Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.11 | ||
Root | \(-0.519068 - 1.65244i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.d.881.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.152807 | + | 1.72530i | −0.0882230 | + | 0.996101i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.72530 | − | 0.152807i | −0.704350 | − | 0.0623831i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.95330 | − | 0.527274i | −0.984433 | − | 0.175758i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | − | 0.476459i | − | 0.143658i | −0.997417 | − | 0.0718290i | \(-0.977116\pi\) | ||
0.997417 | − | 0.0718290i | \(-0.0228836\pi\) | |||||||
\(12\) | 0.152807 | − | 1.72530i | 0.0441115 | − | 0.498050i | ||||
\(13\) | − | 4.96165i | − | 1.37611i | −0.725656 | − | 0.688057i | \(-0.758464\pi\) | ||
0.725656 | − | 0.688057i | \(-0.241536\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.152807 | + | 1.72530i | −0.0394545 | + | 0.445470i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.31590 | −1.28930 | −0.644648 | − | 0.764479i | \(-0.722996\pi\) | ||||
−0.644648 | + | 0.764479i | \(0.722996\pi\) | |||||||
\(18\) | 0.527274 | − | 2.95330i | 0.124280 | − | 0.696100i | ||||
\(19\) | − | 5.18049i | − | 1.18849i | −0.804286 | − | 0.594243i | \(-0.797452\pi\) | ||
0.804286 | − | 0.594243i | \(-0.202548\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.476459 | 0.101581 | ||||||||
\(23\) | − | 3.71381i | − | 0.774383i | −0.921999 | − | 0.387191i | \(-0.873445\pi\) | ||
0.921999 | − | 0.387191i | \(-0.126555\pi\) | |||||||
\(24\) | 1.72530 | + | 0.152807i | 0.352175 | + | 0.0311915i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.96165 | 0.973060 | ||||||||
\(27\) | 1.36099 | − | 5.01475i | 0.261922 | − | 0.965089i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.80278i | − | 0.891853i | −0.895070 | − | 0.445926i | \(-0.852874\pi\) | ||
0.895070 | − | 0.445926i | \(-0.147126\pi\) | |||||||
\(30\) | −1.72530 | − | 0.152807i | −0.314995 | − | 0.0278986i | ||||
\(31\) | 2.47917i | 0.445271i | 0.974902 | + | 0.222636i | \(0.0714660\pi\) | ||||
−0.974902 | + | 0.222636i | \(0.928534\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.822034 | + | 0.0728062i | 0.143098 | + | 0.0126739i | ||||
\(34\) | − | 5.31590i | − | 0.911670i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.95330 | + | 0.527274i | 0.492217 | + | 0.0878790i | ||||
\(37\) | 2.38410 | 0.391943 | 0.195972 | − | 0.980610i | \(-0.437214\pi\) | ||||
0.195972 | + | 0.980610i | \(0.437214\pi\) | |||||||
\(38\) | 5.18049 | 0.840386 | ||||||||
\(39\) | 8.56033 | + | 0.758174i | 1.37075 | + | 0.121405i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | −11.4897 | −1.79439 | −0.897194 | − | 0.441636i | \(-0.854398\pi\) | ||||
−0.897194 | + | 0.441636i | \(0.854398\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.38323 | 0.210940 | 0.105470 | − | 0.994422i | \(-0.466365\pi\) | ||||
0.105470 | + | 0.994422i | \(0.466365\pi\) | |||||||
\(44\) | 0.476459i | 0.0718290i | ||||||||
\(45\) | −2.95330 | − | 0.527274i | −0.440252 | − | 0.0786013i | ||||
\(46\) | 3.71381 | 0.547571 | ||||||||
\(47\) | −11.8319 | −1.72585 | −0.862927 | − | 0.505329i | \(-0.831371\pi\) | ||||
−0.862927 | + | 0.505329i | \(0.831371\pi\) | |||||||
\(48\) | −0.152807 | + | 1.72530i | −0.0220557 | + | 0.249025i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 0.812306 | − | 9.17151i | 0.113746 | − | 1.28427i | ||||
\(52\) | 4.96165i | 0.688057i | ||||||||
\(53\) | 0.305714i | 0.0419931i | 0.999780 | + | 0.0209965i | \(0.00668390\pi\) | ||||
−0.999780 | + | 0.0209965i | \(0.993316\pi\) | |||||||
\(54\) | 5.01475 | + | 1.36099i | 0.682421 | + | 0.185207i | ||||
\(55\) | − | 0.476459i | − | 0.0642458i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.93788 | + | 0.791613i | 1.18385 | + | 0.104852i | ||||
\(58\) | 4.80278 | 0.630635 | ||||||||
\(59\) | 0.441038 | 0.0574182 | 0.0287091 | − | 0.999588i | \(-0.490860\pi\) | ||||
0.0287091 | + | 0.999588i | \(0.490860\pi\) | |||||||
\(60\) | 0.152807 | − | 1.72530i | 0.0197273 | − | 0.222735i | ||||
\(61\) | − | 12.2202i | − | 1.56463i | −0.622881 | − | 0.782317i | \(-0.714038\pi\) | ||
0.622881 | − | 0.782317i | \(-0.285962\pi\) | |||||||
\(62\) | −2.47917 | −0.314854 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 4.96165i | − | 0.615417i | ||||||
\(66\) | −0.0728062 | + | 0.822034i | −0.00896182 | + | 0.101185i | ||||
\(67\) | 3.11989 | 0.381155 | 0.190577 | − | 0.981672i | \(-0.438964\pi\) | ||||
0.190577 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(68\) | 5.31590 | 0.644648 | ||||||||
\(69\) | 6.40743 | + | 0.567495i | 0.771363 | + | 0.0683184i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.78061i | − | 1.04207i | −0.853536 | − | 0.521033i | \(-0.825547\pi\) | ||
0.853536 | − | 0.521033i | \(-0.174453\pi\) | |||||||
\(72\) | −0.527274 | + | 2.95330i | −0.0621398 | + | 0.348050i | ||||
\(73\) | 15.0920i | 1.76639i | 0.469009 | + | 0.883193i | \(0.344611\pi\) | ||||
−0.469009 | + | 0.883193i | \(0.655389\pi\) | |||||||
\(74\) | 2.38410i | 0.277146i | ||||||||
\(75\) | −0.152807 | + | 1.72530i | −0.0176446 | + | 0.199220i | ||||
\(76\) | 5.18049i | 0.594243i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.758174 | + | 8.56033i | −0.0858463 | + | 0.969266i | ||||
\(79\) | 1.77425 | 0.199618 | 0.0998091 | − | 0.995007i | \(-0.468177\pi\) | ||||
0.0998091 | + | 0.995007i | \(0.468177\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.44396 | + | 3.11440i | 0.938218 | + | 0.346044i | ||||
\(82\) | − | 11.4897i | − | 1.26882i | ||||||
\(83\) | 14.2002 | 1.55867 | 0.779335 | − | 0.626607i | \(-0.215557\pi\) | ||||
0.779335 | + | 0.626607i | \(0.215557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.31590 | −0.576591 | ||||||||
\(86\) | 1.38323i | 0.149157i | ||||||||
\(87\) | 8.28621 | + | 0.733896i | 0.888375 | + | 0.0786819i | ||||
\(88\) | −0.476459 | −0.0507907 | ||||||||
\(89\) | −5.22255 | −0.553590 | −0.276795 | − | 0.960929i | \(-0.589272\pi\) | ||||
−0.276795 | + | 0.960929i | \(0.589272\pi\) | |||||||
\(90\) | 0.527274 | − | 2.95330i | 0.0555795 | − | 0.311305i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.71381i | 0.387191i | ||||||||
\(93\) | −4.27730 | − | 0.378833i | −0.443535 | − | 0.0392832i | ||||
\(94\) | − | 11.8319i | − | 1.22036i | ||||||
\(95\) | − | 5.18049i | − | 0.531507i | ||||||
\(96\) | −1.72530 | − | 0.152807i | −0.176087 | − | 0.0155958i | ||||
\(97\) | 8.50932i | 0.863991i | 0.901876 | + | 0.431995i | \(0.142190\pi\) | ||||
−0.901876 | + | 0.431995i | \(0.857810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.251225 | + | 1.40713i | −0.0252490 | + | 0.141422i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −16.8555 | −1.67719 | −0.838593 | − | 0.544759i | \(-0.816621\pi\) | ||||
−0.838593 | + | 0.544759i | \(0.816621\pi\) | |||||||
\(102\) | 9.17151 | + | 0.812306i | 0.908115 | + | 0.0804302i | ||||
\(103\) | − | 8.84632i | − | 0.871654i | −0.900030 | − | 0.435827i | \(-0.856456\pi\) | ||
0.900030 | − | 0.435827i | \(-0.143544\pi\) | |||||||
\(104\) | −4.96165 | −0.486530 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.305714 | −0.0296936 | ||||||||
\(107\) | 12.0789i | 1.16771i | 0.811859 | + | 0.583853i | \(0.198456\pi\) | ||||
−0.811859 | + | 0.583853i | \(0.801544\pi\) | |||||||
\(108\) | −1.36099 | + | 5.01475i | −0.130961 | + | 0.482544i | ||||
\(109\) | 17.0390 | 1.63204 | 0.816021 | − | 0.578023i | \(-0.196176\pi\) | ||||
0.816021 | + | 0.578023i | \(0.196176\pi\) | |||||||
\(110\) | 0.476459 | 0.0454286 | ||||||||
\(111\) | −0.364306 | + | 4.11328i | −0.0345784 | + | 0.390415i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.63769i | 0.530349i | 0.964200 | + | 0.265175i | \(0.0854296\pi\) | ||||
−0.964200 | + | 0.265175i | \(0.914570\pi\) | |||||||
\(114\) | −0.791613 | + | 8.93788i | −0.0741414 | + | 0.837110i | ||||
\(115\) | − | 3.71381i | − | 0.346315i | ||||||
\(116\) | 4.80278i | 0.445926i | ||||||||
\(117\) | −2.61615 | + | 14.6533i | −0.241863 | + | 1.35469i | ||||
\(118\) | 0.441038i | 0.0406008i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.72530 | + | 0.152807i | 0.157497 | + | 0.0139493i | ||||
\(121\) | 10.7730 | 0.979362 | ||||||||
\(122\) | 12.2202 | 1.10636 | ||||||||
\(123\) | 1.75570 | − | 19.8231i | 0.158306 | − | 1.78739i | ||||
\(124\) | − | 2.47917i | − | 0.222636i | ||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.02146 | −0.711789 | −0.355895 | − | 0.934526i | \(-0.615824\pi\) | ||||
−0.355895 | + | 0.934526i | \(0.615824\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −0.211366 | + | 2.38648i | −0.0186098 | + | 0.210118i | ||||
\(130\) | 4.96165 | 0.435166 | ||||||||
\(131\) | −0.177016 | −0.0154660 | −0.00773298 | − | 0.999970i | \(-0.502462\pi\) | ||||
−0.00773298 | + | 0.999970i | \(0.502462\pi\) | |||||||
\(132\) | −0.822034 | − | 0.0728062i | −0.0715489 | − | 0.00633696i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.11989i | 0.269517i | ||||||||
\(135\) | 1.36099 | − | 5.01475i | 0.117135 | − | 0.431601i | ||||
\(136\) | 5.31590i | 0.455835i | ||||||||
\(137\) | 17.5798i | 1.50194i | 0.660334 | + | 0.750972i | \(0.270415\pi\) | ||||
−0.660334 | + | 0.750972i | \(0.729585\pi\) | |||||||
\(138\) | −0.567495 | + | 6.40743i | −0.0483084 | + | 0.545436i | ||||
\(139\) | − | 10.6911i | − | 0.906811i | −0.891304 | − | 0.453406i | \(-0.850209\pi\) | ||
0.891304 | − | 0.453406i | \(-0.149791\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.80799 | − | 20.4135i | 0.152260 | − | 1.71912i | ||||
\(142\) | 8.78061 | 0.736853 | ||||||||
\(143\) | −2.36403 | −0.197690 | ||||||||
\(144\) | −2.95330 | − | 0.527274i | −0.246108 | − | 0.0439395i | ||||
\(145\) | − | 4.80278i | − | 0.398849i | ||||||
\(146\) | −15.0920 | −1.24902 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.38410 | −0.195972 | ||||||||
\(149\) | 18.1696i | 1.48851i | 0.667895 | + | 0.744256i | \(0.267196\pi\) | ||||
−0.667895 | + | 0.744256i | \(0.732804\pi\) | |||||||
\(150\) | −1.72530 | − | 0.152807i | −0.140870 | − | 0.0124766i | ||||
\(151\) | −18.2521 | −1.48533 | −0.742665 | − | 0.669663i | \(-0.766439\pi\) | ||||
−0.742665 | + | 0.669663i | \(0.766439\pi\) | |||||||
\(152\) | −5.18049 | −0.420193 | ||||||||
\(153\) | 15.6995 | + | 2.80294i | 1.26923 | + | 0.226604i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.47917i | 0.199131i | ||||||||
\(156\) | −8.56033 | − | 0.758174i | −0.685375 | − | 0.0607025i | ||||
\(157\) | − | 4.46872i | − | 0.356643i | −0.983972 | − | 0.178321i | \(-0.942933\pi\) | ||
0.983972 | − | 0.178321i | \(-0.0570666\pi\) | |||||||
\(158\) | 1.77425i | 0.141151i | ||||||||
\(159\) | −0.527448 | − | 0.0467152i | −0.0418293 | − | 0.00370475i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.11440 | + | 8.44396i | −0.244690 | + | 0.663421i | ||||
\(163\) | 20.9070 | 1.63756 | 0.818780 | − | 0.574107i | \(-0.194651\pi\) | ||||
0.818780 | + | 0.574107i | \(0.194651\pi\) | |||||||
\(164\) | 11.4897 | 0.897194 | ||||||||
\(165\) | 0.822034 | + | 0.0728062i | 0.0639953 | + | 0.00566795i | ||||
\(166\) | 14.2002i | 1.10215i | ||||||||
\(167\) | 8.40082 | 0.650075 | 0.325038 | − | 0.945701i | \(-0.394623\pi\) | ||||
0.325038 | + | 0.945701i | \(0.394623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6180 | −0.893692 | ||||||||
\(170\) | − | 5.31590i | − | 0.407711i | ||||||
\(171\) | −2.73154 | + | 15.2995i | −0.208886 | + | 1.16999i | ||||
\(172\) | −1.38323 | −0.105470 | ||||||||
\(173\) | 4.69254 | 0.356767 | 0.178383 | − | 0.983961i | \(-0.442913\pi\) | ||||
0.178383 | + | 0.983961i | \(0.442913\pi\) | |||||||
\(174\) | −0.733896 | + | 8.28621i | −0.0556365 | + | 0.628176i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.476459i | − | 0.0359145i | ||||||
\(177\) | −0.0673935 | + | 0.760921i | −0.00506561 | + | 0.0571943i | ||||
\(178\) | − | 5.22255i | − | 0.391447i | ||||||
\(179\) | − | 21.6928i | − | 1.62140i | −0.585462 | − | 0.810700i | \(-0.699087\pi\) | ||
0.585462 | − | 0.810700i | \(-0.300913\pi\) | |||||||
\(180\) | 2.95330 | + | 0.527274i | 0.220126 | + | 0.0393007i | ||||
\(181\) | − | 8.38421i | − | 0.623193i | −0.950214 | − | 0.311597i | \(-0.899136\pi\) | ||
0.950214 | − | 0.311597i | \(-0.100864\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.0834 | + | 1.86732i | 1.55853 | + | 0.138037i | ||||
\(184\) | −3.71381 | −0.273786 | ||||||||
\(185\) | 2.38410 | 0.175282 | ||||||||
\(186\) | 0.378833 | − | 4.27730i | 0.0277774 | − | 0.313627i | ||||
\(187\) | 2.53281i | 0.185218i | ||||||||
\(188\) | 11.8319 | 0.862927 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.18049 | 0.375832 | ||||||||
\(191\) | 8.58536i | 0.621215i | 0.950538 | + | 0.310607i | \(0.100532\pi\) | ||||
−0.950538 | + | 0.310607i | \(0.899468\pi\) | |||||||
\(192\) | 0.152807 | − | 1.72530i | 0.0110279 | − | 0.124513i | ||||
\(193\) | −11.9098 | −0.857289 | −0.428644 | − | 0.903473i | \(-0.641009\pi\) | ||||
−0.428644 | + | 0.903473i | \(0.641009\pi\) | |||||||
\(194\) | −8.50932 | −0.610934 | ||||||||
\(195\) | 8.56033 | + | 0.758174i | 0.613018 | + | 0.0542939i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0983i | − | 1.28945i | −0.764413 | − | 0.644726i | \(-0.776971\pi\) | ||
0.764413 | − | 0.644726i | \(-0.223029\pi\) | |||||||
\(198\) | −1.40713 | − | 0.251225i | −0.100000 | − | 0.0178538i | ||||
\(199\) | − | 10.6113i | − | 0.752218i | −0.926575 | − | 0.376109i | \(-0.877262\pi\) | ||
0.926575 | − | 0.376109i | \(-0.122738\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | −0.476740 | + | 5.38273i | −0.0336266 | + | 0.379669i | ||||
\(202\) | − | 16.8555i | − | 1.18595i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.812306 | + | 9.17151i | −0.0568728 | + | 0.642134i | ||||
\(205\) | −11.4897 | −0.802475 | ||||||||
\(206\) | 8.84632 | 0.616353 | ||||||||
\(207\) | −1.95819 | + | 10.9680i | −0.136104 | + | 0.762328i | ||||
\(208\) | − | 4.96165i | − | 0.344029i | ||||||
\(209\) | −2.46829 | −0.170735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8286 | −0.952000 | −0.476000 | − | 0.879445i | \(-0.657914\pi\) | ||||
−0.476000 | + | 0.879445i | \(0.657914\pi\) | |||||||
\(212\) | − | 0.305714i | − | 0.0209965i | ||||||
\(213\) | 15.1492 | + | 1.34174i | 1.03800 | + | 0.0919342i | ||||
\(214\) | −12.0789 | −0.825693 | ||||||||
\(215\) | 1.38323 | 0.0943353 | ||||||||
\(216\) | −5.01475 | − | 1.36099i | −0.341210 | − | 0.0926035i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.0390i | 1.15403i | ||||||||
\(219\) | −26.0382 | − | 2.30616i | −1.75950 | − | 0.155836i | ||||
\(220\) | 0.476459i | 0.0321229i | ||||||||
\(221\) | 26.3757i | 1.77422i | ||||||||
\(222\) | −4.11328 | − | 0.364306i | −0.276065 | − | 0.0244506i | ||||
\(223\) | − | 1.39419i | − | 0.0933618i | −0.998910 | − | 0.0466809i | \(-0.985136\pi\) | ||
0.998910 | − | 0.0466809i | \(-0.0148644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.95330 | − | 0.527274i | −0.196887 | − | 0.0351516i | ||||
\(226\) | −5.63769 | −0.375014 | ||||||||
\(227\) | −4.57266 | −0.303498 | −0.151749 | − | 0.988419i | \(-0.548491\pi\) | ||||
−0.151749 | + | 0.988419i | \(0.548491\pi\) | |||||||
\(228\) | −8.93788 | − | 0.791613i | −0.591926 | − | 0.0524259i | ||||
\(229\) | 3.35629i | 0.221790i | 0.993832 | + | 0.110895i | \(0.0353717\pi\) | ||||
−0.993832 | + | 0.110895i | \(0.964628\pi\) | |||||||
\(230\) | 3.71381 | 0.244881 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.80278 | −0.315318 | ||||||||
\(233\) | − | 8.18807i | − | 0.536418i | −0.963361 | − | 0.268209i | \(-0.913568\pi\) | ||
0.963361 | − | 0.268209i | \(-0.0864318\pi\) | |||||||
\(234\) | −14.6533 | − | 2.61615i | −0.957913 | − | 0.171023i | ||||
\(235\) | −11.8319 | −0.771825 | ||||||||
\(236\) | −0.441038 | −0.0287091 | ||||||||
\(237\) | −0.271117 | + | 3.06110i | −0.0176109 | + | 0.198840i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 14.1670i | − | 0.916387i | −0.888853 | − | 0.458193i | \(-0.848497\pi\) | ||
0.888853 | − | 0.458193i | \(-0.151503\pi\) | |||||||
\(240\) | −0.152807 | + | 1.72530i | −0.00986363 | + | 0.111367i | ||||
\(241\) | − | 17.2184i | − | 1.10914i | −0.832139 | − | 0.554568i | \(-0.812884\pi\) | ||
0.832139 | − | 0.554568i | \(-0.187116\pi\) | |||||||
\(242\) | 10.7730i | 0.692514i | ||||||||
\(243\) | −6.66355 | + | 14.0924i | −0.427467 | + | 0.904031i | ||||
\(244\) | 12.2202i | 0.782317i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.8231 | + | 1.75570i | 1.26388 | + | 0.111939i | ||||
\(247\) | −25.7038 | −1.63549 | ||||||||
\(248\) | 2.47917 | 0.157427 | ||||||||
\(249\) | −2.16988 | + | 24.4995i | −0.137511 | + | 1.55259i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −28.2916 | −1.78575 | −0.892875 | − | 0.450304i | \(-0.851316\pi\) | ||||
−0.892875 | + | 0.450304i | \(0.851316\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.76948 | −0.111246 | ||||||||
\(254\) | − | 8.02146i | − | 0.503311i | ||||||
\(255\) | 0.812306 | − | 9.17151i | 0.0508686 | − | 0.574342i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.66976 | 0.603183 | 0.301591 | − | 0.953437i | \(-0.402482\pi\) | ||||
0.301591 | + | 0.953437i | \(0.402482\pi\) | |||||||
\(258\) | −2.38648 | − | 0.211366i | −0.148576 | − | 0.0131591i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.96165i | 0.307709i | ||||||||
\(261\) | −2.53238 | + | 14.1840i | −0.156750 | + | 0.877970i | ||||
\(262\) | − | 0.177016i | − | 0.0109361i | ||||||
\(263\) | − | 28.8130i | − | 1.77668i | −0.459183 | − | 0.888342i | \(-0.651858\pi\) | ||
0.459183 | − | 0.888342i | \(-0.348142\pi\) | |||||||
\(264\) | 0.0728062 | − | 0.822034i | 0.00448091 | − | 0.0505927i | ||||
\(265\) | 0.305714i | 0.0187799i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.798041 | − | 9.01046i | 0.0488393 | − | 0.551431i | ||||
\(268\) | −3.11989 | −0.190577 | ||||||||
\(269\) | −8.09812 | −0.493751 | −0.246876 | − | 0.969047i | \(-0.579404\pi\) | ||||
−0.246876 | + | 0.969047i | \(0.579404\pi\) | |||||||
\(270\) | 5.01475 | + | 1.36099i | 0.305188 | + | 0.0828271i | ||||
\(271\) | − | 9.70895i | − | 0.589777i | −0.955532 | − | 0.294888i | \(-0.904718\pi\) | ||
0.955532 | − | 0.294888i | \(-0.0952825\pi\) | |||||||
\(272\) | −5.31590 | −0.322324 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.5798 | −1.06203 | ||||||||
\(275\) | − | 0.476459i | − | 0.0287316i | ||||||
\(276\) | −6.40743 | − | 0.567495i | −0.385682 | − | 0.0341592i | ||||
\(277\) | −30.2568 | −1.81795 | −0.908977 | − | 0.416846i | \(-0.863135\pi\) | ||||
−0.908977 | + | 0.416846i | \(0.863135\pi\) | |||||||
\(278\) | 10.6911 | 0.641212 | ||||||||
\(279\) | 1.30720 | − | 7.32172i | 0.0782600 | − | 0.438340i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.61243i | 0.454120i | 0.973881 | + | 0.227060i | \(0.0729113\pi\) | ||||
−0.973881 | + | 0.227060i | \(0.927089\pi\) | |||||||
\(282\) | 20.4135 | + | 1.80799i | 1.21560 | + | 0.107664i | ||||
\(283\) | − | 20.9933i | − | 1.24792i | −0.781456 | − | 0.623960i | \(-0.785523\pi\) | ||
0.781456 | − | 0.623960i | \(-0.214477\pi\) | |||||||
\(284\) | 8.78061i | 0.521033i | ||||||||
\(285\) | 8.93788 | + | 0.791613i | 0.529435 | + | 0.0468911i | ||||
\(286\) | − | 2.36403i | − | 0.139788i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.527274 | − | 2.95330i | 0.0310699 | − | 0.174025i | ||||
\(289\) | 11.2588 | 0.662285 | ||||||||
\(290\) | 4.80278 | 0.282029 | ||||||||
\(291\) | −14.6811 | − | 1.30028i | −0.860622 | − | 0.0762239i | ||||
\(292\) | − | 15.0920i | − | 0.883193i | ||||||
\(293\) | 30.8856 | 1.80435 | 0.902177 | − | 0.431365i | \(-0.141968\pi\) | ||||
0.902177 | + | 0.431365i | \(0.141968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.441038 | 0.0256782 | ||||||||
\(296\) | − | 2.38410i | − | 0.138573i | ||||||
\(297\) | −2.38932 | − | 0.648456i | −0.138643 | − | 0.0376272i | ||||
\(298\) | −18.1696 | −1.05254 | ||||||||
\(299\) | −18.4266 | −1.06564 | ||||||||
\(300\) | 0.152807 | − | 1.72530i | 0.00882230 | − | 0.0996101i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 18.2521i | − | 1.05029i | ||||||
\(303\) | 2.57563 | − | 29.0808i | 0.147966 | − | 1.67065i | ||||
\(304\) | − | 5.18049i | − | 0.297121i | ||||||
\(305\) | − | 12.2202i | − | 0.699725i | ||||||
\(306\) | −2.80294 | + | 15.6995i | −0.160233 | + | 0.897478i | ||||
\(307\) | 24.0737i | 1.37396i | 0.726678 | + | 0.686979i | \(0.241063\pi\) | ||||
−0.726678 | + | 0.686979i | \(0.758937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.2625 | + | 1.35178i | 0.868255 | + | 0.0768999i | ||||
\(310\) | −2.47917 | −0.140807 | ||||||||
\(311\) | 12.3799 | 0.702000 | 0.351000 | − | 0.936375i | \(-0.385842\pi\) | ||||
0.351000 | + | 0.936375i | \(0.385842\pi\) | |||||||
\(312\) | 0.758174 | − | 8.56033i | 0.0429231 | − | 0.484633i | ||||
\(313\) | 8.19263i | 0.463075i | 0.972826 | + | 0.231538i | \(0.0743756\pi\) | ||||
−0.972826 | + | 0.231538i | \(0.925624\pi\) | |||||||
\(314\) | 4.46872 | 0.252184 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.77425 | −0.0998091 | ||||||||
\(317\) | 6.33601i | 0.355866i | 0.984043 | + | 0.177933i | \(0.0569410\pi\) | ||||
−0.984043 | + | 0.177933i | \(0.943059\pi\) | |||||||
\(318\) | 0.0467152 | − | 0.527448i | 0.00261966 | − | 0.0295778i | ||||
\(319\) | −2.28833 | −0.128122 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −20.8396 | − | 1.84573i | −1.16315 | − | 0.103019i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.5390i | 1.53231i | ||||||||
\(324\) | −8.44396 | − | 3.11440i | −0.469109 | − | 0.173022i | ||||
\(325\) | − | 4.96165i | − | 0.275223i | ||||||
\(326\) | 20.9070i | 1.15793i | ||||||||
\(327\) | −2.60367 | + | 29.3974i | −0.143984 | + | 1.62568i | ||||
\(328\) | 11.4897i | 0.634412i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0728062 | + | 0.822034i | −0.00400785 | + | 0.0452515i | ||||
\(331\) | 15.6010 | 0.857508 | 0.428754 | − | 0.903421i | \(-0.358953\pi\) | ||||
0.428754 | + | 0.903421i | \(0.358953\pi\) | |||||||
\(332\) | −14.2002 | −0.779335 | ||||||||
\(333\) | −7.04096 | − | 1.25707i | −0.385842 | − | 0.0688872i | ||||
\(334\) | 8.40082i | 0.459673i | ||||||||
\(335\) | 3.11989 | 0.170458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.76611 | 0.150679 | 0.0753397 | − | 0.997158i | \(-0.475996\pi\) | ||||
0.0753397 | + | 0.997158i | \(0.475996\pi\) | |||||||
\(338\) | − | 11.6180i | − | 0.631936i | ||||||
\(339\) | −9.72669 | − | 0.861477i | −0.528281 | − | 0.0467890i | ||||
\(340\) | 5.31590 | 0.288295 | ||||||||
\(341\) | 1.18122 | 0.0639667 | ||||||||
\(342\) | −15.2995 | − | 2.73154i | −0.827305 | − | 0.147705i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1.38323i | − | 0.0745786i | ||||||
\(345\) | 6.40743 | + | 0.567495i | 0.344964 | + | 0.0305529i | ||||
\(346\) | 4.69254i | 0.252272i | ||||||||
\(347\) | − | 31.4496i | − | 1.68830i | −0.536106 | − | 0.844151i | \(-0.680105\pi\) | ||
0.536106 | − | 0.844151i | \(-0.319895\pi\) | |||||||
\(348\) | −8.28621 | − | 0.733896i | −0.444188 | − | 0.0393410i | ||||
\(349\) | − | 6.51210i | − | 0.348585i | −0.984694 | − | 0.174292i | \(-0.944236\pi\) | ||
0.984694 | − | 0.174292i | \(-0.0557638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.8814 | − | 6.75275i | −1.32807 | − | 0.360435i | ||||
\(352\) | 0.476459 | 0.0253954 | ||||||||
\(353\) | −33.0035 | −1.75660 | −0.878299 | − | 0.478111i | \(-0.841322\pi\) | ||||
−0.878299 | + | 0.478111i | \(0.841322\pi\) | |||||||
\(354\) | −0.760921 | − | 0.0673935i | −0.0404425 | − | 0.00358192i | ||||
\(355\) | − | 8.78061i | − | 0.466026i | ||||||
\(356\) | 5.22255 | 0.276795 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.6928 | 1.14650 | ||||||||
\(359\) | − | 21.2601i | − | 1.12207i | −0.827793 | − | 0.561033i | \(-0.810404\pi\) | ||
0.827793 | − | 0.561033i | \(-0.189596\pi\) | |||||||
\(360\) | −0.527274 | + | 2.95330i | −0.0277898 | + | 0.155653i | ||||
\(361\) | −7.83748 | −0.412499 | ||||||||
\(362\) | 8.38421 | 0.440664 | ||||||||
\(363\) | −1.64618 | + | 18.5866i | −0.0864023 | + | 0.975544i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0920i | 0.789952i | ||||||||
\(366\) | −1.86732 | + | 21.0834i | −0.0976066 | + | 1.10205i | ||||
\(367\) | 0.576702i | 0.0301036i | 0.999887 | + | 0.0150518i | \(0.00479132\pi\) | ||||
−0.999887 | + | 0.0150518i | \(0.995209\pi\) | |||||||
\(368\) | − | 3.71381i | − | 0.193596i | ||||||
\(369\) | 33.9325 | + | 6.05821i | 1.76646 | + | 0.315378i | ||||
\(370\) | 2.38410i | 0.123943i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.27730 | + | 0.378833i | 0.221768 | + | 0.0196416i | ||||
\(373\) | −11.2196 | −0.580929 | −0.290465 | − | 0.956886i | \(-0.593810\pi\) | ||||
−0.290465 | + | 0.956886i | \(0.593810\pi\) | |||||||
\(374\) | −2.53281 | −0.130969 | ||||||||
\(375\) | −0.152807 | + | 1.72530i | −0.00789090 | + | 0.0890940i | ||||
\(376\) | 11.8319i | 0.610181i | ||||||||
\(377\) | −23.8297 | −1.22729 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4189 | 0.689283 | 0.344641 | − | 0.938734i | \(-0.388000\pi\) | ||||
0.344641 | + | 0.938734i | \(0.388000\pi\) | |||||||
\(380\) | 5.18049i | 0.265754i | ||||||||
\(381\) | 1.22573 | − | 13.8394i | 0.0627962 | − | 0.709014i | ||||
\(382\) | −8.58536 | −0.439265 | ||||||||
\(383\) | 27.0366 | 1.38151 | 0.690754 | − | 0.723090i | \(-0.257279\pi\) | ||||
0.690754 | + | 0.723090i | \(0.257279\pi\) | |||||||
\(384\) | 1.72530 | + | 0.152807i | 0.0880437 | + | 0.00779788i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11.9098i | − | 0.606195i | ||||||
\(387\) | −4.08509 | − | 0.729340i | −0.207657 | − | 0.0370744i | ||||
\(388\) | − | 8.50932i | − | 0.431995i | ||||||
\(389\) | 1.50672i | 0.0763938i | 0.999270 | + | 0.0381969i | \(0.0121614\pi\) | ||||
−0.999270 | + | 0.0381969i | \(0.987839\pi\) | |||||||
\(390\) | −0.758174 | + | 8.56033i | −0.0383916 | + | 0.433469i | ||||
\(391\) | 19.7423i | 0.998409i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0270492 | − | 0.305405i | 0.00136445 | − | 0.0154057i | ||||
\(394\) | 18.0983 | 0.911781 | ||||||||
\(395\) | 1.77425 | 0.0892720 | ||||||||
\(396\) | 0.251225 | − | 1.40713i | 0.0126245 | − | 0.0707108i | ||||
\(397\) | 17.3237i | 0.869449i | 0.900563 | + | 0.434725i | \(0.143154\pi\) | ||||
−0.900563 | + | 0.434725i | \(0.856846\pi\) | |||||||
\(398\) | 10.6113 | 0.531899 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 12.6888i | 0.633647i | 0.948485 | + | 0.316823i | \(0.102616\pi\) | ||||
−0.948485 | + | 0.316823i | \(0.897384\pi\) | |||||||
\(402\) | −5.38273 | − | 0.476740i | −0.268466 | − | 0.0237776i | ||||
\(403\) | 12.3008 | 0.612744 | ||||||||
\(404\) | 16.8555 | 0.838593 | ||||||||
\(405\) | 8.44396 | + | 3.11440i | 0.419584 | + | 0.154756i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.13593i | − | 0.0563058i | ||||||
\(408\) | −9.17151 | − | 0.812306i | −0.454058 | − | 0.0402151i | ||||
\(409\) | − | 20.8434i | − | 1.03064i | −0.856998 | − | 0.515320i | \(-0.827673\pi\) | ||
0.856998 | − | 0.515320i | \(-0.172327\pi\) | |||||||
\(410\) | − | 11.4897i | − | 0.567435i | ||||||
\(411\) | −30.3304 | − | 2.68631i | −1.49609 | − | 0.132506i | ||||
\(412\) | 8.84632i | 0.435827i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −10.9680 | − | 1.95819i | −0.539048 | − | 0.0962400i | ||||
\(415\) | 14.2002 | 0.697058 | ||||||||
\(416\) | 4.96165 | 0.243265 | ||||||||
\(417\) | 18.4454 | + | 1.63368i | 0.903275 | + | 0.0800016i | ||||
\(418\) | − | 2.46829i | − | 0.120728i | ||||||
\(419\) | −29.3248 | −1.43261 | −0.716306 | − | 0.697787i | \(-0.754168\pi\) | ||||
−0.716306 | + | 0.697787i | \(0.754168\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3254 | −0.941861 | −0.470931 | − | 0.882170i | \(-0.656082\pi\) | ||||
−0.470931 | + | 0.882170i | \(0.656082\pi\) | |||||||
\(422\) | − | 13.8286i | − | 0.673166i | ||||||
\(423\) | 34.9430 | + | 6.23863i | 1.69899 | + | 0.303332i | ||||
\(424\) | 0.305714 | 0.0148468 | ||||||||
\(425\) | −5.31590 | −0.257859 | ||||||||
\(426\) | −1.34174 | + | 15.1492i | −0.0650073 | + | 0.733979i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 12.0789i | − | 0.583853i | ||||||
\(429\) | 0.361239 | − | 4.07865i | 0.0174408 | − | 0.196919i | ||||
\(430\) | 1.38323i | 0.0667052i | ||||||||
\(431\) | 17.9318i | 0.863743i | 0.901935 | + | 0.431871i | \(0.142147\pi\) | ||||
−0.901935 | + | 0.431871i | \(0.857853\pi\) | |||||||
\(432\) | 1.36099 | − | 5.01475i | 0.0654806 | − | 0.241272i | ||||
\(433\) | 2.79305i | 0.134225i | 0.997745 | + | 0.0671127i | \(0.0213787\pi\) | ||||
−0.997745 | + | 0.0671127i | \(0.978621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.28621 | + | 0.733896i | 0.397294 | + | 0.0351876i | ||||
\(436\) | −17.0390 | −0.816021 | ||||||||
\(437\) | −19.2394 | −0.920343 | ||||||||
\(438\) | 2.30616 | − | 26.0382i | 0.110193 | − | 1.24415i | ||||
\(439\) | 15.1652i | 0.723795i | 0.932218 | + | 0.361898i | \(0.117871\pi\) | ||||
−0.932218 | + | 0.361898i | \(0.882129\pi\) | |||||||
\(440\) | −0.476459 | −0.0227143 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −26.3757 | −1.25456 | ||||||||
\(443\) | − | 5.62647i | − | 0.267322i | −0.991027 | − | 0.133661i | \(-0.957327\pi\) | ||
0.991027 | − | 0.133661i | \(-0.0426733\pi\) | |||||||
\(444\) | 0.364306 | − | 4.11328i | 0.0172892 | − | 0.195208i | ||||
\(445\) | −5.22255 | −0.247573 | ||||||||
\(446\) | 1.39419 | 0.0660168 | ||||||||
\(447\) | −31.3480 | − | 2.77644i | −1.48271 | − | 0.131321i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.6625i | 0.644775i | 0.946608 | + | 0.322388i | \(0.104485\pi\) | ||||
−0.946608 | + | 0.322388i | \(0.895515\pi\) | |||||||
\(450\) | 0.527274 | − | 2.95330i | 0.0248559 | − | 0.139220i | ||||
\(451\) | 5.47437i | 0.257778i | ||||||||
\(452\) | − | 5.63769i | − | 0.265175i | ||||||
\(453\) | 2.78904 | − | 31.4902i | 0.131040 | − | 1.47954i | ||||
\(454\) | − | 4.57266i | − | 0.214606i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.791613 | − | 8.93788i | 0.0370707 | − | 0.418555i | ||||
\(457\) | −3.70391 | −0.173262 | −0.0866309 | − | 0.996240i | \(-0.527610\pi\) | ||||
−0.0866309 | + | 0.996240i | \(0.527610\pi\) | |||||||
\(458\) | −3.35629 | −0.156829 | ||||||||
\(459\) | −7.23488 | + | 26.6579i | −0.337695 | + | 1.24429i | ||||
\(460\) | 3.71381i | 0.173157i | ||||||||
\(461\) | 23.6183 | 1.10001 | 0.550007 | − | 0.835160i | \(-0.314625\pi\) | ||||
0.550007 | + | 0.835160i | \(0.314625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8440 | −1.15460 | −0.577298 | − | 0.816533i | \(-0.695893\pi\) | ||||
−0.577298 | + | 0.816533i | \(0.695893\pi\) | |||||||
\(464\) | − | 4.80278i | − | 0.222963i | ||||||
\(465\) | −4.27730 | − | 0.378833i | −0.198355 | − | 0.0175680i | ||||
\(466\) | 8.18807 | 0.379305 | ||||||||
\(467\) | 18.2254 | 0.843369 | 0.421685 | − | 0.906743i | \(-0.361439\pi\) | ||||
0.421685 | + | 0.906743i | \(0.361439\pi\) | |||||||
\(468\) | 2.61615 | − | 14.6533i | 0.120932 | − | 0.677347i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 11.8319i | − | 0.545763i | ||||||
\(471\) | 7.70987 | + | 0.682850i | 0.355252 | + | 0.0314641i | ||||
\(472\) | − | 0.441038i | − | 0.0203004i | ||||||
\(473\) | − | 0.659052i | − | 0.0303032i | ||||||
\(474\) | −3.06110 | − | 0.271117i | −0.140601 | − | 0.0124528i | ||||
\(475\) | − | 5.18049i | − | 0.237697i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.161195 | − | 0.902866i | 0.00738062 | − | 0.0413394i | ||||
\(478\) | 14.1670 | 0.647983 | ||||||||
\(479\) | 31.2048 | 1.42578 | 0.712891 | − | 0.701275i | \(-0.247386\pi\) | ||||
0.712891 | + | 0.701275i | \(0.247386\pi\) | |||||||
\(480\) | −1.72530 | − | 0.152807i | −0.0787487 | − | 0.00697464i | ||||
\(481\) | − | 11.8291i | − | 0.539359i | ||||||
\(482\) | 17.2184 | 0.784277 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7730 | −0.489681 | ||||||||
\(485\) | 8.50932i | 0.386389i | ||||||||
\(486\) | −14.0924 | − | 6.66355i | −0.639246 | − | 0.302265i | ||||
\(487\) | 4.62293 | 0.209485 | 0.104743 | − | 0.994499i | \(-0.466598\pi\) | ||||
0.104743 | + | 0.994499i | \(0.466598\pi\) | |||||||
\(488\) | −12.2202 | −0.553181 | ||||||||
\(489\) | −3.19472 | + | 36.0707i | −0.144470 | + | 1.63118i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.9468i | − | 0.674540i | −0.941408 | − | 0.337270i | \(-0.890496\pi\) | ||
0.941408 | − | 0.337270i | \(-0.109504\pi\) | |||||||
\(492\) | −1.75570 | + | 19.8231i | −0.0791531 | + | 0.893696i | ||||
\(493\) | 25.5311i | 1.14986i | ||||||||
\(494\) | − | 25.7038i | − | 1.15647i | ||||||
\(495\) | −0.251225 | + | 1.40713i | −0.0112917 | + | 0.0632457i | ||||
\(496\) | 2.47917i | 0.111318i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −24.4995 | − | 2.16988i | −1.09785 | − | 0.0972346i | ||||
\(499\) | −12.5355 | −0.561166 | −0.280583 | − | 0.959830i | \(-0.590528\pi\) | ||||
−0.280583 | + | 0.959830i | \(0.590528\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −1.28370 | + | 14.4939i | −0.0573516 | + | 0.647541i | ||||
\(502\) | − | 28.2916i | − | 1.26272i | ||||||
\(503\) | 26.5310 | 1.18296 | 0.591479 | − | 0.806320i | \(-0.298544\pi\) | ||||
0.591479 | + | 0.806320i | \(0.298544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8555 | −0.750060 | ||||||||
\(506\) | − | 1.76948i | − | 0.0786630i | ||||||
\(507\) | 1.77531 | − | 20.0445i | 0.0788442 | − | 0.890208i | ||||
\(508\) | 8.02146 | 0.355895 | ||||||||
\(509\) | −25.8107 | −1.14404 | −0.572020 | − | 0.820240i | \(-0.693840\pi\) | ||||
−0.572020 | + | 0.820240i | \(0.693840\pi\) | |||||||
\(510\) | 9.17151 | + | 0.812306i | 0.406121 | + | 0.0359695i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −25.9789 | − | 7.05058i | −1.14699 | − | 0.311291i | ||||
\(514\) | 9.66976i | 0.426515i | ||||||||
\(515\) | − | 8.84632i | − | 0.389816i | ||||||
\(516\) | 0.211366 | − | 2.38648i | 0.00930489 | − | 0.105059i | ||||
\(517\) | 5.63740i | 0.247933i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.717051 | + | 8.09602i | −0.0314750 | + | 0.355376i | ||||
\(520\) | −4.96165 | −0.217583 | ||||||||
\(521\) | −7.06140 | −0.309366 | −0.154683 | − | 0.987964i | \(-0.549436\pi\) | ||||
−0.154683 | + | 0.987964i | \(0.549436\pi\) | |||||||
\(522\) | −14.1840 | − | 2.53238i | −0.620818 | − | 0.110839i | ||||
\(523\) | 37.2776i | 1.63003i | 0.579437 | + | 0.815017i | \(0.303273\pi\) | ||||
−0.579437 | + | 0.815017i | \(0.696727\pi\) | |||||||
\(524\) | 0.177016 | 0.00773298 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.8130 | 1.25630 | ||||||||
\(527\) | − | 13.1790i | − | 0.574087i | ||||||
\(528\) | 0.822034 | + | 0.0728062i | 0.0357744 | + | 0.00316848i | ||||
\(529\) | 9.20762 | 0.400331 | ||||||||
\(530\) | −0.305714 | −0.0132794 | ||||||||
\(531\) | −1.30252 | − | 0.232548i | −0.0565244 | − | 0.0100917i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 57.0079i | 2.46928i | ||||||||
\(534\) | 9.01046 | + | 0.798041i | 0.389921 | + | 0.0345346i | ||||
\(535\) | 12.0789i | 0.522214i | ||||||||
\(536\) | − | 3.11989i | − | 0.134759i | ||||||
\(537\) | 37.4266 | + | 3.31481i | 1.61508 | + | 0.143045i | ||||
\(538\) | − | 8.09812i | − | 0.349135i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.36099 | + | 5.01475i | −0.0585676 | + | 0.215800i | ||||
\(541\) | 35.2331 | 1.51479 | 0.757395 | − | 0.652957i | \(-0.226472\pi\) | ||||
0.757395 | + | 0.652957i | \(0.226472\pi\) | |||||||
\(542\) | 9.70895 | 0.417035 | ||||||||
\(543\) | 14.4652 | + | 1.28116i | 0.620763 | + | 0.0549799i | ||||
\(544\) | − | 5.31590i | − | 0.227918i | ||||||
\(545\) | 17.0390 | 0.729871 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.3886 | 1.51311 | 0.756554 | − | 0.653932i | \(-0.226882\pi\) | ||||
0.756554 | + | 0.653932i | \(0.226882\pi\) | |||||||
\(548\) | − | 17.5798i | − | 0.750972i | ||||||
\(549\) | −6.44338 | + | 36.0899i | −0.274997 | + | 1.54028i | ||||
\(550\) | 0.476459 | 0.0203163 | ||||||||
\(551\) | −24.8807 | −1.05995 | ||||||||
\(552\) | 0.567495 | − | 6.40743i | 0.0241542 | − | 0.272718i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 30.2568i | − | 1.28549i | ||||||
\(555\) | −0.364306 | + | 4.11328i | −0.0154639 | + | 0.174599i | ||||
\(556\) | 10.6911i | 0.453406i | ||||||||
\(557\) | 29.1977i | 1.23715i | 0.785727 | + | 0.618574i | \(0.212289\pi\) | ||||
−0.785727 | + | 0.618574i | \(0.787711\pi\) | |||||||
\(558\) | 7.32172 | + | 1.30720i | 0.309953 | + | 0.0553382i | ||||
\(559\) | − | 6.86310i | − | 0.290278i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.36985 | − | 0.387031i | −0.184495 | − | 0.0163404i | ||||
\(562\) | −7.61243 | −0.321111 | ||||||||
\(563\) | 2.62310 | 0.110551 | 0.0552753 | − | 0.998471i | \(-0.482396\pi\) | ||||
0.0552753 | + | 0.998471i | \(0.482396\pi\) | |||||||
\(564\) | −1.80799 | + | 20.4135i | −0.0761300 | + | 0.859562i | ||||
\(565\) | 5.63769i | 0.237179i | ||||||||
\(566\) | 20.9933 | 0.882412 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.78061 | −0.368426 | ||||||||
\(569\) | − | 35.1149i | − | 1.47209i | −0.676931 | − | 0.736046i | \(-0.736691\pi\) | ||
0.676931 | − | 0.736046i | \(-0.263309\pi\) | |||||||
\(570\) | −0.791613 | + | 8.93788i | −0.0331570 | + | 0.374367i | ||||
\(571\) | 27.9169 | 1.16829 | 0.584143 | − | 0.811651i | \(-0.301431\pi\) | ||||
0.584143 | + | 0.811651i | \(0.301431\pi\) | |||||||
\(572\) | 2.36403 | 0.0988449 | ||||||||
\(573\) | −14.8123 | − | 1.31190i | −0.618792 | − | 0.0548054i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.71381i | − | 0.154877i | ||||||
\(576\) | 2.95330 | + | 0.527274i | 0.123054 | + | 0.0219697i | ||||
\(577\) | 29.2752i | 1.21874i | 0.792884 | + | 0.609372i | \(0.208578\pi\) | ||||
−0.792884 | + | 0.609372i | \(0.791422\pi\) | |||||||
\(578\) | 11.2588i | 0.468306i | ||||||||
\(579\) | 1.81990 | − | 20.5480i | 0.0756326 | − | 0.853946i | ||||
\(580\) | 4.80278i | 0.199424i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.30028 | − | 14.6811i | 0.0538984 | − | 0.608552i | ||||
\(583\) | 0.145660 | 0.00603264 | ||||||||
\(584\) | 15.0920 | 0.624512 | ||||||||
\(585\) | −2.61615 | + | 14.6533i | −0.108164 | + | 0.605837i | ||||
\(586\) | 30.8856i | 1.27587i | ||||||||
\(587\) | −32.6568 | −1.34789 | −0.673944 | − | 0.738782i | \(-0.735401\pi\) | ||||
−0.673944 | + | 0.738782i | \(0.735401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8433 | 0.529199 | ||||||||
\(590\) | 0.441038i | 0.0181572i | ||||||||
\(591\) | 31.2250 | + | 2.76555i | 1.28442 | + | 0.113759i | ||||
\(592\) | 2.38410 | 0.0979858 | ||||||||
\(593\) | 29.8459 | 1.22562 | 0.612812 | − | 0.790228i | \(-0.290038\pi\) | ||||
0.612812 | + | 0.790228i | \(0.290038\pi\) | |||||||
\(594\) | 0.648456 | − | 2.38932i | 0.0266065 | − | 0.0980352i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 18.1696i | − | 0.744256i | ||||||
\(597\) | 18.3077 | + | 1.62148i | 0.749285 | + | 0.0663630i | ||||
\(598\) | − | 18.4266i | − | 0.753521i | ||||||
\(599\) | − | 38.9952i | − | 1.59330i | −0.604441 | − | 0.796650i | \(-0.706604\pi\) | ||
0.604441 | − | 0.796650i | \(-0.293396\pi\) | |||||||
\(600\) | 1.72530 | + | 0.152807i | 0.0704350 | + | 0.00623831i | ||||
\(601\) | − | 12.0833i | − | 0.492890i | −0.969157 | − | 0.246445i | \(-0.920738\pi\) | ||
0.969157 | − | 0.246445i | \(-0.0792624\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.21396 | − | 1.64503i | −0.375222 | − | 0.0669910i | ||||
\(604\) | 18.2521 | 0.742665 | ||||||||
\(605\) | 10.7730 | 0.437984 | ||||||||
\(606\) | 29.0808 | + | 2.57563i | 1.18132 | + | 0.104628i | ||||
\(607\) | − | 9.81922i | − | 0.398550i | −0.979944 | − | 0.199275i | \(-0.936141\pi\) | ||
0.979944 | − | 0.199275i | \(-0.0638587\pi\) | |||||||
\(608\) | 5.18049 | 0.210097 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.2202 | 0.494781 | ||||||||
\(611\) | 58.7056i | 2.37497i | ||||||||
\(612\) | −15.6995 | − | 2.80294i | −0.634613 | − | 0.113302i | ||||
\(613\) | −9.51280 | −0.384218 | −0.192109 | − | 0.981374i | \(-0.561533\pi\) | ||||
−0.192109 | + | 0.981374i | \(0.561533\pi\) | |||||||
\(614\) | −24.0737 | −0.971534 | ||||||||
\(615\) | 1.75570 | − | 19.8231i | 0.0707967 | − | 0.799346i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.8611i | 1.20216i | 0.799188 | + | 0.601081i | \(0.205263\pi\) | ||||
−0.799188 | + | 0.601081i | \(0.794737\pi\) | |||||||
\(618\) | −1.35178 | + | 15.2625i | −0.0543765 | + | 0.613949i | ||||
\(619\) | 39.2407i | 1.57722i | 0.614895 | + | 0.788609i | \(0.289198\pi\) | ||||
−0.614895 | + | 0.788609i | \(0.710802\pi\) | |||||||
\(620\) | − | 2.47917i | − | 0.0995657i | ||||||
\(621\) | −18.6238 | − | 5.05445i | −0.747348 | − | 0.202828i | ||||
\(622\) | 12.3799i | 0.496389i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.56033 | + | 0.758174i | 0.342687 | + | 0.0303512i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.19263 | −0.327443 | ||||||||
\(627\) | 0.377172 | − | 4.25854i | 0.0150628 | − | 0.170070i | ||||
\(628\) | 4.46872i | 0.178321i | ||||||||
\(629\) | −12.6736 | −0.505331 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6654 | 0.782868 | 0.391434 | − | 0.920206i | \(-0.371979\pi\) | ||||
0.391434 | + | 0.920206i | \(0.371979\pi\) | |||||||
\(632\) | − | 1.77425i | − | 0.0705757i | ||||||
\(633\) | 2.11310 | − | 23.8585i | 0.0839883 | − | 0.948288i | ||||
\(634\) | −6.33601 | −0.251635 | ||||||||
\(635\) | −8.02146 | −0.318322 | ||||||||
\(636\) | 0.527448 | + | 0.0467152i | 0.0209147 | + | 0.00185238i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.28833i | − | 0.0905958i | ||||||
\(639\) | −4.62979 | + | 25.9318i | −0.183152 | + | 1.02585i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 14.8980i | 0.588435i | 0.955739 | + | 0.294217i | \(0.0950590\pi\) | ||||
−0.955739 | + | 0.294217i | \(0.904941\pi\) | |||||||
\(642\) | 1.84573 | − | 20.8396i | 0.0728451 | − | 0.822474i | ||||
\(643\) | − | 46.9493i | − | 1.85150i | −0.378134 | − | 0.925751i | \(-0.623434\pi\) | ||
0.378134 | − | 0.925751i | \(-0.376566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.211366 | + | 2.38648i | −0.00832254 | + | 0.0939675i | ||||
\(646\) | −27.5390 | −1.08351 | ||||||||
\(647\) | 9.56306 | 0.375963 | 0.187981 | − | 0.982173i | \(-0.439806\pi\) | ||||
0.187981 | + | 0.982173i | \(0.439806\pi\) | |||||||
\(648\) | 3.11440 | − | 8.44396i | 0.122345 | − | 0.331710i | ||||
\(649\) | − | 0.210137i | − | 0.00824858i | ||||||
\(650\) | 4.96165 | 0.194612 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.9070 | −0.818780 | ||||||||
\(653\) | 7.62005i | 0.298195i | 0.988822 | + | 0.149098i | \(0.0476369\pi\) | ||||
−0.988822 | + | 0.149098i | \(0.952363\pi\) | |||||||
\(654\) | −29.3974 | − | 2.60367i | −1.14953 | − | 0.101812i | ||||
\(655\) | −0.177016 | −0.00691659 | ||||||||
\(656\) | −11.4897 | −0.448597 | ||||||||
\(657\) | 7.95762 | − | 44.5712i | 0.310456 | − | 1.73889i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.0410i | 0.741731i | 0.928686 | + | 0.370866i | \(0.120939\pi\) | ||||
−0.928686 | + | 0.370866i | \(0.879061\pi\) | |||||||
\(660\) | −0.822034 | − | 0.0728062i | −0.0319976 | − | 0.00283398i | ||||
\(661\) | − | 37.8335i | − | 1.47155i | −0.677224 | − | 0.735777i | \(-0.736817\pi\) | ||
0.677224 | − | 0.735777i | \(-0.263183\pi\) | |||||||
\(662\) | 15.6010i | 0.606349i | ||||||||
\(663\) | −45.5059 | − | 4.03038i | −1.76730 | − | 0.156527i | ||||
\(664\) | − | 14.2002i | − | 0.551073i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.25707 | − | 7.04096i | 0.0487106 | − | 0.272832i | ||||
\(667\) | −17.8366 | −0.690636 | ||||||||
\(668\) | −8.40082 | −0.325038 | ||||||||
\(669\) | 2.40539 | + | 0.213041i | 0.0929978 | + | 0.00823666i | ||||
\(670\) | 3.11989i | 0.120532i | ||||||||
\(671\) | −5.82242 | −0.224772 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.8824 | 0.882052 | 0.441026 | − | 0.897494i | \(-0.354615\pi\) | ||||
0.441026 | + | 0.897494i | \(0.354615\pi\) | |||||||
\(674\) | 2.76611i | 0.106546i | ||||||||
\(675\) | 1.36099 | − | 5.01475i | 0.0523845 | − | 0.193018i | ||||
\(676\) | 11.6180 | 0.446846 | ||||||||
\(677\) | −11.0909 | −0.426257 | −0.213128 | − | 0.977024i | \(-0.568365\pi\) | ||||
−0.213128 | + | 0.977024i | \(0.568365\pi\) | |||||||
\(678\) | 0.861477 | − | 9.72669i | 0.0330848 | − | 0.373551i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.31590i | 0.203856i | ||||||||
\(681\) | 0.698734 | − | 7.88920i | 0.0267755 | − | 0.302315i | ||||
\(682\) | 1.18122i | 0.0452313i | ||||||||
\(683\) | 6.84051i | 0.261745i | 0.991399 | + | 0.130873i | \(0.0417779\pi\) | ||||
−0.991399 | + | 0.130873i | \(0.958222\pi\) | |||||||
\(684\) | 2.73154 | − | 15.2995i | 0.104443 | − | 0.584993i | ||||
\(685\) | 17.5798i | 0.671690i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.79059 | − | 0.512863i | −0.220925 | − | 0.0195669i | ||||
\(688\) | 1.38323 | 0.0527351 | ||||||||
\(689\) | 1.51685 | 0.0577873 | ||||||||
\(690\) | −0.567495 | + | 6.40743i | −0.0216042 | + | 0.243927i | ||||
\(691\) | − | 44.5919i | − | 1.69635i | −0.529713 | − | 0.848177i | \(-0.677700\pi\) | ||
0.529713 | − | 0.848177i | \(-0.322300\pi\) | |||||||
\(692\) | −4.69254 | −0.178383 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.4496 | 1.19381 | ||||||||
\(695\) | − | 10.6911i | − | 0.405538i | ||||||
\(696\) | 0.733896 | − | 8.28621i | 0.0278183 | − | 0.314088i | ||||
\(697\) | 61.0781 | 2.31350 | ||||||||
\(698\) | 6.51210 | 0.246487 | ||||||||
\(699\) | 14.1268 | + | 1.25119i | 0.534326 | + | 0.0473244i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.2838i | 1.14380i | 0.820323 | + | 0.571901i | \(0.193794\pi\) | ||||
−0.820323 | + | 0.571901i | \(0.806206\pi\) | |||||||
\(702\) | 6.75275 | − | 24.8814i | 0.254866 | − | 0.939090i | ||||
\(703\) | − | 12.3508i | − | 0.465819i | ||||||
\(704\) | 0.476459i | 0.0179572i | ||||||||
\(705\) | 1.80799 | − | 20.4135i | 0.0680927 | − | 0.768816i | ||||
\(706\) | − | 33.0035i | − | 1.24210i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.0673935 | − | 0.760921i | 0.00253280 | − | 0.0285972i | ||||
\(709\) | 8.53467 | 0.320526 | 0.160263 | − | 0.987074i | \(-0.448766\pi\) | ||||
0.160263 | + | 0.987074i | \(0.448766\pi\) | |||||||
\(710\) | 8.78061 | 0.329530 | ||||||||
\(711\) | −5.23988 | − | 0.935513i | −0.196511 | − | 0.0350845i | ||||
\(712\) | 5.22255i | 0.195723i | ||||||||
\(713\) | 9.20715 | 0.344810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.36403 | −0.0884096 | ||||||||
\(716\) | 21.6928i | 0.810700i | ||||||||
\(717\) | 24.4423 | + | 2.16481i | 0.912813 | + | 0.0808464i | ||||
\(718\) | 21.2601 | 0.793421 | ||||||||
\(719\) | −4.23143 | −0.157806 | −0.0789029 | − | 0.996882i | \(-0.525142\pi\) | ||||
−0.0789029 | + | 0.996882i | \(0.525142\pi\) | |||||||
\(720\) | −2.95330 | − | 0.527274i | −0.110063 | − | 0.0196503i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 7.83748i | − | 0.291681i | ||||||
\(723\) | 29.7069 | + | 2.63109i | 1.10481 | + | 0.0978512i | ||||
\(724\) | 8.38421i | 0.311597i | ||||||||
\(725\) | − | 4.80278i | − | 0.178371i | ||||||
\(726\) | −18.5866 | − | 1.64618i | −0.689814 | − | 0.0610956i | ||||
\(727\) | 5.91343i | 0.219317i | 0.993969 | + | 0.109658i | \(0.0349757\pi\) | ||||
−0.993969 | + | 0.109658i | \(0.965024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.2954 | − | 13.6500i | −0.862793 | − | 0.505557i | ||||
\(730\) | −15.0920 | −0.558580 | ||||||||
\(731\) | −7.35311 | −0.271964 | ||||||||
\(732\) | −21.0834 | − | 1.86732i | −0.779266 | − | 0.0690183i | ||||
\(733\) | − | 33.5690i | − | 1.23990i | −0.784642 | − | 0.619949i | \(-0.787153\pi\) | ||
0.784642 | − | 0.619949i | \(-0.212847\pi\) | |||||||
\(734\) | −0.576702 | −0.0212865 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.71381 | 0.136893 | ||||||||
\(737\) | − | 1.48650i | − | 0.0547559i | ||||||
\(738\) | −6.05821 | + | 33.9325i | −0.223006 | + | 1.24907i | ||||
\(739\) | −40.3871 | −1.48566 | −0.742831 | − | 0.669479i | \(-0.766517\pi\) | ||||
−0.742831 | + | 0.669479i | \(0.766517\pi\) | |||||||
\(740\) | −2.38410 | −0.0876412 | ||||||||
\(741\) | 3.92771 | − | 44.3467i | 0.144288 | − | 1.62912i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.9431i | − | 0.878386i | −0.898393 | − | 0.439193i | \(-0.855264\pi\) | ||
0.898393 | − | 0.439193i | \(-0.144736\pi\) | |||||||
\(744\) | −0.378833 | + | 4.27730i | −0.0138887 | + | 0.156813i | ||||
\(745\) | 18.1696i | 0.665683i | ||||||||
\(746\) | − | 11.2196i | − | 0.410779i | ||||||
\(747\) | −41.9373 | − | 7.48737i | −1.53441 | − | 0.273949i | ||||
\(748\) | − | 2.53281i | − | 0.0926088i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.72530 | − | 0.152807i | −0.0629989 | − | 0.00557971i | ||||
\(751\) | −25.5556 | −0.932535 | −0.466268 | − | 0.884644i | \(-0.654402\pi\) | ||||
−0.466268 | + | 0.884644i | \(0.654402\pi\) | |||||||
\(752\) | −11.8319 | −0.431463 | ||||||||
\(753\) | 4.32315 | − | 48.8114i | 0.157544 | − | 1.77879i | ||||
\(754\) | − | 23.8297i | − | 0.867827i | ||||||
\(755\) | −18.2521 | −0.664260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.0619 | 1.60146 | 0.800728 | − | 0.599028i | \(-0.204446\pi\) | ||||
0.800728 | + | 0.599028i | \(0.204446\pi\) | |||||||
\(758\) | 13.4189i | 0.487397i | ||||||||
\(759\) | 0.270388 | − | 3.05288i | 0.00981447 | − | 0.110812i | ||||
\(760\) | −5.18049 | −0.187916 | ||||||||
\(761\) | 38.9175 | 1.41076 | 0.705380 | − | 0.708830i | \(-0.250776\pi\) | ||||
0.705380 | + | 0.708830i | \(0.250776\pi\) | |||||||
\(762\) | 13.8394 | + | 1.22573i | 0.501348 | + | 0.0444036i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 8.58536i | − | 0.310607i | ||||||
\(765\) | 15.6995 | + | 2.80294i | 0.567615 | + | 0.101340i | ||||
\(766\) | 27.0366i | 0.976873i | ||||||||
\(767\) | − | 2.18828i | − | 0.0790141i | ||||||
\(768\) | −0.152807 | + | 1.72530i | −0.00551394 | + | 0.0622563i | ||||
\(769\) | 11.2174i | 0.404508i | 0.979333 | + | 0.202254i | \(0.0648267\pi\) | ||||
−0.979333 | + | 0.202254i | \(0.935173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.47760 | + | 16.6832i | −0.0532146 | + | 0.600831i | ||||
\(772\) | 11.9098 | 0.428644 | ||||||||
\(773\) | 15.9211 | 0.572642 | 0.286321 | − | 0.958134i | \(-0.407568\pi\) | ||||
0.286321 | + | 0.958134i | \(0.407568\pi\) | |||||||
\(774\) | 0.729340 | − | 4.08509i | 0.0262156 | − | 0.146835i | ||||
\(775\) | 2.47917i | 0.0890543i | ||||||||
\(776\) | 8.50932 | 0.305467 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.50672 | −0.0540186 | ||||||||
\(779\) | 59.5222i | 2.13261i | ||||||||
\(780\) | −8.56033 | − | 0.758174i | −0.306509 | − | 0.0271470i | ||||
\(781\) | −4.18360 | −0.149701 | ||||||||
\(782\) | −19.7423 | −0.705982 | ||||||||
\(783\) | −24.0847 | − | 6.53652i | −0.860717 | − | 0.233596i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.46872i | − | 0.159495i | ||||||
\(786\) | 0.305405 | + | 0.0270492i | 0.0108934 | + | 0.000964815i | ||||
\(787\) | 14.9125i | 0.531574i | 0.964032 | + | 0.265787i | \(0.0856318\pi\) | ||||
−0.964032 | + | 0.265787i | \(0.914368\pi\) | |||||||
\(788\) | 18.0983i | 0.644726i | ||||||||
\(789\) | 49.7109 | + | 4.40281i | 1.76976 | + | 0.156744i | ||||
\(790\) | 1.77425i | 0.0631248i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.40713 | + | 0.251225i | 0.0500001 | + | 0.00892688i | ||||
\(793\) | −60.6323 | −2.15312 | ||||||||
\(794\) | −17.3237 | −0.614794 | ||||||||
\(795\) | −0.527448 | − | 0.0467152i | −0.0187066 | − | 0.00165682i | ||||
\(796\) | 10.6113i | 0.376109i | ||||||||
\(797\) | 32.9042 | 1.16553 | 0.582763 | − | 0.812642i | \(-0.301972\pi\) | ||||
0.582763 | + | 0.812642i | \(0.301972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.8970 | 2.22514 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 15.4238 | + | 2.75372i | 0.544972 | + | 0.0972978i | ||||
\(802\) | −12.6888 | −0.448056 | ||||||||
\(803\) | 7.19073 | 0.253755 | ||||||||
\(804\) | 0.476740 | − | 5.38273i | 0.0168133 | − | 0.189834i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.3008i | 0.433276i | ||||||||
\(807\) | 1.23745 | − | 13.9717i | 0.0435602 | − | 0.491826i | ||||
\(808\) | 16.8555i | 0.592975i | ||||||||
\(809\) | − | 18.8026i | − | 0.661065i | −0.943795 | − | 0.330533i | \(-0.892772\pi\) | ||
0.943795 | − | 0.330533i | \(-0.107228\pi\) | |||||||
\(810\) | −3.11440 | + | 8.44396i | −0.109429 | + | 0.296691i | ||||
\(811\) | 24.4435i | 0.858328i | 0.903227 | + | 0.429164i | \(0.141192\pi\) | ||||
−0.903227 | + | 0.429164i | \(0.858808\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.7508 | + | 1.48359i | 0.587477 | + | 0.0520319i | ||||
\(814\) | 1.13593 | 0.0398142 | ||||||||
\(815\) | 20.9070 | 0.732339 | ||||||||
\(816\) | 0.812306 | − | 9.17151i | 0.0284364 | − | 0.321067i | ||||
\(817\) | − | 7.16580i | − | 0.250700i | ||||||
\(818\) | 20.8434 | 0.728772 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.4897 | 0.401237 | ||||||||
\(821\) | − | 2.67349i | − | 0.0933054i | −0.998911 | − | 0.0466527i | \(-0.985145\pi\) | ||
0.998911 | − | 0.0466527i | \(-0.0148554\pi\) | |||||||
\(822\) | 2.68631 | − | 30.3304i | 0.0936959 | − | 1.05789i | ||||
\(823\) | 38.5503 | 1.34378 | 0.671890 | − | 0.740651i | \(-0.265483\pi\) | ||||
0.671890 | + | 0.740651i | \(0.265483\pi\) | |||||||
\(824\) | −8.84632 | −0.308176 | ||||||||
\(825\) | 0.822034 | + | 0.0728062i | 0.0286196 | + | 0.00253479i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.9672i | − | 1.14638i | −0.819422 | − | 0.573190i | \(-0.805706\pi\) | ||
0.819422 | − | 0.573190i | \(-0.194294\pi\) | |||||||
\(828\) | 1.95819 | − | 10.9680i | 0.0680520 | − | 0.381164i | ||||
\(829\) | 41.6039i | 1.44496i | 0.691389 | + | 0.722482i | \(0.256999\pi\) | ||||
−0.691389 | + | 0.722482i | \(0.743001\pi\) | |||||||
\(830\) | 14.2002i | 0.492895i | ||||||||
\(831\) | 4.62344 | − | 52.2019i | 0.160385 | − | 1.81087i | ||||
\(832\) | 4.96165i | 0.172014i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.63368 | + | 18.4454i | −0.0565697 | + | 0.638712i | ||||
\(835\) | 8.40082 | 0.290723 | ||||||||
\(836\) | 2.46829 | 0.0853677 | ||||||||
\(837\) | 12.4324 | + | 3.37411i | 0.429726 | + | 0.116626i | ||||
\(838\) | − | 29.3248i | − | 1.01301i | ||||||
\(839\) | −20.1022 | −0.694006 | −0.347003 | − | 0.937864i | \(-0.612801\pi\) | ||||
−0.347003 | + | 0.937864i | \(0.612801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.93335 | 0.204598 | ||||||||
\(842\) | − | 19.3254i | − | 0.665996i | ||||||
\(843\) | −13.1337 | − | 1.16323i | −0.452349 | − | 0.0400638i | ||||
\(844\) | 13.8286 | 0.476000 | ||||||||
\(845\) | −11.6180 | −0.399671 | ||||||||
\(846\) | −6.23863 | + | 34.9430i | −0.214488 | + | 1.20137i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.305714i | 0.0104983i | ||||||||
\(849\) | 36.2196 | + | 3.20791i | 1.24305 | + | 0.110095i | ||||
\(850\) | − | 5.31590i | − | 0.182334i | ||||||
\(851\) | − | 8.85409i | − | 0.303514i | ||||||
\(852\) | −15.1492 | − | 1.34174i | −0.519002 | − | 0.0459671i | ||||
\(853\) | − | 19.5492i | − | 0.669351i | −0.942333 | − | 0.334676i | \(-0.891373\pi\) | ||
0.942333 | − | 0.334676i | \(-0.108627\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.73154 | + | 15.2995i | −0.0934166 | + | 0.523233i | ||||
\(856\) | 12.0789 | 0.412847 | ||||||||
\(857\) | 0.558864 | 0.0190904 | 0.00954522 | − | 0.999954i | \(-0.496962\pi\) | ||||
0.00954522 | + | 0.999954i | \(0.496962\pi\) | |||||||
\(858\) | 4.07865 | + | 0.361239i | 0.139243 | + | 0.0123325i | ||||
\(859\) | 38.8641i | 1.32603i | 0.748608 | + | 0.663013i | \(0.230722\pi\) | ||||
−0.748608 | + | 0.663013i | \(0.769278\pi\) | |||||||
\(860\) | −1.38323 | −0.0471677 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.9318 | −0.610758 | ||||||||
\(863\) | 30.6717i | 1.04408i | 0.852922 | + | 0.522038i | \(0.174828\pi\) | ||||
−0.852922 | + | 0.522038i | \(0.825172\pi\) | |||||||
\(864\) | 5.01475 | + | 1.36099i | 0.170605 | + | 0.0463018i | ||||
\(865\) | 4.69254 | 0.159551 | ||||||||
\(866\) | −2.79305 | −0.0949117 | ||||||||
\(867\) | −1.72043 | + | 19.4248i | −0.0584287 | + | 0.659702i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 0.845356i | − | 0.0286767i | ||||||
\(870\) | −0.733896 | + | 8.28621i | −0.0248814 | + | 0.280929i | ||||
\(871\) | − | 15.4798i | − | 0.524513i | ||||||
\(872\) | − | 17.0390i | − | 0.577014i | ||||||
\(873\) | 4.48674 | − | 25.1306i | 0.151853 | − | 0.850542i | ||||
\(874\) | − | 19.2394i | − | 0.650781i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26.0382 | + | 2.30616i | 0.879750 | + | 0.0779179i | ||||
\(877\) | −38.9520 | −1.31532 | −0.657658 | − | 0.753317i | \(-0.728453\pi\) | ||||
−0.657658 | + | 0.753317i | \(0.728453\pi\) | |||||||
\(878\) | −15.1652 | −0.511801 | ||||||||
\(879\) | −4.71952 | + | 53.2868i | −0.159186 | + | 1.79732i | ||||
\(880\) | − | 0.476459i | − | 0.0160614i | ||||||
\(881\) | −3.74997 | −0.126340 | −0.0631698 | − | 0.998003i | \(-0.520121\pi\) | ||||
−0.0631698 | + | 0.998003i | \(0.520121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.0043 | −1.11068 | −0.555342 | − | 0.831622i | \(-0.687413\pi\) | ||||
−0.555342 | + | 0.831622i | \(0.687413\pi\) | |||||||
\(884\) | − | 26.3757i | − | 0.887110i | ||||||
\(885\) | −0.0673935 | + | 0.760921i | −0.00226541 | + | 0.0255781i | ||||
\(886\) | 5.62647 | 0.189025 | ||||||||
\(887\) | 17.3301 | 0.581889 | 0.290944 | − | 0.956740i | \(-0.406031\pi\) | ||||
0.290944 | + | 0.956740i | \(0.406031\pi\) | |||||||
\(888\) | 4.11328 | + | 0.364306i | 0.138033 | + | 0.0122253i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 5.22255i | − | 0.175060i | ||||||
\(891\) | 1.48388 | − | 4.02321i | 0.0497120 | − | 0.134782i | ||||
\(892\) | 1.39419i | 0.0466809i | ||||||||
\(893\) | 61.2948i | 2.05115i | ||||||||
\(894\) | 2.77644 | − | 31.3480i | 0.0928579 | − | 1.04843i | ||||
\(895\) | − | 21.6928i | − | 0.725112i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.81571 | − | 31.7914i | 0.0940139 | − | 1.06148i | ||||
\(898\) | −13.6625 | −0.455925 | ||||||||
\(899\) | 11.9069 | 0.397117 | ||||||||
\(900\) | 2.95330 | + | 0.527274i | 0.0984433 | + | 0.0175758i | ||||
\(901\) | − | 1.62515i | − | 0.0541415i | ||||||
\(902\) | −5.47437 | −0.182277 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.63769 | 0.187507 | ||||||||
\(905\) | − | 8.38421i | − | 0.278700i | ||||||
\(906\) | 31.4902 | + | 2.78904i | 1.04619 | + | 0.0926595i | ||||
\(907\) | 34.4274 | 1.14314 | 0.571572 | − | 0.820552i | \(-0.306334\pi\) | ||||
0.571572 | + | 0.820552i | \(0.306334\pi\) | |||||||
\(908\) | 4.57266 | 0.151749 | ||||||||
\(909\) | 49.7794 | + | 8.88747i | 1.65108 | + | 0.294779i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.90076i | 0.195501i | 0.995211 | + | 0.0977505i | \(0.0311647\pi\) | ||||
−0.995211 | + | 0.0977505i | \(0.968835\pi\) | |||||||
\(912\) | 8.93788 | + | 0.791613i | 0.295963 | + | 0.0262129i | ||||
\(913\) | − | 6.76580i | − | 0.223915i | ||||||
\(914\) | − | 3.70391i | − | 0.122515i | ||||||
\(915\) | 21.0834 | + | 1.86732i | 0.696997 | + | 0.0617319i | ||||
\(916\) | − | 3.35629i | − | 0.110895i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −26.6579 | − | 7.23488i | −0.879843 | − | 0.238787i | ||||
\(919\) | 29.8749 | 0.985481 | 0.492741 | − | 0.870176i | \(-0.335995\pi\) | ||||
0.492741 | + | 0.870176i | \(0.335995\pi\) | |||||||
\(920\) | −3.71381 | −0.122441 | ||||||||
\(921\) | −41.5342 | − | 3.67862i | −1.36860 | − | 0.121215i | ||||
\(922\) | 23.6183i | 0.777827i | ||||||||
\(923\) | −43.5663 | −1.43400 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.38410 | 0.0783887 | ||||||||
\(926\) | − | 24.8440i | − | 0.816423i | ||||||
\(927\) | −4.66443 | + | 26.1258i | −0.153200 | + | 0.858085i | ||||
\(928\) | 4.80278 | 0.157659 | ||||||||
\(929\) | 15.7278 | 0.516011 | 0.258006 | − | 0.966143i | \(-0.416935\pi\) | ||||
0.258006 | + | 0.966143i | \(0.416935\pi\) | |||||||
\(930\) | 0.378833 | − | 4.27730i | 0.0124224 | − | 0.140258i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.18807i | 0.268209i | ||||||||
\(933\) | −1.89173 | + | 21.3590i | −0.0619325 | + | 0.699263i | ||||
\(934\) | 18.2254i | 0.596352i | ||||||||
\(935\) | 2.53281i | 0.0828318i | ||||||||
\(936\) | 14.6533 | + | 2.61615i | 0.478957 | + | 0.0855115i | ||||
\(937\) | − | 19.1459i | − | 0.625469i | −0.949841 | − | 0.312735i | \(-0.898755\pi\) | ||
0.949841 | − | 0.312735i | \(-0.101245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.1347 | − | 1.25189i | −0.461269 | − | 0.0408539i | ||||
\(940\) | 11.8319 | 0.385913 | ||||||||
\(941\) | −2.89249 | −0.0942926 | −0.0471463 | − | 0.998888i | \(-0.515013\pi\) | ||||
−0.0471463 | + | 0.998888i | \(0.515013\pi\) | |||||||
\(942\) | −0.682850 | + | 7.70987i | −0.0222485 | + | 0.251201i | ||||
\(943\) | 42.6705i | 1.38954i | ||||||||
\(944\) | 0.441038 | 0.0143546 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.659052 | 0.0214276 | ||||||||
\(947\) | 7.90756i | 0.256961i | 0.991712 | + | 0.128481i | \(0.0410100\pi\) | ||||
−0.991712 | + | 0.128481i | \(0.958990\pi\) | |||||||
\(948\) | 0.271117 | − | 3.06110i | 0.00880546 | − | 0.0994199i | ||||
\(949\) | 74.8813 | 2.43075 | ||||||||
\(950\) | 5.18049 | 0.168077 | ||||||||
\(951\) | −10.9315 | − | 0.968185i | −0.354478 | − | 0.0313956i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35.2895i | − | 1.14314i | −0.820554 | − | 0.571569i | \(-0.806335\pi\) | ||
0.820554 | − | 0.571569i | \(-0.193665\pi\) | |||||||
\(954\) | 0.902866 | + | 0.161195i | 0.0292314 | + | 0.00521888i | ||||
\(955\) | 8.58536i | 0.277816i | ||||||||
\(956\) | 14.1670i | 0.458193i | ||||||||
\(957\) | 0.349672 | − | 3.94804i | 0.0113033 | − | 0.127622i | ||||
\(958\) | 31.2048i | 1.00818i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.152807 | − | 1.72530i | 0.00493181 | − | 0.0556837i | ||||
\(961\) | 24.8537 | 0.801733 | ||||||||
\(962\) | 11.8291 | 0.381384 | ||||||||
\(963\) | 6.36886 | − | 35.6725i | 0.205234 | − | 1.14953i | ||||
\(964\) | 17.2184i | 0.554568i | ||||||||
\(965\) | −11.9098 | −0.383391 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.4327 | −0.367650 | −0.183825 | − | 0.982959i | \(-0.558848\pi\) | ||||
−0.183825 | + | 0.982959i | \(0.558848\pi\) | |||||||
\(968\) | − | 10.7730i | − | 0.346257i | ||||||
\(969\) | −47.5129 | − | 4.20814i | −1.52634 | − | 0.135185i | ||||
\(970\) | −8.50932 | −0.273218 | ||||||||
\(971\) | 14.7667 | 0.473885 | 0.236942 | − | 0.971524i | \(-0.423855\pi\) | ||||
0.236942 | + | 0.971524i | \(0.423855\pi\) | |||||||
\(972\) | 6.66355 | − | 14.0924i | 0.213734 | − | 0.452015i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.62293i | 0.148128i | ||||||||
\(975\) | 8.56033 | + | 0.758174i | 0.274150 | + | 0.0242810i | ||||
\(976\) | − | 12.2202i | − | 0.391158i | ||||||
\(977\) | − | 25.5402i | − | 0.817102i | −0.912736 | − | 0.408551i | \(-0.866034\pi\) | ||
0.912736 | − | 0.408551i | \(-0.133966\pi\) | |||||||
\(978\) | −36.0707 | − | 3.19472i | −1.15341 | − | 0.102156i | ||||
\(979\) | 2.48834i | 0.0795275i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −50.3213 | − | 8.98422i | −1.60664 | − | 0.286844i | ||||
\(982\) | 14.9468 | 0.476972 | ||||||||
\(983\) | 1.63102 | 0.0520214 | 0.0260107 | − | 0.999662i | \(-0.491720\pi\) | ||||
0.0260107 | + | 0.999662i | \(0.491720\pi\) | |||||||
\(984\) | −19.8231 | − | 1.75570i | −0.631938 | − | 0.0559697i | ||||
\(985\) | − | 18.0983i | − | 0.576661i | ||||||
\(986\) | −25.5311 | −0.813076 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.7038 | 0.817747 | ||||||||
\(989\) | − | 5.13704i | − | 0.163349i | ||||||
\(990\) | −1.40713 | − | 0.251225i | −0.0447215 | − | 0.00798444i | ||||
\(991\) | 27.2180 | 0.864607 | 0.432304 | − | 0.901728i | \(-0.357701\pi\) | ||||
0.432304 | + | 0.901728i | \(0.357701\pi\) | |||||||
\(992\) | −2.47917 | −0.0787136 | ||||||||
\(993\) | −2.38393 | + | 26.9163i | −0.0756519 | + | 0.854164i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 10.6113i | − | 0.336402i | ||||||
\(996\) | 2.16988 | − | 24.4995i | 0.0687553 | − | 0.776296i | ||||
\(997\) | − | 11.7113i | − | 0.370901i | −0.982654 | − | 0.185451i | \(-0.940625\pi\) | ||
0.982654 | − | 0.185451i | \(-0.0593745\pi\) | |||||||
\(998\) | − | 12.5355i | − | 0.396804i | ||||||
\(999\) | 3.24473 | − | 11.9557i | 0.102659 | − | 0.378260i |
(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 | 1470.2.b.d.881.11 | yes | 16 | |
3.2 | odd | 2 | 1470.2.b.c.881.6 | ✓ | 16 | ||
7.6 | odd | 2 | 1470.2.b.c.881.14 | yes | 16 | ||
21.20 | even | 2 | inner | 1470.2.b.d.881.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.b.c.881.6 | ✓ | 16 | 3.2 | odd | 2 | ||
1470.2.b.c.881.14 | yes | 16 | 7.6 | odd | 2 | ||
1470.2.b.d.881.3 | yes | 16 | 21.20 | even | 2 | inner | |
1470.2.b.d.881.11 | yes | 16 | 1.1 | even | 1 | trivial |