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 | 1.5 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.39566 | −1.55410 | −0.777050 | − | 0.629439i | \(-0.783285\pi\) | ||||
−0.777050 | + | 0.629439i | \(0.783285\pi\) | |||||||
\(3\) | −7.85436 | −1.51157 | −0.755786 | − | 0.654818i | \(-0.772745\pi\) | ||||
−0.755786 | + | 0.654818i | \(0.772745\pi\) | |||||||
\(4\) | 11.3218 | 1.41523 | ||||||||
\(5\) | −5.85216 | −0.523433 | −0.261716 | − | 0.965145i | \(-0.584288\pi\) | ||||
−0.261716 | + | 0.965145i | \(0.584288\pi\) | |||||||
\(6\) | 34.5251 | 2.34914 | ||||||||
\(7\) | −12.3980 | −0.669428 | −0.334714 | − | 0.942320i | \(-0.608640\pi\) | ||||
−0.334714 | + | 0.942320i | \(0.608640\pi\) | |||||||
\(8\) | −14.6016 | −0.645305 | ||||||||
\(9\) | 34.6910 | 1.28485 | ||||||||
\(10\) | 25.7241 | 0.813467 | ||||||||
\(11\) | 50.9011 | 1.39520 | 0.697602 | − | 0.716485i | \(-0.254250\pi\) | ||||
0.697602 | + | 0.716485i | \(0.254250\pi\) | |||||||
\(12\) | −88.9257 | −2.13922 | ||||||||
\(13\) | −72.3797 | −1.54419 | −0.772096 | − | 0.635506i | \(-0.780792\pi\) | ||||
−0.772096 | + | 0.635506i | \(0.780792\pi\) | |||||||
\(14\) | 54.4973 | 1.04036 | ||||||||
\(15\) | 45.9650 | 0.791207 | ||||||||
\(16\) | −26.3910 | −0.412359 | ||||||||
\(17\) | 72.1180 | 1.02889 | 0.514446 | − | 0.857523i | \(-0.327997\pi\) | ||||
0.514446 | + | 0.857523i | \(0.327997\pi\) | |||||||
\(18\) | −152.490 | −1.99679 | ||||||||
\(19\) | −47.7505 | −0.576564 | −0.288282 | − | 0.957546i | \(-0.593084\pi\) | ||||
−0.288282 | + | 0.957546i | \(0.593084\pi\) | |||||||
\(20\) | −66.2570 | −0.740776 | ||||||||
\(21\) | 97.3782 | 1.01189 | ||||||||
\(22\) | −223.744 | −2.16829 | ||||||||
\(23\) | 194.454 | 1.76289 | 0.881444 | − | 0.472289i | \(-0.156572\pi\) | ||||
0.881444 | + | 0.472289i | \(0.156572\pi\) | |||||||
\(24\) | 114.686 | 0.975425 | ||||||||
\(25\) | −90.7523 | −0.726018 | ||||||||
\(26\) | 318.156 | 2.39983 | ||||||||
\(27\) | −60.4081 | −0.430576 | ||||||||
\(28\) | −140.368 | −0.947392 | ||||||||
\(29\) | −114.570 | −0.733627 | −0.366813 | − | 0.930295i | \(-0.619551\pi\) | ||||
−0.366813 | + | 0.930295i | \(0.619551\pi\) | |||||||
\(30\) | −202.046 | −1.22961 | ||||||||
\(31\) | −108.300 | −0.627461 | −0.313731 | − | 0.949512i | \(-0.601579\pi\) | ||||
−0.313731 | + | 0.949512i | \(0.601579\pi\) | |||||||
\(32\) | 232.818 | 1.28615 | ||||||||
\(33\) | −399.795 | −2.10895 | ||||||||
\(34\) | −317.006 | −1.59900 | ||||||||
\(35\) | 72.5549 | 0.350400 | ||||||||
\(36\) | 392.765 | 1.81836 | ||||||||
\(37\) | −19.4210 | −0.0862918 | −0.0431459 | − | 0.999069i | \(-0.513738\pi\) | ||||
−0.0431459 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(38\) | 209.895 | 0.896038 | ||||||||
\(39\) | 568.496 | 2.33416 | ||||||||
\(40\) | 85.4507 | 0.337774 | ||||||||
\(41\) | −485.191 | −1.84815 | −0.924074 | − | 0.382214i | \(-0.875162\pi\) | ||||
−0.924074 | + | 0.382214i | \(0.875162\pi\) | |||||||
\(42\) | −428.041 | −1.57258 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 576.293 | 1.97453 | ||||||||
\(45\) | −203.017 | −0.672534 | ||||||||
\(46\) | −854.753 | −2.73970 | ||||||||
\(47\) | −20.2520 | −0.0628523 | −0.0314262 | − | 0.999506i | \(-0.510005\pi\) | ||||
−0.0314262 | + | 0.999506i | \(0.510005\pi\) | |||||||
\(48\) | 207.284 | 0.623311 | ||||||||
\(49\) | −189.290 | −0.551866 | ||||||||
\(50\) | 398.916 | 1.12830 | ||||||||
\(51\) | −566.441 | −1.55525 | ||||||||
\(52\) | −819.469 | −2.18538 | ||||||||
\(53\) | 276.032 | 0.715396 | 0.357698 | − | 0.933837i | \(-0.383562\pi\) | ||||
0.357698 | + | 0.933837i | \(0.383562\pi\) | |||||||
\(54\) | 265.533 | 0.669158 | ||||||||
\(55\) | −297.881 | −0.730296 | ||||||||
\(56\) | 181.030 | 0.431985 | ||||||||
\(57\) | 375.050 | 0.871519 | ||||||||
\(58\) | 503.612 | 1.14013 | ||||||||
\(59\) | −65.3849 | −0.144278 | −0.0721389 | − | 0.997395i | \(-0.522982\pi\) | ||||
−0.0721389 | + | 0.997395i | \(0.522982\pi\) | |||||||
\(60\) | 520.407 | 1.11974 | ||||||||
\(61\) | 330.113 | 0.692896 | 0.346448 | − | 0.938069i | \(-0.387388\pi\) | ||||
0.346448 | + | 0.938069i | \(0.387388\pi\) | |||||||
\(62\) | 476.051 | 0.975138 | ||||||||
\(63\) | −430.098 | −0.860116 | ||||||||
\(64\) | −812.262 | −1.58645 | ||||||||
\(65\) | 423.577 | 0.808281 | ||||||||
\(66\) | 1757.36 | 3.27752 | ||||||||
\(67\) | −522.685 | −0.953077 | −0.476538 | − | 0.879154i | \(-0.658109\pi\) | ||||
−0.476538 | + | 0.879154i | \(0.658109\pi\) | |||||||
\(68\) | 816.506 | 1.45612 | ||||||||
\(69\) | −1527.31 | −2.66473 | ||||||||
\(70\) | −318.927 | −0.544557 | ||||||||
\(71\) | −155.769 | −0.260371 | −0.130185 | − | 0.991490i | \(-0.541557\pi\) | ||||
−0.130185 | + | 0.991490i | \(0.541557\pi\) | |||||||
\(72\) | −506.544 | −0.829122 | ||||||||
\(73\) | −543.223 | −0.870951 | −0.435476 | − | 0.900201i | \(-0.643420\pi\) | ||||
−0.435476 | + | 0.900201i | \(0.643420\pi\) | |||||||
\(74\) | 85.3682 | 0.134106 | ||||||||
\(75\) | 712.801 | 1.09743 | ||||||||
\(76\) | −540.622 | −0.815969 | ||||||||
\(77\) | −631.070 | −0.933988 | ||||||||
\(78\) | −2498.91 | −3.62752 | ||||||||
\(79\) | 1153.53 | 1.64281 | 0.821407 | − | 0.570342i | \(-0.193189\pi\) | ||||
0.821407 | + | 0.570342i | \(0.193189\pi\) | |||||||
\(80\) | 154.444 | 0.215842 | ||||||||
\(81\) | −462.190 | −0.634006 | ||||||||
\(82\) | 2132.73 | 2.87221 | ||||||||
\(83\) | 781.141 | 1.03303 | 0.516514 | − | 0.856279i | \(-0.327229\pi\) | ||||
0.516514 | + | 0.856279i | \(0.327229\pi\) | |||||||
\(84\) | 1102.50 | 1.43205 | ||||||||
\(85\) | −422.046 | −0.538556 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 899.877 | 1.10893 | ||||||||
\(88\) | −743.236 | −0.900332 | ||||||||
\(89\) | −515.449 | −0.613904 | −0.306952 | − | 0.951725i | \(-0.599309\pi\) | ||||
−0.306952 | + | 0.951725i | \(0.599309\pi\) | |||||||
\(90\) | 892.395 | 1.04519 | ||||||||
\(91\) | 897.361 | 1.03373 | ||||||||
\(92\) | 2201.57 | 2.49489 | ||||||||
\(93\) | 850.630 | 0.948454 | ||||||||
\(94\) | 89.0210 | 0.0976788 | ||||||||
\(95\) | 279.443 | 0.301792 | ||||||||
\(96\) | −1828.64 | −1.94411 | ||||||||
\(97\) | 901.767 | 0.943924 | 0.471962 | − | 0.881619i | \(-0.343546\pi\) | ||||
0.471962 | + | 0.881619i | \(0.343546\pi\) | |||||||
\(98\) | 832.055 | 0.857656 | ||||||||
\(99\) | 1765.81 | 1.79263 | ||||||||
\(100\) | −1027.48 | −1.02748 | ||||||||
\(101\) | −199.561 | −0.196605 | −0.0983024 | − | 0.995157i | \(-0.531341\pi\) | ||||
−0.0983024 | + | 0.995157i | \(0.531341\pi\) | |||||||
\(102\) | 2489.88 | 2.41701 | ||||||||
\(103\) | −881.273 | −0.843052 | −0.421526 | − | 0.906816i | \(-0.638505\pi\) | ||||
−0.421526 | + | 0.906816i | \(0.638505\pi\) | |||||||
\(104\) | 1056.86 | 0.996475 | ||||||||
\(105\) | −569.872 | −0.529656 | ||||||||
\(106\) | −1213.34 | −1.11180 | ||||||||
\(107\) | 1495.28 | 1.35098 | 0.675488 | − | 0.737371i | \(-0.263933\pi\) | ||||
0.675488 | + | 0.737371i | \(0.263933\pi\) | |||||||
\(108\) | −683.930 | −0.609363 | ||||||||
\(109\) | −760.930 | −0.668660 | −0.334330 | − | 0.942456i | \(-0.608510\pi\) | ||||
−0.334330 | + | 0.942456i | \(0.608510\pi\) | |||||||
\(110\) | 1309.38 | 1.13495 | ||||||||
\(111\) | 152.540 | 0.130436 | ||||||||
\(112\) | 327.195 | 0.276045 | ||||||||
\(113\) | 1352.82 | 1.12621 | 0.563107 | − | 0.826384i | \(-0.309606\pi\) | ||||
0.563107 | + | 0.826384i | \(0.309606\pi\) | |||||||
\(114\) | −1648.59 | −1.35443 | ||||||||
\(115\) | −1137.97 | −0.922753 | ||||||||
\(116\) | −1297.14 | −1.03825 | ||||||||
\(117\) | −2510.92 | −1.98406 | ||||||||
\(118\) | 287.410 | 0.224222 | ||||||||
\(119\) | −894.117 | −0.688769 | ||||||||
\(120\) | −671.161 | −0.510570 | ||||||||
\(121\) | 1259.92 | 0.946595 | ||||||||
\(122\) | −1451.06 | −1.07683 | ||||||||
\(123\) | 3810.86 | 2.79361 | ||||||||
\(124\) | −1226.16 | −0.888000 | ||||||||
\(125\) | 1262.62 | 0.903454 | ||||||||
\(126\) | 1890.57 | 1.33671 | ||||||||
\(127\) | 229.260 | 0.160185 | 0.0800926 | − | 0.996787i | \(-0.474478\pi\) | ||||
0.0800926 | + | 0.996787i | \(0.474478\pi\) | |||||||
\(128\) | 1707.88 | 1.17935 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1861.90 | −1.25615 | ||||||||
\(131\) | 1670.22 | 1.11396 | 0.556978 | − | 0.830527i | \(-0.311961\pi\) | ||||
0.556978 | + | 0.830527i | \(0.311961\pi\) | |||||||
\(132\) | −4526.41 | −2.98465 | ||||||||
\(133\) | 592.010 | 0.385968 | ||||||||
\(134\) | 2297.55 | 1.48118 | ||||||||
\(135\) | 353.518 | 0.225377 | ||||||||
\(136\) | −1053.04 | −0.663949 | ||||||||
\(137\) | 2120.54 | 1.32241 | 0.661203 | − | 0.750207i | \(-0.270046\pi\) | ||||
0.661203 | + | 0.750207i | \(0.270046\pi\) | |||||||
\(138\) | 6713.54 | 4.14126 | ||||||||
\(139\) | −546.720 | −0.333613 | −0.166806 | − | 0.985990i | \(-0.553346\pi\) | ||||
−0.166806 | + | 0.985990i | \(0.553346\pi\) | |||||||
\(140\) | 821.453 | 0.495896 | ||||||||
\(141\) | 159.067 | 0.0950059 | ||||||||
\(142\) | 684.706 | 0.404642 | ||||||||
\(143\) | −3684.20 | −2.15446 | ||||||||
\(144\) | −915.530 | −0.529821 | ||||||||
\(145\) | 670.483 | 0.384004 | ||||||||
\(146\) | 2387.82 | 1.35355 | ||||||||
\(147\) | 1486.75 | 0.834186 | ||||||||
\(148\) | −219.881 | −0.122123 | ||||||||
\(149\) | 3202.06 | 1.76056 | 0.880280 | − | 0.474455i | \(-0.157355\pi\) | ||||
0.880280 | + | 0.474455i | \(0.157355\pi\) | |||||||
\(150\) | −3133.23 | −1.70552 | ||||||||
\(151\) | 1219.91 | 0.657452 | 0.328726 | − | 0.944425i | \(-0.393381\pi\) | ||||
0.328726 | + | 0.944425i | \(0.393381\pi\) | |||||||
\(152\) | 697.233 | 0.372060 | ||||||||
\(153\) | 2501.85 | 1.32198 | ||||||||
\(154\) | 2773.97 | 1.45151 | ||||||||
\(155\) | 633.790 | 0.328434 | ||||||||
\(156\) | 6436.41 | 3.30337 | ||||||||
\(157\) | −1934.69 | −0.983472 | −0.491736 | − | 0.870744i | \(-0.663637\pi\) | ||||
−0.491736 | + | 0.870744i | \(0.663637\pi\) | |||||||
\(158\) | −5070.53 | −2.55310 | ||||||||
\(159\) | −2168.06 | −1.08137 | ||||||||
\(160\) | −1362.49 | −0.673214 | ||||||||
\(161\) | −2410.83 | −1.18013 | ||||||||
\(162\) | 2031.63 | 0.985309 | ||||||||
\(163\) | −1091.52 | −0.524505 | −0.262253 | − | 0.964999i | \(-0.584465\pi\) | ||||
−0.262253 | + | 0.964999i | \(0.584465\pi\) | |||||||
\(164\) | −5493.24 | −2.61555 | ||||||||
\(165\) | 2339.67 | 1.10390 | ||||||||
\(166\) | −3433.63 | −1.60543 | ||||||||
\(167\) | 2286.50 | 1.05949 | 0.529744 | − | 0.848157i | \(-0.322288\pi\) | ||||
0.529744 | + | 0.848157i | \(0.322288\pi\) | |||||||
\(168\) | −1421.88 | −0.652977 | ||||||||
\(169\) | 3041.81 | 1.38453 | ||||||||
\(170\) | 1855.17 | 0.836970 | ||||||||
\(171\) | −1656.51 | −0.740800 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1171.22 | −0.514720 | −0.257360 | − | 0.966316i | \(-0.582853\pi\) | ||||
−0.257360 | + | 0.966316i | \(0.582853\pi\) | |||||||
\(174\) | −3955.55 | −1.72339 | ||||||||
\(175\) | 1125.14 | 0.486017 | ||||||||
\(176\) | −1343.33 | −0.575325 | ||||||||
\(177\) | 513.557 | 0.218087 | ||||||||
\(178\) | 2265.74 | 0.954069 | ||||||||
\(179\) | −931.735 | −0.389057 | −0.194528 | − | 0.980897i | \(-0.562318\pi\) | ||||
−0.194528 | + | 0.980897i | \(0.562318\pi\) | |||||||
\(180\) | −2298.52 | −0.951788 | ||||||||
\(181\) | −305.691 | −0.125535 | −0.0627675 | − | 0.998028i | \(-0.519993\pi\) | ||||
−0.0627675 | + | 0.998028i | \(0.519993\pi\) | |||||||
\(182\) | −3944.49 | −1.60651 | ||||||||
\(183\) | −2592.83 | −1.04736 | ||||||||
\(184\) | −2839.33 | −1.13760 | ||||||||
\(185\) | 113.655 | 0.0451680 | ||||||||
\(186\) | −3739.08 | −1.47399 | ||||||||
\(187\) | 3670.88 | 1.43552 | ||||||||
\(188\) | −229.290 | −0.0889503 | ||||||||
\(189\) | 748.938 | 0.288239 | ||||||||
\(190\) | −1228.34 | −0.469016 | ||||||||
\(191\) | −302.996 | −0.114786 | −0.0573928 | − | 0.998352i | \(-0.518279\pi\) | ||||
−0.0573928 | + | 0.998352i | \(0.518279\pi\) | |||||||
\(192\) | 6379.80 | 2.39803 | ||||||||
\(193\) | 3593.56 | 1.34026 | 0.670130 | − | 0.742244i | \(-0.266239\pi\) | ||||
0.670130 | + | 0.742244i | \(0.266239\pi\) | |||||||
\(194\) | −3963.86 | −1.46695 | ||||||||
\(195\) | −3326.93 | −1.22178 | ||||||||
\(196\) | −2143.11 | −0.781017 | ||||||||
\(197\) | −2255.81 | −0.815838 | −0.407919 | − | 0.913018i | \(-0.633745\pi\) | ||||
−0.407919 | + | 0.913018i | \(0.633745\pi\) | |||||||
\(198\) | −7761.90 | −2.78593 | ||||||||
\(199\) | 533.234 | 0.189950 | 0.0949748 | − | 0.995480i | \(-0.469723\pi\) | ||||
0.0949748 | + | 0.995480i | \(0.469723\pi\) | |||||||
\(200\) | 1325.13 | 0.468503 | ||||||||
\(201\) | 4105.36 | 1.44065 | ||||||||
\(202\) | 877.203 | 0.305543 | ||||||||
\(203\) | 1420.44 | 0.491110 | ||||||||
\(204\) | −6413.14 | −2.20103 | ||||||||
\(205\) | 2839.41 | 0.967381 | ||||||||
\(206\) | 3873.78 | 1.31019 | ||||||||
\(207\) | 6745.80 | 2.26505 | ||||||||
\(208\) | 1910.17 | 0.636762 | ||||||||
\(209\) | −2430.55 | −0.804425 | ||||||||
\(210\) | 2504.96 | 0.823138 | ||||||||
\(211\) | 4938.57 | 1.61130 | 0.805651 | − | 0.592390i | \(-0.201816\pi\) | ||||
0.805651 | + | 0.592390i | \(0.201816\pi\) | |||||||
\(212\) | 3125.19 | 1.01245 | ||||||||
\(213\) | 1223.46 | 0.393570 | ||||||||
\(214\) | −6572.75 | −2.09955 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 882.054 | 0.277853 | ||||||||
\(217\) | 1342.70 | 0.420040 | ||||||||
\(218\) | 3344.79 | 1.03916 | ||||||||
\(219\) | 4266.67 | 1.31651 | ||||||||
\(220\) | −3372.55 | −1.03353 | ||||||||
\(221\) | −5219.87 | −1.58881 | ||||||||
\(222\) | −670.513 | −0.202711 | ||||||||
\(223\) | 1407.81 | 0.422752 | 0.211376 | − | 0.977405i | \(-0.432206\pi\) | ||||
0.211376 | + | 0.977405i | \(0.432206\pi\) | |||||||
\(224\) | −2886.48 | −0.860986 | ||||||||
\(225\) | −3148.29 | −0.932827 | ||||||||
\(226\) | −5946.52 | −1.75025 | ||||||||
\(227\) | 297.127 | 0.0868766 | 0.0434383 | − | 0.999056i | \(-0.486169\pi\) | ||||
0.0434383 | + | 0.999056i | \(0.486169\pi\) | |||||||
\(228\) | 4246.25 | 1.23340 | ||||||||
\(229\) | 3885.00 | 1.12108 | 0.560542 | − | 0.828126i | \(-0.310593\pi\) | ||||
0.560542 | + | 0.828126i | \(0.310593\pi\) | |||||||
\(230\) | 5002.15 | 1.43405 | ||||||||
\(231\) | 4956.65 | 1.41179 | ||||||||
\(232\) | 1672.91 | 0.473413 | ||||||||
\(233\) | 5538.50 | 1.55725 | 0.778625 | − | 0.627489i | \(-0.215917\pi\) | ||||
0.778625 | + | 0.627489i | \(0.215917\pi\) | |||||||
\(234\) | 11037.2 | 3.08343 | ||||||||
\(235\) | 118.518 | 0.0328990 | ||||||||
\(236\) | −740.276 | −0.204186 | ||||||||
\(237\) | −9060.25 | −2.48323 | ||||||||
\(238\) | 3930.23 | 1.07042 | ||||||||
\(239\) | −2719.79 | −0.736103 | −0.368052 | − | 0.929805i | \(-0.619975\pi\) | ||||
−0.368052 | + | 0.929805i | \(0.619975\pi\) | |||||||
\(240\) | −1213.06 | −0.326261 | ||||||||
\(241\) | −1477.37 | −0.394878 | −0.197439 | − | 0.980315i | \(-0.563262\pi\) | ||||
−0.197439 | + | 0.980315i | \(0.563262\pi\) | |||||||
\(242\) | −5538.17 | −1.47110 | ||||||||
\(243\) | 5261.23 | 1.38892 | ||||||||
\(244\) | 3737.48 | 0.980605 | ||||||||
\(245\) | 1107.76 | 0.288865 | ||||||||
\(246\) | −16751.3 | −4.34155 | ||||||||
\(247\) | 3456.16 | 0.890326 | ||||||||
\(248\) | 1581.35 | 0.404904 | ||||||||
\(249\) | −6135.36 | −1.56150 | ||||||||
\(250\) | −5550.03 | −1.40406 | ||||||||
\(251\) | −3405.07 | −0.856280 | −0.428140 | − | 0.903712i | \(-0.640831\pi\) | ||||
−0.428140 | + | 0.903712i | \(0.640831\pi\) | |||||||
\(252\) | −4869.50 | −1.21726 | ||||||||
\(253\) | 9897.90 | 2.45959 | ||||||||
\(254\) | −1007.75 | −0.248944 | ||||||||
\(255\) | 3314.90 | 0.814067 | ||||||||
\(256\) | −1009.17 | −0.246378 | ||||||||
\(257\) | −2338.70 | −0.567642 | −0.283821 | − | 0.958877i | \(-0.591602\pi\) | ||||
−0.283821 | + | 0.958877i | \(0.591602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 240.781 | 0.0577661 | ||||||||
\(260\) | 4795.66 | 1.14390 | ||||||||
\(261\) | −3974.56 | −0.942602 | ||||||||
\(262\) | −7341.74 | −1.73120 | ||||||||
\(263\) | 2652.29 | 0.621854 | 0.310927 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310927 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(264\) | 5837.65 | 1.36092 | ||||||||
\(265\) | −1615.38 | −0.374462 | ||||||||
\(266\) | −2602.27 | −0.599833 | ||||||||
\(267\) | 4048.52 | 0.927961 | ||||||||
\(268\) | −5917.75 | −1.34882 | ||||||||
\(269\) | −3751.84 | −0.850387 | −0.425193 | − | 0.905103i | \(-0.639794\pi\) | ||||
−0.425193 | + | 0.905103i | \(0.639794\pi\) | |||||||
\(270\) | −1553.94 | −0.350259 | ||||||||
\(271\) | −6834.16 | −1.53190 | −0.765952 | − | 0.642898i | \(-0.777732\pi\) | ||||
−0.765952 | + | 0.642898i | \(0.777732\pi\) | |||||||
\(272\) | −1903.26 | −0.424273 | ||||||||
\(273\) | −7048.20 | −1.56255 | ||||||||
\(274\) | −9321.16 | −2.05515 | ||||||||
\(275\) | −4619.39 | −1.01294 | ||||||||
\(276\) | −17291.9 | −3.77120 | ||||||||
\(277\) | −3328.70 | −0.722029 | −0.361015 | − | 0.932560i | \(-0.617570\pi\) | ||||
−0.361015 | + | 0.932560i | \(0.617570\pi\) | |||||||
\(278\) | 2403.20 | 0.518468 | ||||||||
\(279\) | −3757.05 | −0.806195 | ||||||||
\(280\) | −1059.42 | −0.226115 | ||||||||
\(281\) | −273.014 | −0.0579596 | −0.0289798 | − | 0.999580i | \(-0.509226\pi\) | ||||
−0.0289798 | + | 0.999580i | \(0.509226\pi\) | |||||||
\(282\) | −699.203 | −0.147649 | ||||||||
\(283\) | 4738.49 | 0.995314 | 0.497657 | − | 0.867374i | \(-0.334194\pi\) | ||||
0.497657 | + | 0.867374i | \(0.334194\pi\) | |||||||
\(284\) | −1763.58 | −0.368484 | ||||||||
\(285\) | −2194.85 | −0.456181 | ||||||||
\(286\) | 16194.5 | 3.34825 | ||||||||
\(287\) | 6015.38 | 1.23720 | ||||||||
\(288\) | 8076.71 | 1.65252 | ||||||||
\(289\) | 287.999 | 0.0586199 | ||||||||
\(290\) | −2947.22 | −0.596781 | ||||||||
\(291\) | −7082.81 | −1.42681 | ||||||||
\(292\) | −6150.27 | −1.23259 | ||||||||
\(293\) | 6636.13 | 1.32316 | 0.661581 | − | 0.749873i | \(-0.269886\pi\) | ||||
0.661581 | + | 0.749873i | \(0.269886\pi\) | |||||||
\(294\) | −6535.26 | −1.29641 | ||||||||
\(295\) | 382.643 | 0.0755198 | ||||||||
\(296\) | 283.578 | 0.0556845 | ||||||||
\(297\) | −3074.84 | −0.600741 | ||||||||
\(298\) | −14075.2 | −2.73609 | ||||||||
\(299\) | −14074.5 | −2.72224 | ||||||||
\(300\) | 8070.21 | 1.55311 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5362.33 | −1.02175 | ||||||||
\(303\) | 1567.43 | 0.297182 | ||||||||
\(304\) | 1260.18 | 0.237751 | ||||||||
\(305\) | −1931.87 | −0.362684 | ||||||||
\(306\) | −10997.3 | −2.05448 | ||||||||
\(307\) | 6964.04 | 1.29465 | 0.647327 | − | 0.762212i | \(-0.275887\pi\) | ||||
0.647327 | + | 0.762212i | \(0.275887\pi\) | |||||||
\(308\) | −7144.86 | −1.32181 | ||||||||
\(309\) | 6921.84 | 1.27434 | ||||||||
\(310\) | −2785.92 | −0.510419 | ||||||||
\(311\) | −1532.20 | −0.279366 | −0.139683 | − | 0.990196i | \(-0.544608\pi\) | ||||
−0.139683 | + | 0.990196i | \(0.544608\pi\) | |||||||
\(312\) | −8300.94 | −1.50624 | ||||||||
\(313\) | −7971.39 | −1.43952 | −0.719760 | − | 0.694223i | \(-0.755748\pi\) | ||||
−0.719760 | + | 0.694223i | \(0.755748\pi\) | |||||||
\(314\) | 8504.24 | 1.52841 | ||||||||
\(315\) | 2517.00 | 0.450213 | ||||||||
\(316\) | 13060.1 | 2.32496 | ||||||||
\(317\) | −3644.45 | −0.645719 | −0.322860 | − | 0.946447i | \(-0.604644\pi\) | ||||
−0.322860 | + | 0.946447i | \(0.604644\pi\) | |||||||
\(318\) | 9530.05 | 1.68056 | ||||||||
\(319\) | −5831.75 | −1.02356 | ||||||||
\(320\) | 4753.49 | 0.830400 | ||||||||
\(321\) | −11744.5 | −2.04210 | ||||||||
\(322\) | 10597.2 | 1.83403 | ||||||||
\(323\) | −3443.67 | −0.593222 | ||||||||
\(324\) | −5232.84 | −0.897263 | ||||||||
\(325\) | 6568.62 | 1.12111 | ||||||||
\(326\) | 4797.94 | 0.815133 | ||||||||
\(327\) | 5976.62 | 1.01073 | ||||||||
\(328\) | 7084.55 | 1.19262 | ||||||||
\(329\) | 251.084 | 0.0420751 | ||||||||
\(330\) | −10284.4 | −1.71556 | ||||||||
\(331\) | −5229.57 | −0.868409 | −0.434204 | − | 0.900814i | \(-0.642970\pi\) | ||||
−0.434204 | + | 0.900814i | \(0.642970\pi\) | |||||||
\(332\) | 8843.93 | 1.46197 | ||||||||
\(333\) | −673.735 | −0.110872 | ||||||||
\(334\) | −10050.7 | −1.64655 | ||||||||
\(335\) | 3058.83 | 0.498872 | ||||||||
\(336\) | −2569.91 | −0.417261 | ||||||||
\(337\) | −4729.01 | −0.764408 | −0.382204 | − | 0.924078i | \(-0.624835\pi\) | ||||
−0.382204 | + | 0.924078i | \(0.624835\pi\) | |||||||
\(338\) | −13370.8 | −2.15170 | ||||||||
\(339\) | −10625.5 | −1.70236 | ||||||||
\(340\) | −4778.32 | −0.762179 | ||||||||
\(341\) | −5512.60 | −0.875437 | ||||||||
\(342\) | 7281.47 | 1.15128 | ||||||||
\(343\) | 6599.32 | 1.03886 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8938.06 | 1.39481 | ||||||||
\(346\) | 5148.31 | 0.799927 | ||||||||
\(347\) | −10045.8 | −1.55415 | −0.777074 | − | 0.629409i | \(-0.783297\pi\) | ||||
−0.777074 | + | 0.629409i | \(0.783297\pi\) | |||||||
\(348\) | 10188.2 | 1.56939 | ||||||||
\(349\) | −2985.23 | −0.457867 | −0.228933 | − | 0.973442i | \(-0.573524\pi\) | ||||
−0.228933 | + | 0.973442i | \(0.573524\pi\) | |||||||
\(350\) | −4945.75 | −0.755319 | ||||||||
\(351\) | 4372.32 | 0.664892 | ||||||||
\(352\) | 11850.7 | 1.79444 | ||||||||
\(353\) | 4066.23 | 0.613098 | 0.306549 | − | 0.951855i | \(-0.400826\pi\) | ||||
0.306549 | + | 0.951855i | \(0.400826\pi\) | |||||||
\(354\) | −2257.42 | −0.338928 | ||||||||
\(355\) | 911.582 | 0.136287 | ||||||||
\(356\) | −5835.82 | −0.868814 | ||||||||
\(357\) | 7022.72 | 1.04112 | ||||||||
\(358\) | 4095.59 | 0.604633 | ||||||||
\(359\) | −5734.13 | −0.842996 | −0.421498 | − | 0.906829i | \(-0.638496\pi\) | ||||
−0.421498 | + | 0.906829i | \(0.638496\pi\) | |||||||
\(360\) | 2964.37 | 0.433989 | ||||||||
\(361\) | −4578.89 | −0.667574 | ||||||||
\(362\) | 1343.71 | 0.195094 | ||||||||
\(363\) | −9895.85 | −1.43085 | ||||||||
\(364\) | 10159.8 | 1.46296 | ||||||||
\(365\) | 3179.02 | 0.455884 | ||||||||
\(366\) | 11397.2 | 1.62771 | ||||||||
\(367\) | −7460.30 | −1.06110 | −0.530551 | − | 0.847653i | \(-0.678015\pi\) | ||||
−0.530551 | + | 0.847653i | \(0.678015\pi\) | |||||||
\(368\) | −5131.83 | −0.726943 | ||||||||
\(369\) | −16831.8 | −2.37460 | ||||||||
\(370\) | −499.588 | −0.0701955 | ||||||||
\(371\) | −3422.24 | −0.478906 | ||||||||
\(372\) | 9630.67 | 1.34228 | ||||||||
\(373\) | −5646.39 | −0.783805 | −0.391902 | − | 0.920007i | \(-0.628183\pi\) | ||||
−0.391902 | + | 0.920007i | \(0.628183\pi\) | |||||||
\(374\) | −16135.9 | −2.23093 | ||||||||
\(375\) | −9917.04 | −1.36564 | ||||||||
\(376\) | 295.711 | 0.0405589 | ||||||||
\(377\) | 8292.56 | 1.13286 | ||||||||
\(378\) | −3292.08 | −0.447953 | ||||||||
\(379\) | −3098.26 | −0.419912 | −0.209956 | − | 0.977711i | \(-0.567332\pi\) | ||||
−0.209956 | + | 0.977711i | \(0.567332\pi\) | |||||||
\(380\) | 3163.81 | 0.427105 | ||||||||
\(381\) | −1800.69 | −0.242132 | ||||||||
\(382\) | 1331.87 | 0.178388 | ||||||||
\(383\) | −4625.15 | −0.617060 | −0.308530 | − | 0.951215i | \(-0.599837\pi\) | ||||
−0.308530 | + | 0.951215i | \(0.599837\pi\) | |||||||
\(384\) | −13414.3 | −1.78267 | ||||||||
\(385\) | 3693.12 | 0.488880 | ||||||||
\(386\) | −15796.1 | −2.08290 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10209.6 | 1.33587 | ||||||||
\(389\) | 13403.3 | 1.74698 | 0.873488 | − | 0.486845i | \(-0.161852\pi\) | ||||
0.873488 | + | 0.486845i | \(0.161852\pi\) | |||||||
\(390\) | 14624.0 | 1.89876 | ||||||||
\(391\) | 14023.6 | 1.81382 | ||||||||
\(392\) | 2763.94 | 0.356122 | ||||||||
\(393\) | −13118.6 | −1.68383 | ||||||||
\(394\) | 9915.79 | 1.26789 | ||||||||
\(395\) | −6750.64 | −0.859903 | ||||||||
\(396\) | 19992.2 | 2.53698 | ||||||||
\(397\) | 8906.42 | 1.12595 | 0.562973 | − | 0.826475i | \(-0.309657\pi\) | ||||
0.562973 | + | 0.826475i | \(0.309657\pi\) | |||||||
\(398\) | −2343.92 | −0.295201 | ||||||||
\(399\) | −4649.86 | −0.583419 | ||||||||
\(400\) | 2395.04 | 0.299380 | ||||||||
\(401\) | −10.3507 | −0.00128900 | −0.000644499 | − | 1.00000i | \(-0.500205\pi\) | ||||
−0.000644499 | 1.00000i | \(0.500205\pi\) | ||||||||
\(402\) | −18045.8 | −2.23891 | ||||||||
\(403\) | 7838.73 | 0.968921 | ||||||||
\(404\) | −2259.40 | −0.278240 | ||||||||
\(405\) | 2704.81 | 0.331860 | ||||||||
\(406\) | −6243.77 | −0.763234 | ||||||||
\(407\) | −988.551 | −0.120395 | ||||||||
\(408\) | 8270.93 | 1.00361 | ||||||||
\(409\) | 7522.58 | 0.909456 | 0.454728 | − | 0.890630i | \(-0.349736\pi\) | ||||
0.454728 | + | 0.890630i | \(0.349736\pi\) | |||||||
\(410\) | −12481.1 | −1.50341 | ||||||||
\(411\) | −16655.5 | −1.99891 | ||||||||
\(412\) | −9977.61 | −1.19311 | ||||||||
\(413\) | 810.641 | 0.0965836 | ||||||||
\(414\) | −29652.2 | −3.52012 | ||||||||
\(415\) | −4571.36 | −0.540721 | ||||||||
\(416\) | −16851.3 | −1.98607 | ||||||||
\(417\) | 4294.14 | 0.504280 | ||||||||
\(418\) | 10683.9 | 1.25016 | ||||||||
\(419\) | 109.458 | 0.0127622 | 0.00638110 | − | 0.999980i | \(-0.497969\pi\) | ||||
0.00638110 | + | 0.999980i | \(0.497969\pi\) | |||||||
\(420\) | −6451.99 | −0.749583 | ||||||||
\(421\) | 8920.89 | 1.03273 | 0.516363 | − | 0.856370i | \(-0.327286\pi\) | ||||
0.516363 | + | 0.856370i | \(0.327286\pi\) | |||||||
\(422\) | −21708.3 | −2.50413 | ||||||||
\(423\) | −702.563 | −0.0807560 | ||||||||
\(424\) | −4030.51 | −0.461648 | ||||||||
\(425\) | −6544.87 | −0.746995 | ||||||||
\(426\) | −5377.93 | −0.611647 | ||||||||
\(427\) | −4092.73 | −0.463844 | ||||||||
\(428\) | 16929.3 | 1.91194 | ||||||||
\(429\) | 28937.1 | 3.25663 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16280.0 | −1.81944 | −0.909720 | − | 0.415223i | \(-0.863703\pi\) | ||||
−0.909720 | + | 0.415223i | \(0.863703\pi\) | |||||||
\(432\) | 1594.23 | 0.177552 | ||||||||
\(433\) | −12363.2 | −1.37214 | −0.686070 | − | 0.727535i | \(-0.740666\pi\) | ||||
−0.686070 | + | 0.727535i | \(0.740666\pi\) | |||||||
\(434\) | −5902.07 | −0.652784 | ||||||||
\(435\) | −5266.22 | −0.580450 | ||||||||
\(436\) | −8615.12 | −0.946306 | ||||||||
\(437\) | −9285.27 | −1.01642 | ||||||||
\(438\) | −18754.8 | −2.04598 | ||||||||
\(439\) | −15673.1 | −1.70396 | −0.851979 | − | 0.523576i | \(-0.824598\pi\) | ||||
−0.851979 | + | 0.523576i | \(0.824598\pi\) | |||||||
\(440\) | 4349.53 | 0.471263 | ||||||||
\(441\) | −6566.67 | −0.709067 | ||||||||
\(442\) | 22944.8 | 2.46917 | ||||||||
\(443\) | 8049.79 | 0.863335 | 0.431667 | − | 0.902033i | \(-0.357925\pi\) | ||||
0.431667 | + | 0.902033i | \(0.357925\pi\) | |||||||
\(444\) | 1727.03 | 0.184597 | ||||||||
\(445\) | 3016.49 | 0.321338 | ||||||||
\(446\) | −6188.23 | −0.656999 | ||||||||
\(447\) | −25150.2 | −2.66121 | ||||||||
\(448\) | 10070.4 | 1.06201 | ||||||||
\(449\) | −7655.72 | −0.804668 | −0.402334 | − | 0.915493i | \(-0.631801\pi\) | ||||
−0.402334 | + | 0.915493i | \(0.631801\pi\) | |||||||
\(450\) | 13838.8 | 1.44971 | ||||||||
\(451\) | −24696.7 | −2.57854 | ||||||||
\(452\) | 15316.3 | 1.59385 | ||||||||
\(453\) | −9581.65 | −0.993787 | ||||||||
\(454\) | −1306.07 | −0.135015 | ||||||||
\(455\) | −5251.50 | −0.541086 | ||||||||
\(456\) | −5476.32 | −0.562395 | ||||||||
\(457\) | 5935.62 | 0.607563 | 0.303782 | − | 0.952742i | \(-0.401751\pi\) | ||||
0.303782 | + | 0.952742i | \(0.401751\pi\) | |||||||
\(458\) | −17077.1 | −1.74228 | ||||||||
\(459\) | −4356.51 | −0.443016 | ||||||||
\(460\) | −12883.9 | −1.30591 | ||||||||
\(461\) | 14649.8 | 1.48007 | 0.740033 | − | 0.672571i | \(-0.234810\pi\) | ||||
0.740033 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(462\) | −21787.8 | −2.19407 | ||||||||
\(463\) | 8724.18 | 0.875695 | 0.437848 | − | 0.899049i | \(-0.355741\pi\) | ||||
0.437848 | + | 0.899049i | \(0.355741\pi\) | |||||||
\(464\) | 3023.62 | 0.302518 | ||||||||
\(465\) | −4978.02 | −0.496452 | ||||||||
\(466\) | −24345.4 | −2.42012 | ||||||||
\(467\) | −211.747 | −0.0209818 | −0.0104909 | − | 0.999945i | \(-0.503339\pi\) | ||||
−0.0104909 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(468\) | −28428.2 | −2.80790 | ||||||||
\(469\) | 6480.24 | 0.638016 | ||||||||
\(470\) | −520.964 | −0.0511283 | ||||||||
\(471\) | 15195.8 | 1.48659 | ||||||||
\(472\) | 954.724 | 0.0931032 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 39825.8 | 3.85919 | ||||||||
\(475\) | 4333.47 | 0.418596 | ||||||||
\(476\) | −10123.0 | −0.974765 | ||||||||
\(477\) | 9575.85 | 0.919178 | ||||||||
\(478\) | 11955.3 | 1.14398 | ||||||||
\(479\) | 8169.97 | 0.779323 | 0.389661 | − | 0.920958i | \(-0.372592\pi\) | ||||
0.389661 | + | 0.920958i | \(0.372592\pi\) | |||||||
\(480\) | 10701.5 | 1.01761 | ||||||||
\(481\) | 1405.69 | 0.133251 | ||||||||
\(482\) | 6494.00 | 0.613679 | ||||||||
\(483\) | 18935.6 | 1.78385 | ||||||||
\(484\) | 14264.6 | 1.33965 | ||||||||
\(485\) | −5277.28 | −0.494080 | ||||||||
\(486\) | −23126.6 | −2.15852 | ||||||||
\(487\) | 8646.83 | 0.804570 | 0.402285 | − | 0.915515i | \(-0.368216\pi\) | ||||
0.402285 | + | 0.915515i | \(0.368216\pi\) | |||||||
\(488\) | −4820.17 | −0.447129 | ||||||||
\(489\) | 8573.18 | 0.792828 | ||||||||
\(490\) | −4869.32 | −0.448925 | ||||||||
\(491\) | 7773.64 | 0.714500 | 0.357250 | − | 0.934009i | \(-0.383714\pi\) | ||||
0.357250 | + | 0.934009i | \(0.383714\pi\) | |||||||
\(492\) | 43145.9 | 3.95359 | ||||||||
\(493\) | −8262.58 | −0.754823 | ||||||||
\(494\) | −15192.1 | −1.38366 | ||||||||
\(495\) | −10333.8 | −0.938322 | ||||||||
\(496\) | 2858.15 | 0.258739 | ||||||||
\(497\) | 1931.22 | 0.174299 | ||||||||
\(498\) | 26969.0 | 2.42672 | ||||||||
\(499\) | 17480.8 | 1.56823 | 0.784114 | − | 0.620617i | \(-0.213118\pi\) | ||||
0.784114 | + | 0.620617i | \(0.213118\pi\) | |||||||
\(500\) | 14295.1 | 1.27859 | ||||||||
\(501\) | −17959.0 | −1.60149 | ||||||||
\(502\) | 14967.5 | 1.33075 | ||||||||
\(503\) | −10065.2 | −0.892218 | −0.446109 | − | 0.894979i | \(-0.647191\pi\) | ||||
−0.446109 | + | 0.894979i | \(0.647191\pi\) | |||||||
\(504\) | 6280.12 | 0.555037 | ||||||||
\(505\) | 1167.86 | 0.102909 | ||||||||
\(506\) | −43507.8 | −3.82245 | ||||||||
\(507\) | −23891.5 | −2.09282 | ||||||||
\(508\) | 2595.64 | 0.226698 | ||||||||
\(509\) | 5106.23 | 0.444656 | 0.222328 | − | 0.974972i | \(-0.428634\pi\) | ||||
0.222328 | + | 0.974972i | \(0.428634\pi\) | |||||||
\(510\) | −14571.2 | −1.26514 | ||||||||
\(511\) | 6734.86 | 0.583039 | ||||||||
\(512\) | −9227.10 | −0.796454 | ||||||||
\(513\) | 2884.52 | 0.248255 | ||||||||
\(514\) | 10280.1 | 0.882172 | ||||||||
\(515\) | 5157.35 | 0.441281 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1030.85 | −0.0876919 | ||||||||
\(518\) | −1058.39 | −0.0897743 | ||||||||
\(519\) | 9199.23 | 0.778037 | ||||||||
\(520\) | −6184.89 | −0.521588 | ||||||||
\(521\) | −7651.54 | −0.643416 | −0.321708 | − | 0.946839i | \(-0.604257\pi\) | ||||
−0.321708 | + | 0.946839i | \(0.604257\pi\) | |||||||
\(522\) | 17470.8 | 1.46490 | ||||||||
\(523\) | −3318.37 | −0.277442 | −0.138721 | − | 0.990331i | \(-0.544299\pi\) | ||||
−0.138721 | + | 0.990331i | \(0.544299\pi\) | |||||||
\(524\) | 18910.0 | 1.57650 | ||||||||
\(525\) | −8837.29 | −0.734650 | ||||||||
\(526\) | −11658.6 | −0.966423 | ||||||||
\(527\) | −7810.39 | −0.645590 | ||||||||
\(528\) | 10551.0 | 0.869646 | ||||||||
\(529\) | 25645.3 | 2.10777 | ||||||||
\(530\) | 7100.68 | 0.581951 | ||||||||
\(531\) | −2268.27 | −0.185376 | ||||||||
\(532\) | 6702.62 | 0.546232 | ||||||||
\(533\) | 35117.9 | 2.85390 | ||||||||
\(534\) | −17795.9 | −1.44214 | ||||||||
\(535\) | −8750.63 | −0.707145 | ||||||||
\(536\) | 7632.03 | 0.615025 | ||||||||
\(537\) | 7318.18 | 0.588087 | ||||||||
\(538\) | 16491.8 | 1.32159 | ||||||||
\(539\) | −9635.07 | −0.769966 | ||||||||
\(540\) | 4002.46 | 0.318960 | ||||||||
\(541\) | 3001.86 | 0.238558 | 0.119279 | − | 0.992861i | \(-0.461942\pi\) | ||||
0.119279 | + | 0.992861i | \(0.461942\pi\) | |||||||
\(542\) | 30040.7 | 2.38073 | ||||||||
\(543\) | 2401.01 | 0.189755 | ||||||||
\(544\) | 16790.4 | 1.32331 | ||||||||
\(545\) | 4453.08 | 0.349998 | ||||||||
\(546\) | 30981.5 | 2.42836 | ||||||||
\(547\) | −7159.56 | −0.559636 | −0.279818 | − | 0.960053i | \(-0.590274\pi\) | ||||
−0.279818 | + | 0.960053i | \(0.590274\pi\) | |||||||
\(548\) | 24008.3 | 1.87151 | ||||||||
\(549\) | 11452.0 | 0.890269 | ||||||||
\(550\) | 20305.3 | 1.57422 | ||||||||
\(551\) | 5470.79 | 0.422983 | ||||||||
\(552\) | 22301.2 | 1.71957 | ||||||||
\(553\) | −14301.4 | −1.09975 | ||||||||
\(554\) | 14631.8 | 1.12211 | ||||||||
\(555\) | −892.687 | −0.0682747 | ||||||||
\(556\) | −6189.87 | −0.472138 | ||||||||
\(557\) | −8290.11 | −0.630634 | −0.315317 | − | 0.948986i | \(-0.602111\pi\) | ||||
−0.315317 | + | 0.948986i | \(0.602111\pi\) | |||||||
\(558\) | 16514.7 | 1.25291 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1914.79 | −0.144491 | ||||||||
\(561\) | −28832.4 | −2.16989 | ||||||||
\(562\) | 1200.08 | 0.0900751 | ||||||||
\(563\) | 11830.8 | 0.885630 | 0.442815 | − | 0.896613i | \(-0.353980\pi\) | ||||
0.442815 | + | 0.896613i | \(0.353980\pi\) | |||||||
\(564\) | 1800.92 | 0.134455 | ||||||||
\(565\) | −7916.89 | −0.589498 | ||||||||
\(566\) | −20828.8 | −1.54682 | ||||||||
\(567\) | 5730.23 | 0.424421 | ||||||||
\(568\) | 2274.47 | 0.168019 | ||||||||
\(569\) | −661.208 | −0.0487158 | −0.0243579 | − | 0.999703i | \(-0.507754\pi\) | ||||
−0.0243579 | + | 0.999703i | \(0.507754\pi\) | |||||||
\(570\) | 9647.81 | 0.708951 | ||||||||
\(571\) | 13866.7 | 1.01629 | 0.508146 | − | 0.861271i | \(-0.330331\pi\) | ||||
0.508146 | + | 0.861271i | \(0.330331\pi\) | |||||||
\(572\) | −41711.9 | −3.04906 | ||||||||
\(573\) | 2379.84 | 0.173507 | ||||||||
\(574\) | −26441.6 | −1.92273 | ||||||||
\(575\) | −17647.1 | −1.27989 | ||||||||
\(576\) | −28178.2 | −2.03835 | ||||||||
\(577\) | 15498.6 | 1.11822 | 0.559112 | − | 0.829092i | \(-0.311142\pi\) | ||||
0.559112 | + | 0.829092i | \(0.311142\pi\) | |||||||
\(578\) | −1265.95 | −0.0911011 | ||||||||
\(579\) | −28225.1 | −2.02590 | ||||||||
\(580\) | 7591.09 | 0.543453 | ||||||||
\(581\) | −9684.56 | −0.691538 | ||||||||
\(582\) | 31133.6 | 2.21740 | ||||||||
\(583\) | 14050.3 | 0.998123 | ||||||||
\(584\) | 7931.91 | 0.562029 | ||||||||
\(585\) | 14694.3 | 1.03852 | ||||||||
\(586\) | −29170.2 | −2.05633 | ||||||||
\(587\) | 21748.6 | 1.52923 | 0.764617 | − | 0.644485i | \(-0.222928\pi\) | ||||
0.764617 | + | 0.644485i | \(0.222928\pi\) | |||||||
\(588\) | 16832.8 | 1.18056 | ||||||||
\(589\) | 5171.39 | 0.361772 | ||||||||
\(590\) | −1681.97 | −0.117365 | ||||||||
\(591\) | 17718.0 | 1.23320 | ||||||||
\(592\) | 512.540 | 0.0355832 | ||||||||
\(593\) | 22274.2 | 1.54248 | 0.771240 | − | 0.636545i | \(-0.219637\pi\) | ||||
0.771240 | + | 0.636545i | \(0.219637\pi\) | |||||||
\(594\) | 13515.9 | 0.933612 | ||||||||
\(595\) | 5232.51 | 0.360524 | ||||||||
\(596\) | 36253.2 | 2.49159 | ||||||||
\(597\) | −4188.22 | −0.287123 | ||||||||
\(598\) | 61866.7 | 4.23063 | ||||||||
\(599\) | 22572.5 | 1.53971 | 0.769856 | − | 0.638217i | \(-0.220328\pi\) | ||||
0.769856 | + | 0.638217i | \(0.220328\pi\) | |||||||
\(600\) | −10408.0 | −0.708176 | ||||||||
\(601\) | −22982.2 | −1.55984 | −0.779918 | − | 0.625881i | \(-0.784739\pi\) | ||||
−0.779918 | + | 0.625881i | \(0.784739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18132.5 | −1.22456 | ||||||||
\(604\) | 13811.7 | 0.930444 | ||||||||
\(605\) | −7373.24 | −0.495479 | ||||||||
\(606\) | −6889.87 | −0.461851 | ||||||||
\(607\) | −9708.39 | −0.649178 | −0.324589 | − | 0.945855i | \(-0.605226\pi\) | ||||
−0.324589 | + | 0.945855i | \(0.605226\pi\) | |||||||
\(608\) | −11117.2 | −0.741549 | ||||||||
\(609\) | −11156.7 | −0.742349 | ||||||||
\(610\) | 8491.86 | 0.563648 | ||||||||
\(611\) | 1465.83 | 0.0970561 | ||||||||
\(612\) | 28325.4 | 1.87090 | ||||||||
\(613\) | 13924.3 | 0.917450 | 0.458725 | − | 0.888578i | \(-0.348306\pi\) | ||||
0.458725 | + | 0.888578i | \(0.348306\pi\) | |||||||
\(614\) | −30611.5 | −2.01202 | ||||||||
\(615\) | −22301.8 | −1.46227 | ||||||||
\(616\) | 9214.62 | 0.602707 | ||||||||
\(617\) | 7924.09 | 0.517037 | 0.258519 | − | 0.966006i | \(-0.416766\pi\) | ||||
0.258519 | + | 0.966006i | \(0.416766\pi\) | |||||||
\(618\) | −30426.0 | −1.98044 | ||||||||
\(619\) | −7645.23 | −0.496426 | −0.248213 | − | 0.968705i | \(-0.579843\pi\) | ||||
−0.248213 | + | 0.968705i | \(0.579843\pi\) | |||||||
\(620\) | 7175.66 | 0.464808 | ||||||||
\(621\) | −11746.6 | −0.759057 | ||||||||
\(622\) | 6735.02 | 0.434163 | ||||||||
\(623\) | 6390.53 | 0.410965 | ||||||||
\(624\) | −15003.2 | −0.962512 | ||||||||
\(625\) | 3955.01 | 0.253121 | ||||||||
\(626\) | 35039.5 | 2.23716 | ||||||||
\(627\) | 19090.4 | 1.21595 | ||||||||
\(628\) | −21904.2 | −1.39184 | ||||||||
\(629\) | −1400.60 | −0.0887850 | ||||||||
\(630\) | −11063.9 | −0.699676 | ||||||||
\(631\) | −10857.9 | −0.685020 | −0.342510 | − | 0.939514i | \(-0.611277\pi\) | ||||
−0.342510 | + | 0.939514i | \(0.611277\pi\) | |||||||
\(632\) | −16843.4 | −1.06012 | ||||||||
\(633\) | −38789.3 | −2.43560 | ||||||||
\(634\) | 16019.8 | 1.00351 | ||||||||
\(635\) | −1341.66 | −0.0838461 | ||||||||
\(636\) | −24546.4 | −1.53039 | ||||||||
\(637\) | 13700.8 | 0.852188 | ||||||||
\(638\) | 25634.4 | 1.59071 | ||||||||
\(639\) | −5403.77 | −0.334538 | ||||||||
\(640\) | −9994.79 | −0.617310 | ||||||||
\(641\) | −9993.21 | −0.615769 | −0.307885 | − | 0.951424i | \(-0.599621\pi\) | ||||
−0.307885 | + | 0.951424i | \(0.599621\pi\) | |||||||
\(642\) | 51624.8 | 3.17363 | ||||||||
\(643\) | 4952.30 | 0.303732 | 0.151866 | − | 0.988401i | \(-0.451472\pi\) | ||||
0.151866 | + | 0.988401i | \(0.451472\pi\) | |||||||
\(644\) | −27295.0 | −1.67015 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15137.2 | 0.921927 | ||||||||
\(647\) | −12682.7 | −0.770644 | −0.385322 | − | 0.922782i | \(-0.625910\pi\) | ||||
−0.385322 | + | 0.922782i | \(0.625910\pi\) | |||||||
\(648\) | 6748.71 | 0.409127 | ||||||||
\(649\) | −3328.16 | −0.201297 | ||||||||
\(650\) | −28873.4 | −1.74232 | ||||||||
\(651\) | −10546.1 | −0.634921 | ||||||||
\(652\) | −12358.0 | −0.742294 | ||||||||
\(653\) | −599.654 | −0.0359361 | −0.0179681 | − | 0.999839i | \(-0.505720\pi\) | ||||
−0.0179681 | + | 0.999839i | \(0.505720\pi\) | |||||||
\(654\) | −26271.2 | −1.57077 | ||||||||
\(655\) | −9774.42 | −0.583081 | ||||||||
\(656\) | 12804.7 | 0.762100 | ||||||||
\(657\) | −18845.0 | −1.11904 | ||||||||
\(658\) | −1103.68 | −0.0653889 | ||||||||
\(659\) | −19082.8 | −1.12801 | −0.564007 | − | 0.825770i | \(-0.690741\pi\) | ||||
−0.564007 | + | 0.825770i | \(0.690741\pi\) | |||||||
\(660\) | 26489.3 | 1.56226 | ||||||||
\(661\) | 30565.8 | 1.79860 | 0.899298 | − | 0.437336i | \(-0.144078\pi\) | ||||
0.899298 | + | 0.437336i | \(0.144078\pi\) | |||||||
\(662\) | 22987.4 | 1.34959 | ||||||||
\(663\) | 40998.8 | 2.40160 | ||||||||
\(664\) | −11405.9 | −0.666618 | ||||||||
\(665\) | −3464.53 | −0.202028 | ||||||||
\(666\) | 2961.51 | 0.172307 | ||||||||
\(667\) | −22278.6 | −1.29330 | ||||||||
\(668\) | 25887.3 | 1.49942 | ||||||||
\(669\) | −11057.4 | −0.639020 | ||||||||
\(670\) | −13445.6 | −0.775296 | ||||||||
\(671\) | 16803.1 | 0.966732 | ||||||||
\(672\) | 22671.4 | 1.30144 | ||||||||
\(673\) | 16705.8 | 0.956850 | 0.478425 | − | 0.878128i | \(-0.341208\pi\) | ||||
0.478425 | + | 0.878128i | \(0.341208\pi\) | |||||||
\(674\) | 20787.1 | 1.18797 | ||||||||
\(675\) | 5482.17 | 0.312606 | ||||||||
\(676\) | 34438.9 | 1.95943 | ||||||||
\(677\) | 11786.3 | 0.669105 | 0.334553 | − | 0.942377i | \(-0.391415\pi\) | ||||
0.334553 | + | 0.942377i | \(0.391415\pi\) | |||||||
\(678\) | 46706.1 | 2.64563 | ||||||||
\(679\) | −11180.1 | −0.631889 | ||||||||
\(680\) | 6162.53 | 0.347533 | ||||||||
\(681\) | −2333.74 | −0.131320 | ||||||||
\(682\) | 24231.5 | 1.36052 | ||||||||
\(683\) | −2424.38 | −0.135822 | −0.0679110 | − | 0.997691i | \(-0.521633\pi\) | ||||
−0.0679110 | + | 0.997691i | \(0.521633\pi\) | |||||||
\(684\) | −18754.7 | −1.04840 | ||||||||
\(685\) | −12409.7 | −0.692191 | ||||||||
\(686\) | −29008.4 | −1.61450 | ||||||||
\(687\) | −30514.2 | −1.69460 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19979.1 | −1.10471 | ||||||||
\(690\) | −39288.7 | −2.16767 | ||||||||
\(691\) | −3786.01 | −0.208432 | −0.104216 | − | 0.994555i | \(-0.533233\pi\) | ||||
−0.104216 | + | 0.994555i | \(0.533233\pi\) | |||||||
\(692\) | −13260.4 | −0.728446 | ||||||||
\(693\) | −21892.5 | −1.20004 | ||||||||
\(694\) | 44158.1 | 2.41530 | ||||||||
\(695\) | 3199.49 | 0.174624 | ||||||||
\(696\) | −13139.6 | −0.715598 | ||||||||
\(697\) | −34991.0 | −1.90155 | ||||||||
\(698\) | 13122.0 | 0.711571 | ||||||||
\(699\) | −43501.4 | −2.35390 | ||||||||
\(700\) | 12738.7 | 0.687824 | ||||||||
\(701\) | 2332.79 | 0.125689 | 0.0628447 | − | 0.998023i | \(-0.479983\pi\) | ||||
0.0628447 | + | 0.998023i | \(0.479983\pi\) | |||||||
\(702\) | −19219.2 | −1.03331 | ||||||||
\(703\) | 927.364 | 0.0497527 | ||||||||
\(704\) | −41345.0 | −2.21342 | ||||||||
\(705\) | −930.883 | −0.0497292 | ||||||||
\(706\) | −17873.8 | −0.952815 | ||||||||
\(707\) | 2474.15 | 0.131613 | ||||||||
\(708\) | 5814.40 | 0.308642 | ||||||||
\(709\) | −33435.9 | −1.77110 | −0.885550 | − | 0.464544i | \(-0.846218\pi\) | ||||
−0.885550 | + | 0.464544i | \(0.846218\pi\) | |||||||
\(710\) | −4007.00 | −0.211803 | ||||||||
\(711\) | 40017.2 | 2.11077 | ||||||||
\(712\) | 7526.37 | 0.396155 | ||||||||
\(713\) | −21059.4 | −1.10614 | ||||||||
\(714\) | −30869.5 | −1.61801 | ||||||||
\(715\) | 21560.5 | 1.12772 | ||||||||
\(716\) | −10548.9 | −0.550603 | ||||||||
\(717\) | 21362.2 | 1.11267 | ||||||||
\(718\) | 25205.3 | 1.31010 | ||||||||
\(719\) | 21181.7 | 1.09867 | 0.549334 | − | 0.835603i | \(-0.314881\pi\) | ||||
0.549334 | + | 0.835603i | \(0.314881\pi\) | |||||||
\(720\) | 5357.82 | 0.277325 | ||||||||
\(721\) | 10926.0 | 0.564363 | ||||||||
\(722\) | 20127.2 | 1.03748 | ||||||||
\(723\) | 11603.8 | 0.596886 | ||||||||
\(724\) | −3460.98 | −0.177661 | ||||||||
\(725\) | 10397.5 | 0.532626 | ||||||||
\(726\) | 43498.8 | 2.22368 | ||||||||
\(727\) | −29543.9 | −1.50718 | −0.753592 | − | 0.657343i | \(-0.771680\pi\) | ||||
−0.753592 | + | 0.657343i | \(0.771680\pi\) | |||||||
\(728\) | −13102.9 | −0.667068 | ||||||||
\(729\) | −28844.5 | −1.46545 | ||||||||
\(730\) | −13973.9 | −0.708490 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −29355.5 | −1.48226 | ||||||||
\(733\) | −17766.9 | −0.895273 | −0.447637 | − | 0.894216i | \(-0.647734\pi\) | ||||
−0.447637 | + | 0.894216i | \(0.647734\pi\) | |||||||
\(734\) | 32793.0 | 1.64906 | ||||||||
\(735\) | −8700.72 | −0.436640 | ||||||||
\(736\) | 45272.4 | 2.26734 | ||||||||
\(737\) | −26605.2 | −1.32974 | ||||||||
\(738\) | 73986.7 | 3.69036 | ||||||||
\(739\) | −21245.7 | −1.05756 | −0.528778 | − | 0.848760i | \(-0.677350\pi\) | ||||
−0.528778 | + | 0.848760i | \(0.677350\pi\) | |||||||
\(740\) | 1286.78 | 0.0639229 | ||||||||
\(741\) | −27146.0 | −1.34579 | ||||||||
\(742\) | 15043.0 | 0.744268 | ||||||||
\(743\) | −397.687 | −0.0196362 | −0.00981812 | − | 0.999952i | \(-0.503125\pi\) | ||||
−0.00981812 | + | 0.999952i | \(0.503125\pi\) | |||||||
\(744\) | −12420.5 | −0.612042 | ||||||||
\(745\) | −18739.0 | −0.921534 | ||||||||
\(746\) | 24819.6 | 1.21811 | ||||||||
\(747\) | 27098.6 | 1.32729 | ||||||||
\(748\) | 41561.0 | 2.03158 | ||||||||
\(749\) | −18538.5 | −0.904381 | ||||||||
\(750\) | 43591.9 | 2.12234 | ||||||||
\(751\) | 4939.05 | 0.239985 | 0.119992 | − | 0.992775i | \(-0.461713\pi\) | ||||
0.119992 | + | 0.992775i | \(0.461713\pi\) | |||||||
\(752\) | 534.470 | 0.0259177 | ||||||||
\(753\) | 26744.7 | 1.29433 | ||||||||
\(754\) | −36451.3 | −1.76058 | ||||||||
\(755\) | −7139.13 | −0.344132 | ||||||||
\(756\) | 8479.34 | 0.407924 | ||||||||
\(757\) | −32519.8 | −1.56136 | −0.780682 | − | 0.624928i | \(-0.785128\pi\) | ||||
−0.780682 | + | 0.624928i | \(0.785128\pi\) | |||||||
\(758\) | 13618.9 | 0.652585 | ||||||||
\(759\) | −77741.7 | −3.71785 | ||||||||
\(760\) | −4080.31 | −0.194748 | ||||||||
\(761\) | 2808.28 | 0.133771 | 0.0668856 | − | 0.997761i | \(-0.478694\pi\) | ||||
0.0668856 | + | 0.997761i | \(0.478694\pi\) | |||||||
\(762\) | 7915.22 | 0.376297 | ||||||||
\(763\) | 9434.00 | 0.447619 | ||||||||
\(764\) | −3430.47 | −0.162448 | ||||||||
\(765\) | −14641.2 | −0.691965 | ||||||||
\(766\) | 20330.6 | 0.958973 | ||||||||
\(767\) | 4732.54 | 0.222793 | ||||||||
\(768\) | 7926.35 | 0.372419 | ||||||||
\(769\) | −2452.64 | −0.115012 | −0.0575061 | − | 0.998345i | \(-0.518315\pi\) | ||||
−0.0575061 | + | 0.998345i | \(0.518315\pi\) | |||||||
\(770\) | −16233.7 | −0.759769 | ||||||||
\(771\) | 18369.0 | 0.858032 | ||||||||
\(772\) | 40685.6 | 1.89677 | ||||||||
\(773\) | −15873.4 | −0.738584 | −0.369292 | − | 0.929313i | \(-0.620400\pi\) | ||||
−0.369292 | + | 0.929313i | \(0.620400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9828.49 | 0.455548 | ||||||||
\(776\) | −13167.2 | −0.609118 | ||||||||
\(777\) | −1891.18 | −0.0873177 | ||||||||
\(778\) | −58916.3 | −2.71498 | ||||||||
\(779\) | 23168.1 | 1.06558 | ||||||||
\(780\) | −37666.9 | −1.72909 | ||||||||
\(781\) | −7928.79 | −0.363271 | ||||||||
\(782\) | −61643.0 | −2.81886 | ||||||||
\(783\) | 6920.98 | 0.315882 | ||||||||
\(784\) | 4995.55 | 0.227567 | ||||||||
\(785\) | 11322.1 | 0.514781 | ||||||||
\(786\) | 57664.7 | 2.61683 | ||||||||
\(787\) | −5695.97 | −0.257992 | −0.128996 | − | 0.991645i | \(-0.541175\pi\) | ||||
−0.128996 | + | 0.991645i | \(0.541175\pi\) | |||||||
\(788\) | −25539.9 | −1.15460 | ||||||||
\(789\) | −20832.1 | −0.939977 | ||||||||
\(790\) | 29673.5 | 1.33638 | ||||||||
\(791\) | −16772.2 | −0.753919 | ||||||||
\(792\) | −25783.6 | −1.15679 | ||||||||
\(793\) | −23893.5 | −1.06996 | ||||||||
\(794\) | −39149.6 | −1.74983 | ||||||||
\(795\) | 12687.8 | 0.566026 | ||||||||
\(796\) | 6037.18 | 0.268822 | ||||||||
\(797\) | −2203.96 | −0.0979528 | −0.0489764 | − | 0.998800i | \(-0.515596\pi\) | ||||
−0.0489764 | + | 0.998800i | \(0.515596\pi\) | |||||||
\(798\) | 20439.2 | 0.906691 | ||||||||
\(799\) | −1460.53 | −0.0646683 | ||||||||
\(800\) | −21128.8 | −0.933770 | ||||||||
\(801\) | −17881.5 | −0.788777 | ||||||||
\(802\) | 45.4980 | 0.00200323 | ||||||||
\(803\) | −27650.6 | −1.21515 | ||||||||
\(804\) | 46480.1 | 2.03884 | ||||||||
\(805\) | 14108.6 | 0.617717 | ||||||||
\(806\) | −34456.4 | −1.50580 | ||||||||
\(807\) | 29468.4 | 1.28542 | ||||||||
\(808\) | 2913.91 | 0.126870 | ||||||||
\(809\) | −247.927 | −0.0107746 | −0.00538730 | − | 0.999985i | \(-0.501715\pi\) | ||||
−0.00538730 | + | 0.999985i | \(0.501715\pi\) | |||||||
\(810\) | −11889.4 | −0.515743 | ||||||||
\(811\) | 16460.2 | 0.712694 | 0.356347 | − | 0.934354i | \(-0.384022\pi\) | ||||
0.356347 | + | 0.934354i | \(0.384022\pi\) | |||||||
\(812\) | 16082.0 | 0.695032 | ||||||||
\(813\) | 53678.0 | 2.31558 | ||||||||
\(814\) | 4345.33 | 0.187105 | ||||||||
\(815\) | 6387.74 | 0.274543 | ||||||||
\(816\) | 14948.9 | 0.641320 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −33066.7 | −1.41339 | ||||||||
\(819\) | 31130.4 | 1.32818 | ||||||||
\(820\) | 32147.3 | 1.36906 | ||||||||
\(821\) | 26642.8 | 1.13257 | 0.566286 | − | 0.824209i | \(-0.308380\pi\) | ||||
0.566286 | + | 0.824209i | \(0.308380\pi\) | |||||||
\(822\) | 73211.7 | 3.10651 | ||||||||
\(823\) | 13805.3 | 0.584716 | 0.292358 | − | 0.956309i | \(-0.405560\pi\) | ||||
0.292358 | + | 0.956309i | \(0.405560\pi\) | |||||||
\(824\) | 12868.0 | 0.544026 | ||||||||
\(825\) | 36282.3 | 1.53114 | ||||||||
\(826\) | −3563.30 | −0.150101 | ||||||||
\(827\) | −42308.6 | −1.77898 | −0.889488 | − | 0.456959i | \(-0.848939\pi\) | ||||
−0.889488 | + | 0.456959i | \(0.848939\pi\) | |||||||
\(828\) | 76374.7 | 3.20556 | ||||||||
\(829\) | −1206.36 | −0.0505412 | −0.0252706 | − | 0.999681i | \(-0.508045\pi\) | ||||
−0.0252706 | + | 0.999681i | \(0.508045\pi\) | |||||||
\(830\) | 20094.1 | 0.840334 | ||||||||
\(831\) | 26144.8 | 1.09140 | ||||||||
\(832\) | 58791.3 | 2.44978 | ||||||||
\(833\) | −13651.2 | −0.567811 | ||||||||
\(834\) | −18875.6 | −0.783702 | ||||||||
\(835\) | −13381.0 | −0.554571 | ||||||||
\(836\) | −27518.3 | −1.13844 | ||||||||
\(837\) | 6542.21 | 0.270170 | ||||||||
\(838\) | −481.139 | −0.0198338 | ||||||||
\(839\) | −23105.7 | −0.950773 | −0.475386 | − | 0.879777i | \(-0.657692\pi\) | ||||
−0.475386 | + | 0.879777i | \(0.657692\pi\) | |||||||
\(840\) | 8321.04 | 0.341789 | ||||||||
\(841\) | −11262.6 | −0.461792 | ||||||||
\(842\) | −39213.2 | −1.60496 | ||||||||
\(843\) | 2144.35 | 0.0876102 | ||||||||
\(844\) | 55913.5 | 2.28036 | ||||||||
\(845\) | −17801.2 | −0.724709 | ||||||||
\(846\) | 3088.23 | 0.125503 | ||||||||
\(847\) | −15620.4 | −0.633677 | ||||||||
\(848\) | −7284.77 | −0.295000 | ||||||||
\(849\) | −37217.8 | −1.50449 | ||||||||
\(850\) | 28769.0 | 1.16090 | ||||||||
\(851\) | −3776.49 | −0.152123 | ||||||||
\(852\) | 13851.8 | 0.556990 | ||||||||
\(853\) | −16448.8 | −0.660253 | −0.330126 | − | 0.943937i | \(-0.607091\pi\) | ||||
−0.330126 | + | 0.943937i | \(0.607091\pi\) | |||||||
\(854\) | 17990.3 | 0.720860 | ||||||||
\(855\) | 9694.18 | 0.387759 | ||||||||
\(856\) | −21833.5 | −0.871791 | ||||||||
\(857\) | 35801.6 | 1.42702 | 0.713512 | − | 0.700643i | \(-0.247103\pi\) | ||||
0.713512 | + | 0.700643i | \(0.247103\pi\) | |||||||
\(858\) | −127197. | −5.06113 | ||||||||
\(859\) | 10727.9 | 0.426113 | 0.213057 | − | 0.977040i | \(-0.431658\pi\) | ||||
0.213057 | + | 0.977040i | \(0.431658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −47247.0 | −1.87012 | ||||||||
\(862\) | 71561.2 | 2.82759 | ||||||||
\(863\) | −16939.7 | −0.668172 | −0.334086 | − | 0.942543i | \(-0.608428\pi\) | ||||
−0.334086 | + | 0.942543i | \(0.608428\pi\) | |||||||
\(864\) | −14064.1 | −0.553786 | ||||||||
\(865\) | 6854.19 | 0.269421 | ||||||||
\(866\) | 54344.4 | 2.13244 | ||||||||
\(867\) | −2262.05 | −0.0886082 | ||||||||
\(868\) | 15201.9 | 0.594452 | ||||||||
\(869\) | 58715.9 | 2.29206 | ||||||||
\(870\) | 23148.5 | 0.902078 | ||||||||
\(871\) | 37831.8 | 1.47173 | ||||||||
\(872\) | 11110.8 | 0.431489 | ||||||||
\(873\) | 31283.2 | 1.21280 | ||||||||
\(874\) | 40814.9 | 1.57961 | ||||||||
\(875\) | −15653.9 | −0.604797 | ||||||||
\(876\) | 48306.5 | 1.86316 | ||||||||
\(877\) | −9358.04 | −0.360318 | −0.180159 | − | 0.983638i | \(-0.557661\pi\) | ||||
−0.180159 | + | 0.983638i | \(0.557661\pi\) | |||||||
\(878\) | 68893.7 | 2.64812 | ||||||||
\(879\) | −52122.6 | −2.00006 | ||||||||
\(880\) | 7861.37 | 0.301144 | ||||||||
\(881\) | 11704.6 | 0.447603 | 0.223801 | − | 0.974635i | \(-0.428153\pi\) | ||||
0.223801 | + | 0.974635i | \(0.428153\pi\) | |||||||
\(882\) | 28864.8 | 1.10196 | ||||||||
\(883\) | 3294.49 | 0.125559 | 0.0627794 | − | 0.998027i | \(-0.480004\pi\) | ||||
0.0627794 | + | 0.998027i | \(0.480004\pi\) | |||||||
\(884\) | −59098.4 | −2.24852 | ||||||||
\(885\) | −3005.42 | −0.114154 | ||||||||
\(886\) | −35384.2 | −1.34171 | ||||||||
\(887\) | −19593.1 | −0.741683 | −0.370842 | − | 0.928696i | \(-0.620931\pi\) | ||||
−0.370842 | + | 0.928696i | \(0.620931\pi\) | |||||||
\(888\) | −2227.32 | −0.0841712 | ||||||||
\(889\) | −2842.36 | −0.107232 | ||||||||
\(890\) | −13259.5 | −0.499391 | ||||||||
\(891\) | −23526.0 | −0.884568 | ||||||||
\(892\) | 15938.9 | 0.598290 | ||||||||
\(893\) | 967.044 | 0.0362384 | ||||||||
\(894\) | 110552. | 4.13579 | ||||||||
\(895\) | 5452.66 | 0.203645 | ||||||||
\(896\) | −21174.3 | −0.789490 | ||||||||
\(897\) | 110546. | 4.11486 | ||||||||
\(898\) | 33652.0 | 1.25053 | ||||||||
\(899\) | 12408.0 | 0.460322 | ||||||||
\(900\) | −35644.4 | −1.32016 | ||||||||
\(901\) | 19906.9 | 0.736065 | ||||||||
\(902\) | 108558. | 4.00731 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19753.3 | −0.726752 | ||||||||
\(905\) | 1788.95 | 0.0657092 | ||||||||
\(906\) | 42117.7 | 1.54444 | ||||||||
\(907\) | −33443.1 | −1.22432 | −0.612162 | − | 0.790733i | \(-0.709700\pi\) | ||||
−0.612162 | + | 0.790733i | \(0.709700\pi\) | |||||||
\(908\) | 3364.02 | 0.122950 | ||||||||
\(909\) | −6922.98 | −0.252608 | ||||||||
\(910\) | 23083.8 | 0.840901 | ||||||||
\(911\) | 31893.5 | 1.15991 | 0.579955 | − | 0.814649i | \(-0.303070\pi\) | ||||
0.579955 | + | 0.814649i | \(0.303070\pi\) | |||||||
\(912\) | −9897.93 | −0.359379 | ||||||||
\(913\) | 39760.9 | 1.44129 | ||||||||
\(914\) | −26090.9 | −0.944214 | ||||||||
\(915\) | 15173.6 | 0.548224 | ||||||||
\(916\) | 43985.3 | 1.58659 | ||||||||
\(917\) | −20707.4 | −0.745713 | ||||||||
\(918\) | 19149.7 | 0.688492 | ||||||||
\(919\) | 15843.1 | 0.568678 | 0.284339 | − | 0.958724i | \(-0.408226\pi\) | ||||
0.284339 | + | 0.958724i | \(0.408226\pi\) | |||||||
\(920\) | 16616.2 | 0.595457 | ||||||||
\(921\) | −54698.1 | −1.95696 | ||||||||
\(922\) | −64395.6 | −2.30017 | ||||||||
\(923\) | 11274.5 | 0.402063 | ||||||||
\(924\) | 56118.3 | 1.99801 | ||||||||
\(925\) | 1762.50 | 0.0626494 | ||||||||
\(926\) | −38348.5 | −1.36092 | ||||||||
\(927\) | −30572.3 | −1.08320 | ||||||||
\(928\) | −26674.1 | −0.943555 | ||||||||
\(929\) | 5624.10 | 0.198623 | 0.0993114 | − | 0.995056i | \(-0.468336\pi\) | ||||
0.0993114 | + | 0.995056i | \(0.468336\pi\) | |||||||
\(930\) | 21881.7 | 0.771536 | ||||||||
\(931\) | 9038.70 | 0.318186 | ||||||||
\(932\) | 62705.9 | 2.20386 | ||||||||
\(933\) | 12034.4 | 0.422283 | ||||||||
\(934\) | 930.767 | 0.0326077 | ||||||||
\(935\) | −21482.6 | −0.751396 | ||||||||
\(936\) | 36663.5 | 1.28032 | ||||||||
\(937\) | −24982.7 | −0.871024 | −0.435512 | − | 0.900183i | \(-0.643433\pi\) | ||||
−0.435512 | + | 0.900183i | \(0.643433\pi\) | |||||||
\(938\) | −28484.9 | −0.991541 | ||||||||
\(939\) | 62610.2 | 2.17594 | ||||||||
\(940\) | 1341.84 | 0.0465595 | ||||||||
\(941\) | −2409.74 | −0.0834806 | −0.0417403 | − | 0.999128i | \(-0.513290\pi\) | ||||
−0.0417403 | + | 0.999128i | \(0.513290\pi\) | |||||||
\(942\) | −66795.4 | −2.31031 | ||||||||
\(943\) | −94347.2 | −3.25808 | ||||||||
\(944\) | 1725.57 | 0.0594943 | ||||||||
\(945\) | −4382.90 | −0.150874 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13276.4 | 0.455569 | 0.227785 | − | 0.973712i | \(-0.426852\pi\) | ||||
0.227785 | + | 0.973712i | \(0.426852\pi\) | |||||||
\(948\) | −102579. | −3.51434 | ||||||||
\(949\) | 39318.3 | 1.34492 | ||||||||
\(950\) | −19048.4 | −0.650540 | ||||||||
\(951\) | 28624.9 | 0.976051 | ||||||||
\(952\) | 13055.5 | 0.444466 | ||||||||
\(953\) | 16222.6 | 0.551418 | 0.275709 | − | 0.961241i | \(-0.411087\pi\) | ||||
0.275709 | + | 0.961241i | \(0.411087\pi\) | |||||||
\(954\) | −42092.2 | −1.42849 | ||||||||
\(955\) | 1773.18 | 0.0600825 | ||||||||
\(956\) | −30793.0 | −1.04175 | ||||||||
\(957\) | 45804.7 | 1.54718 | ||||||||
\(958\) | −35912.4 | −1.21115 | ||||||||
\(959\) | −26290.4 | −0.885255 | ||||||||
\(960\) | −37335.6 | −1.25521 | ||||||||
\(961\) | −18062.1 | −0.606292 | ||||||||
\(962\) | −6178.92 | −0.207086 | ||||||||
\(963\) | 51872.9 | 1.73581 | ||||||||
\(964\) | −16726.5 | −0.558842 | ||||||||
\(965\) | −21030.1 | −0.701535 | ||||||||
\(966\) | −83234.3 | −2.77228 | ||||||||
\(967\) | 22602.3 | 0.751647 | 0.375823 | − | 0.926691i | \(-0.377360\pi\) | ||||
0.375823 | + | 0.926691i | \(0.377360\pi\) | |||||||
\(968\) | −18396.8 | −0.610842 | ||||||||
\(969\) | 27047.8 | 0.896699 | ||||||||
\(970\) | 23197.1 | 0.767851 | ||||||||
\(971\) | 8215.32 | 0.271516 | 0.135758 | − | 0.990742i | \(-0.456653\pi\) | ||||
0.135758 | + | 0.990742i | \(0.456653\pi\) | |||||||
\(972\) | 59566.7 | 1.96564 | ||||||||
\(973\) | 6778.22 | 0.223330 | ||||||||
\(974\) | −38008.5 | −1.25038 | ||||||||
\(975\) | −51592.3 | −1.69464 | ||||||||
\(976\) | −8712.01 | −0.285722 | ||||||||
\(977\) | 13701.3 | 0.448662 | 0.224331 | − | 0.974513i | \(-0.427980\pi\) | ||||
0.224331 | + | 0.974513i | \(0.427980\pi\) | |||||||
\(978\) | −37684.8 | −1.23213 | ||||||||
\(979\) | −26236.9 | −0.856522 | ||||||||
\(980\) | 12541.8 | 0.408810 | ||||||||
\(981\) | −26397.5 | −0.859129 | ||||||||
\(982\) | −34170.3 | −1.11040 | ||||||||
\(983\) | 35295.3 | 1.14521 | 0.572606 | − | 0.819830i | \(-0.305932\pi\) | ||||
0.572606 | + | 0.819830i | \(0.305932\pi\) | |||||||
\(984\) | −55644.6 | −1.80273 | ||||||||
\(985\) | 13201.4 | 0.427036 | ||||||||
\(986\) | 36319.5 | 1.17307 | ||||||||
\(987\) | −1972.10 | −0.0635996 | ||||||||
\(988\) | 39130.1 | 1.26001 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 45423.8 | 1.45825 | ||||||||
\(991\) | −10086.0 | −0.323302 | −0.161651 | − | 0.986848i | \(-0.551682\pi\) | ||||
−0.161651 | + | 0.986848i | \(0.551682\pi\) | |||||||
\(992\) | −25214.3 | −0.807011 | ||||||||
\(993\) | 41075.0 | 1.31266 | ||||||||
\(994\) | −8488.96 | −0.270879 | ||||||||
\(995\) | −3120.57 | −0.0994259 | ||||||||
\(996\) | −69463.5 | −2.20987 | ||||||||
\(997\) | −14690.8 | −0.466662 | −0.233331 | − | 0.972397i | \(-0.574963\pi\) | ||||
−0.233331 | + | 0.972397i | \(0.574963\pi\) | |||||||
\(998\) | −76839.4 | −2.43718 | ||||||||
\(999\) | 1173.19 | 0.0371552 |
(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.1.5 | 30 | ||
43.8 | odd | 14 | 43.4.e.a.21.2 | ✓ | 60 | ||
43.27 | odd | 14 | 43.4.e.a.41.2 | yes | 60 | ||
43.42 | odd | 2 | 1849.4.a.h.1.26 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.21.2 | ✓ | 60 | 43.8 | odd | 14 | ||
43.4.e.a.41.2 | yes | 60 | 43.27 | odd | 14 | ||
1849.4.a.g.1.5 | 30 | 1.1 | even | 1 | trivial | ||
1849.4.a.h.1.26 | 30 | 43.42 | odd | 2 |