Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(337,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.337 |
Dual form | 546.2.c.e.337.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.561553i | 0.251134i | 0.992085 | + | 0.125567i | \(0.0400750\pi\) | ||||
−0.992085 | + | 0.125567i | \(0.959925\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.561553 | 0.177579 | ||||||||
\(11\) | − | 1.43845i | − | 0.433708i | −0.976204 | − | 0.216854i | \(-0.930420\pi\) | ||
0.976204 | − | 0.216854i | \(-0.0695796\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.561553 | − | 3.56155i | −0.155747 | − | 0.987797i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | − | 0.561553i | − | 0.144992i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.68466 | 1.37873 | 0.689366 | − | 0.724413i | \(-0.257889\pi\) | ||||
0.689366 | + | 0.724413i | \(0.257889\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | − | 2.56155i | − | 0.587661i | −0.955858 | − | 0.293830i | \(-0.905070\pi\) | ||
0.955858 | − | 0.293830i | \(-0.0949300\pi\) | |||||||
\(20\) | − | 0.561553i | − | 0.125567i | ||||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | −1.43845 | −0.306678 | ||||||||
\(23\) | 5.68466 | 1.18533 | 0.592667 | − | 0.805448i | \(-0.298075\pi\) | ||||
0.592667 | + | 0.805448i | \(0.298075\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | 4.68466 | 0.936932 | ||||||||
\(26\) | −3.56155 | + | 0.561553i | −0.698478 | + | 0.110130i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | −2.56155 | −0.475668 | −0.237834 | − | 0.971306i | \(-0.576437\pi\) | ||||
−0.237834 | + | 0.971306i | \(0.576437\pi\) | |||||||
\(30\) | −0.561553 | −0.102525 | ||||||||
\(31\) | − | 10.2462i | − | 1.84027i | −0.391597 | − | 0.920137i | \(-0.628077\pi\) | ||
0.391597 | − | 0.920137i | \(-0.371923\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.43845i | 0.250402i | ||||||||
\(34\) | − | 5.68466i | − | 0.974911i | ||||||
\(35\) | −0.561553 | −0.0949197 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.68466i | 0.276956i | 0.990366 | + | 0.138478i | \(0.0442210\pi\) | ||||
−0.990366 | + | 0.138478i | \(0.955779\pi\) | |||||||
\(38\) | −2.56155 | −0.415539 | ||||||||
\(39\) | 0.561553 | + | 3.56155i | 0.0899204 | + | 0.570305i | ||||
\(40\) | −0.561553 | −0.0887893 | ||||||||
\(41\) | − | 4.00000i | − | 0.624695i | −0.949968 | − | 0.312348i | \(-0.898885\pi\) | ||
0.949968 | − | 0.312348i | \(-0.101115\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −10.5616 | −1.61062 | −0.805311 | − | 0.592853i | \(-0.798002\pi\) | ||||
−0.805311 | + | 0.592853i | \(0.798002\pi\) | |||||||
\(44\) | 1.43845i | 0.216854i | ||||||||
\(45\) | 0.561553i | 0.0837114i | ||||||||
\(46\) | − | 5.68466i | − | 0.838157i | ||||||
\(47\) | − | 6.24621i | − | 0.911104i | −0.890209 | − | 0.455552i | \(-0.849442\pi\) | ||
0.890209 | − | 0.455552i | \(-0.150558\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | − | 4.68466i | − | 0.662511i | ||||||
\(51\) | −5.68466 | −0.796011 | ||||||||
\(52\) | 0.561553 | + | 3.56155i | 0.0778734 | + | 0.493899i | ||||
\(53\) | 13.1231 | 1.80260 | 0.901299 | − | 0.433198i | \(-0.142615\pi\) | ||||
0.901299 | + | 0.433198i | \(0.142615\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 0.807764 | 0.108919 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 2.56155i | 0.339286i | ||||||||
\(58\) | 2.56155i | 0.336348i | ||||||||
\(59\) | 12.2462i | 1.59432i | 0.603768 | + | 0.797160i | \(0.293666\pi\) | ||||
−0.603768 | + | 0.797160i | \(0.706334\pi\) | |||||||
\(60\) | 0.561553i | 0.0724962i | ||||||||
\(61\) | 2.56155 | 0.327973 | 0.163987 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163987 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(62\) | −10.2462 | −1.30127 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000 | − | 0.315342i | 0.248069 | − | 0.0391133i | ||||
\(66\) | 1.43845 | 0.177061 | ||||||||
\(67\) | − | 7.12311i | − | 0.870226i | −0.900376 | − | 0.435113i | \(-0.856708\pi\) | ||
0.900376 | − | 0.435113i | \(-0.143292\pi\) | |||||||
\(68\) | −5.68466 | −0.689366 | ||||||||
\(69\) | −5.68466 | −0.684352 | ||||||||
\(70\) | 0.561553i | 0.0671184i | ||||||||
\(71\) | 15.3693i | 1.82400i | 0.410188 | + | 0.912001i | \(0.365463\pi\) | ||||
−0.410188 | + | 0.912001i | \(0.634537\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − | 7.43845i | − | 0.870604i | −0.900284 | − | 0.435302i | \(-0.856642\pi\) | ||
0.900284 | − | 0.435302i | \(-0.143358\pi\) | |||||||
\(74\) | 1.68466 | 0.195838 | ||||||||
\(75\) | −4.68466 | −0.540938 | ||||||||
\(76\) | 2.56155i | 0.293830i | ||||||||
\(77\) | 1.43845 | 0.163926 | ||||||||
\(78\) | 3.56155 | − | 0.561553i | 0.403266 | − | 0.0635833i | ||||
\(79\) | 16.0000 | 1.80014 | 0.900070 | − | 0.435745i | \(-0.143515\pi\) | ||||
0.900070 | + | 0.435745i | \(0.143515\pi\) | |||||||
\(80\) | 0.561553i | 0.0627835i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.00000 | −0.441726 | ||||||||
\(83\) | 2.00000i | 0.219529i | 0.993958 | + | 0.109764i | \(0.0350096\pi\) | ||||
−0.993958 | + | 0.109764i | \(0.964990\pi\) | |||||||
\(84\) | 1.00000i | 0.109109i | ||||||||
\(85\) | 3.19224i | 0.346247i | ||||||||
\(86\) | 10.5616i | 1.13888i | ||||||||
\(87\) | 2.56155 | 0.274627 | ||||||||
\(88\) | 1.43845 | 0.153339 | ||||||||
\(89\) | 8.00000i | 0.847998i | 0.905663 | + | 0.423999i | \(0.139374\pi\) | ||||
−0.905663 | + | 0.423999i | \(0.860626\pi\) | |||||||
\(90\) | 0.561553 | 0.0591929 | ||||||||
\(91\) | 3.56155 | − | 0.561553i | 0.373352 | − | 0.0588667i | ||||
\(92\) | −5.68466 | −0.592667 | ||||||||
\(93\) | 10.2462i | 1.06248i | ||||||||
\(94\) | −6.24621 | −0.644247 | ||||||||
\(95\) | 1.43845 | 0.147582 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | − | 1.43845i | − | 0.144569i | ||||||
\(100\) | −4.68466 | −0.468466 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 5.68466i | 0.562865i | ||||||||
\(103\) | −18.8078 | −1.85318 | −0.926592 | − | 0.376068i | \(-0.877276\pi\) | ||||
−0.926592 | + | 0.376068i | \(0.877276\pi\) | |||||||
\(104\) | 3.56155 | − | 0.561553i | 0.349239 | − | 0.0550648i | ||||
\(105\) | 0.561553 | 0.0548019 | ||||||||
\(106\) | − | 13.1231i | − | 1.27463i | ||||||
\(107\) | −13.1231 | −1.26866 | −0.634329 | − | 0.773063i | \(-0.718724\pi\) | ||||
−0.634329 | + | 0.773063i | \(0.718724\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 15.9309i | 1.52590i | 0.646457 | + | 0.762950i | \(0.276250\pi\) | ||||
−0.646457 | + | 0.762950i | \(0.723750\pi\) | |||||||
\(110\) | − | 0.807764i | − | 0.0770173i | ||||||
\(111\) | − | 1.68466i | − | 0.159901i | ||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 3.75379 | 0.353127 | 0.176563 | − | 0.984289i | \(-0.443502\pi\) | ||||
0.176563 | + | 0.984289i | \(0.443502\pi\) | |||||||
\(114\) | 2.56155 | 0.239911 | ||||||||
\(115\) | 3.19224i | 0.297678i | ||||||||
\(116\) | 2.56155 | 0.237834 | ||||||||
\(117\) | −0.561553 | − | 3.56155i | −0.0519156 | − | 0.329266i | ||||
\(118\) | 12.2462 | 1.12736 | ||||||||
\(119\) | 5.68466i | 0.521112i | ||||||||
\(120\) | 0.561553 | 0.0512625 | ||||||||
\(121\) | 8.93087 | 0.811897 | ||||||||
\(122\) | − | 2.56155i | − | 0.231912i | ||||||
\(123\) | 4.00000i | 0.360668i | ||||||||
\(124\) | 10.2462i | 0.920137i | ||||||||
\(125\) | 5.43845i | 0.486430i | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −6.24621 | −0.554262 | −0.277131 | − | 0.960832i | \(-0.589384\pi\) | ||||
−0.277131 | + | 0.960832i | \(0.589384\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 10.5616 | 0.929893 | ||||||||
\(130\) | −0.315342 | − | 2.00000i | −0.0276573 | − | 0.175412i | ||||
\(131\) | 2.56155 | 0.223804 | 0.111902 | − | 0.993719i | \(-0.464306\pi\) | ||||
0.111902 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(132\) | − | 1.43845i | − | 0.125201i | ||||||
\(133\) | 2.56155 | 0.222115 | ||||||||
\(134\) | −7.12311 | −0.615343 | ||||||||
\(135\) | − | 0.561553i | − | 0.0483308i | ||||||
\(136\) | 5.68466i | 0.487455i | ||||||||
\(137\) | 5.68466i | 0.485673i | 0.970067 | + | 0.242837i | \(0.0780779\pi\) | ||||
−0.970067 | + | 0.242837i | \(0.921922\pi\) | |||||||
\(138\) | 5.68466i | 0.483910i | ||||||||
\(139\) | −6.24621 | −0.529797 | −0.264898 | − | 0.964276i | \(-0.585338\pi\) | ||||
−0.264898 | + | 0.964276i | \(0.585338\pi\) | |||||||
\(140\) | 0.561553 | 0.0474599 | ||||||||
\(141\) | 6.24621i | 0.526026i | ||||||||
\(142\) | 15.3693 | 1.28976 | ||||||||
\(143\) | −5.12311 | + | 0.807764i | −0.428416 | + | 0.0675486i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − | 1.43845i | − | 0.119457i | ||||||
\(146\) | −7.43845 | −0.615610 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | − | 1.68466i | − | 0.138478i | ||||||
\(149\) | − | 10.0000i | − | 0.819232i | −0.912258 | − | 0.409616i | \(-0.865663\pi\) | ||
0.912258 | − | 0.409616i | \(-0.134337\pi\) | |||||||
\(150\) | 4.68466i | 0.382501i | ||||||||
\(151\) | − | 4.31534i | − | 0.351178i | −0.984464 | − | 0.175589i | \(-0.943817\pi\) | ||
0.984464 | − | 0.175589i | \(-0.0561829\pi\) | |||||||
\(152\) | 2.56155 | 0.207769 | ||||||||
\(153\) | 5.68466 | 0.459577 | ||||||||
\(154\) | − | 1.43845i | − | 0.115913i | ||||||
\(155\) | 5.75379 | 0.462155 | ||||||||
\(156\) | −0.561553 | − | 3.56155i | −0.0449602 | − | 0.285152i | ||||
\(157\) | 8.80776 | 0.702936 | 0.351468 | − | 0.936200i | \(-0.385683\pi\) | ||||
0.351468 | + | 0.936200i | \(0.385683\pi\) | |||||||
\(158\) | − | 16.0000i | − | 1.27289i | ||||||
\(159\) | −13.1231 | −1.04073 | ||||||||
\(160\) | 0.561553 | 0.0443946 | ||||||||
\(161\) | 5.68466i | 0.448014i | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 0.876894i | − | 0.0686837i | −0.999410 | − | 0.0343418i | \(-0.989067\pi\) | ||
0.999410 | − | 0.0343418i | \(-0.0109335\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | −0.807764 | −0.0628843 | ||||||||
\(166\) | 2.00000 | 0.155230 | ||||||||
\(167\) | − | 8.80776i | − | 0.681565i | −0.940142 | − | 0.340783i | \(-0.889308\pi\) | ||
0.940142 | − | 0.340783i | \(-0.110692\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −12.3693 | + | 4.00000i | −0.951486 | + | 0.307692i | ||||
\(170\) | 3.19224 | 0.244833 | ||||||||
\(171\) | − | 2.56155i | − | 0.195887i | ||||||
\(172\) | 10.5616 | 0.805311 | ||||||||
\(173\) | −20.2462 | −1.53929 | −0.769645 | − | 0.638471i | \(-0.779567\pi\) | ||||
−0.769645 | + | 0.638471i | \(0.779567\pi\) | |||||||
\(174\) | − | 2.56155i | − | 0.194191i | ||||||
\(175\) | 4.68466i | 0.354127i | ||||||||
\(176\) | − | 1.43845i | − | 0.108427i | ||||||
\(177\) | − | 12.2462i | − | 0.920482i | ||||||
\(178\) | 8.00000 | 0.599625 | ||||||||
\(179\) | 2.87689 | 0.215029 | 0.107515 | − | 0.994204i | \(-0.465711\pi\) | ||||
0.107515 | + | 0.994204i | \(0.465711\pi\) | |||||||
\(180\) | − | 0.561553i | − | 0.0418557i | ||||||
\(181\) | 11.3693 | 0.845075 | 0.422537 | − | 0.906346i | \(-0.361140\pi\) | ||||
0.422537 | + | 0.906346i | \(0.361140\pi\) | |||||||
\(182\) | −0.561553 | − | 3.56155i | −0.0416251 | − | 0.264000i | ||||
\(183\) | −2.56155 | −0.189355 | ||||||||
\(184\) | 5.68466i | 0.419079i | ||||||||
\(185\) | −0.946025 | −0.0695531 | ||||||||
\(186\) | 10.2462 | 0.751289 | ||||||||
\(187\) | − | 8.17708i | − | 0.597967i | ||||||
\(188\) | 6.24621i | 0.455552i | ||||||||
\(189\) | − | 1.00000i | − | 0.0727393i | ||||||
\(190\) | − | 1.43845i | − | 0.104356i | ||||||
\(191\) | 13.0540 | 0.944553 | 0.472276 | − | 0.881451i | \(-0.343432\pi\) | ||||
0.472276 | + | 0.881451i | \(0.343432\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 12.0000i | 0.863779i | 0.901927 | + | 0.431889i | \(0.142153\pi\) | ||||
−0.901927 | + | 0.431889i | \(0.857847\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | −2.00000 | + | 0.315342i | −0.143223 | + | 0.0225821i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | −1.43845 | −0.102226 | ||||||||
\(199\) | −23.9309 | −1.69641 | −0.848207 | − | 0.529665i | \(-0.822318\pi\) | ||||
−0.848207 | + | 0.529665i | \(0.822318\pi\) | |||||||
\(200\) | 4.68466i | 0.331255i | ||||||||
\(201\) | 7.12311i | 0.502425i | ||||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | − | 2.56155i | − | 0.179786i | ||||||
\(204\) | 5.68466 | 0.398006 | ||||||||
\(205\) | 2.24621 | 0.156882 | ||||||||
\(206\) | 18.8078i | 1.31040i | ||||||||
\(207\) | 5.68466 | 0.395111 | ||||||||
\(208\) | −0.561553 | − | 3.56155i | −0.0389367 | − | 0.246949i | ||||
\(209\) | −3.68466 | −0.254873 | ||||||||
\(210\) | − | 0.561553i | − | 0.0387508i | ||||||
\(211\) | −12.8078 | −0.881723 | −0.440861 | − | 0.897575i | \(-0.645327\pi\) | ||||
−0.440861 | + | 0.897575i | \(0.645327\pi\) | |||||||
\(212\) | −13.1231 | −0.901299 | ||||||||
\(213\) | − | 15.3693i | − | 1.05309i | ||||||
\(214\) | 13.1231i | 0.897077i | ||||||||
\(215\) | − | 5.93087i | − | 0.404482i | ||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 10.2462 | 0.695558 | ||||||||
\(218\) | 15.9309 | 1.07897 | ||||||||
\(219\) | 7.43845i | 0.502644i | ||||||||
\(220\) | −0.807764 | −0.0544594 | ||||||||
\(221\) | −3.19224 | − | 20.2462i | −0.214733 | − | 1.36191i | ||||
\(222\) | −1.68466 | −0.113067 | ||||||||
\(223\) | 18.2462i | 1.22186i | 0.791686 | + | 0.610928i | \(0.209204\pi\) | ||||
−0.791686 | + | 0.610928i | \(0.790796\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 4.68466 | 0.312311 | ||||||||
\(226\) | − | 3.75379i | − | 0.249698i | ||||||
\(227\) | − | 23.6155i | − | 1.56742i | −0.621128 | − | 0.783709i | \(-0.713325\pi\) | ||
0.621128 | − | 0.783709i | \(-0.286675\pi\) | |||||||
\(228\) | − | 2.56155i | − | 0.169643i | ||||||
\(229\) | − | 2.00000i | − | 0.132164i | −0.997814 | − | 0.0660819i | \(-0.978950\pi\) | ||
0.997814 | − | 0.0660819i | \(-0.0210498\pi\) | |||||||
\(230\) | 3.19224 | 0.210490 | ||||||||
\(231\) | −1.43845 | −0.0946429 | ||||||||
\(232\) | − | 2.56155i | − | 0.168174i | ||||||
\(233\) | 2.00000 | 0.131024 | 0.0655122 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655122 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(234\) | −3.56155 | + | 0.561553i | −0.232826 | + | 0.0367099i | ||||
\(235\) | 3.50758 | 0.228809 | ||||||||
\(236\) | − | 12.2462i | − | 0.797160i | ||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 5.68466 | 0.368482 | ||||||||
\(239\) | 2.24621i | 0.145295i | 0.997358 | + | 0.0726477i | \(0.0231449\pi\) | ||||
−0.997358 | + | 0.0726477i | \(0.976855\pi\) | |||||||
\(240\) | − | 0.561553i | − | 0.0362481i | ||||||
\(241\) | − | 6.00000i | − | 0.386494i | −0.981150 | − | 0.193247i | \(-0.938098\pi\) | ||
0.981150 | − | 0.193247i | \(-0.0619019\pi\) | |||||||
\(242\) | − | 8.93087i | − | 0.574098i | ||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.56155 | −0.163987 | ||||||||
\(245\) | − | 0.561553i | − | 0.0358763i | ||||||
\(246\) | 4.00000 | 0.255031 | ||||||||
\(247\) | −9.12311 | + | 1.43845i | −0.580489 | + | 0.0915262i | ||||
\(248\) | 10.2462 | 0.650635 | ||||||||
\(249\) | − | 2.00000i | − | 0.126745i | ||||||
\(250\) | 5.43845 | 0.343958 | ||||||||
\(251\) | −15.0540 | −0.950198 | −0.475099 | − | 0.879932i | \(-0.657588\pi\) | ||||
−0.475099 | + | 0.879932i | \(0.657588\pi\) | |||||||
\(252\) | − | 1.00000i | − | 0.0629941i | ||||||
\(253\) | − | 8.17708i | − | 0.514089i | ||||||
\(254\) | 6.24621i | 0.391922i | ||||||||
\(255\) | − | 3.19224i | − | 0.199906i | ||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.0000 | −1.62184 | −0.810918 | − | 0.585160i | \(-0.801032\pi\) | ||||
−0.810918 | + | 0.585160i | \(0.801032\pi\) | |||||||
\(258\) | − | 10.5616i | − | 0.657534i | ||||||
\(259\) | −1.68466 | −0.104680 | ||||||||
\(260\) | −2.00000 | + | 0.315342i | −0.124035 | + | 0.0195567i | ||||
\(261\) | −2.56155 | −0.158556 | ||||||||
\(262\) | − | 2.56155i | − | 0.158253i | ||||||
\(263\) | 1.36932 | 0.0844357 | 0.0422178 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422178 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(264\) | −1.43845 | −0.0885303 | ||||||||
\(265\) | 7.36932i | 0.452694i | ||||||||
\(266\) | − | 2.56155i | − | 0.157059i | ||||||
\(267\) | − | 8.00000i | − | 0.489592i | ||||||
\(268\) | 7.12311i | 0.435113i | ||||||||
\(269\) | 6.63068 | 0.404280 | 0.202140 | − | 0.979357i | \(-0.435210\pi\) | ||||
0.202140 | + | 0.979357i | \(0.435210\pi\) | |||||||
\(270\) | −0.561553 | −0.0341750 | ||||||||
\(271\) | 8.00000i | 0.485965i | 0.970031 | + | 0.242983i | \(0.0781258\pi\) | ||||
−0.970031 | + | 0.242983i | \(0.921874\pi\) | |||||||
\(272\) | 5.68466 | 0.344683 | ||||||||
\(273\) | −3.56155 | + | 0.561553i | −0.215555 | + | 0.0339867i | ||||
\(274\) | 5.68466 | 0.343423 | ||||||||
\(275\) | − | 6.73863i | − | 0.406355i | ||||||
\(276\) | 5.68466 | 0.342176 | ||||||||
\(277\) | −19.1231 | −1.14900 | −0.574498 | − | 0.818506i | \(-0.694803\pi\) | ||||
−0.574498 | + | 0.818506i | \(0.694803\pi\) | |||||||
\(278\) | 6.24621i | 0.374623i | ||||||||
\(279\) | − | 10.2462i | − | 0.613425i | ||||||
\(280\) | − | 0.561553i | − | 0.0335592i | ||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 6.24621 | 0.371956 | ||||||||
\(283\) | −13.1231 | −0.780088 | −0.390044 | − | 0.920796i | \(-0.627540\pi\) | ||||
−0.390044 | + | 0.920796i | \(0.627540\pi\) | |||||||
\(284\) | − | 15.3693i | − | 0.912001i | ||||||
\(285\) | −1.43845 | −0.0852063 | ||||||||
\(286\) | 0.807764 | + | 5.12311i | 0.0477641 | + | 0.302936i | ||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 15.3153 | 0.900902 | ||||||||
\(290\) | −1.43845 | −0.0844685 | ||||||||
\(291\) | 10.0000i | 0.586210i | ||||||||
\(292\) | 7.43845i | 0.435302i | ||||||||
\(293\) | 24.2462i | 1.41648i | 0.705972 | + | 0.708239i | \(0.250510\pi\) | ||||
−0.705972 | + | 0.708239i | \(0.749490\pi\) | |||||||
\(294\) | − | 1.00000i | − | 0.0583212i | ||||||
\(295\) | −6.87689 | −0.400388 | ||||||||
\(296\) | −1.68466 | −0.0979188 | ||||||||
\(297\) | 1.43845i | 0.0834672i | ||||||||
\(298\) | −10.0000 | −0.579284 | ||||||||
\(299\) | −3.19224 | − | 20.2462i | −0.184612 | − | 1.17087i | ||||
\(300\) | 4.68466 | 0.270469 | ||||||||
\(301\) | − | 10.5616i | − | 0.608758i | ||||||
\(302\) | −4.31534 | −0.248320 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | − | 2.56155i | − | 0.146915i | ||||||
\(305\) | 1.43845i | 0.0823652i | ||||||||
\(306\) | − | 5.68466i | − | 0.324970i | ||||||
\(307\) | − | 9.75379i | − | 0.556678i | −0.960483 | − | 0.278339i | \(-0.910216\pi\) | ||
0.960483 | − | 0.278339i | \(-0.0897839\pi\) | |||||||
\(308\) | −1.43845 | −0.0819631 | ||||||||
\(309\) | 18.8078 | 1.06994 | ||||||||
\(310\) | − | 5.75379i | − | 0.326793i | ||||||
\(311\) | 32.4924 | 1.84248 | 0.921238 | − | 0.388999i | \(-0.127179\pi\) | ||||
0.921238 | + | 0.388999i | \(0.127179\pi\) | |||||||
\(312\) | −3.56155 | + | 0.561553i | −0.201633 | + | 0.0317917i | ||||
\(313\) | 15.7538 | 0.890457 | 0.445228 | − | 0.895417i | \(-0.353122\pi\) | ||||
0.445228 | + | 0.895417i | \(0.353122\pi\) | |||||||
\(314\) | − | 8.80776i | − | 0.497051i | ||||||
\(315\) | −0.561553 | −0.0316399 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | − | 21.3693i | − | 1.20022i | −0.799917 | − | 0.600110i | \(-0.795123\pi\) | ||
0.799917 | − | 0.600110i | \(-0.204877\pi\) | |||||||
\(318\) | 13.1231i | 0.735907i | ||||||||
\(319\) | 3.68466i | 0.206301i | ||||||||
\(320\) | − | 0.561553i | − | 0.0313918i | ||||||
\(321\) | 13.1231 | 0.732460 | ||||||||
\(322\) | 5.68466 | 0.316794 | ||||||||
\(323\) | − | 14.5616i | − | 0.810226i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −2.63068 | − | 16.6847i | −0.145924 | − | 0.925498i | ||||
\(326\) | −0.876894 | −0.0485667 | ||||||||
\(327\) | − | 15.9309i | − | 0.880979i | ||||||
\(328\) | 4.00000 | 0.220863 | ||||||||
\(329\) | 6.24621 | 0.344365 | ||||||||
\(330\) | 0.807764i | 0.0444659i | ||||||||
\(331\) | − | 7.12311i | − | 0.391521i | −0.980652 | − | 0.195761i | \(-0.937282\pi\) | ||
0.980652 | − | 0.195761i | \(-0.0627176\pi\) | |||||||
\(332\) | − | 2.00000i | − | 0.109764i | ||||||
\(333\) | 1.68466i | 0.0923187i | ||||||||
\(334\) | −8.80776 | −0.481939 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | − | 1.00000i | − | 0.0545545i | ||||||
\(337\) | −17.0540 | −0.928989 | −0.464495 | − | 0.885576i | \(-0.653764\pi\) | ||||
−0.464495 | + | 0.885576i | \(0.653764\pi\) | |||||||
\(338\) | 4.00000 | + | 12.3693i | 0.217571 | + | 0.672802i | ||||
\(339\) | −3.75379 | −0.203878 | ||||||||
\(340\) | − | 3.19224i | − | 0.173123i | ||||||
\(341\) | −14.7386 | −0.798142 | ||||||||
\(342\) | −2.56155 | −0.138513 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 10.5616i | − | 0.569441i | ||||||
\(345\) | − | 3.19224i | − | 0.171864i | ||||||
\(346\) | 20.2462i | 1.08844i | ||||||||
\(347\) | 8.49242 | 0.455897 | 0.227949 | − | 0.973673i | \(-0.426798\pi\) | ||||
0.227949 | + | 0.973673i | \(0.426798\pi\) | |||||||
\(348\) | −2.56155 | −0.137314 | ||||||||
\(349\) | 21.3693i | 1.14387i | 0.820298 | + | 0.571937i | \(0.193808\pi\) | ||||
−0.820298 | + | 0.571937i | \(0.806192\pi\) | |||||||
\(350\) | 4.68466 | 0.250406 | ||||||||
\(351\) | 0.561553 | + | 3.56155i | 0.0299735 | + | 0.190102i | ||||
\(352\) | −1.43845 | −0.0766695 | ||||||||
\(353\) | 1.75379i | 0.0933448i | 0.998910 | + | 0.0466724i | \(0.0148617\pi\) | ||||
−0.998910 | + | 0.0466724i | \(0.985138\pi\) | |||||||
\(354\) | −12.2462 | −0.650879 | ||||||||
\(355\) | −8.63068 | −0.458069 | ||||||||
\(356\) | − | 8.00000i | − | 0.423999i | ||||||
\(357\) | − | 5.68466i | − | 0.300864i | ||||||
\(358\) | − | 2.87689i | − | 0.152049i | ||||||
\(359\) | 17.6155i | 0.929712i | 0.885386 | + | 0.464856i | \(0.153894\pi\) | ||||
−0.885386 | + | 0.464856i | \(0.846106\pi\) | |||||||
\(360\) | −0.561553 | −0.0295964 | ||||||||
\(361\) | 12.4384 | 0.654655 | ||||||||
\(362\) | − | 11.3693i | − | 0.597558i | ||||||
\(363\) | −8.93087 | −0.468749 | ||||||||
\(364\) | −3.56155 | + | 0.561553i | −0.186676 | + | 0.0294334i | ||||
\(365\) | 4.17708 | 0.218638 | ||||||||
\(366\) | 2.56155i | 0.133895i | ||||||||
\(367\) | 25.3693 | 1.32427 | 0.662134 | − | 0.749386i | \(-0.269651\pi\) | ||||
0.662134 | + | 0.749386i | \(0.269651\pi\) | |||||||
\(368\) | 5.68466 | 0.296333 | ||||||||
\(369\) | − | 4.00000i | − | 0.208232i | ||||||
\(370\) | 0.946025i | 0.0491815i | ||||||||
\(371\) | 13.1231i | 0.681318i | ||||||||
\(372\) | − | 10.2462i | − | 0.531241i | ||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | −8.17708 | −0.422827 | ||||||||
\(375\) | − | 5.43845i | − | 0.280840i | ||||||
\(376\) | 6.24621 | 0.322124 | ||||||||
\(377\) | 1.43845 | + | 9.12311i | 0.0740838 | + | 0.469864i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 27.1231i | 1.39322i | 0.717450 | + | 0.696610i | \(0.245309\pi\) | ||||
−0.717450 | + | 0.696610i | \(0.754691\pi\) | |||||||
\(380\) | −1.43845 | −0.0737908 | ||||||||
\(381\) | 6.24621 | 0.320003 | ||||||||
\(382\) | − | 13.0540i | − | 0.667899i | ||||||
\(383\) | − | 13.4384i | − | 0.686673i | −0.939213 | − | 0.343336i | \(-0.888443\pi\) | ||
0.939213 | − | 0.343336i | \(-0.111557\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 0.807764i | 0.0411675i | ||||||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | −10.5616 | −0.536874 | ||||||||
\(388\) | 10.0000i | 0.507673i | ||||||||
\(389\) | 18.8769 | 0.957097 | 0.478548 | − | 0.878061i | \(-0.341163\pi\) | ||||
0.478548 | + | 0.878061i | \(0.341163\pi\) | |||||||
\(390\) | 0.315342 | + | 2.00000i | 0.0159679 | + | 0.101274i | ||||
\(391\) | 32.3153 | 1.63426 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | −2.56155 | −0.129213 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 8.98485i | 0.452077i | ||||||||
\(396\) | 1.43845i | 0.0722847i | ||||||||
\(397\) | 9.36932i | 0.470233i | 0.971967 | + | 0.235116i | \(0.0755471\pi\) | ||||
−0.971967 | + | 0.235116i | \(0.924453\pi\) | |||||||
\(398\) | 23.9309i | 1.19955i | ||||||||
\(399\) | −2.56155 | −0.128238 | ||||||||
\(400\) | 4.68466 | 0.234233 | ||||||||
\(401\) | − | 34.9848i | − | 1.74706i | −0.486771 | − | 0.873530i | \(-0.661825\pi\) | ||
0.486771 | − | 0.873530i | \(-0.338175\pi\) | |||||||
\(402\) | 7.12311 | 0.355268 | ||||||||
\(403\) | −36.4924 | + | 5.75379i | −1.81782 | + | 0.286617i | ||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0.561553i | 0.0279038i | ||||||||
\(406\) | −2.56155 | −0.127128 | ||||||||
\(407\) | 2.42329 | 0.120118 | ||||||||
\(408\) | − | 5.68466i | − | 0.281433i | ||||||
\(409\) | 6.80776i | 0.336622i | 0.985734 | + | 0.168311i | \(0.0538313\pi\) | ||||
−0.985734 | + | 0.168311i | \(0.946169\pi\) | |||||||
\(410\) | − | 2.24621i | − | 0.110932i | ||||||
\(411\) | − | 5.68466i | − | 0.280404i | ||||||
\(412\) | 18.8078 | 0.926592 | ||||||||
\(413\) | −12.2462 | −0.602597 | ||||||||
\(414\) | − | 5.68466i | − | 0.279386i | ||||||
\(415\) | −1.12311 | −0.0551311 | ||||||||
\(416\) | −3.56155 | + | 0.561553i | −0.174619 | + | 0.0275324i | ||||
\(417\) | 6.24621 | 0.305878 | ||||||||
\(418\) | 3.68466i | 0.180223i | ||||||||
\(419\) | −8.31534 | −0.406231 | −0.203116 | − | 0.979155i | \(-0.565107\pi\) | ||||
−0.203116 | + | 0.979155i | \(0.565107\pi\) | |||||||
\(420\) | −0.561553 | −0.0274010 | ||||||||
\(421\) | 10.0000i | 0.487370i | 0.969854 | + | 0.243685i | \(0.0783563\pi\) | ||||
−0.969854 | + | 0.243685i | \(0.921644\pi\) | |||||||
\(422\) | 12.8078i | 0.623472i | ||||||||
\(423\) | − | 6.24621i | − | 0.303701i | ||||||
\(424\) | 13.1231i | 0.637314i | ||||||||
\(425\) | 26.6307 | 1.29178 | ||||||||
\(426\) | −15.3693 | −0.744646 | ||||||||
\(427\) | 2.56155i | 0.123962i | ||||||||
\(428\) | 13.1231 | 0.634329 | ||||||||
\(429\) | 5.12311 | − | 0.807764i | 0.247346 | − | 0.0389992i | ||||
\(430\) | −5.93087 | −0.286012 | ||||||||
\(431\) | 27.8617i | 1.34205i | 0.741433 | + | 0.671026i | \(0.234146\pi\) | ||||
−0.741433 | + | 0.671026i | \(0.765854\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −1.36932 | −0.0658052 | −0.0329026 | − | 0.999459i | \(-0.510475\pi\) | ||||
−0.0329026 | + | 0.999459i | \(0.510475\pi\) | |||||||
\(434\) | − | 10.2462i | − | 0.491834i | ||||||
\(435\) | 1.43845i | 0.0689683i | ||||||||
\(436\) | − | 15.9309i | − | 0.762950i | ||||||
\(437\) | − | 14.5616i | − | 0.696574i | ||||||
\(438\) | 7.43845 | 0.355423 | ||||||||
\(439\) | 19.9309 | 0.951249 | 0.475624 | − | 0.879649i | \(-0.342222\pi\) | ||||
0.475624 | + | 0.879649i | \(0.342222\pi\) | |||||||
\(440\) | 0.807764i | 0.0385086i | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −20.2462 | + | 3.19224i | −0.963014 | + | 0.151839i | ||||
\(443\) | 31.3693 | 1.49040 | 0.745201 | − | 0.666840i | \(-0.232354\pi\) | ||||
0.745201 | + | 0.666840i | \(0.232354\pi\) | |||||||
\(444\) | 1.68466i | 0.0799504i | ||||||||
\(445\) | −4.49242 | −0.212961 | ||||||||
\(446\) | 18.2462 | 0.863983 | ||||||||
\(447\) | 10.0000i | 0.472984i | ||||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | 21.6847i | 1.02336i | 0.859175 | + | 0.511681i | \(0.170977\pi\) | ||||
−0.859175 | + | 0.511681i | \(0.829023\pi\) | |||||||
\(450\) | − | 4.68466i | − | 0.220837i | ||||||
\(451\) | −5.75379 | −0.270935 | ||||||||
\(452\) | −3.75379 | −0.176563 | ||||||||
\(453\) | 4.31534i | 0.202752i | ||||||||
\(454\) | −23.6155 | −1.10833 | ||||||||
\(455\) | 0.315342 | + | 2.00000i | 0.0147834 | + | 0.0937614i | ||||
\(456\) | −2.56155 | −0.119956 | ||||||||
\(457\) | 16.0000i | 0.748448i | 0.927338 | + | 0.374224i | \(0.122091\pi\) | ||||
−0.927338 | + | 0.374224i | \(0.877909\pi\) | |||||||
\(458\) | −2.00000 | −0.0934539 | ||||||||
\(459\) | −5.68466 | −0.265337 | ||||||||
\(460\) | − | 3.19224i | − | 0.148839i | ||||||
\(461\) | − | 8.06913i | − | 0.375817i | −0.982187 | − | 0.187908i | \(-0.939829\pi\) | ||
0.982187 | − | 0.187908i | \(-0.0601708\pi\) | |||||||
\(462\) | 1.43845i | 0.0669226i | ||||||||
\(463\) | − | 39.5464i | − | 1.83788i | −0.394401 | − | 0.918938i | \(-0.629048\pi\) | ||
0.394401 | − | 0.918938i | \(-0.370952\pi\) | |||||||
\(464\) | −2.56155 | −0.118917 | ||||||||
\(465\) | −5.75379 | −0.266826 | ||||||||
\(466\) | − | 2.00000i | − | 0.0926482i | ||||||
\(467\) | −2.56155 | −0.118535 | −0.0592673 | − | 0.998242i | \(-0.518876\pi\) | ||||
−0.0592673 | + | 0.998242i | \(0.518876\pi\) | |||||||
\(468\) | 0.561553 | + | 3.56155i | 0.0259578 | + | 0.164633i | ||||
\(469\) | 7.12311 | 0.328914 | ||||||||
\(470\) | − | 3.50758i | − | 0.161792i | ||||||
\(471\) | −8.80776 | −0.405840 | ||||||||
\(472\) | −12.2462 | −0.563678 | ||||||||
\(473\) | 15.1922i | 0.698540i | ||||||||
\(474\) | 16.0000i | 0.734904i | ||||||||
\(475\) | − | 12.0000i | − | 0.550598i | ||||||
\(476\) | − | 5.68466i | − | 0.260556i | ||||||
\(477\) | 13.1231 | 0.600866 | ||||||||
\(478\) | 2.24621 | 0.102739 | ||||||||
\(479\) | 41.3002i | 1.88705i | 0.331296 | + | 0.943527i | \(0.392514\pi\) | ||||
−0.331296 | + | 0.943527i | \(0.607486\pi\) | |||||||
\(480\) | −0.561553 | −0.0256313 | ||||||||
\(481\) | 6.00000 | − | 0.946025i | 0.273576 | − | 0.0431350i | ||||
\(482\) | −6.00000 | −0.273293 | ||||||||
\(483\) | − | 5.68466i | − | 0.258661i | ||||||
\(484\) | −8.93087 | −0.405949 | ||||||||
\(485\) | 5.61553 | 0.254988 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 30.2462i | 1.37059i | 0.728267 | + | 0.685293i | \(0.240326\pi\) | ||||
−0.728267 | + | 0.685293i | \(0.759674\pi\) | |||||||
\(488\) | 2.56155i | 0.115956i | ||||||||
\(489\) | 0.876894i | 0.0396545i | ||||||||
\(490\) | −0.561553 | −0.0253684 | ||||||||
\(491\) | 6.24621 | 0.281888 | 0.140944 | − | 0.990018i | \(-0.454986\pi\) | ||||
0.140944 | + | 0.990018i | \(0.454986\pi\) | |||||||
\(492\) | − | 4.00000i | − | 0.180334i | ||||||
\(493\) | −14.5616 | −0.655819 | ||||||||
\(494\) | 1.43845 | + | 9.12311i | 0.0647188 | + | 0.410468i | ||||
\(495\) | 0.807764 | 0.0363063 | ||||||||
\(496\) | − | 10.2462i | − | 0.460068i | ||||||
\(497\) | −15.3693 | −0.689408 | ||||||||
\(498\) | −2.00000 | −0.0896221 | ||||||||
\(499\) | 34.4924i | 1.54409i | 0.635566 | + | 0.772046i | \(0.280767\pi\) | ||||
−0.635566 | + | 0.772046i | \(0.719233\pi\) | |||||||
\(500\) | − | 5.43845i | − | 0.243215i | ||||||
\(501\) | 8.80776i | 0.393502i | ||||||||
\(502\) | 15.0540i | 0.671892i | ||||||||
\(503\) | −5.61553 | −0.250384 | −0.125192 | − | 0.992133i | \(-0.539955\pi\) | ||||
−0.125192 | + | 0.992133i | \(0.539955\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 3.36932i | 0.149933i | ||||||||
\(506\) | −8.17708 | −0.363516 | ||||||||
\(507\) | 12.3693 | − | 4.00000i | 0.549341 | − | 0.177646i | ||||
\(508\) | 6.24621 | 0.277131 | ||||||||
\(509\) | 9.68466i | 0.429265i | 0.976695 | + | 0.214632i | \(0.0688554\pi\) | ||||
−0.976695 | + | 0.214632i | \(0.931145\pi\) | |||||||
\(510\) | −3.19224 | −0.141355 | ||||||||
\(511\) | 7.43845 | 0.329058 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.56155i | 0.113095i | ||||||||
\(514\) | 26.0000i | 1.14681i | ||||||||
\(515\) | − | 10.5616i | − | 0.465398i | ||||||
\(516\) | −10.5616 | −0.464946 | ||||||||
\(517\) | −8.98485 | −0.395153 | ||||||||
\(518\) | 1.68466i | 0.0740196i | ||||||||
\(519\) | 20.2462 | 0.888710 | ||||||||
\(520\) | 0.315342 | + | 2.00000i | 0.0138286 | + | 0.0877058i | ||||
\(521\) | −29.0540 | −1.27288 | −0.636439 | − | 0.771327i | \(-0.719593\pi\) | ||||
−0.636439 | + | 0.771327i | \(0.719593\pi\) | |||||||
\(522\) | 2.56155i | 0.112116i | ||||||||
\(523\) | 24.4924 | 1.07098 | 0.535489 | − | 0.844542i | \(-0.320127\pi\) | ||||
0.535489 | + | 0.844542i | \(0.320127\pi\) | |||||||
\(524\) | −2.56155 | −0.111902 | ||||||||
\(525\) | − | 4.68466i | − | 0.204455i | ||||||
\(526\) | − | 1.36932i | − | 0.0597051i | ||||||
\(527\) | − | 58.2462i | − | 2.53724i | ||||||
\(528\) | 1.43845i | 0.0626004i | ||||||||
\(529\) | 9.31534 | 0.405015 | ||||||||
\(530\) | 7.36932 | 0.320103 | ||||||||
\(531\) | 12.2462i | 0.531440i | ||||||||
\(532\) | −2.56155 | −0.111057 | ||||||||
\(533\) | −14.2462 | + | 2.24621i | −0.617072 | + | 0.0972942i | ||||
\(534\) | −8.00000 | −0.346194 | ||||||||
\(535\) | − | 7.36932i | − | 0.318603i | ||||||
\(536\) | 7.12311 | 0.307671 | ||||||||
\(537\) | −2.87689 | −0.124147 | ||||||||
\(538\) | − | 6.63068i | − | 0.285869i | ||||||
\(539\) | 1.43845i | 0.0619583i | ||||||||
\(540\) | 0.561553i | 0.0241654i | ||||||||
\(541\) | 26.8078i | 1.15256i | 0.817254 | + | 0.576278i | \(0.195495\pi\) | ||||
−0.817254 | + | 0.576278i | \(0.804505\pi\) | |||||||
\(542\) | 8.00000 | 0.343629 | ||||||||
\(543\) | −11.3693 | −0.487904 | ||||||||
\(544\) | − | 5.68466i | − | 0.243728i | ||||||
\(545\) | −8.94602 | −0.383206 | ||||||||
\(546\) | 0.561553 | + | 3.56155i | 0.0240322 | + | 0.152420i | ||||
\(547\) | −36.9848 | −1.58136 | −0.790679 | − | 0.612231i | \(-0.790272\pi\) | ||||
−0.790679 | + | 0.612231i | \(0.790272\pi\) | |||||||
\(548\) | − | 5.68466i | − | 0.242837i | ||||||
\(549\) | 2.56155 | 0.109324 | ||||||||
\(550\) | −6.73863 | −0.287336 | ||||||||
\(551\) | 6.56155i | 0.279532i | ||||||||
\(552\) | − | 5.68466i | − | 0.241955i | ||||||
\(553\) | 16.0000i | 0.680389i | ||||||||
\(554\) | 19.1231i | 0.812463i | ||||||||
\(555\) | 0.946025 | 0.0401565 | ||||||||
\(556\) | 6.24621 | 0.264898 | ||||||||
\(557\) | 0.246211i | 0.0104323i | 0.999986 | + | 0.00521615i | \(0.00166036\pi\) | ||||
−0.999986 | + | 0.00521615i | \(0.998340\pi\) | |||||||
\(558\) | −10.2462 | −0.433757 | ||||||||
\(559\) | 5.93087 | + | 37.6155i | 0.250849 | + | 1.59097i | ||||
\(560\) | −0.561553 | −0.0237299 | ||||||||
\(561\) | 8.17708i | 0.345237i | ||||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | 0.946025 | 0.0398702 | 0.0199351 | − | 0.999801i | \(-0.493654\pi\) | ||||
0.0199351 | + | 0.999801i | \(0.493654\pi\) | |||||||
\(564\) | − | 6.24621i | − | 0.263013i | ||||||
\(565\) | 2.10795i | 0.0886821i | ||||||||
\(566\) | 13.1231i | 0.551605i | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | −15.3693 | −0.644882 | ||||||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 1.43845i | 0.0602499i | ||||||||
\(571\) | −1.75379 | −0.0733938 | −0.0366969 | − | 0.999326i | \(-0.511684\pi\) | ||||
−0.0366969 | + | 0.999326i | \(0.511684\pi\) | |||||||
\(572\) | 5.12311 | − | 0.807764i | 0.214208 | − | 0.0337743i | ||||
\(573\) | −13.0540 | −0.545338 | ||||||||
\(574\) | − | 4.00000i | − | 0.166957i | ||||||
\(575\) | 26.6307 | 1.11058 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − | 24.2462i | − | 1.00938i | −0.863300 | − | 0.504691i | \(-0.831606\pi\) | ||
0.863300 | − | 0.504691i | \(-0.168394\pi\) | |||||||
\(578\) | − | 15.3153i | − | 0.637034i | ||||||
\(579\) | − | 12.0000i | − | 0.498703i | ||||||
\(580\) | 1.43845i | 0.0597283i | ||||||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | 10.0000 | 0.414513 | ||||||||
\(583\) | − | 18.8769i | − | 0.781801i | ||||||
\(584\) | 7.43845 | 0.307805 | ||||||||
\(585\) | 2.00000 | − | 0.315342i | 0.0826898 | − | 0.0130378i | ||||
\(586\) | 24.2462 | 1.00160 | ||||||||
\(587\) | 28.8769i | 1.19188i | 0.803030 | + | 0.595938i | \(0.203220\pi\) | ||||
−0.803030 | + | 0.595938i | \(0.796780\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −26.2462 | −1.08146 | ||||||||
\(590\) | 6.87689i | 0.283117i | ||||||||
\(591\) | − | 6.00000i | − | 0.246807i | ||||||
\(592\) | 1.68466i | 0.0692390i | ||||||||
\(593\) | 28.0000i | 1.14982i | 0.818216 | + | 0.574911i | \(0.194963\pi\) | ||||
−0.818216 | + | 0.574911i | \(0.805037\pi\) | |||||||
\(594\) | 1.43845 | 0.0590202 | ||||||||
\(595\) | −3.19224 | −0.130869 | ||||||||
\(596\) | 10.0000i | 0.409616i | ||||||||
\(597\) | 23.9309 | 0.979425 | ||||||||
\(598\) | −20.2462 | + | 3.19224i | −0.827929 | + | 0.130540i | ||||
\(599\) | −23.3002 | −0.952020 | −0.476010 | − | 0.879440i | \(-0.657917\pi\) | ||||
−0.476010 | + | 0.879440i | \(0.657917\pi\) | |||||||
\(600\) | − | 4.68466i | − | 0.191250i | ||||||
\(601\) | 25.8617 | 1.05492 | 0.527461 | − | 0.849579i | \(-0.323144\pi\) | ||||
0.527461 | + | 0.849579i | \(0.323144\pi\) | |||||||
\(602\) | −10.5616 | −0.430457 | ||||||||
\(603\) | − | 7.12311i | − | 0.290075i | ||||||
\(604\) | 4.31534i | 0.175589i | ||||||||
\(605\) | 5.01515i | 0.203895i | ||||||||
\(606\) | 6.00000i | 0.243733i | ||||||||
\(607\) | 41.5464 | 1.68632 | 0.843158 | − | 0.537666i | \(-0.180694\pi\) | ||||
0.843158 | + | 0.537666i | \(0.180694\pi\) | |||||||
\(608\) | −2.56155 | −0.103885 | ||||||||
\(609\) | 2.56155i | 0.103799i | ||||||||
\(610\) | 1.43845 | 0.0582410 | ||||||||
\(611\) | −22.2462 | + | 3.50758i | −0.899985 | + | 0.141901i | ||||
\(612\) | −5.68466 | −0.229789 | ||||||||
\(613\) | − | 18.8078i | − | 0.759638i | −0.925061 | − | 0.379819i | \(-0.875986\pi\) | ||
0.925061 | − | 0.379819i | \(-0.124014\pi\) | |||||||
\(614\) | −9.75379 | −0.393631 | ||||||||
\(615\) | −2.24621 | −0.0905760 | ||||||||
\(616\) | 1.43845i | 0.0579567i | ||||||||
\(617\) | − | 26.8078i | − | 1.07924i | −0.841909 | − | 0.539620i | \(-0.818568\pi\) | ||
0.841909 | − | 0.539620i | \(-0.181432\pi\) | |||||||
\(618\) | − | 18.8078i | − | 0.756559i | ||||||
\(619\) | 2.06913i | 0.0831654i | 0.999135 | + | 0.0415827i | \(0.0132400\pi\) | ||||
−0.999135 | + | 0.0415827i | \(0.986760\pi\) | |||||||
\(620\) | −5.75379 | −0.231078 | ||||||||
\(621\) | −5.68466 | −0.228117 | ||||||||
\(622\) | − | 32.4924i | − | 1.30283i | ||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0.561553 | + | 3.56155i | 0.0224801 | + | 0.142576i | ||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | − | 15.7538i | − | 0.629648i | ||||||
\(627\) | 3.68466 | 0.147151 | ||||||||
\(628\) | −8.80776 | −0.351468 | ||||||||
\(629\) | 9.57671i | 0.381848i | ||||||||
\(630\) | 0.561553i | 0.0223728i | ||||||||
\(631\) | − | 0.315342i | − | 0.0125535i | −0.999980 | − | 0.00627677i | \(-0.998002\pi\) | ||
0.999980 | − | 0.00627677i | \(-0.00199797\pi\) | |||||||
\(632\) | 16.0000i | 0.636446i | ||||||||
\(633\) | 12.8078 | 0.509063 | ||||||||
\(634\) | −21.3693 | −0.848684 | ||||||||
\(635\) | − | 3.50758i | − | 0.139194i | ||||||
\(636\) | 13.1231 | 0.520365 | ||||||||
\(637\) | 0.561553 | + | 3.56155i | 0.0222495 | + | 0.141114i | ||||
\(638\) | 3.68466 | 0.145877 | ||||||||
\(639\) | 15.3693i | 0.608001i | ||||||||
\(640\) | −0.561553 | −0.0221973 | ||||||||
\(641\) | −44.1080 | −1.74216 | −0.871080 | − | 0.491142i | \(-0.836580\pi\) | ||||
−0.871080 | + | 0.491142i | \(0.836580\pi\) | |||||||
\(642\) | − | 13.1231i | − | 0.517928i | ||||||
\(643\) | 20.8078i | 0.820578i | 0.911956 | + | 0.410289i | \(0.134572\pi\) | ||||
−0.911956 | + | 0.410289i | \(0.865428\pi\) | |||||||
\(644\) | − | 5.68466i | − | 0.224007i | ||||||
\(645\) | 5.93087i | 0.233528i | ||||||||
\(646\) | −14.5616 | −0.572917 | ||||||||
\(647\) | 35.3693 | 1.39051 | 0.695256 | − | 0.718763i | \(-0.255291\pi\) | ||||
0.695256 | + | 0.718763i | \(0.255291\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 17.6155 | 0.691470 | ||||||||
\(650\) | −16.6847 | + | 2.63068i | −0.654426 | + | 0.103184i | ||||
\(651\) | −10.2462 | −0.401581 | ||||||||
\(652\) | 0.876894i | 0.0343418i | ||||||||
\(653\) | −25.4384 | −0.995483 | −0.497742 | − | 0.867325i | \(-0.665837\pi\) | ||||
−0.497742 | + | 0.867325i | \(0.665837\pi\) | |||||||
\(654\) | −15.9309 | −0.622946 | ||||||||
\(655\) | 1.43845i | 0.0562048i | ||||||||
\(656\) | − | 4.00000i | − | 0.156174i | ||||||
\(657\) | − | 7.43845i | − | 0.290201i | ||||||
\(658\) | − | 6.24621i | − | 0.243503i | ||||||
\(659\) | 21.1231 | 0.822839 | 0.411420 | − | 0.911446i | \(-0.365033\pi\) | ||||
0.411420 | + | 0.911446i | \(0.365033\pi\) | |||||||
\(660\) | 0.807764 | 0.0314422 | ||||||||
\(661\) | − | 4.73863i | − | 0.184311i | −0.995745 | − | 0.0921557i | \(-0.970624\pi\) | ||
0.995745 | − | 0.0921557i | \(-0.0293758\pi\) | |||||||
\(662\) | −7.12311 | −0.276847 | ||||||||
\(663\) | 3.19224 | + | 20.2462i | 0.123976 | + | 0.786298i | ||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | 1.43845i | 0.0557806i | ||||||||
\(666\) | 1.68466 | 0.0652792 | ||||||||
\(667\) | −14.5616 | −0.563826 | ||||||||
\(668\) | 8.80776i | 0.340783i | ||||||||
\(669\) | − | 18.2462i | − | 0.705439i | ||||||
\(670\) | − | 4.00000i | − | 0.154533i | ||||||
\(671\) | − | 3.68466i | − | 0.142245i | ||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 17.1922 | 0.662712 | 0.331356 | − | 0.943506i | \(-0.392494\pi\) | ||||
0.331356 | + | 0.943506i | \(0.392494\pi\) | |||||||
\(674\) | 17.0540i | 0.656895i | ||||||||
\(675\) | −4.68466 | −0.180313 | ||||||||
\(676\) | 12.3693 | − | 4.00000i | 0.475743 | − | 0.153846i | ||||
\(677\) | 6.63068 | 0.254838 | 0.127419 | − | 0.991849i | \(-0.459331\pi\) | ||||
0.127419 | + | 0.991849i | \(0.459331\pi\) | |||||||
\(678\) | 3.75379i | 0.144163i | ||||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | −3.19224 | −0.122417 | ||||||||
\(681\) | 23.6155i | 0.904949i | ||||||||
\(682\) | 14.7386i | 0.564371i | ||||||||
\(683\) | 11.6847i | 0.447101i | 0.974692 | + | 0.223551i | \(0.0717648\pi\) | ||||
−0.974692 | + | 0.223551i | \(0.928235\pi\) | |||||||
\(684\) | 2.56155i | 0.0979434i | ||||||||
\(685\) | −3.19224 | −0.121969 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | −10.5616 | −0.402655 | ||||||||
\(689\) | −7.36932 | − | 46.7386i | −0.280749 | − | 1.78060i | ||||
\(690\) | −3.19224 | −0.121526 | ||||||||
\(691\) | − | 3.50758i | − | 0.133435i | −0.997772 | − | 0.0667173i | \(-0.978747\pi\) | ||
0.997772 | − | 0.0667173i | \(-0.0212526\pi\) | |||||||
\(692\) | 20.2462 | 0.769645 | ||||||||
\(693\) | 1.43845 | 0.0546421 | ||||||||
\(694\) | − | 8.49242i | − | 0.322368i | ||||||
\(695\) | − | 3.50758i | − | 0.133050i | ||||||
\(696\) | 2.56155i | 0.0970954i | ||||||||
\(697\) | − | 22.7386i | − | 0.861287i | ||||||
\(698\) | 21.3693 | 0.808841 | ||||||||
\(699\) | −2.00000 | −0.0756469 | ||||||||
\(700\) | − | 4.68466i | − | 0.177063i | ||||||
\(701\) | 37.6155 | 1.42072 | 0.710359 | − | 0.703839i | \(-0.248532\pi\) | ||||
0.710359 | + | 0.703839i | \(0.248532\pi\) | |||||||
\(702\) | 3.56155 | − | 0.561553i | 0.134422 | − | 0.0211944i | ||||
\(703\) | 4.31534 | 0.162756 | ||||||||
\(704\) | 1.43845i | 0.0542135i | ||||||||
\(705\) | −3.50758 | −0.132103 | ||||||||
\(706\) | 1.75379 | 0.0660047 | ||||||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | 12.2462i | 0.460241i | ||||||||
\(709\) | − | 48.2462i | − | 1.81192i | −0.423358 | − | 0.905962i | \(-0.639149\pi\) | ||
0.423358 | − | 0.905962i | \(-0.360851\pi\) | |||||||
\(710\) | 8.63068i | 0.323904i | ||||||||
\(711\) | 16.0000 | 0.600047 | ||||||||
\(712\) | −8.00000 | −0.299813 | ||||||||
\(713\) | − | 58.2462i | − | 2.18134i | ||||||
\(714\) | −5.68466 | −0.212743 | ||||||||
\(715\) | −0.453602 | − | 2.87689i | −0.0169638 | − | 0.107590i | ||||
\(716\) | −2.87689 | −0.107515 | ||||||||
\(717\) | − | 2.24621i | − | 0.0838863i | ||||||
\(718\) | 17.6155 | 0.657406 | ||||||||
\(719\) | 30.2462 | 1.12799 | 0.563997 | − | 0.825777i | \(-0.309263\pi\) | ||||
0.563997 | + | 0.825777i | \(0.309263\pi\) | |||||||
\(720\) | 0.561553i | 0.0209278i | ||||||||
\(721\) | − | 18.8078i | − | 0.700438i | ||||||
\(722\) | − | 12.4384i | − | 0.462911i | ||||||
\(723\) | 6.00000i | 0.223142i | ||||||||
\(724\) | −11.3693 | −0.422537 | ||||||||
\(725\) | −12.0000 | −0.445669 | ||||||||
\(726\) | 8.93087i | 0.331456i | ||||||||
\(727\) | −20.0691 | −0.744323 | −0.372161 | − | 0.928168i | \(-0.621383\pi\) | ||||
−0.372161 | + | 0.928168i | \(0.621383\pi\) | |||||||
\(728\) | 0.561553 | + | 3.56155i | 0.0208125 | + | 0.132000i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 4.17708i | − | 0.154601i | ||||||
\(731\) | −60.0388 | −2.22062 | ||||||||
\(732\) | 2.56155 | 0.0946777 | ||||||||
\(733\) | 31.1231i | 1.14956i | 0.818309 | + | 0.574779i | \(0.194912\pi\) | ||||
−0.818309 | + | 0.574779i | \(0.805088\pi\) | |||||||
\(734\) | − | 25.3693i | − | 0.936399i | ||||||
\(735\) | 0.561553i | 0.0207132i | ||||||||
\(736\) | − | 5.68466i | − | 0.209539i | ||||||
\(737\) | −10.2462 | −0.377424 | ||||||||
\(738\) | −4.00000 | −0.147242 | ||||||||
\(739\) | − | 23.6155i | − | 0.868711i | −0.900741 | − | 0.434356i | \(-0.856976\pi\) | ||
0.900741 | − | 0.434356i | \(-0.143024\pi\) | |||||||
\(740\) | 0.946025 | 0.0347766 | ||||||||
\(741\) | 9.12311 | − | 1.43845i | 0.335146 | − | 0.0528427i | ||||
\(742\) | 13.1231 | 0.481764 | ||||||||
\(743\) | 16.0000i | 0.586983i | 0.955962 | + | 0.293492i | \(0.0948173\pi\) | ||||
−0.955962 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(744\) | −10.2462 | −0.375644 | ||||||||
\(745\) | 5.61553 | 0.205737 | ||||||||
\(746\) | 6.00000i | 0.219676i | ||||||||
\(747\) | 2.00000i | 0.0731762i | ||||||||
\(748\) | 8.17708i | 0.298984i | ||||||||
\(749\) | − | 13.1231i | − | 0.479508i | ||||||
\(750\) | −5.43845 | −0.198584 | ||||||||
\(751\) | −14.2462 | −0.519852 | −0.259926 | − | 0.965629i | \(-0.583698\pi\) | ||||
−0.259926 | + | 0.965629i | \(0.583698\pi\) | |||||||
\(752\) | − | 6.24621i | − | 0.227776i | ||||||
\(753\) | 15.0540 | 0.548597 | ||||||||
\(754\) | 9.12311 | − | 1.43845i | 0.332244 | − | 0.0523852i | ||||
\(755\) | 2.42329 | 0.0881926 | ||||||||
\(756\) | 1.00000i | 0.0363696i | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 27.1231 | 0.985156 | ||||||||
\(759\) | 8.17708i | 0.296809i | ||||||||
\(760\) | 1.43845i | 0.0521780i | ||||||||
\(761\) | 30.8769i | 1.11929i | 0.828734 | + | 0.559643i | \(0.189062\pi\) | ||||
−0.828734 | + | 0.559643i | \(0.810938\pi\) | |||||||
\(762\) | − | 6.24621i | − | 0.226276i | ||||||
\(763\) | −15.9309 | −0.576736 | ||||||||
\(764\) | −13.0540 | −0.472276 | ||||||||
\(765\) | 3.19224i | 0.115416i | ||||||||
\(766\) | −13.4384 | −0.485551 | ||||||||
\(767\) | 43.6155 | − | 6.87689i | 1.57487 | − | 0.248310i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.5616i | 0.452981i | 0.974013 | + | 0.226491i | \(0.0727253\pi\) | ||||
−0.974013 | + | 0.226491i | \(0.927275\pi\) | |||||||
\(770\) | 0.807764 | 0.0291098 | ||||||||
\(771\) | 26.0000 | 0.936367 | ||||||||
\(772\) | − | 12.0000i | − | 0.431889i | ||||||
\(773\) | 15.9309i | 0.572994i | 0.958081 | + | 0.286497i | \(0.0924908\pi\) | ||||
−0.958081 | + | 0.286497i | \(0.907509\pi\) | |||||||
\(774\) | 10.5616i | 0.379627i | ||||||||
\(775\) | − | 48.0000i | − | 1.72421i | ||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 1.68466 | 0.0604368 | ||||||||
\(778\) | − | 18.8769i | − | 0.676769i | ||||||
\(779\) | −10.2462 | −0.367109 | ||||||||
\(780\) | 2.00000 | − | 0.315342i | 0.0716115 | − | 0.0112910i | ||||
\(781\) | 22.1080 | 0.791085 | ||||||||
\(782\) | − | 32.3153i | − | 1.15559i | ||||||
\(783\) | 2.56155 | 0.0915424 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 4.94602i | 0.176531i | ||||||||
\(786\) | 2.56155i | 0.0913676i | ||||||||
\(787\) | − | 45.9309i | − | 1.63726i | −0.574322 | − | 0.818629i | \(-0.694734\pi\) | ||
0.574322 | − | 0.818629i | \(-0.305266\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | −1.36932 | −0.0487490 | ||||||||
\(790\) | 8.98485 | 0.319666 | ||||||||
\(791\) | 3.75379i | 0.133469i | ||||||||
\(792\) | 1.43845 | 0.0511130 | ||||||||
\(793\) | −1.43845 | − | 9.12311i | −0.0510808 | − | 0.323971i | ||||
\(794\) | 9.36932 | 0.332505 | ||||||||
\(795\) | − | 7.36932i | − | 0.261363i | ||||||
\(796\) | 23.9309 | 0.848207 | ||||||||
\(797\) | 20.2462 | 0.717158 | 0.358579 | − | 0.933499i | \(-0.383261\pi\) | ||||
0.358579 | + | 0.933499i | \(0.383261\pi\) | |||||||
\(798\) | 2.56155i | 0.0906780i | ||||||||
\(799\) | − | 35.5076i | − | 1.25617i | ||||||
\(800\) | − | 4.68466i | − | 0.165628i | ||||||
\(801\) | 8.00000i | 0.282666i | ||||||||
\(802\) | −34.9848 | −1.23536 | ||||||||
\(803\) | −10.6998 | −0.377588 | ||||||||
\(804\) | − | 7.12311i | − | 0.251213i | ||||||
\(805\) | −3.19224 | −0.112512 | ||||||||
\(806\) | 5.75379 | + | 36.4924i | 0.202669 | + | 1.28539i | ||||
\(807\) | −6.63068 | −0.233411 | ||||||||
\(808\) | 6.00000i | 0.211079i | ||||||||
\(809\) | −30.6307 | −1.07692 | −0.538459 | − | 0.842652i | \(-0.680993\pi\) | ||||
−0.538459 | + | 0.842652i | \(0.680993\pi\) | |||||||
\(810\) | 0.561553 | 0.0197310 | ||||||||
\(811\) | − | 35.0540i | − | 1.23091i | −0.788171 | − | 0.615456i | \(-0.788972\pi\) | ||
0.788171 | − | 0.615456i | \(-0.211028\pi\) | |||||||
\(812\) | 2.56155i | 0.0898929i | ||||||||
\(813\) | − | 8.00000i | − | 0.280572i | ||||||
\(814\) | − | 2.42329i | − | 0.0849363i | ||||||
\(815\) | 0.492423 | 0.0172488 | ||||||||
\(816\) | −5.68466 | −0.199003 | ||||||||
\(817\) | 27.0540i | 0.946499i | ||||||||
\(818\) | 6.80776 | 0.238028 | ||||||||
\(819\) | 3.56155 | − | 0.561553i | 0.124451 | − | 0.0196222i | ||||
\(820\) | −2.24621 | −0.0784411 | ||||||||
\(821\) | 39.1231i | 1.36541i | 0.730696 | + | 0.682703i | \(0.239196\pi\) | ||||
−0.730696 | + | 0.682703i | \(0.760804\pi\) | |||||||
\(822\) | −5.68466 | −0.198275 | ||||||||
\(823\) | 18.7386 | 0.653188 | 0.326594 | − | 0.945165i | \(-0.394099\pi\) | ||||
0.326594 | + | 0.945165i | \(0.394099\pi\) | |||||||
\(824\) | − | 18.8078i | − | 0.655200i | ||||||
\(825\) | 6.73863i | 0.234609i | ||||||||
\(826\) | 12.2462i | 0.426100i | ||||||||
\(827\) | 15.0540i | 0.523478i | 0.965139 | + | 0.261739i | \(0.0842960\pi\) | ||||
−0.965139 | + | 0.261739i | \(0.915704\pi\) | |||||||
\(828\) | −5.68466 | −0.197556 | ||||||||
\(829\) | 4.94602 | 0.171783 | 0.0858913 | − | 0.996305i | \(-0.472626\pi\) | ||||
0.0858913 | + | 0.996305i | \(0.472626\pi\) | |||||||
\(830\) | 1.12311i | 0.0389836i | ||||||||
\(831\) | 19.1231 | 0.663373 | ||||||||
\(832\) | 0.561553 | + | 3.56155i | 0.0194683 | + | 0.123475i | ||||
\(833\) | −5.68466 | −0.196962 | ||||||||
\(834\) | − | 6.24621i | − | 0.216289i | ||||||
\(835\) | 4.94602 | 0.171164 | ||||||||
\(836\) | 3.68466 | 0.127437 | ||||||||
\(837\) | 10.2462i | 0.354161i | ||||||||
\(838\) | 8.31534i | 0.287249i | ||||||||
\(839\) | − | 42.2462i | − | 1.45850i | −0.684247 | − | 0.729251i | \(-0.739869\pi\) | ||
0.684247 | − | 0.729251i | \(-0.260131\pi\) | |||||||
\(840\) | 0.561553i | 0.0193754i | ||||||||
\(841\) | −22.4384 | −0.773740 | ||||||||
\(842\) | 10.0000 | 0.344623 | ||||||||
\(843\) | 6.00000i | 0.206651i | ||||||||
\(844\) | 12.8078 | 0.440861 | ||||||||
\(845\) | −2.24621 | − | 6.94602i | −0.0772720 | − | 0.238951i | ||||
\(846\) | −6.24621 | −0.214749 | ||||||||
\(847\) | 8.93087i | 0.306868i | ||||||||
\(848\) | 13.1231 | 0.450649 | ||||||||
\(849\) | 13.1231 | 0.450384 | ||||||||
\(850\) | − | 26.6307i | − | 0.913425i | ||||||
\(851\) | 9.57671i | 0.328285i | ||||||||
\(852\) | 15.3693i | 0.526544i | ||||||||
\(853\) | − | 19.1231i | − | 0.654763i | −0.944892 | − | 0.327381i | \(-0.893834\pi\) | ||
0.944892 | − | 0.327381i | \(-0.106166\pi\) | |||||||
\(854\) | 2.56155 | 0.0876545 | ||||||||
\(855\) | 1.43845 | 0.0491939 | ||||||||
\(856\) | − | 13.1231i | − | 0.448539i | ||||||
\(857\) | −38.0000 | −1.29806 | −0.649028 | − | 0.760765i | \(-0.724824\pi\) | ||||
−0.649028 | + | 0.760765i | \(0.724824\pi\) | |||||||
\(858\) | −0.807764 | − | 5.12311i | −0.0275766 | − | 0.174900i | ||||
\(859\) | 41.6155 | 1.41990 | 0.709952 | − | 0.704250i | \(-0.248717\pi\) | ||||
0.709952 | + | 0.704250i | \(0.248717\pi\) | |||||||
\(860\) | 5.93087i | 0.202241i | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | 27.8617 | 0.948975 | ||||||||
\(863\) | − | 6.73863i | − | 0.229386i | −0.993401 | − | 0.114693i | \(-0.963412\pi\) | ||
0.993401 | − | 0.114693i | \(-0.0365884\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − | 11.3693i | − | 0.386568i | ||||||
\(866\) | 1.36932i | 0.0465313i | ||||||||
\(867\) | −15.3153 | −0.520136 | ||||||||
\(868\) | −10.2462 | −0.347779 | ||||||||
\(869\) | − | 23.0152i | − | 0.780736i | ||||||
\(870\) | 1.43845 | 0.0487679 | ||||||||
\(871\) | −25.3693 | + | 4.00000i | −0.859607 | + | 0.135535i | ||||
\(872\) | −15.9309 | −0.539487 | ||||||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | −14.5616 | −0.492552 | ||||||||
\(875\) | −5.43845 | −0.183853 | ||||||||
\(876\) | − | 7.43845i | − | 0.251322i | ||||||
\(877\) | − | 42.9848i | − | 1.45150i | −0.687961 | − | 0.725748i | \(-0.741494\pi\) | ||
0.687961 | − | 0.725748i | \(-0.258506\pi\) | |||||||
\(878\) | − | 19.9309i | − | 0.672634i | ||||||
\(879\) | − | 24.2462i | − | 0.817804i | ||||||
\(880\) | 0.807764 | 0.0272297 | ||||||||
\(881\) | −39.3002 | −1.32406 | −0.662028 | − | 0.749479i | \(-0.730304\pi\) | ||||
−0.662028 | + | 0.749479i | \(0.730304\pi\) | |||||||
\(882\) | 1.00000i | 0.0336718i | ||||||||
\(883\) | −18.5616 | −0.624646 | −0.312323 | − | 0.949976i | \(-0.601107\pi\) | ||||
−0.312323 | + | 0.949976i | \(0.601107\pi\) | |||||||
\(884\) | 3.19224 | + | 20.2462i | 0.107367 | + | 0.680954i | ||||
\(885\) | 6.87689 | 0.231164 | ||||||||
\(886\) | − | 31.3693i | − | 1.05387i | ||||||
\(887\) | 19.8617 | 0.666892 | 0.333446 | − | 0.942769i | \(-0.391789\pi\) | ||||
0.333446 | + | 0.942769i | \(0.391789\pi\) | |||||||
\(888\) | 1.68466 | 0.0565334 | ||||||||
\(889\) | − | 6.24621i | − | 0.209491i | ||||||
\(890\) | 4.49242i | 0.150586i | ||||||||
\(891\) | − | 1.43845i | − | 0.0481898i | ||||||
\(892\) | − | 18.2462i | − | 0.610928i | ||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | 10.0000 | 0.334450 | ||||||||
\(895\) | 1.61553i | 0.0540011i | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 3.19224 | + | 20.2462i | 0.106586 | + | 0.676001i | ||||
\(898\) | 21.6847 | 0.723626 | ||||||||
\(899\) | 26.2462i | 0.875360i | ||||||||
\(900\) | −4.68466 | −0.156155 | ||||||||
\(901\) | 74.6004 | 2.48530 | ||||||||
\(902\) | 5.75379i | 0.191580i | ||||||||
\(903\) | 10.5616i | 0.351466i | ||||||||
\(904\) | 3.75379i | 0.124849i | ||||||||
\(905\) | 6.38447i | 0.212227i | ||||||||
\(906\) | 4.31534 | 0.143368 | ||||||||
\(907\) | 8.49242 | 0.281986 | 0.140993 | − | 0.990011i | \(-0.454970\pi\) | ||||
0.140993 | + | 0.990011i | \(0.454970\pi\) | |||||||
\(908\) | 23.6155i | 0.783709i | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 2.00000 | − | 0.315342i | 0.0662994 | − | 0.0104535i | ||||
\(911\) | −8.56155 | −0.283657 | −0.141828 | − | 0.989891i | \(-0.545298\pi\) | ||||
−0.141828 | + | 0.989891i | \(0.545298\pi\) | |||||||
\(912\) | 2.56155i | 0.0848215i | ||||||||
\(913\) | 2.87689 | 0.0952113 | ||||||||
\(914\) | 16.0000 | 0.529233 | ||||||||
\(915\) | − | 1.43845i | − | 0.0475536i | ||||||
\(916\) | 2.00000i | 0.0660819i | ||||||||
\(917\) | 2.56155i | 0.0845899i | ||||||||
\(918\) | 5.68466i | 0.187622i | ||||||||
\(919\) | 39.8617 | 1.31492 | 0.657459 | − | 0.753491i | \(-0.271631\pi\) | ||||
0.657459 | + | 0.753491i | \(0.271631\pi\) | |||||||
\(920\) | −3.19224 | −0.105245 | ||||||||
\(921\) | 9.75379i | 0.321398i | ||||||||
\(922\) | −8.06913 | −0.265743 | ||||||||
\(923\) | 54.7386 | − | 8.63068i | 1.80174 | − | 0.284082i | ||||
\(924\) | 1.43845 | 0.0473214 | ||||||||
\(925\) | 7.89205i | 0.259489i | ||||||||
\(926\) | −39.5464 | −1.29958 | ||||||||
\(927\) | −18.8078 | −0.617728 | ||||||||
\(928\) | 2.56155i | 0.0840871i | ||||||||
\(929\) | 49.1231i | 1.61168i | 0.592136 | + | 0.805838i | \(0.298285\pi\) | ||||
−0.592136 | + | 0.805838i | \(0.701715\pi\) | |||||||
\(930\) | 5.75379i | 0.188674i | ||||||||
\(931\) | 2.56155i | 0.0839515i | ||||||||
\(932\) | −2.00000 | −0.0655122 | ||||||||
\(933\) | −32.4924 | −1.06375 | ||||||||
\(934\) | 2.56155i | 0.0838166i | ||||||||
\(935\) | 4.59186 | 0.150170 | ||||||||
\(936\) | 3.56155 | − | 0.561553i | 0.116413 | − | 0.0183549i | ||||
\(937\) | 37.8617 | 1.23689 | 0.618445 | − | 0.785828i | \(-0.287763\pi\) | ||||
0.618445 | + | 0.785828i | \(0.287763\pi\) | |||||||
\(938\) | − | 7.12311i | − | 0.232578i | ||||||
\(939\) | −15.7538 | −0.514105 | ||||||||
\(940\) | −3.50758 | −0.114405 | ||||||||
\(941\) | − | 6.49242i | − | 0.211647i | −0.994385 | − | 0.105823i | \(-0.966252\pi\) | ||
0.994385 | − | 0.105823i | \(-0.0337478\pi\) | |||||||
\(942\) | 8.80776i | 0.286972i | ||||||||
\(943\) | − | 22.7386i | − | 0.740472i | ||||||
\(944\) | 12.2462i | 0.398580i | ||||||||
\(945\) | 0.561553 | 0.0182673 | ||||||||
\(946\) | 15.1922 | 0.493942 | ||||||||
\(947\) | − | 7.19224i | − | 0.233716i | −0.993149 | − | 0.116858i | \(-0.962718\pi\) | ||
0.993149 | − | 0.116858i | \(-0.0372823\pi\) | |||||||
\(948\) | 16.0000 | 0.519656 | ||||||||
\(949\) | −26.4924 | + | 4.17708i | −0.859980 | + | 0.135594i | ||||
\(950\) | −12.0000 | −0.389331 | ||||||||
\(951\) | 21.3693i | 0.692948i | ||||||||
\(952\) | −5.68466 | −0.184241 | ||||||||
\(953\) | −48.7386 | −1.57880 | −0.789400 | − | 0.613880i | \(-0.789608\pi\) | ||||
−0.789400 | + | 0.613880i | \(0.789608\pi\) | |||||||
\(954\) | − | 13.1231i | − | 0.424876i | ||||||
\(955\) | 7.33050i | 0.237209i | ||||||||
\(956\) | − | 2.24621i | − | 0.0726477i | ||||||
\(957\) | − | 3.68466i | − | 0.119108i | ||||||
\(958\) | 41.3002 | 1.33435 | ||||||||
\(959\) | −5.68466 | −0.183567 | ||||||||
\(960\) | 0.561553i | 0.0181240i | ||||||||
\(961\) | −73.9848 | −2.38661 | ||||||||
\(962\) | −0.946025 | − | 6.00000i | −0.0305011 | − | 0.193448i | ||||
\(963\) | −13.1231 | −0.422886 | ||||||||
\(964\) | 6.00000i | 0.193247i | ||||||||
\(965\) | −6.73863 | −0.216924 | ||||||||
\(966\) | −5.68466 | −0.182901 | ||||||||
\(967\) | 25.9309i | 0.833881i | 0.908934 | + | 0.416940i | \(0.136898\pi\) | ||||
−0.908934 | + | 0.416940i | \(0.863102\pi\) | |||||||
\(968\) | 8.93087i | 0.287049i | ||||||||
\(969\) | 14.5616i | 0.467784i | ||||||||
\(970\) | − | 5.61553i | − | 0.180304i | ||||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − | 6.24621i | − | 0.200244i | ||||||
\(974\) | 30.2462 | 0.969151 | ||||||||
\(975\) | 2.63068 | + | 16.6847i | 0.0842493 | + | 0.534337i | ||||
\(976\) | 2.56155 | 0.0819933 | ||||||||
\(977\) | − | 39.7926i | − | 1.27308i | −0.771244 | − | 0.636539i | \(-0.780365\pi\) | ||
0.771244 | − | 0.636539i | \(-0.219635\pi\) | |||||||
\(978\) | 0.876894 | 0.0280400 | ||||||||
\(979\) | 11.5076 | 0.367784 | ||||||||
\(980\) | 0.561553i | 0.0179381i | ||||||||
\(981\) | 15.9309i | 0.508634i | ||||||||
\(982\) | − | 6.24621i | − | 0.199325i | ||||||
\(983\) | 6.56155i | 0.209281i | 0.994510 | + | 0.104641i | \(0.0333692\pi\) | ||||
−0.994510 | + | 0.104641i | \(0.966631\pi\) | |||||||
\(984\) | −4.00000 | −0.127515 | ||||||||
\(985\) | −3.36932 | −0.107355 | ||||||||
\(986\) | 14.5616i | 0.463734i | ||||||||
\(987\) | −6.24621 | −0.198819 | ||||||||
\(988\) | 9.12311 | − | 1.43845i | 0.290245 | − | 0.0457631i | ||||
\(989\) | −60.0388 | −1.90912 | ||||||||
\(990\) | − | 0.807764i | − | 0.0256724i | ||||||
\(991\) | −13.7538 | −0.436903 | −0.218452 | − | 0.975848i | \(-0.570101\pi\) | ||||
−0.218452 | + | 0.975848i | \(0.570101\pi\) | |||||||
\(992\) | −10.2462 | −0.325318 | ||||||||
\(993\) | 7.12311i | 0.226045i | ||||||||
\(994\) | 15.3693i | 0.487485i | ||||||||
\(995\) | − | 13.4384i | − | 0.426027i | ||||||
\(996\) | 2.00000i | 0.0633724i | ||||||||
\(997\) | −59.3693 | −1.88025 | −0.940123 | − | 0.340837i | \(-0.889290\pi\) | ||||
−0.940123 | + | 0.340837i | \(0.889290\pi\) | |||||||
\(998\) | 34.4924 | 1.09184 | ||||||||
\(999\) | − | 1.68466i | − | 0.0533002i |
(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 | 546.2.c.e.337.2 | ✓ | 4 | |
3.2 | odd | 2 | 1638.2.c.h.883.3 | 4 | |||
4.3 | odd | 2 | 4368.2.h.n.337.3 | 4 | |||
7.6 | odd | 2 | 3822.2.c.h.883.1 | 4 | |||
13.5 | odd | 4 | 7098.2.a.bg.1.2 | 2 | |||
13.8 | odd | 4 | 7098.2.a.bv.1.1 | 2 | |||
13.12 | even | 2 | inner | 546.2.c.e.337.3 | yes | 4 | |
39.38 | odd | 2 | 1638.2.c.h.883.2 | 4 | |||
52.51 | odd | 2 | 4368.2.h.n.337.2 | 4 | |||
91.90 | odd | 2 | 3822.2.c.h.883.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.c.e.337.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
546.2.c.e.337.3 | yes | 4 | 13.12 | even | 2 | inner | |
1638.2.c.h.883.2 | 4 | 39.38 | odd | 2 | |||
1638.2.c.h.883.3 | 4 | 3.2 | odd | 2 | |||
3822.2.c.h.883.1 | 4 | 7.6 | odd | 2 | |||
3822.2.c.h.883.4 | 4 | 91.90 | odd | 2 | |||
4368.2.h.n.337.2 | 4 | 52.51 | odd | 2 | |||
4368.2.h.n.337.3 | 4 | 4.3 | odd | 2 | |||
7098.2.a.bg.1.2 | 2 | 13.5 | odd | 4 | |||
7098.2.a.bv.1.1 | 2 | 13.8 | odd | 4 |