Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4680,2,Mod(2809,4680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 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("4680.2809");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4680.l (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: | \(37.3699881460\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2809.4 | ||
Root | \(0.432320 - 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4680.2809 |
Dual form | 4680.2.l.e.2809.3 |
$q$-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 \(\left(\mathbb{Z}/4680\mathbb{Z}\right)^\times\).
\(n\) | \(937\) | \(1081\) | \(2081\) | \(2341\) | \(3511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.432320 | + | 2.19388i | −0.193340 | + | 0.981132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.86464 | 0.863722 | 0.431861 | − | 0.901940i | \(-0.357857\pi\) | ||||
0.431861 | + | 0.901940i | \(0.357857\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.52311i | 1.33955i | 0.742563 | + | 0.669776i | \(0.233610\pi\) | ||||
−0.742563 | + | 0.669776i | \(0.766390\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.52311 | −0.808258 | −0.404129 | − | 0.914702i | \(-0.632425\pi\) | ||||
−0.404129 | + | 0.914702i | \(0.632425\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.52311i | − | 1.56868i | −0.620333 | − | 0.784339i | \(-0.713002\pi\) | ||
0.620333 | − | 0.784339i | \(-0.286998\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62620 | − | 1.89692i | −0.925240 | − | 0.379383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.77551 | 1.25818 | 0.629090 | − | 0.777332i | \(-0.283428\pi\) | ||||
0.629090 | + | 0.777332i | \(0.283428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.72928 | 1.02901 | 0.514505 | − | 0.857488i | \(-0.327976\pi\) | ||||
0.514505 | + | 0.857488i | \(0.327976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.72928i | 0.613090i | 0.951856 | + | 0.306545i | \(0.0991730\pi\) | ||||
−0.951856 | + | 0.306545i | \(0.900827\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1170 | 1.58002 | 0.790008 | − | 0.613097i | \(-0.210076\pi\) | ||||
0.790008 | + | 0.613097i | \(0.210076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.52311i | − | 0.842267i | −0.906999 | − | 0.421134i | \(-0.861632\pi\) | ||
0.906999 | − | 0.421134i | \(-0.138368\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.65847i | 1.26297i | 0.775389 | + | 0.631484i | \(0.217554\pi\) | ||||
−0.775389 | + | 0.631484i | \(0.782446\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.77551i | 0.930688i | 0.885130 | + | 0.465344i | \(0.154069\pi\) | ||||
−0.885130 | + | 0.465344i | \(0.845931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.23844 | + | 6.28467i | −0.166992 | + | 0.847425i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.593923 | 0.0773221 | 0.0386611 | − | 0.999252i | \(-0.487691\pi\) | ||||
0.0386611 | + | 0.999252i | \(0.487691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.25240 | −0.672500 | −0.336250 | − | 0.941773i | \(-0.609159\pi\) | ||||
−0.336250 | + | 0.941773i | \(0.609159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.19388 | + | 0.432320i | 0.272117 | + | 0.0536228i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5048i | 1.28336i | 0.766971 | + | 0.641682i | \(0.221763\pi\) | ||||
−0.766971 | + | 0.641682i | \(0.778237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.38776 | 0.283374 | 0.141687 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141687 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.45856i | 0.638877i | 0.947607 | + | 0.319438i | \(0.103494\pi\) | ||||
−0.947607 | + | 0.319438i | \(0.896506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.47689 | −0.278671 | −0.139336 | − | 0.990245i | \(-0.544497\pi\) | ||||
−0.139336 | + | 0.990245i | \(0.544497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.11704i | − | 0.890961i | −0.895292 | − | 0.445480i | \(-0.853033\pi\) | ||
0.895292 | − | 0.445480i | \(-0.146967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1170 | − | 2.38776i | −1.31428 | − | 0.258988i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.1170 | −1.49640 | −0.748201 | − | 0.663472i | \(-0.769082\pi\) | ||||
−0.748201 | + | 0.663472i | \(0.769082\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.52311 | − | 7.72928i | 0.156268 | − | 0.793008i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.00000i | − | 0.609208i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7293 | 1.16711 | 0.583554 | − | 0.812075i | \(-0.301662\pi\) | ||||
0.583554 | + | 0.812075i | \(0.301662\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7755i | 1.45587i | 0.685644 | + | 0.727937i | \(0.259521\pi\) | ||||
−0.685644 | + | 0.727937i | \(0.740479\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.72928i | 0.167176i | 0.996500 | + | 0.0835880i | \(0.0266380\pi\) | ||||
−0.996500 | + | 0.0835880i | \(0.973362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0279 | −1.15206 | −0.576032 | − | 0.817427i | \(-0.695400\pi\) | ||||
−0.576032 | + | 0.817427i | \(0.695400\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.25240i | 0.682248i | 0.940018 | + | 0.341124i | \(0.110808\pi\) | ||||
−0.940018 | + | 0.341124i | \(0.889192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.5048 | + | 3.25240i | 1.53908 | + | 0.303288i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.79383 | −0.253985 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.16160 | − | 9.32924i | 0.551110 | − | 0.834432i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.2524i | − | 1.53090i | −0.643494 | − | 0.765451i | \(-0.722516\pi\) | ||
0.643494 | − | 0.765451i | \(-0.277484\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.77551 | 0.766720 | 0.383360 | − | 0.923599i | \(-0.374767\pi\) | ||||
0.383360 | + | 0.923599i | \(0.374767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.4340i | 1.66036i | 0.557497 | + | 0.830179i | \(0.311762\pi\) | ||||
−0.557497 | + | 0.830179i | \(0.688238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.58767 | −0.643577 | −0.321789 | − | 0.946812i | \(-0.604284\pi\) | ||||
−0.321789 | + | 0.946812i | \(0.604284\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.86464i | − | 0.239553i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.92919 | + | 14.8646i | −0.243256 | + | 1.23444i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.40608 | −0.115190 | −0.0575952 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575952 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.31695 | −0.107172 | −0.0535858 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535858 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47689 | + | 12.5693i | −0.198948 | + | 1.00959i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.7110i | − | 1.65291i | −0.562999 | − | 0.826457i | \(-0.690353\pi\) | ||
0.562999 | − | 0.826457i | \(-0.309647\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.27072i | 0.177856i | 0.996038 | + | 0.0889282i | \(0.0283442\pi\) | ||||
−0.996038 | + | 0.0889282i | \(0.971656\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.34153i | 0.568104i | 0.958809 | + | 0.284052i | \(0.0916789\pi\) | ||||
−0.958809 | + | 0.284052i | \(0.908321\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0925i | 1.22349i | 0.791056 | + | 0.611743i | \(0.209532\pi\) | ||||
−0.791056 | + | 0.611743i | \(0.790468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0462 | 1.12461 | 0.562304 | − | 0.826931i | \(-0.309915\pi\) | ||||
0.562304 | + | 0.826931i | \(0.309915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.58767 | 0.415328 | 0.207664 | − | 0.978200i | \(-0.433414\pi\) | ||||
0.207664 | + | 0.978200i | \(0.433414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.18159 | − | 1.61224i | −0.601522 | − | 0.118535i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8217i | 1.15700i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.5510 | −1.26995 | −0.634974 | − | 0.772534i | \(-0.718989\pi\) | ||||
−0.634974 | + | 0.772534i | \(0.718989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8217i | 0.994911i | 0.867490 | + | 0.497455i | \(0.165732\pi\) | ||||
−0.867490 | + | 0.497455i | \(0.834268\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.3511i | 1.87744i | 0.344682 | + | 0.938719i | \(0.387987\pi\) | ||||
−0.344682 | + | 0.938719i | \(0.612013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0741 | 1.63568 | 0.817841 | − | 0.575444i | \(-0.195171\pi\) | ||||
0.817841 | + | 0.575444i | \(0.195171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.37380 | + | 22.1955i | −0.305480 | + | 1.55020i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0925 | −0.698110 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.52311 | 0.104856 | 0.0524278 | − | 0.998625i | \(-0.483304\pi\) | ||||
0.0524278 | + | 0.998625i | \(0.483304\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.1170 | + | 2.38776i | 0.826375 | + | 0.162844i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.52311 | 0.371525 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3169i | 0.891769i | 0.895091 | + | 0.445884i | \(0.147111\pi\) | ||||
−0.895091 | + | 0.445884i | \(0.852889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.80009i | − | 0.451338i | −0.974204 | − | 0.225669i | \(-0.927543\pi\) | ||
0.974204 | − | 0.225669i | \(-0.0724568\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.52311 | −0.100650 | −0.0503251 | − | 0.998733i | \(-0.516026\pi\) | ||||
−0.0503251 | + | 0.998733i | \(0.516026\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7110i | 0.701698i | 0.936432 | + | 0.350849i | \(0.114107\pi\) | ||||
−0.936432 | + | 0.350849i | \(0.885893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.9956 | − | 3.74324i | −1.23914 | − | 0.244182i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.65847 | 0.301332 | 0.150666 | − | 0.988585i | \(-0.451858\pi\) | ||||
0.150666 | + | 0.988585i | \(0.451858\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.22449 | 0.336539 | 0.168269 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168269 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.02624 | + | 15.3571i | −0.193340 | + | 0.981132i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52311i | 0.224170i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.85838 | −0.369778 | −0.184889 | − | 0.982759i | \(-0.559193\pi\) | ||||
−0.184889 | + | 0.982759i | \(0.559193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.5510i | − | 1.35490i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.29862i | − | 0.143384i | −0.997427 | − | 0.0716921i | \(-0.977160\pi\) | ||
0.997427 | − | 0.0716921i | \(-0.0228399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.5789i | 1.94724i | 0.228175 | + | 0.973620i | \(0.426724\pi\) | ||||
−0.228175 | + | 0.973620i | \(0.573276\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.8646 | − | 2.92919i | −0.913128 | − | 0.179939i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.3632 | −1.85128 | −0.925638 | − | 0.378411i | \(-0.876471\pi\) | ||||
−0.925638 | + | 0.378411i | \(0.876471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.5972 | 1.73716 | 0.868580 | − | 0.495550i | \(-0.165033\pi\) | ||||
0.868580 | + | 0.495550i | \(0.165033\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.2524 | − | 5.43398i | −0.799150 | − | 0.327682i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.79383i | − | 0.107781i | −0.998547 | − | 0.0538905i | \(-0.982838\pi\) | ||
0.998547 | − | 0.0538905i | \(-0.0171622\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.2095 | −1.92146 | −0.960729 | − | 0.277489i | \(-0.910498\pi\) | ||||
−0.960729 | + | 0.277489i | \(0.910498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0925i | 1.07548i | 0.843109 | + | 0.537742i | \(0.180723\pi\) | ||||
−0.843109 | + | 0.537742i | \(0.819277\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5048 | −0.794400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6218i | 0.737375i | 0.929553 | + | 0.368688i | \(0.120193\pi\) | ||||
−0.929553 | + | 0.368688i | \(0.879807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.256765 | + | 1.30299i | −0.0149494 | + | 0.0758632i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.52311 | −0.435073 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.27072 | − | 11.5231i | 0.130021 | − | 0.659812i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.0000i | − | 1.14146i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) | ||
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.8217 | 1.80445 | 0.902223 | − | 0.431271i | \(-0.141935\pi\) | ||||
0.902223 | + | 0.431271i | \(0.141935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.7938i | 0.666627i | 0.942816 | + | 0.333313i | \(0.108167\pi\) | ||||
−0.942816 | + | 0.333313i | \(0.891833\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.4340i | 0.642197i | 0.947046 | + | 0.321098i | \(0.104052\pi\) | ||||
−0.947046 | + | 0.321098i | \(0.895948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.4094 | 1.08672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 19.4586i | − | 1.08270i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.89692 | + | 4.62620i | −0.105222 | + | 0.256615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.20617 | 0.121262 | 0.0606310 | − | 0.998160i | \(-0.480689\pi\) | ||||
0.0606310 | + | 0.998160i | \(0.480689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.0462 | − | 4.54144i | −1.25915 | − | 0.248125i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8034i | 0.915340i | 0.889122 | + | 0.457670i | \(0.151316\pi\) | ||||
−0.889122 | + | 0.457670i | \(0.848684\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.4123 | 0.888778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.96336i | 0.534861i | 0.963577 | + | 0.267430i | \(0.0861746\pi\) | ||||
−0.963577 | + | 0.267430i | \(0.913825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3449 | 1.14256 | 0.571282 | − | 0.820754i | \(-0.306446\pi\) | ||||
0.571282 | + | 0.820754i | \(0.306446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 33.3973i | − | 1.77756i | −0.458333 | − | 0.888781i | \(-0.651553\pi\) | ||
0.458333 | − | 0.888781i | \(-0.348447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.03228 | + | 5.23844i | −0.0547875 | + | 0.278028i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9754 | 1.15982 | 0.579909 | − | 0.814681i | \(-0.303088\pi\) | ||||
0.579909 | + | 0.814681i | \(0.303088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58767 | −0.346719 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.9754 | − | 2.35985i | −0.626822 | − | 0.123520i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 29.2803i | − | 1.52842i | −0.644968 | − | 0.764210i | \(-0.723129\pi\) | ||
0.644968 | − | 0.764210i | \(-0.276871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.41233i | 0.124906i | 0.998048 | + | 0.0624530i | \(0.0198923\pi\) | ||||
−0.998048 | + | 0.0624530i | \(0.980108\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.77551i | − | 0.348957i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.5231 | −1.00284 | −0.501418 | − | 0.865205i | \(-0.667188\pi\) | ||||
−0.501418 | + | 0.865205i | \(0.667188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.7047i | 1.21125i | 0.795749 | + | 0.605627i | \(0.207078\pi\) | ||||
−0.795749 | + | 0.605627i | \(0.792922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0000 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5510 | 2.10133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.07081 | − | 5.43398i | 0.0538782 | − | 0.273413i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.8680i | − | 1.44884i | −0.689358 | − | 0.724421i | \(-0.742107\pi\) | ||
0.689358 | − | 0.724421i | \(-0.257893\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.0804 | −1.00277 | −0.501383 | − | 0.865225i | \(-0.667175\pi\) | ||||
−0.501383 | + | 0.865225i | \(0.667175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.72928i | − | 0.285396i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6831i | 0.529539i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6926 | 0.677057 | 0.338529 | − | 0.940956i | \(-0.390071\pi\) | ||||
0.338529 | + | 0.940956i | \(0.390071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.8078 | + | 3.50916i | 0.874150 | + | 0.172258i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3632 | −0.799393 | −0.399697 | − | 0.916647i | \(-0.630885\pi\) | ||||
−0.399697 | + | 0.916647i | \(0.630885\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9817 | 1.21753 | 0.608766 | − | 0.793350i | \(-0.291665\pi\) | ||||
0.608766 | + | 0.793350i | \(0.291665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.4769 | − | 25.5510i | 0.508204 | − | 1.23941i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.9388 | 1.34576 | 0.672882 | − | 0.739750i | \(-0.265056\pi\) | ||||
0.672882 | + | 0.739750i | \(0.265056\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.7110i | − | 1.28365i | −0.766852 | − | 0.641823i | \(-0.778178\pi\) | ||
0.766852 | − | 0.641823i | \(-0.221822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.5048i | 1.26790i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.00958 | 0.239094 | 0.119547 | − | 0.992829i | \(-0.461856\pi\) | ||||
0.119547 | + | 0.992829i | \(0.461856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6926i | 0.935625i | 0.883828 | + | 0.467813i | \(0.154958\pi\) | ||||
−0.883828 | + | 0.467813i | \(0.845042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.10308 | − | 30.9711i | 0.289314 | − | 1.46817i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.7143 | 1.82704 | 0.913520 | − | 0.406794i | \(-0.133353\pi\) | ||||
0.913520 | + | 0.406794i | \(0.133353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9817 | 1.36469 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.9538i | − | 0.512396i | −0.966624 | − | 0.256198i | \(-0.917530\pi\) | ||
0.966624 | − | 0.256198i | \(-0.0824699\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.864641 | 0.0402703 | 0.0201352 | − | 0.999797i | \(-0.493590\pi\) | ||||
0.0201352 | + | 0.999797i | \(0.493590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.7755i | 0.961376i | 0.876892 | + | 0.480688i | \(0.159613\pi\) | ||||
−0.876892 | + | 0.480688i | \(0.840387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 15.8217i | − | 0.727484i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.2986 | + | 6.68305i | 0.747832 | + | 0.306640i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6585 | 0.943910 | 0.471955 | − | 0.881623i | \(-0.343549\pi\) | ||||
0.471955 | + | 0.881623i | \(0.343549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.72928 | 0.170041 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.1633 | + | 2.59392i | 0.597713 | + | 0.117784i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3632i | 0.741486i | 0.928735 | + | 0.370743i | \(0.120897\pi\) | ||||
−0.928735 | + | 0.370743i | \(0.879103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.7389 | −1.20671 | −0.603354 | − | 0.797473i | \(-0.706169\pi\) | ||||
−0.603354 | + | 0.797473i | \(0.706169\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.4219i | 1.68540i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.24281 | −0.189934 | −0.0949672 | − | 0.995480i | \(-0.530275\pi\) | ||||
−0.0949672 | + | 0.995480i | \(0.530275\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.889220i | 0.0396484i | 0.999803 | + | 0.0198242i | \(0.00631065\pi\) | ||||
−0.999803 | + | 0.0198242i | \(0.993689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.07081 | + | 25.7326i | −0.225648 | + | 1.14509i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.3694 | −0.503941 | −0.251971 | − | 0.967735i | \(-0.581079\pi\) | ||||
−0.251971 | + | 0.967735i | \(0.581079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.4157 | − | 6.38776i | −1.42840 | − | 0.281478i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.8034i | 1.09085i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.18785 | −0.139662 | −0.0698310 | − | 0.997559i | \(-0.522246\pi\) | ||||
−0.0698310 | + | 0.997559i | \(0.522246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 37.1666i | − | 1.62518i | −0.582835 | − | 0.812591i | \(-0.698056\pi\) | ||
0.582835 | − | 0.812591i | \(-0.301944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.6435i | 1.37841i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −33.5972 | −1.46075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.1170i | − | 0.438218i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.79383 | − | 0.747604i | −0.164022 | − | 0.0323217i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.0525 | 0.863722 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.02791 | −0.345147 | −0.172573 | − | 0.984997i | \(-0.555208\pi\) | ||||
−0.172573 | + | 0.984997i | \(0.555208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.19991 | − | 26.3878i | 0.222740 | − | 1.13033i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 31.2032i | − | 1.33415i | −0.744989 | − | 0.667077i | \(-0.767545\pi\) | ||
0.744989 | − | 0.667077i | \(-0.232455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.8709 | −1.01693 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 29.2191i | − | 1.23805i | −0.785370 | − | 0.619026i | \(-0.787528\pi\) | ||
0.785370 | − | 0.619026i | \(-0.212472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.52311 | −0.233603 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 30.5048i | − | 1.28562i | −0.766024 | − | 0.642812i | \(-0.777768\pi\) | ||
0.766024 | − | 0.642812i | \(-0.222232\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.9109 | − | 3.13536i | −0.669375 | − | 0.131906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.1416 | −0.509003 | −0.254502 | − | 0.967072i | \(-0.581911\pi\) | ||||
−0.254502 | + | 0.967072i | \(0.581911\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.85258 | −0.370469 | −0.185234 | − | 0.982694i | \(-0.559304\pi\) | ||||
−0.185234 | + | 0.982694i | \(0.559304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.2707 | + | 34.8034i | −0.595130 | + | 1.45140i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.2341i | 1.25866i | 0.777138 | + | 0.629330i | \(0.216671\pi\) | ||||
−0.777138 | + | 0.629330i | \(0.783329\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.4094i | 0.803855i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 23.0342i | − | 0.950722i | −0.879791 | − | 0.475361i | \(-0.842318\pi\) | ||
0.879791 | − | 0.475361i | \(-0.157682\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1849 | −0.831705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 27.9754i | − | 1.14881i | −0.818570 | − | 0.574406i | \(-0.805233\pi\) | ||
0.818570 | − | 0.574406i | \(-0.194767\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.7389 | 0.929085 | 0.464542 | − | 0.885551i | \(-0.346219\pi\) | ||||
0.464542 | + | 0.885551i | \(0.346219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2158 | −0.457500 | −0.228750 | − | 0.973485i | \(-0.573464\pi\) | ||||
−0.228750 | + | 0.973485i | \(0.573464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.20783 | − | 6.12933i | 0.0491053 | − | 0.249193i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 23.7293i | − | 0.963142i | −0.876407 | − | 0.481571i | \(-0.840066\pi\) | ||
0.876407 | − | 0.481571i | \(-0.159934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.65847 | 0.350284 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 18.2341i | − | 0.736467i | −0.929733 | − | 0.368234i | \(-0.879963\pi\) | ||
0.929733 | − | 0.368234i | \(-0.120037\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0245796i | 0.000989536i | 1.00000 | 0.000494768i | \(0.000157490\pi\) | |||||
−1.00000 | 0.000494768i | \(0.999843\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.2158 | −1.25467 | −0.627334 | − | 0.778751i | \(-0.715854\pi\) | ||||
−0.627334 | + | 0.778751i | \(0.715854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | + | 17.5510i | 0.712137 | + | 0.702041i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.5972 | −0.821266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.4460 | 0.535279 | 0.267639 | − | 0.963519i | \(-0.413756\pi\) | ||||
0.267639 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.8496 | + | 7.45856i | 1.50202 | + | 0.295984i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.00000i | − | 0.277350i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.54144 | −0.100381 | −0.0501904 | − | 0.998740i | \(-0.515983\pi\) | ||||
−0.0501904 | + | 0.998740i | \(0.515983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9634i | 0.550661i | 0.961350 | + | 0.275330i | \(0.0887873\pi\) | ||||
−0.961350 | + | 0.275330i | \(0.911213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.8034i | − | 1.21101i | −0.795843 | − | 0.605504i | \(-0.792972\pi\) | ||
0.795843 | − | 0.605504i | \(-0.207028\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.70138 | 0.0667848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.00000i | − | 0.0782660i | −0.999234 | − | 0.0391330i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391330i | \(-0.0124596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.79383 | + | 19.2524i | −0.148237 | + | 0.752253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.05581 | −0.157992 | −0.0789960 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789960 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.9325 | −1.28093 | −0.640463 | − | 0.767989i | \(-0.721258\pi\) | ||||
−0.640463 | + | 0.767989i | \(0.721258\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 50.9729i | − | 1.97368i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0462 | −0.580853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.42192i | 0.363188i | 0.983374 | + | 0.181594i | \(0.0581257\pi\) | ||||
−0.983374 | + | 0.181594i | \(0.941874\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.2341i | 1.62319i | 0.584222 | + | 0.811594i | \(0.301400\pi\) | ||||
−0.584222 | + | 0.811594i | \(0.698600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7509i | 0.717484i | 0.933437 | + | 0.358742i | \(0.116794\pi\) | ||||
−0.933437 | + | 0.358742i | \(0.883206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.6358 | − | 8.40171i | −1.62903 | − | 0.321013i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.77551 | 0.258126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.2524 | 1.72148 | 0.860741 | − | 0.509043i | \(-0.170001\pi\) | ||||
0.860741 | + | 0.509043i | \(0.170001\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.28030 | − | 16.6464i | 0.124429 | − | 0.631434i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.8776i | 2.11651i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.4586 | 1.41479 | 0.707395 | − | 0.706818i | \(-0.249870\pi\) | ||||
0.707395 | + | 0.706818i | \(0.249870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.1387i | − | 0.495535i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.8988 | −0.446869 | −0.223435 | − | 0.974719i | \(-0.571727\pi\) | ||||
−0.223435 | + | 0.974719i | \(0.571727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 43.1020i | − | 1.61418i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.28467 | + | 1.23844i | 0.235033 | + | 0.0463151i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.7851 | 0.961622 | 0.480811 | − | 0.876824i | \(-0.340342\pi\) | ||||
0.480811 | + | 0.876824i | \(0.340342\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.3449 | − | 12.8526i | −1.16412 | − | 0.477333i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 34.8034i | − | 1.29079i | −0.763850 | − | 0.645394i | \(-0.776693\pi\) | ||
0.763850 | − | 0.645394i | \(-0.223307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.5048 | 1.12826 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5510i | 0.722133i | 0.932540 | + | 0.361067i | \(0.117587\pi\) | ||||
−0.932540 | + | 0.361067i | \(0.882413\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.0925i | 1.10847i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2986 | −0.452412 | −0.226206 | − | 0.974079i | \(-0.572632\pi\) | ||||
−0.226206 | + | 0.974079i | \(0.572632\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.9975i | − | 1.50405i | −0.659133 | − | 0.752027i | \(-0.729076\pi\) | ||
0.659133 | − | 0.752027i | \(-0.270924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.607876 | − | 3.08476i | 0.0222709 | − | 0.113017i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.5510 | 1.22429 | 0.612147 | − | 0.790744i | \(-0.290306\pi\) | ||||
0.612147 | + | 0.790744i | \(0.290306\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.569343 | − | 2.88922i | 0.0207205 | − | 0.105149i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.1020i | − | 0.912349i | −0.889890 | − | 0.456175i | \(-0.849219\pi\) | ||
0.889890 | − | 0.456175i | \(-0.150781\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.9021 | 1.44645 | 0.723226 | − | 0.690612i | \(-0.242659\pi\) | ||||
0.723226 | + | 0.690612i | \(0.242659\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.593923i | − | 0.0214453i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5510 | 0.560784 | 0.280392 | − | 0.959886i | \(-0.409536\pi\) | ||||
0.280392 | + | 0.959886i | \(0.409536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 27.7972i | − | 0.999794i | −0.866085 | − | 0.499897i | \(-0.833371\pi\) | ||
0.866085 | − | 0.499897i | \(-0.166629\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.5048 | − | 10.8680i | −0.952080 | − | 0.390389i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.6435 | −1.27706 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.84006 | 0.244757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 45.4373 | + | 8.95377i | 1.62173 | + | 0.319574i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.6339i | 1.09198i | 0.837792 | + | 0.545990i | \(0.183846\pi\) | ||||
−0.837792 | + | 0.545990i | \(0.816154\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.25240i | 0.186518i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 18.6464i | − | 0.660490i | −0.943895 | − | 0.330245i | \(-0.892869\pi\) | ||
0.943895 | − | 0.330245i | \(-0.107131\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.8217 | −1.69181 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 |