Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(143,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.143");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.i (of order \(6\), degree \(2\), 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: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 143.17 | ||
Character | \(\chi\) | \(=\) | 189.143 |
Dual form | 189.4.i.a.152.6 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.46625i | 1.22550i | 0.790275 | + | 0.612752i | \(0.209938\pi\) | ||||
−0.790275 | + | 0.612752i | \(0.790062\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.01488 | −0.501860 | ||||||||
\(5\) | −9.02701 | + | 15.6352i | −0.807400 | + | 1.39846i | 0.107259 | + | 0.994231i | \(0.465793\pi\) |
−0.914659 | + | 0.404227i | \(0.867541\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.1650 | − | 3.61017i | −0.980817 | − | 0.194931i | ||||
\(8\) | 13.8134i | 0.610473i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −54.1956 | − | 31.2898i | −1.71382 | − | 0.989472i | ||||
\(11\) | 10.2147 | − | 5.89746i | 0.279986 | − | 0.161650i | −0.353431 | − | 0.935461i | \(-0.614985\pi\) |
0.633417 | + | 0.773810i | \(0.281652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.9746 | − | 26.5435i | 0.980851 | − | 0.566295i | 0.0783244 | − | 0.996928i | \(-0.475043\pi\) |
0.902527 | + | 0.430633i | \(0.141710\pi\) | |||||||
\(14\) | 12.5137 | − | 62.9644i | 0.238888 | − | 1.20200i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.9998 | −1.25000 | ||||||||
\(17\) | −5.93967 | + | 10.2878i | −0.0847401 | + | 0.146774i | −0.905280 | − | 0.424814i | \(-0.860339\pi\) |
0.820540 | + | 0.571589i | \(0.193673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.1984 | + | 7.04273i | −0.147289 | + | 0.0850376i | −0.571834 | − | 0.820370i | \(-0.693768\pi\) |
0.424544 | + | 0.905407i | \(0.360434\pi\) | |||||||
\(20\) | 36.2423 | − | 62.7736i | 0.405202 | − | 0.701830i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 20.4421 | + | 35.4067i | 0.198103 | + | 0.343124i | ||||
\(23\) | −139.665 | − | 80.6357i | −1.26618 | − | 0.731031i | −0.291919 | − | 0.956443i | \(-0.594294\pi\) |
−0.974263 | + | 0.225412i | \(0.927627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −100.474 | − | 174.026i | −0.803790 | − | 1.39220i | ||||
\(26\) | 92.0062 | + | 159.359i | 0.693997 | + | 1.20204i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 72.9302 | + | 14.4944i | 0.492233 | + | 0.0978278i | ||||
\(29\) | −131.443 | − | 75.8889i | −0.841670 | − | 0.485939i | 0.0161612 | − | 0.999869i | \(-0.494855\pi\) |
−0.857832 | + | 0.513931i | \(0.828189\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 90.1597i | − | 0.522360i | −0.965290 | − | 0.261180i | \(-0.915888\pi\) | ||
0.965290 | − | 0.261180i | \(-0.0841116\pi\) | |||||||
\(32\) | − | 166.792i | − | 0.921403i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −35.6601 | − | 20.5884i | −0.179872 | − | 0.103849i | ||||
\(35\) | 220.421 | − | 251.425i | 1.06451 | − | 1.21424i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 185.189 | + | 320.757i | 0.822835 | + | 1.42519i | 0.903563 | + | 0.428456i | \(0.140942\pi\) |
−0.0807273 | + | 0.996736i | \(0.525724\pi\) | |||||||
\(38\) | −24.4119 | − | 42.2826i | −0.104214 | − | 0.180504i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −215.976 | − | 124.694i | −0.853721 | − | 0.492896i | ||||
\(41\) | 129.206 | + | 223.791i | 0.492161 | + | 0.852447i | 0.999959 | − | 0.00902843i | \(-0.00287388\pi\) |
−0.507798 | + | 0.861476i | \(0.669541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −173.288 | + | 300.144i | −0.614563 | + | 1.06446i | 0.375897 | + | 0.926661i | \(0.377334\pi\) |
−0.990461 | + | 0.137794i | \(0.955999\pi\) | |||||||
\(44\) | −41.0108 | + | 23.6776i | −0.140514 | + | 0.0811257i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 279.503 | − | 484.114i | 0.895881 | − | 1.55171i | ||||
\(47\) | 71.6618 | 0.222403 | 0.111202 | − | 0.993798i | \(-0.464530\pi\) | ||||
0.111202 | + | 0.993798i | \(0.464530\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 316.933 | + | 131.157i | 0.924004 | + | 0.382383i | ||||
\(50\) | 603.216 | − | 348.267i | 1.70615 | − | 0.985047i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −184.583 | + | 106.569i | −0.492250 | + | 0.284201i | ||||
\(53\) | −143.612 | − | 82.9146i | −0.372201 | − | 0.214890i | 0.302219 | − | 0.953239i | \(-0.402273\pi\) |
−0.674420 | + | 0.738348i | \(0.735606\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 212.946i | 0.522065i | ||||||||
\(56\) | 49.8687 | − | 250.921i | 0.119000 | − | 0.598762i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 263.050 | − | 455.616i | 0.595520 | − | 1.03147i | ||||
\(59\) | −575.335 | −1.26953 | −0.634765 | − | 0.772706i | \(-0.718903\pi\) | ||||
−0.634765 | + | 0.772706i | \(0.718903\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 496.392i | − | 1.04191i | −0.853585 | − | 0.520954i | \(-0.825576\pi\) | ||
0.853585 | − | 0.520954i | \(-0.174424\pi\) | |||||||
\(62\) | 312.516 | 0.640154 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −61.8567 | −0.120814 | ||||||||
\(65\) | 958.432i | 1.82891i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −700.848 | −1.27794 | −0.638971 | − | 0.769231i | \(-0.720640\pi\) | ||||
−0.638971 | + | 0.769231i | \(0.720640\pi\) | |||||||
\(68\) | 23.8471 | − | 41.3043i | 0.0425276 | − | 0.0736600i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 871.501 | + | 764.035i | 1.48806 | + | 1.30457i | ||||
\(71\) | 1134.69i | 1.89666i | 0.317289 | + | 0.948329i | \(0.397228\pi\) | ||||
−0.317289 | + | 0.948329i | \(0.602772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 281.645 | + | 162.608i | 0.451563 | + | 0.260710i | 0.708490 | − | 0.705721i | \(-0.249377\pi\) |
−0.256927 | + | 0.966431i | \(0.582710\pi\) | |||||||
\(74\) | −1111.82 | + | 641.911i | −1.74658 | + | 1.00839i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 48.9750 | − | 28.2757i | 0.0739186 | − | 0.0426769i | ||||
\(77\) | −206.841 | + | 70.2505i | −0.306126 | + | 0.103971i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −523.879 | −0.746088 | −0.373044 | − | 0.927814i | \(-0.621686\pi\) | ||||
−0.373044 | + | 0.927814i | \(0.621686\pi\) | |||||||
\(80\) | 722.159 | − | 1250.82i | 1.00925 | − | 1.74807i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −775.717 | + | 447.860i | −1.04468 | + | 0.603145i | ||||
\(83\) | −410.436 | + | 710.896i | −0.542786 | + | 0.940133i | 0.455957 | + | 0.890002i | \(0.349297\pi\) |
−0.998743 | + | 0.0501309i | \(0.984036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −107.235 | − | 185.736i | −0.136838 | − | 0.237011i | ||||
\(86\) | −1040.37 | − | 600.661i | −1.30449 | − | 0.753150i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 81.4641 | + | 141.100i | 0.0986830 | + | 0.170924i | ||||
\(89\) | 181.259 | + | 313.950i | 0.215881 | + | 0.373917i | 0.953545 | − | 0.301251i | \(-0.0974043\pi\) |
−0.737664 | + | 0.675168i | \(0.764071\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −930.955 | + | 316.186i | −1.07242 | + | 0.364234i | ||||
\(92\) | 560.739 | + | 323.743i | 0.635446 | + | 0.366875i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 248.398i | 0.272556i | ||||||||
\(95\) | − | 254.299i | − | 0.274637i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 273.568 | + | 157.944i | 0.286357 | + | 0.165328i | 0.636298 | − | 0.771444i | \(-0.280465\pi\) |
−0.349941 | + | 0.936772i | \(0.613798\pi\) | |||||||
\(98\) | −454.624 | + | 1098.57i | −0.468611 | + | 1.13237i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 403.390 | + | 698.691i | 0.403390 | + | 0.698691i | ||||
\(101\) | −376.181 | − | 651.565i | −0.370608 | − | 0.641912i | 0.619051 | − | 0.785351i | \(-0.287517\pi\) |
−0.989659 | + | 0.143439i | \(0.954184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1521.17 | + | 878.247i | 1.45520 | + | 0.840158i | 0.998769 | − | 0.0496033i | \(-0.0157957\pi\) |
0.456427 | + | 0.889761i | \(0.349129\pi\) | |||||||
\(104\) | 366.656 | + | 635.067i | 0.345708 | + | 0.598783i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 287.402 | − | 497.796i | 0.263349 | − | 0.456134i | ||||
\(107\) | −1162.99 | + | 671.452i | −1.05075 | + | 0.606652i | −0.922860 | − | 0.385137i | \(-0.874154\pi\) |
−0.127892 | + | 0.991788i | \(0.540821\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −40.4130 | + | 69.9973i | −0.0355125 | + | 0.0615094i | −0.883235 | − | 0.468930i | \(-0.844640\pi\) |
0.847723 | + | 0.530439i | \(0.177973\pi\) | |||||||
\(110\) | −738.123 | −0.639793 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1453.19 | + | 288.812i | 1.22602 | + | 0.243663i | ||||
\(113\) | 1113.30 | − | 642.766i | 0.926821 | − | 0.535100i | 0.0410161 | − | 0.999158i | \(-0.486941\pi\) |
0.885805 | + | 0.464058i | \(0.153607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2521.52 | − | 1455.80i | 2.04463 | − | 1.18047i | ||||
\(116\) | 527.730 | + | 304.685i | 0.422401 | + | 0.243873i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1994.25i | − | 1.55581i | ||||||
\(119\) | 145.035 | − | 165.435i | 0.111725 | − | 0.127440i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −595.940 | + | 1032.20i | −0.447738 | + | 0.775506i | ||||
\(122\) | 1720.62 | 1.27686 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 361.980i | 0.262151i | ||||||||
\(125\) | 1371.16 | 0.981119 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −817.285 | −0.571042 | −0.285521 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285521 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(128\) | − | 1548.74i | − | 1.06946i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3322.16 | −2.24133 | ||||||||
\(131\) | 457.664 | − | 792.697i | 0.305239 | − | 0.528689i | −0.672076 | − | 0.740482i | \(-0.734597\pi\) |
0.977314 | + | 0.211793i | \(0.0679304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 247.009 | − | 83.8930i | 0.161040 | − | 0.0546951i | ||||
\(134\) | − | 2429.31i | − | 1.56612i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −142.110 | − | 82.0472i | −0.0896016 | − | 0.0517315i | ||||
\(137\) | −641.359 | + | 370.289i | −0.399963 | + | 0.230919i | −0.686468 | − | 0.727160i | \(-0.740840\pi\) |
0.286505 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 106.660 | − | 61.5800i | 0.0650846 | − | 0.0375766i | −0.467105 | − | 0.884202i | \(-0.654703\pi\) |
0.532189 | + | 0.846625i | \(0.321370\pi\) | |||||||
\(140\) | −884.964 | + | 1009.44i | −0.534237 | + | 0.609380i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3933.11 | −2.32436 | ||||||||
\(143\) | 313.078 | − | 542.267i | 0.183083 | − | 0.317110i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2373.08 | − | 1370.10i | 1.35913 | − | 0.784694i | ||||
\(146\) | −563.640 | + | 976.252i | −0.319501 | + | 0.553392i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −743.512 | − | 1287.80i | −0.412948 | − | 0.715247i | ||||
\(149\) | 355.076 | + | 205.003i | 0.195228 | + | 0.112715i | 0.594428 | − | 0.804149i | \(-0.297379\pi\) |
−0.399200 | + | 0.916864i | \(0.630712\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 163.759 | + | 283.639i | 0.0882550 | + | 0.152862i | 0.906774 | − | 0.421618i | \(-0.138538\pi\) |
−0.818519 | + | 0.574480i | \(0.805204\pi\) | |||||||
\(152\) | −97.2842 | − | 168.501i | −0.0519131 | − | 0.0899162i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −243.506 | − | 716.961i | −0.127417 | − | 0.375158i | ||||
\(155\) | 1409.67 | + | 813.872i | 0.730499 | + | 0.421754i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1445.64i | 0.734869i | 0.930049 | + | 0.367435i | \(0.119764\pi\) | ||||
−0.930049 | + | 0.367435i | \(0.880236\pi\) | |||||||
\(158\) | − | 1815.89i | − | 0.914334i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2607.83 | + | 1505.63i | 1.28854 | + | 0.743941i | ||||
\(161\) | 2245.91 | + | 1968.96i | 1.09939 | + | 0.963825i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −66.7405 | − | 115.598i | −0.0320707 | − | 0.0555481i | 0.849545 | − | 0.527517i | \(-0.176877\pi\) |
−0.881615 | + | 0.471969i | \(0.843544\pi\) | |||||||
\(164\) | −518.746 | − | 898.495i | −0.246996 | − | 0.427809i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2464.14 | − | 1422.67i | −1.15214 | − | 0.665186i | ||||
\(167\) | −1258.17 | − | 2179.21i | −0.582994 | − | 1.00978i | −0.995122 | − | 0.0986499i | \(-0.968548\pi\) |
0.412128 | − | 0.911126i | \(-0.364786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 310.611 | − | 537.994i | 0.141380 | − | 0.244877i | ||||
\(170\) | 643.808 | − | 371.703i | 0.290458 | − | 0.167696i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 695.732 | − | 1205.04i | 0.308425 | − | 0.534207i | ||||
\(173\) | 3687.50 | 1.62055 | 0.810275 | − | 0.586050i | \(-0.199318\pi\) | ||||
0.810275 | + | 0.586050i | \(0.199318\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1196.84 | + | 3523.90i | 0.516987 | + | 1.52218i | ||||
\(176\) | −817.174 | + | 471.796i | −0.349982 | + | 0.202062i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1088.23 | + | 628.289i | −0.458237 | + | 0.264563i | ||||
\(179\) | −1545.34 | − | 892.205i | −0.645276 | − | 0.372550i | 0.141368 | − | 0.989957i | \(-0.454850\pi\) |
−0.786644 | + | 0.617407i | \(0.788183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1168.16i | − | 0.479717i | −0.970808 | − | 0.239859i | \(-0.922899\pi\) | ||
0.970808 | − | 0.239859i | \(-0.0771011\pi\) | |||||||
\(182\) | −1095.98 | − | 3226.92i | −0.446370 | − | 1.31426i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1113.86 | − | 1929.25i | 0.446274 | − | 0.772970i | ||||
\(185\) | −6686.81 | −2.65743 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 140.116i | 0.0547930i | ||||||||
\(188\) | −287.713 | −0.111615 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 881.464 | 0.336569 | ||||||||
\(191\) | − | 1054.37i | − | 0.399434i | −0.979854 | − | 0.199717i | \(-0.935998\pi\) | ||
0.979854 | − | 0.199717i | \(-0.0640022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1225.74 | 0.457155 | 0.228578 | − | 0.973526i | \(-0.426593\pi\) | ||||
0.228578 | + | 0.973526i | \(0.426593\pi\) | |||||||
\(194\) | −547.475 | + | 948.254i | −0.202610 | + | 0.350931i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1272.45 | − | 526.580i | −0.463720 | − | 0.191902i | ||||
\(197\) | − | 799.520i | − | 0.289155i | −0.989494 | − | 0.144577i | \(-0.953818\pi\) | ||
0.989494 | − | 0.144577i | \(-0.0461822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2275.00 | − | 1313.47i | −0.810406 | − | 0.467888i | 0.0366911 | − | 0.999327i | \(-0.488318\pi\) |
−0.847097 | + | 0.531439i | \(0.821652\pi\) | |||||||
\(200\) | 2403.89 | − | 1387.89i | 0.849903 | − | 0.490692i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2258.49 | − | 1303.94i | 0.786666 | − | 0.454182i | ||||
\(203\) | 2113.70 | + | 1853.05i | 0.730800 | + | 0.640684i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4665.37 | −1.58948 | ||||||||
\(206\) | −3044.22 | + | 5272.75i | −1.02962 | + | 1.78335i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3677.96 | + | 2123.47i | −1.22606 | + | 0.707867i | ||||
\(209\) | −83.0685 | + | 143.879i | −0.0274927 | + | 0.0476187i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1004.95 | − | 1740.62i | −0.327883 | − | 0.567911i | 0.654208 | − | 0.756315i | \(-0.273002\pi\) |
−0.982092 | + | 0.188404i | \(0.939669\pi\) | |||||||
\(212\) | 576.586 | + | 332.892i | 0.186793 | + | 0.107845i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2327.42 | − | 4031.21i | −0.743454 | − | 1.28770i | ||||
\(215\) | −3128.55 | − | 5418.81i | −0.992397 | − | 1.71888i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −325.492 | + | 1637.75i | −0.101824 | + | 0.512340i | ||||
\(218\) | −242.628 | − | 140.081i | −0.0753800 | − | 0.0435207i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 854.951i | − | 0.262004i | ||||||
\(221\) | 630.638i | 0.191952i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3897.23 | + | 2250.07i | 1.17030 | + | 0.675676i | 0.953752 | − | 0.300595i | \(-0.0971854\pi\) |
0.216553 | + | 0.976271i | \(0.430519\pi\) | |||||||
\(224\) | −602.146 | + | 3029.77i | −0.179610 | + | 0.903728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2227.99 | + | 3858.98i | 0.655767 | + | 1.13582i | ||||
\(227\) | 1637.48 | + | 2836.19i | 0.478780 | + | 0.829271i | 0.999704 | − | 0.0243318i | \(-0.00774581\pi\) |
−0.520924 | + | 0.853603i | \(0.674412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1155.01 | − | 666.848i | −0.333299 | − | 0.192430i | 0.324006 | − | 0.946055i | \(-0.394970\pi\) |
−0.657305 | + | 0.753625i | \(0.728304\pi\) | |||||||
\(230\) | 5046.16 | + | 8740.20i | 1.44667 | + | 2.50570i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1048.29 | − | 1815.68i | 0.296652 | − | 0.513817i | ||||
\(233\) | −678.031 | + | 391.461i | −0.190641 | + | 0.110066i | −0.592282 | − | 0.805730i | \(-0.701773\pi\) |
0.401642 | + | 0.915797i | \(0.368440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −646.892 | + | 1120.45i | −0.179568 | + | 0.311022i | ||||
\(236\) | 2309.90 | 0.637126 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 573.438 | + | 502.726i | 0.156178 | + | 0.136920i | ||||
\(239\) | 4512.91 | − | 2605.53i | 1.22141 | − | 0.705179i | 0.256188 | − | 0.966627i | \(-0.417534\pi\) |
0.965217 | + | 0.261449i | \(0.0842002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2328.71 | + | 1344.48i | −0.622428 | + | 0.359359i | −0.777814 | − | 0.628495i | \(-0.783671\pi\) |
0.155386 | + | 0.987854i | \(0.450338\pi\) | |||||||
\(242\) | −3577.86 | − | 2065.68i | −0.950385 | − | 0.548705i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1992.95i | 0.522892i | ||||||||
\(245\) | −4911.63 | + | 3771.37i | −1.28079 | + | 0.983445i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −373.877 | + | 647.574i | −0.0963127 | + | 0.166818i | ||||
\(248\) | 1245.41 | 0.318887 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4752.77i | 1.20237i | ||||||||
\(251\) | 2540.09 | 0.638762 | 0.319381 | − | 0.947626i | \(-0.396525\pi\) | ||||
0.319381 | + | 0.947626i | \(0.396525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1902.18 | −0.472685 | ||||||||
\(254\) | − | 2832.91i | − | 0.699814i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4873.48 | 1.18981 | ||||||||
\(257\) | −1934.85 | + | 3351.25i | −0.469620 | + | 0.813406i | −0.999397 | − | 0.0347315i | \(-0.988942\pi\) |
0.529777 | + | 0.848137i | \(0.322276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2205.97 | − | 6495.11i | −0.529237 | − | 1.55825i | ||||
\(260\) | − | 3847.99i | − | 0.917854i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2747.68 | + | 1586.38i | 0.647910 | + | 0.374071i | ||||
\(263\) | 1965.36 | − | 1134.70i | 0.460796 | − | 0.266041i | −0.251583 | − | 0.967836i | \(-0.580951\pi\) |
0.712379 | + | 0.701795i | \(0.247618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2592.78 | − | 1496.94i | 0.601030 | − | 0.347005i | ||||
\(266\) | 290.794 | + | 856.193i | 0.0670290 | + | 0.197356i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2813.82 | 0.641348 | ||||||||
\(269\) | 1363.14 | − | 2361.02i | 0.308967 | − | 0.535146i | −0.669170 | − | 0.743109i | \(-0.733350\pi\) |
0.978137 | + | 0.207964i | \(0.0666836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5611.15 | − | 3239.60i | 1.25776 | − | 0.726168i | 0.285122 | − | 0.958491i | \(-0.407966\pi\) |
0.972639 | + | 0.232323i | \(0.0746326\pi\) | |||||||
\(272\) | 475.172 | − | 823.023i | 0.105925 | − | 0.183467i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1283.51 | − | 2223.11i | −0.282992 | − | 0.490157i | ||||
\(275\) | −2052.62 | − | 1185.08i | −0.450100 | − | 0.259865i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4101.30 | + | 7103.66i | 0.889615 | + | 1.54086i | 0.840331 | + | 0.542074i | \(0.182361\pi\) |
0.0492841 | + | 0.998785i | \(0.484306\pi\) | |||||||
\(278\) | 213.452 | + | 369.709i | 0.0460503 | + | 0.0797614i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3473.04 | + | 3044.77i | 0.741263 | + | 0.649857i | ||||
\(281\) | −586.668 | − | 338.713i | −0.124547 | − | 0.0719072i | 0.436432 | − | 0.899737i | \(-0.356242\pi\) |
−0.560979 | + | 0.827830i | \(0.689575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2464.61i | 0.517688i | 0.965919 | + | 0.258844i | \(0.0833415\pi\) | ||||
−0.965919 | + | 0.258844i | \(0.916658\pi\) | |||||||
\(284\) | − | 4555.63i | − | 0.951856i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1879.63 | + | 1085.21i | 0.388619 | + | 0.224369i | ||||
\(287\) | −1539.10 | − | 4531.62i | −0.316552 | − | 0.932032i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2385.94 | + | 4132.57i | 0.485638 | + | 0.841150i | ||||
\(290\) | 4749.11 | + | 8225.69i | 0.961645 | + | 1.66562i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1130.77 | − | 652.851i | −0.226621 | − | 0.130840i | ||||
\(293\) | 3122.10 | + | 5407.64i | 0.622510 | + | 1.07822i | 0.989017 | + | 0.147803i | \(0.0472202\pi\) |
−0.366507 | + | 0.930415i | \(0.619446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5193.55 | − | 8995.49i | 1.02502 | − | 1.77538i | ||||
\(296\) | −4430.75 | + | 2558.10i | −0.870041 | + | 0.502319i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −710.591 | + | 1230.78i | −0.138132 | + | 0.239252i | ||||
\(299\) | −8561.41 | −1.65592 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4231.35 | − | 4826.52i | 0.810269 | − | 0.924238i | ||||
\(302\) | −983.162 | + | 567.629i | −0.187333 | + | 0.108157i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 975.867 | − | 563.417i | 0.184111 | − | 0.106297i | ||||
\(305\) | 7761.20 | + | 4480.93i | 1.45707 | + | 0.841237i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6996.15i | 1.30062i | 0.759667 | + | 0.650312i | \(0.225362\pi\) | ||||
−0.759667 | + | 0.650312i | \(0.774638\pi\) | |||||||
\(308\) | 830.440 | − | 282.047i | 0.153632 | − | 0.0521790i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2821.08 | + | 4886.26i | −0.516861 | + | 0.895229i | ||||
\(311\) | −2141.91 | −0.390535 | −0.195268 | − | 0.980750i | \(-0.562558\pi\) | ||||
−0.195268 | + | 0.980750i | \(0.562558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5422.41i | 0.979210i | 0.871944 | + | 0.489605i | \(0.162859\pi\) | ||||
−0.871944 | + | 0.489605i | \(0.837141\pi\) | |||||||
\(314\) | −5010.94 | −0.900585 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2103.31 | 0.374432 | ||||||||
\(317\) | − | 1525.39i | − | 0.270266i | −0.990827 | − | 0.135133i | \(-0.956854\pi\) | ||
0.990827 | − | 0.135133i | \(-0.0431461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1790.21 | −0.314208 | ||||||||
\(320\) | 558.381 | − | 967.144i | 0.0975451 | − | 0.168953i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6824.91 | + | 7784.87i | −1.18117 | + | 1.34731i | ||||
\(323\) | − | 167.326i | − | 0.0288244i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9238.48 | − | 5333.84i | −1.57680 | − | 0.910364i | ||||
\(326\) | 400.691 | − | 231.339i | 0.0680744 | − | 0.0393027i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3091.33 | + | 1784.78i | −0.520396 | + | 0.300451i | ||||
\(329\) | −1301.74 | − | 258.711i | −0.218137 | − | 0.0433532i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 178.450 | 0.0296330 | 0.0148165 | − | 0.999890i | \(-0.495284\pi\) | ||||
0.0148165 | + | 0.999890i | \(0.495284\pi\) | |||||||
\(332\) | 1647.85 | − | 2854.16i | 0.272402 | − | 0.471815i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7553.69 | − | 4361.13i | 1.23748 | − | 0.714462i | ||||
\(335\) | 6326.56 | − | 10957.9i | 1.03181 | − | 1.78715i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1570.00 | − | 2719.33i | −0.253779 | − | 0.439558i | 0.710784 | − | 0.703410i | \(-0.248340\pi\) |
−0.964563 | + | 0.263852i | \(0.915007\pi\) | |||||||
\(338\) | 1864.82 | + | 1076.66i | 0.300098 | + | 0.173261i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 430.535 | + | 745.708i | 0.0686736 | + | 0.118946i | ||||
\(341\) | −531.713 | − | 920.955i | −0.0844396 | − | 0.146254i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5283.59 | − | 3526.65i | −0.831741 | − | 0.555164i | ||||
\(344\) | −4146.02 | − | 2393.71i | −0.649821 | − | 0.375174i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12781.8i | 1.98599i | ||||||||
\(347\) | 3602.36i | 0.557305i | 0.960392 | + | 0.278653i | \(0.0898878\pi\) | ||||
−0.960392 | + | 0.278653i | \(0.910112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4656.87 | − | 2688.64i | −0.714259 | − | 0.412378i | 0.0983769 | − | 0.995149i | \(-0.468635\pi\) |
−0.812636 | + | 0.582772i | \(0.801968\pi\) | |||||||
\(350\) | −12214.7 | + | 4148.55i | −1.86544 | + | 0.633570i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −983.648 | − | 1703.73i | −0.148945 | − | 0.257980i | ||||
\(353\) | 2022.86 | + | 3503.70i | 0.305003 | + | 0.528281i | 0.977262 | − | 0.212035i | \(-0.0680091\pi\) |
−0.672259 | + | 0.740316i | \(0.734676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17741.1 | − | 10242.8i | −2.65240 | − | 1.53136i | ||||
\(356\) | −727.733 | − | 1260.47i | −0.108342 | − | 0.187654i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3092.60 | − | 5356.55i | 0.456562 | − | 0.790788i | ||||
\(359\) | −254.213 | + | 146.770i | −0.0373729 | + | 0.0215772i | −0.518570 | − | 0.855035i | \(-0.673535\pi\) |
0.481197 | + | 0.876612i | \(0.340202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3330.30 | + | 5768.25i | −0.485537 | + | 0.840975i | ||||
\(362\) | 4049.14 | 0.587896 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3737.67 | − | 1269.45i | 0.538206 | − | 0.182794i | ||||
\(365\) | −5084.83 | + | 2935.73i | −0.729184 | + | 0.420994i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6468.89 | + | 3734.81i | −0.920090 | + | 0.531214i | −0.883664 | − | 0.468122i | \(-0.844931\pi\) |
−0.0364264 | + | 0.999336i | \(0.511597\pi\) | |||||||
\(368\) | 11173.2 | + | 6450.84i | 1.58272 | + | 0.913786i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 23178.2i | − | 3.25669i | ||||||
\(371\) | 2309.38 | + | 2024.61i | 0.323172 | + | 0.283322i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6519.35 | − | 11291.8i | 0.904984 | − | 1.56748i | 0.0840463 | − | 0.996462i | \(-0.473216\pi\) |
0.820938 | − | 0.571017i | \(-0.193451\pi\) | |||||||
\(374\) | −485.676 | −0.0671490 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 989.895i | 0.135771i | ||||||||
\(377\) | −8057.42 | −1.10074 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8544.38 | −1.15803 | −0.579017 | − | 0.815315i | \(-0.696564\pi\) | ||||
−0.579017 | + | 0.815315i | \(0.696564\pi\) | |||||||
\(380\) | 1020.98i | 0.137829i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3654.72 | 0.489508 | ||||||||
\(383\) | 4417.82 | − | 7651.89i | 0.589400 | − | 1.02087i | −0.404911 | − | 0.914356i | \(-0.632698\pi\) |
0.994311 | − | 0.106514i | \(-0.0339690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 768.769 | − | 3868.16i | 0.101767 | − | 0.512051i | ||||
\(386\) | 4248.73i | 0.560246i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1098.34 | − | 634.128i | −0.143711 | − | 0.0829716i | ||||
\(389\) | −5438.84 | + | 3140.11i | −0.708895 | + | 0.409281i | −0.810652 | − | 0.585529i | \(-0.800887\pi\) |
0.101757 | + | 0.994809i | \(0.467554\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1659.13 | − | 957.899i | 0.214593 | − | 0.123895i | ||||
\(392\) | −1811.73 | + | 4377.94i | −0.233434 | + | 0.564079i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2771.34 | 0.354360 | ||||||||
\(395\) | 4729.06 | − | 8190.96i | 0.602391 | − | 1.04337i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10068.6 | − | 5813.13i | 1.27287 | − | 0.734893i | 0.297345 | − | 0.954770i | \(-0.403899\pi\) |
0.975528 | + | 0.219877i | \(0.0705655\pi\) | |||||||
\(398\) | 4552.83 | − | 7885.73i | 0.573398 | − | 0.993155i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8037.87 | + | 13922.0i | 1.00473 | + | 1.74025i | ||||
\(401\) | −9999.11 | − | 5772.99i | −1.24522 | − | 0.718926i | −0.275064 | − | 0.961426i | \(-0.588699\pi\) |
−0.970151 | + | 0.242500i | \(0.922032\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2393.15 | − | 4145.06i | −0.295810 | − | 0.512358i | ||||
\(404\) | 1510.32 | + | 2615.95i | 0.185993 | + | 0.322150i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6423.15 | + | 7326.60i | −0.785161 | + | 0.895599i | ||||
\(407\) | 3783.30 | + | 2184.29i | 0.460765 | + | 0.266023i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10939.3i | 1.32253i | 0.750154 | + | 0.661263i | \(0.229979\pi\) | ||||
−0.750154 | + | 0.661263i | \(0.770021\pi\) | |||||||
\(410\) | − | 16171.3i | − | 1.94792i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6107.31 | − | 3526.05i | −0.730304 | − | 0.421641i | ||||
\(413\) | 10450.9 | + | 2077.05i | 1.24518 | + | 0.247470i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7410.02 | − | 12834.5i | −0.876491 | − | 1.51813i | ||||
\(416\) | −4427.23 | − | 7668.19i | −0.521786 | − | 0.903759i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −498.720 | − | 287.936i | −0.0583569 | − | 0.0336924i | ||||
\(419\) | 236.117 | + | 408.966i | 0.0275300 | + | 0.0476833i | 0.879462 | − | 0.475969i | \(-0.157902\pi\) |
−0.851932 | + | 0.523652i | \(0.824569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8133.40 | + | 14087.5i | −0.941562 | + | 1.63083i | −0.179070 | + | 0.983836i | \(0.557309\pi\) |
−0.762492 | + | 0.646998i | \(0.776024\pi\) | |||||||
\(422\) | 6033.42 | − | 3483.40i | 0.695977 | − | 0.401822i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1145.33 | − | 1983.78i | 0.131185 | − | 0.227219i | ||||
\(425\) | 2387.12 | 0.272453 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1792.06 | + | 9016.95i | −0.203100 | + | 1.02192i | ||||
\(428\) | 4669.26 | − | 2695.80i | 0.527330 | − | 0.304454i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18782.9 | − | 10844.3i | 2.10650 | − | 1.21619i | ||||
\(431\) | 7130.94 | + | 4117.05i | 0.796949 | + | 0.460119i | 0.842403 | − | 0.538847i | \(-0.181140\pi\) |
−0.0454539 | + | 0.998966i | \(0.514473\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8661.16i | 0.961268i | 0.876921 | + | 0.480634i | \(0.159593\pi\) | ||||
−0.876921 | + | 0.480634i | \(0.840407\pi\) | |||||||
\(434\) | −5676.85 | − | 1128.23i | −0.627874 | − | 0.124786i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 162.253 | − | 281.031i | 0.0178223 | − | 0.0308691i | ||||
\(437\) | 2271.58 | 0.248660 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 12326.7i | − | 1.34014i | −0.742299 | − | 0.670069i | \(-0.766264\pi\) | ||
0.742299 | − | 0.670069i | \(-0.233736\pi\) | |||||||
\(440\) | −2941.51 | −0.318707 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2185.95 | −0.235237 | ||||||||
\(443\) | 4487.07i | 0.481236i | 0.970620 | + | 0.240618i | \(0.0773500\pi\) | ||||
−0.970620 | + | 0.240618i | \(0.922650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6544.91 | −0.697210 | ||||||||
\(446\) | −7799.29 | + | 13508.8i | −0.828043 | + | 1.43421i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1123.63 | + | 223.313i | 0.118496 | + | 0.0235503i | ||||
\(449\) | − | 14430.4i | − | 1.51674i | −0.651827 | − | 0.758368i | \(-0.725997\pi\) | ||
0.651827 | − | 0.758368i | \(-0.274003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2639.60 | + | 1523.98i | 0.275596 | + | 0.159116i | ||||
\(452\) | −4469.78 | + | 2580.63i | −0.465134 | + | 0.268545i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9830.94 | + | 5675.90i | −1.01628 | + | 0.586747i | ||||
\(455\) | 3460.10 | − | 17409.9i | 0.356510 | − | 1.79382i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11998.9 | 1.22820 | 0.614099 | − | 0.789229i | \(-0.289519\pi\) | ||||
0.614099 | + | 0.789229i | \(0.289519\pi\) | |||||||
\(458\) | 2311.46 | − | 4003.57i | 0.235824 | − | 0.408460i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10123.6 | + | 5844.85i | −1.02612 | + | 0.592430i | ||||
\(461\) | −8143.25 | + | 14104.5i | −0.822709 | + | 1.42497i | 0.0809488 | + | 0.996718i | \(0.474205\pi\) |
−0.903658 | + | 0.428255i | \(0.859128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1256.95 | + | 2177.11i | 0.126168 | + | 0.218529i | 0.922189 | − | 0.386740i | \(-0.126399\pi\) |
−0.796021 | + | 0.605269i | \(0.793066\pi\) | |||||||
\(464\) | 10515.4 | + | 6071.10i | 1.05209 | + | 0.607422i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1356.90 | − | 2350.22i | −0.134887 | − | 0.233631i | ||||
\(467\) | 3861.82 | + | 6688.87i | 0.382663 | + | 0.662793i | 0.991442 | − | 0.130548i | \(-0.0416735\pi\) |
−0.608779 | + | 0.793340i | \(0.708340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12730.9 | + | 2530.18i | 1.25343 | + | 0.249110i | ||||
\(470\) | −3883.76 | − | 2242.29i | −0.381158 | − | 0.220062i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 7947.34i | − | 0.775013i | ||||||
\(473\) | 4087.85i | 0.397377i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2451.23 | + | 1415.22i | 0.236779 | + | 0.136705i | ||||
\(476\) | −582.297 | + | 664.200i | −0.0560704 | + | 0.0639571i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9031.41 | + | 15642.9i | 0.864199 | + | 1.49684i | ||||
\(479\) | 42.4285 | + | 73.4883i | 0.00404720 | + | 0.00700995i | 0.868042 | − | 0.496491i | \(-0.165378\pi\) |
−0.863995 | + | 0.503501i | \(0.832045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17028.0 | + | 9831.12i | 1.61416 | + | 0.931935i | ||||
\(482\) | −4660.30 | − | 8071.87i | −0.440396 | − | 0.762788i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2392.63 | − | 4144.15i | 0.224702 | − | 0.389195i | ||||
\(485\) | −4939.00 | + | 2851.53i | −0.462409 | + | 0.266972i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2652.69 | − | 4594.60i | 0.246828 | − | 0.427518i | −0.715816 | − | 0.698289i | \(-0.753945\pi\) |
0.962644 | + | 0.270771i | \(0.0872785\pi\) | |||||||
\(488\) | 6856.87 | 0.636057 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13072.5 | − | 17024.9i | −1.20522 | − | 1.56961i | ||||
\(491\) | −752.365 | + | 434.378i | −0.0691523 | + | 0.0399251i | −0.534177 | − | 0.845372i | \(-0.679379\pi\) |
0.465025 | + | 0.885297i | \(0.346045\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1561.46 | − | 901.510i | 0.142646 | − | 0.0823570i | ||||
\(494\) | −2244.65 | − | 1295.95i | −0.204437 | − | 0.118032i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7212.76i | 0.652948i | ||||||||
\(497\) | 4096.41 | − | 20611.6i | 0.369717 | − | 1.86027i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 899.130 | − | 1557.34i | 0.0806625 | − | 0.139712i | −0.822872 | − | 0.568227i | \(-0.807630\pi\) |
0.903535 | + | 0.428515i | \(0.140963\pi\) | |||||||
\(500\) | −5505.02 | −0.492384 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8804.59i | 0.782805i | ||||||||
\(503\) | −307.609 | −0.0272676 | −0.0136338 | − | 0.999907i | \(-0.504340\pi\) | ||||
−0.0136338 | + | 0.999907i | \(0.504340\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13583.2 | 1.19692 | ||||||||
\(506\) | − | 6593.44i | − | 0.579277i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3281.30 | 0.286583 | ||||||||
\(509\) | −1405.20 | + | 2433.88i | −0.122367 | + | 0.211945i | −0.920700 | − | 0.390270i | \(-0.872382\pi\) |
0.798334 | + | 0.602215i | \(0.205715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4529.04 | − | 3970.56i | −0.392080 | − | 0.343732i | ||||
\(512\) | 4502.73i | 0.388661i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11616.3 | − | 6706.65i | −0.996832 | − | 0.575521i | ||||
\(515\) | −27463.2 | + | 15855.9i | −2.34985 | + | 1.35669i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 732.004 | − | 422.623i | 0.0622698 | − | 0.0359515i | ||||
\(518\) | 22513.7 | − | 7646.45i | 1.90964 | − | 0.648582i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13239.2 | −1.11650 | ||||||||
\(521\) | 2227.32 | − | 3857.83i | 0.187295 | − | 0.324405i | −0.757052 | − | 0.653354i | \(-0.773361\pi\) |
0.944348 | + | 0.328950i | \(0.106695\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6168.37 | − | 3561.31i | 0.515724 | − | 0.297754i | −0.219459 | − | 0.975622i | \(-0.570429\pi\) |
0.735184 | + | 0.677868i | \(0.237096\pi\) | |||||||
\(524\) | −1837.46 | + | 3182.58i | −0.153187 | + | 0.265328i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3933.16 | + | 6812.43i | 0.326034 | + | 0.564708i | ||||
\(527\) | 927.546 | + | 535.519i | 0.0766690 | + | 0.0442648i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6920.74 | + | 11987.1i | 0.568812 | + | 0.985211i | ||||
\(530\) | 5188.77 | + | 8987.21i | 0.425256 | + | 0.736565i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −991.710 | + | 336.820i | −0.0808197 | + | 0.0274493i | ||||
\(533\) | 11880.4 | + | 6859.15i | 0.965473 | + | 0.557416i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 24244.8i | − | 1.95924i | ||||||
\(536\) | − | 9681.10i | − | 0.780149i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8183.90 | + | 4724.98i | 0.655823 | + | 0.378640i | ||||
\(539\) | 4010.88 | − | 529.370i | 0.320521 | − | 0.0423035i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4251.18 | − | 7363.26i | −0.337842 | − | 0.585159i | 0.646185 | − | 0.763181i | \(-0.276364\pi\) |
−0.984027 | + | 0.178022i | \(0.943030\pi\) | |||||||
\(542\) | 11229.3 | + | 19449.6i | 0.889922 | + | 1.54139i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1715.92 | + | 990.688i | 0.135238 | + | 0.0780798i | ||||
\(545\) | −729.616 | − | 1263.73i | −0.0573456 | − | 0.0993254i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9900.32 | + | 17147.9i | −0.773870 | + | 1.34038i | 0.161557 | + | 0.986863i | \(0.448348\pi\) |
−0.935427 | + | 0.353519i | \(0.884985\pi\) | |||||||
\(548\) | 2574.98 | − | 1486.66i | 0.200725 | − | 0.115889i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4107.78 | − | 7114.88i | 0.318466 | − | 0.551599i | ||||
\(551\) | 2137.86 | 0.165292 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9516.25 | + | 1891.29i | 0.731776 | + | 0.145435i | ||||
\(554\) | −24623.1 | + | 14216.1i | −1.88833 | + | 1.09023i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −428.226 | + | 247.236i | −0.0326633 | + | 0.0188582i | ||||
\(557\) | −1286.96 | − | 743.026i | −0.0978998 | − | 0.0565225i | 0.450251 | − | 0.892902i | \(-0.351335\pi\) |
−0.548151 | + | 0.836380i | \(0.684668\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18398.7i | 1.39210i | ||||||||
\(560\) | −17633.7 | + | 20113.9i | −1.33064 | + | 1.51780i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1174.06 | − | 2033.54i | 0.0881226 | − | 0.152633i | ||||
\(563\) | −3428.18 | −0.256626 | −0.128313 | − | 0.991734i | \(-0.540956\pi\) | ||||
−0.128313 | + | 0.991734i | \(0.540956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23209.0i | 1.72816i | ||||||||
\(566\) | −8542.94 | −0.634428 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15673.9 | −1.15786 | ||||||||
\(569\) | 15518.2i | 1.14333i | 0.820486 | + | 0.571667i | \(0.193703\pi\) | ||||
−0.820486 | + | 0.571667i | \(0.806297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3775.08 | −0.276676 | −0.138338 | − | 0.990385i | \(-0.544176\pi\) | ||||
−0.138338 | + | 0.990385i | \(0.544176\pi\) | |||||||
\(572\) | −1256.97 | + | 2177.14i | −0.0918821 | + | 0.159145i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15707.7 | − | 5334.91i | 1.14221 | − | 0.387935i | ||||
\(575\) | 32407.1i | 2.35038i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8116.59 | + | 4686.12i | 0.585612 | + | 0.338103i | 0.763361 | − | 0.645973i | \(-0.223548\pi\) |
−0.177748 | + | 0.984076i | \(0.556881\pi\) | |||||||
\(578\) | −14324.5 | + | 8270.26i | −1.03083 | + | 0.595152i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9527.64 | + | 5500.78i | −0.682092 | + | 0.393806i | ||||
\(581\) | 10022.0 | − | 11431.7i | 0.715634 | − | 0.816293i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1955.94 | −0.138948 | ||||||||
\(584\) | −2246.17 | + | 3890.49i | −0.159156 | + | 0.275667i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18744.2 | + | 10822.0i | −1.32136 | + | 0.762888i | ||||
\(587\) | 4412.41 | − | 7642.52i | 0.310255 | − | 0.537377i | −0.668162 | − | 0.744015i | \(-0.732919\pi\) |
0.978417 | + | 0.206638i | \(0.0662522\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 634.971 | + | 1099.80i | 0.0444202 | + | 0.0769381i | ||||
\(590\) | 31180.6 | + | 18002.1i | 2.17574 | + | 1.25616i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14815.1 | − | 25660.5i | −1.02854 | − | 1.78149i | ||||
\(593\) | −7130.68 | − | 12350.7i | −0.493797 | − | 0.855282i | 0.506177 | − | 0.862430i | \(-0.331058\pi\) |
−0.999974 | + | 0.00714731i | \(0.997725\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1277.38 | + | 3761.03i | 0.0880127 | + | 0.259138i | ||||
\(596\) | −1425.59 | − | 823.062i | −0.0979769 | − | 0.0565670i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 29676.0i | − | 2.02933i | ||||||
\(599\) | − | 6963.46i | − | 0.474991i | −0.971389 | − | 0.237495i | \(-0.923674\pi\) | ||
0.971389 | − | 0.237495i | \(-0.0763265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17885.4 | − | 10326.1i | −1.21391 | − | 0.700850i | −0.250300 | − | 0.968168i | \(-0.580529\pi\) |
−0.963608 | + | 0.267318i | \(0.913863\pi\) | |||||||
\(602\) | 16729.9 | + | 14666.9i | 1.13266 | + | 0.992988i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −657.472 | − | 1138.77i | −0.0442916 | − | 0.0767154i | ||||
\(605\) | −10759.1 | − | 18635.3i | −0.723008 | − | 1.25229i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9603.08 | − | 5544.34i | −0.642137 | − | 0.370738i | 0.143300 | − | 0.989679i | \(-0.454229\pi\) |
−0.785437 | + | 0.618941i | \(0.787562\pi\) | |||||||
\(608\) | 1174.67 | + | 2034.59i | 0.0783539 | + | 0.135713i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15532.0 | + | 26902.2i | −1.03094 | + | 1.78564i | ||||
\(611\) | 3294.63 | − | 1902.15i | 0.218145 | − | 0.125946i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2166.52 | − | 3752.52i | 0.142748 | − | 0.247248i | −0.785782 | − | 0.618503i | \(-0.787739\pi\) |
0.928531 | + | 0.371256i | \(0.121073\pi\) | |||||||
\(614\) | −24250.4 | −1.59392 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −970.400 | − | 2857.18i | −0.0634717 | − | 0.186882i | ||||
\(617\) | −17477.3 | + | 10090.5i | −1.14037 | + | 0.658393i | −0.946522 | − | 0.322639i | \(-0.895430\pi\) |
−0.193848 | + | 0.981032i | \(0.562097\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1788.20 | − | 1032.42i | 0.116113 | − | 0.0670378i | −0.440819 | − | 0.897596i | \(-0.645312\pi\) |
0.556932 | + | 0.830558i | \(0.311979\pi\) | |||||||
\(620\) | −5659.65 | − | 3267.60i | −0.366608 | − | 0.211661i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 7424.39i | − | 0.478603i | ||||||
\(623\) | −2159.16 | − | 6357.27i | −0.138852 | − | 0.408826i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 181.780 | − | 314.852i | 0.0116339 | − | 0.0201505i | ||||
\(626\) | −18795.4 | −1.20003 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 5804.06i | − | 0.368801i | ||||||
\(629\) | −4399.85 | −0.278909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21996.0 | 1.38771 | 0.693856 | − | 0.720114i | \(-0.255911\pi\) | ||||
0.693856 | + | 0.720114i | \(0.255911\pi\) | |||||||
\(632\) | − | 7236.56i | − | 0.455466i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5287.36 | 0.331211 | ||||||||
\(635\) | 7377.64 | − | 12778.4i | 0.461059 | − | 0.798578i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18052.3 | − | 2382.61i | 1.12285 | − | 0.148198i | ||||
\(638\) | − | 6205.31i | − | 0.385063i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24215.0 | + | 13980.5i | 1.49560 | + | 0.863483i | ||||
\(641\) | 15031.3 | − | 8678.33i | 0.926211 | − | 0.534748i | 0.0405997 | − | 0.999175i | \(-0.487073\pi\) |
0.885611 | + | 0.464427i | \(0.153740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6891.57 | + | 3978.85i | −0.422670 | + | 0.244029i | −0.696219 | − | 0.717829i | \(-0.745136\pi\) |
0.273549 | + | 0.961858i | \(0.411802\pi\) | |||||||
\(644\) | −9017.04 | − | 7905.14i | −0.551741 | − | 0.483705i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 579.994 | 0.0353244 | ||||||||
\(647\) | −1066.63 | + | 1847.45i | −0.0648120 | + | 0.112258i | −0.896611 | − | 0.442820i | \(-0.853978\pi\) |
0.831799 | + | 0.555078i | \(0.187311\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5876.87 | + | 3393.01i | −0.355451 | + | 0.205220i | ||||
\(650\) | 18488.4 | − | 32022.9i | 1.11565 | − | 1.93237i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 267.955 | + | 464.112i | 0.0160950 | + | 0.0278773i | ||||
\(653\) | 8113.61 | + | 4684.40i | 0.486233 | + | 0.280727i | 0.723010 | − | 0.690837i | \(-0.242758\pi\) |
−0.236777 | + | 0.971564i | \(0.576091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8262.67 | + | 14311.4i | 0.492899 | + | 0.853727i | ||||
\(656\) | −10336.5 | − | 17903.3i | −0.615199 | − | 1.06556i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 896.757 | − | 4512.14i | 0.0531295 | − | 0.267328i | ||||
\(659\) | 25364.6 | + | 14644.3i | 1.49934 | + | 0.865645i | 1.00000 | 0.000759530i | \(-0.000241766\pi\) | |
0.499342 | + | 0.866405i | \(0.333575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21972.3i | 1.29293i | 0.762945 | + | 0.646464i | \(0.223753\pi\) | ||||
−0.762945 | + | 0.646464i | \(0.776247\pi\) | |||||||
\(662\) | 618.553i | 0.0363153i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9819.91 | − | 5669.53i | −0.573926 | − | 0.331356i | ||||
\(665\) | −918.062 | + | 4619.34i | −0.0535352 | + | 0.269369i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12238.7 | + | 21198.1i | 0.710472 | + | 1.23057i | ||||
\(668\) | 5051.40 | + | 8749.27i | 0.292581 | + | 0.506766i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 37982.9 | + | 21929.4i | 2.19016 | + | 1.26449i | ||||
\(671\) | −2927.45 | − | 5070.49i | −0.168425 | − | 0.291720i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16676.4 | − | 28884.4i | 0.955168 | − | 1.65440i | 0.221184 | − | 0.975232i | \(-0.429008\pi\) |
0.733984 | − | 0.679167i | \(-0.237659\pi\) | |||||||
\(674\) | 9425.86 | − | 5442.03i | 0.538681 | − | 0.311007i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1247.07 | + | 2159.98i | −0.0709528 | + | 0.122894i | ||||
\(677\) | 16326.4 | 0.926843 | 0.463422 | − | 0.886138i | \(-0.346622\pi\) | ||||
0.463422 | + | 0.886138i | \(0.346622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4399.15 | − | 3856.68i | −0.248636 | − | 0.217976i | ||||
\(680\) | 2565.65 | − | 1481.28i | 0.144689 | − | 0.0835361i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3192.26 | − | 1843.05i | 0.179234 | − | 0.103481i | ||||
\(683\) | −8855.85 | − | 5112.93i | −0.496134 | − | 0.286443i | 0.230982 | − | 0.972958i | \(-0.425806\pi\) |
−0.727116 | + | 0.686515i | \(0.759140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 13370.4i | − | 0.745776i | ||||||
\(686\) | 12224.2 | − | 18314.2i | 0.680356 | − | 1.01930i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13863.0 | − | 24011.5i | 0.768202 | − | 1.33057i | ||||
\(689\) | −8803.36 | −0.486765 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14449.2i | − | 0.795473i | −0.917500 | − | 0.397737i | \(-0.869796\pi\) | ||
0.917500 | − | 0.397737i | \(-0.130204\pi\) | |||||||
\(692\) | −14804.8 | −0.813289 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12486.7 | −0.682980 | ||||||||
\(695\) | 2223.53i | 0.121357i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3069.76 | −0.166823 | ||||||||
\(698\) | 9319.51 | − | 16141.9i | 0.505370 | − | 0.875327i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4805.18 | − | 14148.0i | −0.259455 | − | 0.763921i | ||||
\(701\) | 9044.78i | 0.487328i | 0.969860 | + | 0.243664i | \(0.0783494\pi\) | ||||
−0.969860 | + | 0.243664i | \(0.921651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4518.01 | − | 2608.48i | −0.242390 | − | 0.139944i | ||||
\(704\) | −631.848 | + | 364.797i | −0.0338262 | + | 0.0195296i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12144.7 | + | 7011.75i | −0.647411 | + | 0.373783i | ||||
\(707\) | 4481.07 | + | 13193.7i | 0.238370 | + | 0.701841i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15902.0 | −0.842330 | −0.421165 | − | 0.906984i | \(-0.638379\pi\) | ||||
−0.421165 | + | 0.906984i | \(0.638379\pi\) | |||||||
\(710\) | 35504.2 | − | 61495.1i | 1.87669 | − | 3.25052i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4336.72 | + | 2503.81i | −0.228266 | + | 0.131790i | ||||
\(713\) | −7270.09 | + | 12592.2i | −0.381861 | + | 0.661403i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5652.32 | + | 9790.10i | 0.295643 | + | 0.512069i | ||||
\(716\) | 6204.37 | + | 3582.09i | 0.323838 | + | 0.186968i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −508.742 | − | 881.166i | −0.0264430 | − | 0.0458006i | ||||
\(719\) | −5718.63 | − | 9904.97i | −0.296619 | − | 0.513759i | 0.678741 | − | 0.734378i | \(-0.262526\pi\) |
−0.975360 | + | 0.220618i | \(0.929192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24461.4 | − | 21445.0i | −1.26351 | − | 1.10770i | ||||
\(722\) | −19994.2 | − | 11543.6i | −1.03062 | − | 0.595028i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4690.03i | 0.240751i | ||||||||
\(725\) | 30499.4i | 1.56237i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18614.6 | − | 10747.1i | −0.949623 | − | 0.548265i | −0.0566590 | − | 0.998394i | \(-0.518045\pi\) |
−0.892964 | + | 0.450129i | \(0.851378\pi\) | |||||||
\(728\) | −4367.61 | − | 12859.7i | −0.222355 | − | 0.654686i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10176.0 | − | 17625.3i | −0.515930 | − | 0.893617i | ||||
\(731\) | −2058.55 | − | 3565.52i | −0.104156 | − | 0.180404i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1111.43 | + | 641.684i | 0.0560048 | + | 0.0323344i | 0.527741 | − | 0.849405i | \(-0.323039\pi\) |
−0.471736 | + | 0.881740i | \(0.656373\pi\) | |||||||
\(734\) | −12945.8 | − | 22422.8i | −0.651005 | − | 1.12757i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13449.4 | + | 23295.0i | −0.673574 | + | 1.16666i | ||||
\(737\) | −7158.95 | + | 4133.22i | −0.357806 | + | 0.206580i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1436.13 | + | 2487.45i | −0.0714870 | + | 0.123819i | −0.899553 | − | 0.436811i | \(-0.856108\pi\) |
0.828066 | + | 0.560630i | \(0.189441\pi\) | |||||||
\(740\) | 26846.7 | 1.33366 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7017.79 | + | 8004.88i | −0.347212 | + | 0.396049i | ||||
\(743\) | 8010.40 | − | 4624.80i | 0.395522 | − | 0.228355i | −0.289028 | − | 0.957321i | \(-0.593332\pi\) |
0.684550 | + | 0.728966i | \(0.259999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6410.54 | + | 3701.13i | −0.315254 | + | 0.182012i | ||||
\(746\) | 39140.3 | + | 22597.7i | 1.92095 | + | 1.10906i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 562.548i | − | 0.0274984i | ||||||
\(749\) | 23549.7 | − | 7998.33i | 1.14885 | − | 0.390191i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12652.0 | + | 21913.9i | −0.614750 | + | 1.06478i | 0.375678 | + | 0.926750i | \(0.377410\pi\) |
−0.990428 | + | 0.138028i | \(0.955923\pi\) | |||||||
\(752\) | −5732.93 | −0.278003 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 27929.0i | − | 1.34896i | ||||||
\(755\) | −5913.01 | −0.285028 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16874.0 | 0.810166 | 0.405083 | − | 0.914280i | \(-0.367243\pi\) | ||||
0.405083 | + | 0.914280i | \(0.367243\pi\) | |||||||
\(758\) | − | 29616.9i | − | 1.41918i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3512.74 | 0.167659 | ||||||||
\(761\) | −18604.3 | + | 32223.6i | −0.886210 | + | 1.53496i | −0.0418900 | + | 0.999122i | \(0.513338\pi\) |
−0.844320 | + | 0.535839i | \(0.819995\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 986.803 | − | 1125.60i | 0.0468213 | − | 0.0534070i | ||||
\(764\) | 4233.18i | 0.200460i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26523.4 | + | 15313.3i | 1.25108 | + | 0.722312i | ||||
\(767\) | −26450.8 | + | 15271.4i | −1.24522 | + | 0.718928i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10136.5 | − | 5852.32i | 0.475335 | − | 0.274435i | −0.243136 | − | 0.969992i | \(-0.578176\pi\) |
0.718470 | + | 0.695558i | \(0.244843\pi\) | |||||||
\(770\) | 13408.0 | + | 2664.75i | 0.627520 | + | 0.124715i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4921.21 | −0.229428 | ||||||||
\(773\) | −8887.85 | + | 15394.2i | −0.413549 | + | 0.716288i | −0.995275 | − | 0.0970966i | \(-0.969044\pi\) |
0.581726 | + | 0.813385i | \(0.302378\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15690.1 | + | 9058.68i | −0.727232 | + | 0.419868i | ||||
\(776\) | −2181.75 | + | 3778.91i | −0.100928 | + | 0.174813i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10884.4 | − | 18852.4i | −0.501575 | − | 0.868753i | ||||
\(779\) | −3152.21 | − | 1819.93i | −0.144980 | − | 0.0837043i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6691.78 | + | 11590.5i | 0.306595 | + | 0.531038i | ||||
\(782\) | 3320.32 | + | 5750.96i | 0.151834 | + | 0.262984i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25354.6 | − | 10492.5i | −1.15500 | − | 0.477977i | ||||
\(785\) | −22602.9 | − | 13049.8i | −1.02768 | − | 0.593334i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33310.5i | − | 1.50876i | −0.656441 | − | 0.754378i | \(-0.727939\pi\) | ||
0.656441 | − | 0.754378i | \(-0.272061\pi\) | |||||||
\(788\) | 3209.98i | 0.145115i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 28391.9 | + | 16392.1i | 1.27866 | + | 0.738233i | ||||
\(791\) | −22543.6 | + | 7656.62i | −1.01335 | + | 0.344170i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13176.0 | − | 22821.4i | −0.590027 | − | 1.02196i | ||||
\(794\) | 20149.8 | + | 34900.4i | 0.900615 | + | 1.55991i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9133.86 | + | 5273.44i | 0.406710 | + | 0.234814i | ||||
\(797\) | 10344.8 | + | 17917.7i | 0.459763 | + | 0.796334i | 0.998948 | − | 0.0458540i | \(-0.0146009\pi\) |
−0.539185 | + | 0.842187i | \(0.681268\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −425.648 | + | 737.243i | −0.0188465 | + | 0.0326430i | ||||
\(800\) | −29026.0 | + | 16758.2i | −1.28278 | + | 0.740614i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20010.6 | − | 34659.4i | 0.881046 | − | 1.52602i | ||||
\(803\) | 3835.90 | 0.168575 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −51059.0 | + | 17341.5i | −2.23552 | + | 0.759262i | ||||
\(806\) | 14367.8 | − | 8295.26i | 0.627896 | − | 0.362516i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9000.34 | − | 5196.35i | 0.391870 | − | 0.226246i | ||||
\(809\) | 17821.9 | + | 10289.5i | 0.774517 | + | 0.447168i | 0.834484 | − | 0.551033i | \(-0.185766\pi\) |
−0.0599663 | + | 0.998200i | \(0.519099\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19388.9i | − | 0.839502i | −0.907639 | − | 0.419751i | \(-0.862117\pi\) | ||
0.907639 | − | 0.419751i | \(-0.137883\pi\) | |||||||
\(812\) | −8486.24 | − | 7439.79i | −0.366759 | − | 0.321534i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7571.30 | + | 13113.9i | −0.326012 | + | 0.564669i | ||||
\(815\) | 2409.87 | 0.103575 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4881.69i | − | 0.209044i | ||||||
\(818\) | −37918.3 | −1.62076 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18730.9 | 0.797697 | ||||||||
\(821\) | 18742.9i | 0.796751i | 0.917222 | + | 0.398376i | \(0.130426\pi\) | ||||
−0.917222 | + | 0.398376i | \(0.869574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.5746 | −0.00180323 | −0.000901614 | − | 1.00000i | \(-0.500287\pi\) | ||||
−0.000901614 | 1.00000i | \(0.500287\pi\) | ||||||||
\(824\) | −12131.6 | + | 21012.5i | −0.512893 | + | 0.888357i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7199.59 | + | 36225.6i | −0.303276 | + | 1.52597i | ||||
\(827\) | − | 9687.74i | − | 0.407347i | −0.979039 | − | 0.203673i | \(-0.934712\pi\) | ||
0.979039 | − | 0.203673i | \(-0.0652880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19027.2 | − | 10985.4i | −0.797157 | − | 0.460239i | 0.0453189 | − | 0.998973i | \(-0.485570\pi\) |
−0.842476 | + | 0.538734i | \(0.818903\pi\) | |||||||
\(830\) | 44487.7 | − | 25685.0i | 1.86047 | − | 1.07414i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2843.84 | + | 1641.89i | −0.118500 | + | 0.0684163i | ||||
\(833\) | −3231.80 | + | 2481.52i | −0.134424 | + | 0.103217i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45430.0 | 1.88284 | ||||||||
\(836\) | 333.510 | − | 577.656i | 0.0137975 | − | 0.0238979i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1417.58 | + | 818.439i | −0.0584361 | + | 0.0337381i | ||||
\(839\) | 24130.1 | − | 41794.6i | 0.992926 | − | 1.71980i | 0.393635 | − | 0.919267i | \(-0.371217\pi\) |
0.599291 | − | 0.800531i | \(-0.295449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −676.240 | − | 1171.28i | −0.0277272 | − | 0.0480250i | ||||
\(842\) | −48830.7 | − | 28192.4i | −1.99859 | − | 1.15389i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4034.74 | + | 6988.38i | 0.164552 | + | 0.285012i | ||||
\(845\) | 5607.78 | + | 9712.96i | 0.228300 | + | 0.395427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14551.6 | − | 16598.4i | 0.590319 | − | 0.673351i | ||||
\(848\) | 11488.9 | + | 6633.15i | 0.465250 | + | 0.268612i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8274.36i | 0.333892i | ||||||||
\(851\) | − | 59731.4i | − | 2.40607i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5301.14 | − | 3060.61i | −0.212787 | − | 0.122853i | 0.389819 | − | 0.920892i | \(-0.372538\pi\) |
−0.602606 | + | 0.798039i | \(0.705871\pi\) | |||||||
\(854\) | −31255.0 | − | 6211.71i | −1.25237 | − | 0.248900i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9275.05 | − | 16064.9i | −0.370344 | − | 0.641455i | ||||
\(857\) | 1830.74 | + | 3170.93i | 0.0729718 | + | 0.126391i | 0.900202 | − | 0.435472i | \(-0.143418\pi\) |
−0.827231 | + | 0.561862i | \(0.810085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15149.0 | + | 8746.28i | 0.601719 | + | 0.347403i | 0.769718 | − | 0.638384i | \(-0.220397\pi\) |
−0.167998 | + | 0.985787i | \(0.553730\pi\) | |||||||
\(860\) | 12560.7 | + | 21755.9i | 0.498044 | + | 0.862638i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14270.7 | + | 24717.6i | −0.563878 | + | 0.976665i | ||||
\(863\) | 15522.1 | − | 8961.66i | 0.612256 | − | 0.353486i | −0.161592 | − | 0.986858i | \(-0.551663\pi\) |
0.773848 | + | 0.633371i | \(0.218329\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33287.1 | + | 57654.9i | −1.30843 | + | 2.26627i | ||||
\(866\) | −30021.7 | −1.17804 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1306.81 | − | 6575.37i | 0.0511014 | − | 0.257123i | ||||
\(869\) | −5351.26 | + | 3089.55i | −0.208894 | + | 0.120605i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32221.2 | + | 18602.9i | −1.25347 | + | 0.723692i | ||||
\(872\) | −966.902 | − | 558.241i | −0.0375498 | − | 0.0216794i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7873.87i | 0.304734i | ||||||||
\(875\) | −24907.0 | − | 4950.10i | −0.962299 | − | 0.191250i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2140.57 | + | 3707.58i | −0.0824196 | + | 0.142755i | −0.904289 | − | 0.426921i | \(-0.859598\pi\) |
0.821869 | + | 0.569676i | \(0.192931\pi\) | |||||||
\(878\) | 42727.4 | 1.64234 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 17035.6i | − | 0.652580i | ||||||
\(881\) | −19495.6 | −0.745542 | −0.372771 | − | 0.927923i | \(-0.621592\pi\) | ||||
−0.372771 | + | 0.927923i | \(0.621592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6455.82 | −0.246043 | −0.123021 | − | 0.992404i | \(-0.539258\pi\) | ||||
−0.123021 | + | 0.992404i | \(0.539258\pi\) | |||||||
\(884\) | − | 2531.93i | − | 0.0963327i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15553.3 | −0.589756 | ||||||||
\(887\) | −5910.02 | + | 10236.5i | −0.223719 | + | 0.387493i | −0.955934 | − | 0.293580i | \(-0.905153\pi\) |
0.732215 | + | 0.681073i | \(0.238487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14846.0 | + | 2950.54i | 0.560088 | + | 0.111314i | ||||
\(890\) | − | 22686.3i | − | 0.854433i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15646.9 | − | 9033.75i | −0.587329 | − | 0.339094i | ||||
\(893\) | −874.157 | + | 504.695i | −0.0327576 | + | 0.0189126i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27899.7 | − | 16107.9i | 1.04199 | − | 0.601594i | ||||
\(896\) | −5591.22 | + | 28132.9i | −0.208471 | + | 1.04895i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 50019.5 | 1.85877 | ||||||||
\(899\) | −6842.12 | + | 11850.9i | −0.253835 | + | 0.439655i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1706.02 | − | 984.970i | 0.0630807 | − | 0.0364197i | ||||
\(902\) | −5282.48 | + | 9149.52i | −0.194997 | + | 0.337745i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8878.80 | + | 15378.5i | 0.326664 | + | 0.565799i | ||||
\(905\) | 18264.5 | + | 10545.0i | 0.670865 | + | 0.387324i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21758.7 | + | 37687.1i | 0.796565 | + | 1.37969i | 0.921841 | + | 0.387569i | \(0.126685\pi\) |
−0.125275 | + | 0.992122i | \(0.539981\pi\) | |||||||
\(908\) | −6574.26 | − | 11387.0i | −0.240280 | − | 0.416178i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 60347.1 | + | 11993.6i | 2.19834 | + | 0.436904i | ||||
\(911\) | −40124.4 | − | 23165.8i | −1.45926 | − | 0.842501i | −0.460280 | − | 0.887774i | \(-0.652251\pi\) |
−0.998975 | + | 0.0452723i | \(0.985584\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9682.13i | 0.350966i | ||||||||
\(914\) | 41591.3i | 1.50516i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4637.24 | + | 2677.31i | 0.167269 | + | 0.0965731i | ||||
\(917\) | −11175.2 | + | 12747.1i | −0.402441 | + | 0.459047i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13311.5 | + | 23056.1i | 0.477807 | + | 0.827586i | 0.999676 | − | 0.0254393i | \(-0.00809846\pi\) |
−0.521869 | + | 0.853025i | \(0.674765\pi\) | |||||||
\(920\) | 20109.6 | + | 34830.8i | 0.720644 | + | 1.24819i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48889.8 | − | 28226.5i | −1.74631 | − | 1.00823i | ||||
\(923\) | 30118.6 | + | 52166.9i | 1.07407 | + | 1.86034i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37213.3 | − | 64455.3i | 1.32277 | − | 2.29111i | ||||
\(926\) | −7546.40 | + | 4356.92i | −0.267808 | + | 0.154619i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12657.6 | + | 21923.7i | −0.447745 | + | 0.775517i | ||||
\(929\) | 44617.3 | 1.57572 | 0.787862 | − | 0.615852i | \(-0.211188\pi\) | ||||
0.787862 | + | 0.615852i | \(0.211188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4789.78 | + | 632.173i | −0.168613 | + | 0.0222542i | ||||
\(932\) | 2722.21 | − | 1571.67i | 0.0956749 | − | 0.0552379i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23185.3 | + | 13386.0i | −0.812255 | + | 0.468956i | ||||
\(935\) | −2190.74 | − | 1264.83i | −0.0766257 | − | 0.0442399i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37694.9i | 1.31423i | 0.753789 | + | 0.657117i | \(0.228224\pi\) | ||||
−0.753789 | + | 0.657117i | \(0.771776\pi\) | |||||||
\(938\) | −8770.22 | + | 44128.4i | −0.305286 | + | 1.53608i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2597.19 | − | 4498.47i | 0.0901181 | − | 0.156089i | ||||
\(941\) | −26365.3 | −0.913373 | −0.456686 | − | 0.889628i | \(-0.650964\pi\) | ||||
−0.456686 | + | 0.889628i | \(0.650964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 41674.5i | − | 1.43914i | ||||||
\(944\) | 46026.7 | 1.58691 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14169.5 | −0.486987 | ||||||||
\(947\) | 387.274i | 0.0132890i | 0.999978 | + | 0.00664452i | \(0.00211503\pi\) | ||||
−0.999978 | + | 0.00664452i | \(0.997885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17264.7 | 0.590555 | ||||||||
\(950\) | −4905.50 | + | 8496.58i | −0.167532 | + | 0.290174i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2285.22 | + | 2003.43i | 0.0777987 | + | 0.0682053i | ||||
\(953\) | − | 33969.5i | − | 1.15465i | −0.816514 | − | 0.577325i | \(-0.804097\pi\) | ||
0.816514 | − | 0.577325i | \(-0.195903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16485.4 | + | 9517.85i | 0.558591 | + | 0.322503i | ||||
\(956\) | −18118.8 | + | 10460.9i | −0.612974 | + | 0.353901i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −254.729 | + | 147.068i | −0.00859072 | + | 0.00495985i | ||||
\(959\) | 12987.1 | − | 4410.88i | 0.437304 | − | 0.148524i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21662.2 | 0.727140 | ||||||||
\(962\) | −34077.1 | + | 59023.3i | −1.14209 | + | 1.97816i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9349.47 | − | 5397.92i | 0.312371 | − | 0.180348i | ||||
\(965\) | −11064.8 | + | 19164.8i | −0.369107 | + | 0.639312i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9966.96 | + | 17263.3i | 0.331454 | + | 0.574095i | 0.982797 | − | 0.184688i | \(-0.0591276\pi\) |
−0.651343 | + | 0.758783i | \(0.725794\pi\) | |||||||
\(968\) | −14258.2 | − | 8231.97i | −0.473425 | − | 0.273332i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9884.12 | − | 17119.8i | −0.327175 | − | 0.566684i | ||||
\(971\) | −6280.64 | − | 10878.4i | −0.207575 | − | 0.359530i | 0.743375 | − | 0.668875i | \(-0.233224\pi\) |
−0.950950 | + | 0.309344i | \(0.899890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2159.79 | + | 733.541i | −0.0711609 | + | 0.0241688i | ||||
\(974\) | 15926.0 | + | 9194.90i | 0.523925 | + | 0.302488i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39711.2i | 1.30238i | ||||||||
\(977\) | − | 22456.1i | − | 0.735348i | −0.929955 | − | 0.367674i | \(-0.880154\pi\) | ||
0.929955 | − | 0.367674i | \(-0.119846\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3703.01 | + | 2137.94i | 0.120888 | + | 0.0697944i | ||||
\(980\) | 19719.6 | − | 15141.6i | 0.642775 | − | 0.493552i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1505.66 | − | 2607.88i | −0.0489283 | − | 0.0847464i | ||||
\(983\) | −24435.3 | − | 42323.2i | −0.792844 | − | 1.37325i | −0.924199 | − | 0.381911i | \(-0.875266\pi\) |
0.131355 | − | 0.991335i | \(-0.458067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12500.7 | + | 7217.27i | 0.404370 | + | 0.233463i | ||||
\(986\) | 3124.86 | + | 5412.41i | 0.100929 | + | 0.174814i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1501.07 | − | 2599.93i | 0.0483355 | − | 0.0837195i | ||||
\(989\) | 48404.7 | − | 27946.5i | 1.55630 | − | 0.898530i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20255.7 | − | 35083.8i | 0.649286 | − | 1.12460i | −0.334008 | − | 0.942570i | \(-0.608401\pi\) |
0.983294 | − | 0.182026i | \(-0.0582654\pi\) | |||||||
\(992\) | −15037.9 | −0.481304 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 71444.9 | + | 14199.2i | 2.27977 | + | 0.453089i | ||||
\(995\) | 41072.9 | − | 23713.5i | 1.30864 | − | 0.755545i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52677.3 | + | 30413.3i | −1.67333 | + | 0.966096i | −0.707573 | + | 0.706640i | \(0.750210\pi\) |
−0.965755 | + | 0.259456i | \(0.916457\pi\) | |||||||
\(998\) | 5398.13 | + | 3116.61i | 0.171217 | + | 0.0988522i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 189.4.i.a.143.17 | 44 | ||
3.2 | odd | 2 | 63.4.i.a.38.6 | yes | 44 | ||
7.5 | odd | 6 | 189.4.s.a.89.17 | 44 | |||
9.4 | even | 3 | 63.4.s.a.59.6 | yes | 44 | ||
9.5 | odd | 6 | 189.4.s.a.17.17 | 44 | |||
21.5 | even | 6 | 63.4.s.a.47.6 | yes | 44 | ||
63.5 | even | 6 | inner | 189.4.i.a.152.6 | 44 | ||
63.40 | odd | 6 | 63.4.i.a.5.17 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.17 | ✓ | 44 | 63.40 | odd | 6 | ||
63.4.i.a.38.6 | yes | 44 | 3.2 | odd | 2 | ||
63.4.s.a.47.6 | yes | 44 | 21.5 | even | 6 | ||
63.4.s.a.59.6 | yes | 44 | 9.4 | even | 3 | ||
189.4.i.a.143.17 | 44 | 1.1 | even | 1 | trivial | ||
189.4.i.a.152.6 | 44 | 63.5 | even | 6 | inner | ||
189.4.s.a.17.17 | 44 | 9.5 | odd | 6 | |||
189.4.s.a.89.17 | 44 | 7.5 | odd | 6 |