Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.184225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 45x^{2} + 46x + 449 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.28229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −19.2398 | −1.72086 | −0.860428 | − | 0.509572i | \(-0.829804\pi\) | ||||
−0.860428 | + | 0.509572i | \(0.829804\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −18.0653 | −0.975434 | −0.487717 | − | 0.873002i | \(-0.662170\pi\) | ||||
−0.487717 | + | 0.873002i | \(0.662170\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −38.4795 | −1.21683 | ||||||||
\(11\) | 16.3023 | 0.446847 | 0.223424 | − | 0.974721i | \(-0.428277\pi\) | ||||
0.223424 | + | 0.974721i | \(0.428277\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 28.5122 | 0.608298 | 0.304149 | − | 0.952624i | \(-0.401628\pi\) | ||||
0.304149 | + | 0.952624i | \(0.401628\pi\) | |||||||
\(14\) | −36.1306 | −0.689736 | ||||||||
\(15\) | −57.7193 | −0.993537 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 21.7450 | 0.310232 | 0.155116 | − | 0.987896i | \(-0.450425\pi\) | ||||
0.155116 | + | 0.987896i | \(0.450425\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −76.9590 | −0.860428 | ||||||||
\(21\) | −54.1959 | −0.563167 | ||||||||
\(22\) | 32.6046 | 0.315969 | ||||||||
\(23\) | −115.106 | −1.04353 | −0.521767 | − | 0.853088i | \(-0.674727\pi\) | ||||
−0.521767 | + | 0.853088i | \(0.674727\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 245.168 | 1.96134 | ||||||||
\(26\) | 57.0245 | 0.430132 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −72.2611 | −0.487717 | ||||||||
\(29\) | 295.362 | 1.89129 | 0.945644 | − | 0.325203i | \(-0.105433\pi\) | ||||
0.945644 | + | 0.325203i | \(0.105433\pi\) | |||||||
\(30\) | −115.439 | −0.702536 | ||||||||
\(31\) | 250.965 | 1.45402 | 0.727010 | − | 0.686627i | \(-0.240909\pi\) | ||||
0.727010 | + | 0.686627i | \(0.240909\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 48.9068 | 0.257987 | ||||||||
\(34\) | 43.4900 | 0.219367 | ||||||||
\(35\) | 347.572 | 1.67858 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 126.485 | 0.561998 | 0.280999 | − | 0.959708i | \(-0.409334\pi\) | ||||
0.280999 | + | 0.959708i | \(0.409334\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 85.5367 | 0.351201 | ||||||||
\(40\) | −153.918 | −0.608414 | ||||||||
\(41\) | −484.330 | −1.84487 | −0.922434 | − | 0.386154i | \(-0.873803\pi\) | ||||
−0.922434 | + | 0.386154i | \(0.873803\pi\) | |||||||
\(42\) | −108.392 | −0.398219 | ||||||||
\(43\) | 24.1636 | 0.0856956 | 0.0428478 | − | 0.999082i | \(-0.486357\pi\) | ||||
0.0428478 | + | 0.999082i | \(0.486357\pi\) | |||||||
\(44\) | 65.2091 | 0.223424 | ||||||||
\(45\) | −173.158 | −0.573619 | ||||||||
\(46\) | −230.212 | −0.737890 | ||||||||
\(47\) | 76.4066 | 0.237129 | 0.118564 | − | 0.992946i | \(-0.462171\pi\) | ||||
0.118564 | + | 0.992946i | \(0.462171\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −16.6454 | −0.0485289 | ||||||||
\(50\) | 490.336 | 1.38688 | ||||||||
\(51\) | 65.2350 | 0.179112 | ||||||||
\(52\) | 114.049 | 0.304149 | ||||||||
\(53\) | −600.523 | −1.55638 | −0.778190 | − | 0.628028i | \(-0.783862\pi\) | ||||
−0.778190 | + | 0.628028i | \(0.783862\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | −313.652 | −0.768960 | ||||||||
\(56\) | −144.522 | −0.344868 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 590.724 | 1.33734 | ||||||||
\(59\) | −605.562 | −1.33623 | −0.668114 | − | 0.744059i | \(-0.732898\pi\) | ||||
−0.668114 | + | 0.744059i | \(0.732898\pi\) | |||||||
\(60\) | −230.877 | −0.496768 | ||||||||
\(61\) | −440.230 | −0.924028 | −0.462014 | − | 0.886873i | \(-0.652873\pi\) | ||||
−0.462014 | + | 0.886873i | \(0.652873\pi\) | |||||||
\(62\) | 501.930 | 1.02815 | ||||||||
\(63\) | −162.588 | −0.325145 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −548.568 | −1.04679 | ||||||||
\(66\) | 97.8137 | 0.182425 | ||||||||
\(67\) | −898.734 | −1.63877 | −0.819387 | − | 0.573240i | \(-0.805686\pi\) | ||||
−0.819387 | + | 0.573240i | \(0.805686\pi\) | |||||||
\(68\) | 86.9800 | 0.155116 | ||||||||
\(69\) | −345.319 | −0.602485 | ||||||||
\(70\) | 695.143 | 1.18694 | ||||||||
\(71\) | −812.354 | −1.35787 | −0.678935 | − | 0.734199i | \(-0.737558\pi\) | ||||
−0.678935 | + | 0.734199i | \(0.737558\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 794.385 | 1.27364 | 0.636820 | − | 0.771012i | \(-0.280249\pi\) | ||||
0.636820 | + | 0.771012i | \(0.280249\pi\) | |||||||
\(74\) | 252.969 | 0.397393 | ||||||||
\(75\) | 735.504 | 1.13238 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −294.505 | −0.435870 | ||||||||
\(78\) | 171.073 | 0.248337 | ||||||||
\(79\) | −637.672 | −0.908148 | −0.454074 | − | 0.890964i | \(-0.650030\pi\) | ||||
−0.454074 | + | 0.890964i | \(0.650030\pi\) | |||||||
\(80\) | −307.836 | −0.430214 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −968.660 | −1.30452 | ||||||||
\(83\) | −19.5995 | −0.0259195 | −0.0129598 | − | 0.999916i | \(-0.504125\pi\) | ||||
−0.0129598 | + | 0.999916i | \(0.504125\pi\) | |||||||
\(84\) | −216.783 | −0.281583 | ||||||||
\(85\) | −418.369 | −0.533864 | ||||||||
\(86\) | 48.3271 | 0.0605959 | ||||||||
\(87\) | 886.086 | 1.09194 | ||||||||
\(88\) | 130.418 | 0.157984 | ||||||||
\(89\) | 847.436 | 1.00930 | 0.504652 | − | 0.863323i | \(-0.331621\pi\) | ||||
0.504652 | + | 0.863323i | \(0.331621\pi\) | |||||||
\(90\) | −346.316 | −0.405610 | ||||||||
\(91\) | −515.082 | −0.593354 | ||||||||
\(92\) | −460.425 | −0.521767 | ||||||||
\(93\) | 752.895 | 0.839479 | ||||||||
\(94\) | 152.813 | 0.167675 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −1145.18 | −1.19872 | −0.599358 | − | 0.800481i | \(-0.704578\pi\) | ||||
−0.599358 | + | 0.800481i | \(0.704578\pi\) | |||||||
\(98\) | −33.2909 | −0.0343151 | ||||||||
\(99\) | 146.720 | 0.148949 | ||||||||
\(100\) | 980.672 | 0.980672 | ||||||||
\(101\) | 846.280 | 0.833743 | 0.416871 | − | 0.908966i | \(-0.363127\pi\) | ||||
0.416871 | + | 0.908966i | \(0.363127\pi\) | |||||||
\(102\) | 130.470 | 0.126652 | ||||||||
\(103\) | −153.479 | −0.146823 | −0.0734114 | − | 0.997302i | \(-0.523389\pi\) | ||||
−0.0734114 | + | 0.997302i | \(0.523389\pi\) | |||||||
\(104\) | 228.098 | 0.215066 | ||||||||
\(105\) | 1042.71 | 0.969129 | ||||||||
\(106\) | −1201.05 | −1.10053 | ||||||||
\(107\) | −905.591 | −0.818194 | −0.409097 | − | 0.912491i | \(-0.634156\pi\) | ||||
−0.409097 | + | 0.912491i | \(0.634156\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 908.945 | 0.798726 | 0.399363 | − | 0.916793i | \(-0.369231\pi\) | ||||
0.399363 | + | 0.916793i | \(0.369231\pi\) | |||||||
\(110\) | −627.304 | −0.543737 | ||||||||
\(111\) | 379.454 | 0.324470 | ||||||||
\(112\) | −289.045 | −0.243858 | ||||||||
\(113\) | −380.502 | −0.316766 | −0.158383 | − | 0.987378i | \(-0.550628\pi\) | ||||
−0.158383 | + | 0.987378i | \(0.550628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2214.61 | 1.79577 | ||||||||
\(116\) | 1181.45 | 0.945644 | ||||||||
\(117\) | 256.610 | 0.202766 | ||||||||
\(118\) | −1211.12 | −0.944856 | ||||||||
\(119\) | −392.830 | −0.302611 | ||||||||
\(120\) | −461.754 | −0.351268 | ||||||||
\(121\) | −1065.24 | −0.800327 | ||||||||
\(122\) | −880.460 | −0.653386 | ||||||||
\(123\) | −1452.99 | −1.06514 | ||||||||
\(124\) | 1003.86 | 0.727010 | ||||||||
\(125\) | −2312.00 | −1.65434 | ||||||||
\(126\) | −325.175 | −0.229912 | ||||||||
\(127\) | −364.339 | −0.254566 | −0.127283 | − | 0.991866i | \(-0.540626\pi\) | ||||
−0.127283 | + | 0.991866i | \(0.540626\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 72.4907 | 0.0494764 | ||||||||
\(130\) | −1097.14 | −0.740194 | ||||||||
\(131\) | −2503.63 | −1.66980 | −0.834899 | − | 0.550403i | \(-0.814474\pi\) | ||||
−0.834899 | + | 0.550403i | \(0.814474\pi\) | |||||||
\(132\) | 195.627 | 0.128994 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1797.47 | −1.15879 | ||||||||
\(135\) | −519.473 | −0.331179 | ||||||||
\(136\) | 173.960 | 0.109683 | ||||||||
\(137\) | 1553.08 | 0.968528 | 0.484264 | − | 0.874922i | \(-0.339087\pi\) | ||||
0.484264 | + | 0.874922i | \(0.339087\pi\) | |||||||
\(138\) | −690.637 | −0.426021 | ||||||||
\(139\) | −652.442 | −0.398125 | −0.199062 | − | 0.979987i | \(-0.563790\pi\) | ||||
−0.199062 | + | 0.979987i | \(0.563790\pi\) | |||||||
\(140\) | 1390.29 | 0.839290 | ||||||||
\(141\) | 229.220 | 0.136906 | ||||||||
\(142\) | −1624.71 | −0.960158 | ||||||||
\(143\) | 464.814 | 0.271816 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −5682.69 | −3.25463 | ||||||||
\(146\) | 1588.77 | 0.900600 | ||||||||
\(147\) | −49.9363 | −0.0280182 | ||||||||
\(148\) | 505.938 | 0.280999 | ||||||||
\(149\) | 2840.42 | 1.56172 | 0.780860 | − | 0.624706i | \(-0.214781\pi\) | ||||
0.780860 | + | 0.624706i | \(0.214781\pi\) | |||||||
\(150\) | 1471.01 | 0.800716 | ||||||||
\(151\) | −786.715 | −0.423987 | −0.211993 | − | 0.977271i | \(-0.567995\pi\) | ||||
−0.211993 | + | 0.977271i | \(0.567995\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 195.705 | 0.103411 | ||||||||
\(154\) | −589.011 | −0.308207 | ||||||||
\(155\) | −4828.50 | −2.50216 | ||||||||
\(156\) | 342.147 | 0.175600 | ||||||||
\(157\) | −2202.50 | −1.11961 | −0.559804 | − | 0.828625i | \(-0.689124\pi\) | ||||
−0.559804 | + | 0.828625i | \(0.689124\pi\) | |||||||
\(158\) | −1275.34 | −0.642158 | ||||||||
\(159\) | −1801.57 | −0.898577 | ||||||||
\(160\) | −615.672 | −0.304207 | ||||||||
\(161\) | 2079.43 | 1.01790 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −2675.07 | −1.28544 | −0.642722 | − | 0.766099i | \(-0.722195\pi\) | ||||
−0.642722 | + | 0.766099i | \(0.722195\pi\) | |||||||
\(164\) | −1937.32 | −0.922434 | ||||||||
\(165\) | −940.955 | −0.443959 | ||||||||
\(166\) | −39.1989 | −0.0183279 | ||||||||
\(167\) | 250.094 | 0.115885 | 0.0579426 | − | 0.998320i | \(-0.481546\pi\) | ||||
0.0579426 | + | 0.998320i | \(0.481546\pi\) | |||||||
\(168\) | −433.567 | −0.199110 | ||||||||
\(169\) | −1384.05 | −0.629974 | ||||||||
\(170\) | −836.737 | −0.377499 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 96.6543 | 0.0428478 | ||||||||
\(173\) | 1071.62 | 0.470946 | 0.235473 | − | 0.971881i | \(-0.424336\pi\) | ||||
0.235473 | + | 0.971881i | \(0.424336\pi\) | |||||||
\(174\) | 1772.17 | 0.772115 | ||||||||
\(175\) | −4429.03 | −1.91316 | ||||||||
\(176\) | 260.836 | 0.111712 | ||||||||
\(177\) | −1816.69 | −0.771471 | ||||||||
\(178\) | 1694.87 | 0.713685 | ||||||||
\(179\) | 1751.48 | 0.731351 | 0.365676 | − | 0.930742i | \(-0.380838\pi\) | ||||
0.365676 | + | 0.930742i | \(0.380838\pi\) | |||||||
\(180\) | −692.631 | −0.286809 | ||||||||
\(181\) | −45.6569 | −0.0187495 | −0.00937473 | − | 0.999956i | \(-0.502984\pi\) | ||||
−0.00937473 | + | 0.999956i | \(0.502984\pi\) | |||||||
\(182\) | −1030.16 | −0.419565 | ||||||||
\(183\) | −1320.69 | −0.533488 | ||||||||
\(184\) | −920.849 | −0.368945 | ||||||||
\(185\) | −2433.53 | −0.967117 | ||||||||
\(186\) | 1505.79 | 0.593601 | ||||||||
\(187\) | 354.493 | 0.138626 | ||||||||
\(188\) | 305.626 | 0.118564 | ||||||||
\(189\) | −487.763 | −0.187722 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4572.58 | −1.73225 | −0.866127 | − | 0.499823i | \(-0.833398\pi\) | ||||
−0.866127 | + | 0.499823i | \(0.833398\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 3703.26 | 1.38117 | 0.690586 | − | 0.723250i | \(-0.257353\pi\) | ||||
0.690586 | + | 0.723250i | \(0.257353\pi\) | |||||||
\(194\) | −2290.36 | −0.847621 | ||||||||
\(195\) | −1645.71 | −0.604366 | ||||||||
\(196\) | −66.5817 | −0.0242645 | ||||||||
\(197\) | 1839.32 | 0.665210 | 0.332605 | − | 0.943066i | \(-0.392072\pi\) | ||||
0.332605 | + | 0.943066i | \(0.392072\pi\) | |||||||
\(198\) | 293.441 | 0.105323 | ||||||||
\(199\) | 4362.59 | 1.55405 | 0.777025 | − | 0.629470i | \(-0.216728\pi\) | ||||
0.777025 | + | 0.629470i | \(0.216728\pi\) | |||||||
\(200\) | 1961.34 | 0.693440 | ||||||||
\(201\) | −2696.20 | −0.946147 | ||||||||
\(202\) | 1692.56 | 0.589545 | ||||||||
\(203\) | −5335.80 | −1.84483 | ||||||||
\(204\) | 260.940 | 0.0895562 | ||||||||
\(205\) | 9318.39 | 3.17475 | ||||||||
\(206\) | −306.958 | −0.103819 | ||||||||
\(207\) | −1035.96 | −0.347845 | ||||||||
\(208\) | 456.196 | 0.152074 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2085.43 | 0.685278 | ||||||||
\(211\) | 3887.74 | 1.26845 | 0.634225 | − | 0.773149i | \(-0.281319\pi\) | ||||
0.634225 | + | 0.773149i | \(0.281319\pi\) | |||||||
\(212\) | −2402.09 | −0.778190 | ||||||||
\(213\) | −2437.06 | −0.783966 | ||||||||
\(214\) | −1811.18 | −0.578550 | ||||||||
\(215\) | −464.901 | −0.147470 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −4533.75 | −1.41830 | ||||||||
\(218\) | 1817.89 | 0.564784 | ||||||||
\(219\) | 2383.16 | 0.735336 | ||||||||
\(220\) | −1254.61 | −0.384480 | ||||||||
\(221\) | 619.999 | 0.188713 | ||||||||
\(222\) | 758.907 | 0.229435 | ||||||||
\(223\) | 3410.33 | 1.02409 | 0.512047 | − | 0.858958i | \(-0.328888\pi\) | ||||
0.512047 | + | 0.858958i | \(0.328888\pi\) | |||||||
\(224\) | −578.089 | −0.172434 | ||||||||
\(225\) | 2206.51 | 0.653781 | ||||||||
\(226\) | −761.004 | −0.223988 | ||||||||
\(227\) | −4292.40 | −1.25505 | −0.627525 | − | 0.778597i | \(-0.715932\pi\) | ||||
−0.627525 | + | 0.778597i | \(0.715932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1852.15 | −0.534468 | −0.267234 | − | 0.963632i | \(-0.586110\pi\) | ||||
−0.267234 | + | 0.963632i | \(0.586110\pi\) | |||||||
\(230\) | 4429.23 | 1.26980 | ||||||||
\(231\) | −883.516 | −0.251650 | ||||||||
\(232\) | 2362.90 | 0.668671 | ||||||||
\(233\) | 604.211 | 0.169885 | 0.0849425 | − | 0.996386i | \(-0.472929\pi\) | ||||
0.0849425 | + | 0.996386i | \(0.472929\pi\) | |||||||
\(234\) | 513.220 | 0.143377 | ||||||||
\(235\) | −1470.04 | −0.408064 | ||||||||
\(236\) | −2422.25 | −0.668114 | ||||||||
\(237\) | −1913.02 | −0.524320 | ||||||||
\(238\) | −785.660 | −0.213978 | ||||||||
\(239\) | −7110.26 | −1.92437 | −0.962185 | − | 0.272398i | \(-0.912183\pi\) | ||||
−0.962185 | + | 0.272398i | \(0.912183\pi\) | |||||||
\(240\) | −923.508 | −0.248384 | ||||||||
\(241\) | −28.1168 | −0.00751519 | −0.00375759 | − | 0.999993i | \(-0.501196\pi\) | ||||
−0.00375759 | + | 0.999993i | \(0.501196\pi\) | |||||||
\(242\) | −2130.47 | −0.565917 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1760.92 | −0.462014 | ||||||||
\(245\) | 320.254 | 0.0835113 | ||||||||
\(246\) | −2905.98 | −0.753165 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2007.72 | 0.514074 | ||||||||
\(249\) | −58.7984 | −0.0149646 | ||||||||
\(250\) | −4624.01 | −1.16979 | ||||||||
\(251\) | 4155.34 | 1.04495 | 0.522476 | − | 0.852654i | \(-0.325008\pi\) | ||||
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(252\) | −650.350 | −0.162572 | ||||||||
\(253\) | −1876.49 | −0.466301 | ||||||||
\(254\) | −728.679 | −0.180005 | ||||||||
\(255\) | −1255.11 | −0.308227 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −4305.97 | −1.04513 | −0.522566 | − | 0.852599i | \(-0.675025\pi\) | ||||
−0.522566 | + | 0.852599i | \(0.675025\pi\) | |||||||
\(258\) | 144.981 | 0.0349851 | ||||||||
\(259\) | −2284.98 | −0.548192 | ||||||||
\(260\) | −2194.27 | −0.523396 | ||||||||
\(261\) | 2658.26 | 0.630430 | ||||||||
\(262\) | −5007.27 | −1.18073 | ||||||||
\(263\) | 4735.18 | 1.11020 | 0.555102 | − | 0.831782i | \(-0.312679\pi\) | ||||
0.555102 | + | 0.831782i | \(0.312679\pi\) | |||||||
\(264\) | 391.255 | 0.0912123 | ||||||||
\(265\) | 11553.9 | 2.67831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2542.31 | 0.582722 | ||||||||
\(268\) | −3594.94 | −0.819387 | ||||||||
\(269\) | −5555.76 | −1.25926 | −0.629630 | − | 0.776895i | \(-0.716793\pi\) | ||||
−0.629630 | + | 0.776895i | \(0.716793\pi\) | |||||||
\(270\) | −1038.95 | −0.234179 | ||||||||
\(271\) | −889.827 | −0.199458 | −0.0997290 | − | 0.995015i | \(-0.531798\pi\) | ||||
−0.0997290 | + | 0.995015i | \(0.531798\pi\) | |||||||
\(272\) | 347.920 | 0.0775579 | ||||||||
\(273\) | −1545.25 | −0.342573 | ||||||||
\(274\) | 3106.16 | 0.684853 | ||||||||
\(275\) | 3996.80 | 0.876422 | ||||||||
\(276\) | −1381.27 | −0.301243 | ||||||||
\(277\) | 718.326 | 0.155812 | 0.0779062 | − | 0.996961i | \(-0.475177\pi\) | ||||
0.0779062 | + | 0.996961i | \(0.475177\pi\) | |||||||
\(278\) | −1304.88 | −0.281517 | ||||||||
\(279\) | 2258.68 | 0.484673 | ||||||||
\(280\) | 2780.57 | 0.593468 | ||||||||
\(281\) | −6371.16 | −1.35257 | −0.676284 | − | 0.736641i | \(-0.736411\pi\) | ||||
−0.676284 | + | 0.736641i | \(0.736411\pi\) | |||||||
\(282\) | 458.440 | 0.0968074 | ||||||||
\(283\) | 322.116 | 0.0676601 | 0.0338300 | − | 0.999428i | \(-0.489230\pi\) | ||||
0.0338300 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(284\) | −3249.42 | −0.678935 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 929.629 | 0.192203 | ||||||||
\(287\) | 8749.56 | 1.79955 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4440.15 | −0.903756 | ||||||||
\(290\) | −11365.4 | −2.30137 | ||||||||
\(291\) | −3435.54 | −0.692079 | ||||||||
\(292\) | 3177.54 | 0.636820 | ||||||||
\(293\) | −8788.72 | −1.75236 | −0.876182 | − | 0.481980i | \(-0.839918\pi\) | ||||
−0.876182 | + | 0.481980i | \(0.839918\pi\) | |||||||
\(294\) | −99.8726 | −0.0198119 | ||||||||
\(295\) | 11650.9 | 2.29946 | ||||||||
\(296\) | 1011.88 | 0.198696 | ||||||||
\(297\) | 440.161 | 0.0859958 | ||||||||
\(298\) | 5680.84 | 1.10430 | ||||||||
\(299\) | −3281.94 | −0.634780 | ||||||||
\(300\) | 2942.02 | 0.566191 | ||||||||
\(301\) | −436.522 | −0.0835903 | ||||||||
\(302\) | −1573.43 | −0.299804 | ||||||||
\(303\) | 2538.84 | 0.481362 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8469.92 | 1.59012 | ||||||||
\(306\) | 391.410 | 0.0731223 | ||||||||
\(307\) | −5862.73 | −1.08991 | −0.544957 | − | 0.838464i | \(-0.683454\pi\) | ||||
−0.544957 | + | 0.838464i | \(0.683454\pi\) | |||||||
\(308\) | −1178.02 | −0.217935 | ||||||||
\(309\) | −460.438 | −0.0847682 | ||||||||
\(310\) | −9657.01 | −1.76929 | ||||||||
\(311\) | 3932.00 | 0.716924 | 0.358462 | − | 0.933544i | \(-0.383301\pi\) | ||||
0.358462 | + | 0.933544i | \(0.383301\pi\) | |||||||
\(312\) | 684.294 | 0.124168 | ||||||||
\(313\) | 8991.00 | 1.62365 | 0.811823 | − | 0.583903i | \(-0.198475\pi\) | ||||
0.811823 | + | 0.583903i | \(0.198475\pi\) | |||||||
\(314\) | −4405.00 | −0.791682 | ||||||||
\(315\) | 3128.14 | 0.559527 | ||||||||
\(316\) | −2550.69 | −0.454074 | ||||||||
\(317\) | 7803.21 | 1.38256 | 0.691280 | − | 0.722587i | \(-0.257047\pi\) | ||||
0.691280 | + | 0.722587i | \(0.257047\pi\) | |||||||
\(318\) | −3603.14 | −0.635390 | ||||||||
\(319\) | 4815.08 | 0.845117 | ||||||||
\(320\) | −1231.34 | −0.215107 | ||||||||
\(321\) | −2716.77 | −0.472384 | ||||||||
\(322\) | 4158.85 | 0.719763 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 6990.29 | 1.19308 | ||||||||
\(326\) | −5350.13 | −0.908946 | ||||||||
\(327\) | 2726.83 | 0.461145 | ||||||||
\(328\) | −3874.64 | −0.652260 | ||||||||
\(329\) | −1380.31 | −0.231303 | ||||||||
\(330\) | −1881.91 | −0.313927 | ||||||||
\(331\) | 4567.99 | 0.758548 | 0.379274 | − | 0.925284i | \(-0.376174\pi\) | ||||
0.379274 | + | 0.925284i | \(0.376174\pi\) | |||||||
\(332\) | −78.3978 | −0.0129598 | ||||||||
\(333\) | 1138.36 | 0.187333 | ||||||||
\(334\) | 500.187 | 0.0819432 | ||||||||
\(335\) | 17291.4 | 2.82009 | ||||||||
\(336\) | −867.134 | −0.140792 | ||||||||
\(337\) | −10244.1 | −1.65589 | −0.827944 | − | 0.560811i | \(-0.810489\pi\) | ||||
−0.827944 | + | 0.560811i | \(0.810489\pi\) | |||||||
\(338\) | −2768.10 | −0.445459 | ||||||||
\(339\) | −1141.51 | −0.182885 | ||||||||
\(340\) | −1673.47 | −0.266932 | ||||||||
\(341\) | 4091.30 | 0.649725 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6497.10 | 1.02277 | ||||||||
\(344\) | 193.309 | 0.0302980 | ||||||||
\(345\) | 6643.84 | 1.03679 | ||||||||
\(346\) | 2143.24 | 0.333009 | ||||||||
\(347\) | −10463.8 | −1.61880 | −0.809402 | − | 0.587254i | \(-0.800209\pi\) | ||||
−0.809402 | + | 0.587254i | \(0.800209\pi\) | |||||||
\(348\) | 3544.35 | 0.545968 | ||||||||
\(349\) | −4023.52 | −0.617118 | −0.308559 | − | 0.951205i | \(-0.599847\pi\) | ||||
−0.308559 | + | 0.951205i | \(0.599847\pi\) | |||||||
\(350\) | −8858.06 | −1.35281 | ||||||||
\(351\) | 769.830 | 0.117067 | ||||||||
\(352\) | 521.673 | 0.0789922 | ||||||||
\(353\) | −3273.39 | −0.493556 | −0.246778 | − | 0.969072i | \(-0.579372\pi\) | ||||
−0.246778 | + | 0.969072i | \(0.579372\pi\) | |||||||
\(354\) | −3633.37 | −0.545513 | ||||||||
\(355\) | 15629.5 | 2.33670 | ||||||||
\(356\) | 3389.74 | 0.504652 | ||||||||
\(357\) | −1178.49 | −0.174712 | ||||||||
\(358\) | 3502.96 | 0.517143 | ||||||||
\(359\) | −11181.2 | −1.64379 | −0.821893 | − | 0.569642i | \(-0.807082\pi\) | ||||
−0.821893 | + | 0.569642i | \(0.807082\pi\) | |||||||
\(360\) | −1385.26 | −0.202805 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −91.3138 | −0.0132579 | ||||||||
\(363\) | −3195.71 | −0.462069 | ||||||||
\(364\) | −2060.33 | −0.296677 | ||||||||
\(365\) | −15283.8 | −2.19175 | ||||||||
\(366\) | −2641.38 | −0.377233 | ||||||||
\(367\) | 7343.64 | 1.04451 | 0.522255 | − | 0.852790i | \(-0.325091\pi\) | ||||
0.522255 | + | 0.852790i | \(0.325091\pi\) | |||||||
\(368\) | −1841.70 | −0.260884 | ||||||||
\(369\) | −4358.97 | −0.614956 | ||||||||
\(370\) | −4867.06 | −0.683855 | ||||||||
\(371\) | 10848.6 | 1.51815 | ||||||||
\(372\) | 3011.58 | 0.419739 | ||||||||
\(373\) | 1947.63 | 0.270361 | 0.135180 | − | 0.990821i | \(-0.456839\pi\) | ||||
0.135180 | + | 0.990821i | \(0.456839\pi\) | |||||||
\(374\) | 708.986 | 0.0980236 | ||||||||
\(375\) | −6936.01 | −0.955131 | ||||||||
\(376\) | 611.253 | 0.0838376 | ||||||||
\(377\) | 8421.44 | 1.15047 | ||||||||
\(378\) | −975.525 | −0.132740 | ||||||||
\(379\) | −4998.26 | −0.677424 | −0.338712 | − | 0.940890i | \(-0.609991\pi\) | ||||
−0.338712 | + | 0.940890i | \(0.609991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1093.02 | −0.146974 | ||||||||
\(382\) | −9145.17 | −1.22489 | ||||||||
\(383\) | −60.4794 | −0.00806881 | −0.00403441 | − | 0.999992i | \(-0.501284\pi\) | ||||
−0.00403441 | + | 0.999992i | \(0.501284\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 5666.21 | 0.750070 | ||||||||
\(386\) | 7406.51 | 0.976636 | ||||||||
\(387\) | 217.472 | 0.0285652 | ||||||||
\(388\) | −4580.72 | −0.599358 | ||||||||
\(389\) | −13025.1 | −1.69768 | −0.848841 | − | 0.528648i | \(-0.822699\pi\) | ||||
−0.848841 | + | 0.528648i | \(0.822699\pi\) | |||||||
\(390\) | −3291.41 | −0.427351 | ||||||||
\(391\) | −2502.99 | −0.323738 | ||||||||
\(392\) | −133.163 | −0.0171576 | ||||||||
\(393\) | −7510.90 | −0.964058 | ||||||||
\(394\) | 3678.65 | 0.470374 | ||||||||
\(395\) | 12268.6 | 1.56279 | ||||||||
\(396\) | 586.882 | 0.0744746 | ||||||||
\(397\) | −1406.48 | −0.177807 | −0.0889036 | − | 0.996040i | \(-0.528336\pi\) | ||||
−0.0889036 | + | 0.996040i | \(0.528336\pi\) | |||||||
\(398\) | 8725.18 | 1.09888 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3922.69 | 0.490336 | ||||||||
\(401\) | −12553.6 | −1.56333 | −0.781665 | − | 0.623699i | \(-0.785629\pi\) | ||||
−0.781665 | + | 0.623699i | \(0.785629\pi\) | |||||||
\(402\) | −5392.41 | −0.669027 | ||||||||
\(403\) | 7155.57 | 0.884477 | ||||||||
\(404\) | 3385.12 | 0.416871 | ||||||||
\(405\) | −1558.42 | −0.191206 | ||||||||
\(406\) | −10671.6 | −1.30449 | ||||||||
\(407\) | 2061.99 | 0.251127 | ||||||||
\(408\) | 521.880 | 0.0633258 | ||||||||
\(409\) | 6624.84 | 0.800922 | 0.400461 | − | 0.916314i | \(-0.368850\pi\) | ||||
0.400461 | + | 0.916314i | \(0.368850\pi\) | |||||||
\(410\) | 18636.8 | 2.24489 | ||||||||
\(411\) | 4659.23 | 0.559180 | ||||||||
\(412\) | −613.917 | −0.0734114 | ||||||||
\(413\) | 10939.6 | 1.30340 | ||||||||
\(414\) | −2071.91 | −0.245963 | ||||||||
\(415\) | 377.089 | 0.0446037 | ||||||||
\(416\) | 912.392 | 0.107533 | ||||||||
\(417\) | −1957.32 | −0.229858 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8837.39 | 1.03039 | 0.515196 | − | 0.857072i | \(-0.327719\pi\) | ||||
0.515196 | + | 0.857072i | \(0.327719\pi\) | |||||||
\(420\) | 4170.86 | 0.484565 | ||||||||
\(421\) | −2167.46 | −0.250916 | −0.125458 | − | 0.992099i | \(-0.540040\pi\) | ||||
−0.125458 | + | 0.992099i | \(0.540040\pi\) | |||||||
\(422\) | 7775.47 | 0.896929 | ||||||||
\(423\) | 687.659 | 0.0790429 | ||||||||
\(424\) | −4804.18 | −0.550264 | ||||||||
\(425\) | 5331.18 | 0.608471 | ||||||||
\(426\) | −4874.13 | −0.554348 | ||||||||
\(427\) | 7952.89 | 0.901328 | ||||||||
\(428\) | −3622.36 | −0.409097 | ||||||||
\(429\) | 1394.44 | 0.156933 | ||||||||
\(430\) | −929.802 | −0.104277 | ||||||||
\(431\) | −8512.46 | −0.951348 | −0.475674 | − | 0.879622i | \(-0.657796\pi\) | ||||
−0.475674 | + | 0.879622i | \(0.657796\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 15189.2 | 1.68579 | 0.842894 | − | 0.538079i | \(-0.180850\pi\) | ||||
0.842894 | + | 0.538079i | \(0.180850\pi\) | |||||||
\(434\) | −9067.51 | −1.00289 | ||||||||
\(435\) | −17048.1 | −1.87906 | ||||||||
\(436\) | 3635.78 | 0.399363 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 4766.31 | 0.519961 | ||||||||
\(439\) | 7930.92 | 0.862237 | 0.431118 | − | 0.902295i | \(-0.358119\pi\) | ||||
0.431118 | + | 0.902295i | \(0.358119\pi\) | |||||||
\(440\) | −2509.21 | −0.271868 | ||||||||
\(441\) | −149.809 | −0.0161763 | ||||||||
\(442\) | 1240.00 | 0.133440 | ||||||||
\(443\) | −6766.59 | −0.725712 | −0.362856 | − | 0.931845i | \(-0.618198\pi\) | ||||
−0.362856 | + | 0.931845i | \(0.618198\pi\) | |||||||
\(444\) | 1517.81 | 0.162235 | ||||||||
\(445\) | −16304.5 | −1.73687 | ||||||||
\(446\) | 6820.67 | 0.724143 | ||||||||
\(447\) | 8521.26 | 0.901660 | ||||||||
\(448\) | −1156.18 | −0.121929 | ||||||||
\(449\) | 5064.96 | 0.532361 | 0.266181 | − | 0.963923i | \(-0.414238\pi\) | ||||
0.266181 | + | 0.963923i | \(0.414238\pi\) | |||||||
\(450\) | 4413.03 | 0.462293 | ||||||||
\(451\) | −7895.68 | −0.824375 | ||||||||
\(452\) | −1522.01 | −0.158383 | ||||||||
\(453\) | −2360.15 | −0.244789 | ||||||||
\(454\) | −8584.79 | −0.887454 | ||||||||
\(455\) | 9910.05 | 1.02108 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8306.44 | −0.850238 | −0.425119 | − | 0.905137i | \(-0.639768\pi\) | ||||
−0.425119 | + | 0.905137i | \(0.639768\pi\) | |||||||
\(458\) | −3704.29 | −0.377926 | ||||||||
\(459\) | 587.115 | 0.0597041 | ||||||||
\(460\) | 8858.46 | 0.897886 | ||||||||
\(461\) | −2196.28 | −0.221890 | −0.110945 | − | 0.993827i | \(-0.535388\pi\) | ||||
−0.110945 | + | 0.993827i | \(0.535388\pi\) | |||||||
\(462\) | −1767.03 | −0.177943 | ||||||||
\(463\) | −4257.93 | −0.427393 | −0.213696 | − | 0.976900i | \(-0.568550\pi\) | ||||
−0.213696 | + | 0.976900i | \(0.568550\pi\) | |||||||
\(464\) | 4725.79 | 0.472822 | ||||||||
\(465\) | −14485.5 | −1.44462 | ||||||||
\(466\) | 1208.42 | 0.120127 | ||||||||
\(467\) | −4618.14 | −0.457606 | −0.228803 | − | 0.973473i | \(-0.573481\pi\) | ||||
−0.228803 | + | 0.973473i | \(0.573481\pi\) | |||||||
\(468\) | 1026.44 | 0.101383 | ||||||||
\(469\) | 16235.9 | 1.59852 | ||||||||
\(470\) | −2940.09 | −0.288545 | ||||||||
\(471\) | −6607.49 | −0.646406 | ||||||||
\(472\) | −4844.49 | −0.472428 | ||||||||
\(473\) | 393.921 | 0.0382928 | ||||||||
\(474\) | −3826.03 | −0.370750 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1571.32 | −0.151305 | ||||||||
\(477\) | −5404.71 | −0.518794 | ||||||||
\(478\) | −14220.5 | −1.36073 | ||||||||
\(479\) | −1727.99 | −0.164831 | −0.0824155 | − | 0.996598i | \(-0.526263\pi\) | ||||
−0.0824155 | + | 0.996598i | \(0.526263\pi\) | |||||||
\(480\) | −1847.02 | −0.175634 | ||||||||
\(481\) | 3606.36 | 0.341862 | ||||||||
\(482\) | −56.2335 | −0.00531404 | ||||||||
\(483\) | 6238.28 | 0.587684 | ||||||||
\(484\) | −4260.94 | −0.400164 | ||||||||
\(485\) | 22033.0 | 2.06282 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 12555.5 | 1.16827 | 0.584134 | − | 0.811657i | \(-0.301434\pi\) | ||||
0.584134 | + | 0.811657i | \(0.301434\pi\) | |||||||
\(488\) | −3521.84 | −0.326693 | ||||||||
\(489\) | −8025.20 | −0.742152 | ||||||||
\(490\) | 640.508 | 0.0590514 | ||||||||
\(491\) | 9491.11 | 0.872358 | 0.436179 | − | 0.899860i | \(-0.356332\pi\) | ||||
0.436179 | + | 0.899860i | \(0.356332\pi\) | |||||||
\(492\) | −5811.96 | −0.532568 | ||||||||
\(493\) | 6422.65 | 0.586738 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2822.87 | −0.256320 | ||||||||
\(496\) | 4015.44 | 0.363505 | ||||||||
\(497\) | 14675.4 | 1.32451 | ||||||||
\(498\) | −117.597 | −0.0105816 | ||||||||
\(499\) | 2930.59 | 0.262909 | 0.131454 | − | 0.991322i | \(-0.458035\pi\) | ||||
0.131454 | + | 0.991322i | \(0.458035\pi\) | |||||||
\(500\) | −9248.01 | −0.827168 | ||||||||
\(501\) | 750.281 | 0.0669064 | ||||||||
\(502\) | 8310.68 | 0.738892 | ||||||||
\(503\) | −2343.87 | −0.207769 | −0.103885 | − | 0.994589i | \(-0.533127\pi\) | ||||
−0.103885 | + | 0.994589i | \(0.533127\pi\) | |||||||
\(504\) | −1300.70 | −0.114956 | ||||||||
\(505\) | −16282.2 | −1.43475 | ||||||||
\(506\) | −3752.99 | −0.329724 | ||||||||
\(507\) | −4152.16 | −0.363715 | ||||||||
\(508\) | −1457.36 | −0.127283 | ||||||||
\(509\) | 8976.91 | 0.781718 | 0.390859 | − | 0.920451i | \(-0.372178\pi\) | ||||
0.390859 | + | 0.920451i | \(0.372178\pi\) | |||||||
\(510\) | −2510.21 | −0.217949 | ||||||||
\(511\) | −14350.8 | −1.24235 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8611.93 | −0.739019 | ||||||||
\(515\) | 2952.90 | 0.252661 | ||||||||
\(516\) | 289.963 | 0.0247382 | ||||||||
\(517\) | 1245.60 | 0.105960 | ||||||||
\(518\) | −4569.96 | −0.387630 | ||||||||
\(519\) | 3214.86 | 0.271901 | ||||||||
\(520\) | −4388.55 | −0.370097 | ||||||||
\(521\) | −16201.3 | −1.36236 | −0.681182 | − | 0.732114i | \(-0.738534\pi\) | ||||
−0.681182 | + | 0.732114i | \(0.738534\pi\) | |||||||
\(522\) | 5316.52 | 0.445781 | ||||||||
\(523\) | −16705.1 | −1.39668 | −0.698340 | − | 0.715766i | \(-0.746078\pi\) | ||||
−0.698340 | + | 0.715766i | \(0.746078\pi\) | |||||||
\(524\) | −10014.5 | −0.834899 | ||||||||
\(525\) | −13287.1 | −1.10456 | ||||||||
\(526\) | 9470.36 | 0.785033 | ||||||||
\(527\) | 5457.23 | 0.451083 | ||||||||
\(528\) | 782.509 | 0.0644969 | ||||||||
\(529\) | 1082.43 | 0.0889647 | ||||||||
\(530\) | 23107.8 | 1.89385 | ||||||||
\(531\) | −5450.06 | −0.445409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13809.3 | −1.12223 | ||||||||
\(534\) | 5084.61 | 0.412046 | ||||||||
\(535\) | 17423.3 | 1.40799 | ||||||||
\(536\) | −7189.88 | −0.579394 | ||||||||
\(537\) | 5254.44 | 0.422246 | ||||||||
\(538\) | −11111.5 | −0.890431 | ||||||||
\(539\) | −271.358 | −0.0216850 | ||||||||
\(540\) | −2077.89 | −0.165589 | ||||||||
\(541\) | −21446.0 | −1.70431 | −0.852157 | − | 0.523286i | \(-0.824706\pi\) | ||||
−0.852157 | + | 0.523286i | \(0.824706\pi\) | |||||||
\(542\) | −1779.65 | −0.141038 | ||||||||
\(543\) | −136.971 | −0.0108250 | ||||||||
\(544\) | 695.840 | 0.0548417 | ||||||||
\(545\) | −17487.9 | −1.37449 | ||||||||
\(546\) | −3090.49 | −0.242236 | ||||||||
\(547\) | 14560.4 | 1.13813 | 0.569067 | − | 0.822291i | \(-0.307305\pi\) | ||||
0.569067 | + | 0.822291i | \(0.307305\pi\) | |||||||
\(548\) | 6212.31 | 0.484264 | ||||||||
\(549\) | −3962.07 | −0.308009 | ||||||||
\(550\) | 7993.60 | 0.619724 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2762.55 | −0.213011 | ||||||||
\(553\) | 11519.7 | 0.885838 | ||||||||
\(554\) | 1436.65 | 0.110176 | ||||||||
\(555\) | −7300.59 | −0.558365 | ||||||||
\(556\) | −2609.77 | −0.199062 | ||||||||
\(557\) | 15148.7 | 1.15238 | 0.576188 | − | 0.817317i | \(-0.304540\pi\) | ||||
0.576188 | + | 0.817317i | \(0.304540\pi\) | |||||||
\(558\) | 4517.37 | 0.342716 | ||||||||
\(559\) | 688.957 | 0.0521284 | ||||||||
\(560\) | 5561.15 | 0.419645 | ||||||||
\(561\) | 1063.48 | 0.0800359 | ||||||||
\(562\) | −12742.3 | −0.956410 | ||||||||
\(563\) | 581.773 | 0.0435503 | 0.0217751 | − | 0.999763i | \(-0.493068\pi\) | ||||
0.0217751 | + | 0.999763i | \(0.493068\pi\) | |||||||
\(564\) | 916.879 | 0.0684532 | ||||||||
\(565\) | 7320.76 | 0.545109 | ||||||||
\(566\) | 644.232 | 0.0478429 | ||||||||
\(567\) | −1463.29 | −0.108382 | ||||||||
\(568\) | −6498.83 | −0.480079 | ||||||||
\(569\) | 13602.6 | 1.00220 | 0.501098 | − | 0.865390i | \(-0.332930\pi\) | ||||
0.501098 | + | 0.865390i | \(0.332930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21086.1 | −1.54540 | −0.772700 | − | 0.634771i | \(-0.781094\pi\) | ||||
−0.772700 | + | 0.634771i | \(0.781094\pi\) | |||||||
\(572\) | 1859.26 | 0.135908 | ||||||||
\(573\) | −13717.8 | −1.00012 | ||||||||
\(574\) | 17499.1 | 1.27247 | ||||||||
\(575\) | −28220.4 | −2.04673 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 5631.33 | 0.406300 | 0.203150 | − | 0.979148i | \(-0.434882\pi\) | ||||
0.203150 | + | 0.979148i | \(0.434882\pi\) | |||||||
\(578\) | −8880.31 | −0.639052 | ||||||||
\(579\) | 11109.8 | 0.797420 | ||||||||
\(580\) | −22730.8 | −1.62732 | ||||||||
\(581\) | 354.070 | 0.0252828 | ||||||||
\(582\) | −6871.09 | −0.489374 | ||||||||
\(583\) | −9789.89 | −0.695465 | ||||||||
\(584\) | 6355.08 | 0.450300 | ||||||||
\(585\) | −4937.12 | −0.348931 | ||||||||
\(586\) | −17577.4 | −1.23911 | ||||||||
\(587\) | 4246.10 | 0.298561 | 0.149281 | − | 0.988795i | \(-0.452304\pi\) | ||||
0.149281 | + | 0.988795i | \(0.452304\pi\) | |||||||
\(588\) | −199.745 | −0.0140091 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 23301.7 | 1.62596 | ||||||||
\(591\) | 5517.97 | 0.384059 | ||||||||
\(592\) | 2023.75 | 0.140499 | ||||||||
\(593\) | 5040.63 | 0.349062 | 0.174531 | − | 0.984652i | \(-0.444159\pi\) | ||||
0.174531 | + | 0.984652i | \(0.444159\pi\) | |||||||
\(594\) | 880.323 | 0.0608082 | ||||||||
\(595\) | 7557.95 | 0.520749 | ||||||||
\(596\) | 11361.7 | 0.780860 | ||||||||
\(597\) | 13087.8 | 0.897231 | ||||||||
\(598\) | −6563.87 | −0.448857 | ||||||||
\(599\) | −8562.91 | −0.584092 | −0.292046 | − | 0.956404i | \(-0.594336\pi\) | ||||
−0.292046 | + | 0.956404i | \(0.594336\pi\) | |||||||
\(600\) | 5884.03 | 0.400358 | ||||||||
\(601\) | 2352.29 | 0.159654 | 0.0798269 | − | 0.996809i | \(-0.474563\pi\) | ||||
0.0798269 | + | 0.996809i | \(0.474563\pi\) | |||||||
\(602\) | −873.043 | −0.0591073 | ||||||||
\(603\) | −8088.61 | −0.546258 | ||||||||
\(604\) | −3146.86 | −0.211993 | ||||||||
\(605\) | 20494.9 | 1.37725 | ||||||||
\(606\) | 5077.68 | 0.340374 | ||||||||
\(607\) | −15735.1 | −1.05217 | −0.526084 | − | 0.850433i | \(-0.676340\pi\) | ||||
−0.526084 | + | 0.850433i | \(0.676340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16007.4 | −1.06511 | ||||||||
\(610\) | 16939.8 | 1.12438 | ||||||||
\(611\) | 2178.52 | 0.144245 | ||||||||
\(612\) | 782.820 | 0.0517053 | ||||||||
\(613\) | 6399.92 | 0.421681 | 0.210841 | − | 0.977520i | \(-0.432380\pi\) | ||||
0.210841 | + | 0.977520i | \(0.432380\pi\) | |||||||
\(614\) | −11725.5 | −0.770685 | ||||||||
\(615\) | 27955.2 | 1.83294 | ||||||||
\(616\) | −2356.04 | −0.154103 | ||||||||
\(617\) | −21863.0 | −1.42653 | −0.713267 | − | 0.700892i | \(-0.752785\pi\) | ||||
−0.713267 | + | 0.700892i | \(0.752785\pi\) | |||||||
\(618\) | −920.875 | −0.0599402 | ||||||||
\(619\) | 8081.41 | 0.524749 | 0.262374 | − | 0.964966i | \(-0.415494\pi\) | ||||
0.262374 | + | 0.964966i | \(0.415494\pi\) | |||||||
\(620\) | −19314.0 | −1.25108 | ||||||||
\(621\) | −3107.87 | −0.200828 | ||||||||
\(622\) | 7864.01 | 0.506942 | ||||||||
\(623\) | −15309.2 | −0.984509 | ||||||||
\(624\) | 1368.59 | 0.0878002 | ||||||||
\(625\) | 13836.4 | 0.885528 | ||||||||
\(626\) | 17982.0 | 1.14809 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8809.99 | −0.559804 | ||||||||
\(629\) | 2750.41 | 0.174350 | ||||||||
\(630\) | 6256.29 | 0.395645 | ||||||||
\(631\) | 21717.0 | 1.37011 | 0.685055 | − | 0.728491i | \(-0.259778\pi\) | ||||
0.685055 | + | 0.728491i | \(0.259778\pi\) | |||||||
\(632\) | −5101.38 | −0.321079 | ||||||||
\(633\) | 11663.2 | 0.732339 | ||||||||
\(634\) | 15606.4 | 0.977618 | ||||||||
\(635\) | 7009.80 | 0.438072 | ||||||||
\(636\) | −7206.28 | −0.449288 | ||||||||
\(637\) | −474.598 | −0.0295201 | ||||||||
\(638\) | 9630.15 | 0.597588 | ||||||||
\(639\) | −7311.19 | −0.452623 | ||||||||
\(640\) | −2462.69 | −0.152104 | ||||||||
\(641\) | 18967.7 | 1.16876 | 0.584382 | − | 0.811479i | \(-0.301337\pi\) | ||||
0.584382 | + | 0.811479i | \(0.301337\pi\) | |||||||
\(642\) | −5433.54 | −0.334026 | ||||||||
\(643\) | −19322.9 | −1.18510 | −0.592552 | − | 0.805532i | \(-0.701880\pi\) | ||||
−0.592552 | + | 0.805532i | \(0.701880\pi\) | |||||||
\(644\) | 8317.70 | 0.508949 | ||||||||
\(645\) | −1394.70 | −0.0851417 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11022.5 | 0.669764 | 0.334882 | − | 0.942260i | \(-0.391303\pi\) | ||||
0.334882 | + | 0.942260i | \(0.391303\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −9872.04 | −0.597090 | ||||||||
\(650\) | 13980.6 | 0.843636 | ||||||||
\(651\) | −13601.3 | −0.818856 | ||||||||
\(652\) | −10700.3 | −0.642722 | ||||||||
\(653\) | 7031.74 | 0.421399 | 0.210699 | − | 0.977551i | \(-0.432426\pi\) | ||||
0.210699 | + | 0.977551i | \(0.432426\pi\) | |||||||
\(654\) | 5453.67 | 0.326078 | ||||||||
\(655\) | 48169.3 | 2.87348 | ||||||||
\(656\) | −7749.28 | −0.461217 | ||||||||
\(657\) | 7149.47 | 0.424547 | ||||||||
\(658\) | −2760.61 | −0.163556 | ||||||||
\(659\) | −26220.9 | −1.54996 | −0.774978 | − | 0.631989i | \(-0.782239\pi\) | ||||
−0.774978 | + | 0.631989i | \(0.782239\pi\) | |||||||
\(660\) | −3763.82 | −0.221980 | ||||||||
\(661\) | 9214.18 | 0.542194 | 0.271097 | − | 0.962552i | \(-0.412614\pi\) | ||||
0.271097 | + | 0.962552i | \(0.412614\pi\) | |||||||
\(662\) | 9135.98 | 0.536374 | ||||||||
\(663\) | 1860.00 | 0.108954 | ||||||||
\(664\) | −156.796 | −0.00916393 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2276.72 | 0.132464 | ||||||||
\(667\) | −33998.0 | −1.97363 | ||||||||
\(668\) | 1000.37 | 0.0579426 | ||||||||
\(669\) | 10231.0 | 0.591260 | ||||||||
\(670\) | 34582.9 | 1.99411 | ||||||||
\(671\) | −7176.76 | −0.412900 | ||||||||
\(672\) | −1734.27 | −0.0995548 | ||||||||
\(673\) | −4760.01 | −0.272637 | −0.136319 | − | 0.990665i | \(-0.543527\pi\) | ||||
−0.136319 | + | 0.990665i | \(0.543527\pi\) | |||||||
\(674\) | −20488.3 | −1.17089 | ||||||||
\(675\) | 6619.54 | 0.377461 | ||||||||
\(676\) | −5536.21 | −0.314987 | ||||||||
\(677\) | −9064.23 | −0.514574 | −0.257287 | − | 0.966335i | \(-0.582829\pi\) | ||||
−0.257287 | + | 0.966335i | \(0.582829\pi\) | |||||||
\(678\) | −2283.01 | −0.129319 | ||||||||
\(679\) | 20688.0 | 1.16927 | ||||||||
\(680\) | −3346.95 | −0.188749 | ||||||||
\(681\) | −12877.2 | −0.724603 | ||||||||
\(682\) | 8182.60 | 0.459425 | ||||||||
\(683\) | −21037.2 | −1.17858 | −0.589288 | − | 0.807923i | \(-0.700592\pi\) | ||||
−0.589288 | + | 0.807923i | \(0.700592\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29880.8 | −1.66670 | ||||||||
\(686\) | 12994.2 | 0.723208 | ||||||||
\(687\) | −5556.44 | −0.308575 | ||||||||
\(688\) | 386.617 | 0.0214239 | ||||||||
\(689\) | −17122.3 | −0.946743 | ||||||||
\(690\) | 13287.7 | 0.733121 | ||||||||
\(691\) | −33207.3 | −1.82817 | −0.914086 | − | 0.405520i | \(-0.867090\pi\) | ||||
−0.914086 | + | 0.405520i | \(0.867090\pi\) | |||||||
\(692\) | 4286.48 | 0.235473 | ||||||||
\(693\) | −2650.55 | −0.145290 | ||||||||
\(694\) | −20927.6 | −1.14467 | ||||||||
\(695\) | 12552.8 | 0.685116 | ||||||||
\(696\) | 7088.69 | 0.386058 | ||||||||
\(697\) | −10531.8 | −0.572337 | ||||||||
\(698\) | −8047.04 | −0.436368 | ||||||||
\(699\) | 1812.63 | 0.0980831 | ||||||||
\(700\) | −17716.1 | −0.956581 | ||||||||
\(701\) | 12181.8 | 0.656347 | 0.328173 | − | 0.944618i | \(-0.393567\pi\) | ||||
0.328173 | + | 0.944618i | \(0.393567\pi\) | |||||||
\(702\) | 1539.66 | 0.0827789 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1043.35 | 0.0558559 | ||||||||
\(705\) | −4410.13 | −0.235596 | ||||||||
\(706\) | −6546.79 | −0.348997 | ||||||||
\(707\) | −15288.3 | −0.813261 | ||||||||
\(708\) | −7266.74 | −0.385736 | ||||||||
\(709\) | −19592.1 | −1.03779 | −0.518897 | − | 0.854837i | \(-0.673657\pi\) | ||||
−0.518897 | + | 0.854837i | \(0.673657\pi\) | |||||||
\(710\) | 31259.0 | 1.65229 | ||||||||
\(711\) | −5739.05 | −0.302716 | ||||||||
\(712\) | 6779.49 | 0.356843 | ||||||||
\(713\) | −28887.6 | −1.51732 | ||||||||
\(714\) | −2356.98 | −0.123540 | ||||||||
\(715\) | −8942.91 | −0.467757 | ||||||||
\(716\) | 7005.93 | 0.365676 | ||||||||
\(717\) | −21330.8 | −1.11104 | ||||||||
\(718\) | −22362.3 | −1.16233 | ||||||||
\(719\) | 12211.3 | 0.633387 | 0.316693 | − | 0.948528i | \(-0.397427\pi\) | ||||
0.316693 | + | 0.948528i | \(0.397427\pi\) | |||||||
\(720\) | −2770.52 | −0.143405 | ||||||||
\(721\) | 2772.65 | 0.143216 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −84.3503 | −0.00433890 | ||||||||
\(724\) | −182.628 | −0.00937473 | ||||||||
\(725\) | 72413.4 | 3.70947 | ||||||||
\(726\) | −6391.41 | −0.326732 | ||||||||
\(727\) | 22063.4 | 1.12556 | 0.562782 | − | 0.826606i | \(-0.309731\pi\) | ||||
0.562782 | + | 0.826606i | \(0.309731\pi\) | |||||||
\(728\) | −4120.65 | −0.209782 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −30567.5 | −1.54980 | ||||||||
\(731\) | 525.437 | 0.0265855 | ||||||||
\(732\) | −5282.76 | −0.266744 | ||||||||
\(733\) | −25069.2 | −1.26323 | −0.631617 | − | 0.775281i | \(-0.717608\pi\) | ||||
−0.631617 | + | 0.775281i | \(0.717608\pi\) | |||||||
\(734\) | 14687.3 | 0.738580 | ||||||||
\(735\) | 960.762 | 0.0482153 | ||||||||
\(736\) | −3683.40 | −0.184473 | ||||||||
\(737\) | −14651.4 | −0.732282 | ||||||||
\(738\) | −8717.94 | −0.434840 | ||||||||
\(739\) | 9709.63 | 0.483322 | 0.241661 | − | 0.970361i | \(-0.422308\pi\) | ||||
0.241661 | + | 0.970361i | \(0.422308\pi\) | |||||||
\(740\) | −9734.12 | −0.483559 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21697.2 | 1.07349 | ||||||||
\(743\) | −23381.1 | −1.15447 | −0.577233 | − | 0.816580i | \(-0.695867\pi\) | ||||
−0.577233 | + | 0.816580i | \(0.695867\pi\) | |||||||
\(744\) | 6023.16 | 0.296801 | ||||||||
\(745\) | −54649.0 | −2.68750 | ||||||||
\(746\) | 3895.27 | 0.191174 | ||||||||
\(747\) | −176.395 | −0.00863984 | ||||||||
\(748\) | 1417.97 | 0.0693131 | ||||||||
\(749\) | 16359.8 | 0.798094 | ||||||||
\(750\) | −13872.0 | −0.675379 | ||||||||
\(751\) | −1585.42 | −0.0770344 | −0.0385172 | − | 0.999258i | \(-0.512263\pi\) | ||||
−0.0385172 | + | 0.999258i | \(0.512263\pi\) | |||||||
\(752\) | 1222.51 | 0.0592822 | ||||||||
\(753\) | 12466.0 | 0.603303 | ||||||||
\(754\) | 16842.9 | 0.813503 | ||||||||
\(755\) | 15136.2 | 0.729620 | ||||||||
\(756\) | −1951.05 | −0.0938612 | ||||||||
\(757\) | 30847.9 | 1.48109 | 0.740546 | − | 0.672005i | \(-0.234567\pi\) | ||||
0.740546 | + | 0.672005i | \(0.234567\pi\) | |||||||
\(758\) | −9996.53 | −0.479011 | ||||||||
\(759\) | −5629.48 | −0.269219 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28714.9 | −1.36783 | −0.683913 | − | 0.729564i | \(-0.739723\pi\) | ||||
−0.683913 | + | 0.729564i | \(0.739723\pi\) | |||||||
\(762\) | −2186.04 | −0.103926 | ||||||||
\(763\) | −16420.3 | −0.779104 | ||||||||
\(764\) | −18290.3 | −0.866127 | ||||||||
\(765\) | −3765.32 | −0.177955 | ||||||||
\(766\) | −120.959 | −0.00570551 | ||||||||
\(767\) | −17265.9 | −0.812825 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 21245.5 | 0.996270 | 0.498135 | − | 0.867100i | \(-0.334018\pi\) | ||||
0.498135 | + | 0.867100i | \(0.334018\pi\) | |||||||
\(770\) | 11332.4 | 0.530379 | ||||||||
\(771\) | −12917.9 | −0.603407 | ||||||||
\(772\) | 14813.0 | 0.690586 | ||||||||
\(773\) | −135.106 | −0.00628647 | −0.00314324 | − | 0.999995i | \(-0.501001\pi\) | ||||
−0.00314324 | + | 0.999995i | \(0.501001\pi\) | |||||||
\(774\) | 434.944 | 0.0201986 | ||||||||
\(775\) | 61528.6 | 2.85183 | ||||||||
\(776\) | −9161.45 | −0.423810 | ||||||||
\(777\) | −6854.94 | −0.316499 | ||||||||
\(778\) | −26050.2 | −1.20044 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −6582.82 | −0.302183 | ||||||||
\(781\) | −13243.2 | −0.606760 | ||||||||
\(782\) | −5005.97 | −0.228917 | ||||||||
\(783\) | 7974.78 | 0.363979 | ||||||||
\(784\) | −266.327 | −0.0121322 | ||||||||
\(785\) | 42375.5 | 1.92668 | ||||||||
\(786\) | −15021.8 | −0.681692 | ||||||||
\(787\) | 32506.1 | 1.47232 | 0.736161 | − | 0.676807i | \(-0.236637\pi\) | ||||
0.736161 | + | 0.676807i | \(0.236637\pi\) | |||||||
\(788\) | 7357.29 | 0.332605 | ||||||||
\(789\) | 14205.5 | 0.640977 | ||||||||
\(790\) | 24537.3 | 1.10506 | ||||||||
\(791\) | 6873.87 | 0.308985 | ||||||||
\(792\) | 1173.76 | 0.0526615 | ||||||||
\(793\) | −12552.0 | −0.562084 | ||||||||
\(794\) | −2812.97 | −0.125729 | ||||||||
\(795\) | 34661.7 | 1.54632 | ||||||||
\(796\) | 17450.4 | 0.777025 | ||||||||
\(797\) | −8254.37 | −0.366857 | −0.183428 | − | 0.983033i | \(-0.558720\pi\) | ||||
−0.183428 | + | 0.983033i | \(0.558720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1661.46 | 0.0735648 | ||||||||
\(800\) | 7845.38 | 0.346720 | ||||||||
\(801\) | 7626.92 | 0.336434 | ||||||||
\(802\) | −25107.1 | −1.10544 | ||||||||
\(803\) | 12950.3 | 0.569123 | ||||||||
\(804\) | −10784.8 | −0.473073 | ||||||||
\(805\) | −40007.6 | −1.75166 | ||||||||
\(806\) | 14311.1 | 0.625420 | ||||||||
\(807\) | −16667.3 | −0.727034 | ||||||||
\(808\) | 6770.24 | 0.294773 | ||||||||
\(809\) | 9189.24 | 0.399353 | 0.199676 | − | 0.979862i | \(-0.436011\pi\) | ||||
0.199676 | + | 0.979862i | \(0.436011\pi\) | |||||||
\(810\) | −3116.84 | −0.135203 | ||||||||
\(811\) | 12785.8 | 0.553601 | 0.276801 | − | 0.960927i | \(-0.410726\pi\) | ||||
0.276801 | + | 0.960927i | \(0.410726\pi\) | |||||||
\(812\) | −21343.2 | −0.922413 | ||||||||
\(813\) | −2669.48 | −0.115157 | ||||||||
\(814\) | 4123.97 | 0.177574 | ||||||||
\(815\) | 51467.6 | 2.21206 | ||||||||
\(816\) | 1043.76 | 0.0447781 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 13249.7 | 0.566337 | ||||||||
\(819\) | −4635.74 | −0.197785 | ||||||||
\(820\) | 37273.5 | 1.58738 | ||||||||
\(821\) | 6581.97 | 0.279796 | 0.139898 | − | 0.990166i | \(-0.455323\pi\) | ||||
0.139898 | + | 0.990166i | \(0.455323\pi\) | |||||||
\(822\) | 9318.47 | 0.395400 | ||||||||
\(823\) | 21262.6 | 0.900570 | 0.450285 | − | 0.892885i | \(-0.351322\pi\) | ||||
0.450285 | + | 0.892885i | \(0.351322\pi\) | |||||||
\(824\) | −1227.83 | −0.0519097 | ||||||||
\(825\) | 11990.4 | 0.506002 | ||||||||
\(826\) | 21879.3 | 0.921644 | ||||||||
\(827\) | 27797.1 | 1.16880 | 0.584401 | − | 0.811465i | \(-0.301329\pi\) | ||||
0.584401 | + | 0.811465i | \(0.301329\pi\) | |||||||
\(828\) | −4143.82 | −0.173922 | ||||||||
\(829\) | 460.755 | 0.0193036 | 0.00965179 | − | 0.999953i | \(-0.496928\pi\) | ||||
0.00965179 | + | 0.999953i | \(0.496928\pi\) | |||||||
\(830\) | 754.177 | 0.0315396 | ||||||||
\(831\) | 2154.98 | 0.0899583 | ||||||||
\(832\) | 1824.78 | 0.0760372 | ||||||||
\(833\) | −361.955 | −0.0150552 | ||||||||
\(834\) | −3914.65 | −0.162534 | ||||||||
\(835\) | −4811.74 | −0.199422 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6776.05 | 0.279826 | ||||||||
\(838\) | 17674.8 | 0.728598 | ||||||||
\(839\) | −31987.0 | −1.31623 | −0.658113 | − | 0.752919i | \(-0.728645\pi\) | ||||
−0.658113 | + | 0.752919i | \(0.728645\pi\) | |||||||
\(840\) | 8341.72 | 0.342639 | ||||||||
\(841\) | 62849.8 | 2.57697 | ||||||||
\(842\) | −4334.92 | −0.177424 | ||||||||
\(843\) | −19113.5 | −0.780906 | ||||||||
\(844\) | 15550.9 | 0.634225 | ||||||||
\(845\) | 26628.8 | 1.08409 | ||||||||
\(846\) | 1375.32 | 0.0558918 | ||||||||
\(847\) | 19243.8 | 0.780666 | ||||||||
\(848\) | −9608.37 | −0.389095 | ||||||||
\(849\) | 966.348 | 0.0390636 | ||||||||
\(850\) | 10662.4 | 0.430254 | ||||||||
\(851\) | −14559.1 | −0.586464 | ||||||||
\(852\) | −9748.25 | −0.391983 | ||||||||
\(853\) | −5713.39 | −0.229335 | −0.114668 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114668 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(854\) | 15905.8 | 0.637335 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7244.72 | −0.289275 | ||||||||
\(857\) | −14860.3 | −0.592322 | −0.296161 | − | 0.955138i | \(-0.595706\pi\) | ||||
−0.296161 | + | 0.955138i | \(0.595706\pi\) | |||||||
\(858\) | 2788.89 | 0.110969 | ||||||||
\(859\) | 29495.6 | 1.17157 | 0.585784 | − | 0.810467i | \(-0.300787\pi\) | ||||
0.585784 | + | 0.810467i | \(0.300787\pi\) | |||||||
\(860\) | −1859.60 | −0.0737348 | ||||||||
\(861\) | 26248.7 | 1.03897 | ||||||||
\(862\) | −17024.9 | −0.672705 | ||||||||
\(863\) | 11431.9 | 0.450923 | 0.225461 | − | 0.974252i | \(-0.427611\pi\) | ||||
0.225461 | + | 0.974252i | \(0.427611\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −20617.7 | −0.810431 | ||||||||
\(866\) | 30378.4 | 1.19203 | ||||||||
\(867\) | −13320.5 | −0.521784 | ||||||||
\(868\) | −18135.0 | −0.709150 | ||||||||
\(869\) | −10395.5 | −0.405804 | ||||||||
\(870\) | −34096.2 | −1.32870 | ||||||||
\(871\) | −25624.9 | −0.996863 | ||||||||
\(872\) | 7271.56 | 0.282392 | ||||||||
\(873\) | −10306.6 | −0.399572 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41767.0 | 1.61369 | ||||||||
\(876\) | 9532.62 | 0.367668 | ||||||||
\(877\) | −23593.6 | −0.908437 | −0.454218 | − | 0.890890i | \(-0.650081\pi\) | ||||
−0.454218 | + | 0.890890i | \(0.650081\pi\) | |||||||
\(878\) | 15861.8 | 0.609694 | ||||||||
\(879\) | −26366.2 | −1.01173 | ||||||||
\(880\) | −5018.43 | −0.192240 | ||||||||
\(881\) | −13012.7 | −0.497626 | −0.248813 | − | 0.968552i | \(-0.580040\pi\) | ||||
−0.248813 | + | 0.968552i | \(0.580040\pi\) | |||||||
\(882\) | −299.618 | −0.0114384 | ||||||||
\(883\) | −11832.9 | −0.450971 | −0.225485 | − | 0.974247i | \(-0.572397\pi\) | ||||
−0.225485 | + | 0.974247i | \(0.572397\pi\) | |||||||
\(884\) | 2480.00 | 0.0943567 | ||||||||
\(885\) | 34952.6 | 1.32759 | ||||||||
\(886\) | −13533.2 | −0.513156 | ||||||||
\(887\) | 50764.2 | 1.92164 | 0.960821 | − | 0.277169i | \(-0.0893963\pi\) | ||||
0.960821 | + | 0.277169i | \(0.0893963\pi\) | |||||||
\(888\) | 3035.63 | 0.114717 | ||||||||
\(889\) | 6581.90 | 0.248312 | ||||||||
\(890\) | −32608.9 | −1.22815 | ||||||||
\(891\) | 1320.48 | 0.0496497 | ||||||||
\(892\) | 13641.3 | 0.512047 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 17042.5 | 0.637570 | ||||||||
\(895\) | −33698.1 | −1.25855 | ||||||||
\(896\) | −2312.36 | −0.0862170 | ||||||||
\(897\) | −9845.81 | −0.366490 | ||||||||
\(898\) | 10129.9 | 0.376436 | ||||||||
\(899\) | 74125.5 | 2.74997 | ||||||||
\(900\) | 8826.05 | 0.326891 | ||||||||
\(901\) | −13058.4 | −0.482839 | ||||||||
\(902\) | −15791.4 | −0.582921 | ||||||||
\(903\) | −1309.57 | −0.0482609 | ||||||||
\(904\) | −3044.01 | −0.111994 | ||||||||
\(905\) | 878.428 | 0.0322651 | ||||||||
\(906\) | −4720.29 | −0.173092 | ||||||||
\(907\) | 14457.8 | 0.529286 | 0.264643 | − | 0.964346i | \(-0.414746\pi\) | ||||
0.264643 | + | 0.964346i | \(0.414746\pi\) | |||||||
\(908\) | −17169.6 | −0.627525 | ||||||||
\(909\) | 7616.52 | 0.277914 | ||||||||
\(910\) | 19820.1 | 0.722011 | ||||||||
\(911\) | −9841.83 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −319.516 | −0.0115821 | ||||||||
\(914\) | −16612.9 | −0.601209 | ||||||||
\(915\) | 25409.8 | 0.918056 | ||||||||
\(916\) | −7408.58 | −0.267234 | ||||||||
\(917\) | 45228.9 | 1.62878 | ||||||||
\(918\) | 1174.23 | 0.0422172 | ||||||||
\(919\) | 16698.0 | 0.599363 | 0.299682 | − | 0.954039i | \(-0.403120\pi\) | ||||
0.299682 | + | 0.954039i | \(0.403120\pi\) | |||||||
\(920\) | 17716.9 | 0.634902 | ||||||||
\(921\) | −17588.2 | −0.629262 | ||||||||
\(922\) | −4392.57 | −0.156900 | ||||||||
\(923\) | −23162.0 | −0.825989 | ||||||||
\(924\) | −3534.06 | −0.125825 | ||||||||
\(925\) | 31010.0 | 1.10227 | ||||||||
\(926\) | −8515.86 | −0.302212 | ||||||||
\(927\) | −1381.31 | −0.0489410 | ||||||||
\(928\) | 9451.59 | 0.334336 | ||||||||
\(929\) | −45149.9 | −1.59453 | −0.797266 | − | 0.603629i | \(-0.793721\pi\) | ||||
−0.797266 | + | 0.603629i | \(0.793721\pi\) | |||||||
\(930\) | −28971.0 | −1.02150 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2416.84 | 0.0849425 | ||||||||
\(933\) | 11796.0 | 0.413917 | ||||||||
\(934\) | −9236.27 | −0.323576 | ||||||||
\(935\) | −6820.36 | −0.238556 | ||||||||
\(936\) | 2052.88 | 0.0716886 | ||||||||
\(937\) | −21364.8 | −0.744885 | −0.372442 | − | 0.928055i | \(-0.621480\pi\) | ||||
−0.372442 | + | 0.928055i | \(0.621480\pi\) | |||||||
\(938\) | 32471.8 | 1.13032 | ||||||||
\(939\) | 26973.0 | 0.937413 | ||||||||
\(940\) | −5880.18 | −0.204032 | ||||||||
\(941\) | 21552.4 | 0.746639 | 0.373320 | − | 0.927703i | \(-0.378219\pi\) | ||||
0.373320 | + | 0.927703i | \(0.378219\pi\) | |||||||
\(942\) | −13215.0 | −0.457078 | ||||||||
\(943\) | 55749.4 | 1.92518 | ||||||||
\(944\) | −9688.99 | −0.334057 | ||||||||
\(945\) | 9384.43 | 0.323043 | ||||||||
\(946\) | 787.842 | 0.0270771 | ||||||||
\(947\) | −17111.1 | −0.587155 | −0.293578 | − | 0.955935i | \(-0.594846\pi\) | ||||
−0.293578 | + | 0.955935i | \(0.594846\pi\) | |||||||
\(948\) | −7652.06 | −0.262160 | ||||||||
\(949\) | 22649.7 | 0.774753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23409.6 | 0.798222 | ||||||||
\(952\) | −3142.64 | −0.106989 | ||||||||
\(953\) | 15347.7 | 0.521680 | 0.260840 | − | 0.965382i | \(-0.416000\pi\) | ||||
0.260840 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(954\) | −10809.4 | −0.366842 | ||||||||
\(955\) | 87975.4 | 2.98096 | ||||||||
\(956\) | −28441.0 | −0.962185 | ||||||||
\(957\) | 14445.2 | 0.487929 | ||||||||
\(958\) | −3455.99 | −0.116553 | ||||||||
\(959\) | −28056.8 | −0.944735 | ||||||||
\(960\) | −3694.03 | −0.124192 | ||||||||
\(961\) | 33192.4 | 1.11417 | ||||||||
\(962\) | 7212.71 | 0.241733 | ||||||||
\(963\) | −8150.31 | −0.272731 | ||||||||
\(964\) | −112.467 | −0.00375759 | ||||||||
\(965\) | −71249.7 | −2.37680 | ||||||||
\(966\) | 12476.6 | 0.415556 | ||||||||
\(967\) | 28429.3 | 0.945424 | 0.472712 | − | 0.881217i | \(-0.343275\pi\) | ||||
0.472712 | + | 0.881217i | \(0.343275\pi\) | |||||||
\(968\) | −8521.89 | −0.282958 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 44066.0 | 1.45863 | ||||||||
\(971\) | 469.588 | 0.0155199 | 0.00775994 | − | 0.999970i | \(-0.497530\pi\) | ||||
0.00775994 | + | 0.999970i | \(0.497530\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 11786.5 | 0.388345 | ||||||||
\(974\) | 25111.1 | 0.826090 | ||||||||
\(975\) | 20970.9 | 0.688826 | ||||||||
\(976\) | −7043.68 | −0.231007 | ||||||||
\(977\) | 26778.2 | 0.876879 | 0.438440 | − | 0.898761i | \(-0.355531\pi\) | ||||
0.438440 | + | 0.898761i | \(0.355531\pi\) | |||||||
\(978\) | −16050.4 | −0.524780 | ||||||||
\(979\) | 13815.1 | 0.451005 | ||||||||
\(980\) | 1281.02 | 0.0417557 | ||||||||
\(981\) | 8180.50 | 0.266242 | ||||||||
\(982\) | 18982.2 | 0.616850 | ||||||||
\(983\) | −34172.3 | −1.10878 | −0.554389 | − | 0.832258i | \(-0.687048\pi\) | ||||
−0.554389 | + | 0.832258i | \(0.687048\pi\) | |||||||
\(984\) | −11623.9 | −0.376582 | ||||||||
\(985\) | −35388.1 | −1.14473 | ||||||||
\(986\) | 12845.3 | 0.414886 | ||||||||
\(987\) | −4140.92 | −0.133543 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2781.38 | −0.0894263 | ||||||||
\(990\) | −5645.73 | −0.181246 | ||||||||
\(991\) | 34846.5 | 1.11699 | 0.558494 | − | 0.829508i | \(-0.311379\pi\) | ||||
0.558494 | + | 0.829508i | \(0.311379\pi\) | |||||||
\(992\) | 8030.88 | 0.257037 | ||||||||
\(993\) | 13704.0 | 0.437948 | ||||||||
\(994\) | 29350.8 | 0.936571 | ||||||||
\(995\) | −83935.2 | −2.67429 | ||||||||
\(996\) | −235.193 | −0.00748232 | ||||||||
\(997\) | 49622.2 | 1.57628 | 0.788140 | − | 0.615497i | \(-0.211044\pi\) | ||||
0.788140 | + | 0.615497i | \(0.211044\pi\) | |||||||
\(998\) | 5861.19 | 0.185904 | ||||||||
\(999\) | 3415.08 | 0.108157 |
(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 | 2166.4.a.ba.1.1 | yes | 4 | |
19.18 | odd | 2 | 2166.4.a.x.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.4.a.x.1.1 | ✓ | 4 | 19.18 | odd | 2 | ||
2166.4.a.ba.1.1 | yes | 4 | 1.1 | even | 1 | trivial |