Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(33,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.i (of order \(16\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{16})\) |
Twist minimal: | no (minimal twist has level 64) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Character | \(\chi\) | \(=\) | 512.97 |
Dual form | 512.2.i.b.417.1 |
$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{13}{16}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.553854 | − | 2.78441i | −0.319768 | − | 1.60758i | −0.721898 | − | 0.691999i | \(-0.756730\pi\) |
0.402131 | − | 0.915582i | \(-0.368270\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.59756 | + | 1.73564i | −1.16167 | + | 0.776200i | −0.978371 | − | 0.206858i | \(-0.933676\pi\) |
−0.183295 | + | 0.983058i | \(0.558676\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.96508 | − | 0.813965i | −0.742732 | − | 0.307650i | −0.0209598 | − | 0.999780i | \(-0.506672\pi\) |
−0.721772 | + | 0.692131i | \(0.756672\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.67456 | + | 1.93627i | −1.55819 | + | 0.645422i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.02382 | + | 0.402563i | 0.610205 | + | 0.121377i | 0.490513 | − | 0.871434i | \(-0.336809\pi\) |
0.119692 | + | 0.992811i | \(0.461809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.99644 | + | 1.33398i | 0.553713 | + | 0.369979i | 0.800724 | − | 0.599033i | \(-0.204448\pi\) |
−0.247011 | + | 0.969013i | \(0.579448\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.27140 | + | 6.27140i | 1.61927 | + | 1.61927i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.31120 | + | 2.31120i | −0.560547 | + | 0.560547i | −0.929463 | − | 0.368916i | \(-0.879729\pi\) |
0.368916 | + | 0.929463i | \(0.379729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.37703 | + | 3.55748i | −0.545328 | + | 0.816142i | −0.997109 | − | 0.0759875i | \(-0.975789\pi\) |
0.451780 | + | 0.892129i | \(0.350789\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.17804 | + | 5.92242i | −0.257070 | + | 1.29238i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.993213 | + | 2.39783i | 0.207099 | + | 0.499982i | 0.992964 | − | 0.118417i | \(-0.0377819\pi\) |
−0.785865 | + | 0.618398i | \(0.787782\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82149 | − | 4.39746i | 0.364297 | − | 0.879491i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.24866 | + | 4.86196i | 0.625205 | + | 0.935685i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.34079 | + | 0.465613i | −0.434674 | + | 0.0864621i | −0.407577 | − | 0.913171i | \(-0.633626\pi\) |
−0.0270970 | + | 0.999633i | \(0.508626\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.81094i | − | 0.325254i | −0.986688 | − | 0.162627i | \(-0.948003\pi\) | ||
0.986688 | − | 0.162627i | \(-0.0519967\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.85811i | − | 1.01977i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.51718 | − | 1.29635i | 1.10160 | − | 0.219123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.40742 | − | 2.10635i | −0.231378 | − | 0.346282i | 0.697554 | − | 0.716533i | \(-0.254272\pi\) |
−0.928932 | + | 0.370250i | \(0.879272\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.60861 | − | 6.29775i | 0.417712 | − | 1.00845i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.66056 | + | 11.2516i | 0.727858 | + | 1.75720i | 0.649607 | + | 0.760270i | \(0.274933\pi\) |
0.0782501 | + | 0.996934i | \(0.475067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.452227 | + | 2.27350i | −0.0689639 | + | 0.346705i | −0.999826 | − | 0.0186663i | \(-0.994058\pi\) |
0.930862 | + | 0.365371i | \(0.119058\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.78181 | − | 13.1429i | 1.30912 | − | 1.95923i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.27298 | + | 2.27298i | −0.331549 | + | 0.331549i | −0.853174 | − | 0.521626i | \(-0.825326\pi\) |
0.521626 | + | 0.853174i | \(0.325326\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.75073 | − | 1.75073i | −0.250104 | − | 0.250104i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.71539 | + | 5.15526i | 1.08037 | + | 0.721881i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.98970 | − | 1.58925i | −1.09747 | − | 0.218300i | −0.387036 | − | 0.922065i | \(-0.626501\pi\) |
−0.710433 | + | 0.703764i | \(0.751501\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.95570 | + | 2.46693i | −0.803067 | + | 0.332641i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.2220 | + | 4.64831i | 1.48639 | + | 0.615684i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.08029 | + | 4.73090i | −0.921775 | + | 0.615911i | −0.923296 | − | 0.384088i | \(-0.874516\pi\) |
0.00152111 | + | 0.999999i | \(0.499516\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.95998 | + | 9.85346i | 0.250949 | + | 1.26161i | 0.876492 | + | 0.481417i | \(0.159878\pi\) |
−0.625543 | + | 0.780190i | \(0.715122\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.7620 | 1.35588 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.50119 | −0.930408 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.88943 | − | 14.5262i | −0.353000 | − | 1.77465i | −0.594342 | − | 0.804212i | \(-0.702587\pi\) |
0.241342 | − | 0.970440i | \(-0.422413\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.12645 | − | 4.09356i | 0.737537 | − | 0.492807i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.41451 | − | 2.65698i | −0.761263 | − | 0.315325i | −0.0319351 | − | 0.999490i | \(-0.510167\pi\) |
−0.729328 | + | 0.684165i | \(0.760167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.36337 | + | 1.39315i | −0.393653 | + | 0.163056i | −0.570724 | − | 0.821142i | \(-0.693338\pi\) |
0.177072 | + | 0.984198i | \(0.443338\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.2532 | − | 2.63622i | −1.53034 | − | 0.304404i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.64930 | − | 2.43839i | −0.415877 | − | 0.277880i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9490 | − | 10.9490i | −1.23186 | − | 1.23186i | −0.963247 | − | 0.268617i | \(-0.913433\pi\) |
−0.268617 | − | 0.963247i | \(-0.586567\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00516 | − | 1.00516i | 0.111685 | − | 0.111685i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.72793 | − | 5.57925i | 0.409194 | − | 0.612402i | −0.568438 | − | 0.822726i | \(-0.692452\pi\) |
0.977632 | + | 0.210324i | \(0.0674520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.99208 | − | 10.0149i | 0.216072 | − | 1.08627i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.59292 | + | 6.25985i | 0.277990 | + | 0.671126i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.10595 | + | 7.49842i | −0.329230 | + | 0.794831i | 0.669420 | + | 0.742884i | \(0.266543\pi\) |
−0.998650 | + | 0.0519471i | \(0.983457\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.83736 | − | 4.24642i | −0.297437 | − | 0.445145i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.04240 | + | 1.00299i | −0.522872 | + | 0.104006i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 13.3664i | − | 1.37137i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.49286i | − | 0.862319i | −0.902276 | − | 0.431160i | \(-0.858105\pi\) | ||
0.902276 | − | 0.431160i | \(-0.141895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.2399 | + | 2.03685i | −1.02915 | + | 0.204711i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.24152 | + | 12.3343i | 0.820062 | + | 1.22731i | 0.971074 | + | 0.238777i | \(0.0767465\pi\) |
−0.151013 | + | 0.988532i | \(0.548253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.14828 | + | 5.18641i | −0.211676 | + | 0.511032i | −0.993681 | − | 0.112241i | \(-0.964197\pi\) |
0.782005 | + | 0.623273i | \(0.214197\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.21913 | − | 17.4285i | −0.704515 | − | 1.70085i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.52870 | + | 12.7126i | −0.244458 | + | 1.22897i | 0.642195 | + | 0.766541i | \(0.278024\pi\) |
−0.886654 | + | 0.462434i | \(0.846976\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.38971 | + | 8.06626i | −0.516240 | + | 0.772608i | −0.994402 | − | 0.105664i | \(-0.966303\pi\) |
0.478162 | + | 0.878272i | \(0.341303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.08545 | + | 5.08545i | −0.482689 | + | 0.482689i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.75634 | + | 4.75634i | 0.447439 | + | 0.447439i | 0.894502 | − | 0.447063i | \(-0.147530\pi\) |
−0.447063 | + | 0.894502i | \(0.647530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.74169 | − | 4.50465i | −0.628666 | − | 0.420061i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.9154 | − | 2.37013i | −1.10158 | − | 0.219118i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.42293 | − | 2.66046i | 0.588789 | − | 0.243884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.22889 | − | 2.58009i | −0.566262 | − | 0.234554i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.7478 | − | 19.2087i | 2.59210 | − | 1.73199i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.146412 | − | 0.736062i | −0.0130955 | − | 0.0658354i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.302397 | 0.0268334 | 0.0134167 | − | 0.999910i | \(-0.495729\pi\) | ||||
0.0134167 | + | 0.999910i | \(0.495729\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.58082 | 0.579409 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.05063 | + | 5.28186i | 0.0917938 | + | 0.461478i | 0.999154 | + | 0.0411246i | \(0.0130941\pi\) |
−0.907360 | + | 0.420354i | \(0.861906\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.56673 | − | 5.05593i | 0.656119 | − | 0.438404i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.8772 | − | 6.99077i | −1.45256 | − | 0.601669i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.9084 | − | 6.58948i | 1.35915 | − | 0.562978i | 0.420324 | − | 0.907374i | \(-0.361917\pi\) |
0.938824 | + | 0.344397i | \(0.111917\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.7049 | − | 2.32824i | −0.992793 | − | 0.197479i | −0.328138 | − | 0.944630i | \(-0.606421\pi\) |
−0.664654 | + | 0.747151i | \(0.731421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.58783 | + | 5.07002i | 0.639010 | + | 0.426973i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.50343 | + | 3.50343i | 0.292971 | + | 0.292971i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.27222 | − | 5.27222i | 0.437834 | − | 0.437834i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.90511 | + | 5.84440i | −0.322088 | + | 0.482038i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.62919 | − | 13.2179i | 0.215392 | − | 1.08285i | −0.710106 | − | 0.704095i | \(-0.751353\pi\) |
0.925498 | − | 0.378753i | \(-0.123647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.726711 | − | 1.75444i | −0.0591389 | − | 0.142774i | 0.891548 | − | 0.452926i | \(-0.149620\pi\) |
−0.950687 | + | 0.310152i | \(0.899620\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.32873 | − | 15.2789i | 0.511648 | − | 1.23523i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.14313 | + | 4.70402i | 0.252462 | + | 0.377836i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.2962 | − | 3.63933i | 1.46019 | − | 0.290450i | 0.599828 | − | 0.800129i | \(-0.295236\pi\) |
0.860365 | + | 0.509679i | \(0.170236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.1268i | 1.83408i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.52037i | − | 0.435066i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.25039 | − | 0.646543i | 0.254590 | − | 0.0506412i | −0.0661449 | − | 0.997810i | \(-0.521070\pi\) |
0.320735 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.1676 | + | 15.2168i | 0.791543 | + | 1.18463i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.0933446 | − | 0.225354i | 0.00722322 | − | 0.0174384i | −0.920227 | − | 0.391386i | \(-0.871996\pi\) |
0.927450 | + | 0.373947i | \(0.121996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.76861 | − | 6.68401i | −0.212970 | − | 0.514154i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.22335 | − | 21.2322i | 0.322968 | − | 1.62367i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.24361 | − | 12.3374i | 0.626750 | − | 0.937998i | −0.373197 | − | 0.927752i | \(-0.621739\pi\) |
0.999948 | − | 0.0102459i | \(-0.00326144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.15875 | + | 7.15875i | −0.541151 | + | 0.541151i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.0942 | + | 17.0942i | 1.28488 | + | 1.28488i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.58585 | − | 6.40506i | −0.716480 | − | 0.478736i | 0.143119 | − | 0.989705i | \(-0.454287\pi\) |
−0.859599 | + | 0.510969i | \(0.829287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.33755 | + | 1.65844i | 0.619726 | + | 0.123271i | 0.494961 | − | 0.868915i | \(-0.335182\pi\) |
0.124765 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.3506 | − | 10.9148i | 1.94789 | − | 0.806842i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.31172 | + | 3.02862i | 0.537569 | + | 0.222668i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.60785 | + | 3.74704i | −0.410086 | + | 0.274011i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.42642 | − | 12.1985i | −0.176496 | − | 0.887307i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.31207 | 0.456725 | 0.228363 | − | 0.973576i | \(-0.426663\pi\) | ||||
0.228363 | + | 0.973576i | \(0.426663\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5158 | −0.756940 | −0.378470 | − | 0.925614i | \(-0.623550\pi\) | ||||
−0.378470 | + | 0.925614i | \(0.623550\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.15456 | + | 20.8864i | 0.297515 | + | 1.49571i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0604 | + | 8.72666i | −0.930513 | + | 0.621749i | −0.925708 | − | 0.378240i | \(-0.876530\pi\) |
−0.00480529 | + | 0.999988i | \(0.501530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4075 | + | 10.5241i | 1.80109 | + | 0.746037i | 0.986008 | + | 0.166695i | \(0.0533095\pi\) |
0.815085 | + | 0.579342i | \(0.196690\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −38.8465 | + | 16.0907i | −2.74002 | + | 1.13495i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.97885 | + | 0.990354i | 0.349447 | + | 0.0695092i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.6348 | − | 21.1377i | −2.20947 | − | 1.47632i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.28566 | − | 9.28566i | −0.645398 | − | 0.645398i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.24279 | + | 6.24279i | −0.431823 | + | 0.431823i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5416 | + | 18.7698i | −0.863399 | + | 1.29217i | 0.0916719 | + | 0.995789i | \(0.470779\pi\) |
−0.955071 | + | 0.296378i | \(0.904221\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.84542 | + | 19.3322i | −0.263484 | + | 1.32462i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.77128 | − | 6.69045i | −0.189000 | − | 0.456285i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.47404 | + | 3.55864i | −0.100064 | + | 0.241576i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.74193 | + | 8.59341i | 0.388004 | + | 0.580689i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.69726 | + | 1.53108i | −0.517774 | + | 0.102992i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.11318i | − | 0.543298i | −0.962396 | − | 0.271649i | \(-0.912431\pi\) | ||
0.962396 | − | 0.271649i | \(-0.0875690\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 24.0831i | 1.60554i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.3933 | − | 2.26626i | 0.756197 | − | 0.150417i | 0.198087 | − | 0.980184i | \(-0.436527\pi\) |
0.558109 | + | 0.829767i | \(0.311527\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2867 | − | 18.3883i | −0.811926 | − | 1.21513i | −0.973594 | − | 0.228288i | \(-0.926687\pi\) |
0.161668 | − | 0.986845i | \(-0.448313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.76829 | + | 11.5117i | −0.313731 | + | 0.757413i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.609526 | + | 1.47153i | 0.0399314 | + | 0.0964028i | 0.942587 | − | 0.333961i | \(-0.108385\pi\) |
−0.902656 | + | 0.430364i | \(0.858385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.95915 | − | 9.84930i | 0.127801 | − | 0.642497i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.4225 | + | 36.5508i | −1.58641 | + | 2.37423i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.07033 | + | 1.07033i | −0.0692337 | + | 0.0692337i | −0.740876 | − | 0.671642i | \(-0.765589\pi\) |
0.671642 | + | 0.740876i | \(0.265589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5889 | + | 11.5889i | 0.746509 | + | 0.746509i | 0.973822 | − | 0.227313i | \(-0.0729940\pi\) |
−0.227313 | + | 0.973822i | \(0.572994\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.2304 | + | 7.50390i | 0.720429 | + | 0.481375i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.58626 | + | 1.50900i | 0.484669 | + | 0.0964066i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.49121 | + | 3.93139i | −0.603911 | + | 0.250148i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.5997 | − | 7.29002i | −1.11533 | − | 0.461986i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.20465 | − | 2.14128i | 0.202276 | − | 0.135156i | −0.450307 | − | 0.892874i | \(-0.648685\pi\) |
0.652583 | + | 0.757717i | \(0.273685\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.04481 | + | 5.25260i | 0.0656865 | + | 0.330228i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −28.9889 | −1.81535 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.4093 | −0.774071 | −0.387035 | − | 0.922065i | \(-0.626501\pi\) | ||||
−0.387035 | + | 0.922065i | \(0.626501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.05120 | + | 5.28475i | 0.0653185 | + | 0.328378i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0406 | − | 6.70893i | 0.621499 | − | 0.415272i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.63628 | + | 0.677769i | 0.100897 | + | 0.0417930i | 0.432561 | − | 0.901605i | \(-0.357610\pi\) |
−0.331664 | + | 0.943398i | \(0.607610\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.5121 | − | 9.73904i | 1.44434 | − | 0.598264i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.5989 | + | 4.49521i | 1.38303 | + | 0.275102i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.2384 | + | 17.5320i | 1.59978 | + | 1.06894i | 0.951547 | + | 0.307505i | \(0.0994939\pi\) |
0.648238 | + | 0.761438i | \(0.275506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.58765 | − | 1.58765i | −0.0964427 | − | 0.0964427i | 0.657239 | − | 0.753682i | \(-0.271724\pi\) |
−0.753682 | + | 0.657239i | \(0.771724\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.2523 | + | 10.2523i | −0.620497 | + | 0.620497i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.45661 | − | 8.16640i | 0.329046 | − | 0.492452i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.970436 | − | 4.87871i | 0.0583079 | − | 0.293133i | −0.940618 | − | 0.339466i | \(-0.889754\pi\) |
0.998926 | + | 0.0463330i | \(0.0147535\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.50646 | + | 8.46533i | 0.209926 | + | 0.506806i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.758051 | + | 1.83010i | −0.0452216 | + | 0.109175i | −0.944876 | − | 0.327428i | \(-0.893818\pi\) |
0.899655 | + | 0.436602i | \(0.143818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.42628 | − | 8.12100i | −0.322559 | − | 0.482744i | 0.634385 | − | 0.773018i | \(-0.281254\pi\) |
−0.956944 | + | 0.290274i | \(0.906254\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −37.2177 | + | 7.40306i | −2.20459 | + | 0.438519i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 25.9039i | − | 1.52906i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31674i | 0.371573i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.6476 | + | 4.70380i | −1.38625 | + | 0.275742i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.65651 | − | 9.96217i | −0.388877 | − | 0.581996i | 0.584446 | − | 0.811432i | \(-0.301312\pi\) |
−0.973324 | + | 0.229436i | \(0.926312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1804 | − | 24.5776i | 0.592725 | − | 1.43096i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.61746 | + | 11.1475i | 0.267932 | + | 0.646845i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.21576 | + | 6.11205i | −0.0703093 | + | 0.353469i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.73921 | − | 4.09952i | 0.157885 | − | 0.236292i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.7792 | − | 29.7792i | 1.71077 | − | 1.71077i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.1932 | − | 22.1932i | −1.27078 | − | 1.27078i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.59801 | + | 6.41318i | 0.547787 | + | 0.366020i | 0.798456 | − | 0.602053i | \(-0.205650\pi\) |
−0.250669 | + | 0.968073i | \(0.580650\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.6309 | + | 3.10919i | 0.889213 | + | 0.176875i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.5704 | + | 8.93477i | −1.22315 | + | 0.506644i | −0.898409 | − | 0.439160i | \(-0.855276\pi\) |
−0.324738 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.66011 | − | 0.687642i | −0.0938352 | − | 0.0388678i | 0.335272 | − | 0.942121i | \(-0.391172\pi\) |
−0.429107 | + | 0.903254i | \(0.641172\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −27.9549 | + | 18.6788i | −1.57508 | + | 1.05243i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.90261 | + | 14.5924i | 0.163027 | + | 0.819590i | 0.972584 | + | 0.232550i | \(0.0747069\pi\) |
−0.809558 | + | 0.587040i | \(0.800293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.92478 | −0.275735 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.7977 | 2.05385 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.72825 | − | 13.7158i | −0.151804 | − | 0.763169i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.50261 | − | 6.34944i | 0.527110 | − | 0.352204i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.4449 | + | 10.5396i | 1.40711 | + | 0.582843i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.31673 | − | 2.61648i | 0.348253 | − | 0.144251i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.51285 | − | 1.09657i | −0.303014 | − | 0.0602732i | 0.0412418 | − | 0.999149i | \(-0.486869\pi\) |
−0.344255 | + | 0.938876i | \(0.611869\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.6575 | + | 7.12113i | 0.584029 | + | 0.390236i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.7176 | + | 32.7176i | 1.78755 | + | 1.78755i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.17791 | − | 2.17791i | 0.118638 | − | 0.118638i | −0.645295 | − | 0.763933i | \(-0.723266\pi\) |
0.763933 | + | 0.645295i | \(0.223266\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.6093 | − | 15.8779i | 0.576218 | − | 0.862371i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.729016 | − | 3.66501i | 0.0394784 | − | 0.198471i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.71305 | + | 18.6210i | 0.416466 | + | 1.00544i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.80890 | + | 21.2666i | −0.474255 | + | 1.14495i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.32825 | − | 7.97430i | −0.286036 | − | 0.428083i | 0.660430 | − | 0.750888i | \(-0.270374\pi\) |
−0.946465 | + | 0.322805i | \(0.895374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.63592 | − | 0.325405i | 0.0875689 | − | 0.0174185i | −0.151111 | − | 0.988517i | \(-0.548285\pi\) |
0.238680 | + | 0.971098i | \(0.423285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0403i | 0.749414i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5.92592i | − | 0.315405i | −0.987487 | − | 0.157702i | \(-0.949591\pi\) | ||
0.987487 | − | 0.157702i | \(-0.0504087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.2737 | − | 4.23159i | 1.12909 | − | 0.224590i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.9652 | − | 16.4106i | −0.580340 | − | 0.868539i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0537 | + | 29.1002i | −0.636170 | + | 1.53585i | 0.195573 | + | 0.980689i | \(0.437343\pi\) |
−0.831743 | + | 0.555161i | \(0.812657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.265606 | + | 0.641230i | 0.0139793 | + | 0.0337489i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.73414 | + | 18.7728i | −0.195991 | + | 0.985315i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.31856 | − | 9.45639i | 0.330729 | − | 0.494970i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.9541 | + | 18.9541i | −0.989396 | + | 0.989396i | −0.999944 | − | 0.0105483i | \(-0.996642\pi\) |
0.0105483 | + | 0.999944i | \(0.496642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −43.5722 | − | 43.5722i | −2.26828 | − | 2.26828i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.4068 | + | 9.62634i | 0.747966 | + | 0.499775i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.0597 | + | 4.18903i | 1.09043 | + | 0.216899i | 0.707383 | − | 0.706830i | \(-0.249876\pi\) |
0.383044 | + | 0.923730i | \(0.374876\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.96841 | + | 0.815342i | −0.101648 | + | 0.0421041i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.29437 | − | 2.19300i | −0.272674 | − | 0.112945i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.08942 | + | 2.06428i | −0.158693 | + | 0.106035i | −0.632381 | − | 0.774657i | \(-0.717922\pi\) |
0.473688 | + | 0.880693i | \(0.342922\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.167484 | − | 0.841999i | −0.00858046 | − | 0.0431369i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.3597 | 0.835942 | 0.417971 | − | 0.908460i | \(-0.362741\pi\) | ||||
0.417971 | + | 0.908460i | \(0.362741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.7115 | 0.698800 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.28813 | − | 11.5032i | −0.116312 | − | 0.584742i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.6591 | + | 14.4722i | −1.09816 | + | 0.733768i | −0.966279 | − | 0.257498i | \(-0.917102\pi\) |
−0.131882 | + | 0.991265i | \(0.542102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.83736 | − | 3.24634i | −0.396352 | − | 0.164174i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.1250 | − | 5.85076i | 0.712511 | − | 0.295132i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.4444 | + | 9.43728i | 2.38719 | + | 0.474841i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.68511 | − | 2.46232i | −0.184951 | − | 0.123580i | 0.459648 | − | 0.888101i | \(-0.347976\pi\) |
−0.644599 | + | 0.764521i | \(0.722976\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.2686 | − | 18.2686i | −0.914576 | − | 0.914576i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.30297 | − | 8.30297i | 0.414630 | − | 0.414630i | −0.468718 | − | 0.883348i | \(-0.655284\pi\) |
0.883348 | + | 0.468718i | \(0.155284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.41575 | − | 3.61543i | 0.120337 | − | 0.180097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.866379 | + | 4.35558i | −0.0430507 | + | 0.216431i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00042 | − | 4.82945i | −0.0991573 | − | 0.239387i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9503 | − | 31.2648i | 0.640350 | − | 1.54594i | −0.185857 | − | 0.982577i | \(-0.559506\pi\) |
0.826207 | − | 0.563366i | \(-0.190494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.1588 | − | 40.6460i | −1.33964 | − | 2.00492i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.7641 | − | 3.53351i | 0.874117 | − | 0.173873i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.9628i | 1.02902i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.8806i | 1.65914i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.5325 | + | 3.08960i | −0.758811 | + | 0.150937i | −0.559307 | − | 0.828960i | \(-0.688933\pi\) |
−0.199503 | + | 0.979897i | \(0.563933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.42193 | − | 2.12807i | −0.0693006 | − | 0.103716i | 0.795201 | − | 0.606346i | \(-0.207366\pi\) |
−0.864501 | + | 0.502631i | \(0.832366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.22410 | − | 15.0263i | 0.302626 | − | 0.730604i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.95357 | + | 14.3732i | 0.288791 | + | 0.697203i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.16885 | − | 20.9582i | 0.201745 | − | 1.01424i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.81460 | − | 11.6954i | 0.377292 | − | 0.564658i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.2163 | − | 13.2163i | 0.636606 | − | 0.636606i | −0.313111 | − | 0.949717i | \(-0.601371\pi\) |
0.949717 | + | 0.313111i | \(0.101371\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.42276 | − | 5.42276i | −0.260601 | − | 0.260601i | 0.564697 | − | 0.825298i | \(-0.308993\pi\) |
−0.825298 | + | 0.564697i | \(0.808993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.6001 | − | 11.7600i | −0.843860 | − | 0.563849i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.8911 | − | 2.16638i | −0.520993 | − | 0.103632i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4472 | + | 6.39844i | −0.737255 | + | 0.305381i | −0.719530 | − | 0.694462i | \(-0.755643\pi\) |
−0.0177256 | + | 0.999843i | \(0.505643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.5738 | + | 4.79401i | 0.551132 | + | 0.228286i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.77140 | + | 5.86086i | −0.416742 | + | 0.278458i | −0.746213 | − | 0.665708i | \(-0.768130\pi\) |
0.329471 | + | 0.944166i | \(0.393130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.94664 | − | 24.8684i | −0.234493 | − | 1.17888i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −38.2601 | −1.80964 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.0927 | 0.523498 | 0.261749 | − | 0.965136i | \(-0.415701\pi\) | ||||
0.261749 | + | 0.965136i | \(0.415701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.90267 | + | 24.6474i | 0.230857 | + | 1.16060i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.48258 | + | 2.99516i | −0.210610 | + | 0.140725i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.7405 | + | 6.10570i | 0.691044 | + | 0.286240i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.2978 | − | 8.40761i | 0.949490 | − | 0.393292i | 0.146451 | − | 0.989218i | \(-0.453215\pi\) |
0.803039 | + | 0.595926i | \(0.203215\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.7452 | − | 3.72866i | −0.874953 | − | 0.174039i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.1714 | − | 12.8099i | −0.892903 | − | 0.596619i | 0.0222379 | − | 0.999753i | \(-0.492921\pi\) |
−0.915141 | + | 0.403134i | \(0.867921\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.19024 | − | 9.19024i | −0.427107 | − | 0.427107i | 0.460535 | − | 0.887642i | \(-0.347658\pi\) |
−0.887642 | + | 0.460535i | \(0.847658\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.3571 | − | 11.3571i | 0.526673 | − | 0.526673i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.319653 | + | 0.478395i | −0.0147918 | + | 0.0221375i | −0.838792 | − | 0.544452i | \(-0.816738\pi\) |
0.824000 | + | 0.566590i | \(0.191738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.14580 | + | 30.8970i | −0.283787 | + | 1.42669i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.2668 | − | 48.9284i | −0.933845 | − | 2.25450i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.83045 | + | 4.41910i | −0.0841642 | + | 0.203190i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3141 | + | 16.9328i | 0.519128 | + | 0.776930i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 40.4255 | − | 8.04114i | 1.85096 | − | 0.368178i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.0010i | 1.50786i | 0.656957 | + | 0.753928i | \(0.271843\pi\) | ||||
−0.656957 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.08268i | − | 0.277346i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.3710 | + | 3.05748i | −0.699404 | + | 0.139120i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.7405 | + | 22.0607i | 0.669332 | + | 1.00173i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4792 | − | 34.9559i | 0.656116 | − | 1.58400i | −0.147637 | − | 0.989042i | \(-0.547167\pi\) |
0.803753 | − | 0.594963i | \(-0.202833\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.60049 | − | 8.69235i | −0.162820 | − | 0.393081i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.13764 | + | 20.8013i | −0.186729 | + | 0.938750i | 0.767813 | + | 0.640674i | \(0.221345\pi\) |
−0.954542 | + | 0.298076i | \(0.903655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.33391 | − | 6.48615i | 0.195189 | − | 0.292122i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.0637 | − | 23.0637i | 1.03663 | − | 1.03663i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.4424 | + | 10.4424i | 0.468404 | + | 0.468404i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.2079 | − | 22.8570i | −1.53135 | − | 1.02322i | −0.982275 | − | 0.187448i | \(-0.939979\pi\) |
−0.549079 | − | 0.835770i | \(-0.685021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.679177 | − | 0.135097i | −0.0303434 | − | 0.00603568i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.6755 | + | 6.90723i | −0.743525 | + | 0.307978i | −0.722097 | − | 0.691792i | \(-0.756821\pi\) |
−0.0214284 | + | 0.999770i | \(0.506821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.8157 | − | 17.7349i | −1.90528 | − | 0.789191i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.0776 | + | 11.4109i | −0.758444 | + | 0.506776i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.55107 | − | 22.8798i | −0.201722 | − | 1.01413i | −0.940401 | − | 0.340069i | \(-0.889550\pi\) |
0.738678 | − | 0.674058i | \(-0.235450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.74328 | 0.342543 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.0185 | −1.10459 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.42142 | − | 17.2007i | −0.150766 | − | 0.757952i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.51513 | + | 3.68509i | −0.242555 | + | 0.162070i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −38.9183 | − | 16.1205i | −1.70832 | − | 0.707610i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.8128 | + | 10.6920i | −1.13088 | + | 0.468426i | −0.868080 | − | 0.496424i | \(-0.834646\pi\) |
−0.262801 | + | 0.964850i | \(0.584646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.91430 | + | 0.778602i | 0.171160 | + | 0.0340459i | 0.279926 | − | 0.960021i | \(-0.409690\pi\) |
−0.108766 | + | 0.994067i | \(0.534690\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 23.8978 | + | 15.9680i | 1.04299 | + | 0.696901i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.18543 | + | 4.18543i | 0.182320 | + | 0.182320i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5004 | − | 11.5004i | 0.500015 | − | 0.500015i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.9370 | − | 35.8242i | 1.03878 | − | 1.55464i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.70486 | + | 28.6802i | −0.247105 | + | 1.24228i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4960 | − | 37.4107i | −0.669952 | − | 1.61741i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.5252 | + | 30.2384i | −0.540501 | + | 1.30488i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.83838 | − | 4.24794i | −0.122258 | − | 0.182972i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.5841 | − | 4.69116i | 1.01396 | − | 0.201689i | 0.339974 | − | 0.940435i | \(-0.389582\pi\) |
0.673984 | + | 0.738746i | \(0.264582\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 24.1337i | − | 1.03568i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 30.3072i | − | 1.29822i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.9505 | − | 3.76948i | 0.810263 | − | 0.161171i | 0.227463 | − | 0.973787i | \(-0.426957\pi\) |
0.582800 | + | 0.812615i | \(0.301957\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.2409 | − | 42.2656i | −1.20529 | − | 1.80385i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.90773 | − | 9.43410i | 0.166475 | − | 0.401906i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.6037 | + | 30.4279i | 0.535962 | + | 1.29393i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.38329 | − | 22.0363i | 0.186060 | − | 0.935387i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.35372 | + | 13.9988i | −0.396330 | + | 0.593149i | −0.974944 | − | 0.222452i | \(-0.928594\pi\) |
0.578614 | + | 0.815602i | \(0.303594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.93564 | + | 3.93564i | −0.166460 | + | 0.166460i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5392 | + | 13.5392i | 0.571627 | + | 0.571627i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.2172 | − | 22.1950i | −1.39994 | − | 0.935409i | −0.999821 | − | 0.0189460i | \(-0.993969\pi\) |
−0.400119 | − | 0.916463i | \(-0.631031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.6102 | − | 4.09962i | −0.867077 | − | 0.172472i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.79340 | + | 1.15706i | −0.117312 | + | 0.0485922i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.9275 | + | 6.18318i | 0.625794 | + | 0.259212i | 0.672965 | − | 0.739674i | \(-0.265020\pi\) |
−0.0471707 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.6636 | − | 7.12517i | 0.446257 | − | 0.298179i | −0.312064 | − | 0.950061i | \(-0.601020\pi\) |
0.758320 | + | 0.651882i | \(0.226020\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.49596 | − | 17.5754i | −0.146046 | − | 0.734223i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.3535 | 0.515175 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.6883 | −0.778002 | −0.389001 | − | 0.921237i | \(-0.627180\pi\) | ||||
−0.389001 | + | 0.921237i | \(0.627180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.82419 | + | 29.2802i | 0.242045 | + | 1.21684i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8670 | + | 7.92928i | −0.492327 | + | 0.328962i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.5299 | − | 6.43271i | −0.643184 | − | 0.266416i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.0648 | − | 14.5243i | 1.44975 | − | 0.600506i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.9938 | − | 3.38028i | −0.701409 | − | 0.139519i | −0.168513 | − | 0.985699i | \(-0.553896\pi\) |
−0.532896 | + | 0.846180i | \(0.678896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.44237 | + | 4.30465i | 0.265453 | + | 0.177370i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.5322 | + | 31.5322i | 1.29706 | + | 1.29706i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.79685 | + | 5.79685i | −0.238048 | + | 0.238048i | −0.816042 | − | 0.577993i | \(-0.803836\pi\) |
0.577993 | + | 0.816042i | \(0.303836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0664 | + | 18.0586i | −0.494673 | + | 0.740330i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.2315 | − | 76.5739i | 0.623384 | − | 3.13396i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.07554 | − | 14.6677i | −0.248240 | − | 0.599304i | 0.749815 | − | 0.661648i | \(-0.230143\pi\) |
−0.998055 | + | 0.0623435i | \(0.980143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.70092 | + | 23.4201i | −0.395709 | + | 0.955325i | 0.592963 | + | 0.805230i | \(0.297958\pi\) |
−0.988672 | + | 0.150095i | \(0.952042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.6333 | + | 62.3087i | 1.69544 | + | 2.53741i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.6580 | − | 4.10914i | 0.839868 | − | 0.167060i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.795354i | 0.0322824i | 0.999870 | + | 0.0161412i | \(0.00513813\pi\) | ||||
−0.999870 | + | 0.0161412i | \(0.994862\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 14.4117i | − | 0.583991i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.57000 | + | 1.50577i | −0.306249 | + | 0.0609168i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.28756 | + | 3.42358i | 0.0923939 | + | 0.138277i | 0.874787 | − | 0.484508i | \(-0.161001\pi\) |
−0.782393 | + | 0.622785i | \(0.786001\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.3350 | + | 99.7915i | −1.66679 | + | 4.02398i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.1612 | − | 39.0166i | −0.650626 | − | 1.57075i | −0.811872 | − | 0.583836i | \(-0.801551\pi\) |
0.161246 | − | 0.986914i | \(-0.448449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.87121 | + | 14.4345i | −0.115404 | + | 0.580173i | 0.879202 | + | 0.476448i | \(0.158076\pi\) |
−0.994606 | + | 0.103725i | \(0.966924\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.43154 | + | 12.6187i | −0.338346 | + | 0.506370i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.2069 | − | 12.2069i | 0.489059 | − | 0.489059i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.4862 | + | 18.4862i | 0.739448 | + | 0.739448i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.8401 | + | 13.9249i | 0.832274 | + | 0.556107i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.12102 | + | 1.61537i | 0.323806 | + | 0.0644090i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.2699 | − | 14.6093i | 1.40407 | − | 0.581586i | 0.453268 | − | 0.891374i | \(-0.350258\pi\) |
0.950806 | + | 0.309788i | \(0.100258\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 59.2091 | + | 24.5252i | 2.35335 | + | 0.974790i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.785496 | + | 0.524852i | −0.0311715 | + | 0.0208281i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.15979 | − | 5.83067i | −0.0459526 | − | 0.231020i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.1296 | 1.38971 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.8042 | 0.466237 | 0.233119 | − | 0.972448i | \(-0.425107\pi\) | ||||
0.233119 | + | 0.972448i | \(0.425107\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.84656 | + | 14.3106i | 0.112257 | + | 0.564355i | 0.995445 | + | 0.0953360i | \(0.0303926\pi\) |
−0.883188 | + | 0.469019i | \(0.844607\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.0941 | + | 11.4219i | −0.673080 | + | 0.449737i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.76078 | − | 2.80041i | −0.265794 | − | 0.110095i | 0.245807 | − | 0.969319i | \(-0.420947\pi\) |
−0.511600 | + | 0.859224i | \(0.670947\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.2337 | + | 6.72422i | −0.637229 | + | 0.263949i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.7251 | + | 2.13336i | 0.420351 | + | 0.0836130i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.41350 | − | 6.28990i | −0.368379 | − | 0.246143i | 0.357578 | − | 0.933883i | \(-0.383603\pi\) |
−0.725957 | + | 0.687741i | \(0.758603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.8965 | − | 11.8965i | −0.464833 | − | 0.464833i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.0248 | − | 13.0248i | 0.508144 | − | 0.508144i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.27371 | − | 9.38927i | 0.244389 | − | 0.365754i | −0.688914 | − | 0.724843i | \(-0.741912\pi\) |
0.933303 | + | 0.359089i | \(0.116912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.0233980 | − | 0.117629i | 0.000910075 | − | 0.00457526i | −0.980328 | − | 0.197377i | \(-0.936758\pi\) |
0.981238 | + | 0.192802i | \(0.0617576\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.52632 | + | 20.5843i | 0.331135 | + | 0.799430i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.8798 | + | 26.2662i | −0.421901 | + | 1.01856i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.44136 | − | 5.15036i | −0.133250 | − | 0.199423i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.5904 | + | 4.49352i | −0.873396 | + | 0.173729i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.7306i | 0.800298i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.1783i | 1.58731i | 0.608371 | + | 0.793653i | \(0.291823\pi\) | ||||
−0.608371 | + | 0.793653i | \(0.708177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.2977 | − | 5.42984i | 1.05069 | − | 0.208995i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.0241 | + | 19.4920i | 0.500557 | + | 0.749137i | 0.992599 | − | 0.121435i | \(-0.0387495\pi\) |
−0.492042 | + | 0.870571i | \(0.663749\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.91289 | + | 16.6892i | −0.265292 | + | 0.640472i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.6204 | − | 30.4683i | −0.483615 | − | 1.16755i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.94439 | + | 14.8024i | −0.112664 | + | 0.566399i | 0.882677 | + | 0.469980i | \(0.155739\pi\) |
−0.995341 | + | 0.0964191i | \(0.969261\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.8862 | + | 44.7278i | −1.14189 | + | 1.70896i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −44.3956 | + | 44.3956i | −1.69380 | + | 1.69380i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.8309 | − | 13.8309i | −0.526917 | − | 0.526917i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.4953 | + | 15.6991i | 0.893805 | + | 0.597221i | 0.915400 | − | 0.402546i | \(-0.131875\pi\) |
−0.0215953 | + | 0.999767i | \(0.506875\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21.7803 | + | 4.33236i | 0.827364 | + | 0.164573i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34.4451 | − | 14.2676i | 1.30658 | − | 0.541202i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.7761 | − | 15.2332i | −1.39299 | − | 0.576997i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.75975 | − | 2.51218i | 0.142207 | − | 0.0950194i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.68037 | − | 8.44781i | −0.0634668 | − | 0.319069i | 0.935990 | − | 0.352027i | \(-0.114507\pi\) |
−0.999457 | + | 0.0329575i | \(0.989507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8388 | 0.408792 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.5096 | −1.07373 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.15559 | − | 30.9462i | −0.231505 | − | 1.16385i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.70687 | − | 6.48592i | 0.364549 | − | 0.243584i | −0.359782 | − | 0.933036i | \(-0.617149\pi\) |
0.724331 | + | 0.689453i | \(0.242149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 72.3823 | + | 29.9817i | 2.71455 | + | 1.12440i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.34231 | − | 1.79865i | 0.162621 | − | 0.0673598i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.1811 | − | 3.01970i | −0.567739 | − | 0.112930i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.57303 | + | 2.38743i | 0.133437 | + | 0.0891600i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6553 | − | 22.6553i | −0.844899 | − | 0.844899i | 0.144592 | − | 0.989491i | \(-0.453813\pi\) |
−0.989491 | + | 0.144592i | \(0.953813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.44310 | − | 8.44310i | 0.314438 | − | 0.314438i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.8498 | − | 38.6869i | 0.961364 | − | 1.43878i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.21621 | + | 11.1416i | −0.0823080 | + | 0.413790i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.7776 | + | 35.6764i | 0.548072 | + | 1.32316i | 0.918911 | + | 0.394466i | \(0.129070\pi\) |
−0.370839 | + | 0.928697i | \(0.620930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.3059 | − | 39.3660i | 0.603923 | − | 1.45800i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.20931 | − | 6.29968i | −0.155687 | − | 0.233002i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.4550 | + | 2.47746i | −0.460037 | + | 0.0915071i | −0.419668 | − | 0.907678i | \(-0.637853\pi\) |
−0.0403693 | + | 0.999185i | \(0.512853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 21.9591i | − | 0.809972i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 30.5615i | − | 1.12575i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.370926 | + | 0.0737817i | −0.0136447 | + | 0.00271410i | −0.201908 | − | 0.979405i | \(-0.564714\pi\) |
0.188263 | + | 0.982119i | \(0.439714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.2034 | + | 24.2500i | 0.595245 | + | 0.890847i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5484 | + | 25.4660i | −0.386983 | + | 0.934259i | 0.603593 | + | 0.797292i | \(0.293735\pi\) |
−0.990576 | + | 0.136966i | \(0.956265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.1119 | + | 38.8975i | 0.590294 | + | 1.42510i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.62354 | + | 33.2988i | −0.242343 | + | 1.21834i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.3167 | − | 22.9231i | 0.559661 | − | 0.837591i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.7123 | − | 33.7123i | 1.23018 | − | 1.23018i | 0.266286 | − | 0.963894i | \(-0.414203\pi\) |
0.963894 | − | 0.266286i | \(-0.0857967\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.73712 | − | 7.73712i | −0.281956 | − | 0.281956i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.93274 | + | 3.29595i | 0.179521 | + | 0.119952i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.880215 | − | 0.175086i | −0.0319920 | − | 0.00636360i | 0.179068 | − | 0.983837i | \(-0.442692\pi\) |
−0.211060 | + | 0.977473i | \(0.567692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.0467 | − | 5.81835i | 0.509864 | − | 0.211193i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.8419 | + | 10.7040i | 0.936766 | + | 0.388021i | 0.798241 | − | 0.602338i | \(-0.205764\pi\) |
0.138525 | + | 0.990359i | \(0.455764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.1569 | − | 11.4639i | 0.621121 | − | 0.415020i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.0794 | + | 50.6724i | 0.364420 | + | 1.83206i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.4463 | −0.738273 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.4304 | −1.09735 | −0.548674 | − | 0.836036i | \(-0.684867\pi\) | ||||
−0.548674 | + | 0.836036i | \(0.684867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.87294 | + | 34.5526i | 0.247523 | + | 1.24438i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.79837 | − | 5.21070i | 0.280488 | − | 0.187416i | −0.407366 | − | 0.913265i | \(-0.633553\pi\) |
0.687854 | + | 0.725849i | \(0.258553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.96352 | − | 3.29860i | −0.286058 | − | 0.118489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.1327 | − | 5.85396i | 0.507008 | − | 0.210010i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −51.1056 | − | 10.1655i | −1.83105 | − | 0.364218i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.9122 | − | 7.95949i | −0.426253 | − | 0.284813i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.86823 | − | 9.86823i | −0.352662 | − | 0.352662i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −41.2089 | + | 41.2089i | −1.47081 | + | 1.47081i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4919 | + | 29.1717i | −0.694813 | + | 1.03986i | 0.301450 | + | 0.953482i | \(0.402529\pi\) |
−0.996262 | + | 0.0863785i | \(0.972471\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.980928 | − | 4.93146i | 0.0349220 | − | 0.175565i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.47512 | − | 13.2181i | −0.194673 | − | 0.469982i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.23134 | + | 22.2864i | −0.327815 | + | 0.791414i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −40.1398 | − | 60.0734i | −1.42361 | − | 2.13058i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.1662 | − | 2.22109i | 0.395526 | − | 0.0786751i | 0.00667994 | − | 0.999978i | \(-0.497874\pi\) |
0.388846 | + | 0.921303i | \(0.372874\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.5066i | − | 0.371698i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 41.0658i | − | 1.45099i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.36769 | + | 1.46552i | −0.260000 | + | 0.0517172i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.58136 | + | 14.3395i | 0.337699 | + | 0.505402i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.2839 | − | 82.7687i | 1.20685 | − | 2.91360i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.82483 | − | 9.23396i | −0.134474 | − | 0.324649i | 0.842271 | − | 0.539055i | \(-0.181218\pi\) |
−0.976745 | + | 0.214406i | \(0.931218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.50273 | − | 47.7735i | 0.333686 | − | 1.67755i | −0.341482 | − | 0.939888i | \(-0.610929\pi\) |
0.675168 | − | 0.737664i | \(-0.264071\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.54134 | + | 5.29999i | −0.124200 | + | 0.185879i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.32094 | + | 7.32094i | −0.256441 | + | 0.256441i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.01296 | − | 7.01296i | −0.245352 | − | 0.245352i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.4856 | + | 14.3562i | 0.750768 | + | 0.501647i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.9146 | − | 2.76779i | −0.485623 | − | 0.0965965i | −0.0537945 | − | 0.998552i | \(-0.517132\pi\) |
−0.431829 | + | 0.901956i | \(0.642132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.1742 | + | 17.4691i | −1.47010 | + | 0.608935i | −0.966882 | − | 0.255225i | \(-0.917850\pi\) |
−0.503217 | + | 0.864160i | \(0.667850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.7608 | − | 10.6705i | −0.896876 | − | 0.371498i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.5286 | − | 12.3804i | 0.644302 | − | 0.430509i | −0.190025 | − | 0.981779i | \(-0.560857\pi\) |
0.834326 | + | 0.551271i | \(0.185857\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.53766 | + | 42.9217i | 0.296525 | + | 1.49073i | 0.785733 | + | 0.618565i | \(0.212286\pi\) |
−0.489208 | + | 0.872167i | \(0.662714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.1218 | −0.489881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.09256 | 0.280391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.148664 | + | 0.747383i | 0.00514472 | + | 0.0258643i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.80471 | − | 5.88312i | 0.304335 | − | 0.203350i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.4108 | − | 13.0108i | −1.08442 | − | 0.449182i | −0.232364 | − | 0.972629i | \(-0.574646\pi\) |
−0.852059 | + | 0.523446i | \(0.824646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.5300 | + | 8.91801i | −0.742414 | + | 0.307518i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.51560 | + | 1.09712i | 0.189967 | + | 0.0377868i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.7926 | + | 12.5568i | 0.646487 | + | 0.431969i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.1402 | + | 10.1402i | 0.348421 | + | 0.348421i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.6069 | + | 19.6069i | −0.672906 | + | 0.672906i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.65280 | − | 5.46680i | 0.125216 | − | 0.187400i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.2217 | + | 51.3880i | −0.349984 | + | 1.75949i | 0.258583 | + | 0.965989i | \(0.416744\pi\) |
−0.608568 | + | 0.793502i | \(0.708256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.8810 | + | 62.4822i | 0.885111 | + | 2.13685i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.90193 | − | 14.2485i | 0.201606 | − | 0.486720i | −0.790448 | − | 0.612529i | \(-0.790152\pi\) |
0.992055 | + | 0.125808i | \(0.0401524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.4534 | + | 48.5700i | 1.10730 | + | 1.65719i | 0.622747 | + | 0.782423i | \(0.286017\pi\) |
0.484550 | + | 0.874764i | \(0.338983\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −72.1270 | + | 14.3470i | −2.45808 | + | 0.488943i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.8866i | 1.11947i | 0.828671 | + | 0.559736i | \(0.189098\pi\) | ||||
−0.828671 | + | 0.559736i | \(0.810902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.3552i | 1.57612i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.5884 | − | 3.49855i | 0.597334 | − | 0.118817i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.7512 | − | 26.5666i | −0.602169 | − | 0.901209i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6090 | − | 32.8551i | 0.461124 | − | 1.11325i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4444 | + | 39.7004i | 0.556560 | + | 1.34365i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.311417 | + | 1.56560i | −0.0105278 | + | 0.0529269i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.14533 | + | 9.19714i | −0.207513 | + | 0.310565i | −0.920597 | − | 0.390513i | \(-0.872298\pi\) |
0.713084 | + | 0.701078i | \(0.247298\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.0520 | + | 24.0520i | −0.811255 | + | 0.811255i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.2198 | + | 11.2198i | 0.378006 | + | 0.378006i | 0.870382 | − | 0.492376i | \(-0.163872\pi\) |
−0.492376 | + | 0.870382i | \(0.663872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.8483 | − | 19.9440i | −1.00447 | − | 0.671168i | −0.0594714 | − | 0.998230i | \(-0.518941\pi\) |
−0.945003 | + | 0.327062i | \(0.893941\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −74.0727 | − | 14.7340i | −2.48993 | − | 0.495277i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.5314 | + | 13.4749i | −1.09230 | + | 0.452444i | −0.854807 | − | 0.518946i | \(-0.826324\pi\) |
−0.237489 | + | 0.971390i | \(0.576324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.594236 | − | 0.246141i | −0.0199300 | − | 0.00825529i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.43891 | − | 1.62963i | 0.0817067 | − | 0.0545947i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.68314 | − | 13.4891i | −0.0897878 | − | 0.451394i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0167 | 1.20391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.6918 | 0.590713 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.843195 | + | 4.23903i | 0.0281221 | + | 0.141379i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.1388 | − | 14.7927i | 0.737551 | − | 0.492816i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.9319 | − | 5.35655i | −0.430346 | − | 0.178255i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.5358 | + | 10.1631i | −0.815597 | + | 0.337831i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.0725 | + | 9.76113i | 1.62943 | + | 0.324113i | 0.923331 | − | 0.384004i | \(-0.125455\pi\) |
0.706095 | + | 0.708117i | \(0.250455\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −62.4080 | − | 41.6997i | −2.06994 | − | 1.38309i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.673519 | − | 0.673519i | −0.0223147 | − | 0.0223147i | 0.695861 | − | 0.718176i | \(-0.255023\pi\) |
−0.718176 | + | 0.695861i | \(0.755023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.79066 | − | 9.79066i | 0.324024 | − | 0.324024i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −49.5032 | + | 74.0868i | −1.63653 | + | 2.44923i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.23468 | − | 11.2345i | 0.0737955 | − | 0.370995i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.8450 | + | 45.4958i | 0.621639 | + | 1.50077i | 0.849778 | + | 0.527140i | \(0.176736\pi\) |
−0.228139 | + | 0.973628i | \(0.573264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.5411 | − | 30.2768i | 0.413242 | − | 0.997654i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.26185 | − | 13.8613i | −0.304857 | − | 0.456251i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8262 | + | 2.35238i | −0.388843 | + | 0.0773456i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 28.4038i | − | 0.932904i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.0292i | 1.21489i | 0.794362 | + | 0.607445i | \(0.207805\pi\) | ||||
−0.794362 | + | 0.607445i | \(0.792195\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3897 | − | 2.06664i | 0.340510 | − | 0.0677316i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.8250 | + | 55.1124i | 1.20559 | + | 1.80430i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.06323 | − | 19.4664i | 0.263696 | − | 0.636618i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0321 | − | 31.4623i | −0.425740 | − | 1.02783i | −0.980624 | − | 0.195900i | \(-0.937237\pi\) |
0.554884 | − | 0.831928i | \(-0.312763\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.995217 | + | 5.00329i | −0.0324777 | + | 0.163276i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.1954 | − | 21.2450i | 0.462758 | − | 0.692566i | −0.524551 | − | 0.851379i | \(-0.675767\pi\) |
0.987309 | + | 0.158813i | \(0.0507666\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.3504 | + | 22.3504i | −0.727831 | + | 0.727831i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.4749 | + | 27.4749i | 0.893758 | + | 0.893758i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.8404 | + | 29.2932i | 1.42462 | + | 0.951902i | 0.998892 | + | 0.0470518i | \(0.0149826\pi\) |
0.425730 | + | 0.904850i | \(0.360017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.57321 | − | 1.70532i | −0.278298 | − | 0.0553570i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.0236 | − | 16.1641i | 1.26543 | − | 0.524157i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.18380 | + | 0.904560i | 0.0707403 | + | 0.0293016i | 0.417773 | − | 0.908551i | \(-0.362811\pi\) |
−0.347033 | + | 0.937853i | \(0.612811\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.3960 | + | 10.9555i | −0.530562 | + | 0.354510i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.72761 | + | 13.7126i | 0.0881711 | + | 0.443266i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.6250 | −1.18268 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7205 | 0.894210 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.7945 | − | 64.3221i | −0.412296 | − | 2.07275i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.3153 | − | 18.2515i | 0.879312 | − | 0.587537i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.4518 | + | 18.4125i | 1.42947 | + | 0.592107i | 0.957221 | − | 0.289357i | \(-0.0934415\pi\) |
0.472251 | + | 0.881464i | \(0.343441\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.6794 | + | 15.1931i | −1.17831 | + | 0.488074i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.20968 | + | 1.63301i | 0.263461 | + | 0.0524057i | 0.325053 | − | 0.945696i | \(-0.394618\pi\) |
−0.0615920 | + | 0.998101i | \(0.519618\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.1059 | + | 14.1025i | 0.676625 | + | 0.452106i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.9425 | − | 22.9425i | −0.734749 | − | 0.734749i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.9697 | − | 13.9697i | 0.446930 | − | 0.446930i | −0.447403 | − | 0.894333i | \(-0.647651\pi\) |
0.894333 | + | 0.447403i | \(0.147651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.30447 | + | 13.9251i | −0.297372 | + | 0.445049i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.57607 | − | 48.1421i | 0.305740 | − | 1.53706i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.1142 | − | 43.7315i | −0.577753 | − | 1.39482i | −0.894825 | − | 0.446417i | \(-0.852700\pi\) |
0.317072 | − | 0.948401i | \(-0.397300\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.7788 | − | 45.3361i | 0.598344 | − | 1.44453i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.7839 | − | 16.1392i | −0.343255 | − | 0.513718i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.90061 | + | 1.17370i | −0.187628 | + | 0.0373216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.8761i | 0.472553i | 0.971686 | + | 0.236277i | \(0.0759272\pi\) | ||||
−0.971686 | + | 0.236277i | \(0.924073\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.9574i | 0.506392i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −84.2638 | + | 16.7611i | −2.67134 | + | 0.531363i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6104 | − | 26.3559i | −0.557728 | − | 0.834698i | 0.440276 | − | 0.897863i | \(-0.354881\pi\) |
−0.998003 | + | 0.0631644i | \(0.979881\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.66878 | − | 13.6856i | 0.179352 | − | 0.432994i |
(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 | 512.2.i.b.97.1 | 56 | ||
4.3 | odd | 2 | 512.2.i.a.97.7 | 56 | |||
8.3 | odd | 2 | 256.2.i.a.177.1 | 56 | |||
8.5 | even | 2 | 64.2.i.a.21.4 | ✓ | 56 | ||
24.5 | odd | 2 | 576.2.bd.a.469.4 | 56 | |||
64.3 | odd | 16 | 512.2.i.a.417.7 | 56 | |||
64.29 | even | 16 | 64.2.i.a.61.4 | yes | 56 | ||
64.35 | odd | 16 | 256.2.i.a.81.1 | 56 | |||
64.61 | even | 16 | inner | 512.2.i.b.417.1 | 56 | ||
192.29 | odd | 16 | 576.2.bd.a.253.4 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.2.i.a.21.4 | ✓ | 56 | 8.5 | even | 2 | ||
64.2.i.a.61.4 | yes | 56 | 64.29 | even | 16 | ||
256.2.i.a.81.1 | 56 | 64.35 | odd | 16 | |||
256.2.i.a.177.1 | 56 | 8.3 | odd | 2 | |||
512.2.i.a.97.7 | 56 | 4.3 | odd | 2 | |||
512.2.i.a.417.7 | 56 | 64.3 | odd | 16 | |||
512.2.i.b.97.1 | 56 | 1.1 | even | 1 | trivial | ||
512.2.i.b.417.1 | 56 | 64.61 | even | 16 | inner | ||
576.2.bd.a.253.4 | 56 | 192.29 | odd | 16 | |||
576.2.bd.a.469.4 | 56 | 24.5 | odd | 2 |