Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2700,2,Mod(593,2700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2700, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2700.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.j (of order \(4\), 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: | \(21.5596085457\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.3 | ||
Root | \(1.54779 + 1.54779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2700.1457 |
Dual form | 2700.2.j.i.593.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1351\) | \(2377\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.79129 | + | 1.79129i | 0.677043 | + | 0.677043i | 0.959330 | − | 0.282287i | \(-0.0910930\pi\) |
−0.282287 | + | 0.959330i | \(0.591093\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.646084i | − | 0.194802i | −0.995245 | − | 0.0974008i | \(-0.968947\pi\) | ||
0.995245 | − | 0.0974008i | \(-0.0310529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.79129 | + | 3.79129i | −1.05151 | + | 1.05151i | −0.0529150 | + | 0.998599i | \(0.516851\pi\) |
−0.998599 | + | 0.0529150i | \(0.983149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.96640 | − | 4.96640i | 1.20453 | − | 1.20453i | 0.231755 | − | 0.972774i | \(-0.425553\pi\) |
0.972774 | − | 0.231755i | \(-0.0744469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.58258i | − | 1.51015i | −0.655640 | − | 0.755073i | \(-0.727601\pi\) | ||
0.655640 | − | 0.755073i | \(-0.272399\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.87083 | + | 1.87083i | 0.390095 | + | 0.390095i | 0.874721 | − | 0.484626i | \(-0.161044\pi\) |
−0.484626 | + | 0.874721i | \(0.661044\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.99455 | 1.48455 | 0.742276 | − | 0.670095i | \(-0.233747\pi\) | ||||
0.742276 | + | 0.670095i | \(0.233747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.582576 | −0.104634 | −0.0523168 | − | 0.998631i | \(-0.516661\pi\) | ||||
−0.0523168 | + | 0.998631i | \(0.516661\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.25290i | 0.664191i | 0.943246 | + | 0.332095i | \(0.107756\pi\) | ||||
−0.943246 | + | 0.332095i | \(0.892244\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.791288 | − | 0.791288i | 0.120670 | − | 0.120670i | −0.644193 | − | 0.764863i | \(-0.722807\pi\) |
0.764863 | + | 0.644193i | \(0.222807\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.93825 | + | 1.93825i | −0.282723 | + | 0.282723i | −0.834194 | − | 0.551471i | \(-0.814067\pi\) |
0.551471 | + | 0.834194i | \(0.314067\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 0.582576i | − | 0.0832251i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.47764 | + | 5.47764i | 0.752412 | + | 0.752412i | 0.974929 | − | 0.222517i | \(-0.0714273\pi\) |
−0.222517 | + | 0.974929i | \(0.571427\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8935 | 1.67859 | 0.839297 | − | 0.543672i | \(-0.182967\pi\) | ||||
0.839297 | + | 0.543672i | \(0.182967\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.16515 | 0.789367 | 0.394683 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394683 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | + | 7.00000i | 0.855186 | + | 0.855186i | 0.990766 | − | 0.135580i | \(-0.0432899\pi\) |
−0.135580 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3205i | 1.69954i | 0.527157 | + | 0.849768i | \(0.323258\pi\) | ||||
−0.527157 | + | 0.849768i | \(0.676742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.20871 | − | 1.20871i | 0.141469 | − | 0.141469i | −0.632825 | − | 0.774294i | \(-0.718105\pi\) |
0.774294 | + | 0.632825i | \(0.218105\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.15732 | − | 1.15732i | 0.131889 | − | 0.131889i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.16515i | 0.693634i | 0.937933 | + | 0.346817i | \(0.112737\pi\) | ||||
−0.937933 | + | 0.346817i | \(0.887263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.22474 | − | 1.22474i | −0.134433 | − | 0.134433i | 0.636688 | − | 0.771121i | \(-0.280304\pi\) |
−0.771121 | + | 0.636688i | \(0.780304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.42157 | −0.998684 | −0.499342 | − | 0.866405i | \(-0.666425\pi\) | ||||
−0.499342 | + | 0.866405i | \(0.666425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.5826 | −1.42384 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.58258 | − | 7.58258i | −0.769894 | − | 0.769894i | 0.208194 | − | 0.978088i | \(-0.433242\pi\) |
−0.978088 | + | 0.208194i | \(0.933242\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.50579i | 0.846358i | 0.906046 | + | 0.423179i | \(0.139086\pi\) | ||||
−0.906046 | + | 0.423179i | \(0.860914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.58258 | − | 3.58258i | 0.353002 | − | 0.353002i | −0.508224 | − | 0.861225i | \(-0.669698\pi\) |
0.861225 | + | 0.508224i | \(0.169698\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.5396 | − | 13.5396i | 1.30892 | − | 1.30892i | 0.386732 | − | 0.922192i | \(-0.373604\pi\) |
0.922192 | − | 0.386732i | \(-0.126396\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.7477i | 1.50836i | 0.656668 | + | 0.754179i | \(0.271965\pi\) | ||||
−0.656668 | + | 0.754179i | \(0.728035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.03383 | − | 5.03383i | −0.473542 | − | 0.473542i | 0.429517 | − | 0.903059i | \(-0.358684\pi\) |
−0.903059 | + | 0.429517i | \(0.858684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.7925 | 1.63104 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5826 | 0.962052 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.58258 | − | 6.58258i | −0.584109 | − | 0.584109i | 0.351921 | − | 0.936030i | \(-0.385529\pi\) |
−0.936030 | + | 0.351921i | \(0.885529\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.93280i | − | 0.867833i | −0.900953 | − | 0.433917i | \(-0.857131\pi\) | ||
0.900953 | − | 0.433917i | \(-0.142869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.7913 | − | 11.7913i | 1.02243 | − | 1.02243i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.22474 | − | 1.22474i | 0.104637 | − | 0.104637i | −0.652850 | − | 0.757487i | \(-0.726427\pi\) |
0.757487 | + | 0.652850i | \(0.226427\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.1652i | 0.947016i | 0.880790 | + | 0.473508i | \(0.157012\pi\) | ||||
−0.880790 | + | 0.473508i | \(0.842988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.44949 | + | 2.44949i | 0.204837 | + | 0.204837i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7362 | 0.961468 | 0.480734 | − | 0.876867i | \(-0.340370\pi\) | ||||
0.480734 | + | 0.876867i | \(0.340370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.1652 | −1.39688 | −0.698440 | − | 0.715669i | \(-0.746122\pi\) | ||||
−0.698440 | + | 0.715669i | \(0.746122\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.62614 | + | 3.62614i | 0.289397 | + | 0.289397i | 0.836842 | − | 0.547445i | \(-0.184399\pi\) |
−0.547445 | + | 0.836842i | \(0.684399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.70239i | 0.528222i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.58258 | − | 8.58258i | 0.672239 | − | 0.672239i | −0.285993 | − | 0.958232i | \(-0.592323\pi\) |
0.958232 | + | 0.285993i | \(0.0923233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.76981 | − | 6.76981i | 0.523863 | − | 0.523863i | −0.394872 | − | 0.918736i | \(-0.629211\pi\) |
0.918736 | + | 0.394872i | \(0.129211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 15.7477i | − | 1.21136i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.6070 | + | 13.6070i | 1.03452 | + | 1.03452i | 0.999382 | + | 0.0351417i | \(0.0111883\pi\) |
0.0351417 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.7646 | 1.85099 | 0.925496 | − | 0.378757i | \(-0.123648\pi\) | ||||
0.925496 | + | 0.378757i | \(0.123648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.41742 | −0.402674 | −0.201337 | − | 0.979522i | \(-0.564529\pi\) | ||||
−0.201337 | + | 0.979522i | \(0.564529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.20871 | − | 3.20871i | −0.234644 | − | 0.234644i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.74166i | − | 0.270737i | −0.990795 | − | 0.135368i | \(-0.956778\pi\) | ||
0.990795 | − | 0.135368i | \(-0.0432218\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7913 | + | 15.7913i | −1.13668 | + | 1.13668i | −0.147641 | + | 0.989041i | \(0.547168\pi\) |
−0.989041 | + | 0.147641i | \(0.952832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.12372 | + | 6.12372i | −0.436297 | + | 0.436297i | −0.890764 | − | 0.454467i | \(-0.849830\pi\) |
0.454467 | + | 0.890764i | \(0.349830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.5826i | − | 0.962843i | −0.876489 | − | 0.481422i | \(-0.840121\pi\) | ||
0.876489 | − | 0.481422i | \(-0.159879\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.3205 | + | 14.3205i | 1.00511 | + | 1.00511i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.25290 | −0.294179 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.1652 | 1.80128 | 0.900642 | − | 0.434563i | \(-0.143097\pi\) | ||||
0.900642 | + | 0.434563i | \(0.143097\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.04356 | − | 1.04356i | −0.0708415 | − | 0.0708415i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.6581i | 2.53316i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1652 | + | 12.1652i | −0.814639 | + | 0.814639i | −0.985325 | − | 0.170687i | \(-0.945401\pi\) |
0.170687 | + | 0.985325i | \(0.445401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.5453 | − | 15.5453i | 1.03178 | − | 1.03178i | 0.0322989 | − | 0.999478i | \(-0.489717\pi\) |
0.999478 | − | 0.0322989i | \(-0.0102829\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0000i | 0.991228i | 0.868543 | + | 0.495614i | \(0.165057\pi\) | ||||
−0.868543 | + | 0.495614i | \(0.834943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.38774 | + | 4.38774i | 0.287450 | + | 0.287450i | 0.836071 | − | 0.548621i | \(-0.184847\pi\) |
−0.548621 | + | 0.836071i | \(0.684847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.1015 | −0.976833 | −0.488417 | − | 0.872611i | \(-0.662425\pi\) | ||||
−0.488417 | + | 0.872611i | \(0.662425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.74773 | −0.241412 | −0.120706 | − | 0.992688i | \(-0.538516\pi\) | ||||
−0.120706 | + | 0.992688i | \(0.538516\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.9564 | + | 24.9564i | 1.58794 | + | 1.58794i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 27.3489i | − | 1.72625i | −0.504991 | − | 0.863124i | \(-0.668504\pi\) | ||
0.504991 | − | 0.863124i | \(-0.331496\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.20871 | − | 1.20871i | 0.0759911 | − | 0.0759911i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.87083 | − | 1.87083i | 0.116699 | − | 0.116699i | −0.646346 | − | 0.763045i | \(-0.723704\pi\) |
0.763045 | + | 0.646346i | \(0.223704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 10.7477i | − | 0.667831i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.7700 | − | 16.7700i | −1.03408 | − | 1.03408i | −0.999398 | − | 0.0346864i | \(-0.988957\pi\) |
−0.0346864 | − | 0.999398i | \(-0.511043\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.8318 | 0.904310 | 0.452155 | − | 0.891939i | \(-0.350655\pi\) | ||||
0.452155 | + | 0.891939i | \(0.350655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7477 | 0.835115 | 0.417557 | − | 0.908651i | \(-0.362886\pi\) | ||||
0.417557 | + | 0.908651i | \(0.362886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.791288 | − | 0.791288i | −0.0475439 | − | 0.0475439i | 0.682935 | − | 0.730479i | \(-0.260703\pi\) |
−0.730479 | + | 0.682935i | \(0.760703\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.511238i | − | 0.0304979i | −0.999884 | − | 0.0152490i | \(-0.995146\pi\) | ||
0.999884 | − | 0.0152490i | \(-0.00485408\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7913 | + | 14.7913i | −0.879251 | + | 0.879251i | −0.993457 | − | 0.114206i | \(-0.963568\pi\) |
0.114206 | + | 0.993457i | \(0.463568\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.61816 | + | 7.61816i | −0.449686 | + | 0.449686i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 32.3303i | − | 1.90178i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.73598 | + | 1.73598i | 0.101417 | + | 0.101417i | 0.755995 | − | 0.654578i | \(-0.227153\pi\) |
−0.654578 | + | 0.755995i | \(0.727153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.1857 | −0.820380 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.83485 | 0.163398 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0000 | − | 15.0000i | −0.856095 | − | 0.856095i | 0.134780 | − | 0.990876i | \(-0.456967\pi\) |
−0.990876 | + | 0.134780i | \(0.956967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 26.2983i | − | 1.49124i | −0.666371 | − | 0.745620i | \(-0.732153\pi\) | ||
0.666371 | − | 0.745620i | \(-0.267847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.16515 | + | 9.16515i | −0.518045 | + | 0.518045i | −0.916979 | − | 0.398934i | \(-0.869380\pi\) |
0.398934 | + | 0.916979i | \(0.369380\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.22474 | − | 1.22474i | 0.0687885 | − | 0.0687885i | −0.671876 | − | 0.740664i | \(-0.734511\pi\) |
0.740664 | + | 0.671876i | \(0.234511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.16515i | − | 0.289193i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.6917 | − | 32.6917i | −1.81902 | − | 1.81902i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.94393 | −0.382831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.58258 | −0.526706 | −0.263353 | − | 0.964700i | \(-0.584828\pi\) | ||||
−0.263353 | + | 0.964700i | \(0.584828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9564 | + | 18.9564i | 1.03262 | + | 1.03262i | 0.999450 | + | 0.0331734i | \(0.0105614\pi\) |
0.0331734 | + | 0.999450i | \(0.489439\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.376393i | 0.0203828i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5826 | − | 13.5826i | 0.733390 | − | 0.733390i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.50579 | + | 8.50579i | −0.456615 | + | 0.456615i | −0.897543 | − | 0.440928i | \(-0.854649\pi\) |
0.440928 | + | 0.897543i | \(0.354649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.252273i | − | 0.0135039i | −0.999977 | − | 0.00675193i | \(-0.997851\pi\) | ||
0.999977 | − | 0.00675193i | \(-0.00214922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79796 | + | 9.79796i | 0.521493 | + | 0.521493i | 0.918022 | − | 0.396529i | \(-0.129785\pi\) |
−0.396529 | + | 0.918022i | \(0.629785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.134846 | −0.00711688 | −0.00355844 | − | 0.999994i | \(-0.501133\pi\) | ||||
−0.00355844 | + | 0.999994i | \(0.501133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24.3303 | −1.28054 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.7913 | − | 17.7913i | −0.928698 | − | 0.928698i | 0.0689242 | − | 0.997622i | \(-0.478043\pi\) |
−0.997622 | + | 0.0689242i | \(0.978043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.6241i | 1.01883i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.74773 | − | 6.74773i | 0.349384 | − | 0.349384i | −0.510496 | − | 0.859880i | \(-0.670538\pi\) |
0.859880 | + | 0.510496i | \(0.170538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.3097 | + | 30.3097i | −1.56103 | + | 1.56103i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000i | 0.0513665i | 0.999670 | + | 0.0256833i | \(0.00817614\pi\) | ||||
−0.999670 | + | 0.0256833i | \(0.991824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.3487 | − | 17.3487i | −0.886477 | − | 0.886477i | 0.107706 | − | 0.994183i | \(-0.465650\pi\) |
−0.994183 | + | 0.107706i | \(0.965650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −39.0851 | −1.98169 | −0.990847 | − | 0.134986i | \(-0.956901\pi\) | ||||
−0.990847 | + | 0.134986i | \(0.956901\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.5826 | 0.939761 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.9564 | − | 16.9564i | −0.851019 | − | 0.851019i | 0.139239 | − | 0.990259i | \(-0.455534\pi\) |
−0.990259 | + | 0.139239i | \(0.955534\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.44949i | 0.122322i | 0.998128 | + | 0.0611608i | \(0.0194803\pi\) | ||||
−0.998128 | + | 0.0611608i | \(0.980520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.20871 | − | 2.20871i | 0.110024 | − | 0.110024i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.93825 | + | 1.93825i | −0.0960756 | + | 0.0960756i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.1652i | 0.601528i | 0.953699 | + | 0.300764i | \(0.0972417\pi\) | ||||
−0.953699 | + | 0.300764i | \(0.902758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.0960 | + | 23.0960i | 1.13648 | + | 1.13648i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6127 | −0.762731 | −0.381365 | − | 0.924424i | \(-0.624546\pi\) | ||||
−0.381365 | + | 0.924424i | \(0.624546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4174 | −0.556451 | −0.278226 | − | 0.960516i | \(-0.589746\pi\) | ||||
−0.278226 | + | 0.960516i | \(0.589746\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.0436 | + | 11.0436i | 0.534435 | + | 0.534435i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.67991i | 0.273592i | 0.990599 | + | 0.136796i | \(0.0436804\pi\) | ||||
−0.990599 | + | 0.136796i | \(0.956320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.79129 | + | 5.79129i | −0.278312 | + | 0.278312i | −0.832435 | − | 0.554123i | \(-0.813054\pi\) |
0.554123 | + | 0.832435i | \(0.313054\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.3149 | − | 12.3149i | 0.589100 | − | 0.589100i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.1652i | 1.24879i | 0.781107 | + | 0.624397i | \(0.214655\pi\) | ||||
−0.781107 | + | 0.624397i | \(0.785345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5115 | + | 10.5115i | 0.499415 | + | 0.499415i | 0.911256 | − | 0.411841i | \(-0.135114\pi\) |
−0.411841 | + | 0.911256i | \(0.635114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.6238 | −0.595756 | −0.297878 | − | 0.954604i | \(-0.596279\pi\) | ||||
−0.297878 | + | 0.954604i | \(0.596279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.74773 | 0.129385 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.7477 | + | 22.7477i | 1.06409 | + | 1.06409i | 0.997800 | + | 0.0662936i | \(0.0211174\pi\) |
0.0662936 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.74166i | 0.174266i | 0.996197 | + | 0.0871332i | \(0.0277706\pi\) | ||||
−0.996197 | + | 0.0871332i | \(0.972229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.74773 | + | 3.74773i | −0.174172 | + | 0.174172i | −0.788809 | − | 0.614638i | \(-0.789302\pi\) |
0.614638 | + | 0.788809i | \(0.289302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5678 | + | 16.5678i | −0.766665 | + | 0.766665i | −0.977518 | − | 0.210853i | \(-0.932376\pi\) |
0.210853 | + | 0.977518i | \(0.432376\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.0780i | 1.15800i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.511238 | − | 0.511238i | −0.0235068 | − | 0.0235068i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.2981 | 0.607604 | 0.303802 | − | 0.952735i | \(-0.401744\pi\) | ||||
0.303802 | + | 0.952735i | \(0.401744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.7477 | 1.03721 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.37386 | − | 8.37386i | −0.379456 | − | 0.379456i | 0.491450 | − | 0.870906i | \(-0.336467\pi\) |
−0.870906 | + | 0.491450i | \(0.836467\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 27.2141i | − | 1.22815i | −0.789246 | − | 0.614077i | \(-0.789528\pi\) | ||
0.789246 | − | 0.614077i | \(-0.210472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.7042 | − | 39.7042i | 1.78819 | − | 1.78819i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.6522 | + | 25.6522i | −1.15066 | + | 1.15066i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.5826i | 0.831870i | 0.909394 | + | 0.415935i | \(0.136546\pi\) | ||||
−0.909394 | + | 0.415935i | \(0.863454\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.9610 | − | 12.9610i | −0.577900 | − | 0.577900i | 0.356424 | − | 0.934324i | \(-0.383996\pi\) |
−0.934324 | + | 0.356424i | \(0.883996\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.21362 | −0.319738 | −0.159869 | − | 0.987138i | \(-0.551107\pi\) | ||||
−0.159869 | + | 0.987138i | \(0.551107\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.33030 | 0.191561 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.25227 | + | 1.25227i | 0.0550749 | + | 0.0550749i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.4331i | − | 1.15806i | −0.815307 | − | 0.579029i | \(-0.803432\pi\) | ||
0.815307 | − | 0.579029i | \(-0.196568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.04356 | − | 5.04356i | 0.220540 | − | 0.220540i | −0.588186 | − | 0.808726i | \(-0.700158\pi\) |
0.808726 | + | 0.588186i | \(0.200158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.89331 | + | 2.89331i | −0.126034 | + | 0.126034i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 16.0000i | − | 0.695652i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.1240 | − | 16.1240i | −0.698406 | − | 0.698406i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.376393 | −0.0162124 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.1652 | −1.76983 | −0.884914 | − | 0.465754i | \(-0.845783\pi\) | ||||
−0.884914 | + | 0.465754i | \(0.845783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.5390 | − | 29.5390i | −1.26300 | − | 1.26300i | −0.949633 | − | 0.313364i | \(-0.898544\pi\) |
−0.313364 | − | 0.949633i | \(-0.601456\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 52.6248i | − | 2.24189i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0436 | + | 11.0436i | −0.469620 | + | 0.469620i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.6745 | − | 13.6745i | 0.579406 | − | 0.579406i | −0.355334 | − | 0.934739i | \(-0.615633\pi\) |
0.934739 | + | 0.355334i | \(0.115633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.00000i | 0.253773i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.47197 | − | 3.47197i | −0.146326 | − | 0.146326i | 0.630149 | − | 0.776475i | \(-0.282994\pi\) |
−0.776475 | + | 0.630149i | \(0.782994\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.4895 | −1.36203 | −0.681014 | − | 0.732270i | \(-0.738461\pi\) | ||||
−0.681014 | + | 0.732270i | \(0.738461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.9129 | −0.624085 | −0.312042 | − | 0.950068i | \(-0.601013\pi\) | ||||
−0.312042 | + | 0.950068i | \(0.601013\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.37386 | + | 4.37386i | 0.182086 | + | 0.182086i | 0.792264 | − | 0.610178i | \(-0.208902\pi\) |
−0.610178 | + | 0.792264i | \(0.708902\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.38774i | − | 0.182034i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.53901 | − | 3.53901i | 0.146571 | − | 0.146571i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.2477 | − | 22.2477i | 0.918260 | − | 0.918260i | −0.0786430 | − | 0.996903i | \(-0.525059\pi\) |
0.996903 | + | 0.0786430i | \(0.0250587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.83485i | 0.158012i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.45516 | − | 4.45516i | −0.182952 | − | 0.182952i | 0.609689 | − | 0.792641i | \(-0.291294\pi\) |
−0.792641 | + | 0.609689i | \(0.791294\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.82588 | −0.115462 | −0.0577312 | − | 0.998332i | \(-0.518387\pi\) | ||||
−0.0577312 | + | 0.998332i | \(0.518387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7477 | 0.642363 | 0.321182 | − | 0.947018i | \(-0.395920\pi\) | ||||
0.321182 | + | 0.947018i | \(0.395920\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.1216 | − | 25.1216i | −1.01965 | − | 1.01965i | −0.999803 | − | 0.0198510i | \(-0.993681\pi\) |
−0.0198510 | − | 0.999803i | \(-0.506319\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.6969i | − | 0.594574i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3303 | − | 24.3303i | 0.982692 | − | 0.982692i | −0.0171611 | − | 0.999853i | \(-0.505463\pi\) |
0.999853 | + | 0.0171611i | \(0.00546280\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2702 | + | 23.2702i | −0.936821 | + | 0.936821i | −0.998119 | − | 0.0612984i | \(-0.980476\pi\) |
0.0612984 | + | 0.998119i | \(0.480476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.7477i | 0.431988i | 0.976395 | + | 0.215994i | \(0.0692991\pi\) | ||||
−0.976395 | + | 0.215994i | \(0.930701\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.8767 | − | 16.8767i | −0.676152 | − | 0.676152i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.7984 | −1.18814 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.16515 | −0.0861933 | −0.0430967 | − | 0.999071i | \(-0.513722\pi\) | ||||
−0.0430967 | + | 0.999071i | \(0.513722\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.20871 | + | 2.20871i | 0.0875124 | + | 0.0875124i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 0.269691i | − | 0.0106522i | −0.999986 | − | 0.00532608i | \(-0.998305\pi\) | ||
0.999986 | − | 0.00532608i | \(-0.00169535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.53901 | + | 8.53901i | −0.336746 | + | 0.336746i | −0.855141 | − | 0.518395i | \(-0.826530\pi\) |
0.518395 | + | 0.855141i | \(0.326530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.4835 | − | 17.4835i | 0.687349 | − | 0.687349i | −0.274296 | − | 0.961645i | \(-0.588445\pi\) |
0.961645 | + | 0.274296i | \(0.0884449\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.33030i | − | 0.326993i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.59001 | − | 4.59001i | −0.179621 | − | 0.179621i | 0.611570 | − | 0.791191i | \(-0.290538\pi\) |
−0.791191 | + | 0.611570i | \(0.790538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.7700 | −0.653268 | −0.326634 | − | 0.945151i | \(-0.605914\pi\) | ||||
−0.326634 | + | 0.945151i | \(0.605914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.4955 | −1.22503 | −0.612516 | − | 0.790459i | \(-0.709842\pi\) | ||||
−0.612516 | + | 0.790459i | \(0.709842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.9564 | + | 14.9564i | 0.579116 | + | 0.579116i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.98320i | − | 0.153770i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.04356 | − | 7.04356i | 0.271509 | − | 0.271509i | −0.558198 | − | 0.829708i | \(-0.688507\pi\) |
0.829708 | + | 0.558198i | \(0.188507\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.05630 | + | 6.05630i | −0.232763 | + | 0.232763i | −0.813845 | − | 0.581082i | \(-0.802629\pi\) |
0.581082 | + | 0.813845i | \(0.302629\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 27.1652i | − | 1.04250i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.4497 | + | 12.4497i | 0.476375 | + | 0.476375i | 0.903970 | − | 0.427595i | \(-0.140639\pi\) |
−0.427595 | + | 0.903970i | \(0.640639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.5346 | −1.58234 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.6606 | 1.50876 | 0.754380 | − | 0.656438i | \(-0.227938\pi\) | ||||
0.754380 | + | 0.656438i | \(0.227938\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.1216 | + | 21.1216i | 0.800037 | + | 0.800037i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.2141i | 1.02786i | 0.857832 | + | 0.513931i | \(0.171811\pi\) | ||||
−0.857832 | + | 0.513931i | \(0.828189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.7477 | + | 19.7477i | −0.744800 | + | 0.744800i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.2363 | + | 15.2363i | −0.573021 | + | 0.573021i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 26.0000i | − | 0.976450i | −0.872718 | − | 0.488225i | \(-0.837644\pi\) | ||
0.872718 | − | 0.488225i | \(-0.162356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.08990 | − | 1.08990i | −0.0408171 | − | 0.0408171i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.0120 | −1.38032 | −0.690158 | − | 0.723659i | \(-0.742459\pi\) | ||||
−0.690158 | + | 0.723659i | \(0.742459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8348 | 0.477995 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3303 | + | 12.3303i | 0.457306 | + | 0.457306i | 0.897770 | − | 0.440464i | \(-0.145186\pi\) |
−0.440464 | + | 0.897770i | \(0.645186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.85971i | − | 0.290702i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.9129 | + | 23.9129i | −0.883242 | + | 0.883242i | −0.993863 | − | 0.110620i | \(-0.964716\pi\) |
0.110620 | + | 0.993863i | \(0.464716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.52259 | − | 4.52259i | 0.166592 | − | 0.166592i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.4174i | − | 0.419997i | −0.977702 | − | 0.209998i | \(-0.932654\pi\) | ||
0.977702 | − | 0.209998i | \(-0.0673459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.8656 | + | 19.8656i | 0.728799 | + | 0.728799i | 0.970380 | − | 0.241582i | \(-0.0776663\pi\) |
−0.241582 | + | 0.970380i | \(0.577666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.5067 | 1.77240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0000 | 0.547358 | 0.273679 | − | 0.961821i | \(-0.411759\pi\) | ||||
0.273679 | + | 0.961821i | \(0.411759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | − | 15.0000i | −0.545184 | − | 0.545184i | 0.379860 | − | 0.925044i | \(-0.375972\pi\) |
−0.925044 | + | 0.379860i | \(0.875972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.1523i | 1.05677i | 0.849005 | + | 0.528386i | \(0.177202\pi\) | ||||
−0.849005 | + | 0.528386i | \(0.822798\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.2087 | + | 28.2087i | −1.02122 | + | 1.02122i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.8831 | + | 48.8831i | −1.76507 | + | 1.76507i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.0000i | 0.829401i | 0.909958 | + | 0.414701i | \(0.136114\pi\) | ||||
−0.909958 | + | 0.414701i | \(0.863886\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6129 | − | 25.6129i | −0.921233 | − | 0.921233i | 0.0758833 | − | 0.997117i | \(-0.475822\pi\) |
−0.997117 | + | 0.0758833i | \(0.975822\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.9950 | 1.00303 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.25227 | 0.331072 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.7042 | + | 28.7042i | 1.02319 | + | 1.02319i | 0.999725 | + | 0.0234684i | \(0.00747093\pi\) |
0.0234684 | + | 0.999725i | \(0.492529\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 18.0341i | − | 0.641217i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.3739 | + | 23.3739i | −0.830030 | + | 0.830030i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.0849 | + | 29.0849i | −1.03024 | + | 1.03024i | −0.0307120 | + | 0.999528i | \(0.509777\pi\) |
−0.999528 | + | 0.0307120i | \(0.990223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.2523i | 0.681096i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.780929 | − | 0.780929i | −0.0275584 | − | 0.0275584i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.8379 | −1.40063 | −0.700313 | − | 0.713836i | \(-0.746956\pi\) | ||||
−0.700313 | + | 0.713836i | \(0.746956\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.3303 | −0.573434 | −0.286717 | − | 0.958015i | \(-0.592564\pi\) | ||||
−0.286717 | + | 0.958015i | \(0.592564\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.20871 | − | 5.20871i | −0.182230 | − | 0.182230i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.91033i | − | 0.310973i | −0.987838 | − | 0.155486i | \(-0.950306\pi\) | ||
0.987838 | − | 0.155486i | \(-0.0496944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.1216 | − | 11.1216i | 0.387674 | − | 0.387674i | −0.486183 | − | 0.873857i | \(-0.661611\pi\) |
0.873857 | + | 0.486183i | \(0.161611\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.16300 | + | 3.16300i | −0.109988 | + | 0.109988i | −0.759959 | − | 0.649971i | \(-0.774781\pi\) |
0.649971 | + | 0.759959i | \(0.274781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 33.0780i | − | 1.14885i | −0.818558 | − | 0.574424i | \(-0.805226\pi\) | ||
0.818558 | − | 0.574424i | \(-0.194774\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.89331 | − | 2.89331i | −0.100247 | − | 0.100247i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.3605 | 1.53149 | 0.765747 | − | 0.643141i | \(-0.222369\pi\) | ||||
0.765747 | + | 0.643141i | \(0.222369\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.9129 | 1.20389 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9564 | + | 18.9564i | 0.651351 | + | 0.651351i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 11.2250i | − | 0.384787i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3303 | + | 16.3303i | −0.559139 | + | 0.559139i | −0.929062 | − | 0.369923i | \(-0.879384\pi\) |
0.369923 | + | 0.929062i | \(0.379384\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.59001 | + | 4.59001i | −0.156792 | + | 0.156792i | −0.781143 | − | 0.624352i | \(-0.785363\pi\) |
0.624352 | + | 0.781143i | \(0.285363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.9129i | − | 1.53241i | −0.642598 | − | 0.766204i | \(-0.722143\pi\) | ||
0.642598 | − | 0.766204i | \(-0.277857\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.1800 | + | 12.1800i | 0.414613 | + | 0.414613i | 0.883342 | − | 0.468729i | \(-0.155288\pi\) |
−0.468729 | + | 0.883342i | \(0.655288\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.98320 | 0.135121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.0780 | −1.79848 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.2087 | − | 17.2087i | −0.581097 | − | 0.581097i | 0.354108 | − | 0.935205i | \(-0.384785\pi\) |
−0.935205 | + | 0.354108i | \(0.884785\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.3319i | 0.617617i | 0.951124 | + | 0.308809i | \(0.0999303\pi\) | ||||
−0.951124 | + | 0.308809i | \(0.900070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7913 | − | 17.7913i | 0.598725 | − | 0.598725i | −0.341249 | − | 0.939973i | \(-0.610850\pi\) |
0.939973 | + | 0.341249i | \(0.110850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.0456 | − | 32.0456i | 1.07599 | − | 1.07599i | 0.0791222 | − | 0.996865i | \(-0.474788\pi\) |
0.996865 | − | 0.0791222i | \(-0.0252117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23.5826i | − | 0.790934i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7587 | + | 12.7587i | 0.426953 | + | 0.426953i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.65743 | −0.155334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.4083 | 1.81260 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.7477 | + | 18.7477i | 0.622508 | + | 0.622508i | 0.946172 | − | 0.323664i | \(-0.104915\pi\) |
−0.323664 | + | 0.946172i | \(0.604915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.01703i | 0.298748i | 0.988781 | + | 0.149374i | \(0.0477258\pi\) | ||||
−0.988781 | + | 0.149374i | \(0.952274\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.791288 | + | 0.791288i | −0.0261878 | + | 0.0261878i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.7925 | − | 17.7925i | 0.587561 | − | 0.587561i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.0000i | − | 0.527791i | −0.964551 | − | 0.263896i | \(-0.914993\pi\) | ||
0.964551 | − | 0.263896i | \(-0.0850075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54.2933 | − | 54.2933i | −1.78709 | − | 1.78709i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.8039 | −0.715361 | −0.357681 | − | 0.933844i | \(-0.616432\pi\) | ||||
−0.357681 | + | 0.933844i | \(0.616432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.83485 | −0.125682 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.0780 | − | 27.0780i | −0.884601 | − | 0.884601i | 0.109397 | − | 0.993998i | \(-0.465108\pi\) |
−0.993998 | + | 0.109397i | \(0.965108\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28.7759i | − | 0.938069i | −0.883180 | − | 0.469034i | \(-0.844602\pi\) | ||
0.883180 | − | 0.469034i | \(-0.155398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.95644 | + | 7.95644i | −0.259097 | + | 0.259097i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.7644 | + | 14.7644i | −0.479777 | + | 0.479777i | −0.905060 | − | 0.425283i | \(-0.860175\pi\) |
0.425283 | + | 0.905060i | \(0.360175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.16515i | 0.297513i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.5342 | + | 21.5342i | 0.697560 | + | 0.697560i | 0.963884 | − | 0.266324i | \(-0.0858090\pi\) |
−0.266324 | + | 0.963884i | \(0.585809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.38774 | 0.141688 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6606 | −0.989052 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.252273 | + | 0.252273i | 0.00811255 | + | 0.00811255i | 0.711151 | − | 0.703039i | \(-0.248174\pi\) |
−0.703039 | + | 0.711151i | \(0.748174\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.6073i | 0.757593i | 0.925480 | + | 0.378797i | \(0.123662\pi\) | ||||
−0.925480 | + | 0.378797i | \(0.876338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | + | 20.0000i | −0.641171 | + | 0.641171i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.02248 | + | 1.02248i | −0.0327119 | + | 0.0327119i | −0.723274 | − | 0.690562i | \(-0.757363\pi\) |
0.690562 | + | 0.723274i | \(0.257363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.08712i | 0.194545i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.30352 | − | 8.30352i | −0.264841 | − | 0.264841i | 0.562176 | − | 0.827017i | \(-0.309964\pi\) |
−0.827017 | + | 0.562176i | \(0.809964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.96073 | 0.0941457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.0000 | 0.412959 | 0.206479 | − | 0.978451i | \(-0.433799\pi\) | ||||
0.206479 | + | 0.978451i | \(0.433799\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.0436 | + | 10.0436i | 0.318083 | + | 0.318083i | 0.848030 | − | 0.529948i | \(-0.177788\pi\) |
−0.529948 | + | 0.848030i | \(0.677788\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2700.2.j.i.1457.3 | 8 | ||
3.2 | odd | 2 | inner | 2700.2.j.i.1457.4 | 8 | ||
5.2 | odd | 4 | 540.2.j.b.53.1 | ✓ | 8 | ||
5.3 | odd | 4 | inner | 2700.2.j.i.593.3 | 8 | ||
5.4 | even | 2 | 540.2.j.b.377.3 | yes | 8 | ||
15.2 | even | 4 | 540.2.j.b.53.4 | yes | 8 | ||
15.8 | even | 4 | inner | 2700.2.j.i.593.4 | 8 | ||
15.14 | odd | 2 | 540.2.j.b.377.2 | yes | 8 | ||
20.7 | even | 4 | 2160.2.w.c.593.1 | 8 | |||
20.19 | odd | 2 | 2160.2.w.c.1457.3 | 8 | |||
45.2 | even | 12 | 1620.2.x.c.53.1 | 16 | |||
45.4 | even | 6 | 1620.2.x.c.917.1 | 16 | |||
45.7 | odd | 12 | 1620.2.x.c.53.4 | 16 | |||
45.14 | odd | 6 | 1620.2.x.c.917.4 | 16 | |||
45.22 | odd | 12 | 1620.2.x.c.593.2 | 16 | |||
45.29 | odd | 6 | 1620.2.x.c.377.2 | 16 | |||
45.32 | even | 12 | 1620.2.x.c.593.3 | 16 | |||
45.34 | even | 6 | 1620.2.x.c.377.3 | 16 | |||
60.47 | odd | 4 | 2160.2.w.c.593.4 | 8 | |||
60.59 | even | 2 | 2160.2.w.c.1457.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.2.j.b.53.1 | ✓ | 8 | 5.2 | odd | 4 | ||
540.2.j.b.53.4 | yes | 8 | 15.2 | even | 4 | ||
540.2.j.b.377.2 | yes | 8 | 15.14 | odd | 2 | ||
540.2.j.b.377.3 | yes | 8 | 5.4 | even | 2 | ||
1620.2.x.c.53.1 | 16 | 45.2 | even | 12 | |||
1620.2.x.c.53.4 | 16 | 45.7 | odd | 12 | |||
1620.2.x.c.377.2 | 16 | 45.29 | odd | 6 | |||
1620.2.x.c.377.3 | 16 | 45.34 | even | 6 | |||
1620.2.x.c.593.2 | 16 | 45.22 | odd | 12 | |||
1620.2.x.c.593.3 | 16 | 45.32 | even | 12 | |||
1620.2.x.c.917.1 | 16 | 45.4 | even | 6 | |||
1620.2.x.c.917.4 | 16 | 45.14 | odd | 6 | |||
2160.2.w.c.593.1 | 8 | 20.7 | even | 4 | |||
2160.2.w.c.593.4 | 8 | 60.47 | odd | 4 | |||
2160.2.w.c.1457.2 | 8 | 60.59 | even | 2 | |||
2160.2.w.c.1457.3 | 8 | 20.19 | odd | 2 | |||
2700.2.j.i.593.3 | 8 | 5.3 | odd | 4 | inner | ||
2700.2.j.i.593.4 | 8 | 15.8 | even | 4 | inner | ||
2700.2.j.i.1457.3 | 8 | 1.1 | even | 1 | trivial | ||
2700.2.j.i.1457.4 | 8 | 3.2 | odd | 2 | inner |