Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(1729,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.1729");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.f (of order \(2\), degree \(1\), not 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: | \(22.9969157821\) |
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: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1729.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.1729 |
Dual form | 2880.2.f.x.1729.1 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | + | 1.73205i | −0.632456 | + | 0.774597i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.89898i | − | 1.35873i | −0.733799 | − | 0.679366i | \(-0.762255\pi\) | ||
0.733799 | − | 0.679366i | \(-0.237745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820 | 1.58944 | 0.794719 | − | 0.606977i | \(-0.207618\pi\) | ||||
0.794719 | + | 0.606977i | \(0.207618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 4.89898i | −0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528 | 1.57568 | 0.787839 | − | 0.615882i | \(-0.211200\pi\) | ||||
0.787839 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.92820 | −1.24434 | −0.622171 | − | 0.782881i | \(-0.713749\pi\) | ||||
−0.622171 | + | 0.782881i | \(0.713749\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.89898 | − | 4.00000i | −0.828079 | − | 0.676123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89898i | 0.805387i | 0.915335 | + | 0.402694i | \(0.131926\pi\) | ||||
−0.915335 | + | 0.402694i | \(0.868074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.3137i | − | 1.72532i | −0.505781 | − | 0.862662i | \(-0.668795\pi\) | ||
0.505781 | − | 0.862662i | \(-0.331205\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000i | 0.583460i | 0.956501 | + | 0.291730i | \(0.0942309\pi\) | ||||
−0.956501 | + | 0.291730i | \(0.905769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.46410i | 0.475831i | 0.971286 | + | 0.237915i | \(0.0764641\pi\) | ||||
−0.971286 | + | 0.237915i | \(0.923536\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.92820 | + | 8.48528i | −0.934199 | + | 1.14416i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.48528 | + | 6.92820i | 1.05247 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.65685i | − | 0.691095i | −0.938401 | − | 0.345547i | \(-0.887693\pi\) | ||
0.938401 | − | 0.345547i | \(-0.112307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.79796 | 1.16280 | 0.581402 | − | 0.813617i | \(-0.302504\pi\) | ||||
0.581402 | + | 0.813617i | \(0.302504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.8564i | 1.57908i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.92820 | −0.779484 | −0.389742 | − | 0.920924i | \(-0.627436\pi\) | ||||
−0.389742 | + | 0.920924i | \(0.627436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | − | 4.89898i | −0.650791 | − | 0.531369i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8564 | 1.45255 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.79796 | + | 12.0000i | −1.00525 | + | 1.23117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.79796i | 0.994832i | 0.867512 | + | 0.497416i | \(0.165718\pi\) | ||||
−0.867512 | + | 0.497416i | \(0.834282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.48528 | 0.844317 | 0.422159 | − | 0.906522i | \(-0.361273\pi\) | ||||
0.422159 | + | 0.906522i | \(0.361273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.82843i | − | 0.278693i | −0.990244 | − | 0.139347i | \(-0.955500\pi\) | ||
0.990244 | − | 0.139347i | \(-0.0445002\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.00000i | − | 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.00000 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3205i | 1.62938i | 0.579899 | + | 0.814688i | \(0.303092\pi\) | ||||
−0.579899 | + | 0.814688i | \(0.696908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.92820 | + | 5.65685i | 0.646058 | + | 0.527504i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.79796 | −0.898177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1421i | 1.25491i | 0.778652 | + | 0.627456i | \(0.215904\pi\) | ||||
−0.778652 | + | 0.627456i | \(0.784096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.89898 | −0.428026 | −0.214013 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.5959i | 1.69918i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923i | 0.887875i | 0.896058 | + | 0.443937i | \(0.146419\pi\) | ||||
−0.896058 | + | 0.443937i | \(0.853581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 24.0000i | − | 2.00698i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | + | 14.6969i | −0.996546 | + | 1.22051i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.82843 | −0.231714 | −0.115857 | − | 0.993266i | \(-0.536961\pi\) | ||||
−0.115857 | + | 0.993266i | \(0.536961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.92820 | 0.563809 | 0.281905 | − | 0.959442i | \(-0.409034\pi\) | ||||
0.281905 | + | 0.959442i | \(0.409034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.79796 | − | 12.0000i | 0.786991 | − | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.89898i | − | 0.390981i | −0.980706 | − | 0.195491i | \(-0.937370\pi\) | ||
0.980706 | − | 0.195491i | \(-0.0626299\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137 | 0.891645 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.65685i | − | 0.443079i | −0.975151 | − | 0.221540i | \(-0.928892\pi\) | ||
0.975151 | − | 0.221540i | \(-0.0711082\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.00000i | 0.309529i | 0.987951 | + | 0.154765i | \(0.0494619\pi\) | ||||
−0.987951 | + | 0.154765i | \(0.950538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.2487i | 1.84360i | 0.387671 | + | 0.921798i | \(0.373280\pi\) | ||||
−0.387671 | + | 0.921798i | \(0.626720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.8564 | − | 2.82843i | 1.04745 | − | 0.213809i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6969 | 1.09850 | 0.549250 | − | 0.835658i | \(-0.314913\pi\) | ||||
0.549250 | + | 0.835658i | \(0.314913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.48528 | − | 6.92820i | −0.623850 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9706i | 1.24101i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.79796 | −0.708955 | −0.354478 | − | 0.935064i | \(-0.615341\pi\) | ||||
−0.354478 | + | 0.935064i | \(0.615341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.79796i | − | 0.705273i | −0.935760 | − | 0.352636i | \(-0.885285\pi\) | ||
0.935760 | − | 0.352636i | \(-0.114715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.3923i | − | 0.740421i | −0.928948 | − | 0.370211i | \(-0.879286\pi\) | ||
0.928948 | − | 0.370211i | \(-0.120714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.92820 | −0.491127 | −0.245564 | − | 0.969380i | \(-0.578973\pi\) | ||||
−0.245564 | + | 0.969380i | \(0.578973\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.0000i | 1.68447i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | + | 9.79796i | −0.558744 | + | 0.684319i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.9411 | 2.34776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.7846 | −1.43087 | −0.715436 | − | 0.698679i | \(-0.753772\pi\) | ||||
−0.715436 | + | 0.698679i | \(0.753772\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.5959 | + | 16.0000i | 1.33643 | + | 1.09119i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 19.5959i | − | 1.33026i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.9706 | 1.14156 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.1421i | − | 0.947027i | −0.880786 | − | 0.473514i | \(-0.842985\pi\) | ||
0.880786 | − | 0.473514i | \(-0.157015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 16.0000i | − | 1.06196i | −0.847385 | − | 0.530979i | \(-0.821824\pi\) | ||
0.847385 | − | 0.530979i | \(-0.178176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.46410i | − | 0.226941i | −0.993541 | − | 0.113470i | \(-0.963803\pi\) | ||
0.993541 | − | 0.113470i | \(-0.0361967\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.92820 | − | 5.65685i | −0.451946 | − | 0.369012i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3939 | 1.90133 | 0.950666 | − | 0.310217i | \(-0.100402\pi\) | ||||
0.950666 | + | 0.310217i | \(0.100402\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.41421 | − | 1.73205i | 0.0903508 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.9411i | − | 2.15962i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.89898 | −0.309221 | −0.154610 | − | 0.987976i | \(-0.549412\pi\) | ||||
−0.154610 | + | 0.987976i | \(0.549412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.5959i | − | 1.23198i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3923i | 0.648254i | 0.946014 | + | 0.324127i | \(0.105071\pi\) | ||||
−0.946014 | + | 0.324127i | \(0.894929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.8564 | −0.860995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.0000i | − | 1.72655i | −0.504730 | − | 0.863277i | \(-0.668408\pi\) | ||
0.504730 | − | 0.863277i | \(-0.331592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | − | 4.89898i | −0.368577 | − | 0.300942i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.82843 | 0.172452 | 0.0862261 | − | 0.996276i | \(-0.472519\pi\) | ||||
0.0862261 | + | 0.996276i | \(0.472519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.92820 | 0.420858 | 0.210429 | − | 0.977609i | \(-0.432514\pi\) | ||||
0.210429 | + | 0.977609i | \(0.432514\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.89898 | − | 24.0000i | −0.295420 | − | 1.44725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.4949i | − | 1.47176i | −0.677114 | − | 0.735878i | \(-0.736770\pi\) | ||
0.677114 | − | 0.735878i | \(-0.263230\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.6274 | −1.34984 | −0.674919 | − | 0.737892i | \(-0.735822\pi\) | ||||
−0.674919 | + | 0.737892i | \(0.735822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.2843i | 1.68133i | 0.541559 | + | 0.840663i | \(0.317834\pi\) | ||||
−0.541559 | + | 0.840663i | \(0.682166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0000i | 0.944450i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 17.3205i | − | 1.01187i | −0.862570 | − | 0.505937i | \(-0.831147\pi\) | ||
0.862570 | − | 0.505937i | \(-0.168853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.92820 | − | 8.48528i | 0.403376 | − | 0.494032i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.5959 | −1.13326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.0000 | 1.84445 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.48528 | + | 10.3923i | −0.485866 | + | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.3137i | − | 0.645707i | −0.946449 | − | 0.322854i | \(-0.895358\pi\) | ||
0.946449 | − | 0.322854i | \(-0.104642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.3939 | −1.66677 | −0.833387 | − | 0.552690i | \(-0.813601\pi\) | ||||
−0.833387 | + | 0.552690i | \(0.813601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.3939i | 1.66144i | 0.556690 | + | 0.830720i | \(0.312071\pi\) | ||||
−0.556690 | + | 0.830720i | \(0.687929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.2487i | 1.36194i | 0.732310 | + | 0.680972i | \(0.238442\pi\) | ||||
−0.732310 | + | 0.680972i | \(0.761558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 41.5692 | 2.32743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | + | 4.89898i | −1.33128 | + | 0.271746i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3137 | −0.623745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7846 | −1.14243 | −0.571213 | − | 0.820802i | \(-0.693527\pi\) | ||||
−0.571213 | + | 0.820802i | \(0.693527\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.79796 | + | 8.00000i | 0.535320 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.5959i | − | 1.06746i | −0.845656 | − | 0.533729i | \(-0.820790\pi\) | ||
0.845656 | − | 0.533729i | \(-0.179210\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.9411 | −1.83801 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.00000i | 0.429463i | 0.976673 | + | 0.214731i | \(0.0688876\pi\) | ||||
−0.976673 | + | 0.214731i | \(0.931112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3923i | 0.553127i | 0.960996 | + | 0.276563i | \(0.0891955\pi\) | ||||
−0.960996 | + | 0.276563i | \(0.910804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.8564 | + | 16.9706i | −0.735422 | + | 0.900704i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.5959 | −1.03423 | −0.517116 | − | 0.855915i | \(-0.672995\pi\) | ||||
−0.517116 | + | 0.855915i | \(0.672995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.82843i | 0.147643i | 0.997271 | + | 0.0738213i | \(0.0235195\pi\) | ||||
−0.997271 | + | 0.0738213i | \(0.976481\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.79796 | −0.508685 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 14.6969i | − | 0.760979i | −0.924785 | − | 0.380489i | \(-0.875756\pi\) | ||
0.924785 | − | 0.380489i | \(-0.124244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 41.5692i | − | 2.14092i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.92820 | 0.355878 | 0.177939 | − | 0.984042i | \(-0.443057\pi\) | ||||
0.177939 | + | 0.984042i | \(0.443057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 20.0000i | − | 1.02195i | −0.859595 | − | 0.510976i | \(-0.829284\pi\) | ||
0.859595 | − | 0.510976i | \(-0.170716\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | − | 19.5959i | −1.22315 | − | 0.998700i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1421 | −0.717035 | −0.358517 | − | 0.933523i | \(-0.616718\pi\) | ||||
−0.358517 | + | 0.933523i | \(0.616718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.8564 | 0.700749 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.79796 | − | 12.0000i | 0.492989 | − | 0.603786i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4949i | 1.22936i | 0.788775 | + | 0.614682i | \(0.210716\pi\) | ||||
−0.788775 | + | 0.614682i | \(0.789284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9706 | 0.847469 | 0.423735 | − | 0.905786i | \(-0.360719\pi\) | ||||
0.423735 | + | 0.905786i | \(0.360719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.9411i | 1.69073i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.0000 | −1.48340 | −0.741702 | − | 0.670729i | \(-0.765981\pi\) | ||||
−0.741702 | + | 0.670729i | \(0.765981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13.8564i | − | 0.681829i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.7128 | − | 22.6274i | −1.36037 | − | 1.11074i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4949 | 1.19665 | 0.598327 | − | 0.801252i | \(-0.295832\pi\) | ||||
0.598327 | + | 0.801252i | \(0.295832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.9706 | − | 3.46410i | 0.823193 | − | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.9706i | 0.821263i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.79796i | − | 0.470860i | −0.971891 | − | 0.235430i | \(-0.924350\pi\) | ||
0.971891 | − | 0.235430i | \(-0.0756498\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 27.7128i | − | 1.32568i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.7846 | 0.991995 | 0.495998 | − | 0.868324i | \(-0.334802\pi\) | ||||
0.495998 | + | 0.868324i | \(0.334802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.0000i | 1.52037i | 0.649709 | + | 0.760183i | \(0.274891\pi\) | ||||
−0.649709 | + | 0.760183i | \(0.725109\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.5980 | −1.86874 | −0.934372 | − | 0.356299i | \(-0.884039\pi\) | ||||
−0.934372 | + | 0.356299i | \(0.884039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.7128 | 1.30495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.5959 | + | 24.0000i | −0.918671 | + | 1.12514i | ||||
\(456\) | 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 | ||||||||
\(463\) | 2.82843i | 0.131448i | 0.997838 | + | 0.0657241i | \(0.0209357\pi\) | ||||
−0.997838 | + | 0.0657241i | \(0.979064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 8.00000i | − | 0.370196i | −0.982720 | − | 0.185098i | \(-0.940740\pi\) | ||
0.982720 | − | 0.185098i | \(-0.0592602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 55.4256i | − | 2.54847i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.92820 | − | 33.9411i | −0.317888 | − | 1.55733i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.79796 | −0.447680 | −0.223840 | − | 0.974626i | \(-0.571859\pi\) | ||||
−0.223840 | + | 0.974626i | \(0.571859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | 1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.9706 | − | 13.8564i | −0.770594 | − | 0.629187i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.82843i | − | 0.128168i | −0.997944 | − | 0.0640841i | \(-0.979587\pi\) | ||
0.997944 | − | 0.0640841i | \(-0.0204126\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.89898 | −0.221088 | −0.110544 | − | 0.993871i | \(-0.535259\pi\) | ||||
−0.110544 | + | 0.993871i | \(0.535259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.3939i | 1.32383i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.7128i | 1.24309i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.92820 | −0.310149 | −0.155074 | − | 0.987903i | \(-0.549562\pi\) | ||||
−0.155074 | + | 0.987903i | \(0.549562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.0000i | − | 0.891756i | −0.895094 | − | 0.445878i | \(-0.852892\pi\) | ||
0.895094 | − | 0.445878i | \(-0.147108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | + | 14.6969i | −0.533993 | + | 0.654005i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.48528 | 0.376103 | 0.188052 | − | 0.982159i | \(-0.439783\pi\) | ||||
0.188052 | + | 0.982159i | \(0.439783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.89898 | + | 4.00000i | 0.215875 | + | 0.176261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5959i | 0.861827i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.9706 | −0.743494 | −0.371747 | − | 0.928334i | \(-0.621241\pi\) | ||||
−0.371747 | + | 0.928334i | \(0.621241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.2843i | − | 1.23678i | −0.785869 | − | 0.618392i | \(-0.787784\pi\) | ||
0.785869 | − | 0.618392i | \(-0.212216\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.0000i | − | 1.04546i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 27.7128i | − | 1.20038i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8564 | + | 11.3137i | 0.599065 | + | 0.489134i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.89898 | −0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.48528 | − | 10.3923i | 0.363470 | − | 0.445157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.3137i | − | 0.483739i | −0.970309 | − | 0.241870i | \(-0.922239\pi\) | ||
0.970309 | − | 0.241870i | \(-0.0777606\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 58.7878 | 2.50444 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 19.5959i | − | 0.833303i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 31.1769i | − | 1.32101i | −0.750822 | − | 0.660504i | \(-0.770343\pi\) | ||
0.750822 | − | 0.660504i | \(-0.229657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.4256 | −2.34425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 8.00000i | − | 0.337160i | −0.985688 | − | 0.168580i | \(-0.946082\pi\) | ||
0.985688 | − | 0.168580i | \(-0.0539181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.0000 | − | 24.4949i | −1.26211 | − | 1.03051i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.5980 | −1.66003 | −0.830017 | − | 0.557738i | \(-0.811669\pi\) | ||||
−0.830017 | + | 0.557738i | \(0.811669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.7846 | −0.869809 | −0.434904 | − | 0.900477i | \(-0.643218\pi\) | ||||
−0.434904 | + | 0.900477i | \(0.643218\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.5959 | + | 4.00000i | −0.817206 | + | 0.166812i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.1918i | 1.63158i | 0.578350 | + | 0.815789i | \(0.303697\pi\) | ||||
−0.578350 | + | 0.815789i | \(0.696303\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.2548 | −1.87749 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9706i | 0.702849i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 40.0000i | − | 1.65098i | −0.564419 | − | 0.825488i | \(-0.690900\pi\) | ||
0.564419 | − | 0.825488i | \(-0.309100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.0000 | −1.97781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10.3923i | − | 0.426761i | −0.976969 | − | 0.213380i | \(-0.931553\pi\) | ||
0.976969 | − | 0.213380i | \(-0.0684474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8564 | − | 16.9706i | 0.568057 | − | 0.695725i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.5959 | 0.800668 | 0.400334 | − | 0.916369i | \(-0.368894\pi\) | ||||
0.400334 | + | 0.916369i | \(0.368894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0000 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.3848 | + | 22.5167i | −0.747447 | + | 0.915432i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.82843i | − | 0.114802i | −0.998351 | − | 0.0574012i | \(-0.981719\pi\) | ||
0.998351 | − | 0.0574012i | \(-0.0182814\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.5959 | 0.792766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 4.89898i | − | 0.197868i | −0.995094 | − | 0.0989340i | \(-0.968457\pi\) | ||
0.995094 | − | 0.0989340i | \(-0.0315433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.2487i | − | 0.976216i | −0.872783 | − | 0.488108i | \(-0.837687\pi\) | ||
0.872783 | − | 0.488108i | \(-0.162313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.7846 | 0.835404 | 0.417702 | − | 0.908584i | \(-0.362836\pi\) | ||||
0.417702 | + | 0.908584i | \(0.362836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.9706 | −0.676661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.4974 | −1.93065 | −0.965326 | − | 0.261048i | \(-0.915932\pi\) | ||||
−0.965326 | + | 0.261048i | \(0.915932\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.4949 | − | 20.0000i | −0.972050 | − | 0.793676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.89898i | 0.194105i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.65685 | 0.223432 | 0.111716 | − | 0.993740i | \(-0.464365\pi\) | ||||
0.111716 | + | 0.993740i | \(0.464365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.65685i | 0.223085i | 0.993760 | + | 0.111542i | \(0.0355790\pi\) | ||||
−0.993760 | + | 0.111542i | \(0.964421\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 4.00000i | − | 0.157256i | −0.996904 | − | 0.0786281i | \(-0.974946\pi\) | ||
0.996904 | − | 0.0786281i | \(-0.0250540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.3205i | 0.677804i | 0.940822 | + | 0.338902i | \(0.110055\pi\) | ||||
−0.940822 | + | 0.338902i | \(0.889945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.92820 | − | 8.48528i | 0.270707 | − | 0.331547i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.2929 | −1.33586 | −0.667930 | − | 0.744224i | \(-0.732819\pi\) | ||||
−0.667930 | + | 0.744224i | \(0.732819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.0000 | 1.16686 | 0.583432 | − | 0.812162i | \(-0.301709\pi\) | ||||
0.583432 | + | 0.812162i | \(0.301709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33.9411 | − | 27.7128i | −1.31618 | − | 1.07466i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 33.9411i | − | 1.31421i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.3939 | 1.13474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 9.79796i | − | 0.377684i | −0.982008 | − | 0.188842i | \(-0.939527\pi\) | ||
0.982008 | − | 0.188842i | \(-0.0604733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.46410i | − | 0.133136i | −0.997782 | − | 0.0665681i | \(-0.978795\pi\) | ||
0.997782 | − | 0.0665681i | \(-0.0212050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.7128 | −1.06352 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.00000i | 0.306111i | 0.988218 | + | 0.153056i | \(0.0489114\pi\) | ||||
−0.988218 | + | 0.153056i | \(0.951089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | − | 14.6969i | −0.687745 | − | 0.561541i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.9706 | 0.646527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.6410 | 1.31781 | 0.658903 | − | 0.752228i | \(-0.271021\pi\) | ||||
0.658903 | + | 0.752228i | \(0.271021\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.79796 | − | 12.0000i | 0.371658 | − | 0.455186i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.5959i | 0.742248i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1127 | −1.17511 | −0.587555 | − | 0.809184i | \(-0.699909\pi\) | ||||
−0.587555 | + | 0.809184i | \(0.699909\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.9411i | 1.28011i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.0000i | 0.902613i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | 0.525781 | 0.262891 | − | 0.964826i | \(-0.415324\pi\) | ||||
0.262891 | + | 0.964826i | \(0.415324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.7128i | 1.03785i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.5692 | + | 33.9411i | 1.55460 | + | 1.26933i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.5959 | −0.730804 | −0.365402 | − | 0.930850i | \(-0.619069\pi\) | ||||
−0.365402 | + | 0.930850i | \(0.619069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.48528 | − | 41.5692i | −0.315135 | − | 1.54384i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1127i | 1.15391i | 0.816777 | + | 0.576953i | \(0.195758\pi\) | ||||
−0.816777 | + | 0.576953i | \(0.804242\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.1918 | 1.44956 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4949i | 0.904740i | 0.891830 | + | 0.452370i | \(0.149421\pi\) | ||||
−0.891830 | + | 0.452370i | \(0.850579\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 27.7128i | − | 1.02081i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.7846 | 0.764574 | 0.382287 | − | 0.924044i | \(-0.375137\pi\) | ||||
0.382287 | + | 0.924044i | \(0.375137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.00000i | 0.146746i | 0.997305 | + | 0.0733729i | \(0.0233763\pi\) | ||||
−0.997305 | + | 0.0733729i | \(0.976624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | − | 4.89898i | 0.146549 | − | 0.179485i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.6274 | 0.826788 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.7846 | 0.758441 | 0.379221 | − | 0.925306i | \(-0.376192\pi\) | ||||
0.379221 | + | 0.925306i | \(0.376192\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.79796 | + | 12.0000i | −0.356584 | + | 0.436725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.89898i | − | 0.178056i | −0.996029 | − | 0.0890282i | \(-0.971624\pi\) | ||
0.996029 | − | 0.0890282i | \(-0.0283761\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.9117 | −1.84555 | −0.922774 | − | 0.385342i | \(-0.874083\pi\) | ||||
−0.922774 | + | 0.385342i | \(0.874083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 16.9706i | − | 0.614376i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000i | 0.866590i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 38.1051i | − | 1.37055i | −0.728286 | − | 0.685273i | \(-0.759683\pi\) | ||
0.728286 | − | 0.685273i | \(-0.240317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.92820 | + | 33.9411i | 0.248868 | + | 1.21920i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.1918 | 1.40419 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.0000 | 1.71758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.48528 | + | 6.92820i | 0.302853 | + | 0.247278i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.2843i | − | 1.00823i | −0.863638 | − | 0.504113i | \(-0.831820\pi\) | ||
0.863638 | − | 0.504113i | \(-0.168180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.9898 | −1.74188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 29.3939i | − | 1.04381i | ||||||
\(794\) | 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 | ||||||||
\(799\) | −13.8564 | −0.490204 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.0000 | + | 19.5959i | −0.563926 | + | 0.690665i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.9706 | 0.596653 | 0.298327 | − | 0.954464i | \(-0.403572\pi\) | ||||
0.298327 | + | 0.954464i | \(0.403572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6410 | 1.21641 | 0.608205 | − | 0.793780i | \(-0.291890\pi\) | ||||
0.608205 | + | 0.793780i | \(0.291890\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.79796 | + | 8.00000i | 0.343208 | + | 0.280228i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 78.3837i | − | 2.74230i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.7696 | 1.28327 | 0.641633 | − | 0.767012i | \(-0.278257\pi\) | ||||
0.641633 | + | 0.767012i | \(0.278257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.7990i | − | 0.690149i | −0.938575 | − | 0.345075i | \(-0.887854\pi\) | ||
0.938575 | − | 0.345075i | \(-0.112146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0000i | 0.556375i | 0.960527 | + | 0.278187i | \(0.0897336\pi\) | ||||
−0.960527 | + | 0.278187i | \(0.910266\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.46410i | − | 0.120024i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.92820 | − | 5.65685i | −0.239760 | − | 0.195764i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.5563 | − | 19.0526i | 0.535155 | − | 0.655428i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.7696i | 1.26342i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.5959 | 0.671739 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.0908i | − | 1.50964i | −0.655932 | − | 0.754820i | \(-0.727724\pi\) | ||
0.655932 | − | 0.754820i | \(-0.272276\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 38.1051i | − | 1.30165i | −0.759229 | − | 0.650823i | \(-0.774424\pi\) | ||
0.759229 | − | 0.650823i | \(-0.225576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.7846 | −0.709162 | −0.354581 | − | 0.935025i | \(-0.615376\pi\) | ||||
−0.354581 | + | 0.935025i | \(0.615376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.0000i | 0.953131i | 0.879139 | + | 0.476566i | \(0.158119\pi\) | ||||
−0.879139 | + | 0.476566i | \(0.841881\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.0000 | − | 34.2929i | −1.42804 | − | 1.16599i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.9411 | −1.15137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.7128 | −0.939013 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.6969 | + | 28.0000i | −0.496847 | + | 0.946573i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 44.0908i | − | 1.48884i | −0.667711 | − | 0.744421i | \(-0.732726\pi\) | ||
0.667711 | − | 0.744421i | \(-0.267274\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3137 | −0.381169 | −0.190584 | − | 0.981671i | \(-0.561038\pi\) | ||||
−0.190584 | + | 0.981671i | \(0.561038\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 39.5980i | − | 1.33258i | −0.745694 | − | 0.666289i | \(-0.767882\pi\) | ||
0.745694 | − | 0.666289i | \(-0.232118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 28.0000i | − | 0.940148i | −0.882627 | − | 0.470074i | \(-0.844227\pi\) | ||
0.882627 | − | 0.470074i | \(-0.155773\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.0000 | −1.34156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.7128i | 0.927374i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7846 | + | 25.4558i | −0.694753 | + | 0.850895i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.7878 | −1.96068 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.7990 | + | 24.2487i | −0.658141 | + | 0.806054i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.2548i | 1.50266i | 0.659925 | + | 0.751331i | \(0.270588\pi\) | ||||
−0.659925 | + | 0.751331i | \(0.729412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.1918 | −1.29848 | −0.649242 | − | 0.760582i | \(-0.724914\pi\) | ||||
−0.649242 | + | 0.760582i | \(0.724914\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 78.3837i | 2.59412i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 13.8564i | − | 0.457579i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.92820 | 0.228540 | 0.114270 | − | 0.993450i | \(-0.463547\pi\) | ||||
0.114270 | + | 0.993450i | \(0.463547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 48.0000i | − | 1.57994i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.0000 | − | 4.89898i | 0.789115 | − | 0.161077i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.5980 | 1.29917 | 0.649584 | − | 0.760290i | \(-0.274943\pi\) | ||||
0.649584 | + | 0.760290i | \(0.274943\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.92820 | −0.227063 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.3939 | − | 24.0000i | −0.961283 | − | 0.784884i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.5959i | − | 0.640171i | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||
0.947389 | − | 0.320085i | \(-0.103712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.48528 | −0.276612 | −0.138306 | − | 0.990390i | \(-0.544166\pi\) | ||||
−0.138306 | + | 0.990390i | \(0.544166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 22.6274i | − | 0.736850i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.00000i | 0.259965i | 0.991516 | + | 0.129983i | \(0.0414921\pi\) | ||||
−0.991516 | + | 0.129983i | \(0.958508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 38.1051i | − | 1.23435i | −0.786828 | − | 0.617173i | \(-0.788278\pi\) | ||
0.786828 | − | 0.617173i | \(-0.211722\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.8564 | − | 16.9706i | 0.448383 | − | 0.549155i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.3939 | −0.949178 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.9706 | + | 13.8564i | 0.546302 | + | 0.446054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.1127i | − | 1.00052i | −0.865876 | − | 0.500258i | \(-0.833238\pi\) | ||
0.865876 | − | 0.500258i | \(-0.166762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4949 | −0.786079 | −0.393039 | − | 0.919522i | \(-0.628576\pi\) | ||||
−0.393039 | + | 0.919522i | \(0.628576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 19.5959i | − | 0.628216i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.1769i | 0.997438i | 0.866764 | + | 0.498719i | \(0.166196\pi\) | ||||
−0.866764 | + | 0.498719i | \(0.833804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.00000i | 0.127580i | 0.997963 | + | 0.0637901i | \(0.0203188\pi\) | ||||
−0.997963 | + | 0.0637901i | \(0.979681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | + | 14.6969i | 0.573528 | + | 0.468283i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.2548 | −1.43902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.92820 | −0.220082 | −0.110041 | − | 0.993927i | \(-0.535098\pi\) | ||||
−0.110041 | + | 0.993927i | \(0.535098\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.79796 | − | 12.0000i | 0.310616 | − | 0.380426i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.6969i | 0.465457i | 0.972542 | + | 0.232728i | \(0.0747653\pi\) | ||||
−0.972542 | + | 0.232728i | \(0.925235\pi\) | |||||||
\(998\) | 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 | 2880.2.f.x.1729.4 | 8 | ||
3.2 | odd | 2 | inner | 2880.2.f.x.1729.6 | 8 | ||
4.3 | odd | 2 | inner | 2880.2.f.x.1729.3 | 8 | ||
5.4 | even | 2 | inner | 2880.2.f.x.1729.1 | 8 | ||
8.3 | odd | 2 | 1440.2.f.j.289.5 | yes | 8 | ||
8.5 | even | 2 | 1440.2.f.j.289.6 | yes | 8 | ||
12.11 | even | 2 | inner | 2880.2.f.x.1729.5 | 8 | ||
15.14 | odd | 2 | inner | 2880.2.f.x.1729.7 | 8 | ||
20.19 | odd | 2 | inner | 2880.2.f.x.1729.2 | 8 | ||
24.5 | odd | 2 | 1440.2.f.j.289.4 | yes | 8 | ||
24.11 | even | 2 | 1440.2.f.j.289.3 | yes | 8 | ||
40.3 | even | 4 | 7200.2.a.cs.1.2 | 4 | |||
40.13 | odd | 4 | 7200.2.a.ct.1.3 | 4 | |||
40.19 | odd | 2 | 1440.2.f.j.289.8 | yes | 8 | ||
40.27 | even | 4 | 7200.2.a.ct.1.4 | 4 | |||
40.29 | even | 2 | 1440.2.f.j.289.7 | yes | 8 | ||
40.37 | odd | 4 | 7200.2.a.cs.1.1 | 4 | |||
60.59 | even | 2 | inner | 2880.2.f.x.1729.8 | 8 | ||
120.29 | odd | 2 | 1440.2.f.j.289.1 | ✓ | 8 | ||
120.53 | even | 4 | 7200.2.a.cs.1.4 | 4 | |||
120.59 | even | 2 | 1440.2.f.j.289.2 | yes | 8 | ||
120.77 | even | 4 | 7200.2.a.ct.1.2 | 4 | |||
120.83 | odd | 4 | 7200.2.a.ct.1.1 | 4 | |||
120.107 | odd | 4 | 7200.2.a.cs.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.f.j.289.1 | ✓ | 8 | 120.29 | odd | 2 | ||
1440.2.f.j.289.2 | yes | 8 | 120.59 | even | 2 | ||
1440.2.f.j.289.3 | yes | 8 | 24.11 | even | 2 | ||
1440.2.f.j.289.4 | yes | 8 | 24.5 | odd | 2 | ||
1440.2.f.j.289.5 | yes | 8 | 8.3 | odd | 2 | ||
1440.2.f.j.289.6 | yes | 8 | 8.5 | even | 2 | ||
1440.2.f.j.289.7 | yes | 8 | 40.29 | even | 2 | ||
1440.2.f.j.289.8 | yes | 8 | 40.19 | odd | 2 | ||
2880.2.f.x.1729.1 | 8 | 5.4 | even | 2 | inner | ||
2880.2.f.x.1729.2 | 8 | 20.19 | odd | 2 | inner | ||
2880.2.f.x.1729.3 | 8 | 4.3 | odd | 2 | inner | ||
2880.2.f.x.1729.4 | 8 | 1.1 | even | 1 | trivial | ||
2880.2.f.x.1729.5 | 8 | 12.11 | even | 2 | inner | ||
2880.2.f.x.1729.6 | 8 | 3.2 | odd | 2 | inner | ||
2880.2.f.x.1729.7 | 8 | 15.14 | odd | 2 | inner | ||
2880.2.f.x.1729.8 | 8 | 60.59 | even | 2 | inner | ||
7200.2.a.cs.1.1 | 4 | 40.37 | odd | 4 | |||
7200.2.a.cs.1.2 | 4 | 40.3 | even | 4 | |||
7200.2.a.cs.1.3 | 4 | 120.107 | odd | 4 | |||
7200.2.a.cs.1.4 | 4 | 120.53 | even | 4 | |||
7200.2.a.ct.1.1 | 4 | 120.83 | odd | 4 | |||
7200.2.a.ct.1.2 | 4 | 120.77 | even | 4 | |||
7200.2.a.ct.1.3 | 4 | 40.13 | odd | 4 | |||
7200.2.a.ct.1.4 | 4 | 40.27 | even | 4 |