Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (of order \(6\), degree \(2\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 13x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 30.1 | ||
Root | \(-3.12250 - 1.80278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.30 |
Dual form | 637.2.u.f.361.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | − | 0.866025i | 1.06066 | − | 0.612372i | 0.135045 | − | 0.990839i | \(-0.456882\pi\) |
0.925615 | + | 0.378467i | \(0.123549\pi\) | |||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −3.12250 | − | 1.80278i | −1.39642 | − | 0.806226i | −0.402408 | − | 0.915460i | \(-0.631827\pi\) |
−0.994016 | + | 0.109235i | \(0.965160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | −6.24500 | −1.97484 | ||||||||
\(11\) | − | 3.46410i | − | 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.12250 | − | 1.80278i | −0.866025 | − | 0.500000i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(17\) | −3.12250 | + | 5.40833i | −0.757317 | + | 1.31171i | 0.186897 | + | 0.982380i | \(0.440157\pi\) |
−0.944214 | + | 0.329332i | \(0.893176\pi\) | |||||||
\(18\) | −4.50000 | + | 2.59808i | −1.06066 | + | 0.612372i | ||||
\(19\) | − | 7.21110i | − | 1.65434i | −0.561951 | − | 0.827170i | \(-0.689949\pi\) | ||
0.561951 | − | 0.827170i | \(-0.310051\pi\) | |||||||
\(20\) | −3.12250 | + | 1.80278i | −0.698212 | + | 0.403113i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | − | 5.19615i | −0.639602 | − | 1.10782i | ||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | + | 6.92820i | 0.800000 | + | 1.38564i | ||||
\(26\) | −6.24500 | −1.22474 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.500000 | + | 0.866025i | −0.0928477 | + | 0.160817i | −0.908708 | − | 0.417432i | \(-0.862930\pi\) |
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | 4.50000 | + | 2.59808i | 0.795495 | + | 0.459279i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.8167i | 1.85504i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | 1.50000 | − | 0.866025i | 0.246598 | − | 0.142374i | −0.371607 | − | 0.928390i | \(-0.621193\pi\) |
0.618206 | + | 0.786016i | \(0.287860\pi\) | |||||||
\(38\) | −6.24500 | − | 10.8167i | −1.01307 | − | 1.75469i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.12250 | − | 5.40833i | 0.493710 | − | 0.855132i | ||||
\(41\) | 3.12250 | + | 1.80278i | 0.487652 | + | 0.281546i | 0.723600 | − | 0.690220i | \(-0.242486\pi\) |
−0.235948 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 5.19615i | −0.457496 | − | 0.792406i | 0.541332 | − | 0.840809i | \(-0.317920\pi\) |
−0.998828 | + | 0.0484030i | \(0.984587\pi\) | |||||||
\(44\) | −3.00000 | − | 1.73205i | −0.452267 | − | 0.261116i | ||||
\(45\) | 9.36750 | + | 5.40833i | 1.39642 | + | 0.806226i | ||||
\(46\) | −6.00000 | − | 3.46410i | −0.884652 | − | 0.510754i | ||||
\(47\) | 6.24500 | + | 3.60555i | 0.910927 | + | 0.525924i | 0.880729 | − | 0.473620i | \(-0.157053\pi\) |
0.0301974 | + | 0.999544i | \(0.490386\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 12.0000 | + | 6.92820i | 1.69706 | + | 0.979796i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.12250 | + | 1.80278i | −0.433013 | + | 0.250000i | ||||
\(53\) | −2.50000 | − | 4.33013i | −0.343401 | − | 0.594789i | 0.641661 | − | 0.766989i | \(-0.278246\pi\) |
−0.985062 | + | 0.172200i | \(0.944912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.24500 | + | 10.8167i | −0.842075 | + | 1.45852i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.73205i | 0.227429i | ||||||||
\(59\) | 6.24500 | + | 3.60555i | 0.813029 | + | 0.469403i | 0.848007 | − | 0.529985i | \(-0.177803\pi\) |
−0.0349773 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24500 | −0.799590 | −0.399795 | − | 0.916605i | \(-0.630919\pi\) | ||||
−0.399795 | + | 0.916605i | \(0.630919\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.50000 | + | 11.2583i | 0.806226 | + | 1.39642i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.8564i | − | 1.69283i | −0.532524 | − | 0.846415i | \(-0.678756\pi\) | ||
0.532524 | − | 0.846415i | \(-0.321244\pi\) | |||||||
\(68\) | 3.12250 | + | 5.40833i | 0.378659 | + | 0.655856i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | + | 5.19615i | −1.06810 | + | 0.616670i | −0.927663 | − | 0.373419i | \(-0.878185\pi\) |
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(72\) | − | 5.19615i | − | 0.612372i | ||||||
\(73\) | 9.36750 | − | 5.40833i | 1.09638 | − | 0.632997i | 0.161114 | − | 0.986936i | \(-0.448491\pi\) |
0.935269 | + | 0.353939i | \(0.115158\pi\) | |||||||
\(74\) | 1.50000 | − | 2.59808i | 0.174371 | − | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.24500 | − | 3.60555i | −0.716350 | − | 0.413585i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00000 | − | 5.19615i | 0.337526 | − | 0.584613i | −0.646440 | − | 0.762964i | \(-0.723743\pi\) |
0.983967 | + | 0.178352i | \(0.0570765\pi\) | |||||||
\(80\) | − | 18.0278i | − | 2.01556i | ||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 6.24500 | 0.689645 | ||||||||
\(83\) | − | 7.21110i | − | 0.791521i | −0.918354 | − | 0.395761i | \(-0.870481\pi\) | ||
0.918354 | − | 0.395761i | \(-0.129519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.5000 | − | 11.2583i | 2.11507 | − | 1.22114i | ||||
\(86\) | −9.00000 | − | 5.19615i | −0.970495 | − | 0.560316i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.00000 | 0.639602 | ||||||||
\(89\) | −6.24500 | + | 3.60555i | −0.661968 | + | 0.382188i | −0.793027 | − | 0.609187i | \(-0.791496\pi\) |
0.131058 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(90\) | 18.7350 | 1.97484 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.4900 | 1.28824 | ||||||||
\(95\) | −13.0000 | + | 22.5167i | −1.33377 | + | 2.31016i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.24500 | + | 3.60555i | −0.634083 | + | 0.366088i | −0.782332 | − | 0.622862i | \(-0.785970\pi\) |
0.148248 | + | 0.988950i | \(0.452637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3923i | 1.04447i | ||||||||
\(100\) | 8.00000 | 0.800000 | ||||||||
\(101\) | 6.24500 | 0.621401 | 0.310700 | − | 0.950508i | \(-0.399436\pi\) | ||||
0.310700 | + | 0.950508i | \(0.399436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.24500 | − | 10.8167i | 0.615338 | − | 1.06580i | −0.374987 | − | 0.927030i | \(-0.622353\pi\) |
0.990325 | − | 0.138767i | \(-0.0443138\pi\) | |||||||
\(104\) | 3.12250 | − | 5.40833i | 0.306186 | − | 0.530330i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.50000 | − | 4.33013i | −0.728464 | − | 0.420579i | ||||
\(107\) | −1.00000 | − | 1.73205i | −0.0966736 | − | 0.167444i | 0.813632 | − | 0.581380i | \(-0.197487\pi\) |
−0.910306 | + | 0.413936i | \(0.864154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.00000 | + | 3.46410i | −0.574696 | + | 0.331801i | −0.759023 | − | 0.651064i | \(-0.774323\pi\) |
0.184327 | + | 0.982865i | \(0.440990\pi\) | |||||||
\(110\) | 21.6333i | 2.06265i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.50000 | − | 4.33013i | −0.235180 | − | 0.407344i | 0.724145 | − | 0.689648i | \(-0.242235\pi\) |
−0.959325 | + | 0.282304i | \(0.908901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4222i | 1.34488i | ||||||||
\(116\) | 0.500000 | + | 0.866025i | 0.0464238 | + | 0.0804084i | ||||
\(117\) | 9.36750 | + | 5.40833i | 0.866025 | + | 0.500000i | ||||
\(118\) | 12.4900 | 1.14980 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −9.36750 | + | 5.40833i | −0.848093 | + | 0.489647i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.8167i | − | 0.967471i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.00000 | + | 15.5885i | −0.798621 | + | 1.38325i | 0.121894 | + | 0.992543i | \(0.461103\pi\) |
−0.920514 | + | 0.390709i | \(0.872230\pi\) | |||||||
\(128\) | −10.5000 | + | 6.06218i | −0.928078 | + | 0.535826i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 19.5000 | + | 11.2583i | 1.71026 | + | 0.987421i | ||||
\(131\) | −6.24500 | + | 10.8167i | −0.545628 | + | 0.945055i | 0.452939 | + | 0.891541i | \(0.350375\pi\) |
−0.998567 | + | 0.0535140i | \(0.982958\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.0000 | − | 20.7846i | −1.03664 | − | 1.79552i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.36750 | − | 5.40833i | −0.803256 | − | 0.463760i | ||||
\(137\) | −7.50000 | − | 4.33013i | −0.640768 | − | 0.369948i | 0.144142 | − | 0.989557i | \(-0.453958\pi\) |
−0.784910 | + | 0.619609i | \(0.787291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.24500 | − | 10.8167i | −0.529694 | − | 0.917457i | −0.999400 | − | 0.0346338i | \(-0.988974\pi\) |
0.469706 | − | 0.882823i | \(-0.344360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.00000 | + | 15.5885i | −0.755263 | + | 1.30815i | ||||
\(143\) | −6.24500 | + | 10.8167i | −0.522233 | + | 0.904534i | ||||
\(144\) | −7.50000 | − | 12.9904i | −0.625000 | − | 1.08253i | ||||
\(145\) | 3.12250 | − | 1.80278i | 0.259309 | − | 0.149712i | ||||
\(146\) | 9.36750 | − | 16.2250i | 0.775260 | − | 1.34279i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.73205i | − | 0.142374i | ||||||
\(149\) | 15.5885i | 1.27706i | 0.769599 | + | 0.638528i | \(0.220456\pi\) | ||||
−0.769599 | + | 0.638528i | \(0.779544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | + | 1.73205i | −0.244137 | + | 0.140952i | −0.617076 | − | 0.786903i | \(-0.711683\pi\) |
0.372940 | + | 0.927855i | \(0.378350\pi\) | |||||||
\(152\) | 12.4900 | 1.01307 | ||||||||
\(153\) | 9.36750 | − | 16.2250i | 0.757317 | − | 1.31171i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.12250 | − | 5.40833i | −0.249203 | − | 0.431631i | 0.714102 | − | 0.700041i | \(-0.246835\pi\) |
−0.963305 | + | 0.268410i | \(0.913502\pi\) | |||||||
\(158\) | − | 10.3923i | − | 0.826767i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.36750 | − | 16.2250i | −0.740566 | − | 1.28270i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.5000 | − | 7.79423i | 1.06066 | − | 0.612372i | ||||
\(163\) | − | 10.3923i | − | 0.813988i | −0.913431 | − | 0.406994i | \(-0.866577\pi\) | ||
0.913431 | − | 0.406994i | \(-0.133423\pi\) | |||||||
\(164\) | 3.12250 | − | 1.80278i | 0.243826 | − | 0.140773i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.24500 | − | 10.8167i | −0.484706 | − | 0.839535i | ||||
\(167\) | 6.24500 | + | 3.60555i | 0.483252 | + | 0.279006i | 0.721771 | − | 0.692132i | \(-0.243328\pi\) |
−0.238518 | + | 0.971138i | \(0.576662\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.50000 | + | 11.2583i | 0.500000 | + | 0.866025i | ||||
\(170\) | 19.5000 | − | 33.7750i | 1.49558 | − | 2.59042i | ||||
\(171\) | 21.6333i | 1.65434i | ||||||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | −24.9800 | −1.89919 | −0.949597 | − | 0.313474i | \(-0.898507\pi\) | ||||
−0.949597 | + | 0.313474i | \(0.898507\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.0000 | − | 8.66025i | 1.13067 | − | 0.652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.24500 | + | 10.8167i | −0.468082 | + | 0.810742i | ||||
\(179\) | 16.0000 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(180\) | 9.36750 | − | 5.40833i | 0.698212 | − | 0.403113i | ||||
\(181\) | −6.24500 | −0.464187 | −0.232094 | − | 0.972693i | \(-0.574558\pi\) | ||||
−0.232094 | + | 0.972693i | \(0.574558\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | − | 3.46410i | 0.442326 | − | 0.255377i | ||||
\(185\) | −6.24500 | −0.459141 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.7350 | + | 10.8167i | 1.37004 | + | 0.790992i | ||||
\(188\) | 6.24500 | − | 3.60555i | 0.455463 | − | 0.262962i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 45.0333i | 3.26706i | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.66025i | − | 0.623379i | −0.950184 | − | 0.311689i | \(-0.899105\pi\) | ||
0.950184 | − | 0.311689i | \(-0.100895\pi\) | |||||||
\(194\) | −6.24500 | + | 10.8167i | −0.448365 | + | 0.776590i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(198\) | 9.00000 | + | 15.5885i | 0.639602 | + | 1.10782i | ||||
\(199\) | 6.24500 | − | 10.8167i | 0.442696 | − | 0.766772i | −0.555192 | − | 0.831722i | \(-0.687355\pi\) |
0.997889 | + | 0.0649497i | \(0.0206887\pi\) | |||||||
\(200\) | −12.0000 | + | 6.92820i | −0.848528 | + | 0.489898i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.36750 | − | 5.40833i | 0.659095 | − | 0.380529i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.50000 | − | 11.2583i | −0.453980 | − | 0.786316i | ||||
\(206\) | − | 21.6333i | − | 1.50726i | ||||||
\(207\) | 6.00000 | + | 10.3923i | 0.417029 | + | 0.722315i | ||||
\(208\) | − | 18.0278i | − | 1.25000i | ||||||
\(209\) | −24.9800 | −1.72790 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | − | 17.3205i | 0.688428 | − | 1.19239i | −0.283918 | − | 0.958849i | \(-0.591634\pi\) |
0.972346 | − | 0.233544i | \(-0.0750324\pi\) | |||||||
\(212\) | −5.00000 | −0.343401 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.00000 | − | 1.73205i | −0.205076 | − | 0.118401i | ||||
\(215\) | 21.6333i | 1.47538i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | + | 10.3923i | −0.406371 | + | 0.703856i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.24500 | + | 10.8167i | 0.421038 | + | 0.729259i | ||||
\(221\) | 19.5000 | − | 11.2583i | 1.31171 | − | 0.757317i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.24500 | + | 3.60555i | 0.418196 | + | 0.241446i | 0.694305 | − | 0.719681i | \(-0.255712\pi\) |
−0.276109 | + | 0.961126i | \(0.589045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | − | 20.7846i | −0.800000 | − | 1.38564i | ||||
\(226\) | −7.50000 | − | 4.33013i | −0.498893 | − | 0.288036i | ||||
\(227\) | −12.4900 | − | 7.21110i | −0.828990 | − | 0.478618i | 0.0245166 | − | 0.999699i | \(-0.492195\pi\) |
−0.853507 | + | 0.521082i | \(0.825529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7350 | − | 10.8167i | −1.23804 | − | 0.714785i | −0.269349 | − | 0.963043i | \(-0.586809\pi\) |
−0.968694 | + | 0.248258i | \(0.920142\pi\) | |||||||
\(230\) | 12.4900 | + | 21.6333i | 0.823566 | + | 1.42646i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.50000 | − | 0.866025i | −0.0984798 | − | 0.0568574i | ||||
\(233\) | −1.00000 | + | 1.73205i | −0.0655122 | + | 0.113470i | −0.896921 | − | 0.442191i | \(-0.854201\pi\) |
0.831409 | + | 0.555661i | \(0.187535\pi\) | |||||||
\(234\) | 18.7350 | 1.22474 | ||||||||
\(235\) | −13.0000 | − | 22.5167i | −0.848026 | − | 1.46882i | ||||
\(236\) | 6.24500 | − | 3.60555i | 0.406515 | − | 0.234701i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 17.3205i | − | 1.12037i | −0.828367 | − | 0.560185i | \(-0.810730\pi\) | ||
0.828367 | − | 0.560185i | \(-0.189270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.36750 | − | 5.40833i | −0.603414 | − | 0.348381i | 0.166970 | − | 0.985962i | \(-0.446602\pi\) |
−0.770383 | + | 0.637581i | \(0.779935\pi\) | |||||||
\(242\) | −1.50000 | + | 0.866025i | −0.0964237 | + | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.12250 | + | 5.40833i | −0.199898 | + | 0.346233i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.0000 | + | 22.5167i | −0.827170 | + | 1.43270i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.36750 | − | 16.2250i | −0.592453 | − | 1.02616i | ||||
\(251\) | 6.24500 | + | 10.8167i | 0.394181 | + | 0.682741i | 0.992996 | − | 0.118146i | \(-0.0376950\pi\) |
−0.598815 | + | 0.800887i | \(0.704362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | + | 6.92820i | −0.754434 | + | 0.435572i | ||||
\(254\) | 31.1769i | 1.95621i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | 9.36750 | + | 16.2250i | 0.584328 | + | 1.01209i | 0.994959 | + | 0.100285i | \(0.0319753\pi\) |
−0.410630 | + | 0.911802i | \(0.634691\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.0000 | 0.806226 | ||||||||
\(261\) | 1.50000 | − | 2.59808i | 0.0928477 | − | 0.160817i | ||||
\(262\) | 21.6333i | 1.33651i | ||||||||
\(263\) | 2.00000 | 0.123325 | 0.0616626 | − | 0.998097i | \(-0.480360\pi\) | ||||
0.0616626 | + | 0.998097i | \(0.480360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0278i | 1.10744i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.0000 | − | 6.92820i | −0.733017 | − | 0.423207i | ||||
\(269\) | 12.4900 | − | 21.6333i | 0.761528 | − | 1.31901i | −0.180534 | − | 0.983569i | \(-0.557783\pi\) |
0.942063 | − | 0.335437i | \(-0.108884\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.24500 | − | 3.60555i | 0.379357 | − | 0.219022i | −0.298182 | − | 0.954509i | \(-0.596380\pi\) |
0.677538 | + | 0.735487i | \(0.263047\pi\) | |||||||
\(272\) | −31.2250 | −1.89329 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.0000 | −0.906183 | ||||||||
\(275\) | 24.0000 | − | 13.8564i | 1.44725 | − | 0.835573i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.5000 | + | 21.6506i | −0.751052 | + | 1.30086i | 0.196261 | + | 0.980552i | \(0.437120\pi\) |
−0.947313 | + | 0.320309i | \(0.896213\pi\) | |||||||
\(278\) | −18.7350 | − | 10.8167i | −1.12365 | − | 0.648740i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5167i | 1.34323i | 0.740900 | + | 0.671616i | \(0.234399\pi\) | ||||
−0.740900 | + | 0.671616i | \(0.765601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4900 | −0.742453 | −0.371227 | − | 0.928542i | \(-0.621063\pi\) | ||||
−0.371227 | + | 0.928542i | \(0.621063\pi\) | |||||||
\(284\) | 10.3923i | 0.616670i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.6333i | 1.27920i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −13.5000 | − | 7.79423i | −0.795495 | − | 0.459279i | ||||
\(289\) | −11.0000 | − | 19.0526i | −0.647059 | − | 1.12074i | ||||
\(290\) | 3.12250 | − | 5.40833i | 0.183359 | − | 0.317588i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 10.8167i | − | 0.632997i | ||||||
\(293\) | −15.6125 | + | 9.01388i | −0.912092 | + | 0.526596i | −0.881104 | − | 0.472923i | \(-0.843199\pi\) |
−0.0309881 | + | 0.999520i | \(0.509865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0000 | − | 22.5167i | −0.756889 | − | 1.31097i | ||||
\(296\) | 1.50000 | + | 2.59808i | 0.0871857 | + | 0.151010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.5000 | + | 23.3827i | 0.782034 | + | 1.35452i | ||||
\(299\) | 14.4222i | 0.834058i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.00000 | + | 5.19615i | −0.172631 | + | 0.299005i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 31.2250 | − | 18.0278i | 1.79088 | − | 1.03396i | ||||
\(305\) | 19.5000 | + | 11.2583i | 1.11657 | + | 0.644650i | ||||
\(306\) | − | 32.4500i | − | 1.85504i | ||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4900 | + | 21.6333i | 0.708243 | + | 1.22671i | 0.965508 | + | 0.260372i | \(0.0838451\pi\) |
−0.257266 | + | 0.966341i | \(0.582822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(314\) | −9.36750 | − | 5.40833i | −0.528638 | − | 0.305210i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | − | 5.19615i | −0.168763 | − | 0.292306i | ||||
\(317\) | −13.5000 | − | 7.79423i | −0.758236 | − | 0.437767i | 0.0704263 | − | 0.997517i | \(-0.477564\pi\) |
−0.828662 | + | 0.559749i | \(0.810897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | + | 1.73205i | 0.167968 | + | 0.0969762i | ||||
\(320\) | 3.12250 | + | 1.80278i | 0.174553 | + | 0.100778i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.0000 | + | 22.5167i | 2.17002 | + | 1.25286i | ||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | − | 28.8444i | − | 1.60000i | ||||||
\(326\) | −9.00000 | − | 15.5885i | −0.498464 | − | 0.863365i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.12250 | + | 5.40833i | −0.172411 | + | 0.298625i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3923i | 0.571213i | 0.958347 | + | 0.285606i | \(0.0921950\pi\) | ||||
−0.958347 | + | 0.285606i | \(0.907805\pi\) | |||||||
\(332\) | −6.24500 | − | 3.60555i | −0.342739 | − | 0.197880i | ||||
\(333\) | −4.50000 | + | 2.59808i | −0.246598 | + | 0.142374i | ||||
\(334\) | 12.4900 | 0.683422 | ||||||||
\(335\) | −24.9800 | + | 43.2666i | −1.36480 | + | 2.36391i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | 0.599208 | 0.299604 | − | 0.954064i | \(-0.403145\pi\) | ||||
0.299604 | + | 0.954064i | \(0.403145\pi\) | |||||||
\(338\) | 19.5000 | + | 11.2583i | 1.06066 | + | 0.612372i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 22.5167i | − | 1.22114i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 18.7350 | + | 32.4500i | 1.01307 | + | 1.75469i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.00000 | − | 5.19615i | 0.485247 | − | 0.280158i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −37.4700 | + | 21.6333i | −2.01440 | + | 1.16301i | ||||
\(347\) | 14.0000 | − | 24.2487i | 0.751559 | − | 1.30174i | −0.195507 | − | 0.980702i | \(-0.562635\pi\) |
0.947067 | − | 0.321037i | \(-0.104031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.7350 | + | 10.8167i | 1.00286 | + | 0.579002i | 0.909094 | − | 0.416592i | \(-0.136776\pi\) |
0.0937676 | + | 0.995594i | \(0.470109\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.00000 | − | 15.5885i | 0.479702 | − | 0.830868i | ||||
\(353\) | − | 25.2389i | − | 1.34333i | −0.740855 | − | 0.671664i | \(-0.765580\pi\) | ||
0.740855 | − | 0.671664i | \(-0.234420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.4700 | 1.98870 | ||||||||
\(356\) | 7.21110i | 0.382188i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.0000 | − | 13.8564i | 1.26844 | − | 0.732334i | ||||
\(359\) | −24.0000 | − | 13.8564i | −1.26667 | − | 0.731313i | −0.292315 | − | 0.956322i | \(-0.594426\pi\) |
−0.974357 | + | 0.225009i | \(0.927759\pi\) | |||||||
\(360\) | −9.36750 | + | 16.2250i | −0.493710 | + | 0.855132i | ||||
\(361\) | −33.0000 | −1.73684 | ||||||||
\(362\) | −9.36750 | + | 5.40833i | −0.492345 | + | 0.284255i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.0000 | −2.04135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.9800 | −1.30394 | −0.651972 | − | 0.758243i | \(-0.726058\pi\) | ||||
−0.651972 | + | 0.758243i | \(0.726058\pi\) | |||||||
\(368\) | 10.0000 | − | 17.3205i | 0.521286 | − | 0.902894i | ||||
\(369\) | −9.36750 | − | 5.40833i | −0.487652 | − | 0.281546i | ||||
\(370\) | −9.36750 | + | 5.40833i | −0.486993 | + | 0.281166i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0000 | 0.776671 | 0.388335 | − | 0.921518i | \(-0.373050\pi\) | ||||
0.388335 | + | 0.921518i | \(0.373050\pi\) | |||||||
\(374\) | 37.4700 | 1.93753 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.24500 | + | 10.8167i | −0.322061 | + | 0.557826i | ||||
\(377\) | 3.12250 | − | 1.80278i | 0.160817 | − | 0.0928477i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0000 | + | 10.3923i | 0.924598 | + | 0.533817i | 0.885099 | − | 0.465403i | \(-0.154091\pi\) |
0.0394989 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(380\) | 13.0000 | + | 22.5167i | 0.666886 | + | 1.15508i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.00000 | − | 3.46410i | 0.306987 | − | 0.177239i | ||||
\(383\) | − | 36.0555i | − | 1.84235i | −0.389148 | − | 0.921175i | \(-0.627230\pi\) | ||
0.389148 | − | 0.921175i | \(-0.372770\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.50000 | − | 12.9904i | −0.381740 | − | 0.661193i | ||||
\(387\) | 9.00000 | + | 15.5885i | 0.457496 | + | 0.792406i | ||||
\(388\) | 7.21110i | 0.366088i | ||||||||
\(389\) | −8.50000 | − | 14.7224i | −0.430967 | − | 0.746457i | 0.565990 | − | 0.824412i | \(-0.308494\pi\) |
−0.996957 | + | 0.0779554i | \(0.975161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9800 | 1.26329 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.7350 | + | 10.8167i | −0.942660 | + | 0.544245i | ||||
\(396\) | 9.00000 | + | 5.19615i | 0.452267 | + | 0.261116i | ||||
\(397\) | − | 7.21110i | − | 0.361915i | −0.983491 | − | 0.180957i | \(-0.942080\pi\) | ||
0.983491 | − | 0.180957i | \(-0.0579196\pi\) | |||||||
\(398\) | − | 21.6333i | − | 1.08438i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | + | 34.6410i | −1.00000 | + | 1.73205i | ||||
\(401\) | −7.50000 | + | 4.33013i | −0.374532 | + | 0.216236i | −0.675437 | − | 0.737418i | \(-0.736045\pi\) |
0.300904 | + | 0.953654i | \(0.402711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.12250 | − | 5.40833i | 0.155350 | − | 0.269074i | ||||
\(405\) | −28.1025 | − | 16.2250i | −1.39642 | − | 0.806226i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.00000 | − | 5.19615i | −0.148704 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.8575 | + | 12.6194i | 1.08078 | + | 0.623991i | 0.931108 | − | 0.364744i | \(-0.118844\pi\) |
0.149676 | + | 0.988735i | \(0.452177\pi\) | |||||||
\(410\) | −19.5000 | − | 11.2583i | −0.963036 | − | 0.556009i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.24500 | − | 10.8167i | −0.307669 | − | 0.532898i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.0000 | + | 10.3923i | 0.884652 | + | 0.510754i | ||||
\(415\) | −13.0000 | + | 22.5167i | −0.638145 | + | 1.10530i | ||||
\(416\) | −9.36750 | − | 16.2250i | −0.459279 | − | 0.795495i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −37.4700 | + | 21.6333i | −1.83272 | + | 1.05812i | ||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.5167i | 1.09739i | 0.836021 | + | 0.548697i | \(0.184876\pi\) | ||||
−0.836021 | + | 0.548697i | \(0.815124\pi\) | |||||||
\(422\) | − | 34.6410i | − | 1.68630i | ||||||
\(423\) | −18.7350 | − | 10.8167i | −0.910927 | − | 0.525924i | ||||
\(424\) | 7.50000 | − | 4.33013i | 0.364232 | − | 0.210290i | ||||
\(425\) | −49.9600 | −2.42342 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.7350 | + | 32.4500i | 0.903482 | + | 1.56488i | ||||
\(431\) | 27.7128i | 1.33488i | 0.744664 | + | 0.667440i | \(0.232610\pi\) | ||||
−0.744664 | + | 0.667440i | \(0.767390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.36750 | − | 16.2250i | −0.450173 | − | 0.779723i | 0.548223 | − | 0.836332i | \(-0.315304\pi\) |
−0.998396 | + | 0.0566092i | \(0.981971\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.92820i | 0.331801i | ||||||||
\(437\) | −24.9800 | + | 14.4222i | −1.19496 | + | 0.689908i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.24500 | − | 10.8167i | −0.298057 | − | 0.516251i | 0.677634 | − | 0.735399i | \(-0.263005\pi\) |
−0.975691 | + | 0.219149i | \(0.929672\pi\) | |||||||
\(440\) | −18.7350 | − | 10.8167i | −0.893156 | − | 0.515664i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.5000 | − | 33.7750i | 0.927520 | − | 1.60651i | ||||
\(443\) | −8.00000 | + | 13.8564i | −0.380091 | + | 0.658338i | −0.991075 | − | 0.133306i | \(-0.957441\pi\) |
0.610984 | + | 0.791643i | \(0.290774\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.0000 | 1.23252 | ||||||||
\(446\) | 12.4900 | 0.591418 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | − | 3.46410i | 0.283158 | − | 0.163481i | −0.351694 | − | 0.936115i | \(-0.614394\pi\) |
0.634852 | + | 0.772634i | \(0.281061\pi\) | |||||||
\(450\) | −36.0000 | − | 20.7846i | −1.69706 | − | 0.979796i | ||||
\(451\) | 6.24500 | − | 10.8167i | 0.294065 | − | 0.509336i | ||||
\(452\) | −5.00000 | −0.235180 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.9800 | −1.17237 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.5000 | − | 19.9186i | 1.61384 | − | 0.931752i | 0.625373 | − | 0.780326i | \(-0.284947\pi\) |
0.988469 | − | 0.151426i | \(-0.0483867\pi\) | |||||||
\(458\) | −37.4700 | −1.75086 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.4900 | + | 7.21110i | 0.582349 | + | 0.336219i | ||||
\(461\) | 34.3475 | − | 19.8305i | 1.59972 | − | 0.923600i | 0.608182 | − | 0.793797i | \(-0.291899\pi\) |
0.991540 | − | 0.129802i | \(-0.0414343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.3923i | − | 0.482971i | −0.970404 | − | 0.241486i | \(-0.922365\pi\) | ||
0.970404 | − | 0.241486i | \(-0.0776347\pi\) | |||||||
\(464\) | −5.00000 | −0.232119 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.46410i | 0.160471i | ||||||||
\(467\) | −6.24500 | + | 10.8167i | −0.288984 | + | 0.500535i | −0.973568 | − | 0.228399i | \(-0.926651\pi\) |
0.684583 | + | 0.728934i | \(0.259984\pi\) | |||||||
\(468\) | 9.36750 | − | 5.40833i | 0.433013 | − | 0.250000i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −39.0000 | − | 22.5167i | −1.79894 | − | 1.03862i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.24500 | + | 10.8167i | −0.287449 | + | 0.497877i | ||||
\(473\) | −18.0000 | + | 10.3923i | −0.827641 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 49.9600 | − | 28.8444i | 2.29232 | − | 1.32347i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.50000 | + | 12.9904i | 0.343401 | + | 0.594789i | ||||
\(478\) | −15.0000 | − | 25.9808i | −0.686084 | − | 1.18833i | ||||
\(479\) | − | 14.4222i | − | 0.658967i | −0.944161 | − | 0.329484i | \(-0.893125\pi\) | ||
0.944161 | − | 0.329484i | \(-0.106875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.24500 | −0.284747 | ||||||||
\(482\) | −18.7350 | −0.853356 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | 26.0000 | 1.18060 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0000 | + | 10.3923i | 0.815658 | + | 0.470920i | 0.848917 | − | 0.528526i | \(-0.177255\pi\) |
−0.0332590 | + | 0.999447i | \(0.510589\pi\) | |||||||
\(488\) | − | 10.8167i | − | 0.489647i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | − | 3.46410i | 0.0902587 | − | 0.156333i | −0.817361 | − | 0.576126i | \(-0.804564\pi\) |
0.907620 | + | 0.419793i | \(0.137897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.12250 | − | 5.40833i | −0.140630 | − | 0.243579i | ||||
\(494\) | 45.0333i | 2.02614i | ||||||||
\(495\) | 18.7350 | − | 32.4500i | 0.842075 | − | 1.45852i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.0000 | + | 13.8564i | 1.07439 | + | 0.620298i | 0.929377 | − | 0.369132i | \(-0.120345\pi\) |
0.145011 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(500\) | −9.36750 | − | 5.40833i | −0.418927 | − | 0.241868i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.7350 | + | 10.8167i | 0.836184 | + | 0.482771i | ||||
\(503\) | −6.24500 | − | 10.8167i | −0.278451 | − | 0.482291i | 0.692549 | − | 0.721371i | \(-0.256488\pi\) |
−0.971000 | + | 0.239080i | \(0.923154\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.5000 | − | 11.2583i | −0.867739 | − | 0.500989i | ||||
\(506\) | −12.0000 | + | 20.7846i | −0.533465 | + | 0.923989i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.00000 | + | 15.5885i | 0.399310 | + | 0.691626i | ||||
\(509\) | 3.12250 | − | 1.80278i | 0.138402 | − | 0.0799066i | −0.429200 | − | 0.903209i | \(-0.641204\pi\) |
0.567602 | + | 0.823303i | \(0.307871\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.1025 | + | 16.2250i | 1.23955 | + | 0.715653i | ||||
\(515\) | −39.0000 | + | 22.5167i | −1.71855 | + | 0.992203i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4900 | − | 21.6333i | 0.549309 | − | 0.951432i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −19.5000 | + | 11.2583i | −0.855132 | + | 0.493710i | ||||
\(521\) | −3.12250 | − | 5.40833i | −0.136799 | − | 0.236943i | 0.789484 | − | 0.613771i | \(-0.210348\pi\) |
−0.926283 | + | 0.376828i | \(0.877015\pi\) | |||||||
\(522\) | − | 5.19615i | − | 0.227429i | ||||||
\(523\) | 12.4900 | + | 21.6333i | 0.546149 | + | 0.945958i | 0.998534 | + | 0.0541354i | \(0.0172402\pi\) |
−0.452384 | + | 0.891823i | \(0.649426\pi\) | |||||||
\(524\) | 6.24500 | + | 10.8167i | 0.272814 | + | 0.472528i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.00000 | − | 1.73205i | 0.130806 | − | 0.0755210i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 15.6125 | + | 27.0416i | 0.678163 | + | 1.17461i | ||||
\(531\) | −18.7350 | − | 10.8167i | −0.813029 | − | 0.469403i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.50000 | − | 11.2583i | −0.281546 | − | 0.487652i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.21110i | 0.311763i | ||||||||
\(536\) | 24.0000 | 1.03664 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 43.2666i | − | 1.86536i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.50000 | + | 2.59808i | 0.193470 | + | 0.111700i | 0.593606 | − | 0.804756i | \(-0.297704\pi\) |
−0.400136 | + | 0.916456i | \(0.631037\pi\) | |||||||
\(542\) | 6.24500 | − | 10.8167i | 0.268246 | − | 0.464615i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.1025 | + | 16.2250i | −1.20488 | + | 0.695640i | ||||
\(545\) | 24.9800 | 1.07003 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | −7.50000 | + | 4.33013i | −0.320384 | + | 0.184974i | ||||
\(549\) | 18.7350 | 0.799590 | ||||||||
\(550\) | 24.0000 | − | 41.5692i | 1.02336 | − | 1.77252i | ||||
\(551\) | 6.24500 | + | 3.60555i | 0.266046 | + | 0.153602i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 43.3013i | 1.83969i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.4900 | −0.529694 | ||||||||
\(557\) | 1.73205i | 0.0733893i | 0.999327 | + | 0.0366947i | \(0.0116829\pi\) | ||||
−0.999327 | + | 0.0366947i | \(0.988317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.6333i | 0.914991i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.5000 | + | 33.7750i | 0.822558 | + | 1.42471i | ||||
\(563\) | −6.24500 | + | 10.8167i | −0.263195 | + | 0.455868i | −0.967089 | − | 0.254437i | \(-0.918110\pi\) |
0.703894 | + | 0.710305i | \(0.251443\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0278i | 0.758433i | ||||||||
\(566\) | −18.7350 | + | 10.8167i | −0.787491 | + | 0.454658i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.00000 | − | 15.5885i | −0.377632 | − | 0.654077i | ||||
\(569\) | −5.00000 | − | 8.66025i | −0.209611 | − | 0.363057i | 0.741981 | − | 0.670421i | \(-0.233886\pi\) |
−0.951592 | + | 0.307364i | \(0.900553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | − | 20.7846i | −0.502184 | − | 0.869809i | −0.999997 | − | 0.00252413i | \(-0.999197\pi\) |
0.497812 | − | 0.867285i | \(-0.334137\pi\) | |||||||
\(572\) | 6.24500 | + | 10.8167i | 0.261116 | + | 0.452267i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0000 | − | 27.7128i | 0.667246 | − | 1.15570i | ||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | 15.6125 | − | 9.01388i | 0.649957 | − | 0.375253i | −0.138483 | − | 0.990365i | \(-0.544223\pi\) |
0.788440 | + | 0.615112i | \(0.210889\pi\) | |||||||
\(578\) | −33.0000 | − | 19.0526i | −1.37262 | − | 0.792482i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 3.60555i | − | 0.149712i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.0000 | + | 8.66025i | −0.621237 | + | 0.358671i | ||||
\(584\) | 9.36750 | + | 16.2250i | 0.387630 | + | 0.671394i | ||||
\(585\) | −19.5000 | − | 33.7750i | −0.806226 | − | 1.39642i | ||||
\(586\) | −15.6125 | + | 27.0416i | −0.644946 | + | 1.11708i | ||||
\(587\) | 24.9800 | + | 14.4222i | 1.03103 | + | 0.595268i | 0.917281 | − | 0.398241i | \(-0.130379\pi\) |
0.113754 | + | 0.993509i | \(0.463713\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −39.0000 | − | 22.5167i | −1.60560 | − | 0.926996i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.50000 | + | 4.33013i | 0.308248 | + | 0.177967i | ||||
\(593\) | −15.6125 | − | 9.01388i | −0.641128 | − | 0.370156i | 0.143921 | − | 0.989589i | \(-0.454029\pi\) |
−0.785049 | + | 0.619434i | \(0.787362\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.5000 | + | 7.79423i | 0.552982 | + | 0.319264i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.4900 | + | 21.6333i | 0.510754 | + | 0.884652i | ||||
\(599\) | 5.00000 | + | 8.66025i | 0.204294 | + | 0.353848i | 0.949908 | − | 0.312531i | \(-0.101177\pi\) |
−0.745613 | + | 0.666379i | \(0.767843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.8575 | − | 37.8583i | 0.891586 | − | 1.54427i | 0.0536116 | − | 0.998562i | \(-0.482927\pi\) |
0.837974 | − | 0.545710i | \(-0.183740\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.5692i | 1.69283i | ||||||||
\(604\) | 3.46410i | 0.140952i | ||||||||
\(605\) | 3.12250 | + | 1.80278i | 0.126948 | + | 0.0732933i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.4700 | 1.52086 | 0.760430 | − | 0.649420i | \(-0.224988\pi\) | ||||
0.760430 | + | 0.649420i | \(0.224988\pi\) | |||||||
\(608\) | 18.7350 | − | 32.4500i | 0.759804 | − | 1.31602i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.0000 | 1.57906 | ||||||||
\(611\) | −13.0000 | − | 22.5167i | −0.525924 | − | 0.910927i | ||||
\(612\) | −9.36750 | − | 16.2250i | −0.378659 | − | 0.655856i | ||||
\(613\) | 1.73205i | 0.0699569i | 0.999388 | + | 0.0349784i | \(0.0111363\pi\) | ||||
−0.999388 | + | 0.0349784i | \(0.988864\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.5000 | − | 11.2583i | 0.785040 | − | 0.453243i | −0.0531732 | − | 0.998585i | \(-0.516934\pi\) |
0.838214 | + | 0.545342i | \(0.183600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.2250 | − | 18.0278i | 1.25504 | − | 0.724597i | 0.282933 | − | 0.959140i | \(-0.408693\pi\) |
0.972106 | + | 0.234543i | \(0.0753594\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 37.4700 | + | 21.6333i | 1.50241 | + | 0.867417i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.24500 | −0.249203 | ||||||||
\(629\) | 10.8167i | 0.431288i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0000 | + | 6.92820i | −0.477712 | + | 0.275807i | −0.719463 | − | 0.694531i | \(-0.755612\pi\) |
0.241750 | + | 0.970339i | \(0.422279\pi\) | |||||||
\(632\) | 9.00000 | + | 5.19615i | 0.358001 | + | 0.206692i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.0000 | −1.07231 | ||||||||
\(635\) | 56.2050 | − | 32.4500i | 2.23043 | − | 1.28774i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | 27.0000 | − | 15.5885i | 1.06810 | − | 0.616670i | ||||
\(640\) | 43.7150 | 1.72799 | ||||||||
\(641\) | 14.5000 | − | 25.1147i | 0.572716 | − | 0.991972i | −0.423570 | − | 0.905863i | \(-0.639223\pi\) |
0.996286 | − | 0.0861092i | \(-0.0274434\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 78.0000 | 3.06887 | ||||||||
\(647\) | −12.4900 | −0.491032 | −0.245516 | − | 0.969392i | \(-0.578957\pi\) | ||||
−0.245516 | + | 0.969392i | \(0.578957\pi\) | |||||||
\(648\) | 15.5885i | 0.612372i | ||||||||
\(649\) | 12.4900 | − | 21.6333i | 0.490275 | − | 0.849182i | ||||
\(650\) | −24.9800 | − | 43.2666i | −0.979796 | − | 1.69706i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.00000 | − | 5.19615i | −0.352467 | − | 0.203497i | ||||
\(653\) | −19.0000 | − | 32.9090i | −0.743527 | − | 1.28783i | −0.950880 | − | 0.309561i | \(-0.899818\pi\) |
0.207352 | − | 0.978266i | \(-0.433515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.0000 | − | 22.5167i | 1.52386 | − | 0.879799i | ||||
\(656\) | 18.0278i | 0.703866i | ||||||||
\(657\) | −28.1025 | + | 16.2250i | −1.09638 | + | 0.632997i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00000 | + | 3.46410i | 0.0779089 | + | 0.134942i | 0.902348 | − | 0.431009i | \(-0.141842\pi\) |
−0.824439 | + | 0.565951i | \(0.808509\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.8167i | − | 0.420719i | −0.977624 | − | 0.210360i | \(-0.932537\pi\) | ||
0.977624 | − | 0.210360i | \(-0.0674635\pi\) | |||||||
\(662\) | 9.00000 | + | 15.5885i | 0.349795 | + | 0.605863i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.4900 | 0.484706 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.50000 | + | 7.79423i | −0.174371 | + | 0.302020i | ||||
\(667\) | 4.00000 | 0.154881 | ||||||||
\(668\) | 6.24500 | − | 3.60555i | 0.241626 | − | 0.139503i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 86.5332i | 3.34307i | ||||||||
\(671\) | 21.6333i | 0.835145i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.50000 | + | 2.59808i | −0.0578208 | + | 0.100148i | −0.893487 | − | 0.449089i | \(-0.851749\pi\) |
0.835666 | + | 0.549238i | \(0.185082\pi\) | |||||||
\(674\) | 16.5000 | − | 9.52628i | 0.635556 | − | 0.366939i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | 0.500000 | ||||||||
\(677\) | −12.4900 | + | 21.6333i | −0.480030 | + | 0.831436i | −0.999738 | − | 0.0229084i | \(-0.992707\pi\) |
0.519708 | + | 0.854344i | \(0.326041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 19.5000 | + | 33.7750i | 0.747791 | + | 1.29521i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.0000 | + | 22.5167i | 1.49229 | + | 0.861576i | 0.999961 | − | 0.00883113i | \(-0.00281107\pi\) |
0.492333 | + | 0.870407i | \(0.336144\pi\) | |||||||
\(684\) | 18.7350 | + | 10.8167i | 0.716350 | + | 0.413585i | ||||
\(685\) | 15.6125 | + | 27.0416i | 0.596523 | + | 1.03321i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.0000 | − | 25.9808i | 0.571870 | − | 0.990507i | ||||
\(689\) | 18.0278i | 0.686803i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9800 | − | 14.4222i | 0.950284 | − | 0.548647i | 0.0571146 | − | 0.998368i | \(-0.481810\pi\) |
0.893169 | + | 0.449721i | \(0.148477\pi\) | |||||||
\(692\) | −12.4900 | + | 21.6333i | −0.474798 | + | 0.822375i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 48.4974i | − | 1.84094i | ||||||
\(695\) | 45.0333i | 1.70821i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.5000 | + | 11.2583i | −0.738615 | + | 0.426440i | ||||
\(698\) | 37.4700 | 1.41826 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0000 | 0.528773 | 0.264386 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264386 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.24500 | − | 10.8167i | −0.235535 | − | 0.407958i | ||||
\(704\) | 3.46410i | 0.130558i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.8575 | − | 37.8583i | −0.822618 | − | 1.42482i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.9090i | 1.23592i | 0.786209 | + | 0.617961i | \(0.212041\pi\) | ||||
−0.786209 | + | 0.617961i | \(0.787959\pi\) | |||||||
\(710\) | 56.2050 | − | 32.4500i | 2.10934 | − | 1.21783i | ||||
\(711\) | −9.00000 | + | 15.5885i | −0.337526 | + | 0.584613i | ||||
\(712\) | −6.24500 | − | 10.8167i | −0.234041 | − | 0.405371i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.0000 | − | 22.5167i | 1.45852 | − | 0.842075i | ||||
\(716\) | 8.00000 | − | 13.8564i | 0.298974 | − | 0.517838i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −48.0000 | −1.79134 | ||||||||
\(719\) | −37.4700 | −1.39739 | −0.698697 | − | 0.715417i | \(-0.746237\pi\) | ||||
−0.698697 | + | 0.715417i | \(0.746237\pi\) | |||||||
\(720\) | 54.0833i | 2.01556i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −49.5000 | + | 28.5788i | −1.84220 | + | 1.06359i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.12250 | + | 5.40833i | −0.116047 | + | 0.200999i | ||||
\(725\) | −8.00000 | −0.297113 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.9800 | 0.926457 | 0.463228 | − | 0.886239i | \(-0.346691\pi\) | ||||
0.463228 | + | 0.886239i | \(0.346691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −58.5000 | + | 33.7750i | −2.16518 | + | 1.25007i | ||||
\(731\) | 37.4700 | 1.38588 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.36750 | − | 5.40833i | −0.345996 | − | 0.199761i | 0.316924 | − | 0.948451i | \(-0.397350\pi\) |
−0.662921 | + | 0.748690i | \(0.730683\pi\) | |||||||
\(734\) | −37.4700 | + | 21.6333i | −1.38304 | + | 0.798500i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 20.7846i | − | 0.766131i | ||||||
\(737\) | −48.0000 | −1.76810 | ||||||||
\(738\) | −18.7350 | −0.689645 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | −3.12250 | + | 5.40833i | −0.114785 | + | 0.198814i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0000 | − | 10.3923i | −0.660356 | − | 0.381257i | 0.132057 | − | 0.991242i | \(-0.457842\pi\) |
−0.792413 | + | 0.609985i | \(0.791175\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.1025 | − | 48.6749i | 1.02960 | − | 1.78331i | ||||
\(746\) | 22.5000 | − | 12.9904i | 0.823784 | − | 0.475612i | ||||
\(747\) | 21.6333i | 0.791521i | ||||||||
\(748\) | 18.7350 | − | 10.8167i | 0.685019 | − | 0.395496i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.0000 | − | 36.3731i | −0.766301 | − | 1.32727i | −0.939556 | − | 0.342395i | \(-0.888762\pi\) |
0.173255 | − | 0.984877i | \(-0.444571\pi\) | |||||||
\(752\) | 36.0555i | 1.31481i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.12250 | − | 5.40833i | 0.113715 | − | 0.196960i | ||||
\(755\) | 12.4900 | 0.454557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.00000 | − | 12.1244i | 0.254419 | − | 0.440667i | −0.710318 | − | 0.703881i | \(-0.751449\pi\) |
0.964738 | + | 0.263213i | \(0.0847823\pi\) | |||||||
\(758\) | 36.0000 | 1.30758 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −39.0000 | − | 22.5167i | −1.41468 | − | 0.816765i | ||||
\(761\) | − | 36.0555i | − | 1.30701i | −0.756922 | − | 0.653506i | \(-0.773298\pi\) | ||
0.756922 | − | 0.653506i | \(-0.226702\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.00000 | − | 3.46410i | 0.0723575 | − | 0.125327i | ||||
\(765\) | −58.5000 | + | 33.7750i | −2.11507 | + | 1.22114i | ||||
\(766\) | −31.2250 | − | 54.0833i | −1.12820 | − | 1.95411i | ||||
\(767\) | −13.0000 | − | 22.5167i | −0.469403 | − | 0.813029i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.7350 | + | 10.8167i | 0.675601 | + | 0.390059i | 0.798196 | − | 0.602398i | \(-0.205788\pi\) |
−0.122594 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.50000 | − | 4.33013i | −0.269931 | − | 0.155845i | ||||
\(773\) | −6.24500 | − | 3.60555i | −0.224617 | − | 0.129683i | 0.383469 | − | 0.923554i | \(-0.374729\pi\) |
−0.608086 | + | 0.793871i | \(0.708063\pi\) | |||||||
\(774\) | 27.0000 | + | 15.5885i | 0.970495 | + | 0.560316i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.24500 | − | 10.8167i | −0.224182 | − | 0.388295i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.5000 | − | 14.7224i | −0.914219 | − | 0.527825i | ||||
\(779\) | 13.0000 | − | 22.5167i | 0.465773 | − | 0.806743i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | 37.4700 | − | 21.6333i | 1.33992 | − | 0.773606i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.5167i | 0.803654i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4900 | + | 7.21110i | 0.445220 | + | 0.257048i | 0.705809 | − | 0.708402i | \(-0.250583\pi\) |
−0.260589 | + | 0.965450i | \(0.583917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18.7350 | + | 32.4500i | −0.666561 | + | 1.15452i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −18.0000 | −0.639602 | ||||||||
\(793\) | 19.5000 | + | 11.2583i | 0.692465 | + | 0.399795i | ||||
\(794\) | −6.24500 | − | 10.8167i | −0.221627 | − | 0.383869i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.24500 | − | 10.8167i | −0.221348 | − | 0.383386i | ||||
\(797\) | −12.4900 | − | 21.6333i | −0.442418 | − | 0.766291i | 0.555450 | − | 0.831550i | \(-0.312546\pi\) |
−0.997868 | + | 0.0652589i | \(0.979213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.0000 | + | 22.5167i | −1.37972 | + | 0.796582i | ||||
\(800\) | 41.5692i | 1.46969i | ||||||||
\(801\) | 18.7350 | − | 10.8167i | 0.661968 | − | 0.382188i | ||||
\(802\) | −7.50000 | + | 12.9904i | −0.264834 | + | 0.458706i | ||||
\(803\) | −18.7350 | − | 32.4500i | −0.661144 | − | 1.14513i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.8167i | 0.380529i | ||||||||
\(809\) | −7.00000 | −0.246107 | −0.123053 | − | 0.992400i | \(-0.539269\pi\) | ||||
−0.123053 | + | 0.992400i | \(0.539269\pi\) | |||||||
\(810\) | −56.2050 | −1.97484 | ||||||||
\(811\) | − | 43.2666i | − | 1.51930i | −0.650334 | − | 0.759648i | \(-0.725371\pi\) | ||
0.650334 | − | 0.759648i | \(-0.274629\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.00000 | − | 5.19615i | −0.315450 | − | 0.182125i | ||||
\(815\) | −18.7350 | + | 32.4500i | −0.656258 | + | 1.13667i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.4700 | + | 21.6333i | −1.31091 | + | 0.756854i | ||||
\(818\) | 43.7150 | 1.52846 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.0000 | −0.453980 | ||||||||
\(821\) | 12.0000 | − | 6.92820i | 0.418803 | − | 0.241796i | −0.275762 | − | 0.961226i | \(-0.588930\pi\) |
0.694565 | + | 0.719430i | \(0.255597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | + | 13.8564i | −0.278862 | + | 0.483004i | −0.971102 | − | 0.238664i | \(-0.923291\pi\) |
0.692240 | + | 0.721668i | \(0.256624\pi\) | |||||||
\(824\) | 18.7350 | + | 10.8167i | 0.652664 | + | 0.376816i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3205i | 0.602293i | 0.953578 | + | 0.301147i | \(0.0973693\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902631\pi\) | |||||||
\(828\) | 12.0000 | 0.417029 | ||||||||
\(829\) | 18.7350 | 0.650693 | 0.325347 | − | 0.945595i | \(-0.394519\pi\) | ||||
0.325347 | + | 0.945595i | \(0.394519\pi\) | |||||||
\(830\) | 45.0333i | 1.56313i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.12250 | + | 1.80278i | 0.108253 | + | 0.0625000i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.0000 | − | 22.5167i | −0.449884 | − | 0.779221i | ||||
\(836\) | −12.4900 | + | 21.6333i | −0.431976 | + | 0.748204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.7150 | + | 25.2389i | −1.50921 | + | 0.871342i | −0.509267 | + | 0.860609i | \(0.670083\pi\) |
−0.999942 | + | 0.0107333i | \(0.996583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 19.5000 | + | 33.7750i | 0.672014 | + | 1.16396i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | − | 17.3205i | −0.344214 | − | 0.596196i | ||||
\(845\) | − | 46.8722i | − | 1.61245i | ||||||
\(846\) | −37.4700 | −1.28824 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.5000 | − | 21.6506i | 0.429252 | − | 0.743486i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −74.9400 | + | 43.2666i | −2.57042 | + | 1.48403i | ||||
\(851\) | −6.00000 | − | 3.46410i | −0.205677 | − | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.2389i | 0.864162i | 0.901835 | + | 0.432081i | \(0.142221\pi\) | ||||
−0.901835 | + | 0.432081i | \(0.857779\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 39.0000 | − | 67.5500i | 1.33377 | − | 2.31016i | ||||
\(856\) | 3.00000 | − | 1.73205i | 0.102538 | − | 0.0592003i | ||||
\(857\) | −15.6125 | − | 27.0416i | −0.533313 | − | 0.923725i | −0.999243 | − | 0.0389032i | \(-0.987614\pi\) |
0.465930 | − | 0.884821i | \(-0.345720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.9800 | + | 43.2666i | −0.852306 | + | 1.47624i | 0.0268153 | + | 0.999640i | \(0.491463\pi\) |
−0.879122 | + | 0.476597i | \(0.841870\pi\) | |||||||
\(860\) | 18.7350 | + | 10.8167i | 0.638858 | + | 0.368845i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.0000 | + | 41.5692i | 0.817443 | + | 1.41585i | ||||
\(863\) | 33.0000 | + | 19.0526i | 1.12333 | + | 0.648557i | 0.942250 | − | 0.334911i | \(-0.108706\pi\) |
0.181083 | + | 0.983468i | \(0.442040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 78.0000 | + | 45.0333i | 2.65208 | + | 1.53118i | ||||
\(866\) | −28.1025 | − | 16.2250i | −0.954962 | − | 0.551347i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.0000 | − | 10.3923i | −0.610608 | − | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.9800 | + | 43.2666i | −0.846415 | + | 1.46603i | ||||
\(872\) | −6.00000 | − | 10.3923i | −0.203186 | − | 0.351928i | ||||
\(873\) | 18.7350 | − | 10.8167i | 0.634083 | − | 0.366088i | ||||
\(874\) | −24.9800 | + | 43.2666i | −0.844961 | + | 1.46352i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 46.7654i | − | 1.57915i | −0.613651 | − | 0.789577i | \(-0.710300\pi\) | ||
0.613651 | − | 0.789577i | \(-0.289700\pi\) | |||||||
\(878\) | −18.7350 | − | 10.8167i | −0.632275 | − | 0.365044i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −62.4500 | −2.10519 | ||||||||
\(881\) | 21.8575 | − | 37.8583i | 0.736398 | − | 1.27548i | −0.217710 | − | 0.976014i | \(-0.569859\pi\) |
0.954107 | − | 0.299465i | \(-0.0968080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | − | 22.5167i | − | 0.757317i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.7128i | 0.931030i | ||||||||
\(887\) | −12.4900 | − | 21.6333i | −0.419373 | − | 0.726375i | 0.576503 | − | 0.817095i | \(-0.304417\pi\) |
−0.995877 | + | 0.0907193i | \(0.971083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 39.0000 | − | 22.5167i | 1.30728 | − | 0.754760i | ||||
\(891\) | − | 31.1769i | − | 1.04447i | ||||||
\(892\) | 6.24500 | − | 3.60555i | 0.209098 | − | 0.120723i | ||||
\(893\) | 26.0000 | − | 45.0333i | 0.870057 | − | 1.50698i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49.9600 | − | 28.8444i | −1.66998 | − | 0.964162i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | − | 10.3923i | 0.200223 | − | 0.346796i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −24.0000 | −0.800000 | ||||||||
\(901\) | 31.2250 | 1.04026 | ||||||||
\(902\) | − | 21.6333i | − | 0.720310i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.50000 | − | 4.33013i | 0.249446 | − | 0.144018i | ||||
\(905\) | 19.5000 | + | 11.2583i | 0.648202 | + | 0.374240i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | −0.730498 | −0.365249 | − | 0.930910i | \(-0.619016\pi\) | ||||
−0.365249 | + | 0.930910i | \(0.619016\pi\) | |||||||
\(908\) | −12.4900 | + | 7.21110i | −0.414495 | + | 0.239309i | ||||
\(909\) | −18.7350 | −0.621401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00000 | −0.265052 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.9800 | −0.826717 | ||||||||
\(914\) | 34.5000 | − | 59.7558i | 1.14116 | − | 1.97654i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.7350 | + | 10.8167i | −0.619022 | + | 0.357392i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.00000 | −0.0659739 | −0.0329870 | − | 0.999456i | \(-0.510502\pi\) | ||||
−0.0329870 | + | 0.999456i | \(0.510502\pi\) | |||||||
\(920\) | −24.9800 | −0.823566 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.3475 | − | 59.4916i | 1.13117 | − | 1.95925i | ||||
\(923\) | 37.4700 | 1.23334 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0000 | + | 6.92820i | 0.394558 | + | 0.227798i | ||||
\(926\) | −9.00000 | − | 15.5885i | −0.295758 | − | 0.512268i | ||||
\(927\) | −18.7350 | + | 32.4500i | −0.615338 | + | 1.06580i | ||||
\(928\) | −4.50000 | + | 2.59808i | −0.147720 | + | 0.0852860i | ||||
\(929\) | 25.2389i | 0.828060i | 0.910263 | + | 0.414030i | \(0.135879\pi\) | ||||
−0.910263 | + | 0.414030i | \(0.864121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.00000 | + | 1.73205i | 0.0327561 | + | 0.0567352i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.6333i | 0.707863i | ||||||||
\(935\) | −39.0000 | − | 67.5500i | −1.27544 | − | 2.20912i | ||||
\(936\) | −9.36750 | + | 16.2250i | −0.306186 | + | 0.530330i | ||||
\(937\) | 6.24500 | 0.204015 | 0.102008 | − | 0.994784i | \(-0.467473\pi\) | ||||
0.102008 | + | 0.994784i | \(0.467473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26.0000 | −0.848026 | ||||||||
\(941\) | −6.24500 | + | 3.60555i | −0.203581 | + | 0.117538i | −0.598325 | − | 0.801254i | \(-0.704167\pi\) |
0.394744 | + | 0.918791i | \(0.370833\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.4222i | − | 0.469652i | ||||||
\(944\) | 36.0555i | 1.17351i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.0000 | + | 31.1769i | −0.585230 | + | 1.01365i | ||||
\(947\) | 18.0000 | − | 10.3923i | 0.584921 | − | 0.337705i | −0.178165 | − | 0.984001i | \(-0.557016\pi\) |
0.763087 | + | 0.646296i | \(0.223683\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.0000 | −1.26599 | ||||||||
\(950\) | 49.9600 | − | 86.5332i | 1.62092 | − | 2.80751i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.00000 | + | 8.66025i | 0.161966 | + | 0.280533i | 0.935574 | − | 0.353132i | \(-0.114883\pi\) |
−0.773608 | + | 0.633665i | \(0.781550\pi\) | |||||||
\(954\) | 22.5000 | + | 12.9904i | 0.728464 | + | 0.420579i | ||||
\(955\) | −12.4900 | − | 7.21110i | −0.404167 | − | 0.233346i | ||||
\(956\) | −15.0000 | − | 8.66025i | −0.485135 | − | 0.280093i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.4900 | − | 21.6333i | −0.403533 | − | 0.698940i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5000 | + | 26.8468i | −0.500000 | + | 0.866025i | ||||
\(962\) | −9.36750 | + | 5.40833i | −0.302020 | + | 0.174371i | ||||
\(963\) | 3.00000 | + | 5.19615i | 0.0966736 | + | 0.167444i | ||||
\(964\) | −9.36750 | + | 5.40833i | −0.301707 | + | 0.174190i | ||||
\(965\) | −15.6125 | + | 27.0416i | −0.502584 | + | 0.870501i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.4974i | 1.55957i | 0.626046 | + | 0.779786i | \(0.284672\pi\) | ||||
−0.626046 | + | 0.779786i | \(0.715328\pi\) | |||||||
\(968\) | − | 1.73205i | − | 0.0556702i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 39.0000 | − | 22.5167i | 1.25221 | − | 0.722966i | ||||
\(971\) | 12.4900 | 0.400823 | 0.200412 | − | 0.979712i | \(-0.435772\pi\) | ||||
0.200412 | + | 0.979712i | \(0.435772\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.0000 | 1.15351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.6125 | − | 27.0416i | −0.499744 | − | 0.865582i | ||||
\(977\) | − | 5.19615i | − | 0.166240i | −0.996540 | − | 0.0831198i | \(-0.973512\pi\) | ||
0.996540 | − | 0.0831198i | \(-0.0264884\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4900 | + | 21.6333i | 0.399182 | + | 0.691404i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0000 | − | 10.3923i | 0.574696 | − | 0.331801i | ||||
\(982\) | − | 6.92820i | − | 0.221088i | ||||||
\(983\) | −43.7150 | + | 25.2389i | −1.39429 | + | 0.804995i | −0.993787 | − | 0.111300i | \(-0.964499\pi\) |
−0.400505 | + | 0.916295i | \(0.631165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.36750 | − | 5.40833i | −0.298322 | − | 0.172236i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.0000 | + | 22.5167i | 0.413585 | + | 0.716350i | ||||
\(989\) | −12.0000 | + | 20.7846i | −0.381578 | + | 0.660912i | ||||
\(990\) | − | 64.8999i | − | 2.06265i | ||||||
\(991\) | −12.0000 | −0.381193 | −0.190596 | − | 0.981669i | \(-0.561042\pi\) | ||||
−0.190596 | + | 0.981669i | \(0.561042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.0000 | + | 22.5167i | −1.23638 | + | 0.713826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.6125 | + | 27.0416i | −0.494453 | + | 0.856417i | −0.999980 | − | 0.00639370i | \(-0.997965\pi\) |
0.505527 | + | 0.862811i | \(0.331298\pi\) | |||||||
\(998\) | 48.0000 | 1.51941 | ||||||||
\(999\) | 0 | 0 |
(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 | 637.2.u.f.30.1 | 4 | ||
7.2 | even | 3 | 637.2.q.d.589.2 | yes | 4 | ||
7.3 | odd | 6 | 637.2.k.e.459.1 | 4 | |||
7.4 | even | 3 | 637.2.k.e.459.2 | 4 | |||
7.5 | odd | 6 | 637.2.q.d.589.1 | yes | 4 | ||
7.6 | odd | 2 | inner | 637.2.u.f.30.2 | 4 | ||
13.10 | even | 6 | 637.2.k.e.569.2 | 4 | |||
91.10 | odd | 6 | inner | 637.2.u.f.361.2 | 4 | ||
91.19 | even | 12 | 8281.2.a.br.1.3 | 4 | |||
91.23 | even | 6 | 637.2.q.d.491.1 | ✓ | 4 | ||
91.33 | even | 12 | 8281.2.a.br.1.2 | 4 | |||
91.58 | odd | 12 | 8281.2.a.br.1.4 | 4 | |||
91.62 | odd | 6 | 637.2.k.e.569.1 | 4 | |||
91.72 | odd | 12 | 8281.2.a.br.1.1 | 4 | |||
91.75 | odd | 6 | 637.2.q.d.491.2 | yes | 4 | ||
91.88 | even | 6 | inner | 637.2.u.f.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.e.459.1 | 4 | 7.3 | odd | 6 | |||
637.2.k.e.459.2 | 4 | 7.4 | even | 3 | |||
637.2.k.e.569.1 | 4 | 91.62 | odd | 6 | |||
637.2.k.e.569.2 | 4 | 13.10 | even | 6 | |||
637.2.q.d.491.1 | ✓ | 4 | 91.23 | even | 6 | ||
637.2.q.d.491.2 | yes | 4 | 91.75 | odd | 6 | ||
637.2.q.d.589.1 | yes | 4 | 7.5 | odd | 6 | ||
637.2.q.d.589.2 | yes | 4 | 7.2 | even | 3 | ||
637.2.u.f.30.1 | 4 | 1.1 | even | 1 | trivial | ||
637.2.u.f.30.2 | 4 | 7.6 | odd | 2 | inner | ||
637.2.u.f.361.1 | 4 | 91.88 | even | 6 | inner | ||
637.2.u.f.361.2 | 4 | 91.10 | odd | 6 | inner | ||
8281.2.a.br.1.1 | 4 | 91.72 | odd | 12 | |||
8281.2.a.br.1.2 | 4 | 91.33 | even | 12 | |||
8281.2.a.br.1.3 | 4 | 91.19 | even | 12 | |||
8281.2.a.br.1.4 | 4 | 91.58 | odd | 12 |