Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(209,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.k (of order \(2\), degree \(1\), 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.24 | ||
Character | \(\chi\) | \(=\) | 1680.209 |
Dual form | 1680.2.k.h.209.23 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.70556 | + | 0.301745i | 0.984708 | + | 0.174213i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.04579 | − | 0.902636i | −0.914904 | − | 0.403671i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.30232 | − | 2.30304i | −0.492229 | − | 0.870466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.81790 | + | 1.02929i | 0.939300 | + | 0.343097i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.71375i | 1.72276i | 0.507960 | + | 0.861381i | \(0.330400\pi\) | ||||
−0.507960 | + | 0.861381i | \(0.669600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.76758 | −1.04494 | −0.522469 | − | 0.852658i | \(-0.674989\pi\) | ||||
−0.522469 | + | 0.852658i | \(0.674989\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.21686 | − | 2.15681i | −0.830589 | − | 0.556886i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.22968i | 0.783313i | 0.920112 | + | 0.391656i | \(0.128098\pi\) | ||||
−0.920112 | + | 0.391656i | \(0.871902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.786936i | 0.180536i | 0.995918 | + | 0.0902678i | \(0.0287723\pi\) | ||||
−0.995918 | + | 0.0902678i | \(0.971228\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.52625 | − | 4.32094i | −0.333056 | − | 0.942907i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.52714 | 0.318430 | 0.159215 | − | 0.987244i | \(-0.449104\pi\) | ||||
0.159215 | + | 0.987244i | \(0.449104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.37050 | + | 3.69320i | 0.674099 | + | 0.738641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.49553 | + | 2.60581i | 0.865164 | + | 0.501489i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.77221i | 1.25757i | 0.777580 | + | 0.628784i | \(0.216447\pi\) | ||||
−0.777580 | + | 0.628784i | \(0.783553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.56709i | − | 0.281458i | −0.990048 | − | 0.140729i | \(-0.955055\pi\) | ||
0.990048 | − | 0.140729i | \(-0.0449447\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.72410 | + | 9.74517i | −0.300127 | + | 1.69642i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.585457 | + | 5.88704i | 0.0989603 | + | 0.995091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.83080i | 1.45177i | 0.687814 | + | 0.725887i | \(0.258570\pi\) | ||||
−0.687814 | + | 0.725887i | \(0.741430\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.42585 | − | 1.13685i | −1.02896 | − | 0.182042i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.65914 | 1.03998 | 0.519992 | − | 0.854171i | \(-0.325935\pi\) | ||||
0.519992 | + | 0.854171i | \(0.325935\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.85072i | − | 1.34972i | −0.737945 | − | 0.674861i | \(-0.764204\pi\) | ||
0.737945 | − | 0.674861i | \(-0.235796\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.83575 | − | 4.64925i | −0.720871 | − | 0.693069i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.75054i | − | 0.255342i | −0.991817 | − | 0.127671i | \(-0.959250\pi\) | ||
0.991817 | − | 0.127671i | \(-0.0407502\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.60795 | + | 5.99856i | −0.515421 | + | 0.856937i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.974541 | + | 5.50843i | −0.136463 | + | 0.771335i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.616602 | −0.0846967 | −0.0423484 | − | 0.999103i | \(-0.513484\pi\) | ||||
−0.0423484 | + | 0.999103i | \(0.513484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.15744 | − | 11.6891i | 0.695429 | − | 1.57616i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.237454 | + | 1.34217i | −0.0314516 | + | 0.177775i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.38642 | −0.831441 | −0.415721 | − | 0.909492i | \(-0.636471\pi\) | ||||
−0.415721 | + | 0.909492i | \(0.636471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4554i | 1.85082i | 0.378964 | + | 0.925412i | \(0.376281\pi\) | ||||
−0.378964 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.29930 | − | 7.83019i | −0.163696 | − | 0.986511i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.70767 | + | 3.40075i | 0.956019 | + | 0.421812i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.26557i | 0.765462i | 0.923860 | + | 0.382731i | \(0.125016\pi\) | ||||
−0.923860 | + | 0.382731i | \(0.874984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.60463 | + | 0.460806i | 0.313561 | + | 0.0554746i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.09956i | 0.605206i | 0.953117 | + | 0.302603i | \(0.0978556\pi\) | ||||
−0.953117 | + | 0.302603i | \(0.902144\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.5631 | 1.47039 | 0.735197 | − | 0.677853i | \(-0.237089\pi\) | ||||
0.735197 | + | 0.677853i | \(0.237089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.63419 | + | 7.31603i | 0.535110 | + | 0.844782i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.1590 | − | 7.44111i | 1.49960 | − | 0.847993i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.8517 | 1.44593 | 0.722965 | − | 0.690885i | \(-0.242779\pi\) | ||||
0.722965 | + | 0.690885i | \(0.242779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.88112 | + | 5.80088i | 0.764569 | + | 0.644542i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.5003i | − | 1.15256i | −0.817254 | − | 0.576278i | \(-0.804505\pi\) | ||
0.817254 | − | 0.576278i | \(-0.195495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.91523 | − | 6.60724i | 0.316201 | − | 0.716656i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.04348 | + | 11.5504i | −0.219084 | + | 1.23834i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.6873 | −1.66285 | −0.831423 | − | 0.555640i | \(-0.812473\pi\) | ||||
−0.831423 | + | 0.555640i | \(0.812473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.90658 | + | 8.67687i | 0.514349 | + | 0.909583i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.472863 | − | 2.67278i | 0.0490336 | − | 0.277154i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.710317 | − | 1.60990i | 0.0728770 | − | 0.165173i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.69604 | −0.781414 | −0.390707 | − | 0.920515i | \(-0.627769\pi\) | ||||
−0.390707 | + | 0.920515i | \(0.627769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.88112 | + | 16.1008i | −0.591075 | + | 1.61819i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2658 | −1.02149 | −0.510745 | − | 0.859732i | \(-0.670630\pi\) | ||||
−0.510745 | + | 0.859732i | \(0.670630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.62328 | −0.357013 | −0.178506 | − | 0.983939i | \(-0.557127\pi\) | ||||
−0.178506 | + | 0.983939i | \(0.557127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.777851 | + | 10.2174i | −0.0759105 | + | 0.997115i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.65500 | 0.836710 | 0.418355 | − | 0.908284i | \(-0.362607\pi\) | ||||
0.418355 | + | 0.908284i | \(0.362607\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.32109 | 0.797016 | 0.398508 | − | 0.917165i | \(-0.369528\pi\) | ||||
0.398508 | + | 0.917165i | \(0.369528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.66465 | + | 15.0615i | −0.252917 | + | 1.42957i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0986 | −1.32628 | −0.663142 | − | 0.748494i | \(-0.730777\pi\) | ||||
−0.663142 | + | 0.748494i | \(0.730777\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.12420 | − | 1.37845i | −0.291333 | − | 0.128541i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.6167 | − | 3.87794i | −0.981511 | − | 0.358516i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.43807 | − | 4.20606i | 0.681847 | − | 0.385569i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.6470 | −1.96791 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.3576 | + | 2.00936i | 1.02408 | + | 0.181178i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.56170 | − | 10.5978i | −0.318568 | − | 0.947900i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7643i | 1.13265i | 0.824181 | + | 0.566326i | \(0.191636\pi\) | ||||
−0.824181 | + | 0.566326i | \(0.808364\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.67066 | − | 15.0955i | 0.235139 | − | 1.32908i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9991 | −1.48522 | −0.742610 | − | 0.669724i | \(-0.766412\pi\) | ||||
−0.742610 | + | 0.669724i | \(0.766412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.81234 | − | 1.02484i | 0.157150 | − | 0.0888648i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.84479 | − | 9.38876i | −0.589106 | − | 0.808056i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.3946 | 1.05894 | 0.529470 | − | 0.848329i | \(-0.322391\pi\) | ||||
0.529470 | + | 0.848329i | \(0.322391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.2465i | − | 0.953912i | −0.878927 | − | 0.476956i | \(-0.841740\pi\) | ||
0.878927 | − | 0.476956i | \(-0.158260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.528217 | − | 2.98566i | 0.0444839 | − | 0.251438i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 21.5270i | − | 1.80018i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.11284 | − | 13.8545i | 0.507644 | − | 1.15055i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.96363 | + | 9.14225i | −0.656829 | + | 0.754040i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.85057i | 0.233528i | 0.993160 | + | 0.116764i | \(0.0372521\pi\) | ||||
−0.993160 | + | 0.116764i | \(0.962748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.1515 | −1.31439 | −0.657197 | − | 0.753719i | \(-0.728258\pi\) | ||||
−0.657197 | + | 0.753719i | \(0.728258\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.32428 | + | 9.10092i | −0.268752 | + | 0.735766i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.41452 | + | 3.20594i | −0.113617 | + | 0.257507i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.21577 | 0.575881 | 0.287941 | − | 0.957648i | \(-0.407029\pi\) | ||||
0.287941 | + | 0.957648i | \(0.407029\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.05165 | − | 0.186057i | −0.0834016 | − | 0.0147552i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.98881 | − | 3.51705i | −0.156740 | − | 0.277182i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.50516i | − | 0.274545i | −0.990533 | − | 0.137273i | \(-0.956166\pi\) | ||
0.990533 | − | 0.137273i | \(-0.0438337\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.3235 | − | 18.3803i | 0.959382 | − | 1.43091i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.38365i | − | 0.107070i | −0.998566 | − | 0.0535349i | \(-0.982951\pi\) | ||
0.998566 | − | 0.0535349i | \(-0.0170489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.19466 | 0.0918967 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.809987 | + | 2.21751i | −0.0619413 | + | 0.169577i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1282i | 0.770032i | 0.922910 | + | 0.385016i | \(0.125804\pi\) | ||||
−0.922910 | + | 0.385016i | \(0.874196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.11613 | − | 12.5721i | 0.311151 | − | 0.950361i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.8925 | − | 1.92707i | −0.818727 | − | 0.144848i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.542452i | − | 0.0405447i | −0.999794 | − | 0.0202724i | \(-0.993547\pi\) | ||
0.999794 | − | 0.0202724i | \(-0.00645334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.15745i | − | 0.0860323i | −0.999074 | − | 0.0430162i | \(-0.986303\pi\) | ||
0.999074 | − | 0.0430162i | \(-0.0136967\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.36184 | + | 24.6546i | −0.322437 | + | 1.82252i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.97100 | − | 18.0659i | 0.586039 | − | 1.32823i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.4536 | −1.34946 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.146685 | − | 13.7469i | 0.0106697 | − | 0.999943i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.8558i | − | 0.785495i | −0.919646 | − | 0.392748i | \(-0.871525\pi\) | ||
0.919646 | − | 0.392748i | \(-0.128475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 24.6409i | − | 1.77369i | −0.462067 | − | 0.886845i | \(-0.652892\pi\) | ||
0.462067 | − | 0.886845i | \(-0.347108\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.1198 | + | 8.12596i | 0.867914 | + | 0.581912i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.15816 | −0.225009 | −0.112505 | − | 0.993651i | \(-0.535887\pi\) | ||||
−0.112505 | + | 0.993651i | \(0.535887\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.60377i | 0.255464i | 0.991809 | + | 0.127732i | \(0.0407698\pi\) | ||||
−0.991809 | + | 0.127732i | \(0.959230\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.89061 | + | 10.6863i | −0.133353 | + | 0.753756i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5966 | − | 8.81956i | 1.09467 | − | 0.619011i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.6232 | − | 6.01078i | −0.951485 | − | 0.419811i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.30332 | + | 1.57187i | 0.299101 | + | 0.109252i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.49636 | −0.311020 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.159466 | −0.0109781 | −0.00548905 | − | 0.999985i | \(-0.501747\pi\) | ||||
−0.00548905 | + | 0.999985i | \(0.501747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.53877 | + | 8.69762i | −0.105435 | + | 0.595951i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.98898 | + | 18.1067i | −0.544844 | + | 1.23487i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.60907 | + | 2.04085i | −0.245000 | + | 0.138542i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.4271 | + | 3.79084i | 1.44791 | + | 0.256161i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.1681i | − | 0.818514i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.39412 | −0.294252 | −0.147126 | − | 0.989118i | \(-0.547002\pi\) | ||||
−0.147126 | + | 0.989118i | \(0.547002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.69633 | + | 13.8763i | 0.379756 | + | 0.925087i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.1642i | 1.27197i | 0.771700 | + | 0.635987i | \(0.219407\pi\) | ||||
−0.771700 | + | 0.635987i | \(0.780593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.25651i | − | 0.0830328i | −0.999138 | − | 0.0415164i | \(-0.986781\pi\) | ||
0.999138 | − | 0.0415164i | \(-0.0132189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.6888 | − | 8.72063i | 1.62440 | − | 0.573775i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.73752 | −0.375878 | −0.187939 | − | 0.982181i | \(-0.560181\pi\) | ||||
−0.187939 | + | 0.982181i | \(0.560181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.58010 | + | 3.58123i | −0.103074 | + | 0.233614i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.9194 | + | 3.87794i | 1.42382 | + | 0.251899i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.1836i | − | 1.17620i | −0.808789 | − | 0.588099i | \(-0.799877\pi\) | ||
0.808789 | − | 0.588099i | \(-0.200123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1259i | 1.16759i | 0.811901 | + | 0.583795i | \(0.198433\pi\) | ||||
−0.811901 | + | 0.583795i | \(0.801567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.98580 | + | 11.9701i | 0.640589 | + | 0.767884i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7956 | − | 9.01511i | 0.817482 | − | 0.575954i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.96485i | − | 0.188649i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.16841 | − | 17.9089i | 0.200790 | − | 1.13493i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.598823 | 0.0377974 | 0.0188987 | − | 0.999821i | \(-0.493984\pi\) | ||||
0.0188987 | + | 0.999821i | \(0.493984\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.72568i | 0.548579i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.96581 | − | 10.3894i | 0.436216 | − | 0.650611i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 15.4070i | − | 0.961063i | −0.876977 | − | 0.480532i | \(-0.840444\pi\) | ||
0.876977 | − | 0.480532i | \(-0.159556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.3376 | − | 11.5005i | 1.26372 | − | 0.714605i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.97058 | + | 19.0834i | −0.431468 | + | 1.18123i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.66296 | 0.595843 | 0.297922 | − | 0.954590i | \(-0.403707\pi\) | ||||
0.297922 | + | 0.954590i | \(0.403707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.26144 | + | 0.556567i | 0.0774894 | + | 0.0341896i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.7556 | − | 4.73355i | −1.63742 | − | 0.289689i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.2397 | 0.807241 | 0.403620 | − | 0.914927i | \(-0.367752\pi\) | ||||
0.403620 | + | 0.914927i | \(0.367752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6372i | 0.949890i | 0.880016 | + | 0.474945i | \(0.157532\pi\) | ||||
−0.880016 | + | 0.474945i | \(0.842468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.75028 | + | 16.2795i | 0.348023 | + | 0.985280i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.1021 | + | 19.2582i | −1.27250 | + | 1.16131i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.48524i | − | 0.209408i | −0.994503 | − | 0.104704i | \(-0.966611\pi\) | ||
0.994503 | − | 0.104704i | \(-0.0333895\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.61300 | − | 4.41591i | 0.0965676 | − | 0.264374i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4311i | 1.27847i | 0.769011 | + | 0.639236i | \(0.220749\pi\) | ||||
−0.769011 | + | 0.639236i | \(0.779251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.97240 | 0.473910 | 0.236955 | − | 0.971521i | \(-0.423851\pi\) | ||||
0.236955 | + | 0.971521i | \(0.423851\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.69727 | − | 2.53146i | 0.100538 | − | 0.149951i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.67230 | − | 15.3362i | −0.511910 | − | 0.905270i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.56915 | 0.386421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1261 | − | 2.32224i | −0.769465 | − | 0.136132i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.8728i | 0.752035i | 0.926613 | + | 0.376018i | \(0.122707\pi\) | ||||
−0.926613 | + | 0.376018i | \(0.877293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0653 | + | 5.76461i | 0.760689 | + | 0.335629i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.8890 | + | 25.6863i | −0.863945 | + | 1.49047i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.75361 | −0.332740 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.3835 | + | 11.5264i | −1.17489 | + | 0.664372i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.5091 | − | 3.09767i | −1.00587 | − | 0.177956i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.0480 | − | 29.5727i | 0.747124 | − | 1.69333i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.16507 | 0.408932 | 0.204466 | − | 0.978874i | \(-0.434454\pi\) | ||||
0.204466 | + | 0.978874i | \(0.434454\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.17974 | − | 1.09331i | −0.351553 | − | 0.0621961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.4684 | 1.95453 | 0.977263 | − | 0.212030i | \(-0.0680076\pi\) | ||||
0.977263 | + | 0.212030i | \(0.0680076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.5587 | 1.61423 | 0.807117 | − | 0.590392i | \(-0.201027\pi\) | ||||
0.807117 | + | 0.590392i | \(0.201027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.40972 | + | 17.1917i | −0.248460 | + | 0.968642i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.9809 | −1.17840 | −0.589202 | − | 0.807986i | \(-0.700558\pi\) | ||||
−0.589202 | + | 0.807986i | \(0.700558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.6947 | −2.16649 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.7617 | + | 2.61160i | 0.823915 | + | 0.145766i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.54155 | −0.141416 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.6986 | − | 13.9144i | −0.704392 | − | 0.771834i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.1922 | + | 2.51085i | 0.784828 | + | 0.138850i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.03156 | + | 2.27975i | −0.222267 | + | 0.125687i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9404 | −0.601340 | −0.300670 | − | 0.953728i | \(-0.597210\pi\) | ||||
−0.300670 | + | 0.953728i | \(0.597210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.08946 | + | 24.8843i | −0.498100 | + | 1.36365i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.65553 | − | 12.8180i | 0.308995 | − | 0.700324i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.98022i | − | 0.325763i | −0.986646 | − | 0.162882i | \(-0.947921\pi\) | ||
0.986646 | − | 0.162882i | \(-0.0520789\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.0460 | − | 4.25418i | −1.30600 | − | 0.231055i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.95399 | 0.484886 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5136 | + | 0.497225i | 0.999640 | + | 0.0268476i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.91258 | − | 3.29375i | −0.264484 | − | 0.177329i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.3200 | 1.73503 | 0.867514 | − | 0.497412i | \(-0.165716\pi\) | ||||
0.867514 | + | 0.497412i | \(0.165716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.9630i | − | 0.693896i | −0.937884 | − | 0.346948i | \(-0.887218\pi\) | ||
0.937884 | − | 0.346948i | \(-0.112782\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.9373 | − | 9.81760i | −0.904044 | − | 0.524025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 18.4705i | − | 0.983083i | −0.870854 | − | 0.491541i | \(-0.836434\pi\) | ||
0.870854 | − | 0.491541i | \(-0.163566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.60304 | − | 10.4326i | 0.244304 | − | 0.553705i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9553 | − | 4.92931i | 0.738591 | − | 0.260887i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.2434i | − | 1.27952i | −0.768576 | − | 0.639759i | \(-0.779034\pi\) | ||
0.768576 | − | 0.639759i | \(-0.220966\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3807 | 0.967407 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −36.9203 | − | 6.53187i | −1.93781 | − | 0.342834i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.7014 | − | 11.3399i | −1.34527 | − | 0.593556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.55647 | 0.0812468 | 0.0406234 | − | 0.999175i | \(-0.487066\pi\) | ||||
0.0406234 | + | 0.999175i | \(0.487066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.7648 | + | 6.85420i | 0.976856 | + | 0.356815i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.803010 | + | 1.42006i | 0.0416902 | + | 0.0737256i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0453i | 1.14146i | 0.821137 | + | 0.570731i | \(0.193340\pi\) | ||||
−0.821137 | + | 0.570731i | \(0.806660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.87686 | − | 19.1500i | −0.148560 | − | 0.988903i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 25.5149i | − | 1.31408i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.42384 | −0.484070 | −0.242035 | − | 0.970268i | \(-0.577815\pi\) | ||||
−0.242035 | + | 0.970268i | \(0.577815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.85158 | + | 21.7704i | −0.197322 | + | 1.11533i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 27.3334i | − | 1.39667i | −0.715771 | − | 0.698335i | \(-0.753925\pi\) | ||
0.715771 | − | 0.698335i | \(-0.246075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −33.6371 | + | 3.34516i | −1.71430 | + | 0.170485i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.10997 | − | 24.9404i | 0.463086 | − | 1.26779i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.3761i | 0.678195i | 0.940751 | + | 0.339097i | \(0.110122\pi\) | ||||
−0.940751 | + | 0.339097i | \(0.889878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.93217i | 0.249430i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.9931 | − | 5.12940i | −1.46251 | − | 0.258744i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.2919 | − | 11.6004i | −1.32289 | − | 0.583680i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.36101 | −0.469815 | −0.234908 | − | 0.972018i | \(-0.575479\pi\) | ||||
−0.234908 | + | 0.972018i | \(0.575479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.40031 | − | 1.20106i | 0.170228 | − | 0.0601284i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.5115i | − | 1.22405i | −0.790840 | − | 0.612024i | \(-0.790356\pi\) | ||
0.790840 | − | 0.612024i | \(-0.209644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.90415i | 0.294107i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.84122 | − | 18.0785i | −0.439324 | − | 0.898329i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −50.4570 | −2.50106 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0679660i | 0.00336070i | 0.999999 | + | 0.00168035i | \(0.000534872\pi\) | ||||
−0.999999 | + | 0.00168035i | \(0.999465\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1397 | + | 3.74000i | 1.04275 | + | 0.184481i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.31713 | + | 14.7082i | 0.409259 | + | 0.723741i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.47794 | + | 21.4814i | −0.465254 | + | 1.05448i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.39356 | − | 19.1816i | 0.166184 | − | 0.939325i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.7469 | 1.59979 | 0.799896 | − | 0.600138i | \(-0.204888\pi\) | ||||
0.799896 | + | 0.600138i | \(0.204888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8869 | 0.823017 | 0.411508 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411508 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.80182 | − | 4.93285i | 0.0876073 | − | 0.239843i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.9279 | + | 10.8856i | −0.578587 | + | 0.528031i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.2913 | − | 18.8255i | 1.61108 | − | 0.911029i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.49567 | − | 36.7157i | 0.313614 | − | 1.77265i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 29.7369i | − | 1.43238i | −0.697907 | − | 0.716188i | \(-0.745885\pi\) | ||
0.697907 | − | 0.716188i | \(-0.254115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.1503 | −0.728076 | −0.364038 | − | 0.931384i | \(-0.618602\pi\) | ||||
−0.364038 | + | 0.931384i | \(0.618602\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.6064 | − | 21.7852i | 0.700322 | − | 1.04452i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.20176i | 0.0574880i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.26454i | 0.442172i | 0.975254 | + | 0.221086i | \(0.0709602\pi\) | ||||
−0.975254 | + | 0.221086i | \(0.929040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.3411 | + | 13.1897i | −0.778148 | + | 0.628081i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.88820 | −0.279757 | −0.139878 | − | 0.990169i | \(-0.544671\pi\) | ||||
−0.139878 | + | 0.990169i | \(0.544671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.0928 | + | 14.1599i | 1.52134 | + | 0.671243i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.860147 | + | 4.86184i | −0.0406836 | + | 0.229957i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14.4606i | − | 0.682439i | −0.939984 | − | 0.341219i | \(-0.889160\pi\) | ||
0.939984 | − | 0.341219i | \(-0.110840\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.0487i | 1.79164i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.5475 | − | 4.87365i | −1.29429 | − | 0.228984i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.20576 | − | 22.1799i | −0.103407 | − | 1.03981i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.9157i | 0.931617i | 0.884885 | + | 0.465809i | \(0.154236\pi\) | ||||
−0.884885 | + | 0.465809i | \(0.845764\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.41594 | + | 14.5191i | −0.392822 | + | 0.677694i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.4755 | 1.97828 | 0.989142 | − | 0.146966i | \(-0.0469507\pi\) | ||||
0.989142 | + | 0.146966i | \(0.0469507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 34.4952i | − | 1.60313i | −0.597910 | − | 0.801564i | \(-0.704002\pi\) | ||
0.597910 | − | 0.801564i | \(-0.295998\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.37992 | + | 5.04112i | −0.156740 | + | 0.233776i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 5.47336i | − | 0.253277i | −0.991949 | − | 0.126639i | \(-0.959581\pi\) | ||
0.991949 | − | 0.126639i | \(-0.0404188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4298 | − | 8.15975i | 0.666308 | − | 0.376782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.3070 | + | 2.17732i | 0.567075 | + | 0.100326i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.5708 | 2.32525 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.90632 | + | 2.65237i | −0.133351 | + | 0.121699i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.73752 | − | 0.634663i | −0.0795556 | − | 0.0290592i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.9132 | 1.18400 | 0.592001 | − | 0.805937i | \(-0.298338\pi\) | ||||
0.592001 | + | 0.805937i | \(0.298338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 33.2707i | − | 1.51701i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.33080 | − | 6.59867i | −0.106055 | − | 0.300250i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.7445 | + | 6.94672i | 0.714919 | + | 0.315434i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.92087i | − | 0.404243i | −0.979360 | − | 0.202122i | \(-0.935216\pi\) | ||
0.979360 | − | 0.202122i | \(-0.0647836\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.05767 | − | 5.97828i | 0.0478293 | − | 0.270347i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.1241i | 1.63026i | 0.579278 | + | 0.815130i | \(0.303334\pi\) | ||||
−0.579278 | + | 0.815130i | \(0.696666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8721 | −0.985070 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 26.5647 | − | 27.6303i | 1.19399 | − | 1.24189i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.7445 | − | 6.64123i | 0.526811 | − | 0.297900i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.8816 | 1.11385 | 0.556927 | − | 0.830562i | \(-0.311980\pi\) | ||||
0.556927 | + | 0.830562i | \(0.311980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.417509 | − | 2.35990i | 0.0186529 | − | 0.105433i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.3029i | 1.57408i | 0.616902 | + | 0.787040i | \(0.288388\pi\) | ||||
−0.616902 | + | 0.787040i | \(0.711612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.0017 | + | 9.26632i | 0.934565 | + | 0.412346i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.03756 | + | 0.360482i | 0.0904914 | + | 0.0160096i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.6651 | −0.605696 | −0.302848 | − | 0.953039i | \(-0.597938\pi\) | ||||
−0.302848 | + | 0.953039i | \(0.597938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3611 | − | 28.9332i | −0.723771 | − | 1.27993i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.05061 | + | 3.53769i | −0.0905365 | + | 0.156193i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.41247 | + | 3.27051i | 0.326632 | + | 0.144116i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.0022 | 0.439894 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.05613 | + | 17.2743i | −0.134149 | + | 0.758257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.66702 | −0.423520 | −0.211760 | − | 0.977322i | \(-0.567919\pi\) | ||||
−0.211760 | + | 0.977322i | \(0.567919\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.51766 | −0.153817 | −0.0769083 | − | 0.997038i | \(-0.524505\pi\) | ||||
−0.0769083 | + | 0.997038i | \(0.524505\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.8139 | − | 20.2005i | 0.471957 | − | 0.881621i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.06121 | 0.220470 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6679 | −0.898602 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.9963 | − | 6.57349i | −0.780973 | − | 0.285265i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.0888 | −1.08672 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.7063 | − | 7.81231i | −0.765510 | − | 0.337756i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.163682 | − | 0.925186i | 0.00706341 | − | 0.0399247i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.2743 | − | 20.6149i | −1.47630 | − | 0.887948i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.55020 | −0.238622 | −0.119311 | − | 0.992857i | \(-0.538069\pi\) | ||||
−0.119311 | + | 0.992857i | \(0.538069\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.349254 | − | 1.97410i | 0.0149879 | − | 0.0847167i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.0232 | − | 7.51092i | −0.729193 | − | 0.321732i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5496i | 0.707609i | 0.935319 | + | 0.353805i | \(0.115112\pi\) | ||||
−0.935319 | + | 0.353805i | \(0.884888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.8788 | + | 40.7338i | −0.635012 | + | 1.73848i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.32930 | −0.227036 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.7370 | − | 29.5979i | −0.711728 | − | 1.25863i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.0464 | − | 28.4074i | 0.808473 | − | 1.20583i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.7014 | −1.08900 | −0.544501 | − | 0.838760i | \(-0.683281\pi\) | ||||
−0.544501 | + | 0.838760i | \(0.683281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.3458i | 1.41038i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.4738 | − | 5.56829i | −1.32883 | − | 0.235093i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.70532i | 0.0718707i | 0.999354 | + | 0.0359354i | \(0.0114410\pi\) | ||||
−0.999354 | + | 0.0359354i | \(0.988559\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.8427 | + | 12.7259i | 1.21342 | + | 0.535382i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.39825 | − | 23.4020i | 0.184709 | − | 0.982793i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.2249i | 1.51863i | 0.650725 | + | 0.759314i | \(0.274465\pi\) | ||||
−0.650725 | + | 0.759314i | \(0.725535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.2875 | −0.514215 | −0.257107 | − | 0.966383i | \(-0.582769\pi\) | ||||
−0.257107 | + | 0.966383i | \(0.582769\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.27567 | − | 18.5152i | 0.136843 | − | 0.773483i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.14721 | + | 5.64003i | 0.214653 | + | 0.235205i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.9917 | −0.832265 | −0.416132 | − | 0.909304i | \(-0.636615\pi\) | ||||
−0.416132 | + | 0.909304i | \(0.636615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.43527 | − | 42.0266i | 0.308999 | − | 1.74657i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.1825 | + | 13.6747i | −1.00326 | + | 0.567321i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.52311i | − | 0.145912i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.2191 | + | 17.5164i | 0.753266 | + | 0.724215i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.6341i | − | 0.521465i | −0.965411 | − | 0.260733i | \(-0.916036\pi\) | ||
0.965411 | − | 0.260733i | \(-0.0839641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.23320 | 0.0508132 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.38644 | − | 0.952958i | −0.221568 | − | 0.0391995i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.1383i | − | 1.03231i | −0.856496 | − | 0.516153i | \(-0.827364\pi\) | ||
0.856496 | − | 0.516153i | \(-0.172636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.0133 | + | 1.89084i | −0.779468 | + | 0.0775169i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.08742 | + | 6.14645i | −0.0445051 | + | 0.251558i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.03306i | − | 0.287363i | −0.989624 | − | 0.143682i | \(-0.954106\pi\) | ||
0.989624 | − | 0.143682i | \(-0.0458941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.7407i | 1.70264i | 0.524646 | + | 0.851320i | \(0.324198\pi\) | ||||
−0.524646 | + | 0.851320i | \(0.675802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.44910 | + | 17.6558i | −0.262628 | + | 0.718998i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 44.2851 | + | 19.5393i | 1.80045 | + | 0.794387i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.5247 | −1.76661 | −0.883306 | − | 0.468797i | \(-0.844688\pi\) | ||||
−0.883306 | + | 0.468797i | \(0.844688\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.2623 | − | 10.3361i | 1.18577 | − | 0.418840i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.59530i | 0.266817i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.7849i | − | 0.920272i | −0.887849 | − | 0.460136i | \(-0.847801\pi\) | ||
0.887849 | − | 0.460136i | \(-0.152199\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.4215 | − | 14.3625i | −0.863798 | − | 0.579152i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.44461 | 0.339967 | 0.169984 | − | 0.985447i | \(-0.445629\pi\) | ||||
0.169984 | + | 0.985447i | \(0.445629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.1187i | − | 1.13018i | −0.825028 | − | 0.565092i | \(-0.808841\pi\) | ||
0.825028 | − | 0.565092i | \(-0.191159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.86528 | + | 3.97943i | 0.275494 | + | 0.159689i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.4298 | + | 36.1283i | 0.818501 | + | 1.44745i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.27952 | + | 24.8959i | −0.0911807 | + | 0.995834i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.66883 | − | 1.35675i | −0.306264 | − | 0.0541836i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.5207 | −1.13719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.462386 | −0.0184073 | −0.00920365 | − | 0.999958i | \(-0.502930\pi\) | ||||
−0.00920365 | + | 0.999958i | \(0.502930\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.271980 | − | 0.0481181i | −0.0108102 | − | 0.00191252i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.5216 | − | 26.1131i | 0.457219 | − | 1.03627i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5932 | − | 22.6000i | 0.538584 | − | 0.895446i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.24893 | + | 14.3700i | −0.207644 | + | 0.568470i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 38.3510i | − | 1.51477i | −0.652967 | − | 0.757387i | \(-0.726476\pi\) | ||
0.652967 | − | 0.757387i | \(-0.273524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0759 | 0.910024 | 0.455012 | − | 0.890485i | \(-0.349635\pi\) | ||||
0.455012 | + | 0.890485i | \(0.349635\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.0893 | + | 28.4715i | −0.751642 | + | 1.12106i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 28.2861i | − | 1.11204i | −0.831169 | − | 0.556020i | \(-0.812328\pi\) | ||
0.831169 | − | 0.556020i | \(-0.187672\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.4904i | − | 1.43237i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.77132 | + | 2.39178i | −0.265389 | + | 0.0937413i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.6348 | 0.729238 | 0.364619 | − | 0.931157i | \(-0.381199\pi\) | ||||
0.364619 | + | 0.931157i | \(0.381199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.7766 | + | 15.3440i | 1.35883 | + | 0.599540i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.4014 | + | 12.9311i | 1.38114 | + | 0.504488i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.86589i | 0.228503i | 0.993452 | + | 0.114251i | \(0.0364469\pi\) | ||||
−0.993452 | + | 0.114251i | \(0.963553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.13161i | − | 0.238492i | −0.992865 | − | 0.119246i | \(-0.961952\pi\) | ||
0.992865 | − | 0.119246i | \(-0.0380477\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.67166 | − | 20.7535i | 0.142595 | − | 0.805997i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.63273 | + | 0.460717i | −0.179649 | + | 0.0178659i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3421i | 0.400448i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.49445 | − | 1.32590i | −0.289752 | − | 0.0512624i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −82.5945 | −3.18853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.78377i | − | 0.338589i | −0.985565 | − | 0.169295i | \(-0.945851\pi\) | ||
0.985565 | − | 0.169295i | \(-0.0541490\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.52836 | + | 25.3858i | 0.212787 | + | 0.977099i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.7594i | 1.48964i | 0.667264 | + | 0.744822i | \(0.267465\pi\) | ||||
−0.667264 | + | 0.744822i | \(0.732535\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0227 | + | 17.7243i | 0.384635 | + | 0.680194i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.78271 | + | 32.6858i | −0.221594 | + | 1.25252i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.80345 | −0.183799 | −0.0918994 | − | 0.995768i | \(-0.529294\pi\) | ||||
−0.0918994 | + | 0.995768i | \(0.529294\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.3566 | − | 11.1878i | −0.968828 | − | 0.427463i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.379147 | − | 2.14307i | 0.0144654 | − | 0.0817631i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.32310 | 0.0885029 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.9522i | 1.90027i | 0.311836 | + | 0.950136i | \(0.399056\pi\) | ||||
−0.311836 | + | 0.950136i | \(0.600944\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.7397 | − | 7.42387i | 1.69952 | − | 0.282009i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1515 | + | 23.0079i | −0.385067 | + | 0.872738i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.5069i | 0.814632i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.78571 | − | 1.73127i | −0.370130 | − | 0.0654826i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.56829i | 0.0970031i | 0.998823 | + | 0.0485016i | \(0.0154446\pi\) | ||||
−0.998823 | + | 0.0485016i | \(0.984555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.94927 | −0.262097 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.77558 | + | 5.63124i | −0.142197 | + | 0.212085i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.3694 | + | 23.6426i | 0.502807 | + | 0.889172i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.70387 | 0.101546 | 0.0507730 | − | 0.998710i | \(-0.483832\pi\) | ||||
0.0507730 | + | 0.998710i | \(0.483832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.2148 | + | 13.2281i | 1.35816 | + | 0.496094i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.39317i | − | 0.0896248i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.4311 | + | 44.0397i | −0.726681 | + | 1.64699i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.48681 | − | 31.0133i | 0.204909 | − | 1.15821i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.3073 | 0.794627 | 0.397313 | − | 0.917683i | \(-0.369943\pi\) | ||||
0.397313 | + | 0.917683i | \(0.369943\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.71866 | + | 8.34455i | 0.175732 | + | 0.310767i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.46939 | + | 30.9148i | −0.203409 | + | 1.14973i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.0112 | + | 22.8257i | −0.928891 | + | 0.847726i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.9056 | 1.36875 | 0.684377 | − | 0.729129i | \(-0.260074\pi\) | ||||
0.684377 | + | 0.729129i | \(0.260074\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.4195 | + | 23.4290i | 0.497019 | + | 0.867740i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.5850 | 1.05725 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.8436 | 1.17617 | 0.588086 | − | 0.808798i | \(-0.299882\pi\) | ||||
0.588086 | + | 0.808798i | \(0.299882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.5440 | − | 11.5148i | 0.905320 | − | 0.424731i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.7999 | −1.31871 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.76708 | 0.101789 | 0.0508944 | − | 0.998704i | \(-0.483793\pi\) | ||||
0.0508944 | + | 0.998704i | \(0.483793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.894628 | − | 5.05673i | 0.0328650 | − | 0.185764i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.7284 | −1.38412 | −0.692060 | − | 0.721840i | \(-0.743297\pi\) | ||||
−0.692060 | + | 0.721840i | \(0.743297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.57303 | − | 5.83167i | 0.0942686 | − | 0.213656i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.8079 | − | 29.5887i | 0.395439 | − | 1.08260i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.2715 | − | 19.9328i | −0.411853 | − | 0.728328i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.7810 | 0.393403 | 0.196701 | − | 0.980463i | \(-0.436977\pi\) | ||||
0.196701 | + | 0.980463i | \(0.436977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.02133 | + | 0.180692i | 0.0372194 | + | 0.00658478i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.0426 | + | 14.5790i | 1.20254 | + | 0.530583i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.0222i | − | 0.800409i | −0.916426 | − | 0.400205i | \(-0.868939\pi\) | ||
0.916426 | − | 0.400205i | \(-0.131061\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.63293 | + | 14.8822i | −0.0955694 | + | 0.540190i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.133605 | −0.00484319 | −0.00242160 | − | 0.999997i | \(-0.500771\pi\) | ||||
−0.00242160 | + | 0.999997i | \(0.500771\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8367 | − | 19.1638i | −0.392314 | − | 0.693775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.0156 | − | 15.6179i | 0.542890 | − | 0.564668i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0613 | 0.868805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.2686i | 0.947269i | 0.880722 | + | 0.473634i | \(0.157058\pi\) | ||||
−0.880722 | + | 0.473634i | \(0.842942\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.64899 | − | 26.2777i | 0.167429 | − | 0.946367i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.91789i | 0.176884i | 0.996081 | + | 0.0884422i | \(0.0281889\pi\) | ||||
−0.996081 | + | 0.0884422i | \(0.971811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.78760 | − | 5.28188i | 0.207897 | − | 0.189731i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38.1574 | − | 13.4780i | 1.36889 | − | 0.483521i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.24032i | 0.187754i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.1376 | −1.04263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.6471 | + | 30.4447i | −0.630656 | + | 1.08800i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.7619 | − | 6.51322i | −0.526876 | − | 0.232467i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2704 | −0.758207 | −0.379104 | − | 0.925354i | \(-0.623768\pi\) | ||||
−0.379104 | + | 0.925354i | \(0.623768\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.4808 | + | 2.91575i | 0.586732 | + | 0.103803i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.3608 | + | 32.4695i | 0.652835 | + | 1.15448i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 54.4618i | − | 1.93400i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.98352 | + | 1.32989i | 0.0703482 | + | 0.0471664i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.3045i | 0.967175i | 0.875296 | + | 0.483588i | \(0.160667\pi\) | ||||
−0.875296 | + | 0.483588i | \(0.839333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.65369 | 0.200013 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.2051 | − | 16.1468i | −1.56191 | − | 0.570518i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 71.7822i | 2.53314i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.894073 | + | 8.99032i | 0.0315119 | + | 0.316867i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.5812 | + | 3.99503i | 0.794896 | + | 0.140632i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.9979i | 1.33593i | 0.744191 | + | 0.667967i | \(0.232835\pi\) | ||||
−0.744191 | + | 0.667967i | \(0.767165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.6063i | 1.63657i | 0.574813 | + | 0.818285i | \(0.305075\pi\) | ||||
−0.574813 | + | 0.818285i | \(0.694925\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.71844 | + | 26.6702i | −0.165483 | + | 0.935364i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.16389 | + | 7.17082i | −0.110826 | + | 0.251183i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.96495 | 0.243673 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.89521 | + | 29.5009i | 0.171052 | + | 1.03084i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 13.3057i | − | 0.464371i | −0.972672 | − | 0.232185i | \(-0.925412\pi\) | ||
0.972672 | − | 0.232185i | \(-0.0745876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.85875i | 0.239081i | 0.992829 | + | 0.119541i | \(0.0381421\pi\) | ||||
−0.992829 | + | 0.119541i | \(0.961858\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −41.8020 | + | 26.4786i | −1.45536 | + | 0.921867i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.9117 | −0.622852 | −0.311426 | − | 0.950270i | \(-0.600807\pi\) | ||||
−0.311426 | + | 0.950270i | \(0.600807\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 45.4320i | − | 1.57792i | −0.614445 | − | 0.788960i | \(-0.710620\pi\) | ||
0.614445 | − | 0.788960i | \(-0.289380\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.05165 | − | 5.94430i | 0.0364815 | − | 0.206205i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.3734 | − | 11.6525i | −0.671250 | − | 0.403736i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.24893 | + | 2.83065i | −0.0432210 | + | 0.0979587i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.08355 | − | 7.04491i | 0.141148 | − | 0.243508i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.18091 | −0.282436 | −0.141218 | − | 0.989979i | \(-0.545102\pi\) | ||||
−0.141218 | + | 0.989979i | \(0.545102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.8629 | −0.581478 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.46673 | + | 36.5521i | −0.222726 | + | 1.25892i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.44401 | − | 1.07834i | −0.0840766 | − | 0.0370960i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.1912 | + | 49.8537i | 0.968660 | + | 1.71299i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5974 | + | 2.40563i | 0.466663 | + | 0.0825611i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.4858i | 0.462288i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.25962 | −0.0431287 | −0.0215644 | − | 0.999767i | \(-0.506865\pi\) | ||||
−0.0215644 | + | 0.999767i | \(0.506865\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.65866 | − | 3.80543i | 0.125124 | − | 0.130143i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 0.221305i | − | 0.00755962i | −0.999993 | − | 0.00377981i | \(-0.998797\pi\) | ||
0.999993 | − | 0.00377981i | \(-0.00120315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.2694i | − | 0.828062i | −0.910263 | − | 0.414031i | \(-0.864120\pi\) | ||
0.910263 | − | 0.414031i | \(-0.135880\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.1635 | − | 28.7738i | −0.346372 | − | 0.980607i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.515972 | 0.0175639 | 0.00878194 | − | 0.999961i | \(-0.497205\pi\) | ||||
0.00878194 | + | 0.999961i | \(0.497205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.14207 | − | 20.7201i | 0.310840 | − | 0.704506i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.2041 | + | 1.98221i | 0.380512 | + | 0.0673194i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 73.4314i | 2.49099i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 23.6060i | − | 0.799860i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.6867 | − | 7.92147i | −0.733982 | − | 0.268101i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.7688 | + | 22.0045i | −0.668306 | + | 0.743886i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 45.4080i | − | 1.53332i | −0.642053 | − | 0.766660i | \(-0.721917\pi\) | ||
0.642053 | − | 0.766660i | \(-0.278083\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.88430 | + | 21.9553i | −0.131014 | + | 0.740535i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.6497 | 1.03262 | 0.516308 | − | 0.856403i | \(-0.327306\pi\) | ||||
0.516308 | + | 0.856403i | \(0.327306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1004i | 0.676433i | 0.941068 | + | 0.338217i | \(0.109824\pi\) | ||||
−0.941068 | + | 0.338217i | \(0.890176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.5442 | + | 13.7743i | 0.690586 | + | 0.463018i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.4432i | 1.29080i | 0.763846 | + | 0.645398i | \(0.223309\pi\) | ||||
−0.763846 | + | 0.645398i | \(0.776691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.3967 | − | 16.6232i | 0.985934 | − | 0.557524i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.1448 | + | 39.3170i | −1.11039 | + | 1.31717i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.37756 | 0.0460984 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.489636 | + | 1.10974i | −0.0163667 | + | 0.0370945i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.81315 | − | 1.73612i | −0.327652 | − | 0.0579675i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.6127 | 0.353953 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.99143i | − | 0.0663440i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38.2435 | + | 13.5084i | −1.27266 | + | 0.449533i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.04475 | + | 2.36789i | −0.0347288 | + | 0.0787113i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.7121i | − | 0.787346i | −0.919251 | − | 0.393673i | \(-0.871204\pi\) | ||
0.919251 | − | 0.393673i | \(-0.128796\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.9281 | − | 10.5665i | −0.959485 | − | 0.350470i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.4931i | 1.17594i | 0.808883 | + | 0.587970i | \(0.200073\pi\) | ||||
−0.808883 | + | 0.587970i | \(0.799927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.9960 | 1.98558 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.1775 | − | 46.5009i | 1.03070 | − | 1.53727i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.1382 | + | 39.1496i | 0.731068 | + | 1.29283i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.0530 | −1.35421 | −0.677106 | − | 0.735885i | \(-0.736766\pi\) | ||||
−0.677106 | + | 0.735885i | \(0.736766\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.2205 | + | 2.16203i | 0.402679 | + | 0.0712412i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 19.2130i | − | 0.632403i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.6139 | + | 29.7642i | −1.07234 | + | 0.978640i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.2101 | − | 3.72942i | −0.335342 | − | 0.122490i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.1710 | 0.563362 | 0.281681 | − | 0.959508i | \(-0.409108\pi\) | ||||
0.281681 | + | 0.959508i | \(0.409108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.72048 | − | 2.83923i | −0.154708 | − | 0.0930519i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 58.7882 | + | 10.4007i | 1.92464 | + | 0.340503i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 37.7522 | + | 16.6569i | 1.23463 | + | 0.544739i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.1075 | −0.689550 | −0.344775 | − | 0.938685i | \(-0.612045\pi\) | ||||
−0.344775 | + | 0.938685i | \(0.612045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.7087 | + | 8.61745i | 1.58955 | + | 0.281220i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.7526 | 0.969908 | 0.484954 | − | 0.874540i | \(-0.338836\pi\) | ||||
0.484954 | + | 0.874540i | \(0.338836\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1694 | 0.331162 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.7086 | + | 27.9909i | −0.413410 | + | 0.910545i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4259 | −0.501274 | −0.250637 | − | 0.968081i | \(-0.580640\pi\) | ||||
−0.250637 | + | 0.968081i | \(0.580640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.3323 | −1.53647 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −35.7842 | − | 6.33088i | −1.16038 | − | 0.205293i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.6225 | 1.41307 | 0.706535 | − | 0.707678i | \(-0.250257\pi\) | ||||
0.706535 | + | 0.707678i | \(0.250257\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.79880 | + | 22.2086i | −0.317082 | + | 0.718653i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −65.9964 | − | 11.6760i | −2.13336 | − | 0.377430i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.1416 | − | 28.5451i | −0.521240 | − | 0.921770i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5442 | 0.920781 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.3889 | + | 8.90852i | 0.785922 | + | 0.287073i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.2418 | + | 50.4100i | −0.715988 | + | 1.62276i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.6963i | − | 1.08360i | −0.840508 | − | 0.541799i | \(-0.817743\pi\) | ||
0.840508 | − | 0.541799i | \(-0.182257\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.33478 | − | 0.766902i | −0.139253 | − | 0.0246364i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.74825 | −0.280745 | −0.140372 | − | 0.990099i | \(-0.544830\pi\) | ||||
−0.140372 | + | 0.990099i | \(0.544830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.9010 | + | 14.6464i | −0.830348 | + | 0.469543i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.4597 | − | 27.5637i | −0.559157 | − | 0.882746i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.2690 | 1.41629 | 0.708145 | − | 0.706067i | \(-0.249532\pi\) | ||||
0.708145 | + | 0.706067i | \(0.249532\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 89.6331i | − | 2.86469i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.4480 | + | 8.56483i | 0.748637 | + | 0.273454i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.9368i | 1.21000i | 0.796227 | + | 0.604998i | \(0.206826\pi\) | ||||
−0.796227 | + | 0.604998i | \(0.793174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.46092 | + | 2.85067i | 0.205862 | + | 0.0908298i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.56398 | + | 2.67177i | −0.240764 | + | 0.0850432i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 13.5163i | − | 0.429792i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7568 | 1.45351 | 0.726757 | − | 0.686895i | \(-0.241027\pi\) | ||||
0.726757 | + | 0.686895i | \(0.241027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.6596 | − | 3.30122i | −0.592145 | − | 0.104761i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.25289 | − | 7.37254i | 0.103124 | − | 0.233725i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.7188 | 1.13122 | 0.565612 | − | 0.824671i | \(-0.308640\pi\) | ||||
0.565612 | + | 0.824671i | \(0.308640\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.0114 | + | 39.6991i | −0.728048 | + | 1.25602i |
(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 | 1680.2.k.h.209.24 | 24 | ||
3.2 | odd | 2 | 1680.2.k.i.209.23 | 24 | |||
4.3 | odd | 2 | 840.2.k.b.209.1 | yes | 24 | ||
5.4 | even | 2 | 1680.2.k.i.209.1 | 24 | |||
7.6 | odd | 2 | inner | 1680.2.k.h.209.1 | 24 | ||
12.11 | even | 2 | 840.2.k.a.209.2 | yes | 24 | ||
15.14 | odd | 2 | inner | 1680.2.k.h.209.2 | 24 | ||
20.19 | odd | 2 | 840.2.k.a.209.24 | yes | 24 | ||
21.20 | even | 2 | 1680.2.k.i.209.2 | 24 | |||
28.27 | even | 2 | 840.2.k.b.209.24 | yes | 24 | ||
35.34 | odd | 2 | 1680.2.k.i.209.24 | 24 | |||
60.59 | even | 2 | 840.2.k.b.209.23 | yes | 24 | ||
84.83 | odd | 2 | 840.2.k.a.209.23 | yes | 24 | ||
105.104 | even | 2 | inner | 1680.2.k.h.209.23 | 24 | ||
140.139 | even | 2 | 840.2.k.a.209.1 | ✓ | 24 | ||
420.419 | odd | 2 | 840.2.k.b.209.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.k.a.209.1 | ✓ | 24 | 140.139 | even | 2 | ||
840.2.k.a.209.2 | yes | 24 | 12.11 | even | 2 | ||
840.2.k.a.209.23 | yes | 24 | 84.83 | odd | 2 | ||
840.2.k.a.209.24 | yes | 24 | 20.19 | odd | 2 | ||
840.2.k.b.209.1 | yes | 24 | 4.3 | odd | 2 | ||
840.2.k.b.209.2 | yes | 24 | 420.419 | odd | 2 | ||
840.2.k.b.209.23 | yes | 24 | 60.59 | even | 2 | ||
840.2.k.b.209.24 | yes | 24 | 28.27 | even | 2 | ||
1680.2.k.h.209.1 | 24 | 7.6 | odd | 2 | inner | ||
1680.2.k.h.209.2 | 24 | 15.14 | odd | 2 | inner | ||
1680.2.k.h.209.23 | 24 | 105.104 | even | 2 | inner | ||
1680.2.k.h.209.24 | 24 | 1.1 | even | 1 | trivial | ||
1680.2.k.i.209.1 | 24 | 5.4 | even | 2 | |||
1680.2.k.i.209.2 | 24 | 21.20 | even | 2 | |||
1680.2.k.i.209.23 | 24 | 3.2 | odd | 2 | |||
1680.2.k.i.209.24 | 24 | 35.34 | odd | 2 |