Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73308 | −1.93258 | −0.966291 | − | 0.257454i | \(-0.917116\pi\) | ||||
−0.966291 | + | 0.257454i | \(0.917116\pi\) | |||||||
\(3\) | 2.04263 | 1.17931 | 0.589657 | − | 0.807654i | \(-0.299263\pi\) | ||||
0.589657 | + | 0.807654i | \(0.299263\pi\) | |||||||
\(4\) | 5.46974 | 2.73487 | ||||||||
\(5\) | 2.78212 | 1.24420 | 0.622100 | − | 0.782938i | \(-0.286280\pi\) | ||||
0.622100 | + | 0.782938i | \(0.286280\pi\) | |||||||
\(6\) | −5.58268 | −2.27912 | ||||||||
\(7\) | 3.87331 | 1.46397 | 0.731987 | − | 0.681319i | \(-0.238593\pi\) | ||||
0.731987 | + | 0.681319i | \(0.238593\pi\) | |||||||
\(8\) | −9.48308 | −3.35278 | ||||||||
\(9\) | 1.17234 | 0.390781 | ||||||||
\(10\) | −7.60375 | −2.40452 | ||||||||
\(11\) | −0.942573 | −0.284196 | −0.142098 | − | 0.989853i | \(-0.545385\pi\) | ||||
−0.142098 | + | 0.989853i | \(0.545385\pi\) | |||||||
\(12\) | 11.1727 | 3.22527 | ||||||||
\(13\) | 6.23637 | 1.72966 | 0.864829 | − | 0.502067i | \(-0.167427\pi\) | ||||
0.864829 | + | 0.502067i | \(0.167427\pi\) | |||||||
\(14\) | −10.5861 | −2.82925 | ||||||||
\(15\) | 5.68284 | 1.46730 | ||||||||
\(16\) | 14.9786 | 3.74464 | ||||||||
\(17\) | −5.28749 | −1.28240 | −0.641202 | − | 0.767372i | \(-0.721564\pi\) | ||||
−0.641202 | + | 0.767372i | \(0.721564\pi\) | |||||||
\(18\) | −3.20411 | −0.755216 | ||||||||
\(19\) | 2.29285 | 0.526017 | 0.263008 | − | 0.964794i | \(-0.415285\pi\) | ||||
0.263008 | + | 0.964794i | \(0.415285\pi\) | |||||||
\(20\) | 15.2175 | 3.40273 | ||||||||
\(21\) | 7.91174 | 1.72648 | ||||||||
\(22\) | 2.57613 | 0.549232 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −19.3704 | −3.95398 | ||||||||
\(25\) | 2.74017 | 0.548035 | ||||||||
\(26\) | −17.0445 | −3.34270 | ||||||||
\(27\) | −3.73323 | −0.718460 | ||||||||
\(28\) | 21.1860 | 4.00378 | ||||||||
\(29\) | −4.07188 | −0.756129 | −0.378065 | − | 0.925779i | \(-0.623410\pi\) | ||||
−0.378065 | + | 0.925779i | \(0.623410\pi\) | |||||||
\(30\) | −15.5317 | −2.83568 | ||||||||
\(31\) | 8.08494 | 1.45210 | 0.726049 | − | 0.687643i | \(-0.241355\pi\) | ||||
0.726049 | + | 0.687643i | \(0.241355\pi\) | |||||||
\(32\) | −21.9715 | −3.88405 | ||||||||
\(33\) | −1.92533 | −0.335157 | ||||||||
\(34\) | 14.4511 | 2.47835 | ||||||||
\(35\) | 10.7760 | 1.82148 | ||||||||
\(36\) | 6.41241 | 1.06874 | ||||||||
\(37\) | −2.48169 | −0.407987 | −0.203993 | − | 0.978972i | \(-0.565392\pi\) | ||||
−0.203993 | + | 0.978972i | \(0.565392\pi\) | |||||||
\(38\) | −6.26656 | −1.01657 | ||||||||
\(39\) | 12.7386 | 2.03981 | ||||||||
\(40\) | −26.3830 | −4.17153 | ||||||||
\(41\) | 0.934218 | 0.145900 | 0.0729502 | − | 0.997336i | \(-0.476759\pi\) | ||||
0.0729502 | + | 0.997336i | \(0.476759\pi\) | |||||||
\(42\) | −21.6235 | −3.33657 | ||||||||
\(43\) | 8.66302 | 1.32110 | 0.660549 | − | 0.750783i | \(-0.270324\pi\) | ||||
0.660549 | + | 0.750783i | \(0.270324\pi\) | |||||||
\(44\) | −5.15563 | −0.777240 | ||||||||
\(45\) | 3.26160 | 0.486210 | ||||||||
\(46\) | −2.73308 | −0.402971 | ||||||||
\(47\) | 0.619143 | 0.0903113 | 0.0451557 | − | 0.998980i | \(-0.485622\pi\) | ||||
0.0451557 | + | 0.998980i | \(0.485622\pi\) | |||||||
\(48\) | 30.5957 | 4.41611 | ||||||||
\(49\) | 8.00253 | 1.14322 | ||||||||
\(50\) | −7.48912 | −1.05912 | ||||||||
\(51\) | −10.8004 | −1.51236 | ||||||||
\(52\) | 34.1113 | 4.73039 | ||||||||
\(53\) | 7.33471 | 1.00750 | 0.503750 | − | 0.863850i | \(-0.331953\pi\) | ||||
0.503750 | + | 0.863850i | \(0.331953\pi\) | |||||||
\(54\) | 10.2032 | 1.38848 | ||||||||
\(55\) | −2.62235 | −0.353597 | ||||||||
\(56\) | −36.7309 | −4.90838 | ||||||||
\(57\) | 4.68345 | 0.620339 | ||||||||
\(58\) | 11.1288 | 1.46128 | ||||||||
\(59\) | −8.98731 | −1.17005 | −0.585024 | − | 0.811016i | \(-0.698915\pi\) | ||||
−0.585024 | + | 0.811016i | \(0.698915\pi\) | |||||||
\(60\) | 31.0836 | 4.01288 | ||||||||
\(61\) | 3.84620 | 0.492455 | 0.246228 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246228 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(62\) | −22.0968 | −2.80630 | ||||||||
\(63\) | 4.54085 | 0.572093 | ||||||||
\(64\) | 30.0928 | 3.76160 | ||||||||
\(65\) | 17.3503 | 2.15204 | ||||||||
\(66\) | 5.26208 | 0.647717 | ||||||||
\(67\) | −1.86292 | −0.227592 | −0.113796 | − | 0.993504i | \(-0.536301\pi\) | ||||
−0.113796 | + | 0.993504i | \(0.536301\pi\) | |||||||
\(68\) | −28.9212 | −3.50721 | ||||||||
\(69\) | 2.04263 | 0.245904 | ||||||||
\(70\) | −29.4517 | −3.52015 | ||||||||
\(71\) | 11.9901 | 1.42296 | 0.711481 | − | 0.702705i | \(-0.248025\pi\) | ||||
0.711481 | + | 0.702705i | \(0.248025\pi\) | |||||||
\(72\) | −11.1174 | −1.31020 | ||||||||
\(73\) | −10.9820 | −1.28535 | −0.642674 | − | 0.766140i | \(-0.722175\pi\) | ||||
−0.642674 | + | 0.766140i | \(0.722175\pi\) | |||||||
\(74\) | 6.78266 | 0.788468 | ||||||||
\(75\) | 5.59716 | 0.646305 | ||||||||
\(76\) | 12.5413 | 1.43859 | ||||||||
\(77\) | −3.65088 | −0.416056 | ||||||||
\(78\) | −34.8157 | −3.94210 | ||||||||
\(79\) | 4.89120 | 0.550302 | 0.275151 | − | 0.961401i | \(-0.411272\pi\) | ||||
0.275151 | + | 0.961401i | \(0.411272\pi\) | |||||||
\(80\) | 41.6721 | 4.65909 | ||||||||
\(81\) | −11.1426 | −1.23807 | ||||||||
\(82\) | −2.55329 | −0.281964 | ||||||||
\(83\) | 14.3163 | 1.57142 | 0.785709 | − | 0.618597i | \(-0.212298\pi\) | ||||
0.785709 | + | 0.618597i | \(0.212298\pi\) | |||||||
\(84\) | 43.2752 | 4.72171 | ||||||||
\(85\) | −14.7104 | −1.59557 | ||||||||
\(86\) | −23.6767 | −2.55313 | ||||||||
\(87\) | −8.31735 | −0.891714 | ||||||||
\(88\) | 8.93849 | 0.952847 | ||||||||
\(89\) | −7.02322 | −0.744460 | −0.372230 | − | 0.928141i | \(-0.621407\pi\) | ||||
−0.372230 | + | 0.928141i | \(0.621407\pi\) | |||||||
\(90\) | −8.91421 | −0.939640 | ||||||||
\(91\) | 24.1554 | 2.53217 | ||||||||
\(92\) | 5.46974 | 0.570260 | ||||||||
\(93\) | 16.5146 | 1.71248 | ||||||||
\(94\) | −1.69217 | −0.174534 | ||||||||
\(95\) | 6.37898 | 0.654470 | ||||||||
\(96\) | −44.8797 | −4.58051 | ||||||||
\(97\) | 0.753121 | 0.0764679 | 0.0382339 | − | 0.999269i | \(-0.487827\pi\) | ||||
0.0382339 | + | 0.999269i | \(0.487827\pi\) | |||||||
\(98\) | −21.8716 | −2.20936 | ||||||||
\(99\) | −1.10502 | −0.111059 | ||||||||
\(100\) | 14.9880 | 1.49880 | ||||||||
\(101\) | 2.80490 | 0.279098 | 0.139549 | − | 0.990215i | \(-0.455435\pi\) | ||||
0.139549 | + | 0.990215i | \(0.455435\pi\) | |||||||
\(102\) | 29.5184 | 2.92275 | ||||||||
\(103\) | −4.53348 | −0.446697 | −0.223349 | − | 0.974739i | \(-0.571699\pi\) | ||||
−0.223349 | + | 0.974739i | \(0.571699\pi\) | |||||||
\(104\) | −59.1400 | −5.79915 | ||||||||
\(105\) | 22.0114 | 2.14809 | ||||||||
\(106\) | −20.0464 | −1.94707 | ||||||||
\(107\) | 2.00021 | 0.193368 | 0.0966838 | − | 0.995315i | \(-0.469176\pi\) | ||||
0.0966838 | + | 0.995315i | \(0.469176\pi\) | |||||||
\(108\) | −20.4198 | −1.96490 | ||||||||
\(109\) | −5.36771 | −0.514134 | −0.257067 | − | 0.966394i | \(-0.582756\pi\) | ||||
−0.257067 | + | 0.966394i | \(0.582756\pi\) | |||||||
\(110\) | 7.16709 | 0.683355 | ||||||||
\(111\) | −5.06917 | −0.481145 | ||||||||
\(112\) | 58.0166 | 5.48206 | ||||||||
\(113\) | −11.1257 | −1.04662 | −0.523308 | − | 0.852143i | \(-0.675302\pi\) | ||||
−0.523308 | + | 0.852143i | \(0.675302\pi\) | |||||||
\(114\) | −12.8003 | −1.19885 | ||||||||
\(115\) | 2.78212 | 0.259434 | ||||||||
\(116\) | −22.2721 | −2.06792 | ||||||||
\(117\) | 7.31116 | 0.675917 | ||||||||
\(118\) | 24.5631 | 2.26121 | ||||||||
\(119\) | −20.4801 | −1.87741 | ||||||||
\(120\) | −53.8908 | −4.91954 | ||||||||
\(121\) | −10.1116 | −0.919232 | ||||||||
\(122\) | −10.5120 | −0.951709 | ||||||||
\(123\) | 1.90826 | 0.172062 | ||||||||
\(124\) | 44.2225 | 3.97130 | ||||||||
\(125\) | −6.28710 | −0.562336 | ||||||||
\(126\) | −12.4105 | −1.10562 | ||||||||
\(127\) | 4.25550 | 0.377614 | 0.188807 | − | 0.982014i | \(-0.439538\pi\) | ||||
0.188807 | + | 0.982014i | \(0.439538\pi\) | |||||||
\(128\) | −38.3030 | −3.38554 | ||||||||
\(129\) | 17.6954 | 1.55799 | ||||||||
\(130\) | −47.4198 | −4.15899 | ||||||||
\(131\) | −19.0901 | −1.66791 | −0.833955 | − | 0.551833i | \(-0.813929\pi\) | ||||
−0.833955 | + | 0.551833i | \(0.813929\pi\) | |||||||
\(132\) | −10.5310 | −0.916610 | ||||||||
\(133\) | 8.88093 | 0.770074 | ||||||||
\(134\) | 5.09151 | 0.439839 | ||||||||
\(135\) | −10.3863 | −0.893909 | ||||||||
\(136\) | 50.1417 | 4.29961 | ||||||||
\(137\) | 3.44025 | 0.293921 | 0.146960 | − | 0.989142i | \(-0.453051\pi\) | ||||
0.146960 | + | 0.989142i | \(0.453051\pi\) | |||||||
\(138\) | −5.58268 | −0.475229 | ||||||||
\(139\) | 10.9624 | 0.929820 | 0.464910 | − | 0.885358i | \(-0.346087\pi\) | ||||
0.464910 | + | 0.885358i | \(0.346087\pi\) | |||||||
\(140\) | 58.9419 | 4.98150 | ||||||||
\(141\) | 1.26468 | 0.106505 | ||||||||
\(142\) | −32.7699 | −2.74999 | ||||||||
\(143\) | −5.87823 | −0.491562 | ||||||||
\(144\) | 17.5600 | 1.46334 | ||||||||
\(145\) | −11.3284 | −0.940777 | ||||||||
\(146\) | 30.0147 | 2.48404 | ||||||||
\(147\) | 16.3462 | 1.34821 | ||||||||
\(148\) | −13.5742 | −1.11579 | ||||||||
\(149\) | −4.59518 | −0.376452 | −0.188226 | − | 0.982126i | \(-0.560274\pi\) | ||||
−0.188226 | + | 0.982126i | \(0.560274\pi\) | |||||||
\(150\) | −15.2975 | −1.24904 | ||||||||
\(151\) | −7.46353 | −0.607373 | −0.303687 | − | 0.952772i | \(-0.598218\pi\) | ||||
−0.303687 | + | 0.952772i | \(0.598218\pi\) | |||||||
\(152\) | −21.7433 | −1.76362 | ||||||||
\(153\) | −6.19875 | −0.501139 | ||||||||
\(154\) | 9.97814 | 0.804062 | ||||||||
\(155\) | 22.4932 | 1.80670 | ||||||||
\(156\) | 69.6768 | 5.57861 | ||||||||
\(157\) | 14.0427 | 1.12073 | 0.560365 | − | 0.828245i | \(-0.310661\pi\) | ||||
0.560365 | + | 0.828245i | \(0.310661\pi\) | |||||||
\(158\) | −13.3680 | −1.06350 | ||||||||
\(159\) | 14.9821 | 1.18816 | ||||||||
\(160\) | −61.1273 | −4.83253 | ||||||||
\(161\) | 3.87331 | 0.305260 | ||||||||
\(162\) | 30.4538 | 2.39267 | ||||||||
\(163\) | −14.2419 | −1.11551 | −0.557755 | − | 0.830006i | \(-0.688337\pi\) | ||||
−0.557755 | + | 0.830006i | \(0.688337\pi\) | |||||||
\(164\) | 5.10993 | 0.399018 | ||||||||
\(165\) | −5.35649 | −0.417002 | ||||||||
\(166\) | −39.1276 | −3.03689 | ||||||||
\(167\) | 19.2444 | 1.48918 | 0.744588 | − | 0.667525i | \(-0.232646\pi\) | ||||
0.744588 | + | 0.667525i | \(0.232646\pi\) | |||||||
\(168\) | −75.0277 | −5.78852 | ||||||||
\(169\) | 25.8923 | 1.99172 | ||||||||
\(170\) | 40.2048 | 3.08356 | ||||||||
\(171\) | 2.68801 | 0.205557 | ||||||||
\(172\) | 47.3845 | 3.61303 | ||||||||
\(173\) | 16.7795 | 1.27572 | 0.637861 | − | 0.770151i | \(-0.279819\pi\) | ||||
0.637861 | + | 0.770151i | \(0.279819\pi\) | |||||||
\(174\) | 22.7320 | 1.72331 | ||||||||
\(175\) | 10.6135 | 0.802308 | ||||||||
\(176\) | −14.1184 | −1.06421 | ||||||||
\(177\) | −18.3578 | −1.37985 | ||||||||
\(178\) | 19.1950 | 1.43873 | ||||||||
\(179\) | 18.4207 | 1.37683 | 0.688415 | − | 0.725317i | \(-0.258307\pi\) | ||||
0.688415 | + | 0.725317i | \(0.258307\pi\) | |||||||
\(180\) | 17.8401 | 1.32972 | ||||||||
\(181\) | −1.81569 | −0.134959 | −0.0674797 | − | 0.997721i | \(-0.521496\pi\) | ||||
−0.0674797 | + | 0.997721i | \(0.521496\pi\) | |||||||
\(182\) | −66.0187 | −4.89363 | ||||||||
\(183\) | 7.85636 | 0.580759 | ||||||||
\(184\) | −9.48308 | −0.699102 | ||||||||
\(185\) | −6.90434 | −0.507617 | ||||||||
\(186\) | −45.1356 | −3.30951 | ||||||||
\(187\) | 4.98384 | 0.364455 | ||||||||
\(188\) | 3.38655 | 0.246990 | ||||||||
\(189\) | −14.4600 | −1.05181 | ||||||||
\(190\) | −17.4343 | −1.26482 | ||||||||
\(191\) | 14.1955 | 1.02715 | 0.513574 | − | 0.858045i | \(-0.328321\pi\) | ||||
0.513574 | + | 0.858045i | \(0.328321\pi\) | |||||||
\(192\) | 61.4684 | 4.43610 | ||||||||
\(193\) | −21.4627 | −1.54492 | −0.772460 | − | 0.635064i | \(-0.780974\pi\) | ||||
−0.772460 | + | 0.635064i | \(0.780974\pi\) | |||||||
\(194\) | −2.05834 | −0.147780 | ||||||||
\(195\) | 35.4403 | 2.53793 | ||||||||
\(196\) | 43.7718 | 3.12655 | ||||||||
\(197\) | 1.70146 | 0.121224 | 0.0606119 | − | 0.998161i | \(-0.480695\pi\) | ||||
0.0606119 | + | 0.998161i | \(0.480695\pi\) | |||||||
\(198\) | 3.02011 | 0.214630 | ||||||||
\(199\) | 22.4715 | 1.59296 | 0.796479 | − | 0.604666i | \(-0.206693\pi\) | ||||
0.796479 | + | 0.604666i | \(0.206693\pi\) | |||||||
\(200\) | −25.9853 | −1.83744 | ||||||||
\(201\) | −3.80526 | −0.268402 | ||||||||
\(202\) | −7.66602 | −0.539379 | ||||||||
\(203\) | −15.7717 | −1.10695 | ||||||||
\(204\) | −59.0753 | −4.13610 | ||||||||
\(205\) | 2.59910 | 0.181529 | ||||||||
\(206\) | 12.3904 | 0.863279 | ||||||||
\(207\) | 1.17234 | 0.0814835 | ||||||||
\(208\) | 93.4119 | 6.47695 | ||||||||
\(209\) | −2.16118 | −0.149492 | ||||||||
\(210\) | −60.1590 | −4.15136 | ||||||||
\(211\) | −19.3898 | −1.33485 | −0.667424 | − | 0.744678i | \(-0.732603\pi\) | ||||
−0.667424 | + | 0.744678i | \(0.732603\pi\) | |||||||
\(212\) | 40.1189 | 2.75538 | ||||||||
\(213\) | 24.4913 | 1.67812 | ||||||||
\(214\) | −5.46674 | −0.373698 | ||||||||
\(215\) | 24.1015 | 1.64371 | ||||||||
\(216\) | 35.4025 | 2.40884 | ||||||||
\(217\) | 31.3155 | 2.12583 | ||||||||
\(218\) | 14.6704 | 0.993605 | ||||||||
\(219\) | −22.4322 | −1.51583 | ||||||||
\(220\) | −14.3436 | −0.967042 | ||||||||
\(221\) | −32.9747 | −2.21812 | ||||||||
\(222\) | 13.8545 | 0.929851 | ||||||||
\(223\) | −7.89058 | −0.528392 | −0.264196 | − | 0.964469i | \(-0.585107\pi\) | ||||
−0.264196 | + | 0.964469i | \(0.585107\pi\) | |||||||
\(224\) | −85.1024 | −5.68614 | ||||||||
\(225\) | 3.21242 | 0.214162 | ||||||||
\(226\) | 30.4074 | 2.02267 | ||||||||
\(227\) | 19.9342 | 1.32308 | 0.661538 | − | 0.749911i | \(-0.269904\pi\) | ||||
0.661538 | + | 0.749911i | \(0.269904\pi\) | |||||||
\(228\) | 25.6173 | 1.69655 | ||||||||
\(229\) | −0.278942 | −0.0184330 | −0.00921649 | − | 0.999958i | \(-0.502934\pi\) | ||||
−0.00921649 | + | 0.999958i | \(0.502934\pi\) | |||||||
\(230\) | −7.60375 | −0.501377 | ||||||||
\(231\) | −7.45739 | −0.490660 | ||||||||
\(232\) | 38.6140 | 2.53513 | ||||||||
\(233\) | −23.5257 | −1.54122 | −0.770611 | − | 0.637306i | \(-0.780049\pi\) | ||||
−0.770611 | + | 0.637306i | \(0.780049\pi\) | |||||||
\(234\) | −19.9820 | −1.30627 | ||||||||
\(235\) | 1.72253 | 0.112365 | ||||||||
\(236\) | −49.1583 | −3.19993 | ||||||||
\(237\) | 9.99091 | 0.648979 | ||||||||
\(238\) | 55.9737 | 3.62824 | ||||||||
\(239\) | −6.77337 | −0.438133 | −0.219066 | − | 0.975710i | \(-0.570301\pi\) | ||||
−0.219066 | + | 0.975710i | \(0.570301\pi\) | |||||||
\(240\) | 85.1208 | 5.49452 | ||||||||
\(241\) | 16.6401 | 1.07188 | 0.535942 | − | 0.844255i | \(-0.319956\pi\) | ||||
0.535942 | + | 0.844255i | \(0.319956\pi\) | |||||||
\(242\) | 27.6357 | 1.77649 | ||||||||
\(243\) | −11.5606 | −0.741614 | ||||||||
\(244\) | 21.0377 | 1.34680 | ||||||||
\(245\) | 22.2640 | 1.42239 | ||||||||
\(246\) | −5.21544 | −0.332524 | ||||||||
\(247\) | 14.2991 | 0.909829 | ||||||||
\(248\) | −76.6702 | −4.86856 | ||||||||
\(249\) | 29.2429 | 1.85319 | ||||||||
\(250\) | 17.1832 | 1.08676 | ||||||||
\(251\) | 24.9509 | 1.57489 | 0.787443 | − | 0.616387i | \(-0.211404\pi\) | ||||
0.787443 | + | 0.616387i | \(0.211404\pi\) | |||||||
\(252\) | 24.8373 | 1.56460 | ||||||||
\(253\) | −0.942573 | −0.0592590 | ||||||||
\(254\) | −11.6306 | −0.729770 | ||||||||
\(255\) | −30.0479 | −1.88168 | ||||||||
\(256\) | 44.4998 | 2.78124 | ||||||||
\(257\) | 17.4782 | 1.09026 | 0.545130 | − | 0.838352i | \(-0.316480\pi\) | ||||
0.545130 | + | 0.838352i | \(0.316480\pi\) | |||||||
\(258\) | −48.3629 | −3.01094 | ||||||||
\(259\) | −9.61234 | −0.597282 | ||||||||
\(260\) | 94.9017 | 5.88555 | ||||||||
\(261\) | −4.77364 | −0.295481 | ||||||||
\(262\) | 52.1748 | 3.22337 | ||||||||
\(263\) | 10.8108 | 0.666624 | 0.333312 | − | 0.942817i | \(-0.391834\pi\) | ||||
0.333312 | + | 0.942817i | \(0.391834\pi\) | |||||||
\(264\) | 18.2580 | 1.12371 | ||||||||
\(265\) | 20.4060 | 1.25353 | ||||||||
\(266\) | −24.2723 | −1.48823 | ||||||||
\(267\) | −14.3459 | −0.877952 | ||||||||
\(268\) | −10.1897 | −0.622434 | ||||||||
\(269\) | 11.0911 | 0.676237 | 0.338118 | − | 0.941104i | \(-0.390210\pi\) | ||||
0.338118 | + | 0.941104i | \(0.390210\pi\) | |||||||
\(270\) | 28.3866 | 1.72755 | ||||||||
\(271\) | −12.7216 | −0.772785 | −0.386392 | − | 0.922335i | \(-0.626279\pi\) | ||||
−0.386392 | + | 0.922335i | \(0.626279\pi\) | |||||||
\(272\) | −79.1990 | −4.80215 | ||||||||
\(273\) | 49.3406 | 2.98623 | ||||||||
\(274\) | −9.40250 | −0.568026 | ||||||||
\(275\) | −2.58281 | −0.155749 | ||||||||
\(276\) | 11.1727 | 0.672515 | ||||||||
\(277\) | −25.5788 | −1.53688 | −0.768440 | − | 0.639922i | \(-0.778967\pi\) | ||||
−0.768440 | + | 0.639922i | \(0.778967\pi\) | |||||||
\(278\) | −29.9612 | −1.79695 | ||||||||
\(279\) | 9.47832 | 0.567452 | ||||||||
\(280\) | −102.190 | −6.10700 | ||||||||
\(281\) | 18.0598 | 1.07736 | 0.538678 | − | 0.842511i | \(-0.318924\pi\) | ||||
0.538678 | + | 0.842511i | \(0.318924\pi\) | |||||||
\(282\) | −3.45648 | −0.205830 | ||||||||
\(283\) | −6.89252 | −0.409718 | −0.204859 | − | 0.978792i | \(-0.565674\pi\) | ||||
−0.204859 | + | 0.978792i | \(0.565674\pi\) | |||||||
\(284\) | 65.5827 | 3.89162 | ||||||||
\(285\) | 13.0299 | 0.771826 | ||||||||
\(286\) | 16.0657 | 0.949984 | ||||||||
\(287\) | 3.61852 | 0.213594 | ||||||||
\(288\) | −25.7581 | −1.51781 | ||||||||
\(289\) | 10.9575 | 0.644561 | ||||||||
\(290\) | 30.9616 | 1.81813 | ||||||||
\(291\) | 1.53835 | 0.0901796 | ||||||||
\(292\) | −60.0687 | −3.51526 | ||||||||
\(293\) | −14.1139 | −0.824545 | −0.412272 | − | 0.911061i | \(-0.635265\pi\) | ||||
−0.412272 | + | 0.911061i | \(0.635265\pi\) | |||||||
\(294\) | −44.6756 | −2.60553 | ||||||||
\(295\) | −25.0038 | −1.45577 | ||||||||
\(296\) | 23.5340 | 1.36789 | ||||||||
\(297\) | 3.51884 | 0.204184 | ||||||||
\(298\) | 12.5590 | 0.727523 | ||||||||
\(299\) | 6.23637 | 0.360659 | ||||||||
\(300\) | 30.6150 | 1.76756 | ||||||||
\(301\) | 33.5546 | 1.93405 | ||||||||
\(302\) | 20.3984 | 1.17380 | ||||||||
\(303\) | 5.72937 | 0.329144 | ||||||||
\(304\) | 34.3437 | 1.96974 | ||||||||
\(305\) | 10.7006 | 0.612713 | ||||||||
\(306\) | 16.9417 | 0.968492 | ||||||||
\(307\) | −21.4365 | −1.22345 | −0.611724 | − | 0.791071i | \(-0.709524\pi\) | ||||
−0.611724 | + | 0.791071i | \(0.709524\pi\) | |||||||
\(308\) | −19.9693 | −1.13786 | ||||||||
\(309\) | −9.26023 | −0.526796 | ||||||||
\(310\) | −61.4759 | −3.49160 | ||||||||
\(311\) | 14.7226 | 0.834841 | 0.417420 | − | 0.908714i | \(-0.362934\pi\) | ||||
0.417420 | + | 0.908714i | \(0.362934\pi\) | |||||||
\(312\) | −120.801 | −6.83902 | ||||||||
\(313\) | 7.13170 | 0.403107 | 0.201554 | − | 0.979477i | \(-0.435401\pi\) | ||||
0.201554 | + | 0.979477i | \(0.435401\pi\) | |||||||
\(314\) | −38.3799 | −2.16590 | ||||||||
\(315\) | 12.6332 | 0.711798 | ||||||||
\(316\) | 26.7536 | 1.50501 | ||||||||
\(317\) | 24.4872 | 1.37534 | 0.687669 | − | 0.726024i | \(-0.258634\pi\) | ||||
0.687669 | + | 0.726024i | \(0.258634\pi\) | |||||||
\(318\) | −40.9473 | −2.29621 | ||||||||
\(319\) | 3.83804 | 0.214889 | ||||||||
\(320\) | 83.7216 | 4.68018 | ||||||||
\(321\) | 4.08569 | 0.228041 | ||||||||
\(322\) | −10.5861 | −0.589939 | ||||||||
\(323\) | −12.1234 | −0.674566 | ||||||||
\(324\) | −60.9473 | −3.38596 | ||||||||
\(325\) | 17.0887 | 0.947912 | ||||||||
\(326\) | 38.9242 | 2.15581 | ||||||||
\(327\) | −10.9643 | −0.606325 | ||||||||
\(328\) | −8.85927 | −0.489171 | ||||||||
\(329\) | 2.39813 | 0.132213 | ||||||||
\(330\) | 14.6397 | 0.805890 | ||||||||
\(331\) | 24.6321 | 1.35390 | 0.676951 | − | 0.736028i | \(-0.263301\pi\) | ||||
0.676951 | + | 0.736028i | \(0.263301\pi\) | |||||||
\(332\) | 78.3064 | 4.29762 | ||||||||
\(333\) | −2.90939 | −0.159434 | ||||||||
\(334\) | −52.5965 | −2.87795 | ||||||||
\(335\) | −5.18286 | −0.283170 | ||||||||
\(336\) | 118.507 | 6.46507 | ||||||||
\(337\) | −23.9929 | −1.30697 | −0.653487 | − | 0.756938i | \(-0.726695\pi\) | ||||
−0.653487 | + | 0.756938i | \(0.726695\pi\) | |||||||
\(338\) | −70.7658 | −3.84915 | ||||||||
\(339\) | −22.7257 | −1.23429 | ||||||||
\(340\) | −80.4621 | −4.36367 | ||||||||
\(341\) | −7.62064 | −0.412681 | ||||||||
\(342\) | −7.34655 | −0.397256 | ||||||||
\(343\) | 3.88311 | 0.209668 | ||||||||
\(344\) | −82.1521 | −4.42935 | ||||||||
\(345\) | 5.68284 | 0.305954 | ||||||||
\(346\) | −45.8598 | −2.46544 | ||||||||
\(347\) | −22.3332 | −1.19891 | −0.599453 | − | 0.800410i | \(-0.704615\pi\) | ||||
−0.599453 | + | 0.800410i | \(0.704615\pi\) | |||||||
\(348\) | −45.4938 | −2.43872 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −29.0077 | −1.55053 | ||||||||
\(351\) | −23.2818 | −1.24269 | ||||||||
\(352\) | 20.7097 | 1.10383 | ||||||||
\(353\) | 34.9582 | 1.86064 | 0.930318 | − | 0.366754i | \(-0.119531\pi\) | ||||
0.930318 | + | 0.366754i | \(0.119531\pi\) | |||||||
\(354\) | 50.1733 | 2.66668 | ||||||||
\(355\) | 33.3578 | 1.77045 | ||||||||
\(356\) | −38.4152 | −2.03600 | ||||||||
\(357\) | −41.8333 | −2.21405 | ||||||||
\(358\) | −50.3454 | −2.66084 | ||||||||
\(359\) | −14.4297 | −0.761571 | −0.380786 | − | 0.924663i | \(-0.624346\pi\) | ||||
−0.380786 | + | 0.924663i | \(0.624346\pi\) | |||||||
\(360\) | −30.9300 | −1.63015 | ||||||||
\(361\) | −13.7428 | −0.723307 | ||||||||
\(362\) | 4.96244 | 0.260820 | ||||||||
\(363\) | −20.6542 | −1.08406 | ||||||||
\(364\) | 132.124 | 6.92516 | ||||||||
\(365\) | −30.5532 | −1.59923 | ||||||||
\(366\) | −21.4721 | −1.12236 | ||||||||
\(367\) | 17.8581 | 0.932183 | 0.466092 | − | 0.884736i | \(-0.345662\pi\) | ||||
0.466092 | + | 0.884736i | \(0.345662\pi\) | |||||||
\(368\) | 14.9786 | 0.780812 | ||||||||
\(369\) | 1.09522 | 0.0570151 | ||||||||
\(370\) | 18.8701 | 0.981012 | ||||||||
\(371\) | 28.4096 | 1.47495 | ||||||||
\(372\) | 90.3303 | 4.68341 | ||||||||
\(373\) | −28.1443 | −1.45726 | −0.728629 | − | 0.684909i | \(-0.759842\pi\) | ||||
−0.728629 | + | 0.684909i | \(0.759842\pi\) | |||||||
\(374\) | −13.6212 | −0.704338 | ||||||||
\(375\) | −12.8422 | −0.663170 | ||||||||
\(376\) | −5.87139 | −0.302794 | ||||||||
\(377\) | −25.3938 | −1.30785 | ||||||||
\(378\) | 39.5202 | 2.03270 | ||||||||
\(379\) | −13.8648 | −0.712187 | −0.356093 | − | 0.934450i | \(-0.615891\pi\) | ||||
−0.356093 | + | 0.934450i | \(0.615891\pi\) | |||||||
\(380\) | 34.8914 | 1.78989 | ||||||||
\(381\) | 8.69241 | 0.445326 | ||||||||
\(382\) | −38.7974 | −1.98505 | ||||||||
\(383\) | 9.54260 | 0.487604 | 0.243802 | − | 0.969825i | \(-0.421605\pi\) | ||||
0.243802 | + | 0.969825i | \(0.421605\pi\) | |||||||
\(384\) | −78.2390 | −3.99262 | ||||||||
\(385\) | −10.1572 | −0.517657 | ||||||||
\(386\) | 58.6594 | 2.98568 | ||||||||
\(387\) | 10.1560 | 0.516260 | ||||||||
\(388\) | 4.11938 | 0.209130 | ||||||||
\(389\) | −6.82269 | −0.345924 | −0.172962 | − | 0.984928i | \(-0.555334\pi\) | ||||
−0.172962 | + | 0.984928i | \(0.555334\pi\) | |||||||
\(390\) | −96.8612 | −4.90476 | ||||||||
\(391\) | −5.28749 | −0.267400 | ||||||||
\(392\) | −75.8887 | −3.83296 | ||||||||
\(393\) | −38.9940 | −1.96699 | ||||||||
\(394\) | −4.65022 | −0.234275 | ||||||||
\(395\) | 13.6079 | 0.684687 | ||||||||
\(396\) | −6.04416 | −0.303731 | ||||||||
\(397\) | −38.6015 | −1.93735 | −0.968677 | − | 0.248325i | \(-0.920120\pi\) | ||||
−0.968677 | + | 0.248325i | \(0.920120\pi\) | |||||||
\(398\) | −61.4163 | −3.07852 | ||||||||
\(399\) | 18.1405 | 0.908159 | ||||||||
\(400\) | 41.0439 | 2.05219 | ||||||||
\(401\) | 1.44966 | 0.0723926 | 0.0361963 | − | 0.999345i | \(-0.488476\pi\) | ||||
0.0361963 | + | 0.999345i | \(0.488476\pi\) | |||||||
\(402\) | 10.4001 | 0.518709 | ||||||||
\(403\) | 50.4207 | 2.51163 | ||||||||
\(404\) | 15.3421 | 0.763296 | ||||||||
\(405\) | −31.0001 | −1.54041 | ||||||||
\(406\) | 43.1052 | 2.13928 | ||||||||
\(407\) | 2.33917 | 0.115948 | ||||||||
\(408\) | 102.421 | 5.07059 | ||||||||
\(409\) | 5.40343 | 0.267182 | 0.133591 | − | 0.991037i | \(-0.457349\pi\) | ||||
0.133591 | + | 0.991037i | \(0.457349\pi\) | |||||||
\(410\) | −7.10356 | −0.350820 | ||||||||
\(411\) | 7.02717 | 0.346625 | ||||||||
\(412\) | −24.7970 | −1.22166 | ||||||||
\(413\) | −34.8106 | −1.71292 | ||||||||
\(414\) | −3.20411 | −0.157473 | ||||||||
\(415\) | 39.8296 | 1.95516 | ||||||||
\(416\) | −137.022 | −6.71807 | ||||||||
\(417\) | 22.3922 | 1.09655 | ||||||||
\(418\) | 5.90668 | 0.288905 | ||||||||
\(419\) | 28.6602 | 1.40014 | 0.700071 | − | 0.714073i | \(-0.253152\pi\) | ||||
0.700071 | + | 0.714073i | \(0.253152\pi\) | |||||||
\(420\) | 120.397 | 5.87475 | ||||||||
\(421\) | −30.3688 | −1.48008 | −0.740042 | − | 0.672560i | \(-0.765195\pi\) | ||||
−0.740042 | + | 0.672560i | \(0.765195\pi\) | |||||||
\(422\) | 52.9939 | 2.57970 | ||||||||
\(423\) | 0.725848 | 0.0352919 | ||||||||
\(424\) | −69.5556 | −3.37792 | ||||||||
\(425\) | −14.4886 | −0.702802 | ||||||||
\(426\) | −66.9369 | −3.24310 | ||||||||
\(427\) | 14.8975 | 0.720941 | ||||||||
\(428\) | 10.9406 | 0.528835 | ||||||||
\(429\) | −12.0071 | −0.579706 | ||||||||
\(430\) | −65.8715 | −3.17660 | ||||||||
\(431\) | −25.3620 | −1.22165 | −0.610823 | − | 0.791767i | \(-0.709161\pi\) | ||||
−0.610823 | + | 0.791767i | \(0.709161\pi\) | |||||||
\(432\) | −55.9184 | −2.69038 | ||||||||
\(433\) | −3.49367 | −0.167895 | −0.0839475 | − | 0.996470i | \(-0.526753\pi\) | ||||
−0.0839475 | + | 0.996470i | \(0.526753\pi\) | |||||||
\(434\) | −85.5878 | −4.10835 | ||||||||
\(435\) | −23.1398 | −1.10947 | ||||||||
\(436\) | −29.3600 | −1.40609 | ||||||||
\(437\) | 2.29285 | 0.109682 | ||||||||
\(438\) | 61.3091 | 2.92946 | ||||||||
\(439\) | −38.6739 | −1.84581 | −0.922903 | − | 0.385032i | \(-0.874190\pi\) | ||||
−0.922903 | + | 0.385032i | \(0.874190\pi\) | |||||||
\(440\) | 24.8679 | 1.18553 | ||||||||
\(441\) | 9.38171 | 0.446748 | ||||||||
\(442\) | 90.1226 | 4.28670 | ||||||||
\(443\) | 35.5796 | 1.69044 | 0.845218 | − | 0.534422i | \(-0.179471\pi\) | ||||
0.845218 | + | 0.534422i | \(0.179471\pi\) | |||||||
\(444\) | −27.7271 | −1.31587 | ||||||||
\(445\) | −19.5394 | −0.926257 | ||||||||
\(446\) | 21.5656 | 1.02116 | ||||||||
\(447\) | −9.38625 | −0.443954 | ||||||||
\(448\) | 116.559 | 5.50688 | ||||||||
\(449\) | 27.5738 | 1.30129 | 0.650645 | − | 0.759382i | \(-0.274499\pi\) | ||||
0.650645 | + | 0.759382i | \(0.274499\pi\) | |||||||
\(450\) | −8.77982 | −0.413884 | ||||||||
\(451\) | −0.880568 | −0.0414643 | ||||||||
\(452\) | −60.8546 | −2.86236 | ||||||||
\(453\) | −15.2452 | −0.716284 | ||||||||
\(454\) | −54.4817 | −2.55695 | ||||||||
\(455\) | 67.2031 | 3.15053 | ||||||||
\(456\) | −44.4136 | −2.07986 | ||||||||
\(457\) | −6.11373 | −0.285988 | −0.142994 | − | 0.989724i | \(-0.545673\pi\) | ||||
−0.142994 | + | 0.989724i | \(0.545673\pi\) | |||||||
\(458\) | 0.762370 | 0.0356232 | ||||||||
\(459\) | 19.7394 | 0.921357 | ||||||||
\(460\) | 15.2175 | 0.709517 | ||||||||
\(461\) | −10.1165 | −0.471171 | −0.235586 | − | 0.971854i | \(-0.575701\pi\) | ||||
−0.235586 | + | 0.971854i | \(0.575701\pi\) | |||||||
\(462\) | 20.3817 | 0.948241 | ||||||||
\(463\) | 11.2538 | 0.523009 | 0.261505 | − | 0.965202i | \(-0.415781\pi\) | ||||
0.261505 | + | 0.965202i | \(0.415781\pi\) | |||||||
\(464\) | −60.9910 | −2.83143 | ||||||||
\(465\) | 45.9454 | 2.13067 | ||||||||
\(466\) | 64.2978 | 2.97854 | ||||||||
\(467\) | −24.2736 | −1.12325 | −0.561624 | − | 0.827393i | \(-0.689823\pi\) | ||||
−0.561624 | + | 0.827393i | \(0.689823\pi\) | |||||||
\(468\) | 39.9902 | 1.84855 | ||||||||
\(469\) | −7.21566 | −0.333188 | ||||||||
\(470\) | −4.70781 | −0.217155 | ||||||||
\(471\) | 28.6841 | 1.32169 | ||||||||
\(472\) | 85.2274 | 3.92291 | ||||||||
\(473\) | −8.16552 | −0.375451 | ||||||||
\(474\) | −27.3060 | −1.25421 | ||||||||
\(475\) | 6.28281 | 0.288275 | ||||||||
\(476\) | −112.021 | −5.13446 | ||||||||
\(477\) | 8.59879 | 0.393712 | ||||||||
\(478\) | 18.5122 | 0.846727 | ||||||||
\(479\) | 5.02143 | 0.229435 | 0.114717 | − | 0.993398i | \(-0.463404\pi\) | ||||
0.114717 | + | 0.993398i | \(0.463404\pi\) | |||||||
\(480\) | −124.860 | −5.69908 | ||||||||
\(481\) | −15.4767 | −0.705678 | ||||||||
\(482\) | −45.4788 | −2.07150 | ||||||||
\(483\) | 7.91174 | 0.359997 | ||||||||
\(484\) | −55.3076 | −2.51398 | ||||||||
\(485\) | 2.09527 | 0.0951413 | ||||||||
\(486\) | 31.5961 | 1.43323 | ||||||||
\(487\) | −4.00272 | −0.181380 | −0.0906902 | − | 0.995879i | \(-0.528907\pi\) | ||||
−0.0906902 | + | 0.995879i | \(0.528907\pi\) | |||||||
\(488\) | −36.4738 | −1.65109 | ||||||||
\(489\) | −29.0909 | −1.31554 | ||||||||
\(490\) | −60.8493 | −2.74889 | ||||||||
\(491\) | −30.3756 | −1.37083 | −0.685415 | − | 0.728152i | \(-0.740379\pi\) | ||||
−0.685415 | + | 0.728152i | \(0.740379\pi\) | |||||||
\(492\) | 10.4377 | 0.470568 | ||||||||
\(493\) | 21.5300 | 0.969664 | ||||||||
\(494\) | −39.0806 | −1.75832 | ||||||||
\(495\) | −3.07429 | −0.138179 | ||||||||
\(496\) | 121.101 | 5.43759 | ||||||||
\(497\) | 46.4414 | 2.08318 | ||||||||
\(498\) | −79.9233 | −3.58145 | ||||||||
\(499\) | 44.0095 | 1.97013 | 0.985067 | − | 0.172172i | \(-0.0550786\pi\) | ||||
0.985067 | + | 0.172172i | \(0.0550786\pi\) | |||||||
\(500\) | −34.3888 | −1.53791 | ||||||||
\(501\) | 39.3092 | 1.75621 | ||||||||
\(502\) | −68.1928 | −3.04360 | ||||||||
\(503\) | −39.8200 | −1.77549 | −0.887744 | − | 0.460338i | \(-0.847728\pi\) | ||||
−0.887744 | + | 0.460338i | \(0.847728\pi\) | |||||||
\(504\) | −43.0612 | −1.91810 | ||||||||
\(505\) | 7.80356 | 0.347254 | ||||||||
\(506\) | 2.57613 | 0.114523 | ||||||||
\(507\) | 52.8884 | 2.34886 | ||||||||
\(508\) | 23.2764 | 1.03273 | ||||||||
\(509\) | 6.46687 | 0.286639 | 0.143319 | − | 0.989676i | \(-0.454222\pi\) | ||||
0.143319 | + | 0.989676i | \(0.454222\pi\) | |||||||
\(510\) | 82.1235 | 3.63649 | ||||||||
\(511\) | −42.5367 | −1.88171 | ||||||||
\(512\) | −45.0156 | −1.98943 | ||||||||
\(513\) | −8.55975 | −0.377922 | ||||||||
\(514\) | −47.7694 | −2.10702 | ||||||||
\(515\) | −12.6127 | −0.555781 | ||||||||
\(516\) | 96.7890 | 4.26090 | ||||||||
\(517\) | −0.583587 | −0.0256661 | ||||||||
\(518\) | 26.2713 | 1.15430 | ||||||||
\(519\) | 34.2743 | 1.50448 | ||||||||
\(520\) | −164.534 | −7.21531 | ||||||||
\(521\) | −32.7710 | −1.43572 | −0.717861 | − | 0.696187i | \(-0.754879\pi\) | ||||
−0.717861 | + | 0.696187i | \(0.754879\pi\) | |||||||
\(522\) | 13.0468 | 0.571041 | ||||||||
\(523\) | −21.4335 | −0.937223 | −0.468611 | − | 0.883404i | \(-0.655246\pi\) | ||||
−0.468611 | + | 0.883404i | \(0.655246\pi\) | |||||||
\(524\) | −104.418 | −4.56151 | ||||||||
\(525\) | 21.6795 | 0.946173 | ||||||||
\(526\) | −29.5469 | −1.28830 | ||||||||
\(527\) | −42.7490 | −1.86218 | ||||||||
\(528\) | −28.8387 | −1.25504 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −55.7713 | −2.42255 | ||||||||
\(531\) | −10.5362 | −0.457233 | ||||||||
\(532\) | 48.5764 | 2.10605 | ||||||||
\(533\) | 5.82613 | 0.252358 | ||||||||
\(534\) | 39.2084 | 1.69671 | ||||||||
\(535\) | 5.56482 | 0.240588 | ||||||||
\(536\) | 17.6662 | 0.763064 | ||||||||
\(537\) | 37.6268 | 1.62372 | ||||||||
\(538\) | −30.3129 | −1.30688 | ||||||||
\(539\) | −7.54297 | −0.324899 | ||||||||
\(540\) | −56.8102 | −2.44472 | ||||||||
\(541\) | −15.1599 | −0.651773 | −0.325887 | − | 0.945409i | \(-0.605663\pi\) | ||||
−0.325887 | + | 0.945409i | \(0.605663\pi\) | |||||||
\(542\) | 34.7693 | 1.49347 | ||||||||
\(543\) | −3.70879 | −0.159159 | ||||||||
\(544\) | 116.174 | 4.98092 | ||||||||
\(545\) | −14.9336 | −0.639685 | ||||||||
\(546\) | −134.852 | −5.77113 | ||||||||
\(547\) | 16.8025 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(548\) | 18.8173 | 0.803835 | ||||||||
\(549\) | 4.50906 | 0.192442 | ||||||||
\(550\) | 7.05904 | 0.300998 | ||||||||
\(551\) | −9.33623 | −0.397737 | ||||||||
\(552\) | −19.3704 | −0.824461 | ||||||||
\(553\) | 18.9451 | 0.805628 | ||||||||
\(554\) | 69.9089 | 2.97015 | ||||||||
\(555\) | −14.1030 | −0.598640 | ||||||||
\(556\) | 59.9615 | 2.54294 | ||||||||
\(557\) | −20.8609 | −0.883905 | −0.441952 | − | 0.897038i | \(-0.645714\pi\) | ||||
−0.441952 | + | 0.897038i | \(0.645714\pi\) | |||||||
\(558\) | −25.9050 | −1.09665 | ||||||||
\(559\) | 54.0258 | 2.28505 | ||||||||
\(560\) | 161.409 | 6.82078 | ||||||||
\(561\) | 10.1802 | 0.429806 | ||||||||
\(562\) | −49.3589 | −2.08208 | ||||||||
\(563\) | 17.9910 | 0.758232 | 0.379116 | − | 0.925349i | \(-0.376228\pi\) | ||||
0.379116 | + | 0.925349i | \(0.376228\pi\) | |||||||
\(564\) | 6.91748 | 0.291278 | ||||||||
\(565\) | −30.9530 | −1.30220 | ||||||||
\(566\) | 18.8378 | 0.791813 | ||||||||
\(567\) | −43.1589 | −1.81250 | ||||||||
\(568\) | −113.703 | −4.77087 | ||||||||
\(569\) | 6.51137 | 0.272971 | 0.136485 | − | 0.990642i | \(-0.456419\pi\) | ||||
0.136485 | + | 0.990642i | \(0.456419\pi\) | |||||||
\(570\) | −35.6118 | −1.49162 | ||||||||
\(571\) | 25.2674 | 1.05741 | 0.528704 | − | 0.848806i | \(-0.322678\pi\) | ||||
0.528704 | + | 0.848806i | \(0.322678\pi\) | |||||||
\(572\) | −32.1524 | −1.34436 | ||||||||
\(573\) | 28.9961 | 1.21133 | ||||||||
\(574\) | −9.88970 | −0.412788 | ||||||||
\(575\) | 2.74017 | 0.114273 | ||||||||
\(576\) | 35.2791 | 1.46996 | ||||||||
\(577\) | −29.9989 | −1.24887 | −0.624436 | − | 0.781076i | \(-0.714671\pi\) | ||||
−0.624436 | + | 0.781076i | \(0.714671\pi\) | |||||||
\(578\) | −29.9478 | −1.24567 | ||||||||
\(579\) | −43.8404 | −1.82195 | ||||||||
\(580\) | −61.9637 | −2.57290 | ||||||||
\(581\) | 55.4514 | 2.30051 | ||||||||
\(582\) | −4.20443 | −0.174279 | ||||||||
\(583\) | −6.91349 | −0.286328 | ||||||||
\(584\) | 104.143 | 4.30948 | ||||||||
\(585\) | 20.3405 | 0.840977 | ||||||||
\(586\) | 38.5745 | 1.59350 | ||||||||
\(587\) | −12.7845 | −0.527671 | −0.263836 | − | 0.964568i | \(-0.584988\pi\) | ||||
−0.263836 | + | 0.964568i | \(0.584988\pi\) | |||||||
\(588\) | 89.4096 | 3.68719 | ||||||||
\(589\) | 18.5376 | 0.763828 | ||||||||
\(590\) | 68.3373 | 2.81340 | ||||||||
\(591\) | 3.47545 | 0.142961 | ||||||||
\(592\) | −37.1721 | −1.52777 | ||||||||
\(593\) | −21.5496 | −0.884935 | −0.442468 | − | 0.896784i | \(-0.645897\pi\) | ||||
−0.442468 | + | 0.896784i | \(0.645897\pi\) | |||||||
\(594\) | −9.61728 | −0.394602 | ||||||||
\(595\) | −56.9780 | −2.33587 | ||||||||
\(596\) | −25.1344 | −1.02955 | ||||||||
\(597\) | 45.9009 | 1.87860 | ||||||||
\(598\) | −17.0445 | −0.697002 | ||||||||
\(599\) | 25.7240 | 1.05105 | 0.525527 | − | 0.850777i | \(-0.323868\pi\) | ||||
0.525527 | + | 0.850777i | \(0.323868\pi\) | |||||||
\(600\) | −53.0784 | −2.16692 | ||||||||
\(601\) | 18.8968 | 0.770816 | 0.385408 | − | 0.922746i | \(-0.374061\pi\) | ||||
0.385408 | + | 0.922746i | \(0.374061\pi\) | |||||||
\(602\) | −91.7074 | −3.73771 | ||||||||
\(603\) | −2.18398 | −0.0889385 | ||||||||
\(604\) | −40.8235 | −1.66109 | ||||||||
\(605\) | −28.1315 | −1.14371 | ||||||||
\(606\) | −15.6589 | −0.636097 | ||||||||
\(607\) | 3.69895 | 0.150136 | 0.0750678 | − | 0.997178i | \(-0.476083\pi\) | ||||
0.0750678 | + | 0.997178i | \(0.476083\pi\) | |||||||
\(608\) | −50.3774 | −2.04307 | ||||||||
\(609\) | −32.2157 | −1.30545 | ||||||||
\(610\) | −29.2455 | −1.18412 | ||||||||
\(611\) | 3.86120 | 0.156208 | ||||||||
\(612\) | −33.9055 | −1.37055 | ||||||||
\(613\) | 18.9216 | 0.764236 | 0.382118 | − | 0.924114i | \(-0.375195\pi\) | ||||
0.382118 | + | 0.924114i | \(0.375195\pi\) | |||||||
\(614\) | 58.5878 | 2.36441 | ||||||||
\(615\) | 5.30901 | 0.214080 | ||||||||
\(616\) | 34.6216 | 1.39494 | ||||||||
\(617\) | 7.26011 | 0.292281 | 0.146140 | − | 0.989264i | \(-0.453315\pi\) | ||||
0.146140 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(618\) | 25.3090 | 1.01808 | ||||||||
\(619\) | −37.9918 | −1.52702 | −0.763510 | − | 0.645796i | \(-0.776526\pi\) | ||||
−0.763510 | + | 0.645796i | \(0.776526\pi\) | |||||||
\(620\) | 123.032 | 4.94109 | ||||||||
\(621\) | −3.73323 | −0.149809 | ||||||||
\(622\) | −40.2380 | −1.61340 | ||||||||
\(623\) | −27.2031 | −1.08987 | ||||||||
\(624\) | 190.806 | 7.63836 | ||||||||
\(625\) | −31.1923 | −1.24769 | ||||||||
\(626\) | −19.4915 | −0.779038 | ||||||||
\(627\) | −4.41449 | −0.176298 | ||||||||
\(628\) | 76.8100 | 3.06505 | ||||||||
\(629\) | 13.1219 | 0.523204 | ||||||||
\(630\) | −34.5275 | −1.37561 | ||||||||
\(631\) | −27.6573 | −1.10102 | −0.550510 | − | 0.834829i | \(-0.685567\pi\) | ||||
−0.550510 | + | 0.834829i | \(0.685567\pi\) | |||||||
\(632\) | −46.3836 | −1.84504 | ||||||||
\(633\) | −39.6062 | −1.57421 | ||||||||
\(634\) | −66.9256 | −2.65795 | ||||||||
\(635\) | 11.8393 | 0.469828 | ||||||||
\(636\) | 81.9482 | 3.24946 | ||||||||
\(637\) | 49.9067 | 1.97738 | ||||||||
\(638\) | −10.4897 | −0.415291 | ||||||||
\(639\) | 14.0565 | 0.556067 | ||||||||
\(640\) | −106.564 | −4.21229 | ||||||||
\(641\) | −23.6208 | −0.932964 | −0.466482 | − | 0.884531i | \(-0.654479\pi\) | ||||
−0.466482 | + | 0.884531i | \(0.654479\pi\) | |||||||
\(642\) | −11.1665 | −0.440708 | ||||||||
\(643\) | −25.4284 | −1.00280 | −0.501400 | − | 0.865216i | \(-0.667181\pi\) | ||||
−0.501400 | + | 0.865216i | \(0.667181\pi\) | |||||||
\(644\) | 21.1860 | 0.834845 | ||||||||
\(645\) | 49.2305 | 1.93845 | ||||||||
\(646\) | 33.1343 | 1.30365 | ||||||||
\(647\) | −19.5984 | −0.770494 | −0.385247 | − | 0.922813i | \(-0.625884\pi\) | ||||
−0.385247 | + | 0.922813i | \(0.625884\pi\) | |||||||
\(648\) | 105.667 | 4.15098 | ||||||||
\(649\) | 8.47119 | 0.332523 | ||||||||
\(650\) | −46.7049 | −1.83192 | ||||||||
\(651\) | 63.9660 | 2.50702 | ||||||||
\(652\) | −77.8994 | −3.05077 | ||||||||
\(653\) | −33.3385 | −1.30464 | −0.652318 | − | 0.757945i | \(-0.726203\pi\) | ||||
−0.652318 | + | 0.757945i | \(0.726203\pi\) | |||||||
\(654\) | 29.9662 | 1.17177 | ||||||||
\(655\) | −53.1109 | −2.07521 | ||||||||
\(656\) | 13.9932 | 0.546345 | ||||||||
\(657\) | −12.8747 | −0.502289 | ||||||||
\(658\) | −6.55430 | −0.255513 | ||||||||
\(659\) | −12.8480 | −0.500488 | −0.250244 | − | 0.968183i | \(-0.580511\pi\) | ||||
−0.250244 | + | 0.968183i | \(0.580511\pi\) | |||||||
\(660\) | −29.2986 | −1.14045 | ||||||||
\(661\) | −38.7225 | −1.50613 | −0.753066 | − | 0.657945i | \(-0.771426\pi\) | ||||
−0.753066 | + | 0.657945i | \(0.771426\pi\) | |||||||
\(662\) | −67.3215 | −2.61652 | ||||||||
\(663\) | −67.3552 | −2.61586 | ||||||||
\(664\) | −135.763 | −5.26861 | ||||||||
\(665\) | 24.7078 | 0.958127 | ||||||||
\(666\) | 7.95160 | 0.308118 | ||||||||
\(667\) | −4.07188 | −0.157664 | ||||||||
\(668\) | 105.262 | 4.07270 | ||||||||
\(669\) | −16.1176 | −0.623141 | ||||||||
\(670\) | 14.1652 | 0.547248 | ||||||||
\(671\) | −3.62532 | −0.139954 | ||||||||
\(672\) | −173.833 | −6.70575 | ||||||||
\(673\) | −4.39145 | −0.169278 | −0.0846390 | − | 0.996412i | \(-0.526974\pi\) | ||||
−0.0846390 | + | 0.996412i | \(0.526974\pi\) | |||||||
\(674\) | 65.5745 | 2.52583 | ||||||||
\(675\) | −10.2297 | −0.393741 | ||||||||
\(676\) | 141.624 | 5.44708 | ||||||||
\(677\) | 45.8801 | 1.76332 | 0.881658 | − | 0.471888i | \(-0.156427\pi\) | ||||
0.881658 | + | 0.471888i | \(0.156427\pi\) | |||||||
\(678\) | 62.1112 | 2.38536 | ||||||||
\(679\) | 2.91707 | 0.111947 | ||||||||
\(680\) | 139.500 | 5.34958 | ||||||||
\(681\) | 40.7181 | 1.56032 | ||||||||
\(682\) | 20.8278 | 0.797539 | ||||||||
\(683\) | 19.2047 | 0.734847 | 0.367424 | − | 0.930054i | \(-0.380240\pi\) | ||||
0.367424 | + | 0.930054i | \(0.380240\pi\) | |||||||
\(684\) | 14.7027 | 0.562172 | ||||||||
\(685\) | 9.57119 | 0.365696 | ||||||||
\(686\) | −10.6129 | −0.405201 | ||||||||
\(687\) | −0.569775 | −0.0217383 | ||||||||
\(688\) | 129.760 | 4.94704 | ||||||||
\(689\) | 45.7419 | 1.74263 | ||||||||
\(690\) | −15.5317 | −0.591280 | ||||||||
\(691\) | −22.6353 | −0.861089 | −0.430544 | − | 0.902569i | \(-0.641678\pi\) | ||||
−0.430544 | + | 0.902569i | \(0.641678\pi\) | |||||||
\(692\) | 91.7795 | 3.48893 | ||||||||
\(693\) | −4.28008 | −0.162587 | ||||||||
\(694\) | 61.0384 | 2.31698 | ||||||||
\(695\) | 30.4987 | 1.15688 | ||||||||
\(696\) | 78.8742 | 2.98972 | ||||||||
\(697\) | −4.93967 | −0.187103 | ||||||||
\(698\) | 2.73308 | 0.103449 | ||||||||
\(699\) | −48.0544 | −1.81758 | ||||||||
\(700\) | 58.0533 | 2.19421 | ||||||||
\(701\) | −0.676650 | −0.0255567 | −0.0127784 | − | 0.999918i | \(-0.504068\pi\) | ||||
−0.0127784 | + | 0.999918i | \(0.504068\pi\) | |||||||
\(702\) | 63.6311 | 2.40160 | ||||||||
\(703\) | −5.69014 | −0.214608 | ||||||||
\(704\) | −28.3646 | −1.06903 | ||||||||
\(705\) | 3.51849 | 0.132514 | ||||||||
\(706\) | −95.5436 | −3.59583 | ||||||||
\(707\) | 10.8642 | 0.408592 | ||||||||
\(708\) | −100.412 | −3.77372 | ||||||||
\(709\) | 40.9875 | 1.53932 | 0.769659 | − | 0.638456i | \(-0.220426\pi\) | ||||
0.769659 | + | 0.638456i | \(0.220426\pi\) | |||||||
\(710\) | −91.1697 | −3.42154 | ||||||||
\(711\) | 5.73416 | 0.215048 | ||||||||
\(712\) | 66.6018 | 2.49601 | ||||||||
\(713\) | 8.08494 | 0.302783 | ||||||||
\(714\) | 114.334 | 4.27883 | ||||||||
\(715\) | −16.3539 | −0.611602 | ||||||||
\(716\) | 100.757 | 3.76545 | ||||||||
\(717\) | −13.8355 | −0.516696 | ||||||||
\(718\) | 39.4376 | 1.47180 | ||||||||
\(719\) | 40.4073 | 1.50694 | 0.753468 | − | 0.657484i | \(-0.228379\pi\) | ||||
0.753468 | + | 0.657484i | \(0.228379\pi\) | |||||||
\(720\) | 48.8540 | 1.82068 | ||||||||
\(721\) | −17.5596 | −0.653953 | ||||||||
\(722\) | 37.5603 | 1.39785 | ||||||||
\(723\) | 33.9897 | 1.26409 | ||||||||
\(724\) | −9.93136 | −0.369096 | ||||||||
\(725\) | −11.1577 | −0.414385 | ||||||||
\(726\) | 56.4496 | 2.09504 | ||||||||
\(727\) | 0.588702 | 0.0218337 | 0.0109169 | − | 0.999940i | \(-0.496525\pi\) | ||||
0.0109169 | + | 0.999940i | \(0.496525\pi\) | |||||||
\(728\) | −229.068 | −8.48981 | ||||||||
\(729\) | 9.81384 | 0.363475 | ||||||||
\(730\) | 83.5045 | 3.09064 | ||||||||
\(731\) | −45.8056 | −1.69418 | ||||||||
\(732\) | 42.9723 | 1.58830 | ||||||||
\(733\) | 16.3991 | 0.605714 | 0.302857 | − | 0.953036i | \(-0.402060\pi\) | ||||
0.302857 | + | 0.953036i | \(0.402060\pi\) | |||||||
\(734\) | −48.8076 | −1.80152 | ||||||||
\(735\) | 45.4771 | 1.67745 | ||||||||
\(736\) | −21.9715 | −0.809880 | ||||||||
\(737\) | 1.75594 | 0.0646807 | ||||||||
\(738\) | −2.99334 | −0.110186 | ||||||||
\(739\) | 7.30562 | 0.268741 | 0.134371 | − | 0.990931i | \(-0.457099\pi\) | ||||
0.134371 | + | 0.990931i | \(0.457099\pi\) | |||||||
\(740\) | −37.7650 | −1.38827 | ||||||||
\(741\) | 29.2077 | 1.07297 | ||||||||
\(742\) | −77.6458 | −2.85047 | ||||||||
\(743\) | 4.26066 | 0.156308 | 0.0781542 | − | 0.996941i | \(-0.475097\pi\) | ||||
0.0781542 | + | 0.996941i | \(0.475097\pi\) | |||||||
\(744\) | −156.609 | −5.74156 | ||||||||
\(745\) | −12.7843 | −0.468381 | ||||||||
\(746\) | 76.9207 | 2.81627 | ||||||||
\(747\) | 16.7836 | 0.614080 | ||||||||
\(748\) | 27.2603 | 0.996736 | ||||||||
\(749\) | 7.74743 | 0.283085 | ||||||||
\(750\) | 35.0989 | 1.28163 | ||||||||
\(751\) | −18.9634 | −0.691985 | −0.345992 | − | 0.938237i | \(-0.612458\pi\) | ||||
−0.345992 | + | 0.938237i | \(0.612458\pi\) | |||||||
\(752\) | 9.27388 | 0.338184 | ||||||||
\(753\) | 50.9655 | 1.85728 | ||||||||
\(754\) | 69.4032 | 2.52752 | ||||||||
\(755\) | −20.7644 | −0.755694 | ||||||||
\(756\) | −79.0922 | −2.87656 | ||||||||
\(757\) | 43.4896 | 1.58065 | 0.790327 | − | 0.612685i | \(-0.209910\pi\) | ||||
0.790327 | + | 0.612685i | \(0.209910\pi\) | |||||||
\(758\) | 37.8936 | 1.37636 | ||||||||
\(759\) | −1.92533 | −0.0698850 | ||||||||
\(760\) | −60.4924 | −2.19429 | ||||||||
\(761\) | −19.0485 | −0.690507 | −0.345253 | − | 0.938509i | \(-0.612207\pi\) | ||||
−0.345253 | + | 0.938509i | \(0.612207\pi\) | |||||||
\(762\) | −23.7571 | −0.860628 | ||||||||
\(763\) | −20.7908 | −0.752678 | ||||||||
\(764\) | 77.6455 | 2.80912 | ||||||||
\(765\) | −17.2456 | −0.623518 | ||||||||
\(766\) | −26.0807 | −0.942335 | ||||||||
\(767\) | −56.0482 | −2.02378 | ||||||||
\(768\) | 90.8967 | 3.27995 | ||||||||
\(769\) | 21.7746 | 0.785212 | 0.392606 | − | 0.919707i | \(-0.371574\pi\) | ||||
0.392606 | + | 0.919707i | \(0.371574\pi\) | |||||||
\(770\) | 27.7604 | 1.00041 | ||||||||
\(771\) | 35.7015 | 1.28576 | ||||||||
\(772\) | −117.395 | −4.22515 | ||||||||
\(773\) | 22.1364 | 0.796192 | 0.398096 | − | 0.917344i | \(-0.369671\pi\) | ||||
0.398096 | + | 0.917344i | \(0.369671\pi\) | |||||||
\(774\) | −27.7573 | −0.997714 | ||||||||
\(775\) | 22.1541 | 0.795800 | ||||||||
\(776\) | −7.14191 | −0.256380 | ||||||||
\(777\) | −19.6345 | −0.704383 | ||||||||
\(778\) | 18.6470 | 0.668527 | ||||||||
\(779\) | 2.14202 | 0.0767460 | ||||||||
\(780\) | 193.849 | 6.94091 | ||||||||
\(781\) | −11.3015 | −0.404401 | ||||||||
\(782\) | 14.4511 | 0.516772 | ||||||||
\(783\) | 15.2013 | 0.543249 | ||||||||
\(784\) | 119.866 | 4.28095 | ||||||||
\(785\) | 39.0685 | 1.39441 | ||||||||
\(786\) | 106.574 | 3.80136 | ||||||||
\(787\) | −40.0312 | −1.42696 | −0.713480 | − | 0.700676i | \(-0.752882\pi\) | ||||
−0.713480 | + | 0.700676i | \(0.752882\pi\) | |||||||
\(788\) | 9.30653 | 0.331531 | ||||||||
\(789\) | 22.0825 | 0.786159 | ||||||||
\(790\) | −37.1914 | −1.32321 | ||||||||
\(791\) | −43.0932 | −1.53222 | ||||||||
\(792\) | 10.4790 | 0.372354 | ||||||||
\(793\) | 23.9863 | 0.851779 | ||||||||
\(794\) | 105.501 | 3.74409 | ||||||||
\(795\) | 41.6820 | 1.47831 | ||||||||
\(796\) | 122.913 | 4.35654 | ||||||||
\(797\) | −15.4518 | −0.547330 | −0.273665 | − | 0.961825i | \(-0.588236\pi\) | ||||
−0.273665 | + | 0.961825i | \(0.588236\pi\) | |||||||
\(798\) | −49.5794 | −1.75509 | ||||||||
\(799\) | −3.27371 | −0.115816 | ||||||||
\(800\) | −60.2057 | −2.12859 | ||||||||
\(801\) | −8.23362 | −0.290921 | ||||||||
\(802\) | −3.96204 | −0.139904 | ||||||||
\(803\) | 10.3513 | 0.365291 | ||||||||
\(804\) | −20.8138 | −0.734045 | ||||||||
\(805\) | 10.7760 | 0.379804 | ||||||||
\(806\) | −137.804 | −4.85393 | ||||||||
\(807\) | 22.6550 | 0.797495 | ||||||||
\(808\) | −26.5991 | −0.935753 | ||||||||
\(809\) | −37.6144 | −1.32245 | −0.661226 | − | 0.750187i | \(-0.729964\pi\) | ||||
−0.661226 | + | 0.750187i | \(0.729964\pi\) | |||||||
\(810\) | 84.7259 | 2.97696 | ||||||||
\(811\) | 15.7131 | 0.551760 | 0.275880 | − | 0.961192i | \(-0.411031\pi\) | ||||
0.275880 | + | 0.961192i | \(0.411031\pi\) | |||||||
\(812\) | −86.2669 | −3.02737 | ||||||||
\(813\) | −25.9856 | −0.911356 | ||||||||
\(814\) | −6.39315 | −0.224080 | ||||||||
\(815\) | −39.6226 | −1.38792 | ||||||||
\(816\) | −161.774 | −5.66324 | ||||||||
\(817\) | 19.8630 | 0.694920 | ||||||||
\(818\) | −14.7680 | −0.516351 | ||||||||
\(819\) | 28.3184 | 0.989525 | ||||||||
\(820\) | 14.2164 | 0.496459 | ||||||||
\(821\) | 6.17012 | 0.215339 | 0.107669 | − | 0.994187i | \(-0.465661\pi\) | ||||
0.107669 | + | 0.994187i | \(0.465661\pi\) | |||||||
\(822\) | −19.2058 | −0.669880 | ||||||||
\(823\) | 0.237237 | 0.00826955 | 0.00413478 | − | 0.999991i | \(-0.498684\pi\) | ||||
0.00413478 | + | 0.999991i | \(0.498684\pi\) | |||||||
\(824\) | 42.9914 | 1.49768 | ||||||||
\(825\) | −5.27573 | −0.183677 | ||||||||
\(826\) | 95.1404 | 3.31036 | ||||||||
\(827\) | −7.61192 | −0.264692 | −0.132346 | − | 0.991204i | \(-0.542251\pi\) | ||||
−0.132346 | + | 0.991204i | \(0.542251\pi\) | |||||||
\(828\) | 6.41241 | 0.222847 | ||||||||
\(829\) | −48.3466 | −1.67915 | −0.839573 | − | 0.543247i | \(-0.817195\pi\) | ||||
−0.839573 | + | 0.543247i | \(0.817195\pi\) | |||||||
\(830\) | −108.858 | −3.77850 | ||||||||
\(831\) | −52.2480 | −1.81246 | ||||||||
\(832\) | 187.670 | 6.50627 | ||||||||
\(833\) | −42.3133 | −1.46607 | ||||||||
\(834\) | −61.1996 | −2.11917 | ||||||||
\(835\) | 53.5401 | 1.85283 | ||||||||
\(836\) | −11.8211 | −0.408841 | ||||||||
\(837\) | −30.1829 | −1.04327 | ||||||||
\(838\) | −78.3307 | −2.70589 | ||||||||
\(839\) | −42.3724 | −1.46286 | −0.731430 | − | 0.681917i | \(-0.761147\pi\) | ||||
−0.731430 | + | 0.681917i | \(0.761147\pi\) | |||||||
\(840\) | −208.736 | −7.20207 | ||||||||
\(841\) | −12.4198 | −0.428268 | ||||||||
\(842\) | 83.0004 | 2.86038 | ||||||||
\(843\) | 36.8895 | 1.27054 | ||||||||
\(844\) | −106.057 | −3.65064 | ||||||||
\(845\) | 72.0354 | 2.47809 | ||||||||
\(846\) | −1.98380 | −0.0682045 | ||||||||
\(847\) | −39.1652 | −1.34573 | ||||||||
\(848\) | 109.863 | 3.77273 | ||||||||
\(849\) | −14.0789 | −0.483186 | ||||||||
\(850\) | 39.5986 | 1.35822 | ||||||||
\(851\) | −2.48169 | −0.0850711 | ||||||||
\(852\) | 133.961 | 4.58944 | ||||||||
\(853\) | 32.1190 | 1.09973 | 0.549866 | − | 0.835253i | \(-0.314679\pi\) | ||||
0.549866 | + | 0.835253i | \(0.314679\pi\) | |||||||
\(854\) | −40.7161 | −1.39328 | ||||||||
\(855\) | 7.47836 | 0.255754 | ||||||||
\(856\) | −18.9682 | −0.648318 | ||||||||
\(857\) | −24.7390 | −0.845067 | −0.422534 | − | 0.906347i | \(-0.638859\pi\) | ||||
−0.422534 | + | 0.906347i | \(0.638859\pi\) | |||||||
\(858\) | 32.8163 | 1.12033 | ||||||||
\(859\) | −26.5520 | −0.905943 | −0.452971 | − | 0.891525i | \(-0.649636\pi\) | ||||
−0.452971 | + | 0.891525i | \(0.649636\pi\) | |||||||
\(860\) | 131.829 | 4.49533 | ||||||||
\(861\) | 7.39129 | 0.251895 | ||||||||
\(862\) | 69.3165 | 2.36093 | ||||||||
\(863\) | −17.5678 | −0.598015 | −0.299007 | − | 0.954251i | \(-0.596656\pi\) | ||||
−0.299007 | + | 0.954251i | \(0.596656\pi\) | |||||||
\(864\) | 82.0246 | 2.79054 | ||||||||
\(865\) | 46.6825 | 1.58725 | ||||||||
\(866\) | 9.54848 | 0.324471 | ||||||||
\(867\) | 22.3822 | 0.760139 | ||||||||
\(868\) | 171.288 | 5.81388 | ||||||||
\(869\) | −4.61031 | −0.156394 | ||||||||
\(870\) | 63.2431 | 2.14414 | ||||||||
\(871\) | −11.6178 | −0.393656 | ||||||||
\(872\) | 50.9025 | 1.72377 | ||||||||
\(873\) | 0.882916 | 0.0298822 | ||||||||
\(874\) | −6.26656 | −0.211969 | ||||||||
\(875\) | −24.3519 | −0.823244 | ||||||||
\(876\) | −122.698 | −4.14559 | ||||||||
\(877\) | 8.87287 | 0.299615 | 0.149808 | − | 0.988715i | \(-0.452135\pi\) | ||||
0.149808 | + | 0.988715i | \(0.452135\pi\) | |||||||
\(878\) | 105.699 | 3.56717 | ||||||||
\(879\) | −28.8296 | −0.972397 | ||||||||
\(880\) | −39.2790 | −1.32409 | ||||||||
\(881\) | −24.7791 | −0.834828 | −0.417414 | − | 0.908717i | \(-0.637063\pi\) | ||||
−0.417414 | + | 0.908717i | \(0.637063\pi\) | |||||||
\(882\) | −25.6410 | −0.863377 | ||||||||
\(883\) | 36.4867 | 1.22788 | 0.613938 | − | 0.789354i | \(-0.289585\pi\) | ||||
0.613938 | + | 0.789354i | \(0.289585\pi\) | |||||||
\(884\) | −180.363 | −6.06627 | ||||||||
\(885\) | −51.0734 | −1.71682 | ||||||||
\(886\) | −97.2418 | −3.26690 | ||||||||
\(887\) | 24.5993 | 0.825962 | 0.412981 | − | 0.910740i | \(-0.364488\pi\) | ||||
0.412981 | + | 0.910740i | \(0.364488\pi\) | |||||||
\(888\) | 48.0714 | 1.61317 | ||||||||
\(889\) | 16.4829 | 0.552817 | ||||||||
\(890\) | 53.4028 | 1.79007 | ||||||||
\(891\) | 10.5027 | 0.351855 | ||||||||
\(892\) | −43.1594 | −1.44508 | ||||||||
\(893\) | 1.41960 | 0.0475052 | ||||||||
\(894\) | 25.6534 | 0.857978 | ||||||||
\(895\) | 51.2486 | 1.71305 | ||||||||
\(896\) | −148.360 | −4.95634 | ||||||||
\(897\) | 12.7386 | 0.425330 | ||||||||
\(898\) | −75.3615 | −2.51485 | ||||||||
\(899\) | −32.9209 | −1.09797 | ||||||||
\(900\) | 17.5711 | 0.585704 | ||||||||
\(901\) | −38.7822 | −1.29202 | ||||||||
\(902\) | 2.40667 | 0.0801332 | ||||||||
\(903\) | 68.5396 | 2.28086 | ||||||||
\(904\) | 105.506 | 3.50907 | ||||||||
\(905\) | −5.05147 | −0.167916 | ||||||||
\(906\) | 41.6665 | 1.38428 | ||||||||
\(907\) | 25.9062 | 0.860201 | 0.430100 | − | 0.902781i | \(-0.358478\pi\) | ||||
0.430100 | + | 0.902781i | \(0.358478\pi\) | |||||||
\(908\) | 109.035 | 3.61844 | ||||||||
\(909\) | 3.28830 | 0.109066 | ||||||||
\(910\) | −183.672 | −6.08866 | ||||||||
\(911\) | −42.2403 | −1.39948 | −0.699741 | − | 0.714396i | \(-0.746701\pi\) | ||||
−0.699741 | + | 0.714396i | \(0.746701\pi\) | |||||||
\(912\) | 70.1514 | 2.32295 | ||||||||
\(913\) | −13.4941 | −0.446591 | ||||||||
\(914\) | 16.7093 | 0.552695 | ||||||||
\(915\) | 21.8573 | 0.722581 | ||||||||
\(916\) | −1.52574 | −0.0504118 | ||||||||
\(917\) | −73.9418 | −2.44177 | ||||||||
\(918\) | −53.9494 | −1.78060 | ||||||||
\(919\) | −16.8877 | −0.557075 | −0.278538 | − | 0.960425i | \(-0.589850\pi\) | ||||
−0.278538 | + | 0.960425i | \(0.589850\pi\) | |||||||
\(920\) | −26.3830 | −0.869823 | ||||||||
\(921\) | −43.7870 | −1.44283 | ||||||||
\(922\) | 27.6492 | 0.910577 | ||||||||
\(923\) | 74.7747 | 2.46124 | ||||||||
\(924\) | −40.7900 | −1.34189 | ||||||||
\(925\) | −6.80025 | −0.223591 | ||||||||
\(926\) | −30.7576 | −1.01076 | ||||||||
\(927\) | −5.31480 | −0.174561 | ||||||||
\(928\) | 89.4653 | 2.93684 | ||||||||
\(929\) | −22.8538 | −0.749809 | −0.374905 | − | 0.927063i | \(-0.622325\pi\) | ||||
−0.374905 | + | 0.927063i | \(0.622325\pi\) | |||||||
\(930\) | −125.573 | −4.11769 | ||||||||
\(931\) | 18.3486 | 0.601352 | ||||||||
\(932\) | −128.680 | −4.21504 | ||||||||
\(933\) | 30.0728 | 0.984539 | ||||||||
\(934\) | 66.3417 | 2.17077 | ||||||||
\(935\) | 13.8656 | 0.453454 | ||||||||
\(936\) | −69.3324 | −2.26620 | ||||||||
\(937\) | −15.7344 | −0.514021 | −0.257011 | − | 0.966409i | \(-0.582738\pi\) | ||||
−0.257011 | + | 0.966409i | \(0.582738\pi\) | |||||||
\(938\) | 19.7210 | 0.643913 | ||||||||
\(939\) | 14.5674 | 0.475390 | ||||||||
\(940\) | 9.42178 | 0.307305 | ||||||||
\(941\) | −30.0213 | −0.978666 | −0.489333 | − | 0.872097i | \(-0.662760\pi\) | ||||
−0.489333 | + | 0.872097i | \(0.662760\pi\) | |||||||
\(942\) | −78.3960 | −2.55428 | ||||||||
\(943\) | 0.934218 | 0.0304223 | ||||||||
\(944\) | −134.617 | −4.38141 | ||||||||
\(945\) | −40.2293 | −1.30866 | ||||||||
\(946\) | 22.3171 | 0.725590 | ||||||||
\(947\) | −43.7036 | −1.42018 | −0.710088 | − | 0.704113i | \(-0.751345\pi\) | ||||
−0.710088 | + | 0.704113i | \(0.751345\pi\) | |||||||
\(948\) | 54.6477 | 1.77487 | ||||||||
\(949\) | −68.4879 | −2.22321 | ||||||||
\(950\) | −17.1714 | −0.557115 | ||||||||
\(951\) | 50.0183 | 1.62196 | ||||||||
\(952\) | 194.214 | 6.29452 | ||||||||
\(953\) | 25.3980 | 0.822723 | 0.411362 | − | 0.911472i | \(-0.365053\pi\) | ||||
0.411362 | + | 0.911472i | \(0.365053\pi\) | |||||||
\(954\) | −23.5012 | −0.760880 | ||||||||
\(955\) | 39.4934 | 1.27798 | ||||||||
\(956\) | −37.0485 | −1.19824 | ||||||||
\(957\) | 7.83971 | 0.253422 | ||||||||
\(958\) | −13.7240 | −0.443401 | ||||||||
\(959\) | 13.3252 | 0.430292 | ||||||||
\(960\) | 171.012 | 5.51940 | ||||||||
\(961\) | 34.3663 | 1.10859 | ||||||||
\(962\) | 42.2991 | 1.36378 | ||||||||
\(963\) | 2.34493 | 0.0755644 | ||||||||
\(964\) | 91.0172 | 2.93147 | ||||||||
\(965\) | −59.7118 | −1.92219 | ||||||||
\(966\) | −21.6235 | −0.695723 | ||||||||
\(967\) | 35.9116 | 1.15484 | 0.577419 | − | 0.816448i | \(-0.304060\pi\) | ||||
0.577419 | + | 0.816448i | \(0.304060\pi\) | |||||||
\(968\) | 95.8887 | 3.08198 | ||||||||
\(969\) | −24.7637 | −0.795525 | ||||||||
\(970\) | −5.72655 | −0.183868 | ||||||||
\(971\) | 1.29273 | 0.0414858 | 0.0207429 | − | 0.999785i | \(-0.493397\pi\) | ||||
0.0207429 | + | 0.999785i | \(0.493397\pi\) | |||||||
\(972\) | −63.2336 | −2.02822 | ||||||||
\(973\) | 42.4608 | 1.36123 | ||||||||
\(974\) | 10.9398 | 0.350532 | ||||||||
\(975\) | 34.9060 | 1.11789 | ||||||||
\(976\) | 57.6105 | 1.84407 | ||||||||
\(977\) | −17.8166 | −0.570005 | −0.285002 | − | 0.958527i | \(-0.591994\pi\) | ||||
−0.285002 | + | 0.958527i | \(0.591994\pi\) | |||||||
\(978\) | 79.5078 | 2.54238 | ||||||||
\(979\) | 6.61990 | 0.211573 | ||||||||
\(980\) | 121.778 | 3.89006 | ||||||||
\(981\) | −6.29280 | −0.200914 | ||||||||
\(982\) | 83.0189 | 2.64924 | ||||||||
\(983\) | −35.9823 | −1.14766 | −0.573829 | − | 0.818975i | \(-0.694543\pi\) | ||||
−0.573829 | + | 0.818975i | \(0.694543\pi\) | |||||||
\(984\) | −18.0962 | −0.576886 | ||||||||
\(985\) | 4.73365 | 0.150827 | ||||||||
\(986\) | −58.8433 | −1.87395 | ||||||||
\(987\) | 4.89850 | 0.155921 | ||||||||
\(988\) | 78.2122 | 2.48826 | ||||||||
\(989\) | 8.66302 | 0.275468 | ||||||||
\(990\) | 8.40229 | 0.267042 | ||||||||
\(991\) | 28.4414 | 0.903472 | 0.451736 | − | 0.892152i | \(-0.350805\pi\) | ||||
0.451736 | + | 0.892152i | \(0.350805\pi\) | |||||||
\(992\) | −177.638 | −5.64002 | ||||||||
\(993\) | 50.3143 | 1.59667 | ||||||||
\(994\) | −126.928 | −4.02591 | ||||||||
\(995\) | 62.5182 | 1.98196 | ||||||||
\(996\) | 159.951 | 5.06824 | ||||||||
\(997\) | 29.7994 | 0.943758 | 0.471879 | − | 0.881663i | \(-0.343576\pi\) | ||||
0.471879 | + | 0.881663i | \(0.343576\pi\) | |||||||
\(998\) | −120.281 | −3.80744 | ||||||||
\(999\) | 9.26471 | 0.293122 |
(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 | 8027.2.a.f.1.5 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.5 | ✓ | 176 | 1.1 | even | 1 | trivial |