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 | 1.10 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.88871 | −1.37487 | −0.687433 | − | 0.726248i | \(-0.741263\pi\) | ||||
−0.687433 | + | 0.726248i | \(0.741263\pi\) | |||||||
\(3\) | 9.09520 | 1.75037 | 0.875186 | − | 0.483787i | \(-0.160739\pi\) | ||||
0.875186 | + | 0.483787i | \(0.160739\pi\) | |||||||
\(4\) | 7.12206 | 0.890257 | ||||||||
\(5\) | −19.0468 | −1.70359 | −0.851797 | − | 0.523872i | \(-0.824487\pi\) | ||||
−0.851797 | + | 0.523872i | \(0.824487\pi\) | |||||||
\(6\) | −35.3686 | −2.40653 | ||||||||
\(7\) | 18.7927 | 1.01471 | 0.507355 | − | 0.861737i | \(-0.330623\pi\) | ||||
0.507355 | + | 0.861737i | \(0.330623\pi\) | |||||||
\(8\) | 3.41407 | 0.150882 | ||||||||
\(9\) | 55.7226 | 2.06380 | ||||||||
\(10\) | 74.0673 | 2.34221 | ||||||||
\(11\) | 4.37373 | 0.119884 | 0.0599422 | − | 0.998202i | \(-0.480908\pi\) | ||||
0.0599422 | + | 0.998202i | \(0.480908\pi\) | |||||||
\(12\) | 64.7765 | 1.55828 | ||||||||
\(13\) | 45.6452 | 0.973822 | 0.486911 | − | 0.873452i | \(-0.338124\pi\) | ||||
0.486911 | + | 0.873452i | \(0.338124\pi\) | |||||||
\(14\) | −73.0793 | −1.39509 | ||||||||
\(15\) | −173.234 | −2.98192 | ||||||||
\(16\) | −70.2528 | −1.09770 | ||||||||
\(17\) | −62.8152 | −0.896172 | −0.448086 | − | 0.893990i | \(-0.647894\pi\) | ||||
−0.448086 | + | 0.893990i | \(0.647894\pi\) | |||||||
\(18\) | −216.689 | −2.83745 | ||||||||
\(19\) | 33.1127 | 0.399819 | 0.199910 | − | 0.979814i | \(-0.435935\pi\) | ||||
0.199910 | + | 0.979814i | \(0.435935\pi\) | |||||||
\(20\) | −135.652 | −1.51664 | ||||||||
\(21\) | 170.923 | 1.77612 | ||||||||
\(22\) | −17.0082 | −0.164825 | ||||||||
\(23\) | −32.0896 | −0.290919 | −0.145459 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145459 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(24\) | 31.0516 | 0.264100 | ||||||||
\(25\) | 237.779 | 1.90223 | ||||||||
\(26\) | −177.501 | −1.33888 | ||||||||
\(27\) | 261.237 | 1.86204 | ||||||||
\(28\) | 133.843 | 0.903352 | ||||||||
\(29\) | −291.097 | −1.86398 | −0.931988 | − | 0.362490i | \(-0.881927\pi\) | ||||
−0.931988 | + | 0.362490i | \(0.881927\pi\) | |||||||
\(30\) | 673.657 | 4.09974 | ||||||||
\(31\) | −83.9237 | −0.486231 | −0.243115 | − | 0.969997i | \(-0.578169\pi\) | ||||
−0.243115 | + | 0.969997i | \(0.578169\pi\) | |||||||
\(32\) | 245.880 | 1.35831 | ||||||||
\(33\) | 39.7799 | 0.209842 | ||||||||
\(34\) | 244.270 | 1.23212 | ||||||||
\(35\) | −357.940 | −1.72865 | ||||||||
\(36\) | 396.859 | 1.83731 | ||||||||
\(37\) | −90.1795 | −0.400687 | −0.200343 | − | 0.979726i | \(-0.564206\pi\) | ||||
−0.200343 | + | 0.979726i | \(0.564206\pi\) | |||||||
\(38\) | −128.766 | −0.549698 | ||||||||
\(39\) | 415.152 | 1.70455 | ||||||||
\(40\) | −65.0270 | −0.257042 | ||||||||
\(41\) | −422.014 | −1.60750 | −0.803750 | − | 0.594967i | \(-0.797165\pi\) | ||||
−0.803750 | + | 0.594967i | \(0.797165\pi\) | |||||||
\(42\) | −664.670 | −2.44192 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 31.1499 | 0.106728 | ||||||||
\(45\) | −1061.33 | −3.51588 | ||||||||
\(46\) | 124.787 | 0.399974 | ||||||||
\(47\) | −363.055 | −1.12675 | −0.563373 | − | 0.826203i | \(-0.690497\pi\) | ||||
−0.563373 | + | 0.826203i | \(0.690497\pi\) | |||||||
\(48\) | −638.963 | −1.92138 | ||||||||
\(49\) | 10.1649 | 0.0296352 | ||||||||
\(50\) | −924.654 | −2.61532 | ||||||||
\(51\) | −571.316 | −1.56863 | ||||||||
\(52\) | 325.087 | 0.866952 | ||||||||
\(53\) | 387.946 | 1.00544 | 0.502722 | − | 0.864448i | \(-0.332332\pi\) | ||||
0.502722 | + | 0.864448i | \(0.332332\pi\) | |||||||
\(54\) | −1015.88 | −2.56006 | ||||||||
\(55\) | −83.3054 | −0.204234 | ||||||||
\(56\) | 64.1595 | 0.153101 | ||||||||
\(57\) | 301.166 | 0.699832 | ||||||||
\(58\) | 1131.99 | 2.56272 | ||||||||
\(59\) | −248.120 | −0.547500 | −0.273750 | − | 0.961801i | \(-0.588264\pi\) | ||||
−0.273750 | + | 0.961801i | \(0.588264\pi\) | |||||||
\(60\) | −1233.78 | −2.65468 | ||||||||
\(61\) | 64.5638 | 0.135517 | 0.0677586 | − | 0.997702i | \(-0.478415\pi\) | ||||
0.0677586 | + | 0.997702i | \(0.478415\pi\) | |||||||
\(62\) | 326.355 | 0.668502 | ||||||||
\(63\) | 1047.18 | 2.09416 | ||||||||
\(64\) | −394.134 | −0.769792 | ||||||||
\(65\) | −869.393 | −1.65900 | ||||||||
\(66\) | −154.692 | −0.288505 | ||||||||
\(67\) | 80.6113 | 0.146989 | 0.0734943 | − | 0.997296i | \(-0.476585\pi\) | ||||
0.0734943 | + | 0.997296i | \(0.476585\pi\) | |||||||
\(68\) | −447.373 | −0.797823 | ||||||||
\(69\) | −291.861 | −0.509216 | ||||||||
\(70\) | 1391.92 | 2.37667 | ||||||||
\(71\) | 936.123 | 1.56475 | 0.782375 | − | 0.622807i | \(-0.214008\pi\) | ||||
0.782375 | + | 0.622807i | \(0.214008\pi\) | |||||||
\(72\) | 190.241 | 0.311390 | ||||||||
\(73\) | −651.084 | −1.04389 | −0.521943 | − | 0.852980i | \(-0.674793\pi\) | ||||
−0.521943 | + | 0.852980i | \(0.674793\pi\) | |||||||
\(74\) | 350.682 | 0.550891 | ||||||||
\(75\) | 2162.65 | 3.32962 | ||||||||
\(76\) | 235.830 | 0.355942 | ||||||||
\(77\) | 82.1941 | 0.121648 | ||||||||
\(78\) | −1614.40 | −2.34353 | ||||||||
\(79\) | 1114.36 | 1.58703 | 0.793516 | − | 0.608549i | \(-0.208248\pi\) | ||||
0.793516 | + | 0.608549i | \(0.208248\pi\) | |||||||
\(80\) | 1338.09 | 1.87003 | ||||||||
\(81\) | 871.496 | 1.19547 | ||||||||
\(82\) | 1641.09 | 2.21010 | ||||||||
\(83\) | 26.3884 | 0.0348976 | 0.0174488 | − | 0.999848i | \(-0.494446\pi\) | ||||
0.0174488 | + | 0.999848i | \(0.494446\pi\) | |||||||
\(84\) | 1217.32 | 1.58120 | ||||||||
\(85\) | 1196.43 | 1.52671 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2647.58 | −3.26265 | ||||||||
\(88\) | 14.9322 | 0.0180884 | ||||||||
\(89\) | −347.849 | −0.414292 | −0.207146 | − | 0.978310i | \(-0.566417\pi\) | ||||
−0.207146 | + | 0.978310i | \(0.566417\pi\) | |||||||
\(90\) | 4127.22 | 4.83386 | ||||||||
\(91\) | 857.795 | 0.988147 | ||||||||
\(92\) | −228.544 | −0.258993 | ||||||||
\(93\) | −763.303 | −0.851084 | ||||||||
\(94\) | 1411.82 | 1.54912 | ||||||||
\(95\) | −630.689 | −0.681130 | ||||||||
\(96\) | 2236.33 | 2.37754 | ||||||||
\(97\) | 291.207 | 0.304821 | 0.152410 | − | 0.988317i | \(-0.451296\pi\) | ||||
0.152410 | + | 0.988317i | \(0.451296\pi\) | |||||||
\(98\) | −39.5283 | −0.0407445 | ||||||||
\(99\) | 243.715 | 0.247417 | ||||||||
\(100\) | 1693.48 | 1.69348 | ||||||||
\(101\) | −1176.57 | −1.15913 | −0.579567 | − | 0.814924i | \(-0.696778\pi\) | ||||
−0.579567 | + | 0.814924i | \(0.696778\pi\) | |||||||
\(102\) | 2221.68 | 2.15666 | ||||||||
\(103\) | 457.000 | 0.437181 | 0.218590 | − | 0.975817i | \(-0.429854\pi\) | ||||
0.218590 | + | 0.975817i | \(0.429854\pi\) | |||||||
\(104\) | 155.836 | 0.146932 | ||||||||
\(105\) | −3255.53 | −3.02579 | ||||||||
\(106\) | −1508.61 | −1.38235 | ||||||||
\(107\) | −731.873 | −0.661242 | −0.330621 | − | 0.943764i | \(-0.607258\pi\) | ||||
−0.330621 | + | 0.943764i | \(0.607258\pi\) | |||||||
\(108\) | 1860.55 | 1.65770 | ||||||||
\(109\) | −119.276 | −0.104813 | −0.0524063 | − | 0.998626i | \(-0.516689\pi\) | ||||
−0.0524063 | + | 0.998626i | \(0.516689\pi\) | |||||||
\(110\) | 323.950 | 0.280795 | ||||||||
\(111\) | −820.200 | −0.701351 | ||||||||
\(112\) | −1320.24 | −1.11385 | ||||||||
\(113\) | 1149.02 | 0.956554 | 0.478277 | − | 0.878209i | \(-0.341261\pi\) | ||||
0.478277 | + | 0.878209i | \(0.341261\pi\) | |||||||
\(114\) | −1171.15 | −0.962176 | ||||||||
\(115\) | 611.202 | 0.495608 | ||||||||
\(116\) | −2073.21 | −1.65942 | ||||||||
\(117\) | 2543.47 | 2.00977 | ||||||||
\(118\) | 964.868 | 0.752740 | ||||||||
\(119\) | −1180.47 | −0.909354 | ||||||||
\(120\) | −591.433 | −0.449919 | ||||||||
\(121\) | −1311.87 | −0.985628 | ||||||||
\(122\) | −251.070 | −0.186318 | ||||||||
\(123\) | −3838.30 | −2.81372 | ||||||||
\(124\) | −597.710 | −0.432870 | ||||||||
\(125\) | −2148.08 | −1.53704 | ||||||||
\(126\) | −4072.17 | −2.87918 | ||||||||
\(127\) | −1354.82 | −0.946621 | −0.473310 | − | 0.880896i | \(-0.656941\pi\) | ||||
−0.473310 | + | 0.880896i | \(0.656941\pi\) | |||||||
\(128\) | −434.370 | −0.299947 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3380.81 | 2.28090 | ||||||||
\(131\) | 986.023 | 0.657628 | 0.328814 | − | 0.944395i | \(-0.393351\pi\) | ||||
0.328814 | + | 0.944395i | \(0.393351\pi\) | |||||||
\(132\) | 283.315 | 0.186813 | ||||||||
\(133\) | 622.276 | 0.405701 | ||||||||
\(134\) | −313.474 | −0.202090 | ||||||||
\(135\) | −4975.73 | −3.17217 | ||||||||
\(136\) | −214.456 | −0.135216 | ||||||||
\(137\) | 876.858 | 0.546825 | 0.273412 | − | 0.961897i | \(-0.411848\pi\) | ||||
0.273412 | + | 0.961897i | \(0.411848\pi\) | |||||||
\(138\) | 1134.96 | 0.700104 | ||||||||
\(139\) | −1371.22 | −0.836731 | −0.418365 | − | 0.908279i | \(-0.637397\pi\) | ||||
−0.418365 | + | 0.908279i | \(0.637397\pi\) | |||||||
\(140\) | −2549.27 | −1.53895 | ||||||||
\(141\) | −3302.06 | −1.97222 | ||||||||
\(142\) | −3640.31 | −2.15132 | ||||||||
\(143\) | 199.639 | 0.116746 | ||||||||
\(144\) | −3914.67 | −2.26543 | ||||||||
\(145\) | 5544.45 | 3.17546 | ||||||||
\(146\) | 2531.88 | 1.43520 | ||||||||
\(147\) | 92.4516 | 0.0518727 | ||||||||
\(148\) | −642.263 | −0.356714 | ||||||||
\(149\) | 2597.36 | 1.42808 | 0.714040 | − | 0.700105i | \(-0.246863\pi\) | ||||
0.714040 | + | 0.700105i | \(0.246863\pi\) | |||||||
\(150\) | −8409.91 | −4.57778 | ||||||||
\(151\) | 285.155 | 0.153679 | 0.0768397 | − | 0.997043i | \(-0.475517\pi\) | ||||
0.0768397 | + | 0.997043i | \(0.475517\pi\) | |||||||
\(152\) | 113.049 | 0.0603256 | ||||||||
\(153\) | −3500.22 | −1.84952 | ||||||||
\(154\) | −319.629 | −0.167250 | ||||||||
\(155\) | 1598.48 | 0.828340 | ||||||||
\(156\) | 2956.73 | 1.51749 | ||||||||
\(157\) | 1326.53 | 0.674323 | 0.337161 | − | 0.941447i | \(-0.390533\pi\) | ||||
0.337161 | + | 0.941447i | \(0.390533\pi\) | |||||||
\(158\) | −4333.43 | −2.18196 | ||||||||
\(159\) | 3528.45 | 1.75990 | ||||||||
\(160\) | −4683.22 | −2.31401 | ||||||||
\(161\) | −603.049 | −0.295198 | ||||||||
\(162\) | −3388.99 | −1.64361 | ||||||||
\(163\) | −182.755 | −0.0878191 | −0.0439095 | − | 0.999036i | \(-0.513981\pi\) | ||||
−0.0439095 | + | 0.999036i | \(0.513981\pi\) | |||||||
\(164\) | −3005.61 | −1.43109 | ||||||||
\(165\) | −757.679 | −0.357486 | ||||||||
\(166\) | −102.617 | −0.0479795 | ||||||||
\(167\) | −2822.36 | −1.30779 | −0.653894 | − | 0.756586i | \(-0.726866\pi\) | ||||
−0.653894 | + | 0.756586i | \(0.726866\pi\) | |||||||
\(168\) | 583.544 | 0.267984 | ||||||||
\(169\) | −113.520 | −0.0516704 | ||||||||
\(170\) | −4652.55 | −2.09903 | ||||||||
\(171\) | 1845.12 | 0.825147 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2917.04 | −1.28196 | −0.640978 | − | 0.767559i | \(-0.721471\pi\) | ||||
−0.640978 | + | 0.767559i | \(0.721471\pi\) | |||||||
\(174\) | 10295.7 | 4.48571 | ||||||||
\(175\) | 4468.51 | 1.93022 | ||||||||
\(176\) | −307.267 | −0.131597 | ||||||||
\(177\) | −2256.70 | −0.958329 | ||||||||
\(178\) | 1352.68 | 0.569595 | ||||||||
\(179\) | −2240.14 | −0.935397 | −0.467699 | − | 0.883888i | \(-0.654917\pi\) | ||||
−0.467699 | + | 0.883888i | \(0.654917\pi\) | |||||||
\(180\) | −7558.89 | −3.13003 | ||||||||
\(181\) | −4100.39 | −1.68387 | −0.841934 | − | 0.539581i | \(-0.818583\pi\) | ||||
−0.841934 | + | 0.539581i | \(0.818583\pi\) | |||||||
\(182\) | −3335.71 | −1.35857 | ||||||||
\(183\) | 587.221 | 0.237205 | ||||||||
\(184\) | −109.556 | −0.0438944 | ||||||||
\(185\) | 1717.63 | 0.682608 | ||||||||
\(186\) | 2968.26 | 1.17013 | ||||||||
\(187\) | −274.737 | −0.107437 | ||||||||
\(188\) | −2585.70 | −1.00309 | ||||||||
\(189\) | 4909.35 | 1.88943 | ||||||||
\(190\) | 2452.57 | 0.936463 | ||||||||
\(191\) | 3114.34 | 1.17982 | 0.589910 | − | 0.807469i | \(-0.299163\pi\) | ||||
0.589910 | + | 0.807469i | \(0.299163\pi\) | |||||||
\(192\) | −3584.72 | −1.34742 | ||||||||
\(193\) | 1369.02 | 0.510590 | 0.255295 | − | 0.966863i | \(-0.417827\pi\) | ||||
0.255295 | + | 0.966863i | \(0.417827\pi\) | |||||||
\(194\) | −1132.42 | −0.419088 | ||||||||
\(195\) | −7907.30 | −2.90386 | ||||||||
\(196\) | 72.3949 | 0.0263830 | ||||||||
\(197\) | −4821.42 | −1.74372 | −0.871858 | − | 0.489758i | \(-0.837085\pi\) | ||||
−0.871858 | + | 0.489758i | \(0.837085\pi\) | |||||||
\(198\) | −947.738 | −0.340166 | ||||||||
\(199\) | −3469.11 | −1.23577 | −0.617887 | − | 0.786267i | \(-0.712011\pi\) | ||||
−0.617887 | + | 0.786267i | \(0.712011\pi\) | |||||||
\(200\) | 811.795 | 0.287013 | ||||||||
\(201\) | 733.175 | 0.257285 | ||||||||
\(202\) | 4575.32 | 1.59366 | ||||||||
\(203\) | −5470.49 | −1.89139 | ||||||||
\(204\) | −4068.95 | −1.39649 | ||||||||
\(205\) | 8038.00 | 2.73853 | ||||||||
\(206\) | −1777.14 | −0.601065 | ||||||||
\(207\) | −1788.11 | −0.600398 | ||||||||
\(208\) | −3206.70 | −1.06896 | ||||||||
\(209\) | 144.826 | 0.0479321 | ||||||||
\(210\) | 12659.8 | 4.16005 | ||||||||
\(211\) | −949.908 | −0.309926 | −0.154963 | − | 0.987920i | \(-0.549526\pi\) | ||||
−0.154963 | + | 0.987920i | \(0.549526\pi\) | |||||||
\(212\) | 2762.97 | 0.895103 | ||||||||
\(213\) | 8514.22 | 2.73889 | ||||||||
\(214\) | 2846.04 | 0.909119 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 891.883 | 0.280949 | ||||||||
\(217\) | −1577.15 | −0.493383 | ||||||||
\(218\) | 463.830 | 0.144103 | ||||||||
\(219\) | −5921.74 | −1.82719 | ||||||||
\(220\) | −593.305 | −0.181821 | ||||||||
\(221\) | −2867.21 | −0.872712 | ||||||||
\(222\) | 3189.52 | 0.964264 | ||||||||
\(223\) | −5128.19 | −1.53995 | −0.769976 | − | 0.638073i | \(-0.779732\pi\) | ||||
−0.769976 | + | 0.638073i | \(0.779732\pi\) | |||||||
\(224\) | 4620.74 | 1.37829 | ||||||||
\(225\) | 13249.7 | 3.92583 | ||||||||
\(226\) | −4468.20 | −1.31513 | ||||||||
\(227\) | 3818.68 | 1.11654 | 0.558270 | − | 0.829659i | \(-0.311465\pi\) | ||||
0.558270 | + | 0.829659i | \(0.311465\pi\) | |||||||
\(228\) | 2144.92 | 0.623031 | ||||||||
\(229\) | −2587.09 | −0.746548 | −0.373274 | − | 0.927721i | \(-0.621765\pi\) | ||||
−0.373274 | + | 0.927721i | \(0.621765\pi\) | |||||||
\(230\) | −2376.79 | −0.681394 | ||||||||
\(231\) | 747.571 | 0.212929 | ||||||||
\(232\) | −993.825 | −0.281240 | ||||||||
\(233\) | 3660.55 | 1.02923 | 0.514615 | − | 0.857421i | \(-0.327935\pi\) | ||||
0.514615 | + | 0.857421i | \(0.327935\pi\) | |||||||
\(234\) | −9890.80 | −2.76317 | ||||||||
\(235\) | 6915.03 | 1.91952 | ||||||||
\(236\) | −1767.13 | −0.487416 | ||||||||
\(237\) | 10135.3 | 2.77789 | ||||||||
\(238\) | 4590.49 | 1.25024 | ||||||||
\(239\) | 840.112 | 0.227374 | 0.113687 | − | 0.993517i | \(-0.463734\pi\) | ||||
0.113687 | + | 0.993517i | \(0.463734\pi\) | |||||||
\(240\) | 12170.2 | 3.27326 | ||||||||
\(241\) | −1237.68 | −0.330813 | −0.165406 | − | 0.986226i | \(-0.552894\pi\) | ||||
−0.165406 | + | 0.986226i | \(0.552894\pi\) | |||||||
\(242\) | 5101.48 | 1.35511 | ||||||||
\(243\) | 873.016 | 0.230469 | ||||||||
\(244\) | 459.827 | 0.120645 | ||||||||
\(245\) | −193.608 | −0.0504864 | ||||||||
\(246\) | 14926.0 | 3.86849 | ||||||||
\(247\) | 1511.43 | 0.389353 | ||||||||
\(248\) | −286.522 | −0.0733635 | ||||||||
\(249\) | 240.007 | 0.0610837 | ||||||||
\(250\) | 8353.26 | 2.11323 | ||||||||
\(251\) | −4783.43 | −1.20290 | −0.601449 | − | 0.798911i | \(-0.705410\pi\) | ||||
−0.601449 | + | 0.798911i | \(0.705410\pi\) | |||||||
\(252\) | 7458.05 | 1.86434 | ||||||||
\(253\) | −140.351 | −0.0348766 | ||||||||
\(254\) | 5268.50 | 1.30148 | ||||||||
\(255\) | 10881.7 | 2.67232 | ||||||||
\(256\) | 4842.20 | 1.18218 | ||||||||
\(257\) | 3254.28 | 0.789869 | 0.394935 | − | 0.918709i | \(-0.370767\pi\) | ||||
0.394935 | + | 0.918709i | \(0.370767\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1694.71 | −0.406581 | ||||||||
\(260\) | −6191.86 | −1.47693 | ||||||||
\(261\) | −16220.7 | −3.84687 | ||||||||
\(262\) | −3834.36 | −0.904150 | ||||||||
\(263\) | −4499.66 | −1.05498 | −0.527492 | − | 0.849560i | \(-0.676868\pi\) | ||||
−0.527492 | + | 0.849560i | \(0.676868\pi\) | |||||||
\(264\) | 135.811 | 0.0316614 | ||||||||
\(265\) | −7389.12 | −1.71287 | ||||||||
\(266\) | −2419.85 | −0.557784 | ||||||||
\(267\) | −3163.76 | −0.725164 | ||||||||
\(268\) | 574.118 | 0.130858 | ||||||||
\(269\) | 4396.09 | 0.996409 | 0.498205 | − | 0.867059i | \(-0.333993\pi\) | ||||
0.498205 | + | 0.867059i | \(0.333993\pi\) | |||||||
\(270\) | 19349.2 | 4.36131 | ||||||||
\(271\) | 489.737 | 0.109776 | 0.0548882 | − | 0.998493i | \(-0.482520\pi\) | ||||
0.0548882 | + | 0.998493i | \(0.482520\pi\) | |||||||
\(272\) | 4412.94 | 0.983728 | ||||||||
\(273\) | 7801.81 | 1.72962 | ||||||||
\(274\) | −3409.84 | −0.751811 | ||||||||
\(275\) | 1039.98 | 0.228048 | ||||||||
\(276\) | −2078.65 | −0.453333 | ||||||||
\(277\) | −2576.01 | −0.558762 | −0.279381 | − | 0.960180i | \(-0.590129\pi\) | ||||
−0.279381 | + | 0.960180i | \(0.590129\pi\) | |||||||
\(278\) | 5332.28 | 1.15039 | ||||||||
\(279\) | −4676.45 | −1.00348 | ||||||||
\(280\) | −1222.03 | −0.260823 | ||||||||
\(281\) | 6339.36 | 1.34582 | 0.672908 | − | 0.739726i | \(-0.265045\pi\) | ||||
0.672908 | + | 0.739726i | \(0.265045\pi\) | |||||||
\(282\) | 12840.7 | 2.71154 | ||||||||
\(283\) | 3492.92 | 0.733684 | 0.366842 | − | 0.930283i | \(-0.380439\pi\) | ||||
0.366842 | + | 0.930283i | \(0.380439\pi\) | |||||||
\(284\) | 6667.12 | 1.39303 | ||||||||
\(285\) | −5736.24 | −1.19223 | ||||||||
\(286\) | −776.340 | −0.160510 | ||||||||
\(287\) | −7930.77 | −1.63115 | ||||||||
\(288\) | 13701.1 | 2.80327 | ||||||||
\(289\) | −967.251 | −0.196876 | ||||||||
\(290\) | −21560.8 | −4.36583 | ||||||||
\(291\) | 2648.59 | 0.533550 | ||||||||
\(292\) | −4637.06 | −0.929327 | ||||||||
\(293\) | −6042.69 | −1.20484 | −0.602419 | − | 0.798180i | \(-0.705796\pi\) | ||||
−0.602419 | + | 0.798180i | \(0.705796\pi\) | |||||||
\(294\) | −359.517 | −0.0713180 | ||||||||
\(295\) | 4725.89 | 0.932719 | ||||||||
\(296\) | −307.879 | −0.0604565 | ||||||||
\(297\) | 1142.58 | 0.223230 | ||||||||
\(298\) | −10100.4 | −1.96342 | ||||||||
\(299\) | −1464.73 | −0.283303 | ||||||||
\(300\) | 15402.5 | 2.96421 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1108.89 | −0.211289 | ||||||||
\(303\) | −10701.1 | −2.02892 | ||||||||
\(304\) | −2326.26 | −0.438882 | ||||||||
\(305\) | −1229.73 | −0.230866 | ||||||||
\(306\) | 13611.4 | 2.54284 | ||||||||
\(307\) | 7899.54 | 1.46857 | 0.734285 | − | 0.678842i | \(-0.237518\pi\) | ||||
0.734285 | + | 0.678842i | \(0.237518\pi\) | |||||||
\(308\) | 585.391 | 0.108298 | ||||||||
\(309\) | 4156.51 | 0.765228 | ||||||||
\(310\) | −6216.01 | −1.13886 | ||||||||
\(311\) | −10690.9 | −1.94927 | −0.974636 | − | 0.223798i | \(-0.928154\pi\) | ||||
−0.974636 | + | 0.223798i | \(0.928154\pi\) | |||||||
\(312\) | 1417.36 | 0.257186 | ||||||||
\(313\) | −1211.51 | −0.218782 | −0.109391 | − | 0.993999i | \(-0.534890\pi\) | ||||
−0.109391 | + | 0.993999i | \(0.534890\pi\) | |||||||
\(314\) | −5158.49 | −0.927103 | ||||||||
\(315\) | −19945.3 | −3.56759 | ||||||||
\(316\) | 7936.55 | 1.41287 | ||||||||
\(317\) | −6471.09 | −1.14654 | −0.573269 | − | 0.819367i | \(-0.694325\pi\) | ||||
−0.573269 | + | 0.819367i | \(0.694325\pi\) | |||||||
\(318\) | −13721.1 | −2.41963 | ||||||||
\(319\) | −1273.18 | −0.223462 | ||||||||
\(320\) | 7506.97 | 1.31141 | ||||||||
\(321\) | −6656.53 | −1.15742 | ||||||||
\(322\) | 2345.08 | 0.405858 | ||||||||
\(323\) | −2079.98 | −0.358307 | ||||||||
\(324\) | 6206.84 | 1.06427 | ||||||||
\(325\) | 10853.5 | 1.85244 | ||||||||
\(326\) | 710.682 | 0.120739 | ||||||||
\(327\) | −1084.84 | −0.183461 | ||||||||
\(328\) | −1440.79 | −0.242543 | ||||||||
\(329\) | −6822.78 | −1.14332 | ||||||||
\(330\) | 2946.39 | 0.491496 | ||||||||
\(331\) | 1395.83 | 0.231788 | 0.115894 | − | 0.993262i | \(-0.463027\pi\) | ||||
0.115894 | + | 0.993262i | \(0.463027\pi\) | |||||||
\(332\) | 187.939 | 0.0310678 | ||||||||
\(333\) | −5025.03 | −0.826937 | ||||||||
\(334\) | 10975.3 | 1.79803 | ||||||||
\(335\) | −1535.38 | −0.250409 | ||||||||
\(336\) | −12007.8 | −1.94964 | ||||||||
\(337\) | 11548.8 | 1.86678 | 0.933391 | − | 0.358860i | \(-0.116835\pi\) | ||||
0.933391 | + | 0.358860i | \(0.116835\pi\) | |||||||
\(338\) | 441.446 | 0.0710399 | ||||||||
\(339\) | 10450.6 | 1.67432 | ||||||||
\(340\) | 8521.02 | 1.35917 | ||||||||
\(341\) | −367.060 | −0.0582915 | ||||||||
\(342\) | −7175.15 | −1.13447 | ||||||||
\(343\) | −6254.86 | −0.984638 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5559.00 | 0.867498 | ||||||||
\(346\) | 11343.5 | 1.76252 | ||||||||
\(347\) | 3970.96 | 0.614330 | 0.307165 | − | 0.951656i | \(-0.400620\pi\) | ||||
0.307165 | + | 0.951656i | \(0.400620\pi\) | |||||||
\(348\) | −18856.2 | −2.90460 | ||||||||
\(349\) | −1461.92 | −0.224226 | −0.112113 | − | 0.993695i | \(-0.535762\pi\) | ||||
−0.112113 | + | 0.993695i | \(0.535762\pi\) | |||||||
\(350\) | −17376.7 | −2.65379 | ||||||||
\(351\) | 11924.2 | 1.81330 | ||||||||
\(352\) | 1075.41 | 0.162840 | ||||||||
\(353\) | −4652.97 | −0.701565 | −0.350783 | − | 0.936457i | \(-0.614084\pi\) | ||||
−0.350783 | + | 0.936457i | \(0.614084\pi\) | |||||||
\(354\) | 8775.66 | 1.31757 | ||||||||
\(355\) | −17830.1 | −2.66570 | ||||||||
\(356\) | −2477.40 | −0.368826 | ||||||||
\(357\) | −10736.6 | −1.59171 | ||||||||
\(358\) | 8711.26 | 1.28605 | ||||||||
\(359\) | 84.9556 | 0.0124897 | 0.00624483 | − | 0.999981i | \(-0.498012\pi\) | ||||
0.00624483 | + | 0.999981i | \(0.498012\pi\) | |||||||
\(360\) | −3623.47 | −0.530483 | ||||||||
\(361\) | −5762.55 | −0.840144 | ||||||||
\(362\) | 15945.2 | 2.31509 | ||||||||
\(363\) | −11931.7 | −1.72521 | ||||||||
\(364\) | 6109.26 | 0.879704 | ||||||||
\(365\) | 12401.1 | 1.77836 | ||||||||
\(366\) | −2283.53 | −0.326126 | ||||||||
\(367\) | −5121.53 | −0.728452 | −0.364226 | − | 0.931311i | \(-0.618666\pi\) | ||||
−0.364226 | + | 0.931311i | \(0.618666\pi\) | |||||||
\(368\) | 2254.38 | 0.319341 | ||||||||
\(369\) | −23515.7 | −3.31756 | ||||||||
\(370\) | −6679.35 | −0.938495 | ||||||||
\(371\) | 7290.55 | 1.02023 | ||||||||
\(372\) | −5436.29 | −0.757683 | ||||||||
\(373\) | −898.596 | −0.124739 | −0.0623693 | − | 0.998053i | \(-0.519866\pi\) | ||||
−0.0623693 | + | 0.998053i | \(0.519866\pi\) | |||||||
\(374\) | 1068.37 | 0.147712 | ||||||||
\(375\) | −19537.2 | −2.69039 | ||||||||
\(376\) | −1239.50 | −0.170006 | ||||||||
\(377\) | −13287.2 | −1.81518 | ||||||||
\(378\) | −19091.0 | −2.59772 | ||||||||
\(379\) | 9099.47 | 1.23327 | 0.616634 | − | 0.787250i | \(-0.288496\pi\) | ||||
0.616634 | + | 0.787250i | \(0.288496\pi\) | |||||||
\(380\) | −4491.81 | −0.606381 | ||||||||
\(381\) | −12322.3 | −1.65694 | ||||||||
\(382\) | −12110.8 | −1.62209 | ||||||||
\(383\) | −6069.35 | −0.809738 | −0.404869 | − | 0.914375i | \(-0.632683\pi\) | ||||
−0.404869 | + | 0.914375i | \(0.632683\pi\) | |||||||
\(384\) | −3950.68 | −0.525018 | ||||||||
\(385\) | −1565.53 | −0.207239 | ||||||||
\(386\) | −5323.70 | −0.701993 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2073.99 | 0.271369 | ||||||||
\(389\) | 8283.52 | 1.07967 | 0.539834 | − | 0.841771i | \(-0.318487\pi\) | ||||
0.539834 | + | 0.841771i | \(0.318487\pi\) | |||||||
\(390\) | 30749.2 | 3.99242 | ||||||||
\(391\) | 2015.71 | 0.260713 | ||||||||
\(392\) | 34.7036 | 0.00447142 | ||||||||
\(393\) | 8968.08 | 1.15109 | ||||||||
\(394\) | 18749.1 | 2.39738 | ||||||||
\(395\) | −21225.0 | −2.70366 | ||||||||
\(396\) | 1735.75 | 0.220265 | ||||||||
\(397\) | 5831.90 | 0.737266 | 0.368633 | − | 0.929575i | \(-0.379826\pi\) | ||||
0.368633 | + | 0.929575i | \(0.379826\pi\) | |||||||
\(398\) | 13490.4 | 1.69902 | ||||||||
\(399\) | 5659.72 | 0.710127 | ||||||||
\(400\) | −16704.7 | −2.08808 | ||||||||
\(401\) | −14041.3 | −1.74860 | −0.874299 | − | 0.485389i | \(-0.838678\pi\) | ||||
−0.874299 | + | 0.485389i | \(0.838678\pi\) | |||||||
\(402\) | −2851.10 | −0.353732 | ||||||||
\(403\) | −3830.71 | −0.473502 | ||||||||
\(404\) | −8379.56 | −1.03193 | ||||||||
\(405\) | −16599.2 | −2.03659 | ||||||||
\(406\) | 21273.1 | 2.60041 | ||||||||
\(407\) | −394.421 | −0.0480361 | ||||||||
\(408\) | −1950.51 | −0.236679 | ||||||||
\(409\) | 2456.40 | 0.296971 | 0.148486 | − | 0.988915i | \(-0.452560\pi\) | ||||
0.148486 | + | 0.988915i | \(0.452560\pi\) | |||||||
\(410\) | −31257.4 | −3.76511 | ||||||||
\(411\) | 7975.19 | 0.957147 | ||||||||
\(412\) | 3254.78 | 0.389203 | ||||||||
\(413\) | −4662.85 | −0.555554 | ||||||||
\(414\) | 6953.45 | 0.825467 | ||||||||
\(415\) | −502.613 | −0.0594513 | ||||||||
\(416\) | 11223.2 | 1.32275 | ||||||||
\(417\) | −12471.5 | −1.46459 | ||||||||
\(418\) | −563.186 | −0.0659003 | ||||||||
\(419\) | 9412.48 | 1.09745 | 0.548723 | − | 0.836004i | \(-0.315114\pi\) | ||||
0.548723 | + | 0.836004i | \(0.315114\pi\) | |||||||
\(420\) | −23186.1 | −2.69373 | ||||||||
\(421\) | −7475.80 | −0.865435 | −0.432718 | − | 0.901529i | \(-0.642445\pi\) | ||||
−0.432718 | + | 0.901529i | \(0.642445\pi\) | |||||||
\(422\) | 3693.92 | 0.426107 | ||||||||
\(423\) | −20230.4 | −2.32538 | ||||||||
\(424\) | 1324.48 | 0.151703 | ||||||||
\(425\) | −14936.2 | −1.70473 | ||||||||
\(426\) | −33109.3 | −3.76561 | ||||||||
\(427\) | 1213.33 | 0.137511 | ||||||||
\(428\) | −5212.44 | −0.588675 | ||||||||
\(429\) | 1815.76 | 0.204349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12819.7 | 1.43273 | 0.716363 | − | 0.697728i | \(-0.245806\pi\) | ||||
0.716363 | + | 0.697728i | \(0.245806\pi\) | |||||||
\(432\) | −18352.7 | −2.04396 | ||||||||
\(433\) | −8929.20 | −0.991017 | −0.495508 | − | 0.868603i | \(-0.665018\pi\) | ||||
−0.495508 | + | 0.868603i | \(0.665018\pi\) | |||||||
\(434\) | 6133.09 | 0.678335 | ||||||||
\(435\) | 50427.9 | 5.55823 | ||||||||
\(436\) | −849.490 | −0.0933101 | ||||||||
\(437\) | −1062.57 | −0.116315 | ||||||||
\(438\) | 23027.9 | 2.51214 | ||||||||
\(439\) | −9033.45 | −0.982103 | −0.491051 | − | 0.871131i | \(-0.663387\pi\) | ||||
−0.491051 | + | 0.871131i | \(0.663387\pi\) | |||||||
\(440\) | −284.410 | −0.0308153 | ||||||||
\(441\) | 566.414 | 0.0611612 | ||||||||
\(442\) | 11149.7 | 1.19986 | ||||||||
\(443\) | 7257.25 | 0.778335 | 0.389167 | − | 0.921167i | \(-0.372763\pi\) | ||||
0.389167 | + | 0.921167i | \(0.372763\pi\) | |||||||
\(444\) | −5841.51 | −0.624382 | ||||||||
\(445\) | 6625.40 | 0.705785 | ||||||||
\(446\) | 19942.1 | 2.11723 | ||||||||
\(447\) | 23623.5 | 2.49967 | ||||||||
\(448\) | −7406.83 | −0.781115 | ||||||||
\(449\) | 11843.1 | 1.24479 | 0.622394 | − | 0.782704i | \(-0.286160\pi\) | ||||
0.622394 | + | 0.782704i | \(0.286160\pi\) | |||||||
\(450\) | −51524.1 | −5.39749 | ||||||||
\(451\) | −1845.77 | −0.192714 | ||||||||
\(452\) | 8183.38 | 0.851579 | ||||||||
\(453\) | 2593.54 | 0.268996 | ||||||||
\(454\) | −14849.7 | −1.53509 | ||||||||
\(455\) | −16338.2 | −1.68340 | ||||||||
\(456\) | 1028.20 | 0.105592 | ||||||||
\(457\) | 6136.43 | 0.628119 | 0.314059 | − | 0.949403i | \(-0.398311\pi\) | ||||
0.314059 | + | 0.949403i | \(0.398311\pi\) | |||||||
\(458\) | 10060.4 | 1.02640 | ||||||||
\(459\) | −16409.7 | −1.66871 | ||||||||
\(460\) | 4353.02 | 0.441218 | ||||||||
\(461\) | 1927.73 | 0.194758 | 0.0973788 | − | 0.995247i | \(-0.468954\pi\) | ||||
0.0973788 | + | 0.995247i | \(0.468954\pi\) | |||||||
\(462\) | −2907.09 | −0.292749 | ||||||||
\(463\) | −10705.1 | −1.07453 | −0.537264 | − | 0.843414i | \(-0.680542\pi\) | ||||
−0.537264 | + | 0.843414i | \(0.680542\pi\) | |||||||
\(464\) | 20450.3 | 2.04609 | ||||||||
\(465\) | 14538.5 | 1.44990 | ||||||||
\(466\) | −14234.8 | −1.41505 | ||||||||
\(467\) | −13219.7 | −1.30992 | −0.654962 | − | 0.755661i | \(-0.727316\pi\) | ||||
−0.654962 | + | 0.755661i | \(0.727316\pi\) | |||||||
\(468\) | 18114.7 | 1.78921 | ||||||||
\(469\) | 1514.90 | 0.149151 | ||||||||
\(470\) | −26890.5 | −2.63908 | ||||||||
\(471\) | 12065.1 | 1.18032 | ||||||||
\(472\) | −847.101 | −0.0826080 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −39413.4 | −3.81923 | ||||||||
\(475\) | 7873.51 | 0.760550 | ||||||||
\(476\) | −8407.34 | −0.809559 | ||||||||
\(477\) | 21617.4 | 2.07503 | ||||||||
\(478\) | −3266.95 | −0.312608 | ||||||||
\(479\) | −2249.15 | −0.214543 | −0.107271 | − | 0.994230i | \(-0.534211\pi\) | ||||
−0.107271 | + | 0.994230i | \(0.534211\pi\) | |||||||
\(480\) | −42594.8 | −4.05037 | ||||||||
\(481\) | −4116.26 | −0.390198 | ||||||||
\(482\) | 4812.97 | 0.454823 | ||||||||
\(483\) | −5484.85 | −0.516706 | ||||||||
\(484\) | −9343.21 | −0.877462 | ||||||||
\(485\) | −5546.56 | −0.519291 | ||||||||
\(486\) | −3394.90 | −0.316864 | ||||||||
\(487\) | 17135.5 | 1.59443 | 0.797213 | − | 0.603698i | \(-0.206307\pi\) | ||||
0.797213 | + | 0.603698i | \(0.206307\pi\) | |||||||
\(488\) | 220.425 | 0.0204471 | ||||||||
\(489\) | −1662.20 | −0.153716 | ||||||||
\(490\) | 752.886 | 0.0694121 | ||||||||
\(491\) | −17052.6 | −1.56736 | −0.783680 | − | 0.621165i | \(-0.786660\pi\) | ||||
−0.783680 | + | 0.621165i | \(0.786660\pi\) | |||||||
\(492\) | −27336.6 | −2.50494 | ||||||||
\(493\) | 18285.3 | 1.67044 | ||||||||
\(494\) | −5877.52 | −0.535308 | ||||||||
\(495\) | −4641.99 | −0.421499 | ||||||||
\(496\) | 5895.88 | 0.533735 | ||||||||
\(497\) | 17592.3 | 1.58777 | ||||||||
\(498\) | −933.319 | −0.0839820 | ||||||||
\(499\) | 7199.58 | 0.645887 | 0.322944 | − | 0.946418i | \(-0.395328\pi\) | ||||
0.322944 | + | 0.946418i | \(0.395328\pi\) | |||||||
\(500\) | −15298.8 | −1.36836 | ||||||||
\(501\) | −25669.9 | −2.28911 | ||||||||
\(502\) | 18601.4 | 1.65382 | ||||||||
\(503\) | −17120.4 | −1.51761 | −0.758807 | − | 0.651316i | \(-0.774217\pi\) | ||||
−0.758807 | + | 0.651316i | \(0.774217\pi\) | |||||||
\(504\) | 3575.14 | 0.315971 | ||||||||
\(505\) | 22409.8 | 1.97470 | ||||||||
\(506\) | 545.784 | 0.0479507 | ||||||||
\(507\) | −1032.49 | −0.0904424 | ||||||||
\(508\) | −9649.10 | −0.842735 | ||||||||
\(509\) | 12743.3 | 1.10970 | 0.554848 | − | 0.831952i | \(-0.312776\pi\) | ||||
0.554848 | + | 0.831952i | \(0.312776\pi\) | |||||||
\(510\) | −42315.9 | −3.67408 | ||||||||
\(511\) | −12235.6 | −1.05924 | ||||||||
\(512\) | −15355.0 | −1.32539 | ||||||||
\(513\) | 8650.27 | 0.744481 | ||||||||
\(514\) | −12655.0 | −1.08596 | ||||||||
\(515\) | −8704.38 | −0.744778 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1587.91 | −0.135079 | ||||||||
\(518\) | 6590.25 | 0.558994 | ||||||||
\(519\) | −26531.1 | −2.24390 | ||||||||
\(520\) | −2968.17 | −0.250313 | ||||||||
\(521\) | −15646.4 | −1.31570 | −0.657851 | − | 0.753148i | \(-0.728535\pi\) | ||||
−0.657851 | + | 0.753148i | \(0.728535\pi\) | |||||||
\(522\) | 63077.4 | 5.28893 | ||||||||
\(523\) | 11556.5 | 0.966213 | 0.483106 | − | 0.875562i | \(-0.339508\pi\) | ||||
0.483106 | + | 0.875562i | \(0.339508\pi\) | |||||||
\(524\) | 7022.51 | 0.585458 | ||||||||
\(525\) | 40642.0 | 3.37859 | ||||||||
\(526\) | 17497.9 | 1.45046 | ||||||||
\(527\) | 5271.69 | 0.435746 | ||||||||
\(528\) | −2794.65 | −0.230344 | ||||||||
\(529\) | −11137.3 | −0.915366 | ||||||||
\(530\) | 28734.1 | 2.35496 | ||||||||
\(531\) | −13825.9 | −1.12993 | ||||||||
\(532\) | 4431.88 | 0.361178 | ||||||||
\(533\) | −19262.9 | −1.56542 | ||||||||
\(534\) | 12302.9 | 0.997003 | ||||||||
\(535\) | 13939.8 | 1.12649 | ||||||||
\(536\) | 275.213 | 0.0221779 | ||||||||
\(537\) | −20374.5 | −1.63729 | ||||||||
\(538\) | −17095.1 | −1.36993 | ||||||||
\(539\) | 44.4584 | 0.00355280 | ||||||||
\(540\) | −35437.4 | −2.82404 | ||||||||
\(541\) | 4750.49 | 0.377523 | 0.188761 | − | 0.982023i | \(-0.439553\pi\) | ||||
0.188761 | + | 0.982023i | \(0.439553\pi\) | |||||||
\(542\) | −1904.44 | −0.150928 | ||||||||
\(543\) | −37293.9 | −2.94739 | ||||||||
\(544\) | −15445.0 | −1.21728 | ||||||||
\(545\) | 2271.82 | 0.178558 | ||||||||
\(546\) | −30339.0 | −2.37800 | ||||||||
\(547\) | −3938.22 | −0.307836 | −0.153918 | − | 0.988084i | \(-0.549189\pi\) | ||||
−0.153918 | + | 0.988084i | \(0.549189\pi\) | |||||||
\(548\) | 6245.03 | 0.486815 | ||||||||
\(549\) | 3597.66 | 0.279680 | ||||||||
\(550\) | −4044.19 | −0.313536 | ||||||||
\(551\) | −9638.99 | −0.745254 | ||||||||
\(552\) | −996.433 | −0.0768315 | ||||||||
\(553\) | 20941.9 | 1.61038 | ||||||||
\(554\) | 10017.3 | 0.768223 | ||||||||
\(555\) | 15622.2 | 1.19482 | ||||||||
\(556\) | −9765.92 | −0.744905 | ||||||||
\(557\) | −8504.39 | −0.646934 | −0.323467 | − | 0.946239i | \(-0.604849\pi\) | ||||
−0.323467 | + | 0.946239i | \(0.604849\pi\) | |||||||
\(558\) | 18185.3 | 1.37965 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 25146.3 | 1.89754 | ||||||||
\(561\) | −2498.78 | −0.188055 | ||||||||
\(562\) | −24651.9 | −1.85032 | ||||||||
\(563\) | −18079.0 | −1.35335 | −0.676676 | − | 0.736281i | \(-0.736580\pi\) | ||||
−0.676676 | + | 0.736281i | \(0.736580\pi\) | |||||||
\(564\) | −23517.4 | −1.75579 | ||||||||
\(565\) | −21885.1 | −1.62958 | ||||||||
\(566\) | −13582.9 | −1.00872 | ||||||||
\(567\) | 16377.7 | 1.21305 | ||||||||
\(568\) | 3195.99 | 0.236093 | ||||||||
\(569\) | 18686.5 | 1.37677 | 0.688383 | − | 0.725347i | \(-0.258321\pi\) | ||||
0.688383 | + | 0.725347i | \(0.258321\pi\) | |||||||
\(570\) | 22306.6 | 1.63916 | ||||||||
\(571\) | 5322.93 | 0.390119 | 0.195059 | − | 0.980791i | \(-0.437510\pi\) | ||||
0.195059 | + | 0.980791i | \(0.437510\pi\) | |||||||
\(572\) | 1421.84 | 0.103934 | ||||||||
\(573\) | 28325.5 | 2.06512 | ||||||||
\(574\) | 30840.5 | 2.24261 | ||||||||
\(575\) | −7630.23 | −0.553396 | ||||||||
\(576\) | −21962.1 | −1.58870 | ||||||||
\(577\) | −8955.95 | −0.646171 | −0.323086 | − | 0.946370i | \(-0.604720\pi\) | ||||
−0.323086 | + | 0.946370i | \(0.604720\pi\) | |||||||
\(578\) | 3761.36 | 0.270678 | ||||||||
\(579\) | 12451.5 | 0.893722 | ||||||||
\(580\) | 39487.9 | 2.82697 | ||||||||
\(581\) | 495.908 | 0.0354109 | ||||||||
\(582\) | −10299.6 | −0.733559 | ||||||||
\(583\) | 1696.77 | 0.120537 | ||||||||
\(584\) | −2222.85 | −0.157504 | ||||||||
\(585\) | −48444.8 | −3.42384 | ||||||||
\(586\) | 23498.2 | 1.65649 | ||||||||
\(587\) | −15496.4 | −1.08962 | −0.544810 | − | 0.838560i | \(-0.683398\pi\) | ||||
−0.544810 | + | 0.838560i | \(0.683398\pi\) | |||||||
\(588\) | 658.446 | 0.0461800 | ||||||||
\(589\) | −2778.94 | −0.194404 | ||||||||
\(590\) | −18377.6 | −1.28236 | ||||||||
\(591\) | −43851.8 | −3.05215 | ||||||||
\(592\) | 6335.36 | 0.439834 | ||||||||
\(593\) | −4288.84 | −0.297001 | −0.148500 | − | 0.988912i | \(-0.547445\pi\) | ||||
−0.148500 | + | 0.988912i | \(0.547445\pi\) | |||||||
\(594\) | −4443.17 | −0.306911 | ||||||||
\(595\) | 22484.1 | 1.54917 | ||||||||
\(596\) | 18498.5 | 1.27136 | ||||||||
\(597\) | −31552.3 | −2.16306 | ||||||||
\(598\) | 5695.92 | 0.389504 | ||||||||
\(599\) | 9242.19 | 0.630427 | 0.315213 | − | 0.949021i | \(-0.397924\pi\) | ||||
0.315213 | + | 0.949021i | \(0.397924\pi\) | |||||||
\(600\) | 7383.44 | 0.502379 | ||||||||
\(601\) | −2151.32 | −0.146014 | −0.0730068 | − | 0.997331i | \(-0.523259\pi\) | ||||
−0.0730068 | + | 0.997331i | \(0.523259\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4491.87 | 0.303355 | ||||||||
\(604\) | 2030.89 | 0.136814 | ||||||||
\(605\) | 24986.9 | 1.67911 | ||||||||
\(606\) | 41613.4 | 2.78949 | ||||||||
\(607\) | 3764.19 | 0.251703 | 0.125851 | − | 0.992049i | \(-0.459834\pi\) | ||||
0.125851 | + | 0.992049i | \(0.459834\pi\) | |||||||
\(608\) | 8141.75 | 0.543078 | ||||||||
\(609\) | −49755.1 | −3.31064 | ||||||||
\(610\) | 4782.07 | 0.317410 | ||||||||
\(611\) | −16571.7 | −1.09725 | ||||||||
\(612\) | −24928.8 | −1.64655 | ||||||||
\(613\) | −22176.0 | −1.46114 | −0.730571 | − | 0.682837i | \(-0.760746\pi\) | ||||
−0.730571 | + | 0.682837i | \(0.760746\pi\) | |||||||
\(614\) | −30719.0 | −2.01909 | ||||||||
\(615\) | 73107.2 | 4.79344 | ||||||||
\(616\) | 280.616 | 0.0183545 | ||||||||
\(617\) | −8804.57 | −0.574487 | −0.287244 | − | 0.957858i | \(-0.592739\pi\) | ||||
−0.287244 | + | 0.957858i | \(0.592739\pi\) | |||||||
\(618\) | −16163.5 | −1.05209 | ||||||||
\(619\) | −11451.5 | −0.743579 | −0.371789 | − | 0.928317i | \(-0.621256\pi\) | ||||
−0.371789 | + | 0.928317i | \(0.621256\pi\) | |||||||
\(620\) | 11384.4 | 0.737435 | ||||||||
\(621\) | −8382.99 | −0.541704 | ||||||||
\(622\) | 41573.7 | 2.67999 | ||||||||
\(623\) | −6537.02 | −0.420386 | ||||||||
\(624\) | −29165.5 | −1.87108 | ||||||||
\(625\) | 11191.6 | 0.716262 | ||||||||
\(626\) | 4711.23 | 0.300796 | ||||||||
\(627\) | 1317.22 | 0.0838990 | ||||||||
\(628\) | 9447.62 | 0.600320 | ||||||||
\(629\) | 5664.64 | 0.359084 | ||||||||
\(630\) | 77561.6 | 4.90496 | ||||||||
\(631\) | 1972.40 | 0.124437 | 0.0622187 | − | 0.998063i | \(-0.480182\pi\) | ||||
0.0622187 | + | 0.998063i | \(0.480182\pi\) | |||||||
\(632\) | 3804.51 | 0.239455 | ||||||||
\(633\) | −8639.60 | −0.542486 | ||||||||
\(634\) | 25164.2 | 1.57634 | ||||||||
\(635\) | 25804.9 | 1.61266 | ||||||||
\(636\) | 25129.8 | 1.56676 | ||||||||
\(637\) | 463.978 | 0.0288594 | ||||||||
\(638\) | 4951.02 | 0.307230 | ||||||||
\(639\) | 52163.2 | 3.22933 | ||||||||
\(640\) | 8273.34 | 0.510988 | ||||||||
\(641\) | 4829.62 | 0.297595 | 0.148798 | − | 0.988868i | \(-0.452460\pi\) | ||||
0.148798 | + | 0.988868i | \(0.452460\pi\) | |||||||
\(642\) | 25885.3 | 1.59130 | ||||||||
\(643\) | 7867.97 | 0.482554 | 0.241277 | − | 0.970456i | \(-0.422434\pi\) | ||||
0.241277 | + | 0.970456i | \(0.422434\pi\) | |||||||
\(644\) | −4294.95 | −0.262802 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8088.43 | 0.492624 | ||||||||
\(647\) | 378.715 | 0.0230121 | 0.0115060 | − | 0.999934i | \(-0.496337\pi\) | ||||
0.0115060 | + | 0.999934i | \(0.496337\pi\) | |||||||
\(648\) | 2975.35 | 0.180375 | ||||||||
\(649\) | −1085.21 | −0.0656368 | ||||||||
\(650\) | −42206.0 | −2.54685 | ||||||||
\(651\) | −14344.5 | −0.863603 | ||||||||
\(652\) | −1301.59 | −0.0781815 | ||||||||
\(653\) | −4432.62 | −0.265639 | −0.132819 | − | 0.991140i | \(-0.542403\pi\) | ||||
−0.132819 | + | 0.991140i | \(0.542403\pi\) | |||||||
\(654\) | 4218.62 | 0.252234 | ||||||||
\(655\) | −18780.6 | −1.12033 | ||||||||
\(656\) | 29647.6 | 1.76455 | ||||||||
\(657\) | −36280.1 | −2.15437 | ||||||||
\(658\) | 26531.8 | 1.57191 | ||||||||
\(659\) | 24352.2 | 1.43950 | 0.719748 | − | 0.694236i | \(-0.244257\pi\) | ||||
0.719748 | + | 0.694236i | \(0.244257\pi\) | |||||||
\(660\) | −5396.23 | −0.318254 | ||||||||
\(661\) | −7875.21 | −0.463404 | −0.231702 | − | 0.972787i | \(-0.574429\pi\) | ||||
−0.231702 | + | 0.972787i | \(0.574429\pi\) | |||||||
\(662\) | −5427.98 | −0.318678 | ||||||||
\(663\) | −26077.8 | −1.52757 | ||||||||
\(664\) | 90.0918 | 0.00526542 | ||||||||
\(665\) | −11852.3 | −0.691149 | ||||||||
\(666\) | 19540.9 | 1.13693 | ||||||||
\(667\) | 9341.16 | 0.542266 | ||||||||
\(668\) | −20101.0 | −1.16427 | ||||||||
\(669\) | −46641.9 | −2.69549 | ||||||||
\(670\) | 5970.66 | 0.344279 | ||||||||
\(671\) | 282.385 | 0.0162464 | ||||||||
\(672\) | 42026.6 | 2.41252 | ||||||||
\(673\) | 3508.40 | 0.200949 | 0.100475 | − | 0.994940i | \(-0.467964\pi\) | ||||
0.100475 | + | 0.994940i | \(0.467964\pi\) | |||||||
\(674\) | −44910.1 | −2.56658 | ||||||||
\(675\) | 62116.9 | 3.54204 | ||||||||
\(676\) | −808.495 | −0.0459999 | ||||||||
\(677\) | −18304.0 | −1.03912 | −0.519558 | − | 0.854435i | \(-0.673903\pi\) | ||||
−0.519558 | + | 0.854435i | \(0.673903\pi\) | |||||||
\(678\) | −40639.1 | −2.30197 | ||||||||
\(679\) | 5472.57 | 0.309305 | ||||||||
\(680\) | 4084.68 | 0.230354 | ||||||||
\(681\) | 34731.6 | 1.95436 | ||||||||
\(682\) | 1427.39 | 0.0801430 | ||||||||
\(683\) | 14143.7 | 0.792378 | 0.396189 | − | 0.918169i | \(-0.370332\pi\) | ||||
0.396189 | + | 0.918169i | \(0.370332\pi\) | |||||||
\(684\) | 13141.1 | 0.734593 | ||||||||
\(685\) | −16701.3 | −0.931568 | ||||||||
\(686\) | 24323.3 | 1.35375 | ||||||||
\(687\) | −23530.0 | −1.30674 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17707.9 | 0.979123 | ||||||||
\(690\) | −21617.3 | −1.19269 | ||||||||
\(691\) | 2755.08 | 0.151676 | 0.0758380 | − | 0.997120i | \(-0.475837\pi\) | ||||
0.0758380 | + | 0.997120i | \(0.475837\pi\) | |||||||
\(692\) | −20775.3 | −1.14127 | ||||||||
\(693\) | 4580.07 | 0.251057 | ||||||||
\(694\) | −15441.9 | −0.844621 | ||||||||
\(695\) | 26117.4 | 1.42545 | ||||||||
\(696\) | −9039.03 | −0.492275 | ||||||||
\(697\) | 26508.9 | 1.44060 | ||||||||
\(698\) | 5684.98 | 0.308281 | ||||||||
\(699\) | 33293.4 | 1.80153 | ||||||||
\(700\) | 31825.0 | 1.71839 | ||||||||
\(701\) | −27986.8 | −1.50792 | −0.753958 | − | 0.656923i | \(-0.771858\pi\) | ||||
−0.753958 | + | 0.656923i | \(0.771858\pi\) | |||||||
\(702\) | −46369.8 | −2.49304 | ||||||||
\(703\) | −2986.08 | −0.160202 | ||||||||
\(704\) | −1723.83 | −0.0922861 | ||||||||
\(705\) | 62893.5 | 3.35987 | ||||||||
\(706\) | 18094.0 | 0.964559 | ||||||||
\(707\) | −22110.8 | −1.17618 | ||||||||
\(708\) | −16072.4 | −0.853159 | ||||||||
\(709\) | 18906.6 | 1.00148 | 0.500741 | − | 0.865597i | \(-0.333061\pi\) | ||||
0.500741 | + | 0.865597i | \(0.333061\pi\) | |||||||
\(710\) | 69336.1 | 3.66498 | ||||||||
\(711\) | 62095.1 | 3.27532 | ||||||||
\(712\) | −1187.58 | −0.0625092 | ||||||||
\(713\) | 2693.08 | 0.141454 | ||||||||
\(714\) | 41751.4 | 2.18838 | ||||||||
\(715\) | −3802.49 | −0.198888 | ||||||||
\(716\) | −15954.4 | −0.832744 | ||||||||
\(717\) | 7640.98 | 0.397988 | ||||||||
\(718\) | −330.368 | −0.0171716 | ||||||||
\(719\) | 25788.9 | 1.33764 | 0.668820 | − | 0.743424i | \(-0.266800\pi\) | ||||
0.668820 | + | 0.743424i | \(0.266800\pi\) | |||||||
\(720\) | 74561.7 | 3.85938 | ||||||||
\(721\) | 8588.26 | 0.443611 | ||||||||
\(722\) | 22408.9 | 1.15509 | ||||||||
\(723\) | −11256.9 | −0.579045 | ||||||||
\(724\) | −29203.2 | −1.49907 | ||||||||
\(725\) | −69216.8 | −3.54572 | ||||||||
\(726\) | 46399.0 | 2.37194 | ||||||||
\(727\) | 15335.9 | 0.782364 | 0.391182 | − | 0.920313i | \(-0.372066\pi\) | ||||
0.391182 | + | 0.920313i | \(0.372066\pi\) | |||||||
\(728\) | 2928.57 | 0.149094 | ||||||||
\(729\) | −15590.1 | −0.792061 | ||||||||
\(730\) | −48224.1 | −2.44500 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4182.22 | 0.211174 | ||||||||
\(733\) | −36179.3 | −1.82308 | −0.911538 | − | 0.411217i | \(-0.865104\pi\) | ||||
−0.911538 | + | 0.411217i | \(0.865104\pi\) | |||||||
\(734\) | 19916.2 | 1.00152 | ||||||||
\(735\) | −1760.90 | −0.0883700 | ||||||||
\(736\) | −7890.18 | −0.395157 | ||||||||
\(737\) | 352.572 | 0.0176216 | ||||||||
\(738\) | 91445.7 | 4.56120 | ||||||||
\(739\) | 26665.5 | 1.32735 | 0.663673 | − | 0.748023i | \(-0.268997\pi\) | ||||
0.663673 | + | 0.748023i | \(0.268997\pi\) | |||||||
\(740\) | 12233.0 | 0.607697 | ||||||||
\(741\) | 13746.8 | 0.681512 | ||||||||
\(742\) | −28350.8 | −1.40268 | ||||||||
\(743\) | −18545.2 | −0.915692 | −0.457846 | − | 0.889032i | \(-0.651379\pi\) | ||||
−0.457846 | + | 0.889032i | \(0.651379\pi\) | |||||||
\(744\) | −2605.97 | −0.128413 | ||||||||
\(745\) | −49471.3 | −2.43287 | ||||||||
\(746\) | 3494.38 | 0.171499 | ||||||||
\(747\) | 1470.43 | 0.0720216 | ||||||||
\(748\) | −1956.69 | −0.0956466 | ||||||||
\(749\) | −13753.9 | −0.670968 | ||||||||
\(750\) | 75974.5 | 3.69893 | ||||||||
\(751\) | 19902.5 | 0.967048 | 0.483524 | − | 0.875331i | \(-0.339357\pi\) | ||||
0.483524 | + | 0.875331i | \(0.339357\pi\) | |||||||
\(752\) | 25505.6 | 1.23683 | ||||||||
\(753\) | −43506.2 | −2.10552 | ||||||||
\(754\) | 51669.9 | 2.49563 | ||||||||
\(755\) | −5431.28 | −0.261808 | ||||||||
\(756\) | 34964.7 | 1.68208 | ||||||||
\(757\) | −34693.7 | −1.66574 | −0.832869 | − | 0.553470i | \(-0.813303\pi\) | ||||
−0.832869 | + | 0.553470i | \(0.813303\pi\) | |||||||
\(758\) | −35385.2 | −1.69558 | ||||||||
\(759\) | −1276.52 | −0.0610471 | ||||||||
\(760\) | −2153.22 | −0.102770 | ||||||||
\(761\) | 6333.20 | 0.301680 | 0.150840 | − | 0.988558i | \(-0.451802\pi\) | ||||
0.150840 | + | 0.988558i | \(0.451802\pi\) | |||||||
\(762\) | 47918.0 | 2.27807 | ||||||||
\(763\) | −2241.52 | −0.106354 | ||||||||
\(764\) | 22180.5 | 1.05034 | ||||||||
\(765\) | 66668.0 | 3.15083 | ||||||||
\(766\) | 23602.0 | 1.11328 | ||||||||
\(767\) | −11325.5 | −0.533168 | ||||||||
\(768\) | 44040.8 | 2.06925 | ||||||||
\(769\) | −7479.29 | −0.350729 | −0.175364 | − | 0.984504i | \(-0.556110\pi\) | ||||
−0.175364 | + | 0.984504i | \(0.556110\pi\) | |||||||
\(770\) | 6087.90 | 0.284925 | ||||||||
\(771\) | 29598.3 | 1.38256 | ||||||||
\(772\) | 9750.20 | 0.454556 | ||||||||
\(773\) | −18737.7 | −0.871860 | −0.435930 | − | 0.899981i | \(-0.643580\pi\) | ||||
−0.435930 | + | 0.899981i | \(0.643580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19955.3 | −0.924925 | ||||||||
\(776\) | 994.202 | 0.0459920 | ||||||||
\(777\) | −15413.8 | −0.711667 | ||||||||
\(778\) | −32212.2 | −1.48440 | ||||||||
\(779\) | −13974.0 | −0.642710 | ||||||||
\(780\) | −56316.2 | −2.58518 | ||||||||
\(781\) | 4094.35 | 0.187589 | ||||||||
\(782\) | −7838.51 | −0.358446 | ||||||||
\(783\) | −76045.3 | −3.47080 | ||||||||
\(784\) | −714.111 | −0.0325306 | ||||||||
\(785\) | −25266.1 | −1.14877 | ||||||||
\(786\) | −34874.2 | −1.58260 | ||||||||
\(787\) | −29807.9 | −1.35011 | −0.675054 | − | 0.737768i | \(-0.735880\pi\) | ||||
−0.675054 | + | 0.737768i | \(0.735880\pi\) | |||||||
\(788\) | −34338.4 | −1.55236 | ||||||||
\(789\) | −40925.3 | −1.84661 | ||||||||
\(790\) | 82537.8 | 3.71717 | ||||||||
\(791\) | 21593.1 | 0.970624 | ||||||||
\(792\) | 832.062 | 0.0373308 | ||||||||
\(793\) | 2947.03 | 0.131970 | ||||||||
\(794\) | −22678.6 | −1.01364 | ||||||||
\(795\) | −67205.5 | −2.99815 | ||||||||
\(796\) | −24707.2 | −1.10016 | ||||||||
\(797\) | −23158.3 | −1.02924 | −0.514622 | − | 0.857417i | \(-0.672068\pi\) | ||||
−0.514622 | + | 0.857417i | \(0.672068\pi\) | |||||||
\(798\) | −22009.0 | −0.976329 | ||||||||
\(799\) | 22805.4 | 1.00976 | ||||||||
\(800\) | 58465.2 | 2.58382 | ||||||||
\(801\) | −19383.1 | −0.855015 | ||||||||
\(802\) | 54602.4 | 2.40409 | ||||||||
\(803\) | −2847.67 | −0.125146 | ||||||||
\(804\) | 5221.71 | 0.229049 | ||||||||
\(805\) | 11486.1 | 0.502898 | ||||||||
\(806\) | 14896.5 | 0.651002 | ||||||||
\(807\) | 39983.3 | 1.74409 | ||||||||
\(808\) | −4016.88 | −0.174893 | ||||||||
\(809\) | −18381.5 | −0.798836 | −0.399418 | − | 0.916769i | \(-0.630788\pi\) | ||||
−0.399418 | + | 0.916769i | \(0.630788\pi\) | |||||||
\(810\) | 64549.4 | 2.80004 | ||||||||
\(811\) | 32529.5 | 1.40847 | 0.704233 | − | 0.709969i | \(-0.251291\pi\) | ||||
0.704233 | + | 0.709969i | \(0.251291\pi\) | |||||||
\(812\) | −38961.1 | −1.68383 | ||||||||
\(813\) | 4454.25 | 0.192149 | ||||||||
\(814\) | 1533.79 | 0.0660432 | ||||||||
\(815\) | 3480.90 | 0.149608 | ||||||||
\(816\) | 40136.6 | 1.72189 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −9552.23 | −0.408296 | ||||||||
\(819\) | 47798.5 | 2.03934 | ||||||||
\(820\) | 57247.1 | 2.43799 | ||||||||
\(821\) | 24119.8 | 1.02532 | 0.512660 | − | 0.858592i | \(-0.328660\pi\) | ||||
0.512660 | + | 0.858592i | \(0.328660\pi\) | |||||||
\(822\) | −31013.2 | −1.31595 | ||||||||
\(823\) | −22679.7 | −0.960588 | −0.480294 | − | 0.877108i | \(-0.659470\pi\) | ||||
−0.480294 | + | 0.877108i | \(0.659470\pi\) | |||||||
\(824\) | 1560.23 | 0.0659627 | ||||||||
\(825\) | 9458.84 | 0.399169 | ||||||||
\(826\) | 18132.5 | 0.763812 | ||||||||
\(827\) | 7335.57 | 0.308443 | 0.154222 | − | 0.988036i | \(-0.450713\pi\) | ||||
0.154222 | + | 0.988036i | \(0.450713\pi\) | |||||||
\(828\) | −12735.0 | −0.534509 | ||||||||
\(829\) | 2389.09 | 0.100092 | 0.0500461 | − | 0.998747i | \(-0.484063\pi\) | ||||
0.0500461 | + | 0.998747i | \(0.484063\pi\) | |||||||
\(830\) | 1954.52 | 0.0817376 | ||||||||
\(831\) | −23429.3 | −0.978042 | ||||||||
\(832\) | −17990.3 | −0.749641 | ||||||||
\(833\) | −638.509 | −0.0265583 | ||||||||
\(834\) | 48498.2 | 2.01361 | ||||||||
\(835\) | 53756.8 | 2.22794 | ||||||||
\(836\) | 1031.46 | 0.0426719 | ||||||||
\(837\) | −21924.0 | −0.905383 | ||||||||
\(838\) | −36602.4 | −1.50884 | ||||||||
\(839\) | −6893.41 | −0.283656 | −0.141828 | − | 0.989891i | \(-0.545298\pi\) | ||||
−0.141828 | + | 0.989891i | \(0.545298\pi\) | |||||||
\(840\) | −11114.6 | −0.456537 | ||||||||
\(841\) | 60348.3 | 2.47440 | ||||||||
\(842\) | 29071.2 | 1.18986 | ||||||||
\(843\) | 57657.7 | 2.35568 | ||||||||
\(844\) | −6765.30 | −0.275914 | ||||||||
\(845\) | 2162.19 | 0.0880254 | ||||||||
\(846\) | 78670.0 | 3.19708 | ||||||||
\(847\) | −24653.6 | −1.00013 | ||||||||
\(848\) | −27254.3 | −1.10367 | ||||||||
\(849\) | 31768.8 | 1.28422 | ||||||||
\(850\) | 58082.4 | 2.34377 | ||||||||
\(851\) | 2893.82 | 0.116567 | ||||||||
\(852\) | 60638.7 | 2.43832 | ||||||||
\(853\) | −6006.16 | −0.241087 | −0.120543 | − | 0.992708i | \(-0.538464\pi\) | ||||
−0.120543 | + | 0.992708i | \(0.538464\pi\) | |||||||
\(854\) | −4718.28 | −0.189059 | ||||||||
\(855\) | −35143.6 | −1.40572 | ||||||||
\(856\) | −2498.67 | −0.0997695 | ||||||||
\(857\) | 9759.72 | 0.389015 | 0.194507 | − | 0.980901i | \(-0.437689\pi\) | ||||
0.194507 | + | 0.980901i | \(0.437689\pi\) | |||||||
\(858\) | −7060.96 | −0.280953 | ||||||||
\(859\) | 12026.8 | 0.477705 | 0.238853 | − | 0.971056i | \(-0.423229\pi\) | ||||
0.238853 | + | 0.971056i | \(0.423229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −72131.9 | −2.85511 | ||||||||
\(862\) | −49852.2 | −1.96981 | ||||||||
\(863\) | 36262.9 | 1.43036 | 0.715182 | − | 0.698938i | \(-0.246344\pi\) | ||||
0.715182 | + | 0.698938i | \(0.246344\pi\) | |||||||
\(864\) | 64233.1 | 2.52923 | ||||||||
\(865\) | 55560.2 | 2.18393 | ||||||||
\(866\) | 34723.1 | 1.36252 | ||||||||
\(867\) | −8797.34 | −0.344606 | ||||||||
\(868\) | −11232.6 | −0.439237 | ||||||||
\(869\) | 4873.92 | 0.190260 | ||||||||
\(870\) | −196099. | −7.64182 | ||||||||
\(871\) | 3679.51 | 0.143141 | ||||||||
\(872\) | −407.217 | −0.0158143 | ||||||||
\(873\) | 16226.8 | 0.629089 | ||||||||
\(874\) | 4132.03 | 0.159918 | ||||||||
\(875\) | −40368.2 | −1.55965 | ||||||||
\(876\) | −42175.0 | −1.62667 | ||||||||
\(877\) | −3560.34 | −0.137086 | −0.0685429 | − | 0.997648i | \(-0.521835\pi\) | ||||
−0.0685429 | + | 0.997648i | \(0.521835\pi\) | |||||||
\(878\) | 35128.5 | 1.35026 | ||||||||
\(879\) | −54959.4 | −2.10891 | ||||||||
\(880\) | 5852.43 | 0.224188 | ||||||||
\(881\) | 45565.8 | 1.74251 | 0.871255 | − | 0.490831i | \(-0.163307\pi\) | ||||
0.871255 | + | 0.490831i | \(0.163307\pi\) | |||||||
\(882\) | −2202.62 | −0.0840884 | ||||||||
\(883\) | −12993.7 | −0.495214 | −0.247607 | − | 0.968861i | \(-0.579644\pi\) | ||||
−0.247607 | + | 0.968861i | \(0.579644\pi\) | |||||||
\(884\) | −20420.4 | −0.776938 | ||||||||
\(885\) | 42982.9 | 1.63260 | ||||||||
\(886\) | −28221.3 | −1.07011 | ||||||||
\(887\) | 33676.4 | 1.27480 | 0.637398 | − | 0.770535i | \(-0.280011\pi\) | ||||
0.637398 | + | 0.770535i | \(0.280011\pi\) | |||||||
\(888\) | −2800.22 | −0.105821 | ||||||||
\(889\) | −25460.7 | −0.960545 | ||||||||
\(890\) | −25764.3 | −0.970360 | ||||||||
\(891\) | 3811.69 | 0.143318 | ||||||||
\(892\) | −36523.3 | −1.37095 | ||||||||
\(893\) | −12021.7 | −0.450495 | ||||||||
\(894\) | −91864.9 | −3.43671 | ||||||||
\(895\) | 42667.5 | 1.59354 | ||||||||
\(896\) | −8162.97 | −0.304359 | ||||||||
\(897\) | −13322.0 | −0.495886 | ||||||||
\(898\) | −46054.3 | −1.71142 | ||||||||
\(899\) | 24429.9 | 0.906322 | ||||||||
\(900\) | 94364.9 | 3.49500 | ||||||||
\(901\) | −24368.9 | −0.901050 | ||||||||
\(902\) | 7177.68 | 0.264956 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3922.83 | 0.144327 | ||||||||
\(905\) | 78099.3 | 2.86863 | ||||||||
\(906\) | −10085.5 | −0.369834 | ||||||||
\(907\) | 22376.4 | 0.819180 | 0.409590 | − | 0.912270i | \(-0.365672\pi\) | ||||
0.409590 | + | 0.912270i | \(0.365672\pi\) | |||||||
\(908\) | 27196.8 | 0.994008 | ||||||||
\(909\) | −65561.2 | −2.39222 | ||||||||
\(910\) | 63534.6 | 2.31445 | ||||||||
\(911\) | 52260.5 | 1.90062 | 0.950312 | − | 0.311298i | \(-0.100764\pi\) | ||||
0.950312 | + | 0.311298i | \(0.100764\pi\) | |||||||
\(912\) | −21157.8 | −0.768206 | ||||||||
\(913\) | 115.416 | 0.00418368 | ||||||||
\(914\) | −23862.8 | −0.863579 | ||||||||
\(915\) | −11184.7 | −0.404102 | ||||||||
\(916\) | −18425.4 | −0.664619 | ||||||||
\(917\) | 18530.0 | 0.667301 | ||||||||
\(918\) | 63812.5 | 2.29425 | ||||||||
\(919\) | −30391.1 | −1.09087 | −0.545436 | − | 0.838153i | \(-0.683636\pi\) | ||||
−0.545436 | + | 0.838153i | \(0.683636\pi\) | |||||||
\(920\) | 2086.69 | 0.0747783 | ||||||||
\(921\) | 71847.9 | 2.57054 | ||||||||
\(922\) | −7496.37 | −0.267766 | ||||||||
\(923\) | 42729.5 | 1.52379 | ||||||||
\(924\) | 5324.24 | 0.189561 | ||||||||
\(925\) | −21442.8 | −0.762201 | ||||||||
\(926\) | 41628.9 | 1.47733 | ||||||||
\(927\) | 25465.2 | 0.902253 | ||||||||
\(928\) | −71574.8 | −2.53185 | ||||||||
\(929\) | −9900.90 | −0.349664 | −0.174832 | − | 0.984598i | \(-0.555938\pi\) | ||||
−0.174832 | + | 0.984598i | \(0.555938\pi\) | |||||||
\(930\) | −56535.8 | −1.99342 | ||||||||
\(931\) | 336.587 | 0.0118487 | ||||||||
\(932\) | 26070.6 | 0.916279 | ||||||||
\(933\) | −97235.5 | −3.41195 | ||||||||
\(934\) | 51407.6 | 1.80097 | ||||||||
\(935\) | 5232.84 | 0.183029 | ||||||||
\(936\) | 8683.57 | 0.303239 | ||||||||
\(937\) | −24469.5 | −0.853131 | −0.426566 | − | 0.904457i | \(-0.640277\pi\) | ||||
−0.426566 | + | 0.904457i | \(0.640277\pi\) | |||||||
\(938\) | −5891.01 | −0.205062 | ||||||||
\(939\) | −11019.0 | −0.382950 | ||||||||
\(940\) | 49249.2 | 1.70886 | ||||||||
\(941\) | 8819.85 | 0.305546 | 0.152773 | − | 0.988261i | \(-0.451180\pi\) | ||||
0.152773 | + | 0.988261i | \(0.451180\pi\) | |||||||
\(942\) | −46917.5 | −1.62278 | ||||||||
\(943\) | 13542.2 | 0.467652 | ||||||||
\(944\) | 17431.1 | 0.600991 | ||||||||
\(945\) | −93507.3 | −3.21883 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46001.3 | 1.57850 | 0.789250 | − | 0.614072i | \(-0.210469\pi\) | ||||
0.789250 | + | 0.614072i | \(0.210469\pi\) | |||||||
\(948\) | 72184.5 | 2.47304 | ||||||||
\(949\) | −29718.9 | −1.01656 | ||||||||
\(950\) | −30617.8 | −1.04565 | ||||||||
\(951\) | −58855.8 | −2.00687 | ||||||||
\(952\) | −4030.19 | −0.137205 | ||||||||
\(953\) | 12737.3 | 0.432950 | 0.216475 | − | 0.976288i | \(-0.430544\pi\) | ||||
0.216475 | + | 0.976288i | \(0.430544\pi\) | |||||||
\(954\) | −84063.6 | −2.85289 | ||||||||
\(955\) | −59318.1 | −2.00994 | ||||||||
\(956\) | 5983.32 | 0.202421 | ||||||||
\(957\) | −11579.8 | −0.391141 | ||||||||
\(958\) | 8746.27 | 0.294968 | ||||||||
\(959\) | 16478.5 | 0.554868 | ||||||||
\(960\) | 68277.3 | 2.29546 | ||||||||
\(961\) | −22747.8 | −0.763580 | ||||||||
\(962\) | 16006.9 | 0.536470 | ||||||||
\(963\) | −40781.9 | −1.36467 | ||||||||
\(964\) | −8814.81 | −0.294508 | ||||||||
\(965\) | −26075.3 | −0.869838 | ||||||||
\(966\) | 21329.0 | 0.710402 | ||||||||
\(967\) | 28175.8 | 0.936992 | 0.468496 | − | 0.883466i | \(-0.344796\pi\) | ||||
0.468496 | + | 0.883466i | \(0.344796\pi\) | |||||||
\(968\) | −4478.82 | −0.148714 | ||||||||
\(969\) | −18917.8 | −0.627170 | ||||||||
\(970\) | 21568.9 | 0.713956 | ||||||||
\(971\) | 14012.5 | 0.463113 | 0.231557 | − | 0.972821i | \(-0.425618\pi\) | ||||
0.231557 | + | 0.972821i | \(0.425618\pi\) | |||||||
\(972\) | 6217.67 | 0.205177 | ||||||||
\(973\) | −25768.9 | −0.849039 | ||||||||
\(974\) | −66635.2 | −2.19212 | ||||||||
\(975\) | 98714.5 | 3.24245 | ||||||||
\(976\) | −4535.79 | −0.148757 | ||||||||
\(977\) | 25344.3 | 0.829924 | 0.414962 | − | 0.909839i | \(-0.363795\pi\) | ||||
0.414962 | + | 0.909839i | \(0.363795\pi\) | |||||||
\(978\) | 6463.80 | 0.211339 | ||||||||
\(979\) | −1521.40 | −0.0496671 | ||||||||
\(980\) | −1378.89 | −0.0449459 | ||||||||
\(981\) | −6646.37 | −0.216312 | ||||||||
\(982\) | 66312.6 | 2.15491 | ||||||||
\(983\) | −31795.3 | −1.03165 | −0.515825 | − | 0.856694i | \(-0.672514\pi\) | ||||
−0.515825 | + | 0.856694i | \(0.672514\pi\) | |||||||
\(984\) | −13104.2 | −0.424540 | ||||||||
\(985\) | 91832.5 | 2.97059 | ||||||||
\(986\) | −71106.2 | −2.29663 | ||||||||
\(987\) | −62054.5 | −2.00123 | ||||||||
\(988\) | 10764.5 | 0.346624 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 18051.3 | 0.579505 | ||||||||
\(991\) | −57046.1 | −1.82859 | −0.914294 | − | 0.405051i | \(-0.867254\pi\) | ||||
−0.914294 | + | 0.405051i | \(0.867254\pi\) | |||||||
\(992\) | −20635.2 | −0.660451 | ||||||||
\(993\) | 12695.4 | 0.405715 | ||||||||
\(994\) | −68411.2 | −2.18297 | ||||||||
\(995\) | 66075.4 | 2.10526 | ||||||||
\(996\) | 1709.35 | 0.0543802 | ||||||||
\(997\) | −14197.2 | −0.450984 | −0.225492 | − | 0.974245i | \(-0.572399\pi\) | ||||
−0.225492 | + | 0.974245i | \(0.572399\pi\) | |||||||
\(998\) | −27997.1 | −0.888008 | ||||||||
\(999\) | −23558.3 | −0.746096 |
(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.j.1.10 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.41 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.41 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.10 | yes | 50 | 1.1 | even | 1 | trivial |