Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 13.9 | ||
Character | \(\chi\) | \(=\) | 108.13 |
Dual form | 108.4.i.a.25.9 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 5.19029 | − | 0.246754i | 0.998872 | − | 0.0474878i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.7004 | + | 13.1742i | 1.40428 | + | 1.17833i | 0.959160 | + | 0.282863i | \(0.0912840\pi\) |
0.445122 | + | 0.895470i | \(0.353160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.81657 | − | 3.20897i | −0.476050 | − | 0.173268i | 0.0928410 | − | 0.995681i | \(-0.470405\pi\) |
−0.568891 | + | 0.822413i | \(0.692627\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.8782 | − | 2.56145i | 0.995490 | − | 0.0948684i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −45.7414 | + | 38.3816i | −1.25378 | + | 1.05204i | −0.257462 | + | 0.966288i | \(0.582886\pi\) |
−0.996316 | + | 0.0857561i | \(0.972669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.61377 | − | 14.8234i | 0.0557638 | − | 0.316252i | −0.944148 | − | 0.329521i | \(-0.893113\pi\) |
0.999912 | + | 0.0132689i | \(0.00422374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 84.7402 | + | 64.5036i | 1.45865 | + | 1.11032i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 44.8278 | − | 77.6441i | 0.639550 | − | 1.10773i | −0.345982 | − | 0.938241i | \(-0.612454\pi\) |
0.985532 | − | 0.169491i | \(-0.0542124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.79866 | − | 6.57947i | −0.0458669 | − | 0.0794439i | 0.842180 | − | 0.539196i | \(-0.181272\pi\) |
−0.888047 | + | 0.459752i | \(0.847938\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −46.5524 | − | 14.4800i | −0.483741 | − | 0.150466i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 126.350 | − | 45.9876i | 1.14547 | − | 0.416917i | 0.301584 | − | 0.953440i | \(-0.402485\pi\) |
0.843886 | + | 0.536523i | \(0.180262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 51.2365 | + | 290.577i | 0.409892 | + | 2.32462i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 138.874 | − | 19.9270i | 0.989862 | − | 0.142035i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.0600 | − | 142.122i | −0.160466 | − | 0.910049i | −0.953617 | − | 0.301023i | \(-0.902672\pi\) |
0.793151 | − | 0.609026i | \(-0.208439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −243.712 | + | 88.7037i | −1.41200 | + | 0.513925i | −0.931715 | − | 0.363190i | \(-0.881688\pi\) |
−0.480281 | + | 0.877115i | \(0.659465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −227.940 | + | 210.499i | −1.20240 | + | 1.11040i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −96.1478 | − | 166.533i | −0.464341 | − | 0.804263i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 113.051 | − | 195.811i | 0.502312 | − | 0.870030i | −0.497684 | − | 0.867358i | \(-0.665816\pi\) |
0.999996 | − | 0.00267179i | \(-0.000850458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.90850 | − | 77.5829i | 0.0406828 | − | 0.318544i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 32.6776 | − | 185.324i | 0.124473 | − | 0.705921i | −0.857147 | − | 0.515072i | \(-0.827765\pi\) |
0.981620 | − | 0.190848i | \(-0.0611238\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −45.0211 | + | 37.7772i | −0.159667 | + | 0.133976i | −0.719121 | − | 0.694885i | \(-0.755455\pi\) |
0.559454 | + | 0.828861i | \(0.311011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 455.743 | + | 313.882i | 1.50974 | + | 1.03980i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −298.842 | − | 108.770i | −0.927459 | − | 0.337568i | −0.166257 | − | 0.986082i | \(-0.553168\pi\) |
−0.761202 | + | 0.648515i | \(0.775390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −195.319 | − | 163.892i | −0.569443 | − | 0.477819i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 213.510 | − | 414.057i | 0.586224 | − | 1.13685i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −170.290 | −0.441341 | −0.220671 | − | 0.975348i | \(-0.570825\pi\) | ||||
−0.220671 | + | 0.975348i | \(0.570825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1223.80 | −3.00032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.3396 | − | 33.2120i | −0.0495878 | − | 0.0771761i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −82.5952 | − | 69.3056i | −0.182254 | − | 0.152929i | 0.547096 | − | 0.837070i | \(-0.315733\pi\) |
−0.729350 | + | 0.684140i | \(0.760178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −324.349 | − | 118.053i | −0.680797 | − | 0.247790i | −0.0216072 | − | 0.999767i | \(-0.506878\pi\) |
−0.659190 | + | 0.751977i | \(0.729101\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −245.193 | − | 63.6682i | −0.490341 | − | 0.127324i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 236.323 | − | 198.299i | 0.450959 | − | 0.378399i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.02407 | − | 5.80776i | 0.00186731 | − | 0.0105900i | −0.983860 | − | 0.178941i | \(-0.942733\pi\) |
0.985727 | + | 0.168351i | \(0.0538441\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 644.446 | − | 269.867i | 1.12438 | − | 0.470842i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −205.653 | + | 356.202i | −0.343754 | + | 0.595400i | −0.985127 | − | 0.171830i | \(-0.945032\pi\) |
0.641372 | + | 0.767230i | \(0.278365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 602.689 | + | 1043.89i | 0.966294 | + | 1.67367i | 0.706098 | + | 0.708115i | \(0.250454\pi\) |
0.260196 | + | 0.965556i | \(0.416213\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 337.634 | + | 1495.54i | 0.519821 | + | 2.30253i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 526.448 | − | 191.611i | 0.779147 | − | 0.283586i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19.8089 | + | 112.342i | 0.0282111 | + | 0.159993i | 0.995659 | − | 0.0930777i | \(-0.0296705\pi\) |
−0.967448 | + | 0.253071i | \(0.918559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 715.878 | − | 137.694i | 0.982000 | − | 0.188881i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −245.975 | − | 1394.99i | −0.325292 | − | 1.84482i | −0.507616 | − | 0.861583i | \(-0.669473\pi\) |
0.182324 | − | 0.983238i | \(-0.441638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1726.71 | − | 628.470i | 2.20339 | − | 0.801967i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −165.138 | − | 731.472i | −0.203501 | − | 0.901402i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 683.369 | + | 1183.63i | 0.813899 | + | 1.40971i | 0.910116 | + | 0.414354i | \(0.135992\pi\) |
−0.0962172 | + | 0.995360i | \(0.530674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −70.6125 | + | 122.304i | −0.0813428 | + | 0.140890i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1243.05 | + | 520.535i | −1.38600 | + | 0.580397i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.0387 | − | 153.344i | 0.0292012 | − | 0.165608i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −294.392 | + | 247.025i | −0.308155 | + | 0.258573i | −0.783729 | − | 0.621103i | \(-0.786685\pi\) |
0.475574 | + | 0.879676i | \(0.342240\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1131.14 | + | 1148.79i | −1.14832 | + | 1.16624i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 586.611 | + | 213.509i | 0.577920 | + | 0.210346i | 0.614408 | − | 0.788988i | \(-0.289395\pi\) |
−0.0364880 | + | 0.999334i | \(0.511617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 801.072 | + | 672.179i | 0.766330 | + | 0.643027i | 0.939766 | − | 0.341818i | \(-0.111043\pi\) |
−0.173436 | + | 0.984845i | \(0.555487\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −540.128 | − | 840.629i | −0.502010 | − | 0.781305i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 219.340 | 0.198172 | 0.0990860 | − | 0.995079i | \(-0.468408\pi\) | ||||
0.0990860 | + | 0.995079i | \(0.468408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2066.92 | −1.81628 | −0.908142 | − | 0.418663i | \(-0.862499\pi\) | ||||
−0.908142 | + | 0.418663i | \(0.862499\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 538.453 | − | 1044.21i | 0.460430 | − | 0.892902i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −126.524 | − | 106.166i | −0.105331 | − | 0.0883828i | 0.588601 | − | 0.808423i | \(-0.299679\pi\) |
−0.693932 | + | 0.720041i | \(0.744123\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2589.59 | + | 942.533i | 2.09983 | + | 0.764275i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32.2841 | − | 405.123i | 0.0255100 | − | 0.320116i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −644.385 | + | 540.703i | −0.496392 | + | 0.416523i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 388.004 | − | 2200.48i | 0.291513 | − | 1.65325i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 123.877 | − | 969.949i | 0.0908098 | − | 0.711035i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1742.72 | + | 3018.47i | −1.24699 | + | 2.15984i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −801.591 | − | 1388.40i | −0.560077 | − | 0.970081i | −0.997489 | − | 0.0708201i | \(-0.977438\pi\) |
0.437413 | − | 0.899261i | \(-0.355895\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −224.351 | + | 207.184i | −0.153124 | + | 0.141407i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1986.87 | − | 723.162i | 1.32514 | − | 0.482313i | 0.420040 | − | 0.907505i | \(-0.362016\pi\) |
0.905103 | + | 0.425193i | \(0.139794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.3778 | + | 70.1981i | 0.00806988 | + | 0.0457665i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2442.89 | + | 1516.68i | 1.55741 | + | 0.966929i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 174.325 | + | 988.647i | 0.108712 | + | 0.616539i | 0.989672 | + | 0.143348i | \(0.0457868\pi\) |
−0.880960 | + | 0.473191i | \(0.843102\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −141.218 | + | 51.3992i | −0.0861724 | + | 0.0313642i | −0.384747 | − | 0.923022i | \(-0.625711\pi\) |
0.298574 | + | 0.954386i | \(0.403489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1577.92 | − | 490.805i | −0.942443 | − | 0.293144i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 449.390 | + | 778.366i | 0.262796 | + | 0.455176i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1478.89 | − | 2561.51i | 0.847001 | − | 1.46705i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1054.20 | − | 802.451i | −0.591491 | − | 0.450238i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −353.047 | + | 2002.23i | −0.194112 | + | 1.10087i | 0.719565 | + | 0.694426i | \(0.244341\pi\) |
−0.913677 | + | 0.406441i | \(0.866770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −998.407 | + | 837.763i | −0.538074 | + | 0.451498i | −0.870879 | − | 0.491498i | \(-0.836450\pi\) |
0.332804 | + | 0.942996i | \(0.392005\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1006.01 | − | 2201.76i | 0.531576 | − | 1.16341i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4994.95 | − | 1818.01i | −2.58842 | − | 0.942106i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1497.76 | − | 1256.77i | −0.761366 | − | 0.638862i | 0.177116 | − | 0.984190i | \(-0.443323\pi\) |
−0.938482 | + | 0.345328i | \(0.887768\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −883.853 | + | 42.0196i | −0.440844 | + | 0.0209583i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1261.55 | −0.617539 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 304.483 | 0.146312 | 0.0731562 | − | 0.997320i | \(-0.476693\pi\) | ||||
0.0731562 | + | 0.997320i | \(0.476693\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6351.89 | + | 301.978i | −2.99693 | + | 0.142478i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1927.52 | + | 1617.38i | 0.893150 | + | 0.749442i | 0.968839 | − | 0.247690i | \(-0.0796714\pi\) |
−0.0756896 | + | 0.997131i | \(0.524116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1851.60 | + | 673.928i | 0.842787 | + | 0.306749i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −118.954 | − | 167.114i | −0.0531968 | − | 0.0747342i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −416.652 | + | 349.613i | −0.183107 | + | 0.153645i | −0.729734 | − | 0.683731i | \(-0.760356\pi\) |
0.546627 | + | 0.837376i | \(0.315912\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 480.722 | − | 2726.31i | 0.207652 | − | 1.17765i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −445.795 | − | 339.336i | −0.189311 | − | 0.144102i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1487.78 | − | 2576.91i | 0.621238 | − | 1.07602i | −0.368017 | − | 0.929819i | \(-0.619963\pi\) |
0.989255 | − | 0.146197i | \(-0.0467034\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.47319 | − | 11.2119i | −0.00265828 | − | 0.00460427i | 0.864693 | − | 0.502300i | \(-0.167513\pi\) |
−0.867351 | + | 0.497696i | \(0.834179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1712.59 | − | 532.697i | −0.691796 | − | 0.215181i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4354.59 | − | 1584.94i | 1.73057 | − | 0.629877i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 929.616 | + | 5272.11i | 0.363531 | + | 2.06168i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1288.34 | − | 269.954i | −0.495834 | − | 0.103896i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 107.185 | + | 607.875i | 0.0406053 | + | 0.230284i | 0.998356 | − | 0.0573151i | \(-0.0182540\pi\) |
−0.957751 | + | 0.287599i | \(0.907143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1940.91 | − | 706.433i | 0.723884 | − | 0.263472i | 0.0463102 | − | 0.998927i | \(-0.485254\pi\) |
0.677574 | + | 0.735455i | \(0.263032\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1177.66 | − | 1087.54i | 0.432481 | − | 0.399387i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −300.362 | − | 520.241i | −0.108629 | − | 0.188151i | 0.806586 | − | 0.591116i | \(-0.201313\pi\) |
−0.915215 | + | 0.402966i | \(0.867979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1860.07 | + | 3221.74i | −0.662597 | + | 1.14765i | 0.317333 | + | 0.948314i | \(0.397213\pi\) |
−0.979931 | + | 0.199338i | \(0.936121\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.88211 | − | 30.3967i | 0.00136230 | − | 0.0106667i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −235.123 | + | 1333.45i | −0.0812925 | + | 0.461033i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2954.54 | − | 2479.15i | 1.00660 | − | 0.844641i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3278.27 | − | 1559.71i | 1.10075 | − | 0.523705i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 426.287 | + | 155.156i | 0.141085 | + | 0.0513509i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1236.66 | + | 1037.68i | 0.403484 | + | 0.338563i | 0.821838 | − | 0.569721i | \(-0.192949\pi\) |
−0.418355 | + | 0.908284i | \(0.637393\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −979.506 | + | 1899.54i | −0.315092 | + | 0.611052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1204.53 | −0.382085 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2433.35 | 0.761228 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3385.72 | + | 5269.37i | 1.04468 | + | 1.62589i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1033.78 | − | 867.446i | −0.314659 | − | 0.264031i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3267.43 | − | 1189.25i | −0.981182 | − | 0.357121i | −0.198882 | − | 0.980023i | \(-0.563731\pi\) |
−0.782299 | + | 0.622902i | \(0.785953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2121.45 | + | 7678.95i | 0.628576 | + | 2.27524i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 573.716 | − | 481.405i | 0.167748 | − | 0.140758i | −0.555049 | − | 0.831818i | \(-0.687300\pi\) |
0.722797 | + | 0.691060i | \(0.242856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −628.614 | + | 3565.05i | −0.181397 | + | 1.02875i | 0.749100 | + | 0.662457i | \(0.230486\pi\) |
−0.930498 | + | 0.366298i | \(0.880625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2685.14 | − | 1124.42i | 0.764801 | − | 0.320266i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2041.89 | + | 3536.65i | −0.574113 | + | 0.994393i | 0.422024 | + | 0.906585i | \(0.361320\pi\) |
−0.996137 | + | 0.0878086i | \(0.972014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3258.98 | − | 5644.71i | −0.904648 | − | 1.56690i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 130.535 | + | 578.200i | 0.0357770 | + | 0.158473i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2769.51 | − | 1008.02i | 0.749560 | − | 0.272817i | 0.0611393 | − | 0.998129i | \(-0.480527\pi\) |
0.688421 | + | 0.725312i | \(0.258304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.3695 | − | 98.5075i | −0.00464261 | − | 0.0263296i | 0.982398 | − | 0.186797i | \(-0.0598108\pi\) |
−0.987041 | + | 0.160468i | \(0.948700\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3681.64 | − | 891.319i | 0.971923 | − | 0.235301i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −907.435 | − | 5146.32i | −0.236628 | − | 1.34199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −107.459 | + | 39.1119i | −0.0276820 | + | 0.0100754i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1620.90 | − | 7179.72i | −0.412531 | − | 1.82729i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2244.88 | + | 3888.24i | 0.564524 | + | 0.977783i | 0.997094 | + | 0.0761832i | \(0.0242734\pi\) |
−0.432570 | + | 0.901600i | \(0.642393\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4014.35 | + | 6953.06i | −0.997549 | + | 1.72781i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8807.04 | − | 3688.01i | 2.16282 | − | 0.905696i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −537.383 | + | 3047.65i | −0.130432 | + | 0.739717i | 0.847500 | + | 0.530795i | \(0.178107\pi\) |
−0.977932 | + | 0.208922i | \(0.933005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1625.08 | + | 1363.60i | −0.389874 | + | 0.327143i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1037.61 | − | 3755.80i | −0.246077 | − | 0.890721i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5048.21 | + | 1837.40i | 1.18360 | + | 0.430794i | 0.857471 | − | 0.514533i | \(-0.172035\pi\) |
0.326125 | + | 0.945327i | \(0.394257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2673.61 | − | 2243.42i | −0.619768 | − | 0.520047i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3838.95 | + | 5974.76i | 0.879925 | + | 1.36947i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3518.17 | 0.797422 | 0.398711 | − | 0.917077i | \(-0.369458\pi\) | ||||
0.398711 | + | 0.917077i | \(0.369458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 168.611 | 0.0377948 | 0.0188974 | − | 0.999821i | \(-0.493984\pi\) | ||||
0.0188974 | + | 0.999821i | \(0.493984\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −336.320 | + | 652.219i | −0.0745605 | + | 0.144594i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13496.4 | − | 11324.9i | −2.95951 | − | 2.48333i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2582.12 | − | 939.815i | −0.560088 | − | 0.203856i | 0.0464347 | − | 0.998921i | \(-0.485214\pi\) |
−0.606523 | + | 0.795066i | \(0.707436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6323.32 | + | 3008.45i | −1.35687 | + | 0.645561i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3848.57 | − | 3229.33i | 0.817034 | − | 0.685573i | −0.135242 | − | 0.990813i | \(-0.543181\pi\) |
0.952275 | + | 0.305240i | \(0.0987367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 63.6653 | − | 361.064i | 0.0133728 | − | 0.0758411i | −0.977391 | − | 0.211440i | \(-0.932185\pi\) |
0.990764 | + | 0.135599i | \(0.0432958\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 102.500 | − | 802.572i | 0.0213039 | − | 0.166808i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −882.804 | + | 1529.06i | −0.181569 | + | 0.314486i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1562.57 | − | 2706.44i | −0.318047 | − | 0.550874i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1467.03 | + | 1354.77i | −0.295528 | + | 0.272914i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1101.03 | + | 400.741i | −0.219532 | + | 0.0799029i | −0.449445 | − | 0.893308i | \(-0.648378\pi\) |
0.229913 | + | 0.973211i | \(0.426156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −383.731 | − | 2176.25i | −0.0757345 | − | 0.429511i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5587.45 | + | 6241.69i | −1.09164 | + | 1.21946i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −351.445 | − | 1993.14i | −0.0679752 | − | 0.385506i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 518.158 | − | 188.594i | 0.0992230 | − | 0.0361142i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3097.36 | + | 963.424i | 0.587257 | + | 0.182664i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3537.14 | − | 6126.50i | −0.664052 | − | 1.15017i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4212.00 | + | 7295.40i | −0.783034 | + | 1.35626i | 0.147132 | + | 0.989117i | \(0.452996\pi\) |
−0.930166 | + | 0.367139i | \(0.880337\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4323.66 | + | 3291.14i | 0.796001 | + | 0.605910i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1088.82 | − | 6175.03i | 0.198526 | − | 1.12590i | −0.708781 | − | 0.705428i | \(-0.750755\pi\) |
0.907307 | − | 0.420468i | \(-0.138134\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1561.71 | + | 1310.43i | −0.282022 | + | 0.236645i | −0.772815 | − | 0.634632i | \(-0.781152\pi\) |
0.490792 | + | 0.871277i | \(0.336707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3010.85 | − | 4229.83i | −0.538546 | − | 0.756584i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4935.72 | − | 1796.45i | −0.874503 | − | 0.318293i | −0.134514 | − | 0.990912i | \(-0.542947\pi\) |
−0.739989 | + | 0.672619i | \(0.765170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6601.16 | + | 5539.03i | 1.15860 | + | 0.972182i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1138.44 | − | 54.1230i | 0.197948 | − | 0.00941075i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −681.142 | −0.117337 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4441.27 | 0.758023 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10727.9 | + | 510.020i | −1.81423 | + | 0.0862513i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2285.72 | + | 1917.95i | 0.383027 | + | 0.321398i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5265.15 | − | 1916.36i | −0.874317 | − | 0.318225i | −0.134403 | − | 0.990927i | \(-0.542912\pi\) |
−0.739914 | + | 0.672702i | \(0.765134\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2537.06 | − | 5552.62i | 0.417508 | − | 0.913760i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 92.5906 | − | 77.6927i | 0.0151008 | − | 0.0126711i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1242.81 | + | 7048.32i | −0.200890 | + | 1.13931i | 0.702886 | + | 0.711302i | \(0.251894\pi\) |
−0.903777 | + | 0.428004i | \(0.859217\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −682.891 | − | 519.812i | −0.109409 | − | 0.0832812i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7743.12 | − | 13411.5i | 1.22966 | − | 2.12983i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2805.20 | + | 4858.75i | 0.441593 | + | 0.764862i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13673.3 | + | 4253.03i | 2.13375 | + | 0.663697i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6609.62 | − | 2405.70i | 1.02254 | − | 0.372176i | 0.224307 | − | 0.974519i | \(-0.427988\pi\) |
0.798237 | + | 0.602343i | \(0.205766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2117.69 | − | 12010.0i | −0.324806 | − | 1.84207i | −0.511032 | − | 0.859562i | \(-0.670737\pi\) |
0.186226 | − | 0.982507i | \(-0.440374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 67.5982 | − | 2110.67i | 0.0102796 | − | 0.320967i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1121.15 | + | 6358.37i | 0.169045 | + | 0.958702i | 0.944795 | + | 0.327662i | \(0.106261\pi\) |
−0.775750 | + | 0.631040i | \(0.782628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7921.49 | + | 2883.19i | −1.18431 | + | 0.431053i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3211.12 | + | 2965.41i | −0.476053 | + | 0.439625i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2838.30 | − | 4916.07i | −0.417269 | − | 0.722731i | 0.578395 | − | 0.815757i | \(-0.303679\pi\) |
−0.995664 | + | 0.0930261i | \(0.970346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3400.64 | − | 5890.08i | 0.495792 | − | 0.858738i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1470.88 | − | 11516.9i | 0.212675 | − | 1.66523i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4289.92 | + | 24329.3i | −0.615191 | + | 3.48892i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5167.88 | + | 4336.37i | −0.735045 | + | 0.616776i | −0.931502 | − | 0.363737i | \(-0.881501\pi\) |
0.196457 | + | 0.980512i | \(0.437056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 403.619 | − | 5064.88i | 0.0569419 | − | 0.714545i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1501.37 | + | 546.455i | 0.210101 | + | 0.0764704i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6570.17 | − | 5513.03i | −0.912039 | − | 0.765292i | 0.0604669 | − | 0.998170i | \(-0.480741\pi\) |
−0.972506 | + | 0.232879i | \(0.925185\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8300.38 | + | 16096.8i | −1.14301 | + | 2.21662i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2172.24 | −0.296754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2072.06 | 0.280830 | 0.140415 | − | 0.990093i | \(-0.455156\pi\) | ||||
0.140415 | + | 0.990093i | \(0.455156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4503.08 | − | 7008.39i | −0.605512 | − | 0.942390i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8567.05 | − | 7188.61i | −1.14297 | − | 0.959062i | −0.143434 | − | 0.989660i | \(-0.545815\pi\) |
−0.999532 | + | 0.0305975i | \(0.990259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10789.7 | + | 3927.14i | 1.42830 | + | 0.519859i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1113.32 | + | 1130.70i | −0.146236 | + | 0.148519i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7629.67 | + | 6402.06i | −0.994447 | + | 0.834440i | −0.986205 | − | 0.165526i | \(-0.947068\pi\) |
−0.00824146 | + | 0.999966i | \(0.502623\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2093.33 | − | 11871.9i | 0.270752 | − | 1.53551i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10134.0 | − | 4243.69i | 1.30074 | − | 0.544697i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1169.00 | + | 2024.78i | −0.148909 | + | 0.257918i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1696.82 | + | 2938.98i | 0.214511 | + | 0.371545i | 0.953121 | − | 0.302588i | \(-0.0978508\pi\) |
−0.738610 | + | 0.674133i | \(0.764517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 81.5662 | + | 361.294i | 0.0102341 | + | 0.0453317i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4357.03 | − | 1585.83i | 0.542593 | − | 0.197488i | −0.0561597 | − | 0.998422i | \(-0.517886\pi\) |
0.598752 | + | 0.800934i | \(0.295663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 677.888 | + | 3844.49i | 0.0837916 | + | 0.475206i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13053.5 | + | 7269.24i | 1.60157 | + | 0.891880i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2344.40 | + | 13295.8i | 0.285523 | + | 1.61928i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12927.5 | + | 4705.22i | −1.56289 | + | 0.568846i | −0.971397 | − | 0.237463i | \(-0.923684\pi\) |
−0.591495 | + | 0.806309i | \(0.701462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1148.75 | + | 5088.35i | 0.137868 | + | 0.610681i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 505.807 | + | 876.083i | 0.0602643 | + | 0.104381i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14516.0 | − | 25142.4i | 1.71701 | − | 2.97395i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −720.280 | + | 301.623i | −0.0845858 | + | 0.0354209i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2243.12 | + | 12721.3i | −0.261536 | + | 1.48324i | 0.517186 | + | 0.855873i | \(0.326979\pi\) |
−0.778722 | + | 0.627369i | \(0.784132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9277.02 | − | 7784.35i | 1.07395 | − | 0.901154i | 0.0785486 | − | 0.996910i | \(-0.474971\pi\) |
0.995405 | + | 0.0957563i | \(0.0305270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8310.95 | − | 2158.07i | −0.955301 | − | 0.248058i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24858.4 | + | 9047.71i | 2.83720 | + | 1.03266i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2480.81 | + | 2081.65i | 0.281159 | + | 0.235921i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2524.53 | + | 3929.06i | 0.284115 | + | 0.442183i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8454.10 | 0.944826 | 0.472413 | − | 0.881377i | \(-0.343383\pi\) | ||||
0.472413 | + | 0.881377i | \(0.343383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16108.8 | 1.78785 | 0.893926 | − | 0.448214i | \(-0.147940\pi\) | ||||
0.893926 | + | 0.448214i | \(0.147940\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7043.80 | − | 13659.9i | 0.776378 | − | 1.50562i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −782.535 | − | 656.625i | −0.0856607 | − | 0.0718778i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4859.34 | + | 1768.65i | 0.528300 | + | 0.192285i | 0.592379 | − | 0.805659i | \(-0.298189\pi\) |
−0.0640794 | + | 0.997945i | \(0.520411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5669.62 | − | 3904.83i | −0.612204 | − | 0.421642i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4319.54 | + | 3624.52i | −0.463267 | + | 0.388728i | −0.844332 | − | 0.535821i | \(-0.820002\pi\) |
0.381064 | + | 0.924549i | \(0.375558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4864.20 | + | 27586.2i | −0.518169 | + | 2.93868i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1338.36 | + | 10479.3i | −0.141616 | + | 1.10884i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1788.29 | − | 3097.40i | 0.187961 | − | 0.325558i | −0.756609 | − | 0.653867i | \(-0.773146\pi\) |
0.944570 | + | 0.328309i | \(0.106479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5618.31 | + | 9731.20i | 0.586599 | + | 1.01602i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4975.30 | + | 4594.59i | −0.516027 | + | 0.476541i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2719.90 | + | 989.962i | −0.280244 | + | 0.102000i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1008.03 | − | 5716.82i | −0.103181 | − | 0.585168i | −0.991931 | − | 0.126776i | \(-0.959537\pi\) |
0.888750 | − | 0.458391i | \(-0.151574\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4678.20 | − | 11676.0i | 0.475729 | − | 1.18734i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1782.29 | − | 10107.9i | −0.180065 | − | 1.02120i | −0.932134 | − | 0.362113i | \(-0.882055\pi\) |
0.752070 | − | 0.659084i | \(-0.229056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4506.47 | − | 1640.22i | 0.452340 | − | 0.164638i | −0.105796 | − | 0.994388i | \(-0.533739\pi\) |
0.558136 | + | 0.829750i | \(0.311517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −26373.9 | − | 8203.50i | −2.63023 | − | 0.818125i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −517.986 | − | 897.177i | −0.0513266 | − | 0.0889003i | 0.839221 | − | 0.543791i | \(-0.183012\pi\) |
−0.890547 | + | 0.454891i | \(0.849678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.6657 | + | 47.9184i | −0.00272384 | + | 0.00471783i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8083.94 | − | 6153.44i | −0.790846 | − | 0.601986i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 609.380 | − | 3455.97i | 0.0592375 | − | 0.335953i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1717.21 | − | 1440.91i | 0.165876 | − | 0.139186i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4577.09 | + | 436.188i | −0.439351 | + | 0.0418694i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7302.87 | − | 2658.03i | −0.696611 | − | 0.253546i | −0.0306475 | − | 0.999530i | \(-0.509757\pi\) |
−0.665963 | + | 0.745985i | \(0.731979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2607.10 | − | 2187.62i | −0.247138 | − | 0.207374i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6547.79 | + | 311.292i | −0.616843 | + | 0.0293256i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7876.40 | −0.737421 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6402.34 | −0.595724 | −0.297862 | − | 0.954609i | \(-0.596274\pi\) | ||||
−0.297862 | + | 0.954609i | \(0.596274\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1580.35 | − | 75.1323i | 0.146147 | − | 0.00694806i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1539.64 | − | 1291.91i | −0.141513 | − | 0.118743i | 0.569283 | − | 0.822141i | \(-0.307221\pi\) |
−0.710796 | + | 0.703398i | \(0.751665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12158.3 | − | 4425.27i | −1.11072 | − | 0.404268i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32893.6 | + | 3134.70i | −2.98678 | + | 0.284635i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2956.20 | − | 2480.55i | 0.266808 | − | 0.223879i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1717.87 | − | 9742.54i | 0.154113 | − | 0.874020i | −0.805479 | − | 0.592625i | \(-0.798092\pi\) |
0.959592 | − | 0.281395i | \(-0.0907972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10403.5 | + | 7919.06i | 0.927731 | + | 0.706182i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3388.43 | − | 5868.93i | 0.300363 | − | 0.520244i | −0.675855 | − | 0.737034i | \(-0.736226\pi\) |
0.976218 | + | 0.216791i | \(0.0695589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6397.19 | + | 11080.3i | 0.563706 | + | 0.976367i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9776.65 | + | 3040.99i | 0.856403 | + | 0.266381i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1383.55 | + | 503.573i | −0.120481 | + | 0.0438516i | −0.401557 | − | 0.915834i | \(-0.631531\pi\) |
0.281076 | + | 0.959686i | \(0.409309\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1963.85 | − | 11137.5i | −0.170011 | − | 0.964179i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −658.643 | − | 838.020i | −0.0566857 | − | 0.0721237i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3721.72 | + | 21106.9i | 0.318444 | + | 1.80598i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17844.2 | − | 6494.76i | 1.51796 | − | 0.552494i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2076.28 | + | 1917.40i | −0.175604 | + | 0.162167i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6864.02 | − | 11888.8i | −0.577194 | − | 0.999730i | −0.995799 | − | 0.0915615i | \(-0.970814\pi\) |
0.418605 | − | 0.908168i | \(-0.362519\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2877.17 | − | 4983.40i | 0.240554 | − | 0.416652i | −0.720318 | − | 0.693644i | \(-0.756004\pi\) |
0.960872 | + | 0.276992i | \(0.0893376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1822.36 | − | 14269.0i | 0.151494 | − | 1.18619i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4037.74 | + | 22899.1i | −0.333751 | + | 1.89279i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4529.00 | − | 3800.28i | 0.372236 | − | 0.312343i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2397.54 | − | 1651.25i | −0.195940 | − | 0.134949i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2661.73 | − | 968.789i | −0.216308 | − | 0.0787297i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3443.72 | + | 2889.62i | 0.278289 | + | 0.233513i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7086.13 | − | 13742.0i | 0.569440 | − | 1.10430i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15224.6 | 1.21664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17020.2 | −1.35260 | −0.676298 | − | 0.736628i | \(-0.736417\pi\) | ||||
−0.676298 | + | 0.736628i | \(0.736417\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.3643 | − | 56.5957i | −0.00287393 | − | 0.00447284i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32451.3 | − | 27229.9i | −2.55057 | − | 2.14019i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18304.3 | − | 6662.21i | −1.43078 | − | 0.520760i | −0.493623 | − | 0.869676i | \(-0.664328\pi\) |
−0.937154 | + | 0.348916i | \(0.886550\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9020.31 | − | 2342.26i | −0.701234 | − | 0.182086i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −839.894 | + | 704.755i | −0.0649377 | + | 0.0544892i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 185.855 | − | 1054.04i | 0.0142918 | − | 0.0810529i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22210.5 | − | 9300.82i | 1.69871 | − | 0.711347i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2898.44 | + | 5020.24i | −0.220486 | + | 0.381893i | −0.954956 | − | 0.296748i | \(-0.904098\pi\) |
0.734469 | + | 0.678642i | \(0.237431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 442.313 | + | 766.109i | 0.0334667 | + | 0.0579660i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6125.89 | + | 27134.4i | 0.461025 | + | 2.04210i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8296.09 | − | 3019.53i | 0.621027 | − | 0.226035i | −0.0122940 | − | 0.999924i | \(-0.503913\pi\) |
0.633321 | + | 0.773889i | \(0.281691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −587.819 | − | 3333.69i | −0.0437694 | − | 0.248229i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6753.45 | − | 1083.24i | −0.500208 | − | 0.0802324i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1083.07 | + | 6142.40i | 0.0797973 | + | 0.452553i | 0.998358 | + | 0.0572742i | \(0.0182409\pi\) |
−0.918561 | + | 0.395279i | \(0.870648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4348.11 | − | 1582.58i | 0.318674 | − | 0.115988i | −0.177730 | − | 0.984079i | \(-0.556876\pi\) |
0.496404 | + | 0.868091i | \(0.334653\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 706.316 | + | 3128.60i | 0.0514952 | + | 0.228096i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19836.7 | + | 34358.1i | 1.43869 | + | 2.49188i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3232.20 | + | 5598.33i | −0.233203 | + | 0.403920i | −0.958749 | − | 0.284254i | \(-0.908254\pi\) |
0.725546 | + | 0.688174i | \(0.241587\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9899.56 | − | 4145.52i | 0.710555 | − | 0.297551i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2307.83 | + | 13088.4i | −0.164793 | + | 0.934590i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7789.30 | − | 6536.00i | 0.553344 | − | 0.464311i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5844.02 | − | 5935.25i | 0.413027 | − | 0.419474i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1888.52 | − | 687.365i | −0.132790 | − | 0.0483315i | 0.274771 | − | 0.961510i | \(-0.411398\pi\) |
−0.407560 | + | 0.913178i | \(0.633620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1509.40 | + | 1266.54i | 0.105592 | + | 0.0886023i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1687.34 | − | 2626.09i | −0.117441 | − | 0.182780i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22078.4 | −1.52892 | −0.764460 | − | 0.644671i | \(-0.776994\pi\) | ||||
−0.764460 | + | 0.644671i | \(0.776994\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17240.4 | −1.18788 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8859.33 | + | 17180.7i | −0.607350 | + | 1.17782i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 512.637 | + | 430.153i | 0.0349679 | + | 0.0293415i | 0.660104 | − | 0.751174i | \(-0.270512\pi\) |
−0.625136 | + | 0.780516i | \(0.714957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25139.4 | − | 9150.01i | −1.70626 | − | 0.621026i | −0.709742 | − | 0.704462i | \(-0.751188\pi\) |
−0.996513 | + | 0.0834358i | \(0.973411\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.6488 | − | 158.725i | 0.000854225 | − | 0.0107194i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35081.3 | − | 29436.7i | 2.35745 | − | 1.97813i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −768.770 | + | 4359.91i | −0.0514059 | + | 0.291538i | −0.999663 | − | 0.0259666i | \(-0.991734\pi\) |
0.948257 | + | 0.317504i | \(0.102845\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −891.322 | + | 6978.99i | −0.0593074 | + | 0.464373i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2393.44 | + | 4145.57i | −0.158475 | + | 0.274487i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12641.3 | + | 21895.3i | 0.832915 | + | 1.44265i | 0.895717 | + | 0.444624i | \(0.146663\pi\) |
−0.0628026 | + | 0.998026i | \(0.520004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14723.2 | − | 13596.6i | 0.965359 | − | 0.891490i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5179.38 | + | 1885.14i | −0.337948 | + | 0.123003i | −0.505419 | − | 0.862874i | \(-0.668662\pi\) |
0.167471 | + | 0.985877i | \(0.446440\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2252.52 | + | 12774.7i | 0.146263 | + | 0.829497i | 0.966345 | + | 0.257251i | \(0.0828166\pi\) |
−0.820082 | + | 0.572246i | \(0.806072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16630.3 | − | 8904.25i | 1.07464 | − | 0.575387i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2226.74 | − | 12628.5i | −0.143198 | − | 0.812117i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −32468.9 | + | 11817.7i | −2.07801 | + | 0.756334i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2250.84 | + | 700.115i | 0.143365 | + | 0.0445931i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10135.7 | − | 17555.5i | −0.642507 | − | 1.11285i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7534.06 | − | 13049.4i | 0.475319 | − | 0.823276i | −0.524282 | − | 0.851545i | \(-0.675666\pi\) |
0.999600 | + | 0.0282687i | \(0.00899939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6674.67 | + | 5080.71i | 0.419106 | + | 0.319021i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5705.70 | − | 32358.6i | 0.356573 | − | 2.02222i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2939.96 | + | 2466.92i | −0.182866 | + | 0.153443i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4615.20 | + | 10100.8i | −0.285719 | + | 0.625326i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 859.168 | + | 312.712i | 0.0529409 | + | 0.0192689i | 0.368355 | − | 0.929685i | \(-0.379921\pi\) |
−0.315414 | + | 0.948954i | \(0.602143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15011.2 | + | 12595.9i | 0.920657 | + | 0.772523i | 0.974116 | − | 0.226047i | \(-0.0725804\pi\) |
−0.0534597 | + | 0.998570i | \(0.517025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6251.87 | + | 297.223i | −0.381654 | + | 0.0181444i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13286.6 | 0.807339 | 0.403670 | − | 0.914905i | \(-0.367735\pi\) | ||||
0.403670 | + | 0.914905i | \(0.367735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6438.08 | 0.389394 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12629.8 | − | 600.438i | 0.760369 | − | 0.0361490i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4349.80 | + | 3649.92i | 0.260675 | + | 0.218733i | 0.763753 | − | 0.645509i | \(-0.223355\pi\) |
−0.503078 | + | 0.864241i | \(0.667799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40721.6 | + | 14821.5i | 2.42920 | + | 0.884156i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18873.1 | + | 26514.1i | 1.12071 | + | 1.57445i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9412.25 | + | 7897.82i | −0.556372 | + | 0.466852i | −0.877092 | − | 0.480322i | \(-0.840520\pi\) |
0.320720 | + | 0.947174i | \(0.396075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1355.06 | − | 7684.91i | 0.0797362 | − | 0.452206i | −0.918633 | − | 0.395113i | \(-0.870706\pi\) |
0.998369 | − | 0.0570936i | \(-0.0181833\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5579.68 | − | 4247.21i | −0.326843 | − | 0.248790i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −730.465 | + | 1265.20i | −0.0425958 | + | 0.0737781i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9702.19 | − | 16804.7i | −0.563224 | − | 0.975533i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17252.4 | − | 5366.29i | −0.997034 | − | 0.310124i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19367.3 | − | 7049.10i | 1.11425 | − | 0.405555i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4431.14 | + | 25130.2i | 0.253800 | + | 1.43937i | 0.799133 | + | 0.601154i | \(0.205292\pi\) |
−0.545333 | + | 0.838220i | \(0.683597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12905.7 | + | 39332.5i | 0.735914 | + | 2.24283i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4224.47 | − | 23958.2i | −0.239822 | − | 1.36010i | −0.832216 | − | 0.554451i | \(-0.812928\pi\) |
0.592394 | − | 0.805648i | \(-0.298183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3388.23 | − | 1233.21i | 0.191499 | − | 0.0697001i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2858.97 | − | 2640.20i | 0.160875 | − | 0.148565i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12807.8 | − | 22183.8i | −0.717535 | − | 1.24281i | −0.961973 | − | 0.273143i | \(-0.911937\pi\) |
0.244438 | − | 0.969665i | \(-0.421397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10287.6 | + | 17818.7i | −0.573825 | + | 0.993894i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2383.00 | + | 18658.7i | −0.132339 | + | 1.03621i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −445.099 | + | 2524.28i | −0.0246109 | + | 0.139575i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7664.03 | + | 6430.89i | −0.421930 | + | 0.354041i | −0.828897 | − | 0.559402i | \(-0.811031\pi\) |
0.406967 | + | 0.913443i | \(0.366586\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13659.2 | − | 6498.64i | 0.748729 | − | 0.356224i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2894.31 | − | 1053.44i | −0.157968 | − | 0.0574956i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12924.4 | − | 10844.9i | −0.702365 | − | 0.589354i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9725.30 | + | 18860.1i | −0.526244 | + | 1.02053i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18295.6 | 0.985758 | 0.492879 | − | 0.870098i | \(-0.335945\pi\) | ||||
0.492879 | + | 0.870098i | \(0.335945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1717.78 | −0.0921581 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18307.9 | − | 28493.5i | −0.978035 | − | 1.52217i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4486.75 | − | 3764.83i | −0.238673 | − | 0.200270i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8676.97 | + | 3158.16i | 0.459620 | + | 0.167288i | 0.561445 | − | 0.827514i | \(-0.310246\pi\) |
−0.101824 | + | 0.994802i | \(0.532468\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 820.187 | + | 2968.81i | 0.0432622 | + | 0.156595i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26713.7 | + | 22415.4i | −1.40313 | + | 1.17737i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3198.74 | + | 18141.0i | −0.167309 | + | 0.948858i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14125.8 | − | 5915.30i | 0.735759 | − | 0.308105i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8925.75 | − | 15459.9i | 0.462968 | − | 0.801885i | −0.536139 | − | 0.844130i | \(-0.680118\pi\) |
0.999107 | + | 0.0422449i | \(0.0134510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4905.71 | − | 8496.93i | −0.253395 | − | 0.438894i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −114.460 | − | 506.997i | −0.00588771 | − | 0.0260794i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40013.4 | − | 14563.7i | 2.04974 | − | 0.746044i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1140.17 | − | 6466.24i | −0.0581660 | − | 0.329876i | 0.941814 | − | 0.336133i | \(-0.109119\pi\) |
−0.999980 | + | 0.00625749i | \(0.998008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18888.8 | − | 5534.66i | 0.959652 | − | 0.281190i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 914.977 | + | 5189.09i | 0.0462950 | + | 0.262552i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11643.6 | + | 4237.94i | −0.586723 | + | 0.213550i | −0.618287 | − | 0.785952i | \(-0.712173\pi\) |
0.0315647 | + | 0.999502i | \(0.489951\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5979.73 | − | 26487.0i | −0.300089 | − | 1.32923i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 176.069 | + | 304.961i | 0.00879998 | + | 0.0152420i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14098.2 | + | 24418.8i | −0.701773 | + | 1.21551i | 0.266070 | + | 0.963954i | \(0.414275\pi\) |
−0.967843 | + | 0.251554i | \(0.919059\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −548.093 | + | 229.518i | −0.0271723 | + | 0.0113786i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4020.09 | + | 22799.1i | −0.198497 | + | 1.12573i | 0.708854 | + | 0.705355i | \(0.249213\pi\) |
−0.907351 | + | 0.420375i | \(0.861899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31920.7 | + | 26784.6i | −1.56978 | + | 1.31720i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10184.6 | − | 36864.8i | −0.498840 | − | 1.80564i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1933.83 | − | 703.855i | −0.0943398 | − | 0.0343369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16955.6 | − | 14227.4i | −0.823859 | − | 0.691300i | 0.130013 | − | 0.991512i | \(-0.458498\pi\) |
−0.953872 | + | 0.300212i | \(0.902942\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12611.0 | + | 19627.2i | 0.610319 | + | 0.949872i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26712.2 | −1.28762 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22131.8 | 1.06261 | 0.531303 | − | 0.847182i | \(-0.321703\pi\) | ||||
0.531303 | + | 0.847182i | \(0.321703\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19119.9 | + | 37078.9i | −0.914374 | + | 1.77323i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29295.5 | + | 24581.8i | 1.39548 | + | 1.17095i | 0.963064 | + | 0.269274i | \(0.0867837\pi\) |
0.432417 | + | 0.901674i | \(0.357661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18223.1 | + | 6632.68i | 0.864642 | + | 0.314704i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 44801.0 | − | 21315.0i | 2.11737 | − | 1.00738i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1243.23 | + | 1043.20i | −0.0585274 | + | 0.0491103i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7186.45 | − | 40756.4i | 0.336996 | − | 1.91120i | −0.0695665 | − | 0.997577i | \(-0.522162\pi\) |
0.406563 | − | 0.913623i | \(-0.366727\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2037.15 | + | 15950.8i | −0.0951573 | + | 0.745076i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11033.1 | + | 19110.0i | −0.513370 | + | 0.889182i | 0.486510 | + | 0.873675i | \(0.338270\pi\) |
−0.999880 | + | 0.0155073i | \(0.995064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38262.2 | − | 66272.1i | −1.77344 | − | 3.07169i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8098.15 | + | 7478.48i | −0.373899 | + | 0.345288i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1343.46 | + | 488.981i | −0.0617903 | + | 0.0224898i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4264.73 | − | 24186.5i | −0.195396 | − | 1.10814i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6312.24 | − | 19237.7i | −0.288098 | − | 0.878031i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6958.49 | − | 39463.5i | −0.316381 | − | 1.79429i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30214.2 | − | 10997.1i | 1.36851 | − | 0.498098i | 0.449838 | − | 0.893110i | \(-0.351482\pi\) |
0.918676 | + | 0.395012i | \(0.129260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26655.0 | + | 8290.96i | 1.20272 | + | 0.374101i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 774.822 | + | 1342.03i | 0.0348287 | + | 0.0603250i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2597.73 | + | 4499.40i | −0.116328 | + | 0.201486i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14430.4 | − | 10984.3i | −0.643765 | − | 0.490029i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2366.52 | − | 13421.2i | 0.105178 | − | 0.596492i | −0.885972 | − | 0.463740i | \(-0.846507\pi\) |
0.991149 | − | 0.132753i | \(-0.0423816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21841.7 | + | 18327.4i | −0.967091 | + | 0.811485i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21399.6 | + | 30063.5i | 0.943965 | + | 1.32614i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −67634.0 | − | 24616.8i | −2.97229 | − | 1.08183i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19806.7 | − | 16619.8i | −0.867199 | − | 0.727667i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18260.3 | − | 868.122i | 0.796522 | − | 0.0378678i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36411.3 | −1.58239 | −0.791194 | − | 0.611565i | \(-0.790540\pi\) | ||||
−0.791194 | + | 0.611565i | \(0.790540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1772.50 | 0.0767460 | 0.0383730 | − | 0.999263i | \(-0.487782\pi\) | ||||
0.0383730 | + | 0.999263i | \(0.487782\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 875.141 | − | 41.6055i | 0.0377522 | − | 0.00179479i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4780.49 | + | 4011.30i | 0.205464 | + | 0.172405i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 419.574 | + | 152.712i | 0.0179670 | + | 0.00653945i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1584.66 | + | 3468.20i | −0.0676100 | + | 0.147971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17618.5 | + | 14783.6i | −0.748951 | + | 0.628444i | −0.935225 | − | 0.354053i | \(-0.884803\pi\) |
0.186274 | + | 0.982498i | \(0.440359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 150.455 | − | 853.275i | 0.00637248 | − | 0.0361401i | −0.981456 | − | 0.191689i | \(-0.938604\pi\) |
0.987828 | + | 0.155549i | \(0.0497146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −72844.9 | − | 55449.0i | −3.07410 | − | 2.33998i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4302.27 | − | 7451.75i | 0.180900 | − | 0.313328i | −0.761287 | − | 0.648415i | \(-0.775432\pi\) |
0.942187 | + | 0.335086i | \(0.108766\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −178.808 | − | 309.705i | −0.00749127 | − | 0.0129753i | 0.862255 | − | 0.506474i | \(-0.169051\pi\) |
−0.869747 | + | 0.493498i | \(0.835718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13633.9 | − | 4240.76i | −0.569137 | − | 0.177028i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21480.9 | + | 7818.43i | −0.893482 | + | 0.325201i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8955.10 | + | 50786.9i | 0.371143 | + | 2.10486i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32077.5 | + | 17175.1i | −1.32469 | + | 0.709267i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5844.26 | + | 33144.5i | 0.240484 | + | 1.36385i | 0.830750 | + | 0.556645i | \(0.187912\pi\) |
−0.590266 | + | 0.807209i | \(0.700977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3347.45 | − | 1218.37i | 0.137253 | − | 0.0499558i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19178.3 | − | 17710.8i | 0.783555 | − | 0.723598i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20192.4 | + | 34974.2i | 0.822058 | + | 1.42385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10482.1 | + | 18155.6i | −0.425231 | + | 0.736521i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 241.348 | − | 1889.74i | 0.00975621 | − | 0.0763906i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5279.17 | − | 29939.7i | 0.212653 | − | 1.20602i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23937.0 | − | 20085.6i | 0.960830 | − | 0.806232i | −0.0202575 | − | 0.999795i | \(-0.506449\pi\) |
0.981088 | + | 0.193562i | \(0.0620042\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 333.969 | − | 4190.88i | 0.0133585 | − | 0.167631i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22316.3 | + | 8122.48i | 0.889511 | + | 0.323756i | 0.746042 | − | 0.665899i | \(-0.231952\pi\) |
0.143469 | + | 0.989655i | \(0.454174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5888.94 | + | 4941.40i | 0.233909 | + | 0.196273i | 0.752207 | − | 0.658927i | \(-0.228990\pi\) |
−0.518297 | + | 0.855200i | \(0.673434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4204.71 | + | 8154.10i | −0.166430 | + | 0.322754i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48145.1 | 1.89905 | 0.949525 | − | 0.313692i | \(-0.101566\pi\) | ||||
0.949525 | + | 0.313692i | \(0.101566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11147.4 | −0.438178 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8778.00 | − | 13661.7i | −0.343848 | − | 0.535149i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5217.96 | − | 4378.39i | −0.203690 | − | 0.170917i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −83.4143 | − | 30.3603i | −0.00324499 | − | 0.00118108i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7280.00 | + | 7393.65i | −0.282235 | + | 0.286641i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25051.0 | − | 21020.2i | 0.967859 | − | 0.812130i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2077.55 | − | 11782.4i | 0.0799929 | − | 0.453662i | −0.918332 | − | 0.395810i | \(-0.870464\pi\) |
0.998325 | − | 0.0578519i | \(-0.0184251\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5615.77 | + | 2351.65i | −0.215489 | + | 0.0902379i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2602.29 | + | 4507.29i | −0.0995156 | + | 0.172366i | −0.911484 | − | 0.411335i | \(-0.865063\pi\) |
0.811969 | + | 0.583701i | \(0.198396\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 558.434 | + | 967.235i | 0.0212829 | + | 0.0368630i | 0.876471 | − | 0.481455i | \(-0.159892\pi\) |
−0.855188 | + | 0.518318i | \(0.826558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2528.67 | − | 11200.7i | −0.0960456 | − | 0.425430i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36086.5 | − | 13134.4i | 1.36603 | − | 0.497193i | 0.448114 | − | 0.893977i | \(-0.352096\pi\) |
0.917912 | + | 0.396784i | \(0.129874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2611.96 | + | 14813.2i | 0.0985404 | + | 0.558851i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27460.3 | + | 33774.9i | −1.03250 | + | 1.26992i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 419.552 | + | 2379.40i | 0.0157220 | + | 0.0891642i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 57307.2 | − | 20858.1i | 2.14030 | − | 0.779005i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2315.92 | − | 10258.3i | −0.0862054 | − | 0.381844i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18714.2 | + | 32413.9i | 0.694274 | + | 1.20252i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7633.72 | + | 13222.0i | −0.282260 | + | 0.488888i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2642.85 | − | 1106.72i | 0.0973961 | − | 0.0407854i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46.0759 | − | 261.309i | 0.00169239 | − | 0.00959803i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26611.2 | − | 22329.4i | 0.974211 | − | 0.817460i | −0.00899504 | − | 0.999960i | \(-0.502863\pi\) |
0.983206 | + | 0.182500i | \(0.0584188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16313.9 | + | 4236.16i | 0.595269 | + | 0.154571i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7266.12 | + | 2644.65i | 0.264256 | + | 0.0961814i | 0.470750 | − | 0.882266i | \(-0.343983\pi\) |
−0.206494 | + | 0.978448i | \(0.566205\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 64793.2 | + | 54368.0i | 2.34868 | + | 1.97078i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19870.5 | − | 30925.5i | −0.717922 | − | 1.11734i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19838.0 | −0.714404 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3458.97 | 0.124158 | 0.0620788 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620788 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20061.3 | + | 38904.6i | −0.717745 | + | 1.39191i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4742.61 | + | 3979.52i | 0.169128 | + | 0.141915i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62690.5 | + | 22817.5i | 2.22838 | + | 0.811064i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23253.1 | + | 16015.1i | 0.823877 | + | 0.567426i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26175.9 | − | 21964.2i | 0.924440 | − | 0.775697i | −0.0503710 | − | 0.998731i | \(-0.516040\pi\) |
0.974811 | + | 0.223033i | \(0.0715959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −336.373 | + | 1907.66i | −0.0118412 | + | 0.0671548i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4127.60 | − | 32318.9i | 0.144836 | − | 1.13405i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −54860.4 | + | 95020.9i | −1.91885 | + | 3.32355i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10113.2 | − | 17516.6i | −0.352598 | − | 0.610717i | 0.634106 | − | 0.773246i | \(-0.281368\pi\) |
−0.986704 | + | 0.162529i | \(0.948035\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7782.37 | + | 7186.87i | −0.270466 | + | 0.249771i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10035.5 | + | 3652.62i | −0.347659 | + | 0.126538i | −0.509947 | − | 0.860206i | \(-0.670335\pi\) |
0.162288 | + | 0.986744i | \(0.448113\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4393.80 | − | 24918.5i | −0.151730 | − | 0.860505i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16670.9 | − | 21211.1i | −0.573867 | − | 0.730156i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7980.48 | − | 45259.5i | −0.273844 | − | 1.55305i | −0.742608 | − | 0.669726i | \(-0.766412\pi\) |
0.468764 | − | 0.883323i | \(-0.344699\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17049.3 | − | 6205.44i | 0.583187 | − | 0.212263i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26061.1 | − | 8106.21i | −0.888632 | − | 0.276406i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11800.2 | + | 20438.5i | 0.401096 | + | 0.694718i | 0.993858 | − | 0.110659i | \(-0.0352961\pi\) |
−0.592763 | + | 0.805377i | \(0.701963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6325.40 | + | 10955.9i | −0.214330 | + | 0.371231i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35628.7 | + | 27120.3i | 1.20346 | + | 0.916066i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1635.59 | − | 9275.88i | 0.0550739 | − | 0.312340i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28705.7 | − | 24087.0i | 0.963571 | − | 0.808532i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5895.47 | − | 561.828i | 0.197278 | − | 0.0188003i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39779.6 | + | 14478.6i | 1.32699 | + | 0.482987i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30114.9 | − | 25269.4i | −1.00148 | − | 0.840339i | −0.0142886 | − | 0.999898i | \(-0.504548\pi\) |
−0.987188 | + | 0.159559i | \(0.948993\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3535.33 | + | 168.074i | −0.117204 | + | 0.00557206i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20618.9 | −0.681455 | −0.340728 | − | 0.940162i | \(-0.610673\pi\) | ||||
−0.340728 | + | 0.940162i | \(0.610673\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1410.00 | 0.0464568 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23051.5 | − | 1095.90i | 0.757167 | − | 0.0359968i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26281.1 | + | 22052.5i | 0.860602 | + | 0.722131i | 0.962098 | − | 0.272705i | \(-0.0879184\pi\) |
−0.101496 | + | 0.994836i | \(0.532363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −76687.9 | − | 27912.1i | −2.50353 | − | 0.911211i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −55555.1 | + | 5294.30i | −1.80809 | + | 0.172308i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30850.4 | + | 25886.6i | −1.00099 | + | 0.839932i | −0.987122 | − | 0.159971i | \(-0.948860\pi\) |
−0.0138709 | + | 0.999904i | \(0.504415\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2137.96 | − | 12125.0i | 0.0691585 | − | 0.392217i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12336.8 | + | 9390.71i | 0.397858 | + | 0.302846i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3951.14 | + | 6843.57i | −0.127036 | + | 0.220033i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10507.4 | + | 18199.3i | 0.336809 | + | 0.583370i | 0.983831 | − | 0.179102i | \(-0.0573192\pi\) |
−0.647022 | + | 0.762471i | \(0.723986\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27800.5 | − | 8647.26i | −0.888442 | − | 0.276347i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −71647.4 | + | 26077.5i | −2.28279 | + | 0.830868i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1859.20 | − | 10544.0i | −0.0590586 | − | 0.334938i | 0.940935 | − | 0.338588i | \(-0.109949\pi\) |
−0.999993 | + | 0.00365000i | \(0.998838\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11798.0 | − | 29445.8i | 0.373645 | − | 0.932555i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.4.i.a.13.9 | ✓ | 54 | |
3.2 | odd | 2 | 324.4.i.a.253.1 | 54 | |||
27.2 | odd | 18 | 324.4.i.a.73.1 | 54 | |||
27.25 | even | 9 | inner | 108.4.i.a.25.9 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.13.9 | ✓ | 54 | 1.1 | even | 1 | trivial | |
108.4.i.a.25.9 | yes | 54 | 27.25 | even | 9 | inner | |
324.4.i.a.73.1 | 54 | 27.2 | odd | 18 | |||
324.4.i.a.253.1 | 54 | 3.2 | odd | 2 |