Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,2,Mod(129,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.c (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: | \(5.11042572936\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.129 |
Dual form | 640.2.c.a.129.6 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.90321i | − | 1.67617i | −0.545540 | − | 0.838085i | \(-0.683675\pi\) | ||
0.545540 | − | 0.838085i | \(-0.316325\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.311108 | − | 2.21432i | −0.139132 | − | 0.990274i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.52543i | − | 1.33249i | −0.745735 | − | 0.666243i | \(-0.767901\pi\) | ||
0.745735 | − | 0.666243i | \(-0.232099\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.42864 | −1.80955 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.80642 | 1.14768 | 0.573840 | − | 0.818967i | \(-0.305453\pi\) | ||||
0.573840 | + | 0.818967i | \(0.305453\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.62222i | − | 0.727272i | −0.931541 | − | 0.363636i | \(-0.881535\pi\) | ||
0.931541 | − | 0.363636i | \(-0.118465\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.42864 | + | 0.903212i | −1.65987 | + | 0.233208i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.80642i | 1.40826i | 0.710069 | + | 0.704132i | \(0.248664\pi\) | ||||
−0.710069 | + | 0.704132i | \(0.751336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.05086 | 1.15875 | 0.579373 | − | 0.815063i | \(-0.303298\pi\) | ||||
0.579373 | + | 0.815063i | \(0.303298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.2351 | −2.23347 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.474572i | 0.0989552i | 0.998775 | + | 0.0494776i | \(0.0157556\pi\) | ||||
−0.998775 | + | 0.0494776i | \(0.984244\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80642 | + | 1.37778i | −0.961285 | + | 0.275557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.05086i | 1.35694i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.75557 | 0.494915 | 0.247457 | − | 0.968899i | \(-0.420405\pi\) | ||||
0.247457 | + | 0.968899i | \(0.420405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 11.0509i | − | 1.92371i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.80642 | + | 1.09679i | −1.31953 | + | 0.185391i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.18421i | 1.18108i | 0.807010 | + | 0.590538i | \(0.201085\pi\) | ||||
−0.807010 | + | 0.590538i | \(0.798915\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.61285 | −1.21903 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.18421 | 0.809637 | 0.404819 | − | 0.914397i | \(-0.367335\pi\) | ||||
0.404819 | + | 0.914397i | \(0.367335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.95407i | 0.297992i | 0.988838 | + | 0.148996i | \(0.0476042\pi\) | ||||
−0.988838 | + | 0.148996i | \(0.952396\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.68889 | + | 12.0207i | 0.251765 | + | 1.79195i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.33185i | 0.777730i | 0.921295 | + | 0.388865i | \(0.127133\pi\) | ||||
−0.921295 | + | 0.388865i | \(0.872867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.42864 | −0.775520 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.8573 | 2.36049 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.37778i | − | 0.738695i | −0.929291 | − | 0.369348i | \(-0.879581\pi\) | ||
0.929291 | − | 0.369348i | \(-0.120419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18421 | − | 8.42864i | −0.159679 | − | 1.13652i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 14.6637i | − | 1.94225i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.05086 | −0.657565 | −0.328783 | − | 0.944406i | \(-0.606638\pi\) | ||||
−0.328783 | + | 0.944406i | \(0.606638\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2351 | −1.56654 | −0.783270 | − | 0.621682i | \(-0.786450\pi\) | ||||
−0.783270 | + | 0.621682i | \(0.786450\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.1383i | 2.41120i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.80642 | + | 0.815792i | −0.720198 | + | 0.101187i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.76049i | − | 0.948095i | −0.880499 | − | 0.474047i | \(-0.842793\pi\) | ||
0.880499 | − | 0.474047i | \(-0.157207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.37778 | 0.165866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.85728 | 0.576453 | 0.288226 | − | 0.957562i | \(-0.406934\pi\) | ||||
0.288226 | + | 0.957562i | \(0.406934\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.66370i | 0.779927i | 0.920830 | + | 0.389964i | \(0.127512\pi\) | ||||
−0.920830 | + | 0.389964i | \(0.872488\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | + | 13.9541i | 0.461880 | + | 1.61128i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13.4193i | − | 1.52927i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.24443 | −0.590045 | −0.295022 | − | 0.955490i | \(-0.595327\pi\) | ||||
−0.295022 | + | 0.955490i | \(0.595327\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.18421 | 0.464912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.1476i | − | 1.33338i | −0.745336 | − | 0.666689i | \(-0.767711\pi\) | ||
0.745336 | − | 0.666689i | \(-0.232289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.8573 | − | 1.80642i | 1.39457 | − | 0.195934i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.80642i | − | 0.622514i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.1017 | 1.28278 | 0.641389 | − | 0.767216i | \(-0.278358\pi\) | ||||
0.641389 | + | 0.767216i | \(0.278358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.24443 | −0.969080 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.00000i | − | 0.829561i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.57136 | − | 11.1842i | −0.161218 | − | 1.14748i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8064i | 1.40183i | 0.713245 | + | 0.700915i | \(0.247225\pi\) | ||||
−0.713245 | + | 0.700915i | \(0.752775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.6637 | −2.07678 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.7146 | 1.96167 | 0.980836 | − | 0.194836i | \(-0.0624173\pi\) | ||||
0.980836 | + | 0.194836i | \(0.0624173\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.13828i | − | 0.309223i | −0.987975 | − | 0.154612i | \(-0.950587\pi\) | ||
0.987975 | − | 0.154612i | \(-0.0494127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.18421 | + | 22.6637i | 0.310747 | + | 2.21175i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.39207i | − | 0.521272i | −0.965437 | − | 0.260636i | \(-0.916068\pi\) | ||
0.965437 | − | 0.260636i | \(-0.0839322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.62222 | −0.825858 | −0.412929 | − | 0.910763i | \(-0.635494\pi\) | ||||
−0.412929 | + | 0.910763i | \(0.635494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.8573 | 1.97969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.51114i | − | 0.518444i | −0.965818 | − | 0.259222i | \(-0.916534\pi\) | ||
0.965818 | − | 0.259222i | \(-0.0834662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.05086 | − | 0.147643i | 0.0979927 | − | 0.0137678i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.2351i | 1.31603i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.4701 | 1.87649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.48886 | 0.317169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 15.0509i | − | 1.35709i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.54617 | + | 10.2143i | 0.406622 | + | 0.913597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2810i | − | 0.912291i | −0.889905 | − | 0.456145i | \(-0.849230\pi\) | ||
0.889905 | − | 0.456145i | \(-0.150770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.67307 | 0.499486 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.66370 | −0.407470 | −0.203735 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203735 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 17.8064i | − | 1.54401i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.6128 | − | 2.19358i | 1.34374 | − | 0.188793i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3461i | 0.969366i | 0.874690 | + | 0.484683i | \(0.161065\pi\) | ||||
−0.874690 | + | 0.484683i | \(0.838935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8064 | 1.00141 | 0.500704 | − | 0.865619i | \(-0.333075\pi\) | ||||
0.500704 | + | 0.865619i | \(0.333075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.4795 | 1.30361 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 9.98126i | − | 0.834675i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.622216 | − | 4.42864i | −0.0516722 | − | 0.367778i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.7605i | 1.29990i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.47949 | 0.448898 | 0.224449 | − | 0.974486i | \(-0.427942\pi\) | ||||
0.224449 | + | 0.974486i | \(0.427942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.6128 | −1.92159 | −0.960793 | − | 0.277266i | \(-0.910572\pi\) | ||||
−0.960793 | + | 0.277266i | \(0.910572\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 31.5210i | − | 2.54832i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.857279 | − | 6.10171i | −0.0688583 | − | 0.490101i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.815792i | 0.0651073i | 0.999470 | + | 0.0325536i | \(0.0103640\pi\) | ||||
−0.999470 | + | 0.0325536i | \(0.989636\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.6128 | −1.23818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.67307 | 0.131856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.9032i | − | 0.854005i | −0.904250 | − | 0.427003i | \(-0.859569\pi\) | ||
0.904250 | − | 0.427003i | \(-0.140431\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −24.4701 | + | 3.43801i | −1.90500 | + | 0.267649i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.57628i | 0.508888i | 0.967088 | + | 0.254444i | \(0.0818925\pi\) | ||||
−0.967088 | + | 0.254444i | \(0.918108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.12399 | 0.471076 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −27.4193 | −2.09680 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5303i | 0.800608i | 0.916382 | + | 0.400304i | \(0.131095\pi\) | ||||
−0.916382 | + | 0.400304i | \(0.868905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.85728 | + | 16.9447i | 0.367176 | + | 1.28090i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6637i | 1.10219i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.29529 | −0.470532 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.488863 | −0.0363369 | −0.0181684 | − | 0.999835i | \(-0.505784\pi\) | ||||
−0.0181684 | + | 0.999835i | \(0.505784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.5210i | 2.62579i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.9081 | − | 2.23506i | 1.16959 | − | 0.164325i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.1017i | 1.61624i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 24.8573 | 1.80810 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4889 | 0.758947 | 0.379474 | − | 0.925203i | \(-0.376105\pi\) | ||||
0.379474 | + | 0.925203i | \(0.376105\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.8064i | − | 0.993808i | −0.867805 | − | 0.496904i | \(-0.834470\pi\) | ||
0.867805 | − | 0.496904i | \(-0.165530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.36842 | + | 16.8573i | 0.169606 | + | 1.20717i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7239i | 1.19153i | 0.803159 | + | 0.595765i | \(0.203151\pi\) | ||||
−0.803159 | + | 0.595765i | \(0.796849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.8573 | 1.47853 | 0.739267 | − | 0.673413i | \(-0.235172\pi\) | ||||
0.739267 | + | 0.673413i | \(0.235172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.5303 | −1.58917 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 7.05086i | − | 0.494873i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.61285 | − | 11.4795i | −0.112646 | − | 0.801763i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.57628i | − | 0.179064i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.2257 | 1.32987 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.66370 | −0.321063 | −0.160531 | − | 0.987031i | \(-0.551321\pi\) | ||||
−0.160531 | + | 0.987031i | \(0.551321\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 14.1017i | − | 0.966233i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.32693 | − | 0.607926i | 0.295094 | − | 0.0414602i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.71456i | − | 0.659467i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.3461 | 1.30729 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.2257 | 1.02419 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.4558i | 1.77161i | 0.464054 | + | 0.885807i | \(0.346394\pi\) | ||||
−0.464054 | + | 0.885807i | \(0.653606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26.0923 | − | 7.47949i | 1.73949 | − | 0.498633i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.3225i | 0.817872i | 0.912563 | + | 0.408936i | \(0.134100\pi\) | ||||
−0.912563 | + | 0.408936i | \(0.865900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.2257 | −0.873979 | −0.436989 | − | 0.899467i | \(-0.643955\pi\) | ||||
−0.436989 | + | 0.899467i | \(0.643955\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −38.9590 | −2.56331 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.66370i | 0.436554i | 0.975887 | + | 0.218277i | \(0.0700436\pi\) | ||||
−0.975887 | + | 0.218277i | \(0.929956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8064 | − | 1.65878i | 0.770166 | − | 0.108207i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.2257i | 0.989015i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.9590 | 1.48509 | 0.742547 | − | 0.669794i | \(-0.233618\pi\) | ||||
0.742547 | + | 0.669794i | \(0.233618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0415 | −0.904492 | −0.452246 | − | 0.891893i | \(-0.649377\pi\) | ||||
−0.452246 | + | 0.891893i | \(0.649377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.00492i | 0.577666i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.68889 | + | 12.0207i | 0.107899 | + | 0.767977i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 13.2444i | − | 0.842723i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35.2672 | −2.23497 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9304 | −1.57359 | −0.786797 | − | 0.617212i | \(-0.788262\pi\) | ||||
−0.786797 | + | 0.617212i | \(0.788262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.80642i | 0.113569i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.24443 | − | 37.3274i | −0.328419 | − | 2.33753i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 25.7146i | − | 1.60403i | −0.597304 | − | 0.802015i | \(-0.703761\pi\) | ||
0.597304 | − | 0.802015i | \(-0.296239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.3274 | 1.57377 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.8573 | −0.672049 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.57628i | 0.158860i | 0.996840 | + | 0.0794302i | \(0.0253101\pi\) | ||||
−0.996840 | + | 0.0794302i | \(0.974690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.9081 | + | 1.67307i | −0.731511 | + | 0.102776i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 35.1338i | − | 2.15016i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.7462 | −1.56977 | −0.784887 | − | 0.619639i | \(-0.787279\pi\) | ||||
−0.784887 | + | 0.619639i | \(0.787279\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.1847 | −1.83359 | −0.916795 | − | 0.399359i | \(-0.869233\pi\) | ||||
−0.916795 | + | 0.399359i | \(0.869233\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.8385i | 1.62434i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.2953 | + | 5.24443i | −1.10325 | + | 0.316251i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.5303i | − | 0.632707i | −0.948641 | − | 0.316354i | \(-0.897541\pi\) | ||
0.948641 | − | 0.316354i | \(-0.102459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.9590 | −0.895571 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.93978 | −0.473647 | −0.236824 | − | 0.971553i | \(-0.576106\pi\) | ||||
−0.236824 | + | 0.971553i | \(0.576106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.9032i | − | 0.648129i | −0.946035 | − | 0.324064i | \(-0.894951\pi\) | ||
0.946035 | − | 0.324064i | \(-0.105049\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −32.4701 | + | 4.56199i | −1.92336 | + | 0.270229i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 18.2766i | − | 1.07883i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7146 | −0.983209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 40.0830 | 2.34971 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.42864i | − | 0.258724i | −0.991597 | − | 0.129362i | \(-0.958707\pi\) | ||
0.991597 | − | 0.129362i | \(-0.0412929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.57136 | + | 11.1842i | 0.0914881 | + | 0.651170i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.8385i | 1.55733i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.24443 | 0.0719673 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.88892 | 0.397071 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 57.2355i | − | 3.28810i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.80642 | + | 27.0923i | 0.217955 | + | 1.55130i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.27163i | − | 0.300868i | −0.988620 | − | 0.150434i | \(-0.951933\pi\) | ||
0.988620 | − | 0.150434i | \(-0.0480671\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.11108 | −0.518311 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.387152 | −0.0219534 | −0.0109767 | − | 0.999940i | \(-0.503494\pi\) | ||||
−0.0109767 | + | 0.999940i | \(0.503494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.3461i | − | 0.641322i | −0.947194 | − | 0.320661i | \(-0.896095\pi\) | ||
0.947194 | − | 0.320661i | \(-0.103905\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 42.3783 | − | 5.95407i | 2.38774 | − | 0.335474i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 16.7239i | − | 0.939309i | −0.882850 | − | 0.469655i | \(-0.844378\pi\) | ||
0.882850 | − | 0.469655i | \(-0.155622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.61285 | 0.426238 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6543 | −0.873740 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3274i | 1.63182i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.61285 | + | 12.6035i | 0.200405 | + | 0.699115i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.0321i | 1.38428i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.7971 | 1.03632 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.33630 | −0.183379 | −0.0916897 | − | 0.995788i | \(-0.529227\pi\) | ||||
−0.0916897 | + | 0.995788i | \(0.529227\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 39.0005i | − | 2.13721i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.1842 | + | 2.41435i | −0.938874 | + | 0.131910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.61285i | − | 0.196804i | −0.995147 | − | 0.0984022i | \(-0.968627\pi\) | ||
0.995147 | − | 0.0984022i | \(-0.0313732\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.0000 | −0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4889 | 0.568004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5.53972i | − | 0.299117i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.428639 | − | 3.05086i | −0.0230772 | − | 0.164253i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 15.7605i | − | 0.846067i | −0.906114 | − | 0.423034i | \(-0.860965\pi\) | ||
0.906114 | − | 0.423034i | \(-0.139035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.285442 | 0.0152794 | 0.00763968 | − | 0.999971i | \(-0.497568\pi\) | ||||
0.00763968 | + | 0.999971i | \(0.497568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.4889 | 0.986862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.38715i | 0.233505i | 0.993161 | + | 0.116752i | \(0.0372484\pi\) | ||||
−0.993161 | + | 0.116752i | \(0.962752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.51114 | − | 10.7556i | −0.0802028 | − | 0.570846i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 59.4291i | − | 3.14532i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5906 | −1.08673 | −0.543364 | − | 0.839497i | \(-0.682850\pi\) | ||||
−0.543364 | + | 0.839497i | \(0.682850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.51114 | 0.342691 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.1289i | − | 0.531630i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7556 | − | 2.07313i | 0.772342 | − | 0.108513i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5575i | 0.864297i | 0.901802 | + | 0.432148i | \(0.142244\pi\) | ||||
−0.901802 | + | 0.432148i | \(0.857756\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.1432 | −1.46508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.9590 | −0.984302 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8988i | 1.28921i | 0.764516 | + | 0.644605i | \(0.222978\pi\) | ||||
−0.764516 | + | 0.644605i | \(0.777022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.6543 | − | 13.1985i | 1.53134 | − | 0.681568i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.24443i | − | 0.270102i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.31756 | 0.478611 | 0.239305 | − | 0.970944i | \(-0.423080\pi\) | ||||
0.239305 | + | 0.970944i | \(0.423080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.8479 | −1.52915 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.5575i | 1.66361i | 0.555066 | + | 0.831806i | \(0.312693\pi\) | ||||
−0.555066 | + | 0.831806i | \(0.687307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.7146 | + | 4.17484i | −1.51439 | + | 0.212770i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 10.6079i | − | 0.539231i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.9906 | 0.962863 | 0.481432 | − | 0.876484i | \(-0.340117\pi\) | ||||
0.481432 | + | 0.876484i | \(0.340117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.75557 | −0.139355 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5397i | 0.682988i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.63158 | + | 11.6128i | 0.0820939 | + | 0.584306i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.9906i | 1.65575i | 0.560911 | + | 0.827876i | \(0.310451\pi\) | ||||
−0.560911 | + | 0.827876i | \(0.689549\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −51.6958 | −2.58803 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.1017 | −0.804081 | −0.402041 | − | 0.915622i | \(-0.631699\pi\) | ||||
−0.402041 | + | 0.915622i | \(0.631699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.22570i | − | 0.359938i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.30174 | − | 9.26517i | −0.0646840 | − | 0.460390i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.3461i | 1.35550i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3876 | 1.65091 | 0.825456 | − | 0.564466i | \(-0.190918\pi\) | ||||
0.825456 | + | 0.564466i | \(0.190918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.9403 | 1.62482 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.8064i | 0.876197i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.8988 | + | 3.77923i | −1.32041 | + | 0.185515i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 34.2766i | − | 1.67853i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4193 | 1.33952 | 0.669760 | − | 0.742578i | \(-0.266397\pi\) | ||||
0.669760 | + | 0.742578i | \(0.266397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2351 | −0.596301 | −0.298150 | − | 0.954519i | \(-0.596370\pi\) | ||||
−0.298150 | + | 0.954519i | \(0.596370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 28.9447i | − | 1.40734i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.00000 | − | 27.9081i | −0.388057 | − | 1.35374i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.1338i | 2.08739i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.9777 | −1.39906 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.4701 | 1.37136 | 0.685679 | − | 0.727904i | \(-0.259505\pi\) | ||||
0.685679 | + | 0.727904i | \(0.259505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.0098i | − | 1.63441i | −0.576348 | − | 0.817204i | \(-0.695523\pi\) | ||
0.576348 | − | 0.817204i | \(-0.304477\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.8573 | + | 1.80642i | −0.616459 | + | 0.0866114i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.39700i | 0.114664i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8385 | −0.708205 | −0.354103 | − | 0.935207i | \(-0.615214\pi\) | ||||
−0.354103 | + | 0.935207i | \(0.615214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.4701 | 1.40334 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.0968i | 0.622247i | 0.950369 | + | 0.311124i | \(0.100705\pi\) | ||||
−0.950369 | + | 0.311124i | \(0.899295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.76494 | − | 26.7971i | −0.178475 | − | 1.27030i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 15.9081i | − | 0.752429i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.3876 | 1.00934 | 0.504672 | − | 0.863311i | \(-0.331613\pi\) | ||||
0.504672 | + | 0.863311i | \(0.331613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.7333 | 0.929205 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 68.5531i | 3.22091i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.87601 | + | 20.4701i | 0.134830 | + | 0.959654i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9813i | 0.841128i | 0.907263 | + | 0.420564i | \(0.138168\pi\) | ||||
−0.907263 | + | 0.420564i | \(0.861832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −40.9403 | −1.91093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7368 | −0.500064 | −0.250032 | − | 0.968238i | \(-0.580441\pi\) | ||||
−0.250032 | + | 0.968238i | \(0.580441\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.30327i | − | 0.432360i | −0.976354 | − | 0.216180i | \(-0.930640\pi\) | ||
0.976354 | − | 0.216180i | \(-0.0693598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.7146 | + | 2.48886i | −0.821493 | + | 0.115418i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.70964i | 0.403034i | 0.979485 | + | 0.201517i | \(0.0645871\pi\) | ||||
−0.979485 | + | 0.201517i | \(0.935413\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.3590 | −1.26332 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.36842 | 0.109131 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.43801i | 0.342000i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.2766 | + | 6.95899i | −1.11388 | + | 0.319300i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.1941i | 1.33670i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.2257 | 1.06121 | 0.530605 | − | 0.847619i | \(-0.321965\pi\) | ||||
0.530605 | + | 0.847619i | \(0.321965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.8385 | 0.858964 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.85728i | − | 0.221014i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.5718 | − | 4.29529i | 1.38820 | − | 0.195039i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.8528i | − | 1.48870i | −0.667787 | − | 0.744352i | \(-0.732759\pi\) | ||
0.667787 | − | 0.744352i | \(-0.267241\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.6543 | −1.43146 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.94914 | 0.133093 | 0.0665465 | − | 0.997783i | \(-0.478802\pi\) | ||||
0.0665465 | + | 0.997783i | \(0.478802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6128i | 0.523016i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.42864 | + | 45.7560i | 0.288946 | + | 2.05658i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 17.1240i | − | 0.768116i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.0321 | −1.56825 | −0.784127 | − | 0.620601i | \(-0.786889\pi\) | ||||
−0.784127 | + | 0.620601i | \(0.786889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.0923 | 0.852983 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.2908i | 0.726373i | 0.931717 | + | 0.363186i | \(0.118311\pi\) | ||||
−0.931717 | + | 0.363186i | \(0.881689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.13335 | − | 43.6543i | −0.272931 | − | 1.94259i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 17.7792i | − | 0.789603i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.0000 | 1.15243 | 0.576215 | − | 0.817298i | \(-0.304529\pi\) | ||||
0.576215 | + | 0.817298i | \(0.304529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.4924 | 1.03924 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.6128i | 1.57235i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.94914 | + | 0.976342i | −0.306216 | + | 0.0430228i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2953i | 0.892586i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.5718 | 1.34195 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7146 | 0.513224 | 0.256612 | − | 0.966514i | \(-0.417394\pi\) | ||||
0.256612 | + | 0.966514i | \(0.417394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.0370i | 1.66324i | 0.555342 | + | 0.831622i | \(0.312587\pi\) | ||||
−0.555342 | + | 0.831622i | \(0.687413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 49.1941 | − | 14.1017i | 2.14700 | − | 0.615449i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0000i | 0.696971i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7748 | 0.990208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.4193 | 1.18990 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13.5941i | − | 0.588826i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.9398 | + | 1.67752i | −0.516202 | + | 0.0725254i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.2766i | 0.788691i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.6637 | −0.890049 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.5111 | −0.494902 | −0.247451 | − | 0.968900i | \(-0.579593\pi\) | ||||
−0.247451 | + | 0.968900i | \(0.579593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.41927i | 0.0609068i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.68244 | + | 19.0923i | 0.114903 | + | 0.817826i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.2208i | 1.29215i | 0.763275 | + | 0.646073i | \(0.223590\pi\) | ||||
−0.763275 | + | 0.646073i | \(0.776410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 66.4197 | 2.83473 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1017 | 0.430347 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.4889i | 0.786226i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.48886 | − | 46.1847i | −0.275437 | − | 1.96043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.75605i | 0.413377i | 0.978407 | + | 0.206688i | \(0.0662687\pi\) | ||||
−0.978407 | + | 0.206688i | \(0.933731\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12399 | 0.216721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 64.1659 | 2.70909 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.50622i | 0.189914i | 0.995481 | + | 0.0949572i | \(0.0302714\pi\) | ||||
−0.995481 | + | 0.0949572i | \(0.969729\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2034 | + | 1.71456i | −0.513402 | + | 0.0721320i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 14.7511i | − | 0.619489i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.30465 | −0.222383 | −0.111191 | − | 0.993799i | \(-0.535467\pi\) | ||||
−0.111191 | + | 0.993799i | \(0.535467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.3970 | −0.686193 | −0.343096 | − | 0.939300i | \(-0.611476\pi\) | ||||
−0.343096 | + | 0.939300i | \(0.611476\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 30.4514i | − | 1.27213i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.653858 | − | 2.28100i | −0.0272678 | − | 0.0951241i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.8163i | 1.65757i | 0.559565 | + | 0.828786i | \(0.310968\pi\) | ||||
−0.559565 | + | 0.828786i | \(0.689032\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.0830 | −1.66579 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.8256 | −1.77671 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 20.4701i | − | 0.847786i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.5210 | − | 4.42864i | 1.30323 | − | 0.183102i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 15.1699i | − | 0.626130i | −0.949732 | − | 0.313065i | \(-0.898644\pi\) | ||
0.949732 | − | 0.313065i | \(-0.101356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.9180 | 0.573480 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 48.5531 | 1.99721 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.00000i | 0.328521i | 0.986417 | + | 0.164260i | \(0.0525237\pi\) | ||||
−0.986417 | + | 0.164260i | \(0.947476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.36842 | − | 45.3274i | −0.261080 | − | 1.85824i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 60.5531i | − | 2.47827i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.83500 | 0.0749762 | 0.0374881 | − | 0.999297i | \(-0.488064\pi\) | ||||
0.0374881 | + | 0.999297i | \(0.488064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.1432 | −1.47431 | −0.737156 | − | 0.675723i | \(-0.763832\pi\) | ||||
−0.737156 | + | 0.675723i | \(0.763832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 42.1289i | 1.71562i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.08541 | − | 7.72546i | −0.0441283 | − | 0.314084i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.5353i | 0.711735i | 0.934536 | + | 0.355867i | \(0.115815\pi\) | ||||
−0.934536 | + | 0.355867i | \(0.884185\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.4701 | −0.829491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.9813 | 0.565621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 33.9309i | − | 1.37046i | −0.728329 | − | 0.685228i | \(-0.759703\pi\) | ||
0.728329 | − | 0.685228i | \(-0.240297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.3274 | + | 4.68244i | −1.34389 | + | 0.188814i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.68598i | − | 0.389943i | −0.980809 | − | 0.194971i | \(-0.937539\pi\) | ||
0.980809 | − | 0.194971i | \(-0.0624614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.4005 | 1.66403 | 0.832014 | − | 0.554755i | \(-0.187188\pi\) | ||||
0.832014 | + | 0.554755i | \(0.187188\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.34614 | −0.134276 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 42.6637i | − | 1.70929i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | − | 13.2444i | 0.848137 | − | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 55.8163i | − | 2.22909i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41.7146 | −1.66327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.8163 | 1.10735 | 0.553674 | − | 0.832733i | \(-0.313225\pi\) | ||||
0.553674 | + | 0.832733i | \(0.313225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.5397i | 0.538155i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.7654 | + | 3.19850i | −0.903418 | + | 0.126929i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.2351i | 0.564014i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.3684 | −1.04312 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.8988 | 1.69440 | 0.847200 | − | 0.531275i | \(-0.178287\pi\) | ||||
0.847200 | + | 0.531275i | \(0.178287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.9639i | − | 1.10279i | −0.834245 | − | 0.551395i | \(-0.814096\pi\) | ||
0.834245 | − | 0.551395i | \(-0.185904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.76494 | − | 12.5620i | −0.0694943 | − | 0.494628i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.13828i | − | 0.280635i | −0.990107 | − | 0.140317i | \(-0.955188\pi\) | ||
0.990107 | − | 0.140317i | \(-0.0448123\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.2257 | −0.754675 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.2034 | −1.10538 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.7649i | 0.695196i | 0.937644 | + | 0.347598i | \(0.113003\pi\) | ||||
−0.937644 | + | 0.347598i | \(0.886997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.45091 | + | 10.3269i | 0.0566919 | + | 0.403507i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 36.1748i | − | 1.41131i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.1936 | 0.786630 | 0.393315 | − | 0.919404i | \(-0.371328\pi\) | ||||
0.393315 | + | 0.919404i | \(0.371328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0701 | 0.858426 | 0.429213 | − | 0.903203i | \(-0.358791\pi\) | ||||
0.429213 | + | 0.903203i | \(0.358791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 44.2034i | − | 1.71672i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −39.4291 | + | 5.53972i | −1.52900 | + | 0.214821i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.949145i | 0.0367510i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 76.8069 | 2.96953 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −46.5718 | −1.79789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0098i | 1.00261i | 0.865272 | + | 0.501303i | \(0.167146\pi\) | ||||
−0.865272 | + | 0.501303i | \(0.832854\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.71456 | − | 33.8894i | −0.373914 | − | 1.30440i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 7.86665i | − | 0.302340i | −0.988508 | − | 0.151170i | \(-0.951696\pi\) | ||
0.988508 | − | 0.151170i | \(-0.0483041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.6735 | 1.86792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35.7748 | 1.37089 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18.2494i | − | 0.698292i | −0.937068 | − | 0.349146i | \(-0.886472\pi\) | ||
0.937068 | − | 0.349146i | \(-0.113528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.1240 | − | 3.52987i | 0.959938 | − | 0.134870i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.3970i | 1.46494i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.1017 | −0.537232 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2543 | 0.960718 | 0.480359 | − | 0.877072i | \(-0.340506\pi\) | ||||
0.480359 | + | 0.877072i | \(0.340506\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 72.8484i | 2.76728i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.67307 | − | 26.1432i | −0.139328 | − | 0.991668i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.1017i | 1.14018i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.3461 | 0.731738 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.8069 | 1.31464 | 0.657319 | − | 0.753612i | \(-0.271690\pi\) | ||||
0.657319 | + | 0.753612i | \(0.271690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.2864i | 1.36857i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.81579 | − | 34.2766i | −0.181373 | − | 1.29093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 69.5022i | − | 2.61390i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.51114 | 0.282087 | 0.141043 | − | 0.990003i | \(-0.454954\pi\) | ||||
0.141043 | + | 0.990003i | \(0.454954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.4701 | 1.06771 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.30772i | 0.0489744i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.1017 | + | 3.10525i | −0.826557 | + | 0.116130i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 66.6548i | − | 2.48927i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.7556 | 0.997814 | 0.498907 | − | 0.866655i | \(-0.333735\pi\) | ||||
0.498907 | + | 0.866655i | \(0.333735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0638 | −0.412036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.7654i | 1.51608i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.61285 | + | 2.75557i | −0.357012 | + | 0.102339i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.6271i | − | 0.950458i | −0.879862 | − | 0.475229i | \(-0.842365\pi\) | ||
0.879862 | − | 0.475229i | \(-0.157635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.6958 | 1.43318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.3461 | −0.419652 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6543i | 0.725949i | 0.931799 | + | 0.362975i | \(0.118239\pi\) | ||||
−0.931799 | + | 0.362975i | \(0.881761\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.8988 | − | 4.90321i | 1.28726 | − | 0.180858i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 29.5397i | − | 1.08811i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.5433 | −1.19712 | −0.598562 | − | 0.801077i | \(-0.704261\pi\) | ||||
−0.598562 | + | 0.801077i | \(0.704261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.4514 | −1.41255 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.1383i | − | 0.848861i | −0.905461 | − | 0.424430i | \(-0.860474\pi\) | ||
0.905461 | − | 0.424430i | \(-0.139526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.70471 | − | 12.1334i | −0.0624559 | − | 0.444532i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 65.9452i | 2.41281i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.0094 | −0.694587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.48886 | 0.0908199 | 0.0454099 | − | 0.998968i | \(-0.485541\pi\) | ||||
0.0454099 | + | 0.998968i | \(0.485541\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 72.3783i | 2.63761i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.34614 | + | 52.2864i | 0.267353 | + | 1.90290i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2859i | 0.773650i | 0.922153 | + | 0.386825i | \(0.126428\pi\) | ||||
−0.922153 | + | 0.386825i | \(0.873572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.24443 | 0.190361 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1240 | 0.693244 | 0.346622 | − | 0.938005i | \(-0.387329\pi\) | ||||
0.346622 | + | 0.938005i | \(0.387329\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.3970i | 1.10045i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −69.7975 | + | 9.80642i | −2.52354 | + | 0.354552i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2444i | 0.478229i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.9625 | 1.22472 | 0.612360 | − | 0.790579i | \(-0.290220\pi\) | ||||
0.612360 | + | 0.790579i | \(0.290220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −74.6548 | −2.68863 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.133353i | 0.00479638i | 0.999997 | + | 0.00239819i | \(0.000763368\pi\) | ||||
−0.999997 | + | 0.00239819i | \(0.999237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.2444 | + | 3.79658i | −0.475754 | + | 0.136377i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 73.5308i | − | 2.63790i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.1847 | 0.938164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.4889 | 0.661584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1017i | 0.503954i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.80642 | − | 0.253799i | 0.0644740 | − | 0.00905848i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.12537i | − | 0.0401150i | −0.999799 | − | 0.0200575i | \(-0.993615\pi\) | ||
0.999799 | − | 0.0200575i | \(-0.00638494\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.47949 | 0.266277 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.4291 | −0.690820 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0830i | 1.13930i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.85728 | + | 34.5718i | 0.172270 | + | 1.22614i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.11108i | − | 0.181044i | −0.995894 | − | 0.0905218i | \(-0.971147\pi\) | ||
0.995894 | − | 0.0905218i | \(-0.0288535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.9590 | −1.09525 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −65.6958 | −2.32125 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.3649i | 0.895107i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.520505 | − | 3.70471i | −0.0183454 | − | 0.130574i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 74.7467i | 2.63121i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.7368 | −0.658752 | −0.329376 | − | 0.944199i | \(-0.606838\pi\) | ||||
−0.329376 | + | 0.944199i | \(0.606838\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5210 | 1.31754 | 0.658770 | − | 0.752344i | \(-0.271077\pi\) | ||||
0.658770 | + | 0.752344i | \(0.271077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 87.6325i | 3.07341i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.1432 | + | 3.39207i | −0.845699 | + | 0.118819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.86971i | 0.345297i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 50.1847 | 1.75359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4001 | 0.642166 | 0.321083 | − | 0.947051i | \(-0.395953\pi\) | ||||
0.321083 | + | 0.947051i | \(0.395953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.649413i | − | 0.0226371i | −0.999936 | − | 0.0113186i | \(-0.996397\pi\) | ||
0.999936 | − | 0.0113186i | \(-0.00360288\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.2257 | + | 53.1151i | 0.530091 | + | 1.84923i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29.8622i | − | 1.03841i | −0.854650 | − | 0.519205i | \(-0.826228\pi\) | ||
0.854650 | − | 0.519205i | \(-0.173772\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1753 | −0.735449 | −0.367725 | − | 0.929935i | \(-0.619863\pi\) | ||||
−0.367725 | + | 0.929935i | \(0.619863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.5718 | −1.06053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 31.5210i | − | 1.09214i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.5620 | − | 2.04593i | 0.503939 | − | 0.0708024i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.4291i | 0.671568i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.8163 | −1.51271 | −0.756353 | − | 0.654164i | \(-0.773021\pi\) | ||||
−0.756353 | + | 0.654164i | \(0.773021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.0509i | 0.793914i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.90522 | − | 13.5605i | −0.0655415 | − | 0.466494i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.2997i | − | 0.422624i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.6543 | −1.08637 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.40943 | −0.116874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 37.7846i | − | 1.29372i | −0.762608 | − | 0.646860i | \(-0.776082\pi\) | ||
0.762608 | − | 0.646860i | \(-0.223918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.53035 | + | 60.7150i | 0.291732 | + | 2.07641i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.5299i | − | 0.667128i | −0.942727 | − | 0.333564i | \(-0.891749\pi\) | ||
0.942727 | − | 0.333564i | \(-0.108251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.2543 | −1.13462 | −0.567311 | − | 0.823504i | \(-0.692016\pi\) | ||||
−0.567311 | + | 0.823504i | \(0.692016\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −53.0607 | −1.80830 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 44.9733i | − | 1.53091i | −0.643490 | − | 0.765454i | \(-0.722514\pi\) | ||
0.643490 | − | 0.765454i | \(-0.277486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.3176 | − | 3.27607i | 0.792821 | − | 0.111390i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48.5259i | 1.64803i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.9625 | −0.677182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.3497 | −0.689523 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 74.9501i | − | 2.53668i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.0098 | − | 16.0272i | 1.21735 | − | 0.541818i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8.30819i | − | 0.280548i | −0.990113 | − | 0.140274i | \(-0.955202\pi\) | ||
0.990113 | − | 0.140274i | \(-0.0447983\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.8573 | −0.433665 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3689 | −1.32637 | −0.663186 | − | 0.748455i | \(-0.730796\pi\) | ||||
−0.663186 | + | 0.748455i | \(0.730796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.29036i | − | 0.245340i | −0.992447 | − | 0.122670i | \(-0.960854\pi\) | ||
0.992447 | − | 0.122670i | \(-0.0391457\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.4701 | − | 4.56199i | 1.09147 | − | 0.153350i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.1097i | 0.373027i | 0.982452 | + | 0.186514i | \(0.0597188\pi\) | ||||
−0.982452 | + | 0.186514i | \(0.940281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.2449 | −1.21562 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.9269 | 0.533570 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.9304i | 0.901192i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.95851 | + | 13.9398i | 0.0654659 | + | 0.465955i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 3.61285i | − | 0.120629i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.51114 | 0.183807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.2257 | 1.04028 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 20.0000i | − | 0.665558i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.152089 | + | 1.08250i | 0.00505561 | + | 0.0359835i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.5383i | − | 0.582351i | −0.956670 | − | 0.291175i | \(-0.905954\pi\) | ||
0.956670 | − | 0.291175i | \(-0.0940463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −107.023 | −3.54974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.4701 | −1.47336 | −0.736681 | − | 0.676241i | \(-0.763608\pi\) | ||||
−0.736681 | + | 0.676241i | \(0.763608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 46.2391i | − | 1.53029i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 78.6548 | − | 11.0509i | 2.60025 | − | 0.365330i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4415i | 0.542948i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.87955 | 0.259922 | 0.129961 | − | 0.991519i | \(-0.458515\pi\) | ||||
0.129961 | + | 0.991519i | \(0.458515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3047 | −0.504306 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 12.7368i | − | 0.419238i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.89829 | − | 34.5303i | −0.325454 | − | 1.13535i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.0366i | 0.559554i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.7560 | −0.516939 | −0.258470 | − | 0.966019i | \(-0.583218\pi\) | ||||
−0.258470 | + | 0.966019i | \(0.583218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.4193 | −0.898630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.12399i | 0.0367976i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 48.9403 | − | 6.87601i | 1.60052 | − | 0.224870i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 10.2766i | − | 0.335720i | −0.985811 | − | 0.167860i | \(-0.946314\pi\) | ||
0.985811 | − | 0.167860i | \(-0.0536857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.9403 | −1.07496 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.53341 | 0.0825869 | 0.0412934 | − | 0.999147i | \(-0.486852\pi\) | ||||
0.0412934 | + | 0.999147i | \(0.486852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.46028i | 0.0801178i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.73329 | − | 55.0420i | −0.251564 | − | 1.79052i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.06821i | − | 0.0347121i | −0.999849 | − | 0.0173560i | \(-0.994475\pi\) | ||
0.999849 | − | 0.0173560i | \(-0.00552488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.4737 | 0.567219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.5531 | −1.57444 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.6958i | 1.67459i | 0.546750 | + | 0.837296i | \(0.315865\pi\) | ||||
−0.546750 | + | 0.837296i | \(0.684135\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.26317 | − | 23.2257i | −0.105594 | − | 0.751566i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 22.1017i | − | 0.714447i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.0000 | 1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4068 | −0.755059 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.2716i | 0.943265i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.5718 | + | 4.29529i | −0.984142 | + | 0.138270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.2623i | − | 1.68064i | −0.542090 | − | 0.840320i | \(-0.682367\pi\) | ||
0.542090 | − | 0.840320i | \(-0.317633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 85.1437 | 2.73521 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.3560 | 1.90482 | 0.952412 | − | 0.304813i | \(-0.0985941\pi\) | ||||
0.952412 | + | 0.304813i | \(0.0985941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 41.6227i | − | 1.33436i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 36.5906 | − | 10.4889i | 1.17184 | − | 0.335912i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.8707i | 1.53152i | 0.643128 | + | 0.765759i | \(0.277637\pi\) | ||||
−0.643128 | + | 0.765759i | \(0.722363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.0642 | 1.47222 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.8069 | 1.49443 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.01429i | − | 0.191826i | −0.995390 | − | 0.0959130i | \(-0.969423\pi\) | ||
0.995390 | − | 0.0959130i | \(-0.0305771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.0321 | − | 5.20294i | 1.17994 | − | 0.165780i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 54.5718i | − | 1.73704i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.927346 | −0.0294879 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.4291 | 0.617186 | 0.308593 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308593 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.68598i | 0.307375i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.48886 | − | 46.1847i | −0.205711 | − | 1.46415i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.1334i | 1.01767i | 0.860863 | + | 0.508837i | \(0.169924\pi\) | ||||
−0.860863 | + | 0.508837i | \(0.830076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −50.6548 | −1.60265 |
(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 | 640.2.c.a.129.1 | ✓ | 6 | |
4.3 | odd | 2 | 640.2.c.b.129.6 | yes | 6 | ||
5.2 | odd | 4 | 3200.2.a.bq.1.1 | 3 | |||
5.3 | odd | 4 | 3200.2.a.bs.1.3 | 3 | |||
5.4 | even | 2 | inner | 640.2.c.a.129.6 | yes | 6 | |
8.3 | odd | 2 | 640.2.c.c.129.1 | yes | 6 | ||
8.5 | even | 2 | 640.2.c.d.129.6 | yes | 6 | ||
16.3 | odd | 4 | 1280.2.f.j.129.2 | 6 | |||
16.5 | even | 4 | 1280.2.f.i.129.1 | 6 | |||
16.11 | odd | 4 | 1280.2.f.k.129.5 | 6 | |||
16.13 | even | 4 | 1280.2.f.l.129.6 | 6 | |||
20.3 | even | 4 | 3200.2.a.br.1.1 | 3 | |||
20.7 | even | 4 | 3200.2.a.bt.1.3 | 3 | |||
20.19 | odd | 2 | 640.2.c.b.129.1 | yes | 6 | ||
40.3 | even | 4 | 3200.2.a.bu.1.3 | 3 | |||
40.13 | odd | 4 | 3200.2.a.bp.1.1 | 3 | |||
40.19 | odd | 2 | 640.2.c.c.129.6 | yes | 6 | ||
40.27 | even | 4 | 3200.2.a.bo.1.1 | 3 | |||
40.29 | even | 2 | 640.2.c.d.129.1 | yes | 6 | ||
40.37 | odd | 4 | 3200.2.a.bv.1.3 | 3 | |||
80.19 | odd | 4 | 1280.2.f.k.129.6 | 6 | |||
80.29 | even | 4 | 1280.2.f.i.129.2 | 6 | |||
80.59 | odd | 4 | 1280.2.f.j.129.1 | 6 | |||
80.69 | even | 4 | 1280.2.f.l.129.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
640.2.c.a.129.6 | yes | 6 | 5.4 | even | 2 | inner | |
640.2.c.b.129.1 | yes | 6 | 20.19 | odd | 2 | ||
640.2.c.b.129.6 | yes | 6 | 4.3 | odd | 2 | ||
640.2.c.c.129.1 | yes | 6 | 8.3 | odd | 2 | ||
640.2.c.c.129.6 | yes | 6 | 40.19 | odd | 2 | ||
640.2.c.d.129.1 | yes | 6 | 40.29 | even | 2 | ||
640.2.c.d.129.6 | yes | 6 | 8.5 | even | 2 | ||
1280.2.f.i.129.1 | 6 | 16.5 | even | 4 | |||
1280.2.f.i.129.2 | 6 | 80.29 | even | 4 | |||
1280.2.f.j.129.1 | 6 | 80.59 | odd | 4 | |||
1280.2.f.j.129.2 | 6 | 16.3 | odd | 4 | |||
1280.2.f.k.129.5 | 6 | 16.11 | odd | 4 | |||
1280.2.f.k.129.6 | 6 | 80.19 | odd | 4 | |||
1280.2.f.l.129.5 | 6 | 80.69 | even | 4 | |||
1280.2.f.l.129.6 | 6 | 16.13 | even | 4 | |||
3200.2.a.bo.1.1 | 3 | 40.27 | even | 4 | |||
3200.2.a.bp.1.1 | 3 | 40.13 | odd | 4 | |||
3200.2.a.bq.1.1 | 3 | 5.2 | odd | 4 | |||
3200.2.a.br.1.1 | 3 | 20.3 | even | 4 | |||
3200.2.a.bs.1.3 | 3 | 5.3 | odd | 4 | |||
3200.2.a.bt.1.3 | 3 | 20.7 | even | 4 | |||
3200.2.a.bu.1.3 | 3 | 40.3 | even | 4 | |||
3200.2.a.bv.1.3 | 3 | 40.37 | odd | 4 |