Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [668,2,Mod(667,668)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(668, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("668.667");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 668 = 2^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 668.b (of order \(2\), degree \(1\), 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: | \(5.33400685502\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 667.18 | ||
Character | \(\chi\) | \(=\) | 668.667 |
Dual form | 668.2.b.a.667.17 |
$q$-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 \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(335\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.06600 | + | 0.929330i | 0.753773 | + | 0.657135i | ||||
\(3\) | 2.77291i | 1.60094i | 0.599372 | + | 0.800470i | \(0.295417\pi\) | ||||
−0.599372 | + | 0.800470i | \(0.704583\pi\) | |||||||
\(4\) | 0.272692 | + | 1.98132i | 0.136346 | + | 0.990661i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | −2.57695 | + | 2.95591i | −1.05203 | + | 1.20675i | ||||
\(7\) | 0.0155204i | 0.00586616i | 0.999996 | + | 0.00293308i | \(0.000933630\pi\) | ||||
−0.999996 | + | 0.00293308i | \(0.999066\pi\) | |||||||
\(8\) | −1.55061 | + | 2.36550i | −0.548225 | + | 0.836331i | ||||
\(9\) | −4.68903 | −1.56301 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.605002i | 0.182415i | 0.995832 | + | 0.0912075i | \(0.0290727\pi\) | ||||
−0.995832 | + | 0.0912075i | \(0.970927\pi\) | |||||||
\(12\) | −5.49403 | + | 0.756151i | −1.58599 | + | 0.218282i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −0.0144236 | + | 0.0165447i | −0.00385486 | + | 0.00442175i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.85128 | + | 1.08058i | −0.962820 | + | 0.270146i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −4.99849 | − | 4.35766i | −1.17815 | − | 1.02711i | ||||
\(19\) | − | 3.70465i | − | 0.849905i | −0.905216 | − | 0.424952i | \(-0.860291\pi\) | ||
0.905216 | − | 0.424952i | \(-0.139709\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0430367 | −0.00939138 | ||||||||
\(22\) | −0.562247 | + | 0.644930i | −0.119871 | + | 0.137499i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −6.55932 | − | 4.29971i | −1.33892 | − | 0.877675i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.68354i | − | 0.901347i | ||||||
\(28\) | −0.0307509 | + | 0.00423229i | −0.00581138 | + | 0.000799828i | ||||
\(29\) | 4.56421 | 0.847552 | 0.423776 | − | 0.905767i | \(-0.360704\pi\) | ||||
0.423776 | + | 0.905767i | \(0.360704\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.0698i | 1.98820i | 0.108465 | + | 0.994100i | \(0.465406\pi\) | ||||
−0.108465 | + | 0.994100i | \(0.534594\pi\) | |||||||
\(32\) | −5.10966 | − | 2.42721i | −0.903269 | − | 0.429075i | ||||
\(33\) | −1.67762 | −0.292036 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.27866 | − | 9.29049i | −0.213110 | − | 1.54841i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 3.44284 | − | 3.94914i | 0.558502 | − | 0.640635i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | −0.0458769 | − | 0.0399953i | −0.00707896 | − | 0.00617141i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −1.19870 | + | 0.164979i | −0.180712 | + | 0.0248716i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.81007i | − | 1.13922i | −0.821917 | − | 0.569608i | \(-0.807095\pi\) | ||
0.821917 | − | 0.569608i | \(-0.192905\pi\) | |||||||
\(48\) | −2.99636 | − | 10.6792i | −0.432487 | − | 1.54142i | ||||
\(49\) | 6.99976 | 0.999966 | ||||||||
\(50\) | 5.32998 | + | 4.64665i | 0.753773 | + | 0.657135i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 4.35255 | − | 4.99263i | 0.592307 | − | 0.679411i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0367135 | − | 0.0240662i | −0.00490605 | − | 0.00321597i | ||||
\(57\) | 10.2727 | 1.36065 | ||||||||
\(58\) | 4.86542 | + | 4.24165i | 0.638861 | + | 0.556956i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.17625 | −1.17490 | −0.587449 | − | 0.809261i | \(-0.699868\pi\) | ||||
−0.587449 | + | 0.809261i | \(0.699868\pi\) | |||||||
\(62\) | −10.2875 | + | 11.8004i | −1.30652 | + | 1.49865i | ||||
\(63\) | − | 0.0727757i | − | 0.00916888i | ||||||
\(64\) | −3.19119 | − | 7.33596i | −0.398899 | − | 0.916995i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.78833 | − | 1.55906i | −0.220128 | − | 0.191907i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 7.27088 | − | 11.0919i | 0.856881 | − | 1.30719i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.8646i | 1.60094i | ||||||||
\(76\) | 7.34010 | − | 1.01023i | 0.841968 | − | 0.115881i | ||||
\(77\) | −0.00938988 | −0.00107008 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.08007 | −0.120007 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −0.0117358 | − | 0.0852696i | −0.00128048 | − | 0.00930367i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.6561i | 1.35688i | ||||||||
\(88\) | −1.43113 | − | 0.938125i | −0.152559 | − | 0.100004i | ||||
\(89\) | 5.02368 | 0.532509 | 0.266254 | − | 0.963903i | \(-0.414214\pi\) | ||||
0.266254 | + | 0.963903i | \(0.414214\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −30.6957 | −3.18299 | ||||||||
\(94\) | 7.25813 | − | 8.32549i | 0.748619 | − | 0.858709i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.73044 | − | 14.1686i | 0.686923 | − | 1.44608i | ||||
\(97\) | 18.7260 | 1.90134 | 0.950670 | − | 0.310203i | \(-0.100397\pi\) | ||||
0.950670 | + | 0.310203i | \(0.100397\pi\) | |||||||
\(98\) | 7.46171 | + | 6.50508i | 0.753747 | + | 0.657113i | ||||
\(99\) | − | 2.83688i | − | 0.285117i | ||||||
\(100\) | 1.36346 | + | 9.90661i | 0.136346 | + | 0.990661i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.5574i | 1.89068i | 0.326081 | + | 0.945342i | \(0.394272\pi\) | ||||
−0.326081 | + | 0.945342i | \(0.605728\pi\) | |||||||
\(108\) | 9.27960 | − | 1.27716i | 0.892930 | − | 0.122895i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0167711 | − | 0.0597734i | −0.00158472 | − | 0.00564805i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 10.9506 | + | 9.54669i | 1.02562 | + | 0.894129i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.24462 | + | 9.04317i | 0.115560 | + | 0.839637i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6340 | 0.966725 | ||||||||
\(122\) | −9.78184 | − | 8.52776i | −0.885606 | − | 0.772068i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −21.9329 | + | 3.01866i | −1.96963 | + | 0.271083i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0676326 | − | 0.0775786i | 0.00602519 | − | 0.00691125i | ||||
\(127\) | 14.0356i | 1.24546i | 0.782438 | + | 0.622728i | \(0.213976\pi\) | ||||
−0.782438 | + | 0.622728i | \(0.786024\pi\) | |||||||
\(128\) | 3.41573 | − | 10.7858i | 0.301910 | − | 0.953336i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −0.457473 | − | 3.32390i | −0.0398179 | − | 0.289308i | ||||
\(133\) | 0.0574976 | 0.00498568 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.33330 | −0.284783 | −0.142391 | − | 0.989810i | \(-0.545479\pi\) | ||||
−0.142391 | + | 0.989810i | \(0.545479\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.6566 | 1.82382 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 18.0588 | − | 5.06689i | 1.50490 | − | 0.422240i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.4097i | 1.60089i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | −12.8847 | + | 14.7795i | −1.05203 | + | 1.20675i | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 8.76335 | + | 5.74448i | 0.710802 | + | 0.465939i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0100096 | − | 0.00872630i | −0.000806594 | − | 0.000703185i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5841 | −0.924514 | −0.462257 | − | 0.886746i | \(-0.652960\pi\) | ||||
−0.462257 | + | 0.886746i | \(0.652960\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.15135 | − | 1.00374i | −0.0904583 | − | 0.0788611i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.9228i | − | 1.00000i | ||||||
\(168\) | 0.0667333 | − | 0.101803i | 0.00514858 | − | 0.00785430i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.3712i | 1.32841i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.87791 | −0.751003 | −0.375502 | − | 0.926822i | \(-0.622530\pi\) | ||||
−0.375502 | + | 0.926822i | \(0.622530\pi\) | |||||||
\(174\) | −11.7617 | + | 13.4914i | −0.891654 | + | 1.02278i | ||||
\(175\) | 0.0776020i | 0.00586616i | ||||||||
\(176\) | −0.653755 | − | 2.33003i | −0.0492786 | − | 0.175633i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.35522 | + | 4.66865i | 0.401391 | + | 0.349930i | ||||
\(179\) | − | 26.7341i | − | 1.99820i | −0.0424302 | − | 0.999099i | \(-0.513510\pi\) | ||
0.0424302 | − | 0.999099i | \(-0.486490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7159 | 0.796505 | 0.398252 | − | 0.917276i | \(-0.369617\pi\) | ||||
0.398252 | + | 0.917276i | \(0.369617\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 25.4449i | − | 1.88094i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −32.7214 | − | 28.5264i | −2.39925 | − | 2.09166i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 15.4743 | − | 2.12974i | 1.12858 | − | 0.155328i | ||||
\(189\) | 0.0726904 | 0.00528745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.3402i | − | 1.32705i | −0.748153 | − | 0.663526i | \(-0.769059\pi\) | ||
0.748153 | − | 0.663526i | \(-0.230941\pi\) | |||||||
\(192\) | 20.3420 | − | 8.84890i | 1.46805 | − | 0.638614i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 19.9619 | + | 17.4027i | 1.43318 | + | 1.24944i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.90878 | + | 13.8688i | 0.136341 | + | 0.990627i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 2.63639 | − | 3.02410i | 0.187360 | − | 0.214913i | ||||
\(199\) | − | 17.6656i | − | 1.25228i | −0.779711 | − | 0.626140i | \(-0.784634\pi\) | ||
0.779711 | − | 0.626140i | \(-0.215366\pi\) | |||||||
\(200\) | −7.75307 | + | 11.8275i | −0.548225 | + | 0.836331i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0708383i | 0.00497188i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.24132 | 0.155035 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.2341i | − | 0.773386i | −0.922208 | − | 0.386693i | \(-0.873617\pi\) | ||
0.922208 | − | 0.386693i | \(-0.126383\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.1753 | + | 20.8481i | −1.24244 | + | 1.42515i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.0789 | + | 7.26236i | 0.753825 | + | 0.494141i | ||||
\(217\) | −0.171808 | −0.0116631 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.9634i | − | 1.13595i | −0.823045 | − | 0.567976i | \(-0.807727\pi\) | ||
0.823045 | − | 0.567976i | \(-0.192273\pi\) | |||||||
\(224\) | 0.0376713 | − | 0.0793040i | 0.00251702 | − | 0.00529872i | ||||
\(225\) | −23.4452 | −1.56301 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 2.80127 | + | 20.3535i | 0.185519 | + | 1.34794i | ||||
\(229\) | 7.47330 | 0.493850 | 0.246925 | − | 0.969035i | \(-0.420580\pi\) | ||||
0.246925 | + | 0.969035i | \(0.420580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.0260373i | − | 0.00171313i | ||||||
\(232\) | −7.07732 | + | 10.7966i | −0.464649 | + | 0.708834i | ||||
\(233\) | −7.88743 | −0.516722 | −0.258361 | − | 0.966048i | \(-0.583182\pi\) | ||||
−0.258361 | + | 0.966048i | \(0.583182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.4176i | 0.738541i | 0.929322 | + | 0.369271i | \(0.120392\pi\) | ||||
−0.929322 | + | 0.369271i | \(0.879608\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 11.3358 | + | 9.88247i | 0.728691 | + | 0.635269i | ||||
\(243\) | − | 17.0455i | − | 1.09347i | ||||||
\(244\) | −2.50229 | − | 18.1811i | −0.160193 | − | 1.16393i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −26.1857 | − | 17.1650i | −1.66279 | − | 1.08998i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.4643i | − | 1.22857i | −0.789083 | − | 0.614287i | \(-0.789444\pi\) | ||
0.789083 | − | 0.614287i | \(-0.210556\pi\) | |||||||
\(252\) | 0.144192 | − | 0.0198454i | 0.00908325 | − | 0.00125014i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.0437 | + | 14.9619i | −0.818433 | + | 0.938790i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.6647 | − | 8.32324i | 0.854043 | − | 0.520203i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.4017 | −1.32473 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.0550i | − | 1.72995i | −0.501817 | − | 0.864974i | \(-0.667335\pi\) | ||
0.501817 | − | 0.864974i | \(-0.332665\pi\) | |||||||
\(264\) | 2.60134 | − | 3.96841i | 0.160101 | − | 0.244238i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0612922 | + | 0.0534343i | 0.00375807 | + | 0.00327627i | ||||
\(267\) | 13.9302i | 0.852515i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.55328 | − | 3.09773i | −0.214661 | − | 0.187141i | ||||
\(275\) | 3.02501i | 0.182415i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 51.9068i | − | 3.10758i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.9391 | 1.78602 | 0.893009 | − | 0.450039i | \(-0.148590\pi\) | ||||
0.893009 | + | 0.450039i | \(0.148590\pi\) | |||||||
\(282\) | 23.0859 | + | 20.1261i | 1.37474 | + | 1.19849i | ||||
\(283\) | 29.8862i | 1.77655i | 0.459314 | + | 0.888274i | \(0.348095\pi\) | ||||
−0.459314 | + | 0.888274i | \(0.651905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 23.9594 | + | 11.3813i | 1.41182 | + | 0.670648i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 51.9256i | 3.04393i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −33.4713 | −1.95542 | −0.977708 | − | 0.209971i | \(-0.932663\pi\) | ||||
−0.977708 | + | 0.209971i | \(0.932663\pi\) | |||||||
\(294\) | −18.0380 | + | 20.6907i | −1.05200 | + | 1.20670i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.83355 | 0.164419 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −27.4702 | + | 3.78075i | −1.58599 | + | 0.218282i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00318 | + | 14.2676i | 0.229598 | + | 0.818305i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −0.00256055 | − | 0.0186044i | −0.000145901 | − | 0.00106008i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 25.8457i | − | 1.46557i | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||
0.680458 | − | 0.732787i | \(-0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | −12.3486 | − | 10.7655i | −0.696873 | − | 0.607531i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.43404 | 0.417537 | 0.208769 | − | 0.977965i | \(-0.433054\pi\) | ||||
0.208769 | + | 0.977965i | \(0.433054\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.76136i | 0.154606i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −54.2309 | −3.02687 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.294526 | − | 2.13996i | −0.0163625 | − | 0.118887i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.121215 | 0.00668282 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0096 | − | 13.7757i | 0.657135 | − | 0.753773i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.165746 | − | 0.0465047i | 0.00904220 | − | 0.00253704i | ||||
\(337\) | 36.6331 | 1.99553 | 0.997765 | − | 0.0668248i | \(-0.0212868\pi\) | ||||
0.997765 | + | 0.0668248i | \(0.0212868\pi\) | |||||||
\(338\) | 13.8579 | + | 12.0813i | 0.753773 | + | 0.657135i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.69727 | −0.362678 | ||||||||
\(342\) | −16.1436 | + | 18.5176i | −0.872946 | + | 1.00132i | ||||
\(343\) | 0.217282i | 0.0117321i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.5298 | − | 9.17983i | −0.566086 | − | 0.493511i | ||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | −25.0759 | + | 3.45123i | −1.34421 | + | 0.185005i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | −0.0721179 | + | 0.0827234i | −0.00385486 | + | 0.00442175i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.46847 | − | 3.09136i | 0.0782696 | − | 0.164770i | ||||
\(353\) | −36.3131 | −1.93275 | −0.966375 | − | 0.257136i | \(-0.917221\pi\) | ||||
−0.966375 | + | 0.257136i | \(0.917221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.36992 | + | 9.95353i | 0.0726055 | + | 0.527536i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.8448 | − | 28.4984i | 1.31309 | − | 1.50619i | ||||
\(359\) | − | 3.47094i | − | 0.183189i | −0.995796 | − | 0.0915946i | \(-0.970804\pi\) | ||
0.995796 | − | 0.0915946i | \(-0.0291964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.27558 | 0.277662 | ||||||||
\(362\) | 11.4231 | + | 9.95858i | 0.600383 | + | 0.523411i | ||||
\(363\) | 29.4871i | 1.54767i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 23.6467 | − | 27.1242i | 1.23603 | − | 1.41780i | ||||
\(367\) | 38.2488i | 1.99657i | 0.0585343 | + | 0.998285i | \(0.481357\pi\) | ||||
−0.0585343 | + | 0.998285i | \(0.518643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.37046 | − | 60.8180i | −0.433988 | − | 3.15327i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.4747 | + | 12.1104i | 0.952761 | + | 0.624546i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.0774876 | + | 0.0675534i | 0.00398553 | + | 0.00347457i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.9194 | −1.99390 | ||||||||
\(382\) | 17.0441 | − | 19.5506i | 0.872053 | − | 1.00030i | ||||
\(383\) | − | 39.0682i | − | 1.99629i | −0.0608672 | − | 0.998146i | \(-0.519387\pi\) | ||
0.0608672 | − | 0.998146i | \(-0.480613\pi\) | |||||||
\(384\) | 29.9080 | + | 9.47150i | 1.52623 | + | 0.483341i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.10644 | + | 37.1023i | 0.259240 | + | 1.88358i | ||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −10.8539 | + | 16.5579i | −0.548206 | + | 0.836302i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.62077 | − | 0.773594i | 0.282454 | − | 0.0388745i | ||||
\(397\) | −34.0917 | −1.71101 | −0.855507 | − | 0.517792i | \(-0.826754\pi\) | ||||
−0.855507 | + | 0.517792i | \(0.826754\pi\) | |||||||
\(398\) | 16.4172 | − | 18.8314i | 0.822918 | − | 0.943934i | ||||
\(399\) | 0.159436i | 0.00798177i | ||||||||
\(400\) | −19.2564 | + | 5.40291i | −0.962820 | + | 0.270146i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0658322 | + | 0.0755133i | −0.00326720 | + | 0.00374766i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3630 | 0.710203 | 0.355101 | − | 0.934828i | \(-0.384446\pi\) | ||||
0.355101 | + | 0.934828i | \(0.384446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 9.24293i | − | 0.455920i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.38924 | + | 2.08293i | 0.116861 | + | 0.101879i | ||||
\(419\) | − | 40.6441i | − | 1.98560i | −0.119801 | − | 0.992798i | \(-0.538226\pi\) | ||
0.119801 | − | 0.992798i | \(-0.461774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.6392 | 1.39579 | 0.697895 | − | 0.716200i | \(-0.254120\pi\) | ||||
0.697895 | + | 0.716200i | \(0.254120\pi\) | |||||||
\(422\) | 10.4402 | − | 11.9755i | 0.508219 | − | 0.582957i | ||||
\(423\) | 36.6217i | 1.78061i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.142419i | − | 0.00689215i | ||||||
\(428\) | −38.7495 | + | 5.33314i | −1.87303 | + | 0.257787i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.21990i | 0.251434i | 0.992066 | + | 0.125717i | \(0.0401231\pi\) | ||||
−0.992066 | + | 0.125717i | \(0.959877\pi\) | |||||||
\(432\) | 5.06095 | + | 18.0376i | 0.243495 | + | 0.867835i | ||||
\(433\) | −26.4989 | −1.27345 | −0.636727 | − | 0.771090i | \(-0.719712\pi\) | ||||
−0.636727 | + | 0.771090i | \(0.719712\pi\) | |||||||
\(434\) | −0.183147 | − | 0.159667i | −0.00879133 | − | 0.00766424i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.8221 | −1.56296 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.7646 | − | 18.0829i | 0.746475 | − | 0.856250i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.113857 | − | 0.0495286i | 0.00537924 | − | 0.00234001i | ||||
\(449\) | −40.0111 | −1.88824 | −0.944121 | − | 0.329600i | \(-0.893086\pi\) | ||||
−0.944121 | + | 0.329600i | \(0.893086\pi\) | |||||||
\(450\) | −24.9924 | − | 21.7883i | −1.17815 | − | 1.02711i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.9289 | + | 24.3000i | −0.745940 | + | 1.13795i | ||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 7.96650 | + | 6.94516i | 0.372250 | + | 0.324526i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.6062 | −1.28575 | −0.642875 | − | 0.765971i | \(-0.722258\pi\) | ||||
−0.642875 | + | 0.765971i | \(0.722258\pi\) | |||||||
\(462\) | 0.0241972 | − | 0.0277556i | 0.00112576 | − | 0.00129131i | ||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | −17.5780 | + | 4.93200i | −0.816040 | + | 0.228962i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.40796 | − | 7.33002i | −0.389491 | − | 0.339557i | ||||
\(467\) | − | 19.6505i | − | 0.909317i | −0.890666 | − | 0.454658i | \(-0.849761\pi\) | ||
0.890666 | − | 0.454658i | \(-0.150239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 32.1218i | − | 1.48009i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 18.5232i | − | 0.849905i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.6107 | + | 12.1711i | −0.485321 | + | 0.556692i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.89980 | + | 21.0693i | 0.131809 | + | 0.957697i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.8409 | − | 18.1705i | 0.718559 | − | 0.824229i | ||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 14.2288 | − | 21.7064i | 0.644108 | − | 0.982604i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8457i | 1.16640i | 0.812329 | + | 0.583200i | \(0.198200\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.9619 | − | 42.6330i | −0.537103 | − | 1.91428i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.8339 | 1.60094 | ||||||||
\(502\) | 18.0887 | − | 20.7488i | 0.807339 | − | 0.926065i | ||||
\(503\) | 44.6925i | 1.99274i | 0.0851292 | + | 0.996370i | \(0.472870\pi\) | ||||
−0.0851292 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(504\) | 0.172151 | + | 0.112847i | 0.00766822 | + | 0.00502660i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 36.0478i | 1.60094i | ||||||||
\(508\) | −27.8090 | + | 3.82739i | −1.23382 | + | 0.169813i | ||||
\(509\) | −36.3003 | −1.60898 | −0.804492 | − | 0.593964i | \(-0.797562\pi\) | ||||
−0.804492 | + | 0.593964i | \(0.797562\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.3015 | + | 3.82646i | 0.985598 | + | 0.169107i | ||||
\(513\) | −17.3509 | −0.766059 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.72511 | 0.207810 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 27.3906i | − | 1.20231i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | −22.8141 | − | 19.8893i | −0.998547 | − | 0.870529i | ||||
\(523\) | 33.0452i | 1.44497i | 0.691388 | + | 0.722484i | \(0.257000\pi\) | ||||
−0.691388 | + | 0.722484i | \(0.743000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.215183 | −0.00939138 | ||||||||
\(526\) | 26.0724 | − | 29.9065i | 1.13681 | − | 1.30399i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 6.46097 | − | 1.81280i | 0.281178 | − | 0.0788921i | ||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.0156792 | + | 0.113921i | 0.000679778 | + | 0.00493912i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.9458 | + | 14.8495i | −0.560218 | + | 0.642602i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 74.1312 | 3.19900 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.23487i | 0.182409i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.7142i | 1.27516i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | −0.908964 | − | 6.60433i | −0.0388290 | − | 0.282123i | ||||
\(549\) | 43.0278 | 1.83638 | ||||||||
\(550\) | −2.81123 | + | 3.22465i | −0.119871 | + | 0.137499i | ||||
\(551\) | − | 16.9088i | − | 0.720338i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.9669 | 1.82057 | 0.910283 | − | 0.413986i | \(-0.135864\pi\) | ||||
0.910283 | + | 0.413986i | \(0.135864\pi\) | |||||||
\(558\) | 48.2385 | − | 55.3324i | 2.04210 | − | 2.34241i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.9150 | + | 27.8233i | 1.34625 | + | 1.17366i | ||||
\(563\) | 42.3542i | 1.78502i | 0.451030 | + | 0.892509i | \(0.351057\pi\) | ||||
−0.451030 | + | 0.892509i | \(0.648943\pi\) | |||||||
\(564\) | 5.90559 | + | 42.9087i | 0.248670 | + | 1.80678i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.7741 | + | 31.8585i | −1.16743 | + | 1.33911i | ||||
\(567\) | − | 0.0167631i | − | 0.000703983i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 50.8558 | 2.12453 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 14.9636 | + | 34.3986i | 0.623484 | + | 1.43327i | ||||
\(577\) | 18.8310 | 0.783946 | 0.391973 | − | 0.919977i | \(-0.371793\pi\) | ||||
0.391973 | + | 0.919977i | \(0.371793\pi\) | |||||||
\(578\) | 18.1219 | + | 15.7986i | 0.753773 | + | 0.657135i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −48.2560 | + | 55.3525i | −2.00028 | + | 2.29443i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.6803 | − | 31.1059i | −1.47394 | − | 1.28497i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −38.4569 | + | 5.29287i | −1.58594 | + | 0.218274i | ||||
\(589\) | 41.0098 | 1.68978 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 3.02055 | + | 2.63330i | 0.123935 | + | 0.108046i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 48.9851 | 2.00483 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.1613i | 1.60009i | 0.599941 | + | 0.800044i | \(0.295191\pi\) | ||||
−0.599941 | + | 0.800044i | \(0.704809\pi\) | |||||||
\(600\) | −32.7966 | − | 21.4986i | −1.33892 | − | 0.877675i | ||||
\(601\) | −39.2222 | −1.59991 | −0.799953 | − | 0.600063i | \(-0.795142\pi\) | ||||
−0.799953 | + | 0.600063i | \(0.795142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | −8.99197 | + | 18.9295i | −0.364672 | + | 0.767693i | ||||
\(609\) | −0.196428 | −0.00795968 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.4149 | 1.79390 | 0.896951 | − | 0.442131i | \(-0.145777\pi\) | ||||
0.896951 | + | 0.442131i | \(0.145777\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0145601 | − | 0.0222118i | 0.000586642 | − | 0.000894938i | ||||
\(617\) | 8.92785 | 0.359422 | 0.179711 | − | 0.983719i | \(-0.442484\pi\) | ||||
0.179711 | + | 0.983719i | \(0.442484\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0192 | − | 27.5514i | 0.963081 | − | 1.10471i | ||||
\(623\) | 0.0779695i | 0.00312378i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.21498i | 0.248202i | ||||||||
\(628\) | −3.15890 | − | 22.9519i | −0.126054 | − | 0.915880i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 50.2383i | − | 1.99996i | −0.00664970 | − | 0.999978i | \(-0.502117\pi\) | ||
0.00664970 | − | 0.999978i | \(-0.497883\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.1511 | 1.23815 | ||||||||
\(634\) | 7.92465 | + | 6.90868i | 0.314728 | + | 0.274379i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.56621 | + | 2.94359i | −0.101597 | + | 0.116538i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | −57.8099 | − | 50.3984i | −2.28157 | − | 1.98906i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 1.67477 | − | 2.55490i | 0.0657910 | − | 0.100366i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 0.476409i | − | 0.0186719i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −50.5272 | −1.97728 | −0.988642 | − | 0.150291i | \(-0.951979\pi\) | ||||
−0.988642 | + | 0.150291i | \(0.951979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.129215 | + | 0.112649i | 0.00503733 | + | 0.00439152i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 25.6043 | − | 3.52396i | 0.990661 | − | 0.136346i | ||||
\(669\) | 47.0380 | 1.81859 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.55165i | − | 0.214319i | ||||||
\(672\) | 0.219903 | + | 0.104459i | 0.00848294 | + | 0.00402960i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 39.0507 | + | 34.0442i | 1.50418 | + | 1.31133i | ||||
\(675\) | − | 23.4177i | − | 0.901347i | ||||||
\(676\) | 3.54500 | + | 25.7572i | 0.136346 | + | 0.990661i | ||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.290636i | 0.0111536i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.13926 | − | 6.22398i | −0.273376 | − | 0.238328i | ||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | −34.4180 | + | 4.73699i | −1.31600 | + | 0.181124i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.201927 | + | 0.231622i | −0.00770959 | + | 0.00884335i | ||||
\(687\) | 20.7228i | 0.790624i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | −2.69363 | − | 19.5713i | −0.102396 | − | 0.743990i | ||||
\(693\) | 0.0440295 | 0.00167254 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −29.9381 | − | 19.6248i | −1.13480 | − | 0.743875i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 21.8711i | − | 0.827242i | ||||||
\(700\) | −0.153755 | + | 0.0211615i | −0.00581138 | + | 0.000799828i | ||||
\(701\) | −42.3968 | −1.60131 | −0.800653 | − | 0.599128i | \(-0.795514\pi\) | ||||
−0.800653 | + | 0.599128i | \(0.795514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.43827 | − | 1.93068i | 0.167274 | − | 0.0727652i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −38.7096 | − | 33.7468i | −1.45685 | − | 1.27008i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.78978 | + | 11.8835i | −0.291934 | + | 0.445354i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 52.9688 | − | 7.29017i | 1.97954 | − | 0.272447i | ||||
\(717\) | −31.6599 | −1.18236 | ||||||||
\(718\) | 3.22565 | − | 3.70001i | 0.120380 | − | 0.138083i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.62374 | + | 4.90275i | 0.209294 | + | 0.182462i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.92213 | + | 21.2316i | 0.108600 | + | 0.789066i | ||||
\(725\) | 22.8210 | 0.847552 | ||||||||
\(726\) | −27.4032 | + | 31.4331i | −1.01703 | + | 1.16659i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 44.0256 | 1.63058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 50.4146 | − | 6.93863i | 1.86338 | − | 0.256459i | ||||
\(733\) | 30.9843 | 1.14443 | 0.572215 | − | 0.820104i | \(-0.306084\pi\) | ||||
0.572215 | + | 0.820104i | \(0.306084\pi\) | |||||||
\(734\) | −35.5457 | + | 40.7730i | −1.31202 | + | 1.50496i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 25.8457i | − | 0.948187i | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||
0.880475 | − | 0.474093i | \(-0.157224\pi\) | |||||||
\(744\) | 47.5971 | − | 72.6106i | 1.74499 | − | 2.66203i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.303538 | −0.0110911 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 8.43942 | + | 30.0787i | 0.307754 | + | 1.09686i | ||||
\(753\) | 53.9726 | 1.96687 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.0198221 | + | 0.144023i | 0.000720923 | + | 0.00523807i | ||||
\(757\) | 12.1814 | 0.442741 | 0.221371 | − | 0.975190i | \(-0.428947\pi\) | ||||
0.221371 | + | 0.975190i | \(0.428947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.8918 | −0.721076 | −0.360538 | − | 0.932745i | \(-0.617407\pi\) | ||||
−0.360538 | + | 0.932745i | \(0.617407\pi\) | |||||||
\(762\) | −41.4879 | − | 36.1690i | −1.50295 | − | 1.31026i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 36.3379 | − | 5.00123i | 1.31466 | − | 0.180938i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.3072 | − | 41.6465i | 1.31183 | − | 1.50475i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 23.0796 | + | 37.8909i | 0.832814 | + | 1.36727i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.3492i | 1.98820i | ||||||||
\(776\) | −29.0368 | + | 44.2965i | −1.04236 | + | 1.59015i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 21.3766i | − | 0.763939i | ||||||
\(784\) | −26.9580 | + | 7.56381i | −0.962786 | + | 0.270136i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 77.7941 | 2.76954 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.71063 | + | 4.39890i | 0.238452 | + | 0.156308i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −36.3416 | − | 31.6824i | −1.28971 | − | 1.12437i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 35.0012 | − | 4.81727i | 1.24059 | − | 0.170743i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | −0.148168 | + | 0.169958i | −0.00524511 | + | 0.00601644i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −25.5483 | − | 12.1361i | −0.903269 | − | 0.429075i | ||||
\(801\) | −23.5562 | −0.832317 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.5115 | 1.74073 | 0.870366 | − | 0.492405i | \(-0.163882\pi\) | ||||
0.870366 | + | 0.492405i | \(0.163882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | −0.140354 | + | 0.0193171i | −0.00492545 | + | 0.000677896i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 15.3109 | + | 13.3479i | 0.535331 | + | 0.466699i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 8.58973 | − | 9.85292i | 0.299601 | − | 0.343660i | ||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.38809 | −0.292036 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.611190 | + | 4.44078i | 0.0211385 | + | 0.153588i | ||||
\(837\) | 51.8460 | 1.79206 | ||||||||
\(838\) | 37.7718 | − | 43.3265i | 1.30481 | − | 1.49669i | ||||
\(839\) | − | 21.8574i | − | 0.754600i | −0.926091 | − | 0.377300i | \(-0.876853\pi\) | ||
0.926091 | − | 0.377300i | \(-0.123147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.16802 | −0.281656 | ||||||||
\(842\) | 30.5293 | + | 26.6153i | 1.05211 | + | 0.917223i | ||||
\(843\) | 83.0185i | 2.85931i | ||||||||
\(844\) | 22.2583 | − | 3.06345i | 0.766164 | − | 0.105448i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −34.0336 | + | 39.0385i | −1.17010 | + | 1.34217i | ||||
\(847\) | 0.165044i | 0.00567096i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −82.8716 | −2.84415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −58.3596 | −1.99820 | −0.999098 | − | 0.0424614i | \(-0.986480\pi\) | ||||
−0.999098 | + | 0.0424614i | \(0.986480\pi\) | |||||||
\(854\) | 0.132354 | − | 0.151818i | 0.00452907 | − | 0.00519511i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −46.2630 | − | 30.3259i | −1.58124 | − | 1.03652i | ||||
\(857\) | −19.7427 | −0.674398 | −0.337199 | − | 0.941433i | \(-0.609480\pi\) | ||||
−0.337199 | + | 0.941433i | \(0.609480\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 58.6101i | − | 1.99975i | −0.0158288 | − | 0.999875i | \(-0.505039\pi\) | ||
0.0158288 | − | 0.999875i | \(-0.494961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.85101 | + | 5.56439i | −0.165226 | + | 0.189524i | ||||
\(863\) | 43.3167i | 1.47452i | 0.675610 | + | 0.737259i | \(0.263880\pi\) | ||||
−0.675610 | + | 0.737259i | \(0.736120\pi\) | |||||||
\(864\) | −11.3679 | + | 23.9313i | −0.386745 | + | 0.814159i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.2477 | − | 24.6262i | −0.959894 | − | 0.836831i | ||||
\(867\) | 47.1395i | 1.60094i | ||||||||
\(868\) | −0.0468508 | − | 0.340408i | −0.00159022 | − | 0.0115542i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −87.8070 | −2.97182 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.581676 | −0.0196418 | −0.00982090 | − | 0.999952i | \(-0.503126\pi\) | ||||
−0.00982090 | + | 0.999952i | \(0.503126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 92.8130i | − | 3.13050i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −34.9882 | − | 30.5026i | −1.17811 | − | 1.02707i | ||||
\(883\) | 58.6411i | 1.97343i | 0.162460 | + | 0.986715i | \(0.448057\pi\) | ||||
−0.162460 | + | 0.986715i | \(0.551943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.217838 | −0.00730604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 0.653443i | − | 0.0218912i | ||||||
\(892\) | 33.6099 | − | 4.62578i | 1.12534 | − | 0.154883i | ||||
\(893\) | −28.9336 | −0.968224 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.167400 | + | 0.0530134i | 0.00559243 | + | 0.00177105i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −42.6517 | − | 37.1835i | −1.42330 | − | 1.24083i | ||||
\(899\) | 50.5250i | 1.68510i | ||||||||
\(900\) | −6.39331 | − | 46.4524i | −0.213110 | − | 1.54841i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.2455i | 1.40274i | 0.712798 | + | 0.701370i | \(0.247428\pi\) | ||||
−0.712798 | + | 0.701370i | \(0.752572\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14.4178i | − | 0.477684i | −0.971058 | − | 0.238842i | \(-0.923232\pi\) | ||
0.971058 | − | 0.238842i | \(-0.0767678\pi\) | |||||||
\(912\) | −39.5629 | + | 11.1005i | −1.31006 | + | 0.367573i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.03791 | + | 14.8070i | 0.0673344 | + | 0.489238i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.0674i | 1.75053i | 0.483642 | + | 0.875266i | \(0.339314\pi\) | ||||
−0.483642 | + | 0.875266i | \(0.660686\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.4281 | − | 25.6553i | −0.969163 | − | 0.844911i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.0515883 | − | 0.00710017i | 0.00169713 | − | 0.000233578i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.3216 | − | 11.0783i | −0.765567 | − | 0.363663i | ||||
\(929\) | −59.0552 | −1.93754 | −0.968769 | − | 0.247964i | \(-0.920238\pi\) | ||||
−0.968769 | + | 0.247964i | \(0.920238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 25.9316i | − | 0.849875i | ||||||
\(932\) | −2.15084 | − | 15.6275i | −0.0704531 | − | 0.511897i | ||||
\(933\) | 71.6678 | 2.34630 | ||||||||
\(934\) | 18.2618 | − | 20.9473i | 0.597544 | − | 0.685418i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 29.8517 | − | 34.2416i | 0.972621 | − | 1.11565i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 47.7913i | − | 1.55301i | −0.630111 | − | 0.776505i | \(-0.716991\pi\) | ||
0.630111 | − | 0.776505i | \(-0.283009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 17.2142 | − | 19.7457i | 0.558502 | − | 0.640635i | ||||
\(951\) | 20.6139i | 0.668453i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.6219 | + | 3.11348i | −0.731644 | + | 0.100697i | ||||
\(957\) | −7.65699 | −0.247515 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 0.0517341i | − | 0.00167058i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −91.5412 | −2.95294 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 91.7052i | − | 2.95516i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.5380i | − | 1.07851i | −0.842143 | − | 0.539255i | \(-0.818706\pi\) | ||
0.842143 | − | 0.539255i | \(-0.181294\pi\) | |||||||
\(968\) | −16.4892 | + | 25.1547i | −0.529982 | + | 0.808502i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 33.7727 | − | 4.64819i | 1.08326 | − | 0.149091i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35.3403 | − | 9.91569i | 1.13122 | − | 0.317394i | ||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.03934i | 0.0971376i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.0192 | + | 27.5514i | −0.766483 | + | 0.879200i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.336119i | 0.0106988i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 26.8688 | − | 56.5631i | 0.853086 | − | 1.79588i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56.0245 | −1.77431 | −0.887156 | − | 0.461469i | \(-0.847322\pi\) | ||||
−0.887156 | + | 0.461469i | \(0.847322\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 668.2.b.a.667.18 | yes | 22 | |
4.3 | odd | 2 | inner | 668.2.b.a.667.17 | ✓ | 22 | |
167.166 | odd | 2 | CM | 668.2.b.a.667.18 | yes | 22 | |
668.667 | even | 2 | inner | 668.2.b.a.667.17 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
668.2.b.a.667.17 | ✓ | 22 | 4.3 | odd | 2 | inner | |
668.2.b.a.667.17 | ✓ | 22 | 668.667 | even | 2 | inner | |
668.2.b.a.667.18 | yes | 22 | 1.1 | even | 1 | trivial | |
668.2.b.a.667.18 | yes | 22 | 167.166 | odd | 2 | CM |