Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(109.684550701\) |
Analytic rank: | \(0\) |
Dimension: | \(51\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.92218 | −1.03315 | −0.516574 | − | 0.856243i | \(-0.672793\pi\) | ||||
−0.516574 | + | 0.856243i | \(0.672793\pi\) | |||||||
\(3\) | −6.70384 | −1.29015 | −0.645077 | − | 0.764118i | \(-0.723175\pi\) | ||||
−0.645077 | + | 0.764118i | \(0.723175\pi\) | |||||||
\(4\) | 0.539146 | 0.0673933 | ||||||||
\(5\) | 12.5727 | 1.12453 | 0.562267 | − | 0.826956i | \(-0.309929\pi\) | ||||
0.562267 | + | 0.826956i | \(0.309929\pi\) | |||||||
\(6\) | 19.5898 | 1.33292 | ||||||||
\(7\) | −15.7135 | −0.848449 | −0.424224 | − | 0.905557i | \(-0.639453\pi\) | ||||
−0.424224 | + | 0.905557i | \(0.639453\pi\) | |||||||
\(8\) | 21.8020 | 0.963520 | ||||||||
\(9\) | 17.9414 | 0.664497 | ||||||||
\(10\) | −36.7396 | −1.16181 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −3.61435 | −0.0869477 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 45.9177 | 0.876572 | ||||||||
\(15\) | −84.2851 | −1.45082 | ||||||||
\(16\) | −68.0225 | −1.06285 | ||||||||
\(17\) | 88.6878 | 1.26529 | 0.632646 | − | 0.774441i | \(-0.281969\pi\) | ||||
0.632646 | + | 0.774441i | \(0.281969\pi\) | |||||||
\(18\) | −52.4281 | −0.686523 | ||||||||
\(19\) | 129.741 | 1.56656 | 0.783282 | − | 0.621666i | \(-0.213544\pi\) | ||||
0.783282 | + | 0.621666i | \(0.213544\pi\) | |||||||
\(20\) | 6.77851 | 0.0757861 | ||||||||
\(21\) | 105.341 | 1.09463 | ||||||||
\(22\) | −32.1440 | −0.311506 | ||||||||
\(23\) | −172.749 | −1.56611 | −0.783057 | − | 0.621949i | \(-0.786341\pi\) | ||||
−0.783057 | + | 0.621949i | \(0.786341\pi\) | |||||||
\(24\) | −146.157 | −1.24309 | ||||||||
\(25\) | 33.0721 | 0.264577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 60.7273 | 0.432851 | ||||||||
\(28\) | −8.47187 | −0.0571798 | ||||||||
\(29\) | 5.46969 | 0.0350240 | 0.0175120 | − | 0.999847i | \(-0.494425\pi\) | ||||
0.0175120 | + | 0.999847i | \(0.494425\pi\) | |||||||
\(30\) | 246.296 | 1.49891 | ||||||||
\(31\) | 222.253 | 1.28767 | 0.643836 | − | 0.765164i | \(-0.277342\pi\) | ||||
0.643836 | + | 0.765164i | \(0.277342\pi\) | |||||||
\(32\) | 24.3583 | 0.134562 | ||||||||
\(33\) | −73.7422 | −0.388996 | ||||||||
\(34\) | −259.162 | −1.30723 | ||||||||
\(35\) | −197.561 | −0.954109 | ||||||||
\(36\) | 9.67305 | 0.0447826 | ||||||||
\(37\) | 351.233 | 1.56060 | 0.780302 | − | 0.625403i | \(-0.215066\pi\) | ||||
0.780302 | + | 0.625403i | \(0.215066\pi\) | |||||||
\(38\) | −379.128 | −1.61849 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 274.109 | 1.08351 | ||||||||
\(41\) | 424.792 | 1.61808 | 0.809042 | − | 0.587751i | \(-0.199987\pi\) | ||||
0.809042 | + | 0.587751i | \(0.199987\pi\) | |||||||
\(42\) | −307.825 | −1.13091 | ||||||||
\(43\) | −155.625 | −0.551920 | −0.275960 | − | 0.961169i | \(-0.588996\pi\) | ||||
−0.275960 | + | 0.961169i | \(0.588996\pi\) | |||||||
\(44\) | 5.93061 | 0.0203198 | ||||||||
\(45\) | 225.571 | 0.747249 | ||||||||
\(46\) | 504.804 | 1.61803 | ||||||||
\(47\) | 406.439 | 1.26139 | 0.630694 | − | 0.776031i | \(-0.282770\pi\) | ||||
0.630694 | + | 0.776031i | \(0.282770\pi\) | |||||||
\(48\) | 456.012 | 1.37124 | ||||||||
\(49\) | −96.0862 | −0.280135 | ||||||||
\(50\) | −96.6427 | −0.273347 | ||||||||
\(51\) | −594.548 | −1.63242 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 280.727 | 0.727562 | 0.363781 | − | 0.931485i | \(-0.381486\pi\) | ||||
0.363781 | + | 0.931485i | \(0.381486\pi\) | |||||||
\(54\) | −177.456 | −0.447199 | ||||||||
\(55\) | 138.299 | 0.339060 | ||||||||
\(56\) | −342.585 | −0.817497 | ||||||||
\(57\) | −869.765 | −2.02111 | ||||||||
\(58\) | −15.9834 | −0.0361849 | ||||||||
\(59\) | −108.495 | −0.239405 | −0.119702 | − | 0.992810i | \(-0.538194\pi\) | ||||
−0.119702 | + | 0.992810i | \(0.538194\pi\) | |||||||
\(60\) | −45.4420 | −0.0977757 | ||||||||
\(61\) | 388.485 | 0.815416 | 0.407708 | − | 0.913112i | \(-0.366328\pi\) | ||||
0.407708 | + | 0.913112i | \(0.366328\pi\) | |||||||
\(62\) | −649.464 | −1.33035 | ||||||||
\(63\) | −281.922 | −0.563791 | ||||||||
\(64\) | 473.000 | 0.923829 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 215.488 | 0.401890 | ||||||||
\(67\) | −651.390 | −1.18776 | −0.593881 | − | 0.804553i | \(-0.702405\pi\) | ||||
−0.593881 | + | 0.804553i | \(0.702405\pi\) | |||||||
\(68\) | 47.8157 | 0.0852722 | ||||||||
\(69\) | 1158.08 | 2.02053 | ||||||||
\(70\) | 577.308 | 0.985736 | ||||||||
\(71\) | 382.632 | 0.639578 | 0.319789 | − | 0.947489i | \(-0.396388\pi\) | ||||
0.319789 | + | 0.947489i | \(0.396388\pi\) | |||||||
\(72\) | 391.158 | 0.640256 | ||||||||
\(73\) | −211.476 | −0.339060 | −0.169530 | − | 0.985525i | \(-0.554225\pi\) | ||||
−0.169530 | + | 0.985525i | \(0.554225\pi\) | |||||||
\(74\) | −1026.37 | −1.61233 | ||||||||
\(75\) | −221.710 | −0.341345 | ||||||||
\(76\) | 69.9496 | 0.105576 | ||||||||
\(77\) | −172.848 | −0.255817 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 313.752 | 0.446834 | 0.223417 | − | 0.974723i | \(-0.428279\pi\) | ||||
0.223417 | + | 0.974723i | \(0.428279\pi\) | |||||||
\(80\) | −855.225 | −1.19521 | ||||||||
\(81\) | −891.524 | −1.22294 | ||||||||
\(82\) | −1241.32 | −1.67172 | ||||||||
\(83\) | 1127.22 | 1.49070 | 0.745351 | − | 0.666673i | \(-0.232282\pi\) | ||||
0.745351 | + | 0.666673i | \(0.232282\pi\) | |||||||
\(84\) | 56.7940 | 0.0737707 | ||||||||
\(85\) | 1115.04 | 1.42286 | ||||||||
\(86\) | 454.764 | 0.570214 | ||||||||
\(87\) | −36.6679 | −0.0451863 | ||||||||
\(88\) | 239.822 | 0.290512 | ||||||||
\(89\) | −591.138 | −0.704051 | −0.352025 | − | 0.935990i | \(-0.614507\pi\) | ||||
−0.352025 | + | 0.935990i | \(0.614507\pi\) | |||||||
\(90\) | −659.161 | −0.772018 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −93.1370 | −0.105546 | ||||||||
\(93\) | −1489.95 | −1.66129 | ||||||||
\(94\) | −1187.69 | −1.30320 | ||||||||
\(95\) | 1631.20 | 1.76165 | ||||||||
\(96\) | −163.294 | −0.173606 | ||||||||
\(97\) | −490.807 | −0.513751 | −0.256876 | − | 0.966444i | \(-0.582693\pi\) | ||||
−0.256876 | + | 0.966444i | \(0.582693\pi\) | |||||||
\(98\) | 280.781 | 0.289421 | ||||||||
\(99\) | 197.356 | 0.200353 | ||||||||
\(100\) | 17.8307 | 0.0178307 | ||||||||
\(101\) | 1763.94 | 1.73781 | 0.868904 | − | 0.494980i | \(-0.164825\pi\) | ||||
0.868904 | + | 0.494980i | \(0.164825\pi\) | |||||||
\(102\) | 1737.38 | 1.68653 | ||||||||
\(103\) | −1850.35 | −1.77010 | −0.885049 | − | 0.465497i | \(-0.845876\pi\) | ||||
−0.885049 | + | 0.465497i | \(0.845876\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1324.41 | 1.23095 | ||||||||
\(106\) | −820.335 | −0.751679 | ||||||||
\(107\) | −1214.07 | −1.09690 | −0.548452 | − | 0.836182i | \(-0.684783\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(108\) | 32.7409 | 0.0291712 | ||||||||
\(109\) | −890.434 | −0.782460 | −0.391230 | − | 0.920293i | \(-0.627950\pi\) | ||||
−0.391230 | + | 0.920293i | \(0.627950\pi\) | |||||||
\(110\) | −404.136 | −0.350299 | ||||||||
\(111\) | −2354.61 | −2.01342 | ||||||||
\(112\) | 1068.87 | 0.901775 | ||||||||
\(113\) | 511.933 | 0.426183 | 0.213091 | − | 0.977032i | \(-0.431647\pi\) | ||||
0.213091 | + | 0.977032i | \(0.431647\pi\) | |||||||
\(114\) | 2541.61 | 2.08810 | ||||||||
\(115\) | −2171.92 | −1.76115 | ||||||||
\(116\) | 2.94896 | 0.00236038 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 317.043 | 0.247340 | ||||||||
\(119\) | −1393.59 | −1.07353 | ||||||||
\(120\) | −1837.58 | −1.39790 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1135.22 | −0.842445 | ||||||||
\(123\) | −2847.74 | −2.08758 | ||||||||
\(124\) | 119.827 | 0.0867804 | ||||||||
\(125\) | −1155.78 | −0.827008 | ||||||||
\(126\) | 823.828 | 0.582480 | ||||||||
\(127\) | 770.909 | 0.538639 | 0.269319 | − | 0.963051i | \(-0.413201\pi\) | ||||
0.269319 | + | 0.963051i | \(0.413201\pi\) | |||||||
\(128\) | −1577.06 | −1.08901 | ||||||||
\(129\) | 1043.28 | 0.712061 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −910.833 | −0.607480 | −0.303740 | − | 0.952755i | \(-0.598235\pi\) | ||||
−0.303740 | + | 0.952755i | \(0.598235\pi\) | |||||||
\(132\) | −39.7578 | −0.0262157 | ||||||||
\(133\) | −2038.69 | −1.32915 | ||||||||
\(134\) | 1903.48 | 1.22713 | ||||||||
\(135\) | 763.504 | 0.486755 | ||||||||
\(136\) | 1933.57 | 1.21913 | ||||||||
\(137\) | 639.809 | 0.398997 | 0.199498 | − | 0.979898i | \(-0.436069\pi\) | ||||
0.199498 | + | 0.979898i | \(0.436069\pi\) | |||||||
\(138\) | −3384.12 | −2.08750 | ||||||||
\(139\) | −1313.92 | −0.801765 | −0.400882 | − | 0.916130i | \(-0.631296\pi\) | ||||
−0.400882 | + | 0.916130i | \(0.631296\pi\) | |||||||
\(140\) | −106.514 | −0.0643006 | ||||||||
\(141\) | −2724.70 | −1.62739 | ||||||||
\(142\) | −1118.12 | −0.660778 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1220.42 | −0.706261 | ||||||||
\(145\) | 68.7686 | 0.0393857 | ||||||||
\(146\) | 617.971 | 0.350299 | ||||||||
\(147\) | 644.146 | 0.361417 | ||||||||
\(148\) | 189.366 | 0.105174 | ||||||||
\(149\) | −179.585 | −0.0987394 | −0.0493697 | − | 0.998781i | \(-0.515721\pi\) | ||||
−0.0493697 | + | 0.998781i | \(0.515721\pi\) | |||||||
\(150\) | 647.876 | 0.352659 | ||||||||
\(151\) | −113.223 | −0.0610193 | −0.0305097 | − | 0.999534i | \(-0.509713\pi\) | ||||
−0.0305097 | + | 0.999534i | \(0.509713\pi\) | |||||||
\(152\) | 2828.62 | 1.50942 | ||||||||
\(153\) | 1591.18 | 0.840782 | ||||||||
\(154\) | 505.094 | 0.264297 | ||||||||
\(155\) | 2794.31 | 1.44803 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −704.857 | −0.358304 | −0.179152 | − | 0.983821i | \(-0.557335\pi\) | ||||
−0.179152 | + | 0.983821i | \(0.557335\pi\) | |||||||
\(158\) | −916.841 | −0.461645 | ||||||||
\(159\) | −1881.95 | −0.938667 | ||||||||
\(160\) | 306.249 | 0.151320 | ||||||||
\(161\) | 2714.49 | 1.32877 | ||||||||
\(162\) | 2605.19 | 1.26348 | ||||||||
\(163\) | −2260.35 | −1.08616 | −0.543080 | − | 0.839681i | \(-0.682742\pi\) | ||||
−0.543080 | + | 0.839681i | \(0.682742\pi\) | |||||||
\(164\) | 229.025 | 0.109048 | ||||||||
\(165\) | −927.136 | −0.437439 | ||||||||
\(166\) | −3293.93 | −1.54011 | ||||||||
\(167\) | −923.890 | −0.428100 | −0.214050 | − | 0.976823i | \(-0.568666\pi\) | ||||
−0.214050 | + | 0.976823i | \(0.568666\pi\) | |||||||
\(168\) | 2296.63 | 1.05470 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3258.36 | −1.47003 | ||||||||
\(171\) | 2327.74 | 1.04098 | ||||||||
\(172\) | −83.9045 | −0.0371957 | ||||||||
\(173\) | 1403.82 | 0.616939 | 0.308469 | − | 0.951234i | \(-0.400183\pi\) | ||||
0.308469 | + | 0.951234i | \(0.400183\pi\) | |||||||
\(174\) | 107.150 | 0.0466841 | ||||||||
\(175\) | −519.678 | −0.224480 | ||||||||
\(176\) | −748.247 | −0.320462 | ||||||||
\(177\) | 727.334 | 0.308869 | ||||||||
\(178\) | 1727.41 | 0.727388 | ||||||||
\(179\) | 1096.26 | 0.457754 | 0.228877 | − | 0.973455i | \(-0.426495\pi\) | ||||
0.228877 | + | 0.973455i | \(0.426495\pi\) | |||||||
\(180\) | 121.616 | 0.0503596 | ||||||||
\(181\) | −2728.67 | −1.12055 | −0.560277 | − | 0.828305i | \(-0.689305\pi\) | ||||
−0.560277 | + | 0.828305i | \(0.689305\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2604.34 | −1.05201 | ||||||||
\(184\) | −3766.27 | −1.50898 | ||||||||
\(185\) | 4415.94 | 1.75495 | ||||||||
\(186\) | 4353.90 | 1.71636 | ||||||||
\(187\) | 975.566 | 0.381500 | ||||||||
\(188\) | 219.130 | 0.0850092 | ||||||||
\(189\) | −954.238 | −0.367252 | ||||||||
\(190\) | −4766.65 | −1.82005 | ||||||||
\(191\) | −4359.38 | −1.65149 | −0.825743 | − | 0.564046i | \(-0.809244\pi\) | ||||
−0.825743 | + | 0.564046i | \(0.809244\pi\) | |||||||
\(192\) | −3170.92 | −1.19188 | ||||||||
\(193\) | −3799.30 | −1.41699 | −0.708496 | − | 0.705715i | \(-0.750626\pi\) | ||||
−0.708496 | + | 0.705715i | \(0.750626\pi\) | |||||||
\(194\) | 1434.23 | 0.530781 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −51.8046 | −0.0188792 | ||||||||
\(197\) | 3685.29 | 1.33282 | 0.666411 | − | 0.745585i | \(-0.267830\pi\) | ||||
0.666411 | + | 0.745585i | \(0.267830\pi\) | |||||||
\(198\) | −576.709 | −0.206994 | ||||||||
\(199\) | −1531.37 | −0.545506 | −0.272753 | − | 0.962084i | \(-0.587934\pi\) | ||||
−0.272753 | + | 0.962084i | \(0.587934\pi\) | |||||||
\(200\) | 721.037 | 0.254925 | ||||||||
\(201\) | 4366.81 | 1.53239 | ||||||||
\(202\) | −5154.56 | −1.79541 | ||||||||
\(203\) | −85.9479 | −0.0297160 | ||||||||
\(204\) | −320.549 | −0.110014 | ||||||||
\(205\) | 5340.77 | 1.81959 | ||||||||
\(206\) | 5407.05 | 1.82877 | ||||||||
\(207\) | −3099.36 | −1.04068 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1427.16 | 0.472337 | ||||||||
\(210\) | −3870.18 | −1.27175 | ||||||||
\(211\) | 2857.26 | 0.932237 | 0.466118 | − | 0.884722i | \(-0.345652\pi\) | ||||
0.466118 | + | 0.884722i | \(0.345652\pi\) | |||||||
\(212\) | 151.353 | 0.0490328 | ||||||||
\(213\) | −2565.10 | −0.825154 | ||||||||
\(214\) | 3547.74 | 1.13326 | ||||||||
\(215\) | −1956.62 | −0.620653 | ||||||||
\(216\) | 1323.97 | 0.417060 | ||||||||
\(217\) | −3492.37 | −1.09252 | ||||||||
\(218\) | 2602.01 | 0.808396 | ||||||||
\(219\) | 1417.70 | 0.437439 | ||||||||
\(220\) | 74.5636 | 0.0228504 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6880.59 | 2.08016 | ||||||||
\(223\) | −1800.43 | −0.540654 | −0.270327 | − | 0.962769i | \(-0.587132\pi\) | ||||
−0.270327 | + | 0.962769i | \(0.587132\pi\) | |||||||
\(224\) | −382.754 | −0.114169 | ||||||||
\(225\) | 593.360 | 0.175810 | ||||||||
\(226\) | −1495.96 | −0.440309 | ||||||||
\(227\) | −967.195 | −0.282797 | −0.141399 | − | 0.989953i | \(-0.545160\pi\) | ||||
−0.141399 | + | 0.989953i | \(0.545160\pi\) | |||||||
\(228\) | −468.931 | −0.136209 | ||||||||
\(229\) | 6011.19 | 1.73463 | 0.867316 | − | 0.497758i | \(-0.165843\pi\) | ||||
0.867316 | + | 0.497758i | \(0.165843\pi\) | |||||||
\(230\) | 6346.73 | 1.81953 | ||||||||
\(231\) | 1158.75 | 0.330043 | ||||||||
\(232\) | 119.250 | 0.0337463 | ||||||||
\(233\) | 3591.35 | 1.00977 | 0.504887 | − | 0.863185i | \(-0.331534\pi\) | ||||
0.504887 | + | 0.863185i | \(0.331534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5110.03 | 1.41847 | ||||||||
\(236\) | −58.4948 | −0.0161343 | ||||||||
\(237\) | −2103.34 | −0.576484 | ||||||||
\(238\) | 4072.34 | 1.10912 | ||||||||
\(239\) | −344.523 | −0.0932441 | −0.0466221 | − | 0.998913i | \(-0.514846\pi\) | ||||
−0.0466221 | + | 0.998913i | \(0.514846\pi\) | |||||||
\(240\) | 5733.28 | 1.54201 | ||||||||
\(241\) | 6225.31 | 1.66393 | 0.831965 | − | 0.554828i | \(-0.187216\pi\) | ||||
0.831965 | + | 0.554828i | \(0.187216\pi\) | |||||||
\(242\) | −353.584 | −0.0939225 | ||||||||
\(243\) | 4336.99 | 1.14493 | ||||||||
\(244\) | 209.450 | 0.0549536 | ||||||||
\(245\) | −1208.06 | −0.315021 | ||||||||
\(246\) | 8321.61 | 2.15677 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4845.55 | 1.24070 | ||||||||
\(249\) | −7556.68 | −1.92323 | ||||||||
\(250\) | 3377.40 | 0.854422 | ||||||||
\(251\) | 2041.80 | 0.513456 | 0.256728 | − | 0.966484i | \(-0.417355\pi\) | ||||
0.256728 | + | 0.966484i | \(0.417355\pi\) | |||||||
\(252\) | −151.997 | −0.0379958 | ||||||||
\(253\) | −1900.24 | −0.472201 | ||||||||
\(254\) | −2252.74 | −0.556493 | ||||||||
\(255\) | −7475.06 | −1.83571 | ||||||||
\(256\) | 824.452 | 0.201282 | ||||||||
\(257\) | 4146.55 | 1.00644 | 0.503219 | − | 0.864159i | \(-0.332149\pi\) | ||||
0.503219 | + | 0.864159i | \(0.332149\pi\) | |||||||
\(258\) | −3048.66 | −0.735664 | ||||||||
\(259\) | −5519.09 | −1.32409 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 98.1339 | 0.0232733 | ||||||||
\(262\) | 2661.62 | 0.627616 | ||||||||
\(263\) | 5697.94 | 1.33593 | 0.667966 | − | 0.744192i | \(-0.267165\pi\) | ||||
0.667966 | + | 0.744192i | \(0.267165\pi\) | |||||||
\(264\) | −1607.73 | −0.374805 | ||||||||
\(265\) | 3529.49 | 0.818168 | ||||||||
\(266\) | 5957.42 | 1.37321 | ||||||||
\(267\) | 3962.89 | 0.908334 | ||||||||
\(268\) | −351.195 | −0.0800471 | ||||||||
\(269\) | −407.309 | −0.0923200 | −0.0461600 | − | 0.998934i | \(-0.514698\pi\) | ||||
−0.0461600 | + | 0.998934i | \(0.514698\pi\) | |||||||
\(270\) | −2231.10 | −0.502890 | ||||||||
\(271\) | −1527.40 | −0.342373 | −0.171187 | − | 0.985239i | \(-0.554760\pi\) | ||||
−0.171187 | + | 0.985239i | \(0.554760\pi\) | |||||||
\(272\) | −6032.77 | −1.34482 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1869.64 | −0.412222 | ||||||||
\(275\) | 363.793 | 0.0797729 | ||||||||
\(276\) | 624.375 | 0.136170 | ||||||||
\(277\) | 2903.33 | 0.629762 | 0.314881 | − | 0.949131i | \(-0.398035\pi\) | ||||
0.314881 | + | 0.949131i | \(0.398035\pi\) | |||||||
\(278\) | 3839.51 | 0.828341 | ||||||||
\(279\) | 3987.53 | 0.855654 | ||||||||
\(280\) | −4307.21 | −0.919304 | ||||||||
\(281\) | −1930.54 | −0.409844 | −0.204922 | − | 0.978778i | \(-0.565694\pi\) | ||||
−0.204922 | + | 0.978778i | \(0.565694\pi\) | |||||||
\(282\) | 7962.08 | 1.68133 | ||||||||
\(283\) | 4950.15 | 1.03977 | 0.519887 | − | 0.854235i | \(-0.325974\pi\) | ||||
0.519887 | + | 0.854235i | \(0.325974\pi\) | |||||||
\(284\) | 206.294 | 0.0431033 | ||||||||
\(285\) | −10935.3 | −2.27281 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6674.97 | −1.37286 | ||||||||
\(288\) | 437.023 | 0.0894160 | ||||||||
\(289\) | 2952.53 | 0.600962 | ||||||||
\(290\) | −200.954 | −0.0406912 | ||||||||
\(291\) | 3290.29 | 0.662818 | ||||||||
\(292\) | −114.016 | −0.0228504 | ||||||||
\(293\) | −4052.66 | −0.808051 | −0.404025 | − | 0.914748i | \(-0.632389\pi\) | ||||
−0.404025 | + | 0.914748i | \(0.632389\pi\) | |||||||
\(294\) | −1882.31 | −0.373397 | ||||||||
\(295\) | −1364.07 | −0.269219 | ||||||||
\(296\) | 7657.57 | 1.50367 | ||||||||
\(297\) | 668.000 | 0.130509 | ||||||||
\(298\) | 524.780 | 0.102012 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −119.534 | −0.0230043 | ||||||||
\(301\) | 2445.41 | 0.468276 | ||||||||
\(302\) | 330.857 | 0.0630420 | ||||||||
\(303\) | −11825.2 | −2.24204 | ||||||||
\(304\) | −8825.33 | −1.66503 | ||||||||
\(305\) | 4884.29 | 0.916963 | ||||||||
\(306\) | −4649.73 | −0.868651 | ||||||||
\(307\) | −8180.84 | −1.52086 | −0.760432 | − | 0.649418i | \(-0.775013\pi\) | ||||
−0.760432 | + | 0.649418i | \(0.775013\pi\) | |||||||
\(308\) | −93.1906 | −0.0172403 | ||||||||
\(309\) | 12404.4 | 2.28370 | ||||||||
\(310\) | −8165.49 | −1.49603 | ||||||||
\(311\) | 4985.56 | 0.909019 | 0.454509 | − | 0.890742i | \(-0.349815\pi\) | ||||
0.454509 | + | 0.890742i | \(0.349815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −102.182 | −0.0184527 | −0.00922633 | − | 0.999957i | \(-0.502937\pi\) | ||||
−0.00922633 | + | 0.999957i | \(0.502937\pi\) | |||||||
\(314\) | 2059.72 | 0.370181 | ||||||||
\(315\) | −3544.52 | −0.634003 | ||||||||
\(316\) | 169.158 | 0.0301136 | ||||||||
\(317\) | 749.307 | 0.132761 | 0.0663806 | − | 0.997794i | \(-0.478855\pi\) | ||||
0.0663806 | + | 0.997794i | \(0.478855\pi\) | |||||||
\(318\) | 5499.39 | 0.969781 | ||||||||
\(319\) | 60.1666 | 0.0105601 | ||||||||
\(320\) | 5946.88 | 1.03888 | ||||||||
\(321\) | 8138.94 | 1.41518 | ||||||||
\(322\) | −7932.23 | −1.37281 | ||||||||
\(323\) | 11506.5 | 1.98216 | ||||||||
\(324\) | −480.662 | −0.0824180 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6605.15 | 1.12216 | ||||||||
\(327\) | 5969.32 | 1.00949 | ||||||||
\(328\) | 9261.31 | 1.55906 | ||||||||
\(329\) | −6386.58 | −1.07022 | ||||||||
\(330\) | 2709.26 | 0.451939 | ||||||||
\(331\) | 10513.1 | 1.74577 | 0.872886 | − | 0.487924i | \(-0.162246\pi\) | ||||
0.872886 | + | 0.487924i | \(0.162246\pi\) | |||||||
\(332\) | 607.735 | 0.100463 | ||||||||
\(333\) | 6301.61 | 1.03702 | ||||||||
\(334\) | 2699.77 | 0.442291 | ||||||||
\(335\) | −8189.72 | −1.33568 | ||||||||
\(336\) | −7165.53 | −1.16343 | ||||||||
\(337\) | −3157.75 | −0.510426 | −0.255213 | − | 0.966885i | \(-0.582146\pi\) | ||||
−0.255213 | + | 0.966885i | \(0.582146\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3431.92 | −0.549841 | ||||||||
\(340\) | 601.171 | 0.0958914 | ||||||||
\(341\) | 2444.78 | 0.388248 | ||||||||
\(342\) | −6802.09 | −1.07548 | ||||||||
\(343\) | 6899.58 | 1.08613 | ||||||||
\(344\) | −3392.93 | −0.531786 | ||||||||
\(345\) | 14560.2 | 2.27215 | ||||||||
\(346\) | −4102.22 | −0.637389 | ||||||||
\(347\) | 8642.04 | 1.33697 | 0.668486 | − | 0.743725i | \(-0.266943\pi\) | ||||
0.668486 | + | 0.743725i | \(0.266943\pi\) | |||||||
\(348\) | −19.7694 | −0.00304526 | ||||||||
\(349\) | −8480.84 | −1.30077 | −0.650385 | − | 0.759604i | \(-0.725393\pi\) | ||||
−0.650385 | + | 0.759604i | \(0.725393\pi\) | |||||||
\(350\) | 1518.59 | 0.231921 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 267.942 | 0.0405720 | ||||||||
\(353\) | 12797.4 | 1.92957 | 0.964784 | − | 0.263044i | \(-0.0847264\pi\) | ||||
0.964784 | + | 0.263044i | \(0.0847264\pi\) | |||||||
\(354\) | −2125.40 | −0.319107 | ||||||||
\(355\) | 4810.70 | 0.719227 | ||||||||
\(356\) | −318.710 | −0.0474483 | ||||||||
\(357\) | 9342.43 | 1.38502 | ||||||||
\(358\) | −3203.46 | −0.472927 | ||||||||
\(359\) | 11231.4 | 1.65118 | 0.825589 | − | 0.564272i | \(-0.190843\pi\) | ||||
0.825589 | + | 0.564272i | \(0.190843\pi\) | |||||||
\(360\) | 4917.90 | 0.719990 | ||||||||
\(361\) | 9973.84 | 1.45412 | ||||||||
\(362\) | 7973.66 | 1.15770 | ||||||||
\(363\) | −811.164 | −0.117287 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2658.82 | −0.381284 | ||||||||
\(366\) | 7610.35 | 1.08688 | ||||||||
\(367\) | 3920.84 | 0.557673 | 0.278836 | − | 0.960339i | \(-0.410051\pi\) | ||||
0.278836 | + | 0.960339i | \(0.410051\pi\) | |||||||
\(368\) | 11750.8 | 1.66455 | ||||||||
\(369\) | 7621.37 | 1.07521 | ||||||||
\(370\) | −12904.2 | −1.81312 | ||||||||
\(371\) | −4411.20 | −0.617299 | ||||||||
\(372\) | −803.300 | −0.111960 | ||||||||
\(373\) | −9140.22 | −1.26880 | −0.634401 | − | 0.773004i | \(-0.718753\pi\) | ||||
−0.634401 | + | 0.773004i | \(0.718753\pi\) | |||||||
\(374\) | −2850.78 | −0.394145 | ||||||||
\(375\) | 7748.16 | 1.06697 | ||||||||
\(376\) | 8861.18 | 1.21537 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2788.46 | 0.379425 | ||||||||
\(379\) | −2568.60 | −0.348127 | −0.174063 | − | 0.984734i | \(-0.555690\pi\) | ||||
−0.174063 | + | 0.984734i | \(0.555690\pi\) | |||||||
\(380\) | 879.454 | 0.118724 | ||||||||
\(381\) | −5168.05 | −0.694927 | ||||||||
\(382\) | 12738.9 | 1.70623 | ||||||||
\(383\) | −8400.48 | −1.12074 | −0.560372 | − | 0.828241i | \(-0.689342\pi\) | ||||
−0.560372 | + | 0.828241i | \(0.689342\pi\) | |||||||
\(384\) | 10572.4 | 1.40499 | ||||||||
\(385\) | −2173.17 | −0.287675 | ||||||||
\(386\) | 11102.2 | 1.46396 | ||||||||
\(387\) | −2792.13 | −0.366749 | ||||||||
\(388\) | −264.617 | −0.0346234 | ||||||||
\(389\) | −1411.45 | −0.183968 | −0.0919839 | − | 0.995760i | \(-0.529321\pi\) | ||||
−0.0919839 | + | 0.995760i | \(0.529321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15320.7 | −1.98159 | ||||||||
\(392\) | −2094.87 | −0.269916 | ||||||||
\(393\) | 6106.07 | 0.783742 | ||||||||
\(394\) | −10769.1 | −1.37700 | ||||||||
\(395\) | 3944.70 | 0.502480 | ||||||||
\(396\) | 106.404 | 0.0135025 | ||||||||
\(397\) | −10352.7 | −1.30878 | −0.654391 | − | 0.756156i | \(-0.727075\pi\) | ||||
−0.654391 | + | 0.756156i | \(0.727075\pi\) | |||||||
\(398\) | 4474.93 | 0.563588 | ||||||||
\(399\) | 13667.0 | 1.71481 | ||||||||
\(400\) | −2249.65 | −0.281206 | ||||||||
\(401\) | 11410.4 | 1.42097 | 0.710484 | − | 0.703714i | \(-0.248476\pi\) | ||||
0.710484 | + | 0.703714i | \(0.248476\pi\) | |||||||
\(402\) | −12760.6 | −1.58319 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 951.022 | 0.117117 | ||||||||
\(405\) | −11208.8 | −1.37524 | ||||||||
\(406\) | 251.155 | 0.0307011 | ||||||||
\(407\) | 3863.56 | 0.470540 | ||||||||
\(408\) | −12962.3 | −1.57287 | ||||||||
\(409\) | 2454.14 | 0.296698 | 0.148349 | − | 0.988935i | \(-0.452604\pi\) | ||||
0.148349 | + | 0.988935i | \(0.452604\pi\) | |||||||
\(410\) | −15606.7 | −1.87990 | ||||||||
\(411\) | −4289.17 | −0.514767 | ||||||||
\(412\) | −997.608 | −0.119293 | ||||||||
\(413\) | 1704.84 | 0.203122 | ||||||||
\(414\) | 9056.89 | 1.07517 | ||||||||
\(415\) | 14172.1 | 1.67634 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8808.31 | 1.03440 | ||||||||
\(418\) | −4170.41 | −0.487994 | ||||||||
\(419\) | −13489.0 | −1.57274 | −0.786372 | − | 0.617753i | \(-0.788043\pi\) | ||||
−0.786372 | + | 0.617753i | \(0.788043\pi\) | |||||||
\(420\) | 714.053 | 0.0829576 | ||||||||
\(421\) | 11358.3 | 1.31489 | 0.657446 | − | 0.753502i | \(-0.271637\pi\) | ||||
0.657446 | + | 0.753502i | \(0.271637\pi\) | |||||||
\(422\) | −8349.44 | −0.963138 | ||||||||
\(423\) | 7292.10 | 0.838189 | ||||||||
\(424\) | 6120.40 | 0.701021 | ||||||||
\(425\) | 2933.09 | 0.334767 | ||||||||
\(426\) | 7495.69 | 0.852505 | ||||||||
\(427\) | −6104.45 | −0.691839 | ||||||||
\(428\) | −654.563 | −0.0739240 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5717.60 | 0.641225 | ||||||||
\(431\) | 12014.1 | 1.34269 | 0.671344 | − | 0.741146i | \(-0.265718\pi\) | ||||
0.671344 | + | 0.741146i | \(0.265718\pi\) | |||||||
\(432\) | −4130.82 | −0.460056 | ||||||||
\(433\) | 9197.86 | 1.02083 | 0.510417 | − | 0.859927i | \(-0.329491\pi\) | ||||
0.510417 | + | 0.859927i | \(0.329491\pi\) | |||||||
\(434\) | 10205.3 | 1.12874 | ||||||||
\(435\) | −461.013 | −0.0508135 | ||||||||
\(436\) | −480.074 | −0.0527325 | ||||||||
\(437\) | −22412.7 | −2.45342 | ||||||||
\(438\) | −4142.77 | −0.451939 | ||||||||
\(439\) | 6367.85 | 0.692302 | 0.346151 | − | 0.938179i | \(-0.387488\pi\) | ||||
0.346151 | + | 0.938179i | \(0.387488\pi\) | |||||||
\(440\) | 3015.20 | 0.326691 | ||||||||
\(441\) | −1723.92 | −0.186149 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11022.3 | −1.18214 | −0.591068 | − | 0.806622i | \(-0.701293\pi\) | ||||
−0.591068 | + | 0.806622i | \(0.701293\pi\) | |||||||
\(444\) | −1269.48 | −0.135691 | ||||||||
\(445\) | −7432.19 | −0.791729 | ||||||||
\(446\) | 5261.19 | 0.558575 | ||||||||
\(447\) | 1203.91 | 0.127389 | ||||||||
\(448\) | −7432.49 | −0.783822 | ||||||||
\(449\) | 1296.75 | 0.136298 | 0.0681488 | − | 0.997675i | \(-0.478291\pi\) | ||||
0.0681488 | + | 0.997675i | \(0.478291\pi\) | |||||||
\(450\) | −1733.91 | −0.181638 | ||||||||
\(451\) | 4672.72 | 0.487870 | ||||||||
\(452\) | 276.007 | 0.0287219 | ||||||||
\(453\) | 759.025 | 0.0787243 | ||||||||
\(454\) | 2826.32 | 0.292171 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18962.6 | −1.94738 | ||||||||
\(457\) | 12474.9 | 1.27692 | 0.638458 | − | 0.769656i | \(-0.279572\pi\) | ||||
0.638458 | + | 0.769656i | \(0.279572\pi\) | |||||||
\(458\) | −17565.8 | −1.79213 | ||||||||
\(459\) | 5385.77 | 0.547682 | ||||||||
\(460\) | −1170.98 | −0.118690 | ||||||||
\(461\) | −11524.1 | −1.16427 | −0.582136 | − | 0.813091i | \(-0.697783\pi\) | ||||
−0.582136 | + | 0.813091i | \(0.697783\pi\) | |||||||
\(462\) | −3386.07 | −0.340983 | ||||||||
\(463\) | −11186.2 | −1.12282 | −0.561412 | − | 0.827537i | \(-0.689742\pi\) | ||||
−0.561412 | + | 0.827537i | \(0.689742\pi\) | |||||||
\(464\) | −372.062 | −0.0372253 | ||||||||
\(465\) | −18732.6 | −1.86818 | ||||||||
\(466\) | −10494.6 | −1.04325 | ||||||||
\(467\) | −2751.87 | −0.272680 | −0.136340 | − | 0.990662i | \(-0.543534\pi\) | ||||
−0.136340 | + | 0.990662i | \(0.543534\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10235.6 | 1.00775 | ||||||||
\(470\) | −14932.4 | −1.46549 | ||||||||
\(471\) | 4725.24 | 0.462267 | ||||||||
\(472\) | −2365.41 | −0.230671 | ||||||||
\(473\) | −1711.87 | −0.166410 | ||||||||
\(474\) | 6146.35 | 0.595593 | ||||||||
\(475\) | 4290.82 | 0.414476 | ||||||||
\(476\) | −751.352 | −0.0723490 | ||||||||
\(477\) | 5036.63 | 0.483463 | ||||||||
\(478\) | 1006.76 | 0.0963349 | ||||||||
\(479\) | −14990.4 | −1.42991 | −0.714955 | − | 0.699170i | \(-0.753553\pi\) | ||||
−0.714955 | + | 0.699170i | \(0.753553\pi\) | |||||||
\(480\) | −2053.04 | −0.195225 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18191.5 | −1.71909 | ||||||||
\(483\) | −18197.5 | −1.71432 | ||||||||
\(484\) | 65.2367 | 0.00612666 | ||||||||
\(485\) | −6170.75 | −0.577731 | ||||||||
\(486\) | −12673.5 | −1.18288 | ||||||||
\(487\) | −14043.7 | −1.30674 | −0.653369 | − | 0.757040i | \(-0.726645\pi\) | ||||
−0.653369 | + | 0.757040i | \(0.726645\pi\) | |||||||
\(488\) | 8469.74 | 0.785670 | ||||||||
\(489\) | 15153.0 | 1.40131 | ||||||||
\(490\) | 3530.17 | 0.325463 | ||||||||
\(491\) | −11747.4 | −1.07974 | −0.539871 | − | 0.841748i | \(-0.681527\pi\) | ||||
−0.539871 | + | 0.841748i | \(0.681527\pi\) | |||||||
\(492\) | −1535.35 | −0.140689 | ||||||||
\(493\) | 485.095 | 0.0443155 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2481.29 | 0.225304 | ||||||||
\(496\) | −15118.2 | −1.36860 | ||||||||
\(497\) | −6012.48 | −0.542649 | ||||||||
\(498\) | 22082.0 | 1.98698 | ||||||||
\(499\) | 894.096 | 0.0802109 | 0.0401055 | − | 0.999195i | \(-0.487231\pi\) | ||||
0.0401055 | + | 0.999195i | \(0.487231\pi\) | |||||||
\(500\) | −623.134 | −0.0557348 | ||||||||
\(501\) | 6193.61 | 0.552315 | ||||||||
\(502\) | −5966.52 | −0.530476 | ||||||||
\(503\) | −18061.6 | −1.60105 | −0.800525 | − | 0.599300i | \(-0.795446\pi\) | ||||
−0.800525 | + | 0.599300i | \(0.795446\pi\) | |||||||
\(504\) | −6146.46 | −0.543224 | ||||||||
\(505\) | 22177.4 | 1.95422 | ||||||||
\(506\) | 5552.84 | 0.487854 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 415.633 | 0.0363006 | ||||||||
\(509\) | 17066.9 | 1.48621 | 0.743103 | − | 0.669177i | \(-0.233353\pi\) | ||||
0.743103 | + | 0.669177i | \(0.233353\pi\) | |||||||
\(510\) | 21843.5 | 1.89656 | ||||||||
\(511\) | 3323.02 | 0.287675 | ||||||||
\(512\) | 10207.3 | 0.881059 | ||||||||
\(513\) | 7878.84 | 0.678089 | ||||||||
\(514\) | −12117.0 | −1.03980 | ||||||||
\(515\) | −23263.8 | −1.99054 | ||||||||
\(516\) | 562.482 | 0.0479882 | ||||||||
\(517\) | 4470.83 | 0.380323 | ||||||||
\(518\) | 16127.8 | 1.36798 | ||||||||
\(519\) | −9410.98 | −0.795946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6638.80 | −0.558256 | −0.279128 | − | 0.960254i | \(-0.590045\pi\) | ||||
−0.279128 | + | 0.960254i | \(0.590045\pi\) | |||||||
\(522\) | −286.765 | −0.0240448 | ||||||||
\(523\) | 3961.57 | 0.331219 | 0.165609 | − | 0.986191i | \(-0.447041\pi\) | ||||
0.165609 | + | 0.986191i | \(0.447041\pi\) | |||||||
\(524\) | −491.072 | −0.0409401 | ||||||||
\(525\) | 3483.84 | 0.289613 | ||||||||
\(526\) | −16650.4 | −1.38021 | ||||||||
\(527\) | 19711.1 | 1.62928 | ||||||||
\(528\) | 5016.13 | 0.413445 | ||||||||
\(529\) | 17675.2 | 1.45272 | ||||||||
\(530\) | −10313.8 | −0.845288 | ||||||||
\(531\) | −1946.56 | −0.159084 | ||||||||
\(532\) | −1099.15 | −0.0895758 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −11580.3 | −0.938442 | ||||||||
\(535\) | −15264.1 | −1.23351 | ||||||||
\(536\) | −14201.6 | −1.14443 | ||||||||
\(537\) | −7349.11 | −0.590573 | ||||||||
\(538\) | 1190.23 | 0.0953801 | ||||||||
\(539\) | −1056.95 | −0.0844638 | ||||||||
\(540\) | 411.641 | 0.0328041 | ||||||||
\(541\) | 3050.55 | 0.242428 | 0.121214 | − | 0.992626i | \(-0.461321\pi\) | ||||
0.121214 | + | 0.992626i | \(0.461321\pi\) | |||||||
\(542\) | 4463.35 | 0.353722 | ||||||||
\(543\) | 18292.5 | 1.44569 | ||||||||
\(544\) | 2160.29 | 0.170260 | ||||||||
\(545\) | −11195.1 | −0.879902 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1239.50 | 0.0968870 | 0.0484435 | − | 0.998826i | \(-0.484574\pi\) | ||||
0.0484435 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(548\) | 344.951 | 0.0268897 | ||||||||
\(549\) | 6969.97 | 0.541841 | ||||||||
\(550\) | −1063.07 | −0.0824171 | ||||||||
\(551\) | 709.645 | 0.0548673 | ||||||||
\(552\) | 25248.4 | 1.94682 | ||||||||
\(553\) | −4930.14 | −0.379116 | ||||||||
\(554\) | −8484.05 | −0.650636 | ||||||||
\(555\) | −29603.7 | −2.26416 | ||||||||
\(556\) | −708.396 | −0.0540336 | ||||||||
\(557\) | 11458.5 | 0.871659 | 0.435830 | − | 0.900029i | \(-0.356455\pi\) | ||||
0.435830 | + | 0.900029i | \(0.356455\pi\) | |||||||
\(558\) | −11652.3 | −0.884016 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 13438.6 | 1.01408 | ||||||||
\(561\) | −6540.03 | −0.492193 | ||||||||
\(562\) | 5641.38 | 0.423429 | ||||||||
\(563\) | −4582.32 | −0.343022 | −0.171511 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171511 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(564\) | −1469.01 | −0.109675 | ||||||||
\(565\) | 6436.37 | 0.479257 | ||||||||
\(566\) | −14465.2 | −1.07424 | ||||||||
\(567\) | 14009.0 | 1.03760 | ||||||||
\(568\) | 8342.12 | 0.616246 | ||||||||
\(569\) | 2749.09 | 0.202544 | 0.101272 | − | 0.994859i | \(-0.467709\pi\) | ||||
0.101272 | + | 0.994859i | \(0.467709\pi\) | |||||||
\(570\) | 31954.9 | 2.34814 | ||||||||
\(571\) | 1449.90 | 0.106264 | 0.0531318 | − | 0.998588i | \(-0.483080\pi\) | ||||
0.0531318 | + | 0.998588i | \(0.483080\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29224.6 | 2.13067 | ||||||||
\(574\) | 19505.5 | 1.41837 | ||||||||
\(575\) | −5713.17 | −0.414358 | ||||||||
\(576\) | 8486.30 | 0.613881 | ||||||||
\(577\) | 11347.4 | 0.818713 | 0.409357 | − | 0.912375i | \(-0.365753\pi\) | ||||
0.409357 | + | 0.912375i | \(0.365753\pi\) | |||||||
\(578\) | −8627.82 | −0.620882 | ||||||||
\(579\) | 25469.9 | 1.82814 | ||||||||
\(580\) | 37.0763 | 0.00265433 | ||||||||
\(581\) | −17712.5 | −1.26478 | ||||||||
\(582\) | −9614.82 | −0.684789 | ||||||||
\(583\) | 3087.99 | 0.219368 | ||||||||
\(584\) | −4610.59 | −0.326691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11842.6 | 0.834836 | ||||||||
\(587\) | −16081.3 | −1.13075 | −0.565373 | − | 0.824835i | \(-0.691268\pi\) | ||||
−0.565373 | + | 0.824835i | \(0.691268\pi\) | |||||||
\(588\) | 347.289 | 0.0243571 | ||||||||
\(589\) | 28835.4 | 2.01722 | ||||||||
\(590\) | 3986.07 | 0.278142 | ||||||||
\(591\) | −24705.6 | −1.71955 | ||||||||
\(592\) | −23891.7 | −1.65869 | ||||||||
\(593\) | −26318.9 | −1.82257 | −0.911287 | − | 0.411771i | \(-0.864910\pi\) | ||||
−0.911287 | + | 0.411771i | \(0.864910\pi\) | |||||||
\(594\) | −1952.02 | −0.134835 | ||||||||
\(595\) | −17521.2 | −1.20723 | ||||||||
\(596\) | −96.8225 | −0.00665437 | ||||||||
\(597\) | 10266.0 | 0.703786 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25996.4 | −1.77327 | −0.886633 | − | 0.462474i | \(-0.846962\pi\) | ||||
−0.886633 | + | 0.462474i | \(0.846962\pi\) | |||||||
\(600\) | −4833.71 | −0.328892 | ||||||||
\(601\) | 19672.9 | 1.33523 | 0.667617 | − | 0.744505i | \(-0.267314\pi\) | ||||
0.667617 | + | 0.744505i | \(0.267314\pi\) | |||||||
\(602\) | −7145.93 | −0.483798 | ||||||||
\(603\) | −11686.9 | −0.789263 | ||||||||
\(604\) | −61.0435 | −0.00411230 | ||||||||
\(605\) | 1521.29 | 0.102230 | ||||||||
\(606\) | 34555.3 | 2.31636 | ||||||||
\(607\) | −19916.4 | −1.33177 | −0.665883 | − | 0.746057i | \(-0.731945\pi\) | ||||
−0.665883 | + | 0.746057i | \(0.731945\pi\) | |||||||
\(608\) | 3160.28 | 0.210800 | ||||||||
\(609\) | 576.180 | 0.0383383 | ||||||||
\(610\) | −14272.8 | −0.947358 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 857.881 | 0.0566631 | ||||||||
\(613\) | −630.454 | −0.0415396 | −0.0207698 | − | 0.999784i | \(-0.506612\pi\) | ||||
−0.0207698 | + | 0.999784i | \(0.506612\pi\) | |||||||
\(614\) | 23905.9 | 1.57128 | ||||||||
\(615\) | −35803.7 | −2.34755 | ||||||||
\(616\) | −3768.44 | −0.246485 | ||||||||
\(617\) | −2499.88 | −0.163114 | −0.0815569 | − | 0.996669i | \(-0.525989\pi\) | ||||
−0.0815569 | + | 0.996669i | \(0.525989\pi\) | |||||||
\(618\) | −36248.0 | −2.35940 | ||||||||
\(619\) | 26887.2 | 1.74586 | 0.872930 | − | 0.487846i | \(-0.162217\pi\) | ||||
0.872930 | + | 0.487846i | \(0.162217\pi\) | |||||||
\(620\) | 1506.54 | 0.0975876 | ||||||||
\(621\) | −10490.6 | −0.677894 | ||||||||
\(622\) | −14568.7 | −0.939150 | ||||||||
\(623\) | 9288.84 | 0.597351 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18665.2 | −1.19458 | ||||||||
\(626\) | 298.595 | 0.0190643 | ||||||||
\(627\) | −9567.42 | −0.609387 | ||||||||
\(628\) | −380.021 | −0.0241473 | ||||||||
\(629\) | 31150.1 | 1.97462 | ||||||||
\(630\) | 10357.7 | 0.655018 | ||||||||
\(631\) | 20589.6 | 1.29898 | 0.649492 | − | 0.760369i | \(-0.274982\pi\) | ||||
0.649492 | + | 0.760369i | \(0.274982\pi\) | |||||||
\(632\) | 6840.42 | 0.430533 | ||||||||
\(633\) | −19154.6 | −1.20273 | ||||||||
\(634\) | −2189.61 | −0.137162 | ||||||||
\(635\) | 9692.39 | 0.605718 | ||||||||
\(636\) | −1014.64 | −0.0632599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −175.818 | −0.0109102 | ||||||||
\(639\) | 6864.95 | 0.424997 | ||||||||
\(640\) | −19827.9 | −1.22463 | ||||||||
\(641\) | −15597.9 | −0.961126 | −0.480563 | − | 0.876960i | \(-0.659568\pi\) | ||||
−0.480563 | + | 0.876960i | \(0.659568\pi\) | |||||||
\(642\) | −23783.5 | −1.46208 | ||||||||
\(643\) | −17616.1 | −1.08042 | −0.540209 | − | 0.841531i | \(-0.681655\pi\) | ||||
−0.540209 | + | 0.841531i | \(0.681655\pi\) | |||||||
\(644\) | 1463.51 | 0.0895501 | ||||||||
\(645\) | 13116.9 | 0.800737 | ||||||||
\(646\) | −33624.0 | −2.04786 | ||||||||
\(647\) | 23071.4 | 1.40190 | 0.700951 | − | 0.713210i | \(-0.252759\pi\) | ||||
0.700951 | + | 0.713210i | \(0.252759\pi\) | |||||||
\(648\) | −19437.0 | −1.17833 | ||||||||
\(649\) | −1193.45 | −0.0721832 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23412.3 | 1.40952 | ||||||||
\(652\) | −1218.66 | −0.0731999 | ||||||||
\(653\) | 28718.7 | 1.72105 | 0.860527 | − | 0.509405i | \(-0.170135\pi\) | ||||
0.860527 | + | 0.509405i | \(0.170135\pi\) | |||||||
\(654\) | −17443.4 | −1.04296 | ||||||||
\(655\) | −11451.6 | −0.683131 | ||||||||
\(656\) | −28895.4 | −1.71978 | ||||||||
\(657\) | −3794.17 | −0.225304 | ||||||||
\(658\) | 18662.7 | 1.10570 | ||||||||
\(659\) | 12960.6 | 0.766118 | 0.383059 | − | 0.923724i | \(-0.374871\pi\) | ||||
0.383059 | + | 0.923724i | \(0.374871\pi\) | |||||||
\(660\) | −499.862 | −0.0294805 | ||||||||
\(661\) | −10384.9 | −0.611081 | −0.305541 | − | 0.952179i | \(-0.598837\pi\) | ||||
−0.305541 | + | 0.952179i | \(0.598837\pi\) | |||||||
\(662\) | −30721.1 | −1.80364 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24575.6 | 1.43632 | ||||||||
\(665\) | −25631.8 | −1.49467 | ||||||||
\(666\) | −18414.5 | −1.07139 | ||||||||
\(667\) | −944.883 | −0.0548516 | ||||||||
\(668\) | −498.112 | −0.0288511 | ||||||||
\(669\) | 12069.8 | 0.697527 | ||||||||
\(670\) | 23931.8 | 1.37995 | ||||||||
\(671\) | 4273.33 | 0.245857 | ||||||||
\(672\) | 2565.92 | 0.147296 | ||||||||
\(673\) | −23524.6 | −1.34741 | −0.673706 | − | 0.739000i | \(-0.735298\pi\) | ||||
−0.673706 | + | 0.739000i | \(0.735298\pi\) | |||||||
\(674\) | 9227.52 | 0.527345 | ||||||||
\(675\) | 2008.38 | 0.114522 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 349.546 | 0.0198436 | 0.00992182 | − | 0.999951i | \(-0.496842\pi\) | ||||
0.00992182 | + | 0.999951i | \(0.496842\pi\) | |||||||
\(678\) | 10028.7 | 0.568067 | ||||||||
\(679\) | 7712.29 | 0.435892 | ||||||||
\(680\) | 24310.1 | 1.37096 | ||||||||
\(681\) | 6483.92 | 0.364852 | ||||||||
\(682\) | −7144.10 | −0.401117 | ||||||||
\(683\) | 29509.5 | 1.65322 | 0.826611 | − | 0.562774i | \(-0.190266\pi\) | ||||
0.826611 | + | 0.562774i | \(0.190266\pi\) | |||||||
\(684\) | 1254.99 | 0.0701549 | ||||||||
\(685\) | 8044.10 | 0.448685 | ||||||||
\(686\) | −20161.8 | −1.12213 | ||||||||
\(687\) | −40298.0 | −2.23794 | ||||||||
\(688\) | 10586.0 | 0.586609 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −42547.5 | −2.34747 | ||||||||
\(691\) | −13847.6 | −0.762358 | −0.381179 | − | 0.924501i | \(-0.624482\pi\) | ||||
−0.381179 | + | 0.924501i | \(0.624482\pi\) | |||||||
\(692\) | 756.864 | 0.0415775 | ||||||||
\(693\) | −3101.14 | −0.169989 | ||||||||
\(694\) | −25253.6 | −1.38129 | ||||||||
\(695\) | −16519.5 | −0.901612 | ||||||||
\(696\) | −799.432 | −0.0435379 | ||||||||
\(697\) | 37673.9 | 2.04735 | ||||||||
\(698\) | 24782.6 | 1.34389 | ||||||||
\(699\) | −24075.9 | −1.30276 | ||||||||
\(700\) | −280.182 | −0.0151284 | ||||||||
\(701\) | 11463.4 | 0.617639 | 0.308819 | − | 0.951121i | \(-0.400066\pi\) | ||||
0.308819 | + | 0.951121i | \(0.400066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45569.4 | 2.44479 | ||||||||
\(704\) | 5203.01 | 0.278545 | ||||||||
\(705\) | −34256.8 | −1.83005 | ||||||||
\(706\) | −37396.4 | −1.99353 | ||||||||
\(707\) | −27717.7 | −1.47444 | ||||||||
\(708\) | 392.139 | 0.0208157 | ||||||||
\(709\) | −23414.0 | −1.24024 | −0.620121 | − | 0.784507i | \(-0.712916\pi\) | ||||
−0.620121 | + | 0.784507i | \(0.712916\pi\) | |||||||
\(710\) | −14057.7 | −0.743067 | ||||||||
\(711\) | 5629.16 | 0.296920 | ||||||||
\(712\) | −12888.0 | −0.678367 | ||||||||
\(713\) | −38394.0 | −2.01664 | ||||||||
\(714\) | −27300.3 | −1.43093 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 591.042 | 0.0308496 | ||||||||
\(717\) | 2309.63 | 0.120299 | ||||||||
\(718\) | −32820.3 | −1.70591 | ||||||||
\(719\) | 12468.3 | 0.646718 | 0.323359 | − | 0.946276i | \(-0.395188\pi\) | ||||
0.323359 | + | 0.946276i | \(0.395188\pi\) | |||||||
\(720\) | −15343.9 | −0.794215 | ||||||||
\(721\) | 29075.4 | 1.50184 | ||||||||
\(722\) | −29145.4 | −1.50232 | ||||||||
\(723\) | −41733.4 | −2.14673 | ||||||||
\(724\) | −1471.15 | −0.0755178 | ||||||||
\(725\) | 180.894 | 0.00926653 | ||||||||
\(726\) | 2370.37 | 0.121174 | ||||||||
\(727\) | 33013.9 | 1.68421 | 0.842103 | − | 0.539317i | \(-0.181318\pi\) | ||||
0.842103 | + | 0.539317i | \(0.181318\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5003.34 | −0.254196 | ||||||||
\(730\) | 7769.54 | 0.393923 | ||||||||
\(731\) | −13802.0 | −0.698339 | ||||||||
\(732\) | −1404.12 | −0.0708986 | ||||||||
\(733\) | −17188.8 | −0.866142 | −0.433071 | − | 0.901360i | \(-0.642570\pi\) | ||||
−0.433071 | + | 0.901360i | \(0.642570\pi\) | |||||||
\(734\) | −11457.4 | −0.576158 | ||||||||
\(735\) | 8098.64 | 0.406426 | ||||||||
\(736\) | −4207.87 | −0.210740 | ||||||||
\(737\) | −7165.29 | −0.358123 | ||||||||
\(738\) | −22271.0 | −1.11085 | ||||||||
\(739\) | 9120.36 | 0.453989 | 0.226995 | − | 0.973896i | \(-0.427110\pi\) | ||||
0.226995 | + | 0.973896i | \(0.427110\pi\) | |||||||
\(740\) | 2380.84 | 0.118272 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12890.3 | 0.637761 | ||||||||
\(743\) | 38627.2 | 1.90726 | 0.953629 | − | 0.300984i | \(-0.0973152\pi\) | ||||
0.953629 | + | 0.300984i | \(0.0973152\pi\) | |||||||
\(744\) | −32483.8 | −1.60069 | ||||||||
\(745\) | −2257.86 | −0.111036 | ||||||||
\(746\) | 26709.4 | 1.31086 | ||||||||
\(747\) | 20223.9 | 0.990566 | ||||||||
\(748\) | 525.973 | 0.0257105 | ||||||||
\(749\) | 19077.3 | 0.930667 | ||||||||
\(750\) | −22641.5 | −1.10234 | ||||||||
\(751\) | 28140.4 | 1.36732 | 0.683661 | − | 0.729799i | \(-0.260387\pi\) | ||||
0.683661 | + | 0.729799i | \(0.260387\pi\) | |||||||
\(752\) | −27647.0 | −1.34067 | ||||||||
\(753\) | −13687.9 | −0.662438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1423.51 | −0.0686183 | ||||||||
\(756\) | −514.474 | −0.0247503 | ||||||||
\(757\) | −8906.12 | −0.427607 | −0.213803 | − | 0.976877i | \(-0.568585\pi\) | ||||
−0.213803 | + | 0.976877i | \(0.568585\pi\) | |||||||
\(758\) | 7505.91 | 0.359666 | ||||||||
\(759\) | 12738.9 | 0.609212 | ||||||||
\(760\) | 35563.3 | 1.69739 | ||||||||
\(761\) | 31956.1 | 1.52222 | 0.761108 | − | 0.648625i | \(-0.224656\pi\) | ||||
0.761108 | + | 0.648625i | \(0.224656\pi\) | |||||||
\(762\) | 15102.0 | 0.717962 | ||||||||
\(763\) | 13991.8 | 0.663877 | ||||||||
\(764\) | −2350.35 | −0.111299 | ||||||||
\(765\) | 20005.4 | 0.945488 | ||||||||
\(766\) | 24547.7 | 1.15789 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −5526.99 | −0.259685 | ||||||||
\(769\) | 21225.7 | 0.995342 | 0.497671 | − | 0.867366i | \(-0.334189\pi\) | ||||
0.497671 | + | 0.867366i | \(0.334189\pi\) | |||||||
\(770\) | 6350.39 | 0.297210 | ||||||||
\(771\) | −27797.8 | −1.29846 | ||||||||
\(772\) | −2048.38 | −0.0954958 | ||||||||
\(773\) | −1379.06 | −0.0641672 | −0.0320836 | − | 0.999485i | \(-0.510214\pi\) | ||||
−0.0320836 | + | 0.999485i | \(0.510214\pi\) | |||||||
\(774\) | 8159.10 | 0.378906 | ||||||||
\(775\) | 7350.37 | 0.340688 | ||||||||
\(776\) | −10700.6 | −0.495010 | ||||||||
\(777\) | 36999.1 | 1.70828 | ||||||||
\(778\) | 4124.52 | 0.190066 | ||||||||
\(779\) | 55113.2 | 2.53483 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4208.95 | 0.192840 | ||||||||
\(782\) | 44769.9 | 2.04728 | ||||||||
\(783\) | 332.159 | 0.0151602 | ||||||||
\(784\) | 6536.03 | 0.297742 | ||||||||
\(785\) | −8861.93 | −0.402925 | ||||||||
\(786\) | −17843.1 | −0.809721 | ||||||||
\(787\) | 32672.8 | 1.47987 | 0.739935 | − | 0.672678i | \(-0.234856\pi\) | ||||
0.739935 | + | 0.672678i | \(0.234856\pi\) | |||||||
\(788\) | 1986.91 | 0.0898233 | ||||||||
\(789\) | −38198.0 | −1.72356 | ||||||||
\(790\) | −11527.1 | −0.519136 | ||||||||
\(791\) | −8044.26 | −0.361594 | ||||||||
\(792\) | 4302.74 | 0.193044 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 30252.4 | 1.35216 | ||||||||
\(795\) | −23661.1 | −1.05556 | ||||||||
\(796\) | −825.630 | −0.0367634 | ||||||||
\(797\) | 7048.81 | 0.313277 | 0.156639 | − | 0.987656i | \(-0.449934\pi\) | ||||
0.156639 | + | 0.987656i | \(0.449934\pi\) | |||||||
\(798\) | −39937.6 | −1.77165 | ||||||||
\(799\) | 36046.2 | 1.59602 | ||||||||
\(800\) | 805.581 | 0.0356020 | ||||||||
\(801\) | −10605.9 | −0.467839 | ||||||||
\(802\) | −33343.2 | −1.46807 | ||||||||
\(803\) | −2326.23 | −0.102230 | ||||||||
\(804\) | 2354.35 | 0.103273 | ||||||||
\(805\) | 34128.4 | 1.49424 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2730.53 | 0.119107 | ||||||||
\(808\) | 38457.4 | 1.67441 | ||||||||
\(809\) | 23849.5 | 1.03647 | 0.518234 | − | 0.855239i | \(-0.326590\pi\) | ||||
0.518234 | + | 0.855239i | \(0.326590\pi\) | |||||||
\(810\) | 32754.3 | 1.42082 | ||||||||
\(811\) | −13844.2 | −0.599426 | −0.299713 | − | 0.954029i | \(-0.596891\pi\) | ||||
−0.299713 | + | 0.954029i | \(0.596891\pi\) | |||||||
\(812\) | −46.3385 | −0.00200266 | ||||||||
\(813\) | 10239.5 | 0.441714 | ||||||||
\(814\) | −11290.0 | −0.486137 | ||||||||
\(815\) | −28418.6 | −1.22142 | ||||||||
\(816\) | 40442.7 | 1.73502 | ||||||||
\(817\) | −20191.0 | −0.864618 | ||||||||
\(818\) | −7171.44 | −0.306532 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2879.46 | 0.122628 | ||||||||
\(821\) | −8548.53 | −0.363393 | −0.181697 | − | 0.983355i | \(-0.558159\pi\) | ||||
−0.181697 | + | 0.983355i | \(0.558159\pi\) | |||||||
\(822\) | 12533.7 | 0.531830 | ||||||||
\(823\) | 26379.4 | 1.11729 | 0.558644 | − | 0.829407i | \(-0.311322\pi\) | ||||
0.558644 | + | 0.829407i | \(0.311322\pi\) | |||||||
\(824\) | −40341.2 | −1.70553 | ||||||||
\(825\) | −2438.81 | −0.102919 | ||||||||
\(826\) | −4981.85 | −0.209855 | ||||||||
\(827\) | −9853.94 | −0.414335 | −0.207167 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207167 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(828\) | −1671.01 | −0.0701347 | ||||||||
\(829\) | 32349.2 | 1.35529 | 0.677645 | − | 0.735390i | \(-0.263001\pi\) | ||||
0.677645 | + | 0.735390i | \(0.263001\pi\) | |||||||
\(830\) | −41413.6 | −1.73191 | ||||||||
\(831\) | −19463.4 | −0.812489 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8521.68 | −0.354452 | ||||||||
\(834\) | −25739.5 | −1.06869 | ||||||||
\(835\) | −11615.8 | −0.481413 | ||||||||
\(836\) | 769.446 | 0.0318323 | ||||||||
\(837\) | 13496.8 | 0.557370 | ||||||||
\(838\) | 39417.2 | 1.62488 | ||||||||
\(839\) | 9431.30 | 0.388087 | 0.194043 | − | 0.980993i | \(-0.437840\pi\) | ||||
0.194043 | + | 0.980993i | \(0.437840\pi\) | |||||||
\(840\) | 28874.8 | 1.18604 | ||||||||
\(841\) | −24359.1 | −0.998773 | ||||||||
\(842\) | −33191.0 | −1.35848 | ||||||||
\(843\) | 12942.0 | 0.528762 | ||||||||
\(844\) | 1540.48 | 0.0628265 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21308.8 | −0.865972 | ||||||||
\(847\) | −1901.33 | −0.0771317 | ||||||||
\(848\) | −19095.7 | −0.773290 | ||||||||
\(849\) | −33185.0 | −1.34147 | ||||||||
\(850\) | −8571.02 | −0.345863 | ||||||||
\(851\) | −60675.1 | −2.44408 | ||||||||
\(852\) | −1382.96 | −0.0556098 | ||||||||
\(853\) | −34267.5 | −1.37550 | −0.687748 | − | 0.725950i | \(-0.741401\pi\) | ||||
−0.687748 | + | 0.725950i | \(0.741401\pi\) | |||||||
\(854\) | 17838.3 | 0.714771 | ||||||||
\(855\) | 29266.0 | 1.17061 | ||||||||
\(856\) | −26469.2 | −1.05689 | ||||||||
\(857\) | −14640.9 | −0.583577 | −0.291788 | − | 0.956483i | \(-0.594250\pi\) | ||||
−0.291788 | + | 0.956483i | \(0.594250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20542.6 | 0.815952 | 0.407976 | − | 0.912993i | \(-0.366235\pi\) | ||||
0.407976 | + | 0.912993i | \(0.366235\pi\) | |||||||
\(860\) | −1054.90 | −0.0418278 | ||||||||
\(861\) | 44747.9 | 1.77120 | ||||||||
\(862\) | −35107.3 | −1.38719 | ||||||||
\(863\) | −12466.2 | −0.491721 | −0.245861 | − | 0.969305i | \(-0.579071\pi\) | ||||
−0.245861 | + | 0.969305i | \(0.579071\pi\) | |||||||
\(864\) | 1479.22 | 0.0582453 | ||||||||
\(865\) | 17649.8 | 0.693769 | ||||||||
\(866\) | −26877.8 | −1.05467 | ||||||||
\(867\) | −19793.2 | −0.775333 | ||||||||
\(868\) | −1882.90 | −0.0736288 | ||||||||
\(869\) | 3451.27 | 0.134726 | ||||||||
\(870\) | 1347.16 | 0.0524979 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −19413.2 | −0.753916 | ||||||||
\(873\) | −8805.76 | −0.341386 | ||||||||
\(874\) | 65494.0 | 2.53474 | ||||||||
\(875\) | 18161.3 | 0.701674 | ||||||||
\(876\) | 764.347 | 0.0294805 | ||||||||
\(877\) | −11451.9 | −0.440939 | −0.220470 | − | 0.975394i | \(-0.570759\pi\) | ||||
−0.220470 | + | 0.975394i | \(0.570759\pi\) | |||||||
\(878\) | −18608.0 | −0.715250 | ||||||||
\(879\) | 27168.4 | 1.04251 | ||||||||
\(880\) | −9407.47 | −0.360370 | ||||||||
\(881\) | 12598.4 | 0.481784 | 0.240892 | − | 0.970552i | \(-0.422560\pi\) | ||||
0.240892 | + | 0.970552i | \(0.422560\pi\) | |||||||
\(882\) | 5037.62 | 0.192319 | ||||||||
\(883\) | −2803.60 | −0.106850 | −0.0534251 | − | 0.998572i | \(-0.517014\pi\) | ||||
−0.0534251 | + | 0.998572i | \(0.517014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9144.53 | 0.347333 | ||||||||
\(886\) | 32209.2 | 1.22132 | ||||||||
\(887\) | −12962.9 | −0.490700 | −0.245350 | − | 0.969435i | \(-0.578903\pi\) | ||||
−0.245350 | + | 0.969435i | \(0.578903\pi\) | |||||||
\(888\) | −51335.1 | −1.93997 | ||||||||
\(889\) | −12113.7 | −0.457007 | ||||||||
\(890\) | 21718.2 | 0.817973 | ||||||||
\(891\) | −9806.76 | −0.368731 | ||||||||
\(892\) | −970.697 | −0.0364365 | ||||||||
\(893\) | 52732.0 | 1.97605 | ||||||||
\(894\) | −3518.04 | −0.131612 | ||||||||
\(895\) | 13782.9 | 0.514760 | ||||||||
\(896\) | 24781.1 | 0.923972 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3789.35 | −0.140815 | ||||||||
\(899\) | 1215.65 | 0.0450994 | ||||||||
\(900\) | 319.908 | 0.0118484 | ||||||||
\(901\) | 24897.0 | 0.920578 | ||||||||
\(902\) | −13654.5 | −0.504042 | ||||||||
\(903\) | −16393.6 | −0.604148 | ||||||||
\(904\) | 11161.2 | 0.410636 | ||||||||
\(905\) | −34306.6 | −1.26010 | ||||||||
\(906\) | −2218.01 | −0.0813338 | ||||||||
\(907\) | −15508.9 | −0.567766 | −0.283883 | − | 0.958859i | \(-0.591623\pi\) | ||||
−0.283883 | + | 0.958859i | \(0.591623\pi\) | |||||||
\(908\) | −521.460 | −0.0190586 | ||||||||
\(909\) | 31647.6 | 1.15477 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11245.1 | 0.408963 | 0.204482 | − | 0.978870i | \(-0.434449\pi\) | ||||
0.204482 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(912\) | 59163.6 | 2.14814 | ||||||||
\(913\) | 12399.4 | 0.449463 | ||||||||
\(914\) | −36453.9 | −1.31924 | ||||||||
\(915\) | −32743.5 | −1.18302 | ||||||||
\(916\) | 3240.91 | 0.116903 | ||||||||
\(917\) | 14312.4 | 0.515415 | ||||||||
\(918\) | −15738.2 | −0.565837 | ||||||||
\(919\) | 5457.33 | 0.195887 | 0.0979437 | − | 0.995192i | \(-0.468773\pi\) | ||||
0.0979437 | + | 0.995192i | \(0.468773\pi\) | |||||||
\(920\) | −47352.0 | −1.69690 | ||||||||
\(921\) | 54843.0 | 1.96215 | ||||||||
\(922\) | 33675.4 | 1.20287 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 624.734 | 0.0222427 | ||||||||
\(925\) | 11616.0 | 0.412899 | ||||||||
\(926\) | 32688.1 | 1.16004 | ||||||||
\(927\) | −33197.8 | −1.17622 | ||||||||
\(928\) | 133.232 | 0.00471290 | ||||||||
\(929\) | −5746.40 | −0.202942 | −0.101471 | − | 0.994838i | \(-0.532355\pi\) | ||||
−0.101471 | + | 0.994838i | \(0.532355\pi\) | |||||||
\(930\) | 54740.1 | 1.93011 | ||||||||
\(931\) | −12466.4 | −0.438849 | ||||||||
\(932\) | 1936.27 | 0.0680520 | ||||||||
\(933\) | −33422.3 | −1.17277 | ||||||||
\(934\) | 8041.47 | 0.281718 | ||||||||
\(935\) | 12265.5 | 0.429009 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26289.8 | 0.916595 | 0.458297 | − | 0.888799i | \(-0.348459\pi\) | ||||
0.458297 | + | 0.888799i | \(0.348459\pi\) | |||||||
\(938\) | −29910.3 | −1.04116 | ||||||||
\(939\) | 685.013 | 0.0238068 | ||||||||
\(940\) | 2755.05 | 0.0955957 | ||||||||
\(941\) | 9889.52 | 0.342603 | 0.171301 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171301 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(942\) | −13808.0 | −0.477590 | ||||||||
\(943\) | −73382.4 | −2.53410 | ||||||||
\(944\) | 7380.11 | 0.254451 | ||||||||
\(945\) | −11997.3 | −0.412987 | ||||||||
\(946\) | 5002.40 | 0.171926 | ||||||||
\(947\) | 9671.32 | 0.331865 | 0.165932 | − | 0.986137i | \(-0.446937\pi\) | ||||
0.165932 | + | 0.986137i | \(0.446937\pi\) | |||||||
\(948\) | −1134.01 | −0.0388512 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12538.6 | −0.428215 | ||||||||
\(951\) | −5023.23 | −0.171282 | ||||||||
\(952\) | −30383.1 | −1.03437 | ||||||||
\(953\) | 10982.2 | 0.373294 | 0.186647 | − | 0.982427i | \(-0.440238\pi\) | ||||
0.186647 | + | 0.982427i | \(0.440238\pi\) | |||||||
\(954\) | −14718.0 | −0.499488 | ||||||||
\(955\) | −54809.1 | −1.85715 | ||||||||
\(956\) | −185.748 | −0.00628403 | ||||||||
\(957\) | −403.347 | −0.0136242 | ||||||||
\(958\) | 43804.6 | 1.47731 | ||||||||
\(959\) | −10053.6 | −0.338528 | ||||||||
\(960\) | −39866.9 | −1.34031 | ||||||||
\(961\) | 19605.4 | 0.658098 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21782.2 | −0.728889 | ||||||||
\(964\) | 3356.35 | 0.112138 | ||||||||
\(965\) | −47767.3 | −1.59346 | ||||||||
\(966\) | 53176.4 | 1.77114 | ||||||||
\(967\) | −53005.8 | −1.76272 | −0.881361 | − | 0.472443i | \(-0.843372\pi\) | ||||
−0.881361 | + | 0.472443i | \(0.843372\pi\) | |||||||
\(968\) | 2638.04 | 0.0875927 | ||||||||
\(969\) | −77137.6 | −2.55729 | ||||||||
\(970\) | 18032.1 | 0.596881 | ||||||||
\(971\) | −15906.8 | −0.525720 | −0.262860 | − | 0.964834i | \(-0.584666\pi\) | ||||
−0.262860 | + | 0.964834i | \(0.584666\pi\) | |||||||
\(972\) | 2338.27 | 0.0771607 | ||||||||
\(973\) | 20646.3 | 0.680256 | ||||||||
\(974\) | 41038.3 | 1.35005 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26425.7 | −0.866666 | ||||||||
\(977\) | 5306.33 | 0.173761 | 0.0868805 | − | 0.996219i | \(-0.472310\pi\) | ||||
0.0868805 | + | 0.996219i | \(0.472310\pi\) | |||||||
\(978\) | −44279.8 | −1.44776 | ||||||||
\(979\) | −6502.52 | −0.212279 | ||||||||
\(980\) | −651.322 | −0.0212303 | ||||||||
\(981\) | −15975.6 | −0.519942 | ||||||||
\(982\) | 34328.0 | 1.11553 | ||||||||
\(983\) | 27448.6 | 0.890613 | 0.445307 | − | 0.895378i | \(-0.353095\pi\) | ||||
0.445307 | + | 0.895378i | \(0.353095\pi\) | |||||||
\(984\) | −62086.3 | −2.01142 | ||||||||
\(985\) | 46333.9 | 1.49880 | ||||||||
\(986\) | −1417.53 | −0.0457845 | ||||||||
\(987\) | 42814.6 | 1.38075 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26884.0 | 0.864370 | ||||||||
\(990\) | −7250.77 | −0.232772 | ||||||||
\(991\) | −26958.2 | −0.864132 | −0.432066 | − | 0.901842i | \(-0.642215\pi\) | ||||
−0.432066 | + | 0.901842i | \(0.642215\pi\) | |||||||
\(992\) | 5413.71 | 0.173272 | ||||||||
\(993\) | −70477.9 | −2.25231 | ||||||||
\(994\) | 17569.6 | 0.560636 | ||||||||
\(995\) | −19253.4 | −0.613440 | ||||||||
\(996\) | −4074.16 | −0.129613 | ||||||||
\(997\) | −3569.84 | −0.113398 | −0.0566991 | − | 0.998391i | \(-0.518058\pi\) | ||||
−0.0566991 | + | 0.998391i | \(0.518058\pi\) | |||||||
\(998\) | −2612.71 | −0.0828697 | ||||||||
\(999\) | 21329.4 | 0.675508 |
(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 | 1859.4.a.q.1.16 | yes | 51 | |
13.12 | even | 2 | 1859.4.a.p.1.36 | ✓ | 51 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.4.a.p.1.36 | ✓ | 51 | 13.12 | even | 2 | ||
1859.4.a.q.1.16 | yes | 51 | 1.1 | even | 1 | trivial |