Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1264,2,Mod(735,1264)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1264, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1264.735");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1264 = 2^{4} \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1264.n (of order \(6\), 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: | \(10.0930908155\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 767.1 | ||
Character | \(\chi\) | \(=\) | 1264.767 |
Dual form | 1264.2.n.i.735.1 |
$q$-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 \(\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times\).
\(n\) | \(159\) | \(161\) | \(949\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.60192 | − | 2.77460i | −0.924867 | − | 1.60192i | −0.791774 | − | 0.610814i | \(-0.790842\pi\) |
−0.133093 | − | 0.991104i | \(-0.542491\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.45498 | + | 2.52010i | −0.650688 | + | 1.12702i | 0.332268 | + | 0.943185i | \(0.392186\pi\) |
−0.982956 | + | 0.183839i | \(0.941147\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.195200 | − | 0.338096i | 0.0737785 | − | 0.127788i | −0.826776 | − | 0.562531i | \(-0.809828\pi\) |
0.900554 | + | 0.434743i | \(0.143161\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.63228 | + | 6.29129i | −1.21076 | + | 2.09710i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.62575 | − | 2.67068i | −1.39472 | − | 0.805240i | −0.400883 | − | 0.916129i | \(-0.631297\pi\) |
−0.993833 | + | 0.110890i | \(0.964630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.74986 | − | 4.76289i | −0.762673 | − | 1.32099i | −0.941468 | − | 0.337101i | \(-0.890553\pi\) |
0.178796 | − | 0.983886i | \(-0.442780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.32304 | 2.40720 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.03669i | 0.979040i | 0.871992 | + | 0.489520i | \(0.162828\pi\) | ||||
−0.871992 | + | 0.489520i | \(0.837172\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.77958 | + | 1.02744i | 0.408265 | + | 0.235712i | 0.690044 | − | 0.723768i | \(-0.257591\pi\) |
−0.281779 | + | 0.959479i | \(0.590925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.25077 | −0.272941 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.40983 | − | 1.96867i | −0.710999 | − | 0.410495i | 0.100432 | − | 0.994944i | \(-0.467977\pi\) |
−0.811431 | + | 0.584449i | \(0.801311\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.73395 | − | 3.00328i | −0.346789 | − | 0.600657i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.6629 | 2.62943 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.52756 | + | 2.61399i | 0.840746 | + | 0.485405i | 0.857518 | − | 0.514454i | \(-0.172006\pi\) |
−0.0167717 | + | 0.999859i | \(0.505339\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.25404 | + | 3.03342i | 0.943653 | + | 0.544819i | 0.891104 | − | 0.453800i | \(-0.149932\pi\) |
0.0525498 | + | 0.998618i | \(0.483265\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.1128i | 2.97896i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.568024 | + | 0.983847i | 0.0960136 | + | 0.166300i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.16671 | − | 4.71505i | 1.34260 | − | 0.775150i | 0.355411 | − | 0.934710i | \(-0.384341\pi\) |
0.987188 | + | 0.159561i | \(0.0510077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.81008 | + | 15.2595i | −1.41074 | + | 2.44348i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.64388i | − | 0.256731i | −0.991727 | − | 0.128366i | \(-0.959027\pi\) | ||
0.991727 | − | 0.128366i | \(-0.0409731\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.59109 | + | 9.68406i | 0.852634 | + | 1.47680i | 0.878823 | + | 0.477148i | \(0.158329\pi\) |
−0.0261897 | + | 0.999657i | \(0.508337\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.5698 | − | 18.3074i | −1.57565 | − | 2.72911i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.568024 | + | 0.983847i | −0.0828548 | + | 0.143509i | −0.904475 | − | 0.426526i | \(-0.859737\pi\) |
0.821620 | + | 0.570035i | \(0.193070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.42379 | + | 5.93019i | 0.489113 | + | 0.847169i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.2002 | − | 6.46644i | 1.56834 | − | 0.905482i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.76663 | − | 3.90672i | −0.929469 | − | 0.536629i | −0.0428251 | − | 0.999083i | \(-0.513636\pi\) |
−0.886643 | + | 0.462454i | \(0.846969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.4608 | − | 7.77158i | 1.81505 | − | 1.04792i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.58352i | − | 0.872008i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.41419 | − | 5.91355i | −0.444489 | − | 0.769878i | 0.553527 | − | 0.832831i | \(-0.313282\pi\) |
−0.998017 | + | 0.0629529i | \(0.979948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6214i | 1.35993i | 0.733245 | + | 0.679965i | \(0.238005\pi\) | ||||
−0.733245 | + | 0.679965i | \(0.761995\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.41804 | + | 2.45612i | 0.178656 | + | 0.309441i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.0040 | 1.98505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.02785i | − | 0.858589i | −0.903165 | − | 0.429294i | \(-0.858762\pi\) | ||
0.903165 | − | 0.429294i | \(-0.141238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.6146i | 1.51861i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.42312 | −0.287572 | −0.143786 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143786 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.34552 | − | 7.52666i | 0.508604 | − | 0.880928i | −0.491346 | − | 0.870964i | \(-0.663495\pi\) |
0.999950 | − | 0.00996406i | \(-0.00317171\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.55528 | + | 9.62202i | −0.641468 | + | 1.11106i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.80589 | + | 1.04263i | −0.205800 | + | 0.118819i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.66466 | + | 8.47936i | −0.299798 | + | 0.954003i | ||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9900 | − | 19.0353i | −1.22112 | − | 2.11504i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.07404 | + | 2.92950i | 0.556948 | + | 0.321554i | 0.751920 | − | 0.659255i | \(-0.229128\pi\) |
−0.194972 | + | 0.980809i | \(0.562461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.1729 | − | 5.87331i | −1.10340 | − | 0.637050i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 16.7496i | − | 1.79574i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.86283 | 0.621458 | 0.310729 | − | 0.950499i | \(-0.399427\pi\) | ||||
0.310729 | + | 0.950499i | \(0.399427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.14708 | −0.225076 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 19.4372i | − | 2.01554i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.17853 | + | 2.98982i | −0.531306 | + | 0.306750i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3343 | 1.04929 | 0.524644 | − | 0.851321i | \(-0.324198\pi\) | ||||
0.524644 | + | 0.851321i | \(0.324198\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33.6040 | − | 19.4013i | 3.37733 | − | 1.94990i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.37021 | −0.832867 | −0.416433 | − | 0.909166i | \(-0.636720\pi\) | ||||
−0.416433 | + | 0.909166i | \(0.636720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.23535 | − | 7.33584i | −0.417321 | − | 0.722822i | 0.578348 | − | 0.815790i | \(-0.303698\pi\) |
−0.995669 | + | 0.0929686i | \(0.970364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.81986 | − | 3.15208i | 0.177600 | − | 0.307612i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.29855 | + | 16.1056i | 0.898925 | + | 1.55698i | 0.828871 | + | 0.559440i | \(0.188984\pi\) |
0.0700538 | + | 0.997543i | \(0.477683\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.38428 | − | 2.53126i | 0.419937 | − | 0.242451i | −0.275113 | − | 0.961412i | \(-0.588715\pi\) |
0.695051 | + | 0.718961i | \(0.255382\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.1648 | − | 15.1062i | −2.48345 | − | 1.43382i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.88546 | − | 1.08857i | 0.177369 | − | 0.102404i | −0.408687 | − | 0.912675i | \(-0.634013\pi\) |
0.586056 | + | 0.810270i | \(0.300680\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.92248 | − | 5.72875i | 0.925276 | − | 0.534208i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 39.9529 | 3.69365 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.36479 | + | 0.787960i | 0.125110 | + | 0.0722322i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.76504 | + | 15.1815i | 0.796821 | + | 1.38014i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.56112 | + | 2.63337i | −0.411263 | + | 0.237443i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.45838 | −0.398770 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.76729 | − | 13.4533i | 0.689235 | − | 1.19379i | −0.282850 | − | 0.959164i | \(-0.591280\pi\) |
0.972086 | − | 0.234626i | \(-0.0753867\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.9129 | − | 31.0261i | 1.57715 | − | 2.73170i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.47705i | 0.216421i | 0.994128 | + | 0.108210i | \(0.0345120\pi\) | ||||
−0.994128 | + | 0.108210i | \(0.965488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.694749 | − | 0.401113i | 0.0602424 | − | 0.0347809i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.8793 | + | 34.4320i | −1.71094 | + | 2.96343i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.7591i | 1.85900i | 0.368819 | + | 0.929501i | \(0.379762\pi\) | ||||
−0.368819 | + | 0.929501i | \(0.620238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.56919 | − | 2.71791i | 0.133097 | − | 0.230530i | −0.791772 | − | 0.610817i | \(-0.790841\pi\) |
0.924869 | + | 0.380286i | \(0.124175\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.63971 | 0.306519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.3759i | 2.45654i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.1750 | + | 7.60660i | −1.09413 | + | 0.631694i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9693 | − | 18.9993i | 0.904730 | − | 1.56704i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.04383 | + | 1.18001i | 0.167437 | + | 0.0966698i | 0.581377 | − | 0.813634i | \(-0.302514\pi\) |
−0.413940 | + | 0.910304i | \(0.635848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4028 | + | 6.00605i | 0.846567 | + | 0.488766i | 0.859491 | − | 0.511151i | \(-0.170781\pi\) |
−0.0129240 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −25.3960 | − | 14.6624i | −2.05314 | − | 1.18538i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2891 | + | 8.82715i | −1.22805 | + | 0.709014i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.7842i | 1.57895i | 0.613783 | + | 0.789475i | \(0.289647\pi\) | ||||
−0.613783 | + | 0.789475i | \(0.710353\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.0330i | 1.98524i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.33120 | + | 0.768566i | −0.104913 | + | 0.0605715i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.1216 | − | 11.6172i | −1.57605 | − | 0.909931i | −0.995403 | − | 0.0957726i | \(-0.969468\pi\) |
−0.580643 | − | 0.814158i | \(-0.697199\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −43.1261 | − | 24.8988i | −3.35736 | − | 1.93837i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4676 | − | 6.62083i | −0.887391 | − | 0.512335i | −0.0143026 | − | 0.999898i | \(-0.504553\pi\) |
−0.873088 | + | 0.487562i | \(0.837886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.62341 | + | 14.9362i | −0.663339 | + | 1.14894i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.9279 | + | 7.46392i | −0.988620 | + | 0.570780i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.53473i | − | 0.116683i | −0.998297 | − | 0.0583417i | \(-0.981419\pi\) | ||
0.998297 | − | 0.0583417i | \(-0.0185813\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.35386 | −0.102342 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.9385 | + | 18.9460i | −0.822188 | + | 1.42407i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 7.49569i | − | 0.560254i | −0.959963 | − | 0.280127i | \(-0.909623\pi\) | ||
0.959963 | − | 0.280127i | \(-0.0903766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.75853 | + | 13.4382i | −0.576687 | + | 0.998852i | 0.419169 | + | 0.907908i | \(0.362322\pi\) |
−0.995856 | + | 0.0909434i | \(0.971012\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.4701 | − | 17.0146i | 2.17849 | − | 1.25775i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.4413i | 2.01752i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7807 | − | 18.6727i | 0.788362 | − | 1.36548i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.66700 | − | 4.61938i | 0.193996 | − | 0.336010i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6808 | −0.989909 | −0.494954 | − | 0.868919i | \(-0.664815\pi\) | ||||
−0.494954 | + | 0.868919i | \(0.664815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.40819 | + | 1.39037i | −0.173345 | + | 0.100081i | −0.584162 | − | 0.811637i | \(-0.698577\pi\) |
0.410817 | + | 0.911718i | \(0.365243\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −25.6370 | − | 44.4046i | −1.83591 | − | 3.17988i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.75802 | − | 2.16969i | −0.267748 | − | 0.154584i | 0.360116 | − | 0.932908i | \(-0.382737\pi\) |
−0.627864 | + | 0.778323i | \(0.716071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.261147 | 0.0185122 | 0.00925610 | − | 0.999957i | \(-0.497054\pi\) | ||||
0.00925610 | + | 0.999957i | \(0.497054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.4995 | + | 11.2580i | −1.37539 | + | 0.794081i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.76755 | − | 1.02050i | 0.124058 | − | 0.0716249i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.14276 | + | 2.39182i | 0.289343 | + | 0.167052i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24.7709 | − | 14.3015i | 1.72170 | − | 0.994022i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.48794 | − | 9.50539i | −0.379609 | − | 0.657502i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4634 | + | 19.8552i | −0.789175 | + | 1.36689i | 0.137299 | + | 0.990530i | \(0.456158\pi\) |
−0.926473 | + | 0.376361i | \(0.877175\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.88164 | + | 6.72320i | 0.265966 | + | 0.460666i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.5398 | −2.21919 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.05117 | − | 1.18425i | 0.139243 | − | 0.0803918i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.8446 | −1.88157 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.2263 | − | 11.1003i | 1.29330 | − | 0.746687i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6107i | 0.978407i | 0.872170 | + | 0.489204i | \(0.162713\pi\) | ||||
−0.872170 | + | 0.489204i | \(0.837287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 25.1927 | 1.67951 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.5626 | 1.16567 | 0.582834 | − | 0.812591i | \(-0.301944\pi\) | ||||
0.582834 | + | 0.812591i | \(0.301944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.01062i | − | 0.132866i | −0.997791 | − | 0.0664328i | \(-0.978838\pi\) | ||
0.997791 | − | 0.0664328i | \(-0.0211618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.78577 | + | 3.34042i | 0.380676 | + | 0.219783i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3326 | + | 8.27492i | 0.938958 | + | 0.542108i | 0.889634 | − | 0.456675i | \(-0.150960\pi\) |
0.0493246 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.65293 | − | 2.86296i | −0.107825 | − | 0.186759i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.7954 | − | 6.18985i | 1.80551 | − | 0.402074i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2392 | − | 8.79836i | 0.985742 | − | 0.569119i | 0.0817434 | − | 0.996653i | \(-0.473951\pi\) |
0.903999 | + | 0.427535i | \(0.140618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2977 | + | 23.0323i | −0.856581 | + | 1.48364i | 0.0185899 | + | 0.999827i | \(0.494082\pi\) |
−0.875171 | + | 0.483814i | \(0.839251\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7159 | + | 25.4887i | −0.944025 | + | 1.63510i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.9262 | −1.27304 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 11.3013i | − | 0.719084i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 18.7712i | − | 1.18958i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.75669 | −0.174001 | −0.0870005 | − | 0.996208i | \(-0.527728\pi\) | ||||
−0.0870005 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5153 | + | 18.2131i | 0.661094 | + | 1.14505i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.6342i | 2.35675i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.27509 | + | 3.94057i | 0.141916 | + | 0.245806i | 0.928218 | − | 0.372036i | \(-0.121340\pi\) |
−0.786302 | + | 0.617842i | \(0.788007\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.68151i | − | 0.228758i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32.8907 | + | 18.9894i | −2.03588 | + | 1.17542i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.22556 | + | 4.17168i | 0.445547 | + | 0.257237i | 0.705948 | − | 0.708264i | \(-0.250521\pi\) |
−0.260401 | + | 0.965501i | \(0.583855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.6907 | − | 11.3684i | 1.20959 | − | 0.698356i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.39176 | − | 16.2670i | −0.574766 | − | 0.995525i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.34783 | + | 10.9948i | −0.387034 | + | 0.670362i | −0.992049 | − | 0.125852i | \(-0.959834\pi\) |
0.605015 | + | 0.796214i | \(0.293167\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.83603 | − | 4.91216i | −0.172277 | − | 0.298392i | 0.766939 | − | 0.641720i | \(-0.221779\pi\) |
−0.939216 | + | 0.343328i | \(0.888446\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.43945 | + | 5.95730i | 0.208165 | + | 0.360552i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.5232i | 1.11699i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.09536 | − | 14.0216i | 0.486403 | − | 0.842475i | −0.513475 | − | 0.858105i | \(-0.671642\pi\) |
0.999878 | + | 0.0156300i | \(0.00497537\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −38.1683 | + | 22.0365i | −2.28507 | + | 1.31929i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.58390 | + | 13.1357i | 0.452418 | + | 0.783611i | 0.998536 | − | 0.0540978i | \(-0.0172283\pi\) |
−0.546118 | + | 0.837708i | \(0.683895\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3501i | 1.03136i | 0.856782 | + | 0.515679i | \(0.172460\pi\) | ||||
−0.856782 | + | 0.515679i | \(0.827540\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.5911 | + | 9.57890i | 0.982775 | + | 0.567405i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.555790 | − | 0.320886i | −0.0328073 | − | 0.0189413i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.705159 | 0.0414800 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.5547 | − | 28.6736i | −0.970453 | − | 1.68087i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.47971 | − | 1.43166i | −0.144866 | − | 0.0836387i | 0.425815 | − | 0.904810i | \(-0.359987\pi\) |
−0.570681 | + | 0.821172i | \(0.693321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.8703 | 1.15690 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −63.2013 | − | 36.4893i | −3.66731 | − | 2.11732i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.6542i | 1.25229i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.36552 | 0.251624 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.4084 | + | 23.2240i | 0.770291 | + | 1.33418i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.7670 | − | 15.4539i | −1.53267 | − | 0.884889i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.29065 | + | 9.16368i | −0.301953 | + | 0.522999i | −0.976578 | − | 0.215162i | \(-0.930972\pi\) |
0.674625 | + | 0.738161i | \(0.264305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.5694 | + | 23.5028i | −0.771934 | + | 1.33703i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.8213 | + | 20.4751i | −0.670325 | + | 1.16104i | 0.307486 | + | 0.951552i | \(0.400512\pi\) |
−0.977812 | + | 0.209485i | \(0.932821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.87629 | − | 10.1780i | −0.332148 | − | 0.575296i | 0.650785 | − | 0.759262i | \(-0.274440\pi\) |
−0.982933 | + | 0.183966i | \(0.941107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.25288 | −0.464997 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.1531 | 1.91823 | 0.959114 | − | 0.283021i | \(-0.0913367\pi\) | ||||
0.959114 | + | 0.283021i | \(0.0913367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.9622 | − | 24.1833i | −0.781734 | − | 1.35400i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.7910 | − | 51.5995i | 1.66277 | − | 2.88001i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.14747 | + | 7.18363i | −0.230771 | + | 0.399708i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.53620 | + | 16.5172i | −0.528973 | + | 0.916209i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0465 | − | 8.10975i | −0.776773 | − | 0.448470i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.221756 | + | 0.384093i | 0.0122258 | + | 0.0211757i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3014 | 0.786074 | 0.393037 | − | 0.919523i | \(-0.371424\pi\) | ||||
0.393037 | + | 0.919523i | \(0.371424\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 68.5055i | 3.75408i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.7109 | + | 10.2254i | 0.967650 | + | 0.558673i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.6553 | 1.61543 | 0.807713 | − | 0.589576i | \(-0.200705\pi\) | ||||
0.807713 | + | 0.589576i | \(0.200705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.04071 | − | 3.48760i | −0.328086 | − | 0.189421i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.2026 | − | 28.0637i | −0.877419 | − | 1.51973i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.40609 | 0.291901 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −31.7900 | − | 18.3540i | −1.71152 | − | 0.988144i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.4051 | + | 14.0903i | 1.31013 | + | 0.756407i | 0.982118 | − | 0.188265i | \(-0.0602865\pi\) |
0.328016 | + | 0.944672i | \(0.393620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.7093i | − | 1.16207i | −0.813877 | − | 0.581037i | \(-0.802647\pi\) | ||
0.813877 | − | 0.581037i | \(-0.197353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −37.5711 | − | 65.0750i | −2.00540 | − | 3.47345i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.2928 | − | 14.0254i | 1.29297 | − | 0.746498i | 0.313793 | − | 0.949492i | \(-0.398400\pi\) |
0.979180 | + | 0.202993i | \(0.0650670\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.52560 | − | 6.10651i | 0.187119 | − | 0.324100i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 5.04899i | − | 0.267221i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.64332 | + | 8.04247i | 0.245065 | + | 0.424465i | 0.962150 | − | 0.272521i | \(-0.0878573\pi\) |
−0.717085 | + | 0.696986i | \(0.754524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.38872 | − | 12.7976i | −0.388880 | − | 0.673560i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.0817 | − | 48.6390i | 1.47391 | − | 2.55288i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6453 | + | 21.9023i | 0.661885 | + | 1.14642i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3331 | + | 6.54315i | −0.591582 | + | 0.341550i | −0.765723 | − | 0.643171i | \(-0.777618\pi\) |
0.174141 | + | 0.984721i | \(0.444285\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3421 | + | 5.97104i | 0.538391 | + | 0.310840i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.64169 | + | 1.52518i | −0.137150 | + | 0.0791834i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.20691i | − | 0.476716i | −0.971177 | − | 0.238358i | \(-0.923391\pi\) | ||
0.971177 | − | 0.238358i | \(-0.0766091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.14195 | + | 12.3702i | 0.368809 | + | 0.638796i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 28.7523i | − | 1.48082i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.24066 | + | 3.88093i | 0.115095 | + | 0.199350i | 0.917818 | − | 0.397002i | \(-0.129950\pi\) |
−0.802723 | + | 0.596352i | \(0.796616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −49.7702 | −2.54980 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.0667i | − | 1.07646i | −0.842798 | − | 0.538229i | \(-0.819093\pi\) | ||
0.842798 | − | 0.538229i | \(-0.180907\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.06804i | − | 0.309256i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −81.2336 | −4.12934 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.46359 | + | 5.99912i | −0.175611 | + | 0.304168i | −0.940373 | − | 0.340146i | \(-0.889523\pi\) |
0.764761 | + | 0.644314i | \(0.222857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.94689 | − | 13.7644i | 0.401891 | − | 0.696096i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.87283 | − | 3.96803i | 0.346688 | − | 0.200161i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.4918 | − | 19.0525i | −0.880109 | − | 0.958638i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.13492 | + | 10.6260i | 0.307903 | + | 0.533303i | 0.977903 | − | 0.209057i | \(-0.0670395\pi\) |
−0.670001 | + | 0.742360i | \(0.733706\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.22586 | − | 1.28510i | −0.111432 | − | 0.0643355i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.1585 | + | 19.1441i | 1.65586 | + | 0.956009i | 0.974597 | + | 0.223966i | \(0.0719004\pi\) |
0.681259 | + | 0.732043i | \(0.261433\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 33.3659i | − | 1.66207i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 63.9613 | 3.17826 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −50.3695 | −2.49672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.6418i | − | 0.674543i | −0.941407 | − | 0.337272i | \(-0.890496\pi\) | ||
0.941407 | − | 0.337272i | \(-0.109504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 60.3728 | − | 34.8562i | 2.97797 | − | 1.71933i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.66579 | −0.131175 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.7653 | + | 8.52473i | −0.724799 | + | 0.418463i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0548 | −0.492387 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6863 | − | 27.1695i | −0.766326 | − | 1.32732i | −0.939543 | − | 0.342432i | \(-0.888749\pi\) |
0.173216 | − | 0.984884i | \(-0.444584\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6308 | − | 25.3413i | 0.713061 | − | 1.23506i | −0.250641 | − | 0.968080i | \(-0.580642\pi\) |
0.963703 | − | 0.266978i | \(-0.0860252\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.12644 | − | 7.14721i | −0.200634 | − | 0.347509i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.1233 | − | 6.99940i | 0.588067 | − | 0.339521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.59105 | + | 2.07329i | 0.173783 | + | 0.100334i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 81.5064 | − | 47.0578i | 3.93517 | − | 2.27197i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.940875 | + | 0.543214i | −0.0453204 | + | 0.0261657i | −0.522489 | − | 0.852646i | \(-0.674996\pi\) |
0.477169 | + | 0.878812i | \(0.341663\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.8383 | −1.28977 | −0.644884 | − | 0.764280i | \(-0.723094\pi\) | ||||
−0.644884 | + | 0.764280i | \(0.723094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 42.2106 | + | 24.3703i | 2.02384 | + | 1.16847i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.04539 | − | 7.00682i | −0.193517 | − | 0.335181i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.15394 | − | 4.70768i | 0.389167 | − | 0.224685i | −0.292632 | − | 0.956225i | \(-0.594531\pi\) |
0.681799 | + | 0.731540i | \(0.261198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49.7447 | −2.36879 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3494 | + | 26.5859i | −0.729272 | + | 1.26314i | 0.227920 | + | 0.973680i | \(0.426808\pi\) |
−0.957191 | + | 0.289456i | \(0.906526\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.53031 | + | 14.7749i | −0.404375 | + | 0.700399i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.56109i | − | 0.357627i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.41358 | + | 3.12553i | −0.255483 | + | 0.147503i | −0.622272 | − | 0.782801i | \(-0.713790\pi\) |
0.366790 | + | 0.930304i | \(0.380457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.39028 | + | 7.60419i | −0.206730 | + | 0.358067i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 38.4848i | − | 1.80817i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.12397 | − | 5.41087i | 0.146454 | − | 0.253666i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6901 | 0.874288 | 0.437144 | − | 0.899391i | \(-0.355990\pi\) | ||||
0.437144 | + | 0.899391i | \(0.355990\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 55.1530i | 2.57432i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.1386 | + | 8.74026i | −0.705074 | + | 0.407075i | −0.809234 | − | 0.587486i | \(-0.800118\pi\) |
0.104161 | + | 0.994561i | \(0.466784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.11709 | − | 10.5951i | 0.284285 | − | 0.492397i | −0.688150 | − | 0.725568i | \(-0.741577\pi\) |
0.972436 | + | 0.233171i | \(0.0749103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 48.9836 | + | 28.2807i | 2.27156 | + | 1.31149i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.833852 | − | 0.481425i | −0.0385861 | − | 0.0222777i | 0.480583 | − | 0.876949i | \(-0.340425\pi\) |
−0.519169 | + | 0.854672i | \(0.673758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.37609 | − | 1.37183i | −0.109717 | − | 0.0633454i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 54.8933 | − | 31.6926i | 2.52935 | − | 1.46032i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 59.7280i | − | 2.74630i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7.12613i | − | 0.326969i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 49.1566 | − | 28.3806i | 2.25073 | − | 1.29946i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.96154 | − | 1.70985i | −0.135316 | − | 0.0781249i | 0.430814 | − | 0.902441i | \(-0.358227\pi\) |
−0.566130 | + | 0.824316i | \(0.691560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.9145 | − | 25.9314i | −2.04793 | − | 1.18237i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.26493 | + | 2.46236i | 0.194061 | + | 0.112041i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.0362 | + | 26.0435i | −0.682759 | + | 1.18257i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5321 | + | 10.6995i | −0.839768 | + | 0.484840i | −0.857185 | − | 0.515008i | \(-0.827789\pi\) |
0.0174174 | + | 0.999848i | \(0.494456\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 74.4393i | 3.36626i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.56262 | 0.296167 | 0.148084 | − | 0.988975i | \(-0.452690\pi\) | ||||
0.148084 | + | 0.988975i | \(0.452690\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.5518 | + | 18.2763i | −0.475231 | + | 0.823124i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 112.914i | 5.07511i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.472992 | + | 0.819247i | −0.0212166 | + | 0.0367483i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.5059 | + | 12.4165i | −0.962738 | + | 0.555837i | −0.897015 | − | 0.442001i | \(-0.854269\pi\) |
−0.0657235 | + | 0.997838i | \(0.520936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.4241i | 1.89537i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.4878 | + | 32.0217i | −0.824328 | + | 1.42778i | 0.0781037 | + | 0.996945i | \(0.475113\pi\) |
−0.902432 | + | 0.430833i | \(0.858220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1785 | − | 21.0938i | 0.541936 | − | 0.938661i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 55.2559 | 2.45400 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.64391 | + | 3.25851i | −0.250162 | + | 0.144431i | −0.619838 | − | 0.784730i | \(-0.712802\pi\) |
0.369677 | + | 0.929161i | \(0.379469\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.69649 | − | 2.93840i | −0.0750482 | − | 0.129987i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.3143 | + | 14.0379i | 1.07350 | + | 0.619788i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.6494 | 1.08618 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.25507 | − | 3.03402i | 0.231118 | − | 0.133436i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.25827 | + | 2.45851i | −0.186917 | + | 0.107917i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.9156 | − | 13.8077i | −1.04776 | − | 0.604926i | −0.125740 | − | 0.992063i | \(-0.540130\pi\) |
−0.922022 | + | 0.387138i | \(0.873464\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.5394 | + | 13.5905i | −1.02930 | + | 0.594269i | −0.916785 | − | 0.399381i | \(-0.869225\pi\) |
−0.112519 | + | 0.993650i | \(0.535892\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.16878 | + | 3.75643i | 0.0946532 | + | 0.163944i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.2450 | + | 21.2089i | −0.533399 | + | 0.923875i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.74871 | − | 6.49296i | −0.162987 | − | 0.282302i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 49.6051 | 2.15268 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.82963 | + | 4.52044i | −0.339139 | + | 0.195802i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −54.1169 | −2.33968 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.7976 | + | 12.0075i | −0.897481 | + | 0.518161i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 36.5754i | − | 1.57541i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.5630 | −0.927067 | −0.463533 | − | 0.886079i | \(-0.653419\pi\) | ||||
−0.463533 | + | 0.886079i | \(0.653419\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 49.7141 | 2.13344 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7318i | 0.631040i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8376 | + | 8.56648i | 0.634409 | + | 0.366276i | 0.782458 | − | 0.622704i | \(-0.213966\pi\) |
−0.148048 | + | 0.988980i | \(0.547299\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −66.8222 | − | 38.5798i | −2.85190 | − | 1.64655i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.37145 | + | 9.30362i | 0.228831 | + | 0.396347i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.34669 | + | 2.55608i | 0.0997916 | + | 0.108696i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 76.1386 | − | 43.9586i | 3.23190 | − | 1.86594i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.63282 | + | 16.6845i | −0.408156 | + | 0.706946i | −0.994683 | − | 0.102983i | \(-0.967161\pi\) |
0.586528 | + | 0.809929i | \(0.300495\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.7494 | − | 53.2595i | 1.30056 | − | 2.25264i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −69.0791 | −2.91652 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 3.74425i | − | 0.157801i | −0.996882 | − | 0.0789006i | \(-0.974859\pi\) | ||
0.996882 | − | 0.0789006i | \(-0.0251410\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.33541i | 0.266533i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.58101 | −0.360369 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.19461 | + | 12.4614i | 0.301614 | + | 0.522410i | 0.976502 | − | 0.215510i | \(-0.0691414\pi\) |
−0.674888 | + | 0.737920i | \(0.735808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.9037i | 0.581851i | 0.956746 | + | 0.290926i | \(0.0939632\pi\) | ||||
−0.956746 | + | 0.290926i | \(0.906037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.9155 | + | 37.9588i | 0.915534 | + | 1.58575i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.6542i | 0.569421i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7705 | − | 16.6107i | 1.19773 | − | 0.691510i | 0.237682 | − | 0.971343i | \(-0.423612\pi\) |
0.960049 | + | 0.279832i | \(0.0902789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.71544 | + | 4.45451i | 0.320643 | + | 0.185123i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.98090 | − | 1.14367i | 0.0821816 | − | 0.0474476i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.8672 | + | 36.1430i | 0.864230 | + | 1.49689i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −58.1308 | + | 100.686i | −2.40341 | + | 4.16283i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2798 | + | 29.9295i | 0.713214 | + | 1.23532i | 0.963644 | + | 0.267188i | \(0.0860946\pi\) |
−0.250430 | + | 0.968135i | \(0.580572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.23334 | + | 10.7965i | 0.256840 | + | 0.444860i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.9027i | 0.571880i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.6761 | − | 18.4915i | 0.438413 | − | 0.759354i | −0.559154 | − | 0.829064i | \(-0.688874\pi\) |
0.997567 | + | 0.0697097i | \(0.0222073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.97148 | + | 2.29294i | −0.162815 | + | 0.0940012i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.418335 | − | 0.724578i | −0.0171213 | − | 0.0296550i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 18.1660i | − | 0.742242i | −0.928585 | − | 0.371121i | \(-0.878974\pi\) | ||
0.928585 | − | 0.371121i | \(-0.121026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7458 | + | 6.78143i | 0.479120 | + | 0.276620i | 0.720050 | − | 0.693922i | \(-0.244119\pi\) |
−0.240930 | + | 0.970543i | \(0.577452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.2142 | + | 25.5271i | 1.80054 | + | 1.03954i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −51.0119 | −2.07393 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.6617 | − | 21.9307i | −0.513924 | − | 0.890142i | −0.999870 | − | 0.0161528i | \(-0.994858\pi\) |
0.485946 | − | 0.873989i | \(-0.338475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.66295 | − | 3.26951i | −0.229474 | − | 0.132487i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.24794 | 0.252764 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.01933 | − | 1.16586i | −0.0815598 | − | 0.0470886i | 0.458665 | − | 0.888609i | \(-0.348328\pi\) |
−0.540225 | + | 0.841520i | \(0.681661\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 15.3260i | − | 0.618004i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.27330 | 0.0915196 | 0.0457598 | − | 0.998952i | \(-0.485429\pi\) | ||||
0.0457598 | + | 0.998952i | \(0.485429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.59454 | + | 6.22593i | 0.144477 | + | 0.250241i | 0.929178 | − | 0.369634i | \(-0.120517\pi\) |
−0.784701 | + | 0.619875i | \(0.787183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −46.5882 | − | 26.8977i | −1.86952 | − | 1.07937i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.14442 | − | 1.98220i | 0.0458503 | − | 0.0794150i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.1566 | − | 26.2520i | 0.606264 | − | 1.05008i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.5825 | + | 30.4537i | −0.702176 | + | 1.21620i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.0332 | + | 32.9664i | 0.758903 | + | 1.31446i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.3375 | 1.52619 | 0.763095 | − | 0.646286i | \(-0.223679\pi\) | ||||
0.763095 | + | 0.646286i | \(0.223679\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 73.4538 | 2.91953 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.6025 | + | 39.1487i | 0.896954 | + | 1.55357i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.8299 | − | 32.6143i | 0.746067 | − | 1.29223i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.80145 | − | 15.2446i | 0.348180 | − | 0.603065i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0812 | − | 17.4611i | 0.398182 | − | 0.689672i | −0.595320 | − | 0.803489i | \(-0.702975\pi\) |
0.993502 | + | 0.113817i | \(0.0363078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.7713 | − | 9.10555i | −0.621959 | − | 0.359088i | 0.155672 | − | 0.987809i | \(-0.450246\pi\) |
−0.777631 | + | 0.628721i | \(0.783579\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 52.1260 | + | 90.2849i | 2.05246 | + | 3.55496i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.1531 | −0.635044 | −0.317522 | − | 0.948251i | \(-0.602851\pi\) | ||||
−0.317522 | + | 0.948251i | \(0.602851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.4728i | 1.43168i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.57162 | − | 3.79413i | −0.257562 | − | 0.148704i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.1793 | 0.515745 | 0.257873 | − | 0.966179i | \(-0.416979\pi\) | ||||
0.257873 | + | 0.966179i | \(0.416979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.24242 | − | 3.60406i | −0.243912 | − | 0.140822i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.5682 | + | 54.6778i | 1.23159 | + | 2.13318i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.0528 | 1.44337 | 0.721686 | − | 0.692221i | \(-0.243368\pi\) | ||||
0.721686 | + | 0.692221i | \(0.243368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.26003 | − | 1.88218i | −0.126800 | − | 0.0732082i | 0.435258 | − | 0.900306i | \(-0.356657\pi\) |
−0.562059 | + | 0.827097i | \(0.689990\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −61.5979 | − | 35.5635i | −2.39226 | − | 1.38117i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.33445i | 0.0905261i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.2921 | − | 17.8265i | −0.398513 | − | 0.690244i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.5390 | − | 23.4052i | 1.56733 | − | 0.904897i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.3663 | − | 49.1319i | 1.09507 | − | 1.89671i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.16670i | 0.0835201i | 0.999128 | + | 0.0417600i | \(0.0132965\pi\) | ||||
−0.999128 | + | 0.0417600i | \(0.986703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.6908 | − | 41.0336i | −0.911858 | − | 1.57939i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.53173 | + | 6.11714i | 0.135736 | + | 0.235101i | 0.925878 | − | 0.377822i | \(-0.123327\pi\) |
−0.790143 | + | 0.612923i | \(0.789994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.01725 | − | 3.49398i | 0.0774150 | − | 0.134087i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.1338 | − | 48.7291i | −1.07809 | − | 1.86730i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.8918 | + | 12.0619i | −0.799403 | + | 0.461535i | −0.843262 | − | 0.537502i | \(-0.819368\pi\) |
0.0438596 | + | 0.999038i | \(0.486035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.8351 | − | 31.6591i | −2.09514 | − | 1.20963i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.57868 | + | 3.22085i | −0.212840 | + | 0.122883i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.9716i | 1.63709i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.24544 | + | 2.15717i | 0.0473789 | + | 0.0820627i | 0.888742 | − | 0.458407i | \(-0.151580\pi\) |
−0.841363 | + | 0.540470i | \(0.818247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 15.1485i | − | 0.575444i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.56628 | + | 7.90903i | 0.173209 | + | 0.300007i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.63584 | 0.251350 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 53.0229i | − | 2.00551i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.6011i | − | 1.30686i | −0.756985 | − | 0.653432i | \(-0.773328\pi\) | ||
0.756985 | − | 0.653432i | \(-0.226672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.3778 | 0.730848 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.29571 | + | 9.17245i | −0.199448 | + | 0.345454i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.63386 | + | 2.82993i | −0.0614477 | + | 0.106431i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.81822 | + | 5.09120i | −0.331175 | + | 0.191204i | −0.656363 | − | 0.754445i | \(-0.727906\pi\) |
0.325188 | + | 0.945650i | \(0.394573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.6673 | − | 47.5636i | −1.63765 | − | 1.78377i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.9436 | − | 20.6869i | −0.447291 | − | 0.774730i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −74.0303 | − | 42.7414i | −2.76858 | − | 1.59844i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.8239 | − | 28.1885i | −1.82336 | − | 1.05272i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.85764i | 0.218453i | 0.994017 | + | 0.109226i | \(0.0348374\pi\) | ||||
−0.994017 | + | 0.109226i | \(0.965163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.30696 | −0.123157 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 85.2073 | 3.16889 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 18.1300i | − | 0.673333i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.1381 | − | 14.5135i | 0.932319 | − | 0.538275i | 0.0447750 | − | 0.998997i | \(-0.485743\pi\) |
0.887544 | + | 0.460722i | \(0.152410\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.3543 | 1.05016 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.0915 | + | 22.5695i | −1.44585 | + | 0.834763i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.2849 | −1.82038 | −0.910189 | − | 0.414193i | \(-0.864064\pi\) | ||||
−0.910189 | + | 0.414193i | \(0.864064\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.9202 | + | 55.2874i | 1.17739 | + | 2.03931i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.7691 | + | 32.5091i | −0.691370 | + | 1.19749i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.87958 | + | 11.9158i | 0.253069 | + | 0.438329i | 0.964369 | − | 0.264560i | \(-0.0852266\pi\) |
−0.711300 | + | 0.702889i | \(0.751893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.3566 | + | 18.1037i | −1.15191 | + | 0.665057i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.1603 | + | 20.2998i | 1.28991 | + | 0.744727i | 0.978637 | − | 0.205595i | \(-0.0659129\pi\) |
0.311268 | + | 0.950322i | \(0.399246\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.94747 | + | 3.43377i | −0.217899 | + | 0.125804i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.8606 | + | 21.2815i | −1.34866 | + | 0.778649i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.26030 | 0.265285 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7859 | + | 10.8460i | 0.685506 | + | 0.395777i | 0.801926 | − | 0.597423i | \(-0.203809\pi\) |
−0.116420 | + | 0.993200i | \(0.537142\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.41600 | + | 7.64873i | 0.160928 | + | 0.278735i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.2718 | + | 17.4774i | −1.10170 | + | 0.636068i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.2915 | −1.50077 | −0.750383 | − | 0.661004i | \(-0.770131\pi\) | ||||
−0.750383 | + | 0.661004i | \(0.770131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.6894 | − | 58.3518i | 1.22285 | − | 2.11804i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.4471 | + | 25.0231i | −0.523706 | + | 0.907085i | 0.475913 | + | 0.879492i | \(0.342118\pi\) |
−0.999619 | + | 0.0275932i | \(0.991216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.97641i | − | 0.0715507i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 73.9013 | − | 42.6670i | 2.67191 | − | 1.54263i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.7770 | + | 32.5228i | −0.678000 | + | 1.17433i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.1430i | 0.978803i | 0.872059 | + | 0.489401i | \(0.162785\pi\) | ||||
−0.872059 | + | 0.489401i | \(0.837215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.28901 | − | 12.6249i | 0.262507 | − | 0.454676i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.22967 | 0.224066 | 0.112033 | − | 0.993705i | \(-0.464264\pi\) | ||||
0.112033 | + | 0.993705i | \(0.464264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 21.0392i | − | 0.755749i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.2147 | + | 5.89747i | −0.366451 | + | 0.211571i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.68900 | − | 2.92543i | 0.0605146 | − | 0.104814i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2088 | + | 6.47137i | 0.401081 | + | 0.231564i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 61.8597 | + | 35.7147i | 2.21068 | + | 1.27634i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49.8582 | − | 28.7856i | −1.77952 | − | 1.02740i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.5087 | + | 22.8104i | −1.40833 | + | 0.813102i | −0.995228 | − | 0.0975810i | \(-0.968890\pi\) |
−0.413106 | + | 0.910683i | \(0.635556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 26.7307i | − | 0.951640i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.849955i | − | 0.0302209i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.5885 | − | 29.2073i | 1.79645 | − | 1.03718i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −63.0856 | − | 36.4225i | −2.23742 | − | 1.29177i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.125834 | − | 0.0726502i | −0.00445726 | − | 0.00257340i | 0.497770 | − | 0.867309i | \(-0.334152\pi\) |
−0.502227 | + | 0.864736i | \(0.667486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.97148 | − | 2.29294i | −0.140501 | − | 0.0811182i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.2954 | + | 36.8847i | −0.752436 | + | 1.30326i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.2025 | + | 23.2109i | −1.41872 | + | 0.819097i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 4.47300i | − | 0.157652i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.6748 | 1.43182 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.5837 | − | 44.3123i | 0.899475 | − | 1.55794i | 0.0713096 | − | 0.997454i | \(-0.477282\pi\) |
0.828166 | − | 0.560483i | \(-0.189384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.6875i | − | 0.550862i | −0.961321 | − | 0.275431i | \(-0.911179\pi\) | ||
0.961321 | − | 0.275431i | \(-0.0888205\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.08619 | + | 15.7377i | −0.318666 | + | 0.551946i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 58.5532 | − | 33.8057i | 2.05103 | − | 1.18416i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.9781i | 0.803903i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.79880 | − | 13.5079i | 0.272512 | − | 0.472005i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.86207 | + | 11.8855i | −0.239488 | + | 0.414805i | −0.960567 | − | 0.278047i | \(-0.910313\pi\) |
0.721079 | + | 0.692852i | \(0.243646\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.4730 | 1.93367 | 0.966834 | − | 0.255406i | \(-0.0822090\pi\) | ||||
0.966834 | + | 0.255406i | \(0.0822090\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 51.3946 | − | 29.6727i | 1.78933 | − | 1.03307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.1047 | + | 22.6980i | 0.455694 | + | 0.789286i | 0.998728 | − | 0.0504254i | \(-0.0160577\pi\) |
−0.543034 | + | 0.839711i | \(0.682724\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.497941 | + | 0.287486i | 0.0172942 | + | 0.00998481i | 0.508622 | − | 0.860990i | \(-0.330155\pi\) |
−0.491328 | + | 0.870975i | \(0.663488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −51.8724 | −1.79943 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.9383 | + | 13.8208i | −0.829413 | + | 0.478862i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.3704 | − | 19.2664i | 1.15483 | − | 0.666741i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 71.7856 | + | 41.4454i | 2.48127 | + | 1.43256i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.1393 | + | 8.16330i | −0.488141 | + | 0.281829i | −0.723803 | − | 0.690007i | \(-0.757608\pi\) |
0.235662 | + | 0.971835i | \(0.424274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.834160 | − | 1.44481i | −0.0287641 | − | 0.0498210i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.2976 | − | 42.0846i | 0.836853 | − | 1.44947i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.0938 | − | 43.4637i | −0.863253 | − | 1.49520i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.84373 | 0.235153 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 48.1397 | − | 27.7934i | 1.65215 | − | 0.953869i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.1294 | −1.27278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.1652 | + | 11.6424i | −0.690445 | + | 0.398628i | −0.803779 | − | 0.594928i | \(-0.797180\pi\) |
0.113334 | + | 0.993557i | \(0.463847\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 43.4395i | − | 1.48560i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.9756 | 1.43386 | 0.716930 | − | 0.697145i | \(-0.245547\pi\) | ||||
0.716930 | + | 0.697145i | \(0.245547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.3667 | 1.20670 | 0.603348 | − | 0.797478i | \(-0.293833\pi\) | ||||
0.603348 | + | 0.797478i | \(0.293833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.05613i | 0.0700727i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.2525 | + | 12.8475i | 0.757483 | + | 0.437333i | 0.828391 | − | 0.560150i | \(-0.189256\pi\) |
−0.0709083 | + | 0.997483i | \(0.522590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.86768 | + | 2.23301i | 0.131505 | + | 0.0759245i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.12961 | − | 1.95654i | −0.0383635 | − | 0.0664475i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.9717 | − | 32.1069i | 1.18633 | − | 1.08915i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.4729 | + | 19.3256i | −1.13419 | + | 0.654822i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.5370 | + | 65.0160i | −1.27044 | + | 2.20046i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.870274 | + | 1.50736i | −0.0294206 | + | 0.0509580i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.51548 | 0.152477 | 0.0762385 | − | 0.997090i | \(-0.475709\pi\) | ||||
0.0762385 | + | 0.997090i | \(0.475709\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.17363i | 0.309419i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.7794i | 0.396858i | 0.980115 | + | 0.198429i | \(0.0635840\pi\) | ||||
−0.980115 | + | 0.198429i | \(0.936416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.26911 | 0.110014 | 0.0550072 | − | 0.998486i | \(-0.482482\pi\) | ||||
0.0550072 | + | 0.998486i | \(0.482482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.8306 | − | 55.1323i | −1.06997 | − | 1.85325i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 56.3309i | − | 1.89141i | −0.325031 | − | 0.945703i | \(-0.605375\pi\) | ||
0.325031 | − | 0.945703i | \(-0.394625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.03234 | − | 5.25217i | −0.101702 | − | 0.176152i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 117.403i | 3.93316i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.02169 | + | 1.16723i | −0.0676534 | + | 0.0390597i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.8899 | + | 10.9061i | 0.631420 | + | 0.364551i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 60.0817 | − | 34.6882i | 2.00607 | − | 1.15821i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.8586 | + | 27.4680i | 0.528915 | + | 0.916108i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7702 | − | 27.3148i | 0.525381 | − | 0.909987i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.99320 | − | 12.1126i | −0.232719 | − | 0.403081i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.5771 | − | 39.1046i | −0.750487 | − | 1.29988i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.0711i | 1.36374i | 0.731471 | + | 0.681872i | \(0.238834\pi\) | ||||
−0.731471 | + | 0.681872i | \(0.761166\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.4029 | − | 52.6594i | 1.00840 | − | 1.74660i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.4655 | + | 25.0948i | −1.44008 | + | 0.831428i | −0.997854 | − | 0.0654773i | \(-0.979143\pi\) |
−0.442222 | + | 0.896906i | \(0.645810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.6475 | − | 27.1022i | −0.517856 | − | 0.896953i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 99.0237i | 3.27362i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.837480 | + | 0.483520i | 0.0276560 | + | 0.0159672i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.25238 | − | 1.30041i | −0.0742991 | − | 0.0428966i | 0.462390 | − | 0.886677i | \(-0.346992\pi\) |
−0.536689 | + | 0.843780i | \(0.680325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.9007 | 1.11707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.66323 | + | 11.5411i | 0.219323 | + | 0.379879i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.3213 | − | 16.3513i | −0.931198 | − | 0.537627i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 61.5359 | 2.02110 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.3124 | − | 20.3876i | −1.15856 | − | 0.668896i | −0.207603 | − | 0.978213i | \(-0.566566\pi\) |
−0.950959 | + | 0.309317i | \(0.899900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0710i | 0.461159i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 75.7471 | 2.47985 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.3714 | + | 54.3369i | 1.02596 | + | 1.77701i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.4564 | + | 14.1199i | 0.798955 | + | 0.461277i | 0.843106 | − | 0.537748i | \(-0.180725\pi\) |
−0.0441504 | + | 0.999025i | \(0.514058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.8267 | + | 32.6087i | −0.614385 | + | 1.06415i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.76069 | + | 3.04961i | −0.0573969 | + | 0.0994144i | −0.893296 | − | 0.449469i | \(-0.851613\pi\) |
0.835899 | + | 0.548883i | \(0.184947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.23626 | + | 5.60536i | −0.105387 | + | 0.182536i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.76087 | + | 13.4422i | 0.252461 | + | 0.437276i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56.4798 | −1.83535 | −0.917673 | − | 0.397337i | \(-0.869934\pi\) | ||||
−0.917673 | + | 0.397337i | \(0.869934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.7982 | −1.55159 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.7104 | − | 94.7612i | −1.77411 | − | 3.07284i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.05293 | + | 12.2160i | −0.228467 | + | 0.395716i | −0.957354 | − | 0.288918i | \(-0.906705\pi\) |
0.728887 | + | 0.684634i | \(0.240038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.9053 | − | 34.4771i | 0.644122 | − | 1.11565i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −44.7327 | + | 77.4792i | −1.44600 | + | 2.50455i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.35665 | + | 4.24736i | 0.237559 | + | 0.137155i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.90329 | + | 5.02865i | 0.0936546 | + | 0.162215i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −135.100 | −4.35352 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 8.09184i | − | 0.260486i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.44552 | + | 5.45337i | 0.303747 | + | 0.175369i | 0.644125 | − | 0.764920i | \(-0.277222\pi\) |
−0.340378 | + | 0.940289i | \(0.610555\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.5756 | 0.853731 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.0135 | + | 19.6377i | 1.09154 | + | 0.630203i | 0.933987 | − | 0.357306i | \(-0.116305\pi\) |
0.157557 | + | 0.987510i | \(0.449638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.612610 | − | 1.06107i | −0.0196394 | − | 0.0340164i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 61.1048 | 1.95692 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.75177 | + | 4.47548i | 0.248001 | + | 0.143183i | 0.618849 | − | 0.785510i | \(-0.287599\pi\) |
−0.370848 | + | 0.928694i | \(0.620933\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.1200 | − | 15.6577i | −0.866758 | − | 0.500423i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.7770i | 1.17420i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.73899 | + | 11.6723i | 0.214940 | + | 0.372288i | 0.953254 | − | 0.302170i | \(-0.0977110\pi\) |
−0.738314 | + | 0.674457i | \(0.764378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.9357 | − | 6.31373i | 0.348441 | − | 0.201172i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.710470 | − | 1.23057i | 0.0226145 | − | 0.0391695i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 44.0280i | − | 1.40001i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6633 | − | 35.7900i | −0.656393 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.9096 | − | 39.6806i | −0.727014 | − | 1.25923i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.379964 | + | 0.658117i | −0.0120457 | + | 0.0208637i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.5717 | − | 20.0428i | −0.366480 | − | 0.634761i | 0.622533 | − | 0.782594i | \(-0.286104\pi\) |
−0.989012 | + | 0.147832i | \(0.952770\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 111.581 | − | 64.4214i | 3.53027 | − | 2.03820i |
(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 | 1264.2.n.i.767.1 | yes | 28 | |
4.3 | odd | 2 | inner | 1264.2.n.i.767.14 | yes | 28 | |
79.24 | odd | 6 | inner | 1264.2.n.i.735.14 | yes | 28 | |
316.103 | even | 6 | inner | 1264.2.n.i.735.1 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1264.2.n.i.735.1 | ✓ | 28 | 316.103 | even | 6 | inner | |
1264.2.n.i.735.14 | yes | 28 | 79.24 | odd | 6 | inner | |
1264.2.n.i.767.1 | yes | 28 | 1.1 | even | 1 | trivial | |
1264.2.n.i.767.14 | yes | 28 | 4.3 | odd | 2 | inner |