Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(601,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.601");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.bg (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 10x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.1 | ||
Root | \(-1.58114 - 2.73861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.841 |
Dual form | 1560.2.bg.e.601.1 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.08114 | − | 3.60464i | −0.786597 | − | 1.36243i | −0.928041 | − | 0.372479i | \(-0.878508\pi\) |
0.141444 | − | 0.989946i | \(-0.454825\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.08114 | + | 1.87259i | 0.854554 | + | 0.519362i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.418861 | + | 0.725489i | 0.101589 | + | 0.175957i | 0.912339 | − | 0.409435i | \(-0.134274\pi\) |
−0.810751 | + | 0.585392i | \(0.800941\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.16228 | −0.908283 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | − | 1.73205i | 0.208514 | − | 0.361158i | −0.742732 | − | 0.669588i | \(-0.766471\pi\) |
0.951247 | + | 0.308431i | \(0.0998038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.58114 | − | 6.20271i | 0.665001 | − | 1.15182i | −0.314284 | − | 0.949329i | \(-0.601765\pi\) |
0.979285 | − | 0.202486i | \(-0.0649021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.32456 | −1.67474 | −0.837370 | − | 0.546637i | \(-0.815908\pi\) | ||||
−0.837370 | + | 0.546637i | \(0.815908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.08114 | + | 3.60464i | 0.351777 | + | 0.609295i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.16228 | + | 7.20928i | −0.684274 | + | 1.18520i | 0.289390 | + | 0.957211i | \(0.406548\pi\) |
−0.973664 | + | 0.227986i | \(0.926786\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.16228 | − | 1.73205i | 0.506370 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.58114 | + | 4.47066i | −0.403106 | + | 0.698200i | −0.994099 | − | 0.108476i | \(-0.965403\pi\) |
0.590993 | + | 0.806677i | \(0.298736\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.08114 | − | 8.80079i | −0.774866 | − | 1.34211i | −0.934870 | − | 0.354991i | \(-0.884484\pi\) |
0.160003 | − | 0.987117i | \(-0.448850\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.48683 | −1.09207 | −0.546033 | − | 0.837763i | \(-0.683863\pi\) | ||||
−0.546033 | + | 0.837763i | \(0.683863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.16228 | + | 8.94133i | −0.737468 | + | 1.27733i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.837722 | 0.117305 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.32456 | −0.868744 | −0.434372 | − | 0.900733i | \(-0.643030\pi\) | ||||
−0.434372 | + | 0.900733i | \(0.643030\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | + | 1.73205i | −0.134840 | + | 0.233550i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.58114 | + | 6.20271i | 0.466225 | + | 0.807525i | 0.999256 | − | 0.0385709i | \(-0.0122805\pi\) |
−0.533031 | + | 0.846096i | \(0.678947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.50000 | − | 11.2583i | −0.832240 | − | 1.44148i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
0.0640184 | − | 0.997949i | \(-0.479608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.08114 | + | 3.60464i | −0.262199 | + | 0.454142i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.08114 | − | 1.87259i | −0.382168 | − | 0.232266i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.08114 | + | 8.80079i | −0.620760 | + | 1.07519i | 0.368585 | + | 0.929594i | \(0.379842\pi\) |
−0.989344 | + | 0.145593i | \(0.953491\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | − | 1.73205i | −0.120386 | − | 0.208514i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.74342 | − | 4.75174i | −0.325584 | − | 0.563927i | 0.656047 | − | 0.754720i | \(-0.272227\pi\) |
−0.981630 | + | 0.190793i | \(0.938894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.16228 | −0.721240 | −0.360620 | − | 0.932713i | \(-0.617435\pi\) | ||||
−0.360620 | + | 0.932713i | \(0.617435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.32456 | −0.948671 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.418861 | − | 0.725489i | −0.0454319 | − | 0.0786903i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.58114 | − | 6.20271i | −0.383938 | − | 0.665001i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.74342 | − | 13.4120i | 0.820801 | − | 1.42167i | −0.0842864 | − | 0.996442i | \(-0.526861\pi\) |
0.905087 | − | 0.425227i | \(-0.139806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.337722 | − | 15.0035i | 0.0354029 | − | 1.57279i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.66228 | + | 8.07530i | −0.483456 | + | 0.837370i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | + | 1.73205i | 0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.40569 | + | 11.0950i | 0.650400 | + | 1.12653i | 0.983026 | + | 0.183467i | \(0.0587319\pi\) |
−0.332626 | + | 0.943059i | \(0.607935\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.162278 | + | 0.281073i | −0.0161472 | + | 0.0279678i | −0.873986 | − | 0.485951i | \(-0.838473\pi\) |
0.857839 | + | 0.513919i | \(0.171807\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4868 | −1.03330 | −0.516649 | − | 0.856197i | \(-0.672821\pi\) | ||||
−0.516649 | + | 0.856197i | \(0.672821\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.16228 | 0.406197 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.74342 | − | 16.8761i | 0.941932 | − | 1.63147i | 0.180150 | − | 0.983639i | \(-0.442342\pi\) |
0.761781 | − | 0.647834i | \(-0.224325\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.32456 | 0.701565 | 0.350783 | − | 0.936457i | \(-0.385916\pi\) | ||||
0.350783 | + | 0.936457i | \(0.385916\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.16228 | + | 7.20928i | 0.395066 | + | 0.684274i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.16228 | + | 3.74517i | 0.203410 | + | 0.352316i | 0.949625 | − | 0.313389i | \(-0.101464\pi\) |
−0.746215 | + | 0.665705i | \(0.768131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | + | 1.73205i | −0.0932505 | + | 0.161515i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0811388 | − | 3.60464i | 0.00750129 | − | 0.333249i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.74342 | − | 3.01969i | 0.159819 | − | 0.276814i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.58114 | + | 4.47066i | 0.232733 | + | 0.403106i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0811388 | + | 0.140537i | −0.00719991 | + | 0.0124706i | −0.869603 | − | 0.493752i | \(-0.835625\pi\) |
0.862403 | + | 0.506222i | \(0.168958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.1623 | −0.894739 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8114 | 1.38145 | 0.690724 | − | 0.723119i | \(-0.257292\pi\) | ||||
0.690724 | + | 0.723119i | \(0.257292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.16228 | + | 7.20928i | −0.360915 | + | 0.625124i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.41886 | − | 11.1178i | −0.548400 | − | 0.949857i | −0.998384 | − | 0.0568206i | \(-0.981904\pi\) |
0.449984 | − | 0.893037i | \(-0.351430\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.662278 | − | 1.14710i | −0.0561737 | − | 0.0972956i | 0.836571 | − | 0.547858i | \(-0.184557\pi\) |
−0.892745 | + | 0.450563i | \(0.851223\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.74342 | + | 6.48379i | −0.315253 | + | 0.546033i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.32456 | − | 3.46410i | 0.528886 | − | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.58114 | + | 6.20271i | −0.297397 | + | 0.515107i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.16228 | + | 8.94133i | 0.425777 | + | 0.737468i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.32456 | 0.351927 | 0.175964 | − | 0.984397i | \(-0.443696\pi\) | ||||
0.175964 | + | 0.984397i | \(0.443696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.418861 | − | 0.725489i | 0.0338629 | − | 0.0586523i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.32456 | 0.748966 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.8114 | −1.18208 | −0.591039 | − | 0.806643i | \(-0.701282\pi\) | ||||
−0.591039 | + | 0.806643i | \(0.701282\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.16228 | + | 5.47723i | −0.250785 | + | 0.434372i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.32456 | −0.656067 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.24342 | + | 7.34981i | 0.332370 | + | 0.575682i | 0.982976 | − | 0.183734i | \(-0.0588184\pi\) |
−0.650606 | + | 0.759415i | \(0.725485\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00000 | + | 1.73205i | 0.0778499 | + | 0.134840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3246 | − | 17.8827i | 0.798938 | − | 1.38380i | −0.121370 | − | 0.992607i | \(-0.538729\pi\) |
0.920308 | − | 0.391194i | \(-0.127938\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.98683 | + | 11.5394i | 0.460526 | + | 0.887646i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | + | 1.73205i | −0.0764719 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.256584 | + | 0.444416i | 0.0195077 | + | 0.0337883i | 0.875614 | − | 0.483011i | \(-0.160457\pi\) |
−0.856107 | + | 0.516799i | \(0.827123\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.08114 | − | 3.60464i | −0.157319 | − | 0.272485i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.16228 | 0.538350 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.256584 | + | 0.444416i | −0.0191780 | + | 0.0332172i | −0.875455 | − | 0.483299i | \(-0.839438\pi\) |
0.856277 | + | 0.516517i | \(0.172772\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.6491 | −1.83215 | −0.916077 | − | 0.401002i | \(-0.868662\pi\) | ||||
−0.916077 | + | 0.401002i | \(0.868662\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0000 | −0.960988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.16228 | − | 7.20928i | 0.306017 | − | 0.530037i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.67544 | 0.122521 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.08114 | + | 3.60464i | 0.151381 | + | 0.262199i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.90569 | − | 10.2290i | −0.427321 | − | 0.740142i | 0.569313 | − | 0.822121i | \(-0.307209\pi\) |
−0.996634 | + | 0.0819791i | \(0.973876\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0811388 | − | 0.140537i | 0.00584050 | − | 0.0101160i | −0.863090 | − | 0.505049i | \(-0.831474\pi\) |
0.868931 | + | 0.494933i | \(0.164808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.16228 | + | 1.73205i | −0.226455 | + | 0.124035i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.83772 | + | 4.91508i | −0.202179 | + | 0.350185i | −0.949230 | − | 0.314582i | \(-0.898136\pi\) |
0.747051 | + | 0.664767i | \(0.231469\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.33772 | + | 5.78110i | 0.236605 | + | 0.409812i | 0.959738 | − | 0.280897i | \(-0.0906320\pi\) |
−0.723133 | + | 0.690709i | \(0.757299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.08114 | + | 8.80079i | 0.358396 | + | 0.620760i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −29.8114 | −2.09235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.58114 | − | 4.47066i | 0.180275 | − | 0.312245i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | −0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8246 | − | 20.4807i | 0.814036 | − | 1.40995i | −0.0959821 | − | 0.995383i | \(-0.530599\pi\) |
0.910018 | − | 0.414569i | \(-0.136068\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.48683 | −0.375952 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.08114 | + | 8.80079i | 0.346531 | + | 0.600209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.4057 | + | 33.6116i | 1.31734 | + | 2.28171i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.08114 | + | 5.33669i | −0.208204 | + | 0.360620i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0679718 | + | 3.01969i | −0.00457228 | + | 0.203126i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | − | 3.46410i | 0.133930 | − | 0.231973i | −0.791258 | − | 0.611482i | \(-0.790574\pi\) |
0.925188 | + | 0.379509i | \(0.123907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.41886 | + | 4.18959i | 0.160545 | + | 0.278073i | 0.935064 | − | 0.354478i | \(-0.115341\pi\) |
−0.774519 | + | 0.632551i | \(0.782008\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.67544 | −0.375044 | −0.187522 | − | 0.982260i | \(-0.560046\pi\) | ||||
−0.187522 | + | 0.982260i | \(0.560046\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.16228 | + | 7.20928i | −0.273858 | + | 0.474336i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3246 | 1.33151 | 0.665753 | − | 0.746172i | \(-0.268110\pi\) | ||||
0.665753 | + | 0.746172i | \(0.268110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.48683 | 0.488387 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.50000 | − | 9.52628i | 0.357263 | − | 0.618798i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.6491 | 1.07694 | 0.538471 | − | 0.842644i | \(-0.319002\pi\) | ||||
0.538471 | + | 0.842644i | \(0.319002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.83772 | − | 4.91508i | −0.182794 | − | 0.316608i | 0.760037 | − | 0.649880i | \(-0.225181\pi\) |
−0.942831 | + | 0.333272i | \(0.891847\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.16228 | − | 8.94133i | 0.329806 | − | 0.571240i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.162278 | − | 7.20928i | 0.0103255 | − | 0.458715i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.48683 | − | 16.4317i | −0.598804 | − | 1.03716i | −0.992998 | − | 0.118131i | \(-0.962310\pi\) |
0.394194 | − | 0.919027i | \(-0.371024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | − | 3.46410i | −0.125739 | − | 0.217786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.837722 | −0.0524602 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.0680 | − | 22.6344i | 0.815158 | − | 1.41189i | −0.0940569 | − | 0.995567i | \(-0.529984\pi\) |
0.909215 | − | 0.416328i | \(-0.136683\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34.6491 | 2.15299 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.16228 | −0.443334 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.74342 | + | 8.21584i | −0.292492 | + | 0.506610i | −0.974398 | − | 0.224829i | \(-0.927818\pi\) |
0.681907 | + | 0.731439i | \(0.261151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.32456 | 0.388514 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.74342 | − | 13.4120i | −0.473889 | − | 0.820801i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7434 | + | 20.3402i | 0.716009 | + | 1.24016i | 0.962569 | + | 0.271036i | \(0.0873663\pi\) |
−0.246560 | + | 0.969127i | \(0.579300\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.82456 | − | 8.35637i | 0.293071 | − | 0.507614i | −0.681463 | − | 0.731852i | \(-0.738656\pi\) |
0.974534 | + | 0.224239i | \(0.0719895\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.8246 | − | 7.79423i | −0.776177 | − | 0.471728i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | − | 1.73205i | 0.0603023 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.83772 | − | 10.1112i | −0.350755 | − | 0.607525i | 0.635627 | − | 0.771996i | \(-0.280742\pi\) |
−0.986382 | + | 0.164471i | \(0.947408\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.66228 | + | 8.07530i | 0.279123 | + | 0.483456i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.16228 | −0.188646 | −0.0943228 | − | 0.995542i | \(-0.530069\pi\) | ||||
−0.0943228 | + | 0.995542i | \(0.530069\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4057 | + | 21.4873i | −0.737442 | + | 1.27729i | 0.216202 | + | 0.976349i | \(0.430633\pi\) |
−0.953644 | + | 0.300938i | \(0.902700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.4868 | 1.26833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.14911 | − | 14.1147i | 0.479359 | − | 0.830275i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.8114 | 0.751017 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.7434 | − | 23.8043i | −0.802899 | − | 1.39066i | −0.917700 | − | 0.397273i | \(-0.869956\pi\) |
0.114801 | − | 0.993388i | \(-0.463377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.58114 | − | 6.20271i | −0.208502 | − | 0.361136i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.32456 | − | 3.46410i | 0.365758 | − | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1491 | + | 36.6313i | −1.21901 | + | 2.11140i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.162278 | + | 0.281073i | 0.00932261 | + | 0.0161472i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.50000 | + | 11.2583i | 0.372189 | + | 0.644650i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.1623 | −1.37901 | −0.689507 | − | 0.724279i | \(-0.742173\pi\) | ||||
−0.689507 | + | 0.724279i | \(0.742173\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.24342 | + | 9.08186i | −0.298288 | + | 0.516649i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.8114 | 1.46363 | 0.731815 | − | 0.681504i | \(-0.238674\pi\) | ||||
0.731815 | + | 0.681504i | \(0.238674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.4868 | 1.04494 | 0.522469 | − | 0.852658i | \(-0.325011\pi\) | ||||
0.522469 | + | 0.852658i | \(0.325011\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.08114 | − | 3.60464i | 0.117259 | − | 0.203098i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.32456 | −0.130560 | −0.0652800 | − | 0.997867i | \(-0.520794\pi\) | ||||
−0.0652800 | + | 0.997867i | \(0.520794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.16228 | − | 12.4054i | −0.401011 | − | 0.694571i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.74342 | − | 16.8761i | −0.543824 | − | 0.941932i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.837722 | − | 1.45098i | 0.0466121 | − | 0.0807346i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.08114 | + | 1.87259i | 0.170911 | + | 0.103872i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.66228 | − | 6.34325i | 0.202524 | − | 0.350783i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.5811 | + | 26.9873i | 0.859016 | + | 1.48786i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.33772 | + | 2.31700i | 0.0735279 | + | 0.127354i | 0.900445 | − | 0.434970i | \(-0.143241\pi\) |
−0.826917 | + | 0.562324i | \(0.809908\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.32456 | 0.456183 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.08114 | − | 8.80079i | 0.277612 | − | 0.480839i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.83772 | −0.100107 | −0.0500536 | − | 0.998747i | \(-0.515939\pi\) | ||||
−0.0500536 | + | 0.998747i | \(0.515939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.32456 | 0.234878 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.32456 | + | 16.1506i | −0.504953 | + | 0.874604i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8377 | 0.747167 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | + | 1.73205i | 0.0538382 | + | 0.0932505i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.1623 | + | 22.7977i | 0.706588 | + | 1.22385i | 0.966115 | + | 0.258111i | \(0.0830999\pi\) |
−0.259527 | + | 0.965736i | \(0.583567\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.662278 | − | 1.14710i | 0.0354509 | − | 0.0614028i | −0.847756 | − | 0.530387i | \(-0.822047\pi\) |
0.883206 | + | 0.468984i | \(0.155380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.08114 | − | 1.87259i | −0.164459 | − | 0.0999513i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.83772 | + | 3.18303i | −0.0978121 | + | 0.169416i | −0.910779 | − | 0.412895i | \(-0.864518\pi\) |
0.812967 | + | 0.582310i | \(0.197851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.74342 | + | 4.75174i | 0.145605 | + | 0.252196i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.74342 | − | 3.01969i | −0.0922714 | − | 0.159819i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.5132 | −0.660420 | −0.330210 | − | 0.943908i | \(-0.607120\pi\) | ||||
−0.330210 | + | 0.943908i | \(0.607120\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.16228 | 0.322548 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0811 | − | 26.1213i | 0.787229 | − | 1.36352i | −0.140429 | − | 0.990091i | \(-0.544848\pi\) |
0.927658 | − | 0.373430i | \(-0.121818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.16228 | 0.268737 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.1623 | + | 22.7977i | 0.683351 | + | 1.18360i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.7302 | − | 27.2456i | −0.814481 | − | 1.41072i | −0.909700 | − | 0.415267i | \(-0.863688\pi\) |
0.0952182 | − | 0.995456i | \(-0.469645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.6491 | − | 12.4054i | 1.16649 | − | 0.638912i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.98683 | − | 3.44130i | 0.102057 | − | 0.176767i | −0.810475 | − | 0.585773i | \(-0.800791\pi\) |
0.912532 | + | 0.409006i | \(0.134124\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0811388 | + | 0.140537i | 0.00415687 | + | 0.00719991i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.74342 | − | 8.21584i | −0.242377 | − | 0.419810i | 0.719014 | − | 0.694996i | \(-0.244594\pi\) |
−0.961391 | + | 0.275186i | \(0.911261\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.32456 | 0.424259 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.08114 | + | 8.80079i | −0.258289 | + | 0.447369i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.9737 | 1.57043 | 0.785214 | − | 0.619225i | \(-0.212553\pi\) | ||||
0.785214 | + | 0.619225i | \(0.212553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.67544 | 0.0847309 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.90569 | − | 13.6931i | 0.398790 | − | 0.690724i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.0000 | −0.553470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.75658 | − | 9.97070i | −0.288915 | − | 0.500415i | 0.684636 | − | 0.728885i | \(-0.259961\pi\) |
−0.973551 | + | 0.228470i | \(0.926628\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.16228 | + | 7.20928i | 0.208375 | + | 0.360915i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.48683 | − | 12.9676i | 0.373875 | − | 0.647570i | −0.616283 | − | 0.787525i | \(-0.711362\pi\) |
0.990158 | + | 0.139955i | \(0.0446957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.7302 | − | 17.4610i | −1.43116 | − | 0.869797i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.32456 | + | 14.4186i | 0.412633 | + | 0.714701i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.8246 | + | 18.7487i | 0.535240 | + | 0.927063i | 0.999152 | + | 0.0411812i | \(0.0131121\pi\) |
−0.463912 | + | 0.885881i | \(0.653555\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.8377 | −0.633238 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.9057 | − | 25.8174i | 0.733461 | − | 1.27039i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.32456 | −0.0648638 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.9057 | + | 32.7456i | −0.923604 | + | 1.59973i | −0.129812 | + | 0.991539i | \(0.541437\pi\) |
−0.793792 | + | 0.608190i | \(0.791896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.32456 | 0.454451 | 0.227226 | − | 0.973842i | \(-0.427035\pi\) | ||||
0.227226 | + | 0.973842i | \(0.427035\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.74342 | + | 6.48379i | 0.182011 | + | 0.315253i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.418861 | + | 0.725489i | 0.0203178 | + | 0.0351914i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.0548 | + | 46.8603i | −1.30927 | + | 2.26773i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.162278 | − | 7.20928i | 0.00783484 | − | 0.348067i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.3246 | + | 24.8109i | −0.689990 | + | 1.19510i | 0.281851 | + | 0.959458i | \(0.409052\pi\) |
−0.971841 | + | 0.235639i | \(0.924282\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2434 | + | 22.9383i | 0.636438 | + | 1.10234i | 0.986209 | + | 0.165508i | \(0.0529262\pi\) |
−0.349771 | + | 0.936835i | \(0.613740\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.58114 | + | 6.20271i | 0.171702 | + | 0.297397i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.00000 | −0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3114 | − | 28.2522i | 0.778500 | − | 1.34840i | −0.154306 | − | 0.988023i | \(-0.549314\pi\) |
0.932806 | − | 0.360379i | \(-0.117352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.3246 | 0.491645 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.13594 | −0.291527 | −0.145764 | − | 0.989319i | \(-0.546564\pi\) | ||||
−0.145764 | + | 0.989319i | \(0.546564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.74342 | + | 13.4120i | −0.367073 | + | 0.635789i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.16228 | − | 3.74517i | −0.102044 | − | 0.176746i | 0.810483 | − | 0.585763i | \(-0.199205\pi\) |
−0.912527 | + | 0.409017i | \(0.865872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.16228 | + | 8.94133i | 0.243082 | + | 0.421031i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.16228 | − | 3.74517i | 0.101593 | − | 0.175964i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.337722 | + | 15.0035i | −0.0158327 | + | 0.703375i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.91886 | + | 13.7159i | −0.370429 | + | 0.641601i | −0.989631 | − | 0.143630i | \(-0.954123\pi\) |
0.619203 | + | 0.785231i | \(0.287456\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.418861 | − | 0.725489i | −0.0195508 | − | 0.0338629i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.41886 | − | 9.38574i | −0.252382 | − | 0.437138i | 0.711799 | − | 0.702383i | \(-0.247880\pi\) |
−0.964181 | + | 0.265245i | \(0.914547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.4868 | −0.766208 | −0.383104 | − | 0.923705i | \(-0.625145\pi\) | ||||
−0.383104 | + | 0.923705i | \(0.625145\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.66228 | − | 8.07530i | 0.216208 | − | 0.374483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.18861 | −0.286375 | −0.143187 | − | 0.989696i | \(-0.545735\pi\) | ||||
−0.143187 | + | 0.989696i | \(0.545735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.2982 | 1.95315 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.40569 | + | 12.8270i | −0.341236 | + | 0.591039i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.3246 | −0.934524 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | − | 1.73205i | −0.0458831 | − | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.16228 | + | 5.47723i | 0.144791 | + | 0.250785i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.5811 | − | 25.2553i | 0.666229 | − | 1.15394i | −0.312721 | − | 0.949845i | \(-0.601241\pi\) |
0.978950 | − | 0.204098i | \(-0.0654261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.3246 | + | 14.4186i | −1.20030 | + | 0.657429i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.16228 | + | 7.20928i | −0.189390 | + | 0.328033i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.40569 | − | 11.0950i | −0.290868 | − | 0.503797i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.00000 | + | 12.1244i | 0.317200 | + | 0.549407i | 0.979903 | − | 0.199476i | \(-0.0639239\pi\) |
−0.662702 | + | 0.748883i | \(0.730591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.48683 | 0.383788 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7434 | − | 29.0004i | 0.755620 | − | 1.30877i | −0.189446 | − | 0.981891i | \(-0.560669\pi\) |
0.945066 | − | 0.326881i | \(-0.105998\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | 0.270226 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | 0.0898933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.4189 | + | 19.7780i | −0.512206 | + | 0.887167i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6491 | 0.655784 | 0.327892 | − | 0.944715i | \(-0.393662\pi\) | ||||
0.327892 | + | 0.944715i | \(0.393662\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.3246 | − | 17.8827i | −0.461267 | − | 0.798938i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.64911 | + | 9.78455i | 0.251881 | + | 0.436271i | 0.964044 | − | 0.265743i | \(-0.0856174\pi\) |
−0.712162 | + | 0.702015i | \(0.752284\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.162278 | − | 0.281073i | 0.00722126 | − | 0.0125076i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9868 | + | 0.584952i | 0.576766 | + | 0.0259786i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.32456 | − | 9.22240i | 0.236007 | − | 0.408776i | −0.723558 | − | 0.690264i | \(-0.757495\pi\) |
0.959565 | + | 0.281488i | \(0.0908279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8246 | + | 22.2128i | 0.567325 | + | 0.982636i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | + | 1.73205i | 0.0441511 | + | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.4868 | 0.462105 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.48683 | + | 12.9676i | −0.329271 | + | 0.570313i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.513167 | 0.0225255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.1359 | 0.531685 | 0.265843 | − | 0.964016i | \(-0.414350\pi\) | ||||
0.265843 | + | 0.964016i | \(0.414350\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.48683 | + | 9.50347i | −0.239922 | + | 0.415558i | −0.960692 | − | 0.277617i | \(-0.910455\pi\) |
0.720769 | + | 0.693175i | \(0.243789\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.16228 | −0.181657 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.90569 | − | 6.76486i | −0.170135 | − | 0.294682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.58114 | − | 6.20271i | 0.155408 | − | 0.269175i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3246 | + | 8.94133i | −0.707095 | + | 0.387292i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.74342 | + | 16.8761i | −0.421245 | + | 0.729617i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.256584 | + | 0.444416i | 0.0110724 | + | 0.0191780i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3246 | + | 17.8827i | 0.444710 | + | 0.770260i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.6228 | 1.57454 | 0.787268 | − | 0.616611i | \(-0.211495\pi\) | ||||
0.787268 | + | 0.616611i | \(0.211495\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.3246 | + | 21.3468i | −0.528897 | + | 0.916077i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.32456 | −0.313749 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.1359 | −1.07474 | −0.537368 | − | 0.843348i | \(-0.680581\pi\) | ||||
−0.537368 | + | 0.843348i | \(0.680581\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.50000 | + | 11.2583i | −0.277413 | + | 0.480494i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.3246 | −0.610247 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.8925 | − | 39.6510i | −0.973489 | − | 1.68613i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.16228 | − | 7.20928i | −0.176679 | − | 0.306017i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.48683 | + | 12.9676i | −0.317227 | + | 0.549454i | −0.979908 | − | 0.199448i | \(-0.936085\pi\) |
0.662681 | + | 0.748902i | \(0.269418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.824555 | − | 36.6313i | 0.0348750 | − | 1.54934i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.837722 | − | 1.45098i | 0.0353687 | − | 0.0612603i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.00000 | + | 15.5885i | 0.379305 | + | 0.656975i | 0.990961 | − | 0.134148i | \(-0.0428299\pi\) |
−0.611656 | + | 0.791123i | \(0.709497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.16228 | − | 3.74517i | −0.0909677 | − | 0.157561i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.16228 | 0.174799 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.5811 | − | 33.9155i | 0.820884 | − | 1.42181i | −0.0841407 | − | 0.996454i | \(-0.526815\pi\) |
0.905025 | − | 0.425359i | \(-0.139852\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.9737 | −0.710326 | −0.355163 | − | 0.934804i | \(-0.615575\pi\) | ||||
−0.355163 | + | 0.934804i | \(0.615575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.8114 | −0.493428 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | − | 1.73205i | 0.0417029 | − | 0.0722315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.6228 | 0.900168 | 0.450084 | − | 0.892986i | \(-0.351394\pi\) | ||||
0.450084 | + | 0.892986i | \(0.351394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.0811388 | − | 0.140537i | −0.00337201 | − | 0.00584050i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.32456 | + | 10.9545i | −0.261936 | + | 0.453687i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0811388 | + | 3.60464i | −0.00335468 | + | 0.149033i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.3925 | − | 28.3927i | 0.676592 | − | 1.17189i | −0.299409 | − | 0.954125i | \(-0.596789\pi\) |
0.976001 | − | 0.217767i | \(-0.0698772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.32456 | + | 16.1506i | 0.384212 | + | 0.665474i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.83772 | + | 4.91508i | 0.116728 | + | 0.202179i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.3246 | 1.32741 | 0.663705 | − | 0.747994i | \(-0.268983\pi\) | ||||
0.663705 | + | 0.747994i | \(0.268983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.74342 | + | 3.01969i | −0.0714731 | + | 0.123795i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.67544 | 0.273208 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.4868 | −1.36823 | −0.684117 | − | 0.729372i | \(-0.739812\pi\) | ||||
−0.684117 | + | 0.729372i | \(0.739812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.6491 | + | 32.3012i | −0.760713 | + | 1.31759i | 0.181770 | + | 0.983341i | \(0.441817\pi\) |
−0.942483 | + | 0.334253i | \(0.891516\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.1623 | 0.413840 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.675445 | − | 1.16990i | −0.0274155 | − | 0.0474850i | 0.851992 | − | 0.523555i | \(-0.175394\pi\) |
−0.879408 | + | 0.476070i | \(0.842061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.9057 | + | 25.8174i | −0.604009 | + | 1.04617i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.0680 | − | 14.0197i | −0.933230 | − | 0.567178i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7302 | − | 23.7815i | 0.554560 | − | 0.960525i | −0.443378 | − | 0.896335i | \(-0.646220\pi\) |
0.997938 | − | 0.0641906i | \(-0.0204466\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.58114 | − | 4.47066i | −0.104082 | − | 0.180275i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.48683 | − | 11.2355i | −0.261150 | − | 0.452325i | 0.705398 | − | 0.708812i | \(-0.250768\pi\) |
−0.966548 | + | 0.256487i | \(0.917435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.6754 | −0.750629 | −0.375315 | − | 0.926897i | \(-0.622465\pi\) | ||||
−0.375315 | + | 0.926897i | \(0.622465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | + | 1.73205i | −0.0401286 | + | 0.0695048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −64.4605 | −2.58256 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.00000 | + | 3.46410i | −0.0798723 | + | 0.138343i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.97367 | −0.278058 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.662278 | − | 1.14710i | −0.0263649 | − | 0.0456653i | 0.852542 | − | 0.522659i | \(-0.175060\pi\) |
−0.878907 | + | 0.476994i | \(0.841727\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.8246 | − | 20.4807i | −0.469984 | − | 0.814036i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0811388 | − | 0.140537i | 0.00321990 | − | 0.00557702i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.6491 | + | 17.8827i | −1.29360 | + | 0.708537i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.74342 | + | 4.75174i | −0.108528 | + | 0.187976i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.83772 | − | 3.18303i | −0.0725857 | − | 0.125722i | 0.827448 | − | 0.561542i | \(-0.189792\pi\) |
−0.900034 | + | 0.435820i | \(0.856458\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.756584 | + | 1.31044i | 0.0298367 | + | 0.0516788i | 0.880558 | − | 0.473938i | \(-0.157168\pi\) |
−0.850721 | + | 0.525617i | \(0.823835\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.1623 | 0.400139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.67544 | − | 11.5622i | 0.262439 | − | 0.454557i | −0.704451 | − | 0.709753i | \(-0.748807\pi\) |
0.966889 | + | 0.255196i | \(0.0821399\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.3246 | 0.562288 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.8114 | 1.52114 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.7434 | − | 29.0004i | 0.655221 | − | 1.13488i | −0.326618 | − | 0.945156i | \(-0.605909\pi\) |
0.981838 | − | 0.189719i | \(-0.0607576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.8114 | −0.617802 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.08114 | + | 5.33669i | 0.120207 | + | 0.208204i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.48683 | + | 2.57527i | 0.0579188 | + | 0.100318i | 0.893531 | − | 0.449002i | \(-0.148220\pi\) |
−0.835612 | + | 0.549320i | \(0.814887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6623 | − | 23.6638i | 0.531401 | − | 0.920414i | −0.467927 | − | 0.883767i | \(-0.654999\pi\) |
0.999328 | − | 0.0366466i | \(-0.0116676\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.58114 | + | 1.56871i | 0.100243 | + | 0.0609236i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.16228 | − | 7.20928i | 0.161406 | − | 0.279564i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.16228 | − | 12.4054i | −0.277324 | − | 0.480340i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.00000 | − | 3.46410i | −0.0773245 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.0000 | −1.00372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9189 | − | 25.8402i | 0.575080 | − | 0.996067i | −0.420953 | − | 0.907082i | \(-0.638304\pi\) |
0.996033 | − | 0.0889851i | \(-0.0283624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.9473 | −1.15097 | −0.575485 | − | 0.817813i | \(-0.695187\pi\) | ||||
−0.575485 | + | 0.817813i | \(0.695187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.6623 | − | 46.1804i | 1.02320 | − | 1.77224i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.83772 | 0.185382 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.7434 | − | 34.1966i | −0.755461 | − | 1.30850i | −0.945145 | − | 0.326651i | \(-0.894080\pi\) |
0.189684 | − | 0.981845i | \(-0.439254\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.41886 | + | 11.1178i | 0.245252 | + | 0.424789i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.83772 | + | 4.91508i | −0.108266 | + | 0.187522i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.4868 | − | 11.8433i | −0.742389 | − | 0.451193i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.82456 | + | 8.35637i | −0.183535 | + | 0.317891i | −0.943082 | − | 0.332561i | \(-0.892087\pi\) |
0.759547 | + | 0.650452i | \(0.225421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.16228 | + | 7.20928i | 0.158112 | + | 0.273858i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.662278 | + | 1.14710i | 0.0251216 | + | 0.0435119i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.32456 | −0.163804 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.1623 | − | 17.6016i | 0.384373 | − | 0.665753i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3246 | −0.692109 | −0.346054 | − | 0.938214i | \(-0.612479\pi\) | ||||
−0.346054 | + | 0.938214i | \(0.612479\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.6491 | 0.627933 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.74342 | − | 6.48379i | 0.140985 | − | 0.244194i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.35089 | 0.0508054 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.3114 | − | 21.3240i | −0.462364 | − | 0.800838i | 0.536714 | − | 0.843764i | \(-0.319665\pi\) |
−0.999078 | + | 0.0429263i | \(0.986332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.32456 | + | 16.1506i | −0.349207 | + | 0.604845i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.32456 | + | 3.46410i | −0.236525 | + | 0.129550i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.32456 | − | 14.4186i | 0.310886 | − | 0.538471i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.0680 | + | 22.6344i | 0.487353 | + | 0.844120i | 0.999894 | − | 0.0145423i | \(-0.00462913\pi\) |
−0.512541 | + | 0.858663i | \(0.671296\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.8246 | + | 37.8012i | 0.812789 | + | 1.40779i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.67544 | −0.211072 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.58114 | − | 6.20271i | 0.133000 | − | 0.230363i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.1623 | −1.48954 | −0.744768 | − | 0.667323i | \(-0.767440\pi\) | ||||
−0.744768 | + | 0.667323i | \(0.767440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.25658 | − | 7.37262i | 0.157435 | − | 0.272686i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8377 | 1.32370 | 0.661848 | − | 0.749638i | \(-0.269772\pi\) | ||||
0.661848 | + | 0.749638i | \(0.269772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.16228 | − | 8.94133i | −0.190413 | − | 0.329806i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.1623 | + | 17.6016i | 0.374332 | + | 0.648363i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.67544 | − | 6.36606i | 0.135203 | − | 0.234179i | −0.790472 | − | 0.612499i | \(-0.790165\pi\) |
0.925675 | + | 0.378319i | \(0.123498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.16228 | − | 3.74517i | −0.226377 | − | 0.137582i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.7171 | + | 42.8112i | −0.906782 | + | 1.57059i | −0.0882744 | + | 0.996096i | \(0.528135\pi\) |
−0.818507 | + | 0.574496i | \(0.805198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −81.1096 | −2.96368 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.64911 | − | 13.2486i | 0.279120 | − | 0.483450i | −0.692046 | − | 0.721853i | \(-0.743291\pi\) |
0.971166 | + | 0.238403i | \(0.0766239\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.9737 | −0.691439 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.32456 | −0.157387 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.8114 | + | 23.9220i | −0.501983 | + | 0.869461i | 0.498014 | + | 0.867169i | \(0.334063\pi\) |
−0.999997 | + | 0.00229180i | \(0.999270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.64911 | + | 4.58839i | 0.0960302 | + | 0.166329i | 0.910038 | − | 0.414525i | \(-0.136052\pi\) |
−0.814008 | + | 0.580854i | \(0.802719\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.2434 | − | 26.4024i | −0.551849 | − | 0.955830i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.418861 | + | 0.725489i | −0.0151440 | + | 0.0262301i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.581139 | + | 25.8174i | −0.0209837 | + | 0.932213i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.4868 | − | 44.1445i | 0.919079 | − | 1.59189i | 0.118261 | − | 0.992983i | \(-0.462268\pi\) |
0.800817 | − | 0.598908i | \(-0.204399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.0680 | − | 22.6344i | −0.470632 | − | 0.815158i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.16228 | + | 7.20928i | 0.149707 | + | 0.259300i | 0.931119 | − | 0.364715i | \(-0.118834\pi\) |
−0.781412 | + | 0.624015i | \(0.785500\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.32456 | −0.334948 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.3246 | − | 30.0070i | 0.621515 | − | 1.07650i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3246 | 0.369916 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9737 | −0.392669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.58114 | + | 6.20271i | −0.127979 | + | 0.221667i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.8114 | 0.528641 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.0811 | − | 20.9251i | −0.430646 | − | 0.745901i | 0.566283 | − | 0.824211i | \(-0.308381\pi\) |
−0.996929 | + | 0.0783100i | \(0.975048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.74342 | + | 8.21584i | 0.168870 | + | 0.292492i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.00000 | − | 15.5885i | 0.320003 | − | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.05480 | − | 46.8603i | 0.0374572 | − | 1.66406i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.16228 | − | 5.47723i | 0.112154 | − | 0.194257i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5811 | + | 20.0591i | 0.410225 | + | 0.710531i | 0.994914 | − | 0.100727i | \(-0.0321168\pi\) |
−0.584689 | + | 0.811257i | \(0.698784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.13594 | − | 5.43161i | −0.110942 | − | 0.192157i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4868 | −0.547200 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.16228 | + | 10.6734i | −0.217462 | + | 0.376655i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.32456 | 0.293402 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.4868 | 0.826776 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.1623 | + | 19.3336i | −0.392445 | + | 0.679734i | −0.992771 | − | 0.120021i | \(-0.961704\pi\) |
0.600327 | + | 0.799755i | \(0.295037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.97367 | −0.139534 | −0.0697671 | − | 0.997563i | \(-0.522226\pi\) | ||||
−0.0697671 | + | 0.997563i | \(0.522226\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.82456 | − | 8.35637i | −0.169205 | − | 0.293071i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.24342 | − | 7.34981i | −0.148640 | − | 0.257453i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.1623 | + | 17.6016i | −0.355533 | + | 0.615801i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.1623 | + | 7.20928i | −0.459927 | + | 0.251913i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0000 | + | 36.3731i | −0.732905 | + | 1.26943i | 0.222731 | + | 0.974880i | \(0.428503\pi\) |
−0.955636 | + | 0.294549i | \(0.904831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.16228 | + | 15.8695i | 0.319377 | + | 0.553177i | 0.980358 | − | 0.197225i | \(-0.0631931\pi\) |
−0.660981 | + | 0.750402i | \(0.729860\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.00000 | − | 1.73205i | −0.0348155 | − | 0.0603023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.4605 | −0.989669 | −0.494834 | − | 0.868987i | \(-0.664771\pi\) | ||||
−0.494834 | + | 0.868987i | \(0.664771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.82456 | − | 8.35637i | 0.167564 | − | 0.290229i | −0.769999 | − | 0.638045i | \(-0.779743\pi\) |
0.937563 | + | 0.347816i | \(0.113077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.6754 | −0.405017 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.64911 | −0.299674 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.3246 | + | 17.8827i | −0.357296 | + | 0.618855i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.32456 | 0.322304 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.4868 | + | 45.8765i | 0.914427 | + | 1.58383i | 0.807738 | + | 0.589542i | \(0.200692\pi\) |
0.106689 | + | 0.994292i | \(0.465975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1491 | − | 19.3108i | −0.384452 | − | 0.665891i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.58114 | + | 2.73861i | −0.0544573 | + | 0.0943228i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.98683 | − | 11.5394i | −0.205953 | − | 0.396968i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.5680 | − | 25.2325i | 0.500561 | − | 0.866998i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.4057 | + | 21.4873i | 0.425762 | + | 0.737442i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.32456 | + | 14.4186i | 0.285362 | + | 0.494262i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.7851 | −1.08830 | −0.544150 | − | 0.838988i | \(-0.683148\pi\) | ||||
−0.544150 | + | 0.838988i | \(0.683148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | − | 1.73205i | 0.0341993 | − | 0.0592349i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.48683 | 0.119108 | 0.0595540 | − | 0.998225i | \(-0.481032\pi\) | ||||
0.0595540 | + | 0.998225i | \(0.481032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.9473 | −1.46534 | −0.732672 | − | 0.680582i | \(-0.761727\pi\) | ||||
−0.732672 | + | 0.680582i | \(0.761727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.7434 | − | 18.6081i | 0.366135 | − | 0.634164i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.6754 | −0.397437 | −0.198718 | − | 0.980057i | \(-0.563678\pi\) | ||||
−0.198718 | + | 0.980057i | \(0.563678\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.256584 | − | 0.444416i | −0.00872410 | − | 0.0151106i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.14911 | − | 14.1147i | −0.276758 | − | 0.479359i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.0000 | − | 19.0526i | 0.373149 | − | 0.646314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.1359 | + | 17.6016i | −1.08888 | + | 0.596407i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.40569 | − | 11.0950i | 0.216800 | − | 0.375508i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.08114 | + | 3.60464i | 0.0703553 | + | 0.121859i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.1623 | − | 21.0657i | −0.410691 | − | 0.711338i | 0.584275 | − | 0.811556i | \(-0.301379\pi\) |
−0.994965 | + | 0.100219i | \(0.968046\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.4868 | −0.927108 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.16228 | + | 8.94133i | −0.173922 | + | 0.301241i | −0.939788 | − | 0.341759i | \(-0.888977\pi\) |
0.765866 | + | 0.643000i | \(0.222311\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.46050 | 0.183760 | 0.0918802 | − | 0.995770i | \(-0.470712\pi\) | ||||
0.0918802 | + | 0.995770i | \(0.470712\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.16228 | −0.240757 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.2302 | + | 33.3078i | −0.645689 | + | 1.11837i | 0.338453 | + | 0.940983i | \(0.390096\pi\) |
−0.984142 | + | 0.177382i | \(0.943237\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.675445 | 0.0226537 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | + | 1.73205i | 0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.48683 | + | 12.9676i | 0.250537 | + | 0.433943i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.256584 | − | 0.444416i | 0.00857664 | − | 0.0148552i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.162278 | − | 7.20928i | 0.00541829 | − | 0.240711i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.3925 | + | 57.8376i | −1.11370 | + | 1.92899i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.64911 | − | 4.58839i | −0.0882547 | − | 0.152862i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.1491 | + | 36.6313i | 0.703798 | + | 1.21901i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.6491 | 0.819364 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.64911 | + | 13.2486i | −0.253985 | + | 0.439914i | −0.964619 | − | 0.263647i | \(-0.915075\pi\) |
0.710635 | + | 0.703561i | \(0.248408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.324555 | 0.0107648 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.97367 | −0.231048 | −0.115524 | − | 0.993305i | \(-0.536855\pi\) | ||||
−0.115524 | + | 0.993305i | \(0.536855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.0000 | 0.429767 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.9057 | − | 56.9943i | −1.08664 | − | 1.88212i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.1623 | + | 24.5298i | 0.467170 | + | 0.809163i | 0.999297 | − | 0.0375022i | \(-0.0119401\pi\) |
−0.532126 | + | 0.846665i | \(0.678607\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0811 | + | 20.9251i | −0.398087 | + | 0.689507i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.445195 | − | 19.7780i | 0.0146538 | − | 0.651002i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.16228 | + | 7.20928i | −0.136855 | + | 0.237040i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.24342 | + | 9.08186i | 0.172216 | + | 0.298288i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.3246 | − | 35.2032i | −0.666827 | − | 1.15498i | −0.978786 | − | 0.204883i | \(-0.934319\pi\) |
0.311959 | − | 0.950095i | \(-0.399015\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.6491 | 0.676747 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.9057 | − | 22.3533i | 0.422513 | − | 0.731815i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.67544 | −0.0547929 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.9737 | 0.685180 | 0.342590 | − | 0.939485i | \(-0.388696\pi\) | ||||
0.342590 | + | 0.939485i | \(0.388696\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.24342 | − | 16.0101i | 0.301647 | − | 0.522469i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.4605 | −1.31897 | −0.659487 | − | 0.751716i | \(-0.729227\pi\) | ||||
−0.659487 | + | 0.751716i | \(0.729227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.16228 | + | 8.94133i | 0.168107 | + | 0.291170i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.08114 | − | 3.60464i | −0.0676995 | − | 0.117259i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.2302 | − | 35.0398i | 0.657395 | − | 1.13864i | −0.323893 | − | 0.946094i | \(-0.604992\pi\) |
0.981288 | − | 0.192547i | \(-0.0616749\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.9868 | − | 11.5394i | −0.616339 | − | 0.374585i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.16228 | + | 2.01312i | −0.0376894 | + | 0.0652800i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.8377 | + | 37.8240i | 0.707393 | + | 1.22524i | 0.965821 | + | 0.259210i | \(0.0834623\pi\) |
−0.258428 | + | 0.966031i | \(0.583204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.90569 | + | 10.2290i | 0.191104 | + | 0.331001i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.3246 | −0.463047 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.7171 | + | 46.2753i | −0.862740 | + | 1.49431i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.9473 | 1.80475 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.4868 | −0.627954 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0811388 | + | 0.140537i | −0.00261195 | + | 0.00452403i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.9737 | −0.996046 | −0.498023 | − | 0.867164i | \(-0.665940\pi\) | ||||
−0.498023 | + | 0.867164i | \(0.665940\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.837722 | − | 1.45098i | −0.0269115 | − | 0.0466121i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.8114 | − | 23.9220i | −0.443229 | − | 0.767694i | 0.554698 | − | 0.832052i | \(-0.312834\pi\) |
−0.997927 | + | 0.0643571i | \(0.979500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.75658 | + | 4.77454i | −0.0883720 | + | 0.153065i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.16228 | − | 1.73205i | 0.101274 | − | 0.0554700i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.4868 | + | 19.8958i | −0.367496 | + | 0.636522i | −0.989173 | − | 0.146751i | \(-0.953118\pi\) |
0.621677 | + | 0.783274i | \(0.286452\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.4868 | − | 26.8240i | −0.494961 | − | 0.857298i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.66228 | − | 6.34325i | −0.116928 | − | 0.202524i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.62278 | 0.306919 | 0.153459 | − | 0.988155i | \(-0.450959\pi\) | ||||
0.153459 | + | 0.988155i | \(0.450959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.83772 | − | 4.91508i | 0.0904174 | − | 0.156607i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.1623 | 0.991906 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.3246 | −0.646283 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.8114 | − | 39.5105i | 0.724628 | − | 1.25509i | −0.234499 | − | 0.972116i | \(-0.575345\pi\) |
0.959127 | − | 0.282976i | \(-0.0913216\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.67544 | 0.0849027 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.33772 | − | 5.78110i | −0.105813 | − | 0.183273i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.75658 | − | 11.7027i | −0.213983 | − | 0.370630i | 0.738974 | − | 0.673734i | \(-0.235310\pi\) |
−0.952958 | + | 0.303104i | \(0.901977\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.16228 | − | 7.20928i | 0.131689 | − | 0.228091i |
(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 | 1560.2.bg.e.841.1 | yes | 4 | |
13.3 | even | 3 | inner | 1560.2.bg.e.601.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.bg.e.601.1 | ✓ | 4 | 13.3 | even | 3 | inner | |
1560.2.bg.e.841.1 | yes | 4 | 1.1 | even | 1 | trivial |