Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(649,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.f (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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.649 |
Dual form | 1080.2.f.e.649.1 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22474 | + | 0.224745i | −0.994936 | + | 0.100509i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) | ||
0.981981 | − | 0.188982i | \(-0.0605189\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.449490 | −0.135526 | −0.0677631 | − | 0.997701i | \(-0.521586\pi\) | ||||
−0.0677631 | + | 0.997701i | \(0.521586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.89898i | 1.08138i | 0.841221 | + | 0.540691i | \(0.181837\pi\) | ||||
−0.841221 | + | 0.540691i | \(0.818163\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.89898 | 1.35332 | 0.676659 | − | 0.736296i | \(-0.263427\pi\) | ||||
0.676659 | + | 0.736296i | \(0.263427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.44949i | 0.927783i | 0.885892 | + | 0.463891i | \(0.153547\pi\) | ||||
−0.885892 | + | 0.463891i | \(0.846453\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | − | 1.00000i | 0.979796 | − | 0.200000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.449490 | 0.0834681 | 0.0417341 | − | 0.999129i | \(-0.486712\pi\) | ||||
0.0417341 | + | 0.999129i | \(0.486712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.224745 | + | 2.22474i | 0.0379888 | + | 0.376051i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.101021i | − | 0.0166077i | −0.999966 | − | 0.00830384i | \(-0.997357\pi\) | ||
0.999966 | − | 0.00830384i | \(-0.00264322\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.34847 | 1.45999 | 0.729993 | − | 0.683455i | \(-0.239523\pi\) | ||||
0.729993 | + | 0.683455i | \(0.239523\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.00000i | − | 0.914991i | −0.889212 | − | 0.457496i | \(-0.848747\pi\) | ||
0.889212 | − | 0.457496i | \(-0.151253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.89898i | 0.714590i | 0.933992 | + | 0.357295i | \(0.116301\pi\) | ||||
−0.933992 | + | 0.357295i | \(0.883699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.44949i | − | 0.611184i | −0.952162 | − | 0.305592i | \(-0.901146\pi\) | ||
0.952162 | − | 0.305592i | \(-0.0988544\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | − | 0.101021i | 0.134840 | − | 0.0136216i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.79796 | 1.12646 | 0.563232 | − | 0.826299i | \(-0.309558\pi\) | ||||
0.563232 | + | 0.826299i | \(0.309558\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.876276 | − | 8.67423i | −0.108689 | − | 1.07591i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.7980i | 1.80786i | 0.427682 | + | 0.903929i | \(0.359330\pi\) | ||||
−0.427682 | + | 0.903929i | \(0.640670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5505 | 1.37079 | 0.685397 | − | 0.728170i | \(-0.259629\pi\) | ||||
0.685397 | + | 0.728170i | \(0.259629\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.89898i | − | 0.456341i | −0.973621 | − | 0.228171i | \(-0.926726\pi\) | ||
0.973621 | − | 0.228171i | \(-0.0732744\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.449490i | 0.0512241i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.89898 | 0.438669 | 0.219335 | − | 0.975650i | \(-0.429611\pi\) | ||||
0.219335 | + | 0.975650i | \(0.429611\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.55051i | 0.828776i | 0.910100 | + | 0.414388i | \(0.136004\pi\) | ||||
−0.910100 | + | 0.414388i | \(0.863996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.10102 | + | 10.8990i | 0.119422 | + | 1.18216i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.89898 | 0.408724 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.1237 | + | 1.32577i | −1.34647 | + | 0.136021i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.8990i | − | 1.61430i | −0.590349 | − | 0.807148i | \(-0.701010\pi\) | ||
0.590349 | − | 0.807148i | \(-0.298990\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.10102 | 0.706578 | 0.353289 | − | 0.935514i | \(-0.385063\pi\) | ||||
0.353289 | + | 0.935514i | \(0.385063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7980i | 1.06395i | 0.846759 | + | 0.531977i | \(0.178551\pi\) | ||||
−0.846759 | + | 0.531977i | \(0.821449\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.2474i | 1.37735i | 0.725069 | + | 0.688676i | \(0.241808\pi\) | ||||
−0.725069 | + | 0.688676i | \(0.758192\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.3485i | − | 1.63201i | −0.578047 | − | 0.816003i | \(-0.696185\pi\) | ||
0.578047 | − | 0.816003i | \(-0.303815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | − | 9.89898i | −0.0932505 | − | 0.923085i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.89898 | −0.449089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7980 | −0.981633 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6742 | + | 3.32577i | −0.954733 | + | 0.297465i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.79796i | − | 0.337014i | −0.985700 | − | 0.168507i | \(-0.946105\pi\) | ||
0.985700 | − | 0.168507i | \(-0.0538946\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.10102 | 0.620419 | 0.310210 | − | 0.950668i | \(-0.399601\pi\) | ||||
0.310210 | + | 0.950668i | \(0.399601\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.89898i | − | 0.511506i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.3485i | − | 1.48218i | −0.671406 | − | 0.741090i | \(-0.734309\pi\) | ||
0.671406 | − | 0.741090i | \(-0.265691\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.69694 | −0.822484 | −0.411242 | − | 0.911526i | \(-0.634905\pi\) | ||||
−0.411242 | + | 0.911526i | \(0.634905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.75255i | − | 0.146556i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | + | 0.101021i | −0.0830455 | + | 0.00838930i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.79796 | 0.802680 | 0.401340 | − | 0.915929i | \(-0.368545\pi\) | ||||
0.401340 | + | 0.915929i | \(0.368545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.10102 | −0.496494 | −0.248247 | − | 0.968697i | \(-0.579854\pi\) | ||||
−0.248247 | + | 0.968697i | \(0.579854\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.3485 | + | 1.34847i | −1.07217 | + | 0.108312i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.44949 | 0.350669 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.00000i | 0.0783260i | 0.999233 | + | 0.0391630i | \(0.0124692\pi\) | ||||
−0.999233 | + | 0.0391630i | \(0.987531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.20204i | 0.170399i | 0.996364 | + | 0.0851995i | \(0.0271528\pi\) | ||||
−0.996364 | + | 0.0851995i | \(0.972847\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.20204 | −0.169388 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8990i | 1.28481i | 0.766367 | + | 0.642403i | \(0.222062\pi\) | ||||
−0.766367 | + | 0.642403i | \(0.777938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 4.89898i | −0.0755929 | − | 0.370328i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.34847 | 0.399763 | 0.199882 | − | 0.979820i | \(-0.435944\pi\) | ||||
0.199882 | + | 0.979820i | \(0.435944\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.00000 | −0.371647 | −0.185824 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185824 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0227038 | + | 0.224745i | 0.00166922 | + | 0.0165236i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.20204i | 0.161029i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7980 | 1.57724 | 0.788622 | − | 0.614878i | \(-0.210795\pi\) | ||||
0.788622 | + | 0.614878i | \(0.210795\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.8990i | 1.72029i | 0.510053 | + | 0.860143i | \(0.329626\pi\) | ||||
−0.510053 | + | 0.860143i | \(0.670374\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6969 | −1.53806 | −0.769028 | − | 0.639216i | \(-0.779259\pi\) | ||||
−0.769028 | + | 0.639216i | \(0.779259\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.449490i | − | 0.0315480i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.7980 | + | 2.10102i | −1.45259 | + | 0.146742i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.65153 | −0.183410 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.69694 | −0.529879 | −0.264940 | − | 0.964265i | \(-0.585352\pi\) | ||||
−0.264940 | + | 0.964265i | \(0.585352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.34847 | + | 13.3485i | 0.0919648 | + | 0.910358i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.00000i | − | 0.407307i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.1010 | 1.28487 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.5959i | − | 1.71403i | −0.515292 | − | 0.857015i | \(-0.672316\pi\) | ||
0.515292 | − | 0.857015i | \(-0.327684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 19.1464i | − | 1.27079i | −0.772186 | − | 0.635397i | \(-0.780837\pi\) | ||
0.772186 | − | 0.635397i | \(-0.219163\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.79796 | −0.647467 | −0.323734 | − | 0.946148i | \(-0.604938\pi\) | ||||
−0.323734 | + | 0.946148i | \(0.604938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 26.6969i | − | 1.74897i | −0.485048 | − | 0.874487i | \(-0.661198\pi\) | ||
0.485048 | − | 0.874487i | \(-0.338802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.10102 | − | 10.8990i | −0.0718227 | − | 0.710971i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.3485 | −1.38092 | −0.690459 | − | 0.723372i | \(-0.742591\pi\) | ||||
−0.690459 | + | 0.723372i | \(0.742591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5959 | −0.940206 | −0.470103 | − | 0.882612i | \(-0.655783\pi\) | ||||
−0.470103 | + | 0.882612i | \(0.655783\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.3485 | + | 1.34847i | −0.852802 | + | 0.0861505i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.0000i | 1.46345i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.3485 | 1.85246 | 0.926229 | − | 0.376960i | \(-0.123031\pi\) | ||||
0.926229 | + | 0.376960i | \(0.123031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.00000i | − | 0.125739i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.10102i | − | 0.442949i | −0.975166 | − | 0.221475i | \(-0.928913\pi\) | ||
0.975166 | − | 0.221475i | \(-0.0710870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.101021 | −0.00627711 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.8990i | 1.04204i | 0.853546 | + | 0.521018i | \(0.174448\pi\) | ||||
−0.853546 | + | 0.521018i | \(0.825552\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | + | 9.89898i | 0.0614295 | + | 0.608089i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.4949 | −1.49348 | −0.746740 | − | 0.665116i | \(-0.768382\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.6969 | −0.953521 | −0.476761 | − | 0.879033i | \(-0.658189\pi\) | ||||
−0.476761 | + | 0.879033i | \(0.658189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.20204 | + | 0.449490i | −0.132788 | + | 0.0271053i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.7980i | − | 1.30971i | −0.755753 | − | 0.654856i | \(-0.772729\pi\) | ||
0.755753 | − | 0.654856i | \(-0.227271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.6969 | 1.59261 | 0.796303 | − | 0.604898i | \(-0.206786\pi\) | ||||
0.796303 | + | 0.604898i | \(0.206786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.5959i | − | 0.808193i | −0.914716 | − | 0.404097i | \(-0.867586\pi\) | ||
0.914716 | − | 0.404097i | \(-0.132414\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.34847i | − | 0.551823i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.9444i | 1.69095i | 0.534016 | + | 0.845475i | \(0.320682\pi\) | ||||
−0.534016 | + | 0.845475i | \(0.679318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8990 | − | 1.10102i | 0.634563 | − | 0.0641039i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.3485 | −1.00329 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | −0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.5732 | + | 1.97730i | −1.12076 | + | 0.113220i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000i | 0.913168i | 0.889680 | + | 0.456584i | \(0.150927\pi\) | ||||
−0.889680 | + | 0.456584i | \(0.849073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.4949 | −1.38898 | −0.694489 | − | 0.719503i | \(-0.744370\pi\) | ||||
−0.694489 | + | 0.719503i | \(0.744370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1010i | 0.797037i | 0.917160 | + | 0.398518i | \(0.130475\pi\) | ||||
−0.917160 | + | 0.398518i | \(0.869525\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.5959i | 1.10062i | 0.834962 | + | 0.550308i | \(0.185490\pi\) | ||||
−0.834962 | + | 0.550308i | \(0.814510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.202041 | −0.0113121 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 28.8990i | − | 1.60798i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.89898 | + | 19.1010i | 0.216276 | + | 1.05953i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.89898 | 0.270089 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.1010 | −0.665132 | −0.332566 | − | 0.943080i | \(-0.607914\pi\) | ||||
−0.332566 | + | 0.943080i | \(0.607914\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.32577 | − | 32.9217i | −0.181706 | − | 1.79870i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.1010i | − | 1.09497i | −0.836815 | − | 0.547486i | \(-0.815585\pi\) | ||
0.836815 | − | 0.547486i | \(-0.184415\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.69694 | −0.146047 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.2474i | 0.550112i | 0.961428 | + | 0.275056i | \(0.0886964\pi\) | ||||
−0.961428 | + | 0.275056i | \(0.911304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.79796 | −0.470944 | −0.235472 | − | 0.971881i | \(-0.575664\pi\) | ||||
−0.235472 | + | 0.971881i | \(0.575664\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2020i | 0.755898i | 0.925826 | + | 0.377949i | \(0.123371\pi\) | ||||
−0.925826 | + | 0.377949i | \(0.876629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.6969 | + | 2.59592i | −1.36385 | + | 0.137777i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1464 | 1.01051 | 0.505255 | − | 0.862970i | \(-0.331398\pi\) | ||||
0.505255 | + | 0.862970i | \(0.331398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.7980 | 0.831472 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.876276 | + | 8.67423i | 0.0458664 | + | 0.454030i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7980i | 1.19004i | 0.803709 | + | 0.595022i | \(0.202857\pi\) | ||||
−0.803709 | + | 0.595022i | \(0.797143\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.44949 | −0.231006 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 21.6969i | − | 1.12342i | −0.827333 | − | 0.561712i | \(-0.810143\pi\) | ||
0.827333 | − | 0.561712i | \(-0.189857\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.75255i | 0.0902610i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.8990 | 0.919409 | 0.459704 | − | 0.888072i | \(-0.347955\pi\) | ||||
0.459704 | + | 0.888072i | \(0.347955\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 29.3939i | − | 1.50196i | −0.660327 | − | 0.750978i | \(-0.729582\pi\) | ||
0.660327 | − | 0.750978i | \(-0.270418\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.101021 | − | 1.00000i | −0.00514848 | − | 0.0509647i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.59592 | −0.385128 | −0.192564 | − | 0.981284i | \(-0.561680\pi\) | ||||
−0.192564 | + | 0.981284i | \(0.561680\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.7980 | 1.10237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.67423 | + | 0.876276i | −0.436448 | + | 0.0440902i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 31.5959i | − | 1.58575i | −0.609382 | − | 0.792877i | \(-0.708582\pi\) | ||
0.609382 | − | 0.792877i | \(-0.291418\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3485 | 0.866341 | 0.433171 | − | 0.901312i | \(-0.357395\pi\) | ||||
0.433171 | + | 0.901312i | \(0.357395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.3939i | 1.16533i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0454077i | 0.00225078i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.79796 | −0.138350 | −0.0691751 | − | 0.997605i | \(-0.522037\pi\) | ||||
−0.0691751 | + | 0.997605i | \(0.522037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.89898i | 0.241063i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.69694 | − | 16.7980i | −0.0832994 | − | 0.824579i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.59592 | 0.371085 | 0.185542 | − | 0.982636i | \(-0.440596\pi\) | ||||
0.185542 | + | 0.982636i | \(0.440596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.7980 | 1.40353 | 0.701763 | − | 0.712410i | \(-0.252396\pi\) | ||||
0.701763 | + | 0.712410i | \(0.252396\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.89898 | − | 24.0000i | −0.237635 | − | 1.16417i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.79796i | − | 0.425763i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.0454 | 0.965553 | 0.482777 | − | 0.875744i | \(-0.339628\pi\) | ||||
0.482777 | + | 0.875744i | \(0.339628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.5959i | 1.51840i | 0.650856 | + | 0.759201i | \(0.274410\pi\) | ||||
−0.650856 | + | 0.759201i | \(0.725590\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.2474i | 1.25559i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.20204 | 0.391462 | 0.195731 | − | 0.980658i | \(-0.437292\pi\) | ||||
0.195731 | + | 0.980658i | \(0.437292\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.1010i | 1.47765i | 0.673895 | + | 0.738827i | \(0.264620\pi\) | ||||
−0.673895 | + | 0.738827i | \(0.735380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.6969 | − | 2.69694i | 1.26556 | − | 0.127847i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.59592 | 0.358474 | 0.179237 | − | 0.983806i | \(-0.442637\pi\) | ||||
0.179237 | + | 0.983806i | \(0.442637\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.20204 | −0.197866 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.67423 | + | 0.876276i | −0.406654 | + | 0.0410804i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.59592i | 0.355322i | 0.984092 | + | 0.177661i | \(0.0568531\pi\) | ||||
−0.984092 | + | 0.177661i | \(0.943147\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.20204 | 0.102559 | 0.0512796 | − | 0.998684i | \(-0.483670\pi\) | ||||
0.0512796 | + | 0.998684i | \(0.483670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.59592i | 0.306538i | 0.988184 | + | 0.153269i | \(0.0489801\pi\) | ||||
−0.988184 | + | 0.153269i | \(0.951020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.0000i | − | 0.555294i | −0.960683 | − | 0.277647i | \(-0.910445\pi\) | ||
0.960683 | − | 0.277647i | \(-0.0895545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.7980 | 0.683306 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.69694i | 0.124005i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8990 | − | 5.89898i | 1.32598 | − | 0.270664i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.9444 | 1.13974 | 0.569869 | − | 0.821736i | \(-0.306994\pi\) | ||||
0.569869 | + | 0.821736i | \(0.306994\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.393877 | 0.0179592 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.57321 | + | 35.3712i | 0.162251 | + | 1.60612i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.3939i | 1.83042i | 0.402976 | + | 0.915211i | \(0.367976\pi\) | ||||
−0.402976 | + | 0.915211i | \(0.632024\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.9444 | 1.30624 | 0.653121 | − | 0.757254i | \(-0.273459\pi\) | ||||
0.653121 | + | 0.757254i | \(0.273459\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.20204i | − | 0.0991749i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 11.5505i | − | 0.518111i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.3939 | 0.957721 | 0.478861 | − | 0.877891i | \(-0.341050\pi\) | ||||
0.478861 | + | 0.877891i | \(0.341050\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 18.6515i | − | 0.831631i | −0.909449 | − | 0.415815i | \(-0.863496\pi\) | ||
0.909449 | − | 0.415815i | \(-0.136504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.7980 | + | 1.59592i | −0.703000 | + | 0.0710174i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.1464 | −0.671354 | −0.335677 | − | 0.941977i | \(-0.608965\pi\) | ||||
−0.335677 | + | 0.941977i | \(0.608965\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.89898 | −0.172481 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.42679 | − | 24.0227i | −0.106937 | − | 1.05857i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.20204i | − | 0.0968457i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0454 | −1.05345 | −0.526724 | − | 0.850036i | \(-0.676580\pi\) | ||||
−0.526724 | + | 0.850036i | \(0.676580\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.79796i | 0.122346i | 0.998127 | + | 0.0611731i | \(0.0194842\pi\) | ||||
−0.998127 | + | 0.0611731i | \(0.980516\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 29.3939i | − | 1.28042i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.20204 | 0.139219 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.4495i | 1.57880i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.20204 | − | 31.6969i | −0.138436 | − | 1.37038i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.69694 | −0.116165 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.595918 | −0.0256205 | −0.0128103 | − | 0.999918i | \(-0.504078\pi\) | ||||
−0.0128103 | + | 0.999918i | \(0.504078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.0000i | 0.470326i | 0.971956 | + | 0.235163i | \(0.0755624\pi\) | ||||
−0.971956 | + | 0.235163i | \(0.924438\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.65153 | 0.112959 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.89898i | − | 0.165801i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.8990i | 1.22449i | 0.790668 | + | 0.612245i | \(0.209733\pi\) | ||||
−0.790668 | + | 0.612245i | \(0.790267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.3939 | 0.989456 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 24.0000i | − | 1.01148i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) | ||
0.862686 | − | 0.505740i | \(-0.168780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.89898 | + | 38.5959i | 0.164031 | + | 1.62374i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.89898 | 0.205376 | 0.102688 | − | 0.994714i | \(-0.467256\pi\) | ||||
0.102688 | + | 0.994714i | \(0.467256\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.6969 | 1.66127 | 0.830633 | − | 0.556821i | \(-0.187979\pi\) | ||||
0.830633 | + | 0.556821i | \(0.187979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.44949 | + | 21.7980i | 0.185557 | + | 0.909038i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.1010i | − | 0.587033i | −0.955954 | − | 0.293517i | \(-0.905174\pi\) | ||
0.955954 | − | 0.293517i | \(-0.0948256\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.55051 | 0.313248 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000i | 0.0828315i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 24.9444i | − | 1.02957i | −0.857321 | − | 0.514783i | \(-0.827873\pi\) | ||
0.857321 | − | 0.514783i | \(-0.172127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.3939 | 1.45838 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.6515i | − | 0.765927i | −0.923764 | − | 0.382963i | \(-0.874904\pi\) | ||
0.923764 | − | 0.382963i | \(-0.125096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.8990 | − | 1.10102i | 0.446815 | − | 0.0451374i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.8434 | −1.70967 | −0.854837 | − | 0.518897i | \(-0.826343\pi\) | ||||
−0.854837 | + | 0.518897i | \(0.826343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.5959 | 1.77831 | 0.889157 | − | 0.457602i | \(-0.151291\pi\) | ||||
0.889157 | + | 0.457602i | \(0.151291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0227 | − | 2.42679i | 0.976662 | − | 0.0986629i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 30.5959i | − | 1.24185i | −0.783870 | − | 0.620925i | \(-0.786757\pi\) | ||
0.783870 | − | 0.620925i | \(-0.213243\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.1010 | −0.772745 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.8990i | − | 0.965271i | −0.875821 | − | 0.482635i | \(-0.839680\pi\) | ||
0.875821 | − | 0.482635i | \(-0.160320\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0454i | − | 0.484930i | −0.970160 | − | 0.242465i | \(-0.922044\pi\) | ||
0.970160 | − | 0.242465i | \(-0.0779559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.4949 | −0.542406 | −0.271203 | − | 0.962522i | \(-0.587421\pi\) | ||||
−0.271203 | + | 0.962522i | \(0.587421\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000i | 0.480770i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | − | 9.79796i | 0.920000 | − | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.494897 | −0.0197329 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6969 | 1.02298 | 0.511489 | − | 0.859290i | \(-0.329094\pi\) | ||||
0.511489 | + | 0.859290i | \(0.329094\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.853572 | + | 8.44949i | 0.0338730 | + | 0.335308i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.3939i | 0.926899i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.7980 | −1.33494 | −0.667470 | − | 0.744637i | \(-0.732623\pi\) | ||||
−0.667470 | + | 0.744637i | \(0.732623\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.7980i | − | 1.56948i | −0.619826 | − | 0.784739i | \(-0.712797\pi\) | ||
0.619826 | − | 0.784739i | \(-0.287203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.2474i | 1.03189i | 0.856621 | + | 0.515947i | \(0.172560\pi\) | ||||
−0.856621 | + | 0.515947i | \(0.827440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.20204 | 0.0864377 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.79796i | − | 0.383424i | −0.981451 | − | 0.191712i | \(-0.938596\pi\) | ||
0.981451 | − | 0.191712i | \(-0.0614039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.7980 | + | 1.59592i | −0.617277 | + | 0.0623577i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.7980 | −1.31658 | −0.658291 | − | 0.752764i | \(-0.728720\pi\) | ||||
−0.658291 | + | 0.752764i | \(0.728720\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.7980 | −1.82023 | −0.910115 | − | 0.414356i | \(-0.864007\pi\) | ||||
−0.910115 | + | 0.414356i | \(0.864007\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.32577 | + | 13.1237i | 0.0514110 | + | 0.508916i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.00000i | 0.0774403i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.95459 | −0.152665 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.6969i | 1.76149i | 0.473593 | + | 0.880744i | \(0.342957\pi\) | ||||
−0.473593 | + | 0.880744i | \(0.657043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.6969i | − | 0.564849i | −0.959289 | − | 0.282425i | \(-0.908861\pi\) | ||
0.959289 | − | 0.282425i | \(-0.0911387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8990 | −0.610147 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 14.6515i | − | 0.560625i | −0.959909 | − | 0.280313i | \(-0.909562\pi\) | ||
0.959909 | − | 0.280313i | \(-0.0904381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.89898 | + | 38.5959i | 0.148972 | + | 1.47467i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.3485 | 0.660924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.5959 | −0.517213 | −0.258607 | − | 0.965983i | \(-0.583263\pi\) | ||||
−0.258607 | + | 0.965983i | \(0.583263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.5732 | − | 2.17934i | 0.818319 | − | 0.0826670i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 45.7980i | − | 1.73472i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.44949 | −0.168055 | −0.0840275 | − | 0.996463i | \(-0.526778\pi\) | ||||
−0.0840275 | + | 0.996463i | \(0.526778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.595918i | − | 0.0224755i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 7.10102i | − | 0.267061i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.595918 | 0.0223802 | 0.0111901 | − | 0.999937i | \(-0.496438\pi\) | ||||
0.0111901 | + | 0.999937i | \(0.496438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.6969i | 0.999808i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.393877 | + | 3.89898i | 0.0147302 | + | 0.145814i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.44949 | 0.165938 | 0.0829690 | − | 0.996552i | \(-0.473560\pi\) | ||||
0.0829690 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7980 | 0.402137 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.20204 | − | 0.449490i | 0.0817818 | − | 0.0166936i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.7980i | 1.47602i | 0.674787 | + | 0.738012i | \(0.264235\pi\) | ||||
−0.674787 | + | 0.738012i | \(0.735765\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.3939 | −1.08717 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.2020i | − | 0.524564i | −0.964991 | − | 0.262282i | \(-0.915525\pi\) | ||
0.964991 | − | 0.262282i | \(-0.0844751\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.65153i | − | 0.245012i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.59592 | −0.0587068 | −0.0293534 | − | 0.999569i | \(-0.509345\pi\) | ||||
−0.0293534 | + | 0.999569i | \(0.509345\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.1010i | 0.700748i | 0.936610 | + | 0.350374i | \(0.113946\pi\) | ||||
−0.936610 | + | 0.350374i | \(0.886054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.7980 | + | 2.20204i | −0.798615 | + | 0.0806765i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.2474 | 0.520590 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8990 | 0.580162 | 0.290081 | − | 0.957002i | \(-0.406318\pi\) | ||||
0.290081 | + | 0.957002i | \(0.406318\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.5732 | − | 1.37117i | 0.493980 | − | 0.0499021i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.6969i | 0.570515i | 0.958451 | + | 0.285257i | \(0.0920791\pi\) | ||||
−0.958451 | + | 0.285257i | \(0.907921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.6515 | −0.676117 | −0.338059 | − | 0.941125i | \(-0.609770\pi\) | ||||
−0.338059 | + | 0.941125i | \(0.609770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 19.1010i | − | 0.689698i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.3939 | 0.591178 | 0.295589 | − | 0.955315i | \(-0.404484\pi\) | ||||
0.295589 | + | 0.955315i | \(0.404484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 26.6515i | − | 0.958589i | −0.877654 | − | 0.479294i | \(-0.840893\pi\) | ||
0.877654 | − | 0.479294i | \(-0.159107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.3939 | − | 6.00000i | 1.05586 | − | 0.215526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 55.1464 | 1.97583 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.19184 | −0.185778 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.449490 | − | 4.44949i | −0.0160430 | − | 0.158809i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.2020i | 0.755771i | 0.925852 | + | 0.377886i | \(0.123349\pi\) | ||||
−0.925852 | + | 0.377886i | \(0.876651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.3485 | −0.616841 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.3031i | 1.21814i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4949i | 0.442592i | 0.975207 | + | 0.221296i | \(0.0710287\pi\) | ||||
−0.975207 | + | 0.221296i | \(0.928971\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 |