Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(41,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 33, 53]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.ba (of order \(66\), degree \(20\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(440\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{66})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{66}]$ |
Embedding invariants
Embedding label | 353.3 | ||
Character | \(\chi\) | \(=\) | 804.353 |
Dual form | 804.2.ba.b.41.3 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{66}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.68954 | + | 0.381398i | −0.975455 | + | 0.220200i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.606307 | + | 4.21696i | 0.271149 | + | 1.88588i | 0.436590 | + | 0.899660i | \(0.356186\pi\) |
−0.165442 | + | 0.986220i | \(0.552905\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.295017 | + | 3.08956i | −0.111506 | + | 1.16774i | 0.750509 | + | 0.660860i | \(0.229808\pi\) |
−0.862015 | + | 0.506883i | \(0.830798\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.70907 | − | 1.28877i | 0.903024 | − | 0.429591i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.34850 | + | 2.14122i | 1.61263 | + | 0.645601i | 0.990525 | − | 0.137330i | \(-0.0438522\pi\) |
0.622108 | + | 0.782931i | \(0.286276\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.06287 | − | 1.11471i | 0.294787 | − | 0.309164i | −0.559639 | − | 0.828736i | \(-0.689060\pi\) |
0.854426 | + | 0.519573i | \(0.173909\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.63272 | − | 6.89346i | −0.679765 | − | 1.77988i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.13592 | + | 1.08535i | 0.760572 | + | 0.263236i | 0.679702 | − | 0.733488i | \(-0.262109\pi\) |
0.0808697 | + | 0.996725i | \(0.474230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.373168 | − | 0.0356332i | 0.0856105 | − | 0.00817481i | −0.0521629 | − | 0.998639i | \(-0.516611\pi\) |
0.137773 | + | 0.990464i | \(0.456005\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.679910 | − | 5.33244i | −0.148369 | − | 1.16363i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.36039 | − | 0.160075i | −0.700690 | − | 0.0333780i | −0.305786 | − | 0.952100i | \(-0.598919\pi\) |
−0.394904 | + | 0.918722i | \(0.629222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.6176 | + | 3.70487i | −2.52353 | + | 0.740975i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.08554 | + | 3.21067i | −0.786262 | + | 0.617893i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.55526 | + | 3.20733i | 1.03159 | + | 0.595586i | 0.917438 | − | 0.397878i | \(-0.130253\pi\) |
0.114147 | + | 0.993464i | \(0.463586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.06664 | − | 5.31374i | −0.909996 | − | 0.954376i | 0.0891369 | − | 0.996019i | \(-0.471589\pi\) |
−0.999133 | + | 0.0416434i | \(0.986741\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.85315 | − | 1.57776i | −1.71521 | − | 0.274652i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.2074 | + | 0.629146i | −2.23246 | + | 0.106345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.92489 | + | 5.06605i | 0.480848 | + | 0.832854i | 0.999759 | − | 0.0219750i | \(-0.00699543\pi\) |
−0.518910 | + | 0.854829i | \(0.673662\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.37061 | + | 2.28871i | −0.219473 | + | 0.366487i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4018 | − | 2.00479i | 1.62449 | − | 0.313095i | 0.705903 | − | 0.708308i | \(-0.250541\pi\) |
0.918590 | + | 0.395213i | \(0.129329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.118743 | − | 0.102891i | 0.0181081 | − | 0.0156908i | −0.645760 | − | 0.763541i | \(-0.723459\pi\) |
0.663868 | + | 0.747850i | \(0.268914\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.07723 | + | 10.6426i | 1.05501 | + | 1.58651i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.91118 | − | 5.64690i | −0.424639 | − | 0.823685i | −0.999983 | − | 0.00577368i | \(-0.998162\pi\) |
0.575344 | − | 0.817911i | \(-0.304868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.58483 | − | 0.498185i | −0.369261 | − | 0.0711692i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.71220 | − | 0.637708i | −0.799868 | − | 0.0892970i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.39615 | + | 1.61125i | −0.191776 | + | 0.221322i | −0.843492 | − | 0.537142i | \(-0.819504\pi\) |
0.651716 | + | 0.758463i | \(0.274050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.78658 | + | 23.8526i | −0.780263 | + | 3.21629i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.616890 | + | 0.202529i | −0.0817091 | + | 0.0268256i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.864195 | + | 2.94318i | −0.112509 | + | 0.383169i | −0.996426 | − | 0.0844747i | \(-0.973079\pi\) |
0.883917 | + | 0.467644i | \(0.154897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.18649 | − | 12.9552i | −0.664062 | − | 1.65875i | −0.749173 | − | 0.662375i | \(-0.769549\pi\) |
0.0851109 | − | 0.996371i | \(-0.472876\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.18252 | + | 8.75004i | 0.400959 | + | 1.10240i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.34509 | + | 3.80622i | 0.662977 | + | 0.472104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.49951 | − | 8.04683i | 0.183194 | − | 0.983077i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.73856 | − | 1.01119i | 0.690841 | − | 0.121734i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.54395 | + | 1.57268i | −0.539268 | + | 0.186642i | −0.583106 | − | 0.812396i | \(-0.698163\pi\) |
0.0438379 | + | 0.999039i | \(0.486041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.76888 | − | 1.10849i | 0.324073 | − | 0.129739i | −0.203921 | − | 0.978987i | \(-0.565369\pi\) |
0.527994 | + | 0.849248i | \(0.322944\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 19.9049 | − | 11.0719i | 2.29842 | − | 1.27847i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.19331 | + | 15.8928i | −0.933714 | + | 1.81115i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.363719 | + | 0.0882373i | 0.0409216 | + | 0.00992748i | 0.256167 | − | 0.966632i | \(-0.417540\pi\) |
−0.215246 | + | 0.976560i | \(0.569055\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.67813 | − | 6.98276i | 0.630903 | − | 0.775862i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.94036 | − | 8.82538i | −0.761803 | − | 0.968712i | 0.238194 | − | 0.971218i | \(-0.423445\pi\) |
−0.999997 | + | 0.00250596i | \(0.999202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.67555 | + | 13.8821i | −0.290204 | + | 1.50572i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.6091 | − | 3.30014i | −1.13741 | − | 0.353812i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.23838 | + | 1.92696i | 0.131268 | + | 0.204258i | 0.900665 | − | 0.434513i | \(-0.143080\pi\) |
−0.769397 | + | 0.638771i | \(0.779443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.13038 | + | 3.61265i | 0.328153 | + | 0.378709i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.5869 | + | 7.04535i | 1.09781 | + | 0.730569i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.376518 | + | 1.55203i | 0.0386299 | + | 0.159235i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.393962 | + | 0.227454i | −0.0400008 | + | 0.0230945i | −0.519867 | − | 0.854247i | \(-0.674019\pi\) |
0.479866 | + | 0.877342i | \(0.340685\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.2490 | − | 1.09230i | 1.73359 | − | 0.109780i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.12702 | − | 10.0085i | −0.709165 | − | 0.995882i | −0.999244 | − | 0.0388797i | \(-0.987621\pi\) |
0.290079 | − | 0.957003i | \(-0.406318\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1880 | + | 12.5747i | −1.29945 | + | 1.23902i | −0.345726 | + | 0.938336i | \(0.612367\pi\) |
−0.953723 | + | 0.300686i | \(0.902784\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.0744 | − | 6.10024i | 2.15424 | − | 0.595323i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.02067 | + | 0.146751i | 0.0986721 | + | 0.0141869i | 0.191474 | − | 0.981498i | \(-0.438673\pi\) |
−0.0928019 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.29791 | − | 11.2316i | −0.315882 | − | 1.07580i | −0.952480 | − | 0.304601i | \(-0.901477\pi\) |
0.636598 | − | 0.771196i | \(-0.280341\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.87389 | − | 7.44373i | −0.652441 | − | 0.706528i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.84294 | + | 6.16776i | 0.737802 | + | 0.580214i | 0.914757 | − | 0.404005i | \(-0.132382\pi\) |
−0.176955 | + | 0.984219i | \(0.556625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.36240 | − | 14.2677i | −0.127044 | − | 1.33047i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.44279 | − | 4.38961i | 0.133386 | − | 0.405820i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.27841 | + | 9.36840i | −0.392201 | + | 0.858800i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0606 | + | 15.3137i | 1.46005 | + | 1.39216i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.8097 | + | 7.35440i | −1.51568 | + | 0.663124i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14.4244 | − | 31.5851i | −1.29016 | − | 2.82506i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.65841 | + | 0.635801i | 0.590839 | + | 0.0564183i | 0.386193 | − | 0.922418i | \(-0.373790\pi\) |
0.204645 | + | 0.978836i | \(0.434396\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.161378 | + | 0.219127i | −0.0142085 | + | 0.0192930i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.72329 | − | 4.23752i | 0.237935 | − | 0.370234i | −0.701666 | − | 0.712506i | \(-0.747560\pi\) |
0.939601 | + | 0.342272i | \(0.111197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.16343i | 0.100883i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.0163 | − | 15.2819i | −1.37847 | − | 1.31526i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.7333 | − | 9.46850i | −1.25875 | − | 0.808948i | −0.270636 | − | 0.962682i | \(-0.587234\pi\) |
−0.988112 | + | 0.153734i | \(0.950870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.55641 | − | 1.23023i | 0.725746 | − | 0.104346i | 0.230466 | − | 0.973080i | \(-0.425975\pi\) |
0.495279 | + | 0.868734i | \(0.335066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.07226 | + | 8.43033i | 0.595592 | + | 0.709962i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.07158 | − | 3.68617i | 0.674980 | − | 0.308253i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.1570 | + | 25.3709i | −0.843491 | + | 2.10694i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.55717 | − | 0.144147i | 0.375869 | − | 0.0118891i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.94457 | + | 4.54153i | 0.814691 | + | 0.372057i | 0.778779 | − | 0.627298i | \(-0.215839\pi\) |
0.0359117 | + | 0.999355i | \(0.488567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.03650 | − | 8.77339i | 0.247107 | − | 0.713968i | −0.751426 | − | 0.659817i | \(-0.770634\pi\) |
0.998533 | − | 0.0541507i | \(-0.0172452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.89420 | − | 1.10119i | 0.799898 | − | 0.0890262i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.3359 | − | 24.5876i | 1.55309 | − | 1.97492i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.126031 | + | 2.64571i | −0.0100584 | + | 0.211151i | 0.988243 | + | 0.152891i | \(0.0488583\pi\) |
−0.998301 | + | 0.0582601i | \(0.981445\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.74433 | − | 3.25475i | 0.138334 | − | 0.258119i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.48593 | − | 10.3349i | 0.117108 | − | 0.814504i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.59768 | − | 13.1596i | 0.595096 | − | 1.03074i | −0.398437 | − | 0.917196i | \(-0.630447\pi\) |
0.993533 | − | 0.113541i | \(-0.0362194\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.679296 | − | 42.5069i | 0.0528831 | − | 3.30916i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.89558 | − | 7.04661i | 0.765743 | − | 0.545283i | −0.129117 | − | 0.991629i | \(-0.541214\pi\) |
0.894860 | + | 0.446346i | \(0.147275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.505688 | + | 10.6157i | 0.0388991 | + | 0.816592i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.965014 | − | 0.577461i | 0.0737965 | − | 0.0441596i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.27092 | − | 1.52131i | 0.476769 | − | 0.115663i | 0.00982875 | − | 0.999952i | \(-0.496871\pi\) |
0.466941 | + | 0.884289i | \(0.345356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.72400 | − | 40.0759i | −0.583880 | − | 3.02946i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.337566 | − | 5.30221i | 0.0253730 | − | 0.398538i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.2913 | − | 12.3978i | 1.44190 | − | 0.926653i | 0.442344 | − | 0.896845i | \(-0.354147\pi\) |
0.999556 | − | 0.0298077i | \(-0.00948948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7407 | + | 6.05273i | −0.872677 | + | 0.449896i | −0.835550 | − | 0.549414i | \(-0.814851\pi\) |
−0.0371268 | + | 0.999311i | \(0.511821\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.7039 | + | 19.9102i | 1.01302 | + | 1.47180i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.5899 | + | 15.4057i | −1.44028 | + | 1.13265i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.4485 | + | 12.5197i | 1.05658 | + | 0.915530i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.71423 | − | 13.5697i | −0.633867 | − | 0.987051i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.68091 | − | 1.38211i | −0.193984 | − | 0.100006i | 0.358498 | − | 0.933530i | \(-0.383289\pi\) |
−0.552482 | + | 0.833525i | \(0.686319\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.64319 | + | 1.95062i | 0.478187 | + | 0.140408i | 0.511939 | − | 0.859022i | \(-0.328927\pi\) |
−0.0337517 | + | 0.999430i | \(0.510746\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.4824 | − | 4.39214i | −0.750661 | − | 0.314528i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.87942 | − | 11.2088i | −0.276397 | − | 0.798596i | −0.994696 | − | 0.102862i | \(-0.967200\pi\) |
0.718299 | − | 0.695735i | \(-0.244921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6192 | + | 16.3169i | −0.823663 | + | 1.15667i | 0.161807 | + | 0.986822i | \(0.448268\pi\) |
−0.985470 | + | 0.169850i | \(0.945672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.535570 | + | 14.1673i | 0.0377762 | + | 0.999286i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.5481 | + | 16.2171i | −0.810519 | + | 1.13822i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.7608 | + | 42.6485i | 1.03094 | + | 2.97870i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.30984 | + | 3.89713i | −0.647079 | + | 0.270869i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.07219 | + | 0.608449i | 0.143336 | + | 0.0420873i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.8993 | + | 11.8054i | 1.57645 | + | 0.812718i | 0.999990 | − | 0.00440540i | \(-0.00140229\pi\) |
0.576463 | + | 0.817123i | \(0.304433\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.07736 | − | 4.39015i | 0.484933 | − | 0.300808i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.505882 | + | 0.438350i | 0.0345009 | + | 0.0298952i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.9118 | − | 14.0860i | 1.21594 | − | 0.956222i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.25534 | + | 2.92888i | −0.287550 | + | 0.197916i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.54292 | − | 2.34204i | 0.305590 | − | 0.157543i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7753 | + | 7.56750i | −0.788530 | + | 0.506757i | −0.871854 | − | 0.489765i | \(-0.837083\pi\) |
0.0833246 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29.4073 | + | 26.2980i | −1.96049 | + | 1.75320i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.97463 | + | 25.8108i | 0.330178 | + | 1.71312i | 0.645177 | + | 0.764033i | \(0.276784\pi\) |
−0.314999 | + | 0.949092i | \(0.602004\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.42665 | − | 1.55909i | 0.424685 | − | 0.103027i | −0.0177199 | − | 0.999843i | \(-0.505641\pi\) |
0.442405 | + | 0.896816i | \(0.354126\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.78141 | − | 29.9764i | 0.511979 | − | 1.97230i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.980955 | + | 20.5928i | 0.0642645 | + | 1.34908i | 0.768837 | + | 0.639445i | \(0.220836\pi\) |
−0.704572 | + | 0.709632i | \(0.748861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.0477 | − | 15.7001i | 1.43823 | − | 1.02416i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.648171 | − | 0.0103583i | −0.0421032 | − | 0.000672845i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.37469 | + | 5.84513i | −0.218290 | + | 0.378090i | −0.954285 | − | 0.298897i | \(-0.903381\pi\) |
0.735995 | + | 0.676987i | \(0.236715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.90362 | − | 27.1503i | 0.251454 | − | 1.74890i | −0.338042 | − | 0.941131i | \(-0.609765\pi\) |
0.589496 | − | 0.807771i | \(-0.299326\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.93019 | + | 13.9633i | −0.444572 | + | 0.895743i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.533624 | − | 11.2022i | 0.0340920 | − | 0.715679i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.356908 | − | 0.453845i | 0.0227095 | − | 0.0288775i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0920 | + | 12.2638i | 0.956415 | + | 0.777185i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.62965 | − | 10.4872i | 0.229101 | − | 0.661945i | −0.770595 | − | 0.637325i | \(-0.780041\pi\) |
0.999697 | − | 0.0246205i | \(-0.00783774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.6303 | − | 8.05149i | −1.10841 | − | 0.506193i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.774159 | − | 24.4747i | −0.0484797 | − | 1.53267i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.02930 | + | 17.5583i | −0.438475 | + | 1.09526i | 0.530408 | + | 0.847742i | \(0.322039\pi\) |
−0.968884 | + | 0.247516i | \(0.920386\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.5147 | + | 7.54203i | −1.02618 | + | 0.468639i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.1831 | + | 1.52941i | 1.18740 | + | 0.0946684i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.9779 | − | 2.00973i | 0.861917 | − | 0.123925i | 0.302841 | − | 0.953041i | \(-0.402065\pi\) |
0.559076 | + | 0.829116i | \(0.311156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.64106 | − | 4.91061i | −0.469386 | − | 0.301656i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.82724 | − | 2.78336i | −0.173024 | − | 0.170339i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.1978i | 0.987597i | 0.869576 | + | 0.493799i | \(0.164392\pi\) | ||||
−0.869576 | + | 0.493799i | \(0.835608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.88664 | − | 4.49170i | 0.175351 | − | 0.272851i | −0.742442 | − | 0.669910i | \(-0.766333\pi\) |
0.917793 | + | 0.397059i | \(0.129969\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.66676 | − | 4.90979i | −0.403490 | − | 0.297154i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −75.4184 | − | 7.20158i | −4.54790 | − | 0.434272i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0366 | − | 21.9772i | −0.603043 | − | 1.32048i | −0.927232 | − | 0.374487i | \(-0.877819\pi\) |
0.324189 | − | 0.945992i | \(-0.394909\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.5741 | − | 7.86555i | −1.23174 | − | 0.470898i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0301 | + | 12.4242i | 0.777312 | + | 0.741166i | 0.970788 | − | 0.239939i | \(-0.0771275\pi\) |
−0.193476 | + | 0.981105i | \(0.561976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.76612 | − | 3.86727i | 0.104985 | − | 0.229885i | −0.849848 | − | 0.527028i | \(-0.823306\pi\) |
0.954833 | + | 0.297142i | \(0.0960336\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.22808 | − | 2.47860i | −0.0727452 | − | 0.146820i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.12519 | + | 32.7285i | 0.184474 | + | 1.93190i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.70691 | − | 3.70155i | −0.276877 | − | 0.217738i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.578863 | − | 0.534549i | 0.0339335 | − | 0.0313358i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.18836 | + | 7.45288i | 0.127845 | + | 0.435402i | 0.998392 | − | 0.0566841i | \(-0.0180528\pi\) |
−0.870547 | + | 0.492086i | \(0.836235\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9352 | − | 1.85980i | −0.753117 | − | 0.108282i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.7262 | + | 8.42422i | −1.66687 | + | 0.488823i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.75010 | + | 3.57571i | −0.216874 | + | 0.206789i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.282857 | + | 0.397217i | 0.0163036 | + | 0.0228952i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.8586 | + | 14.1915i | 0.911052 | + | 0.815280i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 51.4870 | − | 29.7260i | 2.94814 | − | 1.70211i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.30583 | + | 5.38272i | 0.0745279 | + | 0.307208i | 0.996859 | − | 0.0791913i | \(-0.0252338\pi\) |
−0.922332 | + | 0.386399i | \(0.873719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.4856 | − | 26.2753i | 0.994720 | − | 1.49475i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.91488 | + | 9.13426i | 0.448812 | + | 0.517956i | 0.934397 | − | 0.356233i | \(-0.115939\pi\) |
−0.485586 | + | 0.874189i | \(0.661394\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9193 | − | 24.7709i | −0.899813 | − | 1.40014i | −0.916396 | − | 0.400274i | \(-0.868915\pi\) |
0.0165828 | − | 0.999862i | \(-0.494721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34.9689 | + | 18.7257i | −1.97028 | + | 1.05508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.77787 | − | 14.4130i | 0.156021 | − | 0.809514i | −0.816616 | − | 0.577182i | \(-0.804152\pi\) |
0.972637 | − | 0.232332i | \(-0.0746355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.8447 | + | 29.0494i | 1.27906 | + | 1.62646i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.78043 | + | 0.141342i | −0.0993742 | + | 0.00788896i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.20890 | + | 0.293275i | 0.0672649 | + | 0.0163183i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.28107 | + | 18.0028i | −0.514821 | + | 0.998613i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.85567 | + | 17.7185i | 0.545020 | + | 0.979833i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.3053 | − | 7.32832i | 1.00920 | − | 0.404024i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.93615 | − | 1.70842i | 0.271315 | − | 0.0939031i | −0.188023 | − | 0.982165i | \(-0.560208\pi\) |
0.459338 | + | 0.888262i | \(0.348087\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.4527 | + | 9.95478i | 0.792004 | + | 0.545518i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.8423 | + | 1.44452i | 1.90364 | + | 0.0789226i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9342 | + | 11.3467i | 0.867990 | + | 0.618093i | 0.924868 | − | 0.380288i | \(-0.124175\pi\) |
−0.0568779 | + | 0.998381i | \(0.518115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.6033 | − | 7.42937i | −0.847455 | − | 0.403508i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7211 | − | 39.2693i | −0.851343 | − | 2.12655i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.81898 | + | 13.0062i | −0.206206 | + | 0.702271i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.74349 | + | 23.5862i | 0.416896 | + | 1.26984i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.90110 | + | 7.83645i | −0.102056 | + | 0.420683i | −0.999803 | − | 0.0198291i | \(-0.993688\pi\) |
0.897747 | + | 0.440512i | \(0.145203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.25401 | − | 3.75533i | 0.174183 | − | 0.201018i | −0.661945 | − | 0.749553i | \(-0.730269\pi\) |
0.836128 | + | 0.548535i | \(0.184814\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.763449 | + | 7.96669i | −0.0407499 | + | 0.425231i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.5842 | − | 5.12369i | −1.41493 | − | 0.272706i | −0.576228 | − | 0.817289i | \(-0.695476\pi\) |
−0.838707 | + | 0.544583i | \(0.816688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.38694 | − | 18.2081i | −0.498207 | − | 0.966387i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.65543 | − | 17.4600i | 0.193466 | − | 0.924083i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.4265 | + | 13.3671i | −0.814177 | + | 0.705489i | −0.958826 | − | 0.283995i | \(-0.908340\pi\) |
0.144649 | + | 0.989483i | \(0.453795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5187 | + | 3.56918i | −0.974666 | + | 0.187852i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.9756 | − | 19.7476i | −1.73077 | − | 1.03648i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.35325 | + | 11.0041i | 0.332544 | + | 0.575984i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.2173 | + | 0.820159i | −0.898734 | + | 0.0428120i | −0.491862 | − | 0.870673i | \(-0.663684\pi\) |
−0.406872 | + | 0.913485i | \(0.633381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.5956 | − | 18.8367i | 1.33245 | − | 0.980600i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.56615 | − | 4.78884i | −0.237063 | − | 0.248624i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.10626 | − | 3.52545i | −0.316170 | − | 0.182541i | 0.333514 | − | 0.942745i | \(-0.391765\pi\) |
−0.649684 | + | 0.760204i | \(0.725099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.4172 | + | 47.8628i | 1.88057 | + | 2.47162i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.47974 | − | 2.78350i | 0.488232 | − | 0.143358i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.768266 | − | 0.0365970i | −0.0394632 | − | 0.00187986i | 0.0278410 | − | 0.999612i | \(-0.491137\pi\) |
−0.0673042 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.4921 | + | 1.46530i | −0.588760 | + | 0.0750695i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.47379 | − | 0.713661i | 0.381893 | − | 0.0364663i | 0.0976555 | − | 0.995220i | \(-0.468866\pi\) |
0.284237 | + | 0.958754i | \(0.408260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −71.9869 | − | 24.9149i | −3.66879 | − | 1.26978i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.189079 | − | 0.431772i | 0.00961144 | − | 0.0219482i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.1481 | + | 11.6917i | −0.565229 | + | 0.592795i | −0.942872 | − | 0.333156i | \(-0.891886\pi\) |
0.377643 | + | 0.925951i | \(0.376735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3642 | − | 4.14919i | −0.524139 | − | 0.209834i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.98491 | + | 8.19810i | −0.150569 | + | 0.413539i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.151568 | + | 1.58729i | −0.00762619 | + | 0.0798651i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.11736 | + | 21.6817i | 0.156456 | + | 1.08818i | 0.905099 | + | 0.425202i | \(0.139797\pi\) |
−0.748643 | + | 0.662974i | \(0.769294\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.443732 | − | 1.96567i | −0.0222144 | − | 0.0984064i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.5475 | 1.37566 | 0.687829 | − | 0.725873i | \(-0.258564\pi\) | ||||
0.687829 | + | 0.725873i | \(0.258564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3084 | −0.563313 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.8887 | + | 19.7107i | 1.63425 | + | 0.979433i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.79624 | + | 33.3586i | 0.237741 | + | 1.65352i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.08694 | − | 21.8554i | 0.103193 | − | 1.08068i | −0.784464 | − | 0.620175i | \(-0.787062\pi\) |
0.887656 | − | 0.460507i | \(-0.152332\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.5037 | + | 10.3781i | 1.40598 | + | 0.511915i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.83816 | − | 3.53827i | −0.434897 | − | 0.174107i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.0083 | − | 34.6181i | 1.62031 | − | 1.69933i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.9872 | + | 5.34192i | −0.684955 | + | 0.261595i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.6175 | − | 7.13577i | −1.00723 | − | 0.348605i | −0.226862 | − | 0.973927i | \(-0.572847\pi\) |
−0.780367 | + | 0.625322i | \(0.784968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.37835 | − | 0.895524i | 0.457073 | − | 0.0436452i | 0.136019 | − | 0.990706i | \(-0.456569\pi\) |
0.321054 | + | 0.947061i | \(0.395963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.1642 | − | 11.5460i | −0.737307 | − | 0.561386i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −43.5890 | − | 2.07640i | −2.11438 | − | 0.100720i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.5560 | − | 12.2019i | 2.01104 | − | 0.590493i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.2313 | + | 9.30641i | −0.590535 | + | 0.449318i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.2702 | − | 13.4351i | −1.12089 | − | 0.647144i | −0.179260 | − | 0.983802i | \(-0.557370\pi\) |
−0.941627 | + | 0.336657i | \(0.890704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0976 | − | 24.2241i | −1.11000 | − | 1.16414i | −0.985103 | − | 0.171967i | \(-0.944988\pi\) |
−0.124899 | − | 0.992169i | \(-0.539861\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.48417 | − | 46.7389i | 0.358838 | − | 2.24096i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.25969 | + | 0.0600066i | −0.0602593 | + | 0.00287050i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.23239 | − | 12.5269i | −0.345183 | − | 0.597875i | 0.640204 | − | 0.768205i | \(-0.278850\pi\) |
−0.985387 | + | 0.170330i | \(0.945517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.64453 | + | 1.98164i | −0.364025 | + | 0.0943637i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.6488 | − | 7.06347i | 1.74124 | − | 0.335596i | 0.783097 | − | 0.621900i | \(-0.213639\pi\) |
0.958139 | + | 0.286304i | \(0.0924268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.37508 | + | 6.39054i | −0.349612 | + | 0.302941i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.5339 | − | 3.88025i | −0.876621 | − | 0.183529i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.78293 | + | 5.39814i | 0.131335 | + | 0.254754i | 0.945328 | − | 0.326120i | \(-0.105741\pi\) |
−0.813994 | + | 0.580874i | \(0.802711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 59.9269 | + | 11.5500i | 2.82185 | + | 0.543866i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.78412 | + | 15.9811i | −0.0838254 | + | 0.750857i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.3364 | + | 15.3911i | −0.625221 | + | 0.721544i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.94610 | + | 12.1440i | −0.137813 | + | 0.568073i | 0.860470 | + | 0.509501i | \(0.170170\pi\) |
−0.998283 | + | 0.0585720i | \(0.981345\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.2966 | + | 5.63414i | −0.760661 | + | 0.262979i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.50252 | − | 11.9285i | 0.163129 | − | 0.555566i | −0.836838 | − | 0.547450i | \(-0.815599\pi\) |
0.999967 | − | 0.00811540i | \(-0.00258324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.60634 | + | 18.9997i | 0.353497 | + | 0.882992i | 0.993417 | + | 0.114551i | \(0.0365429\pi\) |
−0.639921 | + | 0.768441i | \(0.721033\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.2910 | + | 48.9163i | −1.08009 | + | 2.26844i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.51464 | + | 5.35115i | 0.347736 | + | 0.247622i | 0.740557 | − | 0.671993i | \(-0.234562\pi\) |
−0.392821 | + | 0.919615i | \(0.628501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.4188 | + | 7.00677i | 1.12755 | + | 0.323543i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.796137 | − | 4.51810i | −0.0366841 | − | 0.208183i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.855409 | − | 0.296060i | 0.0393317 | − | 0.0136128i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.57648 | + | 1.83215i | −0.209983 | + | 0.0840646i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.70575 | + | 6.16431i | −0.0781008 | + | 0.282244i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.80975 | + | 17.0885i | −0.402528 | + | 0.780795i | −0.999774 | − | 0.0212630i | \(-0.993231\pi\) |
0.597246 | + | 0.802058i | \(0.296262\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.75593 | + | 2.12417i | 0.399236 | + | 0.0968536i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.43117 | + | 18.0279i | 0.0651206 | + | 0.820299i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.19803 | − | 1.52341i | −0.0543995 | − | 0.0691747i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.0504807 | − | 0.261919i | 0.00228750 | − | 0.0118687i | −0.980767 | − | 0.195182i | \(-0.937470\pi\) |
0.983055 | + | 0.183313i | \(0.0586823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.81752 | + | 25.1313i | −0.353521 | + | 1.13648i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.10090 | + | 6.38112i | 0.185071 | + | 0.287976i | 0.921375 | − | 0.388675i | \(-0.127067\pi\) |
−0.736304 | + | 0.676651i | \(0.763431\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9398 | + | 16.0873i | 0.627815 | + | 0.724537i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.0644 | + | 72.0760i | 0.677093 | + | 3.23958i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.51833 | − | 14.5028i | −0.157819 | − | 0.650538i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5894 | + | 16.5061i | −1.27984 | + | 0.738915i | −0.976818 | − | 0.214070i | \(-0.931328\pi\) |
−0.303019 | + | 0.952984i | \(0.597995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.0314 | + | 15.6797i | −0.626876 | + | 0.700516i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.8092 | + | 17.9880i | 0.571133 | + | 0.802045i | 0.994591 | − | 0.103871i | \(-0.0331230\pi\) |
−0.423457 | + | 0.905916i | \(0.639184\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.8842 | − | 36.1225i | 1.68583 | − | 1.60743i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.90319 | − | 17.7428i | −0.217758 | − | 0.787983i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2173 | + | 1.61280i | 0.497197 | + | 0.0714861i | 0.386352 | − | 0.922352i | \(-0.373735\pi\) |
0.110845 | + | 0.993838i | \(0.464644\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.60788 | + | 8.88163i | 0.115366 | + | 0.392900i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.41018 | + | 1.34370i | −0.0622612 | + | 0.0593257i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −61.0229 | − | 47.9889i | −2.68899 | − | 2.11465i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.47921 | − | 36.4359i | −0.153015 | − | 1.60245i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.0147 | + | 4.96203i | −0.439598 | + | 0.217809i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8525 | + | 25.9534i | −0.519269 | + | 1.13704i | 0.450446 | + | 0.892804i | \(0.351265\pi\) |
−0.969715 | + | 0.244238i | \(0.921462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.57913 | − | 9.13368i | −0.418866 | − | 0.399388i | 0.451121 | − | 0.892463i | \(-0.351024\pi\) |
−0.869987 | + | 0.493075i | \(0.835873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.3349 | + | 64.7638i | 1.23664 | + | 2.82653i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.1213 | − | 22.1625i | −0.440890 | − | 0.965416i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6292 | − | 1.11046i | −0.505619 | − | 0.0482808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.45192 | + | 9.08702i | 0.0630081 | + | 0.394343i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.82104 | − | 13.7258i | 0.382082 | − | 0.594531i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.39311i | 0.189931i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.8649 | + | 28.3042i | −1.20246 | + | 1.22141i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.7582 | − | 8.19921i | −0.549536 | − | 0.353165i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.6342 | − | 4.26075i | 1.27407 | − | 0.183184i | 0.528112 | − | 0.849175i | \(-0.322900\pi\) |
0.745960 | + | 0.665991i | \(0.231991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.5278 | − | 14.7042i | 0.752189 | − | 0.631017i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 45.3638 | − | 20.7170i | 1.94317 | − | 0.887417i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.9717 | − | 32.4018i | 0.554631 | − | 1.38540i | −0.340773 | − | 0.940146i | \(-0.610689\pi\) |
0.895404 | − | 0.445255i | \(-0.146887\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.7469 | − | 28.4124i | −1.31225 | − | 1.21261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.18733 | + | 0.998920i | 0.0931834 | + | 0.0425554i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.379918 | + | 1.09770i | −0.0161557 | + | 0.0466789i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.2222 | − | 33.5001i | 1.15552 | − | 1.42200i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.7885 | + | 17.5335i | −0.584238 | + | 0.742919i | −0.984865 | − | 0.173322i | \(-0.944550\pi\) |
0.400627 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0115147 | − | 0.241723i | 0.000487020 | − | 0.0102238i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.1862 | − | 15.6418i | −1.23224 | − | 0.660399i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.75169 | + | 12.1833i | −0.0738250 | + | 0.513464i | 0.919035 | + | 0.394176i | \(0.128970\pi\) |
−0.992860 | + | 0.119288i | \(0.961939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.2539 | + | 36.8129i | −0.894159 | + | 1.54873i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.8985 | + | 19.6029i | 0.835658 | + | 0.823246i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.8976 | + | 19.1537i | −1.12761 | + | 0.802965i | −0.982465 | − | 0.186446i | \(-0.940303\pi\) |
−0.145141 | + | 0.989411i | \(0.546364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0868183 | + | 1.82254i | 0.00363323 | + | 0.0762710i | 0.999956 | − | 0.00941174i | \(-0.00299589\pi\) |
−0.996322 | + | 0.0856827i | \(0.972693\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.05663 | + | 1.31262i | 0.211244 | + | 0.0548357i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 42.9933 | − | 10.4301i | 1.79294 | − | 0.434963i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.209927 | − | 1.08920i | −0.00873936 | − | 0.0453441i | 0.977297 | − | 0.211873i | \(-0.0679563\pi\) |
−0.986037 | + | 0.166529i | \(0.946744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.9679 | − | 0.761937i | −0.497368 | − | 0.0316650i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.3141 | − | 18.8390i | 1.21615 | − | 0.781573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9174 | + | 5.62829i | −0.452151 | + | 0.233100i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.3856 | + | 3.42271i | 0.801495 | + | 0.141512i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.1258 | − | 11.1087i | 0.583036 | − | 0.458505i | −0.282559 | − | 0.959250i | \(-0.591183\pi\) |
0.865595 | + | 0.500746i | \(0.166941\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.08005 | − | 1.80238i | −0.0857070 | − | 0.0742656i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.8294 | + | 17.4581i | 0.445464 | + | 0.718132i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.58828 | + | 4.94310i | 0.393744 | + | 0.202989i | 0.643717 | − | 0.765264i | \(-0.277392\pi\) |
−0.249973 | + | 0.968253i | \(0.580422\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.1002 | − | 12.3617i | −1.72594 | − | 0.506781i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.4078 | − | 31.9995i | 0.548746 | − | 1.30965i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.04442 | − | 3.01765i | −0.0426738 | − | 0.123298i | 0.921651 | − | 0.388020i | \(-0.126841\pi\) |
−0.964325 | + | 0.264722i | \(0.914720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.69220 | + | 5.18497i | −0.150608 | + | 0.211499i | −0.882986 | − | 0.469399i | \(-0.844471\pi\) |
0.732379 | + | 0.680898i | \(0.238410\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.30826 | − | 23.7320i | −0.256892 | − | 0.966440i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −54.8397 | + | 77.0115i | −2.22955 | + | 3.13096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.49809 | + | 12.9964i | 0.182572 | + | 0.527506i | 0.998733 | − | 0.0503174i | \(-0.0160233\pi\) |
−0.816162 | + | 0.577824i | \(0.803902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.3258 | − | 31.8038i | 0.539989 | − | 1.28875i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.38884 | − | 2.75681i | −0.379832 | − | 0.111529i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.7393 | − | 12.2385i | −0.958823 | − | 0.494308i | −0.0935533 | − | 0.995614i | \(-0.529823\pi\) |
−0.865270 | + | 0.501307i | \(0.832853\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.2050 | − | 66.4265i | −1.66155 | − | 2.67858i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.81268 | − | 4.17021i | −0.193751 | − | 0.167886i | 0.552583 | − | 0.833458i | \(-0.313642\pi\) |
−0.746334 | + | 0.665572i | \(0.768188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.7834 | + | 10.0530i | −0.513809 | + | 0.404064i | −0.841116 | − | 0.540854i | \(-0.818101\pi\) |
0.327308 | + | 0.944918i | \(0.393859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.2430 | − | 10.1351i | 0.571550 | − | 0.406708i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.31881 | + | 3.25757i | −0.253158 | + | 0.130512i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 69.1337 | − | 44.4295i | 2.76535 | − | 1.77718i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.73310 | − | 0.237668i | −0.149085 | − | 0.00949155i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.67376 | + | 19.0613i | 0.146482 | + | 0.760022i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.7069 | − | 8.41980i | 1.38166 | − | 0.335187i | 0.525014 | − | 0.851093i | \(-0.324060\pi\) |
0.856645 | + | 0.515906i | \(0.172545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −43.1918 | − | 11.2119i | −1.71672 | − | 0.445634i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.35589 | + | 28.4637i | 0.0538070 | + | 1.12955i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.30266 | + | 2.35182i | −0.130856 | + | 0.0931823i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.2831 | + | 10.1166i | −0.406792 | + | 0.400207i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.91537 | + | 3.31751i | −0.0756524 | + | 0.131034i | −0.901370 | − | 0.433050i | \(-0.857437\pi\) |
0.825717 | + | 0.564084i | \(0.190771\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.05839 | + | 28.2267i | −0.160047 | + | 1.11315i | 0.738492 | + | 0.674262i | \(0.235538\pi\) |
−0.898540 | + | 0.438892i | \(0.855371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.02189 | − | 0.547665i | −0.0402370 | − | 0.0215643i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.47317 | − | 30.9257i | 0.0579164 | − | 1.21581i | −0.763623 | − | 0.645663i | \(-0.776581\pi\) |
0.821539 | − | 0.570152i | \(-0.193116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9241 | + | 13.8912i | −0.428809 | + | 0.545275i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.8903 | + | 30.6304i | −0.975529 | + | 1.20050i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.31635 | + | 12.4713i | −0.168912 | + | 0.488038i | −0.997408 | − | 0.0719565i | \(-0.977076\pi\) |
0.828496 | + | 0.559995i | \(0.189197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.5206 | + | 8.91475i | 0.762732 | + | 0.348328i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.07249 | − | 6.57144i | 0.236910 | − | 0.256376i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.60925 | − | 11.5134i | 0.179551 | − | 0.448497i | −0.811102 | − | 0.584905i | \(-0.801132\pi\) |
0.990653 | + | 0.136408i | \(0.0435560\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.1537 | + | 17.4242i | −1.48401 | + | 0.677723i | −0.982300 | − | 0.187314i | \(-0.940022\pi\) |
−0.501707 | + | 0.865038i | \(0.667294\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.78218 | + | 5.68962i | −0.263398 | + | 0.220967i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.90615 | + | 0.705398i | −0.190252 | + | 0.0273542i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.1544 | − | 11.6671i | −0.702942 | − | 0.451754i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.0085 | − | 17.2766i | 0.657587 | − | 0.667953i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 80.3964i | − | 3.10367i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.70299 | + | 5.76197i | −0.142740 | + | 0.222107i | −0.905261 | − | 0.424856i | \(-0.860325\pi\) |
0.762521 | + | 0.646963i | \(0.223961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 39.6548 | − | 55.6474i | 1.52631 | − | 2.14187i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.1584 | − | 1.35197i | −0.544153 | − | 0.0519603i | −0.180640 | − | 0.983549i | \(-0.557817\pi\) |
−0.363513 | + | 0.931589i | \(0.618423\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.586507 | − | 1.28427i | −0.0225081 | − | 0.0492858i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.2490 | − | 41.7110i | −0.699304 | − | 1.59837i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.8052 | + | 24.6052i | 0.987407 | + | 0.941490i | 0.998290 | − | 0.0584504i | \(-0.0186160\pi\) |
−0.0108837 | + | 0.999941i | \(0.503464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.9953 | − | 67.8703i | 1.18427 | − | 2.59319i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.2634 | + | 5.08525i | −0.391574 | + | 0.194014i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.312137 | + | 3.26885i | 0.0118915 | + | 0.124533i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.2125 | − | 15.1089i | −0.730879 | − | 0.574770i | 0.181854 | − | 0.983325i | \(-0.441790\pi\) |
−0.912733 | + | 0.408556i | \(0.866033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.71403 | + | 53.6140i | −0.0651108 | + | 2.03663i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3756 | + | 35.3361i | 0.393570 | + | 1.34038i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.7952 | + | 5.00279i | 1.31796 | + | 0.189494i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.51141 | − | 34.4181i | −0.359755 | − | 1.30181i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.2783 | − | 17.4283i | 0.690361 | − | 0.658258i | −0.261353 | − | 0.965243i | \(-0.584169\pi\) |
0.951714 | + | 0.306986i | \(0.0993203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.27199 | + | 1.78626i | 0.0479741 | + | 0.0673702i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.2624 | + | 34.9348i | −1.17741 | + | 1.31572i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.0244 | − | 19.0666i | 1.24201 | − | 0.717075i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.47237 | − | 18.4354i | −0.167964 | − | 0.692355i | −0.992045 | − | 0.125884i | \(-0.959823\pi\) |
0.824081 | − | 0.566471i | \(-0.191692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.09906 | − | 0.229710i | 0.0412179 | − | 0.00861482i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.1753 | + | 18.6673i | 0.605770 | + | 0.699096i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.4383 | + | 31.8026i | 0.764348 | + | 1.18935i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.47234 | − | 11.1627i | 0.129677 | − | 0.416878i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.18605 | − | 6.15381i | 0.0442322 | − | 0.229498i | −0.953085 | − | 0.302704i | \(-0.902111\pi\) |
0.997317 | + | 0.0732054i | \(0.0233229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.9596 | − | 44.4547i | −1.30196 | − | 1.65558i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.75976 | + | 47.3602i | 0.139827 | + | 1.76135i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −81.9770 | − | 19.8874i | −3.04455 | − | 0.738600i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.9554 | − | 42.5875i | 0.814279 | − | 1.57948i | −0.000705458 | − | 1.00000i | \(-0.500225\pi\) |
0.814985 | − | 0.579482i | \(-0.196745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.38326 | − | 26.2346i | 0.236417 | − | 0.971652i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.484041 | − | 0.193781i | 0.0179029 | − | 0.00716724i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7614 | − | 7.87781i | 0.840713 | − | 0.290973i | 0.127428 | − | 0.991848i | \(-0.459328\pi\) |
0.713285 | + | 0.700874i | \(0.247207\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.37090 | + | 19.1300i | 0.124338 | + | 0.705620i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.2501 | − | 39.8277i | 0.930101 | − | 1.46707i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.7241 | + | 10.4850i | 0.541635 | + | 0.385696i | 0.817878 | − | 0.575391i | \(-0.195150\pi\) |
−0.276244 | + | 0.961088i | \(0.589090\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.429913 | + | 0.902913i | −0.0157933 | + | 0.0331693i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.522599 | − | 1.30539i | −0.0191723 | − | 0.0478901i | 0.918473 | − | 0.395484i | \(-0.129423\pi\) |
−0.937645 | + | 0.347594i | \(0.886999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.1220 | + | 44.6894i | −0.480752 | + | 1.63729i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.1758 | − | 14.9640i | −1.10408 | − | 0.547506i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.754510 | + | 3.11013i | −0.0275692 | + | 0.113642i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2455 | − | 27.9808i | 0.884732 | − | 1.02104i | −0.114885 | − | 0.993379i | \(-0.536650\pi\) |
0.999617 | − | 0.0276568i | \(-0.00880456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.13263 | + | 19.1028i | −0.0777175 | + | 0.696146i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.8380 | + | 7.48542i | 1.41346 | + | 0.272422i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.14182 | + | 6.09427i | 0.114191 | + | 0.221500i | 0.939004 | − | 0.343905i | \(-0.111750\pi\) |
−0.824813 | + | 0.565406i | \(0.808720\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.8579 | + | 6.87912i | 1.19267 | + | 0.249696i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.1610 | − | 31.3337i | 1.31084 | − | 1.13585i | 0.329371 | − | 0.944201i | \(-0.393163\pi\) |
0.981464 | − | 0.191645i | \(-0.0613821\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.6738 | − | 6.87555i | 1.29148 | − | 0.248912i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.6426 | + | 41.0557i | 0.384784 | + | 1.48437i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.36225 | + | 4.09154i | 0.0852959 | + | 0.147737i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.6084 | + | 0.981699i | −0.743158 | + | 0.0354010i | −0.415746 | − | 0.909481i | \(-0.636479\pi\) |
−0.327412 | + | 0.944882i | \(0.606176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.17954 | − | 32.3464i | 0.186536 | − | 1.16493i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.8887 | + | 30.2976i | 1.03905 | + | 1.08973i | 0.995882 | + | 0.0906604i | \(0.0288978\pi\) |
0.0431718 | + | 0.999068i | \(0.486254\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 83.6158 | + | 48.2756i | 3.00357 | + | 1.73411i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.0258 | − | 19.0412i | 0.897794 | − | 0.683101i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.81019 | − | 1.11877i | 0.136514 | − | 0.0400842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.6708 | − | 1.31812i | −0.990138 | − | 0.0471661i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32.9939 | + | 4.73240i | −1.17911 | + | 0.169122i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.2333 | + | 1.07265i | −0.400933 | + | 0.0382844i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3927 | + | 4.63524i | 0.477397 | + | 0.165229i | 0.555161 | − | 0.831743i | \(-0.312657\pi\) |
−0.0777638 | + | 0.996972i | \(0.524778\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.8498 | + | 8.72667i | −0.813473 | + | 0.310678i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.3694 | + | 22.4116i | −0.759810 | + | 0.796865i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.9538 | − | 7.98830i | −0.708581 | − | 0.283673i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.7827 | + | 5.38237i | 0.524290 | + | 0.190893i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.0339439 | + | 0.355477i | −0.00120236 | + | 0.0125916i | −0.996053 | − | 0.0887583i | \(-0.971710\pi\) |
0.994851 | + | 0.101350i | \(0.0323162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00035 | − | 20.8679i | −0.106145 | − | 0.738252i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.83829 | + | 3.62428i | 0.206286 | + | 0.128058i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.1829 | 0.606370 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.4827 | 1.56781 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.17781 | − | 27.3668i | −0.217469 | − | 0.963356i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.85633 | + | 19.8662i | 0.100423 | + | 0.698459i | 0.976379 | + | 0.216067i | \(0.0693228\pi\) |
−0.875955 | + | 0.482392i | \(0.839768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.90615 | − | 51.3796i | 0.172278 | − | 1.80418i | −0.334809 | − | 0.942286i | \(-0.608672\pi\) |
0.507088 | − | 0.861894i | \(-0.330722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.16396 | + | 8.68985i | −0.110965 | + | 0.304766i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 60.0998 | + | 24.0603i | 2.10521 | + | 0.842797i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0406446 | − | 0.0426269i | 0.00142198 | − | 0.00149133i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.1363 | + | 5.75258i | 0.459020 | + | 0.201011i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.7404 | − | 7.52442i | −0.758744 | − | 0.262604i | −0.0798172 | − | 0.996810i | \(-0.525434\pi\) |
−0.678927 | + | 0.734206i | \(0.737555\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.5999 | + | 3.01742i | −1.10150 | + | 0.105181i | −0.629934 | − | 0.776648i | \(-0.716918\pi\) |
−0.471569 | + | 0.881829i | \(0.656312\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 130.169 | − | 16.5971i | 4.53190 | − | 0.577837i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.2640 | − | 2.06092i | −1.50444 | − | 0.0716651i | −0.720912 | − | 0.693027i | \(-0.756277\pi\) |
−0.783524 | + | 0.621362i | \(0.786580\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.1925 | + | 9.74620i | −1.15282 | + | 0.338499i | −0.801640 | − | 0.597807i | \(-0.796039\pi\) |
−0.351183 | + | 0.936307i | \(0.614221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.3393 | + | 33.3033i | 0.879011 | + | 1.15528i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.56510 | − | 4.36771i | −0.262115 | − | 0.151332i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.7150 | + | 37.4568i | 1.23597 | + | 1.29625i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.7606 | + | 5.44221i | 1.30520 | + | 0.188110i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6174 | − | 1.45849i | 1.05703 | − | 0.0503525i | 0.488139 | − | 0.872766i | \(-0.337676\pi\) |
0.568890 | + | 0.822413i | \(0.307373\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.07393 | + | 10.5204i | 0.209446 | + | 0.362771i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.7535 | − | 16.0215i | −0.921438 | − | 0.551809i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −44.4593 | + | 8.56884i | −1.52945 | + | 0.294777i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −52.0508 | + | 45.1022i | −1.78849 | + | 1.54973i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.50896 | + | 7.20749i | −0.0517874 | + | 0.247361i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.01781 | − | 17.4921i | −0.309127 | − | 0.599622i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.39092 | + | 1.61722i | 0.287300 | + | 0.0553725i | 0.330865 | − | 0.943678i | \(-0.392660\pi\) |
−0.0435653 | + | 0.999051i | \(0.513872\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.02022 | + | 3.71930i | 0.103289 | + | 0.127198i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.8887 | − | 34.4934i | 1.02098 | − | 1.17827i | 0.0371221 | − | 0.999311i | \(-0.488181\pi\) |
0.983856 | − | 0.178961i | \(-0.0572736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.75206 | − | 11.3441i | 0.0938990 | − | 0.387057i | −0.905397 | − | 0.424565i | \(-0.860427\pi\) |
0.999296 | + | 0.0375083i | \(0.0119421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.7627 | − | 54.1041i | −0.605352 | − | 1.84386i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.01477 | − | 13.6730i | 0.136664 | − | 0.465436i | −0.862511 | − | 0.506038i | \(-0.831109\pi\) |
0.999175 | + | 0.0406022i | \(0.0129276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.2174 | + | 25.5218i | 0.347402 | + | 0.867768i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.36426 | + | 4.45871i | 0.318027 | + | 0.151426i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75642 | + | 1.25074i | 0.0595824 | + | 0.0424284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.37606 | − | 10.2242i | −0.249928 | − | 0.346435i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.774134 | + | 1.12392i | −0.0262005 | + | 0.0380388i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 101.840 | − | 35.2470i | 3.44280 | − | 1.19157i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.8715 | + | 9.15635i | −0.772314 | + | 0.309188i | −0.724142 | − | 0.689651i | \(-0.757764\pi\) |
−0.0481723 | + | 0.998839i | \(0.515340\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.53983 | − | 11.7573i | −0.220583 | − | 0.396563i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.0138 | + | 21.3637i | −0.371063 | + | 0.719762i | −0.998252 | − | 0.0591053i | \(-0.981175\pi\) |
0.627189 | + | 0.778867i | \(0.284206\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.596955 | + | 0.144820i | 0.0200891 | + | 0.00487357i | 0.245791 | − | 0.969323i | \(-0.420952\pi\) |
−0.225702 | + | 0.974196i | \(0.572467\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.5638 | − | 1.79126i | 0.758475 | − | 0.0602127i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.6086 | − | 38.9220i | −1.02774 | − | 1.30687i | −0.950790 | − | 0.309836i | \(-0.899726\pi\) |
−0.0769450 | − | 0.997035i | \(-0.524517\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.92869 | + | 20.3840i | −0.131764 | + | 0.683657i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 45.3211 | − | 25.1892i | 1.51831 | − | 0.843869i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.28757 | − | 2.00351i | −0.0430871 | − | 0.0670448i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.9773 | + | 73.8337i | 2.13853 | + | 2.46799i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.97216 | − | 7.47157i | 0.166015 | − | 0.249469i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.1036 | − | 45.7696i | −0.370325 | − | 1.52650i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.12699 | + | 3.53742i | −0.204120 | + | 0.117849i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.629396 | − | 0.563232i | −0.0209450 | − | 0.0187432i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32.6426 | − | 45.8401i | −1.08508 | − | 1.52378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.6881 | + | 16.8655i | −0.587323 | + | 0.560011i | −0.924380 | − | 0.381473i | \(-0.875417\pi\) |
0.337057 | + | 0.941484i | \(0.390568\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.2063 | − | 17.9286i | −1.06821 | − | 0.594654i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.70330 | + | 1.39512i | 0.321485 | + | 0.0462225i | 0.301168 | − | 0.953571i | \(-0.402624\pi\) |
0.0203166 | + | 0.999794i | \(0.493533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.2235 | − | 62.0634i | −0.603108 | − | 2.05400i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −75.6517 | + | 69.8603i | −2.50097 | + | 2.30951i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.2886 | + | 9.66389i | 0.405807 | + | 0.319130i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.71168 | + | 17.9255i | 0.0564632 | + | 0.591309i | 0.978785 | + | 0.204888i | \(0.0656829\pi\) |
−0.922322 | + | 0.386422i | \(0.873711\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.25922 | − | 8.59626i | −0.140346 | − | 0.283257i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.07656 | + | 6.73672i | −0.101266 | + | 0.221742i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −55.6743 | − | 53.0853i | −1.83056 | − | 1.74543i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.5212 | + | 51.0620i | −0.641160 | + | 1.67710i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.5808 | − | 49.4450i | −0.740851 | − | 1.62224i | −0.782149 | − | 0.623091i | \(-0.785877\pi\) |
0.0412978 | − | 0.999147i | \(-0.486851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.982326 | − | 0.0938007i | −0.0321944 | − | 0.00307419i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.8563 | − | 12.4139i | −0.551849 | − | 0.406414i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −44.0347 | + | 68.5194i | −1.44009 | + | 2.24082i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 46.2095i | − | 1.50960i | −0.655956 | − | 0.754799i | \(-0.727734\pi\) | ||
0.655956 | − | 0.754799i | \(-0.272266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.3439 | + | 35.7798i | 1.18604 | + | 1.16763i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.19084 | + | 2.05063i | 0.104018 | + | 0.0668485i | 0.591616 | − | 0.806220i | \(-0.298490\pi\) |
−0.487597 | + | 0.873069i | \(0.662127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.2751 | + | 5.07180i | −1.14872 | + | 0.165161i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 51.9394 | − | 44.9749i | 1.68959 | − | 1.46303i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.4327 | − | 8.87460i | 0.631477 | − | 0.288386i | −0.0738487 | − | 0.997269i | \(-0.523528\pi\) |
0.705325 | + | 0.708884i | \(0.250801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.70731 | − | 4.26467i | 0.0554218 | − | 0.138437i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.803766 | + | 25.4107i | 0.0260639 | + | 0.824000i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.1843 | − | 5.10770i | −0.362295 | − | 0.165454i | 0.225947 | − | 0.974140i | \(-0.427452\pi\) |
−0.588242 | + | 0.808685i | \(0.700180\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.20283 | − | 12.1433i | 0.136000 | − | 0.392947i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −49.6764 | − | 40.3671i | −1.60581 | − | 1.30488i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.6000 | − | 42.7259i | 1.08500 | − | 1.37969i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.08994 | + | 22.8807i | −0.0351595 | + | 0.738088i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.95420 | − | 0.917858i | 0.0951978 | − | 0.0295776i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.19785 | + | 29.1967i | −0.135134 | + | 0.939876i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4017 | + | 35.3368i | −0.656075 | + | 1.13636i | 0.325548 | + | 0.945526i | \(0.394451\pi\) |
−0.981623 | + | 0.190830i | \(0.938882\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.15433 | − | 0.0344281i | −0.0692071 | − | 0.00110599i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.4067 | + | 18.8041i | −0.847432 | + | 0.603453i | −0.919122 | − | 0.393974i | \(-0.871100\pi\) |
0.0716902 | + | 0.997427i | \(0.477161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.27657 | + | 26.7985i | 0.0409249 | + | 0.859119i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.81448 | − | 33.9561i | 0.282289 | − | 1.08747i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.02418 | + | 2.18924i | −0.288709 | + | 0.0700401i | −0.377498 | − | 0.926010i | \(-0.623216\pi\) |
0.0887889 | + | 0.996050i | \(0.471700\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.49745 | + | 12.9580i | 0.0798189 | + | 0.414140i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.4093 | − | 26.1771i | −0.747402 | − | 0.835769i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.6773 | − | 10.0752i | 0.500030 | − | 0.321350i | −0.266198 | − | 0.963918i | \(-0.585768\pi\) |
0.766228 | + | 0.642569i | \(0.222131\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.9150 | − | 23.1553i | 1.43111 | − | 0.737790i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.1324 | + | 19.3631i | −0.895465 | + | 0.616333i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.415493 | + | 0.326747i | −0.0132119 | + | 0.0103900i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.3701 | + | 14.1848i | 0.520015 | + | 0.450595i | 0.874892 | − | 0.484317i | \(-0.160932\pi\) |
−0.354878 | + | 0.934913i | \(0.615477\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.68822 | + | 4.76907i | −0.243978 | + | 0.151342i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −75.8523 | − | 39.1046i | −2.40468 | − | 1.23970i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.9340 | + | 12.6066i | 1.35973 | + | 0.399254i | 0.878669 | − | 0.477431i | \(-0.158432\pi\) |
0.481065 | + | 0.876685i | \(0.340250\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.2151 | − | 11.3067i | −0.892687 | − | 0.357729i |
(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 | 804.2.ba.b.353.3 | yes | 440 | |
3.2 | odd | 2 | inner | 804.2.ba.b.353.13 | yes | 440 | |
67.41 | odd | 66 | inner | 804.2.ba.b.41.13 | yes | 440 | |
201.41 | even | 66 | inner | 804.2.ba.b.41.3 | ✓ | 440 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.ba.b.41.3 | ✓ | 440 | 201.41 | even | 66 | inner | |
804.2.ba.b.41.13 | yes | 440 | 67.41 | odd | 66 | inner | |
804.2.ba.b.353.3 | yes | 440 | 1.1 | even | 1 | trivial | |
804.2.ba.b.353.13 | yes | 440 | 3.2 | odd | 2 | inner |