Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(81,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.ba (of order \(12\), degree \(4\), 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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 81.9 | ||
Character | \(\chi\) | \(=\) | 448.81 |
Dual form | 448.2.ba.c.177.9 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.60845 | − | 0.430984i | 0.928642 | − | 0.248829i | 0.237366 | − | 0.971420i | \(-0.423716\pi\) |
0.691275 | + | 0.722591i | \(0.257049\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.94900 | + | 0.522232i | 0.871618 | + | 0.233549i | 0.666787 | − | 0.745248i | \(-0.267669\pi\) |
0.204831 | + | 0.978797i | \(0.434336\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.89075 | − | 1.85069i | 0.714638 | − | 0.699495i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.196696 | + | 0.113563i | −0.0655654 | + | 0.0378542i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.63411 | − | 6.09856i | −0.492701 | − | 1.83879i | −0.542542 | − | 0.840029i | \(-0.682538\pi\) |
0.0498403 | − | 0.998757i | \(-0.484129\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13388 | + | 1.13388i | 0.314480 | + | 0.314480i | 0.846642 | − | 0.532162i | \(-0.178620\pi\) |
−0.532162 | + | 0.846642i | \(0.678620\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.35995 | 0.867535 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.960789 | + | 1.66414i | −0.233026 | + | 0.403612i | −0.958697 | − | 0.284429i | \(-0.908196\pi\) |
0.725671 | + | 0.688041i | \(0.241529\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.63324 | + | 6.09532i | −0.374690 | + | 1.39836i | 0.479107 | + | 0.877756i | \(0.340960\pi\) |
−0.853797 | + | 0.520605i | \(0.825706\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.24357 | − | 3.79164i | 0.489588 | − | 0.827403i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.924606 | − | 0.533821i | 0.192794 | − | 0.111309i | −0.400496 | − | 0.916298i | \(-0.631162\pi\) |
0.593290 | + | 0.804989i | \(0.297829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.804265 | − | 0.464342i | −0.160853 | − | 0.0928685i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.79985 | + | 3.79985i | −0.731281 | + | 0.731281i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.08936 | + | 5.08936i | 0.945070 | + | 0.945070i | 0.998568 | − | 0.0534979i | \(-0.0170370\pi\) |
−0.0534979 | + | 0.998568i | \(0.517037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.198293 | − | 0.343454i | 0.0356145 | − | 0.0616861i | −0.847669 | − | 0.530526i | \(-0.821994\pi\) |
0.883283 | + | 0.468840i | \(0.155328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.25677 | − | 9.10499i | −0.915086 | − | 1.58498i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.65156 | − | 2.61958i | 0.786257 | − | 0.442789i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.327303 | + | 0.0877006i | 0.0538083 | + | 0.0144179i | 0.285623 | − | 0.958342i | \(-0.407800\pi\) |
−0.231814 | + | 0.972760i | \(0.574466\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.31247 | + | 1.33510i | 0.370291 | + | 0.213788i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.26189i | − | 1.13412i | −0.823678 | − | 0.567058i | \(-0.808081\pi\) | ||
0.823678 | − | 0.567058i | \(-0.191919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.75565 | + | 1.75565i | −0.267734 | + | 0.267734i | −0.828187 | − | 0.560452i | \(-0.810627\pi\) |
0.560452 | + | 0.828187i | \(0.310627\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.442666 | + | 0.118612i | −0.0659888 | + | 0.0176816i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.08118 | + | 1.87265i | 0.157706 | + | 0.273155i | 0.934041 | − | 0.357166i | \(-0.116257\pi\) |
−0.776335 | + | 0.630320i | \(0.782924\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.149895 | − | 6.99839i | 0.0214136 | − | 0.999771i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.828170 | + | 3.09077i | −0.115967 | + | 0.432795i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.111394 | + | 0.415727i | 0.0153011 | + | 0.0571045i | 0.973154 | − | 0.230154i | \(-0.0739229\pi\) |
−0.957853 | + | 0.287258i | \(0.907256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12.7395i | − | 1.71779i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.5079i | 1.39181i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.32453 | + | 8.67527i | 0.302628 | + | 1.12942i | 0.934968 | + | 0.354732i | \(0.115428\pi\) |
−0.632340 | + | 0.774691i | \(0.717905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.72673 | + | 10.1763i | −0.349122 | + | 1.30294i | 0.538601 | + | 0.842561i | \(0.318953\pi\) |
−0.887722 | + | 0.460379i | \(0.847713\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.161735 | + | 0.578743i | −0.0203767 | + | 0.0729147i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.61777 | + | 2.80206i | 0.200660 | + | 0.347553i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.87441 | + | 2.10994i | −0.962012 | + | 0.257770i | −0.705452 | − | 0.708758i | \(-0.749256\pi\) |
−0.256560 | + | 0.966528i | \(0.582589\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.25712 | − | 1.25712i | 0.151339 | − | 0.151339i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.78982i | − | 0.331090i | −0.986202 | − | 0.165545i | \(-0.947062\pi\) | ||
0.986202 | − | 0.165545i | \(-0.0529384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.05730 | + | 1.18779i | 0.240789 | + | 0.139020i | 0.615539 | − | 0.788106i | \(-0.288938\pi\) |
−0.374750 | + | 0.927126i | \(0.622272\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.49375 | − | 0.400248i | −0.172483 | − | 0.0462167i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.3762 | − | 8.50666i | −1.63832 | − | 0.969424i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.10829 | − | 8.84782i | −0.574727 | − | 0.995457i | −0.996071 | − | 0.0885562i | \(-0.971775\pi\) |
0.421344 | − | 0.906901i | \(-0.361559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.13352 | + | 7.15947i | −0.459280 | + | 0.795496i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.17951 | − | 1.17951i | −0.129468 | − | 0.129468i | 0.639404 | − | 0.768871i | \(-0.279181\pi\) |
−0.768871 | + | 0.639404i | \(0.779181\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.74164 | + | 2.74164i | −0.297373 | + | 0.297373i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3794 | + | 5.99257i | 1.11279 | + | 0.642471i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0470 | − | 6.37800i | 1.17098 | − | 0.676066i | 0.217070 | − | 0.976156i | \(-0.430350\pi\) |
0.953911 | + | 0.300089i | \(0.0970165\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.24233 | + | 0.0454269i | 0.444717 | + | 0.00476204i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.170922 | − | 0.637891i | 0.0177238 | − | 0.0661462i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.36634 | + | 11.0268i | −0.653173 | + | 1.13133i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.21148 | −0.224542 | −0.112271 | − | 0.993678i | \(-0.535813\pi\) | ||||
−0.112271 | + | 0.993678i | \(0.535813\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.01399 | + | 1.01399i | 0.101910 | + | 0.101910i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.86231 | + | 6.95024i | 0.185307 | + | 0.691575i | 0.994565 | + | 0.104121i | \(0.0332030\pi\) |
−0.809258 | + | 0.587454i | \(0.800130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.1457 | + | 8.74438i | −1.49235 | + | 0.861609i | −0.999962 | − | 0.00876536i | \(-0.997210\pi\) |
−0.492390 | + | 0.870375i | \(0.663877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.35283 | − | 6.21822i | 0.619973 | − | 0.606836i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.90855 | − | 0.779344i | −0.281180 | − | 0.0753420i | 0.115473 | − | 0.993311i | \(-0.463162\pi\) |
−0.396653 | + | 0.917969i | \(0.629828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.86536 | − | 1.83957i | 0.657583 | − | 0.176199i | 0.0854277 | − | 0.996344i | \(-0.472774\pi\) |
0.572155 | + | 0.820146i | \(0.306108\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.564250 | 0.0535562 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.96535 | −0.561173 | −0.280586 | − | 0.959829i | \(-0.590529\pi\) | ||||
−0.280586 | + | 0.959829i | \(0.590529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.08083 | − | 0.557557i | 0.194039 | − | 0.0519925i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.351795 | − | 0.0942631i | −0.0325234 | − | 0.00871463i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.26318 | + | 4.92459i | 0.115796 | + | 0.451437i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.9959 | + | 14.4314i | −2.27235 | + | 1.31194i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.12976 | − | 11.6804i | −0.282201 | − | 1.05319i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.45884 | − | 8.45884i | −0.756582 | − | 0.756582i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.41296 | −0.569058 | −0.284529 | − | 0.958667i | \(-0.591837\pi\) | ||||
−0.284529 | + | 0.958667i | \(0.591837\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.06723 | + | 3.58055i | −0.182009 | + | 0.315250i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.87298 | − | 14.4542i | 0.338384 | − | 1.26287i | −0.561769 | − | 0.827294i | \(-0.689879\pi\) |
0.900154 | − | 0.435573i | \(-0.143454\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.19250 | + | 14.5474i | 0.710380 | + | 1.26142i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.39029 | + | 5.42149i | −0.808187 | + | 0.466607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50928 | + | 0.871382i | 0.128946 | + | 0.0744472i | 0.563086 | − | 0.826399i | \(-0.309614\pi\) |
−0.434139 | + | 0.900846i | \(0.642947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.84436 | + | 2.84436i | −0.241256 | + | 0.241256i | −0.817370 | − | 0.576114i | \(-0.804569\pi\) |
0.576114 | + | 0.817370i | \(0.304569\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.54611 | + | 2.54611i | 0.214421 | + | 0.214421i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.06214 | − | 8.76788i | 0.423317 | − | 0.733207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.26132 | + | 12.5770i | 0.603020 | + | 1.04446i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.77510 | − | 11.3212i | −0.228886 | − | 0.933757i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.7848 | − | 4.76543i | −1.45699 | − | 0.390399i | −0.558541 | − | 0.829477i | \(-0.688639\pi\) |
−0.898449 | + | 0.439077i | \(0.855305\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.52437 | + | 3.18949i | 0.449567 | + | 0.259557i | 0.707647 | − | 0.706566i | \(-0.249757\pi\) |
−0.258081 | + | 0.966123i | \(0.583090\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.436439i | − | 0.0352840i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.565835 | − | 0.565835i | 0.0454490 | − | 0.0454490i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6177 | − | 4.72065i | 1.40605 | − | 0.376749i | 0.525534 | − | 0.850773i | \(-0.323866\pi\) |
0.880512 | + | 0.474024i | \(0.157199\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.358344 | + | 0.620669i | 0.0284185 | + | 0.0492223i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.760264 | − | 2.72048i | 0.0599172 | − | 0.214404i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.97338 | + | 11.0968i | −0.232893 | + | 0.869170i | 0.746194 | + | 0.665729i | \(0.231879\pi\) |
−0.979087 | + | 0.203441i | \(0.934787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.49051 | − | 20.4909i | −0.427435 | − | 1.59521i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 21.6693i | − | 1.67682i | −0.545040 | − | 0.838410i | \(-0.683486\pi\) | ||
0.545040 | − | 0.838410i | \(-0.316514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.4287i | − | 0.802204i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.370949 | − | 1.38440i | −0.0283672 | − | 0.105868i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.31175 | − | 12.3596i | 0.251788 | − | 0.939684i | −0.718062 | − | 0.695979i | \(-0.754970\pi\) |
0.969849 | − | 0.243705i | \(-0.0783629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.38002 | + | 0.610487i | −0.179913 | + | 0.0461485i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.47780 | + | 12.9519i | 0.562066 | + | 0.973527i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.05939 | + | 0.819762i | −0.228670 | + | 0.0612719i | −0.371334 | − | 0.928499i | \(-0.621100\pi\) |
0.142665 | + | 0.989771i | \(0.454433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.3765 | + | 14.3765i | −1.06860 | + | 1.06860i | −0.0711279 | + | 0.997467i | \(0.522660\pi\) |
−0.997467 | + | 0.0711279i | \(0.977340\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.5433i | 1.29684i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.592113 | + | 0.341857i | 0.0435330 | + | 0.0251338i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.7189 | + | 3.14006i | 0.856969 | + | 0.229624i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.152235 | + | 14.2169i | −0.0110735 | + | 1.03413i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.12089 | + | 10.6017i | 0.442892 | + | 0.767111i | 0.997903 | − | 0.0647319i | \(-0.0206192\pi\) |
−0.555011 | + | 0.831843i | \(0.687286\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.08900 | − | 1.88620i | 0.0783877 | − | 0.135771i | −0.824167 | − | 0.566347i | \(-0.808356\pi\) |
0.902554 | + | 0.430576i | \(0.141689\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.80976 | + | 3.80976i | 0.272823 | + | 0.272823i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.97878 | − | 9.97878i | 0.710959 | − | 0.710959i | −0.255777 | − | 0.966736i | \(-0.582331\pi\) |
0.966736 | + | 0.255777i | \(0.0823313\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.14271 | + | 5.27854i | 0.648109 | + | 0.374186i | 0.787731 | − | 0.616019i | \(-0.211255\pi\) |
−0.139622 | + | 0.990205i | \(0.544589\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.7563 | + | 6.78749i | −0.829224 | + | 0.478753i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.0415 | + | 0.203897i | 1.33645 | + | 0.0143108i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.79239 | − | 14.1534i | 0.264872 | − | 0.988516i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.121244 | + | 0.210001i | −0.00842706 | + | 0.0145961i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 39.8416 | 2.75590 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.20378 | − | 5.20378i | −0.358243 | − | 0.358243i | 0.504922 | − | 0.863165i | \(-0.331521\pi\) |
−0.863165 | + | 0.504922i | \(0.831521\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.20237 | − | 4.48730i | −0.0823849 | − | 0.307464i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.33862 | + | 2.50490i | −0.295891 | + | 0.170833i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.260703 | − | 1.01636i | −0.0176977 | − | 0.0689953i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.82100 | + | 1.02383i | 0.258199 | + | 0.0691843i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.97634 | + | 0.797507i | −0.200210 | + | 0.0536461i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.3888 | 1.49926 | 0.749632 | − | 0.661855i | \(-0.230230\pi\) | ||||
0.749632 | + | 0.661855i | \(0.230230\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.210928 | 0.0140619 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.9753 | − | 4.81647i | 1.19306 | − | 0.319680i | 0.392967 | − | 0.919552i | \(-0.371448\pi\) |
0.800096 | + | 0.599872i | \(0.204782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.12426 | + | 2.17689i | 0.536866 | + | 0.143853i | 0.517057 | − | 0.855951i | \(-0.327027\pi\) |
0.0198093 | + | 0.999804i | \(0.493694\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.7898 | − | 7.48664i | −1.76264 | − | 0.492585i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9278 | − | 8.61859i | 0.977955 | − | 0.564623i | 0.0763032 | − | 0.997085i | \(-0.475688\pi\) |
0.901652 | + | 0.432462i | \(0.142355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.12925 | + | 4.21442i | 0.0736642 | + | 0.274919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0297 | − | 12.0297i | −0.781414 | − | 0.781414i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.572679 | 0.0370435 | 0.0185218 | − | 0.999828i | \(-0.494104\pi\) | ||||
0.0185218 | + | 0.999828i | \(0.494104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.89318 | − | 10.2073i | 0.379613 | − | 0.657510i | −0.611393 | − | 0.791327i | \(-0.709390\pi\) |
0.991006 | + | 0.133818i | \(0.0427237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.609557 | − | 2.27490i | 0.0391031 | − | 0.145935i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.94693 | − | 13.5616i | 0.252160 | − | 0.866417i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.76321 | + | 5.05944i | −0.557590 | + | 0.321925i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.40553 | − | 1.38883i | −0.152444 | − | 0.0880137i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.57539 | − | 5.57539i | 0.351916 | − | 0.351916i | −0.508906 | − | 0.860822i | \(-0.669950\pi\) |
0.860822 | + | 0.508906i | \(0.169950\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.76645 | − | 4.76645i | −0.299664 | − | 0.299664i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.22820 | + | 5.59141i | −0.202158 | + | 0.350148i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.5328 | − | 25.1715i | −0.906528 | − | 1.57015i | −0.818853 | − | 0.574004i | \(-0.805390\pi\) |
−0.0876753 | − | 0.996149i | \(-0.527944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.781156 | − | 0.439916i | 0.0485387 | − | 0.0273351i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.57902 | − | 0.423097i | −0.0977388 | − | 0.0261890i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3142 | + | 8.84163i | 0.944311 | + | 0.545198i | 0.891309 | − | 0.453396i | \(-0.149788\pi\) |
0.0530021 | + | 0.998594i | \(0.483121\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.868424i | 0.0533469i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.0198 | − | 15.0198i | 0.919198 | − | 0.919198i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4268 | − | 3.86566i | 0.879620 | − | 0.235693i | 0.209377 | − | 0.977835i | \(-0.432856\pi\) |
0.670243 | + | 0.742142i | \(0.266190\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.93172 | − | 12.0061i | −0.421072 | − | 0.729319i | 0.574972 | − | 0.818173i | \(-0.305013\pi\) |
−0.996045 | + | 0.0888543i | \(0.971679\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.84317 | − | 1.75531i | 0.414168 | − | 0.106236i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.51757 | + | 5.66364i | −0.0915128 | + | 0.341531i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.597472 | − | 2.22980i | −0.0358986 | − | 0.133975i | 0.945651 | − | 0.325184i | \(-0.105426\pi\) |
−0.981550 | + | 0.191208i | \(0.938759\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0900747i | 0.00539263i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.680351i | 0.0405863i | 0.999794 | + | 0.0202932i | \(0.00645996\pi\) | ||||
−0.999794 | + | 0.0202932i | \(0.993540\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0985120 | − | 0.367652i | −0.00585593 | − | 0.0218546i | 0.962936 | − | 0.269730i | \(-0.0869344\pi\) |
−0.968792 | + | 0.247875i | \(0.920268\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.48759 | + | 20.4799i | −0.325056 | + | 1.21313i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4395 | − | 13.7304i | −0.793309 | − | 0.810482i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.65377 | + | 11.5247i | 0.391398 | + | 0.677921i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.55707 | + | 0.953115i | −0.208519 | + | 0.0558726i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.49220 | − | 7.49220i | 0.437699 | − | 0.437699i | −0.453538 | − | 0.891237i | \(-0.649838\pi\) |
0.891237 | + | 0.453538i | \(0.149838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.1220i | 1.05510i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.3829 | + | 16.9643i | 1.70497 | + | 0.984366i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.65367 | + | 0.443101i | 0.0956345 | + | 0.0256252i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0703375 | + | 6.56867i | −0.00405418 | + | 0.378612i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.99089 | + | 10.3765i | 0.344168 | + | 0.596116i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.6288 | + | 18.4096i | −0.608602 | + | 1.05413i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.27988 | + | 6.27988i | 0.358412 | + | 0.358412i | 0.863227 | − | 0.504816i | \(-0.168439\pi\) |
−0.504816 | + | 0.863227i | \(0.668439\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.5925 | + | 20.5925i | −1.17147 | + | 1.17147i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.55685 | − | 4.94030i | −0.485215 | − | 0.280139i | 0.237372 | − | 0.971419i | \(-0.423714\pi\) |
−0.722587 | + | 0.691280i | \(0.757047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.8734 | + | 8.58714i | −0.840692 | + | 0.485374i | −0.857499 | − | 0.514485i | \(-0.827983\pi\) |
0.0168075 | + | 0.999859i | \(0.494650\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.617459 | + | 1.04350i | −0.0347899 | + | 0.0587948i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.49870 | + | 20.5214i | −0.308838 | + | 1.15260i | 0.620754 | + | 0.784006i | \(0.286827\pi\) |
−0.929591 | + | 0.368592i | \(0.879840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.7212 | − | 39.3543i | 1.27214 | − | 2.20342i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.01416 | −0.279863 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.57424 | − | 8.57424i | −0.477084 | − | 0.477084i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.385429 | − | 1.43844i | −0.0213798 | − | 0.0797904i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.2498 | − | 5.91773i | 0.566815 | − | 0.327251i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.50994 | + | 1.53980i | 0.303773 | + | 0.0848921i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3748 | − | 6.26326i | −1.28479 | − | 0.344260i | −0.449113 | − | 0.893475i | \(-0.648260\pi\) |
−0.835681 | + | 0.549215i | \(0.814927\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0743388 | + | 0.0199190i | −0.00407374 | + | 0.00109156i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.4491 | −0.898709 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.26739 | −0.232460 | −0.116230 | − | 0.993222i | \(-0.537081\pi\) | ||||
−0.116230 | + | 0.993222i | \(0.537081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.59499 | + | 2.57097i | −0.521128 | + | 0.139636i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.41861 | − | 0.648063i | −0.130975 | − | 0.0350946i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6684 | − | 13.5096i | −0.684032 | − | 0.729452i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.10663 | − | 1.79361i | 0.167255 | − | 0.0965648i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.0139833 | + | 0.0521865i | 0.000750664 | + | 0.00280152i | 0.966300 | − | 0.257418i | \(-0.0828717\pi\) |
−0.965549 | + | 0.260220i | \(0.916205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.4928 | − | 15.4928i | −0.829309 | − | 0.829309i | 0.158112 | − | 0.987421i | \(-0.449459\pi\) |
−0.987421 | + | 0.158112i | \(0.949459\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.61710 | −0.459947 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.38161 | + | 14.5174i | −0.446108 | + | 0.772682i | −0.998129 | − | 0.0611484i | \(-0.980524\pi\) |
0.552020 | + | 0.833831i | \(0.313857\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.45693 | − | 5.43735i | 0.0773259 | − | 0.288584i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.15420 | + | 7.37657i | 0.219863 | + | 0.390410i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.8777 | − | 17.2499i | 1.57689 | − | 0.910415i | 0.581595 | − | 0.813479i | \(-0.302429\pi\) |
0.995291 | − | 0.0969365i | \(-0.0309044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0310 | − | 10.4102i | −0.948998 | − | 0.547904i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −33.9851 | + | 33.9851i | −1.78375 | + | 1.78375i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.38938 | + | 3.38938i | 0.177408 | + | 0.177408i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2644 | + | 17.7785i | −0.535799 | + | 0.928032i | 0.463325 | + | 0.886189i | \(0.346656\pi\) |
−0.999124 | + | 0.0418433i | \(0.986677\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.824679 | + | 1.42839i | 0.0429311 | + | 0.0743588i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.980000 | + | 0.579882i | 0.0508791 | + | 0.0301060i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.2773 | + | 4.09353i | 0.791027 | + | 0.211955i | 0.631641 | − | 0.775261i | \(-0.282382\pi\) |
0.159386 | + | 0.987216i | \(0.449049\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.2513 | − | 9.96003i | −0.890853 | − | 0.514334i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.5414i | 0.594412i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2717 | + | 11.2717i | −0.578987 | + | 0.578987i | −0.934624 | − | 0.355637i | \(-0.884264\pi\) |
0.355637 | + | 0.934624i | \(0.384264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.3150 | + | 2.76388i | −0.528451 | + | 0.141598i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.14594 | + | 8.91303i | 0.262945 | + | 0.455434i | 0.967023 | − | 0.254688i | \(-0.0819728\pi\) |
−0.704078 | + | 0.710123i | \(0.748640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.5768 | − | 24.0872i | −1.20158 | − | 1.22760i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.145954 | − | 0.544707i | 0.00741925 | − | 0.0276890i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.30513 | + | 19.7990i | 0.268981 | + | 1.00385i | 0.959769 | + | 0.280792i | \(0.0905972\pi\) |
−0.690788 | + | 0.723058i | \(0.742736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.05156i | 0.103752i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 24.9181i | − | 1.25695i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.33543 | − | 19.9121i | −0.268454 | − | 1.00189i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.02632 | + | 7.56231i | −0.101698 | + | 0.379542i | −0.997950 | − | 0.0640041i | \(-0.979613\pi\) |
0.896252 | + | 0.443546i | \(0.146280\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.4469 | + | 19.8679i | 0.973565 | + | 0.994640i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.09985 | − | 12.2973i | −0.354549 | − | 0.614098i | 0.632491 | − | 0.774567i | \(-0.282032\pi\) |
−0.987041 | + | 0.160470i | \(0.948699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.614273 | − | 0.164594i | 0.0305991 | − | 0.00819901i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.7951 | + | 11.7951i | −0.586104 | + | 0.586104i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.13939i | − | 0.106046i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.8759 | − | 13.2074i | −1.13114 | − | 0.653065i | −0.186920 | − | 0.982375i | \(-0.559851\pi\) |
−0.944222 | + | 0.329310i | \(0.893184\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.80316 | + | 0.751104i | 0.138270 | + | 0.0370492i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.4503 | + | 12.1008i | 1.00630 | + | 0.595442i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.68288 | − | 2.91483i | −0.0826092 | − | 0.143083i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.34915 | + | 5.80091i | −0.164009 | + | 0.284072i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.6893 | + | 15.6893i | 0.766471 | + | 0.766471i | 0.977483 | − | 0.211012i | \(-0.0676759\pi\) |
−0.211012 | + | 0.977483i | \(0.567676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.7068 | − | 25.7068i | 1.25287 | − | 1.25287i | 0.298444 | − | 0.954427i | \(-0.403532\pi\) |
0.954427 | − | 0.298444i | \(-0.0964675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.425327 | − | 0.245563i | −0.0206801 | − | 0.0119397i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.54546 | − | 0.892270i | 0.0749657 | − | 0.0432815i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.6776 | + | 24.2872i | 0.661905 | + | 1.17534i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.36340 | − | 16.2844i | 0.210667 | − | 0.786220i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3981 | + | 21.4741i | −0.597194 | + | 1.03437i | 0.396039 | + | 0.918234i | \(0.370384\pi\) |
−0.993233 | + | 0.116137i | \(0.962949\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.22863 | 0.251272 | 0.125636 | − | 0.992076i | \(-0.459903\pi\) | ||||
0.125636 | + | 0.992076i | \(0.459903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.1000 | + | 17.1000i | 0.819881 | + | 0.819881i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.74371 | + | 6.50762i | 0.0834131 | + | 0.311302i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.1771 | − | 11.0719i | 0.915273 | − | 0.528433i | 0.0331491 | − | 0.999450i | \(-0.489446\pi\) |
0.882124 | + | 0.471017i | \(0.156113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.765272 | + | 1.39358i | 0.0364415 | + | 0.0663610i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.8067 | − | 5.84309i | −1.03607 | − | 0.277614i | −0.299585 | − | 0.954070i | \(-0.596848\pi\) |
−0.736483 | + | 0.676456i | \(0.763515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.8614 | − | 6.66159i | 1.17854 | − | 0.315790i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.6599 | −1.45017 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.3678 | −1.71630 | −0.858152 | − | 0.513396i | \(-0.828387\pi\) | ||||
−0.858152 | + | 0.513396i | \(0.828387\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.2871 | + | 11.8667i | −2.08540 | + | 0.558781i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.2603 | + | 2.74924i | 0.482072 | + | 0.129171i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.24456 | + | 2.30402i | 0.386511 | + | 0.108014i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.5807 | − | 12.4596i | 1.00950 | − | 0.582837i | 0.0984570 | − | 0.995141i | \(-0.468609\pi\) |
0.911046 | + | 0.412304i | \(0.135276\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.67261 | − | 9.97431i | −0.124747 | − | 0.465561i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.60588 | − | 1.60588i | −0.0747933 | − | 0.0747933i | 0.668721 | − | 0.743514i | \(-0.266842\pi\) |
−0.743514 | + | 0.668721i | \(0.766842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.8176 | 0.688634 | 0.344317 | − | 0.938853i | \(-0.388110\pi\) | ||||
0.344317 | + | 0.938853i | \(0.388110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.666254 | − | 1.15399i | 0.0308968 | − | 0.0535148i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.21315 | − | 11.9916i | 0.148687 | − | 0.554907i | −0.850877 | − | 0.525365i | \(-0.823929\pi\) |
0.999564 | − | 0.0295414i | \(-0.00940469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.9837 | + | 18.5625i | −0.507181 | + | 0.857135i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.3028 | − | 15.1859i | 1.21197 | − | 0.699730i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.5759 | + | 7.83804i | 0.624220 | + | 0.360393i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.14387 | − | 4.14387i | 0.190134 | − | 0.190134i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0691218 | − | 0.0691218i | −0.00316487 | − | 0.00316487i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.02709 | + | 1.77897i | −0.0469288 | + | 0.0812831i | −0.888536 | − | 0.458808i | \(-0.848277\pi\) |
0.841607 | + | 0.540091i | \(0.181610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.271679 | + | 0.470563i | 0.0123875 | + | 0.0214558i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0503645 | − | 4.70344i | 0.00229166 | − | 0.214014i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.31018 | − | 1.15491i | −0.195715 | − | 0.0524417i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.4045 | + | 20.4408i | 1.60433 | + | 0.926261i | 0.990607 | + | 0.136740i | \(0.0436625\pi\) |
0.613724 | + | 0.789521i | \(0.289671\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.1302i | 0.865098i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.278015 | − | 0.278015i | 0.0125466 | − | 0.0125466i | −0.700806 | − | 0.713352i | \(-0.747176\pi\) |
0.713352 | + | 0.700806i | \(0.247176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.3592 | + | 3.57958i | −0.601667 | + | 0.161216i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.44673 | + | 2.50580i | 0.0650255 | + | 0.112628i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.16309 | − | 5.27486i | −0.231596 | − | 0.236610i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.19039 | − | 11.9067i | 0.142822 | − | 0.533018i | −0.857021 | − | 0.515281i | \(-0.827687\pi\) |
0.999843 | − | 0.0177363i | \(-0.00564595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.33912 | − | 34.8541i | −0.417241 | − | 1.55717i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 0.367839i | − | 0.0164011i | −0.999966 | − | 0.00820057i | \(-0.997390\pi\) | ||
0.999966 | − | 0.00820057i | \(-0.00261035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.5186i | 0.646068i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.49459 | − | 16.7740i | −0.199612 | − | 0.744960i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.09820 | + | 7.83060i | −0.0930012 | + | 0.347085i | −0.996709 | − | 0.0810649i | \(-0.974168\pi\) |
0.903708 | + | 0.428150i | \(0.140835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.08808 | − | 1.56162i | 0.269321 | − | 0.0690822i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.9552 | − | 29.3673i | −0.748591 | − | 1.29660i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −34.0855 | + | 9.13319i | −1.50199 | + | 0.402457i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.65374 | − | 9.65374i | 0.424571 | − | 0.424571i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 21.3072i | − | 0.935282i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.5215 | − | 6.65193i | −0.504766 | − | 0.291427i | 0.225914 | − | 0.974147i | \(-0.427463\pi\) |
−0.730679 | + | 0.682721i | \(0.760797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.4536 | + | 7.35616i | 1.20046 | + | 0.321663i | 0.803013 | − | 0.595962i | \(-0.203229\pi\) |
0.397448 | + | 0.917625i | \(0.369896\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.56504 | + | 2.00769i | −0.155591 | + | 0.0876229i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.381036 | + | 0.659973i | 0.0165982 | + | 0.0287489i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9301 | + | 18.9314i | −0.475220 | + | 0.823106i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.44241 | − | 1.44241i | −0.0625954 | − | 0.0625954i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.23408 | − | 8.23408i | 0.356657 | − | 0.356657i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.26176 | − | 3.03788i | −0.227486 | − | 0.131339i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.56759 | + | 2.63710i | −0.197106 | + | 0.113799i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −42.9251 | + | 10.5220i | −1.84892 | + | 0.453213i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.75802 | + | 17.7572i | −0.204563 | + | 0.763441i | 0.785019 | + | 0.619472i | \(0.212653\pi\) |
−0.989582 | + | 0.143969i | \(0.954013\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.9279 | + | 29.3199i | −0.726445 | + | 1.25824i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.3413 | 0.614312 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9801 | + | 22.9801i | 0.982558 | + | 0.982558i | 0.999850 | − | 0.0172930i | \(-0.00550479\pi\) |
−0.0172930 | + | 0.999850i | \(0.505505\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.619309 | − | 2.31129i | −0.0264315 | − | 0.0986436i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.3334 | + | 22.7091i | −1.67566 | + | 0.967442i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.0331 | − | 7.27518i | −1.10704 | − | 0.309372i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.09972 | + | 0.294670i | 0.0466806 | + | 0.0125080i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50327 | − | 1.20665i | 0.190810 | − | 0.0511273i | −0.162149 | − | 0.986766i | \(-0.551842\pi\) |
0.352958 | + | 0.935639i | \(0.385176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.98138 | −0.168394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.2026 | 0.852954 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.04301 | − | 1.08332i | 0.170393 | − | 0.0456566i | −0.172614 | − | 0.984990i | \(-0.555221\pi\) |
0.343007 | + | 0.939333i | \(0.388555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.6264 | − | 3.11530i | −0.489128 | − | 0.131061i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.43448 | + | 21.1866i | 0.228227 | + | 0.889755i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.88173 | − | 2.24111i | 0.162730 | − | 0.0939524i | −0.416423 | − | 0.909171i | \(-0.636717\pi\) |
0.579154 | + | 0.815218i | \(0.303383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.126176 | + | 0.470896i | 0.00528031 | + | 0.0197064i | 0.968516 | − | 0.248952i | \(-0.0800863\pi\) |
−0.963235 | + | 0.268659i | \(0.913420\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.4143 | + | 14.4143i | 0.602167 | + | 0.602167i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.991504 | −0.0413486 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.31982 | − | 9.21420i | 0.221467 | − | 0.383592i | −0.733787 | − | 0.679380i | \(-0.762249\pi\) |
0.955254 | + | 0.295788i | \(0.0955821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.938680 | − | 3.50320i | 0.0390102 | − | 0.145588i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.41305 | − | 0.0472550i | −0.183084 | − | 0.00196047i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.35331 | − | 1.35868i | 0.0974641 | − | 0.0562709i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.636420 | − | 0.367437i | −0.0263127 | − | 0.0151917i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2861 | − | 13.2861i | 0.548376 | − | 0.548376i | −0.377595 | − | 0.925971i | \(-0.623249\pi\) |
0.925971 | + | 0.377595i | \(0.123249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.76960 | + | 1.76960i | 0.0729151 | + | 0.0729151i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.7497 | − | 20.3511i | 0.483319 | − | 0.837133i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.198497 | + | 0.343806i | 0.00815128 | + | 0.0141184i | 0.870072 | − | 0.492924i | \(-0.164072\pi\) |
−0.861921 | + | 0.507043i | \(0.830739\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.109840 | + | 10.2577i | −0.00450298 | + | 0.420524i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.9806 | + | 4.54994i | 0.694970 | + | 0.186217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.9718 | − | 6.91190i | −0.489153 | − | 0.282412i | 0.235070 | − | 0.971978i | \(-0.424468\pi\) |
−0.724223 | + | 0.689566i | \(0.757801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.73396i | − | 0.356266i | −0.984006 | − | 0.178133i | \(-0.942994\pi\) | ||
0.984006 | − | 0.178133i | \(-0.0570057\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.30926 | − | 1.30926i | 0.0533170 | − | 0.0533170i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −56.2535 | + | 15.0731i | −2.28703 | + | 0.612807i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.3937 | − | 24.9305i | −0.584220 | − | 1.01190i | −0.994972 | − | 0.100152i | \(-0.968067\pi\) |
0.410752 | − | 0.911747i | \(-0.365266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.7153 | − | 7.87864i | 1.24465 | − | 0.319259i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.897436 | + | 3.34928i | −0.0363064 | + | 0.135497i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.13486 | + | 34.0918i | 0.368954 | + | 1.37695i | 0.861981 | + | 0.506940i | \(0.169223\pi\) |
−0.493028 | + | 0.870014i | \(0.664110\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 24.3996i | − | 0.983886i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4612i | 1.34710i | 0.739143 | + | 0.673548i | \(0.235231\pi\) | ||||
−0.739143 | + | 0.673548i | \(0.764769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.41362 | + | 9.00777i | 0.0970118 | + | 0.362053i | 0.997317 | − | 0.0732067i | \(-0.0233233\pi\) |
−0.900305 | + | 0.435260i | \(0.856657\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.48492 | + | 5.54180i | −0.0595878 | + | 0.222385i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.08349 | − | 32.5038i | 0.363922 | − | 1.30224i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.74706 | − | 16.8824i | −0.389882 | − | 0.675296i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 64.0834 | − | 17.1711i | 2.55924 | − | 0.685747i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.460415 | + | 0.460415i | −0.0183580 | + | 0.0183580i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.2587i | − | 0.886105i | −0.896496 | − | 0.443053i | \(-0.853896\pi\) | ||
0.896496 | − | 0.443053i | \(-0.146104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.6128 | − | 6.12730i | −0.421821 | − | 0.243538i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.4988 | − | 3.34905i | −0.496001 | − | 0.132903i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.10527 | − | 7.76534i | 0.321142 | − | 0.307674i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.316819 | + | 0.548747i | 0.0125332 | + | 0.0217081i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.13758 | − | 7.16649i | 0.163424 | − | 0.283059i | −0.772670 | − | 0.634808i | \(-0.781079\pi\) |
0.936095 | + | 0.351748i | \(0.114413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.19175 | − | 4.19175i | −0.165307 | − | 0.165307i | 0.619606 | − | 0.784913i | \(-0.287292\pi\) |
−0.784913 | + | 0.619606i | \(0.787292\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.89890 | + | 5.89890i | −0.232269 | + | 0.232269i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.2428 | − | 10.5325i | −0.717199 | − | 0.414075i | 0.0965221 | − | 0.995331i | \(-0.469228\pi\) |
−0.813721 | + | 0.581256i | \(0.802561\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49.1081 | − | 28.3526i | 1.92766 | − | 1.11294i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.857366 | − | 1.52242i | −0.0336028 | − | 0.0596683i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.43173 | − | 16.5394i | 0.173427 | − | 0.647239i | −0.823387 | − | 0.567480i | \(-0.807918\pi\) |
0.996814 | − | 0.0797585i | \(-0.0254149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.0969 | − | 26.1485i | 0.589883 | − | 1.02171i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.539552 | −0.0210499 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.9513 | − | 19.9513i | −0.777192 | − | 0.777192i | 0.202161 | − | 0.979352i | \(-0.435204\pi\) |
−0.979352 | + | 0.202161i | \(0.935204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.55822 | − | 20.7436i | −0.216190 | − | 0.806831i | −0.985744 | − | 0.168250i | \(-0.946188\pi\) |
0.769555 | − | 0.638581i | \(-0.220478\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.44359 | + | 2.56551i | −0.172575 | + | 0.0996361i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.37005 | + | 32.6311i | 0.324577 | + | 1.26538i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.42246 | + | 1.98884i | 0.287399 | + | 0.0770083i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.0114 | − | 9.64922i | 1.39228 | − | 0.373060i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 66.5165 | 2.56784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0339 | 0.810796 | 0.405398 | − | 0.914140i | \(-0.367133\pi\) | ||||
0.405398 | + | 0.914140i | \(0.367133\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.82051 | − | 1.29165i | 0.185542 | − | 0.0497157i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.02033 | + | 1.61314i | 0.231380 | + | 0.0619982i | 0.372646 | − | 0.927974i | \(-0.378451\pi\) |
−0.141266 | + | 0.989972i | \(0.545117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.18137 | + | 4.09277i | −0.160466 | + | 0.157066i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.8367 | − | 15.4942i | 1.02838 | − | 0.593737i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.78001 | + | 21.5713i | 0.221166 | + | 0.825402i | 0.983904 | + | 0.178695i | \(0.0571876\pi\) |
−0.762739 | + | 0.646707i | \(0.776146\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.48651 | + | 2.48651i | 0.0950048 | + | 0.0950048i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0057 | 0.534351 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.345076 | + | 0.597689i | −0.0131463 | + | 0.0227701i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.94413 | + | 37.1120i | −0.378292 | + | 1.41181i | 0.470182 | + | 0.882570i | \(0.344188\pi\) |
−0.848474 | + | 0.529237i | \(0.822478\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.79379 | + | 0.0406240i | 0.144114 | + | 0.00154318i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.02907 | + | 4.05824i | −0.266628 | + | 0.153938i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0848 | + | 6.97715i | 0.457743 | + | 0.264278i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.2963 | − | 20.2963i | 0.767676 | − | 0.767676i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.40129 | + | 1.40129i | 0.0529259 | + | 0.0529259i | 0.733074 | − | 0.680148i | \(-0.238085\pi\) |
−0.680148 | + | 0.733074i | \(0.738085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.06913 | + | 1.85178i | −0.0403229 | + | 0.0698413i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.63270 | + | 6.29202i | 0.136815 | + | 0.236971i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.3839 | + | 9.69463i | 0.616181 | + | 0.364604i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.42034 | − | 2.25622i | −0.316232 | − | 0.0847342i | 0.0972117 | − | 0.995264i | \(-0.469008\pi\) |
−0.413444 | + | 0.910530i | \(0.635674\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00956 | + | 1.16022i | 0.0753645 | + | 0.0435117i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.423412i | − | 0.0158569i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.4450 | − | 14.4450i | 0.540211 | − | 0.540211i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.921129 | − | 0.246816i | 0.0344002 | − | 0.00921750i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3330 | + | 23.0934i | 0.497236 | + | 0.861239i | 0.999995 | − | 0.00318810i | \(-0.00101481\pi\) |
−0.502758 | + | 0.864427i | \(0.667681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4537 | + | 44.5635i | −0.463799 | + | 1.65963i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.07974 | − | 18.9578i | 0.188917 | − | 0.705050i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.72999 | − | 6.45640i | −0.0642501 | − | 0.239785i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.7224i | 1.39905i | 0.714610 | + | 0.699523i | \(0.246604\pi\) | ||||
−0.714610 | + | 0.699523i | \(0.753396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 28.7229i | − | 1.06381i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.23483 | − | 4.60846i | −0.0456719 | − | 0.170450i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.88050 | − | 21.9463i | 0.217201 | − | 0.810606i | −0.768179 | − | 0.640235i | \(-0.778837\pi\) |
0.985380 | − | 0.170371i | \(-0.0544965\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.503639 | − | 23.5142i | 0.0185770 | − | 0.867336i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7352 | + | 44.5747i | 0.947969 | + | 1.64193i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.3304 | + | 6.78727i | −0.931795 | + | 0.249674i | −0.692620 | − | 0.721303i | \(-0.743544\pi\) |
−0.239175 | + | 0.970977i | \(0.576877\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.9147 | + | 11.9147i | −0.437697 | + | 0.437697i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.7110i | 0.759812i | 0.925025 | + | 0.379906i | \(0.124044\pi\) | ||||
−0.925025 | + | 0.379906i | \(0.875956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.1739 | − | 18.5756i | −1.17876 | − | 0.680558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.365952 | + | 0.0980566i | 0.0133895 | + | 0.00358770i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.94168 | + | 3.90928i | −0.253643 | + | 0.142842i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.73865 | − | 13.4037i | −0.282387 | − | 0.489109i | 0.689585 | − | 0.724205i | \(-0.257793\pi\) |
−0.971972 | + | 0.235096i | \(0.924460\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.56486 | − | 11.3707i | 0.239237 | − | 0.414370i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.10132 | + | 9.10132i | 0.331231 | + | 0.331231i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4631 | − | 18.4631i | 0.671051 | − | 0.671051i | −0.286907 | − | 0.957958i | \(-0.592627\pi\) |
0.957958 | + | 0.286907i | \(0.0926272\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.72088 | − | 5.61235i | −0.352846 | − | 0.203715i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.1420 | + | 6.43283i | −0.403897 | + | 0.233190i | −0.688164 | − | 0.725555i | \(-0.741583\pi\) |
0.284267 | + | 0.958745i | \(0.408250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.57624 | − | 16.1838i | 0.346683 | − | 0.585894i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.227923 | − | 0.850618i | 0.00824056 | − | 0.0307542i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.20094 | + | 12.4724i | −0.260011 | + | 0.450352i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.5676 | −0.597443 | −0.298722 | − | 0.954340i | \(-0.596560\pi\) | ||||
−0.298722 | + | 0.954340i | \(0.596560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.2238 | − | 34.2238i | −1.23254 | − | 1.23254i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.6807 | − | 47.3250i | −0.456093 | − | 1.70216i | −0.684856 | − | 0.728679i | \(-0.740135\pi\) |
0.228763 | − | 0.973482i | \(-0.426532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.318960 | + | 0.184152i | −0.0114574 | + | 0.00661492i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.06686 | − | 1.04425i | 0.0382733 | − | 0.0374623i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.2635 | + | 11.8604i | 1.58591 | + | 0.424942i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0139 | + | 4.55886i | −0.608805 | + | 0.163129i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.6776 | −1.38222 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.8021 | 1.31352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.05999 | − | 1.35582i | 0.180369 | − | 0.0483298i | −0.167504 | − | 0.985871i | \(-0.553571\pi\) |
0.347873 | + | 0.937542i | \(0.386904\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.4427 | + | 7.62121i | 1.01259 | + | 0.271322i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2790 | + | 11.0400i | −0.401035 | + | 0.392537i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.6304 | + | 8.44687i | −0.519541 | + | 0.299957i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.374277 | + | 1.39682i | 0.0132742 | + | 0.0495401i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.4204 | + | 20.4204i | 0.723329 | + | 0.723329i | 0.969282 | − | 0.245953i | \(-0.0791009\pi\) |
−0.245953 | + | 0.969282i | \(0.579101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.15514 | −0.146998 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.44860 | + | 2.50906i | −0.0511839 | + | 0.0886532i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.88193 | − | 14.4876i | 0.136990 | − | 0.511255i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.90248 | − | 4.90518i | 0.102299 | − | 0.172885i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.5389 | − | 12.4355i | 0.758205 | − | 0.437750i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.6734 | − | 19.4413i | −1.18389 | − | 0.683521i | −0.226981 | − | 0.973899i | \(-0.572886\pi\) |
−0.956912 | + | 0.290378i | \(0.906219\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.4718 | + | 12.4718i | −0.437945 | + | 0.437945i | −0.891320 | − | 0.453375i | \(-0.850220\pi\) |
0.453375 | + | 0.891320i | \(0.350220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.3238 | − | 16.3238i | −0.572501 | − | 0.572501i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5902 | + | 20.0749i | −0.405988 | + | 0.703192i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.83387 | − | 13.5687i | −0.274072 | − | 0.474707i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.839609 | + | 0.472835i | −0.0293383 | + | 0.0165222i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.4979 | − | 4.95650i | −0.645581 | − | 0.172983i | −0.0788511 | − | 0.996886i | \(-0.525125\pi\) |
−0.566730 | + | 0.823903i | \(0.691792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.96748 | − | 5.17738i | −0.312587 | − | 0.180472i | 0.335497 | − | 0.942041i | \(-0.391096\pi\) |
−0.648083 | + | 0.761569i | \(0.724429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.76376i | 0.339931i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.65786 | − | 9.65786i | 0.335837 | − | 0.335837i | −0.518961 | − | 0.854798i | \(-0.673681\pi\) |
0.854798 | + | 0.518961i | \(0.173681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.6983 | − | 6.88583i | 0.892538 | − | 0.239155i | 0.216729 | − | 0.976232i | \(-0.430461\pi\) |
0.675809 | + | 0.737077i | \(0.263795\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.92201 | − | 3.32902i | −0.0666739 | − | 0.115483i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.5023 | + | 6.97343i | 0.398530 | + | 0.241615i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.3164 | − | 42.2334i | 0.391620 | − | 1.46155i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.551588 | + | 2.05855i | 0.0190657 | + | 0.0711540i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.4429i | 1.60339i | 0.597736 | + | 0.801693i | \(0.296067\pi\) | ||||
−0.597736 | + | 0.801693i | \(0.703933\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8031i | 0.786315i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.293220 | + | 1.09431i | 0.0100990 | + | 0.0376902i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.44618 | − | 20.3254i | 0.187354 | − | 0.699216i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.5531 | + | 73.5459i | −0.706211 | + | 2.52707i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.316904 | − | 0.548894i | −0.0108761 | − | 0.0188380i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.349443 | − | 0.0936330i | 0.0119788 | − | 0.00320970i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.3013 | + | 31.3013i | −1.07174 | + | 1.07174i | −0.0745177 | + | 0.997220i | \(0.523742\pi\) |
−0.997220 | + | 0.0745177i | \(0.976258\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.89191i | − | 0.0989014i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.8393 | + | 13.1863i | 0.780175 | + | 0.450434i | 0.836492 | − | 0.547979i | \(-0.184602\pi\) |
−0.0563171 | + | 0.998413i | \(0.517936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.91867 | + | 0.782055i | 0.0995837 | + | 0.0266834i | 0.308267 | − | 0.951300i | \(-0.400251\pi\) |
−0.208683 | + | 0.977983i | \(0.566918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.5344 | − | 16.2926i | −0.938371 | − | 0.555250i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.50456 | + | 6.07008i | 0.119297 | + | 0.206628i | 0.919489 | − | 0.393115i | \(-0.128603\pi\) |
−0.800192 | + | 0.599743i | \(0.795269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.9092 | − | 22.3594i | 0.438925 | − | 0.760241i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6692 | + | 15.6692i | 0.532155 | + | 0.532155i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.6115 | + | 45.6115i | −1.54726 | + | 1.54726i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3210 | − | 6.53619i | −0.383598 | − | 0.221470i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.434991 | − | 0.251142i | 0.0147222 | − | 0.00849987i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.6483 | − | 0.338890i | −1.06991 | − | 0.0114566i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.6267 | − | 39.6594i | 0.358838 | − | 1.33920i | −0.516748 | − | 0.856138i | \(-0.672857\pi\) |
0.875585 | − | 0.483063i | \(-0.160476\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.82185 | − | 15.2799i | 0.297554 | − | 0.515378i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6166 | −0.458755 | −0.229377 | − | 0.973338i | \(-0.573669\pi\) | ||||
−0.229377 | + | 0.973338i | \(0.573669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.2238 | − | 35.2238i | −1.18537 | − | 1.18537i | −0.978332 | − | 0.207042i | \(-0.933616\pi\) |
−0.207042 | − | 0.978332i | \(-0.566384\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.81030 | + | 29.1484i | 0.262540 | + | 0.979814i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.44911 | − | 3.14604i | 0.182963 | − | 0.105634i | −0.405721 | − | 0.913997i | \(-0.632980\pi\) |
0.588684 | + | 0.808363i | \(0.299646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.1253 | + | 11.8684i | −0.406670 | + | 0.398053i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.4171 | + | 13.5092i | 1.68904 | + | 0.452576i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.1802 | + | 3.53163i | −0.441060 | + | 0.118182i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.39085 | −0.213623 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.85083 | 0.0951864 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.75714 | − | 0.738774i | 0.0919559 | − | 0.0246395i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.798852 | − | 0.214052i | −0.0266136 | − | 0.00713110i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.71786 | + | 10.5957i | 0.0904447 | + | 0.352604i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.5276 | + | 20.5118i | −1.18098 | + | 0.681837i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.6035 | − | 43.3049i | −0.385289 | − | 1.43792i | −0.837711 | − | 0.546113i | \(-0.816107\pi\) |
0.452423 | − | 0.891804i | \(-0.350560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.15560 | − | 1.15560i | −0.0383288 | − | 0.0383288i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.8973 | −1.42125 | −0.710625 | − | 0.703571i | \(-0.751588\pi\) | ||||
−0.710625 | + | 0.703571i | \(0.751588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.26585 | + | 9.12073i | −0.174274 | + | 0.301852i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.16166 | + | 34.1918i | −0.302875 | + | 1.13035i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.4273 | − | 34.4970i | −0.641547 | − | 1.13919i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.2242 | + | 15.1405i | −0.865056 | + | 0.499440i | −0.865702 | − | 0.500560i | \(-0.833128\pi\) |
0.000646343 | 1.00000i | \(0.499794\pi\) | ||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.8074 | + | 7.39438i | 0.422019 | + | 0.243653i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.16330 | − | 3.16330i | 0.104121 | − | 0.104121i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.222515 | − | 0.222515i | −0.00731626 | − | 0.00731626i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.98607 | − | 3.43997i | 0.0652311 | − | 0.112984i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.93334 | + | 12.0089i | 0.227475 | + | 0.393999i | 0.957059 | − | 0.289892i | \(-0.0936195\pi\) |
−0.729584 | + | 0.683891i | \(0.760286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.4126 | + | 12.3437i | 1.39002 | + | 0.404548i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.8925 | − | 4.25838i | −0.520297 | − | 0.139413i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.2002 | + | 12.2399i | 0.693321 | + | 0.400289i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.7544i | 1.52740i | 0.645572 | + | 0.763699i | \(0.276619\pi\) | ||||
−0.645572 | + | 0.763699i | \(0.723381\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.2222 | + | 20.2222i | −0.659927 | + | 0.659927i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.04407 | − | 2.15540i | 0.262229 | − | 0.0702641i | −0.125309 | − | 0.992118i | \(-0.539992\pi\) |
0.387538 | + | 0.921854i | \(0.373326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.87655 | − | 6.71439i | −0.126238 | − | 0.218651i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.72123 | + | 27.6292i | −0.251172 | + | 0.898778i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.89988 | + | 7.09044i | −0.0617378 | + | 0.230408i | −0.989900 | − | 0.141767i | \(-0.954722\pi\) |
0.928162 | + | 0.372176i | \(0.121388\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.985926 | + | 3.67953i | 0.0320045 | + | 0.119442i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.3776i | 1.14720i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 41.3553i | − | 1.33963i | −0.742528 | − | 0.669815i | \(-0.766373\pi\) | ||
0.742528 | − | 0.669815i | \(-0.233627\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.39305 | + | 23.8592i | 0.206874 | + | 0.772065i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.5850 | − | 73.0921i | 0.633093 | − | 2.36273i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.46633 | − | 1.14564i | 0.144225 | − | 0.0369945i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4214 | + | 26.7106i | 0.497463 | + | 0.861632i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.660606 | − | 0.177009i | 0.0212877 | − | 0.00570403i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.10748 | − | 3.10748i | 0.100033 | − | 0.100033i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.5984i | − | 1.30556i | −0.757549 | − | 0.652778i | \(-0.773603\pi\) | ||
0.757549 | − | 0.652778i | \(-0.226397\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.4866 | − | 10.0959i | −0.561752 | − | 0.324328i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.4132 | − | 8.41714i | −1.00810 | − | 0.270119i | −0.283263 | − | 0.959042i | \(-0.591417\pi\) |
−0.724834 | + | 0.688924i | \(0.758084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.113955 | + | 10.6420i | −0.00365323 | + | 0.341168i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.23989 | − | 2.14755i | −0.0397083 | − | 0.0687768i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.34286 | − | 14.4503i | 0.266912 | − | 0.462305i | −0.701151 | − | 0.713013i | \(-0.747330\pi\) |
0.968063 | + | 0.250708i | \(0.0806635\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.9486 | − | 56.9486i | −1.82009 | − | 1.82009i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.14148 | + | 1.14148i | −0.0364448 | + | 0.0364448i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.1999 | + | 5.88892i | 0.325326 | + | 0.187827i | 0.653764 | − | 0.756698i | \(-0.273189\pi\) |
−0.328438 | + | 0.944526i | \(0.606522\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.6599 | − | 14.2374i | 0.785728 | − | 0.453640i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.52612 | + | 0.102006i | 0.303220 | + | 0.00324688i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.686082 | + | 2.56049i | −0.0218161 | + | 0.0814189i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.8872 | + | 27.5175i | −0.504675 | + | 0.874122i | 0.495311 | + | 0.868716i | \(0.335054\pi\) |
−0.999985 | + | 0.00540613i | \(0.998279\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.2967 | −1.27878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0625 | + | 15.0625i | 0.477513 | + | 0.477513i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.309461 | − | 1.15492i | −0.00980073 | − | 0.0365768i | 0.960852 | − | 0.277061i | \(-0.0893604\pi\) |
−0.970653 | + | 0.240484i | \(0.922694\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.57695 | + | 0.910453i | −0.0498925 | + | 0.0288055i |
(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 | 448.2.ba.c.81.9 | 48 | ||
4.3 | odd | 2 | 112.2.w.c.109.2 | yes | 48 | ||
7.2 | even | 3 | inner | 448.2.ba.c.401.4 | 48 | ||
8.3 | odd | 2 | 896.2.ba.f.417.9 | 48 | |||
8.5 | even | 2 | 896.2.ba.e.417.4 | 48 | |||
16.3 | odd | 4 | 896.2.ba.f.865.4 | 48 | |||
16.5 | even | 4 | inner | 448.2.ba.c.305.4 | 48 | ||
16.11 | odd | 4 | 112.2.w.c.53.10 | yes | 48 | ||
16.13 | even | 4 | 896.2.ba.e.865.9 | 48 | |||
28.3 | even | 6 | 784.2.m.k.589.6 | 24 | |||
28.11 | odd | 6 | 784.2.m.j.589.6 | 24 | |||
28.19 | even | 6 | 784.2.x.o.765.10 | 48 | |||
28.23 | odd | 6 | 112.2.w.c.93.10 | yes | 48 | ||
28.27 | even | 2 | 784.2.x.o.557.2 | 48 | |||
56.37 | even | 6 | 896.2.ba.e.289.9 | 48 | |||
56.51 | odd | 6 | 896.2.ba.f.289.4 | 48 | |||
112.11 | odd | 12 | 784.2.m.j.197.6 | 24 | |||
112.27 | even | 4 | 784.2.x.o.165.10 | 48 | |||
112.37 | even | 12 | inner | 448.2.ba.c.177.9 | 48 | ||
112.51 | odd | 12 | 896.2.ba.f.737.9 | 48 | |||
112.59 | even | 12 | 784.2.m.k.197.6 | 24 | |||
112.75 | even | 12 | 784.2.x.o.373.2 | 48 | |||
112.93 | even | 12 | 896.2.ba.e.737.4 | 48 | |||
112.107 | odd | 12 | 112.2.w.c.37.2 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.2 | ✓ | 48 | 112.107 | odd | 12 | ||
112.2.w.c.53.10 | yes | 48 | 16.11 | odd | 4 | ||
112.2.w.c.93.10 | yes | 48 | 28.23 | odd | 6 | ||
112.2.w.c.109.2 | yes | 48 | 4.3 | odd | 2 | ||
448.2.ba.c.81.9 | 48 | 1.1 | even | 1 | trivial | ||
448.2.ba.c.177.9 | 48 | 112.37 | even | 12 | inner | ||
448.2.ba.c.305.4 | 48 | 16.5 | even | 4 | inner | ||
448.2.ba.c.401.4 | 48 | 7.2 | even | 3 | inner | ||
784.2.m.j.197.6 | 24 | 112.11 | odd | 12 | |||
784.2.m.j.589.6 | 24 | 28.11 | odd | 6 | |||
784.2.m.k.197.6 | 24 | 112.59 | even | 12 | |||
784.2.m.k.589.6 | 24 | 28.3 | even | 6 | |||
784.2.x.o.165.10 | 48 | 112.27 | even | 4 | |||
784.2.x.o.373.2 | 48 | 112.75 | even | 12 | |||
784.2.x.o.557.2 | 48 | 28.27 | even | 2 | |||
784.2.x.o.765.10 | 48 | 28.19 | even | 6 | |||
896.2.ba.e.289.9 | 48 | 56.37 | even | 6 | |||
896.2.ba.e.417.4 | 48 | 8.5 | even | 2 | |||
896.2.ba.e.737.4 | 48 | 112.93 | even | 12 | |||
896.2.ba.e.865.9 | 48 | 16.13 | even | 4 | |||
896.2.ba.f.289.4 | 48 | 56.51 | odd | 6 | |||
896.2.ba.f.417.9 | 48 | 8.3 | odd | 2 | |||
896.2.ba.f.737.9 | 48 | 112.51 | odd | 12 | |||
896.2.ba.f.865.4 | 48 | 16.3 | odd | 4 |