Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(26,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.p (of order \(6\), degree \(2\), 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: | \(1.50917259820\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.2 | ||
Root | \(-1.90412 + 1.09935i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.80 |
Dual form | 189.2.p.d.26.2 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | \(-0.891271\pi\) |
−0.181014 | + | 0.983481i | \(0.557938\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.682224 | − | 1.18165i | 0.341112 | − | 0.590823i | ||||
\(5\) | 1.90412 | + | 3.29804i | 0.851549 | + | 1.47493i | 0.879810 | + | 0.475326i | \(0.157670\pi\) |
−0.0282601 | + | 0.999601i | \(0.508997\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.11581 | − | 1.58850i | 0.799702 | − | 0.600397i | ||||
\(8\) | − | 1.16576i | − | 0.412157i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.04940 | − | 3.49262i | −1.91299 | − | 1.10446i | ||||
\(11\) | −1.00958 | − | 0.582878i | −0.304398 | − | 0.175744i | 0.340019 | − | 0.940419i | \(-0.389567\pi\) |
−0.644417 | + | 0.764674i | \(0.722900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.54030i | 1.53660i | 0.640089 | + | 0.768301i | \(0.278897\pi\) | ||||
−0.640089 | + | 0.768301i | \(0.721103\pi\) | |||||||
\(14\) | −1.90412 | + | 4.46379i | −0.508898 | + | 1.19300i | ||||
\(15\) | 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 | \(0.356402\pi\) | |||||||
\(20\) | 5.19615 | 1.16190 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.13828 | 0.455883 | ||||||||
\(23\) | 1.52579 | − | 0.880915i | 0.318149 | − | 0.183684i | −0.332418 | − | 0.943132i | \(-0.607865\pi\) |
0.650567 | + | 0.759449i | \(0.274531\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.75136 | + | 8.22961i | −0.950273 | + | 1.64592i | ||||
\(26\) | −5.08112 | − | 8.80077i | −0.996491 | − | 1.72597i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.433589 | − | 3.58386i | −0.0819406 | − | 0.677285i | ||||
\(29\) | − | 4.83424i | − | 0.897696i | −0.893608 | − | 0.448848i | \(-0.851834\pi\) | ||
0.893608 | − | 0.448848i | \(-0.148166\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.70469 | − | 2.13891i | −0.665382 | − | 0.384159i | 0.128942 | − | 0.991652i | \(-0.458842\pi\) |
−0.794325 | + | 0.607493i | \(0.792175\pi\) | |||||||
\(32\) | −5.71237 | − | 3.29804i | −1.00981 | − | 0.583016i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.82739i | − | 0.999390i | ||||||
\(35\) | 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 | \(0.946417\pi\) | |||||||
\(38\) | 0.578926 | − | 1.00273i | 0.0939142 | − | 0.162664i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.84471 | − | 2.21974i | 0.607902 | − | 0.350972i | ||||
\(41\) | 4.56491 | 0.712919 | 0.356460 | − | 0.934311i | \(-0.383984\pi\) | ||||
0.356460 | + | 0.934311i | \(0.383984\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.23163 | 1.10281 | 0.551406 | − | 0.834237i | \(-0.314091\pi\) | ||||
0.551406 | + | 0.834237i | \(0.314091\pi\) | |||||||
\(44\) | −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 | 0.943802 | − | 0.330512i | \(-0.107222\pi\) |
−0.758133 | + | 0.652100i | \(0.773888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.95333 | − | 6.72194i | 0.279047 | − | 0.960277i | ||||
\(50\) | − | 17.4303i | − | 2.46502i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.54667 | + | 3.77972i | 0.907860 | + | 0.524153i | ||||
\(53\) | −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 | ||||||
\(56\) | −1.85181 | − | 2.46652i | −0.247458 | − | 0.329603i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.43359 | + | 7.67920i | 0.582159 | + | 1.00833i | ||||
\(59\) | 3.49262 | − | 6.04940i | 0.454701 | − | 0.787565i | −0.543970 | − | 0.839105i | \(-0.683080\pi\) |
0.998671 | + | 0.0515396i | \(0.0164128\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00273 | − | 4.04303i | 0.896608 | − | 0.517657i | 0.0205096 | − | 0.999790i | \(-0.493471\pi\) |
0.876098 | + | 0.482133i | \(0.160138\pi\) | |||||||
\(62\) | 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 | −0.978678 | − | 0.205398i | \(-0.934151\pi\) |
0.667219 | + | 0.744861i | \(0.267484\pi\) | |||||||
\(68\) | 2.16743 | + | 3.75409i | 0.262839 | + | 0.455251i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −18.3474 | + | 2.21974i | −2.19294 | + | 0.265310i | ||||
\(71\) | 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 | \(0.560440\pi\) | |||||||
\(74\) | 6.72194 | + | 3.88092i | 0.781410 | + | 0.451147i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.861298i | 0.0987976i | ||||||||
\(77\) | −3.06197 | + | 0.370450i | −0.348944 | + | 0.0422166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.54940 | − | 14.8080i | −0.961883 | − | 1.66603i | −0.717766 | − | 0.696284i | \(-0.754835\pi\) |
−0.244116 | − | 0.969746i | \(-0.578498\pi\) | |||||||
\(80\) | −9.26770 | + | 16.0521i | −1.03616 | + | 1.79468i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.25136 | + | 4.18658i | −0.800779 | + | 0.462330i | ||||
\(83\) | 10.1622 | 1.11545 | 0.557726 | − | 0.830025i | \(-0.311674\pi\) | ||||
0.557726 | + | 0.830025i | \(0.311674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0988 | −1.31230 | ||||||||
\(86\) | −11.4874 | + | 6.63228i | −1.23872 | + | 0.715177i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.679494 | + | 1.17692i | −0.0724344 | + | 0.125460i | ||||
\(89\) | −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 | ||||
\(92\) | − | 2.40393i | − | 0.250627i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.04394 | − | 2.33477i | −0.417101 | − | 0.240813i | ||||
\(95\) | −2.08186 | − | 1.20196i | −0.213594 | − | 0.123319i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.688287i | 0.0698849i | 0.999389 | + | 0.0349425i | \(0.0111248\pi\) | ||||
−0.999389 | + | 0.0349425i | \(0.988875\pi\) | |||||||
\(98\) | 3.06197 | + | 12.4693i | 0.309306 | + | 1.25958i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.48299 | + | 11.2289i | 0.648299 | + | 1.12289i | ||||
\(101\) | 3.29203 | − | 5.70196i | 0.327569 | − | 0.567367i | −0.654460 | − | 0.756097i | \(-0.727104\pi\) |
0.982029 | + | 0.188730i | \(0.0604372\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.09607 | + | 4.67427i | −0.797730 | + | 0.460570i | −0.842677 | − | 0.538420i | \(-0.819021\pi\) |
0.0449469 | + | 0.998989i | \(0.485688\pi\) | |||||||
\(104\) | 6.45864 | 0.633322 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.132822 | 0.0129009 | ||||||||
\(107\) | 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 | ||||||||
\(112\) | 11.8447 | + | 5.05260i | 1.11922 | + | 0.477426i | ||||
\(113\) | 19.8606i | 1.86833i | 0.356840 | + | 0.934166i | \(0.383854\pi\) | ||||
−0.356840 | + | 0.934166i | \(0.616146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.81058 | + | 3.35474i | 0.541840 | + | 0.312831i | ||||
\(116\) | −5.71237 | − | 3.29804i | −0.530380 | − | 0.306215i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.8126i | 1.17950i | ||||||||
\(119\) | 1.00958 | + | 8.34471i | 0.0925476 | + | 0.764958i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.82051 | − | 8.34936i | −0.438228 | − | 0.759033i | ||||
\(122\) | −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 | ||||
\(131\) | −3.37760 | − | 5.85017i | −0.295102 | − | 0.511132i | 0.679907 | − | 0.733299i | \(-0.262020\pi\) |
−0.975009 | + | 0.222167i | \(0.928687\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.655291 | + | 1.53618i | −0.0568209 | + | 0.133204i | ||||
\(134\) | − | 9.35245i | − | 0.807928i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.20742 | + | 1.85181i | 0.275034 | + | 0.158791i | ||||
\(137\) | −14.6017 | − | 8.43032i | −1.24751 | − | 0.720251i | −0.276898 | − | 0.960899i | \(-0.589307\pi\) |
−0.970612 | + | 0.240649i | \(0.922640\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.813709i | 0.0690179i | 0.999404 | + | 0.0345089i | \(0.0109867\pi\) | ||||
−0.999404 | + | 0.0345089i | \(0.989013\pi\) | |||||||
\(140\) | 10.9941 | − | 8.25409i | 0.929170 | − | 0.697598i | ||||
\(141\) | 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 | ||||
\(146\) | −10.2669 | −0.849693 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.77383 | −0.474606 | ||||||||
\(149\) | −7.30087 | + | 4.21516i | −0.598110 | + | 0.345319i | −0.768298 | − | 0.640092i | \(-0.778896\pi\) |
0.170187 | + | 0.985412i | \(0.445563\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51974 | + | 2.63227i | −0.123675 | + | 0.214211i | −0.921214 | − | 0.389056i | \(-0.872801\pi\) |
0.797539 | + | 0.603267i | \(0.206135\pi\) | |||||||
\(152\) | 0.367938 | + | 0.637287i | 0.0298437 | + | 0.0516908i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.52420 | − | 3.39666i | 0.364571 | − | 0.273711i | ||||
\(155\) | − | 16.2910i | − | 1.30852i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.29804 | − | 1.90412i | −0.263212 | − | 0.151966i | 0.362587 | − | 0.931950i | \(-0.381894\pi\) |
−0.625799 | + | 0.779984i | \(0.715227\pi\) | |||||||
\(158\) | 27.1615 | + | 15.6817i | 2.16085 | + | 1.24757i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 25.1195i | − | 1.98587i | ||||||
\(161\) | 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 | \(0.690276\pi\) | |||||||
\(164\) | 3.11429 | − | 5.39411i | 0.243185 | − | 0.421209i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.1427 | + | 9.32002i | −1.25292 | + | 0.723374i | ||||
\(167\) | 3.70361 | 0.286594 | 0.143297 | − | 0.989680i | \(-0.454230\pi\) | ||||
0.143297 | + | 0.989680i | \(0.454230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.6949 | −1.36114 | ||||||||
\(170\) | 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 | 0.988983 | − | 0.148032i | \(-0.0472938\pi\) |
−0.622691 | + | 0.782468i | \(0.713960\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.01974 | + | 24.9599i | 0.228271 | + | 1.88679i | ||||
\(176\) | − | 5.67395i | − | 0.427690i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.3474 | + | 10.5929i | 1.37520 | + | 0.793971i | ||||
\(179\) | −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 | \(0.788060\pi\) | |||||||
\(182\) | −24.7307 | − | 10.5494i | −1.83316 | − | 0.781974i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.02693 | − | 1.77870i | −0.0757065 | − | 0.131128i | ||||
\(185\) | 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 | \(-0.583192\pi\) |
0.707421 | + | 0.706793i | \(0.249859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58888 | − | 2.75202i | 0.114370 | − | 0.198095i | −0.803158 | − | 0.595766i | \(-0.796848\pi\) |
0.917528 | + | 0.397672i | \(0.130182\pi\) | |||||||
\(194\) | −0.631243 | − | 1.09334i | −0.0453206 | − | 0.0784975i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.61035 | − | 6.89401i | −0.472168 | − | 0.492430i | ||||
\(197\) | − | 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 | \(0.765977\pi\) | |||||||
\(200\) | 9.59372 | + | 5.53894i | 0.678378 | + | 0.391662i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0768i | 0.849718i | ||||||||
\(203\) | −7.67920 | − | 10.2284i | −0.538974 | − | 0.717890i | ||||
\(204\) | 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 | ||||
\(209\) | 0.735875 | 0.0509016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4183 | 0.854912 | 0.427456 | − | 0.904036i | \(-0.359410\pi\) | ||||
0.427456 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(212\) | −0.0855662 | + | 0.0494016i | −0.00587671 | + | 0.00339292i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.4605 | + | 25.0464i | −0.988501 | + | 1.71213i | ||||
\(215\) | 13.7699 | + | 23.8502i | 0.939099 | + | 1.62657i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2361 | + | 1.35939i | −0.762755 | + | 0.0922811i | ||||
\(218\) | 26.5291i | 1.79678i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.24591 | − | 3.02873i | −0.353679 | − | 0.204197i | ||||
\(221\) | −15.2434 | − | 8.80077i | −1.02538 | − | 0.592004i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.9366i | − | 1.26809i | −0.773297 | − | 0.634044i | \(-0.781394\pi\) | ||
0.773297 | − | 0.634044i | \(-0.218606\pi\) | |||||||
\(224\) | −17.3252 | + | 2.09607i | −1.15759 | + | 0.140050i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.2146 | − | 31.5486i | −1.21162 | − | 2.09858i | ||||
\(227\) | 2.86138 | − | 4.95606i | 0.189917 | − | 0.328945i | −0.755306 | − | 0.655373i | \(-0.772512\pi\) |
0.945222 | + | 0.326428i | \(0.105845\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.64548 | − | 5.56882i | 0.637391 | − | 0.367998i | −0.146218 | − | 0.989252i | \(-0.546710\pi\) |
0.783609 | + | 0.621255i | \(0.213377\pi\) | |||||||
\(230\) | −12.3068 | −0.811488 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.63555 | −0.369992 | ||||||||
\(233\) | −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 | ||||||||
\(238\) | −9.25682 | − | 12.3297i | −0.600031 | − | 0.799214i | ||||
\(239\) | 16.5806i | 1.07251i | 0.844056 | + | 0.536255i | \(0.180161\pi\) | ||||
−0.844056 | + | 0.536255i | \(0.819839\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6921 | + | 11.9466i | 1.33290 | + | 0.769549i | 0.985743 | − | 0.168258i | \(-0.0538143\pi\) |
0.347155 | + | 0.937808i | \(0.387148\pi\) | |||||||
\(242\) | 15.3148 | + | 8.84198i | 0.984470 | + | 0.568384i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.0330i | − | 0.706316i | ||||||
\(245\) | 25.8886 | − | 6.35725i | 1.65396 | − | 0.406150i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.74864 | − | 3.02873i | −0.111263 | − | 0.192713i | ||||
\(248\) | −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 | ||||
\(257\) | −11.6025 | − | 20.0961i | −0.723742 | − | 1.25356i | −0.959490 | − | 0.281744i | \(-0.909087\pi\) |
0.235747 | − | 0.971814i | \(-0.424246\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.2980 | − | 4.39284i | −0.639889 | − | 0.272958i | ||||
\(260\) | 28.7882i | 1.78537i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.7306 | + | 6.19533i | 0.662941 | + | 0.382749i | ||||
\(263\) | 8.33330 | + | 4.81123i | 0.513853 | + | 0.296673i | 0.734416 | − | 0.678699i | \(-0.237456\pi\) |
−0.220563 | + | 0.975373i | \(0.570789\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.275765i | − | 0.0169401i | ||||||
\(266\) | −0.367938 | − | 3.04121i | −0.0225597 | − | 0.186469i | ||||
\(267\) | 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 | \(0.129354\pi\) | |||||||
\(272\) | −15.4630 | −0.937584 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 30.9265 | 1.86834 | ||||||||
\(275\) | 9.59372 | − | 5.53894i | 0.578523 | − | 0.334010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.15802 | + | 7.20190i | −0.249831 | + | 0.432720i | −0.963479 | − | 0.267784i | \(-0.913708\pi\) |
0.713648 | + | 0.700505i | \(0.247042\pi\) | |||||||
\(278\) | −0.746270 | − | 1.29258i | −0.0447583 | − | 0.0775237i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.60862 | − | 10.8039i | 0.275418 | − | 0.645656i | ||||
\(281\) | 22.7618i | 1.35786i | 0.734204 | + | 0.678928i | \(0.237555\pi\) | ||||
−0.734204 | + | 0.678928i | \(0.762445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7514 | − | 8.51670i | −0.876878 | − | 0.506266i | −0.00724998 | − | 0.999974i | \(-0.502308\pi\) |
−0.869628 | + | 0.493708i | \(0.835641\pi\) | |||||||
\(284\) | 5.62680 | + | 3.24864i | 0.333889 | + | 0.192771i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.8467i | 0.700511i | ||||||||
\(287\) | 9.65849 | − | 7.25136i | 0.570123 | − | 0.428035i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.45333 | + | 5.98134i | 0.203137 | + | 0.351843i | ||||
\(290\) | −16.8842 | + | 29.2443i | −0.991474 | + | 1.71728i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.61408 | − | 3.81864i | 0.387060 | − | 0.223469i | ||||
\(293\) | −21.4159 | −1.25113 | −0.625564 | − | 0.780173i | \(-0.715131\pi\) | ||||
−0.625564 | + | 0.780173i | \(0.715131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.6015 | 1.54880 | ||||||||
\(296\) | −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 | ||||||||
\(301\) | 15.3008 | − | 11.4874i | 0.881922 | − | 0.662125i | ||||
\(302\) | − | 5.57514i | − | 0.320813i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.66075 | − | 1.53618i | −0.152604 | − | 0.0881062i | ||||
\(305\) | 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 | \(-0.187336\pi\) | |||||||
\(308\) | −1.65121 | + | 3.87090i | −0.0940866 | + | 0.220565i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.9408 | + | 25.8782i | 0.848579 | + | 1.46978i | ||||
\(311\) | 3.40706 | − | 5.90120i | 0.193197 | − | 0.334626i | −0.753111 | − | 0.657893i | \(-0.771448\pi\) |
0.946308 | + | 0.323267i | \(0.104781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4121 | + | 8.32084i | −0.814621 | + | 0.470322i | −0.848558 | − | 0.529102i | \(-0.822529\pi\) |
0.0339371 | + | 0.999424i | \(0.489195\pi\) | |||||||
\(314\) | 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 | \(-0.621120\pi\) |
0.618386 | + | 0.785874i | \(0.287787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.81778 | + | 4.88053i | −0.157765 | + | 0.273257i | ||||
\(320\) | 4.50220 | + | 7.79804i | 0.251681 | + | 0.435924i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.02693 | + | 8.48818i | 0.0572287 | + | 0.473028i | ||||
\(323\) | − | 2.00546i | − | 0.111587i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −45.5944 | − | 26.3240i | −2.52912 | − | 1.46019i | ||||
\(326\) | −17.6218 | − | 10.1739i | −0.975981 | − | 0.563483i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.32157i | − | 0.293835i | ||||||
\(329\) | 6.19533 | + | 2.64275i | 0.341560 | + | 0.145699i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.16521 | − | 14.1426i | −0.448801 | − | 0.777346i | 0.549507 | − | 0.835489i | \(-0.314815\pi\) |
−0.998308 | + | 0.0581430i | \(0.981482\pi\) | |||||||
\(332\) | 6.93293 | − | 12.0082i | 0.380494 | − | 0.659035i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.88319 | + | 3.39666i | −0.321914 | + | 0.185857i | ||||
\(335\) | −19.4175 | −1.06089 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.95506 | −0.215446 | −0.107723 | − | 0.994181i | \(-0.534356\pi\) | ||||
−0.107723 | + | 0.994181i | \(0.534356\pi\) | |||||||
\(338\) | 28.1083 | − | 16.2284i | 1.52889 | − | 0.882706i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.25409 | + | 14.2965i | −0.447641 | + | 0.775337i | ||||
\(341\) | 2.49344 | + | 4.31877i | 0.135028 | + | 0.233875i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.54494 | − | 17.3252i | −0.353393 | − | 0.935475i | ||||
\(344\) | − | 8.43032i | − | 0.454532i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.3062 | − | 8.83705i | −0.822868 | − | 0.475083i | ||||
\(347\) | 6.35400 | + | 3.66849i | 0.341101 | + | 0.196935i | 0.660759 | − | 0.750598i | \(-0.270235\pi\) |
−0.319658 | + | 0.947533i | \(0.603568\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.5093i | 1.36548i | 0.730660 | + | 0.682741i | \(0.239212\pi\) | ||||
−0.730660 | + | 0.682741i | \(0.760788\pi\) | |||||||
\(350\) | −27.6881 | − | 36.8793i | −1.47999 | − | 1.97128i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.84471 | + | 6.65923i | 0.204924 | + | 0.354938i | ||||
\(353\) | −0.0103948 | + | 0.0180043i | −0.000553260 | + | 0.000958274i | −0.866302 | − | 0.499521i | \(-0.833509\pi\) |
0.865749 | + | 0.500479i | \(0.166843\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.7047 | + | 9.06711i | −0.833519 | + | 0.481232i | ||||
\(356\) | −15.7596 | −0.835257 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 33.8441 | 1.78872 | ||||||||
\(359\) | −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 | ||||||||
\(364\) | 19.8556 | − | 2.40221i | 1.04072 | − | 0.125910i | ||||
\(365\) | 21.3160i | 1.11573i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.68942 | − | 4.43949i | −0.401384 | − | 0.231739i | 0.285697 | − | 0.958320i | \(-0.407775\pi\) |
−0.687081 | + | 0.726581i | \(0.741108\pi\) | |||||||
\(368\) | 7.42629 | + | 4.28757i | 0.387122 | + | 0.223505i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.5590i | 1.53670i | ||||||||
\(371\) | −0.190199 | + | 0.0230110i | −0.00987464 | + | 0.00119467i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.40939 | + | 11.1014i | 0.331865 | + | 0.574808i | 0.982878 | − | 0.184260i | \(-0.0589887\pi\) |
−0.651012 | + | 0.759067i | \(0.725655\pi\) | |||||||
\(374\) | −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 | ||||
\(383\) | 13.7595 | + | 23.8322i | 0.703078 | + | 1.21777i | 0.967381 | + | 0.253327i | \(0.0815248\pi\) |
−0.264303 | + | 0.964440i | \(0.585142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.05213 | − | 9.39312i | −0.359410 | − | 0.478718i | ||||
\(386\) | 5.82878i | 0.296677i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.813312 | + | 0.469566i | 0.0412896 | + | 0.0238386i | ||||
\(389\) | 15.7994 | + | 9.12181i | 0.801064 | + | 0.462494i | 0.843843 | − | 0.536590i | \(-0.180288\pi\) |
−0.0427793 | + | 0.999085i | \(0.513621\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.59734i | 0.283070i | ||||||||
\(392\) | −7.83615 | − | 2.27711i | −0.395785 | − | 0.115011i | ||||
\(393\) | 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 | \(0.323993\pi\) | |||||||
\(398\) | 15.8850 | 0.796244 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −46.2515 | −2.31257 | ||||||||
\(401\) | 12.0892 | − | 6.97972i | 0.603707 | − | 0.348551i | −0.166791 | − | 0.985992i | \(-0.553341\pi\) |
0.770499 | + | 0.637442i | \(0.220007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8502 | − | 20.5251i | 0.590299 | − | 1.02243i | ||||
\(404\) | −4.49180 | − | 7.78003i | −0.223476 | − | 0.387071i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.5791 | + | 9.20499i | 1.07095 | + | 0.456836i | ||||
\(407\) | 4.93305i | 0.244522i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.6427 | + | 10.1860i | 0.872378 | + | 0.503667i | 0.868138 | − | 0.496324i | \(-0.165317\pi\) |
0.00424001 | + | 0.999991i | \(0.498650\pi\) | |||||||
\(410\) | −27.6150 | − | 15.9435i | −1.36381 | − | 0.787394i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.7556i | 0.628423i | ||||||||
\(413\) | −2.21974 | − | 18.3474i | −0.109226 | − | 0.902818i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.3502 | + | 33.5155i | 0.949862 | + | 1.64521i | ||||
\(416\) | 18.2721 | − | 31.6482i | 0.895863 | − | 1.55168i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.16894 | + | 0.674887i | −0.0571747 | + | 0.0330098i | ||||
\(419\) | 25.5207 | 1.24677 | 0.623383 | − | 0.781917i | \(-0.285758\pi\) | ||||
0.623383 | + | 0.781917i | \(0.285758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0933442 | 0.00454932 | 0.00227466 | − | 0.999997i | \(-0.499276\pi\) | ||||
0.00227466 | + | 0.999997i | \(0.499276\pi\) | |||||||
\(422\) | −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 | ||||||||
\(427\) | 8.39411 | − | 19.6781i | 0.406219 | − | 0.952292i | ||||
\(428\) | − | 21.5136i | − | 1.03990i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −43.7470 | − | 25.2573i | −2.10967 | − | 1.21802i | ||||
\(431\) | −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 | \(-0.141964\pi\) | |||||||
\(434\) | 16.6018 | − | 12.4642i | 0.796913 | − | 0.598303i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.86718 | − | 17.0905i | −0.472552 | − | 0.818484i | ||||
\(437\) | −0.556071 | + | 0.963144i | −0.0266005 | + | 0.0460734i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.69215 | + | 5.01841i | −0.414854 | + | 0.239516i | −0.692873 | − | 0.721060i | \(-0.743655\pi\) |
0.278019 | + | 0.960575i | \(0.410322\pi\) | |||||||
\(440\) | −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 | \(-0.451296\pi\) |
0.932114 | + | 0.362166i | \(0.117963\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.9929 | − | 38.0928i | 1.04256 | − | 1.80577i | ||||
\(446\) | 17.3672 | + | 30.0808i | 0.822359 | + | 1.42437i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.00273 | − | 3.75593i | 0.236357 | − | 0.177451i | ||||
\(449\) | − | 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 | ||||
\(452\) | 23.4683 | + | 13.5494i | 1.10385 | + | 0.637310i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.4969i | 0.492646i | ||||||||
\(455\) | −21.9026 | + | 51.3458i | −1.02681 | + | 2.40713i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4111 | − | 18.0326i | −0.487012 | − | 0.843529i | 0.512877 | − | 0.858462i | \(-0.328580\pi\) |
−0.999888 | + | 0.0149333i | \(0.995246\pi\) | |||||||
\(458\) | −10.2146 | + | 17.6921i | −0.477295 | + | 0.826700i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.92824 | − | 4.57737i | 0.369656 | − | 0.213421i | ||||
\(461\) | −8.35237 | −0.389008 | −0.194504 | − | 0.980902i | \(-0.562310\pi\) | ||||
−0.194504 | + | 0.980902i | \(0.562310\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8133 | 0.549011 | 0.274506 | − | 0.961586i | \(-0.411486\pi\) | ||||
0.274506 | + | 0.961586i | \(0.411486\pi\) | |||||||
\(464\) | 20.3768 | − | 11.7646i | 0.945970 | − | 0.546156i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.48026 | − | 16.4203i | 0.439165 | − | 0.760655i | ||||
\(467\) | 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 | ||||
\(470\) | − | 17.7828i | − | 0.820258i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.05213 | − | 4.07155i | −0.324601 | − | 0.187408i | ||||
\(473\) | −7.30087 | − | 4.21516i | −0.335694 | − | 0.193813i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.99853i | − | 0.275231i | ||||||
\(476\) | 10.5493 | + | 4.50000i | 0.483524 | + | 0.206257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.2064 | − | 26.3383i | −0.695526 | − | 1.20469i | ||||
\(479\) | −20.2618 | + | 35.0944i | −0.925785 | + | 1.60351i | −0.135491 | + | 0.990779i | \(0.543261\pi\) |
−0.790294 | + | 0.612728i | \(0.790072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.3035 | − | 11.7222i | 0.925760 | − | 0.534488i | ||||
\(482\) | −43.8260 | −1.99622 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.1547 | −0.597939 | ||||||||
\(485\) | −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 | ||||||||
\(490\) | −35.2937 | + | 33.8415i | −1.59441 | + | 1.52880i | ||||
\(491\) | 6.17122i | 0.278503i | 0.990257 | + | 0.139252i | \(0.0444697\pi\) | ||||
−0.990257 | + | 0.139252i | \(0.955530\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.3008 | + | 7.67920i | 0.599036 | + | 0.345854i | ||||
\(494\) | 5.55542 | + | 3.20742i | 0.249950 | + | 0.144309i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 20.8209i | − | 0.934884i | ||||||
\(497\) | 7.56417 | + | 10.0751i | 0.339300 | + | 0.451932i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.48026 | + | 2.56389i | 0.0662656 | + | 0.114775i | 0.897255 | − | 0.441513i | \(-0.145558\pi\) |
−0.830989 | + | 0.556289i | \(0.812225\pi\) | |||||||
\(500\) | −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 | ||||
\(509\) | −14.4742 | − | 25.0701i | −0.641560 | − | 1.11121i | −0.985085 | − | 0.172071i | \(-0.944954\pi\) |
0.343525 | − | 0.939144i | \(-0.388379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.7020 | − | 1.77870i | 0.650377 | − | 0.0786851i | ||||
\(512\) | − | 20.7564i | − | 0.917311i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 36.8611 | + | 21.2818i | 1.62587 | + | 0.938698i | ||||
\(515\) | −30.8318 | − | 17.8008i | −1.35861 | − | 0.784395i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.96774i | − | 0.130521i | ||||||
\(518\) | 20.3872 | − | 2.46652i | 0.895763 | − | 0.108373i | ||||
\(519\) | 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 | \(0.649060\pi\) | |||||||
\(524\) | −9.21711 | −0.402651 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6499 | −0.769574 | ||||||||
\(527\) | 11.7698 | − | 6.79531i | 0.512701 | − | 0.296008i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.94798 | + | 17.2304i | −0.432521 | + | 0.749148i | ||||
\(530\) | 0.252910 | + | 0.438053i | 0.0109857 | + | 0.0190278i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.36817 | + | 1.82234i | 0.0593178 | + | 0.0790087i | ||||
\(533\) | 25.2910i | 1.09547i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 52.0011 | + | 30.0229i | 2.24820 | + | 1.29800i | ||||
\(536\) | 5.14762 | + | 2.97198i | 0.222344 | + | 0.128370i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 38.2079i | − | 1.64726i | ||||||
\(539\) | −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 | \(0.836811\pi\) | |||||||
\(542\) | −18.0524 | + | 31.2677i | −0.775419 | + | 1.34306i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.1482 | − | 10.4779i | 0.778098 | − | 0.449235i | ||||
\(545\) | 55.0796 | 2.35935 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.2964 | −1.72295 | −0.861475 | − | 0.507800i | \(-0.830459\pi\) | ||||
−0.861475 | + | 0.507800i | \(0.830459\pi\) | |||||||
\(548\) | −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 | ||||||||
\(553\) | −41.6115 | − | 17.7502i | −1.76950 | − | 0.754816i | ||||
\(554\) | − | 15.2536i | − | 0.648065i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.961517 | + | 0.555132i | 0.0407774 | + | 0.0235428i | ||||
\(557\) | 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 | ||||||||
\(560\) | 5.89011 | + | 48.6851i | 0.248902 | + | 2.05732i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.8754 | − | 36.1572i | −0.880574 | − | 1.52520i | ||||
\(563\) | −3.16661 | + | 5.48473i | −0.133457 | + | 0.231154i | −0.925007 | − | 0.379951i | \(-0.875941\pi\) |
0.791550 | + | 0.611104i | \(0.209274\pi\) | |||||||
\(564\) | 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 | \(-0.721873\pi\) |
0.343052 | + | 0.939316i | \(0.388539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.24864 | + | 7.35885i | −0.177800 | + | 0.307958i | −0.941127 | − | 0.338054i | \(-0.890231\pi\) |
0.763327 | + | 0.646013i | \(0.223565\pi\) | |||||||
\(572\) | −4.40624 | − | 7.63183i | −0.184234 | − | 0.319103i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.69215 | + | 20.3768i | −0.362803 | + | 0.850512i | ||||
\(575\) | 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 | \(0.359646\pi\) | |||||||
\(578\) | −10.9712 | − | 6.33424i | −0.456343 | − | 0.263470i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 25.1195i | − | 1.04303i | ||||||
\(581\) | 21.5014 | − | 16.1427i | 0.892029 | − | 0.669714i | ||||
\(582\) | 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 | ||||
\(587\) | −24.1120 | −0.995207 | −0.497603 | − | 0.867405i | \(-0.665787\pi\) | ||||
−0.497603 | + | 0.867405i | \(0.665787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.70034 | 0.111265 | ||||||||
\(590\) | −42.2566 | + | 24.3968i | −1.73968 | + | 1.00440i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.2980 | − | 17.8367i | 0.423247 | − | 0.733085i | ||||
\(593\) | 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 | ||||
\(596\) | 11.5027i | 0.471170i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.5055 | − | 8.95208i | −0.634065 | − | 0.366078i | ||||
\(599\) | −30.0332 | − | 17.3397i | −1.22713 | − | 0.708481i | −0.260698 | − | 0.965420i | \(-0.583953\pi\) |
−0.966427 | + | 0.256939i | \(0.917286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.2709i | − | 0.541330i | −0.962674 | − | 0.270665i | \(-0.912756\pi\) | ||
0.962674 | − | 0.270665i | \(-0.0872436\pi\) | |||||||
\(602\) | −13.7699 | + | 32.2805i | −0.561219 | + | 1.31565i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.07361 | + | 3.59159i | 0.0843738 | + | 0.146140i | ||||
\(605\) | 18.3577 | − | 31.7964i | 0.746345 | − | 1.29271i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.6635 | + | 12.5074i | −0.879294 | + | 0.507660i | −0.870425 | − | 0.492300i | \(-0.836156\pi\) |
−0.00886811 | + | 0.999961i | \(0.502823\pi\) | |||||||
\(608\) | 4.16372 | 0.168861 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −56.4831 | −2.28693 | ||||||||
\(611\) | −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 | ||||||||
\(616\) | 0.431854 | + | 3.56952i | 0.0173999 | + | 0.143820i | ||||
\(617\) | − | 19.3370i | − | 0.778477i | −0.921137 | − | 0.389239i | \(-0.872738\pi\) | ||
0.921137 | − | 0.389239i | \(-0.127262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.57807 | + | 5.52990i | 0.384975 | + | 0.222265i | 0.679981 | − | 0.733230i | \(-0.261988\pi\) |
−0.295006 | + | 0.955496i | \(0.595321\pi\) | |||||||
\(620\) | −19.2501 | − | 11.1141i | −0.773105 | − | 0.446352i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.4987i | 0.501154i | ||||||||
\(623\) | −28.1083 | − | 11.9902i | −1.12614 | − | 0.480377i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.89411 | − | 15.4051i | −0.355764 | − | 0.616202i | ||||
\(626\) | 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 | ||||
\(635\) | −16.9594 | − | 29.3745i | −0.673012 | − | 1.16569i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.2415 | + | 10.8220i | 1.47556 | + | 0.428784i | ||||
\(638\) | − | 10.3370i | − | 0.409245i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 29.2047 | + | 16.8613i | 1.15442 | + | 0.666503i | ||||
\(641\) | −5.25886 | − | 3.03621i | −0.207713 | − | 0.119923i | 0.392535 | − | 0.919737i | \(-0.371598\pi\) |
−0.600248 | + | 0.799814i | \(0.704931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.2709i | 0.523352i | 0.965156 | + | 0.261676i | \(0.0842752\pi\) | ||||
−0.965156 | + | 0.261676i | \(0.915725\pi\) | |||||||
\(644\) | −3.81864 | − | 5.08626i | −0.150475 | − | 0.200427i | ||||
\(645\) | 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 | ||||
\(650\) | 96.5691 | 3.78775 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.1363 | 0.592783 | ||||||||
\(653\) | −32.2322 | + | 18.6093i | −1.26134 | + | 0.728237i | −0.973334 | − | 0.229391i | \(-0.926327\pi\) |
−0.288009 | + | 0.957628i | \(0.592993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.8627 | − | 22.2789i | 0.502588 | − | 0.870508i | ||||
\(656\) | 11.1091 | + | 19.2415i | 0.433738 | + | 0.751256i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.2650 | + | 1.48387i | −0.478140 | + | 0.0578472i | ||||
\(659\) | − | 46.2545i | − | 1.80182i | −0.434005 | − | 0.900911i | \(-0.642900\pi\) | ||
0.434005 | − | 0.900911i | \(-0.357100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.4219 | + | 6.59445i | 0.444262 | + | 0.256495i | 0.705404 | − | 0.708806i | \(-0.250766\pi\) |
−0.261142 | + | 0.965300i | \(0.584099\pi\) | |||||||
\(662\) | 25.9409 | + | 14.9770i | 1.00822 | + | 0.582097i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 11.8467i | − | 0.459742i | ||||||
\(665\) | −6.31415 | + | 0.763910i | −0.244852 | + | 0.0296232i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.25856 | − | 7.37604i | −0.164892 | − | 0.285601i | ||||
\(668\) | 2.52669 | − | 4.37636i | 0.0977607 | − | 0.169326i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 30.8447 | − | 17.8082i | 1.19164 | − | 0.687991i | ||||
\(671\) | −9.42637 | −0.363901 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.9265 | 1.57760 | 0.788800 | − | 0.614649i | \(-0.210703\pi\) | ||||
0.788800 | + | 0.614649i | \(0.210703\pi\) | |||||||
\(674\) | 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 | 0.850061 | − | 0.526684i | \(-0.176565\pi\) |
−0.881153 | + | 0.472832i | \(0.843232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.09334 | + | 1.45629i | 0.0419587 | + | 0.0558871i | ||||
\(680\) | 14.1043i | 0.540874i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.92168 | − | 4.57358i | −0.303337 | − | 0.175131i | ||||
\(683\) | −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 | ||||||
\(686\) | 26.2860 | + | 21.5187i | 1.00360 | + | 0.821586i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.5988 | + | 30.4820i | 0.670948 | + | 1.16212i | ||||
\(689\) | 0.200594 | − | 0.347439i | 0.00764201 | − | 0.0132364i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.5917 | − | 18.8168i | 1.23985 | − | 0.715826i | 0.270784 | − | 0.962640i | \(-0.412717\pi\) |
0.969063 | + | 0.246814i | \(0.0793836\pi\) | |||||||
\(692\) | 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 | ||||
\(698\) | −23.3951 | − | 40.5216i | −0.885519 | − | 1.53376i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 31.5539 | + | 13.4599i | 1.19262 | + | 0.508738i | ||||
\(701\) | − | 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 | ||||
\(704\) | −2.38709 | − | 1.37819i | −0.0899668 | − | 0.0519423i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 0.0381332i | − | 0.00143516i | ||||||
\(707\) | −2.09226 | − | 17.2937i | −0.0786874 | − | 0.650396i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.517010 | − | 0.895487i | −0.0194167 | − | 0.0336307i | 0.856154 | − | 0.516721i | \(-0.172848\pi\) |
−0.875570 | + | 0.483090i | \(0.839514\pi\) | |||||||
\(710\) | 16.6313 | − | 28.8062i | 0.624161 | − | 1.08108i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.6608 | + | 6.73234i | −0.437005 | + | 0.252305i | ||||
\(713\) | −7.53678 | −0.282255 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.5961 | 0.919841 | ||||||||
\(716\) | −21.8029 | + | 12.5879i | −0.814811 | + | 0.470431i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.2218 | − | 57.5419i | 1.23983 | − | 2.14744i | ||||
\(719\) | −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 | ||||
\(722\) | − | 34.1197i | − | 1.26981i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.6400 | + | 11.3392i | 0.729915 | + | 0.421417i | ||||
\(725\) | 39.7839 | + | 22.9693i | 1.47754 | + | 0.853057i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.8976i | 1.22011i | 0.792361 | + | 0.610053i | \(0.208852\pi\) | ||||
−0.792361 | + | 0.610053i | \(0.791148\pi\) | |||||||
\(728\) | 13.6653 | − | 10.2596i | 0.506469 | − | 0.380244i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.5494 | − | 33.8606i | −0.723556 | − | 1.25324i | ||||
\(731\) | −11.4874 | + | 19.8968i | −0.424879 | + | 0.735911i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.2443 | + | 9.95599i | −0.636932 | + | 0.367733i | −0.783432 | − | 0.621478i | \(-0.786533\pi\) |
0.146500 | + | 0.989211i | \(0.453199\pi\) | |||||||
\(734\) | 16.2862 | 0.601135 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.6212 | −0.428362 | ||||||||
\(737\) | 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 | ||||||||
\(742\) | 0.281027 | − | 0.210989i | 0.0103168 | − | 0.00774563i | ||||
\(743\) | − | 44.2491i | − | 1.62334i | −0.584115 | − | 0.811671i | \(-0.698558\pi\) | ||
0.584115 | − | 0.811671i | \(-0.301442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.8035 | − | 16.0524i | −1.01864 | − | 0.588113i | ||||
\(746\) | −20.3626 | − | 11.7564i | −0.745529 | − | 0.430431i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 5.05339i | − | 0.184770i | ||||||
\(749\) | 16.3680 | − | 38.3711i | 0.598073 | − | 1.40205i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.17230 | − | 2.03048i | −0.0427779 | − | 0.0740934i | 0.843844 | − | 0.536589i | \(-0.180287\pi\) |
−0.886622 | + | 0.462496i | \(0.846954\pi\) | |||||||
\(752\) | −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 | ||||
\(761\) | 0.441044 | + | 0.763910i | 0.0159878 | + | 0.0276917i | 0.873909 | − | 0.486090i | \(-0.161577\pi\) |
−0.857921 | + | 0.513782i | \(0.828244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.59607 | − | 37.9892i | −0.166389 | − | 1.37530i | ||||
\(764\) | − | 9.77730i | − | 0.353730i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.7140 | − | 25.2383i | −1.57945 | − | 0.911896i | ||||
\(767\) | 33.5155 | + | 19.3502i | 1.21017 | + | 0.698694i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 20.7049i | − | 0.746638i | −0.927703 | − | 0.373319i | \(-0.878220\pi\) | ||
0.927703 | − | 0.373319i | \(-0.121780\pi\) | |||||||
\(770\) | 19.8170 | + | 8.45333i | 0.714154 | + | 0.304637i | ||||
\(771\) | 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 | ||||
\(776\) | 0.802375 | 0.0288036 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.4633 | −1.19972 | ||||||||
\(779\) | −2.49551 | + | 1.44078i | −0.0894109 | + | 0.0516214i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.77557 | − | 4.80743i | 0.0993176 | − | 0.172023i | ||||
\(782\) | −5.13344 | − | 8.89138i | −0.183571 | − | 0.317955i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 33.0873 | − | 8.12497i | 1.18169 | − | 0.290178i | ||||
\(785\) | − | 14.5027i | − | 0.517625i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.7855 | − | 12.5779i | −0.776569 | − | 0.448352i | 0.0586440 | − | 0.998279i | \(-0.481322\pi\) |
−0.835213 | + | 0.549927i | \(0.814656\pi\) | |||||||
\(788\) | −2.28418 | − | 1.31877i | −0.0813705 | − | 0.0469793i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 119.439i | 4.24946i | ||||||||
\(791\) | 31.5486 | + | 42.0214i | 1.12174 | + | 1.49411i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.3996 | + | 38.7972i | 0.795432 | + | 1.37773i | ||||
\(794\) | −1.07229 | + | 1.85725i | −0.0380540 | + | 0.0659115i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.2334 | + | 5.90823i | −0.362712 | + | 0.209412i | ||||
\(797\) | 30.7168 | 1.08805 | 0.544023 | − | 0.839071i | \(-0.316901\pi\) | ||||
0.544023 | + | 0.839071i | \(0.316901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.08789 | −0.286129 | ||||||||
\(800\) | 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 | ||||||||
\(805\) | 17.6231 | − | 2.13211i | 0.621133 | − | 0.0751471i | ||||
\(806\) | 43.4722i | 1.53124i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.64710 | − | 3.83771i | −0.233844 | − | 0.135010i | ||||
\(809\) | −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 | \(0.943731\pi\) | |||||||
\(812\) | −17.3252 | + | 2.09607i | −0.607997 | + | 0.0735578i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.52420 | − | 7.83615i | −0.158573 | − | 0.274657i | ||||
\(815\) | −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 | \(-0.736438\pi\) |
0.299725 | + | 0.954026i | \(0.403105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.29804 | − | 3.98032i | 0.0801045 | − | 0.138745i | −0.823190 | − | 0.567766i | \(-0.807808\pi\) |
0.903295 | + | 0.429021i | \(0.141141\pi\) | |||||||
\(824\) | 5.44906 | + | 9.43805i | 0.189827 | + | 0.328790i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.3529 | + | 27.1092i | 0.708168 | + | 0.943248i | ||||
\(827\) | − | 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 | \(0.887337\pi\) | |||||||
\(830\) | −61.4755 | − | 35.4929i | −2.13385 | − | 1.23198i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.0997i | 0.454152i | ||||||||
\(833\) | 15.3917 | + | 16.0521i | 0.533289 | + | 0.556173i | ||||
\(834\) | 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 | ||||
\(839\) | −21.3569 | −0.737323 | −0.368662 | − | 0.929564i | \(-0.620184\pi\) | ||||
−0.368662 | + | 0.929564i | \(0.620184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.63009 | 0.194141 | ||||||||
\(842\) | −0.148277 | + | 0.0856080i | −0.00510997 | + | 0.00295025i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.47207 | − | 14.6741i | 0.291621 | − | 0.505102i | ||||
\(845\) | −33.6932 | − | 58.3584i | −1.15908 | − | 2.00759i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.4623 | − | 10.0083i | −0.806173 | − | 0.343889i | ||||
\(848\) | − | 0.352445i | − | 0.0121030i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 47.9572 | + | 27.6881i | 1.64492 | + | 0.949693i | ||||
\(851\) | −6.45657 | − | 3.72770i | −0.221328 | − | 0.127784i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.5031i | 1.69495i | 0.530833 | + | 0.847476i | \(0.321879\pi\) | ||||
−0.530833 | + | 0.847476i | \(0.678121\pi\) | |||||||
\(854\) | 4.71319 | + | 38.9572i | 0.161282 | + | 1.33309i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.19041 | − | 15.9183i | −0.314122 | − | 0.544075i | ||||
\(857\) | 7.00810 | − | 12.1384i | 0.239392 | − | 0.414639i | −0.721148 | − | 0.692781i | \(-0.756385\pi\) |
0.960540 | + | 0.278142i | \(0.0897185\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.05213 | − | 0.607448i | 0.0358983 | − | 0.0207259i | −0.481943 | − | 0.876202i | \(-0.660069\pi\) |
0.517842 | + | 0.855476i | \(0.326736\pi\) | |||||||
\(860\) | 37.5766 | 1.28135 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 60.8441 | 2.07236 | ||||||||
\(863\) | 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 | ||||||||
\(868\) | −6.05922 | + | 14.2045i | −0.205663 | + | 0.482132i | ||||
\(869\) | 19.9330i | 0.676182i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.4642 | − | 14.1244i | −0.828939 | − | 0.478588i | ||||
\(872\) | −14.6017 | − | 8.43032i | −0.494477 | − | 0.285487i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.03994i | − | 0.0690020i | ||||||
\(875\) | −36.2809 | + | 27.2388i | −1.22652 | + | 0.920840i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.59607 | + | 9.69268i | 0.188966 | + | 0.327299i | 0.944906 | − | 0.327342i | \(-0.106153\pi\) |
−0.755940 | + | 0.654641i | \(0.772820\pi\) | |||||||
\(878\) | 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 | ||||
\(887\) | 19.0412 | + | 32.9804i | 0.639342 | + | 1.10737i | 0.985577 | + | 0.169225i | \(0.0541264\pi\) |
−0.346236 | + | 0.938148i | \(0.612540\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.8448 | + | 14.1482i | −0.632035 | + | 0.474517i | ||||
\(890\) | 80.6807i | 2.70442i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.3764 | − | 12.9190i | −0.749216 | − | 0.432560i | ||||
\(893\) | −1.39170 | − | 0.803496i | −0.0465713 | − | 0.0268880i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 70.2669i | − | 2.34876i | ||||||
\(896\) | 9.19253 | − | 21.5499i | 0.307101 | − | 0.719930i | ||||
\(897\) | 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 | ||||
\(902\) | 9.76106 | 0.325008 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23.1527 | 0.770046 | ||||||||
\(905\) | −54.8163 | + | 31.6482i | −1.82216 | + | 1.05202i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.773833 | + | 1.34032i | −0.0256947 | + | 0.0445046i | −0.878587 | − | 0.477583i | \(-0.841513\pi\) |
0.852892 | + | 0.522087i | \(0.174846\pi\) | |||||||
\(908\) | −3.90421 | − | 6.76228i | −0.129566 | − | 0.224414i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.2980 | − | 101.650i | −0.407676 | − | 3.36967i | ||||
\(911\) | 38.9704i | 1.29115i | 0.763699 | + | 0.645573i | \(0.223381\pi\) | ||||
−0.763699 | + | 0.645573i | \(0.776619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.2596 | − | 5.92336i | −0.339542 | − | 0.196034i | ||||
\(914\) | 33.0762 | + | 19.0965i | 1.09406 | + | 0.631657i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 15.1967i | − | 0.502114i | ||||||
\(917\) | −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 | \(0.895360\pi\) | |||||||
\(920\) | 3.91081 | − | 6.77373i | 0.128936 | − | 0.223323i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.2677 | − | 7.66013i | 0.436950 | − | 0.252273i | ||||
\(923\) | −26.3819 | −0.868372 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.2120 | 1.32216 | ||||||||
\(926\) | −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 | 0.955982 | + | 0.293425i | \(0.0947952\pi\) |
−0.223877 | + | 0.974617i | \(0.571871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.05376 | + | 4.29121i | 0.0345355 | + | 0.140639i | ||||
\(932\) | 14.1043i | 0.462000i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −46.3171 | − | 26.7412i | −1.51554 | − | 0.874999i | ||||
\(935\) | 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 | \(-0.183282\pi\) | |||||||
\(938\) | −14.8564 | − | 19.7880i | −0.485078 | − | 0.646102i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.61408 | + | 11.4559i | 0.215727 | + | 0.373651i | ||||
\(941\) | 16.9992 | − | 29.4435i | 0.554159 | − | 0.959831i | −0.443810 | − | 0.896121i | \(-0.646373\pi\) |
0.997968 | − | 0.0637100i | \(-0.0202933\pi\) | |||||||
\(942\) | 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 | \(-0.396829\pi\) |
0.980170 | + | 0.198157i | \(0.0634956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.5055 | + | 26.8562i | −0.503329 | + | 0.871791i | ||||
\(950\) | 5.50138 | + | 9.52867i | 0.178488 | + | 0.309151i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.72790 | − | 1.17692i | 0.315283 | − | 0.0381442i | ||||
\(953\) | − | 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 | ||||
\(956\) | 19.5924 | + | 11.3117i | 0.633664 | + | 0.365846i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 74.3301i | − | 2.40150i | ||||||
\(959\) | −44.2861 | + | 5.35790i | −1.43007 | + | 0.173016i | ||||
\(960\) | 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 | ||||
\(965\) | 12.1017 | 0.389567 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.4148 | −0.431392 | −0.215696 | − | 0.976461i | \(-0.569202\pi\) | ||||
−0.215696 | + | 0.976461i | \(0.569202\pi\) | |||||||
\(968\) | −9.73332 | + | 5.61954i | −0.312841 | + | 0.180619i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.40393 | − | 4.16372i | 0.0771854 | − | 0.133689i | ||||
\(971\) | 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 | ||||
\(974\) | − | 22.7782i | − | 0.729861i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 34.0835 | + | 19.6781i | 1.09099 | + | 0.629882i | ||||
\(977\) | 19.6181 | + | 11.3265i | 0.627638 | + | 0.362367i | 0.779837 | − | 0.625983i | \(-0.215302\pi\) |
−0.152199 | + | 0.988350i | \(0.548635\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4647i | 0.430333i | ||||||||
\(980\) | 10.1498 | − | 34.9282i | 0.324223 | − | 1.11574i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.65976 | − | 9.80298i | −0.180610 | − | 0.312826i | ||||
\(983\) | 19.6704 | − | 34.0701i | 0.627388 | − | 1.08667i | −0.360685 | − | 0.932688i | \(-0.617457\pi\) |
0.988074 | − | 0.153981i | \(-0.0492095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.37526 | − | 3.68076i | 0.203133 | − | 0.117279i | ||||
\(986\) | −28.1710 | −0.897149 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.77184 | −0.151813 | ||||||||
\(989\) | 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 | ||||||||
\(994\) | −21.2558 | − | 9.06711i | −0.674194 | − | 0.287591i | ||||
\(995\) | − | 32.9804i | − | 1.04555i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.2486 | − | 15.7320i | −0.862973 | − | 0.498238i | 0.00203378 | − | 0.999998i | \(-0.499353\pi\) |
−0.865007 | + | 0.501760i | \(0.832686\pi\) | |||||||
\(998\) | −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 | 189.2.p.d.80.2 | yes | 12 | |
3.2 | odd | 2 | inner | 189.2.p.d.80.5 | yes | 12 | |
7.3 | odd | 6 | 1323.2.c.d.1322.4 | 12 | |||
7.4 | even | 3 | 1323.2.c.d.1322.3 | 12 | |||
7.5 | odd | 6 | inner | 189.2.p.d.26.5 | yes | 12 | |
9.2 | odd | 6 | 567.2.s.f.458.2 | 12 | |||
9.4 | even | 3 | 567.2.i.f.269.2 | 12 | |||
9.5 | odd | 6 | 567.2.i.f.269.5 | 12 | |||
9.7 | even | 3 | 567.2.s.f.458.5 | 12 | |||
21.5 | even | 6 | inner | 189.2.p.d.26.2 | ✓ | 12 | |
21.11 | odd | 6 | 1323.2.c.d.1322.10 | 12 | |||
21.17 | even | 6 | 1323.2.c.d.1322.9 | 12 | |||
63.5 | even | 6 | 567.2.s.f.26.5 | 12 | |||
63.40 | odd | 6 | 567.2.s.f.26.2 | 12 | |||
63.47 | even | 6 | 567.2.i.f.215.5 | 12 | |||
63.61 | odd | 6 | 567.2.i.f.215.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.2 | ✓ | 12 | 21.5 | even | 6 | inner | |
189.2.p.d.26.5 | yes | 12 | 7.5 | odd | 6 | inner | |
189.2.p.d.80.2 | yes | 12 | 1.1 | even | 1 | trivial | |
189.2.p.d.80.5 | yes | 12 | 3.2 | odd | 2 | inner | |
567.2.i.f.215.2 | 12 | 63.61 | odd | 6 | |||
567.2.i.f.215.5 | 12 | 63.47 | even | 6 | |||
567.2.i.f.269.2 | 12 | 9.4 | even | 3 | |||
567.2.i.f.269.5 | 12 | 9.5 | odd | 6 | |||
567.2.s.f.26.2 | 12 | 63.40 | odd | 6 | |||
567.2.s.f.26.5 | 12 | 63.5 | even | 6 | |||
567.2.s.f.458.2 | 12 | 9.2 | odd | 6 | |||
567.2.s.f.458.5 | 12 | 9.7 | even | 3 | |||
1323.2.c.d.1322.3 | 12 | 7.4 | even | 3 | |||
1323.2.c.d.1322.4 | 12 | 7.3 | odd | 6 | |||
1323.2.c.d.1322.9 | 12 | 21.17 | even | 6 | |||
1323.2.c.d.1322.10 | 12 | 21.11 | odd | 6 |