Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,4,Mod(5,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.g (of order \(8\), degree \(4\), 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: | \(1.88806112018\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 13.6 | ||
Character | \(\chi\) | \(=\) | 32.13 |
Dual form | 32.4.g.a.5.6 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.582457 | + | 2.76780i | −0.205930 | + | 0.978567i | ||||
\(3\) | −1.90169 | + | 4.59109i | −0.365981 | + | 0.883556i | 0.628419 | + | 0.777875i | \(0.283702\pi\) |
−0.994400 | + | 0.105681i | \(0.966298\pi\) | |||||||
\(4\) | −7.32149 | − | 3.22425i | −0.915186 | − | 0.403032i | ||||
\(5\) | 0.188811 | − | 0.0782080i | 0.0168878 | − | 0.00699514i | −0.374224 | − | 0.927339i | \(-0.622091\pi\) |
0.391111 | + | 0.920343i | \(0.372091\pi\) | |||||||
\(6\) | −11.5996 | − | 7.93763i | −0.789252 | − | 0.540087i | ||||
\(7\) | −11.4103 | + | 11.4103i | −0.616096 | + | 0.616096i | −0.944528 | − | 0.328432i | \(-0.893480\pi\) |
0.328432 | + | 0.944528i | \(0.393480\pi\) | |||||||
\(8\) | 13.1886 | − | 18.3865i | 0.582857 | − | 0.812574i | ||||
\(9\) | 1.63019 | + | 1.63019i | 0.0603773 | + | 0.0603773i | ||||
\(10\) | 0.106490 | + | 0.568145i | 0.00336752 | + | 0.0179663i | ||||
\(11\) | 18.6604 | + | 45.0502i | 0.511483 | + | 1.23483i | 0.943020 | + | 0.332735i | \(0.107971\pi\) |
−0.431537 | + | 0.902095i | \(0.642029\pi\) | |||||||
\(12\) | 28.7261 | − | 27.4821i | 0.691042 | − | 0.661116i | ||||
\(13\) | 18.9369 | + | 7.84392i | 0.404011 | + | 0.167347i | 0.575430 | − | 0.817851i | \(-0.304835\pi\) |
−0.171418 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(14\) | −24.9354 | − | 38.2274i | −0.476019 | − | 0.729764i | ||||
\(15\) | 1.01558i | 0.0174814i | ||||||||
\(16\) | 43.2084 | + | 47.2127i | 0.675131 | + | 0.737698i | ||||
\(17\) | − | 85.7028i | − | 1.22270i | −0.791359 | − | 0.611352i | \(-0.790626\pi\) | ||
0.791359 | − | 0.611352i | \(-0.209374\pi\) | |||||||
\(18\) | −5.46155 | + | 3.56253i | −0.0715167 | + | 0.0466497i | ||||
\(19\) | 110.749 | + | 45.8739i | 1.33725 | + | 0.553905i | 0.932713 | − | 0.360619i | \(-0.117434\pi\) |
0.404532 | + | 0.914524i | \(0.367434\pi\) | |||||||
\(20\) | −1.63454 | − | 0.0361752i | −0.0182747 | − | 0.000404451i | ||||
\(21\) | −30.6868 | − | 74.0844i | −0.318876 | − | 0.769835i | ||||
\(22\) | −135.559 | + | 25.4085i | −1.31369 | + | 0.246233i | ||||
\(23\) | −74.2331 | − | 74.2331i | −0.672985 | − | 0.672985i | 0.285418 | − | 0.958403i | \(-0.407868\pi\) |
−0.958403 | + | 0.285418i | \(0.907868\pi\) | |||||||
\(24\) | 59.3334 | + | 95.5153i | 0.504640 | + | 0.812374i | ||||
\(25\) | −88.3588 | + | 88.3588i | −0.706871 | + | 0.706871i | ||||
\(26\) | −32.7404 | + | 47.8449i | −0.246958 | + | 0.360890i | ||||
\(27\) | −134.544 | + | 55.7299i | −0.959000 | + | 0.397231i | ||||
\(28\) | 120.330 | − | 46.7505i | 0.812149 | − | 0.315536i | ||||
\(29\) | 64.4881 | − | 155.688i | 0.412936 | − | 0.996915i | −0.571410 | − | 0.820665i | \(-0.693603\pi\) |
0.984345 | − | 0.176250i | \(-0.0563967\pi\) | |||||||
\(30\) | −2.81092 | − | 0.591529i | −0.0171067 | − | 0.00359993i | ||||
\(31\) | 36.6720 | 0.212467 | 0.106234 | − | 0.994341i | \(-0.466121\pi\) | ||||
0.106234 | + | 0.994341i | \(0.466121\pi\) | |||||||
\(32\) | −155.842 | + | 92.0930i | −0.860916 | + | 0.508747i | ||||
\(33\) | −242.316 | −1.27824 | ||||||||
\(34\) | 237.209 | + | 49.9182i | 1.19650 | + | 0.251791i | ||||
\(35\) | −1.26201 | + | 3.04676i | −0.00609481 | + | 0.0147142i | ||||
\(36\) | −6.67926 | − | 17.1915i | −0.0309225 | − | 0.0795904i | ||||
\(37\) | 313.271 | − | 129.761i | 1.39193 | − | 0.576557i | 0.444287 | − | 0.895884i | \(-0.353457\pi\) |
0.947644 | + | 0.319328i | \(0.103457\pi\) | |||||||
\(38\) | −191.477 | + | 279.813i | −0.817412 | + | 1.19452i | ||||
\(39\) | −72.0243 | + | 72.0243i | −0.295721 | + | 0.295721i | ||||
\(40\) | 1.05217 | − | 4.50302i | 0.00415909 | − | 0.0177997i | ||||
\(41\) | 196.689 | + | 196.689i | 0.749211 | + | 0.749211i | 0.974331 | − | 0.225120i | \(-0.0722773\pi\) |
−0.225120 | + | 0.974331i | \(0.572277\pi\) | |||||||
\(42\) | 222.925 | − | 41.7840i | 0.819001 | − | 0.153510i | ||||
\(43\) | −20.8770 | − | 50.4016i | −0.0740400 | − | 0.178748i | 0.882526 | − | 0.470263i | \(-0.155841\pi\) |
−0.956566 | + | 0.291514i | \(0.905841\pi\) | |||||||
\(44\) | 8.63137 | − | 390.000i | 0.0295734 | − | 1.33624i | ||||
\(45\) | 0.435291 | + | 0.180303i | 0.00144198 | + | 0.000597290i | ||||
\(46\) | 248.700 | − | 162.225i | 0.797149 | − | 0.519974i | ||||
\(47\) | − | 508.601i | − | 1.57845i | −0.614106 | − | 0.789224i | \(-0.710483\pi\) | ||
0.614106 | − | 0.789224i | \(-0.289517\pi\) | |||||||
\(48\) | −298.927 | + | 108.590i | −0.898883 | + | 0.326533i | ||||
\(49\) | 82.6118i | 0.240851i | ||||||||
\(50\) | −193.095 | − | 296.025i | −0.546154 | − | 0.837286i | ||||
\(51\) | 393.469 | + | 162.980i | 1.08033 | + | 0.447487i | ||||
\(52\) | −113.355 | − | 118.486i | −0.302299 | − | 0.315983i | ||||
\(53\) | 73.8289 | + | 178.239i | 0.191343 | + | 0.461943i | 0.990214 | − | 0.139560i | \(-0.0445689\pi\) |
−0.798871 | + | 0.601503i | \(0.794569\pi\) | |||||||
\(54\) | −75.8835 | − | 404.852i | −0.191230 | − | 1.02025i | ||||
\(55\) | 7.04657 | + | 7.04657i | 0.0172756 | + | 0.0172756i | ||||
\(56\) | 59.3094 | + | 360.279i | 0.141528 | + | 0.859720i | ||||
\(57\) | −421.223 | + | 421.223i | −0.978813 | + | 0.978813i | ||||
\(58\) | 393.352 | + | 269.172i | 0.890512 | + | 0.609379i | ||||
\(59\) | 40.9489 | − | 16.9616i | 0.0903576 | − | 0.0374273i | −0.337047 | − | 0.941488i | \(-0.609428\pi\) |
0.427404 | + | 0.904061i | \(0.359428\pi\) | |||||||
\(60\) | 3.27448 | − | 7.43553i | 0.00704555 | − | 0.0159987i | ||||
\(61\) | −324.831 | + | 784.211i | −0.681809 | + | 1.64603i | 0.0788549 | + | 0.996886i | \(0.474874\pi\) |
−0.760664 | + | 0.649146i | \(0.775126\pi\) | |||||||
\(62\) | −21.3598 | + | 101.501i | −0.0437533 | + | 0.207913i | ||||
\(63\) | −37.2017 | −0.0743964 | ||||||||
\(64\) | −164.124 | − | 484.982i | −0.320554 | − | 0.947230i | ||||
\(65\) | 4.18895 | 0.00799346 | ||||||||
\(66\) | 141.138 | − | 670.683i | 0.263226 | − | 1.25084i | ||||
\(67\) | −49.4427 | + | 119.365i | −0.0901550 | + | 0.217654i | −0.962525 | − | 0.271192i | \(-0.912582\pi\) |
0.872370 | + | 0.488846i | \(0.162582\pi\) | |||||||
\(68\) | −276.328 | + | 627.472i | −0.492789 | + | 1.11900i | ||||
\(69\) | 481.979 | − | 199.642i | 0.840920 | − | 0.348321i | ||||
\(70\) | −7.69776 | − | 5.26760i | −0.0131437 | − | 0.00899426i | ||||
\(71\) | −362.308 | + | 362.308i | −0.605606 | + | 0.605606i | −0.941795 | − | 0.336189i | \(-0.890862\pi\) |
0.336189 | + | 0.941795i | \(0.390862\pi\) | |||||||
\(72\) | 51.4732 | − | 8.47355i | 0.0842524 | − | 0.0138697i | ||||
\(73\) | 239.192 | + | 239.192i | 0.383498 | + | 0.383498i | 0.872361 | − | 0.488863i | \(-0.162588\pi\) |
−0.488863 | + | 0.872361i | \(0.662588\pi\) | |||||||
\(74\) | 176.687 | + | 942.654i | 0.277560 | + | 1.48083i | ||||
\(75\) | −237.632 | − | 573.695i | −0.365859 | − | 0.883261i | ||||
\(76\) | −662.942 | − | 692.950i | −1.00059 | − | 1.04588i | ||||
\(77\) | −726.954 | − | 301.114i | −1.07590 | − | 0.445651i | ||||
\(78\) | −157.398 | − | 241.300i | −0.228485 | − | 0.350280i | ||||
\(79\) | − | 1018.36i | − | 1.45030i | −0.688589 | − | 0.725152i | \(-0.741769\pi\) | ||
0.688589 | − | 0.725152i | \(-0.258231\pi\) | |||||||
\(80\) | 11.8506 | + | 5.53503i | 0.0165617 | + | 0.00773544i | ||||
\(81\) | − | 661.438i | − | 0.907323i | ||||||
\(82\) | −658.960 | + | 429.834i | −0.887438 | + | 0.578869i | ||||
\(83\) | 231.267 | + | 95.7940i | 0.305842 | + | 0.126684i | 0.530326 | − | 0.847794i | \(-0.322070\pi\) |
−0.224484 | + | 0.974478i | \(0.572070\pi\) | |||||||
\(84\) | −14.1942 | + | 641.350i | −0.0184370 | + | 0.833060i | ||||
\(85\) | −6.70265 | − | 16.1816i | −0.00855299 | − | 0.0206487i | ||||
\(86\) | 151.662 | − | 28.4268i | 0.190164 | − | 0.0356435i | ||||
\(87\) | 592.141 | + | 592.141i | 0.729704 | + | 0.729704i | ||||
\(88\) | 1074.42 | + | 251.048i | 1.30151 | + | 0.304112i | ||||
\(89\) | 1103.08 | − | 1103.08i | 1.31378 | − | 1.31378i | 0.395174 | − | 0.918606i | \(-0.370684\pi\) |
0.918606 | − | 0.395174i | \(-0.129316\pi\) | |||||||
\(90\) | −0.752583 | + | 1.09978i | −0.000881435 | + | 0.00128808i | ||||
\(91\) | −305.576 | + | 126.574i | −0.352012 | + | 0.145808i | ||||
\(92\) | 304.150 | + | 782.843i | 0.344672 | + | 0.887141i | ||||
\(93\) | −69.7388 | + | 168.364i | −0.0777589 | + | 0.187727i | ||||
\(94\) | 1407.71 | + | 296.238i | 1.54462 | + | 0.325049i | ||||
\(95\) | 24.4984 | 0.0264577 | ||||||||
\(96\) | −126.443 | − | 890.620i | −0.134427 | − | 0.946860i | ||||
\(97\) | −74.0528 | −0.0775147 | −0.0387573 | − | 0.999249i | \(-0.512340\pi\) | ||||
−0.0387573 | + | 0.999249i | \(0.512340\pi\) | |||||||
\(98\) | −228.653 | − | 48.1178i | −0.235689 | − | 0.0495983i | ||||
\(99\) | −43.0203 | + | 103.860i | −0.0436737 | + | 0.105438i | ||||
\(100\) | 931.809 | − | 362.027i | 0.931809 | − | 0.362027i | ||||
\(101\) | 564.281 | − | 233.733i | 0.555922 | − | 0.230270i | −0.0869918 | − | 0.996209i | \(-0.527725\pi\) |
0.642914 | + | 0.765939i | \(0.277725\pi\) | |||||||
\(102\) | −680.277 | + | 994.118i | −0.660367 | + | 0.965023i | ||||
\(103\) | −504.784 | + | 504.784i | −0.482892 | + | 0.482892i | −0.906054 | − | 0.423162i | \(-0.860920\pi\) |
0.423162 | + | 0.906054i | \(0.360920\pi\) | |||||||
\(104\) | 393.972 | − | 244.732i | 0.371463 | − | 0.230750i | ||||
\(105\) | −11.5880 | − | 11.5880i | −0.0107702 | − | 0.0107702i | ||||
\(106\) | −536.332 | + | 100.528i | −0.491445 | + | 0.0921142i | ||||
\(107\) | −399.644 | − | 964.826i | −0.361075 | − | 0.871713i | −0.995143 | − | 0.0984356i | \(-0.968616\pi\) |
0.634068 | − | 0.773277i | \(-0.281384\pi\) | |||||||
\(108\) | 1164.75 | + | 25.7779i | 1.03776 | + | 0.0229674i | ||||
\(109\) | −1362.55 | − | 564.385i | −1.19732 | − | 0.495948i | −0.307191 | − | 0.951648i | \(-0.599389\pi\) |
−0.890133 | + | 0.455700i | \(0.849389\pi\) | |||||||
\(110\) | −23.6079 | + | 15.3992i | −0.0204629 | + | 0.0133478i | ||||
\(111\) | 1685.02i | 1.44086i | ||||||||
\(112\) | −1031.73 | − | 45.6902i | −0.870439 | − | 0.0385475i | ||||
\(113\) | − | 1171.99i | − | 0.975681i | −0.872933 | − | 0.487840i | \(-0.837785\pi\) | ||
0.872933 | − | 0.487840i | \(-0.162215\pi\) | |||||||
\(114\) | −920.519 | − | 1411.21i | −0.756267 | − | 1.15940i | ||||
\(115\) | −19.8216 | − | 8.21039i | −0.0160728 | − | 0.00665759i | ||||
\(116\) | −974.126 | + | 931.942i | −0.779701 | + | 0.745936i | ||||
\(117\) | 18.0836 | + | 43.6577i | 0.0142892 | + | 0.0344971i | ||||
\(118\) | 23.0954 | + | 123.218i | 0.0180179 | + | 0.0961284i | ||||
\(119\) | 977.891 | + | 977.891i | 0.753304 | + | 0.753304i | ||||
\(120\) | 18.6729 | + | 13.3940i | 0.0142049 | + | 0.0101891i | ||||
\(121\) | −740.147 | + | 740.147i | −0.556084 | + | 0.556084i | ||||
\(122\) | −1981.34 | − | 1355.84i | −1.47035 | − | 1.00616i | ||||
\(123\) | −1277.06 | + | 528.976i | −0.936168 | + | 0.387773i | ||||
\(124\) | −268.493 | − | 118.240i | −0.194447 | − | 0.0856310i | ||||
\(125\) | −19.5487 | + | 47.1948i | −0.0139879 | + | 0.0337699i | ||||
\(126\) | 21.6684 | − | 102.967i | 0.0153204 | − | 0.0728019i | ||||
\(127\) | 2033.56 | 1.42086 | 0.710432 | − | 0.703766i | \(-0.248500\pi\) | ||||
0.710432 | + | 0.703766i | \(0.248500\pi\) | |||||||
\(128\) | 1437.93 | − | 171.782i | 0.992940 | − | 0.118621i | ||||
\(129\) | 271.100 | 0.185031 | ||||||||
\(130\) | −2.43988 | + | 11.5942i | −0.00164609 | + | 0.00782214i | ||||
\(131\) | 268.953 | − | 649.310i | 0.179378 | − | 0.433057i | −0.808458 | − | 0.588553i | \(-0.799698\pi\) |
0.987836 | + | 0.155496i | \(0.0496977\pi\) | |||||||
\(132\) | 1774.11 | + | 781.288i | 1.16982 | + | 0.515169i | ||||
\(133\) | −1787.11 | + | 740.247i | −1.16513 | + | 0.482613i | ||||
\(134\) | −301.581 | − | 206.373i | −0.194423 | − | 0.133044i | ||||
\(135\) | −21.0448 | + | 21.0448i | −0.0134167 | + | 0.0134167i | ||||
\(136\) | −1575.77 | − | 1130.30i | −0.993539 | − | 0.712663i | ||||
\(137\) | 1077.41 | + | 1077.41i | 0.671894 | + | 0.671894i | 0.958152 | − | 0.286259i | \(-0.0924116\pi\) |
−0.286259 | + | 0.958152i | \(0.592412\pi\) | |||||||
\(138\) | 271.839 | + | 1450.31i | 0.167685 | + | 0.894626i | ||||
\(139\) | 285.862 | + | 690.132i | 0.174435 | + | 0.421124i | 0.986783 | − | 0.162050i | \(-0.0518106\pi\) |
−0.812347 | + | 0.583174i | \(0.801811\pi\) | |||||||
\(140\) | 19.0633 | − | 18.2378i | 0.0115082 | − | 0.0110098i | ||||
\(141\) | 2335.03 | + | 967.202i | 1.39465 | + | 0.577682i | ||||
\(142\) | −791.769 | − | 1213.83i | −0.467914 | − | 0.717338i | ||||
\(143\) | 999.480i | 0.584481i | ||||||||
\(144\) | −6.52777 | + | 147.403i | −0.00377764 | + | 0.0853028i | ||||
\(145\) | − | 34.4391i | − | 0.0197242i | ||||||
\(146\) | −801.357 | + | 522.718i | −0.454252 | + | 0.296305i | ||||
\(147\) | −379.278 | − | 157.102i | −0.212805 | − | 0.0881468i | ||||
\(148\) | −2711.99 | − | 60.0211i | −1.50625 | − | 0.0333358i | ||||
\(149\) | −634.226 | − | 1531.16i | −0.348710 | − | 0.841860i | −0.996773 | − | 0.0802736i | \(-0.974421\pi\) |
0.648063 | − | 0.761587i | \(-0.275579\pi\) | |||||||
\(150\) | 1726.29 | − | 323.567i | 0.939671 | − | 0.176128i | ||||
\(151\) | −805.847 | − | 805.847i | −0.434297 | − | 0.434297i | 0.455790 | − | 0.890087i | \(-0.349357\pi\) |
−0.890087 | + | 0.455790i | \(0.849357\pi\) | |||||||
\(152\) | 2304.08 | − | 1431.28i | 1.22951 | − | 0.763764i | ||||
\(153\) | 139.712 | − | 139.712i | 0.0738236 | − | 0.0738236i | ||||
\(154\) | 1256.84 | − | 1836.68i | 0.657659 | − | 0.961065i | ||||
\(155\) | 6.92407 | − | 2.86804i | 0.00358809 | − | 0.00148624i | ||||
\(156\) | 759.550 | − | 295.100i | 0.389825 | − | 0.151455i | ||||
\(157\) | −308.064 | + | 743.733i | −0.156600 | + | 0.378066i | −0.982634 | − | 0.185554i | \(-0.940592\pi\) |
0.826034 | + | 0.563620i | \(0.190592\pi\) | |||||||
\(158\) | 2818.61 | + | 593.149i | 1.41922 | + | 0.298661i | ||||
\(159\) | −958.710 | −0.478180 | ||||||||
\(160\) | −22.2224 | + | 29.5763i | −0.0109802 | + | 0.0146138i | ||||
\(161\) | 1694.04 | 0.829248 | ||||||||
\(162\) | 1830.73 | + | 385.259i | 0.887876 | + | 0.186845i | ||||
\(163\) | 396.959 | − | 958.344i | 0.190750 | − | 0.460511i | −0.799352 | − | 0.600863i | \(-0.794824\pi\) |
0.990102 | + | 0.140353i | \(0.0448236\pi\) | |||||||
\(164\) | −805.881 | − | 2074.23i | −0.383712 | − | 0.987624i | ||||
\(165\) | −45.7519 | + | 18.9510i | −0.0215865 | + | 0.00894143i | ||||
\(166\) | −399.842 | + | 584.306i | −0.186950 | + | 0.273199i | ||||
\(167\) | 307.489 | − | 307.489i | 0.142480 | − | 0.142480i | −0.632269 | − | 0.774749i | \(-0.717876\pi\) |
0.774749 | + | 0.632269i | \(0.217876\pi\) | |||||||
\(168\) | −1766.86 | − | 412.845i | −0.811408 | − | 0.189594i | ||||
\(169\) | −1256.43 | − | 1256.43i | −0.571887 | − | 0.571887i | ||||
\(170\) | 48.6916 | − | 9.12652i | 0.0219675 | − | 0.00411748i | ||||
\(171\) | 105.759 | + | 255.325i | 0.0472960 | + | 0.114183i | ||||
\(172\) | −9.65669 | + | 436.328i | −0.00428090 | + | 0.193428i | ||||
\(173\) | 328.204 | + | 135.946i | 0.144236 | + | 0.0597446i | 0.453634 | − | 0.891188i | \(-0.350127\pi\) |
−0.309398 | + | 0.950933i | \(0.600127\pi\) | |||||||
\(174\) | −1983.83 | + | 1294.04i | −0.864331 | + | 0.563796i | ||||
\(175\) | − | 2016.39i | − | 0.871001i | ||||||
\(176\) | −1320.65 | + | 2827.55i | −0.565614 | + | 1.21099i | ||||
\(177\) | 220.256i | 0.0935337i | ||||||||
\(178\) | 2410.62 | + | 3695.61i | 1.01508 | + | 1.55617i | ||||
\(179\) | −1270.86 | − | 526.407i | −0.530662 | − | 0.219807i | 0.101231 | − | 0.994863i | \(-0.467722\pi\) |
−0.631893 | + | 0.775056i | \(0.717722\pi\) | |||||||
\(180\) | −2.60563 | − | 2.72358i | −0.00107896 | − | 0.00112780i | ||||
\(181\) | 1449.19 | + | 3498.66i | 0.595125 | + | 1.43676i | 0.878496 | + | 0.477749i | \(0.158547\pi\) |
−0.283371 | + | 0.959010i | \(0.591453\pi\) | |||||||
\(182\) | −172.347 | − | 919.499i | −0.0701933 | − | 0.374493i | ||||
\(183\) | −2982.66 | − | 2982.66i | −1.20483 | − | 1.20483i | ||||
\(184\) | −2343.91 | + | 385.856i | −0.939105 | + | 0.154596i | ||||
\(185\) | 49.0007 | − | 49.0007i | 0.0194735 | − | 0.0194735i | ||||
\(186\) | −425.380 | − | 291.089i | −0.167690 | − | 0.114751i | ||||
\(187\) | 3860.92 | − | 1599.25i | 1.50983 | − | 0.625393i | ||||
\(188\) | −1639.86 | + | 3723.71i | −0.636164 | + | 1.44457i | ||||
\(189\) | 899.289 | − | 2171.08i | 0.346104 | − | 0.835569i | ||||
\(190\) | −14.2693 | + | 67.8068i | −0.00544843 | + | 0.0258907i | ||||
\(191\) | −2124.08 | −0.804677 | −0.402338 | − | 0.915491i | \(-0.631803\pi\) | ||||
−0.402338 | + | 0.915491i | \(0.631803\pi\) | |||||||
\(192\) | 2538.71 | + | 168.779i | 0.954248 | + | 0.0634403i | ||||
\(193\) | −2384.50 | −0.889328 | −0.444664 | − | 0.895697i | \(-0.646677\pi\) | ||||
−0.444664 | + | 0.895697i | \(0.646677\pi\) | |||||||
\(194\) | 43.1326 | − | 204.964i | 0.0159626 | − | 0.0758533i | ||||
\(195\) | −7.96609 | + | 19.2319i | −0.00292546 | + | 0.00706268i | ||||
\(196\) | 266.361 | − | 604.841i | 0.0970705 | − | 0.220423i | ||||
\(197\) | −3010.53 | + | 1247.00i | −1.08879 | + | 0.450990i | −0.853584 | − | 0.520956i | \(-0.825576\pi\) |
−0.235204 | + | 0.971946i | \(0.575576\pi\) | |||||||
\(198\) | −262.407 | − | 179.566i | −0.0941841 | − | 0.0644504i | ||||
\(199\) | 2542.97 | − | 2542.97i | 0.905862 | − | 0.905862i | −0.0900734 | − | 0.995935i | \(-0.528710\pi\) |
0.995935 | + | 0.0900734i | \(0.0287102\pi\) | |||||||
\(200\) | 459.281 | + | 2789.93i | 0.162380 | + | 0.986390i | ||||
\(201\) | −453.992 | − | 453.992i | −0.159314 | − | 0.159314i | ||||
\(202\) | 318.258 | + | 1697.96i | 0.110854 | + | 0.591426i | ||||
\(203\) | 1040.61 | + | 2512.27i | 0.359787 | + | 0.868604i | ||||
\(204\) | −2355.29 | − | 2461.90i | −0.808350 | − | 0.844940i | ||||
\(205\) | 52.5197 | + | 21.7544i | 0.0178933 | + | 0.00741167i | ||||
\(206\) | −1103.13 | − | 1691.16i | −0.373100 | − | 0.571984i | ||||
\(207\) | − | 242.028i | − | 0.0812661i | ||||||
\(208\) | 447.900 | + | 1232.98i | 0.149309 | + | 0.411020i | ||||
\(209\) | 5845.30i | 1.93458i | ||||||||
\(210\) | 38.8228 | − | 25.3238i | 0.0127573 | − | 0.00832146i | ||||
\(211\) | 411.497 | + | 170.448i | 0.134259 | + | 0.0556118i | 0.448801 | − | 0.893632i | \(-0.351851\pi\) |
−0.314543 | + | 0.949243i | \(0.601851\pi\) | |||||||
\(212\) | 34.1496 | − | 1543.02i | 0.0110632 | − | 0.499881i | ||||
\(213\) | −974.390 | − | 2352.39i | −0.313447 | − | 0.756727i | ||||
\(214\) | 2903.23 | − | 544.167i | 0.927385 | − | 0.173825i | ||||
\(215\) | −7.88363 | − | 7.88363i | −0.00250074 | − | 0.00250074i | ||||
\(216\) | −749.765 | + | 3208.78i | −0.236181 | + | 1.01079i | ||||
\(217\) | −418.437 | + | 418.437i | −0.130900 | + | 0.130900i | ||||
\(218\) | 2355.73 | − | 3442.53i | 0.731882 | − | 1.06953i | ||||
\(219\) | −1553.02 | + | 643.284i | −0.479195 | + | 0.198489i | ||||
\(220\) | −28.8714 | − | 74.3113i | −0.00884778 | − | 0.0227730i | ||||
\(221\) | 672.246 | − | 1622.94i | 0.204616 | − | 0.493987i | ||||
\(222\) | −4663.81 | − | 981.453i | −1.40998 | − | 0.296715i | ||||
\(223\) | −1847.81 | −0.554880 | −0.277440 | − | 0.960743i | \(-0.589486\pi\) | ||||
−0.277440 | + | 0.960743i | \(0.589486\pi\) | |||||||
\(224\) | 727.399 | − | 2829.01i | 0.216970 | − | 0.843844i | ||||
\(225\) | −288.083 | −0.0853579 | ||||||||
\(226\) | 3243.85 | + | 682.636i | 0.954769 | + | 0.200922i | ||||
\(227\) | −904.304 | + | 2183.18i | −0.264409 | + | 0.638339i | −0.999202 | − | 0.0399527i | \(-0.987279\pi\) |
0.734793 | + | 0.678291i | \(0.237279\pi\) | |||||||
\(228\) | 4442.11 | − | 1725.85i | 1.29029 | − | 0.501303i | ||||
\(229\) | 4319.52 | − | 1789.20i | 1.24647 | − | 0.516305i | 0.340740 | − | 0.940158i | \(-0.389322\pi\) |
0.905731 | + | 0.423852i | \(0.139322\pi\) | |||||||
\(230\) | 34.2700 | − | 50.0802i | 0.00982477 | − | 0.0143574i | ||||
\(231\) | 2764.89 | − | 2764.89i | 0.787516 | − | 0.787516i | ||||
\(232\) | −2012.05 | − | 3239.01i | −0.569385 | − | 0.916600i | ||||
\(233\) | −3523.28 | − | 3523.28i | −0.990634 | − | 0.990634i | 0.00932269 | − | 0.999957i | \(-0.497032\pi\) |
−0.999957 | + | 0.00932269i | \(0.997032\pi\) | |||||||
\(234\) | −131.369 | + | 24.6232i | −0.0367003 | + | 0.00687892i | ||||
\(235\) | −39.7767 | − | 96.0294i | −0.0110415 | − | 0.0266564i | ||||
\(236\) | −354.496 | − | 7.84560i | −0.0977784 | − | 0.00216400i | ||||
\(237\) | 4675.37 | + | 1936.60i | 1.28143 | + | 0.530784i | ||||
\(238\) | −3276.19 | + | 2137.03i | −0.892286 | + | 0.582031i | ||||
\(239\) | 6222.79i | 1.68418i | 0.539337 | + | 0.842090i | \(0.318675\pi\) | ||||
−0.539337 | + | 0.842090i | \(0.681325\pi\) | |||||||
\(240\) | −47.9481 | + | 43.8814i | −0.0128960 | + | 0.0118022i | ||||
\(241\) | 4271.08i | 1.14160i | 0.821091 | + | 0.570798i | \(0.193366\pi\) | ||||
−0.821091 | + | 0.570798i | \(0.806634\pi\) | |||||||
\(242\) | −1617.48 | − | 2479.69i | −0.429651 | − | 0.658679i | ||||
\(243\) | −595.962 | − | 246.856i | −0.157329 | − | 0.0651679i | ||||
\(244\) | 4906.74 | − | 4694.26i | 1.28739 | − | 1.23163i | ||||
\(245\) | 6.46091 | + | 15.5980i | 0.00168478 | + | 0.00406743i | ||||
\(246\) | −720.269 | − | 3842.76i | −0.186677 | − | 0.995956i | ||||
\(247\) | 1737.42 | + | 1737.42i | 0.447568 | + | 0.447568i | ||||
\(248\) | 483.651 | − | 674.268i | 0.123838 | − | 0.172645i | ||||
\(249\) | −879.598 | + | 879.598i | −0.223864 | + | 0.223864i | ||||
\(250\) | −119.240 | − | 81.5961i | −0.0301656 | − | 0.0206424i | ||||
\(251\) | 4861.21 | − | 2013.58i | 1.22246 | − | 0.506358i | 0.324267 | − | 0.945966i | \(-0.394883\pi\) |
0.898190 | + | 0.439608i | \(0.144883\pi\) | |||||||
\(252\) | 272.372 | + | 119.948i | 0.0680866 | + | 0.0299841i | ||||
\(253\) | 1958.99 | − | 4729.43i | 0.486802 | − | 1.17524i | ||||
\(254\) | −1184.46 | + | 5628.51i | −0.292598 | + | 1.39041i | ||||
\(255\) | 87.0377 | 0.0213746 | ||||||||
\(256\) | −362.074 | + | 4079.97i | −0.0883969 | + | 0.996085i | ||||
\(257\) | 2043.19 | 0.495917 | 0.247958 | − | 0.968771i | \(-0.420240\pi\) | ||||
0.247958 | + | 0.968771i | \(0.420240\pi\) | |||||||
\(258\) | −157.904 | + | 750.353i | −0.0381035 | + | 0.181066i | ||||
\(259\) | −2093.90 | + | 5055.12i | −0.502349 | + | 1.21278i | ||||
\(260\) | −30.6693 | − | 13.5062i | −0.00731551 | − | 0.00322162i | ||||
\(261\) | 358.928 | − | 148.673i | 0.0851230 | − | 0.0352591i | ||||
\(262\) | 1640.51 | + | 1122.60i | 0.386836 | + | 0.264713i | ||||
\(263\) | −3376.45 | + | 3376.45i | −0.791638 | + | 0.791638i | −0.981760 | − | 0.190123i | \(-0.939111\pi\) |
0.190123 | + | 0.981760i | \(0.439111\pi\) | |||||||
\(264\) | −3195.80 | + | 4455.33i | −0.745029 | + | 1.03866i | ||||
\(265\) | 27.8794 | + | 27.8794i | 0.00646271 | + | 0.00646271i | ||||
\(266\) | −1007.94 | − | 5377.54i | −0.232334 | − | 1.23954i | ||||
\(267\) | 2966.63 | + | 7162.07i | 0.679980 | + | 1.64162i | ||||
\(268\) | 746.858 | − | 714.515i | 0.170230 | − | 0.162858i | ||||
\(269\) | −3758.60 | − | 1556.86i | −0.851917 | − | 0.352876i | −0.0863762 | − | 0.996263i | \(-0.527529\pi\) |
−0.765541 | + | 0.643387i | \(0.777529\pi\) | |||||||
\(270\) | −45.9903 | − | 70.5057i | −0.0103662 | − | 0.0158920i | ||||
\(271\) | − | 4182.58i | − | 0.937540i | −0.883320 | − | 0.468770i | \(-0.844697\pi\) | ||
0.883320 | − | 0.468770i | \(-0.155303\pi\) | |||||||
\(272\) | 4046.26 | − | 3703.08i | 0.901987 | − | 0.825486i | ||||
\(273\) | − | 1643.63i | − | 0.364385i | ||||||
\(274\) | −3609.61 | + | 2354.52i | −0.795856 | + | 0.519130i | ||||
\(275\) | −5629.39 | − | 2331.77i | −1.23442 | − | 0.511313i | ||||
\(276\) | −4172.50 | − | 92.3447i | −0.909983 | − | 0.0201395i | ||||
\(277\) | −26.8731 | − | 64.8775i | −0.00582906 | − | 0.0140726i | 0.920938 | − | 0.389709i | \(-0.127424\pi\) |
−0.926767 | + | 0.375636i | \(0.877424\pi\) | |||||||
\(278\) | −2076.65 | + | 389.238i | −0.448020 | + | 0.0839747i | ||||
\(279\) | 59.7822 | + | 59.7822i | 0.0128282 | + | 0.0128282i | ||||
\(280\) | 39.3750 | + | 63.3862i | 0.00840395 | + | 0.0135287i | ||||
\(281\) | 3756.73 | − | 3756.73i | 0.797536 | − | 0.797536i | −0.185171 | − | 0.982706i | \(-0.559284\pi\) |
0.982706 | + | 0.185171i | \(0.0592837\pi\) | |||||||
\(282\) | −4037.08 | + | 5899.56i | −0.852499 | + | 1.24579i | ||||
\(283\) | 47.8634 | − | 19.8257i | 0.0100536 | − | 0.00416436i | −0.377651 | − | 0.925948i | \(-0.623268\pi\) |
0.387705 | + | 0.921784i | \(0.373268\pi\) | |||||||
\(284\) | 3820.80 | − | 1484.46i | 0.798321 | − | 0.310164i | ||||
\(285\) | −46.5885 | + | 112.474i | −0.00968303 | + | 0.0233769i | ||||
\(286\) | −2766.37 | − | 582.154i | −0.571953 | − | 0.120362i | ||||
\(287\) | −4488.55 | −0.923173 | ||||||||
\(288\) | −404.181 | − | 103.924i | −0.0826965 | − | 0.0212630i | ||||
\(289\) | −2431.97 | −0.495007 | ||||||||
\(290\) | 95.3206 | + | 20.0593i | 0.0193015 | + | 0.00406180i | ||||
\(291\) | 140.826 | − | 339.983i | 0.0283689 | − | 0.0684886i | ||||
\(292\) | −980.027 | − | 2522.46i | −0.196410 | − | 0.505534i | ||||
\(293\) | −3659.53 | + | 1515.83i | −0.729666 | + | 0.302238i | −0.716415 | − | 0.697674i | \(-0.754218\pi\) |
−0.0132515 | + | 0.999912i | \(0.504218\pi\) | |||||||
\(294\) | 655.742 | − | 958.264i | 0.130080 | − | 0.190092i | ||||
\(295\) | 6.40507 | − | 6.40507i | 0.00126413 | − | 0.00126413i | ||||
\(296\) | 1745.75 | − | 7471.31i | 0.342802 | − | 1.46710i | ||||
\(297\) | −5021.28 | − | 5021.28i | −0.981025 | − | 0.981025i | ||||
\(298\) | 4607.35 | − | 863.580i | 0.895626 | − | 0.167872i | ||||
\(299\) | −823.465 | − | 1988.02i | −0.159272 | − | 0.384516i | ||||
\(300\) | −109.917 | + | 4966.49i | −0.0211535 | + | 0.955801i | ||||
\(301\) | 813.309 | + | 336.883i | 0.155742 | + | 0.0645104i | ||||
\(302\) | 2699.80 | − | 1761.06i | 0.514424 | − | 0.335554i | ||||
\(303\) | 3035.16i | 0.575463i | ||||||||
\(304\) | 2619.47 | + | 7210.92i | 0.494201 | + | 1.36044i | ||||
\(305\) | 173.472i | 0.0325671i | ||||||||
\(306\) | 305.318 | + | 468.070i | 0.0570389 | + | 0.0874438i | ||||
\(307\) | 1166.44 | + | 483.155i | 0.216847 | + | 0.0898211i | 0.488463 | − | 0.872585i | \(-0.337558\pi\) |
−0.271615 | + | 0.962406i | \(0.587558\pi\) | |||||||
\(308\) | 4351.52 | + | 4548.49i | 0.805035 | + | 0.841475i | ||||
\(309\) | −1357.57 | − | 3277.46i | −0.249933 | − | 0.603391i | ||||
\(310\) | 3.90521 | + | 20.8350i | 0.000715488 | + | 0.00381725i | ||||
\(311\) | 811.491 | + | 811.491i | 0.147960 | + | 0.147960i | 0.777206 | − | 0.629246i | \(-0.216636\pi\) |
−0.629246 | + | 0.777206i | \(0.716636\pi\) | |||||||
\(312\) | 374.375 | + | 2274.17i | 0.0679321 | + | 0.412658i | ||||
\(313\) | −748.416 | + | 748.416i | −0.135153 | + | 0.135153i | −0.771447 | − | 0.636294i | \(-0.780467\pi\) |
0.636294 | + | 0.771447i | \(0.280467\pi\) | |||||||
\(314\) | −1879.07 | − | 1285.85i | −0.337714 | − | 0.231099i | ||||
\(315\) | −7.02409 | + | 2.90947i | −0.00125639 | + | 0.000520414i | ||||
\(316\) | −3283.44 | + | 7455.88i | −0.584519 | + | 1.32730i | ||||
\(317\) | −1647.93 | + | 3978.45i | −0.291977 | + | 0.704896i | −0.999999 | − | 0.00129494i | \(-0.999588\pi\) |
0.708022 | + | 0.706191i | \(0.249588\pi\) | |||||||
\(318\) | 558.407 | − | 2653.52i | 0.0984715 | − | 0.467931i | ||||
\(319\) | 8217.14 | 1.44223 | ||||||||
\(320\) | −68.9179 | − | 78.7341i | −0.0120395 | − | 0.0137543i | ||||
\(321\) | 5189.61 | 0.902354 | ||||||||
\(322\) | −986.704 | + | 4688.77i | −0.170767 | + | 0.811474i | ||||
\(323\) | 3931.52 | − | 9491.54i | 0.677263 | − | 1.63506i | ||||
\(324\) | −2132.65 | + | 4842.71i | −0.365680 | + | 0.830369i | ||||
\(325\) | −2366.32 | + | 980.162i | −0.403876 | + | 0.167291i | ||||
\(326\) | 2421.30 | + | 1656.90i | 0.411360 | + | 0.281494i | ||||
\(327\) | 5182.29 | − | 5182.29i | 0.876395 | − | 0.876395i | ||||
\(328\) | 6210.46 | − | 1022.37i | 1.04547 | − | 0.172107i | ||||
\(329\) | 5803.27 | + | 5803.27i | 0.972476 | + | 0.972476i | ||||
\(330\) | −25.8043 | − | 137.670i | −0.00430448 | − | 0.0229652i | ||||
\(331\) | −2379.90 | − | 5745.58i | −0.395199 | − | 0.954095i | −0.988788 | − | 0.149327i | \(-0.952289\pi\) |
0.593589 | − | 0.804769i | \(-0.297711\pi\) | |||||||
\(332\) | −1384.35 | − | 1447.02i | −0.228844 | − | 0.239203i | ||||
\(333\) | 722.225 | + | 299.156i | 0.118852 | + | 0.0492301i | ||||
\(334\) | 671.970 | + | 1030.17i | 0.110086 | + | 0.168767i | ||||
\(335\) | 26.4043i | 0.00430633i | ||||||||
\(336\) | 2171.80 | − | 4649.87i | 0.352623 | − | 0.754974i | ||||
\(337\) | − | 10731.5i | − | 1.73466i | −0.497730 | − | 0.867332i | \(-0.665833\pi\) | ||
0.497730 | − | 0.867332i | \(-0.334167\pi\) | |||||||
\(338\) | 4209.39 | − | 2745.75i | 0.677398 | − | 0.441861i | ||||
\(339\) | 5380.73 | + | 2228.77i | 0.862069 | + | 0.357081i | ||||
\(340\) | −3.10031 | + | 140.085i | −0.000494524 | + | 0.0223446i | ||||
\(341\) | 684.313 | + | 1652.08i | 0.108673 | + | 0.262361i | ||||
\(342\) | −768.291 | + | 144.005i | −0.121475 | + | 0.0227687i | ||||
\(343\) | −4856.34 | − | 4856.34i | −0.764484 | − | 0.764484i | ||||
\(344\) | −1202.05 | − | 280.870i | −0.188401 | − | 0.0440218i | ||||
\(345\) | 75.3893 | − | 75.3893i | 0.0117647 | − | 0.0117647i | ||||
\(346\) | −567.438 | + | 829.221i | −0.0881666 | + | 0.128842i | ||||
\(347\) | −5414.63 | + | 2242.81i | −0.837673 | + | 0.346976i | −0.759936 | − | 0.649998i | \(-0.774770\pi\) |
−0.0777376 | + | 0.996974i | \(0.524770\pi\) | |||||||
\(348\) | −2426.14 | − | 6244.57i | −0.373721 | − | 0.961908i | ||||
\(349\) | −443.942 | + | 1071.77i | −0.0680907 | + | 0.164385i | −0.954261 | − | 0.298973i | \(-0.903356\pi\) |
0.886171 | + | 0.463359i | \(0.153356\pi\) | |||||||
\(350\) | 5580.99 | + | 1174.46i | 0.852332 | + | 0.179365i | ||||
\(351\) | −2984.99 | −0.453922 | ||||||||
\(352\) | −7056.88 | − | 5302.24i | −1.06856 | − | 0.802870i | ||||
\(353\) | 812.561 | 0.122516 | 0.0612582 | − | 0.998122i | \(-0.480489\pi\) | ||||
0.0612582 | + | 0.998122i | \(0.480489\pi\) | |||||||
\(354\) | −609.626 | − | 128.290i | −0.0915290 | − | 0.0192614i | ||||
\(355\) | −40.0723 | + | 96.7430i | −0.00599103 | + | 0.0144636i | ||||
\(356\) | −11632.8 | + | 4519.58i | −1.73185 | + | 0.672858i | ||||
\(357\) | −6349.24 | + | 2629.94i | −0.941281 | + | 0.389891i | ||||
\(358\) | 2197.21 | − | 3210.88i | 0.324375 | − | 0.474023i | ||||
\(359\) | −3733.47 | + | 3733.47i | −0.548871 | + | 0.548871i | −0.926114 | − | 0.377243i | \(-0.876872\pi\) |
0.377243 | + | 0.926114i | \(0.376872\pi\) | |||||||
\(360\) | 9.05600 | − | 5.62552i | 0.00132581 | − | 0.000823585i | ||||
\(361\) | 5310.98 | + | 5310.98i | 0.774308 | + | 0.774308i | ||||
\(362\) | −10527.7 | + | 1973.26i | −1.52852 | + | 0.286498i | ||||
\(363\) | −1990.55 | − | 4805.62i | −0.287815 | − | 0.694847i | ||||
\(364\) | 2645.38 | + | 58.5467i | 0.380922 | + | 0.00843045i | ||||
\(365\) | 63.8689 | + | 26.4554i | 0.00915904 | + | 0.00379380i | ||||
\(366\) | 9992.69 | − | 6518.15i | 1.42712 | − | 0.930899i | ||||
\(367\) | 6820.92i | 0.970161i | 0.874469 | + | 0.485081i | \(0.161210\pi\) | ||||
−0.874469 | + | 0.485081i | \(0.838790\pi\) | |||||||
\(368\) | 297.252 | − | 6712.23i | 0.0421069 | − | 0.950813i | ||||
\(369\) | 641.280i | 0.0904707i | ||||||||
\(370\) | 107.083 | + | 164.165i | 0.0150460 | + | 0.0230663i | ||||
\(371\) | −2876.16 | − | 1191.34i | −0.402487 | − | 0.166716i | ||||
\(372\) | 1053.44 | − | 1007.82i | 0.146824 | − | 0.140466i | ||||
\(373\) | 3875.45 | + | 9356.15i | 0.537970 | + | 1.29878i | 0.926137 | + | 0.377186i | \(0.123108\pi\) |
−0.388167 | + | 0.921589i | \(0.626892\pi\) | |||||||
\(374\) | 2177.58 | + | 11617.8i | 0.301070 | + | 1.60626i | ||||
\(375\) | −179.500 | − | 179.500i | −0.0247183 | − | 0.0247183i | ||||
\(376\) | −9351.37 | − | 6707.71i | −1.28261 | − | 0.920010i | ||||
\(377\) | 2442.41 | − | 2442.41i | 0.333661 | − | 0.333661i | ||||
\(378\) | 5485.32 | + | 3753.61i | 0.746387 | + | 0.510754i | ||||
\(379\) | −4336.19 | + | 1796.11i | −0.587692 | + | 0.243430i | −0.656657 | − | 0.754189i | \(-0.728030\pi\) |
0.0689653 | + | 0.997619i | \(0.478030\pi\) | |||||||
\(380\) | −179.365 | − | 78.9891i | −0.0242137 | − | 0.0106633i | ||||
\(381\) | −3867.22 | + | 9336.29i | −0.520009 | + | 1.25541i | ||||
\(382\) | 1237.19 | − | 5879.05i | 0.165707 | − | 0.787430i | ||||
\(383\) | 8452.79 | 1.12772 | 0.563861 | − | 0.825870i | \(-0.309315\pi\) | ||||
0.563861 | + | 0.825870i | \(0.309315\pi\) | |||||||
\(384\) | −1945.84 | + | 6928.35i | −0.258588 | + | 0.920731i | ||||
\(385\) | −160.806 | −0.0212869 | ||||||||
\(386\) | 1388.87 | − | 6599.84i | 0.183139 | − | 0.870267i | ||||
\(387\) | 48.1306 | − | 116.198i | 0.00632201 | − | 0.0152627i | ||||
\(388\) | 542.177 | + | 238.765i | 0.0709403 | + | 0.0312409i | ||||
\(389\) | −468.925 | + | 194.235i | −0.0611194 | + | 0.0253165i | −0.413034 | − | 0.910716i | \(-0.635531\pi\) |
0.351914 | + | 0.936032i | \(0.385531\pi\) | |||||||
\(390\) | −48.5901 | − | 33.2503i | −0.00630886 | − | 0.00431717i | ||||
\(391\) | −6361.98 | + | 6361.98i | −0.822862 | + | 0.822862i | ||||
\(392\) | 1518.94 | + | 1089.53i | 0.195709 | + | 0.140382i | ||||
\(393\) | 2469.58 | + | 2469.58i | 0.316981 | + | 0.316981i | ||||
\(394\) | −1697.95 | − | 9058.87i | −0.217111 | − | 1.15832i | ||||
\(395\) | −79.6437 | − | 192.277i | −0.0101451 | − | 0.0244924i | ||||
\(396\) | 649.844 | − | 621.702i | 0.0824643 | − | 0.0788932i | ||||
\(397\) | −3306.01 | − | 1369.40i | −0.417945 | − | 0.173118i | 0.163793 | − | 0.986495i | \(-0.447627\pi\) |
−0.581738 | + | 0.813376i | \(0.697627\pi\) | |||||||
\(398\) | 5557.28 | + | 8519.62i | 0.699902 | + | 1.07299i | ||||
\(399\) | − | 9612.53i | − | 1.20609i | ||||||
\(400\) | −7989.50 | − | 353.816i | −0.998687 | − | 0.0442270i | ||||
\(401\) | 3887.84i | 0.484164i | 0.970256 | + | 0.242082i | \(0.0778303\pi\) | ||||
−0.970256 | + | 0.242082i | \(0.922170\pi\) | |||||||
\(402\) | 1520.99 | − | 992.131i | 0.188707 | − | 0.123092i | ||||
\(403\) | 694.453 | + | 287.652i | 0.0858392 | + | 0.0355557i | ||||
\(404\) | −4884.99 | − | 108.113i | −0.601578 | − | 0.0133140i | ||||
\(405\) | −51.7298 | − | 124.887i | −0.00634685 | − | 0.0153227i | ||||
\(406\) | −7559.58 | + | 1416.93i | −0.924078 | + | 0.173205i | ||||
\(407\) | 11691.5 | + | 11691.5i | 1.42390 | + | 1.42390i | ||||
\(408\) | 8185.93 | − | 5085.03i | 0.993294 | − | 0.617026i | ||||
\(409\) | −7188.15 | + | 7188.15i | −0.869025 | + | 0.869025i | −0.992365 | − | 0.123339i | \(-0.960640\pi\) |
0.123339 | + | 0.992365i | \(0.460640\pi\) | |||||||
\(410\) | −90.8023 | + | 132.693i | −0.0109376 | + | 0.0159836i | ||||
\(411\) | −6995.40 | + | 2897.59i | −0.839556 | + | 0.347756i | ||||
\(412\) | 5323.32 | − | 2068.22i | 0.636557 | − | 0.247315i | ||||
\(413\) | −273.702 | + | 660.775i | −0.0326101 | + | 0.0787278i | ||||
\(414\) | 669.885 | + | 140.971i | 0.0795243 | + | 0.0167351i | ||||
\(415\) | 51.1576 | 0.00605115 | ||||||||
\(416\) | −3673.54 | + | 521.539i | −0.432957 | + | 0.0614677i | ||||
\(417\) | −3712.08 | −0.435927 | ||||||||
\(418\) | −16178.7 | − | 3404.64i | −1.89312 | − | 0.398388i | ||||
\(419\) | 4190.33 | − | 10116.4i | 0.488571 | − | 1.17951i | −0.466869 | − | 0.884327i | \(-0.654618\pi\) |
0.955439 | − | 0.295187i | \(-0.0953821\pi\) | |||||||
\(420\) | 47.4787 | + | 122.204i | 0.00551601 | + | 0.0141975i | ||||
\(421\) | 14568.6 | − | 6034.51i | 1.68653 | − | 0.698584i | 0.686927 | − | 0.726726i | \(-0.258959\pi\) |
0.999604 | + | 0.0281419i | \(0.00895901\pi\) | |||||||
\(422\) | −711.445 | + | 1039.66i | −0.0820677 | + | 0.119929i | ||||
\(423\) | 829.114 | − | 829.114i | 0.0953024 | − | 0.0953024i | ||||
\(424\) | 4250.87 | + | 993.259i | 0.486888 | + | 0.113766i | ||||
\(425\) | 7572.60 | + | 7572.60i | 0.864294 | + | 0.864294i | ||||
\(426\) | 7078.49 | − | 1326.76i | 0.805056 | − | 0.150896i | ||||
\(427\) | −5241.65 | − | 12654.5i | −0.594054 | − | 1.43417i | ||||
\(428\) | −184.856 | + | 8352.52i | −0.0208769 | + | 0.943304i | ||||
\(429\) | −4588.71 | − | 1900.70i | −0.516422 | − | 0.213909i | ||||
\(430\) | 26.4122 | − | 17.2285i | 0.00296212 | − | 0.00193216i | ||||
\(431\) | − | 844.040i | − | 0.0943295i | −0.998887 | − | 0.0471647i | \(-0.984981\pi\) | ||
0.998887 | − | 0.0471647i | \(-0.0150186\pi\) | |||||||
\(432\) | −8444.58 | − | 3944.18i | −0.940487 | − | 0.439270i | ||||
\(433\) | − | 11447.7i | − | 1.27053i | −0.772293 | − | 0.635266i | \(-0.780890\pi\) | ||
0.772293 | − | 0.635266i | \(-0.219110\pi\) | |||||||
\(434\) | −914.430 | − | 1401.87i | −0.101138 | − | 0.155051i | ||||
\(435\) | 158.113 | + | 65.4925i | 0.0174274 | + | 0.00721868i | ||||
\(436\) | 8156.15 | + | 8525.34i | 0.895891 | + | 0.936444i | ||||
\(437\) | −4815.91 | − | 11626.6i | −0.527177 | − | 1.27272i | ||||
\(438\) | −875.914 | − | 4673.15i | −0.0955543 | − | 0.509799i | ||||
\(439\) | 2040.34 | + | 2040.34i | 0.221823 | + | 0.221823i | 0.809266 | − | 0.587443i | \(-0.199865\pi\) |
−0.587443 | + | 0.809266i | \(0.699865\pi\) | |||||||
\(440\) | 222.496 | − | 36.6274i | 0.0241070 | − | 0.00396850i | ||||
\(441\) | −134.673 | + | 134.673i | −0.0145419 | + | 0.0145419i | ||||
\(442\) | 4100.44 | + | 2805.94i | 0.441262 | + | 0.301957i | ||||
\(443\) | 12477.8 | − | 5168.47i | 1.33823 | − | 0.554315i | 0.405241 | − | 0.914210i | \(-0.367187\pi\) |
0.932993 | + | 0.359895i | \(0.117187\pi\) | |||||||
\(444\) | 5432.94 | − | 12336.9i | 0.580712 | − | 1.31865i | ||||
\(445\) | 122.004 | − | 294.544i | 0.0129967 | − | 0.0313769i | ||||
\(446\) | 1076.27 | − | 5114.37i | 0.114266 | − | 0.542987i | ||||
\(447\) | 8235.78 | 0.871452 | ||||||||
\(448\) | 7406.47 | + | 3661.07i | 0.781077 | + | 0.386093i | ||||
\(449\) | −3601.74 | −0.378567 | −0.189283 | − | 0.981922i | \(-0.560616\pi\) | ||||
−0.189283 | + | 0.981922i | \(0.560616\pi\) | |||||||
\(450\) | 167.796 | − | 797.357i | 0.0175777 | − | 0.0835284i | ||||
\(451\) | −5190.58 | + | 12531.2i | −0.541940 | + | 1.30836i | ||||
\(452\) | −3778.81 | + | 8580.74i | −0.393230 | + | 0.892930i | ||||
\(453\) | 5232.19 | − | 2167.25i | 0.542671 | − | 0.224782i | ||||
\(454\) | −5515.90 | − | 3774.55i | −0.570207 | − | 0.390194i | ||||
\(455\) | −47.7970 | + | 47.7970i | −0.00492474 | + | 0.00492474i | ||||
\(456\) | 2189.48 | + | 13300.1i | 0.224850 | + | 1.36587i | ||||
\(457\) | −10018.4 | − | 10018.4i | −1.02547 | − | 1.02547i | −0.999667 | − | 0.0258078i | \(-0.991784\pi\) |
−0.0258078 | − | 0.999667i | \(-0.508216\pi\) | |||||||
\(458\) | 2436.23 | + | 12997.7i | 0.248554 | + | 1.32608i | ||||
\(459\) | 4776.21 | + | 11530.8i | 0.485696 | + | 1.17257i | ||||
\(460\) | 118.651 | + | 124.022i | 0.0120264 | + | 0.0125708i | ||||
\(461\) | −1495.66 | − | 619.524i | −0.151106 | − | 0.0625902i | 0.305849 | − | 0.952080i | \(-0.401060\pi\) |
−0.456955 | + | 0.889490i | \(0.651060\pi\) | |||||||
\(462\) | 6042.24 | + | 9263.09i | 0.608464 | + | 0.932810i | ||||
\(463\) | − | 14517.8i | − | 1.45724i | −0.684921 | − | 0.728618i | \(-0.740163\pi\) | ||
0.684921 | − | 0.728618i | \(-0.259837\pi\) | |||||||
\(464\) | 10136.9 | − | 3682.37i | 1.01421 | − | 0.368426i | ||||
\(465\) | 37.2432i | 0.00371422i | ||||||||
\(466\) | 11803.9 | − | 7699.59i | 1.17340 | − | 0.765401i | ||||
\(467\) | 5649.95 | + | 2340.29i | 0.559847 | + | 0.231896i | 0.644619 | − | 0.764504i | \(-0.277016\pi\) |
−0.0847717 | + | 0.996400i | \(0.527016\pi\) | |||||||
\(468\) | 8.36459 | − | 377.946i | 0.000826182 | − | 0.0373302i | ||||
\(469\) | −797.835 | − | 1926.14i | −0.0785513 | − | 0.189640i | ||||
\(470\) | 288.959 | − | 54.1611i | 0.0283589 | − | 0.00531546i | ||||
\(471\) | −2828.70 | − | 2828.70i | −0.276730 | − | 0.276730i | ||||
\(472\) | 228.194 | − | 976.605i | 0.0222531 | − | 0.0952371i | ||||
\(473\) | 1881.03 | − | 1881.03i | 0.182854 | − | 0.182854i | ||||
\(474\) | −8083.34 | + | 11812.5i | −0.783291 | + | 1.14466i | ||||
\(475\) | −13839.1 | + | 5732.32i | −1.33680 | + | 0.553720i | ||||
\(476\) | −4006.65 | − | 10312.6i | −0.385808 | − | 0.993018i | ||||
\(477\) | −170.207 | + | 410.917i | −0.0163381 | + | 0.0394436i | ||||
\(478\) | −17223.5 | − | 3624.51i | −1.64808 | − | 0.346823i | ||||
\(479\) | −10244.1 | −0.977172 | −0.488586 | − | 0.872516i | \(-0.662487\pi\) | ||||
−0.488586 | + | 0.872516i | \(0.662487\pi\) | |||||||
\(480\) | −93.5274 | − | 158.270i | −0.00889359 | − | 0.0150500i | ||||
\(481\) | 6950.22 | 0.658841 | ||||||||
\(482\) | −11821.5 | − | 2487.72i | −1.11713 | − | 0.235088i | ||||
\(483\) | −3221.54 | + | 7777.48i | −0.303489 | + | 0.732687i | ||||
\(484\) | 7805.40 | − | 3032.56i | 0.733039 | − | 0.284801i | ||||
\(485\) | −13.9820 | + | 5.79153i | −0.00130905 | + | 0.000542226i | ||||
\(486\) | 1030.37 | − | 1505.72i | 0.0961699 | − | 0.140537i | ||||
\(487\) | −12510.0 | + | 12510.0i | −1.16403 | + | 1.16403i | −0.180446 | + | 0.983585i | \(0.557754\pi\) |
−0.983585 | + | 0.180446i | \(0.942246\pi\) | |||||||
\(488\) | 10134.8 | + | 16315.1i | 0.940126 | + | 1.51342i | ||||
\(489\) | 3644.95 | + | 3644.95i | 0.337076 | + | 0.337076i | ||||
\(490\) | −46.9355 | + | 8.79736i | −0.00432720 | + | 0.000811070i | ||||
\(491\) | −4847.78 | − | 11703.6i | −0.445575 | − | 1.07571i | −0.973962 | − | 0.226710i | \(-0.927203\pi\) |
0.528387 | − | 0.849004i | \(-0.322797\pi\) | |||||||
\(492\) | 11055.5 | + | 244.678i | 1.01305 | + | 0.0224206i | ||||
\(493\) | −13342.9 | − | 5526.81i | −1.21893 | − | 0.504898i | ||||
\(494\) | −5820.81 | + | 3796.86i | −0.530143 | + | 0.345808i | ||||
\(495\) | 22.9744i | 0.00208611i | ||||||||
\(496\) | 1584.54 | + | 1731.38i | 0.143443 | + | 0.156737i | ||||
\(497\) | − | 8268.05i | − | 0.746223i | ||||||
\(498\) | −1922.23 | − | 2946.88i | −0.172966 | − | 0.265167i | ||||
\(499\) | 18011.3 | + | 7460.51i | 1.61582 | + | 0.669295i | 0.993538 | − | 0.113498i | \(-0.0362055\pi\) |
0.622282 | + | 0.782793i | \(0.286206\pi\) | |||||||
\(500\) | 295.294 | − | 282.506i | 0.0264119 | − | 0.0252681i | ||||
\(501\) | 826.961 | + | 1996.46i | 0.0737443 | + | 0.178034i | ||||
\(502\) | 2741.75 | + | 14627.7i | 0.243765 | + | 1.30053i | ||||
\(503\) | −3687.97 | − | 3687.97i | −0.326915 | − | 0.326915i | 0.524497 | − | 0.851412i | \(-0.324253\pi\) |
−0.851412 | + | 0.524497i | \(0.824253\pi\) | |||||||
\(504\) | −490.637 | + | 684.008i | −0.0433625 | + | 0.0604527i | ||||
\(505\) | 88.2627 | − | 88.2627i | 0.00777750 | − | 0.00777750i | ||||
\(506\) | 11949.1 | + | 8176.80i | 1.04981 | + | 0.718386i | ||||
\(507\) | 8157.76 | − | 3379.06i | 0.714594 | − | 0.295994i | ||||
\(508\) | −14888.7 | − | 6556.73i | −1.30035 | − | 0.572653i | ||||
\(509\) | 1071.88 | − | 2587.76i | 0.0933407 | − | 0.225344i | −0.870313 | − | 0.492499i | \(-0.836083\pi\) |
0.963654 | + | 0.267155i | \(0.0860835\pi\) | |||||||
\(510\) | −50.6957 | + | 240.903i | −0.00440166 | + | 0.0209164i | ||||
\(511\) | −5458.49 | −0.472543 | ||||||||
\(512\) | −11081.7 | − | 3378.55i | −0.956532 | − | 0.291626i | ||||
\(513\) | −17457.2 | −1.50245 | ||||||||
\(514\) | −1190.07 | + | 5655.15i | −0.102124 | + | 0.485287i | ||||
\(515\) | −55.8306 | + | 134.787i | −0.00477707 | + | 0.0115329i | ||||
\(516\) | −1984.86 | − | 874.097i | −0.169338 | − | 0.0745736i | ||||
\(517\) | 22912.5 | − | 9490.68i | 1.94911 | − | 0.807350i | ||||
\(518\) | −12772.0 | − | 8739.89i | −1.08334 | − | 0.741329i | ||||
\(519\) | −1248.29 | + | 1248.29i | −0.105575 | + | 0.105575i | ||||
\(520\) | 55.2462 | − | 77.0199i | 0.00465905 | − | 0.00649528i | ||||
\(521\) | −8038.89 | − | 8038.89i | −0.675988 | − | 0.675988i | 0.283102 | − | 0.959090i | \(-0.408637\pi\) |
−0.959090 | + | 0.283102i | \(0.908637\pi\) | |||||||
\(522\) | 202.437 | + | 1080.04i | 0.0169740 | + | 0.0905594i | ||||
\(523\) | 7860.76 | + | 18977.6i | 0.657222 | + | 1.58667i | 0.802076 | + | 0.597222i | \(0.203729\pi\) |
−0.144854 | + | 0.989453i | \(0.546271\pi\) | |||||||
\(524\) | −4062.68 | + | 3886.74i | −0.338700 | + | 0.324033i | ||||
\(525\) | 9257.45 | + | 3834.56i | 0.769578 | + | 0.318770i | ||||
\(526\) | −7378.71 | − | 11312.0i | −0.611649 | − | 0.937692i | ||||
\(527\) | − | 3142.89i | − | 0.259785i | ||||||
\(528\) | −10470.1 | − | 11440.4i | −0.862976 | − | 0.942952i | ||||
\(529\) | − | 1145.90i | − | 0.0941813i | ||||||
\(530\) | −93.4033 | + | 60.9262i | −0.00765505 | + | 0.00499333i | ||||
\(531\) | 94.4050 | + | 39.1038i | 0.00771531 | + | 0.00319579i | ||||
\(532\) | 15471.1 | + | 342.402i | 1.26082 | + | 0.0279041i | ||||
\(533\) | 2181.87 | + | 5267.49i | 0.177312 | + | 0.428068i | ||||
\(534\) | −21551.2 | + | 4039.45i | −1.74646 | + | 0.327348i | ||||
\(535\) | −150.914 | − | 150.914i | −0.0121955 | − | 0.0121955i | ||||
\(536\) | 1542.63 | + | 2483.33i | 0.124312 | + | 0.200119i | ||||
\(537\) | 4833.57 | − | 4833.57i | 0.388424 | − | 0.388424i | ||||
\(538\) | 6498.31 | − | 9496.26i | 0.520748 | − | 0.760991i | ||||
\(539\) | −3721.67 | + | 1541.57i | −0.297410 | + | 0.123191i | ||||
\(540\) | 221.933 | − | 86.2256i | 0.0176861 | − | 0.00687141i | ||||
\(541\) | −1316.22 | + | 3177.63i | −0.104600 | + | 0.252527i | −0.967511 | − | 0.252829i | \(-0.918639\pi\) |
0.862911 | + | 0.505356i | \(0.168639\pi\) | |||||||
\(542\) | 11576.6 | + | 2436.17i | 0.917446 | + | 0.193067i | ||||
\(543\) | −18818.6 | −1.48726 | ||||||||
\(544\) | 7892.63 | + | 13356.1i | 0.622047 | + | 1.05265i | ||||
\(545\) | −301.403 | −0.0236893 | ||||||||
\(546\) | 4549.25 | + | 957.345i | 0.356575 | + | 0.0750377i | ||||
\(547\) | −6431.02 | + | 15525.9i | −0.502689 | + | 1.21360i | 0.445325 | + | 0.895369i | \(0.353088\pi\) |
−0.948014 | + | 0.318229i | \(0.896912\pi\) | |||||||
\(548\) | −4414.41 | − | 11362.1i | −0.344113 | − | 0.885702i | ||||
\(549\) | −1807.95 | + | 748.876i | −0.140549 | + | 0.0582172i | ||||
\(550\) | 9732.76 | − | 14222.9i | 0.754557 | − | 1.10267i | ||||
\(551\) | 14284.0 | − | 14284.0i | 1.10439 | − | 1.10439i | ||||
\(552\) | 2685.90 | − | 11494.9i | 0.207100 | − | 0.886332i | ||||
\(553\) | 11619.7 | + | 11619.7i | 0.893527 | + | 0.893527i | ||||
\(554\) | 195.221 | − | 36.5912i | 0.0149713 | − | 0.00280616i | ||||
\(555\) | 131.782 | + | 318.151i | 0.0100790 | + | 0.0243329i | ||||
\(556\) | 132.226 | − | 5974.49i | 0.0100856 | − | 0.455710i | ||||
\(557\) | −5335.11 | − | 2209.88i | −0.405846 | − | 0.168107i | 0.170416 | − | 0.985372i | \(-0.445489\pi\) |
−0.576261 | + | 0.817266i | \(0.695489\pi\) | |||||||
\(558\) | −200.286 | + | 130.645i | −0.0151949 | + | 0.00991154i | ||||
\(559\) | − | 1118.21i | − | 0.0846068i | ||||||
\(560\) | −198.375 | + | 72.0626i | −0.0149694 | + | 0.00543786i | ||||
\(561\) | 20767.1i | 1.56290i | ||||||||
\(562\) | 8209.76 | + | 12586.0i | 0.616206 | + | 0.944678i | ||||
\(563\) | 5228.46 | + | 2165.70i | 0.391391 | + | 0.162120i | 0.569696 | − | 0.821856i | \(-0.307061\pi\) |
−0.178304 | + | 0.983975i | \(0.557061\pi\) | |||||||
\(564\) | −13977.4 | − | 14610.1i | −1.04354 | − | 1.09077i | ||||
\(565\) | −91.6594 | − | 221.285i | −0.00682502 | − | 0.0164771i | ||||
\(566\) | 26.9952 | + | 144.024i | 0.00200476 | + | 0.0106957i | ||||
\(567\) | 7547.18 | + | 7547.18i | 0.558998 | + | 0.558998i | ||||
\(568\) | 1883.24 | + | 11439.9i | 0.139118 | + | 0.845082i | ||||
\(569\) | −4183.25 | + | 4183.25i | −0.308209 | + | 0.308209i | −0.844215 | − | 0.536005i | \(-0.819933\pi\) |
0.536005 | + | 0.844215i | \(0.319933\pi\) | |||||||
\(570\) | −284.172 | − | 194.459i | −0.0208818 | − | 0.0142895i | ||||
\(571\) | 7441.94 | − | 3082.55i | 0.545421 | − | 0.225921i | −0.0929211 | − | 0.995673i | \(-0.529620\pi\) |
0.638342 | + | 0.769753i | \(0.279620\pi\) | |||||||
\(572\) | 3222.58 | − | 7317.68i | 0.235564 | − | 0.534909i | ||||
\(573\) | 4039.35 | − | 9751.87i | 0.294496 | − | 0.710977i | ||||
\(574\) | 2614.39 | − | 12423.4i | 0.190109 | − | 0.903386i | ||||
\(575\) | 13118.3 | 0.951427 | ||||||||
\(576\) | 523.058 | − | 1058.16i | 0.0378370 | − | 0.0765454i | ||||
\(577\) | 2828.16 | 0.204052 | 0.102026 | − | 0.994782i | \(-0.467468\pi\) | ||||
0.102026 | + | 0.994782i | \(0.467468\pi\) | |||||||
\(578\) | 1416.52 | − | 6731.21i | 0.101937 | − | 0.484397i | ||||
\(579\) | 4534.59 | − | 10947.5i | 0.325477 | − | 0.785771i | ||||
\(580\) | −111.040 | + | 252.145i | −0.00794948 | + | 0.0180513i | ||||
\(581\) | −3731.85 | + | 1545.78i | −0.266477 | + | 0.110379i | ||||
\(582\) | 858.983 | + | 587.804i | 0.0611786 | + | 0.0418647i | ||||
\(583\) | −6652.00 | + | 6652.00i | −0.472552 | + | 0.472552i | ||||
\(584\) | 7552.50 | − | 1243.30i | 0.535145 | − | 0.0880960i | ||||
\(585\) | 6.82877 | + | 6.82877i | 0.000482624 | + | 0.000482624i | ||||
\(586\) | −2064.00 | − | 11011.8i | −0.145500 | − | 0.776267i | ||||
\(587\) | 1835.52 | + | 4431.34i | 0.129063 | + | 0.311586i | 0.975181 | − | 0.221410i | \(-0.0710659\pi\) |
−0.846118 | + | 0.532996i | \(0.821066\pi\) | |||||||
\(588\) | 2270.35 | + | 2373.11i | 0.159230 | + | 0.166438i | ||||
\(589\) | 4061.40 | + | 1682.29i | 0.284121 | + | 0.117687i | ||||
\(590\) | 13.9973 | + | 21.4587i | 0.000976713 | + | 0.00149736i | ||||
\(591\) | − | 16193.0i | − | 1.12706i | ||||||
\(592\) | 19662.3 | + | 9183.60i | 1.36506 | + | 0.637574i | ||||
\(593\) | 13545.0i | 0.937989i | 0.883201 | + | 0.468995i | \(0.155384\pi\) | ||||
−0.883201 | + | 0.468995i | \(0.844616\pi\) | |||||||
\(594\) | 16822.6 | − | 10973.3i | 1.16202 | − | 0.757976i | ||||
\(595\) | 261.116 | + | 108.158i | 0.0179911 | + | 0.00745215i | ||||
\(596\) | −293.361 | + | 13255.2i | −0.0201620 | + | 0.911000i | ||||
\(597\) | 6839.07 | + | 16511.0i | 0.468852 | + | 1.13191i | ||||
\(598\) | 5982.09 | − | 1121.25i | 0.409073 | − | 0.0766748i | ||||
\(599\) | −12379.3 | − | 12379.3i | −0.844414 | − | 0.844414i | 0.145015 | − | 0.989429i | \(-0.453677\pi\) |
−0.989429 | + | 0.145015i | \(0.953677\pi\) | |||||||
\(600\) | −13682.2 | − | 3196.99i | −0.930959 | − | 0.217528i | ||||
\(601\) | −17513.1 | + | 17513.1i | −1.18864 | + | 1.18864i | −0.211202 | + | 0.977442i | \(0.567738\pi\) |
−0.977442 | + | 0.211202i | \(0.932262\pi\) | |||||||
\(602\) | −1406.14 | + | 2054.86i | −0.0951997 | + | 0.139119i | ||||
\(603\) | −275.189 | + | 113.987i | −0.0185846 | + | 0.00769801i | ||||
\(604\) | 3301.74 | + | 8498.26i | 0.222427 | + | 0.572499i | ||||
\(605\) | −81.8624 | + | 197.633i | −0.00550112 | + | 0.0132809i | ||||
\(606\) | −8400.72 | − | 1767.85i | −0.563129 | − | 0.118505i | ||||
\(607\) | 21984.1 | 1.47003 | 0.735013 | − | 0.678053i | \(-0.237176\pi\) | ||||
0.735013 | + | 0.678053i | \(0.237176\pi\) | |||||||
\(608\) | −21484.1 | + | 3050.14i | −1.43305 | + | 0.203453i | ||||
\(609\) | −13513.0 | −0.899135 | ||||||||
\(610\) | −480.137 | − | 101.040i | −0.0318691 | − | 0.00670654i | ||||
\(611\) | 3989.42 | − | 9631.31i | 0.264148 | − | 0.637711i | ||||
\(612\) | −1473.36 | + | 572.431i | −0.0973156 | + | 0.0378091i | ||||
\(613\) | −13582.2 | + | 5625.93i | −0.894910 | + | 0.370684i | −0.782261 | − | 0.622951i | \(-0.785934\pi\) |
−0.112649 | + | 0.993635i | \(0.535934\pi\) | |||||||
\(614\) | −2016.68 | + | 2947.06i | −0.132551 | + | 0.193703i | ||||
\(615\) | −199.753 | + | 199.753i | −0.0130972 | + | 0.0130972i | ||||
\(616\) | −15123.9 | + | 9394.85i | −0.989220 | + | 0.614496i | ||||
\(617\) | −4045.14 | − | 4045.14i | −0.263941 | − | 0.263941i | 0.562712 | − | 0.826653i | \(-0.309758\pi\) |
−0.826653 | + | 0.562712i | \(0.809758\pi\) | |||||||
\(618\) | 9862.08 | − | 1848.50i | 0.641927 | − | 0.120320i | ||||
\(619\) | −4901.51 | − | 11833.3i | −0.318268 | − | 0.768368i | −0.999346 | − | 0.0361568i | \(-0.988488\pi\) |
0.681078 | − | 0.732211i | \(-0.261512\pi\) | |||||||
\(620\) | −59.9418 | − | 1.32662i | −0.00388278 | − | 8.59325e-5i | ||||
\(621\) | 14124.6 | + | 5850.61i | 0.912723 | + | 0.378062i | ||||
\(622\) | −2718.71 | + | 1773.39i | −0.175258 | + | 0.114319i | ||||
\(623\) | 25172.9i | 1.61883i | ||||||||
\(624\) | −6512.51 | − | 288.407i | −0.417803 | − | 0.0185025i | ||||
\(625\) | − | 15609.3i | − | 0.998998i | ||||||
\(626\) | −1635.55 | − | 2507.39i | −0.104424 | − | 0.160089i | ||||
\(627\) | −26836.3 | − | 11116.0i | −1.70931 | − | 0.708021i | ||||
\(628\) | 4653.47 | − | 4451.95i | 0.295691 | − | 0.282886i | ||||
\(629\) | −11120.9 | − | 26848.2i | −0.704959 | − | 1.70192i | ||||
\(630\) | −3.96163 | − | 21.1360i | −0.000250532 | − | 0.00133663i | ||||
\(631\) | −14073.2 | − | 14073.2i | −0.887870 | − | 0.887870i | 0.106448 | − | 0.994318i | \(-0.466052\pi\) |
−0.994318 | + | 0.106448i | \(0.966052\pi\) | |||||||
\(632\) | −18724.0 | − | 13430.7i | −1.17848 | − | 0.845321i | ||||
\(633\) | −1565.08 | + | 1565.08i | −0.0982723 | + | 0.0982723i | ||||
\(634\) | −10051.7 | − | 6878.42i | −0.629661 | − | 0.430878i | ||||
\(635\) | 383.959 | − | 159.041i | 0.0239952 | − | 0.00993914i | ||||
\(636\) | 7019.18 | + | 3091.12i | 0.437624 | + | 0.192722i | ||||
\(637\) | −648.000 | + | 1564.41i | −0.0403057 | + | 0.0973065i | ||||
\(638\) | −4786.13 | + | 22743.4i | −0.296998 | + | 1.41132i | ||||
\(639\) | −1181.26 | −0.0731297 | ||||||||
\(640\) | 258.062 | − | 144.892i | 0.0159388 | − | 0.00894900i | ||||
\(641\) | 14401.9 | 0.887430 | 0.443715 | − | 0.896168i | \(-0.353660\pi\) | ||||
0.443715 | + | 0.896168i | \(0.353660\pi\) | |||||||
\(642\) | −3022.72 | + | 14363.8i | −0.185821 | + | 0.883014i | ||||
\(643\) | 3465.77 | − | 8367.12i | 0.212561 | − | 0.513168i | −0.781254 | − | 0.624213i | \(-0.785420\pi\) |
0.993815 | + | 0.111045i | \(0.0354198\pi\) | |||||||
\(644\) | −12402.9 | − | 5462.01i | −0.758916 | − | 0.334213i | ||||
\(645\) | 51.1867 | − | 21.2022i | 0.00312477 | − | 0.00129432i | ||||
\(646\) | 23980.8 | + | 16410.1i | 1.46054 | + | 0.999453i | ||||
\(647\) | 17607.8 | − | 17607.8i | 1.06991 | − | 1.06991i | 0.0725490 | − | 0.997365i | \(-0.476887\pi\) |
0.997365 | − | 0.0725490i | \(-0.0231134\pi\) | |||||||
\(648\) | −12161.5 | − | 8723.42i | −0.737267 | − | 0.528840i | ||||
\(649\) | 1528.25 | + | 1528.25i | 0.0924328 | + | 0.0924328i | ||||
\(650\) | −1334.62 | − | 7120.42i | −0.0805354 | − | 0.429670i | ||||
\(651\) | −1125.34 | − | 2716.82i | −0.0677507 | − | 0.163565i | ||||
\(652\) | −5996.27 | + | 5736.60i | −0.360172 | + | 0.344575i | ||||
\(653\) | 25243.9 | + | 10456.4i | 1.51282 | + | 0.626629i | 0.976137 | − | 0.217157i | \(-0.0696782\pi\) |
0.536680 | + | 0.843786i | \(0.319678\pi\) | |||||||
\(654\) | 11325.1 | + | 17362.0i | 0.677136 | + | 1.03809i | ||||
\(655\) | − | 143.631i | − | 0.00856814i | ||||||
\(656\) | −787.604 | + | 17784.8i | −0.0468761 | + | 1.05851i | ||||
\(657\) | 779.856i | 0.0463091i | ||||||||
\(658\) | −19442.5 | + | 12682.2i | −1.15189 | + | 0.751371i | ||||
\(659\) | −2555.01 | − | 1058.32i | −0.151030 | − | 0.0625588i | 0.305888 | − | 0.952068i | \(-0.401047\pi\) |
−0.456918 | + | 0.889509i | \(0.651047\pi\) | |||||||
\(660\) | 396.075 | + | 8.76581i | 0.0233594 | + | 0.000516983i | ||||
\(661\) | −1008.92 | − | 2435.76i | −0.0593685 | − | 0.143328i | 0.891412 | − | 0.453195i | \(-0.149716\pi\) |
−0.950780 | + | 0.309866i | \(0.899716\pi\) | |||||||
\(662\) | 17288.8 | − | 3240.54i | 1.01503 | − | 0.190252i | ||||
\(663\) | 6172.68 | + | 6172.68i | 0.361579 | + | 0.361579i | ||||
\(664\) | 4811.39 | − | 2988.80i | 0.281202 | − | 0.174681i | ||||
\(665\) | −279.533 | + | 279.533i | −0.0163005 | + | 0.0163005i | ||||
\(666\) | −1248.67 | + | 1824.73i | −0.0726501 | + | 0.106167i | ||||
\(667\) | −16344.3 | + | 6770.05i | −0.948809 | + | 0.393009i | ||||
\(668\) | −3242.70 | + | 1259.85i | −0.187820 | + | 0.0729719i | ||||
\(669\) | 3513.96 | − | 8483.45i | 0.203076 | − | 0.490268i | ||||
\(670\) | −73.0819 | − | 15.3794i | −0.00421403 | − | 0.000886801i | ||||
\(671\) | −41390.3 | −2.38130 | ||||||||
\(672\) | 11605.0 | + | 8719.46i | 0.666177 | + | 0.500536i | ||||
\(673\) | 23085.3 | 1.32225 | 0.661125 | − | 0.750276i | \(-0.270079\pi\) | ||||
0.661125 | + | 0.750276i | \(0.270079\pi\) | |||||||
\(674\) | 29702.7 | + | 6250.64i | 1.69749 | + | 0.357219i | ||||
\(675\) | 6963.91 | − | 16812.4i | 0.397098 | − | 0.958679i | ||||
\(676\) | 5147.91 | + | 13250.0i | 0.292894 | + | 0.753871i | ||||
\(677\) | −29890.9 | + | 12381.2i | −1.69690 | + | 0.702879i | −0.999899 | − | 0.0141909i | \(-0.995483\pi\) |
−0.697001 | + | 0.717070i | \(0.745483\pi\) | |||||||
\(678\) | −9302.86 | + | 13594.7i | −0.526953 | + | 0.770059i | ||||
\(679\) | 844.962 | − | 844.962i | 0.0477565 | − | 0.0477565i | ||||
\(680\) | −385.921 | − | 90.1743i | −0.0217638 | − | 0.00508533i | ||||
\(681\) | −8303.48 | − | 8303.48i | −0.467240 | − | 0.467240i | ||||
\(682\) | −4971.21 | + | 931.781i | −0.279117 | + | 0.0523163i | ||||
\(683\) | 4968.96 | + | 11996.1i | 0.278378 | + | 0.672063i | 0.999791 | − | 0.0204414i | \(-0.00650715\pi\) |
−0.721413 | + | 0.692505i | \(0.756507\pi\) | |||||||
\(684\) | 48.9190 | − | 2210.36i | 0.00273460 | − | 0.123560i | ||||
\(685\) | 287.689 | + | 119.165i | 0.0160468 | + | 0.00664679i | ||||
\(686\) | 16270.0 | − | 10612.8i | 0.905528 | − | 0.590668i | ||||
\(687\) | 23233.8i | 1.29029i | ||||||||
\(688\) | 1477.53 | − | 3163.43i | 0.0818756 | − | 0.175298i | ||||
\(689\) | 3954.39i | 0.218651i | ||||||||
\(690\) | 164.752 | + | 252.574i | 0.00908985 | + | 0.0139353i | ||||
\(691\) | −7791.33 | − | 3227.27i | −0.428938 | − | 0.177672i | 0.157760 | − | 0.987477i | \(-0.449573\pi\) |
−0.586698 | + | 0.809805i | \(0.699573\pi\) | |||||||
\(692\) | −1964.61 | − | 2053.54i | −0.107924 | − | 0.112809i | ||||
\(693\) | −694.198 | − | 1675.94i | −0.0380525 | − | 0.0918670i | ||||
\(694\) | −3053.88 | − | 16293.0i | −0.167037 | − | 0.891172i | ||||
\(695\) | 107.948 | + | 107.948i | 0.00589165 | + | 0.00589165i | ||||
\(696\) | 18696.9 | − | 3077.89i | 1.01825 | − | 0.167625i | ||||
\(697\) | 16856.8 | − | 16856.8i | 0.916064 | − | 0.916064i | ||||
\(698\) | −2707.87 | − | 1853.00i | −0.146840 | − | 0.100483i | ||||
\(699\) | 22875.9 | − | 9475.51i | 1.23783 | − | 0.512728i | ||||
\(700\) | −6501.37 | + | 14763.0i | −0.351041 | + | 0.797128i | ||||
\(701\) | −3402.06 | + | 8213.30i | −0.183301 | + | 0.442528i | −0.988643 | − | 0.150283i | \(-0.951982\pi\) |
0.805342 | + | 0.592810i | \(0.201982\pi\) | |||||||
\(702\) | 1738.63 | − | 8261.86i | 0.0934760 | − | 0.444193i | ||||
\(703\) | 40647.3 | 2.18071 | ||||||||
\(704\) | 18785.9 | − | 16443.8i | 1.00571 | − | 0.880323i | ||||
\(705\) | 516.523 | 0.0275934 | ||||||||
\(706\) | −473.282 | + | 2249.01i | −0.0252298 | + | 0.119890i | ||||
\(707\) | −3771.64 | + | 9105.55i | −0.200633 | + | 0.484370i | ||||
\(708\) | 710.162 | − | 1612.60i | 0.0376971 | − | 0.0856008i | ||||
\(709\) | −6190.43 | + | 2564.16i | −0.327908 | + | 0.135824i | −0.540563 | − | 0.841303i | \(-0.681789\pi\) |
0.212656 | + | 0.977127i | \(0.431789\pi\) | |||||||
\(710\) | −244.426 | − | 167.261i | −0.0129199 | − | 0.00884111i | ||||
\(711\) | 1660.11 | − | 1660.11i | 0.0875655 | − | 0.0875655i | ||||
\(712\) | −5733.71 | − | 34829.8i | −0.301798 | − | 1.83329i | ||||
\(713\) | −2722.27 | − | 2722.27i | −0.142987 | − | 0.142987i | ||||
\(714\) | −3581.01 | − | 19105.3i | −0.187697 | − | 1.00140i | ||||
\(715\) | 78.1674 | + | 188.713i | 0.00408852 | + | 0.00987057i | ||||
\(716\) | 7607.31 | + | 7951.65i | 0.397065 | + | 0.415038i | ||||
\(717\) | −28569.4 | − | 11833.8i | −1.48807 | − | 0.616378i | ||||
\(718\) | −8158.92 | − | 12508.1i | −0.424078 | − | 0.650136i | ||||
\(719\) | − | 7000.41i | − | 0.363103i | −0.983381 | − | 0.181552i | \(-0.941888\pi\) | ||
0.983381 | − | 0.181552i | \(-0.0581120\pi\) | |||||||
\(720\) | 10.2956 | + | 28.3419i | 0.000532909 | + | 0.00146700i | ||||
\(721\) | − | 11519.4i | − | 0.595016i | ||||||
\(722\) | −17793.2 | + | 11606.3i | −0.917165 | + | 0.598259i | ||||
\(723\) | −19608.9 | − | 8122.29i | −1.00866 | − | 0.417802i | ||||
\(724\) | 670.325 | − | 30288.0i | 0.0344094 | − | 1.55476i | ||||
\(725\) | 8058.32 | + | 19454.5i | 0.412798 | + | 0.996582i | ||||
\(726\) | 14460.4 | − | 2710.39i | 0.739224 | − | 0.138557i | ||||
\(727\) | −4176.48 | − | 4176.48i | −0.213063 | − | 0.213063i | 0.592504 | − | 0.805567i | \(-0.298139\pi\) |
−0.805567 | + | 0.592504i | \(0.798139\pi\) | |||||||
\(728\) | −1702.86 | + | 7287.79i | −0.0866928 | + | 0.371021i | ||||
\(729\) | 14894.8 | − | 14894.8i | 0.756733 | − | 0.756733i | ||||
\(730\) | −110.424 | + | 161.367i | −0.00559860 | + | 0.00818148i | ||||
\(731\) | −4319.56 | + | 1789.22i | −0.218556 | + | 0.0905291i | ||||
\(732\) | 12220.6 | + | 31454.3i | 0.617060 | + | 1.58823i | ||||
\(733\) | 8727.96 | − | 21071.2i | 0.439801 | − | 1.06177i | −0.536216 | − | 0.844081i | \(-0.680147\pi\) |
0.976017 | − | 0.217694i | \(-0.0698533\pi\) | |||||||
\(734\) | −18879.0 | − | 3972.89i | −0.949367 | − | 0.199785i | ||||
\(735\) | −83.8986 | −0.00421040 | ||||||||
\(736\) | 18405.0 | + | 4732.32i | 0.921763 | + | 0.237005i | ||||
\(737\) | −6300.04 | −0.314878 | ||||||||
\(738\) | −1774.94 | − | 373.518i | −0.0885316 | − | 0.0186306i | ||||
\(739\) | −1771.01 | + | 4275.60i | −0.0881566 | + | 0.212829i | −0.961809 | − | 0.273722i | \(-0.911745\pi\) |
0.873652 | + | 0.486551i | \(0.161745\pi\) | |||||||
\(740\) | −516.748 | + | 200.767i | −0.0256703 | + | 0.00997344i | ||||
\(741\) | −11280.7 | + | 4672.61i | −0.559253 | + | 0.231650i | ||||
\(742\) | 4972.64 | − | 7266.73i | 0.246026 | − | 0.359529i | ||||
\(743\) | 331.818 | − | 331.818i | 0.0163839 | − | 0.0163839i | −0.698867 | − | 0.715251i | \(-0.746312\pi\) |
0.715251 | + | 0.698867i | \(0.246312\pi\) | |||||||
\(744\) | 2175.87 | + | 3502.73i | 0.107220 | + | 0.172603i | ||||
\(745\) | −239.497 | − | 239.497i | −0.0117779 | − | 0.0117779i | ||||
\(746\) | −28153.3 | + | 5276.92i | −1.38172 | + | 0.258984i | ||||
\(747\) | 220.846 | + | 533.171i | 0.0108171 | + | 0.0261147i | ||||
\(748\) | −33424.1 | − | 739.733i | −1.63383 | − | 0.0361595i | ||||
\(749\) | 15569.0 | + | 6448.88i | 0.759516 | + | 0.314602i | ||||
\(750\) | 601.373 | − | 392.270i | 0.0292787 | − | 0.0190983i | ||||
\(751\) | 35952.8i | 1.74692i | 0.486897 | + | 0.873459i | \(0.338129\pi\) | ||||
−0.486897 | + | 0.873459i | \(0.661871\pi\) | |||||||
\(752\) | 24012.4 | − | 21975.8i | 1.16442 | − | 1.06566i | ||||
\(753\) | 26147.5i | 1.26543i | ||||||||
\(754\) | 5337.51 | + | 8182.70i | 0.257799 | + | 0.395221i | ||||
\(755\) | −215.177 | − | 89.1290i | −0.0103723 | − | 0.00429634i | ||||
\(756\) | −13584.2 | + | 12996.0i | −0.653510 | + | 0.625210i | ||||
\(757\) | 8248.62 | + | 19913.9i | 0.396038 | + | 0.956121i | 0.988596 | + | 0.150593i | \(0.0481183\pi\) |
−0.592557 | + | 0.805528i | \(0.701882\pi\) | |||||||
\(758\) | −2445.64 | − | 13047.9i | −0.117189 | − | 0.625225i | ||||
\(759\) | 17987.8 | + | 17987.8i | 0.860234 | + | 0.860234i | ||||
\(760\) | 323.099 | − | 450.439i | 0.0154211 | − | 0.0214989i | ||||
\(761\) | 20845.8 | − | 20845.8i | 0.992983 | − | 0.992983i | −0.00699229 | − | 0.999976i | \(-0.502226\pi\) |
0.999976 | + | 0.00699229i | \(0.00222573\pi\) | |||||||
\(762\) | −23588.5 | − | 16141.7i | −1.12142 | − | 0.767390i | ||||
\(763\) | 21986.8 | − | 9107.23i | 1.04322 | − | 0.432115i | ||||
\(764\) | 15551.5 | + | 6848.59i | 0.736429 | + | 0.324310i | ||||
\(765\) | 15.4525 | − | 37.3056i | 0.000730309 | − | 0.00176312i | ||||
\(766\) | −4923.38 | + | 23395.7i | −0.232231 | + | 1.10355i | ||||
\(767\) | 908.491 | 0.0427689 | ||||||||
\(768\) | −18042.9 | − | 9421.16i | −0.847746 | − | 0.442652i | ||||
\(769\) | 14131.4 | 0.662669 | 0.331335 | − | 0.943513i | \(-0.392501\pi\) | ||||
0.331335 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(770\) | 93.6628 | − | 445.081i | 0.00438360 | − | 0.0208306i | ||||
\(771\) | −3885.52 | + | 9380.46i | −0.181496 | + | 0.438170i | ||||
\(772\) | 17458.1 | + | 7688.25i | 0.813901 | + | 0.358428i | ||||
\(773\) | −15774.0 | + | 6533.82i | −0.733962 | + | 0.304017i | −0.718179 | − | 0.695858i | \(-0.755024\pi\) |
−0.0157831 | + | 0.999875i | \(0.505024\pi\) | |||||||
\(774\) | 293.578 | + | 200.896i | 0.0136337 | + | 0.00932954i | ||||
\(775\) | −3240.29 | + | 3240.29i | −0.150187 | + | 0.150187i | ||||
\(776\) | −976.650 | + | 1361.57i | −0.0451800 | + | 0.0629864i | ||||
\(777\) | −19226.6 | − | 19226.6i | −0.887708 | − | 0.887708i | ||||
\(778\) | −264.476 | − | 1411.03i | −0.0121876 | − | 0.0650228i | ||||
\(779\) | 12760.3 | + | 30806.1i | 0.586888 | + | 1.41687i | ||||
\(780\) | 120.332 | − | 115.121i | 0.00552382 | − | 0.00528461i | ||||
\(781\) | −23082.8 | − | 9561.22i | −1.05758 | − | 0.438063i | ||||
\(782\) | −13903.1 | − | 21314.3i | −0.635774 | − | 0.974678i | ||||
\(783\) | 24540.8i | 1.12007i | ||||||||
\(784\) | −3900.32 | + | 3569.52i | −0.177675 | + | 0.162606i | ||||
\(785\) | 164.518i | 0.00748013i | ||||||||
\(786\) | −8273.73 | + | 5396.88i | −0.375463 | + | 0.244912i | ||||
\(787\) | 9893.89 | + | 4098.18i | 0.448131 | + | 0.185622i | 0.595324 | − | 0.803486i | \(-0.297024\pi\) |
−0.147193 | + | 0.989108i | \(0.547024\pi\) | |||||||
\(788\) | 26062.2 | + | 576.801i | 1.17821 | + | 0.0260757i | ||||
\(789\) | −9080.62 | − | 21922.6i | −0.409732 | − | 0.989181i | ||||
\(790\) | 578.574 | − | 108.445i | 0.0260566 | − | 0.00488393i | ||||
\(791\) | 13372.8 | + | 13372.8i | 0.601113 | + | 0.601113i | ||||
\(792\) | 1342.24 | + | 2160.75i | 0.0602204 | + | 0.0969433i | ||||
\(793\) | −12302.6 | + | 12302.6i | −0.550917 | + | 0.550917i | ||||
\(794\) | 5715.83 | − | 8352.79i | 0.255475 | − | 0.373337i | ||||
\(795\) | −181.015 | + | 74.9788i | −0.00807539 | + | 0.00334494i | ||||
\(796\) | −26817.5 | + | 10419.1i | −1.19412 | + | 0.463941i | ||||
\(797\) | −10234.0 | + | 24707.0i | −0.454838 | + | 1.09807i | 0.515623 | + | 0.856815i | \(0.327560\pi\) |
−0.970461 | + | 0.241259i | \(0.922440\pi\) | |||||||
\(798\) | 26605.6 | + | 5598.88i | 1.18024 | + | 0.248369i | ||||
\(799\) | −43588.5 | −1.92998 | ||||||||
\(800\) | 5632.83 | − | 21907.3i | 0.248938 | − | 0.968174i | ||||
\(801\) | 3596.46 | 0.158645 | ||||||||
\(802\) | −10760.8 | − | 2264.50i | −0.473787 | − | 0.0997037i | ||||
\(803\) | −6312.23 | + | 15239.1i | −0.277402 | + | 0.669707i | ||||
\(804\) | 1860.11 | + | 4787.68i | 0.0815934 | + | 0.210011i | ||||
\(805\) | 319.853 | − | 132.487i | 0.0140041 | − | 0.00580070i | ||||
\(806\) | −1200.65 | + | 1754.57i | −0.0524705 | + | 0.0766774i | ||||
\(807\) | 14295.4 | − | 14295.4i | 0.623571 | − | 0.623571i | ||||
\(808\) | 3144.54 | − | 13457.7i | 0.136911 | − | 0.585943i | ||||
\(809\) | −4366.67 | − | 4366.67i | −0.189770 | − | 0.189770i | 0.605827 | − | 0.795597i | \(-0.292843\pi\) |
−0.795597 | + | 0.605827i | \(0.792843\pi\) | |||||||
\(810\) | 375.793 | − | 70.4368i | 0.0163012 | − | 0.00305543i | ||||
\(811\) | −16742.8 | − | 40420.6i | −0.724930 | − | 1.75014i | −0.658792 | − | 0.752325i | \(-0.728932\pi\) |
−0.0661382 | − | 0.997810i | \(-0.521068\pi\) | |||||||
\(812\) | 481.337 | − | 21748.7i | 0.0208025 | − | 0.939940i | ||||
\(813\) | 19202.6 | + | 7953.98i | 0.828370 | + | 0.343122i | ||||
\(814\) | −39169.7 | + | 25550.0i | −1.68660 | + | 1.10016i | ||||
\(815\) | − | 211.991i | − | 0.00911132i | ||||||
\(816\) | 9306.43 | + | 25618.9i | 0.399253 | + | 1.09907i | ||||
\(817\) | − | 6539.67i | − | 0.280042i | ||||||
\(818\) | −15708.6 | − | 24082.2i | −0.671441 | − | 1.02936i | ||||
\(819\) | −704.485 | − | 291.807i | −0.0300570 | − | 0.0124500i | ||||
\(820\) | −314.381 | − | 328.611i | −0.0133886 | − | 0.0139946i | ||||
\(821\) | −2730.75 | − | 6592.63i | −0.116083 | − | 0.280249i | 0.855150 | − | 0.518381i | \(-0.173465\pi\) |
−0.971233 | + | 0.238132i | \(0.923465\pi\) | |||||||
\(822\) | −3945.44 | − | 21049.6i | −0.167413 | − | 0.893175i | ||||
\(823\) | −7832.94 | − | 7832.94i | −0.331761 | − | 0.331761i | 0.521494 | − | 0.853255i | \(-0.325375\pi\) |
−0.853255 | + | 0.521494i | \(0.825375\pi\) | |||||||
\(824\) | 2623.82 | + | 15938.6i | 0.110928 | + | 0.673843i | ||||
\(825\) | 21410.7 | − | 21410.7i | 0.903547 | − | 0.903547i | ||||
\(826\) | −1669.48 | − | 1142.43i | −0.0703251 | − | 0.0481236i | ||||
\(827\) | −18116.8 | + | 7504.23i | −0.761769 | + | 0.315535i | −0.729533 | − | 0.683945i | \(-0.760263\pi\) |
−0.0322359 | + | 0.999480i | \(0.510263\pi\) | |||||||
\(828\) | −780.358 | + | 1772.00i | −0.0327528 | + | 0.0743736i | ||||
\(829\) | −3888.12 | + | 9386.75i | −0.162895 | + | 0.393264i | −0.984160 | − | 0.177284i | \(-0.943269\pi\) |
0.821265 | + | 0.570547i | \(0.193269\pi\) | |||||||
\(830\) | −29.7971 | + | 141.594i | −0.00124611 | + | 0.00592146i | ||||
\(831\) | 348.963 | 0.0145673 | ||||||||
\(832\) | 696.161 | − | 10471.4i | 0.0290085 | − | 0.436336i | ||||
\(833\) | 7080.06 | 0.294489 | ||||||||
\(834\) | 2162.13 | − | 10274.3i | 0.0897703 | − | 0.426584i | ||||
\(835\) | 34.0092 | − | 82.1054i | 0.00140950 | − | 0.00340284i | ||||
\(836\) | 18846.7 | − | 42796.3i | 0.779699 | − | 1.77050i | ||||
\(837\) | −4933.99 | + | 2043.73i | −0.203756 | + | 0.0843985i | ||||
\(838\) | 25559.4 | + | 17490.4i | 1.05362 | + | 0.720996i | ||||
\(839\) | −4919.87 | + | 4919.87i | −0.202447 | + | 0.202447i | −0.801047 | − | 0.598601i | \(-0.795724\pi\) |
0.598601 | + | 0.801047i | \(0.295724\pi\) | |||||||
\(840\) | −365.891 | + | 60.2332i | −0.0150291 | + | 0.00247410i | ||||
\(841\) | −2834.41 | − | 2834.41i | −0.116217 | − | 0.116217i | ||||
\(842\) | 8216.76 | + | 43837.9i | 0.336305 | + | 1.79424i | ||||
\(843\) | 10103.3 | + | 24391.6i | 0.412785 | + | 0.996551i | ||||
\(844\) | −2463.20 | − | 2574.70i | −0.100458 | − | 0.105006i | ||||
\(845\) | −335.492 | − | 138.965i | −0.0136583 | − | 0.00565746i | ||||
\(846\) | 1811.90 | + | 2777.75i | 0.0736342 | + | 0.112885i | ||||
\(847\) | − | 16890.5i | − | 0.685202i | ||||||
\(848\) | −5225.10 | + | 11187.1i | −0.211593 | + | 0.453025i | ||||
\(849\) | 257.447i | 0.0104070i | ||||||||
\(850\) | −25370.2 | + | 16548.8i | −1.02375 | + | 0.667786i | ||||
\(851\) | −32887.6 | − | 13622.5i | −1.32476 | − | 0.548735i | ||||
\(852\) | −450.705 | + | 20364.7i | −0.0181231 | + | 0.818875i | ||||
\(853\) | −2809.03 | − | 6781.60i | −0.112754 | − | 0.272213i | 0.857422 | − | 0.514614i | \(-0.172065\pi\) |
−0.970176 | + | 0.242401i | \(0.922065\pi\) | |||||||
\(854\) | 38078.1 | − | 7137.19i | 1.52577 | − | 0.285983i | ||||
\(855\) | 39.9370 | + | 39.9370i | 0.00159745 | + | 0.00159745i | ||||
\(856\) | −23010.5 | − | 5376.63i | −0.918787 | − | 0.214684i | ||||
\(857\) | −7846.03 | + | 7846.03i | −0.312737 | + | 0.312737i | −0.845969 | − | 0.533232i | \(-0.820977\pi\) |
0.533232 | + | 0.845969i | \(0.320977\pi\) | |||||||
\(858\) | 7933.50 | − | 11593.6i | 0.315671 | − | 0.461303i | ||||
\(859\) | 10278.4 | − | 4257.47i | 0.408261 | − | 0.169107i | −0.169095 | − | 0.985600i | \(-0.554085\pi\) |
0.577356 | + | 0.816493i | \(0.304085\pi\) | |||||||
\(860\) | 32.3011 | + | 83.1387i | 0.00128076 | + | 0.00329652i | ||||
\(861\) | 8535.84 | − | 20607.3i | 0.337864 | − | 0.815675i | ||||
\(862\) | 2336.14 | + | 491.617i | 0.0923077 | + | 0.0194252i | ||||
\(863\) | 28549.2 | 1.12610 | 0.563050 | − | 0.826423i | \(-0.309628\pi\) | ||||
0.563050 | + | 0.826423i | \(0.309628\pi\) | |||||||
\(864\) | 15835.3 | − | 21075.6i | 0.623529 | − | 0.829870i | ||||
\(865\) | 72.6005 | 0.00285375 | ||||||||
\(866\) | 31685.0 | + | 6667.78i | 1.24330 | + | 0.261640i | ||||
\(867\) | 4624.86 | − | 11165.4i | 0.181163 | − | 0.437366i | ||||
\(868\) | 4412.73 | − | 1714.43i | 0.172555 | − | 0.0670411i | ||||
\(869\) | 45877.1 | − | 19002.9i | 1.79088 | − | 0.741807i | ||||
\(870\) | −273.365 | + | 399.479i | −0.0106528 | + | 0.0155674i | ||||
\(871\) | −1872.58 | + | 1872.58i | −0.0728473 | + | 0.0728473i | ||||
\(872\) | −28347.1 | + | 17609.0i | −1.10086 | + | 0.683848i | ||||
\(873\) | −120.720 | − | 120.720i | −0.00468013 | − | 0.00468013i | ||||
\(874\) | 34985.3 | − | 6557.48i | 1.35400 | − | 0.253787i | ||||
\(875\) | −315.449 | − | 761.562i | −0.0121876 | − | 0.0294234i | ||||
\(876\) | 13444.6 | + | 297.551i | 0.518550 | + | 0.0114764i | ||||
\(877\) | −8149.22 | − | 3375.52i | −0.313774 | − | 0.129969i | 0.220239 | − | 0.975446i | \(-0.429316\pi\) |
−0.534012 | + | 0.845477i | \(0.679316\pi\) | |||||||
\(878\) | −6835.68 | + | 4458.86i | −0.262748 | + | 0.171389i | ||||
\(879\) | − | 19683.9i | − | 0.755315i | ||||||
\(880\) | −28.2166 | + | 637.158i | −0.00108089 | + | 0.0244075i | ||||
\(881\) | 22699.0i | 0.868046i | 0.900902 | + | 0.434023i | \(0.142906\pi\) | ||||
−0.900902 | + | 0.434023i | \(0.857094\pi\) | |||||||
\(882\) | −294.307 | − | 451.189i | −0.0112356 | − | 0.0172248i | ||||
\(883\) | −3173.59 | − | 1314.54i | −0.120951 | − | 0.0500995i | 0.321387 | − | 0.946948i | \(-0.395851\pi\) |
−0.442338 | + | 0.896848i | \(0.645851\pi\) | |||||||
\(884\) | −10154.6 | + | 9714.88i | −0.386354 | + | 0.369623i | ||||
\(885\) | 17.2258 | + | 41.5868i | 0.000654282 | + | 0.00157958i | ||||
\(886\) | 7037.54 | + | 37546.5i | 0.266852 | + | 1.42370i | ||||
\(887\) | 389.896 | + | 389.896i | 0.0147592 | + | 0.0147592i | 0.714448 | − | 0.699689i | \(-0.246678\pi\) |
−0.699689 | + | 0.714448i | \(0.746678\pi\) | |||||||
\(888\) | 30981.6 | + | 22223.0i | 1.17080 | + | 0.839815i | ||||
\(889\) | −23203.5 | + | 23203.5i | −0.875389 | + | 0.875389i | ||||
\(890\) | 744.178 | + | 509.242i | 0.0280280 | + | 0.0191796i | ||||
\(891\) | 29797.9 | − | 12342.7i | 1.12039 | − | 0.464081i | ||||
\(892\) | 13528.7 | + | 5957.80i | 0.507818 | + | 0.223634i | ||||
\(893\) | 23331.5 | − | 56327.2i | 0.874310 | − | 2.11077i | ||||
\(894\) | −4796.99 | + | 22795.0i | −0.179458 | + | 0.852774i | ||||
\(895\) | −281.121 | −0.0104993 | ||||||||
\(896\) | −14447.1 | + | 18367.2i | −0.538664 | + | 0.684828i | ||||
\(897\) | 10693.2 | 0.398032 | ||||||||
\(898\) | 2097.86 | − | 9968.91i | 0.0779581 | − | 0.370453i | ||||
\(899\) | 2364.91 | − | 5709.39i | 0.0877353 | − | 0.211812i | ||||
\(900\) | 2109.19 | + | 928.852i | 0.0781183 | + | 0.0344019i | ||||
\(901\) | 15275.6 | − | 6327.34i | 0.564820 | − | 0.233956i | ||||
\(902\) | −31660.5 | − | 21665.4i | −1.16871 | − | 0.799754i | ||||
\(903\) | −3093.33 | + | 3093.33i | −0.113997 | + | 0.113997i | ||||
\(904\) | −21548.8 | − | 15456.9i | −0.792813 | − | 0.568683i | ||||
\(905\) | 547.247 | + | 547.247i | 0.0201007 | + | 0.0201007i | ||||
\(906\) | 2950.99 | + | 15744.0i | 0.108212 | + | 0.577329i | ||||
\(907\) | −14791.8 | − | 35710.6i | −0.541516 | − | 1.30733i | −0.923653 | − | 0.383229i | \(-0.874812\pi\) |
0.382138 | − | 0.924105i | \(-0.375188\pi\) | |||||||
\(908\) | 13660.0 | − | 13068.4i | 0.499254 | − | 0.477634i | ||||
\(909\) | 1300.91 | + | 538.856i | 0.0474682 | + | 0.0196620i | ||||
\(910\) | −104.453 | − | 160.132i | −0.00380504 | − | 0.00583334i | ||||
\(911\) | − | 26874.8i | − | 0.977388i | −0.872455 | − | 0.488694i | \(-0.837473\pi\) | ||
0.872455 | − | 0.488694i | \(-0.162527\pi\) | |||||||
\(912\) | −38087.4 | − | 1686.71i | −1.38289 | − | 0.0612417i | ||||
\(913\) | 12206.2i | 0.442459i | ||||||||
\(914\) | 33564.3 | − | 21893.7i | 1.21467 | − | 0.792320i | ||||
\(915\) | −796.426 | − | 329.891i | −0.0287749 | − | 0.0119190i | ||||
\(916\) | −37394.2 | − | 827.597i | −1.34884 | − | 0.0298522i | ||||
\(917\) | 4339.97 | + | 10477.6i | 0.156291 | + | 0.377319i | ||||
\(918\) | −34696.9 | + | 6503.43i | −1.24746 | + | 0.233818i | ||||
\(919\) | 9495.37 | + | 9495.37i | 0.340831 | + | 0.340831i | 0.856680 | − | 0.515849i | \(-0.172523\pi\) |
−0.515849 | + | 0.856680i | \(0.672523\pi\) | |||||||
\(920\) | −412.379 | + | 256.167i | −0.0147780 | + | 0.00917996i | ||||
\(921\) | −4436.42 | + | 4436.42i | −0.158724 | + | 0.158724i | ||||
\(922\) | 2585.88 | − | 3778.86i | 0.0923660 | − | 0.134978i | ||||
\(923\) | −9702.89 | + | 4019.07i | −0.346018 | + | 0.143325i | ||||
\(924\) | −29157.8 | + | 11328.4i | −1.03812 | + | 0.403330i | ||||
\(925\) | −16214.7 | + | 39145.8i | −0.576364 | + | 1.39147i | ||||
\(926\) | 40182.5 | + | 8456.00i | 1.42600 | + | 0.300088i | ||||
\(927\) | −1645.79 | −0.0583114 | ||||||||
\(928\) | 4287.79 | + | 30201.7i | 0.151674 | + | 1.06834i | ||||
\(929\) | −51635.3 | −1.82357 | −0.911786 | − | 0.410665i | \(-0.865297\pi\) | ||||
−0.911786 | + | 0.410665i | \(0.865297\pi\) | |||||||
\(930\) | −103.082 | − | 21.6926i | −0.00363461 | − | 0.000764868i | ||||
\(931\) | −3789.73 | + | 9149.21i | −0.133409 | + | 0.322077i | ||||
\(932\) | 14435.7 | + | 37155.6i | 0.507357 | + | 1.30587i | ||||
\(933\) | −5268.84 | + | 2182.42i | −0.184881 | + | 0.0765803i | ||||
\(934\) | −9768.31 | + | 14274.8i | −0.342215 | + | 0.500093i | ||||
\(935\) | 603.911 | − | 603.911i | 0.0211230 | − | 0.0211230i | ||||
\(936\) | 1041.21 | + | 243.289i | 0.0363600 | + | 0.00849587i | ||||
\(937\) | 3704.24 | + | 3704.24i | 0.129149 | + | 0.129149i | 0.768726 | − | 0.639578i | \(-0.220891\pi\) |
−0.639578 | + | 0.768726i | \(0.720891\pi\) | |||||||
\(938\) | 5795.89 | − | 1086.36i | 0.201751 | − | 0.0378153i | ||||
\(939\) | −2012.79 | − | 4859.30i | −0.0699520 | − | 0.168879i | ||||
\(940\) | −18.3987 | + | 831.328i | −0.000638404 | + | 0.0288457i | ||||
\(941\) | 6682.02 | + | 2767.78i | 0.231485 | + | 0.0958843i | 0.495411 | − | 0.868659i | \(-0.335017\pi\) |
−0.263926 | + | 0.964543i | \(0.585017\pi\) | |||||||
\(942\) | 9476.90 | − | 6181.70i | 0.327786 | − | 0.213812i | ||||
\(943\) | − | 29201.7i | − | 1.00842i | ||||||
\(944\) | 2570.14 | + | 1200.43i | 0.0886133 | + | 0.0413883i | ||||
\(945\) | − | 480.254i | − | 0.0165319i | ||||||
\(946\) | 4110.70 | + | 6301.94i | 0.141280 | + | 0.216589i | ||||
\(947\) | 494.002 | + | 204.622i | 0.0169513 | + | 0.00702147i | 0.391143 | − | 0.920330i | \(-0.372080\pi\) |
−0.374192 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(948\) | −27986.6 | − | 29253.4i | −0.958820 | − | 1.00222i | ||||
\(949\) | 2653.35 | + | 6405.76i | 0.0907603 | + | 0.219115i | ||||
\(950\) | −7805.30 | − | 41642.6i | −0.266566 | − | 1.42217i | ||||
\(951\) | −15131.6 | − | 15131.6i | −0.515957 | − | 0.515957i | ||||
\(952\) | 30876.9 | − | 5082.98i | 1.05118 | − | 0.173047i | ||||
\(953\) | −28698.0 | + | 28698.0i | −0.975465 | + | 0.975465i | −0.999706 | − | 0.0242408i | \(-0.992283\pi\) |
0.0242408 | + | 0.999706i | \(0.492283\pi\) | |||||||
\(954\) | −1038.20 | − | 710.443i | −0.0352337 | − | 0.0241105i | ||||
\(955\) | −401.050 | + | 166.120i | −0.0135892 | + | 0.00562883i | ||||
\(956\) | 20063.9 | − | 45560.1i | 0.678778 | − | 1.54134i | ||||
\(957\) | −15626.5 | + | 37725.6i | −0.527829 | + | 1.27429i | ||||
\(958\) | 5966.75 | − | 28353.7i | 0.201229 | − | 0.956228i | ||||
\(959\) | −24587.1 | −0.827903 | ||||||||
\(960\) | 492.536 | − | 166.680i | 0.0165589 | − | 0.00560373i | ||||
\(961\) | −28446.2 | −0.954858 | ||||||||
\(962\) | −4048.20 | + | 19236.8i | −0.135675 | + | 0.644720i | ||||
\(963\) | 921.352 | − | 2224.34i | 0.0308309 | − | 0.0744324i | ||||
\(964\) | 13771.1 | − | 31270.7i | 0.460099 | − | 1.04477i | ||||
\(965\) | −450.220 | + | 186.487i | −0.0150188 | + | 0.00622098i | ||||
\(966\) | −19650.1 | − | 13446.6i | −0.654486 | − | 0.447866i | ||||
\(967\) | 22689.5 | − | 22689.5i | 0.754544 | − | 0.754544i | −0.220780 | − | 0.975324i | \(-0.570860\pi\) |
0.975324 | + | 0.220780i | \(0.0708603\pi\) | |||||||
\(968\) | 3847.21 | + | 23370.2i | 0.127742 | + | 0.775977i | ||||
\(969\) | 36100.0 | + | 36100.0i | 1.19680 | + | 1.19680i | ||||
\(970\) | −7.88591 | − | 42.0727i | −0.000261032 | − | 0.00139265i | ||||
\(971\) | 18313.2 | + | 44211.9i | 0.605250 | + | 1.46120i | 0.868111 | + | 0.496369i | \(0.165334\pi\) |
−0.262861 | + | 0.964834i | \(0.584666\pi\) | |||||||
\(972\) | 3567.40 | + | 3728.88i | 0.117721 | + | 0.123049i | ||||
\(973\) | −11136.4 | − | 4612.83i | −0.366922 | − | 0.151984i | ||||
\(974\) | −27338.7 | − | 41911.8i | −0.899374 | − | 1.37879i | ||||
\(975\) | − | 12728.0i | − | 0.418073i | ||||||
\(976\) | −51060.1 | + | 18548.4i | −1.67458 | + | 0.608318i | ||||
\(977\) | 3076.94i | 0.100757i | 0.998730 | + | 0.0503787i | \(0.0160428\pi\) | ||||
−0.998730 | + | 0.0503787i | \(0.983957\pi\) | |||||||
\(978\) | −12211.5 | + | 7965.48i | −0.399266 | + | 0.260438i | ||||
\(979\) | 70277.9 | + | 29110.1i | 2.29427 | + | 0.950319i | ||||
\(980\) | 2.98850 | − | 135.032i | 9.74123e−5 | − | 0.00440148i | ||||
\(981\) | −1301.15 | − | 3141.26i | −0.0423472 | − | 0.102235i | ||||
\(982\) | 35216.9 | − | 6600.89i | 1.14441 | − | 0.214504i | ||||
\(983\) | −40340.6 | − | 40340.6i | −1.30892 | − | 1.30892i | −0.922197 | − | 0.386722i | \(-0.873607\pi\) |
−0.386722 | − | 0.922197i | \(-0.626393\pi\) | |||||||
\(984\) | −7116.59 | + | 30457.0i | −0.230558 | + | 0.986722i | ||||
\(985\) | −470.895 | + | 470.895i | −0.0152324 | + | 0.0152324i | ||||
\(986\) | 23068.8 | − | 33711.4i | 0.745091 | − | 1.08883i | ||||
\(987\) | −37679.4 | + | 15607.3i | −1.21514 | + | 0.503329i | ||||
\(988\) | −7118.61 | − | 18322.4i | −0.229224 | − | 0.589992i | ||||
\(989\) | −2191.70 | + | 5291.24i | −0.0704672 | + | 0.170123i | ||||
\(990\) | −63.5888 | − | 13.3816i | −0.00204140 | − | 0.000429592i | ||||
\(991\) | 19825.3 | 0.635492 | 0.317746 | − | 0.948176i | \(-0.397074\pi\) | ||||
0.317746 | + | 0.948176i | \(0.397074\pi\) | |||||||
\(992\) | −5715.05 | + | 3377.23i | −0.182916 | + | 0.108092i | ||||
\(993\) | 30904.3 | 0.987632 | ||||||||
\(994\) | 22884.4 | + | 4815.79i | 0.730229 | + | 0.153669i | ||||
\(995\) | 281.260 | − | 679.022i | 0.00896135 | − | 0.0216346i | ||||
\(996\) | 9276.01 | − | 3603.92i | 0.295102 | − | 0.114653i | ||||
\(997\) | −12624.9 | + | 5229.39i | −0.401036 | + | 0.166115i | −0.574079 | − | 0.818800i | \(-0.694640\pi\) |
0.173043 | + | 0.984914i | \(0.444640\pi\) | |||||||
\(998\) | −31140.0 | + | 45506.2i | −0.987695 | + | 1.44336i | ||||
\(999\) | −34917.2 | + | 34917.2i | −1.10584 | + | 1.10584i |
(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 | 32.4.g.a.13.6 | yes | 44 | |
4.3 | odd | 2 | 128.4.g.a.17.9 | 44 | |||
8.3 | odd | 2 | 256.4.g.a.33.3 | 44 | |||
8.5 | even | 2 | 256.4.g.b.33.9 | 44 | |||
32.5 | even | 8 | inner | 32.4.g.a.5.6 | ✓ | 44 | |
32.11 | odd | 8 | 256.4.g.a.225.3 | 44 | |||
32.21 | even | 8 | 256.4.g.b.225.9 | 44 | |||
32.27 | odd | 8 | 128.4.g.a.113.9 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.6 | ✓ | 44 | 32.5 | even | 8 | inner | |
32.4.g.a.13.6 | yes | 44 | 1.1 | even | 1 | trivial | |
128.4.g.a.17.9 | 44 | 4.3 | odd | 2 | |||
128.4.g.a.113.9 | 44 | 32.27 | odd | 8 | |||
256.4.g.a.33.3 | 44 | 8.3 | odd | 2 | |||
256.4.g.a.225.3 | 44 | 32.11 | odd | 8 | |||
256.4.g.b.33.9 | 44 | 8.5 | even | 2 | |||
256.4.g.b.225.9 | 44 | 32.21 | even | 8 |