Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.a (trivial) |
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: | yes |
Analytic conductor: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 46x^{7} + 145x^{6} + 680x^{5} - 1501x^{4} - 3203x^{3} + 4784x^{2} + 3584x - 4096 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.16135\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.16135 | 1.11771 | 0.558853 | − | 0.829267i | \(-0.311241\pi\) | ||||
0.558853 | + | 0.829267i | \(0.311241\pi\) | |||||||
\(3\) | 7.08883 | 1.36425 | 0.682123 | − | 0.731237i | \(-0.261057\pi\) | ||||
0.682123 | + | 0.731237i | \(0.261057\pi\) | |||||||
\(4\) | 1.99415 | 0.249268 | ||||||||
\(5\) | 13.6039 | 1.21677 | 0.608386 | − | 0.793641i | \(-0.291817\pi\) | ||||
0.608386 | + | 0.793641i | \(0.291817\pi\) | |||||||
\(6\) | 22.4103 | 1.52483 | ||||||||
\(7\) | −14.3315 | −0.773827 | −0.386913 | − | 0.922116i | \(-0.626459\pi\) | ||||
−0.386913 | + | 0.922116i | \(0.626459\pi\) | |||||||
\(8\) | −18.9866 | −0.839098 | ||||||||
\(9\) | 23.2516 | 0.861169 | ||||||||
\(10\) | 43.0068 | 1.36000 | ||||||||
\(11\) | 67.7223 | 1.85628 | 0.928138 | − | 0.372237i | \(-0.121409\pi\) | ||||
0.928138 | + | 0.372237i | \(0.121409\pi\) | |||||||
\(12\) | 14.1362 | 0.340063 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −45.3068 | −0.864911 | ||||||||
\(15\) | 96.4360 | 1.65998 | ||||||||
\(16\) | −75.9766 | −1.18713 | ||||||||
\(17\) | 0.337795 | 0.00481925 | 0.00240963 | − | 0.999997i | \(-0.499233\pi\) | ||||
0.00240963 | + | 0.999997i | \(0.499233\pi\) | |||||||
\(18\) | 73.5064 | 0.962535 | ||||||||
\(19\) | −40.5229 | −0.489294 | −0.244647 | − | 0.969612i | \(-0.578672\pi\) | ||||
−0.244647 | + | 0.969612i | \(0.578672\pi\) | |||||||
\(20\) | 27.1282 | 0.303303 | ||||||||
\(21\) | −101.593 | −1.05569 | ||||||||
\(22\) | 214.094 | 2.07477 | ||||||||
\(23\) | −155.632 | −1.41093 | −0.705466 | − | 0.708744i | \(-0.749262\pi\) | ||||
−0.705466 | + | 0.708744i | \(0.749262\pi\) | |||||||
\(24\) | −134.593 | −1.14474 | ||||||||
\(25\) | 60.0670 | 0.480536 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.5720 | −0.189399 | ||||||||
\(28\) | −28.5791 | −0.192890 | ||||||||
\(29\) | −33.7925 | −0.216383 | −0.108192 | − | 0.994130i | \(-0.534506\pi\) | ||||
−0.108192 | + | 0.994130i | \(0.534506\pi\) | |||||||
\(30\) | 304.868 | 1.85537 | ||||||||
\(31\) | 157.397 | 0.911911 | 0.455956 | − | 0.890003i | \(-0.349298\pi\) | ||||
0.455956 | + | 0.890003i | \(0.349298\pi\) | |||||||
\(32\) | −88.2957 | −0.487769 | ||||||||
\(33\) | 480.072 | 2.53242 | ||||||||
\(34\) | 1.06789 | 0.00538651 | ||||||||
\(35\) | −194.964 | −0.941571 | ||||||||
\(36\) | 46.3670 | 0.214662 | ||||||||
\(37\) | 58.6204 | 0.260463 | 0.130231 | − | 0.991484i | \(-0.458428\pi\) | ||||
0.130231 | + | 0.991484i | \(0.458428\pi\) | |||||||
\(38\) | −128.107 | −0.546888 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −258.293 | −1.02099 | ||||||||
\(41\) | −59.3488 | −0.226066 | −0.113033 | − | 0.993591i | \(-0.536057\pi\) | ||||
−0.113033 | + | 0.993591i | \(0.536057\pi\) | |||||||
\(42\) | −321.173 | −1.17995 | ||||||||
\(43\) | −208.311 | −0.738769 | −0.369385 | − | 0.929277i | \(-0.620431\pi\) | ||||
−0.369385 | + | 0.929277i | \(0.620431\pi\) | |||||||
\(44\) | 135.048 | 0.462711 | ||||||||
\(45\) | 316.313 | 1.04785 | ||||||||
\(46\) | −492.006 | −1.57701 | ||||||||
\(47\) | 221.212 | 0.686533 | 0.343266 | − | 0.939238i | \(-0.388467\pi\) | ||||
0.343266 | + | 0.939238i | \(0.388467\pi\) | |||||||
\(48\) | −538.585 | −1.61954 | ||||||||
\(49\) | −137.609 | −0.401192 | ||||||||
\(50\) | 189.893 | 0.537098 | ||||||||
\(51\) | 2.39457 | 0.00657465 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −409.639 | −1.06167 | −0.530833 | − | 0.847477i | \(-0.678121\pi\) | ||||
−0.530833 | + | 0.847477i | \(0.678121\pi\) | |||||||
\(54\) | −84.0035 | −0.211693 | ||||||||
\(55\) | 921.289 | 2.25867 | ||||||||
\(56\) | 272.106 | 0.649316 | ||||||||
\(57\) | −287.260 | −0.667518 | ||||||||
\(58\) | −106.830 | −0.241853 | ||||||||
\(59\) | −173.587 | −0.383036 | −0.191518 | − | 0.981489i | \(-0.561341\pi\) | ||||
−0.191518 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(60\) | 192.308 | 0.413780 | ||||||||
\(61\) | 560.796 | 1.17709 | 0.588546 | − | 0.808464i | \(-0.299701\pi\) | ||||
0.588546 | + | 0.808464i | \(0.299701\pi\) | |||||||
\(62\) | 497.586 | 1.01925 | ||||||||
\(63\) | −333.229 | −0.666396 | ||||||||
\(64\) | 328.679 | 0.641951 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1517.68 | 2.83050 | ||||||||
\(67\) | 269.074 | 0.490635 | 0.245318 | − | 0.969443i | \(-0.421108\pi\) | ||||
0.245318 | + | 0.969443i | \(0.421108\pi\) | |||||||
\(68\) | 0.673613 | 0.00120129 | ||||||||
\(69\) | −1103.25 | −1.92486 | ||||||||
\(70\) | −616.351 | −1.05240 | ||||||||
\(71\) | −60.9754 | −0.101922 | −0.0509609 | − | 0.998701i | \(-0.516228\pi\) | ||||
−0.0509609 | + | 0.998701i | \(0.516228\pi\) | |||||||
\(72\) | −441.469 | −0.722605 | ||||||||
\(73\) | −282.066 | −0.452238 | −0.226119 | − | 0.974100i | \(-0.572604\pi\) | ||||
−0.226119 | + | 0.974100i | \(0.572604\pi\) | |||||||
\(74\) | 185.320 | 0.291121 | ||||||||
\(75\) | 425.805 | 0.655570 | ||||||||
\(76\) | −80.8086 | −0.121966 | ||||||||
\(77\) | −970.560 | −1.43644 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 984.026 | 1.40141 | 0.700706 | − | 0.713450i | \(-0.252868\pi\) | ||||
0.700706 | + | 0.713450i | \(0.252868\pi\) | |||||||
\(80\) | −1033.58 | −1.44447 | ||||||||
\(81\) | −816.157 | −1.11956 | ||||||||
\(82\) | −187.622 | −0.252676 | ||||||||
\(83\) | −1201.86 | −1.58942 | −0.794709 | − | 0.606991i | \(-0.792376\pi\) | ||||
−0.794709 | + | 0.606991i | \(0.792376\pi\) | |||||||
\(84\) | −202.592 | −0.263150 | ||||||||
\(85\) | 4.59534 | 0.00586394 | ||||||||
\(86\) | −658.543 | −0.825727 | ||||||||
\(87\) | −239.550 | −0.295200 | ||||||||
\(88\) | −1285.82 | −1.55760 | ||||||||
\(89\) | 539.899 | 0.643024 | 0.321512 | − | 0.946906i | \(-0.395809\pi\) | ||||
0.321512 | + | 0.946906i | \(0.395809\pi\) | |||||||
\(90\) | 999.976 | 1.17119 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −310.352 | −0.351701 | ||||||||
\(93\) | 1115.76 | 1.24407 | ||||||||
\(94\) | 699.328 | 0.767342 | ||||||||
\(95\) | −551.271 | −0.595360 | ||||||||
\(96\) | −625.913 | −0.665438 | ||||||||
\(97\) | −1587.25 | −1.66146 | −0.830728 | − | 0.556678i | \(-0.812076\pi\) | ||||
−0.830728 | + | 0.556678i | \(0.812076\pi\) | |||||||
\(98\) | −435.030 | −0.448415 | ||||||||
\(99\) | 1574.65 | 1.59857 | ||||||||
\(100\) | 119.782 | 0.119782 | ||||||||
\(101\) | 1160.73 | 1.14353 | 0.571765 | − | 0.820417i | \(-0.306259\pi\) | ||||
0.571765 | + | 0.820417i | \(0.306259\pi\) | |||||||
\(102\) | 7.57009 | 0.00734853 | ||||||||
\(103\) | −82.2962 | −0.0787270 | −0.0393635 | − | 0.999225i | \(-0.512533\pi\) | ||||
−0.0393635 | + | 0.999225i | \(0.512533\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1382.07 | −1.28454 | ||||||||
\(106\) | −1295.01 | −1.18663 | ||||||||
\(107\) | 1322.04 | 1.19446 | 0.597229 | − | 0.802071i | \(-0.296269\pi\) | ||||
0.597229 | + | 0.802071i | \(0.296269\pi\) | |||||||
\(108\) | −52.9885 | −0.0472113 | ||||||||
\(109\) | 2073.41 | 1.82199 | 0.910994 | − | 0.412420i | \(-0.135316\pi\) | ||||
0.910994 | + | 0.412420i | \(0.135316\pi\) | |||||||
\(110\) | 2912.52 | 2.52453 | ||||||||
\(111\) | 415.550 | 0.355336 | ||||||||
\(112\) | 1088.86 | 0.918636 | ||||||||
\(113\) | −1602.82 | −1.33434 | −0.667172 | − | 0.744904i | \(-0.732495\pi\) | ||||
−0.667172 | + | 0.744904i | \(0.732495\pi\) | |||||||
\(114\) | −908.131 | −0.746090 | ||||||||
\(115\) | −2117.20 | −1.71678 | ||||||||
\(116\) | −67.3872 | −0.0539375 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −548.771 | −0.428122 | ||||||||
\(119\) | −4.84110 | −0.00372927 | ||||||||
\(120\) | −1830.99 | −1.39288 | ||||||||
\(121\) | 3255.30 | 2.44576 | ||||||||
\(122\) | 1772.87 | 1.31564 | ||||||||
\(123\) | −420.714 | −0.308410 | ||||||||
\(124\) | 313.872 | 0.227311 | ||||||||
\(125\) | −883.344 | −0.632070 | ||||||||
\(126\) | −1053.45 | −0.744835 | ||||||||
\(127\) | 614.495 | 0.429352 | 0.214676 | − | 0.976685i | \(-0.431131\pi\) | ||||
0.214676 | + | 0.976685i | \(0.431131\pi\) | |||||||
\(128\) | 1745.43 | 1.20528 | ||||||||
\(129\) | −1476.68 | −1.00786 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −330.171 | −0.220208 | −0.110104 | − | 0.993920i | \(-0.535118\pi\) | ||||
−0.110104 | + | 0.993920i | \(0.535118\pi\) | |||||||
\(132\) | 957.333 | 0.631251 | ||||||||
\(133\) | 580.753 | 0.378629 | ||||||||
\(134\) | 850.636 | 0.548386 | ||||||||
\(135\) | −361.484 | −0.230456 | ||||||||
\(136\) | −6.41358 | −0.00404383 | ||||||||
\(137\) | 2302.54 | 1.43591 | 0.717953 | − | 0.696091i | \(-0.245079\pi\) | ||||
0.717953 | + | 0.696091i | \(0.245079\pi\) | |||||||
\(138\) | −3487.75 | −2.15143 | ||||||||
\(139\) | 1207.22 | 0.736656 | 0.368328 | − | 0.929696i | \(-0.379930\pi\) | ||||
0.368328 | + | 0.929696i | \(0.379930\pi\) | |||||||
\(140\) | −388.788 | −0.234704 | ||||||||
\(141\) | 1568.13 | 0.936600 | ||||||||
\(142\) | −192.765 | −0.113919 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1766.57 | −1.02232 | ||||||||
\(145\) | −459.711 | −0.263289 | ||||||||
\(146\) | −891.711 | −0.505470 | ||||||||
\(147\) | −975.486 | −0.547325 | ||||||||
\(148\) | 116.898 | 0.0649251 | ||||||||
\(149\) | 338.938 | 0.186355 | 0.0931774 | − | 0.995650i | \(-0.470298\pi\) | ||||
0.0931774 | + | 0.995650i | \(0.470298\pi\) | |||||||
\(150\) | 1346.12 | 0.732734 | ||||||||
\(151\) | 1694.81 | 0.913386 | 0.456693 | − | 0.889624i | \(-0.349034\pi\) | ||||
0.456693 | + | 0.889624i | \(0.349034\pi\) | |||||||
\(152\) | 769.393 | 0.410566 | ||||||||
\(153\) | 7.85426 | 0.00415019 | ||||||||
\(154\) | −3068.28 | −1.60551 | ||||||||
\(155\) | 2141.21 | 1.10959 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.59250 | 0.00487621 | 0.00243811 | − | 0.999997i | \(-0.499224\pi\) | ||||
0.00243811 | + | 0.999997i | \(0.499224\pi\) | |||||||
\(158\) | 3110.85 | 1.56637 | ||||||||
\(159\) | −2903.86 | −1.44837 | ||||||||
\(160\) | −1201.17 | −0.593504 | ||||||||
\(161\) | 2230.43 | 1.09182 | ||||||||
\(162\) | −2580.16 | −1.25134 | ||||||||
\(163\) | 122.100 | 0.0586725 | 0.0293363 | − | 0.999570i | \(-0.490661\pi\) | ||||
0.0293363 | + | 0.999570i | \(0.490661\pi\) | |||||||
\(164\) | −118.350 | −0.0563512 | ||||||||
\(165\) | 6530.87 | 3.08138 | ||||||||
\(166\) | −3799.51 | −1.77650 | ||||||||
\(167\) | 2211.25 | 1.02462 | 0.512309 | − | 0.858801i | \(-0.328790\pi\) | ||||
0.512309 | + | 0.858801i | \(0.328790\pi\) | |||||||
\(168\) | 1928.92 | 0.885828 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 14.5275 | 0.00655416 | ||||||||
\(171\) | −942.221 | −0.421365 | ||||||||
\(172\) | −415.402 | −0.184152 | ||||||||
\(173\) | −213.874 | −0.0939914 | −0.0469957 | − | 0.998895i | \(-0.514965\pi\) | ||||
−0.0469957 | + | 0.998895i | \(0.514965\pi\) | |||||||
\(174\) | −757.301 | −0.329947 | ||||||||
\(175\) | −860.848 | −0.371852 | ||||||||
\(176\) | −5145.30 | −2.20365 | ||||||||
\(177\) | −1230.53 | −0.522556 | ||||||||
\(178\) | 1706.81 | 0.718712 | ||||||||
\(179\) | 2967.41 | 1.23907 | 0.619537 | − | 0.784967i | \(-0.287320\pi\) | ||||
0.619537 | + | 0.784967i | \(0.287320\pi\) | |||||||
\(180\) | 630.774 | 0.261195 | ||||||||
\(181\) | 2329.44 | 0.956609 | 0.478304 | − | 0.878194i | \(-0.341252\pi\) | ||||
0.478304 | + | 0.878194i | \(0.341252\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3975.39 | 1.60584 | ||||||||
\(184\) | 2954.92 | 1.18391 | ||||||||
\(185\) | 797.467 | 0.316924 | ||||||||
\(186\) | 3527.30 | 1.39051 | ||||||||
\(187\) | 22.8762 | 0.00894586 | ||||||||
\(188\) | 441.128 | 0.171131 | ||||||||
\(189\) | 380.816 | 0.146562 | ||||||||
\(190\) | −1742.76 | −0.665438 | ||||||||
\(191\) | −4479.76 | −1.69709 | −0.848544 | − | 0.529125i | \(-0.822520\pi\) | ||||
−0.848544 | + | 0.529125i | \(0.822520\pi\) | |||||||
\(192\) | 2329.95 | 0.875779 | ||||||||
\(193\) | 1302.63 | 0.485830 | 0.242915 | − | 0.970048i | \(-0.421896\pi\) | ||||
0.242915 | + | 0.970048i | \(0.421896\pi\) | |||||||
\(194\) | −5017.87 | −1.85702 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −274.412 | −0.100004 | ||||||||
\(197\) | −740.954 | −0.267974 | −0.133987 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133987 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(198\) | 4978.02 | 1.78673 | ||||||||
\(199\) | −4688.74 | −1.67023 | −0.835115 | − | 0.550075i | \(-0.814599\pi\) | ||||
−0.835115 | + | 0.550075i | \(0.814599\pi\) | |||||||
\(200\) | −1140.47 | −0.403217 | ||||||||
\(201\) | 1907.42 | 0.669348 | ||||||||
\(202\) | 3669.46 | 1.27813 | ||||||||
\(203\) | 484.297 | 0.167443 | ||||||||
\(204\) | 4.77513 | 0.00163885 | ||||||||
\(205\) | −807.377 | −0.275071 | ||||||||
\(206\) | −260.167 | −0.0879937 | ||||||||
\(207\) | −3618.68 | −1.21505 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2744.30 | −0.908265 | ||||||||
\(210\) | −4369.21 | −1.43573 | ||||||||
\(211\) | −3205.11 | −1.04573 | −0.522865 | − | 0.852416i | \(-0.675137\pi\) | ||||
−0.522865 | + | 0.852416i | \(0.675137\pi\) | |||||||
\(212\) | −816.880 | −0.264640 | ||||||||
\(213\) | −432.244 | −0.139046 | ||||||||
\(214\) | 4179.45 | 1.33505 | ||||||||
\(215\) | −2833.84 | −0.898914 | ||||||||
\(216\) | 504.513 | 0.158925 | ||||||||
\(217\) | −2255.72 | −0.705661 | ||||||||
\(218\) | 6554.78 | 2.03645 | ||||||||
\(219\) | −1999.52 | −0.616964 | ||||||||
\(220\) | 1837.18 | 0.563014 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1313.70 | 0.397161 | ||||||||
\(223\) | 1057.39 | 0.317525 | 0.158762 | − | 0.987317i | \(-0.449250\pi\) | ||||
0.158762 | + | 0.987317i | \(0.449250\pi\) | |||||||
\(224\) | 1265.41 | 0.377449 | ||||||||
\(225\) | 1396.65 | 0.413823 | ||||||||
\(226\) | −5067.09 | −1.49141 | ||||||||
\(227\) | 5159.68 | 1.50863 | 0.754317 | − | 0.656510i | \(-0.227968\pi\) | ||||
0.754317 | + | 0.656510i | \(0.227968\pi\) | |||||||
\(228\) | −572.839 | −0.166391 | ||||||||
\(229\) | 1698.25 | 0.490059 | 0.245030 | − | 0.969516i | \(-0.421202\pi\) | ||||
0.245030 | + | 0.969516i | \(0.421202\pi\) | |||||||
\(230\) | −6693.22 | −1.91886 | ||||||||
\(231\) | −6880.14 | −1.95965 | ||||||||
\(232\) | 641.606 | 0.181567 | ||||||||
\(233\) | 3162.23 | 0.889119 | 0.444559 | − | 0.895749i | \(-0.353360\pi\) | ||||
0.444559 | + | 0.895749i | \(0.353360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3009.35 | 0.835354 | ||||||||
\(236\) | −346.159 | −0.0954788 | ||||||||
\(237\) | 6975.60 | 1.91187 | ||||||||
\(238\) | −15.3044 | −0.00416823 | ||||||||
\(239\) | 2350.04 | 0.636030 | 0.318015 | − | 0.948086i | \(-0.396984\pi\) | ||||
0.318015 | + | 0.948086i | \(0.396984\pi\) | |||||||
\(240\) | −7326.88 | −1.97062 | ||||||||
\(241\) | −5167.18 | −1.38111 | −0.690555 | − | 0.723280i | \(-0.742633\pi\) | ||||
−0.690555 | + | 0.723280i | \(0.742633\pi\) | |||||||
\(242\) | 10291.2 | 2.73364 | ||||||||
\(243\) | −5068.16 | −1.33795 | ||||||||
\(244\) | 1118.31 | 0.293412 | ||||||||
\(245\) | −1872.02 | −0.488159 | ||||||||
\(246\) | −1330.02 | −0.344712 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2988.43 | −0.765183 | ||||||||
\(249\) | −8519.81 | −2.16836 | ||||||||
\(250\) | −2792.56 | −0.706469 | ||||||||
\(251\) | 2894.01 | 0.727761 | 0.363880 | − | 0.931446i | \(-0.381452\pi\) | ||||
0.363880 | + | 0.931446i | \(0.381452\pi\) | |||||||
\(252\) | −664.508 | −0.166111 | ||||||||
\(253\) | −10539.7 | −2.61908 | ||||||||
\(254\) | 1942.64 | 0.479889 | ||||||||
\(255\) | 32.5756 | 0.00799986 | ||||||||
\(256\) | 2888.50 | 0.705201 | ||||||||
\(257\) | −6162.63 | −1.49577 | −0.747887 | − | 0.663826i | \(-0.768932\pi\) | ||||
−0.747887 | + | 0.663826i | \(0.768932\pi\) | |||||||
\(258\) | −4668.30 | −1.12650 | ||||||||
\(259\) | −840.116 | −0.201553 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −785.729 | −0.186343 | ||||||||
\(262\) | −1043.79 | −0.246127 | ||||||||
\(263\) | −199.427 | −0.0467574 | −0.0233787 | − | 0.999727i | \(-0.507442\pi\) | ||||
−0.0233787 | + | 0.999727i | \(0.507442\pi\) | |||||||
\(264\) | −9114.94 | −2.12495 | ||||||||
\(265\) | −5572.70 | −1.29181 | ||||||||
\(266\) | 1835.96 | 0.423196 | ||||||||
\(267\) | 3827.25 | 0.877243 | ||||||||
\(268\) | 536.572 | 0.122300 | ||||||||
\(269\) | 1108.00 | 0.251138 | 0.125569 | − | 0.992085i | \(-0.459924\pi\) | ||||
0.125569 | + | 0.992085i | \(0.459924\pi\) | |||||||
\(270\) | −1142.78 | −0.257582 | ||||||||
\(271\) | 406.054 | 0.0910186 | 0.0455093 | − | 0.998964i | \(-0.485509\pi\) | ||||
0.0455093 | + | 0.998964i | \(0.485509\pi\) | |||||||
\(272\) | −25.6645 | −0.00572110 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7279.13 | 1.60492 | ||||||||
\(275\) | 4067.87 | 0.892007 | ||||||||
\(276\) | −2200.04 | −0.479806 | ||||||||
\(277\) | 288.810 | 0.0626460 | 0.0313230 | − | 0.999509i | \(-0.490028\pi\) | ||||
0.0313230 | + | 0.999509i | \(0.490028\pi\) | |||||||
\(278\) | 3816.45 | 0.823366 | ||||||||
\(279\) | 3659.72 | 0.785310 | ||||||||
\(280\) | 3701.71 | 0.790071 | ||||||||
\(281\) | −5134.93 | −1.09012 | −0.545061 | − | 0.838396i | \(-0.683494\pi\) | ||||
−0.545061 | + | 0.838396i | \(0.683494\pi\) | |||||||
\(282\) | 4957.42 | 1.04684 | ||||||||
\(283\) | 5274.40 | 1.10788 | 0.553940 | − | 0.832556i | \(-0.313124\pi\) | ||||
0.553940 | + | 0.832556i | \(0.313124\pi\) | |||||||
\(284\) | −121.594 | −0.0254059 | ||||||||
\(285\) | −3907.87 | −0.812218 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 850.556 | 0.174936 | ||||||||
\(288\) | −2053.01 | −0.420052 | ||||||||
\(289\) | −4912.89 | −0.999977 | ||||||||
\(290\) | −1453.31 | −0.294280 | ||||||||
\(291\) | −11251.8 | −2.26664 | ||||||||
\(292\) | −562.482 | −0.112729 | ||||||||
\(293\) | −1445.69 | −0.288253 | −0.144127 | − | 0.989559i | \(-0.546037\pi\) | ||||
−0.144127 | + | 0.989559i | \(0.546037\pi\) | |||||||
\(294\) | −3083.86 | −0.611749 | ||||||||
\(295\) | −2361.47 | −0.466068 | ||||||||
\(296\) | −1113.00 | −0.218554 | ||||||||
\(297\) | −1799.52 | −0.351578 | ||||||||
\(298\) | 1071.50 | 0.208290 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 849.117 | 0.163413 | ||||||||
\(301\) | 2985.40 | 0.571679 | ||||||||
\(302\) | 5357.88 | 1.02090 | ||||||||
\(303\) | 8228.19 | 1.56006 | ||||||||
\(304\) | 3078.79 | 0.580858 | ||||||||
\(305\) | 7629.04 | 1.43225 | ||||||||
\(306\) | 24.8301 | 0.00463870 | ||||||||
\(307\) | −9421.42 | −1.75149 | −0.875747 | − | 0.482770i | \(-0.839631\pi\) | ||||
−0.875747 | + | 0.482770i | \(0.839631\pi\) | |||||||
\(308\) | −1935.44 | −0.358058 | ||||||||
\(309\) | −583.384 | −0.107403 | ||||||||
\(310\) | 6769.12 | 1.24019 | ||||||||
\(311\) | 7885.87 | 1.43784 | 0.718918 | − | 0.695095i | \(-0.244638\pi\) | ||||
0.718918 | + | 0.695095i | \(0.244638\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −550.423 | −0.0993986 | −0.0496993 | − | 0.998764i | \(-0.515826\pi\) | ||||
−0.0496993 | + | 0.998764i | \(0.515826\pi\) | |||||||
\(314\) | 30.3253 | 0.00545017 | ||||||||
\(315\) | −4533.23 | −0.810852 | ||||||||
\(316\) | 1962.29 | 0.349328 | ||||||||
\(317\) | 150.974 | 0.0267494 | 0.0133747 | − | 0.999911i | \(-0.495743\pi\) | ||||
0.0133747 | + | 0.999911i | \(0.495743\pi\) | |||||||
\(318\) | −9180.14 | −1.61886 | ||||||||
\(319\) | −2288.51 | −0.401667 | ||||||||
\(320\) | 4471.32 | 0.781108 | ||||||||
\(321\) | 9371.76 | 1.62953 | ||||||||
\(322\) | 7051.18 | 1.22033 | ||||||||
\(323\) | −13.6884 | −0.00235803 | ||||||||
\(324\) | −1627.54 | −0.279070 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 386.002 | 0.0655787 | ||||||||
\(327\) | 14698.1 | 2.48564 | ||||||||
\(328\) | 1126.83 | 0.189692 | ||||||||
\(329\) | −3170.29 | −0.531257 | ||||||||
\(330\) | 20646.4 | 3.44408 | ||||||||
\(331\) | 7079.29 | 1.17557 | 0.587784 | − | 0.809018i | \(-0.300001\pi\) | ||||
0.587784 | + | 0.809018i | \(0.300001\pi\) | |||||||
\(332\) | −2396.69 | −0.396191 | ||||||||
\(333\) | 1363.02 | 0.224303 | ||||||||
\(334\) | 6990.52 | 1.14522 | ||||||||
\(335\) | 3660.46 | 0.596992 | ||||||||
\(336\) | 7718.72 | 1.25325 | ||||||||
\(337\) | −6633.34 | −1.07223 | −0.536114 | − | 0.844145i | \(-0.680108\pi\) | ||||
−0.536114 | + | 0.844145i | \(0.680108\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11362.1 | −1.82037 | ||||||||
\(340\) | 9.16378 | 0.00146169 | ||||||||
\(341\) | 10659.2 | 1.69276 | ||||||||
\(342\) | −2978.69 | −0.470963 | ||||||||
\(343\) | 6887.83 | 1.08428 | ||||||||
\(344\) | 3955.11 | 0.619900 | ||||||||
\(345\) | −15008.5 | −2.34212 | ||||||||
\(346\) | −676.130 | −0.105055 | ||||||||
\(347\) | 6404.17 | 0.990760 | 0.495380 | − | 0.868676i | \(-0.335029\pi\) | ||||
0.495380 | + | 0.868676i | \(0.335029\pi\) | |||||||
\(348\) | −477.697 | −0.0735840 | ||||||||
\(349\) | 168.098 | 0.0257825 | 0.0128913 | − | 0.999917i | \(-0.495896\pi\) | ||||
0.0128913 | + | 0.999917i | \(0.495896\pi\) | |||||||
\(350\) | −2721.45 | −0.415621 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5979.58 | −0.905434 | ||||||||
\(353\) | −8451.92 | −1.27436 | −0.637182 | − | 0.770713i | \(-0.719900\pi\) | ||||
−0.637182 | + | 0.770713i | \(0.719900\pi\) | |||||||
\(354\) | −3890.14 | −0.584065 | ||||||||
\(355\) | −829.505 | −0.124016 | ||||||||
\(356\) | 1076.64 | 0.160285 | ||||||||
\(357\) | −34.3178 | −0.00508764 | ||||||||
\(358\) | 9381.01 | 1.38492 | ||||||||
\(359\) | 2631.92 | 0.386929 | 0.193464 | − | 0.981107i | \(-0.438028\pi\) | ||||
0.193464 | + | 0.981107i | \(0.438028\pi\) | |||||||
\(360\) | −6005.71 | −0.879246 | ||||||||
\(361\) | −5216.89 | −0.760591 | ||||||||
\(362\) | 7364.19 | 1.06921 | ||||||||
\(363\) | 23076.3 | 3.33662 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3837.21 | −0.550271 | ||||||||
\(366\) | 12567.6 | 1.79486 | ||||||||
\(367\) | −13269.9 | −1.88742 | −0.943708 | − | 0.330780i | \(-0.892688\pi\) | ||||
−0.943708 | + | 0.330780i | \(0.892688\pi\) | |||||||
\(368\) | 11824.4 | 1.67496 | ||||||||
\(369\) | −1379.95 | −0.194681 | ||||||||
\(370\) | 2521.07 | 0.354228 | ||||||||
\(371\) | 5870.73 | 0.821545 | ||||||||
\(372\) | 2224.98 | 0.310108 | ||||||||
\(373\) | −11680.1 | −1.62137 | −0.810684 | − | 0.585483i | \(-0.800905\pi\) | ||||
−0.810684 | + | 0.585483i | \(0.800905\pi\) | |||||||
\(374\) | 72.3198 | 0.00999885 | ||||||||
\(375\) | −6261.88 | −0.862299 | ||||||||
\(376\) | −4200.06 | −0.576068 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1203.89 | 0.163814 | ||||||||
\(379\) | −3378.23 | −0.457857 | −0.228928 | − | 0.973443i | \(-0.573522\pi\) | ||||
−0.228928 | + | 0.973443i | \(0.573522\pi\) | |||||||
\(380\) | −1099.31 | −0.148404 | ||||||||
\(381\) | 4356.06 | 0.585742 | ||||||||
\(382\) | −14162.1 | −1.89685 | ||||||||
\(383\) | −4380.92 | −0.584476 | −0.292238 | − | 0.956346i | \(-0.594400\pi\) | ||||
−0.292238 | + | 0.956346i | \(0.594400\pi\) | |||||||
\(384\) | 12373.1 | 1.64430 | ||||||||
\(385\) | −13203.4 | −1.74782 | ||||||||
\(386\) | 4118.06 | 0.543015 | ||||||||
\(387\) | −4843.55 | −0.636205 | ||||||||
\(388\) | −3165.22 | −0.414148 | ||||||||
\(389\) | −12484.0 | −1.62716 | −0.813578 | − | 0.581456i | \(-0.802483\pi\) | ||||
−0.813578 | + | 0.581456i | \(0.802483\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.5716 | −0.00679964 | ||||||||
\(392\) | 2612.73 | 0.336639 | ||||||||
\(393\) | −2340.53 | −0.300417 | ||||||||
\(394\) | −2342.42 | −0.299516 | ||||||||
\(395\) | 13386.6 | 1.70520 | ||||||||
\(396\) | 3140.08 | 0.398472 | ||||||||
\(397\) | 9450.48 | 1.19473 | 0.597363 | − | 0.801971i | \(-0.296215\pi\) | ||||
0.597363 | + | 0.801971i | \(0.296215\pi\) | |||||||
\(398\) | −14822.8 | −1.86683 | ||||||||
\(399\) | 4116.86 | 0.516544 | ||||||||
\(400\) | −4563.68 | −0.570460 | ||||||||
\(401\) | 2906.03 | 0.361895 | 0.180948 | − | 0.983493i | \(-0.442084\pi\) | ||||
0.180948 | + | 0.983493i | \(0.442084\pi\) | |||||||
\(402\) | 6030.02 | 0.748134 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2314.66 | 0.285046 | ||||||||
\(405\) | −11102.9 | −1.36225 | ||||||||
\(406\) | 1531.03 | 0.187152 | ||||||||
\(407\) | 3969.90 | 0.483491 | ||||||||
\(408\) | −45.4648 | −0.00551678 | ||||||||
\(409\) | −5795.93 | −0.700710 | −0.350355 | − | 0.936617i | \(-0.613939\pi\) | ||||
−0.350355 | + | 0.936617i | \(0.613939\pi\) | |||||||
\(410\) | −2552.40 | −0.307449 | ||||||||
\(411\) | 16322.3 | 1.95893 | ||||||||
\(412\) | −164.111 | −0.0196242 | ||||||||
\(413\) | 2487.76 | 0.296404 | ||||||||
\(414\) | −11439.9 | −1.35807 | ||||||||
\(415\) | −16350.1 | −1.93396 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8557.79 | 1.00498 | ||||||||
\(418\) | −8675.71 | −1.01517 | ||||||||
\(419\) | −4142.47 | −0.482990 | −0.241495 | − | 0.970402i | \(-0.577638\pi\) | ||||
−0.241495 | + | 0.970402i | \(0.577638\pi\) | |||||||
\(420\) | −2756.05 | −0.320194 | ||||||||
\(421\) | −1426.92 | −0.165187 | −0.0825935 | − | 0.996583i | \(-0.526320\pi\) | ||||
−0.0825935 | + | 0.996583i | \(0.526320\pi\) | |||||||
\(422\) | −10132.5 | −1.16882 | ||||||||
\(423\) | 5143.52 | 0.591221 | ||||||||
\(424\) | 7777.66 | 0.890841 | ||||||||
\(425\) | 20.2903 | 0.00231582 | ||||||||
\(426\) | −1366.48 | −0.155413 | ||||||||
\(427\) | −8037.04 | −0.910865 | ||||||||
\(428\) | 2636.35 | 0.297740 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8958.78 | −1.00472 | ||||||||
\(431\) | 2543.08 | 0.284213 | 0.142106 | − | 0.989851i | \(-0.454612\pi\) | ||||
0.142106 | + | 0.989851i | \(0.454612\pi\) | |||||||
\(432\) | 2018.85 | 0.224842 | ||||||||
\(433\) | −3448.44 | −0.382728 | −0.191364 | − | 0.981519i | \(-0.561291\pi\) | ||||
−0.191364 | + | 0.981519i | \(0.561291\pi\) | |||||||
\(434\) | −7131.14 | −0.788723 | ||||||||
\(435\) | −3258.82 | −0.359191 | ||||||||
\(436\) | 4134.68 | 0.454164 | ||||||||
\(437\) | 6306.65 | 0.690361 | ||||||||
\(438\) | −6321.19 | −0.689585 | ||||||||
\(439\) | −12642.6 | −1.37448 | −0.687240 | − | 0.726431i | \(-0.741178\pi\) | ||||
−0.687240 | + | 0.726431i | \(0.741178\pi\) | |||||||
\(440\) | −17492.2 | −1.89524 | ||||||||
\(441\) | −3199.62 | −0.345494 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8486.59 | 0.910181 | 0.455091 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455091 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(444\) | 828.667 | 0.0885739 | ||||||||
\(445\) | 7344.74 | 0.782414 | ||||||||
\(446\) | 3342.78 | 0.354900 | ||||||||
\(447\) | 2402.67 | 0.254234 | ||||||||
\(448\) | −4710.45 | −0.496759 | ||||||||
\(449\) | −11369.5 | −1.19502 | −0.597508 | − | 0.801863i | \(-0.703842\pi\) | ||||
−0.597508 | + | 0.801863i | \(0.703842\pi\) | |||||||
\(450\) | 4415.31 | 0.462532 | ||||||||
\(451\) | −4019.23 | −0.419642 | ||||||||
\(452\) | −3196.26 | −0.332610 | ||||||||
\(453\) | 12014.2 | 1.24608 | ||||||||
\(454\) | 16311.6 | 1.68621 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5454.10 | 0.560113 | ||||||||
\(457\) | −11289.0 | −1.15553 | −0.577766 | − | 0.816202i | \(-0.696075\pi\) | ||||
−0.577766 | + | 0.816202i | \(0.696075\pi\) | |||||||
\(458\) | 5368.77 | 0.547742 | ||||||||
\(459\) | −8.97589 | −0.000912764 0 | ||||||||
\(460\) | −4222.01 | −0.427940 | ||||||||
\(461\) | −3834.12 | −0.387359 | −0.193680 | − | 0.981065i | \(-0.562042\pi\) | ||||
−0.193680 | + | 0.981065i | \(0.562042\pi\) | |||||||
\(462\) | −21750.5 | −2.19032 | ||||||||
\(463\) | −1294.44 | −0.129930 | −0.0649651 | − | 0.997888i | \(-0.520694\pi\) | ||||
−0.0649651 | + | 0.997888i | \(0.520694\pi\) | |||||||
\(464\) | 2567.44 | 0.256876 | ||||||||
\(465\) | 15178.7 | 1.51375 | ||||||||
\(466\) | 9996.93 | 0.993774 | ||||||||
\(467\) | 13861.5 | 1.37352 | 0.686760 | − | 0.726884i | \(-0.259032\pi\) | ||||
0.686760 | + | 0.726884i | \(0.259032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3856.22 | −0.379667 | ||||||||
\(470\) | 9513.61 | 0.933681 | ||||||||
\(471\) | 67.9997 | 0.00665235 | ||||||||
\(472\) | 3295.84 | 0.321405 | ||||||||
\(473\) | −14107.3 | −1.37136 | ||||||||
\(474\) | 22052.3 | 2.13691 | ||||||||
\(475\) | −2434.09 | −0.235124 | ||||||||
\(476\) | −9.65386 | −0.000929588 0 | ||||||||
\(477\) | −9524.75 | −0.914274 | ||||||||
\(478\) | 7429.29 | 0.710895 | ||||||||
\(479\) | 9627.66 | 0.918369 | 0.459185 | − | 0.888341i | \(-0.348142\pi\) | ||||
0.459185 | + | 0.888341i | \(0.348142\pi\) | |||||||
\(480\) | −8514.88 | −0.809686 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16335.3 | −1.54368 | ||||||||
\(483\) | 15811.2 | 1.48951 | ||||||||
\(484\) | 6491.55 | 0.609650 | ||||||||
\(485\) | −21592.9 | −2.02162 | ||||||||
\(486\) | −16022.2 | −1.49544 | ||||||||
\(487\) | 11952.8 | 1.11219 | 0.556094 | − | 0.831120i | \(-0.312300\pi\) | ||||
0.556094 | + | 0.831120i | \(0.312300\pi\) | |||||||
\(488\) | −10647.6 | −0.987695 | ||||||||
\(489\) | 865.548 | 0.0800438 | ||||||||
\(490\) | −5918.12 | −0.545619 | ||||||||
\(491\) | 5410.12 | 0.497261 | 0.248631 | − | 0.968598i | \(-0.420020\pi\) | ||||
0.248631 | + | 0.968598i | \(0.420020\pi\) | |||||||
\(492\) | −838.965 | −0.0768769 | ||||||||
\(493\) | −11.4149 | −0.00104281 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21421.4 | 1.94509 | ||||||||
\(496\) | −11958.4 | −1.08256 | ||||||||
\(497\) | 873.867 | 0.0788698 | ||||||||
\(498\) | −26934.1 | −2.42359 | ||||||||
\(499\) | 14472.9 | 1.29838 | 0.649192 | − | 0.760624i | \(-0.275107\pi\) | ||||
0.649192 | + | 0.760624i | \(0.275107\pi\) | |||||||
\(500\) | −1761.52 | −0.157555 | ||||||||
\(501\) | 15675.2 | 1.39783 | ||||||||
\(502\) | 9148.97 | 0.813423 | ||||||||
\(503\) | −601.940 | −0.0533582 | −0.0266791 | − | 0.999644i | \(-0.508493\pi\) | ||||
−0.0266791 | + | 0.999644i | \(0.508493\pi\) | |||||||
\(504\) | 6326.90 | 0.559171 | ||||||||
\(505\) | 15790.4 | 1.39142 | ||||||||
\(506\) | −33319.8 | −2.92736 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1225.39 | 0.107024 | ||||||||
\(509\) | −17420.8 | −1.51702 | −0.758512 | − | 0.651659i | \(-0.774073\pi\) | ||||
−0.758512 | + | 0.651659i | \(0.774073\pi\) | |||||||
\(510\) | 102.983 | 0.00894149 | ||||||||
\(511\) | 4042.43 | 0.349954 | ||||||||
\(512\) | −4831.90 | −0.417074 | ||||||||
\(513\) | 1076.78 | 0.0926721 | ||||||||
\(514\) | −19482.2 | −1.67184 | ||||||||
\(515\) | −1119.55 | −0.0957929 | ||||||||
\(516\) | −2944.71 | −0.251228 | ||||||||
\(517\) | 14981.0 | 1.27439 | ||||||||
\(518\) | −2655.90 | −0.225277 | ||||||||
\(519\) | −1516.11 | −0.128227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12881.5 | 1.08320 | 0.541601 | − | 0.840636i | \(-0.317818\pi\) | ||||
0.541601 | + | 0.840636i | \(0.317818\pi\) | |||||||
\(522\) | −2483.97 | −0.208276 | ||||||||
\(523\) | 16534.0 | 1.38238 | 0.691188 | − | 0.722675i | \(-0.257088\pi\) | ||||
0.691188 | + | 0.722675i | \(0.257088\pi\) | |||||||
\(524\) | −658.410 | −0.0548907 | ||||||||
\(525\) | −6102.41 | −0.507297 | ||||||||
\(526\) | −630.459 | −0.0522611 | ||||||||
\(527\) | 53.1678 | 0.00439473 | ||||||||
\(528\) | −36474.2 | −3.00632 | ||||||||
\(529\) | 12054.2 | 0.990730 | ||||||||
\(530\) | −17617.3 | −1.44386 | ||||||||
\(531\) | −4036.18 | −0.329859 | ||||||||
\(532\) | 1158.11 | 0.0943802 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 12099.3 | 0.980501 | ||||||||
\(535\) | 17985.0 | 1.45338 | ||||||||
\(536\) | −5108.80 | −0.411691 | ||||||||
\(537\) | 21035.4 | 1.69040 | ||||||||
\(538\) | 3502.79 | 0.280699 | ||||||||
\(539\) | −9319.18 | −0.744723 | ||||||||
\(540\) | −720.852 | −0.0574454 | ||||||||
\(541\) | 19026.9 | 1.51207 | 0.756035 | − | 0.654531i | \(-0.227134\pi\) | ||||
0.756035 | + | 0.654531i | \(0.227134\pi\) | |||||||
\(542\) | 1283.68 | 0.101732 | ||||||||
\(543\) | 16513.0 | 1.30505 | ||||||||
\(544\) | −29.8258 | −0.00235068 | ||||||||
\(545\) | 28206.5 | 2.21694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8153.61 | 0.637336 | 0.318668 | − | 0.947866i | \(-0.396764\pi\) | ||||
0.318668 | + | 0.947866i | \(0.396764\pi\) | |||||||
\(548\) | 4591.60 | 0.357926 | ||||||||
\(549\) | 13039.4 | 1.01368 | ||||||||
\(550\) | 12860.0 | 0.997002 | ||||||||
\(551\) | 1369.37 | 0.105875 | ||||||||
\(552\) | 20946.9 | 1.61515 | ||||||||
\(553\) | −14102.5 | −1.08445 | ||||||||
\(554\) | 913.031 | 0.0700198 | ||||||||
\(555\) | 5653.11 | 0.432363 | ||||||||
\(556\) | 2407.38 | 0.183625 | ||||||||
\(557\) | −1308.06 | −0.0995051 | −0.0497525 | − | 0.998762i | \(-0.515843\pi\) | ||||
−0.0497525 | + | 0.998762i | \(0.515843\pi\) | |||||||
\(558\) | 11569.7 | 0.877746 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14812.7 | 1.11777 | ||||||||
\(561\) | 162.166 | 0.0122044 | ||||||||
\(562\) | −16233.3 | −1.21844 | ||||||||
\(563\) | −20736.1 | −1.55226 | −0.776129 | − | 0.630575i | \(-0.782819\pi\) | ||||
−0.776129 | + | 0.630575i | \(0.782819\pi\) | |||||||
\(564\) | 3127.09 | 0.233465 | ||||||||
\(565\) | −21804.7 | −1.62359 | ||||||||
\(566\) | 16674.2 | 1.23829 | ||||||||
\(567\) | 11696.7 | 0.866343 | ||||||||
\(568\) | 1157.72 | 0.0855224 | ||||||||
\(569\) | −14982.0 | −1.10383 | −0.551913 | − | 0.833902i | \(-0.686102\pi\) | ||||
−0.551913 | + | 0.833902i | \(0.686102\pi\) | |||||||
\(570\) | −12354.1 | −0.907822 | ||||||||
\(571\) | −5668.79 | −0.415467 | −0.207734 | − | 0.978185i | \(-0.566609\pi\) | ||||
−0.207734 | + | 0.978185i | \(0.566609\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31756.2 | −2.31525 | ||||||||
\(574\) | 2688.91 | 0.195527 | ||||||||
\(575\) | −9348.32 | −0.678004 | ||||||||
\(576\) | 7642.30 | 0.552828 | ||||||||
\(577\) | −6872.94 | −0.495882 | −0.247941 | − | 0.968775i | \(-0.579754\pi\) | ||||
−0.247941 | + | 0.968775i | \(0.579754\pi\) | |||||||
\(578\) | −15531.4 | −1.11768 | ||||||||
\(579\) | 9234.10 | 0.662791 | ||||||||
\(580\) | −916.731 | −0.0656297 | ||||||||
\(581\) | 17224.5 | 1.22993 | ||||||||
\(582\) | −35570.9 | −2.53344 | ||||||||
\(583\) | −27741.7 | −1.97074 | ||||||||
\(584\) | 5355.49 | 0.379472 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4570.34 | −0.322182 | ||||||||
\(587\) | −18593.4 | −1.30738 | −0.653691 | − | 0.756762i | \(-0.726780\pi\) | ||||
−0.653691 | + | 0.756762i | \(0.726780\pi\) | |||||||
\(588\) | −1945.26 | −0.136431 | ||||||||
\(589\) | −6378.17 | −0.446193 | ||||||||
\(590\) | −7465.44 | −0.520928 | ||||||||
\(591\) | −5252.50 | −0.365582 | ||||||||
\(592\) | −4453.77 | −0.309204 | ||||||||
\(593\) | −15612.6 | −1.08117 | −0.540583 | − | 0.841291i | \(-0.681796\pi\) | ||||
−0.540583 | + | 0.841291i | \(0.681796\pi\) | |||||||
\(594\) | −5688.91 | −0.392961 | ||||||||
\(595\) | −65.8580 | −0.00453767 | ||||||||
\(596\) | 675.892 | 0.0464523 | ||||||||
\(597\) | −33237.7 | −2.27861 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22979.8 | −1.56749 | −0.783747 | − | 0.621081i | \(-0.786694\pi\) | ||||
−0.783747 | + | 0.621081i | \(0.786694\pi\) | |||||||
\(600\) | −8084.60 | −0.550087 | ||||||||
\(601\) | 2781.77 | 0.188803 | 0.0944015 | − | 0.995534i | \(-0.469906\pi\) | ||||
0.0944015 | + | 0.995534i | \(0.469906\pi\) | |||||||
\(602\) | 9437.89 | 0.638970 | ||||||||
\(603\) | 6256.38 | 0.422520 | ||||||||
\(604\) | 3379.69 | 0.227678 | ||||||||
\(605\) | 44284.9 | 2.97593 | ||||||||
\(606\) | 26012.2 | 1.74369 | ||||||||
\(607\) | −4078.57 | −0.272725 | −0.136363 | − | 0.990659i | \(-0.543541\pi\) | ||||
−0.136363 | + | 0.990659i | \(0.543541\pi\) | |||||||
\(608\) | 3578.00 | 0.238663 | ||||||||
\(609\) | 3433.10 | 0.228434 | ||||||||
\(610\) | 24118.1 | 1.60084 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.6625 | 0.00103451 | ||||||||
\(613\) | 26290.1 | 1.73221 | 0.866107 | − | 0.499858i | \(-0.166615\pi\) | ||||
0.866107 | + | 0.499858i | \(0.166615\pi\) | |||||||
\(614\) | −29784.4 | −1.95766 | ||||||||
\(615\) | −5723.36 | −0.375265 | ||||||||
\(616\) | 18427.6 | 1.20531 | ||||||||
\(617\) | −4851.69 | −0.316567 | −0.158283 | − | 0.987394i | \(-0.550596\pi\) | ||||
−0.158283 | + | 0.987394i | \(0.550596\pi\) | |||||||
\(618\) | −1844.28 | −0.120045 | ||||||||
\(619\) | −4957.05 | −0.321875 | −0.160937 | − | 0.986965i | \(-0.551452\pi\) | ||||
−0.160937 | + | 0.986965i | \(0.551452\pi\) | |||||||
\(620\) | 4269.89 | 0.276585 | ||||||||
\(621\) | 4135.45 | 0.267230 | ||||||||
\(622\) | 24930.0 | 1.60708 | ||||||||
\(623\) | −7737.54 | −0.497589 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19525.3 | −1.24962 | ||||||||
\(626\) | −1740.08 | −0.111098 | ||||||||
\(627\) | −19453.9 | −1.23910 | ||||||||
\(628\) | 19.1289 | 0.00121548 | ||||||||
\(629\) | 19.8017 | 0.00125524 | ||||||||
\(630\) | −14331.1 | −0.906295 | ||||||||
\(631\) | −2725.11 | −0.171925 | −0.0859627 | − | 0.996298i | \(-0.527397\pi\) | ||||
−0.0859627 | + | 0.996298i | \(0.527397\pi\) | |||||||
\(632\) | −18683.3 | −1.17592 | ||||||||
\(633\) | −22720.5 | −1.42663 | ||||||||
\(634\) | 477.283 | 0.0298980 | ||||||||
\(635\) | 8359.55 | 0.522423 | ||||||||
\(636\) | −5790.73 | −0.361034 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7234.77 | −0.448946 | ||||||||
\(639\) | −1417.77 | −0.0877719 | ||||||||
\(640\) | 23744.8 | 1.46655 | ||||||||
\(641\) | 21396.3 | 1.31841 | 0.659207 | − | 0.751961i | \(-0.270892\pi\) | ||||
0.659207 | + | 0.751961i | \(0.270892\pi\) | |||||||
\(642\) | 29627.4 | 1.82134 | ||||||||
\(643\) | 21833.8 | 1.33910 | 0.669549 | − | 0.742768i | \(-0.266487\pi\) | ||||
0.669549 | + | 0.742768i | \(0.266487\pi\) | |||||||
\(644\) | 4447.80 | 0.272155 | ||||||||
\(645\) | −20088.6 | −1.22634 | ||||||||
\(646\) | −43.2740 | −0.00263559 | ||||||||
\(647\) | −4869.06 | −0.295861 | −0.147931 | − | 0.988998i | \(-0.547261\pi\) | ||||
−0.147931 | + | 0.988998i | \(0.547261\pi\) | |||||||
\(648\) | 15496.1 | 0.939418 | ||||||||
\(649\) | −11755.7 | −0.711021 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15990.5 | −0.962696 | ||||||||
\(652\) | 243.486 | 0.0146252 | ||||||||
\(653\) | −16847.0 | −1.00961 | −0.504803 | − | 0.863235i | \(-0.668435\pi\) | ||||
−0.504803 | + | 0.863235i | \(0.668435\pi\) | |||||||
\(654\) | 46465.7 | 2.77822 | ||||||||
\(655\) | −4491.63 | −0.267943 | ||||||||
\(656\) | 4509.12 | 0.268371 | ||||||||
\(657\) | −6558.49 | −0.389454 | ||||||||
\(658\) | −10022.4 | −0.593790 | ||||||||
\(659\) | −24741.0 | −1.46248 | −0.731240 | − | 0.682121i | \(-0.761058\pi\) | ||||
−0.731240 | + | 0.682121i | \(0.761058\pi\) | |||||||
\(660\) | 13023.5 | 0.768089 | ||||||||
\(661\) | −16522.0 | −0.972210 | −0.486105 | − | 0.873900i | \(-0.661583\pi\) | ||||
−0.486105 | + | 0.873900i | \(0.661583\pi\) | |||||||
\(662\) | 22380.1 | 1.31394 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22819.3 | 1.33368 | ||||||||
\(665\) | 7900.53 | 0.460706 | ||||||||
\(666\) | 4308.97 | 0.250705 | ||||||||
\(667\) | 5259.19 | 0.305302 | ||||||||
\(668\) | 4409.55 | 0.255405 | ||||||||
\(669\) | 7495.66 | 0.433182 | ||||||||
\(670\) | 11572.0 | 0.667262 | ||||||||
\(671\) | 37978.4 | 2.18501 | ||||||||
\(672\) | 8970.26 | 0.514934 | ||||||||
\(673\) | −20721.5 | −1.18686 | −0.593429 | − | 0.804886i | \(-0.702226\pi\) | ||||
−0.593429 | + | 0.804886i | \(0.702226\pi\) | |||||||
\(674\) | −20970.3 | −1.19844 | ||||||||
\(675\) | −1596.10 | −0.0910133 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32407.3 | 1.83975 | 0.919877 | − | 0.392207i | \(-0.128288\pi\) | ||||
0.919877 | + | 0.392207i | \(0.128288\pi\) | |||||||
\(678\) | −35919.7 | −2.03465 | ||||||||
\(679\) | 22747.7 | 1.28568 | ||||||||
\(680\) | −87.2500 | −0.00492042 | ||||||||
\(681\) | 36576.1 | 2.05815 | ||||||||
\(682\) | 33697.6 | 1.89201 | ||||||||
\(683\) | 10123.8 | 0.567168 | 0.283584 | − | 0.958947i | \(-0.408477\pi\) | ||||
0.283584 | + | 0.958947i | \(0.408477\pi\) | |||||||
\(684\) | −1878.93 | −0.105033 | ||||||||
\(685\) | 31323.6 | 1.74717 | ||||||||
\(686\) | 21774.9 | 1.21191 | ||||||||
\(687\) | 12038.6 | 0.668562 | ||||||||
\(688\) | 15826.7 | 0.877018 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −47447.1 | −2.61780 | ||||||||
\(691\) | 29704.5 | 1.63533 | 0.817665 | − | 0.575695i | \(-0.195268\pi\) | ||||
0.817665 | + | 0.575695i | \(0.195268\pi\) | |||||||
\(692\) | −426.495 | −0.0234291 | ||||||||
\(693\) | −22567.0 | −1.23701 | ||||||||
\(694\) | 20245.8 | 1.10738 | ||||||||
\(695\) | 16423.0 | 0.896343 | ||||||||
\(696\) | 4548.24 | 0.247702 | ||||||||
\(697\) | −20.0477 | −0.00108947 | ||||||||
\(698\) | 531.418 | 0.0288173 | ||||||||
\(699\) | 22416.5 | 1.21298 | ||||||||
\(700\) | −1716.66 | −0.0926908 | ||||||||
\(701\) | −20585.2 | −1.10912 | −0.554558 | − | 0.832145i | \(-0.687113\pi\) | ||||
−0.554558 | + | 0.832145i | \(0.687113\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2375.47 | −0.127443 | ||||||||
\(704\) | 22258.9 | 1.19164 | ||||||||
\(705\) | 21332.8 | 1.13963 | ||||||||
\(706\) | −26719.5 | −1.42437 | ||||||||
\(707\) | −16634.9 | −0.884894 | ||||||||
\(708\) | −2453.86 | −0.130257 | ||||||||
\(709\) | −29660.2 | −1.57110 | −0.785552 | − | 0.618796i | \(-0.787621\pi\) | ||||
−0.785552 | + | 0.618796i | \(0.787621\pi\) | |||||||
\(710\) | −2622.36 | −0.138613 | ||||||||
\(711\) | 22880.1 | 1.20685 | ||||||||
\(712\) | −10250.8 | −0.539560 | ||||||||
\(713\) | −24495.9 | −1.28664 | ||||||||
\(714\) | −108.491 | −0.00568649 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5917.44 | 0.308862 | ||||||||
\(717\) | 16659.0 | 0.867702 | ||||||||
\(718\) | 8320.43 | 0.432473 | ||||||||
\(719\) | 1279.68 | 0.0663758 | 0.0331879 | − | 0.999449i | \(-0.489434\pi\) | ||||
0.0331879 | + | 0.999449i | \(0.489434\pi\) | |||||||
\(720\) | −24032.4 | −1.24393 | ||||||||
\(721\) | 1179.43 | 0.0609211 | ||||||||
\(722\) | −16492.4 | −0.850118 | ||||||||
\(723\) | −36629.3 | −1.88417 | ||||||||
\(724\) | 4645.25 | 0.238452 | ||||||||
\(725\) | −2029.82 | −0.103980 | ||||||||
\(726\) | 72952.3 | 3.72936 | ||||||||
\(727\) | 6202.77 | 0.316435 | 0.158217 | − | 0.987404i | \(-0.449425\pi\) | ||||
0.158217 | + | 0.987404i | \(0.449425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13891.1 | −0.705740 | ||||||||
\(730\) | −12130.8 | −0.615042 | ||||||||
\(731\) | −70.3663 | −0.00356032 | ||||||||
\(732\) | 7927.51 | 0.400286 | ||||||||
\(733\) | 35501.2 | 1.78891 | 0.894453 | − | 0.447162i | \(-0.147565\pi\) | ||||
0.894453 | + | 0.447162i | \(0.147565\pi\) | |||||||
\(734\) | −41950.7 | −2.10958 | ||||||||
\(735\) | −13270.5 | −0.665970 | ||||||||
\(736\) | 13741.6 | 0.688209 | ||||||||
\(737\) | 18222.3 | 0.910754 | ||||||||
\(738\) | −4362.52 | −0.217597 | ||||||||
\(739\) | 3893.52 | 0.193810 | 0.0969050 | − | 0.995294i | \(-0.469106\pi\) | ||||
0.0969050 | + | 0.995294i | \(0.469106\pi\) | |||||||
\(740\) | 1590.27 | 0.0789991 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18559.5 | 0.918247 | ||||||||
\(743\) | 2214.99 | 0.109368 | 0.0546839 | − | 0.998504i | \(-0.482585\pi\) | ||||
0.0546839 | + | 0.998504i | \(0.482585\pi\) | |||||||
\(744\) | −21184.5 | −1.04390 | ||||||||
\(745\) | 4610.89 | 0.226751 | ||||||||
\(746\) | −36924.8 | −1.81221 | ||||||||
\(747\) | −27945.2 | −1.36876 | ||||||||
\(748\) | 45.6186 | 0.00222992 | ||||||||
\(749\) | −18946.9 | −0.924303 | ||||||||
\(750\) | −19796.0 | −0.963797 | ||||||||
\(751\) | 2604.34 | 0.126543 | 0.0632714 | − | 0.997996i | \(-0.479847\pi\) | ||||
0.0632714 | + | 0.997996i | \(0.479847\pi\) | |||||||
\(752\) | −16806.9 | −0.815006 | ||||||||
\(753\) | 20515.1 | 0.992845 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23056.0 | 1.11138 | ||||||||
\(756\) | 759.403 | 0.0365334 | ||||||||
\(757\) | −9685.72 | −0.465037 | −0.232519 | − | 0.972592i | \(-0.574697\pi\) | ||||
−0.232519 | + | 0.972592i | \(0.574697\pi\) | |||||||
\(758\) | −10679.8 | −0.511750 | ||||||||
\(759\) | −74714.4 | −3.57307 | ||||||||
\(760\) | 10466.8 | 0.499565 | ||||||||
\(761\) | 10105.6 | 0.481378 | 0.240689 | − | 0.970602i | \(-0.422627\pi\) | ||||
0.240689 | + | 0.970602i | \(0.422627\pi\) | |||||||
\(762\) | 13771.0 | 0.654687 | ||||||||
\(763\) | −29715.0 | −1.40990 | ||||||||
\(764\) | −8933.29 | −0.423030 | ||||||||
\(765\) | 106.849 | 0.00504984 | ||||||||
\(766\) | −13849.6 | −0.653273 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 20476.1 | 0.962068 | ||||||||
\(769\) | 4573.20 | 0.214452 | 0.107226 | − | 0.994235i | \(-0.465803\pi\) | ||||
0.107226 | + | 0.994235i | \(0.465803\pi\) | |||||||
\(770\) | −41740.7 | −1.95355 | ||||||||
\(771\) | −43685.8 | −2.04061 | ||||||||
\(772\) | 2597.63 | 0.121102 | ||||||||
\(773\) | −7446.13 | −0.346467 | −0.173233 | − | 0.984881i | \(-0.555421\pi\) | ||||
−0.173233 | + | 0.984881i | \(0.555421\pi\) | |||||||
\(774\) | −15312.2 | −0.711091 | ||||||||
\(775\) | 9454.34 | 0.438206 | ||||||||
\(776\) | 30136.6 | 1.39412 | ||||||||
\(777\) | −5955.44 | −0.274968 | ||||||||
\(778\) | −39466.3 | −1.81868 | ||||||||
\(779\) | 2404.99 | 0.110613 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4129.39 | −0.189195 | ||||||||
\(782\) | −166.197 | −0.00760000 | ||||||||
\(783\) | 897.935 | 0.0409829 | ||||||||
\(784\) | 10455.0 | 0.476269 | ||||||||
\(785\) | 130.496 | 0.00593324 | ||||||||
\(786\) | −7399.23 | −0.335779 | ||||||||
\(787\) | −3267.11 | −0.147980 | −0.0739898 | − | 0.997259i | \(-0.523573\pi\) | ||||
−0.0739898 | + | 0.997259i | \(0.523573\pi\) | |||||||
\(788\) | −1477.57 | −0.0667973 | ||||||||
\(789\) | −1413.71 | −0.0637887 | ||||||||
\(790\) | 42319.8 | 1.90591 | ||||||||
\(791\) | 22970.8 | 1.03255 | ||||||||
\(792\) | −29897.3 | −1.34135 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 29876.3 | 1.33535 | ||||||||
\(795\) | −39504.0 | −1.76234 | ||||||||
\(796\) | −9350.03 | −0.416336 | ||||||||
\(797\) | −3165.75 | −0.140698 | −0.0703492 | − | 0.997522i | \(-0.522411\pi\) | ||||
−0.0703492 | + | 0.997522i | \(0.522411\pi\) | |||||||
\(798\) | 13014.9 | 0.577344 | ||||||||
\(799\) | 74.7242 | 0.00330857 | ||||||||
\(800\) | −5303.66 | −0.234391 | ||||||||
\(801\) | 12553.5 | 0.553752 | ||||||||
\(802\) | 9186.97 | 0.404493 | ||||||||
\(803\) | −19102.2 | −0.839478 | ||||||||
\(804\) | 3803.67 | 0.166847 | ||||||||
\(805\) | 30342.6 | 1.32849 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7854.45 | 0.342614 | ||||||||
\(808\) | −22038.3 | −0.959534 | ||||||||
\(809\) | 13589.7 | 0.590592 | 0.295296 | − | 0.955406i | \(-0.404582\pi\) | ||||
0.295296 | + | 0.955406i | \(0.404582\pi\) | |||||||
\(810\) | −35100.3 | −1.52259 | ||||||||
\(811\) | −24977.7 | −1.08149 | −0.540744 | − | 0.841188i | \(-0.681857\pi\) | ||||
−0.540744 | + | 0.841188i | \(0.681857\pi\) | |||||||
\(812\) | 965.758 | 0.0417383 | ||||||||
\(813\) | 2878.45 | 0.124172 | ||||||||
\(814\) | 12550.3 | 0.540401 | ||||||||
\(815\) | 1661.04 | 0.0713911 | ||||||||
\(816\) | −181.931 | −0.00780499 | ||||||||
\(817\) | 8441.35 | 0.361476 | ||||||||
\(818\) | −18323.0 | −0.783188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1610.03 | −0.0685666 | ||||||||
\(821\) | 8317.38 | 0.353567 | 0.176784 | − | 0.984250i | \(-0.443431\pi\) | ||||
0.176784 | + | 0.984250i | \(0.443431\pi\) | |||||||
\(822\) | 51600.6 | 2.18951 | ||||||||
\(823\) | 14462.9 | 0.612571 | 0.306286 | − | 0.951940i | \(-0.400914\pi\) | ||||
0.306286 | + | 0.951940i | \(0.400914\pi\) | |||||||
\(824\) | 1562.53 | 0.0660597 | ||||||||
\(825\) | 28836.5 | 1.21692 | ||||||||
\(826\) | 7864.69 | 0.331293 | ||||||||
\(827\) | −17881.0 | −0.751854 | −0.375927 | − | 0.926649i | \(-0.622676\pi\) | ||||
−0.375927 | + | 0.926649i | \(0.622676\pi\) | |||||||
\(828\) | −7216.18 | −0.302874 | ||||||||
\(829\) | 351.169 | 0.0147124 | 0.00735620 | − | 0.999973i | \(-0.497658\pi\) | ||||
0.00735620 | + | 0.999973i | \(0.497658\pi\) | |||||||
\(830\) | −51688.3 | −2.16160 | ||||||||
\(831\) | 2047.33 | 0.0854646 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.4836 | −0.00193345 | ||||||||
\(834\) | 27054.2 | 1.12327 | ||||||||
\(835\) | 30081.6 | 1.24673 | ||||||||
\(836\) | −5472.54 | −0.226402 | ||||||||
\(837\) | −4182.34 | −0.172716 | ||||||||
\(838\) | −13095.8 | −0.539841 | ||||||||
\(839\) | 33425.9 | 1.37543 | 0.687717 | − | 0.725978i | \(-0.258613\pi\) | ||||
0.687717 | + | 0.725978i | \(0.258613\pi\) | |||||||
\(840\) | 26240.8 | 1.07785 | ||||||||
\(841\) | −23247.1 | −0.953178 | ||||||||
\(842\) | −4510.99 | −0.184631 | ||||||||
\(843\) | −36400.7 | −1.48720 | ||||||||
\(844\) | −6391.46 | −0.260667 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16260.5 | 0.660811 | ||||||||
\(847\) | −46653.3 | −1.89259 | ||||||||
\(848\) | 31123.0 | 1.26034 | ||||||||
\(849\) | 37389.3 | 1.51142 | ||||||||
\(850\) | 64.1449 | 0.00258841 | ||||||||
\(851\) | −9123.18 | −0.367495 | ||||||||
\(852\) | −861.959 | −0.0346599 | ||||||||
\(853\) | 35097.5 | 1.40881 | 0.704406 | − | 0.709797i | \(-0.251213\pi\) | ||||
0.704406 | + | 0.709797i | \(0.251213\pi\) | |||||||
\(854\) | −25407.9 | −1.01808 | ||||||||
\(855\) | −12817.9 | −0.512706 | ||||||||
\(856\) | −25101.2 | −1.00227 | ||||||||
\(857\) | 15015.8 | 0.598519 | 0.299259 | − | 0.954172i | \(-0.403260\pi\) | ||||
0.299259 | + | 0.954172i | \(0.403260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19647.1 | 0.780383 | 0.390192 | − | 0.920734i | \(-0.372409\pi\) | ||||
0.390192 | + | 0.920734i | \(0.372409\pi\) | |||||||
\(860\) | −5651.10 | −0.224071 | ||||||||
\(861\) | 6029.45 | 0.238656 | ||||||||
\(862\) | 8039.57 | 0.317667 | ||||||||
\(863\) | 9035.14 | 0.356385 | 0.178192 | − | 0.983996i | \(-0.442975\pi\) | ||||
0.178192 | + | 0.983996i | \(0.442975\pi\) | |||||||
\(864\) | 2346.19 | 0.0923833 | ||||||||
\(865\) | −2909.52 | −0.114366 | ||||||||
\(866\) | −10901.7 | −0.427778 | ||||||||
\(867\) | −34826.6 | −1.36422 | ||||||||
\(868\) | −4498.24 | −0.175899 | ||||||||
\(869\) | 66640.5 | 2.60141 | ||||||||
\(870\) | −10302.3 | −0.401471 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −39367.0 | −1.52883 | ||||||||
\(873\) | −36906.2 | −1.43080 | ||||||||
\(874\) | 19937.5 | 0.771621 | ||||||||
\(875\) | 12659.6 | 0.489113 | ||||||||
\(876\) | −3987.34 | −0.153790 | ||||||||
\(877\) | 8254.16 | 0.317814 | 0.158907 | − | 0.987294i | \(-0.449203\pi\) | ||||
0.158907 | + | 0.987294i | \(0.449203\pi\) | |||||||
\(878\) | −39967.6 | −1.53627 | ||||||||
\(879\) | −10248.3 | −0.393248 | ||||||||
\(880\) | −69996.4 | −2.68134 | ||||||||
\(881\) | −42107.4 | −1.61026 | −0.805128 | − | 0.593101i | \(-0.797903\pi\) | ||||
−0.805128 | + | 0.593101i | \(0.797903\pi\) | |||||||
\(882\) | −10115.1 | −0.386161 | ||||||||
\(883\) | −17584.7 | −0.670183 | −0.335091 | − | 0.942186i | \(-0.608767\pi\) | ||||
−0.335091 | + | 0.942186i | \(0.608767\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16740.1 | −0.635832 | ||||||||
\(886\) | 26829.1 | 1.01732 | ||||||||
\(887\) | −23845.8 | −0.902666 | −0.451333 | − | 0.892356i | \(-0.649051\pi\) | ||||
−0.451333 | + | 0.892356i | \(0.649051\pi\) | |||||||
\(888\) | −7889.89 | −0.298161 | ||||||||
\(889\) | −8806.63 | −0.332244 | ||||||||
\(890\) | 23219.3 | 0.874509 | ||||||||
\(891\) | −55272.0 | −2.07821 | ||||||||
\(892\) | 2108.59 | 0.0791488 | ||||||||
\(893\) | −8964.14 | −0.335917 | ||||||||
\(894\) | 7595.70 | 0.284159 | ||||||||
\(895\) | 40368.4 | 1.50767 | ||||||||
\(896\) | −25014.6 | −0.932679 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35943.1 | −1.33568 | ||||||||
\(899\) | −5318.83 | −0.197322 | ||||||||
\(900\) | 2785.13 | 0.103153 | ||||||||
\(901\) | −138.374 | −0.00511644 | ||||||||
\(902\) | −12706.2 | −0.469036 | ||||||||
\(903\) | 21163.0 | 0.779912 | ||||||||
\(904\) | 30432.2 | 1.11965 | ||||||||
\(905\) | 31689.6 | 1.16398 | ||||||||
\(906\) | 37981.1 | 1.39276 | ||||||||
\(907\) | 30565.7 | 1.11898 | 0.559492 | − | 0.828836i | \(-0.310996\pi\) | ||||
0.559492 | + | 0.828836i | \(0.310996\pi\) | |||||||
\(908\) | 10289.2 | 0.376055 | ||||||||
\(909\) | 26988.7 | 0.984773 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18556.9 | 0.674882 | 0.337441 | − | 0.941347i | \(-0.390439\pi\) | ||||
0.337441 | + | 0.941347i | \(0.390439\pi\) | |||||||
\(912\) | 21825.0 | 0.792433 | ||||||||
\(913\) | −81392.9 | −2.95040 | ||||||||
\(914\) | −35688.6 | −1.29155 | ||||||||
\(915\) | 54081.0 | 1.95395 | ||||||||
\(916\) | 3386.56 | 0.122156 | ||||||||
\(917\) | 4731.84 | 0.170402 | ||||||||
\(918\) | −28.3760 | −0.00102020 | ||||||||
\(919\) | −9938.82 | −0.356748 | −0.178374 | − | 0.983963i | \(-0.557084\pi\) | ||||
−0.178374 | + | 0.983963i | \(0.557084\pi\) | |||||||
\(920\) | 40198.5 | 1.44055 | ||||||||
\(921\) | −66786.9 | −2.38947 | ||||||||
\(922\) | −12121.0 | −0.432954 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −13720.0 | −0.488479 | ||||||||
\(925\) | 3521.15 | 0.125162 | ||||||||
\(926\) | −4092.18 | −0.145224 | ||||||||
\(927\) | −1913.52 | −0.0677973 | ||||||||
\(928\) | 2983.73 | 0.105545 | ||||||||
\(929\) | 5953.61 | 0.210260 | 0.105130 | − | 0.994458i | \(-0.466474\pi\) | ||||
0.105130 | + | 0.994458i | \(0.466474\pi\) | |||||||
\(930\) | 47985.2 | 1.69193 | ||||||||
\(931\) | 5576.31 | 0.196301 | ||||||||
\(932\) | 6305.95 | 0.221629 | ||||||||
\(933\) | 55901.6 | 1.96156 | ||||||||
\(934\) | 43821.1 | 1.53519 | ||||||||
\(935\) | 311.207 | 0.0108851 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24568.0 | −0.856564 | −0.428282 | − | 0.903645i | \(-0.640881\pi\) | ||||
−0.428282 | + | 0.903645i | \(0.640881\pi\) | |||||||
\(938\) | −12190.9 | −0.424356 | ||||||||
\(939\) | −3901.86 | −0.135604 | ||||||||
\(940\) | 6001.08 | 0.208227 | ||||||||
\(941\) | 11024.8 | 0.381931 | 0.190965 | − | 0.981597i | \(-0.438838\pi\) | ||||
0.190965 | + | 0.981597i | \(0.438838\pi\) | |||||||
\(942\) | 214.971 | 0.00743538 | ||||||||
\(943\) | 9236.55 | 0.318964 | ||||||||
\(944\) | 13188.6 | 0.454715 | ||||||||
\(945\) | 5180.60 | 0.178333 | ||||||||
\(946\) | −44598.0 | −1.53278 | ||||||||
\(947\) | −6171.46 | −0.211769 | −0.105885 | − | 0.994378i | \(-0.533767\pi\) | ||||
−0.105885 | + | 0.994378i | \(0.533767\pi\) | |||||||
\(948\) | 13910.4 | 0.476569 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7695.01 | −0.262799 | ||||||||
\(951\) | 1070.23 | 0.0364928 | ||||||||
\(952\) | 91.9161 | 0.00312922 | ||||||||
\(953\) | −18838.4 | −0.640333 | −0.320166 | − | 0.947361i | \(-0.603739\pi\) | ||||
−0.320166 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(954\) | −30111.1 | −1.02189 | ||||||||
\(955\) | −60942.3 | −2.06497 | ||||||||
\(956\) | 4686.32 | 0.158542 | ||||||||
\(957\) | −16222.8 | −0.547973 | ||||||||
\(958\) | 30436.4 | 1.02647 | ||||||||
\(959\) | −32998.8 | −1.11114 | ||||||||
\(960\) | 31696.5 | 1.06562 | ||||||||
\(961\) | −5017.33 | −0.168418 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30739.6 | 1.02863 | ||||||||
\(964\) | −10304.1 | −0.344267 | ||||||||
\(965\) | 17720.8 | 0.591144 | ||||||||
\(966\) | 49984.6 | 1.66483 | ||||||||
\(967\) | −24934.5 | −0.829203 | −0.414602 | − | 0.910003i | \(-0.636079\pi\) | ||||
−0.414602 | + | 0.910003i | \(0.636079\pi\) | |||||||
\(968\) | −61807.2 | −2.05223 | ||||||||
\(969\) | −97.0351 | −0.00321694 | ||||||||
\(970\) | −68262.8 | −2.25957 | ||||||||
\(971\) | 32161.2 | 1.06293 | 0.531463 | − | 0.847082i | \(-0.321643\pi\) | ||||
0.531463 | + | 0.847082i | \(0.321643\pi\) | |||||||
\(972\) | −10106.6 | −0.333509 | ||||||||
\(973\) | −17301.3 | −0.570044 | ||||||||
\(974\) | 37787.2 | 1.24310 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42607.4 | −1.39737 | ||||||||
\(977\) | 18864.0 | 0.617720 | 0.308860 | − | 0.951107i | \(-0.400052\pi\) | ||||
0.308860 | + | 0.951107i | \(0.400052\pi\) | |||||||
\(978\) | 2736.30 | 0.0894655 | ||||||||
\(979\) | 36563.1 | 1.19363 | ||||||||
\(980\) | −3733.08 | −0.121683 | ||||||||
\(981\) | 48210.0 | 1.56904 | ||||||||
\(982\) | 17103.3 | 0.555792 | ||||||||
\(983\) | 7883.83 | 0.255804 | 0.127902 | − | 0.991787i | \(-0.459176\pi\) | ||||
0.127902 | + | 0.991787i | \(0.459176\pi\) | |||||||
\(984\) | 7987.93 | 0.258786 | ||||||||
\(985\) | −10079.9 | −0.326063 | ||||||||
\(986\) | −36.0867 | −0.00116555 | ||||||||
\(987\) | −22473.6 | −0.724766 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32419.7 | 1.04235 | ||||||||
\(990\) | 67720.6 | 2.17404 | ||||||||
\(991\) | 14172.3 | 0.454286 | 0.227143 | − | 0.973861i | \(-0.427062\pi\) | ||||
0.227143 | + | 0.973861i | \(0.427062\pi\) | |||||||
\(992\) | −13897.4 | −0.444802 | ||||||||
\(993\) | 50183.9 | 1.60376 | ||||||||
\(994\) | 2762.60 | 0.0881533 | ||||||||
\(995\) | −63785.3 | −2.03229 | ||||||||
\(996\) | −16989.7 | −0.540503 | ||||||||
\(997\) | 52462.7 | 1.66651 | 0.833256 | − | 0.552888i | \(-0.186474\pi\) | ||||
0.833256 | + | 0.552888i | \(0.186474\pi\) | |||||||
\(998\) | 45753.8 | 1.45121 | ||||||||
\(999\) | −1557.66 | −0.0493315 |
(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 | 169.4.a.l.1.7 | yes | 9 | |
3.2 | odd | 2 | 1521.4.a.bg.1.3 | 9 | |||
13.2 | odd | 12 | 169.4.e.h.147.14 | 36 | |||
13.3 | even | 3 | 169.4.c.k.22.3 | 18 | |||
13.4 | even | 6 | 169.4.c.l.146.7 | 18 | |||
13.5 | odd | 4 | 169.4.b.g.168.5 | 18 | |||
13.6 | odd | 12 | 169.4.e.h.23.5 | 36 | |||
13.7 | odd | 12 | 169.4.e.h.23.14 | 36 | |||
13.8 | odd | 4 | 169.4.b.g.168.14 | 18 | |||
13.9 | even | 3 | 169.4.c.k.146.3 | 18 | |||
13.10 | even | 6 | 169.4.c.l.22.7 | 18 | |||
13.11 | odd | 12 | 169.4.e.h.147.5 | 36 | |||
13.12 | even | 2 | 169.4.a.k.1.3 | ✓ | 9 | ||
39.38 | odd | 2 | 1521.4.a.bh.1.7 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.4.a.k.1.3 | ✓ | 9 | 13.12 | even | 2 | ||
169.4.a.l.1.7 | yes | 9 | 1.1 | even | 1 | trivial | |
169.4.b.g.168.5 | 18 | 13.5 | odd | 4 | |||
169.4.b.g.168.14 | 18 | 13.8 | odd | 4 | |||
169.4.c.k.22.3 | 18 | 13.3 | even | 3 | |||
169.4.c.k.146.3 | 18 | 13.9 | even | 3 | |||
169.4.c.l.22.7 | 18 | 13.10 | even | 6 | |||
169.4.c.l.146.7 | 18 | 13.4 | even | 6 | |||
169.4.e.h.23.5 | 36 | 13.6 | odd | 12 | |||
169.4.e.h.23.14 | 36 | 13.7 | odd | 12 | |||
169.4.e.h.147.5 | 36 | 13.11 | odd | 12 | |||
169.4.e.h.147.14 | 36 | 13.2 | odd | 12 | |||
1521.4.a.bg.1.3 | 9 | 3.2 | odd | 2 | |||
1521.4.a.bh.1.7 | 9 | 39.38 | odd | 2 |