Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.a (trivial) |
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: | yes |
Analytic conductor: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.561553 | 0.251134 | 0.125567 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.561553 | −0.177579 | ||||||||
\(11\) | 1.43845 | 0.433708 | 0.216854 | − | 0.976204i | \(-0.430420\pi\) | ||||
0.216854 | + | 0.976204i | \(0.430420\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −0.561553 | −0.144992 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.68466 | −1.37873 | −0.689366 | − | 0.724413i | \(-0.742111\pi\) | ||||
−0.689366 | + | 0.724413i | \(0.742111\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.56155 | −0.587661 | −0.293830 | − | 0.955858i | \(-0.594930\pi\) | ||||
−0.293830 | + | 0.955858i | \(0.594930\pi\) | |||||||
\(20\) | 0.561553 | 0.125567 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.43845 | −0.306678 | ||||||||
\(23\) | −5.68466 | −1.18533 | −0.592667 | − | 0.805448i | \(-0.701925\pi\) | ||||
−0.592667 | + | 0.805448i | \(0.701925\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.56155 | −0.475668 | −0.237834 | − | 0.971306i | \(-0.576437\pi\) | ||||
−0.237834 | + | 0.971306i | \(0.576437\pi\) | |||||||
\(30\) | 0.561553 | 0.102525 | ||||||||
\(31\) | −10.2462 | −1.84027 | −0.920137 | − | 0.391597i | \(-0.871923\pi\) | ||||
−0.920137 | + | 0.391597i | \(0.871923\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.43845 | −0.250402 | ||||||||
\(34\) | 5.68466 | 0.974911 | ||||||||
\(35\) | −0.561553 | −0.0949197 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.68466 | −0.276956 | −0.138478 | − | 0.990366i | \(-0.544221\pi\) | ||||
−0.138478 | + | 0.990366i | \(0.544221\pi\) | |||||||
\(38\) | 2.56155 | 0.415539 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.561553 | −0.0887893 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 10.5616 | 1.61062 | 0.805311 | − | 0.592853i | \(-0.201998\pi\) | ||||
0.805311 | + | 0.592853i | \(0.201998\pi\) | |||||||
\(44\) | 1.43845 | 0.216854 | ||||||||
\(45\) | 0.561553 | 0.0837114 | ||||||||
\(46\) | 5.68466 | 0.838157 | ||||||||
\(47\) | 6.24621 | 0.911104 | 0.455552 | − | 0.890209i | \(-0.349442\pi\) | ||||
0.455552 | + | 0.890209i | \(0.349442\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.68466 | 0.662511 | ||||||||
\(51\) | 5.68466 | 0.796011 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1231 | 1.80260 | 0.901299 | − | 0.433198i | \(-0.142615\pi\) | ||||
0.901299 | + | 0.433198i | \(0.142615\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.807764 | 0.108919 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 2.56155 | 0.339286 | ||||||||
\(58\) | 2.56155 | 0.336348 | ||||||||
\(59\) | −12.2462 | −1.59432 | −0.797160 | − | 0.603768i | \(-0.793666\pi\) | ||||
−0.797160 | + | 0.603768i | \(0.793666\pi\) | |||||||
\(60\) | −0.561553 | −0.0724962 | ||||||||
\(61\) | 2.56155 | 0.327973 | 0.163987 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163987 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(62\) | 10.2462 | 1.30127 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.43845 | 0.177061 | ||||||||
\(67\) | −7.12311 | −0.870226 | −0.435113 | − | 0.900376i | \(-0.643292\pi\) | ||||
−0.435113 | + | 0.900376i | \(0.643292\pi\) | |||||||
\(68\) | −5.68466 | −0.689366 | ||||||||
\(69\) | 5.68466 | 0.684352 | ||||||||
\(70\) | 0.561553 | 0.0671184 | ||||||||
\(71\) | 15.3693 | 1.82400 | 0.912001 | − | 0.410188i | \(-0.134537\pi\) | ||||
0.912001 | + | 0.410188i | \(0.134537\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 7.43845 | 0.870604 | 0.435302 | − | 0.900284i | \(-0.356642\pi\) | ||||
0.435302 | + | 0.900284i | \(0.356642\pi\) | |||||||
\(74\) | 1.68466 | 0.195838 | ||||||||
\(75\) | 4.68466 | 0.540938 | ||||||||
\(76\) | −2.56155 | −0.293830 | ||||||||
\(77\) | −1.43845 | −0.163926 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0000 | 1.80014 | 0.900070 | − | 0.435745i | \(-0.143515\pi\) | ||||
0.900070 | + | 0.435745i | \(0.143515\pi\) | |||||||
\(80\) | 0.561553 | 0.0627835 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.00000 | 0.441726 | ||||||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −3.19224 | −0.346247 | ||||||||
\(86\) | −10.5616 | −1.13888 | ||||||||
\(87\) | 2.56155 | 0.274627 | ||||||||
\(88\) | −1.43845 | −0.153339 | ||||||||
\(89\) | −8.00000 | −0.847998 | −0.423999 | − | 0.905663i | \(-0.639374\pi\) | ||||
−0.423999 | + | 0.905663i | \(0.639374\pi\) | |||||||
\(90\) | −0.561553 | −0.0591929 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.68466 | −0.592667 | ||||||||
\(93\) | 10.2462 | 1.06248 | ||||||||
\(94\) | −6.24621 | −0.644247 | ||||||||
\(95\) | −1.43845 | −0.147582 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.43845 | 0.144569 | ||||||||
\(100\) | −4.68466 | −0.468466 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | −5.68466 | −0.562865 | ||||||||
\(103\) | 18.8078 | 1.85318 | 0.926592 | − | 0.376068i | \(-0.122724\pi\) | ||||
0.926592 | + | 0.376068i | \(0.122724\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.561553 | 0.0548019 | ||||||||
\(106\) | −13.1231 | −1.27463 | ||||||||
\(107\) | −13.1231 | −1.26866 | −0.634329 | − | 0.773063i | \(-0.718724\pi\) | ||||
−0.634329 | + | 0.773063i | \(0.718724\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 15.9309 | 1.52590 | 0.762950 | − | 0.646457i | \(-0.223750\pi\) | ||||
0.762950 | + | 0.646457i | \(0.223750\pi\) | |||||||
\(110\) | −0.807764 | −0.0770173 | ||||||||
\(111\) | 1.68466 | 0.159901 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.75379 | 0.353127 | 0.176563 | − | 0.984289i | \(-0.443502\pi\) | ||||
0.176563 | + | 0.984289i | \(0.443502\pi\) | |||||||
\(114\) | −2.56155 | −0.239911 | ||||||||
\(115\) | −3.19224 | −0.297678 | ||||||||
\(116\) | −2.56155 | −0.237834 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.2462 | 1.12736 | ||||||||
\(119\) | 5.68466 | 0.521112 | ||||||||
\(120\) | 0.561553 | 0.0512625 | ||||||||
\(121\) | −8.93087 | −0.811897 | ||||||||
\(122\) | −2.56155 | −0.231912 | ||||||||
\(123\) | 4.00000 | 0.360668 | ||||||||
\(124\) | −10.2462 | −0.920137 | ||||||||
\(125\) | −5.43845 | −0.486430 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 6.24621 | 0.554262 | 0.277131 | − | 0.960832i | \(-0.410616\pi\) | ||||
0.277131 | + | 0.960832i | \(0.410616\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.5616 | −0.929893 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.56155 | 0.223804 | 0.111902 | − | 0.993719i | \(-0.464306\pi\) | ||||
0.111902 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(132\) | −1.43845 | −0.125201 | ||||||||
\(133\) | 2.56155 | 0.222115 | ||||||||
\(134\) | 7.12311 | 0.615343 | ||||||||
\(135\) | −0.561553 | −0.0483308 | ||||||||
\(136\) | 5.68466 | 0.487455 | ||||||||
\(137\) | −5.68466 | −0.485673 | −0.242837 | − | 0.970067i | \(-0.578078\pi\) | ||||
−0.242837 | + | 0.970067i | \(0.578078\pi\) | |||||||
\(138\) | −5.68466 | −0.483910 | ||||||||
\(139\) | −6.24621 | −0.529797 | −0.264898 | − | 0.964276i | \(-0.585338\pi\) | ||||
−0.264898 | + | 0.964276i | \(0.585338\pi\) | |||||||
\(140\) | −0.561553 | −0.0474599 | ||||||||
\(141\) | −6.24621 | −0.526026 | ||||||||
\(142\) | −15.3693 | −1.28976 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.43845 | −0.119457 | ||||||||
\(146\) | −7.43845 | −0.615610 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −1.68466 | −0.138478 | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −4.68466 | −0.382501 | ||||||||
\(151\) | 4.31534 | 0.351178 | 0.175589 | − | 0.984464i | \(-0.443817\pi\) | ||||
0.175589 | + | 0.984464i | \(0.443817\pi\) | |||||||
\(152\) | 2.56155 | 0.207769 | ||||||||
\(153\) | −5.68466 | −0.459577 | ||||||||
\(154\) | 1.43845 | 0.115913 | ||||||||
\(155\) | −5.75379 | −0.462155 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.80776 | 0.702936 | 0.351468 | − | 0.936200i | \(-0.385683\pi\) | ||||
0.351468 | + | 0.936200i | \(0.385683\pi\) | |||||||
\(158\) | −16.0000 | −1.27289 | ||||||||
\(159\) | −13.1231 | −1.04073 | ||||||||
\(160\) | −0.561553 | −0.0443946 | ||||||||
\(161\) | 5.68466 | 0.448014 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 0.876894 | 0.0686837 | 0.0343418 | − | 0.999410i | \(-0.489067\pi\) | ||||
0.0343418 | + | 0.999410i | \(0.489067\pi\) | |||||||
\(164\) | −4.00000 | −0.312348 | ||||||||
\(165\) | −0.807764 | −0.0628843 | ||||||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | 8.80776 | 0.681565 | 0.340783 | − | 0.940142i | \(-0.389308\pi\) | ||||
0.340783 | + | 0.940142i | \(0.389308\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.19224 | 0.244833 | ||||||||
\(171\) | −2.56155 | −0.195887 | ||||||||
\(172\) | 10.5616 | 0.805311 | ||||||||
\(173\) | 20.2462 | 1.53929 | 0.769645 | − | 0.638471i | \(-0.220433\pi\) | ||||
0.769645 | + | 0.638471i | \(0.220433\pi\) | |||||||
\(174\) | −2.56155 | −0.194191 | ||||||||
\(175\) | 4.68466 | 0.354127 | ||||||||
\(176\) | 1.43845 | 0.108427 | ||||||||
\(177\) | 12.2462 | 0.920482 | ||||||||
\(178\) | 8.00000 | 0.599625 | ||||||||
\(179\) | −2.87689 | −0.215029 | −0.107515 | − | 0.994204i | \(-0.534289\pi\) | ||||
−0.107515 | + | 0.994204i | \(0.534289\pi\) | |||||||
\(180\) | 0.561553 | 0.0418557 | ||||||||
\(181\) | −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 | ||||||||
\(184\) | 5.68466 | 0.419079 | ||||||||
\(185\) | −0.946025 | −0.0695531 | ||||||||
\(186\) | −10.2462 | −0.751289 | ||||||||
\(187\) | −8.17708 | −0.597967 | ||||||||
\(188\) | 6.24621 | 0.455552 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.43845 | 0.104356 | ||||||||
\(191\) | 13.0540 | 0.944553 | 0.472276 | − | 0.881451i | \(-0.343432\pi\) | ||||
0.472276 | + | 0.881451i | \(0.343432\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −12.0000 | −0.863779 | −0.431889 | − | 0.901927i | \(-0.642153\pi\) | ||||
−0.431889 | + | 0.901927i | \(0.642153\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | −1.43845 | −0.102226 | ||||||||
\(199\) | 23.9309 | 1.69641 | 0.848207 | − | 0.529665i | \(-0.177682\pi\) | ||||
0.848207 | + | 0.529665i | \(0.177682\pi\) | |||||||
\(200\) | 4.68466 | 0.331255 | ||||||||
\(201\) | 7.12311 | 0.502425 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 2.56155 | 0.179786 | ||||||||
\(204\) | 5.68466 | 0.398006 | ||||||||
\(205\) | −2.24621 | −0.156882 | ||||||||
\(206\) | −18.8078 | −1.31040 | ||||||||
\(207\) | −5.68466 | −0.395111 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.68466 | −0.254873 | ||||||||
\(210\) | −0.561553 | −0.0387508 | ||||||||
\(211\) | −12.8078 | −0.881723 | −0.440861 | − | 0.897575i | \(-0.645327\pi\) | ||||
−0.440861 | + | 0.897575i | \(0.645327\pi\) | |||||||
\(212\) | 13.1231 | 0.901299 | ||||||||
\(213\) | −15.3693 | −1.05309 | ||||||||
\(214\) | 13.1231 | 0.897077 | ||||||||
\(215\) | 5.93087 | 0.404482 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 10.2462 | 0.695558 | ||||||||
\(218\) | −15.9309 | −1.07897 | ||||||||
\(219\) | −7.43845 | −0.502644 | ||||||||
\(220\) | 0.807764 | 0.0544594 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.68466 | −0.113067 | ||||||||
\(223\) | 18.2462 | 1.22186 | 0.610928 | − | 0.791686i | \(-0.290796\pi\) | ||||
0.610928 | + | 0.791686i | \(0.290796\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −4.68466 | −0.312311 | ||||||||
\(226\) | −3.75379 | −0.249698 | ||||||||
\(227\) | −23.6155 | −1.56742 | −0.783709 | − | 0.621128i | \(-0.786675\pi\) | ||||
−0.783709 | + | 0.621128i | \(0.786675\pi\) | |||||||
\(228\) | 2.56155 | 0.169643 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 3.19224 | 0.210490 | ||||||||
\(231\) | 1.43845 | 0.0946429 | ||||||||
\(232\) | 2.56155 | 0.168174 | ||||||||
\(233\) | −2.00000 | −0.131024 | −0.0655122 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655122 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.50758 | 0.228809 | ||||||||
\(236\) | −12.2462 | −0.797160 | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | −5.68466 | −0.368482 | ||||||||
\(239\) | 2.24621 | 0.145295 | 0.0726477 | − | 0.997358i | \(-0.476855\pi\) | ||||
0.0726477 | + | 0.997358i | \(0.476855\pi\) | |||||||
\(240\) | −0.561553 | −0.0362481 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 8.93087 | 0.574098 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.56155 | 0.163987 | ||||||||
\(245\) | 0.561553 | 0.0358763 | ||||||||
\(246\) | −4.00000 | −0.255031 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.2462 | 0.650635 | ||||||||
\(249\) | −2.00000 | −0.126745 | ||||||||
\(250\) | 5.43845 | 0.343958 | ||||||||
\(251\) | 15.0540 | 0.950198 | 0.475099 | − | 0.879932i | \(-0.342412\pi\) | ||||
0.475099 | + | 0.879932i | \(0.342412\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −8.17708 | −0.514089 | ||||||||
\(254\) | −6.24621 | −0.391922 | ||||||||
\(255\) | 3.19224 | 0.199906 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.0000 | 1.62184 | 0.810918 | − | 0.585160i | \(-0.198968\pi\) | ||||
0.810918 | + | 0.585160i | \(0.198968\pi\) | |||||||
\(258\) | 10.5616 | 0.657534 | ||||||||
\(259\) | 1.68466 | 0.104680 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.56155 | −0.158556 | ||||||||
\(262\) | −2.56155 | −0.158253 | ||||||||
\(263\) | 1.36932 | 0.0844357 | 0.0422178 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422178 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(264\) | 1.43845 | 0.0885303 | ||||||||
\(265\) | 7.36932 | 0.452694 | ||||||||
\(266\) | −2.56155 | −0.157059 | ||||||||
\(267\) | 8.00000 | 0.489592 | ||||||||
\(268\) | −7.12311 | −0.435113 | ||||||||
\(269\) | 6.63068 | 0.404280 | 0.202140 | − | 0.979357i | \(-0.435210\pi\) | ||||
0.202140 | + | 0.979357i | \(0.435210\pi\) | |||||||
\(270\) | 0.561553 | 0.0341750 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | −5.68466 | −0.344683 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.68466 | 0.343423 | ||||||||
\(275\) | −6.73863 | −0.406355 | ||||||||
\(276\) | 5.68466 | 0.342176 | ||||||||
\(277\) | 19.1231 | 1.14900 | 0.574498 | − | 0.818506i | \(-0.305197\pi\) | ||||
0.574498 | + | 0.818506i | \(0.305197\pi\) | |||||||
\(278\) | 6.24621 | 0.374623 | ||||||||
\(279\) | −10.2462 | −0.613425 | ||||||||
\(280\) | 0.561553 | 0.0335592 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 6.24621 | 0.371956 | ||||||||
\(283\) | 13.1231 | 0.780088 | 0.390044 | − | 0.920796i | \(-0.372460\pi\) | ||||
0.390044 | + | 0.920796i | \(0.372460\pi\) | |||||||
\(284\) | 15.3693 | 0.912001 | ||||||||
\(285\) | 1.43845 | 0.0852063 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 15.3153 | 0.900902 | ||||||||
\(290\) | 1.43845 | 0.0844685 | ||||||||
\(291\) | 10.0000 | 0.586210 | ||||||||
\(292\) | 7.43845 | 0.435302 | ||||||||
\(293\) | −24.2462 | −1.41648 | −0.708239 | − | 0.705972i | \(-0.750510\pi\) | ||||
−0.708239 | + | 0.705972i | \(0.750510\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −6.87689 | −0.400388 | ||||||||
\(296\) | 1.68466 | 0.0979188 | ||||||||
\(297\) | −1.43845 | −0.0834672 | ||||||||
\(298\) | 10.0000 | 0.579284 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.68466 | 0.270469 | ||||||||
\(301\) | −10.5616 | −0.608758 | ||||||||
\(302\) | −4.31534 | −0.248320 | ||||||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | −2.56155 | −0.146915 | ||||||||
\(305\) | 1.43845 | 0.0823652 | ||||||||
\(306\) | 5.68466 | 0.324970 | ||||||||
\(307\) | 9.75379 | 0.556678 | 0.278339 | − | 0.960483i | \(-0.410216\pi\) | ||||
0.278339 | + | 0.960483i | \(0.410216\pi\) | |||||||
\(308\) | −1.43845 | −0.0819631 | ||||||||
\(309\) | −18.8078 | −1.06994 | ||||||||
\(310\) | 5.75379 | 0.326793 | ||||||||
\(311\) | −32.4924 | −1.84248 | −0.921238 | − | 0.388999i | \(-0.872821\pi\) | ||||
−0.921238 | + | 0.388999i | \(0.872821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7538 | 0.890457 | 0.445228 | − | 0.895417i | \(-0.353122\pi\) | ||||
0.445228 | + | 0.895417i | \(0.353122\pi\) | |||||||
\(314\) | −8.80776 | −0.497051 | ||||||||
\(315\) | −0.561553 | −0.0316399 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | −21.3693 | −1.20022 | −0.600110 | − | 0.799917i | \(-0.704877\pi\) | ||||
−0.600110 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(318\) | 13.1231 | 0.735907 | ||||||||
\(319\) | −3.68466 | −0.206301 | ||||||||
\(320\) | 0.561553 | 0.0313918 | ||||||||
\(321\) | 13.1231 | 0.732460 | ||||||||
\(322\) | −5.68466 | −0.316794 | ||||||||
\(323\) | 14.5616 | 0.810226 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.876894 | −0.0485667 | ||||||||
\(327\) | −15.9309 | −0.880979 | ||||||||
\(328\) | 4.00000 | 0.220863 | ||||||||
\(329\) | −6.24621 | −0.344365 | ||||||||
\(330\) | 0.807764 | 0.0444659 | ||||||||
\(331\) | −7.12311 | −0.391521 | −0.195761 | − | 0.980652i | \(-0.562718\pi\) | ||||
−0.195761 | + | 0.980652i | \(0.562718\pi\) | |||||||
\(332\) | 2.00000 | 0.109764 | ||||||||
\(333\) | −1.68466 | −0.0923187 | ||||||||
\(334\) | −8.80776 | −0.481939 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 17.0540 | 0.928989 | 0.464495 | − | 0.885576i | \(-0.346236\pi\) | ||||
0.464495 | + | 0.885576i | \(0.346236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.75379 | −0.203878 | ||||||||
\(340\) | −3.19224 | −0.173123 | ||||||||
\(341\) | −14.7386 | −0.798142 | ||||||||
\(342\) | 2.56155 | 0.138513 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −10.5616 | −0.569441 | ||||||||
\(345\) | 3.19224 | 0.171864 | ||||||||
\(346\) | −20.2462 | −1.08844 | ||||||||
\(347\) | 8.49242 | 0.455897 | 0.227949 | − | 0.973673i | \(-0.426798\pi\) | ||||
0.227949 | + | 0.973673i | \(0.426798\pi\) | |||||||
\(348\) | 2.56155 | 0.137314 | ||||||||
\(349\) | −21.3693 | −1.14387 | −0.571937 | − | 0.820298i | \(-0.693808\pi\) | ||||
−0.571937 | + | 0.820298i | \(0.693808\pi\) | |||||||
\(350\) | −4.68466 | −0.250406 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.43845 | −0.0766695 | ||||||||
\(353\) | 1.75379 | 0.0933448 | 0.0466724 | − | 0.998910i | \(-0.485138\pi\) | ||||
0.0466724 | + | 0.998910i | \(0.485138\pi\) | |||||||
\(354\) | −12.2462 | −0.650879 | ||||||||
\(355\) | 8.63068 | 0.458069 | ||||||||
\(356\) | −8.00000 | −0.423999 | ||||||||
\(357\) | −5.68466 | −0.300864 | ||||||||
\(358\) | 2.87689 | 0.152049 | ||||||||
\(359\) | −17.6155 | −0.929712 | −0.464856 | − | 0.885386i | \(-0.653894\pi\) | ||||
−0.464856 | + | 0.885386i | \(0.653894\pi\) | |||||||
\(360\) | −0.561553 | −0.0295964 | ||||||||
\(361\) | −12.4384 | −0.654655 | ||||||||
\(362\) | 11.3693 | 0.597558 | ||||||||
\(363\) | 8.93087 | 0.468749 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.17708 | 0.218638 | ||||||||
\(366\) | 2.56155 | 0.133895 | ||||||||
\(367\) | 25.3693 | 1.32427 | 0.662134 | − | 0.749386i | \(-0.269651\pi\) | ||||
0.662134 | + | 0.749386i | \(0.269651\pi\) | |||||||
\(368\) | −5.68466 | −0.296333 | ||||||||
\(369\) | −4.00000 | −0.208232 | ||||||||
\(370\) | 0.946025 | 0.0491815 | ||||||||
\(371\) | −13.1231 | −0.681318 | ||||||||
\(372\) | 10.2462 | 0.531241 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 8.17708 | 0.422827 | ||||||||
\(375\) | 5.43845 | 0.280840 | ||||||||
\(376\) | −6.24621 | −0.322124 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 27.1231 | 1.39322 | 0.696610 | − | 0.717450i | \(-0.254691\pi\) | ||||
0.696610 | + | 0.717450i | \(0.254691\pi\) | |||||||
\(380\) | −1.43845 | −0.0737908 | ||||||||
\(381\) | −6.24621 | −0.320003 | ||||||||
\(382\) | −13.0540 | −0.667899 | ||||||||
\(383\) | −13.4384 | −0.686673 | −0.343336 | − | 0.939213i | \(-0.611557\pi\) | ||||
−0.343336 | + | 0.939213i | \(0.611557\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.807764 | −0.0411675 | ||||||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | 10.5616 | 0.536874 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | −18.8769 | −0.957097 | −0.478548 | − | 0.878061i | \(-0.658837\pi\) | ||||
−0.478548 | + | 0.878061i | \(0.658837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.3153 | 1.63426 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −2.56155 | −0.129213 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 8.98485 | 0.452077 | ||||||||
\(396\) | 1.43845 | 0.0722847 | ||||||||
\(397\) | −9.36932 | −0.470233 | −0.235116 | − | 0.971967i | \(-0.575547\pi\) | ||||
−0.235116 | + | 0.971967i | \(0.575547\pi\) | |||||||
\(398\) | −23.9309 | −1.19955 | ||||||||
\(399\) | −2.56155 | −0.128238 | ||||||||
\(400\) | −4.68466 | −0.234233 | ||||||||
\(401\) | 34.9848 | 1.74706 | 0.873530 | − | 0.486771i | \(-0.161825\pi\) | ||||
0.873530 | + | 0.486771i | \(0.161825\pi\) | |||||||
\(402\) | −7.12311 | −0.355268 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0.561553 | 0.0279038 | ||||||||
\(406\) | −2.56155 | −0.127128 | ||||||||
\(407\) | −2.42329 | −0.120118 | ||||||||
\(408\) | −5.68466 | −0.281433 | ||||||||
\(409\) | 6.80776 | 0.336622 | 0.168311 | − | 0.985734i | \(-0.446169\pi\) | ||||
0.168311 | + | 0.985734i | \(0.446169\pi\) | |||||||
\(410\) | 2.24621 | 0.110932 | ||||||||
\(411\) | 5.68466 | 0.280404 | ||||||||
\(412\) | 18.8078 | 0.926592 | ||||||||
\(413\) | 12.2462 | 0.602597 | ||||||||
\(414\) | 5.68466 | 0.279386 | ||||||||
\(415\) | 1.12311 | 0.0551311 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.24621 | 0.305878 | ||||||||
\(418\) | 3.68466 | 0.180223 | ||||||||
\(419\) | −8.31534 | −0.406231 | −0.203116 | − | 0.979155i | \(-0.565107\pi\) | ||||
−0.203116 | + | 0.979155i | \(0.565107\pi\) | |||||||
\(420\) | 0.561553 | 0.0274010 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 12.8078 | 0.623472 | ||||||||
\(423\) | 6.24621 | 0.303701 | ||||||||
\(424\) | −13.1231 | −0.637314 | ||||||||
\(425\) | 26.6307 | 1.29178 | ||||||||
\(426\) | 15.3693 | 0.744646 | ||||||||
\(427\) | −2.56155 | −0.123962 | ||||||||
\(428\) | −13.1231 | −0.634329 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.93087 | −0.286012 | ||||||||
\(431\) | 27.8617 | 1.34205 | 0.671026 | − | 0.741433i | \(-0.265854\pi\) | ||||
0.671026 | + | 0.741433i | \(0.265854\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 1.36932 | 0.0658052 | 0.0329026 | − | 0.999459i | \(-0.489525\pi\) | ||||
0.0329026 | + | 0.999459i | \(0.489525\pi\) | |||||||
\(434\) | −10.2462 | −0.491834 | ||||||||
\(435\) | 1.43845 | 0.0689683 | ||||||||
\(436\) | 15.9309 | 0.762950 | ||||||||
\(437\) | 14.5616 | 0.696574 | ||||||||
\(438\) | 7.43845 | 0.355423 | ||||||||
\(439\) | −19.9309 | −0.951249 | −0.475624 | − | 0.879649i | \(-0.657778\pi\) | ||||
−0.475624 | + | 0.879649i | \(0.657778\pi\) | |||||||
\(440\) | −0.807764 | −0.0385086 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.3693 | 1.49040 | 0.745201 | − | 0.666840i | \(-0.232354\pi\) | ||||
0.745201 | + | 0.666840i | \(0.232354\pi\) | |||||||
\(444\) | 1.68466 | 0.0799504 | ||||||||
\(445\) | −4.49242 | −0.212961 | ||||||||
\(446\) | −18.2462 | −0.863983 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −21.6847 | −1.02336 | −0.511681 | − | 0.859175i | \(-0.670977\pi\) | ||||
−0.511681 | + | 0.859175i | \(0.670977\pi\) | |||||||
\(450\) | 4.68466 | 0.220837 | ||||||||
\(451\) | −5.75379 | −0.270935 | ||||||||
\(452\) | 3.75379 | 0.176563 | ||||||||
\(453\) | −4.31534 | −0.202752 | ||||||||
\(454\) | 23.6155 | 1.10833 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.56155 | −0.119956 | ||||||||
\(457\) | 16.0000 | 0.748448 | 0.374224 | − | 0.927338i | \(-0.377909\pi\) | ||||
0.374224 | + | 0.927338i | \(0.377909\pi\) | |||||||
\(458\) | −2.00000 | −0.0934539 | ||||||||
\(459\) | 5.68466 | 0.265337 | ||||||||
\(460\) | −3.19224 | −0.148839 | ||||||||
\(461\) | −8.06913 | −0.375817 | −0.187908 | − | 0.982187i | \(-0.560171\pi\) | ||||
−0.187908 | + | 0.982187i | \(0.560171\pi\) | |||||||
\(462\) | −1.43845 | −0.0669226 | ||||||||
\(463\) | 39.5464 | 1.83788 | 0.918938 | − | 0.394401i | \(-0.129048\pi\) | ||||
0.918938 | + | 0.394401i | \(0.129048\pi\) | |||||||
\(464\) | −2.56155 | −0.118917 | ||||||||
\(465\) | 5.75379 | 0.266826 | ||||||||
\(466\) | 2.00000 | 0.0926482 | ||||||||
\(467\) | 2.56155 | 0.118535 | 0.0592673 | − | 0.998242i | \(-0.481124\pi\) | ||||
0.0592673 | + | 0.998242i | \(0.481124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.12311 | 0.328914 | ||||||||
\(470\) | −3.50758 | −0.161792 | ||||||||
\(471\) | −8.80776 | −0.405840 | ||||||||
\(472\) | 12.2462 | 0.563678 | ||||||||
\(473\) | 15.1922 | 0.698540 | ||||||||
\(474\) | 16.0000 | 0.734904 | ||||||||
\(475\) | 12.0000 | 0.550598 | ||||||||
\(476\) | 5.68466 | 0.260556 | ||||||||
\(477\) | 13.1231 | 0.600866 | ||||||||
\(478\) | −2.24621 | −0.102739 | ||||||||
\(479\) | −41.3002 | −1.88705 | −0.943527 | − | 0.331296i | \(-0.892514\pi\) | ||||
−0.943527 | + | 0.331296i | \(0.892514\pi\) | |||||||
\(480\) | 0.561553 | 0.0256313 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −6.00000 | −0.273293 | ||||||||
\(483\) | −5.68466 | −0.258661 | ||||||||
\(484\) | −8.93087 | −0.405949 | ||||||||
\(485\) | −5.61553 | −0.254988 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 30.2462 | 1.37059 | 0.685293 | − | 0.728267i | \(-0.259674\pi\) | ||||
0.685293 | + | 0.728267i | \(0.259674\pi\) | |||||||
\(488\) | −2.56155 | −0.115956 | ||||||||
\(489\) | −0.876894 | −0.0396545 | ||||||||
\(490\) | −0.561553 | −0.0253684 | ||||||||
\(491\) | −6.24621 | −0.281888 | −0.140944 | − | 0.990018i | \(-0.545014\pi\) | ||||
−0.140944 | + | 0.990018i | \(0.545014\pi\) | |||||||
\(492\) | 4.00000 | 0.180334 | ||||||||
\(493\) | 14.5616 | 0.655819 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.807764 | 0.0363063 | ||||||||
\(496\) | −10.2462 | −0.460068 | ||||||||
\(497\) | −15.3693 | −0.689408 | ||||||||
\(498\) | 2.00000 | 0.0896221 | ||||||||
\(499\) | 34.4924 | 1.54409 | 0.772046 | − | 0.635566i | \(-0.219233\pi\) | ||||
0.772046 | + | 0.635566i | \(0.219233\pi\) | |||||||
\(500\) | −5.43845 | −0.243215 | ||||||||
\(501\) | −8.80776 | −0.393502 | ||||||||
\(502\) | −15.0540 | −0.671892 | ||||||||
\(503\) | −5.61553 | −0.250384 | −0.125192 | − | 0.992133i | \(-0.539955\pi\) | ||||
−0.125192 | + | 0.992133i | \(0.539955\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −3.36932 | −0.149933 | ||||||||
\(506\) | 8.17708 | 0.363516 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.24621 | 0.277131 | ||||||||
\(509\) | 9.68466 | 0.429265 | 0.214632 | − | 0.976695i | \(-0.431145\pi\) | ||||
0.214632 | + | 0.976695i | \(0.431145\pi\) | |||||||
\(510\) | −3.19224 | −0.141355 | ||||||||
\(511\) | −7.43845 | −0.329058 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.56155 | 0.113095 | ||||||||
\(514\) | −26.0000 | −1.14681 | ||||||||
\(515\) | 10.5616 | 0.465398 | ||||||||
\(516\) | −10.5616 | −0.464946 | ||||||||
\(517\) | 8.98485 | 0.395153 | ||||||||
\(518\) | −1.68466 | −0.0740196 | ||||||||
\(519\) | −20.2462 | −0.888710 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.0540 | −1.27288 | −0.636439 | − | 0.771327i | \(-0.719593\pi\) | ||||
−0.636439 | + | 0.771327i | \(0.719593\pi\) | |||||||
\(522\) | 2.56155 | 0.112116 | ||||||||
\(523\) | 24.4924 | 1.07098 | 0.535489 | − | 0.844542i | \(-0.320127\pi\) | ||||
0.535489 | + | 0.844542i | \(0.320127\pi\) | |||||||
\(524\) | 2.56155 | 0.111902 | ||||||||
\(525\) | −4.68466 | −0.204455 | ||||||||
\(526\) | −1.36932 | −0.0597051 | ||||||||
\(527\) | 58.2462 | 2.53724 | ||||||||
\(528\) | −1.43845 | −0.0626004 | ||||||||
\(529\) | 9.31534 | 0.405015 | ||||||||
\(530\) | −7.36932 | −0.320103 | ||||||||
\(531\) | −12.2462 | −0.531440 | ||||||||
\(532\) | 2.56155 | 0.111057 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.00000 | −0.346194 | ||||||||
\(535\) | −7.36932 | −0.318603 | ||||||||
\(536\) | 7.12311 | 0.307671 | ||||||||
\(537\) | 2.87689 | 0.124147 | ||||||||
\(538\) | −6.63068 | −0.285869 | ||||||||
\(539\) | 1.43845 | 0.0619583 | ||||||||
\(540\) | −0.561553 | −0.0241654 | ||||||||
\(541\) | −26.8078 | −1.15256 | −0.576278 | − | 0.817254i | \(-0.695495\pi\) | ||||
−0.576278 | + | 0.817254i | \(0.695495\pi\) | |||||||
\(542\) | 8.00000 | 0.343629 | ||||||||
\(543\) | 11.3693 | 0.487904 | ||||||||
\(544\) | 5.68466 | 0.243728 | ||||||||
\(545\) | 8.94602 | 0.383206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9848 | −1.58136 | −0.790679 | − | 0.612231i | \(-0.790272\pi\) | ||||
−0.790679 | + | 0.612231i | \(0.790272\pi\) | |||||||
\(548\) | −5.68466 | −0.242837 | ||||||||
\(549\) | 2.56155 | 0.109324 | ||||||||
\(550\) | 6.73863 | 0.287336 | ||||||||
\(551\) | 6.56155 | 0.279532 | ||||||||
\(552\) | −5.68466 | −0.241955 | ||||||||
\(553\) | −16.0000 | −0.680389 | ||||||||
\(554\) | −19.1231 | −0.812463 | ||||||||
\(555\) | 0.946025 | 0.0401565 | ||||||||
\(556\) | −6.24621 | −0.264898 | ||||||||
\(557\) | −0.246211 | −0.0104323 | −0.00521615 | − | 0.999986i | \(-0.501660\pi\) | ||||
−0.00521615 | + | 0.999986i | \(0.501660\pi\) | |||||||
\(558\) | 10.2462 | 0.433757 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.561553 | −0.0237299 | ||||||||
\(561\) | 8.17708 | 0.345237 | ||||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | −0.946025 | −0.0398702 | −0.0199351 | − | 0.999801i | \(-0.506346\pi\) | ||||
−0.0199351 | + | 0.999801i | \(0.506346\pi\) | |||||||
\(564\) | −6.24621 | −0.263013 | ||||||||
\(565\) | 2.10795 | 0.0886821 | ||||||||
\(566\) | −13.1231 | −0.551605 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −15.3693 | −0.644882 | ||||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | −1.43845 | −0.0602499 | ||||||||
\(571\) | 1.75379 | 0.0733938 | 0.0366969 | − | 0.999326i | \(-0.488316\pi\) | ||||
0.0366969 | + | 0.999326i | \(0.488316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.0540 | −0.545338 | ||||||||
\(574\) | −4.00000 | −0.166957 | ||||||||
\(575\) | 26.6307 | 1.11058 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −24.2462 | −1.00938 | −0.504691 | − | 0.863300i | \(-0.668394\pi\) | ||||
−0.504691 | + | 0.863300i | \(0.668394\pi\) | |||||||
\(578\) | −15.3153 | −0.637034 | ||||||||
\(579\) | 12.0000 | 0.498703 | ||||||||
\(580\) | −1.43845 | −0.0597283 | ||||||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | −10.0000 | −0.414513 | ||||||||
\(583\) | 18.8769 | 0.781801 | ||||||||
\(584\) | −7.43845 | −0.307805 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.2462 | 1.00160 | ||||||||
\(587\) | 28.8769 | 1.19188 | 0.595938 | − | 0.803030i | \(-0.296780\pi\) | ||||
0.595938 | + | 0.803030i | \(0.296780\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 26.2462 | 1.08146 | ||||||||
\(590\) | 6.87689 | 0.283117 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | −1.68466 | −0.0692390 | ||||||||
\(593\) | −28.0000 | −1.14982 | −0.574911 | − | 0.818216i | \(-0.694963\pi\) | ||||
−0.574911 | + | 0.818216i | \(0.694963\pi\) | |||||||
\(594\) | 1.43845 | 0.0590202 | ||||||||
\(595\) | 3.19224 | 0.130869 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | −23.9309 | −0.979425 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.3002 | −0.952020 | −0.476010 | − | 0.879440i | \(-0.657917\pi\) | ||||
−0.476010 | + | 0.879440i | \(0.657917\pi\) | |||||||
\(600\) | −4.68466 | −0.191250 | ||||||||
\(601\) | 25.8617 | 1.05492 | 0.527461 | − | 0.849579i | \(-0.323144\pi\) | ||||
0.527461 | + | 0.849579i | \(0.323144\pi\) | |||||||
\(602\) | 10.5616 | 0.430457 | ||||||||
\(603\) | −7.12311 | −0.290075 | ||||||||
\(604\) | 4.31534 | 0.175589 | ||||||||
\(605\) | −5.01515 | −0.203895 | ||||||||
\(606\) | −6.00000 | −0.243733 | ||||||||
\(607\) | 41.5464 | 1.68632 | 0.843158 | − | 0.537666i | \(-0.180694\pi\) | ||||
0.843158 | + | 0.537666i | \(0.180694\pi\) | |||||||
\(608\) | 2.56155 | 0.103885 | ||||||||
\(609\) | −2.56155 | −0.103799 | ||||||||
\(610\) | −1.43845 | −0.0582410 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.68466 | −0.229789 | ||||||||
\(613\) | −18.8078 | −0.759638 | −0.379819 | − | 0.925061i | \(-0.624014\pi\) | ||||
−0.379819 | + | 0.925061i | \(0.624014\pi\) | |||||||
\(614\) | −9.75379 | −0.393631 | ||||||||
\(615\) | 2.24621 | 0.0905760 | ||||||||
\(616\) | 1.43845 | 0.0579567 | ||||||||
\(617\) | −26.8078 | −1.07924 | −0.539620 | − | 0.841909i | \(-0.681432\pi\) | ||||
−0.539620 | + | 0.841909i | \(0.681432\pi\) | |||||||
\(618\) | 18.8078 | 0.756559 | ||||||||
\(619\) | −2.06913 | −0.0831654 | −0.0415827 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415827 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(620\) | −5.75379 | −0.231078 | ||||||||
\(621\) | 5.68466 | 0.228117 | ||||||||
\(622\) | 32.4924 | 1.30283 | ||||||||
\(623\) | 8.00000 | 0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | −15.7538 | −0.629648 | ||||||||
\(627\) | 3.68466 | 0.147151 | ||||||||
\(628\) | 8.80776 | 0.351468 | ||||||||
\(629\) | 9.57671 | 0.381848 | ||||||||
\(630\) | 0.561553 | 0.0223728 | ||||||||
\(631\) | 0.315342 | 0.0125535 | 0.00627677 | − | 0.999980i | \(-0.498002\pi\) | ||||
0.00627677 | + | 0.999980i | \(0.498002\pi\) | |||||||
\(632\) | −16.0000 | −0.636446 | ||||||||
\(633\) | 12.8078 | 0.509063 | ||||||||
\(634\) | 21.3693 | 0.848684 | ||||||||
\(635\) | 3.50758 | 0.139194 | ||||||||
\(636\) | −13.1231 | −0.520365 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.68466 | 0.145877 | ||||||||
\(639\) | 15.3693 | 0.608001 | ||||||||
\(640\) | −0.561553 | −0.0221973 | ||||||||
\(641\) | 44.1080 | 1.74216 | 0.871080 | − | 0.491142i | \(-0.163420\pi\) | ||||
0.871080 | + | 0.491142i | \(0.163420\pi\) | |||||||
\(642\) | −13.1231 | −0.517928 | ||||||||
\(643\) | 20.8078 | 0.820578 | 0.410289 | − | 0.911956i | \(-0.365428\pi\) | ||||
0.410289 | + | 0.911956i | \(0.365428\pi\) | |||||||
\(644\) | 5.68466 | 0.224007 | ||||||||
\(645\) | −5.93087 | −0.233528 | ||||||||
\(646\) | −14.5616 | −0.572917 | ||||||||
\(647\) | −35.3693 | −1.39051 | −0.695256 | − | 0.718763i | \(-0.744709\pi\) | ||||
−0.695256 | + | 0.718763i | \(0.744709\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −17.6155 | −0.691470 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.2462 | −0.401581 | ||||||||
\(652\) | 0.876894 | 0.0343418 | ||||||||
\(653\) | −25.4384 | −0.995483 | −0.497742 | − | 0.867325i | \(-0.665837\pi\) | ||||
−0.497742 | + | 0.867325i | \(0.665837\pi\) | |||||||
\(654\) | 15.9309 | 0.622946 | ||||||||
\(655\) | 1.43845 | 0.0562048 | ||||||||
\(656\) | −4.00000 | −0.156174 | ||||||||
\(657\) | 7.43845 | 0.290201 | ||||||||
\(658\) | 6.24621 | 0.243503 | ||||||||
\(659\) | 21.1231 | 0.822839 | 0.411420 | − | 0.911446i | \(-0.365033\pi\) | ||||
0.411420 | + | 0.911446i | \(0.365033\pi\) | |||||||
\(660\) | −0.807764 | −0.0314422 | ||||||||
\(661\) | 4.73863 | 0.184311 | 0.0921557 | − | 0.995745i | \(-0.470624\pi\) | ||||
0.0921557 | + | 0.995745i | \(0.470624\pi\) | |||||||
\(662\) | 7.12311 | 0.276847 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | 1.43845 | 0.0557806 | ||||||||
\(666\) | 1.68466 | 0.0652792 | ||||||||
\(667\) | 14.5616 | 0.563826 | ||||||||
\(668\) | 8.80776 | 0.340783 | ||||||||
\(669\) | −18.2462 | −0.705439 | ||||||||
\(670\) | 4.00000 | 0.154533 | ||||||||
\(671\) | 3.68466 | 0.142245 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −17.1922 | −0.662712 | −0.331356 | − | 0.943506i | \(-0.607506\pi\) | ||||
−0.331356 | + | 0.943506i | \(0.607506\pi\) | |||||||
\(674\) | −17.0540 | −0.656895 | ||||||||
\(675\) | 4.68466 | 0.180313 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.63068 | 0.254838 | 0.127419 | − | 0.991849i | \(-0.459331\pi\) | ||||
0.127419 | + | 0.991849i | \(0.459331\pi\) | |||||||
\(678\) | 3.75379 | 0.144163 | ||||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | 3.19224 | 0.122417 | ||||||||
\(681\) | 23.6155 | 0.904949 | ||||||||
\(682\) | 14.7386 | 0.564371 | ||||||||
\(683\) | −11.6847 | −0.447101 | −0.223551 | − | 0.974692i | \(-0.571765\pi\) | ||||
−0.223551 | + | 0.974692i | \(0.571765\pi\) | |||||||
\(684\) | −2.56155 | −0.0979434 | ||||||||
\(685\) | −3.19224 | −0.121969 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | 10.5616 | 0.402655 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.19224 | −0.121526 | ||||||||
\(691\) | −3.50758 | −0.133435 | −0.0667173 | − | 0.997772i | \(-0.521253\pi\) | ||||
−0.0667173 | + | 0.997772i | \(0.521253\pi\) | |||||||
\(692\) | 20.2462 | 0.769645 | ||||||||
\(693\) | −1.43845 | −0.0546421 | ||||||||
\(694\) | −8.49242 | −0.322368 | ||||||||
\(695\) | −3.50758 | −0.133050 | ||||||||
\(696\) | −2.56155 | −0.0970954 | ||||||||
\(697\) | 22.7386 | 0.861287 | ||||||||
\(698\) | 21.3693 | 0.808841 | ||||||||
\(699\) | 2.00000 | 0.0756469 | ||||||||
\(700\) | 4.68466 | 0.177063 | ||||||||
\(701\) | −37.6155 | −1.42072 | −0.710359 | − | 0.703839i | \(-0.751468\pi\) | ||||
−0.710359 | + | 0.703839i | \(0.751468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.31534 | 0.162756 | ||||||||
\(704\) | 1.43845 | 0.0542135 | ||||||||
\(705\) | −3.50758 | −0.132103 | ||||||||
\(706\) | −1.75379 | −0.0660047 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 12.2462 | 0.460241 | ||||||||
\(709\) | 48.2462 | 1.81192 | 0.905962 | − | 0.423358i | \(-0.139149\pi\) | ||||
0.905962 | + | 0.423358i | \(0.139149\pi\) | |||||||
\(710\) | −8.63068 | −0.323904 | ||||||||
\(711\) | 16.0000 | 0.600047 | ||||||||
\(712\) | 8.00000 | 0.299813 | ||||||||
\(713\) | 58.2462 | 2.18134 | ||||||||
\(714\) | 5.68466 | 0.212743 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.87689 | −0.107515 | ||||||||
\(717\) | −2.24621 | −0.0838863 | ||||||||
\(718\) | 17.6155 | 0.657406 | ||||||||
\(719\) | −30.2462 | −1.12799 | −0.563997 | − | 0.825777i | \(-0.690737\pi\) | ||||
−0.563997 | + | 0.825777i | \(0.690737\pi\) | |||||||
\(720\) | 0.561553 | 0.0209278 | ||||||||
\(721\) | −18.8078 | −0.700438 | ||||||||
\(722\) | 12.4384 | 0.462911 | ||||||||
\(723\) | −6.00000 | −0.223142 | ||||||||
\(724\) | −11.3693 | −0.422537 | ||||||||
\(725\) | 12.0000 | 0.445669 | ||||||||
\(726\) | −8.93087 | −0.331456 | ||||||||
\(727\) | 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 | ||||||||
\(730\) | −4.17708 | −0.154601 | ||||||||
\(731\) | −60.0388 | −2.22062 | ||||||||
\(732\) | −2.56155 | −0.0946777 | ||||||||
\(733\) | 31.1231 | 1.14956 | 0.574779 | − | 0.818309i | \(-0.305088\pi\) | ||||
0.574779 | + | 0.818309i | \(0.305088\pi\) | |||||||
\(734\) | −25.3693 | −0.936399 | ||||||||
\(735\) | −0.561553 | −0.0207132 | ||||||||
\(736\) | 5.68466 | 0.209539 | ||||||||
\(737\) | −10.2462 | −0.377424 | ||||||||
\(738\) | 4.00000 | 0.147242 | ||||||||
\(739\) | 23.6155 | 0.868711 | 0.434356 | − | 0.900741i | \(-0.356976\pi\) | ||||
0.434356 | + | 0.900741i | \(0.356976\pi\) | |||||||
\(740\) | −0.946025 | −0.0347766 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.1231 | 0.481764 | ||||||||
\(743\) | 16.0000 | 0.586983 | 0.293492 | − | 0.955962i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955962i | \(0.405183\pi\) | |||||||
\(744\) | −10.2462 | −0.375644 | ||||||||
\(745\) | −5.61553 | −0.205737 | ||||||||
\(746\) | 6.00000 | 0.219676 | ||||||||
\(747\) | 2.00000 | 0.0731762 | ||||||||
\(748\) | −8.17708 | −0.298984 | ||||||||
\(749\) | 13.1231 | 0.479508 | ||||||||
\(750\) | −5.43845 | −0.198584 | ||||||||
\(751\) | 14.2462 | 0.519852 | 0.259926 | − | 0.965629i | \(-0.416302\pi\) | ||||
0.259926 | + | 0.965629i | \(0.416302\pi\) | |||||||
\(752\) | 6.24621 | 0.227776 | ||||||||
\(753\) | −15.0540 | −0.548597 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.42329 | 0.0881926 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | −27.1231 | −0.985156 | ||||||||
\(759\) | 8.17708 | 0.296809 | ||||||||
\(760\) | 1.43845 | 0.0521780 | ||||||||
\(761\) | −30.8769 | −1.11929 | −0.559643 | − | 0.828734i | \(-0.689062\pi\) | ||||
−0.559643 | + | 0.828734i | \(0.689062\pi\) | |||||||
\(762\) | 6.24621 | 0.226276 | ||||||||
\(763\) | −15.9309 | −0.576736 | ||||||||
\(764\) | 13.0540 | 0.472276 | ||||||||
\(765\) | −3.19224 | −0.115416 | ||||||||
\(766\) | 13.4384 | 0.485551 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.5616 | 0.452981 | 0.226491 | − | 0.974013i | \(-0.427275\pi\) | ||||
0.226491 | + | 0.974013i | \(0.427275\pi\) | |||||||
\(770\) | 0.807764 | 0.0291098 | ||||||||
\(771\) | −26.0000 | −0.936367 | ||||||||
\(772\) | −12.0000 | −0.431889 | ||||||||
\(773\) | 15.9309 | 0.572994 | 0.286497 | − | 0.958081i | \(-0.407509\pi\) | ||||
0.286497 | + | 0.958081i | \(0.407509\pi\) | |||||||
\(774\) | −10.5616 | −0.379627 | ||||||||
\(775\) | 48.0000 | 1.72421 | ||||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | −1.68466 | −0.0604368 | ||||||||
\(778\) | 18.8769 | 0.676769 | ||||||||
\(779\) | 10.2462 | 0.367109 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.1080 | 0.791085 | ||||||||
\(782\) | −32.3153 | −1.15559 | ||||||||
\(783\) | 2.56155 | 0.0915424 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 4.94602 | 0.176531 | ||||||||
\(786\) | 2.56155 | 0.0913676 | ||||||||
\(787\) | 45.9309 | 1.63726 | 0.818629 | − | 0.574322i | \(-0.194734\pi\) | ||||
0.818629 | + | 0.574322i | \(0.194734\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | −1.36932 | −0.0487490 | ||||||||
\(790\) | −8.98485 | −0.319666 | ||||||||
\(791\) | −3.75379 | −0.133469 | ||||||||
\(792\) | −1.43845 | −0.0511130 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.36932 | 0.332505 | ||||||||
\(795\) | −7.36932 | −0.261363 | ||||||||
\(796\) | 23.9309 | 0.848207 | ||||||||
\(797\) | −20.2462 | −0.717158 | −0.358579 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358579 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(798\) | 2.56155 | 0.0906780 | ||||||||
\(799\) | −35.5076 | −1.25617 | ||||||||
\(800\) | 4.68466 | 0.165628 | ||||||||
\(801\) | −8.00000 | −0.282666 | ||||||||
\(802\) | −34.9848 | −1.23536 | ||||||||
\(803\) | 10.6998 | 0.377588 | ||||||||
\(804\) | 7.12311 | 0.251213 | ||||||||
\(805\) | 3.19224 | 0.112512 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.63068 | −0.233411 | ||||||||
\(808\) | 6.00000 | 0.211079 | ||||||||
\(809\) | −30.6307 | −1.07692 | −0.538459 | − | 0.842652i | \(-0.680993\pi\) | ||||
−0.538459 | + | 0.842652i | \(0.680993\pi\) | |||||||
\(810\) | −0.561553 | −0.0197310 | ||||||||
\(811\) | −35.0540 | −1.23091 | −0.615456 | − | 0.788171i | \(-0.711028\pi\) | ||||
−0.615456 | + | 0.788171i | \(0.711028\pi\) | |||||||
\(812\) | 2.56155 | 0.0898929 | ||||||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 2.42329 | 0.0849363 | ||||||||
\(815\) | 0.492423 | 0.0172488 | ||||||||
\(816\) | 5.68466 | 0.199003 | ||||||||
\(817\) | −27.0540 | −0.946499 | ||||||||
\(818\) | −6.80776 | −0.238028 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.24621 | −0.0784411 | ||||||||
\(821\) | 39.1231 | 1.36541 | 0.682703 | − | 0.730696i | \(-0.260804\pi\) | ||||
0.682703 | + | 0.730696i | \(0.260804\pi\) | |||||||
\(822\) | −5.68466 | −0.198275 | ||||||||
\(823\) | −18.7386 | −0.653188 | −0.326594 | − | 0.945165i | \(-0.605901\pi\) | ||||
−0.326594 | + | 0.945165i | \(0.605901\pi\) | |||||||
\(824\) | −18.8078 | −0.655200 | ||||||||
\(825\) | 6.73863 | 0.234609 | ||||||||
\(826\) | −12.2462 | −0.426100 | ||||||||
\(827\) | −15.0540 | −0.523478 | −0.261739 | − | 0.965139i | \(-0.584296\pi\) | ||||
−0.261739 | + | 0.965139i | \(0.584296\pi\) | |||||||
\(828\) | −5.68466 | −0.197556 | ||||||||
\(829\) | −4.94602 | −0.171783 | −0.0858913 | − | 0.996305i | \(-0.527374\pi\) | ||||
−0.0858913 | + | 0.996305i | \(0.527374\pi\) | |||||||
\(830\) | −1.12311 | −0.0389836 | ||||||||
\(831\) | −19.1231 | −0.663373 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.68466 | −0.196962 | ||||||||
\(834\) | −6.24621 | −0.216289 | ||||||||
\(835\) | 4.94602 | 0.171164 | ||||||||
\(836\) | −3.68466 | −0.127437 | ||||||||
\(837\) | 10.2462 | 0.354161 | ||||||||
\(838\) | 8.31534 | 0.287249 | ||||||||
\(839\) | 42.2462 | 1.45850 | 0.729251 | − | 0.684247i | \(-0.239869\pi\) | ||||
0.729251 | + | 0.684247i | \(0.239869\pi\) | |||||||
\(840\) | −0.561553 | −0.0193754 | ||||||||
\(841\) | −22.4384 | −0.773740 | ||||||||
\(842\) | −10.0000 | −0.344623 | ||||||||
\(843\) | −6.00000 | −0.206651 | ||||||||
\(844\) | −12.8078 | −0.440861 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.24621 | −0.214749 | ||||||||
\(847\) | 8.93087 | 0.306868 | ||||||||
\(848\) | 13.1231 | 0.450649 | ||||||||
\(849\) | −13.1231 | −0.450384 | ||||||||
\(850\) | −26.6307 | −0.913425 | ||||||||
\(851\) | 9.57671 | 0.328285 | ||||||||
\(852\) | −15.3693 | −0.526544 | ||||||||
\(853\) | 19.1231 | 0.654763 | 0.327381 | − | 0.944892i | \(-0.393834\pi\) | ||||
0.327381 | + | 0.944892i | \(0.393834\pi\) | |||||||
\(854\) | 2.56155 | 0.0876545 | ||||||||
\(855\) | −1.43845 | −0.0491939 | ||||||||
\(856\) | 13.1231 | 0.448539 | ||||||||
\(857\) | 38.0000 | 1.29806 | 0.649028 | − | 0.760765i | \(-0.275176\pi\) | ||||
0.649028 | + | 0.760765i | \(0.275176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.6155 | 1.41990 | 0.709952 | − | 0.704250i | \(-0.248717\pi\) | ||||
0.709952 | + | 0.704250i | \(0.248717\pi\) | |||||||
\(860\) | 5.93087 | 0.202241 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | −27.8617 | −0.948975 | ||||||||
\(863\) | −6.73863 | −0.229386 | −0.114693 | − | 0.993401i | \(-0.536588\pi\) | ||||
−0.114693 | + | 0.993401i | \(0.536588\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 11.3693 | 0.386568 | ||||||||
\(866\) | −1.36932 | −0.0465313 | ||||||||
\(867\) | −15.3153 | −0.520136 | ||||||||
\(868\) | 10.2462 | 0.347779 | ||||||||
\(869\) | 23.0152 | 0.780736 | ||||||||
\(870\) | −1.43845 | −0.0487679 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.9309 | −0.539487 | ||||||||
\(873\) | −10.0000 | −0.338449 | ||||||||
\(874\) | −14.5616 | −0.492552 | ||||||||
\(875\) | 5.43845 | 0.183853 | ||||||||
\(876\) | −7.43845 | −0.251322 | ||||||||
\(877\) | −42.9848 | −1.45150 | −0.725748 | − | 0.687961i | \(-0.758506\pi\) | ||||
−0.725748 | + | 0.687961i | \(0.758506\pi\) | |||||||
\(878\) | 19.9309 | 0.672634 | ||||||||
\(879\) | 24.2462 | 0.817804 | ||||||||
\(880\) | 0.807764 | 0.0272297 | ||||||||
\(881\) | 39.3002 | 1.32406 | 0.662028 | − | 0.749479i | \(-0.269696\pi\) | ||||
0.662028 | + | 0.749479i | \(0.269696\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 18.5616 | 0.624646 | 0.312323 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312323 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.87689 | 0.231164 | ||||||||
\(886\) | −31.3693 | −1.05387 | ||||||||
\(887\) | 19.8617 | 0.666892 | 0.333446 | − | 0.942769i | \(-0.391789\pi\) | ||||
0.333446 | + | 0.942769i | \(0.391789\pi\) | |||||||
\(888\) | −1.68466 | −0.0565334 | ||||||||
\(889\) | −6.24621 | −0.209491 | ||||||||
\(890\) | 4.49242 | 0.150586 | ||||||||
\(891\) | 1.43845 | 0.0481898 | ||||||||
\(892\) | 18.2462 | 0.610928 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | −10.0000 | −0.334450 | ||||||||
\(895\) | −1.61553 | −0.0540011 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.6847 | 0.723626 | ||||||||
\(899\) | 26.2462 | 0.875360 | ||||||||
\(900\) | −4.68466 | −0.156155 | ||||||||
\(901\) | −74.6004 | −2.48530 | ||||||||
\(902\) | 5.75379 | 0.191580 | ||||||||
\(903\) | 10.5616 | 0.351466 | ||||||||
\(904\) | −3.75379 | −0.124849 | ||||||||
\(905\) | −6.38447 | −0.212227 | ||||||||
\(906\) | 4.31534 | 0.143368 | ||||||||
\(907\) | −8.49242 | −0.281986 | −0.140993 | − | 0.990011i | \(-0.545030\pi\) | ||||
−0.140993 | + | 0.990011i | \(0.545030\pi\) | |||||||
\(908\) | −23.6155 | −0.783709 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.56155 | −0.283657 | −0.141828 | − | 0.989891i | \(-0.545298\pi\) | ||||
−0.141828 | + | 0.989891i | \(0.545298\pi\) | |||||||
\(912\) | 2.56155 | 0.0848215 | ||||||||
\(913\) | 2.87689 | 0.0952113 | ||||||||
\(914\) | −16.0000 | −0.529233 | ||||||||
\(915\) | −1.43845 | −0.0475536 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | −2.56155 | −0.0845899 | ||||||||
\(918\) | −5.68466 | −0.187622 | ||||||||
\(919\) | 39.8617 | 1.31492 | 0.657459 | − | 0.753491i | \(-0.271631\pi\) | ||||
0.657459 | + | 0.753491i | \(0.271631\pi\) | |||||||
\(920\) | 3.19224 | 0.105245 | ||||||||
\(921\) | −9.75379 | −0.321398 | ||||||||
\(922\) | 8.06913 | 0.265743 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.43845 | 0.0473214 | ||||||||
\(925\) | 7.89205 | 0.259489 | ||||||||
\(926\) | −39.5464 | −1.29958 | ||||||||
\(927\) | 18.8078 | 0.617728 | ||||||||
\(928\) | 2.56155 | 0.0840871 | ||||||||
\(929\) | 49.1231 | 1.61168 | 0.805838 | − | 0.592136i | \(-0.201715\pi\) | ||||
0.805838 | + | 0.592136i | \(0.201715\pi\) | |||||||
\(930\) | −5.75379 | −0.188674 | ||||||||
\(931\) | −2.56155 | −0.0839515 | ||||||||
\(932\) | −2.00000 | −0.0655122 | ||||||||
\(933\) | 32.4924 | 1.06375 | ||||||||
\(934\) | −2.56155 | −0.0838166 | ||||||||
\(935\) | −4.59186 | −0.150170 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.8617 | 1.23689 | 0.618445 | − | 0.785828i | \(-0.287763\pi\) | ||||
0.618445 | + | 0.785828i | \(0.287763\pi\) | |||||||
\(938\) | −7.12311 | −0.232578 | ||||||||
\(939\) | −15.7538 | −0.514105 | ||||||||
\(940\) | 3.50758 | 0.114405 | ||||||||
\(941\) | −6.49242 | −0.211647 | −0.105823 | − | 0.994385i | \(-0.533748\pi\) | ||||
−0.105823 | + | 0.994385i | \(0.533748\pi\) | |||||||
\(942\) | 8.80776 | 0.286972 | ||||||||
\(943\) | 22.7386 | 0.740472 | ||||||||
\(944\) | −12.2462 | −0.398580 | ||||||||
\(945\) | 0.561553 | 0.0182673 | ||||||||
\(946\) | −15.1922 | −0.493942 | ||||||||
\(947\) | 7.19224 | 0.233716 | 0.116858 | − | 0.993149i | \(-0.462718\pi\) | ||||
0.116858 | + | 0.993149i | \(0.462718\pi\) | |||||||
\(948\) | −16.0000 | −0.519656 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12.0000 | −0.389331 | ||||||||
\(951\) | 21.3693 | 0.692948 | ||||||||
\(952\) | −5.68466 | −0.184241 | ||||||||
\(953\) | 48.7386 | 1.57880 | 0.789400 | − | 0.613880i | \(-0.210392\pi\) | ||||
0.789400 | + | 0.613880i | \(0.210392\pi\) | |||||||
\(954\) | −13.1231 | −0.424876 | ||||||||
\(955\) | 7.33050 | 0.237209 | ||||||||
\(956\) | 2.24621 | 0.0726477 | ||||||||
\(957\) | 3.68466 | 0.119108 | ||||||||
\(958\) | 41.3002 | 1.33435 | ||||||||
\(959\) | 5.68466 | 0.183567 | ||||||||
\(960\) | −0.561553 | −0.0181240 | ||||||||
\(961\) | 73.9848 | 2.38661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.1231 | −0.422886 | ||||||||
\(964\) | 6.00000 | 0.193247 | ||||||||
\(965\) | −6.73863 | −0.216924 | ||||||||
\(966\) | 5.68466 | 0.182901 | ||||||||
\(967\) | 25.9309 | 0.833881 | 0.416940 | − | 0.908934i | \(-0.363102\pi\) | ||||
0.416940 | + | 0.908934i | \(0.363102\pi\) | |||||||
\(968\) | 8.93087 | 0.287049 | ||||||||
\(969\) | −14.5616 | −0.467784 | ||||||||
\(970\) | 5.61553 | 0.180304 | ||||||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 6.24621 | 0.200244 | ||||||||
\(974\) | −30.2462 | −0.969151 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.56155 | 0.0819933 | ||||||||
\(977\) | −39.7926 | −1.27308 | −0.636539 | − | 0.771244i | \(-0.719635\pi\) | ||||
−0.636539 | + | 0.771244i | \(0.719635\pi\) | |||||||
\(978\) | 0.876894 | 0.0280400 | ||||||||
\(979\) | −11.5076 | −0.367784 | ||||||||
\(980\) | 0.561553 | 0.0179381 | ||||||||
\(981\) | 15.9309 | 0.508634 | ||||||||
\(982\) | 6.24621 | 0.199325 | ||||||||
\(983\) | −6.56155 | −0.209281 | −0.104641 | − | 0.994510i | \(-0.533369\pi\) | ||||
−0.104641 | + | 0.994510i | \(0.533369\pi\) | |||||||
\(984\) | −4.00000 | −0.127515 | ||||||||
\(985\) | 3.36932 | 0.107355 | ||||||||
\(986\) | −14.5616 | −0.463734 | ||||||||
\(987\) | 6.24621 | 0.198819 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.0388 | −1.90912 | ||||||||
\(990\) | −0.807764 | −0.0256724 | ||||||||
\(991\) | −13.7538 | −0.436903 | −0.218452 | − | 0.975848i | \(-0.570101\pi\) | ||||
−0.218452 | + | 0.975848i | \(0.570101\pi\) | |||||||
\(992\) | 10.2462 | 0.325318 | ||||||||
\(993\) | 7.12311 | 0.226045 | ||||||||
\(994\) | 15.3693 | 0.487485 | ||||||||
\(995\) | 13.4384 | 0.426027 | ||||||||
\(996\) | −2.00000 | −0.0633724 | ||||||||
\(997\) | −59.3693 | −1.88025 | −0.940123 | − | 0.340837i | \(-0.889290\pi\) | ||||
−0.940123 | + | 0.340837i | \(0.889290\pi\) | |||||||
\(998\) | −34.4924 | −1.09184 | ||||||||
\(999\) | 1.68466 | 0.0533002 |
(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 | 7098.2.a.bg.1.2 | 2 | ||
13.5 | odd | 4 | 546.2.c.e.337.3 | yes | 4 | ||
13.8 | odd | 4 | 546.2.c.e.337.2 | ✓ | 4 | ||
13.12 | even | 2 | 7098.2.a.bv.1.1 | 2 | |||
39.5 | even | 4 | 1638.2.c.h.883.2 | 4 | |||
39.8 | even | 4 | 1638.2.c.h.883.3 | 4 | |||
52.31 | even | 4 | 4368.2.h.n.337.2 | 4 | |||
52.47 | even | 4 | 4368.2.h.n.337.3 | 4 | |||
91.34 | even | 4 | 3822.2.c.h.883.1 | 4 | |||
91.83 | even | 4 | 3822.2.c.h.883.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.c.e.337.2 | ✓ | 4 | 13.8 | odd | 4 | ||
546.2.c.e.337.3 | yes | 4 | 13.5 | odd | 4 | ||
1638.2.c.h.883.2 | 4 | 39.5 | even | 4 | |||
1638.2.c.h.883.3 | 4 | 39.8 | even | 4 | |||
3822.2.c.h.883.1 | 4 | 91.34 | even | 4 | |||
3822.2.c.h.883.4 | 4 | 91.83 | even | 4 | |||
4368.2.h.n.337.2 | 4 | 52.31 | even | 4 | |||
4368.2.h.n.337.3 | 4 | 52.47 | even | 4 | |||
7098.2.a.bg.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7098.2.a.bv.1.1 | 2 | 13.12 | even | 2 |