Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63717 | −1.86476 | −0.932381 | − | 0.361478i | \(-0.882272\pi\) | ||||
−0.932381 | + | 0.361478i | \(0.882272\pi\) | |||||||
\(3\) | 2.57307 | 1.48556 | 0.742780 | − | 0.669535i | \(-0.233507\pi\) | ||||
0.742780 | + | 0.669535i | \(0.233507\pi\) | |||||||
\(4\) | 4.95467 | 2.47734 | ||||||||
\(5\) | −2.90004 | −1.29694 | −0.648470 | − | 0.761240i | \(-0.724591\pi\) | ||||
−0.648470 | + | 0.761240i | \(0.724591\pi\) | |||||||
\(6\) | −6.78562 | −2.77022 | ||||||||
\(7\) | 1.48673 | 0.561931 | 0.280965 | − | 0.959718i | \(-0.409345\pi\) | ||||
0.280965 | + | 0.959718i | \(0.409345\pi\) | |||||||
\(8\) | −7.79198 | −2.75488 | ||||||||
\(9\) | 3.62067 | 1.20689 | ||||||||
\(10\) | 7.64791 | 2.41848 | ||||||||
\(11\) | −3.69629 | −1.11447 | −0.557236 | − | 0.830354i | \(-0.688138\pi\) | ||||
−0.557236 | + | 0.830354i | \(0.688138\pi\) | |||||||
\(12\) | 12.7487 | 3.68023 | ||||||||
\(13\) | −4.29547 | −1.19135 | −0.595674 | − | 0.803226i | \(-0.703115\pi\) | ||||
−0.595674 | + | 0.803226i | \(0.703115\pi\) | |||||||
\(14\) | −3.92076 | −1.04787 | ||||||||
\(15\) | −7.46201 | −1.92668 | ||||||||
\(16\) | 10.6394 | 2.65986 | ||||||||
\(17\) | −6.37694 | −1.54664 | −0.773318 | − | 0.634019i | \(-0.781404\pi\) | ||||
−0.773318 | + | 0.634019i | \(0.781404\pi\) | |||||||
\(18\) | −9.54833 | −2.25056 | ||||||||
\(19\) | −4.90196 | −1.12459 | −0.562293 | − | 0.826938i | \(-0.690081\pi\) | ||||
−0.562293 | + | 0.826938i | \(0.690081\pi\) | |||||||
\(20\) | −14.3688 | −3.21295 | ||||||||
\(21\) | 3.82545 | 0.834782 | ||||||||
\(22\) | 9.74774 | 2.07822 | ||||||||
\(23\) | −4.46996 | −0.932051 | −0.466025 | − | 0.884771i | \(-0.654314\pi\) | ||||
−0.466025 | + | 0.884771i | \(0.654314\pi\) | |||||||
\(24\) | −20.0493 | −4.09254 | ||||||||
\(25\) | 3.41026 | 0.682052 | ||||||||
\(26\) | 11.3279 | 2.22158 | ||||||||
\(27\) | 1.59703 | 0.307349 | ||||||||
\(28\) | 7.36625 | 1.39209 | ||||||||
\(29\) | −3.41264 | −0.633711 | −0.316856 | − | 0.948474i | \(-0.602627\pi\) | ||||
−0.316856 | + | 0.948474i | \(0.602627\pi\) | |||||||
\(30\) | 19.6786 | 3.59280 | ||||||||
\(31\) | 6.91544 | 1.24205 | 0.621025 | − | 0.783791i | \(-0.286717\pi\) | ||||
0.621025 | + | 0.783791i | \(0.286717\pi\) | |||||||
\(32\) | −12.4740 | −2.20512 | ||||||||
\(33\) | −9.51079 | −1.65562 | ||||||||
\(34\) | 16.8171 | 2.88411 | ||||||||
\(35\) | −4.31158 | −0.728790 | ||||||||
\(36\) | 17.9392 | 2.98987 | ||||||||
\(37\) | 5.19098 | 0.853392 | 0.426696 | − | 0.904395i | \(-0.359677\pi\) | ||||
0.426696 | + | 0.904395i | \(0.359677\pi\) | |||||||
\(38\) | 12.9273 | 2.09709 | ||||||||
\(39\) | −11.0525 | −1.76982 | ||||||||
\(40\) | 22.5971 | 3.57291 | ||||||||
\(41\) | 3.22172 | 0.503149 | 0.251574 | − | 0.967838i | \(-0.419052\pi\) | ||||
0.251574 | + | 0.967838i | \(0.419052\pi\) | |||||||
\(42\) | −10.0884 | −1.55667 | ||||||||
\(43\) | −0.0314304 | −0.00479310 | −0.00239655 | − | 0.999997i | \(-0.500763\pi\) | ||||
−0.00239655 | + | 0.999997i | \(0.500763\pi\) | |||||||
\(44\) | −18.3139 | −2.76092 | ||||||||
\(45\) | −10.5001 | −1.56526 | ||||||||
\(46\) | 11.7880 | 1.73805 | ||||||||
\(47\) | −8.50271 | −1.24025 | −0.620124 | − | 0.784504i | \(-0.712918\pi\) | ||||
−0.620124 | + | 0.784504i | \(0.712918\pi\) | |||||||
\(48\) | 27.3760 | 3.95138 | ||||||||
\(49\) | −4.78964 | −0.684234 | ||||||||
\(50\) | −8.99343 | −1.27186 | ||||||||
\(51\) | −16.4083 | −2.29762 | ||||||||
\(52\) | −21.2826 | −2.95137 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | −4.21165 | −0.573133 | ||||||||
\(55\) | 10.7194 | 1.44540 | ||||||||
\(56\) | −11.5846 | −1.54805 | ||||||||
\(57\) | −12.6131 | −1.67064 | ||||||||
\(58\) | 8.99971 | 1.18172 | ||||||||
\(59\) | −0.680943 | −0.0886512 | −0.0443256 | − | 0.999017i | \(-0.514114\pi\) | ||||
−0.0443256 | + | 0.999017i | \(0.514114\pi\) | |||||||
\(60\) | −36.9718 | −4.77304 | ||||||||
\(61\) | 2.90398 | 0.371816 | 0.185908 | − | 0.982567i | \(-0.440477\pi\) | ||||
0.185908 | + | 0.982567i | \(0.440477\pi\) | |||||||
\(62\) | −18.2372 | −2.31613 | ||||||||
\(63\) | 5.38296 | 0.678189 | ||||||||
\(64\) | 11.6173 | 1.45217 | ||||||||
\(65\) | 12.4570 | 1.54511 | ||||||||
\(66\) | 25.0816 | 3.08733 | ||||||||
\(67\) | 8.26279 | 1.00946 | 0.504730 | − | 0.863277i | \(-0.331592\pi\) | ||||
0.504730 | + | 0.863277i | \(0.331592\pi\) | |||||||
\(68\) | −31.5957 | −3.83154 | ||||||||
\(69\) | −11.5015 | −1.38462 | ||||||||
\(70\) | 11.3704 | 1.35902 | ||||||||
\(71\) | −5.76751 | −0.684478 | −0.342239 | − | 0.939613i | \(-0.611185\pi\) | ||||
−0.342239 | + | 0.939613i | \(0.611185\pi\) | |||||||
\(72\) | −28.2122 | −3.32484 | ||||||||
\(73\) | 4.37688 | 0.512275 | 0.256138 | − | 0.966640i | \(-0.417550\pi\) | ||||
0.256138 | + | 0.966640i | \(0.417550\pi\) | |||||||
\(74\) | −13.6895 | −1.59137 | ||||||||
\(75\) | 8.77482 | 1.01323 | ||||||||
\(76\) | −24.2876 | −2.78598 | ||||||||
\(77\) | −5.49537 | −0.626256 | ||||||||
\(78\) | 29.1474 | 3.30029 | ||||||||
\(79\) | −9.74121 | −1.09597 | −0.547986 | − | 0.836488i | \(-0.684605\pi\) | ||||
−0.547986 | + | 0.836488i | \(0.684605\pi\) | |||||||
\(80\) | −30.8548 | −3.44967 | ||||||||
\(81\) | −6.75275 | −0.750305 | ||||||||
\(82\) | −8.49624 | −0.938253 | ||||||||
\(83\) | 4.69891 | 0.515772 | 0.257886 | − | 0.966175i | \(-0.416974\pi\) | ||||
0.257886 | + | 0.966175i | \(0.416974\pi\) | |||||||
\(84\) | 18.9539 | 2.06804 | ||||||||
\(85\) | 18.4934 | 2.00589 | ||||||||
\(86\) | 0.0828874 | 0.00893798 | ||||||||
\(87\) | −8.78095 | −0.941417 | ||||||||
\(88\) | 28.8014 | 3.07024 | ||||||||
\(89\) | 13.2060 | 1.39984 | 0.699918 | − | 0.714223i | \(-0.253220\pi\) | ||||
0.699918 | + | 0.714223i | \(0.253220\pi\) | |||||||
\(90\) | 27.6906 | 2.91884 | ||||||||
\(91\) | −6.38619 | −0.669455 | ||||||||
\(92\) | −22.1472 | −2.30900 | ||||||||
\(93\) | 17.7939 | 1.84514 | ||||||||
\(94\) | 22.4231 | 2.31277 | ||||||||
\(95\) | 14.2159 | 1.45852 | ||||||||
\(96\) | −32.0965 | −3.27584 | ||||||||
\(97\) | 8.75996 | 0.889439 | 0.444720 | − | 0.895670i | \(-0.353303\pi\) | ||||
0.444720 | + | 0.895670i | \(0.353303\pi\) | |||||||
\(98\) | 12.6311 | 1.27593 | ||||||||
\(99\) | −13.3830 | −1.34505 | ||||||||
\(100\) | 16.8967 | 1.68967 | ||||||||
\(101\) | 9.15275 | 0.910733 | 0.455367 | − | 0.890304i | \(-0.349508\pi\) | ||||
0.455367 | + | 0.890304i | \(0.349508\pi\) | |||||||
\(102\) | 43.2715 | 4.28452 | ||||||||
\(103\) | −5.15534 | −0.507971 | −0.253985 | − | 0.967208i | \(-0.581741\pi\) | ||||
−0.253985 | + | 0.967208i | \(0.581741\pi\) | |||||||
\(104\) | 33.4702 | 3.28202 | ||||||||
\(105\) | −11.0940 | −1.08266 | ||||||||
\(106\) | −2.63717 | −0.256145 | ||||||||
\(107\) | −9.54415 | −0.922668 | −0.461334 | − | 0.887227i | \(-0.652629\pi\) | ||||
−0.461334 | + | 0.887227i | \(0.652629\pi\) | |||||||
\(108\) | 7.91277 | 0.761407 | ||||||||
\(109\) | −6.27584 | −0.601117 | −0.300558 | − | 0.953763i | \(-0.597173\pi\) | ||||
−0.300558 | + | 0.953763i | \(0.597173\pi\) | |||||||
\(110\) | −28.2689 | −2.69533 | ||||||||
\(111\) | 13.3567 | 1.26777 | ||||||||
\(112\) | 15.8179 | 1.49465 | ||||||||
\(113\) | 15.1481 | 1.42501 | 0.712507 | − | 0.701665i | \(-0.247560\pi\) | ||||
0.712507 | + | 0.701665i | \(0.247560\pi\) | |||||||
\(114\) | 33.2628 | 3.11535 | ||||||||
\(115\) | 12.9631 | 1.20881 | ||||||||
\(116\) | −16.9085 | −1.56992 | ||||||||
\(117\) | −15.5525 | −1.43783 | ||||||||
\(118\) | 1.79576 | 0.165313 | ||||||||
\(119\) | −9.48078 | −0.869102 | ||||||||
\(120\) | 58.1438 | 5.30778 | ||||||||
\(121\) | 2.66253 | 0.242048 | ||||||||
\(122\) | −7.65829 | −0.693349 | ||||||||
\(123\) | 8.28971 | 0.747458 | ||||||||
\(124\) | 34.2637 | 3.07697 | ||||||||
\(125\) | 4.61032 | 0.412360 | ||||||||
\(126\) | −14.1958 | −1.26466 | ||||||||
\(127\) | 10.6958 | 0.949100 | 0.474550 | − | 0.880228i | \(-0.342611\pi\) | ||||
0.474550 | + | 0.880228i | \(0.342611\pi\) | |||||||
\(128\) | −5.68881 | −0.502824 | ||||||||
\(129\) | −0.0808726 | −0.00712043 | ||||||||
\(130\) | −32.8513 | −2.88125 | ||||||||
\(131\) | 10.2277 | 0.893600 | 0.446800 | − | 0.894634i | \(-0.352563\pi\) | ||||
0.446800 | + | 0.894634i | \(0.352563\pi\) | |||||||
\(132\) | −47.1228 | −4.10152 | ||||||||
\(133\) | −7.28788 | −0.631939 | ||||||||
\(134\) | −21.7904 | −1.88240 | ||||||||
\(135\) | −4.63147 | −0.398613 | ||||||||
\(136\) | 49.6890 | 4.26079 | ||||||||
\(137\) | 9.60311 | 0.820449 | 0.410225 | − | 0.911985i | \(-0.365450\pi\) | ||||
0.410225 | + | 0.911985i | \(0.365450\pi\) | |||||||
\(138\) | 30.3314 | 2.58198 | ||||||||
\(139\) | −10.7069 | −0.908149 | −0.454074 | − | 0.890964i | \(-0.650030\pi\) | ||||
−0.454074 | + | 0.890964i | \(0.650030\pi\) | |||||||
\(140\) | −21.3625 | −1.80546 | ||||||||
\(141\) | −21.8780 | −1.84246 | ||||||||
\(142\) | 15.2099 | 1.27639 | ||||||||
\(143\) | 15.8773 | 1.32772 | ||||||||
\(144\) | 38.5219 | 3.21016 | ||||||||
\(145\) | 9.89681 | 0.821885 | ||||||||
\(146\) | −11.5426 | −0.955271 | ||||||||
\(147\) | −12.3241 | −1.01647 | ||||||||
\(148\) | 25.7196 | 2.11414 | ||||||||
\(149\) | 0.971180 | 0.0795622 | 0.0397811 | − | 0.999208i | \(-0.487334\pi\) | ||||
0.0397811 | + | 0.999208i | \(0.487334\pi\) | |||||||
\(150\) | −23.1407 | −1.88943 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 38.1959 | 3.09810 | ||||||||
\(153\) | −23.0888 | −1.86662 | ||||||||
\(154\) | 14.4922 | 1.16782 | ||||||||
\(155\) | −20.0551 | −1.61086 | ||||||||
\(156\) | −54.7616 | −4.38444 | ||||||||
\(157\) | 1.07348 | 0.0856731 | 0.0428365 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428365 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(158\) | 25.6892 | 2.04373 | ||||||||
\(159\) | 2.57307 | 0.204057 | ||||||||
\(160\) | 36.1753 | 2.85991 | ||||||||
\(161\) | −6.64561 | −0.523748 | ||||||||
\(162\) | 17.8082 | 1.39914 | ||||||||
\(163\) | 1.68888 | 0.132283 | 0.0661415 | − | 0.997810i | \(-0.478931\pi\) | ||||
0.0661415 | + | 0.997810i | \(0.478931\pi\) | |||||||
\(164\) | 15.9626 | 1.24647 | ||||||||
\(165\) | 27.5817 | 2.14723 | ||||||||
\(166\) | −12.3918 | −0.961793 | ||||||||
\(167\) | −18.9897 | −1.46947 | −0.734733 | − | 0.678356i | \(-0.762693\pi\) | ||||
−0.734733 | + | 0.678356i | \(0.762693\pi\) | |||||||
\(168\) | −29.8078 | −2.29972 | ||||||||
\(169\) | 5.45102 | 0.419309 | ||||||||
\(170\) | −48.7703 | −3.74051 | ||||||||
\(171\) | −17.7484 | −1.35725 | ||||||||
\(172\) | −0.155727 | −0.0118741 | ||||||||
\(173\) | 20.7337 | 1.57635 | 0.788175 | − | 0.615451i | \(-0.211026\pi\) | ||||
0.788175 | + | 0.615451i | \(0.211026\pi\) | |||||||
\(174\) | 23.1569 | 1.75552 | ||||||||
\(175\) | 5.07013 | 0.383266 | ||||||||
\(176\) | −39.3264 | −2.96434 | ||||||||
\(177\) | −1.75211 | −0.131697 | ||||||||
\(178\) | −34.8265 | −2.61036 | ||||||||
\(179\) | −7.01718 | −0.524489 | −0.262244 | − | 0.965002i | \(-0.584463\pi\) | ||||
−0.262244 | + | 0.965002i | \(0.584463\pi\) | |||||||
\(180\) | −52.0246 | −3.87769 | ||||||||
\(181\) | 3.04172 | 0.226089 | 0.113045 | − | 0.993590i | \(-0.463940\pi\) | ||||
0.113045 | + | 0.993590i | \(0.463940\pi\) | |||||||
\(182\) | 16.8415 | 1.24837 | ||||||||
\(183\) | 7.47213 | 0.552356 | ||||||||
\(184\) | 34.8298 | 2.56769 | ||||||||
\(185\) | −15.0541 | −1.10680 | ||||||||
\(186\) | −46.9255 | −3.44075 | ||||||||
\(187\) | 23.5710 | 1.72368 | ||||||||
\(188\) | −42.1281 | −3.07251 | ||||||||
\(189\) | 2.37435 | 0.172709 | ||||||||
\(190\) | −37.4898 | −2.71979 | ||||||||
\(191\) | 5.31681 | 0.384711 | 0.192355 | − | 0.981325i | \(-0.438387\pi\) | ||||
0.192355 | + | 0.981325i | \(0.438387\pi\) | |||||||
\(192\) | 29.8922 | 2.15728 | ||||||||
\(193\) | −25.0274 | −1.80152 | −0.900758 | − | 0.434322i | \(-0.856988\pi\) | ||||
−0.900758 | + | 0.434322i | \(0.856988\pi\) | |||||||
\(194\) | −23.1015 | −1.65859 | ||||||||
\(195\) | 32.0528 | 2.29535 | ||||||||
\(196\) | −23.7311 | −1.69508 | ||||||||
\(197\) | 13.0527 | 0.929967 | 0.464984 | − | 0.885319i | \(-0.346060\pi\) | ||||
0.464984 | + | 0.885319i | \(0.346060\pi\) | |||||||
\(198\) | 35.2934 | 2.50819 | ||||||||
\(199\) | 14.9935 | 1.06286 | 0.531430 | − | 0.847102i | \(-0.321655\pi\) | ||||
0.531430 | + | 0.847102i | \(0.321655\pi\) | |||||||
\(200\) | −26.5726 | −1.87897 | ||||||||
\(201\) | 21.2607 | 1.49962 | ||||||||
\(202\) | −24.1374 | −1.69830 | ||||||||
\(203\) | −5.07367 | −0.356102 | ||||||||
\(204\) | −81.2977 | −5.69198 | ||||||||
\(205\) | −9.34314 | −0.652553 | ||||||||
\(206\) | 13.5955 | 0.947244 | ||||||||
\(207\) | −16.1843 | −1.12488 | ||||||||
\(208\) | −45.7013 | −3.16881 | ||||||||
\(209\) | 18.1190 | 1.25332 | ||||||||
\(210\) | 29.2567 | 2.01891 | ||||||||
\(211\) | 2.74882 | 0.189237 | 0.0946185 | − | 0.995514i | \(-0.469837\pi\) | ||||
0.0946185 | + | 0.995514i | \(0.469837\pi\) | |||||||
\(212\) | 4.95467 | 0.340288 | ||||||||
\(213\) | −14.8402 | −1.01683 | ||||||||
\(214\) | 25.1696 | 1.72056 | ||||||||
\(215\) | 0.0911496 | 0.00621635 | ||||||||
\(216\) | −12.4440 | −0.846709 | ||||||||
\(217\) | 10.2814 | 0.697946 | ||||||||
\(218\) | 16.5505 | 1.12094 | ||||||||
\(219\) | 11.2620 | 0.761016 | ||||||||
\(220\) | 53.1111 | 3.58075 | ||||||||
\(221\) | 27.3919 | 1.84258 | ||||||||
\(222\) | −35.2240 | −2.36408 | ||||||||
\(223\) | −18.1285 | −1.21397 | −0.606986 | − | 0.794712i | \(-0.707622\pi\) | ||||
−0.606986 | + | 0.794712i | \(0.707622\pi\) | |||||||
\(224\) | −18.5455 | −1.23912 | ||||||||
\(225\) | 12.3474 | 0.823162 | ||||||||
\(226\) | −39.9482 | −2.65731 | ||||||||
\(227\) | 9.58649 | 0.636278 | 0.318139 | − | 0.948044i | \(-0.396942\pi\) | ||||
0.318139 | + | 0.948044i | \(0.396942\pi\) | |||||||
\(228\) | −62.4936 | −4.13874 | ||||||||
\(229\) | 21.2902 | 1.40689 | 0.703447 | − | 0.710748i | \(-0.251643\pi\) | ||||
0.703447 | + | 0.710748i | \(0.251643\pi\) | |||||||
\(230\) | −34.1858 | −2.25415 | ||||||||
\(231\) | −14.1400 | −0.930341 | ||||||||
\(232\) | 26.5912 | 1.74580 | ||||||||
\(233\) | 13.8308 | 0.906086 | 0.453043 | − | 0.891489i | \(-0.350338\pi\) | ||||
0.453043 | + | 0.891489i | \(0.350338\pi\) | |||||||
\(234\) | 41.0145 | 2.68120 | ||||||||
\(235\) | 24.6582 | 1.60853 | ||||||||
\(236\) | −3.37385 | −0.219619 | ||||||||
\(237\) | −25.0648 | −1.62813 | ||||||||
\(238\) | 25.0024 | 1.62067 | ||||||||
\(239\) | 22.8217 | 1.47621 | 0.738107 | − | 0.674684i | \(-0.235720\pi\) | ||||
0.738107 | + | 0.674684i | \(0.235720\pi\) | |||||||
\(240\) | −79.3915 | −5.12470 | ||||||||
\(241\) | 1.00428 | 0.0646911 | 0.0323456 | − | 0.999477i | \(-0.489702\pi\) | ||||
0.0323456 | + | 0.999477i | \(0.489702\pi\) | |||||||
\(242\) | −7.02154 | −0.451361 | ||||||||
\(243\) | −22.1664 | −1.42197 | ||||||||
\(244\) | 14.3883 | 0.921114 | ||||||||
\(245\) | 13.8902 | 0.887410 | ||||||||
\(246\) | −21.8614 | −1.39383 | ||||||||
\(247\) | 21.0562 | 1.33977 | ||||||||
\(248\) | −53.8849 | −3.42170 | ||||||||
\(249\) | 12.0906 | 0.766211 | ||||||||
\(250\) | −12.1582 | −0.768953 | ||||||||
\(251\) | −7.75507 | −0.489496 | −0.244748 | − | 0.969587i | \(-0.578705\pi\) | ||||
−0.244748 | + | 0.969587i | \(0.578705\pi\) | |||||||
\(252\) | 26.6708 | 1.68010 | ||||||||
\(253\) | 16.5222 | 1.03874 | ||||||||
\(254\) | −28.2067 | −1.76985 | ||||||||
\(255\) | 47.5848 | 2.97988 | ||||||||
\(256\) | −8.23231 | −0.514519 | ||||||||
\(257\) | 3.31503 | 0.206786 | 0.103393 | − | 0.994641i | \(-0.467030\pi\) | ||||
0.103393 | + | 0.994641i | \(0.467030\pi\) | |||||||
\(258\) | 0.213275 | 0.0132779 | ||||||||
\(259\) | 7.71758 | 0.479547 | ||||||||
\(260\) | 61.7205 | 3.82775 | ||||||||
\(261\) | −12.3561 | −0.764820 | ||||||||
\(262\) | −26.9723 | −1.66635 | ||||||||
\(263\) | 16.4652 | 1.01529 | 0.507644 | − | 0.861567i | \(-0.330516\pi\) | ||||
0.507644 | + | 0.861567i | \(0.330516\pi\) | |||||||
\(264\) | 74.1078 | 4.56102 | ||||||||
\(265\) | −2.90004 | −0.178148 | ||||||||
\(266\) | 19.2194 | 1.17842 | ||||||||
\(267\) | 33.9800 | 2.07954 | ||||||||
\(268\) | 40.9394 | 2.50077 | ||||||||
\(269\) | 3.91928 | 0.238962 | 0.119481 | − | 0.992836i | \(-0.461877\pi\) | ||||
0.119481 | + | 0.992836i | \(0.461877\pi\) | |||||||
\(270\) | 12.2140 | 0.743318 | ||||||||
\(271\) | −16.2709 | −0.988386 | −0.494193 | − | 0.869352i | \(-0.664536\pi\) | ||||
−0.494193 | + | 0.869352i | \(0.664536\pi\) | |||||||
\(272\) | −67.8470 | −4.11383 | ||||||||
\(273\) | −16.4321 | −0.994516 | ||||||||
\(274\) | −25.3250 | −1.52994 | ||||||||
\(275\) | −12.6053 | −0.760127 | ||||||||
\(276\) | −56.9862 | −3.43016 | ||||||||
\(277\) | −24.9225 | −1.49745 | −0.748724 | − | 0.662882i | \(-0.769333\pi\) | ||||
−0.748724 | + | 0.662882i | \(0.769333\pi\) | |||||||
\(278\) | 28.2360 | 1.69348 | ||||||||
\(279\) | 25.0385 | 1.49902 | ||||||||
\(280\) | 33.5957 | 2.00773 | ||||||||
\(281\) | −30.9217 | −1.84463 | −0.922317 | − | 0.386435i | \(-0.873706\pi\) | ||||
−0.922317 | + | 0.386435i | \(0.873706\pi\) | |||||||
\(282\) | 57.6961 | 3.43576 | ||||||||
\(283\) | −13.0306 | −0.774587 | −0.387293 | − | 0.921957i | \(-0.626590\pi\) | ||||
−0.387293 | + | 0.921957i | \(0.626590\pi\) | |||||||
\(284\) | −28.5761 | −1.69568 | ||||||||
\(285\) | 36.5785 | 2.16672 | ||||||||
\(286\) | −41.8711 | −2.47589 | ||||||||
\(287\) | 4.78983 | 0.282735 | ||||||||
\(288\) | −45.1644 | −2.66134 | ||||||||
\(289\) | 23.6654 | 1.39208 | ||||||||
\(290\) | −26.0996 | −1.53262 | ||||||||
\(291\) | 22.5400 | 1.32132 | ||||||||
\(292\) | 21.6860 | 1.26908 | ||||||||
\(293\) | 8.72238 | 0.509567 | 0.254784 | − | 0.966998i | \(-0.417996\pi\) | ||||
0.254784 | + | 0.966998i | \(0.417996\pi\) | |||||||
\(294\) | 32.5007 | 1.89548 | ||||||||
\(295\) | 1.97476 | 0.114975 | ||||||||
\(296\) | −40.4480 | −2.35099 | ||||||||
\(297\) | −5.90309 | −0.342532 | ||||||||
\(298\) | −2.56117 | −0.148365 | ||||||||
\(299\) | 19.2005 | 1.11040 | ||||||||
\(300\) | 43.4764 | 2.51011 | ||||||||
\(301\) | −0.0467285 | −0.00269339 | ||||||||
\(302\) | 2.63717 | 0.151752 | ||||||||
\(303\) | 23.5506 | 1.35295 | ||||||||
\(304\) | −52.1540 | −2.99124 | ||||||||
\(305\) | −8.42166 | −0.482223 | ||||||||
\(306\) | 60.8892 | 3.48080 | ||||||||
\(307\) | 33.6079 | 1.91810 | 0.959051 | − | 0.283233i | \(-0.0914071\pi\) | ||||
0.959051 | + | 0.283233i | \(0.0914071\pi\) | |||||||
\(308\) | −27.2278 | −1.55145 | ||||||||
\(309\) | −13.2650 | −0.754621 | ||||||||
\(310\) | 52.8887 | 3.00388 | ||||||||
\(311\) | −24.9450 | −1.41450 | −0.707251 | − | 0.706962i | \(-0.750065\pi\) | ||||
−0.707251 | + | 0.706962i | \(0.750065\pi\) | |||||||
\(312\) | 86.1210 | 4.87564 | ||||||||
\(313\) | 22.5492 | 1.27456 | 0.637279 | − | 0.770633i | \(-0.280060\pi\) | ||||
0.637279 | + | 0.770633i | \(0.280060\pi\) | |||||||
\(314\) | −2.83095 | −0.159760 | ||||||||
\(315\) | −15.6108 | −0.879570 | ||||||||
\(316\) | −48.2645 | −2.71509 | ||||||||
\(317\) | 28.2208 | 1.58504 | 0.792519 | − | 0.609848i | \(-0.208769\pi\) | ||||
0.792519 | + | 0.609848i | \(0.208769\pi\) | |||||||
\(318\) | −6.78562 | −0.380519 | ||||||||
\(319\) | 12.6141 | 0.706253 | ||||||||
\(320\) | −33.6908 | −1.88337 | ||||||||
\(321\) | −24.5577 | −1.37068 | ||||||||
\(322\) | 17.5256 | 0.976665 | ||||||||
\(323\) | 31.2595 | 1.73933 | ||||||||
\(324\) | −33.4576 | −1.85876 | ||||||||
\(325\) | −14.6486 | −0.812561 | ||||||||
\(326\) | −4.45386 | −0.246676 | ||||||||
\(327\) | −16.1482 | −0.892995 | ||||||||
\(328\) | −25.1036 | −1.38611 | ||||||||
\(329\) | −12.6412 | −0.696933 | ||||||||
\(330\) | −72.7377 | −4.00408 | ||||||||
\(331\) | −0.799618 | −0.0439510 | −0.0219755 | − | 0.999759i | \(-0.506996\pi\) | ||||
−0.0219755 | + | 0.999759i | \(0.506996\pi\) | |||||||
\(332\) | 23.2816 | 1.27774 | ||||||||
\(333\) | 18.7949 | 1.02995 | ||||||||
\(334\) | 50.0791 | 2.74020 | ||||||||
\(335\) | −23.9625 | −1.30921 | ||||||||
\(336\) | 40.7006 | 2.22040 | ||||||||
\(337\) | −9.58027 | −0.521870 | −0.260935 | − | 0.965356i | \(-0.584031\pi\) | ||||
−0.260935 | + | 0.965356i | \(0.584031\pi\) | |||||||
\(338\) | −14.3753 | −0.781912 | ||||||||
\(339\) | 38.9771 | 2.11695 | ||||||||
\(340\) | 91.6288 | 4.96927 | ||||||||
\(341\) | −25.5614 | −1.38423 | ||||||||
\(342\) | 46.8055 | 2.53095 | ||||||||
\(343\) | −17.5280 | −0.946423 | ||||||||
\(344\) | 0.244905 | 0.0132044 | ||||||||
\(345\) | 33.3549 | 1.79577 | ||||||||
\(346\) | −54.6782 | −2.93952 | ||||||||
\(347\) | −16.1218 | −0.865462 | −0.432731 | − | 0.901523i | \(-0.642450\pi\) | ||||
−0.432731 | + | 0.901523i | \(0.642450\pi\) | |||||||
\(348\) | −43.5067 | −2.33221 | ||||||||
\(349\) | −25.1886 | −1.34831 | −0.674157 | − | 0.738588i | \(-0.735493\pi\) | ||||
−0.674157 | + | 0.738588i | \(0.735493\pi\) | |||||||
\(350\) | −13.3708 | −0.714699 | ||||||||
\(351\) | −6.86000 | −0.366160 | ||||||||
\(352\) | 46.1076 | 2.45754 | ||||||||
\(353\) | 27.6568 | 1.47202 | 0.736011 | − | 0.676969i | \(-0.236707\pi\) | ||||
0.736011 | + | 0.676969i | \(0.236707\pi\) | |||||||
\(354\) | 4.62062 | 0.245583 | ||||||||
\(355\) | 16.7260 | 0.887727 | ||||||||
\(356\) | 65.4315 | 3.46786 | ||||||||
\(357\) | −24.3947 | −1.29110 | ||||||||
\(358\) | 18.5055 | 0.978046 | ||||||||
\(359\) | −18.3900 | −0.970585 | −0.485292 | − | 0.874352i | \(-0.661287\pi\) | ||||
−0.485292 | + | 0.874352i | \(0.661287\pi\) | |||||||
\(360\) | 81.8166 | 4.31211 | ||||||||
\(361\) | 5.02919 | 0.264694 | ||||||||
\(362\) | −8.02154 | −0.421603 | ||||||||
\(363\) | 6.85086 | 0.359577 | ||||||||
\(364\) | −31.6415 | −1.65846 | ||||||||
\(365\) | −12.6931 | −0.664390 | ||||||||
\(366\) | −19.7053 | −1.03001 | ||||||||
\(367\) | −21.3033 | −1.11203 | −0.556013 | − | 0.831174i | \(-0.687669\pi\) | ||||
−0.556013 | + | 0.831174i | \(0.687669\pi\) | |||||||
\(368\) | −47.5578 | −2.47912 | ||||||||
\(369\) | 11.6648 | 0.607246 | ||||||||
\(370\) | 39.7002 | 2.06391 | ||||||||
\(371\) | 1.48673 | 0.0771871 | ||||||||
\(372\) | 88.1629 | 4.57103 | ||||||||
\(373\) | 26.5523 | 1.37482 | 0.687412 | − | 0.726268i | \(-0.258747\pi\) | ||||
0.687412 | + | 0.726268i | \(0.258747\pi\) | |||||||
\(374\) | −62.1608 | −3.21426 | ||||||||
\(375\) | 11.8627 | 0.612585 | ||||||||
\(376\) | 66.2529 | 3.41673 | ||||||||
\(377\) | 14.6589 | 0.754970 | ||||||||
\(378\) | −6.26158 | −0.322061 | ||||||||
\(379\) | 1.33021 | 0.0683284 | 0.0341642 | − | 0.999416i | \(-0.489123\pi\) | ||||
0.0341642 | + | 0.999416i | \(0.489123\pi\) | |||||||
\(380\) | 70.4351 | 3.61324 | ||||||||
\(381\) | 27.5211 | 1.40995 | ||||||||
\(382\) | −14.0213 | −0.717394 | ||||||||
\(383\) | 5.59909 | 0.286100 | 0.143050 | − | 0.989715i | \(-0.454309\pi\) | ||||
0.143050 | + | 0.989715i | \(0.454309\pi\) | |||||||
\(384\) | −14.6377 | −0.746976 | ||||||||
\(385\) | 15.9368 | 0.812216 | ||||||||
\(386\) | 66.0017 | 3.35940 | ||||||||
\(387\) | −0.113799 | −0.00578474 | ||||||||
\(388\) | 43.4027 | 2.20344 | ||||||||
\(389\) | −24.1642 | −1.22518 | −0.612588 | − | 0.790402i | \(-0.709872\pi\) | ||||
−0.612588 | + | 0.790402i | \(0.709872\pi\) | |||||||
\(390\) | −84.5287 | −4.28028 | ||||||||
\(391\) | 28.5047 | 1.44154 | ||||||||
\(392\) | 37.3207 | 1.88498 | ||||||||
\(393\) | 26.3166 | 1.32750 | ||||||||
\(394\) | −34.4222 | −1.73417 | ||||||||
\(395\) | 28.2499 | 1.42141 | ||||||||
\(396\) | −66.3086 | −3.33213 | ||||||||
\(397\) | 29.4144 | 1.47627 | 0.738134 | − | 0.674654i | \(-0.235707\pi\) | ||||
0.738134 | + | 0.674654i | \(0.235707\pi\) | |||||||
\(398\) | −39.5404 | −1.98198 | ||||||||
\(399\) | −18.7522 | −0.938784 | ||||||||
\(400\) | 36.2832 | 1.81416 | ||||||||
\(401\) | 28.2144 | 1.40896 | 0.704480 | − | 0.709724i | \(-0.251180\pi\) | ||||
0.704480 | + | 0.709724i | \(0.251180\pi\) | |||||||
\(402\) | −56.0681 | −2.79642 | ||||||||
\(403\) | −29.7050 | −1.47971 | ||||||||
\(404\) | 45.3489 | 2.25619 | ||||||||
\(405\) | 19.5833 | 0.973100 | ||||||||
\(406\) | 13.3801 | 0.664045 | ||||||||
\(407\) | −19.1874 | −0.951082 | ||||||||
\(408\) | 127.853 | 6.32967 | ||||||||
\(409\) | 27.7090 | 1.37012 | 0.685060 | − | 0.728486i | \(-0.259776\pi\) | ||||
0.685060 | + | 0.728486i | \(0.259776\pi\) | |||||||
\(410\) | 24.6395 | 1.21686 | ||||||||
\(411\) | 24.7094 | 1.21883 | ||||||||
\(412\) | −25.5430 | −1.25841 | ||||||||
\(413\) | −1.01238 | −0.0498158 | ||||||||
\(414\) | 42.6806 | 2.09764 | ||||||||
\(415\) | −13.6271 | −0.668926 | ||||||||
\(416\) | 53.5818 | 2.62707 | ||||||||
\(417\) | −27.5496 | −1.34911 | ||||||||
\(418\) | −47.7830 | −2.33714 | ||||||||
\(419\) | −34.3433 | −1.67778 | −0.838889 | − | 0.544303i | \(-0.816794\pi\) | ||||
−0.838889 | + | 0.544303i | \(0.816794\pi\) | |||||||
\(420\) | −54.9670 | −2.68212 | ||||||||
\(421\) | −12.9770 | −0.632459 | −0.316230 | − | 0.948683i | \(-0.602417\pi\) | ||||
−0.316230 | + | 0.948683i | \(0.602417\pi\) | |||||||
\(422\) | −7.24912 | −0.352882 | ||||||||
\(423\) | −30.7855 | −1.49684 | ||||||||
\(424\) | −7.79198 | −0.378412 | ||||||||
\(425\) | −21.7470 | −1.05489 | ||||||||
\(426\) | 39.1361 | 1.89615 | ||||||||
\(427\) | 4.31743 | 0.208935 | ||||||||
\(428\) | −47.2881 | −2.28576 | ||||||||
\(429\) | 40.8533 | 1.97241 | ||||||||
\(430\) | −0.240377 | −0.0115920 | ||||||||
\(431\) | −8.34407 | −0.401920 | −0.200960 | − | 0.979599i | \(-0.564406\pi\) | ||||
−0.200960 | + | 0.979599i | \(0.564406\pi\) | |||||||
\(432\) | 16.9915 | 0.817505 | ||||||||
\(433\) | 1.28569 | 0.0617865 | 0.0308932 | − | 0.999523i | \(-0.490165\pi\) | ||||
0.0308932 | + | 0.999523i | \(0.490165\pi\) | |||||||
\(434\) | −27.1138 | −1.30150 | ||||||||
\(435\) | 25.4651 | 1.22096 | ||||||||
\(436\) | −31.0947 | −1.48917 | ||||||||
\(437\) | 21.9115 | 1.04817 | ||||||||
\(438\) | −29.6998 | −1.41911 | ||||||||
\(439\) | −7.87133 | −0.375678 | −0.187839 | − | 0.982200i | \(-0.560148\pi\) | ||||
−0.187839 | + | 0.982200i | \(0.560148\pi\) | |||||||
\(440\) | −83.5252 | −3.98191 | ||||||||
\(441\) | −17.3417 | −0.825796 | ||||||||
\(442\) | −72.2372 | −3.43597 | ||||||||
\(443\) | 6.94662 | 0.330044 | 0.165022 | − | 0.986290i | \(-0.447231\pi\) | ||||
0.165022 | + | 0.986290i | \(0.447231\pi\) | |||||||
\(444\) | 66.1783 | 3.14068 | ||||||||
\(445\) | −38.2981 | −1.81550 | ||||||||
\(446\) | 47.8079 | 2.26377 | ||||||||
\(447\) | 2.49891 | 0.118194 | ||||||||
\(448\) | 17.2718 | 0.816017 | ||||||||
\(449\) | −9.40260 | −0.443736 | −0.221868 | − | 0.975077i | \(-0.571215\pi\) | ||||
−0.221868 | + | 0.975077i | \(0.571215\pi\) | |||||||
\(450\) | −32.5623 | −1.53500 | ||||||||
\(451\) | −11.9084 | −0.560745 | ||||||||
\(452\) | 75.0539 | 3.53024 | ||||||||
\(453\) | −2.57307 | −0.120893 | ||||||||
\(454\) | −25.2812 | −1.18651 | ||||||||
\(455\) | 18.5202 | 0.868242 | ||||||||
\(456\) | 98.2807 | 4.60242 | ||||||||
\(457\) | 24.8208 | 1.16107 | 0.580533 | − | 0.814236i | \(-0.302844\pi\) | ||||
0.580533 | + | 0.814236i | \(0.302844\pi\) | |||||||
\(458\) | −56.1458 | −2.62352 | ||||||||
\(459\) | −10.1842 | −0.475357 | ||||||||
\(460\) | 64.2278 | 2.99464 | ||||||||
\(461\) | 17.1494 | 0.798725 | 0.399363 | − | 0.916793i | \(-0.369231\pi\) | ||||
0.399363 | + | 0.916793i | \(0.369231\pi\) | |||||||
\(462\) | 37.2895 | 1.73486 | ||||||||
\(463\) | 9.77502 | 0.454284 | 0.227142 | − | 0.973862i | \(-0.427062\pi\) | ||||
0.227142 | + | 0.973862i | \(0.427062\pi\) | |||||||
\(464\) | −36.3085 | −1.68558 | ||||||||
\(465\) | −51.6031 | −2.39304 | ||||||||
\(466\) | −36.4742 | −1.68964 | ||||||||
\(467\) | −22.2334 | −1.02884 | −0.514419 | − | 0.857539i | \(-0.671992\pi\) | ||||
−0.514419 | + | 0.857539i | \(0.671992\pi\) | |||||||
\(468\) | −77.0574 | −3.56198 | ||||||||
\(469\) | 12.2845 | 0.567247 | ||||||||
\(470\) | −65.0280 | −2.99952 | ||||||||
\(471\) | 2.76214 | 0.127273 | ||||||||
\(472\) | 5.30589 | 0.244223 | ||||||||
\(473\) | 0.116176 | 0.00534177 | ||||||||
\(474\) | 66.1001 | 3.03608 | ||||||||
\(475\) | −16.7169 | −0.767026 | ||||||||
\(476\) | −46.9742 | −2.15306 | ||||||||
\(477\) | 3.62067 | 0.165779 | ||||||||
\(478\) | −60.1847 | −2.75279 | ||||||||
\(479\) | −36.5836 | −1.67155 | −0.835775 | − | 0.549072i | \(-0.814981\pi\) | ||||
−0.835775 | + | 0.549072i | \(0.814981\pi\) | |||||||
\(480\) | 93.0814 | 4.24857 | ||||||||
\(481\) | −22.2977 | −1.01669 | ||||||||
\(482\) | −2.64845 | −0.120634 | ||||||||
\(483\) | −17.0996 | −0.778059 | ||||||||
\(484\) | 13.1919 | 0.599634 | ||||||||
\(485\) | −25.4043 | −1.15355 | ||||||||
\(486\) | 58.4565 | 2.65164 | ||||||||
\(487\) | −20.8560 | −0.945076 | −0.472538 | − | 0.881310i | \(-0.656662\pi\) | ||||
−0.472538 | + | 0.881310i | \(0.656662\pi\) | |||||||
\(488\) | −22.6277 | −1.02431 | ||||||||
\(489\) | 4.34559 | 0.196515 | ||||||||
\(490\) | −36.6307 | −1.65481 | ||||||||
\(491\) | −7.18588 | −0.324294 | −0.162147 | − | 0.986767i | \(-0.551842\pi\) | ||||
−0.162147 | + | 0.986767i | \(0.551842\pi\) | |||||||
\(492\) | 41.0728 | 1.85170 | ||||||||
\(493\) | 21.7622 | 0.980120 | ||||||||
\(494\) | −55.5288 | −2.49836 | ||||||||
\(495\) | 38.8114 | 1.74444 | ||||||||
\(496\) | 73.5763 | 3.30368 | ||||||||
\(497\) | −8.57473 | −0.384629 | ||||||||
\(498\) | −31.8850 | −1.42880 | ||||||||
\(499\) | −32.7283 | −1.46512 | −0.732561 | − | 0.680702i | \(-0.761675\pi\) | ||||
−0.732561 | + | 0.680702i | \(0.761675\pi\) | |||||||
\(500\) | 22.8426 | 1.02155 | ||||||||
\(501\) | −48.8617 | −2.18298 | ||||||||
\(502\) | 20.4515 | 0.912793 | ||||||||
\(503\) | −27.1250 | −1.20944 | −0.604722 | − | 0.796437i | \(-0.706716\pi\) | ||||
−0.604722 | + | 0.796437i | \(0.706716\pi\) | |||||||
\(504\) | −41.9439 | −1.86833 | ||||||||
\(505\) | −26.5434 | −1.18117 | ||||||||
\(506\) | −43.5720 | −1.93701 | ||||||||
\(507\) | 14.0258 | 0.622909 | ||||||||
\(508\) | 52.9943 | 2.35124 | ||||||||
\(509\) | −13.3052 | −0.589742 | −0.294871 | − | 0.955537i | \(-0.595277\pi\) | ||||
−0.294871 | + | 0.955537i | \(0.595277\pi\) | |||||||
\(510\) | −125.489 | −5.55676 | ||||||||
\(511\) | 6.50723 | 0.287863 | ||||||||
\(512\) | 33.0876 | 1.46228 | ||||||||
\(513\) | −7.82859 | −0.345641 | ||||||||
\(514\) | −8.74230 | −0.385606 | ||||||||
\(515\) | 14.9507 | 0.658807 | ||||||||
\(516\) | −0.400697 | −0.0176397 | ||||||||
\(517\) | 31.4284 | 1.38222 | ||||||||
\(518\) | −20.3526 | −0.894241 | ||||||||
\(519\) | 53.3491 | 2.34176 | ||||||||
\(520\) | −97.0649 | −4.25658 | ||||||||
\(521\) | 4.51369 | 0.197749 | 0.0988743 | − | 0.995100i | \(-0.468476\pi\) | ||||
0.0988743 | + | 0.995100i | \(0.468476\pi\) | |||||||
\(522\) | 32.5850 | 1.42621 | ||||||||
\(523\) | −10.4701 | −0.457826 | −0.228913 | − | 0.973447i | \(-0.573517\pi\) | ||||
−0.228913 | + | 0.973447i | \(0.573517\pi\) | |||||||
\(524\) | 50.6750 | 2.21375 | ||||||||
\(525\) | 13.0458 | 0.569364 | ||||||||
\(526\) | −43.4216 | −1.89327 | ||||||||
\(527\) | −44.0994 | −1.92100 | ||||||||
\(528\) | −101.189 | −4.40370 | ||||||||
\(529\) | −3.01948 | −0.131282 | ||||||||
\(530\) | 7.64791 | 0.332204 | ||||||||
\(531\) | −2.46547 | −0.106992 | ||||||||
\(532\) | −36.1091 | −1.56553 | ||||||||
\(533\) | −13.8388 | −0.599425 | ||||||||
\(534\) | −89.6110 | −3.87785 | ||||||||
\(535\) | 27.6785 | 1.19664 | ||||||||
\(536\) | −64.3835 | −2.78094 | ||||||||
\(537\) | −18.0557 | −0.779160 | ||||||||
\(538\) | −10.3358 | −0.445608 | ||||||||
\(539\) | 17.7039 | 0.762560 | ||||||||
\(540\) | −22.9474 | −0.987498 | ||||||||
\(541\) | 2.83582 | 0.121922 | 0.0609608 | − | 0.998140i | \(-0.480584\pi\) | ||||
0.0609608 | + | 0.998140i | \(0.480584\pi\) | |||||||
\(542\) | 42.9091 | 1.84310 | ||||||||
\(543\) | 7.82656 | 0.335870 | ||||||||
\(544\) | 79.5463 | 3.41052 | ||||||||
\(545\) | 18.2002 | 0.779612 | ||||||||
\(546\) | 43.3342 | 1.85453 | ||||||||
\(547\) | 15.0891 | 0.645163 | 0.322582 | − | 0.946542i | \(-0.395449\pi\) | ||||
0.322582 | + | 0.946542i | \(0.395449\pi\) | |||||||
\(548\) | 47.5803 | 2.03253 | ||||||||
\(549\) | 10.5144 | 0.448742 | ||||||||
\(550\) | 33.2423 | 1.41746 | ||||||||
\(551\) | 16.7286 | 0.712663 | ||||||||
\(552\) | 89.6194 | 3.81445 | ||||||||
\(553\) | −14.4825 | −0.615860 | ||||||||
\(554\) | 65.7249 | 2.79238 | ||||||||
\(555\) | −38.7352 | −1.64422 | ||||||||
\(556\) | −53.0493 | −2.24979 | ||||||||
\(557\) | 13.5015 | 0.572078 | 0.286039 | − | 0.958218i | \(-0.407661\pi\) | ||||
0.286039 | + | 0.958218i | \(0.407661\pi\) | |||||||
\(558\) | −66.0309 | −2.79531 | ||||||||
\(559\) | 0.135008 | 0.00571024 | ||||||||
\(560\) | −45.8727 | −1.93848 | ||||||||
\(561\) | 60.6498 | 2.56063 | ||||||||
\(562\) | 81.5458 | 3.43980 | ||||||||
\(563\) | −41.1858 | −1.73577 | −0.867887 | − | 0.496761i | \(-0.834523\pi\) | ||||
−0.867887 | + | 0.496761i | \(0.834523\pi\) | |||||||
\(564\) | −108.399 | −4.56440 | ||||||||
\(565\) | −43.9302 | −1.84816 | ||||||||
\(566\) | 34.3638 | 1.44442 | ||||||||
\(567\) | −10.0395 | −0.421619 | ||||||||
\(568\) | 44.9403 | 1.88565 | ||||||||
\(569\) | 1.46558 | 0.0614401 | 0.0307201 | − | 0.999528i | \(-0.490220\pi\) | ||||
0.0307201 | + | 0.999528i | \(0.490220\pi\) | |||||||
\(570\) | −96.4636 | −4.04042 | ||||||||
\(571\) | 10.3343 | 0.432478 | 0.216239 | − | 0.976340i | \(-0.430621\pi\) | ||||
0.216239 | + | 0.976340i | \(0.430621\pi\) | |||||||
\(572\) | 78.6666 | 3.28922 | ||||||||
\(573\) | 13.6805 | 0.571511 | ||||||||
\(574\) | −12.6316 | −0.527233 | ||||||||
\(575\) | −15.2437 | −0.635707 | ||||||||
\(576\) | 42.0626 | 1.75261 | ||||||||
\(577\) | −17.8421 | −0.742777 | −0.371388 | − | 0.928478i | \(-0.621118\pi\) | ||||
−0.371388 | + | 0.928478i | \(0.621118\pi\) | |||||||
\(578\) | −62.4097 | −2.59590 | ||||||||
\(579\) | −64.3973 | −2.67626 | ||||||||
\(580\) | 49.0354 | 2.03609 | ||||||||
\(581\) | 6.98600 | 0.289828 | ||||||||
\(582\) | −59.4417 | −2.46394 | ||||||||
\(583\) | −3.69629 | −0.153084 | ||||||||
\(584\) | −34.1045 | −1.41126 | ||||||||
\(585\) | 45.1029 | 1.86477 | ||||||||
\(586\) | −23.0024 | −0.950221 | ||||||||
\(587\) | 15.7618 | 0.650560 | 0.325280 | − | 0.945618i | \(-0.394541\pi\) | ||||
0.325280 | + | 0.945618i | \(0.394541\pi\) | |||||||
\(588\) | −61.0617 | −2.51814 | ||||||||
\(589\) | −33.8992 | −1.39679 | ||||||||
\(590\) | −5.20779 | −0.214401 | ||||||||
\(591\) | 33.5855 | 1.38152 | ||||||||
\(592\) | 55.2291 | 2.26990 | ||||||||
\(593\) | −35.8669 | −1.47288 | −0.736439 | − | 0.676504i | \(-0.763494\pi\) | ||||
−0.736439 | + | 0.676504i | \(0.763494\pi\) | |||||||
\(594\) | 15.5675 | 0.638740 | ||||||||
\(595\) | 27.4947 | 1.12717 | ||||||||
\(596\) | 4.81188 | 0.197102 | ||||||||
\(597\) | 38.5792 | 1.57894 | ||||||||
\(598\) | −50.6351 | −2.07062 | ||||||||
\(599\) | 42.9173 | 1.75355 | 0.876776 | − | 0.480899i | \(-0.159690\pi\) | ||||
0.876776 | + | 0.480899i | \(0.159690\pi\) | |||||||
\(600\) | −68.3732 | −2.79132 | ||||||||
\(601\) | −14.4177 | −0.588109 | −0.294055 | − | 0.955789i | \(-0.595005\pi\) | ||||
−0.294055 | + | 0.955789i | \(0.595005\pi\) | |||||||
\(602\) | 0.123231 | 0.00502252 | ||||||||
\(603\) | 29.9169 | 1.21831 | ||||||||
\(604\) | −4.95467 | −0.201603 | ||||||||
\(605\) | −7.72144 | −0.313921 | ||||||||
\(606\) | −62.1071 | −2.52293 | ||||||||
\(607\) | −16.0990 | −0.653439 | −0.326720 | − | 0.945121i | \(-0.605943\pi\) | ||||
−0.326720 | + | 0.945121i | \(0.605943\pi\) | |||||||
\(608\) | 61.1472 | 2.47985 | ||||||||
\(609\) | −13.0549 | −0.529011 | ||||||||
\(610\) | 22.2094 | 0.899231 | ||||||||
\(611\) | 36.5231 | 1.47757 | ||||||||
\(612\) | −114.398 | −4.62425 | ||||||||
\(613\) | −26.5491 | −1.07231 | −0.536154 | − | 0.844120i | \(-0.680123\pi\) | ||||
−0.536154 | + | 0.844120i | \(0.680123\pi\) | |||||||
\(614\) | −88.6297 | −3.57680 | ||||||||
\(615\) | −24.0405 | −0.969408 | ||||||||
\(616\) | 42.8198 | 1.72526 | ||||||||
\(617\) | −6.10564 | −0.245804 | −0.122902 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122902 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(618\) | 34.9822 | 1.40719 | ||||||||
\(619\) | 19.4193 | 0.780527 | 0.390263 | − | 0.920703i | \(-0.372384\pi\) | ||||
0.390263 | + | 0.920703i | \(0.372384\pi\) | |||||||
\(620\) | −99.3664 | −3.99065 | ||||||||
\(621\) | −7.13867 | −0.286465 | ||||||||
\(622\) | 65.7843 | 2.63771 | ||||||||
\(623\) | 19.6338 | 0.786610 | ||||||||
\(624\) | −117.592 | −4.70747 | ||||||||
\(625\) | −30.4214 | −1.21686 | ||||||||
\(626\) | −59.4662 | −2.37675 | ||||||||
\(627\) | 46.6215 | 1.86188 | ||||||||
\(628\) | 5.31874 | 0.212241 | ||||||||
\(629\) | −33.1026 | −1.31989 | ||||||||
\(630\) | 41.1684 | 1.64019 | ||||||||
\(631\) | 34.0860 | 1.35694 | 0.678471 | − | 0.734627i | \(-0.262643\pi\) | ||||
0.678471 | + | 0.734627i | \(0.262643\pi\) | |||||||
\(632\) | 75.9033 | 3.01927 | ||||||||
\(633\) | 7.07291 | 0.281123 | ||||||||
\(634\) | −74.4230 | −2.95572 | ||||||||
\(635\) | −31.0184 | −1.23093 | ||||||||
\(636\) | 12.7487 | 0.505519 | ||||||||
\(637\) | 20.5737 | 0.815161 | ||||||||
\(638\) | −33.2655 | −1.31699 | ||||||||
\(639\) | −20.8823 | −0.826090 | ||||||||
\(640\) | 16.4978 | 0.652132 | ||||||||
\(641\) | 8.33126 | 0.329065 | 0.164533 | − | 0.986372i | \(-0.447388\pi\) | ||||
0.164533 | + | 0.986372i | \(0.447388\pi\) | |||||||
\(642\) | 64.7630 | 2.55599 | ||||||||
\(643\) | −22.7920 | −0.898827 | −0.449414 | − | 0.893324i | \(-0.648367\pi\) | ||||
−0.449414 | + | 0.893324i | \(0.648367\pi\) | |||||||
\(644\) | −32.9268 | −1.29750 | ||||||||
\(645\) | 0.234534 | 0.00923477 | ||||||||
\(646\) | −82.4367 | −3.24343 | ||||||||
\(647\) | −49.5113 | −1.94649 | −0.973245 | − | 0.229771i | \(-0.926202\pi\) | ||||
−0.973245 | + | 0.229771i | \(0.926202\pi\) | |||||||
\(648\) | 52.6172 | 2.06700 | ||||||||
\(649\) | 2.51696 | 0.0987993 | ||||||||
\(650\) | 38.6310 | 1.51523 | ||||||||
\(651\) | 26.4547 | 1.03684 | ||||||||
\(652\) | 8.36783 | 0.327710 | ||||||||
\(653\) | 38.6818 | 1.51374 | 0.756868 | − | 0.653568i | \(-0.226729\pi\) | ||||
0.756868 | + | 0.653568i | \(0.226729\pi\) | |||||||
\(654\) | 42.5855 | 1.66522 | ||||||||
\(655\) | −29.6609 | −1.15895 | ||||||||
\(656\) | 34.2773 | 1.33830 | ||||||||
\(657\) | 15.8473 | 0.618260 | ||||||||
\(658\) | 33.3371 | 1.29961 | ||||||||
\(659\) | −44.5685 | −1.73614 | −0.868071 | − | 0.496441i | \(-0.834640\pi\) | ||||
−0.868071 | + | 0.496441i | \(0.834640\pi\) | |||||||
\(660\) | 136.658 | 5.31942 | ||||||||
\(661\) | 26.2480 | 1.02093 | 0.510465 | − | 0.859898i | \(-0.329473\pi\) | ||||
0.510465 | + | 0.859898i | \(0.329473\pi\) | |||||||
\(662\) | 2.10873 | 0.0819581 | ||||||||
\(663\) | 70.4813 | 2.73727 | ||||||||
\(664\) | −36.6138 | −1.42089 | ||||||||
\(665\) | 21.1352 | 0.819587 | ||||||||
\(666\) | −49.5652 | −1.92061 | ||||||||
\(667\) | 15.2544 | 0.590651 | ||||||||
\(668\) | −94.0877 | −3.64036 | ||||||||
\(669\) | −46.6458 | −1.80343 | ||||||||
\(670\) | 63.1931 | 2.44136 | ||||||||
\(671\) | −10.7339 | −0.414379 | ||||||||
\(672\) | −47.7189 | −1.84079 | ||||||||
\(673\) | 9.36570 | 0.361021 | 0.180511 | − | 0.983573i | \(-0.442225\pi\) | ||||
0.180511 | + | 0.983573i | \(0.442225\pi\) | |||||||
\(674\) | 25.2648 | 0.973164 | ||||||||
\(675\) | 5.44629 | 0.209628 | ||||||||
\(676\) | 27.0080 | 1.03877 | ||||||||
\(677\) | −28.1827 | −1.08315 | −0.541575 | − | 0.840652i | \(-0.682172\pi\) | ||||
−0.541575 | + | 0.840652i | \(0.682172\pi\) | |||||||
\(678\) | −102.789 | −3.94760 | ||||||||
\(679\) | 13.0237 | 0.499803 | ||||||||
\(680\) | −144.100 | −5.52599 | ||||||||
\(681\) | 24.6667 | 0.945229 | ||||||||
\(682\) | 67.4099 | 2.58126 | ||||||||
\(683\) | −34.7040 | −1.32791 | −0.663956 | − | 0.747772i | \(-0.731124\pi\) | ||||
−0.663956 | + | 0.747772i | \(0.731124\pi\) | |||||||
\(684\) | −87.9374 | −3.36237 | ||||||||
\(685\) | −27.8494 | −1.06407 | ||||||||
\(686\) | 46.2243 | 1.76485 | ||||||||
\(687\) | 54.7810 | 2.09003 | ||||||||
\(688\) | −0.334402 | −0.0127489 | ||||||||
\(689\) | −4.29547 | −0.163644 | ||||||||
\(690\) | −87.9625 | −3.34867 | ||||||||
\(691\) | −32.7369 | −1.24537 | −0.622686 | − | 0.782472i | \(-0.713959\pi\) | ||||
−0.622686 | + | 0.782472i | \(0.713959\pi\) | |||||||
\(692\) | 102.728 | 3.90515 | ||||||||
\(693\) | −19.8969 | −0.755822 | ||||||||
\(694\) | 42.5159 | 1.61388 | ||||||||
\(695\) | 31.0505 | 1.17781 | ||||||||
\(696\) | 68.4209 | 2.59349 | ||||||||
\(697\) | −20.5447 | −0.778188 | ||||||||
\(698\) | 66.4266 | 2.51428 | ||||||||
\(699\) | 35.5876 | 1.34605 | ||||||||
\(700\) | 25.1208 | 0.949478 | ||||||||
\(701\) | 5.40409 | 0.204110 | 0.102055 | − | 0.994779i | \(-0.467458\pi\) | ||||
0.102055 | + | 0.994779i | \(0.467458\pi\) | |||||||
\(702\) | 18.0910 | 0.682800 | ||||||||
\(703\) | −25.4460 | −0.959713 | ||||||||
\(704\) | −42.9410 | −1.61840 | ||||||||
\(705\) | 63.4473 | 2.38956 | ||||||||
\(706\) | −72.9357 | −2.74497 | ||||||||
\(707\) | 13.6077 | 0.511769 | ||||||||
\(708\) | −8.68114 | −0.326257 | ||||||||
\(709\) | 42.2359 | 1.58620 | 0.793101 | − | 0.609090i | \(-0.208465\pi\) | ||||
0.793101 | + | 0.609090i | \(0.208465\pi\) | |||||||
\(710\) | −44.1095 | −1.65540 | ||||||||
\(711\) | −35.2697 | −1.32272 | ||||||||
\(712\) | −102.901 | −3.85638 | ||||||||
\(713\) | −30.9117 | −1.15765 | ||||||||
\(714\) | 64.3330 | 2.40760 | ||||||||
\(715\) | −46.0448 | −1.72198 | ||||||||
\(716\) | −34.7678 | −1.29933 | ||||||||
\(717\) | 58.7218 | 2.19300 | ||||||||
\(718\) | 48.4975 | 1.80991 | ||||||||
\(719\) | 16.6282 | 0.620127 | 0.310063 | − | 0.950716i | \(-0.399650\pi\) | ||||
0.310063 | + | 0.950716i | \(0.399650\pi\) | |||||||
\(720\) | −111.715 | −4.16338 | ||||||||
\(721\) | −7.66459 | −0.285444 | ||||||||
\(722\) | −13.2628 | −0.493592 | ||||||||
\(723\) | 2.58407 | 0.0961026 | ||||||||
\(724\) | 15.0707 | 0.560100 | ||||||||
\(725\) | −11.6380 | −0.432224 | ||||||||
\(726\) | −18.0669 | −0.670525 | ||||||||
\(727\) | 50.0953 | 1.85793 | 0.928966 | − | 0.370164i | \(-0.120699\pi\) | ||||
0.928966 | + | 0.370164i | \(0.120699\pi\) | |||||||
\(728\) | 49.7610 | 1.84427 | ||||||||
\(729\) | −36.7773 | −1.36212 | ||||||||
\(730\) | 33.4740 | 1.23893 | ||||||||
\(731\) | 0.200430 | 0.00741317 | ||||||||
\(732\) | 37.0219 | 1.36837 | ||||||||
\(733\) | 36.2651 | 1.33948 | 0.669741 | − | 0.742595i | \(-0.266405\pi\) | ||||
0.669741 | + | 0.742595i | \(0.266405\pi\) | |||||||
\(734\) | 56.1806 | 2.07366 | ||||||||
\(735\) | 35.7403 | 1.31830 | ||||||||
\(736\) | 55.7584 | 2.05528 | ||||||||
\(737\) | −30.5416 | −1.12502 | ||||||||
\(738\) | −30.7621 | −1.13237 | ||||||||
\(739\) | 1.94419 | 0.0715180 | 0.0357590 | − | 0.999360i | \(-0.488615\pi\) | ||||
0.0357590 | + | 0.999360i | \(0.488615\pi\) | |||||||
\(740\) | −74.5880 | −2.74191 | ||||||||
\(741\) | 54.1790 | 1.99031 | ||||||||
\(742\) | −3.92076 | −0.143936 | ||||||||
\(743\) | 9.92315 | 0.364045 | 0.182022 | − | 0.983294i | \(-0.441736\pi\) | ||||
0.182022 | + | 0.983294i | \(0.441736\pi\) | |||||||
\(744\) | −138.650 | −5.08314 | ||||||||
\(745\) | −2.81647 | −0.103187 | ||||||||
\(746\) | −70.0229 | −2.56372 | ||||||||
\(747\) | 17.0132 | 0.622481 | ||||||||
\(748\) | 116.787 | 4.27014 | ||||||||
\(749\) | −14.1896 | −0.518475 | ||||||||
\(750\) | −31.2839 | −1.14233 | ||||||||
\(751\) | 40.3651 | 1.47294 | 0.736472 | − | 0.676468i | \(-0.236490\pi\) | ||||
0.736472 | + | 0.676468i | \(0.236490\pi\) | |||||||
\(752\) | −90.4640 | −3.29888 | ||||||||
\(753\) | −19.9543 | −0.727176 | ||||||||
\(754\) | −38.6580 | −1.40784 | ||||||||
\(755\) | 2.90004 | 0.105543 | ||||||||
\(756\) | 11.7641 | 0.427858 | ||||||||
\(757\) | −10.1163 | −0.367684 | −0.183842 | − | 0.982956i | \(-0.558853\pi\) | ||||
−0.183842 | + | 0.982956i | \(0.558853\pi\) | |||||||
\(758\) | −3.50800 | −0.127416 | ||||||||
\(759\) | 42.5128 | 1.54312 | ||||||||
\(760\) | −110.770 | −4.01805 | ||||||||
\(761\) | 18.6996 | 0.677860 | 0.338930 | − | 0.940812i | \(-0.389935\pi\) | ||||
0.338930 | + | 0.940812i | \(0.389935\pi\) | |||||||
\(762\) | −72.5777 | −2.62921 | ||||||||
\(763\) | −9.33047 | −0.337786 | ||||||||
\(764\) | 26.3431 | 0.953058 | ||||||||
\(765\) | 66.9586 | 2.42089 | ||||||||
\(766\) | −14.7658 | −0.533508 | ||||||||
\(767\) | 2.92497 | 0.105614 | ||||||||
\(768\) | −21.1823 | −0.764350 | ||||||||
\(769\) | −28.9857 | −1.04525 | −0.522625 | − | 0.852563i | \(-0.675047\pi\) | ||||
−0.522625 | + | 0.852563i | \(0.675047\pi\) | |||||||
\(770\) | −42.0281 | −1.51459 | ||||||||
\(771\) | 8.52979 | 0.307193 | ||||||||
\(772\) | −124.003 | −4.46296 | ||||||||
\(773\) | −21.9410 | −0.789164 | −0.394582 | − | 0.918861i | \(-0.629111\pi\) | ||||
−0.394582 | + | 0.918861i | \(0.629111\pi\) | |||||||
\(774\) | 0.300108 | 0.0107872 | ||||||||
\(775\) | 23.5834 | 0.847142 | ||||||||
\(776\) | −68.2574 | −2.45030 | ||||||||
\(777\) | 19.8579 | 0.712397 | ||||||||
\(778\) | 63.7253 | 2.28466 | ||||||||
\(779\) | −15.7928 | −0.565834 | ||||||||
\(780\) | 158.811 | 5.68635 | ||||||||
\(781\) | 21.3184 | 0.762832 | ||||||||
\(782\) | −75.1717 | −2.68813 | ||||||||
\(783\) | −5.45010 | −0.194771 | ||||||||
\(784\) | −50.9590 | −1.81996 | ||||||||
\(785\) | −3.11314 | −0.111113 | ||||||||
\(786\) | −69.4014 | −2.47547 | ||||||||
\(787\) | −19.3800 | −0.690821 | −0.345411 | − | 0.938452i | \(-0.612260\pi\) | ||||
−0.345411 | + | 0.938452i | \(0.612260\pi\) | |||||||
\(788\) | 64.6719 | 2.30384 | ||||||||
\(789\) | 42.3661 | 1.50827 | ||||||||
\(790\) | −74.4999 | −2.65059 | ||||||||
\(791\) | 22.5211 | 0.800759 | ||||||||
\(792\) | 104.280 | 3.70544 | ||||||||
\(793\) | −12.4739 | −0.442962 | ||||||||
\(794\) | −77.5709 | −2.75289 | ||||||||
\(795\) | −7.46201 | −0.264650 | ||||||||
\(796\) | 74.2878 | 2.63306 | ||||||||
\(797\) | −25.8944 | −0.917228 | −0.458614 | − | 0.888635i | \(-0.651654\pi\) | ||||
−0.458614 | + | 0.888635i | \(0.651654\pi\) | |||||||
\(798\) | 49.4528 | 1.75061 | ||||||||
\(799\) | 54.2213 | 1.91821 | ||||||||
\(800\) | −42.5397 | −1.50401 | ||||||||
\(801\) | 47.8147 | 1.68945 | ||||||||
\(802\) | −74.4062 | −2.62737 | ||||||||
\(803\) | −16.1782 | −0.570916 | ||||||||
\(804\) | 105.340 | 3.71505 | ||||||||
\(805\) | 19.2726 | 0.679269 | ||||||||
\(806\) | 78.3373 | 2.75931 | ||||||||
\(807\) | 10.0846 | 0.354993 | ||||||||
\(808\) | −71.3180 | −2.50896 | ||||||||
\(809\) | −36.2889 | −1.27585 | −0.637926 | − | 0.770098i | \(-0.720207\pi\) | ||||
−0.637926 | + | 0.770098i | \(0.720207\pi\) | |||||||
\(810\) | −51.6444 | −1.81460 | ||||||||
\(811\) | 40.6657 | 1.42796 | 0.713982 | − | 0.700164i | \(-0.246890\pi\) | ||||
0.713982 | + | 0.700164i | \(0.246890\pi\) | |||||||
\(812\) | −25.1384 | −0.882183 | ||||||||
\(813\) | −41.8661 | −1.46831 | ||||||||
\(814\) | 50.6003 | 1.77354 | ||||||||
\(815\) | −4.89782 | −0.171563 | ||||||||
\(816\) | −174.575 | −6.11134 | ||||||||
\(817\) | 0.154071 | 0.00539025 | ||||||||
\(818\) | −73.0733 | −2.55495 | ||||||||
\(819\) | −23.1223 | −0.807959 | ||||||||
\(820\) | −46.2922 | −1.61659 | ||||||||
\(821\) | 24.5384 | 0.856397 | 0.428198 | − | 0.903685i | \(-0.359148\pi\) | ||||
0.428198 | + | 0.903685i | \(0.359148\pi\) | |||||||
\(822\) | −65.1630 | −2.27282 | ||||||||
\(823\) | 22.1881 | 0.773430 | 0.386715 | − | 0.922199i | \(-0.373610\pi\) | ||||
0.386715 | + | 0.922199i | \(0.373610\pi\) | |||||||
\(824\) | 40.1703 | 1.39940 | ||||||||
\(825\) | −32.4342 | −1.12922 | ||||||||
\(826\) | 2.66981 | 0.0928946 | ||||||||
\(827\) | 28.2855 | 0.983584 | 0.491792 | − | 0.870713i | \(-0.336342\pi\) | ||||
0.491792 | + | 0.870713i | \(0.336342\pi\) | |||||||
\(828\) | −80.1877 | −2.78671 | ||||||||
\(829\) | 44.9937 | 1.56270 | 0.781348 | − | 0.624096i | \(-0.214532\pi\) | ||||
0.781348 | + | 0.624096i | \(0.214532\pi\) | |||||||
\(830\) | 35.9369 | 1.24739 | ||||||||
\(831\) | −64.1273 | −2.22455 | ||||||||
\(832\) | −49.9018 | −1.73004 | ||||||||
\(833\) | 30.5432 | 1.05826 | ||||||||
\(834\) | 72.6530 | 2.51577 | ||||||||
\(835\) | 55.0709 | 1.90581 | ||||||||
\(836\) | 89.7739 | 3.10489 | ||||||||
\(837\) | 11.0442 | 0.381743 | ||||||||
\(838\) | 90.5691 | 3.12866 | ||||||||
\(839\) | 44.5379 | 1.53762 | 0.768810 | − | 0.639477i | \(-0.220849\pi\) | ||||
0.768810 | + | 0.639477i | \(0.220849\pi\) | |||||||
\(840\) | 86.4440 | 2.98260 | ||||||||
\(841\) | −17.3539 | −0.598410 | ||||||||
\(842\) | 34.2225 | 1.17939 | ||||||||
\(843\) | −79.5636 | −2.74031 | ||||||||
\(844\) | 13.6195 | 0.468803 | ||||||||
\(845\) | −15.8082 | −0.543819 | ||||||||
\(846\) | 81.1867 | 2.79126 | ||||||||
\(847\) | 3.95845 | 0.136014 | ||||||||
\(848\) | 10.6394 | 0.365359 | ||||||||
\(849\) | −33.5285 | −1.15070 | ||||||||
\(850\) | 57.3506 | 1.96711 | ||||||||
\(851\) | −23.2035 | −0.795405 | ||||||||
\(852\) | −73.5283 | −2.51904 | ||||||||
\(853\) | −5.89725 | −0.201918 | −0.100959 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100959 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(854\) | −11.3858 | −0.389614 | ||||||||
\(855\) | 51.4711 | 1.76027 | ||||||||
\(856\) | 74.3678 | 2.54184 | ||||||||
\(857\) | −21.4682 | −0.733339 | −0.366669 | − | 0.930351i | \(-0.619502\pi\) | ||||
−0.366669 | + | 0.930351i | \(0.619502\pi\) | |||||||
\(858\) | −107.737 | −3.67808 | ||||||||
\(859\) | 7.81771 | 0.266737 | 0.133368 | − | 0.991067i | \(-0.457421\pi\) | ||||
0.133368 | + | 0.991067i | \(0.457421\pi\) | |||||||
\(860\) | 0.451617 | 0.0154000 | ||||||||
\(861\) | 12.3245 | 0.420020 | ||||||||
\(862\) | 22.0047 | 0.749485 | ||||||||
\(863\) | 19.3770 | 0.659600 | 0.329800 | − | 0.944051i | \(-0.393019\pi\) | ||||
0.329800 | + | 0.944051i | \(0.393019\pi\) | |||||||
\(864\) | −19.9215 | −0.677742 | ||||||||
\(865\) | −60.1285 | −2.04443 | ||||||||
\(866\) | −3.39059 | −0.115217 | ||||||||
\(867\) | 60.8926 | 2.06802 | ||||||||
\(868\) | 50.9409 | 1.72905 | ||||||||
\(869\) | 36.0063 | 1.22143 | ||||||||
\(870\) | −67.1559 | −2.27680 | ||||||||
\(871\) | −35.4925 | −1.20262 | ||||||||
\(872\) | 48.9012 | 1.65600 | ||||||||
\(873\) | 31.7170 | 1.07346 | ||||||||
\(874\) | −57.7845 | −1.95459 | ||||||||
\(875\) | 6.85430 | 0.231718 | ||||||||
\(876\) | 55.7995 | 1.88529 | ||||||||
\(877\) | 40.9518 | 1.38285 | 0.691423 | − | 0.722450i | \(-0.256984\pi\) | ||||
0.691423 | + | 0.722450i | \(0.256984\pi\) | |||||||
\(878\) | 20.7580 | 0.700550 | ||||||||
\(879\) | 22.4433 | 0.756993 | ||||||||
\(880\) | 114.048 | 3.84456 | ||||||||
\(881\) | 8.97015 | 0.302212 | 0.151106 | − | 0.988518i | \(-0.451717\pi\) | ||||
0.151106 | + | 0.988518i | \(0.451717\pi\) | |||||||
\(882\) | 45.7331 | 1.53991 | ||||||||
\(883\) | 32.0250 | 1.07773 | 0.538864 | − | 0.842393i | \(-0.318854\pi\) | ||||
0.538864 | + | 0.842393i | \(0.318854\pi\) | |||||||
\(884\) | 135.718 | 4.56469 | ||||||||
\(885\) | 5.08120 | 0.170803 | ||||||||
\(886\) | −18.3194 | −0.615453 | ||||||||
\(887\) | 3.53183 | 0.118587 | 0.0592936 | − | 0.998241i | \(-0.481115\pi\) | ||||
0.0592936 | + | 0.998241i | \(0.481115\pi\) | |||||||
\(888\) | −104.075 | −3.49254 | ||||||||
\(889\) | 15.9018 | 0.533329 | ||||||||
\(890\) | 100.999 | 3.38548 | ||||||||
\(891\) | 24.9601 | 0.836194 | ||||||||
\(892\) | −89.8207 | −3.00742 | ||||||||
\(893\) | 41.6799 | 1.39477 | ||||||||
\(894\) | −6.59006 | −0.220405 | ||||||||
\(895\) | 20.3501 | 0.680230 | ||||||||
\(896\) | −8.45771 | −0.282552 | ||||||||
\(897\) | 49.4043 | 1.64956 | ||||||||
\(898\) | 24.7963 | 0.827462 | ||||||||
\(899\) | −23.5999 | −0.787101 | ||||||||
\(900\) | 61.1775 | 2.03925 | ||||||||
\(901\) | −6.37694 | −0.212447 | ||||||||
\(902\) | 31.4045 | 1.04566 | ||||||||
\(903\) | −0.120236 | −0.00400119 | ||||||||
\(904\) | −118.034 | −3.92574 | ||||||||
\(905\) | −8.82113 | −0.293224 | ||||||||
\(906\) | 6.78562 | 0.225437 | ||||||||
\(907\) | −56.2770 | −1.86865 | −0.934323 | − | 0.356427i | \(-0.883995\pi\) | ||||
−0.934323 | + | 0.356427i | \(0.883995\pi\) | |||||||
\(908\) | 47.4979 | 1.57627 | ||||||||
\(909\) | 33.1391 | 1.09916 | ||||||||
\(910\) | −48.8410 | −1.61906 | ||||||||
\(911\) | 31.0489 | 1.02869 | 0.514347 | − | 0.857582i | \(-0.328034\pi\) | ||||
0.514347 | + | 0.857582i | \(0.328034\pi\) | |||||||
\(912\) | −134.196 | −4.44367 | ||||||||
\(913\) | −17.3685 | −0.574814 | ||||||||
\(914\) | −65.4566 | −2.16511 | ||||||||
\(915\) | −21.6695 | −0.716372 | ||||||||
\(916\) | 105.486 | 3.48535 | ||||||||
\(917\) | 15.2058 | 0.502141 | ||||||||
\(918\) | 26.8574 | 0.886427 | ||||||||
\(919\) | −41.8810 | −1.38153 | −0.690764 | − | 0.723081i | \(-0.742725\pi\) | ||||
−0.690764 | + | 0.723081i | \(0.742725\pi\) | |||||||
\(920\) | −101.008 | −3.33013 | ||||||||
\(921\) | 86.4753 | 2.84946 | ||||||||
\(922\) | −45.2258 | −1.48943 | ||||||||
\(923\) | 24.7742 | 0.815451 | ||||||||
\(924\) | −70.0589 | −2.30477 | ||||||||
\(925\) | 17.7026 | 0.582058 | ||||||||
\(926\) | −25.7784 | −0.847131 | ||||||||
\(927\) | −18.6658 | −0.613065 | ||||||||
\(928\) | 42.5694 | 1.39741 | ||||||||
\(929\) | 8.89587 | 0.291864 | 0.145932 | − | 0.989295i | \(-0.453382\pi\) | ||||
0.145932 | + | 0.989295i | \(0.453382\pi\) | |||||||
\(930\) | 136.086 | 4.46244 | ||||||||
\(931\) | 23.4786 | 0.769480 | ||||||||
\(932\) | 68.5271 | 2.24468 | ||||||||
\(933\) | −64.1852 | −2.10133 | ||||||||
\(934\) | 58.6332 | 1.91854 | ||||||||
\(935\) | −68.3569 | −2.23551 | ||||||||
\(936\) | 121.184 | 3.96104 | ||||||||
\(937\) | 25.1324 | 0.821041 | 0.410520 | − | 0.911851i | \(-0.365347\pi\) | ||||
0.410520 | + | 0.911851i | \(0.365347\pi\) | |||||||
\(938\) | −32.3964 | −1.05778 | ||||||||
\(939\) | 58.0207 | 1.89343 | ||||||||
\(940\) | 122.173 | 3.98486 | ||||||||
\(941\) | −23.2201 | −0.756955 | −0.378478 | − | 0.925610i | \(-0.623552\pi\) | ||||
−0.378478 | + | 0.925610i | \(0.623552\pi\) | |||||||
\(942\) | −7.28423 | −0.237333 | ||||||||
\(943\) | −14.4010 | −0.468960 | ||||||||
\(944\) | −7.24484 | −0.235800 | ||||||||
\(945\) | −6.88573 | −0.223993 | ||||||||
\(946\) | −0.306376 | −0.00996113 | ||||||||
\(947\) | −3.51095 | −0.114091 | −0.0570453 | − | 0.998372i | \(-0.518168\pi\) | ||||
−0.0570453 | + | 0.998372i | \(0.518168\pi\) | |||||||
\(948\) | −124.188 | −4.03343 | ||||||||
\(949\) | −18.8007 | −0.610298 | ||||||||
\(950\) | 44.0854 | 1.43032 | ||||||||
\(951\) | 72.6140 | 2.35467 | ||||||||
\(952\) | 73.8740 | 2.39427 | ||||||||
\(953\) | 18.6789 | 0.605068 | 0.302534 | − | 0.953139i | \(-0.402167\pi\) | ||||
0.302534 | + | 0.953139i | \(0.402167\pi\) | |||||||
\(954\) | −9.54833 | −0.309139 | ||||||||
\(955\) | −15.4190 | −0.498947 | ||||||||
\(956\) | 113.074 | 3.65708 | ||||||||
\(957\) | 32.4569 | 1.04918 | ||||||||
\(958\) | 96.4773 | 3.11704 | ||||||||
\(959\) | 14.2772 | 0.461035 | ||||||||
\(960\) | −86.6886 | −2.79786 | ||||||||
\(961\) | 16.8233 | 0.542688 | ||||||||
\(962\) | 58.8028 | 1.89588 | ||||||||
\(963\) | −34.5563 | −1.11356 | ||||||||
\(964\) | 4.97586 | 0.160262 | ||||||||
\(965\) | 72.5807 | 2.33646 | ||||||||
\(966\) | 45.0946 | 1.45089 | ||||||||
\(967\) | 12.9642 | 0.416901 | 0.208451 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208451 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(968\) | −20.7463 | −0.666812 | ||||||||
\(969\) | 80.4328 | 2.58387 | ||||||||
\(970\) | 66.9954 | 2.15109 | ||||||||
\(971\) | 49.7705 | 1.59721 | 0.798605 | − | 0.601855i | \(-0.205571\pi\) | ||||
0.798605 | + | 0.601855i | \(0.205571\pi\) | |||||||
\(972\) | −109.827 | −3.52270 | ||||||||
\(973\) | −15.9183 | −0.510317 | ||||||||
\(974\) | 55.0009 | 1.76234 | ||||||||
\(975\) | −37.6919 | −1.20711 | ||||||||
\(976\) | 30.8967 | 0.988978 | ||||||||
\(977\) | 29.0302 | 0.928758 | 0.464379 | − | 0.885637i | \(-0.346278\pi\) | ||||
0.464379 | + | 0.885637i | \(0.346278\pi\) | |||||||
\(978\) | −11.4601 | −0.366453 | ||||||||
\(979\) | −48.8132 | −1.56008 | ||||||||
\(980\) | 68.8212 | 2.19841 | ||||||||
\(981\) | −22.7228 | −0.725482 | ||||||||
\(982\) | 18.9504 | 0.604732 | ||||||||
\(983\) | −30.5622 | −0.974782 | −0.487391 | − | 0.873184i | \(-0.662051\pi\) | ||||
−0.487391 | + | 0.873184i | \(0.662051\pi\) | |||||||
\(984\) | −64.5932 | −2.05916 | ||||||||
\(985\) | −37.8534 | −1.20611 | ||||||||
\(986\) | −57.3907 | −1.82769 | ||||||||
\(987\) | −32.5267 | −1.03534 | ||||||||
\(988\) | 104.327 | 3.31907 | ||||||||
\(989\) | 0.140493 | 0.00446741 | ||||||||
\(990\) | −102.352 | −3.25297 | ||||||||
\(991\) | 11.8419 | 0.376169 | 0.188084 | − | 0.982153i | \(-0.439772\pi\) | ||||
0.188084 | + | 0.982153i | \(0.439772\pi\) | |||||||
\(992\) | −86.2635 | −2.73887 | ||||||||
\(993\) | −2.05747 | −0.0652918 | ||||||||
\(994\) | 22.6130 | 0.717242 | ||||||||
\(995\) | −43.4818 | −1.37846 | ||||||||
\(996\) | 59.9050 | 1.89816 | ||||||||
\(997\) | 40.4466 | 1.28096 | 0.640478 | − | 0.767977i | \(-0.278736\pi\) | ||||
0.640478 | + | 0.767977i | \(0.278736\pi\) | |||||||
\(998\) | 86.3102 | 2.73210 | ||||||||
\(999\) | 8.29017 | 0.262289 |
(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 | 8003.2.a.d.1.8 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.d.1.8 | ✓ | 179 | 1.1 | even | 1 | trivial |