Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 | ||||||||
\(3\) | −1.90629 | −1.10060 | −0.550298 | − | 0.834968i | \(-0.685486\pi\) | ||||
−0.550298 | + | 0.834968i | \(0.685486\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.44864 | −1.54228 | −0.771139 | − | 0.636667i | \(-0.780313\pi\) | ||||
−0.771139 | + | 0.636667i | \(0.780313\pi\) | |||||||
\(6\) | 1.90629 | 0.778239 | ||||||||
\(7\) | 0.576337 | 0.217835 | 0.108917 | − | 0.994051i | \(-0.465262\pi\) | ||||
0.108917 | + | 0.994051i | \(0.465262\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.633932 | 0.211311 | ||||||||
\(10\) | 3.44864 | 1.09056 | ||||||||
\(11\) | −2.52760 | −0.762101 | −0.381051 | − | 0.924554i | \(-0.624438\pi\) | ||||
−0.381051 | + | 0.924554i | \(0.624438\pi\) | |||||||
\(12\) | −1.90629 | −0.550298 | ||||||||
\(13\) | −3.72282 | −1.03252 | −0.516262 | − | 0.856431i | \(-0.672677\pi\) | ||||
−0.516262 | + | 0.856431i | \(0.672677\pi\) | |||||||
\(14\) | −0.576337 | −0.154032 | ||||||||
\(15\) | 6.57409 | 1.69742 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.135390 | −0.0328369 | −0.0164185 | − | 0.999865i | \(-0.505226\pi\) | ||||
−0.0164185 | + | 0.999865i | \(0.505226\pi\) | |||||||
\(18\) | −0.633932 | −0.149419 | ||||||||
\(19\) | 6.77310 | 1.55386 | 0.776928 | − | 0.629589i | \(-0.216777\pi\) | ||||
0.776928 | + | 0.629589i | \(0.216777\pi\) | |||||||
\(20\) | −3.44864 | −0.771139 | ||||||||
\(21\) | −1.09866 | −0.239748 | ||||||||
\(22\) | 2.52760 | 0.538887 | ||||||||
\(23\) | 6.42164 | 1.33900 | 0.669502 | − | 0.742810i | \(-0.266507\pi\) | ||||
0.669502 | + | 0.742810i | \(0.266507\pi\) | |||||||
\(24\) | 1.90629 | 0.389119 | ||||||||
\(25\) | 6.89310 | 1.37862 | ||||||||
\(26\) | 3.72282 | 0.730105 | ||||||||
\(27\) | 4.51041 | 0.868028 | ||||||||
\(28\) | 0.576337 | 0.108917 | ||||||||
\(29\) | 3.64156 | 0.676220 | 0.338110 | − | 0.941107i | \(-0.390212\pi\) | ||||
0.338110 | + | 0.941107i | \(0.390212\pi\) | |||||||
\(30\) | −6.57409 | −1.20026 | ||||||||
\(31\) | −3.48116 | −0.625235 | −0.312617 | − | 0.949879i | \(-0.601206\pi\) | ||||
−0.312617 | + | 0.949879i | \(0.601206\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.81834 | 0.838765 | ||||||||
\(34\) | 0.135390 | 0.0232192 | ||||||||
\(35\) | −1.98758 | −0.335962 | ||||||||
\(36\) | 0.633932 | 0.105655 | ||||||||
\(37\) | −6.73560 | −1.10733 | −0.553663 | − | 0.832741i | \(-0.686770\pi\) | ||||
−0.553663 | + | 0.832741i | \(0.686770\pi\) | |||||||
\(38\) | −6.77310 | −1.09874 | ||||||||
\(39\) | 7.09676 | 1.13639 | ||||||||
\(40\) | 3.44864 | 0.545278 | ||||||||
\(41\) | 6.30497 | 0.984671 | 0.492335 | − | 0.870406i | \(-0.336143\pi\) | ||||
0.492335 | + | 0.870406i | \(0.336143\pi\) | |||||||
\(42\) | 1.09866 | 0.169527 | ||||||||
\(43\) | −9.94360 | −1.51638 | −0.758192 | − | 0.652031i | \(-0.773917\pi\) | ||||
−0.758192 | + | 0.652031i | \(0.773917\pi\) | |||||||
\(44\) | −2.52760 | −0.381051 | ||||||||
\(45\) | −2.18620 | −0.325899 | ||||||||
\(46\) | −6.42164 | −0.946820 | ||||||||
\(47\) | −10.9283 | −1.59405 | −0.797025 | − | 0.603947i | \(-0.793594\pi\) | ||||
−0.797025 | + | 0.603947i | \(0.793594\pi\) | |||||||
\(48\) | −1.90629 | −0.275149 | ||||||||
\(49\) | −6.66784 | −0.952548 | ||||||||
\(50\) | −6.89310 | −0.974832 | ||||||||
\(51\) | 0.258093 | 0.0361402 | ||||||||
\(52\) | −3.72282 | −0.516262 | ||||||||
\(53\) | 7.21285 | 0.990761 | 0.495381 | − | 0.868676i | \(-0.335029\pi\) | ||||
0.495381 | + | 0.868676i | \(0.335029\pi\) | |||||||
\(54\) | −4.51041 | −0.613789 | ||||||||
\(55\) | 8.71679 | 1.17537 | ||||||||
\(56\) | −0.576337 | −0.0770162 | ||||||||
\(57\) | −12.9115 | −1.71017 | ||||||||
\(58\) | −3.64156 | −0.478160 | ||||||||
\(59\) | 9.89885 | 1.28872 | 0.644360 | − | 0.764722i | \(-0.277124\pi\) | ||||
0.644360 | + | 0.764722i | \(0.277124\pi\) | |||||||
\(60\) | 6.57409 | 0.848712 | ||||||||
\(61\) | 4.83709 | 0.619327 | 0.309663 | − | 0.950846i | \(-0.399784\pi\) | ||||
0.309663 | + | 0.950846i | \(0.399784\pi\) | |||||||
\(62\) | 3.48116 | 0.442108 | ||||||||
\(63\) | 0.365358 | 0.0460308 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.8386 | 1.59244 | ||||||||
\(66\) | −4.81834 | −0.593097 | ||||||||
\(67\) | −8.17945 | −0.999278 | −0.499639 | − | 0.866234i | \(-0.666534\pi\) | ||||
−0.499639 | + | 0.866234i | \(0.666534\pi\) | |||||||
\(68\) | −0.135390 | −0.0164185 | ||||||||
\(69\) | −12.2415 | −1.47370 | ||||||||
\(70\) | 1.98758 | 0.237561 | ||||||||
\(71\) | −6.36792 | −0.755733 | −0.377867 | − | 0.925860i | \(-0.623342\pi\) | ||||
−0.377867 | + | 0.925860i | \(0.623342\pi\) | |||||||
\(72\) | −0.633932 | −0.0747095 | ||||||||
\(73\) | −15.5985 | −1.82567 | −0.912833 | − | 0.408333i | \(-0.866110\pi\) | ||||
−0.912833 | + | 0.408333i | \(0.866110\pi\) | |||||||
\(74\) | 6.73560 | 0.782997 | ||||||||
\(75\) | −13.1402 | −1.51730 | ||||||||
\(76\) | 6.77310 | 0.776928 | ||||||||
\(77\) | −1.45675 | −0.166012 | ||||||||
\(78\) | −7.09676 | −0.803550 | ||||||||
\(79\) | −9.18127 | −1.03297 | −0.516487 | − | 0.856295i | \(-0.672761\pi\) | ||||
−0.516487 | + | 0.856295i | \(0.672761\pi\) | |||||||
\(80\) | −3.44864 | −0.385569 | ||||||||
\(81\) | −10.4999 | −1.16666 | ||||||||
\(82\) | −6.30497 | −0.696268 | ||||||||
\(83\) | −13.4764 | −1.47923 | −0.739613 | − | 0.673032i | \(-0.764992\pi\) | ||||
−0.739613 | + | 0.673032i | \(0.764992\pi\) | |||||||
\(84\) | −1.09866 | −0.119874 | ||||||||
\(85\) | 0.466912 | 0.0506437 | ||||||||
\(86\) | 9.94360 | 1.07225 | ||||||||
\(87\) | −6.94185 | −0.744244 | ||||||||
\(88\) | 2.52760 | 0.269444 | ||||||||
\(89\) | −9.66471 | −1.02446 | −0.512229 | − | 0.858849i | \(-0.671180\pi\) | ||||
−0.512229 | + | 0.858849i | \(0.671180\pi\) | |||||||
\(90\) | 2.18620 | 0.230446 | ||||||||
\(91\) | −2.14560 | −0.224920 | ||||||||
\(92\) | 6.42164 | 0.669502 | ||||||||
\(93\) | 6.63609 | 0.688131 | ||||||||
\(94\) | 10.9283 | 1.12716 | ||||||||
\(95\) | −23.3580 | −2.39648 | ||||||||
\(96\) | 1.90629 | 0.194560 | ||||||||
\(97\) | 8.55243 | 0.868368 | 0.434184 | − | 0.900824i | \(-0.357037\pi\) | ||||
0.434184 | + | 0.900824i | \(0.357037\pi\) | |||||||
\(98\) | 6.66784 | 0.673553 | ||||||||
\(99\) | −1.60233 | −0.161040 | ||||||||
\(100\) | 6.89310 | 0.689310 | ||||||||
\(101\) | 14.2863 | 1.42154 | 0.710768 | − | 0.703426i | \(-0.248347\pi\) | ||||
0.710768 | + | 0.703426i | \(0.248347\pi\) | |||||||
\(102\) | −0.258093 | −0.0255550 | ||||||||
\(103\) | −4.93742 | −0.486498 | −0.243249 | − | 0.969964i | \(-0.578213\pi\) | ||||
−0.243249 | + | 0.969964i | \(0.578213\pi\) | |||||||
\(104\) | 3.72282 | 0.365052 | ||||||||
\(105\) | 3.78889 | 0.369758 | ||||||||
\(106\) | −7.21285 | −0.700574 | ||||||||
\(107\) | 14.1760 | 1.37045 | 0.685225 | − | 0.728331i | \(-0.259704\pi\) | ||||
0.685225 | + | 0.728331i | \(0.259704\pi\) | |||||||
\(108\) | 4.51041 | 0.434014 | ||||||||
\(109\) | 1.52598 | 0.146162 | 0.0730810 | − | 0.997326i | \(-0.476717\pi\) | ||||
0.0730810 | + | 0.997326i | \(0.476717\pi\) | |||||||
\(110\) | −8.71679 | −0.831113 | ||||||||
\(111\) | 12.8400 | 1.21872 | ||||||||
\(112\) | 0.576337 | 0.0544587 | ||||||||
\(113\) | −9.45088 | −0.889064 | −0.444532 | − | 0.895763i | \(-0.646630\pi\) | ||||
−0.444532 | + | 0.895763i | \(0.646630\pi\) | |||||||
\(114\) | 12.9115 | 1.20927 | ||||||||
\(115\) | −22.1459 | −2.06512 | ||||||||
\(116\) | 3.64156 | 0.338110 | ||||||||
\(117\) | −2.36001 | −0.218183 | ||||||||
\(118\) | −9.89885 | −0.911263 | ||||||||
\(119\) | −0.0780303 | −0.00715303 | ||||||||
\(120\) | −6.57409 | −0.600130 | ||||||||
\(121\) | −4.61122 | −0.419202 | ||||||||
\(122\) | −4.83709 | −0.437930 | ||||||||
\(123\) | −12.0191 | −1.08372 | ||||||||
\(124\) | −3.48116 | −0.312617 | ||||||||
\(125\) | −6.52862 | −0.583938 | ||||||||
\(126\) | −0.365358 | −0.0325487 | ||||||||
\(127\) | −2.57457 | −0.228457 | −0.114228 | − | 0.993455i | \(-0.536440\pi\) | ||||
−0.114228 | + | 0.993455i | \(0.536440\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 18.9554 | 1.66893 | ||||||||
\(130\) | −12.8386 | −1.12602 | ||||||||
\(131\) | −13.0315 | −1.13857 | −0.569284 | − | 0.822141i | \(-0.692780\pi\) | ||||
−0.569284 | + | 0.822141i | \(0.692780\pi\) | |||||||
\(132\) | 4.81834 | 0.419383 | ||||||||
\(133\) | 3.90359 | 0.338484 | ||||||||
\(134\) | 8.17945 | 0.706597 | ||||||||
\(135\) | −15.5548 | −1.33874 | ||||||||
\(136\) | 0.135390 | 0.0116096 | ||||||||
\(137\) | −22.6525 | −1.93533 | −0.967667 | − | 0.252231i | \(-0.918836\pi\) | ||||
−0.967667 | + | 0.252231i | \(0.918836\pi\) | |||||||
\(138\) | 12.2415 | 1.04207 | ||||||||
\(139\) | −1.66687 | −0.141382 | −0.0706911 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706911 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(140\) | −1.98758 | −0.167981 | ||||||||
\(141\) | 20.8324 | 1.75440 | ||||||||
\(142\) | 6.36792 | 0.534384 | ||||||||
\(143\) | 9.40981 | 0.786888 | ||||||||
\(144\) | 0.633932 | 0.0528276 | ||||||||
\(145\) | −12.5584 | −1.04292 | ||||||||
\(146\) | 15.5985 | 1.29094 | ||||||||
\(147\) | 12.7108 | 1.04837 | ||||||||
\(148\) | −6.73560 | −0.553663 | ||||||||
\(149\) | 22.7885 | 1.86691 | 0.933453 | − | 0.358699i | \(-0.116780\pi\) | ||||
0.933453 | + | 0.358699i | \(0.116780\pi\) | |||||||
\(150\) | 13.1402 | 1.07290 | ||||||||
\(151\) | 1.41340 | 0.115021 | 0.0575104 | − | 0.998345i | \(-0.481684\pi\) | ||||
0.0575104 | + | 0.998345i | \(0.481684\pi\) | |||||||
\(152\) | −6.77310 | −0.549371 | ||||||||
\(153\) | −0.0858281 | −0.00693879 | ||||||||
\(154\) | 1.45675 | 0.117388 | ||||||||
\(155\) | 12.0053 | 0.964286 | ||||||||
\(156\) | 7.09676 | 0.568196 | ||||||||
\(157\) | 5.98332 | 0.477521 | 0.238760 | − | 0.971079i | \(-0.423259\pi\) | ||||
0.238760 | + | 0.971079i | \(0.423259\pi\) | |||||||
\(158\) | 9.18127 | 0.730423 | ||||||||
\(159\) | −13.7498 | −1.09043 | ||||||||
\(160\) | 3.44864 | 0.272639 | ||||||||
\(161\) | 3.70103 | 0.291682 | ||||||||
\(162\) | 10.4999 | 0.824952 | ||||||||
\(163\) | −6.36633 | −0.498650 | −0.249325 | − | 0.968420i | \(-0.580209\pi\) | ||||
−0.249325 | + | 0.968420i | \(0.580209\pi\) | |||||||
\(164\) | 6.30497 | 0.492335 | ||||||||
\(165\) | −16.6167 | −1.29361 | ||||||||
\(166\) | 13.4764 | 1.04597 | ||||||||
\(167\) | 13.7345 | 1.06280 | 0.531402 | − | 0.847120i | \(-0.321665\pi\) | ||||
0.531402 | + | 0.847120i | \(0.321665\pi\) | |||||||
\(168\) | 1.09866 | 0.0847637 | ||||||||
\(169\) | 0.859371 | 0.0661055 | ||||||||
\(170\) | −0.466912 | −0.0358105 | ||||||||
\(171\) | 4.29368 | 0.328346 | ||||||||
\(172\) | −9.94360 | −0.758192 | ||||||||
\(173\) | 6.27011 | 0.476708 | 0.238354 | − | 0.971178i | \(-0.423392\pi\) | ||||
0.238354 | + | 0.971178i | \(0.423392\pi\) | |||||||
\(174\) | 6.94185 | 0.526260 | ||||||||
\(175\) | 3.97275 | 0.300311 | ||||||||
\(176\) | −2.52760 | −0.190525 | ||||||||
\(177\) | −18.8700 | −1.41836 | ||||||||
\(178\) | 9.66471 | 0.724401 | ||||||||
\(179\) | −5.74419 | −0.429341 | −0.214671 | − | 0.976687i | \(-0.568868\pi\) | ||||
−0.214671 | + | 0.976687i | \(0.568868\pi\) | |||||||
\(180\) | −2.18620 | −0.162950 | ||||||||
\(181\) | 0.803801 | 0.0597461 | 0.0298730 | − | 0.999554i | \(-0.490490\pi\) | ||||
0.0298730 | + | 0.999554i | \(0.490490\pi\) | |||||||
\(182\) | 2.14560 | 0.159042 | ||||||||
\(183\) | −9.22089 | −0.681628 | ||||||||
\(184\) | −6.42164 | −0.473410 | ||||||||
\(185\) | 23.2286 | 1.70780 | ||||||||
\(186\) | −6.63609 | −0.486582 | ||||||||
\(187\) | 0.342213 | 0.0250251 | ||||||||
\(188\) | −10.9283 | −0.797025 | ||||||||
\(189\) | 2.59951 | 0.189087 | ||||||||
\(190\) | 23.3580 | 1.69457 | ||||||||
\(191\) | 9.23399 | 0.668148 | 0.334074 | − | 0.942547i | \(-0.391576\pi\) | ||||
0.334074 | + | 0.942547i | \(0.391576\pi\) | |||||||
\(192\) | −1.90629 | −0.137574 | ||||||||
\(193\) | 16.6869 | 1.20115 | 0.600576 | − | 0.799568i | \(-0.294938\pi\) | ||||
0.600576 | + | 0.799568i | \(0.294938\pi\) | |||||||
\(194\) | −8.55243 | −0.614029 | ||||||||
\(195\) | −24.4742 | −1.75263 | ||||||||
\(196\) | −6.66784 | −0.476274 | ||||||||
\(197\) | 13.2031 | 0.940684 | 0.470342 | − | 0.882484i | \(-0.344131\pi\) | ||||
0.470342 | + | 0.882484i | \(0.344131\pi\) | |||||||
\(198\) | 1.60233 | 0.113872 | ||||||||
\(199\) | −14.2637 | −1.01113 | −0.505563 | − | 0.862790i | \(-0.668715\pi\) | ||||
−0.505563 | + | 0.862790i | \(0.668715\pi\) | |||||||
\(200\) | −6.89310 | −0.487416 | ||||||||
\(201\) | 15.5924 | 1.09980 | ||||||||
\(202\) | −14.2863 | −1.00518 | ||||||||
\(203\) | 2.09876 | 0.147304 | ||||||||
\(204\) | 0.258093 | 0.0180701 | ||||||||
\(205\) | −21.7436 | −1.51864 | ||||||||
\(206\) | 4.93742 | 0.344006 | ||||||||
\(207\) | 4.07088 | 0.282946 | ||||||||
\(208\) | −3.72282 | −0.258131 | ||||||||
\(209\) | −17.1197 | −1.18420 | ||||||||
\(210\) | −3.78889 | −0.261458 | ||||||||
\(211\) | −22.5826 | −1.55465 | −0.777325 | − | 0.629099i | \(-0.783424\pi\) | ||||
−0.777325 | + | 0.629099i | \(0.783424\pi\) | |||||||
\(212\) | 7.21285 | 0.495381 | ||||||||
\(213\) | 12.1391 | 0.831756 | ||||||||
\(214\) | −14.1760 | −0.969055 | ||||||||
\(215\) | 34.2919 | 2.33869 | ||||||||
\(216\) | −4.51041 | −0.306894 | ||||||||
\(217\) | −2.00632 | −0.136198 | ||||||||
\(218\) | −1.52598 | −0.103352 | ||||||||
\(219\) | 29.7352 | 2.00932 | ||||||||
\(220\) | 8.71679 | 0.587686 | ||||||||
\(221\) | 0.504033 | 0.0339049 | ||||||||
\(222\) | −12.8400 | −0.861763 | ||||||||
\(223\) | −4.37688 | −0.293097 | −0.146549 | − | 0.989203i | \(-0.546816\pi\) | ||||
−0.146549 | + | 0.989203i | \(0.546816\pi\) | |||||||
\(224\) | −0.576337 | −0.0385081 | ||||||||
\(225\) | 4.36976 | 0.291317 | ||||||||
\(226\) | 9.45088 | 0.628663 | ||||||||
\(227\) | 9.73531 | 0.646155 | 0.323078 | − | 0.946372i | \(-0.395283\pi\) | ||||
0.323078 | + | 0.946372i | \(0.395283\pi\) | |||||||
\(228\) | −12.9115 | −0.855084 | ||||||||
\(229\) | −8.75050 | −0.578249 | −0.289125 | − | 0.957291i | \(-0.593364\pi\) | ||||
−0.289125 | + | 0.957291i | \(0.593364\pi\) | |||||||
\(230\) | 22.1459 | 1.46026 | ||||||||
\(231\) | 2.77699 | 0.182712 | ||||||||
\(232\) | −3.64156 | −0.239080 | ||||||||
\(233\) | −18.2084 | −1.19287 | −0.596435 | − | 0.802661i | \(-0.703417\pi\) | ||||
−0.596435 | + | 0.802661i | \(0.703417\pi\) | |||||||
\(234\) | 2.36001 | 0.154279 | ||||||||
\(235\) | 37.6876 | 2.45847 | ||||||||
\(236\) | 9.89885 | 0.644360 | ||||||||
\(237\) | 17.5021 | 1.13689 | ||||||||
\(238\) | 0.0780303 | 0.00505795 | ||||||||
\(239\) | −1.38867 | −0.0898254 | −0.0449127 | − | 0.998991i | \(-0.514301\pi\) | ||||
−0.0449127 | + | 0.998991i | \(0.514301\pi\) | |||||||
\(240\) | 6.57409 | 0.424356 | ||||||||
\(241\) | 25.2339 | 1.62546 | 0.812729 | − | 0.582642i | \(-0.197981\pi\) | ||||
0.812729 | + | 0.582642i | \(0.197981\pi\) | |||||||
\(242\) | 4.61122 | 0.296420 | ||||||||
\(243\) | 6.48466 | 0.415991 | ||||||||
\(244\) | 4.83709 | 0.309663 | ||||||||
\(245\) | 22.9950 | 1.46909 | ||||||||
\(246\) | 12.0191 | 0.766309 | ||||||||
\(247\) | −25.2150 | −1.60439 | ||||||||
\(248\) | 3.48116 | 0.221054 | ||||||||
\(249\) | 25.6899 | 1.62803 | ||||||||
\(250\) | 6.52862 | 0.412906 | ||||||||
\(251\) | −12.5201 | −0.790263 | −0.395132 | − | 0.918624i | \(-0.629301\pi\) | ||||
−0.395132 | + | 0.918624i | \(0.629301\pi\) | |||||||
\(252\) | 0.365358 | 0.0230154 | ||||||||
\(253\) | −16.2314 | −1.02046 | ||||||||
\(254\) | 2.57457 | 0.161543 | ||||||||
\(255\) | −0.890068 | −0.0557382 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.3037 | −0.705103 | −0.352552 | − | 0.935792i | \(-0.614686\pi\) | ||||
−0.352552 | + | 0.935792i | \(0.614686\pi\) | |||||||
\(258\) | −18.9554 | −1.18011 | ||||||||
\(259\) | −3.88197 | −0.241214 | ||||||||
\(260\) | 12.8386 | 0.796219 | ||||||||
\(261\) | 2.30850 | 0.142892 | ||||||||
\(262\) | 13.0315 | 0.805089 | ||||||||
\(263\) | −1.84795 | −0.113949 | −0.0569747 | − | 0.998376i | \(-0.518145\pi\) | ||||
−0.0569747 | + | 0.998376i | \(0.518145\pi\) | |||||||
\(264\) | −4.81834 | −0.296548 | ||||||||
\(265\) | −24.8745 | −1.52803 | ||||||||
\(266\) | −3.90359 | −0.239344 | ||||||||
\(267\) | 18.4237 | 1.12751 | ||||||||
\(268\) | −8.17945 | −0.499639 | ||||||||
\(269\) | −29.0587 | −1.77174 | −0.885870 | − | 0.463934i | \(-0.846437\pi\) | ||||
−0.885870 | + | 0.463934i | \(0.846437\pi\) | |||||||
\(270\) | 15.5548 | 0.946632 | ||||||||
\(271\) | −31.2094 | −1.89584 | −0.947918 | − | 0.318516i | \(-0.896816\pi\) | ||||
−0.947918 | + | 0.318516i | \(0.896816\pi\) | |||||||
\(272\) | −0.135390 | −0.00820923 | ||||||||
\(273\) | 4.09012 | 0.247545 | ||||||||
\(274\) | 22.6525 | 1.36849 | ||||||||
\(275\) | −17.4230 | −1.05065 | ||||||||
\(276\) | −12.2415 | −0.736851 | ||||||||
\(277\) | 0.532600 | 0.0320008 | 0.0160004 | − | 0.999872i | \(-0.494907\pi\) | ||||
0.0160004 | + | 0.999872i | \(0.494907\pi\) | |||||||
\(278\) | 1.66687 | 0.0999723 | ||||||||
\(279\) | −2.20682 | −0.132119 | ||||||||
\(280\) | 1.98758 | 0.118780 | ||||||||
\(281\) | 7.65267 | 0.456520 | 0.228260 | − | 0.973600i | \(-0.426696\pi\) | ||||
0.228260 | + | 0.973600i | \(0.426696\pi\) | |||||||
\(282\) | −20.8324 | −1.24055 | ||||||||
\(283\) | 14.6537 | 0.871072 | 0.435536 | − | 0.900171i | \(-0.356559\pi\) | ||||
0.435536 | + | 0.900171i | \(0.356559\pi\) | |||||||
\(284\) | −6.36792 | −0.377867 | ||||||||
\(285\) | 44.5270 | 2.63755 | ||||||||
\(286\) | −9.40981 | −0.556414 | ||||||||
\(287\) | 3.63379 | 0.214496 | ||||||||
\(288\) | −0.633932 | −0.0373548 | ||||||||
\(289\) | −16.9817 | −0.998922 | ||||||||
\(290\) | 12.5584 | 0.737455 | ||||||||
\(291\) | −16.3034 | −0.955721 | ||||||||
\(292\) | −15.5985 | −0.912833 | ||||||||
\(293\) | −28.3990 | −1.65909 | −0.829543 | − | 0.558442i | \(-0.811399\pi\) | ||||
−0.829543 | + | 0.558442i | \(0.811399\pi\) | |||||||
\(294\) | −12.7108 | −0.741310 | ||||||||
\(295\) | −34.1375 | −1.98756 | ||||||||
\(296\) | 6.73560 | 0.391499 | ||||||||
\(297\) | −11.4005 | −0.661525 | ||||||||
\(298\) | −22.7885 | −1.32010 | ||||||||
\(299\) | −23.9066 | −1.38255 | ||||||||
\(300\) | −13.1402 | −0.758652 | ||||||||
\(301\) | −5.73086 | −0.330321 | ||||||||
\(302\) | −1.41340 | −0.0813320 | ||||||||
\(303\) | −27.2337 | −1.56454 | ||||||||
\(304\) | 6.77310 | 0.388464 | ||||||||
\(305\) | −16.6814 | −0.955173 | ||||||||
\(306\) | 0.0858281 | 0.00490647 | ||||||||
\(307\) | 14.7237 | 0.840326 | 0.420163 | − | 0.907449i | \(-0.361973\pi\) | ||||
0.420163 | + | 0.907449i | \(0.361973\pi\) | |||||||
\(308\) | −1.45675 | −0.0830061 | ||||||||
\(309\) | 9.41213 | 0.535438 | ||||||||
\(310\) | −12.0053 | −0.681853 | ||||||||
\(311\) | 7.71615 | 0.437543 | 0.218771 | − | 0.975776i | \(-0.429795\pi\) | ||||
0.218771 | + | 0.975776i | \(0.429795\pi\) | |||||||
\(312\) | −7.09676 | −0.401775 | ||||||||
\(313\) | −18.3358 | −1.03640 | −0.518201 | − | 0.855259i | \(-0.673398\pi\) | ||||
−0.518201 | + | 0.855259i | \(0.673398\pi\) | |||||||
\(314\) | −5.98332 | −0.337658 | ||||||||
\(315\) | −1.25999 | −0.0709922 | ||||||||
\(316\) | −9.18127 | −0.516487 | ||||||||
\(317\) | 23.1086 | 1.29791 | 0.648954 | − | 0.760827i | \(-0.275207\pi\) | ||||
0.648954 | + | 0.760827i | \(0.275207\pi\) | |||||||
\(318\) | 13.7498 | 0.771049 | ||||||||
\(319\) | −9.20441 | −0.515348 | ||||||||
\(320\) | −3.44864 | −0.192785 | ||||||||
\(321\) | −27.0236 | −1.50831 | ||||||||
\(322\) | −3.70103 | −0.206250 | ||||||||
\(323\) | −0.917011 | −0.0510239 | ||||||||
\(324\) | −10.4999 | −0.583329 | ||||||||
\(325\) | −25.6618 | −1.42346 | ||||||||
\(326\) | 6.36633 | 0.352599 | ||||||||
\(327\) | −2.90895 | −0.160865 | ||||||||
\(328\) | −6.30497 | −0.348134 | ||||||||
\(329\) | −6.29835 | −0.347239 | ||||||||
\(330\) | 16.6167 | 0.914720 | ||||||||
\(331\) | 26.9383 | 1.48067 | 0.740333 | − | 0.672241i | \(-0.234668\pi\) | ||||
0.740333 | + | 0.672241i | \(0.234668\pi\) | |||||||
\(332\) | −13.4764 | −0.739613 | ||||||||
\(333\) | −4.26991 | −0.233989 | ||||||||
\(334\) | −13.7345 | −0.751516 | ||||||||
\(335\) | 28.2079 | 1.54116 | ||||||||
\(336\) | −1.09866 | −0.0599370 | ||||||||
\(337\) | 31.6280 | 1.72289 | 0.861444 | − | 0.507853i | \(-0.169561\pi\) | ||||
0.861444 | + | 0.507853i | \(0.169561\pi\) | |||||||
\(338\) | −0.859371 | −0.0467436 | ||||||||
\(339\) | 18.0161 | 0.978500 | ||||||||
\(340\) | 0.466912 | 0.0253218 | ||||||||
\(341\) | 8.79900 | 0.476492 | ||||||||
\(342\) | −4.29368 | −0.232176 | ||||||||
\(343\) | −7.87727 | −0.425333 | ||||||||
\(344\) | 9.94360 | 0.536123 | ||||||||
\(345\) | 42.2165 | 2.27286 | ||||||||
\(346\) | −6.27011 | −0.337083 | ||||||||
\(347\) | 21.8096 | 1.17080 | 0.585399 | − | 0.810745i | \(-0.300938\pi\) | ||||
0.585399 | + | 0.810745i | \(0.300938\pi\) | |||||||
\(348\) | −6.94185 | −0.372122 | ||||||||
\(349\) | −22.8499 | −1.22313 | −0.611564 | − | 0.791195i | \(-0.709459\pi\) | ||||
−0.611564 | + | 0.791195i | \(0.709459\pi\) | |||||||
\(350\) | −3.97275 | −0.212352 | ||||||||
\(351\) | −16.7914 | −0.896260 | ||||||||
\(352\) | 2.52760 | 0.134722 | ||||||||
\(353\) | −1.94798 | −0.103680 | −0.0518402 | − | 0.998655i | \(-0.516509\pi\) | ||||
−0.0518402 | + | 0.998655i | \(0.516509\pi\) | |||||||
\(354\) | 18.8700 | 1.00293 | ||||||||
\(355\) | 21.9606 | 1.16555 | ||||||||
\(356\) | −9.66471 | −0.512229 | ||||||||
\(357\) | 0.148748 | 0.00787259 | ||||||||
\(358\) | 5.74419 | 0.303590 | ||||||||
\(359\) | 37.4144 | 1.97466 | 0.987328 | − | 0.158692i | \(-0.0507277\pi\) | ||||
0.987328 | + | 0.158692i | \(0.0507277\pi\) | |||||||
\(360\) | 2.18620 | 0.115223 | ||||||||
\(361\) | 26.8749 | 1.41447 | ||||||||
\(362\) | −0.803801 | −0.0422469 | ||||||||
\(363\) | 8.79030 | 0.461371 | ||||||||
\(364\) | −2.14560 | −0.112460 | ||||||||
\(365\) | 53.7936 | 2.81568 | ||||||||
\(366\) | 9.22089 | 0.481984 | ||||||||
\(367\) | −34.5696 | −1.80452 | −0.902259 | − | 0.431194i | \(-0.858093\pi\) | ||||
−0.902259 | + | 0.431194i | \(0.858093\pi\) | |||||||
\(368\) | 6.42164 | 0.334751 | ||||||||
\(369\) | 3.99692 | 0.208071 | ||||||||
\(370\) | −23.2286 | −1.20760 | ||||||||
\(371\) | 4.15703 | 0.215822 | ||||||||
\(372\) | 6.63609 | 0.344065 | ||||||||
\(373\) | −31.4079 | −1.62624 | −0.813120 | − | 0.582096i | \(-0.802233\pi\) | ||||
−0.813120 | + | 0.582096i | \(0.802233\pi\) | |||||||
\(374\) | −0.342213 | −0.0176954 | ||||||||
\(375\) | 12.4454 | 0.642679 | ||||||||
\(376\) | 10.9283 | 0.563582 | ||||||||
\(377\) | −13.5568 | −0.698213 | ||||||||
\(378\) | −2.59951 | −0.133704 | ||||||||
\(379\) | 6.35859 | 0.326619 | 0.163309 | − | 0.986575i | \(-0.447783\pi\) | ||||
0.163309 | + | 0.986575i | \(0.447783\pi\) | |||||||
\(380\) | −23.3580 | −1.19824 | ||||||||
\(381\) | 4.90788 | 0.251438 | ||||||||
\(382\) | −9.23399 | −0.472452 | ||||||||
\(383\) | 29.1724 | 1.49064 | 0.745320 | − | 0.666707i | \(-0.232297\pi\) | ||||
0.745320 | + | 0.666707i | \(0.232297\pi\) | |||||||
\(384\) | 1.90629 | 0.0972798 | ||||||||
\(385\) | 5.02381 | 0.256037 | ||||||||
\(386\) | −16.6869 | −0.849342 | ||||||||
\(387\) | −6.30356 | −0.320428 | ||||||||
\(388\) | 8.55243 | 0.434184 | ||||||||
\(389\) | −1.97966 | −0.100373 | −0.0501864 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501864 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(390\) | 24.4742 | 1.23930 | ||||||||
\(391\) | −0.869427 | −0.0439688 | ||||||||
\(392\) | 6.66784 | 0.336777 | ||||||||
\(393\) | 24.8418 | 1.25310 | ||||||||
\(394\) | −13.2031 | −0.665164 | ||||||||
\(395\) | 31.6629 | 1.59313 | ||||||||
\(396\) | −1.60233 | −0.0805200 | ||||||||
\(397\) | −9.74853 | −0.489265 | −0.244632 | − | 0.969616i | \(-0.578667\pi\) | ||||
−0.244632 | + | 0.969616i | \(0.578667\pi\) | |||||||
\(398\) | 14.2637 | 0.714974 | ||||||||
\(399\) | −7.44136 | −0.372534 | ||||||||
\(400\) | 6.89310 | 0.344655 | ||||||||
\(401\) | −18.9600 | −0.946819 | −0.473410 | − | 0.880842i | \(-0.656977\pi\) | ||||
−0.473410 | + | 0.880842i | \(0.656977\pi\) | |||||||
\(402\) | −15.5924 | −0.777677 | ||||||||
\(403\) | 12.9597 | 0.645570 | ||||||||
\(404\) | 14.2863 | 0.710768 | ||||||||
\(405\) | 36.2104 | 1.79931 | ||||||||
\(406\) | −2.09876 | −0.104160 | ||||||||
\(407\) | 17.0249 | 0.843894 | ||||||||
\(408\) | −0.258093 | −0.0127775 | ||||||||
\(409\) | 25.0401 | 1.23815 | 0.619076 | − | 0.785331i | \(-0.287507\pi\) | ||||
0.619076 | + | 0.785331i | \(0.287507\pi\) | |||||||
\(410\) | 21.7436 | 1.07384 | ||||||||
\(411\) | 43.1822 | 2.13002 | ||||||||
\(412\) | −4.93742 | −0.243249 | ||||||||
\(413\) | 5.70507 | 0.280728 | ||||||||
\(414\) | −4.07088 | −0.200073 | ||||||||
\(415\) | 46.4752 | 2.28138 | ||||||||
\(416\) | 3.72282 | 0.182526 | ||||||||
\(417\) | 3.17754 | 0.155605 | ||||||||
\(418\) | 17.1197 | 0.837353 | ||||||||
\(419\) | 30.8403 | 1.50665 | 0.753324 | − | 0.657650i | \(-0.228449\pi\) | ||||
0.753324 | + | 0.657650i | \(0.228449\pi\) | |||||||
\(420\) | 3.78889 | 0.184879 | ||||||||
\(421\) | −3.22509 | −0.157181 | −0.0785905 | − | 0.996907i | \(-0.525042\pi\) | ||||
−0.0785905 | + | 0.996907i | \(0.525042\pi\) | |||||||
\(422\) | 22.5826 | 1.09930 | ||||||||
\(423\) | −6.92776 | −0.336839 | ||||||||
\(424\) | −7.21285 | −0.350287 | ||||||||
\(425\) | −0.933258 | −0.0452697 | ||||||||
\(426\) | −12.1391 | −0.588141 | ||||||||
\(427\) | 2.78779 | 0.134911 | ||||||||
\(428\) | 14.1760 | 0.685225 | ||||||||
\(429\) | −17.9378 | −0.866045 | ||||||||
\(430\) | −34.2919 | −1.65370 | ||||||||
\(431\) | −19.5169 | −0.940095 | −0.470048 | − | 0.882641i | \(-0.655763\pi\) | ||||
−0.470048 | + | 0.882641i | \(0.655763\pi\) | |||||||
\(432\) | 4.51041 | 0.217007 | ||||||||
\(433\) | −20.0509 | −0.963584 | −0.481792 | − | 0.876286i | \(-0.660014\pi\) | ||||
−0.481792 | + | 0.876286i | \(0.660014\pi\) | |||||||
\(434\) | 2.00632 | 0.0963064 | ||||||||
\(435\) | 23.9399 | 1.14783 | ||||||||
\(436\) | 1.52598 | 0.0730810 | ||||||||
\(437\) | 43.4944 | 2.08062 | ||||||||
\(438\) | −29.7352 | −1.42080 | ||||||||
\(439\) | 6.16608 | 0.294291 | 0.147145 | − | 0.989115i | \(-0.452991\pi\) | ||||
0.147145 | + | 0.989115i | \(0.452991\pi\) | |||||||
\(440\) | −8.71679 | −0.415557 | ||||||||
\(441\) | −4.22695 | −0.201283 | ||||||||
\(442\) | −0.504033 | −0.0239744 | ||||||||
\(443\) | −32.8649 | −1.56146 | −0.780729 | − | 0.624869i | \(-0.785152\pi\) | ||||
−0.780729 | + | 0.624869i | \(0.785152\pi\) | |||||||
\(444\) | 12.8400 | 0.609359 | ||||||||
\(445\) | 33.3301 | 1.58000 | ||||||||
\(446\) | 4.37688 | 0.207251 | ||||||||
\(447\) | −43.4414 | −2.05471 | ||||||||
\(448\) | 0.576337 | 0.0272293 | ||||||||
\(449\) | 7.43141 | 0.350710 | 0.175355 | − | 0.984505i | \(-0.443893\pi\) | ||||
0.175355 | + | 0.984505i | \(0.443893\pi\) | |||||||
\(450\) | −4.36976 | −0.205992 | ||||||||
\(451\) | −15.9365 | −0.750419 | ||||||||
\(452\) | −9.45088 | −0.444532 | ||||||||
\(453\) | −2.69435 | −0.126591 | ||||||||
\(454\) | −9.73531 | −0.456901 | ||||||||
\(455\) | 7.39938 | 0.346888 | ||||||||
\(456\) | 12.9115 | 0.604635 | ||||||||
\(457\) | 10.0225 | 0.468830 | 0.234415 | − | 0.972137i | \(-0.424682\pi\) | ||||
0.234415 | + | 0.972137i | \(0.424682\pi\) | |||||||
\(458\) | 8.75050 | 0.408884 | ||||||||
\(459\) | −0.610665 | −0.0285034 | ||||||||
\(460\) | −22.1459 | −1.03256 | ||||||||
\(461\) | 20.9585 | 0.976134 | 0.488067 | − | 0.872806i | \(-0.337702\pi\) | ||||
0.488067 | + | 0.872806i | \(0.337702\pi\) | |||||||
\(462\) | −2.77699 | −0.129197 | ||||||||
\(463\) | 14.7467 | 0.685337 | 0.342669 | − | 0.939456i | \(-0.388669\pi\) | ||||
0.342669 | + | 0.939456i | \(0.388669\pi\) | |||||||
\(464\) | 3.64156 | 0.169055 | ||||||||
\(465\) | −22.8855 | −1.06129 | ||||||||
\(466\) | 18.2084 | 0.843486 | ||||||||
\(467\) | 15.5836 | 0.721125 | 0.360563 | − | 0.932735i | \(-0.382585\pi\) | ||||
0.360563 | + | 0.932735i | \(0.382585\pi\) | |||||||
\(468\) | −2.36001 | −0.109092 | ||||||||
\(469\) | −4.71411 | −0.217678 | ||||||||
\(470\) | −37.6876 | −1.73840 | ||||||||
\(471\) | −11.4059 | −0.525557 | ||||||||
\(472\) | −9.89885 | −0.455631 | ||||||||
\(473\) | 25.1335 | 1.15564 | ||||||||
\(474\) | −17.5021 | −0.803900 | ||||||||
\(475\) | 46.6877 | 2.14218 | ||||||||
\(476\) | −0.0780303 | −0.00357651 | ||||||||
\(477\) | 4.57245 | 0.209358 | ||||||||
\(478\) | 1.38867 | 0.0635161 | ||||||||
\(479\) | −17.5807 | −0.803285 | −0.401642 | − | 0.915797i | \(-0.631560\pi\) | ||||
−0.401642 | + | 0.915797i | \(0.631560\pi\) | |||||||
\(480\) | −6.57409 | −0.300065 | ||||||||
\(481\) | 25.0754 | 1.14334 | ||||||||
\(482\) | −25.2339 | −1.14937 | ||||||||
\(483\) | −7.05522 | −0.321024 | ||||||||
\(484\) | −4.61122 | −0.209601 | ||||||||
\(485\) | −29.4942 | −1.33926 | ||||||||
\(486\) | −6.48466 | −0.294150 | ||||||||
\(487\) | −29.7599 | −1.34855 | −0.674275 | − | 0.738481i | \(-0.735544\pi\) | ||||
−0.674275 | + | 0.738481i | \(0.735544\pi\) | |||||||
\(488\) | −4.83709 | −0.218965 | ||||||||
\(489\) | 12.1361 | 0.548812 | ||||||||
\(490\) | −22.9950 | −1.03881 | ||||||||
\(491\) | −16.2093 | −0.731515 | −0.365757 | − | 0.930710i | \(-0.619190\pi\) | ||||
−0.365757 | + | 0.930710i | \(0.619190\pi\) | |||||||
\(492\) | −12.0191 | −0.541862 | ||||||||
\(493\) | −0.493031 | −0.0222050 | ||||||||
\(494\) | 25.2150 | 1.13448 | ||||||||
\(495\) | 5.52585 | 0.248368 | ||||||||
\(496\) | −3.48116 | −0.156309 | ||||||||
\(497\) | −3.67007 | −0.164625 | ||||||||
\(498\) | −25.6899 | −1.15119 | ||||||||
\(499\) | −11.6837 | −0.523036 | −0.261518 | − | 0.965199i | \(-0.584223\pi\) | ||||
−0.261518 | + | 0.965199i | \(0.584223\pi\) | |||||||
\(500\) | −6.52862 | −0.291969 | ||||||||
\(501\) | −26.1818 | −1.16972 | ||||||||
\(502\) | 12.5201 | 0.558801 | ||||||||
\(503\) | 11.3788 | 0.507354 | 0.253677 | − | 0.967289i | \(-0.418360\pi\) | ||||
0.253677 | + | 0.967289i | \(0.418360\pi\) | |||||||
\(504\) | −0.365358 | −0.0162743 | ||||||||
\(505\) | −49.2682 | −2.19240 | ||||||||
\(506\) | 16.2314 | 0.721572 | ||||||||
\(507\) | −1.63821 | −0.0727554 | ||||||||
\(508\) | −2.57457 | −0.114228 | ||||||||
\(509\) | 35.1372 | 1.55743 | 0.778713 | − | 0.627380i | \(-0.215873\pi\) | ||||
0.778713 | + | 0.627380i | \(0.215873\pi\) | |||||||
\(510\) | 0.890068 | 0.0394129 | ||||||||
\(511\) | −8.98999 | −0.397694 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 30.5494 | 1.34879 | ||||||||
\(514\) | 11.3037 | 0.498583 | ||||||||
\(515\) | 17.0274 | 0.750315 | ||||||||
\(516\) | 18.9554 | 0.834463 | ||||||||
\(517\) | 27.6223 | 1.21483 | ||||||||
\(518\) | 3.88197 | 0.170564 | ||||||||
\(519\) | −11.9526 | −0.524663 | ||||||||
\(520\) | −12.8386 | −0.563012 | ||||||||
\(521\) | 12.1360 | 0.531687 | 0.265843 | − | 0.964016i | \(-0.414350\pi\) | ||||
0.265843 | + | 0.964016i | \(0.414350\pi\) | |||||||
\(522\) | −2.30850 | −0.101040 | ||||||||
\(523\) | 35.2299 | 1.54050 | 0.770248 | − | 0.637744i | \(-0.220132\pi\) | ||||
0.770248 | + | 0.637744i | \(0.220132\pi\) | |||||||
\(524\) | −13.0315 | −0.569284 | ||||||||
\(525\) | −7.57320 | −0.330521 | ||||||||
\(526\) | 1.84795 | 0.0805744 | ||||||||
\(527\) | 0.471315 | 0.0205308 | ||||||||
\(528\) | 4.81834 | 0.209691 | ||||||||
\(529\) | 18.2375 | 0.792934 | ||||||||
\(530\) | 24.8745 | 1.08048 | ||||||||
\(531\) | 6.27519 | 0.272320 | ||||||||
\(532\) | 3.90359 | 0.169242 | ||||||||
\(533\) | −23.4723 | −1.01670 | ||||||||
\(534\) | −18.4237 | −0.797272 | ||||||||
\(535\) | −48.8880 | −2.11361 | ||||||||
\(536\) | 8.17945 | 0.353298 | ||||||||
\(537\) | 10.9501 | 0.472531 | ||||||||
\(538\) | 29.0587 | 1.25281 | ||||||||
\(539\) | 16.8537 | 0.725938 | ||||||||
\(540\) | −15.5548 | −0.669370 | ||||||||
\(541\) | −4.01099 | −0.172446 | −0.0862229 | − | 0.996276i | \(-0.527480\pi\) | ||||
−0.0862229 | + | 0.996276i | \(0.527480\pi\) | |||||||
\(542\) | 31.2094 | 1.34056 | ||||||||
\(543\) | −1.53228 | −0.0657563 | ||||||||
\(544\) | 0.135390 | 0.00580481 | ||||||||
\(545\) | −5.26254 | −0.225422 | ||||||||
\(546\) | −4.09012 | −0.175041 | ||||||||
\(547\) | 17.6519 | 0.754741 | 0.377370 | − | 0.926062i | \(-0.376828\pi\) | ||||
0.377370 | + | 0.926062i | \(0.376828\pi\) | |||||||
\(548\) | −22.6525 | −0.967667 | ||||||||
\(549\) | 3.06639 | 0.130870 | ||||||||
\(550\) | 17.4230 | 0.742921 | ||||||||
\(551\) | 24.6646 | 1.05075 | ||||||||
\(552\) | 12.2415 | 0.521033 | ||||||||
\(553\) | −5.29150 | −0.225018 | ||||||||
\(554\) | −0.532600 | −0.0226280 | ||||||||
\(555\) | −44.2804 | −1.87960 | ||||||||
\(556\) | −1.66687 | −0.0706911 | ||||||||
\(557\) | −4.11543 | −0.174376 | −0.0871882 | − | 0.996192i | \(-0.527788\pi\) | ||||
−0.0871882 | + | 0.996192i | \(0.527788\pi\) | |||||||
\(558\) | 2.20682 | 0.0934220 | ||||||||
\(559\) | 37.0182 | 1.56570 | ||||||||
\(560\) | −1.98758 | −0.0839904 | ||||||||
\(561\) | −0.652356 | −0.0275425 | ||||||||
\(562\) | −7.65267 | −0.322808 | ||||||||
\(563\) | 17.6904 | 0.745561 | 0.372780 | − | 0.927920i | \(-0.378404\pi\) | ||||
0.372780 | + | 0.927920i | \(0.378404\pi\) | |||||||
\(564\) | 20.8324 | 0.877202 | ||||||||
\(565\) | 32.5927 | 1.37118 | ||||||||
\(566\) | −14.6537 | −0.615941 | ||||||||
\(567\) | −6.05149 | −0.254139 | ||||||||
\(568\) | 6.36792 | 0.267192 | ||||||||
\(569\) | 16.5578 | 0.694140 | 0.347070 | − | 0.937839i | \(-0.387177\pi\) | ||||
0.347070 | + | 0.937839i | \(0.387177\pi\) | |||||||
\(570\) | −44.5270 | −1.86503 | ||||||||
\(571\) | −37.2586 | −1.55922 | −0.779611 | − | 0.626264i | \(-0.784583\pi\) | ||||
−0.779611 | + | 0.626264i | \(0.784583\pi\) | |||||||
\(572\) | 9.40981 | 0.393444 | ||||||||
\(573\) | −17.6026 | −0.735361 | ||||||||
\(574\) | −3.63379 | −0.151671 | ||||||||
\(575\) | 44.2650 | 1.84598 | ||||||||
\(576\) | 0.633932 | 0.0264138 | ||||||||
\(577\) | 30.6031 | 1.27402 | 0.637012 | − | 0.770854i | \(-0.280170\pi\) | ||||
0.637012 | + | 0.770854i | \(0.280170\pi\) | |||||||
\(578\) | 16.9817 | 0.706344 | ||||||||
\(579\) | −31.8101 | −1.32198 | ||||||||
\(580\) | −12.5584 | −0.521459 | ||||||||
\(581\) | −7.76694 | −0.322227 | ||||||||
\(582\) | 16.3034 | 0.675797 | ||||||||
\(583\) | −18.2312 | −0.755061 | ||||||||
\(584\) | 15.5985 | 0.645470 | ||||||||
\(585\) | 8.13882 | 0.336499 | ||||||||
\(586\) | 28.3990 | 1.17315 | ||||||||
\(587\) | 9.23380 | 0.381120 | 0.190560 | − | 0.981676i | \(-0.438970\pi\) | ||||
0.190560 | + | 0.981676i | \(0.438970\pi\) | |||||||
\(588\) | 12.7108 | 0.524185 | ||||||||
\(589\) | −23.5783 | −0.971525 | ||||||||
\(590\) | 34.1375 | 1.40542 | ||||||||
\(591\) | −25.1690 | −1.03531 | ||||||||
\(592\) | −6.73560 | −0.276831 | ||||||||
\(593\) | −34.1880 | −1.40393 | −0.701966 | − | 0.712210i | \(-0.747694\pi\) | ||||
−0.701966 | + | 0.712210i | \(0.747694\pi\) | |||||||
\(594\) | 11.4005 | 0.467769 | ||||||||
\(595\) | 0.269098 | 0.0110320 | ||||||||
\(596\) | 22.7885 | 0.933453 | ||||||||
\(597\) | 27.1907 | 1.11284 | ||||||||
\(598\) | 23.9066 | 0.977614 | ||||||||
\(599\) | 30.1903 | 1.23354 | 0.616770 | − | 0.787143i | \(-0.288441\pi\) | ||||
0.616770 | + | 0.787143i | \(0.288441\pi\) | |||||||
\(600\) | 13.1402 | 0.536448 | ||||||||
\(601\) | 14.5291 | 0.592654 | 0.296327 | − | 0.955087i | \(-0.404238\pi\) | ||||
0.296327 | + | 0.955087i | \(0.404238\pi\) | |||||||
\(602\) | 5.73086 | 0.233572 | ||||||||
\(603\) | −5.18521 | −0.211158 | ||||||||
\(604\) | 1.41340 | 0.0575104 | ||||||||
\(605\) | 15.9024 | 0.646525 | ||||||||
\(606\) | 27.2337 | 1.10629 | ||||||||
\(607\) | 15.5597 | 0.631548 | 0.315774 | − | 0.948834i | \(-0.397736\pi\) | ||||
0.315774 | + | 0.948834i | \(0.397736\pi\) | |||||||
\(608\) | −6.77310 | −0.274686 | ||||||||
\(609\) | −4.00084 | −0.162122 | ||||||||
\(610\) | 16.6814 | 0.675410 | ||||||||
\(611\) | 40.6839 | 1.64589 | ||||||||
\(612\) | −0.0858281 | −0.00346940 | ||||||||
\(613\) | 6.46085 | 0.260951 | 0.130476 | − | 0.991452i | \(-0.458350\pi\) | ||||
0.130476 | + | 0.991452i | \(0.458350\pi\) | |||||||
\(614\) | −14.7237 | −0.594200 | ||||||||
\(615\) | 41.4495 | 1.67140 | ||||||||
\(616\) | 1.45675 | 0.0586942 | ||||||||
\(617\) | −26.6566 | −1.07315 | −0.536577 | − | 0.843851i | \(-0.680283\pi\) | ||||
−0.536577 | + | 0.843851i | \(0.680283\pi\) | |||||||
\(618\) | −9.41213 | −0.378611 | ||||||||
\(619\) | 28.2228 | 1.13437 | 0.567185 | − | 0.823591i | \(-0.308033\pi\) | ||||
0.567185 | + | 0.823591i | \(0.308033\pi\) | |||||||
\(620\) | 12.0053 | 0.482143 | ||||||||
\(621\) | 28.9642 | 1.16229 | ||||||||
\(622\) | −7.71615 | −0.309390 | ||||||||
\(623\) | −5.57013 | −0.223162 | ||||||||
\(624\) | 7.09676 | 0.284098 | ||||||||
\(625\) | −11.9507 | −0.478026 | ||||||||
\(626\) | 18.3358 | 0.732847 | ||||||||
\(627\) | 32.6351 | 1.30332 | ||||||||
\(628\) | 5.98332 | 0.238760 | ||||||||
\(629\) | 0.911933 | 0.0363612 | ||||||||
\(630\) | 1.25999 | 0.0501991 | ||||||||
\(631\) | −21.6497 | −0.861859 | −0.430929 | − | 0.902386i | \(-0.641814\pi\) | ||||
−0.430929 | + | 0.902386i | \(0.641814\pi\) | |||||||
\(632\) | 9.18127 | 0.365211 | ||||||||
\(633\) | 43.0489 | 1.71104 | ||||||||
\(634\) | −23.1086 | −0.917760 | ||||||||
\(635\) | 8.87877 | 0.352343 | ||||||||
\(636\) | −13.7498 | −0.545214 | ||||||||
\(637\) | 24.8231 | 0.983529 | ||||||||
\(638\) | 9.20441 | 0.364406 | ||||||||
\(639\) | −4.03683 | −0.159694 | ||||||||
\(640\) | 3.44864 | 0.136319 | ||||||||
\(641\) | −26.2100 | −1.03523 | −0.517616 | − | 0.855613i | \(-0.673180\pi\) | ||||
−0.517616 | + | 0.855613i | \(0.673180\pi\) | |||||||
\(642\) | 27.0236 | 1.06654 | ||||||||
\(643\) | 36.2107 | 1.42801 | 0.714005 | − | 0.700141i | \(-0.246879\pi\) | ||||
0.714005 | + | 0.700141i | \(0.246879\pi\) | |||||||
\(644\) | 3.70103 | 0.145841 | ||||||||
\(645\) | −65.3702 | −2.57395 | ||||||||
\(646\) | 0.917011 | 0.0360793 | ||||||||
\(647\) | −38.4441 | −1.51139 | −0.755697 | − | 0.654922i | \(-0.772702\pi\) | ||||
−0.755697 | + | 0.654922i | \(0.772702\pi\) | |||||||
\(648\) | 10.4999 | 0.412476 | ||||||||
\(649\) | −25.0204 | −0.982135 | ||||||||
\(650\) | 25.6618 | 1.00654 | ||||||||
\(651\) | 3.82462 | 0.149899 | ||||||||
\(652\) | −6.36633 | −0.249325 | ||||||||
\(653\) | −35.7652 | −1.39960 | −0.699800 | − | 0.714338i | \(-0.746728\pi\) | ||||
−0.699800 | + | 0.714338i | \(0.746728\pi\) | |||||||
\(654\) | 2.90895 | 0.113749 | ||||||||
\(655\) | 44.9410 | 1.75599 | ||||||||
\(656\) | 6.30497 | 0.246168 | ||||||||
\(657\) | −9.88838 | −0.385782 | ||||||||
\(658\) | 6.29835 | 0.245535 | ||||||||
\(659\) | −35.9164 | −1.39910 | −0.699551 | − | 0.714582i | \(-0.746617\pi\) | ||||
−0.699551 | + | 0.714582i | \(0.746617\pi\) | |||||||
\(660\) | −16.6167 | −0.646805 | ||||||||
\(661\) | 1.88757 | 0.0734179 | 0.0367089 | − | 0.999326i | \(-0.488313\pi\) | ||||
0.0367089 | + | 0.999326i | \(0.488313\pi\) | |||||||
\(662\) | −26.9383 | −1.04699 | ||||||||
\(663\) | −0.960832 | −0.0373156 | ||||||||
\(664\) | 13.4764 | 0.522986 | ||||||||
\(665\) | −13.4621 | −0.522036 | ||||||||
\(666\) | 4.26991 | 0.165456 | ||||||||
\(667\) | 23.3848 | 0.905462 | ||||||||
\(668\) | 13.7345 | 0.531402 | ||||||||
\(669\) | 8.34359 | 0.322582 | ||||||||
\(670\) | −28.2079 | −1.08977 | ||||||||
\(671\) | −12.2263 | −0.471990 | ||||||||
\(672\) | 1.09866 | 0.0423819 | ||||||||
\(673\) | 15.5489 | 0.599365 | 0.299683 | − | 0.954039i | \(-0.403119\pi\) | ||||
0.299683 | + | 0.954039i | \(0.403119\pi\) | |||||||
\(674\) | −31.6280 | −1.21827 | ||||||||
\(675\) | 31.0907 | 1.19668 | ||||||||
\(676\) | 0.859371 | 0.0330527 | ||||||||
\(677\) | −37.5728 | −1.44404 | −0.722021 | − | 0.691871i | \(-0.756786\pi\) | ||||
−0.722021 | + | 0.691871i | \(0.756786\pi\) | |||||||
\(678\) | −18.0161 | −0.691904 | ||||||||
\(679\) | 4.92908 | 0.189161 | ||||||||
\(680\) | −0.466912 | −0.0179052 | ||||||||
\(681\) | −18.5583 | −0.711156 | ||||||||
\(682\) | −8.79900 | −0.336931 | ||||||||
\(683\) | 19.2955 | 0.738322 | 0.369161 | − | 0.929365i | \(-0.379645\pi\) | ||||
0.369161 | + | 0.929365i | \(0.379645\pi\) | |||||||
\(684\) | 4.29368 | 0.164173 | ||||||||
\(685\) | 78.1203 | 2.98482 | ||||||||
\(686\) | 7.87727 | 0.300756 | ||||||||
\(687\) | 16.6810 | 0.636418 | ||||||||
\(688\) | −9.94360 | −0.379096 | ||||||||
\(689\) | −26.8521 | −1.02298 | ||||||||
\(690\) | −42.2165 | −1.60715 | ||||||||
\(691\) | 52.0548 | 1.98026 | 0.990129 | − | 0.140161i | \(-0.0447621\pi\) | ||||
0.990129 | + | 0.140161i | \(0.0447621\pi\) | |||||||
\(692\) | 6.27011 | 0.238354 | ||||||||
\(693\) | −0.923480 | −0.0350801 | ||||||||
\(694\) | −21.8096 | −0.827880 | ||||||||
\(695\) | 5.74844 | 0.218051 | ||||||||
\(696\) | 6.94185 | 0.263130 | ||||||||
\(697\) | −0.853631 | −0.0323336 | ||||||||
\(698\) | 22.8499 | 0.864882 | ||||||||
\(699\) | 34.7104 | 1.31287 | ||||||||
\(700\) | 3.97275 | 0.150156 | ||||||||
\(701\) | 36.1598 | 1.36574 | 0.682868 | − | 0.730541i | \(-0.260732\pi\) | ||||
0.682868 | + | 0.730541i | \(0.260732\pi\) | |||||||
\(702\) | 16.7914 | 0.633751 | ||||||||
\(703\) | −45.6209 | −1.72062 | ||||||||
\(704\) | −2.52760 | −0.0952627 | ||||||||
\(705\) | −71.8434 | −2.70578 | ||||||||
\(706\) | 1.94798 | 0.0733131 | ||||||||
\(707\) | 8.23370 | 0.309660 | ||||||||
\(708\) | −18.8700 | −0.709180 | ||||||||
\(709\) | 9.49204 | 0.356481 | 0.178240 | − | 0.983987i | \(-0.442960\pi\) | ||||
0.178240 | + | 0.983987i | \(0.442960\pi\) | |||||||
\(710\) | −21.9606 | −0.824168 | ||||||||
\(711\) | −5.82030 | −0.218278 | ||||||||
\(712\) | 9.66471 | 0.362200 | ||||||||
\(713\) | −22.3548 | −0.837193 | ||||||||
\(714\) | −0.148748 | −0.00556676 | ||||||||
\(715\) | −32.4510 | −1.21360 | ||||||||
\(716\) | −5.74419 | −0.214671 | ||||||||
\(717\) | 2.64720 | 0.0988614 | ||||||||
\(718\) | −37.4144 | −1.39629 | ||||||||
\(719\) | −13.8502 | −0.516526 | −0.258263 | − | 0.966075i | \(-0.583150\pi\) | ||||
−0.258263 | + | 0.966075i | \(0.583150\pi\) | |||||||
\(720\) | −2.18620 | −0.0814749 | ||||||||
\(721\) | −2.84561 | −0.105976 | ||||||||
\(722\) | −26.8749 | −1.00018 | ||||||||
\(723\) | −48.1030 | −1.78897 | ||||||||
\(724\) | 0.803801 | 0.0298730 | ||||||||
\(725\) | 25.1016 | 0.932250 | ||||||||
\(726\) | −8.79030 | −0.326239 | ||||||||
\(727\) | −23.7377 | −0.880382 | −0.440191 | − | 0.897904i | \(-0.645089\pi\) | ||||
−0.440191 | + | 0.897904i | \(0.645089\pi\) | |||||||
\(728\) | 2.14560 | 0.0795211 | ||||||||
\(729\) | 19.1382 | 0.708821 | ||||||||
\(730\) | −53.7936 | −1.99099 | ||||||||
\(731\) | 1.34627 | 0.0497934 | ||||||||
\(732\) | −9.22089 | −0.340814 | ||||||||
\(733\) | 12.1388 | 0.448358 | 0.224179 | − | 0.974548i | \(-0.428030\pi\) | ||||
0.224179 | + | 0.974548i | \(0.428030\pi\) | |||||||
\(734\) | 34.5696 | 1.27599 | ||||||||
\(735\) | −43.8350 | −1.61688 | ||||||||
\(736\) | −6.42164 | −0.236705 | ||||||||
\(737\) | 20.6744 | 0.761551 | ||||||||
\(738\) | −3.99692 | −0.147129 | ||||||||
\(739\) | 32.6045 | 1.19938 | 0.599689 | − | 0.800233i | \(-0.295291\pi\) | ||||
0.599689 | + | 0.800233i | \(0.295291\pi\) | |||||||
\(740\) | 23.2286 | 0.853901 | ||||||||
\(741\) | 48.0671 | 1.76579 | ||||||||
\(742\) | −4.15703 | −0.152609 | ||||||||
\(743\) | 39.2689 | 1.44064 | 0.720318 | − | 0.693644i | \(-0.243996\pi\) | ||||
0.720318 | + | 0.693644i | \(0.243996\pi\) | |||||||
\(744\) | −6.63609 | −0.243291 | ||||||||
\(745\) | −78.5893 | −2.87929 | ||||||||
\(746\) | 31.4079 | 1.14993 | ||||||||
\(747\) | −8.54311 | −0.312576 | ||||||||
\(748\) | 0.342213 | 0.0125125 | ||||||||
\(749\) | 8.17017 | 0.298532 | ||||||||
\(750\) | −12.4454 | −0.454443 | ||||||||
\(751\) | −20.7734 | −0.758031 | −0.379015 | − | 0.925390i | \(-0.623737\pi\) | ||||
−0.379015 | + | 0.925390i | \(0.623737\pi\) | |||||||
\(752\) | −10.9283 | −0.398512 | ||||||||
\(753\) | 23.8670 | 0.869760 | ||||||||
\(754\) | 13.5568 | 0.493711 | ||||||||
\(755\) | −4.87430 | −0.177394 | ||||||||
\(756\) | 2.59951 | 0.0945433 | ||||||||
\(757\) | 27.2570 | 0.990672 | 0.495336 | − | 0.868701i | \(-0.335045\pi\) | ||||
0.495336 | + | 0.868701i | \(0.335045\pi\) | |||||||
\(758\) | −6.35859 | −0.230954 | ||||||||
\(759\) | 30.9417 | 1.12311 | ||||||||
\(760\) | 23.3580 | 0.847283 | ||||||||
\(761\) | 52.8286 | 1.91504 | 0.957518 | − | 0.288373i | \(-0.0931142\pi\) | ||||
0.957518 | + | 0.288373i | \(0.0931142\pi\) | |||||||
\(762\) | −4.90788 | −0.177794 | ||||||||
\(763\) | 0.879476 | 0.0318392 | ||||||||
\(764\) | 9.23399 | 0.334074 | ||||||||
\(765\) | 0.295990 | 0.0107015 | ||||||||
\(766\) | −29.1724 | −1.05404 | ||||||||
\(767\) | −36.8516 | −1.33063 | ||||||||
\(768\) | −1.90629 | −0.0687872 | ||||||||
\(769\) | 36.6265 | 1.32078 | 0.660392 | − | 0.750921i | \(-0.270390\pi\) | ||||
0.660392 | + | 0.750921i | \(0.270390\pi\) | |||||||
\(770\) | −5.02381 | −0.181045 | ||||||||
\(771\) | 21.5480 | 0.776034 | ||||||||
\(772\) | 16.6869 | 0.600576 | ||||||||
\(773\) | −39.6994 | −1.42789 | −0.713944 | − | 0.700202i | \(-0.753093\pi\) | ||||
−0.713944 | + | 0.700202i | \(0.753093\pi\) | |||||||
\(774\) | 6.30356 | 0.226577 | ||||||||
\(775\) | −23.9960 | −0.861962 | ||||||||
\(776\) | −8.55243 | −0.307014 | ||||||||
\(777\) | 7.40015 | 0.265479 | ||||||||
\(778\) | 1.97966 | 0.0709744 | ||||||||
\(779\) | 42.7042 | 1.53004 | ||||||||
\(780\) | −24.4742 | −0.876315 | ||||||||
\(781\) | 16.0956 | 0.575945 | ||||||||
\(782\) | 0.869427 | 0.0310907 | ||||||||
\(783\) | 16.4249 | 0.586978 | ||||||||
\(784\) | −6.66784 | −0.238137 | ||||||||
\(785\) | −20.6343 | −0.736470 | ||||||||
\(786\) | −24.8418 | −0.886078 | ||||||||
\(787\) | 31.9123 | 1.13755 | 0.568775 | − | 0.822493i | \(-0.307417\pi\) | ||||
0.568775 | + | 0.822493i | \(0.307417\pi\) | |||||||
\(788\) | 13.2031 | 0.470342 | ||||||||
\(789\) | 3.52272 | 0.125412 | ||||||||
\(790\) | −31.6629 | −1.12652 | ||||||||
\(791\) | −5.44689 | −0.193669 | ||||||||
\(792\) | 1.60233 | 0.0569362 | ||||||||
\(793\) | −18.0076 | −0.639469 | ||||||||
\(794\) | 9.74853 | 0.345962 | ||||||||
\(795\) | 47.4180 | 1.68174 | ||||||||
\(796\) | −14.2637 | −0.505563 | ||||||||
\(797\) | −16.7485 | −0.593262 | −0.296631 | − | 0.954992i | \(-0.595863\pi\) | ||||
−0.296631 | + | 0.954992i | \(0.595863\pi\) | |||||||
\(798\) | 7.44136 | 0.263421 | ||||||||
\(799\) | 1.47958 | 0.0523437 | ||||||||
\(800\) | −6.89310 | −0.243708 | ||||||||
\(801\) | −6.12676 | −0.216479 | ||||||||
\(802\) | 18.9600 | 0.669502 | ||||||||
\(803\) | 39.4268 | 1.39134 | ||||||||
\(804\) | 15.5924 | 0.549901 | ||||||||
\(805\) | −12.7635 | −0.449854 | ||||||||
\(806\) | −12.9597 | −0.456487 | ||||||||
\(807\) | 55.3942 | 1.94997 | ||||||||
\(808\) | −14.2863 | −0.502589 | ||||||||
\(809\) | −21.8531 | −0.768314 | −0.384157 | − | 0.923268i | \(-0.625508\pi\) | ||||
−0.384157 | + | 0.923268i | \(0.625508\pi\) | |||||||
\(810\) | −36.2104 | −1.27231 | ||||||||
\(811\) | 21.7456 | 0.763591 | 0.381796 | − | 0.924247i | \(-0.375306\pi\) | ||||
0.381796 | + | 0.924247i | \(0.375306\pi\) | |||||||
\(812\) | 2.09876 | 0.0736521 | ||||||||
\(813\) | 59.4941 | 2.08655 | ||||||||
\(814\) | −17.0249 | −0.596723 | ||||||||
\(815\) | 21.9552 | 0.769056 | ||||||||
\(816\) | 0.258093 | 0.00903505 | ||||||||
\(817\) | −67.3490 | −2.35624 | ||||||||
\(818\) | −25.0401 | −0.875505 | ||||||||
\(819\) | −1.36016 | −0.0475279 | ||||||||
\(820\) | −21.7436 | −0.759318 | ||||||||
\(821\) | 5.37457 | 0.187574 | 0.0937869 | − | 0.995592i | \(-0.470103\pi\) | ||||
0.0937869 | + | 0.995592i | \(0.470103\pi\) | |||||||
\(822\) | −43.1822 | −1.50615 | ||||||||
\(823\) | −49.4288 | −1.72298 | −0.861489 | − | 0.507776i | \(-0.830468\pi\) | ||||
−0.861489 | + | 0.507776i | \(0.830468\pi\) | |||||||
\(824\) | 4.93742 | 0.172003 | ||||||||
\(825\) | 33.2133 | 1.15634 | ||||||||
\(826\) | −5.70507 | −0.198505 | ||||||||
\(827\) | 2.33601 | 0.0812311 | 0.0406156 | − | 0.999175i | \(-0.487068\pi\) | ||||
0.0406156 | + | 0.999175i | \(0.487068\pi\) | |||||||
\(828\) | 4.07088 | 0.141473 | ||||||||
\(829\) | −46.0698 | −1.60007 | −0.800035 | − | 0.599953i | \(-0.795186\pi\) | ||||
−0.800035 | + | 0.599953i | \(0.795186\pi\) | |||||||
\(830\) | −46.4752 | −1.61318 | ||||||||
\(831\) | −1.01529 | −0.0352200 | ||||||||
\(832\) | −3.72282 | −0.129065 | ||||||||
\(833\) | 0.902759 | 0.0312788 | ||||||||
\(834\) | −3.17754 | −0.110029 | ||||||||
\(835\) | −47.3652 | −1.63914 | ||||||||
\(836\) | −17.1197 | −0.592098 | ||||||||
\(837\) | −15.7014 | −0.542721 | ||||||||
\(838\) | −30.8403 | −1.06536 | ||||||||
\(839\) | −28.3472 | −0.978653 | −0.489327 | − | 0.872101i | \(-0.662757\pi\) | ||||
−0.489327 | + | 0.872101i | \(0.662757\pi\) | |||||||
\(840\) | −3.78889 | −0.130729 | ||||||||
\(841\) | −15.7391 | −0.542727 | ||||||||
\(842\) | 3.22509 | 0.111144 | ||||||||
\(843\) | −14.5882 | −0.502444 | ||||||||
\(844\) | −22.5826 | −0.777325 | ||||||||
\(845\) | −2.96366 | −0.101953 | ||||||||
\(846\) | 6.92776 | 0.238181 | ||||||||
\(847\) | −2.65761 | −0.0913167 | ||||||||
\(848\) | 7.21285 | 0.247690 | ||||||||
\(849\) | −27.9341 | −0.958698 | ||||||||
\(850\) | 0.933258 | 0.0320105 | ||||||||
\(851\) | −43.2536 | −1.48271 | ||||||||
\(852\) | 12.1391 | 0.415878 | ||||||||
\(853\) | −29.7236 | −1.01772 | −0.508858 | − | 0.860851i | \(-0.669932\pi\) | ||||
−0.508858 | + | 0.860851i | \(0.669932\pi\) | |||||||
\(854\) | −2.78779 | −0.0953964 | ||||||||
\(855\) | −14.8074 | −0.506401 | ||||||||
\(856\) | −14.1760 | −0.484527 | ||||||||
\(857\) | −39.5164 | −1.34985 | −0.674927 | − | 0.737884i | \(-0.735825\pi\) | ||||
−0.674927 | + | 0.737884i | \(0.735825\pi\) | |||||||
\(858\) | 17.9378 | 0.612386 | ||||||||
\(859\) | 42.8183 | 1.46094 | 0.730471 | − | 0.682944i | \(-0.239301\pi\) | ||||
0.730471 | + | 0.682944i | \(0.239301\pi\) | |||||||
\(860\) | 34.2919 | 1.16934 | ||||||||
\(861\) | −6.92704 | −0.236073 | ||||||||
\(862\) | 19.5169 | 0.664748 | ||||||||
\(863\) | 22.7744 | 0.775248 | 0.387624 | − | 0.921818i | \(-0.373296\pi\) | ||||
0.387624 | + | 0.921818i | \(0.373296\pi\) | |||||||
\(864\) | −4.51041 | −0.153447 | ||||||||
\(865\) | −21.6234 | −0.735216 | ||||||||
\(866\) | 20.0509 | 0.681357 | ||||||||
\(867\) | 32.3719 | 1.09941 | ||||||||
\(868\) | −2.00632 | −0.0680989 | ||||||||
\(869\) | 23.2066 | 0.787231 | ||||||||
\(870\) | −23.9399 | −0.811640 | ||||||||
\(871\) | 30.4506 | 1.03178 | ||||||||
\(872\) | −1.52598 | −0.0516761 | ||||||||
\(873\) | 5.42165 | 0.183495 | ||||||||
\(874\) | −43.4944 | −1.47122 | ||||||||
\(875\) | −3.76269 | −0.127202 | ||||||||
\(876\) | 29.7352 | 1.00466 | ||||||||
\(877\) | 17.2325 | 0.581901 | 0.290951 | − | 0.956738i | \(-0.406028\pi\) | ||||
0.290951 | + | 0.956738i | \(0.406028\pi\) | |||||||
\(878\) | −6.16608 | −0.208095 | ||||||||
\(879\) | 54.1366 | 1.82598 | ||||||||
\(880\) | 8.71679 | 0.293843 | ||||||||
\(881\) | 12.4888 | 0.420760 | 0.210380 | − | 0.977620i | \(-0.432530\pi\) | ||||
0.210380 | + | 0.977620i | \(0.432530\pi\) | |||||||
\(882\) | 4.22695 | 0.142329 | ||||||||
\(883\) | −12.8737 | −0.433234 | −0.216617 | − | 0.976257i | \(-0.569502\pi\) | ||||
−0.216617 | + | 0.976257i | \(0.569502\pi\) | |||||||
\(884\) | 0.504033 | 0.0169525 | ||||||||
\(885\) | 65.0760 | 2.18750 | ||||||||
\(886\) | 32.8649 | 1.10412 | ||||||||
\(887\) | −49.5840 | −1.66487 | −0.832434 | − | 0.554124i | \(-0.813053\pi\) | ||||
−0.832434 | + | 0.554124i | \(0.813053\pi\) | |||||||
\(888\) | −12.8400 | −0.430882 | ||||||||
\(889\) | −1.48382 | −0.0497658 | ||||||||
\(890\) | −33.3301 | −1.11723 | ||||||||
\(891\) | 26.5397 | 0.889112 | ||||||||
\(892\) | −4.37688 | −0.146549 | ||||||||
\(893\) | −74.0182 | −2.47692 | ||||||||
\(894\) | 43.4414 | 1.45290 | ||||||||
\(895\) | 19.8096 | 0.662163 | ||||||||
\(896\) | −0.576337 | −0.0192541 | ||||||||
\(897\) | 45.5729 | 1.52163 | ||||||||
\(898\) | −7.43141 | −0.247989 | ||||||||
\(899\) | −12.6768 | −0.422796 | ||||||||
\(900\) | 4.36976 | 0.145659 | ||||||||
\(901\) | −0.976549 | −0.0325336 | ||||||||
\(902\) | 15.9365 | 0.530626 | ||||||||
\(903\) | 10.9247 | 0.363550 | ||||||||
\(904\) | 9.45088 | 0.314331 | ||||||||
\(905\) | −2.77202 | −0.0921451 | ||||||||
\(906\) | 2.69435 | 0.0895137 | ||||||||
\(907\) | 14.9870 | 0.497635 | 0.248818 | − | 0.968550i | \(-0.419958\pi\) | ||||
0.248818 | + | 0.968550i | \(0.419958\pi\) | |||||||
\(908\) | 9.73531 | 0.323078 | ||||||||
\(909\) | 9.05651 | 0.300386 | ||||||||
\(910\) | −7.39938 | −0.245287 | ||||||||
\(911\) | 11.9578 | 0.396179 | 0.198090 | − | 0.980184i | \(-0.436526\pi\) | ||||
0.198090 | + | 0.980184i | \(0.436526\pi\) | |||||||
\(912\) | −12.9115 | −0.427542 | ||||||||
\(913\) | 34.0630 | 1.12732 | ||||||||
\(914\) | −10.0225 | −0.331513 | ||||||||
\(915\) | 31.7995 | 1.05126 | ||||||||
\(916\) | −8.75050 | −0.289125 | ||||||||
\(917\) | −7.51054 | −0.248020 | ||||||||
\(918\) | 0.610665 | 0.0201549 | ||||||||
\(919\) | 19.4404 | 0.641281 | 0.320640 | − | 0.947201i | \(-0.396102\pi\) | ||||
0.320640 | + | 0.947201i | \(0.396102\pi\) | |||||||
\(920\) | 22.1459 | 0.730129 | ||||||||
\(921\) | −28.0676 | −0.924859 | ||||||||
\(922\) | −20.9585 | −0.690231 | ||||||||
\(923\) | 23.7066 | 0.780312 | ||||||||
\(924\) | 2.77699 | 0.0913561 | ||||||||
\(925\) | −46.4292 | −1.52658 | ||||||||
\(926\) | −14.7467 | −0.484607 | ||||||||
\(927\) | −3.12998 | −0.102802 | ||||||||
\(928\) | −3.64156 | −0.119540 | ||||||||
\(929\) | 14.3654 | 0.471312 | 0.235656 | − | 0.971837i | \(-0.424276\pi\) | ||||
0.235656 | + | 0.971837i | \(0.424276\pi\) | |||||||
\(930\) | 22.8855 | 0.750444 | ||||||||
\(931\) | −45.1619 | −1.48012 | ||||||||
\(932\) | −18.2084 | −0.596435 | ||||||||
\(933\) | −14.7092 | −0.481558 | ||||||||
\(934\) | −15.5836 | −0.509913 | ||||||||
\(935\) | −1.18017 | −0.0385956 | ||||||||
\(936\) | 2.36001 | 0.0771394 | ||||||||
\(937\) | 19.2693 | 0.629502 | 0.314751 | − | 0.949174i | \(-0.398079\pi\) | ||||
0.314751 | + | 0.949174i | \(0.398079\pi\) | |||||||
\(938\) | 4.71411 | 0.153921 | ||||||||
\(939\) | 34.9533 | 1.14066 | ||||||||
\(940\) | 37.6876 | 1.22923 | ||||||||
\(941\) | −14.4648 | −0.471539 | −0.235769 | − | 0.971809i | \(-0.575761\pi\) | ||||
−0.235769 | + | 0.971809i | \(0.575761\pi\) | |||||||
\(942\) | 11.4059 | 0.371625 | ||||||||
\(943\) | 40.4883 | 1.31848 | ||||||||
\(944\) | 9.89885 | 0.322180 | ||||||||
\(945\) | −8.96478 | −0.291624 | ||||||||
\(946\) | −25.1335 | −0.817160 | ||||||||
\(947\) | 25.5035 | 0.828751 | 0.414376 | − | 0.910106i | \(-0.364000\pi\) | ||||
0.414376 | + | 0.910106i | \(0.364000\pi\) | |||||||
\(948\) | 17.5021 | 0.568443 | ||||||||
\(949\) | 58.0704 | 1.88504 | ||||||||
\(950\) | −46.6877 | −1.51475 | ||||||||
\(951\) | −44.0516 | −1.42847 | ||||||||
\(952\) | 0.0780303 | 0.00252898 | ||||||||
\(953\) | 2.16988 | 0.0702893 | 0.0351446 | − | 0.999382i | \(-0.488811\pi\) | ||||
0.0351446 | + | 0.999382i | \(0.488811\pi\) | |||||||
\(954\) | −4.57245 | −0.148039 | ||||||||
\(955\) | −31.8447 | −1.03047 | ||||||||
\(956\) | −1.38867 | −0.0449127 | ||||||||
\(957\) | 17.5463 | 0.567190 | ||||||||
\(958\) | 17.5807 | 0.568008 | ||||||||
\(959\) | −13.0555 | −0.421583 | ||||||||
\(960\) | 6.57409 | 0.212178 | ||||||||
\(961\) | −18.8815 | −0.609081 | ||||||||
\(962\) | −25.0754 | −0.808463 | ||||||||
\(963\) | 8.98664 | 0.289591 | ||||||||
\(964\) | 25.2339 | 0.812729 | ||||||||
\(965\) | −57.5472 | −1.85251 | ||||||||
\(966\) | 7.05522 | 0.226998 | ||||||||
\(967\) | −33.1569 | −1.06625 | −0.533127 | − | 0.846035i | \(-0.678983\pi\) | ||||
−0.533127 | + | 0.846035i | \(0.678983\pi\) | |||||||
\(968\) | 4.61122 | 0.148210 | ||||||||
\(969\) | 1.74809 | 0.0561567 | ||||||||
\(970\) | 29.4942 | 0.947003 | ||||||||
\(971\) | −4.59929 | −0.147598 | −0.0737992 | − | 0.997273i | \(-0.523512\pi\) | ||||
−0.0737992 | + | 0.997273i | \(0.523512\pi\) | |||||||
\(972\) | 6.48466 | 0.207995 | ||||||||
\(973\) | −0.960679 | −0.0307980 | ||||||||
\(974\) | 29.7599 | 0.953568 | ||||||||
\(975\) | 48.9187 | 1.56665 | ||||||||
\(976\) | 4.83709 | 0.154832 | ||||||||
\(977\) | 2.37261 | 0.0759067 | 0.0379533 | − | 0.999280i | \(-0.487916\pi\) | ||||
0.0379533 | + | 0.999280i | \(0.487916\pi\) | |||||||
\(978\) | −12.1361 | −0.388068 | ||||||||
\(979\) | 24.4286 | 0.780740 | ||||||||
\(980\) | 22.9950 | 0.734547 | ||||||||
\(981\) | 0.967364 | 0.0308856 | ||||||||
\(982\) | 16.2093 | 0.517259 | ||||||||
\(983\) | 12.2578 | 0.390963 | 0.195482 | − | 0.980707i | \(-0.437373\pi\) | ||||
0.195482 | + | 0.980707i | \(0.437373\pi\) | |||||||
\(984\) | 12.0191 | 0.383154 | ||||||||
\(985\) | −45.5328 | −1.45080 | ||||||||
\(986\) | 0.493031 | 0.0157013 | ||||||||
\(987\) | 12.0065 | 0.382170 | ||||||||
\(988\) | −25.2150 | −0.802197 | ||||||||
\(989\) | −63.8542 | −2.03045 | ||||||||
\(990\) | −5.52585 | −0.175623 | ||||||||
\(991\) | 45.5090 | 1.44564 | 0.722821 | − | 0.691035i | \(-0.242845\pi\) | ||||
0.722821 | + | 0.691035i | \(0.242845\pi\) | |||||||
\(992\) | 3.48116 | 0.110527 | ||||||||
\(993\) | −51.3522 | −1.62961 | ||||||||
\(994\) | 3.67007 | 0.116407 | ||||||||
\(995\) | 49.1903 | 1.55944 | ||||||||
\(996\) | 25.6899 | 0.814015 | ||||||||
\(997\) | 28.4724 | 0.901730 | 0.450865 | − | 0.892592i | \(-0.351115\pi\) | ||||
0.450865 | + | 0.892592i | \(0.351115\pi\) | |||||||
\(998\) | 11.6837 | 0.369842 | ||||||||
\(999\) | −30.3803 | −0.961189 |
(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 | 8026.2.a.c.1.18 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.c.1.18 | ✓ | 86 | 1.1 | even | 1 | trivial |