Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(881,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.g (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 72x^{12} + 1296x^{10} + 8245x^{8} + 18780x^{6} + 20808x^{4} - 3672x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(-0.579826 + 1.39982i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.881 |
Dual form | 1386.2.g.b.881.11 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.79965 | −1.25204 | −0.626020 | − | 0.779807i | \(-0.715317\pi\) | ||||
−0.626020 | + | 0.779807i | \(0.715317\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.20231 | + | 1.46623i | −0.832394 | + | 0.554184i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.79965i | 0.885326i | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.14713i | 1.15021i | 0.818080 | + | 0.575104i | \(0.195038\pi\) | ||||
−0.818080 | + | 0.575104i | \(0.804962\pi\) | |||||||
\(14\) | 1.46623 | + | 2.20231i | 0.391867 | + | 0.588592i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.73211 | 1.39024 | 0.695121 | − | 0.718893i | \(-0.255351\pi\) | ||||
0.695121 | + | 0.718893i | \(0.255351\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.15965i | − | 0.266042i | −0.991113 | − | 0.133021i | \(-0.957532\pi\) | ||
0.991113 | − | 0.133021i | \(-0.0424678\pi\) | |||||||
\(20\) | 2.79965 | 0.626020 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.83802 | 0.567605 | ||||||||
\(26\) | 4.14713 | 0.813320 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.20231 | − | 1.46623i | 0.416197 | − | 0.277092i | ||||
\(29\) | − | 10.0479i | − | 1.86585i | −0.360074 | − | 0.932924i | \(-0.617249\pi\) | ||
0.360074 | − | 0.932924i | \(-0.382751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.77281i | − | 0.318407i | −0.987246 | − | 0.159203i | \(-0.949107\pi\) | ||
0.987246 | − | 0.159203i | \(-0.0508926\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.73211i | − | 0.983049i | ||||||
\(35\) | 6.16569 | − | 4.10494i | 1.04219 | − | 0.693861i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40064 | 0.230264 | 0.115132 | − | 0.993350i | \(-0.463271\pi\) | ||||
0.115132 | + | 0.993350i | \(0.463271\pi\) | |||||||
\(38\) | −1.15965 | −0.188120 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 2.79965i | − | 0.442663i | ||||||
\(41\) | 2.37432 | 0.370806 | 0.185403 | − | 0.982663i | \(-0.440641\pi\) | ||||
0.185403 | + | 0.982663i | \(0.440641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.00398 | −1.06810 | −0.534048 | − | 0.845454i | \(-0.679330\pi\) | ||||
−0.534048 | + | 0.845454i | \(0.679330\pi\) | |||||||
\(44\) | 1.00000i | 0.150756i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.69141 | −1.41364 | −0.706819 | − | 0.707395i | \(-0.749870\pi\) | ||||
−0.706819 | + | 0.707395i | \(0.749870\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.70032 | − | 6.45819i | 0.385760 | − | 0.922599i | ||||
\(50\) | − | 2.83802i | − | 0.401357i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.14713i | − | 0.575104i | ||||||
\(53\) | − | 11.8053i | − | 1.62158i | −0.585339 | − | 0.810788i | \(-0.699039\pi\) | ||
0.585339 | − | 0.810788i | \(-0.300961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.79965i | 0.377504i | ||||||||
\(56\) | −1.46623 | − | 2.20231i | −0.195934 | − | 0.294296i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.0479 | −1.31935 | ||||||||
\(59\) | 13.8936 | 1.80879 | 0.904394 | − | 0.426699i | \(-0.140323\pi\) | ||||
0.904394 | + | 0.426699i | \(0.140323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.71780i | − | 0.219942i | −0.993935 | − | 0.109971i | \(-0.964924\pi\) | ||
0.993935 | − | 0.109971i | \(-0.0350757\pi\) | |||||||
\(62\) | −1.77281 | −0.225148 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 11.6105i | − | 1.44011i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0479 | 1.47188 | 0.735942 | − | 0.677044i | \(-0.236739\pi\) | ||||
0.735942 | + | 0.677044i | \(0.236739\pi\) | |||||||
\(68\) | −5.73211 | −0.695121 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.10494 | − | 6.16569i | −0.490634 | − | 0.736940i | ||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2929i | 1.20469i | 0.798234 | + | 0.602347i | \(0.205768\pi\) | ||||
−0.798234 | + | 0.602347i | \(0.794232\pi\) | |||||||
\(74\) | − | 1.40064i | − | 0.162821i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.15965i | 0.133021i | ||||||||
\(77\) | 1.46623 | + | 2.20231i | 0.167093 | + | 0.250976i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.43341 | 0.161271 | 0.0806356 | − | 0.996744i | \(-0.474305\pi\) | ||||
0.0806356 | + | 0.996744i | \(0.474305\pi\) | |||||||
\(80\) | −2.79965 | −0.313010 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 2.37432i | − | 0.262200i | ||||||
\(83\) | 7.55994 | 0.829812 | 0.414906 | − | 0.909864i | \(-0.363815\pi\) | ||||
0.414906 | + | 0.909864i | \(0.363815\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0479 | −1.74064 | ||||||||
\(86\) | 7.00398i | 0.755258i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 2.33096 | 0.247081 | 0.123541 | − | 0.992340i | \(-0.460575\pi\) | ||||
0.123541 | + | 0.992340i | \(0.460575\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.08067 | − | 9.13327i | −0.637427 | − | 0.957426i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.69141i | 0.999593i | ||||||||
\(95\) | 3.24662i | 0.333096i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.91860i | 0.804012i | 0.915637 | + | 0.402006i | \(0.131687\pi\) | ||||
−0.915637 | + | 0.402006i | \(0.868313\pi\) | |||||||
\(98\) | −6.45819 | − | 2.70032i | −0.652376 | − | 0.272774i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.83802 | −0.283802 | ||||||||
\(101\) | 3.77146 | 0.375275 | 0.187637 | − | 0.982238i | \(-0.439917\pi\) | ||||
0.187637 | + | 0.982238i | \(0.439917\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18.0635i | − | 1.77985i | −0.456109 | − | 0.889924i | \(-0.650757\pi\) | ||
0.456109 | − | 0.889924i | \(-0.349243\pi\) | |||||||
\(104\) | −4.14713 | −0.406660 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.8053 | −1.14663 | ||||||||
\(107\) | 8.20987i | 0.793678i | 0.917888 | + | 0.396839i | \(0.129893\pi\) | ||||
−0.917888 | + | 0.396839i | \(0.870107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.7239 | 1.69765 | 0.848823 | − | 0.528677i | \(-0.177312\pi\) | ||||
0.848823 | + | 0.528677i | \(0.177312\pi\) | |||||||
\(110\) | 2.79965 | 0.266936 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.20231 | + | 1.46623i | −0.208099 | + | 0.138546i | ||||
\(113\) | − | 6.08067i | − | 0.572021i | −0.958226 | − | 0.286010i | \(-0.907671\pi\) | ||
0.958226 | − | 0.286010i | \(-0.0923292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.0479i | 0.932924i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 13.8936i | − | 1.27901i | ||||||
\(119\) | −12.6239 | + | 8.40462i | −1.15723 | + | 0.770450i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −1.71780 | −0.155522 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.77281i | 0.159203i | ||||||||
\(125\) | 6.05277 | 0.541376 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0519 | 0.980695 | 0.490348 | − | 0.871527i | \(-0.336870\pi\) | ||||
0.490348 | + | 0.871527i | \(0.336870\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.6105 | −1.01831 | ||||||||
\(131\) | 16.3457 | 1.42813 | 0.714065 | − | 0.700080i | \(-0.246852\pi\) | ||||
0.714065 | + | 0.700080i | \(0.246852\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70032 | + | 2.55391i | 0.147436 | + | 0.221452i | ||||
\(134\) | − | 12.0479i | − | 1.04078i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.73211i | 0.491525i | ||||||||
\(137\) | 3.48131i | 0.297428i | 0.988880 | + | 0.148714i | \(0.0475134\pi\) | ||||
−0.988880 | + | 0.148714i | \(0.952487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.53172i | − | 0.808470i | −0.914655 | − | 0.404235i | \(-0.867538\pi\) | ||
0.914655 | − | 0.404235i | \(-0.132462\pi\) | |||||||
\(140\) | −6.16569 | + | 4.10494i | −0.521096 | + | 0.346930i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.48528 | −0.712069 | ||||||||
\(143\) | 4.14713 | 0.346801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.1306i | 2.33612i | ||||||||
\(146\) | 10.2929 | 0.851848 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.40064 | −0.115132 | ||||||||
\(149\) | 3.40064i | 0.278591i | 0.990251 | + | 0.139296i | \(0.0444838\pi\) | ||||
−0.990251 | + | 0.139296i | \(0.955516\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0918 | −1.39091 | −0.695456 | − | 0.718568i | \(-0.744798\pi\) | ||||
−0.695456 | + | 0.718568i | \(0.744798\pi\) | |||||||
\(152\) | 1.15965 | 0.0940602 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.20231 | − | 1.46623i | 0.177467 | − | 0.118152i | ||||
\(155\) | 4.96326i | 0.398658i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.77281i | 0.141486i | 0.997495 | + | 0.0707430i | \(0.0225370\pi\) | ||||
−0.997495 | + | 0.0707430i | \(0.977463\pi\) | |||||||
\(158\) | − | 1.43341i | − | 0.114036i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.79965i | 0.221332i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.07669 | −0.397637 | −0.198819 | − | 0.980036i | \(-0.563710\pi\) | ||||
−0.198819 | + | 0.980036i | \(0.563710\pi\) | |||||||
\(164\) | −2.37432 | −0.185403 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 7.55994i | − | 0.586765i | ||||||
\(167\) | −20.0944 | −1.55495 | −0.777474 | − | 0.628915i | \(-0.783499\pi\) | ||||
−0.777474 | + | 0.628915i | \(0.783499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.19872 | −0.322978 | ||||||||
\(170\) | 16.0479i | 1.23082i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.00398 | 0.534048 | ||||||||
\(173\) | −7.31709 | −0.556308 | −0.278154 | − | 0.960536i | \(-0.589723\pi\) | ||||
−0.278154 | + | 0.960536i | \(0.589723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.25020 | + | 4.16121i | −0.472471 | + | 0.314558i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 2.33096i | − | 0.174713i | ||||||
\(179\) | 7.72395i | 0.577315i | 0.957432 | + | 0.288657i | \(0.0932089\pi\) | ||||
−0.957432 | + | 0.288657i | \(0.906791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.49061i | 0.259455i | 0.991550 | + | 0.129728i | \(0.0414103\pi\) | ||||
−0.991550 | + | 0.129728i | \(0.958590\pi\) | |||||||
\(182\) | −9.13327 | + | 6.08067i | −0.677003 | + | 0.450729i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.92130 | −0.288300 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.73211i | − | 0.419174i | ||||||
\(188\) | 9.69141 | 0.706819 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.24662 | 0.235534 | ||||||||
\(191\) | − | 8.48528i | − | 0.613973i | −0.951714 | − | 0.306987i | \(-0.900679\pi\) | ||
0.951714 | − | 0.306987i | \(-0.0993207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0958 | 1.30256 | 0.651282 | − | 0.758836i | \(-0.274232\pi\) | ||||
0.651282 | + | 0.758836i | \(0.274232\pi\) | |||||||
\(194\) | 7.91860 | 0.568522 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.70032 | + | 6.45819i | −0.192880 | + | 0.461300i | ||||
\(197\) | − | 23.3424i | − | 1.66308i | −0.555466 | − | 0.831539i | \(-0.687460\pi\) | ||
0.555466 | − | 0.831539i | \(-0.312540\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.95705i | 0.705837i | 0.935654 | + | 0.352918i | \(0.114811\pi\) | ||||
−0.935654 | + | 0.352918i | \(0.885189\pi\) | |||||||
\(200\) | 2.83802i | 0.200679i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.77146i | − | 0.265359i | ||||||
\(203\) | 14.7326 | + | 22.1286i | 1.03402 | + | 1.55312i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.64726 | −0.464265 | ||||||||
\(206\) | −18.0635 | −1.25854 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.14713i | 0.287552i | ||||||||
\(209\) | −1.15965 | −0.0802148 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.29054 | 0.433058 | 0.216529 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216529 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(212\) | 11.8053i | 0.810788i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.20987 | 0.561215 | ||||||||
\(215\) | 19.6087 | 1.33730 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.59936 | + | 3.90428i | 0.176456 | + | 0.265040i | ||||
\(218\) | − | 17.7239i | − | 1.20042i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 2.79965i | − | 0.188752i | ||||||
\(221\) | 23.7718i | 1.59907i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.74778i | − | 0.518830i | −0.965766 | − | 0.259415i | \(-0.916470\pi\) | ||
0.965766 | − | 0.259415i | \(-0.0835297\pi\) | |||||||
\(224\) | 1.46623 | + | 2.20231i | 0.0979668 | + | 0.147148i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.08067 | −0.404480 | ||||||||
\(227\) | −14.7057 | −0.976051 | −0.488025 | − | 0.872829i | \(-0.662283\pi\) | ||||
−0.488025 | + | 0.872829i | \(0.662283\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.0429i | − | 0.795820i | −0.917424 | − | 0.397910i | \(-0.869736\pi\) | ||
0.917424 | − | 0.397910i | \(-0.130264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0479 | 0.659677 | ||||||||
\(233\) | − | 7.13318i | − | 0.467310i | −0.972320 | − | 0.233655i | \(-0.924931\pi\) | ||
0.972320 | − | 0.233655i | \(-0.0750687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.1325 | 1.76993 | ||||||||
\(236\) | −13.8936 | −0.904394 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.40462 | + | 12.6239i | 0.544790 | + | 0.818285i | ||||
\(239\) | − | 1.07669i | − | 0.0696453i | −0.999394 | − | 0.0348226i | \(-0.988913\pi\) | ||
0.999394 | − | 0.0348226i | \(-0.0110866\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.6856i | − | 1.46131i | −0.682748 | − | 0.730654i | \(-0.739215\pi\) | ||
0.682748 | − | 0.730654i | \(-0.260785\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.71780i | 0.109971i | ||||||||
\(245\) | −7.55994 | + | 18.0807i | −0.482987 | + | 1.15513i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.80923 | 0.306004 | ||||||||
\(248\) | 1.77281 | 0.112574 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 6.05277i | − | 0.382811i | ||||||
\(251\) | −24.3971 | −1.53993 | −0.769966 | − | 0.638085i | \(-0.779727\pi\) | ||||
−0.769966 | + | 0.638085i | \(0.779727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 11.0519i | − | 0.693456i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.6654 | −1.72572 | −0.862861 | − | 0.505441i | \(-0.831330\pi\) | ||||
−0.862861 | + | 0.505441i | \(0.831330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.08464 | + | 2.05367i | −0.191670 | + | 0.127609i | ||||
\(260\) | 11.6105i | 0.720053i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 16.3457i | − | 1.00984i | ||||||
\(263\) | − | 11.2387i | − | 0.693006i | −0.938049 | − | 0.346503i | \(-0.887369\pi\) | ||
0.938049 | − | 0.346503i | \(-0.112631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.0506i | 2.03028i | ||||||||
\(266\) | 2.55391 | − | 1.70032i | 0.156590 | − | 0.104253i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.0479 | −0.735942 | ||||||||
\(269\) | 11.1717 | 0.681152 | 0.340576 | − | 0.940217i | \(-0.389378\pi\) | ||||
0.340576 | + | 0.940217i | \(0.389378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.2948i | − | 0.989836i | −0.868940 | − | 0.494918i | \(-0.835198\pi\) | ||
0.868940 | − | 0.494918i | \(-0.164802\pi\) | |||||||
\(272\) | 5.73211 | 0.347560 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.48131 | 0.210313 | ||||||||
\(275\) | − | 2.83802i | − | 0.171139i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.8492 | 1.49304 | 0.746521 | − | 0.665362i | \(-0.231723\pi\) | ||||
0.746521 | + | 0.665362i | \(0.231723\pi\) | |||||||
\(278\) | −9.53172 | −0.571675 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.10494 | + | 6.16569i | 0.245317 | + | 0.368470i | ||||
\(281\) | − | 4.00795i | − | 0.239094i | −0.992829 | − | 0.119547i | \(-0.961856\pi\) | ||
0.992829 | − | 0.119547i | \(-0.0381443\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.496831i | − | 0.0295335i | −0.999891 | − | 0.0147668i | \(-0.995299\pi\) | ||
0.999891 | − | 0.0147668i | \(-0.00470058\pi\) | |||||||
\(284\) | 8.48528i | 0.503509i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4.14713i | − | 0.245225i | ||||||
\(287\) | −5.22898 | + | 3.48131i | −0.308657 | + | 0.205495i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8571 | 0.932772 | ||||||||
\(290\) | 28.1306 | 1.65188 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 10.2929i | − | 0.602347i | ||||||
\(293\) | −12.6507 | −0.739065 | −0.369532 | − | 0.929218i | \(-0.620482\pi\) | ||||
−0.369532 | + | 0.929218i | \(0.620482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.8971 | −2.26468 | ||||||||
\(296\) | 1.40064i | 0.0814106i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.40064 | 0.196994 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4249 | − | 10.2695i | 0.889077 | − | 0.591922i | ||||
\(302\) | 17.0918i | 0.983524i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1.15965i | − | 0.0665106i | ||||||
\(305\) | 4.80923i | 0.275376i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4011i | 1.44972i | 0.688896 | + | 0.724860i | \(0.258096\pi\) | ||||
−0.688896 | + | 0.724860i | \(0.741904\pi\) | |||||||
\(308\) | −1.46623 | − | 2.20231i | −0.0835464 | − | 0.125488i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.96326 | 0.281894 | ||||||||
\(311\) | −34.2764 | −1.94363 | −0.971817 | − | 0.235738i | \(-0.924249\pi\) | ||||
−0.971817 | + | 0.235738i | \(0.924249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.9450i | 1.18388i | 0.805981 | + | 0.591941i | \(0.201638\pi\) | ||||
−0.805981 | + | 0.591941i | \(0.798362\pi\) | |||||||
\(314\) | 1.77281 | 0.100046 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.43341 | −0.0806356 | ||||||||
\(317\) | 31.9010i | 1.79174i | 0.444315 | + | 0.895871i | \(0.353447\pi\) | ||||
−0.444315 | + | 0.895871i | \(0.646553\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0479 | −0.562574 | ||||||||
\(320\) | 2.79965 | 0.156505 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.64726i | − | 0.369863i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7697i | 0.652864i | ||||||||
\(326\) | 5.07669i | 0.281172i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.37432i | 0.131100i | ||||||||
\(329\) | 21.3435 | − | 14.2099i | 1.17670 | − | 0.783416i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5332 | 0.908746 | 0.454373 | − | 0.890812i | \(-0.349863\pi\) | ||||
0.454373 | + | 0.890812i | \(0.349863\pi\) | |||||||
\(332\) | −7.55994 | −0.414906 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0944i | 1.09951i | ||||||||
\(335\) | −33.7299 | −1.84286 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.61051 | 0.523518 | 0.261759 | − | 0.965133i | \(-0.415697\pi\) | ||||
0.261759 | + | 0.965133i | \(0.415697\pi\) | |||||||
\(338\) | 4.19872i | 0.228380i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.0479 | 0.870319 | ||||||||
\(341\) | −1.77281 | −0.0960033 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.52228 | + | 18.1822i | 0.190185 | + | 0.981748i | ||||
\(344\) | − | 7.00398i | − | 0.377629i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.31709i | 0.393369i | ||||||||
\(347\) | − | 1.40859i | − | 0.0756171i | −0.999285 | − | 0.0378086i | \(-0.987962\pi\) | ||
0.999285 | − | 0.0378086i | \(-0.0120377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 32.2992i | − | 1.72894i | −0.502687 | − | 0.864469i | \(-0.667655\pi\) | ||
0.502687 | − | 0.864469i | \(-0.332345\pi\) | |||||||
\(350\) | 4.16121 | + | 6.25020i | 0.222426 | + | 0.334087i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 18.6994 | 0.995271 | 0.497635 | − | 0.867386i | \(-0.334202\pi\) | ||||
0.497635 | + | 0.867386i | \(0.334202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.7558i | 1.26083i | ||||||||
\(356\) | −2.33096 | −0.123541 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.72395 | 0.408223 | ||||||||
\(359\) | − | 7.44854i | − | 0.393119i | −0.980492 | − | 0.196559i | \(-0.937023\pi\) | ||
0.980492 | − | 0.196559i | \(-0.0629768\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.6552 | 0.929221 | ||||||||
\(362\) | 3.49061 | 0.183463 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.08067 | + | 9.13327i | 0.318713 | + | 0.478713i | ||||
\(365\) | − | 28.8165i | − | 1.50833i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3291i | 0.956772i | 0.878150 | + | 0.478386i | \(0.158778\pi\) | ||||
−0.878150 | + | 0.478386i | \(0.841222\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.92130i | 0.203859i | ||||||||
\(371\) | 17.3093 | + | 25.9988i | 0.898652 | + | 1.34979i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5540 | 0.701801 | 0.350900 | − | 0.936413i | \(-0.385876\pi\) | ||||
0.350900 | + | 0.936413i | \(0.385876\pi\) | |||||||
\(374\) | −5.73211 | −0.296401 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 9.69141i | − | 0.499796i | ||||||
\(377\) | 41.6700 | 2.14611 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.07669 | −0.466238 | −0.233119 | − | 0.972448i | \(-0.574893\pi\) | ||||
−0.233119 | + | 0.972448i | \(0.574893\pi\) | |||||||
\(380\) | − | 3.24662i | − | 0.166548i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.48528 | −0.434145 | ||||||||
\(383\) | 13.9866 | 0.714681 | 0.357340 | − | 0.933974i | \(-0.383684\pi\) | ||||
0.357340 | + | 0.933974i | \(0.383684\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.10494 | − | 6.16569i | −0.209207 | − | 0.314232i | ||||
\(386\) | − | 18.0958i | − | 0.921052i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 7.91860i | − | 0.402006i | ||||||
\(389\) | − | 20.1292i | − | 1.02059i | −0.859999 | − | 0.510296i | \(-0.829536\pi\) | ||
0.859999 | − | 0.510296i | \(-0.170464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.45819 | + | 2.70032i | 0.326188 | + | 0.136387i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.3424 | −1.17597 | ||||||||
\(395\) | −4.01304 | −0.201918 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.3206i | 1.12024i | 0.828411 | + | 0.560121i | \(0.189245\pi\) | ||||
−0.828411 | + | 0.560121i | \(0.810755\pi\) | |||||||
\(398\) | 9.95705 | 0.499102 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.83802 | 0.141901 | ||||||||
\(401\) | − | 8.68003i | − | 0.433460i | −0.976232 | − | 0.216730i | \(-0.930461\pi\) | ||
0.976232 | − | 0.216730i | \(-0.0695391\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.35210 | 0.366234 | ||||||||
\(404\) | −3.77146 | −0.187637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.1286 | − | 14.7326i | 1.09822 | − | 0.731165i | ||||
\(407\) | − | 1.40064i | − | 0.0694272i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.9512i | − | 1.13487i | −0.823420 | − | 0.567433i | \(-0.807937\pi\) | ||
0.823420 | − | 0.567433i | \(-0.192063\pi\) | |||||||
\(410\) | 6.64726i | 0.328285i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.0635i | 0.889924i | ||||||||
\(413\) | −30.5979 | + | 20.3712i | −1.50562 | + | 1.00240i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.1652 | −1.03896 | ||||||||
\(416\) | 4.14713 | 0.203330 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.15965i | 0.0567204i | ||||||||
\(419\) | −15.0099 | −0.733279 | −0.366640 | − | 0.930363i | \(-0.619492\pi\) | ||||
−0.366640 | + | 0.930363i | \(0.619492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.4006 | −0.653107 | −0.326554 | − | 0.945179i | \(-0.605887\pi\) | ||||
−0.326554 | + | 0.945179i | \(0.605887\pi\) | |||||||
\(422\) | − | 6.29054i | − | 0.306219i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.8053 | 0.573314 | ||||||||
\(425\) | 16.2679 | 0.789108 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.51869 | + | 3.78312i | 0.121888 | + | 0.183078i | ||||
\(428\) | − | 8.20987i | − | 0.396839i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 19.6087i | − | 0.945614i | ||||||
\(431\) | 28.2092i | 1.35879i | 0.733772 | + | 0.679395i | \(0.237758\pi\) | ||||
−0.733772 | + | 0.679395i | \(0.762242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.48079i | − | 0.455618i | −0.973706 | − | 0.227809i | \(-0.926844\pi\) | ||
0.973706 | − | 0.227809i | \(-0.0731561\pi\) | |||||||
\(434\) | 3.90428 | − | 2.59936i | 0.187412 | − | 0.124773i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.7239 | −0.848823 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0246i | 1.33754i | 0.743468 | + | 0.668771i | \(0.233179\pi\) | ||||
−0.743468 | + | 0.668771i | \(0.766821\pi\) | |||||||
\(440\) | −2.79965 | −0.133468 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.7718 | 1.13071 | ||||||||
\(443\) | − | 4.43738i | − | 0.210827i | −0.994429 | − | 0.105413i | \(-0.966383\pi\) | ||
0.994429 | − | 0.105413i | \(-0.0336165\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.52587 | −0.309356 | ||||||||
\(446\) | −7.74778 | −0.366868 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.20231 | − | 1.46623i | 0.104049 | − | 0.0692730i | ||||
\(449\) | 29.5298i | 1.39360i | 0.717266 | + | 0.696800i | \(0.245393\pi\) | ||||
−0.717266 | + | 0.696800i | \(0.754607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.37432i | − | 0.111802i | ||||||
\(452\) | 6.08067i | 0.286010i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.7057i | 0.690172i | ||||||||
\(455\) | 17.0237 | + | 25.5699i | 0.798084 | + | 1.19874i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.2866 | 0.621519 | 0.310760 | − | 0.950489i | \(-0.399417\pi\) | ||||
0.310760 | + | 0.950489i | \(0.399417\pi\) | |||||||
\(458\) | −12.0429 | −0.562730 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.7035 | 1.89575 | 0.947876 | − | 0.318640i | \(-0.103226\pi\) | ||||
0.947876 | + | 0.318640i | \(0.103226\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9706 | −0.974585 | −0.487292 | − | 0.873239i | \(-0.662015\pi\) | ||||
−0.487292 | + | 0.873239i | \(0.662015\pi\) | |||||||
\(464\) | − | 10.0479i | − | 0.466462i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.13318 | −0.330438 | ||||||||
\(467\) | 4.13065 | 0.191144 | 0.0955718 | − | 0.995423i | \(-0.469532\pi\) | ||||
0.0955718 | + | 0.995423i | \(0.469532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.5332 | + | 17.6650i | −1.22519 | + | 0.815695i | ||||
\(470\) | − | 27.1325i | − | 1.25153i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.8936i | 0.639503i | ||||||||
\(473\) | 7.00398i | 0.322043i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.29112i | − | 0.151007i | ||||||
\(476\) | 12.6239 | − | 8.40462i | 0.578615 | − | 0.385225i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.07669 | −0.0492467 | ||||||||
\(479\) | −13.7670 | −0.629032 | −0.314516 | − | 0.949252i | \(-0.601842\pi\) | ||||
−0.314516 | + | 0.949252i | \(0.601842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.80864i | 0.264851i | ||||||||
\(482\) | −22.6856 | −1.03330 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | − | 22.1693i | − | 1.00666i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.7516 | 1.21223 | 0.606116 | − | 0.795376i | \(-0.292727\pi\) | ||||
0.606116 | + | 0.795376i | \(0.292727\pi\) | |||||||
\(488\) | 1.71780 | 0.0777611 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.0807 | + | 7.55994i | 0.816801 | + | 0.341523i | ||||
\(491\) | − | 15.5620i | − | 0.702302i | −0.936319 | − | 0.351151i | \(-0.885790\pi\) | ||
0.936319 | − | 0.351151i | \(-0.114210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 57.5957i | − | 2.59398i | ||||||
\(494\) | − | 4.80923i | − | 0.216378i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.77281i | − | 0.0796017i | ||||||
\(497\) | 12.4414 | + | 18.6872i | 0.558073 | + | 0.838236i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.0479 | −1.61373 | −0.806863 | − | 0.590739i | \(-0.798836\pi\) | ||||
−0.806863 | + | 0.590739i | \(0.798836\pi\) | |||||||
\(500\) | −6.05277 | −0.270688 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.3971i | 1.08890i | ||||||||
\(503\) | 13.0031 | 0.579780 | 0.289890 | − | 0.957060i | \(-0.406381\pi\) | ||||
0.289890 | + | 0.957060i | \(0.406381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5588 | −0.469859 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.0519 | −0.490348 | ||||||||
\(509\) | −9.30409 | −0.412396 | −0.206198 | − | 0.978510i | \(-0.566109\pi\) | ||||
−0.206198 | + | 0.978510i | \(0.566109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0918 | − | 22.6682i | −0.667623 | − | 1.00278i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 27.6654i | 1.22027i | ||||||||
\(515\) | 50.5714i | 2.22844i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.69141i | 0.426228i | ||||||||
\(518\) | 2.05367 | + | 3.08464i | 0.0902329 | + | 0.135531i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 11.6105 | 0.509155 | ||||||||
\(521\) | −21.9794 | −0.962936 | −0.481468 | − | 0.876464i | \(-0.659896\pi\) | ||||
−0.481468 | + | 0.876464i | \(0.659896\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.5953i | − | 1.07548i | −0.843111 | − | 0.537739i | \(-0.819279\pi\) | ||
0.843111 | − | 0.537739i | \(-0.180721\pi\) | |||||||
\(524\) | −16.3457 | −0.714065 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.2387 | −0.490029 | ||||||||
\(527\) | − | 10.1620i | − | 0.442663i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 33.0506 | 1.43562 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.70032 | − | 2.55391i | −0.0737182 | − | 0.110726i | ||||
\(533\) | 9.84662i | 0.426504i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 22.9847i | − | 0.993717i | ||||||
\(536\) | 12.0479i | 0.520390i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 11.1717i | − | 0.481647i | ||||||
\(539\) | −6.45819 | − | 2.70032i | −0.278174 | − | 0.116311i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.7989 | 1.84007 | 0.920034 | − | 0.391838i | \(-0.128161\pi\) | ||||
0.920034 | + | 0.391838i | \(0.128161\pi\) | |||||||
\(542\) | −16.2948 | −0.699920 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 5.73211i | − | 0.245762i | ||||||
\(545\) | −49.6208 | −2.12552 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.0918 | −1.07285 | −0.536424 | − | 0.843948i | \(-0.680225\pi\) | ||||
−0.536424 | + | 0.843948i | \(0.680225\pi\) | |||||||
\(548\) | − | 3.48131i | − | 0.148714i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.83802 | −0.121014 | ||||||||
\(551\) | −11.6521 | −0.496395 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.15681 | + | 2.10171i | −0.134241 | + | 0.0893739i | ||||
\(554\) | − | 24.8492i | − | 1.05574i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.53172i | 0.404235i | ||||||||
\(557\) | − | 18.7613i | − | 0.794943i | −0.917614 | − | 0.397472i | \(-0.869888\pi\) | ||
0.917614 | − | 0.397472i | \(-0.130112\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 29.0464i | − | 1.22853i | ||||||
\(560\) | 6.16569 | − | 4.10494i | 0.260548 | − | 0.173465i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.00795 | −0.169065 | ||||||||
\(563\) | 15.9155 | 0.670760 | 0.335380 | − | 0.942083i | \(-0.391135\pi\) | ||||
0.335380 | + | 0.942083i | \(0.391135\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.0237i | 0.716193i | ||||||||
\(566\) | −0.496831 | −0.0208833 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.48528 | 0.356034 | ||||||||
\(569\) | − | 28.4773i | − | 1.19383i | −0.802304 | − | 0.596916i | \(-0.796393\pi\) | ||
0.802304 | − | 0.596916i | \(-0.203607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.2985 | −1.18425 | −0.592127 | − | 0.805844i | \(-0.701712\pi\) | ||||
−0.592127 | + | 0.805844i | \(0.701712\pi\) | |||||||
\(572\) | −4.14713 | −0.173400 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.48131 | + | 5.22898i | 0.145307 | + | 0.218253i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11.4642i | − | 0.477262i | −0.971110 | − | 0.238631i | \(-0.923301\pi\) | ||
0.971110 | − | 0.238631i | \(-0.0766986\pi\) | |||||||
\(578\) | − | 15.8571i | − | 0.659570i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 28.1306i | − | 1.16806i | ||||||
\(581\) | −16.6493 | + | 11.0846i | −0.690730 | + | 0.459868i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.8053 | −0.488924 | ||||||||
\(584\) | −10.2929 | −0.425924 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.6507i | 0.522598i | ||||||||
\(587\) | 21.5921 | 0.891201 | 0.445601 | − | 0.895232i | \(-0.352990\pi\) | ||||
0.445601 | + | 0.895232i | \(0.352990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.05585 | −0.0847097 | ||||||||
\(590\) | 38.8971i | 1.60137i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.40064 | 0.0575660 | ||||||||
\(593\) | −1.62298 | −0.0666478 | −0.0333239 | − | 0.999445i | \(-0.510609\pi\) | ||||
−0.0333239 | + | 0.999445i | \(0.510609\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.3424 | − | 23.5300i | 1.44890 | − | 0.964634i | ||||
\(596\) | − | 3.40064i | − | 0.139296i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.8172i | 0.605414i | 0.953084 | + | 0.302707i | \(0.0978903\pi\) | ||||
−0.953084 | + | 0.302707i | \(0.902110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 33.4092i | − | 1.36279i | −0.731916 | − | 0.681395i | \(-0.761374\pi\) | ||
0.731916 | − | 0.681395i | \(-0.238626\pi\) | |||||||
\(602\) | −10.2695 | − | 15.4249i | −0.418552 | − | 0.628672i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.0918 | 0.695456 | ||||||||
\(605\) | 2.79965 | 0.113822 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.2804i | − | 0.539035i | −0.962996 | − | 0.269517i | \(-0.913136\pi\) | ||
0.962996 | − | 0.269517i | \(-0.0868642\pi\) | |||||||
\(608\) | −1.15965 | −0.0470301 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.80923 | 0.194720 | ||||||||
\(611\) | − | 40.1916i | − | 1.62598i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.9706 | −1.08933 | −0.544665 | − | 0.838653i | \(-0.683343\pi\) | ||||
−0.544665 | + | 0.838653i | \(0.683343\pi\) | |||||||
\(614\) | 25.4011 | 1.02511 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.20231 | + | 1.46623i | −0.0887335 | + | 0.0590762i | ||||
\(617\) | 15.1095i | 0.608284i | 0.952627 | + | 0.304142i | \(0.0983697\pi\) | ||||
−0.952627 | + | 0.304142i | \(0.901630\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.58494i | − | 0.103898i | −0.998650 | − | 0.0519488i | \(-0.983457\pi\) | ||
0.998650 | − | 0.0519488i | \(-0.0165433\pi\) | |||||||
\(620\) | − | 4.96326i | − | 0.199329i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.2764i | 1.37436i | ||||||||
\(623\) | −5.13350 | + | 3.41773i | −0.205669 | + | 0.136929i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1357 | −1.24543 | ||||||||
\(626\) | 20.9450 | 0.837131 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 1.77281i | − | 0.0707430i | ||||||
\(629\) | 8.02863 | 0.320122 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4118 | −0.414487 | −0.207243 | − | 0.978289i | \(-0.566449\pi\) | ||||
−0.207243 | + | 0.978289i | \(0.566449\pi\) | |||||||
\(632\) | 1.43341i | 0.0570180i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.9010 | 1.26695 | ||||||||
\(635\) | −30.9413 | −1.22787 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.7830 | + | 11.1986i | 1.06118 | + | 0.443704i | ||||
\(638\) | 10.0479i | 0.397800i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 2.79965i | − | 0.110666i | ||||||
\(641\) | 10.5745i | 0.417669i | 0.977951 | + | 0.208835i | \(0.0669670\pi\) | ||||
−0.977951 | + | 0.208835i | \(0.933033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.8220i | − | 1.45212i | −0.687632 | − | 0.726059i | \(-0.741350\pi\) | ||
0.687632 | − | 0.726059i | \(-0.258650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.64726 | −0.261533 | ||||||||
\(647\) | −37.4463 | −1.47217 | −0.736083 | − | 0.676891i | \(-0.763327\pi\) | ||||
−0.736083 | + | 0.676891i | \(0.763327\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.8936i | − | 0.545370i | ||||||
\(650\) | 11.7697 | 0.461644 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.07669 | 0.198819 | ||||||||
\(653\) | − | 32.0624i | − | 1.25470i | −0.778738 | − | 0.627349i | \(-0.784140\pi\) | ||
0.778738 | − | 0.627349i | \(-0.215860\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.7622 | −1.78808 | ||||||||
\(656\) | 2.37432 | 0.0927016 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.2099 | − | 21.3435i | −0.553958 | − | 0.832055i | ||||
\(659\) | − | 27.4479i | − | 1.06922i | −0.845099 | − | 0.534609i | \(-0.820459\pi\) | ||
0.845099 | − | 0.534609i | \(-0.179541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.5143i | 1.73140i | 0.500560 | + | 0.865702i | \(0.333127\pi\) | ||||
−0.500560 | + | 0.865702i | \(0.666873\pi\) | |||||||
\(662\) | − | 16.5332i | − | 0.642580i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.55994i | 0.293383i | ||||||||
\(665\) | −4.76030 | − | 7.15005i | −0.184596 | − | 0.277267i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 20.0944 | 0.777474 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 33.7299i | 1.30310i | ||||||||
\(671\) | −1.71780 | −0.0663149 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.6185 | −1.37299 | −0.686495 | − | 0.727134i | \(-0.740852\pi\) | ||||
−0.686495 | + | 0.727134i | \(0.740852\pi\) | |||||||
\(674\) | − | 9.61051i | − | 0.370183i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.19872 | 0.161489 | ||||||||
\(677\) | 42.4271 | 1.63061 | 0.815303 | − | 0.579035i | \(-0.196571\pi\) | ||||
0.815303 | + | 0.579035i | \(0.196571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.6105 | − | 17.4392i | −0.445571 | − | 0.669255i | ||||
\(680\) | − | 16.0479i | − | 0.615409i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.77281i | 0.0678846i | ||||||||
\(683\) | − | 32.4676i | − | 1.24234i | −0.783676 | − | 0.621170i | \(-0.786658\pi\) | ||
0.783676 | − | 0.621170i | \(-0.213342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.74643i | − | 0.372392i | ||||||
\(686\) | 18.1822 | − | 3.52228i | 0.694201 | − | 0.134481i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.00398 | −0.267024 | ||||||||
\(689\) | 48.9580 | 1.86515 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25.4678i | − | 0.968842i | −0.874835 | − | 0.484421i | \(-0.839030\pi\) | ||
0.874835 | − | 0.484421i | \(-0.160970\pi\) | |||||||
\(692\) | 7.31709 | 0.278154 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.40859 | −0.0534694 | ||||||||
\(695\) | 26.6855i | 1.01224i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.6099 | 0.515511 | ||||||||
\(698\) | −32.2992 | −1.22254 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.25020 | − | 4.16121i | 0.236236 | − | 0.157279i | ||||
\(701\) | 39.6185i | 1.49637i | 0.663491 | + | 0.748184i | \(0.269074\pi\) | ||||
−0.663491 | + | 0.748184i | \(0.730926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.62426i | − | 0.0612599i | ||||||
\(704\) | 1.00000i | 0.0376889i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.6994i | − | 0.703763i | ||||||
\(707\) | −8.30593 | + | 5.52985i | −0.312376 | + | 0.207971i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.2210 | −0.947195 | −0.473598 | − | 0.880741i | \(-0.657045\pi\) | ||||
−0.473598 | + | 0.880741i | \(0.657045\pi\) | |||||||
\(710\) | 23.7558 | 0.891539 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.33096i | 0.0873565i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.6105 | −0.434209 | ||||||||
\(716\) | − | 7.72395i | − | 0.288657i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.44854 | −0.277977 | ||||||||
\(719\) | −36.9383 | −1.37757 | −0.688784 | − | 0.724967i | \(-0.741855\pi\) | ||||
−0.688784 | + | 0.724967i | \(0.741855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.4853 | + | 39.7814i | 0.986363 | + | 1.48154i | ||||
\(722\) | − | 17.6552i | − | 0.657059i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3.49061i | − | 0.129728i | ||||||
\(725\) | − | 28.5162i | − | 1.05906i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.33280i | − | 0.309046i | −0.987989 | − | 0.154523i | \(-0.950616\pi\) | ||
0.987989 | − | 0.154523i | \(-0.0493841\pi\) | |||||||
\(728\) | 9.13327 | − | 6.08067i | 0.338501 | − | 0.225364i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28.8165 | −1.06655 | ||||||||
\(731\) | −40.1476 | −1.48491 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 42.6927i | − | 1.57689i | −0.615104 | − | 0.788446i | \(-0.710886\pi\) | ||
0.615104 | − | 0.788446i | \(-0.289114\pi\) | |||||||
\(734\) | 18.3291 | 0.676540 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.0479i | − | 0.443790i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.45187 | −0.237336 | −0.118668 | − | 0.992934i | \(-0.537862\pi\) | ||||
−0.118668 | + | 0.992934i | \(0.537862\pi\) | |||||||
\(740\) | 3.92130 | 0.144150 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.9988 | − | 17.3093i | 0.954446 | − | 0.635443i | ||||
\(743\) | − | 27.0112i | − | 0.990943i | −0.868624 | − | 0.495472i | \(-0.834995\pi\) | ||
0.868624 | − | 0.495472i | \(-0.165005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.52059i | − | 0.348808i | ||||||
\(746\) | − | 13.5540i | − | 0.496248i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.73211i | 0.209587i | ||||||||
\(749\) | −12.0376 | − | 18.0807i | −0.439844 | − | 0.660653i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0303 | −1.31476 | −0.657381 | − | 0.753558i | \(-0.728336\pi\) | ||||
−0.657381 | + | 0.753558i | \(0.728336\pi\) | |||||||
\(752\) | −9.69141 | −0.353409 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 41.6700i | − | 1.51753i | ||||||
\(755\) | 47.8511 | 1.74148 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4288 | −0.597115 | −0.298557 | − | 0.954392i | \(-0.596505\pi\) | ||||
−0.298557 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(758\) | 9.07669i | 0.329680i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.24662 | −0.117767 | ||||||||
\(761\) | 13.4091 | 0.486081 | 0.243040 | − | 0.970016i | \(-0.421855\pi\) | ||||
0.243040 | + | 0.970016i | \(0.421855\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.0336 | + | 25.9874i | −1.41311 | + | 0.940808i | ||||
\(764\) | 8.48528i | 0.306987i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 13.9866i | − | 0.505356i | ||||||
\(767\) | 57.6185i | 2.08048i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.16227i | 0.222217i | 0.993808 | + | 0.111109i | \(0.0354401\pi\) | ||||
−0.993808 | + | 0.111109i | \(0.964560\pi\) | |||||||
\(770\) | −6.16569 | + | 4.10494i | −0.222196 | + | 0.147932i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.0958 | −0.651282 | ||||||||
\(773\) | 27.7603 | 0.998467 | 0.499233 | − | 0.866468i | \(-0.333615\pi\) | ||||
0.499233 | + | 0.866468i | \(0.333615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.03129i | − | 0.180729i | ||||||
\(776\) | −7.91860 | −0.284261 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.1292 | −0.721667 | ||||||||
\(779\) | − | 2.75338i | − | 0.0986502i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.48528 | −0.303627 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.70032 | − | 6.45819i | 0.0964400 | − | 0.230650i | ||||
\(785\) | − | 4.96326i | − | 0.177146i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.49957i | − | 0.267331i | −0.991027 | − | 0.133665i | \(-0.957325\pi\) | ||
0.991027 | − | 0.133665i | \(-0.0426747\pi\) | |||||||
\(788\) | 23.3424i | 0.831539i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.01304i | 0.142778i | ||||||||
\(791\) | 8.91567 | + | 13.3915i | 0.317005 | + | 0.476147i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.12394 | 0.252979 | ||||||||
\(794\) | 22.3206 | 0.792130 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 9.95705i | − | 0.352918i | ||||||
\(797\) | 45.9168 | 1.62645 | 0.813227 | − | 0.581946i | \(-0.197708\pi\) | ||||
0.813227 | + | 0.581946i | \(0.197708\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.5523 | −1.96530 | ||||||||
\(800\) | − | 2.83802i | − | 0.100339i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.68003 | −0.306502 | ||||||||
\(803\) | 10.2929 | 0.363229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 7.35210i | − | 0.258967i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.77146i | 0.132680i | ||||||||
\(809\) | − | 38.0958i | − | 1.33938i | −0.742642 | − | 0.669688i | \(-0.766428\pi\) | ||
0.742642 | − | 0.669688i | \(-0.233572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.7929i | 0.695024i | 0.937676 | + | 0.347512i | \(0.112973\pi\) | ||||
−0.937676 | + | 0.347512i | \(0.887027\pi\) | |||||||
\(812\) | −14.7326 | − | 22.1286i | −0.517012 | − | 0.776560i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.40064 | −0.0490924 | ||||||||
\(815\) | 14.2129 | 0.497858 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.12217i | 0.284159i | ||||||||
\(818\) | −22.9512 | −0.802471 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.64726 | 0.232132 | ||||||||
\(821\) | − | 7.99205i | − | 0.278924i | −0.990227 | − | 0.139462i | \(-0.955463\pi\) | ||
0.990227 | − | 0.139462i | \(-0.0445374\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.6026 | −0.613587 | −0.306793 | − | 0.951776i | \(-0.599256\pi\) | ||||
−0.306793 | + | 0.951776i | \(0.599256\pi\) | |||||||
\(824\) | 18.0635 | 0.629271 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.3712 | + | 30.5979i | 0.708805 | + | 1.06464i | ||||
\(827\) | − | 23.5779i | − | 0.819883i | −0.912112 | − | 0.409941i | \(-0.865549\pi\) | ||
0.912112 | − | 0.409941i | \(-0.134451\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.5385i | 1.40796i | 0.710220 | + | 0.703980i | \(0.248595\pi\) | ||||
−0.710220 | + | 0.703980i | \(0.751405\pi\) | |||||||
\(830\) | 21.1652i | 0.734654i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.14713i | − | 0.143776i | ||||||
\(833\) | 15.4785 | − | 37.0191i | 0.536300 | − | 1.28264i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 56.2571 | 1.94686 | ||||||||
\(836\) | 1.15965 | 0.0401074 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.0099i | 0.518507i | ||||||||
\(839\) | 10.5510 | 0.364260 | 0.182130 | − | 0.983274i | \(-0.441701\pi\) | ||||
0.182130 | + | 0.983274i | \(0.441701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −71.9602 | −2.48139 | ||||||||
\(842\) | 13.4006i | 0.461817i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.29054 | −0.216529 | ||||||||
\(845\) | 11.7549 | 0.404382 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.20231 | − | 1.46623i | 0.0756722 | − | 0.0503804i | ||||
\(848\) | − | 11.8053i | − | 0.405394i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 16.2679i | − | 0.557984i | ||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.9835i | 1.50597i | 0.658040 | + | 0.752983i | \(0.271386\pi\) | ||||
−0.658040 | + | 0.752983i | \(0.728614\pi\) | |||||||
\(854\) | 3.78312 | − | 2.51869i | 0.129456 | − | 0.0861879i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.20987 | −0.280608 | ||||||||
\(857\) | −14.2920 | −0.488206 | −0.244103 | − | 0.969749i | \(-0.578494\pi\) | ||||
−0.244103 | + | 0.969749i | \(0.578494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 43.9893i | − | 1.50089i | −0.660930 | − | 0.750447i | \(-0.729838\pi\) | ||
0.660930 | − | 0.750447i | \(-0.270162\pi\) | |||||||
\(860\) | −19.6087 | −0.668650 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.2092 | 0.960810 | ||||||||
\(863\) | 2.81718i | 0.0958980i | 0.998850 | + | 0.0479490i | \(0.0152685\pi\) | ||||
−0.998850 | + | 0.0479490i | \(0.984732\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.4853 | 0.696520 | ||||||||
\(866\) | −9.48079 | −0.322170 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.59936 | − | 3.90428i | −0.0882280 | − | 0.132520i | ||||
\(869\) | − | 1.43341i | − | 0.0486251i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.9642i | 1.69297i | ||||||||
\(872\) | 17.7239i | 0.600209i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.3301 | + | 8.87477i | −0.450638 | + | 0.300022i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.8277 | 1.34489 | 0.672443 | − | 0.740149i | \(-0.265245\pi\) | ||||
0.672443 | + | 0.740149i | \(0.265245\pi\) | |||||||
\(878\) | 28.0246 | 0.945785 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.79965i | 0.0943761i | ||||||||
\(881\) | 10.4589 | 0.352370 | 0.176185 | − | 0.984357i | \(-0.443624\pi\) | ||||
0.176185 | + | 0.984357i | \(0.443624\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.2762 | 1.86019 | 0.930097 | − | 0.367315i | \(-0.119723\pi\) | ||||
0.930097 | + | 0.367315i | \(0.119723\pi\) | |||||||
\(884\) | − | 23.7718i | − | 0.799534i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.43738 | −0.149077 | ||||||||
\(887\) | 32.5813 | 1.09397 | 0.546987 | − | 0.837141i | \(-0.315775\pi\) | ||||
0.546987 | + | 0.837141i | \(0.315775\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.3396 | + | 16.2046i | −0.816325 | + | 0.543486i | ||||
\(890\) | 6.52587i | 0.218748i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.74778i | 0.259415i | ||||||||
\(893\) | 11.2387i | 0.376088i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 21.6243i | − | 0.722821i | ||||||
\(896\) | −1.46623 | − | 2.20231i | −0.0489834 | − | 0.0735739i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.5298 | 0.985424 | ||||||||
\(899\) | −17.8131 | −0.594099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 67.6691i | − | 2.25438i | ||||||
\(902\) | −2.37432 | −0.0790562 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.08067 | 0.202240 | ||||||||
\(905\) | − | 9.77249i | − | 0.324848i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.88657 | 0.261869 | 0.130935 | − | 0.991391i | \(-0.458202\pi\) | ||||
0.130935 | + | 0.991391i | \(0.458202\pi\) | |||||||
\(908\) | 14.7057 | 0.488025 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 25.5699 | − | 17.0237i | 0.847635 | − | 0.564331i | ||||
\(911\) | 19.0756i | 0.632003i | 0.948759 | + | 0.316001i | \(0.102340\pi\) | ||||
−0.948759 | + | 0.316001i | \(0.897660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.55994i | − | 0.250198i | ||||||
\(914\) | − | 13.2866i | − | 0.439480i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.0429i | 0.397910i | ||||||||
\(917\) | −35.9982 | + | 23.9666i | −1.18877 | + | 0.791446i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0624 | 0.595823 | 0.297911 | − | 0.954593i | \(-0.403710\pi\) | ||||
0.297911 | + | 0.954593i | \(0.403710\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 40.7035i | − | 1.34050i | ||||||
\(923\) | 35.1896 | 1.15828 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.97505 | 0.130699 | ||||||||
\(926\) | 20.9706i | 0.689135i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.0479 | −0.329838 | ||||||||
\(929\) | −25.8667 | −0.848659 | −0.424329 | − | 0.905508i | \(-0.639490\pi\) | ||||
−0.424329 | + | 0.905508i | \(0.639490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.48926 | − | 3.13143i | −0.245450 | − | 0.102629i | ||||
\(932\) | 7.13318i | 0.233655i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 4.13065i | − | 0.135159i | ||||||
\(935\) | 16.0479i | 0.524822i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.2920i | 1.18561i | 0.805347 | + | 0.592804i | \(0.201979\pi\) | ||||
−0.805347 | + | 0.592804i | \(0.798021\pi\) | |||||||
\(938\) | 17.6650 | + | 26.5332i | 0.576784 | + | 0.866339i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −27.1325 | −0.884966 | ||||||||
\(941\) | 33.6811 | 1.09797 | 0.548987 | − | 0.835831i | \(-0.315014\pi\) | ||||
0.548987 | + | 0.835831i | \(0.315014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 13.8936 | 0.452197 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.00398 | 0.227719 | ||||||||
\(947\) | − | 25.3510i | − | 0.823797i | −0.911230 | − | 0.411898i | \(-0.864866\pi\) | ||
0.911230 | − | 0.411898i | \(-0.135134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.6861 | −1.38565 | ||||||||
\(950\) | −3.29112 | −0.106778 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.40462 | − | 12.6239i | −0.272395 | − | 0.409142i | ||||
\(953\) | − | 22.1916i | − | 0.718856i | −0.933173 | − | 0.359428i | \(-0.882972\pi\) | ||
0.933173 | − | 0.359428i | \(-0.117028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.7558i | 0.768719i | ||||||||
\(956\) | 1.07669i | 0.0348226i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.7670i | 0.444793i | ||||||||
\(959\) | −5.10441 | − | 7.66691i | −0.164830 | − | 0.247577i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.8571 | 0.898617 | ||||||||
\(962\) | 5.80864 | 0.187278 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.6856i | 0.730654i | ||||||||
\(965\) | −50.6618 | −1.63086 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.9554 | 0.545250 | 0.272625 | − | 0.962120i | \(-0.412108\pi\) | ||||
0.272625 | + | 0.962120i | \(0.412108\pi\) | |||||||
\(968\) | − | 1.00000i | − | 0.0321412i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.1693 | −0.711813 | ||||||||
\(971\) | −21.0152 | −0.674411 | −0.337206 | − | 0.941431i | \(-0.609482\pi\) | ||||
−0.337206 | + | 0.941431i | \(0.609482\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.9757 | + | 20.9918i | 0.448041 | + | 0.672966i | ||||
\(974\) | − | 26.7516i | − | 0.857178i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 1.71780i | − | 0.0549854i | ||||||
\(977\) | 33.1318i | 1.05998i | 0.848004 | + | 0.529990i | \(0.177804\pi\) | ||||
−0.848004 | + | 0.529990i | \(0.822196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.33096i | − | 0.0744979i | ||||||
\(980\) | 7.55994 | − | 18.0807i | 0.241494 | − | 0.577566i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.5620 | −0.496602 | ||||||||
\(983\) | −5.13952 | −0.163925 | −0.0819626 | − | 0.996635i | \(-0.526119\pi\) | ||||
−0.0819626 | + | 0.996635i | \(0.526119\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65.3505i | 2.08224i | ||||||||
\(986\) | −57.5957 | −1.83422 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.80923 | −0.153002 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.6546 | −0.846710 | −0.423355 | − | 0.905964i | \(-0.639148\pi\) | ||||
−0.423355 | + | 0.905964i | \(0.639148\pi\) | |||||||
\(992\) | −1.77281 | −0.0562869 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.6872 | − | 12.4414i | 0.592722 | − | 0.394617i | ||||
\(995\) | − | 27.8762i | − | 0.883736i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.6122i | 1.12785i | 0.825826 | + | 0.563925i | \(0.190709\pi\) | ||||
−0.825826 | + | 0.563925i | \(0.809291\pi\) | |||||||
\(998\) | 36.0479i | 1.14108i | ||||||||
\(999\) | 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 | 1386.2.g.b.881.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1386.2.g.b.881.14 | yes | 16 | |
7.6 | odd | 2 | inner | 1386.2.g.b.881.6 | yes | 16 | |
21.20 | even | 2 | inner | 1386.2.g.b.881.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.g.b.881.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1386.2.g.b.881.6 | yes | 16 | 7.6 | odd | 2 | inner | |
1386.2.g.b.881.11 | yes | 16 | 21.20 | even | 2 | inner | |
1386.2.g.b.881.14 | yes | 16 | 3.2 | odd | 2 | inner |