Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 17.9 | ||
Character | \(\chi\) | \(=\) | 128.17 |
Dual form | 128.4.g.a.113.9 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.90169 | − | 4.59109i | 0.365981 | − | 0.883556i | −0.628419 | − | 0.777875i | \(-0.716298\pi\) |
0.994400 | − | 0.105681i | \(-0.0337023\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.188811 | − | 0.0782080i | 0.0168878 | − | 0.00699514i | −0.374224 | − | 0.927339i | \(-0.622091\pi\) |
0.391111 | + | 0.920343i | \(0.372091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.4103 | − | 11.4103i | 0.616096 | − | 0.616096i | −0.328432 | − | 0.944528i | \(-0.606520\pi\) |
0.944528 | + | 0.328432i | \(0.106520\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.63019 | + | 1.63019i | 0.0603773 | + | 0.0603773i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.6604 | − | 45.0502i | −0.511483 | − | 1.23483i | −0.943020 | − | 0.332735i | \(-0.892029\pi\) |
0.431537 | − | 0.902095i | \(-0.357971\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.9369 | + | 7.84392i | 0.404011 | + | 0.167347i | 0.575430 | − | 0.817851i | \(-0.304835\pi\) |
−0.171418 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.01558i | − | 0.0174814i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 85.7028i | − | 1.22270i | −0.791359 | − | 0.611352i | \(-0.790626\pi\) | ||
0.791359 | − | 0.611352i | \(-0.209374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −110.749 | − | 45.8739i | −1.33725 | − | 0.553905i | −0.404532 | − | 0.914524i | \(-0.632566\pi\) |
−0.932713 | + | 0.360619i | \(0.882566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −30.6868 | − | 74.0844i | −0.318876 | − | 0.769835i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 74.2331 | + | 74.2331i | 0.672985 | + | 0.672985i | 0.958403 | − | 0.285418i | \(-0.0921324\pi\) |
−0.285418 | + | 0.958403i | \(0.592132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −88.3588 | + | 88.3588i | −0.706871 | + | 0.706871i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 134.544 | − | 55.7299i | 0.959000 | − | 0.397231i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 64.4881 | − | 155.688i | 0.412936 | − | 0.996915i | −0.571410 | − | 0.820665i | \(-0.693603\pi\) |
0.984345 | − | 0.176250i | \(-0.0563967\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.6720 | −0.212467 | −0.106234 | − | 0.994341i | \(-0.533879\pi\) | ||||
−0.106234 | + | 0.994341i | \(0.533879\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −242.316 | −1.27824 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26201 | − | 3.04676i | 0.00609481 | − | 0.0147142i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 313.271 | − | 129.761i | 1.39193 | − | 0.576557i | 0.444287 | − | 0.895884i | \(-0.353457\pi\) |
0.947644 | + | 0.319328i | \(0.103457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 72.0243 | − | 72.0243i | 0.295721 | − | 0.295721i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 196.689 | + | 196.689i | 0.749211 | + | 0.749211i | 0.974331 | − | 0.225120i | \(-0.0722773\pi\) |
−0.225120 | + | 0.974331i | \(0.572277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.8770 | + | 50.4016i | 0.0740400 | + | 0.178748i | 0.956566 | − | 0.291514i | \(-0.0941591\pi\) |
−0.882526 | + | 0.470263i | \(0.844159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.435291 | + | 0.180303i | 0.00144198 | + | 0.000597290i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 508.601i | 1.57845i | 0.614106 | + | 0.789224i | \(0.289517\pi\) | ||||
−0.614106 | + | 0.789224i | \(0.710483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 82.6118i | 0.240851i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −393.469 | − | 162.980i | −1.08033 | − | 0.447487i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 73.8289 | + | 178.239i | 0.191343 | + | 0.461943i | 0.990214 | − | 0.139560i | \(-0.0445689\pi\) |
−0.798871 | + | 0.601503i | \(0.794569\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.04657 | − | 7.04657i | −0.0172756 | − | 0.0172756i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −421.223 | + | 421.223i | −0.978813 | + | 0.978813i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −40.9489 | + | 16.9616i | −0.0903576 | + | 0.0374273i | −0.427404 | − | 0.904061i | \(-0.640572\pi\) |
0.337047 | + | 0.941488i | \(0.390572\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −324.831 | + | 784.211i | −0.681809 | + | 1.64603i | 0.0788549 | + | 0.996886i | \(0.474874\pi\) |
−0.760664 | + | 0.649146i | \(0.775126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 37.2017 | 0.0743964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.18895 | 0.00799346 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49.4427 | − | 119.365i | 0.0901550 | − | 0.217654i | −0.872370 | − | 0.488846i | \(-0.837418\pi\) |
0.962525 | + | 0.271192i | \(0.0874180\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 481.979 | − | 199.642i | 0.840920 | − | 0.348321i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 362.308 | − | 362.308i | 0.605606 | − | 0.605606i | −0.336189 | − | 0.941795i | \(-0.609138\pi\) |
0.941795 | + | 0.336189i | \(0.109138\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 239.192 | + | 239.192i | 0.383498 | + | 0.383498i | 0.872361 | − | 0.488863i | \(-0.162588\pi\) |
−0.488863 | + | 0.872361i | \(0.662588\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 237.632 | + | 573.695i | 0.365859 | + | 0.883261i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −726.954 | − | 301.114i | −1.07590 | − | 0.445651i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1018.36i | 1.45030i | 0.688589 | + | 0.725152i | \(0.258231\pi\) | ||||
−0.688589 | + | 0.725152i | \(0.741769\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 661.438i | − | 0.907323i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −231.267 | − | 95.7940i | −0.305842 | − | 0.126684i | 0.224484 | − | 0.974478i | \(-0.427930\pi\) |
−0.530326 | + | 0.847794i | \(0.677930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.70265 | − | 16.1816i | −0.00855299 | − | 0.0206487i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −592.141 | − | 592.141i | −0.729704 | − | 0.729704i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1103.08 | − | 1103.08i | 1.31378 | − | 1.31378i | 0.395174 | − | 0.918606i | \(-0.370684\pi\) |
0.918606 | − | 0.395174i | \(-0.129316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 305.576 | − | 126.574i | 0.352012 | − | 0.145808i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −69.7388 | + | 168.364i | −0.0777589 | + | 0.187727i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24.4984 | −0.0264577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −74.0528 | −0.0775147 | −0.0387573 | − | 0.999249i | \(-0.512340\pi\) | ||||
−0.0387573 | + | 0.999249i | \(0.512340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43.0203 | − | 103.860i | 0.0436737 | − | 0.105438i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 564.281 | − | 233.733i | 0.555922 | − | 0.230270i | −0.0869918 | − | 0.996209i | \(-0.527725\pi\) |
0.642914 | + | 0.765939i | \(0.277725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 504.784 | − | 504.784i | 0.482892 | − | 0.482892i | −0.423162 | − | 0.906054i | \(-0.639080\pi\) |
0.906054 | + | 0.423162i | \(0.139080\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.5880 | − | 11.5880i | −0.0107702 | − | 0.0107702i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 399.644 | + | 964.826i | 0.361075 | + | 0.871713i | 0.995143 | + | 0.0984356i | \(0.0313839\pi\) |
−0.634068 | + | 0.773277i | \(0.718616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1362.55 | − | 564.385i | −1.19732 | − | 0.495948i | −0.307191 | − | 0.951648i | \(-0.599389\pi\) |
−0.890133 | + | 0.455700i | \(0.849389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1685.02i | − | 1.44086i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1171.99i | − | 0.975681i | −0.872933 | − | 0.487840i | \(-0.837785\pi\) | ||
0.872933 | − | 0.487840i | \(-0.162215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.8216 | + | 8.21039i | 0.0160728 | + | 0.00665759i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.0836 | + | 43.6577i | 0.0142892 | + | 0.0344971i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −977.891 | − | 977.891i | −0.753304 | − | 0.753304i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −740.147 | + | 740.147i | −0.556084 | + | 0.556084i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1277.06 | − | 528.976i | 0.936168 | − | 0.387773i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −19.5487 | + | 47.1948i | −0.0139879 | + | 0.0337699i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2033.56 | −1.42086 | −0.710432 | − | 0.703766i | \(-0.751500\pi\) | ||||
−0.710432 | + | 0.703766i | \(0.751500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 271.100 | 0.185031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −268.953 | + | 649.310i | −0.179378 | + | 0.433057i | −0.987836 | − | 0.155496i | \(-0.950302\pi\) |
0.808458 | + | 0.588553i | \(0.200302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1787.11 | + | 740.247i | −1.16513 | + | 0.482613i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.0448 | − | 21.0448i | 0.0134167 | − | 0.0134167i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1077.41 | + | 1077.41i | 0.671894 | + | 0.671894i | 0.958152 | − | 0.286259i | \(-0.0924116\pi\) |
−0.286259 | + | 0.958152i | \(0.592412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −285.862 | − | 690.132i | −0.174435 | − | 0.421124i | 0.812347 | − | 0.583174i | \(-0.198189\pi\) |
−0.986783 | + | 0.162050i | \(0.948189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2335.03 | + | 967.202i | 1.39465 | + | 0.577682i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 999.480i | − | 0.584481i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 34.4391i | − | 0.0197242i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 379.278 | + | 157.102i | 0.212805 | + | 0.0881468i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −634.226 | − | 1531.16i | −0.348710 | − | 0.841860i | −0.996773 | − | 0.0802736i | \(-0.974421\pi\) |
0.648063 | − | 0.761587i | \(-0.275579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 805.847 | + | 805.847i | 0.434297 | + | 0.434297i | 0.890087 | − | 0.455790i | \(-0.150643\pi\) |
−0.455790 | + | 0.890087i | \(0.650643\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 139.712 | − | 139.712i | 0.0738236 | − | 0.0738236i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.92407 | + | 2.86804i | −0.00358809 | + | 0.00148624i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −308.064 | + | 743.733i | −0.156600 | + | 0.378066i | −0.982634 | − | 0.185554i | \(-0.940592\pi\) |
0.826034 | + | 0.563620i | \(0.190592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 958.710 | 0.478180 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1694.04 | 0.829248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −396.959 | + | 958.344i | −0.190750 | + | 0.460511i | −0.990102 | − | 0.140353i | \(-0.955176\pi\) |
0.799352 | + | 0.600863i | \(0.205176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −45.7519 | + | 18.9510i | −0.0215865 | + | 0.00894143i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −307.489 | + | 307.489i | −0.142480 | + | 0.142480i | −0.774749 | − | 0.632269i | \(-0.782124\pi\) |
0.632269 | + | 0.774749i | \(0.282124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1256.43 | − | 1256.43i | −0.571887 | − | 0.571887i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −105.759 | − | 255.325i | −0.0472960 | − | 0.114183i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 328.204 | + | 135.946i | 0.144236 | + | 0.0597446i | 0.453634 | − | 0.891188i | \(-0.350127\pi\) |
−0.309398 | + | 0.950933i | \(0.600127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2016.39i | 0.871001i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 220.256i | 0.0935337i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1270.86 | + | 526.407i | 0.530662 | + | 0.219807i | 0.631893 | − | 0.775056i | \(-0.282278\pi\) |
−0.101231 | + | 0.994863i | \(0.532278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1449.19 | + | 3498.66i | 0.595125 | + | 1.43676i | 0.878496 | + | 0.477749i | \(0.158547\pi\) |
−0.283371 | + | 0.959010i | \(0.591453\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2982.66 | + | 2982.66i | 1.20483 | + | 1.20483i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 49.0007 | − | 49.0007i | 0.0194735 | − | 0.0194735i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3860.92 | + | 1599.25i | −1.50983 | + | 0.625393i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 899.289 | − | 2171.08i | 0.346104 | − | 0.835569i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2124.08 | 0.804677 | 0.402338 | − | 0.915491i | \(-0.368197\pi\) | ||||
0.402338 | + | 0.915491i | \(0.368197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2384.50 | −0.889328 | −0.444664 | − | 0.895697i | \(-0.646677\pi\) | ||||
−0.444664 | + | 0.895697i | \(0.646677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.96609 | − | 19.2319i | 0.00292546 | − | 0.00706268i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3010.53 | + | 1247.00i | −1.08879 | + | 0.450990i | −0.853584 | − | 0.520956i | \(-0.825576\pi\) |
−0.235204 | + | 0.971946i | \(0.575576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2542.97 | + | 2542.97i | −0.905862 | + | 0.905862i | −0.995935 | − | 0.0900734i | \(-0.971290\pi\) |
0.0900734 | + | 0.995935i | \(0.471290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −453.992 | − | 453.992i | −0.159314 | − | 0.159314i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1040.61 | − | 2512.27i | −0.359787 | − | 0.868604i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 52.5197 | + | 21.7544i | 0.0178933 | + | 0.00741167i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 242.028i | 0.0812661i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5845.30i | 1.93458i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −411.497 | − | 170.448i | −0.134259 | − | 0.0556118i | 0.314543 | − | 0.949243i | \(-0.398149\pi\) |
−0.448801 | + | 0.893632i | \(0.648149\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −974.390 | − | 2352.39i | −0.313447 | − | 0.756727i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.88363 | + | 7.88363i | 0.00250074 | + | 0.00250074i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −418.437 | + | 418.437i | −0.130900 | + | 0.130900i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1553.02 | − | 643.284i | 0.479195 | − | 0.198489i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 672.246 | − | 1622.94i | 0.204616 | − | 0.493987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1847.81 | 0.554880 | 0.277440 | − | 0.960743i | \(-0.410514\pi\) | ||||
0.277440 | + | 0.960743i | \(0.410514\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −288.083 | −0.0853579 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 904.304 | − | 2183.18i | 0.264409 | − | 0.638339i | −0.734793 | − | 0.678291i | \(-0.762721\pi\) |
0.999202 | + | 0.0399527i | \(0.0127207\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4319.52 | − | 1789.20i | 1.24647 | − | 0.516305i | 0.340740 | − | 0.940158i | \(-0.389322\pi\) |
0.905731 | + | 0.423852i | \(0.139322\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2764.89 | + | 2764.89i | −0.787516 | + | 0.787516i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3523.28 | − | 3523.28i | −0.990634 | − | 0.990634i | 0.00932269 | − | 0.999957i | \(-0.497032\pi\) |
−0.999957 | + | 0.00932269i | \(0.997032\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.7767 | + | 96.0294i | 0.0110415 | + | 0.0266564i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4675.37 | + | 1936.60i | 1.28143 | + | 0.530784i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6222.79i | − | 1.68418i | −0.539337 | − | 0.842090i | \(-0.681325\pi\) | ||
0.539337 | − | 0.842090i | \(-0.318675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4271.08i | 1.14160i | 0.821091 | + | 0.570798i | \(0.193366\pi\) | ||||
−0.821091 | + | 0.570798i | \(0.806634\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 595.962 | + | 246.856i | 0.157329 | + | 0.0651679i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.46091 | + | 15.5980i | 0.00168478 | + | 0.00406743i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1737.42 | − | 1737.42i | −0.447568 | − | 0.447568i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −879.598 | + | 879.598i | −0.223864 | + | 0.223864i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4861.21 | + | 2013.58i | −1.22246 | + | 0.506358i | −0.898190 | − | 0.439608i | \(-0.855117\pi\) |
−0.324267 | + | 0.945966i | \(0.605117\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1958.99 | − | 4729.43i | 0.486802 | − | 1.17524i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −87.0377 | −0.0213746 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2043.19 | 0.495917 | 0.247958 | − | 0.968771i | \(-0.420240\pi\) | ||||
0.247958 | + | 0.968771i | \(0.420240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2093.90 | − | 5055.12i | 0.502349 | − | 1.21278i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 358.928 | − | 148.673i | 0.0851230 | − | 0.0352591i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3376.45 | − | 3376.45i | 0.791638 | − | 0.791638i | −0.190123 | − | 0.981760i | \(-0.560889\pi\) |
0.981760 | + | 0.190123i | \(0.0608886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.8794 | + | 27.8794i | 0.00646271 | + | 0.00646271i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2966.63 | − | 7162.07i | −0.679980 | − | 1.64162i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3758.60 | − | 1556.86i | −0.851917 | − | 0.352876i | −0.0863762 | − | 0.996263i | \(-0.527529\pi\) |
−0.765541 | + | 0.643387i | \(0.777529\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4182.58i | 0.937540i | 0.883320 | + | 0.468770i | \(0.155303\pi\) | ||||
−0.883320 | + | 0.468770i | \(0.844697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1643.63i | − | 0.364385i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5629.39 | + | 2331.77i | 1.23442 | + | 0.511313i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.8731 | − | 64.8775i | −0.00582906 | − | 0.0140726i | 0.920938 | − | 0.389709i | \(-0.127424\pi\) |
−0.926767 | + | 0.375636i | \(0.877424\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −59.7822 | − | 59.7822i | −0.0128282 | − | 0.0128282i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3756.73 | − | 3756.73i | 0.797536 | − | 0.797536i | −0.185171 | − | 0.982706i | \(-0.559284\pi\) |
0.982706 | + | 0.185171i | \(0.0592837\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −47.8634 | + | 19.8257i | −0.0100536 | + | 0.00416436i | −0.387705 | − | 0.921784i | \(-0.626732\pi\) |
0.377651 | + | 0.925948i | \(0.376732\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −46.5885 | + | 112.474i | −0.00968303 | + | 0.0233769i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4488.55 | 0.923173 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2431.97 | −0.495007 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −140.826 | + | 339.983i | −0.0283689 | + | 0.0684886i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3659.53 | + | 1515.83i | −0.729666 | + | 0.302238i | −0.716415 | − | 0.697674i | \(-0.754218\pi\) |
−0.0132515 | + | 0.999912i | \(0.504218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.40507 | + | 6.40507i | −0.00126413 | + | 0.00126413i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5021.28 | − | 5021.28i | −0.981025 | − | 0.981025i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 823.465 | + | 1988.02i | 0.159272 | + | 0.384516i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 813.309 | + | 336.883i | 0.155742 | + | 0.0645104i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3035.16i | − | 0.575463i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 173.472i | 0.0325671i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1166.44 | − | 483.155i | −0.216847 | − | 0.0898211i | 0.271615 | − | 0.962406i | \(-0.412442\pi\) |
−0.488463 | + | 0.872585i | \(0.662442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1357.57 | − | 3277.46i | −0.249933 | − | 0.603391i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −811.491 | − | 811.491i | −0.147960 | − | 0.147960i | 0.629246 | − | 0.777206i | \(-0.283364\pi\) |
−0.777206 | + | 0.629246i | \(0.783364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −748.416 | + | 748.416i | −0.135153 | + | 0.135153i | −0.771447 | − | 0.636294i | \(-0.780467\pi\) |
0.636294 | + | 0.771447i | \(0.280467\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.02409 | − | 2.90947i | 0.00125639 | − | 0.000520414i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1647.93 | + | 3978.45i | −0.291977 | + | 0.704896i | −0.999999 | − | 0.00129494i | \(-0.999588\pi\) |
0.708022 | + | 0.706191i | \(0.249588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8217.14 | −1.44223 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5189.61 | 0.902354 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3931.52 | + | 9491.54i | −0.677263 | + | 1.63506i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2366.32 | + | 980.162i | −0.403876 | + | 0.167291i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5182.29 | + | 5182.29i | −0.876395 | + | 0.876395i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5803.27 | + | 5803.27i | 0.972476 | + | 0.972476i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2379.90 | + | 5745.58i | 0.395199 | + | 0.954095i | 0.988788 | + | 0.149327i | \(0.0477106\pi\) |
−0.593589 | + | 0.804769i | \(0.702289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 722.225 | + | 299.156i | 0.118852 | + | 0.0492301i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 26.4043i | − | 0.00430633i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10731.5i | − | 1.73466i | −0.497730 | − | 0.867332i | \(-0.665833\pi\) | ||
0.497730 | − | 0.867332i | \(-0.334167\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5380.73 | − | 2228.77i | −0.862069 | − | 0.357081i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 684.313 | + | 1652.08i | 0.108673 | + | 0.262361i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4856.34 | + | 4856.34i | 0.764484 | + | 0.764484i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 75.3893 | − | 75.3893i | 0.0117647 | − | 0.0117647i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5414.63 | − | 2242.81i | 0.837673 | − | 0.346976i | 0.0777376 | − | 0.996974i | \(-0.475230\pi\) |
0.759936 | + | 0.649998i | \(0.225230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −443.942 | + | 1071.77i | −0.0680907 | + | 0.164385i | −0.954261 | − | 0.298973i | \(-0.903356\pi\) |
0.886171 | + | 0.463359i | \(0.153356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2984.99 | 0.453922 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 812.561 | 0.122516 | 0.0612582 | − | 0.998122i | \(-0.480489\pi\) | ||||
0.0612582 | + | 0.998122i | \(0.480489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 40.0723 | − | 96.7430i | 0.00599103 | − | 0.0144636i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6349.24 | + | 2629.94i | −0.941281 | + | 0.389891i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3733.47 | − | 3733.47i | 0.548871 | − | 0.548871i | −0.377243 | − | 0.926114i | \(-0.623128\pi\) |
0.926114 | + | 0.377243i | \(0.123128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5310.98 | + | 5310.98i | 0.774308 | + | 0.774308i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1990.55 | + | 4805.62i | 0.287815 | + | 0.694847i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 63.8689 | + | 26.4554i | 0.00915904 | + | 0.00379380i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6820.92i | − | 0.970161i | −0.874469 | − | 0.485081i | \(-0.838790\pi\) | ||
0.874469 | − | 0.485081i | \(-0.161210\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 641.280i | 0.0904707i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2876.16 | + | 1191.34i | 0.402487 | + | 0.166716i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3875.45 | + | 9356.15i | 0.537970 | + | 1.29878i | 0.926137 | + | 0.377186i | \(0.123108\pi\) |
−0.388167 | + | 0.921589i | \(0.626892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 179.500 | + | 179.500i | 0.0247183 | + | 0.0247183i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2442.41 | − | 2442.41i | 0.333661 | − | 0.333661i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4336.19 | − | 1796.11i | 0.587692 | − | 0.243430i | −0.0689653 | − | 0.997619i | \(-0.521970\pi\) |
0.656657 | + | 0.754189i | \(0.271970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3867.22 | + | 9336.29i | −0.520009 | + | 1.25541i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8452.79 | −1.12772 | −0.563861 | − | 0.825870i | \(-0.690685\pi\) | ||||
−0.563861 | + | 0.825870i | \(0.690685\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −160.806 | −0.0212869 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −48.1306 | + | 116.198i | −0.00632201 | + | 0.0152627i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −468.925 | + | 194.235i | −0.0611194 | + | 0.0253165i | −0.413034 | − | 0.910716i | \(-0.635531\pi\) |
0.351914 | + | 0.936032i | \(0.385531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6361.98 | − | 6361.98i | 0.822862 | − | 0.822862i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2469.58 | + | 2469.58i | 0.316981 | + | 0.316981i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 79.6437 | + | 192.277i | 0.0101451 | + | 0.0244924i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3306.01 | − | 1369.40i | −0.417945 | − | 0.173118i | 0.163793 | − | 0.986495i | \(-0.447627\pi\) |
−0.581738 | + | 0.813376i | \(0.697627\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9612.53i | 1.20609i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3887.84i | 0.484164i | 0.970256 | + | 0.242082i | \(0.0778303\pi\) | ||||
−0.970256 | + | 0.242082i | \(0.922170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −694.453 | − | 287.652i | −0.0858392 | − | 0.0355557i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −51.7298 | − | 124.887i | −0.00634685 | − | 0.0153227i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11691.5 | − | 11691.5i | −1.42390 | − | 1.42390i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7188.15 | + | 7188.15i | −0.869025 | + | 0.869025i | −0.992365 | − | 0.123339i | \(-0.960640\pi\) |
0.123339 | + | 0.992365i | \(0.460640\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6995.40 | − | 2897.59i | 0.839556 | − | 0.347756i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −273.702 | + | 660.775i | −0.0326101 | + | 0.0787278i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −51.1576 | −0.00605115 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3712.08 | −0.435927 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4190.33 | + | 10116.4i | −0.488571 | + | 1.17951i | 0.466869 | + | 0.884327i | \(0.345382\pi\) |
−0.955439 | + | 0.295187i | \(0.904618\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14568.6 | − | 6034.51i | 1.68653 | − | 0.698584i | 0.686927 | − | 0.726726i | \(-0.258959\pi\) |
0.999604 | + | 0.0281419i | \(0.00895901\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −829.114 | + | 829.114i | −0.0953024 | + | 0.0953024i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7572.60 | + | 7572.60i | 0.864294 | + | 0.864294i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5241.65 | + | 12654.5i | 0.594054 | + | 1.43417i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4588.71 | − | 1900.70i | −0.516422 | − | 0.213909i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 844.040i | 0.0943295i | 0.998887 | + | 0.0471647i | \(0.0150186\pi\) | ||||
−0.998887 | + | 0.0471647i | \(0.984981\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11447.7i | − | 1.27053i | −0.772293 | − | 0.635266i | \(-0.780890\pi\) | ||
0.772293 | − | 0.635266i | \(-0.219110\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −158.113 | − | 65.4925i | −0.0174274 | − | 0.00721868i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4815.91 | − | 11626.6i | −0.527177 | − | 1.27272i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2040.34 | − | 2040.34i | −0.221823 | − | 0.221823i | 0.587443 | − | 0.809266i | \(-0.300135\pi\) |
−0.809266 | + | 0.587443i | \(0.800135\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −134.673 | + | 134.673i | −0.0145419 | + | 0.0145419i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12477.8 | + | 5168.47i | −1.33823 | + | 0.554315i | −0.932993 | − | 0.359895i | \(-0.882813\pi\) |
−0.405241 | + | 0.914210i | \(0.632813\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 122.004 | − | 294.544i | 0.0129967 | − | 0.0313769i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8235.78 | −0.871452 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3601.74 | −0.378567 | −0.189283 | − | 0.981922i | \(-0.560616\pi\) | ||||
−0.189283 | + | 0.981922i | \(0.560616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5190.58 | − | 12531.2i | 0.541940 | − | 1.30836i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5232.19 | − | 2167.25i | 0.542671 | − | 0.224782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 47.7970 | − | 47.7970i | 0.00492474 | − | 0.00492474i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10018.4 | − | 10018.4i | −1.02547 | − | 1.02547i | −0.999667 | − | 0.0258078i | \(-0.991784\pi\) |
−0.0258078 | − | 0.999667i | \(-0.508216\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4776.21 | − | 11530.8i | −0.485696 | − | 1.17257i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1495.66 | − | 619.524i | −0.151106 | − | 0.0625902i | 0.305849 | − | 0.952080i | \(-0.401060\pi\) |
−0.456955 | + | 0.889490i | \(0.651060\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14517.8i | 1.45724i | 0.684921 | + | 0.728618i | \(0.259837\pi\) | ||||
−0.684921 | + | 0.728618i | \(0.740163\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.2432i | 0.00371422i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5649.95 | − | 2340.29i | −0.559847 | − | 0.231896i | 0.0847717 | − | 0.996400i | \(-0.472984\pi\) |
−0.644619 | + | 0.764504i | \(0.722984\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −797.835 | − | 1926.14i | −0.0785513 | − | 0.189640i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2828.70 | + | 2828.70i | 0.276730 | + | 0.276730i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1881.03 | − | 1881.03i | 0.182854 | − | 0.182854i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13839.1 | − | 5732.32i | 1.33680 | − | 0.553720i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −170.207 | + | 410.917i | −0.0163381 | + | 0.0394436i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10244.1 | 0.977172 | 0.488586 | − | 0.872516i | \(-0.337513\pi\) | ||||
0.488586 | + | 0.872516i | \(0.337513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6950.22 | 0.658841 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3221.54 | − | 7777.48i | 0.303489 | − | 0.732687i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.9820 | + | 5.79153i | −0.00130905 | + | 0.000542226i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12510.0 | − | 12510.0i | 1.16403 | − | 1.16403i | 0.180446 | − | 0.983585i | \(-0.442246\pi\) |
0.983585 | − | 0.180446i | \(-0.0577542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3644.95 | + | 3644.95i | 0.337076 | + | 0.337076i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4847.78 | + | 11703.6i | 0.445575 | + | 1.07571i | 0.973962 | + | 0.226710i | \(0.0727970\pi\) |
−0.528387 | + | 0.849004i | \(0.677203\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13342.9 | − | 5526.81i | −1.21893 | − | 0.504898i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 22.9744i | − | 0.00208611i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8268.05i | − | 0.746223i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18011.3 | − | 7460.51i | −1.61582 | − | 0.669295i | −0.622282 | − | 0.782793i | \(-0.713794\pi\) |
−0.993538 | + | 0.113498i | \(0.963794\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 826.961 | + | 1996.46i | 0.0737443 | + | 0.178034i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3687.97 | + | 3687.97i | 0.326915 | + | 0.326915i | 0.851412 | − | 0.524497i | \(-0.175747\pi\) |
−0.524497 | + | 0.851412i | \(0.675747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 88.2627 | − | 88.2627i | 0.00777750 | − | 0.00777750i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8157.76 | + | 3379.06i | −0.714594 | + | 0.295994i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1071.88 | − | 2587.76i | 0.0933407 | − | 0.225344i | −0.870313 | − | 0.492499i | \(-0.836083\pi\) |
0.963654 | + | 0.267155i | \(0.0860835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5458.49 | 0.472543 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17457.2 | −1.50245 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 55.8306 | − | 134.787i | 0.00477707 | − | 0.0115329i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22912.5 | − | 9490.68i | 1.94911 | − | 0.807350i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1248.29 | − | 1248.29i | 0.105575 | − | 0.105575i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8038.89 | − | 8038.89i | −0.675988 | − | 0.675988i | 0.283102 | − | 0.959090i | \(-0.408637\pi\) |
−0.959090 | + | 0.283102i | \(0.908637\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7860.76 | − | 18977.6i | −0.657222 | − | 1.58667i | −0.802076 | − | 0.597222i | \(-0.796271\pi\) |
0.144854 | − | 0.989453i | \(-0.453729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9257.45 | + | 3834.56i | 0.769578 | + | 0.318770i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3142.89i | 0.259785i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1145.90i | − | 0.0941813i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −94.4050 | − | 39.1038i | −0.00771531 | − | 0.00319579i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2181.87 | + | 5267.49i | 0.177312 | + | 0.428068i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 150.914 | + | 150.914i | 0.0121955 | + | 0.0121955i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4833.57 | − | 4833.57i | 0.388424 | − | 0.388424i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3721.67 | − | 1541.57i | 0.297410 | − | 0.123191i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1316.22 | + | 3177.63i | −0.104600 | + | 0.252527i | −0.967511 | − | 0.252829i | \(-0.918639\pi\) |
0.862911 | + | 0.505356i | \(0.168639\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18818.6 | 1.48726 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −301.403 | −0.0236893 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6431.02 | − | 15525.9i | 0.502689 | − | 1.21360i | −0.445325 | − | 0.895369i | \(-0.646912\pi\) |
0.948014 | − | 0.318229i | \(-0.103088\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1807.95 | + | 748.876i | −0.140549 | + | 0.0582172i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14284.0 | + | 14284.0i | −1.10439 | + | 1.10439i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11619.7 | + | 11619.7i | 0.893527 | + | 0.893527i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −131.782 | − | 318.151i | −0.0100790 | − | 0.0243329i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5335.11 | − | 2209.88i | −0.405846 | − | 0.168107i | 0.170416 | − | 0.985372i | \(-0.445489\pi\) |
−0.576261 | + | 0.817266i | \(0.695489\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1118.21i | 0.0846068i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20767.1i | 1.56290i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5228.46 | − | 2165.70i | −0.391391 | − | 0.162120i | 0.178304 | − | 0.983975i | \(-0.442939\pi\) |
−0.569696 | + | 0.821856i | \(0.692939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −91.6594 | − | 221.285i | −0.00682502 | − | 0.0164771i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7547.18 | − | 7547.18i | −0.558998 | − | 0.558998i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4183.25 | + | 4183.25i | −0.308209 | + | 0.308209i | −0.844215 | − | 0.536005i | \(-0.819933\pi\) |
0.536005 | + | 0.844215i | \(0.319933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7441.94 | + | 3082.55i | −0.545421 | + | 0.225921i | −0.638342 | − | 0.769753i | \(-0.720380\pi\) |
0.0929211 | + | 0.995673i | \(0.470380\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4039.35 | − | 9751.87i | 0.294496 | − | 0.710977i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13118.3 | −0.951427 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2828.16 | 0.204052 | 0.102026 | − | 0.994782i | \(-0.467468\pi\) | ||||
0.102026 | + | 0.994782i | \(0.467468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4534.59 | + | 10947.5i | −0.325477 | + | 0.785771i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3731.85 | + | 1545.78i | −0.266477 | + | 0.110379i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6652.00 | − | 6652.00i | 0.472552 | − | 0.472552i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.82877 | + | 6.82877i | 0.000482624 | + | 0.000482624i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1835.52 | − | 4431.34i | −0.129063 | − | 0.311586i | 0.846118 | − | 0.532996i | \(-0.178934\pi\) |
−0.975181 | + | 0.221410i | \(0.928934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4061.40 | + | 1682.29i | 0.284121 | + | 0.117687i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16193.0i | 1.12706i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13545.0i | 0.937989i | 0.883201 | + | 0.468995i | \(0.155384\pi\) | ||||
−0.883201 | + | 0.468995i | \(0.844616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −261.116 | − | 108.158i | −0.0179911 | − | 0.00745215i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6839.07 | + | 16511.0i | 0.468852 | + | 1.13191i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12379.3 | + | 12379.3i | 0.844414 | + | 0.844414i | 0.989429 | − | 0.145015i | \(-0.0463231\pi\) |
−0.145015 | + | 0.989429i | \(0.546323\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17513.1 | + | 17513.1i | −1.18864 | + | 1.18864i | −0.211202 | + | 0.977442i | \(0.567738\pi\) |
−0.977442 | + | 0.211202i | \(0.932262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 275.189 | − | 113.987i | 0.0185846 | − | 0.00769801i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −81.8624 | + | 197.633i | −0.00550112 | + | 0.0132809i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21984.1 | −1.47003 | −0.735013 | − | 0.678053i | \(-0.762824\pi\) | ||||
−0.735013 | + | 0.678053i | \(0.762824\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13513.0 | −0.899135 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3989.42 | + | 9631.31i | −0.264148 | + | 0.637711i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13582.2 | + | 5625.93i | −0.894910 | + | 0.370684i | −0.782261 | − | 0.622951i | \(-0.785934\pi\) |
−0.112649 | + | 0.993635i | \(0.535934\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 199.753 | − | 199.753i | 0.0130972 | − | 0.0130972i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4045.14 | − | 4045.14i | −0.263941 | − | 0.263941i | 0.562712 | − | 0.826653i | \(-0.309758\pi\) |
−0.826653 | + | 0.562712i | \(0.809758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4901.51 | + | 11833.3i | 0.318268 | + | 0.768368i | 0.999346 | + | 0.0361568i | \(0.0115116\pi\) |
−0.681078 | + | 0.732211i | \(0.738488\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14124.6 | + | 5850.61i | 0.912723 | + | 0.378062i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 25172.9i | − | 1.61883i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 15609.3i | − | 0.998998i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26836.3 | + | 11116.0i | 1.70931 | + | 0.708021i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11120.9 | − | 26848.2i | −0.704959 | − | 1.70192i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14073.2 | + | 14073.2i | 0.887870 | + | 0.887870i | 0.994318 | − | 0.106448i | \(-0.0339478\pi\) |
−0.106448 | + | 0.994318i | \(0.533948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1565.08 | + | 1565.08i | −0.0982723 | + | 0.0982723i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −383.959 | + | 159.041i | −0.0239952 | + | 0.00993914i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −648.000 | + | 1564.41i | −0.0403057 | + | 0.0973065i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1181.26 | 0.0731297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14401.9 | 0.887430 | 0.443715 | − | 0.896168i | \(-0.353660\pi\) | ||||
0.443715 | + | 0.896168i | \(0.353660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3465.77 | + | 8367.12i | −0.212561 | + | 0.513168i | −0.993815 | − | 0.111045i | \(-0.964580\pi\) |
0.781254 | + | 0.624213i | \(0.214580\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 51.1867 | − | 21.2022i | 0.00312477 | − | 0.00129432i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17607.8 | + | 17607.8i | −1.06991 | + | 1.06991i | −0.0725490 | + | 0.997365i | \(0.523113\pi\) |
−0.997365 | + | 0.0725490i | \(0.976887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1528.25 | + | 1528.25i | 0.0924328 | + | 0.0924328i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1125.34 | + | 2716.82i | 0.0677507 | + | 0.163565i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25243.9 | + | 10456.4i | 1.51282 | + | 0.626629i | 0.976137 | − | 0.217157i | \(-0.0696782\pi\) |
0.536680 | + | 0.843786i | \(0.319678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 143.631i | 0.00856814i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 779.856i | 0.0463091i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2555.01 | + | 1058.32i | 0.151030 | + | 0.0625588i | 0.456918 | − | 0.889509i | \(-0.348953\pi\) |
−0.305888 | + | 0.952068i | \(0.598953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1008.92 | − | 2435.76i | −0.0593685 | − | 0.143328i | 0.891412 | − | 0.453195i | \(-0.149716\pi\) |
−0.950780 | + | 0.309866i | \(0.899716\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6172.68 | − | 6172.68i | −0.361579 | − | 0.361579i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −279.533 | + | 279.533i | −0.0163005 | + | 0.0163005i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16344.3 | − | 6770.05i | 0.948809 | − | 0.393009i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3513.96 | − | 8483.45i | 0.203076 | − | 0.490268i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41390.3 | 2.38130 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23085.3 | 1.32225 | 0.661125 | − | 0.750276i | \(-0.270079\pi\) | ||||
0.661125 | + | 0.750276i | \(0.270079\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6963.91 | + | 16812.4i | −0.397098 | + | 0.958679i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29890.9 | + | 12381.2i | −1.69690 | + | 0.702879i | −0.999899 | − | 0.0141909i | \(-0.995483\pi\) |
−0.697001 | + | 0.717070i | \(0.745483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −844.962 | + | 844.962i | −0.0477565 | + | 0.0477565i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8303.48 | − | 8303.48i | −0.467240 | − | 0.467240i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4968.96 | − | 11996.1i | −0.278378 | − | 0.672063i | 0.721413 | − | 0.692505i | \(-0.243493\pi\) |
−0.999791 | + | 0.0204414i | \(0.993493\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 287.689 | + | 119.165i | 0.0160468 | + | 0.00664679i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 23233.8i | − | 1.29029i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3954.39i | 0.218651i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7791.33 | + | 3227.27i | 0.428938 | + | 0.177672i | 0.586698 | − | 0.809805i | \(-0.300427\pi\) |
−0.157760 | + | 0.987477i | \(0.550427\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −694.198 | − | 1675.94i | −0.0380525 | − | 0.0918670i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −107.948 | − | 107.948i | −0.00589165 | − | 0.00589165i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16856.8 | − | 16856.8i | 0.916064 | − | 0.916064i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22875.9 | + | 9475.51i | −1.23783 | + | 0.512728i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3402.06 | + | 8213.30i | −0.183301 | + | 0.442528i | −0.988643 | − | 0.150283i | \(-0.951982\pi\) |
0.805342 | + | 0.592810i | \(0.201982\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40647.3 | −2.18071 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 516.523 | 0.0275934 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3771.64 | − | 9105.55i | 0.200633 | − | 0.484370i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6190.43 | + | 2564.16i | −0.327908 | + | 0.135824i | −0.540563 | − | 0.841303i | \(-0.681789\pi\) |
0.212656 | + | 0.977127i | \(0.431789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1660.11 | + | 1660.11i | −0.0875655 | + | 0.0875655i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2722.27 | − | 2722.27i | −0.142987 | − | 0.142987i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −78.1674 | − | 188.713i | −0.00408852 | − | 0.00987057i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28569.4 | − | 11833.8i | −1.48807 | − | 0.616378i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7000.41i | 0.363103i | 0.983381 | + | 0.181552i | \(0.0581120\pi\) | ||||
−0.983381 | + | 0.181552i | \(0.941888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 11519.4i | − | 0.595016i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19608.9 | + | 8122.29i | 1.00866 | + | 0.417802i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8058.32 | + | 19454.5i | 0.412798 | + | 0.996582i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4176.48 | + | 4176.48i | 0.213063 | + | 0.213063i | 0.805567 | − | 0.592504i | \(-0.201861\pi\) |
−0.592504 | + | 0.805567i | \(0.701861\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14894.8 | − | 14894.8i | 0.756733 | − | 0.756733i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4319.56 | − | 1789.22i | 0.218556 | − | 0.0905291i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8727.96 | − | 21071.2i | 0.439801 | − | 1.06177i | −0.536216 | − | 0.844081i | \(-0.680147\pi\) |
0.976017 | − | 0.217694i | \(-0.0698533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 83.8986 | 0.00421040 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6300.04 | −0.314878 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1771.01 | − | 4275.60i | 0.0881566 | − | 0.212829i | −0.873652 | − | 0.486551i | \(-0.838255\pi\) |
0.961809 | + | 0.273722i | \(0.0882548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11280.7 | + | 4672.61i | −0.559253 | + | 0.231650i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −331.818 | + | 331.818i | −0.0163839 | + | 0.0163839i | −0.715251 | − | 0.698867i | \(-0.753688\pi\) |
0.698867 | + | 0.715251i | \(0.253688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −239.497 | − | 239.497i | −0.0117779 | − | 0.0117779i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −220.846 | − | 533.171i | −0.0108171 | − | 0.0261147i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15569.0 | + | 6448.88i | 0.759516 | + | 0.314602i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 35952.8i | − | 1.74692i | −0.486897 | − | 0.873459i | \(-0.661871\pi\) | ||
0.486897 | − | 0.873459i | \(-0.338129\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26147.5i | 1.26543i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 215.177 | + | 89.1290i | 0.0103723 | + | 0.00429634i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8248.62 | + | 19913.9i | 0.396038 | + | 0.956121i | 0.988596 | + | 0.150593i | \(0.0481183\pi\) |
−0.592557 | + | 0.805528i | \(0.701882\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17987.8 | − | 17987.8i | −0.860234 | − | 0.860234i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20845.8 | − | 20845.8i | 0.992983 | − | 0.992983i | −0.00699229 | − | 0.999976i | \(-0.502226\pi\) |
0.999976 | + | 0.00699229i | \(0.00222573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21986.8 | + | 9107.23i | −1.04322 | + | 0.432115i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.4525 | − | 37.3056i | 0.000730309 | − | 0.00176312i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −908.491 | −0.0427689 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14131.4 | 0.662669 | 0.331335 | − | 0.943513i | \(-0.392501\pi\) | ||||
0.331335 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3885.52 | − | 9380.46i | 0.181496 | − | 0.438170i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15774.0 | + | 6533.82i | −0.733962 | + | 0.304017i | −0.718179 | − | 0.695858i | \(-0.755024\pi\) |
−0.0157831 | + | 0.999875i | \(0.505024\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3240.29 | − | 3240.29i | 0.150187 | − | 0.150187i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19226.6 | − | 19226.6i | −0.887708 | − | 0.887708i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12760.3 | − | 30806.1i | −0.586888 | − | 1.41687i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23082.8 | − | 9561.22i | −1.05758 | − | 0.438063i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 24540.8i | − | 1.12007i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 164.518i | 0.00748013i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9893.89 | − | 4098.18i | −0.448131 | − | 0.185622i | 0.147193 | − | 0.989108i | \(-0.452976\pi\) |
−0.595324 | + | 0.803486i | \(0.702976\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9080.62 | − | 21922.6i | −0.409732 | − | 0.989181i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13372.8 | − | 13372.8i | −0.601113 | − | 0.601113i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12302.6 | + | 12302.6i | −0.550917 | + | 0.550917i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 181.015 | − | 74.9788i | 0.00807539 | − | 0.00334494i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10234.0 | + | 24707.0i | −0.454838 | + | 1.09807i | 0.515623 | + | 0.856815i | \(0.327560\pi\) |
−0.970461 | + | 0.241259i | \(0.922440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43588.5 | 1.92998 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3596.46 | 0.158645 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6312.23 | − | 15239.1i | 0.277402 | − | 0.669707i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 319.853 | − | 132.487i | 0.0140041 | − | 0.00580070i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14295.4 | + | 14295.4i | −0.623571 | + | 0.623571i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4366.67 | − | 4366.67i | −0.189770 | − | 0.189770i | 0.605827 | − | 0.795597i | \(-0.292843\pi\) |
−0.795597 | + | 0.605827i | \(0.792843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16742.8 | + | 40420.6i | 0.724930 | + | 1.75014i | 0.658792 | + | 0.752325i | \(0.271068\pi\) |
0.0661382 | + | 0.997810i | \(0.478932\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19202.6 | + | 7953.98i | 0.828370 | + | 0.343122i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 211.991i | 0.00911132i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6539.67i | − | 0.280042i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 704.485 | + | 291.807i | 0.0300570 | + | 0.0124500i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2730.75 | − | 6592.63i | −0.116083 | − | 0.280249i | 0.855150 | − | 0.518381i | \(-0.173465\pi\) |
−0.971233 | + | 0.238132i | \(0.923465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7832.94 | + | 7832.94i | 0.331761 | + | 0.331761i | 0.853255 | − | 0.521494i | \(-0.174625\pi\) |
−0.521494 | + | 0.853255i | \(0.674625\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21410.7 | − | 21410.7i | 0.903547 | − | 0.903547i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18116.8 | − | 7504.23i | 0.761769 | − | 0.315535i | 0.0322359 | − | 0.999480i | \(-0.489737\pi\) |
0.729533 | + | 0.683945i | \(0.239737\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3888.12 | + | 9386.75i | −0.162895 | + | 0.393264i | −0.984160 | − | 0.177284i | \(-0.943269\pi\) |
0.821265 | + | 0.570547i | \(0.193269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −348.963 | −0.0145673 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7080.06 | 0.294489 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.0092 | + | 82.1054i | −0.00140950 | + | 0.00340284i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4933.99 | + | 2043.73i | −0.203756 | + | 0.0843985i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4919.87 | − | 4919.87i | 0.202447 | − | 0.202447i | −0.598601 | − | 0.801047i | \(-0.704276\pi\) |
0.801047 | + | 0.598601i | \(0.204276\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2834.41 | − | 2834.41i | −0.116217 | − | 0.116217i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10103.3 | − | 24391.6i | −0.412785 | − | 0.996551i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −335.492 | − | 138.965i | −0.0136583 | − | 0.00565746i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16890.5i | 0.685202i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 257.447i | 0.0104070i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32887.6 | + | 13622.5i | 1.32476 | + | 0.548735i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2809.03 | − | 6781.60i | −0.112754 | − | 0.272213i | 0.857422 | − | 0.514614i | \(-0.172065\pi\) |
−0.970176 | + | 0.242401i | \(0.922065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −39.9370 | − | 39.9370i | −0.00159745 | − | 0.00159745i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7846.03 | + | 7846.03i | −0.312737 | + | 0.312737i | −0.845969 | − | 0.533232i | \(-0.820977\pi\) |
0.533232 | + | 0.845969i | \(0.320977\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10278.4 | + | 4257.47i | −0.408261 | + | 0.169107i | −0.577356 | − | 0.816493i | \(-0.695915\pi\) |
0.169095 | + | 0.985600i | \(0.445915\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8535.84 | − | 20607.3i | 0.337864 | − | 0.815675i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28549.2 | −1.12610 | −0.563050 | − | 0.826423i | \(-0.690372\pi\) | ||||
−0.563050 | + | 0.826423i | \(0.690372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 72.6005 | 0.00285375 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4624.86 | + | 11165.4i | −0.181163 | + | 0.437366i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45877.1 | − | 19002.9i | 1.79088 | − | 0.741807i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1872.58 | − | 1872.58i | 0.0728473 | − | 0.0728473i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −120.720 | − | 120.720i | −0.00468013 | − | 0.00468013i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 315.449 | + | 761.562i | 0.0121876 | + | 0.0294234i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8149.22 | − | 3375.52i | −0.313774 | − | 0.129969i | 0.220239 | − | 0.975446i | \(-0.429316\pi\) |
−0.534012 | + | 0.845477i | \(0.679316\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19683.9i | 0.755315i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22699.0i | 0.868046i | 0.900902 | + | 0.434023i | \(0.142906\pi\) | ||||
−0.900902 | + | 0.434023i | \(0.857094\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3173.59 | + | 1314.54i | 0.120951 | + | 0.0500995i | 0.442338 | − | 0.896848i | \(-0.354149\pi\) |
−0.321387 | + | 0.946948i | \(0.604149\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.2258 | + | 41.5868i | 0.000654282 | + | 0.00157958i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −389.896 | − | 389.896i | −0.0147592 | − | 0.0147592i | 0.699689 | − | 0.714448i | \(-0.253322\pi\) |
−0.714448 | + | 0.699689i | \(0.753322\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23203.5 | + | 23203.5i | −0.875389 | + | 0.875389i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29797.9 | + | 12342.7i | −1.12039 | + | 0.464081i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23331.5 | − | 56327.2i | 0.874310 | − | 2.11077i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 281.121 | 0.0104993 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10693.2 | 0.398032 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2364.91 | + | 5709.39i | −0.0877353 | + | 0.211812i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15275.6 | − | 6327.34i | 0.564820 | − | 0.233956i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3093.33 | − | 3093.33i | 0.113997 | − | 0.113997i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 547.247 | + | 547.247i | 0.0201007 | + | 0.0201007i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14791.8 | + | 35710.6i | 0.541516 | + | 1.30733i | 0.923653 | + | 0.383229i | \(0.125188\pi\) |
−0.382138 | + | 0.924105i | \(0.624812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1300.91 | + | 538.856i | 0.0474682 | + | 0.0196620i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26874.8i | 0.977388i | 0.872455 | + | 0.488694i | \(0.162527\pi\) | ||||
−0.872455 | + | 0.488694i | \(0.837473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12206.2i | 0.442459i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 796.426 | + | 329.891i | 0.0287749 | + | 0.0119190i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4339.97 | + | 10477.6i | 0.156291 | + | 0.377319i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9495.37 | − | 9495.37i | −0.340831 | − | 0.340831i | 0.515849 | − | 0.856680i | \(-0.327477\pi\) |
−0.856680 | + | 0.515849i | \(0.827477\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4436.42 | + | 4436.42i | −0.158724 | + | 0.158724i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9702.89 | − | 4019.07i | 0.346018 | − | 0.143325i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16214.7 | + | 39145.8i | −0.576364 | + | 1.39147i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1645.79 | 0.0583114 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51635.3 | −1.82357 | −0.911786 | − | 0.410665i | \(-0.865297\pi\) | ||||
−0.911786 | + | 0.410665i | \(0.865297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3789.73 | − | 9149.21i | 0.133409 | − | 0.322077i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5268.84 | + | 2182.42i | −0.184881 | + | 0.0765803i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −603.911 | + | 603.911i | −0.0211230 | + | 0.0211230i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3704.24 | + | 3704.24i | 0.129149 | + | 0.129149i | 0.768726 | − | 0.639578i | \(-0.220891\pi\) |
−0.639578 | + | 0.768726i | \(0.720891\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2012.79 | + | 4859.30i | 0.0699520 | + | 0.168879i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6682.02 | + | 2767.78i | 0.231485 | + | 0.0958843i | 0.495411 | − | 0.868659i | \(-0.335017\pi\) |
−0.263926 | + | 0.964543i | \(0.585017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29201.7i | 1.00842i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 480.254i | − | 0.0165319i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −494.002 | − | 204.622i | −0.0169513 | − | 0.00702147i | 0.374192 | − | 0.927351i | \(-0.377920\pi\) |
−0.391143 | + | 0.920330i | \(0.627920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2653.35 | + | 6405.76i | 0.0907603 | + | 0.219115i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15131.6 | + | 15131.6i | 0.515957 | + | 0.515957i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28698.0 | + | 28698.0i | −0.975465 | + | 0.975465i | −0.999706 | − | 0.0242408i | \(-0.992283\pi\) |
0.0242408 | + | 0.999706i | \(0.492283\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 401.050 | − | 166.120i | 0.0135892 | − | 0.00562883i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15626.5 | + | 37725.6i | −0.527829 | + | 1.27429i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24587.1 | 0.827903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28446.2 | −0.954858 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −921.352 | + | 2224.34i | −0.0308309 | + | 0.0744324i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −450.220 | + | 186.487i | −0.0150188 | + | 0.00622098i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22689.5 | + | 22689.5i | −0.754544 | + | 0.754544i | −0.975324 | − | 0.220780i | \(-0.929140\pi\) |
0.220780 | + | 0.975324i | \(0.429140\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36100.0 | + | 36100.0i | 1.19680 | + | 1.19680i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18313.2 | − | 44211.9i | −0.605250 | − | 1.46120i | −0.868111 | − | 0.496369i | \(-0.834666\pi\) |
0.262861 | − | 0.964834i | \(-0.415334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11136.4 | − | 4612.83i | −0.366922 | − | 0.151984i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12728.0i | 0.418073i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3076.94i | 0.100757i | 0.998730 | + | 0.0503787i | \(0.0160428\pi\) | ||||
−0.998730 | + | 0.0503787i | \(0.983957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −70277.9 | − | 29110.1i | −2.29427 | − | 0.950319i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1301.15 | − | 3141.26i | −0.0423472 | − | 0.102235i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40340.6 | + | 40340.6i | 1.30892 | + | 1.30892i | 0.922197 | + | 0.386722i | \(0.126393\pi\) |
0.386722 | + | 0.922197i | \(0.373607\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −470.895 | + | 470.895i | −0.0152324 | + | 0.0152324i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 37679.4 | − | 15607.3i | 1.21514 | − | 0.503329i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2191.70 | + | 5291.24i | −0.0704672 | + | 0.170123i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19825.3 | −0.635492 | −0.317746 | − | 0.948176i | \(-0.602926\pi\) | ||||
−0.317746 | + | 0.948176i | \(0.602926\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30904.3 | 0.987632 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −281.260 | + | 679.022i | −0.00896135 | + | 0.0216346i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12624.9 | + | 5229.39i | −0.401036 | + | 0.166115i | −0.574079 | − | 0.818800i | \(-0.694640\pi\) |
0.173043 | + | 0.984914i | \(0.444640\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 128.4.g.a.17.9 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.13.6 | yes | 44 | ||
8.3 | odd | 2 | 256.4.g.b.33.9 | 44 | |||
8.5 | even | 2 | 256.4.g.a.33.3 | 44 | |||
32.5 | even | 8 | inner | 128.4.g.a.113.9 | 44 | ||
32.11 | odd | 8 | 256.4.g.b.225.9 | 44 | |||
32.21 | even | 8 | 256.4.g.a.225.3 | 44 | |||
32.27 | odd | 8 | 32.4.g.a.5.6 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.6 | ✓ | 44 | 32.27 | odd | 8 | ||
32.4.g.a.13.6 | yes | 44 | 4.3 | odd | 2 | ||
128.4.g.a.17.9 | 44 | 1.1 | even | 1 | trivial | ||
128.4.g.a.113.9 | 44 | 32.5 | even | 8 | inner | ||
256.4.g.a.33.3 | 44 | 8.5 | even | 2 | |||
256.4.g.a.225.3 | 44 | 32.21 | even | 8 | |||
256.4.g.b.33.9 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.225.9 | 44 | 32.11 | odd | 8 |