Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(49,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.bb (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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 49.7 | ||
Character | \(\chi\) | \(=\) | 576.49 |
Dual form | 576.2.bb.e.529.7 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −0.841300 | + | 1.51401i | −0.485725 | + | 0.874112i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0691269 | + | 0.0185225i | −0.0309145 | + | 0.00828352i | −0.274243 | − | 0.961660i | \(-0.588427\pi\) |
0.243329 | + | 0.969944i | \(0.421761\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.28192 | + | 0.740118i | −0.484521 | + | 0.279738i | −0.722299 | − | 0.691581i | \(-0.756914\pi\) |
0.237778 | + | 0.971320i | \(0.423581\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.58443 | − | 2.54747i | −0.528142 | − | 0.849156i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.587070 | + | 2.19098i | −0.177008 | + | 0.660604i | 0.819192 | + | 0.573519i | \(0.194422\pi\) |
−0.996201 | + | 0.0870855i | \(0.972245\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.104109 | + | 0.388539i | 0.0288745 | + | 0.107761i | 0.978859 | − | 0.204535i | \(-0.0655684\pi\) |
−0.949985 | + | 0.312297i | \(0.898902\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0301133 | − | 0.120242i | 0.00777523 | − | 0.0310462i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.851000 | −0.206398 | −0.103199 | − | 0.994661i | \(-0.532908\pi\) | ||||
−0.103199 | + | 0.994661i | \(0.532908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.75230 | + | 3.75230i | −0.860837 | + | 0.860837i | −0.991435 | − | 0.130598i | \(-0.958310\pi\) |
0.130598 | + | 0.991435i | \(0.458310\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0420615 | − | 2.56350i | −0.00917857 | − | 0.559401i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.44629 | − | 4.29912i | −1.55266 | − | 0.896428i | −0.997924 | − | 0.0643999i | \(-0.979487\pi\) |
−0.554734 | − | 0.832028i | \(-0.687180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.32569 | + | 2.49744i | −0.865138 | + | 0.499488i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.18986 | − | 0.255647i | 0.998789 | − | 0.0491992i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.77230 | − | 1.27873i | −0.886193 | − | 0.237455i | −0.213116 | − | 0.977027i | \(-0.568361\pi\) |
−0.673077 | + | 0.739572i | \(0.735028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50318 | − | 7.79974i | 0.808796 | − | 1.40088i | −0.104902 | − | 0.994483i | \(-0.533453\pi\) |
0.913698 | − | 0.406393i | \(-0.133214\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82325 | − | 2.73210i | −0.491464 | − | 0.475597i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0749065 | − | 0.0749065i | 0.0126615 | − | 0.0126615i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.13315 | + | 4.13315i | 0.679485 | + | 0.679485i | 0.959884 | − | 0.280399i | \(-0.0904666\pi\) |
−0.280399 | + | 0.959884i | \(0.590467\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.675837 | − | 0.169257i | −0.108220 | − | 0.0271028i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.05305 | − | 1.18533i | −0.320633 | − | 0.185118i | 0.331042 | − | 0.943616i | \(-0.392600\pi\) |
−0.651675 | + | 0.758499i | \(0.725933\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.669562 | − | 2.49884i | 0.102107 | − | 0.381070i | −0.895894 | − | 0.444269i | \(-0.853464\pi\) |
0.998001 | + | 0.0631989i | \(0.0201303\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.156712 | + | 0.146751i | 0.0233613 | + | 0.0218764i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.42005 | − | 5.92370i | −0.498865 | − | 0.864060i | 0.501134 | − | 0.865370i | \(-0.332916\pi\) |
−0.999999 | + | 0.00130966i | \(0.999583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.40445 | + | 4.16463i | −0.343493 | + | 0.594947i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.715947 | − | 1.28842i | 0.100253 | − | 0.180415i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.95421 | + | 3.95421i | 0.543152 | + | 0.543152i | 0.924452 | − | 0.381300i | \(-0.124523\pi\) |
−0.381300 | + | 0.924452i | \(0.624523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.162329i | − | 0.0218885i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.52419 | − | 8.83782i | −0.334338 | − | 1.17060i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.7811 | + | 3.69264i | −1.79415 | + | 0.480741i | −0.993040 | − | 0.117777i | \(-0.962423\pi\) |
−0.801109 | + | 0.598518i | \(0.795756\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.28936 | − | 0.881382i | −0.421160 | − | 0.112849i | 0.0420139 | − | 0.999117i | \(-0.486623\pi\) |
−0.463173 | + | 0.886268i | \(0.653289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.91654 | + | 2.09299i | 0.493438 | + | 0.263692i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0143934 | − | 0.0249301i | −0.00178528 | − | 0.00309220i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.73506 | + | 6.47532i | 0.211971 | + | 0.791086i | 0.987211 | + | 0.159419i | \(0.0509622\pi\) |
−0.775240 | + | 0.631667i | \(0.782371\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.7735 | − | 7.65687i | 1.53774 | − | 0.921779i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.362864i | 0.0430640i | 0.999768 | + | 0.0215320i | \(0.00685439\pi\) | ||||
−0.999768 | + | 0.0215320i | \(0.993146\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.8744i | 1.85796i | 0.370128 | + | 0.928981i | \(0.379314\pi\) | ||||
−0.370128 | + | 0.928981i | \(0.620686\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.141931 | − | 8.65022i | −0.0163888 | − | 0.998841i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.869003 | − | 3.24316i | −0.0990321 | − | 0.369593i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.45338 | + | 9.44553i | 0.613553 | + | 1.06271i | 0.990637 | + | 0.136526i | \(0.0435937\pi\) |
−0.377083 | + | 0.926179i | \(0.623073\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.97918 | + | 8.07255i | −0.442131 | + | 0.896950i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.37105 | + | 1.43917i | 0.589549 | + | 0.157969i | 0.541247 | − | 0.840863i | \(-0.317952\pi\) |
0.0483022 | + | 0.998833i | \(0.484619\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0588270 | − | 0.0157627i | 0.00638069 | − | 0.00170970i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.95094 | − | 6.14948i | 0.638008 | − | 0.659294i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.1832i | − | 1.39741i | −0.715408 | − | 0.698707i | \(-0.753759\pi\) | ||
0.715408 | − | 0.698707i | \(-0.246241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.421024 | − | 0.421024i | −0.0441353 | − | 0.0441353i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.02033 | + | 13.3798i | 0.831669 | + | 1.38742i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.189883 | − | 0.328887i | 0.0194816 | − | 0.0337431i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.627593 | − | 1.08702i | −0.0637224 | − | 0.110370i | 0.832404 | − | 0.554169i | \(-0.186964\pi\) |
−0.896127 | + | 0.443799i | \(0.853631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.51161 | − | 1.97590i | 0.654442 | − | 0.198585i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.43047 | + | 5.33858i | −0.142337 | + | 0.531209i | 0.857522 | + | 0.514446i | \(0.172003\pi\) |
−0.999860 | + | 0.0167625i | \(0.994664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.59933 | + | 5.54217i | 0.945850 | + | 0.546087i | 0.891789 | − | 0.452451i | \(-0.149450\pi\) |
0.0540605 | + | 0.998538i | \(0.482784\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0503900 | + | 0.176428i | 0.00491756 | + | 0.0172176i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.90288 | + | 6.90288i | 0.667327 | + | 0.667327i | 0.957096 | − | 0.289770i | \(-0.0935787\pi\) |
−0.289770 | + | 0.957096i | \(0.593579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.39169 | − | 9.39169i | 0.899560 | − | 0.899560i | −0.0958367 | − | 0.995397i | \(-0.530553\pi\) |
0.995397 | + | 0.0958367i | \(0.0305527\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.73483 | + | 2.78039i | −0.923989 | + | 0.263903i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.81166 | + | 10.0661i | −0.546715 | + | 0.946938i | 0.451782 | + | 0.892128i | \(0.350789\pi\) |
−0.998497 | + | 0.0548097i | \(0.982545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.594369 | + | 0.159261i | 0.0554252 | + | 0.0148511i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.824837 | − | 0.880825i | 0.0762562 | − | 0.0814323i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.09092 | − | 0.629841i | 0.100004 | − | 0.0577374i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.07055 | + | 2.92749i | 0.460959 | + | 0.266135i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.52183 | − | 2.11111i | 0.317553 | − | 0.190353i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.505785 | − | 0.505785i | 0.0452388 | − | 0.0452388i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1965 | 0.904796 | 0.452398 | − | 0.891816i | \(-0.350569\pi\) | ||||
0.452398 | + | 0.891816i | \(0.350569\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.21996 | + | 3.11600i | 0.283501 | + | 0.274348i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.82077 | + | 6.79522i | 0.159082 | + | 0.593701i | 0.998721 | + | 0.0505571i | \(0.0160997\pi\) |
−0.839639 | + | 0.543144i | \(0.817234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.03301 | − | 7.58731i | 0.176285 | − | 0.657903i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.354024 | + | 0.113801i | −0.0304695 | + | 0.00979445i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.5671 | − | 7.25564i | 1.07368 | − | 0.619891i | 0.144497 | − | 0.989505i | \(-0.453843\pi\) |
0.929185 | + | 0.369614i | \(0.120510\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.09570 | + | 1.36539i | −0.432212 | + | 0.115811i | −0.468364 | − | 0.883535i | \(-0.655157\pi\) |
0.0361523 | + | 0.999346i | \(0.488490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.8458 | − | 0.194364i | 0.997596 | − | 0.0163684i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.912398 | −0.0762986 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.353579 | 0.0293632 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.28241 | − | 7.14406i | −0.353207 | − | 0.589232i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.3330 | + | 5.18027i | −1.58382 | + | 0.424384i | −0.940107 | − | 0.340879i | \(-0.889275\pi\) |
−0.643717 | + | 0.765264i | \(0.722609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0910 | + | 6.40336i | −0.902569 | + | 0.521098i | −0.878033 | − | 0.478601i | \(-0.841144\pi\) |
−0.0245362 | + | 0.999699i | \(0.507811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.34835 | + | 2.16790i | 0.109007 | + | 0.175264i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.166821 | + | 0.622583i | −0.0133993 | + | 0.0500070i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.98067 | + | 7.39195i | 0.158074 | + | 0.589942i | 0.998822 | + | 0.0485153i | \(0.0154490\pi\) |
−0.840748 | + | 0.541427i | \(0.817884\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.31337 | + | 2.66002i | −0.738598 | + | 0.210953i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.7274 | 1.00306 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3989 | + | 10.3989i | −0.814504 | + | 0.814504i | −0.985305 | − | 0.170802i | \(-0.945364\pi\) |
0.170802 | + | 0.985305i | \(0.445364\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.245768 | + | 0.136568i | 0.0191330 | + | 0.0106318i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.44443 | + | 3.14334i | 0.421302 | + | 0.243239i | 0.695634 | − | 0.718396i | \(-0.255123\pi\) |
−0.274332 | + | 0.961635i | \(0.588457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1182 | − | 6.41910i | 0.855247 | − | 0.493777i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.5041 | + | 3.61362i | 1.18563 | + | 0.276340i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3578 | − | 3.04333i | −0.863521 | − | 0.231380i | −0.200237 | − | 0.979748i | \(-0.564171\pi\) |
−0.663284 | + | 0.748368i | \(0.730838\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.69680 | − | 6.40305i | 0.279452 | − | 0.484025i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00338 | − | 23.9713i | 0.451242 | − | 1.80179i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.21801 | − | 9.21801i | 0.688986 | − | 0.688986i | −0.273021 | − | 0.962008i | \(-0.588023\pi\) |
0.962008 | + | 0.273021i | \(0.0880230\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5919 | − | 11.5919i | −0.861621 | − | 0.861621i | 0.129905 | − | 0.991526i | \(-0.458533\pi\) |
−0.991526 | + | 0.129905i | \(0.958533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.10176 | − | 4.23861i | 0.303211 | − | 0.313327i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.362268 | − | 0.209155i | −0.0266345 | − | 0.0153774i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.499597 | − | 1.86452i | 0.0365341 | − | 0.136347i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.46379 | + | 4.16883i | −0.470171 | + | 0.303238i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1864 | − | 19.3755i | −0.809423 | − | 1.40196i | −0.913264 | − | 0.407368i | \(-0.866447\pi\) |
0.103842 | − | 0.994594i | \(-0.466887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.17911 | − | 12.4346i | 0.516764 | − | 0.895061i | −0.483047 | − | 0.875594i | \(-0.660470\pi\) |
0.999811 | − | 0.0194663i | \(-0.00619671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0498536 | 0.000817989i | 0.00357009 | 5.85774e-5i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.57538 | + | 1.57538i | 0.112241 | + | 0.112241i | 0.760997 | − | 0.648756i | \(-0.224710\pi\) |
−0.648756 | + | 0.760997i | \(0.724710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.72755i | − | 0.122463i | −0.998124 | − | 0.0612313i | \(-0.980497\pi\) | ||
0.998124 | − | 0.0612313i | \(-0.0195027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.2634 | − | 2.82080i | −0.794457 | − | 0.198964i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.06413 | − | 1.89283i | 0.495804 | − | 0.132850i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.163877 | + | 0.0439106i | 0.0114456 | + | 0.00306685i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.846243 | + | 25.7808i | 0.0588179 | + | 1.79189i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.01834 | − | 10.4241i | −0.416297 | − | 0.721048i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.19942 | − | 11.9404i | −0.220257 | − | 0.822011i | −0.984249 | − | 0.176785i | \(-0.943430\pi\) |
0.763992 | − | 0.645225i | \(-0.223236\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.549378 | − | 0.305278i | −0.0376428 | − | 0.0209173i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.185139i | 0.0126264i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.3316i | 0.905005i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.0340 | − | 13.3552i | −1.62407 | − | 0.902458i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0885965 | − | 0.330647i | −0.00595964 | − | 0.0222417i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.22081 | + | 12.5068i | 0.483541 | + | 0.837518i | 0.999821 | − | 0.0189019i | \(-0.00601703\pi\) |
−0.516280 | + | 0.856420i | \(0.672684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.2159 | + | 7.06255i | 0.881059 | + | 0.470837i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.61577 | + | 0.432945i | 0.107243 | + | 0.0287356i | 0.312041 | − | 0.950069i | \(-0.398987\pi\) |
−0.204799 | + | 0.978804i | \(0.565654\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6207 | + | 5.25735i | −1.29657 | + | 0.347416i | −0.840153 | − | 0.542349i | \(-0.817535\pi\) |
−0.456420 | + | 0.889765i | \(0.650868\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.64126 | + | 1.41280i | 0.371168 | + | 0.0929553i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.5814i | 1.54487i | 0.635094 | + | 0.772435i | \(0.280961\pi\) | ||||
−0.635094 | + | 0.772435i | \(0.719039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.346139 | + | 0.346139i | 0.0225796 | + | 0.0225796i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.8885 | + | 0.309920i | −1.22694 | + | 0.0201315i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.28400 | + | 7.42011i | −0.277109 | + | 0.479967i | −0.970665 | − | 0.240436i | \(-0.922710\pi\) |
0.693556 | + | 0.720403i | \(0.256043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.69013 | + | 6.39149i | 0.237702 | + | 0.411712i | 0.960055 | − | 0.279813i | \(-0.0902725\pi\) |
−0.722352 | + | 0.691525i | \(0.756939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.87421 | − | 12.8159i | −0.569281 | − | 0.822143i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0890729 | − | 0.332424i | 0.00569066 | − | 0.0212378i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.84856 | − | 1.06727i | −0.117621 | − | 0.0679086i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.69758 | + | 6.92103i | −0.424442 | + | 0.438602i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.74661 | + | 8.74661i | 0.552081 | + | 0.552081i | 0.927041 | − | 0.374960i | \(-0.122343\pi\) |
−0.374960 | + | 0.927041i | \(0.622343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7908 | − | 13.7908i | 0.867017 | − | 0.867017i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0256265 | + | 0.102326i | −0.00160479 | + | 0.00640788i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.21071 | − | 3.82905i | 0.137900 | − | 0.238850i | −0.788802 | − | 0.614648i | \(-0.789298\pi\) |
0.926702 | + | 0.375798i | \(0.122631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.35739 | − | 2.23936i | −0.519303 | − | 0.139147i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.30383 | + | 14.1833i | 0.266400 | + | 0.877926i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.48601 | − | 5.47675i | 0.584932 | − | 0.337711i | −0.178159 | − | 0.984002i | \(-0.557014\pi\) |
0.763091 | + | 0.646291i | \(0.223681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.346584 | − | 0.200100i | −0.0212905 | − | 0.0122921i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.9594 | + | 11.0910i | 1.22150 | + | 0.678759i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6376 | + | 10.6376i | −0.648586 | + | 0.648586i | −0.952651 | − | 0.304065i | \(-0.901656\pi\) |
0.304065 | + | 0.952651i | \(0.401656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1209 | −1.16151 | −0.580757 | − | 0.814077i | \(-0.697243\pi\) | ||||
−0.580757 | + | 0.814077i | \(0.697243\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.991640 | − | 0.283225i | 0.0600168 | − | 0.0171416i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.93235 | − | 10.9437i | −0.176827 | − | 0.659928i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.70176 | − | 10.0831i | 0.162333 | − | 0.605835i | −0.836032 | − | 0.548680i | \(-0.815130\pi\) |
0.998365 | − | 0.0571550i | \(-0.0182029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.0046 | + | 0.886412i | −1.61672 | + | 0.0530681i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.1779 | − | 7.03092i | 0.726473 | − | 0.419429i | −0.0906576 | − | 0.995882i | \(-0.528897\pi\) |
0.817130 | + | 0.576453i | \(0.195564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.6641 | + | 6.60872i | −1.46613 | + | 0.392848i | −0.901601 | − | 0.432568i | \(-0.857608\pi\) |
−0.564526 | + | 0.825415i | \(0.690941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.338188 | + | 0.564177i | 0.0200325 | + | 0.0334190i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.50914 | 0.207138 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2758 | −0.957400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.17375 | − | 0.0356666i | 0.127428 | − | 0.00209081i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.2569 | + | 3.55218i | −0.774476 | + | 0.207520i | −0.624348 | − | 0.781146i | \(-0.714635\pi\) |
−0.150128 | + | 0.988667i | \(0.547969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.884250 | − | 0.510522i | 0.0514830 | − | 0.0297237i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.48670 | + | 11.5209i | −0.144293 | + | 0.668513i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.895150 | − | 3.34075i | 0.0517679 | − | 0.193200i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.991111 | + | 3.69888i | 0.0571267 | + | 0.213200i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.87919 | − | 6.65709i | −0.395199 | − | 0.382440i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.243709 | 0.0139547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1122 | − | 14.1122i | 0.805426 | − | 0.805426i | −0.178512 | − | 0.983938i | \(-0.557128\pi\) |
0.983938 | + | 0.178512i | \(0.0571283\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.4668 | + | 9.87080i | −0.936763 | + | 0.561530i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.2914 | + | 6.51907i | 0.640274 | + | 0.369662i | 0.784720 | − | 0.619850i | \(-0.212807\pi\) |
−0.144446 | + | 0.989513i | \(0.546140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.50512 | + | 3.75573i | −0.367691 | + | 0.212287i | −0.672449 | − | 0.740143i | \(-0.734758\pi\) |
0.304758 | + | 0.952430i | \(0.401424\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.309506 | − | 0.0721380i | −0.0174387 | − | 0.00406451i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.45660 | + | 0.390294i | 0.0818107 | + | 0.0219211i | 0.299492 | − | 0.954099i | \(-0.403183\pi\) |
−0.217682 | + | 0.976020i | \(0.569849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.60335 | − | 9.70528i | 0.313727 | − | 0.543391i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.2584 | + | 4.64361i | −0.907456 | + | 0.259181i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.19321 | − | 3.19321i | 0.177675 | − | 0.177675i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.42069 | − | 1.42069i | −0.0788059 | − | 0.0788059i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.31784 | + | 22.1203i | 0.349377 | + | 1.22326i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.76847 | + | 5.06248i | 0.483422 | + | 0.279104i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.29948 | − | 19.7779i | 0.291286 | − | 1.08709i | −0.652837 | − | 0.757499i | \(-0.726421\pi\) |
0.944122 | − | 0.329595i | \(-0.106912\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.98039 | − | 17.0777i | 0.218124 | − | 0.935854i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.239878 | − | 0.415481i | −0.0131059 | − | 0.0227002i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.81432 | − | 8.33864i | 0.262253 | − | 0.454235i | −0.704588 | − | 0.709617i | \(-0.748868\pi\) |
0.966840 | + | 0.255382i | \(0.0822013\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3508 | − | 17.2675i | −0.562177 | − | 0.937842i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.4454 | + | 14.4454i | 0.782261 | + | 0.782261i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.4800i | − | 0.943829i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.741165 | + | 0.765892i | −0.0399030 | + | 0.0412343i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.72145 | + | 2.33691i | −0.468192 | + | 0.125452i | −0.485199 | − | 0.874404i | \(-0.661253\pi\) |
0.0170070 | + | 0.999855i | \(0.494586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.4971 | − | 7.09989i | −1.41836 | − | 0.380048i | −0.533458 | − | 0.845826i | \(-0.679108\pi\) |
−0.884902 | + | 0.465778i | \(0.845775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.639638 | + | 1.98985i | 0.0341413 | + | 0.106210i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.21080 | − | 3.82922i | −0.117669 | − | 0.203809i | 0.801174 | − | 0.598431i | \(-0.204209\pi\) |
−0.918844 | + | 0.394622i | \(0.870876\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.00672115 | − | 0.0250837i | −0.000356722 | − | 0.00133130i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0357943 | + | 2.18154i | 0.00189444 | + | 0.115459i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.7288i | 1.14680i | 0.819275 | + | 0.573400i | \(0.194376\pi\) | ||||
−0.819275 | + | 0.573400i | \(0.805624\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 9.15954i | − | 0.482081i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.69809 | + | 5.21395i | −0.456531 | + | 0.273662i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.294034 | − | 1.09735i | −0.0153905 | − | 0.0574380i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.28705 | − | 2.22924i | −0.0671835 | − | 0.116365i | 0.830477 | − | 0.557053i | \(-0.188068\pi\) |
−0.897660 | + | 0.440688i | \(0.854735\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.233322 | + | 7.10816i | 0.0121462 | + | 0.370036i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.99556 | − | 2.14241i | −0.415109 | − | 0.111228i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.42780 | − | 0.382578i | 0.0739287 | − | 0.0198091i | −0.221665 | − | 0.975123i | \(-0.571149\pi\) |
0.295594 | + | 0.955314i | \(0.404483\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.340244 | + | 1.19128i | 0.0175701 | + | 0.0615174i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.98735i | − | 0.102354i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.66662 | − | 4.66662i | −0.239708 | − | 0.239708i | 0.577021 | − | 0.816729i | \(-0.304215\pi\) |
−0.816729 | + | 0.577021i | \(0.804215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.57835 | + | 15.4376i | −0.439482 | + | 0.790893i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.48376 | − | 2.56995i | 0.0758165 | − | 0.131318i | −0.825625 | − | 0.564220i | \(-0.809177\pi\) |
0.901441 | + | 0.432902i | \(0.142510\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.120143 | + | 0.208094i | 0.00612305 | + | 0.0106054i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.42659 | + | 2.25354i | −0.377515 | + | 0.114554i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.85632 | − | 29.3202i | 0.398331 | − | 1.48659i | −0.417700 | − | 0.908585i | \(-0.637164\pi\) |
0.816031 | − | 0.578008i | \(-0.196170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.33679 | + | 3.65855i | 0.320465 | + | 0.185021i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.8198 | − | 2.96016i | −0.596231 | − | 0.149320i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.551930 | − | 0.551930i | −0.0277706 | − | 0.0277706i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.6823 | − | 11.6823i | 0.586319 | − | 0.586319i | −0.350314 | − | 0.936632i | \(-0.613925\pi\) |
0.936632 | + | 0.350314i | \(0.113925\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.77685 | + | 9.46120i | 0.489455 | + | 0.473652i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.390756 | − | 0.676809i | 0.0195134 | − | 0.0337982i | −0.856104 | − | 0.516804i | \(-0.827122\pi\) |
0.875617 | + | 0.483006i | \(0.160455\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.49932 | + | 0.937641i | 0.174314 | + | 0.0467072i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.125545 | − | 0.631735i | 0.00623836 | − | 0.0313912i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.4821 | + | 6.62918i | −0.569145 | + | 0.328596i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.9864 | − | 15.5806i | −1.33439 | − | 0.770412i | −0.348423 | − | 0.937338i | \(-0.613283\pi\) |
−0.985969 | + | 0.166926i | \(0.946616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.412344 | + | 25.1309i | 0.0203394 | + | 1.23962i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.9333 | − | 14.9333i | 0.734822 | − | 0.734822i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.397941 | −0.0195342 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.21981 | − | 8.86363i | 0.108705 | − | 0.434054i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.93759 | + | 22.1594i | 0.290070 | + | 1.08256i | 0.945054 | + | 0.326914i | \(0.106009\pi\) |
−0.654984 | + | 0.755643i | \(0.727325\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.71096 | + | 25.0456i | −0.327072 | + | 1.22065i | 0.585140 | + | 0.810932i | \(0.301039\pi\) |
−0.912212 | + | 0.409718i | \(0.865627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.67161 | + | 18.0981i | −0.470250 | + | 0.879961i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.68116 | − | 2.12532i | 0.178563 | − | 0.103093i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.86903 | − | 1.30465i | 0.235629 | − | 0.0631366i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.767601 | − | 1.38138i | 0.0370601 | − | 0.0666935i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.53959 | −0.411338 | −0.205669 | − | 0.978622i | \(-0.565937\pi\) | ||||
−0.205669 | + | 0.978622i | \(0.565937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.28283 | −0.446104 | −0.223052 | − | 0.974807i | \(-0.571602\pi\) | ||||
−0.223052 | + | 0.974807i | \(0.571602\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.297467 | + | 0.535321i | −0.0142624 | + | 0.0256667i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 44.0723 | − | 11.8091i | 2.10826 | − | 0.564908i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0947 | − | 6.98286i | 0.577247 | − | 0.333274i | −0.182792 | − | 0.983152i | \(-0.558513\pi\) |
0.760038 | + | 0.649878i | \(0.225180\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.4189 | − | 0.473295i | 0.686616 | − | 0.0225378i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.19925 | − | 11.9398i | 0.152001 | − | 0.567276i | −0.847343 | − | 0.531047i | \(-0.821799\pi\) |
0.999344 | − | 0.0362287i | \(-0.0115345\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.244185 | + | 0.911312i | 0.0115755 | + | 0.0432004i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.42193 | − | 33.6285i | 0.398344 | − | 1.59057i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.5226 | 0.732554 | 0.366277 | − | 0.930506i | \(-0.380632\pi\) | ||||
0.366277 | + | 0.930506i | \(0.380632\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.80232 | − | 3.80232i | 0.179044 | − | 0.179044i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.363908 | − | 22.1789i | −0.0170979 | − | 1.04206i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0369025 | + | 0.0213057i | 0.00173002 | + | 0.000998825i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.3712 | − | 13.4934i | 1.09326 | − | 0.631194i | 0.158817 | − | 0.987308i | \(-0.449232\pi\) |
0.934442 | + | 0.356114i | \(0.115899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.41657 | + | 0.217555i | −0.206148 | + | 0.0101546i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.8014 | + | 6.10962i | 1.06197 | + | 0.284554i | 0.747189 | − | 0.664611i | \(-0.231403\pi\) |
0.314779 | + | 0.949165i | \(0.398070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.7055 | + | 20.2745i | −0.544001 | + | 0.942238i | 0.454668 | + | 0.890661i | \(0.349758\pi\) |
−0.998669 | + | 0.0515769i | \(0.983575\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.802248 | − | 0.776346i | −0.0372033 | − | 0.0360022i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.4581 | + | 17.4581i | −0.807865 | + | 0.807865i | −0.984310 | − | 0.176446i | \(-0.943540\pi\) |
0.176446 | + | 0.984310i | \(0.443540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.01671 | − | 7.01671i | −0.324001 | − | 0.324001i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.8578 | − | 3.22011i | −0.592456 | − | 0.148375i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.08182 | + | 2.93399i | 0.233662 | + | 0.134905i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.86016 | − | 25.6024i | 0.314766 | − | 1.17472i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.80806 | − | 16.3384i | 0.174359 | − | 0.748082i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.62715 | + | 16.6747i | 0.439876 | + | 0.761887i | 0.997679 | − | 0.0680859i | \(-0.0216892\pi\) |
−0.557804 | + | 0.829973i | \(0.688356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.17559 | + | 2.03618i | −0.0536023 | + | 0.0928420i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.7076 | + | 19.2694i | −0.487212 | + | 0.876787i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0635180 | + | 0.0635180i | 0.00288420 | + | 0.00288420i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.8010i | − | 0.716012i | −0.933719 | − | 0.358006i | \(-0.883457\pi\) | ||
0.933719 | − | 0.358006i | \(-0.116543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.99539 | − | 24.4926i | −0.316342 | − | 1.10759i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9388 | − | 2.93103i | 0.493659 | − | 0.132276i | −0.00339642 | − | 0.999994i | \(-0.501081\pi\) |
0.497056 | + | 0.867719i | \(0.334414\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.06122 | + | 1.08820i | 0.182908 | + | 0.0490101i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.413529 | + | 0.257199i | −0.0185867 | + | 0.0115602i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.268562 | − | 0.465164i | −0.0120467 | − | 0.0208654i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.04051 | + | 3.88323i | 0.0465796 | + | 0.173837i | 0.985297 | − | 0.170850i | \(-0.0546515\pi\) |
−0.938717 | + | 0.344688i | \(0.887985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.33943 | + | 5.59840i | −0.417255 | + | 0.250118i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 24.1846i | − | 1.07834i | −0.842198 | − | 0.539169i | \(-0.818739\pi\) | ||
0.842198 | − | 0.539169i | \(-0.181261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.395536i | − | 0.0176011i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.364802 | + | 22.2334i | 0.0162014 | + | 0.987421i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.36446 | + | 12.5563i | 0.149127 | + | 0.556550i | 0.999537 | + | 0.0304290i | \(0.00968734\pi\) |
−0.850410 | + | 0.526121i | \(0.823646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7490 | − | 20.3498i | −0.519743 | − | 0.900222i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.5147 | + | 20.4332i | −0.817442 | + | 0.902147i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.766227 | − | 0.205310i | −0.0337640 | − | 0.00904703i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9865 | − | 4.01562i | 0.659105 | − | 0.176607i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1630 | − | 14.6355i | 0.621685 | − | 0.642427i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.39592i | 0.148778i | 0.997229 | + | 0.0743889i | \(0.0237006\pi\) | ||||
−0.997229 | + | 0.0743889i | \(0.976299\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.4956 | + | 21.4956i | 0.939938 | + | 0.939938i | 0.998296 | − | 0.0583574i | \(-0.0185863\pi\) |
−0.0583574 | + | 0.998296i | \(0.518586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.58413 | + | 10.9839i | 0.287355 | + | 0.479375i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.83221 | + | 6.63758i | −0.166934 | + | 0.289138i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.4648 | + | 44.1063i | 1.10716 | + | 1.91767i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.2421 | + | 29.2562i | 1.35579 | + | 1.26961i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.246806 | − | 0.921094i | 0.0106904 | − | 0.0398970i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.605034 | − | 0.349316i | −0.0261579 | − | 0.0151023i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.20101 | + | 21.7112i | 0.267593 | + | 0.936909i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.71302 | − | 7.71302i | −0.332223 | − | 0.332223i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.7438 | + | 14.7438i | −0.633886 | + | 0.633886i | −0.949041 | − | 0.315154i | \(-0.897944\pi\) |
0.315154 | + | 0.949041i | \(0.397944\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.3025 | − | 7.79795i | 1.17166 | − | 0.334642i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.475261 | + | 0.823176i | −0.0203579 | + | 0.0352610i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.6555 | + | 8.21413i | 1.31074 | + | 0.351211i | 0.845500 | − | 0.533976i | \(-0.179303\pi\) |
0.465236 | + | 0.885186i | \(0.345969\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.96646 | + | 9.77603i | 0.126606 | + | 0.417231i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.7053 | − | 13.1089i | 0.967278 | − | 0.558458i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.9816 | − | 8.07229i | −0.594559 | − | 0.343269i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.621439 | − | 0.372513i | 0.0263786 | − | 0.0158123i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.6150 | + | 16.6150i | −0.704002 | + | 0.704002i | −0.965267 | − | 0.261265i | \(-0.915860\pi\) |
0.261265 | + | 0.965267i | \(0.415860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.04060 | 0.0440129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.40259 | + | 2.32502i | 0.101437 | + | 0.0981622i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.625738 | + | 2.33528i | 0.0263717 | + | 0.0984205i | 0.977857 | − | 0.209273i | \(-0.0671096\pi\) |
−0.951486 | + | 0.307693i | \(0.900443\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.215293 | − | 0.803484i | 0.00905745 | − | 0.0338028i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.873644 | − | 13.2935i | −0.0366896 | − | 0.558272i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.83926 | + | 5.10335i | −0.370561 | + | 0.213943i | −0.673703 | − | 0.739002i | \(-0.735297\pi\) |
0.303143 | + | 0.952945i | \(0.401964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9394 | + | 5.61069i | −0.876285 | + | 0.234800i | −0.668804 | − | 0.743439i | \(-0.733193\pi\) |
−0.207481 | + | 0.978239i | \(0.566527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.7458 | − | 0.635734i | 1.61863 | − | 0.0265582i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 42.9471 | 1.79102 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0725 | −0.710737 | −0.355369 | − | 0.934726i | \(-0.615645\pi\) | ||||
−0.355369 | + | 0.934726i | \(0.615645\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.7862 | + | 21.3304i | 0.531378 | + | 0.886462i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.95043 | + | 2.13031i | −0.329839 | + | 0.0883802i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9850 | + | 6.34217i | −0.454951 | + | 0.262666i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0407034 | + | 0.0761668i | −0.00168288 | + | 0.00314911i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.63287 | − | 13.5581i | 0.149945 | − | 0.559602i | −0.849541 | − | 0.527523i | \(-0.823121\pi\) |
0.999485 | − | 0.0320783i | \(-0.0102126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3697 | + | 46.1643i | 0.509684 | + | 1.90217i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.71049 | + | 1.05976i | −0.152629 | + | 0.0435928i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.5850 | −1.13278 | −0.566390 | − | 0.824137i | \(-0.691660\pi\) | ||||
−0.566390 | + | 0.824137i | \(0.691660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0637455 | + | 0.0637455i | −0.00261331 | + | 0.00261331i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.61552 | + | 1.45339i | 0.107046 | + | 0.0594832i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.8788 | − | 20.1373i | −1.42511 | − | 0.822788i | −0.428380 | − | 0.903598i | \(-0.640916\pi\) |
−0.996729 | + | 0.0808109i | \(0.974249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.90297 | − | 3.40808i | 0.240787 | − | 0.139018i | −0.374751 | − | 0.927125i | \(-0.622272\pi\) |
0.615538 | + | 0.788107i | \(0.288939\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.7466 | − | 14.6797i | 0.559804 | − | 0.597802i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.404736 | − | 0.108449i | −0.0164549 | − | 0.00440907i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.09235 | − | 1.89200i | 0.0443370 | − | 0.0767939i | −0.843005 | − | 0.537905i | \(-0.819216\pi\) |
0.887342 | + | 0.461111i | \(0.152549\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.07730 | + | 12.2876i | −0.124699 | + | 0.497917i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.94553 | − | 1.94553i | 0.0787077 | − | 0.0787077i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.3068 | + | 15.3068i | 0.618236 | + | 0.618236i | 0.945079 | − | 0.326843i | \(-0.105985\pi\) |
−0.326843 | + | 0.945079i | \(0.605985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.204350 | + | 0.211168i | −0.00824020 | + | 0.00851512i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1056 | − | 5.83447i | −0.406836 | − | 0.234887i | 0.282593 | − | 0.959240i | \(-0.408805\pi\) |
−0.689429 | + | 0.724353i | \(0.742139\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.13744 | − | 4.24500i | 0.0457178 | − | 0.170621i | −0.939292 | − | 0.343118i | \(-0.888517\pi\) |
0.985010 | + | 0.172497i | \(0.0551835\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.7442 | − | 20.4082i | −1.59488 | − | 0.818952i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.75711 | + | 16.8998i | 0.390910 | + | 0.677076i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.4616 | − | 21.5841i | 0.498464 | − | 0.863365i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.8453 | − | 0.342027i | 0.832483 | − | 0.0136592i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.51731 | − | 3.51731i | −0.140244 | − | 0.140244i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.5374i | − | 1.25548i | −0.778422 | − | 0.627742i | \(-0.783979\pi\) | ||
0.778422 | − | 0.627742i | \(-0.216021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.7695 | + | 5.20152i | 0.825513 | + | 0.206742i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.704855 | + | 0.188865i | −0.0279713 | + | 0.00749489i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.86844 | − | 0.500648i | −0.0740304 | − | 0.0198364i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.924384 | − | 0.574932i | 0.0365681 | − | 0.0227439i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.38996 | + | 16.2639i | 0.370881 | + | 0.642385i | 0.989701 | − | 0.143148i | \(-0.0457225\pi\) |
−0.618820 | + | 0.785533i | \(0.712389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.94427 | + | 25.9164i | 0.273855 | + | 1.02204i | 0.956605 | + | 0.291389i | \(0.0941175\pi\) |
−0.682749 | + | 0.730653i | \(0.739216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.280302 | − | 0.155758i | −0.0110369 | − | 0.00613295i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.5176i | 0.649373i | 0.945822 | + | 0.324686i | \(0.105259\pi\) | ||||
−0.945822 | + | 0.324686i | \(0.894741\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 32.3620i | − | 1.27032i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.1841 | − | 11.2158i | −0.791075 | − | 0.439584i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.8252 | + | 40.4003i | 0.423624 | + | 1.58099i | 0.766909 | + | 0.641756i | \(0.221794\pi\) |
−0.343285 | + | 0.939231i | \(0.611540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.251729 | − | 0.436008i | −0.00983587 | − | 0.0170362i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 40.4396 | − | 25.1519i | 1.57770 | − | 0.981268i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.3797 | + | 3.04918i | 0.443290 | + | 0.118779i | 0.473558 | − | 0.880763i | \(-0.342969\pi\) |
−0.0302682 | + | 0.999542i | \(0.509636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.1808 | − | 10.4985i | 1.52396 | − | 0.408343i | 0.602913 | − | 0.797807i | \(-0.294006\pi\) |
0.921042 | + | 0.389464i | \(0.127340\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.575137 | + | 0.144037i | 0.0223365 | + | 0.00559395i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.562144i | 0.0217990i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.0385 | + | 30.0385i | 1.16309 | + | 1.16309i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.0102 | + | 0.410364i | −0.966952 | + | 0.0158656i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.86217 | − | 6.68948i | 0.149098 | − | 0.258245i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.73175 | − | 11.6597i | −0.259490 | − | 0.449450i | 0.706615 | − | 0.707598i | \(-0.250221\pi\) |
−0.966105 | + | 0.258148i | \(0.916888\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.8113 | + | 14.0672i | −0.839516 | + | 0.541447i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.56756 | − | 9.58227i | 0.0986794 | − | 0.368277i | −0.898872 | − | 0.438211i | \(-0.855612\pi\) |
0.997552 | + | 0.0699343i | \(0.0222790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.60905 | + | 0.928986i | 0.0617497 | + | 0.0356512i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.01483 | + | 2.08205i | −0.0772085 | + | 0.0797844i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.48800 | − | 4.48800i | −0.171728 | − | 0.171728i | 0.616010 | − | 0.787738i | \(-0.288748\pi\) |
−0.787738 | + | 0.616010i | \(0.788748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.734335 | + | 0.734335i | −0.0280575 | + | 0.0280575i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.54725 | − | 34.1289i | 0.326098 | − | 1.30210i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.12470 | + | 1.94803i | −0.0428475 | + | 0.0742140i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.9149 | − | 9.62336i | −1.36627 | − | 0.366090i | −0.500153 | − | 0.865937i | \(-0.666723\pi\) |
−0.866114 | + | 0.499847i | \(0.833390\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.88498 | + | 7.35231i | −0.261539 | + | 0.279291i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.326960 | − | 0.188770i | 0.0124023 | − | 0.00716047i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.74715 | + | 1.00872i | 0.0661780 | + | 0.0382079i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.7024 | − | 19.8391i | −1.35039 | − | 0.750382i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.9558 | − | 36.9558i | 1.39580 | − | 1.39580i | 0.584175 | − | 0.811628i | \(-0.301418\pi\) |
0.811628 | − | 0.584175i | \(-0.198582\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.0176 | −1.16985 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.815264 | + | 0.232850i | −0.0307046 | + | 0.00876963i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.11743 | − | 7.90237i | −0.0796343 | − | 0.297199i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.53529 | + | 5.72979i | −0.0576591 | + | 0.215187i | −0.988744 | − | 0.149615i | \(-0.952197\pi\) |
0.931085 | + | 0.364802i | \(0.118863\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.4217 | − | 28.8581i | 0.578359 | − | 1.08226i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −67.0640 | + | 38.7194i | −2.51157 | + | 1.45005i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0630713 | − | 0.0168999i | 0.00235873 | − | 0.000632021i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.62996 | − | 12.7285i | −0.284946 | − | 0.475356i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.58462 | −0.357446 | −0.178723 | − | 0.983899i | \(-0.557197\pi\) | ||||
−0.178723 | + | 0.983899i | \(0.557197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.4075 | −0.611046 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.7813 | + | 0.209713i | −0.475340 | + | 0.00779931i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.8370 | − | 6.38711i | 0.885285 | − | 0.237211i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.4374 | + | 19.8824i | −1.27721 | + | 0.737399i | −0.976335 | − | 0.216264i | \(-0.930613\pi\) |
−0.300877 | + | 0.953663i | \(0.597279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.8693 | − | 2.65354i | 0.995159 | − | 0.0982793i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.569798 | + | 2.12651i | −0.0210747 | + | 0.0786520i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.37557 | − | 34.9901i | −0.346295 | − | 1.29239i | −0.891092 | − | 0.453822i | \(-0.850060\pi\) |
0.544798 | − | 0.838567i | \(-0.316606\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.428356 | + | 0.414526i | 0.0158001 | + | 0.0152900i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.2059 | −0.560115 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.78860 | − | 7.78860i | 0.286508 | − | 0.286508i | −0.549190 | − | 0.835698i | \(-0.685064\pi\) |
0.835698 | + | 0.549190i | \(0.185064\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.17105 | − | 1.90084i | 0.116491 | − | 0.0698291i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.75539 | + | 2.16817i | 0.137772 | + | 0.0795426i | 0.567302 | − | 0.823510i | \(-0.307987\pi\) |
−0.429530 | + | 0.903053i | \(0.641321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.24048 | − | 0.716193i | 0.0454477 | − | 0.0262393i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.84380 | − | 15.9628i | −0.177226 | − | 0.584050i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.9579 | − | 3.74001i | −0.510011 | − | 0.136657i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.74026 | − | 11.6745i | 0.245956 | − | 0.426008i | −0.716444 | − | 0.697644i | \(-0.754232\pi\) |
0.962400 | + | 0.271637i | \(0.0875649\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.6010 | + | 5.88389i | −0.750741 | + | 0.214421i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.648077 | − | 0.648077i | 0.0235859 | − | 0.0235859i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.9901 | + | 25.9901i | 0.944625 | + | 0.944625i | 0.998545 | − | 0.0539205i | \(-0.0171718\pi\) |
−0.0539205 | + | 0.998545i | \(0.517172\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.27712 | + | 32.4815i | 0.336738 | + | 1.17900i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3955 | − | 16.9715i | −1.06558 | − | 0.615216i | −0.138613 | − | 0.990347i | \(-0.544264\pi\) |
−0.926972 | + | 0.375131i | \(0.877598\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.08845 | + | 18.9904i | −0.184214 | + | 0.687498i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.133362 | − | 0.124885i | −0.00482171 | − | 0.00451523i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.86947 | − | 4.97006i | −0.103610 | − | 0.179459i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.38011 | − | 4.12248i | 0.0858291 | − | 0.148660i | −0.819915 | − | 0.572485i | \(-0.805979\pi\) |
0.905744 | + | 0.423825i | \(0.139313\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.93734 | + | 6.56840i | 0.141800 | + | 0.236555i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.1267 | − | 38.1267i | −1.37132 | − | 1.37132i | −0.858486 | − | 0.512837i | \(-0.828595\pi\) |
−0.512837 | − | 0.858486i | \(-0.671405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.9857i | 1.61593i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.4215 | − | 10.7692i | 0.373868 | − | 0.386342i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.1514 | − | 3.25596i | 0.435369 | − | 0.116657i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.795027 | − | 0.213027i | −0.0284483 | − | 0.00762270i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.0944 | − | 5.41642i | −0.896802 | − | 0.193567i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.273835 | − | 0.474296i | −0.00977359 | − | 0.0169284i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.10176 | − | 22.7721i | −0.217504 | − | 0.811736i | −0.985270 | − | 0.171006i | \(-0.945298\pi\) |
0.767766 | − | 0.640730i | \(-0.221368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.311248 | + | 18.9695i | 0.0110807 | + | 0.675331i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 17.2053i | − | 0.611749i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.36980i | − | 0.0486432i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.594534 | − | 0.356386i | 0.0210860 | − | 0.0126397i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.8678 | − | 44.2911i | −0.420378 | − | 1.56887i | −0.773814 | − | 0.633413i | \(-0.781654\pi\) |
0.353436 | − | 0.935459i | \(-0.385013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.91046 | + | 5.04107i | 0.102965 | + | 0.178340i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.5837 | + | 20.8878i | −1.18662 | + | 0.738034i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.7805 | − | 9.31941i | −1.22738 | − | 0.328875i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.879807 | + | 0.235744i | −0.0310091 | + | 0.00830887i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.15597 | − | 25.0548i | −0.251902 | − | 0.881971i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 8.89301i | − | 0.312662i | −0.987705 | − | 0.156331i | \(-0.950033\pi\) | ||
0.987705 | − | 0.156331i | \(-0.0499666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.7492 | + | 31.7492i | 1.11487 | + | 1.11487i | 0.992483 | + | 0.122384i | \(0.0390538\pi\) |
0.122384 | + | 0.992483i | \(0.460946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0865 | − | 28.9492i | 0.564177 | − | 1.01529i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.526230 | − | 0.911457i | 0.0184330 | − | 0.0319269i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.86401 | + | 11.8888i | 0.240141 | + | 0.415937i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.405463 | + | 1.73963i | −0.0141680 | + | 0.0607875i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5747 | + | 46.9294i | −0.438860 | + | 1.63785i | 0.292797 | + | 0.956175i | \(0.405414\pi\) |
−0.731657 | + | 0.681673i | \(0.761253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.69600 | + | 5.59799i | 0.337981 | + | 0.195134i | 0.659379 | − | 0.751811i | \(-0.270819\pi\) |
−0.321398 | + | 0.946944i | \(0.604153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.0357 | + | 4.76732i | 0.662740 | + | 0.165977i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.9898 | − | 11.9898i | −0.416927 | − | 0.416927i | 0.467216 | − | 0.884143i | \(-0.345257\pi\) |
−0.884143 | + | 0.467216i | \(0.845257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.3253 | + | 34.3253i | −1.19217 | + | 1.19217i | −0.215708 | + | 0.976458i | \(0.569206\pi\) |
−0.976458 | + | 0.215708i | \(0.930794\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.9929 | + | 12.5734i | 0.450718 | + | 0.436167i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.04619 | − | 3.54410i | 0.0708962 | − | 0.122796i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.434579 | − | 0.116445i | −0.0150392 | − | 0.00402975i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.3769 | − | 41.6308i | 0.738894 | − | 1.43897i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.4830 | + | 25.1049i | −1.50120 | + | 0.866719i | −0.501202 | + | 0.865331i | \(0.667109\pi\) |
−0.999999 | + | 0.00138814i | \(0.999558\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.97509 | − | 2.29502i | −0.137072 | − | 0.0791386i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.399572 | + | 24.3525i | 0.0137620 | + | 0.838746i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.649670 | + | 0.649670i | −0.0223493 | + | 0.0223493i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.66674 | −0.297793 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.7443 | − | 42.9015i | 0.368742 | − | 1.47237i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.0077 | − | 48.5455i | −0.445899 | − | 1.66412i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.97320 | − | 26.0243i | 0.238758 | − | 0.891056i | −0.737661 | − | 0.675171i | \(-0.764070\pi\) |
0.976419 | − | 0.215885i | \(-0.0692635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.13869 | + | 0.0373768i | −0.0389422 | + | 0.00127826i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.5955 | + | 7.27203i | −0.430255 | + | 0.248408i | −0.699455 | − | 0.714676i | \(-0.746574\pi\) |
0.269200 | + | 0.963084i | \(0.413241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.49231 | + | 1.20371i | −0.153276 | + | 0.0410701i | −0.334641 | − | 0.942346i | \(-0.608615\pi\) |
0.181365 | + | 0.983416i | \(0.441948\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.95224 | + | 5.31286i | −0.100612 | + | 0.181062i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.06219 | −0.206359 | −0.103180 | − | 0.994663i | \(-0.532902\pi\) | ||||
−0.103180 | + | 0.994663i | \(0.532902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.841503 | 0.0286120 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.6928 | − | 24.6417i | 0.465033 | − | 0.836874i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.8965 | + | 6.40303i | −0.810632 | + | 0.217208i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.33528 | + | 1.34827i | −0.0791278 | + | 0.0456845i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.77478 | + | 3.32108i | −0.0600672 | + | 0.112402i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.274036 | + | 1.02272i | −0.00926412 | + | 0.0345742i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.44913 | + | 20.3364i | 0.184004 | + | 0.686713i | 0.994842 | + | 0.101441i | \(0.0323454\pi\) |
−0.810837 | + | 0.585271i | \(0.800988\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.77502 | − | 23.0595i | 0.194787 | − | 0.777777i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.07747 | 0.103682 | 0.0518412 | − | 0.998655i | \(-0.483491\pi\) | ||||
0.0518412 | + | 0.998655i | \(0.483491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.89268 | − | 2.89268i | 0.0973465 | − | 0.0973465i | −0.656756 | − | 0.754103i | \(-0.728072\pi\) |
0.754103 | + | 0.656756i | \(0.228072\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0290134 | + | 1.76826i | 0.000975273 | + | 0.0594395i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.0227 | + | 24.8392i | 1.44456 | + | 0.834017i | 0.998149 | − | 0.0608108i | \(-0.0193686\pi\) |
0.446411 | + | 0.894828i | \(0.352702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.0712 | + | 7.54664i | −0.438393 | + | 0.253106i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.3507 | − | 13.4574i | −0.514268 | − | 0.450841i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.0606 | + | 9.39445i | 1.17326 | + | 0.314373i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.466472 | + | 0.807953i | −0.0155924 | + | 0.0270069i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.30482 | + | 4.16583i | 0.143734 | + | 0.139093i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.4643 | + | 31.4643i | −1.04939 | + | 1.04939i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.36503 | − | 3.36503i | −0.112105 | − | 0.112105i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.43394 | − | 1.61132i | −0.214108 | − | 0.0536213i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.01603 | + | 0.586603i | 0.0337738 | + | 0.0194993i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.27515 | + | 12.2230i | −0.108750 | + | 0.405859i | −0.998744 | − | 0.0501131i | \(-0.984042\pi\) |
0.889994 | + | 0.455973i | \(0.150708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.8663 | − | 4.81452i | 0.526253 | − | 0.159688i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6903 | + | 46.2289i | 0.884289 | + | 1.53163i | 0.846526 | + | 0.532347i | \(0.178690\pi\) |
0.0377625 | + | 0.999287i | \(0.487977\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.30637 | + | 10.9230i | −0.208710 | + | 0.361497i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.205032 | + | 0.368977i | −0.00677816 | + | 0.0121980i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.36336 | − | 7.36336i | −0.243160 | − | 0.243160i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.5309i | 1.27102i | 0.772094 | + | 0.635509i | \(0.219210\pi\) | ||||
−0.772094 | + | 0.635509i | \(0.780790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.49335 | + | 33.2386i | 0.312817 | + | 1.09525i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.140987 | + | 0.0377773i | −0.00464064 | + | 0.00124345i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.2010 | − | 7.55643i | −0.927243 | − | 0.248454i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.09093 | − | 33.2351i | −0.0358308 | − | 1.09159i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.92500 | + | 10.2624i | 0.194393 | + | 0.336699i | 0.946701 | − | 0.322113i | \(-0.104393\pi\) |
−0.752308 | + | 0.658811i | \(0.771060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.60473 | − | 24.6492i | −0.216461 | − | 0.807844i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.3693 | + | 11.6107i | −0.634124 | + | 0.380117i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.138142i | 0.00451774i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.288917i | − | 0.00943850i | −0.999989 | − | 0.00471925i | \(-0.998498\pi\) | ||
0.999989 | − | 0.00471925i | \(-0.00150219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.213441 | − | 13.0085i | −0.00696539 | − | 0.424516i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.87473 | − | 33.1209i | −0.289308 | − | 1.07971i | −0.945634 | − | 0.325234i | \(-0.894557\pi\) |
0.656326 | − | 0.754478i | \(-0.272110\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1917 | + | 17.6526i | 0.331889 | + | 0.574849i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.369605 | − | 0.407904i | 0.0120232 | − | 0.0132691i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.3187 | − | 5.98027i | −0.725259 | − | 0.194333i | −0.122742 | − | 0.992439i | \(-0.539169\pi\) |
−0.602517 | + | 0.798106i | \(0.705835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.16783 | + | 1.65267i | −0.200216 | + | 0.0536478i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.81634 | + | 1.87694i | −0.0588990 | + | 0.0608640i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31.0900i | − | 1.00710i | −0.863965 | − | 0.503552i | \(-0.832026\pi\) | ||
0.863965 | − | 0.503552i | \(-0.167974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.13217 | + | 1.13217i | 0.0366361 | + | 0.0366361i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.97975 | + | 16.6486i | 0.322600 | + | 0.538171i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.7401 | + | 18.6023i | −0.346815 | + | 0.600701i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0573 | − | 43.4006i | −0.808302 | − | 1.40002i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.64775 | − | 28.5220i | 0.214221 | − | 0.919108i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.265950 | + | 0.992539i | −0.00856124 | + | 0.0319510i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.9481 | + | 14.4038i | 0.802277 | + | 0.463195i | 0.844267 | − | 0.535923i | \(-0.180036\pi\) |
−0.0419899 | + | 0.999118i | \(0.513370\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.14809 | + | 7.52099i | 0.0690066 | + | 0.241609i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.6466 | − | 11.6466i | −0.373757 | − | 0.373757i | 0.495087 | − | 0.868844i | \(-0.335136\pi\) |
−0.868844 | + | 0.495087i | \(0.835136\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.52175 | − | 5.52175i | 0.177019 | − | 0.177019i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.34617 | − | 0.955708i | 0.107163 | − | 0.0306072i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.0661 | + | 20.8990i | −0.386028 | + | 0.668619i | −0.991911 | − | 0.126934i | \(-0.959486\pi\) |
0.605884 | + | 0.795553i | \(0.292820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.8840 | + | 7.73945i | 0.923137 | + | 0.247354i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.8055 | − | 9.04457i | −1.23896 | − | 0.288771i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.5016 | + | 10.6819i | −0.590109 | + | 0.340700i | −0.765141 | − | 0.643863i | \(-0.777331\pi\) |
0.175031 | + | 0.984563i | \(0.443997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.138081 | − | 0.0797210i | −0.00439962 | − | 0.00254012i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.0415 | + | 9.01645i | −0.478778 | + | 0.286997i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.7286 | + | 15.7286i | −0.500139 | + | 0.500139i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.0624 | −0.891433 | −0.445717 | − | 0.895174i | \(-0.647051\pi\) | ||||
−0.445717 | + | 0.895174i | \(0.647051\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.4855 | + | 24.6626i | 0.808756 | + | 0.782645i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0319985 | + | 0.119420i | 0.00101442 | + | 0.00378587i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.0100 | + | 56.0181i | −0.475372 | + | 1.77411i | 0.144603 | + | 0.989490i | \(0.453810\pi\) |
−0.619975 | + | 0.784622i | \(0.712857\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.5071 | + | 20.3938i | 0.712092 | + | 0.645232i |
(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 | 576.2.bb.e.49.7 | 72 | ||
3.2 | odd | 2 | 1728.2.bc.e.1009.10 | 72 | |||
4.3 | odd | 2 | 144.2.x.e.85.2 | yes | 72 | ||
9.2 | odd | 6 | 1728.2.bc.e.1585.9 | 72 | |||
9.7 | even | 3 | inner | 576.2.bb.e.241.4 | 72 | ||
12.11 | even | 2 | 432.2.y.e.37.17 | 72 | |||
16.3 | odd | 4 | 144.2.x.e.13.12 | ✓ | 72 | ||
16.13 | even | 4 | inner | 576.2.bb.e.337.4 | 72 | ||
36.7 | odd | 6 | 144.2.x.e.133.12 | yes | 72 | ||
36.11 | even | 6 | 432.2.y.e.181.7 | 72 | |||
48.29 | odd | 4 | 1728.2.bc.e.145.9 | 72 | |||
48.35 | even | 4 | 432.2.y.e.253.7 | 72 | |||
144.29 | odd | 12 | 1728.2.bc.e.721.10 | 72 | |||
144.61 | even | 12 | inner | 576.2.bb.e.529.7 | 72 | ||
144.83 | even | 12 | 432.2.y.e.397.17 | 72 | |||
144.115 | odd | 12 | 144.2.x.e.61.2 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.12 | ✓ | 72 | 16.3 | odd | 4 | ||
144.2.x.e.61.2 | yes | 72 | 144.115 | odd | 12 | ||
144.2.x.e.85.2 | yes | 72 | 4.3 | odd | 2 | ||
144.2.x.e.133.12 | yes | 72 | 36.7 | odd | 6 | ||
432.2.y.e.37.17 | 72 | 12.11 | even | 2 | |||
432.2.y.e.181.7 | 72 | 36.11 | even | 6 | |||
432.2.y.e.253.7 | 72 | 48.35 | even | 4 | |||
432.2.y.e.397.17 | 72 | 144.83 | even | 12 | |||
576.2.bb.e.49.7 | 72 | 1.1 | even | 1 | trivial | ||
576.2.bb.e.241.4 | 72 | 9.7 | even | 3 | inner | ||
576.2.bb.e.337.4 | 72 | 16.13 | even | 4 | inner | ||
576.2.bb.e.529.7 | 72 | 144.61 | even | 12 | inner | ||
1728.2.bc.e.145.9 | 72 | 48.29 | odd | 4 | |||
1728.2.bc.e.721.10 | 72 | 144.29 | odd | 12 | |||
1728.2.bc.e.1009.10 | 72 | 3.2 | odd | 2 | |||
1728.2.bc.e.1585.9 | 72 | 9.2 | odd | 6 |