Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(188,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.188");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 188.1 | ||
Root | \(0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.188 |
Dual form | 189.2.c.c.188.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.44949i | 0.774597i | ||||||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | −3.46410 | − | 1.41421i | −0.925820 | − | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 5.19615 | 1.26025 | 0.630126 | − | 0.776493i | \(-0.283003\pi\) | ||||
0.630126 | + | 0.776493i | \(0.283003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.34847i | 1.68585i | 0.538028 | + | 0.842927i | \(0.319170\pi\) | ||||
−0.538028 | + | 0.842927i | \(0.680830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | −3.46410 | −0.679366 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.07107i | 1.31306i | 0.754298 | + | 0.656532i | \(0.227977\pi\) | ||||
−0.754298 | + | 0.656532i | \(0.772023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.44949i | − | 0.439941i | −0.975506 | − | 0.219971i | \(-0.929404\pi\) | ||
0.975506 | − | 0.219971i | \(-0.0705962\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 7.34847i | − | 1.26025i | ||||||
\(35\) | −1.73205 | + | 4.24264i | −0.292770 | + | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | 10.3923 | 1.68585 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.89898i | 0.774597i | ||||||||
\(41\) | 8.66025 | 1.35250 | 0.676252 | − | 0.736670i | \(-0.263603\pi\) | ||||
0.676252 | + | 0.736670i | \(0.263603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | −8.66025 | −1.26323 | −0.631614 | − | 0.775283i | \(-0.717607\pi\) | ||||
−0.631614 | + | 0.775283i | \(0.717607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 2.82843i | 0.400000i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3137i | 1.55406i | 0.629465 | + | 0.777029i | \(0.283274\pi\) | ||||
−0.629465 | + | 0.777029i | \(0.716726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.44949i | 0.330289i | ||||||||
\(56\) | −6.92820 | − | 2.82843i | −0.925820 | − | 0.377964i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.0000 | 1.31306 | ||||||||
\(59\) | 8.66025 | 1.12747 | 0.563735 | − | 0.825956i | \(-0.309364\pi\) | ||||
0.563735 | + | 0.825956i | \(0.309364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.44949i | 0.313625i | 0.987628 | + | 0.156813i | \(0.0501218\pi\) | ||||
−0.987628 | + | 0.156813i | \(0.949878\pi\) | |||||||
\(62\) | −3.46410 | −0.439941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 4.24264i | 0.526235i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | + | 2.44949i | 0.717137 | + | 0.292770i | ||||
\(71\) | − | 14.1421i | − | 1.67836i | −0.543852 | − | 0.839181i | \(-0.683035\pi\) | ||
0.543852 | − | 0.839181i | \(-0.316965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | − | 7.07107i | − | 0.821995i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | − | 1.41421i | −0.394771 | − | 0.161165i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0000 | −1.46261 | −0.731307 | − | 0.682048i | \(-0.761089\pi\) | ||||
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 6.92820 | 0.774597 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 12.2474i | − | 1.35250i | ||||||
\(83\) | 1.73205 | 0.190117 | 0.0950586 | − | 0.995472i | \(-0.469696\pi\) | ||||
0.0950586 | + | 0.995472i | \(0.469696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | −0.976187 | ||||||||
\(86\) | − | 7.07107i | − | 0.762493i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.00000 | −0.426401 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | − | 2.44949i | −0.628971 | − | 0.256776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.2474i | 1.26323i | ||||||||
\(95\) | − | 12.7279i | − | 1.30586i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1464i | 1.74096i | 0.492207 | + | 0.870478i | \(0.336190\pi\) | ||||
−0.492207 | + | 0.870478i | \(0.663810\pi\) | |||||||
\(98\) | −6.92820 | + | 7.07107i | −0.699854 | + | 0.714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.46410 | −0.344691 | −0.172345 | − | 0.985037i | \(-0.555135\pi\) | ||||
−0.172345 | + | 0.985037i | \(0.555135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.79796i | − | 0.965422i | −0.875780 | − | 0.482711i | \(-0.839652\pi\) | ||
0.875780 | − | 0.482711i | \(-0.160348\pi\) | |||||||
\(104\) | −6.92820 | −0.679366 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.0000 | 1.55406 | ||||||||
\(107\) | − | 14.1421i | − | 1.36717i | −0.729870 | − | 0.683586i | \(-0.760419\pi\) | ||
0.729870 | − | 0.683586i | \(-0.239581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 3.46410 | 0.330289 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | + | 9.79796i | −0.377964 | + | 0.925820i | ||||
\(113\) | 7.07107i | 0.665190i | 0.943070 | + | 0.332595i | \(0.107924\pi\) | ||||
−0.943070 | + | 0.332595i | \(0.892076\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.89898i | − | 0.456832i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 12.2474i | − | 1.12747i | ||||||
\(119\) | 5.19615 | − | 12.7279i | 0.476331 | − | 1.16677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 3.46410 | 0.313625 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 11.3137i | 1.00000i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | 0.526235 | ||||||||
\(131\) | −17.3205 | −1.51330 | −0.756650 | − | 0.653820i | \(-0.773165\pi\) | ||||
−0.756650 | + | 0.653820i | \(0.773165\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.0000 | + | 7.34847i | 1.56080 | + | 0.637193i | ||||
\(134\) | − | 2.82843i | − | 0.244339i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 14.6969i | − | 1.26025i | ||||||
\(137\) | − | 1.41421i | − | 0.120824i | −0.998174 | − | 0.0604122i | \(-0.980758\pi\) | ||
0.998174 | − | 0.0604122i | \(-0.0192415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2474i | 1.03882i | 0.854527 | + | 0.519408i | \(0.173847\pi\) | ||||
−0.854527 | + | 0.519408i | \(0.826153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20.0000 | −1.67836 | ||||||||
\(143\) | −3.46410 | −0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 12.2474i | − | 1.01710i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.07107i | 0.579284i | 0.957135 | + | 0.289642i | \(0.0935363\pi\) | ||||
−0.957135 | + | 0.289642i | \(0.906464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | 0.406894 | 0.203447 | − | 0.979086i | \(-0.434786\pi\) | ||||
0.203447 | + | 0.979086i | \(0.434786\pi\) | |||||||
\(152\) | 20.7846 | 1.68585 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | + | 4.89898i | −0.161165 | + | 0.394771i | ||||
\(155\) | 4.24264i | 0.340777i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.1464i | − | 1.36843i | −0.729279 | − | 0.684217i | \(-0.760144\pi\) | ||
0.729279 | − | 0.684217i | \(-0.239856\pi\) | |||||||
\(158\) | 18.3848i | 1.46261i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | + | 2.82843i | 0.546019 | + | 0.222911i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000 | 0.391630 | 0.195815 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195815 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 2.44949i | − | 0.190117i | ||||||
\(167\) | −12.1244 | −0.938211 | −0.469105 | − | 0.883142i | \(-0.655424\pi\) | ||||
−0.469105 | + | 0.883142i | \(0.655424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 12.7279i | 0.976187i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.92820 | 0.526742 | 0.263371 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263371 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 4.89898i | −0.151186 | + | 0.370328i | ||||
\(176\) | 5.65685i | 0.426401i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.6969i | 1.10158i | ||||||||
\(179\) | 7.07107i | 0.528516i | 0.964452 | + | 0.264258i | \(0.0851271\pi\) | ||||
−0.964452 | + | 0.264258i | \(0.914873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.6969i | 1.09241i | 0.837650 | + | 0.546207i | \(0.183929\pi\) | ||||
−0.837650 | + | 0.546207i | \(0.816071\pi\) | |||||||
\(182\) | −3.46410 | + | 8.48528i | −0.256776 | + | 0.628971i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | −8.66025 | −0.636715 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.34847i | − | 0.537373i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | −1.30586 | ||||||||
\(191\) | − | 14.1421i | − | 1.02329i | −0.859197 | − | 0.511645i | \(-0.829036\pi\) | ||
0.859197 | − | 0.511645i | \(-0.170964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | −0.0719816 | −0.0359908 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359908 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(194\) | 24.2487 | 1.74096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.41421i | − | 0.100759i | −0.998730 | − | 0.0503793i | \(-0.983957\pi\) | ||
0.998730 | − | 0.0503793i | \(-0.0160430\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 5.65685i | 0.400000i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.89898i | 0.344691i | ||||||||
\(203\) | 17.3205 | + | 7.07107i | 1.21566 | + | 0.496292i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.0000 | −1.04765 | ||||||||
\(206\) | −13.8564 | −0.965422 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.79796i | 0.679366i | ||||||||
\(209\) | 10.3923 | 0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.0000 | −1.36717 | ||||||||
\(215\) | −8.66025 | −0.590624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 2.44949i | −0.407307 | − | 0.166282i | ||||
\(218\) | 9.89949i | 0.670478i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.7279i | − | 0.856173i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.2474i | − | 0.820150i | −0.912052 | − | 0.410075i | \(-0.865503\pi\) | ||
0.912052 | − | 0.410075i | \(-0.134497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0000 | 0.665190 | ||||||||
\(227\) | −13.8564 | −0.919682 | −0.459841 | − | 0.888001i | \(-0.652094\pi\) | ||||
−0.459841 | + | 0.888001i | \(0.652094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.89898i | 0.323734i | 0.986813 | + | 0.161867i | \(0.0517515\pi\) | ||||
−0.986813 | + | 0.161867i | \(0.948248\pi\) | |||||||
\(230\) | −6.92820 | −0.456832 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.0000 | 1.31306 | ||||||||
\(233\) | 7.07107i | 0.463241i | 0.972806 | + | 0.231621i | \(0.0744028\pi\) | ||||
−0.972806 | + | 0.231621i | \(0.925597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.0000 | 0.978492 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.0000 | − | 7.34847i | −1.16677 | − | 0.476331i | ||||
\(239\) | − | 18.3848i | − | 1.18921i | −0.804017 | − | 0.594606i | \(-0.797308\pi\) | ||
0.804017 | − | 0.594606i | \(-0.202692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.44949i | 0.157786i | 0.996883 | + | 0.0788928i | \(0.0251385\pi\) | ||||
−0.996883 | + | 0.0788928i | \(0.974862\pi\) | |||||||
\(242\) | − | 12.7279i | − | 0.818182i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.66025 | + | 8.48528i | 0.553283 | + | 0.542105i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.0000 | 1.14531 | ||||||||
\(248\) | −6.92820 | −0.439941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 17.1464i | − | 1.08444i | ||||||
\(251\) | −5.19615 | −0.327978 | −0.163989 | − | 0.986462i | \(-0.552436\pi\) | ||||
−0.163989 | + | 0.986462i | \(0.552436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | − | 7.07107i | − | 0.443678i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.46410 | 0.216085 | 0.108042 | − | 0.994146i | \(-0.465542\pi\) | ||||
0.108042 | + | 0.994146i | \(0.465542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | − | 12.2474i | 0.310685 | − | 0.761019i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.4949i | 1.51330i | ||||||||
\(263\) | − | 1.41421i | − | 0.0872041i | −0.999049 | − | 0.0436021i | \(-0.986117\pi\) | ||
0.999049 | − | 0.0436021i | \(-0.0138834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 19.5959i | − | 1.20377i | ||||||
\(266\) | 10.3923 | − | 25.4558i | 0.637193 | − | 1.56080i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.9808 | −1.58408 | −0.792038 | − | 0.610472i | \(-0.790980\pi\) | ||||
−0.792038 | + | 0.610472i | \(0.790980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6969i | 0.892775i | 0.894840 | + | 0.446388i | \(0.147290\pi\) | ||||
−0.894840 | + | 0.446388i | \(0.852710\pi\) | |||||||
\(272\) | −20.7846 | −1.26025 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 2.82843i | 0.170561i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | 17.3205 | 1.03882 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0000 | + | 4.89898i | 0.717137 | + | 0.292770i | ||||
\(281\) | − | 14.1421i | − | 0.843649i | −0.906677 | − | 0.421825i | \(-0.861390\pi\) | ||
0.906677 | − | 0.421825i | \(-0.138610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2474i | 0.728035i | 0.931392 | + | 0.364018i | \(0.118595\pi\) | ||||
−0.931392 | + | 0.364018i | \(0.881405\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.89898i | 0.289683i | ||||||||
\(287\) | 8.66025 | − | 21.2132i | 0.511199 | − | 1.25218i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0000 | 0.588235 | ||||||||
\(290\) | −17.3205 | −1.01710 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.0526 | 1.11306 | 0.556531 | − | 0.830827i | \(-0.312132\pi\) | ||||
0.556531 | + | 0.830827i | \(0.312132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0000 | −0.873334 | ||||||||
\(296\) | − | 14.1421i | − | 0.821995i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.0000 | 0.579284 | ||||||||
\(299\) | 6.92820 | 0.400668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000 | − | 12.2474i | 0.288195 | − | 0.705931i | ||||
\(302\) | − | 7.07107i | − | 0.406894i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 29.3939i | − | 1.68585i | ||||||
\(305\) | − | 4.24264i | − | 0.242933i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.00000 | 0.340777 | ||||||||
\(311\) | −12.1244 | −0.687509 | −0.343755 | − | 0.939060i | \(-0.611699\pi\) | ||||
−0.343755 | + | 0.939060i | \(0.611699\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4949i | 1.38453i | 0.721642 | + | 0.692267i | \(0.243388\pi\) | ||||
−0.721642 | + | 0.692267i | \(0.756612\pi\) | |||||||
\(314\) | −24.2487 | −1.36843 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.65685i | − | 0.317721i | −0.987301 | − | 0.158860i | \(-0.949218\pi\) | ||
0.987301 | − | 0.158860i | \(-0.0507819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000 | 0.559893 | ||||||||
\(320\) | 13.8564 | 0.774597 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.00000 | − | 9.79796i | 0.222911 | − | 0.546019i | ||||
\(323\) | 38.1838i | 2.12460i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.89898i | 0.271746i | ||||||||
\(326\) | − | 7.07107i | − | 0.391630i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 24.4949i | − | 1.35250i | ||||||
\(329\) | −8.66025 | + | 21.2132i | −0.477455 | + | 1.16952i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.0000 | −1.37412 | −0.687062 | − | 0.726599i | \(-0.741100\pi\) | ||||
−0.687062 | + | 0.726599i | \(0.741100\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.1464i | 0.938211i | ||||||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.00000 | −0.381314 | −0.190657 | − | 0.981657i | \(-0.561062\pi\) | ||||
−0.190657 | + | 0.981657i | \(0.561062\pi\) | |||||||
\(338\) | − | 9.89949i | − | 0.538462i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.46410 | −0.187592 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | − | 14.1421i | − | 0.762493i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 9.79796i | − | 0.526742i | ||||||
\(347\) | 7.07107i | 0.379595i | 0.981823 | + | 0.189797i | \(0.0607831\pi\) | ||||
−0.981823 | + | 0.189797i | \(0.939217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.5959i | − | 1.04895i | −0.851427 | − | 0.524473i | \(-0.824262\pi\) | ||
0.851427 | − | 0.524473i | \(-0.175738\pi\) | |||||||
\(350\) | 6.92820 | + | 2.82843i | 0.370328 | + | 0.151186i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.66025 | −0.460939 | −0.230469 | − | 0.973080i | \(-0.574026\pi\) | ||||
−0.230469 | + | 0.973080i | \(0.574026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.4949i | 1.30005i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000 | 0.528516 | ||||||||
\(359\) | 11.3137i | 0.597115i | 0.954392 | + | 0.298557i | \(0.0965054\pi\) | ||||
−0.954392 | + | 0.298557i | \(0.903495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.0000 | −1.84211 | ||||||||
\(362\) | 20.7846 | 1.09241 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.89898i | − | 0.255725i | −0.991792 | − | 0.127862i | \(-0.959188\pi\) | ||
0.991792 | − | 0.127862i | \(-0.0408116\pi\) | |||||||
\(368\) | − | 11.3137i | − | 0.589768i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.2474i | 0.636715i | ||||||||
\(371\) | 27.7128 | + | 11.3137i | 1.43878 | + | 0.587378i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.0000 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724071\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | −10.3923 | −0.537373 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.4949i | 1.26323i | ||||||||
\(377\) | 17.3205 | 0.892052 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0000 | 1.18143 | 0.590715 | − | 0.806880i | \(-0.298846\pi\) | ||||
0.590715 | + | 0.806880i | \(0.298846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.0000 | −1.02329 | ||||||||
\(383\) | −1.73205 | −0.0885037 | −0.0442518 | − | 0.999020i | \(-0.514090\pi\) | ||||
−0.0442518 | + | 0.999020i | \(0.514090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 2.44949i | 0.305788 | + | 0.124838i | ||||
\(386\) | 1.41421i | 0.0719816i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.5269i | 1.64918i | 0.565731 | + | 0.824590i | \(0.308594\pi\) | ||||
−0.565731 | + | 0.824590i | \(0.691406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6969i | 0.743256i | ||||||||
\(392\) | −13.8564 | + | 14.1421i | −0.699854 | + | 0.714286i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.00000 | −0.100759 | ||||||||
\(395\) | 22.5167 | 1.13294 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.00000 | 0.400000 | ||||||||
\(401\) | 19.7990i | 0.988714i | 0.869259 | + | 0.494357i | \(0.164597\pi\) | ||||
−0.869259 | + | 0.494357i | \(0.835403\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00000 | −0.298881 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.0000 | − | 24.4949i | 0.496292 | − | 1.21566i | ||||
\(407\) | − | 7.07107i | − | 0.350500i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5959i | 0.968956i | 0.874804 | + | 0.484478i | \(0.160990\pi\) | ||||
−0.874804 | + | 0.484478i | \(0.839010\pi\) | |||||||
\(410\) | 21.2132i | 1.04765i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.66025 | − | 21.2132i | 0.426143 | − | 1.04383i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | −0.147264 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 14.6969i | − | 0.718851i | ||||||
\(419\) | −1.73205 | −0.0846162 | −0.0423081 | − | 0.999105i | \(-0.513471\pi\) | ||||
−0.0423081 | + | 0.999105i | \(0.513471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 22.6274i | 1.10149i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32.0000 | 1.55406 | ||||||||
\(425\) | −10.3923 | −0.504101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 2.44949i | 0.290360 | + | 0.118539i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.2474i | 0.590624i | ||||||||
\(431\) | − | 5.65685i | − | 0.272481i | −0.990676 | − | 0.136241i | \(-0.956498\pi\) | ||
0.990676 | − | 0.136241i | \(-0.0435020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.7423i | − | 1.76572i | −0.469632 | − | 0.882862i | \(-0.655613\pi\) | ||
0.469632 | − | 0.882862i | \(-0.344387\pi\) | |||||||
\(434\) | −3.46410 | + | 8.48528i | −0.166282 | + | 0.407307i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 19.5959i | − | 0.935262i | −0.883924 | − | 0.467631i | \(-0.845108\pi\) | ||
0.883924 | − | 0.467631i | \(-0.154892\pi\) | |||||||
\(440\) | 6.92820 | 0.330289 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.0000 | −0.856173 | ||||||||
\(443\) | 32.5269i | 1.54540i | 0.634771 | + | 0.772700i | \(0.281094\pi\) | ||||
−0.634771 | + | 0.772700i | \(0.718906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | 0.853282 | ||||||||
\(446\) | −17.3205 | −0.820150 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.00000 | + | 19.5959i | −0.377964 | + | 0.925820i | ||||
\(449\) | 24.0416i | 1.13459i | 0.823513 | + | 0.567297i | \(0.192011\pi\) | ||||
−0.823513 | + | 0.567297i | \(0.807989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.2474i | − | 0.576710i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.5959i | 0.919682i | ||||||||
\(455\) | 10.3923 | + | 4.24264i | 0.487199 | + | 0.198898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0000 | 1.49690 | 0.748448 | − | 0.663193i | \(-0.230799\pi\) | ||||
0.748448 | + | 0.663193i | \(0.230799\pi\) | |||||||
\(458\) | 6.92820 | 0.323734 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.1244 | 0.564688 | 0.282344 | − | 0.959313i | \(-0.408888\pi\) | ||||
0.282344 | + | 0.959313i | \(0.408888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | 0.511213 | 0.255607 | − | 0.966781i | \(-0.417725\pi\) | ||||
0.255607 | + | 0.966781i | \(0.417725\pi\) | |||||||
\(464\) | − | 28.2843i | − | 1.31306i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0000 | 0.463241 | ||||||||
\(467\) | 20.7846 | 0.961797 | 0.480899 | − | 0.876776i | \(-0.340311\pi\) | ||||
0.480899 | + | 0.876776i | \(0.340311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | − | 4.89898i | 0.0923514 | − | 0.226214i | ||||
\(470\) | − | 21.2132i | − | 0.978492i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 24.4949i | − | 1.12747i | ||||||
\(473\) | − | 7.07107i | − | 0.325128i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 14.6969i | − | 0.674342i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −26.0000 | −1.18921 | ||||||||
\(479\) | 32.9090 | 1.50365 | 0.751825 | − | 0.659363i | \(-0.229174\pi\) | ||||
0.751825 | + | 0.659363i | \(0.229174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 12.2474i | − | 0.558436i | ||||||
\(482\) | 3.46410 | 0.157786 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 29.6985i | − | 1.34854i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.0000 | −0.996915 | −0.498458 | − | 0.866914i | \(-0.666100\pi\) | ||||
−0.498458 | + | 0.866914i | \(0.666100\pi\) | |||||||
\(488\) | 6.92820 | 0.313625 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.0000 | − | 12.2474i | 0.542105 | − | 0.553283i | ||||
\(491\) | 15.5563i | 0.702048i | 0.936366 | + | 0.351024i | \(0.114166\pi\) | ||||
−0.936366 | + | 0.351024i | \(0.885834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.7423i | 1.65479i | ||||||||
\(494\) | − | 25.4558i | − | 1.14531i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.79796i | 0.439941i | ||||||||
\(497\) | −34.6410 | − | 14.1421i | −1.55386 | − | 0.634361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0000 | 0.761025 | 0.380512 | − | 0.924776i | \(-0.375748\pi\) | ||||
0.380512 | + | 0.924776i | \(0.375748\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.34847i | 0.327978i | ||||||||
\(503\) | −36.3731 | −1.62179 | −0.810897 | − | 0.585188i | \(-0.801021\pi\) | ||||
−0.810897 | + | 0.585188i | \(0.801021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | − | 5.65685i | − | 0.251478i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.66025 | 0.383859 | 0.191930 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191930 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 4.89898i | − | 0.216085i | ||||||
\(515\) | 16.9706i | 0.747812i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2474i | 0.538642i | ||||||||
\(518\) | −17.3205 | − | 7.07107i | −0.761019 | − | 0.310685i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0000 | 0.526235 | ||||||||
\(521\) | −5.19615 | −0.227648 | −0.113824 | − | 0.993501i | \(-0.536310\pi\) | ||||
−0.113824 | + | 0.993501i | \(0.536310\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 36.7423i | − | 1.60663i | −0.595554 | − | 0.803315i | \(-0.703067\pi\) | ||
0.595554 | − | 0.803315i | \(-0.296933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | − | 12.7279i | − | 0.554437i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | −27.7128 | −1.20377 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21.2132i | − | 0.918846i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.4949i | 1.05901i | ||||||||
\(536\) | − | 5.65685i | − | 0.244339i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 36.7423i | 1.58408i | ||||||||
\(539\) | −6.92820 | + | 7.07107i | −0.298419 | + | 0.304572i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | 0.214967 | 0.107483 | − | 0.994207i | \(-0.465721\pi\) | ||||
0.107483 | + | 0.994207i | \(0.465721\pi\) | |||||||
\(542\) | 20.7846 | 0.892775 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1244 | 0.519350 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.0000 | −0.555840 | −0.277920 | − | 0.960604i | \(-0.589645\pi\) | ||||
−0.277920 | + | 0.960604i | \(0.589645\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.00000 | 0.170561 | ||||||||
\(551\) | −51.9615 | −2.21364 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.0000 | + | 31.8434i | −0.552816 | + | 1.35412i | ||||
\(554\) | − | 7.07107i | − | 0.300421i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14.1421i | − | 0.599222i | −0.954062 | − | 0.299611i | \(-0.903143\pi\) | ||
0.954062 | − | 0.299611i | \(-0.0968568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.2474i | − | 0.518012i | ||||||
\(560\) | 6.92820 | − | 16.9706i | 0.292770 | − | 0.717137i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0000 | −0.843649 | ||||||||
\(563\) | 34.6410 | 1.45994 | 0.729972 | − | 0.683477i | \(-0.239533\pi\) | ||||
0.729972 | + | 0.683477i | \(0.239533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12.2474i | − | 0.515254i | ||||||
\(566\) | 17.3205 | 0.728035 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −40.0000 | −1.67836 | ||||||||
\(569\) | − | 39.5980i | − | 1.66003i | −0.557738 | − | 0.830017i | \(-0.688331\pi\) | ||
0.557738 | − | 0.830017i | \(-0.311669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.0000 | −0.795125 | −0.397563 | − | 0.917575i | \(-0.630144\pi\) | ||||
−0.397563 | + | 0.917575i | \(0.630144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −30.0000 | − | 12.2474i | −1.25218 | − | 0.511199i | ||||
\(575\) | − | 5.65685i | − | 0.235907i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 29.3939i | − | 1.22368i | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||
0.790980 | − | 0.611842i | \(-0.209571\pi\) | |||||||
\(578\) | − | 14.1421i | − | 0.588235i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.73205 | − | 4.24264i | 0.0718576 | − | 0.176014i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.0000 | 0.662652 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 26.9444i | − | 1.11306i | ||||||
\(587\) | −13.8564 | −0.571915 | −0.285958 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285958 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | 0.741677 | ||||||||
\(590\) | 21.2132i | 0.873334i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.0000 | −0.821995 | ||||||||
\(593\) | −15.5885 | −0.640141 | −0.320071 | − | 0.947394i | \(-0.603707\pi\) | ||||
−0.320071 | + | 0.947394i | \(0.603707\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00000 | + | 22.0454i | −0.368964 | + | 0.903774i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 9.79796i | − | 0.400668i | ||||||
\(599\) | − | 18.3848i | − | 0.751182i | −0.926786 | − | 0.375591i | \(-0.877440\pi\) | ||
0.926786 | − | 0.375591i | \(-0.122560\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.5403i | 1.89842i | 0.314645 | + | 0.949209i | \(0.398114\pi\) | ||||
−0.314645 | + | 0.949209i | \(0.601886\pi\) | |||||||
\(602\) | −17.3205 | − | 7.07107i | −0.705931 | − | 0.288195i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.5885 | −0.633761 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.2474i | 0.497109i | 0.968618 | + | 0.248554i | \(0.0799554\pi\) | ||||
−0.968618 | + | 0.248554i | \(0.920045\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | −0.242933 | ||||||||
\(611\) | 21.2132i | 0.858194i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | −0.161558 | −0.0807792 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807792 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | + | 9.79796i | −0.161165 | + | 0.394771i | ||||
\(617\) | − | 48.0833i | − | 1.93576i | −0.251414 | − | 0.967880i | \(-0.580896\pi\) | ||
0.251414 | − | 0.967880i | \(-0.419104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.9444i | − | 1.08299i | −0.840705 | − | 0.541493i | \(-0.817859\pi\) | ||
0.840705 | − | 0.541493i | \(-0.182141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.1464i | 0.687509i | ||||||||
\(623\) | −10.3923 | + | 25.4558i | −0.416359 | + | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 34.6410 | 1.38453 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.9808 | 1.03592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | 36.7696i | 1.46261i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.00000 | −0.317721 | ||||||||
\(635\) | −8.66025 | −0.343672 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0000 | + | 12.2474i | −0.475457 | + | 0.485262i | ||||
\(638\) | − | 14.1421i | − | 0.559893i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 19.5959i | − | 0.774597i | ||||||
\(641\) | − | 1.41421i | − | 0.0558581i | −0.999610 | − | 0.0279290i | \(-0.991109\pi\) | ||
0.999610 | − | 0.0279290i | \(-0.00889125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.4949i | − | 0.965984i | −0.875625 | − | 0.482992i | \(-0.839550\pi\) | ||
0.875625 | − | 0.482992i | \(-0.160450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 54.0000 | 2.12460 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.2474i | − | 0.480754i | ||||||
\(650\) | 6.92820 | 0.271746 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 18.3848i | − | 0.719452i | −0.933058 | − | 0.359726i | \(-0.882870\pi\) | ||
0.933058 | − | 0.359726i | \(-0.117130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.0000 | 1.17220 | ||||||||
\(656\) | −34.6410 | −1.35250 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.0000 | + | 12.2474i | 1.16952 | + | 0.477455i | ||||
\(659\) | 11.3137i | 0.440720i | 0.975419 | + | 0.220360i | \(0.0707231\pi\) | ||||
−0.975419 | + | 0.220360i | \(0.929277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.1464i | − | 0.666919i | −0.942764 | − | 0.333459i | \(-0.891784\pi\) | ||
0.942764 | − | 0.333459i | \(-0.108216\pi\) | |||||||
\(662\) | 35.3553i | 1.37412i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 4.89898i | − | 0.190117i | ||||||
\(665\) | −31.1769 | − | 12.7279i | −1.20899 | − | 0.493568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.0000 | −0.774403 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.89898i | 0.189264i | ||||||||
\(671\) | 3.46410 | 0.133730 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 9.89949i | 0.381314i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3205 | 0.665681 | 0.332841 | − | 0.942983i | \(-0.391993\pi\) | ||||
0.332841 | + | 0.942983i | \(0.391993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.0000 | + | 17.1464i | 1.61181 | + | 0.658020i | ||||
\(680\) | 25.4558i | 0.976187i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.89898i | 0.187592i | ||||||||
\(683\) | 24.0416i | 0.919927i | 0.887938 | + | 0.459964i | \(0.152138\pi\) | ||||
−0.887938 | + | 0.459964i | \(0.847862\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.44949i | 0.0935902i | ||||||||
\(686\) | 10.3923 | + | 24.0416i | 0.396780 | + | 0.917914i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0000 | −0.762493 | ||||||||
\(689\) | 27.7128 | 1.05577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 26.9444i | − | 1.02501i | −0.858683 | − | 0.512506i | \(-0.828717\pi\) | ||
0.858683 | − | 0.512506i | \(-0.171283\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.0000 | 0.379595 | ||||||||
\(695\) | − | 21.2132i | − | 0.804663i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.0000 | 1.70450 | ||||||||
\(698\) | −27.7128 | −1.04895 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.41421i | − | 0.0534141i | −0.999643 | − | 0.0267071i | \(-0.991498\pi\) | ||
0.999643 | − | 0.0267071i | \(-0.00850213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.7423i | 1.38576i | ||||||||
\(704\) | 11.3137i | 0.426401i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.2474i | 0.460939i | ||||||||
\(707\) | −3.46410 | + | 8.48528i | −0.130281 | + | 0.319122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | 0.187779 | 0.0938895 | − | 0.995583i | \(-0.470070\pi\) | ||||
0.0938895 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(710\) | 34.6410 | 1.30005 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 29.3939i | 1.10158i | ||||||||
\(713\) | 6.92820 | 0.259463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.0000 | 0.597115 | ||||||||
\(719\) | 15.5885 | 0.581351 | 0.290676 | − | 0.956822i | \(-0.406120\pi\) | ||||
0.290676 | + | 0.956822i | \(0.406120\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | − | 9.79796i | −0.893807 | − | 0.364895i | ||||
\(722\) | 49.4975i | 1.84211i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 14.1421i | − | 0.525226i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.2474i | − | 0.454233i | −0.973868 | − | 0.227116i | \(-0.927070\pi\) | ||
0.973868 | − | 0.227116i | \(-0.0729298\pi\) | |||||||
\(728\) | −6.92820 | + | 16.9706i | −0.256776 | + | 0.628971i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.9808 | 0.960933 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.1918i | − | 1.44758i | −0.690018 | − | 0.723792i | \(-0.742398\pi\) | ||
0.690018 | − | 0.723792i | \(-0.257602\pi\) | |||||||
\(734\) | −6.92820 | −0.255725 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.82843i | − | 0.104186i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0000 | −0.809283 | −0.404642 | − | 0.914475i | \(-0.632604\pi\) | ||||
−0.404642 | + | 0.914475i | \(0.632604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.0000 | − | 39.1918i | 0.587378 | − | 1.43878i | ||||
\(743\) | 7.07107i | 0.259412i | 0.991552 | + | 0.129706i | \(0.0414034\pi\) | ||||
−0.991552 | + | 0.129706i | \(0.958597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 12.2474i | − | 0.448712i | ||||||
\(746\) | 35.3553i | 1.29445i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.6410 | − | 14.1421i | −1.26576 | − | 0.516742i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.0000 | −1.24068 | −0.620339 | − | 0.784334i | \(-0.713005\pi\) | ||||
−0.620339 | + | 0.784334i | \(0.713005\pi\) | |||||||
\(752\) | 34.6410 | 1.26323 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 24.4949i | − | 0.892052i | ||||||
\(755\) | −8.66025 | −0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.0000 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(758\) | − | 32.5269i | − | 1.18143i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36.0000 | −1.30586 | ||||||||
\(761\) | −12.1244 | −0.439508 | −0.219754 | − | 0.975555i | \(-0.570525\pi\) | ||||
−0.219754 | + | 0.975555i | \(0.570525\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.00000 | + | 17.1464i | −0.253417 | + | 0.620742i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.44949i | 0.0885037i | ||||||||
\(767\) | − | 21.2132i | − | 0.765964i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.89898i | 0.176662i | 0.996091 | + | 0.0883309i | \(0.0281533\pi\) | ||||
−0.996091 | + | 0.0883309i | \(0.971847\pi\) | |||||||
\(770\) | 3.46410 | − | 8.48528i | 0.124838 | − | 0.305788i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.5885 | −0.560678 | −0.280339 | − | 0.959901i | \(-0.590447\pi\) | ||||
−0.280339 | + | 0.959901i | \(0.590447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.89898i | 0.175977i | ||||||||
\(776\) | 48.4974 | 1.74096 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.0000 | 1.64918 | ||||||||
\(779\) | 63.6396i | 2.28013i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0000 | −0.715656 | ||||||||
\(782\) | 20.7846 | 0.743256 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.0000 | + | 19.5959i | 0.714286 | + | 0.699854i | ||||
\(785\) | 29.6985i | 1.05998i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.89898i | 0.174630i | 0.996181 | + | 0.0873149i | \(0.0278286\pi\) | ||||
−0.996181 | + | 0.0873149i | \(0.972171\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 31.8434i | − | 1.13294i | ||||||
\(791\) | 17.3205 | + | 7.07107i | 0.615846 | + | 0.251418i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | 0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 |