Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 22 x^{10} + 92 x^{9} + 125 x^{8} - 620 x^{7} - 94 x^{6} + 1280 x^{5} - 234 x^{4} + \cdots - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 441) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.14082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.72661 | −1.22090 | −0.610449 | − | 0.792056i | \(-0.709011\pi\) | ||||
−0.610449 | + | 0.792056i | \(0.709011\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.981184 | 0.490592 | ||||||||
\(5\) | 3.51231 | 1.57075 | 0.785377 | − | 0.619018i | \(-0.212469\pi\) | ||||
0.785377 | + | 0.619018i | \(0.212469\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.75910 | 0.621935 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.06439 | −1.91773 | ||||||||
\(11\) | −6.09064 | −1.83640 | −0.918199 | − | 0.396120i | \(-0.870356\pi\) | ||||
−0.918199 | + | 0.396120i | \(0.870356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.12028 | −0.310709 | −0.155355 | − | 0.987859i | \(-0.549652\pi\) | ||||
−0.155355 | + | 0.987859i | \(0.549652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99965 | −1.24991 | ||||||||
\(17\) | 1.20396 | 0.292002 | 0.146001 | − | 0.989284i | \(-0.453360\pi\) | ||||
0.146001 | + | 0.989284i | \(0.453360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.20537 | −0.505947 | −0.252974 | − | 0.967473i | \(-0.581409\pi\) | ||||
−0.252974 | + | 0.967473i | \(0.581409\pi\) | |||||||
\(20\) | 3.44622 | 0.770599 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.5162 | 2.24205 | ||||||||
\(23\) | −1.27339 | −0.265520 | −0.132760 | − | 0.991148i | \(-0.542384\pi\) | ||||
−0.132760 | + | 0.991148i | \(0.542384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.33633 | 1.46727 | ||||||||
\(26\) | 1.93429 | 0.379345 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.20524 | 1.15228 | 0.576142 | − | 0.817350i | \(-0.304557\pi\) | ||||
0.576142 | + | 0.817350i | \(0.304557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.188404 | −0.0338383 | −0.0169192 | − | 0.999857i | \(-0.505386\pi\) | ||||
−0.0169192 | + | 0.999857i | \(0.505386\pi\) | |||||||
\(32\) | 5.11425 | 0.904079 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.07876 | −0.356505 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.57670 | 0.588006 | 0.294003 | − | 0.955804i | \(-0.405012\pi\) | ||||
0.294003 | + | 0.955804i | \(0.405012\pi\) | |||||||
\(38\) | 3.80782 | 0.617710 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.17850 | 0.976907 | ||||||||
\(41\) | −3.36640 | −0.525743 | −0.262871 | − | 0.964831i | \(-0.584669\pi\) | ||||
−0.262871 | + | 0.964831i | \(0.584669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.80551 | 0.580336 | 0.290168 | − | 0.956976i | \(-0.406289\pi\) | ||||
0.290168 | + | 0.956976i | \(0.406289\pi\) | |||||||
\(44\) | −5.97604 | −0.900922 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.19865 | 0.324173 | ||||||||
\(47\) | −5.72070 | −0.834449 | −0.417225 | − | 0.908803i | \(-0.636997\pi\) | ||||
−0.417225 | + | 0.908803i | \(0.636997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.6670 | −1.79138 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.09920 | −0.152432 | ||||||||
\(53\) | −8.33827 | −1.14535 | −0.572675 | − | 0.819783i | \(-0.694094\pi\) | ||||
−0.572675 | + | 0.819783i | \(0.694094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.3922 | −2.88453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.7140 | −1.40682 | ||||||||
\(59\) | −11.2685 | −1.46704 | −0.733519 | − | 0.679669i | \(-0.762123\pi\) | ||||
−0.733519 | + | 0.679669i | \(0.762123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0022 | 1.53672 | 0.768361 | − | 0.640017i | \(-0.221073\pi\) | ||||
0.768361 | + | 0.640017i | \(0.221073\pi\) | |||||||
\(62\) | 0.325300 | 0.0413131 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.16898 | 0.146123 | ||||||||
\(65\) | −3.93477 | −0.488048 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.91303 | −0.966731 | −0.483366 | − | 0.875419i | \(-0.660586\pi\) | ||||
−0.483366 | + | 0.875419i | \(0.660586\pi\) | |||||||
\(68\) | 1.18130 | 0.143254 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2052 | −1.44850 | −0.724248 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724248 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.31473 | −0.622042 | −0.311021 | − | 0.950403i | \(-0.600671\pi\) | ||||
−0.311021 | + | 0.950403i | \(0.600671\pi\) | |||||||
\(74\) | −6.17557 | −0.717896 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.16388 | −0.248214 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.21711 | 1.03701 | 0.518503 | − | 0.855076i | \(-0.326490\pi\) | ||||
0.518503 | + | 0.855076i | \(0.326490\pi\) | |||||||
\(80\) | −17.5603 | −1.96330 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.81246 | 0.641878 | ||||||||
\(83\) | −1.24990 | −0.137194 | −0.0685972 | − | 0.997644i | \(-0.521852\pi\) | ||||
−0.0685972 | + | 0.997644i | \(0.521852\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.22867 | 0.458663 | ||||||||
\(86\) | −6.57064 | −0.708531 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.7140 | −1.14212 | ||||||||
\(89\) | 5.54131 | 0.587378 | 0.293689 | − | 0.955901i | \(-0.405117\pi\) | ||||
0.293689 | + | 0.955901i | \(0.405117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.24943 | −0.130262 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.87741 | 1.01878 | ||||||||
\(95\) | −7.74596 | −0.794718 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4855 | −1.67385 | −0.836926 | − | 0.547316i | \(-0.815650\pi\) | ||||
−0.836926 | + | 0.547316i | \(0.815650\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.19829 | 0.719829 | ||||||||
\(101\) | −12.9638 | −1.28995 | −0.644975 | − | 0.764203i | \(-0.723132\pi\) | ||||
−0.644975 | + | 0.764203i | \(0.723132\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.70182 | 0.266218 | 0.133109 | − | 0.991101i | \(-0.457504\pi\) | ||||
0.133109 | + | 0.991101i | \(0.457504\pi\) | |||||||
\(104\) | −1.97068 | −0.193241 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.3969 | 1.39835 | ||||||||
\(107\) | −0.178480 | −0.0172544 | −0.00862718 | − | 0.999963i | \(-0.502746\pi\) | ||||
−0.00862718 | + | 0.999963i | \(0.502746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.35853 | 0.896385 | 0.448192 | − | 0.893937i | \(-0.352068\pi\) | ||||
0.448192 | + | 0.893937i | \(0.352068\pi\) | |||||||
\(110\) | 36.9360 | 3.52171 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.42038 | −0.792123 | −0.396061 | − | 0.918224i | \(-0.629623\pi\) | ||||
−0.396061 | + | 0.918224i | \(0.629623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.47254 | −0.417067 | ||||||||
\(116\) | 6.08848 | 0.565302 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.4564 | 1.79110 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.0959 | 2.37235 | ||||||||
\(122\) | −20.7231 | −1.87618 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.184859 | −0.0166008 | ||||||||
\(125\) | 8.20593 | 0.733960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.92438 | −0.880647 | −0.440323 | − | 0.897839i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897839i | \(0.645136\pi\) | |||||||
\(128\) | −12.2469 | −1.08248 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.79381 | 0.595857 | ||||||||
\(131\) | −15.2467 | −1.33211 | −0.666055 | − | 0.745902i | \(-0.732019\pi\) | ||||
−0.666055 | + | 0.745902i | \(0.732019\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.6627 | 1.18028 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.11788 | 0.181606 | ||||||||
\(137\) | 6.14700 | 0.525174 | 0.262587 | − | 0.964908i | \(-0.415424\pi\) | ||||
0.262587 | + | 0.964908i | \(0.415424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.877375 | −0.0744179 | −0.0372090 | − | 0.999308i | \(-0.511847\pi\) | ||||
−0.0372090 | + | 0.999308i | \(0.511847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.0737 | 1.76847 | ||||||||
\(143\) | 6.82321 | 0.570586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.7947 | 1.80995 | ||||||||
\(146\) | 9.17647 | 0.759450 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.50940 | 0.288471 | ||||||||
\(149\) | 5.77553 | 0.473150 | 0.236575 | − | 0.971613i | \(-0.423975\pi\) | ||||
0.236575 | + | 0.971613i | \(0.423975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.02643 | −0.164908 | −0.0824541 | − | 0.996595i | \(-0.526276\pi\) | ||||
−0.0824541 | + | 0.996595i | \(0.526276\pi\) | |||||||
\(152\) | −3.87947 | −0.314666 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.661733 | −0.0531516 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.04756 | −0.243222 | −0.121611 | − | 0.992578i | \(-0.538806\pi\) | ||||
−0.121611 | + | 0.992578i | \(0.538806\pi\) | |||||||
\(158\) | −15.9144 | −1.26608 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.9628 | 1.42009 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.38891 | −0.422092 | −0.211046 | − | 0.977476i | \(-0.567687\pi\) | ||||
−0.211046 | + | 0.977476i | \(0.567687\pi\) | |||||||
\(164\) | −3.30306 | −0.257925 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.15809 | 0.167500 | ||||||||
\(167\) | 16.6096 | 1.28529 | 0.642645 | − | 0.766164i | \(-0.277837\pi\) | ||||
0.642645 | + | 0.766164i | \(0.277837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7450 | −0.903460 | ||||||||
\(170\) | −7.30126 | −0.559981 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.73391 | 0.284708 | ||||||||
\(173\) | −17.6503 | −1.34193 | −0.670965 | − | 0.741489i | \(-0.734120\pi\) | ||||
−0.670965 | + | 0.741489i | \(0.734120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30.4510 | 2.29533 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.56769 | −0.717128 | ||||||||
\(179\) | 2.62844 | 0.196459 | 0.0982294 | − | 0.995164i | \(-0.468682\pi\) | ||||
0.0982294 | + | 0.995164i | \(0.468682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.97391 | 0.295378 | 0.147689 | − | 0.989034i | \(-0.452816\pi\) | ||||
0.147689 | + | 0.989034i | \(0.452816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.24002 | −0.165136 | ||||||||
\(185\) | 12.5625 | 0.923613 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.33286 | −0.536232 | ||||||||
\(188\) | −5.61306 | −0.409374 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3743 | 0.970270 | ||||||||
\(191\) | −18.2059 | −1.31733 | −0.658666 | − | 0.752435i | \(-0.728879\pi\) | ||||
−0.658666 | + | 0.752435i | \(0.728879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.202385 | −0.0145680 | −0.00728401 | − | 0.999973i | \(-0.502319\pi\) | ||||
−0.00728401 | + | 0.999973i | \(0.502319\pi\) | |||||||
\(194\) | 28.4641 | 2.04360 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.63136 | −0.116229 | −0.0581147 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581147 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.29211 | 0.446036 | 0.223018 | − | 0.974814i | \(-0.428409\pi\) | ||||
0.223018 | + | 0.974814i | \(0.428409\pi\) | |||||||
\(200\) | 12.9053 | 0.912544 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.3835 | 1.57490 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8238 | −0.825812 | ||||||||
\(206\) | −4.66499 | −0.325025 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.60100 | 0.388359 | ||||||||
\(209\) | 13.4321 | 0.929120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.2874 | −1.12127 | −0.560634 | − | 0.828064i | \(-0.689442\pi\) | ||||
−0.560634 | + | 0.828064i | \(0.689442\pi\) | |||||||
\(212\) | −8.18138 | −0.561899 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.308166 | 0.0210658 | ||||||||
\(215\) | 13.3662 | 0.911564 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.1585 | −1.09439 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −20.9897 | −1.41513 | ||||||||
\(221\) | −1.34877 | −0.0907278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.9694 | 1.33725 | 0.668626 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668626 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.5387 | 0.967101 | ||||||||
\(227\) | 3.61283 | 0.239792 | 0.119896 | − | 0.992786i | \(-0.461744\pi\) | ||||
0.119896 | + | 0.992786i | \(0.461744\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.7147 | 0.906290 | 0.453145 | − | 0.891437i | \(-0.350302\pi\) | ||||
0.453145 | + | 0.891437i | \(0.350302\pi\) | |||||||
\(230\) | 7.72234 | 0.509196 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.9156 | 0.716646 | ||||||||
\(233\) | −25.2542 | −1.65445 | −0.827227 | − | 0.561867i | \(-0.810083\pi\) | ||||
−0.827227 | + | 0.561867i | \(0.810083\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.0929 | −1.31071 | ||||||||
\(236\) | −11.0565 | −0.719717 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.98991 | 0.581509 | 0.290754 | − | 0.956798i | \(-0.406094\pi\) | ||||
0.290754 | + | 0.956798i | \(0.406094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.25724 | 0.596311 | 0.298156 | − | 0.954517i | \(-0.403629\pi\) | ||||
0.298156 | + | 0.954517i | \(0.403629\pi\) | |||||||
\(242\) | −45.0575 | −2.89640 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.7763 | 0.753903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.47063 | 0.157203 | ||||||||
\(248\) | −0.331421 | −0.0210452 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.1684 | −0.896091 | ||||||||
\(251\) | 20.6517 | 1.30353 | 0.651763 | − | 0.758422i | \(-0.274030\pi\) | ||||
0.651763 | + | 0.758422i | \(0.274030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.75576 | 0.487600 | ||||||||
\(254\) | 17.1355 | 1.07518 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.8076 | 1.17548 | ||||||||
\(257\) | −2.44579 | −0.152564 | −0.0762819 | − | 0.997086i | \(-0.524305\pi\) | ||||
−0.0762819 | + | 0.997086i | \(0.524305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.86073 | −0.239432 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 26.3251 | 1.62637 | ||||||||
\(263\) | −24.5628 | −1.51460 | −0.757302 | − | 0.653065i | \(-0.773483\pi\) | ||||
−0.757302 | + | 0.653065i | \(0.773483\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.2866 | −1.79906 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.76415 | −0.474271 | ||||||||
\(269\) | −29.5703 | −1.80293 | −0.901466 | − | 0.432849i | \(-0.857508\pi\) | ||||
−0.901466 | + | 0.432849i | \(0.857508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.7915 | −1.50598 | −0.752989 | − | 0.658034i | \(-0.771388\pi\) | ||||
−0.752989 | + | 0.658034i | \(0.771388\pi\) | |||||||
\(272\) | −6.01935 | −0.364977 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.6135 | −0.641184 | ||||||||
\(275\) | −44.6830 | −2.69448 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.87850 | 0.112868 | 0.0564340 | − | 0.998406i | \(-0.482027\pi\) | ||||
0.0564340 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(278\) | 1.51488 | 0.0908567 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0793 | −0.720590 | −0.360295 | − | 0.932838i | \(-0.617324\pi\) | ||||
−0.360295 | + | 0.932838i | \(0.617324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.9719 | −1.66276 | −0.831378 | − | 0.555708i | \(-0.812447\pi\) | ||||
−0.831378 | + | 0.555708i | \(0.812447\pi\) | |||||||
\(284\) | −11.9756 | −0.710620 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.7810 | −0.696627 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5505 | −0.914735 | ||||||||
\(290\) | −37.6310 | −2.20977 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.21473 | −0.305169 | ||||||||
\(293\) | 8.82326 | 0.515460 | 0.257730 | − | 0.966217i | \(-0.417025\pi\) | ||||
0.257730 | + | 0.966217i | \(0.417025\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.5786 | −2.30435 | ||||||||
\(296\) | 6.29177 | 0.365702 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.97209 | −0.577668 | ||||||||
\(299\) | 1.42655 | 0.0824996 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.49885 | 0.201336 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.0261 | 0.632389 | ||||||||
\(305\) | 42.1554 | 2.41381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.05532 | 0.0602304 | 0.0301152 | − | 0.999546i | \(-0.490413\pi\) | ||||
0.0301152 | + | 0.999546i | \(0.490413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.14255 | 0.0648927 | ||||||||
\(311\) | 3.07215 | 0.174206 | 0.0871029 | − | 0.996199i | \(-0.472239\pi\) | ||||
0.0871029 | + | 0.996199i | \(0.472239\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.1621 | 1.59181 | 0.795907 | − | 0.605419i | \(-0.206994\pi\) | ||||
0.795907 | + | 0.605419i | \(0.206994\pi\) | |||||||
\(314\) | 5.26196 | 0.296949 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04368 | 0.508747 | ||||||||
\(317\) | 12.8465 | 0.721530 | 0.360765 | − | 0.932657i | \(-0.382516\pi\) | ||||
0.360765 | + | 0.932657i | \(0.382516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.7939 | −2.11605 | ||||||||
\(320\) | 4.10582 | 0.229523 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.65517 | −0.147738 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.21874 | −0.455893 | ||||||||
\(326\) | 9.30454 | 0.515331 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.92182 | −0.326978 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.5560 | −1.18483 | −0.592413 | − | 0.805634i | \(-0.701825\pi\) | ||||
−0.592413 | + | 0.805634i | \(0.701825\pi\) | |||||||
\(332\) | −1.22638 | −0.0673065 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.6783 | −1.56921 | ||||||||
\(335\) | −27.7930 | −1.51850 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.6068 | −0.686736 | −0.343368 | − | 0.939201i | \(-0.611568\pi\) | ||||
−0.343368 | + | 0.939201i | \(0.611568\pi\) | |||||||
\(338\) | 20.2790 | 1.10303 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.14910 | 0.225017 | ||||||||
\(341\) | 1.14750 | 0.0621406 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.69427 | 0.360931 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.4752 | 1.63836 | ||||||||
\(347\) | 23.1366 | 1.24204 | 0.621020 | − | 0.783795i | \(-0.286719\pi\) | ||||
0.621020 | + | 0.783795i | \(0.286719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.4869 | −0.882524 | −0.441262 | − | 0.897378i | \(-0.645469\pi\) | ||||
−0.441262 | + | 0.897378i | \(0.645469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −31.1490 | −1.66025 | ||||||||
\(353\) | −24.4875 | −1.30334 | −0.651669 | − | 0.758503i | \(-0.725931\pi\) | ||||
−0.651669 | + | 0.758503i | \(0.725931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42.8686 | −2.27523 | ||||||||
\(356\) | 5.43705 | 0.288163 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.53829 | −0.239856 | ||||||||
\(359\) | 20.4777 | 1.08077 | 0.540386 | − | 0.841417i | \(-0.318278\pi\) | ||||
0.540386 | + | 0.841417i | \(0.318278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1363 | −0.744017 | ||||||||
\(362\) | −6.86139 | −0.360627 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.6670 | −0.977075 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2539 | 1.16164 | 0.580821 | − | 0.814031i | \(-0.302732\pi\) | ||||
0.580821 | + | 0.814031i | \(0.302732\pi\) | |||||||
\(368\) | 6.36650 | 0.331877 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.6905 | −1.12764 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.5369 | −1.68469 | −0.842347 | − | 0.538935i | \(-0.818827\pi\) | ||||
−0.842347 | + | 0.538935i | \(0.818827\pi\) | |||||||
\(374\) | 12.6610 | 0.654685 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.0633 | −0.518973 | ||||||||
\(377\) | −6.95160 | −0.358026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54440 | 0.0793306 | 0.0396653 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396653 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(380\) | −7.60021 | −0.389883 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 31.4345 | 1.60833 | ||||||||
\(383\) | 31.6294 | 1.61619 | 0.808093 | − | 0.589055i | \(-0.200500\pi\) | ||||
0.808093 | + | 0.589055i | \(0.200500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.349441 | 0.0177861 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.1753 | −0.821179 | ||||||||
\(389\) | −5.24626 | −0.265996 | −0.132998 | − | 0.991116i | \(-0.542460\pi\) | ||||
−0.132998 | + | 0.991116i | \(0.542460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53310 | −0.0775324 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.81672 | 0.141904 | ||||||||
\(395\) | 32.3734 | 1.62888 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0276349 | 0.00138696 | 0.000693478 | − | 1.00000i | \(-0.499779\pi\) | ||||
0.000693478 | 1.00000i | \(0.499779\pi\) | ||||||||
\(398\) | −10.8640 | −0.544564 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −36.6791 | −1.83395 | ||||||||
\(401\) | 12.1377 | 0.606127 | 0.303064 | − | 0.952970i | \(-0.401991\pi\) | ||||
0.303064 | + | 0.952970i | \(0.401991\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.211065 | 0.0105139 | ||||||||
\(404\) | −12.7199 | −0.632840 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.7844 | −1.07981 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3453 | 1.54993 | 0.774963 | − | 0.632007i | \(-0.217769\pi\) | ||||
0.774963 | + | 0.632007i | \(0.217769\pi\) | |||||||
\(410\) | 20.4152 | 1.00823 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.65098 | 0.130604 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.39004 | −0.215499 | ||||||||
\(416\) | −5.72938 | −0.280906 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.1921 | −1.13436 | ||||||||
\(419\) | −14.8864 | −0.727247 | −0.363623 | − | 0.931546i | \(-0.618461\pi\) | ||||
−0.363623 | + | 0.931546i | \(0.618461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.08427 | 0.442740 | 0.221370 | − | 0.975190i | \(-0.428947\pi\) | ||||
0.221370 | + | 0.975190i | \(0.428947\pi\) | |||||||
\(422\) | 28.1219 | 1.36895 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.6678 | −0.712333 | ||||||||
\(425\) | 8.83262 | 0.428445 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.175122 | −0.00846485 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −23.0781 | −1.11293 | ||||||||
\(431\) | −16.6355 | −0.801305 | −0.400652 | − | 0.916230i | \(-0.631216\pi\) | ||||
−0.400652 | + | 0.916230i | \(0.631216\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7423 | 0.948756 | 0.474378 | − | 0.880321i | \(-0.342673\pi\) | ||||
0.474378 | + | 0.880321i | \(0.342673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.18244 | 0.439759 | ||||||||
\(437\) | 2.80830 | 0.134339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.73514 | −0.321451 | −0.160725 | − | 0.986999i | \(-0.551383\pi\) | ||||
−0.160725 | + | 0.986999i | \(0.551383\pi\) | |||||||
\(440\) | −37.6310 | −1.79399 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.32879 | 0.110769 | ||||||||
\(443\) | 28.6403 | 1.36074 | 0.680372 | − | 0.732867i | \(-0.261818\pi\) | ||||
0.680372 | + | 0.732867i | \(0.261818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.4628 | 0.922626 | ||||||||
\(446\) | −34.4794 | −1.63265 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.66872 | −0.314716 | −0.157358 | − | 0.987542i | \(-0.550298\pi\) | ||||
−0.157358 | + | 0.987542i | \(0.550298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.5035 | 0.965473 | ||||||||
\(452\) | −8.26194 | −0.388609 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.23795 | −0.292762 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6573 | −1.34053 | −0.670266 | − | 0.742121i | \(-0.733820\pi\) | ||||
−0.670266 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(458\) | −23.6799 | −1.10649 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.38839 | −0.204610 | ||||||||
\(461\) | 20.0173 | 0.932299 | 0.466150 | − | 0.884706i | \(-0.345641\pi\) | ||||
0.466150 | + | 0.884706i | \(0.345641\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.91578 | 0.460825 | 0.230413 | − | 0.973093i | \(-0.425992\pi\) | ||||
0.230413 | + | 0.973093i | \(0.425992\pi\) | |||||||
\(464\) | −31.0240 | −1.44025 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 43.6041 | 2.01992 | ||||||||
\(467\) | −16.0807 | −0.744126 | −0.372063 | − | 0.928207i | \(-0.621349\pi\) | ||||
−0.372063 | + | 0.928207i | \(0.621349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 34.6926 | 1.60025 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.8225 | −0.912402 | ||||||||
\(473\) | −23.1780 | −1.06573 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.1793 | −0.742359 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.5221 | −0.709963 | ||||||||
\(479\) | 8.20255 | 0.374784 | 0.187392 | − | 0.982285i | \(-0.439997\pi\) | ||||
0.187392 | + | 0.982285i | \(0.439997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00690 | −0.182699 | ||||||||
\(482\) | −15.9837 | −0.728036 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.6049 | 1.16386 | ||||||||
\(485\) | −57.9023 | −2.62921 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.73680 | 0.124016 | 0.0620081 | − | 0.998076i | \(-0.480250\pi\) | ||||
0.0620081 | + | 0.998076i | \(0.480250\pi\) | |||||||
\(488\) | 21.1130 | 0.955741 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7096 | −0.889483 | −0.444742 | − | 0.895659i | \(-0.646705\pi\) | ||||
−0.444742 | + | 0.895659i | \(0.646705\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.47084 | 0.336470 | ||||||||
\(494\) | −4.26582 | −0.191928 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.941952 | 0.0422949 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.0960 | −1.48158 | −0.740789 | − | 0.671737i | \(-0.765548\pi\) | ||||
−0.740789 | + | 0.671737i | \(0.765548\pi\) | |||||||
\(500\) | 8.05153 | 0.360075 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −35.6575 | −1.59147 | ||||||||
\(503\) | −12.1860 | −0.543346 | −0.271673 | − | 0.962390i | \(-0.587577\pi\) | ||||
−0.271673 | + | 0.962390i | \(0.587577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.5331 | −2.02619 | ||||||||
\(506\) | −13.3912 | −0.595310 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.73765 | −0.432038 | ||||||||
\(509\) | −13.6393 | −0.604551 | −0.302276 | − | 0.953221i | \(-0.597746\pi\) | ||||
−0.302276 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.97968 | −0.352656 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.22292 | 0.186265 | ||||||||
\(515\) | 9.48962 | 0.418163 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.8427 | 1.53238 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.92164 | −0.303534 | ||||||||
\(521\) | 35.5490 | 1.55743 | 0.778714 | − | 0.627379i | \(-0.215872\pi\) | ||||
0.778714 | + | 0.627379i | \(0.215872\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.7187 | −1.16833 | −0.584163 | − | 0.811636i | \(-0.698577\pi\) | ||||
−0.584163 | + | 0.811636i | \(0.698577\pi\) | |||||||
\(524\) | −14.9598 | −0.653523 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.4103 | 1.84918 | ||||||||
\(527\) | −0.226830 | −0.00988086 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3785 | −0.929499 | ||||||||
\(530\) | 50.5665 | 2.19647 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.77130 | 0.163353 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.626879 | −0.0271023 | ||||||||
\(536\) | −13.9198 | −0.601244 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 51.0564 | 2.20120 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.5855 | 1.61593 | 0.807963 | − | 0.589233i | \(-0.200570\pi\) | ||||
0.807963 | + | 0.589233i | \(0.200570\pi\) | |||||||
\(542\) | 42.8053 | 1.83864 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.15733 | 0.263993 | ||||||||
\(545\) | 32.8701 | 1.40800 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2676 | 0.781067 | 0.390533 | − | 0.920589i | \(-0.372291\pi\) | ||||
0.390533 | + | 0.920589i | \(0.372291\pi\) | |||||||
\(548\) | 6.03134 | 0.257646 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 77.1501 | 3.28969 | ||||||||
\(551\) | −13.6849 | −0.582995 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.24343 | −0.137800 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.860866 | −0.0365089 | ||||||||
\(557\) | −3.89272 | −0.164940 | −0.0824698 | − | 0.996594i | \(-0.526281\pi\) | ||||
−0.0824698 | + | 0.996594i | \(0.526281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.26324 | −0.180316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.8562 | 0.879767 | ||||||||
\(563\) | 3.32855 | 0.140282 | 0.0701409 | − | 0.997537i | \(-0.477655\pi\) | ||||
0.0701409 | + | 0.997537i | \(0.477655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.5750 | −1.24423 | ||||||||
\(566\) | 48.2965 | 2.03006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.4702 | −0.900870 | ||||||||
\(569\) | −36.6244 | −1.53538 | −0.767688 | − | 0.640824i | \(-0.778593\pi\) | ||||
−0.767688 | + | 0.640824i | \(0.778593\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.5824 | −0.945044 | −0.472522 | − | 0.881319i | \(-0.656656\pi\) | ||||
−0.472522 | + | 0.881319i | \(0.656656\pi\) | |||||||
\(572\) | 6.69483 | 0.279925 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.34201 | −0.389589 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5449 | 0.938557 | 0.469279 | − | 0.883050i | \(-0.344514\pi\) | ||||
0.469279 | + | 0.883050i | \(0.344514\pi\) | |||||||
\(578\) | 26.8496 | 1.11680 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.3847 | 0.887949 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.7854 | 2.10332 | ||||||||
\(584\) | −9.34913 | −0.386870 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.2343 | −0.629325 | ||||||||
\(587\) | 24.2396 | 1.00047 | 0.500237 | − | 0.865888i | \(-0.333246\pi\) | ||||
0.500237 | + | 0.865888i | \(0.333246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.415501 | 0.0171204 | ||||||||
\(590\) | 68.3368 | 2.81338 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.8822 | −0.734956 | ||||||||
\(593\) | −45.7326 | −1.87801 | −0.939007 | − | 0.343898i | \(-0.888253\pi\) | ||||
−0.939007 | + | 0.343898i | \(0.888253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.66686 | 0.232123 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.46310 | −0.100724 | ||||||||
\(599\) | −30.1668 | −1.23258 | −0.616290 | − | 0.787519i | \(-0.711365\pi\) | ||||
−0.616290 | + | 0.787519i | \(0.711365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.7387 | −0.601202 | −0.300601 | − | 0.953750i | \(-0.597187\pi\) | ||||
−0.300601 | + | 0.953750i | \(0.597187\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.98830 | −0.0809027 | ||||||||
\(605\) | 91.6569 | 3.72638 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.07836 | −0.246713 | −0.123356 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123356 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(608\) | −11.2788 | −0.457417 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −72.7859 | −2.94702 | ||||||||
\(611\) | 6.40877 | 0.259271 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7734 | 0.475522 | 0.237761 | − | 0.971324i | \(-0.423587\pi\) | ||||
0.237761 | + | 0.971324i | \(0.423587\pi\) | |||||||
\(614\) | −1.82213 | −0.0735352 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.0637 | 1.29084 | 0.645418 | − | 0.763829i | \(-0.276683\pi\) | ||||
0.645418 | + | 0.763829i | \(0.276683\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5518 | −0.504498 | −0.252249 | − | 0.967662i | \(-0.581170\pi\) | ||||
−0.252249 | + | 0.967662i | \(0.581170\pi\) | |||||||
\(620\) | −0.649282 | −0.0260758 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.30441 | −0.212688 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.85989 | −0.314396 | ||||||||
\(626\) | −48.6249 | −1.94344 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.99022 | −0.119323 | ||||||||
\(629\) | 4.30619 | 0.171699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4642 | 1.33219 | 0.666095 | − | 0.745867i | \(-0.267964\pi\) | ||||
0.666095 | + | 0.745867i | \(0.267964\pi\) | |||||||
\(632\) | 16.2138 | 0.644950 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.1809 | −0.880915 | ||||||||
\(635\) | −34.8575 | −1.38328 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 65.2553 | 2.58348 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −43.0148 | −1.70031 | ||||||||
\(641\) | −18.9837 | −0.749809 | −0.374905 | − | 0.927063i | \(-0.622325\pi\) | ||||
−0.374905 | + | 0.927063i | \(0.622325\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.62695 | −0.379650 | −0.189825 | − | 0.981818i | \(-0.560792\pi\) | ||||
−0.189825 | + | 0.981818i | \(0.560792\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.58445 | 0.180373 | ||||||||
\(647\) | −7.81214 | −0.307127 | −0.153564 | − | 0.988139i | \(-0.549075\pi\) | ||||
−0.153564 | + | 0.988139i | \(0.549075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 68.6326 | 2.69406 | ||||||||
\(650\) | 14.1906 | 0.556599 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.28751 | −0.207075 | ||||||||
\(653\) | 31.7429 | 1.24219 | 0.621097 | − | 0.783734i | \(-0.286687\pi\) | ||||
0.621097 | + | 0.783734i | \(0.286687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.5512 | −2.09242 | ||||||||
\(656\) | 16.8308 | 0.657132 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.21370 | −0.242051 | −0.121026 | − | 0.992649i | \(-0.538618\pi\) | ||||
−0.121026 | + | 0.992649i | \(0.538618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5263 | 1.07065 | 0.535324 | − | 0.844647i | \(-0.320190\pi\) | ||||
0.535324 | + | 0.844647i | \(0.320190\pi\) | |||||||
\(662\) | 37.2189 | 1.44655 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.19870 | −0.0853260 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.90169 | −0.305955 | ||||||||
\(668\) | 16.2971 | 0.630553 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 47.9878 | 1.85393 | ||||||||
\(671\) | −73.1010 | −2.82203 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2179 | 0.625154 | 0.312577 | − | 0.949892i | \(-0.398808\pi\) | ||||
0.312577 | + | 0.949892i | \(0.398808\pi\) | |||||||
\(674\) | 21.7670 | 0.838434 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5240 | −0.443230 | ||||||||
\(677\) | −20.5090 | −0.788225 | −0.394112 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394112 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.43864 | 0.285259 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.98128 | −0.0758673 | ||||||||
\(683\) | −0.112308 | −0.00429736 | −0.00214868 | − | 0.999998i | \(-0.500684\pi\) | ||||
−0.00214868 | + | 0.999998i | \(0.500684\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5902 | 0.824918 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.0262 | −0.725368 | ||||||||
\(689\) | 9.34118 | 0.355871 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8670 | 0.717735 | 0.358868 | − | 0.933388i | \(-0.383163\pi\) | ||||
0.358868 | + | 0.933388i | \(0.383163\pi\) | |||||||
\(692\) | −17.3182 | −0.658340 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.9480 | −1.51640 | ||||||||
\(695\) | −3.08161 | −0.116892 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.05299 | −0.153518 | ||||||||
\(698\) | 28.4665 | 1.07747 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.16006 | −0.119354 | −0.0596770 | − | 0.998218i | \(-0.519007\pi\) | ||||
−0.0596770 | + | 0.998218i | \(0.519007\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.88796 | −0.297500 | ||||||||
\(704\) | −7.11984 | −0.268339 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 42.2804 | 1.59124 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5211 | −0.808243 | −0.404121 | − | 0.914705i | \(-0.632423\pi\) | ||||
−0.404121 | + | 0.914705i | \(0.632423\pi\) | |||||||
\(710\) | 74.0174 | 2.77782 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.74771 | 0.365311 | ||||||||
\(713\) | 0.239911 | 0.00898475 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.9653 | 0.896250 | ||||||||
\(716\) | 2.57898 | 0.0963812 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.3570 | −1.31951 | ||||||||
\(719\) | −18.8302 | −0.702246 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.4079 | 0.908369 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.89914 | 0.144910 | ||||||||
\(725\) | 45.5237 | 1.69071 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.0853 | 1.44959 | 0.724797 | − | 0.688963i | \(-0.241934\pi\) | ||||
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 32.2306 | 1.19291 | ||||||||
\(731\) | 4.58167 | 0.169459 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.5985 | 0.686951 | 0.343475 | − | 0.939162i | \(-0.388396\pi\) | ||||
0.343475 | + | 0.939162i | \(0.388396\pi\) | |||||||
\(734\) | −38.4237 | −1.41825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.51243 | −0.240051 | ||||||||
\(737\) | 48.1954 | 1.77530 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.50136 | 0.202371 | 0.101185 | − | 0.994868i | \(-0.467736\pi\) | ||||
0.101185 | + | 0.994868i | \(0.467736\pi\) | |||||||
\(740\) | 12.3261 | 0.453117 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.4653 | −0.750797 | −0.375399 | − | 0.926863i | \(-0.622494\pi\) | ||||
−0.375399 | + | 0.926863i | \(0.622494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.2855 | 0.743201 | ||||||||
\(746\) | 56.1785 | 2.05684 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.19489 | −0.263071 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.0460 | 1.38832 | 0.694159 | − | 0.719822i | \(-0.255777\pi\) | ||||
0.694159 | + | 0.719822i | \(0.255777\pi\) | |||||||
\(752\) | 28.6015 | 1.04299 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0027 | 0.437113 | ||||||||
\(755\) | −7.11744 | −0.259030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.0780 | −1.85646 | −0.928230 | − | 0.372006i | \(-0.878670\pi\) | ||||
−0.928230 | + | 0.372006i | \(0.878670\pi\) | |||||||
\(758\) | −2.66658 | −0.0968546 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.6259 | −0.494263 | ||||||||
\(761\) | −40.0749 | −1.45271 | −0.726357 | − | 0.687317i | \(-0.758788\pi\) | ||||
−0.726357 | + | 0.687317i | \(0.758788\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.8633 | −0.646273 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −54.6116 | −1.97320 | ||||||||
\(767\) | 12.6239 | 0.455822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.9656 | −1.62150 | −0.810751 | − | 0.585391i | \(-0.800941\pi\) | ||||
−0.810751 | + | 0.585391i | \(0.800941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.198577 | −0.00714695 | ||||||||
\(773\) | −24.3561 | −0.876029 | −0.438014 | − | 0.898968i | \(-0.644318\pi\) | ||||
−0.438014 | + | 0.898968i | \(0.644318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.38219 | −0.0496498 | ||||||||
\(776\) | −28.9997 | −1.04103 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.05826 | 0.324754 | ||||||||
\(779\) | 7.42416 | 0.265998 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 74.3377 | 2.66001 | ||||||||
\(782\) | 2.64707 | 0.0946592 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.7040 | −0.382042 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.5233 | 1.48015 | 0.740073 | − | 0.672526i | \(-0.234791\pi\) | ||||
0.740073 | + | 0.672526i | \(0.234791\pi\) | |||||||
\(788\) | −1.60066 | −0.0570212 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −55.8962 | −1.98870 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.4458 | −0.477474 | ||||||||
\(794\) | −0.0477147 | −0.00169333 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.17372 | 0.218822 | ||||||||
\(797\) | 34.6036 | 1.22572 | 0.612861 | − | 0.790191i | \(-0.290019\pi\) | ||||
0.612861 | + | 0.790191i | \(0.290019\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.88747 | −0.243661 | ||||||||
\(800\) | 37.5198 | 1.32653 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.9571 | −0.740020 | ||||||||
\(803\) | 32.3701 | 1.14232 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.364427 | −0.0128364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22.8047 | −0.802266 | ||||||||
\(809\) | −11.2519 | −0.395597 | −0.197799 | − | 0.980243i | \(-0.563379\pi\) | ||||
−0.197799 | + | 0.980243i | \(0.563379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6803 | −1.04222 | −0.521108 | − | 0.853491i | \(-0.674481\pi\) | ||||
−0.521108 | + | 0.853491i | \(0.674481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 37.6132 | 1.31834 | ||||||||
\(815\) | −18.9275 | −0.663002 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.39258 | −0.293619 | ||||||||
\(818\) | −54.1211 | −1.89230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6014 | −0.405137 | ||||||||
\(821\) | 34.6431 | 1.20905 | 0.604526 | − | 0.796585i | \(-0.293362\pi\) | ||||
0.604526 | + | 0.796585i | \(0.293362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.3870 | 1.26837 | 0.634186 | − | 0.773180i | \(-0.281335\pi\) | ||||
0.634186 | + | 0.773180i | \(0.281335\pi\) | |||||||
\(824\) | 4.75276 | 0.165570 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.3576 | −0.846997 | −0.423498 | − | 0.905897i | \(-0.639198\pi\) | ||||
−0.423498 | + | 0.905897i | \(0.639198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.1702 | 1.36044 | 0.680219 | − | 0.733009i | \(-0.261885\pi\) | ||||
0.680219 | + | 0.733009i | \(0.261885\pi\) | |||||||
\(830\) | 7.57989 | 0.263102 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.30958 | −0.0454017 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.3381 | 2.01887 | ||||||||
\(836\) | 13.1794 | 0.455819 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.7030 | 0.887894 | ||||||||
\(839\) | 34.3477 | 1.18581 | 0.592907 | − | 0.805271i | \(-0.297980\pi\) | ||||
0.592907 | + | 0.805271i | \(0.297980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.50500 | 0.327759 | ||||||||
\(842\) | −15.6850 | −0.540541 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.9809 | −0.550085 | ||||||||
\(845\) | −41.2520 | −1.41911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 41.6884 | 1.43159 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.2505 | −0.523088 | ||||||||
\(851\) | −4.55454 | −0.156127 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.6743 | 1.11875 | 0.559373 | − | 0.828916i | \(-0.311042\pi\) | ||||
0.559373 | + | 0.828916i | \(0.311042\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.313965 | −0.0107311 | ||||||||
\(857\) | −57.6679 | −1.96990 | −0.984950 | − | 0.172841i | \(-0.944705\pi\) | ||||
−0.984950 | + | 0.172841i | \(0.944705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.9768 | 1.02279 | 0.511397 | − | 0.859344i | \(-0.329128\pi\) | ||||
0.511397 | + | 0.859344i | \(0.329128\pi\) | |||||||
\(860\) | 13.1147 | 0.447206 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.7231 | 0.978311 | ||||||||
\(863\) | −23.1776 | −0.788974 | −0.394487 | − | 0.918901i | \(-0.629078\pi\) | ||||
−0.394487 | + | 0.918901i | \(0.629078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.9934 | −2.10784 | ||||||||
\(866\) | −34.0873 | −1.15833 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −56.1381 | −1.90435 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.86480 | 0.300372 | ||||||||
\(872\) | 16.4626 | 0.557493 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.84884 | −0.164014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.739956 | −0.0249865 | −0.0124933 | − | 0.999922i | \(-0.503977\pi\) | ||||
−0.0124933 | + | 0.999922i | \(0.503977\pi\) | |||||||
\(878\) | 11.6290 | 0.392458 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 106.954 | 3.60540 | ||||||||
\(881\) | −18.0285 | −0.607395 | −0.303697 | − | 0.952769i | \(-0.598221\pi\) | ||||
−0.303697 | + | 0.952769i | \(0.598221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0928 | 1.45019 | 0.725095 | − | 0.688649i | \(-0.241796\pi\) | ||||
0.725095 | + | 0.688649i | \(0.241796\pi\) | |||||||
\(884\) | −1.32339 | −0.0445104 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.4507 | −1.66133 | ||||||||
\(887\) | −30.9527 | −1.03929 | −0.519645 | − | 0.854382i | \(-0.673936\pi\) | ||||
−0.519645 | + | 0.854382i | \(0.673936\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −33.6047 | −1.12643 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.5937 | 0.656046 | ||||||||
\(893\) | 12.6163 | 0.422187 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.23190 | 0.308588 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.5143 | 0.384236 | ||||||||
\(899\) | −1.16909 | −0.0389913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0389 | −0.334444 | ||||||||
\(902\) | −35.4016 | −1.17874 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.8123 | −0.492649 | ||||||||
\(905\) | 13.9576 | 0.463966 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.8083 | −1.42143 | −0.710714 | − | 0.703481i | \(-0.751628\pi\) | ||||
−0.710714 | + | 0.703481i | \(0.751628\pi\) | |||||||
\(908\) | 3.54485 | 0.117640 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.09738 | −0.202015 | −0.101008 | − | 0.994886i | \(-0.532207\pi\) | ||||
−0.101008 | + | 0.994886i | \(0.532207\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.61269 | 0.251943 | ||||||||
\(914\) | 49.4800 | 1.63665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.4566 | 0.444619 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8613 | 0.820100 | 0.410050 | − | 0.912063i | \(-0.365511\pi\) | ||||
0.410050 | + | 0.912063i | \(0.365511\pi\) | |||||||
\(920\) | −7.86764 | −0.259388 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.5621 | −1.13824 | ||||||||
\(923\) | 13.6733 | 0.450061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.2399 | 0.862762 | ||||||||
\(926\) | −17.1207 | −0.562621 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 31.7351 | 1.04176 | ||||||||
\(929\) | −41.8402 | −1.37273 | −0.686366 | − | 0.727256i | \(-0.740795\pi\) | ||||
−0.686366 | + | 0.727256i | \(0.740795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.7790 | −0.811663 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.7651 | 0.908502 | ||||||||
\(935\) | −25.7553 | −0.842288 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.2537 | −0.955676 | −0.477838 | − | 0.878448i | \(-0.658579\pi\) | ||||
−0.477838 | + | 0.878448i | \(0.658579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.7148 | −0.643026 | ||||||||
\(941\) | −3.35737 | −0.109447 | −0.0547236 | − | 0.998502i | \(-0.517428\pi\) | ||||
−0.0547236 | + | 0.998502i | \(0.517428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.28673 | 0.139595 | ||||||||
\(944\) | 56.3387 | 1.83367 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0194 | 1.30114 | ||||||||
\(947\) | 5.26601 | 0.171122 | 0.0855612 | − | 0.996333i | \(-0.472732\pi\) | ||||
0.0855612 | + | 0.996333i | \(0.472732\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.95398 | 0.193274 | ||||||||
\(950\) | 27.9354 | 0.906345 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.2520 | 1.82218 | 0.911090 | − | 0.412208i | \(-0.135242\pi\) | ||||
0.911090 | + | 0.412208i | \(0.135242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.9448 | −2.06921 | ||||||||
\(956\) | 8.82075 | 0.285284 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.1626 | −0.457573 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9645 | −0.998855 | ||||||||
\(962\) | 6.91836 | 0.223057 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.08306 | 0.292546 | ||||||||
\(965\) | −0.710840 | −0.0228828 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.7728 | 0.442904 | 0.221452 | − | 0.975171i | \(-0.428920\pi\) | ||||
0.221452 | + | 0.975171i | \(0.428920\pi\) | |||||||
\(968\) | 45.9052 | 1.47545 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 99.9748 | 3.21000 | ||||||||
\(971\) | 51.3254 | 1.64711 | 0.823555 | − | 0.567236i | \(-0.191987\pi\) | ||||
0.823555 | + | 0.567236i | \(0.191987\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.72538 | −0.151411 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −60.0066 | −1.92077 | ||||||||
\(977\) | 17.6850 | 0.565794 | 0.282897 | − | 0.959150i | \(-0.408704\pi\) | ||||
0.282897 | + | 0.959150i | \(0.408704\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.7501 | −1.07866 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34.0309 | 1.08597 | ||||||||
\(983\) | 16.0041 | 0.510453 | 0.255226 | − | 0.966881i | \(-0.417850\pi\) | ||||
0.255226 | + | 0.966881i | \(0.417850\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.72984 | −0.182568 | ||||||||
\(986\) | −12.8992 | −0.410795 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.42415 | 0.0771224 | ||||||||
\(989\) | −4.84590 | −0.154091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.8664 | −0.345182 | −0.172591 | − | 0.984994i | \(-0.555214\pi\) | ||||
−0.172591 | + | 0.984994i | \(0.555214\pi\) | |||||||
\(992\) | −0.963543 | −0.0305925 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.0998 | 0.700612 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.0375 | −1.29967 | −0.649835 | − | 0.760075i | \(-0.725162\pi\) | ||||
−0.649835 | + | 0.760075i | \(0.725162\pi\) | |||||||
\(998\) | 57.1438 | 1.80886 | ||||||||
\(999\) | 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 | 3969.2.a.bh.1.4 | 12 | ||
3.2 | odd | 2 | 3969.2.a.bi.1.9 | 12 | |||
7.6 | odd | 2 | inner | 3969.2.a.bh.1.3 | 12 | ||
9.2 | odd | 6 | 1323.2.f.h.442.4 | 24 | |||
9.4 | even | 3 | 441.2.f.h.295.10 | yes | 24 | ||
9.5 | odd | 6 | 1323.2.f.h.883.4 | 24 | |||
9.7 | even | 3 | 441.2.f.h.148.10 | yes | 24 | ||
21.20 | even | 2 | 3969.2.a.bi.1.10 | 12 | |||
63.2 | odd | 6 | 1323.2.g.h.361.3 | 24 | |||
63.4 | even | 3 | 441.2.g.h.79.10 | 24 | |||
63.5 | even | 6 | 1323.2.h.h.802.10 | 24 | |||
63.11 | odd | 6 | 1323.2.h.h.226.9 | 24 | |||
63.13 | odd | 6 | 441.2.f.h.295.9 | yes | 24 | ||
63.16 | even | 3 | 441.2.g.h.67.10 | 24 | |||
63.20 | even | 6 | 1323.2.f.h.442.3 | 24 | |||
63.23 | odd | 6 | 1323.2.h.h.802.9 | 24 | |||
63.25 | even | 3 | 441.2.h.h.373.3 | 24 | |||
63.31 | odd | 6 | 441.2.g.h.79.9 | 24 | |||
63.32 | odd | 6 | 1323.2.g.h.667.3 | 24 | |||
63.34 | odd | 6 | 441.2.f.h.148.9 | ✓ | 24 | ||
63.38 | even | 6 | 1323.2.h.h.226.10 | 24 | |||
63.40 | odd | 6 | 441.2.h.h.214.4 | 24 | |||
63.41 | even | 6 | 1323.2.f.h.883.3 | 24 | |||
63.47 | even | 6 | 1323.2.g.h.361.4 | 24 | |||
63.52 | odd | 6 | 441.2.h.h.373.4 | 24 | |||
63.58 | even | 3 | 441.2.h.h.214.3 | 24 | |||
63.59 | even | 6 | 1323.2.g.h.667.4 | 24 | |||
63.61 | odd | 6 | 441.2.g.h.67.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.9 | ✓ | 24 | 63.34 | odd | 6 | ||
441.2.f.h.148.10 | yes | 24 | 9.7 | even | 3 | ||
441.2.f.h.295.9 | yes | 24 | 63.13 | odd | 6 | ||
441.2.f.h.295.10 | yes | 24 | 9.4 | even | 3 | ||
441.2.g.h.67.9 | 24 | 63.61 | odd | 6 | |||
441.2.g.h.67.10 | 24 | 63.16 | even | 3 | |||
441.2.g.h.79.9 | 24 | 63.31 | odd | 6 | |||
441.2.g.h.79.10 | 24 | 63.4 | even | 3 | |||
441.2.h.h.214.3 | 24 | 63.58 | even | 3 | |||
441.2.h.h.214.4 | 24 | 63.40 | odd | 6 | |||
441.2.h.h.373.3 | 24 | 63.25 | even | 3 | |||
441.2.h.h.373.4 | 24 | 63.52 | odd | 6 | |||
1323.2.f.h.442.3 | 24 | 63.20 | even | 6 | |||
1323.2.f.h.442.4 | 24 | 9.2 | odd | 6 | |||
1323.2.f.h.883.3 | 24 | 63.41 | even | 6 | |||
1323.2.f.h.883.4 | 24 | 9.5 | odd | 6 | |||
1323.2.g.h.361.3 | 24 | 63.2 | odd | 6 | |||
1323.2.g.h.361.4 | 24 | 63.47 | even | 6 | |||
1323.2.g.h.667.3 | 24 | 63.32 | odd | 6 | |||
1323.2.g.h.667.4 | 24 | 63.59 | even | 6 | |||
1323.2.h.h.226.9 | 24 | 63.11 | odd | 6 | |||
1323.2.h.h.226.10 | 24 | 63.38 | even | 6 | |||
1323.2.h.h.802.9 | 24 | 63.23 | odd | 6 | |||
1323.2.h.h.802.10 | 24 | 63.5 | even | 6 | |||
3969.2.a.bh.1.3 | 12 | 7.6 | odd | 2 | inner | ||
3969.2.a.bh.1.4 | 12 | 1.1 | even | 1 | trivial | ||
3969.2.a.bi.1.9 | 12 | 3.2 | odd | 2 | |||
3969.2.a.bi.1.10 | 12 | 21.20 | even | 2 |