Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.89764 | −1.67295 | −0.836477 | − | 0.548002i | \(-0.815389\pi\) | ||||
−0.836477 | + | 0.548002i | \(0.815389\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.79029 | 1.69507 | 0.847535 | − | 0.530740i | \(-0.178086\pi\) | ||||
0.847535 | + | 0.530740i | \(0.178086\pi\) | |||||||
\(6\) | −2.89764 | −1.18296 | ||||||||
\(7\) | −4.56649 | −1.72597 | −0.862986 | − | 0.505227i | \(-0.831409\pi\) | ||||
−0.862986 | + | 0.505227i | \(0.831409\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.39633 | 1.79878 | ||||||||
\(10\) | 3.79029 | 1.19860 | ||||||||
\(11\) | 3.65865 | 1.10313 | 0.551563 | − | 0.834133i | \(-0.314032\pi\) | ||||
0.551563 | + | 0.834133i | \(0.314032\pi\) | |||||||
\(12\) | −2.89764 | −0.836477 | ||||||||
\(13\) | 2.26961 | 0.629477 | 0.314738 | − | 0.949178i | \(-0.398083\pi\) | ||||
0.314738 | + | 0.949178i | \(0.398083\pi\) | |||||||
\(14\) | −4.56649 | −1.22045 | ||||||||
\(15\) | −10.9829 | −2.83578 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.61568 | 0.391859 | 0.195929 | − | 0.980618i | \(-0.437228\pi\) | ||||
0.195929 | + | 0.980618i | \(0.437228\pi\) | |||||||
\(18\) | 5.39633 | 1.27193 | ||||||||
\(19\) | −6.07444 | −1.39357 | −0.696787 | − | 0.717279i | \(-0.745387\pi\) | ||||
−0.696787 | + | 0.717279i | \(0.745387\pi\) | |||||||
\(20\) | 3.79029 | 0.847535 | ||||||||
\(21\) | 13.2321 | 2.88747 | ||||||||
\(22\) | 3.65865 | 0.780027 | ||||||||
\(23\) | −6.86880 | −1.43224 | −0.716122 | − | 0.697975i | \(-0.754084\pi\) | ||||
−0.716122 | + | 0.697975i | \(0.754084\pi\) | |||||||
\(24\) | −2.89764 | −0.591479 | ||||||||
\(25\) | 9.36631 | 1.87326 | ||||||||
\(26\) | 2.26961 | 0.445107 | ||||||||
\(27\) | −6.94371 | −1.33632 | ||||||||
\(28\) | −4.56649 | −0.862986 | ||||||||
\(29\) | −7.67395 | −1.42502 | −0.712509 | − | 0.701663i | \(-0.752441\pi\) | ||||
−0.712509 | + | 0.701663i | \(0.752441\pi\) | |||||||
\(30\) | −10.9829 | −2.00520 | ||||||||
\(31\) | 2.27430 | 0.408477 | 0.204238 | − | 0.978921i | \(-0.434528\pi\) | ||||
0.204238 | + | 0.978921i | \(0.434528\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −10.6015 | −1.84548 | ||||||||
\(34\) | 1.61568 | 0.277086 | ||||||||
\(35\) | −17.3083 | −2.92564 | ||||||||
\(36\) | 5.39633 | 0.899388 | ||||||||
\(37\) | −9.40992 | −1.54698 | −0.773491 | − | 0.633807i | \(-0.781491\pi\) | ||||
−0.773491 | + | 0.633807i | \(0.781491\pi\) | |||||||
\(38\) | −6.07444 | −0.985405 | ||||||||
\(39\) | −6.57652 | −1.05309 | ||||||||
\(40\) | 3.79029 | 0.599298 | ||||||||
\(41\) | −10.6980 | −1.67075 | −0.835377 | − | 0.549677i | \(-0.814751\pi\) | ||||
−0.835377 | + | 0.549677i | \(0.814751\pi\) | |||||||
\(42\) | 13.2321 | 2.04175 | ||||||||
\(43\) | 6.27023 | 0.956200 | 0.478100 | − | 0.878305i | \(-0.341326\pi\) | ||||
0.478100 | + | 0.878305i | \(0.341326\pi\) | |||||||
\(44\) | 3.65865 | 0.551563 | ||||||||
\(45\) | 20.4537 | 3.04905 | ||||||||
\(46\) | −6.86880 | −1.01275 | ||||||||
\(47\) | −5.99379 | −0.874284 | −0.437142 | − | 0.899393i | \(-0.644009\pi\) | ||||
−0.437142 | + | 0.899393i | \(0.644009\pi\) | |||||||
\(48\) | −2.89764 | −0.418239 | ||||||||
\(49\) | 13.8529 | 1.97898 | ||||||||
\(50\) | 9.36631 | 1.32460 | ||||||||
\(51\) | −4.68165 | −0.655562 | ||||||||
\(52\) | 2.26961 | 0.314738 | ||||||||
\(53\) | 7.10368 | 0.975766 | 0.487883 | − | 0.872909i | \(-0.337769\pi\) | ||||
0.487883 | + | 0.872909i | \(0.337769\pi\) | |||||||
\(54\) | −6.94371 | −0.944919 | ||||||||
\(55\) | 13.8674 | 1.86987 | ||||||||
\(56\) | −4.56649 | −0.610223 | ||||||||
\(57\) | 17.6016 | 2.33138 | ||||||||
\(58\) | −7.67395 | −1.00764 | ||||||||
\(59\) | −13.0409 | −1.69778 | −0.848892 | − | 0.528567i | \(-0.822730\pi\) | ||||
−0.848892 | + | 0.528567i | \(0.822730\pi\) | |||||||
\(60\) | −10.9829 | −1.41789 | ||||||||
\(61\) | 1.80554 | 0.231176 | 0.115588 | − | 0.993297i | \(-0.463125\pi\) | ||||
0.115588 | + | 0.993297i | \(0.463125\pi\) | |||||||
\(62\) | 2.27430 | 0.288837 | ||||||||
\(63\) | −24.6423 | −3.10464 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.60249 | 1.06701 | ||||||||
\(66\) | −10.6015 | −1.30495 | ||||||||
\(67\) | 9.50832 | 1.16163 | 0.580813 | − | 0.814037i | \(-0.302735\pi\) | ||||
0.580813 | + | 0.814037i | \(0.302735\pi\) | |||||||
\(68\) | 1.61568 | 0.195929 | ||||||||
\(69\) | 19.9033 | 2.39608 | ||||||||
\(70\) | −17.3083 | −2.06874 | ||||||||
\(71\) | 2.25981 | 0.268190 | 0.134095 | − | 0.990968i | \(-0.457187\pi\) | ||||
0.134095 | + | 0.990968i | \(0.457187\pi\) | |||||||
\(72\) | 5.39633 | 0.635964 | ||||||||
\(73\) | 8.78795 | 1.02855 | 0.514276 | − | 0.857625i | \(-0.328061\pi\) | ||||
0.514276 | + | 0.857625i | \(0.328061\pi\) | |||||||
\(74\) | −9.40992 | −1.09388 | ||||||||
\(75\) | −27.1402 | −3.13388 | ||||||||
\(76\) | −6.07444 | −0.696787 | ||||||||
\(77\) | −16.7072 | −1.90396 | ||||||||
\(78\) | −6.57652 | −0.744644 | ||||||||
\(79\) | −5.00610 | −0.563231 | −0.281615 | − | 0.959527i | \(-0.590870\pi\) | ||||
−0.281615 | + | 0.959527i | \(0.590870\pi\) | |||||||
\(80\) | 3.79029 | 0.423767 | ||||||||
\(81\) | 3.93139 | 0.436822 | ||||||||
\(82\) | −10.6980 | −1.18140 | ||||||||
\(83\) | 2.74130 | 0.300897 | 0.150449 | − | 0.988618i | \(-0.451928\pi\) | ||||
0.150449 | + | 0.988618i | \(0.451928\pi\) | |||||||
\(84\) | 13.2321 | 1.44374 | ||||||||
\(85\) | 6.12388 | 0.664228 | ||||||||
\(86\) | 6.27023 | 0.676136 | ||||||||
\(87\) | 22.2364 | 2.38399 | ||||||||
\(88\) | 3.65865 | 0.390014 | ||||||||
\(89\) | −13.2225 | −1.40158 | −0.700792 | − | 0.713366i | \(-0.747170\pi\) | ||||
−0.700792 | + | 0.713366i | \(0.747170\pi\) | |||||||
\(90\) | 20.4537 | 2.15601 | ||||||||
\(91\) | −10.3642 | −1.08646 | ||||||||
\(92\) | −6.86880 | −0.716122 | ||||||||
\(93\) | −6.59012 | −0.683363 | ||||||||
\(94\) | −5.99379 | −0.618212 | ||||||||
\(95\) | −23.0239 | −2.36220 | ||||||||
\(96\) | −2.89764 | −0.295739 | ||||||||
\(97\) | 7.22829 | 0.733922 | 0.366961 | − | 0.930236i | \(-0.380398\pi\) | ||||
0.366961 | + | 0.930236i | \(0.380398\pi\) | |||||||
\(98\) | 13.8529 | 1.39935 | ||||||||
\(99\) | 19.7433 | 1.98428 | ||||||||
\(100\) | 9.36631 | 0.936631 | ||||||||
\(101\) | 2.14597 | 0.213532 | 0.106766 | − | 0.994284i | \(-0.465950\pi\) | ||||
0.106766 | + | 0.994284i | \(0.465950\pi\) | |||||||
\(102\) | −4.68165 | −0.463552 | ||||||||
\(103\) | 18.3353 | 1.80663 | 0.903316 | − | 0.428975i | \(-0.141125\pi\) | ||||
0.903316 | + | 0.428975i | \(0.141125\pi\) | |||||||
\(104\) | 2.26961 | 0.222554 | ||||||||
\(105\) | 50.1534 | 4.89447 | ||||||||
\(106\) | 7.10368 | 0.689971 | ||||||||
\(107\) | −14.3251 | −1.38486 | −0.692432 | − | 0.721483i | \(-0.743461\pi\) | ||||
−0.692432 | + | 0.721483i | \(0.743461\pi\) | |||||||
\(108\) | −6.94371 | −0.668159 | ||||||||
\(109\) | −19.8425 | −1.90057 | −0.950283 | − | 0.311386i | \(-0.899207\pi\) | ||||
−0.950283 | + | 0.311386i | \(0.899207\pi\) | |||||||
\(110\) | 13.8674 | 1.32220 | ||||||||
\(111\) | 27.2666 | 2.58803 | ||||||||
\(112\) | −4.56649 | −0.431493 | ||||||||
\(113\) | −15.5873 | −1.46633 | −0.733166 | − | 0.680050i | \(-0.761958\pi\) | ||||
−0.733166 | + | 0.680050i | \(0.761958\pi\) | |||||||
\(114\) | 17.6016 | 1.64854 | ||||||||
\(115\) | −26.0348 | −2.42775 | ||||||||
\(116\) | −7.67395 | −0.712509 | ||||||||
\(117\) | 12.2476 | 1.13229 | ||||||||
\(118\) | −13.0409 | −1.20051 | ||||||||
\(119\) | −7.37797 | −0.676338 | ||||||||
\(120\) | −10.9829 | −1.00260 | ||||||||
\(121\) | 2.38574 | 0.216886 | ||||||||
\(122\) | 1.80554 | 0.163466 | ||||||||
\(123\) | 30.9991 | 2.79510 | ||||||||
\(124\) | 2.27430 | 0.204238 | ||||||||
\(125\) | 16.5496 | 1.48024 | ||||||||
\(126\) | −24.6423 | −2.19531 | ||||||||
\(127\) | 3.64159 | 0.323139 | 0.161569 | − | 0.986861i | \(-0.448344\pi\) | ||||
0.161569 | + | 0.986861i | \(0.448344\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −18.1689 | −1.59968 | ||||||||
\(130\) | 8.60249 | 0.754488 | ||||||||
\(131\) | 10.1897 | 0.890276 | 0.445138 | − | 0.895462i | \(-0.353155\pi\) | ||||
0.445138 | + | 0.895462i | \(0.353155\pi\) | |||||||
\(132\) | −10.6015 | −0.922739 | ||||||||
\(133\) | 27.7389 | 2.40527 | ||||||||
\(134\) | 9.50832 | 0.821394 | ||||||||
\(135\) | −26.3187 | −2.26515 | ||||||||
\(136\) | 1.61568 | 0.138543 | ||||||||
\(137\) | 8.19163 | 0.699858 | 0.349929 | − | 0.936776i | \(-0.386206\pi\) | ||||
0.349929 | + | 0.936776i | \(0.386206\pi\) | |||||||
\(138\) | 19.9033 | 1.69428 | ||||||||
\(139\) | −0.273303 | −0.0231813 | −0.0115906 | − | 0.999933i | \(-0.503689\pi\) | ||||
−0.0115906 | + | 0.999933i | \(0.503689\pi\) | |||||||
\(140\) | −17.3083 | −1.46282 | ||||||||
\(141\) | 17.3678 | 1.46264 | ||||||||
\(142\) | 2.25981 | 0.189639 | ||||||||
\(143\) | 8.30372 | 0.694392 | ||||||||
\(144\) | 5.39633 | 0.449694 | ||||||||
\(145\) | −29.0865 | −2.41550 | ||||||||
\(146\) | 8.78795 | 0.727296 | ||||||||
\(147\) | −40.1407 | −3.31075 | ||||||||
\(148\) | −9.40992 | −0.773491 | ||||||||
\(149\) | 11.0896 | 0.908497 | 0.454248 | − | 0.890875i | \(-0.349908\pi\) | ||||
0.454248 | + | 0.890875i | \(0.349908\pi\) | |||||||
\(150\) | −27.1402 | −2.21599 | ||||||||
\(151\) | −5.89412 | −0.479657 | −0.239828 | − | 0.970815i | \(-0.577091\pi\) | ||||
−0.239828 | + | 0.970815i | \(0.577091\pi\) | |||||||
\(152\) | −6.07444 | −0.492702 | ||||||||
\(153\) | 8.71872 | 0.704867 | ||||||||
\(154\) | −16.7072 | −1.34631 | ||||||||
\(155\) | 8.62027 | 0.692397 | ||||||||
\(156\) | −6.57652 | −0.526543 | ||||||||
\(157\) | 13.8986 | 1.10923 | 0.554615 | − | 0.832107i | \(-0.312865\pi\) | ||||
0.554615 | + | 0.832107i | \(0.312865\pi\) | |||||||
\(158\) | −5.00610 | −0.398264 | ||||||||
\(159\) | −20.5839 | −1.63241 | ||||||||
\(160\) | 3.79029 | 0.299649 | ||||||||
\(161\) | 31.3663 | 2.47201 | ||||||||
\(162\) | 3.93139 | 0.308880 | ||||||||
\(163\) | −5.81128 | −0.455175 | −0.227587 | − | 0.973758i | \(-0.573084\pi\) | ||||
−0.227587 | + | 0.973758i | \(0.573084\pi\) | |||||||
\(164\) | −10.6980 | −0.835377 | ||||||||
\(165\) | −40.1827 | −3.12822 | ||||||||
\(166\) | 2.74130 | 0.212766 | ||||||||
\(167\) | −13.9647 | −1.08062 | −0.540309 | − | 0.841467i | \(-0.681693\pi\) | ||||
−0.540309 | + | 0.841467i | \(0.681693\pi\) | |||||||
\(168\) | 13.2321 | 1.02088 | ||||||||
\(169\) | −7.84887 | −0.603759 | ||||||||
\(170\) | 6.12388 | 0.469680 | ||||||||
\(171\) | −32.7797 | −2.50673 | ||||||||
\(172\) | 6.27023 | 0.478100 | ||||||||
\(173\) | −21.7129 | −1.65080 | −0.825400 | − | 0.564548i | \(-0.809050\pi\) | ||||
−0.825400 | + | 0.564548i | \(0.809050\pi\) | |||||||
\(174\) | 22.2364 | 1.68574 | ||||||||
\(175\) | −42.7712 | −3.23320 | ||||||||
\(176\) | 3.65865 | 0.275781 | ||||||||
\(177\) | 37.7879 | 2.84031 | ||||||||
\(178\) | −13.2225 | −0.991070 | ||||||||
\(179\) | −19.7679 | −1.47753 | −0.738763 | − | 0.673966i | \(-0.764589\pi\) | ||||
−0.738763 | + | 0.673966i | \(0.764589\pi\) | |||||||
\(180\) | 20.4537 | 1.52453 | ||||||||
\(181\) | −6.86724 | −0.510438 | −0.255219 | − | 0.966883i | \(-0.582148\pi\) | ||||
−0.255219 | + | 0.966883i | \(0.582148\pi\) | |||||||
\(182\) | −10.3642 | −0.768243 | ||||||||
\(183\) | −5.23182 | −0.386747 | ||||||||
\(184\) | −6.86880 | −0.506375 | ||||||||
\(185\) | −35.6664 | −2.62224 | ||||||||
\(186\) | −6.59012 | −0.483211 | ||||||||
\(187\) | 5.91120 | 0.432270 | ||||||||
\(188\) | −5.99379 | −0.437142 | ||||||||
\(189\) | 31.7084 | 2.30645 | ||||||||
\(190\) | −23.0239 | −1.67033 | ||||||||
\(191\) | −20.5068 | −1.48382 | −0.741911 | − | 0.670499i | \(-0.766080\pi\) | ||||
−0.741911 | + | 0.670499i | \(0.766080\pi\) | |||||||
\(192\) | −2.89764 | −0.209119 | ||||||||
\(193\) | −6.04232 | −0.434936 | −0.217468 | − | 0.976067i | \(-0.569780\pi\) | ||||
−0.217468 | + | 0.976067i | \(0.569780\pi\) | |||||||
\(194\) | 7.22829 | 0.518961 | ||||||||
\(195\) | −24.9269 | −1.78505 | ||||||||
\(196\) | 13.8529 | 0.989491 | ||||||||
\(197\) | 22.0543 | 1.57130 | 0.785652 | − | 0.618668i | \(-0.212328\pi\) | ||||
0.785652 | + | 0.618668i | \(0.212328\pi\) | |||||||
\(198\) | 19.7433 | 1.40310 | ||||||||
\(199\) | −25.3534 | −1.79725 | −0.898627 | − | 0.438714i | \(-0.855434\pi\) | ||||
−0.898627 | + | 0.438714i | \(0.855434\pi\) | |||||||
\(200\) | 9.36631 | 0.662298 | ||||||||
\(201\) | −27.5517 | −1.94335 | ||||||||
\(202\) | 2.14597 | 0.150990 | ||||||||
\(203\) | 35.0431 | 2.45954 | ||||||||
\(204\) | −4.68165 | −0.327781 | ||||||||
\(205\) | −40.5487 | −2.83205 | ||||||||
\(206\) | 18.3353 | 1.27748 | ||||||||
\(207\) | −37.0663 | −2.57629 | ||||||||
\(208\) | 2.26961 | 0.157369 | ||||||||
\(209\) | −22.2243 | −1.53729 | ||||||||
\(210\) | 50.1534 | 3.46091 | ||||||||
\(211\) | 23.5618 | 1.62206 | 0.811032 | − | 0.585002i | \(-0.198906\pi\) | ||||
0.811032 | + | 0.585002i | \(0.198906\pi\) | |||||||
\(212\) | 7.10368 | 0.487883 | ||||||||
\(213\) | −6.54812 | −0.448670 | ||||||||
\(214\) | −14.3251 | −0.979247 | ||||||||
\(215\) | 23.7660 | 1.62083 | ||||||||
\(216\) | −6.94371 | −0.472460 | ||||||||
\(217\) | −10.3856 | −0.705020 | ||||||||
\(218\) | −19.8425 | −1.34390 | ||||||||
\(219\) | −25.4643 | −1.72072 | ||||||||
\(220\) | 13.8674 | 0.934937 | ||||||||
\(221\) | 3.66696 | 0.246666 | ||||||||
\(222\) | 27.2666 | 1.83001 | ||||||||
\(223\) | 18.3676 | 1.22998 | 0.614992 | − | 0.788533i | \(-0.289159\pi\) | ||||
0.614992 | + | 0.788533i | \(0.289159\pi\) | |||||||
\(224\) | −4.56649 | −0.305112 | ||||||||
\(225\) | 50.5437 | 3.36958 | ||||||||
\(226\) | −15.5873 | −1.03685 | ||||||||
\(227\) | 1.23503 | 0.0819718 | 0.0409859 | − | 0.999160i | \(-0.486950\pi\) | ||||
0.0409859 | + | 0.999160i | \(0.486950\pi\) | |||||||
\(228\) | 17.6016 | 1.16569 | ||||||||
\(229\) | −3.42062 | −0.226041 | −0.113020 | − | 0.993593i | \(-0.536053\pi\) | ||||
−0.113020 | + | 0.993593i | \(0.536053\pi\) | |||||||
\(230\) | −26.0348 | −1.71668 | ||||||||
\(231\) | 48.4115 | 3.18525 | ||||||||
\(232\) | −7.67395 | −0.503820 | ||||||||
\(233\) | −21.3961 | −1.40170 | −0.700852 | − | 0.713306i | \(-0.747197\pi\) | ||||
−0.700852 | + | 0.713306i | \(0.747197\pi\) | |||||||
\(234\) | 12.2476 | 0.800649 | ||||||||
\(235\) | −22.7182 | −1.48197 | ||||||||
\(236\) | −13.0409 | −0.848892 | ||||||||
\(237\) | 14.5059 | 0.942259 | ||||||||
\(238\) | −7.37797 | −0.478243 | ||||||||
\(239\) | −12.8100 | −0.828611 | −0.414306 | − | 0.910138i | \(-0.635976\pi\) | ||||
−0.414306 | + | 0.910138i | \(0.635976\pi\) | |||||||
\(240\) | −10.9829 | −0.708944 | ||||||||
\(241\) | 2.55865 | 0.164817 | 0.0824087 | − | 0.996599i | \(-0.473739\pi\) | ||||
0.0824087 | + | 0.996599i | \(0.473739\pi\) | |||||||
\(242\) | 2.38574 | 0.153361 | ||||||||
\(243\) | 9.43935 | 0.605535 | ||||||||
\(244\) | 1.80554 | 0.115588 | ||||||||
\(245\) | 52.5064 | 3.35451 | ||||||||
\(246\) | 30.9991 | 1.97643 | ||||||||
\(247\) | −13.7866 | −0.877222 | ||||||||
\(248\) | 2.27430 | 0.144418 | ||||||||
\(249\) | −7.94331 | −0.503387 | ||||||||
\(250\) | 16.5496 | 1.04669 | ||||||||
\(251\) | −13.2223 | −0.834583 | −0.417291 | − | 0.908773i | \(-0.637021\pi\) | ||||
−0.417291 | + | 0.908773i | \(0.637021\pi\) | |||||||
\(252\) | −24.6423 | −1.55232 | ||||||||
\(253\) | −25.1306 | −1.57994 | ||||||||
\(254\) | 3.64159 | 0.228494 | ||||||||
\(255\) | −17.7448 | −1.11122 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.88848 | 0.429692 | 0.214846 | − | 0.976648i | \(-0.431075\pi\) | ||||
0.214846 | + | 0.976648i | \(0.431075\pi\) | |||||||
\(258\) | −18.1689 | −1.13114 | ||||||||
\(259\) | 42.9704 | 2.67005 | ||||||||
\(260\) | 8.60249 | 0.533504 | ||||||||
\(261\) | −41.4112 | −2.56329 | ||||||||
\(262\) | 10.1897 | 0.629520 | ||||||||
\(263\) | 6.88858 | 0.424768 | 0.212384 | − | 0.977186i | \(-0.431877\pi\) | ||||
0.212384 | + | 0.977186i | \(0.431877\pi\) | |||||||
\(264\) | −10.6015 | −0.652475 | ||||||||
\(265\) | 26.9250 | 1.65399 | ||||||||
\(266\) | 27.7389 | 1.70078 | ||||||||
\(267\) | 38.3141 | 2.34479 | ||||||||
\(268\) | 9.50832 | 0.580813 | ||||||||
\(269\) | 0.730619 | 0.0445467 | 0.0222733 | − | 0.999752i | \(-0.492910\pi\) | ||||
0.0222733 | + | 0.999752i | \(0.492910\pi\) | |||||||
\(270\) | −26.3187 | −1.60170 | ||||||||
\(271\) | 29.9786 | 1.82107 | 0.910534 | − | 0.413435i | \(-0.135671\pi\) | ||||
0.910534 | + | 0.413435i | \(0.135671\pi\) | |||||||
\(272\) | 1.61568 | 0.0979647 | ||||||||
\(273\) | 30.0316 | 1.81760 | ||||||||
\(274\) | 8.19163 | 0.494874 | ||||||||
\(275\) | 34.2681 | 2.06644 | ||||||||
\(276\) | 19.9033 | 1.19804 | ||||||||
\(277\) | 14.5178 | 0.872288 | 0.436144 | − | 0.899877i | \(-0.356344\pi\) | ||||
0.436144 | + | 0.899877i | \(0.356344\pi\) | |||||||
\(278\) | −0.273303 | −0.0163916 | ||||||||
\(279\) | 12.2729 | 0.734759 | ||||||||
\(280\) | −17.3083 | −1.03437 | ||||||||
\(281\) | −5.12599 | −0.305791 | −0.152896 | − | 0.988242i | \(-0.548860\pi\) | ||||
−0.152896 | + | 0.988242i | \(0.548860\pi\) | |||||||
\(282\) | 17.3678 | 1.03424 | ||||||||
\(283\) | −17.9473 | −1.06686 | −0.533429 | − | 0.845845i | \(-0.679097\pi\) | ||||
−0.533429 | + | 0.845845i | \(0.679097\pi\) | |||||||
\(284\) | 2.25981 | 0.134095 | ||||||||
\(285\) | 66.7151 | 3.95186 | ||||||||
\(286\) | 8.30372 | 0.491009 | ||||||||
\(287\) | 48.8526 | 2.88368 | ||||||||
\(288\) | 5.39633 | 0.317982 | ||||||||
\(289\) | −14.3896 | −0.846447 | ||||||||
\(290\) | −29.0865 | −1.70802 | ||||||||
\(291\) | −20.9450 | −1.22782 | ||||||||
\(292\) | 8.78795 | 0.514276 | ||||||||
\(293\) | 27.1006 | 1.58323 | 0.791616 | − | 0.611018i | \(-0.209240\pi\) | ||||
0.791616 | + | 0.611018i | \(0.209240\pi\) | |||||||
\(294\) | −40.1407 | −2.34105 | ||||||||
\(295\) | −49.4289 | −2.87786 | ||||||||
\(296\) | −9.40992 | −0.546941 | ||||||||
\(297\) | −25.4046 | −1.47413 | ||||||||
\(298\) | 11.0896 | 0.642404 | ||||||||
\(299\) | −15.5895 | −0.901564 | ||||||||
\(300\) | −27.1402 | −1.56694 | ||||||||
\(301\) | −28.6330 | −1.65038 | ||||||||
\(302\) | −5.89412 | −0.339169 | ||||||||
\(303\) | −6.21825 | −0.357229 | ||||||||
\(304\) | −6.07444 | −0.348393 | ||||||||
\(305\) | 6.84353 | 0.391859 | ||||||||
\(306\) | 8.71872 | 0.498416 | ||||||||
\(307\) | −23.5113 | −1.34186 | −0.670931 | − | 0.741520i | \(-0.734105\pi\) | ||||
−0.670931 | + | 0.741520i | \(0.734105\pi\) | |||||||
\(308\) | −16.7072 | −0.951982 | ||||||||
\(309\) | −53.1292 | −3.02241 | ||||||||
\(310\) | 8.62027 | 0.489599 | ||||||||
\(311\) | 4.10835 | 0.232963 | 0.116481 | − | 0.993193i | \(-0.462838\pi\) | ||||
0.116481 | + | 0.993193i | \(0.462838\pi\) | |||||||
\(312\) | −6.57652 | −0.372322 | ||||||||
\(313\) | 18.3293 | 1.03603 | 0.518016 | − | 0.855371i | \(-0.326671\pi\) | ||||
0.518016 | + | 0.855371i | \(0.326671\pi\) | |||||||
\(314\) | 13.8986 | 0.784345 | ||||||||
\(315\) | −93.4016 | −5.26258 | ||||||||
\(316\) | −5.00610 | −0.281615 | ||||||||
\(317\) | −31.1070 | −1.74714 | −0.873572 | − | 0.486695i | \(-0.838202\pi\) | ||||
−0.873572 | + | 0.486695i | \(0.838202\pi\) | |||||||
\(318\) | −20.5839 | −1.15429 | ||||||||
\(319\) | −28.0763 | −1.57197 | ||||||||
\(320\) | 3.79029 | 0.211884 | ||||||||
\(321\) | 41.5092 | 2.31682 | ||||||||
\(322\) | 31.3663 | 1.74798 | ||||||||
\(323\) | −9.81433 | −0.546084 | ||||||||
\(324\) | 3.93139 | 0.218411 | ||||||||
\(325\) | 21.2579 | 1.17918 | ||||||||
\(326\) | −5.81128 | −0.321857 | ||||||||
\(327\) | 57.4965 | 3.17956 | ||||||||
\(328\) | −10.6980 | −0.590701 | ||||||||
\(329\) | 27.3706 | 1.50899 | ||||||||
\(330\) | −40.1827 | −2.21198 | ||||||||
\(331\) | −16.9778 | −0.933183 | −0.466591 | − | 0.884473i | \(-0.654518\pi\) | ||||
−0.466591 | + | 0.884473i | \(0.654518\pi\) | |||||||
\(332\) | 2.74130 | 0.150449 | ||||||||
\(333\) | −50.7791 | −2.78268 | ||||||||
\(334\) | −13.9647 | −0.764112 | ||||||||
\(335\) | 36.0393 | 1.96904 | ||||||||
\(336\) | 13.2321 | 0.721868 | ||||||||
\(337\) | −6.86104 | −0.373745 | −0.186872 | − | 0.982384i | \(-0.559835\pi\) | ||||
−0.186872 | + | 0.982384i | \(0.559835\pi\) | |||||||
\(338\) | −7.84887 | −0.426922 | ||||||||
\(339\) | 45.1665 | 2.45311 | ||||||||
\(340\) | 6.12388 | 0.332114 | ||||||||
\(341\) | 8.32089 | 0.450601 | ||||||||
\(342\) | −32.7797 | −1.77252 | ||||||||
\(343\) | −31.2936 | −1.68970 | ||||||||
\(344\) | 6.27023 | 0.338068 | ||||||||
\(345\) | 75.4394 | 4.06152 | ||||||||
\(346\) | −21.7129 | −1.16729 | ||||||||
\(347\) | 7.51465 | 0.403408 | 0.201704 | − | 0.979447i | \(-0.435352\pi\) | ||||
0.201704 | + | 0.979447i | \(0.435352\pi\) | |||||||
\(348\) | 22.2364 | 1.19199 | ||||||||
\(349\) | −23.9846 | −1.28387 | −0.641934 | − | 0.766760i | \(-0.721868\pi\) | ||||
−0.641934 | + | 0.766760i | \(0.721868\pi\) | |||||||
\(350\) | −42.7712 | −2.28622 | ||||||||
\(351\) | −15.7595 | −0.841181 | ||||||||
\(352\) | 3.65865 | 0.195007 | ||||||||
\(353\) | −24.4745 | −1.30265 | −0.651324 | − | 0.758800i | \(-0.725786\pi\) | ||||
−0.651324 | + | 0.758800i | \(0.725786\pi\) | |||||||
\(354\) | 37.7879 | 2.00841 | ||||||||
\(355\) | 8.56534 | 0.454601 | ||||||||
\(356\) | −13.2225 | −0.700792 | ||||||||
\(357\) | 21.3787 | 1.13148 | ||||||||
\(358\) | −19.7679 | −1.04477 | ||||||||
\(359\) | −2.53346 | −0.133711 | −0.0668553 | − | 0.997763i | \(-0.521297\pi\) | ||||
−0.0668553 | + | 0.997763i | \(0.521297\pi\) | |||||||
\(360\) | 20.4537 | 1.07800 | ||||||||
\(361\) | 17.8989 | 0.942046 | ||||||||
\(362\) | −6.86724 | −0.360934 | ||||||||
\(363\) | −6.91303 | −0.362840 | ||||||||
\(364\) | −10.3642 | −0.543230 | ||||||||
\(365\) | 33.3089 | 1.74347 | ||||||||
\(366\) | −5.23182 | −0.273471 | ||||||||
\(367\) | −11.8394 | −0.618013 | −0.309007 | − | 0.951060i | \(-0.599997\pi\) | ||||
−0.309007 | + | 0.951060i | \(0.599997\pi\) | |||||||
\(368\) | −6.86880 | −0.358061 | ||||||||
\(369\) | −57.7302 | −3.00531 | ||||||||
\(370\) | −35.6664 | −1.85421 | ||||||||
\(371\) | −32.4389 | −1.68415 | ||||||||
\(372\) | −6.59012 | −0.341682 | ||||||||
\(373\) | 23.6275 | 1.22339 | 0.611694 | − | 0.791095i | \(-0.290488\pi\) | ||||
0.611694 | + | 0.791095i | \(0.290488\pi\) | |||||||
\(374\) | 5.91120 | 0.305661 | ||||||||
\(375\) | −47.9548 | −2.47638 | ||||||||
\(376\) | −5.99379 | −0.309106 | ||||||||
\(377\) | −17.4169 | −0.897015 | ||||||||
\(378\) | 31.7084 | 1.63090 | ||||||||
\(379\) | −7.20684 | −0.370190 | −0.185095 | − | 0.982721i | \(-0.559259\pi\) | ||||
−0.185095 | + | 0.982721i | \(0.559259\pi\) | |||||||
\(380\) | −23.0239 | −1.18110 | ||||||||
\(381\) | −10.5520 | −0.540596 | ||||||||
\(382\) | −20.5068 | −1.04922 | ||||||||
\(383\) | −18.1294 | −0.926370 | −0.463185 | − | 0.886262i | \(-0.653294\pi\) | ||||
−0.463185 | + | 0.886262i | \(0.653294\pi\) | |||||||
\(384\) | −2.89764 | −0.147870 | ||||||||
\(385\) | −63.3252 | −3.22735 | ||||||||
\(386\) | −6.04232 | −0.307546 | ||||||||
\(387\) | 33.8362 | 1.71999 | ||||||||
\(388\) | 7.22829 | 0.366961 | ||||||||
\(389\) | 29.6967 | 1.50568 | 0.752841 | − | 0.658202i | \(-0.228683\pi\) | ||||
0.752841 | + | 0.658202i | \(0.228683\pi\) | |||||||
\(390\) | −24.9269 | −1.26222 | ||||||||
\(391\) | −11.0978 | −0.561237 | ||||||||
\(392\) | 13.8529 | 0.699676 | ||||||||
\(393\) | −29.5260 | −1.48939 | ||||||||
\(394\) | 22.0543 | 1.11108 | ||||||||
\(395\) | −18.9746 | −0.954715 | ||||||||
\(396\) | 19.7433 | 0.992138 | ||||||||
\(397\) | −21.4192 | −1.07500 | −0.537498 | − | 0.843265i | \(-0.680631\pi\) | ||||
−0.537498 | + | 0.843265i | \(0.680631\pi\) | |||||||
\(398\) | −25.3534 | −1.27085 | ||||||||
\(399\) | −80.3775 | −4.02391 | ||||||||
\(400\) | 9.36631 | 0.468316 | ||||||||
\(401\) | −24.5090 | −1.22392 | −0.611960 | − | 0.790889i | \(-0.709619\pi\) | ||||
−0.611960 | + | 0.790889i | \(0.709619\pi\) | |||||||
\(402\) | −27.5517 | −1.37415 | ||||||||
\(403\) | 5.16178 | 0.257127 | ||||||||
\(404\) | 2.14597 | 0.106766 | ||||||||
\(405\) | 14.9011 | 0.740443 | ||||||||
\(406\) | 35.0431 | 1.73916 | ||||||||
\(407\) | −34.4276 | −1.70651 | ||||||||
\(408\) | −4.68165 | −0.231776 | ||||||||
\(409\) | 7.65341 | 0.378437 | 0.189218 | − | 0.981935i | \(-0.439405\pi\) | ||||
0.189218 | + | 0.981935i | \(0.439405\pi\) | |||||||
\(410\) | −40.5487 | −2.00256 | ||||||||
\(411\) | −23.7364 | −1.17083 | ||||||||
\(412\) | 18.3353 | 0.903316 | ||||||||
\(413\) | 59.5513 | 2.93033 | ||||||||
\(414\) | −37.0663 | −1.82171 | ||||||||
\(415\) | 10.3903 | 0.510041 | ||||||||
\(416\) | 2.26961 | 0.111277 | ||||||||
\(417\) | 0.791934 | 0.0387812 | ||||||||
\(418\) | −22.2243 | −1.08703 | ||||||||
\(419\) | 9.03421 | 0.441350 | 0.220675 | − | 0.975347i | \(-0.429174\pi\) | ||||
0.220675 | + | 0.975347i | \(0.429174\pi\) | |||||||
\(420\) | 50.1534 | 2.44724 | ||||||||
\(421\) | −19.0591 | −0.928882 | −0.464441 | − | 0.885604i | \(-0.653745\pi\) | ||||
−0.464441 | + | 0.885604i | \(0.653745\pi\) | |||||||
\(422\) | 23.5618 | 1.14697 | ||||||||
\(423\) | −32.3445 | −1.57264 | ||||||||
\(424\) | 7.10368 | 0.344985 | ||||||||
\(425\) | 15.1329 | 0.734055 | ||||||||
\(426\) | −6.54812 | −0.317257 | ||||||||
\(427\) | −8.24500 | −0.399003 | ||||||||
\(428\) | −14.3251 | −0.692432 | ||||||||
\(429\) | −24.0612 | −1.16169 | ||||||||
\(430\) | 23.7660 | 1.14610 | ||||||||
\(431\) | −32.1407 | −1.54816 | −0.774080 | − | 0.633087i | \(-0.781787\pi\) | ||||
−0.774080 | + | 0.633087i | \(0.781787\pi\) | |||||||
\(432\) | −6.94371 | −0.334079 | ||||||||
\(433\) | −3.96443 | −0.190518 | −0.0952592 | − | 0.995453i | \(-0.530368\pi\) | ||||
−0.0952592 | + | 0.995453i | \(0.530368\pi\) | |||||||
\(434\) | −10.3856 | −0.498525 | ||||||||
\(435\) | 84.2824 | 4.04103 | ||||||||
\(436\) | −19.8425 | −0.950283 | ||||||||
\(437\) | 41.7241 | 1.99594 | ||||||||
\(438\) | −25.4643 | −1.21673 | ||||||||
\(439\) | 23.9432 | 1.14275 | 0.571374 | − | 0.820690i | \(-0.306410\pi\) | ||||
0.571374 | + | 0.820690i | \(0.306410\pi\) | |||||||
\(440\) | 13.8674 | 0.661101 | ||||||||
\(441\) | 74.7547 | 3.55975 | ||||||||
\(442\) | 3.66696 | 0.174419 | ||||||||
\(443\) | 8.73126 | 0.414834 | 0.207417 | − | 0.978253i | \(-0.433494\pi\) | ||||
0.207417 | + | 0.978253i | \(0.433494\pi\) | |||||||
\(444\) | 27.2666 | 1.29402 | ||||||||
\(445\) | −50.1172 | −2.37578 | ||||||||
\(446\) | 18.3676 | 0.869730 | ||||||||
\(447\) | −32.1337 | −1.51987 | ||||||||
\(448\) | −4.56649 | −0.215747 | ||||||||
\(449\) | −12.3418 | −0.582446 | −0.291223 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291223 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(450\) | 50.5437 | 2.38265 | ||||||||
\(451\) | −39.1404 | −1.84305 | ||||||||
\(452\) | −15.5873 | −0.733166 | ||||||||
\(453\) | 17.0791 | 0.802444 | ||||||||
\(454\) | 1.23503 | 0.0579628 | ||||||||
\(455\) | −39.2832 | −1.84163 | ||||||||
\(456\) | 17.6016 | 0.824269 | ||||||||
\(457\) | 8.92101 | 0.417307 | 0.208654 | − | 0.977990i | \(-0.433092\pi\) | ||||
0.208654 | + | 0.977990i | \(0.433092\pi\) | |||||||
\(458\) | −3.42062 | −0.159835 | ||||||||
\(459\) | −11.2188 | −0.523648 | ||||||||
\(460\) | −26.0348 | −1.21388 | ||||||||
\(461\) | −6.74591 | −0.314188 | −0.157094 | − | 0.987584i | \(-0.550213\pi\) | ||||
−0.157094 | + | 0.987584i | \(0.550213\pi\) | |||||||
\(462\) | 48.4115 | 2.25231 | ||||||||
\(463\) | 9.99033 | 0.464290 | 0.232145 | − | 0.972681i | \(-0.425426\pi\) | ||||
0.232145 | + | 0.972681i | \(0.425426\pi\) | |||||||
\(464\) | −7.67395 | −0.356254 | ||||||||
\(465\) | −24.9785 | −1.15835 | ||||||||
\(466\) | −21.3961 | −0.991155 | ||||||||
\(467\) | 20.1174 | 0.930922 | 0.465461 | − | 0.885068i | \(-0.345889\pi\) | ||||
0.465461 | + | 0.885068i | \(0.345889\pi\) | |||||||
\(468\) | 12.2476 | 0.566144 | ||||||||
\(469\) | −43.4197 | −2.00494 | ||||||||
\(470\) | −22.7182 | −1.04791 | ||||||||
\(471\) | −40.2732 | −1.85569 | ||||||||
\(472\) | −13.0409 | −0.600257 | ||||||||
\(473\) | 22.9406 | 1.05481 | ||||||||
\(474\) | 14.5059 | 0.666278 | ||||||||
\(475\) | −56.8951 | −2.61053 | ||||||||
\(476\) | −7.37797 | −0.338169 | ||||||||
\(477\) | 38.3338 | 1.75519 | ||||||||
\(478\) | −12.8100 | −0.585917 | ||||||||
\(479\) | −4.31252 | −0.197044 | −0.0985221 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985221 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(480\) | −10.9829 | −0.501299 | ||||||||
\(481\) | −21.3569 | −0.973789 | ||||||||
\(482\) | 2.55865 | 0.116544 | ||||||||
\(483\) | −90.8884 | −4.13557 | ||||||||
\(484\) | 2.38574 | 0.108443 | ||||||||
\(485\) | 27.3973 | 1.24405 | ||||||||
\(486\) | 9.43935 | 0.428178 | ||||||||
\(487\) | 9.56529 | 0.433445 | 0.216722 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216722 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(488\) | 1.80554 | 0.0817331 | ||||||||
\(489\) | 16.8390 | 0.761487 | ||||||||
\(490\) | 52.5064 | 2.37200 | ||||||||
\(491\) | −1.40407 | −0.0633648 | −0.0316824 | − | 0.999498i | \(-0.510087\pi\) | ||||
−0.0316824 | + | 0.999498i | \(0.510087\pi\) | |||||||
\(492\) | 30.9991 | 1.39755 | ||||||||
\(493\) | −12.3986 | −0.558406 | ||||||||
\(494\) | −13.7866 | −0.620289 | ||||||||
\(495\) | 74.8329 | 3.36349 | ||||||||
\(496\) | 2.27430 | 0.102119 | ||||||||
\(497\) | −10.3194 | −0.462889 | ||||||||
\(498\) | −7.94331 | −0.355948 | ||||||||
\(499\) | 30.8884 | 1.38275 | 0.691376 | − | 0.722495i | \(-0.257005\pi\) | ||||
0.691376 | + | 0.722495i | \(0.257005\pi\) | |||||||
\(500\) | 16.5496 | 0.740120 | ||||||||
\(501\) | 40.4646 | 1.80782 | ||||||||
\(502\) | −13.2223 | −0.590139 | ||||||||
\(503\) | −10.8726 | −0.484786 | −0.242393 | − | 0.970178i | \(-0.577932\pi\) | ||||
−0.242393 | + | 0.970178i | \(0.577932\pi\) | |||||||
\(504\) | −24.6423 | −1.09766 | ||||||||
\(505\) | 8.13385 | 0.361952 | ||||||||
\(506\) | −25.1306 | −1.11719 | ||||||||
\(507\) | 22.7432 | 1.01006 | ||||||||
\(508\) | 3.64159 | 0.161569 | ||||||||
\(509\) | −18.3173 | −0.811902 | −0.405951 | − | 0.913895i | \(-0.633060\pi\) | ||||
−0.405951 | + | 0.913895i | \(0.633060\pi\) | |||||||
\(510\) | −17.7448 | −0.785754 | ||||||||
\(511\) | −40.1301 | −1.77525 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 42.1792 | 1.86226 | ||||||||
\(514\) | 6.88848 | 0.303838 | ||||||||
\(515\) | 69.4962 | 3.06237 | ||||||||
\(516\) | −18.1689 | −0.799840 | ||||||||
\(517\) | −21.9292 | −0.964444 | ||||||||
\(518\) | 42.9704 | 1.88801 | ||||||||
\(519\) | 62.9162 | 2.76171 | ||||||||
\(520\) | 8.60249 | 0.377244 | ||||||||
\(521\) | −19.2444 | −0.843113 | −0.421557 | − | 0.906802i | \(-0.638516\pi\) | ||||
−0.421557 | + | 0.906802i | \(0.638516\pi\) | |||||||
\(522\) | −41.4112 | −1.81252 | ||||||||
\(523\) | −13.9335 | −0.609271 | −0.304636 | − | 0.952469i | \(-0.598535\pi\) | ||||
−0.304636 | + | 0.952469i | \(0.598535\pi\) | |||||||
\(524\) | 10.1897 | 0.445138 | ||||||||
\(525\) | 123.936 | 5.40900 | ||||||||
\(526\) | 6.88858 | 0.300356 | ||||||||
\(527\) | 3.67454 | 0.160065 | ||||||||
\(528\) | −10.6015 | −0.461370 | ||||||||
\(529\) | 24.1804 | 1.05132 | ||||||||
\(530\) | 26.9250 | 1.16955 | ||||||||
\(531\) | −70.3731 | −3.05393 | ||||||||
\(532\) | 27.7389 | 1.20263 | ||||||||
\(533\) | −24.2804 | −1.05170 | ||||||||
\(534\) | 38.3141 | 1.65801 | ||||||||
\(535\) | −54.2965 | −2.34744 | ||||||||
\(536\) | 9.50832 | 0.410697 | ||||||||
\(537\) | 57.2804 | 2.47183 | ||||||||
\(538\) | 0.730619 | 0.0314992 | ||||||||
\(539\) | 50.6829 | 2.18307 | ||||||||
\(540\) | −26.3187 | −1.13258 | ||||||||
\(541\) | 13.2662 | 0.570358 | 0.285179 | − | 0.958474i | \(-0.407947\pi\) | ||||
0.285179 | + | 0.958474i | \(0.407947\pi\) | |||||||
\(542\) | 29.9786 | 1.28769 | ||||||||
\(543\) | 19.8988 | 0.853939 | ||||||||
\(544\) | 1.61568 | 0.0692715 | ||||||||
\(545\) | −75.2089 | −3.22159 | ||||||||
\(546\) | 30.0316 | 1.28524 | ||||||||
\(547\) | −13.3252 | −0.569745 | −0.284872 | − | 0.958565i | \(-0.591951\pi\) | ||||
−0.284872 | + | 0.958565i | \(0.591951\pi\) | |||||||
\(548\) | 8.19163 | 0.349929 | ||||||||
\(549\) | 9.74330 | 0.415834 | ||||||||
\(550\) | 34.2681 | 1.46120 | ||||||||
\(551\) | 46.6150 | 1.98587 | ||||||||
\(552\) | 19.9033 | 0.847142 | ||||||||
\(553\) | 22.8603 | 0.972121 | ||||||||
\(554\) | 14.5178 | 0.616801 | ||||||||
\(555\) | 103.348 | 4.38689 | ||||||||
\(556\) | −0.273303 | −0.0115906 | ||||||||
\(557\) | −12.3910 | −0.525025 | −0.262512 | − | 0.964929i | \(-0.584551\pi\) | ||||
−0.262512 | + | 0.964929i | \(0.584551\pi\) | |||||||
\(558\) | 12.2729 | 0.519553 | ||||||||
\(559\) | 14.2310 | 0.601906 | ||||||||
\(560\) | −17.3083 | −0.731411 | ||||||||
\(561\) | −17.1285 | −0.723167 | ||||||||
\(562\) | −5.12599 | −0.216227 | ||||||||
\(563\) | −3.97975 | −0.167726 | −0.0838632 | − | 0.996477i | \(-0.526726\pi\) | ||||
−0.0838632 | + | 0.996477i | \(0.526726\pi\) | |||||||
\(564\) | 17.3678 | 0.731318 | ||||||||
\(565\) | −59.0805 | −2.48554 | ||||||||
\(566\) | −17.9473 | −0.754382 | ||||||||
\(567\) | −17.9527 | −0.753942 | ||||||||
\(568\) | 2.25981 | 0.0948195 | ||||||||
\(569\) | −21.1758 | −0.887737 | −0.443869 | − | 0.896092i | \(-0.646394\pi\) | ||||
−0.443869 | + | 0.896092i | \(0.646394\pi\) | |||||||
\(570\) | 66.7151 | 2.79439 | ||||||||
\(571\) | 27.4574 | 1.14906 | 0.574528 | − | 0.818485i | \(-0.305186\pi\) | ||||
0.574528 | + | 0.818485i | \(0.305186\pi\) | |||||||
\(572\) | 8.30372 | 0.347196 | ||||||||
\(573\) | 59.4214 | 2.48237 | ||||||||
\(574\) | 48.8526 | 2.03907 | ||||||||
\(575\) | −64.3353 | −2.68297 | ||||||||
\(576\) | 5.39633 | 0.224847 | ||||||||
\(577\) | −25.3723 | −1.05626 | −0.528131 | − | 0.849163i | \(-0.677107\pi\) | ||||
−0.528131 | + | 0.849163i | \(0.677107\pi\) | |||||||
\(578\) | −14.3896 | −0.598528 | ||||||||
\(579\) | 17.5085 | 0.727628 | ||||||||
\(580\) | −29.0865 | −1.20775 | ||||||||
\(581\) | −12.5181 | −0.519340 | ||||||||
\(582\) | −20.9450 | −0.868198 | ||||||||
\(583\) | 25.9899 | 1.07639 | ||||||||
\(584\) | 8.78795 | 0.363648 | ||||||||
\(585\) | 46.4219 | 1.91931 | ||||||||
\(586\) | 27.1006 | 1.11951 | ||||||||
\(587\) | 45.3591 | 1.87217 | 0.936086 | − | 0.351772i | \(-0.114421\pi\) | ||||
0.936086 | + | 0.351772i | \(0.114421\pi\) | |||||||
\(588\) | −40.1407 | −1.65537 | ||||||||
\(589\) | −13.8151 | −0.569243 | ||||||||
\(590\) | −49.4289 | −2.03496 | ||||||||
\(591\) | −63.9055 | −2.62872 | ||||||||
\(592\) | −9.40992 | −0.386745 | ||||||||
\(593\) | −29.5729 | −1.21442 | −0.607208 | − | 0.794543i | \(-0.707710\pi\) | ||||
−0.607208 | + | 0.794543i | \(0.707710\pi\) | |||||||
\(594\) | −25.4046 | −1.04236 | ||||||||
\(595\) | −27.9647 | −1.14644 | ||||||||
\(596\) | 11.0896 | 0.454248 | ||||||||
\(597\) | 73.4650 | 3.00672 | ||||||||
\(598\) | −15.5895 | −0.637502 | ||||||||
\(599\) | 24.1337 | 0.986076 | 0.493038 | − | 0.870008i | \(-0.335886\pi\) | ||||
0.493038 | + | 0.870008i | \(0.335886\pi\) | |||||||
\(600\) | −27.1402 | −1.10799 | ||||||||
\(601\) | 24.3385 | 0.992788 | 0.496394 | − | 0.868097i | \(-0.334657\pi\) | ||||
0.496394 | + | 0.868097i | \(0.334657\pi\) | |||||||
\(602\) | −28.6330 | −1.16699 | ||||||||
\(603\) | 51.3101 | 2.08951 | ||||||||
\(604\) | −5.89412 | −0.239828 | ||||||||
\(605\) | 9.04266 | 0.367636 | ||||||||
\(606\) | −6.21825 | −0.252599 | ||||||||
\(607\) | −24.4757 | −0.993438 | −0.496719 | − | 0.867911i | \(-0.665462\pi\) | ||||
−0.496719 | + | 0.867911i | \(0.665462\pi\) | |||||||
\(608\) | −6.07444 | −0.246351 | ||||||||
\(609\) | −101.542 | −4.11470 | ||||||||
\(610\) | 6.84353 | 0.277086 | ||||||||
\(611\) | −13.6036 | −0.550341 | ||||||||
\(612\) | 8.71872 | 0.352433 | ||||||||
\(613\) | −27.2523 | −1.10071 | −0.550356 | − | 0.834930i | \(-0.685508\pi\) | ||||
−0.550356 | + | 0.834930i | \(0.685508\pi\) | |||||||
\(614\) | −23.5113 | −0.948840 | ||||||||
\(615\) | 117.496 | 4.73788 | ||||||||
\(616\) | −16.7072 | −0.673153 | ||||||||
\(617\) | 17.8664 | 0.719272 | 0.359636 | − | 0.933093i | \(-0.382901\pi\) | ||||
0.359636 | + | 0.933093i | \(0.382901\pi\) | |||||||
\(618\) | −53.1292 | −2.13717 | ||||||||
\(619\) | 16.5922 | 0.666898 | 0.333449 | − | 0.942768i | \(-0.391787\pi\) | ||||
0.333449 | + | 0.942768i | \(0.391787\pi\) | |||||||
\(620\) | 8.62027 | 0.346199 | ||||||||
\(621\) | 47.6949 | 1.91393 | ||||||||
\(622\) | 4.10835 | 0.164730 | ||||||||
\(623\) | 60.3806 | 2.41910 | ||||||||
\(624\) | −6.57652 | −0.263271 | ||||||||
\(625\) | 15.8962 | 0.635849 | ||||||||
\(626\) | 18.3293 | 0.732585 | ||||||||
\(627\) | 64.3980 | 2.57181 | ||||||||
\(628\) | 13.8986 | 0.554615 | ||||||||
\(629\) | −15.2034 | −0.606199 | ||||||||
\(630\) | −93.4016 | −3.72121 | ||||||||
\(631\) | −23.5990 | −0.939460 | −0.469730 | − | 0.882810i | \(-0.655649\pi\) | ||||
−0.469730 | + | 0.882810i | \(0.655649\pi\) | |||||||
\(632\) | −5.00610 | −0.199132 | ||||||||
\(633\) | −68.2738 | −2.71364 | ||||||||
\(634\) | −31.1070 | −1.23542 | ||||||||
\(635\) | 13.8027 | 0.547743 | ||||||||
\(636\) | −20.5839 | −0.816206 | ||||||||
\(637\) | 31.4406 | 1.24572 | ||||||||
\(638\) | −28.0763 | −1.11155 | ||||||||
\(639\) | 12.1947 | 0.482414 | ||||||||
\(640\) | 3.79029 | 0.149824 | ||||||||
\(641\) | −26.0328 | −1.02823 | −0.514116 | − | 0.857721i | \(-0.671880\pi\) | ||||
−0.514116 | + | 0.857721i | \(0.671880\pi\) | |||||||
\(642\) | 41.5092 | 1.63824 | ||||||||
\(643\) | 11.5997 | 0.457448 | 0.228724 | − | 0.973491i | \(-0.426545\pi\) | ||||
0.228724 | + | 0.973491i | \(0.426545\pi\) | |||||||
\(644\) | 31.3663 | 1.23601 | ||||||||
\(645\) | −68.8653 | −2.71157 | ||||||||
\(646\) | −9.81433 | −0.386140 | ||||||||
\(647\) | 28.0427 | 1.10247 | 0.551236 | − | 0.834350i | \(-0.314157\pi\) | ||||
0.551236 | + | 0.834350i | \(0.314157\pi\) | |||||||
\(648\) | 3.93139 | 0.154440 | ||||||||
\(649\) | −47.7122 | −1.87287 | ||||||||
\(650\) | 21.2579 | 0.833803 | ||||||||
\(651\) | 30.0937 | 1.17947 | ||||||||
\(652\) | −5.81128 | −0.227587 | ||||||||
\(653\) | 10.4246 | 0.407946 | 0.203973 | − | 0.978977i | \(-0.434615\pi\) | ||||
0.203973 | + | 0.978977i | \(0.434615\pi\) | |||||||
\(654\) | 57.4965 | 2.24829 | ||||||||
\(655\) | 38.6218 | 1.50908 | ||||||||
\(656\) | −10.6980 | −0.417689 | ||||||||
\(657\) | 47.4227 | 1.85014 | ||||||||
\(658\) | 27.3706 | 1.06702 | ||||||||
\(659\) | −0.724819 | −0.0282349 | −0.0141175 | − | 0.999900i | \(-0.504494\pi\) | ||||
−0.0141175 | + | 0.999900i | \(0.504494\pi\) | |||||||
\(660\) | −40.1827 | −1.56411 | ||||||||
\(661\) | 3.96086 | 0.154060 | 0.0770298 | − | 0.997029i | \(-0.475456\pi\) | ||||
0.0770298 | + | 0.997029i | \(0.475456\pi\) | |||||||
\(662\) | −16.9778 | −0.659860 | ||||||||
\(663\) | −10.6255 | −0.412661 | ||||||||
\(664\) | 2.74130 | 0.106383 | ||||||||
\(665\) | 105.139 | 4.07710 | ||||||||
\(666\) | −50.7791 | −1.96765 | ||||||||
\(667\) | 52.7109 | 2.04097 | ||||||||
\(668\) | −13.9647 | −0.540309 | ||||||||
\(669\) | −53.2227 | −2.05771 | ||||||||
\(670\) | 36.0393 | 1.39232 | ||||||||
\(671\) | 6.60585 | 0.255016 | ||||||||
\(672\) | 13.2321 | 0.510438 | ||||||||
\(673\) | 12.5805 | 0.484944 | 0.242472 | − | 0.970158i | \(-0.422042\pi\) | ||||
0.242472 | + | 0.970158i | \(0.422042\pi\) | |||||||
\(674\) | −6.86104 | −0.264277 | ||||||||
\(675\) | −65.0369 | −2.50327 | ||||||||
\(676\) | −7.84887 | −0.301880 | ||||||||
\(677\) | −22.7523 | −0.874442 | −0.437221 | − | 0.899354i | \(-0.644037\pi\) | ||||
−0.437221 | + | 0.899354i | \(0.644037\pi\) | |||||||
\(678\) | 45.1665 | 1.73461 | ||||||||
\(679\) | −33.0080 | −1.26673 | ||||||||
\(680\) | 6.12388 | 0.234840 | ||||||||
\(681\) | −3.57868 | −0.137135 | ||||||||
\(682\) | 8.32089 | 0.318623 | ||||||||
\(683\) | −30.5002 | −1.16706 | −0.583529 | − | 0.812092i | \(-0.698329\pi\) | ||||
−0.583529 | + | 0.812092i | \(0.698329\pi\) | |||||||
\(684\) | −32.7797 | −1.25336 | ||||||||
\(685\) | 31.0487 | 1.18631 | ||||||||
\(686\) | −31.2936 | −1.19480 | ||||||||
\(687\) | 9.91173 | 0.378156 | ||||||||
\(688\) | 6.27023 | 0.239050 | ||||||||
\(689\) | 16.1226 | 0.614222 | ||||||||
\(690\) | 75.4394 | 2.87193 | ||||||||
\(691\) | −6.05370 | −0.230293 | −0.115147 | − | 0.993348i | \(-0.536734\pi\) | ||||
−0.115147 | + | 0.993348i | \(0.536734\pi\) | |||||||
\(692\) | −21.7129 | −0.825400 | ||||||||
\(693\) | −90.1577 | −3.42481 | ||||||||
\(694\) | 7.51465 | 0.285252 | ||||||||
\(695\) | −1.03590 | −0.0392938 | ||||||||
\(696\) | 22.2364 | 0.842868 | ||||||||
\(697\) | −17.2846 | −0.654700 | ||||||||
\(698\) | −23.9846 | −0.907831 | ||||||||
\(699\) | 61.9982 | 2.34499 | ||||||||
\(700\) | −42.7712 | −1.61660 | ||||||||
\(701\) | 14.1688 | 0.535149 | 0.267575 | − | 0.963537i | \(-0.413778\pi\) | ||||
0.267575 | + | 0.963537i | \(0.413778\pi\) | |||||||
\(702\) | −15.7595 | −0.594805 | ||||||||
\(703\) | 57.1600 | 2.15583 | ||||||||
\(704\) | 3.65865 | 0.137891 | ||||||||
\(705\) | 65.8292 | 2.47927 | ||||||||
\(706\) | −24.4745 | −0.921111 | ||||||||
\(707\) | −9.79956 | −0.368550 | ||||||||
\(708\) | 37.7879 | 1.42016 | ||||||||
\(709\) | 25.8582 | 0.971124 | 0.485562 | − | 0.874202i | \(-0.338615\pi\) | ||||
0.485562 | + | 0.874202i | \(0.338615\pi\) | |||||||
\(710\) | 8.56534 | 0.321451 | ||||||||
\(711\) | −27.0146 | −1.01313 | ||||||||
\(712\) | −13.2225 | −0.495535 | ||||||||
\(713\) | −15.6217 | −0.585039 | ||||||||
\(714\) | 21.3787 | 0.800079 | ||||||||
\(715\) | 31.4735 | 1.17704 | ||||||||
\(716\) | −19.7679 | −0.738763 | ||||||||
\(717\) | 37.1189 | 1.38623 | ||||||||
\(718\) | −2.53346 | −0.0945477 | ||||||||
\(719\) | −43.6512 | −1.62792 | −0.813958 | − | 0.580923i | \(-0.802692\pi\) | ||||
−0.813958 | + | 0.580923i | \(0.802692\pi\) | |||||||
\(720\) | 20.4537 | 0.762263 | ||||||||
\(721\) | −83.7281 | −3.11820 | ||||||||
\(722\) | 17.8989 | 0.666127 | ||||||||
\(723\) | −7.41407 | −0.275732 | ||||||||
\(724\) | −6.86724 | −0.255219 | ||||||||
\(725\) | −71.8766 | −2.66943 | ||||||||
\(726\) | −6.91303 | −0.256567 | ||||||||
\(727\) | −29.2645 | −1.08536 | −0.542679 | − | 0.839940i | \(-0.682590\pi\) | ||||
−0.542679 | + | 0.839940i | \(0.682590\pi\) | |||||||
\(728\) | −10.3642 | −0.384121 | ||||||||
\(729\) | −39.1461 | −1.44985 | ||||||||
\(730\) | 33.3089 | 1.23282 | ||||||||
\(731\) | 10.1307 | 0.374696 | ||||||||
\(732\) | −5.23182 | −0.193373 | ||||||||
\(733\) | 34.1905 | 1.26285 | 0.631427 | − | 0.775436i | \(-0.282470\pi\) | ||||
0.631427 | + | 0.775436i | \(0.282470\pi\) | |||||||
\(734\) | −11.8394 | −0.437001 | ||||||||
\(735\) | −152.145 | −5.61195 | ||||||||
\(736\) | −6.86880 | −0.253187 | ||||||||
\(737\) | 34.7877 | 1.28142 | ||||||||
\(738\) | −57.7302 | −2.12508 | ||||||||
\(739\) | 38.2664 | 1.40765 | 0.703826 | − | 0.710372i | \(-0.251473\pi\) | ||||
0.703826 | + | 0.710372i | \(0.251473\pi\) | |||||||
\(740\) | −35.6664 | −1.31112 | ||||||||
\(741\) | 39.9487 | 1.46755 | ||||||||
\(742\) | −32.4389 | −1.19087 | ||||||||
\(743\) | −6.53713 | −0.239824 | −0.119912 | − | 0.992785i | \(-0.538261\pi\) | ||||
−0.119912 | + | 0.992785i | \(0.538261\pi\) | |||||||
\(744\) | −6.59012 | −0.241605 | ||||||||
\(745\) | 42.0329 | 1.53997 | ||||||||
\(746\) | 23.6275 | 0.865066 | ||||||||
\(747\) | 14.7930 | 0.541247 | ||||||||
\(748\) | 5.91120 | 0.216135 | ||||||||
\(749\) | 65.4157 | 2.39024 | ||||||||
\(750\) | −47.9548 | −1.75106 | ||||||||
\(751\) | 17.0455 | 0.622000 | 0.311000 | − | 0.950410i | \(-0.399336\pi\) | ||||
0.311000 | + | 0.950410i | \(0.399336\pi\) | |||||||
\(752\) | −5.99379 | −0.218571 | ||||||||
\(753\) | 38.3134 | 1.39622 | ||||||||
\(754\) | −17.4169 | −0.634286 | ||||||||
\(755\) | −22.3404 | −0.813052 | ||||||||
\(756\) | 31.7084 | 1.15322 | ||||||||
\(757\) | 28.5345 | 1.03710 | 0.518552 | − | 0.855046i | \(-0.326471\pi\) | ||||
0.518552 | + | 0.855046i | \(0.326471\pi\) | |||||||
\(758\) | −7.20684 | −0.261764 | ||||||||
\(759\) | 72.8194 | 2.64318 | ||||||||
\(760\) | −23.0239 | −0.835165 | ||||||||
\(761\) | 24.3824 | 0.883861 | 0.441930 | − | 0.897049i | \(-0.354294\pi\) | ||||
0.441930 | + | 0.897049i | \(0.354294\pi\) | |||||||
\(762\) | −10.5520 | −0.382259 | ||||||||
\(763\) | 90.6107 | 3.28033 | ||||||||
\(764\) | −20.5068 | −0.741911 | ||||||||
\(765\) | 33.0465 | 1.19480 | ||||||||
\(766\) | −18.1294 | −0.655043 | ||||||||
\(767\) | −29.5978 | −1.06872 | ||||||||
\(768\) | −2.89764 | −0.104560 | ||||||||
\(769\) | 29.2580 | 1.05507 | 0.527535 | − | 0.849534i | \(-0.323117\pi\) | ||||
0.527535 | + | 0.849534i | \(0.323117\pi\) | |||||||
\(770\) | −63.3252 | −2.28208 | ||||||||
\(771\) | −19.9604 | −0.718854 | ||||||||
\(772\) | −6.04232 | −0.217468 | ||||||||
\(773\) | −4.01873 | −0.144544 | −0.0722718 | − | 0.997385i | \(-0.523025\pi\) | ||||
−0.0722718 | + | 0.997385i | \(0.523025\pi\) | |||||||
\(774\) | 33.8362 | 1.21622 | ||||||||
\(775\) | 21.3018 | 0.765185 | ||||||||
\(776\) | 7.22829 | 0.259481 | ||||||||
\(777\) | −124.513 | −4.46687 | ||||||||
\(778\) | 29.6967 | 1.06468 | ||||||||
\(779\) | 64.9847 | 2.32832 | ||||||||
\(780\) | −24.9269 | −0.892527 | ||||||||
\(781\) | 8.26786 | 0.295847 | ||||||||
\(782\) | −11.0978 | −0.396855 | ||||||||
\(783\) | 53.2857 | 1.90428 | ||||||||
\(784\) | 13.8529 | 0.494745 | ||||||||
\(785\) | 52.6798 | 1.88022 | ||||||||
\(786\) | −29.5260 | −1.05316 | ||||||||
\(787\) | 14.5095 | 0.517207 | 0.258604 | − | 0.965984i | \(-0.416738\pi\) | ||||
0.258604 | + | 0.965984i | \(0.416738\pi\) | |||||||
\(788\) | 22.0543 | 0.785652 | ||||||||
\(789\) | −19.9606 | −0.710618 | ||||||||
\(790\) | −18.9746 | −0.675086 | ||||||||
\(791\) | 71.1794 | 2.53085 | ||||||||
\(792\) | 19.7433 | 0.701548 | ||||||||
\(793\) | 4.09788 | 0.145520 | ||||||||
\(794\) | −21.4192 | −0.760138 | ||||||||
\(795\) | −78.0191 | −2.76705 | ||||||||
\(796\) | −25.3534 | −0.898627 | ||||||||
\(797\) | −40.6870 | −1.44121 | −0.720604 | − | 0.693347i | \(-0.756135\pi\) | ||||
−0.720604 | + | 0.693347i | \(0.756135\pi\) | |||||||
\(798\) | −80.3775 | −2.84533 | ||||||||
\(799\) | −9.68401 | −0.342596 | ||||||||
\(800\) | 9.36631 | 0.331149 | ||||||||
\(801\) | −71.3531 | −2.52114 | ||||||||
\(802\) | −24.5090 | −0.865442 | ||||||||
\(803\) | 32.1521 | 1.13462 | ||||||||
\(804\) | −27.5517 | −0.971674 | ||||||||
\(805\) | 118.888 | 4.19024 | ||||||||
\(806\) | 5.16178 | 0.181816 | ||||||||
\(807\) | −2.11707 | −0.0745245 | ||||||||
\(808\) | 2.14597 | 0.0754949 | ||||||||
\(809\) | −7.60488 | −0.267373 | −0.133687 | − | 0.991024i | \(-0.542682\pi\) | ||||
−0.133687 | + | 0.991024i | \(0.542682\pi\) | |||||||
\(810\) | 14.9011 | 0.523572 | ||||||||
\(811\) | 47.6003 | 1.67147 | 0.835736 | − | 0.549131i | \(-0.185041\pi\) | ||||
0.835736 | + | 0.549131i | \(0.185041\pi\) | |||||||
\(812\) | 35.0431 | 1.22977 | ||||||||
\(813\) | −86.8671 | −3.04656 | ||||||||
\(814\) | −34.4276 | −1.20669 | ||||||||
\(815\) | −22.0265 | −0.771553 | ||||||||
\(816\) | −4.68165 | −0.163891 | ||||||||
\(817\) | −38.0881 | −1.33254 | ||||||||
\(818\) | 7.65341 | 0.267595 | ||||||||
\(819\) | −55.9285 | −1.95430 | ||||||||
\(820\) | −40.5487 | −1.41602 | ||||||||
\(821\) | 34.3313 | 1.19817 | 0.599086 | − | 0.800685i | \(-0.295531\pi\) | ||||
0.599086 | + | 0.800685i | \(0.295531\pi\) | |||||||
\(822\) | −23.7364 | −0.827902 | ||||||||
\(823\) | −28.5005 | −0.993463 | −0.496732 | − | 0.867904i | \(-0.665467\pi\) | ||||
−0.496732 | + | 0.867904i | \(0.665467\pi\) | |||||||
\(824\) | 18.3353 | 0.638741 | ||||||||
\(825\) | −99.2967 | −3.45707 | ||||||||
\(826\) | 59.5513 | 2.07205 | ||||||||
\(827\) | −4.08419 | −0.142021 | −0.0710107 | − | 0.997476i | \(-0.522622\pi\) | ||||
−0.0710107 | + | 0.997476i | \(0.522622\pi\) | |||||||
\(828\) | −37.0663 | −1.28814 | ||||||||
\(829\) | −37.6237 | −1.30673 | −0.653363 | − | 0.757044i | \(-0.726643\pi\) | ||||
−0.653363 | + | 0.757044i | \(0.726643\pi\) | |||||||
\(830\) | 10.3903 | 0.360654 | ||||||||
\(831\) | −42.0673 | −1.45930 | ||||||||
\(832\) | 2.26961 | 0.0786846 | ||||||||
\(833\) | 22.3818 | 0.775482 | ||||||||
\(834\) | 0.791934 | 0.0274224 | ||||||||
\(835\) | −52.9301 | −1.83172 | ||||||||
\(836\) | −22.2243 | −0.768643 | ||||||||
\(837\) | −15.7921 | −0.545855 | ||||||||
\(838\) | 9.03421 | 0.312081 | ||||||||
\(839\) | 12.1751 | 0.420330 | 0.210165 | − | 0.977666i | \(-0.432600\pi\) | ||||
0.210165 | + | 0.977666i | \(0.432600\pi\) | |||||||
\(840\) | 50.1534 | 1.73046 | ||||||||
\(841\) | 29.8896 | 1.03068 | ||||||||
\(842\) | −19.0591 | −0.656818 | ||||||||
\(843\) | 14.8533 | 0.511575 | ||||||||
\(844\) | 23.5618 | 0.811032 | ||||||||
\(845\) | −29.7495 | −1.02341 | ||||||||
\(846\) | −32.3445 | −1.11203 | ||||||||
\(847\) | −10.8945 | −0.374339 | ||||||||
\(848\) | 7.10368 | 0.243941 | ||||||||
\(849\) | 52.0049 | 1.78480 | ||||||||
\(850\) | 15.1329 | 0.519055 | ||||||||
\(851\) | 64.6349 | 2.21565 | ||||||||
\(852\) | −6.54812 | −0.224335 | ||||||||
\(853\) | 18.8656 | 0.645945 | 0.322972 | − | 0.946408i | \(-0.395318\pi\) | ||||
0.322972 | + | 0.946408i | \(0.395318\pi\) | |||||||
\(854\) | −8.24500 | −0.282138 | ||||||||
\(855\) | −124.245 | −4.24908 | ||||||||
\(856\) | −14.3251 | −0.489624 | ||||||||
\(857\) | 42.6515 | 1.45695 | 0.728473 | − | 0.685074i | \(-0.240230\pi\) | ||||
0.728473 | + | 0.685074i | \(0.240230\pi\) | |||||||
\(858\) | −24.0612 | −0.821436 | ||||||||
\(859\) | 41.6830 | 1.42221 | 0.711103 | − | 0.703088i | \(-0.248196\pi\) | ||||
0.711103 | + | 0.703088i | \(0.248196\pi\) | |||||||
\(860\) | 23.7660 | 0.810413 | ||||||||
\(861\) | −141.557 | −4.82426 | ||||||||
\(862\) | −32.1407 | −1.09471 | ||||||||
\(863\) | −10.3409 | −0.352010 | −0.176005 | − | 0.984389i | \(-0.556317\pi\) | ||||
−0.176005 | + | 0.984389i | \(0.556317\pi\) | |||||||
\(864\) | −6.94371 | −0.236230 | ||||||||
\(865\) | −82.2982 | −2.79822 | ||||||||
\(866\) | −3.96443 | −0.134717 | ||||||||
\(867\) | 41.6959 | 1.41607 | ||||||||
\(868\) | −10.3856 | −0.352510 | ||||||||
\(869\) | −18.3156 | −0.621314 | ||||||||
\(870\) | 84.2824 | 2.85744 | ||||||||
\(871\) | 21.5802 | 0.731217 | ||||||||
\(872\) | −19.8425 | −0.671952 | ||||||||
\(873\) | 39.0063 | 1.32016 | ||||||||
\(874\) | 41.7241 | 1.41134 | ||||||||
\(875\) | −75.5736 | −2.55485 | ||||||||
\(876\) | −25.4643 | −0.860360 | ||||||||
\(877\) | 22.9723 | 0.775721 | 0.387860 | − | 0.921718i | \(-0.373214\pi\) | ||||
0.387860 | + | 0.921718i | \(0.373214\pi\) | |||||||
\(878\) | 23.9432 | 0.808045 | ||||||||
\(879\) | −78.5278 | −2.64868 | ||||||||
\(880\) | 13.8674 | 0.467469 | ||||||||
\(881\) | −11.8291 | −0.398531 | −0.199266 | − | 0.979946i | \(-0.563856\pi\) | ||||
−0.199266 | + | 0.979946i | \(0.563856\pi\) | |||||||
\(882\) | 74.7547 | 2.51712 | ||||||||
\(883\) | 7.91811 | 0.266466 | 0.133233 | − | 0.991085i | \(-0.457464\pi\) | ||||
0.133233 | + | 0.991085i | \(0.457464\pi\) | |||||||
\(884\) | 3.66696 | 0.123333 | ||||||||
\(885\) | 143.227 | 4.81453 | ||||||||
\(886\) | 8.73126 | 0.293332 | ||||||||
\(887\) | 37.6103 | 1.26283 | 0.631416 | − | 0.775445i | \(-0.282474\pi\) | ||||
0.631416 | + | 0.775445i | \(0.282474\pi\) | |||||||
\(888\) | 27.2666 | 0.915007 | ||||||||
\(889\) | −16.6293 | −0.557729 | ||||||||
\(890\) | −50.1172 | −1.67993 | ||||||||
\(891\) | 14.3836 | 0.481869 | ||||||||
\(892\) | 18.3676 | 0.614992 | ||||||||
\(893\) | 36.4089 | 1.21838 | ||||||||
\(894\) | −32.1337 | −1.07471 | ||||||||
\(895\) | −74.9262 | −2.50451 | ||||||||
\(896\) | −4.56649 | −0.152556 | ||||||||
\(897\) | 45.1728 | 1.50828 | ||||||||
\(898\) | −12.3418 | −0.411851 | ||||||||
\(899\) | −17.4529 | −0.582087 | ||||||||
\(900\) | 50.5437 | 1.68479 | ||||||||
\(901\) | 11.4772 | 0.382363 | ||||||||
\(902\) | −39.1404 | −1.30323 | ||||||||
\(903\) | 82.9681 | 2.76100 | ||||||||
\(904\) | −15.5873 | −0.518427 | ||||||||
\(905\) | −26.0288 | −0.865228 | ||||||||
\(906\) | 17.0791 | 0.567414 | ||||||||
\(907\) | 1.49096 | 0.0495064 | 0.0247532 | − | 0.999694i | \(-0.492120\pi\) | ||||
0.0247532 | + | 0.999694i | \(0.492120\pi\) | |||||||
\(908\) | 1.23503 | 0.0409859 | ||||||||
\(909\) | 11.5804 | 0.384096 | ||||||||
\(910\) | −39.2832 | −1.30223 | ||||||||
\(911\) | −38.8643 | −1.28763 | −0.643816 | − | 0.765181i | \(-0.722650\pi\) | ||||
−0.643816 | + | 0.765181i | \(0.722650\pi\) | |||||||
\(912\) | 17.6016 | 0.582846 | ||||||||
\(913\) | 10.0295 | 0.331927 | ||||||||
\(914\) | 8.92101 | 0.295081 | ||||||||
\(915\) | −19.8301 | −0.655563 | ||||||||
\(916\) | −3.42062 | −0.113020 | ||||||||
\(917\) | −46.5311 | −1.53659 | ||||||||
\(918\) | −11.2188 | −0.370275 | ||||||||
\(919\) | −57.9899 | −1.91291 | −0.956456 | − | 0.291877i | \(-0.905720\pi\) | ||||
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(920\) | −26.0348 | −0.858340 | ||||||||
\(921\) | 68.1274 | 2.24487 | ||||||||
\(922\) | −6.74591 | −0.222165 | ||||||||
\(923\) | 5.12889 | 0.168819 | ||||||||
\(924\) | 48.4115 | 1.59262 | ||||||||
\(925\) | −88.1363 | −2.89790 | ||||||||
\(926\) | 9.99033 | 0.328303 | ||||||||
\(927\) | 98.9434 | 3.24973 | ||||||||
\(928\) | −7.67395 | −0.251910 | ||||||||
\(929\) | −7.73785 | −0.253871 | −0.126935 | − | 0.991911i | \(-0.540514\pi\) | ||||
−0.126935 | + | 0.991911i | \(0.540514\pi\) | |||||||
\(930\) | −24.9785 | −0.819076 | ||||||||
\(931\) | −84.1485 | −2.75786 | ||||||||
\(932\) | −21.3961 | −0.700852 | ||||||||
\(933\) | −11.9045 | −0.389736 | ||||||||
\(934\) | 20.1174 | 0.658261 | ||||||||
\(935\) | 22.4052 | 0.732727 | ||||||||
\(936\) | 12.2476 | 0.400324 | ||||||||
\(937\) | 14.4494 | 0.472043 | 0.236021 | − | 0.971748i | \(-0.424156\pi\) | ||||
0.236021 | + | 0.971748i | \(0.424156\pi\) | |||||||
\(938\) | −43.4197 | −1.41770 | ||||||||
\(939\) | −53.1117 | −1.73323 | ||||||||
\(940\) | −22.7182 | −0.740986 | ||||||||
\(941\) | 6.43072 | 0.209635 | 0.104818 | − | 0.994491i | \(-0.466574\pi\) | ||||
0.104818 | + | 0.994491i | \(0.466574\pi\) | |||||||
\(942\) | −40.2732 | −1.31217 | ||||||||
\(943\) | 73.4827 | 2.39293 | ||||||||
\(944\) | −13.0409 | −0.424446 | ||||||||
\(945\) | 120.184 | 3.90959 | ||||||||
\(946\) | 22.9406 | 0.745863 | ||||||||
\(947\) | 2.16728 | 0.0704272 | 0.0352136 | − | 0.999380i | \(-0.488789\pi\) | ||||
0.0352136 | + | 0.999380i | \(0.488789\pi\) | |||||||
\(948\) | 14.5059 | 0.471130 | ||||||||
\(949\) | 19.9452 | 0.647449 | ||||||||
\(950\) | −56.8951 | −1.84592 | ||||||||
\(951\) | 90.1370 | 2.92289 | ||||||||
\(952\) | −7.37797 | −0.239122 | ||||||||
\(953\) | −17.9623 | −0.581857 | −0.290928 | − | 0.956745i | \(-0.593964\pi\) | ||||
−0.290928 | + | 0.956745i | \(0.593964\pi\) | |||||||
\(954\) | 38.3338 | 1.24110 | ||||||||
\(955\) | −77.7268 | −2.51518 | ||||||||
\(956\) | −12.8100 | −0.414306 | ||||||||
\(957\) | 81.3552 | 2.62984 | ||||||||
\(958\) | −4.31252 | −0.139331 | ||||||||
\(959\) | −37.4070 | −1.20794 | ||||||||
\(960\) | −10.9829 | −0.354472 | ||||||||
\(961\) | −25.8275 | −0.833147 | ||||||||
\(962\) | −21.3569 | −0.688573 | ||||||||
\(963\) | −77.3032 | −2.49106 | ||||||||
\(964\) | 2.55865 | 0.0824087 | ||||||||
\(965\) | −22.9022 | −0.737246 | ||||||||
\(966\) | −90.8884 | −2.92429 | ||||||||
\(967\) | −3.64174 | −0.117110 | −0.0585552 | − | 0.998284i | \(-0.518649\pi\) | ||||
−0.0585552 | + | 0.998284i | \(0.518649\pi\) | |||||||
\(968\) | 2.38574 | 0.0766807 | ||||||||
\(969\) | 28.4384 | 0.913574 | ||||||||
\(970\) | 27.3973 | 0.879675 | ||||||||
\(971\) | 41.9662 | 1.34676 | 0.673380 | − | 0.739297i | \(-0.264842\pi\) | ||||
0.673380 | + | 0.739297i | \(0.264842\pi\) | |||||||
\(972\) | 9.43935 | 0.302767 | ||||||||
\(973\) | 1.24804 | 0.0400102 | ||||||||
\(974\) | 9.56529 | 0.306492 | ||||||||
\(975\) | −61.5977 | −1.97271 | ||||||||
\(976\) | 1.80554 | 0.0577940 | ||||||||
\(977\) | 47.9869 | 1.53524 | 0.767619 | − | 0.640906i | \(-0.221441\pi\) | ||||
0.767619 | + | 0.640906i | \(0.221441\pi\) | |||||||
\(978\) | 16.8390 | 0.538452 | ||||||||
\(979\) | −48.3766 | −1.54612 | ||||||||
\(980\) | 52.5064 | 1.67726 | ||||||||
\(981\) | −107.077 | −3.41870 | ||||||||
\(982\) | −1.40407 | −0.0448057 | ||||||||
\(983\) | 6.16410 | 0.196604 | 0.0983021 | − | 0.995157i | \(-0.468659\pi\) | ||||
0.0983021 | + | 0.995157i | \(0.468659\pi\) | |||||||
\(984\) | 30.9991 | 0.988216 | ||||||||
\(985\) | 83.5923 | 2.66347 | ||||||||
\(986\) | −12.3986 | −0.394853 | ||||||||
\(987\) | −79.3102 | −2.52447 | ||||||||
\(988\) | −13.7866 | −0.438611 | ||||||||
\(989\) | −43.0689 | −1.36951 | ||||||||
\(990\) | 74.8329 | 2.37835 | ||||||||
\(991\) | −21.9291 | −0.696600 | −0.348300 | − | 0.937383i | \(-0.613241\pi\) | ||||
−0.348300 | + | 0.937383i | \(0.613241\pi\) | |||||||
\(992\) | 2.27430 | 0.0722092 | ||||||||
\(993\) | 49.1955 | 1.56117 | ||||||||
\(994\) | −10.3194 | −0.327312 | ||||||||
\(995\) | −96.0967 | −3.04647 | ||||||||
\(996\) | −7.94331 | −0.251694 | ||||||||
\(997\) | −22.7246 | −0.719695 | −0.359848 | − | 0.933011i | \(-0.617171\pi\) | ||||
−0.359848 | + | 0.933011i | \(0.617171\pi\) | |||||||
\(998\) | 30.8884 | 0.977754 | ||||||||
\(999\) | 65.3398 | 2.06726 |
(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 | 6046.2.a.e.1.6 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.e.1.6 | ✓ | 56 | 1.1 | even | 1 | trivial |