Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1249,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, 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("1560.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.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: | \(12.4566627153\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.2 | ||
Root | \(0.432320 + 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1249 |
Dual form | 1560.2.l.c.1249.5 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 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 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.86464 | −0.863722 | −0.431861 | − | 0.901940i | \(-0.642143\pi\) | ||||
−0.431861 | + | 0.901940i | \(0.642143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.19388 | − | 0.432320i | −0.566457 | − | 0.111625i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.52311i | − | 1.33955i | −0.742563 | − | 0.669776i | \(-0.766390\pi\) | ||
0.742563 | − | 0.669776i | \(-0.233610\pi\) | |||||||
\(18\) | 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 | \(0.286998\pi\) | ||||
−0.620333 | + | 0.784339i | \(0.713002\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62620 | − | 1.89692i | −0.925240 | − | 0.379383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.77551 | −1.25818 | −0.629090 | − | 0.777332i | \(-0.716572\pi\) | ||||
−0.629090 | + | 0.777332i | \(0.716572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.72928 | 1.02901 | 0.514505 | − | 0.857488i | \(-0.327976\pi\) | ||||
0.514505 | + | 0.857488i | \(0.327976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.86464i | 0.498670i | ||||||||
\(34\) | 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 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.1170 | −1.58002 | −0.790008 | − | 0.613097i | \(-0.789924\pi\) | ||||
−0.790008 | + | 0.613097i | \(0.789924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.52311i | − | 0.842267i | −0.906999 | − | 0.421134i | \(-0.861632\pi\) | ||
0.906999 | − | 0.421134i | \(-0.138368\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.432320 | + | 2.19388i | −0.0644465 | + | 0.327044i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.65847i | − | 1.26297i | −0.775389 | − | 0.631484i | \(-0.782446\pi\) | ||
0.775389 | − | 0.631484i | \(-0.217554\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.52311 | −0.773391 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.77551i | − | 0.930688i | −0.885130 | − | 0.465344i | \(-0.845931\pi\) | ||
0.885130 | − | 0.465344i | \(-0.154069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.23844 | + | 6.28467i | −0.166992 | + | 0.847425i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.52311i | 0.466648i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.593923 | −0.0773221 | −0.0386611 | − | 0.999252i | \(-0.512309\pi\) | ||||
−0.0386611 | + | 0.999252i | \(0.512309\pi\) | |||||||
\(60\) | 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 | ||||||||
\(69\) | 7.52311 | 0.905677 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.38776 | −0.283374 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.45856i | 0.638877i | 0.947607 | + | 0.319438i | \(0.103494\pi\) | ||||
−0.947607 | + | 0.319438i | \(0.896506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.89692 | + | 4.62620i | −0.219037 | + | 0.534187i | ||||
\(76\) | 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 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.11704i | 0.890961i | 0.895292 | + | 0.445480i | \(0.146967\pi\) | ||||
−0.895292 | + | 0.445480i | \(0.853033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1170 | − | 2.38776i | −1.31428 | − | 0.258988i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.77551i | 0.726411i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.1170 | 1.49640 | 0.748201 | − | 0.663472i | \(-0.230918\pi\) | ||||
0.748201 | + | 0.663472i | \(0.230918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5.72928i | − | 0.594099i | ||||||
\(94\) | 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 | ||||||||
\(99\) | 2.86464 | 0.287907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.7293 | −1.16711 | −0.583554 | − | 0.812075i | \(-0.698338\pi\) | ||||
−0.583554 | + | 0.812075i | \(0.698338\pi\) | |||||||
\(102\) | 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 | \(-0.973362\pi\) | ||
0.996500 | − | 0.0835880i | \(-0.0266380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0279 | −1.15206 | −0.576032 | − | 0.817427i | \(-0.695400\pi\) | ||||
−0.576032 | + | 0.817427i | \(0.695400\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.72928 | 0.353968 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.25240i | − | 0.682248i | −0.940018 | − | 0.341124i | \(-0.889192\pi\) | ||
0.940018 | − | 0.341124i | \(-0.110808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.5048 | + | 3.25240i | 1.53908 | + | 0.303288i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.79383 | −0.253985 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.1170i | 0.912223i | ||||||||
\(124\) | 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 | ||||||||
\(129\) | −5.52311 | −0.486283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.77551 | −0.766720 | −0.383360 | − | 0.923599i | \(-0.625233\pi\) | ||||
−0.383360 | + | 0.923599i | \(0.625233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.19388 | + | 0.432320i | 0.188819 | + | 0.0372082i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 19.4340i | − | 1.66036i | −0.557497 | − | 0.830179i | \(-0.688238\pi\) | ||
0.557497 | − | 0.830179i | \(-0.311762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.58767 | −0.643577 | −0.321789 | − | 0.946812i | \(-0.604284\pi\) | ||||
−0.321789 | + | 0.946812i | \(0.604284\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.65847 | −0.729175 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.86464i | 0.239553i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.92919 | + | 14.8646i | −0.243256 | + | 1.23444i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 7.00000i | − | 0.577350i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.40608 | 0.115190 | 0.0575952 | − | 0.998340i | \(-0.481657\pi\) | ||||
0.0575952 | + | 0.998340i | \(0.481657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.31695 | −0.107172 | −0.0535858 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535858 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.52311i | 0.446517i | ||||||||
\(154\) | 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 | ||||||||
\(159\) | −6.77551 | −0.537333 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 6.28467 | + | 1.23844i | 0.489261 | + | 0.0964126i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.34153i | − | 0.568104i | −0.958809 | − | 0.284052i | \(-0.908321\pi\) | ||
0.958809 | − | 0.284052i | \(-0.0916789\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.52311 | 0.269419 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 16.0925i | − | 1.22349i | −0.791056 | − | 0.611743i | \(-0.790468\pi\) | ||
0.791056 | − | 0.611743i | \(-0.209532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.593923i | 0.0446420i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0462 | −1.12461 | −0.562304 | − | 0.826931i | \(-0.690085\pi\) | ||||
−0.562304 | + | 0.826931i | \(0.690085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.58767 | 0.415328 | 0.207664 | − | 0.978200i | \(-0.433414\pi\) | ||||
0.207664 | + | 0.978200i | \(0.433414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.25240i | 0.388268i | ||||||||
\(184\) | 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 | \(-0.281011\pi\) | ||||
0.634974 | + | 0.772534i | \(0.281011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8217i | 0.994911i | 0.867490 | + | 0.497455i | \(0.165732\pi\) | ||||
−0.867490 | + | 0.497455i | \(0.834268\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.432320 | + | 2.19388i | −0.0309591 | + | 0.157107i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26.3511i | − | 1.87744i | −0.344682 | − | 0.938719i | \(-0.612013\pi\) | ||
0.344682 | − | 0.938719i | \(-0.387987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0741 | 1.63568 | 0.817841 | − | 0.575444i | \(-0.195171\pi\) | ||||
0.817841 | + | 0.575444i | \(0.195171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5048 | 0.740951 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.37380 | + | 22.1955i | −0.305480 | + | 1.55020i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.52311i | − | 0.522893i | ||||||
\(208\) | 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 | ||||||||
\(213\) | 2.38776i | 0.163606i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.1170 | − | 2.38776i | −0.826375 | − | 0.162844i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.45856 | 0.368856 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 4.62620 | + | 1.89692i | 0.308413 | + | 0.126461i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.80009i | 0.451338i | 0.974204 | + | 0.225669i | \(0.0724568\pi\) | ||||
−0.974204 | + | 0.225669i | \(0.927543\pi\) | |||||||
\(228\) | 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 | \(-0.885893\pi\) | ||
0.936432 | − | 0.350849i | \(-0.114107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.9956 | − | 3.74324i | −1.23914 | − | 0.244182i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.47689i | 0.160891i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.65847 | −0.301332 | −0.150666 | − | 0.988585i | \(-0.548142\pi\) | ||||
−0.150666 | + | 0.988585i | \(0.548142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.22449 | 0.336539 | 0.168269 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168269 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.02624 | − | 15.3571i | 0.193340 | − | 0.981132i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52311i | 0.224170i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.11704 | 0.514396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.85838 | 0.369778 | 0.184889 | − | 0.982759i | \(-0.440807\pi\) | ||||
0.184889 | + | 0.982759i | \(0.440807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.5510i | − | 1.35490i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.38776 | + | 12.1170i | −0.149527 | + | 0.758798i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.29862i | 0.143384i | 0.997427 | + | 0.0716921i | \(0.0228399\pi\) | ||||
−0.997427 | + | 0.0716921i | \(0.977160\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.77551 | 0.419394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 31.5789i | − | 1.94724i | −0.228175 | − | 0.973620i | \(-0.573276\pi\) | ||
0.228175 | − | 0.973620i | \(-0.426724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.8646 | − | 2.92919i | −0.913128 | − | 0.179939i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.1170i | − | 0.863949i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.3632 | 1.85128 | 0.925638 | − | 0.378411i | \(-0.123529\pi\) | ||||
0.925638 | + | 0.378411i | \(0.123529\pi\) | |||||||
\(270\) | 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 | ||||||||
\(279\) | −5.72928 | −0.343003 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.2095 | 1.92146 | 0.960729 | − | 0.277489i | \(-0.0895024\pi\) | ||||
0.960729 | + | 0.277489i | \(0.0895024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0925i | 1.07548i | 0.843109 | + | 0.537742i | \(0.180723\pi\) | ||||
−0.843109 | + | 0.537742i | \(0.819277\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.72928 | + | 1.52311i | 0.457843 | + | 0.0902215i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5048 | −0.794400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 12.6218i | − | 0.737375i | −0.929553 | − | 0.368688i | \(-0.879807\pi\) | ||
0.929553 | − | 0.368688i | \(-0.120193\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.256765 | + | 1.30299i | −0.0149494 | + | 0.0758632i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.86464i | − | 0.166223i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.52311 | 0.435073 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.7293i | 0.673830i | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 14.7755 | 0.840549 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.8217 | −1.80445 | −0.902223 | − | 0.431271i | \(-0.858065\pi\) | ||||
−0.902223 | + | 0.431271i | \(0.858065\pi\) | |||||||
\(312\) | 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 | \(-0.895948\pi\) | ||
0.947046 | − | 0.321098i | \(-0.104052\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.4094 | 1.08672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.72928 | −0.0965191 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4586i | 1.08270i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.89692 | + | 4.62620i | −0.105222 | + | 0.256615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0279i | 0.665145i | ||||||||
\(328\) | 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 | ||||||||
\(333\) | − | 3.72928i | − | 0.204363i | ||||||
\(334\) | 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 | ||||||||
\(339\) | −7.25240 | −0.393896 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4123 | −0.888778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.25240 | − | 16.5048i | 0.175103 | − | 0.888588i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 9.96336i | − | 0.534861i | −0.963577 | − | 0.267430i | \(-0.913825\pi\) | ||
0.963577 | − | 0.267430i | \(-0.0861746\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3449 | 1.14256 | 0.571282 | − | 0.820754i | \(-0.306446\pi\) | ||||
0.571282 | + | 0.820754i | \(0.306446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.3973i | 1.77756i | 0.458333 | + | 0.888781i | \(0.348447\pi\) | ||||
−0.458333 | + | 0.888781i | \(0.651553\pi\) | |||||||
\(354\) | 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 | \(-0.696912\pi\) | ||||
−0.579909 | + | 0.814681i | \(0.696912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58767 | −0.346719 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.79383i | 0.146638i | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 10.1170 | 0.526672 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 9.32924 | + | 6.16160i | 0.481760 | + | 0.318184i | ||||
\(376\) | 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 | ||||||||
\(381\) | −17.2524 | −0.883867 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 23.7047i | − | 1.21125i | −0.795749 | − | 0.605627i | \(-0.792922\pi\) | ||
0.795749 | − | 0.605627i | \(-0.207078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.52311i | 0.280756i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0000 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5510 | 2.10133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.77551i | 0.442666i | ||||||||
\(394\) | 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 | \(-0.332825\pi\) | ||||
0.501383 | + | 0.865225i | \(0.332825\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.72928i | − | 0.285396i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.432320 | − | 2.19388i | 0.0214822 | − | 0.109015i | ||||
\(406\) | 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 | ||||||||
\(411\) | −19.4340 | −0.958608 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.8078 | + | 3.50916i | 0.874150 | + | 0.172258i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.58767i | 0.371570i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.3632 | 0.799393 | 0.399697 | − | 0.916647i | \(-0.369115\pi\) | ||||
0.399697 | + | 0.916647i | \(0.369115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9817 | 1.21753 | 0.608766 | − | 0.793350i | \(-0.291665\pi\) | ||||
0.608766 | + | 0.793350i | \(0.291665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.65847i | 0.420989i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.4769 | + | 25.5510i | −0.508204 | + | 1.23941i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.86464 | 0.138306 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.9388 | −1.34576 | −0.672882 | − | 0.739750i | \(-0.734944\pi\) | ||||
−0.672882 | + | 0.739750i | \(0.734944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.7110i | − | 1.28365i | −0.766852 | − | 0.641823i | \(-0.778178\pi\) | ||
0.766852 | − | 0.641823i | \(-0.221822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.8646 | + | 2.92919i | 0.712705 | + | 0.140444i | ||||
\(436\) | 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 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 19.6926i | − | 0.935625i | −0.883828 | − | 0.467813i | \(-0.845042\pi\) | ||
0.883828 | − | 0.467813i | \(-0.154958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.10308 | − | 30.9711i | 0.289314 | − | 1.46817i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.40608i | − | 0.0665052i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.7143 | −1.82704 | −0.913520 | − | 0.406794i | \(-0.866647\pi\) | ||||
−0.913520 | + | 0.406794i | \(0.866647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9817 | 1.36469 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.31695i | 0.0618756i | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 5.52311 | 0.257797 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.864641 | −0.0402703 | −0.0201352 | − | 0.999797i | \(-0.506410\pi\) | ||||
−0.0201352 | + | 0.999797i | \(0.506410\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.5693 | − | 2.47689i | −0.582889 | − | 0.114863i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 20.7755i | − | 0.961376i | −0.876892 | − | 0.480688i | \(-0.840387\pi\) | ||
0.876892 | − | 0.480688i | \(-0.159613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.7110 | −0.954311 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.8217i | 0.727484i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.2986 | + | 6.68305i | 0.747832 | + | 0.306640i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.77551i | 0.310229i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.6585 | −0.943910 | −0.471955 | − | 0.881623i | \(-0.656451\pi\) | ||||
−0.471955 | + | 0.881623i | \(0.656451\pi\) | |||||||
\(480\) | 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 | ||||||||
\(489\) | 2.27072 | 0.102685 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.7389 | 1.20671 | 0.603354 | − | 0.797473i | \(-0.293831\pi\) | ||||
0.603354 | + | 0.797473i | \(0.293831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.4219i | 1.68540i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.23844 | − | 6.28467i | 0.0556639 | − | 0.282475i | ||||
\(496\) | 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 | ||||||||
\(501\) | −7.34153 | −0.327995 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 0.889220i | − | 0.0396484i | −0.999803 | − | 0.0198242i | \(-0.993689\pi\) | ||
0.999803 | − | 0.0198242i | \(-0.00631065\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.07081 | + | 25.7326i | −0.225648 | + | 1.14509i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.3694 | 0.503941 | 0.251971 | − | 0.967735i | \(-0.418921\pi\) | ||||
0.251971 | + | 0.967735i | \(0.418921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.52311i | − | 0.155549i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.4157 | + | 6.38776i | 1.42840 | + | 0.281478i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.8034i | 1.09085i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0925 | −0.706380 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.18785 | 0.139662 | 0.0698310 | − | 0.997559i | \(-0.477754\pi\) | ||||
0.0698310 | + | 0.997559i | \(0.477754\pi\) | |||||||
\(522\) | 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 | ||||||||
\(531\) | 0.593923 | 0.0257740 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.1170i | 0.438218i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.79383 | − | 0.747604i | −0.164022 | − | 0.0323217i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.0462i | 0.649293i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − | 5.58767i | − | 0.239790i | ||||||
\(544\) | 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 | ||||||||
\(549\) | 5.25240 | 0.224167 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.8709 | 1.01693 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.61224 | − | 8.18159i | 0.0684360 | − | 0.347289i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.2191i | 1.23805i | 0.785370 | + | 0.619026i | \(0.212472\pi\) | ||||
−0.785370 | + | 0.619026i | \(0.787528\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.52311 | −0.233603 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8217 | 0.667994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.5048i | 1.28562i | 0.766024 | + | 0.642812i | \(0.222232\pi\) | ||||
−0.766024 | + | 0.642812i | \(0.777768\pi\) | |||||||
\(564\) | 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 | \(-0.418089\pi\) | ||||
0.254502 | + | 0.967072i | \(0.418089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.85258 | −0.370469 | −0.185234 | − | 0.982694i | \(-0.559304\pi\) | ||||
−0.185234 | + | 0.982694i | \(0.559304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 17.5510i | − | 0.733204i | ||||||
\(574\) | 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 | ||||||||
\(579\) | 13.8217 | 0.574412 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.4094i | 0.803855i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.19388 | + | 0.432320i | 0.0907057 | + | 0.0178743i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.0342i | 0.950722i | 0.879791 | + | 0.475361i | \(0.157682\pi\) | ||||
−0.879791 | + | 0.475361i | \(0.842318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1849 | −0.831705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.3511 | −1.08394 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.9754i | 1.14881i | 0.818570 | + | 0.574406i | \(0.194767\pi\) | ||||
−0.818570 | + | 0.574406i | \(0.805233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 23.0741i | − | 0.944361i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.7389 | −0.929085 | −0.464542 | − | 0.885551i | \(-0.653781\pi\) | ||||
−0.464542 | + | 0.885551i | \(0.653781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2158 | −0.457500 | −0.228750 | − | 0.973485i | \(-0.573464\pi\) | ||||
−0.228750 | + | 0.973485i | \(0.573464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 10.5048i | − | 0.427788i | ||||||
\(604\) | 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 | ||||||||
\(615\) | 22.1955 | + | 4.37380i | 0.895011 | + | 0.176369i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 0.0245796i | − | 0.000989536i | −1.00000 | 0.000494768i | \(-0.999843\pi\) | |||
1.00000 | 0.000494768i | \(-0.000157490\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.2158 | −1.25467 | −0.627334 | − | 0.778751i | \(-0.715854\pi\) | ||||
−0.627334 | + | 0.778751i | \(0.715854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.52311 | −0.301892 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | + | 17.5510i | 0.712137 | + | 0.702041i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 10.0925i | − | 0.403054i | ||||||
\(628\) | 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 | ||||||||
\(633\) | − | 1.52311i | − | 0.0605384i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.8496 | − | 7.45856i | −1.50202 | − | 0.295984i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.00000i | − | 0.277350i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.38776 | 0.0944581 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.54144 | 0.100381 | 0.0501904 | − | 0.998740i | \(-0.484017\pi\) | ||||
0.0501904 | + | 0.998740i | \(0.484017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9634i | 0.550661i | 0.961350 | + | 0.275330i | \(0.0887873\pi\) | ||||
−0.961350 | + | 0.275330i | \(0.911213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.38776 | + | 12.1170i | −0.0940178 | + | 0.477108i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.8034i | 1.21101i | 0.795843 | + | 0.605504i | \(0.207028\pi\) | ||||
−0.795843 | + | 0.605504i | \(0.792972\pi\) | |||||||
\(648\) | 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 | \(0.0124596\pi\) | ||||
−0.999234 | + | 0.0391330i | \(0.987540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.79383 | + | 19.2524i | −0.148237 | + | 0.752253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.45856i | − | 0.212959i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.05581 | 0.157992 | 0.0789960 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789960 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.9325 | −1.28093 | −0.640463 | − | 0.767989i | \(-0.721258\pi\) | ||||
−0.640463 | + | 0.767989i | \(0.721258\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.52311i | 0.214500i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 50.9729i | − | 1.97368i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.3169 | 0.514863 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 1.89692 | − | 4.62620i | 0.0730123 | − | 0.178062i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 42.2341i | − | 1.62319i | −0.584222 | − | 0.811594i | \(-0.698600\pi\) | ||
0.584222 | − | 0.811594i | \(-0.301400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.80009 | 0.260580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18.7509i | − | 0.717484i | −0.933437 | − | 0.358742i | \(-0.883206\pi\) | ||
0.933437 | − | 0.358742i | \(-0.116794\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.6358 | − | 8.40171i | −1.62903 | − | 0.321013i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.52311i | 0.0581104i | ||||||||
\(688\) | 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 | ||||||||
\(699\) | −10.7110 | −0.405126 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.4586 | −1.41479 | −0.707395 | − | 0.706818i | \(-0.750130\pi\) | ||||
−0.707395 | + | 0.706818i | \(0.750130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.1387i | − | 0.495535i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.74324 | + | 18.9956i | −0.140978 | + | 0.715417i | ||||
\(706\) | 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 | ||||||||
\(711\) | 2.47689 | 0.0928905 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.1020i | 1.61418i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.28467 | + | 1.23844i | 0.235033 | + | 0.0463151i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.65847i | 0.173974i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.7851 | −0.961622 | −0.480811 | − | 0.876824i | \(-0.659658\pi\) | ||||
−0.480811 | + | 0.876824i | \(0.659658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.22449i | − | 0.194301i | ||||||
\(724\) | 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 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | −15.3571 | − | 3.02624i | −0.566457 | − | 0.111625i | ||||
\(736\) | 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 | ||||||||
\(741\) | 3.52311 | 0.129425 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.9975i | 1.50405i | 0.659133 | + | 0.752027i | \(0.270924\pi\) | ||||
−0.659133 | + | 0.752027i | \(0.729076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.607876 | − | 3.08476i | 0.0222709 | − | 0.113017i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 8.11704i | − | 0.296987i | ||||||
\(748\) | 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 | ||||||||
\(753\) | − | 5.85838i | − | 0.213491i | ||||||
\(754\) | 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 | ||||||||
\(759\) | −21.5510 | −0.782253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9021 | −1.44645 | −0.723226 | − | 0.690612i | \(-0.757341\pi\) | ||||
−0.723226 | + | 0.690612i | \(0.757341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.1170 | + | 2.38776i | 0.438092 | + | 0.0863295i | ||||
\(766\) | 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 | ||||||||
\(771\) | 2.29862 | 0.0827830 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.7972i | 0.999794i | 0.866085 | + | 0.499897i | \(0.166629\pi\) | ||||
−0.866085 | + | 0.499897i | \(0.833371\pi\) | |||||||
\(774\) | 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 | ||||||||
\(783\) | − | 6.77551i | − | 0.242137i | ||||||
\(784\) | 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 | ||||||||
\(789\) | −31.5789 | −1.12424 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.25240i | 0.186518i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.92919 | + | 14.8646i | −0.103888 | + | 0.527194i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.6464i | 0.660490i | 0.943895 | + | 0.330245i | \(0.107131\pi\) | ||||
−0.943895 | + | 0.330245i | \(0.892869\pi\) |