Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(59,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.59");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(44\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 59.10 | ||
Character | \(\chi\) | \(=\) | 105.59 |
Dual form | 105.4.p.a.89.10 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82858 | − | 3.16720i | −0.646502 | − | 1.11977i | −0.983952 | − | 0.178431i | \(-0.942898\pi\) |
0.337450 | − | 0.941343i | \(-0.390436\pi\) | |||||||
\(3\) | 2.73604 | − | 4.41747i | 0.526552 | − | 0.850143i | ||||
\(4\) | −2.68744 | + | 4.65479i | −0.335931 | + | 0.581849i | ||||
\(5\) | 4.42501 | + | 10.2674i | 0.395785 | + | 0.918343i | ||||
\(6\) | −18.9941 | − | 0.587877i | −1.29239 | − | 0.0399999i | ||||
\(7\) | −2.93091 | − | 18.2869i | −0.158255 | − | 0.987398i | ||||
\(8\) | −9.60048 | −0.424285 | ||||||||
\(9\) | −12.0281 | − | 24.1728i | −0.445487 | − | 0.895289i | ||||
\(10\) | 24.4274 | − | 32.7897i | 0.772461 | − | 1.03690i | ||||
\(11\) | −49.5536 | − | 28.6098i | −1.35827 | − | 0.784197i | −0.368879 | − | 0.929477i | \(-0.620258\pi\) |
−0.989391 | + | 0.145280i | \(0.953592\pi\) | |||||||
\(12\) | 13.2094 | + | 24.6074i | 0.317770 | + | 0.591963i | ||||
\(13\) | −28.2640 | −0.603001 | −0.301500 | − | 0.953466i | \(-0.597487\pi\) | ||||
−0.301500 | + | 0.953466i | \(0.597487\pi\) | |||||||
\(14\) | −52.5588 | + | 42.7219i | −1.00335 | + | 0.815565i | ||||
\(15\) | 57.4629 | + | 8.54463i | 0.989124 | + | 0.147081i | ||||
\(16\) | 39.0548 | + | 67.6450i | 0.610232 | + | 1.05695i | ||||
\(17\) | 50.7431 | + | 29.2965i | 0.723941 | + | 0.417968i | 0.816202 | − | 0.577767i | \(-0.196076\pi\) |
−0.0922602 | + | 0.995735i | \(0.529409\pi\) | |||||||
\(18\) | −54.5656 | + | 82.2975i | −0.714514 | + | 1.07765i | ||||
\(19\) | 57.2243 | − | 33.0385i | 0.690956 | − | 0.398924i | −0.113014 | − | 0.993593i | \(-0.536051\pi\) |
0.803970 | + | 0.594670i | \(0.202717\pi\) | |||||||
\(20\) | −59.6845 | − | 6.99552i | −0.667293 | − | 0.0782123i | ||||
\(21\) | −88.8009 | − | 37.0864i | −0.922759 | − | 0.385377i | ||||
\(22\) | 209.262i | 2.02794i | ||||||||
\(23\) | −49.5701 | − | 85.8580i | −0.449395 | − | 0.778375i | 0.548952 | − | 0.835854i | \(-0.315027\pi\) |
−0.998347 | + | 0.0574792i | \(0.981694\pi\) | |||||||
\(24\) | −26.2673 | + | 42.4098i | −0.223408 | + | 0.360703i | ||||
\(25\) | −85.8385 | + | 90.8667i | −0.686708 | + | 0.726933i | ||||
\(26\) | 51.6830 | + | 89.5176i | 0.389841 | + | 0.675225i | ||||
\(27\) | −139.692 | − | 13.0038i | −0.995695 | − | 0.0926885i | ||||
\(28\) | 92.9982 | + | 35.5022i | 0.627679 | + | 0.239617i | ||||
\(29\) | − | 146.774i | − | 0.939834i | −0.882710 | − | 0.469917i | \(-0.844284\pi\) | ||
0.882710 | − | 0.469917i | \(-0.155716\pi\) | |||||||
\(30\) | −78.0133 | − | 197.621i | −0.474774 | − | 1.20268i | ||||
\(31\) | 219.604 | + | 126.789i | 1.27233 | + | 0.734577i | 0.975425 | − | 0.220331i | \(-0.0707138\pi\) |
0.296900 | + | 0.954909i | \(0.404047\pi\) | |||||||
\(32\) | 104.428 | − | 180.875i | 0.576890 | − | 0.999203i | ||||
\(33\) | −261.964 | + | 140.624i | −1.38188 | + | 0.741803i | ||||
\(34\) | − | 214.285i | − | 1.08087i | ||||||
\(35\) | 174.789 | − | 111.013i | 0.844136 | − | 0.536130i | ||||
\(36\) | 144.844 | + | 8.97459i | 0.670575 | + | 0.0415490i | ||||
\(37\) | 44.6243 | − | 25.7639i | 0.198275 | − | 0.114474i | −0.397575 | − | 0.917570i | \(-0.630148\pi\) |
0.595851 | + | 0.803095i | \(0.296815\pi\) | |||||||
\(38\) | −209.279 | − | 120.827i | −0.893409 | − | 0.515810i | ||||
\(39\) | −77.3314 | + | 124.855i | −0.317511 | + | 0.512637i | ||||
\(40\) | −42.4822 | − | 98.5718i | −0.167926 | − | 0.389639i | ||||
\(41\) | 178.366 | 0.679416 | 0.339708 | − | 0.940531i | \(-0.389672\pi\) | ||||
0.339708 | + | 0.940531i | \(0.389672\pi\) | |||||||
\(42\) | 44.9197 | + | 349.066i | 0.165030 | + | 1.28243i | ||||
\(43\) | − | 435.043i | − | 1.54287i | −0.636308 | − | 0.771435i | \(-0.719539\pi\) | ||
0.636308 | − | 0.771435i | \(-0.280461\pi\) | |||||||
\(44\) | 266.345 | − | 153.774i | 0.912568 | − | 0.526872i | ||||
\(45\) | 194.967 | − | 230.463i | 0.645865 | − | 0.763452i | ||||
\(46\) | −181.286 | + | 313.997i | −0.581070 | + | 1.00644i | ||||
\(47\) | 80.0881 | − | 46.2389i | 0.248554 | − | 0.143503i | −0.370548 | − | 0.928813i | \(-0.620830\pi\) |
0.619102 | + | 0.785311i | \(0.287497\pi\) | |||||||
\(48\) | 405.676 | + | 12.5558i | 1.21988 | + | 0.0377558i | ||||
\(49\) | −325.819 | + | 107.195i | −0.949911 | + | 0.312520i | ||||
\(50\) | 444.756 | + | 105.710i | 1.25796 | + | 0.298994i | ||||
\(51\) | 268.252 | − | 144.000i | 0.736525 | − | 0.395372i | ||||
\(52\) | 75.9578 | − | 131.563i | 0.202566 | − | 0.350855i | ||||
\(53\) | −129.101 | + | 223.609i | −0.334592 | + | 0.579531i | −0.983406 | − | 0.181416i | \(-0.941932\pi\) |
0.648814 | + | 0.760947i | \(0.275265\pi\) | |||||||
\(54\) | 214.253 | + | 466.212i | 0.539929 | + | 1.17488i | ||||
\(55\) | 74.4723 | − | 635.384i | 0.182579 | − | 1.55773i | ||||
\(56\) | 28.1382 | + | 175.563i | 0.0671450 | + | 0.418938i | ||||
\(57\) | 10.6216 | − | 343.182i | 0.0246819 | − | 0.797465i | ||||
\(58\) | −464.862 | + | 268.388i | −1.05240 | + | 0.607605i | ||||
\(59\) | 90.0724 | − | 156.010i | 0.198753 | − | 0.344250i | −0.749371 | − | 0.662150i | \(-0.769644\pi\) |
0.948124 | + | 0.317900i | \(0.102978\pi\) | |||||||
\(60\) | −194.202 | + | 244.515i | −0.417856 | + | 0.526112i | ||||
\(61\) | 514.517 | − | 297.056i | 1.07995 | − | 0.623511i | 0.149069 | − | 0.988827i | \(-0.452372\pi\) |
0.930884 | + | 0.365316i | \(0.119039\pi\) | |||||||
\(62\) | − | 927.375i | − | 1.89962i | ||||||
\(63\) | −406.791 | + | 290.805i | −0.813506 | + | 0.581556i | ||||
\(64\) | −138.946 | −0.271380 | ||||||||
\(65\) | −125.068 | − | 290.197i | −0.238659 | − | 0.553762i | ||||
\(66\) | 924.407 | + | 572.549i | 1.72404 | + | 1.06782i | ||||
\(67\) | 399.169 | + | 230.461i | 0.727855 | + | 0.420227i | 0.817637 | − | 0.575734i | \(-0.195284\pi\) |
−0.0897819 | + | 0.995961i | \(0.528617\pi\) | |||||||
\(68\) | −272.738 | + | 157.466i | −0.486388 | + | 0.280816i | ||||
\(69\) | −514.901 | − | 15.9364i | −0.898360 | − | 0.0278046i | ||||
\(70\) | −671.216 | − | 350.596i | −1.14608 | − | 0.598633i | ||||
\(71\) | − | 628.406i | − | 1.05040i | −0.850980 | − | 0.525198i | \(-0.823991\pi\) | ||
0.850980 | − | 0.525198i | \(-0.176009\pi\) | |||||||
\(72\) | 115.476 | + | 232.070i | 0.189013 | + | 0.379858i | ||||
\(73\) | −432.969 | + | 749.925i | −0.694181 | + | 1.20236i | 0.276275 | + | 0.961079i | \(0.410900\pi\) |
−0.970456 | + | 0.241278i | \(0.922433\pi\) | |||||||
\(74\) | −163.199 | − | 94.2228i | −0.256371 | − | 0.148016i | ||||
\(75\) | 166.543 | + | 627.804i | 0.256410 | + | 0.966568i | ||||
\(76\) | 355.156i | 0.536043i | ||||||||
\(77\) | −377.946 | + | 990.033i | −0.559363 | + | 1.46526i | ||||
\(78\) | 536.849 | + | 16.6157i | 0.779310 | + | 0.0241200i | ||||
\(79\) | −95.1045 | − | 164.726i | −0.135444 | − | 0.234596i | 0.790323 | − | 0.612691i | \(-0.209913\pi\) |
−0.925767 | + | 0.378094i | \(0.876579\pi\) | |||||||
\(80\) | −521.719 | + | 700.321i | −0.729124 | + | 0.978729i | ||||
\(81\) | −439.648 | + | 581.507i | −0.603084 | + | 0.797678i | ||||
\(82\) | −326.157 | − | 564.920i | −0.439244 | − | 0.760793i | ||||
\(83\) | − | 939.466i | − | 1.24241i | −0.783649 | − | 0.621203i | \(-0.786644\pi\) | ||
0.783649 | − | 0.621203i | \(-0.213356\pi\) | |||||||
\(84\) | 411.277 | − | 313.682i | 0.534214 | − | 0.407446i | ||||
\(85\) | −76.2599 | + | 650.636i | −0.0973124 | + | 0.830252i | ||||
\(86\) | −1377.87 | + | 795.513i | −1.72767 | + | 0.997470i | ||||
\(87\) | −648.369 | − | 401.579i | −0.798994 | − | 0.494871i | ||||
\(88\) | 475.738 | + | 274.667i | 0.576293 | + | 0.332723i | ||||
\(89\) | −348.672 | − | 603.917i | −0.415271 | − | 0.719271i | 0.580186 | − | 0.814484i | \(-0.302980\pi\) |
−0.995457 | + | 0.0952136i | \(0.969647\pi\) | |||||||
\(90\) | −1086.43 | − | 196.079i | −1.27245 | − | 0.229650i | ||||
\(91\) | 82.8392 | + | 516.859i | 0.0954276 | + | 0.595402i | ||||
\(92\) | 532.868 | 0.603862 | ||||||||
\(93\) | 1160.93 | − | 623.197i | 1.29444 | − | 0.694866i | ||||
\(94\) | −292.896 | − | 169.103i | −0.321382 | − | 0.185550i | ||||
\(95\) | 592.438 | + | 441.349i | 0.639819 | + | 0.476646i | ||||
\(96\) | −513.290 | − | 956.191i | −0.545703 | − | 1.01657i | ||||
\(97\) | 307.162 | 0.321522 | 0.160761 | − | 0.986993i | \(-0.448605\pi\) | ||||
0.160761 | + | 0.986993i | \(0.448605\pi\) | |||||||
\(98\) | 935.295 | + | 835.922i | 0.964072 | + | 0.861641i | ||||
\(99\) | −95.5409 | + | 1541.97i | −0.0969921 | + | 1.56539i | ||||
\(100\) | −192.279 | − | 643.759i | −0.192279 | − | 0.643759i | ||||
\(101\) | −183.970 | + | 318.646i | −0.181245 | + | 0.313925i | −0.942305 | − | 0.334756i | \(-0.891346\pi\) |
0.761060 | + | 0.648682i | \(0.224679\pi\) | |||||||
\(102\) | −946.597 | − | 586.292i | −0.918893 | − | 0.569133i | ||||
\(103\) | −426.332 | − | 738.428i | −0.407842 | − | 0.706403i | 0.586806 | − | 0.809728i | \(-0.300385\pi\) |
−0.994648 | + | 0.103325i | \(0.967052\pi\) | |||||||
\(104\) | 271.347 | 0.255844 | ||||||||
\(105\) | −12.1644 | − | 1075.86i | −0.0113059 | − | 0.999936i | ||||
\(106\) | 944.288 | 0.865258 | ||||||||
\(107\) | 575.600 | + | 996.968i | 0.520050 | + | 0.900752i | 0.999728 | + | 0.0233081i | \(0.00741988\pi\) |
−0.479679 | + | 0.877444i | \(0.659247\pi\) | |||||||
\(108\) | 435.945 | − | 615.291i | 0.388415 | − | 0.548207i | ||||
\(109\) | 621.897 | − | 1077.16i | 0.546486 | − | 0.946541i | −0.452026 | − | 0.892005i | \(-0.649299\pi\) |
0.998512 | − | 0.0545365i | \(-0.0173681\pi\) | |||||||
\(110\) | −2148.57 | + | 925.985i | −1.86235 | + | 0.802629i | ||||
\(111\) | 8.28289 | − | 267.618i | 0.00708268 | − | 0.228839i | ||||
\(112\) | 1122.55 | − | 912.453i | 0.947061 | − | 0.769809i | ||||
\(113\) | 2097.75 | 1.74637 | 0.873184 | − | 0.487390i | \(-0.162051\pi\) | ||||
0.873184 | + | 0.487390i | \(0.162051\pi\) | |||||||
\(114\) | −1106.35 | + | 593.896i | −0.908939 | + | 0.487925i | ||||
\(115\) | 662.188 | − | 888.878i | 0.536951 | − | 0.720768i | ||||
\(116\) | 683.201 | + | 394.446i | 0.546842 | + | 0.315719i | ||||
\(117\) | 339.963 | + | 683.219i | 0.268629 | + | 0.539860i | ||||
\(118\) | −658.820 | −0.513977 | ||||||||
\(119\) | 387.018 | − | 1013.80i | 0.298134 | − | 0.780964i | ||||
\(120\) | −551.672 | − | 82.0325i | −0.419671 | − | 0.0624043i | ||||
\(121\) | 971.538 | + | 1682.75i | 0.729931 | + | 1.26428i | ||||
\(122\) | −1881.68 | − | 1086.39i | −1.39638 | − | 0.806203i | ||||
\(123\) | 488.016 | − | 787.926i | 0.357748 | − | 0.577601i | ||||
\(124\) | −1180.35 | + | 681.474i | −0.854826 | + | 0.493534i | ||||
\(125\) | −1312.80 | − | 479.251i | −0.939363 | − | 0.342924i | ||||
\(126\) | 1664.89 | + | 756.628i | 1.17715 | + | 0.534967i | ||||
\(127\) | 1004.72i | 0.702004i | 0.936375 | + | 0.351002i | \(0.114159\pi\) | ||||
−0.936375 | + | 0.351002i | \(0.885841\pi\) | |||||||
\(128\) | −581.351 | − | 1006.93i | −0.401443 | − | 0.695319i | ||||
\(129\) | −1921.79 | − | 1190.30i | −1.31166 | − | 0.812401i | ||||
\(130\) | −690.414 | + | 926.767i | −0.465795 | + | 0.625252i | ||||
\(131\) | 322.188 | + | 558.046i | 0.214883 | + | 0.372189i | 0.953236 | − | 0.302225i | \(-0.0977296\pi\) |
−0.738353 | + | 0.674414i | \(0.764396\pi\) | |||||||
\(132\) | 49.4373 | − | 1597.30i | 0.0325982 | − | 1.05324i | ||||
\(133\) | −771.890 | − | 949.621i | −0.503243 | − | 0.619117i | ||||
\(134\) | − | 1685.67i | − | 1.08671i | ||||||
\(135\) | −484.624 | − | 1491.82i | −0.308962 | − | 0.951074i | ||||
\(136\) | −487.158 | − | 281.261i | −0.307158 | − | 0.177337i | ||||
\(137\) | −940.296 | + | 1628.64i | −0.586386 | + | 1.01565i | 0.408315 | + | 0.912841i | \(0.366117\pi\) |
−0.994701 | + | 0.102810i | \(0.967217\pi\) | |||||||
\(138\) | 891.067 | + | 1659.94i | 0.549657 | + | 1.02394i | ||||
\(139\) | 2275.93i | 1.38879i | 0.719595 | + | 0.694394i | \(0.244328\pi\) | ||||
−0.719595 | + | 0.694394i | \(0.755672\pi\) | |||||||
\(140\) | 47.0041 | + | 1111.95i | 0.0283755 | + | 0.671262i | ||||
\(141\) | 14.8655 | − | 480.298i | 0.00887870 | − | 0.286868i | ||||
\(142\) | −1990.29 | + | 1149.09i | −1.17621 | + | 0.679084i | ||||
\(143\) | 1400.58 | + | 808.625i | 0.819037 | + | 0.472872i | ||||
\(144\) | 1165.41 | − | 1757.71i | 0.674428 | − | 1.01719i | ||||
\(145\) | 1506.98 | − | 649.476i | 0.863090 | − | 0.371973i | ||||
\(146\) | 3166.88 | 1.79516 | ||||||||
\(147\) | −417.927 | + | 1732.59i | −0.234490 | + | 0.972118i | ||||
\(148\) | 276.956i | 0.153822i | ||||||||
\(149\) | 1923.41 | − | 1110.48i | 1.05753 | − | 0.610565i | 0.132781 | − | 0.991145i | \(-0.457609\pi\) |
0.924748 | + | 0.380581i | \(0.124276\pi\) | |||||||
\(150\) | 1683.84 | − | 1675.47i | 0.916569 | − | 0.912010i | ||||
\(151\) | 1015.59 | − | 1759.05i | 0.547334 | − | 0.948011i | −0.451122 | − | 0.892463i | \(-0.648976\pi\) |
0.998456 | − | 0.0555486i | \(-0.0176908\pi\) | |||||||
\(152\) | −549.381 | + | 317.185i | −0.293162 | + | 0.169257i | ||||
\(153\) | 97.8343 | − | 1578.98i | 0.0516957 | − | 0.834336i | ||||
\(154\) | 3826.74 | − | 613.328i | 2.00239 | − | 0.320931i | ||||
\(155\) | −330.035 | + | 2815.80i | −0.171026 | + | 1.45917i | ||||
\(156\) | −373.351 | − | 695.503i | −0.191616 | − | 0.356954i | ||||
\(157\) | −137.130 | + | 237.517i | −0.0697082 | + | 0.120738i | −0.898773 | − | 0.438415i | \(-0.855540\pi\) |
0.829065 | + | 0.559153i | \(0.188873\pi\) | |||||||
\(158\) | −347.813 | + | 602.430i | −0.175130 | + | 0.303334i | ||||
\(159\) | 634.563 | + | 1182.11i | 0.316504 | + | 0.589604i | ||||
\(160\) | 2319.21 | + | 271.831i | 1.14594 | + | 0.134313i | ||||
\(161\) | −1424.79 | + | 1158.12i | −0.697447 | + | 0.566913i | ||||
\(162\) | 2645.68 | + | 329.118i | 1.28311 | + | 0.159617i | ||||
\(163\) | −1352.29 | + | 780.744i | −0.649812 | + | 0.375169i | −0.788384 | − | 0.615183i | \(-0.789082\pi\) |
0.138572 | + | 0.990352i | \(0.455749\pi\) | |||||||
\(164\) | −479.348 | + | 830.255i | −0.228237 | + | 0.395317i | ||||
\(165\) | −2603.03 | − | 2067.42i | −1.22816 | − | 0.975444i | ||||
\(166\) | −2975.48 | + | 1717.89i | −1.39122 | + | 0.803219i | ||||
\(167\) | 979.278i | 0.453765i | 0.973922 | + | 0.226883i | \(0.0728534\pi\) | ||||
−0.973922 | + | 0.226883i | \(0.927147\pi\) | |||||||
\(168\) | 852.531 | + | 356.047i | 0.391513 | + | 0.163510i | ||||
\(169\) | −1398.15 | −0.636390 | ||||||||
\(170\) | 2200.14 | − | 948.213i | 0.992608 | − | 0.427792i | ||||
\(171\) | −1486.93 | − | 985.881i | −0.664963 | − | 0.440890i | ||||
\(172\) | 2025.03 | + | 1169.15i | 0.897718 | + | 0.518298i | ||||
\(173\) | −1795.98 | + | 1036.91i | −0.789280 | + | 0.455691i | −0.839709 | − | 0.543036i | \(-0.817275\pi\) |
0.0504287 | + | 0.998728i | \(0.483941\pi\) | |||||||
\(174\) | −86.2848 | + | 2787.84i | −0.0375933 | + | 1.21463i | ||||
\(175\) | 1913.25 | + | 1303.40i | 0.826448 | + | 0.563014i | ||||
\(176\) | − | 4469.40i | − | 1.91417i | ||||||
\(177\) | −442.728 | − | 824.742i | −0.188008 | − | 0.350234i | ||||
\(178\) | −1275.15 | + | 2208.63i | −0.536947 | + | 0.930020i | ||||
\(179\) | 2360.86 | + | 1363.04i | 0.985804 | + | 0.569154i | 0.904017 | − | 0.427496i | \(-0.140604\pi\) |
0.0817868 | + | 0.996650i | \(0.473937\pi\) | |||||||
\(180\) | 548.792 | + | 1526.88i | 0.227248 | + | 0.632263i | ||||
\(181\) | − | 1220.84i | − | 0.501350i | −0.968071 | − | 0.250675i | \(-0.919347\pi\) | ||
0.968071 | − | 0.250675i | \(-0.0806526\pi\) | |||||||
\(182\) | 1485.52 | − | 1207.49i | 0.605022 | − | 0.491786i | ||||
\(183\) | 95.5015 | − | 3085.62i | 0.0385774 | − | 1.24643i | ||||
\(184\) | 475.897 | + | 824.277i | 0.190672 | + | 0.330253i | ||||
\(185\) | 461.991 | + | 344.170i | 0.183601 | + | 0.136778i | ||||
\(186\) | −4096.65 | − | 2537.34i | −1.61495 | − | 1.00025i | ||||
\(187\) | −1676.33 | − | 2903.50i | −0.655538 | − | 1.13543i | ||||
\(188\) | 497.058i | 0.192828i | ||||||||
\(189\) | 171.626 | + | 2592.65i | 0.0660528 | + | 0.997816i | ||||
\(190\) | 314.518 | − | 2683.41i | 0.120092 | − | 1.02461i | ||||
\(191\) | −2259.34 | + | 1304.43i | −0.855918 | + | 0.494165i | −0.862643 | − | 0.505813i | \(-0.831193\pi\) |
0.00672504 | + | 0.999977i | \(0.497859\pi\) | |||||||
\(192\) | −380.163 | + | 613.792i | −0.142895 | + | 0.230711i | ||||
\(193\) | 524.703 | + | 302.937i | 0.195694 | + | 0.112984i | 0.594645 | − | 0.803988i | \(-0.297292\pi\) |
−0.398951 | + | 0.916972i | \(0.630626\pi\) | |||||||
\(194\) | −561.672 | − | 972.845i | −0.207864 | − | 0.360032i | ||||
\(195\) | −1624.13 | − | 241.505i | −0.596443 | − | 0.0886899i | ||||
\(196\) | 376.654 | − | 1804.70i | 0.137264 | − | 0.657690i | ||||
\(197\) | 357.481 | 0.129287 | 0.0646433 | − | 0.997908i | \(-0.479409\pi\) | ||||
0.0646433 | + | 0.997908i | \(0.479409\pi\) | |||||||
\(198\) | 5058.44 | − | 2517.03i | 1.81559 | − | 0.903421i | ||||
\(199\) | −2955.87 | − | 1706.57i | −1.05295 | − | 0.607919i | −0.129473 | − | 0.991583i | \(-0.541329\pi\) |
−0.923473 | + | 0.383664i | \(0.874662\pi\) | |||||||
\(200\) | 824.090 | − | 872.363i | 0.291360 | − | 0.308427i | ||||
\(201\) | 2110.20 | − | 1132.77i | 0.740507 | − | 0.397510i | ||||
\(202\) | 1345.62 | 0.468701 | ||||||||
\(203\) | −2684.03 | + | 430.181i | −0.927991 | + | 0.148733i | ||||
\(204\) | −50.6240 | + | 1635.65i | −0.0173745 | + | 0.561364i | ||||
\(205\) | 789.271 | + | 1831.35i | 0.268903 | + | 0.623937i | ||||
\(206\) | −1559.17 | + | 2700.56i | −0.527341 | + | 0.913382i | ||||
\(207\) | −1479.19 | + | 2230.96i | −0.496671 | + | 0.749094i | ||||
\(208\) | −1103.84 | − | 1911.91i | −0.367970 | − | 0.637343i | ||||
\(209\) | −3780.89 | −1.25134 | ||||||||
\(210\) | −3385.23 | + | 2005.83i | −1.11239 | + | 0.659121i | ||||
\(211\) | −2652.97 | −0.865581 | −0.432791 | − | 0.901494i | \(-0.642471\pi\) | ||||
−0.432791 | + | 0.901494i | \(0.642471\pi\) | |||||||
\(212\) | −693.904 | − | 1201.88i | −0.224799 | − | 0.389364i | ||||
\(213\) | −2775.97 | − | 1719.35i | −0.892987 | − | 0.553088i | ||||
\(214\) | 2105.07 | − | 3646.08i | 0.672427 | − | 1.16468i | ||||
\(215\) | 4466.76 | − | 1925.07i | 1.41688 | − | 0.610646i | ||||
\(216\) | 1341.11 | + | 124.843i | 0.422459 | + | 0.0393264i | ||||
\(217\) | 1674.93 | − | 4387.48i | 0.523969 | − | 1.37254i | ||||
\(218\) | −4548.77 | −1.41322 | ||||||||
\(219\) | 2128.15 | + | 3964.46i | 0.656653 | + | 1.22326i | ||||
\(220\) | 2757.44 | + | 2054.21i | 0.845030 | + | 0.629523i | ||||
\(221\) | −1434.20 | − | 828.036i | −0.436537 | − | 0.252035i | ||||
\(222\) | −862.745 | + | 463.128i | −0.260827 | + | 0.140014i | ||||
\(223\) | −1380.68 | −0.414606 | −0.207303 | − | 0.978277i | \(-0.566469\pi\) | ||||
−0.207303 | + | 0.978277i | \(0.566469\pi\) | |||||||
\(224\) | −3613.71 | − | 1379.54i | −1.07791 | − | 0.411492i | ||||
\(225\) | 3228.98 | + | 981.999i | 0.956734 | + | 0.290963i | ||||
\(226\) | −3835.91 | − | 6644.00i | −1.12903 | − | 1.95554i | ||||
\(227\) | 3589.25 | + | 2072.25i | 1.04946 | + | 0.605904i | 0.922497 | − | 0.386004i | \(-0.126145\pi\) |
0.126959 | + | 0.991908i | \(0.459478\pi\) | |||||||
\(228\) | 1568.89 | + | 971.723i | 0.455713 | + | 0.282254i | ||||
\(229\) | −2579.33 | + | 1489.18i | −0.744310 | + | 0.429727i | −0.823634 | − | 0.567121i | \(-0.808057\pi\) |
0.0793244 | + | 0.996849i | \(0.474724\pi\) | |||||||
\(230\) | −4026.12 | − | 471.895i | −1.15424 | − | 0.135286i | ||||
\(231\) | 3339.37 | + | 4378.34i | 0.951144 | + | 1.24707i | ||||
\(232\) | 1409.10i | 0.398758i | ||||||||
\(233\) | 419.190 | + | 726.058i | 0.117863 | + | 0.204144i | 0.918921 | − | 0.394443i | \(-0.129062\pi\) |
−0.801058 | + | 0.598587i | \(0.795729\pi\) | |||||||
\(234\) | 1542.24 | − | 2326.05i | 0.430852 | − | 0.649824i | ||||
\(235\) | 829.143 | + | 617.687i | 0.230159 | + | 0.171462i | ||||
\(236\) | 484.129 | + | 838.536i | 0.133534 | + | 0.231288i | ||||
\(237\) | −987.882 | − | 30.5754i | −0.270759 | − | 0.00838011i | ||||
\(238\) | −3918.60 | + | 628.050i | −1.06725 | + | 0.171052i | ||||
\(239\) | 3628.72i | 0.982102i | 0.871131 | + | 0.491051i | \(0.163387\pi\) | ||||
−0.871131 | + | 0.491051i | \(0.836613\pi\) | |||||||
\(240\) | 1666.20 | + | 4220.79i | 0.448138 | + | 1.13521i | ||||
\(241\) | −916.908 | − | 529.377i | −0.245076 | − | 0.141495i | 0.372432 | − | 0.928060i | \(-0.378524\pi\) |
−0.617507 | + | 0.786565i | \(0.711857\pi\) | |||||||
\(242\) | 3553.08 | − | 6154.11i | 0.943804 | − | 1.63472i | ||||
\(243\) | 1365.90 | + | 3533.16i | 0.360586 | + | 0.932726i | ||||
\(244\) | 3193.29i | 0.837826i | ||||||||
\(245\) | −2542.36 | − | 2870.98i | −0.662962 | − | 0.748653i | ||||
\(246\) | −3387.90 | − | 104.857i | −0.878067 | − | 0.0271766i | ||||
\(247\) | −1617.39 | + | 933.798i | −0.416647 | + | 0.240551i | ||||
\(248\) | −2108.31 | − | 1217.23i | −0.539829 | − | 0.311670i | ||||
\(249\) | −4150.06 | − | 2570.42i | −1.05622 | − | 0.654191i | ||||
\(250\) | 882.683 | + | 5034.25i | 0.223303 | + | 1.27358i | ||||
\(251\) | 5528.72 | 1.39032 | 0.695159 | − | 0.718856i | \(-0.255334\pi\) | ||||
0.695159 | + | 0.718856i | \(0.255334\pi\) | |||||||
\(252\) | −260.409 | − | 2675.05i | −0.0650961 | − | 0.668700i | ||||
\(253\) | 5672.76i | 1.40966i | ||||||||
\(254\) | 3182.15 | − | 1837.22i | 0.786086 | − | 0.453847i | ||||
\(255\) | 2665.52 | + | 2117.05i | 0.654593 | + | 0.519900i | ||||
\(256\) | −2681.88 | + | 4645.16i | −0.654757 | + | 1.13407i | ||||
\(257\) | 432.019 | − | 249.426i | 0.104858 | − | 0.0605400i | −0.446654 | − | 0.894707i | \(-0.647384\pi\) |
0.551512 | + | 0.834167i | \(0.314051\pi\) | |||||||
\(258\) | −255.752 | + | 8263.26i | −0.0617147 | + | 1.99398i | ||||
\(259\) | −601.931 | − | 740.528i | −0.144410 | − | 0.177661i | ||||
\(260\) | 1686.92 | + | 197.721i | 0.402378 | + | 0.0471621i | ||||
\(261\) | −3547.93 | + | 1765.41i | −0.841423 | + | 0.418684i | ||||
\(262\) | 1178.30 | − | 2040.87i | 0.277845 | − | 0.481242i | ||||
\(263\) | −1060.43 | + | 1836.72i | −0.248627 | + | 0.430634i | −0.963145 | − | 0.268982i | \(-0.913313\pi\) |
0.714518 | + | 0.699617i | \(0.246646\pi\) | |||||||
\(264\) | 2514.97 | − | 1350.06i | 0.586311 | − | 0.314736i | ||||
\(265\) | −2867.16 | − | 336.055i | −0.664635 | − | 0.0779006i | ||||
\(266\) | −1596.18 | + | 4181.20i | −0.367924 | + | 0.963780i | ||||
\(267\) | −3621.77 | − | 112.095i | −0.830145 | − | 0.0256934i | ||||
\(268\) | −2145.49 | + | 1238.70i | −0.489018 | + | 0.282334i | ||||
\(269\) | −957.671 | + | 1658.73i | −0.217064 | + | 0.375966i | −0.953909 | − | 0.300096i | \(-0.902981\pi\) |
0.736845 | + | 0.676062i | \(0.236315\pi\) | |||||||
\(270\) | −3838.70 | + | 4262.81i | −0.865245 | + | 0.960839i | ||||
\(271\) | 5730.09 | − | 3308.27i | 1.28442 | − | 0.741561i | 0.306767 | − | 0.951785i | \(-0.400753\pi\) |
0.977653 | + | 0.210224i | \(0.0674193\pi\) | |||||||
\(272\) | 4576.69i | 1.02023i | ||||||||
\(273\) | 2509.86 | + | 1048.21i | 0.556424 | + | 0.232383i | ||||
\(274\) | 6877.64 | 1.51640 | ||||||||
\(275\) | 6853.28 | − | 2046.95i | 1.50279 | − | 0.448857i | ||||
\(276\) | 1457.95 | − | 2353.93i | 0.317965 | − | 0.513369i | ||||
\(277\) | 4004.78 | + | 2312.16i | 0.868678 | + | 0.501532i | 0.866909 | − | 0.498467i | \(-0.166103\pi\) |
0.00176954 | + | 0.999998i | \(0.499437\pi\) | |||||||
\(278\) | 7208.32 | − | 4161.73i | 1.55513 | − | 0.897855i | ||||
\(279\) | 423.404 | − | 6833.48i | 0.0908550 | − | 1.46634i | ||||
\(280\) | −1678.06 | + | 1065.77i | −0.358154 | + | 0.227472i | ||||
\(281\) | − | 9354.56i | − | 1.98593i | −0.118413 | − | 0.992964i | \(-0.537781\pi\) | ||
0.118413 | − | 0.992964i | \(-0.462219\pi\) | |||||||
\(282\) | −1548.38 | + | 831.184i | −0.326968 | + | 0.175519i | ||||
\(283\) | 1226.31 | − | 2124.03i | 0.257585 | − | 0.446150i | −0.708009 | − | 0.706203i | \(-0.750407\pi\) |
0.965594 | + | 0.260053i | \(0.0837400\pi\) | |||||||
\(284\) | 2925.10 | + | 1688.81i | 0.611172 | + | 0.352860i | ||||
\(285\) | 3570.58 | − | 1409.53i | 0.742116 | − | 0.292959i | ||||
\(286\) | − | 5914.56i | − | 1.22285i | ||||||
\(287\) | −522.775 | − | 3261.75i | −0.107521 | − | 0.670854i | ||||
\(288\) | −5628.33 | − | 348.733i | −1.15157 | − | 0.0713517i | ||||
\(289\) | −739.927 | − | 1281.59i | −0.150606 | − | 0.260857i | ||||
\(290\) | −4812.67 | − | 3585.30i | −0.974516 | − | 0.725986i | ||||
\(291\) | 840.409 | − | 1356.88i | 0.169298 | − | 0.273339i | ||||
\(292\) | −2327.16 | − | 4030.76i | −0.466393 | − | 0.807817i | ||||
\(293\) | − | 5920.48i | − | 1.18047i | −0.807231 | − | 0.590236i | \(-0.799035\pi\) | ||
0.807231 | − | 0.590236i | \(-0.200965\pi\) | |||||||
\(294\) | 6251.67 | − | 1844.52i | 1.24015 | − | 0.365901i | ||||
\(295\) | 2000.39 | + | 234.462i | 0.394803 | + | 0.0462742i | ||||
\(296\) | −428.415 | + | 247.345i | −0.0841253 | + | 0.0485698i | ||||
\(297\) | 6550.21 | + | 4640.95i | 1.27974 | + | 0.906717i | ||||
\(298\) | −7034.23 | − | 4061.22i | −1.36739 | − | 0.789463i | ||||
\(299\) | 1401.05 | + | 2426.69i | 0.270985 | + | 0.469361i | ||||
\(300\) | −3369.87 | − | 911.965i | −0.648533 | − | 0.175508i | ||||
\(301\) | −7955.58 | + | 1275.07i | −1.52343 | + | 0.244166i | ||||
\(302\) | −7428.37 | −1.41541 | ||||||||
\(303\) | 904.259 | + | 1684.51i | 0.171447 | + | 0.319382i | ||||
\(304\) | 4469.77 | + | 2580.63i | 0.843287 | + | 0.486872i | ||||
\(305\) | 5326.74 | + | 3968.26i | 1.00003 | + | 0.744991i | ||||
\(306\) | −5179.86 | + | 2577.45i | −0.967689 | + | 0.481512i | ||||
\(307\) | 4247.09 | 0.789557 | 0.394779 | − | 0.918776i | \(-0.370821\pi\) | ||||
0.394779 | + | 0.918776i | \(0.370821\pi\) | |||||||
\(308\) | −3592.69 | − | 4419.92i | −0.664650 | − | 0.817689i | ||||
\(309\) | −4428.45 | − | 137.063i | −0.815293 | − | 0.0252337i | ||||
\(310\) | 9521.71 | − | 4103.65i | 1.74451 | − | 0.751843i | ||||
\(311\) | −1806.62 | + | 3129.16i | −0.329402 | + | 0.570541i | −0.982393 | − | 0.186824i | \(-0.940181\pi\) |
0.652991 | + | 0.757366i | \(0.273514\pi\) | |||||||
\(312\) | 742.418 | − | 1198.67i | 0.134715 | − | 0.217504i | ||||
\(313\) | 365.112 | + | 632.393i | 0.0659341 | + | 0.114201i | 0.897108 | − | 0.441811i | \(-0.145664\pi\) |
−0.831174 | + | 0.556013i | \(0.812331\pi\) | |||||||
\(314\) | 1003.02 | 0.180266 | ||||||||
\(315\) | −4785.87 | − | 2889.87i | −0.856042 | − | 0.516906i | ||||
\(316\) | 1022.35 | 0.181999 | ||||||||
\(317\) | −3385.50 | − | 5863.86i | −0.599838 | − | 1.03895i | −0.992845 | − | 0.119414i | \(-0.961898\pi\) |
0.393007 | − | 0.919536i | \(-0.371435\pi\) | |||||||
\(318\) | 2583.61 | − | 4171.37i | 0.455603 | − | 0.735594i | ||||
\(319\) | −4199.16 | + | 7273.16i | −0.737016 | + | 1.27655i | ||||
\(320\) | −614.840 | − | 1426.62i | −0.107408 | − | 0.249220i | ||||
\(321\) | 5978.94 | + | 185.051i | 1.03960 | + | 0.0321761i | ||||
\(322\) | 6273.36 | + | 2394.86i | 1.08572 | + | 0.414473i | ||||
\(323\) | 3871.65 | 0.666949 | ||||||||
\(324\) | −1525.27 | − | 3609.24i | −0.261534 | − | 0.618868i | ||||
\(325\) | 2426.13 | − | 2568.25i | 0.414085 | − | 0.438341i | ||||
\(326\) | 4945.54 | + | 2855.31i | 0.840210 | + | 0.485095i | ||||
\(327\) | −3056.78 | − | 5694.36i | −0.516942 | − | 0.962994i | ||||
\(328\) | −1712.40 | −0.288266 | ||||||||
\(329\) | −1080.30 | − | 1329.04i | −0.181029 | − | 0.222712i | ||||
\(330\) | −1788.06 | + | 12024.8i | −0.298272 | + | 2.00589i | ||||
\(331\) | 3113.99 | + | 5393.59i | 0.517101 | + | 0.895646i | 0.999803 | + | 0.0198607i | \(0.00632226\pi\) |
−0.482702 | + | 0.875785i | \(0.660344\pi\) | |||||||
\(332\) | 4373.02 | + | 2524.76i | 0.722893 | + | 0.417362i | ||||
\(333\) | −1159.53 | − | 768.803i | −0.190817 | − | 0.126517i | ||||
\(334\) | 3101.57 | − | 1790.69i | 0.508115 | − | 0.293360i | ||||
\(335\) | −599.897 | + | 5118.22i | −0.0978385 | + | 0.834740i | ||||
\(336\) | −959.393 | − | 7455.34i | −0.155771 | − | 1.21048i | ||||
\(337\) | − | 829.936i | − | 0.134153i | −0.997748 | − | 0.0670764i | \(-0.978633\pi\) | ||
0.997748 | − | 0.0670764i | \(-0.0213671\pi\) | |||||||
\(338\) | 2556.63 | + | 4428.22i | 0.411428 | + | 0.712614i | ||||
\(339\) | 5739.53 | − | 9266.75i | 0.919554 | − | 1.48466i | ||||
\(340\) | −2823.63 | − | 2103.52i | −0.450391 | − | 0.335528i | ||||
\(341\) | −7254.78 | − | 12565.7i | −1.15211 | − | 1.99551i | ||||
\(342\) | −403.497 | + | 6512.19i | −0.0637971 | + | 1.02965i | ||||
\(343\) | 2915.20 | + | 5644.04i | 0.458910 | + | 0.888483i | ||||
\(344\) | 4176.62i | 0.654617i | ||||||||
\(345\) | −2114.82 | − | 5357.21i | −0.330023 | − | 0.836007i | ||||
\(346\) | 6568.19 | + | 3792.15i | 1.02054 | + | 0.589211i | ||||
\(347\) | 366.463 | − | 634.732i | 0.0566938 | − | 0.0981966i | −0.836286 | − | 0.548294i | \(-0.815277\pi\) |
0.892979 | + | 0.450098i | \(0.148611\pi\) | |||||||
\(348\) | 3611.72 | − | 1938.80i | 0.556347 | − | 0.298651i | ||||
\(349\) | 1401.15i | 0.214905i | 0.994210 | + | 0.107452i | \(0.0342693\pi\) | ||||
−0.994210 | + | 0.107452i | \(0.965731\pi\) | |||||||
\(350\) | 629.570 | − | 8443.03i | 0.0961484 | − | 1.28942i | ||||
\(351\) | 3948.25 | + | 367.540i | 0.600405 | + | 0.0558912i | ||||
\(352\) | −10349.6 | + | 5975.34i | −1.56714 | + | 0.904791i | ||||
\(353\) | 8882.44 | + | 5128.28i | 1.33928 | + | 0.773231i | 0.986700 | − | 0.162552i | \(-0.0519725\pi\) |
0.352576 | + | 0.935783i | \(0.385306\pi\) | |||||||
\(354\) | −1802.56 | + | 2910.32i | −0.270635 | + | 0.436954i | ||||
\(355\) | 6452.09 | − | 2780.71i | 0.964624 | − | 0.415731i | ||||
\(356\) | 3748.14 | 0.558009 | ||||||||
\(357\) | −3419.53 | − | 4483.44i | −0.506948 | − | 0.664674i | ||||
\(358\) | − | 9969.76i | − | 1.47184i | ||||||
\(359\) | −6080.19 | + | 3510.40i | −0.893872 | + | 0.516077i | −0.875207 | − | 0.483748i | \(-0.839275\pi\) |
−0.0186652 | + | 0.999826i | \(0.505942\pi\) | |||||||
\(360\) | −1871.77 | + | 2212.55i | −0.274031 | + | 0.323921i | ||||
\(361\) | −1246.42 | + | 2158.86i | −0.181720 | + | 0.314748i | ||||
\(362\) | −3866.65 | + | 2232.41i | −0.561400 | + | 0.324124i | ||||
\(363\) | 10091.7 | + | 312.342i | 1.45916 | + | 0.0451617i | ||||
\(364\) | −2628.50 | − | 1003.43i | −0.378491 | − | 0.144489i | ||||
\(365\) | −9615.66 | − | 1127.03i | −1.37892 | − | 0.161621i | ||||
\(366\) | −9947.43 | + | 5339.85i | −1.42066 | + | 0.762619i | ||||
\(367\) | −4123.71 | + | 7142.48i | −0.586529 | + | 1.01590i | 0.408154 | + | 0.912913i | \(0.366172\pi\) |
−0.994683 | + | 0.102984i | \(0.967161\pi\) | |||||||
\(368\) | 3871.91 | − | 6706.34i | 0.548470 | − | 0.949978i | ||||
\(369\) | −2145.41 | − | 4311.60i | −0.302671 | − | 0.608273i | ||||
\(370\) | 245.265 | − | 2092.56i | 0.0344615 | − | 0.294019i | ||||
\(371\) | 4467.50 | + | 1705.47i | 0.625178 | + | 0.238662i | ||||
\(372\) | −219.089 | + | 7078.70i | −0.0305356 | + | 0.986596i | ||||
\(373\) | 1931.24 | − | 1115.00i | 0.268086 | − | 0.154779i | −0.359932 | − | 0.932979i | \(-0.617200\pi\) |
0.628017 | + | 0.778199i | \(0.283867\pi\) | |||||||
\(374\) | −6130.64 | + | 10618.6i | −0.847614 | + | 1.46811i | ||||
\(375\) | −5708.95 | + | 4488.01i | −0.786158 | + | 0.618026i | ||||
\(376\) | −768.883 | + | 443.915i | −0.105458 | + | 0.0608861i | ||||
\(377\) | 4148.41i | 0.566721i | ||||||||
\(378\) | 7897.60 | − | 5284.45i | 1.07463 | − | 0.719055i | ||||
\(379\) | −6282.27 | −0.851447 | −0.425723 | − | 0.904853i | \(-0.639980\pi\) | ||||
−0.425723 | + | 0.904853i | \(0.639980\pi\) | |||||||
\(380\) | −3646.53 | + | 1571.57i | −0.492271 | + | 0.212158i | ||||
\(381\) | 4438.32 | + | 2748.96i | 0.596804 | + | 0.369641i | ||||
\(382\) | 8262.80 | + | 4770.53i | 1.10671 | + | 0.638957i | ||||
\(383\) | 2425.65 | − | 1400.45i | 0.323616 | − | 0.186840i | −0.329387 | − | 0.944195i | \(-0.606842\pi\) |
0.653003 | + | 0.757355i | \(0.273509\pi\) | |||||||
\(384\) | −6038.69 | − | 186.900i | −0.802501 | − | 0.0248378i | ||||
\(385\) | −11837.5 | + | 500.392i | −1.56699 | + | 0.0662399i | ||||
\(386\) | − | 2215.79i | − | 0.292178i | ||||||
\(387\) | −10516.2 | + | 5232.76i | −1.38131 | + | 0.687328i | ||||
\(388\) | −825.481 | + | 1429.78i | −0.108009 | + | 0.187077i | ||||
\(389\) | 5033.86 | + | 2906.30i | 0.656110 | + | 0.378805i | 0.790793 | − | 0.612083i | \(-0.209668\pi\) |
−0.134683 | + | 0.990889i | \(0.543002\pi\) | |||||||
\(390\) | 2204.96 | + | 5585.56i | 0.286289 | + | 0.725220i | ||||
\(391\) | − | 5808.93i | − | 0.751330i | ||||||
\(392\) | 3128.02 | − | 1029.12i | 0.403033 | − | 0.132598i | ||||
\(393\) | 3346.68 | + | 103.581i | 0.429561 | + | 0.0132951i | ||||
\(394\) | −653.684 | − | 1132.21i | −0.0835841 | − | 0.144772i | ||||
\(395\) | 1270.46 | − | 1705.39i | 0.161833 | − | 0.217234i | ||||
\(396\) | −6920.79 | − | 4588.68i | −0.878239 | − | 0.582298i | ||||
\(397\) | −562.602 | − | 974.455i | −0.0711239 | − | 0.123190i | 0.828270 | − | 0.560329i | \(-0.189325\pi\) |
−0.899394 | + | 0.437139i | \(0.855992\pi\) | |||||||
\(398\) | 12482.5i | 1.57208i | ||||||||
\(399\) | −6306.85 | + | 811.600i | −0.791322 | + | 0.101832i | ||||
\(400\) | −9499.08 | − | 2257.76i | −1.18739 | − | 0.282220i | ||||
\(401\) | −3095.66 | + | 1787.28i | −0.385511 | + | 0.222575i | −0.680213 | − | 0.733014i | \(-0.738113\pi\) |
0.294702 | + | 0.955589i | \(0.404780\pi\) | |||||||
\(402\) | −7446.39 | − | 4612.06i | −0.923861 | − | 0.572210i | ||||
\(403\) | −6206.88 | − | 3583.55i | −0.767213 | − | 0.442951i | ||||
\(404\) | −988.820 | − | 1712.69i | −0.121771 | − | 0.210914i | ||||
\(405\) | −7916.01 | − | 1940.86i | −0.971234 | − | 0.238128i | ||||
\(406\) | 6270.45 | + | 7714.25i | 0.766496 | + | 0.942985i | ||||
\(407\) | −2948.39 | −0.359082 | ||||||||
\(408\) | −2575.35 | + | 1382.46i | −0.312497 | + | 0.167751i | ||||
\(409\) | 4005.27 | + | 2312.44i | 0.484225 | + | 0.279567i | 0.722175 | − | 0.691710i | \(-0.243142\pi\) |
−0.237951 | + | 0.971277i | \(0.576476\pi\) | |||||||
\(410\) | 4357.01 | − | 5848.56i | 0.524822 | − | 0.704487i | ||||
\(411\) | 4621.78 | + | 8609.76i | 0.554686 | + | 1.03330i | ||||
\(412\) | 4582.97 | 0.548026 | ||||||||
\(413\) | −3116.93 | − | 1189.89i | −0.371366 | − | 0.141769i | ||||
\(414\) | 9770.72 | + | 605.397i | 1.15992 | + | 0.0718687i | ||||
\(415\) | 9645.86 | − | 4157.15i | 1.14096 | − | 0.491726i | ||||
\(416\) | −2951.56 | + | 5112.24i | −0.347865 | + | 0.602520i | ||||
\(417\) | 10053.8 | + | 6227.04i | 1.18067 | + | 0.731269i | ||||
\(418\) | 6913.68 | + | 11974.9i | 0.808994 | + | 1.40122i | ||||
\(419\) | 1241.95 | 0.144805 | 0.0724025 | − | 0.997375i | \(-0.476933\pi\) | ||||
0.0724025 | + | 0.997375i | \(0.476933\pi\) | |||||||
\(420\) | 5040.60 | + | 2834.69i | 0.585610 | + | 0.329331i | ||||
\(421\) | 6728.40 | 0.778913 | 0.389456 | − | 0.921045i | \(-0.372663\pi\) | ||||
0.389456 | + | 0.921045i | \(0.372663\pi\) | |||||||
\(422\) | 4851.17 | + | 8402.48i | 0.559600 | + | 0.969256i | ||||
\(423\) | −2081.03 | − | 1379.78i | −0.239204 | − | 0.158599i | ||||
\(424\) | 1239.43 | − | 2146.76i | 0.141962 | − | 0.245886i | ||||
\(425\) | −7017.79 | + | 2096.09i | −0.800971 | + | 0.239235i | ||||
\(426\) | −369.425 | + | 11936.0i | −0.0420158 | + | 1.35752i | ||||
\(427\) | −6940.24 | − | 8538.26i | −0.786561 | − | 0.967670i | ||||
\(428\) | −6187.57 | −0.698802 | ||||||||
\(429\) | 7404.13 | − | 3974.59i | 0.833274 | − | 0.447308i | ||||
\(430\) | −14264.9 | − | 10627.0i | −1.59981 | − | 1.19181i | ||||
\(431\) | −5318.21 | − | 3070.47i | −0.594360 | − | 0.343154i | 0.172460 | − | 0.985017i | \(-0.444829\pi\) |
−0.766820 | + | 0.641863i | \(0.778162\pi\) | |||||||
\(432\) | −4576.01 | − | 9957.33i | −0.509638 | − | 1.10896i | ||||
\(433\) | −12165.7 | −1.35022 | −0.675109 | − | 0.737718i | \(-0.735904\pi\) | ||||
−0.675109 | + | 0.737718i | \(0.735904\pi\) | |||||||
\(434\) | −16958.8 | + | 2718.06i | −1.87569 | + | 0.300624i | ||||
\(435\) | 1254.13 | − | 8434.05i | 0.138232 | − | 0.929613i | ||||
\(436\) | 3342.63 | + | 5789.60i | 0.367163 | + | 0.635944i | ||||
\(437\) | −5673.23 | − | 3275.44i | −0.621024 | − | 0.358548i | ||||
\(438\) | 8664.73 | − | 13989.6i | 0.945244 | − | 1.52614i | ||||
\(439\) | −6199.80 | + | 3579.45i | −0.674032 | + | 0.389153i | −0.797603 | − | 0.603183i | \(-0.793899\pi\) |
0.123570 | + | 0.992336i | \(0.460566\pi\) | |||||||
\(440\) | −714.969 | + | 6099.99i | −0.0774655 | + | 0.660922i | ||||
\(441\) | 6510.19 | + | 6586.62i | 0.702969 | + | 0.711221i | ||||
\(442\) | 6056.53i | 0.651765i | ||||||||
\(443\) | −4004.38 | − | 6935.79i | −0.429467 | − | 0.743859i | 0.567359 | − | 0.823471i | \(-0.307965\pi\) |
−0.996826 | + | 0.0796117i | \(0.974632\pi\) | |||||||
\(444\) | 1223.44 | + | 757.763i | 0.130771 | + | 0.0809951i | ||||
\(445\) | 4657.77 | − | 6252.29i | 0.496179 | − | 0.666038i | ||||
\(446\) | 2524.69 | + | 4372.89i | 0.268044 | + | 0.464266i | ||||
\(447\) | 357.011 | − | 11534.9i | 0.0377764 | − | 1.22054i | ||||
\(448\) | 407.240 | + | 2540.89i | 0.0429470 | + | 0.267960i | ||||
\(449\) | − | 5413.91i | − | 0.569038i | −0.958670 | − | 0.284519i | \(-0.908166\pi\) | ||
0.958670 | − | 0.284519i | \(-0.0918339\pi\) | |||||||
\(450\) | −2794.27 | − | 12022.5i | −0.292718 | − | 1.25944i | ||||
\(451\) | −8838.66 | − | 5103.00i | −0.922830 | − | 0.532796i | ||||
\(452\) | −5637.59 | + | 9764.58i | −0.586659 | + | 1.01612i | ||||
\(453\) | −4991.87 | − | 9299.18i | −0.517745 | − | 0.964490i | ||||
\(454\) | − | 15157.2i | − | 1.56687i | ||||||
\(455\) | −4940.23 | + | 3137.65i | −0.509014 | + | 0.323287i | ||||
\(456\) | −101.973 | + | 3294.71i | −0.0104722 | + | 0.338353i | ||||
\(457\) | 13022.1 | − | 7518.29i | 1.33292 | − | 0.769564i | 0.347177 | − | 0.937800i | \(-0.387140\pi\) |
0.985747 | + | 0.168236i | \(0.0538071\pi\) | |||||||
\(458\) | 9433.05 | + | 5446.17i | 0.962396 | + | 0.555640i | ||||
\(459\) | −6707.44 | − | 4752.35i | −0.682084 | − | 0.483270i | ||||
\(460\) | 2357.95 | + | 5471.16i | 0.239000 | + | 0.554552i | ||||
\(461\) | 7696.93 | 0.777618 | 0.388809 | − | 0.921318i | \(-0.372887\pi\) | ||||
0.388809 | + | 0.921318i | \(0.372887\pi\) | |||||||
\(462\) | 7760.76 | − | 18582.6i | 0.781523 | − | 1.87130i | ||||
\(463\) | − | 3089.56i | − | 0.310117i | −0.987905 | − | 0.155058i | \(-0.950443\pi\) | ||
0.987905 | − | 0.155058i | \(-0.0495566\pi\) | |||||||
\(464\) | 9928.50 | − | 5732.22i | 0.993360 | − | 0.573517i | ||||
\(465\) | 11535.7 | + | 9162.08i | 1.15045 | + | 0.913723i | ||||
\(466\) | 1533.05 | − | 2655.32i | 0.152397 | − | 0.263960i | ||||
\(467\) | 13115.7 | − | 7572.33i | 1.29961 | − | 0.750333i | 0.319277 | − | 0.947661i | \(-0.396560\pi\) |
0.980337 | + | 0.197328i | \(0.0632265\pi\) | |||||||
\(468\) | −4093.87 | − | 253.657i | −0.404357 | − | 0.0250541i | ||||
\(469\) | 3044.47 | − | 7975.02i | 0.299745 | − | 0.785186i | ||||
\(470\) | 440.182 | − | 3755.56i | 0.0432002 | − | 0.368577i | ||||
\(471\) | 674.029 | + | 1255.63i | 0.0659398 | + | 0.122837i | ||||
\(472\) | −864.738 | + | 1497.77i | −0.0843279 | + | 0.146060i | ||||
\(473\) | −12446.5 | + | 21557.9i | −1.20992 | + | 2.09563i | ||||
\(474\) | 1709.59 | + | 3184.73i | 0.165662 | + | 0.308607i | ||||
\(475\) | −1909.95 | + | 8035.76i | −0.184494 | + | 0.776223i | ||||
\(476\) | 3678.93 | + | 4526.01i | 0.354251 | + | 0.435818i | ||||
\(477\) | 6958.11 | + | 431.126i | 0.667903 | + | 0.0413835i | ||||
\(478\) | 11492.9 | − | 6635.42i | 1.09973 | − | 0.634931i | ||||
\(479\) | 2366.30 | − | 4098.55i | 0.225718 | − | 0.390955i | −0.730817 | − | 0.682574i | \(-0.760861\pi\) |
0.956535 | + | 0.291619i | \(0.0941939\pi\) | |||||||
\(480\) | 7546.27 | − | 9501.31i | 0.717580 | − | 0.903487i | ||||
\(481\) | −1261.26 | + | 728.189i | −0.119560 | + | 0.0690281i | ||||
\(482\) | 3872.05i | 0.365906i | ||||||||
\(483\) | 1217.70 | + | 9462.64i | 0.114715 | + | 0.891439i | ||||
\(484\) | −10443.8 | −0.980824 | ||||||||
\(485\) | 1359.20 | + | 3153.75i | 0.127254 | + | 0.295267i | ||||
\(486\) | 8692.58 | − | 10786.8i | 0.811324 | − | 1.00678i | ||||
\(487\) | −3459.37 | − | 1997.27i | −0.321887 | − | 0.185842i | 0.330346 | − | 0.943860i | \(-0.392834\pi\) |
−0.652233 | + | 0.758018i | \(0.726168\pi\) | |||||||
\(488\) | −4939.61 | + | 2851.88i | −0.458208 | + | 0.264547i | ||||
\(489\) | −251.003 | + | 8109.84i | −0.0232122 | + | 0.749979i | ||||
\(490\) | −4444.04 | + | 13302.0i | −0.409717 | + | 1.22637i | ||||
\(491\) | − | 8902.22i | − | 0.818231i | −0.912483 | − | 0.409116i | \(-0.865837\pi\) | ||
0.912483 | − | 0.409116i | \(-0.134163\pi\) | |||||||
\(492\) | 2356.11 | + | 4389.12i | 0.215898 | + | 0.402189i | ||||
\(493\) | 4299.96 | − | 7447.75i | 0.392821 | − | 0.680385i | ||||
\(494\) | 5915.05 | + | 3415.06i | 0.538727 | + | 0.311034i | ||||
\(495\) | −16254.8 | + | 5842.29i | −1.47596 | + | 0.530487i | ||||
\(496\) | 19806.8i | 1.79305i | ||||||||
\(497\) | −11491.6 | + | 1841.81i | −1.03716 | + | 0.166230i | ||||
\(498\) | −552.290 | + | 17844.3i | −0.0496962 | + | 1.60567i | ||||
\(499\) | −9451.17 | − | 16369.9i | −0.847881 | − | 1.46857i | −0.883096 | − | 0.469193i | \(-0.844545\pi\) |
0.0352153 | − | 0.999380i | \(-0.488788\pi\) | |||||||
\(500\) | 5758.89 | − | 4822.85i | 0.515091 | − | 0.431369i | ||||
\(501\) | 4325.93 | + | 2679.35i | 0.385765 | + | 0.238931i | ||||
\(502\) | −10109.7 | − | 17510.6i | −0.898843 | − | 1.55684i | ||||
\(503\) | − | 17198.7i | − | 1.52455i | −0.647251 | − | 0.762277i | \(-0.724081\pi\) | ||
0.647251 | − | 0.762277i | \(-0.275919\pi\) | |||||||
\(504\) | 3905.39 | − | 2791.87i | 0.345159 | − | 0.246746i | ||||
\(505\) | −4085.73 | − | 478.882i | −0.360025 | − | 0.0421979i | ||||
\(506\) | 17966.8 | − | 10373.1i | 1.57850 | − | 0.911347i | ||||
\(507\) | −3825.40 | + | 6176.29i | −0.335092 | + | 0.541023i | ||||
\(508\) | −4676.76 | − | 2700.13i | −0.408460 | − | 0.235825i | ||||
\(509\) | 6930.54 | + | 12004.0i | 0.603518 | + | 1.04532i | 0.992284 | + | 0.123987i | \(0.0395682\pi\) |
−0.388766 | + | 0.921337i | \(0.627098\pi\) | |||||||
\(510\) | 1830.98 | − | 12313.4i | 0.158975 | − | 1.06911i | ||||
\(511\) | 14982.8 | + | 5719.69i | 1.29706 | + | 0.495155i | ||||
\(512\) | 10314.6 | 0.890322 | ||||||||
\(513\) | −8423.42 | + | 3871.08i | −0.724957 | + | 0.333163i | ||||
\(514\) | −1579.97 | − | 912.194i | −0.135582 | − | 0.0782785i | ||||
\(515\) | 5695.20 | − | 7644.87i | 0.487302 | − | 0.654123i | ||||
\(516\) | 10705.3 | − | 5746.68i | 0.913322 | − | 0.490278i | ||||
\(517\) | −5291.53 | −0.450138 | ||||||||
\(518\) | −1244.72 | + | 3260.55i | −0.105579 | + | 0.276565i | ||||
\(519\) | −333.358 | + | 10770.7i | −0.0281942 | + | 0.910946i | ||||
\(520\) | 1200.72 | + | 2786.03i | 0.101259 | + | 0.234953i | ||||
\(521\) | −5717.97 | + | 9903.82i | −0.480823 | + | 0.832810i | −0.999758 | − | 0.0220037i | \(-0.992995\pi\) |
0.518935 | + | 0.854814i | \(0.326329\pi\) | |||||||
\(522\) | 12079.1 | + | 8008.80i | 1.01281 | + | 0.671525i | ||||
\(523\) | 10835.6 | + | 18767.7i | 0.905939 | + | 1.56913i | 0.819652 | + | 0.572862i | \(0.194167\pi\) |
0.0862877 | + | 0.996270i | \(0.472500\pi\) | |||||||
\(524\) | −3463.45 | −0.288743 | ||||||||
\(525\) | 10992.5 | − | 4885.60i | 0.913810 | − | 0.406143i | ||||
\(526\) | 7756.34 | 0.642951 | ||||||||
\(527\) | 7428.93 | + | 12867.3i | 0.614059 | + | 1.06358i | ||||
\(528\) | −19743.5 | − | 12228.5i | −1.62732 | − | 1.00791i | ||||
\(529\) | 1169.11 | − | 2024.95i | 0.0960884 | − | 0.166430i | ||||
\(530\) | 4178.49 | + | 9695.38i | 0.342457 | + | 0.794604i | ||||
\(531\) | −4854.60 | − | 300.792i | −0.396745 | − | 0.0245824i | ||||
\(532\) | 6494.70 | − | 1040.93i | 0.529288 | − | 0.0848312i | ||||
\(533\) | −5041.32 | −0.409688 | ||||||||
\(534\) | 6267.68 | + | 11675.8i | 0.507920 | + | 0.946186i | ||||
\(535\) | −7689.22 | + | 10321.5i | −0.621372 | + | 0.834089i | ||||
\(536\) | −3832.22 | − | 2212.53i | −0.308818 | − | 0.178296i | ||||
\(537\) | 12480.6 | − | 6699.69i | 1.00294 | − | 0.538385i | ||||
\(538\) | 7004.73 | 0.561330 | ||||||||
\(539\) | 19212.3 | + | 4009.75i | 1.53531 | + | 0.320431i | ||||
\(540\) | 8246.49 | + | 1753.35i | 0.657171 | + | 0.139726i | ||||
\(541\) | 5202.43 | + | 9010.88i | 0.413438 | + | 0.716096i | 0.995263 | − | 0.0972182i | \(-0.0309945\pi\) |
−0.581825 | + | 0.813314i | \(0.697661\pi\) | |||||||
\(542\) | −20955.9 | − | 12098.9i | −1.66076 | − | 0.958841i | ||||
\(543\) | −5393.03 | − | 3340.27i | −0.426220 | − | 0.263987i | ||||
\(544\) | 10598.0 | − | 6118.77i | 0.835269 | − | 0.482243i | ||||
\(545\) | 13811.5 | + | 1618.82i | 1.08554 | + | 0.127234i | ||||
\(546\) | −1269.61 | − | 9865.98i | −0.0995132 | − | 0.773306i | ||||
\(547\) | 3193.07i | 0.249590i | 0.992183 | + | 0.124795i | \(0.0398273\pi\) | ||||
−0.992183 | + | 0.124795i | \(0.960173\pi\) | |||||||
\(548\) | −5053.99 | − | 8753.76i | −0.393970 | − | 0.682376i | ||||
\(549\) | −13369.4 | − | 8864.27i | −1.03933 | − | 0.689104i | ||||
\(550\) | −19014.9 | − | 17962.7i | −1.47418 | − | 1.39260i | ||||
\(551\) | −4849.18 | − | 8399.03i | −0.374922 | − | 0.649384i | ||||
\(552\) | 4943.30 | + | 152.997i | 0.381161 | + | 0.0117971i | ||||
\(553\) | −2733.58 | + | 2221.96i | −0.210205 | + | 0.170863i | ||||
\(554\) | − | 16911.9i | − | 1.29697i | ||||||
\(555\) | 2784.39 | − | 1099.17i | 0.212956 | − | 0.0840669i | ||||
\(556\) | −10594.0 | − | 6116.43i | −0.808065 | − | 0.466537i | ||||
\(557\) | 7060.98 | − | 12230.0i | 0.537134 | − | 0.930343i | −0.461923 | − | 0.886920i | \(-0.652840\pi\) |
0.999057 | − | 0.0434229i | \(-0.0138263\pi\) | |||||||
\(558\) | −22417.2 | + | 11154.6i | −1.70071 | + | 0.846257i | ||||
\(559\) | 12296.0i | 0.930352i | ||||||||
\(560\) | 14335.8 | + | 7488.02i | 1.08178 | + | 0.565048i | ||||
\(561\) | −17412.6 | − | 538.929i | −1.31045 | − | 0.0405590i | ||||
\(562\) | −29627.8 | + | 17105.6i | −2.22379 | + | 1.28391i | ||||
\(563\) | 3222.99 | + | 1860.80i | 0.241266 | + | 0.139295i | 0.615759 | − | 0.787935i | \(-0.288850\pi\) |
−0.374492 | + | 0.927230i | \(0.622183\pi\) | |||||||
\(564\) | 2195.74 | + | 1359.97i | 0.163931 | + | 0.101534i | ||||
\(565\) | 9282.57 | + | 21538.4i | 0.691187 | + | 1.60377i | ||||
\(566\) | −8969.64 | −0.666117 | ||||||||
\(567\) | 11922.5 | + | 6335.44i | 0.883067 | + | 0.469248i | ||||
\(568\) | 6033.00i | 0.445667i | ||||||||
\(569\) | −11508.4 | + | 6644.40i | −0.847906 | + | 0.489539i | −0.859944 | − | 0.510389i | \(-0.829502\pi\) |
0.0120377 | + | 0.999928i | \(0.496168\pi\) | |||||||
\(570\) | −10993.4 | − | 8731.31i | −0.807827 | − | 0.641604i | ||||
\(571\) | 8163.22 | − | 14139.1i | 0.598284 | − | 1.03626i | −0.394790 | − | 0.918771i | \(-0.629183\pi\) |
0.993074 | − | 0.117487i | \(-0.0374839\pi\) | |||||||
\(572\) | −7527.96 | + | 4346.27i | −0.550279 | + | 0.317704i | ||||
\(573\) | −419.366 | + | 13549.6i | −0.0305746 | + | 0.987856i | ||||
\(574\) | −9374.69 | + | 7620.12i | −0.681693 | + | 0.554108i | ||||
\(575\) | 12056.7 | + | 2865.65i | 0.874430 | + | 0.207836i | ||||
\(576\) | 1671.27 | + | 3358.72i | 0.120896 | + | 0.242963i | ||||
\(577\) | 9451.10 | − | 16369.8i | 0.681897 | − | 1.18108i | −0.292504 | − | 0.956264i | \(-0.594489\pi\) |
0.974401 | − | 0.224816i | \(-0.0721781\pi\) | |||||||
\(578\) | −2706.04 | + | 4686.99i | −0.194734 | + | 0.337289i | ||||
\(579\) | 2773.83 | − | 1489.01i | 0.199096 | − | 0.106876i | ||||
\(580\) | −1026.76 | + | 8760.12i | −0.0735066 | + | 0.627145i | ||||
\(581\) | −17179.9 | + | 2753.49i | −1.22675 | + | 0.196616i | ||||
\(582\) | −5834.27 | − | 180.573i | −0.415530 | − | 0.0128608i | ||||
\(583\) | 12794.8 | − | 7387.10i | 0.908933 | − | 0.524772i | ||||
\(584\) | 4156.71 | − | 7199.63i | 0.294531 | − | 0.510142i | ||||
\(585\) | −5510.53 | + | 6513.78i | −0.389457 | + | 0.460362i | ||||
\(586\) | −18751.4 | + | 10826.1i | −1.32186 | + | 0.763178i | ||||
\(587\) | − | 27857.8i | − | 1.95879i | −0.201942 | − | 0.979397i | \(-0.564725\pi\) | ||
0.201942 | − | 0.979397i | \(-0.435275\pi\) | |||||||
\(588\) | −6941.68 | − | 6601.60i | −0.486854 | − | 0.463002i | ||||
\(589\) | 16755.6 | 1.17216 | ||||||||
\(590\) | −2915.29 | − | 6764.36i | −0.203425 | − | 0.472007i | ||||
\(591\) | 978.083 | − | 1579.16i | 0.0680761 | − | 0.109912i | ||||
\(592\) | 3485.59 | + | 2012.41i | 0.241988 | + | 0.139712i | ||||
\(593\) | −2724.87 | + | 1573.20i | −0.188697 | + | 0.108944i | −0.591372 | − | 0.806399i | \(-0.701414\pi\) |
0.402676 | + | 0.915343i | \(0.368080\pi\) | |||||||
\(594\) | 2721.20 | − | 29232.2i | 0.187967 | − | 2.01921i | ||||
\(595\) | 12121.6 | − | 512.404i | 0.835190 | − | 0.0353051i | ||||
\(596\) | 11937.4i | 0.820429i | ||||||||
\(597\) | −15626.1 | + | 8388.23i | −1.07125 | + | 0.575054i | ||||
\(598\) | 5123.87 | − | 8874.80i | 0.350385 | − | 0.606885i | ||||
\(599\) | −17180.9 | − | 9919.42i | −1.17194 | − | 0.676622i | −0.217807 | − | 0.975992i | \(-0.569890\pi\) |
−0.954137 | + | 0.299370i | \(0.903224\pi\) | |||||||
\(600\) | −1598.90 | − | 6027.22i | −0.108791 | − | 0.410100i | ||||
\(601\) | 6956.27i | 0.472133i | 0.971737 | + | 0.236067i | \(0.0758583\pi\) | ||||
−0.971737 | + | 0.236067i | \(0.924142\pi\) | |||||||
\(602\) | 18585.9 | + | 22865.3i | 1.25831 | + | 1.54804i | ||||
\(603\) | 769.611 | − | 12421.0i | 0.0519751 | − | 0.838846i | ||||
\(604\) | 5458.68 | + | 9454.71i | 0.367733 | + | 0.636932i | ||||
\(605\) | −12978.4 | + | 17421.4i | −0.872144 | + | 1.17071i | ||||
\(606\) | 3681.68 | − | 5944.25i | 0.246795 | − | 0.398463i | ||||
\(607\) | −3693.67 | − | 6397.63i | −0.246988 | − | 0.427795i | 0.715701 | − | 0.698407i | \(-0.246107\pi\) |
−0.962689 | + | 0.270612i | \(0.912774\pi\) | |||||||
\(608\) | − | 13800.6i | − | 0.920540i | ||||||
\(609\) | −5443.31 | + | 13033.6i | −0.362191 | + | 0.867241i | ||||
\(610\) | 2827.90 | − | 24127.2i | 0.187702 | − | 1.60144i | ||||
\(611\) | −2263.61 | + | 1306.89i | −0.149878 | + | 0.0865323i | ||||
\(612\) | 7086.92 | + | 4698.83i | 0.468091 | + | 0.310358i | ||||
\(613\) | −3129.62 | − | 1806.88i | −0.206206 | − | 0.119053i | 0.393341 | − | 0.919393i | \(-0.371319\pi\) |
−0.599547 | + | 0.800340i | \(0.704652\pi\) | |||||||
\(614\) | −7766.16 | − | 13451.4i | −0.510451 | − | 0.884127i | ||||
\(615\) | 10249.4 | + | 1524.07i | 0.672027 | + | 0.0999291i | ||||
\(616\) | 3628.46 | − | 9504.78i | 0.237329 | − | 0.621686i | ||||
\(617\) | 9799.49 | 0.639405 | 0.319702 | − | 0.947518i | \(-0.396417\pi\) | ||||
0.319702 | + | 0.947518i | \(0.396417\pi\) | |||||||
\(618\) | 7663.69 | + | 14276.4i | 0.498833 | + | 0.929259i | ||||
\(619\) | 24554.3 | + | 14176.4i | 1.59438 | + | 0.920513i | 0.992543 | + | 0.121891i | \(0.0388959\pi\) |
0.601832 | + | 0.798622i | \(0.294437\pi\) | |||||||
\(620\) | −12220.0 | − | 9103.56i | −0.791561 | − | 0.589690i | ||||
\(621\) | 5808.07 | + | 12638.3i | 0.375314 | + | 0.816678i | ||||
\(622\) | 13214.2 | 0.851837 | ||||||||
\(623\) | −10021.8 | + | 8146.14i | −0.644488 | + | 0.523866i | ||||
\(624\) | −11466.0 | − | 354.878i | −0.735588 | − | 0.0227668i | ||||
\(625\) | −888.508 | − | 15599.7i | −0.0568645 | − | 0.998382i | ||||
\(626\) | 1335.28 | − | 2312.77i | 0.0852531 | − | 0.147663i | ||||
\(627\) | −10344.7 | + | 16702.0i | −0.658895 | + | 1.06382i | ||||
\(628\) | −737.060 | − | 1276.63i | −0.0468343 | − | 0.0811193i | ||||
\(629\) | 3019.17 | 0.191386 | ||||||||
\(630\) | −401.422 | + | 20442.2i | −0.0253858 | + | 1.29276i | ||||
\(631\) | 4670.05 | 0.294630 | 0.147315 | − | 0.989090i | \(-0.452937\pi\) | ||||
0.147315 | + | 0.989090i | \(0.452937\pi\) | |||||||
\(632\) | 913.048 | + | 1581.45i | 0.0574669 | + | 0.0995357i | ||||
\(633\) | −7258.63 | + | 11719.4i | −0.455773 | + | 0.735868i | ||||
\(634\) | −12381.3 | + | 21445.1i | −0.775593 | + | 1.34337i | ||||
\(635\) | −10315.8 | + | 4445.90i | −0.644680 | + | 0.277843i | ||||
\(636\) | −7207.81 | − | 223.085i | −0.449384 | − | 0.0139086i | ||||
\(637\) | 9208.95 | − | 3029.74i | 0.572797 | − | 0.188450i | ||||
\(638\) | 30714.1 | 1.90593 | ||||||||
\(639\) | −15190.3 | + | 7558.56i | −0.940408 | + | 0.467937i | ||||
\(640\) | 7766.05 | − | 10424.6i | 0.479656 | − | 0.643859i | ||||
\(641\) | 25125.2 | + | 14506.0i | 1.54818 | + | 0.893843i | 0.998281 | + | 0.0586122i | \(0.0186675\pi\) |
0.549900 | + | 0.835230i | \(0.314666\pi\) | |||||||
\(642\) | −10346.9 | − | 19274.9i | −0.636075 | − | 1.18492i | ||||
\(643\) | 4817.00 | 0.295434 | 0.147717 | − | 0.989030i | \(-0.452808\pi\) | ||||
0.147717 | + | 0.989030i | \(0.452808\pi\) | |||||||
\(644\) | −1561.79 | − | 9744.48i | −0.0955639 | − | 0.596252i | ||||
\(645\) | 3717.28 | − | 24998.9i | 0.226927 | − | 1.52609i | ||||
\(646\) | −7079.64 | − | 12262.3i | −0.431184 | − | 0.746833i | ||||
\(647\) | 394.988 | + | 228.046i | 0.0240009 | + | 0.0138569i | 0.511952 | − | 0.859014i | \(-0.328922\pi\) |
−0.487952 | + | 0.872871i | \(0.662256\pi\) | |||||||
\(648\) | 4220.83 | − | 5582.75i | 0.255879 | − | 0.338443i | ||||
\(649\) | −8926.81 | + | 5153.90i | −0.539920 | + | 0.311723i | ||||
\(650\) | −12570.6 | − | 2987.79i | −0.758551 | − | 0.180294i | ||||
\(651\) | −14798.9 | − | 19403.3i | −0.890960 | − | 1.16816i | ||||
\(652\) | − | 8392.82i | − | 0.504123i | ||||||
\(653\) | −11166.2 | − | 19340.4i | −0.669168 | − | 1.15903i | −0.978137 | − | 0.207961i | \(-0.933317\pi\) |
0.308969 | − | 0.951072i | \(-0.400016\pi\) | |||||||
\(654\) | −12445.6 | + | 20094.1i | −0.744132 | + | 1.20144i | ||||
\(655\) | −4303.99 | + | 5777.39i | −0.256749 | + | 0.344643i | ||||
\(656\) | 6966.05 | + | 12065.5i | 0.414601 | + | 0.718110i | ||||
\(657\) | 23335.6 | + | 1445.88i | 1.38570 | + | 0.0858586i | ||||
\(658\) | −2233.92 | + | 5851.77i | −0.132351 | + | 0.346696i | ||||
\(659\) | 6124.90i | 0.362052i | 0.983478 | + | 0.181026i | \(0.0579418\pi\) | ||||
−0.983478 | + | 0.181026i | \(0.942058\pi\) | |||||||
\(660\) | 16618.9 | − | 6560.51i | 0.980137 | − | 0.386920i | ||||
\(661\) | −2884.22 | − | 1665.21i | −0.169718 | − | 0.0979865i | 0.412735 | − | 0.910851i | \(-0.364574\pi\) |
−0.582453 | + | 0.812865i | \(0.697907\pi\) | |||||||
\(662\) | 11388.4 | − | 19725.3i | 0.668614 | − | 1.15807i | ||||
\(663\) | −7581.86 | + | 4070.00i | −0.444125 | + | 0.238410i | ||||
\(664\) | 9019.32i | 0.527135i | ||||||||
\(665\) | 6334.50 | − | 12127.4i | 0.369386 | − | 0.707188i | ||||
\(666\) | −314.652 | + | 5078.29i | −0.0183071 | + | 0.295465i | ||||
\(667\) | −12601.7 | + | 7275.59i | −0.731543 | + | 0.422357i | ||||
\(668\) | −4558.33 | − | 2631.76i | −0.264023 | − | 0.152434i | ||||
\(669\) | −3777.60 | + | 6099.12i | −0.218312 | + | 0.352475i | ||||
\(670\) | 17307.4 | − | 7459.10i | 0.997974 | − | 0.430105i | ||||
\(671\) | −33994.9 | −1.95582 | ||||||||
\(672\) | −15981.3 | + | 12189.0i | −0.917401 | + | 0.699703i | ||||
\(673\) | − | 1875.76i | − | 0.107437i | −0.998556 | − | 0.0537186i | \(-0.982893\pi\) | ||
0.998556 | − | 0.0537186i | \(-0.0171074\pi\) | |||||||
\(674\) | −2628.57 | + | 1517.61i | −0.150221 | + | 0.0867301i | ||||
\(675\) | 13172.6 | − | 11577.1i | 0.751130 | − | 0.660154i | ||||
\(676\) | 3757.45 | − | 6508.09i | 0.213783 | − | 0.370283i | ||||
\(677\) | −22553.4 | + | 13021.2i | −1.28035 | + | 0.739211i | −0.976912 | − | 0.213640i | \(-0.931468\pi\) |
−0.303438 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(678\) | −39844.9 | − | 1233.22i | −2.25698 | − | 0.0698546i | ||||
\(679\) | −900.266 | − | 5617.04i | −0.0508822 | − | 0.317470i | ||||
\(680\) | 732.132 | − | 6246.42i | 0.0412882 | − | 0.352264i | ||||
\(681\) | 18974.4 | − | 10185.6i | 1.06770 | − | 0.573148i | ||||
\(682\) | −26532.0 | + | 45954.7i | −1.48968 | + | 2.58020i | ||||
\(683\) | −12143.0 | + | 21032.4i | −0.680294 | + | 1.17830i | 0.294598 | + | 0.955621i | \(0.404814\pi\) |
−0.974891 | + | 0.222682i | \(0.928519\pi\) | |||||||
\(684\) | 8585.12 | − | 4271.87i | 0.479913 | − | 0.238800i | ||||
\(685\) | −20882.7 | − | 2447.63i | −1.16480 | − | 0.136524i | ||||
\(686\) | 12545.1 | − | 19553.6i | 0.698214 | − | 1.08828i | ||||
\(687\) | −478.760 | + | 15468.6i | −0.0265878 | + | 0.859044i | ||||
\(688\) | 29428.5 | − | 16990.5i | 1.63074 | − | 0.941509i | ||||
\(689\) | 3648.90 | − | 6320.09i | 0.201759 | − | 0.349457i | ||||
\(690\) | −13100.2 | + | 16494.2i | −0.722779 | + | 0.910032i | ||||
\(691\) | −1566.38 | + | 904.352i | −0.0862345 | + | 0.0497875i | −0.542497 | − | 0.840058i | \(-0.682521\pi\) |
0.456263 | + | 0.889845i | \(0.349188\pi\) | |||||||
\(692\) | − | 11146.5i | − | 0.612323i | ||||||
\(693\) | 28477.8 | − | 2772.24i | 1.56102 | − | 0.151961i | ||||
\(694\) | −2680.43 | −0.146611 | ||||||||
\(695\) | −23367.8 | + | 10071.0i | −1.27538 | + | 0.549662i | ||||
\(696\) | 6224.65 | + | 3855.35i | 0.339001 | + | 0.209967i | ||||
\(697\) | 9050.83 | + | 5225.50i | 0.491857 | + | 0.283974i | ||||
\(698\) | 4437.72 | − | 2562.12i | 0.240645 | − | 0.138936i | ||||
\(699\) | 4354.26 | + | 134.766i | 0.235613 | + | 0.00729233i | ||||
\(700\) | −11208.8 | + | 5402.99i | −0.605218 | + | 0.291734i | ||||
\(701\) | 30533.4i | 1.64512i | 0.568676 | + | 0.822561i | \(0.307456\pi\) | ||||
−0.568676 | + | 0.822561i | \(0.692544\pi\) | |||||||
\(702\) | −6055.64 | − | 13177.0i | −0.325578 | − | 0.708452i | ||||
\(703\) | 1702.40 | − | 2948.64i | 0.0913331 | − | 0.158194i | ||||
\(704\) | 6885.29 | + | 3975.22i | 0.368607 | + | 0.212815i | ||||
\(705\) | 4997.19 | − | 1972.70i | 0.266958 | − | 0.105385i | ||||
\(706\) | − | 37510.0i | − | 1.99958i | ||||||
\(707\) | 6366.24 | + | 2430.32i | 0.338652 | + | 0.129281i | ||||
\(708\) | 5028.81 | + | 155.644i | 0.266941 | + | 0.00826194i | ||||
\(709\) | −6699.23 | − | 11603.4i | −0.354859 | − | 0.614633i | 0.632235 | − | 0.774777i | \(-0.282138\pi\) |
−0.987094 | + | 0.160143i | \(0.948804\pi\) | |||||||
\(710\) | −20605.3 | − | 15350.3i | −1.08916 | − | 0.811390i | ||||
\(711\) | −2837.95 | + | 4280.29i | −0.149693 | + | 0.225771i | ||||
\(712\) | 3347.41 | + | 5797.89i | 0.176193 | + | 0.305176i | ||||
\(713\) | − | 25139.7i | − | 1.32046i | ||||||
\(714\) | −7947.06 | + | 19028.7i | −0.416542 | + | 0.997381i | ||||
\(715\) | −2104.88 | + | 17958.5i | −0.110095 | + | 0.939313i | ||||
\(716\) | −12689.4 | + | 7326.21i | −0.662324 | + | 0.382393i | ||||
\(717\) | 16029.8 | + | 9928.34i | 0.834927 | + | 0.517128i | ||||
\(718\) | 22236.3 | + | 12838.1i | 1.15578 | + | 0.667290i | ||||
\(719\) | −11691.5 | − | 20250.3i | −0.606424 | − | 1.05036i | −0.991825 | − | 0.127608i | \(-0.959270\pi\) |
0.385400 | − | 0.922749i | \(-0.374063\pi\) | |||||||
\(720\) | 23204.0 | + | 4187.84i | 1.20106 | + | 0.216766i | ||||
\(721\) | −12254.0 | + | 9960.54i | −0.632958 | + | 0.514494i | ||||
\(722\) | 9116.71 | 0.469929 | ||||||||
\(723\) | −4847.21 | + | 2602.02i | −0.249336 | + | 0.133845i | ||||
\(724\) | 5682.76 | + | 3280.94i | 0.291710 | + | 0.168419i | ||||
\(725\) | 13336.8 | + | 12598.8i | 0.683197 | + | 0.645392i | ||||
\(726\) | −17464.2 | − | 32533.5i | −0.892781 | − | 1.66313i | ||||
\(727\) | −24256.5 | −1.23745 | −0.618723 | − | 0.785609i | \(-0.712350\pi\) | ||||
−0.618723 | + | 0.785609i | \(0.712350\pi\) | |||||||
\(728\) | −795.296 | − | 4962.10i | −0.0404885 | − | 0.252620i | ||||
\(729\) | 19344.8 | + | 3633.07i | 0.982818 | + | 0.184579i | ||||
\(730\) | 14013.5 | + | 32515.6i | 0.710497 | + | 1.64857i | ||||
\(731\) | 12745.3 | − | 22075.4i | 0.644870 | − | 1.11695i | ||||
\(732\) | 14106.3 | + | 8736.98i | 0.712272 | + | 0.441159i | ||||
\(733\) | −5083.73 | − | 8805.28i | −0.256169 | − | 0.443698i | 0.709043 | − | 0.705165i | \(-0.249127\pi\) |
−0.965212 | + | 0.261467i | \(0.915794\pi\) | |||||||
\(734\) | 30162.2 | 1.51677 | ||||||||
\(735\) | −19638.5 | + | 3375.71i | −0.985546 | + | 0.169408i | ||||
\(736\) | −20706.1 | −1.03701 | ||||||||
\(737\) | −13186.8 | − | 22840.3i | −0.659082 | − | 1.14156i | ||||
\(738\) | −9732.64 | + | 14679.1i | −0.485452 | + | 0.732173i | ||||
\(739\) | −4828.03 | + | 8362.40i | −0.240328 | + | 0.416260i | −0.960808 | − | 0.277216i | \(-0.910588\pi\) |
0.720480 | + | 0.693476i | \(0.243922\pi\) | |||||||
\(740\) | −2843.61 | + | 1225.53i | −0.141261 | + | 0.0608804i | ||||
\(741\) | −300.209 | + | 9699.67i | −0.0148832 | + | 0.480872i | ||||
\(742\) | −2767.63 | − | 17268.1i | −0.136931 | − | 0.854355i | ||||
\(743\) | 23051.5 | 1.13819 | 0.569097 | − | 0.822270i | \(-0.307293\pi\) | ||||
0.569097 | + | 0.822270i | \(0.307293\pi\) | |||||||
\(744\) | −11145.5 | + | 5982.99i | −0.549212 | + | 0.294821i | ||||
\(745\) | 19912.8 | + | 14834.5i | 0.979262 | + | 0.729522i | ||||
\(746\) | −7062.88 | − | 4077.76i | −0.346636 | − | 0.200130i | ||||
\(747\) | −22709.5 | + | 11300.0i | −1.11231 | + | 0.553476i | ||||
\(748\) | 18020.2 | 0.880861 | ||||||||
\(749\) | 16544.4 | − | 13447.9i | 0.807101 | − | 0.656044i | ||||
\(750\) | 24653.7 | + | 9874.70i | 1.20030 | + | 0.480764i | ||||
\(751\) | −15368.6 | − | 26619.2i | −0.746749 | − | 1.29341i | −0.949373 | − | 0.314151i | \(-0.898280\pi\) |
0.202623 | − | 0.979257i | \(-0.435053\pi\) | |||||||
\(752\) | 6255.65 | + | 3611.70i | 0.303351 | + | 0.175140i | ||||
\(753\) | 15126.8 | − | 24423.0i | 0.732074 | − | 1.18197i | ||||
\(754\) | 13138.8 | − | 7585.71i | 0.634600 | − | 0.366386i | ||||
\(755\) | 22554.9 | + | 2643.62i | 1.08723 | + | 0.127432i | ||||
\(756\) | −12529.5 | − | 6168.71i | −0.602767 | − | 0.296764i | ||||
\(757\) | 25957.3i | 1.24628i | 0.782111 | + | 0.623140i | \(0.214143\pi\) | ||||
−0.782111 | + | 0.623140i | \(0.785857\pi\) | |||||||
\(758\) | 11487.7 | + | 19897.2i | 0.550462 | + | 0.953429i | ||||
\(759\) | 25059.3 | + | 15520.9i | 1.19841 | + | 0.742257i | ||||
\(760\) | −5687.68 | − | 4237.16i | −0.271466 | − | 0.202234i | ||||
\(761\) | 4938.41 | + | 8553.57i | 0.235239 | + | 0.407446i | 0.959342 | − | 0.282245i | \(-0.0910793\pi\) |
−0.724103 | + | 0.689692i | \(0.757746\pi\) | |||||||
\(762\) | 590.651 | − | 19083.8i | 0.0280801 | − | 0.907260i | ||||
\(763\) | −21520.6 | − | 8215.50i | −1.02110 | − | 0.389805i | ||||
\(764\) | − | 14022.4i | − | 0.664020i | ||||||
\(765\) | 16645.0 | − | 5982.53i | 0.786667 | − | 0.282743i | ||||
\(766\) | −8871.01 | − | 5121.68i | −0.418437 | − | 0.241585i | ||||
\(767\) | −2545.80 | + | 4409.46i | −0.119848 | + | 0.207583i | ||||
\(768\) | 13182.1 | + | 24556.5i | 0.619360 | + | 1.15378i | ||||
\(769\) | − | 33326.9i | − | 1.56281i | −0.624026 | − | 0.781404i | \(-0.714504\pi\) | ||
0.624026 | − | 0.781404i | \(-0.285496\pi\) | |||||||
\(770\) | 23230.7 | + | 36576.6i | 1.08724 | + | 1.71186i | ||||
\(771\) | 80.1887 | − | 2590.87i | 0.00374569 | − | 0.121022i | ||||
\(772\) | −2820.22 | + | 1628.26i | −0.131479 | + | 0.0759096i | ||||
\(773\) | 21335.2 | + | 12317.9i | 0.992722 | + | 0.573148i | 0.906087 | − | 0.423092i | \(-0.139055\pi\) |
0.0866350 | + | 0.996240i | \(0.472389\pi\) | |||||||
\(774\) | 35803.0 | + | 23738.4i | 1.66268 | + | 1.10240i | ||||
\(775\) | −30371.4 | + | 9071.37i | −1.40770 | + | 0.420456i | ||||
\(776\) | −2948.90 | −0.136417 | ||||||||
\(777\) | −4918.17 | + | 632.897i | −0.227076 | + | 0.0292214i | ||||
\(778\) | − | 21257.7i | − | 0.979594i | ||||||
\(779\) | 10206.9 | − | 5892.93i | 0.469446 | − | 0.271035i | ||||
\(780\) | 5488.91 | − | 6910.95i | 0.251967 | − | 0.317246i | ||||
\(781\) | −17978.6 | + | 31139.8i | −0.823718 | + | 1.42672i | ||||
\(782\) | −18398.1 | + | 10622.1i | −0.841321 | + | 0.485737i | ||||
\(783\) | −1908.62 | + | 20503.1i | −0.0871119 | + | 0.935789i | ||||
\(784\) | −19976.0 | − | 17853.6i | −0.909985 | − | 0.813301i | ||||
\(785\) | −3045.48 | − | 356.955i | −0.138469 | − | 0.0162297i | ||||
\(786\) | −5791.62 | − | 10789.0i | −0.262825 | − | 0.489607i | ||||
\(787\) | 18821.5 | − | 32599.7i | 0.852494 | − | 1.47656i | −0.0264570 | − | 0.999650i | \(-0.508423\pi\) |
0.878951 | − | 0.476913i | \(-0.158244\pi\) | |||||||
\(788\) | −960.710 | + | 1664.00i | −0.0434313 | + | 0.0752253i | ||||
\(789\) | 5212.27 | + | 9709.76i | 0.235186 | + | 0.438120i | ||||
\(790\) | −7724.46 | − | 905.371i | −0.347879 | − | 0.0407742i | ||||
\(791\) | −6148.32 | − | 38361.3i | −0.276371 | − | 1.72436i | ||||
\(792\) | 917.238 | − | 14803.6i | 0.0411523 | − | 0.664173i | ||||
\(793\) | −14542.3 | + | 8395.99i | −0.651213 | + | 0.375978i | ||||
\(794\) | −2057.53 | + | 3563.75i | −0.0919635 | + | 0.159285i | ||||
\(795\) | −9329.18 | + | 11746.1i | −0.416191 | + | 0.524016i | ||||
\(796\) | 15887.5 | − | 9172.65i | 0.707434 | − | 0.408437i | ||||
\(797\) | 34063.3i | 1.51391i | 0.653467 | + | 0.756955i | \(0.273314\pi\) | ||||
−0.653467 | + | 0.756955i | \(0.726686\pi\) | |||||||
\(798\) | 14103.1 | + | 18491.0i | 0.625620 | + | 0.820268i | ||||
\(799\) | 5418.55 | 0.239918 | ||||||||
\(800\) | 7471.55 | + | 25015.1i | 0.330199 | + | 1.10552i | ||||
\(801\) | −10404.5 | + | 15692.4i | −0.458957 | + | 0.692213i | ||||
\(802\) | 11321.4 | + | 6536.39i | 0.498468 | + | 0.287791i | ||||
\(803\) | 42910.3 | − | 24774.3i | 1.88577 | − | 1.08875i | ||||
\(804\) | −398.233 | + | 12866.8i | −0.0174684 | + | 0.564399i | ||||
\(805\) | −18195.6 | − | 9504.13i | −0.796660 | − | 0.416120i | ||||
\(806\) | 26211.3i | 1.14547i | ||||||||
\(807\) | 4707.19 | + | 8768.86i | 0.205329 | + | 0.382501i | ||||
\(808\) | 1766.20 | − | 3059.15i | 0.0768995 | − | 0.133194i | ||||
\(809\) | 1514.08 | + | 874.157i | 0.0658002 | + | 0.0379898i | 0.532539 | − | 0.846405i | \(-0.321238\pi\) |
−0.466739 | + | 0.884395i | \(0.654571\pi\) | |||||||
\(810\) | 8328.01 | + | 28620.6i | 0.361255 | + | 1.24151i | ||||
\(811\) | − | 33427.6i | − | 1.44735i | −0.690140 | − | 0.723676i | \(-0.742451\pi\) | ||
0.690140 | − | 0.723676i | \(-0.257549\pi\) | |||||||
\(812\) | 5210.79 | − | 13649.7i | 0.225200 | − | 0.589914i | ||||
\(813\) | 1063.58 | − | 34364.1i | 0.0458813 | − | 1.48241i | ||||
\(814\) | 5391.39 | + | 9338.15i | 0.232147 | + | 0.402091i | ||||
\(815\) | −14000.1 | − | 10429.7i | −0.601720 | − | 0.448264i | ||||
\(816\) | 20217.4 | + | 12522.0i | 0.867341 | + | 0.537203i | ||||
\(817\) | −14373.2 | − | 24895.1i | −0.615488 | − | 1.06606i | ||||
\(818\) | − | 16914.0i | − | 0.722963i | ||||||
\(819\) | 11497.5 | − | 8219.31i | 0.490545 | − | 0.350679i | ||||
\(820\) | −10645.7 | − | 1247.76i | −0.453370 | − | 0.0531386i | ||||
\(821\) | 32936.9 | − | 19016.2i | 1.40013 | − | 0.808366i | 0.405725 | − | 0.913995i | \(-0.367019\pi\) |
0.994406 | + | 0.105629i | \(0.0336857\pi\) | |||||||
\(822\) | 18817.5 | − | 30381.8i | 0.798463 | − | 1.28916i | ||||
\(823\) | 13824.9 | + | 7981.82i | 0.585549 | + | 0.338067i | 0.763335 | − | 0.646002i | \(-0.223560\pi\) |
−0.177787 | + | 0.984069i | \(0.556894\pi\) | |||||||
\(824\) | 4092.99 | + | 7089.26i | 0.173041 | + | 0.299716i | ||||
\(825\) | 9708.52 | − | 35874.7i | 0.409706 | − | 1.51394i | ||||
\(826\) | 1930.94 | + | 12047.8i | 0.0813392 | + | 0.507500i | ||||
\(827\) | −20921.9 | −0.879716 | −0.439858 | − | 0.898067i | \(-0.644971\pi\) | ||||
−0.439858 | + | 0.898067i | \(0.644971\pi\) | |||||||
\(828\) | −6409.41 | − | 12880.9i | −0.269012 | − | 0.540631i | ||||
\(829\) | 11903.3 | + | 6872.36i | 0.498695 | + | 0.287922i | 0.728174 | − | 0.685392i | \(-0.240369\pi\) |
−0.229480 | + | 0.973313i | \(0.573702\pi\) | |||||||
\(830\) | −30804.8 | − | 22948.7i | −1.28825 | − | 0.959711i | ||||
\(831\) | 21171.2 | − | 11364.8i | 0.883778 | − | 0.474419i | ||||
\(832\) | 3927.17 | 0.163642 | ||||||||
\(833\) | −19673.5 | − | 4106.00i | −0.818303 | − | 0.170786i | ||||
\(834\) | 1337.96 | − | 43229.2i | 0.0555515 | − | 1.79485i | ||||
\(835\) | −10054.6 | + | 4333.32i | −0.416712 | + | 0.179594i | ||||
\(836\) | 10160.9 | − | 17599.3i | 0.420363 | − | 0.728090i | ||||
\(837\) | −29028.3 | − | 20567.1i | −1.19876 | − | 0.849345i | ||||
\(838\) | −2271.01 | − | 3933.51i | −0.0936168 | − | 0.162149i | ||||
\(839\) | −31709.8 | −1.30482 | −0.652409 | − | 0.757867i | \(-0.726242\pi\) | ||||
−0.652409 | + | 0.757867i | \(0.726242\pi\) | |||||||
\(840\) | 116.784 | + | 10328.8i | 0.00479694 | + | 0.424258i | ||||
\(841\) | 2846.47 | 0.116711 | ||||||||
\(842\) | −12303.5 | − | 21310.2i | −0.503569 | − | 0.872207i | ||||
\(843\) | −41323.5 | − | 25594.5i | −1.68832 | − | 1.04569i | ||||
\(844\) | 7129.70 | − | 12349.0i | 0.290775 | − | 0.503637i | ||||
\(845\) | −6186.83 | − | 14355.3i | −0.251874 | − | 0.584424i | ||||
\(846\) | −564.712 | + | 9114.10i | −0.0229494 | + | 0.370389i | ||||
\(847\) | 27924.8 | − | 22698.4i | 1.13283 | − | 0.920810i | ||||
\(848\) | −20168.1 | −0.816715 | ||||||||
\(849\) | −6027.61 | − | 11228.6i | −0.243660 | − | 0.453905i | ||||
\(850\) | 19471.3 | + | 18393.9i | 0.785720 | + | 0.742241i | ||||
\(851\) | −4424.06 | − | 2554.24i | −0.178208 | − | 0.102888i | ||||
\(852\) | 15463.5 | − | 8300.90i | 0.621795 | − | 0.333784i | ||||
\(853\) | 42434.5 | 1.70332 | 0.851659 | − | 0.524096i | \(-0.175597\pi\) | ||||
0.851659 | + | 0.524096i | \(0.175597\pi\) | |||||||
\(854\) | −14351.6 | + | 37594.1i | −0.575059 | + | 1.50637i | ||||
\(855\) | 3542.71 | − | 19629.5i | 0.141705 | − | 0.785162i | ||||
\(856\) | −5526.03 | − | 9571.36i | −0.220649 | − | 0.382176i | ||||
\(857\) | −4662.38 | − | 2691.83i | −0.185839 | − | 0.107294i | 0.404194 | − | 0.914673i | \(-0.367552\pi\) |
−0.590033 | + | 0.807379i | \(0.700885\pi\) | |||||||
\(858\) | −26127.4 | − | 16182.5i | −1.03960 | − | 0.643894i | ||||
\(859\) | 1603.60 | − | 925.839i | 0.0636951 | − | 0.0367744i | −0.467814 | − | 0.883827i | \(-0.654958\pi\) |
0.531509 | + | 0.847052i | \(0.321625\pi\) | |||||||
\(860\) | −3043.35 | + | 25965.3i | −0.120671 | + | 1.02955i | ||||
\(861\) | −15839.0 | − | 6614.95i | −0.626937 | − | 0.261831i | ||||
\(862\) | 22458.5i | 0.887399i | ||||||||
\(863\) | 11492.3 | + | 19905.3i | 0.453307 | + | 0.785151i | 0.998589 | − | 0.0531017i | \(-0.0169108\pi\) |
−0.545282 | + | 0.838253i | \(0.683577\pi\) | |||||||
\(864\) | −16939.9 | + | 23908.9i | −0.667021 | + | 0.941431i | ||||
\(865\) | −18593.5 | − | 13851.7i | −0.730867 | − | 0.544474i | ||||
\(866\) | 22246.0 | + | 38531.1i | 0.872919 | + | 1.51194i | ||||
\(867\) | −7685.86 | − | 237.881i | −0.301068 | − | 0.00931818i | ||||
\(868\) | 15921.5 | + | 19587.5i | 0.622595 | + | 0.765950i | ||||
\(869\) | 10883.7i | 0.424860i | ||||||||
\(870\) | −29005.6 | + | 11450.3i | −1.13032 | + | 0.446209i | ||||
\(871\) | −11282.1 | − | 6513.72i | −0.438897 | − | 0.253397i | ||||
\(872\) | −5970.51 | + | 10341.2i | −0.231866 | + | 0.401603i | ||||
\(873\) | −3694.59 | − | 7424.97i | −0.143234 | − | 0.287855i | ||||
\(874\) | 23957.7i | 0.927210i | ||||||||
\(875\) | −4916.29 | + | 25411.7i | −0.189944 | + | 0.981795i | ||||
\(876\) | −24173.0 | − | 748.165i | −0.932340 | − | 0.0288563i | ||||
\(877\) | −13256.8 | + | 7653.80i | −0.510433 | + | 0.294698i | −0.733011 | − | 0.680216i | \(-0.761886\pi\) |
0.222579 | + | 0.974915i | \(0.428553\pi\) | |||||||
\(878\) | 22673.7 | + | 13090.7i | 0.871527 | + | 0.503176i | ||||
\(879\) | −26153.6 | − | 16198.7i | −1.00357 | − | 0.621579i | ||||
\(880\) | 45889.1 | − | 19777.2i | 1.75786 | − | 0.757600i | ||||
\(881\) | −30324.5 | −1.15966 | −0.579828 | − | 0.814739i | \(-0.696880\pi\) | ||||
−0.579828 | + | 0.814739i | \(0.696880\pi\) | |||||||
\(882\) | 8956.71 | − | 32663.3i | 0.341936 | − | 1.24697i | ||||
\(883\) | − | 4515.96i | − | 0.172111i | −0.996290 | − | 0.0860555i | \(-0.972574\pi\) | ||
0.996290 | − | 0.0860555i | \(-0.0274262\pi\) | |||||||
\(884\) | 7708.67 | − | 4450.60i | 0.293292 | − | 0.169332i | ||||
\(885\) | 6508.87 | − | 8195.15i | 0.247224 | − | 0.311273i | ||||
\(886\) | −14644.7 | + | 25365.4i | −0.555303 | + | 0.961813i | ||||
\(887\) | 6630.98 | − | 3828.40i | 0.251011 | − | 0.144921i | −0.369216 | − | 0.929344i | \(-0.620374\pi\) |
0.620227 | + | 0.784422i | \(0.287040\pi\) | |||||||
\(888\) | −79.5197 | + | 2569.26i | −0.00300507 | + | 0.0970931i | ||||
\(889\) | 18373.2 | − | 2944.75i | 0.693157 | − | 0.111095i | ||||
\(890\) | −28319.4 | − | 3319.27i | −1.06659 | − | 0.125014i | ||||
\(891\) | 38422.9 | − | 16237.5i | 1.44469 | − | 0.610525i | ||||
\(892\) | 3710.50 | − | 6426.78i | 0.139279 | − | 0.241238i | ||||
\(893\) | 3055.32 | − | 5291.98i | 0.114493 | − | 0.198308i | ||||
\(894\) | −37186.3 | + | 19961.9i | −1.39116 | + | 0.746784i | ||||
\(895\) | −3548.05 | + | 30271.3i | −0.132512 | + | 1.13057i | ||||
\(896\) | −16709.7 | + | 13582.3i | −0.623027 | + | 0.506421i | ||||
\(897\) | 14553.1 | + | 450.426i | 0.541712 | + | 0.0167662i | ||||
\(898\) | −17146.9 | + | 9899.79i | −0.637195 | + | 0.367885i | ||||
\(899\) | 18609.2 | − | 32232.1i | 0.690381 | − | 1.19578i | ||||
\(900\) | −13248.7 | + | 12391.2i | −0.490693 | + | 0.458931i | ||||
\(901\) | −13102.0 | + | 7564.42i | −0.484450 | + | 0.279697i | ||||
\(902\) | 37325.1i | 1.37782i | ||||||||
\(903\) | −16134.2 | + | 38632.2i | −0.594588 | + | 1.42370i | ||||
\(904\) | −20139.4 | −0.740958 | ||||||||
\(905\) | 12534.9 | − | 5402.24i | 0.460412 | − | 0.198427i | ||||
\(906\) | −20324.3 | + | 32814.6i | −0.745288 | + | 1.20330i | ||||
\(907\) | 34886.0 | + | 20141.4i | 1.27715 | + | 0.737360i | 0.976323 | − | 0.216320i | \(-0.0694054\pi\) |
0.300823 | + | 0.953680i | \(0.402739\pi\) | |||||||
\(908\) | −19291.8 | + | 11138.1i | −0.705089 | + | 0.407083i | ||||
\(909\) | 9915.38 | + | 614.360i | 0.361796 | + | 0.0224170i | ||||
\(910\) | 18971.2 | + | 9909.24i | 0.691087 | + | 0.360976i | ||||
\(911\) | 42780.3i | 1.55585i | 0.628360 | + | 0.777923i | \(0.283727\pi\) | ||||
−0.628360 | + | 0.777923i | \(0.716273\pi\) | |||||||
\(912\) | 23629.3 | − | 12684.4i | 0.857945 | − | 0.460551i | ||||
\(913\) | −26877.9 | + | 46553.9i | −0.974292 | + | 1.68752i | ||||
\(914\) | −47623.9 | − | 27495.6i | −1.72348 | − | 0.995049i | ||||
\(915\) | 32103.9 | − | 12673.4i | 1.15991 | − | 0.457890i | ||||
\(916\) | − | 16008.3i | − | 0.577434i | ||||||
\(917\) | 9260.62 | − | 7527.40i | 0.333492 | − | 0.271076i | ||||
\(918\) | −2786.52 | + | 29933.9i | −0.100184 | + | 1.07622i | ||||
\(919\) | 19701.4 | + | 34123.8i | 0.707170 | + | 1.22485i | 0.965903 | + | 0.258906i | \(0.0833619\pi\) |
−0.258732 | + | 0.965949i | \(0.583305\pi\) | |||||||
\(920\) | −6357.32 | + | 8533.65i | −0.227820 | + | 0.305811i | ||||
\(921\) | 11620.2 | − | 18761.4i | 0.415743 | − | 0.671237i | ||||
\(922\) | −14074.5 | − | 24377.7i | −0.502732 | − | 0.870757i | ||||
\(923\) | 17761.2i | 0.633390i | ||||||||
\(924\) | −29354.6 | + | 3777.51i | −1.04513 | + | 0.134492i | ||||
\(925\) | −1489.41 | + | 6266.39i | −0.0529421 | + | 0.222744i | ||||
\(926\) | −9785.26 | + | 5649.52i | −0.347261 | + | 0.200491i | ||||
\(927\) | −12721.9 | + | 19187.5i | −0.450746 | + | 0.679829i | ||||
\(928\) | −26547.7 | − | 15327.3i | −0.939085 | − | 0.542181i | ||||
\(929\) | 6621.49 | + | 11468.8i | 0.233847 | + | 0.405035i | 0.958937 | − | 0.283619i | \(-0.0915351\pi\) |
−0.725090 | + | 0.688654i | \(0.758202\pi\) | |||||||
\(930\) | 7924.07 | − | 53289.7i | 0.279398 | − | 1.87896i | ||||
\(931\) | −15103.3 | + | 16898.7i | −0.531675 | + | 0.594880i | ||||
\(932\) | −4506.20 | −0.158375 | ||||||||
\(933\) | 8879.99 | + | 16542.2i | 0.311595 | + | 0.580459i | ||||
\(934\) | −47966.2 | − | 27693.3i | −1.68041 | − | 0.970184i | ||||
\(935\) | 22393.5 | − | 30059.6i | 0.783258 | − | 1.05139i | ||||
\(936\) | −3263.80 | − | 6559.22i | −0.113975 | − | 0.229054i | ||||
\(937\) | −4524.54 | −0.157748 | −0.0788742 | − | 0.996885i | \(-0.525133\pi\) | ||||
−0.0788742 | + | 0.996885i | \(0.525133\pi\) | |||||||
\(938\) | −30825.6 | + | 4940.54i | −1.07302 | + | 0.171977i | ||||
\(939\) | 3792.54 | + | 117.381i | 0.131805 | + | 0.00407943i | ||||
\(940\) | −5103.48 | + | 2199.49i | −0.177082 | + | 0.0763185i | ||||
\(941\) | 10508.1 | − | 18200.5i | 0.364032 | − | 0.630522i | −0.624588 | − | 0.780954i | \(-0.714733\pi\) |
0.988620 | + | 0.150432i | \(0.0480666\pi\) | |||||||
\(942\) | 2744.30 | − | 4430.80i | 0.0949195 | − | 0.153252i | ||||
\(943\) | −8841.61 | − | 15314.1i | −0.305326 | − | 0.528840i | ||||
\(944\) | 14071.0 | 0.485141 | ||||||||
\(945\) | −25860.3 | + | 13234.7i | −0.890195 | + | 0.455580i | ||||
\(946\) | 91037.8 | 3.12885 | ||||||||
\(947\) | 25315.2 | + | 43847.2i | 0.868672 | + | 1.50458i | 0.863354 | + | 0.504599i | \(0.168360\pi\) |
0.00531866 | + | 0.999986i | \(0.498307\pi\) | |||||||
\(948\) | 2797.20 | − | 4516.21i | 0.0958321 | − | 0.154726i | ||||
\(949\) | 12237.4 | − | 21195.8i | 0.418592 | − | 0.725022i | ||||
\(950\) | 28943.4 | − | 8644.86i | 0.988471 | − | 0.295238i | ||||
\(951\) | −35166.3 | − | 1088.41i | −1.19910 | − | 0.0371127i | ||||
\(952\) | −3715.56 | + | 9732.94i | −0.126494 | + | 0.331351i | ||||
\(953\) | −42764.4 | −1.45359 | −0.726797 | − | 0.686852i | \(-0.758992\pi\) | ||||
−0.726797 | + | 0.686852i | \(0.758992\pi\) | |||||||
\(954\) | −11358.0 | − | 22826.1i | −0.385461 | − | 0.774656i | ||||
\(955\) | −23390.7 | − | 17425.4i | −0.792573 | − | 0.590443i | ||||
\(956\) | −16890.9 | − | 9751.99i | −0.571435 | − | 0.329918i | ||||
\(957\) | 20639.9 | + | 38449.4i | 0.697172 | + | 1.29874i | ||||
\(958\) | −17307.9 | −0.583709 | ||||||||
\(959\) | 32538.7 | + | 12421.7i | 1.09565 | + | 0.418265i | ||||
\(960\) | −7984.26 | − | 1187.25i | −0.268428 | − | 0.0399148i | ||||
\(961\) | 17255.2 | + | 29886.8i | 0.579208 | + | 1.00322i | ||||
\(962\) | 4612.64 | + | 2663.11i | 0.154592 | + | 0.0892537i | ||||
\(963\) | 17176.1 | − | 25905.5i | 0.574758 | − | 0.866868i | ||||
\(964\) | 4928.28 | − | 2845.34i | 0.164657 | − | 0.0950647i | ||||
\(965\) | −788.557 | + | 6727.83i | −0.0263052 | + | 0.224432i | ||||
\(966\) | 27743.4 | − | 21160.0i | 0.924047 | − | 0.704773i | ||||
\(967\) | − | 5439.52i | − | 0.180893i | −0.995901 | − | 0.0904463i | \(-0.971171\pi\) | ||
0.995901 | − | 0.0904463i | \(-0.0288293\pi\) | |||||||
\(968\) | −9327.22 | − | 16155.2i | −0.309699 | − | 0.536414i | ||||
\(969\) | 10593.0 | − | 17102.9i | 0.351183 | − | 0.567002i | ||||
\(970\) | 7503.17 | − | 10071.8i | 0.248363 | − | 0.333386i | ||||
\(971\) | −1568.07 | − | 2715.99i | −0.0518248 | − | 0.0897632i | 0.838949 | − | 0.544210i | \(-0.183170\pi\) |
−0.890774 | + | 0.454446i | \(0.849837\pi\) | |||||||
\(972\) | −20116.9 | − | 3137.21i | −0.663837 | − | 0.103525i | ||||
\(973\) | 41619.6 | − | 6670.55i | 1.37129 | − | 0.219782i | ||||
\(974\) | 14608.7i | 0.480588i | ||||||||
\(975\) | −4707.17 | − | 17744.2i | −0.154616 | − | 0.582841i | ||||
\(976\) | 40188.7 | + | 23203.0i | 1.31804 | + | 0.760973i | ||||
\(977\) | −17645.5 | + | 30563.0i | −0.577821 | + | 1.00081i | 0.417908 | + | 0.908489i | \(0.362763\pi\) |
−0.995729 | + | 0.0923255i | \(0.970570\pi\) | |||||||
\(978\) | 26144.5 | − | 14034.6i | 0.854814 | − | 0.458871i | ||||
\(979\) | 39901.7i | 1.30262i | ||||||||
\(980\) | 20196.3 | − | 4118.58i | 0.658312 | − | 0.134248i | ||||
\(981\) | −33518.2 | − | 2076.80i | −1.09088 | − | 0.0675912i | ||||
\(982\) | −28195.1 | + | 16278.5i | −0.916235 | + | 0.528988i | ||||
\(983\) | 10381.3 | + | 5993.64i | 0.336838 | + | 0.194473i | 0.658873 | − | 0.752254i | \(-0.271034\pi\) |
−0.322035 | + | 0.946728i | \(0.604367\pi\) | |||||||
\(984\) | −4685.19 | + | 7564.46i | −0.151787 | + | 0.245067i | ||||
\(985\) | 1581.86 | + | 3670.40i | 0.0511697 | + | 0.118729i | ||||
\(986\) | −31451.4 | −1.01584 | ||||||||
\(987\) | −8826.73 | + | 1135.87i | −0.284658 | + | 0.0366314i | ||||
\(988\) | − | 10038.1i | − | 0.323234i | ||||||
\(989\) | −37351.9 | + | 21565.1i | −1.20093 | + | 0.693358i | ||||
\(990\) | 48226.9 | + | 40799.0i | 1.54824 | + | 1.30978i | ||||
\(991\) | 18186.2 | − | 31499.4i | 0.582950 | − | 1.00970i | −0.412177 | − | 0.911104i | \(-0.635232\pi\) |
0.995128 | − | 0.0985959i | \(-0.0314351\pi\) | |||||||
\(992\) | 45865.8 | − | 26480.6i | 1.46798 | − | 0.847541i | ||||
\(993\) | 32346.1 | + | 1001.13i | 1.03371 | + | 0.0319937i | ||||
\(994\) | 26846.7 | + | 33028.3i | 0.856666 | + | 1.05392i | ||||
\(995\) | 4442.27 | − | 37900.7i | 0.141537 | − | 1.20757i | ||||
\(996\) | 23117.8 | − | 12409.8i | 0.735458 | − | 0.394800i | ||||
\(997\) | −7354.79 | + | 12738.9i | −0.233630 | + | 0.404658i | −0.958874 | − | 0.283834i | \(-0.908394\pi\) |
0.725244 | + | 0.688492i | \(0.241727\pi\) | |||||||
\(998\) | −34564.5 | + | 59867.5i | −1.09631 | + | 1.89887i | ||||
\(999\) | −6568.70 | + | 3018.72i | −0.208032 | + | 0.0956037i |
(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.p.a.59.10 | yes | 88 | |
3.2 | odd | 2 | inner | 105.4.p.a.59.36 | yes | 88 | |
5.4 | even | 2 | inner | 105.4.p.a.59.35 | yes | 88 | |
7.5 | odd | 6 | inner | 105.4.p.a.89.9 | yes | 88 | |
15.14 | odd | 2 | inner | 105.4.p.a.59.9 | ✓ | 88 | |
21.5 | even | 6 | inner | 105.4.p.a.89.35 | yes | 88 | |
35.19 | odd | 6 | inner | 105.4.p.a.89.36 | yes | 88 | |
105.89 | even | 6 | inner | 105.4.p.a.89.10 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.p.a.59.9 | ✓ | 88 | 15.14 | odd | 2 | inner | |
105.4.p.a.59.10 | yes | 88 | 1.1 | even | 1 | trivial | |
105.4.p.a.59.35 | yes | 88 | 5.4 | even | 2 | inner | |
105.4.p.a.59.36 | yes | 88 | 3.2 | odd | 2 | inner | |
105.4.p.a.89.9 | yes | 88 | 7.5 | odd | 6 | inner | |
105.4.p.a.89.10 | yes | 88 | 105.89 | even | 6 | inner | |
105.4.p.a.89.35 | yes | 88 | 21.5 | even | 6 | inner | |
105.4.p.a.89.36 | yes | 88 | 35.19 | odd | 6 | inner |