Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(883,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.883");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
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: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 883.4 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.883 |
Dual form | 3822.2.c.h.883.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times\).
\(n\) | \(1471\) | \(2549\) | \(3433\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.561553 | −0.177579 | ||||||||
\(11\) | 1.43845i | 0.433708i | 0.976204 | + | 0.216854i | \(0.0695796\pi\) | ||||
−0.976204 | + | 0.216854i | \(0.930420\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.561553 | − | 3.56155i | 0.155747 | − | 0.987797i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.561553i | 0.144992i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.68466 | −1.37873 | −0.689366 | − | 0.724413i | \(-0.742111\pi\) | ||||
−0.689366 | + | 0.724413i | \(0.742111\pi\) | |||||||
\(18\) | 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 | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −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 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −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 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 1.68466i | − | 0.276956i | −0.990366 | − | 0.138478i | \(-0.955779\pi\) | ||
0.990366 | − | 0.138478i | \(-0.0442210\pi\) | |||||||
\(38\) | 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 | \(-0.101115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −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 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 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 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 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 | \(-0.552435\pi\) | ||||
−0.163987 | + | 0.986463i | \(0.552435\pi\) | |||||||
\(62\) | 10.2462 | 1.30127 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −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 | \(0.143292\pi\) | ||||
−0.900376 | + | 0.435113i | \(0.856708\pi\) | |||||||
\(68\) | 5.68466 | 0.689366 | ||||||||
\(69\) | 5.68466 | 0.684352 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.3693i | − | 1.82400i | −0.410188 | − | 0.912001i | \(-0.634537\pi\) | ||
0.410188 | − | 0.912001i | \(-0.365463\pi\) | |||||||
\(72\) | − | 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 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | \(0.964990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 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 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −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 | \(-0.169494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.43845i | 0.144569i | ||||||||
\(100\) | −4.68466 | −0.468466 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | − | 5.68466i | − | 0.562865i | ||||||
\(103\) | 18.8078 | 1.85318 | 0.926592 | − | 0.376068i | \(-0.122724\pi\) | ||||
0.926592 | + | 0.376068i | \(0.122724\pi\) | |||||||
\(104\) | −3.56155 | − | 0.561553i | −0.349239 | − | 0.0550648i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | \(-0.723750\pi\) | ||
0.646457 | − | 0.762950i | \(-0.276250\pi\) | |||||||
\(110\) | − | 0.807764i | − | 0.0770173i | ||||||
\(111\) | − | 1.68466i | − | 0.159901i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 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 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | \(-0.535694\pi\) | ||||
−0.111902 | + | 0.993719i | \(0.535694\pi\) | |||||||
\(132\) | − | 1.43845i | − | 0.125201i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.12311 | −0.615343 | ||||||||
\(135\) | 0.561553i | 0.0483308i | ||||||||
\(136\) | 5.68466i | 0.487455i | ||||||||
\(137\) | − | 5.68466i | − | 0.485673i | −0.970067 | − | 0.242837i | \(-0.921922\pi\) | ||
0.970067 | − | 0.242837i | \(-0.0780779\pi\) | |||||||
\(138\) | 5.68466i | 0.483910i | ||||||||
\(139\) | 6.24621 | 0.529797 | 0.264898 | − | 0.964276i | \(-0.414662\pi\) | ||||
0.264898 | + | 0.964276i | \(0.414662\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.68466i | 0.138478i | ||||||||
\(149\) | 10.0000i | 0.819232i | 0.912258 | + | 0.409616i | \(0.134337\pi\) | ||||
−0.912258 | + | 0.409616i | \(0.865663\pi\) | |||||||
\(150\) | 4.68466i | 0.382501i | ||||||||
\(151\) | 4.31534i | 0.351178i | 0.984464 | + | 0.175589i | \(0.0561829\pi\) | ||||
−0.984464 | + | 0.175589i | \(0.943817\pi\) | |||||||
\(152\) | −2.56155 | −0.207769 | ||||||||
\(153\) | −5.68466 | −0.459577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.75379 | 0.462155 | ||||||||
\(156\) | −0.561553 | + | 3.56155i | −0.0449602 | + | 0.285152i | ||||
\(157\) | −8.80776 | −0.702936 | −0.351468 | − | 0.936200i | \(-0.614317\pi\) | ||||
−0.351468 | + | 0.936200i | \(0.614317\pi\) | |||||||
\(158\) | 16.0000i | 1.27289i | ||||||||
\(159\) | 13.1231 | 1.04073 | ||||||||
\(160\) | −0.561553 | −0.0443946 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 0.876894i | 0.0686837i | 0.999410 | + | 0.0343418i | \(0.0109335\pi\) | ||||
−0.999410 | + | 0.0343418i | \(0.989067\pi\) | |||||||
\(164\) | 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 | \(-0.110692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −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 | \(-0.220433\pi\) | ||||
0.769645 | + | 0.638471i | \(0.220433\pi\) | |||||||
\(174\) | − | 2.56155i | − | 0.194191i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | \(-0.638860\pi\) | ||||
−0.422537 | + | 0.906346i | \(0.638860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.857847\pi\) | ||
0.901927 | − | 0.431889i | \(-0.142153\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 2.00000 | + | 0.315342i | 0.143223 | + | 0.0225821i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | −1.43845 | −0.102226 | ||||||||
\(199\) | 23.9309 | 1.69641 | 0.848207 | − | 0.529665i | \(-0.177682\pi\) | ||||
0.848207 | + | 0.529665i | \(0.177682\pi\) | |||||||
\(200\) | − | 4.68466i | − | 0.331255i | ||||||
\(201\) | 7.12311i | 0.502425i | ||||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 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 | 0 | ||||||||
\(211\) | −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 | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 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 | \(0.790796\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.24621i | − | 0.145295i | −0.997358 | − | 0.0726477i | \(-0.976855\pi\) | ||
0.997358 | − | 0.0726477i | \(-0.0231449\pi\) | |||||||
\(240\) | 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 | 0 | ||||||||
\(246\) | 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 | \(-0.342412\pi\) | ||||
0.475099 | + | 0.879932i | \(0.342412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | \(-0.198968\pi\) | ||||
0.810918 | + | 0.585160i | \(0.198968\pi\) | |||||||
\(258\) | − | 10.5616i | − | 0.657534i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.00000i | 0.489592i | ||||||||
\(268\) | − | 7.12311i | − | 0.435113i | ||||||
\(269\) | −6.63068 | −0.404280 | −0.202140 | − | 0.979357i | \(-0.564790\pi\) | ||||
−0.202140 | + | 0.979357i | \(0.564790\pi\) | |||||||
\(270\) | −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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | 0 | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 6.24621 | 0.371956 | ||||||||
\(283\) | 13.1231 | 0.780088 | 0.390044 | − | 0.920796i | \(-0.372460\pi\) | ||||
0.390044 | + | 0.920796i | \(0.372460\pi\) | |||||||
\(284\) | 15.3693i | 0.912001i | ||||||||
\(285\) | 1.43845 | 0.0852063 | ||||||||
\(286\) | −0.807764 | + | 5.12311i | −0.0477641 | + | 0.302936i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 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 | \(0.749490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −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 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −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 | \(-0.0897839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.8078 | 1.06994 | ||||||||
\(310\) | 5.75379i | 0.326793i | ||||||||
\(311\) | −32.4924 | −1.84248 | −0.921238 | − | 0.388999i | \(-0.872821\pi\) | ||||
−0.921238 | + | 0.388999i | \(0.872821\pi\) | |||||||
\(312\) | −3.56155 | − | 0.561553i | −0.201633 | − | 0.0317917i | ||||
\(313\) | −15.7538 | −0.890457 | −0.445228 | − | 0.895417i | \(-0.646878\pi\) | ||||
−0.445228 | + | 0.895417i | \(0.646878\pi\) | |||||||
\(314\) | − | 8.80776i | − | 0.497051i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 21.3693i | 1.20022i | 0.799917 | + | 0.600110i | \(0.204877\pi\) | ||||
−0.799917 | + | 0.600110i | \(0.795123\pi\) | |||||||
\(318\) | 13.1231i | 0.735907i | ||||||||
\(319\) | − | 3.68466i | − | 0.206301i | ||||||
\(320\) | − | 0.561553i | − | 0.0313918i | ||||||
\(321\) | −13.1231 | −0.732460 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 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 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 0.807764i | − | 0.0444659i | ||||||
\(331\) | 7.12311i | 0.391521i | 0.980652 | + | 0.195761i | \(0.0627176\pi\) | ||||
−0.980652 | + | 0.195761i | \(0.937282\pi\) | |||||||
\(332\) | − | 2.00000i | − | 0.109764i | ||||||
\(333\) | − | 1.68466i | − | 0.0923187i | ||||||
\(334\) | 8.80776 | 0.481939 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 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 | \(0.806192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 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 | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.87689i | 0.152049i | ||||||||
\(359\) | − | 17.6155i | − | 0.929712i | −0.885386 | − | 0.464856i | \(-0.846106\pi\) | ||
0.885386 | − | 0.464856i | \(-0.153894\pi\) | |||||||
\(360\) | 0.561553 | 0.0295964 | ||||||||
\(361\) | 12.4384 | 0.654655 | ||||||||
\(362\) | − | 11.3693i | − | 0.597558i | ||||||
\(363\) | 8.93087 | 0.468749 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.17708 | 0.218638 | ||||||||
\(366\) | − | 2.56155i | − | 0.133895i | ||||||
\(367\) | −25.3693 | −1.32427 | −0.662134 | − | 0.749386i | \(-0.730349\pi\) | ||||
−0.662134 | + | 0.749386i | \(0.730349\pi\) | |||||||
\(368\) | 5.68466 | 0.296333 | ||||||||
\(369\) | − | 4.00000i | − | 0.208232i | ||||||
\(370\) | 0.946025i | 0.0491815i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.1231i | − | 1.39322i | −0.717450 | − | 0.696610i | \(-0.754691\pi\) | ||
0.717450 | − | 0.696610i | \(-0.245309\pi\) | |||||||
\(380\) | −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 | 0 | ||||||||
\(386\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.68466 | 0.234233 | ||||||||
\(401\) | 34.9848i | 1.74706i | 0.486771 | + | 0.873530i | \(0.338175\pi\) | ||||
−0.486771 | + | 0.873530i | \(0.661825\pi\) | |||||||
\(402\) | −7.12311 | −0.355268 | ||||||||
\(403\) | −36.4924 | − | 5.75379i | −1.81782 | − | 0.286617i | ||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0.561553i | 0.0279038i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 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 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 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 | \(-0.434893\pi\) | ||||
0.203116 | + | 0.979155i | \(0.434893\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10.0000i | − | 0.487370i | −0.969854 | − | 0.243685i | \(-0.921644\pi\) | ||
0.969854 | − | 0.243685i | \(-0.0783563\pi\) | |||||||
\(422\) | − | 12.8078i | − | 0.623472i | ||||||
\(423\) | − | 6.24621i | − | 0.303701i | ||||||
\(424\) | − | 13.1231i | − | 0.637314i | ||||||
\(425\) | −26.6307 | −1.29178 | ||||||||
\(426\) | 15.3693 | 0.744646 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | \(-0.765854\pi\) | ||
0.741433 | − | 0.671026i | \(-0.234146\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 1.36932 | 0.0658052 | 0.0329026 | − | 0.999459i | \(-0.489525\pi\) | ||||
0.0329026 | + | 0.999459i | \(0.489525\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 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 | \(-0.657778\pi\) | ||||
−0.475624 | + | 0.879649i | \(0.657778\pi\) | |||||||
\(440\) | 0.807764i | 0.0385086i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −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 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 21.6847i | − | 1.02336i | −0.859175 | − | 0.511681i | \(-0.829023\pi\) | ||
0.859175 | − | 0.511681i | \(-0.170977\pi\) | |||||||
\(450\) | 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 | 0 | ||||||||
\(456\) | −2.56155 | −0.119956 | ||||||||
\(457\) | − | 16.0000i | − | 0.748448i | −0.927338 | − | 0.374224i | \(-0.877909\pi\) | ||
0.927338 | − | 0.374224i | \(-0.122091\pi\) | |||||||
\(458\) | 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 | \(-0.0601708\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.5464i | 1.83788i | 0.394401 | + | 0.918938i | \(0.370952\pi\) | ||||
−0.394401 | + | 0.918938i | \(0.629048\pi\) | |||||||
\(464\) | −2.56155 | −0.118917 | ||||||||
\(465\) | 5.75379 | 0.266826 | ||||||||
\(466\) | 2.00000i | 0.0926482i | ||||||||
\(467\) | 2.56155 | 0.118535 | 0.0592673 | − | 0.998242i | \(-0.481124\pi\) | ||||
0.0592673 | + | 0.998242i | \(0.481124\pi\) | |||||||
\(468\) | −0.561553 | + | 3.56155i | −0.0259578 | + | 0.164633i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.93087 | −0.405949 | ||||||||
\(485\) | 5.61553 | 0.254988 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − | 30.2462i | − | 1.37059i | −0.728267 | − | 0.685293i | \(-0.759674\pi\) | ||
0.728267 | − | 0.685293i | \(-0.240326\pi\) | |||||||
\(488\) | 2.56155i | 0.115956i | ||||||||
\(489\) | 0.876894i | 0.0396545i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.00000 | −0.0896221 | ||||||||
\(499\) | − | 34.4924i | − | 1.54409i | −0.635566 | − | 0.772046i | \(-0.719233\pi\) | ||
0.635566 | − | 0.772046i | \(-0.280767\pi\) | |||||||
\(500\) | − | 5.43845i | − | 0.243215i | ||||||
\(501\) | − | 8.80776i | − | 0.393502i | ||||||
\(502\) | 15.0540i | 0.671892i | ||||||||
\(503\) | 5.61553 | 0.250384 | 0.125192 | − | 0.992133i | \(-0.460045\pi\) | ||||
0.125192 | + | 0.992133i | \(0.460045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 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 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 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 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.2462 | 0.888710 | ||||||||
\(520\) | 0.315342 | − | 2.00000i | 0.0138286 | − | 0.0877058i | ||||
\(521\) | 29.0540 | 1.27288 | 0.636439 | − | 0.771327i | \(-0.280407\pi\) | ||||
0.636439 | + | 0.771327i | \(0.280407\pi\) | |||||||
\(522\) | − | 2.56155i | − | 0.112116i | ||||||
\(523\) | −24.4924 | −1.07098 | −0.535489 | − | 0.844542i | \(-0.679873\pi\) | ||||
−0.535489 | + | 0.844542i | \(0.679873\pi\) | |||||||
\(524\) | 2.56155 | 0.111902 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −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 | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 0.561553i | − | 0.0241654i | ||||||
\(541\) | − | 26.8078i | − | 1.15256i | −0.817254 | − | 0.576278i | \(-0.804505\pi\) | ||
0.817254 | − | 0.576278i | \(-0.195495\pi\) | |||||||
\(542\) | −8.00000 | −0.343629 | ||||||||
\(543\) | −11.3693 | −0.487904 | ||||||||
\(544\) | − | 5.68466i | − | 0.243728i | ||||||
\(545\) | 8.94602 | 0.383206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −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 | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 19.1231i | − | 0.812463i | ||||||
\(555\) | 0.946025 | 0.0401565 | ||||||||
\(556\) | −6.24621 | −0.264898 | ||||||||
\(557\) | − | 0.246211i | − | 0.0104323i | −0.999986 | − | 0.00521615i | \(-0.998340\pi\) | ||
0.999986 | − | 0.00521615i | \(-0.00166036\pi\) | |||||||
\(558\) | 10.2462 | 0.433757 | ||||||||
\(559\) | −5.93087 | + | 37.6155i | −0.250849 | + | 1.59097i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 8.17708i | − | 0.345237i | ||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | −0.946025 | −0.0398702 | −0.0199351 | − | 0.999801i | \(-0.506346\pi\) | ||||
−0.0199351 | + | 0.999801i | \(0.506346\pi\) | |||||||
\(564\) | 6.24621i | 0.263013i | ||||||||
\(565\) | 2.10795i | 0.0886821i | ||||||||
\(566\) | 13.1231i | 0.551605i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 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 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 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 | \(0.796780\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −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 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 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 | \(-0.676856\pi\) | ||||
−0.527461 | + | 0.849579i | \(0.676856\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 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 | \(-0.819306\pi\) | ||||
−0.843158 | + | 0.537666i | \(0.819306\pi\) | |||||||
\(608\) | 2.56155 | 0.103885 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | \(0.124014\pi\) | ||||
−0.925061 | + | 0.379819i | \(0.875986\pi\) | |||||||
\(614\) | 9.75379 | 0.393631 | ||||||||
\(615\) | 2.24621 | 0.0905760 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.8078i | 1.07924i | 0.841909 | + | 0.539620i | \(0.181432\pi\) | ||||
−0.841909 | + | 0.539620i | \(0.818568\pi\) | |||||||
\(618\) | 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 | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 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 | 0 | ||||||||
\(631\) | 0.315342i | 0.0125535i | 0.999980 | + | 0.00627677i | \(0.00199797\pi\) | ||||
−0.999980 | + | 0.00627677i | \(0.998002\pi\) | |||||||
\(632\) | − | 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 | 0 | ||||||||
\(638\) | 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 | \(0.865428\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 5.93087i | − | 0.233528i | ||||||
\(646\) | −14.5616 | −0.572917 | ||||||||
\(647\) | −35.3693 | −1.39051 | −0.695256 | − | 0.718763i | \(-0.744709\pi\) | ||||
−0.695256 | + | 0.718763i | \(0.744709\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −17.6155 | −0.691470 | ||||||||
\(650\) | 16.6847 | + | 2.63068i | 0.654426 | + | 0.103184i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 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 | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 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 | \(-0.540669\pi\) | ||||
−0.127419 | + | 0.991849i | \(0.540669\pi\) | |||||||
\(678\) | 3.75379i | 0.144163i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.19224 | −0.122417 | ||||||||
\(681\) | − | 23.6155i | − | 0.904949i | ||||||
\(682\) | 14.7386i | 0.564371i | ||||||||
\(683\) | − | 11.6847i | − | 0.447101i | −0.974692 | − | 0.223551i | \(-0.928235\pi\) | ||
0.974692 | − | 0.223551i | \(-0.0717648\pi\) | |||||||
\(684\) | 2.56155i | 0.0979434i | ||||||||
\(685\) | 3.19224 | 0.121969 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 12.2462i | − | 0.460241i | ||||||
\(709\) | 48.2462i | 1.81192i | 0.423358 | + | 0.905962i | \(0.360851\pi\) | ||||
−0.423358 | + | 0.905962i | \(0.639149\pi\) | |||||||
\(710\) | 8.63068i | 0.323904i | ||||||||
\(711\) | 16.0000 | 0.600047 | ||||||||
\(712\) | 8.00000 | 0.299813 | ||||||||
\(713\) | − | 58.2462i | − | 2.18134i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −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 | \(-0.690737\pi\) | ||||
−0.563997 | + | 0.825777i | \(0.690737\pi\) | |||||||
\(720\) | 0.561553i | 0.0209278i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 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 | \(-0.378617\pi\) | ||||
0.372161 | + | 0.928168i | \(0.378617\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 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 | 0 | ||||||||
\(736\) | 5.68466i | 0.209539i | ||||||||
\(737\) | −10.2462 | −0.377424 | ||||||||
\(738\) | 4.00000 | 0.147242 | ||||||||
\(739\) | 23.6155i | 0.868711i | 0.900741 | + | 0.434356i | \(0.143024\pi\) | ||||
−0.900741 | + | 0.434356i | \(0.856976\pi\) | |||||||
\(740\) | −0.946025 | −0.0347766 | ||||||||
\(741\) | −9.12311 | − | 1.43845i | −0.335146 | − | 0.0528427i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.0000i | − | 0.586983i | −0.955962 | − | 0.293492i | \(-0.905183\pi\) | ||
0.955962 | − | 0.293492i | \(-0.0948173\pi\) | |||||||
\(744\) | −10.2462 | −0.375644 | ||||||||
\(745\) | −5.61553 | −0.205737 | ||||||||
\(746\) | − | 6.00000i | − | 0.219676i | ||||||
\(747\) | 2.00000i | 0.0731762i | ||||||||
\(748\) | 8.17708i | 0.298984i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −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 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 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 | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −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 | 0 | ||||||||
\(771\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 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 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | \(-0.616739\pi\) | ||||
−0.358579 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 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 | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(-0.211028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.24621 | −0.0784411 | ||||||||
\(821\) | − | 39.1231i | − | 1.36541i | −0.730696 | − | 0.682703i | \(-0.760804\pi\) | ||
0.730696 | − | 0.682703i | \(-0.239196\pi\) | |||||||
\(822\) | 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 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.0540i | − | 0.523478i | −0.965139 | − | 0.261739i | \(-0.915704\pi\) | ||
0.965139 | − | 0.261739i | \(-0.0842960\pi\) | |||||||
\(828\) | −5.68466 | −0.197556 | ||||||||
\(829\) | −4.94602 | −0.171783 | −0.0858913 | − | 0.996305i | \(-0.527374\pi\) | ||||
−0.0858913 | + | 0.996305i | \(0.527374\pi\) | |||||||
\(830\) | − | 1.12311i | − | 0.0389836i | ||||||
\(831\) | −19.1231 | −0.663373 | ||||||||
\(832\) | −0.561553 | + | 3.56155i | −0.0194683 | + | 0.123475i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 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 | 0 | ||||||||
\(841\) | −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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 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 | \(-0.106166\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.43845 | 0.0491939 | ||||||||
\(856\) | 13.1231i | 0.448539i | ||||||||
\(857\) | 38.0000 | 1.29806 | 0.649028 | − | 0.760765i | \(-0.275176\pi\) | ||||
0.649028 | + | 0.760765i | \(0.275176\pi\) | |||||||
\(858\) | −0.807764 | + | 5.12311i | −0.0275766 | + | 0.174900i | ||||
\(859\) | −41.6155 | −1.41990 | −0.709952 | − | 0.704250i | \(-0.751283\pi\) | ||||
−0.709952 | + | 0.704250i | \(0.751283\pi\) | |||||||
\(860\) | 5.93087i | 0.202241i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.8617 | 0.948975 | ||||||||
\(863\) | 6.73863i | 0.229386i | 0.993401 | + | 0.114693i | \(0.0365884\pi\) | ||||
−0.993401 | + | 0.114693i | \(0.963412\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 11.3693i | 0.386568i | ||||||||
\(866\) | 1.36932i | 0.0465313i | ||||||||
\(867\) | 15.3153 | 0.520136 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.43845i | 0.251322i | ||||||||
\(877\) | 42.9848i | 1.45150i | 0.687961 | + | 0.725748i | \(0.258506\pi\) | ||||
−0.687961 | + | 0.725748i | \(0.741494\pi\) | |||||||
\(878\) | − | 19.9309i | − | 0.672634i | ||||||
\(879\) | 24.2462i | 0.817804i | ||||||||
\(880\) | −0.807764 | −0.0272297 | ||||||||
\(881\) | 39.3002 | 1.32406 | 0.662028 | − | 0.749479i | \(-0.269696\pi\) | ||||
0.662028 | + | 0.749479i | \(0.269696\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −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 | \(-0.608211\pi\) | ||||
−0.333446 | + | 0.942769i | \(0.608211\pi\) | |||||||
\(888\) | −1.68466 | −0.0565334 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 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 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 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 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 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 | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 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 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −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 | \(-0.712237\pi\) | ||||
−0.618445 | + | 0.785828i | \(0.712237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −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 | 0 | ||||||||
\(946\) | 15.1922 | 0.493942 | ||||||||
\(947\) | 7.19224i | 0.233716i | 0.993149 | + | 0.116858i | \(0.0372823\pi\) | ||||
−0.993149 | + | 0.116858i | \(0.962718\pi\) | |||||||
\(948\) | −16.0000 | −0.519656 | ||||||||
\(949\) | −26.4924 | − | 4.17708i | −0.859980 | − | 0.135594i | ||||
\(950\) | 12.0000 | 0.389331 | ||||||||
\(951\) | 21.3693i | 0.692948i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −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 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 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 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25.9309i | − | 0.833881i | −0.908934 | − | 0.416940i | \(-0.863102\pi\) | ||
0.908934 | − | 0.416940i | \(-0.136898\pi\) | |||||||
\(968\) | − | 8.93087i | − | 0.287049i | ||||||
\(969\) | 14.5616i | 0.467784i | ||||||||
\(970\) | 5.61553i | 0.180304i | ||||||||
\(971\) | −4.00000 | −0.128366 | −0.0641831 | − | 0.997938i | \(-0.520444\pi\) | ||||
−0.0641831 | + | 0.997938i | \(0.520444\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | \(0.219635\pi\) | ||||
−0.771244 | + | 0.636539i | \(0.780365\pi\) | |||||||
\(978\) | −0.876894 | −0.0280400 | ||||||||
\(979\) | −11.5076 | −0.367784 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.4384i | 0.426027i | ||||||||
\(996\) | − | 2.00000i | − | 0.0633724i | ||||||
\(997\) | 59.3693 | 1.88025 | 0.940123 | − | 0.340837i | \(-0.110710\pi\) | ||||
0.940123 | + | 0.340837i | \(0.110710\pi\) | |||||||
\(998\) | 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 | 3822.2.c.h.883.4 | 4 | ||
7.6 | odd | 2 | 546.2.c.e.337.3 | yes | 4 | ||
13.12 | even | 2 | inner | 3822.2.c.h.883.1 | 4 | ||
21.20 | even | 2 | 1638.2.c.h.883.2 | 4 | |||
28.27 | even | 2 | 4368.2.h.n.337.2 | 4 | |||
91.34 | even | 4 | 7098.2.a.bg.1.2 | 2 | |||
91.83 | even | 4 | 7098.2.a.bv.1.1 | 2 | |||
91.90 | odd | 2 | 546.2.c.e.337.2 | ✓ | 4 | ||
273.272 | even | 2 | 1638.2.c.h.883.3 | 4 | |||
364.363 | even | 2 | 4368.2.h.n.337.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.c.e.337.2 | ✓ | 4 | 91.90 | odd | 2 | ||
546.2.c.e.337.3 | yes | 4 | 7.6 | odd | 2 | ||
1638.2.c.h.883.2 | 4 | 21.20 | even | 2 | |||
1638.2.c.h.883.3 | 4 | 273.272 | even | 2 | |||
3822.2.c.h.883.1 | 4 | 13.12 | even | 2 | inner | ||
3822.2.c.h.883.4 | 4 | 1.1 | even | 1 | trivial | ||
4368.2.h.n.337.2 | 4 | 28.27 | even | 2 | |||
4368.2.h.n.337.3 | 4 | 364.363 | even | 2 | |||
7098.2.a.bg.1.2 | 2 | 91.34 | even | 4 | |||
7098.2.a.bv.1.1 | 2 | 91.83 | even | 4 |