Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9408,2,Mod(1,9408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9408, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9408.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9408.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: | \(75.1232582216\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.14510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9408.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.74657 | −1.22830 | −0.614151 | − | 0.789188i | \(-0.710502\pi\) | ||||
−0.614151 | + | 0.789188i | \(0.710502\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.54364 | −0.465424 | −0.232712 | − | 0.972546i | \(-0.574760\pi\) | ||||
−0.232712 | + | 0.972546i | \(0.574760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.03677 | −1.67430 | −0.837150 | − | 0.546974i | \(-0.815780\pi\) | ||||
−0.837150 | + | 0.546974i | \(0.815780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.74657 | 0.709161 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.49314 | 1.81735 | 0.908676 | − | 0.417501i | \(-0.137094\pi\) | ||||
0.908676 | + | 0.417501i | \(0.137094\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.03677 | 1.38493 | 0.692465 | − | 0.721451i | \(-0.256525\pi\) | ||||
0.692465 | + | 0.721451i | \(0.256525\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.49314 | −1.56243 | −0.781213 | − | 0.624264i | \(-0.785399\pi\) | ||||
−0.781213 | + | 0.624264i | \(0.785399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.54364 | 0.508727 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.25343 | −0.232756 | −0.116378 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116378 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.29021 | 0.950149 | 0.475074 | − | 0.879946i | \(-0.342421\pi\) | ||||
0.475074 | + | 0.879946i | \(0.342421\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.54364 | 0.268713 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.94950 | −0.813693 | −0.406846 | − | 0.913497i | \(-0.633372\pi\) | ||||
−0.406846 | + | 0.913497i | \(0.633372\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.03677 | 0.966657 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.08727 | −0.794499 | −0.397249 | − | 0.917711i | \(-0.630035\pi\) | ||||
−0.397249 | + | 0.917711i | \(0.630035\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.45636 | −0.527090 | −0.263545 | − | 0.964647i | \(-0.584892\pi\) | ||||
−0.263545 | + | 0.964647i | \(0.584892\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.74657 | −0.409434 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.49314 | 1.38472 | 0.692358 | − | 0.721554i | \(-0.256572\pi\) | ||||
0.692358 | + | 0.721554i | \(0.256572\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.49314 | −1.04925 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.83384 | 0.526619 | 0.263309 | − | 0.964711i | \(-0.415186\pi\) | ||||
0.263309 | + | 0.964711i | \(0.415186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.23970 | 0.571682 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.03677 | −0.799590 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.54364 | −0.721720 | −0.360860 | − | 0.932620i | \(-0.617517\pi\) | ||||
−0.360860 | + | 0.932620i | \(0.617517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5804 | 1.86683 | 0.933415 | − | 0.358798i | \(-0.116813\pi\) | ||||
0.933415 | + | 0.358798i | \(0.116813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.5804 | 2.05655 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.03677 | 0.493170 | 0.246585 | − | 0.969121i | \(-0.420691\pi\) | ||||
0.246585 | + | 0.969121i | \(0.420691\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.49314 | 0.902068 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.49314 | −0.651915 | −0.325958 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325958 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.5436 | 1.46812 | 0.734061 | − | 0.679084i | \(-0.237623\pi\) | ||||
0.734061 | + | 0.679084i | \(0.237623\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.54364 | −0.293714 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.79707 | −0.877239 | −0.438619 | − | 0.898673i | \(-0.644532\pi\) | ||||
−0.438619 | + | 0.898673i | \(0.644532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.52991 | 0.716751 | 0.358375 | − | 0.933578i | \(-0.383331\pi\) | ||||
0.358375 | + | 0.933578i | \(0.383331\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.5804 | −2.23226 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.25343 | 0.134382 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.49314 | −1.00627 | −0.503135 | − | 0.864208i | \(-0.667820\pi\) | ||||
−0.503135 | + | 0.864208i | \(0.667820\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.29021 | −0.548569 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.5804 | −1.70111 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.54364 | 0.156733 | 0.0783663 | − | 0.996925i | \(-0.475030\pi\) | ||||
0.0783663 | + | 0.996925i | \(0.475030\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.54364 | −0.155141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.58041 | 0.256760 | 0.128380 | − | 0.991725i | \(-0.459022\pi\) | ||||
0.128380 | + | 0.991725i | \(0.459022\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.54364 | 0.644764 | 0.322382 | − | 0.946610i | \(-0.395516\pi\) | ||||
0.322382 | + | 0.946610i | \(0.395516\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.52991 | 0.437923 | 0.218961 | − | 0.975734i | \(-0.429733\pi\) | ||||
0.218961 | + | 0.975734i | \(0.429733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.44264 | 0.617093 | 0.308546 | − | 0.951209i | \(-0.400158\pi\) | ||||
0.308546 | + | 0.951209i | \(0.400158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.94950 | 0.469786 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.5804 | 1.91913 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.03677 | −0.558100 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.61718 | −0.783380 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.08727 | 0.458704 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.74657 | 0.603431 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.79707 | 0.336935 | 0.168468 | − | 0.985707i | \(-0.446118\pi\) | ||||
0.168468 | + | 0.985707i | \(0.446118\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.45636 | 0.304316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.54364 | −0.134868 | −0.0674341 | − | 0.997724i | \(-0.521481\pi\) | ||||
−0.0674341 | + | 0.997724i | \(0.521481\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.74657 | 0.236387 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.49314 | 0.127567 | 0.0637836 | − | 0.997964i | \(-0.479683\pi\) | ||||
0.0637836 | + | 0.997964i | \(0.479683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.94950 | 0.250173 | 0.125087 | − | 0.992146i | \(-0.460079\pi\) | ||||
0.125087 | + | 0.992146i | \(0.460079\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.49314 | −0.799466 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.31859 | 0.779259 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.44264 | 0.285895 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.49314 | 0.122323 | 0.0611613 | − | 0.998128i | \(-0.480520\pi\) | ||||
0.0611613 | + | 0.998128i | \(0.480520\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.73284 | 0.792047 | 0.396024 | − | 0.918240i | \(-0.370390\pi\) | ||||
0.396024 | + | 0.918240i | \(0.370390\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.49314 | 0.605784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.5299 | −1.16707 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.08727 | −0.725243 | −0.362622 | − | 0.931936i | \(-0.618118\pi\) | ||||
−0.362622 | + | 0.931936i | \(0.618118\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.83384 | −0.304043 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.5667 | −1.53258 | −0.766290 | − | 0.642494i | \(-0.777900\pi\) | ||||
−0.766290 | + | 0.642494i | \(0.777900\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.23970 | −0.330061 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.8990 | −0.920772 | −0.460386 | − | 0.887719i | \(-0.652289\pi\) | ||||
−0.460386 | + | 0.887719i | \(0.652289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.4426 | 1.80328 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.03677 | 0.461644 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.58041 | −0.196185 | −0.0980925 | − | 0.995177i | \(-0.531274\pi\) | ||||
−0.0980925 | + | 0.995177i | \(0.531274\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.54364 | 0.416685 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.98627 | 0.223205 | 0.111602 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111602 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5436 | 0.783702 | 0.391851 | − | 0.920029i | \(-0.371835\pi\) | ||||
0.391851 | + | 0.920029i | \(0.371835\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.5804 | −1.07781 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.5941 | 0.999461 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.5667 | −0.845840 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.1608 | 1.24171 | 0.620857 | − | 0.783924i | \(-0.286785\pi\) | ||||
0.620857 | + | 0.783924i | \(0.286785\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8990 | 0.784527 | 0.392264 | − | 0.919853i | \(-0.371692\pi\) | ||||
0.392264 | + | 0.919853i | \(0.371692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.5804 | −1.18735 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.41959 | −0.386130 | −0.193065 | − | 0.981186i | \(-0.561843\pi\) | ||||
−0.193065 | + | 0.981186i | \(0.561843\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.9863 | −1.62945 | −0.814727 | − | 0.579845i | \(-0.803113\pi\) | ||||
−0.814727 | + | 0.579845i | \(0.803113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.03677 | −0.284732 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9725 | 0.975885 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.49314 | −0.520809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.31859 | −0.644580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.08727 | −0.212537 | −0.106268 | − | 0.994337i | \(-0.533890\pi\) | ||||
−0.106268 | + | 0.994337i | \(0.533890\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.49314 | 0.376384 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.49314 | 0.647427 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.5436 | −0.847620 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −45.2344 | −3.04279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.7466 | −1.52322 | −0.761611 | − | 0.648034i | \(-0.775591\pi\) | ||||
−0.761611 | + | 0.648034i | \(0.775591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.54364 | 0.169576 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.6035 | −1.50024 | −0.750122 | − | 0.661299i | \(-0.770005\pi\) | ||||
−0.750122 | + | 0.661299i | \(0.770005\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3554 | 0.750383 | 0.375192 | − | 0.926947i | \(-0.377577\pi\) | ||||
0.375192 | + | 0.926947i | \(0.377577\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.41959 | 0.224025 | 0.112012 | − | 0.993707i | \(-0.464270\pi\) | ||||
0.112012 | + | 0.993707i | \(0.464270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.0735 | −1.70085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.79707 | 0.506474 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.49314 | −0.484691 | −0.242345 | − | 0.970190i | \(-0.577917\pi\) | ||||
−0.242345 | + | 0.970190i | \(0.577917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6035 | −1.19835 | −0.599177 | − | 0.800617i | \(-0.704505\pi\) | ||||
−0.599177 | + | 0.800617i | \(0.704505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.4426 | −2.31879 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.52991 | −0.413816 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.5299 | −1.54831 | −0.774157 | − | 0.632994i | \(-0.781826\pi\) | ||||
−0.774157 | + | 0.632994i | \(0.781826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5667 | 0.727191 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.5804 | 1.28880 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.4931 | −1.09119 | −0.545596 | − | 0.838048i | \(-0.683697\pi\) | ||||
−0.545596 | + | 0.838048i | \(0.683697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.25343 | −0.0775855 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.4931 | −0.832022 | −0.416011 | − | 0.909359i | \(-0.636572\pi\) | ||||
−0.416011 | + | 0.909359i | \(0.636572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5299 | −0.646847 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.49314 | 0.580971 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.34071 | −0.386600 | −0.193300 | − | 0.981140i | \(-0.561919\pi\) | ||||
−0.193300 | + | 0.981140i | \(0.561919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2397 | −1.22947 | −0.614737 | − | 0.788732i | \(-0.710738\pi\) | ||||
−0.614737 | + | 0.788732i | \(0.710738\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.92645 | −0.236774 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.54364 | 0.152832 | 0.0764162 | − | 0.997076i | \(-0.475652\pi\) | ||||
0.0764162 | + | 0.997076i | \(0.475652\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.29021 | 0.316716 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.5804 | 1.58565 | 0.792827 | − | 0.609447i | \(-0.208608\pi\) | ||||
0.792827 | + | 0.609447i | \(0.208608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.5436 | 1.22119 | 0.610596 | − | 0.791942i | \(-0.290930\pi\) | ||||
0.610596 | + | 0.791942i | \(0.290930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.5804 | 0.982139 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.1471 | 2.30277 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.54364 | −0.0904896 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.25343 | −0.306909 | −0.153454 | − | 0.988156i | \(-0.549040\pi\) | ||||
−0.153454 | + | 0.988156i | \(0.549040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2260 | 0.886491 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.54364 | 0.0895709 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 45.2344 | 2.61597 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.58041 | −0.148241 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.0461 | −2.29303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.8485 | −0.847449 | −0.423724 | − | 0.905791i | \(-0.639277\pi\) | ||||
−0.423724 | + | 0.905791i | \(0.639277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.54364 | −0.372255 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.89900 | −0.107682 | −0.0538412 | − | 0.998550i | \(-0.517146\pi\) | ||||
−0.0538412 | + | 0.998550i | \(0.517146\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.0872743 | −0.00493303 | −0.00246652 | − | 0.999997i | \(-0.500785\pi\) | ||||
−0.00246652 | + | 0.999997i | \(0.500785\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.23970 | −0.462788 | −0.231394 | − | 0.972860i | \(-0.574329\pi\) | ||||
−0.231394 | + | 0.972860i | \(0.574329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.93484 | 0.108330 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.52991 | −0.252835 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.2344 | 2.51691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.3554 | −0.851762 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.44264 | −0.356279 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.52991 | 0.303951 | 0.151976 | − | 0.988384i | \(-0.451436\pi\) | ||||
0.151976 | + | 0.988384i | \(0.451436\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.94950 | −0.271231 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0873 | −0.605763 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.17455 | 0.390823 | 0.195411 | − | 0.980721i | \(-0.437396\pi\) | ||||
0.195411 | + | 0.980721i | \(0.437396\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.00000 | −0.434500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.16616 | −0.442222 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.5804 | −1.10801 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0735 | −1.29234 | −0.646168 | − | 0.763195i | \(-0.723629\pi\) | ||||
−0.646168 | + | 0.763195i | \(0.723629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.1608 | 1.66800 | 0.834000 | − | 0.551764i | \(-0.186045\pi\) | ||||
0.834000 | + | 0.551764i | \(0.186045\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.03677 | 0.322219 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.1745 | −0.541537 | −0.270768 | − | 0.962645i | \(-0.587278\pi\) | ||||
−0.270768 | + | 0.962645i | \(0.587278\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.0873 | 0.800749 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.2481 | −1.70199 | −0.850995 | − | 0.525174i | \(-0.824000\pi\) | ||||
−0.850995 | + | 0.525174i | \(0.824000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4426 | 0.918033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.61718 | 0.452285 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.4520 | −1.80330 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.87062 | 0.202045 | 0.101022 | − | 0.994884i | \(-0.467789\pi\) | ||||
0.101022 | + | 0.994884i | \(0.467789\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.08727 | −0.264833 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.6907 | −1.79622 | −0.898109 | − | 0.439773i | \(-0.855059\pi\) | ||||
−0.898109 | + | 0.439773i | \(0.855059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.74657 | −0.348391 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.56668 | 0.389704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4564 | −0.691207 | −0.345603 | − | 0.938381i | \(-0.612326\pi\) | ||||
−0.345603 | + | 0.938381i | \(0.612326\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.79707 | −0.194530 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.17455 | 0.213309 | 0.106655 | − | 0.994296i | \(-0.465986\pi\) | ||||
0.106655 | + | 0.994296i | \(0.465986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.45636 | −0.175697 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.6540 | 0.945793 | 0.472897 | − | 0.881118i | \(-0.343208\pi\) | ||||
0.472897 | + | 0.881118i | \(0.343208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −56.1471 | −2.83948 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.54364 | 0.0778662 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.4152 | 1.07751 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.45636 | 0.0730928 | 0.0365464 | − | 0.999332i | \(-0.488364\pi\) | ||||
0.0365464 | + | 0.999332i | \(0.488364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.2344 | −1.45989 | −0.729947 | − | 0.683503i | \(-0.760455\pi\) | ||||
−0.729947 | + | 0.683503i | \(0.760455\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.9358 | −1.59083 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.74657 | −0.136478 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.64023 | 0.378712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0598 | 1.28858 | 0.644288 | − | 0.764783i | \(-0.277154\pi\) | ||||
0.644288 | + | 0.764783i | \(0.277154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.49314 | −0.0736510 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.9348 | −0.880387 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.94950 | −0.144438 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.8853 | −1.60655 | −0.803275 | − | 0.595608i | \(-0.796911\pi\) | ||||
−0.803275 | + | 0.595608i | \(0.796911\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1976 | 0.838160 | 0.419080 | − | 0.907949i | \(-0.362353\pi\) | ||||
0.419080 | + | 0.907949i | \(0.362353\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.49314 | 0.461572 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.0598 | 0.924537 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.31859 | −0.449906 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.98627 | 0.143844 | 0.0719219 | − | 0.997410i | \(-0.477087\pi\) | ||||
0.0719219 | + | 0.997410i | \(0.477087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.4426 | 0.886297 | 0.443148 | − | 0.896448i | \(-0.353862\pi\) | ||||
0.443148 | + | 0.896448i | \(0.353862\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.44264 | −0.165062 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45.2344 | −2.16385 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.572020 | 0.0273010 | 0.0136505 | − | 0.999907i | \(-0.495655\pi\) | ||||
0.0136505 | + | 0.999907i | \(0.495655\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.5299 | −1.73559 | −0.867794 | − | 0.496924i | \(-0.834463\pi\) | ||||
−0.867794 | + | 0.496924i | \(0.834463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.0735 | 1.23600 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.49314 | −0.0706229 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.5530 | −1.06434 | −0.532170 | − | 0.846638i | \(-0.678623\pi\) | ||||
−0.532170 | + | 0.846638i | \(0.678623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.85291 | 0.369779 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.73284 | −0.457289 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.2344 | 0.946524 | 0.473262 | − | 0.880922i | \(-0.343076\pi\) | ||||
0.473262 | + | 0.880922i | \(0.343076\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.49314 | −0.349750 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.4931 | −1.18733 | −0.593667 | − | 0.804711i | \(-0.702320\pi\) | ||||
−0.593667 | + | 0.804711i | \(0.702320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.70446 | −0.358057 | −0.179028 | − | 0.983844i | \(-0.557295\pi\) | ||||
−0.179028 | + | 0.983844i | \(0.557295\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.5299 | 0.673808 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.1471 | −1.67269 | −0.836344 | − | 0.548205i | \(-0.815311\pi\) | ||||
−0.836344 | + | 0.548205i | \(0.815311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.08727 | 0.418719 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.33537 | 0.245321 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.3554 | 0.704552 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.83384 | 0.175540 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.5804 | 1.21449 | 0.607245 | − | 0.794515i | \(-0.292275\pi\) | ||||
0.607245 | + | 0.794515i | \(0.292275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.8790 | 1.36237 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.23970 | −0.192515 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.4236 | −1.83177 | −0.915883 | − | 0.401444i | \(-0.868508\pi\) | ||||
−0.915883 | + | 0.401444i | \(0.868508\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.5667 | 0.884836 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6309 | −0.660284 | −0.330142 | − | 0.943931i | \(-0.607097\pi\) | ||||
−0.330142 | + | 0.943931i | \(0.607097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.39214 | −0.423000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.23970 | 0.190561 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.1103 | 1.61652 | 0.808260 | − | 0.588826i | \(-0.200410\pi\) | ||||
0.808260 | + | 0.588826i | \(0.200410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.8990 | 0.531608 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.4931 | 0.869156 | 0.434578 | − | 0.900634i | \(-0.356898\pi\) | ||||
0.434578 | + | 0.900634i | \(0.356898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.08727 | −0.315380 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.4426 | −1.04112 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.9074 | 1.05968 | 0.529838 | − | 0.848099i | \(-0.322253\pi\) | ||||
0.529838 | + | 0.848099i | \(0.322253\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.03677 | −0.266530 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.9725 | −0.791965 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.6540 | −0.644480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.58041 | 0.113267 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.08727 | −0.310499 | −0.155250 | − | 0.987875i | \(-0.549618\pi\) | ||||
−0.155250 | + | 0.987875i | \(0.549618\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.7475 | 1.25704 | 0.628520 | − | 0.777793i | \(-0.283661\pi\) | ||||
0.628520 | + | 0.777793i | \(0.283661\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.6402 | 1.72676 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.1471 | 1.44118 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.54364 | −0.240573 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.7107 | 1.33023 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.4417 | −0.537902 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.98627 | −0.128867 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.02305 | 0.301944 | 0.150972 | − | 0.988538i | \(-0.451760\pi\) | ||||
0.150972 | + | 0.988538i | \(0.451760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.5436 | −0.452471 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.6951 | −0.757976 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.59414 | −0.239188 | −0.119594 | − | 0.992823i | \(-0.538159\pi\) | ||||
−0.119594 | + | 0.992823i | \(0.538159\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.5804 | 0.622277 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.56668 | −0.322352 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.5941 | −0.577039 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.6456 | −1.21375 | −0.606876 | − | 0.794797i | \(-0.707577\pi\) | ||||
−0.606876 | + | 0.794797i | \(0.707577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.8653 | 0.882507 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.5667 | 0.488346 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.8927 | 0.838379 | 0.419189 | − | 0.907899i | \(-0.362314\pi\) | ||||
0.419189 | + | 0.907899i | \(0.362314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.9725 | −0.924392 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.6402 | 1.49412 | 0.747058 | − | 0.664759i | \(-0.231466\pi\) | ||||
0.747058 | + | 0.664759i | \(0.231466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.6770 | 1.15825 | 0.579123 | − | 0.815240i | \(-0.303395\pi\) | ||||
0.579123 | + | 0.815240i | \(0.303395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.1608 | −0.716904 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.0598 | −0.794849 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.01373 | −0.250355 | −0.125177 | − | 0.992134i | \(-0.539950\pi\) | ||||
−0.125177 | + | 0.992134i | \(0.539950\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.8990 | −0.452947 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.91806 | −0.245101 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.5804 | 0.685516 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5436 | −0.641555 | −0.320777 | − | 0.947155i | \(-0.603944\pi\) | ||||
−0.320777 | + | 0.947155i | \(0.603944\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.9358 | 1.31589 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.41959 | 0.222932 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −48.6540 | −1.99798 | −0.998989 | − | 0.0449488i | \(-0.985688\pi\) | ||||
−0.998989 | + | 0.0449488i | \(0.985688\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.9863 | 0.940766 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.9127 | −0.854471 | −0.427235 | − | 0.904140i | \(-0.640512\pi\) | ||||
−0.427235 | + | 0.904140i | \(0.640512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.98627 | −0.325767 | −0.162883 | − | 0.986645i | \(-0.552079\pi\) | ||||
−0.162883 | + | 0.986645i | \(0.552079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.03677 | 0.164390 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.6677 | 0.962228 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.70979 | 0.109987 | 0.0549936 | − | 0.998487i | \(-0.482486\pi\) | ||||
0.0549936 | + | 0.998487i | \(0.482486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −57.3079 | −2.31843 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.5069 | 0.666706 | 0.333353 | − | 0.942802i | \(-0.391820\pi\) | ||||
0.333353 | + | 0.942802i | \(0.391820\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.9725 | −0.563427 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.1608 | −0.932420 | −0.466210 | − | 0.884674i | \(-0.654381\pi\) | ||||
−0.466210 | + | 0.884674i | \(0.654381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.4289 | 1.18285 | 0.591424 | − | 0.806361i | \(-0.298566\pi\) | ||||
0.591424 | + | 0.806361i | \(0.298566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.49314 | 0.300689 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2481 | −1.24992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.31859 | 0.372149 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.0873 | −1.47877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7054 | −1.42141 | −0.710705 | − | 0.703491i | \(-0.751624\pi\) | ||||
−0.710705 | + | 0.703491i | \(0.751624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.08727 | 0.122708 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4289 | −0.413859 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.49314 | −0.217305 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.36282 | −0.132824 | −0.0664118 | − | 0.997792i | \(-0.521155\pi\) | ||||
−0.0664118 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.2113 | −0.402695 | −0.201348 | − | 0.979520i | \(-0.564532\pi\) | ||||
−0.201348 | + | 0.979520i | \(0.564532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.49314 | −0.373792 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.5530 | −0.808020 | −0.404010 | − | 0.914755i | \(-0.632384\pi\) | ||||
−0.404010 | + | 0.914755i | \(0.632384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.55736 | 0.335906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3544 | 0.444333 | 0.222167 | − | 0.975009i | \(-0.428687\pi\) | ||||
0.222167 | + | 0.975009i | \(0.428687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.23970 | 0.165659 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.5436 | 0.489374 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.2344 | −0.827174 | −0.413587 | − | 0.910465i | \(-0.635724\pi\) | ||||
−0.413587 | + | 0.910465i | \(0.635724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9220 | 1.12494 | 0.562469 | − | 0.826819i | \(-0.309852\pi\) | ||||
0.562469 | + | 0.826819i | \(0.309852\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 45.2344 | 1.75676 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.39214 | 0.363665 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.7466 | 0.879433 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.5069 | −0.868868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.2618 | −1.32070 | −0.660348 | − | 0.750960i | \(-0.729591\pi\) | ||||
−0.660348 | + | 0.750960i | \(0.729591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.54364 | −0.0979046 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.7466 | −1.33542 | −0.667710 | − | 0.744422i | \(-0.732725\pi\) | ||||
−0.667710 | + | 0.744422i | \(0.732725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.6035 | 0.866166 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.281814 | −0.0107833 | −0.00539166 | − | 0.999985i | \(-0.501716\pi\) | ||||
−0.00539166 | + | 0.999985i | \(0.501716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.10100 | −0.156691 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.3554 | −0.433234 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.1440 | −0.881718 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.4152 | −1.30922 | −0.654608 | − | 0.755969i | \(-0.727166\pi\) | ||||
−0.654608 | + | 0.755969i | \(0.727166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.10100 | −0.307288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.1196 | −1.44388 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.41959 | −0.129341 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.498472 | 0.0188270 | 0.00941352 | − | 0.999956i | \(-0.497004\pi\) | ||||
0.00941352 | + | 0.999956i | \(0.497004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.8790 | −1.12691 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.0735 | 0.981987 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.17455 | 0.156778 | 0.0783892 | − | 0.996923i | \(-0.475022\pi\) | ||||
0.0783892 | + | 0.996923i | \(0.475022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.79707 | −0.292413 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.6402 | −1.48454 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.5941 | −0.957166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.49314 | 0.279836 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.986273 | −0.0367818 | −0.0183909 | − | 0.999831i | \(-0.505854\pi\) | ||||
−0.0183909 | + | 0.999831i | \(0.505854\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.6035 | 0.691870 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.18828 | −0.118410 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.9304 | −1.29550 | −0.647749 | − | 0.761854i | \(-0.724289\pi\) | ||||
−0.647749 | + | 0.761854i | \(0.724289\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8990 | −0.957909 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.12405 | −0.189261 | −0.0946305 | − | 0.995512i | \(-0.530167\pi\) | ||||
−0.0946305 | + | 0.995512i | \(0.530167\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.23131 | −0.229533 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9220 | 0.622488 | 0.311244 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311244 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.4426 | 1.33875 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.81172 | 0.249898 | 0.124949 | − | 0.992163i | \(-0.460123\pi\) | ||||
0.124949 | + | 0.992163i | \(0.460123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.10100 | −0.150249 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.52991 | 0.238917 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.1755 | −0.955157 | −0.477578 | − | 0.878589i | \(-0.658485\pi\) | ||||
−0.477578 | + | 0.878589i | \(0.658485\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.5299 | 0.893920 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.7319 | −0.972874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.7138 | −1.80688 | −0.903439 | − | 0.428717i | \(-0.858966\pi\) | ||||
−0.903439 | + | 0.428717i | \(0.858966\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.5667 | −0.419844 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.6540 | −0.458706 | −0.229353 | − | 0.973343i | \(-0.573661\pi\) | ||||
−0.229353 | + | 0.973343i | \(0.573661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.5804 | −0.744086 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.4657 | 1.20838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.2344 | −0.729670 | −0.364835 | − | 0.931072i | \(-0.618875\pi\) | ||||
−0.364835 | + | 0.931072i | \(0.618875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.4931 | 0.630000 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.7412 | 0.710043 | 0.355021 | − | 0.934858i | \(-0.384474\pi\) | ||||
0.355021 | + | 0.934858i | \(0.384474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.4564 | 0.483367 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.7107 | −1.10033 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.47941 | 0.303417 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.25343 | 0.0447940 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.9588 | 0.890818 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.9127 | 0.602874 | 0.301437 | − | 0.953486i | \(-0.402534\pi\) | ||||
0.301437 | + | 0.953486i | \(0.402534\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.4931 | 0.480368 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −88.0186 | −3.12563 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.5299 | 0.373457 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.48475 | −0.123436 | −0.0617180 | − | 0.998094i | \(-0.519658\pi\) | ||||
−0.0617180 | + | 0.998094i | \(0.519658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 71.1334 | 2.51652 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.49314 | −0.335423 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.3628 | −0.683299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.34071 | 0.223203 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.1883 | −0.674624 | −0.337312 | − | 0.941393i | \(-0.609518\pi\) | ||||
−0.337312 | + | 0.941393i | \(0.609518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.8285 | 1.71460 | 0.857300 | − | 0.514817i | \(-0.172140\pi\) | ||||
0.857300 | + | 0.514817i | \(0.172140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.2397 | 0.709837 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.7412 | 1.88247 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.8653 | −0.729984 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5446 | 0.926412 | 0.463206 | − | 0.886251i | \(-0.346699\pi\) | ||||
0.463206 | + | 0.886251i | \(0.346699\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9588 | 0.591147 | 0.295574 | − | 0.955320i | \(-0.404489\pi\) | ||||
0.295574 | + | 0.955320i | \(0.404489\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.92645 | 0.136702 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.4289 | −1.47540 | −0.737699 | − | 0.675130i | \(-0.764088\pi\) | ||||
−0.737699 | + | 0.675130i | \(0.764088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.9358 | 1.10918 | 0.554588 | − | 0.832125i | \(-0.312876\pi\) | ||||
0.554588 | + | 0.832125i | \(0.312876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.54364 | −0.0882378 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.6814 | 1.13099 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.29021 | −0.182856 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.5392 | 1.71028 | 0.855142 | − | 0.518394i | \(-0.173470\pi\) | ||||
0.855142 | + | 0.518394i | \(0.173470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4289 | −0.945824 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.5804 | −0.915478 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −64.3868 | −2.21497 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.5436 | −0.705056 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.0873 | 1.27134 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4564 | −0.392258 | −0.196129 | − | 0.980578i | \(-0.562837\pi\) | ||||
−0.196129 | + | 0.980578i | \(0.562837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.5804 | −0.567038 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.2481 | −1.10157 | −0.550787 | − | 0.834646i | \(-0.685672\pi\) | ||||
−0.550787 | + | 0.834646i | \(0.685672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.08727 | 0.105336 | 0.0526682 | − | 0.998612i | \(-0.483227\pi\) | ||||
0.0526682 | + | 0.998612i | \(0.483227\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.1471 | −0.617734 | −0.308867 | − | 0.951105i | \(-0.599950\pi\) | ||||
−0.308867 | + | 0.951105i | \(0.599950\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.08727 | 0.240975 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.1471 | −1.32951 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0358 | 0.408288 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.3691 | −0.825715 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.54364 | 0.0522442 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.88527 | −0.300034 | −0.150017 | − | 0.988683i | \(-0.547933\pi\) | ||||
−0.150017 | + | 0.988683i | \(0.547933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.25343 | 0.177194 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.5667 | −1.40042 | −0.700209 | − | 0.713938i | \(-0.746910\pi\) | ||||
−0.700209 | + | 0.713938i | \(0.746910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.7182 | 0.966444 | 0.483222 | − | 0.875498i | \(-0.339466\pi\) | ||||
0.483222 | + | 0.875498i | \(0.339466\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.2260 | −0.511816 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.8148 | −1.40400 | −0.702001 | − | 0.712176i | \(-0.747710\pi\) | ||||
−0.702001 | + | 0.712176i | \(0.747710\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.54364 | −0.0517138 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.3079 | 1.91774 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.20200 | −0.274163 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −45.2344 | −1.51033 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.63091 | −0.221153 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.7275 | 0.957052 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.9588 | −0.962624 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.1701 | −1.89830 | −0.949152 | − | 0.314819i | \(-0.898056\pi\) | ||||
−0.949152 | + | 0.314819i | \(0.898056\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.58041 | 0.0855868 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.4059 | 0.808602 | 0.404301 | − | 0.914626i | \(-0.367515\pi\) | ||||
0.404301 | + | 0.914626i | \(0.367515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0798 | −0.333593 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40.0461 | 1.32388 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.7045 | −1.57362 | −0.786812 | − | 0.617192i | \(-0.788270\pi\) | ||||
−0.786812 | + | 0.617192i | \(0.788270\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.8485 | 0.489275 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.1608 | 1.09150 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.5897 | −0.413948 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.54364 | 0.214921 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.2344 | 1.28724 | 0.643619 | − | 0.765346i | \(-0.277432\pi\) | ||||
0.643619 | + | 0.765346i | \(0.277432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.89900 | 0.0621704 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.7687 | 1.03895 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.3491 | 0.501433 | 0.250717 | − | 0.968061i | \(-0.419334\pi\) | ||||
0.250717 | + | 0.968061i | \(0.419334\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.0872743 | 0.00284809 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.1662 | 0.396605 | 0.198303 | − | 0.980141i | \(-0.436457\pi\) | ||||
0.198303 | + | 0.980141i | \(0.436457\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.1196 | 1.24135 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.0598 | −0.619361 | −0.309680 | − | 0.950841i | \(-0.600222\pi\) | ||||
−0.309680 | + | 0.950841i | \(0.600222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −75.7231 | −2.45808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.23970 | 0.267191 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.1334 | 0.555004 | 0.277502 | − | 0.960725i | \(-0.410493\pi\) | ||||
0.277502 | + | 0.960725i | \(0.410493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.1334 | −1.52520 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.93484 | −0.0625446 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.01373 | −0.0972170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.52991 | 0.145974 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.9348 | −0.963637 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7833 | −0.861294 | −0.430647 | − | 0.902520i | \(-0.641715\pi\) | ||||
−0.430647 | + | 0.902520i | \(0.641715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45.2344 | −1.45314 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.5162 | 0.369572 | 0.184786 | − | 0.982779i | \(-0.440841\pi\) | ||||
0.184786 | + | 0.982779i | \(0.440841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.3554 | 0.491765 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.3354 | 0.682579 | 0.341289 | − | 0.939958i | \(-0.389136\pi\) | ||||
0.341289 | + | 0.939958i | \(0.389136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.6540 | 0.468343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.44264 | 0.205698 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.3952 | 1.60736 | 0.803678 | − | 0.595064i | \(-0.202873\pi\) | ||||
0.803678 | + | 0.595064i | \(0.202873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.8853 | 0.474284 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.8990 | 0.823540 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.6823 | −0.402868 | −0.201434 | − | 0.979502i | \(-0.564560\pi\) | ||||
−0.201434 | + | 0.979502i | \(0.564560\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.52991 | −0.175486 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 63.1334 | 2.00146 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.3416 | 1.27763 | 0.638816 | − | 0.769359i | \(-0.279424\pi\) | ||||
0.638816 | + | 0.769359i | \(0.279424\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.94950 | 0.156595 |
(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 | 9408.2.a.eh.1.1 | 3 | ||
4.3 | odd | 2 | 9408.2.a.ej.1.1 | 3 | |||
7.2 | even | 3 | 1344.2.q.z.193.3 | 6 | |||
7.4 | even | 3 | 1344.2.q.z.961.3 | 6 | |||
7.6 | odd | 2 | 9408.2.a.ei.1.3 | 3 | |||
8.3 | odd | 2 | 4704.2.a.bs.1.3 | 3 | |||
8.5 | even | 2 | 4704.2.a.bu.1.3 | 3 | |||
28.11 | odd | 6 | 1344.2.q.y.961.3 | 6 | |||
28.23 | odd | 6 | 1344.2.q.y.193.3 | 6 | |||
28.27 | even | 2 | 9408.2.a.eg.1.3 | 3 | |||
56.11 | odd | 6 | 672.2.q.l.289.1 | yes | 6 | ||
56.13 | odd | 2 | 4704.2.a.bt.1.1 | 3 | |||
56.27 | even | 2 | 4704.2.a.bv.1.1 | 3 | |||
56.37 | even | 6 | 672.2.q.k.193.1 | ✓ | 6 | ||
56.51 | odd | 6 | 672.2.q.l.193.1 | yes | 6 | ||
56.53 | even | 6 | 672.2.q.k.289.1 | yes | 6 | ||
168.11 | even | 6 | 2016.2.s.v.289.3 | 6 | |||
168.53 | odd | 6 | 2016.2.s.u.289.3 | 6 | |||
168.107 | even | 6 | 2016.2.s.v.865.3 | 6 | |||
168.149 | odd | 6 | 2016.2.s.u.865.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.k.193.1 | ✓ | 6 | 56.37 | even | 6 | ||
672.2.q.k.289.1 | yes | 6 | 56.53 | even | 6 | ||
672.2.q.l.193.1 | yes | 6 | 56.51 | odd | 6 | ||
672.2.q.l.289.1 | yes | 6 | 56.11 | odd | 6 | ||
1344.2.q.y.193.3 | 6 | 28.23 | odd | 6 | |||
1344.2.q.y.961.3 | 6 | 28.11 | odd | 6 | |||
1344.2.q.z.193.3 | 6 | 7.2 | even | 3 | |||
1344.2.q.z.961.3 | 6 | 7.4 | even | 3 | |||
2016.2.s.u.289.3 | 6 | 168.53 | odd | 6 | |||
2016.2.s.u.865.3 | 6 | 168.149 | odd | 6 | |||
2016.2.s.v.289.3 | 6 | 168.11 | even | 6 | |||
2016.2.s.v.865.3 | 6 | 168.107 | even | 6 | |||
4704.2.a.bs.1.3 | 3 | 8.3 | odd | 2 | |||
4704.2.a.bt.1.1 | 3 | 56.13 | odd | 2 | |||
4704.2.a.bu.1.3 | 3 | 8.5 | even | 2 | |||
4704.2.a.bv.1.1 | 3 | 56.27 | even | 2 | |||
9408.2.a.eg.1.3 | 3 | 28.27 | even | 2 | |||
9408.2.a.eh.1.1 | 3 | 1.1 | even | 1 | trivial | ||
9408.2.a.ei.1.3 | 3 | 7.6 | odd | 2 | |||
9408.2.a.ej.1.1 | 3 | 4.3 | odd | 2 |