Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.39 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.07922 | 1.08867 | 0.544335 | − | 0.838868i | \(-0.316782\pi\) | ||||
0.544335 | + | 0.838868i | \(0.316782\pi\) | |||||||
\(3\) | 5.77516 | 1.11143 | 0.555715 | − | 0.831373i | \(-0.312444\pi\) | ||||
0.555715 | + | 0.831373i | \(0.312444\pi\) | |||||||
\(4\) | 1.48163 | 0.185203 | ||||||||
\(5\) | 13.4757 | 1.20530 | 0.602651 | − | 0.798005i | \(-0.294111\pi\) | ||||
0.602651 | + | 0.798005i | \(0.294111\pi\) | |||||||
\(6\) | 17.7830 | 1.20998 | ||||||||
\(7\) | −34.2458 | −1.84910 | −0.924551 | − | 0.381059i | \(-0.875559\pi\) | ||||
−0.924551 | + | 0.381059i | \(0.875559\pi\) | |||||||
\(8\) | −20.0715 | −0.887045 | ||||||||
\(9\) | 6.35250 | 0.235278 | ||||||||
\(10\) | 41.4947 | 1.31218 | ||||||||
\(11\) | 24.2940 | 0.665903 | 0.332951 | − | 0.942944i | \(-0.391955\pi\) | ||||
0.332951 | + | 0.942944i | \(0.391955\pi\) | |||||||
\(12\) | 8.55663 | 0.205840 | ||||||||
\(13\) | 11.8136 | 0.252040 | 0.126020 | − | 0.992028i | \(-0.459780\pi\) | ||||
0.126020 | + | 0.992028i | \(0.459780\pi\) | |||||||
\(14\) | −105.451 | −2.01306 | ||||||||
\(15\) | 77.8243 | 1.33961 | ||||||||
\(16\) | −73.6578 | −1.15090 | ||||||||
\(17\) | 110.941 | 1.58278 | 0.791389 | − | 0.611313i | \(-0.209359\pi\) | ||||
0.791389 | + | 0.611313i | \(0.209359\pi\) | |||||||
\(18\) | 19.5608 | 0.256140 | ||||||||
\(19\) | −45.6852 | −0.551627 | −0.275813 | − | 0.961211i | \(-0.588947\pi\) | ||||
−0.275813 | + | 0.961211i | \(0.588947\pi\) | |||||||
\(20\) | 19.9659 | 0.223226 | ||||||||
\(21\) | −197.775 | −2.05515 | ||||||||
\(22\) | 74.8068 | 0.724949 | ||||||||
\(23\) | −214.470 | −1.94435 | −0.972176 | − | 0.234254i | \(-0.924735\pi\) | ||||
−0.972176 | + | 0.234254i | \(0.924735\pi\) | |||||||
\(24\) | −115.916 | −0.985889 | ||||||||
\(25\) | 56.5941 | 0.452753 | ||||||||
\(26\) | 36.3769 | 0.274388 | ||||||||
\(27\) | −119.243 | −0.849936 | ||||||||
\(28\) | −50.7395 | −0.342459 | ||||||||
\(29\) | 57.4470 | 0.367850 | 0.183925 | − | 0.982940i | \(-0.441120\pi\) | ||||
0.183925 | + | 0.982940i | \(0.441120\pi\) | |||||||
\(30\) | 239.638 | 1.45839 | ||||||||
\(31\) | −181.469 | −1.05138 | −0.525689 | − | 0.850677i | \(-0.676193\pi\) | ||||
−0.525689 | + | 0.850677i | \(0.676193\pi\) | |||||||
\(32\) | −66.2366 | −0.365909 | ||||||||
\(33\) | 140.302 | 0.740105 | ||||||||
\(34\) | 341.613 | 1.72312 | ||||||||
\(35\) | −461.486 | −2.22873 | ||||||||
\(36\) | 9.41203 | 0.0435742 | ||||||||
\(37\) | −156.106 | −0.693613 | −0.346806 | − | 0.937937i | \(-0.612734\pi\) | ||||
−0.346806 | + | 0.937937i | \(0.612734\pi\) | |||||||
\(38\) | −140.675 | −0.600540 | ||||||||
\(39\) | 68.2257 | 0.280124 | ||||||||
\(40\) | −270.478 | −1.06916 | ||||||||
\(41\) | 0.775433 | 0.00295371 | 0.00147686 | − | 0.999999i | \(-0.499530\pi\) | ||||
0.00147686 | + | 0.999999i | \(0.499530\pi\) | |||||||
\(42\) | −608.995 | −2.23738 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 35.9947 | 0.123327 | ||||||||
\(45\) | 85.6043 | 0.283581 | ||||||||
\(46\) | −660.401 | −2.11676 | ||||||||
\(47\) | −146.038 | −0.453232 | −0.226616 | − | 0.973984i | \(-0.572766\pi\) | ||||
−0.226616 | + | 0.973984i | \(0.572766\pi\) | |||||||
\(48\) | −425.386 | −1.27915 | ||||||||
\(49\) | 829.777 | 2.41918 | ||||||||
\(50\) | 174.266 | 0.492898 | ||||||||
\(51\) | 640.704 | 1.75915 | ||||||||
\(52\) | 17.5034 | 0.0466785 | ||||||||
\(53\) | −282.368 | −0.731815 | −0.365908 | − | 0.930651i | \(-0.619241\pi\) | ||||
−0.365908 | + | 0.930651i | \(0.619241\pi\) | |||||||
\(54\) | −367.175 | −0.925300 | ||||||||
\(55\) | 327.379 | 0.802614 | ||||||||
\(56\) | 687.367 | 1.64024 | ||||||||
\(57\) | −263.840 | −0.613095 | ||||||||
\(58\) | 176.892 | 0.400467 | ||||||||
\(59\) | −698.452 | −1.54120 | −0.770599 | − | 0.637320i | \(-0.780043\pi\) | ||||
−0.770599 | + | 0.637320i | \(0.780043\pi\) | |||||||
\(60\) | 115.306 | 0.248100 | ||||||||
\(61\) | −98.7249 | −0.207220 | −0.103610 | − | 0.994618i | \(-0.533039\pi\) | ||||
−0.103610 | + | 0.994618i | \(0.533039\pi\) | |||||||
\(62\) | −558.783 | −1.14461 | ||||||||
\(63\) | −217.547 | −0.435053 | ||||||||
\(64\) | 385.305 | 0.752549 | ||||||||
\(65\) | 159.197 | 0.303784 | ||||||||
\(66\) | 432.022 | 0.805730 | ||||||||
\(67\) | −517.724 | −0.944031 | −0.472015 | − | 0.881590i | \(-0.656473\pi\) | ||||
−0.472015 | + | 0.881590i | \(0.656473\pi\) | |||||||
\(68\) | 164.373 | 0.293135 | ||||||||
\(69\) | −1238.60 | −2.16101 | ||||||||
\(70\) | −1421.02 | −2.42635 | ||||||||
\(71\) | 29.8847 | 0.0499529 | 0.0249765 | − | 0.999688i | \(-0.492049\pi\) | ||||
0.0249765 | + | 0.999688i | \(0.492049\pi\) | |||||||
\(72\) | −127.505 | −0.208702 | ||||||||
\(73\) | −75.4773 | −0.121013 | −0.0605065 | − | 0.998168i | \(-0.519272\pi\) | ||||
−0.0605065 | + | 0.998168i | \(0.519272\pi\) | |||||||
\(74\) | −480.686 | −0.755116 | ||||||||
\(75\) | 326.840 | 0.503203 | ||||||||
\(76\) | −67.6884 | −0.102163 | ||||||||
\(77\) | −831.970 | −1.23132 | ||||||||
\(78\) | 210.082 | 0.304963 | ||||||||
\(79\) | 882.904 | 1.25740 | 0.628699 | − | 0.777649i | \(-0.283588\pi\) | ||||
0.628699 | + | 0.777649i | \(0.283588\pi\) | |||||||
\(80\) | −992.589 | −1.38719 | ||||||||
\(81\) | −860.163 | −1.17992 | ||||||||
\(82\) | 2.38773 | 0.00321562 | ||||||||
\(83\) | 716.095 | 0.947008 | 0.473504 | − | 0.880792i | \(-0.342989\pi\) | ||||
0.473504 | + | 0.880792i | \(0.342989\pi\) | |||||||
\(84\) | −293.029 | −0.380620 | ||||||||
\(85\) | 1495.01 | 1.90772 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 331.766 | 0.408839 | ||||||||
\(88\) | −487.619 | −0.590686 | ||||||||
\(89\) | 142.143 | 0.169293 | 0.0846466 | − | 0.996411i | \(-0.473024\pi\) | ||||
0.0846466 | + | 0.996411i | \(0.473024\pi\) | |||||||
\(90\) | 263.595 | 0.308726 | ||||||||
\(91\) | −404.568 | −0.466047 | ||||||||
\(92\) | −317.764 | −0.360100 | ||||||||
\(93\) | −1048.01 | −1.16853 | ||||||||
\(94\) | −449.685 | −0.493420 | ||||||||
\(95\) | −615.640 | −0.664877 | ||||||||
\(96\) | −382.527 | −0.406682 | ||||||||
\(97\) | −352.135 | −0.368597 | −0.184299 | − | 0.982870i | \(-0.559001\pi\) | ||||
−0.184299 | + | 0.982870i | \(0.559001\pi\) | |||||||
\(98\) | 2555.07 | 2.63369 | ||||||||
\(99\) | 154.328 | 0.156672 | ||||||||
\(100\) | 83.8512 | 0.0838512 | ||||||||
\(101\) | 1101.97 | 1.08564 | 0.542820 | − | 0.839849i | \(-0.317357\pi\) | ||||
0.542820 | + | 0.839849i | \(0.317357\pi\) | |||||||
\(102\) | 1972.87 | 1.91513 | ||||||||
\(103\) | −909.666 | −0.870214 | −0.435107 | − | 0.900379i | \(-0.643290\pi\) | ||||
−0.435107 | + | 0.900379i | \(0.643290\pi\) | |||||||
\(104\) | −237.118 | −0.223570 | ||||||||
\(105\) | −2665.16 | −2.47707 | ||||||||
\(106\) | −869.474 | −0.796706 | ||||||||
\(107\) | −1868.64 | −1.68830 | −0.844150 | − | 0.536107i | \(-0.819894\pi\) | ||||
−0.844150 | + | 0.536107i | \(0.819894\pi\) | |||||||
\(108\) | −176.673 | −0.157411 | ||||||||
\(109\) | 1049.08 | 0.921869 | 0.460935 | − | 0.887434i | \(-0.347514\pi\) | ||||
0.460935 | + | 0.887434i | \(0.347514\pi\) | |||||||
\(110\) | 1008.07 | 0.873782 | ||||||||
\(111\) | −901.538 | −0.770903 | ||||||||
\(112\) | 2522.47 | 2.12814 | ||||||||
\(113\) | −739.032 | −0.615242 | −0.307621 | − | 0.951509i | \(-0.599533\pi\) | ||||
−0.307621 | + | 0.951509i | \(0.599533\pi\) | |||||||
\(114\) | −812.421 | −0.667458 | ||||||||
\(115\) | −2890.13 | −2.34353 | ||||||||
\(116\) | 85.1149 | 0.0681269 | ||||||||
\(117\) | 75.0462 | 0.0592993 | ||||||||
\(118\) | −2150.69 | −1.67786 | ||||||||
\(119\) | −3799.28 | −2.92672 | ||||||||
\(120\) | −1562.05 | −1.18829 | ||||||||
\(121\) | −740.799 | −0.556573 | ||||||||
\(122\) | −303.996 | −0.225594 | ||||||||
\(123\) | 4.47825 | 0.00328285 | ||||||||
\(124\) | −268.869 | −0.194719 | ||||||||
\(125\) | −921.817 | −0.659598 | ||||||||
\(126\) | −669.876 | −0.473629 | ||||||||
\(127\) | 1516.44 | 1.05955 | 0.529773 | − | 0.848140i | \(-0.322277\pi\) | ||||
0.529773 | + | 0.848140i | \(0.322277\pi\) | |||||||
\(128\) | 1716.33 | 1.18519 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 490.203 | 0.330720 | ||||||||
\(131\) | −1383.75 | −0.922893 | −0.461446 | − | 0.887168i | \(-0.652669\pi\) | ||||
−0.461446 | + | 0.887168i | \(0.652669\pi\) | |||||||
\(132\) | 207.875 | 0.137070 | ||||||||
\(133\) | 1564.53 | 1.02001 | ||||||||
\(134\) | −1594.19 | −1.02774 | ||||||||
\(135\) | −1606.88 | −1.02443 | ||||||||
\(136\) | −2226.76 | −1.40399 | ||||||||
\(137\) | 1180.51 | 0.736190 | 0.368095 | − | 0.929788i | \(-0.380010\pi\) | ||||
0.368095 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(138\) | −3813.92 | −2.35263 | ||||||||
\(139\) | −2967.86 | −1.81101 | −0.905505 | − | 0.424336i | \(-0.860507\pi\) | ||||
−0.905505 | + | 0.424336i | \(0.860507\pi\) | |||||||
\(140\) | −683.749 | −0.412767 | ||||||||
\(141\) | −843.396 | −0.503736 | ||||||||
\(142\) | 92.0216 | 0.0543823 | ||||||||
\(143\) | 287.001 | 0.167834 | ||||||||
\(144\) | −467.911 | −0.270782 | ||||||||
\(145\) | 774.138 | 0.443370 | ||||||||
\(146\) | −232.412 | −0.131743 | ||||||||
\(147\) | 4792.10 | 2.68875 | ||||||||
\(148\) | −231.291 | −0.128459 | ||||||||
\(149\) | −568.440 | −0.312540 | −0.156270 | − | 0.987714i | \(-0.549947\pi\) | ||||
−0.156270 | + | 0.987714i | \(0.549947\pi\) | |||||||
\(150\) | 1006.41 | 0.547822 | ||||||||
\(151\) | −1740.05 | −0.937772 | −0.468886 | − | 0.883259i | \(-0.655344\pi\) | ||||
−0.468886 | + | 0.883259i | \(0.655344\pi\) | |||||||
\(152\) | 916.973 | 0.489318 | ||||||||
\(153\) | 704.755 | 0.372393 | ||||||||
\(154\) | −2561.82 | −1.34050 | ||||||||
\(155\) | −2445.42 | −1.26723 | ||||||||
\(156\) | 101.085 | 0.0518799 | ||||||||
\(157\) | 1742.13 | 0.885587 | 0.442793 | − | 0.896624i | \(-0.353988\pi\) | ||||
0.442793 | + | 0.896624i | \(0.353988\pi\) | |||||||
\(158\) | 2718.66 | 1.36889 | ||||||||
\(159\) | −1630.72 | −0.813362 | ||||||||
\(160\) | −892.583 | −0.441030 | ||||||||
\(161\) | 7344.70 | 3.59530 | ||||||||
\(162\) | −2648.64 | −1.28455 | ||||||||
\(163\) | 1870.73 | 0.898939 | 0.449469 | − | 0.893296i | \(-0.351613\pi\) | ||||
0.449469 | + | 0.893296i | \(0.351613\pi\) | |||||||
\(164\) | 1.14890 | 0.000547037 0 | ||||||||
\(165\) | 1890.67 | 0.892050 | ||||||||
\(166\) | 2205.02 | 1.03098 | ||||||||
\(167\) | 295.044 | 0.136714 | 0.0683568 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683568 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(168\) | 3969.65 | 1.82301 | ||||||||
\(169\) | −2057.44 | −0.936476 | ||||||||
\(170\) | 4603.47 | 2.07688 | ||||||||
\(171\) | −290.216 | −0.129786 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1615.88 | −0.710132 | −0.355066 | − | 0.934841i | \(-0.615542\pi\) | ||||
−0.355066 | + | 0.934841i | \(0.615542\pi\) | |||||||
\(174\) | 1021.58 | 0.445091 | ||||||||
\(175\) | −1938.11 | −0.837186 | ||||||||
\(176\) | −1789.45 | −0.766390 | ||||||||
\(177\) | −4033.67 | −1.71294 | ||||||||
\(178\) | 437.689 | 0.184305 | ||||||||
\(179\) | −2117.02 | −0.883987 | −0.441993 | − | 0.897018i | \(-0.645729\pi\) | ||||
−0.441993 | + | 0.897018i | \(0.645729\pi\) | |||||||
\(180\) | 126.834 | 0.0525201 | ||||||||
\(181\) | 297.604 | 0.122214 | 0.0611070 | − | 0.998131i | \(-0.480537\pi\) | ||||
0.0611070 | + | 0.998131i | \(0.480537\pi\) | |||||||
\(182\) | −1245.76 | −0.507371 | ||||||||
\(183\) | −570.152 | −0.230311 | ||||||||
\(184\) | 4304.74 | 1.72473 | ||||||||
\(185\) | −2103.64 | −0.836013 | ||||||||
\(186\) | −3227.06 | −1.27215 | ||||||||
\(187\) | 2695.21 | 1.05398 | ||||||||
\(188\) | −216.374 | −0.0839400 | ||||||||
\(189\) | 4083.56 | 1.57162 | ||||||||
\(190\) | −1895.69 | −0.723832 | ||||||||
\(191\) | 4542.23 | 1.72075 | 0.860377 | − | 0.509659i | \(-0.170228\pi\) | ||||
0.860377 | + | 0.509659i | \(0.170228\pi\) | |||||||
\(192\) | 2225.20 | 0.836406 | ||||||||
\(193\) | 3262.95 | 1.21696 | 0.608478 | − | 0.793571i | \(-0.291781\pi\) | ||||
0.608478 | + | 0.793571i | \(0.291781\pi\) | |||||||
\(194\) | −1084.30 | −0.401281 | ||||||||
\(195\) | 919.388 | 0.337635 | ||||||||
\(196\) | 1229.42 | 0.448039 | ||||||||
\(197\) | −868.209 | −0.313997 | −0.156998 | − | 0.987599i | \(-0.550182\pi\) | ||||
−0.156998 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(198\) | 475.211 | 0.170564 | ||||||||
\(199\) | −4215.53 | −1.50166 | −0.750832 | − | 0.660493i | \(-0.770347\pi\) | ||||
−0.750832 | + | 0.660493i | \(0.770347\pi\) | |||||||
\(200\) | −1135.93 | −0.401612 | ||||||||
\(201\) | −2989.94 | −1.04922 | ||||||||
\(202\) | 3393.20 | 1.18190 | ||||||||
\(203\) | −1967.32 | −0.680191 | ||||||||
\(204\) | 949.283 | 0.325800 | ||||||||
\(205\) | 10.4495 | 0.00356012 | ||||||||
\(206\) | −2801.07 | −0.947377 | ||||||||
\(207\) | −1362.42 | −0.457463 | ||||||||
\(208\) | −870.167 | −0.290073 | ||||||||
\(209\) | −1109.88 | −0.367330 | ||||||||
\(210\) | −8206.62 | −2.69672 | ||||||||
\(211\) | 2905.47 | 0.947964 | 0.473982 | − | 0.880534i | \(-0.342816\pi\) | ||||
0.473982 | + | 0.880534i | \(0.342816\pi\) | |||||||
\(212\) | −418.363 | −0.135535 | ||||||||
\(213\) | 172.589 | 0.0555192 | ||||||||
\(214\) | −5753.96 | −1.83800 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2393.38 | 0.753931 | ||||||||
\(217\) | 6214.55 | 1.94411 | ||||||||
\(218\) | 3230.36 | 1.00361 | ||||||||
\(219\) | −435.894 | −0.134498 | ||||||||
\(220\) | 485.053 | 0.148647 | ||||||||
\(221\) | 1310.62 | 0.398922 | ||||||||
\(222\) | −2776.04 | −0.839259 | ||||||||
\(223\) | −2146.80 | −0.644667 | −0.322333 | − | 0.946626i | \(-0.604467\pi\) | ||||
−0.322333 | + | 0.946626i | \(0.604467\pi\) | |||||||
\(224\) | 2268.33 | 0.676602 | ||||||||
\(225\) | 359.514 | 0.106523 | ||||||||
\(226\) | −2275.65 | −0.669795 | ||||||||
\(227\) | −873.162 | −0.255303 | −0.127652 | − | 0.991819i | \(-0.540744\pi\) | ||||
−0.127652 | + | 0.991819i | \(0.540744\pi\) | |||||||
\(228\) | −390.911 | −0.113547 | ||||||||
\(229\) | 3489.37 | 1.00692 | 0.503459 | − | 0.864019i | \(-0.332061\pi\) | ||||
0.503459 | + | 0.864019i | \(0.332061\pi\) | |||||||
\(230\) | −8899.36 | −2.55133 | ||||||||
\(231\) | −4804.76 | −1.36853 | ||||||||
\(232\) | −1153.05 | −0.326299 | ||||||||
\(233\) | 5132.13 | 1.44299 | 0.721496 | − | 0.692418i | \(-0.243455\pi\) | ||||
0.721496 | + | 0.692418i | \(0.243455\pi\) | |||||||
\(234\) | 231.084 | 0.0645574 | ||||||||
\(235\) | −1967.97 | −0.546281 | ||||||||
\(236\) | −1034.84 | −0.285435 | ||||||||
\(237\) | 5098.91 | 1.39751 | ||||||||
\(238\) | −11698.8 | −3.18623 | ||||||||
\(239\) | 3497.81 | 0.946672 | 0.473336 | − | 0.880882i | \(-0.343050\pi\) | ||||
0.473336 | + | 0.880882i | \(0.343050\pi\) | |||||||
\(240\) | −5732.36 | −1.54176 | ||||||||
\(241\) | 5168.03 | 1.38134 | 0.690669 | − | 0.723171i | \(-0.257316\pi\) | ||||
0.690669 | + | 0.723171i | \(0.257316\pi\) | |||||||
\(242\) | −2281.09 | −0.605925 | ||||||||
\(243\) | −1748.03 | −0.461466 | ||||||||
\(244\) | −146.273 | −0.0383778 | ||||||||
\(245\) | 11181.8 | 2.91584 | ||||||||
\(246\) | 13.7895 | 0.00357394 | ||||||||
\(247\) | −539.709 | −0.139032 | ||||||||
\(248\) | 3642.36 | 0.932621 | ||||||||
\(249\) | 4135.57 | 1.05253 | ||||||||
\(250\) | −2838.48 | −0.718085 | ||||||||
\(251\) | 2060.88 | 0.518253 | 0.259126 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259126 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(252\) | −322.323 | −0.0805731 | ||||||||
\(253\) | −5210.34 | −1.29475 | ||||||||
\(254\) | 4669.46 | 1.15350 | ||||||||
\(255\) | 8633.92 | 2.12030 | ||||||||
\(256\) | 2202.54 | 0.537728 | ||||||||
\(257\) | 2254.70 | 0.547254 | 0.273627 | − | 0.961836i | \(-0.411777\pi\) | ||||
0.273627 | + | 0.961836i | \(0.411777\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5345.98 | 1.28256 | ||||||||
\(260\) | 235.870 | 0.0562617 | ||||||||
\(261\) | 364.932 | 0.0865469 | ||||||||
\(262\) | −4260.88 | −1.00473 | ||||||||
\(263\) | 6481.38 | 1.51962 | 0.759808 | − | 0.650147i | \(-0.225293\pi\) | ||||
0.759808 | + | 0.650147i | \(0.225293\pi\) | |||||||
\(264\) | −2816.08 | −0.656506 | ||||||||
\(265\) | −3805.10 | −0.882059 | ||||||||
\(266\) | 4817.53 | 1.11046 | ||||||||
\(267\) | 820.897 | 0.188158 | ||||||||
\(268\) | −767.073 | −0.174837 | ||||||||
\(269\) | 2971.06 | 0.673415 | 0.336708 | − | 0.941609i | \(-0.390687\pi\) | ||||
0.336708 | + | 0.941609i | \(0.390687\pi\) | |||||||
\(270\) | −4947.93 | −1.11527 | ||||||||
\(271\) | −5738.03 | −1.28620 | −0.643100 | − | 0.765782i | \(-0.722352\pi\) | ||||
−0.643100 | + | 0.765782i | \(0.722352\pi\) | |||||||
\(272\) | −8171.69 | −1.82162 | ||||||||
\(273\) | −2336.45 | −0.517979 | ||||||||
\(274\) | 3635.06 | 0.801468 | ||||||||
\(275\) | 1374.90 | 0.301489 | ||||||||
\(276\) | −1835.14 | −0.400226 | ||||||||
\(277\) | −1591.55 | −0.345224 | −0.172612 | − | 0.984990i | \(-0.555221\pi\) | ||||
−0.172612 | + | 0.984990i | \(0.555221\pi\) | |||||||
\(278\) | −9138.70 | −1.97159 | ||||||||
\(279\) | −1152.78 | −0.247366 | ||||||||
\(280\) | 9262.74 | 1.97698 | ||||||||
\(281\) | −1279.65 | −0.271665 | −0.135832 | − | 0.990732i | \(-0.543371\pi\) | ||||
−0.135832 | + | 0.990732i | \(0.543371\pi\) | |||||||
\(282\) | −2597.01 | −0.548402 | ||||||||
\(283\) | 8416.02 | 1.76778 | 0.883888 | − | 0.467699i | \(-0.154917\pi\) | ||||
0.883888 | + | 0.467699i | \(0.154917\pi\) | |||||||
\(284\) | 44.2779 | 0.00925144 | ||||||||
\(285\) | −3555.42 | −0.738964 | ||||||||
\(286\) | 883.741 | 0.182716 | ||||||||
\(287\) | −26.5553 | −0.00546171 | ||||||||
\(288\) | −420.768 | −0.0860902 | ||||||||
\(289\) | 7394.97 | 1.50518 | ||||||||
\(290\) | 2383.74 | 0.482684 | ||||||||
\(291\) | −2033.64 | −0.409670 | ||||||||
\(292\) | −111.829 | −0.0224120 | ||||||||
\(293\) | −3718.98 | −0.741519 | −0.370760 | − | 0.928729i | \(-0.620903\pi\) | ||||
−0.370760 | + | 0.928729i | \(0.620903\pi\) | |||||||
\(294\) | 14756.0 | 2.92716 | ||||||||
\(295\) | −9412.12 | −1.85761 | ||||||||
\(296\) | 3133.29 | 0.615266 | ||||||||
\(297\) | −2896.89 | −0.565974 | ||||||||
\(298\) | −1750.35 | −0.340253 | ||||||||
\(299\) | −2533.67 | −0.490053 | ||||||||
\(300\) | 484.254 | 0.0931948 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5358.02 | −1.02092 | ||||||||
\(303\) | 6364.03 | 1.20661 | ||||||||
\(304\) | 3365.07 | 0.634869 | ||||||||
\(305\) | −1330.39 | −0.249763 | ||||||||
\(306\) | 2170.10 | 0.405413 | ||||||||
\(307\) | 6406.06 | 1.19092 | 0.595461 | − | 0.803384i | \(-0.296969\pi\) | ||||
0.595461 | + | 0.803384i | \(0.296969\pi\) | |||||||
\(308\) | −1232.67 | −0.228045 | ||||||||
\(309\) | −5253.47 | −0.967183 | ||||||||
\(310\) | −7529.98 | −1.37959 | ||||||||
\(311\) | −3626.35 | −0.661194 | −0.330597 | − | 0.943772i | \(-0.607250\pi\) | ||||
−0.330597 | + | 0.943772i | \(0.607250\pi\) | |||||||
\(312\) | −1369.39 | −0.248483 | ||||||||
\(313\) | −6160.29 | −1.11246 | −0.556230 | − | 0.831028i | \(-0.687753\pi\) | ||||
−0.556230 | + | 0.831028i | \(0.687753\pi\) | |||||||
\(314\) | 5364.41 | 0.964112 | ||||||||
\(315\) | −2931.59 | −0.524370 | ||||||||
\(316\) | 1308.13 | 0.232874 | ||||||||
\(317\) | −1508.62 | −0.267294 | −0.133647 | − | 0.991029i | \(-0.542669\pi\) | ||||
−0.133647 | + | 0.991029i | \(0.542669\pi\) | |||||||
\(318\) | −5021.36 | −0.885483 | ||||||||
\(319\) | 1395.62 | 0.244952 | ||||||||
\(320\) | 5192.25 | 0.907049 | ||||||||
\(321\) | −10791.7 | −1.87643 | ||||||||
\(322\) | 22616.0 | 3.91410 | ||||||||
\(323\) | −5068.38 | −0.873102 | ||||||||
\(324\) | −1274.44 | −0.218525 | ||||||||
\(325\) | 668.582 | 0.114112 | ||||||||
\(326\) | 5760.40 | 0.978648 | ||||||||
\(327\) | 6058.61 | 1.02459 | ||||||||
\(328\) | −15.5641 | −0.00262008 | ||||||||
\(329\) | 5001.21 | 0.838072 | ||||||||
\(330\) | 5821.79 | 0.971148 | ||||||||
\(331\) | −2373.17 | −0.394082 | −0.197041 | − | 0.980395i | \(-0.563133\pi\) | ||||
−0.197041 | + | 0.980395i | \(0.563133\pi\) | |||||||
\(332\) | 1060.98 | 0.175389 | ||||||||
\(333\) | −991.664 | −0.163192 | ||||||||
\(334\) | 908.506 | 0.148836 | ||||||||
\(335\) | −6976.69 | −1.13784 | ||||||||
\(336\) | 14567.7 | 2.36528 | ||||||||
\(337\) | −6631.98 | −1.07201 | −0.536005 | − | 0.844215i | \(-0.680067\pi\) | ||||
−0.536005 | + | 0.844215i | \(0.680067\pi\) | |||||||
\(338\) | −6335.31 | −1.01951 | ||||||||
\(339\) | −4268.03 | −0.683798 | ||||||||
\(340\) | 2215.04 | 0.353317 | ||||||||
\(341\) | −4408.61 | −0.700116 | ||||||||
\(342\) | −893.639 | −0.141294 | ||||||||
\(343\) | −16670.1 | −2.62420 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16691.0 | −2.60467 | ||||||||
\(346\) | −4975.64 | −0.773099 | ||||||||
\(347\) | 4392.54 | 0.679551 | 0.339775 | − | 0.940507i | \(-0.389649\pi\) | ||||
0.339775 | + | 0.940507i | \(0.389649\pi\) | |||||||
\(348\) | 491.553 | 0.0757183 | ||||||||
\(349\) | −1187.57 | −0.182147 | −0.0910736 | − | 0.995844i | \(-0.529030\pi\) | ||||
−0.0910736 | + | 0.995844i | \(0.529030\pi\) | |||||||
\(350\) | −5967.88 | −0.911419 | ||||||||
\(351\) | −1408.69 | −0.214217 | ||||||||
\(352\) | −1609.15 | −0.243660 | ||||||||
\(353\) | −6116.11 | −0.922175 | −0.461088 | − | 0.887355i | \(-0.652541\pi\) | ||||
−0.461088 | + | 0.887355i | \(0.652541\pi\) | |||||||
\(354\) | −12420.6 | −1.86482 | ||||||||
\(355\) | 402.716 | 0.0602084 | ||||||||
\(356\) | 210.602 | 0.0313536 | ||||||||
\(357\) | −21941.4 | −3.25284 | ||||||||
\(358\) | −6518.79 | −0.962370 | ||||||||
\(359\) | −867.123 | −0.127479 | −0.0637396 | − | 0.997967i | \(-0.520303\pi\) | ||||
−0.0637396 | + | 0.997967i | \(0.520303\pi\) | |||||||
\(360\) | −1718.21 | −0.251549 | ||||||||
\(361\) | −4771.86 | −0.695708 | ||||||||
\(362\) | 916.390 | 0.133051 | ||||||||
\(363\) | −4278.24 | −0.618593 | ||||||||
\(364\) | −599.418 | −0.0863133 | ||||||||
\(365\) | −1017.11 | −0.145857 | ||||||||
\(366\) | −1755.63 | −0.250733 | ||||||||
\(367\) | 7941.70 | 1.12957 | 0.564787 | − | 0.825237i | \(-0.308959\pi\) | ||||
0.564787 | + | 0.825237i | \(0.308959\pi\) | |||||||
\(368\) | 15797.4 | 2.23776 | ||||||||
\(369\) | 4.92594 | 0.000694943 0 | ||||||||
\(370\) | −6477.57 | −0.910143 | ||||||||
\(371\) | 9669.93 | 1.35320 | ||||||||
\(372\) | −1552.76 | −0.216416 | ||||||||
\(373\) | −200.374 | −0.0278149 | −0.0139075 | − | 0.999903i | \(-0.504427\pi\) | ||||
−0.0139075 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(374\) | 8299.17 | 1.14743 | ||||||||
\(375\) | −5323.64 | −0.733098 | ||||||||
\(376\) | 2931.22 | 0.402037 | ||||||||
\(377\) | 678.658 | 0.0927127 | ||||||||
\(378\) | 12574.2 | 1.71097 | ||||||||
\(379\) | 9566.94 | 1.29662 | 0.648312 | − | 0.761375i | \(-0.275475\pi\) | ||||
0.648312 | + | 0.761375i | \(0.275475\pi\) | |||||||
\(380\) | −912.147 | −0.123137 | ||||||||
\(381\) | 8757.69 | 1.17761 | ||||||||
\(382\) | 13986.5 | 1.87333 | ||||||||
\(383\) | −5373.45 | −0.716894 | −0.358447 | − | 0.933550i | \(-0.616694\pi\) | ||||
−0.358447 | + | 0.933550i | \(0.616694\pi\) | |||||||
\(384\) | 9912.10 | 1.31725 | ||||||||
\(385\) | −11211.4 | −1.48411 | ||||||||
\(386\) | 10047.4 | 1.32486 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −521.733 | −0.0682654 | ||||||||
\(389\) | −7774.81 | −1.01336 | −0.506682 | − | 0.862133i | \(-0.669128\pi\) | ||||
−0.506682 | + | 0.862133i | \(0.669128\pi\) | |||||||
\(390\) | 2831.00 | 0.367573 | ||||||||
\(391\) | −23793.6 | −3.07747 | ||||||||
\(392\) | −16654.9 | −2.14592 | ||||||||
\(393\) | −7991.39 | −1.02573 | ||||||||
\(394\) | −2673.41 | −0.341839 | ||||||||
\(395\) | 11897.7 | 1.51554 | ||||||||
\(396\) | 228.656 | 0.0290162 | ||||||||
\(397\) | 974.462 | 0.123191 | 0.0615955 | − | 0.998101i | \(-0.480381\pi\) | ||||
0.0615955 | + | 0.998101i | \(0.480381\pi\) | |||||||
\(398\) | −12980.6 | −1.63482 | ||||||||
\(399\) | 9035.41 | 1.13367 | ||||||||
\(400\) | −4168.59 | −0.521074 | ||||||||
\(401\) | 3270.33 | 0.407263 | 0.203631 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203631 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(402\) | −9206.70 | −1.14226 | ||||||||
\(403\) | −2143.81 | −0.264989 | ||||||||
\(404\) | 1632.70 | 0.201064 | ||||||||
\(405\) | −11591.3 | −1.42216 | ||||||||
\(406\) | −6057.82 | −0.740504 | ||||||||
\(407\) | −3792.45 | −0.461879 | ||||||||
\(408\) | −12859.9 | −1.56044 | ||||||||
\(409\) | 5108.88 | 0.617647 | 0.308824 | − | 0.951119i | \(-0.400065\pi\) | ||||
0.308824 | + | 0.951119i | \(0.400065\pi\) | |||||||
\(410\) | 32.1763 | 0.00387579 | ||||||||
\(411\) | 6817.65 | 0.818224 | ||||||||
\(412\) | −1347.78 | −0.161166 | ||||||||
\(413\) | 23919.1 | 2.84983 | ||||||||
\(414\) | −4195.20 | −0.498026 | ||||||||
\(415\) | 9649.87 | 1.14143 | ||||||||
\(416\) | −782.495 | −0.0922235 | ||||||||
\(417\) | −17139.9 | −2.01281 | ||||||||
\(418\) | −3417.57 | −0.399901 | ||||||||
\(419\) | −4610.75 | −0.537590 | −0.268795 | − | 0.963197i | \(-0.586625\pi\) | ||||
−0.268795 | + | 0.963197i | \(0.586625\pi\) | |||||||
\(420\) | −3948.76 | −0.458762 | ||||||||
\(421\) | −8130.00 | −0.941168 | −0.470584 | − | 0.882355i | \(-0.655957\pi\) | ||||
−0.470584 | + | 0.882355i | \(0.655957\pi\) | |||||||
\(422\) | 8946.58 | 1.03202 | ||||||||
\(423\) | −927.710 | −0.106635 | ||||||||
\(424\) | 5667.56 | 0.649153 | ||||||||
\(425\) | 6278.62 | 0.716607 | ||||||||
\(426\) | 531.440 | 0.0604421 | ||||||||
\(427\) | 3380.92 | 0.383171 | ||||||||
\(428\) | −2768.62 | −0.312678 | ||||||||
\(429\) | 1657.48 | 0.186536 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10180.0 | −1.13771 | −0.568853 | − | 0.822439i | \(-0.692613\pi\) | ||||
−0.568853 | + | 0.822439i | \(0.692613\pi\) | |||||||
\(432\) | 8783.15 | 0.978193 | ||||||||
\(433\) | −3809.91 | −0.422846 | −0.211423 | − | 0.977395i | \(-0.567810\pi\) | ||||
−0.211423 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(434\) | 19136.0 | 2.11649 | ||||||||
\(435\) | 4470.77 | 0.492775 | ||||||||
\(436\) | 1554.35 | 0.170733 | ||||||||
\(437\) | 9798.11 | 1.07256 | ||||||||
\(438\) | −1342.21 | −0.146423 | ||||||||
\(439\) | −13805.3 | −1.50090 | −0.750448 | − | 0.660930i | \(-0.770162\pi\) | ||||
−0.750448 | + | 0.660930i | \(0.770162\pi\) | |||||||
\(440\) | −6571.00 | −0.711955 | ||||||||
\(441\) | 5271.16 | 0.569179 | ||||||||
\(442\) | 4035.69 | 0.434295 | ||||||||
\(443\) | −3291.23 | −0.352982 | −0.176491 | − | 0.984302i | \(-0.556475\pi\) | ||||
−0.176491 | + | 0.984302i | \(0.556475\pi\) | |||||||
\(444\) | −1335.74 | −0.142774 | ||||||||
\(445\) | 1915.47 | 0.204049 | ||||||||
\(446\) | −6610.49 | −0.701830 | ||||||||
\(447\) | −3282.83 | −0.347366 | ||||||||
\(448\) | −13195.1 | −1.39154 | ||||||||
\(449\) | 17505.7 | 1.83997 | 0.919986 | − | 0.391952i | \(-0.128200\pi\) | ||||
0.919986 | + | 0.391952i | \(0.128200\pi\) | |||||||
\(450\) | 1107.02 | 0.115968 | ||||||||
\(451\) | 18.8384 | 0.00196689 | ||||||||
\(452\) | −1094.97 | −0.113945 | ||||||||
\(453\) | −10049.1 | −1.04227 | ||||||||
\(454\) | −2688.66 | −0.277941 | ||||||||
\(455\) | −5451.83 | −0.561727 | ||||||||
\(456\) | 5295.67 | 0.543843 | ||||||||
\(457\) | 6024.93 | 0.616706 | 0.308353 | − | 0.951272i | \(-0.400222\pi\) | ||||
0.308353 | + | 0.951272i | \(0.400222\pi\) | |||||||
\(458\) | 10744.6 | 1.09620 | ||||||||
\(459\) | −13228.9 | −1.34526 | ||||||||
\(460\) | −4282.09 | −0.434029 | ||||||||
\(461\) | 9644.81 | 0.974411 | 0.487205 | − | 0.873287i | \(-0.338016\pi\) | ||||
0.487205 | + | 0.873287i | \(0.338016\pi\) | |||||||
\(462\) | −14794.9 | −1.48988 | ||||||||
\(463\) | −8578.11 | −0.861034 | −0.430517 | − | 0.902583i | \(-0.641669\pi\) | ||||
−0.430517 | + | 0.902583i | \(0.641669\pi\) | |||||||
\(464\) | −4231.42 | −0.423359 | ||||||||
\(465\) | −14122.7 | −1.40844 | ||||||||
\(466\) | 15803.0 | 1.57094 | ||||||||
\(467\) | 3847.04 | 0.381199 | 0.190599 | − | 0.981668i | \(-0.438957\pi\) | ||||
0.190599 | + | 0.981668i | \(0.438957\pi\) | |||||||
\(468\) | 111.190 | 0.0109824 | ||||||||
\(469\) | 17729.9 | 1.74561 | ||||||||
\(470\) | −6059.82 | −0.594720 | ||||||||
\(471\) | 10061.1 | 0.984268 | ||||||||
\(472\) | 14019.0 | 1.36711 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 15700.7 | 1.52143 | ||||||||
\(475\) | −2585.51 | −0.249750 | ||||||||
\(476\) | −5629.10 | −0.542037 | ||||||||
\(477\) | −1793.74 | −0.172180 | ||||||||
\(478\) | 10770.5 | 1.03061 | ||||||||
\(479\) | −3588.42 | −0.342295 | −0.171147 | − | 0.985245i | \(-0.554747\pi\) | ||||
−0.171147 | + | 0.985245i | \(0.554747\pi\) | |||||||
\(480\) | −5154.81 | −0.490175 | ||||||||
\(481\) | −1844.18 | −0.174818 | ||||||||
\(482\) | 15913.5 | 1.50382 | ||||||||
\(483\) | 42416.9 | 3.99593 | ||||||||
\(484\) | −1097.59 | −0.103079 | ||||||||
\(485\) | −4745.27 | −0.444271 | ||||||||
\(486\) | −5382.58 | −0.502384 | ||||||||
\(487\) | −14142.4 | −1.31592 | −0.657962 | − | 0.753051i | \(-0.728581\pi\) | ||||
−0.657962 | + | 0.753051i | \(0.728581\pi\) | |||||||
\(488\) | 1981.56 | 0.183814 | ||||||||
\(489\) | 10803.8 | 0.999108 | ||||||||
\(490\) | 34431.3 | 3.17439 | ||||||||
\(491\) | 7516.33 | 0.690850 | 0.345425 | − | 0.938446i | \(-0.387735\pi\) | ||||
0.345425 | + | 0.938446i | \(0.387735\pi\) | |||||||
\(492\) | 6.63509 | 0.000607993 0 | ||||||||
\(493\) | 6373.24 | 0.582224 | ||||||||
\(494\) | −1661.88 | −0.151360 | ||||||||
\(495\) | 2079.68 | 0.188837 | ||||||||
\(496\) | 13366.6 | 1.21004 | ||||||||
\(497\) | −1023.43 | −0.0923680 | ||||||||
\(498\) | 12734.3 | 1.14586 | ||||||||
\(499\) | 7452.63 | 0.668588 | 0.334294 | − | 0.942469i | \(-0.391502\pi\) | ||||
0.334294 | + | 0.942469i | \(0.391502\pi\) | |||||||
\(500\) | −1365.79 | −0.122160 | ||||||||
\(501\) | 1703.93 | 0.151948 | ||||||||
\(502\) | 6345.90 | 0.564206 | ||||||||
\(503\) | 13585.0 | 1.20422 | 0.602112 | − | 0.798412i | \(-0.294326\pi\) | ||||
0.602112 | + | 0.798412i | \(0.294326\pi\) | |||||||
\(504\) | 4366.50 | 0.385911 | ||||||||
\(505\) | 14849.7 | 1.30852 | ||||||||
\(506\) | −16043.8 | −1.40955 | ||||||||
\(507\) | −11882.0 | −1.04083 | ||||||||
\(508\) | 2246.80 | 0.196231 | ||||||||
\(509\) | −3781.95 | −0.329336 | −0.164668 | − | 0.986349i | \(-0.552655\pi\) | ||||
−0.164668 | + | 0.986349i | \(0.552655\pi\) | |||||||
\(510\) | 26585.8 | 2.30831 | ||||||||
\(511\) | 2584.78 | 0.223765 | ||||||||
\(512\) | −6948.56 | −0.599778 | ||||||||
\(513\) | 5447.63 | 0.468847 | ||||||||
\(514\) | 6942.72 | 0.595779 | ||||||||
\(515\) | −12258.4 | −1.04887 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3547.87 | −0.301808 | ||||||||
\(518\) | 16461.5 | 1.39629 | ||||||||
\(519\) | −9331.94 | −0.789262 | ||||||||
\(520\) | −3195.33 | −0.269470 | ||||||||
\(521\) | 5698.91 | 0.479220 | 0.239610 | − | 0.970869i | \(-0.422980\pi\) | ||||
0.239610 | + | 0.970869i | \(0.422980\pi\) | |||||||
\(522\) | 1123.71 | 0.0942211 | ||||||||
\(523\) | 19344.4 | 1.61734 | 0.808671 | − | 0.588262i | \(-0.200187\pi\) | ||||
0.808671 | + | 0.588262i | \(0.200187\pi\) | |||||||
\(524\) | −2050.20 | −0.170923 | ||||||||
\(525\) | −11192.9 | −0.930474 | ||||||||
\(526\) | 19957.6 | 1.65436 | ||||||||
\(527\) | −20132.4 | −1.66410 | ||||||||
\(528\) | −10334.3 | −0.851789 | ||||||||
\(529\) | 33830.4 | 2.78050 | ||||||||
\(530\) | −11716.8 | −0.960271 | ||||||||
\(531\) | −4436.92 | −0.362610 | ||||||||
\(532\) | 2318.04 | 0.188910 | ||||||||
\(533\) | 9.16068 | 0.000744452 0 | ||||||||
\(534\) | 2527.73 | 0.204842 | ||||||||
\(535\) | −25181.2 | −2.03491 | ||||||||
\(536\) | 10391.5 | 0.837398 | ||||||||
\(537\) | −12226.1 | −0.982490 | ||||||||
\(538\) | 9148.56 | 0.733127 | ||||||||
\(539\) | 20158.7 | 1.61094 | ||||||||
\(540\) | −2380.79 | −0.189727 | ||||||||
\(541\) | 4375.41 | 0.347714 | 0.173857 | − | 0.984771i | \(-0.444377\pi\) | ||||
0.173857 | + | 0.984771i | \(0.444377\pi\) | |||||||
\(542\) | −17668.7 | −1.40025 | ||||||||
\(543\) | 1718.71 | 0.135832 | ||||||||
\(544\) | −7348.37 | −0.579152 | ||||||||
\(545\) | 14137.1 | 1.11113 | ||||||||
\(546\) | −7194.44 | −0.563908 | ||||||||
\(547\) | −22211.1 | −1.73616 | −0.868080 | − | 0.496424i | \(-0.834646\pi\) | ||||
−0.868080 | + | 0.496424i | \(0.834646\pi\) | |||||||
\(548\) | 1749.08 | 0.136345 | ||||||||
\(549\) | −627.150 | −0.0487543 | ||||||||
\(550\) | 4233.62 | 0.328222 | ||||||||
\(551\) | −2624.48 | −0.202916 | ||||||||
\(552\) | 24860.6 | 1.91691 | ||||||||
\(553\) | −30235.8 | −2.32506 | ||||||||
\(554\) | −4900.74 | −0.375835 | ||||||||
\(555\) | −12148.8 | −0.929170 | ||||||||
\(556\) | −4397.25 | −0.335405 | ||||||||
\(557\) | 2299.41 | 0.174918 | 0.0874590 | − | 0.996168i | \(-0.472125\pi\) | ||||
0.0874590 | + | 0.996168i | \(0.472125\pi\) | |||||||
\(558\) | −3549.67 | −0.269300 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 33992.0 | 2.56505 | ||||||||
\(561\) | 15565.3 | 1.17142 | ||||||||
\(562\) | −3940.34 | −0.295753 | ||||||||
\(563\) | 10335.3 | 0.773677 | 0.386839 | − | 0.922147i | \(-0.373567\pi\) | ||||
0.386839 | + | 0.922147i | \(0.373567\pi\) | |||||||
\(564\) | −1249.60 | −0.0932935 | ||||||||
\(565\) | −9958.96 | −0.741552 | ||||||||
\(566\) | 25914.8 | 1.92453 | ||||||||
\(567\) | 29457.0 | 2.18180 | ||||||||
\(568\) | −599.831 | −0.0443105 | ||||||||
\(569\) | 3082.61 | 0.227117 | 0.113559 | − | 0.993531i | \(-0.463775\pi\) | ||||
0.113559 | + | 0.993531i | \(0.463775\pi\) | |||||||
\(570\) | −10947.9 | −0.804489 | ||||||||
\(571\) | −3788.95 | −0.277693 | −0.138846 | − | 0.990314i | \(-0.544339\pi\) | ||||
−0.138846 | + | 0.990314i | \(0.544339\pi\) | |||||||
\(572\) | 425.228 | 0.0310834 | ||||||||
\(573\) | 26232.1 | 1.91250 | ||||||||
\(574\) | −81.7699 | −0.00594601 | ||||||||
\(575\) | −12137.7 | −0.880310 | ||||||||
\(576\) | 2447.65 | 0.177058 | ||||||||
\(577\) | −11757.4 | −0.848296 | −0.424148 | − | 0.905593i | \(-0.639426\pi\) | ||||
−0.424148 | + | 0.905593i | \(0.639426\pi\) | |||||||
\(578\) | 22770.8 | 1.63865 | ||||||||
\(579\) | 18844.1 | 1.35256 | ||||||||
\(580\) | 1146.98 | 0.0821135 | ||||||||
\(581\) | −24523.3 | −1.75111 | ||||||||
\(582\) | −6262.03 | −0.445996 | ||||||||
\(583\) | −6859.86 | −0.487318 | ||||||||
\(584\) | 1514.95 | 0.107344 | ||||||||
\(585\) | 1011.30 | 0.0714736 | ||||||||
\(586\) | −11451.6 | −0.807270 | ||||||||
\(587\) | 9782.37 | 0.687839 | 0.343919 | − | 0.938999i | \(-0.388245\pi\) | ||||
0.343919 | + | 0.938999i | \(0.388245\pi\) | |||||||
\(588\) | 7100.09 | 0.497964 | ||||||||
\(589\) | 8290.44 | 0.579969 | ||||||||
\(590\) | −28982.0 | −2.02232 | ||||||||
\(591\) | −5014.05 | −0.348985 | ||||||||
\(592\) | 11498.4 | 0.798281 | ||||||||
\(593\) | 19483.1 | 1.34920 | 0.674600 | − | 0.738183i | \(-0.264316\pi\) | ||||
0.674600 | + | 0.738183i | \(0.264316\pi\) | |||||||
\(594\) | −8920.17 | −0.616160 | ||||||||
\(595\) | −51197.9 | −3.52758 | ||||||||
\(596\) | −842.215 | −0.0578833 | ||||||||
\(597\) | −24345.4 | −1.66900 | ||||||||
\(598\) | −7801.74 | −0.533507 | ||||||||
\(599\) | −4655.42 | −0.317555 | −0.158778 | − | 0.987314i | \(-0.550755\pi\) | ||||
−0.158778 | + | 0.987314i | \(0.550755\pi\) | |||||||
\(600\) | −6560.18 | −0.446364 | ||||||||
\(601\) | −13673.1 | −0.928014 | −0.464007 | − | 0.885832i | \(-0.653589\pi\) | ||||
−0.464007 | + | 0.885832i | \(0.653589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3288.84 | −0.222110 | ||||||||
\(604\) | −2578.11 | −0.173678 | ||||||||
\(605\) | −9982.78 | −0.670839 | ||||||||
\(606\) | 19596.3 | 1.31360 | ||||||||
\(607\) | −7757.17 | −0.518705 | −0.259352 | − | 0.965783i | \(-0.583509\pi\) | ||||
−0.259352 | + | 0.965783i | \(0.583509\pi\) | |||||||
\(608\) | 3026.03 | 0.201845 | ||||||||
\(609\) | −11361.6 | −0.755986 | ||||||||
\(610\) | −4096.56 | −0.271909 | ||||||||
\(611\) | −1725.25 | −0.114232 | ||||||||
\(612\) | 1044.18 | 0.0689683 | ||||||||
\(613\) | 14088.9 | 0.928297 | 0.464148 | − | 0.885757i | \(-0.346360\pi\) | ||||
0.464148 | + | 0.885757i | \(0.346360\pi\) | |||||||
\(614\) | 19725.7 | 1.29652 | ||||||||
\(615\) | 60.3475 | 0.00395682 | ||||||||
\(616\) | 16698.9 | 1.09224 | ||||||||
\(617\) | 12906.3 | 0.842122 | 0.421061 | − | 0.907032i | \(-0.361658\pi\) | ||||
0.421061 | + | 0.907032i | \(0.361658\pi\) | |||||||
\(618\) | −16176.6 | −1.05294 | ||||||||
\(619\) | −23723.2 | −1.54041 | −0.770206 | − | 0.637795i | \(-0.779847\pi\) | ||||
−0.770206 | + | 0.637795i | \(0.779847\pi\) | |||||||
\(620\) | −3623.19 | −0.234695 | ||||||||
\(621\) | 25574.0 | 1.65257 | ||||||||
\(622\) | −11166.3 | −0.719823 | ||||||||
\(623\) | −4867.80 | −0.313040 | ||||||||
\(624\) | −5025.35 | −0.322396 | ||||||||
\(625\) | −19496.4 | −1.24777 | ||||||||
\(626\) | −18968.9 | −1.21110 | ||||||||
\(627\) | −6409.73 | −0.408262 | ||||||||
\(628\) | 2581.18 | 0.164013 | ||||||||
\(629\) | −17318.6 | −1.09783 | ||||||||
\(630\) | −9027.03 | −0.570866 | ||||||||
\(631\) | −12214.1 | −0.770578 | −0.385289 | − | 0.922796i | \(-0.625898\pi\) | ||||
−0.385289 | + | 0.922796i | \(0.625898\pi\) | |||||||
\(632\) | −17721.2 | −1.11537 | ||||||||
\(633\) | 16779.5 | 1.05360 | ||||||||
\(634\) | −4645.37 | −0.290995 | ||||||||
\(635\) | 20435.1 | 1.27707 | ||||||||
\(636\) | −2416.12 | −0.150637 | ||||||||
\(637\) | 9802.69 | 0.609728 | ||||||||
\(638\) | 4297.43 | 0.266672 | ||||||||
\(639\) | 189.842 | 0.0117528 | ||||||||
\(640\) | 23128.8 | 1.42851 | ||||||||
\(641\) | 16542.4 | 1.01932 | 0.509662 | − | 0.860375i | \(-0.329771\pi\) | ||||
0.509662 | + | 0.860375i | \(0.329771\pi\) | |||||||
\(642\) | −33230.0 | −2.04281 | ||||||||
\(643\) | 6165.28 | 0.378126 | 0.189063 | − | 0.981965i | \(-0.439455\pi\) | ||||
0.189063 | + | 0.981965i | \(0.439455\pi\) | |||||||
\(644\) | 10882.1 | 0.665861 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15606.7 | −0.950520 | ||||||||
\(647\) | 1033.87 | 0.0628217 | 0.0314108 | − | 0.999507i | \(-0.490000\pi\) | ||||
0.0314108 | + | 0.999507i | \(0.490000\pi\) | |||||||
\(648\) | 17264.8 | 1.04664 | ||||||||
\(649\) | −16968.2 | −1.02629 | ||||||||
\(650\) | 2058.71 | 0.124230 | ||||||||
\(651\) | 35890.0 | 2.16074 | ||||||||
\(652\) | 2771.72 | 0.166486 | ||||||||
\(653\) | −10363.9 | −0.621085 | −0.310543 | − | 0.950559i | \(-0.600511\pi\) | ||||
−0.310543 | + | 0.950559i | \(0.600511\pi\) | |||||||
\(654\) | 18655.8 | 1.11544 | ||||||||
\(655\) | −18647.0 | −1.11236 | ||||||||
\(656\) | −57.1166 | −0.00339944 | ||||||||
\(657\) | −479.470 | −0.0284717 | ||||||||
\(658\) | 15399.8 | 0.912384 | ||||||||
\(659\) | 27813.2 | 1.64408 | 0.822039 | − | 0.569431i | \(-0.192837\pi\) | ||||
0.822039 | + | 0.569431i | \(0.192837\pi\) | |||||||
\(660\) | 2801.26 | 0.165210 | ||||||||
\(661\) | −12139.7 | −0.714344 | −0.357172 | − | 0.934039i | \(-0.616259\pi\) | ||||
−0.357172 | + | 0.934039i | \(0.616259\pi\) | |||||||
\(662\) | −7307.52 | −0.429026 | ||||||||
\(663\) | 7569.05 | 0.443375 | ||||||||
\(664\) | −14373.1 | −0.840039 | ||||||||
\(665\) | 21083.1 | 1.22942 | ||||||||
\(666\) | −3053.56 | −0.177662 | ||||||||
\(667\) | −12320.7 | −0.715229 | ||||||||
\(668\) | 437.144 | 0.0253198 | ||||||||
\(669\) | −12398.1 | −0.716502 | ||||||||
\(670\) | −21482.8 | −1.23873 | ||||||||
\(671\) | −2398.43 | −0.137988 | ||||||||
\(672\) | 13100.0 | 0.751996 | ||||||||
\(673\) | −14488.3 | −0.829842 | −0.414921 | − | 0.909857i | \(-0.636191\pi\) | ||||
−0.414921 | + | 0.909857i | \(0.636191\pi\) | |||||||
\(674\) | −20421.4 | −1.16706 | ||||||||
\(675\) | −6748.43 | −0.384811 | ||||||||
\(676\) | −3048.35 | −0.173438 | ||||||||
\(677\) | −6394.53 | −0.363016 | −0.181508 | − | 0.983389i | \(-0.558098\pi\) | ||||
−0.181508 | + | 0.983389i | \(0.558098\pi\) | |||||||
\(678\) | −13142.2 | −0.744431 | ||||||||
\(679\) | 12059.2 | 0.681574 | ||||||||
\(680\) | −30007.1 | −1.69224 | ||||||||
\(681\) | −5042.65 | −0.283752 | ||||||||
\(682\) | −13575.1 | −0.762196 | ||||||||
\(683\) | 24918.6 | 1.39602 | 0.698011 | − | 0.716087i | \(-0.254069\pi\) | ||||
0.698011 | + | 0.716087i | \(0.254069\pi\) | |||||||
\(684\) | −429.991 | −0.0240367 | ||||||||
\(685\) | 15908.2 | 0.887331 | ||||||||
\(686\) | −51331.0 | −2.85689 | ||||||||
\(687\) | 20151.7 | 1.11912 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3335.79 | −0.184446 | ||||||||
\(690\) | −51395.2 | −2.83563 | ||||||||
\(691\) | −26390.3 | −1.45287 | −0.726434 | − | 0.687236i | \(-0.758824\pi\) | ||||
−0.726434 | + | 0.687236i | \(0.758824\pi\) | |||||||
\(692\) | −2394.12 | −0.131519 | ||||||||
\(693\) | −5285.09 | −0.289703 | ||||||||
\(694\) | 13525.6 | 0.739807 | ||||||||
\(695\) | −39993.9 | −2.18281 | ||||||||
\(696\) | −6659.05 | −0.362659 | ||||||||
\(697\) | 86.0275 | 0.00467507 | ||||||||
\(698\) | −3656.81 | −0.198298 | ||||||||
\(699\) | 29638.9 | 1.60379 | ||||||||
\(700\) | −2871.55 | −0.155049 | ||||||||
\(701\) | −16215.7 | −0.873693 | −0.436846 | − | 0.899536i | \(-0.643905\pi\) | ||||
−0.436846 | + | 0.899536i | \(0.643905\pi\) | |||||||
\(702\) | −4337.67 | −0.233212 | ||||||||
\(703\) | 7131.74 | 0.382615 | ||||||||
\(704\) | 9360.62 | 0.501125 | ||||||||
\(705\) | −11365.3 | −0.607154 | ||||||||
\(706\) | −18832.9 | −1.00394 | ||||||||
\(707\) | −37737.7 | −2.00746 | ||||||||
\(708\) | −5976.39 | −0.317241 | ||||||||
\(709\) | −4007.85 | −0.212296 | −0.106148 | − | 0.994350i | \(-0.533852\pi\) | ||||
−0.106148 | + | 0.994350i | \(0.533852\pi\) | |||||||
\(710\) | 1240.05 | 0.0655471 | ||||||||
\(711\) | 5608.65 | 0.295838 | ||||||||
\(712\) | −2853.02 | −0.150171 | ||||||||
\(713\) | 38919.6 | 2.04425 | ||||||||
\(714\) | −67562.6 | −3.54127 | ||||||||
\(715\) | 3867.54 | 0.202290 | ||||||||
\(716\) | −3136.63 | −0.163717 | ||||||||
\(717\) | 20200.4 | 1.05216 | ||||||||
\(718\) | −2670.07 | −0.138783 | ||||||||
\(719\) | −27845.1 | −1.44429 | −0.722147 | − | 0.691740i | \(-0.756844\pi\) | ||||
−0.722147 | + | 0.691740i | \(0.756844\pi\) | |||||||
\(720\) | −6305.43 | −0.326374 | ||||||||
\(721\) | 31152.3 | 1.60911 | ||||||||
\(722\) | −14693.6 | −0.757397 | ||||||||
\(723\) | 29846.2 | 1.53526 | ||||||||
\(724\) | 440.938 | 0.0226344 | ||||||||
\(725\) | 3251.16 | 0.166545 | ||||||||
\(726\) | −13173.6 | −0.673443 | ||||||||
\(727\) | −17757.5 | −0.905899 | −0.452949 | − | 0.891536i | \(-0.649628\pi\) | ||||
−0.452949 | + | 0.891536i | \(0.649628\pi\) | |||||||
\(728\) | 8120.30 | 0.413405 | ||||||||
\(729\) | 13129.2 | 0.667035 | ||||||||
\(730\) | −3131.90 | −0.158790 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −844.752 | −0.0426543 | ||||||||
\(733\) | −37573.6 | −1.89333 | −0.946667 | − | 0.322212i | \(-0.895573\pi\) | ||||
−0.946667 | + | 0.322212i | \(0.895573\pi\) | |||||||
\(734\) | 24454.3 | 1.22973 | ||||||||
\(735\) | 64576.8 | 3.24075 | ||||||||
\(736\) | 14205.7 | 0.711455 | ||||||||
\(737\) | −12577.6 | −0.628633 | ||||||||
\(738\) | 15.1681 | 0.000756564 0 | ||||||||
\(739\) | −5146.38 | −0.256174 | −0.128087 | − | 0.991763i | \(-0.540884\pi\) | ||||
−0.128087 | + | 0.991763i | \(0.540884\pi\) | |||||||
\(740\) | −3116.80 | −0.154832 | ||||||||
\(741\) | −3116.91 | −0.154524 | ||||||||
\(742\) | 29775.9 | 1.47319 | ||||||||
\(743\) | 14021.8 | 0.692342 | 0.346171 | − | 0.938171i | \(-0.387482\pi\) | ||||
0.346171 | + | 0.938171i | \(0.387482\pi\) | |||||||
\(744\) | 21035.2 | 1.03654 | ||||||||
\(745\) | −7660.12 | −0.376705 | ||||||||
\(746\) | −616.996 | −0.0302813 | ||||||||
\(747\) | 4549.00 | 0.222810 | ||||||||
\(748\) | 3993.29 | 0.195200 | ||||||||
\(749\) | 63993.1 | 3.12184 | ||||||||
\(750\) | −16392.7 | −0.798102 | ||||||||
\(751\) | −7633.53 | −0.370907 | −0.185454 | − | 0.982653i | \(-0.559375\pi\) | ||||
−0.185454 | + | 0.982653i | \(0.559375\pi\) | |||||||
\(752\) | 10756.9 | 0.521626 | ||||||||
\(753\) | 11901.9 | 0.576002 | ||||||||
\(754\) | 2089.74 | 0.100934 | ||||||||
\(755\) | −23448.4 | −1.13030 | ||||||||
\(756\) | 6050.31 | 0.291068 | ||||||||
\(757\) | −9584.30 | −0.460168 | −0.230084 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230084 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(758\) | 29458.7 | 1.41160 | ||||||||
\(759\) | −30090.6 | −1.43902 | ||||||||
\(760\) | 12356.8 | 0.589776 | ||||||||
\(761\) | −12340.8 | −0.587849 | −0.293925 | − | 0.955829i | \(-0.594961\pi\) | ||||
−0.293925 | + | 0.955829i | \(0.594961\pi\) | |||||||
\(762\) | 26966.9 | 1.28203 | ||||||||
\(763\) | −35926.7 | −1.70463 | ||||||||
\(764\) | 6729.87 | 0.318689 | ||||||||
\(765\) | 9497.05 | 0.448845 | ||||||||
\(766\) | −16546.1 | −0.780461 | ||||||||
\(767\) | −8251.26 | −0.388443 | ||||||||
\(768\) | 12720.0 | 0.597648 | ||||||||
\(769\) | −6270.07 | −0.294024 | −0.147012 | − | 0.989135i | \(-0.546966\pi\) | ||||
−0.147012 | + | 0.989135i | \(0.546966\pi\) | |||||||
\(770\) | −34522.3 | −1.61571 | ||||||||
\(771\) | 13021.2 | 0.608234 | ||||||||
\(772\) | 4834.47 | 0.225384 | ||||||||
\(773\) | 29116.0 | 1.35476 | 0.677379 | − | 0.735634i | \(-0.263116\pi\) | ||||
0.677379 | + | 0.735634i | \(0.263116\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10270.1 | −0.476015 | ||||||||
\(776\) | 7067.90 | 0.326962 | ||||||||
\(777\) | 30873.9 | 1.42548 | ||||||||
\(778\) | −23940.4 | −1.10322 | ||||||||
\(779\) | −35.4258 | −0.00162935 | ||||||||
\(780\) | 1362.19 | 0.0625310 | ||||||||
\(781\) | 726.020 | 0.0332638 | ||||||||
\(782\) | −73265.7 | −3.35036 | ||||||||
\(783\) | −6850.13 | −0.312649 | ||||||||
\(784\) | −61119.6 | −2.78424 | ||||||||
\(785\) | 23476.4 | 1.06740 | ||||||||
\(786\) | −24607.3 | −1.11668 | ||||||||
\(787\) | 28536.0 | 1.29250 | 0.646250 | − | 0.763126i | \(-0.276336\pi\) | ||||
0.646250 | + | 0.763126i | \(0.276336\pi\) | |||||||
\(788\) | −1286.36 | −0.0581531 | ||||||||
\(789\) | 37431.0 | 1.68895 | ||||||||
\(790\) | 36635.8 | 1.64993 | ||||||||
\(791\) | 25308.8 | 1.13764 | ||||||||
\(792\) | −3097.60 | −0.138975 | ||||||||
\(793\) | −1166.30 | −0.0522277 | ||||||||
\(794\) | 3000.59 | 0.134114 | ||||||||
\(795\) | −21975.1 | −0.980347 | ||||||||
\(796\) | −6245.84 | −0.278113 | ||||||||
\(797\) | −16273.3 | −0.723248 | −0.361624 | − | 0.932324i | \(-0.617778\pi\) | ||||
−0.361624 | + | 0.932324i | \(0.617778\pi\) | |||||||
\(798\) | 27822.0 | 1.23420 | ||||||||
\(799\) | −16201.7 | −0.717365 | ||||||||
\(800\) | −3748.60 | −0.165666 | ||||||||
\(801\) | 902.962 | 0.0398310 | ||||||||
\(802\) | 10070.1 | 0.443375 | ||||||||
\(803\) | −1833.65 | −0.0805829 | ||||||||
\(804\) | −4429.97 | −0.194320 | ||||||||
\(805\) | 98974.9 | 4.33342 | ||||||||
\(806\) | −6601.26 | −0.288486 | ||||||||
\(807\) | 17158.4 | 0.748454 | ||||||||
\(808\) | −22118.1 | −0.963012 | ||||||||
\(809\) | −22873.9 | −0.994073 | −0.497037 | − | 0.867730i | \(-0.665579\pi\) | ||||
−0.497037 | + | 0.867730i | \(0.665579\pi\) | |||||||
\(810\) | −35692.2 | −1.54827 | ||||||||
\(811\) | −1107.97 | −0.0479728 | −0.0239864 | − | 0.999712i | \(-0.507636\pi\) | ||||
−0.0239864 | + | 0.999712i | \(0.507636\pi\) | |||||||
\(812\) | −2914.83 | −0.125974 | ||||||||
\(813\) | −33138.0 | −1.42952 | ||||||||
\(814\) | −11677.8 | −0.502834 | ||||||||
\(815\) | 25209.4 | 1.08349 | ||||||||
\(816\) | −47192.8 | −2.02461 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 15731.4 | 0.672414 | ||||||||
\(819\) | −2570.02 | −0.109651 | ||||||||
\(820\) | 15.4822 | 0.000659345 0 | ||||||||
\(821\) | −24233.1 | −1.03014 | −0.515068 | − | 0.857149i | \(-0.672233\pi\) | ||||
−0.515068 | + | 0.857149i | \(0.672233\pi\) | |||||||
\(822\) | 20993.1 | 0.890776 | ||||||||
\(823\) | −15663.8 | −0.663435 | −0.331717 | − | 0.943379i | \(-0.607628\pi\) | ||||
−0.331717 | + | 0.943379i | \(0.607628\pi\) | |||||||
\(824\) | 18258.4 | 0.771920 | ||||||||
\(825\) | 7940.27 | 0.335084 | ||||||||
\(826\) | 73652.2 | 3.10253 | ||||||||
\(827\) | −13112.5 | −0.551349 | −0.275674 | − | 0.961251i | \(-0.588901\pi\) | ||||
−0.275674 | + | 0.961251i | \(0.588901\pi\) | |||||||
\(828\) | −2018.60 | −0.0847236 | ||||||||
\(829\) | 23726.4 | 0.994030 | 0.497015 | − | 0.867742i | \(-0.334429\pi\) | ||||
0.497015 | + | 0.867742i | \(0.334429\pi\) | |||||||
\(830\) | 29714.1 | 1.24264 | ||||||||
\(831\) | −9191.47 | −0.383692 | ||||||||
\(832\) | 4551.86 | 0.189672 | ||||||||
\(833\) | 92056.6 | 3.82902 | ||||||||
\(834\) | −52777.5 | −2.19129 | ||||||||
\(835\) | 3975.92 | 0.164781 | ||||||||
\(836\) | −1644.42 | −0.0680306 | ||||||||
\(837\) | 21638.8 | 0.893604 | ||||||||
\(838\) | −14197.5 | −0.585258 | ||||||||
\(839\) | 10199.7 | 0.419704 | 0.209852 | − | 0.977733i | \(-0.432702\pi\) | ||||
0.209852 | + | 0.977733i | \(0.432702\pi\) | |||||||
\(840\) | 53493.8 | 2.19728 | ||||||||
\(841\) | −21088.8 | −0.864687 | ||||||||
\(842\) | −25034.1 | −1.02462 | ||||||||
\(843\) | −7390.21 | −0.301936 | ||||||||
\(844\) | 4304.81 | 0.175566 | ||||||||
\(845\) | −27725.4 | −1.12874 | ||||||||
\(846\) | −2856.63 | −0.116091 | ||||||||
\(847\) | 25369.3 | 1.02916 | ||||||||
\(848\) | 20798.6 | 0.842249 | ||||||||
\(849\) | 48603.9 | 1.96476 | ||||||||
\(850\) | 19333.3 | 0.780148 | ||||||||
\(851\) | 33480.1 | 1.34863 | ||||||||
\(852\) | 255.712 | 0.0102823 | ||||||||
\(853\) | 23124.5 | 0.928214 | 0.464107 | − | 0.885779i | \(-0.346375\pi\) | ||||
0.464107 | + | 0.885779i | \(0.346375\pi\) | |||||||
\(854\) | 10410.6 | 0.417147 | ||||||||
\(855\) | −3910.85 | −0.156431 | ||||||||
\(856\) | 37506.5 | 1.49760 | ||||||||
\(857\) | −2642.41 | −0.105324 | −0.0526621 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526621 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(858\) | 5103.75 | 0.203076 | ||||||||
\(859\) | 20573.1 | 0.817166 | 0.408583 | − | 0.912721i | \(-0.366023\pi\) | ||||
0.408583 | + | 0.912721i | \(0.366023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −153.361 | −0.00607032 | ||||||||
\(862\) | −31346.4 | −1.23859 | ||||||||
\(863\) | −20572.4 | −0.811465 | −0.405732 | − | 0.913992i | \(-0.632983\pi\) | ||||
−0.405732 | + | 0.913992i | \(0.632983\pi\) | |||||||
\(864\) | 7898.22 | 0.310999 | ||||||||
\(865\) | −21775.0 | −0.855923 | ||||||||
\(866\) | −11731.6 | −0.460340 | ||||||||
\(867\) | 42707.1 | 1.67291 | ||||||||
\(868\) | 9207.63 | 0.360055 | ||||||||
\(869\) | 21449.3 | 0.837305 | ||||||||
\(870\) | 13766.5 | 0.536469 | ||||||||
\(871\) | −6116.20 | −0.237933 | ||||||||
\(872\) | −21056.7 | −0.817740 | ||||||||
\(873\) | −2236.94 | −0.0867228 | ||||||||
\(874\) | 30170.6 | 1.16766 | ||||||||
\(875\) | 31568.4 | 1.21966 | ||||||||
\(876\) | −645.831 | −0.0249094 | ||||||||
\(877\) | −50009.6 | −1.92555 | −0.962773 | − | 0.270313i | \(-0.912873\pi\) | ||||
−0.962773 | + | 0.270313i | \(0.912873\pi\) | |||||||
\(878\) | −42509.8 | −1.63398 | ||||||||
\(879\) | −21477.7 | −0.824147 | ||||||||
\(880\) | −24114.0 | −0.923731 | ||||||||
\(881\) | 32839.4 | 1.25583 | 0.627915 | − | 0.778282i | \(-0.283909\pi\) | ||||
0.627915 | + | 0.778282i | \(0.283909\pi\) | |||||||
\(882\) | 16231.1 | 0.619648 | ||||||||
\(883\) | 5095.20 | 0.194187 | 0.0970935 | − | 0.995275i | \(-0.469045\pi\) | ||||
0.0970935 | + | 0.995275i | \(0.469045\pi\) | |||||||
\(884\) | 1941.85 | 0.0738817 | ||||||||
\(885\) | −54356.5 | −2.06460 | ||||||||
\(886\) | −10134.4 | −0.384281 | ||||||||
\(887\) | 41889.4 | 1.58569 | 0.792845 | − | 0.609423i | \(-0.208599\pi\) | ||||
0.792845 | + | 0.609423i | \(0.208599\pi\) | |||||||
\(888\) | 18095.3 | 0.683826 | ||||||||
\(889\) | −51931.8 | −1.95921 | ||||||||
\(890\) | 5898.16 | 0.222143 | ||||||||
\(891\) | −20896.9 | −0.785714 | ||||||||
\(892\) | −3180.76 | −0.119394 | ||||||||
\(893\) | 6671.80 | 0.250015 | ||||||||
\(894\) | −10108.6 | −0.378167 | ||||||||
\(895\) | −28528.3 | −1.06547 | ||||||||
\(896\) | −58777.3 | −2.19153 | ||||||||
\(897\) | −14632.4 | −0.544660 | ||||||||
\(898\) | 53904.1 | 2.00312 | ||||||||
\(899\) | −10424.8 | −0.386749 | ||||||||
\(900\) | 532.665 | 0.0197283 | ||||||||
\(901\) | −31326.3 | −1.15830 | ||||||||
\(902\) | 58.0077 | 0.00214129 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14833.5 | 0.545747 | ||||||||
\(905\) | 4010.42 | 0.147305 | ||||||||
\(906\) | −30943.4 | −1.13469 | ||||||||
\(907\) | −7205.23 | −0.263777 | −0.131889 | − | 0.991265i | \(-0.542104\pi\) | ||||
−0.131889 | + | 0.991265i | \(0.542104\pi\) | |||||||
\(908\) | −1293.70 | −0.0472829 | ||||||||
\(909\) | 7000.24 | 0.255427 | ||||||||
\(910\) | −16787.4 | −0.611536 | ||||||||
\(911\) | 11977.2 | 0.435591 | 0.217796 | − | 0.975994i | \(-0.430113\pi\) | ||||
0.217796 | + | 0.975994i | \(0.430113\pi\) | |||||||
\(912\) | 19433.8 | 0.705613 | ||||||||
\(913\) | 17396.9 | 0.630615 | ||||||||
\(914\) | 18552.1 | 0.671389 | ||||||||
\(915\) | −7683.19 | −0.277594 | ||||||||
\(916\) | 5169.94 | 0.186484 | ||||||||
\(917\) | 47387.7 | 1.70652 | ||||||||
\(918\) | −40734.9 | −1.46454 | ||||||||
\(919\) | −54968.3 | −1.97305 | −0.986527 | − | 0.163597i | \(-0.947690\pi\) | ||||
−0.986527 | + | 0.163597i | \(0.947690\pi\) | |||||||
\(920\) | 58009.3 | 2.07882 | ||||||||
\(921\) | 36996.0 | 1.32363 | ||||||||
\(922\) | 29698.5 | 1.06081 | ||||||||
\(923\) | 353.047 | 0.0125901 | ||||||||
\(924\) | −7118.86 | −0.253456 | ||||||||
\(925\) | −8834.68 | −0.314035 | ||||||||
\(926\) | −26413.9 | −0.937382 | ||||||||
\(927\) | −5778.66 | −0.204742 | ||||||||
\(928\) | −3805.09 | −0.134599 | ||||||||
\(929\) | −49645.6 | −1.75330 | −0.876652 | − | 0.481125i | \(-0.840228\pi\) | ||||
−0.876652 | + | 0.481125i | \(0.840228\pi\) | |||||||
\(930\) | −43486.9 | −1.53332 | ||||||||
\(931\) | −37908.6 | −1.33448 | ||||||||
\(932\) | 7603.90 | 0.267247 | ||||||||
\(933\) | −20942.8 | −0.734872 | ||||||||
\(934\) | 11845.9 | 0.415000 | ||||||||
\(935\) | 36319.8 | 1.27036 | ||||||||
\(936\) | −1506.29 | −0.0526012 | ||||||||
\(937\) | −4460.11 | −0.155502 | −0.0777510 | − | 0.996973i | \(-0.524774\pi\) | ||||
−0.0777510 | + | 0.996973i | \(0.524774\pi\) | |||||||
\(938\) | 54594.3 | 1.90039 | ||||||||
\(939\) | −35576.7 | −1.23642 | ||||||||
\(940\) | −2915.79 | −0.101173 | ||||||||
\(941\) | −41928.2 | −1.45252 | −0.726259 | − | 0.687421i | \(-0.758743\pi\) | ||||
−0.726259 | + | 0.687421i | \(0.758743\pi\) | |||||||
\(942\) | 30980.3 | 1.07154 | ||||||||
\(943\) | −166.307 | −0.00574305 | ||||||||
\(944\) | 51446.4 | 1.77377 | ||||||||
\(945\) | 55028.8 | 1.89427 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37529.0 | 1.28778 | 0.643890 | − | 0.765118i | \(-0.277320\pi\) | ||||
0.643890 | + | 0.765118i | \(0.277320\pi\) | |||||||
\(948\) | 7554.68 | 0.258823 | ||||||||
\(949\) | −891.661 | −0.0305001 | ||||||||
\(950\) | −7961.37 | −0.271896 | ||||||||
\(951\) | −8712.50 | −0.297079 | ||||||||
\(952\) | 76257.3 | 2.59613 | ||||||||
\(953\) | 6351.12 | 0.215879 | 0.107940 | − | 0.994157i | \(-0.465575\pi\) | ||||
0.107940 | + | 0.994157i | \(0.465575\pi\) | |||||||
\(954\) | −5523.34 | −0.187447 | ||||||||
\(955\) | 61209.6 | 2.07403 | ||||||||
\(956\) | 5182.44 | 0.175327 | ||||||||
\(957\) | 8059.94 | 0.272247 | ||||||||
\(958\) | −11049.6 | −0.372646 | ||||||||
\(959\) | −40427.6 | −1.36129 | ||||||||
\(960\) | 29986.1 | 1.00812 | ||||||||
\(961\) | 3139.90 | 0.105398 | ||||||||
\(962\) | −5678.65 | −0.190319 | ||||||||
\(963\) | −11870.5 | −0.397220 | ||||||||
\(964\) | 7657.09 | 0.255828 | ||||||||
\(965\) | 43970.5 | 1.46680 | ||||||||
\(966\) | 130611. | 4.35025 | ||||||||
\(967\) | −15622.6 | −0.519535 | −0.259768 | − | 0.965671i | \(-0.583646\pi\) | ||||
−0.259768 | + | 0.965671i | \(0.583646\pi\) | |||||||
\(968\) | 14869.0 | 0.493706 | ||||||||
\(969\) | −29270.7 | −0.970392 | ||||||||
\(970\) | −14611.7 | −0.483665 | ||||||||
\(971\) | 5920.86 | 0.195684 | 0.0978422 | − | 0.995202i | \(-0.468806\pi\) | ||||
0.0978422 | + | 0.995202i | \(0.468806\pi\) | |||||||
\(972\) | −2589.93 | −0.0854650 | ||||||||
\(973\) | 101637. | 3.34874 | ||||||||
\(974\) | −43547.8 | −1.43261 | ||||||||
\(975\) | 3861.17 | 0.126827 | ||||||||
\(976\) | 7271.86 | 0.238490 | ||||||||
\(977\) | −36549.5 | −1.19685 | −0.598424 | − | 0.801179i | \(-0.704206\pi\) | ||||
−0.598424 | + | 0.801179i | \(0.704206\pi\) | |||||||
\(978\) | 33267.3 | 1.08770 | ||||||||
\(979\) | 3453.22 | 0.112733 | ||||||||
\(980\) | 16567.3 | 0.540022 | ||||||||
\(981\) | 6664.29 | 0.216896 | ||||||||
\(982\) | 23144.5 | 0.752108 | ||||||||
\(983\) | 52748.6 | 1.71152 | 0.855758 | − | 0.517377i | \(-0.173091\pi\) | ||||
0.855758 | + | 0.517377i | \(0.173091\pi\) | |||||||
\(984\) | −89.8854 | −0.00291203 | ||||||||
\(985\) | −11699.7 | −0.378461 | ||||||||
\(986\) | 19624.7 | 0.633850 | ||||||||
\(987\) | 28882.8 | 0.931459 | ||||||||
\(988\) | −799.646 | −0.0257491 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6403.79 | 0.205582 | ||||||||
\(991\) | 56108.6 | 1.79854 | 0.899268 | − | 0.437397i | \(-0.144100\pi\) | ||||
0.899268 | + | 0.437397i | \(0.144100\pi\) | |||||||
\(992\) | 12019.9 | 0.384709 | ||||||||
\(993\) | −13705.4 | −0.437995 | ||||||||
\(994\) | −3151.36 | −0.100558 | ||||||||
\(995\) | −56807.2 | −1.80996 | ||||||||
\(996\) | 6127.36 | 0.194933 | ||||||||
\(997\) | 23518.2 | 0.747071 | 0.373536 | − | 0.927616i | \(-0.378145\pi\) | ||||
0.373536 | + | 0.927616i | \(0.378145\pi\) | |||||||
\(998\) | 22948.3 | 0.727872 | ||||||||
\(999\) | 18614.5 | 0.589526 |
(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 | 1849.4.a.i.1.39 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.12 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.39 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.12 | yes | 50 | 43.42 | odd | 2 |