Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1119,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1119");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.n (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1119.4 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1119 |
Dual form | 2240.2.n.c.1119.2 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | + | 1.73205i | −0.632456 | + | 0.774597i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949 | − | 1.00000i | 0.925820 | − | 0.377964i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.89898 | −1.02151 | −0.510754 | − | 0.859727i | \(-0.670634\pi\) | ||||
−0.510754 | + | 0.859727i | \(0.670634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 4.89898i | −0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.92820i | 1.28654i | 0.765641 | + | 0.643268i | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.79796 | −1.75977 | −0.879883 | − | 0.475191i | \(-0.842379\pi\) | ||||
−0.879883 | + | 0.475191i | \(0.842379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.73205 | + | 5.65685i | −0.292770 | + | 0.956183i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65685 | 0.929981 | 0.464991 | − | 0.885316i | \(-0.346058\pi\) | ||||
0.464991 | + | 0.885316i | \(0.346058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.79796i | − | 1.53018i | −0.643921 | − | 0.765092i | \(-0.722693\pi\) | ||
0.643921 | − | 0.765092i | \(-0.277307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.82843i | 0.431331i | 0.976467 | + | 0.215666i | \(0.0691921\pi\) | ||||
−0.976467 | + | 0.215666i | \(0.930808\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.24264 | − | 5.19615i | 0.632456 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0000i | 1.45865i | 0.684167 | + | 0.729325i | \(0.260166\pi\) | ||||
−0.684167 | + | 0.729325i | \(0.739834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | − | 4.89898i | 0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.3137 | −1.55406 | −0.777029 | − | 0.629465i | \(-0.783274\pi\) | ||||
−0.777029 | + | 0.629465i | \(0.783274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.89898 | + | 6.00000i | −0.660578 | + | 0.809040i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.48528i | − | 1.10469i | −0.833616 | − | 0.552345i | \(-0.813733\pi\) | ||
0.833616 | − | 0.552345i | \(-0.186267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1421 | 1.81071 | 0.905357 | − | 0.424650i | \(-0.139603\pi\) | ||||
0.905357 | + | 0.424650i | \(0.139603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.34847 | + | 3.00000i | −0.925820 | + | 0.377964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | + | 4.89898i | 0.744208 | + | 0.607644i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.1421i | − | 1.72774i | −0.503718 | − | 0.863868i | \(-0.668035\pi\) | ||
0.503718 | − | 0.863868i | \(-0.331965\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.00000i | − | 0.474713i | −0.971423 | − | 0.237356i | \(-0.923719\pi\) | ||
0.971423 | − | 0.237356i | \(-0.0762809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0000 | −1.40449 | −0.702247 | − | 0.711934i | \(-0.747820\pi\) | ||||
−0.702247 | + | 0.711934i | \(0.747820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.48528 | − | 3.46410i | 0.966988 | − | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.0000i | − | 1.35011i | −0.737769 | − | 0.675053i | \(-0.764121\pi\) | ||
0.737769 | − | 0.675053i | \(-0.235879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8564 | −1.52094 | −0.760469 | − | 0.649374i | \(-0.775031\pi\) | ||||
−0.760469 | + | 0.649374i | \(0.775031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.65685 | − | 6.92820i | 0.613572 | − | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.79796i | − | 1.03858i | −0.854598 | − | 0.519291i | \(-0.826196\pi\) | ||
0.854598 | − | 0.519291i | \(-0.173804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.46410 | − | 8.48528i | −0.363137 | − | 0.889499i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.89898 | + | 4.00000i | 0.502625 | + | 0.410391i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | −0.406138 | −0.203069 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203069 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.3923 | −1.04447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.48528 | −0.844317 | −0.422159 | − | 0.906522i | \(-0.638727\pi\) | ||||
−0.422159 | + | 0.906522i | \(0.638727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843i | 0.273434i | 0.990610 | + | 0.136717i | \(0.0436552\pi\) | ||||
−0.990610 | + | 0.136717i | \(0.956345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.92820i | − | 0.663602i | −0.943349 | − | 0.331801i | \(-0.892344\pi\) | ||
0.943349 | − | 0.331801i | \(-0.107656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.79796i | − | 0.921714i | −0.887474 | − | 0.460857i | \(-0.847542\pi\) | ||
0.887474 | − | 0.460857i | \(-0.152458\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.92820 | − | 8.48528i | 0.646058 | − | 0.791257i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3923i | 0.960769i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.79796 | + | 4.00000i | −0.898177 | + | 0.366679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.89898 | −0.434714 | −0.217357 | − | 0.976092i | \(-0.569744\pi\) | ||||
−0.217357 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.82843i | − | 0.247121i | −0.992337 | − | 0.123560i | \(-0.960569\pi\) | ||
0.992337 | − | 0.123560i | \(-0.0394313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.82843 | − | 6.92820i | −0.245256 | − | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.82843i | 0.239904i | 0.992780 | + | 0.119952i | \(0.0382741\pi\) | ||||
−0.992780 | + | 0.119952i | \(0.961726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | − | 9.79796i | −0.996546 | − | 0.813676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.92820i | 0.567581i | 0.958886 | + | 0.283790i | \(0.0915919\pi\) | ||||
−0.958886 | + | 0.283790i | \(0.908408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8564 | − | 16.9706i | 1.11297 | − | 1.36311i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.3923i | − | 0.829396i | −0.909959 | − | 0.414698i | \(-0.863887\pi\) | ||
0.909959 | − | 0.414698i | \(-0.136113\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | + | 4.89898i | −0.945732 | + | 0.386094i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.7990i | 1.55078i | 0.631485 | + | 0.775388i | \(0.282446\pi\) | ||||
−0.631485 | + | 0.775388i | \(0.717554\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0000i | 0.773823i | 0.922117 | + | 0.386912i | \(0.126458\pi\) | ||||
−0.922117 | + | 0.386912i | \(0.873542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.48528i | 0.648886i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 17.3205i | − | 1.31685i | −0.752645 | − | 0.658427i | \(-0.771222\pi\) | ||
0.752645 | − | 0.658427i | \(-0.228778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.34847 | − | 11.0000i | −0.555492 | − | 0.831522i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923 | 0.776757 | 0.388379 | − | 0.921500i | \(-0.373035\pi\) | ||||
0.388379 | + | 0.921500i | \(0.373035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.82843 | 0.210235 | 0.105118 | − | 0.994460i | \(-0.466478\pi\) | ||||
0.105118 | + | 0.994460i | \(0.466478\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.00000 | + | 9.79796i | −0.588172 | + | 0.720360i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.8564 | −1.01328 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0000i | 1.44715i | 0.690246 | + | 0.723575i | \(0.257502\pi\) | ||||
−0.690246 | + | 0.723575i | \(0.742498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 19.5959i | − | 1.41055i | −0.708936 | − | 0.705273i | \(-0.750825\pi\) | ||
0.708936 | − | 0.705273i | \(-0.249175\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.3137 | −0.806068 | −0.403034 | − | 0.915185i | \(-0.632044\pi\) | ||||
−0.403034 | + | 0.915185i | \(0.632044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.5959 | −1.38912 | −0.694559 | − | 0.719436i | \(-0.744400\pi\) | ||||
−0.694559 | + | 0.719436i | \(0.744400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820 | + | 16.9706i | 0.486265 | + | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.9706 | + | 13.8564i | 1.18528 | + | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.6969 | 1.02151 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.79796i | − | 0.677739i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3923 | 0.715436 | 0.357718 | − | 0.933830i | \(-0.383555\pi\) | ||||
0.357718 | + | 0.933830i | \(0.383555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.89898 | − | 4.00000i | −0.334108 | − | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0000 | + | 9.79796i | −1.62923 | + | 0.665129i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8564i | 0.932083i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0000i | 1.20537i | 0.797980 | + | 0.602685i | \(0.205902\pi\) | ||||
−0.797980 | + | 0.602685i | \(0.794098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | + | 14.6969i | 0.200000 | + | 0.979796i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.8564 | 0.919682 | 0.459841 | − | 0.888001i | \(-0.347906\pi\) | ||||
0.459841 | + | 0.888001i | \(0.347906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.82843 | −0.186908 | −0.0934539 | − | 0.995624i | \(-0.529791\pi\) | ||||
−0.0934539 | + | 0.995624i | \(0.529791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.79796i | − | 0.641886i | −0.947099 | − | 0.320943i | \(-0.896000\pi\) | ||
0.947099 | − | 0.320943i | \(-0.104000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.3205 | − | 14.1421i | −1.12987 | − | 0.922531i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.00000i | − | 0.258738i | −0.991596 | − | 0.129369i | \(-0.958705\pi\) | ||
0.991596 | − | 0.129369i | \(-0.0412952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.41421 | + | 15.5885i | 0.0903508 | + | 0.995910i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.79796 | −0.623429 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.82843i | 0.178529i | 0.996008 | + | 0.0892644i | \(0.0284516\pi\) | ||||
−0.996008 | + | 0.0892644i | \(0.971548\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.9706 | −1.06693 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.0000 | 1.24757 | 0.623783 | − | 0.781598i | \(-0.285595\pi\) | ||||
0.623783 | + | 0.781598i | \(0.285595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.8564 | − | 5.65685i | 0.860995 | − | 0.351500i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 20.7846i | − | 1.28654i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6969 | −0.906252 | −0.453126 | − | 0.891446i | \(-0.649691\pi\) | ||||
−0.453126 | + | 0.891446i | \(0.649691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.0000 | − | 19.5959i | 0.982872 | − | 1.20377i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.48528 | 0.517357 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.46410 | − | 16.9706i | −0.208893 | − | 1.02336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.65685 | 0.339887 | 0.169944 | − | 0.985454i | \(-0.445641\pi\) | ||||
0.169944 | + | 0.985454i | \(0.445641\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.3939 | 1.75977 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.7128 | −1.64736 | −0.823678 | − | 0.567058i | \(-0.808082\pi\) | ||||
−0.823678 | + | 0.567058i | \(0.808082\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.79796 | − | 24.0000i | −0.578355 | − | 1.41668i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.2487i | 1.41662i | 0.705899 | + | 0.708312i | \(0.250543\pi\) | ||||
−0.705899 | + | 0.708312i | \(0.749457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.6969 | + | 12.0000i | 0.855689 | + | 0.698667i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9706i | 0.981433i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.82843 | + | 6.92820i | 0.163028 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.0000 | + | 24.4949i | −1.14520 | + | 1.40257i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.79796 | 0.555591 | 0.277796 | − | 0.960640i | \(-0.410396\pi\) | ||||
0.277796 | + | 0.960640i | \(0.410396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0000 | 0.678280 | 0.339140 | − | 0.940736i | \(-0.389864\pi\) | ||||
0.339140 | + | 0.940736i | \(0.389864\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.19615 | − | 16.9706i | 0.292770 | − | 0.956183i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000i | 1.34374i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.3137i | 0.629512i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.9706 | + | 3.46410i | −0.941357 | + | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0000 | + | 24.4949i | 0.551318 | + | 1.35045i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.46410 | 0.190404 | 0.0952021 | − | 0.995458i | \(-0.469650\pi\) | ||||
0.0952021 | + | 0.995458i | \(0.469650\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.9706 | −0.929981 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.4949 | + | 20.0000i | 1.33830 | + | 1.09272i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.79796i | − | 0.533729i | −0.963734 | − | 0.266864i | \(-0.914012\pi\) | ||
0.963734 | − | 0.266864i | \(-0.0859876\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.9411 | −1.83801 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.34847 | − | 17.0000i | 0.396780 | − | 0.917914i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.48528i | 0.455514i | 0.973718 | + | 0.227757i | \(0.0731391\pi\) | ||||
−0.973718 | + | 0.227757i | \(0.926861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.7990 | 1.05982 | 0.529908 | − | 0.848055i | \(-0.322227\pi\) | ||||
0.529908 | + | 0.848055i | \(0.322227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.00000 | 0.212899 | 0.106449 | − | 0.994318i | \(-0.466052\pi\) | ||||
0.106449 | + | 0.994318i | \(0.466052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.92820 | + | 5.65685i | 0.367711 | + | 0.300235i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000i | 0.211112i | 0.994413 | + | 0.105556i | \(0.0336622\pi\) | ||||
−0.994413 | + | 0.105556i | \(0.966338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9706 | − | 20.7846i | 0.888280 | − | 1.08792i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.00000i | − | 0.104399i | −0.998637 | − | 0.0521996i | \(-0.983377\pi\) | ||
0.998637 | − | 0.0521996i | \(-0.0166232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.3939i | 1.53018i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.7128 | + | 11.3137i | −1.43878 | + | 0.587378i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.2843 | −1.46450 | −0.732252 | − | 0.681034i | \(-0.761531\pi\) | ||||
−0.732252 | + | 0.681034i | \(0.761531\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.46410 | −0.177939 | −0.0889695 | − | 0.996034i | \(-0.528357\pi\) | ||||
−0.0889695 | + | 0.996034i | \(0.528357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 22.0000i | − | 1.12415i | −0.827087 | − | 0.562074i | \(-0.810004\pi\) | ||
0.827087 | − | 0.562074i | \(-0.189996\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | + | 19.5959i | −0.305788 | + | 0.998700i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 8.48528i | − | 0.431331i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 20.7846i | − | 1.05382i | −0.849921 | − | 0.526911i | \(-0.823350\pi\) | ||
0.849921 | − | 0.526911i | \(-0.176650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5959 | 0.991008 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.7846 | + | 16.9706i | 1.04579 | + | 0.853882i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.46410i | 0.173858i | 0.996214 | + | 0.0869291i | \(0.0277054\pi\) | ||||
−0.996214 | + | 0.0869291i | \(0.972295\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.9411i | 1.69073i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.7279 | + | 15.5885i | −0.632456 | + | 0.774597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.5959 | 0.971334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.79796i | 0.484478i | 0.970217 | + | 0.242239i | \(0.0778818\pi\) | ||||
−0.970217 | + | 0.242239i | \(0.922118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.48528 | − | 20.7846i | −0.417533 | − | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.5959 | − | 24.0000i | 0.961926 | − | 1.17811i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4558i | 1.24360i | 0.783176 | + | 0.621800i | \(0.213598\pi\) | ||||
−0.783176 | + | 0.621800i | \(0.786402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.92820i | 0.337660i | 0.985645 | + | 0.168830i | \(0.0539989\pi\) | ||||
−0.985645 | + | 0.168830i | \(0.946001\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 30.0000i | − | 1.45865i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.00000 | + | 19.5959i | 0.194029 | + | 0.950542i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.6410 | − | 14.1421i | 1.67640 | − | 0.684386i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.0000i | − | 0.963366i | −0.876346 | − | 0.481683i | \(-0.840026\pi\) | ||
0.876346 | − | 0.481683i | \(-0.159974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0000 | 1.34559 | 0.672797 | − | 0.739827i | \(-0.265093\pi\) | ||||
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8564i | 0.662842i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.79796 | 0.467631 | 0.233816 | − | 0.972281i | \(-0.424879\pi\) | ||||
0.233816 | + | 0.972281i | \(0.424879\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | + | 14.6969i | −0.714286 | + | 0.699854i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.48528i | 0.403148i | 0.979473 | + | 0.201574i | \(0.0646056\pi\) | ||||
−0.979473 | + | 0.201574i | \(0.935394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.9706 | + | 13.8564i | 0.804482 | + | 0.656857i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.0000 | −1.03824 | −0.519122 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519122 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 33.9411i | − | 1.59823i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.5959 | + | 6.00000i | 0.918671 | + | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3939i | 1.37499i | 0.726190 | + | 0.687494i | \(0.241289\pi\) | ||||
−0.726190 | + | 0.687494i | \(0.758711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.4558 | 1.18560 | 0.592798 | − | 0.805351i | \(-0.298023\pi\) | ||||
0.592798 | + | 0.805351i | \(0.298023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.2929 | −1.59372 | −0.796862 | − | 0.604161i | \(-0.793508\pi\) | ||||
−0.796862 | + | 0.604161i | \(0.793508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.1421 | − | 34.6410i | −0.653023 | − | 1.59957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.79796i | 0.450511i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.8564 | + | 2.82843i | −0.635776 | + | 0.129777i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.9411 | 1.55406 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.79796 | 0.447680 | 0.223840 | − | 0.974626i | \(-0.428141\pi\) | ||||
0.223840 | + | 0.974626i | \(0.428141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 19.5959i | − | 0.893497i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.65685 | − | 6.92820i | 0.256865 | − | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.89898 | −0.221994 | −0.110997 | − | 0.993821i | \(-0.535404\pi\) | ||||
−0.110997 | + | 0.993821i | \(0.535404\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.1769 | −1.40699 | −0.703497 | − | 0.710698i | \(-0.748379\pi\) | ||||
−0.703497 | + | 0.710698i | \(0.748379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 27.7128i | − | 1.24812i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.6969 | − | 18.0000i | 0.660578 | − | 0.809040i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.00000 | − | 9.79796i | −0.179425 | − | 0.439499i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3205 | −0.775372 | −0.387686 | − | 0.921791i | \(-0.626726\pi\) | ||||
−0.387686 | + | 0.921791i | \(0.626726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.0000i | 0.624229i | 0.950044 | + | 0.312115i | \(0.101037\pi\) | ||||
−0.950044 | + | 0.312115i | \(0.898963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | − | 14.6969i | 0.533993 | − | 0.654005i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.1421 | 0.626839 | 0.313420 | − | 0.949615i | \(-0.398525\pi\) | ||||
0.313420 | + | 0.949615i | \(0.398525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.3939 | + | 12.0000i | −1.30031 | + | 0.530849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.3923 | − | 8.48528i | −0.457940 | − | 0.373906i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.6410i | 1.52351i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.1918i | 1.71703i | 0.512792 | + | 0.858513i | \(0.328611\pi\) | ||||
−0.512792 | + | 0.858513i | \(0.671389\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.1918 | 1.70722 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.4558i | 1.10469i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.9411 | −1.47015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.89898 | − | 4.00000i | −0.211801 | − | 0.172935i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.3205 | − | 16.9706i | 0.746047 | − | 0.730974i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 20.7846i | − | 0.893600i | −0.894634 | − | 0.446800i | \(-0.852564\pi\) | ||
0.894634 | − | 0.446800i | \(-0.147436\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | + | 9.79796i | 0.514024 | + | 0.419698i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.1421i | − | 0.604674i | −0.953201 | − | 0.302337i | \(-0.902233\pi\) | ||
0.953201 | − | 0.302337i | \(-0.0977668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −42.4264 | −1.81071 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.5959 | 0.834814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0000 | − | 29.3939i | −0.510292 | − | 1.24995i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.9706 | 0.719066 | 0.359533 | − | 0.933132i | \(-0.382936\pi\) | ||||
0.359533 | + | 0.933132i | \(0.382936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.79796 | 0.414410 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.5692 | 1.75193 | 0.875967 | − | 0.482371i | \(-0.160224\pi\) | ||||
0.875967 | + | 0.482371i | \(0.160224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.9706 | + | 13.8564i | 0.713957 | + | 0.582943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.0454 | − | 9.00000i | 0.925820 | − | 0.377964i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.2487 | 1.01478 | 0.507388 | − | 0.861717i | \(-0.330611\pi\) | ||||
0.507388 | + | 0.861717i | \(0.330611\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.89898 | + | 24.0000i | 0.204302 | + | 1.00087i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0000 | −0.499567 | −0.249783 | − | 0.968302i | \(-0.580359\pi\) | ||||
−0.249783 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.9411 | + | 13.8564i | −1.40812 | + | 0.574861i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.1918 | −1.62316 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.0000 | − | 14.6969i | −0.744208 | − | 0.607644i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8564 | −0.571915 | −0.285958 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285958 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.7128i | 1.14189i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.00000 | 0.164260 | 0.0821302 | − | 0.996622i | \(-0.473828\pi\) | ||||
0.0821302 | + | 0.996622i | \(0.473828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.92820 | − | 22.6274i | 0.284029 | − | 0.927634i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.00000i | − | 0.163436i | −0.996656 | − | 0.0817178i | \(-0.973959\pi\) | ||
0.996656 | − | 0.0817178i | \(-0.0260406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.5959i | − | 0.799334i | −0.916660 | − | 0.399667i | \(-0.869126\pi\) | ||
0.916660 | − | 0.399667i | \(-0.130874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 42.4264i | 1.72774i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.41421 | + | 1.73205i | −0.0574960 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.0000i | 1.21766i | 0.793300 | + | 0.608831i | \(0.208361\pi\) | ||||
−0.793300 | + | 0.608831i | \(0.791639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.6410 | 1.40143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.3137 | −0.456956 | −0.228478 | − | 0.973549i | \(-0.573375\pi\) | ||||
−0.228478 | + | 0.973549i | \(0.573375\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1918i | 1.57780i | 0.614519 | + | 0.788902i | \(0.289350\pi\) | ||||
−0.614519 | + | 0.788902i | \(0.710650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1127i | 1.25052i | 0.780415 | + | 0.625262i | \(0.215008\pi\) | ||||
−0.780415 | + | 0.625262i | \(0.784992\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.79796 | − | 24.0000i | −0.392547 | − | 0.961540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.6274 | −0.902214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.00000i | − | 0.159237i | −0.996825 | − | 0.0796187i | \(-0.974630\pi\) | ||
0.996825 | − | 0.0796187i | \(-0.0253703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.92820 | − | 8.48528i | 0.274937 | − | 0.336728i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.9706 | − | 17.3205i | −0.672398 | − | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000i | 0.474713i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.5692 | −1.63933 | −0.819665 | − | 0.572843i | \(-0.805840\pi\) | ||||
−0.819665 | + | 0.572843i | \(0.805840\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 38.0000i | − | 1.49393i | −0.664861 | − | 0.746967i | \(-0.731509\pi\) | ||
0.664861 | − | 0.746967i | \(-0.268491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.3939i | − | 1.15381i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.9411 | −1.32822 | −0.664109 | − | 0.747635i | \(-0.731189\pi\) | ||||
−0.664109 | + | 0.747635i | \(0.731189\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.89898 | + | 4.00000i | 0.191419 | + | 0.156293i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.0000 | 1.40449 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3923 | −0.404827 | −0.202413 | − | 0.979300i | \(-0.564878\pi\) | ||||
−0.202413 | + | 0.979300i | \(0.564878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.1421 | 0.550065 | 0.275033 | − | 0.961435i | \(-0.411311\pi\) | ||||
0.275033 | + | 0.961435i | \(0.411311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000 | + | 4.89898i | 0.620453 | + | 0.189974i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 33.9411i | − | 1.31421i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.9898 | 1.89123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.79796i | 0.377684i | 0.982008 | + | 0.188842i | \(0.0604733\pi\) | ||||
−0.982008 | + | 0.188842i | \(0.939527\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3205i | 0.665681i | 0.942983 | + | 0.332841i | \(0.108007\pi\) | ||||
−0.942983 | + | 0.332841i | \(0.891993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.79796 | + | 4.00000i | −0.376011 | + | 0.153506i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.7696i | 1.40695i | 0.710721 | + | 0.703474i | \(0.248369\pi\) | ||||
−0.710721 | + | 0.703474i | \(0.751631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.1918i | 1.49309i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1127i | 1.18358i | 0.806091 | + | 0.591791i | \(0.201579\pi\) | ||||
−0.806091 | + | 0.591791i | \(0.798421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.4558 | + | 10.3923i | −0.966988 | + | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.89898 | − | 4.00000i | −0.185829 | − | 0.151729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.1918i | 1.48450i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7846i | 0.785024i | 0.919747 | + | 0.392512i | \(0.128394\pi\) | ||||
−0.919747 | + | 0.392512i | \(0.871606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.0000i | − | 0.603451i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.7846 | + | 8.48528i | −0.781686 | + | 0.319122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.4974i | 1.82136i | 0.413114 | + | 0.910679i | \(0.364441\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.0000i | 1.35011i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.0000 | 1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.7846 | + | 16.9706i | 0.777300 | + | 0.634663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.79796 | 0.365402 | 0.182701 | − | 0.983169i | \(-0.441516\pi\) | ||||
0.182701 | + | 0.983169i | \(0.441516\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | + | 14.6969i | 0.223452 | + | 0.547343i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.9411 | − | 6.92820i | 1.26054 | − | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.0000i | 1.55769i | 0.627214 | + | 0.778847i | \(0.284195\pi\) | ||||
−0.627214 | + | 0.778847i | \(0.715805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.3137i | − | 0.418453i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.3205i | 0.639748i | 0.947460 | + | 0.319874i | \(0.103641\pi\) | ||||
−0.947460 | + | 0.319874i | \(0.896359\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 48.9898i | − | 1.80456i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3923 | −0.382287 | −0.191144 | − | 0.981562i | \(-0.561220\pi\) | ||||
−0.191144 | + | 0.981562i | \(0.561220\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.89898 | 0.179726 | 0.0898631 | − | 0.995954i | \(-0.471357\pi\) | ||||
0.0898631 | + | 0.995954i | \(0.471357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0000 | − | 9.79796i | −0.439646 | − | 0.358969i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.5692 | 1.52094 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.82843 | + | 6.92820i | 0.103348 | + | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.0000i | 1.60558i | 0.596260 | + | 0.802791i | \(0.296653\pi\) | ||||
−0.596260 | + | 0.802791i | \(0.703347\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.7846 | + | 16.9706i | 0.756429 | + | 0.617622i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.5980 | 1.43921 | 0.719607 | − | 0.694382i | \(-0.244322\pi\) | ||||
0.719607 | + | 0.694382i | \(0.244322\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.5959i | 0.710351i | 0.934800 | + | 0.355176i | \(0.115579\pi\) | ||||
−0.934800 | + | 0.355176i | \(0.884421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.92820 | − | 16.9706i | −0.250818 | − | 0.614376i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.9706 | + | 20.7846i | −0.613572 | + | 0.751469i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.3939 | −1.06135 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 48.9898i | − | 1.76662i | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||
0.468792 | − | 0.883309i | \(-0.344689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 10.3923i | − | 0.373785i | −0.982380 | − | 0.186893i | \(-0.940158\pi\) | ||
0.982380 | − | 0.186893i | \(-0.0598416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.79796 | + | 48.0000i | 0.351953 | + | 1.72421i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.7128 | −0.992915 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 13.8564i | − | 0.495821i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.0000 | + | 14.6969i | 0.642448 | + | 0.524556i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.7128 | 0.987855 | 0.493928 | − | 0.869503i | \(-0.335561\pi\) | ||||
0.493928 | + | 0.869503i | \(0.335561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.79796 | − | 24.0000i | −0.348375 | − | 0.853342i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 48.9898i | − | 1.73968i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.46410i | 0.122705i | 0.998116 | + | 0.0613524i | \(0.0195413\pi\) | ||||
−0.998116 | + | 0.0613524i | \(0.980459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 40.0000i | − | 1.41510i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.3939i | 1.03858i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.5692 | −1.46695 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.48528 | − | 27.7128i | 0.299067 | − | 0.976748i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.00000 | 0.0703163 | 0.0351581 | − | 0.999382i | \(-0.488807\pi\) | ||||
0.0351581 | + | 0.999382i | \(0.488807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.7990i | 0.695237i | 0.937636 | + | 0.347618i | \(0.113009\pi\) | ||||
−0.937636 | + | 0.347618i | \(0.886991\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.2929 | − | 28.0000i | −1.20123 | − | 0.980797i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | 0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3923 | + | 25.4558i | 0.363137 | + | 0.889499i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 48.4974i | − | 1.69257i | −0.532729 | − | 0.846286i | \(-0.678834\pi\) | ||
0.532729 | − | 0.846286i | \(-0.321166\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.89898 | −0.170768 | −0.0853838 | − | 0.996348i | \(-0.527212\pi\) | ||||
−0.0853838 | + | 0.996348i | \(0.527212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.4558i | − | 0.885186i | −0.896723 | − | 0.442593i | \(-0.854059\pi\) | ||
0.896723 | − | 0.442593i | \(-0.145941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.82843 | −0.0982353 | −0.0491177 | − | 0.998793i | \(-0.515641\pi\) | ||||
−0.0491177 | + | 0.998793i | \(0.515641\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.0000 | + | 19.5959i | −0.692959 | + | 0.678958i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.3205 | − | 14.1421i | −0.599401 | − | 0.489409i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.41421 | + | 1.73205i | −0.0486504 | + | 0.0595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.44949 | − | 1.00000i | 0.0841655 | − | 0.0343604i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7128 | −0.949983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.1051i | − | 1.30469i | −0.757920 | − | 0.652347i | \(-0.773784\pi\) | ||
0.757920 | − | 0.652347i | \(-0.226216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.6969 | − | 12.0000i | −0.502625 | − | 0.410391i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.0000 | −1.77629 | −0.888143 | − | 0.459567i | \(-0.848005\pi\) | ||||
−0.888143 | + | 0.459567i | \(0.848005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 53.7401i | − | 1.83359i | −0.399359 | − | 0.916795i | \(-0.630767\pi\) | ||
0.399359 | − | 0.916795i | \(-0.369233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.2929 | 1.16734 | 0.583671 | − | 0.811990i | \(-0.301616\pi\) | ||||
0.583671 | + | 0.811990i | \(0.301616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.0000 | + | 24.4949i | 1.02003 | + | 0.832851i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 41.5692i | − | 1.41014i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.9898 | −1.65996 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0000 | 0.406138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.4449 | + | 2.82843i | 0.995418 | + | 0.0956183i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.2843 | 0.955092 | 0.477546 | − | 0.878607i | \(-0.341526\pi\) | ||||
0.477546 | + | 0.878607i | \(0.341526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.3939i | − | 0.990305i | −0.868806 | − | 0.495152i | \(-0.835112\pi\) | ||
0.868806 | − | 0.495152i | \(-0.164888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1421i | 0.475921i | 0.971275 | + | 0.237960i | \(0.0764788\pi\) | ||||
−0.971275 | + | 0.237960i | \(0.923521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 26.0000i | − | 0.872995i | −0.899706 | − | 0.436497i | \(-0.856219\pi\) | ||
0.899706 | − | 0.436497i | \(-0.143781\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | + | 4.89898i | −0.402467 | + | 0.164306i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.1769 | 1.04447 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.2843 | 0.946497 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.6969 | + | 18.0000i | −0.491264 | + | 0.601674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 67.8823i | − | 2.26400i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.2548 | 1.50766 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.00000 | + | 4.89898i | −0.132964 | + | 0.162848i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.82843i | − | 0.0939164i | −0.998897 | − | 0.0469582i | \(-0.985047\pi\) | ||
0.998897 | − | 0.0469582i | \(-0.0149528\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.4558 | 0.844317 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 20.0000i | − | 0.662630i | −0.943520 | − | 0.331315i | \(-0.892508\pi\) | ||
0.943520 | − | 0.331315i | \(-0.107492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.0000 | −1.58857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.82843 | − | 6.92820i | −0.0934029 | − | 0.228789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20.0000i | − | 0.659739i | −0.944027 | − | 0.329870i | \(-0.892995\pi\) | ||
0.944027 | − | 0.329870i | \(-0.107005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.8564 | −0.456089 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.65685 | − | 27.7128i | −0.185996 | − | 0.911192i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 18.0000i | − | 0.591198i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.5959i | − | 0.642921i | −0.946923 | − | 0.321461i | \(-0.895826\pi\) | ||
0.946923 | − | 0.321461i | \(-0.104174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8564 | − | 14.1421i | −0.454125 | − | 0.463490i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959 | − | 24.0000i | 0.640855 | − | 0.784884i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.0000 | −0.914720 | −0.457360 | − | 0.889282i | \(-0.651205\pi\) | ||||
−0.457360 | + | 0.889282i | \(0.651205\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.4558 | −0.829837 | −0.414918 | − | 0.909859i | \(-0.636190\pi\) | ||||
−0.414918 | + | 0.909859i | \(0.636190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.0000i | 1.56310i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.1421i | 0.459558i | 0.973243 | + | 0.229779i | \(0.0738003\pi\) | ||||
−0.973243 | + | 0.229779i | \(0.926200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.5692i | 1.34939i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 58.7878i | − | 1.90432i | −0.305597 | − | 0.952161i | \(-0.598856\pi\) | ||
0.305597 | − | 0.952161i | \(-0.401144\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.6410 | − | 28.2843i | −1.12096 | − | 0.915258i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65.0000 | 2.09677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 8.48528i | − | 0.273434i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.9411 | + | 27.7128i | 1.09260 | + | 0.892107i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.89898 | 0.157541 | 0.0787703 | − | 0.996893i | \(-0.474901\pi\) | ||||
0.0787703 | + | 0.996893i | \(0.474901\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.82843i | − | 0.0907685i | −0.998970 | − | 0.0453843i | \(-0.985549\pi\) | ||
0.998970 | − | 0.0453843i | \(-0.0144512\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.82843 | + | 6.92820i | 0.0906752 | + | 0.222108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 29.3939i | − | 0.940393i | −0.882562 | − | 0.470197i | \(-0.844183\pi\) | ||
0.882562 | − | 0.470197i | \(-0.155817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 33.9411i | − | 1.08476i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.7846i | 0.663602i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.0000i | 0.829271i | 0.909988 | + | 0.414636i | \(0.136091\pi\) | ||||
−0.909988 | + | 0.414636i | \(0.863909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | − | 19.5959i | 0.509802 | − | 0.624378i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 13.8564i | − | 0.440608i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 44.0000i | − | 1.39771i | −0.715265 | − | 0.698853i | \(-0.753694\pi\) | ||
0.715265 | − | 0.698853i | \(-0.246306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.7128 | − | 33.9411i | 0.878555 | − | 1.07601i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 45.0333i | − | 1.42622i | −0.701052 | − | 0.713110i | \(-0.747286\pi\) | ||
0.701052 | − | 0.713110i | \(-0.252714\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2240.2.n.c.1119.4 | yes | 8 | |
4.3 | odd | 2 | inner | 2240.2.n.c.1119.3 | yes | 8 | |
5.4 | even | 2 | 2240.2.n.e.1119.1 | yes | 8 | ||
7.6 | odd | 2 | 2240.2.n.e.1119.6 | yes | 8 | ||
8.3 | odd | 2 | inner | 2240.2.n.c.1119.5 | yes | 8 | |
8.5 | even | 2 | inner | 2240.2.n.c.1119.6 | yes | 8 | |
20.19 | odd | 2 | 2240.2.n.e.1119.2 | yes | 8 | ||
28.27 | even | 2 | 2240.2.n.e.1119.5 | yes | 8 | ||
35.34 | odd | 2 | inner | 2240.2.n.c.1119.7 | yes | 8 | |
40.19 | odd | 2 | 2240.2.n.e.1119.8 | yes | 8 | ||
40.29 | even | 2 | 2240.2.n.e.1119.7 | yes | 8 | ||
56.13 | odd | 2 | 2240.2.n.e.1119.4 | yes | 8 | ||
56.27 | even | 2 | 2240.2.n.e.1119.3 | yes | 8 | ||
140.139 | even | 2 | inner | 2240.2.n.c.1119.8 | yes | 8 | |
280.69 | odd | 2 | inner | 2240.2.n.c.1119.1 | ✓ | 8 | |
280.139 | even | 2 | inner | 2240.2.n.c.1119.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.n.c.1119.1 | ✓ | 8 | 280.69 | odd | 2 | inner | |
2240.2.n.c.1119.2 | yes | 8 | 280.139 | even | 2 | inner | |
2240.2.n.c.1119.3 | yes | 8 | 4.3 | odd | 2 | inner | |
2240.2.n.c.1119.4 | yes | 8 | 1.1 | even | 1 | trivial | |
2240.2.n.c.1119.5 | yes | 8 | 8.3 | odd | 2 | inner | |
2240.2.n.c.1119.6 | yes | 8 | 8.5 | even | 2 | inner | |
2240.2.n.c.1119.7 | yes | 8 | 35.34 | odd | 2 | inner | |
2240.2.n.c.1119.8 | yes | 8 | 140.139 | even | 2 | inner | |
2240.2.n.e.1119.1 | yes | 8 | 5.4 | even | 2 | ||
2240.2.n.e.1119.2 | yes | 8 | 20.19 | odd | 2 | ||
2240.2.n.e.1119.3 | yes | 8 | 56.27 | even | 2 | ||
2240.2.n.e.1119.4 | yes | 8 | 56.13 | odd | 2 | ||
2240.2.n.e.1119.5 | yes | 8 | 28.27 | even | 2 | ||
2240.2.n.e.1119.6 | yes | 8 | 7.6 | odd | 2 | ||
2240.2.n.e.1119.7 | yes | 8 | 40.29 | even | 2 | ||
2240.2.n.e.1119.8 | yes | 8 | 40.19 | odd | 2 |