Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2548,2,Mod(1145,2548)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2548, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2548.1145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2548.j (of order \(3\), 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: | \(20.3458824350\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 52) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1353.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2548.1353 |
Dual form | 2548.2.j.e.1145.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) | \(1275\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 5.19615i | 0.688247 | − | 1.19208i | −0.284157 | − | 0.958778i | \(-0.591714\pi\) |
0.972404 | − | 0.233301i | \(-0.0749529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | + | 6.92820i | −0.834058 | + | 1.44463i | 0.0607377 | + | 0.998154i | \(0.480655\pi\) |
−0.894795 | + | 0.446476i | \(0.852679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | − | 8.66025i | −0.898027 | − | 1.55543i | −0.830014 | − | 0.557743i | \(-0.811667\pi\) |
−0.0680129 | − | 0.997684i | \(-0.521666\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 5.19615i | 0.493197 | − | 0.854242i | −0.506772 | − | 0.862080i | \(-0.669162\pi\) |
0.999969 | + | 0.00783774i | \(0.00249486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | + | 5.19615i | 0.447214 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000 | − | 1.73205i | 0.145865 | − | 0.252646i | −0.783830 | − | 0.620975i | \(-0.786737\pi\) |
0.929695 | + | 0.368329i | \(0.120070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00000 | + | 8.66025i | 0.650945 | + | 1.12747i | 0.982894 | + | 0.184172i | \(0.0589603\pi\) |
−0.331949 | + | 0.943297i | \(0.607706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | − | 8.66025i | −0.610847 | − | 1.05802i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.380251 | − | 0.924883i | \(-0.375838\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | + | 10.3923i | 0.615587 | + | 1.06623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | − | 6.92820i | 0.394132 | − | 0.682656i | −0.598858 | − | 0.800855i | \(-0.704379\pi\) |
0.992990 | + | 0.118199i | \(0.0377120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.00000 | − | 13.8564i | 0.773389 | − | 1.33955i | −0.162306 | − | 0.986740i | \(-0.551893\pi\) |
0.935695 | − | 0.352809i | \(-0.114773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | + | 12.1244i | 0.670478 | + | 1.16130i | 0.977769 | + | 0.209687i | \(0.0672444\pi\) |
−0.307290 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | − | 13.8564i | −0.746004 | − | 1.29212i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50000 | + | 2.59808i | −0.138675 | + | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000 | − | 13.8564i | 0.698963 | − | 1.21064i | −0.269863 | − | 0.962899i | \(-0.586978\pi\) |
0.968826 | − | 0.247741i | \(-0.0796882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00000 | − | 15.5885i | −0.768922 | − | 1.33181i | −0.938148 | − | 0.346235i | \(-0.887460\pi\) |
0.169226 | − | 0.985577i | \(-0.445873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | − | 1.73205i | −0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | + | 3.46410i | −0.166091 | + | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | − | 5.19615i | −0.244137 | − | 0.422857i | 0.717752 | − | 0.696299i | \(-0.245171\pi\) |
−0.961888 | + | 0.273442i | \(0.911838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.0000 | −1.45521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.0000 | 1.60644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | − | 1.73205i | −0.0798087 | − | 0.138233i | 0.823359 | − | 0.567521i | \(-0.192098\pi\) |
−0.903167 | + | 0.429289i | \(0.858764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000 | − | 8.66025i | 0.391630 | − | 0.678323i | −0.601035 | − | 0.799223i | \(-0.705245\pi\) |
0.992665 | + | 0.120900i | \(0.0385779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.00000 | − | 15.5885i | −0.688247 | − | 1.19208i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.00000 | − | 8.66025i | 0.380143 | − | 0.658427i | −0.610939 | − | 0.791677i | \(-0.709208\pi\) |
0.991082 | + | 0.133250i | \(0.0425415\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | − | 10.3923i | −0.448461 | − | 0.776757i | 0.549825 | − | 0.835280i | \(-0.314694\pi\) |
−0.998286 | + | 0.0585225i | \(0.981361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | + | 10.3923i | 0.441129 | + | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | − | 10.3923i | 0.438763 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.73205i | −0.0719816 | − | 0.124676i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | + | 13.8564i | 0.567105 | + | 0.982255i | 0.996850 | + | 0.0793045i | \(0.0252700\pi\) |
−0.429745 | + | 0.902950i | \(0.641397\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | − | 10.3923i | 0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.0000 | + | 20.7846i | 0.834058 | + | 1.44463i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | + | 6.92820i | −0.272798 | + | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.00000 | −0.401790 | −0.200895 | − | 0.979613i | \(-0.564385\pi\) | ||||
−0.200895 | + | 0.979613i | \(0.564385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.00000 | + | 15.5885i | −0.594737 | + | 1.03011i | 0.398847 | + | 0.917017i | \(0.369410\pi\) |
−0.993584 | + | 0.113097i | \(0.963923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.00000 | + | 8.66025i | −0.327561 | + | 0.567352i | −0.982027 | − | 0.188739i | \(-0.939560\pi\) |
0.654466 | + | 0.756091i | \(0.272893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | + | 3.46410i | 0.130466 | + | 0.225973i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.00000 | + | 5.19615i | 0.193247 | + | 0.334714i | 0.946324 | − | 0.323218i | \(-0.104765\pi\) |
−0.753077 | + | 0.657932i | \(0.771431\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | + | 5.19615i | −0.190885 | + | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0000 | −1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.00000 | − | 1.73205i | 0.0607457 | − | 0.105215i | −0.834053 | − | 0.551684i | \(-0.813985\pi\) |
0.894799 | + | 0.446469i | \(0.147319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0000 | − | 25.9808i | −0.901263 | − | 1.56103i | −0.825857 | − | 0.563880i | \(-0.809308\pi\) |
−0.0754058 | − | 0.997153i | \(-0.524025\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.0000 | −1.79605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.0000 | −1.16445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00000 | − | 6.92820i | 0.231326 | − | 0.400668i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | + | 3.46410i | 0.114520 | + | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.0000 | −1.94048 | −0.970241 | − | 0.242140i | \(-0.922151\pi\) | ||||
−0.970241 | + | 0.242140i | \(0.922151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | + | 3.46410i | 0.111979 | + | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.0000 | −2.00309 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.500000 | − | 0.866025i | −0.0277350 | − | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0000 | − | 19.0526i | 0.604615 | − | 1.04722i | −0.387498 | − | 0.921871i | \(-0.626660\pi\) |
0.992112 | − | 0.125353i | \(-0.0400062\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.00000 | − | 15.5885i | −0.493197 | − | 0.854242i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.0000 | 1.09272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0000 | − | 17.3205i | 0.541530 | − | 0.937958i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | + | 20.7846i | 0.644194 | + | 1.11578i | 0.984487 | + | 0.175457i | \(0.0561403\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.00000 | + | 12.1244i | 0.372572 | + | 0.645314i | 0.989960 | − | 0.141344i | \(-0.0451425\pi\) |
−0.617388 | + | 0.786659i | \(0.711809\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0000 | + | 17.3205i | −0.530745 | + | 0.919277i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0000 | + | 25.9808i | −0.791670 | + | 1.37121i | 0.133263 | + | 0.991081i | \(0.457455\pi\) |
−0.924932 | + | 0.380131i | \(0.875879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.00000 | + | 15.5885i | −0.468521 | + | 0.811503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | − | 19.0526i | 0.569558 | − | 0.986504i | −0.427051 | − | 0.904227i | \(-0.640448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.00000 | + | 15.5885i | −0.459879 | + | 0.796533i | −0.998954 | − | 0.0457244i | \(-0.985440\pi\) |
0.539076 | + | 0.842257i | \(0.318774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00000 | − | 10.3923i | 0.304997 | − | 0.528271i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 48.0000 | 2.42746 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | + | 6.92820i | 0.201262 | + | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | + | 1.73205i | −0.0501886 | + | 0.0869291i | −0.890028 | − | 0.455905i | \(-0.849316\pi\) |
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00000 | + | 8.66025i | 0.249068 | + | 0.431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00000 | + | 12.1244i | 0.346128 | + | 0.599511i | 0.985558 | − | 0.169338i | \(-0.0541630\pi\) |
−0.639430 | + | 0.768849i | \(0.720830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | − | 10.3923i | 0.294528 | − | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.0000 | + | 41.5692i | 1.14808 | + | 1.98853i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | − | 13.8564i | 0.381819 | − | 0.661330i | −0.609503 | − | 0.792784i | \(-0.708631\pi\) |
0.991322 | + | 0.131453i | \(0.0419644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | − | 20.7846i | 0.570137 | − | 0.987507i | −0.426414 | − | 0.904528i | \(-0.640223\pi\) |
0.996551 | − | 0.0829786i | \(-0.0264433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | + | 10.3923i | 0.284427 | + | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.0000 | −1.79333 | −0.896665 | − | 0.442709i | \(-0.854018\pi\) | ||||
−0.896665 | + | 0.442709i | \(0.854018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0000 | + | 29.4449i | −0.795226 | + | 1.37737i | 0.127469 | + | 0.991843i | \(0.459315\pi\) |
−0.922695 | + | 0.385530i | \(0.874019\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0000 | 1.02243 | 0.511213 | − | 0.859454i | \(-0.329196\pi\) | ||||
0.511213 | + | 0.859454i | \(0.329196\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0000 | + | 17.3205i | −0.462745 | + | 0.801498i | −0.999097 | − | 0.0424970i | \(-0.986469\pi\) |
0.536352 | + | 0.843995i | \(0.319802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | + | 6.92820i | 0.183920 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.0000 | −0.824163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | + | 5.19615i | −0.136788 | + | 0.236924i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | + | 3.46410i | −0.0908153 | + | 0.157297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | − | 1.73205i | −0.0453143 | − | 0.0784867i | 0.842479 | − | 0.538730i | \(-0.181096\pi\) |
−0.887793 | + | 0.460243i | \(0.847762\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0000 | −0.902587 | −0.451294 | − | 0.892375i | \(-0.649037\pi\) | ||||
−0.451294 | + | 0.892375i | \(0.649037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | − | 10.3923i | −0.270226 | − | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | + | 10.3923i | −0.269680 | + | 0.467099i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.00000 | − | 12.1244i | 0.313363 | − | 0.542761i | −0.665725 | − | 0.746197i | \(-0.731878\pi\) |
0.979088 | + | 0.203436i | \(0.0652110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.0000 | 1.24846 | 0.624229 | − | 0.781241i | \(-0.285413\pi\) | ||||
0.624229 | + | 0.781241i | \(0.285413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.00000 | − | 12.1244i | 0.310270 | − | 0.537403i | −0.668151 | − | 0.744026i | \(-0.732914\pi\) |
0.978421 | + | 0.206623i | \(0.0662474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | + | 13.8564i | 0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000 | 0.175920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | − | 5.19615i | −0.131432 | − | 0.227648i | 0.792797 | − | 0.609486i | \(-0.208624\pi\) |
−0.924229 | + | 0.381839i | \(0.875291\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0000 | + | 20.7846i | −0.524723 | + | 0.908848i | 0.474862 | + | 0.880060i | \(0.342498\pi\) |
−0.999586 | + | 0.0287874i | \(0.990835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.0000 | + | 51.9615i | −1.30682 | + | 2.26348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | − | 35.5070i | −0.891304 | − | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.0000 | 1.30189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | 0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.0000 | + | 27.7128i | 0.691740 | + | 1.19813i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.0000 | + | 22.5167i | −0.558914 | + | 0.968067i | 0.438674 | + | 0.898646i | \(0.355448\pi\) |
−0.997587 | + | 0.0694205i | \(0.977885\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.0000 | −1.19939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0000 | −1.36822 | −0.684111 | − | 0.729378i | \(-0.739809\pi\) | ||||
−0.684111 | + | 0.729378i | \(0.739809\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00000 | − | 5.19615i | −0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | − | 10.3923i | 0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0000 | − | 36.3731i | −0.889799 | − | 1.54118i | −0.840113 | − | 0.542411i | \(-0.817511\pi\) |
−0.0496855 | − | 0.998765i | \(-0.515822\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.00000 | + | 3.46410i | 0.0842900 | + | 0.145994i | 0.905088 | − | 0.425223i | \(-0.139804\pi\) |
−0.820798 | + | 0.571218i | \(0.806471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | + | 24.2487i | −0.588984 | + | 1.02015i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00000 | + | 10.3923i | 0.251092 | + | 0.434904i | 0.963827 | − | 0.266529i | \(-0.0858769\pi\) |
−0.712735 | + | 0.701434i | \(0.752544\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.00000 | −0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | + | 5.19615i | 0.124892 | + | 0.216319i | 0.921691 | − | 0.387926i | \(-0.126808\pi\) |
−0.796799 | + | 0.604245i | \(0.793475\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | − | 10.3923i | 0.248495 | − | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.00000 | − | 5.19615i | −0.124035 | − | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.0000 | 1.07313 | 0.536567 | − | 0.843857i | \(-0.319721\pi\) | ||||
0.536567 | + | 0.843857i | \(0.319721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.0000 | −2.47226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0000 | + | 22.5167i | −0.533846 | + | 0.924648i | 0.465372 | + | 0.885115i | \(0.345920\pi\) |
−0.999218 | + | 0.0395334i | \(0.987413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.00000 | − | 3.46410i | −0.0817178 | − | 0.141539i | 0.822270 | − | 0.569097i | \(-0.192707\pi\) |
−0.903988 | + | 0.427558i | \(0.859374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.0000 | −1.22169 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00000 | − | 10.3923i | 0.243532 | − | 0.421811i | −0.718186 | − | 0.695852i | \(-0.755027\pi\) |
0.961718 | + | 0.274041i | \(0.0883604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00000 | + | 1.73205i | −0.0404557 | + | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0000 | − | 22.5167i | −0.525065 | − | 0.909439i | −0.999574 | − | 0.0291886i | \(-0.990708\pi\) |
0.474509 | − | 0.880251i | \(-0.342626\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000 | 1.36879 | 0.684394 | − | 0.729112i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729112i | \(0.260067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.00000 | + | 1.73205i | 0.0401934 | + | 0.0696170i | 0.885422 | − | 0.464787i | \(-0.153869\pi\) |
−0.845229 | + | 0.534404i | \(0.820536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.0000 | −1.43541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0000 | 0.875806 | 0.437903 | − | 0.899022i | \(-0.355721\pi\) | ||||
0.437903 | + | 0.899022i | \(0.355721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | − | 13.8564i | 0.317470 | − | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.0000 | − | 25.9808i | 0.593391 | − | 1.02778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0000 | + | 22.5167i | 0.513469 | + | 0.889355i | 0.999878 | + | 0.0156233i | \(0.00497325\pi\) |
−0.486409 | + | 0.873731i | \(0.661693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | 0.0788723 | 0.0394362 | − | 0.999222i | \(-0.487444\pi\) | ||||
0.0394362 | + | 0.999222i | \(0.487444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0000 | + | 27.7128i | 0.629025 | + | 1.08950i | 0.987748 | + | 0.156059i | \(0.0498790\pi\) |
−0.358723 | + | 0.933444i | \(0.616788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.0000 | + | 17.3205i | −0.392534 | + | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0000 | + | 27.7128i | 0.625172 | + | 1.08283i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | − | 1.73205i | −0.0388955 | − | 0.0673690i | 0.845922 | − | 0.533306i | \(-0.179051\pi\) |
−0.884818 | + | 0.465937i | \(0.845717\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | + | 13.8564i | −0.309761 | + | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.00000 | 0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | + | 5.19615i | −0.115299 | + | 0.199704i | −0.917899 | − | 0.396813i | \(-0.870116\pi\) |
0.802600 | + | 0.596518i | \(0.203449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.00000 | + | 1.73205i | 0.0382639 | + | 0.0662751i | 0.884523 | − | 0.466496i | \(-0.154484\pi\) |
−0.846259 | + | 0.532771i | \(0.821151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.00000 | + | 5.19615i | 0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.0000 | + | 29.4449i | −0.646710 | + | 1.12014i | 0.337193 | + | 0.941435i | \(0.390522\pi\) |
−0.983904 | + | 0.178700i | \(0.942811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0000 | + | 27.7128i | −0.606915 | + | 1.05121i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | − | 31.1769i | −0.678883 | − | 1.17586i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0000 | − | 19.0526i | 0.413114 | − | 0.715534i | −0.582115 | − | 0.813107i | \(-0.697775\pi\) |
0.995228 | + | 0.0975728i | \(0.0311079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | − | 10.3923i | −0.225018 | − | 0.389742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 80.0000 | 2.99602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.0000 | − | 34.6410i | 0.745874 | − | 1.29189i | −0.203911 | − | 0.978989i | \(-0.565365\pi\) |
0.949785 | − | 0.312903i | \(-0.101301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | + | 1.73205i | 0.0371391 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | − | 20.7846i | −0.443836 | − | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.0000 | + | 22.5167i | −0.480166 | + | 0.831672i | −0.999741 | − | 0.0227529i | \(-0.992757\pi\) |
0.519575 | + | 0.854425i | \(0.326090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0000 | − | 17.3205i | 0.368355 | − | 0.638009i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.00000 | − | 5.19615i | −0.110357 | − | 0.191144i | 0.805557 | − | 0.592518i | \(-0.201866\pi\) |
−0.915914 | + | 0.401374i | \(0.868533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.0000 | −0.513610 | −0.256805 | − | 0.966463i | \(-0.582670\pi\) | ||||
−0.256805 | + | 0.966463i | \(0.582670\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | − | 31.1769i | −0.659469 | − | 1.14223i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.00000 | + | 15.5885i | −0.329293 | + | 0.570352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.0000 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.0000 | − | 31.1769i | 0.650791 | − | 1.12720i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.00000 | − | 8.66025i | −0.180540 | − | 0.312704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.0000 | −1.94729 | −0.973645 | − | 0.228069i | \(-0.926759\pi\) | ||||
−0.973645 | + | 0.228069i | \(0.926759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.0000 | + | 39.8372i | 0.827253 | + | 1.43284i | 0.900186 | + | 0.435507i | \(0.143431\pi\) |
−0.0729331 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00000 | − | 8.66025i | 0.179605 | − | 0.311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.0000 | + | 31.1769i | −0.644917 | + | 1.11703i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | + | 17.3205i | 0.357828 | + | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.00000 | 0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0000 | − | 32.9090i | −0.677277 | − | 1.17308i | −0.975798 | − | 0.218675i | \(-0.929827\pi\) |
0.298521 | − | 0.954403i | \(-0.403507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00000 | + | 1.73205i | −0.0355110 | + | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | − | 15.5885i | −0.317999 | − | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00000 | − | 3.46410i | 0.0705785 | − | 0.122245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.00000 | − | 5.19615i | −0.105474 | − | 0.182687i | 0.808458 | − | 0.588555i | \(-0.200303\pi\) |
−0.913932 | + | 0.405868i | \(0.866969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.0000 | + | 17.3205i | 0.350285 | + | 0.606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | − | 20.7846i | 0.419827 | − | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | ||||||||
\(823\) | 12.0000 | + | 20.7846i | 0.418294 | + | 0.724506i | 0.995768 | − | 0.0919029i | \(-0.0292950\pi\) |
−0.577474 | + | 0.816409i | \(0.695962\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.00000 | 0.208640 | 0.104320 | − | 0.994544i | \(-0.466733\pi\) | ||||
0.104320 | + | 0.994544i | \(0.466733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0000 | − | 19.0526i | −0.382046 | − | 0.661723i | 0.609309 | − | 0.792933i | \(-0.291447\pi\) |
−0.991355 | + | 0.131210i | \(0.958114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | + | 10.3923i | −0.207639 | + | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0000 | −0.345238 | −0.172619 | − | 0.984989i | \(-0.555223\pi\) | ||||
−0.172619 | + | 0.984989i | \(0.555223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | + | 1.73205i | −0.0344010 | + | 0.0595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | + | 41.5692i | 0.822709 | + | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.0000 | −1.30110 | −0.650548 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.0000 | 1.23117 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0000 | + | 32.9090i | 0.649028 | + | 1.12415i | 0.983355 | + | 0.181692i | \(0.0581574\pi\) |
−0.334328 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | + | 6.92820i | −0.136478 | + | 0.236387i | −0.926161 | − | 0.377128i | \(-0.876912\pi\) |
0.789683 | + | 0.613515i | \(0.210245\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.0000 | + | 29.4449i | −0.578687 | + | 1.00231i | 0.416944 | + | 0.908932i | \(0.363101\pi\) |
−0.995630 | + | 0.0933825i | \(0.970232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0000 | + | 17.3205i | 0.340010 | + | 0.588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.00000 | + | 8.66025i | 0.169419 | + | 0.293442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | − | 5.19615i | 0.101535 | − | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.00000 | + | 15.5885i | −0.303908 | + | 0.526385i | −0.977018 | − | 0.213158i | \(-0.931625\pi\) |
0.673109 | + | 0.739543i | \(0.264958\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.00000 | + | 3.46410i | −0.0671534 | + | 0.116313i | −0.897647 | − | 0.440715i | \(-0.854725\pi\) |
0.830494 | + | 0.557028i | \(0.188058\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | − | 15.5885i | 0.301511 | − | 0.522233i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | − | 10.3923i | −0.200782 | − | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | 0.802232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.0000 | − | 17.3205i | −0.333519 | − | 0.577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.00000 | − | 10.3923i | 0.199447 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.0000 | − | 31.1769i | −0.597680 | − | 1.03521i | −0.993163 | − | 0.116739i | \(-0.962756\pi\) |
0.395482 | − | 0.918474i | \(-0.370577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.00000 | − | 10.3923i | −0.198571 | − | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.00000 | − | 10.3923i | 0.197922 | − | 0.342811i | −0.749933 | − | 0.661514i | \(-0.769914\pi\) |
0.947854 | + | 0.318704i | \(0.103247\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.0000 | −0.329154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.0000 | − | 20.7846i | −0.394132 | − | 0.682656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.0000 | − | 46.7654i | 0.885841 | − | 1.53432i | 0.0410949 | − | 0.999155i | \(-0.486915\pi\) |
0.844746 | − | 0.535167i | \(-0.179751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | + | 20.7846i | 0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259347\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.00000 | − | 8.66025i | −0.162995 | − | 0.282316i | 0.772946 | − | 0.634472i | \(-0.218782\pi\) |
−0.935942 | + | 0.352155i | \(0.885449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | − | 41.5692i | 0.781548 | − | 1.35368i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.0000 | − | 36.3731i | 0.682408 | − | 1.18197i | −0.291835 | − | 0.956469i | \(-0.594266\pi\) |
0.974244 | − | 0.225497i | \(-0.0724007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00000 | + | 1.73205i | 0.0324614 | + | 0.0562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.0000 | 0.842223 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | − | 6.92820i | −0.129437 | − | 0.224191i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.0000 | − | 41.5692i | −0.773389 | − | 1.33955i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000 | 1.60789 | 0.803946 | − | 0.594703i | \(-0.202730\pi\) | ||||
0.803946 | + | 0.594703i | \(0.202730\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000 | − | 41.5692i | 0.770197 | − | 1.33402i | −0.167258 | − | 0.985913i | \(-0.553491\pi\) |
0.937455 | − | 0.348107i | \(-0.113175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.0000 | 1.34096 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.00000 | − | 12.1244i | −0.223265 | − | 0.386707i | 0.732532 | − | 0.680732i | \(-0.238338\pi\) |
−0.955798 | + | 0.294025i | \(0.905005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | − | 10.3923i | 0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | + | 27.7128i | −0.508770 | + | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.00000 | − | 10.3923i | −0.190596 | − | 0.330122i | 0.754852 | − | 0.655895i | \(-0.227709\pi\) |
−0.945448 | + | 0.325773i | \(0.894375\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.0000 | −1.01447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0000 | + | 50.2295i | 0.918439 | + | 1.59078i | 0.801786 | + | 0.597611i | \(0.203883\pi\) |
0.116653 | + | 0.993173i | \(0.462784\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))