Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.80099 | −1.98060 | −0.990299 | − | 0.138955i | \(-0.955626\pi\) | ||||
−0.990299 | + | 0.138955i | \(0.955626\pi\) | |||||||
\(3\) | 1.23587 | 0.713529 | 0.356765 | − | 0.934194i | \(-0.383880\pi\) | ||||
0.356765 | + | 0.934194i | \(0.383880\pi\) | |||||||
\(4\) | 5.84553 | 2.92277 | ||||||||
\(5\) | −1.08657 | −0.485929 | −0.242965 | − | 0.970035i | \(-0.578120\pi\) | ||||
−0.242965 | + | 0.970035i | \(0.578120\pi\) | |||||||
\(6\) | −3.46165 | −1.41321 | ||||||||
\(7\) | −3.96716 | −1.49945 | −0.749723 | − | 0.661752i | \(-0.769813\pi\) | ||||
−0.749723 | + | 0.661752i | \(0.769813\pi\) | |||||||
\(8\) | −10.7713 | −3.80823 | ||||||||
\(9\) | −1.47263 | −0.490876 | ||||||||
\(10\) | 3.04347 | 0.962430 | ||||||||
\(11\) | 3.26035 | 0.983034 | 0.491517 | − | 0.870868i | \(-0.336443\pi\) | ||||
0.491517 | + | 0.870868i | \(0.336443\pi\) | |||||||
\(12\) | 7.22431 | 2.08548 | ||||||||
\(13\) | −3.69125 | −1.02377 | −0.511884 | − | 0.859054i | \(-0.671052\pi\) | ||||
−0.511884 | + | 0.859054i | \(0.671052\pi\) | |||||||
\(14\) | 11.1120 | 2.96980 | ||||||||
\(15\) | −1.34286 | −0.346725 | ||||||||
\(16\) | 18.4792 | 4.61980 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 4.12481 | 0.972227 | ||||||||
\(19\) | −1.13498 | −0.260383 | −0.130191 | − | 0.991489i | \(-0.541559\pi\) | ||||
−0.130191 | + | 0.991489i | \(0.541559\pi\) | |||||||
\(20\) | −6.35159 | −1.42026 | ||||||||
\(21\) | −4.90289 | −1.06990 | ||||||||
\(22\) | −9.13221 | −1.94699 | ||||||||
\(23\) | −8.02983 | −1.67434 | −0.837168 | − | 0.546946i | \(-0.815790\pi\) | ||||
−0.837168 | + | 0.546946i | \(0.815790\pi\) | |||||||
\(24\) | −13.3119 | −2.71728 | ||||||||
\(25\) | −3.81936 | −0.763873 | ||||||||
\(26\) | 10.3391 | 2.02767 | ||||||||
\(27\) | −5.52758 | −1.06378 | ||||||||
\(28\) | −23.1902 | −4.38253 | ||||||||
\(29\) | −1.02942 | −0.191158 | −0.0955792 | − | 0.995422i | \(-0.530470\pi\) | ||||
−0.0955792 | + | 0.995422i | \(0.530470\pi\) | |||||||
\(30\) | 3.76133 | 0.686722 | ||||||||
\(31\) | 0.676568 | 0.121515 | 0.0607576 | − | 0.998153i | \(-0.480648\pi\) | ||||
0.0607576 | + | 0.998153i | \(0.480648\pi\) | |||||||
\(32\) | −30.2174 | −5.34173 | ||||||||
\(33\) | 4.02937 | 0.701424 | ||||||||
\(34\) | 2.80099 | 0.480365 | ||||||||
\(35\) | 4.31060 | 0.728624 | ||||||||
\(36\) | −8.60829 | −1.43471 | ||||||||
\(37\) | 3.19133 | 0.524651 | 0.262326 | − | 0.964979i | \(-0.415511\pi\) | ||||
0.262326 | + | 0.964979i | \(0.415511\pi\) | |||||||
\(38\) | 3.17907 | 0.515713 | ||||||||
\(39\) | −4.56190 | −0.730489 | ||||||||
\(40\) | 11.7038 | 1.85053 | ||||||||
\(41\) | −4.64636 | −0.725640 | −0.362820 | − | 0.931859i | \(-0.618186\pi\) | ||||
−0.362820 | + | 0.931859i | \(0.618186\pi\) | |||||||
\(42\) | 13.7329 | 2.11904 | ||||||||
\(43\) | −11.1217 | −1.69604 | −0.848021 | − | 0.529962i | \(-0.822206\pi\) | ||||
−0.848021 | + | 0.529962i | \(0.822206\pi\) | |||||||
\(44\) | 19.0585 | 2.87318 | ||||||||
\(45\) | 1.60011 | 0.238531 | ||||||||
\(46\) | 22.4915 | 3.31618 | ||||||||
\(47\) | 0.0565963 | 0.00825542 | 0.00412771 | − | 0.999991i | \(-0.498686\pi\) | ||||
0.00412771 | + | 0.999991i | \(0.498686\pi\) | |||||||
\(48\) | 22.8379 | 3.29636 | ||||||||
\(49\) | 8.73835 | 1.24834 | ||||||||
\(50\) | 10.6980 | 1.51292 | ||||||||
\(51\) | −1.23587 | −0.173056 | ||||||||
\(52\) | −21.5773 | −2.99224 | ||||||||
\(53\) | 12.0838 | 1.65984 | 0.829920 | − | 0.557883i | \(-0.188386\pi\) | ||||
0.829920 | + | 0.557883i | \(0.188386\pi\) | |||||||
\(54\) | 15.4827 | 2.10693 | ||||||||
\(55\) | −3.54261 | −0.477685 | ||||||||
\(56\) | 42.7314 | 5.71023 | ||||||||
\(57\) | −1.40269 | −0.185791 | ||||||||
\(58\) | 2.88339 | 0.378608 | ||||||||
\(59\) | 2.86987 | 0.373625 | 0.186813 | − | 0.982396i | \(-0.440184\pi\) | ||||
0.186813 | + | 0.982396i | \(0.440184\pi\) | |||||||
\(60\) | −7.84973 | −1.01340 | ||||||||
\(61\) | −10.0966 | −1.29273 | −0.646366 | − | 0.763027i | \(-0.723712\pi\) | ||||
−0.646366 | + | 0.763027i | \(0.723712\pi\) | |||||||
\(62\) | −1.89506 | −0.240673 | ||||||||
\(63\) | 5.84215 | 0.736041 | ||||||||
\(64\) | 47.6802 | 5.96002 | ||||||||
\(65\) | 4.01081 | 0.497479 | ||||||||
\(66\) | −11.2862 | −1.38924 | ||||||||
\(67\) | 1.27948 | 0.156313 | 0.0781565 | − | 0.996941i | \(-0.475097\pi\) | ||||
0.0781565 | + | 0.996941i | \(0.475097\pi\) | |||||||
\(68\) | −5.84553 | −0.708875 | ||||||||
\(69\) | −9.92382 | −1.19469 | ||||||||
\(70\) | −12.0739 | −1.44311 | ||||||||
\(71\) | 2.44454 | 0.290113 | 0.145056 | − | 0.989423i | \(-0.453664\pi\) | ||||
0.145056 | + | 0.989423i | \(0.453664\pi\) | |||||||
\(72\) | 15.8621 | 1.86937 | ||||||||
\(73\) | −8.13747 | −0.952419 | −0.476210 | − | 0.879332i | \(-0.657990\pi\) | ||||
−0.476210 | + | 0.879332i | \(0.657990\pi\) | |||||||
\(74\) | −8.93887 | −1.03912 | ||||||||
\(75\) | −4.72023 | −0.545046 | ||||||||
\(76\) | −6.63458 | −0.761038 | ||||||||
\(77\) | −12.9343 | −1.47401 | ||||||||
\(78\) | 12.7778 | 1.44681 | ||||||||
\(79\) | −2.57775 | −0.290019 | −0.145010 | − | 0.989430i | \(-0.546321\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546321\pi\) | |||||||
\(80\) | −20.0790 | −2.24489 | ||||||||
\(81\) | −2.41349 | −0.268165 | ||||||||
\(82\) | 13.0144 | 1.43720 | ||||||||
\(83\) | −5.32068 | −0.584021 | −0.292010 | − | 0.956415i | \(-0.594324\pi\) | ||||
−0.292010 | + | 0.956415i | \(0.594324\pi\) | |||||||
\(84\) | −28.6600 | −3.12706 | ||||||||
\(85\) | 1.08657 | 0.117855 | ||||||||
\(86\) | 31.1517 | 3.35918 | ||||||||
\(87\) | −1.27223 | −0.136397 | ||||||||
\(88\) | −35.1182 | −3.74362 | ||||||||
\(89\) | −10.2723 | −1.08886 | −0.544431 | − | 0.838806i | \(-0.683254\pi\) | ||||
−0.544431 | + | 0.838806i | \(0.683254\pi\) | |||||||
\(90\) | −4.48190 | −0.472434 | ||||||||
\(91\) | 14.6438 | 1.53509 | ||||||||
\(92\) | −46.9386 | −4.89369 | ||||||||
\(93\) | 0.836149 | 0.0867046 | ||||||||
\(94\) | −0.158526 | −0.0163507 | ||||||||
\(95\) | 1.23324 | 0.126528 | ||||||||
\(96\) | −37.3448 | −3.81148 | ||||||||
\(97\) | −6.69182 | −0.679451 | −0.339726 | − | 0.940525i | \(-0.610334\pi\) | ||||
−0.339726 | + | 0.940525i | \(0.610334\pi\) | |||||||
\(98\) | −24.4760 | −2.47245 | ||||||||
\(99\) | −4.80129 | −0.482547 | ||||||||
\(100\) | −22.3262 | −2.23262 | ||||||||
\(101\) | 12.0871 | 1.20271 | 0.601355 | − | 0.798982i | \(-0.294628\pi\) | ||||
0.601355 | + | 0.798982i | \(0.294628\pi\) | |||||||
\(102\) | 3.46165 | 0.342755 | ||||||||
\(103\) | 1.95644 | 0.192774 | 0.0963870 | − | 0.995344i | \(-0.469271\pi\) | ||||
0.0963870 | + | 0.995344i | \(0.469271\pi\) | |||||||
\(104\) | 39.7595 | 3.89874 | ||||||||
\(105\) | 5.32734 | 0.519895 | ||||||||
\(106\) | −33.8466 | −3.28747 | ||||||||
\(107\) | −8.84782 | −0.855351 | −0.427675 | − | 0.903932i | \(-0.640667\pi\) | ||||
−0.427675 | + | 0.903932i | \(0.640667\pi\) | |||||||
\(108\) | −32.3117 | −3.10919 | ||||||||
\(109\) | 6.62183 | 0.634256 | 0.317128 | − | 0.948383i | \(-0.397281\pi\) | ||||
0.317128 | + | 0.948383i | \(0.397281\pi\) | |||||||
\(110\) | 9.92280 | 0.946102 | ||||||||
\(111\) | 3.94406 | 0.374354 | ||||||||
\(112\) | −73.3099 | −6.92713 | ||||||||
\(113\) | 0.102681 | 0.00965940 | 0.00482970 | − | 0.999988i | \(-0.498463\pi\) | ||||
0.00482970 | + | 0.999988i | \(0.498463\pi\) | |||||||
\(114\) | 3.92892 | 0.367977 | ||||||||
\(115\) | 8.72498 | 0.813609 | ||||||||
\(116\) | −6.01750 | −0.558711 | ||||||||
\(117\) | 5.43584 | 0.502543 | ||||||||
\(118\) | −8.03847 | −0.740001 | ||||||||
\(119\) | 3.96716 | 0.363669 | ||||||||
\(120\) | 14.4643 | 1.32041 | ||||||||
\(121\) | −0.370087 | −0.0336443 | ||||||||
\(122\) | 28.2804 | 2.56038 | ||||||||
\(123\) | −5.74230 | −0.517766 | ||||||||
\(124\) | 3.95490 | 0.355160 | ||||||||
\(125\) | 9.58286 | 0.857117 | ||||||||
\(126\) | −16.3638 | −1.45780 | ||||||||
\(127\) | 1.11840 | 0.0992415 | 0.0496208 | − | 0.998768i | \(-0.484199\pi\) | ||||
0.0496208 | + | 0.998768i | \(0.484199\pi\) | |||||||
\(128\) | −73.1169 | −6.46268 | ||||||||
\(129\) | −13.7450 | −1.21018 | ||||||||
\(130\) | −11.2342 | −0.985306 | ||||||||
\(131\) | 19.0842 | 1.66739 | 0.833696 | − | 0.552223i | \(-0.186220\pi\) | ||||
0.833696 | + | 0.552223i | \(0.186220\pi\) | |||||||
\(132\) | 23.5538 | 2.05010 | ||||||||
\(133\) | 4.50266 | 0.390430 | ||||||||
\(134\) | −3.58380 | −0.309593 | ||||||||
\(135\) | 6.00611 | 0.516924 | ||||||||
\(136\) | 10.7713 | 0.923631 | ||||||||
\(137\) | 5.17144 | 0.441826 | 0.220913 | − | 0.975294i | \(-0.429096\pi\) | ||||
0.220913 | + | 0.975294i | \(0.429096\pi\) | |||||||
\(138\) | 27.7965 | 2.36620 | ||||||||
\(139\) | −3.93434 | −0.333706 | −0.166853 | − | 0.985982i | \(-0.553361\pi\) | ||||
−0.166853 | + | 0.985982i | \(0.553361\pi\) | |||||||
\(140\) | 25.1978 | 2.12960 | ||||||||
\(141\) | 0.0699457 | 0.00589049 | ||||||||
\(142\) | −6.84711 | −0.574597 | ||||||||
\(143\) | −12.0348 | −1.00640 | ||||||||
\(144\) | −27.2130 | −2.26775 | ||||||||
\(145\) | 1.11854 | 0.0928894 | ||||||||
\(146\) | 22.7930 | 1.88636 | ||||||||
\(147\) | 10.7995 | 0.890725 | ||||||||
\(148\) | 18.6550 | 1.53343 | ||||||||
\(149\) | −19.0412 | −1.55992 | −0.779958 | − | 0.625832i | \(-0.784760\pi\) | ||||
−0.779958 | + | 0.625832i | \(0.784760\pi\) | |||||||
\(150\) | 13.2213 | 1.07952 | ||||||||
\(151\) | 3.93886 | 0.320540 | 0.160270 | − | 0.987073i | \(-0.448764\pi\) | ||||
0.160270 | + | 0.987073i | \(0.448764\pi\) | |||||||
\(152\) | 12.2252 | 0.991597 | ||||||||
\(153\) | 1.47263 | 0.119055 | ||||||||
\(154\) | 36.2289 | 2.91941 | ||||||||
\(155\) | −0.735139 | −0.0590478 | ||||||||
\(156\) | −26.6668 | −2.13505 | ||||||||
\(157\) | −14.6388 | −1.16831 | −0.584153 | − | 0.811644i | \(-0.698573\pi\) | ||||
−0.584153 | + | 0.811644i | \(0.698573\pi\) | |||||||
\(158\) | 7.22024 | 0.574411 | ||||||||
\(159\) | 14.9340 | 1.18434 | ||||||||
\(160\) | 32.8334 | 2.59570 | ||||||||
\(161\) | 31.8556 | 2.51057 | ||||||||
\(162\) | 6.76015 | 0.531128 | ||||||||
\(163\) | 22.5537 | 1.76654 | 0.883270 | − | 0.468865i | \(-0.155337\pi\) | ||||
0.883270 | + | 0.468865i | \(0.155337\pi\) | |||||||
\(164\) | −27.1605 | −2.12088 | ||||||||
\(165\) | −4.37820 | −0.340842 | ||||||||
\(166\) | 14.9032 | 1.15671 | ||||||||
\(167\) | 10.4710 | 0.810274 | 0.405137 | − | 0.914256i | \(-0.367224\pi\) | ||||
0.405137 | + | 0.914256i | \(0.367224\pi\) | |||||||
\(168\) | 52.8105 | 4.07442 | ||||||||
\(169\) | 0.625336 | 0.0481028 | ||||||||
\(170\) | −3.04347 | −0.233424 | ||||||||
\(171\) | 1.67141 | 0.127816 | ||||||||
\(172\) | −65.0122 | −4.95714 | ||||||||
\(173\) | 6.35909 | 0.483473 | 0.241736 | − | 0.970342i | \(-0.422283\pi\) | ||||
0.241736 | + | 0.970342i | \(0.422283\pi\) | |||||||
\(174\) | 3.56349 | 0.270148 | ||||||||
\(175\) | 15.1520 | 1.14539 | ||||||||
\(176\) | 60.2487 | 4.54142 | ||||||||
\(177\) | 3.54678 | 0.266593 | ||||||||
\(178\) | 28.7726 | 2.15660 | ||||||||
\(179\) | −13.1115 | −0.979998 | −0.489999 | − | 0.871723i | \(-0.663003\pi\) | ||||
−0.489999 | + | 0.871723i | \(0.663003\pi\) | |||||||
\(180\) | 9.35352 | 0.697170 | ||||||||
\(181\) | −17.6619 | −1.31280 | −0.656401 | − | 0.754412i | \(-0.727922\pi\) | ||||
−0.656401 | + | 0.754412i | \(0.727922\pi\) | |||||||
\(182\) | −41.0171 | −3.04039 | ||||||||
\(183\) | −12.4780 | −0.922403 | ||||||||
\(184\) | 86.4916 | 6.37625 | ||||||||
\(185\) | −3.46760 | −0.254943 | ||||||||
\(186\) | −2.34204 | −0.171727 | ||||||||
\(187\) | −3.26035 | −0.238421 | ||||||||
\(188\) | 0.330836 | 0.0241287 | ||||||||
\(189\) | 21.9288 | 1.59509 | ||||||||
\(190\) | −3.45429 | −0.250600 | ||||||||
\(191\) | 0.956853 | 0.0692355 | 0.0346177 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346177 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(192\) | 58.9265 | 4.25265 | ||||||||
\(193\) | −17.7873 | −1.28036 | −0.640179 | − | 0.768225i | \(-0.721140\pi\) | ||||
−0.640179 | + | 0.768225i | \(0.721140\pi\) | |||||||
\(194\) | 18.7437 | 1.34572 | ||||||||
\(195\) | 4.95683 | 0.354966 | ||||||||
\(196\) | 51.0803 | 3.64859 | ||||||||
\(197\) | 23.0438 | 1.64180 | 0.820902 | − | 0.571070i | \(-0.193471\pi\) | ||||
0.820902 | + | 0.571070i | \(0.193471\pi\) | |||||||
\(198\) | 13.4483 | 0.955732 | ||||||||
\(199\) | −18.8993 | −1.33974 | −0.669868 | − | 0.742480i | \(-0.733649\pi\) | ||||
−0.669868 | + | 0.742480i | \(0.733649\pi\) | |||||||
\(200\) | 41.1395 | 2.90900 | ||||||||
\(201\) | 1.58127 | 0.111534 | ||||||||
\(202\) | −33.8558 | −2.38208 | ||||||||
\(203\) | 4.08387 | 0.286631 | ||||||||
\(204\) | −7.22431 | −0.505803 | ||||||||
\(205\) | 5.04860 | 0.352610 | ||||||||
\(206\) | −5.47997 | −0.381808 | ||||||||
\(207\) | 11.8249 | 0.821890 | ||||||||
\(208\) | −68.2113 | −4.72960 | ||||||||
\(209\) | −3.70044 | −0.255965 | ||||||||
\(210\) | −14.9218 | −1.02970 | ||||||||
\(211\) | 4.97360 | 0.342397 | 0.171198 | − | 0.985237i | \(-0.445236\pi\) | ||||
0.171198 | + | 0.985237i | \(0.445236\pi\) | |||||||
\(212\) | 70.6363 | 4.85132 | ||||||||
\(213\) | 3.02113 | 0.207004 | ||||||||
\(214\) | 24.7826 | 1.69411 | ||||||||
\(215\) | 12.0845 | 0.824157 | ||||||||
\(216\) | 59.5392 | 4.05113 | ||||||||
\(217\) | −2.68405 | −0.182205 | ||||||||
\(218\) | −18.5477 | −1.25621 | ||||||||
\(219\) | −10.0569 | −0.679579 | ||||||||
\(220\) | −20.7084 | −1.39616 | ||||||||
\(221\) | 3.69125 | 0.248300 | ||||||||
\(222\) | −11.0473 | −0.741445 | ||||||||
\(223\) | −8.41244 | −0.563339 | −0.281669 | − | 0.959512i | \(-0.590888\pi\) | ||||
−0.281669 | + | 0.959512i | \(0.590888\pi\) | |||||||
\(224\) | 119.877 | 8.00964 | ||||||||
\(225\) | 5.62450 | 0.374967 | ||||||||
\(226\) | −0.287608 | −0.0191314 | ||||||||
\(227\) | −9.93965 | −0.659718 | −0.329859 | − | 0.944030i | \(-0.607001\pi\) | ||||
−0.329859 | + | 0.944030i | \(0.607001\pi\) | |||||||
\(228\) | −8.19947 | −0.543023 | ||||||||
\(229\) | −1.22137 | −0.0807102 | −0.0403551 | − | 0.999185i | \(-0.512849\pi\) | ||||
−0.0403551 | + | 0.999185i | \(0.512849\pi\) | |||||||
\(230\) | −24.4386 | −1.61143 | ||||||||
\(231\) | −15.9852 | −1.05175 | ||||||||
\(232\) | 11.0882 | 0.727974 | ||||||||
\(233\) | 20.2392 | 1.32591 | 0.662956 | − | 0.748658i | \(-0.269302\pi\) | ||||
0.662956 | + | 0.748658i | \(0.269302\pi\) | |||||||
\(234\) | −15.2257 | −0.995336 | ||||||||
\(235\) | −0.0614959 | −0.00401155 | ||||||||
\(236\) | 16.7759 | 1.09202 | ||||||||
\(237\) | −3.18576 | −0.206937 | ||||||||
\(238\) | −11.1120 | −0.720282 | ||||||||
\(239\) | 22.2542 | 1.43951 | 0.719753 | − | 0.694230i | \(-0.244255\pi\) | ||||
0.719753 | + | 0.694230i | \(0.244255\pi\) | |||||||
\(240\) | −24.8150 | −1.60180 | ||||||||
\(241\) | −0.938322 | −0.0604427 | −0.0302213 | − | 0.999543i | \(-0.509621\pi\) | ||||
−0.0302213 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(242\) | 1.03661 | 0.0666358 | ||||||||
\(243\) | 13.6000 | 0.872440 | ||||||||
\(244\) | −59.0198 | −3.77836 | ||||||||
\(245\) | −9.49484 | −0.606603 | ||||||||
\(246\) | 16.0841 | 1.02549 | ||||||||
\(247\) | 4.18950 | 0.266572 | ||||||||
\(248\) | −7.28751 | −0.462757 | ||||||||
\(249\) | −6.57567 | −0.416716 | ||||||||
\(250\) | −26.8415 | −1.69760 | ||||||||
\(251\) | 8.51475 | 0.537446 | 0.268723 | − | 0.963217i | \(-0.413398\pi\) | ||||
0.268723 | + | 0.963217i | \(0.413398\pi\) | |||||||
\(252\) | 34.1505 | 2.15128 | ||||||||
\(253\) | −26.1801 | −1.64593 | ||||||||
\(254\) | −3.13261 | −0.196558 | ||||||||
\(255\) | 1.34286 | 0.0840931 | ||||||||
\(256\) | 109.439 | 6.83994 | ||||||||
\(257\) | 16.5579 | 1.03286 | 0.516428 | − | 0.856331i | \(-0.327261\pi\) | ||||
0.516428 | + | 0.856331i | \(0.327261\pi\) | |||||||
\(258\) | 38.4995 | 2.39687 | ||||||||
\(259\) | −12.6605 | −0.786686 | ||||||||
\(260\) | 23.4453 | 1.45402 | ||||||||
\(261\) | 1.51595 | 0.0938350 | ||||||||
\(262\) | −53.4546 | −3.30243 | ||||||||
\(263\) | 7.99093 | 0.492742 | 0.246371 | − | 0.969176i | \(-0.420762\pi\) | ||||
0.246371 | + | 0.969176i | \(0.420762\pi\) | |||||||
\(264\) | −43.4015 | −2.67118 | ||||||||
\(265\) | −13.1299 | −0.806565 | ||||||||
\(266\) | −12.6119 | −0.773284 | ||||||||
\(267\) | −12.6952 | −0.776935 | ||||||||
\(268\) | 7.47922 | 0.456866 | ||||||||
\(269\) | 29.6434 | 1.80739 | 0.903695 | − | 0.428176i | \(-0.140844\pi\) | ||||
0.903695 | + | 0.428176i | \(0.140844\pi\) | |||||||
\(270\) | −16.8230 | −1.02382 | ||||||||
\(271\) | 9.51765 | 0.578156 | 0.289078 | − | 0.957306i | \(-0.406651\pi\) | ||||
0.289078 | + | 0.957306i | \(0.406651\pi\) | |||||||
\(272\) | −18.4792 | −1.12047 | ||||||||
\(273\) | 18.0978 | 1.09533 | ||||||||
\(274\) | −14.4851 | −0.875079 | ||||||||
\(275\) | −12.4525 | −0.750913 | ||||||||
\(276\) | −58.0100 | −3.49179 | ||||||||
\(277\) | −5.15541 | −0.309759 | −0.154879 | − | 0.987933i | \(-0.549499\pi\) | ||||
−0.154879 | + | 0.987933i | \(0.549499\pi\) | |||||||
\(278\) | 11.0200 | 0.660938 | ||||||||
\(279\) | −0.996332 | −0.0596488 | ||||||||
\(280\) | −46.4307 | −2.77477 | ||||||||
\(281\) | −30.7358 | −1.83355 | −0.916773 | − | 0.399408i | \(-0.869216\pi\) | ||||
−0.916773 | + | 0.399408i | \(0.869216\pi\) | |||||||
\(282\) | −0.195917 | −0.0116667 | ||||||||
\(283\) | −23.3022 | −1.38517 | −0.692585 | − | 0.721336i | \(-0.743528\pi\) | ||||
−0.692585 | + | 0.721336i | \(0.743528\pi\) | |||||||
\(284\) | 14.2896 | 0.847932 | ||||||||
\(285\) | 1.52412 | 0.0902812 | ||||||||
\(286\) | 33.7093 | 1.99327 | ||||||||
\(287\) | 18.4329 | 1.08806 | ||||||||
\(288\) | 44.4990 | 2.62213 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −3.13301 | −0.183977 | ||||||||
\(291\) | −8.27021 | −0.484808 | ||||||||
\(292\) | −47.5679 | −2.78370 | ||||||||
\(293\) | −11.4146 | −0.666850 | −0.333425 | − | 0.942777i | \(-0.608204\pi\) | ||||
−0.333425 | + | 0.942777i | \(0.608204\pi\) | |||||||
\(294\) | −30.2492 | −1.76417 | ||||||||
\(295\) | −3.11832 | −0.181555 | ||||||||
\(296\) | −34.3747 | −1.99799 | ||||||||
\(297\) | −18.0219 | −1.04574 | ||||||||
\(298\) | 53.3342 | 3.08957 | ||||||||
\(299\) | 29.6401 | 1.71413 | ||||||||
\(300\) | −27.5923 | −1.59304 | ||||||||
\(301\) | 44.1215 | 2.54312 | ||||||||
\(302\) | −11.0327 | −0.634860 | ||||||||
\(303\) | 14.9381 | 0.858169 | ||||||||
\(304\) | −20.9736 | −1.20292 | ||||||||
\(305\) | 10.9706 | 0.628177 | ||||||||
\(306\) | −4.12481 | −0.235800 | ||||||||
\(307\) | 21.7898 | 1.24361 | 0.621805 | − | 0.783172i | \(-0.286400\pi\) | ||||
0.621805 | + | 0.783172i | \(0.286400\pi\) | |||||||
\(308\) | −75.6081 | −4.30817 | ||||||||
\(309\) | 2.41791 | 0.137550 | ||||||||
\(310\) | 2.05911 | 0.116950 | ||||||||
\(311\) | −25.2616 | −1.43245 | −0.716226 | − | 0.697868i | \(-0.754132\pi\) | ||||
−0.716226 | + | 0.697868i | \(0.754132\pi\) | |||||||
\(312\) | 49.1376 | 2.78187 | ||||||||
\(313\) | −5.65005 | −0.319360 | −0.159680 | − | 0.987169i | \(-0.551046\pi\) | ||||
−0.159680 | + | 0.987169i | \(0.551046\pi\) | |||||||
\(314\) | 41.0032 | 2.31394 | ||||||||
\(315\) | −6.34791 | −0.357664 | ||||||||
\(316\) | −15.0683 | −0.847658 | ||||||||
\(317\) | 15.4510 | 0.867814 | 0.433907 | − | 0.900958i | \(-0.357135\pi\) | ||||
0.433907 | + | 0.900958i | \(0.357135\pi\) | |||||||
\(318\) | −41.8300 | −2.34571 | ||||||||
\(319\) | −3.35627 | −0.187915 | ||||||||
\(320\) | −51.8079 | −2.89615 | ||||||||
\(321\) | −10.9347 | −0.610318 | ||||||||
\(322\) | −89.2272 | −4.97244 | ||||||||
\(323\) | 1.13498 | 0.0631521 | ||||||||
\(324\) | −14.1081 | −0.783785 | ||||||||
\(325\) | 14.0982 | 0.782029 | ||||||||
\(326\) | −63.1726 | −3.49880 | ||||||||
\(327\) | 8.18372 | 0.452561 | ||||||||
\(328\) | 50.0473 | 2.76340 | ||||||||
\(329\) | −0.224527 | −0.0123786 | ||||||||
\(330\) | 12.2633 | 0.675071 | ||||||||
\(331\) | 22.3967 | 1.23103 | 0.615517 | − | 0.788124i | \(-0.288947\pi\) | ||||
0.615517 | + | 0.788124i | \(0.288947\pi\) | |||||||
\(332\) | −31.1022 | −1.70696 | ||||||||
\(333\) | −4.69964 | −0.257538 | ||||||||
\(334\) | −29.3293 | −1.60483 | ||||||||
\(335\) | −1.39024 | −0.0759570 | ||||||||
\(336\) | −90.6014 | −4.94271 | ||||||||
\(337\) | −5.27920 | −0.287576 | −0.143788 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143788 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(338\) | −1.75156 | −0.0952722 | ||||||||
\(339\) | 0.126900 | 0.00689227 | ||||||||
\(340\) | 6.35159 | 0.344463 | ||||||||
\(341\) | 2.20585 | 0.119453 | ||||||||
\(342\) | −4.68159 | −0.253151 | ||||||||
\(343\) | −6.89632 | −0.372366 | ||||||||
\(344\) | 119.795 | 6.45891 | ||||||||
\(345\) | 10.7829 | 0.580534 | ||||||||
\(346\) | −17.8117 | −0.957565 | ||||||||
\(347\) | −11.8084 | −0.633910 | −0.316955 | − | 0.948441i | \(-0.602660\pi\) | ||||
−0.316955 | + | 0.948441i | \(0.602660\pi\) | |||||||
\(348\) | −7.43685 | −0.398657 | ||||||||
\(349\) | 28.7365 | 1.53823 | 0.769116 | − | 0.639110i | \(-0.220697\pi\) | ||||
0.769116 | + | 0.639110i | \(0.220697\pi\) | |||||||
\(350\) | −42.4406 | −2.26855 | ||||||||
\(351\) | 20.4037 | 1.08907 | ||||||||
\(352\) | −98.5195 | −5.25110 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −9.93450 | −0.528013 | ||||||||
\(355\) | −2.65616 | −0.140974 | ||||||||
\(356\) | −60.0471 | −3.18249 | ||||||||
\(357\) | 4.90289 | 0.259488 | ||||||||
\(358\) | 36.7251 | 1.94098 | ||||||||
\(359\) | −21.0653 | −1.11178 | −0.555891 | − | 0.831255i | \(-0.687623\pi\) | ||||
−0.555891 | + | 0.831255i | \(0.687623\pi\) | |||||||
\(360\) | −17.2353 | −0.908380 | ||||||||
\(361\) | −17.7118 | −0.932201 | ||||||||
\(362\) | 49.4709 | 2.60013 | ||||||||
\(363\) | −0.457379 | −0.0240062 | ||||||||
\(364\) | 85.6007 | 4.48670 | ||||||||
\(365\) | 8.84194 | 0.462808 | ||||||||
\(366\) | 34.9508 | 1.82691 | ||||||||
\(367\) | 1.78964 | 0.0934183 | 0.0467091 | − | 0.998909i | \(-0.485127\pi\) | ||||
0.0467091 | + | 0.998909i | \(0.485127\pi\) | |||||||
\(368\) | −148.385 | −7.73509 | ||||||||
\(369\) | 6.84236 | 0.356199 | ||||||||
\(370\) | 9.71272 | 0.504940 | ||||||||
\(371\) | −47.9384 | −2.48884 | ||||||||
\(372\) | 4.88774 | 0.253417 | ||||||||
\(373\) | −20.2554 | −1.04878 | −0.524391 | − | 0.851477i | \(-0.675707\pi\) | ||||
−0.524391 | + | 0.851477i | \(0.675707\pi\) | |||||||
\(374\) | 9.13221 | 0.472216 | ||||||||
\(375\) | 11.8432 | 0.611579 | ||||||||
\(376\) | −0.609616 | −0.0314385 | ||||||||
\(377\) | 3.79984 | 0.195702 | ||||||||
\(378\) | −61.4223 | −3.15922 | ||||||||
\(379\) | −19.1858 | −0.985508 | −0.492754 | − | 0.870169i | \(-0.664010\pi\) | ||||
−0.492754 | + | 0.870169i | \(0.664010\pi\) | |||||||
\(380\) | 7.20894 | 0.369811 | ||||||||
\(381\) | 1.38219 | 0.0708118 | ||||||||
\(382\) | −2.68013 | −0.137128 | ||||||||
\(383\) | 31.8381 | 1.62685 | 0.813426 | − | 0.581668i | \(-0.197600\pi\) | ||||
0.813426 | + | 0.581668i | \(0.197600\pi\) | |||||||
\(384\) | −90.3629 | −4.61131 | ||||||||
\(385\) | 14.0541 | 0.716263 | ||||||||
\(386\) | 49.8221 | 2.53588 | ||||||||
\(387\) | 16.3781 | 0.832546 | ||||||||
\(388\) | −39.1172 | −1.98588 | ||||||||
\(389\) | 0.0769479 | 0.00390141 | 0.00195071 | − | 0.999998i | \(-0.499379\pi\) | ||||
0.00195071 | + | 0.999998i | \(0.499379\pi\) | |||||||
\(390\) | −13.8840 | −0.703045 | ||||||||
\(391\) | 8.02983 | 0.406086 | ||||||||
\(392\) | −94.1233 | −4.75395 | ||||||||
\(393\) | 23.5856 | 1.18973 | ||||||||
\(394\) | −64.5454 | −3.25175 | ||||||||
\(395\) | 2.80090 | 0.140929 | ||||||||
\(396\) | −28.0661 | −1.41037 | ||||||||
\(397\) | 21.3845 | 1.07326 | 0.536628 | − | 0.843819i | \(-0.319698\pi\) | ||||
0.536628 | + | 0.843819i | \(0.319698\pi\) | |||||||
\(398\) | 52.9367 | 2.65348 | ||||||||
\(399\) | 5.56469 | 0.278583 | ||||||||
\(400\) | −70.5787 | −3.52894 | ||||||||
\(401\) | −23.0251 | −1.14982 | −0.574909 | − | 0.818217i | \(-0.694963\pi\) | ||||
−0.574909 | + | 0.818217i | \(0.694963\pi\) | |||||||
\(402\) | −4.42911 | −0.220904 | ||||||||
\(403\) | −2.49738 | −0.124403 | ||||||||
\(404\) | 70.6554 | 3.51524 | ||||||||
\(405\) | 2.62243 | 0.130309 | ||||||||
\(406\) | −11.4389 | −0.567701 | ||||||||
\(407\) | 10.4049 | 0.515750 | ||||||||
\(408\) | 13.3119 | 0.659038 | ||||||||
\(409\) | 22.5260 | 1.11384 | 0.556918 | − | 0.830567i | \(-0.311984\pi\) | ||||
0.556918 | + | 0.830567i | \(0.311984\pi\) | |||||||
\(410\) | −14.1411 | −0.698378 | ||||||||
\(411\) | 6.39122 | 0.315256 | ||||||||
\(412\) | 11.4364 | 0.563433 | ||||||||
\(413\) | −11.3852 | −0.560231 | ||||||||
\(414\) | −33.1215 | −1.62783 | ||||||||
\(415\) | 5.78130 | 0.283793 | ||||||||
\(416\) | 111.540 | 5.46870 | ||||||||
\(417\) | −4.86233 | −0.238109 | ||||||||
\(418\) | 10.3649 | 0.506964 | ||||||||
\(419\) | 35.7560 | 1.74679 | 0.873397 | − | 0.487008i | \(-0.161912\pi\) | ||||
0.873397 | + | 0.487008i | \(0.161912\pi\) | |||||||
\(420\) | 31.1411 | 1.51953 | ||||||||
\(421\) | 1.86920 | 0.0910992 | 0.0455496 | − | 0.998962i | \(-0.485496\pi\) | ||||
0.0455496 | + | 0.998962i | \(0.485496\pi\) | |||||||
\(422\) | −13.9310 | −0.678150 | ||||||||
\(423\) | −0.0833453 | −0.00405239 | ||||||||
\(424\) | −130.158 | −6.32104 | ||||||||
\(425\) | 3.81936 | 0.185266 | ||||||||
\(426\) | −8.46214 | −0.409992 | ||||||||
\(427\) | 40.0547 | 1.93838 | ||||||||
\(428\) | −51.7202 | −2.49999 | ||||||||
\(429\) | −14.8734 | −0.718096 | ||||||||
\(430\) | −33.8486 | −1.63232 | ||||||||
\(431\) | −18.9943 | −0.914923 | −0.457461 | − | 0.889230i | \(-0.651241\pi\) | ||||
−0.457461 | + | 0.889230i | \(0.651241\pi\) | |||||||
\(432\) | −102.145 | −4.91447 | ||||||||
\(433\) | 14.0952 | 0.677372 | 0.338686 | − | 0.940900i | \(-0.390018\pi\) | ||||
0.338686 | + | 0.940900i | \(0.390018\pi\) | |||||||
\(434\) | 7.51800 | 0.360875 | ||||||||
\(435\) | 1.38237 | 0.0662793 | ||||||||
\(436\) | 38.7081 | 1.85378 | ||||||||
\(437\) | 9.11371 | 0.435968 | ||||||||
\(438\) | 28.1691 | 1.34597 | ||||||||
\(439\) | −32.8500 | −1.56784 | −0.783922 | − | 0.620859i | \(-0.786784\pi\) | ||||
−0.783922 | + | 0.620859i | \(0.786784\pi\) | |||||||
\(440\) | 38.1584 | 1.81913 | ||||||||
\(441\) | −12.8683 | −0.612778 | ||||||||
\(442\) | −10.3391 | −0.491783 | ||||||||
\(443\) | −27.0752 | −1.28638 | −0.643190 | − | 0.765707i | \(-0.722389\pi\) | ||||
−0.643190 | + | 0.765707i | \(0.722389\pi\) | |||||||
\(444\) | 23.0552 | 1.09415 | ||||||||
\(445\) | 11.1616 | 0.529110 | ||||||||
\(446\) | 23.5631 | 1.11575 | ||||||||
\(447\) | −23.5324 | −1.11305 | ||||||||
\(448\) | −189.155 | −8.93673 | ||||||||
\(449\) | 29.8543 | 1.40891 | 0.704456 | − | 0.709748i | \(-0.251191\pi\) | ||||
0.704456 | + | 0.709748i | \(0.251191\pi\) | |||||||
\(450\) | −15.7542 | −0.742658 | ||||||||
\(451\) | −15.1488 | −0.713329 | ||||||||
\(452\) | 0.600224 | 0.0282322 | ||||||||
\(453\) | 4.86791 | 0.228714 | ||||||||
\(454\) | 27.8408 | 1.30664 | ||||||||
\(455\) | −15.9115 | −0.745943 | ||||||||
\(456\) | 15.1088 | 0.707533 | ||||||||
\(457\) | 37.9777 | 1.77652 | 0.888262 | − | 0.459338i | \(-0.151913\pi\) | ||||
0.888262 | + | 0.459338i | \(0.151913\pi\) | |||||||
\(458\) | 3.42103 | 0.159854 | ||||||||
\(459\) | 5.52758 | 0.258005 | ||||||||
\(460\) | 51.0022 | 2.37799 | ||||||||
\(461\) | 34.3481 | 1.59975 | 0.799874 | − | 0.600167i | \(-0.204899\pi\) | ||||
0.799874 | + | 0.600167i | \(0.204899\pi\) | |||||||
\(462\) | 44.7742 | 2.08309 | ||||||||
\(463\) | −2.70740 | −0.125824 | −0.0629119 | − | 0.998019i | \(-0.520039\pi\) | ||||
−0.0629119 | + | 0.998019i | \(0.520039\pi\) | |||||||
\(464\) | −19.0228 | −0.883113 | ||||||||
\(465\) | −0.908535 | −0.0421323 | ||||||||
\(466\) | −56.6897 | −2.62610 | ||||||||
\(467\) | −20.2778 | −0.938344 | −0.469172 | − | 0.883107i | \(-0.655447\pi\) | ||||
−0.469172 | + | 0.883107i | \(0.655447\pi\) | |||||||
\(468\) | 31.7754 | 1.46882 | ||||||||
\(469\) | −5.07589 | −0.234383 | ||||||||
\(470\) | 0.172249 | 0.00794527 | ||||||||
\(471\) | −18.0917 | −0.833620 | ||||||||
\(472\) | −30.9122 | −1.42285 | ||||||||
\(473\) | −36.2607 | −1.66727 | ||||||||
\(474\) | 8.92327 | 0.409859 | ||||||||
\(475\) | 4.33491 | 0.198899 | ||||||||
\(476\) | 23.1902 | 1.06292 | ||||||||
\(477\) | −17.7949 | −0.814775 | ||||||||
\(478\) | −62.3338 | −2.85108 | ||||||||
\(479\) | −8.19879 | −0.374612 | −0.187306 | − | 0.982302i | \(-0.559976\pi\) | ||||
−0.187306 | + | 0.982302i | \(0.559976\pi\) | |||||||
\(480\) | 40.5777 | 1.85211 | ||||||||
\(481\) | −11.7800 | −0.537122 | ||||||||
\(482\) | 2.62823 | 0.119713 | ||||||||
\(483\) | 39.3694 | 1.79137 | ||||||||
\(484\) | −2.16336 | −0.0983344 | ||||||||
\(485\) | 7.27113 | 0.330165 | ||||||||
\(486\) | −38.0934 | −1.72795 | ||||||||
\(487\) | −29.0037 | −1.31428 | −0.657141 | − | 0.753768i | \(-0.728234\pi\) | ||||
−0.657141 | + | 0.753768i | \(0.728234\pi\) | |||||||
\(488\) | 108.753 | 4.92302 | ||||||||
\(489\) | 27.8734 | 1.26048 | ||||||||
\(490\) | 26.5949 | 1.20144 | ||||||||
\(491\) | 4.05750 | 0.183112 | 0.0915562 | − | 0.995800i | \(-0.470816\pi\) | ||||
0.0915562 | + | 0.995800i | \(0.470816\pi\) | |||||||
\(492\) | −33.5668 | −1.51331 | ||||||||
\(493\) | 1.02942 | 0.0463627 | ||||||||
\(494\) | −11.7348 | −0.527971 | ||||||||
\(495\) | 5.21694 | 0.234484 | ||||||||
\(496\) | 12.5024 | 0.561375 | ||||||||
\(497\) | −9.69786 | −0.435009 | ||||||||
\(498\) | 18.4184 | 0.825346 | ||||||||
\(499\) | 13.3239 | 0.596459 | 0.298229 | − | 0.954494i | \(-0.403604\pi\) | ||||
0.298229 | + | 0.954494i | \(0.403604\pi\) | |||||||
\(500\) | 56.0169 | 2.50515 | ||||||||
\(501\) | 12.9408 | 0.578154 | ||||||||
\(502\) | −23.8497 | −1.06446 | ||||||||
\(503\) | −13.1590 | −0.586730 | −0.293365 | − | 0.956001i | \(-0.594775\pi\) | ||||
−0.293365 | + | 0.956001i | \(0.594775\pi\) | |||||||
\(504\) | −62.9275 | −2.80301 | ||||||||
\(505\) | −13.1335 | −0.584432 | ||||||||
\(506\) | 73.3301 | 3.25992 | ||||||||
\(507\) | 0.772834 | 0.0343227 | ||||||||
\(508\) | 6.53762 | 0.290060 | ||||||||
\(509\) | 14.3806 | 0.637409 | 0.318705 | − | 0.947854i | \(-0.396752\pi\) | ||||
0.318705 | + | 0.947854i | \(0.396752\pi\) | |||||||
\(510\) | −3.76133 | −0.166555 | ||||||||
\(511\) | 32.2827 | 1.42810 | ||||||||
\(512\) | −160.304 | −7.08449 | ||||||||
\(513\) | 6.27371 | 0.276991 | ||||||||
\(514\) | −46.3786 | −2.04567 | ||||||||
\(515\) | −2.12581 | −0.0936745 | ||||||||
\(516\) | −80.3466 | −3.53706 | ||||||||
\(517\) | 0.184524 | 0.00811536 | ||||||||
\(518\) | 35.4619 | 1.55811 | ||||||||
\(519\) | 7.85900 | 0.344972 | ||||||||
\(520\) | −43.2016 | −1.89451 | ||||||||
\(521\) | −5.04879 | −0.221191 | −0.110596 | − | 0.993865i | \(-0.535276\pi\) | ||||
−0.110596 | + | 0.993865i | \(0.535276\pi\) | |||||||
\(522\) | −4.24616 | −0.185849 | ||||||||
\(523\) | −28.4338 | −1.24333 | −0.621663 | − | 0.783285i | \(-0.713542\pi\) | ||||
−0.621663 | + | 0.783285i | \(0.713542\pi\) | |||||||
\(524\) | 111.557 | 4.87340 | ||||||||
\(525\) | 18.7259 | 0.817266 | ||||||||
\(526\) | −22.3825 | −0.975923 | ||||||||
\(527\) | −0.676568 | −0.0294717 | ||||||||
\(528\) | 74.4595 | 3.24044 | ||||||||
\(529\) | 41.4782 | 1.80340 | ||||||||
\(530\) | 36.7767 | 1.59748 | ||||||||
\(531\) | −4.22625 | −0.183404 | ||||||||
\(532\) | 26.3204 | 1.14113 | ||||||||
\(533\) | 17.1509 | 0.742888 | ||||||||
\(534\) | 35.5592 | 1.53880 | ||||||||
\(535\) | 9.61378 | 0.415640 | ||||||||
\(536\) | −13.7816 | −0.595275 | ||||||||
\(537\) | −16.2041 | −0.699258 | ||||||||
\(538\) | −83.0308 | −3.57971 | ||||||||
\(539\) | 28.4901 | 1.22716 | ||||||||
\(540\) | 35.1089 | 1.51085 | ||||||||
\(541\) | 4.69287 | 0.201762 | 0.100881 | − | 0.994898i | \(-0.467834\pi\) | ||||
0.100881 | + | 0.994898i | \(0.467834\pi\) | |||||||
\(542\) | −26.6588 | −1.14509 | ||||||||
\(543\) | −21.8279 | −0.936723 | ||||||||
\(544\) | 30.2174 | 1.29556 | ||||||||
\(545\) | −7.19509 | −0.308204 | ||||||||
\(546\) | −50.6917 | −2.16941 | ||||||||
\(547\) | −16.9444 | −0.724489 | −0.362245 | − | 0.932083i | \(-0.617990\pi\) | ||||
−0.362245 | + | 0.932083i | \(0.617990\pi\) | |||||||
\(548\) | 30.2298 | 1.29135 | ||||||||
\(549\) | 14.8685 | 0.634571 | ||||||||
\(550\) | 34.8792 | 1.48726 | ||||||||
\(551\) | 1.16837 | 0.0497743 | ||||||||
\(552\) | 106.892 | 4.54964 | ||||||||
\(553\) | 10.2263 | 0.434868 | ||||||||
\(554\) | 14.4402 | 0.613507 | ||||||||
\(555\) | −4.28551 | −0.181910 | ||||||||
\(556\) | −22.9983 | −0.975345 | ||||||||
\(557\) | 7.03238 | 0.297971 | 0.148986 | − | 0.988839i | \(-0.452399\pi\) | ||||
0.148986 | + | 0.988839i | \(0.452399\pi\) | |||||||
\(558\) | 2.79071 | 0.118140 | ||||||||
\(559\) | 41.0530 | 1.73636 | ||||||||
\(560\) | 79.6564 | 3.36610 | ||||||||
\(561\) | −4.02937 | −0.170120 | ||||||||
\(562\) | 86.0907 | 3.63152 | ||||||||
\(563\) | −28.4864 | −1.20056 | −0.600279 | − | 0.799791i | \(-0.704944\pi\) | ||||
−0.600279 | + | 0.799791i | \(0.704944\pi\) | |||||||
\(564\) | 0.408870 | 0.0172165 | ||||||||
\(565\) | −0.111570 | −0.00469379 | ||||||||
\(566\) | 65.2691 | 2.74346 | ||||||||
\(567\) | 9.57469 | 0.402099 | ||||||||
\(568\) | −26.3308 | −1.10482 | ||||||||
\(569\) | −2.21738 | −0.0929572 | −0.0464786 | − | 0.998919i | \(-0.514800\pi\) | ||||
−0.0464786 | + | 0.998919i | \(0.514800\pi\) | |||||||
\(570\) | −4.26905 | −0.178811 | ||||||||
\(571\) | 4.28813 | 0.179453 | 0.0897263 | − | 0.995966i | \(-0.471401\pi\) | ||||
0.0897263 | + | 0.995966i | \(0.471401\pi\) | |||||||
\(572\) | −70.3498 | −2.94147 | ||||||||
\(573\) | 1.18255 | 0.0494015 | ||||||||
\(574\) | −51.6302 | −2.15500 | ||||||||
\(575\) | 30.6688 | 1.27898 | ||||||||
\(576\) | −70.2151 | −2.92563 | ||||||||
\(577\) | 29.1152 | 1.21208 | 0.606040 | − | 0.795434i | \(-0.292757\pi\) | ||||
0.606040 | + | 0.795434i | \(0.292757\pi\) | |||||||
\(578\) | −2.80099 | −0.116506 | ||||||||
\(579\) | −21.9828 | −0.913574 | ||||||||
\(580\) | 6.53844 | 0.271494 | ||||||||
\(581\) | 21.1080 | 0.875707 | ||||||||
\(582\) | 23.1648 | 0.960210 | ||||||||
\(583\) | 39.3975 | 1.63168 | ||||||||
\(584\) | 87.6511 | 3.62703 | ||||||||
\(585\) | −5.90642 | −0.244201 | ||||||||
\(586\) | 31.9722 | 1.32076 | ||||||||
\(587\) | 23.8311 | 0.983615 | 0.491808 | − | 0.870704i | \(-0.336336\pi\) | ||||
0.491808 | + | 0.870704i | \(0.336336\pi\) | |||||||
\(588\) | 63.1286 | 2.60338 | ||||||||
\(589\) | −0.767892 | −0.0316404 | ||||||||
\(590\) | 8.73437 | 0.359588 | ||||||||
\(591\) | 28.4791 | 1.17147 | ||||||||
\(592\) | 58.9732 | 2.42378 | ||||||||
\(593\) | −17.4421 | −0.716260 | −0.358130 | − | 0.933672i | \(-0.616586\pi\) | ||||
−0.358130 | + | 0.933672i | \(0.616586\pi\) | |||||||
\(594\) | 50.4791 | 2.07118 | ||||||||
\(595\) | −4.31060 | −0.176717 | ||||||||
\(596\) | −111.306 | −4.55927 | ||||||||
\(597\) | −23.3571 | −0.955941 | ||||||||
\(598\) | −83.0216 | −3.39501 | ||||||||
\(599\) | −29.5360 | −1.20681 | −0.603405 | − | 0.797435i | \(-0.706190\pi\) | ||||
−0.603405 | + | 0.797435i | \(0.706190\pi\) | |||||||
\(600\) | 50.8430 | 2.07566 | ||||||||
\(601\) | −25.8366 | −1.05390 | −0.526949 | − | 0.849897i | \(-0.676664\pi\) | ||||
−0.526949 | + | 0.849897i | \(0.676664\pi\) | |||||||
\(602\) | −123.584 | −5.03690 | ||||||||
\(603\) | −1.88419 | −0.0767302 | ||||||||
\(604\) | 23.0247 | 0.936862 | ||||||||
\(605\) | 0.402126 | 0.0163487 | ||||||||
\(606\) | −41.8413 | −1.69969 | ||||||||
\(607\) | 12.6508 | 0.513480 | 0.256740 | − | 0.966480i | \(-0.417352\pi\) | ||||
0.256740 | + | 0.966480i | \(0.417352\pi\) | |||||||
\(608\) | 34.2962 | 1.39090 | ||||||||
\(609\) | 5.04713 | 0.204520 | ||||||||
\(610\) | −30.7286 | −1.24417 | ||||||||
\(611\) | −0.208911 | −0.00845165 | ||||||||
\(612\) | 8.60829 | 0.347969 | ||||||||
\(613\) | 41.0528 | 1.65811 | 0.829054 | − | 0.559168i | \(-0.188879\pi\) | ||||
0.829054 | + | 0.559168i | \(0.188879\pi\) | |||||||
\(614\) | −61.0330 | −2.46309 | ||||||||
\(615\) | 6.23942 | 0.251598 | ||||||||
\(616\) | 139.320 | 5.61335 | ||||||||
\(617\) | 16.5051 | 0.664468 | 0.332234 | − | 0.943197i | \(-0.392198\pi\) | ||||
0.332234 | + | 0.943197i | \(0.392198\pi\) | |||||||
\(618\) | −6.77253 | −0.272431 | ||||||||
\(619\) | −1.84972 | −0.0743464 | −0.0371732 | − | 0.999309i | \(-0.511835\pi\) | ||||
−0.0371732 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(620\) | −4.29728 | −0.172583 | ||||||||
\(621\) | 44.3855 | 1.78113 | ||||||||
\(622\) | 70.7574 | 2.83711 | ||||||||
\(623\) | 40.7519 | 1.63269 | ||||||||
\(624\) | −84.3003 | −3.37471 | ||||||||
\(625\) | 8.68436 | 0.347374 | ||||||||
\(626\) | 15.8257 | 0.632523 | ||||||||
\(627\) | −4.57327 | −0.182639 | ||||||||
\(628\) | −85.5717 | −3.41468 | ||||||||
\(629\) | −3.19133 | −0.127247 | ||||||||
\(630\) | 17.7804 | 0.708388 | ||||||||
\(631\) | −44.3479 | −1.76546 | −0.882732 | − | 0.469877i | \(-0.844298\pi\) | ||||
−0.882732 | + | 0.469877i | \(0.844298\pi\) | |||||||
\(632\) | 27.7657 | 1.10446 | ||||||||
\(633\) | 6.14672 | 0.244310 | ||||||||
\(634\) | −43.2780 | −1.71879 | ||||||||
\(635\) | −1.21522 | −0.0482244 | ||||||||
\(636\) | 87.2973 | 3.46156 | ||||||||
\(637\) | −32.2555 | −1.27801 | ||||||||
\(638\) | 9.40087 | 0.372184 | ||||||||
\(639\) | −3.59989 | −0.142409 | ||||||||
\(640\) | 79.4466 | 3.14040 | ||||||||
\(641\) | 21.3463 | 0.843127 | 0.421564 | − | 0.906799i | \(-0.361481\pi\) | ||||
0.421564 | + | 0.906799i | \(0.361481\pi\) | |||||||
\(642\) | 30.6281 | 1.20879 | ||||||||
\(643\) | 18.7513 | 0.739480 | 0.369740 | − | 0.929135i | \(-0.379447\pi\) | ||||
0.369740 | + | 0.929135i | \(0.379447\pi\) | |||||||
\(644\) | 186.213 | 7.33782 | ||||||||
\(645\) | 14.9349 | 0.588060 | ||||||||
\(646\) | −3.17907 | −0.125079 | ||||||||
\(647\) | 31.0739 | 1.22164 | 0.610820 | − | 0.791769i | \(-0.290840\pi\) | ||||
0.610820 | + | 0.791769i | \(0.290840\pi\) | |||||||
\(648\) | 25.9964 | 1.02123 | ||||||||
\(649\) | 9.35679 | 0.367286 | ||||||||
\(650\) | −39.4890 | −1.54888 | ||||||||
\(651\) | −3.31714 | −0.130009 | ||||||||
\(652\) | 131.838 | 5.16318 | ||||||||
\(653\) | −14.1762 | −0.554758 | −0.277379 | − | 0.960761i | \(-0.589466\pi\) | ||||
−0.277379 | + | 0.960761i | \(0.589466\pi\) | |||||||
\(654\) | −22.9225 | −0.896340 | ||||||||
\(655\) | −20.7363 | −0.810235 | ||||||||
\(656\) | −85.8610 | −3.35231 | ||||||||
\(657\) | 11.9835 | 0.467519 | ||||||||
\(658\) | 0.628896 | 0.0245169 | ||||||||
\(659\) | 32.9123 | 1.28208 | 0.641040 | − | 0.767507i | \(-0.278503\pi\) | ||||
0.641040 | + | 0.767507i | \(0.278503\pi\) | |||||||
\(660\) | −25.5929 | −0.996203 | ||||||||
\(661\) | 5.63159 | 0.219043 | 0.109522 | − | 0.993984i | \(-0.465068\pi\) | ||||
0.109522 | + | 0.993984i | \(0.465068\pi\) | |||||||
\(662\) | −62.7328 | −2.43818 | ||||||||
\(663\) | 4.56190 | 0.177170 | ||||||||
\(664\) | 57.3106 | 2.22408 | ||||||||
\(665\) | −4.89245 | −0.189721 | ||||||||
\(666\) | 13.1636 | 0.510080 | ||||||||
\(667\) | 8.26606 | 0.320063 | ||||||||
\(668\) | 61.2088 | 2.36824 | ||||||||
\(669\) | −10.3967 | −0.401959 | ||||||||
\(670\) | 3.89405 | 0.150440 | ||||||||
\(671\) | −32.9184 | −1.27080 | ||||||||
\(672\) | 148.153 | 5.71511 | ||||||||
\(673\) | −24.7137 | −0.952644 | −0.476322 | − | 0.879271i | \(-0.658030\pi\) | ||||
−0.476322 | + | 0.879271i | \(0.658030\pi\) | |||||||
\(674\) | 14.7870 | 0.569572 | ||||||||
\(675\) | 21.1118 | 0.812595 | ||||||||
\(676\) | 3.65542 | 0.140593 | ||||||||
\(677\) | 15.5169 | 0.596363 | 0.298181 | − | 0.954509i | \(-0.403620\pi\) | ||||
0.298181 | + | 0.954509i | \(0.403620\pi\) | |||||||
\(678\) | −0.355446 | −0.0136508 | ||||||||
\(679\) | 26.5475 | 1.01880 | ||||||||
\(680\) | −11.7038 | −0.448819 | ||||||||
\(681\) | −12.2841 | −0.470728 | ||||||||
\(682\) | −6.17856 | −0.236589 | ||||||||
\(683\) | 15.1324 | 0.579027 | 0.289513 | − | 0.957174i | \(-0.406507\pi\) | ||||
0.289513 | + | 0.957174i | \(0.406507\pi\) | |||||||
\(684\) | 9.77026 | 0.373575 | ||||||||
\(685\) | −5.61914 | −0.214696 | ||||||||
\(686\) | 19.3165 | 0.737508 | ||||||||
\(687\) | −1.50945 | −0.0575891 | ||||||||
\(688\) | −205.520 | −7.83537 | ||||||||
\(689\) | −44.6044 | −1.69929 | ||||||||
\(690\) | −30.2029 | −1.14980 | ||||||||
\(691\) | −10.8510 | −0.412793 | −0.206397 | − | 0.978468i | \(-0.566174\pi\) | ||||
−0.206397 | + | 0.978468i | \(0.566174\pi\) | |||||||
\(692\) | 37.1723 | 1.41308 | ||||||||
\(693\) | 19.0475 | 0.723553 | ||||||||
\(694\) | 33.0753 | 1.25552 | ||||||||
\(695\) | 4.27494 | 0.162158 | ||||||||
\(696\) | 13.7035 | 0.519431 | ||||||||
\(697\) | 4.64636 | 0.175994 | ||||||||
\(698\) | −80.4907 | −3.04662 | ||||||||
\(699\) | 25.0130 | 0.946078 | ||||||||
\(700\) | 88.5716 | 3.34769 | ||||||||
\(701\) | 8.62413 | 0.325729 | 0.162864 | − | 0.986648i | \(-0.447927\pi\) | ||||
0.162864 | + | 0.986648i | \(0.447927\pi\) | |||||||
\(702\) | −57.1505 | −2.15701 | ||||||||
\(703\) | −3.62210 | −0.136610 | ||||||||
\(704\) | 155.454 | 5.85891 | ||||||||
\(705\) | −0.0760009 | −0.00286236 | ||||||||
\(706\) | −2.80099 | −0.105417 | ||||||||
\(707\) | −47.9514 | −1.80340 | ||||||||
\(708\) | 20.7328 | 0.779188 | ||||||||
\(709\) | −28.0778 | −1.05448 | −0.527242 | − | 0.849715i | \(-0.676774\pi\) | ||||
−0.527242 | + | 0.849715i | \(0.676774\pi\) | |||||||
\(710\) | 7.43988 | 0.279214 | ||||||||
\(711\) | 3.79606 | 0.142363 | ||||||||
\(712\) | 110.646 | 4.14663 | ||||||||
\(713\) | −5.43272 | −0.203457 | ||||||||
\(714\) | −13.7329 | −0.513942 | ||||||||
\(715\) | 13.0767 | 0.489039 | ||||||||
\(716\) | −76.6436 | −2.86431 | ||||||||
\(717\) | 27.5033 | 1.02713 | ||||||||
\(718\) | 59.0035 | 2.20199 | ||||||||
\(719\) | 48.9331 | 1.82490 | 0.912448 | − | 0.409193i | \(-0.134190\pi\) | ||||
0.912448 | + | 0.409193i | \(0.134190\pi\) | |||||||
\(720\) | 29.5688 | 1.10196 | ||||||||
\(721\) | −7.76152 | −0.289054 | ||||||||
\(722\) | 49.6106 | 1.84631 | ||||||||
\(723\) | −1.15964 | −0.0431276 | ||||||||
\(724\) | −103.243 | −3.83701 | ||||||||
\(725\) | 3.93173 | 0.146021 | ||||||||
\(726\) | 1.28111 | 0.0475466 | ||||||||
\(727\) | 44.7439 | 1.65946 | 0.829729 | − | 0.558166i | \(-0.188495\pi\) | ||||
0.829729 | + | 0.558166i | \(0.188495\pi\) | |||||||
\(728\) | −157.732 | −5.84595 | ||||||||
\(729\) | 24.0483 | 0.890677 | ||||||||
\(730\) | −24.7662 | −0.916637 | ||||||||
\(731\) | 11.1217 | 0.411351 | ||||||||
\(732\) | −72.9408 | −2.69597 | ||||||||
\(733\) | 31.9111 | 1.17866 | 0.589332 | − | 0.807891i | \(-0.299391\pi\) | ||||
0.589332 | + | 0.807891i | \(0.299391\pi\) | |||||||
\(734\) | −5.01275 | −0.185024 | ||||||||
\(735\) | −11.7344 | −0.432829 | ||||||||
\(736\) | 242.641 | 8.94385 | ||||||||
\(737\) | 4.17155 | 0.153661 | ||||||||
\(738\) | −19.1654 | −0.705487 | ||||||||
\(739\) | −53.8269 | −1.98005 | −0.990026 | − | 0.140882i | \(-0.955006\pi\) | ||||
−0.990026 | + | 0.140882i | \(0.955006\pi\) | |||||||
\(740\) | −20.2700 | −0.745140 | ||||||||
\(741\) | 5.17768 | 0.190207 | ||||||||
\(742\) | 134.275 | 4.92939 | ||||||||
\(743\) | −29.1941 | −1.07103 | −0.535513 | − | 0.844527i | \(-0.679882\pi\) | ||||
−0.535513 | + | 0.844527i | \(0.679882\pi\) | |||||||
\(744\) | −9.00641 | −0.330191 | ||||||||
\(745\) | 20.6896 | 0.758009 | ||||||||
\(746\) | 56.7350 | 2.07722 | ||||||||
\(747\) | 7.83538 | 0.286681 | ||||||||
\(748\) | −19.0585 | −0.696848 | ||||||||
\(749\) | 35.1007 | 1.28255 | ||||||||
\(750\) | −33.1726 | −1.21129 | ||||||||
\(751\) | −45.2612 | −1.65161 | −0.825803 | − | 0.563959i | \(-0.809278\pi\) | ||||
−0.825803 | + | 0.563959i | \(0.809278\pi\) | |||||||
\(752\) | 1.04585 | 0.0381384 | ||||||||
\(753\) | 10.5231 | 0.383484 | ||||||||
\(754\) | −10.6433 | −0.387607 | ||||||||
\(755\) | −4.27985 | −0.155760 | ||||||||
\(756\) | 128.186 | 4.66206 | ||||||||
\(757\) | 16.0545 | 0.583512 | 0.291756 | − | 0.956493i | \(-0.405761\pi\) | ||||
0.291756 | + | 0.956493i | \(0.405761\pi\) | |||||||
\(758\) | 53.7392 | 1.95190 | ||||||||
\(759\) | −32.3552 | −1.17442 | ||||||||
\(760\) | −13.2836 | −0.481846 | ||||||||
\(761\) | 18.2604 | 0.661940 | 0.330970 | − | 0.943641i | \(-0.392624\pi\) | ||||
0.330970 | + | 0.943641i | \(0.392624\pi\) | |||||||
\(762\) | −3.87150 | −0.140250 | ||||||||
\(763\) | −26.2699 | −0.951033 | ||||||||
\(764\) | 5.59332 | 0.202359 | ||||||||
\(765\) | −1.60011 | −0.0578522 | ||||||||
\(766\) | −89.1782 | −3.22214 | ||||||||
\(767\) | −10.5934 | −0.382506 | ||||||||
\(768\) | 135.252 | 4.88050 | ||||||||
\(769\) | −8.51815 | −0.307172 | −0.153586 | − | 0.988135i | \(-0.549082\pi\) | ||||
−0.153586 | + | 0.988135i | \(0.549082\pi\) | |||||||
\(770\) | −39.3653 | −1.41863 | ||||||||
\(771\) | 20.4634 | 0.736973 | ||||||||
\(772\) | −103.976 | −3.74219 | ||||||||
\(773\) | −37.7900 | −1.35921 | −0.679606 | − | 0.733577i | \(-0.737849\pi\) | ||||
−0.679606 | + | 0.733577i | \(0.737849\pi\) | |||||||
\(774\) | −45.8749 | −1.64894 | ||||||||
\(775\) | −2.58406 | −0.0928221 | ||||||||
\(776\) | 72.0795 | 2.58750 | ||||||||
\(777\) | −15.6467 | −0.561323 | ||||||||
\(778\) | −0.215530 | −0.00772713 | ||||||||
\(779\) | 5.27354 | 0.188944 | ||||||||
\(780\) | 28.9753 | 1.03748 | ||||||||
\(781\) | 7.97005 | 0.285191 | ||||||||
\(782\) | −22.4915 | −0.804293 | ||||||||
\(783\) | 5.69020 | 0.203351 | ||||||||
\(784\) | 161.478 | 5.76706 | ||||||||
\(785\) | 15.9061 | 0.567714 | ||||||||
\(786\) | −66.0629 | −2.35638 | ||||||||
\(787\) | 1.00198 | 0.0357168 | 0.0178584 | − | 0.999841i | \(-0.494315\pi\) | ||||
0.0178584 | + | 0.999841i | \(0.494315\pi\) | |||||||
\(788\) | 134.703 | 4.79861 | ||||||||
\(789\) | 9.87574 | 0.351586 | ||||||||
\(790\) | −7.84530 | −0.279123 | ||||||||
\(791\) | −0.407351 | −0.0144837 | ||||||||
\(792\) | 51.7161 | 1.83765 | ||||||||
\(793\) | 37.2690 | 1.32346 | ||||||||
\(794\) | −59.8976 | −2.12569 | ||||||||
\(795\) | −16.2269 | −0.575508 | ||||||||
\(796\) | −110.476 | −3.91573 | ||||||||
\(797\) | −10.0509 | −0.356021 | −0.178010 | − | 0.984029i | \(-0.556966\pi\) | ||||
−0.178010 | + | 0.984029i | \(0.556966\pi\) | |||||||
\(798\) | −15.5866 | −0.551761 | ||||||||
\(799\) | −0.0565963 | −0.00200223 | ||||||||
\(800\) | 115.411 | 4.08040 | ||||||||
\(801\) | 15.1273 | 0.534496 | ||||||||
\(802\) | 64.4930 | 2.27733 | ||||||||
\(803\) | −26.5310 | −0.936260 | ||||||||
\(804\) | 9.24334 | 0.325987 | ||||||||
\(805\) | −34.6134 | −1.21996 | ||||||||
\(806\) | 6.99513 | 0.246393 | ||||||||
\(807\) | 36.6354 | 1.28963 | ||||||||
\(808\) | −130.193 | −4.58019 | ||||||||
\(809\) | 15.7934 | 0.555266 | 0.277633 | − | 0.960687i | \(-0.410450\pi\) | ||||
0.277633 | + | 0.960687i | \(0.410450\pi\) | |||||||
\(810\) | −7.34538 | −0.258091 | ||||||||
\(811\) | 21.0943 | 0.740722 | 0.370361 | − | 0.928888i | \(-0.379234\pi\) | ||||
0.370361 | + | 0.928888i | \(0.379234\pi\) | |||||||
\(812\) | 23.8724 | 0.837757 | ||||||||
\(813\) | 11.7626 | 0.412531 | ||||||||
\(814\) | −29.1439 | −1.02149 | ||||||||
\(815\) | −24.5062 | −0.858414 | ||||||||
\(816\) | −22.8379 | −0.799485 | ||||||||
\(817\) | 12.6229 | 0.441620 | ||||||||
\(818\) | −63.0949 | −2.20606 | ||||||||
\(819\) | −21.5648 | −0.753536 | ||||||||
\(820\) | 29.5118 | 1.03060 | ||||||||
\(821\) | −31.4289 | −1.09688 | −0.548438 | − | 0.836191i | \(-0.684777\pi\) | ||||
−0.548438 | + | 0.836191i | \(0.684777\pi\) | |||||||
\(822\) | −17.9017 | −0.624395 | ||||||||
\(823\) | −47.6686 | −1.66162 | −0.830812 | − | 0.556553i | \(-0.812123\pi\) | ||||
−0.830812 | + | 0.556553i | \(0.812123\pi\) | |||||||
\(824\) | −21.0734 | −0.734127 | ||||||||
\(825\) | −15.3896 | −0.535798 | ||||||||
\(826\) | 31.8899 | 1.10959 | ||||||||
\(827\) | 46.3213 | 1.61075 | 0.805374 | − | 0.592767i | \(-0.201964\pi\) | ||||
0.805374 | + | 0.592767i | \(0.201964\pi\) | |||||||
\(828\) | 69.1231 | 2.40219 | ||||||||
\(829\) | −47.5185 | −1.65038 | −0.825192 | − | 0.564852i | \(-0.808933\pi\) | ||||
−0.825192 | + | 0.564852i | \(0.808933\pi\) | |||||||
\(830\) | −16.1933 | −0.562079 | ||||||||
\(831\) | −6.37141 | −0.221022 | ||||||||
\(832\) | −176.000 | −6.10169 | ||||||||
\(833\) | −8.73835 | −0.302766 | ||||||||
\(834\) | 13.6193 | 0.471598 | ||||||||
\(835\) | −11.3775 | −0.393736 | ||||||||
\(836\) | −21.6311 | −0.748126 | ||||||||
\(837\) | −3.73978 | −0.129266 | ||||||||
\(838\) | −100.152 | −3.45970 | ||||||||
\(839\) | 3.89713 | 0.134544 | 0.0672719 | − | 0.997735i | \(-0.478570\pi\) | ||||
0.0672719 | + | 0.997735i | \(0.478570\pi\) | |||||||
\(840\) | −57.3823 | −1.97988 | ||||||||
\(841\) | −27.9403 | −0.963458 | ||||||||
\(842\) | −5.23560 | −0.180431 | ||||||||
\(843\) | −37.9855 | −1.30829 | ||||||||
\(844\) | 29.0733 | 1.00075 | ||||||||
\(845\) | −0.679472 | −0.0233745 | ||||||||
\(846\) | 0.233449 | 0.00802615 | ||||||||
\(847\) | 1.46819 | 0.0504478 | ||||||||
\(848\) | 223.299 | 7.66812 | ||||||||
\(849\) | −28.7984 | −0.988359 | ||||||||
\(850\) | −10.6980 | −0.366938 | ||||||||
\(851\) | −25.6258 | −0.878442 | ||||||||
\(852\) | 17.6601 | 0.605025 | ||||||||
\(853\) | 28.0799 | 0.961436 | 0.480718 | − | 0.876875i | \(-0.340376\pi\) | ||||
0.480718 | + | 0.876875i | \(0.340376\pi\) | |||||||
\(854\) | −112.193 | −3.83915 | ||||||||
\(855\) | −1.81610 | −0.0621093 | ||||||||
\(856\) | 95.3024 | 3.25737 | ||||||||
\(857\) | −44.6206 | −1.52421 | −0.762106 | − | 0.647452i | \(-0.775834\pi\) | ||||
−0.762106 | + | 0.647452i | \(0.775834\pi\) | |||||||
\(858\) | 41.6603 | 1.42226 | ||||||||
\(859\) | 7.51593 | 0.256440 | 0.128220 | − | 0.991746i | \(-0.459074\pi\) | ||||
0.128220 | + | 0.991746i | \(0.459074\pi\) | |||||||
\(860\) | 70.6404 | 2.40882 | ||||||||
\(861\) | 22.7806 | 0.776361 | ||||||||
\(862\) | 53.2028 | 1.81209 | ||||||||
\(863\) | 30.4739 | 1.03734 | 0.518672 | − | 0.854973i | \(-0.326427\pi\) | ||||
0.518672 | + | 0.854973i | \(0.326427\pi\) | |||||||
\(864\) | 167.029 | 5.68245 | ||||||||
\(865\) | −6.90960 | −0.234934 | ||||||||
\(866\) | −39.4805 | −1.34160 | ||||||||
\(867\) | 1.23587 | 0.0419723 | ||||||||
\(868\) | −15.6897 | −0.532543 | ||||||||
\(869\) | −8.40437 | −0.285099 | ||||||||
\(870\) | −3.87199 | −0.131273 | ||||||||
\(871\) | −4.72287 | −0.160028 | ||||||||
\(872\) | −71.3257 | −2.41539 | ||||||||
\(873\) | 9.85455 | 0.333526 | ||||||||
\(874\) | −25.5274 | −0.863477 | ||||||||
\(875\) | −38.0167 | −1.28520 | ||||||||
\(876\) | −58.7877 | −1.98625 | ||||||||
\(877\) | 13.7662 | 0.464851 | 0.232425 | − | 0.972614i | \(-0.425334\pi\) | ||||
0.232425 | + | 0.972614i | \(0.425334\pi\) | |||||||
\(878\) | 92.0124 | 3.10527 | ||||||||
\(879\) | −14.1070 | −0.475817 | ||||||||
\(880\) | −65.4645 | −2.20681 | ||||||||
\(881\) | −45.8523 | −1.54480 | −0.772402 | − | 0.635134i | \(-0.780945\pi\) | ||||
−0.772402 | + | 0.635134i | \(0.780945\pi\) | |||||||
\(882\) | 36.0440 | 1.21367 | ||||||||
\(883\) | −28.7748 | −0.968348 | −0.484174 | − | 0.874972i | \(-0.660880\pi\) | ||||
−0.484174 | + | 0.874972i | \(0.660880\pi\) | |||||||
\(884\) | 21.5773 | 0.725724 | ||||||||
\(885\) | −3.85383 | −0.129545 | ||||||||
\(886\) | 75.8372 | 2.54780 | ||||||||
\(887\) | 35.1629 | 1.18066 | 0.590328 | − | 0.807164i | \(-0.298999\pi\) | ||||
0.590328 | + | 0.807164i | \(0.298999\pi\) | |||||||
\(888\) | −42.4827 | −1.42562 | ||||||||
\(889\) | −4.43685 | −0.148807 | ||||||||
\(890\) | −31.2635 | −1.04795 | ||||||||
\(891\) | −7.86883 | −0.263616 | ||||||||
\(892\) | −49.1752 | −1.64651 | ||||||||
\(893\) | −0.0642358 | −0.00214957 | ||||||||
\(894\) | 65.9141 | 2.20450 | ||||||||
\(895\) | 14.2466 | 0.476210 | ||||||||
\(896\) | 290.066 | 9.69043 | ||||||||
\(897\) | 36.6313 | 1.22308 | ||||||||
\(898\) | −83.6215 | −2.79049 | ||||||||
\(899\) | −0.696472 | −0.0232286 | ||||||||
\(900\) | 32.8782 | 1.09594 | ||||||||
\(901\) | −12.0838 | −0.402570 | ||||||||
\(902\) | 42.4316 | 1.41282 | ||||||||
\(903\) | 54.5285 | 1.81459 | ||||||||
\(904\) | −1.10601 | −0.0367852 | ||||||||
\(905\) | 19.1910 | 0.637929 | ||||||||
\(906\) | −13.6350 | −0.452991 | ||||||||
\(907\) | −2.38274 | −0.0791177 | −0.0395588 | − | 0.999217i | \(-0.512595\pi\) | ||||
−0.0395588 | + | 0.999217i | \(0.512595\pi\) | |||||||
\(908\) | −58.1026 | −1.92820 | ||||||||
\(909\) | −17.7998 | −0.590381 | ||||||||
\(910\) | 44.5679 | 1.47741 | ||||||||
\(911\) | −12.2639 | −0.406322 | −0.203161 | − | 0.979145i | \(-0.565122\pi\) | ||||
−0.203161 | + | 0.979145i | \(0.565122\pi\) | |||||||
\(912\) | −25.9206 | −0.858316 | ||||||||
\(913\) | −17.3473 | −0.574112 | ||||||||
\(914\) | −106.375 | −3.51858 | ||||||||
\(915\) | 13.5583 | 0.448223 | ||||||||
\(916\) | −7.13954 | −0.235897 | ||||||||
\(917\) | −75.7100 | −2.50016 | ||||||||
\(918\) | −15.4827 | −0.511005 | ||||||||
\(919\) | −35.2020 | −1.16121 | −0.580604 | − | 0.814186i | \(-0.697183\pi\) | ||||
−0.580604 | + | 0.814186i | \(0.697183\pi\) | |||||||
\(920\) | −93.9793 | −3.09841 | ||||||||
\(921\) | 26.9294 | 0.887353 | ||||||||
\(922\) | −96.2085 | −3.16846 | ||||||||
\(923\) | −9.02339 | −0.297009 | ||||||||
\(924\) | −93.4418 | −3.07401 | ||||||||
\(925\) | −12.1888 | −0.400767 | ||||||||
\(926\) | 7.58341 | 0.249206 | ||||||||
\(927\) | −2.88111 | −0.0946280 | ||||||||
\(928\) | 31.1064 | 1.02112 | ||||||||
\(929\) | 5.72804 | 0.187931 | 0.0939654 | − | 0.995575i | \(-0.470046\pi\) | ||||
0.0939654 | + | 0.995575i | \(0.470046\pi\) | |||||||
\(930\) | 2.54480 | 0.0834472 | ||||||||
\(931\) | −9.91787 | −0.325045 | ||||||||
\(932\) | 118.309 | 3.87533 | ||||||||
\(933\) | −31.2200 | −1.02210 | ||||||||
\(934\) | 56.7978 | 1.85848 | ||||||||
\(935\) | 3.54261 | 0.115856 | ||||||||
\(936\) | −58.5510 | −1.91380 | ||||||||
\(937\) | −36.6452 | −1.19715 | −0.598573 | − | 0.801068i | \(-0.704265\pi\) | ||||
−0.598573 | + | 0.801068i | \(0.704265\pi\) | |||||||
\(938\) | 14.2175 | 0.464218 | ||||||||
\(939\) | −6.98272 | −0.227873 | ||||||||
\(940\) | −0.359476 | −0.0117248 | ||||||||
\(941\) | −51.6842 | −1.68486 | −0.842429 | − | 0.538808i | \(-0.818875\pi\) | ||||
−0.842429 | + | 0.538808i | \(0.818875\pi\) | |||||||
\(942\) | 50.6745 | 1.65107 | ||||||||
\(943\) | 37.3095 | 1.21496 | ||||||||
\(944\) | 53.0329 | 1.72607 | ||||||||
\(945\) | −23.8272 | −0.775099 | ||||||||
\(946\) | 101.566 | 3.30219 | ||||||||
\(947\) | 39.9617 | 1.29858 | 0.649290 | − | 0.760541i | \(-0.275066\pi\) | ||||
0.649290 | + | 0.760541i | \(0.275066\pi\) | |||||||
\(948\) | −18.6225 | −0.604829 | ||||||||
\(949\) | 30.0375 | 0.975057 | ||||||||
\(950\) | −12.1420 | −0.393939 | ||||||||
\(951\) | 19.0954 | 0.619211 | ||||||||
\(952\) | −42.7314 | −1.38493 | ||||||||
\(953\) | −27.2901 | −0.884013 | −0.442007 | − | 0.897012i | \(-0.645733\pi\) | ||||
−0.442007 | + | 0.897012i | \(0.645733\pi\) | |||||||
\(954\) | 49.8434 | 1.61374 | ||||||||
\(955\) | −1.03969 | −0.0336435 | ||||||||
\(956\) | 130.088 | 4.20734 | ||||||||
\(957\) | −4.14791 | −0.134083 | ||||||||
\(958\) | 22.9647 | 0.741956 | ||||||||
\(959\) | −20.5159 | −0.662494 | ||||||||
\(960\) | −64.0278 | −2.06649 | ||||||||
\(961\) | −30.5423 | −0.985234 | ||||||||
\(962\) | 32.9956 | 1.06382 | ||||||||
\(963\) | 13.0295 | 0.419871 | ||||||||
\(964\) | −5.48499 | −0.176660 | ||||||||
\(965\) | 19.3272 | 0.622164 | ||||||||
\(966\) | −110.273 | −3.54798 | ||||||||
\(967\) | −48.1494 | −1.54838 | −0.774189 | − | 0.632954i | \(-0.781842\pi\) | ||||
−0.774189 | + | 0.632954i | \(0.781842\pi\) | |||||||
\(968\) | 3.98632 | 0.128125 | ||||||||
\(969\) | 1.40269 | 0.0450609 | ||||||||
\(970\) | −20.3664 | −0.653924 | ||||||||
\(971\) | 31.3319 | 1.00549 | 0.502744 | − | 0.864435i | \(-0.332324\pi\) | ||||
0.502744 | + | 0.864435i | \(0.332324\pi\) | |||||||
\(972\) | 79.4992 | 2.54994 | ||||||||
\(973\) | 15.6081 | 0.500374 | ||||||||
\(974\) | 81.2389 | 2.60306 | ||||||||
\(975\) | 17.4236 | 0.558001 | ||||||||
\(976\) | −186.576 | −5.97216 | ||||||||
\(977\) | −45.2133 | −1.44650 | −0.723252 | − | 0.690585i | \(-0.757353\pi\) | ||||
−0.723252 | + | 0.690585i | \(0.757353\pi\) | |||||||
\(978\) | −78.0730 | −2.49650 | ||||||||
\(979\) | −33.4913 | −1.07039 | ||||||||
\(980\) | −55.5024 | −1.77296 | ||||||||
\(981\) | −9.75149 | −0.311341 | ||||||||
\(982\) | −11.3650 | −0.362672 | ||||||||
\(983\) | 6.05395 | 0.193091 | 0.0965455 | − | 0.995329i | \(-0.469221\pi\) | ||||
0.0965455 | + | 0.995329i | \(0.469221\pi\) | |||||||
\(984\) | 61.8520 | 1.97177 | ||||||||
\(985\) | −25.0387 | −0.797800 | ||||||||
\(986\) | −2.88339 | −0.0918259 | ||||||||
\(987\) | −0.277486 | −0.00883246 | ||||||||
\(988\) | 24.4899 | 0.779127 | ||||||||
\(989\) | 89.3053 | 2.83974 | ||||||||
\(990\) | −14.6126 | −0.464418 | ||||||||
\(991\) | 19.9578 | 0.633981 | 0.316991 | − | 0.948429i | \(-0.397328\pi\) | ||||
0.316991 | + | 0.948429i | \(0.397328\pi\) | |||||||
\(992\) | −20.4441 | −0.649101 | ||||||||
\(993\) | 27.6794 | 0.878378 | ||||||||
\(994\) | 27.1636 | 0.861577 | ||||||||
\(995\) | 20.5354 | 0.651017 | ||||||||
\(996\) | −38.4383 | −1.21796 | ||||||||
\(997\) | 51.4394 | 1.62910 | 0.814551 | − | 0.580092i | \(-0.196984\pi\) | ||||
0.814551 | + | 0.580092i | \(0.196984\pi\) | |||||||
\(998\) | −37.3200 | −1.18134 | ||||||||
\(999\) | −17.6403 | −0.558115 |
(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 | 6001.2.a.c.1.1 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.c.1.1 | ✓ | 121 | 1.1 | even | 1 | trivial |