Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, 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("256.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(15.1044889615\) |
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 | 33.3 | ||
Character | \(\chi\) | \(=\) | 256.33 |
Dual form | 256.4.g.a.225.3 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | \(0.283702\pi\) |
−0.994400 | + | 0.105681i | \(0.966298\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.188811 | + | 0.0782080i | −0.0168878 | + | 0.00699514i | −0.391111 | − | 0.920343i | \(-0.627909\pi\) |
0.374224 | + | 0.927339i | \(0.377909\pi\) | |||||||
\(6\) | 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 | \(0.107971\pi\) |
−0.431537 | + | 0.902095i | \(0.642029\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.9369 | − | 7.84392i | −0.404011 | − | 0.167347i | 0.171418 | − | 0.985198i | \(-0.445165\pi\) |
−0.575430 | + | 0.817851i | \(0.695165\pi\) | |||||||
\(14\) | 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 | 0.932713 | − | 0.360619i | \(-0.117434\pi\) |
0.404532 | + | 0.914524i | \(0.367434\pi\) | |||||||
\(20\) | 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 | \(0.306397\pi\) |
−0.984345 | + | 0.176250i | \(0.943603\pi\) | |||||||
\(30\) | 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 | −0.947644 | − | 0.319328i | \(-0.896543\pi\) |
−0.444287 | + | 0.895884i | \(0.646543\pi\) | |||||||
\(38\) | 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 | 0.882526 | − | 0.470263i | \(-0.155841\pi\) |
−0.956566 | + | 0.291514i | \(0.905841\pi\) | |||||||
\(44\) | 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 | 0.798871 | − | 0.601503i | \(-0.205431\pi\) |
−0.990214 | + | 0.139560i | \(0.955431\pi\) | |||||||
\(54\) | 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 | −0.337047 | − | 0.941488i | \(-0.609428\pi\) |
0.427404 | + | 0.904061i | \(0.359428\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 324.831 | − | 784.211i | 0.681809 | − | 1.64603i | −0.0788549 | − | 0.996886i | \(-0.525126\pi\) |
0.760664 | − | 0.649146i | \(-0.224874\pi\) | |||||||
\(62\) | 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 | −0.962525 | − | 0.271192i | \(-0.912582\pi\) |
0.872370 | + | 0.488846i | \(0.162582\pi\) | |||||||
\(68\) | 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 | 0.530326 | − | 0.847794i | \(-0.322070\pi\) |
−0.224484 | + | 0.974478i | \(0.572070\pi\) | |||||||
\(84\) | 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 | −0.642914 | − | 0.765939i | \(-0.722275\pi\) |
0.0869918 | + | 0.996209i | \(0.472275\pi\) | |||||||
\(102\) | 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 | \(-0.968616\pi\) |
0.634068 | − | 0.773277i | \(-0.281384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1362.55 | + | 564.385i | 1.19732 | + | 0.495948i | 0.890133 | − | 0.455700i | \(-0.150611\pi\) |
0.307191 | + | 0.951648i | \(0.400611\pi\) | |||||||
\(110\) | 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 | −0.808458 | − | 0.588553i | \(-0.799698\pi\) |
0.987836 | + | 0.155496i | \(0.0496977\pi\) | |||||||
\(132\) | 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 | 0.986783 | − | 0.162050i | \(-0.0518106\pi\) |
−0.812347 | + | 0.583174i | \(0.801811\pi\) | |||||||
\(140\) | 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 | \(0.0255794\pi\) |
−0.648063 | + | 0.761587i | \(0.724421\pi\) | |||||||
\(150\) | 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 | −0.826034 | − | 0.563620i | \(-0.809408\pi\) |
0.982634 | + | 0.185554i | \(0.0594081\pi\) | |||||||
\(158\) | 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 | −0.799352 | − | 0.600863i | \(-0.794824\pi\) |
0.990102 | + | 0.140353i | \(0.0448236\pi\) | |||||||
\(164\) | 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 | 0.309398 | − | 0.950933i | \(-0.399873\pi\) |
−0.453634 | + | 0.891188i | \(0.649873\pi\) | |||||||
\(174\) | 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 | 0.101231 | − | 0.994863i | \(-0.467722\pi\) |
−0.631893 | + | 0.775056i | \(0.717722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1449.19 | − | 3498.66i | −0.595125 | − | 1.43676i | −0.878496 | − | 0.477749i | \(-0.841453\pi\) |
0.283371 | − | 0.959010i | \(-0.408547\pi\) | |||||||
\(182\) | 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 | 0.235204 | − | 0.971946i | \(-0.424424\pi\) |
0.853584 | + | 0.520956i | \(0.174424\pi\) | |||||||
\(198\) | 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 | 0.448801 | − | 0.893632i | \(-0.351851\pi\) |
−0.314543 | + | 0.949243i | \(0.601851\pi\) | |||||||
\(212\) | 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 | −0.999202 | − | 0.0399527i | \(-0.987279\pi\) |
0.734793 | + | 0.678291i | \(0.237279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4319.52 | + | 1789.20i | −1.24647 | + | 0.516305i | −0.905731 | − | 0.423852i | \(-0.860678\pi\) |
−0.340740 | + | 0.940158i | \(0.610678\pi\) | |||||||
\(230\) | 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 | 0.324267 | − | 0.945966i | \(-0.394883\pi\) |
0.898190 | + | 0.439608i | \(0.144883\pi\) | |||||||
\(252\) | 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 | 0.765541 | − | 0.643387i | \(-0.222471\pi\) |
0.0863762 | + | 0.996263i | \(0.472471\pi\) | |||||||
\(270\) | 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 | 0.926767 | − | 0.375636i | \(-0.122576\pi\) |
−0.920938 | + | 0.389709i | \(0.872576\pi\) | |||||||
\(278\) | 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 | −0.377651 | − | 0.925948i | \(-0.623268\pi\) |
0.387705 | + | 0.921784i | \(0.373268\pi\) | |||||||
\(284\) | 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 | 0.0132515 | − | 0.999912i | \(-0.495782\pi\) |
0.716415 | + | 0.697674i | \(0.245782\pi\) | |||||||
\(294\) | 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 | 0.488463 | − | 0.872585i | \(-0.337558\pi\) |
−0.271615 | + | 0.962406i | \(0.587558\pi\) | |||||||
\(308\) | 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 | −0.708022 | − | 0.706191i | \(-0.750412\pi\) |
0.999999 | + | 0.00129494i | \(0.000412192\pi\) | |||||||
\(318\) | 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 | \(-0.952289\pi\) |
0.593589 | − | 0.804769i | \(-0.297711\pi\) | |||||||
\(332\) | 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 | −0.759936 | − | 0.649998i | \(-0.774770\pi\) |
−0.0777376 | + | 0.996974i | \(0.524770\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 443.942 | − | 1071.77i | 0.0680907 | − | 0.164385i | −0.886171 | − | 0.463359i | \(-0.846644\pi\) |
0.954261 | + | 0.298973i | \(0.0966441\pi\) | |||||||
\(350\) | 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 | \(-0.876892\pi\) |
0.388167 | − | 0.921589i | \(-0.373108\pi\) | |||||||
\(374\) | 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 | −0.656657 | − | 0.754189i | \(-0.728030\pi\) |
0.0689653 | + | 0.997619i | \(0.478030\pi\) | |||||||
\(380\) | 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 | −0.351914 | − | 0.936032i | \(-0.614469\pi\) |
0.413034 | + | 0.910716i | \(0.364469\pi\) | |||||||
\(390\) | 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 | 0.581738 | − | 0.813376i | \(-0.302373\pi\) |
−0.163793 | + | 0.986495i | \(0.552373\pi\) | |||||||
\(398\) | 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 | \(-0.654618\pi\) |
0.955439 | − | 0.295187i | \(-0.0953821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14568.6 | + | 6034.51i | −1.68653 | + | 0.698584i | −0.999604 | − | 0.0281419i | \(-0.991041\pi\) |
−0.686927 | + | 0.726726i | \(0.741041\pi\) | |||||||
\(422\) | 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 | 0.405241 | − | 0.914210i | \(-0.367187\pi\) |
0.932993 | + | 0.359895i | \(0.117187\pi\) | |||||||
\(444\) | 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 | 0.456955 | − | 0.889490i | \(-0.348940\pi\) |
−0.305849 | + | 0.952080i | \(0.598940\pi\) | |||||||
\(462\) | 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 | 0.644619 | − | 0.764504i | \(-0.277016\pi\) |
−0.0847717 | + | 0.996400i | \(0.527016\pi\) | |||||||
\(468\) | 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 | \(-0.927203\pi\) |
0.528387 | − | 0.849004i | \(-0.322797\pi\) | |||||||
\(492\) | 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 | 0.993538 | − | 0.113498i | \(-0.0362055\pi\) |
0.622282 | + | 0.782793i | \(0.286206\pi\) | |||||||
\(500\) | 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 | −0.963654 | − | 0.267155i | \(-0.913917\pi\) |
0.870313 | + | 0.492499i | \(0.163917\pi\) | |||||||
\(510\) | 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 | \(0.203729\pi\) |
−0.144854 | + | 0.989453i | \(0.546271\pi\) | |||||||
\(524\) | 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 | −0.862911 | − | 0.505356i | \(-0.831361\pi\) |
0.967511 | + | 0.252829i | \(0.0813612\pi\) | |||||||
\(542\) | 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 | \(0.353088\pi\) |
−0.948014 | + | 0.318229i | \(0.896912\pi\) | |||||||
\(548\) | 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 | 0.576261 | − | 0.817266i | \(-0.304511\pi\) |
−0.170416 | + | 0.985372i | \(0.554511\pi\) | |||||||
\(558\) | 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 | 0.569696 | − | 0.821856i | \(-0.307061\pi\) |
−0.178304 | + | 0.983975i | \(0.557061\pi\) | |||||||
\(564\) | 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 | −0.0929211 | − | 0.995673i | \(-0.529620\pi\) |
0.638342 | + | 0.769753i | \(0.279620\pi\) | |||||||
\(572\) | 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 | 0.975181 | − | 0.221410i | \(-0.0710659\pi\) |
−0.846118 | + | 0.532996i | \(0.821066\pi\) | |||||||
\(588\) | 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 | 0.112649 | − | 0.993635i | \(-0.464066\pi\) |
0.782261 | + | 0.622951i | \(0.214066\pi\) | |||||||
\(614\) | 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 | \(-0.988488\pi\) |
0.681078 | − | 0.732211i | \(-0.261512\pi\) | |||||||
\(620\) | 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 | −0.781254 | − | 0.624213i | \(-0.785420\pi\) |
0.993815 | + | 0.111045i | \(0.0354198\pi\) | |||||||
\(644\) | 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 | −0.536680 | − | 0.843786i | \(-0.680322\pi\) |
−0.976137 | + | 0.217157i | \(0.930322\pi\) | |||||||
\(654\) | 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 | 0.305888 | − | 0.952068i | \(-0.401047\pi\) |
−0.456918 | + | 0.889509i | \(0.651047\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1008.92 | + | 2435.76i | 0.0593685 | + | 0.143328i | 0.950780 | − | 0.309866i | \(-0.100284\pi\) |
−0.891412 | + | 0.453195i | \(0.850284\pi\) | |||||||
\(662\) | 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 | 0.697001 | − | 0.717070i | \(-0.254517\pi\) |
0.999899 | + | 0.0141909i | \(0.00451726\pi\) | |||||||
\(678\) | 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 | 0.999791 | − | 0.0204414i | \(-0.00650715\pi\) |
−0.721413 | + | 0.692505i | \(0.756507\pi\) | |||||||
\(684\) | 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 | 0.157760 | − | 0.987477i | \(-0.449573\pi\) |
−0.586698 | + | 0.809805i | \(0.699573\pi\) | |||||||
\(692\) | 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 | −0.805342 | − | 0.592810i | \(-0.798018\pi\) |
0.988643 | + | 0.150283i | \(0.0480184\pi\) | |||||||
\(702\) | 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 | −0.212656 | − | 0.977127i | \(-0.568211\pi\) |
0.540563 | + | 0.841303i | \(0.318211\pi\) | |||||||
\(710\) | 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 | \(0.319853\pi\) |
−0.976017 | + | 0.217694i | \(0.930147\pi\) | |||||||
\(734\) | 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 | −0.961809 | − | 0.273722i | \(-0.911745\pi\) |
0.873652 | + | 0.486551i | \(0.161745\pi\) | |||||||
\(740\) | 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 | \(-0.951882\pi\) |
0.592557 | − | 0.805528i | \(-0.298118\pi\) | |||||||
\(758\) | 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 | 0.0157831 | − | 0.999875i | \(-0.494976\pi\) |
0.718179 | + | 0.695858i | \(0.244976\pi\) | |||||||
\(774\) | 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 | 0.595324 | − | 0.803486i | \(-0.297024\pi\) |
−0.147193 | + | 0.989108i | \(0.547024\pi\) | |||||||
\(788\) | 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 | \(-0.672440\pi\) |
0.970461 | − | 0.241259i | \(-0.0775605\pi\) | |||||||
\(798\) | 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 | \(-0.728932\pi\) |
−0.0661382 | − | 0.997810i | \(-0.521068\pi\) | |||||||
\(812\) | 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 | 0.971233 | − | 0.238132i | \(-0.0765351\pi\) |
−0.855150 | + | 0.518381i | \(0.826535\pi\) | |||||||
\(822\) | 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 | −0.729533 | − | 0.683945i | \(-0.760263\pi\) |
−0.0322359 | + | 0.999480i | \(0.510263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3888.12 | − | 9386.75i | 0.162895 | − | 0.393264i | −0.821265 | − | 0.570547i | \(-0.806731\pi\) |
0.984160 | + | 0.177284i | \(0.0567311\pi\) | |||||||
\(830\) | 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 | 0.970176 | − | 0.242401i | \(-0.0779351\pi\) |
−0.857422 | + | 0.514614i | \(0.827935\pi\) | |||||||
\(854\) | 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 | −0.169095 | − | 0.985600i | \(-0.554085\pi\) |
0.577356 | + | 0.816493i | \(0.304085\pi\) | |||||||
\(860\) | 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 | 0.534012 | − | 0.845477i | \(-0.320684\pi\) |
−0.220239 | + | 0.975446i | \(0.570684\pi\) | |||||||
\(878\) | 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 | 0.321387 | − | 0.946948i | \(-0.395851\pi\) |
−0.442338 | + | 0.896848i | \(0.645851\pi\) | |||||||
\(884\) | 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 | \(-0.874812\pi\) |
0.382138 | − | 0.924105i | \(-0.375188\pi\) | |||||||
\(908\) | 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 | 0.263926 | − | 0.964543i | \(-0.414983\pi\) |
−0.495411 | + | 0.868659i | \(0.664983\pi\) | |||||||
\(942\) | 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 | 0.391143 | − | 0.920330i | \(-0.372080\pi\) |
−0.374192 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(948\) | 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 | \(0.165334\pi\) |
−0.262861 | + | 0.964834i | \(0.584666\pi\) | |||||||
\(972\) | 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 | −0.173043 | − | 0.984914i | \(-0.555360\pi\) |
0.574079 | + | 0.818800i | \(0.305360\pi\) | |||||||
\(998\) | 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 | 256.4.g.a.33.3 | 44 | ||
4.3 | odd | 2 | 256.4.g.b.33.9 | 44 | |||
8.3 | odd | 2 | 32.4.g.a.13.6 | yes | 44 | ||
8.5 | even | 2 | 128.4.g.a.17.9 | 44 | |||
32.5 | even | 8 | inner | 256.4.g.a.225.3 | 44 | ||
32.11 | odd | 8 | 32.4.g.a.5.6 | ✓ | 44 | ||
32.21 | even | 8 | 128.4.g.a.113.9 | 44 | |||
32.27 | odd | 8 | 256.4.g.b.225.9 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.6 | ✓ | 44 | 32.11 | odd | 8 | ||
32.4.g.a.13.6 | yes | 44 | 8.3 | odd | 2 | ||
128.4.g.a.17.9 | 44 | 8.5 | even | 2 | |||
128.4.g.a.113.9 | 44 | 32.21 | even | 8 | |||
256.4.g.a.33.3 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.a.225.3 | 44 | 32.5 | even | 8 | inner | ||
256.4.g.b.33.9 | 44 | 4.3 | odd | 2 | |||
256.4.g.b.225.9 | 44 | 32.27 | odd | 8 |