Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,4,Mod(449,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.449");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.g (of order \(2\), degree \(1\), not 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: | \(33.0410696032\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{10} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(-4.31366i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.449 |
Dual form | 560.4.g.f.449.5 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.93939i | 0.373235i | 0.982433 | + | 0.186617i | \(0.0597525\pi\) | ||||
−0.982433 | + | 0.186617i | \(0.940247\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.32771 | + | 10.9353i | −0.208197 | + | 0.978087i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.2388 | 0.860696 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25.5420 | −0.700108 | −0.350054 | − | 0.936730i | \(-0.613837\pi\) | ||||
−0.350054 | + | 0.936730i | \(0.613837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 64.1014i | 1.36758i | 0.729679 | + | 0.683790i | \(0.239670\pi\) | ||||
−0.729679 | + | 0.683790i | \(0.760330\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −21.2079 | − | 4.51433i | −0.365056 | − | 0.0777063i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 27.6952i | − | 0.395122i | −0.980291 | − | 0.197561i | \(-0.936698\pi\) | ||
0.980291 | − | 0.197561i | \(-0.0633020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.792436 | 0.00956828 | 0.00478414 | − | 0.999989i | \(-0.498477\pi\) | ||||
0.00478414 | + | 0.999989i | \(0.498477\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.5757 | 0.141070 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 108.606i | 0.984609i | 0.870423 | + | 0.492305i | \(0.163845\pi\) | ||||
−0.870423 | + | 0.492305i | \(0.836155\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −114.164 | − | 50.9086i | −0.913308 | − | 0.407269i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 97.4324i | 0.694477i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 234.000 | 1.49837 | 0.749186 | − | 0.662360i | \(-0.230445\pi\) | ||||
0.749186 | + | 0.662360i | \(0.230445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −129.204 | −0.748570 | −0.374285 | − | 0.927314i | \(-0.622112\pi\) | ||||
−0.374285 | + | 0.927314i | \(0.622112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 49.5357i | − | 0.261305i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 76.5474 | + | 16.2940i | 0.369682 | + | 0.0786909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.3108i | 0.170223i | 0.996371 | + | 0.0851116i | \(0.0271247\pi\) | ||||
−0.996371 | + | 0.0851116i | \(0.972875\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −124.317 | −0.510429 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −403.216 | −1.53590 | −0.767949 | − | 0.640511i | \(-0.778722\pi\) | ||||
−0.767949 | + | 0.640511i | \(0.778722\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 172.895i | 0.613167i | 0.951844 | + | 0.306584i | \(0.0991859\pi\) | ||||
−0.951844 | + | 0.306584i | \(0.900814\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −54.0931 | + | 254.124i | −0.179194 | + | 0.841835i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 206.943i | − | 0.642250i | −0.947037 | − | 0.321125i | \(-0.895939\pi\) | ||
0.947037 | − | 0.321125i | \(-0.104061\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 53.7117 | 0.147473 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 144.031i | − | 0.373287i | −0.982428 | − | 0.186643i | \(-0.940239\pi\) | ||
0.982428 | − | 0.186643i | \(-0.0597609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 59.4542 | − | 279.310i | 0.145760 | − | 0.684767i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.53684i | 0.00357122i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −679.086 | −1.49846 | −0.749232 | − | 0.662307i | \(-0.769577\pi\) | ||||
−0.749232 | + | 0.662307i | \(0.769577\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −574.717 | −1.20631 | −0.603155 | − | 0.797624i | \(-0.706090\pi\) | ||||
−0.603155 | + | 0.797624i | \(0.706090\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 162.671i | − | 0.325312i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −700.971 | − | 149.209i | −1.33761 | − | 0.284725i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 515.640i | − | 0.940230i | −0.882605 | − | 0.470115i | \(-0.844212\pi\) | ||
0.882605 | − | 0.470115i | \(-0.155788\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −210.630 | −0.367491 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −556.612 | −0.930391 | −0.465195 | − | 0.885208i | \(-0.654016\pi\) | ||||
−0.465195 | + | 0.885208i | \(0.654016\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 173.243i | 0.277762i | 0.990309 | + | 0.138881i | \(0.0443505\pi\) | ||||
−0.990309 | + | 0.138881i | \(0.955650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 98.7314 | − | 221.407i | 0.152007 | − | 0.340879i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 178.794i | 0.264616i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 79.3290 | 0.112977 | 0.0564887 | − | 0.998403i | \(-0.482010\pi\) | ||||
0.0564887 | + | 0.998403i | \(0.482010\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 438.488 | 0.601493 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1043.56i | 1.38007i | 0.723777 | + | 0.690034i | \(0.242404\pi\) | ||||
−0.723777 | + | 0.690034i | \(0.757596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 302.856 | + | 64.4663i | 0.386463 | + | 0.0822630i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 453.817i | 0.559245i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −652.060 | −0.776609 | −0.388304 | − | 0.921531i | \(-0.626939\pi\) | ||||
−0.388304 | + | 0.921531i | \(0.626939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 448.710 | 0.516897 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 250.576i | − | 0.279393i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84456 | + | 8.66556i | −0.00199208 | + | 0.00935861i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 515.714i | 0.539823i | 0.962885 | + | 0.269912i | \(0.0869945\pi\) | ||||
−0.962885 | + | 0.269912i | \(0.913005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −593.564 | −0.602580 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −536.339 | −0.528394 | −0.264197 | − | 0.964469i | \(-0.585107\pi\) | ||||
−0.264197 | + | 0.964469i | \(0.585107\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 381.693i | 0.365139i | 0.983193 | + | 0.182570i | \(0.0584415\pi\) | ||||
−0.983193 | + | 0.182570i | \(0.941559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −31.6003 | + | 148.455i | −0.0293702 | + | 0.137978i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1381.12i | 1.24783i | 0.781492 | + | 0.623915i | \(0.214459\pi\) | ||||
−0.781492 | + | 0.623915i | \(0.785541\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 390.582 | 0.343220 | 0.171610 | − | 0.985165i | \(-0.445103\pi\) | ||||
0.171610 | + | 0.985165i | \(0.445103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −74.2995 | −0.0635333 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1643.15i | − | 1.36792i | −0.729521 | − | 0.683958i | \(-0.760257\pi\) | ||
0.729521 | − | 0.683958i | \(-0.239743\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1187.65 | − | 252.804i | −0.963033 | − | 0.204992i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1489.64i | 1.17707i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −193.866 | −0.149342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −678.609 | −0.509849 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 781.992i | − | 0.573251i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 822.443 | − | 1129.92i | 0.588492 | − | 0.808503i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 192.032i | 0.134174i | 0.997747 | + | 0.0670869i | \(0.0213705\pi\) | ||||
−0.997747 | + | 0.0670869i | \(0.978630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −335.310 | −0.228856 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2082.90 | −1.38919 | −0.694594 | − | 0.719402i | \(-0.744416\pi\) | ||||
−0.694594 | + | 0.719402i | \(0.744416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.54705i | − | 0.00361647i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1065.46 | − | 226.794i | −0.679259 | − | 0.144588i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 78.1709i | − | 0.0487488i | −0.999703 | − | 0.0243744i | \(-0.992241\pi\) | ||
0.999703 | − | 0.0243744i | \(-0.00775939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1393.67 | 0.850426 | 0.425213 | − | 0.905093i | \(-0.360199\pi\) | ||||
0.425213 | + | 0.905093i | \(0.360199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 401.342 | 0.239710 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1637.28i | − | 0.957454i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −544.685 | + | 2558.88i | −0.311956 | + | 1.46554i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 95.0299i | − | 0.0533193i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −32.5002 | −0.0178693 | −0.00893463 | − | 0.999960i | \(-0.502844\pi\) | ||||
−0.00893463 | + | 0.999960i | \(0.502844\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −466.762 | −0.251553 | −0.125777 | − | 0.992059i | \(-0.540142\pi\) | ||||
−0.125777 | + | 0.992059i | \(0.540142\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 643.602i | − | 0.340080i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 300.749 | − | 1412.89i | 0.155850 | − | 0.732167i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1673.50i | 0.850701i | 0.905029 | + | 0.425351i | \(0.139849\pi\) | ||||
−0.905029 | + | 0.425351i | \(0.860151\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 279.332 | 0.139324 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 760.245 | 0.372147 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1869.36i | 0.898279i | 0.893462 | + | 0.449139i | \(0.148269\pi\) | ||||
−0.893462 | + | 0.449139i | \(0.851731\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 541.690 | + | 115.305i | 0.255579 | + | 0.0544028i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 46.5250i | − | 0.0215581i | −0.999942 | − | 0.0107791i | \(-0.996569\pi\) | ||
0.999942 | − | 0.0107791i | \(-0.00343115\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1911.99 | −0.870275 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.4152 | 0.00823538 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2496.28i | − | 1.09704i | −0.836137 | − | 0.548521i | \(-0.815191\pi\) | ||
0.836137 | − | 0.548521i | \(-0.184809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −356.360 | + | 799.145i | −0.153933 | + | 0.345198i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1317.01i | − | 0.559279i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2975.70 | 1.24254 | 0.621269 | − | 0.783598i | \(-0.286618\pi\) | ||||
0.621269 | + | 0.783598i | \(0.286618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 966.273 | 0.396809 | 0.198405 | − | 0.980120i | \(-0.436424\pi\) | ||||
0.198405 | + | 0.980120i | \(0.436424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1114.60i | − | 0.450237i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −418.942 | − | 89.1764i | −0.166493 | − | 0.0354399i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 707.389i | 0.276628i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 682.027 | 0.262488 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1545.50 | 0.585488 | 0.292744 | − | 0.956191i | \(-0.405432\pi\) | ||||
0.292744 | + | 0.956191i | \(0.405432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2304.05i | 0.859322i | 0.902990 | + | 0.429661i | \(0.141367\pi\) | ||||
−0.902990 | + | 0.429661i | \(0.858633\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 289.375 | − | 1359.45i | 0.106270 | − | 0.499244i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 222.021i | − | 0.0802960i | −0.999194 | − | 0.0401480i | \(-0.987217\pi\) | ||
0.999194 | − | 0.0401480i | \(-0.0127829\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3580.56 | 1.27547 | 0.637736 | − | 0.770255i | \(-0.279871\pi\) | ||||
0.637736 | + | 0.770255i | \(0.279871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1000.02 | 0.350927 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1638.00i | − | 0.566331i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 938.570 | − | 4409.31i | 0.319769 | − | 1.50224i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2523.88i | 0.847449i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.2404 | −0.00669883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4181.04 | 1.36415 | 0.682073 | − | 0.731284i | \(-0.261079\pi\) | ||||
0.682073 | + | 0.731284i | \(0.261079\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1079.49i | − | 0.347254i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1890.66 | − | 402.449i | −0.599731 | − | 0.127659i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 904.426i | 0.282933i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −335.986 | −0.103670 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1775.30 | 0.540361 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2361.52i | 0.709145i | 0.935028 | + | 0.354573i | \(0.115374\pi\) | ||||
−0.935028 | + | 0.354573i | \(0.884626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2653.02 | − | 1183.05i | −0.786081 | − | 0.350534i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 586.877i | − | 0.171596i | −0.996313 | − | 0.0857982i | \(-0.972656\pi\) | ||
0.996313 | − | 0.0857982i | \(-0.0273440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4619.55 | 1.33305 | 0.666526 | − | 0.745482i | \(-0.267781\pi\) | ||||
0.666526 | + | 0.745482i | \(0.267781\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −346.750 | −0.0987639 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5120.44i | 1.43971i | 0.694127 | + | 0.719853i | \(0.255791\pi\) | ||||
−0.694127 | + | 0.719853i | \(0.744209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2262.99 | + | 481.703i | 0.628176 | + | 0.133714i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 153.850i | 0.0421671i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1127.51 | 0.305158 | 0.152579 | − | 0.988291i | \(-0.451242\pi\) | ||||
0.152579 | + | 0.988291i | \(0.451242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3549.53 | −0.948736 | −0.474368 | − | 0.880327i | \(-0.657323\pi\) | ||||
−0.474368 | + | 0.880327i | \(0.657323\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3481.07i | 0.918975i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 114.058 | − | 535.832i | 0.0297424 | − | 0.139727i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 50.7963i | 0.0130854i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2023.87 | −0.515090 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4717.19 | −1.18624 | −0.593120 | − | 0.805114i | \(-0.702104\pi\) | ||||
−0.593120 | + | 0.805114i | \(0.702104\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2774.02i | − | 0.689333i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −125.025 | + | 587.355i | −0.0307034 | + | 0.144242i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6260.31i | 1.51948i | 0.650224 | + | 0.759742i | \(0.274675\pi\) | ||||
−0.650224 | + | 0.759742i | \(0.725325\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 268.176 | 0.0643383 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5437.88 | 1.28964 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5753.04i | − | 1.34885i | −0.738344 | − | 0.674425i | \(-0.764392\pi\) | ||
0.738344 | − | 0.674425i | \(-0.235608\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1575.03 | + | 335.262i | 0.365107 | + | 0.0777170i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1264.60i | − | 0.289858i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7059.21 | 1.60003 | 0.800014 | − | 0.599982i | \(-0.204826\pi\) | ||||
0.800014 | + | 0.599982i | \(0.204826\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8534.52 | 1.91305 | 0.956523 | − | 0.291658i | \(-0.0942069\pi\) | ||||
0.956523 | + | 0.291658i | \(0.0942069\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 870.222i | 0.192924i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2915.96 | + | 1300.30i | 0.639415 | + | 0.285132i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1313.94i | − | 0.285008i | −0.989794 | − | 0.142504i | \(-0.954485\pi\) | ||
0.989794 | − | 0.142504i | \(-0.0455154\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3002.54 | −0.644291 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −247.229 | −0.0524856 | −0.0262428 | − | 0.999656i | \(-0.508354\pi\) | ||||
−0.0262428 | + | 0.999656i | \(0.508354\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9074.90i | − | 1.90617i | −0.302697 | − | 0.953087i | \(-0.597887\pi\) | ||
0.302697 | − | 0.953087i | \(-0.402113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.8059 | − | 3.57731i | −0.00349296 | − | 0.000743515i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2822.51i | 0.580515i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4145.98 | 0.843879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1000.17 | −0.201481 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2740.72i | 0.546466i | 0.961948 | + | 0.273233i | \(0.0880930\pi\) | ||||
−0.961948 | + | 0.273233i | \(0.911907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1580.71 | − | 7426.04i | 0.311975 | − | 1.46563i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2488.61i | − | 0.486209i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6961.83 | −1.34653 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1210.26 | 0.231755 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1040.17i | − | 0.197215i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1337.77 | − | 6284.73i | 0.251150 | − | 1.17988i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6985.46i | 1.29864i | 0.760517 | + | 0.649318i | \(0.224946\pi\) | ||||
−0.760517 | + | 0.649318i | \(0.775054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −740.250 | −0.136283 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 356.841 | 0.0650630 | 0.0325315 | − | 0.999471i | \(-0.489643\pi\) | ||||
0.0325315 | + | 0.999471i | \(0.489643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6630.12i | − | 1.19731i | −0.801009 | − | 0.598653i | \(-0.795703\pi\) | ||
0.801009 | − | 0.598653i | \(-0.204297\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1778.87 | + | 378.652i | 0.318184 | + | 0.0677289i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2494.05i | 0.441891i | 0.975286 | + | 0.220946i | \(0.0709144\pi\) | ||||
−0.975286 | + | 0.220946i | \(0.929086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5976.83 | −1.04902 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2678.52 | −0.465734 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 21.9467i | − | 0.00378063i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3263.31 | − | 7318.05i | 0.556973 | − | 1.24902i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 757.489i | 0.128102i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1448.60 | −0.242748 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4682.47 | 0.777558 | 0.388779 | − | 0.921331i | \(-0.372897\pi\) | ||||
0.388779 | + | 0.921331i | \(0.372897\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 890.297i | 0.146510i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5638.70 | + | 1200.26i | 0.919627 | + | 0.195753i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3596.60i | − | 0.581363i | −0.956820 | − | 0.290681i | \(-0.906118\pi\) | ||
0.956820 | − | 0.290681i | \(-0.0938820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3186.70 | 0.510554 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3300.12 | 0.524080 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 490.285 | − | 2303.31i | 0.0765103 | − | 0.359438i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1899.51i | 0.293865i | 0.989147 | + | 0.146932i | \(0.0469400\pi\) | ||||
−0.989147 | + | 0.146932i | \(0.953060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1037.55 | 0.159137 | 0.0795683 | − | 0.996829i | \(-0.474646\pi\) | ||||
0.0795683 | + | 0.996829i | \(0.474646\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6245.56 | −0.949752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4087.08i | − | 0.616242i | −0.951347 | − | 0.308121i | \(-0.900300\pi\) | ||
0.951347 | − | 0.308121i | \(-0.0997001\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1295.63 | − | 6086.75i | 0.193704 | − | 0.910003i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 375.982i | − | 0.0557397i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3472.67 | 0.510530 | 0.255265 | − | 0.966871i | \(-0.417837\pi\) | ||||
0.255265 | + | 0.966871i | \(0.417837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6858.37 | −0.999908 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1316.08i | − | 0.190293i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1894.48 | − | 403.260i | −0.271675 | − | 0.0578290i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8769.14i | 1.24726i | 0.781719 | + | 0.623631i | \(0.214343\pi\) | ||||
−0.781719 | + | 0.623631i | \(0.785657\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9370.25 | −1.32194 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1008.22 | −0.141089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11368.9i | 1.57817i | 0.614284 | + | 0.789085i | \(0.289445\pi\) | ||||
−0.614284 | + | 0.789085i | \(0.710555\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2191.35 | + | 1595.03i | 0.301762 | + | 0.219646i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14999.8i | 2.04914i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12137.4 | −1.64500 | −0.822501 | − | 0.568764i | \(-0.807422\pi\) | ||||
−0.822501 | + | 0.568764i | \(0.807422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −372.424 | −0.0500784 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9869.61i | 1.31675i | 0.752692 | + | 0.658373i | \(0.228755\pi\) | ||||
−0.752692 | + | 0.658373i | \(0.771245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1955.17 | − | 416.180i | −0.258817 | − | 0.0550921i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4017.86i | 0.527751i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −57.1166 | −0.00744454 | −0.00372227 | − | 0.999993i | \(-0.501185\pi\) | ||||
−0.00372227 | + | 0.999993i | \(0.501185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3007.88 | 0.389041 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4039.54i | − | 0.518494i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −184.655 | + | 867.490i | −0.0235215 | + | 0.110502i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7436.17i | 0.940078i | 0.882646 | + | 0.470039i | \(0.155760\pi\) | ||||
−0.882646 | + | 0.470039i | \(0.844240\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.7579 | 0.00134979 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12465.0 | −1.55230 | −0.776149 | − | 0.630550i | \(-0.782829\pi\) | ||||
−0.776149 | + | 0.630550i | \(0.782829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8282.15i | − | 1.02373i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1020.67 | + | 4795.02i | −0.125229 | + | 0.588312i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 978.533i | − | 0.119175i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1708.72 | 0.206578 | 0.103289 | − | 0.994651i | \(-0.467063\pi\) | ||||
0.103289 | + | 0.994651i | \(0.467063\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 151.604 | 0.0181948 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4753.60i | 0.566366i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11411.7 | − | 2429.10i | −1.34983 | − | 0.287325i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2702.86i | 0.317409i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10618.8 | 1.23810 | 0.619050 | − | 0.785352i | \(-0.287518\pi\) | ||||
0.619050 | + | 0.785352i | \(0.287518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13273.5 | 1.53661 | 0.768304 | − | 0.640085i | \(-0.221101\pi\) | ||||
0.768304 | + | 0.640085i | \(0.221101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4809.10i | − | 0.552781i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1409.92 | + | 3161.78i | −0.160921 | + | 0.360868i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4023.02i | 0.455943i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3175.31 | 0.357355 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7918.20 | −0.884934 | −0.442467 | − | 0.896785i | \(-0.645897\pi\) | ||||
−0.442467 | + | 0.896785i | \(0.645897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4433.34i | − | 0.492038i | −0.969265 | − | 0.246019i | \(-0.920877\pi\) | ||
0.969265 | − | 0.246019i | \(-0.0791226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4962.65 | − | 1056.35i | −0.546990 | − | 0.116433i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 86.0637i | 0.00942102i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12958.4 | 1.40882 | 0.704408 | − | 0.709796i | \(-0.251213\pi\) | ||||
0.704408 | + | 0.709796i | \(0.251213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1138.70 | −0.122957 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12040.4i | − | 1.29133i | −0.763621 | − | 0.645664i | \(-0.776580\pi\) | ||
0.763621 | − | 0.645664i | \(-0.223420\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1517.80 | − | 7130.50i | 0.161687 | − | 0.759591i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 63.0304i | − | 0.00666943i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11586.3 | −1.21780 | −0.608899 | − | 0.793247i | \(-0.708389\pi\) | ||||
−0.608899 | + | 0.793247i | \(0.708389\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10298.9 | 1.07529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 905.232i | − | 0.0938886i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1044.47 | + | 4906.80i | −0.107616 | + | 0.505570i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9734.34i | 0.996396i | 0.867063 | + | 0.498198i | \(0.166005\pi\) | ||||
−0.867063 | + | 0.498198i | \(0.833995\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2698.41 | 0.274403 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1343.41 | −0.135724 | −0.0678621 | − | 0.997695i | \(-0.521618\pi\) | ||||
−0.0678621 | + | 0.997695i | \(0.521618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6613.72i | − | 0.663857i | −0.943305 | − | 0.331929i | \(-0.892301\pi\) | ||
0.943305 | − | 0.331929i | \(-0.107699\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2740.13 | + | 583.268i | 0.273270 | + | 0.0581686i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14688.9i | 1.45551i | 0.685838 | + | 0.727755i | \(0.259436\pi\) | ||||
−0.685838 | + | 0.727755i | \(0.740564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3609.48 | −0.355374 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3245.57 | −0.317511 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4416.07i | − | 0.429283i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −90.4673 | − | 40.3418i | −0.00873879 | − | 0.00389686i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3347.11i | − | 0.321286i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15298.6 | −1.45931 | −0.729657 | − | 0.683813i | \(-0.760320\pi\) | ||||
−0.729657 | + | 0.683813i | \(0.760320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2455.78 | −0.232794 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1474.41i | 0.138898i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5639.52 | − | 1200.43i | −0.527994 | − | 0.112389i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9653.80i | 0.898266i | 0.893465 | + | 0.449133i | \(0.148267\pi\) | ||||
−0.893465 | + | 0.449133i | \(0.851733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3625.41 | −0.335269 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20142.6 | −1.85137 | −0.925684 | − | 0.378297i | \(-0.876510\pi\) | ||||
−0.925684 | + | 0.378297i | \(0.876510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6480.69i | − | 0.592039i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1381.64 | − | 6490.83i | 0.125455 | − | 0.589376i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3896.29i | 0.351655i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1309.29 | −0.117459 | −0.0587293 | − | 0.998274i | \(-0.518705\pi\) | ||||
−0.0587293 | + | 0.998274i | \(0.518705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 90.2299 | 0.00804625 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2186.17i | 0.193791i | 0.995295 | + | 0.0968953i | \(0.0308912\pi\) | ||||
−0.995295 | + | 0.0968953i | \(0.969109\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1248.44 | − | 5865.06i | 0.110010 | − | 0.516815i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3708.09i | − | 0.324817i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3591.11 | −0.312718 | −0.156359 | − | 0.987700i | \(-0.549976\pi\) | ||||
−0.156359 | + | 0.987700i | \(0.549976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1212.70 | 0.104984 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 77.2089i | 0.00664495i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4173.94 | − | 888.470i | −0.357138 | − | 0.0760207i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5285.73i | 0.449644i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4841.24 | 0.409455 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8605.34 | −0.723621 | −0.361811 | − | 0.932252i | \(-0.617841\pi\) | ||||
−0.361811 | + | 0.932252i | \(0.617841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22536.4i | 1.88423i | 0.335297 | + | 0.942113i | \(0.391163\pi\) | ||||
−0.335297 | + | 0.942113i | \(0.608837\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1549.85 | − | 691.120i | −0.128840 | − | 0.0574532i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3578.32i | 0.295776i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 371.637 | 0.0305447 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15781.1 | −1.28972 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 25846.7i | − | 2.10046i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15103.0 | − | 3214.84i | −1.22049 | − | 0.259794i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5771.03i | 0.463758i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1251.56 | 0.100015 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8782.44 | 0.697942 | 0.348971 | − | 0.937134i | \(-0.386531\pi\) | ||||
0.348971 | + | 0.937134i | \(0.386531\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1873.98i | 0.148103i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −909.161 | + | 4271.15i | −0.0714572 | + | 0.335699i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 22593.0i | − | 1.76601i | −0.469366 | − | 0.883004i | \(-0.655518\pi\) | ||
0.469366 | − | 0.883004i | \(-0.344482\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13355.7 | −1.03827 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 185.430 | 0.0143368 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 555.303i | − | 0.0427014i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 172.947 | − | 812.490i | 0.0132274 | − | 0.0621411i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7264.13i | − | 0.552587i | −0.961073 | − | 0.276294i | \(-0.910894\pi\) | ||
0.961073 | − | 0.276294i | \(-0.0891062\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11082.8 | −0.838555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1371.90 | −0.103247 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3851.42i | 0.288309i | 0.989555 | + | 0.144154i | \(0.0460462\pi\) | ||||
−0.989555 | + | 0.144154i | \(0.953954\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17968.4 | + | 3824.78i | 1.33794 | + | 0.284796i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3069.42i | − | 0.227343i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16580.3 | −1.22158 | −0.610792 | − | 0.791791i | \(-0.709149\pi\) | ||||
−0.610792 | + | 0.791791i | \(0.709149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6385.86 | −0.468021 | −0.234010 | − | 0.972234i | \(-0.575185\pi\) | ||||
−0.234010 | + | 0.972234i | \(0.575185\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2997.32i | 0.218525i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5529.00 | − | 12398.9i | 0.401001 | − | 0.899252i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11059.1i | − | 0.797912i | −0.916970 | − | 0.398956i | \(-0.869373\pi\) | ||
0.916970 | − | 0.398956i | \(-0.130627\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4468.44 | −0.320729 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7304.92 | 0.521617 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3678.84i | 0.261341i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16289.7 | − | 3467.45i | −1.15128 | − | 0.245062i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7871.25i | 0.553461i | 0.960948 | + | 0.276730i | \(0.0892509\pi\) | ||||
−0.960948 | + | 0.276730i | \(0.910749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −102.386 | −0.00716253 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 430.584 | 0.0299693 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2018.06i | 0.139750i | 0.997556 | + | 0.0698750i | \(0.0222600\pi\) | ||||
−0.997556 | + | 0.0698750i | \(0.977740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 451.264 | − | 2120.00i | 0.0310925 | − | 0.146069i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6944.08i | 0.476051i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1356.67 | −0.0925409 | −0.0462705 | − | 0.998929i | \(-0.514734\pi\) | ||||
−0.0462705 | + | 0.998929i | \(0.514734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11178.7 | 0.758715 | 0.379358 | − | 0.925250i | \(-0.376145\pi\) | ||||
0.379358 | + | 0.925250i | \(0.376145\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 11982.8i | − | 0.809252i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1579.60 | − | 7420.82i | 0.106149 | − | 0.498676i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9404.67i | − | 0.628870i | −0.949279 | − | 0.314435i | \(-0.898185\pi\) | ||
0.949279 | − | 0.314435i | \(-0.101815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3176.72 | 0.211375 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13265.3 | 0.878328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18938.0i | 1.24779i | 0.781507 | + | 0.623897i | \(0.214452\pi\) | ||||
−0.781507 | + | 0.623897i | \(0.785548\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8551.35 | + | 1820.25i | 0.560689 | + | 0.119349i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17716.9i | 1.15600i | 0.816036 | + | 0.578001i | \(0.196167\pi\) | ||||
−0.816036 | + | 0.578001i | \(0.803833\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6240.33 | −0.405202 | −0.202601 | − | 0.979261i | \(-0.564939\pi\) | ||||
−0.202601 | + | 0.979261i | \(0.564939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10581.8 | −0.683788 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4564.42i | 0.293531i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10441.6 | + | 11623.8i | 0.668264 | + | 0.743924i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 39.2539i | − | 0.00250024i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1061.03 | 0.0672589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25887.7 | 1.63323 | 0.816617 | − | 0.577179i | \(-0.195847\pi\) | ||||
0.816617 | + | 0.577179i | \(0.195847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8108.65i | 0.509147i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2099.94 | − | 446.994i | −0.131234 | − | 0.0279345i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3140.97i | − | 0.195369i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12935.0 | −0.800783 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18798.4 | 1.15834 | 0.579168 | − | 0.815208i | \(-0.303378\pi\) | ||||
0.579168 | + | 0.815208i | \(0.303378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2287.70i | − | 0.140308i | −0.997536 | − | 0.0701541i | \(-0.977651\pi\) | ||
0.997536 | − | 0.0701541i | \(-0.0223491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 780.503 | − | 3666.73i | 0.0476469 | − | 0.223841i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1769.31i | − | 0.107510i | −0.998554 | − | 0.0537548i | \(-0.982881\pi\) | ||
0.998554 | − | 0.0537548i | \(-0.0171189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17345.2 | 1.04909 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1754.03 | −0.105600 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3891.48i | − | 0.233209i | −0.993178 | − | 0.116604i | \(-0.962799\pi\) | ||
0.993178 | − | 0.116604i | \(-0.0372010\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4848.38 | − | 22777.2i | 0.289224 | − | 1.35875i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4025.96i | 0.239068i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20097.6 | 1.18800 | 0.594001 | − | 0.804465i | \(-0.297548\pi\) | ||||
0.594001 | + | 0.804465i | \(0.297548\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27167.9 | −1.59865 | −0.799326 | − | 0.600898i | \(-0.794810\pi\) | ||||
−0.799326 | + | 0.600898i | \(0.794810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3442.99i | 0.201681i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 60.6589 | + | 12.9119i | 0.00353722 | + | 0.000752937i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25414.0i | 1.47531i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4579.91 | −0.264678 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14679.4 | 0.844548 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 25909.7i | − | 1.48402i | −0.670389 | − | 0.742010i | \(-0.733873\pi\) | ||
0.670389 | − | 0.742010i | \(-0.266127\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4960.15 | − | 11123.2i | 0.282839 | − | 0.634271i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4359.22i | 0.247472i | 0.992315 | + | 0.123736i | \(0.0394875\pi\) | ||||
−0.992315 | + | 0.123736i | \(0.960512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3610.00 | 0.204034 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1138.18 | 0.0640458 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29721.9i | 1.66512i | 0.553937 | + | 0.832559i | \(0.313125\pi\) | ||||
−0.553937 | + | 0.832559i | \(0.686875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 854.826 | + | 181.959i | 0.0476806 | + | 0.0101493i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8959.10i | 0.497541i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9232.60 | 0.510499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4929.13 | 0.271365 | 0.135682 | − | 0.990752i | \(-0.456677\pi\) | ||||
0.135682 | + | 0.990752i | \(0.456677\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4154.95i | 0.227754i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3244.05 | + | 15240.2i | −0.177056 | + | 0.831791i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11167.1i | 0.606866i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9930.51 | −0.537348 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19358.8 | −1.04304 | −0.521520 | − | 0.853239i | \(-0.674635\pi\) | ||||
−0.521520 | + | 0.853239i | \(0.674635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.3589i | 0.00162874i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −934.208 | + | 4388.82i | −0.0499068 | + | 0.234457i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3754.38i | 0.199714i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17186.3 | 0.910359 | 0.455180 | − | 0.890400i | \(-0.349575\pi\) | ||||
0.455180 | + | 0.890400i | \(0.349575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1843.51 | 0.0972392 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 14032.4i | − | 0.737049i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17904.2 | + | 3811.10i | 0.936473 | + | 0.199339i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2186.68i | 0.113896i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15107.3 | −0.783598 | −0.391799 | − | 0.920051i | \(-0.628147\pi\) | ||||
−0.391799 | + | 0.920051i | \(0.628147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2671.85 | 0.138010 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 6883.91i | − | 0.354102i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26714.3 | − | 11912.6i | −1.36848 | − | 0.610240i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15840.9i | 0.808124i | 0.914732 | + | 0.404062i | \(0.132402\pi\) | ||||
−0.914732 | + | 0.404062i | \(0.867598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5088.04 | 0.258499 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4788.35 | 0.242276 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27639.7i | 1.39276i | 0.717671 | + | 0.696382i | \(0.245208\pi\) | ||||
−0.717671 | + | 0.696382i | \(0.754792\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1039.18 | + | 221.202i | 0.0521509 | + | 0.0111009i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13170.4i | 0.658263i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34874.4 | 1.73596 | 0.867982 | − | 0.496597i | \(-0.165417\pi\) | ||||
0.867982 | + | 0.496597i | \(0.165417\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −98.5136 | −0.00488392 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27686.7i | − | 1.36706i | −0.729922 | − | 0.683530i | \(-0.760444\pi\) | ||
0.729922 | − | 0.683530i | \(-0.239556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 75.6510 | − | 355.401i | 0.00372032 | − | 0.0174777i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24251.1i | 1.18782i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9667.83 | 0.471635 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4806.85 | −0.233561 | −0.116781 | − | 0.993158i | \(-0.537257\pi\) | ||||
−0.116781 | + | 0.993158i | \(0.537257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9148.45i | − | 0.442747i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1086.49 | − | 5104.21i | 0.0523726 | − | 0.246041i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 40166.6i | − | 1.92851i | −0.264983 | − | 0.964253i | \(-0.585366\pi\) | ||
0.264983 | − | 0.964253i | \(-0.414634\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5379.90 | 0.257283 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25912.3 | 1.23432 | 0.617162 | − | 0.786836i | \(-0.288282\pi\) | ||||
0.617162 | + | 0.786836i | \(0.288282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2734.07i | − | 0.129725i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7038.01 | + | 1498.12i | 0.332627 | + | 0.0708034i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 43530.4i | − | 2.04927i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23231.3 | 1.08939 | 0.544697 | − | 0.838633i | \(-0.316645\pi\) | ||||
0.544697 | + | 0.838633i | \(0.316645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12141.2 | −0.567125 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 836.306i | − | 0.0389131i | −0.999811 | − | 0.0194566i | \(-0.993806\pi\) | ||
0.999811 | − | 0.0194566i | \(-0.00619360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14750.4 | + | 6577.58i | 0.683675 | + | 0.304869i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 520.096i | 0.0240133i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −319.523 | −0.0146959 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14217.0 | 0.651374 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22799.2i | 1.04058i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18300.3 | − | 3895.43i | −0.832060 | − | 0.177113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 31945.6i | − | 1.44693i | −0.690359 | − | 0.723467i | \(-0.742547\pi\) | ||
0.690359 | − | 0.723467i | \(-0.257453\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11157.4 | 0.503438 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11502.1 | −0.517024 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 36840.2i | − | 1.64973i | ||||||
\(794\) | 0 | 0 |