Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73352 | −1.22579 | −0.612894 | − | 0.790165i | \(-0.709995\pi\) | ||||
−0.612894 | + | 0.790165i | \(0.709995\pi\) | |||||||
\(3\) | 2.13034 | 1.22995 | 0.614977 | − | 0.788545i | \(-0.289165\pi\) | ||||
0.614977 | + | 0.788545i | \(0.289165\pi\) | |||||||
\(4\) | 1.00511 | 0.502554 | ||||||||
\(5\) | −4.15912 | −1.86002 | −0.930008 | − | 0.367539i | \(-0.880200\pi\) | ||||
−0.930008 | + | 0.367539i | \(0.880200\pi\) | |||||||
\(6\) | −3.69300 | −1.50766 | ||||||||
\(7\) | −1.81917 | −0.687581 | −0.343791 | − | 0.939046i | \(-0.611711\pi\) | ||||
−0.343791 | + | 0.939046i | \(0.611711\pi\) | |||||||
\(8\) | 1.72467 | 0.609763 | ||||||||
\(9\) | 1.53836 | 0.512788 | ||||||||
\(10\) | 7.20994 | 2.27998 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.14123 | 0.618119 | ||||||||
\(13\) | 3.34135 | 0.926722 | 0.463361 | − | 0.886170i | \(-0.346643\pi\) | ||||
0.463361 | + | 0.886170i | \(0.346643\pi\) | |||||||
\(14\) | 3.15357 | 0.842828 | ||||||||
\(15\) | −8.86036 | −2.28774 | ||||||||
\(16\) | −4.99997 | −1.24999 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.66679 | −0.628569 | ||||||||
\(19\) | −0.395669 | −0.0907727 | −0.0453864 | − | 0.998970i | \(-0.514452\pi\) | ||||
−0.0453864 | + | 0.998970i | \(0.514452\pi\) | |||||||
\(20\) | −4.18037 | −0.934759 | ||||||||
\(21\) | −3.87545 | −0.845694 | ||||||||
\(22\) | −1.73352 | −0.369589 | ||||||||
\(23\) | 3.74793 | 0.781498 | 0.390749 | − | 0.920497i | \(-0.372216\pi\) | ||||
0.390749 | + | 0.920497i | \(0.372216\pi\) | |||||||
\(24\) | 3.67414 | 0.749980 | ||||||||
\(25\) | 12.2983 | 2.45966 | ||||||||
\(26\) | −5.79231 | −1.13596 | ||||||||
\(27\) | −3.11379 | −0.599249 | ||||||||
\(28\) | −1.82846 | −0.345547 | ||||||||
\(29\) | 6.92498 | 1.28594 | 0.642969 | − | 0.765893i | \(-0.277703\pi\) | ||||
0.642969 | + | 0.765893i | \(0.277703\pi\) | |||||||
\(30\) | 15.3597 | 2.80428 | ||||||||
\(31\) | −4.77160 | −0.857004 | −0.428502 | − | 0.903541i | \(-0.640959\pi\) | ||||
−0.428502 | + | 0.903541i | \(0.640959\pi\) | |||||||
\(32\) | 5.21824 | 0.922463 | ||||||||
\(33\) | 2.13034 | 0.370845 | ||||||||
\(34\) | 1.73352 | 0.297297 | ||||||||
\(35\) | 7.56615 | 1.27891 | ||||||||
\(36\) | 1.54622 | 0.257704 | ||||||||
\(37\) | 12.0076 | 1.97403 | 0.987015 | − | 0.160628i | \(-0.0513518\pi\) | ||||
0.987015 | + | 0.160628i | \(0.0513518\pi\) | |||||||
\(38\) | 0.685902 | 0.111268 | ||||||||
\(39\) | 7.11821 | 1.13983 | ||||||||
\(40\) | −7.17311 | −1.13417 | ||||||||
\(41\) | 3.93128 | 0.613963 | 0.306981 | − | 0.951716i | \(-0.400681\pi\) | ||||
0.306981 | + | 0.951716i | \(0.400681\pi\) | |||||||
\(42\) | 6.71820 | 1.03664 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 1.00511 | 0.151526 | ||||||||
\(45\) | −6.39824 | −0.953794 | ||||||||
\(46\) | −6.49714 | −0.957951 | ||||||||
\(47\) | 0.482571 | 0.0703902 | 0.0351951 | − | 0.999380i | \(-0.488795\pi\) | ||||
0.0351951 | + | 0.999380i | \(0.488795\pi\) | |||||||
\(48\) | −10.6517 | −1.53743 | ||||||||
\(49\) | −3.69062 | −0.527232 | ||||||||
\(50\) | −21.3194 | −3.01502 | ||||||||
\(51\) | −2.13034 | −0.298308 | ||||||||
\(52\) | 3.35841 | 0.465728 | ||||||||
\(53\) | −5.31367 | −0.729888 | −0.364944 | − | 0.931029i | \(-0.618912\pi\) | ||||
−0.364944 | + | 0.931029i | \(0.618912\pi\) | |||||||
\(54\) | 5.39783 | 0.734552 | ||||||||
\(55\) | −4.15912 | −0.560816 | ||||||||
\(56\) | −3.13746 | −0.419261 | ||||||||
\(57\) | −0.842911 | −0.111646 | ||||||||
\(58\) | −12.0046 | −1.57629 | ||||||||
\(59\) | −5.33453 | −0.694496 | −0.347248 | − | 0.937773i | \(-0.612884\pi\) | ||||
−0.347248 | + | 0.937773i | \(0.612884\pi\) | |||||||
\(60\) | −8.90562 | −1.14971 | ||||||||
\(61\) | −14.4626 | −1.85175 | −0.925873 | − | 0.377834i | \(-0.876669\pi\) | ||||
−0.925873 | + | 0.377834i | \(0.876669\pi\) | |||||||
\(62\) | 8.27168 | 1.05050 | ||||||||
\(63\) | −2.79854 | −0.352583 | ||||||||
\(64\) | 0.953998 | 0.119250 | ||||||||
\(65\) | −13.8971 | −1.72372 | ||||||||
\(66\) | −3.69300 | −0.454577 | ||||||||
\(67\) | −9.55002 | −1.16672 | −0.583360 | − | 0.812213i | \(-0.698262\pi\) | ||||
−0.583360 | + | 0.812213i | \(0.698262\pi\) | |||||||
\(68\) | −1.00511 | −0.121887 | ||||||||
\(69\) | 7.98439 | 0.961207 | ||||||||
\(70\) | −13.1161 | −1.56767 | ||||||||
\(71\) | −10.8443 | −1.28698 | −0.643489 | − | 0.765456i | \(-0.722514\pi\) | ||||
−0.643489 | + | 0.765456i | \(0.722514\pi\) | |||||||
\(72\) | 2.65317 | 0.312679 | ||||||||
\(73\) | 0.787245 | 0.0921400 | 0.0460700 | − | 0.998938i | \(-0.485330\pi\) | ||||
0.0460700 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(74\) | −20.8154 | −2.41974 | ||||||||
\(75\) | 26.1996 | 3.02527 | ||||||||
\(76\) | −0.397690 | −0.0456182 | ||||||||
\(77\) | −1.81917 | −0.207314 | ||||||||
\(78\) | −12.3396 | −1.39718 | ||||||||
\(79\) | −13.0934 | −1.47312 | −0.736559 | − | 0.676373i | \(-0.763551\pi\) | ||||
−0.736559 | + | 0.676373i | \(0.763551\pi\) | |||||||
\(80\) | 20.7955 | 2.32501 | ||||||||
\(81\) | −11.2485 | −1.24984 | ||||||||
\(82\) | −6.81497 | −0.752588 | ||||||||
\(83\) | 6.37930 | 0.700219 | 0.350110 | − | 0.936709i | \(-0.386144\pi\) | ||||
0.350110 | + | 0.936709i | \(0.386144\pi\) | |||||||
\(84\) | −3.89525 | −0.425007 | ||||||||
\(85\) | 4.15912 | 0.451120 | ||||||||
\(86\) | 1.73352 | 0.186931 | ||||||||
\(87\) | 14.7526 | 1.58164 | ||||||||
\(88\) | 1.72467 | 0.183850 | ||||||||
\(89\) | −6.94533 | −0.736204 | −0.368102 | − | 0.929785i | \(-0.619992\pi\) | ||||
−0.368102 | + | 0.929785i | \(0.619992\pi\) | |||||||
\(90\) | 11.0915 | 1.16915 | ||||||||
\(91\) | −6.07847 | −0.637197 | ||||||||
\(92\) | 3.76708 | 0.392745 | ||||||||
\(93\) | −10.1651 | −1.05408 | ||||||||
\(94\) | −0.836549 | −0.0862834 | ||||||||
\(95\) | 1.64564 | 0.168839 | ||||||||
\(96\) | 11.1166 | 1.13459 | ||||||||
\(97\) | 9.60390 | 0.975129 | 0.487564 | − | 0.873087i | \(-0.337885\pi\) | ||||
0.487564 | + | 0.873087i | \(0.337885\pi\) | |||||||
\(98\) | 6.39779 | 0.646274 | ||||||||
\(99\) | 1.53836 | 0.154611 | ||||||||
\(100\) | 12.3611 | 1.23611 | ||||||||
\(101\) | 0.280169 | 0.0278778 | 0.0139389 | − | 0.999903i | \(-0.495563\pi\) | ||||
0.0139389 | + | 0.999903i | \(0.495563\pi\) | |||||||
\(102\) | 3.69300 | 0.365662 | ||||||||
\(103\) | −6.91930 | −0.681778 | −0.340889 | − | 0.940103i | \(-0.610728\pi\) | ||||
−0.340889 | + | 0.940103i | \(0.610728\pi\) | |||||||
\(104\) | 5.76272 | 0.565081 | ||||||||
\(105\) | 16.1185 | 1.57300 | ||||||||
\(106\) | 9.21137 | 0.894688 | ||||||||
\(107\) | −5.02302 | −0.485594 | −0.242797 | − | 0.970077i | \(-0.578065\pi\) | ||||
−0.242797 | + | 0.970077i | \(0.578065\pi\) | |||||||
\(108\) | −3.12970 | −0.301155 | ||||||||
\(109\) | 13.0521 | 1.25016 | 0.625081 | − | 0.780560i | \(-0.285066\pi\) | ||||
0.625081 | + | 0.780560i | \(0.285066\pi\) | |||||||
\(110\) | 7.20994 | 0.687441 | ||||||||
\(111\) | 25.5802 | 2.42797 | ||||||||
\(112\) | 9.09580 | 0.859472 | ||||||||
\(113\) | 4.90543 | 0.461464 | 0.230732 | − | 0.973017i | \(-0.425888\pi\) | ||||
0.230732 | + | 0.973017i | \(0.425888\pi\) | |||||||
\(114\) | 1.46121 | 0.136855 | ||||||||
\(115\) | −15.5881 | −1.45360 | ||||||||
\(116\) | 6.96036 | 0.646253 | ||||||||
\(117\) | 5.14020 | 0.475212 | ||||||||
\(118\) | 9.24753 | 0.851304 | ||||||||
\(119\) | 1.81917 | 0.166763 | ||||||||
\(120\) | −15.2812 | −1.39498 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 25.0713 | 2.26985 | ||||||||
\(123\) | 8.37498 | 0.755146 | ||||||||
\(124\) | −4.79597 | −0.430691 | ||||||||
\(125\) | −30.3545 | −2.71499 | ||||||||
\(126\) | 4.85134 | 0.432192 | ||||||||
\(127\) | 18.8511 | 1.67277 | 0.836384 | − | 0.548144i | \(-0.184665\pi\) | ||||
0.836384 | + | 0.548144i | \(0.184665\pi\) | |||||||
\(128\) | −12.0903 | −1.06864 | ||||||||
\(129\) | −2.13034 | −0.187566 | ||||||||
\(130\) | 24.0909 | 2.11291 | ||||||||
\(131\) | −0.920618 | −0.0804348 | −0.0402174 | − | 0.999191i | \(-0.512805\pi\) | ||||
−0.0402174 | + | 0.999191i | \(0.512805\pi\) | |||||||
\(132\) | 2.14123 | 0.186370 | ||||||||
\(133\) | 0.719789 | 0.0624136 | ||||||||
\(134\) | 16.5552 | 1.43015 | ||||||||
\(135\) | 12.9506 | 1.11461 | ||||||||
\(136\) | −1.72467 | −0.147889 | ||||||||
\(137\) | −6.23598 | −0.532776 | −0.266388 | − | 0.963866i | \(-0.585830\pi\) | ||||
−0.266388 | + | 0.963866i | \(0.585830\pi\) | |||||||
\(138\) | −13.8411 | −1.17824 | ||||||||
\(139\) | −5.62858 | −0.477410 | −0.238705 | − | 0.971092i | \(-0.576723\pi\) | ||||
−0.238705 | + | 0.971092i | \(0.576723\pi\) | |||||||
\(140\) | 7.60480 | 0.642723 | ||||||||
\(141\) | 1.02804 | 0.0865768 | ||||||||
\(142\) | 18.7988 | 1.57756 | ||||||||
\(143\) | 3.34135 | 0.279417 | ||||||||
\(144\) | −7.69178 | −0.640981 | ||||||||
\(145\) | −28.8019 | −2.39186 | ||||||||
\(146\) | −1.36471 | −0.112944 | ||||||||
\(147\) | −7.86230 | −0.648471 | ||||||||
\(148\) | 12.0689 | 0.992057 | ||||||||
\(149\) | 22.5681 | 1.84885 | 0.924425 | − | 0.381363i | \(-0.124545\pi\) | ||||
0.924425 | + | 0.381363i | \(0.124545\pi\) | |||||||
\(150\) | −45.4177 | −3.70834 | ||||||||
\(151\) | −7.25551 | −0.590445 | −0.295223 | − | 0.955429i | \(-0.595394\pi\) | ||||
−0.295223 | + | 0.955429i | \(0.595394\pi\) | |||||||
\(152\) | −0.682398 | −0.0553498 | ||||||||
\(153\) | −1.53836 | −0.124369 | ||||||||
\(154\) | 3.15357 | 0.254122 | ||||||||
\(155\) | 19.8457 | 1.59404 | ||||||||
\(156\) | 7.15458 | 0.572825 | ||||||||
\(157\) | 12.6197 | 1.00716 | 0.503582 | − | 0.863947i | \(-0.332015\pi\) | ||||
0.503582 | + | 0.863947i | \(0.332015\pi\) | |||||||
\(158\) | 22.6977 | 1.80573 | ||||||||
\(159\) | −11.3199 | −0.897729 | ||||||||
\(160\) | −21.7033 | −1.71580 | ||||||||
\(161\) | −6.81813 | −0.537344 | ||||||||
\(162\) | 19.4996 | 1.53203 | ||||||||
\(163\) | 22.8361 | 1.78866 | 0.894330 | − | 0.447409i | \(-0.147653\pi\) | ||||
0.894330 | + | 0.447409i | \(0.147653\pi\) | |||||||
\(164\) | 3.95136 | 0.308550 | ||||||||
\(165\) | −8.86036 | −0.689778 | ||||||||
\(166\) | −11.0587 | −0.858320 | ||||||||
\(167\) | 18.9126 | 1.46350 | 0.731749 | − | 0.681574i | \(-0.238704\pi\) | ||||
0.731749 | + | 0.681574i | \(0.238704\pi\) | |||||||
\(168\) | −6.68388 | −0.515672 | ||||||||
\(169\) | −1.83541 | −0.141186 | ||||||||
\(170\) | −7.20994 | −0.552977 | ||||||||
\(171\) | −0.608683 | −0.0465471 | ||||||||
\(172\) | −1.00511 | −0.0766388 | ||||||||
\(173\) | 7.37677 | 0.560846 | 0.280423 | − | 0.959877i | \(-0.409525\pi\) | ||||
0.280423 | + | 0.959877i | \(0.409525\pi\) | |||||||
\(174\) | −25.5740 | −1.93876 | ||||||||
\(175\) | −22.3727 | −1.69122 | ||||||||
\(176\) | −4.99997 | −0.376887 | ||||||||
\(177\) | −11.3644 | −0.854199 | ||||||||
\(178\) | 12.0399 | 0.902429 | ||||||||
\(179\) | 2.42944 | 0.181585 | 0.0907925 | − | 0.995870i | \(-0.471060\pi\) | ||||
0.0907925 | + | 0.995870i | \(0.471060\pi\) | |||||||
\(180\) | −6.43093 | −0.479333 | ||||||||
\(181\) | −7.53724 | −0.560239 | −0.280119 | − | 0.959965i | \(-0.590374\pi\) | ||||
−0.280119 | + | 0.959965i | \(0.590374\pi\) | |||||||
\(182\) | 10.5372 | 0.781068 | ||||||||
\(183\) | −30.8103 | −2.27756 | ||||||||
\(184\) | 6.46395 | 0.476529 | ||||||||
\(185\) | −49.9409 | −3.67173 | ||||||||
\(186\) | 17.6215 | 1.29207 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 0.485036 | 0.0353749 | ||||||||
\(189\) | 5.66451 | 0.412032 | ||||||||
\(190\) | −2.85275 | −0.206960 | ||||||||
\(191\) | 24.2995 | 1.75825 | 0.879125 | − | 0.476591i | \(-0.158128\pi\) | ||||
0.879125 | + | 0.476591i | \(0.158128\pi\) | |||||||
\(192\) | 2.03234 | 0.146672 | ||||||||
\(193\) | −15.6469 | −1.12629 | −0.563144 | − | 0.826359i | \(-0.690408\pi\) | ||||
−0.563144 | + | 0.826359i | \(0.690408\pi\) | |||||||
\(194\) | −16.6486 | −1.19530 | ||||||||
\(195\) | −29.6055 | −2.12010 | ||||||||
\(196\) | −3.70948 | −0.264963 | ||||||||
\(197\) | 11.5970 | 0.826252 | 0.413126 | − | 0.910674i | \(-0.364437\pi\) | ||||
0.413126 | + | 0.910674i | \(0.364437\pi\) | |||||||
\(198\) | −2.66679 | −0.189521 | ||||||||
\(199\) | −16.7890 | −1.19014 | −0.595069 | − | 0.803674i | \(-0.702875\pi\) | ||||
−0.595069 | + | 0.803674i | \(0.702875\pi\) | |||||||
\(200\) | 21.2105 | 1.49981 | ||||||||
\(201\) | −20.3448 | −1.43501 | ||||||||
\(202\) | −0.485679 | −0.0341723 | ||||||||
\(203\) | −12.5977 | −0.884186 | ||||||||
\(204\) | −2.14123 | −0.149916 | ||||||||
\(205\) | −16.3507 | −1.14198 | ||||||||
\(206\) | 11.9948 | 0.835715 | ||||||||
\(207\) | 5.76568 | 0.400743 | ||||||||
\(208\) | −16.7066 | −1.15840 | ||||||||
\(209\) | −0.395669 | −0.0273690 | ||||||||
\(210\) | −27.9418 | −1.92817 | ||||||||
\(211\) | 25.0401 | 1.72383 | 0.861917 | − | 0.507049i | \(-0.169264\pi\) | ||||
0.861917 | + | 0.507049i | \(0.169264\pi\) | |||||||
\(212\) | −5.34081 | −0.366808 | ||||||||
\(213\) | −23.1020 | −1.58292 | ||||||||
\(214\) | 8.70753 | 0.595234 | ||||||||
\(215\) | 4.15912 | 0.283650 | ||||||||
\(216\) | −5.37026 | −0.365400 | ||||||||
\(217\) | 8.68034 | 0.589260 | ||||||||
\(218\) | −22.6261 | −1.53243 | ||||||||
\(219\) | 1.67710 | 0.113328 | ||||||||
\(220\) | −4.18037 | −0.281840 | ||||||||
\(221\) | −3.34135 | −0.224763 | ||||||||
\(222\) | −44.3439 | −2.97617 | ||||||||
\(223\) | −1.55714 | −0.104274 | −0.0521368 | − | 0.998640i | \(-0.516603\pi\) | ||||
−0.0521368 | + | 0.998640i | \(0.516603\pi\) | |||||||
\(224\) | −9.49286 | −0.634268 | ||||||||
\(225\) | 18.9193 | 1.26128 | ||||||||
\(226\) | −8.50369 | −0.565657 | ||||||||
\(227\) | 19.2961 | 1.28072 | 0.640362 | − | 0.768073i | \(-0.278784\pi\) | ||||
0.640362 | + | 0.768073i | \(0.278784\pi\) | |||||||
\(228\) | −0.847217 | −0.0561083 | ||||||||
\(229\) | 16.6755 | 1.10195 | 0.550974 | − | 0.834523i | \(-0.314256\pi\) | ||||
0.550974 | + | 0.834523i | \(0.314256\pi\) | |||||||
\(230\) | 27.0224 | 1.78180 | ||||||||
\(231\) | −3.87545 | −0.254986 | ||||||||
\(232\) | 11.9433 | 0.784116 | ||||||||
\(233\) | 16.9746 | 1.11204 | 0.556022 | − | 0.831168i | \(-0.312327\pi\) | ||||
0.556022 | + | 0.831168i | \(0.312327\pi\) | |||||||
\(234\) | −8.91067 | −0.582509 | ||||||||
\(235\) | −2.00707 | −0.130927 | ||||||||
\(236\) | −5.36178 | −0.349022 | ||||||||
\(237\) | −27.8934 | −1.81187 | ||||||||
\(238\) | −3.15357 | −0.204416 | ||||||||
\(239\) | −2.40411 | −0.155509 | −0.0777544 | − | 0.996973i | \(-0.524775\pi\) | ||||
−0.0777544 | + | 0.996973i | \(0.524775\pi\) | |||||||
\(240\) | 44.3016 | 2.85965 | ||||||||
\(241\) | −16.4944 | −1.06250 | −0.531249 | − | 0.847216i | \(-0.678277\pi\) | ||||
−0.531249 | + | 0.847216i | \(0.678277\pi\) | |||||||
\(242\) | −1.73352 | −0.111435 | ||||||||
\(243\) | −14.6219 | −0.937993 | ||||||||
\(244\) | −14.5365 | −0.930603 | ||||||||
\(245\) | 15.3498 | 0.980660 | ||||||||
\(246\) | −14.5182 | −0.925648 | ||||||||
\(247\) | −1.32207 | −0.0841211 | ||||||||
\(248\) | −8.22943 | −0.522569 | ||||||||
\(249\) | 13.5901 | 0.861238 | ||||||||
\(250\) | 52.6203 | 3.32800 | ||||||||
\(251\) | 19.0017 | 1.19938 | 0.599689 | − | 0.800233i | \(-0.295291\pi\) | ||||
0.599689 | + | 0.800233i | \(0.295291\pi\) | |||||||
\(252\) | −2.81284 | −0.177192 | ||||||||
\(253\) | 3.74793 | 0.235631 | ||||||||
\(254\) | −32.6789 | −2.05046 | ||||||||
\(255\) | 8.86036 | 0.554857 | ||||||||
\(256\) | 19.0508 | 1.19067 | ||||||||
\(257\) | 17.0767 | 1.06522 | 0.532608 | − | 0.846362i | \(-0.321212\pi\) | ||||
0.532608 | + | 0.846362i | \(0.321212\pi\) | |||||||
\(258\) | 3.69300 | 0.229916 | ||||||||
\(259\) | −21.8438 | −1.35731 | ||||||||
\(260\) | −13.9681 | −0.866262 | ||||||||
\(261\) | 10.6531 | 0.659413 | ||||||||
\(262\) | 1.59591 | 0.0985959 | ||||||||
\(263\) | −6.92502 | −0.427015 | −0.213508 | − | 0.976941i | \(-0.568489\pi\) | ||||
−0.213508 | + | 0.976941i | \(0.568489\pi\) | |||||||
\(264\) | 3.67414 | 0.226128 | ||||||||
\(265\) | 22.1002 | 1.35760 | ||||||||
\(266\) | −1.24777 | −0.0765058 | ||||||||
\(267\) | −14.7959 | −0.905497 | ||||||||
\(268\) | −9.59881 | −0.586340 | ||||||||
\(269\) | −4.89486 | −0.298445 | −0.149223 | − | 0.988804i | \(-0.547677\pi\) | ||||
−0.149223 | + | 0.988804i | \(0.547677\pi\) | |||||||
\(270\) | −22.4502 | −1.36628 | ||||||||
\(271\) | −8.59353 | −0.522020 | −0.261010 | − | 0.965336i | \(-0.584055\pi\) | ||||
−0.261010 | + | 0.965336i | \(0.584055\pi\) | |||||||
\(272\) | 4.99997 | 0.303168 | ||||||||
\(273\) | −12.9492 | −0.783723 | ||||||||
\(274\) | 10.8102 | 0.653070 | ||||||||
\(275\) | 12.2983 | 0.741616 | ||||||||
\(276\) | 8.02518 | 0.483059 | ||||||||
\(277\) | −30.3758 | −1.82511 | −0.912553 | − | 0.408959i | \(-0.865892\pi\) | ||||
−0.912553 | + | 0.408959i | \(0.865892\pi\) | |||||||
\(278\) | 9.75728 | 0.585203 | ||||||||
\(279\) | −7.34045 | −0.439461 | ||||||||
\(280\) | 13.0491 | 0.779833 | ||||||||
\(281\) | −10.8956 | −0.649977 | −0.324989 | − | 0.945718i | \(-0.605360\pi\) | ||||
−0.324989 | + | 0.945718i | \(0.605360\pi\) | |||||||
\(282\) | −1.78214 | −0.106125 | ||||||||
\(283\) | −8.28555 | −0.492525 | −0.246262 | − | 0.969203i | \(-0.579202\pi\) | ||||
−0.246262 | + | 0.969203i | \(0.579202\pi\) | |||||||
\(284\) | −10.8997 | −0.646776 | ||||||||
\(285\) | 3.50577 | 0.207664 | ||||||||
\(286\) | −5.79231 | −0.342506 | ||||||||
\(287\) | −7.15166 | −0.422149 | ||||||||
\(288\) | 8.02755 | 0.473028 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 49.9287 | 2.93192 | ||||||||
\(291\) | 20.4596 | 1.19936 | ||||||||
\(292\) | 0.791267 | 0.0463054 | ||||||||
\(293\) | −13.1064 | −0.765683 | −0.382841 | − | 0.923814i | \(-0.625054\pi\) | ||||
−0.382841 | + | 0.923814i | \(0.625054\pi\) | |||||||
\(294\) | 13.6295 | 0.794888 | ||||||||
\(295\) | 22.1869 | 1.29177 | ||||||||
\(296\) | 20.7091 | 1.20369 | ||||||||
\(297\) | −3.11379 | −0.180680 | ||||||||
\(298\) | −39.1224 | −2.26630 | ||||||||
\(299\) | 12.5231 | 0.724232 | ||||||||
\(300\) | 26.3334 | 1.52036 | ||||||||
\(301\) | 1.81917 | 0.104855 | ||||||||
\(302\) | 12.5776 | 0.723760 | ||||||||
\(303\) | 0.596856 | 0.0342885 | ||||||||
\(304\) | 1.97834 | 0.113465 | ||||||||
\(305\) | 60.1517 | 3.44428 | ||||||||
\(306\) | 2.66679 | 0.152450 | ||||||||
\(307\) | −3.52390 | −0.201120 | −0.100560 | − | 0.994931i | \(-0.532063\pi\) | ||||
−0.100560 | + | 0.994931i | \(0.532063\pi\) | |||||||
\(308\) | −1.82846 | −0.104186 | ||||||||
\(309\) | −14.7405 | −0.838556 | ||||||||
\(310\) | −34.4029 | −1.95396 | ||||||||
\(311\) | 6.21116 | 0.352203 | 0.176101 | − | 0.984372i | \(-0.443651\pi\) | ||||
0.176101 | + | 0.984372i | \(0.443651\pi\) | |||||||
\(312\) | 12.2766 | 0.695024 | ||||||||
\(313\) | −22.4968 | −1.27160 | −0.635798 | − | 0.771855i | \(-0.719329\pi\) | ||||
−0.635798 | + | 0.771855i | \(0.719329\pi\) | |||||||
\(314\) | −21.8766 | −1.23457 | ||||||||
\(315\) | 11.6395 | 0.655811 | ||||||||
\(316\) | −13.1603 | −0.740322 | ||||||||
\(317\) | −4.91928 | −0.276294 | −0.138147 | − | 0.990412i | \(-0.544115\pi\) | ||||
−0.138147 | + | 0.990412i | \(0.544115\pi\) | |||||||
\(318\) | 19.6234 | 1.10042 | ||||||||
\(319\) | 6.92498 | 0.387725 | ||||||||
\(320\) | −3.96780 | −0.221807 | ||||||||
\(321\) | −10.7008 | −0.597258 | ||||||||
\(322\) | 11.8194 | 0.658669 | ||||||||
\(323\) | 0.395669 | 0.0220156 | ||||||||
\(324\) | −11.3060 | −0.628111 | ||||||||
\(325\) | 41.0929 | 2.27942 | ||||||||
\(326\) | −39.5869 | −2.19252 | ||||||||
\(327\) | 27.8054 | 1.53764 | ||||||||
\(328\) | 6.78016 | 0.374372 | ||||||||
\(329\) | −0.877878 | −0.0483990 | ||||||||
\(330\) | 15.3597 | 0.845521 | ||||||||
\(331\) | 29.0547 | 1.59699 | 0.798496 | − | 0.602000i | \(-0.205629\pi\) | ||||
0.798496 | + | 0.602000i | \(0.205629\pi\) | |||||||
\(332\) | 6.41189 | 0.351898 | ||||||||
\(333\) | 18.4720 | 1.01226 | ||||||||
\(334\) | −32.7854 | −1.79394 | ||||||||
\(335\) | 39.7197 | 2.17012 | ||||||||
\(336\) | 19.3772 | 1.05711 | ||||||||
\(337\) | 9.54892 | 0.520163 | 0.260081 | − | 0.965587i | \(-0.416251\pi\) | ||||
0.260081 | + | 0.965587i | \(0.416251\pi\) | |||||||
\(338\) | 3.18173 | 0.173063 | ||||||||
\(339\) | 10.4503 | 0.567580 | ||||||||
\(340\) | 4.18037 | 0.226712 | ||||||||
\(341\) | −4.77160 | −0.258396 | ||||||||
\(342\) | 1.05517 | 0.0570569 | ||||||||
\(343\) | 19.4481 | 1.05010 | ||||||||
\(344\) | −1.72467 | −0.0929879 | ||||||||
\(345\) | −33.2080 | −1.78786 | ||||||||
\(346\) | −12.7878 | −0.687478 | ||||||||
\(347\) | 18.7629 | 1.00725 | 0.503624 | − | 0.863923i | \(-0.332000\pi\) | ||||
0.503624 | + | 0.863923i | \(0.332000\pi\) | |||||||
\(348\) | 14.8280 | 0.794862 | ||||||||
\(349\) | 5.88659 | 0.315102 | 0.157551 | − | 0.987511i | \(-0.449640\pi\) | ||||
0.157551 | + | 0.987511i | \(0.449640\pi\) | |||||||
\(350\) | 38.7836 | 2.07307 | ||||||||
\(351\) | −10.4042 | −0.555337 | ||||||||
\(352\) | 5.21824 | 0.278133 | ||||||||
\(353\) | 18.7976 | 1.00049 | 0.500247 | − | 0.865883i | \(-0.333243\pi\) | ||||
0.500247 | + | 0.865883i | \(0.333243\pi\) | |||||||
\(354\) | 19.7004 | 1.04707 | ||||||||
\(355\) | 45.1026 | 2.39380 | ||||||||
\(356\) | −6.98081 | −0.369982 | ||||||||
\(357\) | 3.87545 | 0.205111 | ||||||||
\(358\) | −4.21150 | −0.222585 | ||||||||
\(359\) | 23.5778 | 1.24439 | 0.622193 | − | 0.782864i | \(-0.286242\pi\) | ||||
0.622193 | + | 0.782864i | \(0.286242\pi\) | |||||||
\(360\) | −11.0349 | −0.581588 | ||||||||
\(361\) | −18.8434 | −0.991760 | ||||||||
\(362\) | 13.0660 | 0.686733 | ||||||||
\(363\) | 2.13034 | 0.111814 | ||||||||
\(364\) | −6.10952 | −0.320226 | ||||||||
\(365\) | −3.27425 | −0.171382 | ||||||||
\(366\) | 53.4104 | 2.79181 | ||||||||
\(367\) | 30.9896 | 1.61764 | 0.808822 | − | 0.588054i | \(-0.200106\pi\) | ||||
0.808822 | + | 0.588054i | \(0.200106\pi\) | |||||||
\(368\) | −18.7396 | −0.976868 | ||||||||
\(369\) | 6.04774 | 0.314833 | ||||||||
\(370\) | 86.5738 | 4.50076 | ||||||||
\(371\) | 9.66646 | 0.501857 | ||||||||
\(372\) | −10.2171 | −0.529730 | ||||||||
\(373\) | −12.5384 | −0.649213 | −0.324607 | − | 0.945849i | \(-0.605232\pi\) | ||||
−0.324607 | + | 0.945849i | \(0.605232\pi\) | |||||||
\(374\) | 1.73352 | 0.0896384 | ||||||||
\(375\) | −64.6656 | −3.33932 | ||||||||
\(376\) | 0.832275 | 0.0429213 | ||||||||
\(377\) | 23.1388 | 1.19171 | ||||||||
\(378\) | −9.81956 | −0.505064 | ||||||||
\(379\) | 7.02346 | 0.360771 | 0.180385 | − | 0.983596i | \(-0.442265\pi\) | ||||
0.180385 | + | 0.983596i | \(0.442265\pi\) | |||||||
\(380\) | 1.65404 | 0.0848506 | ||||||||
\(381\) | 40.1594 | 2.05743 | ||||||||
\(382\) | −42.1238 | −2.15524 | ||||||||
\(383\) | 3.15574 | 0.161251 | 0.0806254 | − | 0.996744i | \(-0.474308\pi\) | ||||
0.0806254 | + | 0.996744i | \(0.474308\pi\) | |||||||
\(384\) | −25.7564 | −1.31438 | ||||||||
\(385\) | 7.56615 | 0.385607 | ||||||||
\(386\) | 27.1243 | 1.38059 | ||||||||
\(387\) | −1.53836 | −0.0781994 | ||||||||
\(388\) | 9.65297 | 0.490055 | ||||||||
\(389\) | 19.4912 | 0.988241 | 0.494121 | − | 0.869393i | \(-0.335490\pi\) | ||||
0.494121 | + | 0.869393i | \(0.335490\pi\) | |||||||
\(390\) | 51.3219 | 2.59879 | ||||||||
\(391\) | −3.74793 | −0.189541 | ||||||||
\(392\) | −6.36511 | −0.321486 | ||||||||
\(393\) | −1.96123 | −0.0989311 | ||||||||
\(394\) | −20.1037 | −1.01281 | ||||||||
\(395\) | 54.4569 | 2.74002 | ||||||||
\(396\) | 1.54622 | 0.0777006 | ||||||||
\(397\) | 4.50829 | 0.226264 | 0.113132 | − | 0.993580i | \(-0.463912\pi\) | ||||
0.113132 | + | 0.993580i | \(0.463912\pi\) | |||||||
\(398\) | 29.1041 | 1.45886 | ||||||||
\(399\) | 1.53340 | 0.0767659 | ||||||||
\(400\) | −61.4912 | −3.07456 | ||||||||
\(401\) | −19.4741 | −0.972492 | −0.486246 | − | 0.873822i | \(-0.661634\pi\) | ||||
−0.486246 | + | 0.873822i | \(0.661634\pi\) | |||||||
\(402\) | 35.2683 | 1.75902 | ||||||||
\(403\) | −15.9436 | −0.794205 | ||||||||
\(404\) | 0.281600 | 0.0140101 | ||||||||
\(405\) | 46.7840 | 2.32472 | ||||||||
\(406\) | 21.8385 | 1.08382 | ||||||||
\(407\) | 12.0076 | 0.595192 | ||||||||
\(408\) | −3.67414 | −0.181897 | ||||||||
\(409\) | −37.4564 | −1.85210 | −0.926051 | − | 0.377398i | \(-0.876819\pi\) | ||||
−0.926051 | + | 0.377398i | \(0.876819\pi\) | |||||||
\(410\) | 28.3443 | 1.39983 | ||||||||
\(411\) | −13.2848 | −0.655290 | ||||||||
\(412\) | −6.95464 | −0.342631 | ||||||||
\(413\) | 9.70440 | 0.477523 | ||||||||
\(414\) | −9.99496 | −0.491225 | ||||||||
\(415\) | −26.5323 | −1.30242 | ||||||||
\(416\) | 17.4359 | 0.854867 | ||||||||
\(417\) | −11.9908 | −0.587192 | ||||||||
\(418\) | 0.685902 | 0.0335486 | ||||||||
\(419\) | −5.37835 | −0.262750 | −0.131375 | − | 0.991333i | \(-0.541939\pi\) | ||||
−0.131375 | + | 0.991333i | \(0.541939\pi\) | |||||||
\(420\) | 16.2008 | 0.790520 | ||||||||
\(421\) | −10.7539 | −0.524112 | −0.262056 | − | 0.965053i | \(-0.584400\pi\) | ||||
−0.262056 | + | 0.965053i | \(0.584400\pi\) | |||||||
\(422\) | −43.4077 | −2.11305 | ||||||||
\(423\) | 0.742370 | 0.0360952 | ||||||||
\(424\) | −9.16432 | −0.445059 | ||||||||
\(425\) | −12.2983 | −0.596555 | ||||||||
\(426\) | 40.0479 | 1.94033 | ||||||||
\(427\) | 26.3099 | 1.27323 | ||||||||
\(428\) | −5.04868 | −0.244037 | ||||||||
\(429\) | 7.11821 | 0.343671 | ||||||||
\(430\) | −7.20994 | −0.347694 | ||||||||
\(431\) | 31.0868 | 1.49740 | 0.748700 | − | 0.662909i | \(-0.230678\pi\) | ||||
0.748700 | + | 0.662909i | \(0.230678\pi\) | |||||||
\(432\) | 15.5689 | 0.749057 | ||||||||
\(433\) | 24.9861 | 1.20075 | 0.600377 | − | 0.799717i | \(-0.295017\pi\) | ||||
0.600377 | + | 0.799717i | \(0.295017\pi\) | |||||||
\(434\) | −15.0476 | −0.722307 | ||||||||
\(435\) | −61.3578 | −2.94188 | ||||||||
\(436\) | 13.1187 | 0.628274 | ||||||||
\(437\) | −1.48294 | −0.0709387 | ||||||||
\(438\) | −2.90730 | −0.138916 | ||||||||
\(439\) | −14.7450 | −0.703742 | −0.351871 | − | 0.936049i | \(-0.614454\pi\) | ||||
−0.351871 | + | 0.936049i | \(0.614454\pi\) | |||||||
\(440\) | −7.17311 | −0.341965 | ||||||||
\(441\) | −5.67752 | −0.270358 | ||||||||
\(442\) | 5.79231 | 0.275512 | ||||||||
\(443\) | 7.33150 | 0.348330 | 0.174165 | − | 0.984716i | \(-0.444277\pi\) | ||||
0.174165 | + | 0.984716i | \(0.444277\pi\) | |||||||
\(444\) | 25.7109 | 1.22019 | ||||||||
\(445\) | 28.8865 | 1.36935 | ||||||||
\(446\) | 2.69933 | 0.127817 | ||||||||
\(447\) | 48.0778 | 2.27400 | ||||||||
\(448\) | −1.73548 | −0.0819939 | ||||||||
\(449\) | 8.64688 | 0.408071 | 0.204036 | − | 0.978963i | \(-0.434594\pi\) | ||||
0.204036 | + | 0.978963i | \(0.434594\pi\) | |||||||
\(450\) | −32.7970 | −1.54607 | ||||||||
\(451\) | 3.93128 | 0.185117 | ||||||||
\(452\) | 4.93049 | 0.231911 | ||||||||
\(453\) | −15.4567 | −0.726220 | ||||||||
\(454\) | −33.4502 | −1.56989 | ||||||||
\(455\) | 25.2811 | 1.18520 | ||||||||
\(456\) | −1.45374 | −0.0680777 | ||||||||
\(457\) | 1.01564 | 0.0475096 | 0.0237548 | − | 0.999718i | \(-0.492438\pi\) | ||||
0.0237548 | + | 0.999718i | \(0.492438\pi\) | |||||||
\(458\) | −28.9074 | −1.35075 | ||||||||
\(459\) | 3.11379 | 0.145339 | ||||||||
\(460\) | −15.6678 | −0.730513 | ||||||||
\(461\) | −18.7447 | −0.873027 | −0.436514 | − | 0.899698i | \(-0.643787\pi\) | ||||
−0.436514 | + | 0.899698i | \(0.643787\pi\) | |||||||
\(462\) | 6.71820 | 0.312559 | ||||||||
\(463\) | −3.26052 | −0.151529 | −0.0757646 | − | 0.997126i | \(-0.524140\pi\) | ||||
−0.0757646 | + | 0.997126i | \(0.524140\pi\) | |||||||
\(464\) | −34.6247 | −1.60741 | ||||||||
\(465\) | 42.2781 | 1.96060 | ||||||||
\(466\) | −29.4259 | −1.36313 | ||||||||
\(467\) | −23.2079 | −1.07393 | −0.536967 | − | 0.843603i | \(-0.680430\pi\) | ||||
−0.536967 | + | 0.843603i | \(0.680430\pi\) | |||||||
\(468\) | 5.16646 | 0.238820 | ||||||||
\(469\) | 17.3731 | 0.802215 | ||||||||
\(470\) | 3.47931 | 0.160489 | ||||||||
\(471\) | 26.8844 | 1.23877 | ||||||||
\(472\) | −9.20029 | −0.423478 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 48.3538 | 2.22097 | ||||||||
\(475\) | −4.86606 | −0.223270 | ||||||||
\(476\) | 1.82846 | 0.0838074 | ||||||||
\(477\) | −8.17435 | −0.374278 | ||||||||
\(478\) | 4.16758 | 0.190621 | ||||||||
\(479\) | −20.1309 | −0.919803 | −0.459902 | − | 0.887970i | \(-0.652115\pi\) | ||||
−0.459902 | + | 0.887970i | \(0.652115\pi\) | |||||||
\(480\) | −46.2355 | −2.11035 | ||||||||
\(481\) | 40.1214 | 1.82938 | ||||||||
\(482\) | 28.5935 | 1.30240 | ||||||||
\(483\) | −14.5249 | −0.660908 | ||||||||
\(484\) | 1.00511 | 0.0456867 | ||||||||
\(485\) | −39.9438 | −1.81376 | ||||||||
\(486\) | 25.3474 | 1.14978 | ||||||||
\(487\) | 16.0837 | 0.728822 | 0.364411 | − | 0.931238i | \(-0.381270\pi\) | ||||
0.364411 | + | 0.931238i | \(0.381270\pi\) | |||||||
\(488\) | −24.9432 | −1.12913 | ||||||||
\(489\) | 48.6487 | 2.19997 | ||||||||
\(490\) | −26.6092 | −1.20208 | ||||||||
\(491\) | 24.4966 | 1.10552 | 0.552759 | − | 0.833341i | \(-0.313575\pi\) | ||||
0.552759 | + | 0.833341i | \(0.313575\pi\) | |||||||
\(492\) | 8.41776 | 0.379502 | ||||||||
\(493\) | −6.92498 | −0.311886 | ||||||||
\(494\) | 2.29184 | 0.103115 | ||||||||
\(495\) | −6.39824 | −0.287580 | ||||||||
\(496\) | 23.8579 | 1.07125 | ||||||||
\(497\) | 19.7276 | 0.884902 | ||||||||
\(498\) | −23.5588 | −1.05569 | ||||||||
\(499\) | −10.6609 | −0.477249 | −0.238625 | − | 0.971112i | \(-0.576697\pi\) | ||||
−0.238625 | + | 0.971112i | \(0.576697\pi\) | |||||||
\(500\) | −30.5096 | −1.36443 | ||||||||
\(501\) | 40.2903 | 1.80004 | ||||||||
\(502\) | −32.9400 | −1.47018 | ||||||||
\(503\) | 3.94210 | 0.175770 | 0.0878849 | − | 0.996131i | \(-0.471989\pi\) | ||||
0.0878849 | + | 0.996131i | \(0.471989\pi\) | |||||||
\(504\) | −4.82656 | −0.214992 | ||||||||
\(505\) | −1.16526 | −0.0518532 | ||||||||
\(506\) | −6.49714 | −0.288833 | ||||||||
\(507\) | −3.91006 | −0.173652 | ||||||||
\(508\) | 18.9474 | 0.840657 | ||||||||
\(509\) | 24.0289 | 1.06506 | 0.532531 | − | 0.846410i | \(-0.321241\pi\) | ||||
0.532531 | + | 0.846410i | \(0.321241\pi\) | |||||||
\(510\) | −15.3597 | −0.680137 | ||||||||
\(511\) | −1.43213 | −0.0633538 | ||||||||
\(512\) | −8.84446 | −0.390874 | ||||||||
\(513\) | 1.23203 | 0.0543955 | ||||||||
\(514\) | −29.6029 | −1.30573 | ||||||||
\(515\) | 28.7782 | 1.26812 | ||||||||
\(516\) | −2.14123 | −0.0942622 | ||||||||
\(517\) | 0.482571 | 0.0212235 | ||||||||
\(518\) | 37.8667 | 1.66377 | ||||||||
\(519\) | 15.7151 | 0.689815 | ||||||||
\(520\) | −23.9678 | −1.05106 | ||||||||
\(521\) | −2.06632 | −0.0905270 | −0.0452635 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452635 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(522\) | −18.4675 | −0.808300 | ||||||||
\(523\) | −40.6133 | −1.77589 | −0.887947 | − | 0.459945i | \(-0.847869\pi\) | ||||
−0.887947 | + | 0.459945i | \(0.847869\pi\) | |||||||
\(524\) | −0.925321 | −0.0404228 | ||||||||
\(525\) | −47.6615 | −2.08012 | ||||||||
\(526\) | 12.0047 | 0.523430 | ||||||||
\(527\) | 4.77160 | 0.207854 | ||||||||
\(528\) | −10.6517 | −0.463554 | ||||||||
\(529\) | −8.95299 | −0.389260 | ||||||||
\(530\) | −38.3112 | −1.66413 | ||||||||
\(531\) | −8.20644 | −0.356129 | ||||||||
\(532\) | 0.723466 | 0.0313662 | ||||||||
\(533\) | 13.1358 | 0.568973 | ||||||||
\(534\) | 25.6491 | 1.10995 | ||||||||
\(535\) | 20.8914 | 0.903212 | ||||||||
\(536\) | −16.4706 | −0.711423 | ||||||||
\(537\) | 5.17555 | 0.223341 | ||||||||
\(538\) | 8.48537 | 0.365830 | ||||||||
\(539\) | −3.69062 | −0.158966 | ||||||||
\(540\) | 13.0168 | 0.560153 | ||||||||
\(541\) | 26.4953 | 1.13912 | 0.569561 | − | 0.821949i | \(-0.307113\pi\) | ||||
0.569561 | + | 0.821949i | \(0.307113\pi\) | |||||||
\(542\) | 14.8971 | 0.639885 | ||||||||
\(543\) | −16.0569 | −0.689068 | ||||||||
\(544\) | −5.21824 | −0.223730 | ||||||||
\(545\) | −54.2851 | −2.32532 | ||||||||
\(546\) | 22.4478 | 0.960678 | ||||||||
\(547\) | −3.85418 | −0.164793 | −0.0823965 | − | 0.996600i | \(-0.526257\pi\) | ||||
−0.0823965 | + | 0.996600i | \(0.526257\pi\) | |||||||
\(548\) | −6.26784 | −0.267749 | ||||||||
\(549\) | −22.2487 | −0.949553 | ||||||||
\(550\) | −21.3194 | −0.909063 | ||||||||
\(551\) | −2.74000 | −0.116728 | ||||||||
\(552\) | 13.7704 | 0.586108 | ||||||||
\(553\) | 23.8190 | 1.01289 | ||||||||
\(554\) | 52.6572 | 2.23719 | ||||||||
\(555\) | −106.391 | −4.51606 | ||||||||
\(556\) | −5.65733 | −0.239924 | ||||||||
\(557\) | 17.8754 | 0.757403 | 0.378702 | − | 0.925519i | \(-0.376371\pi\) | ||||
0.378702 | + | 0.925519i | \(0.376371\pi\) | |||||||
\(558\) | 12.7249 | 0.538686 | ||||||||
\(559\) | −3.34135 | −0.141324 | ||||||||
\(560\) | −37.8305 | −1.59863 | ||||||||
\(561\) | −2.13034 | −0.0899432 | ||||||||
\(562\) | 18.8878 | 0.796734 | ||||||||
\(563\) | 7.87441 | 0.331867 | 0.165933 | − | 0.986137i | \(-0.446936\pi\) | ||||
0.165933 | + | 0.986137i | \(0.446936\pi\) | |||||||
\(564\) | 1.03329 | 0.0435095 | ||||||||
\(565\) | −20.4023 | −0.858331 | ||||||||
\(566\) | 14.3632 | 0.603731 | ||||||||
\(567\) | 20.4630 | 0.859364 | ||||||||
\(568\) | −18.7028 | −0.784751 | ||||||||
\(569\) | −27.4812 | −1.15207 | −0.576036 | − | 0.817424i | \(-0.695401\pi\) | ||||
−0.576036 | + | 0.817424i | \(0.695401\pi\) | |||||||
\(570\) | −6.07734 | −0.254552 | ||||||||
\(571\) | −44.0173 | −1.84207 | −0.921034 | − | 0.389482i | \(-0.872654\pi\) | ||||
−0.921034 | + | 0.389482i | \(0.872654\pi\) | |||||||
\(572\) | 3.35841 | 0.140422 | ||||||||
\(573\) | 51.7663 | 2.16257 | ||||||||
\(574\) | 12.3976 | 0.517465 | ||||||||
\(575\) | 46.0932 | 1.92222 | ||||||||
\(576\) | 1.46760 | 0.0611498 | ||||||||
\(577\) | 12.4992 | 0.520347 | 0.260174 | − | 0.965562i | \(-0.416220\pi\) | ||||
0.260174 | + | 0.965562i | \(0.416220\pi\) | |||||||
\(578\) | −1.73352 | −0.0721051 | ||||||||
\(579\) | −33.3333 | −1.38528 | ||||||||
\(580\) | −28.9490 | −1.20204 | ||||||||
\(581\) | −11.6050 | −0.481458 | ||||||||
\(582\) | −35.4673 | −1.47016 | ||||||||
\(583\) | −5.31367 | −0.220070 | ||||||||
\(584\) | 1.35774 | 0.0561836 | ||||||||
\(585\) | −21.3787 | −0.883902 | ||||||||
\(586\) | 22.7202 | 0.938564 | ||||||||
\(587\) | 39.4789 | 1.62947 | 0.814735 | − | 0.579834i | \(-0.196882\pi\) | ||||
0.814735 | + | 0.579834i | \(0.196882\pi\) | |||||||
\(588\) | −7.90246 | −0.325892 | ||||||||
\(589\) | 1.88797 | 0.0777926 | ||||||||
\(590\) | −38.4616 | −1.58344 | ||||||||
\(591\) | 24.7056 | 1.01625 | ||||||||
\(592\) | −60.0375 | −2.46752 | ||||||||
\(593\) | 37.1415 | 1.52522 | 0.762610 | − | 0.646858i | \(-0.223917\pi\) | ||||
0.762610 | + | 0.646858i | \(0.223917\pi\) | |||||||
\(594\) | 5.39783 | 0.221476 | ||||||||
\(595\) | −7.56615 | −0.310182 | ||||||||
\(596\) | 22.6834 | 0.929148 | ||||||||
\(597\) | −35.7663 | −1.46382 | ||||||||
\(598\) | −21.7092 | −0.887754 | ||||||||
\(599\) | 15.8187 | 0.646334 | 0.323167 | − | 0.946342i | \(-0.395253\pi\) | ||||
0.323167 | + | 0.946342i | \(0.395253\pi\) | |||||||
\(600\) | 45.1857 | 1.84470 | ||||||||
\(601\) | 39.6107 | 1.61575 | 0.807877 | − | 0.589351i | \(-0.200616\pi\) | ||||
0.807877 | + | 0.589351i | \(0.200616\pi\) | |||||||
\(602\) | −3.15357 | −0.128530 | ||||||||
\(603\) | −14.6914 | −0.598280 | ||||||||
\(604\) | −7.29257 | −0.296731 | ||||||||
\(605\) | −4.15912 | −0.169092 | ||||||||
\(606\) | −1.03466 | −0.0420304 | ||||||||
\(607\) | 14.5160 | 0.589188 | 0.294594 | − | 0.955622i | \(-0.404816\pi\) | ||||
0.294594 | + | 0.955622i | \(0.404816\pi\) | |||||||
\(608\) | −2.06470 | −0.0837345 | ||||||||
\(609\) | −26.8375 | −1.08751 | ||||||||
\(610\) | −104.275 | −4.22195 | ||||||||
\(611\) | 1.61244 | 0.0652322 | ||||||||
\(612\) | −1.54622 | −0.0625023 | ||||||||
\(613\) | −32.4613 | −1.31110 | −0.655550 | − | 0.755152i | \(-0.727563\pi\) | ||||
−0.655550 | + | 0.755152i | \(0.727563\pi\) | |||||||
\(614\) | 6.10878 | 0.246530 | ||||||||
\(615\) | −34.8326 | −1.40458 | ||||||||
\(616\) | −3.13746 | −0.126412 | ||||||||
\(617\) | −10.0335 | −0.403935 | −0.201967 | − | 0.979392i | \(-0.564734\pi\) | ||||
−0.201967 | + | 0.979392i | \(0.564734\pi\) | |||||||
\(618\) | 25.5530 | 1.02789 | ||||||||
\(619\) | 14.0314 | 0.563970 | 0.281985 | − | 0.959419i | \(-0.409007\pi\) | ||||
0.281985 | + | 0.959419i | \(0.409007\pi\) | |||||||
\(620\) | 19.9470 | 0.801092 | ||||||||
\(621\) | −11.6703 | −0.468312 | ||||||||
\(622\) | −10.7672 | −0.431725 | ||||||||
\(623\) | 12.6347 | 0.506200 | ||||||||
\(624\) | −35.5909 | −1.42478 | ||||||||
\(625\) | 64.7567 | 2.59027 | ||||||||
\(626\) | 38.9988 | 1.55871 | ||||||||
\(627\) | −0.842911 | −0.0336626 | ||||||||
\(628\) | 12.6842 | 0.506155 | ||||||||
\(629\) | −12.0076 | −0.478773 | ||||||||
\(630\) | −20.1773 | −0.803884 | ||||||||
\(631\) | 30.5604 | 1.21659 | 0.608294 | − | 0.793712i | \(-0.291854\pi\) | ||||
0.608294 | + | 0.793712i | \(0.291854\pi\) | |||||||
\(632\) | −22.5817 | −0.898253 | ||||||||
\(633\) | 53.3441 | 2.12024 | ||||||||
\(634\) | 8.52769 | 0.338678 | ||||||||
\(635\) | −78.4042 | −3.11138 | ||||||||
\(636\) | −11.3778 | −0.451158 | ||||||||
\(637\) | −12.3317 | −0.488598 | ||||||||
\(638\) | −12.0046 | −0.475268 | ||||||||
\(639\) | −16.6824 | −0.659946 | ||||||||
\(640\) | 50.2849 | 1.98768 | ||||||||
\(641\) | −37.1632 | −1.46786 | −0.733929 | − | 0.679226i | \(-0.762315\pi\) | ||||
−0.733929 | + | 0.679226i | \(0.762315\pi\) | |||||||
\(642\) | 18.5500 | 0.732111 | ||||||||
\(643\) | 48.4321 | 1.90997 | 0.954987 | − | 0.296648i | \(-0.0958689\pi\) | ||||
0.954987 | + | 0.296648i | \(0.0958689\pi\) | |||||||
\(644\) | −6.85296 | −0.270044 | ||||||||
\(645\) | 8.86036 | 0.348876 | ||||||||
\(646\) | −0.685902 | −0.0269865 | ||||||||
\(647\) | −6.47105 | −0.254403 | −0.127202 | − | 0.991877i | \(-0.540600\pi\) | ||||
−0.127202 | + | 0.991877i | \(0.540600\pi\) | |||||||
\(648\) | −19.4000 | −0.762104 | ||||||||
\(649\) | −5.33453 | −0.209398 | ||||||||
\(650\) | −71.2355 | −2.79409 | ||||||||
\(651\) | 18.4921 | 0.724763 | ||||||||
\(652\) | 22.9527 | 0.898898 | ||||||||
\(653\) | −6.13116 | −0.239931 | −0.119965 | − | 0.992778i | \(-0.538278\pi\) | ||||
−0.119965 | + | 0.992778i | \(0.538278\pi\) | |||||||
\(654\) | −48.2013 | −1.88482 | ||||||||
\(655\) | 3.82896 | 0.149610 | ||||||||
\(656\) | −19.6563 | −0.767449 | ||||||||
\(657\) | 1.21107 | 0.0472483 | ||||||||
\(658\) | 1.52182 | 0.0593269 | ||||||||
\(659\) | 16.9276 | 0.659407 | 0.329703 | − | 0.944085i | \(-0.393051\pi\) | ||||
0.329703 | + | 0.944085i | \(0.393051\pi\) | |||||||
\(660\) | −8.90562 | −0.346651 | ||||||||
\(661\) | −8.40237 | −0.326814 | −0.163407 | − | 0.986559i | \(-0.552248\pi\) | ||||
−0.163407 | + | 0.986559i | \(0.552248\pi\) | |||||||
\(662\) | −50.3671 | −1.95757 | ||||||||
\(663\) | −7.11821 | −0.276448 | ||||||||
\(664\) | 11.0022 | 0.426968 | ||||||||
\(665\) | −2.99369 | −0.116090 | ||||||||
\(666\) | −32.0216 | −1.24081 | ||||||||
\(667\) | 25.9544 | 1.00496 | ||||||||
\(668\) | 19.0092 | 0.735487 | ||||||||
\(669\) | −3.31723 | −0.128252 | ||||||||
\(670\) | −68.8551 | −2.66010 | ||||||||
\(671\) | −14.4626 | −0.558323 | ||||||||
\(672\) | −20.2231 | −0.780121 | ||||||||
\(673\) | −7.19800 | −0.277462 | −0.138731 | − | 0.990330i | \(-0.544302\pi\) | ||||
−0.138731 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(674\) | −16.5533 | −0.637609 | ||||||||
\(675\) | −38.2943 | −1.47395 | ||||||||
\(676\) | −1.84479 | −0.0709534 | ||||||||
\(677\) | 4.59262 | 0.176509 | 0.0882543 | − | 0.996098i | \(-0.471871\pi\) | ||||
0.0882543 | + | 0.996098i | \(0.471871\pi\) | |||||||
\(678\) | −18.1158 | −0.695732 | ||||||||
\(679\) | −17.4711 | −0.670480 | ||||||||
\(680\) | 7.17311 | 0.275076 | ||||||||
\(681\) | 41.1072 | 1.57523 | ||||||||
\(682\) | 8.27168 | 0.316739 | ||||||||
\(683\) | 20.3470 | 0.778557 | 0.389278 | − | 0.921120i | \(-0.372724\pi\) | ||||
0.389278 | + | 0.921120i | \(0.372724\pi\) | |||||||
\(684\) | −0.611792 | −0.0233925 | ||||||||
\(685\) | 25.9362 | 0.990972 | ||||||||
\(686\) | −33.7137 | −1.28719 | ||||||||
\(687\) | 35.5245 | 1.35534 | ||||||||
\(688\) | 4.99997 | 0.190622 | ||||||||
\(689\) | −17.7548 | −0.676404 | ||||||||
\(690\) | 57.5670 | 2.19154 | ||||||||
\(691\) | −40.6621 | −1.54686 | −0.773429 | − | 0.633883i | \(-0.781460\pi\) | ||||
−0.773429 | + | 0.633883i | \(0.781460\pi\) | |||||||
\(692\) | 7.41446 | 0.281855 | ||||||||
\(693\) | −2.79854 | −0.106308 | ||||||||
\(694\) | −32.5260 | −1.23467 | ||||||||
\(695\) | 23.4099 | 0.887990 | ||||||||
\(696\) | 25.4433 | 0.964427 | ||||||||
\(697\) | −3.93128 | −0.148908 | ||||||||
\(698\) | −10.2045 | −0.386248 | ||||||||
\(699\) | 36.1618 | 1.36776 | ||||||||
\(700\) | −22.4870 | −0.849928 | ||||||||
\(701\) | −3.56567 | −0.134673 | −0.0673367 | − | 0.997730i | \(-0.521450\pi\) | ||||
−0.0673367 | + | 0.997730i | \(0.521450\pi\) | |||||||
\(702\) | 18.0360 | 0.680725 | ||||||||
\(703\) | −4.75102 | −0.179188 | ||||||||
\(704\) | 0.953998 | 0.0359552 | ||||||||
\(705\) | −4.27575 | −0.161034 | ||||||||
\(706\) | −32.5861 | −1.22639 | ||||||||
\(707\) | −0.509674 | −0.0191683 | ||||||||
\(708\) | −11.4224 | −0.429281 | ||||||||
\(709\) | 3.29202 | 0.123634 | 0.0618172 | − | 0.998087i | \(-0.480310\pi\) | ||||
0.0618172 | + | 0.998087i | \(0.480310\pi\) | |||||||
\(710\) | −78.1865 | −2.93429 | ||||||||
\(711\) | −20.1423 | −0.755397 | ||||||||
\(712\) | −11.9784 | −0.448910 | ||||||||
\(713\) | −17.8836 | −0.669747 | ||||||||
\(714\) | −6.71820 | −0.251422 | ||||||||
\(715\) | −13.8971 | −0.519721 | ||||||||
\(716\) | 2.44185 | 0.0912563 | ||||||||
\(717\) | −5.12158 | −0.191269 | ||||||||
\(718\) | −40.8726 | −1.52535 | ||||||||
\(719\) | 22.9828 | 0.857115 | 0.428558 | − | 0.903514i | \(-0.359022\pi\) | ||||
0.428558 | + | 0.903514i | \(0.359022\pi\) | |||||||
\(720\) | 31.9910 | 1.19224 | ||||||||
\(721\) | 12.5874 | 0.468778 | ||||||||
\(722\) | 32.6656 | 1.21569 | ||||||||
\(723\) | −35.1387 | −1.30682 | ||||||||
\(724\) | −7.57574 | −0.281550 | ||||||||
\(725\) | 85.1655 | 3.16297 | ||||||||
\(726\) | −3.69300 | −0.137060 | ||||||||
\(727\) | 25.2996 | 0.938311 | 0.469155 | − | 0.883116i | \(-0.344558\pi\) | ||||
0.469155 | + | 0.883116i | \(0.344558\pi\) | |||||||
\(728\) | −10.4834 | −0.388539 | ||||||||
\(729\) | 2.59599 | 0.0961479 | ||||||||
\(730\) | 5.67599 | 0.210078 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −30.9677 | −1.14460 | ||||||||
\(733\) | 9.34073 | 0.345008 | 0.172504 | − | 0.985009i | \(-0.444814\pi\) | ||||
0.172504 | + | 0.985009i | \(0.444814\pi\) | |||||||
\(734\) | −53.7212 | −1.98289 | ||||||||
\(735\) | 32.7003 | 1.20617 | ||||||||
\(736\) | 19.5576 | 0.720904 | ||||||||
\(737\) | −9.55002 | −0.351780 | ||||||||
\(738\) | −10.4839 | −0.385918 | ||||||||
\(739\) | −15.6028 | −0.573957 | −0.286978 | − | 0.957937i | \(-0.592651\pi\) | ||||
−0.286978 | + | 0.957937i | \(0.592651\pi\) | |||||||
\(740\) | −50.1960 | −1.84524 | ||||||||
\(741\) | −2.81646 | −0.103465 | ||||||||
\(742\) | −16.7570 | −0.615170 | ||||||||
\(743\) | −2.48960 | −0.0913346 | −0.0456673 | − | 0.998957i | \(-0.514541\pi\) | ||||
−0.0456673 | + | 0.998957i | \(0.514541\pi\) | |||||||
\(744\) | −17.5315 | −0.642736 | ||||||||
\(745\) | −93.8635 | −3.43889 | ||||||||
\(746\) | 21.7356 | 0.795797 | ||||||||
\(747\) | 9.81368 | 0.359064 | ||||||||
\(748\) | −1.00511 | −0.0367504 | ||||||||
\(749\) | 9.13772 | 0.333885 | ||||||||
\(750\) | 112.099 | 4.09329 | ||||||||
\(751\) | 16.8503 | 0.614877 | 0.307438 | − | 0.951568i | \(-0.400528\pi\) | ||||
0.307438 | + | 0.951568i | \(0.400528\pi\) | |||||||
\(752\) | −2.41284 | −0.0879873 | ||||||||
\(753\) | 40.4802 | 1.47518 | ||||||||
\(754\) | −40.1116 | −1.46078 | ||||||||
\(755\) | 30.1766 | 1.09824 | ||||||||
\(756\) | 5.69344 | 0.207069 | ||||||||
\(757\) | 25.7264 | 0.935042 | 0.467521 | − | 0.883982i | \(-0.345147\pi\) | ||||
0.467521 | + | 0.883982i | \(0.345147\pi\) | |||||||
\(758\) | −12.1753 | −0.442228 | ||||||||
\(759\) | 7.98439 | 0.289815 | ||||||||
\(760\) | 2.83818 | 0.102952 | ||||||||
\(761\) | 8.56334 | 0.310421 | 0.155210 | − | 0.987881i | \(-0.450394\pi\) | ||||
0.155210 | + | 0.987881i | \(0.450394\pi\) | |||||||
\(762\) | −69.6173 | −2.52197 | ||||||||
\(763\) | −23.7439 | −0.859587 | ||||||||
\(764\) | 24.4236 | 0.883616 | ||||||||
\(765\) | 6.39824 | 0.231329 | ||||||||
\(766\) | −5.47055 | −0.197659 | ||||||||
\(767\) | −17.8245 | −0.643605 | ||||||||
\(768\) | 40.5847 | 1.46447 | ||||||||
\(769\) | 12.4303 | 0.448248 | 0.224124 | − | 0.974561i | \(-0.428048\pi\) | ||||
0.224124 | + | 0.974561i | \(0.428048\pi\) | |||||||
\(770\) | −13.1161 | −0.472672 | ||||||||
\(771\) | 36.3793 | 1.31017 | ||||||||
\(772\) | −15.7268 | −0.566021 | ||||||||
\(773\) | 33.4064 | 1.20154 | 0.600772 | − | 0.799421i | \(-0.294860\pi\) | ||||
0.600772 | + | 0.799421i | \(0.294860\pi\) | |||||||
\(774\) | 2.66679 | 0.0958558 | ||||||||
\(775\) | −58.6826 | −2.10794 | ||||||||
\(776\) | 16.5636 | 0.594597 | ||||||||
\(777\) | −46.5347 | −1.66942 | ||||||||
\(778\) | −33.7884 | −1.21137 | ||||||||
\(779\) | −1.55549 | −0.0557311 | ||||||||
\(780\) | −29.7568 | −1.06546 | ||||||||
\(781\) | −10.8443 | −0.388038 | ||||||||
\(782\) | 6.49714 | 0.232337 | ||||||||
\(783\) | −21.5629 | −0.770596 | ||||||||
\(784\) | 18.4530 | 0.659037 | ||||||||
\(785\) | −52.4870 | −1.87334 | ||||||||
\(786\) | 3.39985 | 0.121268 | ||||||||
\(787\) | −6.95976 | −0.248089 | −0.124044 | − | 0.992277i | \(-0.539587\pi\) | ||||
−0.124044 | + | 0.992277i | \(0.539587\pi\) | |||||||
\(788\) | 11.6562 | 0.415236 | ||||||||
\(789\) | −14.7527 | −0.525209 | ||||||||
\(790\) | −94.4024 | −3.35869 | ||||||||
\(791\) | −8.92381 | −0.317294 | ||||||||
\(792\) | 2.65317 | 0.0942762 | ||||||||
\(793\) | −48.3245 | −1.71606 | ||||||||
\(794\) | −7.81523 | −0.277352 | ||||||||
\(795\) | 47.0810 | 1.66979 | ||||||||
\(796\) | −16.8747 | −0.598109 | ||||||||
\(797\) | 21.1866 | 0.750469 | 0.375234 | − | 0.926930i | \(-0.377562\pi\) | ||||
0.375234 | + | 0.926930i | \(0.377562\pi\) | |||||||
\(798\) | −2.65818 | −0.0940987 | ||||||||
\(799\) | −0.482571 | −0.0170721 | ||||||||
\(800\) | 64.1755 | 2.26895 | ||||||||
\(801\) | −10.6844 | −0.377516 | ||||||||
\(802\) | 33.7589 | 1.19207 | ||||||||
\(803\) | 0.787245 | 0.0277813 | ||||||||
\(804\) | −20.4488 | −0.721172 | ||||||||
\(805\) | 28.3574 | 0.999468 | ||||||||
\(806\) | 27.6385 | 0.973526 | ||||||||
\(807\) | −10.4277 | −0.367074 | ||||||||
\(808\) | 0.483198 | 0.0169989 | ||||||||
\(809\) | −52.0591 | −1.83030 | −0.915151 | − | 0.403111i | \(-0.867929\pi\) | ||||
−0.915151 | + | 0.403111i | \(0.867929\pi\) | |||||||
\(810\) | −81.1012 | −2.84961 | ||||||||
\(811\) | 18.3140 | 0.643092 | 0.321546 | − | 0.946894i | \(-0.395798\pi\) | ||||
0.321546 | + | 0.946894i | \(0.395798\pi\) | |||||||
\(812\) | −12.6621 | −0.444352 | ||||||||
\(813\) | −18.3072 | −0.642060 | ||||||||
\(814\) | −20.8154 | −0.729579 | ||||||||
\(815\) | −94.9780 | −3.32694 | ||||||||
\(816\) | 10.6517 | 0.372883 | ||||||||
\(817\) | 0.395669 | 0.0138427 | ||||||||
\(818\) | 64.9317 | 2.27028 | ||||||||
\(819\) | −9.35090 | −0.326747 | ||||||||
\(820\) | −16.4342 | −0.573907 | ||||||||
\(821\) | −21.6929 | −0.757087 | −0.378543 | − | 0.925584i | \(-0.623575\pi\) | ||||
−0.378543 | + | 0.925584i | \(0.623575\pi\) | |||||||
\(822\) | 23.0295 | 0.803246 | ||||||||
\(823\) | −34.8886 | −1.21614 | −0.608070 | − | 0.793884i | \(-0.708056\pi\) | ||||
−0.608070 | + | 0.793884i | \(0.708056\pi\) | |||||||
\(824\) | −11.9335 | −0.415723 | ||||||||
\(825\) | 26.1996 | 0.912153 | ||||||||
\(826\) | −16.8228 | −0.585341 | ||||||||
\(827\) | 18.4110 | 0.640213 | 0.320107 | − | 0.947382i | \(-0.396281\pi\) | ||||
0.320107 | + | 0.947382i | \(0.396281\pi\) | |||||||
\(828\) | 5.79514 | 0.201395 | ||||||||
\(829\) | 3.47139 | 0.120566 | 0.0602831 | − | 0.998181i | \(-0.480800\pi\) | ||||
0.0602831 | + | 0.998181i | \(0.480800\pi\) | |||||||
\(830\) | 45.9944 | 1.59649 | ||||||||
\(831\) | −64.7109 | −2.24480 | ||||||||
\(832\) | 3.18764 | 0.110511 | ||||||||
\(833\) | 3.69062 | 0.127873 | ||||||||
\(834\) | 20.7864 | 0.719773 | ||||||||
\(835\) | −78.6597 | −2.72213 | ||||||||
\(836\) | −0.397690 | −0.0137544 | ||||||||
\(837\) | 14.8577 | 0.513559 | ||||||||
\(838\) | 9.32350 | 0.322075 | ||||||||
\(839\) | 32.6769 | 1.12813 | 0.564066 | − | 0.825729i | \(-0.309236\pi\) | ||||
0.564066 | + | 0.825729i | \(0.309236\pi\) | |||||||
\(840\) | 27.7991 | 0.959159 | ||||||||
\(841\) | 18.9554 | 0.653634 | ||||||||
\(842\) | 18.6421 | 0.642450 | ||||||||
\(843\) | −23.2114 | −0.799442 | ||||||||
\(844\) | 25.1681 | 0.866320 | ||||||||
\(845\) | 7.63370 | 0.262607 | ||||||||
\(846\) | −1.28692 | −0.0442451 | ||||||||
\(847\) | −1.81917 | −0.0625074 | ||||||||
\(848\) | 26.5682 | 0.912355 | ||||||||
\(849\) | −17.6511 | −0.605783 | ||||||||
\(850\) | 21.3194 | 0.731250 | ||||||||
\(851\) | 45.0035 | 1.54270 | ||||||||
\(852\) | −23.2200 | −0.795505 | ||||||||
\(853\) | 14.5448 | 0.498004 | 0.249002 | − | 0.968503i | \(-0.419897\pi\) | ||||
0.249002 | + | 0.968503i | \(0.419897\pi\) | |||||||
\(854\) | −45.6089 | −1.56070 | ||||||||
\(855\) | 2.53159 | 0.0865784 | ||||||||
\(856\) | −8.66305 | −0.296097 | ||||||||
\(857\) | −57.2896 | −1.95698 | −0.978488 | − | 0.206303i | \(-0.933857\pi\) | ||||
−0.978488 | + | 0.206303i | \(0.933857\pi\) | |||||||
\(858\) | −12.3396 | −0.421267 | ||||||||
\(859\) | 23.2202 | 0.792263 | 0.396131 | − | 0.918194i | \(-0.370352\pi\) | ||||
0.396131 | + | 0.918194i | \(0.370352\pi\) | |||||||
\(860\) | 4.18037 | 0.142549 | ||||||||
\(861\) | −15.2355 | −0.519224 | ||||||||
\(862\) | −53.8898 | −1.83549 | ||||||||
\(863\) | 41.9492 | 1.42797 | 0.713983 | − | 0.700163i | \(-0.246889\pi\) | ||||
0.713983 | + | 0.700163i | \(0.246889\pi\) | |||||||
\(864\) | −16.2485 | −0.552785 | ||||||||
\(865\) | −30.6809 | −1.04318 | ||||||||
\(866\) | −43.3139 | −1.47187 | ||||||||
\(867\) | 2.13034 | 0.0723503 | ||||||||
\(868\) | 8.72468 | 0.296135 | ||||||||
\(869\) | −13.0934 | −0.444162 | ||||||||
\(870\) | 106.365 | 3.60612 | ||||||||
\(871\) | −31.9099 | −1.08123 | ||||||||
\(872\) | 22.5105 | 0.762302 | ||||||||
\(873\) | 14.7743 | 0.500034 | ||||||||
\(874\) | 2.57072 | 0.0869558 | ||||||||
\(875\) | 55.2200 | 1.86678 | ||||||||
\(876\) | 1.68567 | 0.0569535 | ||||||||
\(877\) | 0.187881 | 0.00634430 | 0.00317215 | − | 0.999995i | \(-0.498990\pi\) | ||||
0.00317215 | + | 0.999995i | \(0.498990\pi\) | |||||||
\(878\) | 25.5609 | 0.862638 | ||||||||
\(879\) | −27.9211 | −0.941755 | ||||||||
\(880\) | 20.7955 | 0.701016 | ||||||||
\(881\) | −17.9792 | −0.605736 | −0.302868 | − | 0.953033i | \(-0.597944\pi\) | ||||
−0.302868 | + | 0.953033i | \(0.597944\pi\) | |||||||
\(882\) | 9.84212 | 0.331402 | ||||||||
\(883\) | 12.2957 | 0.413783 | 0.206891 | − | 0.978364i | \(-0.433665\pi\) | ||||
0.206891 | + | 0.978364i | \(0.433665\pi\) | |||||||
\(884\) | −3.35841 | −0.112956 | ||||||||
\(885\) | 47.2658 | 1.58882 | ||||||||
\(886\) | −12.7093 | −0.426978 | ||||||||
\(887\) | 15.8416 | 0.531909 | 0.265954 | − | 0.963986i | \(-0.414313\pi\) | ||||
0.265954 | + | 0.963986i | \(0.414313\pi\) | |||||||
\(888\) | 44.1174 | 1.48048 | ||||||||
\(889\) | −34.2934 | −1.15016 | ||||||||
\(890\) | −50.0755 | −1.67853 | ||||||||
\(891\) | −11.2485 | −0.376840 | ||||||||
\(892\) | −1.56509 | −0.0524031 | ||||||||
\(893\) | −0.190938 | −0.00638951 | ||||||||
\(894\) | −83.3441 | −2.78744 | ||||||||
\(895\) | −10.1043 | −0.337751 | ||||||||
\(896\) | 21.9942 | 0.734776 | ||||||||
\(897\) | 26.6786 | 0.890772 | ||||||||
\(898\) | −14.9896 | −0.500209 | ||||||||
\(899\) | −33.0432 | −1.10205 | ||||||||
\(900\) | 19.0159 | 0.633863 | ||||||||
\(901\) | 5.31367 | 0.177024 | ||||||||
\(902\) | −6.81497 | −0.226914 | ||||||||
\(903\) | 3.87545 | 0.128967 | ||||||||
\(904\) | 8.46025 | 0.281384 | ||||||||
\(905\) | 31.3483 | 1.04205 | ||||||||
\(906\) | 26.7946 | 0.890192 | ||||||||
\(907\) | −0.113375 | −0.00376457 | −0.00188228 | − | 0.999998i | \(-0.500599\pi\) | ||||
−0.00188228 | + | 0.999998i | \(0.500599\pi\) | |||||||
\(908\) | 19.3946 | 0.643633 | ||||||||
\(909\) | 0.431001 | 0.0142954 | ||||||||
\(910\) | −43.8254 | −1.45280 | ||||||||
\(911\) | 50.7226 | 1.68051 | 0.840257 | − | 0.542188i | \(-0.182404\pi\) | ||||
0.840257 | + | 0.542188i | \(0.182404\pi\) | |||||||
\(912\) | 4.21453 | 0.139557 | ||||||||
\(913\) | 6.37930 | 0.211124 | ||||||||
\(914\) | −1.76064 | −0.0582367 | ||||||||
\(915\) | 128.144 | 4.23631 | ||||||||
\(916\) | 16.7607 | 0.553788 | ||||||||
\(917\) | 1.67476 | 0.0553054 | ||||||||
\(918\) | −5.39783 | −0.178155 | ||||||||
\(919\) | 1.42520 | 0.0470129 | 0.0235064 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235064 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(920\) | −26.8844 | −0.886351 | ||||||||
\(921\) | −7.50713 | −0.247368 | ||||||||
\(922\) | 32.4944 | 1.07015 | ||||||||
\(923\) | −36.2344 | −1.19267 | ||||||||
\(924\) | −3.89525 | −0.128144 | ||||||||
\(925\) | 147.673 | 4.85544 | ||||||||
\(926\) | 5.65219 | 0.185743 | ||||||||
\(927\) | −10.6444 | −0.349608 | ||||||||
\(928\) | 36.1362 | 1.18623 | ||||||||
\(929\) | −6.45400 | −0.211749 | −0.105874 | − | 0.994380i | \(-0.533764\pi\) | ||||
−0.105874 | + | 0.994380i | \(0.533764\pi\) | |||||||
\(930\) | −73.2901 | −2.40328 | ||||||||
\(931\) | 1.46027 | 0.0478583 | ||||||||
\(932\) | 17.0613 | 0.558862 | ||||||||
\(933\) | 13.2319 | 0.433193 | ||||||||
\(934\) | 40.2315 | 1.31641 | ||||||||
\(935\) | 4.15912 | 0.136018 | ||||||||
\(936\) | 8.86515 | 0.289766 | ||||||||
\(937\) | −36.7454 | −1.20042 | −0.600210 | − | 0.799843i | \(-0.704916\pi\) | ||||
−0.600210 | + | 0.799843i | \(0.704916\pi\) | |||||||
\(938\) | −30.1167 | −0.983345 | ||||||||
\(939\) | −47.9260 | −1.56401 | ||||||||
\(940\) | −2.01733 | −0.0657979 | ||||||||
\(941\) | −51.8476 | −1.69018 | −0.845092 | − | 0.534622i | \(-0.820454\pi\) | ||||
−0.845092 | + | 0.534622i | \(0.820454\pi\) | |||||||
\(942\) | −46.6047 | −1.51846 | ||||||||
\(943\) | 14.7342 | 0.479811 | ||||||||
\(944\) | 26.6725 | 0.868116 | ||||||||
\(945\) | −23.5594 | −0.766387 | ||||||||
\(946\) | 1.73352 | 0.0563618 | ||||||||
\(947\) | 19.7023 | 0.640239 | 0.320120 | − | 0.947377i | \(-0.396277\pi\) | ||||
0.320120 | + | 0.947377i | \(0.396277\pi\) | |||||||
\(948\) | −28.0359 | −0.910562 | ||||||||
\(949\) | 2.63046 | 0.0853882 | ||||||||
\(950\) | 8.43543 | 0.273682 | ||||||||
\(951\) | −10.4798 | −0.339829 | ||||||||
\(952\) | 3.13746 | 0.101686 | ||||||||
\(953\) | 11.1653 | 0.361681 | 0.180841 | − | 0.983512i | \(-0.442118\pi\) | ||||
0.180841 | + | 0.983512i | \(0.442118\pi\) | |||||||
\(954\) | 14.1704 | 0.458785 | ||||||||
\(955\) | −101.065 | −3.27037 | ||||||||
\(956\) | −2.41639 | −0.0781516 | ||||||||
\(957\) | 14.7526 | 0.476884 | ||||||||
\(958\) | 34.8974 | 1.12748 | ||||||||
\(959\) | 11.3443 | 0.366327 | ||||||||
\(960\) | −8.45277 | −0.272812 | ||||||||
\(961\) | −8.23186 | −0.265544 | ||||||||
\(962\) | −69.5514 | −2.24243 | ||||||||
\(963\) | −7.72723 | −0.249006 | ||||||||
\(964\) | −16.5787 | −0.533963 | ||||||||
\(965\) | 65.0773 | 2.09491 | ||||||||
\(966\) | 25.1794 | 0.810133 | ||||||||
\(967\) | 47.2611 | 1.51982 | 0.759908 | − | 0.650031i | \(-0.225244\pi\) | ||||
0.759908 | + | 0.650031i | \(0.225244\pi\) | |||||||
\(968\) | 1.72467 | 0.0554330 | ||||||||
\(969\) | 0.842911 | 0.0270782 | ||||||||
\(970\) | 69.2436 | 2.22328 | ||||||||
\(971\) | −53.2219 | −1.70797 | −0.853986 | − | 0.520295i | \(-0.825822\pi\) | ||||
−0.853986 | + | 0.520295i | \(0.825822\pi\) | |||||||
\(972\) | −14.6966 | −0.471392 | ||||||||
\(973\) | 10.2393 | 0.328258 | ||||||||
\(974\) | −27.8815 | −0.893381 | ||||||||
\(975\) | 87.5419 | 2.80359 | ||||||||
\(976\) | 72.3126 | 2.31467 | ||||||||
\(977\) | 39.1537 | 1.25264 | 0.626319 | − | 0.779567i | \(-0.284561\pi\) | ||||
0.626319 | + | 0.779567i | \(0.284561\pi\) | |||||||
\(978\) | −84.3337 | −2.69669 | ||||||||
\(979\) | −6.94533 | −0.221974 | ||||||||
\(980\) | 15.4282 | 0.492835 | ||||||||
\(981\) | 20.0788 | 0.641067 | ||||||||
\(982\) | −42.4655 | −1.35513 | ||||||||
\(983\) | 20.0267 | 0.638752 | 0.319376 | − | 0.947628i | \(-0.396527\pi\) | ||||
0.319376 | + | 0.947628i | \(0.396527\pi\) | |||||||
\(984\) | 14.4441 | 0.460460 | ||||||||
\(985\) | −48.2334 | −1.53684 | ||||||||
\(986\) | 12.0046 | 0.382305 | ||||||||
\(987\) | −1.87018 | −0.0595286 | ||||||||
\(988\) | −1.32882 | −0.0422754 | ||||||||
\(989\) | −3.74793 | −0.119177 | ||||||||
\(990\) | 11.0915 | 0.352511 | ||||||||
\(991\) | 17.0975 | 0.543120 | 0.271560 | − | 0.962421i | \(-0.412460\pi\) | ||||
0.271560 | + | 0.962421i | \(0.412460\pi\) | |||||||
\(992\) | −24.8993 | −0.790555 | ||||||||
\(993\) | 61.8965 | 1.96423 | ||||||||
\(994\) | −34.1982 | −1.08470 | ||||||||
\(995\) | 69.8274 | 2.21368 | ||||||||
\(996\) | 13.6595 | 0.432819 | ||||||||
\(997\) | −14.4961 | −0.459097 | −0.229549 | − | 0.973297i | \(-0.573725\pi\) | ||||
−0.229549 | + | 0.973297i | \(0.573725\pi\) | |||||||
\(998\) | 18.4810 | 0.585006 | ||||||||
\(999\) | −37.3890 | −1.18294 |
(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 | 8041.2.a.i.1.17 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.i.1.17 | ✓ | 78 | 1.1 | even | 1 | trivial |