Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(46,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.e (of order \(3\), 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: | \(7.96525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{13} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Root | \(2.65775 - 4.60336i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.91 |
Dual form | 135.4.e.c.46.1 |
$q$-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 \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(82\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65775 | − | 4.60336i | −0.939658 | − | 1.62754i | −0.766110 | − | 0.642710i | \(-0.777810\pi\) |
−0.173548 | − | 0.984825i | \(-0.555523\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −10.1273 | + | 17.5410i | −1.26591 | + | 2.19263i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.71686 | + | 11.6339i | 0.362676 | + | 0.628174i | 0.988400 | − | 0.151871i | \(-0.0485297\pi\) |
−0.625724 | + | 0.780045i | \(0.715196\pi\) | |||||||
\(8\) | 65.1396 | 2.87879 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 26.5775 | 0.840456 | ||||||||
\(11\) | −23.4628 | − | 40.6388i | −0.643119 | − | 1.11391i | −0.984733 | − | 0.174074i | \(-0.944307\pi\) |
0.341614 | − | 0.939840i | \(-0.389026\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.0673 | − | 31.2935i | 0.385460 | − | 0.667636i | −0.606373 | − | 0.795180i | \(-0.707376\pi\) |
0.991833 | + | 0.127544i | \(0.0407095\pi\) | |||||||
\(14\) | 35.7035 | − | 61.8403i | 0.681584 | − | 1.18054i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −92.1064 | − | 159.533i | −1.43916 | − | 2.49270i | ||||
\(17\) | 54.6071 | 0.779069 | 0.389535 | − | 0.921012i | \(-0.372636\pi\) | ||||
0.389535 | + | 0.921012i | \(0.372636\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 111.339 | 1.34436 | 0.672180 | − | 0.740388i | \(-0.265358\pi\) | ||||
0.672180 | + | 0.740388i | \(0.265358\pi\) | |||||||
\(20\) | −50.6366 | − | 87.7051i | −0.566134 | − | 0.980573i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −124.717 | + | 216.016i | −1.20862 | + | 2.09340i | ||||
\(23\) | −17.9870 | + | 31.1544i | −0.163067 | + | 0.282441i | −0.935967 | − | 0.352087i | \(-0.885472\pi\) |
0.772900 | + | 0.634528i | \(0.218805\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −192.074 | −1.44880 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −272.095 | −1.83647 | ||||||||
\(29\) | 29.0588 | + | 50.3312i | 0.186072 | + | 0.322285i | 0.943937 | − | 0.330125i | \(-0.107091\pi\) |
−0.757866 | + | 0.652411i | \(0.773758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 147.833 | − | 256.055i | 0.856506 | − | 1.48351i | −0.0187353 | − | 0.999824i | \(-0.505964\pi\) |
0.875241 | − | 0.483687i | \(-0.160703\pi\) | |||||||
\(32\) | −229.034 | + | 396.699i | −1.26525 | + | 2.19147i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −145.132 | − | 251.377i | −0.732059 | − | 1.26796i | ||||
\(35\) | −67.1686 | −0.324388 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −53.0417 | −0.235676 | −0.117838 | − | 0.993033i | \(-0.537596\pi\) | ||||
−0.117838 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(38\) | −295.911 | − | 512.533i | −1.26324 | − | 2.18799i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −162.849 | + | 282.063i | −0.643717 | + | 1.11495i | ||||
\(41\) | 64.1795 | − | 111.162i | 0.244467 | − | 0.423430i | −0.717514 | − | 0.696544i | \(-0.754720\pi\) |
0.961982 | + | 0.273114i | \(0.0880536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 82.0858 | + | 142.177i | 0.291116 | + | 0.504227i | 0.974074 | − | 0.226230i | \(-0.0726402\pi\) |
−0.682958 | + | 0.730457i | \(0.739307\pi\) | |||||||
\(44\) | 950.461 | 3.25653 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 191.220 | 0.612910 | ||||||||
\(47\) | 43.9159 | + | 76.0646i | 0.136294 | + | 0.236067i | 0.926091 | − | 0.377301i | \(-0.123148\pi\) |
−0.789797 | + | 0.613368i | \(0.789814\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 81.2675 | − | 140.759i | 0.236932 | − | 0.410378i | ||||
\(50\) | −66.4439 | + | 115.084i | −0.187932 | + | 0.325507i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 365.947 | + | 633.839i | 0.975918 | + | 1.69034i | ||||
\(53\) | 479.247 | 1.24207 | 0.621035 | − | 0.783783i | \(-0.286713\pi\) | ||||
0.621035 | + | 0.783783i | \(0.286713\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 234.628 | 0.575223 | ||||||||
\(56\) | 437.533 | + | 757.830i | 1.04407 | + | 1.80838i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 154.462 | − | 267.536i | 0.349687 | − | 0.605676i | ||||
\(59\) | 317.807 | − | 550.458i | 0.701271 | − | 1.21464i | −0.266750 | − | 0.963766i | \(-0.585950\pi\) |
0.968021 | − | 0.250871i | \(-0.0807169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.0128 | − | 41.5915i | −0.0504021 | − | 0.0872990i | 0.839724 | − | 0.543014i | \(-0.182717\pi\) |
−0.890126 | + | 0.455715i | \(0.849384\pi\) | |||||||
\(62\) | −1571.62 | −3.21929 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 961.163 | 1.87727 | ||||||||
\(65\) | 90.3367 | + | 156.468i | 0.172383 | + | 0.298576i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4592 | − | 25.0440i | 0.0263652 | − | 0.0456658i | −0.852542 | − | 0.522659i | \(-0.824940\pi\) |
0.878907 | + | 0.476993i | \(0.158273\pi\) | |||||||
\(68\) | −553.024 | + | 957.865i | −0.986235 | + | 1.70821i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 178.518 | + | 309.202i | 0.304813 | + | 0.527952i | ||||
\(71\) | −576.183 | −0.963103 | −0.481552 | − | 0.876418i | \(-0.659927\pi\) | ||||
−0.481552 | + | 0.876418i | \(0.659927\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 835.057 | 1.33885 | 0.669425 | − | 0.742880i | \(-0.266541\pi\) | ||||
0.669425 | + | 0.742880i | \(0.266541\pi\) | |||||||
\(74\) | 140.972 | + | 244.170i | 0.221455 | + | 0.383571i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1127.56 | + | 1952.99i | −1.70184 | + | 2.94768i | ||||
\(77\) | 315.193 | − | 545.930i | 0.466488 | − | 0.807981i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 101.869 | + | 176.442i | 0.145078 | + | 0.251282i | 0.929402 | − | 0.369069i | \(-0.120324\pi\) |
−0.784324 | + | 0.620351i | \(0.786990\pi\) | |||||||
\(80\) | 921.064 | 1.28723 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −682.294 | −0.918863 | ||||||||
\(83\) | 232.239 | + | 402.249i | 0.307127 | + | 0.531959i | 0.977733 | − | 0.209855i | \(-0.0672991\pi\) |
−0.670606 | + | 0.741814i | \(0.733966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −136.518 | + | 236.456i | −0.174205 | + | 0.301732i | ||||
\(86\) | 436.328 | − | 755.742i | 0.547098 | − | 0.947602i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1528.36 | − | 2647.19i | −1.85140 | − | 3.20672i | ||||
\(89\) | −993.782 | −1.18360 | −0.591801 | − | 0.806084i | \(-0.701583\pi\) | ||||
−0.591801 | + | 0.806084i | \(0.701583\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 485.423 | 0.559189 | ||||||||
\(92\) | −364.320 | − | 631.021i | −0.412859 | − | 0.715092i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 233.435 | − | 404.322i | 0.256139 | − | 0.443645i | ||||
\(95\) | −278.347 | + | 482.111i | −0.300608 | + | 0.520668i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −440.708 | − | 763.328i | −0.461310 | − | 0.799012i | 0.537717 | − | 0.843126i | \(-0.319287\pi\) |
−0.999027 | + | 0.0441134i | \(0.985954\pi\) | |||||||
\(98\) | −863.956 | −0.890538 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 506.366 | 0.506366 | ||||||||
\(101\) | 604.869 | + | 1047.66i | 0.595909 | + | 1.03214i | 0.993418 | + | 0.114546i | \(0.0365412\pi\) |
−0.397509 | + | 0.917598i | \(0.630125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −372.421 | + | 645.053i | −0.356270 | + | 0.617077i | −0.987334 | − | 0.158653i | \(-0.949285\pi\) |
0.631065 | + | 0.775730i | \(0.282618\pi\) | |||||||
\(104\) | 1176.90 | − | 2038.45i | 1.10966 | − | 1.92198i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1273.72 | − | 2206.15i | −1.16712 | − | 2.02151i | ||||
\(107\) | 1000.14 | 0.903622 | 0.451811 | − | 0.892114i | \(-0.350778\pi\) | ||||
0.451811 | + | 0.892114i | \(0.350778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −915.517 | −0.804502 | −0.402251 | − | 0.915530i | \(-0.631772\pi\) | ||||
−0.402251 | + | 0.915530i | \(0.631772\pi\) | |||||||
\(110\) | −623.584 | − | 1080.08i | −0.540513 | − | 0.936196i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1237.33 | − | 2143.12i | 1.04390 | − | 1.80809i | ||||
\(113\) | −662.451 | + | 1147.40i | −0.551488 | + | 0.955206i | 0.446679 | + | 0.894694i | \(0.352606\pi\) |
−0.998168 | + | 0.0605114i | \(0.980727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −89.9350 | − | 155.772i | −0.0729260 | − | 0.126311i | ||||
\(116\) | −1177.15 | −0.942202 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3378.61 | −2.63582 | ||||||||
\(119\) | 366.789 | + | 635.297i | 0.282550 | + | 0.489391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −435.508 | + | 754.321i | −0.327203 | + | 0.566733i | ||||
\(122\) | −127.640 | + | 221.080i | −0.0947215 | + | 0.164062i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2994.31 | + | 5186.30i | 2.16853 | + | 3.75600i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −993.635 | −0.694259 | −0.347129 | − | 0.937817i | \(-0.612843\pi\) | ||||
−0.347129 | + | 0.937817i | \(0.612843\pi\) | |||||||
\(128\) | −722.262 | − | 1251.00i | −0.498747 | − | 0.863855i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 480.185 | − | 831.705i | 0.323962 | − | 0.561118i | ||||
\(131\) | 691.995 | − | 1198.57i | 0.461526 | − | 0.799386i | −0.537512 | − | 0.843256i | \(-0.680636\pi\) |
0.999037 | + | 0.0438704i | \(0.0139689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 747.847 | + | 1295.31i | 0.487568 | + | 0.844492i | ||||
\(134\) | −153.715 | −0.0990970 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3557.09 | 2.24278 | ||||||||
\(137\) | 773.568 | + | 1339.86i | 0.482411 | + | 0.835561i | 0.999796 | − | 0.0201918i | \(-0.00642770\pi\) |
−0.517385 | + | 0.855753i | \(0.673094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 269.752 | − | 467.225i | 0.164605 | − | 0.285104i | −0.771910 | − | 0.635732i | \(-0.780698\pi\) |
0.936515 | + | 0.350628i | \(0.114032\pi\) | |||||||
\(140\) | 680.238 | − | 1178.21i | 0.410647 | − | 0.711261i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1531.35 | + | 2652.38i | 0.904988 | + | 1.56748i | ||||
\(143\) | −1695.64 | −0.991586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −290.588 | −0.166427 | ||||||||
\(146\) | −2219.38 | − | 3844.07i | −1.25806 | − | 2.17902i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 537.170 | − | 930.406i | 0.298345 | − | 0.516749i | ||||
\(149\) | −602.335 | + | 1043.27i | −0.331176 | + | 0.573613i | −0.982743 | − | 0.184978i | \(-0.940779\pi\) |
0.651567 | + | 0.758591i | \(0.274112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1486.46 | − | 2574.62i | −0.801100 | − | 1.38755i | −0.918893 | − | 0.394508i | \(-0.870915\pi\) |
0.117793 | − | 0.993038i | \(-0.462418\pi\) | |||||||
\(152\) | 7252.55 | 3.87013 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3350.82 | −1.75336 | ||||||||
\(155\) | 739.167 | + | 1280.28i | 0.383041 | + | 0.663446i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 197.880 | − | 342.739i | 0.100590 | − | 0.174226i | −0.811338 | − | 0.584577i | \(-0.801260\pi\) |
0.911928 | + | 0.410351i | \(0.134594\pi\) | |||||||
\(158\) | 541.484 | − | 937.877i | 0.272646 | − | 0.472238i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1145.17 | − | 1983.49i | −0.565836 | − | 0.980056i | ||||
\(161\) | −483.265 | −0.236563 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3861.43 | 1.85553 | 0.927764 | − | 0.373169i | \(-0.121729\pi\) | ||||
0.927764 | + | 0.373169i | \(0.121729\pi\) | |||||||
\(164\) | 1299.93 | + | 2251.55i | 0.618949 | + | 1.07205i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1234.47 | − | 2138.16i | 0.577188 | − | 0.999719i | ||||
\(167\) | 1017.49 | − | 1762.34i | 0.471470 | − | 0.816609i | −0.527998 | − | 0.849246i | \(-0.677057\pi\) |
0.999467 | + | 0.0326366i | \(0.0103904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 445.643 | + | 771.876i | 0.202842 | + | 0.351332i | ||||
\(170\) | 1451.32 | 0.654773 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3325.24 | −1.47411 | ||||||||
\(173\) | 773.458 | + | 1339.67i | 0.339913 | + | 0.588746i | 0.984416 | − | 0.175855i | \(-0.0562691\pi\) |
−0.644503 | + | 0.764602i | \(0.722936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 167.922 | − | 290.849i | 0.0725353 | − | 0.125635i | ||||
\(176\) | −4322.15 | + | 7486.19i | −1.85111 | + | 3.20621i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2641.23 | + | 4574.74i | 1.11218 | + | 1.92636i | ||||
\(179\) | 823.973 | 0.344059 | 0.172030 | − | 0.985092i | \(-0.444967\pi\) | ||||
0.172030 | + | 0.985092i | \(0.444967\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4403.55 | −1.80836 | −0.904180 | − | 0.427152i | \(-0.859517\pi\) | ||||
−0.904180 | + | 0.427152i | \(0.859517\pi\) | |||||||
\(182\) | −1290.14 | − | 2234.58i | −0.525446 | − | 0.910099i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1171.67 | + | 2029.38i | −0.469437 | + | 0.813088i | ||||
\(185\) | 132.604 | − | 229.677i | 0.0526987 | − | 0.0912769i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1281.24 | − | 2219.17i | −0.501034 | − | 0.867816i | ||||
\(188\) | −1779.00 | −0.690144 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2959.11 | 1.12988 | ||||||||
\(191\) | −1523.46 | − | 2638.72i | −0.577141 | − | 0.999637i | −0.995805 | − | 0.0914964i | \(-0.970835\pi\) |
0.418664 | − | 0.908141i | \(-0.362498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −945.452 | + | 1637.57i | −0.352617 | + | 0.610751i | −0.986707 | − | 0.162508i | \(-0.948042\pi\) |
0.634090 | + | 0.773259i | \(0.281375\pi\) | |||||||
\(194\) | −2342.58 | + | 4057.48i | −0.866947 | + | 1.50160i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1646.04 | + | 2851.03i | 0.599870 | + | 1.03901i | ||||
\(197\) | −3652.00 | −1.32078 | −0.660392 | − | 0.750921i | \(-0.729610\pi\) | ||||
−0.660392 | + | 0.750921i | \(0.729610\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3217.26 | 1.14606 | 0.573029 | − | 0.819535i | \(-0.305768\pi\) | ||||
0.573029 | + | 0.819535i | \(0.305768\pi\) | |||||||
\(200\) | −814.245 | − | 1410.31i | −0.287879 | − | 0.498621i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3215.19 | − | 5568.87i | 1.11990 | − | 1.93972i | ||||
\(203\) | −390.367 | + | 676.136i | −0.134968 | + | 0.233771i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 320.898 | + | 555.811i | 0.109329 | + | 0.189364i | ||||
\(206\) | 3959.22 | 1.33909 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6656.47 | −2.21896 | ||||||||
\(209\) | −2612.32 | − | 4524.67i | −0.864583 | − | 1.49750i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2473.90 | + | 4284.92i | −0.807159 | + | 1.39804i | 0.107666 | + | 0.994187i | \(0.465662\pi\) |
−0.914824 | + | 0.403853i | \(0.867671\pi\) | |||||||
\(212\) | −4853.49 | + | 8406.48i | −1.57235 | + | 2.72339i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2658.14 | − | 4604.03i | −0.849096 | − | 1.47068i | ||||
\(215\) | −820.858 | −0.260382 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3971.91 | 1.24254 | ||||||||
\(218\) | 2433.22 | + | 4214.46i | 0.755956 | + | 1.30935i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2376.15 | + | 4115.62i | −0.728183 | + | 1.26125i | ||||
\(221\) | 986.606 | − | 1708.85i | 0.300300 | − | 0.520135i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −552.056 | − | 956.189i | −0.165778 | − | 0.287135i | 0.771154 | − | 0.636649i | \(-0.219680\pi\) |
−0.936931 | + | 0.349514i | \(0.886347\pi\) | |||||||
\(224\) | −6153.56 | −1.83550 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7042.53 | 2.07284 | ||||||||
\(227\) | −1910.12 | − | 3308.43i | −0.558498 | − | 0.967348i | −0.997622 | − | 0.0689210i | \(-0.978044\pi\) |
0.439124 | − | 0.898427i | \(-0.355289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −72.3848 | + | 125.374i | −0.0208879 | + | 0.0361788i | −0.876280 | − | 0.481801i | \(-0.839983\pi\) |
0.855393 | + | 0.517980i | \(0.173316\pi\) | |||||||
\(230\) | −478.050 | + | 828.008i | −0.137051 | + | 0.237379i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1892.87 | + | 3278.55i | 0.535661 | + | 0.927792i | ||||
\(233\) | −1286.31 | −0.361670 | −0.180835 | − | 0.983513i | \(-0.557880\pi\) | ||||
−0.180835 | + | 0.983513i | \(0.557880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −439.159 | −0.121905 | ||||||||
\(236\) | 6437.07 | + | 11149.3i | 1.77550 | + | 3.07525i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1949.67 | − | 3376.92i | 0.531001 | − | 0.919721i | ||||
\(239\) | 2109.73 | − | 3654.15i | 0.570991 | − | 0.988986i | −0.425473 | − | 0.904971i | \(-0.639892\pi\) |
0.996465 | − | 0.0840147i | \(-0.0267743\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1141.57 | − | 1977.25i | −0.305124 | − | 0.528490i | 0.672165 | − | 0.740401i | \(-0.265364\pi\) |
−0.977289 | + | 0.211912i | \(0.932031\pi\) | |||||||
\(242\) | 4629.89 | 1.22984 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 972.742 | 0.255219 | ||||||||
\(245\) | 406.338 | + | 703.797i | 0.105959 | + | 0.183526i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2011.59 | − | 3484.18i | 0.518197 | − | 0.897543i | ||||
\(248\) | 9629.81 | − | 16679.3i | 2.46570 | − | 4.27072i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −332.219 | − | 575.421i | −0.0840456 | − | 0.145571i | ||||
\(251\) | 7922.23 | 1.99222 | 0.996109 | − | 0.0881290i | \(-0.0280888\pi\) | ||||
0.996109 | + | 0.0881290i | \(0.0280888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1688.10 | 0.419487 | ||||||||
\(254\) | 2640.84 | + | 4574.06i | 0.652366 | + | 1.12993i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.46197 | − | 9.46041i | 0.00133349 | − | 0.00230967i | ||||
\(257\) | 1131.09 | − | 1959.10i | 0.274535 | − | 0.475508i | −0.695483 | − | 0.718542i | \(-0.744810\pi\) |
0.970018 | + | 0.243035i | \(0.0781429\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −356.274 | − | 617.085i | −0.0854741 | − | 0.148045i | ||||
\(260\) | −3659.47 | −0.872888 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7356.61 | −1.73471 | ||||||||
\(263\) | 81.7349 | + | 141.569i | 0.0191635 | + | 0.0331921i | 0.875448 | − | 0.483312i | \(-0.160566\pi\) |
−0.856285 | + | 0.516504i | \(0.827233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1198.12 | + | 2075.20i | −0.277735 | + | 0.481051i | ||||
\(266\) | 3975.18 | − | 6885.22i | 0.916294 | − | 1.58707i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 292.865 | + | 507.257i | 0.0667521 | + | 0.115618i | ||||
\(269\) | −3304.13 | −0.748908 | −0.374454 | − | 0.927246i | \(-0.622170\pi\) | ||||
−0.374454 | + | 0.927246i | \(0.622170\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1954.96 | −0.438212 | −0.219106 | − | 0.975701i | \(-0.570314\pi\) | ||||
−0.219106 | + | 0.975701i | \(0.570314\pi\) | |||||||
\(272\) | −5029.67 | − | 8711.64i | −1.12121 | − | 1.94199i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4111.91 | − | 7122.03i | 0.906603 | − | 1.57028i | ||||
\(275\) | −586.570 | + | 1015.97i | −0.128624 | + | 0.222783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2121.67 | + | 3674.85i | 0.460213 | + | 0.797112i | 0.998971 | − | 0.0453482i | \(-0.0144397\pi\) |
−0.538758 | + | 0.842460i | \(0.681106\pi\) | |||||||
\(278\) | −2867.74 | −0.618689 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4375.33 | −0.933844 | ||||||||
\(281\) | −1311.15 | − | 2270.97i | −0.278350 | − | 0.482117i | 0.692625 | − | 0.721298i | \(-0.256454\pi\) |
−0.970975 | + | 0.239181i | \(0.923121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.53735 | − | 6.12688i | 0.000743017 | − | 0.00128694i | −0.865654 | − | 0.500643i | \(-0.833097\pi\) |
0.866397 | + | 0.499356i | \(0.166430\pi\) | |||||||
\(284\) | 5835.18 | − | 10106.8i | 1.21921 | − | 2.11173i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4506.60 | + | 7805.66i | 0.931751 | + | 1.61384i | ||||
\(287\) | 1724.34 | 0.354650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1931.06 | −0.393051 | ||||||||
\(290\) | 772.310 | + | 1337.68i | 0.156385 | + | 0.270867i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8456.88 | + | 14647.7i | −1.69487 | + | 2.93560i | ||||
\(293\) | −2238.75 | + | 3877.62i | −0.446378 | + | 0.773150i | −0.998147 | − | 0.0608470i | \(-0.980620\pi\) |
0.551769 | + | 0.833997i | \(0.313953\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1589.04 | + | 2752.29i | 0.313618 | + | 0.543202i | ||||
\(296\) | −3455.12 | −0.678461 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6403.43 | 1.24477 | ||||||||
\(299\) | 649.955 | + | 1125.75i | 0.125712 | + | 0.217739i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1102.72 | + | 1909.96i | −0.211162 | + | 0.365743i | ||||
\(302\) | −7901.27 | + | 13685.4i | −1.50552 | + | 2.60764i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10255.0 | − | 17762.2i | −1.93475 | − | 3.35109i | ||||
\(305\) | 240.128 | 0.0450810 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3889.78 | −0.723132 | −0.361566 | − | 0.932347i | \(-0.617758\pi\) | ||||
−0.361566 | + | 0.932347i | \(0.617758\pi\) | |||||||
\(308\) | 6384.12 | + | 11057.6i | 1.18107 | + | 2.04567i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3929.05 | − | 6805.31i | 0.719855 | − | 1.24683i | ||||
\(311\) | −3647.83 | + | 6318.23i | −0.665111 | + | 1.15201i | 0.314145 | + | 0.949375i | \(0.398282\pi\) |
−0.979255 | + | 0.202630i | \(0.935051\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 318.036 | + | 550.854i | 0.0574328 | + | 0.0994765i | 0.893312 | − | 0.449436i | \(-0.148375\pi\) |
−0.835880 | + | 0.548913i | \(0.815042\pi\) | |||||||
\(314\) | −2103.67 | −0.378080 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4126.62 | −0.734623 | ||||||||
\(317\) | −3073.18 | − | 5322.90i | −0.544501 | − | 0.943104i | −0.998638 | − | 0.0521721i | \(-0.983386\pi\) |
0.454137 | − | 0.890932i | \(-0.349948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1363.60 | − | 2361.83i | 0.239332 | − | 0.414536i | ||||
\(320\) | −2402.91 | + | 4161.96i | −0.419771 | + | 0.727064i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1284.40 | + | 2224.65i | 0.222288 | + | 0.385014i | ||||
\(323\) | 6079.89 | 1.04735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −903.367 | −0.154184 | ||||||||
\(326\) | −10262.7 | − | 17775.6i | −1.74356 | − | 3.01994i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4180.63 | − | 7241.06i | 0.703770 | − | 1.21897i | ||||
\(329\) | −589.954 | + | 1021.83i | −0.0988609 | + | 0.171232i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5867.20 | − | 10162.3i | −0.974291 | − | 1.68752i | −0.682255 | − | 0.731114i | \(-0.739001\pi\) |
−0.292036 | − | 0.956407i | \(-0.594333\pi\) | |||||||
\(332\) | −9407.82 | −1.55518 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10816.9 | −1.77208 | ||||||||
\(335\) | 72.2958 | + | 125.220i | 0.0117909 | + | 0.0204224i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3141.65 | + | 5441.49i | −0.507823 | + | 0.879575i | 0.492136 | + | 0.870518i | \(0.336216\pi\) |
−0.999959 | + | 0.00905696i | \(0.997117\pi\) | |||||||
\(338\) | 2368.82 | − | 4102.91i | 0.381203 | − | 0.660264i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2765.12 | − | 4789.33i | −0.441058 | − | 0.763934i | ||||
\(341\) | −13874.4 | −2.20334 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6791.22 | 1.06907 | ||||||||
\(344\) | 5347.04 | + | 9261.34i | 0.838061 | + | 1.45156i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4111.32 | − | 7121.02i | 0.638803 | − | 1.10644i | ||||
\(347\) | 2400.41 | − | 4157.63i | 0.371357 | − | 0.643209i | −0.618418 | − | 0.785849i | \(-0.712226\pi\) |
0.989775 | + | 0.142641i | \(0.0455594\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1946.23 | + | 3370.97i | 0.298508 | + | 0.517031i | 0.975795 | − | 0.218688i | \(-0.0701778\pi\) |
−0.677287 | + | 0.735719i | \(0.736844\pi\) | |||||||
\(350\) | −1785.18 | −0.272633 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21495.2 | 3.25482 | ||||||||
\(353\) | −1483.14 | − | 2568.87i | −0.223624 | − | 0.387329i | 0.732281 | − | 0.681002i | \(-0.238456\pi\) |
−0.955906 | + | 0.293673i | \(0.905122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1440.46 | − | 2494.94i | 0.215356 | − | 0.373008i | ||||
\(356\) | 10064.3 | − | 17431.9i | 1.49834 | − | 2.59520i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2189.92 | − | 3793.05i | −0.323298 | − | 0.559969i | ||||
\(359\) | 9584.91 | 1.40911 | 0.704557 | − | 0.709647i | \(-0.251146\pi\) | ||||
0.704557 | + | 0.709647i | \(0.251146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5537.30 | 0.807304 | ||||||||
\(362\) | 11703.5 | + | 20271.1i | 1.69924 | + | 2.94317i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4916.03 | + | 8514.82i | −0.707885 | + | 1.22609i | ||||
\(365\) | −2087.64 | + | 3615.90i | −0.299376 | + | 0.518534i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2268.59 | − | 3929.31i | −0.322669 | − | 0.558879i | 0.658369 | − | 0.752695i | \(-0.271247\pi\) |
−0.981038 | + | 0.193817i | \(0.937913\pi\) | |||||||
\(368\) | 6626.88 | 0.938722 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1409.72 | −0.198075 | ||||||||
\(371\) | 3219.04 | + | 5575.54i | 0.450469 | + | 0.780236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6565.65 | + | 11372.0i | −0.911411 | + | 1.57861i | −0.0993385 | + | 0.995054i | \(0.531673\pi\) |
−0.812073 | + | 0.583557i | \(0.801661\pi\) | |||||||
\(374\) | −6810.43 | + | 11796.0i | −0.941601 | + | 1.63090i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2860.66 | + | 4954.82i | 0.392360 | + | 0.679588i | ||||
\(377\) | 2100.06 | 0.286892 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9451.10 | −1.28092 | −0.640462 | − | 0.767990i | \(-0.721257\pi\) | ||||
−0.640462 | + | 0.767990i | \(0.721257\pi\) | |||||||
\(380\) | −5637.81 | − | 9764.97i | −0.761088 | − | 1.31824i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8097.98 | + | 14026.1i | −1.08463 | + | 1.87863i | ||||
\(383\) | −4298.52 | + | 7445.25i | −0.573483 | + | 0.993301i | 0.422722 | + | 0.906260i | \(0.361075\pi\) |
−0.996205 | + | 0.0870420i | \(0.972259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1575.97 | + | 2729.65i | 0.208620 | + | 0.361340i | ||||
\(386\) | 10051.1 | 1.32536 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17852.7 | 2.33592 | ||||||||
\(389\) | 2221.04 | + | 3846.95i | 0.289489 | + | 0.501410i | 0.973688 | − | 0.227886i | \(-0.0731813\pi\) |
−0.684199 | + | 0.729295i | \(0.739848\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −982.219 | + | 1701.25i | −0.127041 | + | 0.220041i | ||||
\(392\) | 5293.73 | − | 9169.01i | 0.682076 | − | 1.18139i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9706.13 | + | 16811.5i | 1.24109 | + | 2.14962i | ||||
\(395\) | −1018.69 | −0.129761 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10445.6 | 1.32053 | 0.660265 | − | 0.751033i | \(-0.270444\pi\) | ||||
0.660265 | + | 0.751033i | \(0.270444\pi\) | |||||||
\(398\) | −8550.68 | − | 14810.2i | −1.07690 | − | 1.86525i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2302.66 | + | 3988.33i | −0.287833 | + | 0.498541i | ||||
\(401\) | −6341.72 | + | 10984.2i | −0.789751 | + | 1.36789i | 0.136368 | + | 0.990658i | \(0.456457\pi\) |
−0.926119 | + | 0.377231i | \(0.876876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5341.91 | − | 9252.47i | −0.660297 | − | 1.14367i | ||||
\(404\) | −24502.8 | −3.01748 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4150.00 | 0.507293 | ||||||||
\(407\) | 1244.51 | + | 2155.55i | 0.151568 | + | 0.262523i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5556.30 | − | 9623.79i | 0.671739 | − | 1.16349i | −0.305671 | − | 0.952137i | \(-0.598881\pi\) |
0.977411 | − | 0.211349i | \(-0.0677858\pi\) | |||||||
\(410\) | 1705.73 | − | 2954.42i | 0.205464 | − | 0.355874i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7543.26 | − | 13065.3i | −0.902014 | − | 1.56233i | ||||
\(413\) | 8538.67 | 1.01734 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2322.39 | −0.274702 | ||||||||
\(416\) | 8276.08 | + | 14334.6i | 0.975404 | + | 1.68945i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13885.8 | + | 24050.9i | −1.62482 | + | 2.81428i | ||||
\(419\) | 1009.26 | − | 1748.09i | 0.117675 | − | 0.203818i | −0.801171 | − | 0.598435i | \(-0.795789\pi\) |
0.918846 | + | 0.394617i | \(0.129123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5478.85 | + | 9489.65i | 0.634259 | + | 1.09857i | 0.986672 | + | 0.162724i | \(0.0520280\pi\) |
−0.352413 | + | 0.935845i | \(0.614639\pi\) | |||||||
\(422\) | 26300.1 | 3.03381 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 31218.0 | 3.57565 | ||||||||
\(425\) | −682.589 | − | 1182.28i | −0.0779069 | − | 0.134939i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 322.582 | − | 558.728i | 0.0365593 | − | 0.0633226i | ||||
\(428\) | −10128.8 | + | 17543.5i | −1.14391 | + | 1.98131i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2181.64 | + | 3778.71i | 0.244670 | + | 0.423781i | ||||
\(431\) | 2124.75 | 0.237460 | 0.118730 | − | 0.992927i | \(-0.462118\pi\) | ||||
0.118730 | + | 0.992927i | \(0.462118\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16169.2 | −1.79456 | −0.897279 | − | 0.441463i | \(-0.854460\pi\) | ||||
−0.897279 | + | 0.441463i | \(0.854460\pi\) | |||||||
\(434\) | −10556.4 | − | 18284.1i | −1.16756 | − | 2.02227i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9271.73 | − | 16059.1i | 1.01843 | − | 1.76397i | ||||
\(437\) | −2002.65 | + | 3468.69i | −0.219221 | + | 0.379702i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −346.098 | − | 599.460i | −0.0376273 | − | 0.0651724i | 0.846598 | − | 0.532232i | \(-0.178647\pi\) |
−0.884226 | + | 0.467060i | \(0.845313\pi\) | |||||||
\(440\) | 15283.6 | 1.65595 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10488.6 | −1.12872 | ||||||||
\(443\) | −3335.26 | − | 5776.83i | −0.357704 | − | 0.619561i | 0.629873 | − | 0.776698i | \(-0.283107\pi\) |
−0.987577 | + | 0.157137i | \(0.949774\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2484.45 | − | 4303.20i | 0.264662 | − | 0.458407i | ||||
\(446\) | −2934.46 | + | 5082.63i | −0.311549 | + | 0.539618i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6456.00 | + | 11182.1i | 0.680843 | + | 1.17925i | ||||
\(449\) | 9743.18 | 1.02407 | 0.512037 | − | 0.858964i | \(-0.328891\pi\) | ||||
0.512037 | + | 0.858964i | \(0.328891\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6023.33 | −0.628886 | ||||||||
\(452\) | −13417.7 | − | 23240.1i | −1.39627 | − | 2.41842i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10153.3 | + | 17586.0i | −1.04959 | + | 1.81795i | ||||
\(455\) | −1213.56 | + | 2101.94i | −0.125038 | + | 0.216573i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2221.36 | − | 3847.51i | −0.227376 | − | 0.393827i | 0.729654 | − | 0.683817i | \(-0.239681\pi\) |
−0.957030 | + | 0.289990i | \(0.906348\pi\) | |||||||
\(458\) | 769.524 | 0.0785098 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3643.20 | 0.369272 | ||||||||
\(461\) | 9469.70 | + | 16402.0i | 0.956720 | + | 1.65709i | 0.730383 | + | 0.683038i | \(0.239342\pi\) |
0.226337 | + | 0.974049i | \(0.427325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8396.10 | − | 14542.5i | 0.842764 | − | 1.45971i | −0.0447846 | − | 0.998997i | \(-0.514260\pi\) |
0.887549 | − | 0.460714i | \(-0.152407\pi\) | |||||||
\(464\) | 5353.00 | − | 9271.66i | 0.535575 | − | 0.927642i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3418.70 | + | 5921.36i | 0.339846 | + | 0.588630i | ||||
\(467\) | −1367.93 | −0.135547 | −0.0677735 | − | 0.997701i | \(-0.521590\pi\) | ||||
−0.0677735 | + | 0.997701i | \(0.521590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 388.480 | 0.0382481 | ||||||||
\(470\) | 1167.18 | + | 2021.61i | 0.114549 | + | 0.198404i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20701.8 | − | 35856.6i | 2.01881 | − | 3.49668i | ||||
\(473\) | 3851.93 | − | 6671.74i | 0.374444 | − | 0.648556i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1391.73 | − | 2410.55i | −0.134436 | − | 0.232850i | ||||
\(476\) | −14858.3 | −1.43074 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22428.5 | −2.14615 | ||||||||
\(479\) | 101.371 | + | 175.579i | 0.00966960 | + | 0.0167482i | 0.870820 | − | 0.491603i | \(-0.163589\pi\) |
−0.861150 | + | 0.508351i | \(0.830255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −958.323 | + | 1659.86i | −0.0908436 | + | 0.157346i | ||||
\(482\) | −6068.01 | + | 10510.1i | −0.573424 | + | 0.993199i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8821.04 | − | 15278.5i | −0.828423 | − | 1.43487i | ||||
\(485\) | 4407.08 | 0.412608 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18961.3 | 1.76431 | 0.882153 | − | 0.470964i | \(-0.156094\pi\) | ||||
0.882153 | + | 0.470964i | \(0.156094\pi\) | |||||||
\(488\) | −1564.19 | − | 2709.25i | −0.145097 | − | 0.251315i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2159.89 | − | 3741.04i | 0.199130 | − | 0.344904i | ||||
\(491\) | 5856.15 | − | 10143.1i | 0.538257 | − | 0.932289i | −0.460741 | − | 0.887535i | \(-0.652416\pi\) |
0.998998 | − | 0.0447541i | \(-0.0142504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1586.82 | + | 2748.45i | 0.144963 | + | 0.251083i | ||||
\(494\) | −21385.3 | −1.94771 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −54465.7 | −4.93061 | ||||||||
\(497\) | −3870.14 | − | 6703.28i | −0.349295 | − | 0.604996i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4312.44 | + | 7469.36i | −0.386876 | + | 0.670089i | −0.992028 | − | 0.126021i | \(-0.959779\pi\) |
0.605151 | + | 0.796110i | \(0.293113\pi\) | |||||||
\(500\) | −1265.91 | + | 2192.63i | −0.113227 | + | 0.196115i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21055.3 | − | 36468.9i | −1.87200 | − | 3.24241i | ||||
\(503\) | −4856.12 | −0.430465 | −0.215232 | − | 0.976563i | \(-0.569051\pi\) | ||||
−0.215232 | + | 0.976563i | \(0.569051\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6048.69 | −0.532997 | ||||||||
\(506\) | −4486.56 | − | 7770.96i | −0.394174 | − | 0.682730i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10062.9 | − | 17429.4i | 0.878872 | − | 1.52225i | ||||
\(509\) | −5425.17 | + | 9396.67i | −0.472429 | + | 0.818271i | −0.999502 | − | 0.0315486i | \(-0.989956\pi\) |
0.527073 | + | 0.849820i | \(0.323289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5608.96 | + | 9715.01i | 0.485569 | + | 0.841030i | ||||
\(512\) | −11614.3 | −1.00251 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12024.6 | −1.03187 | ||||||||
\(515\) | −1862.11 | − | 3225.26i | −0.159329 | − | 0.275965i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2060.78 | − | 3569.38i | 0.175306 | − | 0.303639i | ||||
\(518\) | −1893.78 | + | 3280.12i | −0.160633 | + | 0.278224i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5884.49 | + | 10192.2i | 0.496254 | + | 0.859537i | ||||
\(521\) | −3559.30 | −0.299301 | −0.149651 | − | 0.988739i | \(-0.547815\pi\) | ||||
−0.149651 | + | 0.988739i | \(0.547815\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22191.7 | 1.85540 | 0.927702 | − | 0.373321i | \(-0.121781\pi\) | ||||
0.927702 | + | 0.373321i | \(0.121781\pi\) | |||||||
\(524\) | 14016.1 | + | 24276.6i | 1.16850 | + | 2.02391i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 434.463 | − | 752.511i | 0.0360142 | − | 0.0623784i | ||||
\(527\) | 8072.77 | − | 13982.4i | 0.667277 | − | 1.15576i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5436.44 | + | 9416.18i | 0.446818 | + | 0.773912i | ||||
\(530\) | 12737.2 | 1.04390 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −30294.7 | −2.46888 | ||||||||
\(533\) | −2319.11 | − | 4016.81i | −0.188465 | − | 0.326430i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2500.36 | + | 4330.75i | −0.202056 | + | 0.349971i | ||||
\(536\) | 941.863 | − | 1631.35i | 0.0758998 | − | 0.131462i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8781.56 | + | 15210.1i | 0.703717 | + | 1.21887i | ||||
\(539\) | −7627.06 | −0.609500 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4257.08 | 0.338311 | 0.169155 | − | 0.985589i | \(-0.445896\pi\) | ||||
0.169155 | + | 0.985589i | \(0.445896\pi\) | |||||||
\(542\) | 5195.81 | + | 8999.40i | 0.411770 | + | 0.713206i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12506.9 | + | 21662.6i | −0.985715 | + | 1.70731i | ||||
\(545\) | 2288.79 | − | 3964.31i | 0.179892 | − | 0.311582i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10609.1 | + | 18375.5i | 0.829272 | + | 1.43634i | 0.898610 | + | 0.438748i | \(0.144578\pi\) |
−0.0693385 | + | 0.997593i | \(0.522089\pi\) | |||||||
\(548\) | −31336.7 | −2.44277 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6235.84 | 0.483449 | ||||||||
\(551\) | 3235.36 | + | 5603.81i | 0.250147 | + | 0.433268i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1368.48 | + | 2370.27i | −0.105232 | + | 0.182268i | ||||
\(554\) | 11277.8 | − | 19533.7i | 0.864885 | − | 1.49803i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5463.73 | + | 9463.46i | 0.416752 | + | 0.721835i | ||||
\(557\) | −2506.42 | −0.190665 | −0.0953324 | − | 0.995445i | \(-0.530391\pi\) | ||||
−0.0953324 | + | 0.995445i | \(0.530391\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5932.29 | 0.448854 | ||||||||
\(560\) | 6186.66 | + | 10715.6i | 0.466847 | + | 0.808602i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6969.41 | + | 12071.4i | −0.523108 | + | 0.906050i | ||||
\(563\) | 8639.80 | − | 14964.6i | 0.646757 | − | 1.12022i | −0.337136 | − | 0.941456i | \(-0.609458\pi\) |
0.983893 | − | 0.178759i | \(-0.0572084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3312.26 | − | 5737.00i | −0.246633 | − | 0.427181i | ||||
\(566\) | −37.6057 | −0.00279273 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37532.3 | −2.77257 | ||||||||
\(569\) | −10254.1 | − | 17760.5i | −0.755487 | − | 1.30854i | −0.945132 | − | 0.326689i | \(-0.894067\pi\) |
0.189645 | − | 0.981853i | \(-0.439266\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3412.53 | + | 5910.68i | −0.250105 | + | 0.433195i | −0.963555 | − | 0.267512i | \(-0.913799\pi\) |
0.713449 | + | 0.700707i | \(0.247132\pi\) | |||||||
\(572\) | 17172.3 | − | 29743.3i | 1.25526 | − | 2.17418i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4582.87 | − | 7937.77i | −0.333250 | − | 0.577206i | ||||
\(575\) | 899.350 | 0.0652270 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4249.00 | 0.306565 | 0.153283 | − | 0.988182i | \(-0.451016\pi\) | ||||
0.153283 | + | 0.988182i | \(0.451016\pi\) | |||||||
\(578\) | 5132.28 | + | 8889.37i | 0.369333 | + | 0.639704i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2942.87 | − | 5097.20i | 0.210683 | − | 0.364913i | ||||
\(581\) | −3119.83 | + | 5403.71i | −0.222775 | + | 0.385858i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11244.5 | − | 19476.0i | −0.798798 | − | 1.38356i | ||||
\(584\) | 54395.2 | 3.85426 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23800.1 | 1.67777 | ||||||||
\(587\) | 9344.04 | + | 16184.3i | 0.657018 | + | 1.13799i | 0.981384 | + | 0.192057i | \(0.0615159\pi\) |
−0.324365 | + | 0.945932i | \(0.605151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16459.6 | − | 28508.8i | 1.15145 | − | 1.99437i | ||||
\(590\) | 8446.53 | − | 14629.8i | 0.589387 | − | 1.02085i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4885.48 | + | 8461.91i | 0.339176 | + | 0.587470i | ||||
\(593\) | 12434.5 | 0.861084 | 0.430542 | − | 0.902570i | \(-0.358322\pi\) | ||||
0.430542 | + | 0.902570i | \(0.358322\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3667.89 | −0.252721 | ||||||||
\(596\) | −12200.1 | − | 21131.1i | −0.838480 | − | 1.45229i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3454.84 | − | 5983.96i | 0.236252 | − | 0.409201i | ||||
\(599\) | −3021.52 | + | 5233.42i | −0.206103 | + | 0.356981i | −0.950484 | − | 0.310774i | \(-0.899412\pi\) |
0.744380 | + | 0.667756i | \(0.232745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 315.654 | + | 546.729i | 0.0214239 | + | 0.0371074i | 0.876539 | − | 0.481332i | \(-0.159847\pi\) |
−0.855115 | + | 0.518439i | \(0.826513\pi\) | |||||||
\(602\) | 11723.0 | 0.793679 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 60215.2 | 4.05649 | ||||||||
\(605\) | −2177.54 | − | 3771.61i | −0.146330 | − | 0.253451i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4727.43 | − | 8188.16i | 0.316113 | − | 0.547524i | −0.663560 | − | 0.748123i | \(-0.730955\pi\) |
0.979673 | + | 0.200599i | \(0.0642888\pi\) | |||||||
\(608\) | −25500.4 | + | 44167.9i | −1.70095 | + | 2.94613i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −638.202 | − | 1105.40i | −0.0423607 | − | 0.0733709i | ||||
\(611\) | 3173.77 | 0.210143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2682.66 | −0.176757 | −0.0883783 | − | 0.996087i | \(-0.528168\pi\) | ||||
−0.0883783 | + | 0.996087i | \(0.528168\pi\) | |||||||
\(614\) | 10338.1 | + | 17906.1i | 0.679497 | + | 1.17692i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20531.5 | − | 35561.7i | 1.34292 | − | 2.32601i | ||||
\(617\) | −1169.26 | + | 2025.22i | −0.0762930 | + | 0.132143i | −0.901648 | − | 0.432471i | \(-0.857642\pi\) |
0.825355 | + | 0.564614i | \(0.190975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5965.11 | + | 10331.9i | 0.387331 | + | 0.670878i | 0.992090 | − | 0.125531i | \(-0.0400636\pi\) |
−0.604758 | + | 0.796409i | \(0.706730\pi\) | |||||||
\(620\) | −29943.1 | −1.93959 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 38780.1 | 2.49991 | ||||||||
\(623\) | −6675.09 | − | 11561.6i | −0.429265 | − | 0.743509i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 1690.52 | − | 2928.07i | 0.107934 | − | 0.186948i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4008.00 | + | 6942.05i | 0.254676 | + | 0.441111i | ||||
\(629\) | −2896.46 | −0.183608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4106.81 | 0.259096 | 0.129548 | − | 0.991573i | \(-0.458647\pi\) | ||||
0.129548 | + | 0.991573i | \(0.458647\pi\) | |||||||
\(632\) | 6635.68 | + | 11493.3i | 0.417648 | + | 0.723387i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16335.5 | + | 28293.9i | −1.02329 | + | 1.77239i | ||||
\(635\) | 2484.09 | − | 4302.57i | 0.155241 | − | 0.268885i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2936.58 | − | 5086.30i | −0.182655 | − | 0.316368i | ||||
\(638\) | −14496.5 | −0.899562 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7222.62 | 0.446093 | ||||||||
\(641\) | 7462.65 | + | 12925.7i | 0.459839 | + | 0.796465i | 0.998952 | − | 0.0457684i | \(-0.0145736\pi\) |
−0.539113 | + | 0.842234i | \(0.681240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9502.84 | + | 16459.4i | −0.582823 | + | 1.00948i | 0.412319 | + | 0.911039i | \(0.364719\pi\) |
−0.995143 | + | 0.0984406i | \(0.968615\pi\) | |||||||
\(644\) | 4894.18 | − | 8476.96i | 0.299468 | − | 0.518694i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16158.8 | − | 27987.9i | −0.984151 | − | 1.70460i | ||||
\(647\) | −9252.81 | −0.562234 | −0.281117 | − | 0.959673i | \(-0.590705\pi\) | ||||
−0.281117 | + | 0.959673i | \(0.590705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29826.6 | −1.80400 | ||||||||
\(650\) | 2400.93 | + | 4158.53i | 0.144880 | + | 0.250940i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −39106.0 | + | 67733.5i | −2.34894 | + | 4.06848i | ||||
\(653\) | 11475.3 | − | 19875.9i | 0.687695 | − | 1.19112i | −0.284887 | − | 0.958561i | \(-0.591956\pi\) |
0.972582 | − | 0.232561i | \(-0.0747105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3459.97 | + | 5992.85i | 0.206401 | + | 0.357496i | ||||
\(656\) | −23645.4 | −1.40731 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6271.81 | 0.371582 | ||||||||
\(659\) | 3258.54 | + | 5643.96i | 0.192617 | + | 0.333623i | 0.946117 | − | 0.323826i | \(-0.104969\pi\) |
−0.753500 | + | 0.657448i | \(0.771636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2598.16 | − | 4500.15i | 0.152885 | − | 0.264804i | −0.779402 | − | 0.626524i | \(-0.784477\pi\) |
0.932287 | + | 0.361720i | \(0.117810\pi\) | |||||||
\(662\) | −31187.1 | + | 54017.7i | −1.83100 | + | 3.17139i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15127.9 | + | 26202.3i | 0.884153 | + | 1.53140i | ||||
\(665\) | −7478.47 | −0.436094 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2090.72 | −0.121369 | ||||||||
\(668\) | 20608.8 | + | 35695.5i | 1.19368 | + | 2.06751i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 384.289 | − | 665.607i | 0.0221588 | − | 0.0383801i | ||||
\(671\) | −1126.82 | + | 1951.71i | −0.0648291 | + | 0.112287i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14095.0 | − | 24413.2i | −0.807313 | − | 1.39831i | −0.914718 | − | 0.404093i | \(-0.867587\pi\) |
0.107405 | − | 0.994215i | \(-0.465746\pi\) | |||||||
\(674\) | 33398.9 | 1.90872 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18052.7 | −1.02712 | ||||||||
\(677\) | 4338.44 | + | 7514.40i | 0.246292 | + | 0.426590i | 0.962494 | − | 0.271303i | \(-0.0874544\pi\) |
−0.716202 | + | 0.697893i | \(0.754121\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5920.34 | − | 10254.3i | 0.334613 | − | 0.579566i | ||||
\(680\) | −8892.71 | + | 15402.6i | −0.501500 | + | 0.868624i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 36874.6 | + | 63868.7i | 2.07039 | + | 3.58601i | ||||
\(683\) | −20624.1 | −1.15543 | −0.577714 | − | 0.816239i | \(-0.696055\pi\) | ||||
−0.577714 | + | 0.816239i | \(0.696055\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7735.68 | −0.431482 | ||||||||
\(686\) | −18049.4 | − | 31262.5i | −1.00456 | − | 1.73995i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15121.3 | − | 26190.8i | 0.837926 | − | 1.45133i | ||||
\(689\) | 8658.72 | − | 14997.3i | 0.478768 | − | 0.829250i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3493.03 | − | 6050.10i | −0.192303 | − | 0.333078i | 0.753710 | − | 0.657207i | \(-0.228262\pi\) |
−0.946013 | + | 0.324129i | \(0.894929\pi\) | |||||||
\(692\) | −31332.2 | −1.72120 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25518.8 | −1.39579 | ||||||||
\(695\) | 1348.76 | + | 2336.12i | 0.0736136 | + | 0.127502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3504.66 | − | 6070.25i | 0.190457 | − | 0.329881i | ||||
\(698\) | 10345.2 | − | 17918.4i | 0.560991 | − | 0.971664i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3401.19 | + | 5891.03i | 0.183647 | + | 0.318086i | ||||
\(701\) | −7848.55 | −0.422875 | −0.211438 | − | 0.977391i | \(-0.567815\pi\) | ||||
−0.211438 | + | 0.977391i | \(0.567815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5905.60 | −0.316833 | ||||||||
\(704\) | −22551.6 | − | 39060.5i | −1.20731 | − | 2.09112i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7883.63 | + | 13654.8i | −0.420261 | + | 0.727913i | ||||
\(707\) | −8125.65 | + | 14074.0i | −0.432244 | + | 0.748669i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12712.3 | + | 22018.3i | 0.673371 | + | 1.16631i | 0.976942 | + | 0.213504i | \(0.0684876\pi\) |
−0.303571 | + | 0.952809i | \(0.598179\pi\) | |||||||
\(710\) | −15313.5 | −0.809445 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −64734.5 | −3.40734 | ||||||||
\(713\) | 5318.16 | + | 9211.33i | 0.279336 | + | 0.483825i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4239.11 | − | 7342.35i | 0.221725 | − | 0.384039i | ||||
\(716\) | −8344.63 | + | 14453.3i | −0.435550 | + | 0.754394i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25474.3 | − | 44122.8i | −1.32409 | − | 2.29338i | ||||
\(719\) | −16707.2 | −0.866584 | −0.433292 | − | 0.901254i | \(-0.642648\pi\) | ||||
−0.433292 | + | 0.901254i | \(0.642648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10006.0 | −0.516843 | ||||||||
\(722\) | −14716.8 | − | 25490.2i | −0.758590 | − | 1.31392i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 44596.1 | − | 77242.7i | 2.28923 | − | 3.96506i | ||||
\(725\) | 726.469 | − | 1258.28i | 0.0372143 | − | 0.0644571i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −718.240 | − | 1244.03i | −0.0366410 | − | 0.0634642i | 0.847123 | − | 0.531396i | \(-0.178332\pi\) |
−0.883764 | + | 0.467932i | \(0.844999\pi\) | |||||||
\(728\) | 31620.3 | 1.60979 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22193.8 | 1.12524 | ||||||||
\(731\) | 4482.47 | + | 7763.87i | 0.226799 | + | 0.392828i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5770.44 | + | 9994.70i | −0.290772 | + | 0.503633i | −0.973993 | − | 0.226580i | \(-0.927246\pi\) |
0.683220 | + | 0.730212i | \(0.260579\pi\) | |||||||
\(734\) | −12058.7 | + | 20886.3i | −0.606397 | + | 1.05031i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8239.28 | − | 14270.9i | −0.412641 | − | 0.714715i | ||||
\(737\) | −1357.01 | −0.0678237 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4127.87 | 0.205475 | 0.102737 | − | 0.994709i | \(-0.467240\pi\) | ||||
0.102737 | + | 0.994709i | \(0.467240\pi\) | |||||||
\(740\) | 2685.85 | + | 4652.03i | 0.133424 | + | 0.231097i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17110.8 | − | 29636.8i | 0.846574 | − | 1.46631i | ||||
\(743\) | −13748.5 | + | 23813.1i | −0.678846 | + | 1.17580i | 0.296482 | + | 0.955038i | \(0.404186\pi\) |
−0.975329 | + | 0.220758i | \(0.929147\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3011.67 | − | 5216.37i | −0.148106 | − | 0.256528i | ||||
\(746\) | 69799.5 | 3.42566 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 51902.0 | 2.53706 | ||||||||
\(749\) | 6717.83 | + | 11635.6i | 0.327723 | + | 0.567632i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17197.1 | + | 29786.2i | −0.835592 | + | 1.44729i | 0.0579559 | + | 0.998319i | \(0.481542\pi\) |
−0.893548 | + | 0.448968i | \(0.851792\pi\) | |||||||
\(752\) | 8089.88 | − | 14012.1i | 0.392297 | − | 0.679479i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5581.44 | − | 9667.33i | −0.269581 | − | 0.466928i | ||||
\(755\) | 14864.6 | 0.716526 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30459.8 | −1.46246 | −0.731229 | − | 0.682132i | \(-0.761053\pi\) | ||||
−0.731229 | + | 0.682132i | \(0.761053\pi\) | |||||||
\(758\) | 25118.7 | + | 43506.8i | 1.20363 | + | 2.08475i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18131.4 | + | 31404.5i | −0.865387 | + | 1.49889i | ||||
\(761\) | 223.584 | − | 387.259i | 0.0106504 | − | 0.0184469i | −0.860651 | − | 0.509195i | \(-0.829943\pi\) |
0.871301 | + | 0.490748i | \(0.163276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6149.40 | − | 10651.1i | −0.291774 | − | 0.505367i | ||||
\(764\) | 61714.3 | 2.92244 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45697.6 | 2.15551 | ||||||||
\(767\) | −11483.9 | − | 19890.6i | −0.540623 | − | 0.936387i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4028.59 | − | 6977.71i | 0.188914 | − | 0.327208i | −0.755975 | − | 0.654601i | \(-0.772837\pi\) |
0.944888 | + | 0.327393i | \(0.106170\pi\) | |||||||
\(770\) | 8377.06 | − | 14509.5i | 0.392062 | − | 0.679072i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19149.8 | − | 33168.4i | −0.892767 | − | 1.54632i | ||||
\(773\) | 19600.4 | 0.912001 | 0.456000 | − | 0.889980i | \(-0.349282\pi\) | ||||
0.456000 | + | 0.889980i | \(0.349282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7391.67 | −0.342602 | ||||||||
\(776\) | −28707.5 | − | 49722.8i | −1.32801 | − | 2.30019i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11806.0 | − | 20448.5i | 0.544041 | − | 0.942307i | ||||
\(779\) | 7145.66 | − | 12376.7i | 0.328652 | − | 0.569242i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13518.9 | + | 23415.4i | 0.619390 | + | 1.07281i | ||||
\(782\) | 10442.0 | 0.477500 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −29941.0 | −1.36393 | ||||||||
\(785\) | 989.402 | + | 1713.70i | 0.0449851 | + | 0.0779164i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8968.18 | + | 15533.3i | −0.406202 | + | 0.703563i | −0.994461 | − | 0.105110i | \(-0.966480\pi\) |
0.588258 | + | 0.808673i | \(0.299814\pi\) | |||||||
\(788\) | 36985.0 | − | 64059.9i | 1.67200 | − | 2.89599i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2707.42 | + | 4689.39i | 0.121931 | + | 0.211191i | ||||
\(791\) | −17798.4 | −0.800047 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1735.39 | −0.0777119 | ||||||||
\(794\) | −27761.9 | − | 48085.0i | −1.24085 | − | 2.14921i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32582.2 | + | 56434.0i | −1.45081 | + | 2.51288i | ||||
\(797\) | −8971.31 | + | 15538.8i | −0.398720 | + | 0.690604i | −0.993568 | − | 0.113235i | \(-0.963879\pi\) |
0.594848 | + | 0.803838i | \(0.297212\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2398.12 | + | 4153.67i | 0.106182 | + | 0.183913i | ||||
\(800\) | 11451.7 | 0.506099 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 67418.9 | 2.96838 | ||||||||
\(803\) | −19592.8 | − | 33935.7i | −0.861039 | − | 1.49136i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1208.16 | − | 2092.60i | 0.0528971 | − | 0.0916204i | ||||
\(806\) | −28395.0 | + | 49181.6i | −1.24091 | + | 2.14931i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 39400.9 | + | 68244.4i | 1.71549 | + | 2.97132i | ||||
\(809\) | −29094.2 | −1.26440 | −0.632200 | − | 0.774806i | \(-0.717848\pi\) | ||||
−0.632200 | + | 0.774806i | \(0.717848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1438.31 | 0.0622760 | 0.0311380 | − | 0.999515i | \(-0.490087\pi\) | ||||
0.0311380 | + | 0.999515i | \(0.490087\pi\) | |||||||
\(812\) | −7906.74 | − | 13694.9i | −0.341715 | − | 0.591867i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6615.19 | − | 11457.9i | 0.284843 | − | 0.493363i | ||||
\(815\) | −9653.59 | + | 16720.5i | −0.414908 | + | 0.718643i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9139.33 | + | 15829.8i | 0.391364 | + | 0.677863i | ||||
\(818\) | −59069.1 | −2.52482 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12999.3 | −0.553605 | ||||||||
\(821\) | −121.415 | − | 210.297i | −0.00516128 | − | 0.00893959i | 0.863433 | − | 0.504463i | \(-0.168310\pi\) |
−0.868595 | + | 0.495524i | \(0.834976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9085.50 | + | 15736.5i | −0.384812 | + | 0.666515i | −0.991743 | − | 0.128240i | \(-0.959067\pi\) |
0.606931 | + | 0.794755i | \(0.292401\pi\) | |||||||
\(824\) | −24259.4 | + | 42018.5i | −1.02563 | + | 1.77644i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22693.7 | − | 39306.6i | −0.955949 | − | 1.65575i | ||||
\(827\) | −12181.7 | −0.512213 | −0.256107 | − | 0.966649i | \(-0.582440\pi\) | ||||
−0.256107 | + | 0.966649i | \(0.582440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17370.0 | −0.727724 | −0.363862 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363862 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(830\) | 6172.34 | + | 10690.8i | 0.258126 | + | 0.447088i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17365.7 | − | 30078.2i | 0.723613 | − | 1.25333i | ||||
\(833\) | 4437.79 | − | 7686.47i | 0.184586 | − | 0.319713i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5087.43 | + | 8811.69i | 0.210848 | + | 0.365199i | ||||
\(836\) | 105823. | 4.37795 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10729.5 | −0.442296 | ||||||||
\(839\) | 15681.5 | + | 27161.2i | 0.645275 | + | 1.11765i | 0.984238 | + | 0.176849i | \(0.0565906\pi\) |
−0.338963 | + | 0.940800i | \(0.610076\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10505.7 | − | 18196.4i | 0.430755 | − | 0.746089i | ||||
\(842\) | 29122.9 | − | 50442.3i | 1.19197 | − | 2.06456i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −50108.0 | − | 86789.5i | −2.04359 | − | 3.53960i | ||||
\(845\) | −4456.43 | −0.181427 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11701.0 | −0.474676 | ||||||||
\(848\) | −44141.7 | − | 76455.7i | −1.78754 | − | 3.09611i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3628.31 | + | 6284.42i | −0.146412 | + | 0.253593i | ||||
\(851\) | 954.062 | − | 1652.48i | 0.0384311 | − | 0.0665645i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19838.8 | + | 34361.8i | 0.796326 | + | 1.37928i | 0.921993 | + | 0.387205i | \(0.126560\pi\) |
−0.125667 | + | 0.992072i | \(0.540107\pi\) | |||||||
\(854\) | −3429.37 | −0.137413 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 65149.0 | 2.60134 | ||||||||
\(857\) | 16604.7 | + | 28760.1i | 0.661849 | + | 1.14636i | 0.980129 | + | 0.198360i | \(0.0635614\pi\) |
−0.318280 | + | 0.947997i | \(0.603105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17202.4 | + | 29795.5i | −0.683282 | + | 1.18348i | 0.290691 | + | 0.956817i | \(0.406115\pi\) |
−0.973973 | + | 0.226663i | \(0.927219\pi\) | |||||||
\(860\) | 8313.09 | − | 14398.7i | 0.329621 | − | 0.570920i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5647.05 | − | 9780.98i | −0.223131 | − | 0.386475i | ||||
\(863\) | −12999.7 | −0.512765 | −0.256382 | − | 0.966575i | \(-0.582531\pi\) | ||||
−0.256382 | + | 0.966575i | \(0.582531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7734.58 | −0.304027 | ||||||||
\(866\) | 42973.9 | + | 74432.9i | 1.68627 | + | 2.92071i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −40224.8 | + | 69671.3i | −1.57295 | + | 2.72442i | ||||
\(869\) | 4780.25 | − | 8279.64i | 0.186604 | − | 0.323208i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −522.477 | − | 904.956i | −0.0203254 | − | 0.0352047i | ||||
\(872\) | −59636.4 | −2.31599 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21290.2 | 0.823972 | ||||||||
\(875\) | 839.608 | + | 1454.24i | 0.0324388 | + | 0.0561856i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11415.7 | − | 19772.6i | 0.439546 | − | 0.761317i | −0.558108 | − | 0.829768i | \(-0.688473\pi\) |
0.997654 | + | 0.0684517i | \(0.0218059\pi\) | |||||||
\(878\) | −1839.69 | + | 3186.43i | −0.0707135 | + | 0.122479i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −21610.8 | − | 37430.9i | −0.827839 | − | 1.43386i | ||||
\(881\) | 1889.31 | 0.0722502 | 0.0361251 | − | 0.999347i | \(-0.488499\pi\) | ||||
0.0361251 | + | 0.999347i | \(0.488499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1778.37 | −0.0677768 | −0.0338884 | − | 0.999426i | \(-0.510789\pi\) | ||||
−0.0338884 | + | 0.999426i | \(0.510789\pi\) | |||||||
\(884\) | 19983.3 | + | 34612.1i | 0.760308 | + | 1.31689i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17728.6 | + | 30706.8i | −0.672239 | + | 1.16435i | ||||
\(887\) | 11492.1 | − | 19904.8i | 0.435023 | − | 0.753482i | −0.562274 | − | 0.826951i | \(-0.690073\pi\) |
0.997298 | + | 0.0734685i | \(0.0234068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6674.11 | − | 11559.9i | −0.251791 | − | 0.436115i | ||||
\(890\) | −26412.3 | −0.994766 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22363.4 | 0.839441 | ||||||||
\(893\) | 4889.54 | + | 8468.93i | 0.183228 | + | 0.317359i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2059.93 | + | 3567.91i | −0.0769340 | + | 0.133254i | ||||
\(896\) | 9702.67 | − | 16805.5i | 0.361767 | − | 0.626600i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25895.0 | − | 44851.4i | −0.962279 | − | 1.66672i | ||||
\(899\) | 17183.4 | 0.637485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26170.3 | 0.967658 | ||||||||
\(902\) | 16008.5 | + | 27727.6i | 0.590938 | + | 1.02353i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43151.8 | + | 74741.1i | −1.58762 | + | 2.74984i | ||||
\(905\) | 11008.9 | − | 19067.9i | 0.404362 | − | 0.700375i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22705.0 | − | 39326.3i | −0.831211 | − | 1.43970i | −0.897078 | − | 0.441872i | \(-0.854315\pi\) |
0.0658671 | − | 0.997828i | \(-0.479019\pi\) | |||||||
\(908\) | 77377.5 | 2.82804 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12901.4 | 0.469973 | ||||||||
\(911\) | −15390.9 | − | 26657.8i | −0.559740 | − | 0.969497i | −0.997518 | − | 0.0704143i | \(-0.977568\pi\) |
0.437778 | − | 0.899083i | \(-0.355765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10898.0 | − | 18875.8i | 0.395038 | − | 0.684226i | ||||
\(914\) | −11807.7 | + | 20451.5i | −0.427311 | + | 0.740125i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1466.13 | − | 2539.41i | −0.0528845 | − | 0.0915986i | ||||
\(917\) | 18592.1 | 0.669538 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22457.3 | −0.806093 | −0.403046 | − | 0.915180i | \(-0.632049\pi\) | ||||
−0.403046 | + | 0.915180i | \(0.632049\pi\) | |||||||
\(920\) | −5858.33 | − | 10146.9i | −0.209938 | − | 0.363624i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 50336.3 | − | 87185.0i | 1.79798 | − | 3.11419i | ||||
\(923\) | −10410.1 | + | 18030.8i | −0.371238 | + | 0.643002i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 663.022 | + | 1148.39i | 0.0235676 | + | 0.0408203i | ||||
\(926\) | −89259.1 | −3.16764 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26621.8 | −0.941706 | ||||||||
\(929\) | −21827.1 | − | 37805.7i | −0.770855 | − | 1.33516i | −0.937095 | − | 0.349075i | \(-0.886496\pi\) |
0.166240 | − | 0.986085i | \(-0.446837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9048.22 | − | 15672.0i | 0.318521 | − | 0.551695i | ||||
\(932\) | 13026.9 | − | 22563.2i | 0.457843 | − | 0.793007i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3635.63 | + | 6297.10i | 0.127368 | + | 0.220607i | ||||
\(935\) | 12812.4 | 0.448138 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41123.3 | −1.43377 | −0.716884 | − | 0.697193i | \(-0.754432\pi\) | ||||
−0.716884 | + | 0.697193i | \(0.754432\pi\) | |||||||
\(938\) | −1032.49 | − | 1788.32i | −0.0359401 | − | 0.0622501i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4447.50 | − | 7703.30i | 0.154321 | − | 0.267291i | ||||
\(941\) | 11038.9 | − | 19119.9i | 0.382419 | − | 0.662370i | −0.608988 | − | 0.793179i | \(-0.708424\pi\) |
0.991408 | + | 0.130810i | \(0.0417576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2308.80 | + | 3998.95i | 0.0797293 | + | 0.138095i | ||||
\(944\) | −117088. | −4.03697 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40949.9 | −1.40740 | ||||||||
\(947\) | 4308.20 | + | 7462.03i | 0.147833 | + | 0.256054i | 0.930426 | − | 0.366479i | \(-0.119437\pi\) |
−0.782593 | + | 0.622533i | \(0.786104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15087.3 | − | 26131.9i | 0.516073 | − | 0.893864i | ||||
\(950\) | −7397.77 | + | 12813.3i | −0.252648 | + | 0.437599i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 23892.5 | + | 41382.9i | 0.813402 | + | 1.40885i | ||||
\(953\) | 29558.0 | 1.00470 | 0.502350 | − | 0.864664i | \(-0.332469\pi\) | ||||
0.502350 | + | 0.864664i | \(0.332469\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15234.6 | 0.516211 | ||||||||
\(956\) | 42731.7 | + | 74013.5i | 1.44565 | + | 2.50394i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 538.836 | − | 933.291i | 0.0181722 | − | 0.0314752i | ||||
\(959\) | −10391.9 | + | 17999.3i | −0.349919 | + | 0.606077i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28814.0 | − | 49907.3i | −0.967204 | − | 1.67525i | ||||
\(962\) | 10187.9 | 0.341448 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46244.0 | 1.54504 | ||||||||
\(965\) | −4727.26 | − | 8187.86i | −0.157695 | − | 0.273136i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22288.0 | + | 38603.9i | −0.741192 | + | 1.28378i | 0.210761 | + | 0.977538i | \(0.432406\pi\) |
−0.951953 | + | 0.306244i | \(0.900928\pi\) | |||||||
\(968\) | −28368.8 | + | 49136.2i | −0.941949 | + | 1.63150i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11712.9 | − | 20287.4i | −0.387711 | − | 0.671534i | ||||
\(971\) | −43702.8 | −1.44438 | −0.722188 | − | 0.691696i | \(-0.756864\pi\) | ||||
−0.722188 | + | 0.691696i | \(0.756864\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7247.56 | 0.238793 | ||||||||
\(974\) | −50394.4 | − | 87285.6i | −1.65784 | − | 2.87147i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4423.47 | + | 7661.68i | −0.145074 | + | 0.251275i | ||||
\(977\) | 22670.9 | − | 39267.1i | 0.742381 | − | 1.28584i | −0.209027 | − | 0.977910i | \(-0.567030\pi\) |
0.951408 | − | 0.307932i | \(-0.0996369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23316.9 | + | 40386.1i | 0.761197 | + | 1.31843i | ||||
\(980\) | −16460.4 | −0.536540 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −62256.8 | −2.02311 | ||||||||
\(983\) | 3680.26 | + | 6374.40i | 0.119412 | + | 0.206828i | 0.919535 | − | 0.393009i | \(-0.128566\pi\) |
−0.800123 | + | 0.599836i | \(0.795232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9130.01 | − | 15813.6i | 0.295336 | − | 0.511538i | ||||
\(986\) | 8434.73 | − | 14609.4i | 0.272431 | − | 0.471864i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 40744.1 | + | 70570.8i | 1.31199 | + | 2.27242i | ||||
\(989\) | −5905.91 | −0.189886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33328.4 | 1.06833 | 0.534164 | − | 0.845381i | \(-0.320627\pi\) | ||||
0.534164 | + | 0.845381i | \(0.320627\pi\) | |||||||
\(992\) | 67717.8 | + | 117291.i | 2.16738 | + | 3.75402i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20571.8 | + | 35631.3i | −0.656435 | + | 1.13698i | ||||
\(995\) | −8043.15 | + | 13931.1i | −0.256266 | + | 0.443866i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17665.8 | + | 30598.1i | 0.561166 | + | 0.971968i | 0.997395 | + | 0.0721326i | \(0.0229805\pi\) |
−0.436229 | + | 0.899836i | \(0.643686\pi\) | |||||||
\(998\) | 45845.6 | 1.45412 | ||||||||
\(999\) | 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 | 135.4.e.c.91.1 | 14 | ||
3.2 | odd | 2 | 45.4.e.c.31.7 | yes | 14 | ||
9.2 | odd | 6 | 45.4.e.c.16.7 | ✓ | 14 | ||
9.4 | even | 3 | 405.4.a.n.1.7 | 7 | |||
9.5 | odd | 6 | 405.4.a.m.1.1 | 7 | |||
9.7 | even | 3 | inner | 135.4.e.c.46.1 | 14 | ||
15.2 | even | 4 | 225.4.k.d.49.2 | 28 | |||
15.8 | even | 4 | 225.4.k.d.49.13 | 28 | |||
15.14 | odd | 2 | 225.4.e.d.76.1 | 14 | |||
45.2 | even | 12 | 225.4.k.d.124.13 | 28 | |||
45.4 | even | 6 | 2025.4.a.ba.1.1 | 7 | |||
45.14 | odd | 6 | 2025.4.a.bb.1.7 | 7 | |||
45.29 | odd | 6 | 225.4.e.d.151.1 | 14 | |||
45.38 | even | 12 | 225.4.k.d.124.2 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.7 | ✓ | 14 | 9.2 | odd | 6 | ||
45.4.e.c.31.7 | yes | 14 | 3.2 | odd | 2 | ||
135.4.e.c.46.1 | 14 | 9.7 | even | 3 | inner | ||
135.4.e.c.91.1 | 14 | 1.1 | even | 1 | trivial | ||
225.4.e.d.76.1 | 14 | 15.14 | odd | 2 | |||
225.4.e.d.151.1 | 14 | 45.29 | odd | 6 | |||
225.4.k.d.49.2 | 28 | 15.2 | even | 4 | |||
225.4.k.d.49.13 | 28 | 15.8 | even | 4 | |||
225.4.k.d.124.2 | 28 | 45.38 | even | 12 | |||
225.4.k.d.124.13 | 28 | 45.2 | even | 12 | |||
405.4.a.m.1.1 | 7 | 9.5 | odd | 6 | |||
405.4.a.n.1.7 | 7 | 9.4 | even | 3 | |||
2025.4.a.ba.1.1 | 7 | 45.4 | even | 6 | |||
2025.4.a.bb.1.7 | 7 | 45.14 | odd | 6 |