Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(26,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.s (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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 458.5 | ||
Root | \(1.90412 + 1.09935i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.458 |
Dual form | 567.2.s.f.26.5 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.58850 | + | 0.917122i | 1.12324 | + | 0.648503i | 0.942226 | − | 0.334978i | \(-0.108729\pi\) |
0.181014 | + | 0.983481i | \(0.442062\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.682224 | + | 1.18165i | 0.341112 | + | 0.590823i | ||||
\(5\) | −3.80824 | −1.70310 | −0.851549 | − | 0.524274i | \(-0.824337\pi\) | ||||
−0.851549 | + | 0.524274i | \(0.824337\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.43359 | − | 1.03810i | −0.919810 | − | 0.392364i | ||||
\(8\) | − | 1.16576i | − | 0.412157i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.04940 | − | 3.49262i | −1.91299 | − | 1.10446i | ||||
\(11\) | 1.16576i | 0.351489i | 0.984436 | + | 0.175744i | \(0.0562332\pi\) | ||||
−0.984436 | + | 0.175744i | \(0.943767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.79804 | − | 2.77015i | −1.33074 | − | 0.768301i | −0.345324 | − | 0.938484i | \(-0.612231\pi\) |
−0.985412 | + | 0.170183i | \(0.945564\pi\) | |||||||
\(14\) | −2.91370 | − | 3.88092i | −0.778718 | − | 1.03722i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.43359 | − | 4.21510i | 0.608397 | − | 1.05377i | ||||
\(17\) | −1.58850 | + | 2.75136i | −0.385268 | + | 0.667304i | −0.991806 | − | 0.127750i | \(-0.959224\pi\) |
0.606538 | + | 0.795054i | \(0.292558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.546672 | + | 0.315621i | −0.125415 | + | 0.0724085i | −0.561395 | − | 0.827548i | \(-0.689735\pi\) |
0.435980 | + | 0.899956i | \(0.356402\pi\) | |||||||
\(20\) | −2.59808 | − | 4.50000i | −0.580948 | − | 1.00623i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.06914 | + | 1.85181i | −0.227942 | + | 0.394806i | ||||
\(23\) | 1.76183i | 0.367367i | 0.982985 | + | 0.183684i | \(0.0588022\pi\) | ||||
−0.982985 | + | 0.183684i | \(0.941198\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.50273 | 1.90055 | ||||||||
\(26\) | −5.08112 | − | 8.80077i | −0.996491 | − | 1.72597i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.433589 | − | 3.58386i | −0.0819406 | − | 0.677285i | ||||
\(29\) | −4.18658 | + | 2.41712i | −0.777428 | + | 0.448848i | −0.835518 | − | 0.549463i | \(-0.814832\pi\) |
0.0580901 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.70469 | − | 2.13891i | 0.665382 | − | 0.384159i | −0.128942 | − | 0.991652i | \(-0.541158\pi\) |
0.794325 | + | 0.607493i | \(0.207825\pi\) | |||||||
\(32\) | 5.71237 | − | 3.29804i | 1.00981 | − | 0.583016i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.04667 | + | 2.91370i | −0.865497 | + | 0.499695i | ||||
\(35\) | 9.26770 | + | 3.95333i | 1.56653 | + | 0.668234i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.11581 | − | 3.66470i | −0.347837 | − | 0.602472i | 0.638028 | − | 0.770014i | \(-0.279751\pi\) |
−0.985865 | + | 0.167541i | \(0.946417\pi\) | |||||||
\(38\) | −1.15785 | −0.187828 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.43949i | 0.701945i | ||||||||
\(41\) | −2.28245 | + | 3.95333i | −0.356460 | + | 0.617406i | −0.987367 | − | 0.158452i | \(-0.949350\pi\) |
0.630907 | + | 0.775858i | \(0.282683\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.61581 | − | 6.26277i | −0.551406 | − | 0.955064i | −0.998173 | − | 0.0604134i | \(-0.980758\pi\) |
0.446767 | − | 0.894650i | \(-0.352575\pi\) | |||||||
\(44\) | −1.37751 | + | 0.795307i | −0.207668 | + | 0.119897i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.61581 | + | 2.79867i | −0.238239 | + | 0.412641i | ||||
\(47\) | 1.27288 | − | 2.20469i | 0.185669 | − | 0.321587i | −0.758133 | − | 0.652100i | \(-0.773888\pi\) |
0.943802 | + | 0.330512i | \(0.107222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.84471 | + | 5.05260i | 0.692101 | + | 0.721800i | ||||
\(50\) | 15.0951 | + | 8.71516i | 2.13477 | + | 1.23251i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 7.55945i | − | 1.04831i | ||||||
\(53\) | −0.0627112 | − | 0.0362063i | −0.00861404 | − | 0.00497332i | 0.495687 | − | 0.868501i | \(-0.334916\pi\) |
−0.504301 | + | 0.863528i | \(0.668250\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.43949i | − | 0.598620i | ||||||
\(56\) | −1.21017 | + | 2.83697i | −0.161716 | + | 0.379106i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.86718 | −1.16432 | ||||||||
\(59\) | 3.49262 | + | 6.04940i | 0.454701 | + | 0.787565i | 0.998671 | − | 0.0515396i | \(-0.0164128\pi\) |
−0.543970 | + | 0.839105i | \(0.683080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00273 | − | 4.04303i | −0.896608 | − | 0.517657i | −0.0205096 | − | 0.999790i | \(-0.506529\pi\) |
−0.876098 | + | 0.482133i | \(0.839862\pi\) | |||||||
\(62\) | 7.84655 | 0.996512 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.36445 | 0.295556 | ||||||||
\(65\) | 18.2721 | + | 10.5494i | 2.26638 | + | 1.30849i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.54940 | − | 4.41569i | −0.311459 | − | 0.539463i | 0.667219 | − | 0.744861i | \(-0.267484\pi\) |
−0.978678 | + | 0.205398i | \(0.934151\pi\) | |||||||
\(68\) | −4.33485 | −0.525678 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.0961 | + | 14.7795i | 1.32623 | + | 1.76649i | ||||
\(71\) | 4.76183i | 0.565125i | 0.959249 | + | 0.282563i | \(0.0911845\pi\) | ||||
−0.959249 | + | 0.282563i | \(0.908815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.84744 | + | 2.79867i | 0.567350 | + | 0.327560i | 0.756090 | − | 0.654467i | \(-0.227107\pi\) |
−0.188740 | + | 0.982027i | \(0.560440\pi\) | |||||||
\(74\) | − | 7.76183i | − | 0.902294i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.745906 | − | 0.430649i | −0.0855612 | − | 0.0493988i | ||||
\(77\) | 1.21017 | − | 2.83697i | 0.137912 | − | 0.323303i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.54940 | + | 14.8080i | −0.961883 | + | 1.66603i | −0.244116 | + | 0.969746i | \(0.578498\pi\) |
−0.717766 | + | 0.696284i | \(0.754835\pi\) | |||||||
\(80\) | −9.26770 | + | 16.0521i | −1.03616 | + | 1.79468i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.25136 | + | 4.18658i | −0.800779 | + | 0.462330i | ||||
\(83\) | −5.08112 | − | 8.80077i | −0.557726 | − | 0.966010i | −0.997686 | − | 0.0679922i | \(-0.978341\pi\) |
0.439960 | − | 0.898017i | \(-0.354993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.04940 | − | 10.4779i | 0.656150 | − | 1.13648i | ||||
\(86\) | − | 13.2646i | − | 1.43035i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.35899 | 0.144869 | ||||||||
\(89\) | −5.77508 | − | 10.0027i | −0.612157 | − | 1.06029i | −0.990876 | − | 0.134776i | \(-0.956969\pi\) |
0.378719 | − | 0.925512i | \(-0.376365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.80077 | + | 11.7222i | 0.922571 | + | 1.22882i | ||||
\(92\) | −2.08186 | + | 1.20196i | −0.217049 | + | 0.125313i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.04394 | − | 2.33477i | 0.417101 | − | 0.240813i | ||||
\(95\) | 2.08186 | − | 1.20196i | 0.213594 | − | 0.123319i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.596074 | − | 0.344143i | 0.0605221 | − | 0.0349425i | −0.469434 | − | 0.882968i | \(-0.655542\pi\) |
0.529956 | + | 0.848025i | \(0.322209\pi\) | |||||||
\(98\) | 3.06197 | + | 12.4693i | 0.309306 | + | 1.25958i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.48299 | + | 11.2289i | 0.648299 | + | 1.12289i | ||||
\(101\) | −6.58406 | −0.655138 | −0.327569 | − | 0.944827i | \(-0.606229\pi\) | ||||
−0.327569 | + | 0.944827i | \(0.606229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.34854i | − | 0.921139i | −0.887624 | − | 0.460570i | \(-0.847645\pi\) | ||
0.887624 | − | 0.460570i | \(-0.152355\pi\) | |||||||
\(104\) | −3.22932 | + | 5.59334i | −0.316661 | + | 0.548473i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0664112 | − | 0.115028i | −0.00645043 | − | 0.0111725i | ||||
\(107\) | 13.6549 | − | 7.88364i | 1.32007 | − | 0.762141i | 0.336328 | − | 0.941745i | \(-0.390815\pi\) |
0.983739 | + | 0.179604i | \(0.0574818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.23163 | − | 12.5255i | 0.692664 | − | 1.19973i | −0.278298 | − | 0.960495i | \(-0.589770\pi\) |
0.970962 | − | 0.239235i | \(-0.0768965\pi\) | |||||||
\(110\) | 4.07155 | − | 7.05213i | 0.388207 | − | 0.672394i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.2980 | + | 7.73152i | −0.973073 | + | 0.730560i | ||||
\(113\) | −17.1998 | − | 9.93032i | −1.61802 | − | 0.934166i | −0.987431 | − | 0.158051i | \(-0.949479\pi\) |
−0.630591 | − | 0.776115i | \(-0.717188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.70948i | − | 0.625662i | ||||||
\(116\) | −5.71237 | − | 3.29804i | −0.530380 | − | 0.306215i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.8126i | 1.17950i | ||||||||
\(119\) | 6.72194 | − | 5.04667i | 0.616199 | − | 0.462628i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.64101 | 0.876456 | ||||||||
\(122\) | −7.41590 | − | 12.8447i | −0.671404 | − | 1.16291i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.05486 | + | 2.91843i | 0.453940 | + | 0.262082i | ||||
\(125\) | −17.1475 | −1.53372 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.90666 | −0.790338 | −0.395169 | − | 0.918608i | \(-0.629314\pi\) | ||||
−0.395169 | + | 0.918608i | \(0.629314\pi\) | |||||||
\(128\) | −7.66881 | − | 4.42759i | −0.677833 | − | 0.391347i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 19.3502 | + | 33.5155i | 1.69712 | + | 2.93950i | ||||
\(131\) | 6.75519 | 0.590204 | 0.295102 | − | 0.955466i | \(-0.404646\pi\) | ||||
0.295102 | + | 0.955466i | \(0.404646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.65802 | − | 0.200594i | 0.143769 | − | 0.0173937i | ||||
\(134\) | − | 9.35245i | − | 0.807928i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.20742 | + | 1.85181i | 0.275034 | + | 0.158791i | ||||
\(137\) | 16.8606i | 1.44050i | 0.693714 | + | 0.720251i | \(0.255973\pi\) | ||||
−0.693714 | + | 0.720251i | \(0.744027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.704693 | − | 0.406855i | −0.0597713 | − | 0.0345089i | 0.469817 | − | 0.882764i | \(-0.344320\pi\) |
−0.529588 | + | 0.848255i | \(0.677653\pi\) | |||||||
\(140\) | 1.65121 | + | 13.6482i | 0.139553 | + | 1.15348i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.36718 | + | 7.56417i | −0.366485 | + | 0.634771i | ||||
\(143\) | 3.22932 | − | 5.59334i | 0.270049 | − | 0.467739i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.9435 | − | 9.20499i | 1.32404 | − | 0.764433i | ||||
\(146\) | 5.13344 | + | 8.89138i | 0.424847 | + | 0.735856i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.88692 | − | 5.00029i | 0.237303 | − | 0.411021i | ||||
\(149\) | − | 8.43032i | − | 0.690638i | −0.938485 | − | 0.345319i | \(-0.887771\pi\) | ||
0.938485 | − | 0.345319i | \(-0.112229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.03948 | 0.247349 | 0.123675 | − | 0.992323i | \(-0.460532\pi\) | ||||
0.123675 | + | 0.992323i | \(0.460532\pi\) | |||||||
\(152\) | 0.367938 | + | 0.637287i | 0.0298437 | + | 0.0516908i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.52420 | − | 3.39666i | 0.364571 | − | 0.273711i | ||||
\(155\) | −14.1084 | + | 8.14548i | −1.13321 | + | 0.654260i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.29804 | − | 1.90412i | 0.263212 | − | 0.151966i | −0.362587 | − | 0.931950i | \(-0.618106\pi\) |
0.625799 | + | 0.779984i | \(0.284773\pi\) | |||||||
\(158\) | −27.1615 | + | 15.6817i | −2.16085 | + | 1.24757i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −21.7541 | + | 12.5597i | −1.71981 | + | 0.992934i | ||||
\(161\) | 1.82895 | − | 4.28757i | 0.144142 | − | 0.337908i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.54667 | + | 9.60712i | 0.434449 | + | 0.752488i | 0.997250 | − | 0.0741045i | \(-0.0236098\pi\) |
−0.562802 | + | 0.826592i | \(0.690276\pi\) | |||||||
\(164\) | −6.22858 | −0.486371 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 18.6400i | − | 1.44675i | ||||||
\(167\) | −1.85181 | + | 3.20742i | −0.143297 | + | 0.248198i | −0.928736 | − | 0.370741i | \(-0.879104\pi\) |
0.785439 | + | 0.618939i | \(0.212437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.84744 | + | 15.3242i | 0.680572 | + | 1.17879i | ||||
\(170\) | 19.2190 | − | 11.0961i | 1.47403 | − | 0.851030i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.93359 | − | 8.54523i | 0.376183 | − | 0.651567i | ||||
\(173\) | 4.81782 | − | 8.34471i | 0.366292 | − | 0.634436i | −0.622691 | − | 0.782468i | \(-0.713960\pi\) |
0.988983 | + | 0.148032i | \(0.0472938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.1257 | − | 9.86476i | −1.74814 | − | 0.745705i | ||||
\(176\) | 4.91378 | + | 2.83697i | 0.370390 | + | 0.213845i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 21.1858i | − | 1.58794i | ||||||
\(179\) | −15.9792 | − | 9.22562i | −1.19435 | − | 0.689556i | −0.235056 | − | 0.971982i | \(-0.575527\pi\) |
−0.959289 | + | 0.282426i | \(0.908861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6209i | 1.23542i | 0.786406 | + | 0.617710i | \(0.211940\pi\) | ||||
−0.786406 | + | 0.617710i | \(0.788060\pi\) | |||||||
\(182\) | 3.22932 | + | 26.6921i | 0.239373 | + | 1.97855i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.05387 | 0.151413 | ||||||||
\(185\) | 8.05753 | + | 13.9561i | 0.592402 | + | 1.02607i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.20742 | − | 1.85181i | −0.234550 | − | 0.135417i | ||||
\(188\) | 3.47356 | 0.253335 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.40939 | 0.319890 | ||||||||
\(191\) | −6.20573 | − | 3.58288i | −0.449031 | − | 0.259248i | 0.258390 | − | 0.966041i | \(-0.416808\pi\) |
−0.707421 | + | 0.706793i | \(0.750141\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58888 | + | 2.75202i | 0.114370 | + | 0.198095i | 0.917528 | − | 0.397672i | \(-0.130182\pi\) |
−0.803158 | + | 0.595766i | \(0.796848\pi\) | |||||||
\(194\) | 1.26249 | 0.0906411 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.66521 | + | 9.17174i | −0.190372 | + | 0.655124i | ||||
\(197\) | − | 1.93305i | − | 0.137724i | −0.997626 | − | 0.0688619i | \(-0.978063\pi\) | ||
0.997626 | − | 0.0688619i | \(-0.0219368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.50000 | − | 4.33013i | −0.531661 | − | 0.306955i | 0.210032 | − | 0.977695i | \(-0.432643\pi\) |
−0.741693 | + | 0.670740i | \(0.765977\pi\) | |||||||
\(200\) | − | 11.0779i | − | 0.783324i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.4588 | − | 6.03838i | −0.735878 | − | 0.424859i | ||||
\(203\) | 12.6976 | − | 1.53621i | 0.891198 | − | 0.107821i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.69215 | − | 15.0552i | 0.607086 | − | 1.05150i | ||||
\(206\) | 8.57375 | − | 14.8502i | 0.597361 | − | 1.03466i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −23.3529 | + | 13.4828i | −1.61923 | + | 0.934864i | ||||
\(209\) | −0.367938 | − | 0.637287i | −0.0254508 | − | 0.0440820i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.20916 | + | 10.7546i | −0.427456 | + | 0.740376i | −0.996646 | − | 0.0818303i | \(-0.973923\pi\) |
0.569190 | + | 0.822206i | \(0.307257\pi\) | |||||||
\(212\) | − | 0.0988033i | − | 0.00678584i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.9210 | 1.97700 | ||||||||
\(215\) | 13.7699 | + | 23.8502i | 0.939099 | + | 1.62657i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2361 | + | 1.35939i | −0.762755 | + | 0.0922811i | ||||
\(218\) | 22.9749 | − | 13.2646i | 1.55606 | − | 0.898389i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.24591 | − | 3.02873i | 0.353679 | − | 0.204197i | ||||
\(221\) | 15.2434 | − | 8.80077i | 1.02538 | − | 0.592004i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.3996 | + | 9.46830i | −1.09820 | + | 0.634044i | −0.935747 | − | 0.352673i | \(-0.885273\pi\) |
−0.162450 | + | 0.986717i | \(0.551940\pi\) | |||||||
\(224\) | −17.3252 | + | 2.09607i | −1.15759 | + | 0.140050i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.2146 | − | 31.5486i | −1.21162 | − | 2.09858i | ||||
\(227\) | −5.72276 | −0.379833 | −0.189917 | − | 0.981800i | \(-0.560822\pi\) | ||||
−0.189917 | + | 0.981800i | \(0.560822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.1376i | 0.735996i | 0.929827 | + | 0.367998i | \(0.119957\pi\) | ||||
−0.929827 | + | 0.367998i | \(0.880043\pi\) | |||||||
\(230\) | 6.15341 | − | 10.6580i | 0.405744 | − | 0.702769i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.81778 | + | 4.88053i | 0.184996 | + | 0.320423i | ||||
\(233\) | −8.95208 | + | 5.16849i | −0.586470 | + | 0.338599i | −0.763701 | − | 0.645571i | \(-0.776620\pi\) |
0.177230 | + | 0.984169i | \(0.443286\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.84744 | + | 8.39601i | −0.316212 | + | 0.547695i | ||||
\(236\) | −4.76550 | + | 8.25409i | −0.310208 | + | 0.537296i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.3062 | − | 1.85181i | 0.992155 | − | 0.120035i | ||||
\(239\) | −14.3592 | − | 8.29030i | −0.928821 | − | 0.536255i | −0.0423824 | − | 0.999101i | \(-0.513495\pi\) |
−0.886438 | + | 0.462846i | \(0.846828\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.8932i | − | 1.53910i | −0.638587 | − | 0.769549i | \(-0.720481\pi\) | ||
0.638587 | − | 0.769549i | \(-0.279519\pi\) | |||||||
\(242\) | 15.3148 | + | 8.84198i | 0.984470 | + | 0.568384i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.0330i | − | 0.706316i | ||||||
\(245\) | −18.4498 | − | 19.2415i | −1.17872 | − | 1.22930i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.49727 | 0.222526 | ||||||||
\(248\) | −2.49344 | − | 4.31877i | −0.158334 | − | 0.274242i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −27.2388 | − | 15.7263i | −1.72273 | − | 0.994621i | ||||
\(251\) | −19.9233 | −1.25755 | −0.628774 | − | 0.777588i | \(-0.716443\pi\) | ||||
−0.628774 | + | 0.777588i | \(0.716443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.05387 | −0.129125 | ||||||||
\(254\) | −14.1482 | − | 8.16849i | −0.887739 | − | 0.512536i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.4857 | − | 18.1618i | −0.655358 | − | 1.13511i | ||||
\(257\) | 23.2049 | 1.44748 | 0.723742 | − | 0.690070i | \(-0.242420\pi\) | ||||
0.723742 | + | 0.690070i | \(0.242420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.34471 | + | 11.1148i | 0.0835561 | + | 0.690639i | ||||
\(260\) | 28.7882i | 1.78537i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.7306 | + | 6.19533i | 0.662941 | + | 0.382749i | ||||
\(263\) | − | 9.62246i | − | 0.593347i | −0.954979 | − | 0.296673i | \(-0.904123\pi\) | ||
0.954979 | − | 0.296673i | \(-0.0958772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.238820 | + | 0.137883i | 0.0146706 | + | 0.00847006i | ||||
\(266\) | 2.81774 | + | 1.20196i | 0.172767 | + | 0.0736971i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.47853 | − | 6.02498i | 0.212485 | − | 0.368034i | ||||
\(269\) | −10.4152 | + | 18.0396i | −0.635024 | + | 1.09989i | 0.351487 | + | 0.936193i | \(0.385676\pi\) |
−0.986510 | + | 0.163700i | \(0.947657\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0467 | − | 9.84190i | 1.03551 | − | 0.597853i | 0.116953 | − | 0.993137i | \(-0.462687\pi\) |
0.918559 | + | 0.395285i | \(0.129354\pi\) | |||||||
\(272\) | 7.73152 | + | 13.3914i | 0.468792 | + | 0.811972i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4633 | + | 26.7831i | −0.934169 | + | 1.61803i | ||||
\(275\) | 11.0779i | 0.668021i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.31604 | 0.499662 | 0.249831 | − | 0.968289i | \(-0.419625\pi\) | ||||
0.249831 | + | 0.968289i | \(0.419625\pi\) | |||||||
\(278\) | −0.746270 | − | 1.29258i | −0.0447583 | − | 0.0775237i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.60862 | − | 10.8039i | 0.275418 | − | 0.645656i | ||||
\(281\) | 19.7123 | − | 11.3809i | 1.17594 | − | 0.678928i | 0.220867 | − | 0.975304i | \(-0.429111\pi\) |
0.955072 | + | 0.296375i | \(0.0957780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7514 | − | 8.51670i | 0.876878 | − | 0.506266i | 0.00724998 | − | 0.999974i | \(-0.497692\pi\) |
0.869628 | + | 0.493708i | \(0.164359\pi\) | |||||||
\(284\) | −5.62680 | + | 3.24864i | −0.333889 | + | 0.192771i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.2596 | − | 5.92336i | 0.606660 | − | 0.350255i | ||||
\(287\) | 9.65849 | − | 7.25136i | 0.570123 | − | 0.428035i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.45333 | + | 5.98134i | 0.203137 | + | 0.351843i | ||||
\(290\) | 33.7684 | 1.98295 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.63728i | 0.446938i | ||||||||
\(293\) | 10.7079 | − | 18.5467i | 0.625564 | − | 1.08351i | −0.362868 | − | 0.931841i | \(-0.618202\pi\) |
0.988432 | − | 0.151668i | \(-0.0484643\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.3008 | − | 23.0376i | −0.774401 | − | 1.34130i | ||||
\(296\) | −4.27214 | + | 2.46652i | −0.248313 | + | 0.143364i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.73163 | − | 13.3916i | 0.447881 | − | 0.775753i | ||||
\(299\) | 4.88053 | − | 8.45333i | 0.282248 | − | 0.488869i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.29804 | + | 18.9946i | 0.132457 | + | 1.09483i | ||||
\(302\) | 4.82821 | + | 2.78757i | 0.277833 | + | 0.160407i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.07237i | 0.176212i | ||||||||
\(305\) | 26.6681 | + | 15.3968i | 1.52701 | + | 0.881621i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.4537i | − | 1.11028i | −0.831756 | − | 0.555142i | \(-0.812664\pi\) | ||
0.831756 | − | 0.555142i | \(-0.187336\pi\) | |||||||
\(308\) | 4.17791 | − | 0.505459i | 0.238058 | − | 0.0288012i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −29.8816 | −1.69716 | ||||||||
\(311\) | 3.40706 | + | 5.90120i | 0.193197 | + | 0.334626i | 0.946308 | − | 0.323267i | \(-0.104781\pi\) |
−0.753111 | + | 0.657893i | \(0.771448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4121 | + | 8.32084i | 0.814621 | + | 0.470322i | 0.848558 | − | 0.529102i | \(-0.177471\pi\) |
−0.0339371 | + | 0.999424i | \(0.510805\pi\) | |||||||
\(314\) | 6.98525 | 0.394200 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.3304 | −1.31244 | ||||||||
\(317\) | −4.39757 | − | 2.53894i | −0.246992 | − | 0.142601i | 0.371394 | − | 0.928475i | \(-0.378880\pi\) |
−0.618386 | + | 0.785874i | \(0.712213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.81778 | − | 4.88053i | −0.157765 | − | 0.273257i | ||||
\(320\) | −9.00440 | −0.503361 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.83752 | − | 5.13344i | 0.381040 | − | 0.286075i | ||||
\(323\) | − | 2.00546i | − | 0.111587i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −45.5944 | − | 26.3240i | −2.52912 | − | 1.46019i | ||||
\(326\) | 20.3479i | 1.12697i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.60862 | + | 2.66079i | 0.254468 | + | 0.146917i | ||||
\(329\) | −5.38635 | + | 4.04394i | −0.296959 | + | 0.222950i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.16521 | + | 14.1426i | −0.448801 | + | 0.777346i | −0.998308 | − | 0.0581430i | \(-0.981482\pi\) |
0.549507 | + | 0.835489i | \(0.314815\pi\) | |||||||
\(332\) | 6.93293 | − | 12.0082i | 0.380494 | − | 0.659035i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.88319 | + | 3.39666i | −0.321914 | + | 0.185857i | ||||
\(335\) | 9.70875 | + | 16.8160i | 0.530445 | + | 0.918758i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.97753 | − | 3.42518i | 0.107723 | − | 0.186582i | −0.807124 | − | 0.590381i | \(-0.798977\pi\) |
0.914847 | + | 0.403800i | \(0.132311\pi\) | |||||||
\(338\) | 32.4567i | 1.76541i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.5082 | 0.895282 | ||||||||
\(341\) | 2.49344 | + | 4.31877i | 0.135028 | + | 0.233875i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.54494 | − | 17.3252i | −0.353393 | − | 0.935475i | ||||
\(344\) | −7.30087 | + | 4.21516i | −0.393636 | + | 0.227266i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.3062 | − | 8.83705i | 0.822868 | − | 0.475083i | ||||
\(347\) | −6.35400 | + | 3.66849i | −0.341101 | + | 0.196935i | −0.660759 | − | 0.750598i | \(-0.729765\pi\) |
0.319658 | + | 0.947533i | \(0.396432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0917 | − | 12.7547i | 1.18254 | − | 0.682741i | 0.225941 | − | 0.974141i | \(-0.427454\pi\) |
0.956601 | + | 0.291400i | \(0.0941210\pi\) | |||||||
\(350\) | −27.6881 | − | 36.8793i | −1.47999 | − | 1.97128i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.84471 | + | 6.65923i | 0.204924 | + | 0.354938i | ||||
\(353\) | 0.0207896 | 0.00110652 | 0.000553260 | − | 1.00000i | \(-0.499824\pi\) | ||||
0.000553260 | 1.00000i | \(0.499824\pi\) | ||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 18.1342i | − | 0.962464i | ||||||
\(356\) | 7.87979 | − | 13.6482i | 0.417628 | − | 0.723353i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.9220 | − | 29.3098i | −0.894358 | − | 1.54907i | ||||
\(359\) | −31.3709 | + | 18.1120i | −1.65569 | + | 0.955915i | −0.681024 | + | 0.732261i | \(0.738465\pi\) |
−0.974669 | + | 0.223654i | \(0.928201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.30077 | + | 16.1094i | −0.489514 | + | 0.847863i | ||||
\(362\) | −15.2434 | + | 26.4023i | −0.801174 | + | 1.38767i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.84744 | + | 18.3966i | −0.411318 | + | 0.964243i | ||||
\(365\) | −18.4602 | − | 10.6580i | −0.966253 | − | 0.557866i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.87897i | 0.463479i | 0.972778 | + | 0.231739i | \(0.0744416\pi\) | ||||
−0.972778 | + | 0.231739i | \(0.925558\pi\) | |||||||
\(368\) | 7.42629 | + | 4.28757i | 0.387122 | + | 0.223505i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.5590i | 1.53670i | ||||||||
\(371\) | 0.115028 | + | 0.153212i | 0.00597193 | + | 0.00795435i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8188 | −0.663731 | −0.331865 | − | 0.943327i | \(-0.607678\pi\) | ||||
−0.331865 | + | 0.943327i | \(0.607678\pi\) | |||||||
\(374\) | −3.39666 | − | 5.88319i | −0.175637 | − | 0.304213i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.57014 | − | 1.48387i | −0.132545 | − | 0.0765247i | ||||
\(377\) | 26.7831 | 1.37940 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.13828 | 0.161203 | 0.0806013 | − | 0.996746i | \(-0.474316\pi\) | ||||
0.0806013 | + | 0.996746i | \(0.474316\pi\) | |||||||
\(380\) | 2.84059 | + | 1.64002i | 0.145719 | + | 0.0841311i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.57187 | − | 11.3828i | −0.336246 | − | 0.582395i | ||||
\(383\) | −27.5190 | −1.40616 | −0.703078 | − | 0.711113i | \(-0.748192\pi\) | ||||
−0.703078 | + | 0.711113i | \(0.748192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.60862 | + | 10.8039i | −0.234877 | + | 0.550617i | ||||
\(386\) | 5.82878i | 0.296677i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.813312 | + | 0.469566i | 0.0412896 | + | 0.0238386i | ||||
\(389\) | − | 18.2436i | − | 0.924989i | −0.886622 | − | 0.462494i | \(-0.846955\pi\) | ||
0.886622 | − | 0.462494i | \(-0.153045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.84744 | − | 2.79867i | −0.245146 | − | 0.141535i | ||||
\(392\) | 5.89011 | − | 5.64775i | 0.297495 | − | 0.285255i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.77284 | − | 3.07065i | 0.0893143 | − | 0.154697i | ||||
\(395\) | 32.5582 | − | 56.3925i | 1.63818 | − | 2.83741i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.01255 | − | 0.584593i | 0.0508182 | − | 0.0293399i | −0.474376 | − | 0.880323i | \(-0.657326\pi\) |
0.525194 | + | 0.850983i | \(0.323993\pi\) | |||||||
\(398\) | −7.94251 | − | 13.7568i | −0.398122 | − | 0.689567i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.1257 | − | 40.0550i | 1.15629 | − | 2.00275i | ||||
\(401\) | 13.9594i | 0.697101i | 0.937290 | + | 0.348551i | \(0.113326\pi\) | ||||
−0.937290 | + | 0.348551i | \(0.886674\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.7003 | −1.18060 | ||||||||
\(404\) | −4.49180 | − | 7.78003i | −0.223476 | − | 0.387071i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.5791 | + | 9.20499i | 1.07095 | + | 0.456836i | ||||
\(407\) | 4.27214 | − | 2.46652i | 0.211762 | − | 0.122261i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.6427 | + | 10.1860i | −0.872378 | + | 0.503667i | −0.868138 | − | 0.496324i | \(-0.834683\pi\) |
−0.00424001 | + | 0.999991i | \(0.501350\pi\) | |||||||
\(410\) | 27.6150 | − | 15.9435i | 1.36381 | − | 0.787394i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.0467 | − | 6.37780i | 0.544230 | − | 0.314212i | ||||
\(413\) | −2.21974 | − | 18.3474i | −0.109226 | − | 0.902818i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.3502 | + | 33.5155i | 0.949862 | + | 1.64521i | ||||
\(416\) | −36.5442 | −1.79173 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.34977i | − | 0.0660196i | ||||||
\(419\) | −12.7603 | + | 22.1015i | −0.623383 | + | 1.07973i | 0.365469 | + | 0.930824i | \(0.380909\pi\) |
−0.988851 | + | 0.148907i | \(0.952425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0466721 | − | 0.0808384i | −0.00227466 | − | 0.00393982i | 0.864886 | − | 0.501969i | \(-0.167391\pi\) |
−0.867160 | + | 0.498029i | \(0.834057\pi\) | |||||||
\(422\) | −19.7265 | + | 11.3891i | −0.960271 | + | 0.554413i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.0422078 | + | 0.0731060i | −0.00204979 | + | 0.00355034i | ||||
\(425\) | −15.0951 | + | 26.1455i | −0.732220 | + | 1.26824i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.8447 | + | 17.1086i | 0.621599 | + | 0.827942i | ||||
\(428\) | 18.6314 | + | 10.7568i | 0.900581 | + | 0.519951i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 50.5147i | 2.43603i | ||||||||
\(431\) | −28.7271 | − | 16.5856i | −1.38374 | − | 0.798901i | −0.391137 | − | 0.920333i | \(-0.627918\pi\) |
−0.992600 | + | 0.121432i | \(0.961251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.9518i | − | 0.862706i | −0.902183 | − | 0.431353i | \(-0.858036\pi\) | ||
0.902183 | − | 0.431353i | \(-0.141964\pi\) | |||||||
\(434\) | −19.0953 | − | 8.14548i | −0.916602 | − | 0.390995i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.7344 | 0.945104 | ||||||||
\(437\) | −0.556071 | − | 0.963144i | −0.0266005 | − | 0.0460734i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.69215 | + | 5.01841i | 0.414854 | + | 0.239516i | 0.692873 | − | 0.721060i | \(-0.256345\pi\) |
−0.278019 | + | 0.960575i | \(0.589678\pi\) | |||||||
\(440\) | −5.17536 | −0.246726 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 32.2855 | 1.53566 | ||||||||
\(443\) | −22.8266 | − | 13.1790i | −1.08453 | − | 0.626151i | −0.152412 | − | 0.988317i | \(-0.548704\pi\) |
−0.932114 | + | 0.362166i | \(0.882037\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.9929 | + | 38.0928i | 1.04256 | + | 1.80577i | ||||
\(446\) | −34.7343 | −1.64472 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.75409 | − | 2.45453i | −0.271855 | − | 0.115965i | ||||
\(449\) | − | 24.0264i | − | 1.13388i | −0.823761 | − | 0.566938i | \(-0.808128\pi\) | ||
0.823761 | − | 0.566938i | \(-0.191872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.60862 | − | 2.66079i | −0.217011 | − | 0.125292i | ||||
\(452\) | − | 27.0988i | − | 1.27462i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.09061 | − | 5.24847i | −0.426644 | − | 0.246323i | ||||
\(455\) | −33.5155 | − | 44.6411i | −1.57123 | − | 2.09281i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4111 | + | 18.0326i | −0.487012 | + | 0.843529i | −0.999888 | − | 0.0149333i | \(-0.995246\pi\) |
0.512877 | + | 0.858462i | \(0.328580\pi\) | |||||||
\(458\) | −10.2146 | + | 17.6921i | −0.477295 | + | 0.826700i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.92824 | − | 4.57737i | 0.369656 | − | 0.213421i | ||||
\(461\) | 4.17618 | + | 7.23336i | 0.194504 | + | 0.336891i | 0.946738 | − | 0.322005i | \(-0.104357\pi\) |
−0.752234 | + | 0.658896i | \(0.771024\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.90666 | + | 10.2306i | −0.274506 | + | 0.475458i | −0.970010 | − | 0.243064i | \(-0.921848\pi\) |
0.695505 | + | 0.718522i | \(0.255181\pi\) | |||||||
\(464\) | 23.5291i | 1.09231i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.9605 | −0.878329 | ||||||||
\(467\) | 14.5789 | + | 25.2514i | 0.674630 | + | 1.16849i | 0.976577 | + | 0.215169i | \(0.0690302\pi\) |
−0.301947 | + | 0.953325i | \(0.597636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.62028 | + | 13.3925i | 0.0748174 | + | 0.618409i | ||||
\(470\) | −15.4003 | + | 8.89138i | −0.710364 | + | 0.410129i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.05213 | − | 4.07155i | 0.324601 | − | 0.187408i | ||||
\(473\) | 7.30087 | − | 4.21516i | 0.335694 | − | 0.193813i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.19488 | + | 2.99926i | −0.238357 | + | 0.137616i | ||||
\(476\) | 10.5493 | + | 4.50000i | 0.483524 | + | 0.206257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.2064 | − | 26.3383i | −0.695526 | − | 1.20469i | ||||
\(479\) | 40.5236 | 1.85157 | 0.925785 | − | 0.378051i | \(-0.123406\pi\) | ||||
0.925785 | + | 0.378051i | \(0.123406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.4445i | 1.06898i | ||||||||
\(482\) | 21.9130 | − | 37.9544i | 0.998110 | − | 1.72878i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.57733 | + | 11.3923i | 0.298970 | + | 0.517830i | ||||
\(485\) | −2.26999 | + | 1.31058i | −0.103075 | + | 0.0595105i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.20916 | + | 10.7546i | −0.281364 | + | 0.487336i | −0.971721 | − | 0.236132i | \(-0.924120\pi\) |
0.690357 | + | 0.723469i | \(0.257453\pi\) | |||||||
\(488\) | −4.71319 | + | 8.16348i | −0.213356 | + | 0.369543i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.6608 | − | 47.4860i | −0.526779 | − | 2.14520i | ||||
\(491\) | −5.34443 | − | 3.08561i | −0.241191 | − | 0.139252i | 0.374533 | − | 0.927214i | \(-0.377803\pi\) |
−0.615724 | + | 0.787962i | \(0.711136\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 15.3584i | − | 0.691708i | ||||||
\(494\) | 5.55542 | + | 3.20742i | 0.249950 | + | 0.144309i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 20.8209i | − | 0.934884i | ||||||
\(497\) | 4.94324 | − | 11.5883i | 0.221735 | − | 0.519808i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.96052 | −0.132531 | −0.0662656 | − | 0.997802i | \(-0.521108\pi\) | ||||
−0.0662656 | + | 0.997802i | \(0.521108\pi\) | |||||||
\(500\) | −11.6984 | − | 20.2623i | −0.523170 | − | 0.906157i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31.6482 | − | 18.2721i | −1.41253 | − | 0.815524i | ||||
\(503\) | −4.33485 | −0.193282 | −0.0966408 | − | 0.995319i | \(-0.530810\pi\) | ||||
−0.0966408 | + | 0.995319i | \(0.530810\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.0737 | 1.11577 | ||||||||
\(506\) | −3.26257 | − | 1.88364i | −0.145039 | − | 0.0837382i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.07633 | − | 10.5245i | −0.269594 | − | 0.466950i | ||||
\(509\) | 28.9485 | 1.28312 | 0.641560 | − | 0.767073i | \(-0.278288\pi\) | ||||
0.641560 | + | 0.767073i | \(0.278288\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.89138 | − | 11.8429i | −0.393332 | − | 0.523900i | ||||
\(512\) | − | 20.7564i | − | 0.917311i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 36.8611 | + | 21.2818i | 1.62587 | + | 0.938698i | ||||
\(515\) | 35.6015i | 1.56879i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.57014 | + | 1.48387i | 0.113034 | + | 0.0652605i | ||||
\(518\) | −8.05753 | + | 18.8891i | −0.354028 | + | 0.829940i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.2980 | − | 21.3008i | 0.539305 | − | 0.934103i | ||||
\(521\) | −6.08031 | + | 10.5314i | −0.266383 | + | 0.461389i | −0.967925 | − | 0.251239i | \(-0.919162\pi\) |
0.701542 | + | 0.712628i | \(0.252495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.1564 | + | 19.1429i | −1.44983 | + | 0.837059i | −0.998471 | − | 0.0552848i | \(-0.982393\pi\) |
−0.451357 | + | 0.892343i | \(0.649060\pi\) | |||||||
\(524\) | 4.60855 | + | 7.98225i | 0.201326 | + | 0.348706i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.82497 | − | 15.2853i | 0.384787 | − | 0.666471i | ||||
\(527\) | 13.5906i | 0.592016i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.8960 | 0.865041 | ||||||||
\(530\) | 0.252910 | + | 0.438053i | 0.0109857 | + | 0.0190278i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.36817 | + | 1.82234i | 0.0593178 | + | 0.0790087i | ||||
\(533\) | 21.9026 | − | 12.6455i | 0.948707 | − | 0.547736i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −52.0011 | + | 30.0229i | −2.24820 | + | 1.29800i | ||||
\(536\) | −5.14762 | + | 2.97198i | −0.222344 | + | 0.128370i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −33.0890 | + | 19.1039i | −1.42657 | + | 0.823629i | ||||
\(539\) | −5.89011 | + | 5.64775i | −0.253705 | + | 0.243266i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.254094 | − | 0.440104i | −0.0109244 | − | 0.0189216i | 0.860512 | − | 0.509431i | \(-0.170144\pi\) |
−0.871436 | + | 0.490509i | \(0.836811\pi\) | |||||||
\(542\) | 36.1049 | 1.55084 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.9557i | 0.898470i | ||||||||
\(545\) | −27.5398 | + | 47.7003i | −1.17968 | + | 2.04326i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.1482 | + | 34.8977i | 0.861475 | + | 1.49212i | 0.870505 | + | 0.492159i | \(0.163792\pi\) |
−0.00903012 | + | 0.999959i | \(0.502874\pi\) | |||||||
\(548\) | −19.9233 | + | 11.5027i | −0.851082 | + | 0.491372i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.1598 | + | 17.5972i | −0.433213 | + | 0.750348i | ||||
\(551\) | 1.52579 | − | 2.64275i | 0.0650008 | − | 0.112585i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.1779 | − | 27.1615i | 1.53844 | − | 1.15502i | ||||
\(554\) | 13.2100 | + | 7.62682i | 0.561241 | + | 0.324033i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 1.11026i | − | 0.0470857i | ||||||
\(557\) | 37.6165 | + | 21.7179i | 1.59386 | + | 0.920216i | 0.992636 | + | 0.121137i | \(0.0386541\pi\) |
0.601226 | + | 0.799079i | \(0.294679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.0653i | 1.69458i | ||||||||
\(560\) | 39.2174 | − | 29.4435i | 1.65724 | − | 1.24422i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 41.7507 | 1.76115 | ||||||||
\(563\) | −3.16661 | − | 5.48473i | −0.133457 | − | 0.231154i | 0.791550 | − | 0.611104i | \(-0.209274\pi\) |
−0.925007 | + | 0.379951i | \(0.875941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 65.5011 | + | 37.8171i | 2.75565 | + | 1.59098i | ||||
\(566\) | 31.2434 | 1.31326 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.55114 | 0.232921 | ||||||||
\(569\) | 7.12974 | + | 4.11636i | 0.298894 | + | 0.172567i | 0.641946 | − | 0.766750i | \(-0.278127\pi\) |
−0.343052 | + | 0.939316i | \(0.611461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.24864 | − | 7.35885i | −0.177800 | − | 0.307958i | 0.763327 | − | 0.646013i | \(-0.223565\pi\) |
−0.941127 | + | 0.338054i | \(0.890231\pi\) | |||||||
\(572\) | 8.81248 | 0.368468 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 21.9929 | − | 2.66079i | 0.917966 | − | 0.111059i | ||||
\(575\) | 16.7422i | 0.698198i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.1905 | + | 19.7399i | 1.42337 | + | 0.821783i | 0.996585 | − | 0.0825702i | \(-0.0263129\pi\) |
0.426785 | + | 0.904353i | \(0.359646\pi\) | |||||||
\(578\) | 12.6685i | 0.526940i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.7541 | + | 12.5597i | 0.903290 | + | 0.521514i | ||||
\(581\) | 3.22932 | + | 26.6921i | 0.133975 | + | 1.10738i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0422078 | − | 0.0731060i | 0.00174807 | − | 0.00302774i | ||||
\(584\) | 3.26257 | − | 5.65093i | 0.135006 | − | 0.233837i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.0191 | − | 19.6409i | 1.40532 | − | 0.811360i | ||||
\(587\) | 12.0560 | + | 20.8816i | 0.497603 | + | 0.861874i | 0.999996 | − | 0.00276510i | \(-0.000880160\pi\) |
−0.502393 | + | 0.864640i | \(0.667547\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.35017 | + | 2.33856i | −0.0556327 | + | 0.0963587i | ||||
\(590\) | − | 48.7937i | − | 2.00880i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.5961 | −0.846493 | ||||||||
\(593\) | 9.46830 | + | 16.3996i | 0.388816 | + | 0.673450i | 0.992291 | − | 0.123933i | \(-0.0395507\pi\) |
−0.603474 | + | 0.797382i | \(0.706217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.5988 | + | 19.2190i | −1.04945 | + | 0.787901i | ||||
\(596\) | 9.96166 | − | 5.75136i | 0.408045 | − | 0.235585i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.5055 | − | 8.95208i | 0.634065 | − | 0.366078i | ||||
\(599\) | 30.0332 | − | 17.3397i | 1.22713 | − | 0.708481i | 0.260698 | − | 0.965420i | \(-0.416047\pi\) |
0.966427 | + | 0.256939i | \(0.0827141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.4929 | + | 6.63544i | −0.468806 | + | 0.270665i | −0.715740 | − | 0.698367i | \(-0.753910\pi\) |
0.246934 | + | 0.969032i | \(0.420577\pi\) | |||||||
\(602\) | −13.7699 | + | 32.2805i | −0.561219 | + | 1.31565i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.07361 | + | 3.59159i | 0.0843738 | + | 0.146140i | ||||
\(605\) | −36.7153 | −1.49269 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.0148i | − | 1.01532i | −0.861557 | − | 0.507660i | \(-0.830510\pi\) | ||
0.861557 | − | 0.507660i | \(-0.169490\pi\) | |||||||
\(608\) | −2.08186 | + | 3.60589i | −0.0844306 | + | 0.146238i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.2415 | + | 48.9158i | 1.14347 | + | 1.98054i | ||||
\(611\) | −12.2146 | + | 7.05213i | −0.494152 | + | 0.285299i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0549 | − | 38.2001i | 0.890787 | − | 1.54289i | 0.0518543 | − | 0.998655i | \(-0.483487\pi\) |
0.838933 | − | 0.544234i | \(-0.183180\pi\) | |||||||
\(614\) | 17.8415 | − | 30.9023i | 0.720022 | − | 1.24712i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.30722 | − | 1.41076i | −0.133252 | − | 0.0568412i | ||||
\(617\) | 16.7463 | + | 9.66849i | 0.674181 | + | 0.389239i | 0.797659 | − | 0.603109i | \(-0.206071\pi\) |
−0.123478 | + | 0.992347i | \(0.539405\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 11.0598i | − | 0.444531i | −0.974986 | − | 0.222265i | \(-0.928655\pi\) | ||
0.974986 | − | 0.222265i | \(-0.0713452\pi\) | |||||||
\(620\) | −19.2501 | − | 11.1141i | −0.773105 | − | 0.446352i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.4987i | 0.501154i | ||||||||
\(623\) | 3.67036 | + | 30.3376i | 0.147050 | + | 1.21545i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.7882 | 0.711529 | ||||||||
\(626\) | 15.2624 | + | 26.4353i | 0.610010 | + | 1.05657i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.50000 | + | 2.59808i | 0.179570 | + | 0.103675i | ||||
\(629\) | 13.4439 | 0.536043 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6015 | −1.09880 | −0.549400 | − | 0.835560i | \(-0.685144\pi\) | ||||
−0.549400 | + | 0.835560i | \(0.685144\pi\) | |||||||
\(632\) | 17.2625 | + | 9.96652i | 0.686666 | + | 0.396447i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.65703 | − | 8.06621i | −0.184954 | − | 0.320350i | ||||
\(635\) | 33.9187 | 1.34602 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.24864 | − | 37.6631i | −0.366444 | − | 1.49227i | ||||
\(638\) | − | 10.3370i | − | 0.409245i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 29.2047 | + | 16.8613i | 1.15442 | + | 0.666503i | ||||
\(641\) | 6.07241i | 0.239846i | 0.992783 | + | 0.119923i | \(0.0382648\pi\) | ||||
−0.992783 | + | 0.119923i | \(0.961735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.4929 | − | 6.63544i | −0.453236 | − | 0.261676i | 0.255960 | − | 0.966687i | \(-0.417609\pi\) |
−0.709196 | + | 0.705011i | \(0.750942\pi\) | |||||||
\(644\) | 6.31415 | − | 0.763910i | 0.248812 | − | 0.0301023i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.83925 | − | 3.18567i | 0.0723643 | − | 0.125339i | ||||
\(647\) | −15.3688 | + | 26.6195i | −0.604210 | + | 1.04652i | 0.387966 | + | 0.921674i | \(0.373178\pi\) |
−0.992176 | + | 0.124848i | \(0.960156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.05213 | + | 4.07155i | −0.276820 | + | 0.159822i | ||||
\(650\) | −48.2846 | − | 83.6313i | −1.89388 | − | 3.28029i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.56815 | + | 13.1084i | −0.296391 | + | 0.513365i | ||||
\(653\) | − | 37.2185i | − | 1.45647i | −0.685325 | − | 0.728237i | \(-0.740340\pi\) | ||
0.685325 | − | 0.728237i | \(-0.259660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.7254 | −1.00518 | ||||||||
\(656\) | 11.1091 | + | 19.2415i | 0.433738 | + | 0.751256i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.2650 | + | 1.48387i | −0.478140 | + | 0.0578472i | ||||
\(659\) | −40.0576 | + | 23.1273i | −1.56042 | + | 0.900911i | −0.563209 | + | 0.826314i | \(0.690433\pi\) |
−0.997214 | + | 0.0745963i | \(0.976233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.4219 | + | 6.59445i | −0.444262 | + | 0.256495i | −0.705404 | − | 0.708806i | \(-0.749234\pi\) |
0.261142 | + | 0.965300i | \(0.415901\pi\) | |||||||
\(662\) | −25.9409 | + | 14.9770i | −1.00822 | + | 0.582097i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.2596 | + | 5.92336i | −0.398148 | + | 0.229871i | ||||
\(665\) | −6.31415 | + | 0.763910i | −0.244852 | + | 0.0296232i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.25856 | − | 7.37604i | −0.164892 | − | 0.285601i | ||||
\(668\) | −5.05339 | −0.195521 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.6164i | 1.37598i | ||||||||
\(671\) | 4.71319 | − | 8.16348i | 0.181951 | − | 0.315148i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.4633 | − | 35.4434i | −0.788800 | − | 1.36624i | −0.926702 | − | 0.375796i | \(-0.877369\pi\) |
0.137902 | − | 0.990446i | \(-0.455964\pi\) | |||||||
\(674\) | 6.28262 | − | 3.62727i | 0.241998 | − | 0.139717i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0719 | + | 20.9091i | −0.464303 | + | 0.804196i | ||||
\(677\) | −0.808981 | + | 1.40120i | −0.0310917 | + | 0.0538524i | −0.881153 | − | 0.472832i | \(-0.843232\pi\) |
0.850061 | + | 0.526684i | \(0.176565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.80785 | + | 0.218721i | −0.0693790 | + | 0.00839374i | ||||
\(680\) | −12.2146 | − | 7.05213i | −0.468410 | − | 0.270437i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.14716i | 0.350263i | ||||||||
\(683\) | −22.9977 | − | 13.2778i | −0.879984 | − | 0.508059i | −0.00933109 | − | 0.999956i | \(-0.502970\pi\) |
−0.870653 | + | 0.491897i | \(0.836304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 64.2094i | − | 2.45332i | ||||||
\(686\) | 5.49271 | − | 33.5237i | 0.209713 | − | 1.27994i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −35.1976 | −1.34190 | ||||||||
\(689\) | 0.200594 | + | 0.347439i | 0.00764201 | + | 0.0132364i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.5917 | − | 18.8168i | −1.23985 | − | 0.715826i | −0.270784 | − | 0.962640i | \(-0.587283\pi\) |
−0.969063 | + | 0.246814i | \(0.920616\pi\) | |||||||
\(692\) | 13.1473 | 0.499787 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.4578 | −0.510851 | ||||||||
\(695\) | 2.68364 | + | 1.54940i | 0.101796 | + | 0.0587722i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.25136 | − | 12.5597i | −0.274665 | − | 0.475734i | ||||
\(698\) | 46.7903 | 1.77104 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.12028 | − | 34.0564i | −0.155732 | − | 1.28721i | ||||
\(701\) | − | 24.3228i | − | 0.918659i | −0.888266 | − | 0.459330i | \(-0.848090\pi\) | ||
0.888266 | − | 0.459330i | \(-0.151910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.31331 | + | 1.33559i | 0.0872482 | + | 0.0503728i | ||||
\(704\) | 2.75637i | 0.103885i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.0330243 | + | 0.0190666i | 0.00124289 | + | 0.000717581i | ||||
\(707\) | 16.0229 | + | 6.83489i | 0.602603 | + | 0.257053i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.517010 | + | 0.895487i | −0.0194167 | + | 0.0336307i | −0.875570 | − | 0.483090i | \(-0.839514\pi\) |
0.856154 | + | 0.516721i | \(0.172848\pi\) | |||||||
\(710\) | 16.6313 | − | 28.8062i | 0.624161 | − | 1.08108i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.6608 | + | 6.73234i | −0.437005 | + | 0.252305i | ||||
\(713\) | 3.76839 | + | 6.52704i | 0.141127 | + | 0.244440i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.2980 | + | 21.3008i | −0.459921 | + | 0.796606i | ||||
\(716\) | − | 25.1758i | − | 0.940863i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −66.4436 | −2.47965 | ||||||||
\(719\) | −8.37315 | − | 14.5027i | −0.312266 | − | 0.540861i | 0.666587 | − | 0.745428i | \(-0.267755\pi\) |
−0.978853 | + | 0.204567i | \(0.934421\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.70469 | + | 22.7505i | −0.361422 | + | 0.847273i | ||||
\(722\) | −29.5486 | + | 17.0599i | −1.09968 | + | 0.634903i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.6400 | + | 11.3392i | −0.729915 | + | 0.421417i | ||||
\(725\) | −39.7839 | + | 22.9693i | −1.47754 | + | 0.853057i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.4902 | − | 16.4488i | 1.05664 | − | 0.610053i | 0.132141 | − | 0.991231i | \(-0.457815\pi\) |
0.924502 | + | 0.381178i | \(0.124482\pi\) | |||||||
\(728\) | 13.6653 | − | 10.2596i | 0.506469 | − | 0.380244i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.5494 | − | 33.8606i | −0.723556 | − | 1.25324i | ||||
\(731\) | 22.9749 | 0.849757 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 19.9120i | − | 0.735466i | −0.929931 | − | 0.367733i | \(-0.880134\pi\) | ||
0.929931 | − | 0.367733i | \(-0.119866\pi\) | |||||||
\(734\) | −8.14310 | + | 14.1043i | −0.300567 | + | 0.520598i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.81058 | + | 10.0642i | 0.214181 | + | 0.370972i | ||||
\(737\) | 5.14762 | − | 2.97198i | 0.189615 | − | 0.109474i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.3349 | − | 43.8813i | 0.931959 | − | 1.61420i | 0.151990 | − | 0.988382i | \(-0.451432\pi\) |
0.779969 | − | 0.625819i | \(-0.215235\pi\) | |||||||
\(740\) | −10.9941 | + | 19.0423i | −0.404151 | + | 0.700009i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0422078 | + | 0.348871i | 0.00154950 | + | 0.0128075i | ||||
\(743\) | 38.3208 | + | 22.1245i | 1.40586 | + | 0.811671i | 0.994985 | − | 0.100023i | \(-0.0318917\pi\) |
0.410870 | + | 0.911694i | \(0.365225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.1047i | 1.17623i | ||||||||
\(746\) | −20.3626 | − | 11.7564i | −0.745529 | − | 0.430431i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 5.05339i | − | 0.184770i | ||||||
\(749\) | −41.4143 | + | 5.01047i | −1.51325 | + | 0.183078i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.34460 | 0.0855557 | 0.0427779 | − | 0.999085i | \(-0.486379\pi\) | ||||
0.0427779 | + | 0.999085i | \(0.486379\pi\) | |||||||
\(752\) | −6.19533 | − | 10.7306i | −0.225921 | − | 0.391306i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 42.5450 | + | 24.5634i | 1.54940 | + | 0.894546i | ||||
\(755\) | −11.5751 | −0.421260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.8530 | −0.903298 | −0.451649 | − | 0.892196i | \(-0.649164\pi\) | ||||
−0.451649 | + | 0.892196i | \(0.649164\pi\) | |||||||
\(758\) | 4.98516 | + | 2.87819i | 0.181069 | + | 0.104540i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.40120 | − | 2.42694i | −0.0508267 | − | 0.0880345i | ||||
\(761\) | −0.882087 | −0.0319756 | −0.0159878 | − | 0.999872i | \(-0.505089\pi\) | ||||
−0.0159878 | + | 0.999872i | \(0.505089\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.6015 | + | 22.9749i | −1.10785 | + | 0.831747i | ||||
\(764\) | − | 9.77730i | − | 0.353730i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.7140 | − | 25.2383i | −1.57945 | − | 0.911896i | ||||
\(767\) | − | 38.7003i | − | 1.39739i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9310 | + | 10.3524i | 0.646607 | + | 0.373319i | 0.787155 | − | 0.616755i | \(-0.211553\pi\) |
−0.140548 | + | 0.990074i | \(0.544886\pi\) | |||||||
\(770\) | −17.2293 | + | 12.9353i | −0.620900 | + | 0.466157i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.16794 | + | 3.75499i | −0.0780260 | + | 0.135145i | ||||
\(773\) | −4.70279 | + | 8.14548i | −0.169148 | + | 0.292972i | −0.938120 | − | 0.346309i | \(-0.887435\pi\) |
0.768973 | + | 0.639282i | \(0.220768\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.2047 | − | 20.3254i | 1.26459 | − | 0.730111i | ||||
\(776\) | −0.401187 | − | 0.694877i | −0.0144018 | − | 0.0249446i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.7316 | − | 28.9800i | 0.599858 | − | 1.03898i | ||||
\(779\) | − | 2.88157i | − | 0.103243i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.55114 | −0.198635 | ||||||||
\(782\) | −5.13344 | − | 8.89138i | −0.183571 | − | 0.317955i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 33.0873 | − | 8.12497i | 1.18169 | − | 0.290178i | ||||
\(785\) | −12.5597 | + | 7.25136i | −0.448276 | + | 0.258812i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.7855 | − | 12.5779i | 0.776569 | − | 0.448352i | −0.0586440 | − | 0.998279i | \(-0.518678\pi\) |
0.835213 | + | 0.549927i | \(0.185344\pi\) | |||||||
\(788\) | 2.28418 | − | 1.31877i | 0.0813705 | − | 0.0469793i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 103.438 | − | 59.7197i | 3.68014 | − | 2.12473i | ||||
\(791\) | 31.5486 | + | 42.0214i | 1.12174 | + | 1.49411i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.3996 | + | 38.7972i | 0.795432 | + | 1.37773i | ||||
\(794\) | 2.14457 | 0.0761080 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 11.8165i | − | 0.418824i | ||||||
\(797\) | −15.3584 | + | 26.6015i | −0.544023 | + | 0.942275i | 0.454645 | + | 0.890673i | \(0.349766\pi\) |
−0.998668 | + | 0.0516020i | \(0.983567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.04394 | + | 7.00431i | 0.143064 | + | 0.247795i | ||||
\(800\) | 54.2831 | − | 31.3404i | 1.91920 | − | 1.10805i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.8025 | + | 22.1746i | −0.452072 | + | 0.783012i | ||||
\(803\) | −3.26257 | + | 5.65093i | −0.115134 | + | 0.199417i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.96509 | + | 16.3281i | −0.245487 | + | 0.575491i | ||||
\(806\) | −37.6480 | − | 21.7361i | −1.32609 | − | 0.765621i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.67541i | 0.270020i | ||||||||
\(809\) | −12.3629 | − | 7.13774i | −0.434657 | − | 0.250950i | 0.266671 | − | 0.963788i | \(-0.414076\pi\) |
−0.701329 | + | 0.712838i | \(0.747409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0160i | 0.351711i | 0.984416 | + | 0.175855i | \(0.0562691\pi\) | ||||
−0.984416 | + | 0.175855i | \(0.943731\pi\) | |||||||
\(812\) | 10.4779 | + | 13.9561i | 0.367701 | + | 0.489762i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.04841 | 0.317146 | ||||||||
\(815\) | −21.1231 | − | 36.5863i | −0.739909 | − | 1.28156i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.95333 | + | 2.28245i | 0.138309 | + | 0.0798530i | ||||
\(818\) | −37.3674 | −1.30652 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.7200 | 0.828337 | ||||||||
\(821\) | 10.7914 | + | 6.23043i | 0.376623 | + | 0.217444i | 0.676348 | − | 0.736582i | \(-0.263562\pi\) |
−0.299725 | + | 0.954026i | \(0.596895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.29804 | + | 3.98032i | 0.0801045 | + | 0.138745i | 0.903295 | − | 0.429021i | \(-0.141141\pi\) |
−0.823190 | + | 0.567766i | \(0.807808\pi\) | |||||||
\(824\) | −10.8981 | −0.379654 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.3008 | − | 31.1807i | 0.462793 | − | 1.08492i | ||||
\(827\) | − | 37.9330i | − | 1.31906i | −0.751678 | − | 0.659531i | \(-0.770755\pi\) | ||
0.751678 | − | 0.659531i | \(-0.229245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.8690 | − | 18.3996i | −1.10686 | − | 0.639044i | −0.168843 | − | 0.985643i | \(-0.554003\pi\) |
−0.938013 | + | 0.346599i | \(0.887337\pi\) | |||||||
\(830\) | 70.9858i | 2.46395i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.3447 | − | 6.54987i | −0.393307 | − | 0.227076i | ||||
\(833\) | −21.5974 | + | 5.30350i | −0.748305 | + | 0.183755i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.05213 | − | 12.2146i | 0.244049 | − | 0.422705i | ||||
\(836\) | 0.502032 | − | 0.869545i | 0.0173631 | − | 0.0300738i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40.5396 | + | 23.4055i | −1.40042 | + | 0.808531i | ||||
\(839\) | 10.6785 | + | 18.4956i | 0.368662 | + | 0.638541i | 0.989357 | − | 0.145512i | \(-0.0464828\pi\) |
−0.620695 | + | 0.784052i | \(0.713149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.81505 | + | 4.87580i | −0.0970706 | + | 0.168131i | ||||
\(842\) | − | 0.171216i | − | 0.00590049i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.9441 | −0.583242 | ||||||||
\(845\) | −33.6932 | − | 58.3584i | −1.15908 | − | 2.00759i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.4623 | − | 10.0083i | −0.806173 | − | 0.343889i | ||||
\(848\) | −0.305226 | + | 0.176223i | −0.0104815 | + | 0.00605151i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47.9572 | + | 27.6881i | −1.64492 | + | 0.949693i | ||||
\(851\) | 6.45657 | − | 3.72770i | 0.221328 | − | 0.127784i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.8709 | − | 24.7515i | 1.46787 | − | 0.847476i | 0.468519 | − | 0.883453i | \(-0.344788\pi\) |
0.999353 | + | 0.0359772i | \(0.0114544\pi\) | |||||||
\(854\) | 4.71319 | + | 38.9572i | 0.161282 | + | 1.33309i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.19041 | − | 15.9183i | −0.314122 | − | 0.544075i | ||||
\(857\) | −14.0162 | −0.478784 | −0.239392 | − | 0.970923i | \(-0.576948\pi\) | ||||
−0.239392 | + | 0.970923i | \(0.576948\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.21490i | 0.0414517i | 0.999785 | + | 0.0207259i | \(0.00659772\pi\) | ||||
−0.999785 | + | 0.0207259i | \(0.993402\pi\) | |||||||
\(860\) | −18.7883 | + | 32.5423i | −0.640676 | + | 1.10968i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.4220 | − | 52.6925i | −1.03618 | − | 1.79471i | ||||
\(863\) | 31.2396 | − | 18.0362i | 1.06341 | − | 0.613960i | 0.137036 | − | 0.990566i | \(-0.456242\pi\) |
0.926373 | + | 0.376606i | \(0.122909\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.3474 | + | 31.7787i | −0.623832 | + | 1.08051i | ||||
\(866\) | 16.4639 | − | 28.5164i | 0.559467 | − | 0.969026i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.27184 | − | 12.3497i | −0.314707 | − | 0.419176i | ||||
\(869\) | −17.2625 | − | 9.96652i | −0.585591 | − | 0.338091i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.2489i | 0.957177i | ||||||||
\(872\) | −14.6017 | − | 8.43032i | −0.494477 | − | 0.285487i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.03994i | − | 0.0690020i | ||||||
\(875\) | 41.7300 | + | 17.8008i | 1.41073 | + | 0.601776i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.1921 | −0.377932 | −0.188966 | − | 0.981984i | \(-0.560514\pi\) | ||||
−0.188966 | + | 0.981984i | \(0.560514\pi\) | |||||||
\(878\) | 9.20499 | + | 15.9435i | 0.310653 | + | 0.538067i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −18.7129 | − | 10.8039i | −0.630811 | − | 0.364199i | ||||
\(881\) | −4.16372 | −0.140279 | −0.0701397 | − | 0.997537i | \(-0.522345\pi\) | ||||
−0.0701397 | + | 0.997537i | \(0.522345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.7433 | −1.30382 | −0.651908 | − | 0.758298i | \(-0.726031\pi\) | ||||
−0.651908 | + | 0.758298i | \(0.726031\pi\) | |||||||
\(884\) | 20.7988 | + | 12.0082i | 0.699539 | + | 0.403879i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.1734 | − | 41.8696i | −0.812121 | − | 1.40664i | ||||
\(887\) | −38.0824 | −1.27868 | −0.639342 | − | 0.768923i | \(-0.720793\pi\) | ||||
−0.639342 | + | 0.768923i | \(0.720793\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.6751 | + | 9.24597i | 0.726961 | + | 0.310100i | ||||
\(890\) | 80.6807i | 2.70442i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.3764 | − | 12.9190i | −0.749216 | − | 0.432560i | ||||
\(893\) | 1.60699i | 0.0537759i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 60.8529 | + | 35.1334i | 2.03409 | + | 1.17438i | ||||
\(896\) | 14.0665 | + | 18.7359i | 0.469927 | + | 0.625922i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.0351 | − | 38.1660i | 0.735322 | − | 1.27361i | ||||
\(899\) | −10.3400 | + | 17.9094i | −0.344858 | + | 0.597311i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.199234 | − | 0.115028i | 0.00663743 | − | 0.00383212i | ||||
\(902\) | −4.88053 | − | 8.45333i | −0.162504 | − | 0.281465i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.5763 | + | 20.0508i | −0.385023 | + | 0.666880i | ||||
\(905\) | − | 63.2964i | − | 2.10404i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.54767 | 0.0513894 | 0.0256947 | − | 0.999670i | \(-0.491820\pi\) | ||||
0.0256947 | + | 0.999670i | \(0.491820\pi\) | |||||||
\(908\) | −3.90421 | − | 6.76228i | −0.129566 | − | 0.224414i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.2980 | − | 101.650i | −0.407676 | − | 3.36967i | ||||
\(911\) | 33.7493 | − | 19.4852i | 1.11816 | − | 0.645573i | 0.177233 | − | 0.984169i | \(-0.443285\pi\) |
0.940932 | + | 0.338596i | \(0.109952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.2596 | − | 5.92336i | 0.339542 | − | 0.196034i | ||||
\(914\) | −33.0762 | + | 19.0965i | −1.09406 | + | 0.631657i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.1608 | + | 7.59836i | −0.434843 | + | 0.251057i | ||||
\(917\) | −16.4394 | − | 7.01255i | −0.542875 | − | 0.231575i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.86991 | − | 10.1670i | −0.193630 | − | 0.335378i | 0.752820 | − | 0.658226i | \(-0.228693\pi\) |
−0.946451 | + | 0.322848i | \(0.895360\pi\) | |||||||
\(920\) | −7.82162 | −0.257871 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.3203i | 0.504546i | ||||||||
\(923\) | 13.1910 | − | 22.8474i | 0.434186 | − | 0.752033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.1060 | − | 34.8246i | −0.661081 | − | 1.14503i | ||||
\(926\) | −18.7655 | + | 10.8342i | −0.616671 | + | 0.356035i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.9435 | + | 27.6150i | −0.523371 | + | 0.906506i | ||||
\(929\) | 22.3142 | − | 38.6493i | 0.732105 | − | 1.26804i | −0.223877 | − | 0.974617i | \(-0.571871\pi\) |
0.955982 | − | 0.293425i | \(-0.0947952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.24318 | − | 1.23302i | −0.139064 | − | 0.0404107i | ||||
\(932\) | −12.2146 | − | 7.05213i | −0.400104 | − | 0.231000i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 53.4824i | 1.75000i | ||||||||
\(935\) | 12.2146 | + | 7.05213i | 0.399462 | + | 0.230629i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 33.3351i | − | 1.08901i | −0.838758 | − | 0.544505i | \(-0.816718\pi\) | ||
0.838758 | − | 0.544505i | \(-0.183282\pi\) | |||||||
\(938\) | −9.70875 | + | 22.7600i | −0.317002 | + | 0.743141i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.2282 | −0.431455 | ||||||||
\(941\) | 16.9992 | + | 29.4435i | 0.554159 | + | 0.959831i | 0.997968 | + | 0.0637100i | \(0.0202933\pi\) |
−0.443810 | + | 0.896121i | \(0.646373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.96509 | − | 4.02130i | −0.226815 | − | 0.130952i | ||||
\(944\) | 33.9984 | 1.10655 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.4633 | 0.502754 | ||||||||
\(947\) | −39.9637 | − | 23.0731i | −1.29865 | − | 0.749774i | −0.318476 | − | 0.947931i | \(-0.603171\pi\) |
−0.980170 | + | 0.198157i | \(0.936504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.5055 | − | 26.8562i | −0.503329 | − | 0.871791i | ||||
\(950\) | −11.0028 | −0.356977 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.88319 | − | 7.83615i | −0.190675 | − | 0.253971i | ||||
\(953\) | − | 35.1143i | − | 1.13746i | −0.822523 | − | 0.568731i | \(-0.807434\pi\) | ||
0.822523 | − | 0.568731i | \(-0.192566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.6329 | + | 13.6445i | 0.764744 | + | 0.441525i | ||||
\(956\) | − | 22.6234i | − | 0.731692i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 64.3717 | + | 37.1650i | 2.07976 | + | 1.20075i | ||||
\(959\) | 17.5030 | − | 41.0318i | 0.565201 | − | 1.32499i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.35017 | + | 10.9988i | −0.204844 | + | 0.354800i | ||||
\(962\) | −21.5014 | + | 37.2415i | −0.693234 | + | 1.20072i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28.2334 | − | 16.3005i | 0.909335 | − | 0.525005i | ||||
\(965\) | −6.05084 | − | 10.4804i | −0.194784 | − | 0.337375i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.70742 | − | 11.6176i | 0.215696 | − | 0.373597i | −0.737792 | − | 0.675029i | \(-0.764131\pi\) |
0.953488 | + | 0.301432i | \(0.0974646\pi\) | |||||||
\(968\) | − | 11.2391i | − | 0.361238i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.80785 | −0.154371 | ||||||||
\(971\) | 9.19460 | + | 15.9255i | 0.295069 | + | 0.511074i | 0.975001 | − | 0.222201i | \(-0.0713241\pi\) |
−0.679932 | + | 0.733275i | \(0.737991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.29258 | + | 1.72166i | 0.0414381 | + | 0.0551938i | ||||
\(974\) | −19.7265 | + | 11.3891i | −0.632078 | + | 0.364930i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.0835 | + | 19.6781i | −1.09099 | + | 0.629882i | ||||
\(977\) | −19.6181 | + | 11.3265i | −0.627638 | + | 0.362367i | −0.779837 | − | 0.625983i | \(-0.784698\pi\) |
0.152199 | + | 0.988350i | \(0.451365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.6608 | − | 6.73234i | 0.372679 | − | 0.215166i | ||||
\(980\) | 10.1498 | − | 34.9282i | 0.324223 | − | 1.11574i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.65976 | − | 9.80298i | −0.180610 | − | 0.312826i | ||||
\(983\) | −39.3408 | −1.25478 | −0.627388 | − | 0.778707i | \(-0.715876\pi\) | ||||
−0.627388 | + | 0.778707i | \(0.715876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.36151i | 0.234557i | ||||||||
\(986\) | 14.0855 | − | 24.3968i | 0.448574 | − | 0.776954i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.38592 | + | 4.13254i | 0.0759063 | + | 0.131474i | ||||
\(989\) | 11.0339 | − | 6.37045i | 0.350859 | − | 0.202569i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.475797 | + | 0.824104i | −0.0151142 | + | 0.0261785i | −0.873484 | − | 0.486854i | \(-0.838145\pi\) |
0.858369 | + | 0.513032i | \(0.171478\pi\) | |||||||
\(992\) | 14.1084 | − | 24.4364i | 0.447941 | − | 0.775857i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.4803 | − | 13.8745i | 0.586158 | − | 0.440073i | ||||
\(995\) | 28.5618 | + | 16.4902i | 0.905471 | + | 0.522774i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.4640i | 0.996475i | 0.867041 | + | 0.498238i | \(0.166019\pi\) | ||||
−0.867041 | + | 0.498238i | \(0.833981\pi\) | |||||||
\(998\) | −4.70279 | − | 2.71516i | −0.148864 | − | 0.0859468i | ||||
\(999\) | 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 | 567.2.s.f.458.5 | 12 | ||
3.2 | odd | 2 | inner | 567.2.s.f.458.2 | 12 | ||
7.5 | odd | 6 | 567.2.i.f.215.2 | 12 | |||
9.2 | odd | 6 | 567.2.i.f.269.5 | 12 | |||
9.4 | even | 3 | 189.2.p.d.80.2 | yes | 12 | ||
9.5 | odd | 6 | 189.2.p.d.80.5 | yes | 12 | ||
9.7 | even | 3 | 567.2.i.f.269.2 | 12 | |||
21.5 | even | 6 | 567.2.i.f.215.5 | 12 | |||
63.4 | even | 3 | 1323.2.c.d.1322.3 | 12 | |||
63.5 | even | 6 | 189.2.p.d.26.2 | ✓ | 12 | ||
63.31 | odd | 6 | 1323.2.c.d.1322.4 | 12 | |||
63.32 | odd | 6 | 1323.2.c.d.1322.10 | 12 | |||
63.40 | odd | 6 | 189.2.p.d.26.5 | yes | 12 | ||
63.47 | even | 6 | inner | 567.2.s.f.26.5 | 12 | ||
63.59 | even | 6 | 1323.2.c.d.1322.9 | 12 | |||
63.61 | odd | 6 | inner | 567.2.s.f.26.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.2 | ✓ | 12 | 63.5 | even | 6 | ||
189.2.p.d.26.5 | yes | 12 | 63.40 | odd | 6 | ||
189.2.p.d.80.2 | yes | 12 | 9.4 | even | 3 | ||
189.2.p.d.80.5 | yes | 12 | 9.5 | odd | 6 | ||
567.2.i.f.215.2 | 12 | 7.5 | odd | 6 | |||
567.2.i.f.215.5 | 12 | 21.5 | even | 6 | |||
567.2.i.f.269.2 | 12 | 9.7 | even | 3 | |||
567.2.i.f.269.5 | 12 | 9.2 | odd | 6 | |||
567.2.s.f.26.2 | 12 | 63.61 | odd | 6 | inner | ||
567.2.s.f.26.5 | 12 | 63.47 | even | 6 | inner | ||
567.2.s.f.458.2 | 12 | 3.2 | odd | 2 | inner | ||
567.2.s.f.458.5 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.c.d.1322.3 | 12 | 63.4 | even | 3 | |||
1323.2.c.d.1322.4 | 12 | 63.31 | odd | 6 | |||
1323.2.c.d.1322.9 | 12 | 63.59 | even | 6 | |||
1323.2.c.d.1322.10 | 12 | 63.32 | odd | 6 |