Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.4 | ||
Root | \(0.150493 - 0.260662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.k.3781.4 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.827889 | − | 1.43395i | 0.312913 | − | 0.541981i | −0.666079 | − | 0.745881i | \(-0.732029\pi\) |
0.978992 | + | 0.203901i | \(0.0653620\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.81310 | + | 4.87244i | −0.848182 | + | 1.46909i | 0.0346464 | + | 0.999400i | \(0.488970\pi\) |
−0.882829 | + | 0.469695i | \(0.844364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.800986 | + | 1.38735i | 0.222154 | + | 0.384781i | 0.955462 | − | 0.295115i | \(-0.0953580\pi\) |
−0.733308 | + | 0.679897i | \(0.762025\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.35601 | − | 2.34868i | −0.328882 | − | 0.569640i | 0.653409 | − | 0.757005i | \(-0.273338\pi\) |
−0.982290 | + | 0.187366i | \(0.940005\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.454704 | − | 0.787570i | −0.104316 | − | 0.180681i | 0.809142 | − | 0.587613i | \(-0.199932\pi\) |
−0.913459 | + | 0.406932i | \(0.866599\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.827889 | + | 1.43395i | −0.180660 | + | 0.312913i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.02247 | − | 5.23507i | −0.630228 | − | 1.09159i | −0.987505 | − | 0.157588i | \(-0.949628\pi\) |
0.357277 | − | 0.933999i | \(-0.383705\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.34683 | + | 2.33278i | −0.250100 | + | 0.433186i | −0.963553 | − | 0.267517i | \(-0.913797\pi\) |
0.713453 | + | 0.700703i | \(0.247130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.11431 | − | 8.85825i | 0.918558 | − | 1.59099i | 0.116950 | − | 0.993138i | \(-0.462688\pi\) |
0.801608 | − | 0.597850i | \(-0.203978\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.81310 | − | 4.87244i | 0.489698 | − | 0.848182i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.827889 | − | 1.43395i | 0.139939 | − | 0.242381i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.237490 | − | 0.411344i | −0.0390430 | − | 0.0676245i | 0.845844 | − | 0.533431i | \(-0.179098\pi\) |
−0.884887 | + | 0.465806i | \(0.845764\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.800986 | − | 1.38735i | −0.128260 | − | 0.222154i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.573228 | − | 0.992859i | 0.0895231 | − | 0.155059i | −0.817787 | − | 0.575522i | \(-0.804799\pi\) |
0.907310 | + | 0.420463i | \(0.138132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.46671 | 0.833665 | 0.416833 | − | 0.908983i | \(-0.363140\pi\) | ||||
0.416833 | + | 0.908983i | \(0.363140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.69934 | − | 2.94334i | 0.247874 | − | 0.429330i | −0.715062 | − | 0.699061i | \(-0.753601\pi\) |
0.962936 | + | 0.269731i | \(0.0869348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.12920 | + | 3.68788i | 0.304171 | + | 0.526840i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.35601 | + | 2.34868i | 0.189880 | + | 0.328882i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.97455 | −0.820667 | −0.410334 | − | 0.911935i | \(-0.634588\pi\) | ||||
−0.410334 | + | 0.911935i | \(0.634588\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.81310 | + | 4.87244i | −0.379319 | + | 0.656999i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.454704 | + | 0.787570i | 0.0602270 | + | 0.104316i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.25736 | 1.07502 | 0.537509 | − | 0.843258i | \(-0.319366\pi\) | ||||
0.537509 | + | 0.843258i | \(0.319366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.07988 | + | 8.79861i | 0.650412 | + | 1.12655i | 0.983023 | + | 0.183482i | \(0.0587371\pi\) |
−0.332611 | + | 0.943064i | \(0.607930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.827889 | − | 1.43395i | 0.104304 | − | 0.180660i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.800986 | + | 1.38735i | 0.0993501 | + | 0.172079i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.03367 | + | 1.56851i | 0.981469 | + | 0.191623i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.02247 | + | 5.23507i | 0.363862 | + | 0.630228i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.81642 | − | 3.14614i | 0.215570 | − | 0.373378i | −0.737879 | − | 0.674933i | \(-0.764172\pi\) |
0.953449 | + | 0.301555i | \(0.0975058\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.751860 | − | 1.30226i | −0.0879985 | − | 0.152418i | 0.818667 | − | 0.574269i | \(-0.194714\pi\) |
−0.906665 | + | 0.421851i | \(0.861380\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.65787 | + | 8.06767i | 0.530814 | + | 0.919397i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.38601 | − | 7.59678i | 0.493464 | − | 0.854705i | −0.506507 | − | 0.862236i | \(-0.669064\pi\) |
0.999972 | + | 0.00753058i | \(0.00239708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.96714 | − | 10.3354i | −0.654979 | − | 1.13446i | −0.981899 | − | 0.189405i | \(-0.939344\pi\) |
0.326920 | − | 0.945052i | \(-0.393989\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.35601 | − | 2.34868i | −0.147080 | − | 0.254751i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.34683 | − | 2.33278i | 0.144395 | − | 0.250100i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1310 | 1.07389 | 0.536943 | − | 0.843619i | \(-0.319579\pi\) | ||||
0.536943 | + | 0.843619i | \(0.319579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.65251 | 0.278059 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.11431 | + | 8.85825i | −0.530329 | + | 0.918558i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.454704 | − | 0.787570i | −0.0466516 | − | 0.0808030i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.33139 | + | 4.03809i | 0.236717 | + | 0.410006i | 0.959770 | − | 0.280786i | \(-0.0905952\pi\) |
−0.723053 | + | 0.690792i | \(0.757262\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.81310 | + | 4.87244i | −0.282727 | + | 0.489698i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.05606 | + | 7.02530i | −0.403593 | + | 0.699043i | −0.994157 | − | 0.107948i | \(-0.965572\pi\) |
0.590564 | + | 0.806991i | \(0.298905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.101231 | + | 0.175338i | −0.00997461 | + | 0.0172765i | −0.870970 | − | 0.491337i | \(-0.836508\pi\) |
0.860995 | + | 0.508613i | \(0.169842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.827889 | + | 1.43395i | −0.0807937 | + | 0.139939i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.09586 | −0.685983 | −0.342991 | − | 0.939339i | \(-0.611440\pi\) | ||||
−0.342991 | + | 0.939339i | \(0.611440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.42556 | −0.902805 | −0.451402 | − | 0.892321i | \(-0.649076\pi\) | ||||
−0.451402 | + | 0.892321i | \(0.649076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.237490 | + | 0.411344i | 0.0225415 | + | 0.0390430i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.20764 | − | 9.01990i | 0.489894 | − | 0.848520i | −0.510039 | − | 0.860151i | \(-0.670369\pi\) |
0.999932 | + | 0.0116309i | \(0.00370232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.02247 | − | 5.23507i | −0.281847 | − | 0.488173i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.800986 | + | 1.38735i | 0.0740512 | + | 0.128260i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.49051 | −0.411645 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3271 | − | 17.8870i | −0.938826 | − | 1.62610i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.573228 | + | 0.992859i | −0.0516862 | + | 0.0895231i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.57825 | − | 14.8580i | 0.761196 | − | 1.31843i | −0.181038 | − | 0.983476i | \(-0.557946\pi\) |
0.942234 | − | 0.334955i | \(-0.108721\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.46671 | −0.481317 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.43412 | −0.387411 | −0.193705 | − | 0.981060i | \(-0.562051\pi\) | ||||
−0.193705 | + | 0.981060i | \(0.562051\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50578 | −0.130567 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6451 | 1.16578 | 0.582890 | − | 0.812551i | \(-0.301922\pi\) | ||||
0.582890 | + | 0.812551i | \(0.301922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.07755 | 0.261034 | 0.130517 | − | 0.991446i | \(-0.458336\pi\) | ||||
0.130517 | + | 0.991446i | \(0.458336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.69934 | + | 2.94334i | −0.143110 | + | 0.247874i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.01303 | −0.753707 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.34683 | + | 2.33278i | −0.111848 | + | 0.193727i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.12920 | − | 3.68788i | −0.175613 | − | 0.304171i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.71209 | 0.713722 | 0.356861 | − | 0.934158i | \(-0.383847\pi\) | ||||
0.356861 | + | 0.934158i | \(0.383847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4966 | + | 19.9127i | 0.935582 | + | 1.62048i | 0.773593 | + | 0.633683i | \(0.218458\pi\) |
0.161989 | + | 0.986793i | \(0.448209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.35601 | − | 2.34868i | −0.109627 | − | 0.189880i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.11431 | − | 8.85825i | 0.410791 | − | 0.711512i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0754 | + | 17.4511i | 0.804106 | + | 1.39275i | 0.916893 | + | 0.399134i | \(0.130689\pi\) |
−0.112786 | + | 0.993619i | \(0.535978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.97455 | 0.473812 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0091 | −0.788825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.52114 | − | 7.83085i | 0.354123 | − | 0.613359i | −0.632844 | − | 0.774279i | \(-0.718113\pi\) |
0.986968 | + | 0.160920i | \(0.0514460\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.81310 | − | 4.87244i | 0.219000 | − | 0.379319i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.20616 | − | 5.55323i | 0.248100 | − | 0.429722i | −0.714899 | − | 0.699228i | \(-0.753527\pi\) |
0.962999 | + | 0.269506i | \(0.0868606\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.21684 | − | 9.03584i | 0.401296 | − | 0.695064i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.454704 | − | 0.787570i | −0.0347721 | − | 0.0602270i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.45972 | − | 16.3847i | −0.719209 | − | 1.24571i | −0.961313 | − | 0.275457i | \(-0.911171\pi\) |
0.242104 | − | 0.970250i | \(-0.422162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.827889 | − | 1.43395i | 0.0625825 | − | 0.108396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.25736 | −0.620661 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.01635 | 0.374939 | 0.187470 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187470 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.71426 | + | 8.16533i | −0.350408 | + | 0.606924i | −0.986321 | − | 0.164836i | \(-0.947290\pi\) |
0.635913 | + | 0.771761i | \(0.280624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.07988 | − | 8.79861i | −0.375516 | − | 0.650412i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.237490 | − | 0.411344i | −0.0174606 | − | 0.0302426i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2584 | 1.11581 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.827889 | + | 1.43395i | −0.0602201 | + | 0.104304i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.77371 | + | 6.53626i | 0.273056 | + | 0.472947i | 0.969643 | − | 0.244525i | \(-0.0786322\pi\) |
−0.696587 | + | 0.717473i | \(0.745299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.80997 | 0.706137 | 0.353068 | − | 0.935597i | \(-0.385138\pi\) | ||||
0.353068 | + | 0.935597i | \(0.385138\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.800986 | − | 1.38735i | −0.0573598 | − | 0.0993501i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.16415 | − | 12.4087i | 0.510425 | − | 0.884082i | −0.489502 | − | 0.872002i | \(-0.662822\pi\) |
0.999927 | − | 0.0120795i | \(-0.00384513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8696 | − | 22.2908i | −0.912304 | − | 1.58016i | −0.810802 | − | 0.585321i | \(-0.800969\pi\) |
−0.101502 | − | 0.994835i | \(-0.532365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.03367 | − | 1.56851i | −0.566651 | − | 0.110634i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.23005 | + | 3.86256i | 0.156519 | + | 0.271099i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.573228 | − | 0.992859i | 0.0400360 | − | 0.0693443i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.02247 | − | 5.23507i | −0.210076 | − | 0.363862i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.11651 | 0.353917 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5115 | − | 21.6706i | −0.861329 | − | 1.49187i | −0.870646 | − | 0.491910i | \(-0.836299\pi\) |
0.00931696 | − | 0.999957i | \(-0.497034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.81642 | + | 3.14614i | −0.124459 | + | 0.215570i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.46671 | 0.372826 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.46816 | − | 14.6673i | −0.574856 | − | 0.995681i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.751860 | + | 1.30226i | 0.0508060 | + | 0.0879985i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17230 | − | 3.76253i | 0.146124 | − | 0.253095i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9045 | 1.13201 | 0.566004 | − | 0.824402i | \(-0.308489\pi\) | ||||
0.566004 | + | 0.824402i | \(0.308489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.58831 | + | 9.67924i | −0.370909 | + | 0.642434i | −0.989706 | − | 0.143118i | \(-0.954287\pi\) |
0.618796 | + | 0.785551i | \(0.287621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.62535 | + | 13.2075i | 0.503897 | + | 0.872776i | 0.999990 | + | 0.00450622i | \(0.00143438\pi\) |
−0.496092 | + | 0.868270i | \(0.665232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.65787 | − | 8.06767i | −0.306466 | − | 0.530814i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.94446 | + | 3.36790i | −0.127386 | + | 0.220639i | −0.922663 | − | 0.385607i | \(-0.873992\pi\) |
0.795277 | + | 0.606246i | \(0.207325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.69934 | − | 2.94334i | 0.110853 | − | 0.192002i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.38601 | + | 7.59678i | −0.284902 | + | 0.493464i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.86697 | + | 8.42984i | −0.314818 | + | 0.545281i | −0.979399 | − | 0.201935i | \(-0.935277\pi\) |
0.664581 | + | 0.747217i | \(0.268610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8478 | 1.21409 | 0.607047 | − | 0.794666i | \(-0.292354\pi\) | ||||
0.607047 | + | 0.794666i | \(0.292354\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.12920 | + | 3.68788i | 0.136030 | + | 0.235610i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.728423 | − | 1.26167i | 0.0463484 | − | 0.0802778i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.96714 | + | 10.3354i | 0.378152 | + | 0.654979i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.50889 | + | 4.34552i | 0.158360 | + | 0.274287i | 0.934277 | − | 0.356547i | \(-0.116046\pi\) |
−0.775918 | + | 0.630834i | \(0.782713\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.0100 | 2.13819 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.35601 | + | 2.34868i | 0.0849169 | + | 0.147080i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.989493 | + | 1.71385i | −0.0617229 | + | 0.106907i | −0.895236 | − | 0.445593i | \(-0.852993\pi\) |
0.833513 | + | 0.552500i | \(0.186326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.786460 | −0.0488682 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.34683 | + | 2.33278i | −0.0833667 | + | 0.144395i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.03457 | 0.372107 | 0.186054 | − | 0.982540i | \(-0.440430\pi\) | ||||
0.186054 | + | 0.982540i | \(0.440430\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.97455 | −0.367014 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.1310 | −0.620008 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.0260 | 1.34295 | 0.671474 | − | 0.741028i | \(-0.265662\pi\) | ||||
0.671474 | + | 0.741028i | \(0.265662\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3255 | −0.991705 | −0.495852 | − | 0.868407i | \(-0.665144\pi\) | ||||
−0.495852 | + | 0.868407i | \(0.665144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.65251 | −0.160537 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.81310 | + | 4.87244i | −0.169636 | + | 0.293819i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.6875 | −1.30307 | −0.651537 | − | 0.758617i | \(-0.725875\pi\) | ||||
−0.651537 | + | 0.758617i | \(0.725875\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.11431 | − | 8.85825i | 0.306186 | − | 0.530329i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1094 | − | 19.2421i | −0.662733 | − | 1.14789i | −0.979895 | − | 0.199516i | \(-0.936063\pi\) |
0.317161 | − | 0.948372i | \(-0.397270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.8268 | 1.11914 | 0.559568 | − | 0.828784i | \(-0.310967\pi\) | ||||
0.559568 | + | 0.828784i | \(0.310967\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.454704 | + | 0.787570i | 0.0269343 | + | 0.0466516i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.949138 | − | 1.64395i | −0.0560258 | − | 0.0970396i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.82245 | − | 8.35274i | 0.283674 | − | 0.491337i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.33139 | − | 4.03809i | −0.136669 | − | 0.236717i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.2928 | 1.82814 | 0.914072 | − | 0.405552i | \(-0.132921\pi\) | ||||
0.914072 | + | 0.405552i | \(0.132921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.25736 | 0.480762 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.81310 | − | 4.87244i | 0.163233 | − | 0.282727i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.84191 | − | 8.38643i | 0.280015 | − | 0.485000i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.52583 | − | 7.83896i | 0.260864 | − | 0.451830i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.05606 | − | 7.02530i | 0.233014 | − | 0.403593i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.07988 | + | 8.79861i | 0.290873 | + | 0.503807i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.74426 | − | 3.02115i | −0.0995503 | − | 0.172426i | 0.811948 | − | 0.583729i | \(-0.198407\pi\) |
−0.911499 | + | 0.411303i | \(0.865074\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.101231 | − | 0.175338i | 0.00575884 | − | 0.00997461i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1487 | −0.802300 | −0.401150 | − | 0.916012i | \(-0.631389\pi\) | ||||
−0.401150 | + | 0.916012i | \(0.631389\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0740 | 0.625941 | 0.312971 | − | 0.949763i | \(-0.398676\pi\) | ||||
0.312971 | + | 0.949763i | \(0.398676\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.827889 | − | 1.43395i | 0.0466463 | − | 0.0807937i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.1965 | + | 24.5890i | 0.797353 | + | 1.38106i | 0.921334 | + | 0.388772i | \(0.127101\pi\) |
−0.123981 | + | 0.992285i | \(0.539566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.57754 | − | 13.1247i | −0.424261 | − | 0.734842i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.09586 | 0.396052 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.23317 | + | 2.13591i | −0.0686153 | + | 0.118845i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.800986 | + | 1.38735i | 0.0444307 | + | 0.0769563i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.42556 | 0.521235 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.81373 | − | 4.87352i | −0.155126 | − | 0.268686i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0830 | + | 20.9283i | −0.664140 | + | 1.15032i | 0.315378 | + | 0.948966i | \(0.397869\pi\) |
−0.979518 | + | 0.201358i | \(0.935465\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.237490 | − | 0.411344i | −0.0130143 | − | 0.0225415i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.03367 | + | 1.56851i | 0.438926 | + | 0.0856966i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.35191 | − | 9.26977i | −0.291537 | − | 0.504957i | 0.682636 | − | 0.730758i | \(-0.260833\pi\) |
−0.974173 | + | 0.225801i | \(0.927500\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.20764 | + | 9.01990i | −0.282840 | + | 0.489894i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.7742 | + | 49.8383i | 1.55821 | + | 2.69890i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6414 | 1.00654 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.02247 | + | 5.23507i | 0.162724 | + | 0.281847i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.40314 | − | 12.8226i | 0.397421 | − | 0.688354i | −0.595986 | − | 0.802995i | \(-0.703238\pi\) |
0.993407 | + | 0.114641i | \(0.0365718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.5221 | 0.563236 | 0.281618 | − | 0.959527i | \(-0.409129\pi\) | ||||
0.281618 | + | 0.959527i | \(0.409129\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.800986 | − | 1.38735i | −0.0427535 | − | 0.0740512i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7966 | + | 20.4324i | 0.627872 | + | 1.08751i | 0.987978 | + | 0.154595i | \(0.0494072\pi\) |
−0.360106 | + | 0.932911i | \(0.617259\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.81642 | − | 3.14614i | 0.0964057 | − | 0.166980i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.49051 | 0.237663 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4751 | −1.08063 | −0.540317 | − | 0.841461i | \(-0.681696\pi\) | ||||
−0.540317 | + | 0.841461i | \(0.681696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.08649 | − | 15.7383i | 0.478236 | − | 0.828330i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.3271 | + | 17.8870i | 0.542032 | + | 0.938826i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.751860 | − | 1.30226i | −0.0393541 | − | 0.0681633i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3612 | − | 26.6064i | 0.801848 | − | 1.38884i | −0.116550 | − | 0.993185i | \(-0.537184\pi\) |
0.918398 | − | 0.395657i | \(-0.129483\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.573228 | − | 0.992859i | 0.0298410 | − | 0.0516862i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.94626 | + | 8.56718i | −0.256797 | + | 0.444786i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.9993 | − | 24.2476i | 0.724859 | − | 1.25549i | −0.234173 | − | 0.972195i | \(-0.575238\pi\) |
0.959032 | − | 0.283297i | \(-0.0914283\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.31517 | −0.222243 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.3276 | − | 23.0841i | −0.684594 | − | 1.18575i | −0.973564 | − | 0.228413i | \(-0.926646\pi\) |
0.288970 | − | 0.957338i | \(-0.406687\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.57825 | + | 14.8580i | −0.439477 | + | 0.761196i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.54153 | + | 14.7944i | 0.436452 | + | 0.755957i | 0.997413 | − | 0.0718855i | \(-0.0229016\pi\) |
−0.560961 | + | 0.827842i | \(0.689568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.65787 | + | 8.06767i | 0.237387 | + | 0.411167i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.46671 | 0.277888 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.45917 | + | 2.52735i | 0.0739828 | + | 0.128142i | 0.900643 | − | 0.434559i | \(-0.143096\pi\) |
−0.826661 | + | 0.562701i | \(0.809762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.19701 | + | 14.1976i | −0.414541 | + | 0.718006i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.43412 | 0.223672 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.38601 | − | 7.59678i | 0.220684 | − | 0.382236i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.6606 | −1.78976 | −0.894878 | − | 0.446312i | \(-0.852737\pi\) | ||||
−0.894878 | + | 0.446312i | \(0.852737\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.50578 | 0.0753831 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.4152 | −1.71861 | −0.859306 | − | 0.511462i | \(-0.829104\pi\) | ||||
−0.859306 | + | 0.511462i | \(0.829104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.3860 | 0.816243 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.67233 | 0.132462 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.883687 | + | 1.53059i | −0.0436955 | + | 0.0756829i | −0.887046 | − | 0.461681i | \(-0.847246\pi\) |
0.843350 | + | 0.537364i | \(0.180580\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.6451 | −0.673064 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.83618 | − | 11.8406i | 0.336386 | − | 0.582638i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.96714 | − | 10.3354i | −0.292916 | − | 0.507345i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.07755 | −0.150708 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.414007 | − | 0.717081i | −0.0202256 | − | 0.0350317i | 0.855735 | − | 0.517414i | \(-0.173105\pi\) |
−0.875961 | + | 0.482382i | \(0.839772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.38387 | − | 4.12898i | −0.116183 | − | 0.201234i | 0.802069 | − | 0.597231i | \(-0.203732\pi\) |
−0.918252 | + | 0.395997i | \(0.870399\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.69934 | − | 2.94334i | 0.0826247 | − | 0.143110i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.35601 | − | 2.34868i | −0.0657763 | − | 0.113928i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.8223 | 0.814088 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.01303 | 0.435153 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.53658 | + | 9.58964i | −0.266688 | + | 0.461917i | −0.968004 | − | 0.250933i | \(-0.919263\pi\) |
0.701317 | + | 0.712850i | \(0.252596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.740009 | − | 1.28173i | 0.0355626 | − | 0.0615962i | −0.847696 | − | 0.530482i | \(-0.822011\pi\) |
0.883259 | + | 0.468886i | \(0.155344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.34683 | − | 2.33278i | 0.0645756 | − | 0.111848i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.74865 | + | 4.76081i | −0.131486 | + | 0.227740i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4870 | + | 18.1641i | 0.500519 | + | 0.866924i | 1.00000 | 0.000598899i | \(0.000190636\pi\) | |
−0.499481 | + | 0.866325i | \(0.666476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.12920 | + | 3.68788i | 0.101390 | + | 0.175613i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.1526 | − | 26.2450i | 0.719921 | − | 1.24694i | −0.241110 | − | 0.970498i | \(-0.577512\pi\) |
0.961031 | − | 0.276441i | \(-0.0891551\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1310 | 0.480256 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.71209 | −0.412068 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1124 | − | 24.4433i | 0.666004 | − | 1.15355i | −0.313008 | − | 0.949750i | \(-0.601337\pi\) |
0.979012 | − | 0.203802i | \(-0.0653298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.22510 | + | 5.58603i | 0.151864 | + | 0.263036i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.4966 | − | 19.9127i | −0.540158 | − | 0.935582i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.65251 | 0.124352 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.527111 | − | 0.912983i | 0.0246572 | − | 0.0427076i | −0.853433 | − | 0.521202i | \(-0.825484\pi\) |
0.878091 | + | 0.478494i | \(0.158817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.35601 | + | 2.34868i | 0.0632933 | + | 0.109627i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.0052 | −1.72350 | −0.861751 | − | 0.507331i | \(-0.830632\pi\) | ||||
−0.861751 | + | 0.507331i | \(0.830632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.62376 | + | 4.54448i | 0.121936 | + | 0.211200i | 0.920531 | − | 0.390669i | \(-0.127756\pi\) |
−0.798595 | + | 0.601869i | \(0.794423\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.11431 | + | 8.85825i | −0.237171 | + | 0.410791i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8832 | − | 27.5106i | −0.734989 | − | 1.27304i | −0.954728 | − | 0.297479i | \(-0.903854\pi\) |
0.219740 | − | 0.975559i | \(-0.429479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.90013 | − | 10.2213i | 0.410970 | − | 0.471975i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0754 | − | 17.4511i | −0.464251 | − | 0.804106i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.3784 | + | 26.6362i | −0.707100 | + | 1.22473i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.454704 | − | 0.787570i | −0.0208632 | − | 0.0361362i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.97455 | −0.273556 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.6079 | − | 30.4978i | −0.804527 | − | 1.39348i | −0.916610 | − | 0.399782i | \(-0.869086\pi\) |
0.112084 | − | 0.993699i | \(-0.464248\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.380452 | − | 0.658962i | 0.0173471 | − | 0.0300461i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0091 | 0.455428 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.33139 | + | 4.03809i | 0.105863 | + | 0.183360i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.935906 | − | 1.62104i | −0.0424100 | − | 0.0734562i | 0.844041 | − | 0.536278i | \(-0.180170\pi\) |
−0.886451 | + | 0.462822i | \(0.846837\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.52114 | + | 7.83085i | −0.204453 | + | 0.354123i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.81111 | 0.217122 | 0.108561 | − | 0.994090i | \(-0.465376\pi\) | ||||
0.108561 | + | 0.994090i | \(0.465376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.30528 | 0.329013 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.81310 | + | 4.87244i | −0.126440 | + | 0.219000i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00759 | − | 5.20930i | −0.134909 | − | 0.233669i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.88805 | + | 5.00226i | 0.129287 | + | 0.223932i | 0.923401 | − | 0.383838i | \(-0.125398\pi\) |
−0.794114 | + | 0.607769i | \(0.792064\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.20616 | + | 5.55323i | −0.143241 | + | 0.248100i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.34561 | + | 12.7230i | −0.327525 | + | 0.567289i | −0.982020 | − | 0.188777i | \(-0.939548\pi\) |
0.654495 | + | 0.756066i | \(0.272881\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.05606 | + | 7.02530i | −0.180492 | + | 0.312622i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.21684 | + | 9.03584i | −0.231688 | + | 0.401296i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.1868 | −1.73692 | −0.868462 | − | 0.495756i | \(-0.834891\pi\) | ||||
−0.868462 | + | 0.495756i | \(0.834891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.48982 | −0.110143 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.454704 | + | 0.787570i | 0.0200757 | + | 0.0347721i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.101231 | + | 0.175338i | −0.00446078 | + | 0.00772630i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.56083 | + | 16.5598i | 0.420485 | + | 0.728301i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.45972 | + | 16.3847i | 0.415236 | + | 0.719209i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0438 | −0.659080 | −0.329540 | − | 0.944142i | \(-0.606894\pi\) | ||||
−0.329540 | + | 0.944142i | \(0.606894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.6705 | − | 30.6062i | −0.772677 | − | 1.33832i | −0.936091 | − | 0.351759i | \(-0.885584\pi\) |
0.163413 | − | 0.986558i | \(-0.447750\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.827889 | + | 1.43395i | −0.0361320 | + | 0.0625825i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.7403 | −1.20839 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.77062 | + | 11.7271i | −0.294375 | + | 0.509872i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.25736 | 0.358339 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.83659 | 0.0795515 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.09586 | −0.306781 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.01635 | −0.216471 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.9586 | −1.03197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.01368 | 0.258548 | 0.129274 | − | 0.991609i | \(-0.458735\pi\) | ||||
0.129274 | + | 0.991609i | \(0.458735\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.71426 | − | 8.16533i | 0.202308 | − | 0.350408i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.42556 | −0.403747 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.04360 | − | 12.1999i | 0.301163 | − | 0.521629i | −0.675237 | − | 0.737601i | \(-0.735959\pi\) |
0.976400 | + | 0.215972i | \(0.0692920\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.07988 | + | 8.79861i | 0.216804 | + | 0.375516i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.44963 | 0.104358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.26225 | − | 12.5786i | −0.308822 | − | 0.534896i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.237490 | + | 0.411344i | 0.0100809 | + | 0.0174606i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.4614 | + | 31.9761i | −0.782235 | + | 1.35487i | 0.148401 | + | 0.988927i | \(0.452587\pi\) |
−0.930637 | + | 0.365944i | \(0.880746\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.37876 | + | 7.58423i | 0.185202 | + | 0.320779i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.2584 | −0.644211 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.4229 | −0.818578 | −0.409289 | − | 0.912405i | \(-0.634223\pi\) | ||||
−0.409289 | + | 0.912405i | \(0.634223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.20764 | − | 9.01990i | 0.219087 | − | 0.379470i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.827889 | − | 1.43395i | 0.0347681 | − | 0.0602201i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.90660 | − | 10.2305i | 0.247617 | − | 0.428886i | −0.715247 | − | 0.698872i | \(-0.753686\pi\) |
0.962864 | + | 0.269986i | \(0.0870191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0988 | + | 17.4916i | −0.422620 | + | 0.731999i | −0.996195 | − | 0.0871539i | \(-0.972223\pi\) |
0.573575 | + | 0.819153i | \(0.305556\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.77371 | − | 6.53626i | −0.157649 | − | 0.273056i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.02247 | − | 5.23507i | −0.126046 | − | 0.218317i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.2372 | + | 24.6596i | −0.592703 | + | 1.02659i | 0.401164 | + | 0.916006i | \(0.368606\pi\) |
−0.993867 | + | 0.110585i | \(0.964728\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.80997 | −0.407688 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.7605 | −0.819805 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.8070 | − | 29.1106i | 0.696075 | − | 1.20564i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.800986 | + | 1.38735i | 0.0331167 | + | 0.0573598i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.22117 | − | 14.2395i | −0.339324 | − | 0.587726i | 0.644982 | − | 0.764198i | \(-0.276865\pi\) |
−0.984306 | + | 0.176472i | \(0.943532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.30198 | −0.383282 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.16415 | + | 12.4087i | −0.294694 | + | 0.510425i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.417897 | + | 0.723819i | 0.0171610 | + | 0.0297237i | 0.874478 | − | 0.485065i | \(-0.161204\pi\) |
−0.857317 | + | 0.514788i | \(0.827871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.49051 | −0.184093 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8696 | + | 22.2908i | 0.526719 | + | 0.912304i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8672 | + | 24.0187i | −0.566599 | + | 0.981378i | 0.430300 | + | 0.902686i | \(0.358408\pi\) |
−0.996899 | + | 0.0786922i | \(0.974926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.10975 | + | 5.38625i | 0.126850 | + | 0.219710i | 0.922454 | − | 0.386106i | \(-0.126180\pi\) |
−0.795605 | + | 0.605816i | \(0.792847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.03367 | + | 1.56851i | 0.327156 | + | 0.0638745i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.3271 | − | 17.8870i | −0.419856 | − | 0.727212i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.3997 | − | 31.8692i | 0.746822 | − | 1.29353i | −0.202517 | − | 0.979279i | \(-0.564912\pi\) |
0.949339 | − | 0.314254i | \(-0.101754\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.23005 | − | 3.86256i | −0.0903663 | − | 0.156519i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.44459 | 0.220264 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2977 | − | 26.4965i | −0.617870 | − | 1.07018i | −0.989874 | − | 0.141951i | \(-0.954663\pi\) |
0.372004 | − | 0.928231i | \(-0.378671\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.573228 | + | 0.992859i | −0.0231148 | + | 0.0400360i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.4967 | 0.784906 | 0.392453 | − | 0.919772i | \(-0.371627\pi\) | ||||
0.392453 | + | 0.919772i | \(0.371627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.62543 | + | 11.4756i | 0.266298 | + | 0.461242i | 0.967903 | − | 0.251324i | \(-0.0808660\pi\) |
−0.701605 | + | 0.712567i | \(0.747533\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.02247 | + | 5.23507i | 0.121287 | + | 0.210076i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.38736 | − | 14.5273i | 0.336032 | − | 0.582025i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.11651 | −0.204334 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.644078 | + | 1.11558i | −0.0256811 | + | 0.0444809i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9734 | + | 32.8629i | 0.755320 | + | 1.30825i | 0.945215 | + | 0.326448i | \(0.105852\pi\) |
−0.189896 | + | 0.981804i | \(0.560815\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5115 | + | 21.6706i | 0.497289 | + | 0.861329i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.57825 | − | 14.8580i | 0.340417 | − | 0.589620i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.41092 | + | 5.90789i | −0.135146 | + | 0.234079i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.81642 | − | 3.14614i | 0.0718566 | − | 0.124459i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.2803 | + | 29.9304i | −0.682531 | + | 1.18218i | 0.291675 | + | 0.956517i | \(0.405787\pi\) |
−0.974206 | + | 0.225660i | \(0.927546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.3668 | −0.566570 | −0.283285 | − | 0.959036i | \(-0.591424\pi\) | ||||
−0.283285 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.46671 | −0.215251 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.3641 | + | 24.8794i | 0.564712 | + | 0.978110i | 0.997076 | + | 0.0764108i | \(0.0243461\pi\) |
−0.432364 | + | 0.901699i | \(0.642321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.2288 | + | 40.2335i | −0.911811 | + | 1.57930i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.46816 | + | 14.6673i | 0.331894 | + | 0.574856i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.76966 | + | 6.52924i | 0.147518 | + | 0.255509i | 0.930310 | − | 0.366775i | \(-0.119538\pi\) |
−0.782791 | + | 0.622284i | \(0.786205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.43412 | −0.173255 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.751860 | − | 1.30226i | −0.0293328 | − | 0.0508060i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.82506 | − | 15.2854i | 0.343775 | − | 0.595437i | −0.641355 | − | 0.767244i | \(-0.721627\pi\) |
0.985131 | + | 0.171808i | \(0.0549608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.732720 | 0.0284995 | 0.0142498 | − | 0.999898i | \(-0.495464\pi\) | ||||
0.0142498 | + | 0.999898i | \(0.495464\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.17230 | + | 3.76253i | −0.0843650 | + | 0.146124i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.50578 | −0.0583915 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.2830 | 0.630480 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.9045 | −0.653565 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −57.1609 | −2.20667 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.2787 | 1.70682 | 0.853409 | − | 0.521242i | \(-0.174531\pi\) | ||||
0.853409 | + | 0.521242i | \(0.174531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.6334 | + | 30.5420i | −0.677708 | + | 1.17383i | 0.297961 | + | 0.954578i | \(0.403693\pi\) |
−0.975669 | + | 0.219247i | \(0.929640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.72054 | 0.296287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.58831 | − | 9.67924i | 0.214145 | − | 0.370909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.93772 | + | 5.08828i | 0.112409 | + | 0.194698i | 0.916741 | − | 0.399482i | \(-0.130810\pi\) |
−0.804332 | + | 0.594180i | \(0.797477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6451 | 0.521353 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.62535 | − | 13.2075i | −0.290925 | − | 0.503897i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.78553 | − | 8.28878i | −0.182314 | − | 0.315777i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.1951 | − | 26.3186i | 0.578048 | − | 1.00121i | −0.417655 | − | 0.908606i | \(-0.637148\pi\) |
0.995703 | − | 0.0926028i | \(-0.0295187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.65787 | + | 8.06767i | 0.176938 | + | 0.306466i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.07755 | 0.116738 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.10922 | −0.117770 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.94446 | − | 3.36790i | 0.0735462 | − | 0.127386i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.7302 | − | 30.7097i | 0.669661 | − | 1.15989i | −0.308337 | − | 0.951277i | \(-0.599773\pi\) |
0.977999 | − | 0.208611i | \(-0.0668941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.215975 | + | 0.374079i | −0.00814564 | + | 0.0141087i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.69934 | + | 2.94334i | −0.0640008 | + | 0.110853i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.71593 | + | 11.6323i | 0.252578 | + | 0.437479i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.5341 | − | 21.7097i | −0.470727 | − | 0.815324i | 0.528712 | − | 0.848801i | \(-0.322675\pi\) |
−0.999439 | + | 0.0334774i | \(0.989342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.38601 | − | 7.59678i | 0.164488 | − | 0.284902i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −61.8314 | −2.31560 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.01303 | −0.337068 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.86697 | − | 8.42984i | 0.181760 | − | 0.314818i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.9619 | + | 22.4507i | 0.483397 | + | 0.837269i | 0.999818 | − | 0.0190661i | \(-0.00606931\pi\) |
−0.516421 | + | 0.856335i | \(0.672736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.167616 | + | 0.290320i | 0.00624236 | + | 0.0108121i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.8478 | −0.700958 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.34683 | + | 2.33278i | −0.0500200 | + | 0.0866372i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5361 | + | 33.8375i | 0.724555 | + | 1.25497i | 0.959157 | + | 0.282874i | \(0.0912878\pi\) |
−0.234603 | + | 0.972091i | \(0.575379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.41293 | − | 12.8396i | −0.274177 | − | 0.474889i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.97287 | − | 8.61326i | 0.183677 | − | 0.318138i | −0.759453 | − | 0.650562i | \(-0.774533\pi\) |
0.943130 | + | 0.332424i | \(0.107867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.12920 | − | 3.68788i | −0.0785367 | − | 0.136030i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.2420 | + | 34.7312i | −1.11398 | + | 1.27934i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.5996 | + | 32.2155i | 0.684197 | + | 1.18506i | 0.973688 | + | 0.227884i | \(0.0731807\pi\) |
−0.289491 | + | 0.957181i | \(0.593486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.728423 | + | 1.26167i | −0.0267593 | + | 0.0463484i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.37068 | + | 7.57024i | 0.160345 | + | 0.277725i | 0.934992 | − | 0.354668i | \(-0.115406\pi\) |
−0.774648 | + | 0.632393i | \(0.782073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.71209 | 0.319186 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.96714 | − | 10.3354i | −0.218326 | − | 0.378152i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.87458 | + | 10.1751i | −0.214653 | + | 0.371789i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.5269 | −1.62481 | −0.812405 | − | 0.583094i | \(-0.801842\pi\) | ||||
−0.812405 | + | 0.583094i | \(0.801842\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.50889 | − | 4.34552i | −0.0914290 | − | 0.158360i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4966 | + | 19.9127i | 0.418405 | + | 0.724699i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.1417 | + | 34.8865i | −0.732064 | + | 1.26797i | 0.223936 | + | 0.974604i | \(0.428109\pi\) |
−0.956000 | + | 0.293368i | \(0.905224\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.0100 | −1.23449 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.5812 | −0.746068 | −0.373034 | − | 0.927818i | \(-0.621682\pi\) | ||||
−0.373034 | + | 0.927818i | \(0.621682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.80331 | + | 13.5157i | −0.282499 | + | 0.489303i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.35601 | − | 2.34868i | −0.0490268 | − | 0.0849169i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.61403 | + | 11.4558i | 0.238819 | + | 0.413647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.892739 | − | 1.54627i | 0.0321930 | − | 0.0557599i | −0.849480 | − | 0.527621i | \(-0.823084\pi\) |
0.881673 | + | 0.471861i | \(0.156418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.989493 | − | 1.71385i | 0.0356357 | − | 0.0617229i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.82765 | + | 3.16558i | −0.0657359 | + | 0.113858i | −0.897020 | − | 0.441990i | \(-0.854273\pi\) |
0.831284 | + | 0.555848i | \(0.187606\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.11431 | − | 8.85825i | 0.183712 | − | 0.318198i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.786460 | 0.0282141 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.04259 | −0.0373548 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2196 | + | 17.7008i | 0.365685 | + | 0.633385i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.34683 | − | 2.33278i | 0.0481318 | − | 0.0833667i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0754 | + | 17.4511i | 0.359607 | + | 0.622858i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.99119 | − | 17.3053i | −0.356148 | − | 0.616866i | 0.631166 | − | 0.775648i | \(-0.282577\pi\) |
−0.987314 | + | 0.158782i | \(0.949243\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.03457 | −0.214836 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.62269 | − | 14.9349i | −0.306588 | − | 0.531025i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.13783 | + | 14.0951i | −0.288983 | + | 0.500533i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.97455 | 0.211895 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.17916 | + | 10.7026i | −0.218877 | + | 0.379106i | −0.954465 | − | 0.298323i | \(-0.903573\pi\) |
0.735588 | + | 0.677429i | \(0.236906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.21730 | −0.326085 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.1310 | 0.357962 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.46023 | 0.298555 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0091 | −0.352773 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.0260 | −0.775351 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.09959 | 0.284767 | 0.142383 | − | 0.989812i | \(-0.454523\pi\) | ||||
0.142383 | + | 0.989812i | \(0.454523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.32560 | + | 7.49215i | −0.151892 | + | 0.263085i | −0.931923 | − | 0.362656i | \(-0.881870\pi\) |
0.780031 | + | 0.625741i | \(0.215203\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.3255 | 0.572561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.52114 | − | 7.83085i | 0.158369 | − | 0.274303i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.48573 | − | 4.30541i | −0.0869648 | − | 0.150627i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.65251 | 0.0926862 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.2168 | + | 22.8921i | 0.461268 | + | 0.798940i | 0.999024 | − | 0.0441607i | \(-0.0140614\pi\) |
−0.537756 | + | 0.843100i | \(0.680728\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.33192 | − | 4.03900i | −0.0812855 | − | 0.140791i | 0.822517 | − | 0.568741i | \(-0.192569\pi\) |
−0.903802 | + | 0.427950i | \(0.859236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.81310 | − | 4.87244i | 0.0979397 | − | 0.169636i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6353 | + | 28.8133i | 0.578468 | + | 1.00194i | 0.995655 | + | 0.0931149i | \(0.0296824\pi\) |
−0.417188 | + | 0.908820i | \(0.636984\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.92652 | 0.240568 | 0.120284 | − | 0.992740i | \(-0.461619\pi\) | ||||
0.120284 | + | 0.992740i | \(0.461619\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.6875 | 0.752330 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.77445 | − | 10.0016i | 0.200073 | − | 0.346536i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.20616 | − | 5.55323i | 0.110954 | − | 0.192177i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.11431 | + | 8.85825i | −0.176776 | + | 0.306186i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.78860 | + | 3.09795i | −0.0617495 | + | 0.106953i | −0.895247 | − | 0.445569i | \(-0.853001\pi\) |
0.833498 | + | 0.552522i | \(0.186335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8721 | + | 18.8310i | 0.374900 | + | 0.649346i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.1094 | + | 19.2421i | 0.382629 | + | 0.662733i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.21684 | − | 9.03584i | 0.179465 | − | 0.310842i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.1987 | −1.17508 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.8268 | −0.646134 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.43561 | + | 2.48655i | −0.0492120 | + | 0.0852377i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.55867 | + | 4.43174i | 0.0876071 | + | 0.151740i | 0.906499 | − | 0.422208i | \(-0.138745\pi\) |
−0.818892 | + | 0.573948i | \(0.805411\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.454704 | − | 0.787570i | −0.0155505 | − | 0.0269343i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.2584 | −1.37520 | −0.687600 | − | 0.726090i | \(-0.741336\pi\) | ||||
−0.687600 | + | 0.726090i | \(0.741336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.2959 | − | 31.6894i | 0.624247 | − | 1.08123i | −0.364438 | − | 0.931228i | \(-0.618739\pi\) |
0.988686 | − | 0.150001i | \(-0.0479277\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.949138 | + | 1.64395i | 0.0323465 | + | 0.0560258i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.16219 | 0.311885 | 0.155942 | − | 0.987766i | \(-0.450159\pi\) | ||||
0.155942 | + | 0.987766i | \(0.450159\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.45972 | − | 16.3847i | −0.321640 | − | 0.557097i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.82245 | + | 8.35274i | −0.163779 | + | 0.283674i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.6766 | + | 42.7411i | 0.837095 | + | 1.44989i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.25879 | + | 12.4018i | 0.144304 | + | 0.420221i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.33139 | + | 4.03809i | 0.0789057 | + | 0.136669i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.827889 | − | 1.43395i | 0.0279878 | − | 0.0484762i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.46422 | + | 9.46430i | 0.184513 | + | 0.319587i | 0.943412 | − | 0.331622i | \(-0.107596\pi\) |
−0.758899 | + | 0.651208i | \(0.774262\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.2928 | −1.05548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0875 | + | 20.9362i | 0.407238 | + | 0.705357i | 0.994579 | − | 0.103983i | \(-0.0331586\pi\) |
−0.587341 | + | 0.809339i | \(0.699825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.54851 | + | 4.41415i | −0.0857642 | + | 0.148548i | −0.905717 | − | 0.423884i | \(-0.860667\pi\) |
0.819952 | + | 0.572432i | \(0.194000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.25736 | −0.277568 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.0295 | − | 26.0319i | −0.504642 | − | 0.874065i | −0.999986 | − | 0.00536822i | \(-0.998291\pi\) |
0.495344 | − | 0.868697i | \(-0.335042\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.2037 | − | 24.6015i | −0.476376 | − | 0.825107i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.81310 | + | 4.87244i | −0.0942425 | + | 0.163233i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.09078 | −0.103429 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.01635 | 0.167678 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.84191 | + | 8.38643i | −0.161667 | + | 0.280015i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.7762 | + | 23.8611i | 0.459463 | + | 0.795813i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.10157 | + | 14.0323i | 0.269902 | + | 0.467485i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.52583 | + | 7.83896i | −0.150610 | + | 0.260864i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.71426 | + | 8.16533i | −0.156707 | + | 0.271425i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.80223 | − | 4.85361i | 0.0930466 | − | 0.161161i | −0.815745 | − | 0.578412i | \(-0.803673\pi\) |
0.908792 | + | 0.417250i | \(0.137006\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.05606 | + | 7.02530i | −0.134531 | + | 0.233014i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.8524 | −0.657740 | −0.328870 | − | 0.944375i | \(-0.606668\pi\) | ||||
−0.328870 | + | 0.944375i | \(0.606668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 67.1448 | 2.22217 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.07988 | − | 8.79861i | −0.167936 | − | 0.290873i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.67096 | + | 6.35828i | −0.121226 | + | 0.209969i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.59944 | − | 11.4306i | −0.217695 | − | 0.377060i | 0.736408 | − | 0.676538i | \(-0.236521\pi\) |
−0.954103 | + | 0.299479i | \(0.903187\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.74426 | + | 3.02115i | 0.0574754 | + | 0.0995503i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.81972 | 0.191558 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.237490 | − | 0.411344i | −0.00780861 | − | 0.0135249i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.101231 | + | 0.175338i | −0.00332487 | + | 0.00575884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.7574 | −0.910690 | −0.455345 | − | 0.890315i | \(-0.650484\pi\) | ||||
−0.455345 | + | 0.890315i | \(0.650484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.93631 | − | 3.35379i | 0.0634600 | − | 0.109916i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.1487 | 0.463208 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.2584 | 0.499004 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.5093 | 0.474000 | 0.237000 | − | 0.971510i | \(-0.423836\pi\) | ||||
0.237000 | + | 0.971510i | \(0.423836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.0740 | −0.361387 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.2412 | 1.80081 | 0.900406 | − | 0.435051i | \(-0.143270\pi\) | ||||
0.900406 | + | 0.435051i | \(0.143270\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.93025 | −0.225680 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.827889 | + | 1.43395i | −0.0269312 | + | 0.0466463i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.4760 | 0.697876 | 0.348938 | − | 0.937146i | \(-0.386542\pi\) | ||||
0.348938 | + | 0.937146i | \(0.386542\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.20446 | − | 2.08618i | 0.0390984 | − | 0.0677204i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.1965 | − | 24.5890i | −0.460352 | − | 0.797353i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.20463 | −0.0390219 | −0.0195110 | − | 0.999810i | \(-0.506211\pi\) | ||||
−0.0195110 | + | 0.999810i | \(0.506211\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.77371 | + | 6.53626i | 0.122114 | + | 0.211508i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.57754 | + | 13.1247i | 0.244947 | + | 0.424261i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2966 | − | 19.5663i | 0.364787 | − | 0.631830i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.8124 | − | 63.7609i | −1.18750 | − | 2.05680i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.09586 | −0.228661 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.80997 | 0.315794 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.92337 | + | 11.9916i | −0.222641 | + | 0.385625i | −0.955609 | − | 0.294638i | \(-0.904801\pi\) |
0.732968 | + | 0.680263i | \(0.238134\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.23317 | − | 2.13591i | 0.0396151 | − | 0.0686153i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.56739 | − | 7.91096i | 0.146575 | − | 0.253875i | −0.783385 | − | 0.621537i | \(-0.786508\pi\) |
0.929959 | + | 0.367662i | \(0.119842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.54787 | − | 4.41304i | 0.0816810 | − | 0.141476i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.800986 | − | 1.38735i | −0.0256521 | − | 0.0444307i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.73407 | − | 4.73556i | −0.0874708 | − | 0.151504i | 0.818971 | − | 0.573835i | \(-0.194545\pi\) |
−0.906441 | + | 0.422332i | \(0.861212\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.4996 | + | 49.3627i | −0.910851 | + | 1.57764i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.42556 | −0.300935 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5261 | 0.399522 | 0.199761 | − | 0.979845i | \(-0.435983\pi\) | ||||
0.199761 | + | 0.979845i | \(0.435983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.16415 | − | 12.4087i | 0.228269 | − | 0.395373i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.81373 | + | 4.87352i | 0.0895619 | + | 0.155126i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.5229 | − | 28.6186i | −0.525399 | − | 0.910018i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.90849 | −0.251222 | −0.125611 | − | 0.992080i | \(-0.540089\pi\) | ||||
−0.125611 | + | 0.992080i | \(0.540089\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0830 | − | 20.9283i | 0.383441 | − | 0.664140i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.8696 | − | 22.2908i | −0.407995 | − | 0.706667i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.8026 | −1.41891 | −0.709456 | − | 0.704750i | \(-0.751059\pi\) | ||||
−0.709456 | + | 0.704750i | \(0.751059\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.237490 | + | 0.411344i | 0.00751384 | + | 0.0130143i |
(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 | 4020.2.q.k.841.4 | ✓ | 14 | |
67.29 | even | 3 | inner | 4020.2.q.k.3781.4 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.k.841.4 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4020.2.q.k.3781.4 | yes | 14 | 67.29 | even | 3 | inner |