Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(11,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.v (of order \(18\), degree \(6\), 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: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{18})\) |
Coefficient field: | 12.0.101559956668416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{6} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 131.1 | ||
Root | \(-1.39273 - 0.245576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.131 |
Dual form | 216.2.v.a.155.1 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{11}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.483690 | + | 1.32893i | −0.342020 | + | 0.939693i | ||||
\(3\) | −1.56638 | − | 0.739232i | −0.904348 | − | 0.426796i | ||||
\(4\) | −1.53209 | − | 1.28558i | −0.766044 | − | 0.642788i | ||||
\(5\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(6\) | 1.74002 | − | 1.72404i | 0.710362 | − | 0.703836i | ||||
\(7\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(8\) | 2.44949 | − | 1.41421i | 0.866025 | − | 0.500000i | ||||
\(9\) | 1.90707 | + | 2.31583i | 0.635691 | + | 0.771944i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.93192 | − | 1.04596i | 1.78854 | − | 0.315368i | 0.821541 | − | 0.570149i | \(-0.193114\pi\) |
0.966999 | + | 0.254781i | \(0.0820033\pi\) | |||||||
\(12\) | 1.44949 | + | 3.14626i | 0.418432 | + | 0.908248i | ||||
\(13\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.694593 | + | 3.93923i | 0.173648 | + | 0.984808i | ||||
\(17\) | 6.38072 | + | 3.68391i | 1.54755 | + | 0.893480i | 0.998328 | + | 0.0578055i | \(0.0184103\pi\) |
0.549225 | + | 0.835675i | \(0.314923\pi\) | |||||||
\(18\) | −4.00000 | + | 1.41421i | −0.942809 | + | 0.333333i | ||||
\(19\) | −4.35183 | − | 7.53760i | −0.998379 | − | 1.72924i | −0.548478 | − | 0.836165i | \(-0.684793\pi\) |
−0.449901 | − | 0.893079i | \(-0.648541\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.47921 | + | 8.38900i | −0.315368 | + | 1.78854i | ||||
\(23\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(24\) | −4.88226 | + | 0.404450i | −0.996586 | + | 0.0825579i | ||||
\(25\) | 4.69846 | + | 1.71010i | 0.939693 | + | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.27526 | − | 5.03723i | −0.245423 | − | 0.969416i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(32\) | −5.57091 | − | 0.982302i | −0.984808 | − | 0.173648i | ||||
\(33\) | −10.0648 | − | 2.74670i | −1.75206 | − | 0.478139i | ||||
\(34\) | −7.98194 | + | 6.69764i | −1.36889 | + | 1.14864i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0553729 | − | 5.99974i | 0.00922881 | − | 0.999957i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 12.1218 | − | 2.13741i | 1.96642 | − | 0.346733i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.34901 | − | 3.70637i | −0.210680 | − | 0.578838i | 0.788673 | − | 0.614813i | \(-0.210769\pi\) |
−0.999353 | + | 0.0359748i | \(0.988546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12781 | + | 6.39612i | 0.171989 | + | 0.975399i | 0.941562 | + | 0.336840i | \(0.109358\pi\) |
−0.769573 | + | 0.638559i | \(0.779531\pi\) | |||||||
\(44\) | −10.4329 | − | 6.02343i | −1.57282 | − | 0.908066i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(48\) | 1.82401 | − | 6.68378i | 0.263274 | − | 0.964721i | ||||
\(49\) | 1.21554 | − | 6.89365i | 0.173648 | − | 0.984808i | ||||
\(50\) | −4.54519 | + | 5.41675i | −0.642788 | + | 0.766044i | ||||
\(51\) | −7.27135 | − | 10.4872i | −1.01819 | − | 1.46851i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 7.31094 | + | 0.741737i | 0.994893 | + | 0.100938i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.24458 | + | 15.0237i | 0.164848 | + | 1.98994i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.23753 | + | 1.45250i | 1.07243 | + | 0.189099i | 0.681868 | − | 0.731475i | \(-0.261168\pi\) |
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.00000 | − | 6.92820i | 0.500000 | − | 0.866025i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.51841 | − | 12.0469i | 1.04854 | − | 1.48287i | ||||
\(67\) | −4.95255 | + | 1.80258i | −0.605050 | + | 0.220220i | −0.626336 | − | 0.779553i | \(-0.715446\pi\) |
0.0212861 | + | 0.999773i | \(0.493224\pi\) | |||||||
\(68\) | −5.03989 | − | 13.8470i | −0.611176 | − | 1.67919i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | 7.94643 | + | 2.97560i | 0.936496 | + | 0.350678i | ||||
\(73\) | −1.96244 | − | 3.39905i | −0.229687 | − | 0.397829i | 0.728028 | − | 0.685547i | \(-0.240437\pi\) |
−0.957715 | + | 0.287718i | \(0.907104\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.09540 | − | 6.15192i | −0.703836 | − | 0.710362i | ||||
\(76\) | −3.02275 | + | 17.1429i | −0.346733 | + | 1.96642i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.72616 | + | 8.83292i | −0.191795 | + | 0.981435i | ||||
\(82\) | 5.57800 | 0.615987 | ||||||||
\(83\) | −4.84788 | + | 13.3194i | −0.532124 | + | 1.46200i | 0.324415 | + | 0.945915i | \(0.394833\pi\) |
−0.856539 | + | 0.516083i | \(0.827390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.04548 | − | 1.59496i | −0.975399 | − | 0.171989i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.0510 | − | 10.9511i | 1.39124 | − | 1.16739i | ||||
\(89\) | −15.9495 | + | 9.20844i | −1.69064 | + | 0.976093i | −0.736644 | + | 0.676280i | \(0.763591\pi\) |
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.00000 | + | 5.65685i | 0.816497 | + | 0.577350i | ||||
\(97\) | 0.564013 | + | 3.19868i | 0.0572669 | + | 0.324777i | 0.999961 | − | 0.00888289i | \(-0.00282755\pi\) |
−0.942694 | + | 0.333659i | \(0.891716\pi\) | |||||||
\(98\) | 8.57321 | + | 4.94975i | 0.866025 | + | 0.500000i | ||||
\(99\) | 13.7349 | + | 11.7426i | 1.38040 | + | 1.18018i | ||||
\(100\) | −5.00000 | − | 8.66025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(102\) | 17.4538 | − | 4.59052i | 1.72819 | − | 0.454529i | ||||
\(103\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.5528i | 1.60022i | 0.599851 | + | 0.800112i | \(0.295227\pi\) | ||||
−0.599851 | + | 0.800112i | \(0.704773\pi\) | |||||||
\(108\) | −4.52194 | + | 9.35693i | −0.435124 | + | 0.900371i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.78072 | − | 1.72460i | −0.920093 | − | 0.162237i | −0.306510 | − | 0.951867i | \(-0.599161\pi\) |
−0.613583 | + | 0.789630i | \(0.710272\pi\) | |||||||
\(114\) | −20.5674 | − | 5.61287i | −1.92632 | − | 0.525694i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.91467 | + | 10.2445i | −0.544489 | + | 0.943083i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.7570 | − | 8.64684i | 2.15973 | − | 0.786076i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.626813 | + | 6.80281i | −0.0565179 | + | 0.613389i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 7.27231 | + | 8.66680i | 0.642788 | + | 0.766044i | ||||
\(129\) | 2.96164 | − | 10.8524i | 0.260758 | − | 0.955504i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5653 | − | 17.3582i | 1.27257 | − | 1.51659i | 0.527611 | − | 0.849486i | \(-0.323088\pi\) |
0.744962 | − | 0.667107i | \(-0.232468\pi\) | |||||||
\(132\) | 11.8891 | + | 17.1473i | 1.03481 | + | 1.49248i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 7.45345i | − | 0.643880i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.8394 | 1.78696 | ||||||||
\(137\) | 4.60936 | − | 12.6641i | 0.393805 | − | 1.08197i | −0.571445 | − | 0.820640i | \(-0.693617\pi\) |
0.965250 | − | 0.261329i | \(-0.0841608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0883 | − | 14.3388i | −1.44941 | − | 1.21620i | −0.933008 | − | 0.359856i | \(-0.882826\pi\) |
−0.516404 | − | 0.856345i | \(-0.672730\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.79796 | + | 9.12096i | −0.649830 | + | 0.760080i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.46630 | − | 0.963857i | 0.452395 | − | 0.0797694i | ||||
\(147\) | −7.00000 | + | 9.89949i | −0.577350 | + | 0.816497i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(150\) | 11.1237 | − | 5.12472i | 0.908248 | − | 0.418432i | ||||
\(151\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(152\) | −21.3195 | − | 12.3088i | −1.72924 | − | 0.998379i | ||||
\(153\) | 3.63718 | + | 21.8022i | 0.294048 | + | 1.76260i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −10.9034 | − | 6.56632i | −0.856649 | − | 0.515899i | ||||
\(163\) | −23.0454 | −1.80506 | −0.902528 | − | 0.430632i | \(-0.858291\pi\) | ||||
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(164\) | −2.69802 | + | 7.41275i | −0.210680 | + | 0.578838i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.3557 | − | 12.8849i | −1.19183 | − | 1.00007i | ||||
\(167\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.95858 | − | 8.35624i | 0.766044 | − | 0.642788i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.15655 | − | 24.4529i | 0.700219 | − | 1.86996i | ||||
\(172\) | 6.49479 | − | 11.2493i | 0.495223 | − | 0.857751i | ||||
\(173\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.24053 | + | 22.6407i | 0.621154 | + | 1.70661i | ||||
\(177\) | −11.8293 | − | 8.36460i | −0.889147 | − | 0.628722i | ||||
\(178\) | −4.52274 | − | 25.6497i | −0.338994 | − | 1.92253i | ||||
\(179\) | 4.92679 | + | 2.84448i | 0.368245 | + | 0.212607i | 0.672692 | − | 0.739923i | \(-0.265138\pi\) |
−0.304446 | + | 0.952529i | \(0.598471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.7031 | + | 15.1787i | 3.04964 | + | 1.10998i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(192\) | −11.3871 | + | 7.89525i | −0.821790 | + | 0.569790i | ||||
\(193\) | −15.7292 | − | 13.1984i | −1.13221 | − | 0.950039i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
−0.999156 | + | 0.0410699i | \(0.986923\pi\) | |||||||
\(194\) | −4.52361 | − | 0.797635i | −0.324777 | − | 0.0572669i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.7246 | + | 8.99903i | −0.766044 | + | 0.642788i | ||||
\(197\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(198\) | −22.2485 | + | 12.5728i | −1.58113 | + | 0.893512i | ||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 13.9273 | − | 2.45576i | 0.984808 | − | 0.173648i | ||||
\(201\) | 9.09008 | + | 0.837563i | 0.641164 | + | 0.0590771i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.34177 | + | 25.4152i | −0.163957 | + | 1.77942i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33.6987 | − | 40.1606i | −2.33099 | − | 2.77796i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.04368 | + | 28.6041i | −0.347221 | + | 1.96919i | −0.153151 | + | 0.988203i | \(0.548942\pi\) |
−0.194071 | + | 0.980988i | \(0.562169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −21.9975 | − | 8.00644i | −1.50372 | − | 0.547309i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.2474 | − | 10.5352i | −0.697251 | − | 0.716827i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.561238 | + | 6.77490i | 0.0379249 | + | 0.457805i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | + | 14.1421i | 0.333333 | + | 0.942809i | ||||
\(226\) | 7.02270 | − | 12.1637i | 0.467143 | − | 0.809116i | ||||
\(227\) | −12.7222 | + | 2.24327i | −0.844402 | + | 0.148891i | −0.579082 | − | 0.815270i | \(-0.696589\pi\) |
−0.265320 | + | 0.964160i | \(0.585478\pi\) | |||||||
\(228\) | 17.4073 | − | 24.6177i | 1.15283 | − | 1.63035i | ||||
\(229\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.7354 | + | 14.2810i | 1.62047 | + | 0.935577i | 0.986795 | + | 0.161976i | \(0.0517866\pi\) |
0.633672 | + | 0.773602i | \(0.281547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.7533 | − | 12.8153i | −0.699982 | − | 0.834206i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.9666 | − | 10.5430i | −1.86590 | − | 0.679133i | −0.973845 | − | 0.227213i | \(-0.927039\pi\) |
−0.892058 | − | 0.451920i | \(-0.850739\pi\) | |||||||
\(242\) | 35.7537i | 2.29833i | ||||||||
\(243\) | 9.23338 | − | 12.5596i | 0.592322 | − | 0.805701i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.73725 | − | 4.12344i | −0.557067 | − | 0.262901i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.4398 | − | 17.2795i | 1.10520 | − | 1.09505i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0966 | + | 15.6442i | −1.71032 | + | 0.987456i | −0.776215 | + | 0.630468i | \(0.782863\pi\) |
−0.934109 | + | 0.356988i | \(0.883804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.0351 | + | 5.47232i | −0.939693 | + | 0.342020i | ||||
\(257\) | −3.63117 | − | 9.97655i | −0.226506 | − | 0.622320i | 0.773427 | − | 0.633885i | \(-0.218541\pi\) |
−0.999933 | + | 0.0115651i | \(0.996319\pi\) | |||||||
\(258\) | 12.9896 | + | 9.18502i | 0.808696 | + | 0.571834i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.0227 | + | 27.7521i | 0.989886 | + | 1.71453i | ||||
\(263\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(264\) | −28.5381 | + | 7.50579i | −1.75640 | + | 0.461950i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 31.7901 | − | 2.63351i | 1.94552 | − | 0.161168i | ||||
\(268\) | 9.90509 | + | 3.60516i | 0.605050 | + | 0.220220i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −10.0798 | + | 27.6940i | −0.611176 | + | 1.67919i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.6002 | + | 12.2510i | 0.882029 | + | 0.740111i | ||||
\(275\) | 29.6596 | + | 5.22979i | 1.78854 | + | 0.315368i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(278\) | 27.3206 | − | 15.7736i | 1.63858 | − | 0.946036i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.42435 | − | 0.251151i | 0.0849695 | − | 0.0149824i | −0.131002 | − | 0.991382i | \(-0.541819\pi\) |
0.215971 | + | 0.976400i | \(0.430708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3793 | − | 3.77775i | 0.616985 | − | 0.224564i | −0.0145720 | − | 0.999894i | \(-0.504639\pi\) |
0.631557 | + | 0.775330i | \(0.282416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8.34928 | − | 14.7746i | −0.491986 | − | 0.870603i | ||||
\(289\) | 18.6424 | + | 32.2896i | 1.09661 | + | 1.89939i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.48111 | − | 5.42727i | 0.0868241 | − | 0.318152i | ||||
\(292\) | −1.36310 | + | 7.73052i | −0.0797694 | + | 0.452395i | ||||
\(293\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(294\) | −9.76987 | − | 14.0908i | −0.569790 | − | 0.821790i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.8334 | − | 28.5466i | −0.744672 | − | 1.65644i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.42995 | + | 17.2614i | 0.0825579 | + | 0.996586i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.6696 | − | 22.3784i | 1.52961 | − | 1.28349i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −30.7327 | − | 5.71194i | −1.75687 | − | 0.326530i | ||||
\(307\) | −1.22617 | + | 2.12378i | −0.0699810 | + | 0.121211i | −0.898893 | − | 0.438169i | \(-0.855627\pi\) |
0.828912 | + | 0.559379i | \(0.188961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.50274 | + | 31.2076i | 0.311033 | + | 1.76396i | 0.593650 | + | 0.804723i | \(0.297686\pi\) |
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2364 | − | 25.9280i | 0.682969 | − | 1.44716i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 64.1271i | − | 3.56813i | ||||||
\(324\) | 14.0000 | − | 11.3137i | 0.777778 | − | 0.628539i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.1468 | − | 30.6256i | 0.617365 | − | 1.69620i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.54599 | − | 7.17094i | −0.471873 | − | 0.395949i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.8463 | + | 22.5268i | −1.47561 | + | 1.23818i | −0.564882 | + | 0.825172i | \(0.691078\pi\) |
−0.910726 | + | 0.413011i | \(0.864477\pi\) | |||||||
\(332\) | 24.5505 | − | 14.1742i | 1.34738 | − | 0.777913i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.2708 | − | 8.46987i | 1.26764 | − | 0.461383i | 0.381314 | − | 0.924445i | \(-0.375472\pi\) |
0.886326 | + | 0.463062i | \(0.153249\pi\) | |||||||
\(338\) | 6.28796 | + | 17.2760i | 0.342020 | + | 0.939693i | ||||
\(339\) | 14.0454 | + | 9.93160i | 0.762842 | + | 0.539411i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 28.0671 | + | 23.9960i | 1.51770 | + | 1.29755i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.8080 | + | 14.0723i | 0.636646 | + | 0.758726i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.306044 | − | 0.364729i | 0.0164293 | − | 0.0195797i | −0.757767 | − | 0.652525i | \(-0.773710\pi\) |
0.774197 | + | 0.632945i | \(0.218154\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −34.0736 | −1.81613 | ||||||||
\(353\) | −3.76298 | + | 10.3387i | −0.200283 | + | 0.550273i | −0.998653 | − | 0.0518946i | \(-0.983474\pi\) |
0.798369 | + | 0.602168i | \(0.205696\pi\) | |||||||
\(354\) | 16.8377 | − | 11.6744i | 0.894912 | − | 0.620489i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 36.2742 | + | 6.39612i | 1.92253 | + | 0.338994i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.16314 | + | 5.17149i | −0.325732 | + | 0.273322i | ||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −28.3769 | + | 49.1503i | −1.49352 | + | 2.58686i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −43.6044 | − | 4.01773i | −2.28864 | − | 0.210876i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.01068 | − | 10.1924i | 0.312904 | − | 0.530595i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(374\) | −40.3427 | + | 48.0786i | −2.08607 | + | 2.48609i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9550 | 0.768187 | 0.384093 | − | 0.923294i | \(-0.374514\pi\) | ||||
0.384093 | + | 0.923294i | \(0.374514\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(384\) | −4.98440 | − | 18.9514i | −0.254359 | − | 0.967110i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.1477 | − | 14.5190i | 1.27998 | − | 0.738999i | ||||
\(387\) | −12.6615 | + | 14.8097i | −0.643621 | + | 0.752818i | ||||
\(388\) | 3.24802 | − | 5.62574i | 0.164893 | − | 0.285604i | ||||
\(389\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.77165 | − | 18.6050i | −0.342020 | − | 0.939693i | ||||
\(393\) | −35.6464 | + | 16.4224i | −1.79812 | + | 0.828399i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.94701 | − | 35.6479i | −0.298848 | − | 1.79137i | ||||
\(397\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47296 | + | 19.6962i | −0.173648 | + | 0.984808i | ||||
\(401\) | −8.21802 | + | 9.79385i | −0.410388 | + | 0.489082i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.520770 | + | 0.853697i | \(0.325645\pi\) | |||||||
\(402\) | −5.50983 | + | 11.6749i | −0.274806 | + | 0.582292i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −32.6423 | − | 15.4051i | −1.61603 | − | 0.762667i | ||||
\(409\) | 6.94395 | + | 5.82667i | 0.343356 | + | 0.288110i | 0.798116 | − | 0.602504i | \(-0.205830\pi\) |
−0.454759 | + | 0.890614i | \(0.650275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.5817 | + | 16.4294i | −0.817916 | + | 0.810403i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.1670 | + | 35.0922i | 0.791703 | + | 1.71847i | ||||
\(418\) | 69.6701 | − | 25.3579i | 3.40768 | − | 1.24029i | ||||
\(419\) | −0.956397 | − | 2.62768i | −0.0467231 | − | 0.128371i | 0.914136 | − | 0.405407i | \(-0.132870\pi\) |
−0.960860 | + | 0.277036i | \(0.910648\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(422\) | −35.5732 | − | 20.5382i | −1.73168 | − | 0.999784i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.6797 | + | 28.2204i | 1.14864 | + | 1.36889i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 21.2799 | − | 25.3604i | 1.02860 | − | 1.22584i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 18.9570 | − | 8.52235i | 0.912071 | − | 0.410032i | ||||
\(433\) | −29.9040 | −1.43710 | −0.718548 | − | 0.695477i | \(-0.755193\pi\) | ||||
−0.718548 | + | 0.695477i | \(0.755193\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −9.27481 | − | 2.53111i | −0.443167 | − | 0.120941i | ||||
\(439\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.2827 | − | 10.3317i | 0.870603 | − | 0.491986i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.2499 | + | 7.09714i | −1.91233 | + | 0.337195i | −0.997740 | − | 0.0671913i | \(-0.978596\pi\) |
−0.914588 | + | 0.404386i | \(0.867485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6273 | + | 11.3318i | 0.926271 | + | 0.534783i | 0.885630 | − | 0.464391i | \(-0.153727\pi\) |
0.0406404 | + | 0.999174i | \(0.487060\pi\) | |||||||
\(450\) | −21.2123 | − | 0.195773i | −0.999957 | − | 0.00922881i | ||||
\(451\) | −11.8789 | − | 20.5749i | −0.559357 | − | 0.968834i | ||||
\(452\) | 12.7678 | + | 15.2161i | 0.600548 | + | 0.715705i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.17246 | − | 17.9919i | 0.148891 | − | 0.844402i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.2953 | + | 35.0404i | 1.13773 | + | 1.64092i | ||||
\(457\) | −35.6523 | − | 12.9764i | −1.66774 | − | 0.607008i | −0.676191 | − | 0.736726i | \(-0.736371\pi\) |
−0.991551 | + | 0.129718i | \(0.958593\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.4197 | − | 36.8391i | 0.486349 | − | 1.71950i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.9426 | + | 25.9639i | −1.43339 | + | 1.20275i | ||||
\(467\) | −20.9072 | + | 12.0708i | −0.967470 | + | 0.558569i | −0.898464 | − | 0.439047i | \(-0.855316\pi\) |
−0.0690063 | + | 0.997616i | \(0.521983\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22.2319 | − | 8.09174i | 1.02331 | − | 0.372453i | ||||
\(473\) | 13.3801 | + | 36.7616i | 0.615219 | + | 1.69030i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.55688 | − | 42.8572i | −0.346733 | − | 1.96642i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 28.0217 | − | 33.3950i | 1.27635 | − | 1.52110i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −47.5140 | − | 17.2937i | −2.15973 | − | 0.786076i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.2247 | + | 18.3455i | 0.554526 | + | 0.832167i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.0978 | + | 17.0359i | 1.63240 | + | 0.770390i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.2340 | − | 4.80209i | −1.22905 | − | 0.216715i | −0.478834 | − | 0.877905i | \(-0.658940\pi\) |
−0.750218 | + | 0.661190i | \(0.770052\pi\) | |||||||
\(492\) | 9.70586 | − | 9.61669i | 0.437574 | − | 0.433554i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.5278 | + | 31.5341i | 0.651007 | + | 1.41308i | ||||
\(499\) | −1.27327 | + | 0.463434i | −0.0569995 | + | 0.0207461i | −0.370363 | − | 0.928887i | \(-0.620767\pi\) |
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.68369 | − | 43.5764i | −0.342940 | − | 1.94491i | ||||
\(503\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.7761 | + | 5.72732i | −0.967110 | + | 0.254359i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | −32.4189 | + | 31.5336i | −1.43133 | + | 1.39224i | ||||
\(514\) | 15.0145 | 0.662259 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −18.4891 | + | 12.8195i | −0.813939 | + | 0.564347i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.0511 | − | 20.2368i | 1.53562 | − | 0.886588i | 0.536528 | − | 0.843882i | \(-0.319735\pi\) |
0.999088 | − | 0.0427062i | \(-0.0135979\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.5227 | − | 35.5464i | 0.897395 | − | 1.55433i | 0.0665832 | − | 0.997781i | \(-0.478790\pi\) |
0.830812 | − | 0.556553i | \(-0.187876\pi\) | |||||||
\(524\) | −44.6306 | + | 7.86957i | −1.94969 | + | 0.343784i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.82894 | − | 41.5555i | 0.166633 | − | 1.80847i | ||||
\(529\) | −3.99391 | − | 22.6506i | −0.173648 | − | 0.984808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.3458 | + | 21.8467i | 0.535763 | + | 0.948068i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −11.8768 | + | 43.5205i | −0.513959 | + | 1.88332i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.58198 | + | 11.4194i | −0.413878 | + | 0.493241i | ||||
\(537\) | −5.61447 | − | 8.09757i | −0.242282 | − | 0.349436i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 42.1640i | − | 1.81613i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −31.9277 | − | 26.7906i | −1.36889 | − | 1.14864i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.8898 | − | 25.9196i | 1.32075 | − | 1.10824i | 0.334606 | − | 0.942358i | \(-0.391397\pi\) |
0.986145 | − | 0.165883i | \(-0.0530475\pi\) | |||||||
\(548\) | −23.3426 | + | 13.4769i | −0.997148 | + | 0.575704i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.2960 | + | 36.8858i | −0.908066 | + | 1.57282i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.74721 | + | 43.9366i | 0.328555 | + | 1.86333i | ||||
\(557\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −54.1022 | − | 54.6039i | −2.28420 | − | 2.30538i | ||||
\(562\) | −0.355181 | + | 2.01433i | −0.0149824 | + | 0.0849695i | ||||
\(563\) | 5.71019 | − | 6.80514i | 0.240656 | − | 0.286803i | −0.632175 | − | 0.774826i | \(-0.717837\pi\) |
0.872831 | + | 0.488023i | \(0.162282\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.6206i | 0.656581i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4905 | − | 42.5597i | 0.649395 | − | 1.78420i | 0.0294311 | − | 0.999567i | \(-0.490630\pi\) |
0.619964 | − | 0.784631i | \(-0.287147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.9524 | + | 22.6158i | 1.12792 | + | 0.946441i | 0.998978 | − | 0.0452101i | \(-0.0143957\pi\) |
0.128947 | + | 0.991651i | \(0.458840\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.6728 | − | 3.94925i | 0.986368 | − | 0.164552i | ||||
\(577\) | 23.9312 | − | 41.4501i | 0.996270 | − | 1.72559i | 0.423403 | − | 0.905941i | \(-0.360835\pi\) |
0.572866 | − | 0.819649i | \(-0.305831\pi\) | |||||||
\(578\) | −51.9277 | + | 9.15625i | −2.15991 | + | 0.380850i | ||||
\(579\) | 14.8812 | + | 32.3011i | 0.618441 | + | 1.34239i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.49605 | + | 4.59340i | 0.269270 | + | 0.190402i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.61398 | − | 5.55063i | −0.397829 | − | 0.229687i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1973 | + | 25.2620i | 0.874907 | + | 1.04267i | 0.998731 | + | 0.0503697i | \(0.0160400\pi\) |
−0.123823 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(588\) | 23.4512 | − | 6.16788i | 0.967110 | − | 0.254359i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.03896i | 0.289055i | 0.989501 | + | 0.144528i | \(0.0461663\pi\) | ||||
−0.989501 | + | 0.144528i | \(0.953834\pi\) | |||||||
\(594\) | 44.1437 | − | 3.24700i | 1.81124 | − | 0.133226i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(600\) | −23.6307 | − | 6.44886i | −0.964721 | − | 0.263274i | ||||
\(601\) | −18.6375 | + | 15.6388i | −0.760241 | + | 0.637918i | −0.938190 | − | 0.346122i | \(-0.887498\pi\) |
0.177949 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.6193 | − | 8.03161i | −0.554622 | − | 0.327073i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(608\) | 16.8395 | + | 46.2661i | 0.682932 | + | 1.87634i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 22.4559 | − | 38.0787i | 0.907724 | − | 1.53924i | ||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | −2.22927 | − | 2.65674i | −0.0899659 | − | 0.107217i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.8935 | + | 38.0092i | −1.28398 | + | 1.53019i | −0.603877 | + | 0.797077i | \(0.706378\pi\) |
−0.680106 | + | 0.733114i | \(0.738066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.0195 | + | 12.7461i | 1.40755 | + | 0.512308i | 0.930411 | − | 0.366518i | \(-0.119450\pi\) |
0.477143 | + | 0.878826i | \(0.341672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1511 | + | 16.0697i | 0.766044 | + | 0.642788i | ||||
\(626\) | −44.1342 | − | 7.78205i | −1.76396 | − | 0.311033i | ||||
\(627\) | 23.0969 | + | 87.8178i | 0.922401 | + | 3.50710i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.0454 | − | 41.0764i | 1.15445 | − | 1.63264i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.4299 | + | 27.9226i | 0.925424 | + | 1.10288i | 0.994444 | + | 0.105263i | \(0.0335683\pi\) |
−0.0690201 | + | 0.997615i | \(0.521987\pi\) | |||||||
\(642\) | 28.5378 | + | 28.8024i | 1.12630 | + | 1.13674i | ||||
\(643\) | 5.70399 | − | 32.3490i | 0.224944 | − | 1.27572i | −0.637850 | − | 0.770161i | \(-0.720176\pi\) |
0.862793 | − | 0.505557i | \(-0.168713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 85.2202 | + | 31.0176i | 3.35294 | + | 1.22037i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 8.26343 | + | 24.0773i | 0.324618 | + | 0.945845i | ||||
\(649\) | 50.3836 | 1.97773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 35.3076 | + | 29.6266i | 1.38275 | + | 1.16027i | ||||
\(653\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.6633 | − | 7.88848i | 0.533460 | − | 0.307994i | ||||
\(657\) | 4.12911 | − | 11.0269i | 0.161092 | − | 0.430202i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.0280 | − | 6.88169i | 1.52032 | − | 0.268073i | 0.649759 | − | 0.760140i | \(-0.274870\pi\) |
0.870557 | + | 0.492068i | \(0.163759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(662\) | −16.9511 | − | 46.5728i | −0.658823 | − | 1.81010i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.96170 | + | 39.4817i | 0.270166 | + | 1.53219i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.1303 | − | 16.7900i | −1.77819 | − | 0.647209i | −0.999812 | − | 0.0194154i | \(-0.993820\pi\) |
−0.778380 | − | 0.627793i | \(-0.783958\pi\) | |||||||
\(674\) | 35.0219i | 1.34899i | ||||||||
\(675\) | 2.62244 | − | 25.8481i | 0.100938 | − | 0.994893i | ||||
\(676\) | −26.0000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(678\) | −19.9920 | + | 13.8615i | −0.767787 | + | 0.532348i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.5860 | + | 5.89086i | 0.827179 | + | 0.225738i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.73956 | + | 1.58168i | −0.104826 | + | 0.0605215i | −0.551497 | − | 0.834177i | \(-0.685943\pi\) |
0.446670 | + | 0.894699i | \(0.352610\pi\) | |||||||
\(684\) | −45.4646 | + | 25.6925i | −1.73838 | + | 0.982378i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.4124 | + | 8.88539i | −0.930715 | + | 0.338752i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.165763 | + | 0.940090i | 0.00630593 | + | 0.0357627i | 0.987798 | − | 0.155738i | \(-0.0497756\pi\) |
−0.981492 | + | 0.191501i | \(0.938665\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.336667 | + | 0.583125i | 0.0127797 | + | 0.0221351i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.04630 | − | 28.6190i | 0.191142 | − | 1.08402i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.1879 | − | 40.6545i | −1.06617 | − | 1.53770i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 16.4811 | − | 45.2814i | 0.621154 | − | 1.70661i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.9193 | − | 10.0014i | −0.448587 | − | 0.376409i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.37027 | + | 28.0228i | 0.276992 | + | 1.05316i | ||||
\(709\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −26.0454 | + | 45.1120i | −0.976093 | + | 1.69064i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.89148 | − | 10.6918i | −0.145431 | − | 0.399570i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −51.5914 | − | 61.4843i | −1.92003 | − | 2.28821i | ||||
\(723\) | 37.5789 | + | 37.9273i | 1.39757 | + | 1.41053i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.4303 | − | 56.0037i | 0.980919 | − | 2.07849i | ||||
\(727\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.7474 | + | 12.8475i | −0.879535 | + | 0.475834i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.3665 | + | 44.9666i | −0.605337 | + | 1.66315i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.4927 | + | 15.8729i | −1.01271 | + | 0.584686i | ||||
\(738\) | 10.6376 | + | 12.9177i | 0.391577 | + | 0.475508i | ||||
\(739\) | −0.612829 | + | 1.06145i | −0.0225433 | + | 0.0390461i | −0.877077 | − | 0.480350i | \(-0.840510\pi\) |
0.854534 | + | 0.519396i | \(0.173843\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40.0908 | + | 14.1742i | −1.46685 | + | 0.518608i | ||||
\(748\) | −44.3796 | − | 76.8676i | −1.62268 | − | 2.81056i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 54.0083 | − | 4.47408i | 1.96817 | − | 0.163045i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −7.23358 | + | 19.8741i | −0.262735 | + | 0.721859i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.1418 | − | 1.96460i | −0.403891 | − | 0.0712169i | −0.0319875 | − | 0.999488i | \(-0.510184\pi\) |
−0.371903 | + | 0.928271i | \(0.621295\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 27.5959 | + | 2.54270i | 0.995782 | + | 0.0917517i | ||||
\(769\) | −51.7684 | + | 18.8422i | −1.86682 | + | 0.679466i | −0.893921 | + | 0.448224i | \(0.852057\pi\) |
−0.972896 | + | 0.231242i | \(0.925721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.68721 | + | 18.3113i | −0.0607634 | + | 0.659466i | ||||
\(772\) | 7.13104 | + | 40.4421i | 0.256652 | + | 1.45554i | ||||
\(773\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(774\) | −13.5567 | − | 23.9895i | −0.487286 | − | 0.862285i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.90516 | + | 7.03749i | 0.211983 | + | 0.252631i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.0665 | + | 26.2978i | −0.790614 | + | 0.942217i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.58232 | − | 55.3148i | −0.163446 | − | 1.97301i | ||||
\(787\) | −36.0389 | − | 30.2402i | −1.28465 | − | 1.07795i | −0.992586 | − | 0.121547i | \(-0.961214\pi\) |
−0.292061 | − | 0.956400i | \(-0.594341\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 50.2499 | + | 9.33938i | 1.78555 | + | 0.331861i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −24.4949 | − | 14.1421i | −0.866025 | − | 0.500000i | ||||
\(801\) | −51.7420 | − | 19.3752i | −1.82821 | − | 0.684588i | ||||
\(802\) | −9.04033 | − | 15.6583i | −0.319225 | − | 0.552914i | ||||
\(803\) | −15.1963 | − | 18.1103i | −0.536267 | − | 0.639098i | ||||
\(804\) | −12.8501 | − | 12.9692i | −0.453186 | − | 0.457388i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 55.2092i | − | 1.94105i | −0.240999 | − | 0.970525i | \(-0.577475\pi\) | ||
0.240999 | − | 0.970525i | \(-0.422525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.3809 | 1.97980 | 0.989900 | − | 0.141768i | \(-0.0452789\pi\) | ||||
0.989900 | + | 0.141768i | \(0.0452789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 36.2610 | − | 35.9279i | 1.26939 | − | 1.25773i | ||||
\(817\) | 43.3033 | − | 36.3358i | 1.51499 | − | 1.27123i | ||||
\(818\) | −11.1019 | + | 6.40970i | −0.388170 | + | 0.224110i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(822\) | −13.8130 | − | 29.9826i | −0.481785 | − | 1.04576i | ||||
\(823\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −42.5921 | − | 30.1171i | −1.48287 | − | 1.04854i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.1464 | + | 9.89949i | 0.596240 | + | 0.344239i | 0.767561 | − | 0.640976i | \(-0.221470\pi\) |
−0.171321 | + | 0.985215i | \(0.554804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.1516 | − | 39.5086i | 1.14864 | − | 1.36889i | ||||
\(834\) | −54.4548 | + | 4.51107i | −1.88561 | + | 0.156206i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 104.852i | 3.62638i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.95459 | 0.136609 | ||||||||
\(839\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2153 | − | 18.6408i | −0.766044 | − | 0.642788i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.41673 | − | 0.659527i | −0.0832365 | − | 0.0227153i | ||||
\(844\) | 44.5001 | − | 37.3401i | 1.53176 | − | 1.28530i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.0505 | − | 1.75532i | −0.653812 | − | 0.0602425i | ||||
\(850\) | −48.9565 | + | 17.8187i | −1.67919 | + | 0.611176i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.4093 | + | 40.5460i | 0.800112 | + | 1.38583i | ||||
\(857\) | 14.5446 | + | 17.3336i | 0.496835 | + | 0.592105i | 0.954942 | − | 0.296792i | \(-0.0959169\pi\) |
−0.458107 | + | 0.888897i | \(0.651472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.66241 | + | 49.1269i | −0.295557 | + | 1.67619i | 0.369370 | + | 0.929282i | \(0.379573\pi\) |
−0.664928 | + | 0.746908i | \(0.731538\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 2.15625 | + | 29.3147i | 0.0733571 | + | 0.997306i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.4643 | − | 39.7403i | 0.491516 | − | 1.35043i | ||||
\(867\) | −5.33153 | − | 64.3588i | −0.181068 | − | 2.18574i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.33199 | + | 7.40627i | −0.214305 | + | 0.250664i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.84978 | − | 11.1013i | 0.265219 | − | 0.375077i | ||||
\(877\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.9949 | + | 21.9364i | 1.28008 | + | 0.739055i | 0.976863 | − | 0.213866i | \(-0.0686057\pi\) |
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 4.88695 | + | 29.2936i | 0.164552 | + | 0.986368i | ||||
\(883\) | 11.0972 | + | 19.2209i | 0.373450 | + | 0.646834i | 0.990094 | − | 0.140408i | \(-0.0448416\pi\) |
−0.616644 | + | 0.787242i | \(0.711508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.0369 | − | 56.9219i | 0.337195 | − | 1.91233i | ||||
\(887\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00056 | + | 54.2016i | −0.0335200 | + | 1.81582i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.5527 | + | 20.6022i | −0.819334 | + | 0.687503i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 10.5203 | − | 28.0949i | 0.350678 | − | 0.936496i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 33.0882 | − | 5.83435i | 1.10172 | − | 0.194263i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.3967 | + | 9.60762i | −0.877942 | + | 0.319545i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.96005 | − | 45.1437i | −0.264309 | − | 1.49897i | −0.770996 | − | 0.636841i | \(-0.780241\pi\) |
0.506687 | − | 0.862130i | \(-0.330870\pi\) | |||||||
\(908\) | 22.3754 | + | 12.9185i | 0.742554 | + | 0.428714i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(912\) | −58.3175 | + | 15.3380i | −1.93108 | + | 0.507894i | ||||
\(913\) | −14.8257 | + | 84.0804i | −0.490657 | + | 2.78266i | ||||
\(914\) | 34.4892 | − | 41.1027i | 1.14080 | − | 1.35956i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 43.9166 | + | 31.6657i | 1.44946 | + | 1.04512i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.49061 | − | 2.42022i | 0.115019 | − | 0.0797490i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.8546 | − | 4.91151i | 0.913879 | − | 0.161141i | 0.303115 | − | 0.952954i | \(-0.401973\pi\) |
0.610764 | + | 0.791813i | \(0.290862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −57.2514 | + | 20.8378i | −1.87634 | + | 0.682932i | ||||
\(932\) | −19.5375 | − | 53.6789i | −0.639972 | − | 1.75831i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.92858 | − | 33.6227i | −0.193989 | − | 1.10017i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.5454 | − | 52.9062i | −0.997875 | − | 1.72837i | −0.555366 | − | 0.831606i | \(-0.687422\pi\) |
−0.442509 | − | 0.896764i | \(-0.645912\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.4503 | − | 52.9506i | 0.471567 | − | 1.72798i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 33.4584i | 1.08898i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55.3253 | −1.79878 | ||||||||
\(947\) | 20.7811 | − | 57.0955i | 0.675294 | − | 1.85536i | 0.187860 | − | 0.982196i | \(-0.439845\pi\) |
0.487435 | − | 0.873160i | \(-0.337933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 60.6092 | + | 10.6870i | 1.96642 | + | 0.346733i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.4028 | + | 30.8321i | −1.72989 | + | 0.998751i | −0.839964 | + | 0.542643i | \(0.817424\pi\) |
−0.889924 | + | 0.456109i | \(0.849243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.38309 | + | 30.5290i | 0.173648 | + | 0.984808i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.3336 | + | 31.5675i | −1.23528 | + | 1.01725i | ||||
\(964\) | 30.8256 | + | 53.3915i | 0.992826 | + | 1.71963i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(968\) | 45.9640 | − | 54.7778i | 1.47734 | − | 1.76063i | ||||
\(969\) | −47.4048 | + | 100.447i | −1.52286 | + | 3.22683i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.1127i | 0.998454i | 0.866471 | + | 0.499227i | \(0.166383\pi\) | ||||
−0.866471 | + | 0.499227i | \(0.833617\pi\) | |||||||
\(972\) | −30.2927 | + | 7.37228i | −0.971640 | + | 0.236466i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.82209 | − | 0.850265i | −0.154272 | − | 0.0272024i | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) |
−0.250251 | + | 0.968181i | \(0.580513\pi\) | |||||||
\(978\) | −40.0996 | + | 39.7312i | −1.28224 | + | 1.27046i | ||||
\(979\) | −84.9794 | + | 71.3062i | −2.71595 | + | 2.27896i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.5544 | − | 33.8692i | 0.624006 | − | 1.08081i | ||||
\(983\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(984\) | 8.08525 | + | 17.5499i | 0.257748 | + | 0.559469i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 58.7040 | − | 15.4397i | 1.86291 | − | 0.489964i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −48.9334 | + | 4.05368i | −1.55051 | + | 0.128446i | ||||
\(997\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(998\) | − | 1.91624i | − | 0.0606576i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 216.2.v.a.131.1 | ✓ | 12 | |
3.2 | odd | 2 | 648.2.v.a.179.2 | 12 | |||
4.3 | odd | 2 | 864.2.bh.a.239.2 | 12 | |||
8.3 | odd | 2 | CM | 216.2.v.a.131.1 | ✓ | 12 | |
8.5 | even | 2 | 864.2.bh.a.239.2 | 12 | |||
24.11 | even | 2 | 648.2.v.a.179.2 | 12 | |||
27.7 | even | 9 | 648.2.v.a.467.2 | 12 | |||
27.20 | odd | 18 | inner | 216.2.v.a.155.1 | yes | 12 | |
108.47 | even | 18 | 864.2.bh.a.47.2 | 12 | |||
216.101 | odd | 18 | 864.2.bh.a.47.2 | 12 | |||
216.115 | odd | 18 | 648.2.v.a.467.2 | 12 | |||
216.155 | even | 18 | inner | 216.2.v.a.155.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.a.131.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
216.2.v.a.131.1 | ✓ | 12 | 8.3 | odd | 2 | CM | |
216.2.v.a.155.1 | yes | 12 | 27.20 | odd | 18 | inner | |
216.2.v.a.155.1 | yes | 12 | 216.155 | even | 18 | inner | |
648.2.v.a.179.2 | 12 | 3.2 | odd | 2 | |||
648.2.v.a.179.2 | 12 | 24.11 | even | 2 | |||
648.2.v.a.467.2 | 12 | 27.7 | even | 9 | |||
648.2.v.a.467.2 | 12 | 216.115 | odd | 18 | |||
864.2.bh.a.47.2 | 12 | 108.47 | even | 18 | |||
864.2.bh.a.47.2 | 12 | 216.101 | odd | 18 | |||
864.2.bh.a.239.2 | 12 | 4.3 | odd | 2 | |||
864.2.bh.a.239.2 | 12 | 8.5 | even | 2 |