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: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-3.82341\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.82341 | 1.35178 | 0.675889 | − | 0.737003i | \(-0.263760\pi\) | ||||
0.675889 | + | 0.737003i | \(0.263760\pi\) | |||||||
\(3\) | −7.76517 | −1.49441 | −0.747204 | − | 0.664595i | \(-0.768604\pi\) | ||||
−0.747204 | + | 0.664595i | \(0.768604\pi\) | |||||||
\(4\) | 6.61843 | 0.827303 | ||||||||
\(5\) | 18.1323 | 1.62180 | 0.810901 | − | 0.585184i | \(-0.198978\pi\) | ||||
0.810901 | + | 0.585184i | \(0.198978\pi\) | |||||||
\(6\) | −29.6894 | −2.02011 | ||||||||
\(7\) | 5.19796 | 0.280663 | 0.140332 | − | 0.990105i | \(-0.455183\pi\) | ||||
0.140332 | + | 0.990105i | \(0.455183\pi\) | |||||||
\(8\) | −5.28231 | −0.233447 | ||||||||
\(9\) | 33.2979 | 1.23325 | ||||||||
\(10\) | 69.3271 | 2.19232 | ||||||||
\(11\) | 31.5438 | 0.864620 | 0.432310 | − | 0.901725i | \(-0.357699\pi\) | ||||
0.432310 | + | 0.901725i | \(0.357699\pi\) | |||||||
\(12\) | −51.3932 | −1.23633 | ||||||||
\(13\) | −71.3248 | −1.52169 | −0.760844 | − | 0.648935i | \(-0.775215\pi\) | ||||
−0.760844 | + | 0.648935i | \(0.775215\pi\) | |||||||
\(14\) | 19.8739 | 0.379395 | ||||||||
\(15\) | −140.800 | −2.42363 | ||||||||
\(16\) | −73.1438 | −1.14287 | ||||||||
\(17\) | 136.180 | 1.94286 | 0.971428 | − | 0.237334i | \(-0.0762736\pi\) | ||||
0.971428 | + | 0.237334i | \(0.0762736\pi\) | |||||||
\(18\) | 127.311 | 1.66709 | ||||||||
\(19\) | −1.39966 | −0.0169002 | −0.00845010 | − | 0.999964i | \(-0.502690\pi\) | ||||
−0.00845010 | + | 0.999964i | \(0.502690\pi\) | |||||||
\(20\) | 120.007 | 1.34172 | ||||||||
\(21\) | −40.3630 | −0.419425 | ||||||||
\(22\) | 120.605 | 1.16877 | ||||||||
\(23\) | −60.7163 | −0.550444 | −0.275222 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275222 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(24\) | 41.0180 | 0.348865 | ||||||||
\(25\) | 203.780 | 1.63024 | ||||||||
\(26\) | −272.704 | −2.05698 | ||||||||
\(27\) | −48.9039 | −0.348576 | ||||||||
\(28\) | 34.4023 | 0.232194 | ||||||||
\(29\) | 29.6008 | 0.189542 | 0.0947712 | − | 0.995499i | \(-0.469788\pi\) | ||||
0.0947712 | + | 0.995499i | \(0.469788\pi\) | |||||||
\(30\) | −538.337 | −3.27621 | ||||||||
\(31\) | 87.2661 | 0.505595 | 0.252798 | − | 0.967519i | \(-0.418649\pi\) | ||||
0.252798 | + | 0.967519i | \(0.418649\pi\) | |||||||
\(32\) | −237.400 | −1.31146 | ||||||||
\(33\) | −244.943 | −1.29209 | ||||||||
\(34\) | 520.672 | 2.62631 | ||||||||
\(35\) | 94.2509 | 0.455180 | ||||||||
\(36\) | 220.379 | 1.02028 | ||||||||
\(37\) | 255.642 | 1.13587 | 0.567936 | − | 0.823073i | \(-0.307742\pi\) | ||||
0.567936 | + | 0.823073i | \(0.307742\pi\) | |||||||
\(38\) | −5.35146 | −0.0228453 | ||||||||
\(39\) | 553.849 | 2.27402 | ||||||||
\(40\) | −95.7804 | −0.378605 | ||||||||
\(41\) | 23.1367 | 0.0881302 | 0.0440651 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440651 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(42\) | −154.324 | −0.566970 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 208.771 | 0.715303 | ||||||||
\(45\) | 603.766 | 2.00009 | ||||||||
\(46\) | −232.143 | −0.744079 | ||||||||
\(47\) | −1.08229 | −0.00335890 | −0.00167945 | − | 0.999999i | \(-0.500535\pi\) | ||||
−0.00167945 | + | 0.999999i | \(0.500535\pi\) | |||||||
\(48\) | 567.974 | 1.70792 | ||||||||
\(49\) | −315.981 | −0.921228 | ||||||||
\(50\) | 779.133 | 2.20372 | ||||||||
\(51\) | −1057.46 | −2.90342 | ||||||||
\(52\) | −472.058 | −1.25890 | ||||||||
\(53\) | −66.8923 | −0.173365 | −0.0866827 | − | 0.996236i | \(-0.527627\pi\) | ||||
−0.0866827 | + | 0.996236i | \(0.527627\pi\) | |||||||
\(54\) | −186.979 | −0.471198 | ||||||||
\(55\) | 571.962 | 1.40224 | ||||||||
\(56\) | −27.4572 | −0.0655201 | ||||||||
\(57\) | 10.8686 | 0.0252558 | ||||||||
\(58\) | 113.176 | 0.256219 | ||||||||
\(59\) | 465.968 | 1.02820 | 0.514101 | − | 0.857730i | \(-0.328126\pi\) | ||||
0.514101 | + | 0.857730i | \(0.328126\pi\) | |||||||
\(60\) | −931.877 | −2.00508 | ||||||||
\(61\) | −580.345 | −1.21812 | −0.609062 | − | 0.793123i | \(-0.708454\pi\) | ||||
−0.609062 | + | 0.793123i | \(0.708454\pi\) | |||||||
\(62\) | 333.654 | 0.683452 | ||||||||
\(63\) | 173.081 | 0.346129 | ||||||||
\(64\) | −322.526 | −0.629933 | ||||||||
\(65\) | −1293.28 | −2.46788 | ||||||||
\(66\) | −936.517 | −1.74663 | ||||||||
\(67\) | 328.856 | 0.599644 | 0.299822 | − | 0.953995i | \(-0.403073\pi\) | ||||
0.299822 | + | 0.953995i | \(0.403073\pi\) | |||||||
\(68\) | 901.299 | 1.60733 | ||||||||
\(69\) | 471.472 | 0.822588 | ||||||||
\(70\) | 360.359 | 0.615303 | ||||||||
\(71\) | 832.806 | 1.39205 | 0.696027 | − | 0.718016i | \(-0.254949\pi\) | ||||
0.696027 | + | 0.718016i | \(0.254949\pi\) | |||||||
\(72\) | −175.890 | −0.287900 | ||||||||
\(73\) | −1049.14 | −1.68210 | −0.841048 | − | 0.540961i | \(-0.818061\pi\) | ||||
−0.841048 | + | 0.540961i | \(0.818061\pi\) | |||||||
\(74\) | 977.423 | 1.53545 | ||||||||
\(75\) | −1582.39 | −2.43624 | ||||||||
\(76\) | −9.26354 | −0.0139816 | ||||||||
\(77\) | 163.963 | 0.242667 | ||||||||
\(78\) | 2117.59 | 3.07397 | ||||||||
\(79\) | 808.341 | 1.15121 | 0.575605 | − | 0.817728i | \(-0.304767\pi\) | ||||
0.575605 | + | 0.817728i | \(0.304767\pi\) | |||||||
\(80\) | −1326.27 | −1.85351 | ||||||||
\(81\) | −519.295 | −0.712339 | ||||||||
\(82\) | 88.4608 | 0.119132 | ||||||||
\(83\) | 1038.31 | 1.37312 | 0.686560 | − | 0.727074i | \(-0.259120\pi\) | ||||
0.686560 | + | 0.727074i | \(0.259120\pi\) | |||||||
\(84\) | −267.140 | −0.346992 | ||||||||
\(85\) | 2469.26 | 3.15093 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −229.855 | −0.283254 | ||||||||
\(88\) | −166.624 | −0.201843 | ||||||||
\(89\) | 875.226 | 1.04240 | 0.521201 | − | 0.853434i | \(-0.325484\pi\) | ||||
0.521201 | + | 0.853434i | \(0.325484\pi\) | |||||||
\(90\) | 2308.44 | 2.70368 | ||||||||
\(91\) | −370.744 | −0.427082 | ||||||||
\(92\) | −401.846 | −0.455385 | ||||||||
\(93\) | −677.636 | −0.755565 | ||||||||
\(94\) | −4.13803 | −0.00454048 | ||||||||
\(95\) | −25.3790 | −0.0274088 | ||||||||
\(96\) | 1843.45 | 1.95986 | ||||||||
\(97\) | 88.7982 | 0.0929494 | 0.0464747 | − | 0.998919i | \(-0.485201\pi\) | ||||
0.0464747 | + | 0.998919i | \(0.485201\pi\) | |||||||
\(98\) | −1208.12 | −1.24530 | ||||||||
\(99\) | 1050.34 | 1.06630 | ||||||||
\(100\) | 1348.70 | 1.34870 | ||||||||
\(101\) | 1277.36 | 1.25843 | 0.629216 | − | 0.777230i | \(-0.283376\pi\) | ||||
0.629216 | + | 0.777230i | \(0.283376\pi\) | |||||||
\(102\) | −4043.11 | −3.92478 | ||||||||
\(103\) | −928.067 | −0.887817 | −0.443909 | − | 0.896072i | \(-0.646409\pi\) | ||||
−0.443909 | + | 0.896072i | \(0.646409\pi\) | |||||||
\(104\) | 376.760 | 0.355234 | ||||||||
\(105\) | −731.874 | −0.680225 | ||||||||
\(106\) | −255.757 | −0.234352 | ||||||||
\(107\) | −1194.14 | −1.07890 | −0.539448 | − | 0.842019i | \(-0.681367\pi\) | ||||
−0.539448 | + | 0.842019i | \(0.681367\pi\) | |||||||
\(108\) | −323.667 | −0.288378 | ||||||||
\(109\) | 671.431 | 0.590013 | 0.295007 | − | 0.955495i | \(-0.404678\pi\) | ||||
0.295007 | + | 0.955495i | \(0.404678\pi\) | |||||||
\(110\) | 2186.84 | 1.89552 | ||||||||
\(111\) | −1985.10 | −1.69746 | ||||||||
\(112\) | −380.199 | −0.320762 | ||||||||
\(113\) | −263.783 | −0.219598 | −0.109799 | − | 0.993954i | \(-0.535021\pi\) | ||||
−0.109799 | + | 0.993954i | \(0.535021\pi\) | |||||||
\(114\) | 41.5550 | 0.0341402 | ||||||||
\(115\) | −1100.93 | −0.892712 | ||||||||
\(116\) | 195.911 | 0.156809 | ||||||||
\(117\) | −2374.96 | −1.87663 | ||||||||
\(118\) | 1781.59 | 1.38990 | ||||||||
\(119\) | 707.859 | 0.545289 | ||||||||
\(120\) | 743.751 | 0.565791 | ||||||||
\(121\) | −335.987 | −0.252432 | ||||||||
\(122\) | −2218.89 | −1.64663 | ||||||||
\(123\) | −179.660 | −0.131702 | ||||||||
\(124\) | 577.564 | 0.418281 | ||||||||
\(125\) | 1428.46 | 1.02212 | ||||||||
\(126\) | 661.758 | 0.467890 | ||||||||
\(127\) | −1082.71 | −0.756499 | −0.378249 | − | 0.925704i | \(-0.623474\pi\) | ||||
−0.378249 | + | 0.925704i | \(0.623474\pi\) | |||||||
\(128\) | 666.053 | 0.459932 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4944.74 | −3.33602 | ||||||||
\(131\) | 1370.38 | 0.913972 | 0.456986 | − | 0.889474i | \(-0.348929\pi\) | ||||
0.456986 | + | 0.889474i | \(0.348929\pi\) | |||||||
\(132\) | −1621.14 | −1.06895 | ||||||||
\(133\) | −7.27537 | −0.00474327 | ||||||||
\(134\) | 1257.35 | 0.810586 | ||||||||
\(135\) | −886.739 | −0.565321 | ||||||||
\(136\) | −719.346 | −0.453555 | ||||||||
\(137\) | 1001.07 | 0.624283 | 0.312142 | − | 0.950036i | \(-0.398954\pi\) | ||||
0.312142 | + | 0.950036i | \(0.398954\pi\) | |||||||
\(138\) | 1802.63 | 1.11196 | ||||||||
\(139\) | −598.525 | −0.365225 | −0.182612 | − | 0.983185i | \(-0.558455\pi\) | ||||
−0.182612 | + | 0.983185i | \(0.558455\pi\) | |||||||
\(140\) | 623.793 | 0.376572 | ||||||||
\(141\) | 8.40416 | 0.00501956 | ||||||||
\(142\) | 3184.15 | 1.88175 | ||||||||
\(143\) | −2249.86 | −1.31568 | ||||||||
\(144\) | −2435.53 | −1.40945 | ||||||||
\(145\) | 536.730 | 0.307400 | ||||||||
\(146\) | −4011.30 | −2.27382 | ||||||||
\(147\) | 2453.65 | 1.37669 | ||||||||
\(148\) | 1691.95 | 0.939711 | ||||||||
\(149\) | −710.011 | −0.390378 | −0.195189 | − | 0.980766i | \(-0.562532\pi\) | ||||
−0.195189 | + | 0.980766i | \(0.562532\pi\) | |||||||
\(150\) | −6050.10 | −3.29326 | ||||||||
\(151\) | 1699.83 | 0.916093 | 0.458047 | − | 0.888928i | \(-0.348549\pi\) | ||||
0.458047 | + | 0.888928i | \(0.348549\pi\) | |||||||
\(152\) | 7.39343 | 0.00394531 | ||||||||
\(153\) | 4534.51 | 2.39603 | ||||||||
\(154\) | 626.899 | 0.328032 | ||||||||
\(155\) | 1582.33 | 0.819975 | ||||||||
\(156\) | 3665.61 | 1.88131 | ||||||||
\(157\) | 1361.92 | 0.692311 | 0.346155 | − | 0.938177i | \(-0.387487\pi\) | ||||
0.346155 | + | 0.938177i | \(0.387487\pi\) | |||||||
\(158\) | 3090.62 | 1.55618 | ||||||||
\(159\) | 519.430 | 0.259079 | ||||||||
\(160\) | −4304.61 | −2.12693 | ||||||||
\(161\) | −315.601 | −0.154490 | ||||||||
\(162\) | −1985.48 | −0.962924 | ||||||||
\(163\) | 2881.57 | 1.38467 | 0.692336 | − | 0.721575i | \(-0.256582\pi\) | ||||
0.692336 | + | 0.721575i | \(0.256582\pi\) | |||||||
\(164\) | 153.128 | 0.0729104 | ||||||||
\(165\) | −4441.38 | −2.09552 | ||||||||
\(166\) | 3969.86 | 1.85615 | ||||||||
\(167\) | 986.781 | 0.457242 | 0.228621 | − | 0.973515i | \(-0.426578\pi\) | ||||
0.228621 | + | 0.973515i | \(0.426578\pi\) | |||||||
\(168\) | 213.210 | 0.0979138 | ||||||||
\(169\) | 2890.23 | 1.31554 | ||||||||
\(170\) | 9440.98 | 4.25935 | ||||||||
\(171\) | −46.6056 | −0.0208422 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 595.012 | 0.261491 | 0.130746 | − | 0.991416i | \(-0.458263\pi\) | ||||
0.130746 | + | 0.991416i | \(0.458263\pi\) | |||||||
\(174\) | −878.830 | −0.382896 | ||||||||
\(175\) | 1059.24 | 0.457549 | ||||||||
\(176\) | −2307.24 | −0.988150 | ||||||||
\(177\) | −3618.32 | −1.53655 | ||||||||
\(178\) | 3346.34 | 1.40910 | ||||||||
\(179\) | 2320.31 | 0.968872 | 0.484436 | − | 0.874827i | \(-0.339025\pi\) | ||||
0.484436 | + | 0.874827i | \(0.339025\pi\) | |||||||
\(180\) | 3995.98 | 1.65468 | ||||||||
\(181\) | 1531.17 | 0.628792 | 0.314396 | − | 0.949292i | \(-0.398198\pi\) | ||||
0.314396 | + | 0.949292i | \(0.398198\pi\) | |||||||
\(182\) | −1417.50 | −0.577320 | ||||||||
\(183\) | 4506.48 | 1.82037 | ||||||||
\(184\) | 320.722 | 0.128500 | ||||||||
\(185\) | 4635.37 | 1.84216 | ||||||||
\(186\) | −2590.88 | −1.02136 | ||||||||
\(187\) | 4295.65 | 1.67983 | ||||||||
\(188\) | −7.16306 | −0.00277883 | ||||||||
\(189\) | −254.200 | −0.0978326 | ||||||||
\(190\) | −97.0343 | −0.0370506 | ||||||||
\(191\) | 1733.51 | 0.656714 | 0.328357 | − | 0.944554i | \(-0.393505\pi\) | ||||
0.328357 | + | 0.944554i | \(0.393505\pi\) | |||||||
\(192\) | 2504.47 | 0.941377 | ||||||||
\(193\) | 1109.49 | 0.413798 | 0.206899 | − | 0.978362i | \(-0.433663\pi\) | ||||
0.206899 | + | 0.978362i | \(0.433663\pi\) | |||||||
\(194\) | 339.512 | 0.125647 | ||||||||
\(195\) | 10042.6 | 3.68801 | ||||||||
\(196\) | −2091.30 | −0.762135 | ||||||||
\(197\) | 1579.78 | 0.571343 | 0.285672 | − | 0.958328i | \(-0.407783\pi\) | ||||
0.285672 | + | 0.958328i | \(0.407783\pi\) | |||||||
\(198\) | 4015.88 | 1.44140 | ||||||||
\(199\) | 3596.57 | 1.28118 | 0.640588 | − | 0.767885i | \(-0.278691\pi\) | ||||
0.640588 | + | 0.767885i | \(0.278691\pi\) | |||||||
\(200\) | −1076.43 | −0.380575 | ||||||||
\(201\) | −2553.62 | −0.896112 | ||||||||
\(202\) | 4883.85 | 1.70112 | ||||||||
\(203\) | 153.864 | 0.0531976 | ||||||||
\(204\) | −6998.74 | −2.40201 | ||||||||
\(205\) | 419.521 | 0.142930 | ||||||||
\(206\) | −3548.38 | −1.20013 | ||||||||
\(207\) | −2021.72 | −0.678838 | ||||||||
\(208\) | 5216.97 | 1.73910 | ||||||||
\(209\) | −44.1506 | −0.0146123 | ||||||||
\(210\) | −2798.25 | −0.919513 | ||||||||
\(211\) | 3927.29 | 1.28135 | 0.640676 | − | 0.767811i | \(-0.278654\pi\) | ||||
0.640676 | + | 0.767811i | \(0.278654\pi\) | |||||||
\(212\) | −442.722 | −0.143426 | ||||||||
\(213\) | −6466.88 | −2.08030 | ||||||||
\(214\) | −4565.68 | −1.45843 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 258.326 | 0.0813742 | ||||||||
\(217\) | 453.606 | 0.141902 | ||||||||
\(218\) | 2567.15 | 0.797567 | ||||||||
\(219\) | 8146.78 | 2.51374 | ||||||||
\(220\) | 3785.49 | 1.16008 | ||||||||
\(221\) | −9713.03 | −2.95642 | ||||||||
\(222\) | −7589.85 | −2.29458 | ||||||||
\(223\) | −249.842 | −0.0750255 | −0.0375127 | − | 0.999296i | \(-0.511943\pi\) | ||||
−0.0375127 | + | 0.999296i | \(0.511943\pi\) | |||||||
\(224\) | −1234.00 | −0.368079 | ||||||||
\(225\) | 6785.44 | 2.01050 | ||||||||
\(226\) | −1008.55 | −0.296848 | ||||||||
\(227\) | 5231.99 | 1.52978 | 0.764889 | − | 0.644163i | \(-0.222794\pi\) | ||||
0.764889 | + | 0.644163i | \(0.222794\pi\) | |||||||
\(228\) | 71.9330 | 0.0208942 | ||||||||
\(229\) | −948.401 | −0.273677 | −0.136839 | − | 0.990593i | \(-0.543694\pi\) | ||||
−0.136839 | + | 0.990593i | \(0.543694\pi\) | |||||||
\(230\) | −4209.28 | −1.20675 | ||||||||
\(231\) | −1273.20 | −0.362644 | ||||||||
\(232\) | −156.361 | −0.0442482 | ||||||||
\(233\) | 3452.38 | 0.970699 | 0.485350 | − | 0.874320i | \(-0.338692\pi\) | ||||
0.485350 | + | 0.874320i | \(0.338692\pi\) | |||||||
\(234\) | −9080.45 | −2.53678 | ||||||||
\(235\) | −19.6244 | −0.00544747 | ||||||||
\(236\) | 3083.98 | 0.850635 | ||||||||
\(237\) | −6276.91 | −1.72038 | ||||||||
\(238\) | 2706.43 | 0.737109 | ||||||||
\(239\) | −1033.96 | −0.279838 | −0.139919 | − | 0.990163i | \(-0.544684\pi\) | ||||
−0.139919 | + | 0.990163i | \(0.544684\pi\) | |||||||
\(240\) | 10298.7 | 2.76990 | ||||||||
\(241\) | 925.893 | 0.247477 | 0.123739 | − | 0.992315i | \(-0.460512\pi\) | ||||
0.123739 | + | 0.992315i | \(0.460512\pi\) | |||||||
\(242\) | −1284.62 | −0.341232 | ||||||||
\(243\) | 5352.82 | 1.41310 | ||||||||
\(244\) | −3840.97 | −1.00776 | ||||||||
\(245\) | −5729.46 | −1.49405 | ||||||||
\(246\) | −686.913 | −0.178032 | ||||||||
\(247\) | 99.8304 | 0.0257168 | ||||||||
\(248\) | −460.967 | −0.118030 | ||||||||
\(249\) | −8062.62 | −2.05200 | ||||||||
\(250\) | 5461.59 | 1.38168 | ||||||||
\(251\) | −1376.38 | −0.346120 | −0.173060 | − | 0.984911i | \(-0.555365\pi\) | ||||
−0.173060 | + | 0.984911i | \(0.555365\pi\) | |||||||
\(252\) | 1145.52 | 0.286354 | ||||||||
\(253\) | −1915.22 | −0.475925 | ||||||||
\(254\) | −4139.65 | −1.02262 | ||||||||
\(255\) | −19174.2 | −4.70877 | ||||||||
\(256\) | 5126.80 | 1.25166 | ||||||||
\(257\) | −582.311 | −0.141337 | −0.0706685 | − | 0.997500i | \(-0.522513\pi\) | ||||
−0.0706685 | + | 0.997500i | \(0.522513\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1328.82 | 0.318798 | ||||||||
\(260\) | −8559.50 | −2.04168 | ||||||||
\(261\) | 985.643 | 0.233754 | ||||||||
\(262\) | 5239.50 | 1.23549 | ||||||||
\(263\) | −130.662 | −0.0306348 | −0.0153174 | − | 0.999883i | \(-0.504876\pi\) | ||||
−0.0153174 | + | 0.999883i | \(0.504876\pi\) | |||||||
\(264\) | 1293.87 | 0.301636 | ||||||||
\(265\) | −1212.91 | −0.281164 | ||||||||
\(266\) | −27.8167 | −0.00641184 | ||||||||
\(267\) | −6796.28 | −1.55777 | ||||||||
\(268\) | 2176.51 | 0.496088 | ||||||||
\(269\) | −7250.60 | −1.64341 | −0.821704 | − | 0.569914i | \(-0.806976\pi\) | ||||
−0.821704 | + | 0.569914i | \(0.806976\pi\) | |||||||
\(270\) | −3390.36 | −0.764189 | ||||||||
\(271\) | 4219.91 | 0.945909 | 0.472955 | − | 0.881087i | \(-0.343187\pi\) | ||||
0.472955 | + | 0.881087i | \(0.343187\pi\) | |||||||
\(272\) | −9960.74 | −2.22044 | ||||||||
\(273\) | 2878.89 | 0.638235 | ||||||||
\(274\) | 3827.48 | 0.843892 | ||||||||
\(275\) | 6428.00 | 1.40954 | ||||||||
\(276\) | 3120.40 | 0.680530 | ||||||||
\(277\) | 397.916 | 0.0863121 | 0.0431560 | − | 0.999068i | \(-0.486259\pi\) | ||||
0.0431560 | + | 0.999068i | \(0.486259\pi\) | |||||||
\(278\) | −2288.40 | −0.493703 | ||||||||
\(279\) | 2905.77 | 0.623527 | ||||||||
\(280\) | −497.863 | −0.106261 | ||||||||
\(281\) | −5264.19 | −1.11756 | −0.558781 | − | 0.829315i | \(-0.688731\pi\) | ||||
−0.558781 | + | 0.829315i | \(0.688731\pi\) | |||||||
\(282\) | 32.1325 | 0.00678533 | ||||||||
\(283\) | −4632.62 | −0.973076 | −0.486538 | − | 0.873659i | \(-0.661740\pi\) | ||||
−0.486538 | + | 0.873659i | \(0.661740\pi\) | |||||||
\(284\) | 5511.86 | 1.15165 | ||||||||
\(285\) | 197.072 | 0.0409599 | ||||||||
\(286\) | −8602.12 | −1.77851 | ||||||||
\(287\) | 120.263 | 0.0247349 | ||||||||
\(288\) | −7904.91 | −1.61737 | ||||||||
\(289\) | 13632.1 | 2.77469 | ||||||||
\(290\) | 2052.14 | 0.415537 | ||||||||
\(291\) | −689.533 | −0.138904 | ||||||||
\(292\) | −6943.68 | −1.39160 | ||||||||
\(293\) | −519.305 | −0.103543 | −0.0517716 | − | 0.998659i | \(-0.516487\pi\) | ||||
−0.0517716 | + | 0.998659i | \(0.516487\pi\) | |||||||
\(294\) | 9381.29 | 1.86098 | ||||||||
\(295\) | 8449.08 | 1.66754 | ||||||||
\(296\) | −1350.38 | −0.265166 | ||||||||
\(297\) | −1542.62 | −0.301386 | ||||||||
\(298\) | −2714.66 | −0.527704 | ||||||||
\(299\) | 4330.58 | 0.837605 | ||||||||
\(300\) | −10472.9 | −2.01551 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6499.13 | 1.23835 | ||||||||
\(303\) | −9918.88 | −1.88061 | ||||||||
\(304\) | 102.376 | 0.0193148 | ||||||||
\(305\) | −10523.0 | −1.97555 | ||||||||
\(306\) | 17337.3 | 3.23891 | ||||||||
\(307\) | 1193.72 | 0.221920 | 0.110960 | − | 0.993825i | \(-0.464607\pi\) | ||||
0.110960 | + | 0.993825i | \(0.464607\pi\) | |||||||
\(308\) | 1085.18 | 0.200759 | ||||||||
\(309\) | 7206.60 | 1.32676 | ||||||||
\(310\) | 6049.90 | 1.10842 | ||||||||
\(311\) | −2588.37 | −0.471938 | −0.235969 | − | 0.971761i | \(-0.575826\pi\) | ||||
−0.235969 | + | 0.971761i | \(0.575826\pi\) | |||||||
\(312\) | −2925.60 | −0.530865 | ||||||||
\(313\) | 423.736 | 0.0765208 | 0.0382604 | − | 0.999268i | \(-0.487818\pi\) | ||||
0.0382604 | + | 0.999268i | \(0.487818\pi\) | |||||||
\(314\) | 5207.16 | 0.935851 | ||||||||
\(315\) | 3138.35 | 0.561353 | ||||||||
\(316\) | 5349.95 | 0.952399 | ||||||||
\(317\) | 1368.80 | 0.242522 | 0.121261 | − | 0.992621i | \(-0.461306\pi\) | ||||
0.121261 | + | 0.992621i | \(0.461306\pi\) | |||||||
\(318\) | 1985.99 | 0.350217 | ||||||||
\(319\) | 933.723 | 0.163882 | ||||||||
\(320\) | −5848.13 | −1.02163 | ||||||||
\(321\) | 9272.71 | 1.61231 | ||||||||
\(322\) | −1206.67 | −0.208836 | ||||||||
\(323\) | −190.606 | −0.0328347 | ||||||||
\(324\) | −3436.92 | −0.589320 | ||||||||
\(325\) | −14534.6 | −2.48072 | ||||||||
\(326\) | 11017.4 | 1.87177 | ||||||||
\(327\) | −5213.78 | −0.881720 | ||||||||
\(328\) | −122.215 | −0.0205738 | ||||||||
\(329\) | −5.62570 | −0.000942720 0 | ||||||||
\(330\) | −16981.2 | −2.83268 | ||||||||
\(331\) | −2454.58 | −0.407601 | −0.203801 | − | 0.979012i | \(-0.565329\pi\) | ||||
−0.203801 | + | 0.979012i | \(0.565329\pi\) | |||||||
\(332\) | 6871.95 | 1.13599 | ||||||||
\(333\) | 8512.33 | 1.40082 | ||||||||
\(334\) | 3772.87 | 0.618090 | ||||||||
\(335\) | 5962.91 | 0.972504 | ||||||||
\(336\) | 2952.31 | 0.479350 | ||||||||
\(337\) | 7409.08 | 1.19762 | 0.598810 | − | 0.800891i | \(-0.295640\pi\) | ||||
0.598810 | + | 0.800891i | \(0.295640\pi\) | |||||||
\(338\) | 11050.5 | 1.77831 | ||||||||
\(339\) | 2048.32 | 0.328169 | ||||||||
\(340\) | 16342.6 | 2.60677 | ||||||||
\(341\) | 2752.71 | 0.437148 | ||||||||
\(342\) | −178.192 | −0.0281741 | ||||||||
\(343\) | −3425.36 | −0.539218 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8548.87 | 1.33407 | ||||||||
\(346\) | 2274.97 | 0.353478 | ||||||||
\(347\) | −10125.5 | −1.56647 | −0.783237 | − | 0.621723i | \(-0.786433\pi\) | ||||
−0.783237 | + | 0.621723i | \(0.786433\pi\) | |||||||
\(348\) | −1521.28 | −0.234337 | ||||||||
\(349\) | 67.8059 | 0.0103999 | 0.00519995 | − | 0.999986i | \(-0.498345\pi\) | ||||
0.00519995 | + | 0.999986i | \(0.498345\pi\) | |||||||
\(350\) | 4049.90 | 0.618504 | ||||||||
\(351\) | 3488.06 | 0.530424 | ||||||||
\(352\) | −7488.51 | −1.13392 | ||||||||
\(353\) | −6725.07 | −1.01399 | −0.506996 | − | 0.861948i | \(-0.669244\pi\) | ||||
−0.506996 | + | 0.861948i | \(0.669244\pi\) | |||||||
\(354\) | −13834.3 | −2.07708 | ||||||||
\(355\) | 15100.7 | 2.25764 | ||||||||
\(356\) | 5792.62 | 0.862383 | ||||||||
\(357\) | −5496.65 | −0.814883 | ||||||||
\(358\) | 8871.49 | 1.30970 | ||||||||
\(359\) | −9260.90 | −1.36148 | −0.680740 | − | 0.732525i | \(-0.738342\pi\) | ||||
−0.680740 | + | 0.732525i | \(0.738342\pi\) | |||||||
\(360\) | −3189.28 | −0.466916 | ||||||||
\(361\) | −6857.04 | −0.999714 | ||||||||
\(362\) | 5854.30 | 0.849987 | ||||||||
\(363\) | 2609.00 | 0.377236 | ||||||||
\(364\) | −2453.74 | −0.353327 | ||||||||
\(365\) | −19023.4 | −2.72802 | ||||||||
\(366\) | 17230.1 | 2.46074 | ||||||||
\(367\) | 1180.46 | 0.167901 | 0.0839504 | − | 0.996470i | \(-0.473246\pi\) | ||||
0.0839504 | + | 0.996470i | \(0.473246\pi\) | |||||||
\(368\) | 4441.02 | 0.629088 | ||||||||
\(369\) | 770.401 | 0.108687 | ||||||||
\(370\) | 17722.9 | 2.49019 | ||||||||
\(371\) | −347.704 | −0.0486573 | ||||||||
\(372\) | −4484.88 | −0.625082 | ||||||||
\(373\) | −6144.38 | −0.852933 | −0.426466 | − | 0.904503i | \(-0.640242\pi\) | ||||
−0.426466 | + | 0.904503i | \(0.640242\pi\) | |||||||
\(374\) | 16424.0 | 2.27076 | ||||||||
\(375\) | −11092.2 | −1.52747 | ||||||||
\(376\) | 5.71699 | 0.000784126 0 | ||||||||
\(377\) | −2111.27 | −0.288425 | ||||||||
\(378\) | −971.911 | −0.132248 | ||||||||
\(379\) | −8452.78 | −1.14562 | −0.572810 | − | 0.819688i | \(-0.694147\pi\) | ||||
−0.572810 | + | 0.819688i | \(0.694147\pi\) | |||||||
\(380\) | −167.969 | −0.0226754 | ||||||||
\(381\) | 8407.46 | 1.13052 | ||||||||
\(382\) | 6627.91 | 0.887731 | ||||||||
\(383\) | 3796.02 | 0.506443 | 0.253221 | − | 0.967408i | \(-0.418510\pi\) | ||||
0.253221 | + | 0.967408i | \(0.418510\pi\) | |||||||
\(384\) | −5172.02 | −0.687326 | ||||||||
\(385\) | 2973.03 | 0.393558 | ||||||||
\(386\) | 4242.04 | 0.559363 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 587.705 | 0.0768974 | ||||||||
\(389\) | 12372.4 | 1.61261 | 0.806303 | − | 0.591502i | \(-0.201465\pi\) | ||||
0.806303 | + | 0.591502i | \(0.201465\pi\) | |||||||
\(390\) | 38396.8 | 4.98537 | ||||||||
\(391\) | −8268.36 | −1.06943 | ||||||||
\(392\) | 1669.11 | 0.215058 | ||||||||
\(393\) | −10641.2 | −1.36585 | ||||||||
\(394\) | 6040.14 | 0.772329 | ||||||||
\(395\) | 14657.1 | 1.86703 | ||||||||
\(396\) | 6951.61 | 0.882150 | ||||||||
\(397\) | −12525.5 | −1.58346 | −0.791731 | − | 0.610869i | \(-0.790820\pi\) | ||||
−0.791731 | + | 0.610869i | \(0.790820\pi\) | |||||||
\(398\) | 13751.1 | 1.73186 | ||||||||
\(399\) | 56.4945 | 0.00708837 | ||||||||
\(400\) | −14905.2 | −1.86316 | ||||||||
\(401\) | 8542.42 | 1.06381 | 0.531905 | − | 0.846804i | \(-0.321476\pi\) | ||||
0.531905 | + | 0.846804i | \(0.321476\pi\) | |||||||
\(402\) | −9763.53 | −1.21135 | ||||||||
\(403\) | −6224.24 | −0.769358 | ||||||||
\(404\) | 8454.09 | 1.04111 | ||||||||
\(405\) | −9416.01 | −1.15527 | ||||||||
\(406\) | 588.284 | 0.0719114 | ||||||||
\(407\) | 8063.92 | 0.982098 | ||||||||
\(408\) | 5585.85 | 0.677796 | ||||||||
\(409\) | −9148.33 | −1.10601 | −0.553003 | − | 0.833180i | \(-0.686518\pi\) | ||||
−0.553003 | + | 0.833180i | \(0.686518\pi\) | |||||||
\(410\) | 1604.00 | 0.193209 | ||||||||
\(411\) | −7773.45 | −0.932934 | ||||||||
\(412\) | −6142.34 | −0.734494 | ||||||||
\(413\) | 2422.08 | 0.288579 | ||||||||
\(414\) | −7729.86 | −0.917638 | ||||||||
\(415\) | 18826.9 | 2.22693 | ||||||||
\(416\) | 16932.5 | 1.99564 | ||||||||
\(417\) | 4647.65 | 0.545794 | ||||||||
\(418\) | −168.806 | −0.0197525 | ||||||||
\(419\) | 8781.89 | 1.02392 | 0.511961 | − | 0.859009i | \(-0.328919\pi\) | ||||
0.511961 | + | 0.859009i | \(0.328919\pi\) | |||||||
\(420\) | −4843.86 | −0.562752 | ||||||||
\(421\) | −7723.93 | −0.894160 | −0.447080 | − | 0.894494i | \(-0.647536\pi\) | ||||
−0.447080 | + | 0.894494i | \(0.647536\pi\) | |||||||
\(422\) | 15015.6 | 1.73210 | ||||||||
\(423\) | −36.0379 | −0.00414237 | ||||||||
\(424\) | 353.346 | 0.0404717 | ||||||||
\(425\) | 27750.8 | 3.16732 | ||||||||
\(426\) | −24725.5 | −2.81210 | ||||||||
\(427\) | −3016.61 | −0.341883 | ||||||||
\(428\) | −7903.33 | −0.892575 | ||||||||
\(429\) | 17470.5 | 1.96617 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5925.41 | −0.662221 | −0.331110 | − | 0.943592i | \(-0.607423\pi\) | ||||
−0.331110 | + | 0.943592i | \(0.607423\pi\) | |||||||
\(432\) | 3577.02 | 0.398378 | ||||||||
\(433\) | −3909.25 | −0.433871 | −0.216936 | − | 0.976186i | \(-0.569606\pi\) | ||||
−0.216936 | + | 0.976186i | \(0.569606\pi\) | |||||||
\(434\) | 1734.32 | 0.191820 | ||||||||
\(435\) | −4167.80 | −0.459381 | ||||||||
\(436\) | 4443.82 | 0.488120 | ||||||||
\(437\) | 84.9821 | 0.00930262 | ||||||||
\(438\) | 31148.4 | 3.39801 | ||||||||
\(439\) | −4441.26 | −0.482846 | −0.241423 | − | 0.970420i | \(-0.577614\pi\) | ||||
−0.241423 | + | 0.970420i | \(0.577614\pi\) | |||||||
\(440\) | −3021.28 | −0.327350 | ||||||||
\(441\) | −10521.5 | −1.13611 | ||||||||
\(442\) | −37136.9 | −3.99643 | ||||||||
\(443\) | −7712.27 | −0.827136 | −0.413568 | − | 0.910473i | \(-0.635718\pi\) | ||||
−0.413568 | + | 0.910473i | \(0.635718\pi\) | |||||||
\(444\) | −13138.3 | −1.40431 | ||||||||
\(445\) | 15869.9 | 1.69057 | ||||||||
\(446\) | −955.248 | −0.101418 | ||||||||
\(447\) | 5513.35 | 0.583384 | ||||||||
\(448\) | −1676.48 | −0.176799 | ||||||||
\(449\) | 1293.48 | 0.135954 | 0.0679769 | − | 0.997687i | \(-0.478346\pi\) | ||||
0.0679769 | + | 0.997687i | \(0.478346\pi\) | |||||||
\(450\) | 25943.5 | 2.71775 | ||||||||
\(451\) | 729.818 | 0.0761991 | ||||||||
\(452\) | −1745.83 | −0.181674 | ||||||||
\(453\) | −13199.5 | −1.36902 | ||||||||
\(454\) | 20004.0 | 2.06792 | ||||||||
\(455\) | −6722.43 | −0.692643 | ||||||||
\(456\) | −57.4113 | −0.00589590 | ||||||||
\(457\) | −5561.70 | −0.569290 | −0.284645 | − | 0.958633i | \(-0.591876\pi\) | ||||
−0.284645 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(458\) | −3626.12 | −0.369951 | ||||||||
\(459\) | −6659.74 | −0.677233 | ||||||||
\(460\) | −7286.40 | −0.738543 | ||||||||
\(461\) | −15913.7 | −1.60776 | −0.803878 | − | 0.594795i | \(-0.797233\pi\) | ||||
−0.803878 | + | 0.594795i | \(0.797233\pi\) | |||||||
\(462\) | −4867.98 | −0.490214 | ||||||||
\(463\) | 15646.3 | 1.57051 | 0.785256 | − | 0.619172i | \(-0.212532\pi\) | ||||
0.785256 | + | 0.619172i | \(0.212532\pi\) | |||||||
\(464\) | −2165.12 | −0.216623 | ||||||||
\(465\) | −12287.1 | −1.22538 | ||||||||
\(466\) | 13199.8 | 1.31217 | ||||||||
\(467\) | 9463.86 | 0.937762 | 0.468881 | − | 0.883261i | \(-0.344657\pi\) | ||||
0.468881 | + | 0.883261i | \(0.344657\pi\) | |||||||
\(468\) | −15718.5 | −1.55254 | ||||||||
\(469\) | 1709.38 | 0.168298 | ||||||||
\(470\) | −75.0320 | −0.00736376 | ||||||||
\(471\) | −10575.5 | −1.03459 | ||||||||
\(472\) | −2461.39 | −0.240031 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −23999.2 | −2.32557 | ||||||||
\(475\) | −285.223 | −0.0275514 | ||||||||
\(476\) | 4684.91 | 0.451119 | ||||||||
\(477\) | −2227.37 | −0.213804 | ||||||||
\(478\) | −3953.24 | −0.378278 | ||||||||
\(479\) | 3861.05 | 0.368301 | 0.184150 | − | 0.982898i | \(-0.441047\pi\) | ||||
0.184150 | + | 0.982898i | \(0.441047\pi\) | |||||||
\(480\) | 33426.0 | 3.17850 | ||||||||
\(481\) | −18233.6 | −1.72844 | ||||||||
\(482\) | 3540.06 | 0.334534 | ||||||||
\(483\) | 2450.69 | 0.230870 | ||||||||
\(484\) | −2223.71 | −0.208838 | ||||||||
\(485\) | 1610.12 | 0.150746 | ||||||||
\(486\) | 20466.0 | 1.91020 | ||||||||
\(487\) | 3513.12 | 0.326888 | 0.163444 | − | 0.986553i | \(-0.447740\pi\) | ||||
0.163444 | + | 0.986553i | \(0.447740\pi\) | |||||||
\(488\) | 3065.56 | 0.284368 | ||||||||
\(489\) | −22375.8 | −2.06926 | ||||||||
\(490\) | −21906.1 | −2.01962 | ||||||||
\(491\) | −19277.8 | −1.77188 | −0.885940 | − | 0.463799i | \(-0.846486\pi\) | ||||
−0.885940 | + | 0.463799i | \(0.846486\pi\) | |||||||
\(492\) | −1189.07 | −0.108958 | ||||||||
\(493\) | 4031.04 | 0.368254 | ||||||||
\(494\) | 381.692 | 0.0347635 | ||||||||
\(495\) | 19045.1 | 1.72932 | ||||||||
\(496\) | −6382.98 | −0.577831 | ||||||||
\(497\) | 4328.89 | 0.390699 | ||||||||
\(498\) | −30826.7 | −2.77385 | ||||||||
\(499\) | −7626.32 | −0.684170 | −0.342085 | − | 0.939669i | \(-0.611133\pi\) | ||||
−0.342085 | + | 0.939669i | \(0.611133\pi\) | |||||||
\(500\) | 9454.17 | 0.845607 | ||||||||
\(501\) | −7662.53 | −0.683306 | ||||||||
\(502\) | −5262.45 | −0.467878 | ||||||||
\(503\) | 9139.85 | 0.810190 | 0.405095 | − | 0.914275i | \(-0.367238\pi\) | ||||
0.405095 | + | 0.914275i | \(0.367238\pi\) | |||||||
\(504\) | −914.267 | −0.0808029 | ||||||||
\(505\) | 23161.4 | 2.04093 | ||||||||
\(506\) | −7322.68 | −0.643345 | ||||||||
\(507\) | −22443.1 | −1.96595 | ||||||||
\(508\) | −7165.86 | −0.625854 | ||||||||
\(509\) | −13821.6 | −1.20360 | −0.601799 | − | 0.798647i | \(-0.705549\pi\) | ||||
−0.601799 | + | 0.798647i | \(0.705549\pi\) | |||||||
\(510\) | −73310.8 | −6.36521 | ||||||||
\(511\) | −5453.40 | −0.472103 | ||||||||
\(512\) | 14273.4 | 1.23203 | ||||||||
\(513\) | 68.4488 | 0.00589101 | ||||||||
\(514\) | −2226.41 | −0.191056 | ||||||||
\(515\) | −16828.0 | −1.43986 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.1396 | −0.00290417 | ||||||||
\(518\) | 5080.60 | 0.430944 | ||||||||
\(519\) | −4620.37 | −0.390774 | ||||||||
\(520\) | 6831.52 | 0.576119 | ||||||||
\(521\) | −10933.9 | −0.919427 | −0.459714 | − | 0.888067i | \(-0.652048\pi\) | ||||
−0.459714 | + | 0.888067i | \(0.652048\pi\) | |||||||
\(522\) | 3768.51 | 0.315983 | ||||||||
\(523\) | −15350.3 | −1.28340 | −0.641701 | − | 0.766955i | \(-0.721771\pi\) | ||||
−0.641701 | + | 0.766955i | \(0.721771\pi\) | |||||||
\(524\) | 9069.74 | 0.756132 | ||||||||
\(525\) | −8225.18 | −0.683764 | ||||||||
\(526\) | −499.573 | −0.0414115 | ||||||||
\(527\) | 11883.9 | 0.982299 | ||||||||
\(528\) | 17916.1 | 1.47670 | ||||||||
\(529\) | −8480.53 | −0.697011 | ||||||||
\(530\) | −4637.45 | −0.380072 | ||||||||
\(531\) | 15515.7 | 1.26803 | ||||||||
\(532\) | −48.1515 | −0.00392412 | ||||||||
\(533\) | −1650.22 | −0.134107 | ||||||||
\(534\) | −25984.9 | −2.10576 | ||||||||
\(535\) | −21652.5 | −1.74976 | ||||||||
\(536\) | −1737.12 | −0.139985 | ||||||||
\(537\) | −18017.6 | −1.44789 | ||||||||
\(538\) | −27722.0 | −2.22152 | ||||||||
\(539\) | −9967.26 | −0.796512 | ||||||||
\(540\) | −5868.82 | −0.467692 | ||||||||
\(541\) | 21902.0 | 1.74055 | 0.870277 | − | 0.492562i | \(-0.163940\pi\) | ||||
0.870277 | + | 0.492562i | \(0.163940\pi\) | |||||||
\(542\) | 16134.4 | 1.27866 | ||||||||
\(543\) | −11889.8 | −0.939671 | ||||||||
\(544\) | −32329.2 | −2.54798 | ||||||||
\(545\) | 12174.6 | 0.956884 | ||||||||
\(546\) | 11007.1 | 0.862752 | ||||||||
\(547\) | 3326.60 | 0.260028 | 0.130014 | − | 0.991512i | \(-0.458498\pi\) | ||||
0.130014 | + | 0.991512i | \(0.458498\pi\) | |||||||
\(548\) | 6625.48 | 0.516472 | ||||||||
\(549\) | −19324.2 | −1.50226 | ||||||||
\(550\) | 24576.8 | 1.90538 | ||||||||
\(551\) | −41.4310 | −0.00320331 | ||||||||
\(552\) | −2490.46 | −0.192031 | ||||||||
\(553\) | 4201.73 | 0.323102 | ||||||||
\(554\) | 1521.39 | 0.116675 | ||||||||
\(555\) | −35994.5 | −2.75294 | ||||||||
\(556\) | −3961.29 | −0.302152 | ||||||||
\(557\) | −16723.9 | −1.27220 | −0.636098 | − | 0.771608i | \(-0.719453\pi\) | ||||
−0.636098 | + | 0.771608i | \(0.719453\pi\) | |||||||
\(558\) | 11109.9 | 0.842870 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6893.87 | −0.520213 | ||||||||
\(561\) | −33356.4 | −2.51035 | ||||||||
\(562\) | −20127.1 | −1.51070 | ||||||||
\(563\) | −8139.07 | −0.609273 | −0.304637 | − | 0.952469i | \(-0.598535\pi\) | ||||
−0.304637 | + | 0.952469i | \(0.598535\pi\) | |||||||
\(564\) | 55.6223 | 0.00415270 | ||||||||
\(565\) | −4782.98 | −0.356145 | ||||||||
\(566\) | −17712.4 | −1.31538 | ||||||||
\(567\) | −2699.27 | −0.199927 | ||||||||
\(568\) | −4399.14 | −0.324971 | ||||||||
\(569\) | −10529.4 | −0.775771 | −0.387885 | − | 0.921708i | \(-0.626794\pi\) | ||||
−0.387885 | + | 0.921708i | \(0.626794\pi\) | |||||||
\(570\) | 753.488 | 0.0553686 | ||||||||
\(571\) | 21060.5 | 1.54353 | 0.771765 | − | 0.635908i | \(-0.219374\pi\) | ||||
0.771765 | + | 0.635908i | \(0.219374\pi\) | |||||||
\(572\) | −14890.5 | −1.08847 | ||||||||
\(573\) | −13461.0 | −0.981398 | ||||||||
\(574\) | 459.816 | 0.0334361 | ||||||||
\(575\) | −12372.8 | −0.897356 | ||||||||
\(576\) | −10739.4 | −0.776868 | ||||||||
\(577\) | −832.149 | −0.0600395 | −0.0300198 | − | 0.999549i | \(-0.509557\pi\) | ||||
−0.0300198 | + | 0.999549i | \(0.509557\pi\) | |||||||
\(578\) | 52120.9 | 3.75077 | ||||||||
\(579\) | −8615.40 | −0.618383 | ||||||||
\(580\) | 3552.31 | 0.254313 | ||||||||
\(581\) | 5397.07 | 0.385384 | ||||||||
\(582\) | −2636.37 | −0.187768 | ||||||||
\(583\) | −2110.04 | −0.149895 | ||||||||
\(584\) | 5541.90 | 0.392681 | ||||||||
\(585\) | −43063.5 | −3.04352 | ||||||||
\(586\) | −1985.51 | −0.139967 | ||||||||
\(587\) | −21831.1 | −1.53504 | −0.767519 | − | 0.641027i | \(-0.778509\pi\) | ||||
−0.767519 | + | 0.641027i | \(0.778509\pi\) | |||||||
\(588\) | 16239.3 | 1.13894 | ||||||||
\(589\) | −122.143 | −0.00854466 | ||||||||
\(590\) | 32304.2 | 2.25414 | ||||||||
\(591\) | −12267.3 | −0.853820 | ||||||||
\(592\) | −18698.6 | −1.29816 | ||||||||
\(593\) | 22576.3 | 1.56340 | 0.781702 | − | 0.623653i | \(-0.214352\pi\) | ||||
0.781702 | + | 0.623653i | \(0.214352\pi\) | |||||||
\(594\) | −5898.04 | −0.407407 | ||||||||
\(595\) | 12835.1 | 0.884350 | ||||||||
\(596\) | −4699.15 | −0.322961 | ||||||||
\(597\) | −27928.0 | −1.91460 | ||||||||
\(598\) | 16557.6 | 1.13226 | ||||||||
\(599\) | −2926.37 | −0.199613 | −0.0998065 | − | 0.995007i | \(-0.531822\pi\) | ||||
−0.0998065 | + | 0.995007i | \(0.531822\pi\) | |||||||
\(600\) | 8358.66 | 0.568734 | ||||||||
\(601\) | 26815.7 | 1.82003 | 0.910013 | − | 0.414579i | \(-0.136071\pi\) | ||||
0.910013 | + | 0.414579i | \(0.136071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10950.2 | 0.739513 | ||||||||
\(604\) | 11250.2 | 0.757887 | ||||||||
\(605\) | −6092.22 | −0.409395 | ||||||||
\(606\) | −37923.9 | −2.54217 | ||||||||
\(607\) | 19629.5 | 1.31258 | 0.656290 | − | 0.754508i | \(-0.272125\pi\) | ||||
0.656290 | + | 0.754508i | \(0.272125\pi\) | |||||||
\(608\) | 332.279 | 0.0221640 | ||||||||
\(609\) | −1194.78 | −0.0794989 | ||||||||
\(610\) | −40233.6 | −2.67051 | ||||||||
\(611\) | 77.1941 | 0.00511120 | ||||||||
\(612\) | 30011.3 | 1.98225 | ||||||||
\(613\) | −14870.5 | −0.979793 | −0.489896 | − | 0.871781i | \(-0.662965\pi\) | ||||
−0.489896 | + | 0.871781i | \(0.662965\pi\) | |||||||
\(614\) | 4564.09 | 0.299986 | ||||||||
\(615\) | −3257.65 | −0.213595 | ||||||||
\(616\) | −866.106 | −0.0566500 | ||||||||
\(617\) | 3238.39 | 0.211301 | 0.105650 | − | 0.994403i | \(-0.466308\pi\) | ||||
0.105650 | + | 0.994403i | \(0.466308\pi\) | |||||||
\(618\) | 27553.7 | 1.79349 | ||||||||
\(619\) | 20133.6 | 1.30733 | 0.653666 | − | 0.756783i | \(-0.273230\pi\) | ||||
0.653666 | + | 0.756783i | \(0.273230\pi\) | |||||||
\(620\) | 10472.6 | 0.678368 | ||||||||
\(621\) | 2969.26 | 0.191872 | ||||||||
\(622\) | −9896.37 | −0.637955 | ||||||||
\(623\) | 4549.39 | 0.292564 | ||||||||
\(624\) | −40510.7 | −2.59892 | ||||||||
\(625\) | 428.784 | 0.0274422 | ||||||||
\(626\) | 1620.12 | 0.103439 | ||||||||
\(627\) | 342.837 | 0.0218367 | ||||||||
\(628\) | 9013.75 | 0.572751 | ||||||||
\(629\) | 34813.4 | 2.20684 | ||||||||
\(630\) | 11999.2 | 0.758824 | ||||||||
\(631\) | −6227.34 | −0.392879 | −0.196439 | − | 0.980516i | \(-0.562938\pi\) | ||||
−0.196439 | + | 0.980516i | \(0.562938\pi\) | |||||||
\(632\) | −4269.91 | −0.268747 | ||||||||
\(633\) | −30496.0 | −1.91486 | ||||||||
\(634\) | 5233.47 | 0.327835 | ||||||||
\(635\) | −19632.1 | −1.22689 | ||||||||
\(636\) | 3437.81 | 0.214337 | ||||||||
\(637\) | 22537.3 | 1.40182 | ||||||||
\(638\) | 3570.00 | 0.221532 | ||||||||
\(639\) | 27730.6 | 1.71676 | ||||||||
\(640\) | 12077.1 | 0.745919 | ||||||||
\(641\) | 12495.3 | 0.769945 | 0.384973 | − | 0.922928i | \(-0.374211\pi\) | ||||
0.384973 | + | 0.922928i | \(0.374211\pi\) | |||||||
\(642\) | 35453.3 | 2.17949 | ||||||||
\(643\) | 4940.90 | 0.303033 | 0.151516 | − | 0.988455i | \(-0.451584\pi\) | ||||
0.151516 | + | 0.988455i | \(0.451584\pi\) | |||||||
\(644\) | −2088.78 | −0.127810 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −728.764 | −0.0443852 | ||||||||
\(647\) | 6624.13 | 0.402506 | 0.201253 | − | 0.979539i | \(-0.435499\pi\) | ||||
0.201253 | + | 0.979539i | \(0.435499\pi\) | |||||||
\(648\) | 2743.08 | 0.166294 | ||||||||
\(649\) | 14698.4 | 0.889004 | ||||||||
\(650\) | −55571.6 | −3.35338 | ||||||||
\(651\) | −3522.32 | −0.212060 | ||||||||
\(652\) | 19071.4 | 1.14554 | ||||||||
\(653\) | −4497.38 | −0.269519 | −0.134760 | − | 0.990878i | \(-0.543026\pi\) | ||||
−0.134760 | + | 0.990878i | \(0.543026\pi\) | |||||||
\(654\) | −19934.4 | −1.19189 | ||||||||
\(655\) | 24848.1 | 1.48228 | ||||||||
\(656\) | −1692.30 | −0.100722 | ||||||||
\(657\) | −34934.2 | −2.07445 | ||||||||
\(658\) | −21.5093 | −0.00127435 | ||||||||
\(659\) | 26308.3 | 1.55512 | 0.777562 | − | 0.628806i | \(-0.216456\pi\) | ||||
0.777562 | + | 0.628806i | \(0.216456\pi\) | |||||||
\(660\) | −29395.0 | −1.73363 | ||||||||
\(661\) | 15971.0 | 0.939788 | 0.469894 | − | 0.882723i | \(-0.344292\pi\) | ||||
0.469894 | + | 0.882723i | \(0.344292\pi\) | |||||||
\(662\) | −9384.86 | −0.550986 | ||||||||
\(663\) | 75423.3 | 4.41810 | ||||||||
\(664\) | −5484.66 | −0.320551 | ||||||||
\(665\) | −131.919 | −0.00769264 | ||||||||
\(666\) | 32546.1 | 1.89360 | ||||||||
\(667\) | −1797.25 | −0.104333 | ||||||||
\(668\) | 6530.94 | 0.378278 | ||||||||
\(669\) | 1940.07 | 0.112119 | ||||||||
\(670\) | 22798.6 | 1.31461 | ||||||||
\(671\) | −18306.3 | −1.05321 | ||||||||
\(672\) | 9582.18 | 0.550061 | ||||||||
\(673\) | 3279.61 | 0.187845 | 0.0939226 | − | 0.995580i | \(-0.470059\pi\) | ||||
0.0939226 | + | 0.995580i | \(0.470059\pi\) | |||||||
\(674\) | 28327.9 | 1.61892 | ||||||||
\(675\) | −9965.63 | −0.568263 | ||||||||
\(676\) | 19128.8 | 1.08835 | ||||||||
\(677\) | −33062.8 | −1.87697 | −0.938483 | − | 0.345325i | \(-0.887769\pi\) | ||||
−0.938483 | + | 0.345325i | \(0.887769\pi\) | |||||||
\(678\) | 7831.55 | 0.443612 | ||||||||
\(679\) | 461.570 | 0.0260875 | ||||||||
\(680\) | −13043.4 | −0.735576 | ||||||||
\(681\) | −40627.3 | −2.28611 | ||||||||
\(682\) | 10524.7 | 0.590927 | ||||||||
\(683\) | −28185.8 | −1.57906 | −0.789531 | − | 0.613711i | \(-0.789676\pi\) | ||||
−0.789531 | + | 0.613711i | \(0.789676\pi\) | |||||||
\(684\) | −308.456 | −0.0172429 | ||||||||
\(685\) | 18151.6 | 1.01246 | ||||||||
\(686\) | −13096.5 | −0.728903 | ||||||||
\(687\) | 7364.49 | 0.408985 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4771.08 | 0.263808 | ||||||||
\(690\) | 32685.8 | 1.80337 | ||||||||
\(691\) | −20756.6 | −1.14272 | −0.571359 | − | 0.820700i | \(-0.693584\pi\) | ||||
−0.571359 | + | 0.820700i | \(0.693584\pi\) | |||||||
\(692\) | 3938.05 | 0.216332 | ||||||||
\(693\) | 5459.63 | 0.299270 | ||||||||
\(694\) | −38714.0 | −2.11753 | ||||||||
\(695\) | −10852.6 | −0.592322 | ||||||||
\(696\) | 1214.17 | 0.0661248 | ||||||||
\(697\) | 3150.75 | 0.171224 | ||||||||
\(698\) | 259.249 | 0.0140584 | ||||||||
\(699\) | −26808.3 | −1.45062 | ||||||||
\(700\) | 7010.50 | 0.378532 | ||||||||
\(701\) | −32953.3 | −1.77550 | −0.887751 | − | 0.460324i | \(-0.847733\pi\) | ||||
−0.887751 | + | 0.460324i | \(0.847733\pi\) | |||||||
\(702\) | 13336.3 | 0.717016 | ||||||||
\(703\) | −357.812 | −0.0191965 | ||||||||
\(704\) | −10173.7 | −0.544653 | ||||||||
\(705\) | 152.387 | 0.00814073 | ||||||||
\(706\) | −25712.7 | −1.37069 | ||||||||
\(707\) | 6639.64 | 0.353196 | ||||||||
\(708\) | −23947.6 | −1.27120 | ||||||||
\(709\) | 10596.1 | 0.561276 | 0.280638 | − | 0.959814i | \(-0.409454\pi\) | ||||
0.280638 | + | 0.959814i | \(0.409454\pi\) | |||||||
\(710\) | 57736.0 | 3.05182 | ||||||||
\(711\) | 26916.0 | 1.41973 | ||||||||
\(712\) | −4623.22 | −0.243346 | ||||||||
\(713\) | −5298.47 | −0.278302 | ||||||||
\(714\) | −21015.9 | −1.10154 | ||||||||
\(715\) | −40795.1 | −2.13378 | ||||||||
\(716\) | 15356.8 | 0.801551 | ||||||||
\(717\) | 8028.86 | 0.418191 | ||||||||
\(718\) | −35408.2 | −1.84042 | ||||||||
\(719\) | −27081.5 | −1.40469 | −0.702344 | − | 0.711838i | \(-0.747863\pi\) | ||||
−0.702344 | + | 0.711838i | \(0.747863\pi\) | |||||||
\(720\) | −44161.8 | −2.28585 | ||||||||
\(721\) | −4824.05 | −0.249178 | ||||||||
\(722\) | −26217.2 | −1.35139 | ||||||||
\(723\) | −7189.72 | −0.369832 | ||||||||
\(724\) | 10134.0 | 0.520201 | ||||||||
\(725\) | 6032.05 | 0.309000 | ||||||||
\(726\) | 9975.25 | 0.509940 | ||||||||
\(727\) | −2011.78 | −0.102631 | −0.0513155 | − | 0.998682i | \(-0.516341\pi\) | ||||
−0.0513155 | + | 0.998682i | \(0.516341\pi\) | |||||||
\(728\) | 1958.38 | 0.0997012 | ||||||||
\(729\) | −27544.6 | −1.39941 | ||||||||
\(730\) | −72734.1 | −3.68768 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 29825.8 | 1.50600 | ||||||||
\(733\) | 9401.81 | 0.473757 | 0.236878 | − | 0.971539i | \(-0.423876\pi\) | ||||
0.236878 | + | 0.971539i | \(0.423876\pi\) | |||||||
\(734\) | 4513.38 | 0.226965 | ||||||||
\(735\) | 44490.3 | 2.23272 | ||||||||
\(736\) | 14414.0 | 0.721887 | ||||||||
\(737\) | 10373.4 | 0.518464 | ||||||||
\(738\) | 2945.55 | 0.146921 | ||||||||
\(739\) | −18781.6 | −0.934900 | −0.467450 | − | 0.884019i | \(-0.654827\pi\) | ||||
−0.467450 | + | 0.884019i | \(0.654827\pi\) | |||||||
\(740\) | 30678.9 | 1.52402 | ||||||||
\(741\) | −775.200 | −0.0384314 | ||||||||
\(742\) | −1329.41 | −0.0657739 | ||||||||
\(743\) | 32099.5 | 1.58495 | 0.792474 | − | 0.609906i | \(-0.208793\pi\) | ||||
0.792474 | + | 0.609906i | \(0.208793\pi\) | |||||||
\(744\) | 3579.48 | 0.176385 | ||||||||
\(745\) | −12874.1 | −0.633116 | ||||||||
\(746\) | −23492.4 | −1.15298 | ||||||||
\(747\) | 34573.4 | 1.69340 | ||||||||
\(748\) | 28430.4 | 1.38973 | ||||||||
\(749\) | −6207.09 | −0.302807 | ||||||||
\(750\) | −42410.2 | −2.06480 | ||||||||
\(751\) | −22982.6 | −1.11671 | −0.558353 | − | 0.829603i | \(-0.688567\pi\) | ||||
−0.558353 | + | 0.829603i | \(0.688567\pi\) | |||||||
\(752\) | 79.1628 | 0.00383879 | ||||||||
\(753\) | 10687.8 | 0.517245 | ||||||||
\(754\) | −8072.25 | −0.389886 | ||||||||
\(755\) | 30821.8 | 1.48572 | ||||||||
\(756\) | −1682.41 | −0.0809372 | ||||||||
\(757\) | 4670.82 | 0.224259 | 0.112129 | − | 0.993694i | \(-0.464233\pi\) | ||||
0.112129 | + | 0.993694i | \(0.464233\pi\) | |||||||
\(758\) | −32318.4 | −1.54862 | ||||||||
\(759\) | 14872.0 | 0.711226 | ||||||||
\(760\) | 134.060 | 0.00639851 | ||||||||
\(761\) | −14771.7 | −0.703643 | −0.351821 | − | 0.936067i | \(-0.614438\pi\) | ||||
−0.351821 | + | 0.936067i | \(0.614438\pi\) | |||||||
\(762\) | 32145.1 | 1.52821 | ||||||||
\(763\) | 3490.07 | 0.165595 | ||||||||
\(764\) | 11473.1 | 0.543301 | ||||||||
\(765\) | 82221.0 | 3.88589 | ||||||||
\(766\) | 14513.7 | 0.684598 | ||||||||
\(767\) | −33235.1 | −1.56460 | ||||||||
\(768\) | −39810.5 | −1.87049 | ||||||||
\(769\) | 15650.6 | 0.733910 | 0.366955 | − | 0.930239i | \(-0.380400\pi\) | ||||
0.366955 | + | 0.930239i | \(0.380400\pi\) | |||||||
\(770\) | 11367.1 | 0.532003 | ||||||||
\(771\) | 4521.75 | 0.211215 | ||||||||
\(772\) | 7343.10 | 0.342337 | ||||||||
\(773\) | −31462.6 | −1.46395 | −0.731975 | − | 0.681332i | \(-0.761401\pi\) | ||||
−0.731975 | + | 0.681332i | \(0.761401\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17783.1 | 0.824242 | ||||||||
\(776\) | −469.060 | −0.0216988 | ||||||||
\(777\) | −10318.5 | −0.476414 | ||||||||
\(778\) | 47304.6 | 2.17989 | ||||||||
\(779\) | −32.3834 | −0.00148942 | ||||||||
\(780\) | 66465.9 | 3.05111 | ||||||||
\(781\) | 26269.9 | 1.20360 | ||||||||
\(782\) | −31613.3 | −1.44564 | ||||||||
\(783\) | −1447.59 | −0.0660700 | ||||||||
\(784\) | 23112.1 | 1.05285 | ||||||||
\(785\) | 24694.7 | 1.12279 | ||||||||
\(786\) | −40685.6 | −1.84632 | ||||||||
\(787\) | 14116.6 | 0.639391 | 0.319696 | − | 0.947520i | \(-0.396419\pi\) | ||||
0.319696 | + | 0.947520i | \(0.396419\pi\) | |||||||
\(788\) | 10455.7 | 0.472674 | ||||||||
\(789\) | 1014.61 | 0.0457809 | ||||||||
\(790\) | 56040.0 | 2.52381 | ||||||||
\(791\) | −1371.13 | −0.0616331 | ||||||||
\(792\) | −5548.23 | −0.248924 | ||||||||
\(793\) | 41393.0 | 1.85360 | ||||||||
\(794\) | −47889.9 | −2.14049 | ||||||||
\(795\) | 9418.46 | 0.420174 | ||||||||
\(796\) | 23803.6 | 1.05992 | ||||||||
\(797\) | 21531.5 | 0.956946 | 0.478473 | − | 0.878102i | \(-0.341191\pi\) | ||||
0.478473 | + | 0.878102i | \(0.341191\pi\) | |||||||
\(798\) | 216.001 | 0.00958191 | ||||||||
\(799\) | −147.386 | −0.00652586 | ||||||||
\(800\) | −48377.4 | −2.13800 | ||||||||
\(801\) | 29143.1 | 1.28555 | ||||||||
\(802\) | 32661.1 | 1.43804 | ||||||||
\(803\) | −33094.0 | −1.45437 | ||||||||
\(804\) | −16901.0 | −0.741357 | ||||||||
\(805\) | −5722.56 | −0.250551 | ||||||||
\(806\) | −23797.8 | −1.04000 | ||||||||
\(807\) | 56302.1 | 2.45592 | ||||||||
\(808\) | −6747.39 | −0.293778 | ||||||||
\(809\) | −9241.88 | −0.401641 | −0.200820 | − | 0.979628i | \(-0.564361\pi\) | ||||
−0.200820 | + | 0.979628i | \(0.564361\pi\) | |||||||
\(810\) | −36001.2 | −1.56167 | ||||||||
\(811\) | 25173.8 | 1.08998 | 0.544989 | − | 0.838443i | \(-0.316534\pi\) | ||||
0.544989 | + | 0.838443i | \(0.316534\pi\) | |||||||
\(812\) | 1018.34 | 0.0440106 | ||||||||
\(813\) | −32768.3 | −1.41357 | ||||||||
\(814\) | 30831.6 | 1.32758 | ||||||||
\(815\) | 52249.4 | 2.24566 | ||||||||
\(816\) | 77346.9 | 3.31824 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −34977.8 | −1.49507 | ||||||||
\(819\) | −12345.0 | −0.526701 | ||||||||
\(820\) | 2776.57 | 0.118246 | ||||||||
\(821\) | −10451.1 | −0.444272 | −0.222136 | − | 0.975016i | \(-0.571303\pi\) | ||||
−0.222136 | + | 0.975016i | \(0.571303\pi\) | |||||||
\(822\) | −29721.0 | −1.26112 | ||||||||
\(823\) | 4757.91 | 0.201519 | 0.100760 | − | 0.994911i | \(-0.467873\pi\) | ||||
0.100760 | + | 0.994911i | \(0.467873\pi\) | |||||||
\(824\) | 4902.34 | 0.207259 | ||||||||
\(825\) | −49914.5 | −2.10642 | ||||||||
\(826\) | 9260.61 | 0.390094 | ||||||||
\(827\) | −15905.4 | −0.668785 | −0.334393 | − | 0.942434i | \(-0.608531\pi\) | ||||
−0.334393 | + | 0.942434i | \(0.608531\pi\) | |||||||
\(828\) | −13380.6 | −0.561605 | ||||||||
\(829\) | −3943.21 | −0.165203 | −0.0826016 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826016 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(830\) | 71982.7 | 3.01031 | ||||||||
\(831\) | −3089.88 | −0.128985 | ||||||||
\(832\) | 23004.1 | 0.958562 | ||||||||
\(833\) | −43030.4 | −1.78981 | ||||||||
\(834\) | 17769.8 | 0.737793 | ||||||||
\(835\) | 17892.6 | 0.741556 | ||||||||
\(836\) | −292.208 | −0.0120888 | ||||||||
\(837\) | −4267.65 | −0.176238 | ||||||||
\(838\) | 33576.7 | 1.38411 | ||||||||
\(839\) | −19902.5 | −0.818962 | −0.409481 | − | 0.912319i | \(-0.634290\pi\) | ||||
−0.409481 | + | 0.912319i | \(0.634290\pi\) | |||||||
\(840\) | 3865.99 | 0.158797 | ||||||||
\(841\) | −23512.8 | −0.964074 | ||||||||
\(842\) | −29531.7 | −1.20871 | ||||||||
\(843\) | 40877.3 | 1.67009 | ||||||||
\(844\) | 25992.5 | 1.06007 | ||||||||
\(845\) | 52406.5 | 2.13354 | ||||||||
\(846\) | −137.788 | −0.00559957 | ||||||||
\(847\) | −1746.45 | −0.0708485 | ||||||||
\(848\) | 4892.76 | 0.198135 | ||||||||
\(849\) | 35973.1 | 1.45417 | ||||||||
\(850\) | 106103. | 4.28152 | ||||||||
\(851\) | −15521.6 | −0.625234 | ||||||||
\(852\) | −42800.6 | −1.72104 | ||||||||
\(853\) | 44071.9 | 1.76904 | 0.884521 | − | 0.466500i | \(-0.154485\pi\) | ||||
0.884521 | + | 0.466500i | \(0.154485\pi\) | |||||||
\(854\) | −11533.7 | −0.462150 | ||||||||
\(855\) | −845.067 | −0.0338020 | ||||||||
\(856\) | 6307.82 | 0.251866 | ||||||||
\(857\) | −17150.5 | −0.683606 | −0.341803 | − | 0.939772i | \(-0.611038\pi\) | ||||
−0.341803 | + | 0.939772i | \(0.611038\pi\) | |||||||
\(858\) | 66796.9 | 2.65782 | ||||||||
\(859\) | 48887.4 | 1.94181 | 0.970907 | − | 0.239457i | \(-0.0769695\pi\) | ||||
0.970907 | + | 0.239457i | \(0.0769695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −933.865 | −0.0369640 | ||||||||
\(862\) | −22655.3 | −0.895175 | ||||||||
\(863\) | −38864.3 | −1.53297 | −0.766486 | − | 0.642260i | \(-0.777997\pi\) | ||||
−0.766486 | + | 0.642260i | \(0.777997\pi\) | |||||||
\(864\) | 11609.8 | 0.457145 | ||||||||
\(865\) | 10788.9 | 0.424087 | ||||||||
\(866\) | −14946.6 | −0.586498 | ||||||||
\(867\) | −105855. | −4.14652 | ||||||||
\(868\) | 3002.16 | 0.117396 | ||||||||
\(869\) | 25498.2 | 0.995358 | ||||||||
\(870\) | −15935.2 | −0.620981 | ||||||||
\(871\) | −23455.6 | −0.912471 | ||||||||
\(872\) | −3546.71 | −0.137737 | ||||||||
\(873\) | 2956.79 | 0.114630 | ||||||||
\(874\) | 324.921 | 0.0125751 | ||||||||
\(875\) | 7425.08 | 0.286873 | ||||||||
\(876\) | 53918.9 | 2.07962 | ||||||||
\(877\) | −12583.6 | −0.484515 | −0.242258 | − | 0.970212i | \(-0.577888\pi\) | ||||
−0.242258 | + | 0.970212i | \(0.577888\pi\) | |||||||
\(878\) | −16980.7 | −0.652701 | ||||||||
\(879\) | 4032.49 | 0.154736 | ||||||||
\(880\) | −41835.5 | −1.60258 | ||||||||
\(881\) | −27901.3 | −1.06699 | −0.533495 | − | 0.845803i | \(-0.679122\pi\) | ||||
−0.533495 | + | 0.845803i | \(0.679122\pi\) | |||||||
\(882\) | −40227.9 | −1.53577 | ||||||||
\(883\) | −50179.5 | −1.91243 | −0.956215 | − | 0.292666i | \(-0.905458\pi\) | ||||
−0.956215 | + | 0.292666i | \(0.905458\pi\) | |||||||
\(884\) | −64285.0 | −2.44586 | ||||||||
\(885\) | −65608.5 | −2.49198 | ||||||||
\(886\) | −29487.1 | −1.11810 | ||||||||
\(887\) | −9359.99 | −0.354315 | −0.177158 | − | 0.984182i | \(-0.556690\pi\) | ||||
−0.177158 | + | 0.984182i | \(0.556690\pi\) | |||||||
\(888\) | 10485.9 | 0.396267 | ||||||||
\(889\) | −5627.90 | −0.212321 | ||||||||
\(890\) | 60676.9 | 2.28527 | ||||||||
\(891\) | −16380.6 | −0.615903 | ||||||||
\(892\) | −1653.56 | −0.0620688 | ||||||||
\(893\) | 1.51484 | 5.67660e−5 0 | ||||||||
\(894\) | 21079.8 | 0.788605 | ||||||||
\(895\) | 42072.5 | 1.57132 | ||||||||
\(896\) | 3462.12 | 0.129086 | ||||||||
\(897\) | −33627.7 | −1.25172 | ||||||||
\(898\) | 4945.51 | 0.183779 | ||||||||
\(899\) | 2583.15 | 0.0958318 | ||||||||
\(900\) | 44908.9 | 1.66329 | ||||||||
\(901\) | −9109.41 | −0.336824 | ||||||||
\(902\) | 2790.39 | 0.103004 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1393.38 | 0.0512646 | ||||||||
\(905\) | 27763.7 | 1.01978 | ||||||||
\(906\) | −50466.9 | −1.85061 | ||||||||
\(907\) | −41146.5 | −1.50633 | −0.753167 | − | 0.657829i | \(-0.771475\pi\) | ||||
−0.753167 | + | 0.657829i | \(0.771475\pi\) | |||||||
\(908\) | 34627.6 | 1.26559 | ||||||||
\(909\) | 42533.2 | 1.55197 | ||||||||
\(910\) | −25702.6 | −0.936299 | ||||||||
\(911\) | 16872.6 | 0.613626 | 0.306813 | − | 0.951770i | \(-0.400737\pi\) | ||||
0.306813 | + | 0.951770i | \(0.400737\pi\) | |||||||
\(912\) | −794.970 | −0.0288641 | ||||||||
\(913\) | 32752.1 | 1.18723 | ||||||||
\(914\) | −21264.6 | −0.769554 | ||||||||
\(915\) | 81712.7 | 2.95228 | ||||||||
\(916\) | −6276.92 | −0.226414 | ||||||||
\(917\) | 7123.16 | 0.256519 | ||||||||
\(918\) | −25462.9 | −0.915469 | ||||||||
\(919\) | 47698.3 | 1.71210 | 0.856052 | − | 0.516890i | \(-0.172910\pi\) | ||||
0.856052 | + | 0.516890i | \(0.172910\pi\) | |||||||
\(920\) | 5815.43 | 0.208401 | ||||||||
\(921\) | −9269.46 | −0.331639 | ||||||||
\(922\) | −60844.5 | −2.17333 | ||||||||
\(923\) | −59399.7 | −2.11827 | ||||||||
\(924\) | −8426.61 | −0.300016 | ||||||||
\(925\) | 52094.7 | 1.85174 | ||||||||
\(926\) | 59822.3 | 2.12298 | ||||||||
\(927\) | −30902.6 | −1.09490 | ||||||||
\(928\) | −7027.23 | −0.248578 | ||||||||
\(929\) | 17674.8 | 0.624210 | 0.312105 | − | 0.950048i | \(-0.398966\pi\) | ||||
0.312105 | + | 0.950048i | \(0.398966\pi\) | |||||||
\(930\) | −46978.5 | −1.65644 | ||||||||
\(931\) | 442.266 | 0.0155689 | ||||||||
\(932\) | 22849.3 | 0.803063 | ||||||||
\(933\) | 20099.1 | 0.705268 | ||||||||
\(934\) | 36184.2 | 1.26765 | ||||||||
\(935\) | 77889.9 | 2.72435 | ||||||||
\(936\) | 12545.3 | 0.438094 | ||||||||
\(937\) | 17557.9 | 0.612158 | 0.306079 | − | 0.952006i | \(-0.400983\pi\) | ||||
0.306079 | + | 0.952006i | \(0.400983\pi\) | |||||||
\(938\) | 6535.65 | 0.227502 | ||||||||
\(939\) | −3290.39 | −0.114353 | ||||||||
\(940\) | −129.883 | −0.00450671 | ||||||||
\(941\) | 42936.2 | 1.48744 | 0.743719 | − | 0.668492i | \(-0.233060\pi\) | ||||
0.743719 | + | 0.668492i | \(0.233060\pi\) | |||||||
\(942\) | −40434.5 | −1.39854 | ||||||||
\(943\) | −1404.77 | −0.0485108 | ||||||||
\(944\) | −34082.7 | −1.17510 | ||||||||
\(945\) | −4609.24 | −0.158665 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4691.32 | −0.160979 | −0.0804897 | − | 0.996755i | \(-0.525648\pi\) | ||||
−0.0804897 | + | 0.996755i | \(0.525648\pi\) | |||||||
\(948\) | −41543.3 | −1.42327 | ||||||||
\(949\) | 74830.0 | 2.55962 | ||||||||
\(950\) | −1090.52 | −0.0372433 | ||||||||
\(951\) | −10629.0 | −0.362426 | ||||||||
\(952\) | −3739.13 | −0.127296 | ||||||||
\(953\) | −24602.9 | −0.836271 | −0.418135 | − | 0.908385i | \(-0.637316\pi\) | ||||
−0.418135 | + | 0.908385i | \(0.637316\pi\) | |||||||
\(954\) | −8516.14 | −0.289015 | ||||||||
\(955\) | 31432.5 | 1.06506 | ||||||||
\(956\) | −6843.18 | −0.231511 | ||||||||
\(957\) | −7250.51 | −0.244907 | ||||||||
\(958\) | 14762.4 | 0.497861 | ||||||||
\(959\) | 5203.50 | 0.175213 | ||||||||
\(960\) | 45411.7 | 1.52673 | ||||||||
\(961\) | −22175.6 | −0.744373 | ||||||||
\(962\) | −69714.5 | −2.33647 | ||||||||
\(963\) | −39762.3 | −1.33055 | ||||||||
\(964\) | 6127.96 | 0.204739 | ||||||||
\(965\) | 20117.7 | 0.671099 | ||||||||
\(966\) | 9369.99 | 0.312086 | ||||||||
\(967\) | 1371.38 | 0.0456056 | 0.0228028 | − | 0.999740i | \(-0.492741\pi\) | ||||
0.0228028 | + | 0.999740i | \(0.492741\pi\) | |||||||
\(968\) | 1774.79 | 0.0589296 | ||||||||
\(969\) | 1480.09 | 0.0490684 | ||||||||
\(970\) | 6156.12 | 0.203774 | ||||||||
\(971\) | 33787.3 | 1.11667 | 0.558335 | − | 0.829616i | \(-0.311440\pi\) | ||||
0.558335 | + | 0.829616i | \(0.311440\pi\) | |||||||
\(972\) | 35427.2 | 1.16906 | ||||||||
\(973\) | −3111.11 | −0.102505 | ||||||||
\(974\) | 13432.1 | 0.441880 | ||||||||
\(975\) | 112863. | 3.70720 | ||||||||
\(976\) | 42448.6 | 1.39216 | ||||||||
\(977\) | 9124.24 | 0.298782 | 0.149391 | − | 0.988778i | \(-0.452269\pi\) | ||||
0.149391 | + | 0.988778i | \(0.452269\pi\) | |||||||
\(978\) | −85551.9 | −2.79719 | ||||||||
\(979\) | 27608.0 | 0.901282 | ||||||||
\(980\) | −37920.0 | −1.23603 | ||||||||
\(981\) | 22357.2 | 0.727636 | ||||||||
\(982\) | −73706.7 | −2.39519 | ||||||||
\(983\) | −9300.65 | −0.301775 | −0.150887 | − | 0.988551i | \(-0.548213\pi\) | ||||
−0.150887 | + | 0.988551i | \(0.548213\pi\) | |||||||
\(984\) | 949.020 | 0.0307456 | ||||||||
\(985\) | 28645.0 | 0.926605 | ||||||||
\(986\) | 15412.3 | 0.497797 | ||||||||
\(987\) | 43.6845 | 0.00140881 | ||||||||
\(988\) | 660.721 | 0.0212756 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 72817.1 | 2.33766 | ||||||||
\(991\) | 17367.8 | 0.556717 | 0.278358 | − | 0.960477i | \(-0.410210\pi\) | ||||
0.278358 | + | 0.960477i | \(0.410210\pi\) | |||||||
\(992\) | −20717.0 | −0.663069 | ||||||||
\(993\) | 19060.2 | 0.609122 | ||||||||
\(994\) | 16551.1 | 0.528138 | ||||||||
\(995\) | 65214.0 | 2.07781 | ||||||||
\(996\) | −53361.9 | −1.69763 | ||||||||
\(997\) | −36720.9 | −1.16646 | −0.583230 | − | 0.812307i | \(-0.698211\pi\) | ||||
−0.583230 | + | 0.812307i | \(0.698211\pi\) | |||||||
\(998\) | −29158.5 | −0.924846 | ||||||||
\(999\) | −12501.9 | −0.395938 |
(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.d.1.9 | 10 | ||
43.6 | even | 3 | 43.4.c.a.36.9 | yes | 20 | ||
43.36 | even | 3 | 43.4.c.a.6.9 | ✓ | 20 | ||
43.42 | odd | 2 | 1849.4.a.f.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.c.a.6.9 | ✓ | 20 | 43.36 | even | 3 | ||
43.4.c.a.36.9 | yes | 20 | 43.6 | even | 3 | ||
1849.4.a.d.1.9 | 10 | 1.1 | even | 1 | trivial | ||
1849.4.a.f.1.2 | 10 | 43.42 | odd | 2 |