Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.72 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.92694 | 1.68987 | 0.844936 | − | 0.534867i | \(-0.179638\pi\) | ||||
0.844936 | + | 0.534867i | \(0.179638\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.51878 | 1.57365 | 0.786824 | − | 0.617177i | \(-0.211724\pi\) | ||||
0.786824 | + | 0.617177i | \(0.211724\pi\) | |||||||
\(6\) | −2.92694 | −1.19492 | ||||||||
\(7\) | −2.15404 | −0.814152 | −0.407076 | − | 0.913394i | \(-0.633452\pi\) | ||||
−0.407076 | + | 0.913394i | \(0.633452\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.56701 | 1.85567 | ||||||||
\(10\) | −3.51878 | −1.11274 | ||||||||
\(11\) | −1.41443 | −0.426466 | −0.213233 | − | 0.977001i | \(-0.568399\pi\) | ||||
−0.213233 | + | 0.977001i | \(0.568399\pi\) | |||||||
\(12\) | 2.92694 | 0.844936 | ||||||||
\(13\) | 1.01538 | 0.281616 | 0.140808 | − | 0.990037i | \(-0.455030\pi\) | ||||
0.140808 | + | 0.990037i | \(0.455030\pi\) | |||||||
\(14\) | 2.15404 | 0.575692 | ||||||||
\(15\) | 10.2993 | 2.65926 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.94396 | 0.714015 | 0.357007 | − | 0.934102i | \(-0.383797\pi\) | ||||
0.357007 | + | 0.934102i | \(0.383797\pi\) | |||||||
\(18\) | −5.56701 | −1.31216 | ||||||||
\(19\) | 6.03206 | 1.38385 | 0.691925 | − | 0.721970i | \(-0.256763\pi\) | ||||
0.691925 | + | 0.721970i | \(0.256763\pi\) | |||||||
\(20\) | 3.51878 | 0.786824 | ||||||||
\(21\) | −6.30477 | −1.37581 | ||||||||
\(22\) | 1.41443 | 0.301557 | ||||||||
\(23\) | −2.14527 | −0.447319 | −0.223660 | − | 0.974667i | \(-0.571800\pi\) | ||||
−0.223660 | + | 0.974667i | \(0.571800\pi\) | |||||||
\(24\) | −2.92694 | −0.597460 | ||||||||
\(25\) | 7.38184 | 1.47637 | ||||||||
\(26\) | −1.01538 | −0.199133 | ||||||||
\(27\) | 7.51348 | 1.44597 | ||||||||
\(28\) | −2.15404 | −0.407076 | ||||||||
\(29\) | −0.271618 | −0.0504381 | −0.0252191 | − | 0.999682i | \(-0.508028\pi\) | ||||
−0.0252191 | + | 0.999682i | \(0.508028\pi\) | |||||||
\(30\) | −10.2993 | −1.88038 | ||||||||
\(31\) | 5.07483 | 0.911466 | 0.455733 | − | 0.890117i | \(-0.349377\pi\) | ||||
0.455733 | + | 0.890117i | \(0.349377\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.13995 | −0.720673 | ||||||||
\(34\) | −2.94396 | −0.504885 | ||||||||
\(35\) | −7.57961 | −1.28119 | ||||||||
\(36\) | 5.56701 | 0.927834 | ||||||||
\(37\) | −8.31027 | −1.36620 | −0.683100 | − | 0.730325i | \(-0.739369\pi\) | ||||
−0.683100 | + | 0.730325i | \(0.739369\pi\) | |||||||
\(38\) | −6.03206 | −0.978529 | ||||||||
\(39\) | 2.97197 | 0.475896 | ||||||||
\(40\) | −3.51878 | −0.556369 | ||||||||
\(41\) | 9.15654 | 1.43001 | 0.715006 | − | 0.699118i | \(-0.246424\pi\) | ||||
0.715006 | + | 0.699118i | \(0.246424\pi\) | |||||||
\(42\) | 6.30477 | 0.972846 | ||||||||
\(43\) | 5.82028 | 0.887584 | 0.443792 | − | 0.896130i | \(-0.353633\pi\) | ||||
0.443792 | + | 0.896130i | \(0.353633\pi\) | |||||||
\(44\) | −1.41443 | −0.213233 | ||||||||
\(45\) | 19.5891 | 2.92017 | ||||||||
\(46\) | 2.14527 | 0.316302 | ||||||||
\(47\) | −9.09485 | −1.32662 | −0.663310 | − | 0.748345i | \(-0.730849\pi\) | ||||
−0.663310 | + | 0.748345i | \(0.730849\pi\) | |||||||
\(48\) | 2.92694 | 0.422468 | ||||||||
\(49\) | −2.36010 | −0.337157 | ||||||||
\(50\) | −7.38184 | −1.04395 | ||||||||
\(51\) | 8.61680 | 1.20659 | ||||||||
\(52\) | 1.01538 | 0.140808 | ||||||||
\(53\) | 7.65817 | 1.05193 | 0.525965 | − | 0.850506i | \(-0.323704\pi\) | ||||
0.525965 | + | 0.850506i | \(0.323704\pi\) | |||||||
\(54\) | −7.51348 | −1.02246 | ||||||||
\(55\) | −4.97706 | −0.671107 | ||||||||
\(56\) | 2.15404 | 0.287846 | ||||||||
\(57\) | 17.6555 | 2.33853 | ||||||||
\(58\) | 0.271618 | 0.0356651 | ||||||||
\(59\) | 6.11808 | 0.796506 | 0.398253 | − | 0.917276i | \(-0.369617\pi\) | ||||
0.398253 | + | 0.917276i | \(0.369617\pi\) | |||||||
\(60\) | 10.2993 | 1.32963 | ||||||||
\(61\) | −1.98794 | −0.254530 | −0.127265 | − | 0.991869i | \(-0.540620\pi\) | ||||
−0.127265 | + | 0.991869i | \(0.540620\pi\) | |||||||
\(62\) | −5.07483 | −0.644504 | ||||||||
\(63\) | −11.9916 | −1.51080 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.57291 | 0.443165 | ||||||||
\(66\) | 4.13995 | 0.509593 | ||||||||
\(67\) | 4.12217 | 0.503604 | 0.251802 | − | 0.967779i | \(-0.418977\pi\) | ||||
0.251802 | + | 0.967779i | \(0.418977\pi\) | |||||||
\(68\) | 2.94396 | 0.357007 | ||||||||
\(69\) | −6.27908 | −0.755912 | ||||||||
\(70\) | 7.57961 | 0.905937 | ||||||||
\(71\) | 15.1780 | 1.80129 | 0.900647 | − | 0.434552i | \(-0.143093\pi\) | ||||
0.900647 | + | 0.434552i | \(0.143093\pi\) | |||||||
\(72\) | −5.56701 | −0.656078 | ||||||||
\(73\) | −2.71306 | −0.317539 | −0.158770 | − | 0.987316i | \(-0.550753\pi\) | ||||
−0.158770 | + | 0.987316i | \(0.550753\pi\) | |||||||
\(74\) | 8.31027 | 0.966049 | ||||||||
\(75\) | 21.6062 | 2.49487 | ||||||||
\(76\) | 6.03206 | 0.691925 | ||||||||
\(77\) | 3.04674 | 0.347208 | ||||||||
\(78\) | −2.97197 | −0.336509 | ||||||||
\(79\) | −4.28520 | −0.482122 | −0.241061 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241061 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(80\) | 3.51878 | 0.393412 | ||||||||
\(81\) | 5.29054 | 0.587838 | ||||||||
\(82\) | −9.15654 | −1.01117 | ||||||||
\(83\) | −11.1344 | −1.22215 | −0.611077 | − | 0.791571i | \(-0.709264\pi\) | ||||
−0.611077 | + | 0.791571i | \(0.709264\pi\) | |||||||
\(84\) | −6.30477 | −0.687906 | ||||||||
\(85\) | 10.3591 | 1.12361 | ||||||||
\(86\) | −5.82028 | −0.627617 | ||||||||
\(87\) | −0.795009 | −0.0852340 | ||||||||
\(88\) | 1.41443 | 0.150778 | ||||||||
\(89\) | −15.1343 | −1.60424 | −0.802119 | − | 0.597165i | \(-0.796294\pi\) | ||||
−0.802119 | + | 0.597165i | \(0.796294\pi\) | |||||||
\(90\) | −19.5891 | −2.06487 | ||||||||
\(91\) | −2.18718 | −0.229279 | ||||||||
\(92\) | −2.14527 | −0.223660 | ||||||||
\(93\) | 14.8537 | 1.54026 | ||||||||
\(94\) | 9.09485 | 0.938062 | ||||||||
\(95\) | 21.2255 | 2.17769 | ||||||||
\(96\) | −2.92694 | −0.298730 | ||||||||
\(97\) | −15.5772 | −1.58163 | −0.790813 | − | 0.612057i | \(-0.790342\pi\) | ||||
−0.790813 | + | 0.612057i | \(0.790342\pi\) | |||||||
\(98\) | 2.36010 | 0.238406 | ||||||||
\(99\) | −7.87412 | −0.791379 | ||||||||
\(100\) | 7.38184 | 0.738184 | ||||||||
\(101\) | −0.540634 | −0.0537951 | −0.0268975 | − | 0.999638i | \(-0.508563\pi\) | ||||
−0.0268975 | + | 0.999638i | \(0.508563\pi\) | |||||||
\(102\) | −8.61680 | −0.853190 | ||||||||
\(103\) | 6.79230 | 0.669265 | 0.334632 | − | 0.942349i | \(-0.391388\pi\) | ||||
0.334632 | + | 0.942349i | \(0.391388\pi\) | |||||||
\(104\) | −1.01538 | −0.0995665 | ||||||||
\(105\) | −22.1851 | −2.16504 | ||||||||
\(106\) | −7.65817 | −0.743827 | ||||||||
\(107\) | 13.4644 | 1.30165 | 0.650826 | − | 0.759227i | \(-0.274423\pi\) | ||||
0.650826 | + | 0.759227i | \(0.274423\pi\) | |||||||
\(108\) | 7.51348 | 0.722985 | ||||||||
\(109\) | 6.72962 | 0.644580 | 0.322290 | − | 0.946641i | \(-0.395547\pi\) | ||||
0.322290 | + | 0.946641i | \(0.395547\pi\) | |||||||
\(110\) | 4.97706 | 0.474544 | ||||||||
\(111\) | −24.3237 | −2.30870 | ||||||||
\(112\) | −2.15404 | −0.203538 | ||||||||
\(113\) | −10.2145 | −0.960899 | −0.480450 | − | 0.877022i | \(-0.659526\pi\) | ||||
−0.480450 | + | 0.877022i | \(0.659526\pi\) | |||||||
\(114\) | −17.6555 | −1.65359 | ||||||||
\(115\) | −7.54873 | −0.703923 | ||||||||
\(116\) | −0.271618 | −0.0252191 | ||||||||
\(117\) | 5.65264 | 0.522587 | ||||||||
\(118\) | −6.11808 | −0.563215 | ||||||||
\(119\) | −6.34141 | −0.581316 | ||||||||
\(120\) | −10.2993 | −0.940192 | ||||||||
\(121\) | −8.99940 | −0.818127 | ||||||||
\(122\) | 1.98794 | 0.179980 | ||||||||
\(123\) | 26.8007 | 2.41654 | ||||||||
\(124\) | 5.07483 | 0.455733 | ||||||||
\(125\) | 8.38118 | 0.749635 | ||||||||
\(126\) | 11.9916 | 1.06829 | ||||||||
\(127\) | 8.20947 | 0.728473 | 0.364236 | − | 0.931306i | \(-0.381330\pi\) | ||||
0.364236 | + | 0.931306i | \(0.381330\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 17.0356 | 1.49990 | ||||||||
\(130\) | −3.57291 | −0.313365 | ||||||||
\(131\) | −12.4641 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(132\) | −4.13995 | −0.360336 | ||||||||
\(133\) | −12.9933 | −1.12666 | ||||||||
\(134\) | −4.12217 | −0.356102 | ||||||||
\(135\) | 26.4383 | 2.27545 | ||||||||
\(136\) | −2.94396 | −0.252442 | ||||||||
\(137\) | 0.690596 | 0.0590016 | 0.0295008 | − | 0.999565i | \(-0.490608\pi\) | ||||
0.0295008 | + | 0.999565i | \(0.490608\pi\) | |||||||
\(138\) | 6.27908 | 0.534511 | ||||||||
\(139\) | −15.5473 | −1.31871 | −0.659353 | − | 0.751834i | \(-0.729169\pi\) | ||||
−0.659353 | + | 0.751834i | \(0.729169\pi\) | |||||||
\(140\) | −7.57961 | −0.640594 | ||||||||
\(141\) | −26.6201 | −2.24182 | ||||||||
\(142\) | −15.1780 | −1.27371 | ||||||||
\(143\) | −1.43618 | −0.120100 | ||||||||
\(144\) | 5.56701 | 0.463917 | ||||||||
\(145\) | −0.955763 | −0.0793718 | ||||||||
\(146\) | 2.71306 | 0.224534 | ||||||||
\(147\) | −6.90788 | −0.569752 | ||||||||
\(148\) | −8.31027 | −0.683100 | ||||||||
\(149\) | 8.77859 | 0.719170 | 0.359585 | − | 0.933112i | \(-0.382918\pi\) | ||||
0.359585 | + | 0.933112i | \(0.382918\pi\) | |||||||
\(150\) | −21.6062 | −1.76414 | ||||||||
\(151\) | 6.59271 | 0.536507 | 0.268254 | − | 0.963348i | \(-0.413553\pi\) | ||||
0.268254 | + | 0.963348i | \(0.413553\pi\) | |||||||
\(152\) | −6.03206 | −0.489265 | ||||||||
\(153\) | 16.3890 | 1.32497 | ||||||||
\(154\) | −3.04674 | −0.245513 | ||||||||
\(155\) | 17.8572 | 1.43433 | ||||||||
\(156\) | 2.97197 | 0.237948 | ||||||||
\(157\) | 17.0219 | 1.35850 | 0.679249 | − | 0.733908i | \(-0.262306\pi\) | ||||
0.679249 | + | 0.733908i | \(0.262306\pi\) | |||||||
\(158\) | 4.28520 | 0.340912 | ||||||||
\(159\) | 22.4150 | 1.77763 | ||||||||
\(160\) | −3.51878 | −0.278184 | ||||||||
\(161\) | 4.62100 | 0.364186 | ||||||||
\(162\) | −5.29054 | −0.415664 | ||||||||
\(163\) | −1.29657 | −0.101555 | −0.0507775 | − | 0.998710i | \(-0.516170\pi\) | ||||
−0.0507775 | + | 0.998710i | \(0.516170\pi\) | |||||||
\(164\) | 9.15654 | 0.715006 | ||||||||
\(165\) | −14.5676 | −1.13409 | ||||||||
\(166\) | 11.1344 | 0.864194 | ||||||||
\(167\) | −3.97341 | −0.307472 | −0.153736 | − | 0.988112i | \(-0.549130\pi\) | ||||
−0.153736 | + | 0.988112i | \(0.549130\pi\) | |||||||
\(168\) | 6.30477 | 0.486423 | ||||||||
\(169\) | −11.9690 | −0.920692 | ||||||||
\(170\) | −10.3591 | −0.794511 | ||||||||
\(171\) | 33.5805 | 2.56797 | ||||||||
\(172\) | 5.82028 | 0.443792 | ||||||||
\(173\) | 15.9429 | 1.21212 | 0.606060 | − | 0.795419i | \(-0.292749\pi\) | ||||
0.606060 | + | 0.795419i | \(0.292749\pi\) | |||||||
\(174\) | 0.795009 | 0.0602695 | ||||||||
\(175\) | −15.9008 | −1.20199 | ||||||||
\(176\) | −1.41443 | −0.106616 | ||||||||
\(177\) | 17.9073 | 1.34599 | ||||||||
\(178\) | 15.1343 | 1.13437 | ||||||||
\(179\) | 10.0601 | 0.751924 | 0.375962 | − | 0.926635i | \(-0.377312\pi\) | ||||
0.375962 | + | 0.926635i | \(0.377312\pi\) | |||||||
\(180\) | 19.5891 | 1.46008 | ||||||||
\(181\) | 5.63218 | 0.418636 | 0.209318 | − | 0.977848i | \(-0.432876\pi\) | ||||
0.209318 | + | 0.977848i | \(0.432876\pi\) | |||||||
\(182\) | 2.18718 | 0.162124 | ||||||||
\(183\) | −5.81860 | −0.430124 | ||||||||
\(184\) | 2.14527 | 0.158151 | ||||||||
\(185\) | −29.2420 | −2.14992 | ||||||||
\(186\) | −14.8537 | −1.08913 | ||||||||
\(187\) | −4.16401 | −0.304503 | ||||||||
\(188\) | −9.09485 | −0.663310 | ||||||||
\(189\) | −16.1844 | −1.17724 | ||||||||
\(190\) | −21.2255 | −1.53986 | ||||||||
\(191\) | −17.7971 | −1.28776 | −0.643878 | − | 0.765128i | \(-0.722676\pi\) | ||||
−0.643878 | + | 0.765128i | \(0.722676\pi\) | |||||||
\(192\) | 2.92694 | 0.211234 | ||||||||
\(193\) | 16.1480 | 1.16236 | 0.581179 | − | 0.813776i | \(-0.302591\pi\) | ||||
0.581179 | + | 0.813776i | \(0.302591\pi\) | |||||||
\(194\) | 15.5772 | 1.11838 | ||||||||
\(195\) | 10.4577 | 0.748893 | ||||||||
\(196\) | −2.36010 | −0.168578 | ||||||||
\(197\) | 5.37830 | 0.383188 | 0.191594 | − | 0.981474i | \(-0.438634\pi\) | ||||
0.191594 | + | 0.981474i | \(0.438634\pi\) | |||||||
\(198\) | 7.87412 | 0.559590 | ||||||||
\(199\) | −12.2368 | −0.867447 | −0.433724 | − | 0.901046i | \(-0.642801\pi\) | ||||
−0.433724 | + | 0.901046i | \(0.642801\pi\) | |||||||
\(200\) | −7.38184 | −0.521975 | ||||||||
\(201\) | 12.0654 | 0.851026 | ||||||||
\(202\) | 0.540634 | 0.0380389 | ||||||||
\(203\) | 0.585076 | 0.0410643 | ||||||||
\(204\) | 8.61680 | 0.603297 | ||||||||
\(205\) | 32.2199 | 2.25034 | ||||||||
\(206\) | −6.79230 | −0.473242 | ||||||||
\(207\) | −11.9427 | −0.830076 | ||||||||
\(208\) | 1.01538 | 0.0704041 | ||||||||
\(209\) | −8.53191 | −0.590165 | ||||||||
\(210\) | 22.1851 | 1.53092 | ||||||||
\(211\) | −9.56427 | −0.658431 | −0.329216 | − | 0.944255i | \(-0.606784\pi\) | ||||
−0.329216 | + | 0.944255i | \(0.606784\pi\) | |||||||
\(212\) | 7.65817 | 0.525965 | ||||||||
\(213\) | 44.4251 | 3.04396 | ||||||||
\(214\) | −13.4644 | −0.920407 | ||||||||
\(215\) | 20.4803 | 1.39674 | ||||||||
\(216\) | −7.51348 | −0.511228 | ||||||||
\(217\) | −10.9314 | −0.742072 | ||||||||
\(218\) | −6.72962 | −0.455787 | ||||||||
\(219\) | −7.94097 | −0.536601 | ||||||||
\(220\) | −4.97706 | −0.335554 | ||||||||
\(221\) | 2.98924 | 0.201078 | ||||||||
\(222\) | 24.3237 | 1.63250 | ||||||||
\(223\) | 20.9492 | 1.40286 | 0.701430 | − | 0.712739i | \(-0.252545\pi\) | ||||
0.701430 | + | 0.712739i | \(0.252545\pi\) | |||||||
\(224\) | 2.15404 | 0.143923 | ||||||||
\(225\) | 41.0947 | 2.73965 | ||||||||
\(226\) | 10.2145 | 0.679458 | ||||||||
\(227\) | 25.0539 | 1.66288 | 0.831442 | − | 0.555611i | \(-0.187516\pi\) | ||||
0.831442 | + | 0.555611i | \(0.187516\pi\) | |||||||
\(228\) | 17.6555 | 1.16926 | ||||||||
\(229\) | 11.8010 | 0.779829 | 0.389914 | − | 0.920851i | \(-0.372505\pi\) | ||||
0.389914 | + | 0.920851i | \(0.372505\pi\) | |||||||
\(230\) | 7.54873 | 0.497749 | ||||||||
\(231\) | 8.91763 | 0.586737 | ||||||||
\(232\) | 0.271618 | 0.0178326 | ||||||||
\(233\) | −16.7353 | −1.09636 | −0.548182 | − | 0.836359i | \(-0.684680\pi\) | ||||
−0.548182 | + | 0.836359i | \(0.684680\pi\) | |||||||
\(234\) | −5.65264 | −0.369525 | ||||||||
\(235\) | −32.0028 | −2.08763 | ||||||||
\(236\) | 6.11808 | 0.398253 | ||||||||
\(237\) | −12.5425 | −0.814725 | ||||||||
\(238\) | 6.34141 | 0.411053 | ||||||||
\(239\) | −18.5731 | −1.20140 | −0.600698 | − | 0.799476i | \(-0.705111\pi\) | ||||
−0.600698 | + | 0.799476i | \(0.705111\pi\) | |||||||
\(240\) | 10.2993 | 0.664816 | ||||||||
\(241\) | −5.35589 | −0.345003 | −0.172502 | − | 0.985009i | \(-0.555185\pi\) | ||||
−0.172502 | + | 0.985009i | \(0.555185\pi\) | |||||||
\(242\) | 8.99940 | 0.578503 | ||||||||
\(243\) | −7.05534 | −0.452600 | ||||||||
\(244\) | −1.98794 | −0.127265 | ||||||||
\(245\) | −8.30467 | −0.530566 | ||||||||
\(246\) | −26.8007 | −1.70875 | ||||||||
\(247\) | 6.12485 | 0.389715 | ||||||||
\(248\) | −5.07483 | −0.322252 | ||||||||
\(249\) | −32.5897 | −2.06529 | ||||||||
\(250\) | −8.38118 | −0.530072 | ||||||||
\(251\) | −16.9179 | −1.06785 | −0.533923 | − | 0.845533i | \(-0.679283\pi\) | ||||
−0.533923 | + | 0.845533i | \(0.679283\pi\) | |||||||
\(252\) | −11.9916 | −0.755398 | ||||||||
\(253\) | 3.03432 | 0.190766 | ||||||||
\(254\) | −8.20947 | −0.515108 | ||||||||
\(255\) | 30.3207 | 1.89875 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.30216 | −0.330740 | −0.165370 | − | 0.986232i | \(-0.552882\pi\) | ||||
−0.165370 | + | 0.986232i | \(0.552882\pi\) | |||||||
\(258\) | −17.0356 | −1.06059 | ||||||||
\(259\) | 17.9007 | 1.11229 | ||||||||
\(260\) | 3.57291 | 0.221583 | ||||||||
\(261\) | −1.51210 | −0.0935964 | ||||||||
\(262\) | 12.4641 | 0.770037 | ||||||||
\(263\) | 27.9487 | 1.72339 | 0.861697 | − | 0.507424i | \(-0.169402\pi\) | ||||
0.861697 | + | 0.507424i | \(0.169402\pi\) | |||||||
\(264\) | 4.13995 | 0.254796 | ||||||||
\(265\) | 26.9474 | 1.65537 | ||||||||
\(266\) | 12.9933 | 0.796672 | ||||||||
\(267\) | −44.2974 | −2.71096 | ||||||||
\(268\) | 4.12217 | 0.251802 | ||||||||
\(269\) | 6.57533 | 0.400905 | 0.200452 | − | 0.979703i | \(-0.435759\pi\) | ||||
0.200452 | + | 0.979703i | \(0.435759\pi\) | |||||||
\(270\) | −26.4383 | −1.60899 | ||||||||
\(271\) | 29.0271 | 1.76327 | 0.881634 | − | 0.471934i | \(-0.156444\pi\) | ||||
0.881634 | + | 0.471934i | \(0.156444\pi\) | |||||||
\(272\) | 2.94396 | 0.178504 | ||||||||
\(273\) | −6.40175 | −0.387452 | ||||||||
\(274\) | −0.690596 | −0.0417204 | ||||||||
\(275\) | −10.4411 | −0.629620 | ||||||||
\(276\) | −6.27908 | −0.377956 | ||||||||
\(277\) | 31.1579 | 1.87209 | 0.936047 | − | 0.351874i | \(-0.114456\pi\) | ||||
0.936047 | + | 0.351874i | \(0.114456\pi\) | |||||||
\(278\) | 15.5473 | 0.932465 | ||||||||
\(279\) | 28.2516 | 1.69138 | ||||||||
\(280\) | 7.57961 | 0.452968 | ||||||||
\(281\) | −10.7216 | −0.639599 | −0.319800 | − | 0.947485i | \(-0.603616\pi\) | ||||
−0.319800 | + | 0.947485i | \(0.603616\pi\) | |||||||
\(282\) | 26.6201 | 1.58521 | ||||||||
\(283\) | 27.0020 | 1.60510 | 0.802550 | − | 0.596584i | \(-0.203476\pi\) | ||||
0.802550 | + | 0.596584i | \(0.203476\pi\) | |||||||
\(284\) | 15.1780 | 0.900647 | ||||||||
\(285\) | 62.1259 | 3.68002 | ||||||||
\(286\) | 1.43618 | 0.0849234 | ||||||||
\(287\) | −19.7236 | −1.16425 | ||||||||
\(288\) | −5.56701 | −0.328039 | ||||||||
\(289\) | −8.33312 | −0.490183 | ||||||||
\(290\) | 0.955763 | 0.0561244 | ||||||||
\(291\) | −45.5937 | −2.67275 | ||||||||
\(292\) | −2.71306 | −0.158770 | ||||||||
\(293\) | 1.63516 | 0.0955270 | 0.0477635 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477635 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(294\) | 6.90788 | 0.402876 | ||||||||
\(295\) | 21.5282 | 1.25342 | ||||||||
\(296\) | 8.31027 | 0.483025 | ||||||||
\(297\) | −10.6273 | −0.616657 | ||||||||
\(298\) | −8.77859 | −0.508530 | ||||||||
\(299\) | −2.17827 | −0.125972 | ||||||||
\(300\) | 21.6062 | 1.24744 | ||||||||
\(301\) | −12.5371 | −0.722628 | ||||||||
\(302\) | −6.59271 | −0.379368 | ||||||||
\(303\) | −1.58241 | −0.0909068 | ||||||||
\(304\) | 6.03206 | 0.345962 | ||||||||
\(305\) | −6.99515 | −0.400541 | ||||||||
\(306\) | −16.3890 | −0.936898 | ||||||||
\(307\) | 14.1830 | 0.809464 | 0.404732 | − | 0.914435i | \(-0.367365\pi\) | ||||
0.404732 | + | 0.914435i | \(0.367365\pi\) | |||||||
\(308\) | 3.04674 | 0.173604 | ||||||||
\(309\) | 19.8807 | 1.13097 | ||||||||
\(310\) | −17.8572 | −1.01422 | ||||||||
\(311\) | 1.76971 | 0.100351 | 0.0501755 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501755 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(312\) | −2.97197 | −0.168255 | ||||||||
\(313\) | −5.95556 | −0.336628 | −0.168314 | − | 0.985733i | \(-0.553832\pi\) | ||||
−0.168314 | + | 0.985733i | \(0.553832\pi\) | |||||||
\(314\) | −17.0219 | −0.960603 | ||||||||
\(315\) | −42.1957 | −2.37746 | ||||||||
\(316\) | −4.28520 | −0.241061 | ||||||||
\(317\) | 1.51891 | 0.0853103 | 0.0426552 | − | 0.999090i | \(-0.486418\pi\) | ||||
0.0426552 | + | 0.999090i | \(0.486418\pi\) | |||||||
\(318\) | −22.4150 | −1.25697 | ||||||||
\(319\) | 0.384183 | 0.0215101 | ||||||||
\(320\) | 3.51878 | 0.196706 | ||||||||
\(321\) | 39.4095 | 2.19963 | ||||||||
\(322\) | −4.62100 | −0.257518 | ||||||||
\(323\) | 17.7581 | 0.988089 | ||||||||
\(324\) | 5.29054 | 0.293919 | ||||||||
\(325\) | 7.49539 | 0.415770 | ||||||||
\(326\) | 1.29657 | 0.0718102 | ||||||||
\(327\) | 19.6972 | 1.08926 | ||||||||
\(328\) | −9.15654 | −0.505586 | ||||||||
\(329\) | 19.5907 | 1.08007 | ||||||||
\(330\) | 14.5676 | 0.801919 | ||||||||
\(331\) | −26.2245 | −1.44143 | −0.720713 | − | 0.693233i | \(-0.756186\pi\) | ||||
−0.720713 | + | 0.693233i | \(0.756186\pi\) | |||||||
\(332\) | −11.1344 | −0.611077 | ||||||||
\(333\) | −46.2633 | −2.53521 | ||||||||
\(334\) | 3.97341 | 0.217415 | ||||||||
\(335\) | 14.5050 | 0.792495 | ||||||||
\(336\) | −6.30477 | −0.343953 | ||||||||
\(337\) | −16.2124 | −0.883146 | −0.441573 | − | 0.897225i | \(-0.645579\pi\) | ||||
−0.441573 | + | 0.897225i | \(0.645579\pi\) | |||||||
\(338\) | 11.9690 | 0.651028 | ||||||||
\(339\) | −29.8973 | −1.62380 | ||||||||
\(340\) | 10.3591 | 0.561804 | ||||||||
\(341\) | −7.17797 | −0.388709 | ||||||||
\(342\) | −33.5805 | −1.81583 | ||||||||
\(343\) | 20.1621 | 1.08865 | ||||||||
\(344\) | −5.82028 | −0.313808 | ||||||||
\(345\) | −22.0947 | −1.18954 | ||||||||
\(346\) | −15.9429 | −0.857098 | ||||||||
\(347\) | −12.6302 | −0.678024 | −0.339012 | − | 0.940782i | \(-0.610093\pi\) | ||||
−0.339012 | + | 0.940782i | \(0.610093\pi\) | |||||||
\(348\) | −0.795009 | −0.0426170 | ||||||||
\(349\) | −22.2269 | −1.18978 | −0.594888 | − | 0.803809i | \(-0.702804\pi\) | ||||
−0.594888 | + | 0.803809i | \(0.702804\pi\) | |||||||
\(350\) | 15.9008 | 0.849934 | ||||||||
\(351\) | 7.62906 | 0.407209 | ||||||||
\(352\) | 1.41443 | 0.0753892 | ||||||||
\(353\) | 7.44590 | 0.396305 | 0.198153 | − | 0.980171i | \(-0.436506\pi\) | ||||
0.198153 | + | 0.980171i | \(0.436506\pi\) | |||||||
\(354\) | −17.9073 | −0.951762 | ||||||||
\(355\) | 53.4080 | 2.83460 | ||||||||
\(356\) | −15.1343 | −0.802119 | ||||||||
\(357\) | −18.5610 | −0.982350 | ||||||||
\(358\) | −10.0601 | −0.531691 | ||||||||
\(359\) | 12.3914 | 0.653993 | 0.326996 | − | 0.945026i | \(-0.393964\pi\) | ||||
0.326996 | + | 0.945026i | \(0.393964\pi\) | |||||||
\(360\) | −19.5891 | −1.03244 | ||||||||
\(361\) | 17.3858 | 0.915040 | ||||||||
\(362\) | −5.63218 | −0.296021 | ||||||||
\(363\) | −26.3407 | −1.38253 | ||||||||
\(364\) | −2.18718 | −0.114639 | ||||||||
\(365\) | −9.54666 | −0.499695 | ||||||||
\(366\) | 5.81860 | 0.304143 | ||||||||
\(367\) | −13.6207 | −0.710994 | −0.355497 | − | 0.934677i | \(-0.615688\pi\) | ||||
−0.355497 | + | 0.934677i | \(0.615688\pi\) | |||||||
\(368\) | −2.14527 | −0.111830 | ||||||||
\(369\) | 50.9745 | 2.65363 | ||||||||
\(370\) | 29.2420 | 1.52022 | ||||||||
\(371\) | −16.4960 | −0.856431 | ||||||||
\(372\) | 14.8537 | 0.770131 | ||||||||
\(373\) | 9.21697 | 0.477236 | 0.238618 | − | 0.971113i | \(-0.423306\pi\) | ||||
0.238618 | + | 0.971113i | \(0.423306\pi\) | |||||||
\(374\) | 4.16401 | 0.215316 | ||||||||
\(375\) | 24.5312 | 1.26679 | ||||||||
\(376\) | 9.09485 | 0.469031 | ||||||||
\(377\) | −0.275796 | −0.0142042 | ||||||||
\(378\) | 16.1844 | 0.832434 | ||||||||
\(379\) | −5.15285 | −0.264684 | −0.132342 | − | 0.991204i | \(-0.542250\pi\) | ||||
−0.132342 | + | 0.991204i | \(0.542250\pi\) | |||||||
\(380\) | 21.2255 | 1.08885 | ||||||||
\(381\) | 24.0287 | 1.23103 | ||||||||
\(382\) | 17.7971 | 0.910581 | ||||||||
\(383\) | 25.9053 | 1.32370 | 0.661850 | − | 0.749636i | \(-0.269772\pi\) | ||||
0.661850 | + | 0.749636i | \(0.269772\pi\) | |||||||
\(384\) | −2.92694 | −0.149365 | ||||||||
\(385\) | 10.7208 | 0.546383 | ||||||||
\(386\) | −16.1480 | −0.821912 | ||||||||
\(387\) | 32.4015 | 1.64706 | ||||||||
\(388\) | −15.5772 | −0.790813 | ||||||||
\(389\) | −14.2715 | −0.723595 | −0.361798 | − | 0.932257i | \(-0.617837\pi\) | ||||
−0.361798 | + | 0.932257i | \(0.617837\pi\) | |||||||
\(390\) | −10.4577 | −0.529547 | ||||||||
\(391\) | −6.31558 | −0.319392 | ||||||||
\(392\) | 2.36010 | 0.119203 | ||||||||
\(393\) | −36.4818 | −1.84027 | ||||||||
\(394\) | −5.37830 | −0.270955 | ||||||||
\(395\) | −15.0787 | −0.758691 | ||||||||
\(396\) | −7.87412 | −0.395690 | ||||||||
\(397\) | −28.3844 | −1.42457 | −0.712286 | − | 0.701890i | \(-0.752340\pi\) | ||||
−0.712286 | + | 0.701890i | \(0.752340\pi\) | |||||||
\(398\) | 12.2368 | 0.613378 | ||||||||
\(399\) | −38.0307 | −1.90392 | ||||||||
\(400\) | 7.38184 | 0.369092 | ||||||||
\(401\) | −38.1003 | −1.90264 | −0.951320 | − | 0.308206i | \(-0.900271\pi\) | ||||
−0.951320 | + | 0.308206i | \(0.900271\pi\) | |||||||
\(402\) | −12.0654 | −0.601766 | ||||||||
\(403\) | 5.15289 | 0.256684 | ||||||||
\(404\) | −0.540634 | −0.0268975 | ||||||||
\(405\) | 18.6163 | 0.925049 | ||||||||
\(406\) | −0.585076 | −0.0290368 | ||||||||
\(407\) | 11.7543 | 0.582638 | ||||||||
\(408\) | −8.61680 | −0.426595 | ||||||||
\(409\) | 20.3927 | 1.00836 | 0.504178 | − | 0.863600i | \(-0.331796\pi\) | ||||
0.504178 | + | 0.863600i | \(0.331796\pi\) | |||||||
\(410\) | −32.2199 | −1.59123 | ||||||||
\(411\) | 2.02134 | 0.0997052 | ||||||||
\(412\) | 6.79230 | 0.334632 | ||||||||
\(413\) | −13.1786 | −0.648477 | ||||||||
\(414\) | 11.9427 | 0.586953 | ||||||||
\(415\) | −39.1794 | −1.92324 | ||||||||
\(416\) | −1.01538 | −0.0497832 | ||||||||
\(417\) | −45.5061 | −2.22844 | ||||||||
\(418\) | 8.53191 | 0.417309 | ||||||||
\(419\) | 40.3433 | 1.97090 | 0.985450 | − | 0.169968i | \(-0.0543664\pi\) | ||||
0.985450 | + | 0.169968i | \(0.0543664\pi\) | |||||||
\(420\) | −22.1851 | −1.08252 | ||||||||
\(421\) | 14.5045 | 0.706906 | 0.353453 | − | 0.935452i | \(-0.385007\pi\) | ||||
0.353453 | + | 0.935452i | \(0.385007\pi\) | |||||||
\(422\) | 9.56427 | 0.465581 | ||||||||
\(423\) | −50.6311 | −2.46177 | ||||||||
\(424\) | −7.65817 | −0.371914 | ||||||||
\(425\) | 21.7318 | 1.05415 | ||||||||
\(426\) | −44.4251 | −2.15240 | ||||||||
\(427\) | 4.28212 | 0.207226 | ||||||||
\(428\) | 13.4644 | 0.650826 | ||||||||
\(429\) | −4.20363 | −0.202953 | ||||||||
\(430\) | −20.4803 | −0.987647 | ||||||||
\(431\) | −25.4001 | −1.22348 | −0.611739 | − | 0.791060i | \(-0.709530\pi\) | ||||
−0.611739 | + | 0.791060i | \(0.709530\pi\) | |||||||
\(432\) | 7.51348 | 0.361493 | ||||||||
\(433\) | −25.0402 | −1.20336 | −0.601678 | − | 0.798738i | \(-0.705501\pi\) | ||||
−0.601678 | + | 0.798738i | \(0.705501\pi\) | |||||||
\(434\) | 10.9314 | 0.524724 | ||||||||
\(435\) | −2.79747 | −0.134128 | ||||||||
\(436\) | 6.72962 | 0.322290 | ||||||||
\(437\) | −12.9404 | −0.619023 | ||||||||
\(438\) | 7.94097 | 0.379434 | ||||||||
\(439\) | −13.4799 | −0.643361 | −0.321681 | − | 0.946848i | \(-0.604248\pi\) | ||||
−0.321681 | + | 0.946848i | \(0.604248\pi\) | |||||||
\(440\) | 4.97706 | 0.237272 | ||||||||
\(441\) | −13.1387 | −0.625651 | ||||||||
\(442\) | −2.98924 | −0.142184 | ||||||||
\(443\) | 11.5523 | 0.548867 | 0.274433 | − | 0.961606i | \(-0.411510\pi\) | ||||
0.274433 | + | 0.961606i | \(0.411510\pi\) | |||||||
\(444\) | −24.3237 | −1.15435 | ||||||||
\(445\) | −53.2545 | −2.52450 | ||||||||
\(446\) | −20.9492 | −0.991971 | ||||||||
\(447\) | 25.6944 | 1.21531 | ||||||||
\(448\) | −2.15404 | −0.101769 | ||||||||
\(449\) | −5.54771 | −0.261813 | −0.130906 | − | 0.991395i | \(-0.541789\pi\) | ||||
−0.130906 | + | 0.991395i | \(0.541789\pi\) | |||||||
\(450\) | −41.0947 | −1.93722 | ||||||||
\(451\) | −12.9513 | −0.609851 | ||||||||
\(452\) | −10.2145 | −0.480450 | ||||||||
\(453\) | 19.2965 | 0.906629 | ||||||||
\(454\) | −25.0539 | −1.17584 | ||||||||
\(455\) | −7.69621 | −0.360804 | ||||||||
\(456\) | −17.6555 | −0.826795 | ||||||||
\(457\) | −11.9046 | −0.556876 | −0.278438 | − | 0.960454i | \(-0.589817\pi\) | ||||
−0.278438 | + | 0.960454i | \(0.589817\pi\) | |||||||
\(458\) | −11.8010 | −0.551422 | ||||||||
\(459\) | 22.1194 | 1.03244 | ||||||||
\(460\) | −7.54873 | −0.351961 | ||||||||
\(461\) | −33.4774 | −1.55920 | −0.779599 | − | 0.626279i | \(-0.784577\pi\) | ||||
−0.779599 | + | 0.626279i | \(0.784577\pi\) | |||||||
\(462\) | −8.91763 | −0.414886 | ||||||||
\(463\) | −4.15271 | −0.192993 | −0.0964964 | − | 0.995333i | \(-0.530764\pi\) | ||||
−0.0964964 | + | 0.995333i | \(0.530764\pi\) | |||||||
\(464\) | −0.271618 | −0.0126095 | ||||||||
\(465\) | 52.2671 | 2.42383 | ||||||||
\(466\) | 16.7353 | 0.775246 | ||||||||
\(467\) | 24.1830 | 1.11906 | 0.559528 | − | 0.828811i | \(-0.310982\pi\) | ||||
0.559528 | + | 0.828811i | \(0.310982\pi\) | |||||||
\(468\) | 5.65264 | 0.261293 | ||||||||
\(469\) | −8.87934 | −0.410010 | ||||||||
\(470\) | 32.0028 | 1.47618 | ||||||||
\(471\) | 49.8222 | 2.29569 | ||||||||
\(472\) | −6.11808 | −0.281608 | ||||||||
\(473\) | −8.23236 | −0.378524 | ||||||||
\(474\) | 12.5425 | 0.576098 | ||||||||
\(475\) | 44.5277 | 2.04307 | ||||||||
\(476\) | −6.34141 | −0.290658 | ||||||||
\(477\) | 42.6331 | 1.95203 | ||||||||
\(478\) | 18.5731 | 0.849516 | ||||||||
\(479\) | 27.9934 | 1.27905 | 0.639526 | − | 0.768769i | \(-0.279131\pi\) | ||||
0.639526 | + | 0.768769i | \(0.279131\pi\) | |||||||
\(480\) | −10.2993 | −0.470096 | ||||||||
\(481\) | −8.43810 | −0.384744 | ||||||||
\(482\) | 5.35589 | 0.243954 | ||||||||
\(483\) | 13.5254 | 0.615427 | ||||||||
\(484\) | −8.99940 | −0.409063 | ||||||||
\(485\) | −54.8129 | −2.48892 | ||||||||
\(486\) | 7.05534 | 0.320037 | ||||||||
\(487\) | 6.83469 | 0.309709 | 0.154855 | − | 0.987937i | \(-0.450509\pi\) | ||||
0.154855 | + | 0.987937i | \(0.450509\pi\) | |||||||
\(488\) | 1.98794 | 0.0899900 | ||||||||
\(489\) | −3.79498 | −0.171615 | ||||||||
\(490\) | 8.30467 | 0.375167 | ||||||||
\(491\) | −3.00393 | −0.135565 | −0.0677826 | − | 0.997700i | \(-0.521592\pi\) | ||||
−0.0677826 | + | 0.997700i | \(0.521592\pi\) | |||||||
\(492\) | 26.8007 | 1.20827 | ||||||||
\(493\) | −0.799630 | −0.0360135 | ||||||||
\(494\) | −6.12485 | −0.275570 | ||||||||
\(495\) | −27.7073 | −1.24535 | ||||||||
\(496\) | 5.07483 | 0.227867 | ||||||||
\(497\) | −32.6940 | −1.46653 | ||||||||
\(498\) | 32.5897 | 1.46038 | ||||||||
\(499\) | −11.0943 | −0.496649 | −0.248325 | − | 0.968677i | \(-0.579880\pi\) | ||||
−0.248325 | + | 0.968677i | \(0.579880\pi\) | |||||||
\(500\) | 8.38118 | 0.374818 | ||||||||
\(501\) | −11.6300 | −0.519588 | ||||||||
\(502\) | 16.9179 | 0.755081 | ||||||||
\(503\) | −30.2152 | −1.34723 | −0.673615 | − | 0.739082i | \(-0.735260\pi\) | ||||
−0.673615 | + | 0.739082i | \(0.735260\pi\) | |||||||
\(504\) | 11.9916 | 0.534147 | ||||||||
\(505\) | −1.90237 | −0.0846545 | ||||||||
\(506\) | −3.03432 | −0.134892 | ||||||||
\(507\) | −35.0326 | −1.55585 | ||||||||
\(508\) | 8.20947 | 0.364236 | ||||||||
\(509\) | 14.0591 | 0.623158 | 0.311579 | − | 0.950220i | \(-0.399142\pi\) | ||||
0.311579 | + | 0.950220i | \(0.399142\pi\) | |||||||
\(510\) | −30.3207 | −1.34262 | ||||||||
\(511\) | 5.84404 | 0.258525 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 45.3218 | 2.00101 | ||||||||
\(514\) | 5.30216 | 0.233868 | ||||||||
\(515\) | 23.9006 | 1.05319 | ||||||||
\(516\) | 17.0356 | 0.749952 | ||||||||
\(517\) | 12.8640 | 0.565758 | ||||||||
\(518\) | −17.9007 | −0.786511 | ||||||||
\(519\) | 46.6641 | 2.04833 | ||||||||
\(520\) | −3.57291 | −0.156683 | ||||||||
\(521\) | 11.2641 | 0.493489 | 0.246745 | − | 0.969081i | \(-0.420639\pi\) | ||||
0.246745 | + | 0.969081i | \(0.420639\pi\) | |||||||
\(522\) | 1.51210 | 0.0661827 | ||||||||
\(523\) | −0.483039 | −0.0211218 | −0.0105609 | − | 0.999944i | \(-0.503362\pi\) | ||||
−0.0105609 | + | 0.999944i | \(0.503362\pi\) | |||||||
\(524\) | −12.4641 | −0.544498 | ||||||||
\(525\) | −46.5408 | −2.03121 | ||||||||
\(526\) | −27.9487 | −1.21862 | ||||||||
\(527\) | 14.9401 | 0.650800 | ||||||||
\(528\) | −4.13995 | −0.180168 | ||||||||
\(529\) | −18.3978 | −0.799906 | ||||||||
\(530\) | −26.9474 | −1.17052 | ||||||||
\(531\) | 34.0594 | 1.47805 | ||||||||
\(532\) | −12.9933 | −0.563332 | ||||||||
\(533\) | 9.29739 | 0.402715 | ||||||||
\(534\) | 44.2974 | 1.91694 | ||||||||
\(535\) | 47.3783 | 2.04834 | ||||||||
\(536\) | −4.12217 | −0.178051 | ||||||||
\(537\) | 29.4452 | 1.27066 | ||||||||
\(538\) | −6.57533 | −0.283482 | ||||||||
\(539\) | 3.33819 | 0.143786 | ||||||||
\(540\) | 26.4383 | 1.13772 | ||||||||
\(541\) | 25.4837 | 1.09563 | 0.547814 | − | 0.836600i | \(-0.315460\pi\) | ||||
0.547814 | + | 0.836600i | \(0.315460\pi\) | |||||||
\(542\) | −29.0271 | −1.24682 | ||||||||
\(543\) | 16.4851 | 0.707442 | ||||||||
\(544\) | −2.94396 | −0.126221 | ||||||||
\(545\) | 23.6801 | 1.01434 | ||||||||
\(546\) | 6.40175 | 0.273970 | ||||||||
\(547\) | 8.31873 | 0.355683 | 0.177842 | − | 0.984059i | \(-0.443089\pi\) | ||||
0.177842 | + | 0.984059i | \(0.443089\pi\) | |||||||
\(548\) | 0.690596 | 0.0295008 | ||||||||
\(549\) | −11.0669 | −0.472324 | ||||||||
\(550\) | 10.4411 | 0.445209 | ||||||||
\(551\) | −1.63841 | −0.0697988 | ||||||||
\(552\) | 6.27908 | 0.267255 | ||||||||
\(553\) | 9.23050 | 0.392521 | ||||||||
\(554\) | −31.1579 | −1.32377 | ||||||||
\(555\) | −85.5898 | −3.63309 | ||||||||
\(556\) | −15.5473 | −0.659353 | ||||||||
\(557\) | −16.7477 | −0.709622 | −0.354811 | − | 0.934938i | \(-0.615455\pi\) | ||||
−0.354811 | + | 0.934938i | \(0.615455\pi\) | |||||||
\(558\) | −28.2516 | −1.19599 | ||||||||
\(559\) | 5.90981 | 0.249958 | ||||||||
\(560\) | −7.57961 | −0.320297 | ||||||||
\(561\) | −12.1878 | −0.514571 | ||||||||
\(562\) | 10.7216 | 0.452265 | ||||||||
\(563\) | −32.9048 | −1.38677 | −0.693386 | − | 0.720566i | \(-0.743882\pi\) | ||||
−0.693386 | + | 0.720566i | \(0.743882\pi\) | |||||||
\(564\) | −26.6201 | −1.12091 | ||||||||
\(565\) | −35.9426 | −1.51212 | ||||||||
\(566\) | −27.0020 | −1.13498 | ||||||||
\(567\) | −11.3960 | −0.478589 | ||||||||
\(568\) | −15.1780 | −0.636853 | ||||||||
\(569\) | −26.5208 | −1.11181 | −0.555905 | − | 0.831246i | \(-0.687628\pi\) | ||||
−0.555905 | + | 0.831246i | \(0.687628\pi\) | |||||||
\(570\) | −62.1259 | −2.60217 | ||||||||
\(571\) | −1.48419 | −0.0621114 | −0.0310557 | − | 0.999518i | \(-0.509887\pi\) | ||||
−0.0310557 | + | 0.999518i | \(0.509887\pi\) | |||||||
\(572\) | −1.43618 | −0.0600499 | ||||||||
\(573\) | −52.0913 | −2.17614 | ||||||||
\(574\) | 19.7236 | 0.823247 | ||||||||
\(575\) | −15.8360 | −0.660408 | ||||||||
\(576\) | 5.56701 | 0.231959 | ||||||||
\(577\) | 15.9449 | 0.663794 | 0.331897 | − | 0.943316i | \(-0.392311\pi\) | ||||
0.331897 | + | 0.943316i | \(0.392311\pi\) | |||||||
\(578\) | 8.33312 | 0.346612 | ||||||||
\(579\) | 47.2643 | 1.96424 | ||||||||
\(580\) | −0.955763 | −0.0396859 | ||||||||
\(581\) | 23.9839 | 0.995020 | ||||||||
\(582\) | 45.5937 | 1.88992 | ||||||||
\(583\) | −10.8319 | −0.448612 | ||||||||
\(584\) | 2.71306 | 0.112267 | ||||||||
\(585\) | 19.8904 | 0.822368 | ||||||||
\(586\) | −1.63516 | −0.0675478 | ||||||||
\(587\) | −15.7778 | −0.651219 | −0.325609 | − | 0.945504i | \(-0.605569\pi\) | ||||
−0.325609 | + | 0.945504i | \(0.605569\pi\) | |||||||
\(588\) | −6.90788 | −0.284876 | ||||||||
\(589\) | 30.6117 | 1.26133 | ||||||||
\(590\) | −21.5282 | −0.886302 | ||||||||
\(591\) | 15.7420 | 0.647539 | ||||||||
\(592\) | −8.31027 | −0.341550 | ||||||||
\(593\) | −6.60690 | −0.271313 | −0.135656 | − | 0.990756i | \(-0.543314\pi\) | ||||
−0.135656 | + | 0.990756i | \(0.543314\pi\) | |||||||
\(594\) | 10.6273 | 0.436042 | ||||||||
\(595\) | −22.3141 | −0.914787 | ||||||||
\(596\) | 8.77859 | 0.359585 | ||||||||
\(597\) | −35.8166 | −1.46587 | ||||||||
\(598\) | 2.17827 | 0.0890760 | ||||||||
\(599\) | 2.89962 | 0.118475 | 0.0592376 | − | 0.998244i | \(-0.481133\pi\) | ||||
0.0592376 | + | 0.998244i | \(0.481133\pi\) | |||||||
\(600\) | −21.6062 | −0.882071 | ||||||||
\(601\) | −8.56656 | −0.349437 | −0.174719 | − | 0.984618i | \(-0.555902\pi\) | ||||
−0.174719 | + | 0.984618i | \(0.555902\pi\) | |||||||
\(602\) | 12.5371 | 0.510975 | ||||||||
\(603\) | 22.9482 | 0.934521 | ||||||||
\(604\) | 6.59271 | 0.268254 | ||||||||
\(605\) | −31.6669 | −1.28744 | ||||||||
\(606\) | 1.58241 | 0.0642808 | ||||||||
\(607\) | −11.4992 | −0.466737 | −0.233368 | − | 0.972388i | \(-0.574975\pi\) | ||||
−0.233368 | + | 0.972388i | \(0.574975\pi\) | |||||||
\(608\) | −6.03206 | −0.244632 | ||||||||
\(609\) | 1.71248 | 0.0693934 | ||||||||
\(610\) | 6.99515 | 0.283225 | ||||||||
\(611\) | −9.23475 | −0.373598 | ||||||||
\(612\) | 16.3890 | 0.662487 | ||||||||
\(613\) | −36.6162 | −1.47892 | −0.739458 | − | 0.673203i | \(-0.764918\pi\) | ||||
−0.739458 | + | 0.673203i | \(0.764918\pi\) | |||||||
\(614\) | −14.1830 | −0.572378 | ||||||||
\(615\) | 94.3059 | 3.80278 | ||||||||
\(616\) | −3.04674 | −0.122757 | ||||||||
\(617\) | −4.97994 | −0.200485 | −0.100242 | − | 0.994963i | \(-0.531962\pi\) | ||||
−0.100242 | + | 0.994963i | \(0.531962\pi\) | |||||||
\(618\) | −19.8807 | −0.799718 | ||||||||
\(619\) | −16.3902 | −0.658780 | −0.329390 | − | 0.944194i | \(-0.606843\pi\) | ||||
−0.329390 | + | 0.944194i | \(0.606843\pi\) | |||||||
\(620\) | 17.8572 | 0.717163 | ||||||||
\(621\) | −16.1184 | −0.646811 | ||||||||
\(622\) | −1.76971 | −0.0709589 | ||||||||
\(623\) | 32.6000 | 1.30609 | ||||||||
\(624\) | 2.97197 | 0.118974 | ||||||||
\(625\) | −7.41764 | −0.296706 | ||||||||
\(626\) | 5.95556 | 0.238032 | ||||||||
\(627\) | −24.9724 | −0.997303 | ||||||||
\(628\) | 17.0219 | 0.679249 | ||||||||
\(629\) | −24.4651 | −0.975487 | ||||||||
\(630\) | 42.1957 | 1.68112 | ||||||||
\(631\) | −28.5874 | −1.13805 | −0.569023 | − | 0.822321i | \(-0.692679\pi\) | ||||
−0.569023 | + | 0.822321i | \(0.692679\pi\) | |||||||
\(632\) | 4.28520 | 0.170456 | ||||||||
\(633\) | −27.9941 | −1.11266 | ||||||||
\(634\) | −1.51891 | −0.0603235 | ||||||||
\(635\) | 28.8874 | 1.14636 | ||||||||
\(636\) | 22.4150 | 0.888814 | ||||||||
\(637\) | −2.39640 | −0.0949489 | ||||||||
\(638\) | −0.384183 | −0.0152100 | ||||||||
\(639\) | 84.4958 | 3.34260 | ||||||||
\(640\) | −3.51878 | −0.139092 | ||||||||
\(641\) | −37.5347 | −1.48253 | −0.741265 | − | 0.671212i | \(-0.765774\pi\) | ||||
−0.741265 | + | 0.671212i | \(0.765774\pi\) | |||||||
\(642\) | −39.4095 | −1.55537 | ||||||||
\(643\) | −6.96859 | −0.274814 | −0.137407 | − | 0.990515i | \(-0.543877\pi\) | ||||
−0.137407 | + | 0.990515i | \(0.543877\pi\) | |||||||
\(644\) | 4.62100 | 0.182093 | ||||||||
\(645\) | 59.9447 | 2.36032 | ||||||||
\(646\) | −17.7581 | −0.698684 | ||||||||
\(647\) | 31.5656 | 1.24097 | 0.620485 | − | 0.784218i | \(-0.286936\pi\) | ||||
0.620485 | + | 0.784218i | \(0.286936\pi\) | |||||||
\(648\) | −5.29054 | −0.207832 | ||||||||
\(649\) | −8.65358 | −0.339683 | ||||||||
\(650\) | −7.49539 | −0.293993 | ||||||||
\(651\) | −31.9956 | −1.25401 | ||||||||
\(652\) | −1.29657 | −0.0507775 | ||||||||
\(653\) | −35.5943 | −1.39291 | −0.696457 | − | 0.717599i | \(-0.745241\pi\) | ||||
−0.696457 | + | 0.717599i | \(0.745241\pi\) | |||||||
\(654\) | −19.6972 | −0.770222 | ||||||||
\(655\) | −43.8586 | −1.71370 | ||||||||
\(656\) | 9.15654 | 0.357503 | ||||||||
\(657\) | −15.1036 | −0.589248 | ||||||||
\(658\) | −19.5907 | −0.763725 | ||||||||
\(659\) | 16.9929 | 0.661950 | 0.330975 | − | 0.943640i | \(-0.392622\pi\) | ||||
0.330975 | + | 0.943640i | \(0.392622\pi\) | |||||||
\(660\) | −14.5676 | −0.567043 | ||||||||
\(661\) | −24.8625 | −0.967039 | −0.483520 | − | 0.875333i | \(-0.660642\pi\) | ||||
−0.483520 | + | 0.875333i | \(0.660642\pi\) | |||||||
\(662\) | 26.2245 | 1.01924 | ||||||||
\(663\) | 8.74935 | 0.339797 | ||||||||
\(664\) | 11.1344 | 0.432097 | ||||||||
\(665\) | −45.7207 | −1.77297 | ||||||||
\(666\) | 46.2633 | 1.79267 | ||||||||
\(667\) | 0.582692 | 0.0225619 | ||||||||
\(668\) | −3.97341 | −0.153736 | ||||||||
\(669\) | 61.3170 | 2.37065 | ||||||||
\(670\) | −14.5050 | −0.560378 | ||||||||
\(671\) | 2.81180 | 0.108548 | ||||||||
\(672\) | 6.30477 | 0.243212 | ||||||||
\(673\) | 6.76622 | 0.260819 | 0.130409 | − | 0.991460i | \(-0.458371\pi\) | ||||
0.130409 | + | 0.991460i | \(0.458371\pi\) | |||||||
\(674\) | 16.2124 | 0.624479 | ||||||||
\(675\) | 55.4633 | 2.13478 | ||||||||
\(676\) | −11.9690 | −0.460346 | ||||||||
\(677\) | 30.6185 | 1.17677 | 0.588383 | − | 0.808583i | \(-0.299765\pi\) | ||||
0.588383 | + | 0.808583i | \(0.299765\pi\) | |||||||
\(678\) | 29.8973 | 1.14820 | ||||||||
\(679\) | 33.5540 | 1.28768 | ||||||||
\(680\) | −10.3591 | −0.397255 | ||||||||
\(681\) | 73.3313 | 2.81006 | ||||||||
\(682\) | 7.17797 | 0.274859 | ||||||||
\(683\) | −11.4771 | −0.439158 | −0.219579 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219579 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(684\) | 33.5805 | 1.28398 | ||||||||
\(685\) | 2.43006 | 0.0928477 | ||||||||
\(686\) | −20.1621 | −0.769791 | ||||||||
\(687\) | 34.5407 | 1.31781 | ||||||||
\(688\) | 5.82028 | 0.221896 | ||||||||
\(689\) | 7.77597 | 0.296241 | ||||||||
\(690\) | 22.0947 | 0.841132 | ||||||||
\(691\) | −44.1455 | −1.67937 | −0.839687 | − | 0.543070i | \(-0.817262\pi\) | ||||
−0.839687 | + | 0.543070i | \(0.817262\pi\) | |||||||
\(692\) | 15.9429 | 0.606060 | ||||||||
\(693\) | 16.9612 | 0.644303 | ||||||||
\(694\) | 12.6302 | 0.479435 | ||||||||
\(695\) | −54.7076 | −2.07518 | ||||||||
\(696\) | 0.795009 | 0.0301348 | ||||||||
\(697\) | 26.9565 | 1.02105 | ||||||||
\(698\) | 22.2269 | 0.841299 | ||||||||
\(699\) | −48.9832 | −1.85271 | ||||||||
\(700\) | −15.9008 | −0.600994 | ||||||||
\(701\) | −39.5282 | −1.49296 | −0.746480 | − | 0.665408i | \(-0.768258\pi\) | ||||
−0.746480 | + | 0.665408i | \(0.768258\pi\) | |||||||
\(702\) | −7.62906 | −0.287940 | ||||||||
\(703\) | −50.1281 | −1.89062 | ||||||||
\(704\) | −1.41443 | −0.0533082 | ||||||||
\(705\) | −93.6704 | −3.52783 | ||||||||
\(706\) | −7.44590 | −0.280230 | ||||||||
\(707\) | 1.16455 | 0.0437974 | ||||||||
\(708\) | 17.9073 | 0.672997 | ||||||||
\(709\) | 5.77479 | 0.216877 | 0.108438 | − | 0.994103i | \(-0.465415\pi\) | ||||
0.108438 | + | 0.994103i | \(0.465415\pi\) | |||||||
\(710\) | −53.4080 | −2.00437 | ||||||||
\(711\) | −23.8557 | −0.894659 | ||||||||
\(712\) | 15.1343 | 0.567184 | ||||||||
\(713\) | −10.8869 | −0.407716 | ||||||||
\(714\) | 18.5610 | 0.694627 | ||||||||
\(715\) | −5.05362 | −0.188995 | ||||||||
\(716\) | 10.0601 | 0.375962 | ||||||||
\(717\) | −54.3626 | −2.03021 | ||||||||
\(718\) | −12.3914 | −0.462443 | ||||||||
\(719\) | −43.1721 | −1.61005 | −0.805025 | − | 0.593241i | \(-0.797848\pi\) | ||||
−0.805025 | + | 0.593241i | \(0.797848\pi\) | |||||||
\(720\) | 19.5891 | 0.730042 | ||||||||
\(721\) | −14.6309 | −0.544883 | ||||||||
\(722\) | −17.3858 | −0.647031 | ||||||||
\(723\) | −15.6764 | −0.583012 | ||||||||
\(724\) | 5.63218 | 0.209318 | ||||||||
\(725\) | −2.00504 | −0.0744652 | ||||||||
\(726\) | 26.3407 | 0.977596 | ||||||||
\(727\) | −5.30795 | −0.196861 | −0.0984304 | − | 0.995144i | \(-0.531382\pi\) | ||||
−0.0984304 | + | 0.995144i | \(0.531382\pi\) | |||||||
\(728\) | 2.18718 | 0.0810622 | ||||||||
\(729\) | −36.5222 | −1.35267 | ||||||||
\(730\) | 9.54666 | 0.353338 | ||||||||
\(731\) | 17.1346 | 0.633748 | ||||||||
\(732\) | −5.81860 | −0.215062 | ||||||||
\(733\) | 14.1569 | 0.522896 | 0.261448 | − | 0.965218i | \(-0.415800\pi\) | ||||
0.261448 | + | 0.965218i | \(0.415800\pi\) | |||||||
\(734\) | 13.6207 | 0.502749 | ||||||||
\(735\) | −24.3073 | −0.896589 | ||||||||
\(736\) | 2.14527 | 0.0790756 | ||||||||
\(737\) | −5.83051 | −0.214770 | ||||||||
\(738\) | −50.9745 | −1.87640 | ||||||||
\(739\) | 40.8528 | 1.50279 | 0.751397 | − | 0.659850i | \(-0.229380\pi\) | ||||
0.751397 | + | 0.659850i | \(0.229380\pi\) | |||||||
\(740\) | −29.2420 | −1.07496 | ||||||||
\(741\) | 17.9271 | 0.658568 | ||||||||
\(742\) | 16.4960 | 0.605588 | ||||||||
\(743\) | 30.1773 | 1.10710 | 0.553549 | − | 0.832817i | \(-0.313273\pi\) | ||||
0.553549 | + | 0.832817i | \(0.313273\pi\) | |||||||
\(744\) | −14.8537 | −0.544565 | ||||||||
\(745\) | 30.8900 | 1.13172 | ||||||||
\(746\) | −9.21697 | −0.337457 | ||||||||
\(747\) | −61.9850 | −2.26791 | ||||||||
\(748\) | −4.16401 | −0.152251 | ||||||||
\(749\) | −29.0029 | −1.05974 | ||||||||
\(750\) | −24.5312 | −0.895755 | ||||||||
\(751\) | −16.3337 | −0.596025 | −0.298012 | − | 0.954562i | \(-0.596324\pi\) | ||||
−0.298012 | + | 0.954562i | \(0.596324\pi\) | |||||||
\(752\) | −9.09485 | −0.331655 | ||||||||
\(753\) | −49.5177 | −1.80452 | ||||||||
\(754\) | 0.275796 | 0.0100439 | ||||||||
\(755\) | 23.1983 | 0.844273 | ||||||||
\(756\) | −16.1844 | −0.588620 | ||||||||
\(757\) | −10.7404 | −0.390367 | −0.195184 | − | 0.980767i | \(-0.562530\pi\) | ||||
−0.195184 | + | 0.980767i | \(0.562530\pi\) | |||||||
\(758\) | 5.15285 | 0.187160 | ||||||||
\(759\) | 8.88130 | 0.322371 | ||||||||
\(760\) | −21.2255 | −0.769930 | ||||||||
\(761\) | −47.6840 | −1.72854 | −0.864272 | − | 0.503025i | \(-0.832220\pi\) | ||||
−0.864272 | + | 0.503025i | \(0.832220\pi\) | |||||||
\(762\) | −24.0287 | −0.870467 | ||||||||
\(763\) | −14.4959 | −0.524786 | ||||||||
\(764\) | −17.7971 | −0.643878 | ||||||||
\(765\) | 57.6694 | 2.08504 | ||||||||
\(766\) | −25.9053 | −0.935997 | ||||||||
\(767\) | 6.21219 | 0.224309 | ||||||||
\(768\) | 2.92694 | 0.105617 | ||||||||
\(769\) | 5.92408 | 0.213628 | 0.106814 | − | 0.994279i | \(-0.465935\pi\) | ||||
0.106814 | + | 0.994279i | \(0.465935\pi\) | |||||||
\(770\) | −10.7208 | −0.386351 | ||||||||
\(771\) | −15.5191 | −0.558908 | ||||||||
\(772\) | 16.1480 | 0.581179 | ||||||||
\(773\) | 17.2054 | 0.618837 | 0.309418 | − | 0.950926i | \(-0.399866\pi\) | ||||
0.309418 | + | 0.950926i | \(0.399866\pi\) | |||||||
\(774\) | −32.4015 | −1.16465 | ||||||||
\(775\) | 37.4616 | 1.34566 | ||||||||
\(776\) | 15.5772 | 0.559189 | ||||||||
\(777\) | 52.3943 | 1.87964 | ||||||||
\(778\) | 14.2715 | 0.511659 | ||||||||
\(779\) | 55.2328 | 1.97892 | ||||||||
\(780\) | 10.4577 | 0.374446 | ||||||||
\(781\) | −21.4681 | −0.768190 | ||||||||
\(782\) | 6.31558 | 0.225845 | ||||||||
\(783\) | −2.04079 | −0.0729320 | ||||||||
\(784\) | −2.36010 | −0.0842892 | ||||||||
\(785\) | 59.8965 | 2.13780 | ||||||||
\(786\) | 36.4818 | 1.30126 | ||||||||
\(787\) | 31.0946 | 1.10840 | 0.554201 | − | 0.832383i | \(-0.313024\pi\) | ||||
0.554201 | + | 0.832383i | \(0.313024\pi\) | |||||||
\(788\) | 5.37830 | 0.191594 | ||||||||
\(789\) | 81.8044 | 2.91232 | ||||||||
\(790\) | 15.0787 | 0.536475 | ||||||||
\(791\) | 22.0025 | 0.782318 | ||||||||
\(792\) | 7.87412 | 0.279795 | ||||||||
\(793\) | −2.01852 | −0.0716799 | ||||||||
\(794\) | 28.3844 | 1.00732 | ||||||||
\(795\) | 78.8737 | 2.79736 | ||||||||
\(796\) | −12.2368 | −0.433724 | ||||||||
\(797\) | −18.6722 | −0.661404 | −0.330702 | − | 0.943735i | \(-0.607286\pi\) | ||||
−0.330702 | + | 0.943735i | \(0.607286\pi\) | |||||||
\(798\) | 38.0307 | 1.34627 | ||||||||
\(799\) | −26.7748 | −0.947226 | ||||||||
\(800\) | −7.38184 | −0.260987 | ||||||||
\(801\) | −84.2530 | −2.97693 | ||||||||
\(802\) | 38.1003 | 1.34537 | ||||||||
\(803\) | 3.83742 | 0.135420 | ||||||||
\(804\) | 12.0654 | 0.425513 | ||||||||
\(805\) | 16.2603 | 0.573100 | ||||||||
\(806\) | −5.15289 | −0.181503 | ||||||||
\(807\) | 19.2456 | 0.677478 | ||||||||
\(808\) | 0.540634 | 0.0190194 | ||||||||
\(809\) | 21.5480 | 0.757588 | 0.378794 | − | 0.925481i | \(-0.376339\pi\) | ||||
0.378794 | + | 0.925481i | \(0.376339\pi\) | |||||||
\(810\) | −18.6163 | −0.654109 | ||||||||
\(811\) | −17.4411 | −0.612439 | −0.306219 | − | 0.951961i | \(-0.599064\pi\) | ||||
−0.306219 | + | 0.951961i | \(0.599064\pi\) | |||||||
\(812\) | 0.585076 | 0.0205321 | ||||||||
\(813\) | 84.9606 | 2.97970 | ||||||||
\(814\) | −11.7543 | −0.411987 | ||||||||
\(815\) | −4.56234 | −0.159812 | ||||||||
\(816\) | 8.61680 | 0.301648 | ||||||||
\(817\) | 35.1083 | 1.22828 | ||||||||
\(818\) | −20.3927 | −0.713015 | ||||||||
\(819\) | −12.1760 | −0.425465 | ||||||||
\(820\) | 32.2199 | 1.12517 | ||||||||
\(821\) | −49.2282 | −1.71807 | −0.859037 | − | 0.511913i | \(-0.828937\pi\) | ||||
−0.859037 | + | 0.511913i | \(0.828937\pi\) | |||||||
\(822\) | −2.02134 | −0.0705022 | ||||||||
\(823\) | −39.4215 | −1.37415 | −0.687073 | − | 0.726589i | \(-0.741105\pi\) | ||||
−0.687073 | + | 0.726589i | \(0.741105\pi\) | |||||||
\(824\) | −6.79230 | −0.236621 | ||||||||
\(825\) | −30.5604 | −1.06398 | ||||||||
\(826\) | 13.1786 | 0.458543 | ||||||||
\(827\) | 9.99263 | 0.347478 | 0.173739 | − | 0.984792i | \(-0.444415\pi\) | ||||
0.173739 | + | 0.984792i | \(0.444415\pi\) | |||||||
\(828\) | −11.9427 | −0.415038 | ||||||||
\(829\) | 12.4418 | 0.432120 | 0.216060 | − | 0.976380i | \(-0.430679\pi\) | ||||
0.216060 | + | 0.976380i | \(0.430679\pi\) | |||||||
\(830\) | 39.1794 | 1.35994 | ||||||||
\(831\) | 91.1973 | 3.16360 | ||||||||
\(832\) | 1.01538 | 0.0352021 | ||||||||
\(833\) | −6.94803 | −0.240735 | ||||||||
\(834\) | 45.5061 | 1.57575 | ||||||||
\(835\) | −13.9816 | −0.483852 | ||||||||
\(836\) | −8.53191 | −0.295082 | ||||||||
\(837\) | 38.1296 | 1.31795 | ||||||||
\(838\) | −40.3433 | −1.39364 | ||||||||
\(839\) | 40.2755 | 1.39047 | 0.695233 | − | 0.718785i | \(-0.255301\pi\) | ||||
0.695233 | + | 0.718785i | \(0.255301\pi\) | |||||||
\(840\) | 22.1851 | 0.765459 | ||||||||
\(841\) | −28.9262 | −0.997456 | ||||||||
\(842\) | −14.5045 | −0.499858 | ||||||||
\(843\) | −31.3817 | −1.08084 | ||||||||
\(844\) | −9.56427 | −0.329216 | ||||||||
\(845\) | −42.1163 | −1.44885 | ||||||||
\(846\) | 50.6311 | 1.74073 | ||||||||
\(847\) | 19.3851 | 0.666080 | ||||||||
\(848\) | 7.65817 | 0.262983 | ||||||||
\(849\) | 79.0333 | 2.71242 | ||||||||
\(850\) | −21.7318 | −0.745395 | ||||||||
\(851\) | 17.8278 | 0.611127 | ||||||||
\(852\) | 44.4251 | 1.52198 | ||||||||
\(853\) | 36.3548 | 1.24476 | 0.622382 | − | 0.782714i | \(-0.286165\pi\) | ||||
0.622382 | + | 0.782714i | \(0.286165\pi\) | |||||||
\(854\) | −4.28212 | −0.146531 | ||||||||
\(855\) | 118.163 | 4.04108 | ||||||||
\(856\) | −13.4644 | −0.460204 | ||||||||
\(857\) | −23.1125 | −0.789509 | −0.394755 | − | 0.918787i | \(-0.629170\pi\) | ||||
−0.394755 | + | 0.918787i | \(0.629170\pi\) | |||||||
\(858\) | 4.20363 | 0.143510 | ||||||||
\(859\) | −22.4839 | −0.767141 | −0.383570 | − | 0.923512i | \(-0.625306\pi\) | ||||
−0.383570 | + | 0.923512i | \(0.625306\pi\) | |||||||
\(860\) | 20.4803 | 0.698372 | ||||||||
\(861\) | −57.7299 | −1.96743 | ||||||||
\(862\) | 25.4001 | 0.865130 | ||||||||
\(863\) | 18.5867 | 0.632698 | 0.316349 | − | 0.948643i | \(-0.397543\pi\) | ||||
0.316349 | + | 0.948643i | \(0.397543\pi\) | |||||||
\(864\) | −7.51348 | −0.255614 | ||||||||
\(865\) | 56.0998 | 1.90745 | ||||||||
\(866\) | 25.0402 | 0.850902 | ||||||||
\(867\) | −24.3906 | −0.828347 | ||||||||
\(868\) | −10.9314 | −0.371036 | ||||||||
\(869\) | 6.06110 | 0.205609 | ||||||||
\(870\) | 2.79747 | 0.0948430 | ||||||||
\(871\) | 4.18558 | 0.141823 | ||||||||
\(872\) | −6.72962 | −0.227894 | ||||||||
\(873\) | −86.7185 | −2.93497 | ||||||||
\(874\) | 12.9404 | 0.437715 | ||||||||
\(875\) | −18.0534 | −0.610317 | ||||||||
\(876\) | −7.94097 | −0.268301 | ||||||||
\(877\) | 20.6282 | 0.696564 | 0.348282 | − | 0.937390i | \(-0.386765\pi\) | ||||
0.348282 | + | 0.937390i | \(0.386765\pi\) | |||||||
\(878\) | 13.4799 | 0.454925 | ||||||||
\(879\) | 4.78602 | 0.161429 | ||||||||
\(880\) | −4.97706 | −0.167777 | ||||||||
\(881\) | −14.9572 | −0.503920 | −0.251960 | − | 0.967738i | \(-0.581075\pi\) | ||||
−0.251960 | + | 0.967738i | \(0.581075\pi\) | |||||||
\(882\) | 13.1387 | 0.442402 | ||||||||
\(883\) | −21.2829 | −0.716228 | −0.358114 | − | 0.933678i | \(-0.616580\pi\) | ||||
−0.358114 | + | 0.933678i | \(0.616580\pi\) | |||||||
\(884\) | 2.98924 | 0.100539 | ||||||||
\(885\) | 63.0119 | 2.11812 | ||||||||
\(886\) | −11.5523 | −0.388107 | ||||||||
\(887\) | 14.2275 | 0.477712 | 0.238856 | − | 0.971055i | \(-0.423228\pi\) | ||||
0.238856 | + | 0.971055i | \(0.423228\pi\) | |||||||
\(888\) | 24.3237 | 0.816250 | ||||||||
\(889\) | −17.6836 | −0.593088 | ||||||||
\(890\) | 53.2545 | 1.78509 | ||||||||
\(891\) | −7.48308 | −0.250693 | ||||||||
\(892\) | 20.9492 | 0.701430 | ||||||||
\(893\) | −54.8607 | −1.83584 | ||||||||
\(894\) | −25.6944 | −0.859351 | ||||||||
\(895\) | 35.3992 | 1.18326 | ||||||||
\(896\) | 2.15404 | 0.0719615 | ||||||||
\(897\) | −6.37567 | −0.212877 | ||||||||
\(898\) | 5.54771 | 0.185130 | ||||||||
\(899\) | −1.37841 | −0.0459726 | ||||||||
\(900\) | 41.0947 | 1.36982 | ||||||||
\(901\) | 22.5453 | 0.751093 | ||||||||
\(902\) | 12.9513 | 0.431230 | ||||||||
\(903\) | −36.6955 | −1.22115 | ||||||||
\(904\) | 10.2145 | 0.339729 | ||||||||
\(905\) | 19.8184 | 0.658786 | ||||||||
\(906\) | −19.2965 | −0.641083 | ||||||||
\(907\) | 34.2535 | 1.13737 | 0.568684 | − | 0.822556i | \(-0.307453\pi\) | ||||
0.568684 | + | 0.822556i | \(0.307453\pi\) | |||||||
\(908\) | 25.0539 | 0.831442 | ||||||||
\(909\) | −3.00971 | −0.0998259 | ||||||||
\(910\) | 7.69621 | 0.255127 | ||||||||
\(911\) | 1.47381 | 0.0488297 | 0.0244148 | − | 0.999702i | \(-0.492228\pi\) | ||||
0.0244148 | + | 0.999702i | \(0.492228\pi\) | |||||||
\(912\) | 17.6555 | 0.584632 | ||||||||
\(913\) | 15.7487 | 0.521207 | ||||||||
\(914\) | 11.9046 | 0.393771 | ||||||||
\(915\) | −20.4744 | −0.676863 | ||||||||
\(916\) | 11.8010 | 0.389914 | ||||||||
\(917\) | 26.8483 | 0.886609 | ||||||||
\(918\) | −22.1194 | −0.730048 | ||||||||
\(919\) | 18.9914 | 0.626467 | 0.313234 | − | 0.949676i | \(-0.398588\pi\) | ||||
0.313234 | + | 0.949676i | \(0.398588\pi\) | |||||||
\(920\) | 7.54873 | 0.248874 | ||||||||
\(921\) | 41.5127 | 1.36789 | ||||||||
\(922\) | 33.4774 | 1.10252 | ||||||||
\(923\) | 15.4114 | 0.507274 | ||||||||
\(924\) | 8.91763 | 0.293369 | ||||||||
\(925\) | −61.3451 | −2.01701 | ||||||||
\(926\) | 4.15271 | 0.136467 | ||||||||
\(927\) | 37.8127 | 1.24193 | ||||||||
\(928\) | 0.271618 | 0.00891628 | ||||||||
\(929\) | 29.6480 | 0.972719 | 0.486359 | − | 0.873759i | \(-0.338325\pi\) | ||||
0.486359 | + | 0.873759i | \(0.338325\pi\) | |||||||
\(930\) | −52.2671 | −1.71391 | ||||||||
\(931\) | −14.2363 | −0.466574 | ||||||||
\(932\) | −16.7353 | −0.548182 | ||||||||
\(933\) | 5.17984 | 0.169580 | ||||||||
\(934\) | −24.1830 | −0.791292 | ||||||||
\(935\) | −14.6523 | −0.479180 | ||||||||
\(936\) | −5.65264 | −0.184762 | ||||||||
\(937\) | −32.0794 | −1.04799 | −0.523993 | − | 0.851722i | \(-0.675558\pi\) | ||||
−0.523993 | + | 0.851722i | \(0.675558\pi\) | |||||||
\(938\) | 8.87934 | 0.289921 | ||||||||
\(939\) | −17.4316 | −0.568859 | ||||||||
\(940\) | −32.0028 | −1.04382 | ||||||||
\(941\) | −13.1020 | −0.427113 | −0.213556 | − | 0.976931i | \(-0.568505\pi\) | ||||
−0.213556 | + | 0.976931i | \(0.568505\pi\) | |||||||
\(942\) | −49.8222 | −1.62330 | ||||||||
\(943\) | −19.6432 | −0.639672 | ||||||||
\(944\) | 6.11808 | 0.199127 | ||||||||
\(945\) | −56.9493 | −1.85256 | ||||||||
\(946\) | 8.23236 | 0.267657 | ||||||||
\(947\) | 54.0459 | 1.75625 | 0.878127 | − | 0.478427i | \(-0.158793\pi\) | ||||
0.878127 | + | 0.478427i | \(0.158793\pi\) | |||||||
\(948\) | −12.5425 | −0.407363 | ||||||||
\(949\) | −2.75479 | −0.0894243 | ||||||||
\(950\) | −44.5277 | −1.44467 | ||||||||
\(951\) | 4.44576 | 0.144164 | ||||||||
\(952\) | 6.34141 | 0.205526 | ||||||||
\(953\) | −3.23242 | −0.104708 | −0.0523541 | − | 0.998629i | \(-0.516672\pi\) | ||||
−0.0523541 | + | 0.998629i | \(0.516672\pi\) | |||||||
\(954\) | −42.6331 | −1.38030 | ||||||||
\(955\) | −62.6243 | −2.02648 | ||||||||
\(956\) | −18.5731 | −0.600698 | ||||||||
\(957\) | 1.12448 | 0.0363494 | ||||||||
\(958\) | −27.9934 | −0.904427 | ||||||||
\(959\) | −1.48757 | −0.0480363 | ||||||||
\(960\) | 10.2993 | 0.332408 | ||||||||
\(961\) | −5.24612 | −0.169230 | ||||||||
\(962\) | 8.43810 | 0.272055 | ||||||||
\(963\) | 74.9564 | 2.41544 | ||||||||
\(964\) | −5.35589 | −0.172502 | ||||||||
\(965\) | 56.8213 | 1.82914 | ||||||||
\(966\) | −13.5254 | −0.435173 | ||||||||
\(967\) | 41.9691 | 1.34963 | 0.674817 | − | 0.737985i | \(-0.264222\pi\) | ||||
0.674817 | + | 0.737985i | \(0.264222\pi\) | |||||||
\(968\) | 8.99940 | 0.289252 | ||||||||
\(969\) | 51.9771 | 1.66974 | ||||||||
\(970\) | 54.8129 | 1.75993 | ||||||||
\(971\) | 11.3915 | 0.365571 | 0.182785 | − | 0.983153i | \(-0.441489\pi\) | ||||
0.182785 | + | 0.983153i | \(0.441489\pi\) | |||||||
\(972\) | −7.05534 | −0.226300 | ||||||||
\(973\) | 33.4896 | 1.07363 | ||||||||
\(974\) | −6.83469 | −0.218998 | ||||||||
\(975\) | 21.9386 | 0.702597 | ||||||||
\(976\) | −1.98794 | −0.0636326 | ||||||||
\(977\) | 4.91695 | 0.157307 | 0.0786536 | − | 0.996902i | \(-0.474938\pi\) | ||||
0.0786536 | + | 0.996902i | \(0.474938\pi\) | |||||||
\(978\) | 3.79498 | 0.121350 | ||||||||
\(979\) | 21.4064 | 0.684152 | ||||||||
\(980\) | −8.30467 | −0.265283 | ||||||||
\(981\) | 37.4638 | 1.19613 | ||||||||
\(982\) | 3.00393 | 0.0958591 | ||||||||
\(983\) | −11.2907 | −0.360119 | −0.180059 | − | 0.983656i | \(-0.557629\pi\) | ||||
−0.180059 | + | 0.983656i | \(0.557629\pi\) | |||||||
\(984\) | −26.8007 | −0.854375 | ||||||||
\(985\) | 18.9251 | 0.603003 | ||||||||
\(986\) | 0.799630 | 0.0254654 | ||||||||
\(987\) | 57.3409 | 1.82518 | ||||||||
\(988\) | 6.12485 | 0.194857 | ||||||||
\(989\) | −12.4860 | −0.397033 | ||||||||
\(990\) | 27.7073 | 0.880597 | ||||||||
\(991\) | −43.8862 | −1.39409 | −0.697046 | − | 0.717026i | \(-0.745503\pi\) | ||||
−0.697046 | + | 0.717026i | \(0.745503\pi\) | |||||||
\(992\) | −5.07483 | −0.161126 | ||||||||
\(993\) | −76.7576 | −2.43583 | ||||||||
\(994\) | 32.6940 | 1.03699 | ||||||||
\(995\) | −43.0588 | −1.36506 | ||||||||
\(996\) | −32.5897 | −1.03264 | ||||||||
\(997\) | −37.8524 | −1.19880 | −0.599399 | − | 0.800450i | \(-0.704594\pi\) | ||||
−0.599399 | + | 0.800450i | \(0.704594\pi\) | |||||||
\(998\) | 11.0943 | 0.351184 | ||||||||
\(999\) | −62.4391 | −1.97549 |
(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 | 8002.2.a.e.1.72 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.72 | ✓ | 77 | 1.1 | even | 1 | trivial |