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: | \(60\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.85348 | −1.71596 | −0.857982 | − | 0.513680i | \(-0.828282\pi\) | ||||
−0.857982 | + | 0.513680i | \(0.828282\pi\) | |||||||
\(3\) | 5.30735 | 1.02140 | 0.510700 | − | 0.859759i | \(-0.329386\pi\) | ||||
0.510700 | + | 0.859759i | \(0.329386\pi\) | |||||||
\(4\) | 15.5563 | 1.94453 | ||||||||
\(5\) | 16.1569 | 1.44512 | 0.722559 | − | 0.691309i | \(-0.242966\pi\) | ||||
0.722559 | + | 0.691309i | \(0.242966\pi\) | |||||||
\(6\) | −25.7591 | −1.75269 | ||||||||
\(7\) | 27.9534 | 1.50934 | 0.754670 | − | 0.656104i | \(-0.227797\pi\) | ||||
0.754670 | + | 0.656104i | \(0.227797\pi\) | |||||||
\(8\) | −36.6742 | −1.62078 | ||||||||
\(9\) | 1.16797 | 0.0432582 | ||||||||
\(10\) | −78.4173 | −2.47977 | ||||||||
\(11\) | −13.3801 | −0.366750 | −0.183375 | − | 0.983043i | \(-0.558702\pi\) | ||||
−0.183375 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(12\) | 82.5625 | 1.98615 | ||||||||
\(13\) | −52.0918 | −1.11136 | −0.555679 | − | 0.831397i | \(-0.687542\pi\) | ||||
−0.555679 | + | 0.831397i | \(0.687542\pi\) | |||||||
\(14\) | −135.671 | −2.58997 | ||||||||
\(15\) | 85.7504 | 1.47604 | ||||||||
\(16\) | 53.5471 | 0.836674 | ||||||||
\(17\) | −90.9834 | −1.29804 | −0.649021 | − | 0.760770i | \(-0.724821\pi\) | ||||
−0.649021 | + | 0.760770i | \(0.724821\pi\) | |||||||
\(18\) | −5.66872 | −0.0742295 | ||||||||
\(19\) | −10.5083 | −0.126883 | −0.0634413 | − | 0.997986i | \(-0.520208\pi\) | ||||
−0.0634413 | + | 0.997986i | \(0.520208\pi\) | |||||||
\(20\) | 251.341 | 2.81008 | ||||||||
\(21\) | 148.358 | 1.54164 | ||||||||
\(22\) | 64.9401 | 0.629330 | ||||||||
\(23\) | −195.325 | −1.77079 | −0.885394 | − | 0.464842i | \(-0.846111\pi\) | ||||
−0.885394 | + | 0.464842i | \(0.846111\pi\) | |||||||
\(24\) | −194.643 | −1.65547 | ||||||||
\(25\) | 136.046 | 1.08837 | ||||||||
\(26\) | 252.826 | 1.90705 | ||||||||
\(27\) | −137.100 | −0.977216 | ||||||||
\(28\) | 434.850 | 2.93496 | ||||||||
\(29\) | −168.406 | −1.07835 | −0.539176 | − | 0.842193i | \(-0.681264\pi\) | ||||
−0.539176 | + | 0.842193i | \(0.681264\pi\) | |||||||
\(30\) | −416.188 | −2.53284 | ||||||||
\(31\) | 122.360 | 0.708920 | 0.354460 | − | 0.935071i | \(-0.384665\pi\) | ||||
0.354460 | + | 0.935071i | \(0.384665\pi\) | |||||||
\(32\) | 33.5033 | 0.185081 | ||||||||
\(33\) | −71.0129 | −0.374599 | ||||||||
\(34\) | 441.586 | 2.22739 | ||||||||
\(35\) | 451.641 | 2.18118 | ||||||||
\(36\) | 18.1693 | 0.0841170 | ||||||||
\(37\) | 265.643 | 1.18031 | 0.590155 | − | 0.807290i | \(-0.299067\pi\) | ||||
0.590155 | + | 0.807290i | \(0.299067\pi\) | |||||||
\(38\) | 51.0018 | 0.217726 | ||||||||
\(39\) | −276.469 | −1.13514 | ||||||||
\(40\) | −592.541 | −2.34223 | ||||||||
\(41\) | −250.166 | −0.952911 | −0.476456 | − | 0.879198i | \(-0.658079\pi\) | ||||
−0.476456 | + | 0.879198i | \(0.658079\pi\) | |||||||
\(42\) | −720.054 | −2.64540 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −208.144 | −0.713158 | ||||||||
\(45\) | 18.8708 | 0.0625132 | ||||||||
\(46\) | 948.007 | 3.03861 | ||||||||
\(47\) | 179.800 | 0.558011 | 0.279005 | − | 0.960290i | \(-0.409995\pi\) | ||||
0.279005 | + | 0.960290i | \(0.409995\pi\) | |||||||
\(48\) | 284.193 | 0.854579 | ||||||||
\(49\) | 438.392 | 1.27811 | ||||||||
\(50\) | −660.297 | −1.86760 | ||||||||
\(51\) | −482.881 | −1.32582 | ||||||||
\(52\) | −810.353 | −2.16107 | ||||||||
\(53\) | −63.6412 | −0.164939 | −0.0824697 | − | 0.996594i | \(-0.526281\pi\) | ||||
−0.0824697 | + | 0.996594i | \(0.526281\pi\) | |||||||
\(54\) | 665.410 | 1.67687 | ||||||||
\(55\) | −216.181 | −0.529998 | ||||||||
\(56\) | −1025.17 | −2.44632 | ||||||||
\(57\) | −55.7712 | −0.129598 | ||||||||
\(58\) | 817.355 | 1.85041 | ||||||||
\(59\) | −29.8681 | −0.0659066 | −0.0329533 | − | 0.999457i | \(-0.510491\pi\) | ||||
−0.0329533 | + | 0.999457i | \(0.510491\pi\) | |||||||
\(60\) | 1333.96 | 2.87022 | ||||||||
\(61\) | −215.166 | −0.451626 | −0.225813 | − | 0.974171i | \(-0.572504\pi\) | ||||
−0.225813 | + | 0.974171i | \(0.572504\pi\) | |||||||
\(62\) | −593.872 | −1.21648 | ||||||||
\(63\) | 32.6488 | 0.0652914 | ||||||||
\(64\) | −590.984 | −1.15427 | ||||||||
\(65\) | −841.643 | −1.60605 | ||||||||
\(66\) | 344.660 | 0.642798 | ||||||||
\(67\) | 16.2324 | 0.0295985 | 0.0147992 | − | 0.999890i | \(-0.495289\pi\) | ||||
0.0147992 | + | 0.999890i | \(0.495289\pi\) | |||||||
\(68\) | −1415.36 | −2.52409 | ||||||||
\(69\) | −1036.66 | −1.80868 | ||||||||
\(70\) | −2192.03 | −3.74282 | ||||||||
\(71\) | 806.449 | 1.34800 | 0.673999 | − | 0.738732i | \(-0.264575\pi\) | ||||
0.673999 | + | 0.738732i | \(0.264575\pi\) | |||||||
\(72\) | −42.8344 | −0.0701122 | ||||||||
\(73\) | −30.3032 | −0.0485853 | −0.0242926 | − | 0.999705i | \(-0.507733\pi\) | ||||
−0.0242926 | + | 0.999705i | \(0.507733\pi\) | |||||||
\(74\) | −1289.29 | −2.02537 | ||||||||
\(75\) | 722.044 | 1.11166 | ||||||||
\(76\) | −163.470 | −0.246727 | ||||||||
\(77\) | −374.019 | −0.553551 | ||||||||
\(78\) | 1341.84 | 1.94786 | ||||||||
\(79\) | −379.053 | −0.539833 | −0.269917 | − | 0.962884i | \(-0.586996\pi\) | ||||
−0.269917 | + | 0.962884i | \(0.586996\pi\) | |||||||
\(80\) | 865.157 | 1.20909 | ||||||||
\(81\) | −759.171 | −1.04139 | ||||||||
\(82\) | 1214.18 | 1.63516 | ||||||||
\(83\) | −607.128 | −0.802904 | −0.401452 | − | 0.915880i | \(-0.631494\pi\) | ||||
−0.401452 | + | 0.915880i | \(0.631494\pi\) | |||||||
\(84\) | 2307.90 | 2.99777 | ||||||||
\(85\) | −1470.01 | −1.87583 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −893.790 | −1.10143 | ||||||||
\(88\) | 490.704 | 0.594423 | ||||||||
\(89\) | −1314.18 | −1.56520 | −0.782602 | − | 0.622522i | \(-0.786108\pi\) | ||||
−0.782602 | + | 0.622522i | \(0.786108\pi\) | |||||||
\(90\) | −91.5891 | −0.107270 | ||||||||
\(91\) | −1456.14 | −1.67742 | ||||||||
\(92\) | −3038.53 | −3.44335 | ||||||||
\(93\) | 649.408 | 0.724091 | ||||||||
\(94\) | −872.655 | −0.957526 | ||||||||
\(95\) | −169.782 | −0.183360 | ||||||||
\(96\) | 177.814 | 0.189042 | ||||||||
\(97\) | 229.873 | 0.240619 | 0.120310 | − | 0.992736i | \(-0.461611\pi\) | ||||
0.120310 | + | 0.992736i | \(0.461611\pi\) | |||||||
\(98\) | −2127.72 | −2.19319 | ||||||||
\(99\) | −15.6276 | −0.0158650 | ||||||||
\(100\) | 2116.37 | 2.11637 | ||||||||
\(101\) | 1013.21 | 0.998195 | 0.499098 | − | 0.866546i | \(-0.333665\pi\) | ||||
0.499098 | + | 0.866546i | \(0.333665\pi\) | |||||||
\(102\) | 2343.65 | 2.27506 | ||||||||
\(103\) | 664.636 | 0.635811 | 0.317906 | − | 0.948122i | \(-0.397020\pi\) | ||||
0.317906 | + | 0.948122i | \(0.397020\pi\) | |||||||
\(104\) | 1910.42 | 1.80127 | ||||||||
\(105\) | 2397.01 | 2.22785 | ||||||||
\(106\) | 308.881 | 0.283030 | ||||||||
\(107\) | −785.202 | −0.709424 | −0.354712 | − | 0.934976i | \(-0.615421\pi\) | ||||
−0.354712 | + | 0.934976i | \(0.615421\pi\) | |||||||
\(108\) | −2132.76 | −1.90023 | ||||||||
\(109\) | −1541.98 | −1.35500 | −0.677500 | − | 0.735522i | \(-0.736937\pi\) | ||||
−0.677500 | + | 0.735522i | \(0.736937\pi\) | |||||||
\(110\) | 1049.23 | 0.909457 | ||||||||
\(111\) | 1409.86 | 1.20557 | ||||||||
\(112\) | 1496.82 | 1.26283 | ||||||||
\(113\) | 1142.64 | 0.951248 | 0.475624 | − | 0.879649i | \(-0.342222\pi\) | ||||
0.475624 | + | 0.879649i | \(0.342222\pi\) | |||||||
\(114\) | 270.685 | 0.222385 | ||||||||
\(115\) | −3155.85 | −2.55900 | ||||||||
\(116\) | −2619.77 | −2.09689 | ||||||||
\(117\) | −60.8417 | −0.0480754 | ||||||||
\(118\) | 144.964 | 0.113093 | ||||||||
\(119\) | −2543.29 | −1.95919 | ||||||||
\(120\) | −3144.82 | −2.39235 | ||||||||
\(121\) | −1151.97 | −0.865494 | ||||||||
\(122\) | 1044.30 | 0.774974 | ||||||||
\(123\) | −1327.72 | −0.973304 | ||||||||
\(124\) | 1903.47 | 1.37852 | ||||||||
\(125\) | 178.470 | 0.127703 | ||||||||
\(126\) | −158.460 | −0.112038 | ||||||||
\(127\) | −2422.91 | −1.69290 | −0.846452 | − | 0.532464i | \(-0.821266\pi\) | ||||
−0.846452 | + | 0.532464i | \(0.821266\pi\) | |||||||
\(128\) | 2600.30 | 1.79560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4084.90 | 2.75592 | ||||||||
\(131\) | 1794.68 | 1.19696 | 0.598480 | − | 0.801137i | \(-0.295771\pi\) | ||||
0.598480 | + | 0.801137i | \(0.295771\pi\) | |||||||
\(132\) | −1104.70 | −0.728420 | ||||||||
\(133\) | −293.743 | −0.191509 | ||||||||
\(134\) | −78.7834 | −0.0507899 | ||||||||
\(135\) | −2215.11 | −1.41219 | ||||||||
\(136\) | 3336.74 | 2.10385 | ||||||||
\(137\) | −2170.60 | −1.35362 | −0.676812 | − | 0.736156i | \(-0.736639\pi\) | ||||
−0.676812 | + | 0.736156i | \(0.736639\pi\) | |||||||
\(138\) | 5031.40 | 3.10363 | ||||||||
\(139\) | −245.580 | −0.149855 | −0.0749275 | − | 0.997189i | \(-0.523873\pi\) | ||||
−0.0749275 | + | 0.997189i | \(0.523873\pi\) | |||||||
\(140\) | 7025.84 | 4.24137 | ||||||||
\(141\) | 954.261 | 0.569952 | ||||||||
\(142\) | −3914.08 | −2.31312 | ||||||||
\(143\) | 696.994 | 0.407591 | ||||||||
\(144\) | 62.5415 | 0.0361930 | ||||||||
\(145\) | −2720.92 | −1.55835 | ||||||||
\(146\) | 147.076 | 0.0833705 | ||||||||
\(147\) | 2326.70 | 1.30546 | ||||||||
\(148\) | 4132.41 | 2.29515 | ||||||||
\(149\) | −1142.62 | −0.628237 | −0.314119 | − | 0.949384i | \(-0.601709\pi\) | ||||
−0.314119 | + | 0.949384i | \(0.601709\pi\) | |||||||
\(150\) | −3504.43 | −1.90757 | ||||||||
\(151\) | 1393.59 | 0.751049 | 0.375525 | − | 0.926812i | \(-0.377463\pi\) | ||||
0.375525 | + | 0.926812i | \(0.377463\pi\) | |||||||
\(152\) | 385.383 | 0.205649 | ||||||||
\(153\) | −106.266 | −0.0561510 | ||||||||
\(154\) | 1815.29 | 0.949874 | ||||||||
\(155\) | 1976.96 | 1.02447 | ||||||||
\(156\) | −4300.83 | −2.20732 | ||||||||
\(157\) | −147.109 | −0.0747809 | −0.0373904 | − | 0.999301i | \(-0.511905\pi\) | ||||
−0.0373904 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(158\) | 1839.73 | 0.926335 | ||||||||
\(159\) | −337.766 | −0.168469 | ||||||||
\(160\) | 541.309 | 0.267464 | ||||||||
\(161\) | −5460.00 | −2.67272 | ||||||||
\(162\) | 3684.62 | 1.78698 | ||||||||
\(163\) | −161.544 | −0.0776262 | −0.0388131 | − | 0.999246i | \(-0.512358\pi\) | ||||
−0.0388131 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(164\) | −3891.65 | −1.85297 | ||||||||
\(165\) | −1147.35 | −0.541340 | ||||||||
\(166\) | 2946.68 | 1.37775 | ||||||||
\(167\) | 1901.23 | 0.880970 | 0.440485 | − | 0.897760i | \(-0.354807\pi\) | ||||
0.440485 | + | 0.897760i | \(0.354807\pi\) | |||||||
\(168\) | −5440.92 | −2.49867 | ||||||||
\(169\) | 516.554 | 0.235118 | ||||||||
\(170\) | 7134.67 | 3.21885 | ||||||||
\(171\) | −12.2734 | −0.00548871 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 67.1165 | 0.0294958 | 0.0147479 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147479 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(174\) | 4337.99 | 1.89001 | ||||||||
\(175\) | 3802.95 | 1.64272 | ||||||||
\(176\) | −716.467 | −0.306851 | ||||||||
\(177\) | −158.520 | −0.0673170 | ||||||||
\(178\) | 6378.36 | 2.68583 | ||||||||
\(179\) | 1615.61 | 0.674617 | 0.337308 | − | 0.941394i | \(-0.390483\pi\) | ||||
0.337308 | + | 0.941394i | \(0.390483\pi\) | |||||||
\(180\) | 293.559 | 0.121559 | ||||||||
\(181\) | 1922.60 | 0.789536 | 0.394768 | − | 0.918781i | \(-0.370825\pi\) | ||||
0.394768 | + | 0.918781i | \(0.370825\pi\) | |||||||
\(182\) | 7067.35 | 2.87839 | ||||||||
\(183\) | −1141.96 | −0.461291 | ||||||||
\(184\) | 7163.38 | 2.87006 | ||||||||
\(185\) | 4291.98 | 1.70569 | ||||||||
\(186\) | −3151.89 | −1.24251 | ||||||||
\(187\) | 1217.37 | 0.476058 | ||||||||
\(188\) | 2797.01 | 1.08507 | ||||||||
\(189\) | −3832.40 | −1.47495 | ||||||||
\(190\) | 824.032 | 0.314640 | ||||||||
\(191\) | −3119.14 | −1.18164 | −0.590820 | − | 0.806803i | \(-0.701196\pi\) | ||||
−0.590820 | + | 0.806803i | \(0.701196\pi\) | |||||||
\(192\) | −3136.56 | −1.17897 | ||||||||
\(193\) | −1853.76 | −0.691381 | −0.345691 | − | 0.938349i | \(-0.612355\pi\) | ||||
−0.345691 | + | 0.938349i | \(0.612355\pi\) | |||||||
\(194\) | −1115.68 | −0.412894 | ||||||||
\(195\) | −4466.89 | −1.64041 | ||||||||
\(196\) | 6819.73 | 2.48533 | ||||||||
\(197\) | 189.579 | 0.0685633 | 0.0342817 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342817 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(198\) | 75.8482 | 0.0272237 | ||||||||
\(199\) | −57.5715 | −0.0205082 | −0.0102541 | − | 0.999947i | \(-0.503264\pi\) | ||||
−0.0102541 | + | 0.999947i | \(0.503264\pi\) | |||||||
\(200\) | −4989.37 | −1.76401 | ||||||||
\(201\) | 86.1508 | 0.0302319 | ||||||||
\(202\) | −4917.57 | −1.71287 | ||||||||
\(203\) | −4707.52 | −1.62760 | ||||||||
\(204\) | −7511.82 | −2.57810 | ||||||||
\(205\) | −4041.91 | −1.37707 | ||||||||
\(206\) | −3225.80 | −1.09103 | ||||||||
\(207\) | −228.134 | −0.0766011 | ||||||||
\(208\) | −2789.37 | −0.929845 | ||||||||
\(209\) | 140.602 | 0.0465342 | ||||||||
\(210\) | −11633.9 | −3.82292 | ||||||||
\(211\) | −719.563 | −0.234772 | −0.117386 | − | 0.993086i | \(-0.537451\pi\) | ||||
−0.117386 | + | 0.993086i | \(0.537451\pi\) | |||||||
\(212\) | −990.019 | −0.320730 | ||||||||
\(213\) | 4280.11 | 1.37685 | ||||||||
\(214\) | 3810.96 | 1.21735 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5028.01 | 1.58386 | ||||||||
\(217\) | 3420.38 | 1.07000 | ||||||||
\(218\) | 7483.98 | 2.32513 | ||||||||
\(219\) | −160.830 | −0.0496250 | ||||||||
\(220\) | −3362.97 | −1.03060 | ||||||||
\(221\) | 4739.49 | 1.44259 | ||||||||
\(222\) | −6842.73 | −2.06871 | ||||||||
\(223\) | −32.0202 | −0.00961540 | −0.00480770 | − | 0.999988i | \(-0.501530\pi\) | ||||
−0.00480770 | + | 0.999988i | \(0.501530\pi\) | |||||||
\(224\) | 936.529 | 0.279350 | ||||||||
\(225\) | 158.898 | 0.0470809 | ||||||||
\(226\) | −5545.80 | −1.63231 | ||||||||
\(227\) | −4950.83 | −1.44757 | −0.723785 | − | 0.690026i | \(-0.757599\pi\) | ||||
−0.723785 | + | 0.690026i | \(0.757599\pi\) | |||||||
\(228\) | −867.592 | −0.252007 | ||||||||
\(229\) | 1165.53 | 0.336333 | 0.168166 | − | 0.985759i | \(-0.446215\pi\) | ||||
0.168166 | + | 0.985759i | \(0.446215\pi\) | |||||||
\(230\) | 15316.9 | 4.39115 | ||||||||
\(231\) | −1985.05 | −0.565397 | ||||||||
\(232\) | 6176.15 | 1.74778 | ||||||||
\(233\) | −1071.01 | −0.301135 | −0.150567 | − | 0.988600i | \(-0.548110\pi\) | ||||
−0.150567 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(234\) | 295.294 | 0.0824956 | ||||||||
\(235\) | 2905.01 | 0.806392 | ||||||||
\(236\) | −464.635 | −0.128158 | ||||||||
\(237\) | −2011.77 | −0.551386 | ||||||||
\(238\) | 12343.8 | 3.36190 | ||||||||
\(239\) | −4274.37 | −1.15685 | −0.578423 | − | 0.815737i | \(-0.696332\pi\) | ||||
−0.578423 | + | 0.815737i | \(0.696332\pi\) | |||||||
\(240\) | 4591.69 | 1.23497 | ||||||||
\(241\) | 7024.10 | 1.87744 | 0.938718 | − | 0.344687i | \(-0.112015\pi\) | ||||
0.938718 | + | 0.344687i | \(0.112015\pi\) | |||||||
\(242\) | 5591.08 | 1.48516 | ||||||||
\(243\) | −327.497 | −0.0864565 | ||||||||
\(244\) | −3347.18 | −0.878202 | ||||||||
\(245\) | 7083.06 | 1.84702 | ||||||||
\(246\) | 6444.06 | 1.67015 | ||||||||
\(247\) | 547.396 | 0.141012 | ||||||||
\(248\) | −4487.45 | −1.14901 | ||||||||
\(249\) | −3222.24 | −0.820086 | ||||||||
\(250\) | −866.202 | −0.219134 | ||||||||
\(251\) | 2122.77 | 0.533816 | 0.266908 | − | 0.963722i | \(-0.413998\pi\) | ||||
0.266908 | + | 0.963722i | \(0.413998\pi\) | |||||||
\(252\) | 507.892 | 0.126961 | ||||||||
\(253\) | 2613.47 | 0.649437 | ||||||||
\(254\) | 11759.6 | 2.90496 | ||||||||
\(255\) | −7801.87 | −1.91597 | ||||||||
\(256\) | −7892.65 | −1.92692 | ||||||||
\(257\) | −1456.60 | −0.353543 | −0.176771 | − | 0.984252i | \(-0.556565\pi\) | ||||
−0.176771 | + | 0.984252i | \(0.556565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7425.63 | 1.78149 | ||||||||
\(260\) | −13092.8 | −3.12301 | ||||||||
\(261\) | −196.693 | −0.0466476 | ||||||||
\(262\) | −8710.44 | −2.05394 | ||||||||
\(263\) | 4608.02 | 1.08039 | 0.540195 | − | 0.841540i | \(-0.318350\pi\) | ||||
0.540195 | + | 0.841540i | \(0.318350\pi\) | |||||||
\(264\) | 2604.34 | 0.607144 | ||||||||
\(265\) | −1028.25 | −0.238357 | ||||||||
\(266\) | 1425.67 | 0.328623 | ||||||||
\(267\) | −6974.83 | −1.59870 | ||||||||
\(268\) | 252.515 | 0.0575552 | ||||||||
\(269\) | −3794.78 | −0.860118 | −0.430059 | − | 0.902801i | \(-0.641507\pi\) | ||||
−0.430059 | + | 0.902801i | \(0.641507\pi\) | |||||||
\(270\) | 10751.0 | 2.42327 | ||||||||
\(271\) | 3683.71 | 0.825717 | 0.412859 | − | 0.910795i | \(-0.364530\pi\) | ||||
0.412859 | + | 0.910795i | \(0.364530\pi\) | |||||||
\(272\) | −4871.90 | −1.08604 | ||||||||
\(273\) | −7728.25 | −1.71332 | ||||||||
\(274\) | 10534.9 | 2.32277 | ||||||||
\(275\) | −1820.31 | −0.399160 | ||||||||
\(276\) | −16126.5 | −3.51704 | ||||||||
\(277\) | 4917.90 | 1.06674 | 0.533372 | − | 0.845881i | \(-0.320925\pi\) | ||||
0.533372 | + | 0.845881i | \(0.320925\pi\) | |||||||
\(278\) | 1191.92 | 0.257146 | ||||||||
\(279\) | 142.913 | 0.0306666 | ||||||||
\(280\) | −16563.5 | −3.53522 | ||||||||
\(281\) | −212.734 | −0.0451625 | −0.0225813 | − | 0.999745i | \(-0.507188\pi\) | ||||
−0.0225813 | + | 0.999745i | \(0.507188\pi\) | |||||||
\(282\) | −4631.49 | −0.978018 | ||||||||
\(283\) | −2776.00 | −0.583096 | −0.291548 | − | 0.956556i | \(-0.594170\pi\) | ||||
−0.291548 | + | 0.956556i | \(0.594170\pi\) | |||||||
\(284\) | 12545.3 | 2.62123 | ||||||||
\(285\) | −901.091 | −0.187284 | ||||||||
\(286\) | −3382.84 | −0.699412 | ||||||||
\(287\) | −6992.99 | −1.43827 | ||||||||
\(288\) | 39.1308 | 0.00800627 | ||||||||
\(289\) | 3364.98 | 0.684914 | ||||||||
\(290\) | 13205.9 | 2.67407 | ||||||||
\(291\) | 1220.02 | 0.245769 | ||||||||
\(292\) | −471.405 | −0.0944756 | ||||||||
\(293\) | −7115.75 | −1.41879 | −0.709397 | − | 0.704809i | \(-0.751033\pi\) | ||||
−0.709397 | + | 0.704809i | \(0.751033\pi\) | |||||||
\(294\) | −11292.6 | −2.24012 | ||||||||
\(295\) | −482.576 | −0.0952429 | ||||||||
\(296\) | −9742.24 | −1.91303 | ||||||||
\(297\) | 1834.41 | 0.358394 | ||||||||
\(298\) | 5545.70 | 1.07803 | ||||||||
\(299\) | 10174.8 | 1.96798 | ||||||||
\(300\) | 11232.3 | 2.16166 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6763.74 | −1.28877 | ||||||||
\(303\) | 5377.44 | 1.01956 | ||||||||
\(304\) | −562.689 | −0.106159 | ||||||||
\(305\) | −3476.42 | −0.652653 | ||||||||
\(306\) | 515.760 | 0.0963531 | ||||||||
\(307\) | −3663.91 | −0.681141 | −0.340570 | − | 0.940219i | \(-0.610620\pi\) | ||||
−0.340570 | + | 0.940219i | \(0.610620\pi\) | |||||||
\(308\) | −5818.34 | −1.07640 | ||||||||
\(309\) | 3527.46 | 0.649418 | ||||||||
\(310\) | −9595.14 | −1.75796 | ||||||||
\(311\) | −7474.92 | −1.36291 | −0.681453 | − | 0.731862i | \(-0.738651\pi\) | ||||
−0.681453 | + | 0.731862i | \(0.738651\pi\) | |||||||
\(312\) | 10139.3 | 1.83982 | ||||||||
\(313\) | 6355.18 | 1.14765 | 0.573827 | − | 0.818976i | \(-0.305458\pi\) | ||||
0.573827 | + | 0.818976i | \(0.305458\pi\) | |||||||
\(314\) | 713.992 | 0.128321 | ||||||||
\(315\) | 527.503 | 0.0943538 | ||||||||
\(316\) | −5896.65 | −1.04972 | ||||||||
\(317\) | 2434.32 | 0.431309 | 0.215654 | − | 0.976470i | \(-0.430812\pi\) | ||||
0.215654 | + | 0.976470i | \(0.430812\pi\) | |||||||
\(318\) | 1639.34 | 0.289087 | ||||||||
\(319\) | 2253.29 | 0.395486 | ||||||||
\(320\) | −9548.49 | −1.66805 | ||||||||
\(321\) | −4167.34 | −0.724606 | ||||||||
\(322\) | 26500.0 | 4.58629 | ||||||||
\(323\) | 956.081 | 0.164699 | ||||||||
\(324\) | −11809.9 | −2.02501 | ||||||||
\(325\) | −7086.88 | −1.20957 | ||||||||
\(326\) | 784.049 | 0.133204 | ||||||||
\(327\) | −8183.84 | −1.38400 | ||||||||
\(328\) | 9174.63 | 1.54446 | ||||||||
\(329\) | 5026.01 | 0.842228 | ||||||||
\(330\) | 5568.64 | 0.928920 | ||||||||
\(331\) | 2053.35 | 0.340973 | 0.170487 | − | 0.985360i | \(-0.445466\pi\) | ||||
0.170487 | + | 0.985360i | \(0.445466\pi\) | |||||||
\(332\) | −9444.65 | −1.56127 | ||||||||
\(333\) | 310.264 | 0.0510581 | ||||||||
\(334\) | −9227.60 | −1.51171 | ||||||||
\(335\) | 262.265 | 0.0427733 | ||||||||
\(336\) | 7944.17 | 1.28985 | ||||||||
\(337\) | −7324.43 | −1.18394 | −0.591969 | − | 0.805961i | \(-0.701649\pi\) | ||||
−0.591969 | + | 0.805961i | \(0.701649\pi\) | |||||||
\(338\) | −2507.08 | −0.403454 | ||||||||
\(339\) | 6064.42 | 0.971604 | ||||||||
\(340\) | −22867.9 | −3.64760 | ||||||||
\(341\) | −1637.19 | −0.259997 | ||||||||
\(342\) | 59.5687 | 0.00941843 | ||||||||
\(343\) | 2666.52 | 0.419762 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16749.2 | −2.61376 | ||||||||
\(346\) | −325.749 | −0.0506137 | ||||||||
\(347\) | 210.302 | 0.0325348 | 0.0162674 | − | 0.999868i | \(-0.494822\pi\) | ||||
0.0162674 | + | 0.999868i | \(0.494822\pi\) | |||||||
\(348\) | −13904.0 | −2.14176 | ||||||||
\(349\) | −7982.13 | −1.22428 | −0.612140 | − | 0.790750i | \(-0.709691\pi\) | ||||
−0.612140 | + | 0.790750i | \(0.709691\pi\) | |||||||
\(350\) | −18457.5 | −2.81885 | ||||||||
\(351\) | 7141.76 | 1.08604 | ||||||||
\(352\) | −448.277 | −0.0678786 | ||||||||
\(353\) | −9136.44 | −1.37757 | −0.688787 | − | 0.724964i | \(-0.741856\pi\) | ||||
−0.688787 | + | 0.724964i | \(0.741856\pi\) | |||||||
\(354\) | 769.375 | 0.115514 | ||||||||
\(355\) | 13029.7 | 1.94802 | ||||||||
\(356\) | −20443.8 | −3.04359 | ||||||||
\(357\) | −13498.2 | −2.00112 | ||||||||
\(358\) | −7841.33 | −1.15762 | ||||||||
\(359\) | −6539.79 | −0.961440 | −0.480720 | − | 0.876874i | \(-0.659625\pi\) | ||||
−0.480720 | + | 0.876874i | \(0.659625\pi\) | |||||||
\(360\) | −692.071 | −0.101320 | ||||||||
\(361\) | −6748.58 | −0.983901 | ||||||||
\(362\) | −9331.32 | −1.35482 | ||||||||
\(363\) | −6113.92 | −0.884016 | ||||||||
\(364\) | −22652.1 | −3.26180 | ||||||||
\(365\) | −489.607 | −0.0702115 | ||||||||
\(366\) | 5542.49 | 0.791559 | ||||||||
\(367\) | 7503.05 | 1.06718 | 0.533592 | − | 0.845742i | \(-0.320842\pi\) | ||||
0.533592 | + | 0.845742i | \(0.320842\pi\) | |||||||
\(368\) | −10459.1 | −1.48157 | ||||||||
\(369\) | −292.187 | −0.0412212 | ||||||||
\(370\) | −20831.0 | −2.92690 | ||||||||
\(371\) | −1778.99 | −0.248950 | ||||||||
\(372\) | 10102.4 | 1.40802 | ||||||||
\(373\) | −233.234 | −0.0323764 | −0.0161882 | − | 0.999869i | \(-0.505153\pi\) | ||||
−0.0161882 | + | 0.999869i | \(0.505153\pi\) | |||||||
\(374\) | −5908.47 | −0.816898 | ||||||||
\(375\) | 947.205 | 0.130436 | ||||||||
\(376\) | −6594.01 | −0.904415 | ||||||||
\(377\) | 8772.57 | 1.19844 | ||||||||
\(378\) | 18600.5 | 2.53097 | ||||||||
\(379\) | 7237.58 | 0.980922 | 0.490461 | − | 0.871463i | \(-0.336828\pi\) | ||||
0.490461 | + | 0.871463i | \(0.336828\pi\) | |||||||
\(380\) | −2641.17 | −0.356550 | ||||||||
\(381\) | −12859.3 | −1.72913 | ||||||||
\(382\) | 15138.7 | 2.02765 | ||||||||
\(383\) | 7769.85 | 1.03661 | 0.518304 | − | 0.855197i | \(-0.326564\pi\) | ||||
0.518304 | + | 0.855197i | \(0.326564\pi\) | |||||||
\(384\) | 13800.7 | 1.83402 | ||||||||
\(385\) | −6043.00 | −0.799948 | ||||||||
\(386\) | 8997.19 | 1.18639 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3575.97 | 0.467892 | ||||||||
\(389\) | −8231.01 | −1.07282 | −0.536412 | − | 0.843956i | \(-0.680221\pi\) | ||||
−0.536412 | + | 0.843956i | \(0.680221\pi\) | |||||||
\(390\) | 21680.0 | 2.81489 | ||||||||
\(391\) | 17771.4 | 2.29856 | ||||||||
\(392\) | −16077.6 | −2.07154 | ||||||||
\(393\) | 9524.99 | 1.22258 | ||||||||
\(394\) | −920.120 | −0.117652 | ||||||||
\(395\) | −6124.34 | −0.780124 | ||||||||
\(396\) | −243.107 | −0.0308499 | ||||||||
\(397\) | −8274.41 | −1.04605 | −0.523023 | − | 0.852318i | \(-0.675196\pi\) | ||||
−0.523023 | + | 0.852318i | \(0.675196\pi\) | |||||||
\(398\) | 279.422 | 0.0351914 | ||||||||
\(399\) | −1558.99 | −0.195607 | ||||||||
\(400\) | 7284.88 | 0.910610 | ||||||||
\(401\) | −13688.9 | −1.70472 | −0.852360 | − | 0.522956i | \(-0.824829\pi\) | ||||
−0.852360 | + | 0.522956i | \(0.824829\pi\) | |||||||
\(402\) | −418.131 | −0.0518768 | ||||||||
\(403\) | −6373.95 | −0.787864 | ||||||||
\(404\) | 15761.7 | 1.94102 | ||||||||
\(405\) | −12265.9 | −1.50493 | ||||||||
\(406\) | 22847.8 | 2.79291 | ||||||||
\(407\) | −3554.33 | −0.432879 | ||||||||
\(408\) | 17709.2 | 2.14887 | ||||||||
\(409\) | 13141.7 | 1.58879 | 0.794397 | − | 0.607398i | \(-0.207787\pi\) | ||||
0.794397 | + | 0.607398i | \(0.207787\pi\) | |||||||
\(410\) | 19617.3 | 2.36300 | ||||||||
\(411\) | −11520.1 | −1.38259 | ||||||||
\(412\) | 10339.3 | 1.23636 | ||||||||
\(413\) | −834.914 | −0.0994756 | ||||||||
\(414\) | 1107.24 | 0.131445 | ||||||||
\(415\) | −9809.32 | −1.16029 | ||||||||
\(416\) | −1745.24 | −0.205691 | ||||||||
\(417\) | −1303.38 | −0.153062 | ||||||||
\(418\) | −682.410 | −0.0798511 | ||||||||
\(419\) | 7318.77 | 0.853330 | 0.426665 | − | 0.904410i | \(-0.359688\pi\) | ||||
0.426665 | + | 0.904410i | \(0.359688\pi\) | |||||||
\(420\) | 37288.6 | 4.33214 | ||||||||
\(421\) | −15041.7 | −1.74130 | −0.870651 | − | 0.491901i | \(-0.836302\pi\) | ||||
−0.870651 | + | 0.491901i | \(0.836302\pi\) | |||||||
\(422\) | 3492.39 | 0.402859 | ||||||||
\(423\) | 210.001 | 0.0241385 | ||||||||
\(424\) | 2333.99 | 0.267331 | ||||||||
\(425\) | −12377.9 | −1.41275 | ||||||||
\(426\) | −20773.4 | −2.36262 | ||||||||
\(427\) | −6014.62 | −0.681658 | ||||||||
\(428\) | −12214.8 | −1.37950 | ||||||||
\(429\) | 3699.19 | 0.416314 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4332.46 | 0.484193 | 0.242096 | − | 0.970252i | \(-0.422165\pi\) | ||||
0.242096 | + | 0.970252i | \(0.422165\pi\) | |||||||
\(432\) | −7341.29 | −0.817612 | ||||||||
\(433\) | −1688.95 | −0.187450 | −0.0937249 | − | 0.995598i | \(-0.529877\pi\) | ||||
−0.0937249 | + | 0.995598i | \(0.529877\pi\) | |||||||
\(434\) | −16600.7 | −1.83608 | ||||||||
\(435\) | −14440.9 | −1.59170 | ||||||||
\(436\) | −23987.5 | −2.63484 | ||||||||
\(437\) | 2052.54 | 0.224682 | ||||||||
\(438\) | 780.584 | 0.0851547 | ||||||||
\(439\) | 14355.9 | 1.56075 | 0.780373 | − | 0.625314i | \(-0.215029\pi\) | ||||
0.780373 | + | 0.625314i | \(0.215029\pi\) | |||||||
\(440\) | 7928.27 | 0.859012 | ||||||||
\(441\) | 512.029 | 0.0552887 | ||||||||
\(442\) | −23003.0 | −2.47543 | ||||||||
\(443\) | −1572.96 | −0.168699 | −0.0843493 | − | 0.996436i | \(-0.526881\pi\) | ||||
−0.0843493 | + | 0.996436i | \(0.526881\pi\) | |||||||
\(444\) | 21932.2 | 2.34427 | ||||||||
\(445\) | −21233.2 | −2.26191 | ||||||||
\(446\) | 155.410 | 0.0164997 | ||||||||
\(447\) | −6064.30 | −0.641682 | ||||||||
\(448\) | −16520.0 | −1.74218 | ||||||||
\(449\) | −9925.53 | −1.04324 | −0.521620 | − | 0.853178i | \(-0.674672\pi\) | ||||
−0.521620 | + | 0.853178i | \(0.674672\pi\) | |||||||
\(450\) | −771.208 | −0.0807891 | ||||||||
\(451\) | 3347.25 | 0.349481 | ||||||||
\(452\) | 17775.3 | 1.84973 | ||||||||
\(453\) | 7396.25 | 0.767122 | ||||||||
\(454\) | 24028.8 | 2.48398 | ||||||||
\(455\) | −23526.8 | −2.42407 | ||||||||
\(456\) | 2045.36 | 0.210050 | ||||||||
\(457\) | −18820.4 | −1.92643 | −0.963216 | − | 0.268729i | \(-0.913397\pi\) | ||||
−0.963216 | + | 0.268729i | \(0.913397\pi\) | |||||||
\(458\) | −5656.87 | −0.577135 | ||||||||
\(459\) | 12473.8 | 1.26847 | ||||||||
\(460\) | −49093.3 | −4.97606 | ||||||||
\(461\) | 2178.77 | 0.220120 | 0.110060 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110060 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(462\) | 9634.41 | 0.970202 | ||||||||
\(463\) | 2774.25 | 0.278467 | 0.139234 | − | 0.990260i | \(-0.455536\pi\) | ||||
0.139234 | + | 0.990260i | \(0.455536\pi\) | |||||||
\(464\) | −9017.66 | −0.902229 | ||||||||
\(465\) | 10492.4 | 1.04640 | ||||||||
\(466\) | 5198.14 | 0.516737 | ||||||||
\(467\) | 4212.31 | 0.417393 | 0.208696 | − | 0.977980i | \(-0.433078\pi\) | ||||
0.208696 | + | 0.977980i | \(0.433078\pi\) | |||||||
\(468\) | −946.469 | −0.0934841 | ||||||||
\(469\) | 453.749 | 0.0446742 | ||||||||
\(470\) | −14099.4 | −1.38374 | ||||||||
\(471\) | −780.760 | −0.0763812 | ||||||||
\(472\) | 1095.39 | 0.106820 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9764.08 | 0.946158 | ||||||||
\(475\) | −1429.61 | −0.138095 | ||||||||
\(476\) | −39564.2 | −3.80971 | ||||||||
\(477\) | −74.3311 | −0.00713498 | ||||||||
\(478\) | 20745.6 | 1.98511 | ||||||||
\(479\) | 17700.2 | 1.68839 | 0.844197 | − | 0.536033i | \(-0.180078\pi\) | ||||
0.844197 | + | 0.536033i | \(0.180078\pi\) | |||||||
\(480\) | 2872.92 | 0.273188 | ||||||||
\(481\) | −13837.8 | −1.31175 | ||||||||
\(482\) | −34091.3 | −3.22161 | ||||||||
\(483\) | −28978.1 | −2.72992 | ||||||||
\(484\) | −17920.4 | −1.68298 | ||||||||
\(485\) | 3714.04 | 0.347724 | ||||||||
\(486\) | 1589.50 | 0.148356 | ||||||||
\(487\) | 15614.3 | 1.45288 | 0.726439 | − | 0.687231i | \(-0.241174\pi\) | ||||
0.726439 | + | 0.687231i | \(0.241174\pi\) | |||||||
\(488\) | 7891.03 | 0.731988 | ||||||||
\(489\) | −857.369 | −0.0792874 | ||||||||
\(490\) | −34377.5 | −3.16942 | ||||||||
\(491\) | −18884.0 | −1.73569 | −0.867843 | − | 0.496838i | \(-0.834494\pi\) | ||||
−0.867843 | + | 0.496838i | \(0.834494\pi\) | |||||||
\(492\) | −20654.3 | −1.89262 | ||||||||
\(493\) | 15322.2 | 1.39975 | ||||||||
\(494\) | −2656.78 | −0.241972 | ||||||||
\(495\) | −252.494 | −0.0229268 | ||||||||
\(496\) | 6552.03 | 0.593135 | ||||||||
\(497\) | 22543.0 | 2.03459 | ||||||||
\(498\) | 15639.1 | 1.40724 | ||||||||
\(499\) | 6710.07 | 0.601971 | 0.300986 | − | 0.953629i | \(-0.402684\pi\) | ||||
0.300986 | + | 0.953629i | \(0.402684\pi\) | |||||||
\(500\) | 2776.33 | 0.248323 | ||||||||
\(501\) | 10090.5 | 0.899823 | ||||||||
\(502\) | −10302.8 | −0.916010 | ||||||||
\(503\) | 8300.85 | 0.735819 | 0.367909 | − | 0.929862i | \(-0.380074\pi\) | ||||
0.367909 | + | 0.929862i | \(0.380074\pi\) | |||||||
\(504\) | −1197.37 | −0.105823 | ||||||||
\(505\) | 16370.3 | 1.44251 | ||||||||
\(506\) | −12684.4 | −1.11441 | ||||||||
\(507\) | 2741.53 | 0.240149 | ||||||||
\(508\) | −37691.5 | −3.29191 | ||||||||
\(509\) | −2569.76 | −0.223777 | −0.111889 | − | 0.993721i | \(-0.535690\pi\) | ||||
−0.111889 | + | 0.993721i | \(0.535690\pi\) | |||||||
\(510\) | 37866.2 | 3.28773 | ||||||||
\(511\) | −847.077 | −0.0733317 | ||||||||
\(512\) | 17504.4 | 1.51092 | ||||||||
\(513\) | 1440.68 | 0.123992 | ||||||||
\(514\) | 7069.60 | 0.606667 | ||||||||
\(515\) | 10738.5 | 0.918823 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2405.74 | −0.204651 | ||||||||
\(518\) | −36040.1 | −3.05697 | ||||||||
\(519\) | 356.211 | 0.0301270 | ||||||||
\(520\) | 30866.5 | 2.60305 | ||||||||
\(521\) | −12083.3 | −1.01609 | −0.508043 | − | 0.861332i | \(-0.669631\pi\) | ||||
−0.508043 | + | 0.861332i | \(0.669631\pi\) | |||||||
\(522\) | 954.648 | 0.0800456 | ||||||||
\(523\) | 7343.65 | 0.613988 | 0.306994 | − | 0.951712i | \(-0.400677\pi\) | ||||
0.306994 | + | 0.951712i | \(0.400677\pi\) | |||||||
\(524\) | 27918.5 | 2.32753 | ||||||||
\(525\) | 20183.6 | 1.67787 | ||||||||
\(526\) | −22364.9 | −1.85391 | ||||||||
\(527\) | −11132.7 | −0.920208 | ||||||||
\(528\) | −3802.54 | −0.313417 | ||||||||
\(529\) | 25984.9 | 2.13569 | ||||||||
\(530\) | 4990.57 | 0.409012 | ||||||||
\(531\) | −34.8851 | −0.00285100 | ||||||||
\(532\) | −4569.54 | −0.372396 | ||||||||
\(533\) | 13031.6 | 1.05903 | ||||||||
\(534\) | 33852.2 | 2.74331 | ||||||||
\(535\) | −12686.4 | −1.02520 | ||||||||
\(536\) | −595.308 | −0.0479727 | ||||||||
\(537\) | 8574.61 | 0.689054 | ||||||||
\(538\) | 18417.9 | 1.47593 | ||||||||
\(539\) | −5865.73 | −0.468747 | ||||||||
\(540\) | −34458.8 | −2.74606 | ||||||||
\(541\) | 9216.21 | 0.732414 | 0.366207 | − | 0.930533i | \(-0.380656\pi\) | ||||
0.366207 | + | 0.930533i | \(0.380656\pi\) | |||||||
\(542\) | −17878.8 | −1.41690 | ||||||||
\(543\) | 10203.9 | 0.806432 | ||||||||
\(544\) | −3048.24 | −0.240243 | ||||||||
\(545\) | −24913.7 | −1.95814 | ||||||||
\(546\) | 37508.9 | 2.93999 | ||||||||
\(547\) | −4652.64 | −0.363680 | −0.181840 | − | 0.983328i | \(-0.558205\pi\) | ||||
−0.181840 | + | 0.983328i | \(0.558205\pi\) | |||||||
\(548\) | −33766.4 | −2.63217 | ||||||||
\(549\) | −251.308 | −0.0195365 | ||||||||
\(550\) | 8834.84 | 0.684943 | ||||||||
\(551\) | 1769.66 | 0.136824 | ||||||||
\(552\) | 38018.6 | 2.93148 | ||||||||
\(553\) | −10595.8 | −0.814793 | ||||||||
\(554\) | −23868.9 | −1.83049 | ||||||||
\(555\) | 22779.0 | 1.74219 | ||||||||
\(556\) | −3820.31 | −0.291398 | ||||||||
\(557\) | 14312.2 | 1.08874 | 0.544369 | − | 0.838846i | \(-0.316769\pi\) | ||||
0.544369 | + | 0.838846i | \(0.316769\pi\) | |||||||
\(558\) | −693.626 | −0.0526228 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 24184.1 | 1.82493 | ||||||||
\(561\) | 6461.00 | 0.486245 | ||||||||
\(562\) | 1032.50 | 0.0774973 | ||||||||
\(563\) | −3350.90 | −0.250841 | −0.125421 | − | 0.992104i | \(-0.540028\pi\) | ||||
−0.125421 | + | 0.992104i | \(0.540028\pi\) | |||||||
\(564\) | 14844.7 | 1.10829 | ||||||||
\(565\) | 18461.6 | 1.37467 | ||||||||
\(566\) | 13473.3 | 1.00057 | ||||||||
\(567\) | −21221.4 | −1.57181 | ||||||||
\(568\) | −29575.8 | −2.18481 | ||||||||
\(569\) | 12015.1 | 0.885238 | 0.442619 | − | 0.896710i | \(-0.354050\pi\) | ||||
0.442619 | + | 0.896710i | \(0.354050\pi\) | |||||||
\(570\) | 4373.43 | 0.321373 | ||||||||
\(571\) | 3985.38 | 0.292089 | 0.146045 | − | 0.989278i | \(-0.453346\pi\) | ||||
0.146045 | + | 0.989278i | \(0.453346\pi\) | |||||||
\(572\) | 10842.6 | 0.792574 | ||||||||
\(573\) | −16554.4 | −1.20693 | ||||||||
\(574\) | 33940.3 | 2.46802 | ||||||||
\(575\) | −26573.2 | −1.92727 | ||||||||
\(576\) | −690.253 | −0.0499315 | ||||||||
\(577\) | 12302.3 | 0.887609 | 0.443804 | − | 0.896124i | \(-0.353629\pi\) | ||||
0.443804 | + | 0.896124i | \(0.353629\pi\) | |||||||
\(578\) | −16331.9 | −1.17529 | ||||||||
\(579\) | −9838.56 | −0.706177 | ||||||||
\(580\) | −42327.4 | −3.03026 | ||||||||
\(581\) | −16971.3 | −1.21186 | ||||||||
\(582\) | −5921.33 | −0.421730 | ||||||||
\(583\) | 851.526 | 0.0604916 | ||||||||
\(584\) | 1111.34 | 0.0787462 | ||||||||
\(585\) | −983.015 | −0.0694746 | ||||||||
\(586\) | 34536.2 | 2.43460 | ||||||||
\(587\) | −2130.30 | −0.149791 | −0.0748953 | − | 0.997191i | \(-0.523862\pi\) | ||||
−0.0748953 | + | 0.997191i | \(0.523862\pi\) | |||||||
\(588\) | 36194.7 | 2.53851 | ||||||||
\(589\) | −1285.80 | −0.0899496 | ||||||||
\(590\) | 2342.17 | 0.163433 | ||||||||
\(591\) | 1006.16 | 0.0700306 | ||||||||
\(592\) | 14224.4 | 0.987535 | ||||||||
\(593\) | 15604.8 | 1.08063 | 0.540315 | − | 0.841463i | \(-0.318305\pi\) | ||||
0.540315 | + | 0.841463i | \(0.318305\pi\) | |||||||
\(594\) | −8903.26 | −0.614992 | ||||||||
\(595\) | −41091.8 | −2.83126 | ||||||||
\(596\) | −17774.9 | −1.22163 | ||||||||
\(597\) | −305.552 | −0.0209471 | ||||||||
\(598\) | −49383.4 | −3.37698 | ||||||||
\(599\) | −1690.93 | −0.115342 | −0.0576709 | − | 0.998336i | \(-0.518367\pi\) | ||||
−0.0576709 | + | 0.998336i | \(0.518367\pi\) | |||||||
\(600\) | −26480.4 | −1.80176 | ||||||||
\(601\) | 8333.53 | 0.565610 | 0.282805 | − | 0.959177i | \(-0.408735\pi\) | ||||
0.282805 | + | 0.959177i | \(0.408735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.9589 | 0.00128038 | ||||||||
\(604\) | 21679.0 | 1.46044 | ||||||||
\(605\) | −18612.3 | −1.25074 | ||||||||
\(606\) | −26099.3 | −1.74952 | ||||||||
\(607\) | 17800.5 | 1.19028 | 0.595141 | − | 0.803621i | \(-0.297096\pi\) | ||||
0.595141 | + | 0.803621i | \(0.297096\pi\) | |||||||
\(608\) | −352.062 | −0.0234836 | ||||||||
\(609\) | −24984.5 | −1.66243 | ||||||||
\(610\) | 16872.7 | 1.11993 | ||||||||
\(611\) | −9366.10 | −0.620150 | ||||||||
\(612\) | −1653.10 | −0.109187 | ||||||||
\(613\) | −13015.8 | −0.857594 | −0.428797 | − | 0.903401i | \(-0.641062\pi\) | ||||
−0.428797 | + | 0.903401i | \(0.641062\pi\) | |||||||
\(614\) | 17782.7 | 1.16881 | ||||||||
\(615\) | −21451.8 | −1.40654 | ||||||||
\(616\) | 13716.8 | 0.897187 | ||||||||
\(617\) | −14286.8 | −0.932198 | −0.466099 | − | 0.884733i | \(-0.654341\pi\) | ||||
−0.466099 | + | 0.884733i | \(0.654341\pi\) | |||||||
\(618\) | −17120.4 | −1.11438 | ||||||||
\(619\) | −20191.3 | −1.31108 | −0.655538 | − | 0.755162i | \(-0.727558\pi\) | ||||
−0.655538 | + | 0.755162i | \(0.727558\pi\) | |||||||
\(620\) | 30754.1 | 1.99212 | ||||||||
\(621\) | 26779.0 | 1.73044 | ||||||||
\(622\) | 36279.3 | 2.33870 | ||||||||
\(623\) | −36735.9 | −2.36243 | ||||||||
\(624\) | −14804.1 | −0.949744 | ||||||||
\(625\) | −14122.2 | −0.903823 | ||||||||
\(626\) | −30844.7 | −1.96933 | ||||||||
\(627\) | 746.225 | 0.0475301 | ||||||||
\(628\) | −2288.47 | −0.145414 | ||||||||
\(629\) | −24169.1 | −1.53209 | ||||||||
\(630\) | −2560.23 | −0.161908 | ||||||||
\(631\) | 16981.8 | 1.07137 | 0.535685 | − | 0.844418i | \(-0.320053\pi\) | ||||
0.535685 | + | 0.844418i | \(0.320053\pi\) | |||||||
\(632\) | 13901.5 | 0.874953 | ||||||||
\(633\) | −3818.98 | −0.239796 | ||||||||
\(634\) | −11814.9 | −0.740111 | ||||||||
\(635\) | −39146.8 | −2.44645 | ||||||||
\(636\) | −5254.38 | −0.327594 | ||||||||
\(637\) | −22836.6 | −1.42044 | ||||||||
\(638\) | −10936.3 | −0.678640 | ||||||||
\(639\) | 941.909 | 0.0583120 | ||||||||
\(640\) | 42012.9 | 2.59485 | ||||||||
\(641\) | 17639.8 | 1.08694 | 0.543471 | − | 0.839428i | \(-0.317110\pi\) | ||||
0.543471 | + | 0.839428i | \(0.317110\pi\) | |||||||
\(642\) | 20226.1 | 1.24340 | ||||||||
\(643\) | 23124.0 | 1.41823 | 0.709115 | − | 0.705093i | \(-0.249095\pi\) | ||||
0.709115 | + | 0.705093i | \(0.249095\pi\) | |||||||
\(644\) | −84937.2 | −5.19719 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4640.32 | −0.282618 | ||||||||
\(647\) | −10314.1 | −0.626721 | −0.313360 | − | 0.949634i | \(-0.601455\pi\) | ||||
−0.313360 | + | 0.949634i | \(0.601455\pi\) | |||||||
\(648\) | 27842.0 | 1.68786 | ||||||||
\(649\) | 399.638 | 0.0241713 | ||||||||
\(650\) | 34396.0 | 2.07557 | ||||||||
\(651\) | 18153.1 | 1.09290 | ||||||||
\(652\) | −2513.01 | −0.150947 | ||||||||
\(653\) | 23231.2 | 1.39220 | 0.696099 | − | 0.717946i | \(-0.254917\pi\) | ||||
0.696099 | + | 0.717946i | \(0.254917\pi\) | |||||||
\(654\) | 39720.1 | 2.37489 | ||||||||
\(655\) | 28996.5 | 1.72975 | ||||||||
\(656\) | −13395.7 | −0.797276 | ||||||||
\(657\) | −35.3933 | −0.00210171 | ||||||||
\(658\) | −24393.7 | −1.44523 | ||||||||
\(659\) | 19494.8 | 1.15236 | 0.576182 | − | 0.817321i | \(-0.304542\pi\) | ||||
0.576182 | + | 0.817321i | \(0.304542\pi\) | |||||||
\(660\) | −17848.5 | −1.05265 | ||||||||
\(661\) | 31934.6 | 1.87914 | 0.939571 | − | 0.342354i | \(-0.111224\pi\) | ||||
0.939571 | + | 0.342354i | \(0.111224\pi\) | |||||||
\(662\) | −9965.88 | −0.585098 | ||||||||
\(663\) | 25154.1 | 1.47346 | ||||||||
\(664\) | 22265.9 | 1.30133 | ||||||||
\(665\) | −4745.97 | −0.276753 | ||||||||
\(666\) | −1505.86 | −0.0876138 | ||||||||
\(667\) | 32893.9 | 1.90953 | ||||||||
\(668\) | 29576.1 | 1.71307 | ||||||||
\(669\) | −169.943 | −0.00982117 | ||||||||
\(670\) | −1272.90 | −0.0733974 | ||||||||
\(671\) | 2878.95 | 0.165634 | ||||||||
\(672\) | 4970.49 | 0.285329 | ||||||||
\(673\) | −31725.0 | −1.81710 | −0.908550 | − | 0.417776i | \(-0.862810\pi\) | ||||
−0.908550 | + | 0.417776i | \(0.862810\pi\) | |||||||
\(674\) | 35549.0 | 2.03159 | ||||||||
\(675\) | −18651.9 | −1.06357 | ||||||||
\(676\) | 8035.64 | 0.457194 | ||||||||
\(677\) | 21791.4 | 1.23709 | 0.618545 | − | 0.785749i | \(-0.287722\pi\) | ||||
0.618545 | + | 0.785749i | \(0.287722\pi\) | |||||||
\(678\) | −29433.5 | −1.66724 | ||||||||
\(679\) | 6425.73 | 0.363177 | ||||||||
\(680\) | 53911.4 | 3.04031 | ||||||||
\(681\) | −26275.8 | −1.47855 | ||||||||
\(682\) | 7946.07 | 0.446145 | ||||||||
\(683\) | 5819.39 | 0.326022 | 0.163011 | − | 0.986624i | \(-0.447879\pi\) | ||||
0.163011 | + | 0.986624i | \(0.447879\pi\) | |||||||
\(684\) | −190.928 | −0.0106730 | ||||||||
\(685\) | −35070.1 | −1.95615 | ||||||||
\(686\) | −12941.9 | −0.720297 | ||||||||
\(687\) | 6185.87 | 0.343531 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3315.18 | 0.183307 | ||||||||
\(690\) | 81292.0 | 4.48512 | ||||||||
\(691\) | 28673.5 | 1.57857 | 0.789285 | − | 0.614027i | \(-0.210452\pi\) | ||||
0.789285 | + | 0.614027i | \(0.210452\pi\) | |||||||
\(692\) | 1044.08 | 0.0573556 | ||||||||
\(693\) | −436.844 | −0.0239456 | ||||||||
\(694\) | −1020.69 | −0.0558286 | ||||||||
\(695\) | −3967.82 | −0.216558 | ||||||||
\(696\) | 32779.0 | 1.78518 | ||||||||
\(697\) | 22761.0 | 1.23692 | ||||||||
\(698\) | 38741.1 | 2.10082 | ||||||||
\(699\) | −5684.24 | −0.307579 | ||||||||
\(700\) | 59159.6 | 3.19432 | ||||||||
\(701\) | 14960.3 | 0.806054 | 0.403027 | − | 0.915188i | \(-0.367958\pi\) | ||||
0.403027 | + | 0.915188i | \(0.367958\pi\) | |||||||
\(702\) | −34662.4 | −1.86360 | ||||||||
\(703\) | −2791.46 | −0.149761 | ||||||||
\(704\) | 7907.44 | 0.423328 | ||||||||
\(705\) | 15417.9 | 0.823649 | ||||||||
\(706\) | 44343.5 | 2.36387 | ||||||||
\(707\) | 28322.5 | 1.50662 | ||||||||
\(708\) | −2465.98 | −0.130900 | ||||||||
\(709\) | 3891.22 | 0.206118 | 0.103059 | − | 0.994675i | \(-0.467137\pi\) | ||||
0.103059 | + | 0.994675i | \(0.467137\pi\) | |||||||
\(710\) | −63239.5 | −3.34273 | ||||||||
\(711\) | −442.724 | −0.0233522 | ||||||||
\(712\) | 48196.6 | 2.53686 | ||||||||
\(713\) | −23900.0 | −1.25535 | ||||||||
\(714\) | 65513.0 | 3.43384 | ||||||||
\(715\) | 11261.3 | 0.589018 | ||||||||
\(716\) | 25132.9 | 1.31181 | ||||||||
\(717\) | −22685.6 | −1.18160 | ||||||||
\(718\) | 31740.8 | 1.64980 | ||||||||
\(719\) | 32574.3 | 1.68959 | 0.844796 | − | 0.535088i | \(-0.179722\pi\) | ||||
0.844796 | + | 0.535088i | \(0.179722\pi\) | |||||||
\(720\) | 1010.48 | 0.0523032 | ||||||||
\(721\) | 18578.8 | 0.959656 | ||||||||
\(722\) | 32754.1 | 1.68834 | ||||||||
\(723\) | 37279.3 | 1.91761 | ||||||||
\(724\) | 29908.5 | 1.53528 | ||||||||
\(725\) | −22911.0 | −1.17364 | ||||||||
\(726\) | 29673.8 | 1.51694 | ||||||||
\(727\) | 22352.4 | 1.14031 | 0.570154 | − | 0.821538i | \(-0.306883\pi\) | ||||
0.570154 | + | 0.821538i | \(0.306883\pi\) | |||||||
\(728\) | 53402.8 | 2.71873 | ||||||||
\(729\) | 18759.5 | 0.953080 | ||||||||
\(730\) | 2376.30 | 0.120480 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −17764.7 | −0.896995 | ||||||||
\(733\) | 7894.97 | 0.397827 | 0.198914 | − | 0.980017i | \(-0.436259\pi\) | ||||
0.198914 | + | 0.980017i | \(0.436259\pi\) | |||||||
\(734\) | −36415.9 | −1.83125 | ||||||||
\(735\) | 37592.3 | 1.88655 | ||||||||
\(736\) | −6544.03 | −0.327739 | ||||||||
\(737\) | −217.191 | −0.0108552 | ||||||||
\(738\) | 1418.12 | 0.0707342 | ||||||||
\(739\) | −19992.9 | −0.995196 | −0.497598 | − | 0.867408i | \(-0.665784\pi\) | ||||
−0.497598 | + | 0.867408i | \(0.665784\pi\) | |||||||
\(740\) | 66767.1 | 3.31677 | ||||||||
\(741\) | 2905.22 | 0.144030 | ||||||||
\(742\) | 8634.27 | 0.427189 | ||||||||
\(743\) | −29649.9 | −1.46400 | −0.731999 | − | 0.681305i | \(-0.761413\pi\) | ||||
−0.731999 | + | 0.681305i | \(0.761413\pi\) | |||||||
\(744\) | −23816.5 | −1.17359 | ||||||||
\(745\) | −18461.3 | −0.907878 | ||||||||
\(746\) | 1132.00 | 0.0555567 | ||||||||
\(747\) | −709.109 | −0.0347322 | ||||||||
\(748\) | 18937.7 | 0.925709 | ||||||||
\(749\) | −21949.1 | −1.07076 | ||||||||
\(750\) | −4597.24 | −0.223823 | ||||||||
\(751\) | 16153.5 | 0.784887 | 0.392443 | − | 0.919776i | \(-0.371630\pi\) | ||||
0.392443 | + | 0.919776i | \(0.371630\pi\) | |||||||
\(752\) | 9627.77 | 0.466873 | ||||||||
\(753\) | 11266.3 | 0.545240 | ||||||||
\(754\) | −42577.5 | −2.05647 | ||||||||
\(755\) | 22516.1 | 1.08536 | ||||||||
\(756\) | −59617.8 | −2.86809 | ||||||||
\(757\) | −38932.2 | −1.86924 | −0.934620 | − | 0.355648i | \(-0.884260\pi\) | ||||
−0.934620 | + | 0.355648i | \(0.884260\pi\) | |||||||
\(758\) | −35127.4 | −1.68323 | ||||||||
\(759\) | 13870.6 | 0.663335 | ||||||||
\(760\) | 6226.60 | 0.297188 | ||||||||
\(761\) | 40667.5 | 1.93718 | 0.968592 | − | 0.248656i | \(-0.0799889\pi\) | ||||
0.968592 | + | 0.248656i | \(0.0799889\pi\) | |||||||
\(762\) | 62412.1 | 2.96713 | ||||||||
\(763\) | −43103.6 | −2.04516 | ||||||||
\(764\) | −48522.2 | −2.29774 | ||||||||
\(765\) | −1716.93 | −0.0811448 | ||||||||
\(766\) | −37710.8 | −1.77878 | ||||||||
\(767\) | 1555.88 | 0.0732459 | ||||||||
\(768\) | −41889.1 | −1.96815 | ||||||||
\(769\) | 971.746 | 0.0455684 | 0.0227842 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227842 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(770\) | 29329.6 | 1.37268 | ||||||||
\(771\) | −7730.71 | −0.361109 | ||||||||
\(772\) | −28837.6 | −1.34441 | ||||||||
\(773\) | 15680.2 | 0.729596 | 0.364798 | − | 0.931087i | \(-0.381138\pi\) | ||||
0.364798 | + | 0.931087i | \(0.381138\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16646.6 | 0.771566 | ||||||||
\(776\) | −8430.40 | −0.389992 | ||||||||
\(777\) | 39410.4 | 1.81961 | ||||||||
\(778\) | 39949.0 | 1.84093 | ||||||||
\(779\) | 2628.82 | 0.120908 | ||||||||
\(780\) | −69488.2 | −3.18984 | ||||||||
\(781\) | −10790.4 | −0.494379 | ||||||||
\(782\) | −86252.9 | −3.94424 | ||||||||
\(783\) | 23088.4 | 1.05378 | ||||||||
\(784\) | 23474.6 | 1.06936 | ||||||||
\(785\) | −2376.83 | −0.108067 | ||||||||
\(786\) | −46229.4 | −2.09790 | ||||||||
\(787\) | −9789.83 | −0.443418 | −0.221709 | − | 0.975113i | \(-0.571163\pi\) | ||||
−0.221709 | + | 0.975113i | \(0.571163\pi\) | |||||||
\(788\) | 2949.15 | 0.133324 | ||||||||
\(789\) | 24456.4 | 1.10351 | ||||||||
\(790\) | 29724.3 | 1.33866 | ||||||||
\(791\) | 31940.8 | 1.43576 | ||||||||
\(792\) | 573.128 | 0.0257137 | ||||||||
\(793\) | 11208.4 | 0.501919 | ||||||||
\(794\) | 40159.7 | 1.79498 | ||||||||
\(795\) | −5457.26 | −0.243458 | ||||||||
\(796\) | −895.597 | −0.0398789 | ||||||||
\(797\) | −38193.6 | −1.69747 | −0.848737 | − | 0.528815i | \(-0.822636\pi\) | ||||
−0.848737 | + | 0.528815i | \(0.822636\pi\) | |||||||
\(798\) | 7566.55 | 0.335655 | ||||||||
\(799\) | −16358.8 | −0.724322 | ||||||||
\(800\) | 4557.99 | 0.201436 | ||||||||
\(801\) | −1534.93 | −0.0677079 | ||||||||
\(802\) | 66438.9 | 2.92524 | ||||||||
\(803\) | 405.460 | 0.0178187 | ||||||||
\(804\) | 1340.18 | 0.0587869 | ||||||||
\(805\) | −88216.8 | −3.86240 | ||||||||
\(806\) | 30935.9 | 1.35195 | ||||||||
\(807\) | −20140.2 | −0.878524 | ||||||||
\(808\) | −37158.5 | −1.61786 | ||||||||
\(809\) | −25984.8 | −1.12927 | −0.564634 | − | 0.825342i | \(-0.690983\pi\) | ||||
−0.564634 | + | 0.825342i | \(0.690983\pi\) | |||||||
\(810\) | 59532.1 | 2.58240 | ||||||||
\(811\) | −12058.7 | −0.522120 | −0.261060 | − | 0.965323i | \(-0.584072\pi\) | ||||
−0.261060 | + | 0.965323i | \(0.584072\pi\) | |||||||
\(812\) | −73231.4 | −3.16492 | ||||||||
\(813\) | 19550.7 | 0.843388 | ||||||||
\(814\) | 17250.9 | 0.742805 | ||||||||
\(815\) | −2610.05 | −0.112179 | ||||||||
\(816\) | −25856.9 | −1.10928 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −63783.1 | −2.72631 | ||||||||
\(819\) | −1700.73 | −0.0725621 | ||||||||
\(820\) | −62877.0 | −2.67776 | ||||||||
\(821\) | 10328.1 | 0.439040 | 0.219520 | − | 0.975608i | \(-0.429551\pi\) | ||||
0.219520 | + | 0.975608i | \(0.429551\pi\) | |||||||
\(822\) | 55912.6 | 2.37248 | ||||||||
\(823\) | 1549.44 | 0.0656259 | 0.0328130 | − | 0.999462i | \(-0.489553\pi\) | ||||
0.0328130 | + | 0.999462i | \(0.489553\pi\) | |||||||
\(824\) | −24375.0 | −1.03051 | ||||||||
\(825\) | −9661.03 | −0.407702 | ||||||||
\(826\) | 4052.24 | 0.170697 | ||||||||
\(827\) | −34169.0 | −1.43673 | −0.718364 | − | 0.695668i | \(-0.755109\pi\) | ||||
−0.718364 | + | 0.695668i | \(0.755109\pi\) | |||||||
\(828\) | −3548.91 | −0.148953 | ||||||||
\(829\) | 41058.6 | 1.72017 | 0.860086 | − | 0.510148i | \(-0.170410\pi\) | ||||
0.860086 | + | 0.510148i | \(0.170410\pi\) | |||||||
\(830\) | 47609.4 | 1.99102 | ||||||||
\(831\) | 26101.0 | 1.08957 | ||||||||
\(832\) | 30785.4 | 1.28280 | ||||||||
\(833\) | −39886.4 | −1.65904 | ||||||||
\(834\) | 6325.93 | 0.262649 | ||||||||
\(835\) | 30718.1 | 1.27311 | ||||||||
\(836\) | 2187.24 | 0.0904874 | ||||||||
\(837\) | −16775.5 | −0.692768 | ||||||||
\(838\) | −35521.5 | −1.46428 | ||||||||
\(839\) | −14142.7 | −0.581953 | −0.290977 | − | 0.956730i | \(-0.593980\pi\) | ||||
−0.290977 | + | 0.956730i | \(0.593980\pi\) | |||||||
\(840\) | −87908.5 | −3.61087 | ||||||||
\(841\) | 3971.60 | 0.162844 | ||||||||
\(842\) | 73004.6 | 2.98801 | ||||||||
\(843\) | −1129.06 | −0.0461290 | ||||||||
\(844\) | −11193.7 | −0.456521 | ||||||||
\(845\) | 8345.92 | 0.339773 | ||||||||
\(846\) | −1019.24 | −0.0414209 | ||||||||
\(847\) | −32201.5 | −1.30633 | ||||||||
\(848\) | −3407.80 | −0.138001 | ||||||||
\(849\) | −14733.2 | −0.595574 | ||||||||
\(850\) | 60076.1 | 2.42423 | ||||||||
\(851\) | −51886.8 | −2.09008 | ||||||||
\(852\) | 66582.4 | 2.67732 | ||||||||
\(853\) | 37292.5 | 1.49692 | 0.748459 | − | 0.663181i | \(-0.230794\pi\) | ||||
0.748459 | + | 0.663181i | \(0.230794\pi\) | |||||||
\(854\) | 29191.8 | 1.16970 | ||||||||
\(855\) | −198.300 | −0.00793184 | ||||||||
\(856\) | 28796.6 | 1.14982 | ||||||||
\(857\) | −5517.53 | −0.219924 | −0.109962 | − | 0.993936i | \(-0.535073\pi\) | ||||
−0.109962 | + | 0.993936i | \(0.535073\pi\) | |||||||
\(858\) | −17953.9 | −0.714379 | ||||||||
\(859\) | −35180.3 | −1.39737 | −0.698683 | − | 0.715431i | \(-0.746230\pi\) | ||||
−0.698683 | + | 0.715431i | \(0.746230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37114.2 | −1.46905 | ||||||||
\(862\) | −21027.5 | −0.830857 | ||||||||
\(863\) | −957.480 | −0.0377671 | −0.0188835 | − | 0.999822i | \(-0.506011\pi\) | ||||
−0.0188835 | + | 0.999822i | \(0.506011\pi\) | |||||||
\(864\) | −4593.28 | −0.180864 | ||||||||
\(865\) | 1084.40 | 0.0426249 | ||||||||
\(866\) | 8197.29 | 0.321657 | ||||||||
\(867\) | 17859.1 | 0.699571 | ||||||||
\(868\) | 53208.3 | 2.08065 | ||||||||
\(869\) | 5071.78 | 0.197984 | ||||||||
\(870\) | 70088.6 | 2.73129 | ||||||||
\(871\) | −845.572 | −0.0328945 | ||||||||
\(872\) | 56550.9 | 2.19616 | ||||||||
\(873\) | 268.485 | 0.0104088 | ||||||||
\(874\) | −9961.94 | −0.385546 | ||||||||
\(875\) | 4988.85 | 0.192747 | ||||||||
\(876\) | −2501.91 | −0.0964974 | ||||||||
\(877\) | 2707.29 | 0.104240 | 0.0521201 | − | 0.998641i | \(-0.483402\pi\) | ||||
0.0521201 | + | 0.998641i | \(0.483402\pi\) | |||||||
\(878\) | −69675.9 | −2.67818 | ||||||||
\(879\) | −37765.8 | −1.44916 | ||||||||
\(880\) | −11575.9 | −0.443436 | ||||||||
\(881\) | 10685.3 | 0.408621 | 0.204311 | − | 0.978906i | \(-0.434505\pi\) | ||||
0.204311 | + | 0.978906i | \(0.434505\pi\) | |||||||
\(882\) | −2485.12 | −0.0948735 | ||||||||
\(883\) | 7131.73 | 0.271803 | 0.135901 | − | 0.990722i | \(-0.456607\pi\) | ||||
0.135901 | + | 0.990722i | \(0.456607\pi\) | |||||||
\(884\) | 73728.7 | 2.80516 | ||||||||
\(885\) | −2561.20 | −0.0972811 | ||||||||
\(886\) | 7634.31 | 0.289481 | ||||||||
\(887\) | −8191.54 | −0.310085 | −0.155042 | − | 0.987908i | \(-0.549551\pi\) | ||||
−0.155042 | + | 0.987908i | \(0.549551\pi\) | |||||||
\(888\) | −51705.5 | −1.95397 | ||||||||
\(889\) | −67728.7 | −2.55517 | ||||||||
\(890\) | 103055. | 3.88135 | ||||||||
\(891\) | 10157.8 | 0.381929 | ||||||||
\(892\) | −498.115 | −0.0186975 | ||||||||
\(893\) | −1889.39 | −0.0708019 | ||||||||
\(894\) | 29433.0 | 1.10110 | ||||||||
\(895\) | 26103.3 | 0.974901 | ||||||||
\(896\) | 72687.3 | 2.71017 | ||||||||
\(897\) | 54001.4 | 2.01009 | ||||||||
\(898\) | 48173.3 | 1.79016 | ||||||||
\(899\) | −20606.2 | −0.764466 | ||||||||
\(900\) | 2471.86 | 0.0915503 | ||||||||
\(901\) | 5790.29 | 0.214098 | ||||||||
\(902\) | −16245.8 | −0.599696 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41905.5 | −1.54177 | ||||||||
\(905\) | 31063.4 | 1.14097 | ||||||||
\(906\) | −35897.6 | −1.31635 | ||||||||
\(907\) | −33159.0 | −1.21392 | −0.606960 | − | 0.794732i | \(-0.707611\pi\) | ||||
−0.606960 | + | 0.794732i | \(0.707611\pi\) | |||||||
\(908\) | −77016.5 | −2.81485 | ||||||||
\(909\) | 1183.40 | 0.0431801 | ||||||||
\(910\) | 114187. | 4.15962 | ||||||||
\(911\) | −22979.0 | −0.835705 | −0.417852 | − | 0.908515i | \(-0.637217\pi\) | ||||
−0.417852 | + | 0.908515i | \(0.637217\pi\) | |||||||
\(912\) | −2986.39 | −0.108431 | ||||||||
\(913\) | 8123.44 | 0.294465 | ||||||||
\(914\) | 91344.2 | 3.30569 | ||||||||
\(915\) | −18450.6 | −0.666620 | ||||||||
\(916\) | 18131.3 | 0.654010 | ||||||||
\(917\) | 50167.4 | 1.80662 | ||||||||
\(918\) | −60541.3 | −2.17665 | ||||||||
\(919\) | −28118.8 | −1.00931 | −0.504655 | − | 0.863321i | \(-0.668380\pi\) | ||||
−0.504655 | + | 0.863321i | \(0.668380\pi\) | |||||||
\(920\) | 115738. | 4.14758 | ||||||||
\(921\) | −19445.6 | −0.695717 | ||||||||
\(922\) | −10574.6 | −0.377719 | ||||||||
\(923\) | −42009.3 | −1.49811 | ||||||||
\(924\) | −30880.0 | −1.09943 | ||||||||
\(925\) | 36139.7 | 1.28461 | ||||||||
\(926\) | −13464.8 | −0.477840 | ||||||||
\(927\) | 776.276 | 0.0275041 | ||||||||
\(928\) | −5642.15 | −0.199583 | ||||||||
\(929\) | 34555.2 | 1.22037 | 0.610183 | − | 0.792261i | \(-0.291096\pi\) | ||||
0.610183 | + | 0.792261i | \(0.291096\pi\) | |||||||
\(930\) | −50924.8 | −1.79558 | ||||||||
\(931\) | −4606.75 | −0.162170 | ||||||||
\(932\) | −16661.0 | −0.585567 | ||||||||
\(933\) | −39672.0 | −1.39207 | ||||||||
\(934\) | −20444.4 | −0.716231 | ||||||||
\(935\) | 19668.9 | 0.687960 | ||||||||
\(936\) | 2231.32 | 0.0779198 | ||||||||
\(937\) | −24391.7 | −0.850420 | −0.425210 | − | 0.905095i | \(-0.639800\pi\) | ||||
−0.425210 | + | 0.905095i | \(0.639800\pi\) | |||||||
\(938\) | −2202.26 | −0.0766593 | ||||||||
\(939\) | 33729.2 | 1.17221 | ||||||||
\(940\) | 45191.1 | 1.56806 | ||||||||
\(941\) | −17916.6 | −0.620684 | −0.310342 | − | 0.950625i | \(-0.600444\pi\) | ||||
−0.310342 | + | 0.950625i | \(0.600444\pi\) | |||||||
\(942\) | 3789.40 | 0.131067 | ||||||||
\(943\) | 48863.7 | 1.68740 | ||||||||
\(944\) | −1599.35 | −0.0551424 | ||||||||
\(945\) | −61919.8 | −2.13148 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21343.8 | 0.732398 | 0.366199 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366199 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(948\) | −31295.6 | −1.07219 | ||||||||
\(949\) | 1578.55 | 0.0539956 | ||||||||
\(950\) | 6938.60 | 0.236966 | ||||||||
\(951\) | 12919.8 | 0.440539 | ||||||||
\(952\) | 93273.2 | 3.17542 | ||||||||
\(953\) | −37998.5 | −1.29160 | −0.645799 | − | 0.763508i | \(-0.723476\pi\) | ||||
−0.645799 | + | 0.763508i | \(0.723476\pi\) | |||||||
\(954\) | 360.764 | 0.0122434 | ||||||||
\(955\) | −50395.7 | −1.70761 | ||||||||
\(956\) | −66493.3 | −2.24953 | ||||||||
\(957\) | 11959.0 | 0.403950 | ||||||||
\(958\) | −85907.3 | −2.89722 | ||||||||
\(959\) | −60675.5 | −2.04308 | ||||||||
\(960\) | −50677.2 | −1.70375 | ||||||||
\(961\) | −14819.0 | −0.497432 | ||||||||
\(962\) | 67161.6 | 2.25091 | ||||||||
\(963\) | −917.094 | −0.0306884 | ||||||||
\(964\) | 109269. | 3.65073 | ||||||||
\(965\) | −29951.1 | −0.999128 | ||||||||
\(966\) | 140645. | 4.68444 | ||||||||
\(967\) | 30226.2 | 1.00518 | 0.502590 | − | 0.864525i | \(-0.332381\pi\) | ||||
0.502590 | + | 0.864525i | \(0.332381\pi\) | |||||||
\(968\) | 42247.6 | 1.40278 | ||||||||
\(969\) | 5074.26 | 0.168224 | ||||||||
\(970\) | −18026.0 | −0.596681 | ||||||||
\(971\) | 18868.7 | 0.623611 | 0.311805 | − | 0.950146i | \(-0.399066\pi\) | ||||
0.311805 | + | 0.950146i | \(0.399066\pi\) | |||||||
\(972\) | −5094.63 | −0.168118 | ||||||||
\(973\) | −6864.80 | −0.226182 | ||||||||
\(974\) | −75783.7 | −2.49309 | ||||||||
\(975\) | −37612.6 | −1.23545 | ||||||||
\(976\) | −11521.5 | −0.377864 | ||||||||
\(977\) | 14033.2 | 0.459531 | 0.229766 | − | 0.973246i | \(-0.426204\pi\) | ||||
0.229766 | + | 0.973246i | \(0.426204\pi\) | |||||||
\(978\) | 4161.22 | 0.136054 | ||||||||
\(979\) | 17583.9 | 0.574039 | ||||||||
\(980\) | 110186. | 3.59159 | ||||||||
\(981\) | −1800.99 | −0.0586149 | ||||||||
\(982\) | 91653.0 | 2.97838 | ||||||||
\(983\) | −29136.6 | −0.945386 | −0.472693 | − | 0.881227i | \(-0.656718\pi\) | ||||
−0.472693 | + | 0.881227i | \(0.656718\pi\) | |||||||
\(984\) | 48693.0 | 1.57752 | ||||||||
\(985\) | 3063.02 | 0.0990821 | ||||||||
\(986\) | −74365.8 | −2.40192 | ||||||||
\(987\) | 26674.8 | 0.860252 | ||||||||
\(988\) | 8515.44 | 0.274203 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1225.47 | 0.0393415 | ||||||||
\(991\) | 14864.1 | 0.476463 | 0.238232 | − | 0.971208i | \(-0.423432\pi\) | ||||
0.238232 | + | 0.971208i | \(0.423432\pi\) | |||||||
\(992\) | 4099.46 | 0.131208 | ||||||||
\(993\) | 10897.8 | 0.348270 | ||||||||
\(994\) | −109412. | −3.49128 | ||||||||
\(995\) | −930.178 | −0.0296368 | ||||||||
\(996\) | −50126.1 | −1.59468 | ||||||||
\(997\) | 47590.6 | 1.51174 | 0.755872 | − | 0.654720i | \(-0.227213\pi\) | ||||
0.755872 | + | 0.654720i | \(0.227213\pi\) | |||||||
\(998\) | −32567.2 | −1.03296 | ||||||||
\(999\) | −36419.6 | −1.15342 |
(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.k.1.8 | 60 | ||
43.3 | odd | 42 | 43.4.g.a.9.9 | ✓ | 120 | ||
43.29 | odd | 42 | 43.4.g.a.24.9 | yes | 120 | ||
43.42 | odd | 2 | 1849.4.a.l.1.53 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.g.a.9.9 | ✓ | 120 | 43.3 | odd | 42 | ||
43.4.g.a.24.9 | yes | 120 | 43.29 | odd | 42 | ||
1849.4.a.k.1.8 | 60 | 1.1 | even | 1 | trivial | ||
1849.4.a.l.1.53 | 60 | 43.42 | odd | 2 |