Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5040,2,Mod(1009,5040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5040.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5040.t (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: | \(40.2446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.1 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5040.1009 |
Dual form | 5040.2.t.z.1009.2 |
$q$-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 \(\left(\mathbb{Z}/5040\mathbb{Z}\right)^\times\).
\(n\) | \(2017\) | \(2801\) | \(3151\) | \(3601\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −1.48119 | − | 1.67513i | −0.662410 | − | 0.749141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.31265 | 1.90334 | 0.951668 | − | 0.307129i | \(-0.0993684\pi\) | ||||
0.951668 | + | 0.307129i | \(0.0993684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.96239i | − | 1.93102i | −0.260368 | − | 0.965510i | \(-0.583844\pi\) | ||
0.260368 | − | 0.965510i | \(-0.416156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.57452i | − | 1.59455i | −0.603613 | − | 0.797277i | \(-0.706273\pi\) | ||
0.603613 | − | 0.797277i | \(-0.293727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.73813 | −0.857587 | −0.428793 | − | 0.903403i | \(-0.641061\pi\) | ||||
−0.428793 | + | 0.903403i | \(0.641061\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.73813i | − | 1.19648i | −0.801316 | − | 0.598242i | \(-0.795866\pi\) | ||
0.801316 | − | 0.598242i | \(-0.204134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.612127 | + | 4.96239i | −0.122425 | + | 0.992478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.03761 | 0.186361 | 0.0931803 | − | 0.995649i | \(-0.470297\pi\) | ||||
0.0931803 | + | 0.995649i | \(0.470297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.67513 | − | 1.48119i | 0.283149 | − | 0.250368i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.7005i | 1.75916i | 0.475755 | + | 0.879578i | \(0.342175\pi\) | ||||
−0.475755 | + | 0.879578i | \(0.657825\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.96239 | 1.08734 | 0.543671 | − | 0.839298i | \(-0.317034\pi\) | ||||
0.543671 | + | 0.839298i | \(0.317034\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.92478i | − | 0.903520i | −0.892139 | − | 0.451760i | \(-0.850796\pi\) | ||
0.892139 | − | 0.451760i | \(-0.149204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.03761i | 0.142527i | 0.997458 | + | 0.0712634i | \(0.0227031\pi\) | ||||
−0.997458 | + | 0.0712634i | \(0.977297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.35026 | − | 10.5745i | −1.26079 | − | 1.42587i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.22425 | 0.419762 | 0.209881 | − | 0.977727i | \(-0.432692\pi\) | ||||
0.209881 | + | 0.977727i | \(0.432692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8496 | −1.77325 | −0.886627 | − | 0.462485i | \(-0.846958\pi\) | ||||
−0.886627 | + | 0.462485i | \(0.846958\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.6629 | + | 10.3127i | −1.44661 | + | 1.27913i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.77575i | 0.583450i | 0.956502 | + | 0.291725i | \(0.0942293\pi\) | ||||
−0.956502 | + | 0.291725i | \(0.905771\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.23743 | 0.977603 | 0.488801 | − | 0.872395i | \(-0.337434\pi\) | ||||
0.488801 | + | 0.872395i | \(0.337434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.26187i | − | 0.498814i | −0.968399 | − | 0.249407i | \(-0.919764\pi\) | ||
0.968399 | − | 0.249407i | \(-0.0802356\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.31265i | 0.719393i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.92478 | −0.666590 | −0.333295 | − | 0.942823i | \(-0.608160\pi\) | ||||
−0.333295 | + | 0.942823i | \(0.608160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.22425i | − | 0.353908i | −0.984219 | − | 0.176954i | \(-0.943376\pi\) | ||
0.984219 | − | 0.176954i | \(-0.0566244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.0132 | + | 9.73813i | −1.19455 | + | 1.05625i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.18664 | 0.231784 | 0.115892 | − | 0.993262i | \(-0.463027\pi\) | ||||
0.115892 | + | 0.993262i | \(0.463027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.96239 | 0.729857 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.53690 | + | 6.26187i | 0.568074 | + | 0.642454i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.73813i | 0.379550i | 0.981828 | + | 0.189775i | \(0.0607759\pi\) | ||||
−0.981828 | + | 0.189775i | \(0.939224\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.66291 | −0.961496 | −0.480748 | − | 0.876859i | \(-0.659635\pi\) | ||||
−0.480748 | + | 0.876859i | \(0.659635\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.29948i | 0.128041i | 0.997949 | + | 0.0640206i | \(0.0203923\pi\) | ||||
−0.997949 | + | 0.0640206i | \(0.979608\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.66291i | − | 0.354107i | −0.984201 | − | 0.177054i | \(-0.943343\pi\) | ||
0.984201 | − | 0.177054i | \(-0.0566566\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.77575 | −0.648999 | −0.324499 | − | 0.945886i | \(-0.605196\pi\) | ||||
−0.324499 | + | 0.945886i | \(0.605196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.88717i | − | 0.836034i | −0.908439 | − | 0.418017i | \(-0.862725\pi\) | ||
0.908439 | − | 0.418017i | \(-0.137275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.61213 | + | 8.49929i | −0.896335 | + | 0.792563i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.57452 | 0.602685 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.8496 | 2.62269 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.21933 | − | 6.32487i | 0.824602 | − | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.70052i | 0.239633i | 0.992796 | + | 0.119816i | \(0.0382306\pi\) | ||||
−0.992796 | + | 0.119816i | \(0.961769\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.40105 | −0.821373 | −0.410687 | − | 0.911777i | \(-0.634711\pi\) | ||||
−0.410687 | + | 0.911777i | \(0.634711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.73813i | − | 0.324137i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.66291i | 0.825558i | 0.910831 | + | 0.412779i | \(0.135442\pi\) | ||||
−0.910831 | + | 0.412779i | \(0.864558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.8872 | 1.77163 | 0.885813 | − | 0.464042i | \(-0.153601\pi\) | ||||
0.885813 | + | 0.464042i | \(0.153601\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 43.9511i | − | 3.67538i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.96239 | + | 3.35026i | 0.246013 | + | 0.278224i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0752228 | 0.00616249 | 0.00308125 | − | 0.999995i | \(-0.499019\pi\) | ||||
0.00308125 | + | 0.999995i | \(0.499019\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.70052 | −0.545281 | −0.272640 | − | 0.962116i | \(-0.587897\pi\) | ||||
−0.272640 | + | 0.962116i | \(0.587897\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.53690 | − | 1.73813i | −0.123447 | − | 0.139610i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.66291i | − | 0.451950i | −0.974133 | − | 0.225975i | \(-0.927443\pi\) | ||
0.974133 | − | 0.225975i | \(-0.0725567\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.73813 | 0.452228 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.6253i | − | 1.59603i | −0.602635 | − | 0.798017i | \(-0.705883\pi\) | ||
0.602635 | − | 0.798017i | \(-0.294117\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.4749 | −2.72884 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5745i | 0.803966i | 0.915647 | + | 0.401983i | \(0.131679\pi\) | ||||
−0.915647 | + | 0.401983i | \(0.868321\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.96239 | − | 0.612127i | −0.375121 | − | 0.0462724i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.911603 | −0.0681364 | −0.0340682 | − | 0.999420i | \(-0.510846\pi\) | ||||
−0.0340682 | + | 0.999420i | \(0.510846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3258 | −0.990501 | −0.495250 | − | 0.868750i | \(-0.664924\pi\) | ||||
−0.495250 | + | 0.868750i | \(0.664924\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.9248 | − | 15.8496i | 1.31786 | − | 1.16528i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 41.5026i | − | 3.03497i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.7889 | −1.86602 | −0.933010 | − | 0.359849i | \(-0.882828\pi\) | ||||
−0.933010 | + | 0.359849i | \(0.882828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 15.3258i | − | 1.10318i | −0.834116 | − | 0.551588i | \(-0.814022\pi\) | ||
0.834116 | − | 0.551588i | \(-0.185978\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.513881i | − | 0.0366125i | −0.999832 | − | 0.0183063i | \(-0.994173\pi\) | ||
0.999832 | − | 0.0183063i | \(-0.00582739\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.73813 | 0.264989 | 0.132495 | − | 0.991184i | \(-0.457701\pi\) | ||||
0.132495 | + | 0.991184i | \(0.457701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.00000i | − | 0.140372i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.3127 | − | 11.6629i | −0.720267 | − | 0.814573i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.5975 | −1.63228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.22425 | 0.221967 | 0.110983 | − | 0.993822i | \(-0.464600\pi\) | ||||
0.110983 | + | 0.993822i | \(0.464600\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.92478 | + | 8.77575i | −0.676864 | + | 0.598501i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.03761i | 0.0704377i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −45.7743 | −3.07911 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.8496i | − | 0.793505i | −0.917926 | − | 0.396752i | \(-0.870137\pi\) | ||
0.917926 | − | 0.396752i | \(-0.129863\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.7005i | 0.975708i | 0.872925 | + | 0.487854i | \(0.162220\pi\) | ||||
−0.872925 | + | 0.487854i | \(0.837780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.47627 | −0.626210 | −0.313105 | − | 0.949719i | \(-0.601369\pi\) | ||||
−0.313105 | + | 0.949719i | \(0.601369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.5125i | 1.93343i | 0.255863 | + | 0.966713i | \(0.417640\pi\) | ||||
−0.255863 | + | 0.966713i | \(0.582360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.0132 | 1.61797 | 0.808984 | − | 0.587831i | \(-0.200018\pi\) | ||||
0.808984 | + | 0.587831i | \(0.200018\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.92478 | 0.510480 | 0.255240 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255240 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.48119 | + | 1.67513i | 0.0946300 | + | 0.107020i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0263i | 1.65602i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0738 | −0.951450 | −0.475725 | − | 0.879594i | \(-0.657814\pi\) | ||||
−0.475725 | + | 0.879594i | \(0.657814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 36.2228i | − | 2.27731i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.0508i | − | 1.37549i | −0.725952 | − | 0.687745i | \(-0.758601\pi\) | ||
0.725952 | − | 0.687745i | \(-0.241399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.7005 | −0.664898 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.8134i | − | 0.728443i | −0.931312 | − | 0.364221i | \(-0.881335\pi\) | ||
0.931312 | − | 0.364221i | \(-0.118665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.73813 | − | 1.53690i | 0.106773 | − | 0.0944113i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.0640 | −1.65012 | −0.825059 | − | 0.565046i | \(-0.808858\pi\) | ||||
−0.825059 | + | 0.565046i | \(0.808858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8119 | 0.656779 | 0.328389 | − | 0.944542i | \(-0.393494\pi\) | ||||
0.328389 | + | 0.944542i | \(0.393494\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.86414 | + | 31.3258i | −0.233017 | + | 1.88902i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 22.5501i | − | 1.35490i | −0.735568 | − | 0.677451i | \(-0.763084\pi\) | ||
0.735568 | − | 0.677451i | \(-0.236916\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3733 | 0.618818 | 0.309409 | − | 0.950929i | \(-0.399869\pi\) | ||||
0.309409 | + | 0.950929i | \(0.399869\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.7005i | − | 0.636080i | −0.948077 | − | 0.318040i | \(-0.896975\pi\) | ||
0.948077 | − | 0.318040i | \(-0.103025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.96239i | 0.410977i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.2243 | −1.54260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.5745i | − | 0.617770i | −0.951099 | − | 0.308885i | \(-0.900044\pi\) | ||
0.951099 | − | 0.308885i | \(-0.0999558\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.77575 | − | 5.40105i | −0.278055 | − | 0.314461i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −39.9511 | −2.31043 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.92478 | 0.341498 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.5139 | + | 23.1998i | 1.17462 | + | 1.32842i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.55008i | − | 0.373833i | −0.982376 | − | 0.186916i | \(-0.940151\pi\) | ||
0.982376 | − | 0.186916i | \(-0.0598493\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.2995 | −0.980963 | −0.490482 | − | 0.871452i | \(-0.663179\pi\) | ||||
−0.490482 | + | 0.871452i | \(0.663179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2130i | 1.14251i | 0.820774 | + | 0.571253i | \(0.193542\pi\) | ||||
−0.820774 | + | 0.571253i | \(0.806458\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.3357i | − | 1.08600i | −0.839733 | − | 0.543000i | \(-0.817288\pi\) | ||
0.839733 | − | 0.543000i | \(-0.182712\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.6253 | −0.706881 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.5764i | 1.36747i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.5501 | + | 4.26187i | 1.91649 | + | 0.236406i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6253 | −1.35353 | −0.676764 | − | 0.736200i | \(-0.736618\pi\) | ||||
−0.676764 | + | 0.736200i | \(0.736618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | − | 7.07381i | 0.437087 | − | 0.386483i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.44851i | 0.351273i | 0.984455 | + | 0.175636i | \(0.0561983\pi\) | ||||
−0.984455 | + | 0.175636i | \(0.943802\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.55008 | 0.354707 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 11.6629i | − | 0.626098i | −0.949737 | − | 0.313049i | \(-0.898650\pi\) | ||
0.949737 | − | 0.313049i | \(-0.101350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.4485 | −0.666353 | −0.333177 | − | 0.942864i | \(-0.608121\pi\) | ||||
−0.333177 | + | 0.942864i | \(0.608121\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.0230i | − | 0.693146i | −0.938023 | − | 0.346573i | \(-0.887345\pi\) | ||
0.938023 | − | 0.346573i | \(-0.112655\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2012 | − | 13.7988i | −0.647574 | − | 0.732363i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3879 | 1.07603 | 0.538015 | − | 0.842935i | \(-0.319174\pi\) | ||||
0.538015 | + | 0.842935i | \(0.319174\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.02635 | −0.264545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.13918 | + | 6.31265i | −0.373682 | + | 0.330419i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8496i | 1.03614i | 0.855339 | + | 0.518069i | \(0.173349\pi\) | ||||
−0.855339 | + | 0.518069i | \(0.826651\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.03761 | −0.0538701 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.85097i | − | 0.147618i | −0.997272 | − | 0.0738088i | \(-0.976485\pi\) | ||
0.997272 | − | 0.0738088i | \(-0.0235155\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.9248i | 0.717163i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.29948 | 0.272216 | 0.136108 | − | 0.990694i | \(-0.456541\pi\) | ||||
0.136108 | + | 0.990694i | \(0.456541\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.2520i | 0.626049i | 0.949745 | + | 0.313024i | \(0.101342\pi\) | ||||
−0.949745 | + | 0.313024i | \(0.898658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.5745 | − | 9.35026i | 0.538927 | − | 0.476533i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.4485 | 0.833972 | 0.416986 | − | 0.908913i | \(-0.363086\pi\) | ||||
0.416986 | + | 0.908913i | \(0.363086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.7255 | −1.90786 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.77575 | + | 9.92478i | 0.441556 | + | 0.499370i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.58769i | − | 0.180061i | −0.995939 | − | 0.0900305i | \(-0.971304\pi\) | ||
0.995939 | − | 0.0900305i | \(-0.0286964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.9248 | −0.994996 | −0.497498 | − | 0.867465i | \(-0.665748\pi\) | ||||
−0.497498 | + | 0.867465i | \(0.665748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.22425i | − | 0.359866i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 67.5487i | 3.34826i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1754 | 1.24484 | 0.622421 | − | 0.782682i | \(-0.286149\pi\) | ||||
0.622421 | + | 0.782682i | \(0.286149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.22425i | 0.158655i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.40105 | + | 4.77575i | −0.265127 | + | 0.234432i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.14903 | −0.0561338 | −0.0280669 | − | 0.999606i | \(-0.508935\pi\) | ||||
−0.0280669 | + | 0.999606i | \(0.508935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.176793 | −0.00861637 | −0.00430819 | − | 0.999991i | \(-0.501371\pi\) | ||||
−0.00430819 | + | 0.999991i | \(0.501371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.6253 | + | 4.02444i | 1.58256 | + | 0.195214i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.8496i | − | 0.670227i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3879 | 0.596703 | 0.298351 | − | 0.954456i | \(-0.403563\pi\) | ||||
0.298351 | + | 0.954456i | \(0.403563\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.41090i | 0.0678033i | 0.999425 | + | 0.0339017i | \(0.0107933\pi\) | ||||
−0.999425 | + | 0.0339017i | \(0.989207\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.4499i | 1.02609i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5877 | 1.50760 | 0.753799 | − | 0.657105i | \(-0.228219\pi\) | ||||
0.753799 | + | 0.657105i | \(0.228219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 28.0362i | − | 1.33204i | −0.745934 | − | 0.666020i | \(-0.767997\pi\) | ||
0.745934 | − | 0.666020i | \(-0.232003\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.23884 | − | 3.66291i | −0.153536 | − | 0.173639i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.4010 | −0.915592 | −0.457796 | − | 0.889057i | \(-0.651361\pi\) | ||||
−0.457796 | + | 0.889057i | \(0.651361\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43.9511 | 2.06958 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.3127 | − | 11.6629i | −0.483465 | − | 0.546766i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3258i | 0.904024i | 0.892012 | + | 0.452012i | \(0.149294\pi\) | ||||
−0.892012 | + | 0.452012i | \(0.850706\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.81194 | −0.130965 | −0.0654826 | − | 0.997854i | \(-0.520859\pi\) | ||||
−0.0654826 | + | 0.997854i | \(0.520859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1016i | 1.12009i | 0.828461 | + | 0.560047i | \(0.189217\pi\) | ||||
−0.828461 | + | 0.560047i | \(0.810783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 21.1490i | − | 0.978660i | −0.872099 | − | 0.489330i | \(-0.837241\pi\) | ||
0.872099 | − | 0.489330i | \(-0.162759\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.77575 | −0.220523 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 37.4010i | − | 1.71970i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.28821 | − | 18.5501i | 0.104990 | − | 0.851136i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.2995 | 0.790433 | 0.395217 | − | 0.918588i | \(-0.370670\pi\) | ||||
0.395217 | + | 0.918588i | \(0.370670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 74.5012 | 3.39696 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.26187 | − | 5.53690i | 0.284337 | − | 0.251418i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 40.4749i | − | 1.83409i | −0.398783 | − | 0.917045i | \(-0.630567\pi\) | ||
0.398783 | − | 0.917045i | \(-0.369433\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.9854 | −0.901929 | −0.450964 | − | 0.892542i | \(-0.648920\pi\) | ||||
−0.450964 | + | 0.892542i | \(0.648920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.1490i | 0.592203i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.23743i | 0.369499i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.8510 | 0.664821 | 0.332410 | − | 0.943135i | \(-0.392138\pi\) | ||||
0.332410 | + | 0.943135i | \(0.392138\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.5501i | 1.00546i | 0.864444 | + | 0.502729i | \(0.167671\pi\) | ||||
−0.864444 | + | 0.502729i | \(0.832329\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.3127 | + | 16.1866i | 0.636905 | + | 0.720296i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.5125 | 0.776226 | 0.388113 | − | 0.921612i | \(-0.373127\pi\) | ||||
0.388113 | + | 0.921612i | \(0.373127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.26187 | 0.188534 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.17679 | − | 1.92478i | 0.0959210 | − | 0.0848158i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.4387 | −1.15830 | −0.579149 | − | 0.815221i | \(-0.696615\pi\) | ||||
−0.579149 | + | 0.815221i | \(0.696615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.8496i | 1.39268i | 0.717710 | + | 0.696342i | \(0.245190\pi\) | ||||
−0.717710 | + | 0.696342i | \(0.754810\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 6.82179i | − | 0.297162i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.92619 | −0.431574 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 48.4749i | − | 2.09968i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.13586 | + | 5.42548i | −0.265276 | + | 0.234564i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.31265 | −0.271905 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.1768 | 1.03944 | 0.519721 | − | 0.854336i | \(-0.326036\pi\) | ||||
0.519721 | + | 0.854336i | \(0.326036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0362 | + | 11.3503i | 0.429903 | + | 0.486192i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 34.1768i | − | 1.46129i | −0.682755 | − | 0.730647i | \(-0.739219\pi\) | ||
0.682755 | − | 0.730647i | \(-0.260781\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.47627 | 0.318500 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.92478i | − | 0.251947i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 24.7367i | − | 1.04813i | −0.851679 | − | 0.524064i | \(-0.824415\pi\) | ||
0.851679 | − | 0.524064i | \(-0.175585\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.2506 | −1.74471 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.47627i | 0.315087i | 0.987512 | + | 0.157544i | \(0.0503575\pi\) | ||||
−0.987512 | + | 0.157544i | \(0.949643\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.8872 | + | 13.1636i | −0.626308 | + | 0.553798i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.3258 | 0.726336 | 0.363168 | − | 0.931724i | \(-0.381695\pi\) | ||||
0.363168 | + | 0.931724i | \(0.381695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.8496 | −1.33286 | −0.666431 | − | 0.745567i | \(-0.732179\pi\) | ||||
−0.666431 | + | 0.745567i | \(0.732179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.4749 | + | 3.51247i | 1.18748 | + | 0.146480i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 20.5139i | − | 0.854004i | −0.904251 | − | 0.427002i | \(-0.859570\pi\) | ||
0.904251 | − | 0.427002i | \(-0.140430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.22425 | 0.133765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.55008i | 0.271277i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.8773i | 0.861699i | 0.902424 | + | 0.430850i | \(0.141786\pi\) | ||||
−0.902424 | + | 0.430850i | \(0.858214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.87873 | −0.159820 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.57593i | − | 0.228976i | −0.993425 | − | 0.114488i | \(-0.963477\pi\) | ||
0.993425 | − | 0.114488i | \(-0.0365227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.73813 | − | 11.0132i | −0.399225 | − | 0.451496i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.01317 | −0.0413972 | −0.0206986 | − | 0.999786i | \(-0.506589\pi\) | ||||
−0.0206986 | + | 0.999786i | \(0.506589\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2981 | −0.827975 | −0.413988 | − | 0.910283i | \(-0.635864\pi\) | ||||
−0.413988 | + | 0.910283i | \(0.635864\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −42.7318 | − | 48.3268i | −1.73729 | − | 1.96476i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.9525i | 0.606905i | 0.952847 | + | 0.303452i | \(0.0981393\pi\) | ||||
−0.952847 | + | 0.303452i | \(0.901861\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 19.0738i | − | 0.770384i | −0.922836 | − | 0.385192i | \(-0.874135\pi\) | ||
0.922836 | − | 0.385192i | \(-0.125865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8886i | 0.639650i | 0.947477 | + | 0.319825i | \(0.103624\pi\) | ||||
−0.947477 | + | 0.319825i | \(0.896376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.7367 | 1.31580 | 0.657900 | − | 0.753105i | \(-0.271445\pi\) | ||||
0.657900 | + | 0.753105i | \(0.271445\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.18664i | 0.0876060i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | − | 6.07522i | −0.970024 | − | 0.243009i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 70.3508 | 2.80507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.7269 | 1.62131 | 0.810656 | − | 0.585523i | \(-0.199111\pi\) | ||||
0.810656 | + | 0.585523i | \(0.199111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.52373 | − | 4.00000i | 0.179519 | − | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.96239i | 0.275860i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.1754 | 1.46834 | 0.734170 | − | 0.678966i | \(-0.237572\pi\) | ||||
0.734170 | + | 0.678966i | \(0.237572\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3996i | 0.725611i | 0.931865 | + | 0.362805i | \(0.118181\pi\) | ||||
−0.931865 | + | 0.362805i | \(0.881819\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.2243i | 0.598527i | 0.954170 | + | 0.299264i | \(0.0967410\pi\) | ||||
−0.954170 | + | 0.299264i | \(0.903259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3536 | 0.798948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 0.785595i | − | 0.0307427i | −0.999882 | − | 0.0153714i | \(-0.995107\pi\) | ||
0.999882 | − | 0.0153714i | \(-0.00489305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9248 | + | 15.7480i | 0.544086 | + | 0.615325i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.2652 | 0.828374 | 0.414187 | − | 0.910192i | \(-0.364066\pi\) | ||||
0.414187 | + | 0.910192i | \(0.364066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.4485 | −1.26210 | −0.631050 | − | 0.775742i | \(-0.717376\pi\) | ||||
−0.631050 | + | 0.775742i | \(0.717376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.26187 | + | 5.53690i | −0.242825 | + | 0.214712i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4763i | 0.444363i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −87.4274 | −3.37510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.55149i | 0.213994i | 0.994259 | + | 0.106997i | \(0.0341236\pi\) | ||||
−0.994259 | + | 0.106997i | \(0.965876\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.72355i | 0.296840i | 0.988924 | + | 0.148420i | \(0.0474187\pi\) | ||||
−0.988924 | + | 0.148420i | \(0.952581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.73813 | −0.143456 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5125i | 0.593568i | 0.954945 | + | 0.296784i | \(0.0959141\pi\) | ||||
−0.954945 | + | 0.296784i | \(0.904086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.1866 | − | 14.3127i | 0.618460 | − | 0.546858i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.22425 | 0.275222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.7367 | 0.941029 | 0.470515 | − | 0.882392i | \(-0.344068\pi\) | ||||
0.470515 | + | 0.882392i | \(0.344068\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.9380 | − | 34.9887i | −1.17354 | − | 1.32720i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 45.7743i | − | 1.73383i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.55149 | 0.134138 | 0.0670690 | − | 0.997748i | \(-0.478635\pi\) | ||||
0.0670690 | + | 0.997748i | \(0.478635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 40.0000i | − | 1.50863i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 9.66291i | − | 0.363411i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.6991 | −0.664704 | −0.332352 | − | 0.943155i | \(-0.607842\pi\) | ||||
−0.332352 | + | 0.943155i | \(0.607842\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.95395i | − | 0.222977i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −73.6239 | + | 65.1002i | −2.75338 | + | 2.43461i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.3733 | 0.461446 | 0.230723 | − | 0.973020i | \(-0.425891\pi\) | ||||
0.230723 | + | 0.973020i | \(0.425891\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.29948 | −0.0483950 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.22425 | − | 9.92478i | 0.0454676 | − | 0.368597i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.9511i | 1.77841i | 0.457510 | + | 0.889204i | \(0.348741\pi\) | ||||
−0.457510 | + | 0.889204i | \(0.651259\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.9525 | −1.44071 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 37.9149i | − | 1.40042i | −0.713937 | − | 0.700210i | \(-0.753090\pi\) | ||
0.713937 | − | 0.700210i | \(-0.246910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.1476i | 1.11050i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.4010 | 1.52296 | 0.761481 | − | 0.648187i | \(-0.224473\pi\) | ||||
0.761481 | + | 0.648187i | \(0.224473\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.28963i | − | 0.267430i | −0.991020 | − | 0.133715i | \(-0.957309\pi\) | ||
0.991020 | − | 0.133715i | \(-0.0426908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.111420 | − | 0.126008i | −0.00408210 | − | 0.00461658i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.66291 | 0.133840 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.12127 | −0.150387 | −0.0751936 | − | 0.997169i | \(-0.523957\pi\) | ||||
−0.0751936 | + | 0.997169i | \(0.523957\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.92478 | + | 11.2243i | 0.361200 | + | 0.408492i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 23.4471i | − | 0.852199i | −0.904676 | − | 0.426100i | \(-0.859887\pi\) | ||
0.904676 | − | 0.426100i | \(-0.140113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.7104 | −0.388251 | −0.194125 | − | 0.980977i | \(-0.562187\pi\) | ||||
−0.194125 | + | 0.980977i | \(0.562187\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 6.77575i | − | 0.245298i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 22.4485i | − | 0.810569i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.8496 | 0.787915 | 0.393958 | − | 0.919129i | \(-0.371106\pi\) | ||||
0.393958 | + | 0.919129i | \(0.371106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 31.9756i | − | 1.15008i | −0.818125 | − | 0.575041i | \(-0.804986\pi\) | ||
0.818125 | − | 0.575041i | \(-0.195014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.635150 | + | 5.14903i | −0.0228153 | + | 0.184959i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.0263 | −0.932491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.0000 | 1.86071 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.48612 | + | 8.38787i | −0.338574 | + | 0.299376i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2506i | 1.04267i | 0.853352 | + | 0.521336i | \(0.174566\pi\) | ||||
−0.853352 | + | 0.521336i | \(0.825434\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.88717 | 0.315991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 96.4260i | 3.42419i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.1246i | 1.03165i | 0.856695 | + | 0.515823i | \(0.172514\pi\) | ||||
−0.856695 | + | 0.515823i | \(0.827486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 26.9037i | − | 0.949410i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.49929 | − | 9.61213i | −0.299561 | − | 0.338783i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.95254 | 0.174122 | 0.0870610 | − | 0.996203i | \(-0.472252\pi\) | ||||
0.0870610 | + | 0.996203i | \(0.472252\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.6893 | −1.11276 | −0.556380 | − | 0.830928i | \(-0.687810\pi\) | ||||
−0.556380 | + | 0.830928i | \(0.687810\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.70052 | − | 5.92478i | 0.234709 | − | 0.207536i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.1476i | 0.774847i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.8218 | 0.587085 | 0.293542 | − | 0.955946i | \(-0.405166\pi\) | ||||
0.293542 | + | 0.955946i | \(0.405166\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.7005i | − | 0.930722i | −0.885121 | − | 0.465361i | \(-0.845925\pi\) | ||
0.885121 | − | 0.465361i | \(-0.154075\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.1866i | 1.11924i | 0.828750 | + | 0.559620i | \(0.189053\pi\) | ||||
−0.828750 | + | 0.559620i | \(0.810947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.7269 | −1.62289 | −0.811446 | − | 0.584428i | \(-0.801319\pi\) | ||||
−0.811446 | + | 0.584428i | \(0.801319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.57452i | 0.227793i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.5501 | + | 30.5501i | −1.19565 | + | 1.05723i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.6253 | 1.54064 | 0.770318 | − | 0.637660i | \(-0.220097\pi\) | ||||
0.770318 | + | 0.637660i | \(0.220097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.5452 | + | 59.4250i | 1.80761 | + | 2.04428i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.8496i | 0.991282i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.4010 | 2.10480 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.2422i | 0.830036i | 0.909813 | + | 0.415018i | \(0.136225\pi\) | ||||
−0.909813 | + | 0.415018i | \(0.863775\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 15.6023i | − | 0.532964i | −0.963840 | − | 0.266482i | \(-0.914139\pi\) | ||
0.963840 | − | 0.266482i | \(-0.0858612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.3371 | 1.30804 | 0.654022 | − | 0.756475i | \(-0.273080\pi\) | ||||
0.654022 | + | 0.756475i | \(0.273080\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.0640i | 0.989349i | 0.869078 | + | 0.494674i | \(0.164713\pi\) | ||||
−0.869078 | + | 0.494674i | \(0.835287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.7137 | − | 15.6629i | 0.602284 | − | 0.532555i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.4010 | −1.26874 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.2506 | 1.12665 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.32487 | + | 9.21933i | 0.213820 | + | 0.311670i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7757i | 0.566477i | 0.959050 | + | 0.283238i | \(0.0914088\pi\) | ||||
−0.959050 | + | 0.283238i | \(0.908591\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.6907 | 1.03400 | 0.516998 | − | 0.855987i | \(-0.327050\pi\) | ||||
0.516998 | + | 0.855987i | \(0.327050\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 32.9986i | − | 1.11049i | −0.831687 | − | 0.555245i | \(-0.812624\pi\) | ||
0.831687 | − | 0.555245i | \(-0.187376\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 45.1002i | − | 1.51432i | −0.653232 | − | 0.757158i | \(-0.726588\pi\) | ||
0.653232 | − | 0.757158i | \(-0.273412\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.70052 | −0.0905727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.35026 | + | 1.52705i | 0.0451343 | + | 0.0510438i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.07522 | −0.0692126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.82179 | 0.227267 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.7381 | + | 22.3225i | 0.656118 | + | 0.742025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.9986i | 1.09570i | 0.836577 | + | 0.547850i | \(0.184554\pi\) | ||||
−0.836577 | + | 0.547850i | \(0.815446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.8153 | 1.18661 | 0.593306 | − | 0.804977i | \(-0.297822\pi\) | ||||
0.593306 | + | 0.804977i | \(0.297822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 20.3536i | − | 0.673605i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 9.40105i | − | 0.310450i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.0738 | −0.893083 | −0.446541 | − | 0.894763i | \(-0.647344\pi\) | ||||
−0.446541 | + | 0.894763i | \(0.647344\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 57.3522i | − | 1.88777i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −53.1002 | − | 6.55008i | −1.74592 | − | 0.215365i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.5877 | −0.773887 | −0.386943 | − | 0.922103i | \(-0.626469\pi\) | ||||
−0.386943 | + | 0.922103i | \(0.626469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.73813 | 0.122512 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −69.5223 | + | 61.4734i | −2.27362 | + | 2.01040i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.0625i | 1.57013i | 0.619410 | + | 0.785067i | \(0.287372\pi\) | ||||
−0.619410 | + | 0.785067i | \(0.712628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.4109 | 0.567579 | 0.283789 | − | 0.958887i | \(-0.408408\pi\) | ||||
0.283789 | + | 0.958887i | \(0.408408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 39.9511i | − | 1.30099i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.9610i | 0.453671i | 0.973933 | + | 0.226835i | \(0.0728379\pi\) | ||||
−0.973933 | + | 0.226835i | \(0.927162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.6728 | −0.963219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 27.4861i | − | 0.890363i | −0.895440 | − | 0.445181i | \(-0.853139\pi\) | ||
0.895440 | − | 0.445181i | \(-0.146861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.1984 | + | 43.1998i | 1.23607 | + | 1.39791i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.66291 | −0.312032 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9234 | −0.965270 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.6728 | + | 22.7005i | −0.826435 | + | 0.730756i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.6713i | 0.857693i | 0.903377 | + | 0.428846i | \(0.141080\pi\) | ||||
−0.903377 | + | 0.428846i | \(0.858920\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.6239 | 1.59251 | 0.796253 | − | 0.604964i | \(-0.206812\pi\) | ||||
0.796253 | + | 0.604964i | \(0.206812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.8872i | 0.669612i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 37.5125i | − | 1.20013i | −0.799951 | − | 0.600065i | \(-0.795141\pi\) | ||
0.799951 | − | 0.600065i | \(-0.204859\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.8035 | 0.441162 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 52.2228i | − | 1.66565i | −0.553536 | − | 0.832825i | \(-0.686722\pi\) | ||
0.553536 | − | 0.832825i | \(-0.313278\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.860818 | + | 0.761158i | −0.0274279 | + | 0.0242525i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.9972 | −1.08105 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.3272 | −0.836312 | −0.418156 | − | 0.908375i | \(-0.637324\pi\) | ||||
−0.418156 | + | 0.908375i | \(0.637324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.53690 | − | 6.26187i | −0.175532 | − | 0.198514i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.3620i | 0.929905i | 0.885336 | + | 0.464952i | \(0.153929\pi\) | ||||
−0.885336 | + | 0.464952i | \(0.846071\pi\) | |||||||
\(998\) | 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 | 5040.2.t.z.1009.1 | 6 | ||
3.2 | odd | 2 | 1680.2.t.j.1009.3 | 6 | |||
4.3 | odd | 2 | 2520.2.t.k.1009.1 | 6 | |||
5.4 | even | 2 | inner | 5040.2.t.z.1009.2 | 6 | ||
12.11 | even | 2 | 840.2.t.d.169.6 | yes | 6 | ||
15.2 | even | 4 | 8400.2.a.di.1.1 | 3 | |||
15.8 | even | 4 | 8400.2.a.dl.1.1 | 3 | |||
15.14 | odd | 2 | 1680.2.t.j.1009.6 | 6 | |||
20.19 | odd | 2 | 2520.2.t.k.1009.2 | 6 | |||
60.23 | odd | 4 | 4200.2.a.bn.1.3 | 3 | |||
60.47 | odd | 4 | 4200.2.a.bp.1.3 | 3 | |||
60.59 | even | 2 | 840.2.t.d.169.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.d.169.3 | ✓ | 6 | 60.59 | even | 2 | ||
840.2.t.d.169.6 | yes | 6 | 12.11 | even | 2 | ||
1680.2.t.j.1009.3 | 6 | 3.2 | odd | 2 | |||
1680.2.t.j.1009.6 | 6 | 15.14 | odd | 2 | |||
2520.2.t.k.1009.1 | 6 | 4.3 | odd | 2 | |||
2520.2.t.k.1009.2 | 6 | 20.19 | odd | 2 | |||
4200.2.a.bn.1.3 | 3 | 60.23 | odd | 4 | |||
4200.2.a.bp.1.3 | 3 | 60.47 | odd | 4 | |||
5040.2.t.z.1009.1 | 6 | 1.1 | even | 1 | trivial | ||
5040.2.t.z.1009.2 | 6 | 5.4 | even | 2 | inner | ||
8400.2.a.di.1.1 | 3 | 15.2 | even | 4 | |||
8400.2.a.dl.1.1 | 3 | 15.8 | even | 4 |