 | + | 0.906667i | \(0.638618\pi\) | |||||||
\(602\) | −75.8424 | −0.125984 | ||||||||
\(603\) | −318.542 | + | 513.781i | −0.528262 | + | 0.852041i | ||||
\(604\) | 248.264 | 0.411033 | ||||||||
\(605\) | 943.313 | − | 443.975i | 1.55919 | − | 0.733843i | ||||
\(606\) | 45.7024 | − | 160.446i | 0.0754164 | − | 0.264762i | ||||
\(607\) | 86.8260i | 0.143041i | 0.997439 | + | 0.0715206i | \(0.0227852\pi\) | ||||
−0.997439 | + | 0.0715206i | \(0.977215\pi\) | |||||||
\(608\) | −170.626 | −0.280634 | ||||||||
\(609\) | 35.9330 | + | 10.2354i | 0.0590033 | + | 0.0168068i | ||||
\(610\) | 360.732 | − | 169.780i | 0.591364 | − | 0.278329i | ||||
\(611\) | − | 218.114i | − | 0.356979i | ||||||
\(612\) | −6.99360 | − | 4.33601i | −0.0114275 | − | 0.00708498i | ||||
\(613\) | − | 1109.19i | − | 1.80945i | −0.425996 | − | 0.904725i | \(-0.640076\pi\) | ||
0.425996 | − | 0.904725i | \(-0.359924\pi\) | |||||||
\(614\) | − | 549.920i | − | 0.895635i | ||||||
\(615\) | 55.6433 | + | 339.612i | 0.0904770 | + | 0.552215i | ||||
\(616\) | 135.841 | 0.220521 | ||||||||
\(617\) | 572.163 | 0.927331 | 0.463665 | − | 0.886010i | \(-0.346534\pi\) | ||||
0.463665 | + | 0.886010i | \(0.346534\pi\) | |||||||
\(618\) | −81.6028 | + | 286.481i | −0.132043 | + | 0.463561i | ||||
\(619\) | −535.523 | −0.865143 | −0.432571 | − | 0.901600i | \(-0.642394\pi\) | ||||
−0.432571 | + | 0.901600i | \(0.642394\pi\) | |||||||
\(620\) | −409.568 | + | 192.765i | −0.660594 | + | 0.310912i | ||||
\(621\) | 225.287 | + | 247.571i | 0.362781 | + | 0.398665i | ||||
\(622\) | 217.746i | 0.350073i | ||||||||
\(623\) | −70.9452 | −0.113877 | ||||||||
\(624\) | 74.1240 | − | 260.225i | 0.118788 | − | 0.417027i | ||||
\(625\) | −117.296 | − | 613.895i | −0.187674 | − | 0.982231i | ||||
\(626\) | 162.486i | 0.259562i | ||||||||
\(627\) | −449.984 | + | 1579.75i | −0.717678 | + | 2.51953i | ||||
\(628\) | 100.823i | 0.160547i | ||||||||
\(629\) | − | 15.0810i | − | 0.0239761i | ||||||
\(630\) | −19.3364 | + | 167.261i | −0.0306927 | + | 0.265493i | ||||
\(631\) | 308.871 | 0.489495 | 0.244747 | − | 0.969587i | \(-0.421295\pi\) | ||||
0.244747 | + | 0.969587i | \(0.421295\pi\) | |||||||
\(632\) | −117.110 | −0.185301 | ||||||||
\(633\) | −48.1146 | − | 13.7052i | −0.0760104 | − | 0.0216512i | ||||
\(634\) | −11.6153 | −0.0183206 | ||||||||
\(635\) | 308.869 | + | 656.253i | 0.486408 | + | 1.03347i | ||||
\(636\) | −34.4765 | − | 9.82049i | −0.0542084 | − | 0.0154410i | ||||
\(637\) | − | 157.836i | − | 0.247780i | ||||||
\(638\) | 120.841 | 0.189406 | ||||||||
\(639\) | 99.3074 | − | 160.174i | 0.155411 | − | 0.250664i | ||||
\(640\) | −51.1830 | + | 24.0895i | −0.0799734 | + | 0.0376399i | ||||
\(641\) | 795.563i | 1.24113i | 0.784156 | + | 0.620564i | \(0.213096\pi\) | ||||
−0.784156 | + | 0.620564i | \(0.786904\pi\) | |||||||
\(642\) | 351.076 | + | 100.002i | 0.546847 | + | 0.155767i | ||||
\(643\) | − | 567.428i | − | 0.882469i | −0.897392 | − | 0.441234i | \(-0.854541\pi\) | ||
0.897392 | − | 0.441234i | \(-0.145459\pi\) | |||||||
\(644\) | 65.6013i | 0.101865i | ||||||||
\(645\) | −49.1606 | − | 300.045i | −0.0762179 | − | 0.465186i | ||||
\(646\) | 19.5004 | 0.0301863 | ||||||||
\(647\) | −482.089 | −0.745114 | −0.372557 | − | 0.928009i | \(-0.621519\pi\) | ||||
−0.372557 | + | 0.928009i | \(0.621519\pi\) | |||||||
\(648\) | 101.876 | + | 205.205i | 0.157216 | + | 0.316675i | ||||
\(649\) | 2048.48 | 3.15636 | ||||||||
\(650\) | 614.323 | + | 508.058i | 0.945112 | + | 0.781628i | ||||
\(651\) | −98.4273 | + | 345.546i | −0.151194 | + | 0.530792i | ||||
\(652\) | 263.603i | 0.404300i | ||||||||
\(653\) | 1072.96 | 1.64313 | 0.821565 | − | 0.570114i | \(-0.193101\pi\) | ||||
0.821565 | + | 0.570114i | \(0.193101\pi\) | |||||||
\(654\) | −189.510 | − | 53.9812i | −0.289771 | − | 0.0825401i | ||||
\(655\) | 12.7123 | + | 27.0097i | 0.0194080 | + | 0.0412362i | ||||
\(656\) | 91.7707i | 0.139894i | ||||||||
\(657\) | −463.756 | + | 747.998i | −0.705869 | + | 1.13851i | ||||
\(658\) | 36.1943i | 0.0550065i | ||||||||
\(659\) | 653.498i | 0.991651i | 0.868422 | + | 0.495825i | \(0.165134\pi\) | ||||
−0.868422 | + | 0.495825i | \(0.834866\pi\) | |||||||
\(660\) | 88.0514 | + | 537.410i | 0.133411 | + | 0.814258i | ||||
\(661\) | 1085.85 | 1.64274 | 0.821372 | − | 0.570392i | \(-0.193209\pi\) | ||||
0.821372 | + | 0.570392i | \(0.193209\pi\) | |||||||
\(662\) | −881.393 | −1.33141 | ||||||||
\(663\) | −8.47144 | + | 29.7405i | −0.0127774 | + | 0.0448574i | ||||
\(664\) | 344.860 | 0.519367 | ||||||||
\(665\) | −169.919 | − | 361.026i | −0.255517 | − | 0.542897i | ||||
\(666\) | −221.252 | + | 356.860i | −0.332210 | + | 0.535826i | ||||
\(667\) | 58.3575i | 0.0874925i | ||||||||
\(668\) | 378.171 | 0.566125 | ||||||||
\(669\) | −59.3657 | + | 208.413i | −0.0887379 | + | 0.311530i | ||||
\(670\) | −202.257 | − | 429.735i | −0.301876 | − | 0.641395i | ||||
\(671\) | − | 1023.50i | − | 1.52533i | ||||||
\(672\) | −12.3003 | + | 43.1822i | −0.0183040 | + | 0.0642592i | ||||
\(673\) | − | 199.268i | − | 0.296089i | −0.988981 | − | 0.148044i | \(-0.952702\pi\) | ||
0.988981 | − | 0.148044i | \(-0.0472979\pi\) | |||||||
\(674\) | − | 395.826i | − | 0.587279i | ||||||
\(675\) | −674.245 | + | 31.9192i | −0.998881 | + | 0.0472877i | ||||
\(676\) | −678.826 | −1.00418 | ||||||||
\(677\) | 409.731 | 0.605216 | 0.302608 | − | 0.953115i | \(-0.402143\pi\) | ||||
0.302608 | + | 0.953115i | \(0.402143\pi\) | |||||||
\(678\) | −247.945 | − | 70.6262i | −0.365701 | − | 0.104168i | ||||
\(679\) | 400.864 | 0.590374 | ||||||||
\(680\) | 5.84957 | − | 2.75313i | 0.00860231 | − | 0.00404872i | ||||
\(681\) | 300.266 | + | 85.5295i | 0.440919 | + | 0.125594i | ||||
\(682\) | 1162.06i | 1.70390i | ||||||||
\(683\) | −204.910 | −0.300015 | −0.150008 | − | 0.988685i | \(-0.547930\pi\) | ||||
−0.150008 | + | 0.988685i | \(0.547930\pi\) | |||||||
\(684\) | −461.436 | − | 286.089i | −0.674615 | − | 0.418259i | ||||
\(685\) | −584.925 | + | 275.298i | −0.853905 | + | 0.401895i | ||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | −951.264 | − | 270.964i | −1.38466 | − | 0.394416i | ||||
\(688\) | − | 81.0789i | − | 0.117847i | ||||||
\(689\) | 134.717i | 0.195525i | ||||||||
\(690\) | −259.530 | + | 42.5224i | −0.376130 | + | 0.0616266i | ||||
\(691\) | −437.098 | −0.632558 | −0.316279 | − | 0.948666i | \(-0.602434\pi\) | ||||
−0.316279 | + | 0.948666i | \(0.602434\pi\) | |||||||
\(692\) | 585.228 | 0.845706 | ||||||||
\(693\) | 367.366 | + | 227.765i | 0.530109 | + | 0.328666i | ||||
\(694\) | −659.652 | −0.950507 | ||||||||
\(695\) | −1069.74 | + | 503.479i | −1.53920 | + | 0.724430i | ||||
\(696\) | −10.9421 | + | 38.4140i | −0.0157213 | + | 0.0551925i | ||||
\(697\) | − | 10.4882i | − | 0.0150477i | ||||||
\(698\) | −79.7561 | −0.114264 | ||||||||
\(699\) | −209.949 | − | 59.8032i | −0.300357 | − | 0.0855553i | ||||
\(700\) | −101.942 | − | 84.3081i | −0.145631 | − | 0.120440i | ||||
\(701\) | − | 969.784i | − | 1.38343i | −0.722171 | − | 0.691715i | \(-0.756855\pi\) | ||
0.722171 | − | 0.691715i | \(-0.243145\pi\) | |||||||
\(702\) | 636.780 | − | 579.463i | 0.907094 | − | 0.825446i | ||||
\(703\) | − | 995.038i | − | 1.41542i | ||||||
\(704\) | 145.220i | 0.206279i | ||||||||
\(705\) | −143.191 | + | 23.4609i | −0.203107 | + | 0.0332779i | ||||
\(706\) | 336.042 | 0.475980 | ||||||||
\(707\) | 104.036 | 0.147151 | ||||||||
\(708\) | −185.487 | + | 651.186i | −0.261988 | + | 0.919754i | ||||
\(709\) | −575.519 | −0.811733 | −0.405866 | − | 0.913932i | \(-0.633030\pi\) | ||||
−0.405866 | + | 0.913932i | \(0.633030\pi\) | |||||||
\(710\) | 63.0548 | + | 133.972i | 0.0888096 | + | 0.188694i | ||||
\(711\) | −316.710 | − | 196.359i | −0.445443 | − | 0.276173i | ||||
\(712\) | − | 75.8436i | − | 0.106522i | ||||||
\(713\) | −561.189 | −0.787081 | ||||||||
\(714\) | 1.40577 | − | 4.93518i | 0.00196886 | − | 0.00691202i | ||||
\(715\) | 1851.68 | − | 871.502i | 2.58976 | − | 1.21888i | ||||
\(716\) | 398.872i | 0.557084i | ||||||||
\(717\) | −239.563 | + | 841.027i | −0.334119 | + | 1.17298i | ||||
\(718\) | 442.519i | 0.616321i | ||||||||
\(719\) | 1327.86i | 1.84681i | 0.383825 | + | 0.923406i | \(0.374607\pi\) | ||||
−0.383825 | + | 0.923406i | \(0.625393\pi\) | |||||||
\(720\) | −178.809 | − | 20.6715i | −0.248346 | − | 0.0287104i | ||||
\(721\) | −185.758 | −0.257640 | ||||||||
\(722\) | 776.100 | 1.07493 | ||||||||
\(723\) | −812.721 | − | 231.500i | −1.12409 | − | 0.320194i | ||||
\(724\) | 84.4920 | 0.116702 | ||||||||
\(725\) | −90.6853 | − | 74.9987i | −0.125083 | − | 0.103446i | ||||
\(726\) | 850.807 | + | 242.349i | 1.17191 | + | 0.333814i | ||||
\(727\) | − | 136.854i | − | 0.188245i | −0.995561 | − | 0.0941226i | \(-0.969995\pi\) | ||
0.995561 | − | 0.0941226i | \(-0.0300046\pi\) | |||||||
\(728\) | 168.734 | 0.231777 | ||||||||
\(729\) | −68.5577 | + | 725.769i | −0.0940435 | + | 0.995568i | ||||
\(730\) | −294.460 | − | 625.638i | −0.403370 | − | 0.857039i | ||||
\(731\) | 9.26630i | 0.0126762i | ||||||||
\(732\) | 325.357 | + | 92.6766i | 0.444477 | + | 0.126607i | ||||
\(733\) | − | 345.348i | − | 0.471143i | −0.971857 | − | 0.235572i | \(-0.924304\pi\) | ||
0.971857 | − | 0.235572i | \(-0.0756963\pi\) | |||||||
\(734\) | − | 82.1996i | − | 0.111989i | ||||||
\(735\) | −103.618 | + | 16.9772i | −0.140977 | + | 0.0230983i | ||||
\(736\) | −70.1307 | −0.0952863 | ||||||||
\(737\) | −1219.28 | −1.65438 | ||||||||
\(738\) | −153.872 | + | 248.183i | −0.208499 | + | 0.336291i | ||||
\(739\) | −91.4827 | −0.123793 | −0.0618963 | − | 0.998083i | \(-0.519715\pi\) | ||||
−0.0618963 | + | 0.998083i | \(0.519715\pi\) | |||||||
\(740\) | −140.483 | − | 298.484i | −0.189842 | − | 0.403356i | ||||
\(741\) | −558.944 | + | 1962.27i | −0.754311 | + | 2.64814i | ||||
\(742\) | − | 22.3551i | − | 0.0301282i | ||||||
\(743\) | 86.0672 | 0.115837 | 0.0579187 | − | 0.998321i | \(-0.481554\pi\) | ||||
0.0579187 | + | 0.998321i | \(0.481554\pi\) | |||||||
\(744\) | −369.404 | − | 105.223i | −0.496511 | − | 0.141429i | ||||
\(745\) | 206.945 | + | 439.695i | 0.277778 | + | 0.590195i | ||||
\(746\) | − | 616.388i | − | 0.826258i | ||||||
\(747\) | 932.631 | + | 578.228i | 1.24850 | + | 0.774067i | ||||
\(748\) | − | 16.5968i | − | 0.0221883i | ||||||
\(749\) | 227.643i | 0.303929i | ||||||||
\(750\) | 267.459 | − | 457.947i | 0.356612 | − | 0.610596i | ||||
\(751\) | 107.700 | 0.143408 | 0.0717042 | − | 0.997426i | \(-0.477156\pi\) | ||||
0.0717042 | + | 0.997426i | \(0.477156\pi\) | |||||||
\(752\) | −38.6933 | −0.0514539 | ||||||||
\(753\) | 172.080 | − | 604.117i | 0.228526 | − | 0.802280i | ||||
\(754\) | 150.102 | 0.199074 | ||||||||
\(755\) | −561.570 | + | 264.306i | −0.743801 | + | 0.350074i | ||||
\(756\) | −105.668 | + | 96.1571i | −0.139773 | + | 0.127192i | ||||
\(757\) | − | 485.286i | − | 0.641065i | −0.947238 | − | 0.320532i | \(-0.896138\pi\) | ||
0.947238 | − | 0.320532i | \(-0.103862\pi\) | |||||||
\(758\) | −904.238 | −1.19293 | ||||||||
\(759\) | −184.953 | + | 649.309i | −0.243680 | + | 0.855479i | ||||
\(760\) | 385.953 | − | 181.651i | 0.507833 | − | 0.239014i | ||||
\(761\) | − | 1202.49i | − | 1.58014i | −0.613017 | − | 0.790069i | \(-0.710044\pi\) | ||
0.613017 | − | 0.790069i | \(-0.289956\pi\) | |||||||
\(762\) | −168.600 | + | 591.898i | −0.221259 | + | 0.776769i | ||||
\(763\) | − | 122.881i | − | 0.161050i | ||||||
\(764\) | 425.817i | 0.557353i | ||||||||
\(765\) | 20.4356 | + | 2.36249i | 0.0267132 | + | 0.00308823i | ||||
\(766\) | 340.532 | 0.444559 | ||||||||
\(767\) | 2544.50 | 3.31747 | ||||||||
\(768\) | −46.1637 | − | 13.1495i | −0.0601090 | − | 0.0171218i | ||||
\(769\) | 1020.23 | 1.32670 | 0.663351 | − | 0.748308i | \(-0.269133\pi\) | ||||
0.663351 | + | 0.748308i | \(0.269133\pi\) | |||||||
\(770\) | −307.271 | + | 144.619i | −0.399053 | + | 0.187816i | ||||
\(771\) | 1032.15 | + | 294.004i | 1.33872 | + | 0.381328i | ||||
\(772\) | − | 163.604i | − | 0.211922i | ||||||
\(773\) | −847.386 | −1.09623 | −0.548115 | − | 0.836403i | \(-0.684654\pi\) | ||||
−0.548115 | + | 0.836403i | \(0.684654\pi\) | |||||||
\(774\) | 135.945 | − | 219.268i | 0.175640 | − | 0.283292i | ||||
\(775\) | 721.217 | − | 872.066i | 0.930603 | − | 1.12525i | ||||
\(776\) | 428.542i | 0.552244i | ||||||||
\(777\) | −251.826 | − | 71.7315i | −0.324100 | − | 0.0923185i | ||||
\(778\) | − | 227.290i | − | 0.292146i | ||||||
\(779\) | − | 692.012i | − | 0.888334i | ||||||
\(780\) | 109.372 | + | 667.540i | 0.140221 | + | 0.855820i | ||||
\(781\) | 380.117 | 0.486705 | ||||||||
\(782\) | 8.01506 | 0.0102494 | ||||||||
\(783\) | −94.0004 | + | 85.5393i | −0.120052 | + | 0.109246i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | −107.338 | − | 228.061i | −0.136737 | − | 0.290524i | ||||
\(786\) | −6.93913 | + | 24.3610i | −0.00882841 | + | 0.0309937i | ||||
\(787\) | 515.749i | 0.655336i | 0.944793 | + | 0.327668i | \(0.106263\pi\) | ||||
−0.944793 | + | 0.327668i | \(0.893737\pi\) | |||||||
\(788\) | 281.774 | 0.357581 | ||||||||
\(789\) | 432.756 | + | 123.269i | 0.548487 | + | 0.156234i | ||||
\(790\) | 264.902 | − | 124.677i | 0.335319 | − | 0.157820i | ||||
\(791\) | − | 160.772i | − | 0.203251i | ||||||
\(792\) | −243.491 | + | 392.730i | −0.307439 | + | 0.495872i | ||||
\(793\) | − | 1271.33i | − | 1.60319i | ||||||
\(794\) | − | 300.293i | − | 0.378203i | ||||||
\(795\) | 88.4405 | − | 14.4904i | 0.111246 | − | 0.0182270i | ||||
\(796\) | −238.796 | −0.299995 | ||||||||
\(797\) | 65.3181 | 0.0819550 | 0.0409775 | − | 0.999160i | \(-0.486953\pi\) | ||||
0.0409775 | + | 0.999160i | \(0.486953\pi\) | |||||||
\(798\) | 92.7522 | − | 325.622i | 0.116231 | − | 0.408048i | ||||
\(799\) | 4.42216 | 0.00553462 | ||||||||
\(800\) | 90.1291 | − | 108.980i | 0.112661 | − | 0.136226i | ||||
\(801\) | 127.167 | − | 205.110i | 0.158761 | − | 0.256067i | ||||
\(802\) | 274.975i | 0.342861i | ||||||||
\(803\) | −1775.11 | −2.21060 | ||||||||
\(804\) | 110.404 | − | 387.593i | 0.137319 | − | 0.482081i | ||||
\(805\) | −69.8402 | − | 148.389i | −0.0867580 | − | 0.184335i | ||||
\(806\) | 1443.44i | 1.79087i | ||||||||
\(807\) | −135.605 | + | 476.066i | −0.168036 | + | 0.589921i | ||||
\(808\) | 111.219i | 0.137647i | ||||||||
\(809\) | 984.812i | 1.21732i | 0.793431 | + | 0.608660i | \(0.208293\pi\) | ||||
−0.793431 | + | 0.608660i | \(0.791707\pi\) | |||||||
\(810\) | −448.907 | − | 355.714i | −0.554207 | − | 0.439153i | ||||
\(811\) | −1043.21 | −1.28632 | −0.643162 | − | 0.765730i | \(-0.722378\pi\) | ||||
−0.643162 | + | 0.765730i | \(0.722378\pi\) | |||||||
\(812\) | −24.9082 | −0.0306751 | ||||||||
\(813\) | 0.787755 | + | 0.224389i | 0.000968948 | + | 0.000276001i | ||||
\(814\) | −846.881 | −1.04039 | ||||||||
\(815\) | −280.636 | − | 596.268i | −0.344339 | − | 0.731617i | ||||
\(816\) | 5.27593 | + | 1.50283i | 0.00646561 | + | 0.00184170i | ||||
\(817\) | 611.389i | 0.748334i | ||||||||
\(818\) | 417.124 | 0.509931 | ||||||||
\(819\) | 456.320 | + | 282.917i | 0.557168 | + | 0.345442i | ||||
\(820\) | −97.7006 | − | 207.584i | −0.119147 | − | 0.253152i | ||||
\(821\) | 316.439i | 0.385431i | 0.981255 | + | 0.192716i | \(0.0617295\pi\) | ||||
−0.981255 | + | 0.192716i | \(0.938271\pi\) | |||||||
\(822\) | −527.564 | − | 150.274i | −0.641806 | − | 0.182816i | ||||
\(823\) | − | 770.671i | − | 0.936417i | −0.883618 | − | 0.468209i | \(-0.844900\pi\) | ||
0.883618 | − | 0.468209i | \(-0.155100\pi\) | |||||||
\(824\) | − | 198.584i | − | 0.241000i | ||||||
\(825\) | −771.307 | − | 1121.87i | −0.934917 | − | 1.35985i | ||||
\(826\) | −422.239 | −0.511185 | ||||||||
\(827\) | 1321.39 | 1.59781 | 0.798907 | − | 0.601455i | \(-0.205412\pi\) | ||||
0.798907 | + | 0.601455i | \(0.205412\pi\) | |||||||
\(828\) | −189.660 | − | 117.588i | −0.229058 | − | 0.142015i | ||||
\(829\) | 476.736 | 0.575074 | 0.287537 | − | 0.957770i | \(-0.407164\pi\) | ||||
0.287537 | + | 0.957770i | \(0.407164\pi\) | |||||||
\(830\) | −780.069 | + | 367.143i | −0.939842 | + | 0.442341i | ||||
\(831\) | 71.0530 | − | 249.444i | 0.0855030 | − | 0.300173i | ||||
\(832\) | 180.384i | 0.216808i | ||||||||
\(833\) | 3.20005 | 0.00384160 | ||||||||
\(834\) | −964.837 | − | 274.830i | −1.15688 | − | 0.329532i | ||||
\(835\) | −855.419 | + | 402.607i | −1.02445 | + | 0.482165i | ||||
\(836\) | − | 1095.06i | − | 1.30988i | ||||||
\(837\) | −822.580 | − | 903.945i | −0.982772 | − | 1.07998i | ||||
\(838\) | 874.473i | 1.04352i | ||||||||
\(839\) | − | 920.100i | − | 1.09666i | −0.836261 | − | 0.548331i | \(-0.815263\pi\) | ||
0.836261 | − | 0.548331i | \(-0.184737\pi\) | |||||||
\(840\) | −18.1494 | − | 110.773i | −0.0216065 | − | 0.131872i | ||||
\(841\) | 818.842 | 0.973653 | ||||||||
\(842\) | 243.960 | 0.289739 | ||||||||
\(843\) | 247.797 | − | 869.935i | 0.293947 | − | 1.03195i | ||||
\(844\) | 33.3523 | 0.0395169 | ||||||||
\(845\) | 1535.50 | − | 722.689i | 1.81715 | − | 0.855253i | ||||
\(846\) | −104.641 | − | 64.8773i | −0.123690 | − | 0.0766871i | ||||
\(847\) | 551.676i | 0.651330i | ||||||||
\(848\) | 23.8986 | 0.0281823 | ||||||||
\(849\) | 61.0944 | − | 214.483i | 0.0719605 | − | 0.252630i | ||||
\(850\) | −10.3006 | + | 12.4551i | −0.0121184 | + | 0.0146531i | ||||
\(851\) | − | 408.981i | − | 0.480589i | ||||||
\(852\) | −34.4192 | + | 120.835i | −0.0403981 | + | 0.141825i | ||||
\(853\) | − | 148.026i | − | 0.173536i | −0.996229 | − | 0.0867681i | \(-0.972346\pi\) | ||
0.996229 | − | 0.0867681i | \(-0.0276539\pi\) | |||||||
\(854\) | 210.966i | 0.247033i | ||||||||
\(855\) | 1348.34 | + | 155.877i | 1.57700 | + | 0.182312i | ||||
\(856\) | −243.361 | −0.284300 | ||||||||
\(857\) | −948.093 | −1.10629 | −0.553147 | − | 0.833084i | \(-0.686573\pi\) | ||||
−0.553147 | + | 0.833084i | \(0.686573\pi\) | |||||||
\(858\) | 1670.09 | + | 475.719i | 1.94650 | + | 0.554452i | ||||
\(859\) | −264.436 | −0.307842 | −0.153921 | − | 0.988083i | \(-0.549190\pi\) | ||||
−0.153921 | + | 0.988083i | \(0.549190\pi\) | |||||||
\(860\) | 86.3179 | + | 183.400i | 0.100370 | + | 0.213255i | ||||
\(861\) | −175.135 | − | 49.8866i | −0.203409 | − | 0.0579403i | ||||
\(862\) | − | 255.186i | − | 0.296039i | ||||||
\(863\) | 1553.74 | 1.80040 | 0.900198 | − | 0.435482i | \(-0.143422\pi\) | ||||
0.900198 | + | 0.435482i | \(0.143422\pi\) | |||||||
\(864\) | −102.796 | − | 112.964i | −0.118977 | − | 0.130746i | ||||
\(865\) | −1323.78 | + | 623.044i | −1.53038 | + | 0.720282i | ||||
\(866\) | 622.389i | 0.718694i | ||||||||
\(867\) | 833.229 | + | 237.342i | 0.961049 | + | 0.273751i | ||||
\(868\) | − | 239.527i | − | 0.275953i | ||||||
\(869\) | − | 751.600i | − | 0.864902i | ||||||
\(870\) | −16.1453 | − | 98.5411i | −0.0185579 | − | 0.113266i | ||||
\(871\) | −1514.51 | −1.73882 | ||||||||
\(872\) | 131.366 | 0.150649 | ||||||||
\(873\) | −718.537 | + | 1158.94i | −0.823067 | + | 1.32754i | ||||
\(874\) | 528.832 | 0.605071 | ||||||||
\(875\) | 320.347 | + | 82.1749i | 0.366111 | + | 0.0939142i | ||||
\(876\) | 160.734 | − | 564.285i | 0.183487 | − | 0.644161i | ||||
\(877\) | 1187.32i | 1.35385i | 0.736053 | + | 0.676924i | \(0.236687\pi\) | ||||
−0.736053 | + | 0.676924i | \(0.763313\pi\) | |||||||
\(878\) | 550.619 | 0.627128 | ||||||||
\(879\) | 1022.75 | + | 291.327i | 1.16354 | + | 0.331429i | ||||
\(880\) | −154.604 | − | 328.486i | −0.175686 | − | 0.373280i | ||||
\(881\) | 238.098i | 0.270259i | 0.990828 | + | 0.135129i | \(0.0431450\pi\) | ||||
−0.990828 | + | 0.135129i | \(0.956855\pi\) | |||||||
\(882\) | −75.7226 | − | 46.9477i | −0.0858533 | − | 0.0532287i | ||||
\(883\) | 1720.86i | 1.94888i | 0.224648 | + | 0.974440i | \(0.427877\pi\) | ||||
−0.224648 | + | 0.974440i | \(0.572123\pi\) | |||||||
\(884\) | − | 20.6156i | − | 0.0233209i | ||||||
\(885\) | −273.693 | − | 1670.45i | −0.309257 | − | 1.88751i | ||||
\(886\) | 737.471 | 0.832361 | ||||||||
\(887\) | −186.566 | −0.210333 | −0.105167 | − | 0.994455i | \(-0.533538\pi\) | ||||
−0.105167 | + | 0.994455i | \(0.533538\pi\) | |||||||
\(888\) | 76.6842 | − | 269.213i | 0.0863561 | − | 0.303168i | ||||
\(889\) | −383.796 | −0.431716 | ||||||||
\(890\) | 80.7443 | + | 171.557i | 0.0907240 | + | 0.192761i | ||||
\(891\) | −1316.99 | + | 653.828i | −1.47810 | + | 0.733814i | ||||
\(892\) | − | 144.469i | − | 0.161961i | ||||||
\(893\) | 291.773 | 0.326734 | ||||||||
\(894\) | −112.963 | + | 396.577i | −0.126357 | + | 0.443598i | ||||
\(895\) | −424.646 | − | 902.245i | −0.474465 | − | 1.00809i | ||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | −229.738 | + | 806.534i | −0.256118 | + | 0.899146i | ||||
\(898\) | 843.044i | 0.938802i | ||||||||
\(899\) | − | 213.078i | − | 0.237017i | ||||||
\(900\) | 426.471 | − | 143.604i | 0.473857 | − | 0.159560i | ||||
\(901\) | −2.73131 | −0.00303142 | ||||||||
\(902\) | −588.974 | −0.652965 | ||||||||
\(903\) | 154.731 | + | 44.0745i | 0.171352 | + | 0.0488090i | ||||
\(904\) | 171.872 | 0.190124 | ||||||||
\(905\) | −191.120 | + | 89.9516i | −0.211182 | + | 0.0993940i | ||||
\(906\) | −506.500 | − | 144.274i | −0.559051 | − | 0.159243i | ||||
\(907\) | − | 1079.22i | − | 1.18988i | −0.803771 | − | 0.594939i | \(-0.797176\pi\) | ||
0.803771 | − | 0.594939i | \(-0.202824\pi\) | |||||||
\(908\) | −208.140 | −0.229229 | ||||||||
\(909\) | −186.481 | + | 300.778i | −0.205150 | + | 0.330888i | ||||
\(910\) | −381.674 | + | 179.637i | −0.419422 | + | 0.197403i | ||||
\(911\) | − | 1274.59i | − | 1.39911i | −0.714580 | − | 0.699554i | \(-0.753382\pi\) | ||
0.714580 | − | 0.699554i | \(-0.246618\pi\) | |||||||
\(912\) | 348.105 | + | 99.1563i | 0.381694 | + | 0.108724i | ||||
\(913\) | 2213.27i | 2.42417i | ||||||||
\(914\) | 452.873i | 0.495484i | ||||||||
\(915\) | −834.619 | + | 136.747i | −0.912152 | + | 0.149450i | ||||
\(916\) | 659.402 | 0.719871 | ||||||||
\(917\) | −15.7961 | −0.0172258 | ||||||||
\(918\) | 11.7483 | + | 12.9104i | 0.0127977 | + | 0.0140636i | ||||
\(919\) | 1110.91 | 1.20882 | 0.604412 | − | 0.796672i | \(-0.293408\pi\) | ||||
0.604412 | + | 0.796672i | \(0.293408\pi\) | |||||||
\(920\) | 158.635 | − | 74.6623i | 0.172429 | − | 0.0811547i | ||||
\(921\) | −319.577 | + | 1121.93i | −0.346989 | + | 1.21816i | ||||
\(922\) | − | 200.726i | − | 0.217708i | ||||||
\(923\) | 472.159 | 0.511548 | ||||||||
\(924\) | −277.138 | − | 78.9417i | −0.299933 | − | 0.0854348i | ||||
\(925\) | 635.541 | + | 525.606i | 0.687072 | + | 0.568223i | ||||
\(926\) | − | 330.068i | − | 0.356445i | ||||||
\(927\) | 332.967 | − | 537.047i | 0.359188 | − | 0.579338i | ||||
\(928\) | − | 26.6280i | − | 0.0286940i | ||||||
\(929\) | − | 140.614i | − | 0.151361i | −0.997132 | − | 0.0756803i | \(-0.975887\pi\) | ||
0.997132 | − | 0.0756803i | \(-0.0241129\pi\) | |||||||
\(930\) | 947.610 | − | 155.260i | 1.01894 | − | 0.166946i | ||||
\(931\) | 211.139 | 0.226787 | ||||||||
\(932\) | 145.534 | 0.156152 | ||||||||
\(933\) | 126.539 | − | 444.237i | 0.135626 | − | 0.476139i | ||||
\(934\) | 549.913 | 0.588772 | ||||||||
\(935\) | 17.6693 | + | 37.5419i | 0.0188976 | + | 0.0401517i | ||||
\(936\) | −302.451 | + | 487.827i | −0.323131 | + | 0.521183i | ||||
\(937\) | − | 1469.08i | − | 1.56785i | −0.620853 | − | 0.783927i | \(-0.713214\pi\) | ||
0.620853 | − | 0.783927i | \(-0.286786\pi\) | |||||||
\(938\) | 251.321 | 0.267933 | ||||||||
\(939\) | 94.4259 | − | 331.498i | 0.100560 | − | 0.353033i | ||||
\(940\) | 87.5238 | − | 41.1936i | 0.0931105 | − | 0.0438229i | ||||
\(941\) | 6.07056i | 0.00645118i | 0.999995 | + | 0.00322559i | \(0.00102674\pi\) | ||||
−0.999995 | + | 0.00322559i | \(0.998973\pi\) | |||||||
\(942\) | 58.5918 | − | 205.696i | 0.0621993 | − | 0.218361i | ||||
\(943\) | − | 284.431i | − | 0.301624i | ||||||
\(944\) | − | 451.392i | − | 0.478170i | ||||||
\(945\) | 136.650 | − | 330.003i | 0.144603 | − | 0.349209i | ||||
\(946\) | 520.355 | 0.550058 | ||||||||
\(947\) | −1311.95 | −1.38538 | −0.692688 | − | 0.721237i | \(-0.743574\pi\) | ||||
−0.692688 | + | 0.721237i | \(0.743574\pi\) | |||||||
\(948\) | 238.924 | + | 68.0566i | 0.252030 | + | 0.0717897i | ||||
\(949\) | −2204.94 | −2.32343 | ||||||||
\(950\) | −679.633 | + | 821.785i | −0.715404 | + | 0.865037i | ||||
\(951\) | 23.6971 | + | 6.75002i | 0.0249181 | + | 0.00709781i | ||||
\(952\) | 3.42100i | 0.00359348i | ||||||||
\(953\) | 953.113 | 1.00012 | 0.500059 | − | 0.865991i | \(-0.333312\pi\) | ||||
0.500059 | + | 0.865991i | \(0.333312\pi\) | |||||||
\(954\) | 64.6309 | + | 40.0709i | 0.0677472 | + | 0.0420030i | ||||
\(955\) | −453.332 | − | 963.194i | −0.474694 | − | 1.00858i | ||||
\(956\) | − | 582.987i | − | 0.609819i | ||||||
\(957\) | −246.537 | − | 70.2249i | −0.257614 | − | 0.0733802i | ||||
\(958\) | 1260.84i | 1.31612i | ||||||||
\(959\) | − | 342.081i | − | 0.356706i | ||||||
\(960\) | 118.421 | − | 19.4026i | 0.123355 | − | 0.0202110i | ||||
\(961\) | 1088.05 | 1.13220 | ||||||||
\(962\) | −1051.95 | −1.09350 | ||||||||
\(963\) | −658.139 | − | 408.044i | −0.683426 | − | 0.423721i | ||||
\(964\) | 563.366 | 0.584404 | ||||||||
\(965\) | 174.175 | + | 370.070i | 0.180493 | + | 0.383492i | ||||
\(966\) | 38.1231 | − | 133.838i | 0.0394649 | − | 0.138548i | ||||
\(967\) | 624.295i | 0.645600i | 0.946467 | + | 0.322800i | \(0.104624\pi\) | ||||
−0.946467 | + | 0.322800i | \(0.895376\pi\) | |||||||
\(968\) | −589.767 | −0.609263 | ||||||||
\(969\) | −39.7840 | − | 11.3323i | −0.0410568 | − | 0.0116949i | ||||
\(970\) | −456.232 | − | 969.356i | −0.470343 | − | 0.999336i | ||||
\(971\) | − | 982.557i | − | 1.01190i | −0.862562 | − | 0.505951i | \(-0.831142\pi\) | ||
0.862562 | − | 0.505951i | \(-0.168858\pi\) | |||||||
\(972\) | −88.5924 | − | 477.857i | −0.0911444 | − | 0.491623i | ||||
\(973\) | − | 625.615i | − | 0.642975i | ||||||
\(974\) | − | 323.738i | − | 0.332380i | ||||||
\(975\) | −958.073 | − | 1393.53i | −0.982639 | − | 1.42926i | ||||
\(976\) | −225.533 | −0.231079 | ||||||||
\(977\) | 1520.84 | 1.55664 | 0.778320 | − | 0.627868i | \(-0.216072\pi\) | ||||
0.778320 | + | 0.627868i | \(0.216072\pi\) | |||||||
\(978\) | 153.189 | − | 537.795i | 0.156635 | − | 0.549893i | ||||
\(979\) | 486.755 | 0.497197 | ||||||||
\(980\) | 63.3357 | − | 29.8093i | 0.0646282 | − | 0.0304176i | ||||
\(981\) | 355.262 | + | 220.261i | 0.362143 | + | 0.224527i | ||||
\(982\) | − | 465.206i | − | 0.473734i | ||||||
\(983\) | −366.574 | −0.372914 | −0.186457 | − | 0.982463i | \(-0.559700\pi\) | ||||
−0.186457 | + | 0.982463i | \(0.559700\pi\) | |||||||
\(984\) | 53.3310 | − | 187.228i | 0.0541982 | − | 0.190272i | ||||
\(985\) | −637.369 | + | 299.981i | −0.647075 | + | 0.304549i | ||||
\(986\) | 3.04325i | 0.00308646i | ||||||||
\(987\) | 21.0337 | − | 73.8424i | 0.0213107 | − | 0.0748150i | ||||
\(988\) | − | 1360.22i | − | 1.37674i | ||||||
\(989\) | 251.293i | 0.254088i | ||||||||
\(990\) | 132.667 | − | 1147.58i | 0.134007 | − | 1.15917i | ||||
\(991\) | 1204.07 | 1.21501 | 0.607505 | − | 0.794316i | \(-0.292171\pi\) | ||||
0.607505 | + | 0.794316i | \(0.292171\pi\) | |||||||
\(992\) | 256.065 | 0.258130 | ||||||||
\(993\) | 1798.19 | + | 512.207i | 1.81087 | + | 0.515817i | ||||
\(994\) | −78.3509 | −0.0788239 | ||||||||
\(995\) | 540.153 | − | 254.226i | 0.542867 | − | 0.255503i | ||||
\(996\) | −703.572 | − | 200.409i | −0.706397 | − | 0.201214i | ||||
\(997\) | − | 861.399i | − | 0.863991i | −0.901876 | − | 0.431995i | \(-0.857810\pi\) | ||
0.901876 | − | 0.431995i | \(-0.142190\pi\) | |||||||
\(998\) | 239.925 | 0.240406 | ||||||||
\(999\) | 658.774 | − | 599.477i | 0.659433 | − | 0.600077i |
(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 | 210.3.c.a.29.13 | yes | 24 | |
3.2 | odd | 2 | inner | 210.3.c.a.29.11 | ✓ | 24 | |
5.2 | odd | 4 | 1050.3.e.e.701.23 | 24 | |||
5.3 | odd | 4 | 1050.3.e.e.701.22 | 24 | |||
5.4 | even | 2 | inner | 210.3.c.a.29.12 | yes | 24 | |
15.2 | even | 4 | 1050.3.e.e.701.21 | 24 | |||
15.8 | even | 4 | 1050.3.e.e.701.24 | 24 | |||
15.14 | odd | 2 | inner | 210.3.c.a.29.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.c.a.29.11 | ✓ | 24 | 3.2 | odd | 2 | inner | |
210.3.c.a.29.12 | yes | 24 | 5.4 | even | 2 | inner | |
210.3.c.a.29.13 | yes | 24 | 1.1 | even | 1 | trivial | |
210.3.c.a.29.14 | yes | 24 | 15.14 | odd | 2 | inner | |
1050.3.e.e.701.21 | 24 | 15.2 | even | 4 | |||
1050.3.e.e.701.22 | 24 | 5.3 | odd | 4 | |||
1050.3.e.e.701.23 | 24 | 5.2 | odd | 4 | |||
1050.3.e.e.701.24 | 24 | 15.8 | even | 4 |