Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 1007.4 | ||
Character | \(\chi\) | \(=\) | 1152.1007 |
Dual form | 1152.2.w.a.143.4 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.352978 | − | 0.852163i | −0.157856 | − | 0.381099i | 0.825087 | − | 0.565005i | \(-0.191126\pi\) |
−0.982944 | + | 0.183906i | \(0.941126\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.43393 | + | 3.43393i | 1.29790 | + | 1.29790i | 0.929774 | + | 0.368130i | \(0.120002\pi\) |
0.368130 | + | 0.929774i | \(0.379998\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.44650 | − | 3.49216i | −0.436136 | − | 1.05293i | −0.977272 | − | 0.211991i | \(-0.932005\pi\) |
0.541135 | − | 0.840936i | \(-0.317995\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.258636 | − | 0.107131i | −0.0717328 | − | 0.0297127i | 0.346529 | − | 0.938039i | \(-0.387360\pi\) |
−0.418261 | + | 0.908327i | \(0.637360\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.30575 | 1.28683 | 0.643417 | − | 0.765516i | \(-0.277516\pi\) | ||||
0.643417 | + | 0.765516i | \(0.277516\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.72546 | + | 6.57983i | −0.625263 | + | 1.50952i | 0.220185 | + | 0.975458i | \(0.429334\pi\) |
−0.845447 | + | 0.534059i | \(0.820666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.23882 | + | 2.23882i | 0.466825 | + | 0.466825i | 0.900884 | − | 0.434059i | \(-0.142919\pi\) |
−0.434059 | + | 0.900884i | \(0.642919\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.93394 | − | 2.93394i | 0.586789 | − | 0.586789i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.16953 | + | 1.31286i | 0.588568 | + | 0.243793i | 0.657034 | − | 0.753861i | \(-0.271811\pi\) |
−0.0684666 | + | 0.997653i | \(0.521811\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46749i | − | 0.622779i | −0.950282 | − | 0.311390i | \(-0.899206\pi\) | ||
0.950282 | − | 0.311390i | \(-0.100794\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.71417 | − | 4.13837i | 0.289748 | − | 0.699513i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.27512 | − | 0.528171i | 0.209628 | − | 0.0868308i | −0.275399 | − | 0.961330i | \(-0.588810\pi\) |
0.485027 | + | 0.874499i | \(0.338810\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.28251 | + | 5.28251i | −0.824989 | + | 0.824989i | −0.986819 | − | 0.161830i | \(-0.948260\pi\) |
0.161830 | + | 0.986819i | \(0.448260\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.46955 | + | 1.02292i | −0.376603 | + | 0.155994i | −0.562952 | − | 0.826489i | \(-0.690334\pi\) |
0.186349 | + | 0.982484i | \(0.440334\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.423698i | 0.0618027i | 0.999522 | + | 0.0309013i | \(0.00983776\pi\) | ||||
−0.999522 | + | 0.0309013i | \(0.990162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.5838i | 2.36911i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.5563 | − | 5.20097i | 1.72474 | − | 0.714409i | 0.725066 | − | 0.688679i | \(-0.241809\pi\) |
0.999669 | − | 0.0257295i | \(-0.00819085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.46531 | + | 2.46531i | −0.332422 | + | 0.332422i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.24194 | + | 2.17128i | −0.682442 | + | 0.282677i | −0.696847 | − | 0.717220i | \(-0.745414\pi\) |
0.0144054 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0138304 | − | 0.0333895i | 0.00177080 | − | 0.00427509i | −0.922992 | − | 0.384820i | \(-0.874264\pi\) |
0.924762 | + | 0.380545i | \(0.124264\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.258215i | 0.0320276i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.82224 | + | 4.06850i | 1.19998 | + | 0.497047i | 0.890992 | − | 0.454020i | \(-0.150010\pi\) |
0.308986 | + | 0.951067i | \(0.400010\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.64969 | − | 4.64969i | 0.551817 | − | 0.551817i | −0.375148 | − | 0.926965i | \(-0.622408\pi\) |
0.926965 | + | 0.375148i | \(0.122408\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.96752 | + | 3.96752i | 0.464363 | + | 0.464363i | 0.900082 | − | 0.435720i | \(-0.143506\pi\) |
−0.435720 | + | 0.900082i | \(0.643506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.02466 | − | 16.9590i | 0.800534 | − | 1.93266i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7319 | 1.43245 | 0.716224 | − | 0.697870i | \(-0.245869\pi\) | ||||
0.716224 | + | 0.697870i | \(0.245869\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.867335 | − | 0.359262i | −0.0952024 | − | 0.0394341i | 0.334574 | − | 0.942369i | \(-0.391408\pi\) |
−0.429776 | + | 0.902935i | \(0.641408\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.87281 | − | 4.52137i | −0.203135 | − | 0.490411i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.82033 | − | 4.82033i | −0.510954 | − | 0.510954i | 0.403865 | − | 0.914819i | \(-0.367667\pi\) |
−0.914819 | + | 0.403865i | \(0.867667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.520260 | − | 1.25602i | −0.0545381 | − | 0.131667i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.56912 | 0.673977 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.78058 | 0.891532 | 0.445766 | − | 0.895149i | \(-0.352931\pi\) | ||||
0.445766 | + | 0.895149i | \(0.352931\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.37141 | + | 10.5535i | 0.434972 | + | 1.05011i | 0.977662 | + | 0.210182i | \(0.0674056\pi\) |
−0.542691 | + | 0.839933i | \(0.682594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.54327 | − | 2.54327i | −0.250596 | − | 0.250596i | 0.570619 | − | 0.821215i | \(-0.306703\pi\) |
−0.821215 | + | 0.570619i | \(0.806703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.34953 | − | 3.25806i | −0.130464 | − | 0.314968i | 0.845126 | − | 0.534567i | \(-0.179525\pi\) |
−0.975590 | + | 0.219599i | \(0.929525\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5904 | + | 4.80089i | 1.11016 | + | 0.459842i | 0.860992 | − | 0.508619i | \(-0.169844\pi\) |
0.249165 | + | 0.968461i | \(0.419844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.5004 | −1.55223 | −0.776115 | − | 0.630591i | \(-0.782812\pi\) | ||||
−0.776115 | + | 0.630591i | \(0.782812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11758 | − | 2.69809i | 0.104215 | − | 0.251598i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.2196 | + | 18.2196i | 1.67019 | + | 1.67019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.32465 | + | 2.32465i | −0.211332 | + | 0.211332i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.79663 | − | 3.22947i | −0.697352 | − | 0.288853i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.43014i | − | 0.836790i | −0.908265 | − | 0.418395i | \(-0.862593\pi\) | ||
0.908265 | − | 0.418395i | \(-0.137407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.19791 | − | 14.9631i | 0.541514 | − | 1.30733i | −0.382140 | − | 0.924104i | \(-0.624813\pi\) |
0.923654 | − | 0.383227i | \(-0.125187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.9537 | + | 13.2357i | −2.77074 | + | 1.14768i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.01737 | + | 5.01737i | −0.428663 | + | 0.428663i | −0.888173 | − | 0.459510i | \(-0.848025\pi\) |
0.459510 | + | 0.888173i | \(0.348025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.0610 | + | 7.89534i | −1.61674 | + | 0.669674i | −0.993654 | − | 0.112482i | \(-0.964120\pi\) |
−0.623083 | + | 0.782156i | \(0.714120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.05816i | 0.0884881i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.16437i | − | 0.262787i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.8124 | + | 8.62076i | −1.70502 | + | 0.706240i | −0.999996 | − | 0.00294754i | \(-0.999062\pi\) |
−0.705019 | + | 0.709188i | \(0.749062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.68070 | + | 4.68070i | −0.380910 | + | 0.380910i | −0.871430 | − | 0.490520i | \(-0.836807\pi\) |
0.490520 | + | 0.871430i | \(0.336807\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.95487 | + | 1.22395i | −0.237341 | + | 0.0983097i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.17384 | − | 14.9050i | 0.492726 | − | 1.18955i | −0.460601 | − | 0.887607i | \(-0.652366\pi\) |
0.953327 | − | 0.301939i | \(-0.0976340\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3759i | 1.21179i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.13457 | + | 0.884169i | 0.167193 | + | 0.0692534i | 0.464710 | − | 0.885463i | \(-0.346159\pi\) |
−0.297517 | + | 0.954716i | \(0.596159\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.2052 | + | 14.2052i | −1.09923 | + | 1.09923i | −0.104733 | + | 0.994500i | \(0.533399\pi\) |
−0.994500 | + | 0.104733i | \(0.966601\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.13697 | − | 9.13697i | −0.702844 | − | 0.702844i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.53353 | − | 10.9449i | 0.344678 | − | 0.832127i | −0.652552 | − | 0.757744i | \(-0.726301\pi\) |
0.997230 | − | 0.0743825i | \(-0.0236986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.1499 | 1.52319 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00945 | − | 3.73184i | −0.673398 | − | 0.278931i | 0.0196661 | − | 0.999807i | \(-0.493740\pi\) |
−0.693064 | + | 0.720876i | \(0.743740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.75935 | − | 13.9043i | −0.428089 | − | 1.03350i | −0.979893 | − | 0.199524i | \(-0.936060\pi\) |
0.551804 | − | 0.833974i | \(-0.313940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.900176 | − | 0.900176i | −0.0661823 | − | 0.0661823i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.67477 | − | 18.5285i | −0.561235 | − | 1.35494i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.18207 | −0.447319 | −0.223660 | − | 0.974667i | \(-0.571800\pi\) | ||||
−0.223660 | + | 0.974667i | \(0.571800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2515 | −0.809899 | −0.404949 | − | 0.914339i | \(-0.632711\pi\) | ||||
−0.404949 | + | 0.914339i | \(0.632711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.59303 | − | 6.26014i | −0.184746 | − | 0.446016i | 0.804187 | − | 0.594376i | \(-0.202601\pi\) |
−0.988934 | + | 0.148359i | \(0.952601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.67622 | − | 8.67622i | −0.615041 | − | 0.615041i | 0.329214 | − | 0.944255i | \(-0.393216\pi\) |
−0.944255 | + | 0.329214i | \(0.893216\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.37568 | + | 15.3922i | 0.447485 | + | 1.08032i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.36616 | + | 2.63695i | 0.444632 | + | 0.184173i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.9202 | 1.86211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.18497 | + | 7.68919i | −0.219262 | + | 0.529345i | −0.994787 | − | 0.101971i | \(-0.967485\pi\) |
0.775525 | + | 0.631317i | \(0.217485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.74339 | + | 1.74339i | 0.118898 | + | 0.118898i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.9071 | − | 11.9071i | 0.808308 | − | 0.808308i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.37226 | − | 0.568409i | −0.0923082 | − | 0.0382353i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.9728i | − | 0.868722i | −0.900739 | − | 0.434361i | \(-0.856974\pi\) | ||
0.900739 | − | 0.434361i | \(-0.143026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.79613 | − | 9.16468i | 0.251958 | − | 0.608281i | −0.746404 | − | 0.665493i | \(-0.768221\pi\) |
0.998362 | + | 0.0572122i | \(0.0182212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.91823 | − | 2.03720i | 0.325006 | − | 0.134622i | −0.214214 | − | 0.976787i | \(-0.568719\pi\) |
0.539220 | + | 0.842165i | \(0.318719\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8493 | + | 10.8493i | −0.710759 | + | 0.710759i | −0.966694 | − | 0.255935i | \(-0.917617\pi\) |
0.255935 | + | 0.966694i | \(0.417617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.361060 | − | 0.149556i | 0.0235529 | − | 0.00975594i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.69444i | − | 0.497712i | −0.968540 | − | 0.248856i | \(-0.919945\pi\) | ||
0.968540 | − | 0.248856i | \(-0.0800546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5669i | 0.938338i | 0.883108 | + | 0.469169i | \(0.155447\pi\) | ||||
−0.883108 | + | 0.469169i | \(0.844553\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.1321 | − | 5.85370i | 0.902866 | − | 0.373979i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.40980 | − | 1.40980i | 0.0897037 | − | 0.0897037i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1528 | + | 5.86227i | −0.893315 | + | 0.370023i | −0.781646 | − | 0.623722i | \(-0.785620\pi\) |
−0.111669 | + | 0.993745i | \(0.535620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.57986 | − | 11.0568i | 0.287933 | − | 0.695132i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 19.4990i | − | 1.21632i | −0.793816 | − | 0.608159i | \(-0.791908\pi\) | ||
0.793816 | − | 0.608159i | \(-0.208092\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.19237 | + | 2.56496i | 0.384775 | + | 0.159379i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.65433 | − | 9.65433i | 0.595312 | − | 0.595312i | −0.343750 | − | 0.939061i | \(-0.611697\pi\) |
0.939061 | + | 0.343750i | \(0.111697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.86416 | − | 8.86416i | −0.544521 | − | 0.544521i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.95451 | + | 19.2039i | −0.484995 | + | 1.17088i | 0.472214 | + | 0.881484i | \(0.343455\pi\) |
−0.957209 | + | 0.289397i | \(0.906545\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1213 | −1.16154 | −0.580770 | − | 0.814068i | \(-0.697248\pi\) | ||||
−0.580770 | + | 0.814068i | \(0.697248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.4898 | − | 6.00186i | −0.873765 | − | 0.361926i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.609964 | − | 1.47258i | −0.0366492 | − | 0.0884789i | 0.904495 | − | 0.426484i | \(-0.140248\pi\) |
−0.941144 | + | 0.338005i | \(0.890248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.76628 | − | 8.76628i | −0.522953 | − | 0.522953i | 0.395509 | − | 0.918462i | \(-0.370568\pi\) |
−0.918462 | + | 0.395509i | \(0.870568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.64026 | − | 18.4452i | −0.454166 | − | 1.09645i | −0.970723 | − | 0.240201i | \(-0.922787\pi\) |
0.516557 | − | 0.856253i | \(-0.327213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36.2795 | −2.14151 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1510 | 0.655942 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.73727 | + | 21.0936i | 0.510437 | + | 1.23230i | 0.943630 | + | 0.331002i | \(0.107387\pi\) |
−0.433194 | + | 0.901301i | \(0.642613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.70057 | + | 3.70057i | 0.215456 | + | 0.215456i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.339193 | − | 0.818885i | −0.0196160 | − | 0.0473573i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.9929 | − | 4.96763i | −0.691260 | − | 0.286329i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0333351 | −0.00190876 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.29860 | + | 5.54931i | −0.131188 | + | 0.316716i | −0.975801 | − | 0.218662i | \(-0.929831\pi\) |
0.844613 | + | 0.535378i | \(0.179831\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3351 | − | 12.3351i | −0.699460 | − | 0.699460i | 0.264834 | − | 0.964294i | \(-0.414683\pi\) |
−0.964294 | + | 0.264834i | \(0.914683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.07712 | − | 9.07712i | 0.513069 | − | 0.513069i | −0.402397 | − | 0.915465i | \(-0.631823\pi\) |
0.915465 | + | 0.402397i | \(0.131823\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7317 | + | 6.10208i | 0.827416 | + | 0.342727i | 0.755879 | − | 0.654711i | \(-0.227210\pi\) |
0.0715366 | + | 0.997438i | \(0.477210\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.9676i | − | 0.726045i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.4606 | + | 34.9110i | −0.804609 | + | 1.94250i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.07314 | + | 0.444509i | −0.0595271 | + | 0.0246569i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.45495 | + | 1.45495i | −0.0802139 | + | 0.0802139i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7207 | − | 8.58281i | 1.13892 | − | 0.471754i | 0.268113 | − | 0.963387i | \(-0.413600\pi\) |
0.870802 | + | 0.491633i | \(0.163600\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.80624i | − | 0.535772i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.9981i | 0.708052i | 0.935236 | + | 0.354026i | \(0.115188\pi\) | ||||
−0.935236 | + | 0.354026i | \(0.884812\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.1090 | + | 5.01573i | −0.655741 | + | 0.271617i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −32.9100 | + | 32.9100i | −1.77697 | + | 1.77697i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.4093 | + | 10.1107i | −1.31036 | + | 0.542769i | −0.924990 | − | 0.379992i | \(-0.875927\pi\) |
−0.385372 | + | 0.922762i | \(0.625927\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.82444 | + | 9.23301i | −0.204717 | + | 0.494231i | −0.992576 | − | 0.121624i | \(-0.961190\pi\) |
0.787859 | + | 0.615856i | \(0.211190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.4035i | 1.29887i | 0.760418 | + | 0.649434i | \(0.224994\pi\) | ||||
−0.760418 | + | 0.649434i | \(0.775006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.60353 | − | 2.32106i | −0.297405 | − | 0.123189i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.52733 | − | 6.52733i | 0.344500 | − | 0.344500i | −0.513556 | − | 0.858056i | \(-0.671672\pi\) |
0.858056 | + | 0.513556i | \(0.171672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.4311 | − | 22.4311i | −1.18058 | − | 1.18058i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.98053 | − | 4.78142i | 0.103666 | − | 0.250271i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4291 | −1.01419 | −0.507096 | − | 0.861889i | \(-0.669281\pi\) | ||||
−0.507096 | + | 0.861889i | \(0.669281\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 60.9771 | + | 25.2576i | 3.16577 | + | 1.31131i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.15808 | − | 10.0385i | −0.215297 | − | 0.519773i | 0.778925 | − | 0.627117i | \(-0.215765\pi\) |
−0.994222 | + | 0.107344i | \(0.965765\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.679109 | − | 0.679109i | −0.0349759 | − | 0.0349759i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.96668 | − | 4.74798i | −0.101021 | − | 0.243887i | 0.865286 | − | 0.501279i | \(-0.167137\pi\) |
−0.966307 | + | 0.257392i | \(0.917137\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.30106 | −0.321969 | −0.160985 | − | 0.986957i | \(-0.551467\pi\) | ||||
−0.160985 | + | 0.986957i | \(0.551467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.9314 | −0.862905 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.331782 | + | 0.800993i | 0.0168220 | + | 0.0406119i | 0.932067 | − | 0.362285i | \(-0.118003\pi\) |
−0.915245 | + | 0.402897i | \(0.868003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8786 | + | 11.8786i | 0.600727 | + | 0.600727i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.49407 | − | 10.8496i | −0.226121 | − | 0.545905i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2798 | + | 4.67225i | 0.566118 | + | 0.234494i | 0.647339 | − | 0.762202i | \(-0.275882\pi\) |
−0.0812209 | + | 0.996696i | \(0.525882\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.7890 | 0.538777 | 0.269388 | − | 0.963032i | \(-0.413178\pi\) | ||||
0.269388 | + | 0.963032i | \(0.413178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.371474 | + | 0.896819i | −0.0185045 | + | 0.0446737i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.68892 | − | 3.68892i | −0.182853 | − | 0.182853i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0980818 | + | 0.0980818i | −0.00484983 | + | 0.00484983i | −0.709528 | − | 0.704678i | \(-0.751092\pi\) |
0.704678 | + | 0.709528i | \(0.251092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.4565 | − | 10.5444i | −1.25263 | − | 0.518857i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.865923i | 0.0425065i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.5665 | − | 27.9241i | 0.565063 | − | 1.36418i | −0.340610 | − | 0.940205i | \(-0.610634\pi\) |
0.905673 | − | 0.423977i | \(-0.139366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0670 | − | 7.48361i | 0.880533 | − | 0.364729i | 0.103829 | − | 0.994595i | \(-0.466890\pi\) |
0.776703 | + | 0.629867i | \(0.216890\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.5668 | − | 15.5668i | 0.755100 | − | 0.755100i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.162150 | − | 0.0671647i | 0.00784698 | − | 0.00325033i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6345i | 0.512245i | 0.966644 | + | 0.256123i | \(0.0824451\pi\) | ||||
−0.966644 | + | 0.256123i | \(0.917555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11.8688i | − | 0.570377i | −0.958471 | − | 0.285189i | \(-0.907944\pi\) | ||
0.958471 | − | 0.285189i | \(-0.0920562\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.8328 | + | 8.62924i | −0.996569 | + | 0.412793i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2613 | − | 11.2613i | 0.537471 | − | 0.537471i | −0.385314 | − | 0.922785i | \(-0.625907\pi\) |
0.922785 | + | 0.385314i | \(0.125907\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.1370 | − | 7.09839i | 0.814204 | − | 0.337255i | 0.0635743 | − | 0.997977i | \(-0.479750\pi\) |
0.750630 | + | 0.660723i | \(0.229750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.40624 | + | 5.80918i | −0.114067 | + | 0.275381i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 38.4537i | − | 1.81474i | −0.420331 | − | 0.907371i | \(-0.638086\pi\) | ||
0.420331 | − | 0.907371i | \(-0.361914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0885 | + | 10.8062i | 1.22846 | + | 0.508845i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.886693 | + | 0.886693i | −0.0415688 | + | 0.0415688i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.6258 | − | 11.6258i | −0.543833 | − | 0.543833i | 0.380817 | − | 0.924650i | \(-0.375643\pi\) |
−0.924650 | + | 0.380817i | \(0.875643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.95672 | + | 4.72395i | −0.0911337 | + | 0.220016i | −0.962874 | − | 0.269953i | \(-0.912992\pi\) |
0.871740 | + | 0.489969i | \(0.162992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2082 | 1.12505 | 0.562524 | − | 0.826781i | \(-0.309830\pi\) | ||||
0.562524 | + | 0.826781i | \(0.309830\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.35140 | − | 2.21662i | −0.247633 | − | 0.102573i | 0.255415 | − | 0.966832i | \(-0.417788\pi\) |
−0.503048 | + | 0.864259i | \(0.667788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.7579 | + | 47.6999i | 0.912336 | + | 2.20257i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.14442 | + | 7.14442i | 0.328501 | + | 0.328501i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3085 | + | 27.3012i | 0.518871 | + | 1.25267i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.4282 | 1.20754 | 0.603768 | − | 0.797160i | \(-0.293665\pi\) | ||||
0.603768 | + | 0.797160i | \(0.293665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.386375 | −0.0176172 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.09935 | − | 7.48249i | −0.140734 | − | 0.339762i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.32733 | + | 9.32733i | 0.422662 | + | 0.422662i | 0.886119 | − | 0.463457i | \(-0.153391\pi\) |
−0.463457 | + | 0.886119i | \(0.653391\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.97593 | + | 7.18453i | 0.134302 | + | 0.324233i | 0.976696 | − | 0.214629i | \(-0.0688543\pi\) |
−0.842394 | + | 0.538862i | \(0.818854\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.8168 | + | 6.96573i | 0.757389 | + | 0.313721i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.9334 | 1.43241 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.3839 | − | 25.0689i | 0.464846 | − | 1.12224i | −0.501538 | − | 0.865136i | \(-0.667232\pi\) |
0.966384 | − | 0.257103i | \(-0.0827679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.53224 | + | 3.53224i | 0.157495 | + | 0.157495i | 0.781456 | − | 0.623961i | \(-0.214478\pi\) |
−0.623961 | + | 0.781456i | \(0.714478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.45031 | − | 7.45031i | 0.331535 | − | 0.331535i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0074 | − | 7.87311i | −0.842487 | − | 0.348969i | −0.0806532 | − | 0.996742i | \(-0.525701\pi\) |
−0.761834 | + | 0.647773i | \(0.775701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.2484i | 1.20540i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.26957 | + | 3.06500i | −0.0559437 | + | 0.135060i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.47962 | − | 0.612879i | 0.0650736 | − | 0.0269544i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5687 | − | 12.5687i | 0.550643 | − | 0.550643i | −0.375984 | − | 0.926626i | \(-0.622695\pi\) |
0.926626 | + | 0.375984i | \(0.122695\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.66162 | + | 4.00197i | −0.422473 | + | 0.174994i | −0.583783 | − | 0.811910i | \(-0.698428\pi\) |
0.161310 | + | 0.986904i | \(0.448428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 18.3976i | − | 0.801414i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 12.9754i | − | 0.564148i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.93217 | − | 0.800329i | 0.0836914 | − | 0.0346661i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.30004 | + | 2.30004i | −0.0994395 | + | 0.0994395i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 57.9132 | − | 23.9884i | 2.49450 | − | 1.03326i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.6046 | + | 35.2587i | −0.627901 | + | 1.51589i | 0.214324 | + | 0.976763i | \(0.431245\pi\) |
−0.842225 | + | 0.539125i | \(0.818755\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.5715i | − | 0.495669i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.22367 | + | 3.82057i | 0.394376 | + | 0.163356i | 0.571053 | − | 0.820913i | \(-0.306535\pi\) |
−0.176677 | + | 0.984269i | \(0.556535\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.2769 | + | 17.2769i | −0.736019 | + | 0.736019i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.7204 | + | 43.7204i | 1.85918 | + | 1.85918i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.65349 | + | 20.8914i | −0.366660 | + | 0.885196i | 0.627632 | + | 0.778510i | \(0.284024\pi\) |
−0.994293 | + | 0.106686i | \(0.965976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.748302 | 0.0316498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.53958 | − | 1.46614i | −0.149175 | − | 0.0617905i | 0.306847 | − | 0.951759i | \(-0.400726\pi\) |
−0.456022 | + | 0.889969i | \(0.650726\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.82428 | + | 14.0611i | 0.245029 | + | 0.591553i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.855711 | − | 0.855711i | −0.0358733 | − | 0.0358733i | 0.688943 | − | 0.724816i | \(-0.258075\pi\) |
−0.724816 | + | 0.688943i | \(0.758075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.33854 | − | 10.4742i | −0.181562 | − | 0.438330i | 0.806726 | − | 0.590925i | \(-0.201237\pi\) |
−0.988289 | + | 0.152595i | \(0.951237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.1371 | 0.547856 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.91000 | −0.121145 | −0.0605724 | − | 0.998164i | \(-0.519293\pi\) | ||||
−0.0605724 | + | 0.998164i | \(0.519293\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.74469 | − | 4.21205i | −0.0723819 | − | 0.174745i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.3253 | − | 36.3253i | −1.50444 | − | 1.50444i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.1052 | + | 43.7099i | 0.747283 | + | 1.80410i | 0.573287 | + | 0.819355i | \(0.305668\pi\) |
0.173996 | + | 0.984746i | \(0.444332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.8155 | + | 9.45049i | 0.940096 | + | 0.389401i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.7464 | −1.26260 | −0.631301 | − | 0.775538i | \(-0.717479\pi\) | ||||
−0.631301 | + | 0.775538i | \(0.717479\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.09496 | − | 21.9572i | 0.372857 | − | 0.900157i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.3435 | − | 19.3435i | −0.790354 | − | 0.790354i | 0.191198 | − | 0.981552i | \(-0.438763\pi\) |
−0.981552 | + | 0.191198i | \(0.938763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.4893 | + | 28.4893i | −1.16210 | + | 1.16210i | −0.178087 | + | 0.984015i | \(0.556991\pi\) |
−0.984015 | + | 0.178087i | \(0.943009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.80153 | + | 1.16043i | 0.113899 | + | 0.0471783i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.5078i | 1.27886i | 0.768848 | + | 0.639432i | \(0.220830\pi\) | ||||
−0.768848 | + | 0.639432i | \(0.779170\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0453910 | − | 0.109584i | 0.00183632 | − | 0.00443328i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.5414 | + | 16.7928i | −1.63745 | + | 0.678254i | −0.996037 | − | 0.0889418i | \(-0.971651\pi\) |
−0.641413 | + | 0.767196i | \(0.721651\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.1405 | − | 14.1405i | 0.569276 | − | 0.569276i | −0.362650 | − | 0.931926i | \(-0.618128\pi\) |
0.931926 | + | 0.362650i | \(0.118128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.7763 | − | 7.36320i | 0.714491 | − | 0.295952i | 0.00432943 | − | 0.999991i | \(-0.498622\pi\) |
0.710162 | + | 0.704039i | \(0.248622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 33.1054i | − | 1.32634i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 12.9622i | − | 0.518487i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.76546 | − | 2.80235i | 0.269757 | − | 0.111737i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1654 | − | 14.1654i | 0.563915 | − | 0.563915i | −0.366502 | − | 0.930417i | \(-0.619445\pi\) |
0.930417 | + | 0.366502i | \(0.119445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.03602 | + | 3.32863i | −0.318900 | + | 0.132093i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.77663 | − | 4.28917i | 0.0703927 | − | 0.169943i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.51722i | 0.138922i | 0.997585 | + | 0.0694610i | \(0.0221279\pi\) | ||||
−0.997585 | + | 0.0694610i | \(0.977872\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.4159 | − | 11.7702i | −1.12061 | − | 0.464173i | −0.256032 | − | 0.966668i | \(-0.582415\pi\) |
−0.864580 | + | 0.502496i | \(0.832415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.2793 | − | 22.2793i | 0.875889 | − | 0.875889i | −0.117217 | − | 0.993106i | \(-0.537397\pi\) |
0.993106 | + | 0.117217i | \(0.0373973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.1649 | + | 15.1649i | 0.595275 | + | 0.595275i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.57865 | − | 3.81119i | 0.0617772 | − | 0.149143i | −0.889976 | − | 0.456007i | \(-0.849279\pi\) |
0.951754 | + | 0.306863i | \(0.0992794\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9387 | −0.583704 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.2385 | − | 5.48357i | −0.515699 | − | 0.213610i | 0.109627 | − | 0.993973i | \(-0.465034\pi\) |
−0.625327 | + | 0.780363i | \(0.715034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.61142 | − | 23.2040i | −0.373841 | − | 0.902532i | −0.993092 | − | 0.117339i | \(-0.962564\pi\) |
0.619251 | − | 0.785193i | \(-0.287436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.5579 | + | 22.5579i | 0.874758 | + | 0.874758i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.15674 | + | 10.0353i | 0.160950 | + | 0.388567i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.136607 | −0.00527366 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4509 | −0.479947 | −0.239974 | − | 0.970779i | \(-0.577139\pi\) | ||||
−0.239974 | + | 0.970779i | \(0.577139\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.84859 | + | 16.5340i | 0.263213 | + | 0.635451i | 0.999134 | − | 0.0416159i | \(-0.0132506\pi\) |
−0.735921 | + | 0.677067i | \(0.763251\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.1519 | + | 30.1519i | 1.15712 | + | 1.15712i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.54777 | + | 23.0504i | 0.365335 | + | 0.881997i | 0.994501 | + | 0.104726i | \(0.0333966\pi\) |
−0.629166 | + | 0.777271i | \(0.716603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.04663 | + | 2.50460i | 0.231030 | + | 0.0956958i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.80469 | −0.144947 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.714680 | − | 1.72539i | 0.0271877 | − | 0.0656369i | −0.909703 | − | 0.415260i | \(-0.863690\pi\) |
0.936890 | + | 0.349623i | \(0.113690\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.4562 | + | 13.4562i | 0.510424 | + | 0.510424i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0277 | + | 28.0277i | −1.06162 | + | 1.06162i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2566 | + | 9.63319i | 0.878388 | + | 0.363840i | 0.775872 | − | 0.630891i | \(-0.217310\pi\) |
0.102517 | + | 0.994731i | \(0.467310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.82957i | 0.370729i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.2289 | + | 51.2512i | −0.798396 | + | 1.92750i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.2006 | − | 15.4090i | 1.39710 | − | 0.578698i | 0.448102 | − | 0.893982i | \(-0.352100\pi\) |
0.948997 | + | 0.315285i | \(0.102100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.76307 | − | 7.76307i | 0.290729 | − | 0.290729i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.901729 | − | 0.373508i | 0.0337227 | − | 0.0139684i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.2965i | 0.383996i | 0.981395 | + | 0.191998i | \(0.0614968\pi\) | ||||
−0.981395 | + | 0.191998i | \(0.938503\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 17.4669i | − | 0.650500i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.1511 | − | 5.44737i | 0.488420 | − | 0.202310i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.6565 | + | 13.6565i | −0.506493 | + | 0.506493i | −0.913448 | − | 0.406955i | \(-0.866591\pi\) |
0.406955 | + | 0.913448i | \(0.366591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1028 | + | 5.42737i | −0.484626 | + | 0.200739i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.2351 | − | 29.5382i | 0.451915 | − | 1.09102i | −0.519678 | − | 0.854362i | \(-0.673948\pi\) |
0.971593 | − | 0.236657i | \(-0.0760517\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 40.1859i | − | 1.48027i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.26176 | + | 2.17949i | 0.193557 | + | 0.0801739i | 0.477356 | − | 0.878710i | \(-0.341595\pi\) |
−0.283800 | + | 0.958884i | \(0.591595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.0314 | + | 17.0314i | −0.624823 | + | 0.624823i | −0.946761 | − | 0.321938i | \(-0.895666\pi\) |
0.321938 | + | 0.946761i | \(0.395666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6926 | + | 14.6926i | 0.538295 | + | 0.538295i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.55375 | − | 15.8221i | 0.239469 | − | 0.578129i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.21219 | −0.190196 | −0.0950978 | − | 0.995468i | \(-0.530316\pi\) | ||||
−0.0950978 | + | 0.995468i | \(0.530316\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.64090 | + | 2.33654i | 0.205293 | + | 0.0850353i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.99669 | + | 14.4773i | 0.217953 | + | 0.526186i | 0.994604 | − | 0.103746i | \(-0.0330828\pi\) |
−0.776650 | + | 0.629932i | \(0.783083\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.7870 | − | 16.7870i | −0.608528 | − | 0.608528i | 0.334033 | − | 0.942561i | \(-0.391590\pi\) |
−0.942561 | + | 0.334033i | \(0.891590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.3146 | + | 56.2865i | 0.844046 | + | 2.03771i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.58837 | 0.0573526 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.1933 | 1.19698 | 0.598491 | − | 0.801129i | \(-0.295767\pi\) | ||||
0.598491 | + | 0.801129i | \(0.295767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.41657 | − | 13.0767i | −0.194820 | − | 0.470338i | 0.796038 | − | 0.605247i | \(-0.206926\pi\) |
−0.990858 | + | 0.134909i | \(0.956926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.1734 | − | 10.1734i | −0.365440 | − | 0.365440i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.3608 | − | 49.1552i | −0.729500 | − | 1.76117i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9632 | − | 9.51169i | −0.821689 | − | 0.340355i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.8807 | −0.531115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.2278 | + | 44.0057i | −0.649750 | + | 1.56864i | 0.163387 | + | 0.986562i | \(0.447758\pi\) |
−0.813136 | + | 0.582073i | \(0.802242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56.6614 | − | 56.6614i | −2.01465 | − | 2.01465i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.00715408 | + | 0.00715408i | −0.000254049 | + | 0.000254049i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.3377 | + | 13.8089i | 1.18088 | + | 0.489138i | 0.884776 | − | 0.466017i | \(-0.154311\pi\) |
0.296107 | + | 0.955155i | \(0.404311\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.24803i | 0.0795298i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.11619 | − | 19.5942i | 0.286414 | − | 0.691465i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.1028 | − | 5.42734i | 0.461812 | − | 0.191289i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.3585 | − | 13.3585i | 0.469661 | − | 0.469661i | −0.432144 | − | 0.901805i | \(-0.642243\pi\) |
0.901805 | + | 0.432144i | \(0.142243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.9118 | − | 10.3188i | 0.874772 | − | 0.362343i | 0.100305 | − | 0.994957i | \(-0.468018\pi\) |
0.774467 | + | 0.632614i | \(0.218018\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2.13110i | − | 0.0746490i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 19.0372i | − | 0.666026i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.1686 | + | 16.2242i | −1.36699 | + | 0.566228i | −0.940972 | − | 0.338485i | \(-0.890086\pi\) |
−0.426023 | + | 0.904712i | \(0.640086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.6538 | − | 26.6538i | 0.929095 | − | 0.929095i | −0.0685527 | − | 0.997647i | \(-0.521838\pi\) |
0.997647 | + | 0.0685527i | \(0.0218381\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.4095 | − | 10.5250i | 0.883576 | − | 0.365989i | 0.105693 | − | 0.994399i | \(-0.466294\pi\) |
0.777883 | + | 0.628410i | \(0.216294\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.57539 | + | 13.4602i | −0.193641 | + | 0.467491i | −0.990642 | − | 0.136487i | \(-0.956419\pi\) |
0.797001 | + | 0.603979i | \(0.206419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 87.9894i | 3.04865i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.1193 | + | 7.09105i | 0.592438 | + | 0.245396i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.3694 | − | 20.3694i | 0.703231 | − | 0.703231i | −0.261872 | − | 0.965103i | \(-0.584340\pi\) |
0.965103 | + | 0.261872i | \(0.0843397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.1838 | − | 12.1838i | −0.420130 | − | 0.420130i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.56105 | + | 11.0113i | −0.156905 | + | 0.378802i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.9654 | −0.548577 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.03723 | + | 1.67228i | 0.138395 | + | 0.0573249i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.58123 | + | 6.23163i | 0.0883795 | + | 0.213367i | 0.961889 | − | 0.273440i | \(-0.0881615\pi\) |
−0.873510 | + | 0.486807i | \(0.838161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.2096 | + | 11.2096i | 0.382911 | + | 0.382911i | 0.872150 | − | 0.489239i | \(-0.162725\pi\) |
−0.489239 | + | 0.872150i | \(0.662725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.70400 | + | 6.52804i | 0.0922594 | + | 0.222734i | 0.963272 | − | 0.268526i | \(-0.0865365\pi\) |
−0.871013 | + | 0.491260i | \(0.836537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.1544 | 0.583943 | 0.291972 | − | 0.956427i | \(-0.405689\pi\) | ||||
0.291972 | + | 0.956427i | \(0.405689\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.9271 | −0.371532 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.4167 | − | 44.4618i | −0.624743 | − | 1.50826i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.10453 | − | 2.10453i | −0.0713091 | − | 0.0713091i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.6833 | − | 37.8629i | −0.530193 | − | 1.28000i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.9641 | − | 19.4532i | −1.58586 | − | 0.656886i | −0.596535 | − | 0.802587i | \(-0.703456\pi\) |
−0.989329 | + | 0.145700i | \(0.953456\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.1442 | −0.813438 | −0.406719 | − | 0.913553i | \(-0.633327\pi\) | ||||
−0.406719 | + | 0.913553i | \(0.633327\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.3495 | − | 39.4712i | 0.550205 | − | 1.32831i | −0.367120 | − | 0.930174i | \(-0.619656\pi\) |
0.917325 | − | 0.398140i | \(-0.130344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4225 | + | 22.4225i | 0.752872 | + | 0.752872i | 0.975014 | − | 0.222142i | \(-0.0713049\pi\) |
−0.222142 | + | 0.975014i | \(0.571305\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.3825 | − | 32.3825i | 1.08607 | − | 1.08607i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.78786 | − | 1.15477i | −0.0932922 | − | 0.0386429i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.99478i | 0.300662i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.55234 | − | 10.9903i | 0.151829 | − | 0.366548i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.6204 | − | 27.5951i | 2.21945 | − | 0.919325i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.81581 | + | 9.81581i | −0.326289 | + | 0.326289i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.7879 | + | 6.95376i | −0.557431 | + | 0.230896i | −0.643570 | − | 0.765388i | \(-0.722547\pi\) |
0.0861382 | + | 0.996283i | \(0.472547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.4718i | 1.70534i | 0.522451 | + | 0.852669i | \(0.325018\pi\) | ||||
−0.522451 | + | 0.852669i | \(0.674982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.54855i | 0.117440i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 72.6654 | − | 30.0990i | 2.39962 | − | 0.993957i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8706 | − | 24.8706i | 0.820407 | − | 0.820407i | −0.165760 | − | 0.986166i | \(-0.553008\pi\) |
0.986166 | + | 0.165760i | \(0.0530076\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.70070 | + | 0.704454i | −0.0559793 | + | 0.0231874i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.19150 | − | 5.29075i | 0.0720561 | − | 0.173959i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 10.4466i | − | 0.342740i | −0.985207 | − | 0.171370i | \(-0.945181\pi\) | ||
0.985207 | − | 0.171370i | \(-0.0548194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −109.118 | − | 45.1984i | −3.57621 | − | 1.48132i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.0803 | + | 13.0803i | −0.427772 | + | 0.427772i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.5899 | − | 32.5899i | −1.06466 | − | 1.06466i | −0.997759 | − | 0.0669050i | \(-0.978688\pi\) |
−0.0669050 | − | 0.997759i | \(-0.521312\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8677 | + | 50.3791i | −0.680268 | + | 1.64231i | 0.0832512 | + | 0.996529i | \(0.473470\pi\) |
−0.763520 | + | 0.645785i | \(0.776530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.6531 | −0.770251 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.61124 | − | 1.49582i | −0.117349 | − | 0.0486077i | 0.323236 | − | 0.946318i | \(-0.395229\pi\) |
−0.440586 | + | 0.897711i | \(0.645229\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.601101 | − | 1.45119i | −0.0195126 | − | 0.0471075i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6527 | + | 29.6527i | 0.960544 | + | 0.960544i | 0.999251 | − | 0.0387065i | \(-0.0123237\pi\) |
−0.0387065 | + | 0.999251i | \(0.512324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.18213 | + | 5.26814i | 0.0706122 | + | 0.170473i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.4586 | −1.11273 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.9765 | 0.612146 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.97152 | + | 9.58810i | 0.127848 | + | 0.308652i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.0414 | + | 15.0414i | 0.483697 | + | 0.483697i | 0.906310 | − | 0.422613i | \(-0.138887\pi\) |
−0.422613 | + | 0.906310i | \(0.638887\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.522995 | − | 1.26262i | −0.0167837 | − | 0.0405195i | 0.915266 | − | 0.402851i | \(-0.131981\pi\) |
−0.932049 | + | 0.362332i | \(0.881981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −92.5664 | − | 38.3423i | −2.96754 | − | 1.22920i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.54082 | 0.209259 | 0.104630 | − | 0.994511i | \(-0.466634\pi\) | ||||
0.104630 | + | 0.994511i | \(0.466634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.86076 | + | 23.8060i | −0.315151 | + | 0.760843i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2187 | + | 11.2187i | 0.357820 | + | 0.357820i | 0.863009 | − | 0.505189i | \(-0.168577\pi\) |
−0.505189 | + | 0.863009i | \(0.668577\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.41938 | + | 4.41938i | −0.140813 | + | 0.140813i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.81900 | − | 3.23874i | −0.248630 | − | 0.102986i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.7152i | 0.594507i | 0.954799 | + | 0.297254i | \(0.0960707\pi\) | ||||
−0.954799 | + | 0.297254i | \(0.903929\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.33105 | + | 10.4561i | −0.137303 | + | 0.331480i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.03956 | + | 2.08745i | −0.159604 | + | 0.0661103i | −0.461055 | − | 0.887371i | \(-0.652529\pi\) |
0.301451 | + | 0.953482i | \(0.402529\pi\) | |||||||
\(998\) | 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 | 1152.2.w.a.1007.4 | 32 | ||
3.2 | odd | 2 | 1152.2.w.b.1007.5 | 32 | |||
4.3 | odd | 2 | 288.2.w.b.179.6 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.a.179.3 | ✓ | 32 | ||
32.5 | even | 8 | 288.2.w.a.251.3 | yes | 32 | ||
32.27 | odd | 8 | 1152.2.w.b.143.5 | 32 | |||
96.5 | odd | 8 | 288.2.w.b.251.6 | yes | 32 | ||
96.59 | even | 8 | inner | 1152.2.w.a.143.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.3 | ✓ | 32 | 12.11 | even | 2 | ||
288.2.w.a.251.3 | yes | 32 | 32.5 | even | 8 | ||
288.2.w.b.179.6 | yes | 32 | 4.3 | odd | 2 | ||
288.2.w.b.251.6 | yes | 32 | 96.5 | odd | 8 | ||
1152.2.w.a.143.4 | 32 | 96.59 | even | 8 | inner | ||
1152.2.w.a.1007.4 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.b.143.5 | 32 | 32.27 | odd | 8 | |||
1152.2.w.b.1007.5 | 32 | 3.2 | odd | 2 |