Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(949,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bc (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1549.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1549 |
Dual form | 2100.2.bc.a.949.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59808 | + | 0.500000i | −0.981981 | + | 0.188982i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000i | 0.832050i | 0.909353 | + | 0.416025i | \(0.136577\pi\) | ||||
−0.909353 | + | 0.416025i | \(0.863423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.92820 | − | 4.00000i | 1.68034 | − | 0.970143i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
0.961436 | − | 0.275029i | \(-0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.92820 | + | 4.00000i | 1.44463 | + | 0.834058i | 0.998154 | − | 0.0607377i | \(-0.0193453\pi\) |
0.446476 | + | 0.894795i | \(0.352679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73205 | − | 1.00000i | −0.301511 | − | 0.174078i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.866025 | + | 0.500000i | 0.142374 | + | 0.0821995i | 0.569495 | − | 0.821995i | \(-0.307139\pi\) |
−0.427121 | + | 0.904194i | \(0.640472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50000 | + | 2.59808i | 0.240192 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.0000i | − | 1.67748i | −0.544529 | − | 0.838742i | \(-0.683292\pi\) | ||
0.544529 | − | 0.838742i | \(-0.316708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19615 | − | 3.00000i | −0.757937 | − | 0.437595i | 0.0706177 | − | 0.997503i | \(-0.477503\pi\) |
−0.828554 | + | 0.559908i | \(0.810836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.50000 | − | 2.59808i | 0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | − | 6.92820i | 0.560112 | − | 0.970143i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923 | − | 6.00000i | 1.42749 | − | 0.824163i | 0.430570 | − | 0.902557i | \(-0.358312\pi\) |
0.996922 | + | 0.0783936i | \(0.0249791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 3.46410i | 0.260378 | + | 0.450988i | 0.966342 | − | 0.257260i | \(-0.0828195\pi\) |
−0.705965 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.866025 | + | 2.50000i | −0.109109 | + | 0.314970i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2583 | − | 6.50000i | 1.37542 | − | 0.794101i | 0.383819 | − | 0.923408i | \(-0.374609\pi\) |
0.991605 | + | 0.129307i | \(0.0412752\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0000 | −1.18678 | −0.593391 | − | 0.804914i | \(-0.702211\pi\) | ||||
−0.593391 | + | 0.804914i | \(0.702211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.52628 | − | 5.50000i | 1.11497 | − | 0.643726i | 0.174855 | − | 0.984594i | \(-0.444054\pi\) |
0.940111 | + | 0.340868i | \(0.110721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.46410 | + | 4.00000i | 0.394771 | + | 0.455842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.50000 | + | 2.59808i | −0.168763 | + | 0.292306i | −0.937985 | − | 0.346675i | \(-0.887311\pi\) |
0.769222 | + | 0.638982i | \(0.220644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.00000i | − | 0.219529i | −0.993958 | − | 0.109764i | \(-0.964990\pi\) | ||
0.993958 | − | 0.109764i | \(-0.0350096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.46410 | + | 2.00000i | −0.371391 | + | 0.214423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50000 | − | 7.79423i | −0.157243 | − | 0.817057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.59808 | − | 1.50000i | −0.269408 | − | 0.155543i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00000 | − | 8.66025i | −0.497519 | − | 0.861727i | 0.502477 | − | 0.864590i | \(-0.332422\pi\) |
−0.999996 | + | 0.00286291i | \(0.999089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.52628 | + | 5.50000i | 0.938652 | + | 0.541931i | 0.889538 | − | 0.456862i | \(-0.151027\pi\) |
0.0491146 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.50000 | − | 9.52628i | −0.526804 | − | 0.912452i | −0.999512 | − | 0.0312328i | \(-0.990057\pi\) |
0.472708 | − | 0.881219i | \(-0.343277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.59808 | + | 1.50000i | 0.240192 | + | 0.138675i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.0000 | + | 13.8564i | −1.46672 | + | 1.27021i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.19615 | − | 3.00000i | 0.468521 | − | 0.270501i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00000i | 0.266207i | 0.991102 | + | 0.133103i | \(0.0424943\pi\) | ||||
−0.991102 | + | 0.133103i | \(0.957506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.50000 | − | 9.52628i | −0.484248 | − | 0.838742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | − | 1.73205i | 0.0873704 | − | 0.151330i | −0.819028 | − | 0.573753i | \(-0.805487\pi\) |
0.906399 | + | 0.422423i | \(0.138820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.866025 | − | 2.50000i | 0.0750939 | − | 0.216777i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46410 | − | 2.00000i | 0.295958 | − | 0.170872i | −0.344668 | − | 0.938725i | \(-0.612008\pi\) |
0.640626 | + | 0.767853i | \(0.278675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.19615 | − | 3.00000i | 0.434524 | − | 0.250873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.33013 | − | 5.50000i | 0.357143 | − | 0.453632i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 8.00000i | − | 0.646762i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.73205 | − | 1.00000i | 0.138233 | − | 0.0798087i | −0.429289 | − | 0.903167i | \(-0.641236\pi\) |
0.567521 | + | 0.823359i | \(0.307902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | − | 10.3923i | 0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.0000 | − | 6.92820i | −1.57622 | − | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.46410 | − | 2.00000i | −0.271329 | − | 0.156652i | 0.358162 | − | 0.933659i | \(-0.383403\pi\) |
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.00000i | − | 0.154765i | −0.997001 | − | 0.0773823i | \(-0.975344\pi\) | ||
0.997001 | − | 0.0773823i | \(-0.0246562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | + | 0.866025i | 0.0382360 | + | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.8564 | + | 8.00000i | 1.05348 | + | 0.608229i | 0.923622 | − | 0.383304i | \(-0.125214\pi\) |
0.129861 | + | 0.991532i | \(0.458547\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.46410 | + | 2.00000i | 0.260378 | + | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | + | 5.19615i | 0.224231 | + | 0.388379i | 0.956088 | − | 0.293079i | \(-0.0946798\pi\) |
−0.731858 | + | 0.681457i | \(0.761346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0000 | −1.11494 | −0.557471 | − | 0.830197i | \(-0.688228\pi\) | ||||
−0.557471 | + | 0.830197i | \(0.688228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.00000i | − | 0.443533i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.8564 | − | 8.00000i | −1.01328 | − | 0.585018i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.500000 | + | 2.59808i | 0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.52628 | + | 5.50000i | −0.685717 | + | 0.395899i | −0.802005 | − | 0.597317i | \(-0.796234\pi\) |
0.116289 | + | 0.993215i | \(0.462900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.00000i | 0.569976i | 0.958531 | + | 0.284988i | \(0.0919897\pi\) | ||||
−0.958531 | + | 0.284988i | \(0.908010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | + | 6.92820i | 0.283552 | + | 0.491127i | 0.972257 | − | 0.233915i | \(-0.0751537\pi\) |
−0.688705 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.50000 | − | 11.2583i | 0.458475 | − | 0.794101i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3923 | − | 2.00000i | 0.729397 | − | 0.140372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.92820 | − | 4.00000i | 0.481543 | − | 0.278019i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.66025 | + | 5.00000i | −0.593391 | + | 0.342594i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.19615 | + | 6.00000i | 0.352738 | + | 0.407307i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.50000 | − | 9.52628i | 0.371656 | − | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | + | 20.7846i | 0.807207 | + | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5885 | + | 9.00000i | −1.03464 | + | 0.597351i | −0.918311 | − | 0.395860i | \(-0.870447\pi\) |
−0.116331 | + | 0.993210i | \(0.537113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | − | 0.866025i | 0.0330409 | − | 0.0572286i | −0.849032 | − | 0.528341i | \(-0.822814\pi\) |
0.882073 | + | 0.471113i | \(0.156147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.00000 | + | 1.73205i | 0.328976 | + | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1244 | + | 7.00000i | 0.794293 | + | 0.458585i | 0.841472 | − | 0.540301i | \(-0.181690\pi\) |
−0.0471787 | + | 0.998886i | \(0.515023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000i | 0.194871i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0000 | −1.16432 | −0.582162 | − | 0.813073i | \(-0.697793\pi\) | ||||
−0.582162 | + | 0.813073i | \(0.697793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.59808 | − | 1.50000i | −0.165312 | − | 0.0954427i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.00000 | − | 1.73205i | −0.0633724 | − | 0.109764i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.0000i | − | 1.00591i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.5885 | − | 9.00000i | −0.972381 | − | 0.561405i | −0.0724199 | − | 0.997374i | \(-0.523072\pi\) |
−0.899961 | + | 0.435970i | \(0.856405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | − | 0.866025i | −0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | + | 3.46410i | −0.123797 | + | 0.214423i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3923 | + | 6.00000i | −0.640817 | + | 0.369976i | −0.784929 | − | 0.619586i | \(-0.787301\pi\) |
0.144112 | + | 0.989561i | \(0.453967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | − | 1.73205i | −0.0609711 | − | 0.105605i | 0.833929 | − | 0.551872i | \(-0.186086\pi\) |
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.19615 | − | 6.00000i | −0.314485 | − | 0.363137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7224 | − | 8.50000i | 0.884585 | − | 0.510716i | 0.0124177 | − | 0.999923i | \(-0.496047\pi\) |
0.872167 | + | 0.489207i | \(0.162714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000 | 1.19310 | 0.596550 | − | 0.802576i | \(-0.296538\pi\) | ||||
0.596550 | + | 0.802576i | \(0.296538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.4545 | + | 9.50000i | −0.978117 | + | 0.564716i | −0.901701 | − | 0.432360i | \(-0.857681\pi\) |
−0.0764162 | + | 0.997076i | \(0.524348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.5885 | + | 3.00000i | −0.920158 | + | 0.177084i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.5000 | − | 40.7032i | 1.38235 | − | 2.39431i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0000i | 1.40209i | 0.713115 | + | 0.701047i | \(0.247284\pi\) | ||||
−0.713115 | + | 0.701047i | \(0.752716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.73205 | + | 1.00000i | −0.100504 | + | 0.0580259i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.50000 | + | 28.5788i | 0.317015 | + | 1.64726i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.66025 | − | 5.00000i | −0.497519 | − | 0.287242i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.0000i | − | 1.31268i | −0.754466 | − | 0.656340i | \(-0.772104\pi\) | ||
0.754466 | − | 0.656340i | \(-0.227896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0000 | 0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.00000 | + | 1.73205i | 0.0567048 | + | 0.0982156i | 0.892984 | − | 0.450088i | \(-0.148607\pi\) |
−0.836280 | + | 0.548303i | \(0.815274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7224 | − | 8.50000i | −0.832161 | − | 0.480448i | 0.0224310 | − | 0.999748i | \(-0.492859\pi\) |
−0.854592 | + | 0.519300i | \(0.826193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.7846 | + | 12.0000i | 1.16738 | + | 0.673987i | 0.953062 | − | 0.302777i | \(-0.0979136\pi\) |
0.214318 | + | 0.976764i | \(0.431247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000i | 0.445132i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.52628 | − | 5.50000i | −0.526804 | − | 0.304151i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0000 | + | 5.19615i | 0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.866025 | − | 0.500000i | 0.0474579 | − | 0.0273998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.0000i | 1.14394i | 0.820274 | + | 0.571971i | \(0.193821\pi\) | ||||
−0.820274 | + | 0.571971i | \(0.806179\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.00000 | + | 12.1244i | 0.380188 | + | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | − | 12.0000i | 1.11578 | − | 0.644194i | 0.175457 | − | 0.984487i | \(-0.443860\pi\) |
0.940319 | + | 0.340293i | \(0.110526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.00000 | 0.160128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.19615 | − | 3.00000i | 0.276563 | − | 0.159674i | −0.355303 | − | 0.934751i | \(-0.615622\pi\) |
0.631867 | + | 0.775077i | \(0.282289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.92820 | + | 20.0000i | −0.366679 | + | 1.05851i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.33013 | − | 2.50000i | 0.226031 | − | 0.130499i | −0.382709 | − | 0.923869i | \(-0.625009\pi\) |
0.608740 | + | 0.793370i | \(0.291675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | + | 20.7846i | −1.24602 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.33013 | − | 2.50000i | −0.224205 | − | 0.129445i | 0.383691 | − | 0.923462i | \(-0.374653\pi\) |
−0.607896 | + | 0.794017i | \(0.707986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0000 | −0.667765 | −0.333883 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333883 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50000 | + | 2.59808i | 0.0768473 | + | 0.133103i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.2487 | − | 14.0000i | −1.23905 | − | 0.715367i | −0.270151 | − | 0.962818i | \(-0.587074\pi\) |
−0.968900 | + | 0.247451i | \(0.920407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.52628 | − | 5.50000i | −0.484248 | − | 0.279581i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.00000 | + | 8.66025i | 0.253510 | + | 0.439092i | 0.964490 | − | 0.264120i | \(-0.0850816\pi\) |
−0.710980 | + | 0.703213i | \(0.751748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64.0000 | 3.23662 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.00000i | − | 0.100887i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.59808 | − | 1.50000i | −0.130394 | − | 0.0752828i | 0.433384 | − | 0.901209i | \(-0.357319\pi\) |
−0.563778 | + | 0.825926i | \(0.690653\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.500000 | − | 2.59808i | −0.0250313 | − | 0.130066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.79423 | − | 4.50000i | 0.388258 | − | 0.224161i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.00000i | − | 0.0991363i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.50000 | − | 16.4545i | −0.469745 | − | 0.813622i | 0.529657 | − | 0.848212i | \(-0.322321\pi\) |
−0.999402 | + | 0.0345902i | \(0.988987\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | − | 3.46410i | 0.0986527 | − | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.92820 | − | 8.00000i | −0.340915 | − | 0.393654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.33013 | − | 2.50000i | 0.212047 | − | 0.122426i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0000 | −0.879358 | −0.439679 | − | 0.898155i | \(-0.644908\pi\) | ||||
−0.439679 | + | 0.898155i | \(0.644908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.19615 | + | 3.00000i | −0.252646 | + | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.19615 | + | 15.0000i | −0.251459 | + | 0.725901i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.00000 | − | 5.19615i | 0.144841 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0000 | + | 25.9808i | 0.722525 | + | 1.25145i | 0.959985 | + | 0.280052i | \(0.0903517\pi\) |
−0.237460 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0000i | 1.20142i | 0.799466 | + | 0.600712i | \(0.205116\pi\) | ||||
−0.799466 | + | 0.600712i | \(0.794884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.92820 | + | 4.00000i | −0.331421 | + | 0.191346i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | − | 20.7846i | 0.572729 | − | 0.991995i | −0.423556 | − | 0.905870i | \(-0.639218\pi\) |
0.996284 | − | 0.0861252i | \(-0.0274485\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.46410 | − | 2.00000i | −0.164584 | − | 0.0950229i | 0.415445 | − | 0.909618i | \(-0.363626\pi\) |
−0.580030 | + | 0.814595i | \(0.696959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000i | 0.567581i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.0000 | −1.03824 | −0.519122 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519122 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.92820 | + | 4.00000i | 0.325515 | + | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.2583 | − | 6.50000i | −0.526642 | − | 0.304057i | 0.213006 | − | 0.977051i | \(-0.431675\pi\) |
−0.739648 | + | 0.672994i | \(0.765008\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.00000 | − | 6.92820i | −0.186704 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.00000 | 0.186299 | 0.0931493 | − | 0.995652i | \(-0.470307\pi\) | ||||
0.0931493 | + | 0.995652i | \(0.470307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000i | 0.511213i | 0.966781 | + | 0.255607i | \(0.0822752\pi\) | ||||
−0.966781 | + | 0.255607i | \(0.917725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4449 | − | 17.0000i | −1.36255 | − | 0.786666i | −0.372584 | − | 0.927999i | \(-0.621528\pi\) |
−0.989962 | + | 0.141332i | \(0.954861\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.0000 | + | 22.5167i | −1.20057 | + | 1.03972i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00000 | − | 1.73205i | 0.0460776 | − | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.0526 | + | 11.0000i | −0.876038 | + | 0.505781i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 12.0000i | − | 0.549442i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.0000 | − | 24.2487i | −0.639676 | − | 1.10795i | −0.985504 | − | 0.169654i | \(-0.945735\pi\) |
0.345827 | − | 0.938298i | \(-0.387598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50000 | + | 2.59808i | −0.0683941 | + | 0.118462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.7846 | + | 4.00000i | −0.945732 | + | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4545 | + | 9.50000i | −0.745624 | + | 0.430486i | −0.824110 | − | 0.566429i | \(-0.808325\pi\) |
0.0784867 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.7128 | + | 16.0000i | −1.24812 | + | 0.720604i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.9808 | − | 5.00000i | 1.16540 | − | 0.224281i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5000 | + | 25.1147i | −0.649109 | + | 1.12429i | 0.334227 | + | 0.942493i | \(0.391525\pi\) |
−0.983336 | + | 0.181797i | \(0.941809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | − | 1.73205i | −0.0446767 | − | 0.0773823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.0000i | 1.33763i | 0.743427 | + | 0.668817i | \(0.233199\pi\) | ||||
−0.743427 | + | 0.668817i | \(0.766801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.46410 | − | 2.00000i | 0.153846 | − | 0.0888231i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.00000 | − | 15.5885i | 0.398918 | − | 0.690946i | −0.594675 | − | 0.803966i | \(-0.702719\pi\) |
0.993593 | + | 0.113020i | \(0.0360525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0000 | + | 19.0526i | −0.973223 | + | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.866025 | + | 0.500000i | 0.0382360 | + | 0.0220755i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000i | 0.527759i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0000 | 0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | + | 31.1769i | 0.788594 | + | 1.36589i | 0.926828 | + | 0.375486i | \(0.122524\pi\) |
−0.138234 | + | 0.990400i | \(0.544143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.8468 | − | 15.5000i | −1.17393 | − | 0.677768i | −0.219326 | − | 0.975652i | \(-0.570386\pi\) |
−0.954602 | + | 0.297884i | \(0.903719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7846 | − | 12.0000i | −0.905392 | − | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5000 | + | 35.5070i | 0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.0000i | 0.779667i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.19615 | + | 3.00000i | 0.224231 | + | 0.129460i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.0000 | − | 8.66025i | −0.473804 | − | 0.373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.50000 | − | 12.9904i | 0.322450 | − | 0.558500i | −0.658543 | − | 0.752543i | \(-0.728827\pi\) |
0.980993 | + | 0.194043i | \(0.0621602\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.9904 | + | 7.50000i | −0.557471 | + | 0.321856i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.0000i | − | 0.513083i | −0.966533 | − | 0.256541i | \(-0.917417\pi\) | ||
0.966533 | − | 0.256541i | \(-0.0825830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00000 | − | 5.19615i | −0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | − | 3.46410i | 0.0852029 | − | 0.147576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.59808 | − | 7.50000i | 0.110481 | − | 0.318932i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.0526 | − | 11.0000i | 0.807283 | − | 0.466085i | −0.0387286 | − | 0.999250i | \(-0.512331\pi\) |
0.846011 | + | 0.533165i | \(0.178997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.0000 | 1.39575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0000 | −0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.8372 | − | 23.0000i | 1.67894 | − | 0.969334i | 0.716596 | − | 0.697489i | \(-0.245699\pi\) |
0.962341 | − | 0.271846i | \(-0.0876340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.73205 | + | 2.00000i | 0.0727393 | + | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5000 | + | 18.1865i | 0.439411 | + | 0.761083i | 0.997644 | − | 0.0686016i | \(-0.0218537\pi\) |
−0.558233 | + | 0.829684i | \(0.688520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000i | 0.250654i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.5070 | + | 20.5000i | −1.47818 | + | 0.853426i | −0.999696 | − | 0.0246713i | \(-0.992146\pi\) |
−0.478482 | + | 0.878097i | \(0.658813\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.50000 | + | 9.52628i | −0.228572 | + | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00000 | + | 5.19615i | 0.0414870 | + | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.7846 | − | 12.0000i | −0.860811 | − | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.0000i | 1.32078i | 0.750922 | + | 0.660391i | \(0.229609\pi\) | ||||
−0.750922 | + | 0.660391i | \(0.770391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.00000 | + | 6.92820i | 0.164538 | + | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.19615 | − | 3.00000i | −0.213380 | − | 0.123195i | 0.389501 | − | 0.921026i | \(-0.372647\pi\) |
−0.602881 | + | 0.797831i | \(0.705981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.92820 | + | 4.00000i | 0.283552 | + | 0.163709i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.00000 | − | 10.3923i | −0.245153 | − | 0.424618i | 0.717021 | − | 0.697051i | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | −0.0407909 | −0.0203954 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203954 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 13.0000i | − | 0.529401i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.59808 | + | 1.50000i | 0.105453 | + | 0.0608831i | 0.551799 | − | 0.833977i | \(-0.313942\pi\) |
−0.446346 | + | 0.894860i | \(0.647275\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | − | 6.92820i | 0.324176 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | − | 15.5885i | 0.364101 | − | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.9808 | − | 15.0000i | 1.04935 | − | 0.605844i | 0.126885 | − | 0.991917i | \(-0.459502\pi\) |
0.922468 | + | 0.386073i | \(0.126169\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.0000i | 1.04672i | 0.852111 | + | 0.523360i | \(0.175322\pi\) | ||||
−0.852111 | + | 0.523360i | \(0.824678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.50000 | − | 9.52628i | −0.221064 | − | 0.382893i | 0.734068 | − | 0.679076i | \(-0.237620\pi\) |
−0.955131 | + | 0.296183i | \(0.904286\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | − | 6.92820i | 0.160514 | − | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.73205 | − | 1.00000i | 0.0691714 | − | 0.0399362i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.00000 | 0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.46410 | + | 2.00000i | −0.137686 | + | 0.0794929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.79423 | + | 19.5000i | 0.308819 | + | 0.772618i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.00000 | + | 8.66025i | −0.197797 | + | 0.342594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0000 | + | 34.6410i | 0.789953 | + | 1.36824i | 0.925995 | + | 0.377535i | \(0.123228\pi\) |
−0.136043 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.0000i | − | 1.38027i | −0.723683 | − | 0.690133i | \(-0.757552\pi\) | ||
0.723683 | − | 0.690133i | \(-0.242448\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.19615 | − | 3.00000i | 0.204282 | − | 0.117942i | −0.394369 | − | 0.918952i | \(-0.629037\pi\) |
0.598651 | + | 0.801010i | \(0.295704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | − | 6.92820i | 0.157014 | − | 0.271956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.50000 | + | 2.59808i | 0.293948 | + | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.19615 | − | 3.00000i | −0.203341 | − | 0.117399i | 0.394872 | − | 0.918736i | \(-0.370789\pi\) |
−0.598213 | + | 0.801337i | \(0.704122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 11.0000i | − | 0.429151i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.0000 | 1.09073 | 0.545363 | − | 0.838200i | \(-0.316392\pi\) | ||||
0.545363 | + | 0.838200i | \(0.316392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5000 | + | 25.1147i | 0.563985 | + | 0.976850i | 0.997143 | + | 0.0755324i | \(0.0240656\pi\) |
−0.433159 | + | 0.901318i | \(0.642601\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.7846 | + | 12.0000i | 0.807207 | + | 0.466041i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.7128 | − | 16.0000i | −1.07304 | − | 0.619522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | − | 6.92820i | −0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000i | 0.0385472i | 0.999814 | + | 0.0192736i | \(0.00613535\pi\) | ||||
−0.999814 | + | 0.0192736i | \(0.993865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3923 | − | 6.00000i | −0.399409 | − | 0.230599i | 0.286820 | − | 0.957984i | \(-0.407402\pi\) |
−0.686229 | + | 0.727386i | \(0.740735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.00000 | − | 25.9808i | −0.191882 | − | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | + | 15.5885i | −0.344881 | + | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.1769 | + | 18.0000i | −1.19295 | + | 0.688751i | −0.958975 | − | 0.283491i | \(-0.908507\pi\) |
−0.233977 | + | 0.972242i | \(0.575174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.00000i | − | 0.0381524i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | + | 31.1769i | 0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.5000 | − | 37.2391i | 0.817899 | − | 1.41664i | −0.0893292 | − | 0.996002i | \(-0.528472\pi\) |
0.907228 | − | 0.420640i | \(-0.138194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.19615 | − | 1.00000i | 0.197386 | − | 0.0379869i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.5692 | − | 24.0000i | 1.57455 | − | 0.909065i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.0000 | 0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.00000 | −0.302156 | −0.151078 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151078 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.866025 | + | 0.500000i | −0.0326628 | + | 0.0188579i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.3205 | + | 20.0000i | 0.651405 | + | 0.752177i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.00000 | − | 12.1244i | 0.262891 | − | 0.455340i | −0.704118 | − | 0.710083i | \(-0.748658\pi\) |
0.967009 | + | 0.254743i | \(0.0819909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | + | 2.59808i | 0.0562544 | + | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 24.0000i | − | 0.898807i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.5885 | + | 9.00000i | −0.582162 | + | 0.336111i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.5000 | − | 9.52628i | −1.02415 | − | 0.354777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.1244 | − | 7.00000i | −0.450910 | − | 0.260333i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.0000i | − | 0.853023i | −0.904482 | − | 0.426511i | \(-0.859742\pi\) | ||
0.904482 | − | 0.426511i | \(-0.140258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.0000 | − | 76.2102i | −1.62740 | − | 2.81874i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.9711 | + | 22.5000i | 1.43943 | + | 0.831056i | 0.997810 | − | 0.0661448i | \(-0.0210699\pi\) |
0.441622 | + | 0.897201i | \(0.354403\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.5167 | − | 13.0000i | −0.829412 | − | 0.478861i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.50000 | − | 7.79423i | −0.165535 | − | 0.286715i | 0.771310 | − | 0.636460i | \(-0.219602\pi\) |
−0.936845 | + | 0.349744i | \(0.886268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | −0.110208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000i | 0.660356i | 0.943919 | + | 0.330178i | \(0.107109\pi\) | ||||
−0.943919 | + | 0.330178i | \(0.892891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.73205 | − | 1.00000i | −0.0633724 | − | 0.0365881i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.50000 | + | 12.9904i | −0.273679 | + | 0.474026i | −0.969801 | − | 0.243898i | \(-0.921574\pi\) |
0.696122 | + | 0.717923i | \(0.254907\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000i | 1.52652i | 0.646094 | + | 0.763258i | \(0.276401\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | − | 13.8564i | −0.290382 | − | 0.502956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.00000 | + | 6.92820i | −0.145000 | + | 0.251147i | −0.929373 | − | 0.369142i | \(-0.879652\pi\) |
0.784373 | + | 0.620289i | \(0.212985\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.0526 | + | 22.0000i | 0.689749 | + | 0.796453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.3923 | + | 6.00000i | −0.375244 | + | 0.216647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0000 | −1.11789 | −0.558944 | − | 0.829205i | \(-0.688793\pi\) | ||||
−0.558944 | + | 0.829205i | \(0.688793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.0526 | + | 11.0000i | −0.685273 | + | 0.395643i | −0.801839 | − | 0.597540i | \(-0.796145\pi\) |
0.116566 | + | 0.993183i | \(0.462811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.59808 | + | 0.500000i | −0.0932055 | + | 0.0179374i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | + | 17.3205i | 0.357828 | + | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.00000i | 0.142948i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7846 | − | 12.0000i | 0.740891 | − | 0.427754i | −0.0815020 | − | 0.996673i | \(-0.525972\pi\) |
0.822393 | + | 0.568919i | \(0.192638\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.00000 | + | 10.3923i | −0.213606 | + | 0.369976i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.00000 | − | 36.3731i | −0.248891 | − | 1.29328i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5885 | + | 9.00000i | 0.553562 | + | 0.319599i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 48.0000i | − | 1.70025i | −0.526583 | − | 0.850124i | \(-0.676527\pi\) | ||
0.526583 | − | 0.850124i | \(-0.323473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.0000 | −1.69812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.0526 | − | 11.0000i | −0.672350 | − | 0.388182i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.73205 | − | 1.00000i | −0.0609711 | − | 0.0352017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0000 | + | 19.0526i | 0.386739 | + | 0.669852i | 0.992009 | − | 0.126168i | \(-0.0402680\pi\) |
−0.605269 | + | 0.796021i | \(0.706935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.0000 | −1.12367 | −0.561836 | − | 0.827249i | \(-0.689905\pi\) | ||||
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 24.0000i | − | 0.841717i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.52628 | + | 5.50000i | 0.333282 | + | 0.192421i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.50000 | − | 2.59808i | −0.262071 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.00000 | + | 1.73205i | −0.0349002 | + | 0.0604490i | −0.882948 | − | 0.469471i | \(-0.844445\pi\) |
0.848048 | + | 0.529920i | \(0.177778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.6410 | + | 20.0000i | −1.20751 | + | 0.697156i | −0.962215 | − | 0.272292i | \(-0.912218\pi\) |
−0.245295 | + | 0.969448i | \(0.578885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0000i | 1.87776i | 0.344239 | + | 0.938882i | \(0.388137\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50000 | − | 9.52628i | −0.191023 | − | 0.330861i | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.50000 | − | 14.7224i | 0.294862 | − | 0.510716i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.6410 | − | 44.0000i | 1.20024 | − | 1.52451i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.59808 | + | 1.50000i | −0.0898027 | + | 0.0518476i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.3205 | − | 10.0000i | 0.596550 | − | 0.344418i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.06218 | + | 17.5000i | −0.208299 | + | 0.601307i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.50000 | + | 16.4545i | −0.326039 | + | 0.564716i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | + | 6.92820i | 0.137118 | + | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.0000i | − | 0.787505i | −0.919216 | − | 0.393753i | \(-0.871177\pi\) | ||
0.919216 | − | 0.393753i | \(-0.128823\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | − | 6.92820i | 0.136478 | − | 0.236387i | −0.789683 | − | 0.613515i | \(-0.789755\pi\) |
0.926161 | + | 0.377128i | \(0.123088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | + | 10.3923i | −0.408959 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.8372 | + | 23.0000i | 1.35607 | + | 0.782929i | 0.989092 | − | 0.147299i | \(-0.0470581\pi\) |
0.366981 | + | 0.930228i | \(0.380391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 47.0000i | − | 1.59620i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.00000 | 0.203536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5000 | + | 33.7750i | 0.660732 | + | 1.14442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.66025 | + | 5.00000i | 0.293105 | + | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.9090 | + | 19.0000i | 1.11126 | + | 0.641584i | 0.939155 | − | 0.343495i | \(-0.111611\pi\) |
0.172102 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000 | + | 20.7846i | 0.404750 | + | 0.701047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.0000 | 1.61716 | 0.808581 | − | 0.588386i | \(-0.200236\pi\) | ||||
0.808581 | + | 0.588386i | \(0.200236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.0000i | − | 0.975928i | −0.872864 | − | 0.487964i | \(-0.837740\pi\) | ||
0.872864 | − | 0.487964i | \(-0.162260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.19615 | + | 3.00000i | 0.174470 | + | 0.100730i | 0.584692 | − | 0.811256i | \(-0.301215\pi\) |
−0.410222 | + | 0.911986i | \(0.634549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.50000 | − | 7.79423i | −0.0503084 | − | 0.261410i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.19615 | − | 3.00000i | 0.173883 | − | 0.100391i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000i | 0.801337i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.00000 | + | 10.3923i | 0.200111 | + | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.0000 | − | 83.1384i | 1.59911 | − | 2.76974i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.0526 | + | 22.0000i | 0.634029 | + | 0.732114i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.1865 | − | 10.5000i | 0.603874 | − | 0.348647i | −0.166690 | − | 0.986009i | \(-0.553308\pi\) |
0.770564 | + | 0.637363i | \(0.219975\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.46410 | + | 2.00000i | −0.114645 | + | 0.0661903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.73205 | + | 5.00000i | −0.0571974 | + | 0.165115i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.50000 | + | 9.52628i | −0.181428 | + | 0.314243i | −0.942367 | − | 0.334581i | \(-0.891405\pi\) |
0.760939 | + | 0.648824i | \(0.224739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.5000 | − | 19.9186i | −0.378938 | − | 0.656340i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 30.0000i | − | 0.987462i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.52628 | − | 5.50000i | 0.312884 | − | 0.180644i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | + | 6.92820i | −0.0327737 | + | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.73205 | + | 1.00000i | 0.0567048 | + | 0.0327385i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 49.0000i | − | 1.60076i | −0.599493 | − | 0.800380i | \(-0.704631\pi\) | ||
0.599493 | − | 0.800380i | \(-0.295369\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0000 | −0.554774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0000 | − | 45.0333i | −0.847576 | − | 1.46804i | −0.883365 | − | 0.468685i | \(-0.844728\pi\) |
0.0357896 | − | 0.999359i | \(-0.488605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.5692 | + | 24.0000i | 1.35368 | + | 0.781548i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.66025 | − | 5.00000i | −0.281420 | − | 0.162478i | 0.352646 | − | 0.935757i | \(-0.385282\pi\) |
−0.634066 | + | 0.773279i | \(0.718615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.5000 | + | 28.5788i | 0.535613 | + | 0.927708i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0000 | 0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0000i | 0.907009i | 0.891254 | + | 0.453504i | \(0.149826\pi\) | ||||
−0.891254 | + | 0.453504i | \(0.850174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.92820 | + | 4.00000i | 0.223957 | + | 0.129302i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.00000 | + | 6.92820i | −0.258333 | + | 0.223723i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.0000i | − | 0.996893i | −0.866921 | − | 0.498446i | \(-0.833904\pi\) | ||
0.866921 | − | 0.498446i | \(-0.166096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | + | 6.92820i | 0.128499 | + | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.9904 | + | 2.50000i | −0.416452 | + | 0.0801463i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.5885 | + | 9.00000i | −0.498719 | + | 0.287936i | −0.728184 | − | 0.685381i | \(-0.759636\pi\) |
0.229465 | + | 0.973317i | \(0.426302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0000 | −0.351203 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.3923 | − | 6.00000i | 0.331463 | − | 0.191370i | −0.325027 | − | 0.945705i | \(-0.605374\pi\) |
0.656490 | + | 0.754334i | \(0.272040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.5885 | − | 3.00000i | 0.496186 | − | 0.0954911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.0000 | − | 76.2102i | 1.39912 | − | 2.42334i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.50000 | − | 9.52628i | −0.174713 | − | 0.302612i | 0.765349 | − | 0.643616i | \(-0.222567\pi\) |
−0.940062 | + | 0.341004i | \(0.889233\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0000i | 0.539479i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.866025 | + | 0.500000i | −0.0274273 | + | 0.0158352i | −0.513651 | − | 0.857999i | \(-0.671707\pi\) |
0.486224 | + | 0.873834i | \(0.338374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.500000 | − | 0.866025i | 0.0158193 | − | 0.0273998i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))