Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1305,2,Mod(784,1305)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1305.784");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1305 = 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1305.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4204774638\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 4x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 145) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 784.2 | ||
Root | \(-0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1305.784 |
Dual form | 1305.2.c.f.784.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times\).
\(n\) | \(146\) | \(262\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.517638i | − | 0.366025i | −0.983111 | − | 0.183013i | \(-0.941415\pi\) | ||
0.983111 | − | 0.183013i | \(-0.0585849\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73205 | 0.866025 | ||||||||
\(5\) | 1.73205 | + | 1.41421i | 0.774597 | + | 0.632456i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.44949i | − | 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | − | 1.93185i | − | 0.683013i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.732051 | − | 0.896575i | 0.231495 | − | 0.283522i | ||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.79315i | 0.497331i | 0.968589 | + | 0.248665i | \(0.0799919\pi\) | ||||
−0.968589 | + | 0.248665i | \(0.920008\pi\) | |||||||
\(14\) | −1.26795 | −0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | − | 1.41421i | − | 0.342997i | −0.985184 | − | 0.171499i | \(-0.945139\pi\) | ||
0.985184 | − | 0.171499i | \(-0.0548609\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.26795 | 0.749719 | 0.374859 | − | 0.927082i | \(-0.377691\pi\) | ||||
0.374859 | + | 0.927082i | \(0.377691\pi\) | |||||||
\(20\) | 3.00000 | + | 2.44949i | 0.670820 | + | 0.547723i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.656339i | − | 0.139932i | ||||||
\(23\) | − | 6.31319i | − | 1.31639i | −0.752847 | − | 0.658196i | \(-0.771320\pi\) | ||
0.752847 | − | 0.658196i | \(-0.228680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 4.89898i | 0.200000 | + | 0.979796i | ||||
\(26\) | 0.928203 | 0.182036 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 4.24264i | − | 0.801784i | ||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.73205 | −1.56832 | −0.784161 | − | 0.620557i | \(-0.786907\pi\) | ||||
−0.784161 | + | 0.620557i | \(0.786907\pi\) | |||||||
\(32\) | − | 5.13922i | − | 0.908494i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.732051 | −0.125546 | ||||||||
\(35\) | 3.46410 | − | 4.24264i | 0.585540 | − | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.14162i | 1.50287i | 0.659805 | + | 0.751437i | \(0.270639\pi\) | ||||
−0.659805 | + | 0.751437i | \(0.729361\pi\) | |||||||
\(38\) | − | 1.69161i | − | 0.274416i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.73205 | − | 3.34607i | 0.431975 | − | 0.529059i | ||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.14162i | − | 1.39408i | −0.717030 | − | 0.697042i | \(-0.754499\pi\) | ||
0.717030 | − | 0.697042i | \(-0.245501\pi\) | |||||||
\(44\) | 2.19615 | 0.331082 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.26795 | −0.481833 | ||||||||
\(47\) | − | 1.41421i | − | 0.206284i | −0.994667 | − | 0.103142i | \(-0.967110\pi\) | ||
0.994667 | − | 0.103142i | \(-0.0328896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.53590 | − | 0.517638i | 0.358630 | − | 0.0732051i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.10583i | 0.430701i | ||||||||
\(53\) | 5.93426i | 0.815133i | 0.913176 | + | 0.407566i | \(0.133622\pi\) | ||||
−0.913176 | + | 0.407566i | \(0.866378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.19615 | + | 1.79315i | 0.296129 | + | 0.241788i | ||||
\(56\) | −4.73205 | −0.632347 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 0.517638i | − | 0.0679692i | ||||||
\(59\) | −10.3923 | −1.35296 | −0.676481 | − | 0.736460i | \(-0.736496\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92820 | 0.374918 | 0.187459 | − | 0.982272i | \(-0.439975\pi\) | ||||
0.187459 | + | 0.982272i | \(0.439975\pi\) | |||||||
\(62\) | 4.52004i | 0.574046i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.26795 | 0.283494 | ||||||||
\(65\) | −2.53590 | + | 3.10583i | −0.314539 | + | 0.385231i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.24264i | 0.518321i | 0.965834 | + | 0.259161i | \(0.0834459\pi\) | ||||
−0.965834 | + | 0.259161i | \(0.916554\pi\) | |||||||
\(68\) | − | 2.44949i | − | 0.297044i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.19615 | − | 1.79315i | −0.262490 | − | 0.214323i | ||||
\(71\) | −3.46410 | −0.411113 | −0.205557 | − | 0.978645i | \(-0.565900\pi\) | ||||
−0.205557 | + | 0.978645i | \(0.565900\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34847i | 0.860073i | 0.902811 | + | 0.430037i | \(0.141499\pi\) | ||||
−0.902811 | + | 0.430037i | \(0.858501\pi\) | |||||||
\(74\) | 4.73205 | 0.550090 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.66025 | 0.649276 | ||||||||
\(77\) | − | 3.10583i | − | 0.353942i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.19615 | 0.472104 | 0.236052 | − | 0.971740i | \(-0.424146\pi\) | ||||
0.236052 | + | 0.971740i | \(0.424146\pi\) | |||||||
\(80\) | 4.26795 | + | 3.48477i | 0.477171 | + | 0.389609i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.58630i | − | 0.396041i | ||||||
\(83\) | 10.1769i | 1.11706i | 0.829484 | + | 0.558530i | \(0.188634\pi\) | ||||
−0.829484 | + | 0.558530i | \(0.811366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 2.44949i | 0.216930 | − | 0.265684i | ||||
\(86\) | −4.73205 | −0.510270 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.44949i | − | 0.261116i | ||||||
\(89\) | 10.3923 | 1.10158 | 0.550791 | − | 0.834643i | \(-0.314326\pi\) | ||||
0.550791 | + | 0.834643i | \(0.314326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.39230 | 0.460439 | ||||||||
\(92\) | − | 10.9348i | − | 1.14003i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.732051 | −0.0755053 | ||||||||
\(95\) | 5.66025 | + | 4.62158i | 0.580730 | + | 0.474164i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.9348i | − | 1.11026i | −0.831764 | − | 0.555129i | \(-0.812669\pi\) | ||
0.831764 | − | 0.555129i | \(-0.187331\pi\) | |||||||
\(98\) | − | 0.517638i | − | 0.0522893i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.73205 | + | 8.48528i | 0.173205 | + | 0.848528i | ||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.14162i | − | 0.900751i | −0.892839 | − | 0.450375i | \(-0.851290\pi\) | ||
0.892839 | − | 0.450375i | \(-0.148710\pi\) | |||||||
\(104\) | 3.46410 | 0.339683 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.07180 | 0.298359 | ||||||||
\(107\) | 18.6622i | 1.80414i | 0.431589 | + | 0.902070i | \(0.357953\pi\) | ||||
−0.431589 | + | 0.902070i | \(0.642047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8564 | −1.71033 | −0.855167 | − | 0.518353i | \(-0.826545\pi\) | ||||
−0.855167 | + | 0.518353i | \(0.826545\pi\) | |||||||
\(110\) | 0.928203 | − | 1.13681i | 0.0885007 | − | 0.108391i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 6.03579i | − | 0.570329i | ||||||
\(113\) | − | 13.0053i | − | 1.22344i | −0.791075 | − | 0.611719i | \(-0.790478\pi\) | ||
0.791075 | − | 0.611719i | \(-0.209522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.92820 | − | 10.9348i | 0.832559 | − | 1.01967i | ||||
\(116\) | 1.73205 | 0.160817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.37945i | 0.495219i | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | − | 1.51575i | − | 0.137230i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.1244 | −1.35821 | ||||||||
\(125\) | −5.19615 | + | 9.89949i | −0.464758 | + | 0.885438i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.24264i | 0.376473i | 0.982124 | + | 0.188237i | \(0.0602772\pi\) | ||||
−0.982124 | + | 0.188237i | \(0.939723\pi\) | |||||||
\(128\) | − | 11.4524i | − | 1.01226i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.60770 | + | 1.31268i | 0.141004 | + | 0.115129i | ||||
\(131\) | 4.73205 | 0.413441 | 0.206721 | − | 0.978400i | \(-0.433721\pi\) | ||||
0.206721 | + | 0.978400i | \(0.433721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.00481i | − | 0.694105i | ||||||
\(134\) | 2.19615 | 0.189719 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.73205 | −0.234271 | ||||||||
\(137\) | − | 14.7985i | − | 1.26432i | −0.774838 | − | 0.632159i | \(-0.782169\pi\) | ||
0.774838 | − | 0.632159i | \(-0.217831\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 6.00000 | − | 7.34847i | 0.507093 | − | 0.621059i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.79315i | 0.150478i | ||||||||
\(143\) | 2.27362i | 0.190130i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.73205 | + | 1.41421i | 0.143839 | + | 0.117444i | ||||
\(146\) | 3.80385 | 0.314809 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.8338i | 1.30153i | ||||||||
\(149\) | −0.928203 | −0.0760414 | −0.0380207 | − | 0.999277i | \(-0.512105\pi\) | ||||
−0.0380207 | + | 0.999277i | \(0.512105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7846 | −1.52867 | −0.764335 | − | 0.644819i | \(-0.776933\pi\) | ||||
−0.764335 | + | 0.644819i | \(0.776933\pi\) | |||||||
\(152\) | − | 6.31319i | − | 0.512068i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.60770 | −0.129552 | ||||||||
\(155\) | −15.1244 | − | 12.3490i | −1.21482 | − | 0.991894i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9348i | 0.872690i | 0.899780 | + | 0.436345i | \(0.143727\pi\) | ||||
−0.899780 | + | 0.436345i | \(0.856273\pi\) | |||||||
\(158\) | − | 2.17209i | − | 0.172802i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.26795 | − | 8.90138i | 0.574582 | − | 0.703716i | ||||
\(161\) | −15.4641 | −1.21874 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.0406i | − | 1.09974i | −0.835249 | − | 0.549872i | \(-0.814676\pi\) | ||
0.835249 | − | 0.549872i | \(-0.185324\pi\) | |||||||
\(164\) | 12.0000 | 0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.26795 | 0.408872 | ||||||||
\(167\) | − | 11.2122i | − | 0.867624i | −0.901003 | − | 0.433812i | \(-0.857168\pi\) | ||
0.901003 | − | 0.433812i | \(-0.142832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.78461 | 0.752662 | ||||||||
\(170\) | −1.26795 | − | 1.03528i | −0.0972473 | − | 0.0794021i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 15.8338i | − | 1.20731i | ||||||
\(173\) | 4.62158i | 0.351372i | 0.984446 | + | 0.175686i | \(0.0562144\pi\) | ||||
−0.984446 | + | 0.175686i | \(0.943786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.0000 | − | 2.44949i | 0.907115 | − | 0.185164i | ||||
\(176\) | 3.12436 | 0.235507 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 5.37945i | − | 0.403207i | ||||||
\(179\) | 2.53590 | 0.189542 | 0.0947710 | − | 0.995499i | \(-0.469788\pi\) | ||||
0.0947710 | + | 0.995499i | \(0.469788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | − | 2.27362i | − | 0.168532i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.1962 | −0.899112 | ||||||||
\(185\) | −12.9282 | + | 15.8338i | −0.950500 | + | 1.16412i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.79315i | − | 0.131128i | ||||||
\(188\) | − | 2.44949i | − | 0.178647i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.39230 | − | 2.92996i | 0.173556 | − | 0.212562i | ||||
\(191\) | −15.1244 | −1.09436 | −0.547180 | − | 0.837015i | \(-0.684299\pi\) | ||||
−0.547180 | + | 0.837015i | \(0.684299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.656339i | 0.0472443i | 0.999721 | + | 0.0236222i | \(0.00751986\pi\) | ||||
−0.999721 | + | 0.0236222i | \(0.992480\pi\) | |||||||
\(194\) | −5.66025 | −0.406383 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.73205 | 0.123718 | ||||||||
\(197\) | 22.4243i | 1.59767i | 0.601551 | + | 0.798834i | \(0.294550\pi\) | ||||
−0.601551 | + | 0.798834i | \(0.705450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | 9.46410 | − | 1.93185i | 0.669213 | − | 0.136603i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.10583i | − | 0.218525i | ||||||
\(203\) | − | 2.44949i | − | 0.171920i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | + | 9.79796i | 0.838116 | + | 0.684319i | ||||
\(206\) | −4.73205 | −0.329698 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.41851i | 0.306368i | ||||||||
\(209\) | 4.14359 | 0.286618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7321 | −1.01420 | −0.507098 | − | 0.861888i | \(-0.669282\pi\) | ||||
−0.507098 | + | 0.861888i | \(0.669282\pi\) | |||||||
\(212\) | 10.2784i | 0.705926i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.66025 | 0.660361 | ||||||||
\(215\) | 12.9282 | − | 15.8338i | 0.881696 | − | 1.07985i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.3891i | 1.45198i | ||||||||
\(218\) | 9.24316i | 0.626026i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.80385 | + | 3.10583i | 0.256455 | + | 0.209395i | ||||
\(221\) | 2.53590 | 0.170583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3533i | 1.02813i | 0.857751 | + | 0.514066i | \(0.171861\pi\) | ||||
−0.857751 | + | 0.514066i | \(0.828139\pi\) | |||||||
\(224\) | −12.5885 | −0.841102 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.73205 | −0.447809 | ||||||||
\(227\) | 20.4553i | 1.35767i | 0.734292 | + | 0.678834i | \(0.237514\pi\) | ||||
−0.734292 | + | 0.678834i | \(0.762486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7846 | −1.24132 | −0.620661 | − | 0.784079i | \(-0.713136\pi\) | ||||
−0.620661 | + | 0.784079i | \(0.713136\pi\) | |||||||
\(230\) | −5.66025 | − | 4.62158i | −0.373226 | − | 0.304738i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.93185i | − | 0.126832i | ||||||
\(233\) | − | 3.38323i | − | 0.221643i | −0.993840 | − | 0.110821i | \(-0.964652\pi\) | ||
0.993840 | − | 0.110821i | \(-0.0353481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | − | 2.44949i | 0.130466 | − | 0.159787i | ||||
\(236\) | −18.0000 | −1.17170 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.79315i | 0.116233i | ||||||||
\(239\) | 10.3923 | 0.672222 | 0.336111 | − | 0.941822i | \(-0.390888\pi\) | ||||
0.336111 | + | 0.941822i | \(0.390888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4641 | 0.738468 | 0.369234 | − | 0.929337i | \(-0.379620\pi\) | ||||
0.369234 | + | 0.929337i | \(0.379620\pi\) | |||||||
\(242\) | 4.86181i | 0.312529i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.07180 | 0.324689 | ||||||||
\(245\) | 1.73205 | + | 1.41421i | 0.110657 | + | 0.0903508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.85993i | 0.372858i | ||||||||
\(248\) | 16.8690i | 1.07118i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.12436 | + | 2.68973i | 0.324093 | + | 0.170113i | ||||
\(251\) | −15.1244 | −0.954641 | −0.477320 | − | 0.878729i | \(-0.658392\pi\) | ||||
−0.477320 | + | 0.878729i | \(0.658392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.00481i | − | 0.503258i | ||||||
\(254\) | 2.19615 | 0.137799 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.39230 | −0.0870191 | ||||||||
\(257\) | 9.52056i | 0.593876i | 0.954897 | + | 0.296938i | \(0.0959655\pi\) | ||||
−0.954897 | + | 0.296938i | \(0.904035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.3923 | 1.39139 | ||||||||
\(260\) | −4.39230 | + | 5.37945i | −0.272399 | + | 0.333620i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 2.44949i | − | 0.151330i | ||||||
\(263\) | 4.79744i | 0.295823i | 0.989001 | + | 0.147912i | \(0.0472551\pi\) | ||||
−0.989001 | + | 0.147912i | \(0.952745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.39230 | + | 10.2784i | −0.515535 | + | 0.631399i | ||||
\(266\) | −4.14359 | −0.254060 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.34847i | 0.448879i | ||||||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.7321 | −1.62386 | −0.811928 | − | 0.583757i | \(-0.801582\pi\) | ||||
−0.811928 | + | 0.583757i | \(0.801582\pi\) | |||||||
\(272\) | − | 3.48477i | − | 0.211295i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.66025 | −0.462773 | ||||||||
\(275\) | 1.26795 | + | 6.21166i | 0.0764602 | + | 0.374577i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.7637i | 1.12740i | 0.825979 | + | 0.563701i | \(0.190623\pi\) | ||||
−0.825979 | + | 0.563701i | \(0.809377\pi\) | |||||||
\(278\) | − | 4.14110i | − | 0.248367i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.19615 | − | 6.69213i | −0.489814 | − | 0.399931i | ||||
\(281\) | −32.7846 | −1.95577 | −0.977883 | − | 0.209153i | \(-0.932929\pi\) | ||||
−0.977883 | + | 0.209153i | \(0.932929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.4249i | 1.63024i | 0.579293 | + | 0.815119i | \(0.303329\pi\) | ||||
−0.579293 | + | 0.815119i | \(0.696671\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.17691 | 0.0695924 | ||||||||
\(287\) | − | 16.9706i | − | 1.00174i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0.732051 | − | 0.896575i | 0.0429875 | − | 0.0526487i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.7279i | 0.744845i | ||||||||
\(293\) | 30.7338i | 1.79549i | 0.440520 | + | 0.897743i | \(0.354794\pi\) | ||||
−0.440520 | + | 0.897743i | \(0.645206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.0000 | − | 14.6969i | −1.04800 | − | 0.855689i | ||||
\(296\) | 17.6603 | 1.02648 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.480473i | 0.0278331i | ||||||||
\(299\) | 11.3205 | 0.654682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.3923 | −1.29067 | ||||||||
\(302\) | 9.72363i | 0.559532i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.05256 | 0.461846 | ||||||||
\(305\) | 5.07180 | + | 4.14110i | 0.290410 | + | 0.237119i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4543i | 0.596658i | 0.954463 | + | 0.298329i | \(0.0964293\pi\) | ||||
−0.954463 | + | 0.298329i | \(0.903571\pi\) | |||||||
\(308\) | − | 5.37945i | − | 0.306523i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.39230 | + | 7.82894i | −0.363059 | + | 0.444654i | ||||
\(311\) | 6.58846 | 0.373597 | 0.186799 | − | 0.982398i | \(-0.440189\pi\) | ||||
0.186799 | + | 0.982398i | \(0.440189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.6627i | 1.33749i | 0.743490 | + | 0.668747i | \(0.233169\pi\) | ||||
−0.743490 | + | 0.668747i | \(0.766831\pi\) | |||||||
\(314\) | 5.66025 | 0.319427 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.26795 | 0.408854 | ||||||||
\(317\) | 5.75839i | 0.323423i | 0.986838 | + | 0.161712i | \(0.0517015\pi\) | ||||
−0.986838 | + | 0.161712i | \(0.948299\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.26795 | 0.0709915 | ||||||||
\(320\) | 3.92820 | + | 3.20736i | 0.219593 | + | 0.179297i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.00481i | 0.446091i | ||||||||
\(323\) | − | 4.62158i | − | 0.257151i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.78461 | + | 1.79315i | −0.487282 | + | 0.0994661i | ||||
\(326\) | −7.26795 | −0.402534 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 13.3843i | − | 0.739022i | ||||||
\(329\) | −3.46410 | −0.190982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1962 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(332\) | 17.6269i | 0.967402i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.80385 | −0.317572 | ||||||||
\(335\) | −6.00000 | + | 7.34847i | −0.327815 | + | 0.401490i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.9053i | − | 1.52010i | −0.649864 | − | 0.760050i | \(-0.725174\pi\) | ||
0.649864 | − | 0.760050i | \(-0.274826\pi\) | |||||||
\(338\) | − | 5.06489i | − | 0.275494i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.46410 | − | 4.24264i | 0.187867 | − | 0.230089i | ||||
\(341\) | −11.0718 | −0.599571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5959i | − | 1.05808i | ||||||
\(344\) | −17.6603 | −0.952177 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.39230 | 0.128611 | ||||||||
\(347\) | − | 21.4906i | − | 1.15368i | −0.816859 | − | 0.576838i | \(-0.804286\pi\) | ||
0.816859 | − | 0.576838i | \(-0.195714\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.7846 | 1.21963 | 0.609816 | − | 0.792543i | \(-0.291243\pi\) | ||||
0.609816 | + | 0.792543i | \(0.291243\pi\) | |||||||
\(350\) | −1.26795 | − | 6.21166i | −0.0677747 | − | 0.332027i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 6.51626i | − | 0.347318i | ||||||
\(353\) | − | 31.9449i | − | 1.70026i | −0.526576 | − | 0.850128i | \(-0.676525\pi\) | ||
0.526576 | − | 0.850128i | \(-0.323475\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | − | 4.89898i | −0.318447 | − | 0.260011i | ||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 1.31268i | − | 0.0693772i | ||||||
\(359\) | −7.26795 | −0.383588 | −0.191794 | − | 0.981435i | \(-0.561430\pi\) | ||||
−0.191794 | + | 0.981435i | \(0.561430\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | 8.28221i | 0.435303i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.60770 | 0.398752 | ||||||||
\(365\) | −10.3923 | + | 12.7279i | −0.543958 | + | 0.666210i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.6365i | − | 1.75581i | −0.478833 | − | 0.877906i | \(-0.658940\pi\) | ||
0.478833 | − | 0.877906i | \(-0.341060\pi\) | |||||||
\(368\) | − | 15.5563i | − | 0.810931i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.19615 | + | 6.69213i | 0.426098 | + | 0.347907i | ||||
\(371\) | 14.5359 | 0.754666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5959i | 1.01464i | 0.861758 | + | 0.507319i | \(0.169363\pi\) | ||||
−0.861758 | + | 0.507319i | \(0.830637\pi\) | |||||||
\(374\) | −0.928203 | −0.0479962 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.73205 | −0.140895 | ||||||||
\(377\) | 1.79315i | 0.0923520i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1962 | 0.831940 | 0.415970 | − | 0.909378i | \(-0.363442\pi\) | ||||
0.415970 | + | 0.909378i | \(0.363442\pi\) | |||||||
\(380\) | 9.80385 | + | 8.00481i | 0.502927 | + | 0.410638i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.82894i | 0.400564i | ||||||||
\(383\) | − | 0.933740i | − | 0.0477119i | −0.999715 | − | 0.0238559i | \(-0.992406\pi\) | ||
0.999715 | − | 0.0238559i | \(-0.00759430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.39230 | − | 5.37945i | 0.223853 | − | 0.274162i | ||||
\(386\) | 0.339746 | 0.0172926 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 18.9396i | − | 0.961511i | ||||||
\(389\) | −20.7846 | −1.05382 | −0.526911 | − | 0.849921i | \(-0.676650\pi\) | ||||
−0.526911 | + | 0.849921i | \(0.676650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.92820 | −0.451519 | ||||||||
\(392\) | − | 1.93185i | − | 0.0975732i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.6077 | 0.584787 | ||||||||
\(395\) | 7.26795 | + | 5.93426i | 0.365690 | + | 0.298585i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.89898i | 0.245873i | 0.992415 | + | 0.122936i | \(0.0392311\pi\) | ||||
−0.992415 | + | 0.122936i | \(0.960769\pi\) | |||||||
\(398\) | − | 7.24693i | − | 0.363256i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.46410 | + | 12.0716i | 0.123205 | + | 0.603579i | ||||
\(401\) | −37.8564 | −1.89046 | −0.945229 | − | 0.326407i | \(-0.894162\pi\) | ||||
−0.945229 | + | 0.326407i | \(0.894162\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 15.6579i | − | 0.779975i | ||||||
\(404\) | 10.3923 | 0.517036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.26795 | −0.0629273 | ||||||||
\(407\) | 11.5911i | 0.574550i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.07180 | −0.448571 | −0.224286 | − | 0.974523i | \(-0.572005\pi\) | ||||
−0.224286 | + | 0.974523i | \(0.572005\pi\) | |||||||
\(410\) | 5.07180 | − | 6.21166i | 0.250478 | − | 0.306772i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 15.8338i | − | 0.780073i | ||||||
\(413\) | 25.4558i | 1.25260i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.3923 | + | 17.6269i | −0.706490 | + | 0.865271i | ||||
\(416\) | 9.21539 | 0.451822 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 2.14488i | − | 0.104910i | ||||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.46410 | 0.266304 | 0.133152 | − | 0.991096i | \(-0.457490\pi\) | ||||
0.133152 | + | 0.991096i | \(0.457490\pi\) | |||||||
\(422\) | 7.62587i | 0.371222i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.4641 | 0.556746 | ||||||||
\(425\) | 6.92820 | − | 1.41421i | 0.336067 | − | 0.0685994i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.17260i | − | 0.347107i | ||||||
\(428\) | 32.3238i | 1.56243i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.19615 | − | 6.69213i | −0.395254 | − | 0.322723i | ||||
\(431\) | 37.1769 | 1.79075 | 0.895374 | − | 0.445314i | \(-0.146908\pi\) | ||||
0.895374 | + | 0.445314i | \(0.146908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.92996i | 0.140805i | 0.997519 | + | 0.0704025i | \(0.0224284\pi\) | ||||
−0.997519 | + | 0.0704025i | \(0.977572\pi\) | |||||||
\(434\) | 11.0718 | 0.531463 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.9282 | −1.48119 | ||||||||
\(437\) | − | 20.6312i | − | 0.986924i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.07180 | 0.337518 | 0.168759 | − | 0.985657i | \(-0.446024\pi\) | ||||
0.168759 | + | 0.985657i | \(0.446024\pi\) | |||||||
\(440\) | 3.46410 | − | 4.24264i | 0.165145 | − | 0.202260i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.31268i | − | 0.0624377i | ||||||
\(443\) | 18.1817i | 0.863839i | 0.901912 | + | 0.431919i | \(0.142164\pi\) | ||||
−0.901912 | + | 0.431919i | \(0.857836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | + | 14.6969i | 0.853282 | + | 0.696702i | ||||
\(446\) | 7.94744 | 0.376322 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 5.55532i | − | 0.262464i | ||||||
\(449\) | −25.8564 | −1.22024 | −0.610120 | − | 0.792309i | \(-0.708879\pi\) | ||||
−0.610120 | + | 0.792309i | \(0.708879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.78461 | 0.413651 | ||||||||
\(452\) | − | 22.5259i | − | 1.05953i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.5885 | 0.496941 | ||||||||
\(455\) | 7.60770 | + | 6.21166i | 0.356654 | + | 0.291207i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 23.6627i | − | 1.10689i | −0.832884 | − | 0.553447i | \(-0.813312\pi\) | ||
0.832884 | − | 0.553447i | \(-0.186688\pi\) | |||||||
\(458\) | 9.72363i | 0.454355i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.4641 | − | 18.9396i | 0.721017 | − | 0.883062i | ||||
\(461\) | −24.9282 | −1.16102 | −0.580511 | − | 0.814252i | \(-0.697147\pi\) | ||||
−0.580511 | + | 0.814252i | \(0.697147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.86800i | − | 0.319183i | −0.987183 | − | 0.159591i | \(-0.948982\pi\) | ||
0.987183 | − | 0.159591i | \(-0.0510177\pi\) | |||||||
\(464\) | 2.46410 | 0.114393 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.75129 | −0.0811269 | ||||||||
\(467\) | − | 21.0101i | − | 0.972233i | −0.873894 | − | 0.486116i | \(-0.838413\pi\) | ||
0.873894 | − | 0.486116i | \(-0.161587\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3923 | 0.479872 | ||||||||
\(470\) | −1.26795 | − | 1.03528i | −0.0584861 | − | 0.0477537i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.0764i | 0.924091i | ||||||||
\(473\) | − | 11.5911i | − | 0.532960i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.26795 | + | 16.0096i | 0.149944 | + | 0.734572i | ||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 5.37945i | − | 0.246050i | ||||||
\(479\) | 5.66025 | 0.258624 | 0.129312 | − | 0.991604i | \(-0.458723\pi\) | ||||
0.129312 | + | 0.991604i | \(0.458723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.3923 | −0.747425 | ||||||||
\(482\) | − | 5.93426i | − | 0.270298i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.2679 | −0.739452 | ||||||||
\(485\) | 15.4641 | − | 18.9396i | 0.702189 | − | 0.860002i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.9348i | − | 0.495502i | −0.968824 | − | 0.247751i | \(-0.920309\pi\) | ||
0.968824 | − | 0.247751i | \(-0.0796915\pi\) | |||||||
\(488\) | − | 5.65685i | − | 0.256074i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.732051 | − | 0.896575i | 0.0330707 | − | 0.0405032i | ||||
\(491\) | −7.26795 | −0.327998 | −0.163999 | − | 0.986461i | \(-0.552439\pi\) | ||||
−0.163999 | + | 0.986461i | \(0.552439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.41421i | − | 0.0636930i | ||||||
\(494\) | 3.03332 | 0.136476 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.5167 | −0.966127 | ||||||||
\(497\) | 8.48528i | 0.380617i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.07180 | 0.0479802 | 0.0239901 | − | 0.999712i | \(-0.492363\pi\) | ||||
0.0239901 | + | 0.999712i | \(0.492363\pi\) | |||||||
\(500\) | −9.00000 | + | 17.1464i | −0.402492 | + | 0.766812i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.82894i | 0.349423i | ||||||||
\(503\) | − | 12.1731i | − | 0.542773i | −0.962471 | − | 0.271386i | \(-0.912518\pi\) | ||
0.962471 | − | 0.271386i | \(-0.0874821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3923 | + | 8.48528i | 0.462451 | + | 0.377590i | ||||
\(506\) | −4.14359 | −0.184205 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.34847i | 0.326036i | ||||||||
\(509\) | 33.4641 | 1.48327 | 0.741635 | − | 0.670804i | \(-0.234051\pi\) | ||||
0.741635 | + | 0.670804i | \(0.234051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | 0.796273 | ||||||||
\(512\) | − | 22.1841i | − | 0.980408i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.92820 | 0.217374 | ||||||||
\(515\) | 12.9282 | − | 15.8338i | 0.569685 | − | 0.697718i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.79315i | − | 0.0788627i | ||||||
\(518\) | − | 11.5911i | − | 0.509284i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | + | 4.89898i | 0.263117 | + | 0.214834i | ||||
\(521\) | −4.39230 | −0.192430 | −0.0962152 | − | 0.995361i | \(-0.530674\pi\) | ||||
−0.0962152 | + | 0.995361i | \(0.530674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.61729i | − | 0.0707190i | −0.999375 | − | 0.0353595i | \(-0.988742\pi\) | ||
0.999375 | − | 0.0353595i | \(-0.0112576\pi\) | |||||||
\(524\) | 8.19615 | 0.358051 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.48334 | 0.108279 | ||||||||
\(527\) | 12.3490i | 0.537930i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8564 | −0.732887 | ||||||||
\(530\) | 5.32051 | + | 4.34418i | 0.231108 | + | 0.188699i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 13.8647i | − | 0.601112i | ||||||
\(533\) | 12.4233i | 0.538113i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.3923 | + | 32.3238i | −1.14104 | + | 1.39748i | ||||
\(536\) | 8.19615 | 0.354020 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.21166i | 0.267804i | ||||||||
\(539\) | 1.26795 | 0.0546144 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.3923 | 1.82259 | 0.911294 | − | 0.411757i | \(-0.135085\pi\) | ||||
0.911294 | + | 0.411757i | \(0.135085\pi\) | |||||||
\(542\) | 13.8375i | 0.594373i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.26795 | −0.311611 | ||||||||
\(545\) | −30.9282 | − | 25.2528i | −1.32482 | − | 1.08171i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.44949i | − | 0.104733i | −0.998628 | − | 0.0523663i | \(-0.983324\pi\) | ||
0.998628 | − | 0.0523663i | \(-0.0166763\pi\) | |||||||
\(548\) | − | 25.6317i | − | 1.09493i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.21539 | − | 0.656339i | 0.137105 | − | 0.0279864i | ||||
\(551\) | 3.26795 | 0.139219 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.2784i | − | 0.437083i | ||||||
\(554\) | 9.71281 | 0.412658 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.8564 | 0.587643 | ||||||||
\(557\) | 0.554803i | 0.0235078i | 0.999931 | + | 0.0117539i | \(0.00374146\pi\) | ||||
−0.999931 | + | 0.0117539i | \(0.996259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.3923 | 0.693321 | ||||||||
\(560\) | 8.53590 | − | 10.4543i | 0.360708 | − | 0.441775i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.9706i | 0.715860i | ||||||||
\(563\) | 13.2827i | 0.559800i | 0.960029 | + | 0.279900i | \(0.0903013\pi\) | ||||
−0.960029 | + | 0.279900i | \(0.909699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.3923 | − | 22.5259i | 0.773770 | − | 0.947671i | ||||
\(566\) | 14.1962 | 0.596709 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.69213i | 0.280796i | ||||||||
\(569\) | 21.4641 | 0.899822 | 0.449911 | − | 0.893073i | \(-0.351456\pi\) | ||||
0.449911 | + | 0.893073i | \(0.351456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.3205 | −1.64551 | −0.822756 | − | 0.568395i | \(-0.807565\pi\) | ||||
−0.822756 | + | 0.568395i | \(0.807565\pi\) | |||||||
\(572\) | 3.93803i | 0.164657i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.78461 | −0.366663 | ||||||||
\(575\) | 30.9282 | − | 6.31319i | 1.28980 | − | 0.263278i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.14162i | 0.380571i | 0.981729 | + | 0.190285i | \(0.0609413\pi\) | ||||
−0.981729 | + | 0.190285i | \(0.939059\pi\) | |||||||
\(578\) | − | 7.76457i | − | 0.322964i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.00000 | + | 2.44949i | 0.124568 | + | 0.101710i | ||||
\(581\) | 24.9282 | 1.03420 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.52433i | 0.311626i | ||||||||
\(584\) | 14.1962 | 0.587441 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.9090 | 0.657193 | ||||||||
\(587\) | 15.5563i | 0.642079i | 0.947066 | + | 0.321040i | \(0.104032\pi\) | ||||
−0.947066 | + | 0.321040i | \(0.895968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.5359 | −1.17580 | ||||||||
\(590\) | −7.60770 | + | 9.31749i | −0.313204 | + | 0.383595i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.5259i | 0.925808i | ||||||||
\(593\) | 25.5302i | 1.04840i | 0.851596 | + | 0.524199i | \(0.175635\pi\) | ||||
−0.851596 | + | 0.524199i | \(0.824365\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | − | 4.89898i | −0.245976 | − | 0.200839i | ||||
\(596\) | −1.60770 | −0.0658538 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 5.85993i | − | 0.239630i | ||||||
\(599\) | 1.26795 | 0.0518070 | 0.0259035 | − | 0.999664i | \(-0.491754\pi\) | ||||
0.0259035 | + | 0.999664i | \(0.491754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7846 | 0.684659 | 0.342329 | − | 0.939580i | \(-0.388784\pi\) | ||||
0.342329 | + | 0.939580i | \(0.388784\pi\) | |||||||
\(602\) | 11.5911i | 0.472418i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −32.5359 | −1.32387 | ||||||||
\(605\) | −16.2679 | − | 13.2827i | −0.661386 | − | 0.540020i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3142i | 0.662174i | 0.943600 | + | 0.331087i | \(0.107415\pi\) | ||||
−0.943600 | + | 0.331087i | \(0.892585\pi\) | |||||||
\(608\) | − | 16.7947i | − | 0.681115i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.14359 | − | 2.62536i | 0.0867916 | − | 0.106298i | ||||
\(611\) | 2.53590 | 0.102591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 18.2832i | − | 0.738453i | −0.929339 | − | 0.369227i | \(-0.879623\pi\) | ||
0.929339 | − | 0.369227i | \(-0.120377\pi\) | |||||||
\(614\) | 5.41154 | 0.218392 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | −0.241747 | ||||||||
\(617\) | 32.0464i | 1.29014i | 0.764123 | + | 0.645071i | \(0.223172\pi\) | ||||
−0.764123 | + | 0.645071i | \(0.776828\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.8038 | 0.956757 | 0.478379 | − | 0.878154i | \(-0.341225\pi\) | ||||
0.478379 | + | 0.878154i | \(0.341225\pi\) | |||||||
\(620\) | −26.1962 | − | 21.3891i | −1.05206 | − | 0.859006i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 3.41044i | − | 0.136746i | ||||||
\(623\) | − | 25.4558i | − | 1.01987i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 12.2487 | 0.489557 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.9396i | 0.755771i | ||||||||
\(629\) | 12.9282 | 0.515481 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.6077 | 0.621333 | 0.310666 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310666 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(632\) | − | 8.10634i | − | 0.322453i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.98076 | 0.118381 | ||||||||
\(635\) | −6.00000 | + | 7.34847i | −0.238103 | + | 0.291615i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.79315i | 0.0710472i | ||||||||
\(638\) | − | 0.656339i | − | 0.0259847i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.1962 | − | 19.8362i | 0.640209 | − | 0.784093i | ||||
\(641\) | −34.6410 | −1.36824 | −0.684119 | − | 0.729370i | \(-0.739813\pi\) | ||||
−0.684119 | + | 0.729370i | \(0.739813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4543i | 0.412277i | 0.978523 | + | 0.206139i | \(0.0660898\pi\) | ||||
−0.978523 | + | 0.206139i | \(0.933910\pi\) | |||||||
\(644\) | −26.7846 | −1.05546 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.39230 | −0.0941240 | ||||||||
\(647\) | − | 14.3180i | − | 0.562899i | −0.959576 | − | 0.281449i | \(-0.909185\pi\) | ||
0.959576 | − | 0.281449i | \(-0.0908151\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.1769 | −0.517239 | ||||||||
\(650\) | 0.928203 | + | 4.54725i | 0.0364071 | + | 0.178358i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 24.3190i | − | 0.952407i | ||||||
\(653\) | − | 13.0053i | − | 0.508938i | −0.967081 | − | 0.254469i | \(-0.918099\pi\) | ||
0.967081 | − | 0.254469i | \(-0.0819006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.19615 | + | 6.69213i | 0.320250 | + | 0.261483i | ||||
\(656\) | 17.0718 | 0.666542 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.79315i | 0.0699043i | ||||||||
\(659\) | 32.4449 | 1.26387 | 0.631936 | − | 0.775020i | \(-0.282260\pi\) | ||||
0.631936 | + | 0.775020i | \(0.282260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.784610 | −0.0305178 | −0.0152589 | − | 0.999884i | \(-0.504857\pi\) | ||||
−0.0152589 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(662\) | 9.41902i | 0.366081i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.6603 | 0.762966 | ||||||||
\(665\) | 11.3205 | − | 13.8647i | 0.438990 | − | 0.537651i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.31319i | − | 0.244448i | ||||||
\(668\) | − | 19.4201i | − | 0.751384i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.80385 | + | 3.10583i | 0.146955 | + | 0.119989i | ||||
\(671\) | 3.71281 | 0.143332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 46.3644i | − | 1.78722i | −0.448846 | − | 0.893609i | \(-0.648165\pi\) | ||
0.448846 | − | 0.893609i | \(-0.351835\pi\) | |||||||
\(674\) | −14.4449 | −0.556395 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.9474 | 0.651825 | ||||||||
\(677\) | − | 32.2495i | − | 1.23945i | −0.784819 | − | 0.619725i | \(-0.787244\pi\) | ||
0.784819 | − | 0.619725i | \(-0.212756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.7846 | −1.02790 | ||||||||
\(680\) | −4.73205 | − | 3.86370i | −0.181466 | − | 0.148166i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.73118i | 0.219458i | ||||||||
\(683\) | − | 21.9711i | − | 0.840700i | −0.907362 | − | 0.420350i | \(-0.861907\pi\) | ||
0.907362 | − | 0.420350i | \(-0.138093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.9282 | − | 25.6317i | 0.799626 | − | 0.979337i | ||||
\(686\) | −10.1436 | −0.387284 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 22.5259i | − | 0.858791i | ||||||
\(689\) | −10.6410 | −0.405390 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.7128 | 1.58683 | 0.793415 | − | 0.608681i | \(-0.208301\pi\) | ||||
0.793415 | + | 0.608681i | \(0.208301\pi\) | |||||||
\(692\) | 8.00481i | 0.304297i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.1244 | −0.422275 | ||||||||
\(695\) | 13.8564 | + | 11.3137i | 0.525603 | + | 0.429153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.79796i | − | 0.371124i | ||||||
\(698\) | − | 11.7942i | − | 0.446416i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.7846 | − | 4.24264i | 0.785584 | − | 0.160357i | ||||
\(701\) | −27.7128 | −1.04670 | −0.523349 | − | 0.852118i | \(-0.675318\pi\) | ||||
−0.523349 | + | 0.852118i | \(0.675318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.8744i | 1.12673i | ||||||||
\(704\) | 2.87564 | 0.108380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.5359 | −0.622337 | ||||||||
\(707\) | − | 14.6969i | − | 0.552735i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.3923 | −0.765849 | −0.382925 | − | 0.923780i | \(-0.625083\pi\) | ||||
−0.382925 | + | 0.923780i | \(0.625083\pi\) | |||||||
\(710\) | −2.53590 | + | 3.10583i | −0.0951706 | + | 0.116560i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 20.0764i | − | 0.752395i | ||||||
\(713\) | 55.1271i | 2.06453i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.21539 | + | 3.93803i | −0.120249 | + | 0.147274i | ||||
\(716\) | 4.39230 | 0.164148 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.76217i | 0.140403i | ||||||||
\(719\) | −19.8564 | −0.740519 | −0.370260 | − | 0.928928i | \(-0.620731\pi\) | ||||
−0.370260 | + | 0.928928i | \(0.620731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3923 | −0.833933 | ||||||||
\(722\) | 4.30701i | 0.160290i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.7128 | −1.02994 | ||||||||
\(725\) | 1.00000 | + | 4.89898i | 0.0371391 | + | 0.181944i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 46.6690i | − | 1.73086i | −0.501031 | − | 0.865430i | \(-0.667046\pi\) | ||
0.501031 | − | 0.865430i | \(-0.332954\pi\) | |||||||
\(728\) | − | 8.48528i | − | 0.314485i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.58846 | + | 5.37945i | 0.243850 | + | 0.199102i | ||||
\(731\) | −12.9282 | −0.478167 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.7279i | − | 0.470117i | −0.971981 | − | 0.235058i | \(-0.924472\pi\) | ||
0.971981 | − | 0.235058i | \(-0.0755281\pi\) | |||||||
\(734\) | −17.4115 | −0.642672 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.4449 | −1.19593 | ||||||||
\(737\) | 5.37945i | 0.198155i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.9808 | 0.698219 | 0.349109 | − | 0.937082i | \(-0.386484\pi\) | ||||
0.349109 | + | 0.937082i | \(0.386484\pi\) | |||||||
\(740\) | −22.3923 | + | 27.4249i | −0.823157 | + | 1.00816i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 7.52433i | − | 0.276227i | ||||||
\(743\) | − | 9.89949i | − | 0.363177i | −0.983375 | − | 0.181589i | \(-0.941876\pi\) | ||
0.983375 | − | 0.181589i | \(-0.0581239\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.60770 | − | 1.31268i | −0.0589014 | − | 0.0480928i | ||||
\(746\) | 10.1436 | 0.371383 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.10583i | − | 0.113560i | ||||||
\(749\) | 45.7128 | 1.67031 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.9090 | 1.82120 | 0.910602 | − | 0.413284i | \(-0.135618\pi\) | ||||
0.910602 | + | 0.413284i | \(0.135618\pi\) | |||||||
\(752\) | − | 3.48477i | − | 0.127076i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.928203 | 0.0338032 | ||||||||
\(755\) | −32.5359 | − | 26.5654i | −1.18410 | − | 0.966816i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.9348i | 0.397431i | 0.980057 | + | 0.198716i | \(0.0636770\pi\) | ||||
−0.980057 | + | 0.198716i | \(0.936323\pi\) | |||||||
\(758\) | − | 8.38375i | − | 0.304511i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.92820 | − | 10.9348i | 0.323860 | − | 0.396646i | ||||
\(761\) | 35.5692 | 1.28938 | 0.644692 | − | 0.764443i | \(-0.276986\pi\) | ||||
0.644692 | + | 0.764443i | \(0.276986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.7391i | 1.58346i | ||||||||
\(764\) | −26.1962 | −0.947744 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.483340 | −0.0174638 | ||||||||
\(767\) | − | 18.6350i | − | 0.672870i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.0718 | 0.687747 | 0.343873 | − | 0.939016i | \(-0.388261\pi\) | ||||
0.343873 | + | 0.939016i | \(0.388261\pi\) | |||||||
\(770\) | −2.78461 | − | 2.27362i | −0.100350 | − | 0.0819357i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.13681i | 0.0409148i | ||||||||
\(773\) | − | 11.2122i | − | 0.403274i | −0.979460 | − | 0.201637i | \(-0.935374\pi\) | ||
0.979460 | − | 0.201637i | \(-0.0646261\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.73205 | − | 42.7781i | −0.313665 | − | 1.53664i | ||||
\(776\) | −21.1244 | −0.758320 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.7589i | 0.385725i | ||||||||
\(779\) | 22.6410 | 0.811199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.39230 | −0.157169 | ||||||||
\(782\) | 4.62158i | 0.165267i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.46410 | 0.0880036 | ||||||||
\(785\) | −15.4641 | + | 18.9396i | −0.551937 | + | 0.675983i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.0779i | 1.25039i | 0.780467 | + | 0.625197i | \(0.214981\pi\) | ||||
−0.780467 | + | 0.625197i | \(0.785019\pi\) | |||||||
\(788\) | 38.8401i | 1.38362i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.07180 | − | 3.76217i | 0.109290 | − | 0.133852i | ||||
\(791\) | −31.8564 | −1.13268 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.25071i | 0.186458i | ||||||||
\(794\) | 2.53590 | 0.0899957 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.2487 | 0.859473 | ||||||||
\(797\) | − | 29.0149i | − | 1.02776i | −0.857862 | − | 0.513881i | \(-0.828207\pi\) | ||
0.857862 | − | 0.513881i | \(-0.171793\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.00000 | −0.0707549 | ||||||||
\(800\) | 25.1769 | − | 5.13922i | 0.890138 | − | 0.181699i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.5959i | 0.691956i | ||||||||
\(803\) | 9.31749i | 0.328807i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.7846 | − | 21.8695i | −0.944033 | − | 0.770800i | ||||
\(806\) | −8.10512 | −0.285491 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 11.5911i | − | 0.407774i | ||||||
\(809\) | 13.6077 | 0.478421 | 0.239211 | − | 0.970968i | \(-0.423111\pi\) | ||||
0.239211 | + | 0.970968i | \(0.423111\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.7846 | −1.29168 | −0.645841 | − | 0.763472i | \(-0.723493\pi\) | ||||
−0.645841 | + | 0.763472i | \(0.723493\pi\) | |||||||
\(812\) | − | 4.24264i | − | 0.148888i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | 0.210300 | ||||||||
\(815\) | 19.8564 | − | 24.3190i | 0.695540 | − | 0.851859i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 29.8744i | − | 1.04517i | ||||||
\(818\) | 4.69591i | 0.164189i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.7846 | + | 16.9706i | 0.725830 | + | 0.592638i | ||||
\(821\) | −9.21539 | −0.321619 | −0.160810 | − | 0.986985i | \(-0.551411\pi\) | ||||
−0.160810 | + | 0.986985i | \(0.551411\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.8091i | 1.42252i | 0.702931 | + | 0.711258i | \(0.251874\pi\) | ||||
−0.702931 | + | 0.711258i | \(0.748126\pi\) | |||||||
\(824\) | −17.6603 | −0.615224 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.1769 | 0.458483 | ||||||||
\(827\) | − | 3.68784i | − | 0.128239i | −0.997942 | − | 0.0641193i | \(-0.979576\pi\) | ||
0.997942 | − | 0.0641193i | \(-0.0204238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.7846 | 0.582954 | 0.291477 | − | 0.956578i | \(-0.405853\pi\) | ||||
0.291477 | + | 0.956578i | \(0.405853\pi\) | |||||||
\(830\) | 9.12436 | + | 7.45001i | 0.316711 | + | 0.258593i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.06678i | 0.140990i | ||||||||
\(833\) | − | 1.41421i | − | 0.0489996i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.8564 | − | 19.4201i | 0.548734 | − | 0.672059i | ||||
\(836\) | 7.17691 | 0.248219 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.10583i | 0.107289i | ||||||||
\(839\) | 40.9808 | 1.41481 | 0.707407 | − | 0.706807i | \(-0.249865\pi\) | ||||
0.707407 | + | 0.706807i | \(0.249865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − | 2.82843i | − | 0.0974740i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.5167 | −0.878320 | ||||||||
\(845\) | 16.9474 | + | 13.8375i | 0.583010 | + | 0.476025i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.0064i | 0.790508i | ||||||||
\(848\) | 14.6226i | 0.502142i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.732051 | − | 3.58630i | −0.0251091 | − | 0.123009i | ||||
\(851\) | 57.7128 | 1.97837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 32.3238i | − | 1.10675i | −0.832933 | − | 0.553374i | \(-0.813340\pi\) | ||
0.832933 | − | 0.553374i | \(-0.186660\pi\) | |||||||
\(854\) | −3.71281 | −0.127050 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.0526 | 1.23225 | ||||||||
\(857\) | − | 33.2576i | − | 1.13606i | −0.823009 | − | 0.568029i | \(-0.807706\pi\) | ||
0.823009 | − | 0.568029i | \(-0.192294\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.7321 | 0.639129 | 0.319565 | − | 0.947564i | \(-0.396463\pi\) | ||||
0.319565 | + | 0.947564i | \(0.396463\pi\) | |||||||
\(860\) | 22.3923 | − | 27.4249i | 0.763571 | − | 0.935180i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 19.2442i | − | 0.655460i | ||||||
\(863\) | 1.69161i | 0.0575832i | 0.999585 | + | 0.0287916i | \(0.00916592\pi\) | ||||
−0.999585 | + | 0.0287916i | \(0.990834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.53590 | + | 8.00481i | −0.222227 | + | 0.272172i | ||||
\(866\) | 1.51666 | 0.0515382 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 37.0470i | 1.25746i | ||||||||
\(869\) | 5.32051 | 0.180486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.60770 | −0.257777 | ||||||||
\(872\) | 34.4959i | 1.16818i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.6795 | −0.361239 | ||||||||
\(875\) | 24.2487 | + | 12.7279i | 0.819756 | + | 0.430282i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.9754i | 0.843358i | 0.906745 | + | 0.421679i | \(0.138559\pi\) | ||||
−0.906745 | + | 0.421679i | \(0.861441\pi\) | |||||||
\(878\) | − | 3.66063i | − | 0.123540i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.41154 | + | 4.41851i | 0.182423 | + | 0.148948i | ||||
\(881\) | 50.5359 | 1.70260 | 0.851299 | − | 0.524681i | \(-0.175815\pi\) | ||||
0.851299 | + | 0.524681i | \(0.175815\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.48854i | − | 0.0500935i | −0.999686 | − | 0.0250467i | \(-0.992027\pi\) | ||
0.999686 | − | 0.0250467i | \(-0.00797346\pi\) | |||||||
\(884\) | 4.39230 | 0.147729 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.41154 | 0.316187 | ||||||||
\(887\) | − | 21.0101i | − | 0.705451i | −0.935727 | − | 0.352726i | \(-0.885255\pi\) | ||
0.935727 | − | 0.352726i | \(-0.114745\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3923 | 0.348547 | ||||||||
\(890\) | 7.60770 | − | 9.31749i | 0.255011 | − | 0.312323i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.5927i | 0.890388i | ||||||||
\(893\) | − | 4.62158i | − | 0.154655i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.39230 | + | 3.58630i | 0.146819 | + | 0.119877i | ||||
\(896\) | −28.0526 | −0.937170 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.3843i | 0.446639i | ||||||||
\(899\) | −8.73205 | −0.291230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.39230 | 0.279588 | ||||||||
\(902\) | − | 4.54725i | − | 0.151407i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.1244 | −0.835624 | ||||||||
\(905\) | −27.7128 | − | 22.6274i | −0.921205 | − | 0.752161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 45.7081i | − | 1.51771i | −0.651258 | − | 0.758856i | \(-0.725758\pi\) | ||
0.651258 | − | 0.758856i | \(-0.274242\pi\) | |||||||
\(908\) | 35.4297i | 1.17577i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.21539 | − | 3.93803i | 0.106589 | − | 0.130545i | ||||
\(911\) | 9.80385 | 0.324816 | 0.162408 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162408 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9038i | 0.427053i | ||||||||
\(914\) | −12.2487 | −0.405151 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −32.5359 | −1.07502 | ||||||||
\(917\) | − | 11.5911i | − | 0.382772i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.9615 | −1.45016 | −0.725078 | − | 0.688666i | \(-0.758197\pi\) | ||||
−0.725078 | + | 0.688666i | \(0.758197\pi\) | |||||||
\(920\) | −21.1244 | − | 17.2480i | −0.696449 | − | 0.568649i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.9038i | 0.424964i | ||||||||
\(923\) | − | 6.21166i | − | 0.204459i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.7846 | + | 9.14162i | −1.47251 | + | 0.300575i | ||||
\(926\) | −3.55514 | −0.116829 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 5.13922i | − | 0.168703i | ||||||
\(929\) | 55.8564 | 1.83259 | 0.916295 | − | 0.400505i | \(-0.131165\pi\) | ||||
0.916295 | + | 0.400505i | \(0.131165\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.26795 | 0.107103 | ||||||||
\(932\) | − | 5.85993i | − | 0.191948i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.8756 | −0.355862 | ||||||||
\(935\) | 2.53590 | − | 3.10583i | 0.0829327 | − | 0.101571i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.75410i | 0.0899724i | 0.998988 | + | 0.0449862i | \(0.0143244\pi\) | ||||
−0.998988 | + | 0.0449862i | \(0.985676\pi\) | |||||||
\(938\) | − | 5.37945i | − | 0.175645i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.46410 | − | 4.24264i | 0.112987 | − | 0.138380i | ||||
\(941\) | 7.85641 | 0.256112 | 0.128056 | − | 0.991767i | \(-0.459126\pi\) | ||||
0.128056 | + | 0.991767i | \(0.459126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 43.7391i | − | 1.42434i | ||||||
\(944\) | −25.6077 | −0.833459 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | 27.9797i | 0.909217i | 0.890691 | + | 0.454608i | \(0.150221\pi\) | ||||
−0.890691 | + | 0.454608i | \(0.849779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.1769 | −0.427741 | ||||||||
\(950\) | 8.28719 | − | 1.69161i | 0.268872 | − | 0.0548832i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.69213i | 0.216893i | ||||||||
\(953\) | − | 5.65685i | − | 0.183243i | −0.995794 | − | 0.0916217i | \(-0.970795\pi\) | ||
0.995794 | − | 0.0916217i | \(-0.0292051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.1962 | − | 21.3891i | −0.847688 | − | 0.692134i | ||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2.92996i | − | 0.0946628i | ||||||
\(959\) | −36.2487 | −1.17053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.2487 | 1.45964 | ||||||||
\(962\) | 8.48528i | 0.273576i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.8564 | 0.639532 | ||||||||
\(965\) | −0.928203 | + | 1.13681i | −0.0298799 | + | 0.0365953i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.96902i | − | 0.0633193i | −0.999499 | − | 0.0316596i | \(-0.989921\pi\) | ||
0.999499 | − | 0.0316596i | \(-0.0100793\pi\) | |||||||
\(968\) | 18.1445i | 0.583188i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.80385 | − | 8.00481i | −0.314783 | − | 0.257019i | ||||
\(971\) | 49.5167 | 1.58907 | 0.794533 | − | 0.607221i | \(-0.207716\pi\) | ||||
0.794533 | + | 0.607221i | \(0.207716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 19.5959i | − | 0.628216i | ||||||
\(974\) | −5.66025 | −0.181366 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.21539 | 0.230959 | ||||||||
\(977\) | 22.9048i | 0.732790i | 0.930459 | + | 0.366395i | \(0.119408\pi\) | ||||
−0.930459 | + | 0.366395i | \(0.880592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.1769 | 0.421136 | ||||||||
\(980\) | 3.00000 | + | 2.44949i | 0.0958315 | + | 0.0782461i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.76217i | 0.120056i | ||||||||
\(983\) | 30.2533i | 0.964930i | 0.875915 | + | 0.482465i | \(0.160258\pi\) | ||||
−0.875915 | + | 0.482465i | \(0.839742\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.7128 | + | 38.8401i | −1.01045 | + | 1.23755i | ||||
\(986\) | −0.732051 | −0.0233132 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.1497i | 0.322905i | ||||||||
\(989\) | −57.7128 | −1.83516 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.7846 | 1.10497 | 0.552485 | − | 0.833523i | \(-0.313680\pi\) | ||||
0.552485 | + | 0.833523i | \(0.313680\pi\) | |||||||
\(992\) | 44.8759i | 1.42481i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.39230 | 0.139315 | ||||||||
\(995\) | 24.2487 | + | 19.7990i | 0.768736 | + | 0.627670i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5927i | 0.842198i | 0.907015 | + | 0.421099i | \(0.138355\pi\) | ||||
−0.907015 | + | 0.421099i | \(0.861645\pi\) | |||||||
\(998\) | − | 0.554803i | − | 0.0175620i | ||||||
\(999\) | 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 | 1305.2.c.f.784.2 | 4 | ||
3.2 | odd | 2 | 145.2.b.b.59.3 | yes | 4 | ||
5.2 | odd | 4 | 6525.2.a.bj.1.3 | 4 | |||
5.3 | odd | 4 | 6525.2.a.bj.1.2 | 4 | |||
5.4 | even | 2 | inner | 1305.2.c.f.784.3 | 4 | ||
12.11 | even | 2 | 2320.2.d.f.929.3 | 4 | |||
15.2 | even | 4 | 725.2.a.f.1.2 | 4 | |||
15.8 | even | 4 | 725.2.a.f.1.3 | 4 | |||
15.14 | odd | 2 | 145.2.b.b.59.2 | ✓ | 4 | ||
60.59 | even | 2 | 2320.2.d.f.929.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.b.b.59.2 | ✓ | 4 | 15.14 | odd | 2 | ||
145.2.b.b.59.3 | yes | 4 | 3.2 | odd | 2 | ||
725.2.a.f.1.2 | 4 | 15.2 | even | 4 | |||
725.2.a.f.1.3 | 4 | 15.8 | even | 4 | |||
1305.2.c.f.784.2 | 4 | 1.1 | even | 1 | trivial | ||
1305.2.c.f.784.3 | 4 | 5.4 | even | 2 | inner | ||
2320.2.d.f.929.1 | 4 | 60.59 | even | 2 | |||
2320.2.d.f.929.3 | 4 | 12.11 | even | 2 | |||
6525.2.a.bj.1.2 | 4 | 5.3 | odd | 4 | |||
6525.2.a.bj.1.3 | 4 | 5.2 | odd | 4 |