Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(571,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.571");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 53x^{10} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 571.14 | ||
Root | \(-0.516228 + 1.31663i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.571 |
Dual form | 572.2.b.b.571.13 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.516228 | + | 1.31663i | 0.365029 | + | 0.930996i | ||||
\(3\) | − | 1.51752i | − | 0.876139i | −0.898941 | − | 0.438069i | \(-0.855662\pi\) | ||
0.898941 | − | 0.438069i | \(-0.144338\pi\) | |||||||
\(4\) | −1.46702 | + | 1.35936i | −0.733508 | + | 0.679680i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | 1.99800 | − | 0.783385i | 0.815682 | − | 0.319816i | ||||
\(7\) | − | 2.42385i | − | 0.916128i | −0.888919 | − | 0.458064i | \(-0.848543\pi\) | ||
0.888919 | − | 0.458064i | \(-0.151457\pi\) | |||||||
\(8\) | −2.54709 | − | 1.22977i | −0.900531 | − | 0.434791i | ||||
\(9\) | 0.697144 | 0.232381 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.31662i | − | 1.00000i | ||||||
\(12\) | 2.06285 | + | 2.22622i | 0.595494 | + | 0.642655i | ||||
\(13\) | −3.60555 | −1.00000 | ||||||||
\(14\) | 3.19130 | − | 1.25126i | 0.852912 | − | 0.334413i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.304276 | − | 3.98841i | 0.0760689 | − | 0.997103i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0.359885 | + | 0.917879i | 0.0848258 | + | 0.216346i | ||||
\(19\) | − | 5.06154i | − | 1.16120i | −0.814190 | − | 0.580598i | \(-0.802819\pi\) | ||
0.814190 | − | 0.580598i | \(-0.197181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.67823 | −0.802655 | ||||||||
\(22\) | 4.36676 | − | 1.71214i | 0.930996 | − | 0.365029i | ||||
\(23\) | 0.711862i | 0.148433i | 0.997242 | + | 0.0742167i | \(0.0236456\pi\) | ||||
−0.997242 | + | 0.0742167i | \(0.976354\pi\) | |||||||
\(24\) | −1.86620 | + | 3.86525i | −0.380937 | + | 0.788990i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −1.86129 | − | 4.74717i | −0.365029 | − | 0.930996i | ||||
\(27\) | − | 5.61048i | − | 1.07974i | ||||||
\(28\) | 3.29488 | + | 3.55582i | 0.622674 | + | 0.671987i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 5.40833 | − | 1.65831i | 0.956066 | − | 0.293151i | ||||
\(33\) | −5.03303 | −0.876139 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.02272 | + | 0.947670i | −0.170454 | + | 0.157945i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 6.66416 | − | 2.61291i | 1.08107 | − | 0.423870i | ||||
\(39\) | 5.47148i | 0.876139i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.92280 | 0.612639 | 0.306320 | − | 0.951929i | \(-0.400902\pi\) | ||||
0.306320 | + | 0.951929i | \(0.400902\pi\) | |||||||
\(42\) | −1.89880 | − | 4.84286i | −0.292992 | − | 0.747269i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 4.50849 | + | 4.86554i | 0.679680 | + | 0.733508i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.937257 | + | 0.367483i | −0.138191 | + | 0.0541824i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −6.05248 | − | 0.461743i | −0.873600 | − | 0.0666469i | ||||
\(49\) | 1.12497 | 0.160710 | ||||||||
\(50\) | 2.58114 | + | 6.58314i | 0.365029 | + | 0.930996i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.28940 | − | 4.90125i | 0.733508 | − | 0.679680i | ||||
\(53\) | −1.89692 | −0.260562 | −0.130281 | − | 0.991477i | \(-0.541588\pi\) | ||||
−0.130281 | + | 0.991477i | \(0.541588\pi\) | |||||||
\(54\) | 7.38691 | − | 2.89629i | 1.00523 | − | 0.394135i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.98078 | + | 6.17375i | −0.398324 | + | 0.825002i | ||||
\(57\) | −7.68097 | −1.01737 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.68977i | − | 0.212891i | ||||||
\(64\) | 4.97531 | + | 6.26468i | 0.621914 | + | 0.783086i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.59819 | − | 6.62663i | −0.319816 | − | 0.815682i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.08026 | 0.130048 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −1.77569 | − | 0.857330i | −0.209267 | − | 0.101037i | ||||
\(73\) | −13.2927 | −1.55579 | −0.777896 | − | 0.628394i | \(-0.783713\pi\) | ||||
−0.777896 | + | 0.628394i | \(0.783713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 7.58758i | − | 0.876139i | ||||||
\(76\) | 6.88046 | + | 7.42536i | 0.789243 | + | 0.851747i | ||||
\(77\) | −8.03899 | −0.916128 | ||||||||
\(78\) | −7.20391 | + | 2.82453i | −0.815682 | + | 0.319816i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.42256 | −0.713618 | ||||||||
\(82\) | 2.02506 | + | 5.16487i | 0.223631 | + | 0.570365i | ||||
\(83\) | 17.1097i | 1.87804i | 0.343867 | + | 0.939019i | \(0.388263\pi\) | ||||
−0.343867 | + | 0.939019i | \(0.611737\pi\) | |||||||
\(84\) | 5.39602 | − | 5.00004i | 0.588754 | − | 0.545549i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.07870 | + | 8.44773i | −0.434791 | + | 0.900531i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.73930i | 0.916128i | ||||||||
\(92\) | −0.967677 | − | 1.04431i | −0.100887 | − | 0.108877i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.51652 | − | 8.20722i | −0.256841 | − | 0.837646i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0.580740 | + | 1.48116i | 0.0586636 | + | 0.149620i | ||||
\(99\) | − | 2.31216i | − | 0.232381i | ||||||
\(100\) | −7.33508 | + | 6.79680i | −0.733508 | + | 0.679680i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.6142i | 1.93264i | 0.257337 | + | 0.966322i | \(0.417155\pi\) | ||||
−0.257337 | + | 0.966322i | \(0.582845\pi\) | |||||||
\(104\) | 9.18366 | + | 4.43401i | 0.900531 | + | 0.434791i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.979244 | − | 2.49754i | −0.0951126 | − | 0.242582i | ||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 7.62666 | + | 8.23066i | 0.733876 | + | 0.791996i | ||||
\(109\) | −0.903206 | −0.0865115 | −0.0432557 | − | 0.999064i | \(-0.513773\pi\) | ||||
−0.0432557 | + | 0.999064i | \(0.513773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.66729 | − | 0.737518i | −0.913473 | − | 0.0696889i | ||||
\(113\) | 20.5811 | 1.93610 | 0.968052 | − | 0.250750i | \(-0.0806773\pi\) | ||||
0.968052 | + | 0.250750i | \(0.0806773\pi\) | |||||||
\(114\) | −3.96513 | − | 10.1130i | −0.371369 | − | 0.947167i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.51359 | −0.232381 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.95292i | − | 0.536757i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.22480 | − | 0.872307i | 0.198201 | − | 0.0777113i | ||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | −5.67986 | + | 9.78464i | −0.502033 | + | 0.864848i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 7.38354 | − | 6.84171i | 0.642655 | − | 0.595494i | ||||
\(133\) | −12.2684 | −1.06380 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0.557662 | + | 1.42230i | 0.0474713 | + | 0.121074i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.9583i | 1.00000i | ||||||||
\(144\) | 0.212124 | − | 2.78050i | 0.0176770 | − | 0.231708i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.86206 | − | 17.5015i | −0.567908 | − | 1.44844i | ||||
\(147\) | − | 1.70716i | − | 0.140804i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 24.2995 | 1.99069 | 0.995347 | − | 0.0963598i | \(-0.0307200\pi\) | ||||
0.995347 | + | 0.0963598i | \(0.0307200\pi\) | |||||||
\(150\) | 9.99002 | − | 3.91692i | 0.815682 | − | 0.319816i | ||||
\(151\) | − | 19.8997i | − | 1.61942i | −0.586831 | − | 0.809709i | \(-0.699625\pi\) | ||
0.586831 | − | 0.809709i | \(-0.300375\pi\) | |||||||
\(152\) | −6.22455 | + | 12.8922i | −0.504878 | + | 1.04569i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.14995 | − | 10.5844i | −0.334413 | − | 0.852912i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.43772 | − | 8.02676i | −0.595494 | − | 0.642655i | ||||
\(157\) | 0.644702 | 0.0514528 | 0.0257264 | − | 0.999669i | \(-0.491810\pi\) | ||||
0.0257264 | + | 0.999669i | \(0.491810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.87861i | 0.228288i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.72544 | 0.135984 | ||||||||
\(162\) | −3.31551 | − | 8.45612i | −0.260491 | − | 0.664375i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | −5.75482 | + | 5.33251i | −0.449376 | + | 0.416399i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.5271 | + | 8.83253i | −1.74845 | + | 0.685537i | ||||
\(167\) | 4.65159i | 0.359951i | 0.983671 | + | 0.179976i | \(0.0576019\pi\) | ||||
−0.983671 | + | 0.179976i | \(0.942398\pi\) | |||||||
\(168\) | 9.36877 | + | 4.52339i | 0.722816 | + | 0.348987i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 3.52862i | − | 0.269840i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 12.1192i | − | 0.916128i | ||||||
\(176\) | −13.2281 | − | 1.00917i | −0.997103 | − | 0.0760689i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 23.9165i | − | 1.78760i | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||
0.448461 | − | 0.893802i | \(-0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.8091 | −1.99271 | −0.996353 | − | 0.0853299i | \(-0.972806\pi\) | ||||
−0.996353 | + | 0.0853299i | \(0.972806\pi\) | |||||||
\(182\) | −11.5064 | + | 4.51148i | −0.852912 | + | 0.334413i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.875429 | − | 1.81317i | 0.0645375 | − | 0.133669i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.5989 | −0.989177 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.3197i | 1.75971i | 0.475241 | + | 0.879856i | \(0.342361\pi\) | ||||
−0.475241 | + | 0.879856i | \(0.657639\pi\) | |||||||
\(192\) | 9.50676 | − | 7.55012i | 0.686091 | − | 0.544883i | ||||
\(193\) | 7.04646 | 0.507215 | 0.253608 | − | 0.967307i | \(-0.418383\pi\) | ||||
0.253608 | + | 0.967307i | \(0.418383\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.65035 | + | 1.52924i | −0.117882 | + | 0.109231i | ||||
\(197\) | 19.2289 | 1.37000 | 0.685002 | − | 0.728541i | \(-0.259801\pi\) | ||||
0.685002 | + | 0.728541i | \(0.259801\pi\) | |||||||
\(198\) | 3.04426 | − | 1.19360i | 0.216346 | − | 0.0848258i | ||||
\(199\) | − | 27.3547i | − | 1.93913i | −0.244843 | − | 0.969563i | \(-0.578736\pi\) | ||
0.244843 | − | 0.969563i | \(-0.421264\pi\) | |||||||
\(200\) | −12.7354 | − | 6.14887i | −0.900531 | − | 0.434791i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −25.8246 | + | 10.1254i | −1.79928 | + | 0.705470i | ||||
\(207\) | 0.496270i | 0.0344931i | ||||||||
\(208\) | −1.09708 | + | 14.3804i | −0.0760689 | + | 0.997103i | ||||
\(209\) | −16.7872 | −1.16120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 2.78281 | − | 2.57860i | 0.191124 | − | 0.177099i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.89962 | + | 14.2904i | −0.469460 | + | 0.972337i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.466261 | − | 1.18919i | −0.0315791 | − | 0.0805418i | ||||
\(219\) | 20.1719i | 1.36309i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | −4.01949 | − | 13.1090i | −0.268564 | − | 0.875879i | ||||
\(225\) | 3.48572 | 0.232381 | ||||||||
\(226\) | 10.6245 | + | 27.0976i | 0.706733 | + | 1.80251i | ||||
\(227\) | − | 5.88143i | − | 0.390364i | −0.980767 | − | 0.195182i | \(-0.937470\pi\) | ||
0.980767 | − | 0.195182i | \(-0.0625298\pi\) | |||||||
\(228\) | 11.2681 | − | 10.4412i | 0.746249 | − | 0.691486i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.1993i | 0.802655i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | −1.29759 | − | 3.30946i | −0.0848258 | − | 0.216346i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.7176i | 1.66354i | 0.555124 | + | 0.831768i | \(0.312671\pi\) | ||||
−0.555124 | + | 0.831768i | \(0.687329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.8613 | 1.66587 | 0.832937 | − | 0.553367i | \(-0.186657\pi\) | ||||
0.832937 | + | 0.553367i | \(0.186657\pi\) | |||||||
\(242\) | −5.67851 | − | 14.4829i | −0.365029 | − | 0.930996i | ||||
\(243\) | − | 7.08509i | − | 0.454509i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.83778 | − | 3.07307i | 0.499719 | − | 0.195932i | ||||
\(247\) | 18.2496i | 1.16120i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.9643 | 1.64542 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 29.0654i | − | 1.83459i | −0.398210 | − | 0.917294i | \(-0.630368\pi\) | ||
0.398210 | − | 0.917294i | \(-0.369632\pi\) | |||||||
\(252\) | 2.29701 | + | 2.47892i | 0.144698 | + | 0.156157i | ||||
\(253\) | 2.36098 | 0.148433 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.8148 | − | 2.42715i | −0.988427 | − | 0.151697i | ||||
\(257\) | 27.1694 | 1.69478 | 0.847391 | − | 0.530970i | \(-0.178172\pi\) | ||||
0.847391 | + | 0.530970i | \(0.178172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 12.8196 | + | 6.18949i | 0.788990 | + | 0.380937i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.33329 | − | 16.1529i | −0.388319 | − | 0.990398i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.2219 | 1.84266 | 0.921329 | − | 0.388783i | \(-0.127104\pi\) | ||||
0.921329 | + | 0.388783i | \(0.127104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.5375i | 1.61204i | 0.591888 | + | 0.806020i | \(0.298383\pi\) | ||||
−0.591888 | + | 0.806020i | \(0.701617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.2620 | 0.802655 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 16.5831i | − | 1.00000i | ||||||
\(276\) | −1.58476 | + | 1.46847i | −0.0953914 | + | 0.0883912i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.6184 | 1.88620 | 0.943098 | − | 0.332515i | \(-0.107897\pi\) | ||||
0.943098 | + | 0.332515i | \(0.107897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.7446 | + | 6.17319i | −0.930996 | + | 0.365029i | ||||
\(287\) | − | 9.50828i | − | 0.561256i | ||||||
\(288\) | 3.77038 | − | 1.15608i | 0.222172 | − | 0.0681228i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.5006 | − | 18.0696i | 1.14119 | − | 1.05744i | ||||
\(293\) | 21.6333 | 1.26383 | 0.631916 | − | 0.775037i | \(-0.282269\pi\) | ||||
0.631916 | + | 0.775037i | \(0.282269\pi\) | |||||||
\(294\) | 2.24769 | − | 0.881283i | 0.131088 | − | 0.0513975i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.6078 | −1.07974 | ||||||||
\(298\) | 12.5441 | + | 31.9934i | 0.726660 | + | 1.85333i | ||||
\(299\) | − | 2.56665i | − | 0.148433i | ||||||
\(300\) | 10.3143 | + | 11.1311i | 0.595494 | + | 0.642655i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 26.2006 | − | 10.2728i | 1.50767 | − | 0.591134i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.1875 | − | 1.54010i | −1.15783 | − | 0.0883310i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8997i | 1.13574i | 0.823119 | + | 0.567869i | \(0.192232\pi\) | ||||
−0.823119 | + | 0.567869i | \(0.807768\pi\) | |||||||
\(308\) | 11.7933 | − | 10.9279i | 0.671987 | − | 0.622674i | ||||
\(309\) | 29.7649 | 1.69326 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.2146i | − | 0.862741i | −0.902175 | − | 0.431370i | \(-0.858030\pi\) | ||
0.902175 | − | 0.431370i | \(-0.141970\pi\) | |||||||
\(312\) | 6.72869 | − | 13.9363i | 0.380937 | − | 0.788990i | ||||
\(313\) | −34.5637 | −1.95366 | −0.976828 | − | 0.214026i | \(-0.931342\pi\) | ||||
−0.976828 | + | 0.214026i | \(0.931342\pi\) | |||||||
\(314\) | 0.332813 | + | 0.848832i | 0.0187817 | + | 0.0479024i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(318\) | −3.79006 | + | 1.48602i | −0.212536 | + | 0.0833318i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.890723 | + | 2.27177i | 0.0496380 | + | 0.126601i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.42200 | − | 8.73058i | 0.523444 | − | 0.485032i | ||||
\(325\) | −18.0278 | −1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.37063i | 0.0757960i | ||||||||
\(328\) | −9.99173 | − | 4.82416i | −0.551701 | − | 0.266370i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | −23.2583 | − | 25.1003i | −1.27647 | − | 1.37756i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.12442 | + | 2.40128i | −0.335113 | + | 0.131392i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.11920 | + | 14.6703i | −0.0610571 | + | 0.800329i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 6.71097 | + | 17.1162i | 0.365029 | + | 0.930996i | ||||
\(339\) | − | 31.2321i | − | 1.69629i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.64588 | − | 1.82157i | 0.251220 | − | 0.0984994i | ||||
\(343\) | − | 19.6937i | − | 1.06336i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.2688 | −1.88789 | −0.943947 | − | 0.330097i | \(-0.892919\pi\) | ||||
−0.943947 | + | 0.330097i | \(0.892919\pi\) | |||||||
\(350\) | 15.9565 | − | 6.25629i | 0.852912 | − | 0.334413i | ||||
\(351\) | 20.2289i | 1.07974i | ||||||||
\(352\) | −5.50000 | − | 17.9374i | −0.293151 | − | 0.956066i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 31.4892 | − | 12.3464i | 1.66425 | − | 0.652527i | ||||
\(359\) | 26.9479i | 1.42226i | 0.703062 | + | 0.711129i | \(0.251816\pi\) | ||||
−0.703062 | + | 0.711129i | \(0.748184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.61917 | −0.348377 | ||||||||
\(362\) | −13.8396 | − | 35.2976i | −0.727394 | − | 1.85520i | ||||
\(363\) | 16.6927i | 0.876139i | ||||||||
\(364\) | −11.8799 | − | 12.8207i | −0.622674 | − | 0.671987i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.4598i | 1.90319i | 0.307358 | + | 0.951594i | \(0.400555\pi\) | ||||
−0.307358 | + | 0.951594i | \(0.599445\pi\) | |||||||
\(368\) | 2.83920 | + | 0.216602i | 0.148003 | + | 0.0112912i | ||||
\(369\) | 2.73476 | 0.142366 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.59784i | 0.238708i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −7.02015 | − | 17.9047i | −0.361078 | − | 0.920920i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.0200 | + | 12.5545i | −1.63829 | + | 0.642345i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 14.8484 | + | 8.61928i | 0.757727 | + | 0.439851i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.63758 | + | 9.27756i | 0.185148 | + | 0.472216i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −39.2652 | −1.99082 | −0.995412 | − | 0.0956765i | \(-0.969499\pi\) | ||||
−0.995412 | + | 0.0956765i | \(0.969499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.86539 | − | 1.38346i | −0.144724 | − | 0.0698751i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.92652 | + | 25.3173i | 0.500091 | + | 1.27547i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.14307 | + | 3.39198i | 0.157945 | + | 0.170454i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 36.0160 | − | 14.1213i | 1.80532 | − | 0.707836i | ||||
\(399\) | 18.6175i | 0.932040i | ||||||||
\(400\) | 1.52138 | − | 19.9421i | 0.0760689 | − | 0.997103i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.21110 | 0.356566 | 0.178283 | − | 0.983979i | \(-0.442946\pi\) | ||||
0.178283 | + | 0.983979i | \(0.442946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26.6628 | − | 28.7743i | −1.31358 | − | 1.41761i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.653403 | + | 0.256189i | −0.0321130 | + | 0.0125910i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.5000 | + | 5.97913i | −0.956066 | + | 0.293151i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.66604 | − | 22.1025i | −0.423870 | − | 1.08107i | ||||
\(419\) | − | 31.9128i | − | 1.55904i | −0.626376 | − | 0.779521i | \(-0.715462\pi\) | ||
0.626376 | − | 0.779521i | \(-0.284538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.83162 | + | 2.33278i | 0.234644 | + | 0.113290i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.1469 | 0.876139 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 41.4910i | − | 1.99855i | −0.0380545 | − | 0.999276i | \(-0.512116\pi\) | ||
0.0380545 | − | 0.999276i | \(-0.487884\pi\) | |||||||
\(432\) | −22.3769 | − | 1.70713i | −1.07661 | − | 0.0821344i | ||||
\(433\) | −29.2433 | −1.40534 | −0.702672 | − | 0.711514i | \(-0.748010\pi\) | ||||
−0.702672 | + | 0.711514i | \(0.748010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.32502 | − | 1.22778i | 0.0634569 | − | 0.0588001i | ||||
\(437\) | 3.60311 | 0.172360 | ||||||||
\(438\) | −26.5588 | + | 10.4133i | −1.26903 | + | 0.497566i | ||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.784265 | 0.0373459 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.6416i | 1.31329i | 0.754198 | + | 0.656647i | \(0.228026\pi\) | ||||
−0.754198 | + | 0.656647i | \(0.771974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 36.8749i | − | 1.74412i | ||||||
\(448\) | 15.1846 | − | 12.0594i | 0.717407 | − | 0.569753i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 1.79943 | + | 4.58939i | 0.0848258 | + | 0.216346i | ||||
\(451\) | − | 13.0105i | − | 0.612639i | ||||||
\(452\) | −30.1928 | + | 27.9771i | −1.42015 | + | 1.31593i | ||||
\(453\) | −30.1982 | −1.41883 | ||||||||
\(454\) | 7.74365 | − | 3.03616i | 0.363428 | − | 0.142494i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.5641 | + | 9.44585i | 0.916173 | + | 0.442343i | ||||
\(457\) | −41.6845 | −1.94992 | −0.974959 | − | 0.222386i | \(-0.928615\pi\) | ||||
−0.974959 | + | 0.222386i | \(0.928615\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.9693 | 0.510890 | 0.255445 | − | 0.966824i | \(-0.417778\pi\) | ||||
0.255445 | + | 0.966824i | \(0.417778\pi\) | |||||||
\(462\) | −16.0619 | + | 6.29762i | −0.747269 | + | 0.292992i | ||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 23.9165i | − | 1.10672i | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||
0.832941 | − | 0.553362i | \(-0.186655\pi\) | |||||||
\(468\) | 3.68748 | − | 3.41687i | 0.170454 | − | 0.157945i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 0.978345i | − | 0.0450798i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 25.3077i | − | 1.16120i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.32243 | −0.0605498 | ||||||||
\(478\) | −33.8605 | + | 13.2762i | −1.54875 | + | 0.607238i | ||||
\(479\) | 6.63325i | 0.303081i | 0.988451 | + | 0.151540i | \(0.0484234\pi\) | ||||
−0.988451 | + | 0.151540i | \(0.951577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 13.3504 | + | 34.0497i | 0.608092 | + | 1.55092i | ||||
\(483\) | − | 2.61839i | − | 0.119141i | ||||||
\(484\) | 16.1372 | − | 14.9530i | 0.733508 | − | 0.679680i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.32843 | − | 3.65752i | 0.423146 | − | 0.165909i | ||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 8.09217 | + | 8.73303i | 0.364823 | + | 0.393716i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −24.0280 | + | 9.42098i | −1.08107 | + | 0.423870i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.4035 | + | 34.1853i | 0.600625 | + | 1.53188i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.05887 | 0.315367 | ||||||||
\(502\) | 38.2682 | − | 15.0044i | 1.70800 | − | 0.669677i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −2.07804 | + | 4.30399i | −0.0925630 | + | 0.191715i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.21880 | + | 3.10853i | 0.0541824 | + | 0.138191i | ||||
\(507\) | − | 19.7277i | − | 0.876139i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.2194i | 1.42530i | ||||||||
\(512\) | −4.96841 | − | 22.0752i | −0.219575 | − | 0.975596i | ||||
\(513\) | −28.3976 | −1.25379 | ||||||||
\(514\) | 14.0256 | + | 35.7720i | 0.618644 | + | 1.57784i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.98655 | −0.218465 | −0.109232 | − | 0.994016i | \(-0.534839\pi\) | ||||
−0.109232 | + | 0.994016i | \(0.534839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.3911 | −0.802655 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.53143 | + | 20.0738i | −0.0666469 | + | 0.873600i | ||||
\(529\) | 22.4933 | 0.977968 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.9979 | − | 16.6772i | 0.780309 | − | 0.723047i | ||||
\(533\) | −14.1439 | −0.612639 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.2937 | −1.56619 | ||||||||
\(538\) | 15.6014 | + | 39.7909i | 0.672623 | + | 1.71551i | ||||
\(539\) | − | 3.73110i | − | 0.160710i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.1759 | 0.910421 | 0.455210 | − | 0.890384i | \(-0.349564\pi\) | ||||
0.455210 | + | 0.890384i | \(0.349564\pi\) | |||||||
\(542\) | −34.9400 | + | 13.6994i | −1.50080 | + | 0.588441i | ||||
\(543\) | 40.6833i | 1.74589i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.84624 | + | 17.4612i | 0.292992 | + | 0.747269i | ||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.8338 | − | 8.56068i | 0.930996 | − | 0.365029i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.75152 | − | 1.32848i | −0.117113 | − | 0.0565438i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.60829 | 0.364745 | 0.182372 | − | 0.983230i | \(-0.441622\pi\) | ||||
0.182372 | + | 0.983230i | \(0.441622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.3223 | + | 41.6297i | 0.688515 | + | 1.75604i | ||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.5673i | 0.653765i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | −16.2556 | − | 17.5430i | −0.679680 | − | 0.733508i | ||||
\(573\) | 36.9055 | 1.54175 | ||||||||
\(574\) | 12.5189 | − | 4.90844i | 0.522527 | − | 0.204874i | ||||
\(575\) | 3.55931i | 0.148433i | ||||||||
\(576\) | 3.46851 | + | 4.36739i | 0.144521 | + | 0.181974i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 8.77588 | + | 22.3827i | 0.365029 | + | 0.930996i | ||||
\(579\) | − | 10.6931i | − | 0.444391i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.4714 | 1.72052 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.29137i | 0.260562i | ||||||||
\(584\) | 33.8576 | + | 16.3470i | 1.40104 | + | 0.676444i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1677 | + | 28.4830i | 0.461335 | + | 1.17662i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 2.32064 | + | 2.50443i | 0.0957017 | + | 0.103281i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 29.1802i | − | 1.20031i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.8306 | −1.51245 | −0.756226 | − | 0.654311i | \(-0.772959\pi\) | ||||
−0.756226 | + | 0.654311i | \(0.772959\pi\) | |||||||
\(594\) | −9.60590 | − | 24.4996i | −0.394135 | − | 1.00523i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −35.6478 | + | 33.0318i | −1.46019 | + | 1.35304i | ||||
\(597\) | −41.5113 | −1.69894 | ||||||||
\(598\) | 3.37933 | − | 1.32498i | 0.138191 | − | 0.0541824i | ||||
\(599\) | 42.5299i | 1.73772i | 0.495054 | + | 0.868862i | \(0.335148\pi\) | ||||
−0.495054 | + | 0.868862i | \(0.664852\pi\) | |||||||
\(600\) | −9.33101 | + | 19.3262i | −0.380937 | + | 0.788990i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27.0509 | + | 29.1933i | 1.10069 | + | 1.18786i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | −8.39361 | − | 27.3745i | −0.340406 | − | 1.11018i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.6822 | −1.03729 | −0.518646 | − | 0.854989i | \(-0.673564\pi\) | ||||
−0.518646 | + | 0.854989i | \(0.673564\pi\) | |||||||
\(614\) | −26.2006 | + | 10.2728i | −1.05737 | + | 0.414577i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.4760 | + | 9.88614i | 0.825002 | + | 0.398324i | ||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 15.3655 | + | 39.1892i | 0.618089 | + | 1.57642i | ||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.99388 | 0.160269 | ||||||||
\(622\) | 20.0320 | − | 7.85421i | 0.803209 | − | 0.314925i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 21.8225 | + | 1.66484i | 0.873600 | + | 0.0666469i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −17.8428 | − | 45.5075i | −0.713140 | − | 1.81885i | ||||
\(627\) | 25.4749i | 1.01737i | ||||||||
\(628\) | −0.945788 | + | 0.876382i | −0.0377410 | + | 0.0349715i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.91307 | − | 4.22297i | −0.155163 | − | 0.167452i | ||||
\(637\) | −4.05613 | −0.160710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −49.3523 | −1.94930 | −0.974649 | − | 0.223740i | \(-0.928173\pi\) | ||||
−0.974649 | + | 0.223740i | \(0.928173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | −2.53125 | + | 2.34550i | −0.0997454 | + | 0.0924256i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.10950i | 0.240189i | 0.992762 | + | 0.120095i | \(0.0383198\pi\) | ||||
−0.992762 | + | 0.120095i | \(0.961680\pi\) | |||||||
\(648\) | 16.3588 | + | 7.89830i | 0.642635 | + | 0.310274i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −9.30644 | − | 23.7358i | −0.365029 | − | 0.930996i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | −1.80461 | + | 0.707558i | −0.0705658 | + | 0.0276677i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.19361 | − | 15.6458i | 0.0466028 | − | 0.610864i | ||||
\(657\) | −9.26691 | −0.361537 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.0411 | − | 43.5800i | 0.816553 | − | 1.69123i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −6.32319 | − | 6.82396i | −0.244652 | − | 0.264027i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −19.8931 | + | 6.09965i | −0.767391 | + | 0.235299i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 28.0524i | − | 1.07974i | ||||||
\(676\) | −19.0712 | + | 17.6717i | −0.733508 | + | 0.679680i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 41.1210 | − | 16.1229i | 1.57924 | − | 0.619196i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.92516 | −0.342013 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 4.79667 | + | 5.17654i | 0.183405 | + | 0.197930i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.9292 | − | 10.1664i | 0.989983 | − | 0.388156i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.83944 | 0.260562 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.60433 | −0.212891 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −18.2067 | − | 46.4358i | −0.689135 | − | 1.75762i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.4744 | + | 17.7791i | 0.622674 | + | 0.671987i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | −26.6339 | + | 10.4427i | −1.00523 | + | 0.394135i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 20.7776 | − | 16.5012i | 0.783086 | − | 0.621914i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.5112 | + | 35.0859i | 1.21500 | + | 1.31122i | ||||
\(717\) | 39.0269 | 1.45749 | ||||||||
\(718\) | −35.4804 | + | 13.9113i | −1.32412 | + | 0.519164i | ||||
\(719\) | 23.9165i | 0.891936i | 0.895049 | + | 0.445968i | \(0.147140\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.5418 | 1.77055 | ||||||||
\(722\) | −3.41700 | − | 8.71498i | −0.127168 | − | 0.324338i | ||||
\(723\) | − | 39.2450i | − | 1.45954i | ||||||
\(724\) | 39.3294 | − | 36.4433i | 1.46167 | − | 1.35440i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.9780 | + | 8.61723i | −0.815682 | + | 0.319816i | ||||
\(727\) | − | 37.0928i | − | 1.37570i | −0.725855 | − | 0.687848i | \(-0.758556\pi\) | ||
0.725855 | − | 0.687848i | \(-0.241444\pi\) | |||||||
\(728\) | 10.7474 | − | 22.2598i | 0.398324 | − | 0.825002i | ||||
\(729\) | −30.0194 | −1.11183 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −54.0836 | −1.99763 | −0.998813 | − | 0.0487194i | \(-0.984486\pi\) | ||||
−0.998813 | + | 0.0487194i | \(0.984486\pi\) | |||||||
\(734\) | −48.0040 | + | 18.8216i | −1.77186 | + | 0.694718i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.18049 | + | 3.84998i | 0.0435134 | + | 0.141912i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.41176 | + | 3.60066i | 0.0519676 | + | 0.132542i | ||||
\(739\) | 46.4815i | 1.70985i | 0.518752 | + | 0.854925i | \(0.326397\pi\) | ||||
−0.518752 | + | 0.854925i | \(0.673603\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.6941 | 1.01737 | ||||||||
\(742\) | −6.05365 | + | 2.37354i | −0.222236 | + | 0.0871353i | ||||
\(743\) | 33.1662i | 1.21675i | 0.793649 | + | 0.608376i | \(0.208179\pi\) | ||||
−0.793649 | + | 0.608376i | \(0.791821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.9279i | 0.436421i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 45.5649i | − | 1.66269i | −0.555758 | − | 0.831344i | \(-0.687572\pi\) | ||
0.555758 | − | 0.831344i | \(-0.312428\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −44.1072 | −1.60735 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.9499 | − | 18.4859i | 0.725569 | − | 0.672324i | ||||
\(757\) | 45.0104 | 1.63593 | 0.817966 | − | 0.575267i | \(-0.195102\pi\) | ||||
0.817966 | + | 0.575267i | \(0.195102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3.58282i | − | 0.130048i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.5218 | −1.90391 | −0.951957 | − | 0.306231i | \(-0.900932\pi\) | ||||
−0.951957 | + | 0.306231i | \(0.900932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.18923i | 0.0792556i | ||||||||
\(764\) | −33.0592 | − | 35.6774i | −1.19604 | − | 1.29076i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.68324 | + | 23.9993i | −0.132908 | + | 0.865999i | ||||
\(769\) | −30.5833 | −1.10286 | −0.551431 | − | 0.834221i | \(-0.685918\pi\) | ||||
−0.551431 | + | 0.834221i | \(0.685918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 41.2300i | − | 1.48486i | ||||||
\(772\) | −10.3373 | + | 9.57868i | −0.372047 | + | 0.344744i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.2698 | − | 51.6977i | −0.726708 | − | 1.85345i | ||||
\(779\) | − | 19.8554i | − | 0.711394i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.342301 | − | 4.48683i | 0.0122250 | − | 0.160244i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 41.6338i | − | 1.48409i | −0.670353 | − | 0.742043i | \(-0.733857\pi\) | ||
0.670353 | − | 0.742043i | \(-0.266143\pi\) | |||||||
\(788\) | −28.2092 | + | 26.1390i | −1.00491 | + | 0.931165i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 49.8853i | − | 1.77372i | ||||||
\(792\) | −2.84344 | + | 5.88929i | −0.101037 | + | 0.209267i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37.1850 | + | 40.1298i | 1.31799 | + | 1.42236i | ||||
\(797\) | 30.0000 | 1.06265 | 0.531327 | − | 0.847167i | \(-0.321693\pi\) | ||||
0.531327 | + | 0.847167i | \(0.321693\pi\) | |||||||
\(798\) | −24.5123 | + | 9.61087i | −0.867726 | + | 0.340221i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 27.0416 | − | 8.29156i | 0.956066 | − | 0.293151i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44.0869i | 1.55579i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 45.8622i | − | 1.61442i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.1769i | 1.97264i | 0.164850 | + | 0.986319i | \(0.447286\pi\) | ||||
−0.164850 | + | 0.986319i | \(0.552714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.2711 | 1.41237 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 3.72258 | + | 9.49434i | 0.130157 | + | 0.331962i | ||||
\(819\) | 6.09255i | 0.212891i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.6333 | 0.755008 | 0.377504 | − | 0.926008i | \(-0.376783\pi\) | ||||
0.377504 | + | 0.926008i | \(0.376783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 23.8854i | − | 0.832591i | −0.909229 | − | 0.416296i | \(-0.863328\pi\) | ||
0.909229 | − | 0.416296i | \(-0.136672\pi\) | |||||||
\(824\) | 24.1210 | − | 49.9591i | 0.840296 | − | 1.74041i | ||||
\(825\) | −25.1652 | −0.876139 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 57.3167i | 1.99310i | 0.0830134 | + | 0.996548i | \(0.473546\pi\) | ||||
−0.0830134 | + | 0.996548i | \(0.526454\pi\) | |||||||
\(828\) | −0.674610 | − | 0.728036i | −0.0234443 | − | 0.0253010i | ||||
\(829\) | 21.5382 | 0.748051 | 0.374026 | − | 0.927418i | \(-0.377977\pi\) | ||||
0.374026 | + | 0.927418i | \(0.377977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.9387 | − | 22.5876i | −0.621914 | − | 0.783086i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.6271 | − | 22.8199i | 0.851747 | − | 0.789243i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 42.0173 | − | 16.4743i | 1.45146 | − | 0.569095i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 47.9814i | − | 1.65257i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.6623i | 0.916128i | ||||||||
\(848\) | −0.577187 | + | 7.56570i | −0.0198207 | + | 0.259807i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.0739 | −1.85146 | −0.925728 | − | 0.378189i | \(-0.876547\pi\) | ||||
−0.925728 | + | 0.378189i | \(0.876547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 9.36792 | + | 23.8927i | 0.319816 | + | 0.815682i | ||||
\(859\) | − | 41.0518i | − | 1.40067i | −0.713814 | − | 0.700335i | \(-0.753034\pi\) | ||
0.713814 | − | 0.700335i | \(-0.246966\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.4290 | −0.491738 | ||||||||
\(862\) | 54.6282 | − | 21.4188i | 1.86064 | − | 0.729528i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −9.30392 | − | 30.3433i | −0.316526 | − | 1.03230i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.0962 | − | 38.5026i | −0.512991 | − | 1.30837i | ||||
\(867\) | − | 25.7978i | − | 0.876139i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.30055 | + | 1.11074i | 0.0779063 | + | 0.0376144i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.86003 | + | 4.74396i | 0.0629164 | + | 0.160467i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −27.4208 | − | 29.5925i | −0.926465 | − | 0.999837i | ||||
\(877\) | 55.8804 | 1.88695 | 0.943473 | − | 0.331450i | \(-0.107538\pi\) | ||||
0.943473 | + | 0.331450i | \(0.107538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 32.8289i | − | 1.10729i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.9493 | 1.95236 | 0.976182 | − | 0.216955i | \(-0.0696125\pi\) | ||||
0.976182 | + | 0.216955i | \(0.0696125\pi\) | |||||||
\(882\) | 0.404860 | + | 1.03258i | 0.0136323 | + | 0.0347689i | ||||
\(883\) | − | 59.2620i | − | 1.99433i | −0.0752753 | − | 0.997163i | \(-0.523984\pi\) | ||
0.0752753 | − | 0.997163i | \(-0.476016\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.3937 | + | 14.2694i | −1.22267 | + | 0.479390i | ||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.3012i | 0.713618i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 48.5505 | − | 19.0359i | 1.62377 | − | 0.636655i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23.7165 | + | 13.7671i | 0.792312 | + | 0.459927i | ||||
\(897\) | −3.89494 | −0.130048 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.11361 | + | 4.73835i | −0.170454 | + | 0.157945i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 17.1299 | − | 6.71637i | 0.570365 | − | 0.223631i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.4218 | − | 25.3101i | −1.74352 | − | 0.841800i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.5892 | − | 39.7598i | −0.517915 | − | 1.32093i | ||||
\(907\) | 52.2389i | 1.73456i | 0.497818 | + | 0.867281i | \(0.334135\pi\) | ||||
−0.497818 | + | 0.867281i | \(0.665865\pi\) | |||||||
\(908\) | 7.99498 | + | 8.62815i | 0.265323 | + | 0.286335i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 60.2663i | 1.99671i | 0.0573229 | + | 0.998356i | \(0.481744\pi\) | ||||
−0.0573229 | + | 0.998356i | \(0.518256\pi\) | |||||||
\(912\) | −2.33713 | + | 30.6348i | −0.0773902 | + | 1.01442i | ||||
\(913\) | 56.7466 | 1.87804 | ||||||||
\(914\) | −21.5187 | − | 54.8829i | −0.711775 | − | 1.81537i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.1982 | 0.995064 | ||||||||
\(922\) | 5.66265 | + | 14.4424i | 0.186489 | + | 0.475637i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16.5832 | − | 17.8966i | −0.545549 | − | 0.588754i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.6739i | 0.449110i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.69407i | − | 0.186616i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.0884 | −0.755881 | ||||||||
\(934\) | 31.4892 | − | 12.3464i | 1.03036 | − | 0.403986i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.40233 | + | 3.09115i | 0.209267 | + | 0.101037i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.4510i | 1.71167i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.0079 | 1.43462 | 0.717308 | − | 0.696756i | \(-0.245374\pi\) | ||||
0.717308 | + | 0.696756i | \(0.245374\pi\) | |||||||
\(942\) | 1.28812 | − | 0.505049i | 0.0419691 | − | 0.0164554i | ||||
\(943\) | 2.79249i | 0.0909361i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.9275 | 1.55579 | ||||||||
\(950\) | 33.3208 | − | 13.0645i | 1.08107 | − | 0.423870i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | −0.682674 | − | 1.74114i | −0.0221024 | − | 0.0563716i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −34.9595 | − | 37.7282i | −1.13067 | − | 1.22022i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.73352 | + | 3.42427i | −0.282167 | + | 0.110633i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.9390 | + | 35.1549i | −1.22193 | + | 1.13226i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.44744 | − | 1.35169i | 0.110920 | − | 0.0434898i | ||||
\(967\) | 3.83170i | 0.123219i | 0.998100 | + | 0.0616096i | \(0.0196234\pi\) | ||||
−0.998100 | + | 0.0616096i | \(0.980377\pi\) | |||||||
\(968\) | 28.0180 | + | 13.5275i | 0.900531 | + | 0.434791i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 62.2970i | 1.99921i | 0.0281505 | + | 0.999604i | \(0.491038\pi\) | ||||
−0.0281505 | + | 0.999604i | \(0.508962\pi\) | |||||||
\(972\) | 9.63120 | + | 10.3939i | 0.308921 | + | 0.333386i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.3574i | 0.876139i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.629665 | −0.0201036 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −7.32075 | + | 15.1626i | −0.233377 | + | 0.483366i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.8078 | − | 26.7725i | −0.789243 | − | 0.851747i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0394371i | 0.00125276i | 1.00000 | 0.000626381i | \(0.000199383\pi\) | |||||
−1.00000 | 0.000626381i | \(0.999801\pi\) | ||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −38.0901 | + | 35.2949i | −1.20693 | + | 1.11836i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 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 | 572.2.b.b.571.14 | yes | 20 | |
4.3 | odd | 2 | inner | 572.2.b.b.571.13 | yes | 20 | |
11.10 | odd | 2 | inner | 572.2.b.b.571.7 | ✓ | 20 | |
13.12 | even | 2 | inner | 572.2.b.b.571.7 | ✓ | 20 | |
44.43 | even | 2 | inner | 572.2.b.b.571.8 | yes | 20 | |
52.51 | odd | 2 | inner | 572.2.b.b.571.8 | yes | 20 | |
143.142 | odd | 2 | CM | 572.2.b.b.571.14 | yes | 20 | |
572.571 | even | 2 | inner | 572.2.b.b.571.13 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.b.b.571.7 | ✓ | 20 | 11.10 | odd | 2 | inner | |
572.2.b.b.571.7 | ✓ | 20 | 13.12 | even | 2 | inner | |
572.2.b.b.571.8 | yes | 20 | 44.43 | even | 2 | inner | |
572.2.b.b.571.8 | yes | 20 | 52.51 | odd | 2 | inner | |
572.2.b.b.571.13 | yes | 20 | 4.3 | odd | 2 | inner | |
572.2.b.b.571.13 | yes | 20 | 572.571 | even | 2 | inner | |
572.2.b.b.571.14 | yes | 20 | 1.1 | even | 1 | trivial | |
572.2.b.b.571.14 | yes | 20 | 143.142 | odd | 2 | CM |