Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(104,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.104");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.g (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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 104.35 | ||
Character | \(\chi\) | \(=\) | 105.104 |
Dual form | 105.4.g.b.104.36 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.45958 | 1.57670 | 0.788350 | − | 0.615227i | \(-0.210936\pi\) | ||||
0.788350 | + | 0.615227i | \(0.210936\pi\) | |||||||
\(3\) | 5.00290 | − | 1.40393i | 0.962808 | − | 0.270187i | ||||
\(4\) | 11.8879 | 1.48598 | ||||||||
\(5\) | −0.892950 | − | 11.1446i | −0.0798679 | − | 0.996805i | ||||
\(6\) | 22.3108 | − | 6.26096i | 1.51806 | − | 0.426004i | ||||
\(7\) | −12.5955 | + | 13.5777i | −0.680095 | + | 0.733124i | ||||
\(8\) | 17.3382 | 0.766247 | ||||||||
\(9\) | 23.0579 | − | 14.0475i | 0.853998 | − | 0.520277i | ||||
\(10\) | −3.98218 | − | 49.7003i | −0.125928 | − | 1.57166i | ||||
\(11\) | 30.2834i | 0.830071i | 0.909805 | + | 0.415035i | \(0.136231\pi\) | ||||
−0.909805 | + | 0.415035i | \(0.863769\pi\) | |||||||
\(12\) | 59.4737 | − | 16.6898i | 1.43071 | − | 0.401493i | ||||
\(13\) | −18.9551 | −0.404400 | −0.202200 | − | 0.979344i | \(-0.564809\pi\) | ||||
−0.202200 | + | 0.979344i | \(0.564809\pi\) | |||||||
\(14\) | −56.1708 | + | 60.5506i | −1.07230 | + | 1.15592i | ||||
\(15\) | −20.1137 | − | 54.5018i | −0.346222 | − | 0.938153i | ||||
\(16\) | −17.7818 | −0.277841 | ||||||||
\(17\) | − | 4.59392i | − | 0.0655406i | −0.999463 | − | 0.0327703i | \(-0.989567\pi\) | ||
0.999463 | − | 0.0327703i | \(-0.0104330\pi\) | |||||||
\(18\) | 102.829 | − | 62.6458i | 1.34650 | − | 0.820320i | ||||
\(19\) | 119.595i | 1.44405i | 0.691869 | + | 0.722023i | \(0.256788\pi\) | ||||
−0.691869 | + | 0.722023i | \(0.743212\pi\) | |||||||
\(20\) | −10.6153 | − | 132.486i | −0.118682 | − | 1.48123i | ||||
\(21\) | −43.9520 | + | 85.6109i | −0.456720 | + | 0.889611i | ||||
\(22\) | 135.051i | 1.30877i | ||||||||
\(23\) | 134.577 | 1.22005 | 0.610026 | − | 0.792381i | \(-0.291159\pi\) | ||||
0.610026 | + | 0.792381i | \(0.291159\pi\) | |||||||
\(24\) | 86.7411 | − | 24.3417i | 0.737748 | − | 0.207030i | ||||
\(25\) | −123.405 | + | 19.9032i | −0.987242 | + | 0.159225i | ||||
\(26\) | −84.5318 | −0.637617 | ||||||||
\(27\) | 95.6347 | − | 102.650i | 0.681663 | − | 0.731666i | ||||
\(28\) | −149.734 | + | 161.409i | −1.01061 | + | 1.08941i | ||||
\(29\) | − | 203.146i | − | 1.30080i | −0.759590 | − | 0.650402i | \(-0.774600\pi\) | ||
0.759590 | − | 0.650402i | \(-0.225400\pi\) | |||||||
\(30\) | −89.6985 | − | 243.055i | −0.545887 | − | 1.47919i | ||||
\(31\) | 61.4983i | 0.356304i | 0.984003 | + | 0.178152i | \(0.0570119\pi\) | ||||
−0.984003 | + | 0.178152i | \(0.942988\pi\) | |||||||
\(32\) | −218.005 | −1.20432 | ||||||||
\(33\) | 42.5159 | + | 151.505i | 0.224275 | + | 0.799198i | ||||
\(34\) | − | 20.4870i | − | 0.103338i | ||||||
\(35\) | 162.565 | + | 128.248i | 0.785100 | + | 0.619369i | ||||
\(36\) | 274.109 | − | 166.994i | 1.26902 | − | 0.773122i | ||||
\(37\) | − | 337.592i | − | 1.49999i | −0.661441 | − | 0.749997i | \(-0.730055\pi\) | ||
0.661441 | − | 0.749997i | \(-0.269945\pi\) | |||||||
\(38\) | 533.342i | 2.27683i | ||||||||
\(39\) | −94.8304 | + | 26.6117i | −0.389359 | + | 0.109264i | ||||
\(40\) | −15.4821 | − | 193.227i | −0.0611985 | − | 0.763799i | ||||
\(41\) | −135.603 | −0.516529 | −0.258264 | − | 0.966074i | \(-0.583151\pi\) | ||||
−0.258264 | + | 0.966074i | \(0.583151\pi\) | |||||||
\(42\) | −196.007 | + | 381.789i | −0.720110 | + | 1.40265i | ||||
\(43\) | 270.630i | 0.959785i | 0.877327 | + | 0.479893i | \(0.159324\pi\) | ||||
−0.877327 | + | 0.479893i | \(0.840676\pi\) | |||||||
\(44\) | 360.004i | 1.23347i | ||||||||
\(45\) | −177.143 | − | 244.428i | −0.586822 | − | 0.809716i | ||||
\(46\) | 600.156 | 1.92366 | ||||||||
\(47\) | − | 273.318i | − | 0.848245i | −0.905605 | − | 0.424123i | \(-0.860583\pi\) | ||
0.905605 | − | 0.424123i | \(-0.139417\pi\) | |||||||
\(48\) | −88.9606 | + | 24.9645i | −0.267507 | + | 0.0750691i | ||||
\(49\) | −25.7052 | − | 342.035i | −0.0749424 | − | 0.997188i | ||||
\(50\) | −550.336 | + | 88.7598i | −1.55658 | + | 0.251051i | ||||
\(51\) | −6.44957 | − | 22.9829i | −0.0177082 | − | 0.0631030i | ||||
\(52\) | −225.335 | −0.600931 | ||||||||
\(53\) | 222.861 | 0.577591 | 0.288796 | − | 0.957391i | \(-0.406745\pi\) | ||||
0.288796 | + | 0.957391i | \(0.406745\pi\) | |||||||
\(54\) | 426.491 | − | 457.775i | 1.07478 | − | 1.15362i | ||||
\(55\) | 337.497 | − | 27.0415i | 0.827419 | − | 0.0662960i | ||||
\(56\) | −218.384 | + | 235.412i | −0.521120 | + | 0.561754i | ||||
\(57\) | 167.903 | + | 598.319i | 0.390163 | + | 1.39034i | ||||
\(58\) | − | 905.947i | − | 2.05098i | ||||||
\(59\) | −735.026 | −1.62190 | −0.810951 | − | 0.585114i | \(-0.801050\pi\) | ||||
−0.810951 | + | 0.585114i | \(0.801050\pi\) | |||||||
\(60\) | −239.108 | − | 647.909i | −0.514479 | − | 1.39408i | ||||
\(61\) | 312.240i | 0.655381i | 0.944785 | + | 0.327691i | \(0.106270\pi\) | ||||
−0.944785 | + | 0.327691i | \(0.893730\pi\) | |||||||
\(62\) | 274.257i | 0.561784i | ||||||||
\(63\) | −99.6952 | + | 490.008i | −0.199372 | + | 0.979924i | ||||
\(64\) | −829.955 | −1.62101 | ||||||||
\(65\) | 16.9260 | + | 211.247i | 0.0322986 | + | 0.403108i | ||||
\(66\) | 189.603 | + | 675.646i | 0.353614 | + | 1.26010i | ||||
\(67\) | − | 751.739i | − | 1.37074i | −0.728195 | − | 0.685370i | \(-0.759641\pi\) | ||
0.728195 | − | 0.685370i | \(-0.240359\pi\) | |||||||
\(68\) | − | 54.6119i | − | 0.0973921i | ||||||
\(69\) | 673.274 | − | 188.937i | 1.17468 | − | 0.329643i | ||||
\(70\) | 724.972 | + | 571.933i | 1.23787 | + | 0.976559i | ||||
\(71\) | 640.823i | 1.07115i | 0.844487 | + | 0.535576i | \(0.179905\pi\) | ||||
−0.844487 | + | 0.535576i | \(0.820095\pi\) | |||||||
\(72\) | 399.783 | − | 243.558i | 0.654373 | − | 0.398660i | ||||
\(73\) | 469.117 | 0.752137 | 0.376069 | − | 0.926592i | \(-0.377276\pi\) | ||||
0.376069 | + | 0.926592i | \(0.377276\pi\) | |||||||
\(74\) | − | 1505.52i | − | 2.36504i | ||||||
\(75\) | −589.441 | + | 272.826i | −0.907504 | + | 0.420044i | ||||
\(76\) | 1421.72i | 2.14583i | ||||||||
\(77\) | −411.177 | − | 381.435i | −0.608545 | − | 0.564527i | ||||
\(78\) | −422.904 | + | 118.677i | −0.613903 | + | 0.172276i | ||||
\(79\) | 126.493 | 0.180147 | 0.0900733 | − | 0.995935i | \(-0.471290\pi\) | ||||
0.0900733 | + | 0.995935i | \(0.471290\pi\) | |||||||
\(80\) | 15.8783 | + | 198.172i | 0.0221906 | + | 0.276953i | ||||
\(81\) | 334.337 | − | 647.812i | 0.458624 | − | 0.888630i | ||||
\(82\) | −604.734 | −0.814411 | ||||||||
\(83\) | − | 299.265i | − | 0.395766i | −0.980226 | − | 0.197883i | \(-0.936593\pi\) | ||
0.980226 | − | 0.197883i | \(-0.0634066\pi\) | |||||||
\(84\) | −522.495 | + | 1017.73i | −0.678677 | + | 1.32194i | ||||
\(85\) | −51.1976 | + | 4.10215i | −0.0653312 | + | 0.00523459i | ||||
\(86\) | 1206.90i | 1.51329i | ||||||||
\(87\) | −285.204 | − | 1016.32i | −0.351461 | − | 1.25242i | ||||
\(88\) | 525.058i | 0.636039i | ||||||||
\(89\) | −425.893 | −0.507242 | −0.253621 | − | 0.967304i | \(-0.581622\pi\) | ||||
−0.253621 | + | 0.967304i | \(0.581622\pi\) | |||||||
\(90\) | −789.985 | − | 1090.05i | −0.925242 | − | 1.27668i | ||||
\(91\) | 238.750 | − | 257.366i | 0.275030 | − | 0.296475i | ||||
\(92\) | 1599.83 | 1.81297 | ||||||||
\(93\) | 86.3396 | + | 307.670i | 0.0962688 | + | 0.343052i | ||||
\(94\) | − | 1218.88i | − | 1.33743i | ||||||
\(95\) | 1332.84 | − | 106.792i | 1.43943 | − | 0.115333i | ||||
\(96\) | −1090.66 | + | 306.064i | −1.15953 | + | 0.325391i | ||||
\(97\) | 561.656 | 0.587913 | 0.293957 | − | 0.955819i | \(-0.405028\pi\) | ||||
0.293957 | + | 0.955819i | \(0.405028\pi\) | |||||||
\(98\) | −114.635 | − | 1525.33i | −0.118162 | − | 1.57227i | ||||
\(99\) | 425.405 | + | 698.272i | 0.431867 | + | 0.708878i | ||||
\(100\) | −1467.02 | + | 236.606i | −1.46702 | + | 0.236606i | ||||
\(101\) | 1733.15 | 1.70747 | 0.853736 | − | 0.520706i | \(-0.174331\pi\) | ||||
0.853736 | + | 0.520706i | \(0.174331\pi\) | |||||||
\(102\) | −28.7624 | − | 102.494i | −0.0279206 | − | 0.0994945i | ||||
\(103\) | 1704.95 | 1.63101 | 0.815504 | − | 0.578751i | \(-0.196460\pi\) | ||||
0.815504 | + | 0.578751i | \(0.196460\pi\) | |||||||
\(104\) | −328.647 | −0.309870 | ||||||||
\(105\) | 993.348 | + | 413.382i | 0.923246 | + | 0.384209i | ||||
\(106\) | 993.867 | 0.910688 | ||||||||
\(107\) | 397.788 | 0.359399 | 0.179699 | − | 0.983722i | \(-0.442488\pi\) | ||||
0.179699 | + | 0.983722i | \(0.442488\pi\) | |||||||
\(108\) | 1136.89 | − | 1220.29i | 1.01294 | − | 1.08724i | ||||
\(109\) | 1382.72 | 1.21505 | 0.607526 | − | 0.794300i | \(-0.292162\pi\) | ||||
0.607526 | + | 0.794300i | \(0.292162\pi\) | |||||||
\(110\) | 1505.09 | − | 120.594i | 1.30459 | − | 0.104529i | ||||
\(111\) | −473.957 | − | 1688.94i | −0.405280 | − | 1.44421i | ||||
\(112\) | 223.971 | − | 241.435i | 0.188958 | − | 0.203692i | ||||
\(113\) | −1029.11 | −0.856728 | −0.428364 | − | 0.903606i | \(-0.640910\pi\) | ||||
−0.428364 | + | 0.903606i | \(0.640910\pi\) | |||||||
\(114\) | 748.777 | + | 2668.25i | 0.615170 | + | 2.19215i | ||||
\(115\) | −120.170 | − | 1499.81i | −0.0974430 | − | 1.21615i | ||||
\(116\) | − | 2414.97i | − | 1.93297i | ||||||
\(117\) | −437.066 | + | 266.271i | −0.345357 | + | 0.210400i | ||||
\(118\) | −3277.91 | −2.55725 | ||||||||
\(119\) | 62.3747 | + | 57.8629i | 0.0480494 | + | 0.0445738i | ||||
\(120\) | −348.734 | − | 944.961i | −0.265291 | − | 0.718856i | ||||
\(121\) | 413.918 | 0.310983 | ||||||||
\(122\) | 1392.46i | 1.03334i | ||||||||
\(123\) | −678.409 | + | 190.378i | −0.497318 | + | 0.139559i | ||||
\(124\) | 731.083i | 0.529461i | ||||||||
\(125\) | 332.008 | + | 1357.53i | 0.237566 | + | 0.971371i | ||||
\(126\) | −444.599 | + | 2185.23i | −0.314349 | + | 1.54505i | ||||
\(127\) | 1251.75i | 0.874602i | 0.899315 | + | 0.437301i | \(0.144066\pi\) | ||||
−0.899315 | + | 0.437301i | \(0.855934\pi\) | |||||||
\(128\) | −1957.21 | −1.35152 | ||||||||
\(129\) | 379.947 | + | 1353.94i | 0.259322 | + | 0.924089i | ||||
\(130\) | 75.4827 | + | 942.075i | 0.0509251 | + | 0.635580i | ||||
\(131\) | −1225.39 | −0.817274 | −0.408637 | − | 0.912697i | \(-0.633996\pi\) | ||||
−0.408637 | + | 0.912697i | \(0.633996\pi\) | |||||||
\(132\) | 505.422 | + | 1801.06i | 0.333268 | + | 1.18759i | ||||
\(133\) | −1623.81 | − | 1506.36i | −1.05867 | − | 0.982088i | ||||
\(134\) | − | 3352.44i | − | 2.16124i | ||||||
\(135\) | −1229.39 | − | 974.152i | −0.783772 | − | 0.621049i | ||||
\(136\) | − | 79.6503i | − | 0.0502203i | ||||||
\(137\) | −1748.45 | −1.09037 | −0.545183 | − | 0.838317i | \(-0.683540\pi\) | ||||
−0.545183 | + | 0.838317i | \(0.683540\pi\) | |||||||
\(138\) | 3002.52 | − | 842.579i | 1.85211 | − | 0.519747i | ||||
\(139\) | 2075.28i | 1.26635i | 0.774007 | + | 0.633177i | \(0.218250\pi\) | ||||
−0.774007 | + | 0.633177i | \(0.781750\pi\) | |||||||
\(140\) | 1932.55 | + | 1524.60i | 1.16664 | + | 0.920371i | ||||
\(141\) | −383.720 | − | 1367.38i | −0.229185 | − | 0.816697i | ||||
\(142\) | 2857.80i | 1.68888i | ||||||||
\(143\) | − | 574.024i | − | 0.335681i | ||||||
\(144\) | −410.012 | + | 249.790i | −0.237275 | + | 0.144554i | ||||
\(145\) | −2263.99 | + | 181.399i | −1.29665 | + | 0.103892i | ||||
\(146\) | 2092.07 | 1.18589 | ||||||||
\(147\) | −608.796 | − | 1675.08i | −0.341583 | − | 0.939852i | ||||
\(148\) | − | 4013.25i | − | 2.22896i | ||||||
\(149\) | − | 192.111i | − | 0.105627i | −0.998604 | − | 0.0528133i | \(-0.983181\pi\) | ||
0.998604 | − | 0.0528133i | \(-0.0168188\pi\) | |||||||
\(150\) | −2628.66 | + | 1216.69i | −1.43086 | + | 0.662283i | ||||
\(151\) | −2157.41 | −1.16270 | −0.581350 | − | 0.813654i | \(-0.697475\pi\) | ||||
−0.581350 | + | 0.813654i | \(0.697475\pi\) | |||||||
\(152\) | 2073.55i | 1.10650i | ||||||||
\(153\) | −64.5330 | − | 105.926i | −0.0340993 | − | 0.0559715i | ||||
\(154\) | −1833.68 | − | 1701.04i | −0.959493 | − | 0.890089i | ||||
\(155\) | 685.376 | − | 54.9149i | 0.355166 | − | 0.0284572i | ||||
\(156\) | −1127.33 | + | 316.356i | −0.578581 | + | 0.162364i | ||||
\(157\) | 1016.31 | 0.516625 | 0.258312 | − | 0.966061i | \(-0.416834\pi\) | ||||
0.258312 | + | 0.966061i | \(0.416834\pi\) | |||||||
\(158\) | 564.106 | 0.284037 | ||||||||
\(159\) | 1114.95 | − | 312.882i | 0.556109 | − | 0.156058i | ||||
\(160\) | 194.667 | + | 2429.58i | 0.0961863 | + | 1.20047i | ||||
\(161\) | −1695.07 | + | 1827.24i | −0.829751 | + | 0.894450i | ||||
\(162\) | 1491.00 | − | 2888.97i | 0.723112 | − | 1.40110i | ||||
\(163\) | 2851.10i | 1.37003i | 0.728527 | + | 0.685017i | \(0.240205\pi\) | ||||
−0.728527 | + | 0.685017i | \(0.759795\pi\) | |||||||
\(164\) | −1612.03 | −0.767552 | ||||||||
\(165\) | 1650.50 | − | 609.109i | 0.778733 | − | 0.287388i | ||||
\(166\) | − | 1334.59i | − | 0.624004i | ||||||
\(167\) | − | 1887.62i | − | 0.874662i | −0.899301 | − | 0.437331i | \(-0.855924\pi\) | ||
0.899301 | − | 0.437331i | \(-0.144076\pi\) | |||||||
\(168\) | −762.048 | + | 1484.34i | −0.349960 | + | 0.681661i | ||||
\(169\) | −1837.70 | −0.836461 | ||||||||
\(170\) | −228.320 | + | 18.2938i | −0.103008 | + | 0.00825338i | ||||
\(171\) | 1680.00 | + | 2757.60i | 0.751304 | + | 1.23321i | ||||
\(172\) | 3217.21i | 1.42622i | ||||||||
\(173\) | 3491.67i | 1.53449i | 0.641353 | + | 0.767246i | \(0.278373\pi\) | ||||
−0.641353 | + | 0.767246i | \(0.721627\pi\) | |||||||
\(174\) | −1271.89 | − | 4532.36i | −0.554148 | − | 1.97470i | ||||
\(175\) | 1284.12 | − | 1926.25i | 0.554686 | − | 0.832060i | ||||
\(176\) | − | 538.493i | − | 0.230628i | ||||||
\(177\) | −3677.26 | + | 1031.93i | −1.56158 | + | 0.438217i | ||||
\(178\) | −1899.30 | −0.799769 | ||||||||
\(179\) | 172.498i | 0.0720286i | 0.999351 | + | 0.0360143i | \(0.0114662\pi\) | ||||
−0.999351 | + | 0.0360143i | \(0.988534\pi\) | |||||||
\(180\) | −2105.85 | − | 2905.73i | −0.872006 | − | 1.20322i | ||||
\(181\) | 2106.81i | 0.865182i | 0.901590 | + | 0.432591i | \(0.142401\pi\) | ||||
−0.901590 | + | 0.432591i | \(0.857599\pi\) | |||||||
\(182\) | 1064.72 | − | 1147.74i | 0.433640 | − | 0.467453i | ||||
\(183\) | 438.365 | + | 1562.10i | 0.177076 | + | 0.631006i | ||||
\(184\) | 2333.32 | 0.934861 | ||||||||
\(185\) | −3762.34 | + | 301.453i | −1.49520 | + | 0.119801i | ||||
\(186\) | 385.038 | + | 1372.08i | 0.151787 | + | 0.540890i | ||||
\(187\) | 139.119 | 0.0544033 | ||||||||
\(188\) | − | 3249.16i | − | 1.26048i | ||||||
\(189\) | 189.174 | + | 2591.42i | 0.0728063 | + | 0.997346i | ||||
\(190\) | 5943.89 | − | 476.247i | 2.26955 | − | 0.181845i | ||||
\(191\) | − | 633.737i | − | 0.240082i | −0.992769 | − | 0.120041i | \(-0.961697\pi\) | ||
0.992769 | − | 0.120041i | \(-0.0383026\pi\) | |||||||
\(192\) | −4152.18 | + | 1165.20i | −1.56072 | + | 0.437975i | ||||
\(193\) | − | 4520.88i | − | 1.68611i | −0.537824 | − | 0.843057i | \(-0.680754\pi\) | ||
0.537824 | − | 0.843057i | \(-0.319246\pi\) | |||||||
\(194\) | 2504.75 | 0.926962 | ||||||||
\(195\) | 381.256 | + | 1033.09i | 0.140012 | + | 0.379389i | ||||
\(196\) | −305.580 | − | 4066.07i | −0.111363 | − | 1.48180i | ||||
\(197\) | −3816.25 | −1.38018 | −0.690092 | − | 0.723722i | \(-0.742430\pi\) | ||||
−0.690092 | + | 0.723722i | \(0.742430\pi\) | |||||||
\(198\) | 1897.13 | + | 3114.00i | 0.680924 | + | 1.11769i | ||||
\(199\) | − | 1340.01i | − | 0.477341i | −0.971101 | − | 0.238670i | \(-0.923288\pi\) | ||
0.971101 | − | 0.238670i | \(-0.0767115\pi\) | |||||||
\(200\) | −2139.62 | + | 345.085i | −0.756471 | + | 0.122006i | ||||
\(201\) | −1055.39 | − | 3760.87i | −0.370356 | − | 1.31976i | ||||
\(202\) | 7729.11 | 2.69217 | ||||||||
\(203\) | 2758.25 | + | 2558.73i | 0.953651 | + | 0.884670i | ||||
\(204\) | −76.6715 | − | 273.218i | −0.0263141 | − | 0.0937699i | ||||
\(205\) | 121.087 | + | 1511.25i | 0.0412541 | + | 0.514879i | ||||
\(206\) | 7603.37 | 2.57161 | ||||||||
\(207\) | 3103.06 | − | 1890.46i | 1.04192 | − | 0.634765i | ||||
\(208\) | 337.056 | 0.112359 | ||||||||
\(209\) | −3621.73 | −1.19866 | ||||||||
\(210\) | 4429.91 | + | 1843.51i | 1.45568 | + | 0.605783i | ||||
\(211\) | 729.169 | 0.237905 | 0.118953 | − | 0.992900i | \(-0.462046\pi\) | ||||
0.118953 | + | 0.992900i | \(0.462046\pi\) | |||||||
\(212\) | 2649.34 | 0.858290 | ||||||||
\(213\) | 899.674 | + | 3205.97i | 0.289411 | + | 1.03131i | ||||
\(214\) | 1773.97 | 0.566664 | ||||||||
\(215\) | 3016.07 | − | 241.660i | 0.956719 | − | 0.0766560i | ||||
\(216\) | 1658.13 | − | 1779.76i | 0.522322 | − | 0.560636i | ||||
\(217\) | −835.003 | − | 774.604i | −0.261215 | − | 0.242320i | ||||
\(218\) | 6166.36 | 1.91577 | ||||||||
\(219\) | 2346.95 | − | 658.610i | 0.724164 | − | 0.203218i | ||||
\(220\) | 4012.11 | − | 321.466i | 1.22953 | − | 0.0985146i | ||||
\(221\) | 87.0783i | 0.0265046i | ||||||||
\(222\) | −2113.65 | − | 7531.96i | −0.639004 | − | 2.27708i | ||||
\(223\) | −3259.48 | −0.978793 | −0.489396 | − | 0.872061i | \(-0.662783\pi\) | ||||
−0.489396 | + | 0.872061i | \(0.662783\pi\) | |||||||
\(224\) | 2745.89 | − | 2959.99i | 0.819050 | − | 0.882915i | ||||
\(225\) | −2565.88 | + | 2192.46i | −0.760261 | + | 0.649617i | ||||
\(226\) | −4589.39 | −1.35080 | ||||||||
\(227\) | − | 4188.94i | − | 1.22480i | −0.790548 | − | 0.612401i | \(-0.790204\pi\) | ||
0.790548 | − | 0.612401i | \(-0.209796\pi\) | |||||||
\(228\) | 1996.01 | + | 7112.73i | 0.579775 | + | 2.06602i | ||||
\(229\) | 1996.90i | 0.576240i | 0.957594 | + | 0.288120i | \(0.0930302\pi\) | ||||
−0.957594 | + | 0.288120i | \(0.906970\pi\) | |||||||
\(230\) | −535.909 | − | 6688.51i | −0.153638 | − | 1.91751i | ||||
\(231\) | −2592.59 | − | 1331.01i | −0.738440 | − | 0.379110i | ||||
\(232\) | − | 3522.19i | − | 0.996736i | ||||||
\(233\) | 141.704 | 0.0398425 | 0.0199213 | − | 0.999802i | \(-0.493658\pi\) | ||||
0.0199213 | + | 0.999802i | \(0.493658\pi\) | |||||||
\(234\) | −1949.13 | + | 1187.46i | −0.544524 | + | 0.331737i | ||||
\(235\) | −3046.03 | + | 244.059i | −0.845535 | + | 0.0677476i | ||||
\(236\) | −8737.88 | −2.41012 | ||||||||
\(237\) | 632.832 | − | 177.588i | 0.173447 | − | 0.0486733i | ||||
\(238\) | 278.165 | + | 258.044i | 0.0757595 | + | 0.0702795i | ||||
\(239\) | 2702.30i | 0.731369i | 0.930739 | + | 0.365684i | \(0.119165\pi\) | ||||
−0.930739 | + | 0.365684i | \(0.880835\pi\) | |||||||
\(240\) | 357.657 | + | 969.140i | 0.0961945 | + | 0.260657i | ||||
\(241\) | − | 4299.54i | − | 1.14920i | −0.818434 | − | 0.574601i | \(-0.805157\pi\) | ||
0.818434 | − | 0.574601i | \(-0.194843\pi\) | |||||||
\(242\) | 1845.90 | 0.490326 | ||||||||
\(243\) | 763.168 | − | 3710.32i | 0.201470 | − | 0.979495i | ||||
\(244\) | 3711.86i | 0.973884i | ||||||||
\(245\) | −3788.90 | + | 591.896i | −0.988017 | + | 0.154346i | ||||
\(246\) | −3025.42 | + | 849.006i | −0.784121 | + | 0.220043i | ||||
\(247\) | − | 2266.93i | − | 0.583972i | ||||||
\(248\) | 1066.27i | 0.273017i | ||||||||
\(249\) | −420.148 | − | 1497.19i | −0.106931 | − | 0.381047i | ||||
\(250\) | 1480.62 | + | 6054.03i | 0.374570 | + | 1.53156i | ||||
\(251\) | 3307.05 | 0.831630 | 0.415815 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415815 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(252\) | −1185.16 | + | 5825.14i | −0.296263 | + | 1.45615i | ||||
\(253\) | 4075.44i | 1.01273i | ||||||||
\(254\) | 5582.26i | 1.37898i | ||||||||
\(255\) | −250.377 | + | 92.4006i | −0.0614871 | + | 0.0226916i | ||||
\(256\) | −2088.71 | −0.509938 | ||||||||
\(257\) | 3931.01i | 0.954123i | 0.878870 | + | 0.477061i | \(0.158298\pi\) | ||||
−0.878870 | + | 0.477061i | \(0.841702\pi\) | |||||||
\(258\) | 1694.41 | + | 6037.99i | 0.408872 | + | 1.45701i | ||||
\(259\) | 4583.71 | + | 4252.15i | 1.09968 | + | 1.02014i | ||||
\(260\) | 201.213 | + | 2511.28i | 0.0479951 | + | 0.599011i | ||||
\(261\) | −2853.69 | − | 4684.13i | −0.676778 | − | 1.11088i | ||||
\(262\) | −5464.73 | −1.28860 | ||||||||
\(263\) | −2083.22 | −0.488430 | −0.244215 | − | 0.969721i | \(-0.578530\pi\) | ||||
−0.244215 | + | 0.969721i | \(0.578530\pi\) | |||||||
\(264\) | 737.147 | + | 2626.81i | 0.171850 | + | 0.612383i | ||||
\(265\) | −199.004 | − | 2483.70i | −0.0461310 | − | 0.575746i | ||||
\(266\) | −7241.53 | − | 6717.72i | −1.66920 | − | 1.54846i | ||||
\(267\) | −2130.70 | + | 597.926i | −0.488377 | + | 0.137050i | ||||
\(268\) | − | 8936.56i | − | 2.03689i | ||||||
\(269\) | −2905.93 | −0.658653 | −0.329326 | − | 0.944216i | \(-0.606822\pi\) | ||||
−0.329326 | + | 0.944216i | \(0.606822\pi\) | |||||||
\(270\) | −5482.57 | − | 4344.31i | −1.23577 | − | 0.979208i | ||||
\(271\) | − | 716.004i | − | 0.160495i | −0.996775 | − | 0.0802475i | \(-0.974429\pi\) | ||
0.996775 | − | 0.0802475i | \(-0.0255711\pi\) | |||||||
\(272\) | 81.6883i | 0.0182099i | ||||||||
\(273\) | 833.115 | − | 1622.76i | 0.184697 | − | 0.359759i | ||||
\(274\) | −7797.36 | −1.71918 | ||||||||
\(275\) | −602.735 | − | 3737.13i | −0.132168 | − | 0.819481i | ||||
\(276\) | 8003.78 | − | 2246.05i | 1.74555 | − | 0.489843i | ||||
\(277\) | 101.240i | 0.0219601i | 0.999940 | + | 0.0109801i | \(0.00349513\pi\) | ||||
−0.999940 | + | 0.0109801i | \(0.996505\pi\) | |||||||
\(278\) | 9254.89i | 1.99666i | ||||||||
\(279\) | 863.896 | + | 1418.02i | 0.185377 | + | 0.304283i | ||||
\(280\) | 2818.58 | + | 2223.59i | 0.601580 | + | 0.474589i | ||||
\(281\) | 7745.33i | 1.64430i | 0.569272 | + | 0.822149i | \(0.307225\pi\) | ||||
−0.569272 | + | 0.822149i | \(0.692775\pi\) | |||||||
\(282\) | −1711.23 | − | 6097.95i | −0.361356 | − | 1.28769i | ||||
\(283\) | 381.119 | 0.0800536 | 0.0400268 | − | 0.999199i | \(-0.487256\pi\) | ||||
0.0400268 | + | 0.999199i | \(0.487256\pi\) | |||||||
\(284\) | 7618.01i | 1.59171i | ||||||||
\(285\) | 6518.11 | − | 2405.48i | 1.35474 | − | 0.499960i | ||||
\(286\) | − | 2559.91i | − | 0.529267i | ||||||
\(287\) | 1708.00 | − | 1841.17i | 0.351288 | − | 0.378680i | ||||
\(288\) | −5026.74 | + | 3062.42i | −1.02848 | + | 0.626579i | ||||
\(289\) | 4891.90 | 0.995704 | ||||||||
\(290\) | −10096.4 | + | 808.965i | −2.04442 | + | 0.163807i | ||||
\(291\) | 2809.91 | − | 788.529i | 0.566047 | − | 0.158847i | ||||
\(292\) | 5576.80 | 1.11766 | ||||||||
\(293\) | − | 2325.30i | − | 0.463637i | −0.972759 | − | 0.231818i | \(-0.925532\pi\) | ||
0.972759 | − | 0.231818i | \(-0.0744675\pi\) | |||||||
\(294\) | −2714.97 | − | 7470.15i | −0.538573 | − | 1.48186i | ||||
\(295\) | 656.342 | + | 8191.59i | 0.129538 | + | 1.61672i | ||||
\(296\) | − | 5853.23i | − | 1.14937i | ||||||
\(297\) | 3108.58 | + | 2896.14i | 0.607334 | + | 0.565829i | ||||
\(298\) | − | 856.735i | − | 0.166541i | ||||||
\(299\) | −2550.92 | −0.493389 | ||||||||
\(300\) | −7007.19 | + | 3243.32i | −1.34853 | + | 0.624177i | ||||
\(301\) | −3674.53 | − | 3408.73i | −0.703642 | − | 0.652745i | ||||
\(302\) | −9621.14 | −1.83323 | ||||||||
\(303\) | 8670.76 | − | 2433.23i | 1.64397 | − | 0.461337i | ||||
\(304\) | − | 2126.61i | − | 0.401215i | ||||||
\(305\) | 3479.80 | − | 278.815i | 0.653287 | − | 0.0523439i | ||||
\(306\) | −287.790 | − | 472.387i | −0.0537643 | − | 0.0882503i | ||||
\(307\) | −3447.89 | −0.640981 | −0.320491 | − | 0.947252i | \(-0.603848\pi\) | ||||
−0.320491 | + | 0.947252i | \(0.603848\pi\) | |||||||
\(308\) | −4888.01 | − | 4534.44i | −0.904286 | − | 0.838876i | ||||
\(309\) | 8529.70 | − | 2393.64i | 1.57035 | − | 0.440678i | ||||
\(310\) | 3056.49 | − | 244.897i | 0.559990 | − | 0.0448685i | ||||
\(311\) | 7675.73 | 1.39952 | 0.699760 | − | 0.714378i | \(-0.253290\pi\) | ||||
0.699760 | + | 0.714378i | \(0.253290\pi\) | |||||||
\(312\) | −1644.19 | + | 461.399i | −0.298345 | + | 0.0837230i | ||||
\(313\) | −9734.46 | −1.75790 | −0.878952 | − | 0.476910i | \(-0.841757\pi\) | ||||
−0.878952 | + | 0.476910i | \(0.841757\pi\) | |||||||
\(314\) | 4532.30 | 0.814562 | ||||||||
\(315\) | 5549.98 | + | 673.513i | 0.992717 | + | 0.120470i | ||||
\(316\) | 1503.73 | 0.267694 | ||||||||
\(317\) | 688.561 | 0.121998 | 0.0609991 | − | 0.998138i | \(-0.480571\pi\) | ||||
0.0609991 | + | 0.998138i | \(0.480571\pi\) | |||||||
\(318\) | 4972.21 | − | 1395.32i | 0.876817 | − | 0.246056i | ||||
\(319\) | 6151.95 | 1.07976 | ||||||||
\(320\) | 741.109 | + | 9249.54i | 0.129466 | + | 1.61583i | ||||
\(321\) | 1990.09 | − | 558.469i | 0.346032 | − | 0.0971050i | ||||
\(322\) | −7559.28 | + | 8148.71i | −1.30827 | + | 1.41028i | ||||
\(323\) | 549.409 | 0.0946437 | ||||||||
\(324\) | 3974.55 | − | 7701.09i | 0.681507 | − | 1.32049i | ||||
\(325\) | 2339.16 | − | 377.267i | 0.399241 | − | 0.0643908i | ||||
\(326\) | 12714.7i | 2.16013i | ||||||||
\(327\) | 6917.61 | − | 1941.25i | 1.16986 | − | 0.328292i | ||||
\(328\) | −2351.11 | −0.395788 | ||||||||
\(329\) | 3711.02 | + | 3442.58i | 0.621869 | + | 0.576887i | ||||
\(330\) | 7360.52 | − | 2716.37i | 1.22783 | − | 0.453125i | ||||
\(331\) | 4447.67 | 0.738568 | 0.369284 | − | 0.929317i | \(-0.379603\pi\) | ||||
0.369284 | + | 0.929317i | \(0.379603\pi\) | |||||||
\(332\) | − | 3557.61i | − | 0.588101i | ||||||
\(333\) | −4742.32 | − | 7784.18i | −0.780413 | − | 1.28099i | ||||
\(334\) | − | 8418.00i | − | 1.37908i | ||||||
\(335\) | −8377.85 | + | 671.265i | −1.36636 | + | 0.109478i | ||||
\(336\) | 781.546 | − | 1522.32i | 0.126895 | − | 0.247170i | ||||
\(337\) | 4087.57i | 0.660724i | 0.943854 | + | 0.330362i | \(0.107171\pi\) | ||||
−0.943854 | + | 0.330362i | \(0.892829\pi\) | |||||||
\(338\) | −8195.39 | −1.31885 | ||||||||
\(339\) | −5148.52 | + | 1444.80i | −0.824864 | + | 0.231477i | ||||
\(340\) | −608.629 | + | 48.7657i | −0.0970810 | + | 0.00777850i | ||||
\(341\) | −1862.38 | −0.295757 | ||||||||
\(342\) | 7492.10 | + | 12297.8i | 1.18458 | + | 1.94441i | ||||
\(343\) | 4967.81 | + | 3959.10i | 0.782031 | + | 0.623240i | ||||
\(344\) | 4692.24i | 0.735432i | ||||||||
\(345\) | −2706.83 | − | 7334.67i | −0.422408 | − | 1.14460i | ||||
\(346\) | 15571.4i | 2.41943i | ||||||||
\(347\) | 5812.08 | 0.899161 | 0.449580 | − | 0.893240i | \(-0.351573\pi\) | ||||
0.449580 | + | 0.893240i | \(0.351573\pi\) | |||||||
\(348\) | −3390.46 | − | 12081.9i | −0.522264 | − | 1.86108i | ||||
\(349\) | − | 2804.01i | − | 0.430073i | −0.976606 | − | 0.215036i | \(-0.931013\pi\) | ||
0.976606 | − | 0.215036i | \(-0.0689870\pi\) | |||||||
\(350\) | 5726.62 | − | 8590.24i | 0.874573 | − | 1.31191i | ||||
\(351\) | −1812.77 | + | 1945.74i | −0.275665 | + | 0.295886i | ||||
\(352\) | − | 6601.92i | − | 0.999669i | ||||||
\(353\) | − | 1183.07i | − | 0.178381i | −0.996015 | − | 0.0891907i | \(-0.971572\pi\) | ||
0.996015 | − | 0.0891907i | \(-0.0284281\pi\) | |||||||
\(354\) | −16399.0 | + | 4601.97i | −2.46214 | + | 0.690937i | ||||
\(355\) | 7141.74 | − | 572.223i | 1.06773 | − | 0.0855506i | ||||
\(356\) | −5062.95 | −0.753753 | ||||||||
\(357\) | 393.290 | + | 201.912i | 0.0583056 | + | 0.0299337i | ||||
\(358\) | 769.269i | 0.113567i | ||||||||
\(359\) | − | 8708.99i | − | 1.28034i | −0.768232 | − | 0.640171i | \(-0.778863\pi\) | ||
0.768232 | − | 0.640171i | \(-0.221137\pi\) | |||||||
\(360\) | −3071.34 | − | 4237.94i | −0.449650 | − | 0.620442i | ||||
\(361\) | −7443.86 | −1.08527 | ||||||||
\(362\) | 9395.49i | 1.36413i | ||||||||
\(363\) | 2070.79 | − | 581.114i | 0.299417 | − | 0.0840236i | ||||
\(364\) | 2838.22 | − | 3059.53i | 0.408690 | − | 0.440557i | ||||
\(365\) | −418.898 | − | 5228.14i | −0.0600716 | − | 0.749735i | ||||
\(366\) | 1954.92 | + | 6966.33i | 0.279195 | + | 0.994907i | ||||
\(367\) | −7352.20 | −1.04573 | −0.522864 | − | 0.852416i | \(-0.675136\pi\) | ||||
−0.522864 | + | 0.852416i | \(0.675136\pi\) | |||||||
\(368\) | −2393.02 | −0.338980 | ||||||||
\(369\) | −3126.73 | + | 1904.88i | −0.441114 | + | 0.268738i | ||||
\(370\) | −16778.4 | + | 1344.35i | −2.35749 | + | 0.188891i | ||||
\(371\) | −2807.05 | + | 3025.93i | −0.392817 | + | 0.423446i | ||||
\(372\) | 1026.39 | + | 3657.53i | 0.143054 | + | 0.509769i | ||||
\(373\) | − | 1319.56i | − | 0.183174i | −0.995797 | − | 0.0915872i | \(-0.970806\pi\) | ||
0.995797 | − | 0.0915872i | \(-0.0291940\pi\) | |||||||
\(374\) | 620.414 | 0.0857777 | ||||||||
\(375\) | 3566.89 | + | 6325.48i | 0.491182 | + | 0.871057i | ||||
\(376\) | − | 4738.84i | − | 0.649965i | ||||||
\(377\) | 3850.66i | 0.526045i | ||||||||
\(378\) | 843.637 | + | 11556.7i | 0.114794 | + | 1.57252i | ||||
\(379\) | −10334.2 | −1.40062 | −0.700309 | − | 0.713839i | \(-0.746955\pi\) | ||||
−0.700309 | + | 0.713839i | \(0.746955\pi\) | |||||||
\(380\) | 15844.6 | − | 1269.53i | 2.13897 | − | 0.171383i | ||||
\(381\) | 1757.37 | + | 6262.35i | 0.236306 | + | 0.842074i | ||||
\(382\) | − | 2826.20i | − | 0.378537i | ||||||
\(383\) | − | 13328.0i | − | 1.77815i | −0.457763 | − | 0.889074i | \(-0.651349\pi\) | ||
0.457763 | − | 0.889074i | \(-0.348651\pi\) | |||||||
\(384\) | −9791.74 | + | 2747.80i | −1.30126 | + | 0.365164i | ||||
\(385\) | −3883.79 | + | 4923.01i | −0.514120 | + | 0.651688i | ||||
\(386\) | − | 20161.2i | − | 2.65850i | ||||||
\(387\) | 3801.67 | + | 6240.18i | 0.499354 | + | 0.819654i | ||||
\(388\) | 6676.89 | 0.873628 | ||||||||
\(389\) | 6183.45i | 0.805947i | 0.915212 | + | 0.402973i | \(0.132023\pi\) | ||||
−0.915212 | + | 0.402973i | \(0.867977\pi\) | |||||||
\(390\) | 1700.24 | + | 4607.13i | 0.220757 | + | 0.598182i | ||||
\(391\) | − | 618.236i | − | 0.0799630i | ||||||
\(392\) | −445.682 | − | 5930.27i | −0.0574243 | − | 0.764092i | ||||
\(393\) | −6130.50 | + | 1720.37i | −0.786878 | + | 0.220817i | ||||
\(394\) | −17018.8 | −2.17614 | ||||||||
\(395\) | −112.952 | − | 1409.72i | −0.0143879 | − | 0.179571i | ||||
\(396\) | 5057.15 | + | 8300.95i | 0.641746 | + | 1.05338i | ||||
\(397\) | 2722.53 | 0.344181 | 0.172091 | − | 0.985081i | \(-0.444948\pi\) | ||||
0.172091 | + | 0.985081i | \(0.444948\pi\) | |||||||
\(398\) | − | 5975.88i | − | 0.752623i | ||||||
\(399\) | −10238.6 | − | 5256.42i | −1.28464 | − | 0.659524i | ||||
\(400\) | 2194.37 | − | 353.915i | 0.274296 | − | 0.0442393i | ||||
\(401\) | − | 6359.86i | − | 0.792011i | −0.918248 | − | 0.396005i | \(-0.870396\pi\) | ||
0.918248 | − | 0.396005i | \(-0.129604\pi\) | |||||||
\(402\) | −4706.60 | − | 16771.9i | −0.583941 | − | 2.08086i | ||||
\(403\) | − | 1165.71i | − | 0.144089i | ||||||
\(404\) | 20603.4 | 2.53727 | ||||||||
\(405\) | −7518.16 | − | 3147.60i | −0.922421 | − | 0.386186i | ||||
\(406\) | 12300.6 | + | 11410.9i | 1.50362 | + | 1.39486i | ||||
\(407\) | 10223.4 | 1.24510 | ||||||||
\(408\) | −111.824 | − | 398.482i | −0.0135689 | − | 0.0483525i | ||||
\(409\) | 2243.08i | 0.271181i | 0.990765 | + | 0.135591i | \(0.0432932\pi\) | ||||
−0.990765 | + | 0.135591i | \(0.956707\pi\) | |||||||
\(410\) | 539.997 | + | 6739.53i | 0.0650453 | + | 0.811809i | ||||
\(411\) | −8747.32 | + | 2454.71i | −1.04981 | + | 0.294603i | ||||
\(412\) | 20268.2 | 2.42365 | ||||||||
\(413\) | 9258.04 | − | 9979.93i | 1.10305 | − | 1.18906i | ||||
\(414\) | 13838.4 | − | 8430.67i | 1.64280 | − | 1.00083i | ||||
\(415\) | −3335.19 | + | 267.229i | −0.394502 | + | 0.0316090i | ||||
\(416\) | 4132.30 | 0.487026 | ||||||||
\(417\) | 2913.56 | + | 10382.4i | 0.342153 | + | 1.21926i | ||||
\(418\) | −16151.4 | −1.88993 | ||||||||
\(419\) | 12565.4 | 1.46505 | 0.732527 | − | 0.680738i | \(-0.238341\pi\) | ||||
0.732527 | + | 0.680738i | \(0.238341\pi\) | |||||||
\(420\) | 11808.8 | + | 4914.23i | 1.37193 | + | 0.570928i | ||||
\(421\) | 3903.57 | 0.451896 | 0.225948 | − | 0.974139i | \(-0.427452\pi\) | ||||
0.225948 | + | 0.974139i | \(0.427452\pi\) | |||||||
\(422\) | 3251.79 | 0.375105 | ||||||||
\(423\) | −3839.43 | − | 6302.15i | −0.441322 | − | 0.724399i | ||||
\(424\) | 3864.01 | 0.442577 | ||||||||
\(425\) | 91.4337 | + | 566.915i | 0.0104357 | + | 0.0647045i | ||||
\(426\) | 4012.17 | + | 14297.3i | 0.456315 | + | 1.62607i | ||||
\(427\) | −4239.49 | − | 3932.83i | −0.480476 | − | 0.445721i | ||||
\(428\) | 4728.85 | 0.534060 | ||||||||
\(429\) | −805.892 | − | 2871.78i | −0.0906966 | − | 0.323196i | ||||
\(430\) | 13450.4 | − | 1077.70i | 1.50846 | − | 0.120864i | ||||
\(431\) | − | 5029.93i | − | 0.562142i | −0.959687 | − | 0.281071i | \(-0.909310\pi\) | ||
0.959687 | − | 0.281071i | \(-0.0906897\pi\) | |||||||
\(432\) | −1700.56 | + | 1825.30i | −0.189394 | + | 0.203287i | ||||
\(433\) | 14864.3 | 1.64972 | 0.824862 | − | 0.565334i | \(-0.191253\pi\) | ||||
0.824862 | + | 0.565334i | \(0.191253\pi\) | |||||||
\(434\) | −3723.76 | − | 3454.41i | −0.411858 | − | 0.382066i | ||||
\(435\) | −11071.8 | + | 4086.01i | −1.22035 | + | 0.450366i | ||||
\(436\) | 16437.6 | 1.80555 | ||||||||
\(437\) | 16094.7i | 1.76181i | ||||||||
\(438\) | 10466.4 | − | 2937.12i | 1.14179 | − | 0.320414i | ||||
\(439\) | 11284.2i | 1.22680i | 0.789771 | + | 0.613402i | \(0.210199\pi\) | ||||
−0.789771 | + | 0.613402i | \(0.789801\pi\) | |||||||
\(440\) | 5851.58 | − | 468.851i | 0.634007 | − | 0.0507991i | ||||
\(441\) | −5397.44 | − | 7525.54i | −0.582814 | − | 0.812605i | ||||
\(442\) | 388.333i | 0.0417898i | ||||||||
\(443\) | −6406.23 | −0.687064 | −0.343532 | − | 0.939141i | \(-0.611623\pi\) | ||||
−0.343532 | + | 0.939141i | \(0.611623\pi\) | |||||||
\(444\) | −5634.33 | − | 20077.8i | −0.602238 | − | 2.14606i | ||||
\(445\) | 380.301 | + | 4746.42i | 0.0405124 | + | 0.505622i | ||||
\(446\) | −14535.9 | −1.54326 | ||||||||
\(447\) | −269.712 | − | 961.113i | −0.0285390 | − | 0.101698i | ||||
\(448\) | 10453.7 | − | 11268.8i | 1.10244 | − | 1.18840i | ||||
\(449\) | 5647.45i | 0.593585i | 0.954942 | + | 0.296792i | \(0.0959169\pi\) | ||||
−0.954942 | + | 0.296792i | \(0.904083\pi\) | |||||||
\(450\) | −11442.8 | + | 9777.45i | −1.19870 | + | 1.02425i | ||||
\(451\) | − | 4106.52i | − | 0.428755i | ||||||
\(452\) | −12233.9 | −1.27308 | ||||||||
\(453\) | −10793.3 | + | 3028.86i | −1.11946 | + | 0.314147i | ||||
\(454\) | − | 18680.9i | − | 1.93114i | ||||||
\(455\) | −3081.44 | − | 2430.96i | −0.317494 | − | 0.250473i | ||||
\(456\) | 2911.13 | + | 10373.8i | 0.298961 | + | 1.06534i | ||||
\(457\) | 4027.42i | 0.412243i | 0.978526 | + | 0.206121i | \(0.0660842\pi\) | ||||
−0.978526 | + | 0.206121i | \(0.933916\pi\) | |||||||
\(458\) | 8905.34i | 0.908558i | ||||||||
\(459\) | −471.566 | − | 439.339i | −0.0479538 | − | 0.0446766i | ||||
\(460\) | −1428.57 | − | 17829.5i | −0.144798 | − | 1.80718i | ||||
\(461\) | 4322.13 | 0.436663 | 0.218332 | − | 0.975875i | \(-0.429939\pi\) | ||||
0.218332 | + | 0.975875i | \(0.429939\pi\) | |||||||
\(462\) | −11561.8 | − | 5935.76i | −1.16430 | − | 0.597742i | ||||
\(463\) | − | 13087.8i | − | 1.31370i | −0.754021 | − | 0.656850i | \(-0.771889\pi\) | ||
0.754021 | − | 0.656850i | \(-0.228111\pi\) | |||||||
\(464\) | 3612.31i | 0.361416i | ||||||||
\(465\) | 3351.77 | − | 1236.96i | 0.334268 | − | 0.123360i | ||||
\(466\) | 631.938 | 0.0628197 | ||||||||
\(467\) | 2525.04i | 0.250203i | 0.992144 | + | 0.125102i | \(0.0399257\pi\) | ||||
−0.992144 | + | 0.125102i | \(0.960074\pi\) | |||||||
\(468\) | −5195.77 | + | 3165.39i | −0.513193 | + | 0.312650i | ||||
\(469\) | 10206.8 | + | 9468.55i | 1.00492 | + | 0.932232i | ||||
\(470\) | −13584.0 | + | 1088.40i | −1.33316 | + | 0.106818i | ||||
\(471\) | 5084.47 | − | 1426.83i | 0.497410 | − | 0.139585i | ||||
\(472\) | −12744.0 | −1.24278 | ||||||||
\(473\) | −8195.60 | −0.796689 | ||||||||
\(474\) | 2822.16 | − | 791.968i | 0.273473 | − | 0.0767432i | ||||
\(475\) | −2380.31 | − | 14758.6i | −0.229929 | − | 1.42562i | ||||
\(476\) | 741.501 | + | 687.866i | 0.0714005 | + | 0.0662359i | ||||
\(477\) | 5138.72 | − | 3130.64i | 0.493262 | − | 0.300507i | ||||
\(478\) | 12051.1i | 1.15315i | ||||||||
\(479\) | −3175.55 | −0.302911 | −0.151456 | − | 0.988464i | \(-0.548396\pi\) | ||||
−0.151456 | + | 0.988464i | \(0.548396\pi\) | |||||||
\(480\) | 4384.87 | + | 11881.6i | 0.416961 | + | 1.12983i | ||||
\(481\) | 6399.09i | 0.606598i | ||||||||
\(482\) | − | 19174.1i | − | 1.81195i | ||||||
\(483\) | −5914.92 | + | 11521.2i | −0.557222 | + | 1.08537i | ||||
\(484\) | 4920.59 | 0.462114 | ||||||||
\(485\) | −501.531 | − | 6259.45i | −0.0469554 | − | 0.586035i | ||||
\(486\) | 3403.41 | − | 16546.5i | 0.317658 | − | 1.54437i | ||||
\(487\) | − | 3971.81i | − | 0.369569i | −0.982779 | − | 0.184785i | \(-0.940841\pi\) | ||
0.982779 | − | 0.184785i | \(-0.0591587\pi\) | |||||||
\(488\) | 5413.67i | 0.502183i | ||||||||
\(489\) | 4002.76 | + | 14263.8i | 0.370166 | + | 1.31908i | ||||
\(490\) | −16896.9 | + | 2639.61i | −1.55781 | + | 0.243358i | ||||
\(491\) | 10854.4i | 0.997665i | 0.866698 | + | 0.498833i | \(0.166238\pi\) | ||||
−0.866698 | + | 0.498833i | \(0.833762\pi\) | |||||||
\(492\) | −8064.83 | + | 2263.19i | −0.739005 | + | 0.207383i | ||||
\(493\) | −933.239 | −0.0852555 | ||||||||
\(494\) | − | 10109.5i | − | 0.920749i | ||||||
\(495\) | 7402.11 | − | 5364.50i | 0.672122 | − | 0.487104i | ||||
\(496\) | − | 1093.55i | − | 0.0989958i | ||||||
\(497\) | −8700.88 | − | 8071.51i | −0.785287 | − | 0.728484i | ||||
\(498\) | −1873.68 | − | 6676.84i | −0.168598 | − | 0.600796i | ||||
\(499\) | −4802.55 | −0.430845 | −0.215423 | − | 0.976521i | \(-0.569113\pi\) | ||||
−0.215423 | + | 0.976521i | \(0.569113\pi\) | |||||||
\(500\) | 3946.87 | + | 16138.1i | 0.353018 | + | 1.44344i | ||||
\(501\) | −2650.10 | − | 9443.57i | −0.236323 | − | 0.842131i | ||||
\(502\) | 14748.1 | 1.31123 | ||||||||
\(503\) | 13959.0i | 1.23738i | 0.785636 | + | 0.618689i | \(0.212336\pi\) | ||||
−0.785636 | + | 0.618689i | \(0.787664\pi\) | |||||||
\(504\) | −1728.53 | + | 8495.85i | −0.152768 | + | 0.750863i | ||||
\(505\) | −1547.61 | − | 19315.3i | −0.136372 | − | 1.70202i | ||||
\(506\) | 18174.7i | 1.59677i | ||||||||
\(507\) | −9193.84 | + | 2580.02i | −0.805351 | + | 0.226001i | ||||
\(508\) | 14880.6i | 1.29964i | ||||||||
\(509\) | −13117.5 | −1.14228 | −0.571141 | − | 0.820852i | \(-0.693499\pi\) | ||||
−0.571141 | + | 0.820852i | \(0.693499\pi\) | |||||||
\(510\) | −1116.58 | + | 412.068i | −0.0969467 | + | 0.0357778i | ||||
\(511\) | −5908.78 | + | 6369.51i | −0.511525 | + | 0.551410i | ||||
\(512\) | 6342.96 | 0.547503 | ||||||||
\(513\) | 12276.4 | + | 11437.4i | 1.05656 | + | 0.984354i | ||||
\(514\) | 17530.6i | 1.50436i | ||||||||
\(515\) | −1522.44 | − | 19001.0i | −0.130265 | − | 1.62580i | ||||
\(516\) | 4516.76 | + | 16095.4i | 0.385347 | + | 1.37318i | ||||
\(517\) | 8276.99 | 0.704103 | ||||||||
\(518\) | 20441.4 | + | 18962.8i | 1.73387 | + | 1.60845i | ||||
\(519\) | 4902.08 | + | 17468.5i | 0.414600 | + | 1.47742i | ||||
\(520\) | 293.465 | + | 3662.65i | 0.0247487 | + | 0.308880i | ||||
\(521\) | 3567.96 | 0.300029 | 0.150015 | − | 0.988684i | \(-0.452068\pi\) | ||||
0.150015 | + | 0.988684i | \(0.452068\pi\) | |||||||
\(522\) | −12726.3 | − | 20889.3i | −1.06708 | − | 1.75153i | ||||
\(523\) | 6801.37 | 0.568648 | 0.284324 | − | 0.958728i | \(-0.408231\pi\) | ||||
0.284324 | + | 0.958728i | \(0.408231\pi\) | |||||||
\(524\) | −14567.3 | −1.21445 | ||||||||
\(525\) | 3719.98 | − | 11439.6i | 0.309244 | − | 0.950983i | ||||
\(526\) | −9290.30 | −0.770107 | ||||||||
\(527\) | 282.519 | 0.0233524 | ||||||||
\(528\) | −756.009 | − | 2694.02i | −0.0623126 | − | 0.222050i | ||||
\(529\) | 5943.91 | 0.488527 | ||||||||
\(530\) | −887.474 | − | 11076.3i | −0.0727347 | − | 0.907779i | ||||
\(531\) | −16948.2 | + | 10325.3i | −1.38510 | + | 0.843838i | ||||
\(532\) | −19303.7 | − | 17907.3i | −1.57316 | − | 1.45936i | ||||
\(533\) | 2570.37 | 0.208884 | ||||||||
\(534\) | −9502.02 | + | 2666.50i | −0.770024 | + | 0.216087i | ||||
\(535\) | −355.205 | − | 4433.20i | −0.0287044 | − | 0.358251i | ||||
\(536\) | − | 13033.8i | − | 1.05032i | ||||||
\(537\) | 242.176 | + | 862.991i | 0.0194612 | + | 0.0693497i | ||||
\(538\) | −12959.2 | −1.03850 | ||||||||
\(539\) | 10358.0 | − | 778.441i | 0.827736 | − | 0.0622075i | ||||
\(540\) | −14614.8 | − | 11580.6i | −1.16467 | − | 0.922868i | ||||
\(541\) | 2446.78 | 0.194446 | 0.0972229 | − | 0.995263i | \(-0.469004\pi\) | ||||
0.0972229 | + | 0.995263i | \(0.469004\pi\) | |||||||
\(542\) | − | 3193.07i | − | 0.253052i | ||||||
\(543\) | 2957.82 | + | 10540.2i | 0.233761 | + | 0.833004i | ||||
\(544\) | 1001.50i | 0.0789317i | ||||||||
\(545\) | −1234.70 | − | 15409.9i | −0.0970437 | − | 1.21117i | ||||
\(546\) | 3715.34 | − | 7236.84i | 0.291212 | − | 0.567231i | ||||
\(547\) | − | 11784.9i | − | 0.921179i | −0.887613 | − | 0.460590i | \(-0.847638\pi\) | ||
0.887613 | − | 0.460590i | \(-0.152362\pi\) | |||||||
\(548\) | −20785.3 | −1.62026 | ||||||||
\(549\) | 4386.18 | + | 7199.61i | 0.340980 | + | 0.559694i | ||||
\(550\) | −2687.95 | − | 16666.0i | −0.208390 | − | 1.29208i | ||||
\(551\) | 24295.2 | 1.87842 | ||||||||
\(552\) | 11673.3 | − | 3275.82i | 0.900091 | − | 0.252587i | ||||
\(553\) | −1593.25 | + | 1717.48i | −0.122517 | + | 0.132070i | ||||
\(554\) | 451.490i | 0.0346245i | ||||||||
\(555\) | −18399.4 | + | 6790.21i | −1.40722 | + | 0.519331i | ||||
\(556\) | 24670.7i | 1.88178i | ||||||||
\(557\) | 1115.57 | 0.0848618 | 0.0424309 | − | 0.999099i | \(-0.486490\pi\) | ||||
0.0424309 | + | 0.999099i | \(0.486490\pi\) | |||||||
\(558\) | 3852.61 | + | 6323.79i | 0.292283 | + | 0.479762i | ||||
\(559\) | − | 5129.83i | − | 0.388137i | ||||||
\(560\) | −2890.70 | − | 2280.49i | −0.218133 | − | 0.172086i | ||||
\(561\) | 696.000 | − | 195.315i | 0.0523800 | − | 0.0146991i | ||||
\(562\) | 34540.9i | 2.59256i | ||||||||
\(563\) | 16595.3i | 1.24229i | 0.783696 | + | 0.621145i | \(0.213332\pi\) | ||||
−0.783696 | + | 0.621145i | \(0.786668\pi\) | |||||||
\(564\) | −4561.61 | − | 16255.2i | −0.340565 | − | 1.21360i | ||||
\(565\) | 918.941 | + | 11469.0i | 0.0684251 | + | 0.853991i | ||||
\(566\) | 1699.63 | 0.126220 | ||||||||
\(567\) | 4584.61 | + | 12699.0i | 0.339569 | + | 0.940581i | ||||
\(568\) | 11110.7i | 0.820766i | ||||||||
\(569\) | − | 15891.3i | − | 1.17082i | −0.810736 | − | 0.585412i | \(-0.800933\pi\) | ||
0.810736 | − | 0.585412i | \(-0.199067\pi\) | |||||||
\(570\) | 29068.0 | − | 10727.4i | 2.13601 | − | 0.788287i | ||||
\(571\) | 1303.38 | 0.0955252 | 0.0477626 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477626 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(572\) | − | 6823.91i | − | 0.498815i | ||||||
\(573\) | −889.725 | − | 3170.52i | −0.0648670 | − | 0.231153i | ||||
\(574\) | 7616.94 | − | 8210.86i | 0.553876 | − | 0.597064i | ||||
\(575\) | −16607.5 | + | 2678.51i | −1.20449 | + | 0.194263i | ||||
\(576\) | −19137.1 | + | 11658.8i | −1.38434 | + | 0.843372i | ||||
\(577\) | −8256.36 | −0.595696 | −0.297848 | − | 0.954613i | \(-0.596269\pi\) | ||||
−0.297848 | + | 0.954613i | \(0.596269\pi\) | |||||||
\(578\) | 21815.8 | 1.56993 | ||||||||
\(579\) | −6347.02 | − | 22617.5i | −0.455567 | − | 1.62340i | ||||
\(580\) | −26914.0 | + | 2156.45i | −1.92680 | + | 0.154382i | ||||
\(581\) | 4063.31 | + | 3769.40i | 0.290146 | + | 0.269158i | ||||
\(582\) | 12531.0 | − | 3516.51i | 0.892487 | − | 0.250453i | ||||
\(583\) | 6748.99i | 0.479442i | ||||||||
\(584\) | 8133.64 | 0.576323 | ||||||||
\(585\) | 3357.77 | + | 4633.16i | 0.237311 | + | 0.327449i | ||||
\(586\) | − | 10369.9i | − | 0.731016i | ||||||
\(587\) | 22031.8i | 1.54915i | 0.632484 | + | 0.774573i | \(0.282035\pi\) | ||||
−0.632484 | + | 0.774573i | \(0.717965\pi\) | |||||||
\(588\) | −7237.27 | − | 19913.1i | −0.507585 | − | 1.39660i | ||||
\(589\) | −7354.86 | −0.514519 | ||||||||
\(590\) | 2927.01 | + | 36531.0i | 0.204242 | + | 2.54908i | ||||
\(591\) | −19092.3 | + | 5357.76i | −1.32885 | + | 0.372908i | ||||
\(592\) | 6003.00i | 0.416760i | ||||||||
\(593\) | 11710.2i | 0.810929i | 0.914111 | + | 0.405465i | \(0.132890\pi\) | ||||
−0.914111 | + | 0.405465i | \(0.867110\pi\) | |||||||
\(594\) | 13863.0 | + | 12915.6i | 0.957584 | + | 0.892142i | ||||
\(595\) | 589.163 | − | 746.811i | 0.0405938 | − | 0.0514559i | ||||
\(596\) | − | 2283.79i | − | 0.156959i | ||||||
\(597\) | −1881.29 | − | 6703.93i | −0.128971 | − | 0.459587i | ||||
\(598\) | −11376.0 | −0.777926 | ||||||||
\(599\) | − | 14539.0i | − | 0.991729i | −0.868400 | − | 0.495865i | \(-0.834851\pi\) | ||
0.868400 | − | 0.495865i | \(-0.165149\pi\) | |||||||
\(600\) | −10219.8 | + | 4730.31i | −0.695372 | + | 0.321857i | ||||
\(601\) | − | 20293.0i | − | 1.37732i | −0.725083 | − | 0.688661i | \(-0.758199\pi\) | ||
0.725083 | − | 0.688661i | \(-0.241801\pi\) | |||||||
\(602\) | −16386.8 | − | 15201.5i | −1.10943 | − | 1.02918i | ||||
\(603\) | −10560.0 | − | 17333.5i | −0.713164 | − | 1.17061i | ||||
\(604\) | −25647.0 | −1.72775 | ||||||||
\(605\) | −369.608 | − | 4612.96i | −0.0248375 | − | 0.309989i | ||||
\(606\) | 38667.9 | − | 10851.2i | 2.59204 | − | 0.727390i | ||||
\(607\) | −4143.51 | −0.277068 | −0.138534 | − | 0.990358i | \(-0.544239\pi\) | ||||
−0.138534 | + | 0.990358i | \(0.544239\pi\) | |||||||
\(608\) | − | 26072.2i | − | 1.73909i | ||||||
\(609\) | 17391.5 | + | 8928.68i | 1.15721 | + | 0.594103i | ||||
\(610\) | 15518.4 | − | 1243.40i | 1.03004 | − | 0.0825306i | ||||
\(611\) | 5180.77i | 0.343030i | ||||||||
\(612\) | −767.159 | − | 1259.24i | −0.0506709 | − | 0.0831727i | ||||
\(613\) | 13166.7i | 0.867534i | 0.901025 | + | 0.433767i | \(0.142816\pi\) | ||||
−0.901025 | + | 0.433767i | \(0.857184\pi\) | |||||||
\(614\) | −15376.1 | −1.01063 | ||||||||
\(615\) | 2727.48 | + | 7390.62i | 0.178833 | + | 0.484583i | ||||
\(616\) | −7129.06 | − | 6613.39i | −0.466295 | − | 0.432567i | ||||
\(617\) | 8241.67 | 0.537759 | 0.268880 | − | 0.963174i | \(-0.413347\pi\) | ||||
0.268880 | + | 0.963174i | \(0.413347\pi\) | |||||||
\(618\) | 38038.9 | − | 10674.6i | 2.47597 | − | 0.694816i | ||||
\(619\) | − | 12892.7i | − | 0.837162i | −0.908180 | − | 0.418581i | \(-0.862528\pi\) | ||
0.908180 | − | 0.418581i | \(-0.137472\pi\) | |||||||
\(620\) | 8147.64 | − | 652.820i | 0.527770 | − | 0.0422869i | ||||
\(621\) | 12870.2 | − | 13814.3i | 0.831665 | − | 0.892671i | ||||
\(622\) | 34230.5 | 2.20662 | ||||||||
\(623\) | 5364.35 | − | 5782.63i | 0.344973 | − | 0.371872i | ||||
\(624\) | 1686.26 | − | 473.205i | 0.108180 | − | 0.0303579i | ||||
\(625\) | 14832.7 | − | 4912.32i | 0.949294 | − | 0.314388i | ||||
\(626\) | −43411.6 | −2.77169 | ||||||||
\(627\) | −18119.1 | + | 5084.67i | −1.15408 | + | 0.323863i | ||||
\(628\) | 12081.7 | 0.767695 | ||||||||
\(629\) | −1550.87 | −0.0983106 | ||||||||
\(630\) | 24750.6 | + | 3003.59i | 1.56522 | + | 0.189946i | ||||
\(631\) | 26758.6 | 1.68818 | 0.844092 | − | 0.536198i | \(-0.180140\pi\) | ||||
0.844092 | + | 0.536198i | \(0.180140\pi\) | |||||||
\(632\) | 2193.16 | 0.138037 | ||||||||
\(633\) | 3647.95 | − | 1023.70i | 0.229057 | − | 0.0642790i | ||||
\(634\) | 3070.69 | 0.192355 | ||||||||
\(635\) | 13950.2 | − | 1117.75i | 0.871808 | − | 0.0698526i | ||||
\(636\) | 13254.4 | − | 3719.50i | 0.826368 | − | 0.231899i | ||||
\(637\) | 487.245 | + | 6483.32i | 0.0303067 | + | 0.403263i | ||||
\(638\) | 27435.1 | 1.70246 | ||||||||
\(639\) | 9001.95 | + | 14776.1i | 0.557295 | + | 0.914761i | ||||
\(640\) | 1747.69 | + | 21812.4i | 0.107943 | + | 1.34721i | ||||
\(641\) | 12483.3i | 0.769204i | 0.923082 | + | 0.384602i | \(0.125661\pi\) | ||||
−0.923082 | + | 0.384602i | \(0.874339\pi\) | |||||||
\(642\) | 8874.98 | − | 2490.54i | 0.545588 | − | 0.153105i | ||||
\(643\) | −15859.5 | −0.972689 | −0.486345 | − | 0.873767i | \(-0.661670\pi\) | ||||
−0.486345 | + | 0.873767i | \(0.661670\pi\) | |||||||
\(644\) | −20150.7 | + | 21721.9i | −1.23299 | + | 1.32914i | ||||
\(645\) | 14749.8 | − | 5443.37i | 0.900425 | − | 0.332298i | ||||
\(646\) | 2450.13 | 0.149225 | ||||||||
\(647\) | − | 26235.0i | − | 1.59413i | −0.603893 | − | 0.797066i | \(-0.706384\pi\) | ||
0.603893 | − | 0.797066i | \(-0.293616\pi\) | |||||||
\(648\) | 5796.79 | − | 11231.9i | 0.351419 | − | 0.680910i | ||||
\(649\) | − | 22259.1i | − | 1.34629i | ||||||
\(650\) | 10431.7 | − | 1682.45i | 0.629483 | − | 0.101525i | ||||
\(651\) | −5264.92 | − | 2702.97i | −0.316972 | − | 0.162731i | ||||
\(652\) | 33893.5i | 2.03584i | ||||||||
\(653\) | −11488.0 | −0.688451 | −0.344226 | − | 0.938887i | \(-0.611858\pi\) | ||||
−0.344226 | + | 0.938887i | \(0.611858\pi\) | |||||||
\(654\) | 30849.6 | − | 8657.16i | 1.84452 | − | 0.517617i | ||||
\(655\) | 1094.21 | + | 13656.5i | 0.0652740 | + | 0.814663i | ||||
\(656\) | 2411.27 | 0.143513 | ||||||||
\(657\) | 10816.9 | − | 6589.91i | 0.642324 | − | 0.391320i | ||||
\(658\) | 16549.6 | + | 15352.5i | 0.980501 | + | 0.909578i | ||||
\(659\) | − | 13746.7i | − | 0.812588i | −0.913743 | − | 0.406294i | \(-0.866821\pi\) | ||
0.913743 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(660\) | 19620.9 | − | 7241.00i | 1.15718 | − | 0.427054i | ||||
\(661\) | − | 18205.0i | − | 1.07124i | −0.844458 | − | 0.535621i | \(-0.820077\pi\) | ||
0.844458 | − | 0.535621i | \(-0.179923\pi\) | |||||||
\(662\) | 19834.7 | 1.16450 | ||||||||
\(663\) | 122.252 | + | 435.644i | 0.00716121 | + | 0.0255189i | ||||
\(664\) | − | 5188.71i | − | 0.303254i | ||||||
\(665\) | −15337.8 | + | 19441.9i | −0.894398 | + | 1.13372i | ||||
\(666\) | −21148.7 | − | 34714.2i | −1.23048 | − | 2.01974i | ||||
\(667\) | − | 27338.8i | − | 1.58705i | ||||||
\(668\) | − | 22439.8i | − | 1.29973i | ||||||
\(669\) | −16306.8 | + | 4576.09i | −0.942389 | + | 0.264457i | ||||
\(670\) | −37361.7 | + | 2993.56i | −2.15434 | + | 0.172614i | ||||
\(671\) | −9455.68 | −0.544013 | ||||||||
\(672\) | 9581.75 | − | 18663.6i | 0.550036 | − | 1.07137i | ||||
\(673\) | 2132.80i | 0.122160i | 0.998133 | + | 0.0610799i | \(0.0194544\pi\) | ||||
−0.998133 | + | 0.0610799i | \(0.980546\pi\) | |||||||
\(674\) | 18228.8i | 1.04176i | ||||||||
\(675\) | −9758.77 | + | 14571.0i | −0.556467 | + | 0.830870i | ||||
\(676\) | −21846.4 | −1.24296 | ||||||||
\(677\) | − | 995.751i | − | 0.0565285i | −0.999600 | − | 0.0282643i | \(-0.991002\pi\) | ||
0.999600 | − | 0.0282643i | \(-0.00899799\pi\) | |||||||
\(678\) | −22960.2 | + | 6443.20i | −1.30056 | + | 0.364970i | ||||
\(679\) | −7074.36 | + | 7625.98i | −0.399837 | + | 0.431013i | ||||
\(680\) | −887.673 | + | 71.1237i | −0.0500598 | + | 0.00401099i | ||||
\(681\) | −5881.00 | − | 20956.8i | −0.330926 | − | 1.17925i | ||||
\(682\) | −8305.41 | −0.466321 | ||||||||
\(683\) | −24097.2 | −1.35000 | −0.675002 | − | 0.737816i | \(-0.735857\pi\) | ||||
−0.675002 | + | 0.737816i | \(0.735857\pi\) | |||||||
\(684\) | 19971.6 | + | 32782.0i | 1.11642 | + | 1.83253i | ||||
\(685\) | 1561.28 | + | 19485.8i | 0.0870853 | + | 1.08688i | ||||
\(686\) | 22154.3 | + | 17655.9i | 1.23303 | + | 0.982662i | ||||
\(687\) | 2803.52 | + | 9990.29i | 0.155693 | + | 0.554809i | ||||
\(688\) | − | 4812.30i | − | 0.266667i | ||||||
\(689\) | −4224.36 | −0.233578 | ||||||||
\(690\) | −12071.3 | − | 32709.5i | −0.666011 | − | 1.80468i | ||||
\(691\) | 18883.3i | 1.03959i | 0.854291 | + | 0.519794i | \(0.173991\pi\) | ||||
−0.854291 | + | 0.519794i | \(0.826009\pi\) | |||||||
\(692\) | 41508.5i | 2.28023i | ||||||||
\(693\) | −14839.1 | − | 3019.11i | −0.813406 | − | 0.165493i | ||||
\(694\) | 25919.4 | 1.41771 | ||||||||
\(695\) | 23128.3 | − | 1853.12i | 1.26231 | − | 0.101141i | ||||
\(696\) | −4944.92 | − | 17621.1i | −0.269306 | − | 0.959666i | ||||
\(697\) | 622.951i | 0.0338536i | ||||||||
\(698\) | − | 12504.7i | − | 0.678095i | ||||||
\(699\) | 708.928 | − | 198.942i | 0.0383607 | − | 0.0107649i | ||||
\(700\) | 15265.4 | − | 22898.9i | 0.824253 | − | 1.23643i | ||||
\(701\) | − | 6421.10i | − | 0.345965i | −0.984925 | − | 0.172983i | \(-0.944660\pi\) | ||
0.984925 | − | 0.172983i | \(-0.0553404\pi\) | |||||||
\(702\) | −8084.17 | + | 8677.18i | −0.434640 | + | 0.466523i | ||||
\(703\) | 40374.2 | 2.16606 | ||||||||
\(704\) | − | 25133.8i | − | 1.34555i | ||||||
\(705\) | −14896.3 | + | 5497.42i | −0.795784 | + | 0.293681i | ||||
\(706\) | − | 5276.01i | − | 0.281254i | ||||||
\(707\) | −21829.9 | + | 23532.1i | −1.16124 | + | 1.25179i | ||||
\(708\) | −43714.7 | + | 12267.4i | −2.32048 | + | 0.651183i | ||||
\(709\) | −5206.72 | −0.275800 | −0.137900 | − | 0.990446i | \(-0.544035\pi\) | ||||
−0.137900 | + | 0.990446i | \(0.544035\pi\) | |||||||
\(710\) | 31849.1 | − | 2551.88i | 1.68349 | − | 0.134888i | ||||
\(711\) | 2916.67 | − | 1776.91i | 0.153845 | − | 0.0937261i | ||||
\(712\) | −7384.21 | −0.388673 | ||||||||
\(713\) | 8276.24i | 0.434709i | ||||||||
\(714\) | 1753.91 | + | 900.443i | 0.0919305 | + | 0.0471964i | ||||
\(715\) | −6397.28 | + | 512.575i | −0.334608 | + | 0.0268101i | ||||
\(716\) | 2050.63i | 0.107033i | ||||||||
\(717\) | 3793.85 | + | 13519.3i | 0.197607 | + | 0.704168i | ||||
\(718\) | − | 38838.4i | − | 2.01872i | ||||||
\(719\) | −26323.4 | −1.36537 | −0.682683 | − | 0.730715i | \(-0.739187\pi\) | ||||
−0.682683 | + | 0.730715i | \(0.739187\pi\) | |||||||
\(720\) | 3149.93 | + | 4346.38i | 0.163043 | + | 0.224972i | ||||
\(721\) | −21474.8 | + | 23149.2i | −1.10924 | + | 1.19573i | ||||
\(722\) | −33196.5 | −1.71114 | ||||||||
\(723\) | −6036.27 | − | 21510.2i | −0.310500 | − | 1.10646i | ||||
\(724\) | 25045.5i | 1.28565i | ||||||||
\(725\) | 4043.26 | + | 25069.3i | 0.207121 | + | 1.28421i | ||||
\(726\) | 9234.85 | − | 2591.52i | 0.472090 | − | 0.132480i | ||||
\(727\) | −653.079 | −0.0333169 | −0.0166584 | − | 0.999861i | \(-0.505303\pi\) | ||||
−0.0166584 | + | 0.999861i | \(0.505303\pi\) | |||||||
\(728\) | 4139.48 | − | 4462.25i | 0.210741 | − | 0.227173i | ||||
\(729\) | −1391.00 | − | 19633.8i | −0.0706700 | − | 0.997500i | ||||
\(730\) | −1868.11 | − | 23315.3i | −0.0947149 | − | 1.18211i | ||||
\(731\) | 1243.26 | 0.0629049 | ||||||||
\(732\) | 5211.21 | + | 18570.1i | 0.263131 | + | 0.937663i | ||||
\(733\) | 19283.5 | 0.971696 | 0.485848 | − | 0.874043i | \(-0.338511\pi\) | ||||
0.485848 | + | 0.874043i | \(0.338511\pi\) | |||||||
\(734\) | −32787.7 | −1.64880 | ||||||||
\(735\) | −18124.5 | + | 8280.56i | −0.909568 | + | 0.415555i | ||||
\(736\) | −29338.4 | −1.46933 | ||||||||
\(737\) | 22765.2 | 1.13781 | ||||||||
\(738\) | −13943.9 | + | 8494.98i | −0.695505 | + | 0.423719i | ||||
\(739\) | 11829.3 | 0.588832 | 0.294416 | − | 0.955677i | \(-0.404875\pi\) | ||||
0.294416 | + | 0.955677i | \(0.404875\pi\) | |||||||
\(740\) | −44726.1 | + | 3583.63i | −2.22184 | + | 0.178023i | ||||
\(741\) | −3182.62 | − | 11341.2i | −0.157782 | − | 0.562253i | ||||
\(742\) | −12518.3 | + | 13494.4i | −0.619354 | + | 0.667647i | ||||
\(743\) | 15784.6 | 0.779380 | 0.389690 | − | 0.920946i | \(-0.372582\pi\) | ||||
0.389690 | + | 0.920946i | \(0.372582\pi\) | |||||||
\(744\) | 1496.97 | + | 5334.43i | 0.0737656 | + | 0.262863i | ||||
\(745\) | −2141.01 | + | 171.546i | −0.105289 | + | 0.00843618i | ||||
\(746\) | − | 5884.67i | − | 0.288811i | ||||||
\(747\) | −4203.91 | − | 6900.43i | −0.205908 | − | 0.337983i | ||||
\(748\) | 1653.83 | 0.0808423 | ||||||||
\(749\) | −5010.36 | + | 5401.03i | −0.244425 | + | 0.263484i | ||||
\(750\) | 15906.8 | + | 28209.0i | 0.774447 | + | 1.37339i | ||||
\(751\) | −719.429 | −0.0349565 | −0.0174782 | − | 0.999847i | \(-0.505564\pi\) | ||||
−0.0174782 | + | 0.999847i | \(0.505564\pi\) | |||||||
\(752\) | 4860.09i | 0.235677i | ||||||||
\(753\) | 16544.8 | − | 4642.88i | 0.800700 | − | 0.224696i | ||||
\(754\) | 17172.3i | 0.829415i | ||||||||
\(755\) | 1926.46 | + | 24043.5i | 0.0928623 | + | 1.15899i | ||||
\(756\) | 2248.87 | + | 30806.5i | 0.108189 | + | 1.48204i | ||||
\(757\) | − | 23060.3i | − | 1.10719i | −0.832787 | − | 0.553593i | \(-0.813256\pi\) | ||
0.832787 | − | 0.553593i | \(-0.186744\pi\) | |||||||
\(758\) | −46086.4 | −2.20835 | ||||||||
\(759\) | 5721.65 | + | 20389.0i | 0.273627 | + | 0.975064i | ||||
\(760\) | 23109.0 | − | 1851.58i | 1.10296 | − | 0.0883735i | ||||
\(761\) | 19804.3 | 0.943371 | 0.471686 | − | 0.881767i | \(-0.343646\pi\) | ||||
0.471686 | + | 0.881767i | \(0.343646\pi\) | |||||||
\(762\) | 7837.13 | + | 27927.5i | 0.372584 | + | 1.32770i | ||||
\(763\) | −17416.1 | + | 18774.1i | −0.826351 | + | 0.890784i | ||||
\(764\) | − | 7533.77i | − | 0.356757i | ||||||
\(765\) | −1122.89 | + | 813.784i | −0.0530693 | + | 0.0384607i | ||||
\(766\) | − | 59437.4i | − | 2.80361i | ||||||
\(767\) | 13932.5 | 0.655897 | ||||||||
\(768\) | −10449.6 | + | 2932.41i | −0.490972 | + | 0.137779i | ||||
\(769\) | 14623.5i | 0.685746i | 0.939382 | + | 0.342873i | \(0.111400\pi\) | ||||
−0.939382 | + | 0.342873i | \(0.888600\pi\) | |||||||
\(770\) | −17320.1 | + | 21954.6i | −0.810613 | + | 1.02752i | ||||
\(771\) | 5518.88 | + | 19666.4i | 0.257792 | + | 0.918637i | ||||
\(772\) | − | 53743.5i | − | 2.50553i | ||||||
\(773\) | − | 40353.9i | − | 1.87766i | −0.344384 | − | 0.938829i | \(-0.611912\pi\) | ||
0.344384 | − | 0.938829i | \(-0.388088\pi\) | |||||||
\(774\) | 16953.9 | + | 27828.6i | 0.787331 | + | 1.29235i | ||||
\(775\) | −1224.01 | − | 7589.22i | −0.0567327 | − | 0.351758i | ||||
\(776\) | 9738.10 | 0.450486 | ||||||||
\(777\) | 28901.6 | + | 14837.8i | 1.33441 | + | 0.685077i | ||||
\(778\) | 27575.6i | 1.27074i | ||||||||
\(779\) | − | 16217.4i | − | 0.745891i | ||||||
\(780\) | 4532.32 | + | 12281.2i | 0.208055 | + | 0.563765i | ||||
\(781\) | −19406.3 | −0.889131 | ||||||||
\(782\) | − | 2757.07i | − | 0.126078i | ||||||
\(783\) | −20852.9 | − | 19427.8i | −0.951754 | − | 0.886710i | ||||
\(784\) | 457.086 | + | 6082.01i | 0.0208220 | + | 0.277059i | ||||
\(785\) | −907.511 | − | 11326.4i | −0.0412617 | − | 0.514974i | ||||
\(786\) | −27339.5 | + | 7672.12i | −1.24067 | + | 0.348162i | ||||
\(787\) | −9011.80 | −0.408178 | −0.204089 | − | 0.978952i | \(-0.565423\pi\) | ||||
−0.204089 | + | 0.978952i | \(0.565423\pi\) | |||||||
\(788\) | −45367.0 | −2.05093 | ||||||||
\(789\) | −10422.1 | + | 2924.71i | −0.470264 | + | 0.131968i | ||||
\(790\) | −503.718 | − | 6286.75i | −0.0226854 | − | 0.283130i | ||||
\(791\) | 12962.2 | − | 13972.9i | 0.582656 | − | 0.628088i | ||||
\(792\) | 7375.74 | + | 12106.8i | 0.330916 | + | 0.543176i | ||||
\(793\) | − | 5918.54i | − | 0.265036i | ||||||
\(794\) | 12141.3 | 0.542670 | ||||||||
\(795\) | −4482.55 | − | 12146.3i | −0.199975 | − | 0.541869i | ||||
\(796\) | − | 15929.8i | − | 0.709319i | ||||||
\(797\) | − | 23157.4i | − | 1.02921i | −0.857428 | − | 0.514604i | \(-0.827939\pi\) | ||
0.857428 | − | 0.514604i | \(-0.172061\pi\) | |||||||
\(798\) | −45659.8 | − | 23441.4i | −2.02549 | − | 1.03987i | ||||
\(799\) | −1255.60 | −0.0555945 | ||||||||
\(800\) | 26902.9 | − | 4338.99i | 1.18895 | − | 0.191758i | ||||
\(801\) | −9820.22 | + | 5982.72i | −0.433184 | + | 0.263907i | ||||
\(802\) | − | 28362.3i | − | 1.24876i | ||||||
\(803\) | 14206.4i | 0.624327i | ||||||||
\(804\) | −12546.3 | − | 44708.7i | −0.550342 | − | 1.96114i | ||||
\(805\) | 21877.5 | + | 17259.2i | 0.957863 | + | 0.755663i | ||||
\(806\) | − | 5198.56i | − | 0.227186i | ||||||
\(807\) | −14538.1 | + | 4079.73i | −0.634156 | + | 0.177960i | ||||
\(808\) | 30049.6 | 1.30834 | ||||||||
\(809\) | − | 612.672i | − | 0.0266259i | −0.999911 | − | 0.0133130i | \(-0.995762\pi\) | ||
0.999911 | − | 0.0133130i | \(-0.00423778\pi\) | |||||||
\(810\) | −33527.8 | − | 14037.0i | −1.45438 | − | 0.608899i | ||||
\(811\) | 20636.7i | 0.893529i | 0.894652 | + | 0.446764i | \(0.147424\pi\) | ||||
−0.894652 | + | 0.446764i | \(0.852576\pi\) | |||||||
\(812\) | 32789.7 | + | 30417.9i | 1.41711 | + | 1.31460i | ||||
\(813\) | −1005.22 | − | 3582.09i | −0.0433637 | − | 0.154526i | ||||
\(814\) | 45592.2 | 1.96315 | ||||||||
\(815\) | 31774.4 | − | 2545.89i | 1.36566 | − | 0.109422i | ||||
\(816\) | 114.685 | + | 408.678i | 0.00492007 | + | 0.0175326i | ||||
\(817\) | −32365.9 | −1.38597 | ||||||||
\(818\) | 10003.2i | 0.427571i | ||||||||
\(819\) | 1889.73 | − | 9288.15i | 0.0806259 | − | 0.396281i | ||||
\(820\) | 1439.46 | + | 17965.5i | 0.0613028 | + | 0.765100i | ||||
\(821\) | 29514.0i | 1.25462i | 0.778768 | + | 0.627312i | \(0.215845\pi\) | ||||
−0.778768 | + | 0.627312i | \(0.784155\pi\) | |||||||
\(822\) | −39009.4 | + | 10947.0i | −1.65524 | + | 0.464501i | ||||
\(823\) | 8964.57i | 0.379690i | 0.981814 | + | 0.189845i | \(0.0607986\pi\) | ||||
−0.981814 | + | 0.189845i | \(0.939201\pi\) | |||||||
\(824\) | 29560.8 | 1.24975 | ||||||||
\(825\) | −8262.10 | − | 17850.3i | −0.348666 | − | 0.753292i | ||||
\(826\) | 41287.0 | − | 44506.3i | 1.73917 | − | 1.87478i | ||||
\(827\) | −36886.7 | −1.55100 | −0.775500 | − | 0.631348i | \(-0.782502\pi\) | ||||
−0.775500 | + | 0.631348i | \(0.782502\pi\) | |||||||
\(828\) | 36888.7 | − | 22473.6i | 1.54828 | − | 0.943249i | ||||
\(829\) | − | 29077.8i | − | 1.21823i | −0.793081 | − | 0.609116i | \(-0.791525\pi\) | ||
0.793081 | − | 0.609116i | \(-0.208475\pi\) | |||||||
\(830\) | −14873.6 | + | 1191.73i | −0.622011 | + | 0.0498379i | ||||
\(831\) | 142.135 | + | 506.495i | 0.00593334 | + | 0.0211434i | ||||
\(832\) | 15731.9 | 0.655535 | ||||||||
\(833\) | −1571.29 | + | 118.088i | −0.0653563 | + | 0.00491177i | ||||
\(834\) | 12993.3 | + | 46301.3i | 0.539472 | + | 1.92240i | ||||
\(835\) | −21036.8 | + | 1685.55i | −0.871868 | + | 0.0698574i | ||||
\(836\) | −43054.5 | −1.78119 | ||||||||
\(837\) | 6312.79 | + | 5881.37i | 0.260695 | + | 0.242879i | ||||
\(838\) | 56036.2 | 2.30995 | ||||||||
\(839\) | 32262.6 | 1.32757 | 0.663784 | − | 0.747924i | \(-0.268949\pi\) | ||||
0.663784 | + | 0.747924i | \(0.268949\pi\) | |||||||
\(840\) | 17222.8 | + | 7167.30i | 0.707434 | + | 0.294399i | ||||
\(841\) | −16879.4 | −0.692091 | ||||||||
\(842\) | 17408.3 | 0.712505 | ||||||||
\(843\) | 10873.9 | + | 38749.1i | 0.444268 | + | 1.58314i | ||||
\(844\) | 8668.25 | 0.353523 | ||||||||
\(845\) | 1640.98 | + | 20480.5i | 0.0668063 | + | 0.833789i | ||||
\(846\) | −17122.2 | − | 28104.9i | −0.695833 | − | 1.14216i | ||||
\(847\) | −5213.52 | + | 5620.03i | −0.211498 | + | 0.227989i | ||||
\(848\) | −3962.88 | −0.160478 | ||||||||
\(849\) | 1906.70 | − | 535.066i | 0.0770762 | − | 0.0216295i | ||||
\(850\) | 407.756 | + | 2528.20i | 0.0164540 | + | 0.102019i | ||||
\(851\) | − | 45432.1i | − | 1.83007i | ||||||
\(852\) | 10695.2 | + | 38112.1i | 0.430060 | + | 1.53251i | ||||
\(853\) | −14995.9 | −0.601935 | −0.300968 | − | 0.953634i | \(-0.597310\pi\) | ||||
−0.300968 | + | 0.953634i | \(0.597310\pi\) | |||||||
\(854\) | −18906.3 | − | 17538.8i | −0.757566 | − | 0.702768i | ||||
\(855\) | 29232.3 | − | 21185.4i | 1.16927 | − | 0.847398i | ||||
\(856\) | 6896.93 | 0.275388 | ||||||||
\(857\) | − | 36795.5i | − | 1.46664i | −0.679884 | − | 0.733319i | \(-0.737970\pi\) | ||
0.679884 | − | 0.733319i | \(-0.262030\pi\) | |||||||
\(858\) | −3593.94 | − | 12806.9i | −0.143001 | − | 0.509583i | ||||
\(859\) | 6908.88i | 0.274421i | 0.990542 | + | 0.137211i | \(0.0438137\pi\) | ||||
−0.990542 | + | 0.137211i | \(0.956186\pi\) | |||||||
\(860\) | 35854.6 | − | 2872.81i | 1.42167 | − | 0.113909i | ||||
\(861\) | 5960.04 | − | 11609.1i | 0.235909 | − | 0.459509i | ||||
\(862\) | − | 22431.4i | − | 0.886330i | ||||||
\(863\) | −4307.42 | −0.169903 | −0.0849515 | − | 0.996385i | \(-0.527074\pi\) | ||||
−0.0849515 | + | 0.996385i | \(0.527074\pi\) | |||||||
\(864\) | −20848.8 | + | 22378.2i | −0.820940 | + | 0.881158i | ||||
\(865\) | 38913.4 | − | 3117.89i | 1.52959 | − | 0.122557i | ||||
\(866\) | 66288.3 | 2.60112 | ||||||||
\(867\) | 24473.6 | − | 6867.90i | 0.958672 | − | 0.269027i | ||||
\(868\) | −9926.39 | − | 9208.37i | −0.388161 | − | 0.360084i | ||||
\(869\) | 3830.64i | 0.149534i | ||||||||
\(870\) | −49375.7 | + | 18221.9i | −1.92413 | + | 0.710092i | ||||
\(871\) | 14249.3i | 0.554327i | ||||||||
\(872\) | 23973.9 | 0.931030 | ||||||||
\(873\) | 12950.6 | − | 7889.85i | 0.502076 | − | 0.305878i | ||||
\(874\) | 71775.4i | 2.77785i | ||||||||
\(875\) | −22613.9 | − | 12591.0i | −0.873703 | − | 0.486459i | ||||
\(876\) | 27900.1 | − | 7829.46i | 1.07609 | − | 0.301978i | ||||
\(877\) | 1580.51i | 0.0608552i | 0.999537 | + | 0.0304276i | \(0.00968690\pi\) | ||||
−0.999537 | + | 0.0304276i | \(0.990313\pi\) | |||||||
\(878\) | 50322.9i | 1.93430i | ||||||||
\(879\) | −3264.57 | − | 11633.2i | −0.125269 | − | 0.446393i | ||||
\(880\) | −6001.30 | + | 480.847i | −0.229891 | + | 0.0184197i | ||||
\(881\) | −29644.9 | −1.13367 | −0.566834 | − | 0.823832i | \(-0.691832\pi\) | ||||
−0.566834 | + | 0.823832i | \(0.691832\pi\) | |||||||
\(882\) | −24070.3 | − | 33560.7i | −0.918923 | − | 1.28123i | ||||
\(883\) | 16316.4i | 0.621847i | 0.950435 | + | 0.310923i | \(0.100638\pi\) | ||||
−0.950435 | + | 0.310923i | \(0.899362\pi\) | |||||||
\(884\) | 1035.17i | 0.0393854i | ||||||||
\(885\) | 14784.1 | + | 40060.2i | 0.561538 | + | 1.52159i | ||||
\(886\) | −28569.1 | −1.08329 | ||||||||
\(887\) | − | 16452.1i | − | 0.622783i | −0.950282 | − | 0.311392i | \(-0.899205\pi\) | ||
0.950282 | − | 0.311392i | \(-0.100795\pi\) | |||||||
\(888\) | −8217.56 | − | 29283.1i | −0.310544 | − | 1.10662i | ||||
\(889\) | −16995.8 | − | 15766.4i | −0.641192 | − | 0.594812i | ||||
\(890\) | 1695.98 | + | 21167.0i | 0.0638759 | + | 0.797214i | ||||
\(891\) | 19617.9 | + | 10124.8i | 0.737626 | + | 0.380690i | ||||
\(892\) | −38748.2 | −1.45447 | ||||||||
\(893\) | 32687.4 | 1.22491 | ||||||||
\(894\) | −1202.80 | − | 4286.16i | −0.0449974 | − | 0.160347i | ||||
\(895\) | 1922.43 | − | 154.032i | 0.0717985 | − | 0.00575277i | ||||
\(896\) | 24652.1 | − | 26574.4i | 0.919163 | − | 0.990834i | ||||
\(897\) | −12762.0 | + | 3581.32i | −0.475039 | + | 0.133307i | ||||
\(898\) | 25185.2i | 0.935905i | ||||||||
\(899\) | 12493.2 | 0.463482 | ||||||||
\(900\) | −30502.8 | + | 26063.6i | −1.12973 | + | 0.965319i | ||||
\(901\) | − | 1023.81i | − | 0.0378557i | ||||||
\(902\) | − | 18313.4i | − | 0.676018i | ||||||
\(903\) | −23168.9 | − | 11894.8i | −0.853835 | − | 0.438353i | ||||
\(904\) | −17842.8 | −0.656465 | ||||||||
\(905\) | 23479.6 | − | 1881.28i | 0.862419 | − | 0.0691003i | ||||
\(906\) | −48133.6 | + | 13507.5i | −1.76505 | + | 0.495315i | ||||
\(907\) | 15972.5i | 0.584737i | 0.956306 | + | 0.292369i | \(0.0944434\pi\) | ||||
−0.956306 | + | 0.292369i | \(0.905557\pi\) | |||||||
\(908\) | − | 49797.5i | − | 1.82003i | ||||||
\(909\) | 39962.8 | − | 24346.3i | 1.45818 | − | 0.888358i | ||||
\(910\) | −13741.9 | − | 10841.1i | −0.500593 | − | 0.394920i | ||||
\(911\) | 47647.5i | 1.73285i | 0.499303 | + | 0.866427i | \(0.333589\pi\) | ||||
−0.499303 | + | 0.866427i | \(0.666411\pi\) | |||||||
\(912\) | −2985.62 | − | 10639.2i | −0.108403 | − | 0.386293i | ||||
\(913\) | 9062.74 | 0.328514 | ||||||||
\(914\) | 17960.6i | 0.649983i | ||||||||
\(915\) | 17017.6 | − | 6280.29i | 0.614848 | − | 0.226907i | ||||
\(916\) | 23738.9i | 0.856282i | ||||||||
\(917\) | 15434.4 | − | 16637.9i | 0.555824 | − | 0.599163i | ||||
\(918\) | −2102.99 | − | 1959.27i | −0.0756088 | − | 0.0704416i | ||||
\(919\) | −40628.7 | −1.45834 | −0.729171 | − | 0.684331i | \(-0.760094\pi\) | ||||
−0.729171 | + | 0.684331i | \(0.760094\pi\) | |||||||
\(920\) | −2083.54 | − | 26003.9i | −0.0746654 | − | 0.931874i | ||||
\(921\) | −17249.4 | + | 4840.60i | −0.617142 | + | 0.173185i | ||||
\(922\) | 19274.9 | 0.688487 | ||||||||
\(923\) | − | 12146.9i | − | 0.433174i | ||||||
\(924\) | −30820.3 | − | 15822.9i | −1.09731 | − | 0.563350i | ||||
\(925\) | 6719.16 | + | 41660.7i | 0.238837 | + | 1.48086i | ||||
\(926\) | − | 58366.2i | − | 2.07131i | ||||||
\(927\) | 39312.7 | − | 23950.3i | 1.39288 | − | 0.848576i | ||||
\(928\) | 44286.9i | 1.56658i | ||||||||
\(929\) | −42333.4 | −1.49506 | −0.747532 | − | 0.664226i | \(-0.768761\pi\) | ||||
−0.747532 | + | 0.664226i | \(0.768761\pi\) | |||||||
\(930\) | 14947.5 | − | 5516.30i | 0.527039 | − | 0.194502i | ||||
\(931\) | 40905.6 | − | 3074.21i | 1.43999 | − | 0.108220i | ||||
\(932\) | 1684.55 | 0.0592052 | ||||||||
\(933\) | 38400.9 | − | 10776.2i | 1.34747 | − | 0.378132i | ||||
\(934\) | 11260.6i | 0.394495i | ||||||||
\(935\) | −124.227 | − | 1550.43i | −0.00434508 | − | 0.0542295i | ||||
\(936\) | −7577.92 | + | 4616.66i | −0.264628 | + | 0.161218i | ||||
\(937\) | −14777.6 | −0.515224 | −0.257612 | − | 0.966248i | \(-0.582936\pi\) | ||||
−0.257612 | + | 0.966248i | \(0.582936\pi\) | |||||||
\(938\) | 45518.3 | + | 42225.8i | 1.58446 | + | 1.46985i | ||||
\(939\) | −48700.5 | + | 13666.5i | −1.69252 | + | 0.474963i | ||||
\(940\) | −36210.7 | + | 2901.34i | −1.25645 | + | 0.100672i | ||||
\(941\) | −37729.8 | −1.30707 | −0.653537 | − | 0.756894i | \(-0.726716\pi\) | ||||
−0.653537 | + | 0.756894i | \(0.726716\pi\) | |||||||
\(942\) | 22674.6 | − | 6363.05i | 0.784266 | − | 0.220084i | ||||
\(943\) | −18249.1 | −0.630192 | ||||||||
\(944\) | 13070.1 | 0.450631 | ||||||||
\(945\) | 28711.5 | − | 4422.29i | 0.988345 | − | 0.152230i | ||||
\(946\) | −36548.9 | −1.25614 | ||||||||
\(947\) | −13860.2 | −0.475602 | −0.237801 | − | 0.971314i | \(-0.576427\pi\) | ||||
−0.237801 | + | 0.971314i | \(0.576427\pi\) | |||||||
\(948\) | 7523.01 | − | 2111.14i | 0.257738 | − | 0.0723276i | ||||
\(949\) | −8892.17 | −0.304164 | ||||||||
\(950\) | −10615.2 | − | 65817.2i | −0.362529 | − | 2.24778i | ||||
\(951\) | 3444.80 | − | 966.695i | 0.117461 | − | 0.0329624i | ||||
\(952\) | 1081.46 | + | 1003.24i | 0.0368177 | + | 0.0341545i | ||||
\(953\) | 54882.6 | 1.86550 | 0.932750 | − | 0.360523i | \(-0.117402\pi\) | ||||
0.932750 | + | 0.360523i | \(0.117402\pi\) | |||||||
\(954\) | 22916.5 | − | 13961.3i | 0.777725 | − | 0.473810i | ||||
\(955\) | −7062.76 | + | 565.896i | −0.239315 | + | 0.0191748i | ||||
\(956\) | 32124.5i | 1.08680i | ||||||||
\(957\) | 30777.6 | − | 8636.94i | 1.03960 | − | 0.291737i | ||||
\(958\) | −14161.6 | −0.477600 | ||||||||
\(959\) | 22022.7 | − | 23739.9i | 0.741553 | − | 0.799374i | ||||
\(960\) | 16693.4 | + | 45234.0i | 0.561228 | + | 1.52075i | ||||
\(961\) | 26009.0 | 0.873048 | ||||||||
\(962\) | 28537.3i | 0.956423i | ||||||||
\(963\) | 9172.18 | − | 5587.92i | 0.306926 | − | 0.186987i | ||||
\(964\) | − | 51112.3i | − | 1.70769i | ||||||
\(965\) | −50383.5 | + | 4036.92i | −1.68073 | + | 0.134666i | ||||
\(966\) | −26378.1 | + | 51379.9i | −0.878571 | + | 1.71130i | ||||
\(967\) | − | 21656.2i | − | 0.720183i | −0.932917 | − | 0.360092i | \(-0.882745\pi\) | ||
0.932917 | − | 0.360092i | \(-0.117255\pi\) | |||||||
\(968\) | 7176.58 | 0.238289 | ||||||||
\(969\) | 2748.63 | − | 771.333i | 0.0911237 | − | 0.0255715i | ||||
\(970\) | −2236.62 | − | 27914.5i | −0.0740345 | − | 0.924001i | ||||
\(971\) | 4409.47 | 0.145733 | 0.0728664 | − | 0.997342i | \(-0.476785\pi\) | ||||
0.0728664 | + | 0.997342i | \(0.476785\pi\) | |||||||
\(972\) | 9072.43 | − | 44107.7i | 0.299381 | − | 1.45551i | ||||
\(973\) | −28177.5 | − | 26139.3i | −0.928395 | − | 0.861241i | ||||
\(974\) | − | 17712.6i | − | 0.582699i | ||||||
\(975\) | 11172.9 | − | 5171.45i | 0.366995 | − | 0.169866i | ||||
\(976\) | − | 5552.19i | − | 0.182092i | ||||||
\(977\) | −36452.4 | −1.19367 | −0.596834 | − | 0.802364i | \(-0.703575\pi\) | ||||
−0.596834 | + | 0.802364i | \(0.703575\pi\) | |||||||
\(978\) | 17850.6 | + | 63610.4i | 0.583640 | + | 2.07979i | ||||
\(979\) | − | 12897.5i | − | 0.421047i | ||||||
\(980\) | −45041.9 | + | 7036.37i | −1.46817 | + | 0.229356i | ||||
\(981\) | 31882.7 | − | 19423.7i | 1.03765 | − | 0.632164i | ||||
\(982\) | 48406.2i | 1.57302i | ||||||||
\(983\) | − | 2111.09i | − | 0.0684979i | −0.999413 | − | 0.0342489i | \(-0.989096\pi\) | ||
0.999413 | − | 0.0342489i | \(-0.0109039\pi\) | |||||||
\(984\) | −11762.4 | + | 3300.81i | −0.381068 | + | 0.106937i | ||||
\(985\) | 3407.72 | + | 42530.6i | 0.110232 | + | 1.37577i | ||||
\(986\) | −4161.85 | −0.134422 | ||||||||
\(987\) | 23399.0 | + | 12012.9i | 0.754608 | + | 0.387410i | ||||
\(988\) | − | 26948.9i | − | 0.867772i | ||||||
\(989\) | 36420.6i | 1.17099i | ||||||||
\(990\) | 33010.3 | − | 23923.4i | 1.05973 | − | 0.768016i | ||||
\(991\) | 5791.29 | 0.185637 | 0.0928186 | − | 0.995683i | \(-0.470412\pi\) | ||||
0.0928186 | + | 0.995683i | \(0.470412\pi\) | |||||||
\(992\) | − | 13406.9i | − | 0.429103i | ||||||
\(993\) | 22251.2 | − | 6244.24i | 0.711099 | − | 0.199552i | ||||
\(994\) | −38802.3 | − | 35995.5i | −1.23816 | − | 1.14860i | ||||
\(995\) | −14933.9 | + | 1196.56i | −0.475816 | + | 0.0381242i | ||||
\(996\) | −4994.66 | − | 17798.4i | −0.158897 | − | 0.566228i | ||||
\(997\) | −15024.7 | −0.477269 | −0.238635 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238635 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(998\) | −21417.4 | −0.679314 | ||||||||
\(999\) | −34653.8 | − | 32285.5i | −1.09750 | − | 1.02249i |
(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 | 105.4.g.b.104.35 | yes | 40 | |
3.2 | odd | 2 | inner | 105.4.g.b.104.8 | yes | 40 | |
5.4 | even | 2 | inner | 105.4.g.b.104.6 | yes | 40 | |
7.6 | odd | 2 | inner | 105.4.g.b.104.34 | yes | 40 | |
15.14 | odd | 2 | inner | 105.4.g.b.104.33 | yes | 40 | |
21.20 | even | 2 | inner | 105.4.g.b.104.5 | ✓ | 40 | |
35.34 | odd | 2 | inner | 105.4.g.b.104.7 | yes | 40 | |
105.104 | even | 2 | inner | 105.4.g.b.104.36 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.g.b.104.5 | ✓ | 40 | 21.20 | even | 2 | inner | |
105.4.g.b.104.6 | yes | 40 | 5.4 | even | 2 | inner | |
105.4.g.b.104.7 | yes | 40 | 35.34 | odd | 2 | inner | |
105.4.g.b.104.8 | yes | 40 | 3.2 | odd | 2 | inner | |
105.4.g.b.104.33 | yes | 40 | 15.14 | odd | 2 | inner | |
105.4.g.b.104.34 | yes | 40 | 7.6 | odd | 2 | inner | |
105.4.g.b.104.35 | yes | 40 | 1.1 | even | 1 | trivial | |
105.4.g.b.104.36 | yes | 40 | 105.104 | even | 2 | inner |