Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(215,567)]
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([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.i (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: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 269.2 | ||
Root | \(-1.90412 + 1.09935i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.269 |
Dual form | 567.2.i.f.215.5 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.83424i | − | 1.29701i | −0.761212 | − | 0.648503i | \(-0.775395\pi\) | ||
0.761212 | − | 0.648503i | \(-0.224605\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.36445 | −0.682224 | ||||||||
\(5\) | 1.90412 | − | 3.29804i | 0.851549 | − | 1.47493i | −0.0282601 | − | 0.999601i | \(-0.508997\pi\) |
0.879810 | − | 0.475326i | \(-0.157670\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.317776 | + | 2.62660i | 0.120108 | + | 0.992761i | ||||
\(8\) | − | 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 | \(-0.610433\pi\) |
0.644417 | + | 0.764674i | \(0.277100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.79804 | − | 2.77015i | 1.33074 | − | 0.768301i | 0.345324 | − | 0.938484i | \(-0.387769\pi\) |
0.985412 | + | 0.170183i | \(0.0544359\pi\) | |||||||
\(14\) | 4.81782 | − | 0.582878i | 1.28762 | − | 0.155781i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.86718 | −1.21679 | ||||||||
\(17\) | −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 | ||||
\(23\) | −1.52579 | − | 0.880915i | −0.318149 | − | 0.183684i | 0.332418 | − | 0.943132i | \(-0.392135\pi\) |
−0.650567 | + | 0.759449i | \(0.725469\pi\) | |||||||
\(24\) | 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 | ||||
\(29\) | 4.18658 | + | 2.41712i | 0.777428 | + | 0.448848i | 0.835518 | − | 0.549463i | \(-0.185168\pi\) |
−0.0580901 | + | 0.998311i | \(0.518501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.27781i | 0.768317i | 0.923267 | + | 0.384159i | \(0.125508\pi\) | ||||
−0.923267 | + | 0.384159i | \(0.874492\pi\) | |||||||
\(32\) | 6.59607i | 1.16603i | ||||||||
\(33\) | 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 | \(0.946417\pi\) | |||||||
\(38\) | 0.578926 | + | 1.00273i | 0.0939142 | + | 0.162664i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.84471 | − | 2.21974i | −0.607902 | − | 0.350972i | ||||
\(41\) | −2.28245 | − | 3.95333i | −0.356460 | − | 0.617406i | 0.630907 | − | 0.775858i | \(-0.282683\pi\) |
−0.987367 | + | 0.158452i | \(0.949350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.61581 | + | 6.26277i | −0.551406 | + | 0.955064i | 0.446767 | + | 0.894650i | \(0.352575\pi\) |
−0.998173 | + | 0.0604134i | \(0.980758\pi\) | |||||||
\(44\) | −1.37751 | + | 0.795307i | −0.207668 | + | 0.119897i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.61581 | + | 2.79867i | −0.238239 | + | 0.412641i | ||||
\(47\) | −2.54576 | −0.371337 | −0.185669 | − | 0.982612i | \(-0.559445\pi\) | ||||
−0.185669 | + | 0.982612i | \(0.559445\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.79804 | + | 1.66934i | −0.971148 | + | 0.238477i | ||||
\(50\) | −15.0951 | + | 8.71516i | −2.13477 | + | 1.23251i | ||||
\(51\) | 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 | ||||||
\(56\) | 3.06197 | − | 0.370450i | 0.409174 | − | 0.0495034i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.43359 | − | 7.67920i | 0.582159 | − | 1.00833i | ||||
\(59\) | −6.98525 | −0.909402 | −0.454701 | − | 0.890644i | \(-0.650254\pi\) | ||||
−0.454701 | + | 0.890644i | \(0.650254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.08606i | 1.03531i | 0.855588 | + | 0.517657i | \(0.173196\pi\) | ||||
−0.855588 | + | 0.517657i | \(0.826804\pi\) | |||||||
\(62\) | 7.84655 | 0.996512 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.36445 | 0.295556 | ||||||||
\(65\) | − | 21.0988i | − | 2.61698i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.09880 | 0.622918 | 0.311459 | − | 0.950260i | \(-0.399182\pi\) | ||||
0.311459 | + | 0.950260i | \(0.399182\pi\) | |||||||
\(68\) | 2.16743 | − | 3.75409i | 0.262839 | − | 0.455251i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.25136 | − | 16.9992i | 0.866704 | − | 2.03180i | ||||
\(71\) | 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 | ||||||||
\(76\) | 0.745906 | − | 0.430649i | 0.0855612 | − | 0.0493988i | ||||
\(77\) | 1.85181 | + | 2.46652i | 0.211033 | + | 0.281086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.0988 | 1.92377 | 0.961883 | − | 0.273462i | \(-0.0881687\pi\) | ||||
0.961883 | + | 0.273462i | \(0.0881687\pi\) | |||||||
\(80\) | −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 | 0.439960 | + | 0.898017i | \(0.354993\pi\) |
−0.997686 | + | 0.0679922i | \(0.978341\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.04940 | + | 10.4779i | 0.656150 | + | 1.13648i | ||||
\(86\) | 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 | ||||
\(92\) | 2.08186 | + | 1.20196i | 0.217049 | + | 0.125313i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.66954i | 0.481627i | ||||||||
\(95\) | 2.40393i | 0.246638i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.596074 | − | 0.344143i | −0.0605221 | − | 0.0349425i | 0.469434 | − | 0.882968i | \(-0.344458\pi\) |
−0.529956 | + | 0.848025i | \(0.677791\pi\) | |||||||
\(98\) | 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 | 0.982029 | − | 0.188730i | \(-0.0604372\pi\) |
−0.654460 | + | 0.756097i | \(0.727104\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.09607 | + | 4.67427i | 0.797730 | + | 0.460570i | 0.842677 | − | 0.538420i | \(-0.180979\pi\) |
−0.0449469 | + | 0.998989i | \(0.514312\pi\) | |||||||
\(104\) | −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 | \(-0.0768965\pi\) | |||||||
\(110\) | −8.14310 | −0.776414 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.54667 | − | 12.7841i | −0.146147 | − | 1.20799i | ||||
\(113\) | 17.1998 | − | 9.93032i | 1.61802 | − | 0.934166i | 0.630591 | − | 0.776115i | \(-0.282812\pi\) |
0.987431 | − | 0.158051i | \(-0.0505209\pi\) | |||||||
\(114\) | 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 | ||||||||
\(119\) | −7.73152 | − | 3.29804i | −0.708747 | − | 0.302331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.82051 | + | 8.34936i | −0.438228 | + | 0.759033i | ||||
\(122\) | 14.8318 | 1.34281 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.83685i | − | 0.524165i | ||||||
\(125\) | −17.1475 | −1.53372 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.90666 | −0.790338 | −0.395169 | − | 0.918608i | \(-0.629314\pi\) | ||||
−0.395169 | + | 0.918608i | \(0.629314\pi\) | |||||||
\(128\) | 8.85517i | 0.782694i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −38.7003 | −3.39424 | ||||||||
\(131\) | −3.37760 | + | 5.85017i | −0.295102 | + | 0.511132i | −0.975009 | − | 0.222167i | \(-0.928687\pi\) |
0.679907 | + | 0.733299i | \(0.262020\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00273 | − | 1.33559i | −0.0869477 | − | 0.115810i | ||||
\(134\) | − | 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 | \(-0.410693\pi\) |
0.970612 | + | 0.240649i | \(0.0773602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.704693 | − | 0.406855i | 0.0597713 | − | 0.0345089i | −0.469817 | − | 0.882764i | \(-0.655680\pi\) |
0.529588 | + | 0.848255i | \(0.322347\pi\) | |||||||
\(140\) | −12.6453 | − | 5.39411i | −1.06872 | − | 0.455886i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.73436 | 0.732971 | ||||||||
\(143\) | 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 | ||||
\(149\) | 7.30087 | + | 4.21516i | 0.598110 | + | 0.345319i | 0.768298 | − | 0.640092i | \(-0.221104\pi\) |
−0.170187 | + | 0.985412i | \(0.554437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51974 | − | 2.63227i | −0.123675 | − | 0.214211i | 0.797539 | − | 0.603267i | \(-0.206135\pi\) |
−0.921214 | + | 0.389056i | \(0.872801\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | 3.80824i | 0.303931i | 0.988386 | + | 0.151966i | \(0.0485603\pi\) | ||||
−0.988386 | + | 0.151966i | \(0.951440\pi\) | |||||||
\(158\) | − | 31.3634i | − | 2.49514i | ||||||
\(159\) | 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 | \(0.690276\pi\) | |||||||
\(164\) | 3.11429 | + | 5.39411i | 0.243185 | + | 0.421209i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.1427 | + | 9.32002i | 1.25292 | + | 0.723374i | ||||
\(167\) | −1.85181 | − | 3.20742i | −0.143297 | − | 0.248198i | 0.785439 | − | 0.618939i | \(-0.212437\pi\) |
−0.928736 | + | 0.370741i | \(0.879104\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | −9.63564 | −0.732584 | −0.366292 | − | 0.930500i | \(-0.619373\pi\) | ||||
−0.366292 | + | 0.930500i | \(0.619373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.1060 | − | 15.0951i | 1.51987 | − | 1.14108i | ||||
\(176\) | −4.91378 | + | 2.83697i | −0.370390 | + | 0.213845i | ||||
\(177\) | 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 | \(0.788060\pi\) | |||||||
\(182\) | 21.5014 | − | 16.1427i | 1.59379 | − | 1.19658i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.02693 | + | 1.77870i | −0.0757065 | + | 0.131128i | ||||
\(185\) | −16.1151 | −1.18480 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.70361i | 0.270835i | ||||||||
\(188\) | 3.47356 | 0.253335 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.40939 | 0.319890 | ||||||||
\(191\) | 7.16576i | 0.518496i | 0.965811 | + | 0.259248i | \(0.0834747\pi\) | ||||
−0.965811 | + | 0.259248i | \(0.916525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.17776 | −0.228740 | −0.114370 | − | 0.993438i | \(-0.536485\pi\) | ||||
−0.114370 | + | 0.993438i | \(0.536485\pi\) | |||||||
\(194\) | −0.631243 | + | 1.09334i | −0.0453206 | + | 0.0784975i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.27557 | − | 2.27773i | 0.662541 | − | 0.162695i | ||||
\(197\) | − | 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 | ||||||||
\(202\) | 10.4588 | − | 6.03838i | 0.735878 | − | 0.424859i | ||||
\(203\) | −5.01841 | + | 11.7646i | −0.352224 | + | 0.825710i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.3843 | −1.21417 | ||||||||
\(206\) | 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 | 0.569190 | − | 0.822206i | \(-0.307257\pi\) |
−0.996646 | + | 0.0818303i | \(0.973923\pi\) | |||||||
\(212\) | 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 | ||||
\(218\) | −22.9749 | − | 13.2646i | −1.55606 | − | 0.898389i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.05745i | 0.408393i | ||||||||
\(221\) | 17.6015i | 1.18401i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.3996 | + | 9.46830i | 1.09820 | + | 0.634044i | 0.935747 | − | 0.352673i | \(-0.114727\pi\) |
0.162450 | + | 0.986717i | \(0.448060\pi\) | |||||||
\(224\) | −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 | 0.945222 | − | 0.326428i | \(-0.105845\pi\) |
−0.755306 | + | 0.655373i | \(0.772512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.64548 | − | 5.56882i | −0.637391 | − | 0.367998i | 0.146218 | − | 0.989252i | \(-0.453290\pi\) |
−0.783609 | + | 0.621255i | \(0.786623\pi\) | |||||||
\(230\) | 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 | ||||
\(236\) | 9.53101 | 0.620416 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.04940 | + | 14.1815i | −0.392124 | + | 0.919249i | ||||
\(239\) | 14.3592 | − | 8.29030i | 0.928821 | − | 0.536255i | 0.0423824 | − | 0.999101i | \(-0.486505\pi\) |
0.886438 | + | 0.462846i | \(0.153172\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.6921 | + | 11.9466i | −1.33290 | + | 0.769549i | −0.985743 | − | 0.168258i | \(-0.946186\pi\) |
−0.347155 | + | 0.937808i | \(0.612852\pi\) | |||||||
\(242\) | 15.3148 | + | 8.84198i | 0.984470 | + | 0.568384i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.0330i | − | 0.706316i | ||||||
\(245\) | −7.43875 | + | 25.5988i | −0.475244 | + | 1.63545i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.74864 | + | 3.02873i | −0.111263 | + | 0.192713i | ||||
\(248\) | 4.98689 | 0.316668 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 31.4527i | 1.98924i | ||||||||
\(251\) | −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 | ||||||||
\(254\) | 16.3370i | 1.02507i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9714 | 1.31072 | ||||||||
\(257\) | −11.6025 | + | 20.0961i | −0.723742 | + | 1.25356i | 0.235747 | + | 0.971814i | \(0.424246\pi\) |
−0.959490 | + | 0.281744i | \(0.909087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.95333 | − | 6.72194i | 0.556333 | − | 0.417681i | ||||
\(260\) | 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 | \(-0.762544\pi\) |
0.220563 | + | 0.975373i | \(0.429211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.238820 | + | 0.137883i | −0.0146706 | + | 0.00847006i | ||||
\(266\) | −2.44980 | + | 1.83925i | −0.150207 | + | 0.112772i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.95705 | −0.424970 | ||||||||
\(269\) | −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 | ||||
\(275\) | −9.59372 | − | 5.53894i | −0.578523 | − | 0.334010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.15802 | − | 7.20190i | −0.249831 | − | 0.432720i | 0.713648 | − | 0.700505i | \(-0.247042\pi\) |
−0.963479 | + | 0.267784i | \(0.913708\pi\) | |||||||
\(278\) | −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 | \(-0.570889\pi\) |
−0.955072 | + | 0.296375i | \(0.904222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0334i | 1.01253i | 0.862378 | + | 0.506266i | \(0.168974\pi\) | ||||
−0.862378 | + | 0.506266i | \(0.831026\pi\) | |||||||
\(284\) | − | 6.49727i | − | 0.385542i | ||||||
\(285\) | 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 | ||||
\(290\) | −16.8842 | − | 29.2443i | −0.991474 | − | 1.71728i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.61408 | − | 3.81864i | −0.387060 | − | 0.223469i | ||||
\(293\) | 10.7079 | + | 18.5467i | 0.625564 | + | 1.08351i | 0.988432 | + | 0.151668i | \(0.0484643\pi\) |
−0.362868 | + | 0.931841i | \(0.618202\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | −9.76106 | −0.564497 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.5988 | − | 7.50713i | −1.01438 | − | 0.432704i | ||||
\(302\) | −4.82821 | + | 2.78757i | −0.277833 | + | 0.160407i | ||||
\(303\) | 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 | \(-0.187336\pi\) | |||||||
\(308\) | −2.52669 | − | 3.36544i | −0.143972 | − | 0.191764i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.9408 | − | 25.8782i | 0.848579 | − | 1.46978i | ||||
\(311\) | −6.81412 | −0.386393 | −0.193197 | − | 0.981160i | \(-0.561885\pi\) | ||||
−0.193197 | + | 0.981160i | \(0.561885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.6417i | − | 0.940643i | −0.882495 | − | 0.470322i | \(-0.844138\pi\) | ||
0.882495 | − | 0.470322i | \(-0.155862\pi\) | |||||||
\(314\) | 6.98525 | 0.394200 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.3304 | −1.31244 | ||||||||
\(317\) | 5.07787i | 0.285202i | 0.989780 | + | 0.142601i | \(0.0455465\pi\) | ||||
−0.989780 | + | 0.142601i | \(0.954453\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.63555 | 0.315530 | ||||||||
\(320\) | 4.50220 | − | 7.79804i | 0.251681 | − | 0.435924i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.86445 | − | 3.35474i | −0.438269 | − | 0.186952i | ||||
\(323\) | − | 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 | ||||||||
\(328\) | −4.60862 | + | 2.66079i | −0.254468 | + | 0.146917i | ||||
\(329\) | −0.808981 | − | 6.68669i | −0.0446006 | − | 0.368649i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.3304 | 0.897602 | 0.448801 | − | 0.893632i | \(-0.351851\pi\) | ||||
0.448801 | + | 0.893632i | \(0.351851\pi\) | |||||||
\(332\) | 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 | 0.914847 | − | 0.403800i | \(-0.132311\pi\) |
−0.807124 | + | 0.590381i | \(0.798977\pi\) | |||||||
\(338\) | −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 | ||||
\(344\) | 7.30087 | + | 4.21516i | 0.393636 | + | 0.227266i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.6741i | 0.950166i | ||||||||
\(347\) | − | 7.33697i | − | 0.393869i | −0.980417 | − | 0.196935i | \(-0.936901\pi\) | ||
0.980417 | − | 0.196935i | \(-0.0630987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0917 | − | 12.7547i | −1.18254 | − | 0.682741i | −0.225941 | − | 0.974141i | \(-0.572546\pi\) |
−0.956601 | + | 0.291400i | \(0.905879\pi\) | |||||||
\(350\) | −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 | 0.865749 | − | 0.500479i | \(-0.166843\pi\) |
−0.866302 | + | 0.499521i | \(0.833509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.7047 | + | 9.06711i | 0.833519 | + | 0.481232i | ||||
\(356\) | 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 | ||||
\(362\) | 30.4867 | 1.60235 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0082 | − | 15.9944i | −0.629400 | − | 0.838333i | ||||
\(365\) | 18.4602 | − | 10.6580i | 0.966253 | − | 0.557866i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.68942 | − | 4.43949i | 0.401384 | − | 0.231739i | −0.285697 | − | 0.958320i | \(-0.592225\pi\) |
0.687081 | + | 0.726581i | \(0.258892\pi\) | |||||||
\(368\) | 7.42629 | + | 4.28757i | 0.387122 | + | 0.223505i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.5590i | 1.53670i | ||||||||
\(371\) | 0.0751713 | − | 0.176223i | 0.00390270 | − | 0.00914902i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.40939 | − | 11.1014i | 0.331865 | − | 0.574808i | −0.651012 | − | 0.759067i | \(-0.725655\pi\) |
0.982878 | + | 0.184260i | \(0.0589887\pi\) | |||||||
\(374\) | 6.79333 | 0.351274 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.96774i | 0.153049i | ||||||||
\(377\) | 26.7831 | 1.37940 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.13828 | 0.161203 | 0.0806013 | − | 0.996746i | \(-0.474316\pi\) | ||||
0.0806013 | + | 0.996746i | \(0.474316\pi\) | |||||||
\(380\) | − | 3.28003i | − | 0.168262i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.1437 | 0.672492 | ||||||||
\(383\) | 13.7595 | − | 23.8322i | 0.703078 | − | 1.21777i | −0.264303 | − | 0.964440i | \(-0.585142\pi\) |
0.967381 | − | 0.253327i | \(-0.0815248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.6608 | − | 1.41076i | 0.594287 | − | 0.0718991i | ||||
\(386\) | 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 | \(-0.819712\pi\) |
0.0427793 | + | 0.999085i | \(0.486379\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.84744 | − | 2.79867i | 0.245146 | − | 0.141535i | ||||
\(392\) | 1.94604 | + | 7.92486i | 0.0982901 | + | 0.400266i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.54568 | −0.178629 | ||||||||
\(395\) | 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 | ||||
\(401\) | −12.0892 | − | 6.97972i | −0.603707 | − | 0.348551i | 0.166791 | − | 0.985992i | \(-0.446659\pi\) |
−0.770499 | + | 0.637442i | \(0.779993\pi\) | |||||||
\(402\) | 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 | ||||
\(407\) | −4.27214 | − | 2.46652i | −0.211762 | − | 0.122261i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.3721i | − | 1.00733i | −0.863898 | − | 0.503667i | \(-0.831984\pi\) | ||
0.863898 | − | 0.503667i | \(-0.168016\pi\) | |||||||
\(410\) | 31.8870i | 1.57479i | ||||||||
\(411\) | 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 | ||||
\(416\) | 18.2721 | + | 31.6482i | 0.895863 | + | 1.55168i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.16894 | + | 0.674887i | 0.0571747 | + | 0.0330098i | ||||
\(419\) | −12.7603 | − | 22.1015i | −0.623383 | − | 1.07973i | −0.988851 | − | 0.148907i | \(-0.952425\pi\) |
0.365469 | − | 0.930824i | \(-0.380909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0466721 | + | 0.0808384i | −0.00227466 | + | 0.00393982i | −0.867160 | − | 0.498029i | \(-0.834057\pi\) |
0.864886 | + | 0.501969i | \(0.167391\pi\) | |||||||
\(422\) | −19.7265 | + | 11.3891i | −0.960271 | + | 0.554413i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.0422078 | + | 0.0731060i | −0.00204979 | + | 0.00355034i | ||||
\(425\) | 30.1902 | 1.46444 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.2388 | + | 2.56955i | −1.02782 | + | 0.124349i | ||||
\(428\) | −18.6314 | + | 10.7568i | −0.900581 | + | 0.519951i | ||||
\(429\) | 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 | \(-0.141964\pi\) | |||||||
\(434\) | 2.49344 | + | 20.6097i | 0.119689 | + | 0.989298i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.86718 | + | 17.0905i | −0.472552 | + | 0.818484i | ||||
\(437\) | 1.11214 | 0.0532010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10.0368i | − | 0.479032i | −0.970892 | − | 0.239516i | \(-0.923011\pi\) | ||
0.970892 | − | 0.239516i | \(-0.0769887\pi\) | |||||||
\(440\) | −5.17536 | −0.246726 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 32.2855 | 1.53566 | ||||||||
\(443\) | 26.3579i | 1.25230i | 0.779702 | + | 0.626151i | \(0.215371\pi\) | ||||
−0.779702 | + | 0.626151i | \(0.784629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43.9858 | −2.08513 | ||||||||
\(446\) | 17.3672 | − | 30.0808i | 0.822359 | − | 1.42437i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.751365 | + | 6.21046i | 0.0354986 | + | 0.293416i | ||||
\(449\) | − | 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 | ||||||||
\(454\) | 9.09061 | − | 5.24847i | 0.426644 | − | 0.246323i | ||||
\(455\) | 55.4181 | − | 6.70469i | 2.59804 | − | 0.314321i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8222 | 0.974023 | 0.487012 | − | 0.873395i | \(-0.338087\pi\) | ||||
0.487012 | + | 0.873395i | \(0.338087\pi\) | |||||||
\(458\) | −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 | −0.752234 | − | 0.658896i | \(-0.771024\pi\) |
0.946738 | + | 0.322005i | \(0.104357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.90666 | − | 10.2306i | −0.274506 | − | 0.475458i | 0.695505 | − | 0.718522i | \(-0.255181\pi\) |
−0.970010 | + | 0.243064i | \(0.921848\pi\) | |||||||
\(464\) | −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 | ||||
\(470\) | 15.4003 | + | 8.89138i | 0.710364 | + | 0.410129i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.14310i | 0.374817i | ||||||||
\(473\) | 8.43032i | 0.387626i | ||||||||
\(474\) | 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 | ||||
\(479\) | −20.2618 | − | 35.0944i | −0.925785 | − | 1.60351i | −0.790294 | − | 0.612728i | \(-0.790072\pi\) |
−0.135491 | − | 0.990779i | \(-0.543261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.3035 | − | 11.7222i | −0.925760 | − | 0.534488i | ||||
\(482\) | 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 | \(0.257453\pi\) | |||||||
\(488\) | 9.42637 | 0.426712 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 46.9544 | + | 13.6445i | 2.12118 | + | 0.616395i | ||||
\(491\) | 5.34443 | − | 3.08561i | 0.241191 | − | 0.139252i | −0.374533 | − | 0.927214i | \(-0.622197\pi\) |
0.615724 | + | 0.787962i | \(0.288864\pi\) | |||||||
\(492\) | 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 | ||||||
\(497\) | −12.5074 | + | 1.51320i | −0.561034 | + | 0.0678761i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.48026 | − | 2.56389i | 0.0662656 | − | 0.114775i | −0.830989 | − | 0.556289i | \(-0.812225\pi\) |
0.897255 | + | 0.441513i | \(0.145558\pi\) | |||||||
\(500\) | 23.3969 | 1.04634 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 36.5442i | 1.63105i | ||||||||
\(503\) | −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 | ||||||||
\(506\) | 3.76729i | 0.167476i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.1527 | 0.539188 | ||||||||
\(509\) | −14.4742 | + | 25.0701i | −0.641560 | + | 1.11121i | 0.343525 | + | 0.939144i | \(0.388379\pi\) |
−0.985085 | + | 0.172071i | \(0.944954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.81058 | + | 13.6216i | −0.257045 | + | 0.602585i | ||||
\(512\) | − | 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 | ||||||||
\(517\) | −2.57014 | + | 1.48387i | −0.113034 | + | 0.0652605i | ||||
\(518\) | −12.3297 | − | 16.4226i | −0.541735 | − | 0.721567i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.5961 | −1.07861 | ||||||||
\(521\) | −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 | ||||
\(527\) | −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 | ||||
\(533\) | −21.9026 | − | 12.6455i | −0.948707 | − | 0.547736i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 60.0457i | − | 2.59600i | ||||||
\(536\) | − | 5.94396i | − | 0.256740i | ||||||
\(537\) | 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 | \(0.836811\pi\) | |||||||
\(542\) | −18.0524 | − | 31.2677i | −0.775419 | − | 1.34306i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.1482 | − | 10.4779i | −0.778098 | − | 0.449235i | ||||
\(545\) | −27.5398 | − | 47.7003i | −1.17968 | − | 2.04326i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.1482 | − | 34.8977i | 0.861475 | − | 1.49212i | −0.00903012 | − | 0.999959i | \(-0.502874\pi\) |
0.870505 | − | 0.492159i | \(-0.163792\pi\) | |||||||
\(548\) | −19.9233 | + | 11.5027i | −0.851082 | + | 0.491372i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.1598 | + | 17.5972i | −0.433213 | + | 0.750348i | ||||
\(551\) | −3.05158 | −0.130002 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.43359 | + | 44.9117i | 0.231060 | + | 1.90984i | ||||
\(554\) | −13.2100 | + | 7.62682i | −0.561241 | + | 0.324033i | ||||
\(555\) | 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 | ||||||||
\(560\) | −45.1076 | − | 19.2415i | −1.90614 | − | 0.813104i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.8754 | + | 36.1572i | −0.880574 | + | 1.52520i | ||||
\(563\) | 6.33322 | 0.266913 | 0.133457 | − | 0.991055i | \(-0.457392\pi\) | ||||
0.133457 | + | 0.991055i | \(0.457392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 75.6342i | − | 3.18195i | ||||||
\(566\) | 31.2434 | 1.31326 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.55114 | 0.232921 | ||||||||
\(569\) | − | 8.23271i | − | 0.345133i | −0.984998 | − | 0.172567i | \(-0.944794\pi\) | ||
0.984998 | − | 0.172567i | \(-0.0552060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.49727 | 0.355600 | 0.177800 | − | 0.984067i | \(-0.443102\pi\) | ||||
0.177800 | + | 0.984067i | \(0.443102\pi\) | |||||||
\(572\) | −4.40624 | + | 7.63183i | −0.184234 | + | 0.319103i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.3008 | − | 17.7160i | −0.555163 | − | 0.739453i | ||||
\(575\) | 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 | ||||||||
\(580\) | −21.7541 | + | 12.5597i | −0.903290 | + | 0.521514i | ||||
\(581\) | −24.7307 | − | 10.5494i | −1.02600 | − | 0.437663i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0844155 | −0.00349613 | ||||||||
\(584\) | 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 | −0.502393 | − | 0.864640i | \(-0.667547\pi\) |
0.999996 | + | 0.00276510i | \(0.000880160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.35017 | − | 2.33856i | −0.0556327 | − | 0.0963587i | ||||
\(590\) | 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 | ||||
\(596\) | −9.96166 | − | 5.75136i | −0.408045 | − | 0.235585i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.9042i | 0.732156i | ||||||||
\(599\) | 34.6794i | 1.41696i | 0.705730 | + | 0.708481i | \(0.250619\pi\) | ||||
−0.705730 | + | 0.708481i | \(0.749381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4929 | + | 6.63544i | 0.468806 | + | 0.270665i | 0.715740 | − | 0.698367i | \(-0.246090\pi\) |
−0.246934 | + | 0.969032i | \(0.579423\pi\) | |||||||
\(602\) | −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 | \(-0.163844\pi\) |
0.00886811 | + | 0.999961i | \(0.497177\pi\) | |||||||
\(608\) | −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 | \(-0.183180\pi\) | |||||||
\(614\) | −35.6829 | −1.44004 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.87537 | − | 2.15876i | 0.115852 | − | 0.0869787i | ||||
\(617\) | −16.7463 | + | 9.66849i | −0.674181 | + | 0.389239i | −0.797659 | − | 0.603109i | \(-0.793929\pi\) |
0.123478 | + | 0.992347i | \(0.460595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.57807 | + | 5.52990i | −0.384975 | + | 0.222265i | −0.679981 | − | 0.733230i | \(-0.738012\pi\) |
0.295006 | + | 0.955496i | \(0.404679\pi\) | |||||||
\(620\) | −19.2501 | − | 11.1141i | −0.773105 | − | 0.446352i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.4987i | 0.501154i | ||||||||
\(623\) | 24.4380 | − | 18.3474i | 0.979087 | − | 0.735075i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.89411 | + | 15.4051i | −0.355764 | + | 0.616202i | ||||
\(626\) | −30.5249 | −1.22002 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 5.19615i | − | 0.207349i | ||||||
\(629\) | 13.4439 | 0.536043 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6015 | −1.09880 | −0.549400 | − | 0.835560i | \(-0.685144\pi\) | ||||
−0.549400 | + | 0.835560i | \(0.685144\pi\) | |||||||
\(632\) | − | 19.9330i | − | 0.792894i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.31405 | 0.369908 | ||||||||
\(635\) | −16.9594 | + | 29.3745i | −0.673012 | + | 1.16569i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.9929 | + | 26.8411i | −1.10912 | + | 1.06348i | ||||
\(638\) | − | 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 | \(-0.628402\pi\) |
0.600248 | + | 0.799814i | \(0.295069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.4929 | − | 6.63544i | 0.453236 | − | 0.261676i | −0.255960 | − | 0.966687i | \(-0.582391\pi\) |
0.709196 | + | 0.705011i | \(0.249058\pi\) | |||||||
\(644\) | −2.49551 | + | 5.85017i | −0.0983368 | + | 0.230529i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.67850 | −0.144729 | ||||||||
\(647\) | −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 | ||||
\(653\) | 32.2322 | + | 18.6093i | 1.26134 | + | 0.728237i | 0.973334 | − | 0.229391i | \(-0.0736734\pi\) |
0.288009 | + | 0.957628i | \(0.407007\pi\) | |||||||
\(654\) | 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 | ||||
\(659\) | 40.0576 | + | 23.1273i | 1.56042 | + | 0.900911i | 0.997214 | + | 0.0745963i | \(0.0237668\pi\) |
0.563209 | + | 0.826314i | \(0.309567\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 13.1889i | − | 0.512989i | −0.966546 | − | 0.256495i | \(-0.917432\pi\) | ||
0.966546 | − | 0.256495i | \(-0.0825676\pi\) | |||||||
\(662\) | − | 29.9540i | − | 1.16419i | ||||||
\(663\) | 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 | ||||
\(668\) | 2.52669 | + | 4.37636i | 0.0977607 | + | 0.169326i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −30.8447 | − | 17.8082i | −1.19164 | − | 0.687991i | ||||
\(671\) | 4.71319 | + | 8.16348i | 0.181951 | + | 0.315148i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.4633 | + | 35.4434i | −0.788800 | + | 1.36624i | 0.137902 | + | 0.990446i | \(0.455964\pi\) |
−0.926702 | + | 0.375796i | \(0.877369\pi\) | |||||||
\(674\) | 6.28262 | − | 3.62727i | 0.241998 | − | 0.139717i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0719 | + | 20.9091i | −0.464303 | + | 0.804196i | ||||
\(677\) | 1.61796 | 0.0621834 | 0.0310917 | − | 0.999517i | \(-0.490102\pi\) | ||||
0.0310917 | + | 0.999517i | \(0.490102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.714508 | − | 1.67501i | 0.0274203 | − | 0.0642809i | ||||
\(680\) | 12.2146 | − | 7.05213i | 0.468410 | − | 0.270437i | ||||
\(681\) | 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 | ||||||
\(686\) | −31.7787 | + | 12.0050i | −1.21332 | + | 0.458353i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.5988 | − | 30.4820i | 0.670948 | − | 1.16212i | ||||
\(689\) | −0.401187 | −0.0152840 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.6337i | 1.43165i | 0.698278 | + | 0.715826i | \(0.253950\pi\) | ||||
−0.698278 | + | 0.715826i | \(0.746050\pi\) | |||||||
\(692\) | 13.1473 | 0.499787 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.4578 | −0.510851 | ||||||||
\(695\) | − | 3.09880i | − | 0.117544i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5027 | 0.549330 | ||||||||
\(698\) | −23.3951 | + | 40.5216i | −0.885519 | + | 1.53376i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −27.4336 | + | 20.5965i | −1.03689 | + | 0.778474i | ||||
\(701\) | − | 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 | ||||||||
\(706\) | −0.0330243 | + | 0.0190666i | −0.00124289 | + | 0.000717581i | ||||
\(707\) | −13.9306 | + | 10.4588i | −0.523916 | + | 0.393343i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.03402 | 0.0388334 | 0.0194167 | − | 0.999811i | \(-0.493819\pi\) | ||||
0.0194167 | + | 0.999811i | \(0.493819\pi\) | |||||||
\(710\) | 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 | ||||
\(716\) | 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 | ||||
\(722\) | 29.5486 | + | 17.0599i | 1.09968 | + | 0.634903i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 22.6783i | − | 0.842834i | ||||||
\(725\) | − | 45.9385i | − | 1.70611i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.4902 | − | 16.4488i | −1.05664 | − | 0.610053i | −0.132141 | − | 0.991231i | \(-0.542185\pi\) |
−0.924502 | + | 0.381178i | \(0.875518\pi\) | |||||||
\(728\) | 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 | \(-0.213467\pi\) |
−0.146500 | + | 0.989211i | \(0.546801\pi\) | |||||||
\(734\) | −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 | \(-0.215235\pi\) | |||||||
\(740\) | 21.9882 | 0.808301 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.323235 | − | 0.137883i | −0.0118663 | − | 0.00506183i | ||||
\(743\) | −38.3208 | + | 22.1245i | −1.40586 | + | 0.811671i | −0.994985 | − | 0.100023i | \(-0.968108\pi\) |
−0.410870 | + | 0.911694i | \(0.634775\pi\) | |||||||
\(744\) | 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 | ||||||
\(749\) | 25.0464 | + | 33.3606i | 0.915174 | + | 1.21897i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.17230 | + | 2.03048i | −0.0427779 | + | 0.0740934i | −0.886622 | − | 0.462496i | \(-0.846954\pi\) |
0.843844 | + | 0.536589i | \(0.180287\pi\) | |||||||
\(752\) | 12.3907 | 0.451841 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 49.1268i | − | 1.78909i | ||||||
\(755\) | −11.5751 | −0.421260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.8530 | −0.903298 | −0.451649 | − | 0.892196i | \(-0.649164\pi\) | ||||
−0.451649 | + | 0.892196i | \(0.649164\pi\) | |||||||
\(758\) | − | 5.75637i | − | 0.209081i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.80239 | 0.101653 | ||||||||
\(761\) | 0.441044 | − | 0.763910i | 0.0159878 | − | 0.0276917i | −0.857921 | − | 0.513782i | \(-0.828244\pi\) |
0.873909 | + | 0.486090i | \(0.161577\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.1976 | + | 15.0143i | 1.27424 | + | 0.543553i | ||||
\(764\) | − | 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 | ||||||||
\(769\) | −17.9310 | + | 10.3524i | −0.646607 | + | 0.373319i | −0.787155 | − | 0.616755i | \(-0.788447\pi\) |
0.140548 | + | 0.990074i | \(0.455114\pi\) | |||||||
\(770\) | −2.58768 | − | 21.3887i | −0.0932536 | − | 0.770793i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.33589 | 0.156052 | ||||||||
\(773\) | −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 | ||||
\(779\) | 2.49551 | + | 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 | ||||
\(785\) | 12.5597 | + | 7.25136i | 0.448276 | + | 0.258812i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.1557i | 0.896705i | 0.893857 | + | 0.448352i | \(0.147989\pi\) | ||||
−0.893857 | + | 0.448352i | \(0.852011\pi\) | |||||||
\(788\) | 2.63754i | 0.0939585i | ||||||||
\(789\) | 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 | ||||
\(794\) | −1.07229 | − | 1.85725i | −0.0380540 | − | 0.0659115i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.2334 | + | 5.90823i | 0.362712 | + | 0.209412i | ||||
\(797\) | −15.3584 | − | 26.6015i | −0.544023 | − | 0.942275i | −0.998668 | − | 0.0516020i | \(-0.983567\pi\) |
0.454645 | − | 0.890673i | \(-0.349766\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | 6.52514 | 0.230267 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.6580 | − | 14.1960i | −0.375646 | − | 0.500344i | ||||
\(806\) | 37.6480 | − | 21.7361i | 1.32609 | − | 0.765621i | ||||
\(807\) | 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 | \(0.943731\pi\) | |||||||
\(812\) | 6.84736 | − | 16.0521i | 0.240295 | − | 0.563319i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.52420 | + | 7.83615i | −0.158573 | + | 0.274657i | ||||
\(815\) | 42.2462 | 1.47982 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.56491i | − | 0.159706i | ||||||
\(818\) | −37.3674 | −1.30652 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.7200 | 0.828337 | ||||||||
\(821\) | − | 12.4609i | − | 0.434887i | −0.976073 | − | 0.217444i | \(-0.930228\pi\) | ||
0.976073 | − | 0.217444i | \(-0.0697718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.59607 | −0.160209 | −0.0801045 | − | 0.996786i | \(-0.525525\pi\) | ||||
−0.0801045 | + | 0.996786i | \(0.525525\pi\) | |||||||
\(824\) | 5.44906 | − | 9.43805i | 0.189827 | − | 0.328790i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33.6537 | + | 4.07155i | −1.17096 | + | 0.141667i | ||||
\(827\) | − | 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 | ||||||||
\(832\) | 11.3447 | − | 6.54987i | 0.393307 | − | 0.227076i | ||||
\(833\) | 6.20573 | − | 21.3556i | 0.215016 | − | 0.739929i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1043 | −0.488098 | ||||||||
\(836\) | 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 | −0.620695 | − | 0.784052i | \(-0.713149\pi\) |
0.989357 | + | 0.145512i | \(0.0464828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.81505 | − | 4.87580i | −0.0970706 | − | 0.168131i | ||||
\(842\) | 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 | ||||
\(848\) | 0.305226 | + | 0.176223i | 0.0104815 | + | 0.00605151i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 55.3762i | − | 1.89939i | ||||||
\(851\) | 7.45541i | 0.255568i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.8709 | − | 24.7515i | −1.46787 | − | 0.847476i | −0.468519 | − | 0.883453i | \(-0.655212\pi\) |
−0.999353 | + | 0.0359772i | \(0.988546\pi\) | |||||||
\(854\) | 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 | 0.960540 | − | 0.278142i | \(-0.0897185\pi\) |
−0.721148 | + | 0.692781i | \(0.756385\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.05213 | − | 0.607448i | −0.0358983 | − | 0.0207259i | 0.481943 | − | 0.876202i | \(-0.339931\pi\) |
−0.517842 | + | 0.855476i | \(0.673264\pi\) | |||||||
\(860\) | −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 | ||||
\(866\) | −32.9279 | −1.11893 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.3311 | − | 1.85481i | 0.520370 | − | 0.0629564i | ||||
\(869\) | 17.2625 | − | 9.96652i | 0.585591 | − | 0.338091i | ||||
\(870\) | 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 | ||||||
\(875\) | −5.44906 | − | 45.0396i | −0.184212 | − | 1.52262i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.59607 | − | 9.69268i | 0.188966 | − | 0.327299i | −0.755940 | − | 0.654641i | \(-0.772820\pi\) |
0.944906 | + | 0.327342i | \(0.106153\pi\) | |||||||
\(878\) | −18.4100 | −0.621307 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 21.6078i | 0.728398i | ||||||||
\(881\) | −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 | \(0.726031\pi\) | |||||||
\(884\) | − | 24.0164i | − | 0.807758i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48.3468 | 1.62424 | ||||||||
\(887\) | 19.0412 | − | 32.9804i | 0.639342 | − | 1.10737i | −0.346236 | − | 0.938148i | \(-0.612540\pi\) |
0.985577 | − | 0.169225i | \(-0.0541264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.83032 | − | 23.3942i | −0.0949259 | − | 0.784617i | ||||
\(890\) | 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 | ||||||||
\(895\) | −60.8529 | + | 35.1334i | −2.03409 | + | 1.17438i | ||||
\(896\) | −23.2590 | + | 2.81396i | −0.777028 | + | 0.0940079i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44.0702 | −1.47064 | ||||||||
\(899\) | −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 | ||||
\(905\) | 54.8163 | + | 31.6482i | 1.82216 | + | 1.05202i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.773833 | − | 1.34032i | −0.0256947 | − | 0.0445046i | 0.852892 | − | 0.522087i | \(-0.174846\pi\) |
−0.878587 | + | 0.477583i | \(0.841513\pi\) | |||||||
\(908\) | −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 | \(-0.556715\pi\) |
−0.940932 | + | 0.338596i | \(0.890048\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.8467i | 0.392069i | ||||||||
\(914\) | − | 38.1931i | − | 1.26331i | ||||||
\(915\) | 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 | \(0.895360\pi\) | |||||||
\(920\) | 3.91081 | + | 6.77373i | 0.128936 | + | 0.223323i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.2677 | − | 7.66013i | −0.436950 | − | 0.252273i | ||||
\(923\) | 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 | ||||
\(929\) | −44.6284 | −1.46421 | −0.732105 | − | 0.681192i | \(-0.761462\pi\) | ||||
−0.732105 | + | 0.681192i | \(0.761462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.18942 | − | 3.05819i | 0.104529 | − | 0.100228i | ||||
\(932\) | 12.2146 | − | 7.05213i | 0.400104 | − | 0.231000i | ||||
\(933\) | 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 | \(-0.183282\pi\) | |||||||
\(938\) | 24.5651 | − | 2.97198i | 0.802079 | − | 0.0970387i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.61408 | − | 11.4559i | 0.215727 | − | 0.373651i | ||||
\(941\) | −33.9984 | −1.10832 | −0.554159 | − | 0.832411i | \(-0.686960\pi\) | ||||
−0.554159 | + | 0.832411i | \(0.686960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.04260i | 0.261903i | ||||||||
\(944\) | 33.9984 | 1.10655 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.4633 | 0.502754 | ||||||||
\(947\) | 46.1461i | 1.49955i | 0.661694 | + | 0.749774i | \(0.269838\pi\) | ||||
−0.661694 | + | 0.749774i | \(0.730162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.0109 | 1.00666 | ||||||||
\(950\) | 5.50138 | − | 9.52867i | 0.178488 | − | 0.309151i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.84471 | + | 9.01307i | −0.124608 | + | 0.292115i | ||||
\(953\) | − | 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 | ||||||||
\(958\) | −64.3717 | + | 37.1650i | −2.07976 | + | 1.20075i | ||||
\(959\) | 26.7831 | + | 35.6739i | 0.864873 | + | 1.15197i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7003 | 0.409688 | ||||||||
\(962\) | −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 | 0.953488 | − | 0.301432i | \(-0.0974646\pi\) |
−0.737792 | + | 0.675029i | \(0.764131\pi\) | |||||||
\(968\) | 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 | ||||
\(974\) | 19.7265 | + | 11.3891i | 0.632078 | + | 0.364930i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 39.3563i | − | 1.25976i | ||||||
\(977\) | − | 22.6530i | − | 0.724734i | −0.932035 | − | 0.362367i | \(-0.881969\pi\) | ||
0.932035 | − | 0.362367i | \(-0.118031\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | 19.6704 | + | 34.0701i | 0.627388 | + | 1.08667i | 0.988074 | + | 0.153981i | \(0.0492095\pi\) |
−0.360685 | + | 0.932688i | \(0.617457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.37526 | − | 3.68076i | −0.203133 | − | 0.117279i | ||||
\(986\) | 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 | \(0.171478\pi\) | |||||||
\(992\) | −28.2168 | −0.895883 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.77557 | + | 22.9416i | 0.0880357 | + | 0.727665i | ||||
\(995\) | −28.5618 | + | 16.4902i | −0.905471 | + | 0.522774i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.2486 | − | 15.7320i | 0.862973 | − | 0.498238i | −0.00203378 | − | 0.999998i | \(-0.500647\pi\) |
0.865007 | + | 0.501760i | \(0.167314\pi\) | |||||||
\(998\) | −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.i.f.269.2 | 12 | ||
3.2 | odd | 2 | inner | 567.2.i.f.269.5 | 12 | ||
7.5 | odd | 6 | 567.2.s.f.26.2 | 12 | |||
9.2 | odd | 6 | 189.2.p.d.80.5 | yes | 12 | ||
9.4 | even | 3 | 567.2.s.f.458.5 | 12 | |||
9.5 | odd | 6 | 567.2.s.f.458.2 | 12 | |||
9.7 | even | 3 | 189.2.p.d.80.2 | yes | 12 | ||
21.5 | even | 6 | 567.2.s.f.26.5 | 12 | |||
63.5 | even | 6 | inner | 567.2.i.f.215.5 | 12 | ||
63.11 | odd | 6 | 1323.2.c.d.1322.10 | 12 | |||
63.25 | even | 3 | 1323.2.c.d.1322.3 | 12 | |||
63.38 | even | 6 | 1323.2.c.d.1322.9 | 12 | |||
63.40 | odd | 6 | inner | 567.2.i.f.215.2 | 12 | ||
63.47 | even | 6 | 189.2.p.d.26.2 | ✓ | 12 | ||
63.52 | odd | 6 | 1323.2.c.d.1322.4 | 12 | |||
63.61 | odd | 6 | 189.2.p.d.26.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.2 | ✓ | 12 | 63.47 | even | 6 | ||
189.2.p.d.26.5 | yes | 12 | 63.61 | odd | 6 | ||
189.2.p.d.80.2 | yes | 12 | 9.7 | even | 3 | ||
189.2.p.d.80.5 | yes | 12 | 9.2 | odd | 6 | ||
567.2.i.f.215.2 | 12 | 63.40 | odd | 6 | inner | ||
567.2.i.f.215.5 | 12 | 63.5 | even | 6 | inner | ||
567.2.i.f.269.2 | 12 | 1.1 | even | 1 | trivial | ||
567.2.i.f.269.5 | 12 | 3.2 | odd | 2 | inner | ||
567.2.s.f.26.2 | 12 | 7.5 | odd | 6 | |||
567.2.s.f.26.5 | 12 | 21.5 | even | 6 | |||
567.2.s.f.458.2 | 12 | 9.5 | odd | 6 | |||
567.2.s.f.458.5 | 12 | 9.4 | even | 3 | |||
1323.2.c.d.1322.3 | 12 | 63.25 | even | 3 | |||
1323.2.c.d.1322.4 | 12 | 63.52 | odd | 6 | |||
1323.2.c.d.1322.9 | 12 | 63.38 | even | 6 | |||
1323.2.c.d.1322.10 | 12 | 63.11 | odd | 6 |