Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56619 | 0.553733 | 0.276867 | − | 0.960908i | \(-0.410704\pi\) | ||||
0.276867 | + | 0.960908i | \(0.410704\pi\) | |||||||
\(3\) | 5.42418 | 1.04388 | 0.521942 | − | 0.852981i | \(-0.325208\pi\) | ||||
0.521942 | + | 0.852981i | \(0.325208\pi\) | |||||||
\(4\) | −5.54704 | −0.693380 | ||||||||
\(5\) | −8.12470 | −0.726695 | −0.363348 | − | 0.931654i | \(-0.618366\pi\) | ||||
−0.363348 | + | 0.931654i | \(0.618366\pi\) | |||||||
\(6\) | 8.49531 | 0.578033 | ||||||||
\(7\) | 30.7370 | 1.65964 | 0.829820 | − | 0.558031i | \(-0.188443\pi\) | ||||
0.829820 | + | 0.558031i | \(0.188443\pi\) | |||||||
\(8\) | −21.2173 | −0.937680 | ||||||||
\(9\) | 2.42171 | 0.0896928 | ||||||||
\(10\) | −12.7249 | −0.402395 | ||||||||
\(11\) | 9.06614 | 0.248504 | 0.124252 | − | 0.992251i | \(-0.460347\pi\) | ||||
0.124252 | + | 0.992251i | \(0.460347\pi\) | |||||||
\(12\) | −30.0881 | −0.723808 | ||||||||
\(13\) | −16.1006 | −0.343499 | −0.171750 | − | 0.985141i | \(-0.554942\pi\) | ||||
−0.171750 | + | 0.985141i | \(0.554942\pi\) | |||||||
\(14\) | 48.1400 | 0.918998 | ||||||||
\(15\) | −44.0698 | −0.758585 | ||||||||
\(16\) | 11.1459 | 0.174155 | ||||||||
\(17\) | −13.4280 | −0.191574 | −0.0957872 | − | 0.995402i | \(-0.530537\pi\) | ||||
−0.0957872 | + | 0.995402i | \(0.530537\pi\) | |||||||
\(18\) | 3.79286 | 0.0496659 | ||||||||
\(19\) | 76.7126 | 0.926267 | 0.463134 | − | 0.886288i | \(-0.346725\pi\) | ||||
0.463134 | + | 0.886288i | \(0.346725\pi\) | |||||||
\(20\) | 45.0680 | 0.503876 | ||||||||
\(21\) | 166.723 | 1.73247 | ||||||||
\(22\) | 14.1993 | 0.137605 | ||||||||
\(23\) | −38.4314 | −0.348413 | −0.174207 | − | 0.984709i | \(-0.555736\pi\) | ||||
−0.174207 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(24\) | −115.086 | −0.978829 | ||||||||
\(25\) | −58.9893 | −0.471914 | ||||||||
\(26\) | −25.2166 | −0.190207 | ||||||||
\(27\) | −133.317 | −0.950255 | ||||||||
\(28\) | −170.499 | −1.15076 | ||||||||
\(29\) | −251.400 | −1.60979 | −0.804893 | − | 0.593420i | \(-0.797777\pi\) | ||||
−0.804893 | + | 0.593420i | \(0.797777\pi\) | |||||||
\(30\) | −69.0219 | −0.420054 | ||||||||
\(31\) | −120.743 | −0.699549 | −0.349775 | − | 0.936834i | \(-0.613742\pi\) | ||||
−0.349775 | + | 0.936834i | \(0.613742\pi\) | |||||||
\(32\) | 187.195 | 1.03412 | ||||||||
\(33\) | 49.1764 | 0.259409 | ||||||||
\(34\) | −21.0308 | −0.106081 | ||||||||
\(35\) | −249.729 | −1.20605 | ||||||||
\(36\) | −13.4333 | −0.0621911 | ||||||||
\(37\) | 391.816 | 1.74092 | 0.870462 | − | 0.492235i | \(-0.163820\pi\) | ||||
0.870462 | + | 0.492235i | \(0.163820\pi\) | |||||||
\(38\) | 120.147 | 0.512905 | ||||||||
\(39\) | −87.3323 | −0.358573 | ||||||||
\(40\) | 172.384 | 0.681408 | ||||||||
\(41\) | −338.720 | −1.29022 | −0.645112 | − | 0.764088i | \(-0.723189\pi\) | ||||
−0.645112 | + | 0.764088i | \(0.723189\pi\) | |||||||
\(42\) | 261.120 | 0.959327 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −50.2902 | −0.172308 | ||||||||
\(45\) | −19.6756 | −0.0651793 | ||||||||
\(46\) | −60.1911 | −0.192928 | ||||||||
\(47\) | 120.370 | 0.373568 | 0.186784 | − | 0.982401i | \(-0.440194\pi\) | ||||
0.186784 | + | 0.982401i | \(0.440194\pi\) | |||||||
\(48\) | 60.4574 | 0.181797 | ||||||||
\(49\) | 601.761 | 1.75440 | ||||||||
\(50\) | −92.3886 | −0.261315 | ||||||||
\(51\) | −72.8358 | −0.199981 | ||||||||
\(52\) | 89.3103 | 0.238175 | ||||||||
\(53\) | −480.889 | −1.24633 | −0.623163 | − | 0.782092i | \(-0.714153\pi\) | ||||
−0.623163 | + | 0.782092i | \(0.714153\pi\) | |||||||
\(54\) | −208.800 | −0.526188 | ||||||||
\(55\) | −73.6597 | −0.180587 | ||||||||
\(56\) | −652.155 | −1.55621 | ||||||||
\(57\) | 416.103 | 0.966915 | ||||||||
\(58\) | −393.741 | −0.891392 | ||||||||
\(59\) | 357.983 | 0.789923 | 0.394961 | − | 0.918698i | \(-0.370758\pi\) | ||||
0.394961 | + | 0.918698i | \(0.370758\pi\) | |||||||
\(60\) | 244.457 | 0.525987 | ||||||||
\(61\) | 592.360 | 1.24334 | 0.621672 | − | 0.783278i | \(-0.286454\pi\) | ||||
0.621672 | + | 0.783278i | \(0.286454\pi\) | |||||||
\(62\) | −189.106 | −0.387364 | ||||||||
\(63\) | 74.4359 | 0.148858 | ||||||||
\(64\) | 204.016 | 0.398469 | ||||||||
\(65\) | 130.812 | 0.249619 | ||||||||
\(66\) | 77.0197 | 0.143644 | ||||||||
\(67\) | −672.610 | −1.22645 | −0.613227 | − | 0.789907i | \(-0.710129\pi\) | ||||
−0.613227 | + | 0.789907i | \(0.710129\pi\) | |||||||
\(68\) | 74.4856 | 0.132834 | ||||||||
\(69\) | −208.459 | −0.363703 | ||||||||
\(70\) | −391.123 | −0.667831 | ||||||||
\(71\) | −417.963 | −0.698635 | −0.349318 | − | 0.937004i | \(-0.613587\pi\) | ||||
−0.349318 | + | 0.937004i | \(0.613587\pi\) | |||||||
\(72\) | −51.3820 | −0.0841032 | ||||||||
\(73\) | 922.640 | 1.47927 | 0.739636 | − | 0.673007i | \(-0.234998\pi\) | ||||
0.739636 | + | 0.673007i | \(0.234998\pi\) | |||||||
\(74\) | 613.660 | 0.964008 | ||||||||
\(75\) | −319.968 | −0.492623 | ||||||||
\(76\) | −425.528 | −0.642255 | ||||||||
\(77\) | 278.666 | 0.412427 | ||||||||
\(78\) | −136.779 | −0.198554 | ||||||||
\(79\) | −107.902 | −0.153670 | −0.0768350 | − | 0.997044i | \(-0.524481\pi\) | ||||
−0.0768350 | + | 0.997044i | \(0.524481\pi\) | |||||||
\(80\) | −90.5571 | −0.126557 | ||||||||
\(81\) | −788.521 | −1.08165 | ||||||||
\(82\) | −530.501 | −0.714440 | ||||||||
\(83\) | −1003.60 | −1.32722 | −0.663609 | − | 0.748080i | \(-0.730976\pi\) | ||||
−0.663609 | + | 0.748080i | \(0.730976\pi\) | |||||||
\(84\) | −924.817 | −1.20126 | ||||||||
\(85\) | 109.098 | 0.139216 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1363.64 | −1.68043 | ||||||||
\(88\) | −192.359 | −0.233017 | ||||||||
\(89\) | 188.544 | 0.224558 | 0.112279 | − | 0.993677i | \(-0.464185\pi\) | ||||
0.112279 | + | 0.993677i | \(0.464185\pi\) | |||||||
\(90\) | −30.8158 | −0.0360919 | ||||||||
\(91\) | −494.882 | −0.570085 | ||||||||
\(92\) | 213.181 | 0.241583 | ||||||||
\(93\) | −654.930 | −0.730248 | ||||||||
\(94\) | 188.522 | 0.206857 | ||||||||
\(95\) | −623.267 | −0.673114 | ||||||||
\(96\) | 1015.38 | 1.07950 | ||||||||
\(97\) | 481.540 | 0.504051 | 0.252026 | − | 0.967721i | \(-0.418903\pi\) | ||||
0.252026 | + | 0.967721i | \(0.418903\pi\) | |||||||
\(98\) | 942.474 | 0.971472 | ||||||||
\(99\) | 21.9555 | 0.0222890 | ||||||||
\(100\) | 327.216 | 0.327216 | ||||||||
\(101\) | −1370.30 | −1.35000 | −0.674999 | − | 0.737818i | \(-0.735856\pi\) | ||||
−0.674999 | + | 0.737818i | \(0.735856\pi\) | |||||||
\(102\) | −114.075 | −0.110736 | ||||||||
\(103\) | −823.195 | −0.787494 | −0.393747 | − | 0.919219i | \(-0.628821\pi\) | ||||
−0.393747 | + | 0.919219i | \(0.628821\pi\) | |||||||
\(104\) | 341.610 | 0.322092 | ||||||||
\(105\) | −1354.57 | −1.25898 | ||||||||
\(106\) | −753.166 | −0.690132 | ||||||||
\(107\) | −1936.29 | −1.74943 | −0.874713 | − | 0.484640i | \(-0.838950\pi\) | ||||
−0.874713 | + | 0.484640i | \(0.838950\pi\) | |||||||
\(108\) | 739.515 | 0.658887 | ||||||||
\(109\) | −1765.66 | −1.55155 | −0.775777 | − | 0.631007i | \(-0.782642\pi\) | ||||
−0.775777 | + | 0.631007i | \(0.782642\pi\) | |||||||
\(110\) | −115.365 | −0.0999969 | ||||||||
\(111\) | 2125.28 | 1.81732 | ||||||||
\(112\) | 342.591 | 0.289034 | ||||||||
\(113\) | −1935.29 | −1.61112 | −0.805559 | − | 0.592515i | \(-0.798135\pi\) | ||||
−0.805559 | + | 0.592515i | \(0.798135\pi\) | |||||||
\(114\) | 651.698 | 0.535413 | ||||||||
\(115\) | 312.244 | 0.253190 | ||||||||
\(116\) | 1394.52 | 1.11619 | ||||||||
\(117\) | −38.9908 | −0.0308094 | ||||||||
\(118\) | 560.671 | 0.437406 | ||||||||
\(119\) | −412.736 | −0.317945 | ||||||||
\(120\) | 935.042 | 0.711310 | ||||||||
\(121\) | −1248.81 | −0.938246 | ||||||||
\(122\) | 927.751 | 0.688481 | ||||||||
\(123\) | −1837.28 | −1.34684 | ||||||||
\(124\) | 669.764 | 0.485053 | ||||||||
\(125\) | 1494.86 | 1.06963 | ||||||||
\(126\) | 116.581 | 0.0824275 | ||||||||
\(127\) | 216.846 | 0.151511 | 0.0757556 | − | 0.997126i | \(-0.475863\pi\) | ||||
0.0757556 | + | 0.997126i | \(0.475863\pi\) | |||||||
\(128\) | −1178.03 | −0.813470 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 204.877 | 0.138222 | ||||||||
\(131\) | 629.545 | 0.419875 | 0.209937 | − | 0.977715i | \(-0.432674\pi\) | ||||
0.209937 | + | 0.977715i | \(0.432674\pi\) | |||||||
\(132\) | −272.783 | −0.179869 | ||||||||
\(133\) | 2357.91 | 1.53727 | ||||||||
\(134\) | −1053.44 | −0.679128 | ||||||||
\(135\) | 1083.16 | 0.690545 | ||||||||
\(136\) | 284.906 | 0.179636 | ||||||||
\(137\) | 1799.38 | 1.12212 | 0.561062 | − | 0.827774i | \(-0.310393\pi\) | ||||
0.561062 | + | 0.827774i | \(0.310393\pi\) | |||||||
\(138\) | −326.487 | −0.201394 | ||||||||
\(139\) | 1364.33 | 0.832524 | 0.416262 | − | 0.909245i | \(-0.363340\pi\) | ||||
0.416262 | + | 0.909245i | \(0.363340\pi\) | |||||||
\(140\) | 1385.25 | 0.836252 | ||||||||
\(141\) | 652.906 | 0.389962 | ||||||||
\(142\) | −654.611 | −0.386857 | ||||||||
\(143\) | −145.970 | −0.0853610 | ||||||||
\(144\) | 26.9921 | 0.0156204 | ||||||||
\(145\) | 2042.55 | 1.16982 | ||||||||
\(146\) | 1445.03 | 0.819122 | ||||||||
\(147\) | 3264.06 | 1.83139 | ||||||||
\(148\) | −2173.42 | −1.20712 | ||||||||
\(149\) | 61.1081 | 0.0335984 | 0.0167992 | − | 0.999859i | \(-0.494652\pi\) | ||||
0.0167992 | + | 0.999859i | \(0.494652\pi\) | |||||||
\(150\) | −501.132 | −0.272782 | ||||||||
\(151\) | −1992.02 | −1.07357 | −0.536784 | − | 0.843720i | \(-0.680361\pi\) | ||||
−0.536784 | + | 0.843720i | \(0.680361\pi\) | |||||||
\(152\) | −1627.63 | −0.868543 | ||||||||
\(153\) | −32.5186 | −0.0171828 | ||||||||
\(154\) | 436.445 | 0.228375 | ||||||||
\(155\) | 980.998 | 0.508359 | ||||||||
\(156\) | 484.435 | 0.248627 | ||||||||
\(157\) | −517.016 | −0.262818 | −0.131409 | − | 0.991328i | \(-0.541950\pi\) | ||||
−0.131409 | + | 0.991328i | \(0.541950\pi\) | |||||||
\(158\) | −168.996 | −0.0850922 | ||||||||
\(159\) | −2608.43 | −1.30102 | ||||||||
\(160\) | −1520.90 | −0.751487 | ||||||||
\(161\) | −1181.27 | −0.578241 | ||||||||
\(162\) | −1234.98 | −0.598944 | ||||||||
\(163\) | −1550.46 | −0.745041 | −0.372521 | − | 0.928024i | \(-0.621506\pi\) | ||||
−0.372521 | + | 0.928024i | \(0.621506\pi\) | |||||||
\(164\) | 1878.89 | 0.894615 | ||||||||
\(165\) | −399.543 | −0.188512 | ||||||||
\(166\) | −1571.83 | −0.734924 | ||||||||
\(167\) | −2645.09 | −1.22565 | −0.612825 | − | 0.790219i | \(-0.709967\pi\) | ||||
−0.612825 | + | 0.790219i | \(0.709967\pi\) | |||||||
\(168\) | −3537.40 | −1.62450 | ||||||||
\(169\) | −1937.77 | −0.882008 | ||||||||
\(170\) | 170.869 | 0.0770887 | ||||||||
\(171\) | 185.775 | 0.0830795 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2035.37 | −0.894488 | −0.447244 | − | 0.894412i | \(-0.647594\pi\) | ||||
−0.447244 | + | 0.894412i | \(0.647594\pi\) | |||||||
\(174\) | −2135.72 | −0.930509 | ||||||||
\(175\) | −1813.15 | −0.783208 | ||||||||
\(176\) | 101.050 | 0.0432782 | ||||||||
\(177\) | 1941.76 | 0.824587 | ||||||||
\(178\) | 295.297 | 0.124345 | ||||||||
\(179\) | 3581.88 | 1.49566 | 0.747828 | − | 0.663893i | \(-0.231097\pi\) | ||||
0.747828 | + | 0.663893i | \(0.231097\pi\) | |||||||
\(180\) | 109.141 | 0.0451940 | ||||||||
\(181\) | 142.547 | 0.0585384 | 0.0292692 | − | 0.999572i | \(-0.490682\pi\) | ||||
0.0292692 | + | 0.999572i | \(0.490682\pi\) | |||||||
\(182\) | −775.081 | −0.315675 | ||||||||
\(183\) | 3213.07 | 1.29791 | ||||||||
\(184\) | 815.411 | 0.326700 | ||||||||
\(185\) | −3183.39 | −1.26512 | ||||||||
\(186\) | −1025.75 | −0.404362 | ||||||||
\(187\) | −121.740 | −0.0476070 | ||||||||
\(188\) | −667.694 | −0.259025 | ||||||||
\(189\) | −4097.76 | −1.57708 | ||||||||
\(190\) | −976.157 | −0.372726 | ||||||||
\(191\) | −613.948 | −0.232585 | −0.116292 | − | 0.993215i | \(-0.537101\pi\) | ||||
−0.116292 | + | 0.993215i | \(0.537101\pi\) | |||||||
\(192\) | 1106.62 | 0.415956 | ||||||||
\(193\) | −251.603 | −0.0938381 | −0.0469190 | − | 0.998899i | \(-0.514940\pi\) | ||||
−0.0469190 | + | 0.998899i | \(0.514940\pi\) | |||||||
\(194\) | 754.185 | 0.279110 | ||||||||
\(195\) | 709.548 | 0.260573 | ||||||||
\(196\) | −3337.99 | −1.21647 | ||||||||
\(197\) | −2046.10 | −0.739992 | −0.369996 | − | 0.929033i | \(-0.620641\pi\) | ||||
−0.369996 | + | 0.929033i | \(0.620641\pi\) | |||||||
\(198\) | 34.3866 | 0.0123422 | ||||||||
\(199\) | −602.944 | −0.214782 | −0.107391 | − | 0.994217i | \(-0.534250\pi\) | ||||
−0.107391 | + | 0.994217i | \(0.534250\pi\) | |||||||
\(200\) | 1251.59 | 0.442505 | ||||||||
\(201\) | −3648.36 | −1.28027 | ||||||||
\(202\) | −2146.15 | −0.747539 | ||||||||
\(203\) | −7727.27 | −2.67167 | ||||||||
\(204\) | 404.023 | 0.138663 | ||||||||
\(205\) | 2752.00 | 0.937599 | ||||||||
\(206\) | −1289.28 | −0.436061 | ||||||||
\(207\) | −93.0696 | −0.0312502 | ||||||||
\(208\) | −179.455 | −0.0598220 | ||||||||
\(209\) | 695.488 | 0.230181 | ||||||||
\(210\) | −2121.52 | −0.697138 | ||||||||
\(211\) | −4349.61 | −1.41914 | −0.709572 | − | 0.704633i | \(-0.751112\pi\) | ||||
−0.709572 | + | 0.704633i | \(0.751112\pi\) | |||||||
\(212\) | 2667.51 | 0.864176 | ||||||||
\(213\) | −2267.11 | −0.729294 | ||||||||
\(214\) | −3032.61 | −0.968716 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2828.63 | 0.891035 | ||||||||
\(217\) | −3711.26 | −1.16100 | ||||||||
\(218\) | −2765.36 | −0.859147 | ||||||||
\(219\) | 5004.56 | 1.54419 | ||||||||
\(220\) | 408.593 | 0.125215 | ||||||||
\(221\) | 216.198 | 0.0658057 | ||||||||
\(222\) | 3328.60 | 1.00631 | ||||||||
\(223\) | 2364.75 | 0.710113 | 0.355057 | − | 0.934845i | \(-0.384462\pi\) | ||||
0.355057 | + | 0.934845i | \(0.384462\pi\) | |||||||
\(224\) | 5753.80 | 1.71626 | ||||||||
\(225\) | −142.855 | −0.0423273 | ||||||||
\(226\) | −3031.03 | −0.892130 | ||||||||
\(227\) | −6612.47 | −1.93341 | −0.966707 | − | 0.255886i | \(-0.917633\pi\) | ||||
−0.966707 | + | 0.255886i | \(0.917633\pi\) | |||||||
\(228\) | −2308.14 | −0.670439 | ||||||||
\(229\) | 2165.70 | 0.624950 | 0.312475 | − | 0.949926i | \(-0.398842\pi\) | ||||
0.312475 | + | 0.949926i | \(0.398842\pi\) | |||||||
\(230\) | 489.034 | 0.140200 | ||||||||
\(231\) | 1511.53 | 0.430526 | ||||||||
\(232\) | 5334.02 | 1.50946 | ||||||||
\(233\) | 2568.88 | 0.722286 | 0.361143 | − | 0.932510i | \(-0.382387\pi\) | ||||
0.361143 | + | 0.932510i | \(0.382387\pi\) | |||||||
\(234\) | −61.0671 | −0.0170602 | ||||||||
\(235\) | −977.966 | −0.271470 | ||||||||
\(236\) | −1985.75 | −0.547716 | ||||||||
\(237\) | −585.280 | −0.160414 | ||||||||
\(238\) | −646.424 | −0.176057 | ||||||||
\(239\) | 952.472 | 0.257784 | 0.128892 | − | 0.991659i | \(-0.458858\pi\) | ||||
0.128892 | + | 0.991659i | \(0.458858\pi\) | |||||||
\(240\) | −491.198 | −0.132111 | ||||||||
\(241\) | −2756.95 | −0.736892 | −0.368446 | − | 0.929649i | \(-0.620110\pi\) | ||||
−0.368446 | + | 0.929649i | \(0.620110\pi\) | |||||||
\(242\) | −1955.87 | −0.519538 | ||||||||
\(243\) | −677.520 | −0.178860 | ||||||||
\(244\) | −3285.85 | −0.862109 | ||||||||
\(245\) | −4889.13 | −1.27492 | ||||||||
\(246\) | −2877.53 | −0.745792 | ||||||||
\(247\) | −1235.12 | −0.318172 | ||||||||
\(248\) | 2561.83 | 0.655954 | ||||||||
\(249\) | −5443.69 | −1.38546 | ||||||||
\(250\) | 2341.24 | 0.592291 | ||||||||
\(251\) | −725.383 | −0.182413 | −0.0912067 | − | 0.995832i | \(-0.529072\pi\) | ||||
−0.0912067 | + | 0.995832i | \(0.529072\pi\) | |||||||
\(252\) | −412.898 | −0.103215 | ||||||||
\(253\) | −348.425 | −0.0865822 | ||||||||
\(254\) | 339.622 | 0.0838968 | ||||||||
\(255\) | 591.769 | 0.145326 | ||||||||
\(256\) | −3477.15 | −0.848915 | ||||||||
\(257\) | 3866.44 | 0.938452 | 0.469226 | − | 0.883078i | \(-0.344533\pi\) | ||||
0.469226 | + | 0.883078i | \(0.344533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12043.2 | 2.88931 | ||||||||
\(260\) | −725.620 | −0.173081 | ||||||||
\(261\) | −608.816 | −0.144386 | ||||||||
\(262\) | 985.989 | 0.232499 | ||||||||
\(263\) | −1275.72 | −0.299103 | −0.149552 | − | 0.988754i | \(-0.547783\pi\) | ||||
−0.149552 | + | 0.988754i | \(0.547783\pi\) | |||||||
\(264\) | −1043.39 | −0.243243 | ||||||||
\(265\) | 3907.08 | 0.905699 | ||||||||
\(266\) | 3692.95 | 0.851238 | ||||||||
\(267\) | 1022.70 | 0.234412 | ||||||||
\(268\) | 3730.99 | 0.850398 | ||||||||
\(269\) | −702.374 | −0.159199 | −0.0795994 | − | 0.996827i | \(-0.525364\pi\) | ||||
−0.0795994 | + | 0.996827i | \(0.525364\pi\) | |||||||
\(270\) | 1696.44 | 0.382378 | ||||||||
\(271\) | 6411.84 | 1.43724 | 0.718619 | − | 0.695404i | \(-0.244775\pi\) | ||||
0.718619 | + | 0.695404i | \(0.244775\pi\) | |||||||
\(272\) | −149.667 | −0.0333636 | ||||||||
\(273\) | −2684.33 | −0.595102 | ||||||||
\(274\) | 2818.17 | 0.621358 | ||||||||
\(275\) | −534.805 | −0.117273 | ||||||||
\(276\) | 1156.33 | 0.252184 | ||||||||
\(277\) | −2089.16 | −0.453161 | −0.226580 | − | 0.973992i | \(-0.572755\pi\) | ||||
−0.226580 | + | 0.973992i | \(0.572755\pi\) | |||||||
\(278\) | 2136.80 | 0.460996 | ||||||||
\(279\) | −292.403 | −0.0627445 | ||||||||
\(280\) | 5298.56 | 1.13089 | ||||||||
\(281\) | −3390.64 | −0.719817 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(282\) | 1022.58 | 0.215935 | ||||||||
\(283\) | 6836.92 | 1.43609 | 0.718044 | − | 0.695998i | \(-0.245038\pi\) | ||||
0.718044 | + | 0.695998i | \(0.245038\pi\) | |||||||
\(284\) | 2318.46 | 0.484419 | ||||||||
\(285\) | −3380.71 | −0.702653 | ||||||||
\(286\) | −228.617 | −0.0472672 | ||||||||
\(287\) | −10411.2 | −2.14131 | ||||||||
\(288\) | 453.331 | 0.0927527 | ||||||||
\(289\) | −4732.69 | −0.963299 | ||||||||
\(290\) | 3199.03 | 0.647770 | ||||||||
\(291\) | 2611.96 | 0.526171 | ||||||||
\(292\) | −5117.92 | −1.02570 | ||||||||
\(293\) | 6814.59 | 1.35875 | 0.679373 | − | 0.733793i | \(-0.262252\pi\) | ||||
0.679373 | + | 0.733793i | \(0.262252\pi\) | |||||||
\(294\) | 5112.15 | 1.01410 | ||||||||
\(295\) | −2908.51 | −0.574033 | ||||||||
\(296\) | −8313.28 | −1.63243 | ||||||||
\(297\) | −1208.67 | −0.236142 | ||||||||
\(298\) | 95.7071 | 0.0186046 | ||||||||
\(299\) | 618.767 | 0.119680 | ||||||||
\(300\) | 1774.88 | 0.341575 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3119.90 | −0.594470 | ||||||||
\(303\) | −7432.75 | −1.40924 | ||||||||
\(304\) | 855.032 | 0.161314 | ||||||||
\(305\) | −4812.75 | −0.903532 | ||||||||
\(306\) | −50.9305 | −0.00951471 | ||||||||
\(307\) | 1604.28 | 0.298244 | 0.149122 | − | 0.988819i | \(-0.452355\pi\) | ||||
0.149122 | + | 0.988819i | \(0.452355\pi\) | |||||||
\(308\) | −1545.77 | −0.285969 | ||||||||
\(309\) | −4465.16 | −0.822052 | ||||||||
\(310\) | 1536.43 | 0.281495 | ||||||||
\(311\) | −2318.26 | −0.422690 | −0.211345 | − | 0.977412i | \(-0.567784\pi\) | ||||
−0.211345 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(312\) | 1852.95 | 0.336227 | ||||||||
\(313\) | 4380.98 | 0.791142 | 0.395571 | − | 0.918435i | \(-0.370547\pi\) | ||||
0.395571 | + | 0.918435i | \(0.370547\pi\) | |||||||
\(314\) | −809.748 | −0.145531 | ||||||||
\(315\) | −604.769 | −0.108174 | ||||||||
\(316\) | 598.537 | 0.106552 | ||||||||
\(317\) | 9306.43 | 1.64890 | 0.824450 | − | 0.565934i | \(-0.191484\pi\) | ||||
0.824450 | + | 0.565934i | \(0.191484\pi\) | |||||||
\(318\) | −4085.31 | −0.720417 | ||||||||
\(319\) | −2279.23 | −0.400038 | ||||||||
\(320\) | −1657.57 | −0.289566 | ||||||||
\(321\) | −10502.8 | −1.82620 | ||||||||
\(322\) | −1850.09 | −0.320191 | ||||||||
\(323\) | −1030.10 | −0.177449 | ||||||||
\(324\) | 4373.96 | 0.749993 | ||||||||
\(325\) | 949.760 | 0.162102 | ||||||||
\(326\) | −2428.33 | −0.412554 | ||||||||
\(327\) | −9577.24 | −1.61964 | ||||||||
\(328\) | 7186.72 | 1.20982 | ||||||||
\(329\) | 3699.79 | 0.619989 | ||||||||
\(330\) | −625.762 | −0.104385 | ||||||||
\(331\) | 5183.44 | 0.860749 | 0.430374 | − | 0.902651i | \(-0.358382\pi\) | ||||
0.430374 | + | 0.902651i | \(0.358382\pi\) | |||||||
\(332\) | 5566.99 | 0.920266 | ||||||||
\(333\) | 948.864 | 0.156148 | ||||||||
\(334\) | −4142.73 | −0.678683 | ||||||||
\(335\) | 5464.75 | 0.891258 | ||||||||
\(336\) | 1858.28 | 0.301718 | ||||||||
\(337\) | 3000.12 | 0.484947 | 0.242474 | − | 0.970158i | \(-0.422041\pi\) | ||||
0.242474 | + | 0.970158i | \(0.422041\pi\) | |||||||
\(338\) | −3034.93 | −0.488397 | ||||||||
\(339\) | −10497.3 | −1.68182 | ||||||||
\(340\) | −605.173 | −0.0965297 | ||||||||
\(341\) | −1094.67 | −0.173841 | ||||||||
\(342\) | 290.960 | 0.0460039 | ||||||||
\(343\) | 7953.52 | 1.25204 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1693.67 | 0.264301 | ||||||||
\(346\) | −3187.78 | −0.495307 | ||||||||
\(347\) | −9148.76 | −1.41536 | −0.707682 | − | 0.706531i | \(-0.750259\pi\) | ||||
−0.707682 | + | 0.706531i | \(0.750259\pi\) | |||||||
\(348\) | 7564.15 | 1.16518 | ||||||||
\(349\) | −2096.34 | −0.321531 | −0.160766 | − | 0.986993i | \(-0.551396\pi\) | ||||
−0.160766 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(350\) | −2839.75 | −0.433688 | ||||||||
\(351\) | 2146.48 | 0.326412 | ||||||||
\(352\) | 1697.14 | 0.256982 | ||||||||
\(353\) | 319.106 | 0.0481142 | 0.0240571 | − | 0.999711i | \(-0.492342\pi\) | ||||
0.0240571 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(354\) | 3041.18 | 0.456601 | ||||||||
\(355\) | 3395.82 | 0.507695 | ||||||||
\(356\) | −1045.86 | −0.155704 | ||||||||
\(357\) | −2238.75 | −0.331897 | ||||||||
\(358\) | 5609.92 | 0.828194 | ||||||||
\(359\) | 9112.72 | 1.33970 | 0.669848 | − | 0.742498i | \(-0.266359\pi\) | ||||
0.669848 | + | 0.742498i | \(0.266359\pi\) | |||||||
\(360\) | 417.463 | 0.0611174 | ||||||||
\(361\) | −974.175 | −0.142029 | ||||||||
\(362\) | 223.257 | 0.0324147 | ||||||||
\(363\) | −6773.74 | −0.979419 | ||||||||
\(364\) | 2745.13 | 0.395285 | ||||||||
\(365\) | −7496.17 | −1.07498 | ||||||||
\(366\) | 5032.29 | 0.718694 | ||||||||
\(367\) | −2726.93 | −0.387860 | −0.193930 | − | 0.981015i | \(-0.562123\pi\) | ||||
−0.193930 | + | 0.981015i | \(0.562123\pi\) | |||||||
\(368\) | −428.353 | −0.0606779 | ||||||||
\(369\) | −820.280 | −0.115724 | ||||||||
\(370\) | −4985.81 | −0.700540 | ||||||||
\(371\) | −14781.1 | −2.06845 | ||||||||
\(372\) | 3632.92 | 0.506339 | ||||||||
\(373\) | 13249.6 | 1.83924 | 0.919622 | − | 0.392804i | \(-0.128495\pi\) | ||||
0.919622 | + | 0.392804i | \(0.128495\pi\) | |||||||
\(374\) | −190.669 | −0.0263616 | ||||||||
\(375\) | 8108.37 | 1.11657 | ||||||||
\(376\) | −2553.92 | −0.350288 | ||||||||
\(377\) | 4047.68 | 0.552960 | ||||||||
\(378\) | −6417.89 | −0.873282 | ||||||||
\(379\) | 8778.93 | 1.18982 | 0.594912 | − | 0.803791i | \(-0.297187\pi\) | ||||
0.594912 | + | 0.803791i | \(0.297187\pi\) | |||||||
\(380\) | 3457.28 | 0.466724 | ||||||||
\(381\) | 1176.21 | 0.158160 | ||||||||
\(382\) | −961.562 | −0.128790 | ||||||||
\(383\) | 11141.2 | 1.48639 | 0.743194 | − | 0.669076i | \(-0.233310\pi\) | ||||
0.743194 | + | 0.669076i | \(0.233310\pi\) | |||||||
\(384\) | −6389.85 | −0.849168 | ||||||||
\(385\) | −2264.07 | −0.299709 | ||||||||
\(386\) | −394.058 | −0.0519613 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2671.12 | −0.349499 | ||||||||
\(389\) | −11673.9 | −1.52157 | −0.760786 | − | 0.649003i | \(-0.775186\pi\) | ||||
−0.760786 | + | 0.649003i | \(0.775186\pi\) | |||||||
\(390\) | 1111.29 | 0.144288 | ||||||||
\(391\) | 516.057 | 0.0667471 | ||||||||
\(392\) | −12767.7 | −1.64507 | ||||||||
\(393\) | 3414.76 | 0.438300 | ||||||||
\(394\) | −3204.58 | −0.409758 | ||||||||
\(395\) | 876.672 | 0.111671 | ||||||||
\(396\) | −121.788 | −0.0154548 | ||||||||
\(397\) | 9942.51 | 1.25693 | 0.628464 | − | 0.777839i | \(-0.283684\pi\) | ||||
0.628464 | + | 0.777839i | \(0.283684\pi\) | |||||||
\(398\) | −944.327 | −0.118932 | ||||||||
\(399\) | 12789.7 | 1.60473 | ||||||||
\(400\) | −657.489 | −0.0821861 | ||||||||
\(401\) | 4884.85 | 0.608323 | 0.304162 | − | 0.952620i | \(-0.401624\pi\) | ||||
0.304162 | + | 0.952620i | \(0.401624\pi\) | |||||||
\(402\) | −5714.03 | −0.708930 | ||||||||
\(403\) | 1944.02 | 0.240295 | ||||||||
\(404\) | 7601.10 | 0.936061 | ||||||||
\(405\) | 6406.50 | 0.786028 | ||||||||
\(406\) | −12102.4 | −1.47939 | ||||||||
\(407\) | 3552.26 | 0.432627 | ||||||||
\(408\) | 1545.38 | 0.187519 | ||||||||
\(409\) | −10707.9 | −1.29455 | −0.647276 | − | 0.762256i | \(-0.724092\pi\) | ||||
−0.647276 | + | 0.762256i | \(0.724092\pi\) | |||||||
\(410\) | 4310.16 | 0.519180 | ||||||||
\(411\) | 9760.14 | 1.17137 | ||||||||
\(412\) | 4566.29 | 0.546032 | ||||||||
\(413\) | 11003.3 | 1.31099 | ||||||||
\(414\) | −145.765 | −0.0173043 | ||||||||
\(415\) | 8153.92 | 0.964483 | ||||||||
\(416\) | −3013.94 | −0.355218 | ||||||||
\(417\) | 7400.36 | 0.869058 | ||||||||
\(418\) | 1089.27 | 0.127459 | ||||||||
\(419\) | 5076.87 | 0.591936 | 0.295968 | − | 0.955198i | \(-0.404358\pi\) | ||||
0.295968 | + | 0.955198i | \(0.404358\pi\) | |||||||
\(420\) | 7513.86 | 0.872950 | ||||||||
\(421\) | 3748.60 | 0.433956 | 0.216978 | − | 0.976176i | \(-0.430380\pi\) | ||||
0.216978 | + | 0.976176i | \(0.430380\pi\) | |||||||
\(422\) | −6812.33 | −0.785827 | ||||||||
\(423\) | 291.500 | 0.0335064 | ||||||||
\(424\) | 10203.2 | 1.16865 | ||||||||
\(425\) | 792.107 | 0.0904067 | ||||||||
\(426\) | −3550.73 | −0.403834 | ||||||||
\(427\) | 18207.4 | 2.06350 | ||||||||
\(428\) | 10740.7 | 1.21302 | ||||||||
\(429\) | −791.767 | −0.0891069 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −472.408 | −0.0527960 | −0.0263980 | − | 0.999652i | \(-0.508404\pi\) | ||||
−0.0263980 | + | 0.999652i | \(0.508404\pi\) | |||||||
\(432\) | −1485.94 | −0.165491 | ||||||||
\(433\) | −500.116 | −0.0555058 | −0.0277529 | − | 0.999615i | \(-0.508835\pi\) | ||||
−0.0277529 | + | 0.999615i | \(0.508835\pi\) | |||||||
\(434\) | −5812.56 | −0.642884 | ||||||||
\(435\) | 11079.1 | 1.22116 | ||||||||
\(436\) | 9794.17 | 1.07582 | ||||||||
\(437\) | −2948.18 | −0.322724 | ||||||||
\(438\) | 7838.12 | 0.855068 | ||||||||
\(439\) | −15113.3 | −1.64309 | −0.821544 | − | 0.570144i | \(-0.806887\pi\) | ||||
−0.821544 | + | 0.570144i | \(0.806887\pi\) | |||||||
\(440\) | 1562.86 | 0.169333 | ||||||||
\(441\) | 1457.29 | 0.157357 | ||||||||
\(442\) | 338.608 | 0.0364388 | ||||||||
\(443\) | −8694.15 | −0.932441 | −0.466221 | − | 0.884668i | \(-0.654385\pi\) | ||||
−0.466221 | + | 0.884668i | \(0.654385\pi\) | |||||||
\(444\) | −11789.0 | −1.26009 | ||||||||
\(445\) | −1531.86 | −0.163185 | ||||||||
\(446\) | 3703.65 | 0.393213 | ||||||||
\(447\) | 331.461 | 0.0350729 | ||||||||
\(448\) | 6270.84 | 0.661316 | ||||||||
\(449\) | 15475.4 | 1.62657 | 0.813287 | − | 0.581863i | \(-0.197676\pi\) | ||||
0.813287 | + | 0.581863i | \(0.197676\pi\) | |||||||
\(450\) | −223.738 | −0.0234380 | ||||||||
\(451\) | −3070.88 | −0.320626 | ||||||||
\(452\) | 10735.1 | 1.11712 | ||||||||
\(453\) | −10805.1 | −1.12068 | ||||||||
\(454\) | −10356.4 | −1.07060 | ||||||||
\(455\) | 4020.77 | 0.414278 | ||||||||
\(456\) | −8828.57 | −0.906658 | ||||||||
\(457\) | −7336.32 | −0.750938 | −0.375469 | − | 0.926835i | \(-0.622518\pi\) | ||||
−0.375469 | + | 0.926835i | \(0.622518\pi\) | |||||||
\(458\) | 3391.91 | 0.346056 | ||||||||
\(459\) | 1790.18 | 0.182045 | ||||||||
\(460\) | −1732.03 | −0.175557 | ||||||||
\(461\) | −1976.62 | −0.199698 | −0.0998488 | − | 0.995003i | \(-0.531836\pi\) | ||||
−0.0998488 | + | 0.995003i | \(0.531836\pi\) | |||||||
\(462\) | 2367.35 | 0.238397 | ||||||||
\(463\) | −7644.41 | −0.767313 | −0.383656 | − | 0.923476i | \(-0.625335\pi\) | ||||
−0.383656 | + | 0.923476i | \(0.625335\pi\) | |||||||
\(464\) | −2802.08 | −0.280352 | ||||||||
\(465\) | 5321.11 | 0.530668 | ||||||||
\(466\) | 4023.36 | 0.399954 | ||||||||
\(467\) | 4008.28 | 0.397176 | 0.198588 | − | 0.980083i | \(-0.436365\pi\) | ||||
0.198588 | + | 0.980083i | \(0.436365\pi\) | |||||||
\(468\) | 216.283 | 0.0213626 | ||||||||
\(469\) | −20674.0 | −2.03547 | ||||||||
\(470\) | −1531.69 | −0.150322 | ||||||||
\(471\) | −2804.39 | −0.274351 | ||||||||
\(472\) | −7595.43 | −0.740695 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −916.662 | −0.0888263 | ||||||||
\(475\) | −4525.22 | −0.437119 | ||||||||
\(476\) | 2289.46 | 0.220456 | ||||||||
\(477\) | −1164.57 | −0.111786 | ||||||||
\(478\) | 1491.76 | 0.142743 | ||||||||
\(479\) | −10236.8 | −0.976473 | −0.488236 | − | 0.872711i | \(-0.662360\pi\) | ||||
−0.488236 | + | 0.872711i | \(0.662360\pi\) | |||||||
\(480\) | −8249.65 | −0.784465 | ||||||||
\(481\) | −6308.46 | −0.598006 | ||||||||
\(482\) | −4317.92 | −0.408042 | ||||||||
\(483\) | −6407.39 | −0.603616 | ||||||||
\(484\) | 6927.17 | 0.650560 | ||||||||
\(485\) | −3912.37 | −0.366292 | ||||||||
\(486\) | −1061.13 | −0.0990406 | ||||||||
\(487\) | 4057.87 | 0.377576 | 0.188788 | − | 0.982018i | \(-0.439544\pi\) | ||||
0.188788 | + | 0.982018i | \(0.439544\pi\) | |||||||
\(488\) | −12568.3 | −1.16586 | ||||||||
\(489\) | −8410.00 | −0.777737 | ||||||||
\(490\) | −7657.32 | −0.705964 | ||||||||
\(491\) | 3884.88 | 0.357072 | 0.178536 | − | 0.983933i | \(-0.442864\pi\) | ||||
0.178536 | + | 0.983933i | \(0.442864\pi\) | |||||||
\(492\) | 10191.4 | 0.933874 | ||||||||
\(493\) | 3375.80 | 0.308394 | ||||||||
\(494\) | −1934.43 | −0.176182 | ||||||||
\(495\) | −178.382 | −0.0161973 | ||||||||
\(496\) | −1345.79 | −0.121830 | ||||||||
\(497\) | −12846.9 | −1.15948 | ||||||||
\(498\) | −8525.87 | −0.767176 | ||||||||
\(499\) | 8005.88 | 0.718222 | 0.359111 | − | 0.933295i | \(-0.383080\pi\) | ||||
0.359111 | + | 0.933295i | \(0.383080\pi\) | |||||||
\(500\) | −8292.03 | −0.741662 | ||||||||
\(501\) | −14347.5 | −1.27944 | ||||||||
\(502\) | −1136.09 | −0.101008 | ||||||||
\(503\) | −3167.37 | −0.280767 | −0.140384 | − | 0.990097i | \(-0.544834\pi\) | ||||
−0.140384 | + | 0.990097i | \(0.544834\pi\) | |||||||
\(504\) | −1579.33 | −0.139581 | ||||||||
\(505\) | 11133.3 | 0.981037 | ||||||||
\(506\) | −545.701 | −0.0479434 | ||||||||
\(507\) | −10510.8 | −0.920714 | ||||||||
\(508\) | −1202.85 | −0.105055 | ||||||||
\(509\) | −2437.53 | −0.212262 | −0.106131 | − | 0.994352i | \(-0.533846\pi\) | ||||
−0.106131 | + | 0.994352i | \(0.533846\pi\) | |||||||
\(510\) | 926.825 | 0.0804716 | ||||||||
\(511\) | 28359.2 | 2.45506 | ||||||||
\(512\) | 3978.34 | 0.343398 | ||||||||
\(513\) | −10227.1 | −0.880190 | ||||||||
\(514\) | 6055.60 | 0.519652 | ||||||||
\(515\) | 6688.21 | 0.572268 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1091.29 | 0.0928332 | ||||||||
\(518\) | 18862.1 | 1.59991 | ||||||||
\(519\) | −11040.2 | −0.933741 | ||||||||
\(520\) | −2775.48 | −0.234063 | ||||||||
\(521\) | −12207.6 | −1.02654 | −0.513268 | − | 0.858228i | \(-0.671565\pi\) | ||||
−0.513268 | + | 0.858228i | \(0.671565\pi\) | |||||||
\(522\) | −953.525 | −0.0799514 | ||||||||
\(523\) | 18236.1 | 1.52468 | 0.762340 | − | 0.647177i | \(-0.224050\pi\) | ||||
0.762340 | + | 0.647177i | \(0.224050\pi\) | |||||||
\(524\) | −3492.11 | −0.291133 | ||||||||
\(525\) | −9834.85 | −0.817577 | ||||||||
\(526\) | −1998.02 | −0.165623 | ||||||||
\(527\) | 1621.33 | 0.134016 | ||||||||
\(528\) | 548.115 | 0.0451774 | ||||||||
\(529\) | −10690.0 | −0.878608 | ||||||||
\(530\) | 6119.25 | 0.501515 | ||||||||
\(531\) | 866.930 | 0.0708504 | ||||||||
\(532\) | −13079.4 | −1.06591 | ||||||||
\(533\) | 5453.58 | 0.443191 | ||||||||
\(534\) | 1601.74 | 0.129802 | ||||||||
\(535\) | 15731.8 | 1.27130 | ||||||||
\(536\) | 14271.0 | 1.15002 | ||||||||
\(537\) | 19428.8 | 1.56129 | ||||||||
\(538\) | −1100.05 | −0.0881537 | ||||||||
\(539\) | 5455.65 | 0.435977 | ||||||||
\(540\) | −6008.33 | −0.478810 | ||||||||
\(541\) | −4277.33 | −0.339920 | −0.169960 | − | 0.985451i | \(-0.554364\pi\) | ||||
−0.169960 | + | 0.985451i | \(0.554364\pi\) | |||||||
\(542\) | 10042.2 | 0.795846 | ||||||||
\(543\) | 773.202 | 0.0611073 | ||||||||
\(544\) | −2513.65 | −0.198110 | ||||||||
\(545\) | 14345.4 | 1.12751 | ||||||||
\(546\) | −4204.18 | −0.329528 | ||||||||
\(547\) | 10280.6 | 0.803596 | 0.401798 | − | 0.915728i | \(-0.368385\pi\) | ||||
0.401798 | + | 0.915728i | \(0.368385\pi\) | |||||||
\(548\) | −9981.21 | −0.778058 | ||||||||
\(549\) | 1434.52 | 0.111519 | ||||||||
\(550\) | −837.609 | −0.0649377 | ||||||||
\(551\) | −19285.5 | −1.49109 | ||||||||
\(552\) | 4422.93 | 0.341037 | ||||||||
\(553\) | −3316.58 | −0.255037 | ||||||||
\(554\) | −3272.03 | −0.250930 | ||||||||
\(555\) | −17267.3 | −1.32064 | ||||||||
\(556\) | −7567.98 | −0.577255 | ||||||||
\(557\) | −19282.4 | −1.46683 | −0.733413 | − | 0.679784i | \(-0.762074\pi\) | ||||
−0.733413 | + | 0.679784i | \(0.762074\pi\) | |||||||
\(558\) | −457.960 | −0.0347437 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2783.45 | −0.210040 | ||||||||
\(561\) | −660.340 | −0.0496962 | ||||||||
\(562\) | −5310.40 | −0.398586 | ||||||||
\(563\) | 14877.6 | 1.11371 | 0.556854 | − | 0.830610i | \(-0.312008\pi\) | ||||
0.556854 | + | 0.830610i | \(0.312008\pi\) | |||||||
\(564\) | −3621.69 | −0.270391 | ||||||||
\(565\) | 15723.6 | 1.17079 | ||||||||
\(566\) | 10707.9 | 0.795209 | ||||||||
\(567\) | −24236.8 | −1.79515 | ||||||||
\(568\) | 8868.04 | 0.655096 | ||||||||
\(569\) | −10794.5 | −0.795307 | −0.397654 | − | 0.917536i | \(-0.630175\pi\) | ||||
−0.397654 | + | 0.917536i | \(0.630175\pi\) | |||||||
\(570\) | −5294.85 | −0.389082 | ||||||||
\(571\) | −7995.91 | −0.586022 | −0.293011 | − | 0.956109i | \(-0.594657\pi\) | ||||
−0.293011 | + | 0.956109i | \(0.594657\pi\) | |||||||
\(572\) | 809.700 | 0.0591875 | ||||||||
\(573\) | −3330.16 | −0.242792 | ||||||||
\(574\) | −16306.0 | −1.18571 | ||||||||
\(575\) | 2267.04 | 0.164421 | ||||||||
\(576\) | 494.067 | 0.0357398 | ||||||||
\(577\) | −11565.4 | −0.834444 | −0.417222 | − | 0.908805i | \(-0.636996\pi\) | ||||
−0.417222 | + | 0.908805i | \(0.636996\pi\) | |||||||
\(578\) | −7412.31 | −0.533411 | ||||||||
\(579\) | −1364.74 | −0.0979560 | ||||||||
\(580\) | −11330.1 | −0.811132 | ||||||||
\(581\) | −30847.5 | −2.20270 | ||||||||
\(582\) | 4090.83 | 0.291358 | ||||||||
\(583\) | −4359.81 | −0.309717 | ||||||||
\(584\) | −19575.9 | −1.38708 | ||||||||
\(585\) | 316.788 | 0.0223890 | ||||||||
\(586\) | 10673.0 | 0.752382 | ||||||||
\(587\) | −6354.81 | −0.446833 | −0.223417 | − | 0.974723i | \(-0.571721\pi\) | ||||
−0.223417 | + | 0.974723i | \(0.571721\pi\) | |||||||
\(588\) | −18105.8 | −1.26985 | ||||||||
\(589\) | −9262.49 | −0.647970 | ||||||||
\(590\) | −4555.28 | −0.317861 | ||||||||
\(591\) | −11098.4 | −0.772465 | ||||||||
\(592\) | 4367.15 | 0.303190 | ||||||||
\(593\) | 21747.7 | 1.50602 | 0.753010 | − | 0.658009i | \(-0.228601\pi\) | ||||
0.753010 | + | 0.658009i | \(0.228601\pi\) | |||||||
\(594\) | −1893.01 | −0.130760 | ||||||||
\(595\) | 3353.35 | 0.231049 | ||||||||
\(596\) | −338.969 | −0.0232965 | ||||||||
\(597\) | −3270.47 | −0.224207 | ||||||||
\(598\) | 969.110 | 0.0662706 | ||||||||
\(599\) | 10874.2 | 0.741750 | 0.370875 | − | 0.928683i | \(-0.379058\pi\) | ||||
0.370875 | + | 0.928683i | \(0.379058\pi\) | |||||||
\(600\) | 6788.86 | 0.461923 | ||||||||
\(601\) | −16092.5 | −1.09223 | −0.546113 | − | 0.837712i | \(-0.683893\pi\) | ||||
−0.546113 | + | 0.837712i | \(0.683893\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1628.86 | −0.110004 | ||||||||
\(604\) | 11049.8 | 0.744390 | ||||||||
\(605\) | 10146.2 | 0.681819 | ||||||||
\(606\) | −11641.1 | −0.780344 | ||||||||
\(607\) | 23235.8 | 1.55372 | 0.776862 | − | 0.629671i | \(-0.216810\pi\) | ||||
0.776862 | + | 0.629671i | \(0.216810\pi\) | |||||||
\(608\) | 14360.2 | 0.957868 | ||||||||
\(609\) | −41914.1 | −2.78891 | ||||||||
\(610\) | −7537.70 | −0.500316 | ||||||||
\(611\) | −1938.02 | −0.128320 | ||||||||
\(612\) | 180.382 | 0.0119142 | ||||||||
\(613\) | −14997.4 | −0.988153 | −0.494076 | − | 0.869418i | \(-0.664494\pi\) | ||||
−0.494076 | + | 0.869418i | \(0.664494\pi\) | |||||||
\(614\) | 2512.61 | 0.165148 | ||||||||
\(615\) | 14927.3 | 0.978745 | ||||||||
\(616\) | −5912.53 | −0.386725 | ||||||||
\(617\) | 2016.56 | 0.131578 | 0.0657890 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657890 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(618\) | −6993.30 | −0.455197 | ||||||||
\(619\) | 17984.1 | 1.16776 | 0.583879 | − | 0.811841i | \(-0.301534\pi\) | ||||
0.583879 | + | 0.811841i | \(0.301534\pi\) | |||||||
\(620\) | −5441.63 | −0.352486 | ||||||||
\(621\) | 5123.57 | 0.331081 | ||||||||
\(622\) | −3630.85 | −0.234058 | ||||||||
\(623\) | 5795.27 | 0.372685 | ||||||||
\(624\) | −973.397 | −0.0624472 | ||||||||
\(625\) | −4771.61 | −0.305383 | ||||||||
\(626\) | 6861.46 | 0.438082 | ||||||||
\(627\) | 3772.45 | 0.240282 | ||||||||
\(628\) | 2867.91 | 0.182233 | ||||||||
\(629\) | −5261.31 | −0.333517 | ||||||||
\(630\) | −947.185 | −0.0598996 | ||||||||
\(631\) | 7502.61 | 0.473335 | 0.236667 | − | 0.971591i | \(-0.423945\pi\) | ||||
0.236667 | + | 0.971591i | \(0.423945\pi\) | |||||||
\(632\) | 2289.39 | 0.144093 | ||||||||
\(633\) | −23593.1 | −1.48142 | ||||||||
\(634\) | 14575.7 | 0.913051 | ||||||||
\(635\) | −1761.80 | −0.110103 | ||||||||
\(636\) | 14469.1 | 0.902100 | ||||||||
\(637\) | −9688.68 | −0.602637 | ||||||||
\(638\) | −3569.71 | −0.221515 | ||||||||
\(639\) | −1012.18 | −0.0626625 | ||||||||
\(640\) | 9571.14 | 0.591145 | ||||||||
\(641\) | 17658.5 | 1.08809 | 0.544047 | − | 0.839055i | \(-0.316891\pi\) | ||||
0.544047 | + | 0.839055i | \(0.316891\pi\) | |||||||
\(642\) | −16449.4 | −1.01123 | ||||||||
\(643\) | −12908.4 | −0.791694 | −0.395847 | − | 0.918316i | \(-0.629549\pi\) | ||||
−0.395847 | + | 0.918316i | \(0.629549\pi\) | |||||||
\(644\) | 6552.52 | 0.400940 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1613.33 | −0.0982595 | ||||||||
\(647\) | 20030.3 | 1.21712 | 0.608558 | − | 0.793510i | \(-0.291748\pi\) | ||||
0.608558 | + | 0.793510i | \(0.291748\pi\) | |||||||
\(648\) | 16730.3 | 1.01424 | ||||||||
\(649\) | 3245.53 | 0.196299 | ||||||||
\(650\) | 1487.51 | 0.0897613 | ||||||||
\(651\) | −20130.6 | −1.21195 | ||||||||
\(652\) | 8600.48 | 0.516597 | ||||||||
\(653\) | 3145.07 | 0.188478 | 0.0942391 | − | 0.995550i | \(-0.469958\pi\) | ||||
0.0942391 | + | 0.995550i | \(0.469958\pi\) | |||||||
\(654\) | −14999.8 | −0.896849 | ||||||||
\(655\) | −5114.86 | −0.305121 | ||||||||
\(656\) | −3775.34 | −0.224699 | ||||||||
\(657\) | 2234.36 | 0.132680 | ||||||||
\(658\) | 5794.60 | 0.343308 | ||||||||
\(659\) | −16132.7 | −0.953627 | −0.476813 | − | 0.879005i | \(-0.658208\pi\) | ||||
−0.476813 | + | 0.879005i | \(0.658208\pi\) | |||||||
\(660\) | 2216.28 | 0.130710 | ||||||||
\(661\) | −9134.09 | −0.537481 | −0.268740 | − | 0.963213i | \(-0.586607\pi\) | ||||
−0.268740 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(662\) | 8118.28 | 0.476625 | ||||||||
\(663\) | 1172.70 | 0.0686935 | ||||||||
\(664\) | 21293.6 | 1.24451 | ||||||||
\(665\) | −19157.3 | −1.11713 | ||||||||
\(666\) | 1486.10 | 0.0864645 | ||||||||
\(667\) | 9661.66 | 0.560871 | ||||||||
\(668\) | 14672.4 | 0.849841 | ||||||||
\(669\) | 12826.8 | 0.741275 | ||||||||
\(670\) | 8558.86 | 0.493519 | ||||||||
\(671\) | 5370.42 | 0.308976 | ||||||||
\(672\) | 31209.7 | 1.79158 | ||||||||
\(673\) | 5116.23 | 0.293041 | 0.146520 | − | 0.989208i | \(-0.453193\pi\) | ||||
0.146520 | + | 0.989208i | \(0.453193\pi\) | |||||||
\(674\) | 4698.78 | 0.268531 | ||||||||
\(675\) | 7864.27 | 0.448439 | ||||||||
\(676\) | 10748.9 | 0.611567 | ||||||||
\(677\) | 4972.81 | 0.282305 | 0.141153 | − | 0.989988i | \(-0.454919\pi\) | ||||
0.141153 | + | 0.989988i | \(0.454919\pi\) | |||||||
\(678\) | −16440.9 | −0.931280 | ||||||||
\(679\) | 14801.1 | 0.836543 | ||||||||
\(680\) | −2314.77 | −0.130540 | ||||||||
\(681\) | −35867.2 | −2.01826 | ||||||||
\(682\) | −1714.47 | −0.0962614 | ||||||||
\(683\) | −7581.73 | −0.424754 | −0.212377 | − | 0.977188i | \(-0.568120\pi\) | ||||
−0.212377 | + | 0.977188i | \(0.568120\pi\) | |||||||
\(684\) | −1030.50 | −0.0576056 | ||||||||
\(685\) | −14619.4 | −0.815443 | ||||||||
\(686\) | 12456.8 | 0.693296 | ||||||||
\(687\) | 11747.2 | 0.652375 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7742.58 | 0.428112 | ||||||||
\(690\) | 2652.61 | 0.146352 | ||||||||
\(691\) | 7653.70 | 0.421361 | 0.210681 | − | 0.977555i | \(-0.432432\pi\) | ||||
0.210681 | + | 0.977555i | \(0.432432\pi\) | |||||||
\(692\) | 11290.3 | 0.620219 | ||||||||
\(693\) | 674.846 | 0.0369918 | ||||||||
\(694\) | −14328.7 | −0.783734 | ||||||||
\(695\) | −11084.8 | −0.604991 | ||||||||
\(696\) | 28932.7 | 1.57571 | ||||||||
\(697\) | 4548.33 | 0.247174 | ||||||||
\(698\) | −3283.27 | −0.178043 | ||||||||
\(699\) | 13934.0 | 0.753982 | ||||||||
\(700\) | 10057.6 | 0.543060 | ||||||||
\(701\) | 5942.69 | 0.320189 | 0.160094 | − | 0.987102i | \(-0.448820\pi\) | ||||
0.160094 | + | 0.987102i | \(0.448820\pi\) | |||||||
\(702\) | 3361.80 | 0.180745 | ||||||||
\(703\) | 30057.3 | 1.61256 | ||||||||
\(704\) | 1849.64 | 0.0990213 | ||||||||
\(705\) | −5304.66 | −0.283383 | ||||||||
\(706\) | 499.782 | 0.0266424 | ||||||||
\(707\) | −42118.8 | −2.24051 | ||||||||
\(708\) | −10771.0 | −0.571752 | ||||||||
\(709\) | −5113.78 | −0.270877 | −0.135439 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135439 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(710\) | 5318.52 | 0.281127 | ||||||||
\(711\) | −261.307 | −0.0137831 | ||||||||
\(712\) | −4000.39 | −0.210563 | ||||||||
\(713\) | 4640.31 | 0.243732 | ||||||||
\(714\) | −3506.32 | −0.183783 | ||||||||
\(715\) | 1185.96 | 0.0620314 | ||||||||
\(716\) | −19868.8 | −1.03706 | ||||||||
\(717\) | 5166.38 | 0.269096 | ||||||||
\(718\) | 14272.3 | 0.741835 | ||||||||
\(719\) | 36844.4 | 1.91108 | 0.955538 | − | 0.294869i | \(-0.0952761\pi\) | ||||
0.955538 | + | 0.294869i | \(0.0952761\pi\) | |||||||
\(720\) | −219.303 | −0.0113513 | ||||||||
\(721\) | −25302.5 | −1.30696 | ||||||||
\(722\) | −1525.75 | −0.0786460 | ||||||||
\(723\) | −14954.2 | −0.769230 | ||||||||
\(724\) | −790.715 | −0.0405893 | ||||||||
\(725\) | 14829.9 | 0.759681 | ||||||||
\(726\) | −10609.0 | −0.542337 | ||||||||
\(727\) | 21420.6 | 1.09277 | 0.546387 | − | 0.837533i | \(-0.316003\pi\) | ||||
0.546387 | + | 0.837533i | \(0.316003\pi\) | |||||||
\(728\) | 10500.1 | 0.534558 | ||||||||
\(729\) | 17615.1 | 0.894939 | ||||||||
\(730\) | −11740.5 | −0.595252 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −17823.0 | −0.899942 | ||||||||
\(733\) | 35541.1 | 1.79091 | 0.895457 | − | 0.445148i | \(-0.146849\pi\) | ||||
0.895457 | + | 0.445148i | \(0.146849\pi\) | |||||||
\(734\) | −4270.90 | −0.214771 | ||||||||
\(735\) | −26519.5 | −1.33087 | ||||||||
\(736\) | −7194.17 | −0.360300 | ||||||||
\(737\) | −6097.98 | −0.304779 | ||||||||
\(738\) | −1284.72 | −0.0640801 | ||||||||
\(739\) | −5111.15 | −0.254420 | −0.127210 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127210 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(740\) | 17658.4 | 0.877209 | ||||||||
\(741\) | −6699.49 | −0.332135 | ||||||||
\(742\) | −23150.0 | −1.14537 | ||||||||
\(743\) | −37864.8 | −1.86962 | −0.934808 | − | 0.355153i | \(-0.884429\pi\) | ||||
−0.934808 | + | 0.355153i | \(0.884429\pi\) | |||||||
\(744\) | 13895.8 | 0.684739 | ||||||||
\(745\) | −496.485 | −0.0244158 | ||||||||
\(746\) | 20751.4 | 1.01845 | ||||||||
\(747\) | −2430.42 | −0.119042 | ||||||||
\(748\) | 675.297 | 0.0330098 | ||||||||
\(749\) | −59515.8 | −2.90342 | ||||||||
\(750\) | 12699.3 | 0.618283 | ||||||||
\(751\) | −4814.57 | −0.233937 | −0.116968 | − | 0.993136i | \(-0.537318\pi\) | ||||
−0.116968 | + | 0.993136i | \(0.537318\pi\) | |||||||
\(752\) | 1341.63 | 0.0650587 | ||||||||
\(753\) | −3934.60 | −0.190418 | ||||||||
\(754\) | 6339.45 | 0.306192 | ||||||||
\(755\) | 16184.6 | 0.780156 | ||||||||
\(756\) | 22730.4 | 1.09352 | ||||||||
\(757\) | 13342.1 | 0.640589 | 0.320295 | − | 0.947318i | \(-0.396218\pi\) | ||||
0.320295 | + | 0.947318i | \(0.396218\pi\) | |||||||
\(758\) | 13749.5 | 0.658845 | ||||||||
\(759\) | −1889.92 | −0.0903817 | ||||||||
\(760\) | 13224.0 | 0.631166 | ||||||||
\(761\) | 17924.5 | 0.853826 | 0.426913 | − | 0.904293i | \(-0.359601\pi\) | ||||
0.426913 | + | 0.904293i | \(0.359601\pi\) | |||||||
\(762\) | 1842.17 | 0.0875785 | ||||||||
\(763\) | −54271.0 | −2.57502 | ||||||||
\(764\) | 3405.59 | 0.161270 | ||||||||
\(765\) | 264.204 | 0.0124867 | ||||||||
\(766\) | 17449.2 | 0.823062 | ||||||||
\(767\) | −5763.73 | −0.271338 | ||||||||
\(768\) | −18860.7 | −0.886168 | ||||||||
\(769\) | 4472.87 | 0.209748 | 0.104874 | − | 0.994486i | \(-0.466556\pi\) | ||||
0.104874 | + | 0.994486i | \(0.466556\pi\) | |||||||
\(770\) | −3545.98 | −0.165959 | ||||||||
\(771\) | 20972.3 | 0.979635 | ||||||||
\(772\) | 1395.65 | 0.0650654 | ||||||||
\(773\) | −33168.7 | −1.54333 | −0.771665 | − | 0.636029i | \(-0.780576\pi\) | ||||
−0.771665 | + | 0.636029i | \(0.780576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7122.52 | 0.330127 | ||||||||
\(776\) | −10217.0 | −0.472639 | ||||||||
\(777\) | 65324.7 | 3.01610 | ||||||||
\(778\) | −18283.6 | −0.842544 | ||||||||
\(779\) | −25984.1 | −1.19509 | ||||||||
\(780\) | −3935.89 | −0.180676 | ||||||||
\(781\) | −3789.31 | −0.173614 | ||||||||
\(782\) | 808.245 | 0.0369601 | ||||||||
\(783\) | 33515.9 | 1.52971 | ||||||||
\(784\) | 6707.17 | 0.305538 | ||||||||
\(785\) | 4200.60 | 0.190988 | ||||||||
\(786\) | 5348.18 | 0.242701 | ||||||||
\(787\) | 6452.90 | 0.292276 | 0.146138 | − | 0.989264i | \(-0.453316\pi\) | ||||
0.146138 | + | 0.989264i | \(0.453316\pi\) | |||||||
\(788\) | 11349.8 | 0.513095 | ||||||||
\(789\) | −6919.72 | −0.312229 | ||||||||
\(790\) | 1373.04 | 0.0618361 | ||||||||
\(791\) | −59484.8 | −2.67388 | ||||||||
\(792\) | −465.837 | −0.0209000 | ||||||||
\(793\) | −9537.33 | −0.427088 | ||||||||
\(794\) | 15571.9 | 0.696002 | ||||||||
\(795\) | 21192.7 | 0.945444 | ||||||||
\(796\) | 3344.55 | 0.148925 | ||||||||
\(797\) | 8676.60 | 0.385622 | 0.192811 | − | 0.981236i | \(-0.438240\pi\) | ||||
0.192811 | + | 0.981236i | \(0.438240\pi\) | |||||||
\(798\) | 20031.2 | 0.888593 | ||||||||
\(799\) | −1616.32 | −0.0715661 | ||||||||
\(800\) | −11042.5 | −0.488014 | ||||||||
\(801\) | 456.598 | 0.0201412 | ||||||||
\(802\) | 7650.62 | 0.336849 | ||||||||
\(803\) | 8364.79 | 0.367605 | ||||||||
\(804\) | 20237.6 | 0.887716 | ||||||||
\(805\) | 9597.43 | 0.420205 | ||||||||
\(806\) | 3044.72 | 0.133059 | ||||||||
\(807\) | −3809.80 | −0.166185 | ||||||||
\(808\) | 29074.0 | 1.26587 | ||||||||
\(809\) | 10277.3 | 0.446637 | 0.223319 | − | 0.974745i | \(-0.428311\pi\) | ||||
0.223319 | + | 0.974745i | \(0.428311\pi\) | |||||||
\(810\) | 10033.8 | 0.435250 | ||||||||
\(811\) | −31979.8 | −1.38466 | −0.692332 | − | 0.721579i | \(-0.743416\pi\) | ||||
−0.692332 | + | 0.721579i | \(0.743416\pi\) | |||||||
\(812\) | 42863.4 | 1.85248 | ||||||||
\(813\) | 34779.0 | 1.50031 | ||||||||
\(814\) | 5563.53 | 0.239560 | ||||||||
\(815\) | 12597.1 | 0.541418 | ||||||||
\(816\) | −811.821 | −0.0348277 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −16770.7 | −0.716837 | ||||||||
\(819\) | −1198.46 | −0.0511325 | ||||||||
\(820\) | −15265.4 | −0.650112 | ||||||||
\(821\) | 4889.45 | 0.207848 | 0.103924 | − | 0.994585i | \(-0.466860\pi\) | ||||
0.103924 | + | 0.994585i | \(0.466860\pi\) | |||||||
\(822\) | 15286.3 | 0.648625 | ||||||||
\(823\) | −27193.5 | −1.15177 | −0.575884 | − | 0.817531i | \(-0.695342\pi\) | ||||
−0.575884 | + | 0.817531i | \(0.695342\pi\) | |||||||
\(824\) | 17466.0 | 0.738417 | ||||||||
\(825\) | −2900.88 | −0.122419 | ||||||||
\(826\) | 17233.3 | 0.725937 | ||||||||
\(827\) | −5190.02 | −0.218228 | −0.109114 | − | 0.994029i | \(-0.534801\pi\) | ||||
−0.109114 | + | 0.994029i | \(0.534801\pi\) | |||||||
\(828\) | 516.260 | 0.0216682 | ||||||||
\(829\) | −22048.5 | −0.923733 | −0.461867 | − | 0.886949i | \(-0.652820\pi\) | ||||
−0.461867 | + | 0.886949i | \(0.652820\pi\) | |||||||
\(830\) | 12770.6 | 0.534066 | ||||||||
\(831\) | −11332.0 | −0.473047 | ||||||||
\(832\) | −3284.78 | −0.136874 | ||||||||
\(833\) | −8080.44 | −0.336099 | ||||||||
\(834\) | 11590.4 | 0.481226 | ||||||||
\(835\) | 21490.6 | 0.890674 | ||||||||
\(836\) | −3857.89 | −0.159603 | ||||||||
\(837\) | 16097.1 | 0.664750 | ||||||||
\(838\) | 7951.36 | 0.327775 | ||||||||
\(839\) | 24727.9 | 1.01752 | 0.508761 | − | 0.860908i | \(-0.330104\pi\) | ||||
0.508761 | + | 0.860908i | \(0.330104\pi\) | |||||||
\(840\) | 28740.3 | 1.18052 | ||||||||
\(841\) | 38812.9 | 1.59141 | ||||||||
\(842\) | 5871.03 | 0.240296 | ||||||||
\(843\) | −18391.4 | −0.751405 | ||||||||
\(844\) | 24127.4 | 0.984006 | ||||||||
\(845\) | 15743.8 | 0.640951 | ||||||||
\(846\) | 456.545 | 0.0185536 | ||||||||
\(847\) | −38384.5 | −1.55715 | ||||||||
\(848\) | −5359.95 | −0.217054 | ||||||||
\(849\) | 37084.7 | 1.49911 | ||||||||
\(850\) | 1240.59 | 0.0500612 | ||||||||
\(851\) | −15058.1 | −0.606562 | ||||||||
\(852\) | 12575.7 | 0.505677 | ||||||||
\(853\) | −23989.1 | −0.962922 | −0.481461 | − | 0.876468i | \(-0.659894\pi\) | ||||
−0.481461 | + | 0.876468i | \(0.659894\pi\) | |||||||
\(854\) | 28516.3 | 1.14263 | ||||||||
\(855\) | −1509.37 | −0.0603735 | ||||||||
\(856\) | 41082.9 | 1.64040 | ||||||||
\(857\) | −10224.3 | −0.407534 | −0.203767 | − | 0.979019i | \(-0.565319\pi\) | ||||
−0.203767 | + | 0.979019i | \(0.565319\pi\) | |||||||
\(858\) | −1240.06 | −0.0493414 | ||||||||
\(859\) | 20256.5 | 0.804590 | 0.402295 | − | 0.915510i | \(-0.368213\pi\) | ||||
0.402295 | + | 0.915510i | \(0.368213\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −56472.3 | −2.23527 | ||||||||
\(862\) | −739.882 | −0.0292349 | ||||||||
\(863\) | 21978.0 | 0.866905 | 0.433453 | − | 0.901176i | \(-0.357295\pi\) | ||||
0.433453 | + | 0.901176i | \(0.357295\pi\) | |||||||
\(864\) | −24956.3 | −0.982673 | ||||||||
\(865\) | 16536.8 | 0.650020 | ||||||||
\(866\) | −783.278 | −0.0307354 | ||||||||
\(867\) | −25670.9 | −1.00557 | ||||||||
\(868\) | 20586.5 | 0.805014 | ||||||||
\(869\) | −978.256 | −0.0381876 | ||||||||
\(870\) | 17352.1 | 0.676197 | ||||||||
\(871\) | 10829.4 | 0.421286 | ||||||||
\(872\) | 37462.5 | 1.45486 | ||||||||
\(873\) | 1166.15 | 0.0452097 | ||||||||
\(874\) | −4617.42 | −0.178703 | ||||||||
\(875\) | 45947.4 | 1.77521 | ||||||||
\(876\) | −27760.5 | −1.07071 | ||||||||
\(877\) | −11390.5 | −0.438575 | −0.219287 | − | 0.975660i | \(-0.570373\pi\) | ||||
−0.219287 | + | 0.975660i | \(0.570373\pi\) | |||||||
\(878\) | −23670.3 | −0.909833 | ||||||||
\(879\) | 36963.5 | 1.41837 | ||||||||
\(880\) | −821.004 | −0.0314500 | ||||||||
\(881\) | 36825.6 | 1.40827 | 0.704135 | − | 0.710066i | \(-0.251335\pi\) | ||||
0.704135 | + | 0.710066i | \(0.251335\pi\) | |||||||
\(882\) | 2282.39 | 0.0871340 | ||||||||
\(883\) | −27495.1 | −1.04789 | −0.523943 | − | 0.851754i | \(-0.675539\pi\) | ||||
−0.523943 | + | 0.851754i | \(0.675539\pi\) | |||||||
\(884\) | −1199.26 | −0.0456283 | ||||||||
\(885\) | −15776.2 | −0.599224 | ||||||||
\(886\) | −13616.7 | −0.516324 | ||||||||
\(887\) | 39402.6 | 1.49155 | 0.745777 | − | 0.666195i | \(-0.232078\pi\) | ||||
0.745777 | + | 0.666195i | \(0.232078\pi\) | |||||||
\(888\) | −45092.7 | −1.70407 | ||||||||
\(889\) | 6665.17 | 0.251454 | ||||||||
\(890\) | −2399.20 | −0.0903610 | ||||||||
\(891\) | −7148.85 | −0.268794 | ||||||||
\(892\) | −13117.3 | −0.492378 | ||||||||
\(893\) | 9233.86 | 0.346024 | ||||||||
\(894\) | 519.132 | 0.0194210 | ||||||||
\(895\) | −29101.7 | −1.08689 | ||||||||
\(896\) | −36209.1 | −1.35007 | ||||||||
\(897\) | 3356.30 | 0.124932 | ||||||||
\(898\) | 24237.5 | 0.900687 | ||||||||
\(899\) | 30354.7 | 1.12612 | ||||||||
\(900\) | 792.420 | 0.0293489 | ||||||||
\(901\) | 6457.38 | 0.238764 | ||||||||
\(902\) | −4809.60 | −0.177541 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41061.5 | 1.51071 | ||||||||
\(905\) | −1158.15 | −0.0425396 | ||||||||
\(906\) | −16922.9 | −0.620557 | ||||||||
\(907\) | −842.302 | −0.0308359 | −0.0154180 | − | 0.999881i | \(-0.504908\pi\) | ||||
−0.0154180 | + | 0.999881i | \(0.504908\pi\) | |||||||
\(908\) | 36679.6 | 1.34059 | ||||||||
\(909\) | −3318.46 | −0.121085 | ||||||||
\(910\) | 6297.30 | 0.229399 | ||||||||
\(911\) | 7588.34 | 0.275975 | 0.137987 | − | 0.990434i | \(-0.455937\pi\) | ||||
0.137987 | + | 0.990434i | \(0.455937\pi\) | |||||||
\(912\) | 4637.84 | 0.168393 | ||||||||
\(913\) | −9098.75 | −0.329819 | ||||||||
\(914\) | −11490.1 | −0.415819 | ||||||||
\(915\) | −26105.2 | −0.943182 | ||||||||
\(916\) | −12013.2 | −0.433328 | ||||||||
\(917\) | 19350.3 | 0.696841 | ||||||||
\(918\) | 2803.77 | 0.100804 | ||||||||
\(919\) | 1126.30 | 0.0404278 | 0.0202139 | − | 0.999796i | \(-0.493565\pi\) | ||||
0.0202139 | + | 0.999796i | \(0.493565\pi\) | |||||||
\(920\) | −6624.97 | −0.237412 | ||||||||
\(921\) | 8701.89 | 0.311332 | ||||||||
\(922\) | −3095.78 | −0.110579 | ||||||||
\(923\) | 6729.44 | 0.239981 | ||||||||
\(924\) | −8384.53 | −0.298518 | ||||||||
\(925\) | −23113.0 | −0.821567 | ||||||||
\(926\) | −11972.6 | −0.424887 | ||||||||
\(927\) | −1993.54 | −0.0706325 | ||||||||
\(928\) | −47060.8 | −1.66470 | ||||||||
\(929\) | −12483.2 | −0.440861 | −0.220431 | − | 0.975403i | \(-0.570746\pi\) | ||||
−0.220431 | + | 0.975403i | \(0.570746\pi\) | |||||||
\(930\) | 8333.89 | 0.293848 | ||||||||
\(931\) | 46162.6 | 1.62505 | ||||||||
\(932\) | −14249.6 | −0.500818 | ||||||||
\(933\) | −12574.7 | −0.441239 | ||||||||
\(934\) | 6277.74 | 0.219929 | ||||||||
\(935\) | 989.102 | 0.0345958 | ||||||||
\(936\) | 827.279 | 0.0288894 | ||||||||
\(937\) | −50746.3 | −1.76927 | −0.884636 | − | 0.466282i | \(-0.845593\pi\) | ||||
−0.884636 | + | 0.466282i | \(0.845593\pi\) | |||||||
\(938\) | −32379.5 | −1.12711 | ||||||||
\(939\) | 23763.2 | 0.825860 | ||||||||
\(940\) | 5424.82 | 0.188232 | ||||||||
\(941\) | 21706.6 | 0.751983 | 0.375991 | − | 0.926623i | \(-0.377302\pi\) | ||||
0.375991 | + | 0.926623i | \(0.377302\pi\) | |||||||
\(942\) | −4392.22 | −0.151917 | ||||||||
\(943\) | 13017.5 | 0.449531 | ||||||||
\(944\) | 3990.05 | 0.137569 | ||||||||
\(945\) | 33293.1 | 1.14606 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16594.0 | 0.569412 | 0.284706 | − | 0.958615i | \(-0.408104\pi\) | ||||
0.284706 | + | 0.958615i | \(0.408104\pi\) | |||||||
\(948\) | 3246.57 | 0.111228 | ||||||||
\(949\) | −14855.0 | −0.508129 | ||||||||
\(950\) | −7087.37 | −0.242047 | ||||||||
\(951\) | 50479.8 | 1.72126 | ||||||||
\(952\) | 8757.13 | 0.298131 | ||||||||
\(953\) | −5575.02 | −0.189499 | −0.0947495 | − | 0.995501i | \(-0.530205\pi\) | ||||
−0.0947495 | + | 0.995501i | \(0.530205\pi\) | |||||||
\(954\) | −1823.95 | −0.0618998 | ||||||||
\(955\) | 4988.14 | 0.169018 | ||||||||
\(956\) | −5283.40 | −0.178742 | ||||||||
\(957\) | −12362.9 | −0.417593 | ||||||||
\(958\) | −16032.8 | −0.540705 | ||||||||
\(959\) | 55307.4 | 1.86232 | ||||||||
\(960\) | −8990.96 | −0.302273 | ||||||||
\(961\) | −15212.2 | −0.510631 | ||||||||
\(962\) | −9880.27 | −0.331136 | ||||||||
\(963\) | −4689.13 | −0.156911 | ||||||||
\(964\) | 15292.9 | 0.510946 | ||||||||
\(965\) | 2044.20 | 0.0681917 | ||||||||
\(966\) | −10035.2 | −0.334242 | ||||||||
\(967\) | 25230.5 | 0.839046 | 0.419523 | − | 0.907745i | \(-0.362197\pi\) | ||||
0.419523 | + | 0.907745i | \(0.362197\pi\) | |||||||
\(968\) | 26496.3 | 0.879775 | ||||||||
\(969\) | −5587.43 | −0.185236 | ||||||||
\(970\) | −6127.52 | −0.202828 | ||||||||
\(971\) | 37852.9 | 1.25104 | 0.625519 | − | 0.780209i | \(-0.284887\pi\) | ||||
0.625519 | + | 0.780209i | \(0.284887\pi\) | |||||||
\(972\) | 3758.23 | 0.124018 | ||||||||
\(973\) | 41935.3 | 1.38169 | ||||||||
\(974\) | 6355.41 | 0.209076 | ||||||||
\(975\) | 5151.67 | 0.169216 | ||||||||
\(976\) | 6602.39 | 0.216534 | ||||||||
\(977\) | −24861.4 | −0.814111 | −0.407055 | − | 0.913404i | \(-0.633444\pi\) | ||||
−0.407055 | + | 0.913404i | \(0.633444\pi\) | |||||||
\(978\) | −13171.7 | −0.430659 | ||||||||
\(979\) | 1709.37 | 0.0558035 | ||||||||
\(980\) | 27120.2 | 0.884002 | ||||||||
\(981\) | −4275.90 | −0.139163 | ||||||||
\(982\) | 6084.47 | 0.197722 | ||||||||
\(983\) | 38582.6 | 1.25187 | 0.625937 | − | 0.779873i | \(-0.284717\pi\) | ||||
0.625937 | + | 0.779873i | \(0.284717\pi\) | |||||||
\(984\) | 38982.0 | 1.26291 | ||||||||
\(985\) | 16623.9 | 0.537748 | ||||||||
\(986\) | 5287.15 | 0.170768 | ||||||||
\(987\) | 20068.3 | 0.647196 | ||||||||
\(988\) | 6851.23 | 0.220614 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −279.381 | −0.00896900 | ||||||||
\(991\) | 45385.9 | 1.45483 | 0.727413 | − | 0.686200i | \(-0.240723\pi\) | ||||
0.727413 | + | 0.686200i | \(0.240723\pi\) | |||||||
\(992\) | −22602.4 | −0.723415 | ||||||||
\(993\) | 28115.9 | 0.898521 | ||||||||
\(994\) | −20120.8 | −0.642044 | ||||||||
\(995\) | 4898.74 | 0.156081 | ||||||||
\(996\) | 30196.3 | 0.960650 | ||||||||
\(997\) | −55850.4 | −1.77412 | −0.887061 | − | 0.461653i | \(-0.847257\pi\) | ||||
−0.887061 | + | 0.461653i | \(0.847257\pi\) | |||||||
\(998\) | 12538.8 | 0.397703 | ||||||||
\(999\) | −52235.8 | −1.65432 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1849.4.a.g.1.20 | 30 | ||
43.2 | odd | 14 | 43.4.e.a.4.4 | ✓ | 60 | ||
43.22 | odd | 14 | 43.4.e.a.11.4 | yes | 60 | ||
43.42 | odd | 2 | 1849.4.a.h.1.11 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.4 | ✓ | 60 | 43.2 | odd | 14 | ||
43.4.e.a.11.4 | yes | 60 | 43.22 | odd | 14 | ||
1849.4.a.g.1.20 | 30 | 1.1 | even | 1 | trivial | ||
1849.4.a.h.1.11 | 30 | 43.42 | odd | 2 |