Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,2,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (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: | \(2.55521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.4 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.2.d.b.161.1 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.73205i | 1.57735i | 0.614810 | + | 0.788675i | \(0.289233\pi\) | ||||
−0.614810 | + | 0.788675i | \(0.710767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.73205 | 1.78855 | 0.894274 | − | 0.447521i | \(-0.147693\pi\) | ||||
0.894274 | + | 0.447521i | \(0.147693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.46410 | −1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.46410i | − 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.73205 | −0.705412 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.00000i | − 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.9282i | 2.82117i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.19615 | −0.457929 | −0.228965 | − | 0.973435i | \(-0.573534\pi\) | ||||
−0.228965 | + | 0.973435i | \(0.573534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.53590 | −0.455461 | −0.227730 | − | 0.973724i | \(-0.573130\pi\) | ||||
−0.227730 | + | 0.973724i | \(0.573130\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.46410 | −1.64749 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.73205i | 0.799863i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.00000i | − 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.46410 | 1.51547 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.46410 | 1.47804 | 0.739022 | − | 0.673681i | \(-0.235288\pi\) | ||||
0.739022 | + | 0.673681i | \(0.235288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.196152i | − 0.0299130i | −0.999888 | − | 0.0149565i | \(-0.995239\pi\) | ||||
0.999888 | − | 0.0149565i | \(-0.00476097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4.46410i | − 0.665469i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.19615 | 0.320342 | 0.160171 | − | 0.987089i | \(-0.448795\pi\) | ||||
0.160171 | + | 0.987089i | \(0.448795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.3923 | 2.19890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 9.46410i | − 1.32524i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.3923i | − 1.42749i | −0.700404 | − | 0.713746i | \(-0.746997\pi\) | ||||
0.700404 | − | 0.713746i | \(-0.253003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.46410 | 0.723738 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.928203i | 0.118844i | 0.998233 | + | 0.0594221i | \(0.0189258\pi\) | ||||
−0.998233 | + | 0.0594221i | \(0.981074\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21.1244 | −2.66142 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.46410 | 0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.196152i | − 0.0239638i | −0.999928 | − | 0.0119819i | \(-0.996186\pi\) | ||||
0.999928 | − | 0.0119819i | \(-0.00381405\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.00000i | − 0.722315i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3923 | 1.94541 | 0.972704 | − | 0.232048i | \(-0.0745426\pi\) | ||||
0.972704 | + | 0.232048i | \(0.0745426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.39230 | 0.748163 | 0.374081 | − | 0.927396i | \(-0.377958\pi\) | ||||
0.374081 | + | 0.927396i | \(0.377958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 2.73205i | − 0.315470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.3923i | 1.86808i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.26795i | 0.139176i | 0.997576 | + | 0.0695878i | \(0.0221684\pi\) | ||||
−0.997576 | + | 0.0695878i | \(0.977832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 3.46410i | − 0.375735i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.9282 | −1.37039 | −0.685193 | − | 0.728361i | \(-0.740282\pi\) | ||||
−0.685193 | + | 0.728361i | \(0.740282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 16.3923i | − 1.71838i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 6.92820i | − 0.718421i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3923 | 1.46132 | 0.730659 | − | 0.682743i | \(-0.239213\pi\) | ||||
0.730659 | + | 0.682743i | \(0.239213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 15.4641i | − 1.55420i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 12.0000i | − 1.19404i | −0.802225 | − | 0.597022i | \(-0.796350\pi\) | ||||
0.802225 | − | 0.597022i | \(-0.203650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19615 | −0.216393 | −0.108197 | − | 0.994130i | \(-0.534508\pi\) | ||||
−0.108197 | + | 0.994130i | \(0.534508\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.9282 | −1.26166 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 13.2679i | − 1.28266i | −0.767265 | − | 0.641331i | \(-0.778383\pi\) | ||||
0.767265 | − | 0.641331i | \(-0.221617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9282i | 1.23830i | 0.785274 | + | 0.619149i | \(0.212522\pi\) | ||||
−0.785274 | + | 0.619149i | \(0.787478\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.3923 | 1.55589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9282 | −1.21618 | −0.608092 | − | 0.793867i | \(-0.708065\pi\) | ||||
−0.608092 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.19615i | − 0.204792i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.4641i | 1.42966i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.3923 | −1.50268 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.8564i | 2.33139i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1962 | −1.25970 | −0.629852 | − | 0.776715i | \(-0.716885\pi\) | ||||
−0.629852 | + | 0.776715i | \(0.716885\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.535898 | 0.0471832 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3923i | 0.907980i | 0.891007 | + | 0.453990i | \(0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 9.46410i | − 0.820642i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.928203 | −0.0793018 | −0.0396509 | − | 0.999214i | \(-0.512625\pi\) | ||||
−0.0396509 | + | 0.999214i | \(0.512625\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000i | 0.505291i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 42.0526i | 3.46844i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000i | 1.47462i | 0.675556 | + | 0.737309i | \(0.263904\pi\) | ||||
−0.675556 | + | 0.737309i | \(0.736096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.46410 | 0.770178 | 0.385089 | − | 0.922880i | \(-0.374171\pi\) | ||||
0.385089 | + | 0.922880i | \(0.374171\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.4641 | 1.25020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.53590i | − 0.203688i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.9282i | − 1.03178i | −0.856654 | − | 0.515891i | \(-0.827461\pi\) | ||||
0.856654 | − | 0.515891i | \(-0.172539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.3923 | 2.25166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3923 | −0.819028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.1962i | − 1.26858i | −0.773095 | − | 0.634290i | \(-0.781292\pi\) | ||||
0.773095 | − | 0.634290i | \(-0.218708\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 9.46410i | − 0.736779i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.19615 | 0.169943 | 0.0849717 | − | 0.996383i | \(-0.472920\pi\) | ||||
0.0849717 | + | 0.996383i | \(0.472920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.92820i | 0.682757i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000i | 0.456172i | 0.973641 | + | 0.228086i | \(0.0732467\pi\) | ||||
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.73205 | −0.357709 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.3923 | −1.23212 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.85641i | 0.587215i | 0.955926 | + | 0.293608i | \(0.0948559\pi\) | ||||
−0.955926 | + | 0.293608i | \(0.905144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.92820i | − 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.53590 | −0.187459 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 12.0000i | − 0.877527i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 18.9282i | − 1.37682i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.39230 | −0.317816 | −0.158908 | − | 0.987293i | \(-0.550797\pi\) | ||||
−0.158908 | + | 0.987293i | \(0.550797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3923 | −1.03598 | −0.517990 | − | 0.855386i | \(-0.673320\pi\) | ||||
−0.517990 | + | 0.855386i | \(0.673320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.46410i | 0.677738i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3923i | 0.740421i | 0.928948 | + | 0.370211i | \(0.120714\pi\) | ||||
−0.928948 | + | 0.370211i | \(0.879286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | 0.491127 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.535898 | 0.0377994 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.46410i | 0.661002i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.80385 | 0.681415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820 | 0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 14.3923i | − 0.990807i | −0.868663 | − | 0.495404i | \(-0.835020\pi\) | ||||
0.868663 | − | 0.495404i | \(-0.164980\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 44.7846i | 3.06859i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.196152 | 0.0133775 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0000 | −0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.4641i | 1.18011i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000i | 0.807207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.12436 | 0.611012 | 0.305506 | − | 0.952190i | \(-0.401174\pi\) | ||||
0.305506 | + | 0.952190i | \(0.401174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.5885i | − 0.835525i | −0.908556 | − | 0.417763i | \(-0.862814\pi\) | ||||
0.908556 | − | 0.417763i | \(-0.137186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.07180i | − 0.335154i | −0.985859 | − | 0.167577i | \(-0.946406\pi\) | ||||
0.985859 | − | 0.167577i | \(-0.0535942\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −44.7846 | −2.94661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.3923 | −1.46697 | −0.733484 | − | 0.679706i | \(-0.762107\pi\) | ||||
−0.733484 | + | 0.679706i | \(0.762107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.19615i | 0.143261i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 32.7846i | − 2.12959i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7846 | −1.34444 | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.392305 | 0.0252706 | 0.0126353 | − | 0.999920i | \(-0.495978\pi\) | ||||
0.0126353 | + | 0.999920i | \(0.495978\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 18.7321i | − 1.20166i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.3923i | 0.983378i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92820 | −0.440831 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.46410 | −0.219529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.53590i | 0.538781i | 0.963031 | + | 0.269391i | \(0.0868223\pi\) | ||||
−0.963031 | + | 0.269391i | \(0.913178\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7.60770i | − 0.478292i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.46410 | 0.592665 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 28.3923i | − 1.76421i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.80385 | −0.604531 | −0.302266 | − | 0.953224i | \(-0.597743\pi\) | ||||
−0.302266 | + | 0.953224i | \(0.597743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3923 | 0.638394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 35.3205i | − 2.16158i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 26.7846i | − 1.63309i | −0.577284 | − | 0.816543i | \(-0.695888\pi\) | ||||
0.577284 | − | 0.816543i | \(-0.304112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3923 | −0.995762 | −0.497881 | − | 0.867245i | \(-0.665888\pi\) | ||||
−0.497881 | + | 0.867245i | \(0.665888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 44.7846 | 2.71049 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 3.46410i | − 0.208893i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7.85641i | − 0.472046i | −0.971748 | − | 0.236023i | \(-0.924156\pi\) | ||||
0.971748 | − | 0.236023i | \(-0.0758440\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3205 | 0.677741 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.60770 | −0.453837 | −0.226919 | − | 0.973914i | \(-0.572865\pi\) | ||||
−0.226919 | + | 0.973914i | \(0.572865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 20.5885i | − 1.22386i | −0.790913 | − | 0.611928i | \(-0.790394\pi\) | ||||
0.790913 | − | 0.611928i | \(-0.209606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.46410i | 0.323665i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 44.7846 | 2.64355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 39.3205i | 2.30501i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 30.0000i | − 1.75262i | −0.481749 | − | 0.876309i | \(-0.659998\pi\) | ||||
0.481749 | − | 0.876309i | \(-0.340002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564 | 0.804030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.60770i | 0.439964i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 0.928203i | − 0.0535007i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.7846 | 1.88343 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.928203 | −0.0531488 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8038i | 1.35856i | 0.733880 | + | 0.679279i | \(0.237707\pi\) | ||||
−0.733880 | + | 0.679279i | \(0.762293\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 6.00000i | − 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.3923 | −1.60998 | −0.804990 | − | 0.593288i | \(-0.797829\pi\) | ||||
−0.804990 | + | 0.593288i | \(0.797829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0000 | 1.24351 | 0.621757 | − | 0.783210i | \(-0.286419\pi\) | ||||
0.621757 | + | 0.783210i | \(0.286419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 21.1244i | − 1.19022i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.60770i | − 0.0902972i | −0.998980 | − | 0.0451486i | \(-0.985624\pi\) | ||||
0.998980 | − | 0.0451486i | \(-0.0143761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.2487 | 2.02321 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.92820i | 0.385496i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.46410i | 0.192154i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −35.3205 | −1.95323 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.3923 | 0.572946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3923i | 1.45065i | 0.688405 | + | 0.725326i | \(0.258311\pi\) | ||||
−0.688405 | + | 0.725326i | \(0.741689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.7846i | 1.46779i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.196152 | 0.0107170 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 35.3205i | − 1.91835i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.78461i | − 0.475713i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.7128 | 2.14429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | 0.323029 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0526i | 0.539650i | 0.962909 | + | 0.269825i | \(0.0869658\pi\) | ||||
−0.962909 | + | 0.269825i | \(0.913034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.7846i | 1.75492i | 0.479650 | + | 0.877460i | \(0.340764\pi\) | ||||
−0.479650 | + | 0.877460i | \(0.659236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.8564 | −0.739600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.7846 | 1.42560 | 0.712800 | − | 0.701367i | \(-0.247427\pi\) | ||||
0.712800 | + | 0.701367i | \(0.247427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3923i | 0.870013i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 44.7846i | − 2.37025i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.7846 | −1.73031 | −0.865153 | − | 0.501508i | \(-0.832779\pi\) | ||||
−0.865153 | + | 0.501508i | \(0.832779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.73205i | − 0.143395i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.39230i | 0.334589i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.0526 | −1.46433 | −0.732166 | − | 0.681126i | \(-0.761490\pi\) | ||||
−0.732166 | + | 0.681126i | \(0.761490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −42.2487 | −2.19938 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 49.1769i | − 2.55314i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.8564i | 1.02813i | 0.857753 | + | 0.514063i | \(0.171860\pi\) | ||||
−0.857753 | + | 0.514063i | \(0.828140\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.73205 | 0.141082 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000i | 0.102733i | 0.998680 | + | 0.0513665i | \(0.0163577\pi\) | ||||
−0.998680 | + | 0.0513665i | \(0.983642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 38.7846i | − 1.98700i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.1962 | 0.725390 | 0.362695 | − | 0.931908i | \(-0.381857\pi\) | ||||
0.362695 | + | 0.931908i | \(0.381857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3923 | −0.835429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.875644i | 0.0445115i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 14.7846i | − 0.749609i | −0.927104 | − | 0.374805i | \(-0.877710\pi\) | ||||
0.927104 | − | 0.374805i | \(-0.122290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.60770 | 0.384738 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.3923 | −1.43220 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 12.0000i | − 0.603786i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5359i | 1.03067i | 0.856990 | + | 0.515334i | \(0.172332\pi\) | ||||
−0.856990 | + | 0.515334i | \(0.827668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.8564 | 1.29444 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.8564 | −1.59083 | −0.795417 | − | 0.606063i | \(-0.792748\pi\) | ||||
−0.795417 | + | 0.606063i | \(0.792748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.78461i | 0.437593i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2.46410i | − 0.122442i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.7846 | 1.03025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3923 | 1.20612 | 0.603061 | − | 0.797695i | \(-0.293948\pi\) | ||||
0.603061 | + | 0.797695i | \(0.293948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.53590i | − 0.125087i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.3923i | 1.39709i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.26795 | −0.0622412 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.3205 | −1.33789 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.9282i | 0.631584i | 0.948828 | + | 0.315792i | \(0.102270\pi\) | ||||
−0.948828 | + | 0.315792i | \(0.897730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.00000i | − 0.292422i | −0.989253 | − | 0.146211i | \(-0.953292\pi\) | ||||
0.989253 | − | 0.146211i | \(-0.0467079\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.80385 | −0.476679 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.39230i | 0.212559i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.7846i | 1.58286i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.60770 | 0.366450 | 0.183225 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183225 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.60770 | 0.269489 | 0.134744 | − | 0.990880i | \(-0.456979\pi\) | ||||
0.134744 | + | 0.990880i | \(0.456979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.39230i | 0.210112i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.07180 | 0.242064 | 0.121032 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121032 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −68.7128 | −3.27204 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 17.6603i | − 0.839064i | −0.907741 | − | 0.419532i | \(-0.862194\pi\) | ||||
0.907741 | − | 0.419532i | \(-0.137806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12.9282i | − 0.612856i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −49.1769 | −2.32599 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.46410 | −0.446639 | −0.223319 | − | 0.974745i | \(-0.571689\pi\) | ||||
−0.223319 | + | 0.974745i | \(0.571689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.7846i | 1.54377i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.8564i | 1.21484i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.3923 | 0.768483 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.7846 | −0.878707 | −0.439353 | − | 0.898314i | \(-0.644792\pi\) | ||||
−0.439353 | + | 0.898314i | \(0.644792\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8564i | 0.646762i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 12.0000i | − 0.558896i | −0.960161 | − | 0.279448i | \(-0.909849\pi\) | ||||
0.960161 | − | 0.279448i | \(-0.0901514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.1962 | −1.21744 | −0.608719 | − | 0.793386i | \(-0.708316\pi\) | ||||
−0.608719 | + | 0.793386i | \(0.708316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.92820 | 0.321288 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.9808i | 1.34107i | 0.741878 | + | 0.670535i | \(0.233935\pi\) | ||||
−0.741878 | + | 0.670535i | \(0.766065\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 0.928203i | − 0.0428604i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.3205 | 1.62748 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.679492 | 0.0312431 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000i | 0.0917663i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 46.3923i | 2.12416i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7846 | −0.947697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 28.3923i | − 1.29189i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3923i | 0.653521i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.8756 | 0.674080 | 0.337040 | − | 0.941490i | \(-0.390574\pi\) | ||||
0.337040 | + | 0.941490i | \(0.390574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 44.2487 | 2.00100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.60770i | 0.0725543i | 0.999342 | + | 0.0362771i | \(0.0115499\pi\) | ||||
−0.999342 | + | 0.0362771i | \(0.988450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.4641 | 0.695060 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 77.5692 | 3.47946 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.5692i | 1.95043i | 0.221268 | + | 0.975213i | \(0.428980\pi\) | ||||
−0.221268 | + | 0.975213i | \(0.571020\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000i | 0.268060i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.19615 | −0.0979216 | −0.0489608 | − | 0.998801i | \(-0.515591\pi\) | ||||
−0.0489608 | + | 0.998801i | \(0.515591\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.73205i | 0.121335i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 32.7846i | − 1.45315i | −0.687086 | − | 0.726576i | \(-0.741110\pi\) | ||||
0.687086 | − | 0.726576i | \(-0.258890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.2487 | 1.33812 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.19615i | − 0.0967740i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.60770i | 0.334586i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.3923 | −0.719542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.14359 | 0.181534 | 0.0907671 | − | 0.995872i | \(-0.471068\pi\) | ||||
0.0907671 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.9808i | 1.61706i | 0.588458 | + | 0.808528i | \(0.299735\pi\) | ||||
−0.588458 | + | 0.808528i | \(0.700265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 12.9282i | − 0.564233i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.78461 | 0.382664 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 26.7846i | − 1.16235i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 32.7846i | − 1.42006i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2679 | 0.573623 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.4641 | −0.926244 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 53.3205i | 2.29668i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 39.7128i | − 1.70739i | −0.520776 | − | 0.853694i | \(-0.674357\pi\) | ||||
0.520776 | − | 0.853694i | \(-0.325643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.9282 | 0.812287 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.9282 | −0.553783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.1962i | 0.521470i | 0.965410 | + | 0.260735i | \(0.0839649\pi\) | ||||
−0.965410 | + | 0.260735i | \(0.916035\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.14359i | − 0.176844i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56.7846 | −2.41473 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.3923i | 0.695815i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.7846i | 1.13490i | 0.823408 | + | 0.567450i | \(0.192070\pi\) | ||||
−0.823408 | + | 0.567450i | \(0.807930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.679492 | −0.0287394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.7846 | 1.38417 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.8038i | 0.666053i | 0.942918 | + | 0.333026i | \(0.108070\pi\) | ||||
−0.942918 | + | 0.333026i | \(0.891930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 12.9282i | − 0.543894i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.6603 | −0.489685 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.24871 | 0.261960 | 0.130980 | − | 0.991385i | \(-0.458188\pi\) | ||||
0.130980 | + | 0.991385i | \(0.458188\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 9.60770i | − 0.402070i | −0.979584 | − | 0.201035i | \(-0.935570\pi\) | ||||
0.979584 | − | 0.201035i | \(-0.0644304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 12.0000i | − 0.501307i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.19615 | 0.0915859 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.00000 | −0.0832611 | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416305 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 39.3205i | − 1.63410i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000i | 0.248922i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.0000 | 1.49097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.4641 | −0.639362 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 31.5167i | − 1.30083i | −0.759578 | − | 0.650416i | \(-0.774595\pi\) | ||||
0.759578 | − | 0.650416i | \(-0.225405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.07180i | 0.208980i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.3923 | −1.16790 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9282 | 0.530898 | 0.265449 | − | 0.964125i | \(-0.414480\pi\) | ||||
0.265449 | + | 0.964125i | \(0.414480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 16.3923i | − 0.672019i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.9282i | 0.774680i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.392305 | 0.0160024 | 0.00800122 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800122 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.875644i | 0.0356590i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1.00000i | − 0.0406558i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.19615 | 0.0891391 | 0.0445695 | − | 0.999006i | \(-0.485808\pi\) | ||||
0.0445695 | + | 0.999006i | \(0.485808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 7.60770i | − 0.307774i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.3923i | 1.38909i | 0.719448 | + | 0.694546i | \(0.244395\pi\) | ||||
−0.719448 | + | 0.694546i | \(0.755605\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.8564 | −1.04263 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.3923 | 1.38458 | 0.692291 | − | 0.721618i | \(-0.256601\pi\) | ||||
0.692291 | + | 0.721618i | \(0.256601\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 34.7846i | − 1.39811i | −0.715067 | − | 0.699056i | \(-0.753604\pi\) | ||||
0.715067 | − | 0.699056i | \(-0.246396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.78461i | 0.352514i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −61.1769 | −2.45100 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.9282i | 0.755920i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.7846i | 0.828737i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.5359 | 0.578665 | 0.289332 | − | 0.957229i | \(-0.406567\pi\) | ||||
0.289332 | + | 0.957229i | \(0.406567\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.3205 | 1.56285 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 14.1962i | − 0.563357i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 53.3205i | − 2.11264i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −73.1769 | −2.89483 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.3923 | 0.647457 | 0.323729 | − | 0.946150i | \(-0.395064\pi\) | ||||
0.323729 | + | 0.946150i | \(0.395064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.5885i | − 0.811929i | −0.913889 | − | 0.405965i | \(-0.866936\pi\) | ||||
0.913889 | − | 0.405965i | \(-0.133064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.535898i | 0.0211010i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.41154 | −0.212750 | −0.106375 | − | 0.994326i | \(-0.533924\pi\) | ||||
−0.106375 | + | 0.994326i | \(0.533924\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.7846 | −0.815867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 32.7846i | − 1.28493i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 43.1769i | − 1.68964i | −0.535048 | − | 0.844822i | \(-0.679707\pi\) | ||||
0.535048 | − | 0.844822i | \(-0.320293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3923 | −0.406061 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.5359 | −1.11329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 28.6410i | − 1.11570i | −0.829943 | − | 0.557848i | \(-0.811627\pi\) | ||||
0.829943 | − | 0.557848i | \(-0.188373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.5692i | 1.85023i | 0.379689 | + | 0.925114i | \(0.376031\pi\) | ||||
−0.379689 | + | 0.925114i | \(0.623969\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −32.7846 | −1.27325 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.46410 | 0.367002 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.9282i | 0.963780i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.21539 | −0.124129 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1769 | 0.893404 | 0.446702 | − | 0.894683i | \(-0.352598\pi\) | ||||
0.446702 | + | 0.894683i | \(0.352598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.00000i | 0.153960i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.1769i | 0.737029i | 0.929622 | + | 0.368514i | \(0.120133\pi\) | ||||
−0.929622 | + | 0.368514i | \(0.879867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 68.1051 | 2.61363 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.3923 | 1.31792 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.66025i | 0.216584i | 0.994119 | + | 0.108292i | \(0.0345381\pi\) | ||||
−0.994119 | + | 0.108292i | \(0.965462\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 0.928203i | − 0.0354648i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8564 | 0.528655 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.3923i | 1.00401i | 0.864865 | + | 0.502005i | \(0.167404\pi\) | ||||
−0.864865 | + | 0.502005i | \(0.832596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 73.1769i | − 2.77976i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0000 | −0.379322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.7846 | −1.24181 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 61.1769i | − 2.31392i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.7846i | 1.01164i | 0.862639 | + | 0.505820i | \(0.168810\pi\) | ||||
−0.862639 | + | 0.505820i | \(0.831190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 56.7846i | − 2.13561i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8564i | 1.42173i | 0.703330 | + | 0.710864i | \(0.251696\pi\) | ||||
−0.703330 | + | 0.710864i | \(0.748304\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 53.5692 | 2.00900 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.56922 | 0.208569 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000i | 0.448775i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 56.7846i | − 2.12066i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.21539 | 0.119914 | 0.0599569 | − | 0.998201i | \(-0.480904\pi\) | ||||
0.0599569 | + | 0.998201i | \(0.480904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3923 | −0.387030 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.07180i | 0.0398606i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.05256 | −0.150301 | −0.0751505 | − | 0.997172i | \(-0.523944\pi\) | ||||
−0.0751505 | + | 0.997172i | \(0.523944\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.7846 | 1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.679492i | 0.0251319i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.78461i | − 0.102852i | −0.998677 | − | 0.0514260i | \(-0.983623\pi\) | ||||
0.998677 | − | 0.0514260i | \(-0.0163766\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −42.0526 | −1.55113 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.679492 | 0.0250294 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000i | 0.0735712i | 0.999323 | + | 0.0367856i | \(0.0117119\pi\) | ||||
−0.999323 | + | 0.0367856i | \(0.988288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 18.9282i | − 0.695345i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.41154 | 0.198530 | 0.0992651 | − | 0.995061i | \(-0.468351\pi\) | ||||
0.0992651 | + | 0.995061i | \(0.468351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | −0.659469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5.66025i | − 0.207098i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 62.7846i | − 2.29410i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.6077 | −0.715495 | −0.357747 | − | 0.933818i | \(-0.616455\pi\) | ||||
−0.357747 | + | 0.933818i | \(0.616455\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.3205 | −0.849847 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.46410i | 0.344434i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 36.9282i | − 1.34218i | −0.741377 | − | 0.671089i | \(-0.765827\pi\) | ||||
0.741377 | − | 0.671089i | \(-0.234173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846 | 0.754434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.7128 | 1.22209 | 0.611044 | − | 0.791596i | \(-0.290750\pi\) | ||||
0.611044 | + | 0.791596i | \(0.290750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 61.1769i | 2.21475i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.4641i | 0.559106i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.7846 | 0.750489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.7846 | 1.25437 | 0.627183 | − | 0.778872i | \(-0.284208\pi\) | ||||
0.627183 | + | 0.778872i | \(0.284208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.3923i | 0.590354i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.6077i | 0.921045i | 0.887648 | + | 0.460522i | \(0.152338\pi\) | ||||
−0.887648 | + | 0.460522i | \(0.847662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.53590 | 0.0910922 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 77.5692 | 2.78278 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 18.9282i | − 0.678173i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.7846i | 2.03191i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9282 | 0.461427 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 16.1962i | − 0.577330i | −0.957430 | − | 0.288665i | \(-0.906789\pi\) | ||||
0.957430 | − | 0.288665i | \(-0.0932115\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 26.7846i | − 0.953557i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −61.1769 | −2.17520 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.21539 | 0.114182 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.3923i | 1.00697i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.3923i | 0.793176i | 0.917997 | + | 0.396588i | \(0.129806\pi\) | ||||
−0.917997 | + | 0.396588i | \(0.870194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.60770 | −0.269141 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 57.7128 | 2.03918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.1436i | 0.781430i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 10.3923i | − 0.366281i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 73.1769 | 2.57595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.5692 | −1.67244 | −0.836222 | − | 0.548391i | \(-0.815241\pi\) | ||||
−0.836222 | + | 0.548391i | \(0.815241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 17.6077i | − 0.618290i | −0.951015 | − | 0.309145i | \(-0.899957\pi\) | ||||
0.951015 | − | 0.309145i | \(-0.100043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 44.7846i | − 1.57066i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.1962 | 0.567326 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.392305 | −0.0137250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 73.1769i | 2.55701i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 9.21539i | − 0.321619i | −0.986985 | − | 0.160810i | \(-0.948589\pi\) | ||||
0.986985 | − | 0.160810i | \(-0.0514105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.8372 | −1.70236 | −0.851178 | − | 0.524877i | \(-0.824111\pi\) | ||||
−0.851178 | + | 0.524877i | \(0.824111\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.46410 | 0.329498 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.26795i | 0.0440909i | 0.999757 | + | 0.0220455i | \(0.00701786\pi\) | ||||
−0.999757 | + | 0.0220455i | \(0.992982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 9.21539i | − 0.320064i | −0.987112 | − | 0.160032i | \(-0.948840\pi\) | ||||
0.987112 | − | 0.160032i | \(-0.0511597\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.4641 | 0.744581 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −53.3205 | −1.84745 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.19615i | 0.0760010i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1436i | 0.350614i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.7846 | −1.13185 | −0.565925 | − | 0.824457i | \(-0.691481\pi\) | ||||
−0.565925 | + | 0.824457i | \(0.691481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 20.7846i | − 0.715860i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000i | 0.0344010i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.73205 | −0.162595 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.2487 | 1.93045 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.1769i | 0.451699i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.46410i | − 0.118609i | −0.998240 | − | 0.0593043i | \(-0.981112\pi\) | ||||
0.998240 | − | 0.0593043i | \(-0.0188882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.92820 | −0.305338 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.8564 | −1.49811 | −0.749053 | − | 0.662510i | \(-0.769491\pi\) | ||||
−0.749053 | + | 0.662510i | \(0.769491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.5692i | 1.07713i | 0.842585 | + | 0.538564i | \(0.181033\pi\) | ||||
−0.842585 | + | 0.538564i | \(0.818967\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 122.354i | 4.16981i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.9808 | −0.373789 | −0.186895 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186895 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 13.6603i | − 0.463927i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 41.5692i | − 1.41014i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.679492 | −0.0230237 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −64.2487 | −2.17449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 4.73205i | − 0.159973i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8564i | 0.670503i | 0.942129 | + | 0.335252i | \(0.108821\pi\) | ||||
−0.942129 | + | 0.335252i | \(0.891179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 81.9615 | 2.76449 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3923 | −0.956561 | −0.478281 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478281 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 16.1962i | − 0.545044i | −0.962150 | − | 0.272522i | \(-0.912142\pi\) | ||||
0.962150 | − | 0.272522i | \(-0.0878577\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 16.3923i | − 0.551021i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.3731 | 1.72494 | 0.862469 | − | 0.506109i | \(-0.168917\pi\) | ||||
0.862469 | + | 0.506109i | \(0.168917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −67.1769 | −2.25304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 8.53590i | − 0.285963i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.39230i | − 0.146983i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.85641 | −0.262611 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.7846 | −0.693978 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000i | 1.19933i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.53590 | 0.0843894 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.92820 | 0.230301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.5885i | 1.08208i | 0.840996 | + | 0.541041i | \(0.181970\pi\) | ||||
−0.840996 | + | 0.541041i | \(0.818030\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 53.5692i | 1.77678i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.1769 | 0.834148 | 0.417074 | − | 0.908872i | \(-0.363056\pi\) | ||||
0.417074 | + | 0.908872i | \(0.363056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.39230 | −0.145364 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.53590i | − 0.0838342i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.1769i | 1.62396i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.7128 | −0.518318 | −0.259159 | − | 0.965835i | \(-0.583445\pi\) | ||||
−0.259159 | + | 0.965835i | \(0.583445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −65.0333 | −2.14292 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 56.7846i | − 1.86909i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000i | 0.197279i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.80385 | 0.322001 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.3923 | 0.931521 | 0.465761 | − | 0.884911i | \(-0.345781\pi\) | ||||
0.465761 | + | 0.884911i | \(0.345781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 30.7846i | − 1.00892i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 77.5692i | − 2.53950i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | 0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.3923 | −0.992873 | −0.496437 | − | 0.868073i | \(-0.665359\pi\) | ||||
−0.496437 | + | 0.868073i | \(0.665359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.1051i | 1.96146i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 20.7846i | − 0.677559i | −0.940866 | − | 0.338779i | \(-0.889986\pi\) | ||||
0.940866 | − | 0.338779i | \(-0.110014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7846 | −0.676840 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.9282 | 0.615734 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 56.1962i | − 1.82613i | −0.407815 | − | 0.913065i | \(-0.633709\pi\) | ||||
0.407815 | − | 0.913065i | \(-0.366291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 22.1436i | − 0.718811i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.39230 | 0.142430 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0718 | 0.358651 | 0.179325 | − | 0.983790i | \(-0.442609\pi\) | ||||
0.179325 | + | 0.983790i | \(0.442609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 4.39230i | − 0.142132i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.39230 | −0.141835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5692 | −0.792555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 59.2295i | 1.90864i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 14.3923i | − 0.463305i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.19615 | 0.0706235 | 0.0353118 | − | 0.999376i | \(-0.488758\pi\) | ||||
0.0353118 | + | 0.999376i | \(0.488758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.9282 | −0.608061 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.0333i | 1.83029i | 0.403129 | + | 0.915143i | \(0.367923\pi\) | ||||
−0.403129 | + | 0.915143i | \(0.632077\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.3205i | 1.51703i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.46410 | −0.303094 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.3205 | −0.938046 | −0.469023 | − | 0.883186i | \(-0.655394\pi\) | ||||
−0.469023 | + | 0.883186i | \(0.655394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 44.7846i | − 1.43132i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 57.7128i | − 1.84263i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.5885 | −1.35836 | −0.679180 | − | 0.733971i | \(-0.737665\pi\) | ||||
−0.679180 | + | 0.733971i | \(0.737665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.3923 | −0.331126 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.3923i | 0.903737i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.430781i | 0.0136980i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.1051 | −1.01985 | −0.509926 | − | 0.860218i | \(-0.670327\pi\) | ||||
−0.509926 | + | 0.860218i | \(0.670327\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −72.1051 | −2.28819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.92820i | 0.219639i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.3923i | 1.46926i | 0.678468 | + | 0.734630i | \(0.262644\pi\) | ||||
−0.678468 | + | 0.734630i | \(0.737356\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.0000 | −0.759326 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 320.2.d.b.161.4 | yes | 4 | |
3.2 | odd | 2 | 2880.2.k.l.1441.2 | 4 | |||
4.3 | odd | 2 | 320.2.d.a.161.1 | ✓ | 4 | ||
5.2 | odd | 4 | 1600.2.f.h.1249.4 | 4 | |||
5.3 | odd | 4 | 1600.2.f.d.1249.1 | 4 | |||
5.4 | even | 2 | 1600.2.d.b.801.1 | 4 | |||
8.3 | odd | 2 | 320.2.d.a.161.4 | yes | 4 | ||
8.5 | even | 2 | inner | 320.2.d.b.161.1 | yes | 4 | |
12.11 | even | 2 | 2880.2.k.e.1441.1 | 4 | |||
16.3 | odd | 4 | 1280.2.a.p.1.2 | 2 | |||
16.5 | even | 4 | 1280.2.a.m.1.2 | 2 | |||
16.11 | odd | 4 | 1280.2.a.b.1.1 | 2 | |||
16.13 | even | 4 | 1280.2.a.c.1.1 | 2 | |||
20.3 | even | 4 | 1600.2.f.i.1249.4 | 4 | |||
20.7 | even | 4 | 1600.2.f.e.1249.1 | 4 | |||
20.19 | odd | 2 | 1600.2.d.h.801.4 | 4 | |||
24.5 | odd | 2 | 2880.2.k.l.1441.4 | 4 | |||
24.11 | even | 2 | 2880.2.k.e.1441.3 | 4 | |||
40.3 | even | 4 | 1600.2.f.e.1249.2 | 4 | |||
40.13 | odd | 4 | 1600.2.f.h.1249.3 | 4 | |||
40.19 | odd | 2 | 1600.2.d.h.801.1 | 4 | |||
40.27 | even | 4 | 1600.2.f.i.1249.3 | 4 | |||
40.29 | even | 2 | 1600.2.d.b.801.4 | 4 | |||
40.37 | odd | 4 | 1600.2.f.d.1249.2 | 4 | |||
80.19 | odd | 4 | 6400.2.a.y.1.1 | 2 | |||
80.29 | even | 4 | 6400.2.a.ck.1.2 | 2 | |||
80.59 | odd | 4 | 6400.2.a.cd.1.2 | 2 | |||
80.69 | even | 4 | 6400.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.d.a.161.1 | ✓ | 4 | 4.3 | odd | 2 | ||
320.2.d.a.161.4 | yes | 4 | 8.3 | odd | 2 | ||
320.2.d.b.161.1 | yes | 4 | 8.5 | even | 2 | inner | |
320.2.d.b.161.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1280.2.a.b.1.1 | 2 | 16.11 | odd | 4 | |||
1280.2.a.c.1.1 | 2 | 16.13 | even | 4 | |||
1280.2.a.m.1.2 | 2 | 16.5 | even | 4 | |||
1280.2.a.p.1.2 | 2 | 16.3 | odd | 4 | |||
1600.2.d.b.801.1 | 4 | 5.4 | even | 2 | |||
1600.2.d.b.801.4 | 4 | 40.29 | even | 2 | |||
1600.2.d.h.801.1 | 4 | 40.19 | odd | 2 | |||
1600.2.d.h.801.4 | 4 | 20.19 | odd | 2 | |||
1600.2.f.d.1249.1 | 4 | 5.3 | odd | 4 | |||
1600.2.f.d.1249.2 | 4 | 40.37 | odd | 4 | |||
1600.2.f.e.1249.1 | 4 | 20.7 | even | 4 | |||
1600.2.f.e.1249.2 | 4 | 40.3 | even | 4 | |||
1600.2.f.h.1249.3 | 4 | 40.13 | odd | 4 | |||
1600.2.f.h.1249.4 | 4 | 5.2 | odd | 4 | |||
1600.2.f.i.1249.3 | 4 | 40.27 | even | 4 | |||
1600.2.f.i.1249.4 | 4 | 20.3 | even | 4 | |||
2880.2.k.e.1441.1 | 4 | 12.11 | even | 2 | |||
2880.2.k.e.1441.3 | 4 | 24.11 | even | 2 | |||
2880.2.k.l.1441.2 | 4 | 3.2 | odd | 2 | |||
2880.2.k.l.1441.4 | 4 | 24.5 | odd | 2 | |||
6400.2.a.y.1.1 | 2 | 80.19 | odd | 4 | |||
6400.2.a.bf.1.1 | 2 | 80.69 | even | 4 | |||
6400.2.a.cd.1.2 | 2 | 80.59 | odd | 4 | |||
6400.2.a.ck.1.2 | 2 | 80.29 | even | 4 |