Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(543,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.543");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.o (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 543.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.543 |
Dual form | 1600.2.o.c.607.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | + | 1.00000i | 0.577350 | + | 0.577350i | 0.934172 | − | 0.356822i | \(-0.116140\pi\) |
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 1.00000i | −0.377964 | − | 0.377964i | 0.492403 | − | 0.870367i | \(-0.336119\pi\) |
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | − | 3.00000i | 0.727607 | − | 0.727607i | −0.242536 | − | 0.970143i | \(-0.577979\pi\) |
0.970143 | + | 0.242536i | \(0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.00000i | − | 0.436436i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 3.00000i | −0.625543 | + | 0.625543i | −0.946943 | − | 0.321400i | \(-0.895847\pi\) |
0.321400 | + | 0.946943i | \(0.395847\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | − | 4.00000i | 0.769800 | − | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.00000i | − | 1.07763i | −0.842424 | − | 0.538816i | \(-0.818872\pi\) | ||
0.842424 | − | 0.538816i | \(-0.181128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | − | 4.00000i | −0.696311 | − | 0.696311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 3.00000i | −0.457496 | − | 0.457496i | 0.440337 | − | 0.897833i | \(-0.354859\pi\) |
−0.897833 | + | 0.440337i | \(0.854859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00000 | − | 9.00000i | −1.31278 | − | 1.31278i | −0.919354 | − | 0.393431i | \(-0.871288\pi\) |
−0.393431 | − | 0.919354i | \(-0.628712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00000 | − | 5.00000i | 0.686803 | − | 0.686803i | −0.274721 | − | 0.961524i | \(-0.588586\pi\) |
0.961524 | + | 0.274721i | \(0.0885855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | − | 6.00000i | 0.794719 | − | 0.794719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0000i | 1.30189i | 0.759125 | + | 0.650945i | \(0.225627\pi\) | ||||
−0.759125 | + | 0.650945i | \(0.774373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000i | 1.53644i | 0.640184 | + | 0.768221i | \(0.278858\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | + | 1.00000i | −0.125988 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00000 | + | 9.00000i | −1.09952 | + | 1.09952i | −0.105059 | + | 0.994466i | \(0.533503\pi\) |
−0.994466 | + | 0.105059i | \(0.966497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | − | 5.00000i | −0.585206 | − | 0.585206i | 0.351123 | − | 0.936329i | \(-0.385800\pi\) |
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 4.00000i | 0.455842 | + | 0.455842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.00000 | − | 3.00000i | −0.329293 | − | 0.329293i | 0.523025 | − | 0.852318i | \(-0.324804\pi\) |
−0.852318 | + | 0.523025i | \(0.824804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | − | 2.00000i | −0.214423 | − | 0.214423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | − | 6.00000i | 0.622171 | − | 0.622171i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | − | 7.00000i | 0.710742 | − | 0.710742i | −0.255948 | − | 0.966691i | \(-0.582388\pi\) |
0.966691 | + | 0.255948i | \(0.0823876\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000i | 0.402015i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.00000i | − | 0.796030i | −0.917379 | − | 0.398015i | \(-0.869699\pi\) | ||
0.917379 | − | 0.398015i | \(-0.130301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0000 | + | 11.0000i | −1.08386 | + | 1.08386i | −0.0877167 | + | 0.996145i | \(0.527957\pi\) |
−0.996145 | + | 0.0877167i | \(0.972043\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | − | 3.00000i | 0.290021 | − | 0.290021i | −0.547068 | − | 0.837088i | \(-0.684256\pi\) |
0.837088 | + | 0.547068i | \(0.184256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0000 | 1.72409 | 0.862044 | − | 0.506834i | \(-0.169184\pi\) | ||||
0.862044 | + | 0.506834i | \(0.169184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.00000i | − | 0.569495i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | + | 3.00000i | 0.282216 | + | 0.282216i | 0.833992 | − | 0.551776i | \(-0.186050\pi\) |
−0.551776 | + | 0.833992i | \(0.686050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | + | 3.00000i | 0.277350 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | −0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | + | 6.00000i | 0.541002 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | − | 5.00000i | −0.443678 | − | 0.443678i | 0.449568 | − | 0.893246i | \(-0.351578\pi\) |
−0.893246 | + | 0.449568i | \(0.851578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.00000i | − | 0.528271i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | − | 3.00000i | 0.256307 | − | 0.256307i | −0.567243 | − | 0.823550i | \(-0.691990\pi\) |
0.823550 | + | 0.567243i | \(0.191990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.00000i | − | 0.508913i | −0.967084 | − | 0.254457i | \(-0.918103\pi\) | ||
0.967084 | − | 0.254457i | \(-0.0818966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 18.0000i | − | 1.51587i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | − | 12.0000i | 1.00349 | − | 1.00349i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | − | 5.00000i | 0.412393 | − | 0.412393i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | 0.163846 | 0.0819232 | − | 0.996639i | \(-0.473894\pi\) | ||||
0.0819232 | + | 0.996639i | \(0.473894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | − | 3.00000i | −0.242536 | − | 0.242536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | − | 3.00000i | −0.239426 | − | 0.239426i | 0.577186 | − | 0.816612i | \(-0.304151\pi\) |
−0.816612 | + | 0.577186i | \(0.804151\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.00000 | + | 9.00000i | 0.704934 | + | 0.704934i | 0.965465 | − | 0.260531i | \(-0.0838976\pi\) |
−0.260531 | + | 0.965465i | \(0.583898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000 | + | 3.00000i | 0.232147 | + | 0.232147i | 0.813588 | − | 0.581441i | \(-0.197511\pi\) |
−0.581441 | + | 0.813588i | \(0.697511\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.0000 | + | 15.0000i | −1.14043 | + | 1.14043i | −0.152057 | + | 0.988372i | \(0.548590\pi\) |
−0.988372 | + | 0.152057i | \(0.951410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0000 | + | 10.0000i | −0.751646 | + | 0.751646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000i | 0.149487i | 0.997203 | + | 0.0747435i | \(0.0238138\pi\) | ||||
−0.997203 | + | 0.0747435i | \(0.976186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0000 | + | 12.0000i | −0.887066 | + | 0.887066i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | + | 12.0000i | −0.877527 | + | 0.877527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.00000 | −0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.00000i | − | 0.434145i | −0.976156 | − | 0.217072i | \(-0.930349\pi\) | ||
0.976156 | − | 0.217072i | \(-0.0696508\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | − | 5.00000i | −0.359908 | − | 0.359908i | 0.503871 | − | 0.863779i | \(-0.331909\pi\) |
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | + | 5.00000i | 0.356235 | + | 0.356235i | 0.862423 | − | 0.506188i | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.0000 | −1.26962 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | + | 2.00000i | 0.140372 | + | 0.140372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | + | 3.00000i | 0.208514 | + | 0.208514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000i | 1.66011i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | − | 6.00000i | 0.411113 | − | 0.411113i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | + | 6.00000i | −0.407307 | + | 0.407307i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 10.0000i | − | 0.675737i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000i | 1.21081i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.0000 | − | 13.0000i | 0.870544 | − | 0.870544i | −0.121987 | − | 0.992532i | \(-0.538927\pi\) |
0.992532 | + | 0.121987i | \(0.0389267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000 | − | 11.0000i | 0.730096 | − | 0.730096i | −0.240543 | − | 0.970639i | \(-0.577325\pi\) |
0.970639 | + | 0.240543i | \(0.0773255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000i | 0.526361i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0000 | + | 15.0000i | 0.982683 | + | 0.982683i | 0.999853 | − | 0.0171699i | \(-0.00546562\pi\) |
−0.0171699 | + | 0.999853i | \(0.505466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0000 | −1.15948 | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.00000 | − | 7.00000i | −0.449050 | − | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.0000 | + | 18.0000i | 1.14531 | + | 1.14531i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.00000i | − | 0.380235i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | − | 12.0000i | 0.754434 | − | 0.754434i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00000 | − | 3.00000i | 0.187135 | − | 0.187135i | −0.607321 | − | 0.794456i | \(-0.707756\pi\) |
0.794456 | + | 0.607321i | \(0.207756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000i | 0.372822i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | − | 9.00000i | 0.554964 | − | 0.554964i | −0.372906 | − | 0.927869i | \(-0.621638\pi\) |
0.927869 | + | 0.372906i | \(0.121638\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000i | 0.121491i | 0.998153 | + | 0.0607457i | \(0.0193479\pi\) | ||||
−0.998153 | + | 0.0607457i | \(0.980652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | + | 6.00000i | 0.363137 | + | 0.363137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0000 | − | 15.0000i | −0.901263 | − | 0.901263i | 0.0942828 | − | 0.995545i | \(-0.469944\pi\) |
−0.995545 | + | 0.0942828i | \(0.969944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0000 | − | 15.0000i | −0.891657 | − | 0.891657i | 0.103022 | − | 0.994679i | \(-0.467149\pi\) |
−0.994679 | + | 0.103022i | \(0.967149\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | − | 6.00000i | −0.354169 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0000 | 0.820695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.00000 | − | 1.00000i | 0.0584206 | − | 0.0584206i | −0.677293 | − | 0.735714i | \(-0.736847\pi\) |
0.735714 | + | 0.677293i | \(0.236847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.0000 | + | 16.0000i | −0.928414 | + | 0.928414i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 18.0000i | − | 1.04097i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000i | 0.345834i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.00000 | − | 8.00000i | 0.459588 | − | 0.459588i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0000 | − | 15.0000i | 0.856095 | − | 0.856095i | −0.134780 | − | 0.990876i | \(-0.543033\pi\) |
0.990876 | + | 0.134780i | \(0.0430329\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.0000 | −1.25154 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0000i | 1.02069i | 0.859971 | + | 0.510343i | \(0.170482\pi\) | ||||
−0.859971 | + | 0.510343i | \(0.829518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | − | 1.00000i | −0.0565233 | − | 0.0565233i | 0.678280 | − | 0.734803i | \(-0.262726\pi\) |
−0.734803 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | − | 3.00000i | −0.168497 | − | 0.168497i | 0.617822 | − | 0.786318i | \(-0.288015\pi\) |
−0.786318 | + | 0.617822i | \(0.788015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0000 | − | 18.0000i | −1.00155 | − | 1.00155i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.0000 | + | 18.0000i | 0.995402 | + | 0.995402i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.0000i | 0.992372i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | + | 3.00000i | −0.164399 | + | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.0000 | + | 25.0000i | −1.36184 | + | 1.36184i | −0.490261 | + | 0.871576i | \(0.663099\pi\) |
−0.871576 | + | 0.490261i | \(0.836901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.0000i | 1.29967i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0000 | + | 17.0000i | −0.912608 | + | 0.912608i | −0.996477 | − | 0.0838690i | \(-0.973272\pi\) |
0.0838690 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0000i | 1.28103i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | + | 15.0000i | 0.798369 | + | 0.798369i | 0.982838 | − | 0.184469i | \(-0.0590565\pi\) |
−0.184469 | + | 0.982838i | \(0.559057\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | − | 6.00000i | −0.317554 | − | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | + | 5.00000i | 0.262432 | + | 0.262432i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | + | 11.0000i | 0.574195 | + | 0.574195i | 0.933298 | − | 0.359103i | \(-0.116917\pi\) |
−0.359103 | + | 0.933298i | \(0.616917\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.00000i | − | 0.312348i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0000 | −0.519174 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00000 | + | 3.00000i | −0.155334 | + | 0.155334i | −0.780496 | − | 0.625161i | \(-0.785033\pi\) |
0.625161 | + | 0.780496i | \(0.285033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000 | − | 6.00000i | 0.309016 | − | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0000i | 0.924598i | 0.886724 | + | 0.462299i | \(0.152975\pi\) | ||||
−0.886724 | + | 0.462299i | \(0.847025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 10.0000i | − | 0.512316i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.0000 | − | 21.0000i | 1.07305 | − | 1.07305i | 0.0759373 | − | 0.997113i | \(-0.475805\pi\) |
0.997113 | − | 0.0759373i | \(-0.0241949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | + | 3.00000i | −0.152499 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.0000 | 1.31825 | 0.659126 | − | 0.752032i | \(-0.270926\pi\) | ||||
0.659126 | + | 0.752032i | \(0.270926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000i | 0.910299i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | − | 4.00000i | −0.201773 | − | 0.201773i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.00000 | + | 9.00000i | 0.451697 | + | 0.451697i | 0.895918 | − | 0.444220i | \(-0.146519\pi\) |
−0.444220 | + | 0.895918i | \(0.646519\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.0000 | −0.600751 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | + | 18.0000i | 0.896644 | + | 0.896644i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | + | 12.0000i | 0.594818 | + | 0.594818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.0000 | − | 10.0000i | 0.492068 | − | 0.492068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | − | 6.00000i | 0.293821 | − | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0000i | 0.488532i | 0.969708 | + | 0.244266i | \(0.0785470\pi\) | ||||
−0.969708 | + | 0.244266i | \(0.921453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.0000i | − | 0.584844i | −0.956289 | − | 0.292422i | \(-0.905539\pi\) | ||
0.956289 | − | 0.292422i | \(-0.0944612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.00000 | + | 9.00000i | −0.437595 | + | 0.437595i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | − | 12.0000i | 0.580721 | − | 0.580721i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0000 | 1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 30.0000i | − | 1.44505i | −0.691345 | − | 0.722525i | \(-0.742982\pi\) | ||
0.691345 | − | 0.722525i | \(-0.257018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00000 | + | 7.00000i | 0.336399 | + | 0.336399i | 0.855010 | − | 0.518611i | \(-0.173551\pi\) |
−0.518611 | + | 0.855010i | \(0.673551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.0000 | + | 18.0000i | 0.861057 | + | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.0000 | + | 25.0000i | 1.18779 | + | 1.18779i | 0.977678 | + | 0.210108i | \(0.0673814\pi\) |
0.210108 | + | 0.977678i | \(0.432619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.00000 | + | 2.00000i | 0.0945968 | + | 0.0945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.0000i | − | 0.566315i | −0.959073 | − | 0.283158i | \(-0.908618\pi\) | ||
0.959073 | − | 0.283158i | \(-0.0913819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.0000 | −1.13012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0000 | + | 10.0000i | −0.469841 | + | 0.469841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0000 | + | 17.0000i | −0.795226 | + | 0.795226i | −0.982339 | − | 0.187112i | \(-0.940087\pi\) |
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 24.0000i | − | 1.12022i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 40.0000i | − | 1.86299i | −0.363760 | − | 0.931493i | \(-0.618507\pi\) | ||
0.363760 | − | 0.931493i | \(-0.381493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00000 | − | 1.00000i | 0.0464739 | − | 0.0464739i | −0.683488 | − | 0.729962i | \(-0.739538\pi\) |
0.729962 | + | 0.683488i | \(0.239538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0000 | + | 21.0000i | −0.971764 | + | 0.971764i | −0.999612 | − | 0.0278481i | \(-0.991135\pi\) |
0.0278481 | + | 0.999612i | \(0.491135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000 | 0.831163 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 6.00000i | − | 0.276465i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000 | + | 12.0000i | 0.551761 | + | 0.551761i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.00000 | − | 5.00000i | −0.228934 | − | 0.228934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000 | + | 6.00000i | 0.273009 | + | 0.273009i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | − | 1.00000i | −0.0453143 | − | 0.0453143i | 0.684087 | − | 0.729401i | \(-0.260201\pi\) |
−0.729401 | + | 0.684087i | \(0.760201\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0000i | 0.813988i | ||||||||
\(490\) | 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 | + | 6.00000i | −0.270226 | + | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | + | 6.00000i | −0.269137 | + | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.00000i | − | 0.268597i | −0.990941 | − | 0.134298i | \(-0.957122\pi\) | ||
0.990941 | − | 0.134298i | \(-0.0428781\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000i | 0.268060i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0000 | − | 21.0000i | 0.936344 | − | 0.936344i | −0.0617480 | − | 0.998092i | \(-0.519668\pi\) |
0.998092 | + | 0.0617480i | \(0.0196675\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | − | 5.00000i | 0.222058 | − | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0000i | 0.442374i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.0000 | − | 24.0000i | −1.05963 | − | 1.05963i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0000 | + | 36.0000i | 1.58328 | + | 1.58328i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.0000 | −1.31685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0000 | − | 15.0000i | −0.655904 | − | 0.655904i | 0.298504 | − | 0.954408i | \(-0.403512\pi\) |
−0.954408 | + | 0.298504i | \(0.903512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0000 | − | 18.0000i | −0.784092 | − | 0.784092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.00000i | 0.217391i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | 0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0000 | + | 18.0000i | −0.779667 | + | 0.779667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.00000 | + | 2.00000i | −0.0863064 | + | 0.0863064i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.0000i | 0.861461i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.0000i | − | 1.03184i | −0.856637 | − | 0.515920i | \(-0.827450\pi\) | ||
0.856637 | − | 0.515920i | \(-0.172550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.00000 | − | 3.00000i | 0.128271 | − | 0.128271i | −0.640057 | − | 0.768328i | \(-0.721089\pi\) |
0.768328 | + | 0.640057i | \(0.221089\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0000 | 0.512148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.0000 | − | 31.0000i | −1.31351 | − | 1.31351i | −0.918808 | − | 0.394704i | \(-0.870847\pi\) |
−0.394704 | − | 0.918808i | \(-0.629153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0000 | 0.761319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.00000 | + | 1.00000i | 0.0421450 | + | 0.0421450i | 0.727865 | − | 0.685720i | \(-0.240513\pi\) |
−0.685720 | + | 0.727865i | \(0.740513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.00000 | − | 5.00000i | −0.209980 | − | 0.209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 12.0000i | − | 0.503066i | −0.967849 | − | 0.251533i | \(-0.919065\pi\) | ||
0.967849 | − | 0.251533i | \(-0.0809347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000 | − | 6.00000i | 0.250654 | − | 0.250654i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0000 | − | 19.0000i | 0.790980 | − | 0.790980i | −0.190673 | − | 0.981654i | \(-0.561067\pi\) |
0.981654 | + | 0.190673i | \(0.0610671\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 10.0000i | − | 0.415586i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000i | 0.248922i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.0000 | + | 20.0000i | −0.828315 | + | 0.828315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0000 | − | 15.0000i | 0.619116 | − | 0.619116i | −0.326188 | − | 0.945305i | \(-0.605764\pi\) |
0.945305 | + | 0.326188i | \(0.105764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000i | 0.411345i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0000 | + | 15.0000i | 0.615976 | + | 0.615976i | 0.944497 | − | 0.328521i | \(-0.106550\pi\) |
−0.328521 | + | 0.944497i | \(0.606550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.0000 | − | 16.0000i | −0.654836 | − | 0.654836i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.00000 | + | 9.00000i | 0.366508 | + | 0.366508i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.00000 | + | 7.00000i | 0.284121 | + | 0.284121i | 0.834750 | − | 0.550629i | \(-0.185612\pi\) |
−0.550629 | + | 0.834750i | \(0.685612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000i | 0.162088i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.0000 | 2.18461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.00000 | − | 9.00000i | 0.363507 | − | 0.363507i | −0.501596 | − | 0.865102i | \(-0.667253\pi\) |
0.865102 | + | 0.501596i | \(0.167253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000 | − | 15.0000i | 0.603877 | − | 0.603877i | −0.337462 | − | 0.941339i | \(-0.609568\pi\) |
0.941339 | + | 0.337462i | \(0.109568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.0000i | 1.68812i | 0.536247 | + | 0.844061i | \(0.319842\pi\) | ||||
−0.536247 | + | 0.844061i | \(0.680158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.0000i | 0.963087i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.0000 | + | 24.0000i | −0.958468 | + | 0.958468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0000 | −0.717707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0000i | − | 1.19428i | −0.802137 | − | 0.597141i | \(-0.796303\pi\) | ||
0.802137 | − | 0.597141i | \(-0.203697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | − | 12.0000i | −0.476957 | − | 0.476957i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 15.0000i | 0.594322 | + | 0.594322i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.00000 | − | 3.00000i | −0.118308 | − | 0.118308i | 0.645474 | − | 0.763782i | \(-0.276660\pi\) |
−0.763782 | + | 0.645474i | \(0.776660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.00000 | − | 9.00000i | −0.353827 | − | 0.353827i | 0.507705 | − | 0.861531i | \(-0.330494\pi\) |
−0.861531 | + | 0.507705i | \(0.830494\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 40.0000i | − | 1.57014i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.0000 | − | 33.0000i | 1.29139 | − | 1.29139i | 0.357462 | − | 0.933928i | \(-0.383642\pi\) |
0.933928 | − | 0.357462i | \(-0.116358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.00000 | + | 5.00000i | −0.195069 | + | 0.195069i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.0000i | − | 0.856998i | −0.903542 | − | 0.428499i | \(-0.859042\pi\) | ||
0.903542 | − | 0.428499i | \(-0.140958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0000i | 0.466746i | 0.972387 | + | 0.233373i | \(0.0749763\pi\) | ||||
−0.972387 | + | 0.233373i | \(0.925024\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.0000 | + | 18.0000i | −0.699062 | + | 0.699062i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000 | − | 6.00000i | 0.232321 | − | 0.232321i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.0000 | 1.00522 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 48.0000i | − | 1.85302i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0000 | − | 25.0000i | −0.963679 | − | 0.963679i | 0.0356839 | − | 0.999363i | \(-0.488639\pi\) |
−0.999363 | + | 0.0356839i | \(0.988639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.0000 | − | 27.0000i | −1.03769 | − | 1.03769i | −0.999261 | − | 0.0384331i | \(-0.987763\pi\) |
−0.0384331 | − | 0.999261i | \(-0.512237\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.0000 | −0.537271 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.0000 | 0.843042 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.0000 | − | 27.0000i | −1.03313 | − | 1.03313i | −0.999432 | − | 0.0336941i | \(-0.989273\pi\) |
−0.0336941 | − | 0.999432i | \(-0.510727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | + | 6.00000i | 0.228914 | + | 0.228914i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.0000i | 1.14291i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | − | 4.00000i | 0.151947 | − | 0.151947i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 18.0000i | 0.681799 | − | 0.681799i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.0000i | 1.13470i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.0000i | 0.755390i | 0.925930 | + | 0.377695i | \(0.123283\pi\) | ||||
−0.925930 | + | 0.377695i | \(0.876717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | + | 18.0000i | −0.678883 | + | 0.678883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.00000 | + | 8.00000i | −0.300871 | + | 0.300871i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.0000 | −1.57734 | −0.788672 | − | 0.614815i | \(-0.789231\pi\) | ||||
−0.788672 | + | 0.614815i | \(0.789231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0000 | + | 18.0000i | 0.674105 | + | 0.674105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.0000 | + | 24.0000i | 0.896296 | + | 0.896296i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0000 | 0.819323 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.0000 | − | 18.0000i | −0.669427 | − | 0.669427i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.0000 | − | 25.0000i | −0.927199 | − | 0.927199i | 0.0703254 | − | 0.997524i | \(-0.477596\pi\) |
−0.997524 | + | 0.0703254i | \(0.977596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0000 | −0.665754 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0000 | + | 15.0000i | −0.554038 | + | 0.554038i | −0.927604 | − | 0.373566i | \(-0.878135\pi\) |
0.373566 | + | 0.927604i | \(0.378135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.0000 | − | 36.0000i | 1.32608 | − | 1.32608i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30.0000i | − | 1.10357i | −0.833987 | − | 0.551784i | \(-0.813947\pi\) | ||
0.833987 | − | 0.551784i | \(-0.186053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.0000i | 1.32249i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.00000 | − | 9.00000i | 0.330178 | − | 0.330178i | −0.522476 | − | 0.852654i | \(-0.674992\pi\) |
0.852654 | + | 0.522476i | \(0.174992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | + | 3.00000i | −0.109764 | + | 0.109764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.0000i | 1.53260i | 0.642482 | + | 0.766301i | \(0.277905\pi\) | ||||
−0.642482 | + | 0.766301i | \(0.722095\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.00000 | + | 4.00000i | 0.145768 | + | 0.145768i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | + | 9.00000i | 0.327111 | + | 0.327111i | 0.851487 | − | 0.524376i | \(-0.175701\pi\) |
−0.524376 | + | 0.851487i | \(0.675701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.0000 | 0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000 | 0.652499 | 0.326250 | − | 0.945284i | \(-0.394215\pi\) | ||||
0.326250 | + | 0.945284i | \(0.394215\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0000 | − | 18.0000i | −0.651644 | − | 0.651644i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.0000 | − | 30.0000i | −1.08324 | − | 1.08324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40.0000i | − | 1.44244i | −0.692708 | − | 0.721218i | \(-0.743582\pi\) | ||
0.692708 | − | 0.721218i | \(-0.256418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00000 | 0.216085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.00000 | − | 9.00000i | 0.323708 | − | 0.323708i | −0.526480 | − | 0.850188i | \(-0.676489\pi\) |
0.850188 | + | 0.526480i | \(0.176489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.00000 | + | 6.00000i | −0.215249 | + | 0.215249i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 36.0000i | − | 1.28983i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000i | 0.858788i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.00000 | + | 8.00000i | −0.285897 | + | 0.285897i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | − | 15.0000i | 0.534692 | − | 0.534692i | −0.387273 | − | 0.921965i | \(-0.626583\pi\) |
0.921965 | + | 0.387273i | \(0.126583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.0000 | 0.640817 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.00000i | − | 0.213335i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0000 | − | 36.0000i | −1.27840 | − | 1.27840i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) |