Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75277 | −1.94651 | −0.973253 | − | 0.229737i | \(-0.926213\pi\) | ||||
−0.973253 | + | 0.229737i | \(0.926213\pi\) | |||||||
\(3\) | 3.20644 | 1.85124 | 0.925621 | − | 0.378453i | \(-0.123544\pi\) | ||||
0.925621 | + | 0.378453i | \(0.123544\pi\) | |||||||
\(4\) | 5.57777 | 2.78888 | ||||||||
\(5\) | 3.17240 | 1.41874 | 0.709371 | − | 0.704836i | \(-0.248979\pi\) | ||||
0.709371 | + | 0.704836i | \(0.248979\pi\) | |||||||
\(6\) | −8.82662 | −3.60345 | ||||||||
\(7\) | 4.29647 | 1.62391 | 0.811956 | − | 0.583719i | \(-0.198403\pi\) | ||||
0.811956 | + | 0.583719i | \(0.198403\pi\) | |||||||
\(8\) | −9.84879 | −3.48207 | ||||||||
\(9\) | 7.28128 | 2.42709 | ||||||||
\(10\) | −8.73291 | −2.76159 | ||||||||
\(11\) | −0.263402 | −0.0794186 | −0.0397093 | − | 0.999211i | \(-0.512643\pi\) | ||||
−0.0397093 | + | 0.999211i | \(0.512643\pi\) | |||||||
\(12\) | 17.8848 | 5.16290 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −11.8272 | −3.16095 | ||||||||
\(15\) | 10.1721 | 2.62643 | ||||||||
\(16\) | 15.9560 | 3.98899 | ||||||||
\(17\) | −4.13601 | −1.00313 | −0.501565 | − | 0.865120i | \(-0.667242\pi\) | ||||
−0.501565 | + | 0.865120i | \(0.667242\pi\) | |||||||
\(18\) | −20.0437 | −4.72435 | ||||||||
\(19\) | 2.21339 | 0.507785 | 0.253893 | − | 0.967232i | \(-0.418289\pi\) | ||||
0.253893 | + | 0.967232i | \(0.418289\pi\) | |||||||
\(20\) | 17.6949 | 3.95670 | ||||||||
\(21\) | 13.7764 | 3.00625 | ||||||||
\(22\) | 0.725085 | 0.154589 | ||||||||
\(23\) | −6.65465 | −1.38759 | −0.693795 | − | 0.720172i | \(-0.744063\pi\) | ||||
−0.693795 | + | 0.720172i | \(0.744063\pi\) | |||||||
\(24\) | −31.5796 | −6.44616 | ||||||||
\(25\) | 5.06413 | 1.01283 | ||||||||
\(26\) | −2.75277 | −0.539864 | ||||||||
\(27\) | 13.7277 | 2.64189 | ||||||||
\(28\) | 23.9647 | 4.52890 | ||||||||
\(29\) | 8.73232 | 1.62155 | 0.810775 | − | 0.585357i | \(-0.199046\pi\) | ||||
0.810775 | + | 0.585357i | \(0.199046\pi\) | |||||||
\(30\) | −28.0016 | −5.11236 | ||||||||
\(31\) | −1.55098 | −0.278564 | −0.139282 | − | 0.990253i | \(-0.544479\pi\) | ||||
−0.139282 | + | 0.990253i | \(0.544479\pi\) | |||||||
\(32\) | −24.2256 | −4.28252 | ||||||||
\(33\) | −0.844582 | −0.147023 | ||||||||
\(34\) | 11.3855 | 1.95260 | ||||||||
\(35\) | 13.6301 | 2.30391 | ||||||||
\(36\) | 40.6133 | 6.76888 | ||||||||
\(37\) | 6.95318 | 1.14310 | 0.571548 | − | 0.820569i | \(-0.306343\pi\) | ||||
0.571548 | + | 0.820569i | \(0.306343\pi\) | |||||||
\(38\) | −6.09295 | −0.988407 | ||||||||
\(39\) | 3.20644 | 0.513442 | ||||||||
\(40\) | −31.2443 | −4.94016 | ||||||||
\(41\) | 1.29749 | 0.202634 | 0.101317 | − | 0.994854i | \(-0.467694\pi\) | ||||
0.101317 | + | 0.994854i | \(0.467694\pi\) | |||||||
\(42\) | −37.9233 | −5.85169 | ||||||||
\(43\) | −7.49702 | −1.14328 | −0.571642 | − | 0.820503i | \(-0.693693\pi\) | ||||
−0.571642 | + | 0.820503i | \(0.693693\pi\) | |||||||
\(44\) | −1.46919 | −0.221489 | ||||||||
\(45\) | 23.0991 | 3.44342 | ||||||||
\(46\) | 18.3188 | 2.70095 | ||||||||
\(47\) | −6.36833 | −0.928917 | −0.464458 | − | 0.885595i | \(-0.653751\pi\) | ||||
−0.464458 | + | 0.885595i | \(0.653751\pi\) | |||||||
\(48\) | 51.1619 | 7.38458 | ||||||||
\(49\) | 11.4596 | 1.63709 | ||||||||
\(50\) | −13.9404 | −1.97147 | ||||||||
\(51\) | −13.2619 | −1.85703 | ||||||||
\(52\) | 5.57777 | 0.773497 | ||||||||
\(53\) | 5.38401 | 0.739551 | 0.369775 | − | 0.929121i | \(-0.379435\pi\) | ||||
0.369775 | + | 0.929121i | \(0.379435\pi\) | |||||||
\(54\) | −37.7892 | −5.14246 | ||||||||
\(55\) | −0.835616 | −0.112674 | ||||||||
\(56\) | −42.3150 | −5.65458 | ||||||||
\(57\) | 7.09710 | 0.940033 | ||||||||
\(58\) | −24.0381 | −3.15636 | ||||||||
\(59\) | −1.91259 | −0.248998 | −0.124499 | − | 0.992220i | \(-0.539732\pi\) | ||||
−0.124499 | + | 0.992220i | \(0.539732\pi\) | |||||||
\(60\) | 56.7378 | 7.32481 | ||||||||
\(61\) | 9.65500 | 1.23620 | 0.618098 | − | 0.786101i | \(-0.287904\pi\) | ||||
0.618098 | + | 0.786101i | \(0.287904\pi\) | |||||||
\(62\) | 4.26949 | 0.542226 | ||||||||
\(63\) | 31.2838 | 3.94139 | ||||||||
\(64\) | 34.7756 | 4.34695 | ||||||||
\(65\) | 3.17240 | 0.393488 | ||||||||
\(66\) | 2.32495 | 0.286181 | ||||||||
\(67\) | 3.85262 | 0.470673 | 0.235337 | − | 0.971914i | \(-0.424381\pi\) | ||||
0.235337 | + | 0.971914i | \(0.424381\pi\) | |||||||
\(68\) | −23.0697 | −2.79761 | ||||||||
\(69\) | −21.3378 | −2.56876 | ||||||||
\(70\) | −37.5206 | −4.48457 | ||||||||
\(71\) | −0.984946 | −0.116892 | −0.0584458 | − | 0.998291i | \(-0.518614\pi\) | ||||
−0.0584458 | + | 0.998291i | \(0.518614\pi\) | |||||||
\(72\) | −71.7118 | −8.45132 | ||||||||
\(73\) | −14.2783 | −1.67115 | −0.835575 | − | 0.549377i | \(-0.814865\pi\) | ||||
−0.835575 | + | 0.549377i | \(0.814865\pi\) | |||||||
\(74\) | −19.1405 | −2.22504 | ||||||||
\(75\) | 16.2379 | 1.87499 | ||||||||
\(76\) | 12.3458 | 1.41615 | ||||||||
\(77\) | −1.13170 | −0.128969 | ||||||||
\(78\) | −8.82662 | −0.999418 | ||||||||
\(79\) | 10.5549 | 1.18752 | 0.593762 | − | 0.804641i | \(-0.297642\pi\) | ||||
0.593762 | + | 0.804641i | \(0.297642\pi\) | |||||||
\(80\) | 50.6187 | 5.65934 | ||||||||
\(81\) | 22.1732 | 2.46369 | ||||||||
\(82\) | −3.57170 | −0.394428 | ||||||||
\(83\) | −14.5510 | −1.59718 | −0.798591 | − | 0.601874i | \(-0.794421\pi\) | ||||
−0.798591 | + | 0.601874i | \(0.794421\pi\) | |||||||
\(84\) | 76.8414 | 8.38409 | ||||||||
\(85\) | −13.1211 | −1.42318 | ||||||||
\(86\) | 20.6376 | 2.22541 | ||||||||
\(87\) | 27.9997 | 3.00188 | ||||||||
\(88\) | 2.59419 | 0.276541 | ||||||||
\(89\) | 9.36383 | 0.992564 | 0.496282 | − | 0.868161i | \(-0.334698\pi\) | ||||
0.496282 | + | 0.868161i | \(0.334698\pi\) | |||||||
\(90\) | −63.5867 | −6.70263 | ||||||||
\(91\) | 4.29647 | 0.450392 | ||||||||
\(92\) | −37.1181 | −3.86983 | ||||||||
\(93\) | −4.97312 | −0.515689 | ||||||||
\(94\) | 17.5306 | 1.80814 | ||||||||
\(95\) | 7.02175 | 0.720416 | ||||||||
\(96\) | −77.6779 | −7.92797 | ||||||||
\(97\) | −9.26914 | −0.941139 | −0.470569 | − | 0.882363i | \(-0.655951\pi\) | ||||
−0.470569 | + | 0.882363i | \(0.655951\pi\) | |||||||
\(98\) | −31.5458 | −3.18660 | ||||||||
\(99\) | −1.91790 | −0.192756 | ||||||||
\(100\) | 28.2465 | 2.82465 | ||||||||
\(101\) | −3.87237 | −0.385315 | −0.192658 | − | 0.981266i | \(-0.561711\pi\) | ||||
−0.192658 | + | 0.981266i | \(0.561711\pi\) | |||||||
\(102\) | 36.5070 | 3.61473 | ||||||||
\(103\) | 6.34530 | 0.625221 | 0.312611 | − | 0.949881i | \(-0.398797\pi\) | ||||
0.312611 | + | 0.949881i | \(0.398797\pi\) | |||||||
\(104\) | −9.84879 | −0.965753 | ||||||||
\(105\) | 43.7042 | 4.26509 | ||||||||
\(106\) | −14.8210 | −1.43954 | ||||||||
\(107\) | −17.5470 | −1.69633 | −0.848166 | − | 0.529731i | \(-0.822293\pi\) | ||||
−0.848166 | + | 0.529731i | \(0.822293\pi\) | |||||||
\(108\) | 76.5698 | 7.36794 | ||||||||
\(109\) | −4.66196 | −0.446534 | −0.223267 | − | 0.974757i | \(-0.571672\pi\) | ||||
−0.223267 | + | 0.974757i | \(0.571672\pi\) | |||||||
\(110\) | 2.30026 | 0.219321 | ||||||||
\(111\) | 22.2950 | 2.11615 | ||||||||
\(112\) | 68.5542 | 6.47777 | ||||||||
\(113\) | 2.03834 | 0.191751 | 0.0958754 | − | 0.995393i | \(-0.469435\pi\) | ||||
0.0958754 | + | 0.995393i | \(0.469435\pi\) | |||||||
\(114\) | −19.5367 | −1.82978 | ||||||||
\(115\) | −21.1112 | −1.96863 | ||||||||
\(116\) | 48.7068 | 4.52232 | ||||||||
\(117\) | 7.28128 | 0.673155 | ||||||||
\(118\) | 5.26493 | 0.484676 | ||||||||
\(119\) | −17.7702 | −1.62899 | ||||||||
\(120\) | −100.183 | −9.14543 | ||||||||
\(121\) | −10.9306 | −0.993693 | ||||||||
\(122\) | −26.5780 | −2.40626 | ||||||||
\(123\) | 4.16033 | 0.375125 | ||||||||
\(124\) | −8.65099 | −0.776882 | ||||||||
\(125\) | 0.203451 | 0.0181972 | ||||||||
\(126\) | −86.1172 | −7.67193 | ||||||||
\(127\) | −3.00347 | −0.266515 | −0.133257 | − | 0.991081i | \(-0.542544\pi\) | ||||
−0.133257 | + | 0.991081i | \(0.542544\pi\) | |||||||
\(128\) | −47.2783 | −4.17885 | ||||||||
\(129\) | −24.0388 | −2.11650 | ||||||||
\(130\) | −8.73291 | −0.765927 | ||||||||
\(131\) | 12.5394 | 1.09557 | 0.547786 | − | 0.836618i | \(-0.315471\pi\) | ||||
0.547786 | + | 0.836618i | \(0.315471\pi\) | |||||||
\(132\) | −4.71088 | −0.410030 | ||||||||
\(133\) | 9.50974 | 0.824599 | ||||||||
\(134\) | −10.6054 | −0.916168 | ||||||||
\(135\) | 43.5497 | 3.74816 | ||||||||
\(136\) | 40.7347 | 3.49297 | ||||||||
\(137\) | −18.3770 | −1.57005 | −0.785025 | − | 0.619464i | \(-0.787350\pi\) | ||||
−0.785025 | + | 0.619464i | \(0.787350\pi\) | |||||||
\(138\) | 58.7380 | 5.00011 | ||||||||
\(139\) | −15.9716 | −1.35469 | −0.677346 | − | 0.735665i | \(-0.736870\pi\) | ||||
−0.677346 | + | 0.735665i | \(0.736870\pi\) | |||||||
\(140\) | 76.0256 | 6.42534 | ||||||||
\(141\) | −20.4197 | −1.71965 | ||||||||
\(142\) | 2.71134 | 0.227530 | ||||||||
\(143\) | −0.263402 | −0.0220268 | ||||||||
\(144\) | 116.180 | 9.68165 | ||||||||
\(145\) | 27.7024 | 2.30056 | ||||||||
\(146\) | 39.3050 | 3.25290 | ||||||||
\(147\) | 36.7446 | 3.03065 | ||||||||
\(148\) | 38.7832 | 3.18796 | ||||||||
\(149\) | −16.1325 | −1.32163 | −0.660813 | − | 0.750550i | \(-0.729789\pi\) | ||||
−0.660813 | + | 0.750550i | \(0.729789\pi\) | |||||||
\(150\) | −44.6991 | −3.64967 | ||||||||
\(151\) | −3.08634 | −0.251163 | −0.125582 | − | 0.992083i | \(-0.540080\pi\) | ||||
−0.125582 | + | 0.992083i | \(0.540080\pi\) | |||||||
\(152\) | −21.7992 | −1.76815 | ||||||||
\(153\) | −30.1154 | −2.43469 | ||||||||
\(154\) | 3.11530 | 0.251038 | ||||||||
\(155\) | −4.92032 | −0.395210 | ||||||||
\(156\) | 17.8848 | 1.43193 | ||||||||
\(157\) | −1.38500 | −0.110535 | −0.0552676 | − | 0.998472i | \(-0.517601\pi\) | ||||
−0.0552676 | + | 0.998472i | \(0.517601\pi\) | |||||||
\(158\) | −29.0554 | −2.31152 | ||||||||
\(159\) | 17.2635 | 1.36909 | ||||||||
\(160\) | −76.8533 | −6.07578 | ||||||||
\(161\) | −28.5915 | −2.25332 | ||||||||
\(162\) | −61.0378 | −4.79559 | ||||||||
\(163\) | 0.685117 | 0.0536625 | 0.0268312 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268312 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(164\) | 7.23711 | 0.565123 | ||||||||
\(165\) | −2.67935 | −0.208587 | ||||||||
\(166\) | 40.0557 | 3.10892 | ||||||||
\(167\) | −12.1220 | −0.938031 | −0.469015 | − | 0.883190i | \(-0.655391\pi\) | ||||
−0.469015 | + | 0.883190i | \(0.655391\pi\) | |||||||
\(168\) | −135.681 | −10.4680 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 36.1194 | 2.77023 | ||||||||
\(171\) | 16.1163 | 1.23244 | ||||||||
\(172\) | −41.8166 | −3.18849 | ||||||||
\(173\) | 14.5772 | 1.10828 | 0.554140 | − | 0.832423i | \(-0.313047\pi\) | ||||
0.554140 | + | 0.832423i | \(0.313047\pi\) | |||||||
\(174\) | −77.0768 | −5.84318 | ||||||||
\(175\) | 21.7579 | 1.64474 | ||||||||
\(176\) | −4.20283 | −0.316800 | ||||||||
\(177\) | −6.13261 | −0.460956 | ||||||||
\(178\) | −25.7765 | −1.93203 | ||||||||
\(179\) | −0.995754 | −0.0744261 | −0.0372131 | − | 0.999307i | \(-0.511848\pi\) | ||||
−0.0372131 | + | 0.999307i | \(0.511848\pi\) | |||||||
\(180\) | 128.842 | 9.60329 | ||||||||
\(181\) | −16.9891 | −1.26279 | −0.631393 | − | 0.775463i | \(-0.717517\pi\) | ||||
−0.631393 | + | 0.775463i | \(0.717517\pi\) | |||||||
\(182\) | −11.8272 | −0.876691 | ||||||||
\(183\) | 30.9582 | 2.28850 | ||||||||
\(184\) | 65.5402 | 4.83169 | ||||||||
\(185\) | 22.0583 | 1.62176 | ||||||||
\(186\) | 13.6899 | 1.00379 | ||||||||
\(187\) | 1.08943 | 0.0796671 | ||||||||
\(188\) | −35.5211 | −2.59064 | ||||||||
\(189\) | 58.9805 | 4.29020 | ||||||||
\(190\) | −19.3293 | −1.40229 | ||||||||
\(191\) | 27.1499 | 1.96450 | 0.982248 | − | 0.187586i | \(-0.0600664\pi\) | ||||
0.982248 | + | 0.187586i | \(0.0600664\pi\) | |||||||
\(192\) | 111.506 | 8.04726 | ||||||||
\(193\) | −24.0330 | −1.72993 | −0.864967 | − | 0.501828i | \(-0.832661\pi\) | ||||
−0.864967 | + | 0.501828i | \(0.832661\pi\) | |||||||
\(194\) | 25.5159 | 1.83193 | ||||||||
\(195\) | 10.1721 | 0.728441 | ||||||||
\(196\) | 63.9191 | 4.56565 | ||||||||
\(197\) | −16.4922 | −1.17502 | −0.587510 | − | 0.809217i | \(-0.699892\pi\) | ||||
−0.587510 | + | 0.809217i | \(0.699892\pi\) | |||||||
\(198\) | 5.27955 | 0.375201 | ||||||||
\(199\) | 18.6551 | 1.32243 | 0.661214 | − | 0.750198i | \(-0.270042\pi\) | ||||
0.661214 | + | 0.750198i | \(0.270042\pi\) | |||||||
\(200\) | −49.8756 | −3.52673 | ||||||||
\(201\) | 12.3532 | 0.871329 | ||||||||
\(202\) | 10.6598 | 0.750018 | ||||||||
\(203\) | 37.5181 | 2.63326 | ||||||||
\(204\) | −73.9717 | −5.17905 | ||||||||
\(205\) | 4.11616 | 0.287485 | ||||||||
\(206\) | −17.4672 | −1.21700 | ||||||||
\(207\) | −48.4544 | −3.36781 | ||||||||
\(208\) | 15.9560 | 1.10635 | ||||||||
\(209\) | −0.583009 | −0.0403276 | ||||||||
\(210\) | −120.308 | −8.30203 | ||||||||
\(211\) | 11.4372 | 0.787369 | 0.393684 | − | 0.919246i | \(-0.371200\pi\) | ||||
0.393684 | + | 0.919246i | \(0.371200\pi\) | |||||||
\(212\) | 30.0308 | 2.06252 | ||||||||
\(213\) | −3.15818 | −0.216395 | ||||||||
\(214\) | 48.3029 | 3.30192 | ||||||||
\(215\) | −23.7835 | −1.62202 | ||||||||
\(216\) | −135.201 | −9.19927 | ||||||||
\(217\) | −6.66372 | −0.452363 | ||||||||
\(218\) | 12.8333 | 0.869182 | ||||||||
\(219\) | −45.7826 | −3.09370 | ||||||||
\(220\) | −4.66087 | −0.314236 | ||||||||
\(221\) | −4.13601 | −0.278218 | ||||||||
\(222\) | −61.3731 | −4.11909 | ||||||||
\(223\) | 3.80732 | 0.254957 | 0.127478 | − | 0.991841i | \(-0.459312\pi\) | ||||
0.127478 | + | 0.991841i | \(0.459312\pi\) | |||||||
\(224\) | −104.084 | −6.95443 | ||||||||
\(225\) | 36.8734 | 2.45822 | ||||||||
\(226\) | −5.61109 | −0.373244 | ||||||||
\(227\) | 2.60376 | 0.172818 | 0.0864089 | − | 0.996260i | \(-0.472461\pi\) | ||||
0.0864089 | + | 0.996260i | \(0.472461\pi\) | |||||||
\(228\) | 39.5860 | 2.62164 | ||||||||
\(229\) | 28.1232 | 1.85843 | 0.929215 | − | 0.369538i | \(-0.120484\pi\) | ||||
0.929215 | + | 0.369538i | \(0.120484\pi\) | |||||||
\(230\) | 58.1144 | 3.83195 | ||||||||
\(231\) | −3.62872 | −0.238752 | ||||||||
\(232\) | −86.0028 | −5.64636 | ||||||||
\(233\) | −6.75743 | −0.442694 | −0.221347 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221347 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(234\) | −20.0437 | −1.31030 | ||||||||
\(235\) | −20.2029 | −1.31789 | ||||||||
\(236\) | −10.6680 | −0.694427 | ||||||||
\(237\) | 33.8438 | 2.19839 | ||||||||
\(238\) | 48.9174 | 3.17085 | ||||||||
\(239\) | 17.0715 | 1.10427 | 0.552133 | − | 0.833756i | \(-0.313814\pi\) | ||||
0.552133 | + | 0.833756i | \(0.313814\pi\) | |||||||
\(240\) | 162.306 | 10.4768 | ||||||||
\(241\) | −8.81531 | −0.567844 | −0.283922 | − | 0.958847i | \(-0.591636\pi\) | ||||
−0.283922 | + | 0.958847i | \(0.591636\pi\) | |||||||
\(242\) | 30.0895 | 1.93423 | ||||||||
\(243\) | 29.9141 | 1.91899 | ||||||||
\(244\) | 53.8533 | 3.44761 | ||||||||
\(245\) | 36.3545 | 2.32261 | ||||||||
\(246\) | −11.4525 | −0.730182 | ||||||||
\(247\) | 2.21339 | 0.140834 | ||||||||
\(248\) | 15.2752 | 0.969979 | ||||||||
\(249\) | −46.6570 | −2.95677 | ||||||||
\(250\) | −0.560055 | −0.0354210 | ||||||||
\(251\) | 16.3569 | 1.03244 | 0.516219 | − | 0.856457i | \(-0.327339\pi\) | ||||
0.516219 | + | 0.856457i | \(0.327339\pi\) | |||||||
\(252\) | 174.494 | 10.9921 | ||||||||
\(253\) | 1.75285 | 0.110200 | ||||||||
\(254\) | 8.26787 | 0.518772 | ||||||||
\(255\) | −42.0720 | −2.63465 | ||||||||
\(256\) | 60.5953 | 3.78721 | ||||||||
\(257\) | 17.4386 | 1.08779 | 0.543897 | − | 0.839152i | \(-0.316948\pi\) | ||||
0.543897 | + | 0.839152i | \(0.316948\pi\) | |||||||
\(258\) | 66.1733 | 4.11977 | ||||||||
\(259\) | 29.8741 | 1.85629 | ||||||||
\(260\) | 17.6949 | 1.09739 | ||||||||
\(261\) | 63.5825 | 3.93566 | ||||||||
\(262\) | −34.5181 | −2.13254 | ||||||||
\(263\) | 8.55463 | 0.527501 | 0.263751 | − | 0.964591i | \(-0.415040\pi\) | ||||
0.263751 | + | 0.964591i | \(0.415040\pi\) | |||||||
\(264\) | 8.31811 | 0.511945 | ||||||||
\(265\) | 17.0802 | 1.04923 | ||||||||
\(266\) | −26.1782 | −1.60509 | ||||||||
\(267\) | 30.0246 | 1.83748 | ||||||||
\(268\) | 21.4890 | 1.31265 | ||||||||
\(269\) | −21.1997 | −1.29257 | −0.646283 | − | 0.763098i | \(-0.723677\pi\) | ||||
−0.646283 | + | 0.763098i | \(0.723677\pi\) | |||||||
\(270\) | −119.883 | −7.29582 | ||||||||
\(271\) | 6.62808 | 0.402627 | 0.201314 | − | 0.979527i | \(-0.435479\pi\) | ||||
0.201314 | + | 0.979527i | \(0.435479\pi\) | |||||||
\(272\) | −65.9940 | −4.00147 | ||||||||
\(273\) | 13.7764 | 0.833784 | ||||||||
\(274\) | 50.5876 | 3.05611 | ||||||||
\(275\) | −1.33390 | −0.0804372 | ||||||||
\(276\) | −119.017 | −7.16399 | ||||||||
\(277\) | −6.89556 | −0.414314 | −0.207157 | − | 0.978308i | \(-0.566421\pi\) | ||||
−0.207157 | + | 0.978308i | \(0.566421\pi\) | |||||||
\(278\) | 43.9662 | 2.63692 | ||||||||
\(279\) | −11.2931 | −0.676100 | ||||||||
\(280\) | −134.240 | −8.02238 | ||||||||
\(281\) | −30.7068 | −1.83182 | −0.915908 | − | 0.401388i | \(-0.868528\pi\) | ||||
−0.915908 | + | 0.401388i | \(0.868528\pi\) | |||||||
\(282\) | 56.2108 | 3.34731 | ||||||||
\(283\) | 23.8752 | 1.41924 | 0.709618 | − | 0.704587i | \(-0.248868\pi\) | ||||
0.709618 | + | 0.704587i | \(0.248868\pi\) | |||||||
\(284\) | −5.49380 | −0.325997 | ||||||||
\(285\) | 22.5148 | 1.33366 | ||||||||
\(286\) | 0.725085 | 0.0428752 | ||||||||
\(287\) | 5.57463 | 0.329060 | ||||||||
\(288\) | −176.393 | −10.3941 | ||||||||
\(289\) | 0.106572 | 0.00626894 | ||||||||
\(290\) | −76.2585 | −4.47805 | ||||||||
\(291\) | −29.7210 | −1.74228 | ||||||||
\(292\) | −79.6411 | −4.66064 | ||||||||
\(293\) | 24.2474 | 1.41655 | 0.708274 | − | 0.705938i | \(-0.249474\pi\) | ||||
0.708274 | + | 0.705938i | \(0.249474\pi\) | |||||||
\(294\) | −101.150 | −5.89917 | ||||||||
\(295\) | −6.06751 | −0.353264 | ||||||||
\(296\) | −68.4804 | −3.98034 | ||||||||
\(297\) | −3.61589 | −0.209816 | ||||||||
\(298\) | 44.4092 | 2.57255 | ||||||||
\(299\) | −6.65465 | −0.384848 | ||||||||
\(300\) | 90.5710 | 5.22912 | ||||||||
\(301\) | −32.2107 | −1.85659 | ||||||||
\(302\) | 8.49601 | 0.488890 | ||||||||
\(303\) | −12.4165 | −0.713311 | ||||||||
\(304\) | 35.3167 | 2.02555 | ||||||||
\(305\) | 30.6295 | 1.75384 | ||||||||
\(306\) | 82.9010 | 4.73914 | ||||||||
\(307\) | 25.4891 | 1.45474 | 0.727369 | − | 0.686247i | \(-0.240743\pi\) | ||||
0.727369 | + | 0.686247i | \(0.240743\pi\) | |||||||
\(308\) | −6.31234 | −0.359679 | ||||||||
\(309\) | 20.3459 | 1.15744 | ||||||||
\(310\) | 13.5445 | 0.769278 | ||||||||
\(311\) | 23.0889 | 1.30925 | 0.654627 | − | 0.755952i | \(-0.272826\pi\) | ||||
0.654627 | + | 0.755952i | \(0.272826\pi\) | |||||||
\(312\) | −31.5796 | −1.78784 | ||||||||
\(313\) | 3.94940 | 0.223233 | 0.111617 | − | 0.993751i | \(-0.464397\pi\) | ||||
0.111617 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(314\) | 3.81260 | 0.215157 | ||||||||
\(315\) | 99.2447 | 5.59181 | ||||||||
\(316\) | 58.8730 | 3.31187 | ||||||||
\(317\) | −19.4039 | −1.08983 | −0.544917 | − | 0.838490i | \(-0.683439\pi\) | ||||
−0.544917 | + | 0.838490i | \(0.683439\pi\) | |||||||
\(318\) | −47.5226 | −2.66494 | ||||||||
\(319\) | −2.30011 | −0.128781 | ||||||||
\(320\) | 110.322 | 6.16720 | ||||||||
\(321\) | −56.2634 | −3.14032 | ||||||||
\(322\) | 78.7059 | 4.38611 | ||||||||
\(323\) | −9.15458 | −0.509375 | ||||||||
\(324\) | 123.677 | 6.87094 | ||||||||
\(325\) | 5.06413 | 0.280907 | ||||||||
\(326\) | −1.88597 | −0.104454 | ||||||||
\(327\) | −14.9483 | −0.826643 | ||||||||
\(328\) | −12.7787 | −0.705587 | ||||||||
\(329\) | −27.3613 | −1.50848 | ||||||||
\(330\) | 7.37566 | 0.406017 | ||||||||
\(331\) | 1.76385 | 0.0969502 | 0.0484751 | − | 0.998824i | \(-0.484564\pi\) | ||||
0.0484751 | + | 0.998824i | \(0.484564\pi\) | |||||||
\(332\) | −81.1622 | −4.45435 | ||||||||
\(333\) | 50.6281 | 2.77440 | ||||||||
\(334\) | 33.3692 | 1.82588 | ||||||||
\(335\) | 12.2221 | 0.667763 | ||||||||
\(336\) | 219.815 | 11.9919 | ||||||||
\(337\) | −33.0416 | −1.79989 | −0.899946 | − | 0.436002i | \(-0.856394\pi\) | ||||
−0.899946 | + | 0.436002i | \(0.856394\pi\) | |||||||
\(338\) | −2.75277 | −0.149731 | ||||||||
\(339\) | 6.53582 | 0.354977 | ||||||||
\(340\) | −73.1863 | −3.96909 | ||||||||
\(341\) | 0.408530 | 0.0221231 | ||||||||
\(342\) | −44.3645 | −2.39896 | ||||||||
\(343\) | 19.1606 | 1.03458 | ||||||||
\(344\) | 73.8365 | 3.98100 | ||||||||
\(345\) | −67.6919 | −3.64441 | ||||||||
\(346\) | −40.1276 | −2.15727 | ||||||||
\(347\) | −21.3470 | −1.14597 | −0.572984 | − | 0.819567i | \(-0.694214\pi\) | ||||
−0.572984 | + | 0.819567i | \(0.694214\pi\) | |||||||
\(348\) | 156.176 | 8.37190 | ||||||||
\(349\) | −31.1499 | −1.66742 | −0.833709 | − | 0.552204i | \(-0.813787\pi\) | ||||
−0.833709 | + | 0.552204i | \(0.813787\pi\) | |||||||
\(350\) | −59.8945 | −3.20150 | ||||||||
\(351\) | 13.7277 | 0.732730 | ||||||||
\(352\) | 6.38106 | 0.340111 | ||||||||
\(353\) | 23.0819 | 1.22853 | 0.614263 | − | 0.789102i | \(-0.289454\pi\) | ||||
0.614263 | + | 0.789102i | \(0.289454\pi\) | |||||||
\(354\) | 16.8817 | 0.897252 | ||||||||
\(355\) | −3.12465 | −0.165839 | ||||||||
\(356\) | 52.2293 | 2.76815 | ||||||||
\(357\) | −56.9792 | −3.01566 | ||||||||
\(358\) | 2.74109 | 0.144871 | ||||||||
\(359\) | 0.0369949 | 0.00195252 | 0.000976259 | − | 1.00000i | \(-0.499689\pi\) | ||||
0.000976259 | 1.00000i | \(0.499689\pi\) | ||||||||
\(360\) | −227.499 | −11.9902 | ||||||||
\(361\) | −14.1009 | −0.742154 | ||||||||
\(362\) | 46.7670 | 2.45802 | ||||||||
\(363\) | −35.0484 | −1.83956 | ||||||||
\(364\) | 23.9647 | 1.25609 | ||||||||
\(365\) | −45.2965 | −2.37093 | ||||||||
\(366\) | −85.2209 | −4.45457 | ||||||||
\(367\) | −25.7029 | −1.34168 | −0.670841 | − | 0.741601i | \(-0.734067\pi\) | ||||
−0.670841 | + | 0.741601i | \(0.734067\pi\) | |||||||
\(368\) | −106.181 | −5.53508 | ||||||||
\(369\) | 9.44740 | 0.491812 | ||||||||
\(370\) | −60.7215 | −3.15676 | ||||||||
\(371\) | 23.1322 | 1.20097 | ||||||||
\(372\) | −27.7389 | −1.43820 | ||||||||
\(373\) | 19.4748 | 1.00837 | 0.504183 | − | 0.863597i | \(-0.331794\pi\) | ||||
0.504183 | + | 0.863597i | \(0.331794\pi\) | |||||||
\(374\) | −2.99896 | −0.155073 | ||||||||
\(375\) | 0.652355 | 0.0336875 | ||||||||
\(376\) | 62.7203 | 3.23455 | ||||||||
\(377\) | 8.73232 | 0.449737 | ||||||||
\(378\) | −162.360 | −8.35090 | ||||||||
\(379\) | 25.7206 | 1.32118 | 0.660588 | − | 0.750748i | \(-0.270307\pi\) | ||||
0.660588 | + | 0.750748i | \(0.270307\pi\) | |||||||
\(380\) | 39.1657 | 2.00916 | ||||||||
\(381\) | −9.63045 | −0.493383 | ||||||||
\(382\) | −74.7375 | −3.82390 | ||||||||
\(383\) | 15.7957 | 0.807124 | 0.403562 | − | 0.914952i | \(-0.367772\pi\) | ||||
0.403562 | + | 0.914952i | \(0.367772\pi\) | |||||||
\(384\) | −151.595 | −7.73607 | ||||||||
\(385\) | −3.59020 | −0.182973 | ||||||||
\(386\) | 66.1575 | 3.36733 | ||||||||
\(387\) | −54.5879 | −2.77486 | ||||||||
\(388\) | −51.7011 | −2.62473 | ||||||||
\(389\) | 36.3914 | 1.84512 | 0.922559 | − | 0.385857i | \(-0.126094\pi\) | ||||
0.922559 | + | 0.385857i | \(0.126094\pi\) | |||||||
\(390\) | −28.0016 | −1.41791 | ||||||||
\(391\) | 27.5237 | 1.39193 | ||||||||
\(392\) | −112.863 | −5.70046 | ||||||||
\(393\) | 40.2069 | 2.02817 | ||||||||
\(394\) | 45.3993 | 2.28718 | ||||||||
\(395\) | 33.4845 | 1.68479 | ||||||||
\(396\) | −10.6976 | −0.537575 | ||||||||
\(397\) | 10.5672 | 0.530354 | 0.265177 | − | 0.964200i | \(-0.414570\pi\) | ||||
0.265177 | + | 0.964200i | \(0.414570\pi\) | |||||||
\(398\) | −51.3534 | −2.57411 | ||||||||
\(399\) | 30.4924 | 1.52653 | ||||||||
\(400\) | 80.8031 | 4.04015 | ||||||||
\(401\) | −27.0427 | −1.35045 | −0.675225 | − | 0.737612i | \(-0.735954\pi\) | ||||
−0.675225 | + | 0.737612i | \(0.735954\pi\) | |||||||
\(402\) | −34.0056 | −1.69605 | ||||||||
\(403\) | −1.55098 | −0.0772597 | ||||||||
\(404\) | −21.5992 | −1.07460 | ||||||||
\(405\) | 70.3423 | 3.49534 | ||||||||
\(406\) | −103.279 | −5.12565 | ||||||||
\(407\) | −1.83148 | −0.0907831 | ||||||||
\(408\) | 130.613 | 6.46633 | ||||||||
\(409\) | 6.05597 | 0.299449 | 0.149724 | − | 0.988728i | \(-0.452161\pi\) | ||||
0.149724 | + | 0.988728i | \(0.452161\pi\) | |||||||
\(410\) | −11.3309 | −0.559592 | ||||||||
\(411\) | −58.9247 | −2.90654 | ||||||||
\(412\) | 35.3926 | 1.74367 | ||||||||
\(413\) | −8.21738 | −0.404351 | ||||||||
\(414\) | 133.384 | 6.55546 | ||||||||
\(415\) | −46.1617 | −2.26599 | ||||||||
\(416\) | −24.2256 | −1.18776 | ||||||||
\(417\) | −51.2120 | −2.50786 | ||||||||
\(418\) | 1.60489 | 0.0784979 | ||||||||
\(419\) | 8.89765 | 0.434679 | 0.217339 | − | 0.976096i | \(-0.430262\pi\) | ||||
0.217339 | + | 0.976096i | \(0.430262\pi\) | |||||||
\(420\) | 243.772 | 11.8949 | ||||||||
\(421\) | 22.5612 | 1.09957 | 0.549783 | − | 0.835308i | \(-0.314711\pi\) | ||||
0.549783 | + | 0.835308i | \(0.314711\pi\) | |||||||
\(422\) | −31.4840 | −1.53262 | ||||||||
\(423\) | −46.3696 | −2.25457 | ||||||||
\(424\) | −53.0260 | −2.57517 | ||||||||
\(425\) | −20.9453 | −1.01600 | ||||||||
\(426\) | 8.69374 | 0.421213 | ||||||||
\(427\) | 41.4824 | 2.00747 | ||||||||
\(428\) | −97.8730 | −4.73087 | ||||||||
\(429\) | −0.844582 | −0.0407768 | ||||||||
\(430\) | 65.4707 | 3.15728 | ||||||||
\(431\) | −11.4635 | −0.552176 | −0.276088 | − | 0.961132i | \(-0.589038\pi\) | ||||
−0.276088 | + | 0.961132i | \(0.589038\pi\) | |||||||
\(432\) | 219.038 | 10.5385 | ||||||||
\(433\) | 3.19450 | 0.153518 | 0.0767590 | − | 0.997050i | \(-0.475543\pi\) | ||||
0.0767590 | + | 0.997050i | \(0.475543\pi\) | |||||||
\(434\) | 18.3437 | 0.880527 | ||||||||
\(435\) | 88.8263 | 4.25889 | ||||||||
\(436\) | −26.0033 | −1.24533 | ||||||||
\(437\) | −14.7293 | −0.704598 | ||||||||
\(438\) | 126.029 | 6.02190 | ||||||||
\(439\) | −21.0644 | −1.00535 | −0.502676 | − | 0.864475i | \(-0.667651\pi\) | ||||
−0.502676 | + | 0.864475i | \(0.667651\pi\) | |||||||
\(440\) | 8.22980 | 0.392340 | ||||||||
\(441\) | 83.4408 | 3.97337 | ||||||||
\(442\) | 11.3855 | 0.541553 | ||||||||
\(443\) | 8.00724 | 0.380435 | 0.190218 | − | 0.981742i | \(-0.439081\pi\) | ||||
0.190218 | + | 0.981742i | \(0.439081\pi\) | |||||||
\(444\) | 124.356 | 5.90169 | ||||||||
\(445\) | 29.7058 | 1.40819 | ||||||||
\(446\) | −10.4807 | −0.496275 | ||||||||
\(447\) | −51.7280 | −2.44665 | ||||||||
\(448\) | 149.412 | 7.05907 | ||||||||
\(449\) | −37.6623 | −1.77739 | −0.888697 | − | 0.458496i | \(-0.848388\pi\) | ||||
−0.888697 | + | 0.458496i | \(0.848388\pi\) | |||||||
\(450\) | −101.504 | −4.78495 | ||||||||
\(451\) | −0.341761 | −0.0160929 | ||||||||
\(452\) | 11.3694 | 0.534771 | ||||||||
\(453\) | −9.89619 | −0.464964 | ||||||||
\(454\) | −7.16757 | −0.336391 | ||||||||
\(455\) | 13.6301 | 0.638990 | ||||||||
\(456\) | −69.8978 | −3.27326 | ||||||||
\(457\) | 30.8556 | 1.44337 | 0.721683 | − | 0.692224i | \(-0.243369\pi\) | ||||
0.721683 | + | 0.692224i | \(0.243369\pi\) | |||||||
\(458\) | −77.4167 | −3.61745 | ||||||||
\(459\) | −56.7778 | −2.65016 | ||||||||
\(460\) | −117.753 | −5.49029 | ||||||||
\(461\) | 19.4842 | 0.907470 | 0.453735 | − | 0.891137i | \(-0.350091\pi\) | ||||
0.453735 | + | 0.891137i | \(0.350091\pi\) | |||||||
\(462\) | 9.98905 | 0.464733 | ||||||||
\(463\) | 10.8825 | 0.505750 | 0.252875 | − | 0.967499i | \(-0.418624\pi\) | ||||
0.252875 | + | 0.967499i | \(0.418624\pi\) | |||||||
\(464\) | 139.333 | 6.46835 | ||||||||
\(465\) | −15.7767 | −0.731629 | ||||||||
\(466\) | 18.6017 | 0.861707 | ||||||||
\(467\) | 25.1089 | 1.16190 | 0.580951 | − | 0.813939i | \(-0.302681\pi\) | ||||
0.580951 | + | 0.813939i | \(0.302681\pi\) | |||||||
\(468\) | 40.6133 | 1.87735 | ||||||||
\(469\) | 16.5527 | 0.764331 | ||||||||
\(470\) | 55.6140 | 2.56528 | ||||||||
\(471\) | −4.44093 | −0.204627 | ||||||||
\(472\) | 18.8367 | 0.867029 | ||||||||
\(473\) | 1.97473 | 0.0907980 | ||||||||
\(474\) | −93.1645 | −4.27919 | ||||||||
\(475\) | 11.2089 | 0.514298 | ||||||||
\(476\) | −99.1182 | −4.54307 | ||||||||
\(477\) | 39.2025 | 1.79496 | ||||||||
\(478\) | −46.9941 | −2.14946 | ||||||||
\(479\) | −17.0339 | −0.778300 | −0.389150 | − | 0.921174i | \(-0.627231\pi\) | ||||
−0.389150 | + | 0.921174i | \(0.627231\pi\) | |||||||
\(480\) | −246.426 | −11.2477 | ||||||||
\(481\) | 6.95318 | 0.317038 | ||||||||
\(482\) | 24.2666 | 1.10531 | ||||||||
\(483\) | −91.6770 | −4.17145 | ||||||||
\(484\) | −60.9685 | −2.77129 | ||||||||
\(485\) | −29.4054 | −1.33523 | ||||||||
\(486\) | −82.3467 | −3.73532 | ||||||||
\(487\) | −34.9925 | −1.58566 | −0.792830 | − | 0.609443i | \(-0.791393\pi\) | ||||
−0.792830 | + | 0.609443i | \(0.791393\pi\) | |||||||
\(488\) | −95.0900 | −4.30452 | ||||||||
\(489\) | 2.19679 | 0.0993422 | ||||||||
\(490\) | −100.076 | −4.52097 | ||||||||
\(491\) | −22.8146 | −1.02961 | −0.514804 | − | 0.857308i | \(-0.672135\pi\) | ||||
−0.514804 | + | 0.857308i | \(0.672135\pi\) | |||||||
\(492\) | 23.2054 | 1.04618 | ||||||||
\(493\) | −36.1170 | −1.62663 | ||||||||
\(494\) | −6.09295 | −0.274135 | ||||||||
\(495\) | −6.08435 | −0.273471 | ||||||||
\(496\) | −24.7473 | −1.11119 | ||||||||
\(497\) | −4.23179 | −0.189822 | ||||||||
\(498\) | 128.436 | 5.75537 | ||||||||
\(499\) | −6.12172 | −0.274046 | −0.137023 | − | 0.990568i | \(-0.543753\pi\) | ||||
−0.137023 | + | 0.990568i | \(0.543753\pi\) | |||||||
\(500\) | 1.13480 | 0.0507500 | ||||||||
\(501\) | −38.8686 | −1.73652 | ||||||||
\(502\) | −45.0268 | −2.00965 | ||||||||
\(503\) | −6.01625 | −0.268251 | −0.134126 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134126 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(504\) | −308.107 | −13.7242 | ||||||||
\(505\) | −12.2847 | −0.546662 | ||||||||
\(506\) | −4.82519 | −0.214506 | ||||||||
\(507\) | 3.20644 | 0.142403 | ||||||||
\(508\) | −16.7526 | −0.743278 | ||||||||
\(509\) | −1.37514 | −0.0609519 | −0.0304759 | − | 0.999536i | \(-0.509702\pi\) | ||||
−0.0304759 | + | 0.999536i | \(0.509702\pi\) | |||||||
\(510\) | 115.815 | 5.12836 | ||||||||
\(511\) | −61.3463 | −2.71380 | ||||||||
\(512\) | −72.2486 | −3.19297 | ||||||||
\(513\) | 30.3847 | 1.34152 | ||||||||
\(514\) | −48.0047 | −2.11740 | ||||||||
\(515\) | 20.1298 | 0.887027 | ||||||||
\(516\) | −134.083 | −5.90266 | ||||||||
\(517\) | 1.67743 | 0.0737732 | ||||||||
\(518\) | −82.2367 | −3.61327 | ||||||||
\(519\) | 46.7408 | 2.05169 | ||||||||
\(520\) | −31.2443 | −1.37015 | ||||||||
\(521\) | 5.75248 | 0.252021 | 0.126010 | − | 0.992029i | \(-0.459783\pi\) | ||||
0.126010 | + | 0.992029i | \(0.459783\pi\) | |||||||
\(522\) | −175.028 | −7.66078 | ||||||||
\(523\) | −25.3691 | −1.10931 | −0.554657 | − | 0.832079i | \(-0.687150\pi\) | ||||
−0.554657 | + | 0.832079i | \(0.687150\pi\) | |||||||
\(524\) | 69.9419 | 3.05542 | ||||||||
\(525\) | 69.7654 | 3.04481 | ||||||||
\(526\) | −23.5490 | −1.02678 | ||||||||
\(527\) | 6.41486 | 0.279436 | ||||||||
\(528\) | −13.4761 | −0.586473 | ||||||||
\(529\) | 21.2844 | 0.925407 | ||||||||
\(530\) | −47.0181 | −2.04233 | ||||||||
\(531\) | −13.9261 | −0.604342 | ||||||||
\(532\) | 53.0431 | 2.29971 | ||||||||
\(533\) | 1.29749 | 0.0562006 | ||||||||
\(534\) | −82.6510 | −3.57666 | ||||||||
\(535\) | −55.6661 | −2.40666 | ||||||||
\(536\) | −37.9437 | −1.63892 | ||||||||
\(537\) | −3.19283 | −0.137781 | ||||||||
\(538\) | 58.3579 | 2.51599 | ||||||||
\(539\) | −3.01848 | −0.130015 | ||||||||
\(540\) | 242.910 | 10.4532 | ||||||||
\(541\) | −2.94516 | −0.126622 | −0.0633112 | − | 0.997994i | \(-0.520166\pi\) | ||||
−0.0633112 | + | 0.997994i | \(0.520166\pi\) | |||||||
\(542\) | −18.2456 | −0.783716 | ||||||||
\(543\) | −54.4744 | −2.33772 | ||||||||
\(544\) | 100.197 | 4.29592 | ||||||||
\(545\) | −14.7896 | −0.633517 | ||||||||
\(546\) | −37.9233 | −1.62297 | ||||||||
\(547\) | −39.4876 | −1.68837 | −0.844185 | − | 0.536053i | \(-0.819915\pi\) | ||||
−0.844185 | + | 0.536053i | \(0.819915\pi\) | |||||||
\(548\) | −102.502 | −4.37869 | ||||||||
\(549\) | 70.3007 | 3.00036 | ||||||||
\(550\) | 3.67193 | 0.156572 | ||||||||
\(551\) | 19.3280 | 0.823400 | ||||||||
\(552\) | 210.151 | 8.94462 | ||||||||
\(553\) | 45.3490 | 1.92843 | ||||||||
\(554\) | 18.9819 | 0.806464 | ||||||||
\(555\) | 70.7286 | 3.00226 | ||||||||
\(556\) | −89.0858 | −3.77808 | ||||||||
\(557\) | 5.88433 | 0.249327 | 0.124664 | − | 0.992199i | \(-0.460215\pi\) | ||||
0.124664 | + | 0.992199i | \(0.460215\pi\) | |||||||
\(558\) | 31.0874 | 1.31603 | ||||||||
\(559\) | −7.49702 | −0.317090 | ||||||||
\(560\) | 217.482 | 9.19027 | ||||||||
\(561\) | 3.49320 | 0.147483 | ||||||||
\(562\) | 84.5290 | 3.56564 | ||||||||
\(563\) | 18.8957 | 0.796358 | 0.398179 | − | 0.917308i | \(-0.369642\pi\) | ||||
0.398179 | + | 0.917308i | \(0.369642\pi\) | |||||||
\(564\) | −113.896 | −4.79590 | ||||||||
\(565\) | 6.46643 | 0.272045 | ||||||||
\(566\) | −65.7231 | −2.76255 | ||||||||
\(567\) | 95.2665 | 4.00081 | ||||||||
\(568\) | 9.70053 | 0.407025 | ||||||||
\(569\) | 7.76020 | 0.325324 | 0.162662 | − | 0.986682i | \(-0.447992\pi\) | ||||
0.162662 | + | 0.986682i | \(0.447992\pi\) | |||||||
\(570\) | −61.9783 | −2.59598 | ||||||||
\(571\) | −10.0504 | −0.420597 | −0.210299 | − | 0.977637i | \(-0.567444\pi\) | ||||
−0.210299 | + | 0.977637i | \(0.567444\pi\) | |||||||
\(572\) | −1.46919 | −0.0614301 | ||||||||
\(573\) | 87.0546 | 3.63676 | ||||||||
\(574\) | −15.3457 | −0.640517 | ||||||||
\(575\) | −33.7000 | −1.40539 | ||||||||
\(576\) | 253.211 | 10.5505 | ||||||||
\(577\) | −21.6345 | −0.900656 | −0.450328 | − | 0.892863i | \(-0.648693\pi\) | ||||
−0.450328 | + | 0.892863i | \(0.648693\pi\) | |||||||
\(578\) | −0.293368 | −0.0122025 | ||||||||
\(579\) | −77.0605 | −3.20253 | ||||||||
\(580\) | 154.518 | 6.41600 | ||||||||
\(581\) | −62.5180 | −2.59368 | ||||||||
\(582\) | 81.8152 | 3.39135 | ||||||||
\(583\) | −1.41816 | −0.0587341 | ||||||||
\(584\) | 140.624 | 5.81906 | ||||||||
\(585\) | 23.0991 | 0.955032 | ||||||||
\(586\) | −66.7476 | −2.75732 | ||||||||
\(587\) | −22.8695 | −0.943927 | −0.471963 | − | 0.881618i | \(-0.656455\pi\) | ||||
−0.471963 | + | 0.881618i | \(0.656455\pi\) | |||||||
\(588\) | 204.953 | 8.45212 | ||||||||
\(589\) | −3.43291 | −0.141451 | ||||||||
\(590\) | 16.7025 | 0.687630 | ||||||||
\(591\) | −52.8813 | −2.17525 | ||||||||
\(592\) | 110.945 | 4.55980 | ||||||||
\(593\) | 42.5958 | 1.74920 | 0.874600 | − | 0.484845i | \(-0.161124\pi\) | ||||
0.874600 | + | 0.484845i | \(0.161124\pi\) | |||||||
\(594\) | 9.95374 | 0.408407 | ||||||||
\(595\) | −56.3743 | −2.31112 | ||||||||
\(596\) | −89.9834 | −3.68586 | ||||||||
\(597\) | 59.8166 | 2.44813 | ||||||||
\(598\) | 18.3188 | 0.749109 | ||||||||
\(599\) | −28.6069 | −1.16885 | −0.584423 | − | 0.811449i | \(-0.698679\pi\) | ||||
−0.584423 | + | 0.811449i | \(0.698679\pi\) | |||||||
\(600\) | −159.923 | −6.52884 | ||||||||
\(601\) | −0.863777 | −0.0352342 | −0.0176171 | − | 0.999845i | \(-0.505608\pi\) | ||||
−0.0176171 | + | 0.999845i | \(0.505608\pi\) | |||||||
\(602\) | 88.6688 | 3.61387 | ||||||||
\(603\) | 28.0520 | 1.14237 | ||||||||
\(604\) | −17.2149 | −0.700465 | ||||||||
\(605\) | −34.6763 | −1.40979 | ||||||||
\(606\) | 34.1799 | 1.38846 | ||||||||
\(607\) | 34.2041 | 1.38830 | 0.694152 | − | 0.719829i | \(-0.255780\pi\) | ||||
0.694152 | + | 0.719829i | \(0.255780\pi\) | |||||||
\(608\) | −53.6205 | −2.17460 | ||||||||
\(609\) | 120.300 | 4.87479 | ||||||||
\(610\) | −84.3162 | −3.41386 | ||||||||
\(611\) | −6.36833 | −0.257635 | ||||||||
\(612\) | −167.977 | −6.79007 | ||||||||
\(613\) | 2.10108 | 0.0848619 | 0.0424309 | − | 0.999099i | \(-0.486490\pi\) | ||||
0.0424309 | + | 0.999099i | \(0.486490\pi\) | |||||||
\(614\) | −70.1656 | −2.83166 | ||||||||
\(615\) | 13.1982 | 0.532205 | ||||||||
\(616\) | 11.1458 | 0.449079 | ||||||||
\(617\) | −1.00000 | −0.0402585 | ||||||||
\(618\) | −56.0076 | −2.25295 | ||||||||
\(619\) | 41.1047 | 1.65214 | 0.826069 | − | 0.563569i | \(-0.190572\pi\) | ||||
0.826069 | + | 0.563569i | \(0.190572\pi\) | |||||||
\(620\) | −27.4444 | −1.10219 | ||||||||
\(621\) | −91.3529 | −3.66587 | ||||||||
\(622\) | −63.5587 | −2.54847 | ||||||||
\(623\) | 40.2314 | 1.61184 | ||||||||
\(624\) | 51.1619 | 2.04811 | ||||||||
\(625\) | −24.6752 | −0.987009 | ||||||||
\(626\) | −10.8718 | −0.434525 | ||||||||
\(627\) | −1.86939 | −0.0746561 | ||||||||
\(628\) | −7.72522 | −0.308270 | ||||||||
\(629\) | −28.7584 | −1.14667 | ||||||||
\(630\) | −273.198 | −10.8845 | ||||||||
\(631\) | −23.4955 | −0.935341 | −0.467671 | − | 0.883903i | \(-0.654907\pi\) | ||||
−0.467671 | + | 0.883903i | \(0.654907\pi\) | |||||||
\(632\) | −103.953 | −4.13504 | ||||||||
\(633\) | 36.6727 | 1.45761 | ||||||||
\(634\) | 53.4146 | 2.12137 | ||||||||
\(635\) | −9.52821 | −0.378115 | ||||||||
\(636\) | 96.2920 | 3.81822 | ||||||||
\(637\) | 11.4596 | 0.454047 | ||||||||
\(638\) | 6.33168 | 0.250673 | ||||||||
\(639\) | −7.17167 | −0.283707 | ||||||||
\(640\) | −149.986 | −5.92871 | ||||||||
\(641\) | 30.7230 | 1.21349 | 0.606743 | − | 0.794898i | \(-0.292476\pi\) | ||||
0.606743 | + | 0.794898i | \(0.292476\pi\) | |||||||
\(642\) | 154.881 | 6.11265 | ||||||||
\(643\) | −30.3677 | −1.19759 | −0.598793 | − | 0.800904i | \(-0.704353\pi\) | ||||
−0.598793 | + | 0.800904i | \(0.704353\pi\) | |||||||
\(644\) | −159.477 | −6.28426 | ||||||||
\(645\) | −76.2606 | −3.00276 | ||||||||
\(646\) | 25.2005 | 0.991501 | ||||||||
\(647\) | 20.5713 | 0.808741 | 0.404370 | − | 0.914595i | \(-0.367491\pi\) | ||||
0.404370 | + | 0.914595i | \(0.367491\pi\) | |||||||
\(648\) | −218.379 | −8.57875 | ||||||||
\(649\) | 0.503780 | 0.0197751 | ||||||||
\(650\) | −13.9404 | −0.546788 | ||||||||
\(651\) | −21.3669 | −0.837433 | ||||||||
\(652\) | 3.82142 | 0.149658 | ||||||||
\(653\) | −39.5346 | −1.54711 | −0.773554 | − | 0.633731i | \(-0.781523\pi\) | ||||
−0.773554 | + | 0.633731i | \(0.781523\pi\) | |||||||
\(654\) | 41.1493 | 1.60907 | ||||||||
\(655\) | 39.7800 | 1.55433 | ||||||||
\(656\) | 20.7027 | 0.808305 | ||||||||
\(657\) | −103.964 | −4.05604 | ||||||||
\(658\) | 75.3196 | 2.93626 | ||||||||
\(659\) | −14.3977 | −0.560853 | −0.280427 | − | 0.959875i | \(-0.590476\pi\) | ||||
−0.280427 | + | 0.959875i | \(0.590476\pi\) | |||||||
\(660\) | −14.9448 | −0.581726 | ||||||||
\(661\) | −34.7869 | −1.35305 | −0.676526 | − | 0.736418i | \(-0.736516\pi\) | ||||
−0.676526 | + | 0.736418i | \(0.736516\pi\) | |||||||
\(662\) | −4.85549 | −0.188714 | ||||||||
\(663\) | −13.2619 | −0.515049 | ||||||||
\(664\) | 143.310 | 5.56150 | ||||||||
\(665\) | 30.1687 | 1.16989 | ||||||||
\(666\) | −139.368 | −5.40039 | ||||||||
\(667\) | −58.1105 | −2.25005 | ||||||||
\(668\) | −67.6139 | −2.61606 | ||||||||
\(669\) | 12.2080 | 0.471987 | ||||||||
\(670\) | −33.6446 | −1.29980 | ||||||||
\(671\) | −2.54314 | −0.0981769 | ||||||||
\(672\) | −333.741 | −12.8743 | ||||||||
\(673\) | −28.7714 | −1.10906 | −0.554528 | − | 0.832165i | \(-0.687101\pi\) | ||||
−0.554528 | + | 0.832165i | \(0.687101\pi\) | |||||||
\(674\) | 90.9561 | 3.50350 | ||||||||
\(675\) | 69.5188 | 2.67578 | ||||||||
\(676\) | 5.57777 | 0.214530 | ||||||||
\(677\) | 10.2175 | 0.392690 | 0.196345 | − | 0.980535i | \(-0.437093\pi\) | ||||
0.196345 | + | 0.980535i | \(0.437093\pi\) | |||||||
\(678\) | −17.9916 | −0.690964 | ||||||||
\(679\) | −39.8246 | −1.52833 | ||||||||
\(680\) | 129.227 | 4.95562 | ||||||||
\(681\) | 8.34882 | 0.319927 | ||||||||
\(682\) | −1.12459 | −0.0430628 | ||||||||
\(683\) | −31.1954 | −1.19366 | −0.596830 | − | 0.802368i | \(-0.703573\pi\) | ||||
−0.596830 | + | 0.802368i | \(0.703573\pi\) | |||||||
\(684\) | 89.8929 | 3.43714 | ||||||||
\(685\) | −58.2991 | −2.22749 | ||||||||
\(686\) | −52.7449 | −2.01381 | ||||||||
\(687\) | 90.1753 | 3.44040 | ||||||||
\(688\) | −119.622 | −4.56055 | ||||||||
\(689\) | 5.38401 | 0.205114 | ||||||||
\(690\) | 186.341 | 7.09387 | ||||||||
\(691\) | −10.7091 | −0.407392 | −0.203696 | − | 0.979034i | \(-0.565295\pi\) | ||||
−0.203696 | + | 0.979034i | \(0.565295\pi\) | |||||||
\(692\) | 81.3080 | 3.09087 | ||||||||
\(693\) | −8.24020 | −0.313019 | ||||||||
\(694\) | 58.7635 | 2.23063 | ||||||||
\(695\) | −50.6683 | −1.92196 | ||||||||
\(696\) | −275.763 | −10.4528 | ||||||||
\(697\) | −5.36644 | −0.203268 | ||||||||
\(698\) | 85.7487 | 3.24564 | ||||||||
\(699\) | −21.6673 | −0.819534 | ||||||||
\(700\) | 121.360 | 4.58699 | ||||||||
\(701\) | 0.411144 | 0.0155287 | 0.00776435 | − | 0.999970i | \(-0.497529\pi\) | ||||
0.00776435 | + | 0.999970i | \(0.497529\pi\) | |||||||
\(702\) | −37.7892 | −1.42626 | ||||||||
\(703\) | 15.3901 | 0.580447 | ||||||||
\(704\) | −9.15996 | −0.345229 | ||||||||
\(705\) | −64.7795 | −2.43974 | ||||||||
\(706\) | −63.5393 | −2.39133 | ||||||||
\(707\) | −16.6375 | −0.625718 | ||||||||
\(708\) | −34.2063 | −1.28555 | ||||||||
\(709\) | 13.3940 | 0.503021 | 0.251510 | − | 0.967855i | \(-0.419073\pi\) | ||||
0.251510 | + | 0.967855i | \(0.419073\pi\) | |||||||
\(710\) | 8.60144 | 0.322806 | ||||||||
\(711\) | 76.8535 | 2.88223 | ||||||||
\(712\) | −92.2224 | −3.45618 | ||||||||
\(713\) | 10.3212 | 0.386532 | ||||||||
\(714\) | 156.851 | 5.87000 | ||||||||
\(715\) | −0.835616 | −0.0312503 | ||||||||
\(716\) | −5.55408 | −0.207566 | ||||||||
\(717\) | 54.7389 | 2.04426 | ||||||||
\(718\) | −0.101839 | −0.00380059 | ||||||||
\(719\) | −11.2494 | −0.419532 | −0.209766 | − | 0.977752i | \(-0.567270\pi\) | ||||
−0.209766 | + | 0.977752i | \(0.567270\pi\) | |||||||
\(720\) | 368.569 | 13.7358 | ||||||||
\(721\) | 27.2624 | 1.01530 | ||||||||
\(722\) | 38.8167 | 1.44461 | ||||||||
\(723\) | −28.2658 | −1.05122 | ||||||||
\(724\) | −94.7610 | −3.52176 | ||||||||
\(725\) | 44.2216 | 1.64235 | ||||||||
\(726\) | 96.4804 | 3.58072 | ||||||||
\(727\) | 40.5949 | 1.50558 | 0.752790 | − | 0.658260i | \(-0.228707\pi\) | ||||
0.752790 | + | 0.658260i | \(0.228707\pi\) | |||||||
\(728\) | −42.3150 | −1.56830 | ||||||||
\(729\) | 29.3982 | 1.08882 | ||||||||
\(730\) | 124.691 | 4.61502 | ||||||||
\(731\) | 31.0077 | 1.14686 | ||||||||
\(732\) | 172.678 | 6.38235 | ||||||||
\(733\) | 26.3672 | 0.973893 | 0.486947 | − | 0.873432i | \(-0.338111\pi\) | ||||
0.486947 | + | 0.873432i | \(0.338111\pi\) | |||||||
\(734\) | 70.7543 | 2.61159 | ||||||||
\(735\) | 116.569 | 4.29970 | ||||||||
\(736\) | 161.213 | 5.94238 | ||||||||
\(737\) | −1.01479 | −0.0373802 | ||||||||
\(738\) | −26.0066 | −0.957315 | ||||||||
\(739\) | −12.2731 | −0.451474 | −0.225737 | − | 0.974188i | \(-0.572479\pi\) | ||||
−0.225737 | + | 0.974188i | \(0.572479\pi\) | |||||||
\(740\) | 123.036 | 4.52289 | ||||||||
\(741\) | 7.09710 | 0.260718 | ||||||||
\(742\) | −63.6778 | −2.33769 | ||||||||
\(743\) | 21.9240 | 0.804312 | 0.402156 | − | 0.915571i | \(-0.368261\pi\) | ||||
0.402156 | + | 0.915571i | \(0.368261\pi\) | |||||||
\(744\) | 48.9792 | 1.79567 | ||||||||
\(745\) | −51.1788 | −1.87505 | ||||||||
\(746\) | −53.6097 | −1.96279 | ||||||||
\(747\) | −105.950 | −3.87651 | ||||||||
\(748\) | 6.07660 | 0.222182 | ||||||||
\(749\) | −75.3901 | −2.75469 | ||||||||
\(750\) | −1.79579 | −0.0655728 | ||||||||
\(751\) | 35.5762 | 1.29819 | 0.649096 | − | 0.760706i | \(-0.275147\pi\) | ||||
0.649096 | + | 0.760706i | \(0.275147\pi\) | |||||||
\(752\) | −101.613 | −3.70544 | ||||||||
\(753\) | 52.4475 | 1.91129 | ||||||||
\(754\) | −24.0381 | −0.875416 | ||||||||
\(755\) | −9.79112 | −0.356335 | ||||||||
\(756\) | 328.980 | 11.9649 | ||||||||
\(757\) | −7.87619 | −0.286265 | −0.143132 | − | 0.989704i | \(-0.545717\pi\) | ||||
−0.143132 | + | 0.989704i | \(0.545717\pi\) | |||||||
\(758\) | −70.8029 | −2.57168 | ||||||||
\(759\) | 5.62040 | 0.204008 | ||||||||
\(760\) | −69.1557 | −2.50854 | ||||||||
\(761\) | 8.79464 | 0.318806 | 0.159403 | − | 0.987214i | \(-0.449043\pi\) | ||||
0.159403 | + | 0.987214i | \(0.449043\pi\) | |||||||
\(762\) | 26.5105 | 0.960373 | ||||||||
\(763\) | −20.0299 | −0.725133 | ||||||||
\(764\) | 151.436 | 5.47875 | ||||||||
\(765\) | −95.5383 | −3.45419 | ||||||||
\(766\) | −43.4821 | −1.57107 | ||||||||
\(767\) | −1.91259 | −0.0690596 | ||||||||
\(768\) | 194.295 | 7.01103 | ||||||||
\(769\) | 28.4647 | 1.02646 | 0.513232 | − | 0.858250i | \(-0.328448\pi\) | ||||
0.513232 | + | 0.858250i | \(0.328448\pi\) | |||||||
\(770\) | 9.88300 | 0.356159 | ||||||||
\(771\) | 55.9160 | 2.01377 | ||||||||
\(772\) | −134.051 | −4.82459 | ||||||||
\(773\) | −29.9567 | −1.07747 | −0.538733 | − | 0.842476i | \(-0.681097\pi\) | ||||
−0.538733 | + | 0.842476i | \(0.681097\pi\) | |||||||
\(774\) | 150.268 | 5.40128 | ||||||||
\(775\) | −7.85435 | −0.282137 | ||||||||
\(776\) | 91.2898 | 3.27711 | ||||||||
\(777\) | 95.7896 | 3.43643 | ||||||||
\(778\) | −100.177 | −3.59153 | ||||||||
\(779\) | 2.87185 | 0.102895 | ||||||||
\(780\) | 56.7378 | 2.03154 | ||||||||
\(781\) | 0.259436 | 0.00928337 | ||||||||
\(782\) | −75.7665 | −2.70941 | ||||||||
\(783\) | 119.875 | 4.28397 | ||||||||
\(784\) | 182.849 | 6.53033 | ||||||||
\(785\) | −4.39378 | −0.156821 | ||||||||
\(786\) | −110.680 | −3.94784 | ||||||||
\(787\) | 45.6797 | 1.62831 | 0.814153 | − | 0.580651i | \(-0.197202\pi\) | ||||
0.814153 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(788\) | −91.9897 | −3.27700 | ||||||||
\(789\) | 27.4299 | 0.976532 | ||||||||
\(790\) | −92.1753 | −3.27945 | ||||||||
\(791\) | 8.75765 | 0.311386 | ||||||||
\(792\) | 18.8890 | 0.671191 | ||||||||
\(793\) | 9.65500 | 0.342859 | ||||||||
\(794\) | −29.0892 | −1.03234 | ||||||||
\(795\) | 54.7668 | 1.94238 | ||||||||
\(796\) | 104.054 | 3.68810 | ||||||||
\(797\) | −8.20775 | −0.290733 | −0.145367 | − | 0.989378i | \(-0.546436\pi\) | ||||
−0.145367 | + | 0.989378i | \(0.546436\pi\) | |||||||
\(798\) | −83.9388 | −2.97140 | ||||||||
\(799\) | 26.3395 | 0.931824 | ||||||||
\(800\) | −122.682 | −4.33745 | ||||||||
\(801\) | 68.1807 | 2.40905 | ||||||||
\(802\) | 74.4426 | 2.62866 | ||||||||
\(803\) | 3.76093 | 0.132720 | ||||||||
\(804\) | 68.9034 | 2.43004 | ||||||||
\(805\) | −90.7037 | −3.19688 | ||||||||
\(806\) | 4.26949 | 0.150386 | ||||||||
\(807\) | −67.9755 | −2.39285 | ||||||||
\(808\) | 38.1381 | 1.34169 | ||||||||
\(809\) | −45.9737 | −1.61635 | −0.808175 | − | 0.588943i | \(-0.799544\pi\) | ||||
−0.808175 | + | 0.588943i | \(0.799544\pi\) | |||||||
\(810\) | −193.637 | −6.80369 | ||||||||
\(811\) | 3.55060 | 0.124678 | 0.0623392 | − | 0.998055i | \(-0.480144\pi\) | ||||
0.0623392 | + | 0.998055i | \(0.480144\pi\) | |||||||
\(812\) | 209.267 | 7.34384 | ||||||||
\(813\) | 21.2526 | 0.745360 | ||||||||
\(814\) | 5.04165 | 0.176710 | ||||||||
\(815\) | 2.17347 | 0.0761332 | ||||||||
\(816\) | −211.606 | −7.40769 | ||||||||
\(817\) | −16.5938 | −0.580543 | ||||||||
\(818\) | −16.6707 | −0.582878 | ||||||||
\(819\) | 31.2838 | 1.09314 | ||||||||
\(820\) | 22.9590 | 0.801763 | ||||||||
\(821\) | 22.2205 | 0.775502 | 0.387751 | − | 0.921764i | \(-0.373252\pi\) | ||||
0.387751 | + | 0.921764i | \(0.373252\pi\) | |||||||
\(822\) | 162.206 | 5.65760 | ||||||||
\(823\) | 27.4312 | 0.956192 | 0.478096 | − | 0.878308i | \(-0.341327\pi\) | ||||
0.478096 | + | 0.878308i | \(0.341327\pi\) | |||||||
\(824\) | −62.4935 | −2.17707 | ||||||||
\(825\) | −4.27708 | −0.148909 | ||||||||
\(826\) | 22.6206 | 0.787071 | ||||||||
\(827\) | −26.4634 | −0.920222 | −0.460111 | − | 0.887861i | \(-0.652190\pi\) | ||||
−0.460111 | + | 0.887861i | \(0.652190\pi\) | |||||||
\(828\) | −270.267 | −9.39244 | ||||||||
\(829\) | −38.3939 | −1.33347 | −0.666737 | − | 0.745293i | \(-0.732310\pi\) | ||||
−0.666737 | + | 0.745293i | \(0.732310\pi\) | |||||||
\(830\) | 127.073 | 4.41076 | ||||||||
\(831\) | −22.1102 | −0.766995 | ||||||||
\(832\) | 34.7756 | 1.20563 | ||||||||
\(833\) | −47.3971 | −1.64221 | ||||||||
\(834\) | 140.975 | 4.88157 | ||||||||
\(835\) | −38.4560 | −1.33082 | ||||||||
\(836\) | −3.25189 | −0.112469 | ||||||||
\(837\) | −21.2913 | −0.735936 | ||||||||
\(838\) | −24.4932 | −0.846105 | ||||||||
\(839\) | −28.9443 | −0.999270 | −0.499635 | − | 0.866236i | \(-0.666532\pi\) | ||||
−0.499635 | + | 0.866236i | \(0.666532\pi\) | |||||||
\(840\) | −430.433 | −14.8514 | ||||||||
\(841\) | 47.2534 | 1.62943 | ||||||||
\(842\) | −62.1059 | −2.14031 | ||||||||
\(843\) | −98.4597 | −3.39113 | ||||||||
\(844\) | 63.7940 | 2.19588 | ||||||||
\(845\) | 3.17240 | 0.109134 | ||||||||
\(846\) | 127.645 | 4.38853 | ||||||||
\(847\) | −46.9630 | −1.61367 | ||||||||
\(848\) | 85.9071 | 2.95006 | ||||||||
\(849\) | 76.5546 | 2.62735 | ||||||||
\(850\) | 57.6577 | 1.97764 | ||||||||
\(851\) | −46.2710 | −1.58615 | ||||||||
\(852\) | −17.6156 | −0.603499 | ||||||||
\(853\) | 42.5657 | 1.45742 | 0.728710 | − | 0.684822i | \(-0.240120\pi\) | ||||
0.728710 | + | 0.684822i | \(0.240120\pi\) | |||||||
\(854\) | −114.192 | −3.90756 | ||||||||
\(855\) | 51.1273 | 1.74852 | ||||||||
\(856\) | 172.817 | 5.90675 | ||||||||
\(857\) | 54.2756 | 1.85402 | 0.927009 | − | 0.375039i | \(-0.122371\pi\) | ||||
0.927009 | + | 0.375039i | \(0.122371\pi\) | |||||||
\(858\) | 2.32495 | 0.0793723 | ||||||||
\(859\) | 24.4559 | 0.834424 | 0.417212 | − | 0.908809i | \(-0.363007\pi\) | ||||
0.417212 | + | 0.908809i | \(0.363007\pi\) | |||||||
\(860\) | −132.659 | −4.52364 | ||||||||
\(861\) | 17.8747 | 0.609169 | ||||||||
\(862\) | 31.5563 | 1.07481 | ||||||||
\(863\) | 54.7805 | 1.86475 | 0.932375 | − | 0.361492i | \(-0.117733\pi\) | ||||
0.932375 | + | 0.361492i | \(0.117733\pi\) | |||||||
\(864\) | −332.561 | −11.3140 | ||||||||
\(865\) | 46.2446 | 1.57236 | ||||||||
\(866\) | −8.79374 | −0.298823 | ||||||||
\(867\) | 0.341717 | 0.0116053 | ||||||||
\(868\) | −37.1687 | −1.26159 | ||||||||
\(869\) | −2.78019 | −0.0943115 | ||||||||
\(870\) | −244.519 | −8.28996 | ||||||||
\(871\) | 3.85262 | 0.130541 | ||||||||
\(872\) | 45.9146 | 1.55487 | ||||||||
\(873\) | −67.4912 | −2.28423 | ||||||||
\(874\) | 40.5465 | 1.37150 | ||||||||
\(875\) | 0.874122 | 0.0295507 | ||||||||
\(876\) | −255.365 | −8.62797 | ||||||||
\(877\) | −29.0422 | −0.980686 | −0.490343 | − | 0.871529i | \(-0.663129\pi\) | ||||
−0.490343 | + | 0.871529i | \(0.663129\pi\) | |||||||
\(878\) | 57.9857 | 1.95692 | ||||||||
\(879\) | 77.7479 | 2.62237 | ||||||||
\(880\) | −13.3330 | −0.449457 | ||||||||
\(881\) | −15.5702 | −0.524574 | −0.262287 | − | 0.964990i | \(-0.584477\pi\) | ||||
−0.262287 | + | 0.964990i | \(0.584477\pi\) | |||||||
\(882\) | −229.694 | −7.73419 | ||||||||
\(883\) | −1.48410 | −0.0499440 | −0.0249720 | − | 0.999688i | \(-0.507950\pi\) | ||||
−0.0249720 | + | 0.999688i | \(0.507950\pi\) | |||||||
\(884\) | −23.0697 | −0.775918 | ||||||||
\(885\) | −19.4551 | −0.653977 | ||||||||
\(886\) | −22.0421 | −0.740520 | ||||||||
\(887\) | 42.4750 | 1.42617 | 0.713085 | − | 0.701078i | \(-0.247297\pi\) | ||||
0.713085 | + | 0.701078i | \(0.247297\pi\) | |||||||
\(888\) | −219.579 | −7.36857 | ||||||||
\(889\) | −12.9043 | −0.432796 | ||||||||
\(890\) | −81.7735 | −2.74105 | ||||||||
\(891\) | −5.84046 | −0.195663 | ||||||||
\(892\) | 21.2363 | 0.711045 | ||||||||
\(893\) | −14.0956 | −0.471690 | ||||||||
\(894\) | 142.395 | 4.76242 | ||||||||
\(895\) | −3.15893 | −0.105591 | ||||||||
\(896\) | −203.130 | −6.78609 | ||||||||
\(897\) | −21.3378 | −0.712447 | ||||||||
\(898\) | 103.676 | 3.45971 | ||||||||
\(899\) | −13.5436 | −0.451705 | ||||||||
\(900\) | 205.671 | 6.85570 | ||||||||
\(901\) | −22.2683 | −0.741865 | ||||||||
\(902\) | 0.940792 | 0.0313250 | ||||||||
\(903\) | −103.282 | −3.43700 | ||||||||
\(904\) | −20.0752 | −0.667690 | ||||||||
\(905\) | −53.8961 | −1.79157 | ||||||||
\(906\) | 27.2420 | 0.905054 | ||||||||
\(907\) | 27.1168 | 0.900398 | 0.450199 | − | 0.892928i | \(-0.351353\pi\) | ||||
0.450199 | + | 0.892928i | \(0.351353\pi\) | |||||||
\(908\) | 14.5232 | 0.481969 | ||||||||
\(909\) | −28.1958 | −0.935196 | ||||||||
\(910\) | −37.5206 | −1.24380 | ||||||||
\(911\) | −22.1250 | −0.733033 | −0.366516 | − | 0.930412i | \(-0.619450\pi\) | ||||
−0.366516 | + | 0.930412i | \(0.619450\pi\) | |||||||
\(912\) | 113.241 | 3.74978 | ||||||||
\(913\) | 3.83276 | 0.126846 | ||||||||
\(914\) | −84.9386 | −2.80952 | ||||||||
\(915\) | 98.2118 | 3.24678 | ||||||||
\(916\) | 156.864 | 5.18295 | ||||||||
\(917\) | 53.8751 | 1.77911 | ||||||||
\(918\) | 156.297 | 5.15856 | ||||||||
\(919\) | 16.3792 | 0.540300 | 0.270150 | − | 0.962818i | \(-0.412927\pi\) | ||||
0.270150 | + | 0.962818i | \(0.412927\pi\) | |||||||
\(920\) | 207.920 | 6.85492 | ||||||||
\(921\) | 81.7292 | 2.69307 | ||||||||
\(922\) | −53.6356 | −1.76640 | ||||||||
\(923\) | −0.984946 | −0.0324199 | ||||||||
\(924\) | −20.2402 | −0.665852 | ||||||||
\(925\) | 35.2118 | 1.15776 | ||||||||
\(926\) | −29.9569 | −0.984446 | ||||||||
\(927\) | 46.2019 | 1.51747 | ||||||||
\(928\) | −211.545 | −6.94432 | ||||||||
\(929\) | 23.3057 | 0.764635 | 0.382318 | − | 0.924031i | \(-0.375126\pi\) | ||||
0.382318 | + | 0.924031i | \(0.375126\pi\) | |||||||
\(930\) | 43.4298 | 1.42412 | ||||||||
\(931\) | 25.3646 | 0.831290 | ||||||||
\(932\) | −37.6914 | −1.23462 | ||||||||
\(933\) | 74.0334 | 2.42374 | ||||||||
\(934\) | −69.1192 | −2.26165 | ||||||||
\(935\) | 3.45611 | 0.113027 | ||||||||
\(936\) | −71.7118 | −2.34397 | ||||||||
\(937\) | 31.6897 | 1.03526 | 0.517629 | − | 0.855605i | \(-0.326815\pi\) | ||||
0.517629 | + | 0.855605i | \(0.326815\pi\) | |||||||
\(938\) | −45.5658 | −1.48778 | ||||||||
\(939\) | 12.6635 | 0.413259 | ||||||||
\(940\) | −112.687 | −3.67545 | ||||||||
\(941\) | −36.4720 | −1.18895 | −0.594477 | − | 0.804113i | \(-0.702641\pi\) | ||||
−0.594477 | + | 0.804113i | \(0.702641\pi\) | |||||||
\(942\) | 12.2249 | 0.398308 | ||||||||
\(943\) | −8.63435 | −0.281173 | ||||||||
\(944\) | −30.5172 | −0.993251 | ||||||||
\(945\) | 187.110 | 6.08669 | ||||||||
\(946\) | −5.43598 | −0.176739 | ||||||||
\(947\) | 27.1913 | 0.883598 | 0.441799 | − | 0.897114i | \(-0.354340\pi\) | ||||
0.441799 | + | 0.897114i | \(0.354340\pi\) | |||||||
\(948\) | 188.773 | 6.13106 | ||||||||
\(949\) | −14.2783 | −0.463493 | ||||||||
\(950\) | −30.8555 | −1.00108 | ||||||||
\(951\) | −62.2176 | −2.01754 | ||||||||
\(952\) | 175.015 | 5.67227 | ||||||||
\(953\) | −43.1808 | −1.39876 | −0.699381 | − | 0.714749i | \(-0.746541\pi\) | ||||
−0.699381 | + | 0.714749i | \(0.746541\pi\) | |||||||
\(954\) | −107.916 | −3.49390 | ||||||||
\(955\) | 86.1303 | 2.78711 | ||||||||
\(956\) | 95.2210 | 3.07967 | ||||||||
\(957\) | −7.37516 | −0.238405 | ||||||||
\(958\) | 46.8906 | 1.51497 | ||||||||
\(959\) | −78.9560 | −2.54962 | ||||||||
\(960\) | 353.742 | 11.4170 | ||||||||
\(961\) | −28.5945 | −0.922402 | ||||||||
\(962\) | −19.1405 | −0.617116 | ||||||||
\(963\) | −127.765 | −4.11716 | ||||||||
\(964\) | −49.1697 | −1.58365 | ||||||||
\(965\) | −76.2424 | −2.45433 | ||||||||
\(966\) | 252.366 | 8.11974 | ||||||||
\(967\) | −13.3760 | −0.430142 | −0.215071 | − | 0.976598i | \(-0.568998\pi\) | ||||
−0.215071 | + | 0.976598i | \(0.568998\pi\) | |||||||
\(968\) | 107.653 | 3.46011 | ||||||||
\(969\) | −29.3537 | −0.942975 | ||||||||
\(970\) | 80.9466 | 2.59904 | ||||||||
\(971\) | 8.24212 | 0.264502 | 0.132251 | − | 0.991216i | \(-0.457779\pi\) | ||||
0.132251 | + | 0.991216i | \(0.457779\pi\) | |||||||
\(972\) | 166.854 | 5.35184 | ||||||||
\(973\) | −68.6214 | −2.19990 | ||||||||
\(974\) | 96.3264 | 3.08650 | ||||||||
\(975\) | 16.2379 | 0.520027 | ||||||||
\(976\) | 154.055 | 4.93117 | ||||||||
\(977\) | −2.11960 | −0.0678120 | −0.0339060 | − | 0.999425i | \(-0.510795\pi\) | ||||
−0.0339060 | + | 0.999425i | \(0.510795\pi\) | |||||||
\(978\) | −6.04726 | −0.193370 | ||||||||
\(979\) | −2.46645 | −0.0788281 | ||||||||
\(980\) | 202.777 | 6.47748 | ||||||||
\(981\) | −33.9450 | −1.08378 | ||||||||
\(982\) | 62.8034 | 2.00414 | ||||||||
\(983\) | 25.0743 | 0.799747 | 0.399874 | − | 0.916570i | \(-0.369054\pi\) | ||||
0.399874 | + | 0.916570i | \(0.369054\pi\) | |||||||
\(984\) | −40.9742 | −1.30621 | ||||||||
\(985\) | −52.3199 | −1.66705 | ||||||||
\(986\) | 99.4218 | 3.16624 | ||||||||
\(987\) | −87.7325 | −2.79256 | ||||||||
\(988\) | 12.3458 | 0.392771 | ||||||||
\(989\) | 49.8900 | 1.58641 | ||||||||
\(990\) | 16.7489 | 0.532313 | ||||||||
\(991\) | −26.7446 | −0.849572 | −0.424786 | − | 0.905294i | \(-0.639651\pi\) | ||||
−0.424786 | + | 0.905294i | \(0.639651\pi\) | |||||||
\(992\) | 37.5733 | 1.19295 | ||||||||
\(993\) | 5.65570 | 0.179478 | ||||||||
\(994\) | 11.6492 | 0.369489 | ||||||||
\(995\) | 59.1816 | 1.87618 | ||||||||
\(996\) | −260.242 | −8.24608 | ||||||||
\(997\) | 7.40486 | 0.234514 | 0.117257 | − | 0.993102i | \(-0.462590\pi\) | ||||
0.117257 | + | 0.993102i | \(0.462590\pi\) | |||||||
\(998\) | 16.8517 | 0.533432 | ||||||||
\(999\) | 95.4511 | 3.01994 |
(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 | 8021.2.a.d.1.3 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.d.1.3 | ✓ | 174 | 1.1 | even | 1 | trivial |