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 | 104.5 | ||
Character | \(\chi\) | \(=\) | 105.104 |
Dual form | 105.4.g.b.104.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | \(-0.789064\pi\) | ||||
−0.788350 | + | 0.615227i | \(0.789064\pi\) | |||||||
\(3\) | −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 | \(-0.863769\pi\) | ||
0.909805 | − | 0.415035i | \(-0.136231\pi\) | |||||||
\(12\) | −59.4737 | − | 16.6898i | −1.43071 | − | 0.401493i | ||||
\(13\) | 18.9551 | 0.404400 | 0.202200 | − | 0.979344i | \(-0.435191\pi\) | ||||
0.202200 | + | 0.979344i | \(0.435191\pi\) | |||||||
\(14\) | −56.1708 | − | 60.5506i | −1.07230 | − | 1.15592i | ||||
\(15\) | −11.1790 | + | 57.0090i | −0.192427 | + | 0.981311i | ||||
\(16\) | −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 | \(-0.743212\pi\) | ||
0.691869 | − | 0.722023i | \(-0.256788\pi\) | |||||||
\(20\) | −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 | \(-0.708841\pi\) | ||||
−0.610026 | + | 0.792381i | \(0.708841\pi\) | |||||||
\(24\) | 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 | \(0.225400\pi\) | ||||
−0.759590 | + | 0.650402i | \(0.774600\pi\) | |||||||
\(30\) | 49.8536 | − | 254.236i | 0.303399 | − | 1.54723i | ||||
\(31\) | − | 61.4983i | − | 0.356304i | −0.984003 | − | 0.178152i | \(-0.942988\pi\) | ||
0.984003 | − | 0.178152i | \(-0.0570119\pi\) | |||||||
\(32\) | 218.005 | 1.20432 | ||||||||
\(33\) | −42.5159 | + | 151.505i | −0.224275 | + | 0.799198i | ||||
\(34\) | 20.4870i | 0.103338i | ||||||||
\(35\) | 140.071 | − | 152.497i | 0.676465 | − | 0.736475i | ||||
\(36\) | 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 | ||||||
\(45\) | 135.964 | − | 269.516i | 0.450408 | − | 0.892823i | ||||
\(46\) | 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 | \(-0.593255\pi\) | ||||
−0.288796 | + | 0.957391i | \(0.593255\pi\) | |||||||
\(54\) | 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 | \(0.801050\pi\) | |||||||
\(60\) | −132.894 | + | 677.715i | −0.285943 | + | 1.45821i | ||||
\(61\) | − | 312.240i | − | 0.655381i | −0.944785 | − | 0.327691i | \(-0.893730\pi\) | ||
0.944785 | − | 0.327691i | \(-0.106270\pi\) | |||||||
\(62\) | 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 | ||||
\(70\) | −624.656 | + | 680.071i | −1.06658 | + | 1.16120i | ||||
\(71\) | − | 640.823i | − | 1.07115i | −0.844487 | − | 0.535576i | \(-0.820095\pi\) | ||
0.844487 | − | 0.535576i | \(-0.179905\pi\) | |||||||
\(72\) | −399.783 | − | 243.558i | −0.654373 | − | 0.398660i | ||||
\(73\) | −469.117 | −0.752137 | −0.376069 | − | 0.926592i | \(-0.622724\pi\) | ||||
−0.376069 | + | 0.926592i | \(0.622724\pi\) | |||||||
\(74\) | 1505.52i | 2.36504i | ||||||||
\(75\) | 645.327 | + | 73.6793i | 0.993545 | + | 0.113437i | ||||
\(76\) | − | 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 | \(0.581622\pi\) | |||||||
\(90\) | −606.343 | + | 1201.93i | −0.710158 | + | 1.40771i | ||||
\(91\) | 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 | \(-0.594972\pi\) | ||||
−0.293957 | + | 0.955819i | \(0.594972\pi\) | |||||||
\(98\) | 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 | \(-0.803540\pi\) | ||||
−0.815504 | + | 0.578751i | \(0.803540\pi\) | |||||||
\(104\) | −328.647 | −0.309870 | ||||||||
\(105\) | −914.854 | + | 566.275i | −0.850292 | + | 0.526312i | ||||
\(106\) | 993.867 | 0.910688 | ||||||||
\(107\) | −397.788 | −0.359399 | −0.179699 | − | 0.983722i | \(-0.557512\pi\) | ||||
−0.179699 | + | 0.983722i | \(0.557512\pi\) | |||||||
\(108\) | −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 | \(-0.359090\pi\) | ||||
0.428364 | + | 0.903606i | \(0.359090\pi\) | |||||||
\(114\) | 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 | ||||
\(120\) | 193.823 | − | 988.433i | 0.147446 | − | 0.751926i | ||||
\(121\) | 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 | ||||||||
\(135\) | −1058.60 | + | 1157.47i | −0.674886 | + | 0.737922i | ||||
\(136\) | 79.6503i | 0.0502203i | ||||||||
\(137\) | 1748.45 | 1.09037 | 0.545183 | − | 0.838317i | \(-0.316460\pi\) | ||||
0.545183 | + | 0.838317i | \(0.316460\pi\) | |||||||
\(138\) | −3002.52 | − | 842.579i | −1.85211 | − | 0.519747i | ||||
\(139\) | − | 2075.28i | − | 1.26635i | −0.774007 | − | 0.633177i | \(-0.781750\pi\) | ||
0.774007 | − | 0.633177i | \(-0.218250\pi\) | |||||||
\(140\) | 1665.14 | − | 1812.86i | 1.00521 | − | 1.09439i | ||||
\(141\) | −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 | \(0.0168188\pi\) | ||||
−0.998604 | + | 0.0528133i | \(0.983181\pi\) | |||||||
\(150\) | −2877.89 | − | 328.579i | −1.56652 | − | 0.178856i | ||||
\(151\) | −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 | \(-0.583166\pi\) | ||||
−0.258312 | + | 0.966061i | \(0.583166\pi\) | |||||||
\(158\) | −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 | ||||||||
\(165\) | 1726.43 | + | 338.537i | 0.814558 | + | 0.159728i | ||||
\(166\) | 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 | ||||
\(175\) | −1824.59 | − | 1424.86i | −0.788150 | − | 0.615483i | ||||
\(176\) | 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 | \(-0.988534\pi\) | ||
0.999351 | − | 0.0360143i | \(-0.0114662\pi\) | |||||||
\(180\) | 1616.32 | − | 3203.96i | 0.669298 | − | 1.32672i | ||||
\(181\) | − | 2106.81i | − | 0.865182i | −0.901590 | − | 0.432591i | \(-0.857599\pi\) | ||
0.901590 | − | 0.432591i | \(-0.142401\pi\) | |||||||
\(182\) | −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 | \(0.0383026\pi\) | ||||
−0.992769 | + | 0.120041i | \(0.961697\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −211.899 | + | 1080.61i | −0.0778174 | + | 0.396842i | ||||
\(196\) | −305.580 | + | 4066.07i | −0.111363 | + | 1.48180i | ||||
\(197\) | 3816.25 | 1.38018 | 0.690092 | − | 0.723722i | \(-0.257570\pi\) | ||||
0.690092 | + | 0.723722i | \(0.257570\pi\) | |||||||
\(198\) | −1897.13 | + | 3114.00i | −0.680924 | + | 1.11769i | ||||
\(199\) | 1340.01i | 0.477341i | 0.971101 | + | 0.238670i | \(0.0767115\pi\) | ||||
−0.971101 | + | 0.238670i | \(0.923288\pi\) | |||||||
\(200\) | 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 | ||||||||
\(210\) | 4079.86 | − | 2525.35i | 1.34065 | − | 0.829836i | ||||
\(211\) | 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 | \(-0.337217\pi\) | ||||
0.489396 | + | 0.872061i | \(0.337217\pi\) | |||||||
\(224\) | 2745.89 | + | 2959.99i | 0.819050 | + | 0.882915i | ||||
\(225\) | −3125.06 | − | 1274.61i | −0.925944 | − | 0.377661i | ||||
\(226\) | −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 | \(-0.906970\pi\) | ||
0.957594 | − | 0.288120i | \(-0.0930302\pi\) | |||||||
\(230\) | −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 | \(-0.506342\pi\) | ||||
−0.0199213 | + | 0.999802i | \(0.506342\pi\) | |||||||
\(234\) | −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 | \(-0.880835\pi\) | ||
0.930739 | − | 0.365684i | \(-0.119165\pi\) | |||||||
\(240\) | 198.783 | − | 1013.72i | 0.0534640 | − | 0.272648i | ||||
\(241\) | 4299.54i | 1.14920i | 0.818434 | + | 0.574601i | \(0.194843\pi\) | ||||
−0.818434 | + | 0.574601i | \(0.805157\pi\) | |||||||
\(242\) | −1845.90 | −0.490326 | ||||||||
\(243\) | −763.168 | − | 3710.32i | −0.201470 | − | 0.979495i | ||||
\(244\) | − | 3711.86i | − | 0.973884i | ||||||
\(245\) | 3834.81 | − | 18.9455i | 0.999988 | − | 0.00494033i | ||||
\(246\) | −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 | ||||||
\(255\) | 261.895 | + | 51.3554i | 0.0643157 | + | 0.0126118i | ||||
\(256\) | −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 | \(-0.421470\pi\) | ||||
0.244215 | + | 0.969721i | \(0.421470\pi\) | |||||||
\(264\) | 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 | \(0.606822\pi\) | |||||||
\(270\) | 4720.90 | − | 5161.85i | 1.06409 | − | 1.16348i | ||||
\(271\) | 716.004i | 0.160495i | 0.996775 | + | 0.0802475i | \(0.0255711\pi\) | ||||
−0.996775 | + | 0.0802475i | \(0.974429\pi\) | |||||||
\(272\) | 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 | ||||
\(280\) | −2428.57 | + | 2644.01i | −0.518339 | + | 0.564322i | ||||
\(281\) | − | 7745.33i | − | 1.64430i | −0.569272 | − | 0.822149i | \(-0.692775\pi\) | ||
0.569272 | − | 0.822149i | \(-0.307225\pi\) | |||||||
\(282\) | 1711.23 | − | 6097.95i | 0.361356 | − | 1.28769i | ||||
\(283\) | −381.119 | −0.0800536 | −0.0400268 | − | 0.999199i | \(-0.512744\pi\) | ||||
−0.0400268 | + | 0.999199i | \(0.512744\pi\) | |||||||
\(284\) | − | 7618.01i | − | 1.59171i | ||||||
\(285\) | 6817.97 | + | 1336.95i | 1.41706 | + | 0.277873i | ||||
\(286\) | 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 | ||||||||
\(300\) | 7671.55 | + | 875.889i | 1.47639 | + | 0.168565i | ||||
\(301\) | −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 | \(-0.396152\pi\) | ||||
0.320491 | + | 0.947252i | \(0.396152\pi\) | |||||||
\(308\) | 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 | \(-0.158243\pi\) | ||||
0.878952 | + | 0.476910i | \(0.158243\pi\) | |||||||
\(314\) | 4532.30 | 0.814562 | ||||||||
\(315\) | 5371.93 | − | 1548.62i | 0.960870 | − | 0.276999i | ||||
\(316\) | 1503.73 | 0.267694 | ||||||||
\(317\) | −688.561 | −0.121998 | −0.0609991 | − | 0.998138i | \(-0.519429\pi\) | ||||
−0.0609991 | + | 0.998138i | \(0.519429\pi\) | |||||||
\(318\) | −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 | ||||
\(330\) | −7699.13 | − | 1509.73i | −1.28431 | − | 0.251843i | ||||
\(331\) | 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 | ||||||
\(345\) | 1504.43 | − | 7672.09i | 0.234771 | − | 1.19725i | ||||
\(346\) | − | 15571.4i | − | 2.41943i | ||||||
\(347\) | −5812.08 | −0.899161 | −0.449580 | − | 0.893240i | \(-0.648427\pi\) | ||||
−0.449580 | + | 0.893240i | \(0.648427\pi\) | |||||||
\(348\) | 3390.46 | − | 12081.9i | 0.522264 | − | 1.86108i | ||||
\(349\) | 2804.01i | 0.430073i | 0.976606 | + | 0.215036i | \(0.0689870\pi\) | ||||
−0.976606 | + | 0.215036i | \(0.931013\pi\) | |||||||
\(350\) | 8136.92 | + | 6354.29i | 1.24268 | + | 0.970431i | ||||
\(351\) | −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 | \(0.221137\pi\) | ||||
−0.768232 | + | 0.640171i | \(0.778863\pi\) | |||||||
\(360\) | −2357.37 | + | 4672.91i | −0.345123 | + | 0.684122i | ||||
\(361\) | −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 | \(-0.324864\pi\) | ||||
0.522864 | + | 0.852416i | \(0.324864\pi\) | |||||||
\(368\) | 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 | ||||||||
\(375\) | 244.884 | − | 7257.71i | 0.0337220 | − | 0.999431i | ||||
\(376\) | 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 | ||||
\(385\) | −4618.11 | − | 4241.81i | −0.611326 | − | 0.561513i | ||||
\(386\) | 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 | \(-0.867977\pi\) | ||
0.915212 | − | 0.402973i | \(-0.132023\pi\) | |||||||
\(390\) | 944.979 | − | 4819.08i | 0.122695 | − | 0.625701i | ||||
\(391\) | 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 | \(-0.555052\pi\) | ||||
−0.172091 | + | 0.985081i | \(0.555052\pi\) | |||||||
\(398\) | − | 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 | \(0.129604\pi\) | ||||
−0.918248 | + | 0.396005i | \(0.870396\pi\) | |||||||
\(402\) | 4706.60 | − | 16771.9i | 0.583941 | − | 2.08086i | ||||
\(403\) | − | 1165.71i | − | 0.144089i | ||||||
\(404\) | 20603.4 | 2.53727 | ||||||||
\(405\) | 6921.07 | − | 4304.52i | 0.849162 | − | 0.528132i | ||||
\(406\) | 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 | \(-0.956707\pi\) | ||
0.990765 | − | 0.135591i | \(-0.0432932\pi\) | |||||||
\(410\) | −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 | \(0.238341\pi\) | |||||||
\(420\) | −10875.6 | + | 6731.79i | −1.26352 | + | 0.782090i | ||||
\(421\) | 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 | \(0.0906897\pi\) | ||||
−0.959687 | + | 0.281071i | \(0.909310\pi\) | |||||||
\(432\) | 1700.56 | + | 1825.30i | 0.189394 | + | 0.203287i | ||||
\(433\) | −14864.3 | −1.64972 | −0.824862 | − | 0.565334i | \(-0.808747\pi\) | ||||
−0.824862 | + | 0.565334i | \(0.808747\pi\) | |||||||
\(434\) | −3723.76 | + | 3454.41i | −0.411858 | + | 0.382066i | ||||
\(435\) | −11581.2 | − | 2270.97i | −1.27649 | − | 0.250309i | ||||
\(436\) | 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 | \(-0.789801\pi\) | ||
0.789771 | − | 0.613402i | \(-0.210199\pi\) | |||||||
\(440\) | 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 | \(-0.388377\pi\) | ||||
0.343532 | + | 0.939141i | \(0.388377\pi\) | |||||||
\(444\) | −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 | \(-0.904083\pi\) | ||
0.954942 | − | 0.296792i | \(-0.0959169\pi\) | |||||||
\(450\) | 13936.5 | + | 5684.21i | 1.45994 | + | 0.595458i | ||||
\(451\) | 4106.52i | 0.428755i | ||||||||
\(452\) | 12233.9 | 1.27308 | ||||||||
\(453\) | 10793.3 | + | 3028.86i | 1.11946 | + | 0.314147i | ||||
\(454\) | 18680.9i | 1.93114i | ||||||||
\(455\) | 2655.05 | − | 2890.59i | 0.273562 | − | 0.297831i | ||||
\(456\) | 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 | ||||||
\(465\) | 3505.96 | + | 687.489i | 0.349645 | + | 0.0685624i | ||||
\(466\) | 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 | \(0.548396\pi\) | |||||||
\(480\) | −2437.07 | + | 12428.2i | −0.231743 | + | 1.18181i | ||||
\(481\) | − | 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 | ||||
\(490\) | −17101.6 | + | 84.4888i | −1.57668 | + | 0.00778941i | ||||
\(491\) | − | 10854.4i | − | 0.997665i | −0.866698 | − | 0.498833i | \(-0.833762\pi\) | ||
0.866698 | − | 0.498833i | \(-0.166238\pi\) | |||||||
\(492\) | 8064.83 | + | 2263.19i | 0.739005 | + | 0.207383i | ||||
\(493\) | 933.239 | 0.0852555 | ||||||||
\(494\) | 10109.5i | 0.920749i | ||||||||
\(495\) | −8161.84 | − | 4117.45i | −0.741106 | − | 0.373870i | ||||
\(496\) | 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 | \(0.693499\pi\) | |||||||
\(510\) | −1167.94 | − | 229.024i | −0.101407 | − | 0.0198850i | ||||
\(511\) | −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 | \(-0.591769\pi\) | ||||
−0.284324 | + | 0.958728i | \(0.591769\pi\) | |||||||
\(524\) | −14567.3 | −1.21445 | ||||||||
\(525\) | 7127.84 | + | 9690.05i | 0.592542 | + | 0.805540i | ||||
\(526\) | −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 | ||||
\(540\) | −12584.4 | + | 13759.9i | −1.00287 | + | 1.09654i | ||||
\(541\) | 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 | ||||||
\(555\) | 19245.8 | + | 3773.94i | 1.47196 | + | 0.288639i | ||||
\(556\) | − | 24670.7i | − | 1.88178i | ||||||
\(557\) | −1115.57 | −0.0848618 | −0.0424309 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424309 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(558\) | −3852.61 | + | 6323.79i | −0.292283 | + | 0.479762i | ||||
\(559\) | 5129.83i | 0.388137i | ||||||||
\(560\) | −2490.71 | + | 2711.67i | −0.187949 | + | 0.204623i | ||||
\(561\) | 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 | \(0.199067\pi\) | ||||
−0.810736 | + | 0.585412i | \(0.800933\pi\) | |||||||
\(570\) | −30405.3 | − | 5962.22i | −2.23428 | − | 0.438122i | ||||
\(571\) | 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 | \(-0.403731\pi\) | ||||
0.297848 | + | 0.954613i | \(0.403731\pi\) | |||||||
\(578\) | −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 | ||||||||
\(585\) | 2577.22 | − | 5108.70i | 0.182145 | − | 0.361058i | ||||
\(586\) | 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 | ||||
\(595\) | −700.558 | − | 643.474i | −0.0482690 | − | 0.0443359i | ||||
\(596\) | 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 | \(0.165149\pi\) | ||||
−0.868400 | + | 0.495865i | \(0.834851\pi\) | |||||||
\(600\) | −11188.8 | − | 1277.47i | −0.761301 | − | 0.0869205i | ||||
\(601\) | 20293.0i | 1.37732i | 0.725083 | + | 0.688661i | \(0.241801\pi\) | ||||
−0.725083 | + | 0.688661i | \(0.758199\pi\) | |||||||
\(602\) | 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 | \(-0.455761\pi\) | ||||
0.138534 | + | 0.990358i | \(0.455761\pi\) | |||||||
\(608\) | − | 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 | ||||||||
\(615\) | 1515.91 | − | 7730.61i | 0.0993939 | − | 0.506875i | ||||
\(616\) | −7129.06 | + | 6613.39i | −0.466295 | + | 0.432567i | ||||
\(617\) | −8241.67 | −0.537759 | −0.268880 | − | 0.963174i | \(-0.586653\pi\) | ||||
−0.268880 | + | 0.963174i | \(0.586653\pi\) | |||||||
\(618\) | −38038.9 | − | 10674.6i | −2.47597 | − | 0.694816i | ||||
\(619\) | 12892.7i | 0.837162i | 0.908180 | + | 0.418581i | \(0.137472\pi\) | ||||
−0.908180 | + | 0.418581i | \(0.862528\pi\) | |||||||
\(620\) | −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 | ||||||||
\(630\) | −23956.6 | + | 6906.19i | −1.51500 | + | 0.436745i | ||||
\(631\) | 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 | \(-0.874339\pi\) | ||
0.923082 | − | 0.384602i | \(-0.125661\pi\) | |||||||
\(642\) | −8874.98 | − | 2490.54i | −0.545588 | − | 0.153105i | ||||
\(643\) | 15859.5 | 0.972689 | 0.486345 | − | 0.873767i | \(-0.338330\pi\) | ||||
0.486345 | + | 0.873767i | \(0.338330\pi\) | |||||||
\(644\) | −20150.7 | − | 21721.9i | −1.23299 | − | 1.32914i | ||||
\(645\) | −15428.4 | − | 3025.37i | −0.941848 | − | 0.184688i | ||||
\(646\) | 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 | \(-0.388142\pi\) | ||||
0.344226 | + | 0.938887i | \(0.388142\pi\) | |||||||
\(654\) | 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 | \(0.133179\pi\) | ||||
−0.913743 | + | 0.406294i | \(0.866821\pi\) | |||||||
\(660\) | 20523.5 | + | 4024.48i | 1.21042 | + | 0.237353i | ||||
\(661\) | 18205.0i | 1.07124i | 0.844458 | + | 0.535621i | \(0.179923\pi\) | ||||
−0.844458 | + | 0.535621i | \(0.820077\pi\) | |||||||
\(662\) | −19834.7 | −1.16450 | ||||||||
\(663\) | −122.252 | + | 435.644i | −0.00716121 | + | 0.0255189i | ||||
\(664\) | 5188.71i | 0.303254i | ||||||||
\(665\) | −18237.8 | − | 16751.7i | −1.06350 | − | 0.976846i | ||||
\(666\) | −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 | ||||||
\(675\) | 13844.9 | + | 10764.1i | 0.789467 | + | 0.613793i | ||||
\(676\) | −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 | \(-0.264143\pi\) | ||||
0.675002 | + | 0.737816i | \(0.264143\pi\) | |||||||
\(684\) | 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 | ||||||||
\(690\) | −6709.13 | + | 34214.3i | −0.370163 | + | 1.88771i | ||||
\(691\) | − | 18883.3i | − | 1.03959i | −0.854291 | − | 0.519794i | \(-0.826009\pi\) | ||
0.854291 | − | 0.519794i | \(-0.173991\pi\) | |||||||
\(692\) | 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 | ||||
\(700\) | −21690.5 | − | 16938.6i | −1.17118 | − | 0.914596i | ||||
\(701\) | 6421.10i | 0.345965i | 0.984925 | + | 0.172983i | \(0.0553404\pi\) | ||||
−0.984925 | + | 0.172983i | \(0.944660\pi\) | |||||||
\(702\) | 8084.17 | + | 8677.18i | 0.434640 | + | 0.466523i | ||||
\(703\) | −40374.2 | −2.16606 | ||||||||
\(704\) | 25133.8i | 1.34555i | ||||||||
\(705\) | 15581.6 | + | 3055.42i | 0.832393 | + | 0.163225i | ||||
\(706\) | 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 | \(0.739187\pi\) | |||||||
\(720\) | −2417.69 | + | 4792.48i | −0.125142 | + | 0.248063i | ||||
\(721\) | −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 | \(-0.494697\pi\) | ||||
0.0166584 | + | 0.999861i | \(0.494697\pi\) | |||||||
\(728\) | −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 | \(-0.661489\pi\) | ||||
−0.485848 | + | 0.874043i | \(0.661489\pi\) | |||||||
\(734\) | −32787.7 | −1.64880 | ||||||||
\(735\) | −19211.8 | − | 5289.04i | −0.964131 | − | 0.265427i | ||||
\(736\) | −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 | \(-0.627418\pi\) | ||||
−0.389690 | + | 0.920946i | \(0.627418\pi\) | |||||||
\(744\) | 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 | ||||
\(750\) | −1092.08 | + | 32366.4i | −0.0531695 | + | 1.57580i | ||||
\(751\) | −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 | ||||||||
\(765\) | −1238.14 | − | 624.609i | −0.0585162 | − | 0.0295200i | ||||
\(766\) | 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 | \(-0.888600\pi\) | ||
0.939382 | − | 0.342873i | \(-0.111400\pi\) | |||||||
\(770\) | 20594.8 | + | 18916.7i | 0.963878 | + | 0.885338i | ||||
\(771\) | 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 | ||||||||
\(780\) | −2519.02 | + | 12846.2i | −0.115635 | + | 0.589700i | ||||
\(781\) | −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 | \(-0.434577\pi\) | ||||
0.204089 | + | 0.978952i | \(0.434577\pi\) | |||||||
\(788\) | 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 | ||||||||
\(795\) | 2491.36 | − | 12705.1i | 0.111144 | − | 0.566797i | ||||
\(796\) | 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 | ||||
\(805\) | −18850.3 | + | 20522.5i | −0.825322 | + | 0.898538i | ||||
\(806\) | 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 | \(0.00423778\pi\) | ||||
−0.999911 | + | 0.0133130i | \(0.995762\pi\) | |||||||
\(810\) | −30865.1 | + | 19196.4i | −1.33887 | + | 0.832705i | ||||
\(811\) | − | 20636.7i | − | 0.893529i | −0.894652 | − | 0.446764i | \(-0.852576\pi\) | ||
0.894652 | − | 0.446764i | \(-0.147424\pi\) | |||||||
\(812\) | −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 | \(-0.784155\pi\) | ||
0.778768 | − | 0.627312i | \(-0.215845\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 2231.26 | − | 19542.7i | 0.0941605 | − | 0.824713i | ||||
\(826\) | 41287.0 | + | 44506.3i | 1.73917 | + | 1.87478i | ||||
\(827\) | 36886.7 | 1.55100 | 0.775500 | − | 0.631348i | \(-0.217498\pi\) | ||||
0.775500 | + | 0.631348i | \(0.217498\pi\) | |||||||
\(828\) | −36888.7 | − | 22473.6i | −1.54828 | − | 0.943249i | ||||
\(829\) | 29077.8i | 1.21823i | 0.793081 | + | 0.609116i | \(0.208475\pi\) | ||||
−0.793081 | + | 0.609116i | \(0.791525\pi\) | |||||||
\(830\) | 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 | \(0.268949\pi\) | |||||||
\(840\) | 15861.9 | − | 9818.17i | 0.651533 | − | 0.403285i | ||||
\(841\) | −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 | \(-0.402690\pi\) | ||||
0.300968 | + | 0.953634i | \(0.402690\pi\) | |||||||
\(854\) | −18906.3 | + | 17538.8i | −0.757566 | + | 0.702768i | ||||
\(855\) | −32232.6 | − | 16260.6i | −1.28928 | − | 0.650410i | ||||
\(856\) | 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 | \(-0.956186\pi\) | ||
0.990542 | − | 0.137211i | \(-0.0438137\pi\) | |||||||
\(860\) | 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 | \(-0.472926\pi\) | ||||
0.0849515 | + | 0.996385i | \(0.472926\pi\) | |||||||
\(864\) | −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 | ||||||
\(870\) | 51647.2 | + | 10127.6i | 2.01265 | + | 0.394663i | ||||
\(871\) | − | 14249.3i | − | 0.554327i | ||||||
\(872\) | −23973.9 | −0.931030 | ||||||||
\(873\) | −12950.6 | − | 7889.85i | −0.502076 | − | 0.305878i | ||||
\(874\) | − | 71775.4i | − | 2.77785i | ||||||
\(875\) | −14250.3 | + | 21606.7i | −0.550569 | + | 0.834790i | ||||
\(876\) | 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 | ||||||
\(885\) | 8216.85 | − | 41903.1i | 0.312097 | − | 1.59159i | ||||
\(886\) | −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 | ||||||||
\(900\) | −37150.3 | − | 15152.3i | −1.37594 | − | 0.561197i | ||||
\(901\) | 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 | ||||
\(910\) | −11840.4 | + | 12890.8i | −0.431325 | + | 0.469589i | ||||
\(911\) | − | 47647.5i | − | 1.73285i | −0.499303 | − | 0.866427i | \(-0.666411\pi\) | ||
0.499303 | − | 0.866427i | \(-0.333589\pi\) | |||||||
\(912\) | 2985.62 | − | 10639.2i | 0.108403 | − | 0.386293i | ||||
\(913\) | −9062.74 | −0.328514 | ||||||||
\(914\) | − | 17960.6i | − | 0.649983i | ||||||
\(915\) | 17800.5 | + | 3490.53i | 0.643133 | + | 0.126113i | ||||
\(916\) | − | 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 | \(0.768761\pi\) | |||||||
\(930\) | −15635.1 | − | 3065.91i | −0.551285 | − | 0.108102i | ||||
\(931\) | 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 | \(-0.417064\pi\) | ||||
0.257612 | + | 0.966248i | \(0.417064\pi\) | |||||||
\(938\) | −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 | ||||||||
\(945\) | −29049.4 | + | 205.738i | −0.999975 | + | 0.00708217i | ||||
\(946\) | −36548.9 | −1.25614 | ||||||||
\(947\) | 13860.2 | 0.475602 | 0.237801 | − | 0.971314i | \(-0.423573\pi\) | ||||
0.237801 | + | 0.971314i | \(0.423573\pi\) | |||||||
\(948\) | −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 | \(-0.882598\pi\) | ||||
−0.932750 | + | 0.360523i | \(0.882598\pi\) | |||||||
\(954\) | 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 | ||||
\(960\) | 9278.06 | − | 47315.0i | 0.311925 | − | 1.59071i | ||||
\(961\) | 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 | ||||||||
\(975\) | 12232.2 | + | 1396.60i | 0.401790 | + | 0.0458738i | ||||
\(976\) | 5552.19i | 0.182092i | ||||||||
\(977\) | 36452.4 | 1.19367 | 0.596834 | − | 0.802364i | \(-0.296425\pi\) | ||||
0.596834 | + | 0.802364i | \(0.296425\pi\) | |||||||
\(978\) | −17850.6 | + | 63610.4i | −0.583640 | + | 2.07979i | ||||
\(979\) | 12897.5i | 0.421047i | ||||||||
\(980\) | 45587.6 | − | 225.221i | 1.48596 | − | 0.00734124i | ||||
\(981\) | 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 | ||||||
\(990\) | 36398.4 | + | 18362.1i | 1.16850 | + | 0.589481i | ||||
\(991\) | 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 | \(-0.423300\pi\) | ||||
0.238635 | + | 0.971109i | \(0.423300\pi\) | |||||||
\(998\) | 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.104.5 | ✓ | 40 | |
3.2 | odd | 2 | inner | 105.4.g.b.104.34 | yes | 40 | |
5.4 | even | 2 | inner | 105.4.g.b.104.36 | yes | 40 | |
7.6 | odd | 2 | inner | 105.4.g.b.104.8 | yes | 40 | |
15.14 | odd | 2 | inner | 105.4.g.b.104.7 | yes | 40 | |
21.20 | even | 2 | inner | 105.4.g.b.104.35 | yes | 40 | |
35.34 | odd | 2 | inner | 105.4.g.b.104.33 | yes | 40 | |
105.104 | even | 2 | inner | 105.4.g.b.104.6 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.g.b.104.5 | ✓ | 40 | 1.1 | even | 1 | trivial | |
105.4.g.b.104.6 | yes | 40 | 105.104 | even | 2 | inner | |
105.4.g.b.104.7 | yes | 40 | 15.14 | odd | 2 | inner | |
105.4.g.b.104.8 | yes | 40 | 7.6 | odd | 2 | inner | |
105.4.g.b.104.33 | yes | 40 | 35.34 | odd | 2 | inner | |
105.4.g.b.104.34 | yes | 40 | 3.2 | odd | 2 | inner | |
105.4.g.b.104.35 | yes | 40 | 21.20 | even | 2 | inner | |
105.4.g.b.104.36 | yes | 40 | 5.4 | even | 2 | inner |