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 | 607.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.607 |
Dual form | 1600.2.o.d.543.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
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 | −0.356822 | − | 0.934172i | \(-0.616140\pi\) |
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 1.00000i | 0.377964 | − | 0.377964i | −0.492403 | − | 0.870367i | \(-0.663881\pi\) |
0.870367 | + | 0.492403i | \(0.163881\pi\) | |||||||
\(8\) | 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 | \(-0.0497784\pi\) |
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | + | 3.00000i | 0.727607 | + | 0.727607i | 0.970143 | − | 0.242536i | \(-0.0779791\pi\) |
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.00000i | − | 0.436436i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 3.00000i | 0.625543 | + | 0.625543i | 0.946943 | − | 0.321400i | \(-0.104153\pi\) |
−0.321400 | + | 0.946943i | \(0.604153\pi\) | |||||||
\(24\) | 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 | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 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 | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | 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 | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.440337 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.00000 | − | 9.00000i | 1.31278 | − | 1.31278i | 0.393431 | − | 0.919354i | \(-0.371288\pi\) |
0.919354 | − | 0.393431i | \(-0.128712\pi\) | |||||||
\(48\) | 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 | \(-0.411414\pi\) |
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 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 | \(-0.774373\pi\) | ||
0.759125 | − | 0.650945i | \(-0.225627\pi\) | |||||||
\(60\) | 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 | −0.994466 | − | 0.105059i | \(-0.966497\pi\) |
−0.105059 | − | 0.994466i | \(-0.533503\pi\) | |||||||
\(68\) | 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 | −0.936329 | − | 0.351123i | \(-0.885800\pi\) |
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 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 | −0.852318 | − | 0.523025i | \(-0.824804\pi\) |
0.523025 | + | 0.852318i | \(0.324804\pi\) | |||||||
\(84\) | 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 | 0.966691 | − | 0.255948i | \(-0.0823876\pi\) |
−0.255948 | + | 0.966691i | \(0.582388\pi\) | |||||||
\(98\) | 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 | 0.996145 | + | 0.0877167i | \(0.0279570\pi\) |
0.0877167 | + | 0.996145i | \(0.472043\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | + | 3.00000i | 0.290021 | + | 0.290021i | 0.837088 | − | 0.547068i | \(-0.184256\pi\) |
−0.547068 | + | 0.837088i | \(0.684256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.0000 | −1.72409 | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.00000i | − | 0.569495i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | − | 3.00000i | 0.282216 | − | 0.282216i | −0.551776 | − | 0.833992i | \(-0.686050\pi\) |
0.833992 | + | 0.551776i | \(0.186050\pi\) | |||||||
\(114\) | 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 | \(-0.648422\pi\) |
0.893246 | + | 0.449568i | \(0.148422\pi\) | |||||||
\(128\) | 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 | 0.823550 | − | 0.567243i | \(-0.191990\pi\) |
−0.567243 | + | 0.823550i | \(0.691990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000i | 0.508913i | 0.967084 | + | 0.254457i | \(0.0818966\pi\) | ||||
−0.967084 | + | 0.254457i | \(0.918103\pi\) | |||||||
\(140\) | 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 | \(-0.526106\pi\) | ||||
−0.0819232 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(150\) | 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 | \(-0.695849\pi\) |
0.816612 | + | 0.577186i | \(0.195849\pi\) | |||||||
\(158\) | 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 | −0.260531 | − | 0.965465i | \(-0.583898\pi\) |
0.965465 | + | 0.260531i | \(0.0838976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | + | 3.00000i | −0.232147 | + | 0.232147i | −0.813588 | − | 0.581441i | \(-0.802489\pi\) |
0.581441 | + | 0.813588i | \(0.302489\pi\) | |||||||
\(168\) | 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 | 0.988372 | + | 0.152057i | \(0.0485898\pi\) |
0.152057 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(174\) | 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 | \(-0.976186\pi\) | ||
0.997203 | − | 0.0747435i | \(-0.0238138\pi\) | |||||||
\(180\) | 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 | −0.863779 | − | 0.503871i | \(-0.831909\pi\) |
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.00000 | + | 5.00000i | −0.356235 | + | 0.356235i | −0.862423 | − | 0.506188i | \(-0.831054\pi\) |
0.506188 | + | 0.862423i | \(0.331054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 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 | \(-0.461073\pi\) |
−0.992532 | + | 0.121987i | \(0.961073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000 | + | 11.0000i | 0.730096 | + | 0.730096i | 0.970639 | − | 0.240543i | \(-0.0773255\pi\) |
−0.240543 | + | 0.970639i | \(0.577325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000i | 0.526361i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0000 | − | 15.0000i | 0.982683 | − | 0.982683i | −0.0171699 | − | 0.999853i | \(-0.505466\pi\) |
0.999853 | + | 0.0171699i | \(0.00546562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 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 | 0.794456 | − | 0.607321i | \(-0.207756\pi\) |
−0.607321 | + | 0.794456i | \(0.707756\pi\) | |||||||
\(258\) | 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 | \(-0.378362\pi\) |
−0.927869 | + | 0.372906i | \(0.878362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 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 | \(-0.530056\pi\) |
0.995545 | + | 0.0942828i | \(0.0300558\pi\) | |||||||
\(278\) | 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 | −0.994679 | − | 0.103022i | \(-0.967149\pi\) |
0.103022 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(284\) | 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 | \(-0.263153\pi\) |
−0.735714 | + | 0.677293i | \(0.763153\pi\) | |||||||
\(294\) | 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 | 0.990876 | − | 0.134780i | \(-0.0430329\pi\) |
−0.134780 | + | 0.990876i | \(0.543033\pi\) | |||||||
\(308\) | 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 | −0.734803 | − | 0.678280i | \(-0.762726\pi\) |
0.678280 | + | 0.734803i | \(0.262726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | − | 3.00000i | 0.168497 | − | 0.168497i | −0.617822 | − | 0.786318i | \(-0.711985\pi\) |
0.786318 | + | 0.617822i | \(0.211985\pi\) | |||||||
\(318\) | 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 | −0.871576 | − | 0.490261i | \(-0.836901\pi\) |
−0.490261 | − | 0.871576i | \(-0.663099\pi\) | |||||||
\(338\) | 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 | 0.0838690 | − | 0.996477i | \(-0.473272\pi\) |
−0.996477 | + | 0.0838690i | \(0.973272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0000i | 1.28103i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | − | 15.0000i | 0.798369 | − | 0.798369i | −0.184469 | − | 0.982838i | \(-0.559057\pi\) |
0.982838 | + | 0.184469i | \(0.0590565\pi\) | |||||||
\(354\) | 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 | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 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 | \(-0.883083\pi\) |
0.359103 | + | 0.933298i | \(0.383083\pi\) | |||||||
\(368\) | 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 | \(-0.214967\pi\) |
−0.625161 | + | 0.780496i | \(0.714967\pi\) | |||||||
\(374\) | 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 | \(-0.847025\pi\) | ||
0.886724 | − | 0.462299i | \(-0.152975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 10.0000i | − | 0.512316i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.0000 | − | 21.0000i | −1.07305 | − | 1.07305i | −0.997113 | − | 0.0759373i | \(-0.975805\pi\) |
−0.0759373 | − | 0.997113i | \(-0.524195\pi\) | |||||||
\(384\) | 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 | \(-0.729074\pi\) | ||||
−0.659126 | + | 0.752032i | \(0.729074\pi\) | |||||||
\(390\) | 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 | \(-0.853481\pi\) |
0.444220 | + | 0.895918i | \(0.353481\pi\) | |||||||
\(398\) | 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 | \(-0.904120\pi\) | ||
0.954977 | − | 0.296681i | \(-0.0958798\pi\) | |||||||
\(410\) | 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 | \(-0.921453\pi\) | ||
0.969708 | − | 0.244266i | \(-0.0785470\pi\) | |||||||
\(420\) | 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 | −0.518611 | − | 0.855010i | \(-0.673551\pi\) |
0.855010 | + | 0.518611i | \(0.173551\pi\) | |||||||
\(434\) | 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 | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.0000 | − | 25.0000i | 1.18779 | − | 1.18779i | 0.210108 | − | 0.977678i | \(-0.432619\pi\) |
0.977678 | − | 0.210108i | \(-0.0673814\pi\) | |||||||
\(444\) | 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 | \(0.0913819\pi\) | ||||
−0.959073 | + | 0.283158i | \(0.908618\pi\) | |||||||
\(450\) | 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 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) |
−0.982339 | + | 0.187112i | \(0.940087\pi\) | |||||||
\(458\) | 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 | \(-0.260462\pi\) |
−0.729962 | + | 0.683488i | \(0.760462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0000 | − | 21.0000i | −0.971764 | − | 0.971764i | 0.0278481 | − | 0.999612i | \(-0.491135\pi\) |
−0.999612 | + | 0.0278481i | \(0.991135\pi\) | |||||||
\(468\) | 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 | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 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 | \(-0.739799\pi\) |
0.729401 | + | 0.684087i | \(0.239799\pi\) | |||||||
\(488\) | 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 | \(0.0428781\pi\) | ||||
−0.990941 | + | 0.134298i | \(0.957122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000i | 0.268060i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.0000 | − | 21.0000i | −0.936344 | − | 0.936344i | 0.0617480 | − | 0.998092i | \(-0.480332\pi\) |
−0.998092 | + | 0.0617480i | \(0.980332\pi\) | |||||||
\(504\) | 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 | \(-0.600419\pi\) | ||||
−0.310270 | + | 0.950649i | \(0.600419\pi\) | |||||||
\(510\) | 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 | −0.954408 | − | 0.298504i | \(-0.903512\pi\) |
0.298504 | + | 0.954408i | \(0.403512\pi\) | |||||||
\(524\) | 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 | 0.768328 | − | 0.640057i | \(-0.221089\pi\) |
−0.640057 | + | 0.768328i | \(0.721089\pi\) | |||||||
\(548\) | 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 | 0.394704 | − | 0.918808i | \(-0.370847\pi\) |
0.918808 | − | 0.394704i | \(-0.129153\pi\) | |||||||
\(558\) | 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 | −0.685720 | − | 0.727865i | \(-0.740513\pi\) |
0.727865 | + | 0.685720i | \(0.240513\pi\) | |||||||
\(564\) | 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 | \(0.0809347\pi\) | ||||
−0.967849 | + | 0.251533i | \(0.919065\pi\) | |||||||
\(570\) | 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 | 0.981654 | − | 0.190673i | \(-0.0610671\pi\) |
−0.190673 | + | 0.981654i | \(0.561067\pi\) | |||||||
\(578\) | 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 | 0.945305 | − | 0.326188i | \(-0.105764\pi\) |
−0.326188 | + | 0.945305i | \(0.605764\pi\) | |||||||
\(588\) | 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 | −0.328521 | − | 0.944497i | \(-0.606550\pi\) |
0.944497 | + | 0.328521i | \(0.106550\pi\) | |||||||
\(594\) | 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 | \(-0.814388\pi\) |
0.550629 | + | 0.834750i | \(0.314388\pi\) | |||||||
\(608\) | 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 | \(-0.332747\pi\) |
−0.865102 | + | 0.501596i | \(0.832747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000 | + | 15.0000i | 0.603877 | + | 0.603877i | 0.941339 | − | 0.337462i | \(-0.109568\pi\) |
−0.337462 | + | 0.941339i | \(0.609568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 42.0000i | − | 1.68812i | −0.536247 | − | 0.844061i | \(-0.680158\pi\) | ||
0.536247 | − | 0.844061i | \(-0.319842\pi\) | |||||||
\(620\) | 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 | −0.763782 | − | 0.645474i | \(-0.776660\pi\) |
0.645474 | + | 0.763782i | \(0.276660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000 | − | 9.00000i | 0.353827 | − | 0.353827i | −0.507705 | − | 0.861531i | \(-0.669506\pi\) |
0.861531 | + | 0.507705i | \(0.169506\pi\) | |||||||
\(648\) | 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 | −0.933928 | − | 0.357462i | \(-0.883642\pi\) |
−0.357462 | − | 0.933928i | \(-0.616358\pi\) | |||||||
\(654\) | 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 | \(0.140958\pi\) | ||||
−0.903542 | + | 0.428499i | \(0.859042\pi\) | |||||||
\(660\) | 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 | −0.999363 | − | 0.0356839i | \(-0.988639\pi\) |
0.0356839 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.0000 | − | 27.0000i | 1.03769 | − | 1.03769i | 0.0384331 | − | 0.999261i | \(-0.487763\pi\) |
0.999261 | − | 0.0384331i | \(-0.0122367\pi\) | |||||||
\(678\) | 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 | −0.0336941 | + | 0.999432i | \(0.510727\pi\) |
−0.999432 | + | 0.0336941i | \(0.989273\pi\) | |||||||
\(684\) | 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 | \(-0.210769\pi\) | ||||
0.788672 | + | 0.614815i | \(0.210769\pi\) | |||||||
\(710\) | 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 | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 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 | \(-0.522404\pi\) |
0.997524 | + | 0.0703254i | \(0.0224038\pi\) | |||||||
\(728\) | 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 | \(-0.121865\pi\) |
−0.373566 | + | 0.927604i | \(0.621865\pi\) | |||||||
\(734\) | 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 | \(0.186053\pi\) | ||||
−0.833987 | + | 0.551784i | \(0.813947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.0000i | 1.32249i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.00000 | − | 9.00000i | −0.330178 | − | 0.330178i | 0.522476 | − | 0.852654i | \(-0.325008\pi\) |
−0.852654 | + | 0.522476i | \(0.825008\pi\) | |||||||
\(744\) | 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 | \(-0.824299\pi\) |
0.524376 | + | 0.851487i | \(0.324299\pi\) | |||||||
\(758\) | 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 | \(0.256418\pi\) | ||||
−0.692708 | + | 0.721218i | \(0.743582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00000 | 0.216085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | − | 9.00000i | −0.323708 | − | 0.323708i | 0.526480 | − | 0.850188i | \(-0.323511\pi\) |
−0.850188 | + | 0.526480i | \(0.823511\pi\) | |||||||
\(774\) | 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 | 0.921965 | − | 0.387273i | \(-0.126583\pi\) |
−0.387273 | + | 0.921965i | \(0.626583\pi\) | |||||||
\(788\) | 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 | ||||||||
\(796\) | 0 |