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 | 1.22 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.02286 | −0.361635 | −0.180818 | − | 0.983517i | \(-0.557874\pi\) | ||||
−0.180818 | + | 0.983517i | \(0.557874\pi\) | |||||||
\(3\) | 1.11016 | 0.213651 | 0.106825 | − | 0.994278i | \(-0.465931\pi\) | ||||
0.106825 | + | 0.994278i | \(0.465931\pi\) | |||||||
\(4\) | −6.95376 | −0.869220 | ||||||||
\(5\) | 17.8254 | 1.59435 | 0.797177 | − | 0.603746i | \(-0.206326\pi\) | ||||
0.797177 | + | 0.603746i | \(0.206326\pi\) | |||||||
\(6\) | −1.13554 | −0.0772636 | ||||||||
\(7\) | 19.7420 | 1.06597 | 0.532985 | − | 0.846125i | \(-0.321070\pi\) | ||||
0.532985 | + | 0.846125i | \(0.321070\pi\) | |||||||
\(8\) | 15.2956 | 0.675976 | ||||||||
\(9\) | −25.7675 | −0.954353 | ||||||||
\(10\) | −18.2329 | −0.576575 | ||||||||
\(11\) | 22.7928 | 0.624754 | 0.312377 | − | 0.949958i | \(-0.398875\pi\) | ||||
0.312377 | + | 0.949958i | \(0.398875\pi\) | |||||||
\(12\) | −7.71979 | −0.185709 | ||||||||
\(13\) | 19.7572 | 0.421513 | 0.210757 | − | 0.977539i | \(-0.432407\pi\) | ||||
0.210757 | + | 0.977539i | \(0.432407\pi\) | |||||||
\(14\) | −20.1933 | −0.385493 | ||||||||
\(15\) | 19.7891 | 0.340634 | ||||||||
\(16\) | 39.9848 | 0.624763 | ||||||||
\(17\) | −101.707 | −1.45103 | −0.725515 | − | 0.688206i | \(-0.758399\pi\) | ||||
−0.725515 | + | 0.688206i | \(0.758399\pi\) | |||||||
\(18\) | 26.3566 | 0.345128 | ||||||||
\(19\) | −71.2415 | −0.860206 | −0.430103 | − | 0.902780i | \(-0.641523\pi\) | ||||
−0.430103 | + | 0.902780i | \(0.641523\pi\) | |||||||
\(20\) | −123.954 | −1.38584 | ||||||||
\(21\) | 21.9168 | 0.227745 | ||||||||
\(22\) | −23.3139 | −0.225933 | ||||||||
\(23\) | 39.5390 | 0.358454 | 0.179227 | − | 0.983808i | \(-0.442640\pi\) | ||||
0.179227 | + | 0.983808i | \(0.442640\pi\) | |||||||
\(24\) | 16.9806 | 0.144423 | ||||||||
\(25\) | 192.745 | 1.54196 | ||||||||
\(26\) | −20.2089 | −0.152434 | ||||||||
\(27\) | −58.5805 | −0.417549 | ||||||||
\(28\) | −137.281 | −0.926562 | ||||||||
\(29\) | −100.371 | −0.642703 | −0.321351 | − | 0.946960i | \(-0.604137\pi\) | ||||
−0.321351 | + | 0.946960i | \(0.604137\pi\) | |||||||
\(30\) | −20.2414 | −0.123186 | ||||||||
\(31\) | 188.118 | 1.08990 | 0.544951 | − | 0.838468i | \(-0.316548\pi\) | ||||
0.544951 | + | 0.838468i | \(0.316548\pi\) | |||||||
\(32\) | −163.264 | −0.901913 | ||||||||
\(33\) | 25.3037 | 0.133479 | ||||||||
\(34\) | 104.032 | 0.524744 | ||||||||
\(35\) | 351.910 | 1.69953 | ||||||||
\(36\) | 179.181 | 0.829543 | ||||||||
\(37\) | −431.553 | −1.91748 | −0.958741 | − | 0.284282i | \(-0.908245\pi\) | ||||
−0.958741 | + | 0.284282i | \(0.908245\pi\) | |||||||
\(38\) | 72.8700 | 0.311081 | ||||||||
\(39\) | 21.9337 | 0.0900565 | ||||||||
\(40\) | 272.650 | 1.07775 | ||||||||
\(41\) | −388.086 | −1.47827 | −0.739133 | − | 0.673560i | \(-0.764764\pi\) | ||||
−0.739133 | + | 0.673560i | \(0.764764\pi\) | |||||||
\(42\) | −22.4178 | −0.0823607 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −158.496 | −0.543049 | ||||||||
\(45\) | −459.317 | −1.52158 | ||||||||
\(46\) | −40.4428 | −0.129630 | ||||||||
\(47\) | −444.898 | −1.38075 | −0.690373 | − | 0.723453i | \(-0.742554\pi\) | ||||
−0.690373 | + | 0.723453i | \(0.742554\pi\) | |||||||
\(48\) | 44.3896 | 0.133481 | ||||||||
\(49\) | 46.7482 | 0.136292 | ||||||||
\(50\) | −197.151 | −0.557629 | ||||||||
\(51\) | −112.911 | −0.310014 | ||||||||
\(52\) | −137.387 | −0.366388 | ||||||||
\(53\) | −561.950 | −1.45641 | −0.728206 | − | 0.685359i | \(-0.759645\pi\) | ||||
−0.728206 | + | 0.685359i | \(0.759645\pi\) | |||||||
\(54\) | 59.9196 | 0.151000 | ||||||||
\(55\) | 406.292 | 0.996079 | ||||||||
\(56\) | 301.966 | 0.720570 | ||||||||
\(57\) | −79.0895 | −0.183783 | ||||||||
\(58\) | 102.665 | 0.232424 | ||||||||
\(59\) | −582.977 | −1.28639 | −0.643196 | − | 0.765702i | \(-0.722392\pi\) | ||||
−0.643196 | + | 0.765702i | \(0.722392\pi\) | |||||||
\(60\) | −137.608 | −0.296086 | ||||||||
\(61\) | −490.093 | −1.02869 | −0.514344 | − | 0.857584i | \(-0.671964\pi\) | ||||
−0.514344 | + | 0.857584i | \(0.671964\pi\) | |||||||
\(62\) | −192.418 | −0.394147 | ||||||||
\(63\) | −508.704 | −1.01731 | ||||||||
\(64\) | −152.883 | −0.298599 | ||||||||
\(65\) | 352.181 | 0.672041 | ||||||||
\(66\) | −25.8821 | −0.0482708 | ||||||||
\(67\) | 638.092 | 1.16351 | 0.581756 | − | 0.813363i | \(-0.302366\pi\) | ||||
0.581756 | + | 0.813363i | \(0.302366\pi\) | |||||||
\(68\) | 707.245 | 1.26126 | ||||||||
\(69\) | 43.8946 | 0.0765839 | ||||||||
\(70\) | −359.955 | −0.614611 | ||||||||
\(71\) | −37.3436 | −0.0624207 | −0.0312103 | − | 0.999513i | \(-0.509936\pi\) | ||||
−0.0312103 | + | 0.999513i | \(0.509936\pi\) | |||||||
\(72\) | −394.130 | −0.645120 | ||||||||
\(73\) | 504.541 | 0.808933 | 0.404466 | − | 0.914553i | \(-0.367457\pi\) | ||||
0.404466 | + | 0.914553i | \(0.367457\pi\) | |||||||
\(74\) | 441.418 | 0.693429 | ||||||||
\(75\) | 213.978 | 0.329441 | ||||||||
\(76\) | 495.396 | 0.747708 | ||||||||
\(77\) | 449.977 | 0.665969 | ||||||||
\(78\) | −22.4351 | −0.0325676 | ||||||||
\(79\) | 690.289 | 0.983084 | 0.491542 | − | 0.870854i | \(-0.336433\pi\) | ||||
0.491542 | + | 0.870854i | \(0.336433\pi\) | |||||||
\(80\) | 712.746 | 0.996093 | ||||||||
\(81\) | 630.690 | 0.865144 | ||||||||
\(82\) | 396.958 | 0.534593 | ||||||||
\(83\) | −112.701 | −0.149043 | −0.0745216 | − | 0.997219i | \(-0.523743\pi\) | ||||
−0.0745216 | + | 0.997219i | \(0.523743\pi\) | |||||||
\(84\) | −152.404 | −0.197961 | ||||||||
\(85\) | −1812.97 | −2.31346 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −111.428 | −0.137314 | ||||||||
\(88\) | 348.630 | 0.422319 | ||||||||
\(89\) | −772.926 | −0.920562 | −0.460281 | − | 0.887773i | \(-0.652251\pi\) | ||||
−0.460281 | + | 0.887773i | \(0.652251\pi\) | |||||||
\(90\) | 469.817 | 0.550256 | ||||||||
\(91\) | 390.048 | 0.449321 | ||||||||
\(92\) | −274.945 | −0.311576 | ||||||||
\(93\) | 208.841 | 0.232858 | ||||||||
\(94\) | 455.068 | 0.499327 | ||||||||
\(95\) | −1269.91 | −1.37147 | ||||||||
\(96\) | −181.249 | −0.192694 | ||||||||
\(97\) | −403.914 | −0.422797 | −0.211398 | − | 0.977400i | \(-0.567802\pi\) | ||||
−0.211398 | + | 0.977400i | \(0.567802\pi\) | |||||||
\(98\) | −47.8168 | −0.0492881 | ||||||||
\(99\) | −587.315 | −0.596236 | ||||||||
\(100\) | −1340.30 | −1.34030 | ||||||||
\(101\) | −550.505 | −0.542350 | −0.271175 | − | 0.962530i | \(-0.587412\pi\) | ||||
−0.271175 | + | 0.962530i | \(0.587412\pi\) | |||||||
\(102\) | 115.492 | 0.112112 | ||||||||
\(103\) | 1818.49 | 1.73962 | 0.869812 | − | 0.493384i | \(-0.164240\pi\) | ||||
0.869812 | + | 0.493384i | \(0.164240\pi\) | |||||||
\(104\) | 302.199 | 0.284933 | ||||||||
\(105\) | 390.677 | 0.363106 | ||||||||
\(106\) | 574.796 | 0.526690 | ||||||||
\(107\) | 78.4386 | 0.0708686 | 0.0354343 | − | 0.999372i | \(-0.488719\pi\) | ||||
0.0354343 | + | 0.999372i | \(0.488719\pi\) | |||||||
\(108\) | 407.354 | 0.362942 | ||||||||
\(109\) | −157.371 | −0.138288 | −0.0691440 | − | 0.997607i | \(-0.522027\pi\) | ||||
−0.0691440 | + | 0.997607i | \(0.522027\pi\) | |||||||
\(110\) | −415.579 | −0.360218 | ||||||||
\(111\) | −479.093 | −0.409671 | ||||||||
\(112\) | 789.382 | 0.665978 | ||||||||
\(113\) | −348.983 | −0.290527 | −0.145263 | − | 0.989393i | \(-0.546403\pi\) | ||||
−0.145263 | + | 0.989393i | \(0.546403\pi\) | |||||||
\(114\) | 80.8974 | 0.0664626 | ||||||||
\(115\) | 704.799 | 0.571503 | ||||||||
\(116\) | 697.954 | 0.558650 | ||||||||
\(117\) | −509.096 | −0.402273 | ||||||||
\(118\) | 596.304 | 0.465205 | ||||||||
\(119\) | −2007.90 | −1.54676 | ||||||||
\(120\) | 302.686 | 0.230261 | ||||||||
\(121\) | −811.487 | −0.609682 | ||||||||
\(122\) | 501.296 | 0.372010 | ||||||||
\(123\) | −430.838 | −0.315832 | ||||||||
\(124\) | −1308.12 | −0.947364 | ||||||||
\(125\) | 1207.59 | 0.864081 | ||||||||
\(126\) | 520.333 | 0.367896 | ||||||||
\(127\) | 1286.15 | 0.898643 | 0.449322 | − | 0.893370i | \(-0.351666\pi\) | ||||
0.449322 | + | 0.893370i | \(0.351666\pi\) | |||||||
\(128\) | 1462.49 | 1.00990 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −360.232 | −0.243034 | ||||||||
\(131\) | 2694.05 | 1.79680 | 0.898399 | − | 0.439181i | \(-0.144731\pi\) | ||||
0.898399 | + | 0.439181i | \(0.144731\pi\) | |||||||
\(132\) | −175.956 | −0.116023 | ||||||||
\(133\) | −1406.45 | −0.916954 | ||||||||
\(134\) | −652.678 | −0.420767 | ||||||||
\(135\) | −1044.22 | −0.665720 | ||||||||
\(136\) | −1555.67 | −0.980862 | ||||||||
\(137\) | 21.0377 | 0.0131195 | 0.00655976 | − | 0.999978i | \(-0.497912\pi\) | ||||
0.00655976 | + | 0.999978i | \(0.497912\pi\) | |||||||
\(138\) | −44.8980 | −0.0276955 | ||||||||
\(139\) | 3054.31 | 1.86376 | 0.931882 | − | 0.362761i | \(-0.118166\pi\) | ||||
0.931882 | + | 0.362761i | \(0.118166\pi\) | |||||||
\(140\) | −2447.10 | −1.47727 | ||||||||
\(141\) | −493.909 | −0.294997 | ||||||||
\(142\) | 38.1973 | 0.0225735 | ||||||||
\(143\) | 450.323 | 0.263342 | ||||||||
\(144\) | −1030.31 | −0.596245 | ||||||||
\(145\) | −1789.15 | −1.02470 | ||||||||
\(146\) | −516.075 | −0.292539 | ||||||||
\(147\) | 51.8980 | 0.0291189 | ||||||||
\(148\) | 3000.91 | 1.66671 | ||||||||
\(149\) | −1300.51 | −0.715047 | −0.357524 | − | 0.933904i | \(-0.616379\pi\) | ||||
−0.357524 | + | 0.933904i | \(0.616379\pi\) | |||||||
\(150\) | −218.870 | −0.119138 | ||||||||
\(151\) | −1123.62 | −0.605556 | −0.302778 | − | 0.953061i | \(-0.597914\pi\) | ||||
−0.302778 | + | 0.953061i | \(0.597914\pi\) | |||||||
\(152\) | −1089.68 | −0.581479 | ||||||||
\(153\) | 2620.73 | 1.38480 | ||||||||
\(154\) | −460.263 | −0.240838 | ||||||||
\(155\) | 3353.28 | 1.73769 | ||||||||
\(156\) | −152.522 | −0.0782789 | ||||||||
\(157\) | 2420.82 | 1.23059 | 0.615294 | − | 0.788298i | \(-0.289037\pi\) | ||||
0.615294 | + | 0.788298i | \(0.289037\pi\) | |||||||
\(158\) | −706.069 | −0.355518 | ||||||||
\(159\) | −623.855 | −0.311163 | ||||||||
\(160\) | −2910.24 | −1.43797 | ||||||||
\(161\) | 780.580 | 0.382102 | ||||||||
\(162\) | −645.107 | −0.312867 | ||||||||
\(163\) | −2633.91 | −1.26567 | −0.632834 | − | 0.774288i | \(-0.718108\pi\) | ||||
−0.632834 | + | 0.774288i | \(0.718108\pi\) | |||||||
\(164\) | 2698.66 | 1.28494 | ||||||||
\(165\) | 451.049 | 0.212813 | ||||||||
\(166\) | 115.278 | 0.0538993 | ||||||||
\(167\) | −2477.45 | −1.14797 | −0.573984 | − | 0.818866i | \(-0.694603\pi\) | ||||
−0.573984 | + | 0.818866i | \(0.694603\pi\) | |||||||
\(168\) | 335.231 | 0.153950 | ||||||||
\(169\) | −1806.65 | −0.822327 | ||||||||
\(170\) | 1854.41 | 0.836628 | ||||||||
\(171\) | 1835.72 | 0.820941 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1641.92 | 0.721575 | 0.360788 | − | 0.932648i | \(-0.382508\pi\) | ||||
0.360788 | + | 0.932648i | \(0.382508\pi\) | |||||||
\(174\) | 113.975 | 0.0496575 | ||||||||
\(175\) | 3805.19 | 1.64369 | ||||||||
\(176\) | 911.367 | 0.390323 | ||||||||
\(177\) | −647.198 | −0.274838 | ||||||||
\(178\) | 790.595 | 0.332908 | ||||||||
\(179\) | 197.274 | 0.0823742 | 0.0411871 | − | 0.999151i | \(-0.486886\pi\) | ||||
0.0411871 | + | 0.999151i | \(0.486886\pi\) | |||||||
\(180\) | 3193.98 | 1.32258 | ||||||||
\(181\) | −2120.28 | −0.870714 | −0.435357 | − | 0.900258i | \(-0.643378\pi\) | ||||
−0.435357 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(182\) | −398.965 | −0.162490 | ||||||||
\(183\) | −544.081 | −0.219780 | ||||||||
\(184\) | 604.772 | 0.242307 | ||||||||
\(185\) | −7692.61 | −3.05714 | ||||||||
\(186\) | −213.615 | −0.0842097 | ||||||||
\(187\) | −2318.19 | −0.906538 | ||||||||
\(188\) | 3093.71 | 1.20017 | ||||||||
\(189\) | −1156.50 | −0.445094 | ||||||||
\(190\) | 1298.94 | 0.495973 | ||||||||
\(191\) | −3247.98 | −1.23045 | −0.615223 | − | 0.788353i | \(-0.710934\pi\) | ||||
−0.615223 | + | 0.788353i | \(0.710934\pi\) | |||||||
\(192\) | −169.724 | −0.0637959 | ||||||||
\(193\) | 4635.04 | 1.72869 | 0.864345 | − | 0.502899i | \(-0.167733\pi\) | ||||
0.864345 | + | 0.502899i | \(0.167733\pi\) | |||||||
\(194\) | 413.147 | 0.152898 | ||||||||
\(195\) | 390.978 | 0.143582 | ||||||||
\(196\) | −325.076 | −0.118468 | ||||||||
\(197\) | −2130.99 | −0.770695 | −0.385348 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385348 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(198\) | 600.741 | 0.215620 | ||||||||
\(199\) | −3441.83 | −1.22605 | −0.613027 | − | 0.790062i | \(-0.710048\pi\) | ||||
−0.613027 | + | 0.790062i | \(0.710048\pi\) | |||||||
\(200\) | 2948.16 | 1.04233 | ||||||||
\(201\) | 708.385 | 0.248585 | ||||||||
\(202\) | 563.090 | 0.196133 | ||||||||
\(203\) | −1981.52 | −0.685102 | ||||||||
\(204\) | 785.155 | 0.269470 | ||||||||
\(205\) | −6917.80 | −2.35688 | ||||||||
\(206\) | −1860.06 | −0.629110 | ||||||||
\(207\) | −1018.82 | −0.342092 | ||||||||
\(208\) | 789.990 | 0.263346 | ||||||||
\(209\) | −1623.80 | −0.537417 | ||||||||
\(210\) | −399.607 | −0.131312 | ||||||||
\(211\) | 1835.67 | 0.598922 | 0.299461 | − | 0.954109i | \(-0.403193\pi\) | ||||
0.299461 | + | 0.954109i | \(0.403193\pi\) | |||||||
\(212\) | 3907.67 | 1.26594 | ||||||||
\(213\) | −41.4574 | −0.0133362 | ||||||||
\(214\) | −80.2317 | −0.0256286 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −896.023 | −0.282253 | ||||||||
\(217\) | 3713.83 | 1.16180 | ||||||||
\(218\) | 160.968 | 0.0500098 | ||||||||
\(219\) | 560.122 | 0.172829 | ||||||||
\(220\) | −2825.25 | −0.865812 | ||||||||
\(221\) | −2009.45 | −0.611629 | ||||||||
\(222\) | 490.045 | 0.148152 | ||||||||
\(223\) | −2382.48 | −0.715438 | −0.357719 | − | 0.933829i | \(-0.616445\pi\) | ||||
−0.357719 | + | 0.933829i | \(0.616445\pi\) | |||||||
\(224\) | −3223.16 | −0.961412 | ||||||||
\(225\) | −4966.58 | −1.47158 | ||||||||
\(226\) | 356.960 | 0.105065 | ||||||||
\(227\) | −1427.19 | −0.417294 | −0.208647 | − | 0.977991i | \(-0.566906\pi\) | ||||
−0.208647 | + | 0.977991i | \(0.566906\pi\) | |||||||
\(228\) | 549.969 | 0.159748 | ||||||||
\(229\) | −3610.07 | −1.04175 | −0.520874 | − | 0.853634i | \(-0.674394\pi\) | ||||
−0.520874 | + | 0.853634i | \(0.674394\pi\) | |||||||
\(230\) | −720.910 | −0.206676 | ||||||||
\(231\) | 499.547 | 0.142285 | ||||||||
\(232\) | −1535.23 | −0.434452 | ||||||||
\(233\) | 844.802 | 0.237532 | 0.118766 | − | 0.992922i | \(-0.462106\pi\) | ||||
0.118766 | + | 0.992922i | \(0.462106\pi\) | |||||||
\(234\) | 520.733 | 0.145476 | ||||||||
\(235\) | −7930.50 | −2.20140 | ||||||||
\(236\) | 4053.88 | 1.11816 | ||||||||
\(237\) | 766.332 | 0.210036 | ||||||||
\(238\) | 2053.80 | 0.559362 | ||||||||
\(239\) | 3678.94 | 0.995693 | 0.497846 | − | 0.867265i | \(-0.334124\pi\) | ||||
0.497846 | + | 0.867265i | \(0.334124\pi\) | |||||||
\(240\) | 791.263 | 0.212816 | ||||||||
\(241\) | 2907.74 | 0.777194 | 0.388597 | − | 0.921408i | \(-0.372960\pi\) | ||||
0.388597 | + | 0.921408i | \(0.372960\pi\) | |||||||
\(242\) | 830.037 | 0.220483 | ||||||||
\(243\) | 2281.84 | 0.602387 | ||||||||
\(244\) | 3407.98 | 0.894155 | ||||||||
\(245\) | 833.306 | 0.217298 | ||||||||
\(246\) | 440.687 | 0.114216 | ||||||||
\(247\) | −1407.54 | −0.362588 | ||||||||
\(248\) | 2877.37 | 0.736747 | ||||||||
\(249\) | −125.117 | −0.0318432 | ||||||||
\(250\) | −1235.20 | −0.312482 | ||||||||
\(251\) | 7305.43 | 1.83711 | 0.918555 | − | 0.395294i | \(-0.129357\pi\) | ||||
0.918555 | + | 0.395294i | \(0.129357\pi\) | |||||||
\(252\) | 3537.40 | 0.884268 | ||||||||
\(253\) | 901.205 | 0.223946 | ||||||||
\(254\) | −1315.56 | −0.324981 | ||||||||
\(255\) | −2012.68 | −0.494271 | ||||||||
\(256\) | −272.856 | −0.0666153 | ||||||||
\(257\) | −1564.64 | −0.379765 | −0.189882 | − | 0.981807i | \(-0.560811\pi\) | ||||
−0.189882 | + | 0.981807i | \(0.560811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8519.73 | −2.04398 | ||||||||
\(260\) | −2448.98 | −0.584151 | ||||||||
\(261\) | 2586.31 | 0.613365 | ||||||||
\(262\) | −2755.64 | −0.649786 | ||||||||
\(263\) | −1714.84 | −0.402060 | −0.201030 | − | 0.979585i | \(-0.564429\pi\) | ||||
−0.201030 | + | 0.979585i | \(0.564429\pi\) | |||||||
\(264\) | 387.035 | 0.0902287 | ||||||||
\(265\) | −10017.0 | −2.32203 | ||||||||
\(266\) | 1438.60 | 0.331603 | ||||||||
\(267\) | −858.072 | −0.196678 | ||||||||
\(268\) | −4437.14 | −1.01135 | ||||||||
\(269\) | −5451.01 | −1.23552 | −0.617758 | − | 0.786368i | \(-0.711959\pi\) | ||||
−0.617758 | + | 0.786368i | \(0.711959\pi\) | |||||||
\(270\) | 1068.09 | 0.240748 | ||||||||
\(271\) | −1315.31 | −0.294832 | −0.147416 | − | 0.989075i | \(-0.547096\pi\) | ||||
−0.147416 | + | 0.989075i | \(0.547096\pi\) | |||||||
\(272\) | −4066.73 | −0.906550 | ||||||||
\(273\) | 433.016 | 0.0959976 | ||||||||
\(274\) | −21.5186 | −0.00474448 | ||||||||
\(275\) | 4393.21 | 0.963348 | ||||||||
\(276\) | −305.233 | −0.0665683 | ||||||||
\(277\) | −2640.70 | −0.572795 | −0.286398 | − | 0.958111i | \(-0.592458\pi\) | ||||
−0.286398 | + | 0.958111i | \(0.592458\pi\) | |||||||
\(278\) | −3124.13 | −0.674003 | ||||||||
\(279\) | −4847.33 | −1.04015 | ||||||||
\(280\) | 5382.67 | 1.14884 | ||||||||
\(281\) | −4294.12 | −0.911621 | −0.455811 | − | 0.890077i | \(-0.650651\pi\) | ||||
−0.455811 | + | 0.890077i | \(0.650651\pi\) | |||||||
\(282\) | 505.199 | 0.106681 | ||||||||
\(283\) | −3322.87 | −0.697965 | −0.348983 | − | 0.937129i | \(-0.613473\pi\) | ||||
−0.348983 | + | 0.937129i | \(0.613473\pi\) | |||||||
\(284\) | 259.678 | 0.0542573 | ||||||||
\(285\) | −1409.80 | −0.293016 | ||||||||
\(286\) | −460.618 | −0.0952339 | ||||||||
\(287\) | −7661.62 | −1.57579 | ||||||||
\(288\) | 4206.90 | 0.860743 | ||||||||
\(289\) | 5431.28 | 1.10549 | ||||||||
\(290\) | 1830.05 | 0.370566 | ||||||||
\(291\) | −448.410 | −0.0903307 | ||||||||
\(292\) | −3508.46 | −0.703141 | ||||||||
\(293\) | −190.708 | −0.0380249 | −0.0190125 | − | 0.999819i | \(-0.506052\pi\) | ||||
−0.0190125 | + | 0.999819i | \(0.506052\pi\) | |||||||
\(294\) | −53.0844 | −0.0105304 | ||||||||
\(295\) | −10391.8 | −2.05096 | ||||||||
\(296\) | −6600.86 | −1.29617 | ||||||||
\(297\) | −1335.21 | −0.260865 | ||||||||
\(298\) | 1330.24 | 0.258586 | ||||||||
\(299\) | 781.181 | 0.151093 | ||||||||
\(300\) | −1487.95 | −0.286357 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1149.31 | 0.218990 | ||||||||
\(303\) | −611.149 | −0.115873 | ||||||||
\(304\) | −2848.58 | −0.537425 | ||||||||
\(305\) | −8736.10 | −1.64009 | ||||||||
\(306\) | −2680.64 | −0.500792 | ||||||||
\(307\) | 4341.31 | 0.807073 | 0.403536 | − | 0.914964i | \(-0.367781\pi\) | ||||
0.403536 | + | 0.914964i | \(0.367781\pi\) | |||||||
\(308\) | −3129.03 | −0.578874 | ||||||||
\(309\) | 2018.82 | 0.371672 | ||||||||
\(310\) | −3429.93 | −0.628410 | ||||||||
\(311\) | −6092.04 | −1.11077 | −0.555383 | − | 0.831595i | \(-0.687428\pi\) | ||||
−0.555383 | + | 0.831595i | \(0.687428\pi\) | |||||||
\(312\) | 335.489 | 0.0608761 | ||||||||
\(313\) | 5612.18 | 1.01348 | 0.506740 | − | 0.862099i | \(-0.330851\pi\) | ||||
0.506740 | + | 0.862099i | \(0.330851\pi\) | |||||||
\(314\) | −2476.16 | −0.445024 | ||||||||
\(315\) | −9067.86 | −1.62196 | ||||||||
\(316\) | −4800.10 | −0.854516 | ||||||||
\(317\) | −3963.80 | −0.702299 | −0.351150 | − | 0.936319i | \(-0.614209\pi\) | ||||
−0.351150 | + | 0.936319i | \(0.614209\pi\) | |||||||
\(318\) | 638.116 | 0.112528 | ||||||||
\(319\) | −2287.73 | −0.401531 | ||||||||
\(320\) | −2725.20 | −0.476073 | ||||||||
\(321\) | 87.0794 | 0.0151411 | ||||||||
\(322\) | −798.424 | −0.138181 | ||||||||
\(323\) | 7245.74 | 1.24819 | ||||||||
\(324\) | −4385.67 | −0.752000 | ||||||||
\(325\) | 3808.12 | 0.649958 | ||||||||
\(326\) | 2694.12 | 0.457710 | ||||||||
\(327\) | −174.707 | −0.0295453 | ||||||||
\(328\) | −5936.01 | −0.999273 | ||||||||
\(329\) | −8783.20 | −1.47183 | ||||||||
\(330\) | −461.360 | −0.0769607 | ||||||||
\(331\) | 9099.39 | 1.51102 | 0.755510 | − | 0.655137i | \(-0.227389\pi\) | ||||
0.755510 | + | 0.655137i | \(0.227389\pi\) | |||||||
\(332\) | 783.698 | 0.129551 | ||||||||
\(333\) | 11120.1 | 1.82996 | ||||||||
\(334\) | 2534.08 | 0.415146 | ||||||||
\(335\) | 11374.3 | 1.85505 | ||||||||
\(336\) | 876.341 | 0.142287 | ||||||||
\(337\) | −2484.89 | −0.401663 | −0.200832 | − | 0.979626i | \(-0.564364\pi\) | ||||
−0.200832 | + | 0.979626i | \(0.564364\pi\) | |||||||
\(338\) | 1847.95 | 0.297382 | ||||||||
\(339\) | −387.427 | −0.0620712 | ||||||||
\(340\) | 12606.9 | 2.01090 | ||||||||
\(341\) | 4287.73 | 0.680920 | ||||||||
\(342\) | −1877.68 | −0.296881 | ||||||||
\(343\) | −5848.62 | −0.920687 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 782.440 | 0.122102 | ||||||||
\(346\) | −1679.45 | −0.260947 | ||||||||
\(347\) | −9452.41 | −1.46234 | −0.731170 | − | 0.682196i | \(-0.761025\pi\) | ||||
−0.731170 | + | 0.682196i | \(0.761025\pi\) | |||||||
\(348\) | 774.841 | 0.119356 | ||||||||
\(349\) | 2929.71 | 0.449352 | 0.224676 | − | 0.974434i | \(-0.427868\pi\) | ||||
0.224676 | + | 0.974434i | \(0.427868\pi\) | |||||||
\(350\) | −3892.17 | −0.594415 | ||||||||
\(351\) | −1157.39 | −0.176002 | ||||||||
\(352\) | −3721.24 | −0.563474 | ||||||||
\(353\) | 1497.90 | 0.225851 | 0.112926 | − | 0.993603i | \(-0.463978\pi\) | ||||
0.112926 | + | 0.993603i | \(0.463978\pi\) | |||||||
\(354\) | 661.993 | 0.0993913 | ||||||||
\(355\) | −665.665 | −0.0995207 | ||||||||
\(356\) | 5374.74 | 0.800170 | ||||||||
\(357\) | −2229.09 | −0.330465 | ||||||||
\(358\) | −201.784 | −0.0297894 | ||||||||
\(359\) | 11573.3 | 1.70144 | 0.850721 | − | 0.525618i | \(-0.176166\pi\) | ||||
0.850721 | + | 0.525618i | \(0.176166\pi\) | |||||||
\(360\) | −7025.53 | −1.02855 | ||||||||
\(361\) | −1783.65 | −0.260045 | ||||||||
\(362\) | 2168.75 | 0.314881 | ||||||||
\(363\) | −900.881 | −0.130259 | ||||||||
\(364\) | −2712.30 | −0.390558 | ||||||||
\(365\) | 8993.66 | 1.28973 | ||||||||
\(366\) | 556.519 | 0.0794801 | ||||||||
\(367\) | −3815.58 | −0.542702 | −0.271351 | − | 0.962480i | \(-0.587470\pi\) | ||||
−0.271351 | + | 0.962480i | \(0.587470\pi\) | |||||||
\(368\) | 1580.96 | 0.223949 | ||||||||
\(369\) | 10000.0 | 1.41079 | ||||||||
\(370\) | 7868.46 | 1.10557 | ||||||||
\(371\) | −11094.0 | −1.55249 | ||||||||
\(372\) | −1452.23 | −0.202405 | ||||||||
\(373\) | −1969.77 | −0.273434 | −0.136717 | − | 0.990610i | \(-0.543655\pi\) | ||||
−0.136717 | + | 0.990610i | \(0.543655\pi\) | |||||||
\(374\) | 2371.18 | 0.327836 | ||||||||
\(375\) | 1340.62 | 0.184611 | ||||||||
\(376\) | −6804.98 | −0.933352 | ||||||||
\(377\) | −1983.05 | −0.270908 | ||||||||
\(378\) | 1182.93 | 0.160962 | ||||||||
\(379\) | 1267.89 | 0.171839 | 0.0859194 | − | 0.996302i | \(-0.472617\pi\) | ||||
0.0859194 | + | 0.996302i | \(0.472617\pi\) | |||||||
\(380\) | 8830.64 | 1.19211 | ||||||||
\(381\) | 1427.84 | 0.191996 | ||||||||
\(382\) | 3322.22 | 0.444973 | ||||||||
\(383\) | 2523.67 | 0.336694 | 0.168347 | − | 0.985728i | \(-0.446157\pi\) | ||||
0.168347 | + | 0.985728i | \(0.446157\pi\) | |||||||
\(384\) | 1623.60 | 0.215765 | ||||||||
\(385\) | 8021.03 | 1.06179 | ||||||||
\(386\) | −4740.99 | −0.625156 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2808.72 | 0.367503 | ||||||||
\(389\) | 12576.9 | 1.63926 | 0.819631 | − | 0.572892i | \(-0.194179\pi\) | ||||
0.819631 | + | 0.572892i | \(0.194179\pi\) | |||||||
\(390\) | −399.915 | −0.0519243 | ||||||||
\(391\) | −4021.38 | −0.520128 | ||||||||
\(392\) | 715.041 | 0.0921302 | ||||||||
\(393\) | 2990.83 | 0.383887 | ||||||||
\(394\) | 2179.71 | 0.278711 | ||||||||
\(395\) | 12304.7 | 1.56738 | ||||||||
\(396\) | 4084.05 | 0.518260 | ||||||||
\(397\) | −6253.88 | −0.790613 | −0.395306 | − | 0.918549i | \(-0.629362\pi\) | ||||
−0.395306 | + | 0.918549i | \(0.629362\pi\) | |||||||
\(398\) | 3520.51 | 0.443384 | ||||||||
\(399\) | −1561.39 | −0.195908 | ||||||||
\(400\) | 7706.89 | 0.963361 | ||||||||
\(401\) | 1382.58 | 0.172177 | 0.0860883 | − | 0.996288i | \(-0.472563\pi\) | ||||
0.0860883 | + | 0.996288i | \(0.472563\pi\) | |||||||
\(402\) | −724.578 | −0.0898972 | ||||||||
\(403\) | 3716.69 | 0.459408 | ||||||||
\(404\) | 3828.08 | 0.471421 | ||||||||
\(405\) | 11242.3 | 1.37935 | ||||||||
\(406\) | 2026.82 | 0.247757 | ||||||||
\(407\) | −9836.31 | −1.19795 | ||||||||
\(408\) | −1727.04 | −0.209562 | ||||||||
\(409\) | −13695.7 | −1.65577 | −0.827885 | − | 0.560899i | \(-0.810456\pi\) | ||||
−0.827885 | + | 0.560899i | \(0.810456\pi\) | |||||||
\(410\) | 7075.94 | 0.852331 | ||||||||
\(411\) | 23.3552 | 0.00280299 | ||||||||
\(412\) | −12645.3 | −1.51212 | ||||||||
\(413\) | −11509.2 | −1.37126 | ||||||||
\(414\) | 1042.11 | 0.123713 | ||||||||
\(415\) | −2008.95 | −0.237628 | ||||||||
\(416\) | −3225.64 | −0.380168 | ||||||||
\(417\) | 3390.78 | 0.398194 | ||||||||
\(418\) | 1660.91 | 0.194349 | ||||||||
\(419\) | 10610.7 | 1.23715 | 0.618573 | − | 0.785727i | \(-0.287711\pi\) | ||||
0.618573 | + | 0.785727i | \(0.287711\pi\) | |||||||
\(420\) | −2716.67 | −0.315619 | ||||||||
\(421\) | −2110.80 | −0.244357 | −0.122178 | − | 0.992508i | \(-0.538988\pi\) | ||||
−0.122178 | + | 0.992508i | \(0.538988\pi\) | |||||||
\(422\) | −1877.63 | −0.216592 | ||||||||
\(423\) | 11463.9 | 1.31772 | ||||||||
\(424\) | −8595.36 | −0.984499 | ||||||||
\(425\) | −19603.5 | −2.23744 | ||||||||
\(426\) | 42.4051 | 0.00482285 | ||||||||
\(427\) | −9675.43 | −1.09655 | ||||||||
\(428\) | −545.443 | −0.0616004 | ||||||||
\(429\) | 499.931 | 0.0562632 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12954.3 | 1.44777 | 0.723883 | − | 0.689922i | \(-0.242355\pi\) | ||||
0.723883 | + | 0.689922i | \(0.242355\pi\) | |||||||
\(432\) | −2342.33 | −0.260869 | ||||||||
\(433\) | 1171.99 | 0.130075 | 0.0650374 | − | 0.997883i | \(-0.479283\pi\) | ||||
0.0650374 | + | 0.997883i | \(0.479283\pi\) | |||||||
\(434\) | −3798.72 | −0.420149 | ||||||||
\(435\) | −1986.24 | −0.218927 | ||||||||
\(436\) | 1094.32 | 0.120203 | ||||||||
\(437\) | −2816.82 | −0.308345 | ||||||||
\(438\) | −572.926 | −0.0625011 | ||||||||
\(439\) | −16402.2 | −1.78322 | −0.891609 | − | 0.452807i | \(-0.850423\pi\) | ||||
−0.891609 | + | 0.452807i | \(0.850423\pi\) | |||||||
\(440\) | 6214.47 | 0.673326 | ||||||||
\(441\) | −1204.59 | −0.130071 | ||||||||
\(442\) | 2055.38 | 0.221187 | ||||||||
\(443\) | 10078.9 | 1.08096 | 0.540479 | − | 0.841358i | \(-0.318243\pi\) | ||||
0.540479 | + | 0.841358i | \(0.318243\pi\) | |||||||
\(444\) | 3331.50 | 0.356094 | ||||||||
\(445\) | −13777.7 | −1.46770 | ||||||||
\(446\) | 2436.94 | 0.258728 | ||||||||
\(447\) | −1443.78 | −0.152770 | ||||||||
\(448\) | −3018.22 | −0.318298 | ||||||||
\(449\) | 6527.47 | 0.686081 | 0.343040 | − | 0.939321i | \(-0.388543\pi\) | ||||
0.343040 | + | 0.939321i | \(0.388543\pi\) | |||||||
\(450\) | 5080.11 | 0.532175 | ||||||||
\(451\) | −8845.59 | −0.923553 | ||||||||
\(452\) | 2426.74 | 0.252532 | ||||||||
\(453\) | −1247.40 | −0.129377 | ||||||||
\(454\) | 1459.81 | 0.150908 | ||||||||
\(455\) | 6952.77 | 0.716376 | ||||||||
\(456\) | −1209.72 | −0.124233 | ||||||||
\(457\) | 5400.42 | 0.552782 | 0.276391 | − | 0.961045i | \(-0.410862\pi\) | ||||
0.276391 | + | 0.961045i | \(0.410862\pi\) | |||||||
\(458\) | 3692.60 | 0.376733 | ||||||||
\(459\) | 5958.03 | 0.605876 | ||||||||
\(460\) | −4901.00 | −0.496762 | ||||||||
\(461\) | −6304.64 | −0.636956 | −0.318478 | − | 0.947930i | \(-0.603172\pi\) | ||||
−0.318478 | + | 0.947930i | \(0.603172\pi\) | |||||||
\(462\) | −510.966 | −0.0514552 | ||||||||
\(463\) | −19243.6 | −1.93158 | −0.965792 | − | 0.259317i | \(-0.916503\pi\) | ||||
−0.965792 | + | 0.259317i | \(0.916503\pi\) | |||||||
\(464\) | −4013.30 | −0.401537 | ||||||||
\(465\) | 3722.68 | 0.371258 | ||||||||
\(466\) | −864.114 | −0.0858998 | ||||||||
\(467\) | 2714.13 | 0.268940 | 0.134470 | − | 0.990918i | \(-0.457067\pi\) | ||||
0.134470 | + | 0.990918i | \(0.457067\pi\) | |||||||
\(468\) | 3540.13 | 0.349663 | ||||||||
\(469\) | 12597.2 | 1.24027 | ||||||||
\(470\) | 8111.78 | 0.796104 | ||||||||
\(471\) | 2687.50 | 0.262916 | ||||||||
\(472\) | −8916.98 | −0.869570 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −783.850 | −0.0759566 | ||||||||
\(475\) | −13731.5 | −1.32641 | ||||||||
\(476\) | 13962.5 | 1.34447 | ||||||||
\(477\) | 14480.1 | 1.38993 | ||||||||
\(478\) | −3763.03 | −0.360078 | ||||||||
\(479\) | −11210.3 | −1.06933 | −0.534666 | − | 0.845063i | \(-0.679563\pi\) | ||||
−0.534666 | + | 0.845063i | \(0.679563\pi\) | |||||||
\(480\) | −3230.84 | −0.307223 | ||||||||
\(481\) | −8526.29 | −0.808244 | ||||||||
\(482\) | −2974.21 | −0.281061 | ||||||||
\(483\) | 866.570 | 0.0816362 | ||||||||
\(484\) | 5642.88 | 0.529948 | ||||||||
\(485\) | −7199.94 | −0.674087 | ||||||||
\(486\) | −2334.00 | −0.217845 | ||||||||
\(487\) | 8701.07 | 0.809617 | 0.404808 | − | 0.914402i | \(-0.367338\pi\) | ||||
0.404808 | + | 0.914402i | \(0.367338\pi\) | |||||||
\(488\) | −7496.26 | −0.695368 | ||||||||
\(489\) | −2924.06 | −0.270410 | ||||||||
\(490\) | −852.355 | −0.0785826 | ||||||||
\(491\) | 1624.22 | 0.149288 | 0.0746438 | − | 0.997210i | \(-0.476218\pi\) | ||||
0.0746438 | + | 0.997210i | \(0.476218\pi\) | |||||||
\(492\) | 2995.94 | 0.274528 | ||||||||
\(493\) | 10208.4 | 0.932581 | ||||||||
\(494\) | 1439.71 | 0.131125 | ||||||||
\(495\) | −10469.1 | −0.950612 | ||||||||
\(496\) | 7521.85 | 0.680930 | ||||||||
\(497\) | −737.239 | −0.0665386 | ||||||||
\(498\) | 127.977 | 0.0115156 | ||||||||
\(499\) | 14069.2 | 1.26217 | 0.631084 | − | 0.775714i | \(-0.282610\pi\) | ||||
0.631084 | + | 0.775714i | \(0.282610\pi\) | |||||||
\(500\) | −8397.29 | −0.751076 | ||||||||
\(501\) | −2750.37 | −0.245264 | ||||||||
\(502\) | −7472.43 | −0.664364 | ||||||||
\(503\) | −11488.0 | −1.01834 | −0.509170 | − | 0.860666i | \(-0.670048\pi\) | ||||
−0.509170 | + | 0.860666i | \(0.670048\pi\) | |||||||
\(504\) | −7780.93 | −0.687679 | ||||||||
\(505\) | −9812.98 | −0.864697 | ||||||||
\(506\) | −921.807 | −0.0809868 | ||||||||
\(507\) | −2005.67 | −0.175691 | ||||||||
\(508\) | −8943.60 | −0.781119 | ||||||||
\(509\) | −9359.44 | −0.815030 | −0.407515 | − | 0.913199i | \(-0.633605\pi\) | ||||
−0.407515 | + | 0.913199i | \(0.633605\pi\) | |||||||
\(510\) | 2058.69 | 0.178746 | ||||||||
\(511\) | 9960.68 | 0.862298 | ||||||||
\(512\) | −11420.8 | −0.985806 | ||||||||
\(513\) | 4173.36 | 0.359178 | ||||||||
\(514\) | 1600.41 | 0.137336 | ||||||||
\(515\) | 32415.4 | 2.77358 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10140.5 | −0.862627 | ||||||||
\(518\) | 8714.49 | 0.739175 | ||||||||
\(519\) | 1822.79 | 0.154165 | ||||||||
\(520\) | 5386.82 | 0.454284 | ||||||||
\(521\) | 1027.52 | 0.0864036 | 0.0432018 | − | 0.999066i | \(-0.486244\pi\) | ||||
0.0432018 | + | 0.999066i | \(0.486244\pi\) | |||||||
\(522\) | −2645.43 | −0.221815 | ||||||||
\(523\) | −9348.97 | −0.781648 | −0.390824 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390824 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(524\) | −18733.8 | −1.56181 | ||||||||
\(525\) | 4224.37 | 0.351175 | ||||||||
\(526\) | 1754.04 | 0.145399 | ||||||||
\(527\) | −19132.9 | −1.58148 | ||||||||
\(528\) | 1011.76 | 0.0833928 | ||||||||
\(529\) | −10603.7 | −0.871511 | ||||||||
\(530\) | 10246.0 | 0.839730 | ||||||||
\(531\) | 15021.9 | 1.22767 | ||||||||
\(532\) | 9780.13 | 0.797035 | ||||||||
\(533\) | −7667.51 | −0.623109 | ||||||||
\(534\) | 877.687 | 0.0711259 | ||||||||
\(535\) | 1398.20 | 0.112990 | ||||||||
\(536\) | 9760.00 | 0.786507 | ||||||||
\(537\) | 219.006 | 0.0175993 | ||||||||
\(538\) | 5575.61 | 0.446806 | ||||||||
\(539\) | 1065.52 | 0.0851491 | ||||||||
\(540\) | 7261.26 | 0.578657 | ||||||||
\(541\) | −19965.3 | −1.58664 | −0.793322 | − | 0.608802i | \(-0.791650\pi\) | ||||
−0.793322 | + | 0.608802i | \(0.791650\pi\) | |||||||
\(542\) | 1345.38 | 0.106622 | ||||||||
\(543\) | −2353.85 | −0.186029 | ||||||||
\(544\) | 16605.0 | 1.30870 | ||||||||
\(545\) | −2805.20 | −0.220480 | ||||||||
\(546\) | −442.915 | −0.0347161 | ||||||||
\(547\) | −15813.1 | −1.23605 | −0.618027 | − | 0.786157i | \(-0.712068\pi\) | ||||
−0.618027 | + | 0.786157i | \(0.712068\pi\) | |||||||
\(548\) | −146.291 | −0.0114037 | ||||||||
\(549\) | 12628.5 | 0.981731 | ||||||||
\(550\) | −4493.64 | −0.348381 | ||||||||
\(551\) | 7150.56 | 0.552857 | ||||||||
\(552\) | 671.394 | 0.0517689 | ||||||||
\(553\) | 13627.7 | 1.04794 | ||||||||
\(554\) | 2701.07 | 0.207143 | ||||||||
\(555\) | −8540.03 | −0.653160 | ||||||||
\(556\) | −21238.9 | −1.62002 | ||||||||
\(557\) | −3373.07 | −0.256592 | −0.128296 | − | 0.991736i | \(-0.540951\pi\) | ||||
−0.128296 | + | 0.991736i | \(0.540951\pi\) | |||||||
\(558\) | 4958.14 | 0.376155 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14071.1 | 1.06181 | ||||||||
\(561\) | −2573.56 | −0.193682 | ||||||||
\(562\) | 4392.28 | 0.329675 | ||||||||
\(563\) | 21680.8 | 1.62298 | 0.811489 | − | 0.584368i | \(-0.198657\pi\) | ||||
0.811489 | + | 0.584368i | \(0.198657\pi\) | |||||||
\(564\) | 3434.52 | 0.256417 | ||||||||
\(565\) | −6220.76 | −0.463203 | ||||||||
\(566\) | 3398.83 | 0.252409 | ||||||||
\(567\) | 12451.1 | 0.922218 | ||||||||
\(568\) | −571.193 | −0.0421949 | ||||||||
\(569\) | 3600.43 | 0.265268 | 0.132634 | − | 0.991165i | \(-0.457656\pi\) | ||||
0.132634 | + | 0.991165i | \(0.457656\pi\) | |||||||
\(570\) | 1442.03 | 0.105965 | ||||||||
\(571\) | 15694.5 | 1.15025 | 0.575126 | − | 0.818065i | \(-0.304953\pi\) | ||||
0.575126 | + | 0.818065i | \(0.304953\pi\) | |||||||
\(572\) | −3131.44 | −0.228902 | ||||||||
\(573\) | −3605.78 | −0.262886 | ||||||||
\(574\) | 7836.76 | 0.569861 | ||||||||
\(575\) | 7620.96 | 0.552723 | ||||||||
\(576\) | 3939.41 | 0.284969 | ||||||||
\(577\) | 8951.52 | 0.645852 | 0.322926 | − | 0.946424i | \(-0.395334\pi\) | ||||
0.322926 | + | 0.946424i | \(0.395334\pi\) | |||||||
\(578\) | −5555.43 | −0.399785 | ||||||||
\(579\) | 5145.64 | 0.369336 | ||||||||
\(580\) | 12441.3 | 0.890685 | ||||||||
\(581\) | −2224.96 | −0.158876 | ||||||||
\(582\) | 458.660 | 0.0326668 | ||||||||
\(583\) | −12808.4 | −0.909899 | ||||||||
\(584\) | 7717.26 | 0.546819 | ||||||||
\(585\) | −9074.84 | −0.641365 | ||||||||
\(586\) | 195.068 | 0.0137512 | ||||||||
\(587\) | 4071.25 | 0.286266 | 0.143133 | − | 0.989703i | \(-0.454282\pi\) | ||||
0.143133 | + | 0.989703i | \(0.454282\pi\) | |||||||
\(588\) | −360.886 | −0.0253107 | ||||||||
\(589\) | −13401.8 | −0.937540 | ||||||||
\(590\) | 10629.4 | 0.741701 | ||||||||
\(591\) | −2365.74 | −0.164659 | ||||||||
\(592\) | −17255.6 | −1.19797 | ||||||||
\(593\) | −7458.47 | −0.516497 | −0.258249 | − | 0.966079i | \(-0.583145\pi\) | ||||
−0.258249 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(594\) | 1365.74 | 0.0943382 | ||||||||
\(595\) | −35791.7 | −2.46608 | ||||||||
\(596\) | 9043.44 | 0.621533 | ||||||||
\(597\) | −3820.98 | −0.261947 | ||||||||
\(598\) | −799.039 | −0.0546407 | ||||||||
\(599\) | 3861.66 | 0.263411 | 0.131705 | − | 0.991289i | \(-0.457955\pi\) | ||||
0.131705 | + | 0.991289i | \(0.457955\pi\) | |||||||
\(600\) | 3272.93 | 0.222694 | ||||||||
\(601\) | 3695.64 | 0.250829 | 0.125414 | − | 0.992104i | \(-0.459974\pi\) | ||||
0.125414 | + | 0.992104i | \(0.459974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16442.1 | −1.11040 | ||||||||
\(604\) | 7813.38 | 0.526361 | ||||||||
\(605\) | −14465.1 | −0.972049 | ||||||||
\(606\) | 625.120 | 0.0419039 | ||||||||
\(607\) | 7398.42 | 0.494716 | 0.247358 | − | 0.968924i | \(-0.420438\pi\) | ||||
0.247358 | + | 0.968924i | \(0.420438\pi\) | |||||||
\(608\) | 11631.1 | 0.775831 | ||||||||
\(609\) | −2199.81 | −0.146372 | ||||||||
\(610\) | 8935.81 | 0.593115 | ||||||||
\(611\) | −8789.96 | −0.582003 | ||||||||
\(612\) | −18224.0 | −1.20369 | ||||||||
\(613\) | 18359.2 | 1.20966 | 0.604828 | − | 0.796356i | \(-0.293242\pi\) | ||||
0.604828 | + | 0.796356i | \(0.293242\pi\) | |||||||
\(614\) | −4440.55 | −0.291866 | ||||||||
\(615\) | −7679.87 | −0.503548 | ||||||||
\(616\) | 6882.67 | 0.450179 | ||||||||
\(617\) | −12505.8 | −0.815986 | −0.407993 | − | 0.912985i | \(-0.633771\pi\) | ||||
−0.407993 | + | 0.912985i | \(0.633771\pi\) | |||||||
\(618\) | −2064.97 | −0.134410 | ||||||||
\(619\) | 10523.0 | 0.683288 | 0.341644 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | −23317.9 | −1.51043 | ||||||||
\(621\) | −2316.21 | −0.149672 | ||||||||
\(622\) | 6231.31 | 0.401692 | ||||||||
\(623\) | −15259.1 | −0.981291 | ||||||||
\(624\) | 877.015 | 0.0562640 | ||||||||
\(625\) | −2567.38 | −0.164313 | ||||||||
\(626\) | −5740.47 | −0.366510 | ||||||||
\(627\) | −1802.67 | −0.114820 | ||||||||
\(628\) | −16833.8 | −1.06965 | ||||||||
\(629\) | 43891.8 | 2.78233 | ||||||||
\(630\) | 9275.15 | 0.586557 | ||||||||
\(631\) | 28065.1 | 1.77061 | 0.885306 | − | 0.465010i | \(-0.153949\pi\) | ||||
0.885306 | + | 0.465010i | \(0.153949\pi\) | |||||||
\(632\) | 10558.4 | 0.664541 | ||||||||
\(633\) | 2037.89 | 0.127960 | ||||||||
\(634\) | 4054.41 | 0.253976 | ||||||||
\(635\) | 22926.2 | 1.43276 | ||||||||
\(636\) | 4338.14 | 0.270469 | ||||||||
\(637\) | 923.615 | 0.0574489 | ||||||||
\(638\) | 2340.03 | 0.145208 | ||||||||
\(639\) | 962.253 | 0.0595714 | ||||||||
\(640\) | 26069.4 | 1.61013 | ||||||||
\(641\) | −20560.3 | −1.26690 | −0.633450 | − | 0.773784i | \(-0.718362\pi\) | ||||
−0.633450 | + | 0.773784i | \(0.718362\pi\) | |||||||
\(642\) | −89.0700 | −0.00547557 | ||||||||
\(643\) | 1245.51 | 0.0763889 | 0.0381944 | − | 0.999270i | \(-0.487839\pi\) | ||||
0.0381944 | + | 0.999270i | \(0.487839\pi\) | |||||||
\(644\) | −5427.97 | −0.332130 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7411.38 | −0.451388 | ||||||||
\(647\) | −11323.3 | −0.688047 | −0.344024 | − | 0.938961i | \(-0.611790\pi\) | ||||
−0.344024 | + | 0.938961i | \(0.611790\pi\) | |||||||
\(648\) | 9646.78 | 0.584817 | ||||||||
\(649\) | −13287.7 | −0.803679 | ||||||||
\(650\) | −3895.17 | −0.235048 | ||||||||
\(651\) | 4122.95 | 0.248220 | ||||||||
\(652\) | 18315.6 | 1.10014 | ||||||||
\(653\) | −4387.92 | −0.262960 | −0.131480 | − | 0.991319i | \(-0.541973\pi\) | ||||
−0.131480 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(654\) | 178.701 | 0.0106846 | ||||||||
\(655\) | 48022.6 | 2.86473 | ||||||||
\(656\) | −15517.6 | −0.923566 | ||||||||
\(657\) | −13000.8 | −0.772008 | ||||||||
\(658\) | 8983.98 | 0.532267 | ||||||||
\(659\) | −4067.28 | −0.240423 | −0.120211 | − | 0.992748i | \(-0.538357\pi\) | ||||
−0.120211 | + | 0.992748i | \(0.538357\pi\) | |||||||
\(660\) | −3136.49 | −0.184981 | ||||||||
\(661\) | −700.954 | −0.0412465 | −0.0206233 | − | 0.999787i | \(-0.506565\pi\) | ||||
−0.0206233 | + | 0.999787i | \(0.506565\pi\) | |||||||
\(662\) | −9307.40 | −0.546438 | ||||||||
\(663\) | −2230.81 | −0.130675 | ||||||||
\(664\) | −1723.84 | −0.100750 | ||||||||
\(665\) | −25070.6 | −1.46195 | ||||||||
\(666\) | −11374.3 | −0.661777 | ||||||||
\(667\) | −3968.56 | −0.230379 | ||||||||
\(668\) | 17227.6 | 0.997837 | ||||||||
\(669\) | −2644.94 | −0.152854 | ||||||||
\(670\) | −11634.3 | −0.670852 | ||||||||
\(671\) | −11170.6 | −0.642677 | ||||||||
\(672\) | −3578.22 | −0.205406 | ||||||||
\(673\) | −24721.5 | −1.41597 | −0.707983 | − | 0.706229i | \(-0.750395\pi\) | ||||
−0.707983 | + | 0.706229i | \(0.750395\pi\) | |||||||
\(674\) | 2541.69 | 0.145256 | ||||||||
\(675\) | −11291.1 | −0.643845 | ||||||||
\(676\) | 12563.0 | 0.714783 | ||||||||
\(677\) | −10400.6 | −0.590442 | −0.295221 | − | 0.955429i | \(-0.595393\pi\) | ||||
−0.295221 | + | 0.955429i | \(0.595393\pi\) | |||||||
\(678\) | 396.283 | 0.0224472 | ||||||||
\(679\) | −7974.09 | −0.450688 | ||||||||
\(680\) | −27730.4 | −1.56384 | ||||||||
\(681\) | −1584.41 | −0.0891551 | ||||||||
\(682\) | −4385.75 | −0.246245 | ||||||||
\(683\) | −18255.8 | −1.02275 | −0.511376 | − | 0.859357i | \(-0.670864\pi\) | ||||
−0.511376 | + | 0.859357i | \(0.670864\pi\) | |||||||
\(684\) | −12765.1 | −0.713578 | ||||||||
\(685\) | 375.006 | 0.0209171 | ||||||||
\(686\) | 5982.31 | 0.332953 | ||||||||
\(687\) | −4007.76 | −0.222570 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11102.6 | −0.613897 | ||||||||
\(690\) | −800.326 | −0.0441564 | ||||||||
\(691\) | −30571.0 | −1.68304 | −0.841518 | − | 0.540229i | \(-0.818337\pi\) | ||||
−0.841518 | + | 0.540229i | \(0.818337\pi\) | |||||||
\(692\) | −11417.5 | −0.627208 | ||||||||
\(693\) | −11594.8 | −0.635570 | ||||||||
\(694\) | 9668.49 | 0.528834 | ||||||||
\(695\) | 54444.3 | 2.97150 | ||||||||
\(696\) | −1704.35 | −0.0928208 | ||||||||
\(697\) | 39471.0 | 2.14501 | ||||||||
\(698\) | −2996.68 | −0.162502 | ||||||||
\(699\) | 937.866 | 0.0507487 | ||||||||
\(700\) | −26460.4 | −1.42872 | ||||||||
\(701\) | 9418.96 | 0.507488 | 0.253744 | − | 0.967271i | \(-0.418338\pi\) | ||||
0.253744 | + | 0.967271i | \(0.418338\pi\) | |||||||
\(702\) | 1183.85 | 0.0636487 | ||||||||
\(703\) | 30744.5 | 1.64943 | ||||||||
\(704\) | −3484.63 | −0.186551 | ||||||||
\(705\) | −8804.12 | −0.470330 | ||||||||
\(706\) | −1532.15 | −0.0816757 | ||||||||
\(707\) | −10868.1 | −0.578129 | ||||||||
\(708\) | 4500.46 | 0.238895 | ||||||||
\(709\) | 21799.2 | 1.15471 | 0.577353 | − | 0.816495i | \(-0.304086\pi\) | ||||
0.577353 | + | 0.816495i | \(0.304086\pi\) | |||||||
\(710\) | 680.882 | 0.0359902 | ||||||||
\(711\) | −17787.1 | −0.938209 | ||||||||
\(712\) | −11822.4 | −0.622278 | ||||||||
\(713\) | 7437.98 | 0.390680 | ||||||||
\(714\) | 2280.05 | 0.119508 | ||||||||
\(715\) | 8027.20 | 0.419861 | ||||||||
\(716\) | −1371.80 | −0.0716013 | ||||||||
\(717\) | 4084.21 | 0.212730 | ||||||||
\(718\) | −11837.9 | −0.615302 | ||||||||
\(719\) | 9463.10 | 0.490840 | 0.245420 | − | 0.969417i | \(-0.421074\pi\) | ||||
0.245420 | + | 0.969417i | \(0.421074\pi\) | |||||||
\(720\) | −18365.7 | −0.950625 | ||||||||
\(721\) | 35900.7 | 1.85439 | ||||||||
\(722\) | 1824.43 | 0.0940416 | ||||||||
\(723\) | 3228.06 | 0.166048 | ||||||||
\(724\) | 14743.9 | 0.756842 | ||||||||
\(725\) | −19346.0 | −0.991024 | ||||||||
\(726\) | 921.475 | 0.0471062 | ||||||||
\(727\) | 7627.15 | 0.389099 | 0.194550 | − | 0.980893i | \(-0.437675\pi\) | ||||
0.194550 | + | 0.980893i | \(0.437675\pi\) | |||||||
\(728\) | 5966.02 | 0.303730 | ||||||||
\(729\) | −14495.4 | −0.736444 | ||||||||
\(730\) | −9199.25 | −0.466410 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3783.41 | 0.191037 | ||||||||
\(733\) | 2047.25 | 0.103161 | 0.0515805 | − | 0.998669i | \(-0.483574\pi\) | ||||
0.0515805 | + | 0.998669i | \(0.483574\pi\) | |||||||
\(734\) | 3902.80 | 0.196260 | ||||||||
\(735\) | 925.104 | 0.0464258 | ||||||||
\(736\) | −6455.28 | −0.323294 | ||||||||
\(737\) | 14543.9 | 0.726909 | ||||||||
\(738\) | −10228.6 | −0.510191 | ||||||||
\(739\) | 2538.29 | 0.126350 | 0.0631749 | − | 0.998002i | \(-0.479877\pi\) | ||||
0.0631749 | + | 0.998002i | \(0.479877\pi\) | |||||||
\(740\) | 53492.5 | 2.65733 | ||||||||
\(741\) | −1562.59 | −0.0774672 | ||||||||
\(742\) | 11347.6 | 0.561436 | ||||||||
\(743\) | 18805.1 | 0.928524 | 0.464262 | − | 0.885698i | \(-0.346320\pi\) | ||||
0.464262 | + | 0.885698i | \(0.346320\pi\) | |||||||
\(744\) | 3194.35 | 0.157406 | ||||||||
\(745\) | −23182.2 | −1.14004 | ||||||||
\(746\) | 2014.80 | 0.0988833 | ||||||||
\(747\) | 2904.04 | 0.142240 | ||||||||
\(748\) | 16120.1 | 0.787981 | ||||||||
\(749\) | 1548.54 | 0.0755438 | ||||||||
\(750\) | −1371.27 | −0.0667620 | ||||||||
\(751\) | 33700.0 | 1.63746 | 0.818729 | − | 0.574181i | \(-0.194679\pi\) | ||||
0.818729 | + | 0.574181i | \(0.194679\pi\) | |||||||
\(752\) | −17789.2 | −0.862639 | ||||||||
\(753\) | 8110.20 | 0.392499 | ||||||||
\(754\) | 2028.38 | 0.0979698 | ||||||||
\(755\) | −20029.0 | −0.965470 | ||||||||
\(756\) | 8042.01 | 0.386885 | ||||||||
\(757\) | 28589.4 | 1.37265 | 0.686326 | − | 0.727294i | \(-0.259222\pi\) | ||||
0.686326 | + | 0.727294i | \(0.259222\pi\) | |||||||
\(758\) | −1296.87 | −0.0621430 | ||||||||
\(759\) | 1000.48 | 0.0478461 | ||||||||
\(760\) | −19424.0 | −0.927083 | ||||||||
\(761\) | 16653.2 | 0.793268 | 0.396634 | − | 0.917977i | \(-0.370178\pi\) | ||||
0.396634 | + | 0.917977i | \(0.370178\pi\) | |||||||
\(762\) | −1460.48 | −0.0694324 | ||||||||
\(763\) | −3106.82 | −0.147411 | ||||||||
\(764\) | 22585.6 | 1.06953 | ||||||||
\(765\) | 46715.7 | 2.20785 | ||||||||
\(766\) | −2581.36 | −0.121760 | ||||||||
\(767\) | −11518.0 | −0.542231 | ||||||||
\(768\) | −302.914 | −0.0142324 | ||||||||
\(769\) | 19518.3 | 0.915279 | 0.457640 | − | 0.889138i | \(-0.348695\pi\) | ||||
0.457640 | + | 0.889138i | \(0.348695\pi\) | |||||||
\(770\) | −8204.38 | −0.383981 | ||||||||
\(771\) | −1737.00 | −0.0811370 | ||||||||
\(772\) | −32230.9 | −1.50261 | ||||||||
\(773\) | −633.350 | −0.0294696 | −0.0147348 | − | 0.999891i | \(-0.504690\pi\) | ||||
−0.0147348 | + | 0.999891i | \(0.504690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36258.8 | 1.68059 | ||||||||
\(776\) | −6178.11 | −0.285800 | ||||||||
\(777\) | −9458.27 | −0.436697 | ||||||||
\(778\) | −12864.4 | −0.592815 | ||||||||
\(779\) | 27647.8 | 1.27161 | ||||||||
\(780\) | −2718.76 | −0.124804 | ||||||||
\(781\) | −851.166 | −0.0389976 | ||||||||
\(782\) | 4113.31 | 0.188097 | ||||||||
\(783\) | 5879.76 | 0.268360 | ||||||||
\(784\) | 1869.22 | 0.0851502 | ||||||||
\(785\) | 43152.1 | 1.96199 | ||||||||
\(786\) | −3059.20 | −0.138827 | ||||||||
\(787\) | 22023.2 | 0.997511 | 0.498755 | − | 0.866743i | \(-0.333791\pi\) | ||||
0.498755 | + | 0.866743i | \(0.333791\pi\) | |||||||
\(788\) | 14818.4 | 0.669903 | ||||||||
\(789\) | −1903.75 | −0.0859003 | ||||||||
\(790\) | −12586.0 | −0.566821 | ||||||||
\(791\) | −6889.63 | −0.309693 | ||||||||
\(792\) | −8983.34 | −0.403042 | ||||||||
\(793\) | −9682.88 | −0.433605 | ||||||||
\(794\) | 6396.84 | 0.285914 | ||||||||
\(795\) | −11120.5 | −0.496104 | ||||||||
\(796\) | 23933.6 | 1.06571 | ||||||||
\(797\) | −20062.0 | −0.891635 | −0.445817 | − | 0.895124i | \(-0.647087\pi\) | ||||
−0.445817 | + | 0.895124i | \(0.647087\pi\) | |||||||
\(798\) | 1597.08 | 0.0708472 | ||||||||
\(799\) | 45249.2 | 2.00351 | ||||||||
\(800\) | −31468.3 | −1.39072 | ||||||||
\(801\) | 19916.4 | 0.878541 | ||||||||
\(802\) | −1414.19 | −0.0622652 | ||||||||
\(803\) | 11499.9 | 0.505384 | ||||||||
\(804\) | −4925.93 | −0.216075 | ||||||||
\(805\) | 13914.2 | 0.609205 | ||||||||
\(806\) | −3801.65 | −0.166138 | ||||||||
\(807\) | −6051.49 | −0.263969 | ||||||||
\(808\) | −8420.31 | −0.366615 | ||||||||
\(809\) | 37497.8 | 1.62961 | 0.814804 | − | 0.579736i | \(-0.196845\pi\) | ||||
0.814804 | + | 0.579736i | \(0.196845\pi\) | |||||||
\(810\) | −11499.3 | −0.498820 | ||||||||
\(811\) | 1705.17 | 0.0738304 | 0.0369152 | − | 0.999318i | \(-0.488247\pi\) | ||||
0.0369152 | + | 0.999318i | \(0.488247\pi\) | |||||||
\(812\) | 13779.0 | 0.595504 | ||||||||
\(813\) | −1460.21 | −0.0629910 | ||||||||
\(814\) | 10061.2 | 0.433223 | ||||||||
\(815\) | −46950.5 | −2.01792 | ||||||||
\(816\) | −4514.72 | −0.193685 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 14008.8 | 0.598785 | ||||||||
\(819\) | −10050.6 | −0.428811 | ||||||||
\(820\) | 48104.7 | 2.04865 | ||||||||
\(821\) | −18361.5 | −0.780535 | −0.390267 | − | 0.920702i | \(-0.627617\pi\) | ||||
−0.390267 | + | 0.920702i | \(0.627617\pi\) | |||||||
\(822\) | −23.8891 | −0.00101366 | ||||||||
\(823\) | 14800.1 | 0.626851 | 0.313426 | − | 0.949613i | \(-0.398523\pi\) | ||||
0.313426 | + | 0.949613i | \(0.398523\pi\) | |||||||
\(824\) | 27814.9 | 1.17594 | ||||||||
\(825\) | 4877.17 | 0.205820 | ||||||||
\(826\) | 11772.2 | 0.495895 | ||||||||
\(827\) | 14542.4 | 0.611474 | 0.305737 | − | 0.952116i | \(-0.401097\pi\) | ||||
0.305737 | + | 0.952116i | \(0.401097\pi\) | |||||||
\(828\) | 7084.65 | 0.297353 | ||||||||
\(829\) | −32533.1 | −1.36299 | −0.681496 | − | 0.731822i | \(-0.738670\pi\) | ||||
−0.681496 | + | 0.731822i | \(0.738670\pi\) | |||||||
\(830\) | 2054.87 | 0.0859346 | ||||||||
\(831\) | −2931.60 | −0.122378 | ||||||||
\(832\) | −3020.54 | −0.125864 | ||||||||
\(833\) | −4754.61 | −0.197764 | ||||||||
\(834\) | −3468.29 | −0.144001 | ||||||||
\(835\) | −44161.5 | −1.83027 | ||||||||
\(836\) | 11291.5 | 0.467134 | ||||||||
\(837\) | −11020.0 | −0.455087 | ||||||||
\(838\) | −10853.2 | −0.447396 | ||||||||
\(839\) | 9279.94 | 0.381858 | 0.190929 | − | 0.981604i | \(-0.438850\pi\) | ||||
0.190929 | + | 0.981604i | \(0.438850\pi\) | |||||||
\(840\) | 5975.63 | 0.245451 | ||||||||
\(841\) | −14314.7 | −0.586933 | ||||||||
\(842\) | 2159.05 | 0.0883680 | ||||||||
\(843\) | −4767.16 | −0.194768 | ||||||||
\(844\) | −12764.8 | −0.520595 | ||||||||
\(845\) | −32204.3 | −1.31108 | ||||||||
\(846\) | −11726.0 | −0.476534 | ||||||||
\(847\) | −16020.4 | −0.649903 | ||||||||
\(848\) | −22469.5 | −0.909911 | ||||||||
\(849\) | −3688.92 | −0.149121 | ||||||||
\(850\) | 20051.7 | 0.809136 | ||||||||
\(851\) | −17063.2 | −0.687330 | ||||||||
\(852\) | 288.285 | 0.0115921 | ||||||||
\(853\) | −37303.3 | −1.49735 | −0.748675 | − | 0.662937i | \(-0.769310\pi\) | ||||
−0.748675 | + | 0.662937i | \(0.769310\pi\) | |||||||
\(854\) | 9896.60 | 0.396551 | ||||||||
\(855\) | 32722.4 | 1.30887 | ||||||||
\(856\) | 1199.76 | 0.0479055 | ||||||||
\(857\) | −28599.1 | −1.13994 | −0.569969 | − | 0.821666i | \(-0.693045\pi\) | ||||
−0.569969 | + | 0.821666i | \(0.693045\pi\) | |||||||
\(858\) | −511.360 | −0.0203468 | ||||||||
\(859\) | −17588.9 | −0.698632 | −0.349316 | − | 0.937005i | \(-0.613586\pi\) | ||||
−0.349316 | + | 0.937005i | \(0.613586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8505.63 | −0.336668 | ||||||||
\(862\) | −13250.4 | −0.523564 | ||||||||
\(863\) | −16630.5 | −0.655978 | −0.327989 | − | 0.944681i | \(-0.606371\pi\) | ||||
−0.327989 | + | 0.944681i | \(0.606371\pi\) | |||||||
\(864\) | 9564.06 | 0.376592 | ||||||||
\(865\) | 29267.8 | 1.15045 | ||||||||
\(866\) | −1198.78 | −0.0470397 | ||||||||
\(867\) | 6029.59 | 0.236189 | ||||||||
\(868\) | −25825.1 | −1.00986 | ||||||||
\(869\) | 15733.6 | 0.614186 | ||||||||
\(870\) | 2031.65 | 0.0791716 | ||||||||
\(871\) | 12606.9 | 0.490436 | ||||||||
\(872\) | −2407.08 | −0.0934793 | ||||||||
\(873\) | 10407.9 | 0.403497 | ||||||||
\(874\) | 2881.21 | 0.111508 | ||||||||
\(875\) | 23840.3 | 0.921085 | ||||||||
\(876\) | −3894.95 | −0.150226 | ||||||||
\(877\) | −29568.5 | −1.13849 | −0.569247 | − | 0.822167i | \(-0.692765\pi\) | ||||
−0.569247 | + | 0.822167i | \(0.692765\pi\) | |||||||
\(878\) | 16777.1 | 0.644875 | ||||||||
\(879\) | −211.717 | −0.00812405 | ||||||||
\(880\) | 16245.5 | 0.622313 | ||||||||
\(881\) | 3239.15 | 0.123870 | 0.0619351 | − | 0.998080i | \(-0.480273\pi\) | ||||
0.0619351 | + | 0.998080i | \(0.480273\pi\) | |||||||
\(882\) | 1232.12 | 0.0470382 | ||||||||
\(883\) | 9200.23 | 0.350637 | 0.175318 | − | 0.984512i | \(-0.443904\pi\) | ||||
0.175318 | + | 0.984512i | \(0.443904\pi\) | |||||||
\(884\) | 13973.2 | 0.531640 | ||||||||
\(885\) | −11536.6 | −0.438189 | ||||||||
\(886\) | −10309.3 | −0.390913 | ||||||||
\(887\) | 11534.9 | 0.436643 | 0.218322 | − | 0.975877i | \(-0.429942\pi\) | ||||
0.218322 | + | 0.975877i | \(0.429942\pi\) | |||||||
\(888\) | −7328.01 | −0.276928 | ||||||||
\(889\) | 25391.3 | 0.957927 | ||||||||
\(890\) | 14092.7 | 0.530773 | ||||||||
\(891\) | 14375.2 | 0.540502 | ||||||||
\(892\) | 16567.2 | 0.621873 | ||||||||
\(893\) | 31695.2 | 1.18773 | ||||||||
\(894\) | 1476.78 | 0.0552471 | ||||||||
\(895\) | 3516.50 | 0.131334 | ||||||||
\(896\) | 28872.5 | 1.07652 | ||||||||
\(897\) | 867.237 | 0.0322811 | ||||||||
\(898\) | −6676.68 | −0.248111 | ||||||||
\(899\) | −18881.5 | −0.700482 | ||||||||
\(900\) | 34536.4 | 1.27912 | ||||||||
\(901\) | 57154.2 | 2.11330 | ||||||||
\(902\) | 9047.79 | 0.333990 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5337.90 | −0.196389 | ||||||||
\(905\) | −37794.9 | −1.38823 | ||||||||
\(906\) | 1275.91 | 0.0467874 | ||||||||
\(907\) | 27277.5 | 0.998603 | 0.499302 | − | 0.866428i | \(-0.333590\pi\) | ||||
0.499302 | + | 0.866428i | \(0.333590\pi\) | |||||||
\(908\) | 9924.32 | 0.362720 | ||||||||
\(909\) | 14185.2 | 0.517593 | ||||||||
\(910\) | −7111.71 | −0.259067 | ||||||||
\(911\) | −676.309 | −0.0245962 | −0.0122981 | − | 0.999924i | \(-0.503915\pi\) | ||||
−0.0122981 | + | 0.999924i | \(0.503915\pi\) | |||||||
\(912\) | −3162.38 | −0.114821 | ||||||||
\(913\) | −2568.78 | −0.0931154 | ||||||||
\(914\) | −5523.88 | −0.199905 | ||||||||
\(915\) | −9698.48 | −0.350406 | ||||||||
\(916\) | 25103.6 | 0.905508 | ||||||||
\(917\) | 53186.1 | 1.91533 | ||||||||
\(918\) | −6094.23 | −0.219106 | ||||||||
\(919\) | 1872.82 | 0.0672239 | 0.0336119 | − | 0.999435i | \(-0.489299\pi\) | ||||
0.0336119 | + | 0.999435i | \(0.489299\pi\) | |||||||
\(920\) | 10780.3 | 0.386322 | ||||||||
\(921\) | 4819.55 | 0.172432 | ||||||||
\(922\) | 6448.76 | 0.230346 | ||||||||
\(923\) | −737.806 | −0.0263112 | ||||||||
\(924\) | −3473.73 | −0.123677 | ||||||||
\(925\) | −83179.8 | −2.95669 | ||||||||
\(926\) | 19683.5 | 0.698530 | ||||||||
\(927\) | −46858.0 | −1.66022 | ||||||||
\(928\) | 16386.9 | 0.579662 | ||||||||
\(929\) | 7059.21 | 0.249306 | 0.124653 | − | 0.992200i | \(-0.460218\pi\) | ||||
0.124653 | + | 0.992200i | \(0.460218\pi\) | |||||||
\(930\) | −3807.77 | −0.134260 | ||||||||
\(931\) | −3330.41 | −0.117239 | ||||||||
\(932\) | −5874.55 | −0.206467 | ||||||||
\(933\) | −6763.15 | −0.237316 | ||||||||
\(934\) | −2776.17 | −0.0972582 | ||||||||
\(935\) | −41322.6 | −1.44534 | ||||||||
\(936\) | −7786.92 | −0.271927 | ||||||||
\(937\) | 33383.4 | 1.16392 | 0.581958 | − | 0.813219i | \(-0.302287\pi\) | ||||
0.581958 | + | 0.813219i | \(0.302287\pi\) | |||||||
\(938\) | −12885.2 | −0.448525 | ||||||||
\(939\) | 6230.42 | 0.216530 | ||||||||
\(940\) | 55146.7 | 1.91350 | ||||||||
\(941\) | 24876.3 | 0.861791 | 0.430895 | − | 0.902402i | \(-0.358198\pi\) | ||||
0.430895 | + | 0.902402i | \(0.358198\pi\) | |||||||
\(942\) | −2748.93 | −0.0950797 | ||||||||
\(943\) | −15344.5 | −0.529891 | ||||||||
\(944\) | −23310.2 | −0.803690 | ||||||||
\(945\) | −20615.1 | −0.709638 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44261.5 | −1.51880 | −0.759400 | − | 0.650624i | \(-0.774508\pi\) | ||||
−0.759400 | + | 0.650624i | \(0.774508\pi\) | |||||||
\(948\) | −5328.89 | −0.182568 | ||||||||
\(949\) | 9968.35 | 0.340976 | ||||||||
\(950\) | 14045.4 | 0.479676 | ||||||||
\(951\) | −4400.45 | −0.150047 | ||||||||
\(952\) | −30712.0 | −1.04557 | ||||||||
\(953\) | −5408.14 | −0.183827 | −0.0919133 | − | 0.995767i | \(-0.529298\pi\) | ||||
−0.0919133 | + | 0.995767i | \(0.529298\pi\) | |||||||
\(954\) | −14811.1 | −0.502648 | ||||||||
\(955\) | −57896.5 | −1.96177 | ||||||||
\(956\) | −25582.4 | −0.865476 | ||||||||
\(957\) | −2539.75 | −0.0857873 | ||||||||
\(958\) | 11466.5 | 0.386709 | ||||||||
\(959\) | 415.327 | 0.0139850 | ||||||||
\(960\) | −3025.41 | −0.101713 | ||||||||
\(961\) | 5597.27 | 0.187885 | ||||||||
\(962\) | 8721.20 | 0.292290 | ||||||||
\(963\) | −2021.17 | −0.0676337 | ||||||||
\(964\) | −20219.7 | −0.675553 | ||||||||
\(965\) | 82621.5 | 2.75614 | ||||||||
\(966\) | −886.379 | −0.0295225 | ||||||||
\(967\) | −3500.75 | −0.116418 | −0.0582092 | − | 0.998304i | \(-0.518539\pi\) | ||||
−0.0582092 | + | 0.998304i | \(0.518539\pi\) | |||||||
\(968\) | −12412.2 | −0.412131 | ||||||||
\(969\) | 8043.94 | 0.266676 | ||||||||
\(970\) | 7364.52 | 0.243774 | ||||||||
\(971\) | 988.893 | 0.0326829 | 0.0163414 | − | 0.999866i | \(-0.494798\pi\) | ||||
0.0163414 | + | 0.999866i | \(0.494798\pi\) | |||||||
\(972\) | −15867.4 | −0.523607 | ||||||||
\(973\) | 60298.3 | 1.98672 | ||||||||
\(974\) | −8899.98 | −0.292786 | ||||||||
\(975\) | 4227.62 | 0.138864 | ||||||||
\(976\) | −19596.3 | −0.642685 | ||||||||
\(977\) | 43478.3 | 1.42374 | 0.711870 | − | 0.702311i | \(-0.247848\pi\) | ||||
0.711870 | + | 0.702311i | \(0.247848\pi\) | |||||||
\(978\) | 2990.91 | 0.0977900 | ||||||||
\(979\) | −17617.2 | −0.575125 | ||||||||
\(980\) | −5794.61 | −0.188880 | ||||||||
\(981\) | 4055.06 | 0.131976 | ||||||||
\(982\) | −1661.35 | −0.0539877 | ||||||||
\(983\) | −43582.2 | −1.41410 | −0.707048 | − | 0.707166i | \(-0.749973\pi\) | ||||
−0.707048 | + | 0.707166i | \(0.749973\pi\) | |||||||
\(984\) | −6589.93 | −0.213495 | ||||||||
\(985\) | −37985.8 | −1.22876 | ||||||||
\(986\) | −10441.7 | −0.337254 | ||||||||
\(987\) | −9750.76 | −0.314458 | ||||||||
\(988\) | 9787.66 | 0.315169 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 10708.5 | 0.343775 | ||||||||
\(991\) | 32709.0 | 1.04847 | 0.524236 | − | 0.851573i | \(-0.324351\pi\) | ||||
0.524236 | + | 0.851573i | \(0.324351\pi\) | |||||||
\(992\) | −30712.8 | −0.982996 | ||||||||
\(993\) | 10101.8 | 0.322830 | ||||||||
\(994\) | 754.092 | 0.0240627 | ||||||||
\(995\) | −61352.0 | −1.95476 | ||||||||
\(996\) | 870.031 | 0.0276787 | ||||||||
\(997\) | −29341.0 | −0.932035 | −0.466017 | − | 0.884776i | \(-0.654312\pi\) | ||||
−0.466017 | + | 0.884776i | \(0.654312\pi\) | |||||||
\(998\) | −14390.8 | −0.456445 | ||||||||
\(999\) | 25280.6 | 0.800642 |
(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.1.22 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.29 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.22 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.29 | yes | 50 | 43.42 | odd | 2 |