Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [145,2,Mod(59,145)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(145, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("145.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 145 = 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 145.b (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: | \(1.15783082931\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 59.2 | ||
Root | \(-0.517638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 145.59 |
Dual form | 145.2.b.b.59.3 |
$q$-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 \(\left(\mathbb{Z}/145\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(117\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | \(-0.0585849\pi\) | |||||||
\(3\) | 1.41421i | 0.816497i | 0.912871 | + | 0.408248i | \(0.133860\pi\) | ||||
−0.912871 | + | 0.408248i | \(0.866140\pi\) | |||||||
\(4\) | 1.73205 | 0.866025 | ||||||||
\(5\) | −1.73205 | + | 1.41421i | −0.774597 | + | 0.632456i | ||||
\(6\) | 0.732051 | 0.298858 | ||||||||
\(7\) | 2.44949i | 0.925820i | 0.886405 | + | 0.462910i | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | − | 1.93185i | − | 0.683013i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.732051 | + | 0.896575i | 0.231495 | + | 0.283522i | ||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | 2.44949i | 0.707107i | ||||||||
\(13\) | − | 1.79315i | − | 0.497331i | −0.968589 | − | 0.248665i | \(-0.920008\pi\) | ||
0.968589 | − | 0.248665i | \(-0.0799919\pi\) | |||||||
\(14\) | 1.26795 | 0.338874 | ||||||||
\(15\) | −2.00000 | − | 2.44949i | −0.516398 | − | 0.632456i | ||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | − | 1.41421i | − | 0.342997i | −0.985184 | − | 0.171499i | \(-0.945139\pi\) | ||
0.985184 | − | 0.171499i | \(-0.0548609\pi\) | |||||||
\(18\) | − | 0.517638i | − | 0.122008i | ||||||
\(19\) | 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 | ||||
\(21\) | −3.46410 | −0.755929 | ||||||||
\(22\) | 0.656339i | 0.139932i | ||||||||
\(23\) | − | 6.31319i | − | 1.31639i | −0.752847 | − | 0.658196i | \(-0.771320\pi\) | ||
0.752847 | − | 0.658196i | \(-0.228680\pi\) | |||||||
\(24\) | 2.73205 | 0.557678 | ||||||||
\(25\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(26\) | −0.928203 | −0.182036 | ||||||||
\(27\) | 5.65685i | 1.08866i | ||||||||
\(28\) | 4.24264i | 0.801784i | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.26795 | + | 1.03528i | −0.231495 | + | 0.189015i | ||||
\(31\) | −8.73205 | −1.56832 | −0.784161 | − | 0.620557i | \(-0.786907\pi\) | ||||
−0.784161 | + | 0.620557i | \(0.786907\pi\) | |||||||
\(32\) | − | 5.13922i | − | 0.908494i | ||||||
\(33\) | − | 1.79315i | − | 0.312148i | ||||||
\(34\) | −0.732051 | −0.125546 | ||||||||
\(35\) | −3.46410 | − | 4.24264i | −0.585540 | − | 0.717137i | ||||
\(36\) | 1.73205 | 0.288675 | ||||||||
\(37\) | − | 9.14162i | − | 1.50287i | −0.659805 | − | 0.751437i | \(-0.729361\pi\) | ||
0.659805 | − | 0.751437i | \(-0.270639\pi\) | |||||||
\(38\) | − | 1.69161i | − | 0.274416i | ||||||
\(39\) | 2.53590 | 0.406069 | ||||||||
\(40\) | 2.73205 | + | 3.34607i | 0.431975 | + | 0.529059i | ||||
\(41\) | −6.92820 | −1.08200 | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541002 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(42\) | 1.79315i | 0.276689i | ||||||||
\(43\) | 9.14162i | 1.39408i | 0.717030 | + | 0.697042i | \(0.245501\pi\) | ||||
−0.717030 | + | 0.697042i | \(0.754499\pi\) | |||||||
\(44\) | −2.19615 | −0.331082 | ||||||||
\(45\) | −1.73205 | + | 1.41421i | −0.258199 | + | 0.210819i | ||||
\(46\) | −3.26795 | −0.481833 | ||||||||
\(47\) | − | 1.41421i | − | 0.206284i | −0.994667 | − | 0.103142i | \(-0.967110\pi\) | ||
0.994667 | − | 0.103142i | \(-0.0328896\pi\) | |||||||
\(48\) | 3.48477i | 0.502983i | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.53590 | − | 0.517638i | −0.358630 | − | 0.0732051i | ||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | − | 3.10583i | − | 0.430701i | ||||||
\(53\) | 5.93426i | 0.815133i | 0.913176 | + | 0.407566i | \(0.133622\pi\) | ||||
−0.913176 | + | 0.407566i | \(0.866378\pi\) | |||||||
\(54\) | 2.92820 | 0.398478 | ||||||||
\(55\) | 2.19615 | − | 1.79315i | 0.296129 | − | 0.241788i | ||||
\(56\) | 4.73205 | 0.632347 | ||||||||
\(57\) | 4.62158i | 0.612143i | ||||||||
\(58\) | 0.517638i | 0.0679692i | ||||||||
\(59\) | 10.3923 | 1.35296 | 0.676481 | − | 0.736460i | \(-0.263504\pi\) | ||||
0.676481 | + | 0.736460i | \(0.263504\pi\) | |||||||
\(60\) | −3.46410 | − | 4.24264i | −0.447214 | − | 0.547723i | ||||
\(61\) | 2.92820 | 0.374918 | 0.187459 | − | 0.982272i | \(-0.439975\pi\) | ||||
0.187459 | + | 0.982272i | \(0.439975\pi\) | |||||||
\(62\) | 4.52004i | 0.574046i | ||||||||
\(63\) | 2.44949i | 0.308607i | ||||||||
\(64\) | 2.26795 | 0.283494 | ||||||||
\(65\) | 2.53590 | + | 3.10583i | 0.314539 | + | 0.385231i | ||||
\(66\) | −0.928203 | −0.114254 | ||||||||
\(67\) | − | 4.24264i | − | 0.518321i | −0.965834 | − | 0.259161i | \(-0.916554\pi\) | ||
0.965834 | − | 0.259161i | \(-0.0834459\pi\) | |||||||
\(68\) | − | 2.44949i | − | 0.297044i | ||||||
\(69\) | 8.92820 | 1.07483 | ||||||||
\(70\) | −2.19615 | + | 1.79315i | −0.262490 | + | 0.214323i | ||||
\(71\) | 3.46410 | 0.411113 | 0.205557 | − | 0.978645i | \(-0.434100\pi\) | ||||
0.205557 | + | 0.978645i | \(0.434100\pi\) | |||||||
\(72\) | − | 1.93185i | − | 0.227671i | ||||||
\(73\) | − | 7.34847i | − | 0.860073i | −0.902811 | − | 0.430037i | \(-0.858501\pi\) | ||
0.902811 | − | 0.430037i | \(-0.141499\pi\) | |||||||
\(74\) | −4.73205 | −0.550090 | ||||||||
\(75\) | 6.92820 | + | 1.41421i | 0.800000 | + | 0.163299i | ||||
\(76\) | 5.66025 | 0.649276 | ||||||||
\(77\) | − | 3.10583i | − | 0.353942i | ||||||
\(78\) | − | 1.31268i | − | 0.148631i | ||||||
\(79\) | 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 | ||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 3.58630i | 0.396041i | ||||||||
\(83\) | 10.1769i | 1.11706i | 0.829484 | + | 0.558530i | \(0.188634\pi\) | ||||
−0.829484 | + | 0.558530i | \(0.811366\pi\) | |||||||
\(84\) | −6.00000 | −0.654654 | ||||||||
\(85\) | 2.00000 | + | 2.44949i | 0.216930 | + | 0.265684i | ||||
\(86\) | 4.73205 | 0.510270 | ||||||||
\(87\) | − | 1.41421i | − | 0.151620i | ||||||
\(88\) | 2.44949i | 0.261116i | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0.732051 | + | 0.896575i | 0.0771649 | + | 0.0945074i | ||||
\(91\) | 4.39230 | 0.460439 | ||||||||
\(92\) | − | 10.9348i | − | 1.14003i | ||||||
\(93\) | − | 12.3490i | − | 1.28053i | ||||||
\(94\) | −0.732051 | −0.0755053 | ||||||||
\(95\) | −5.66025 | + | 4.62158i | −0.580730 | + | 0.474164i | ||||
\(96\) | 7.26795 | 0.741782 | ||||||||
\(97\) | 10.9348i | 1.11026i | 0.831764 | + | 0.555129i | \(0.187331\pi\) | ||||
−0.831764 | + | 0.555129i | \(0.812669\pi\) | |||||||
\(98\) | − | 0.517638i | − | 0.0522893i | ||||||
\(99\) | −1.26795 | −0.127434 | ||||||||
\(100\) | 1.73205 | − | 8.48528i | 0.173205 | − | 0.848528i | ||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | − | 1.03528i | − | 0.102508i | ||||||
\(103\) | 9.14162i | 0.900751i | 0.892839 | + | 0.450375i | \(0.148710\pi\) | ||||
−0.892839 | + | 0.450375i | \(0.851290\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | 6.00000 | − | 4.89898i | 0.585540 | − | 0.478091i | ||||
\(106\) | 3.07180 | 0.298359 | ||||||||
\(107\) | 18.6622i | 1.80414i | 0.431589 | + | 0.902070i | \(0.357953\pi\) | ||||
−0.431589 | + | 0.902070i | \(0.642047\pi\) | |||||||
\(108\) | 9.79796i | 0.942809i | ||||||||
\(109\) | −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 | ||||
\(111\) | 12.9282 | 1.22709 | ||||||||
\(112\) | 6.03579i | 0.570329i | ||||||||
\(113\) | − | 13.0053i | − | 1.22344i | −0.791075 | − | 0.611719i | \(-0.790478\pi\) | ||
0.791075 | − | 0.611719i | \(-0.209522\pi\) | |||||||
\(114\) | 2.39230 | 0.224060 | ||||||||
\(115\) | 8.92820 | + | 10.9348i | 0.832559 | + | 1.01967i | ||||
\(116\) | −1.73205 | −0.160817 | ||||||||
\(117\) | − | 1.79315i | − | 0.165777i | ||||||
\(118\) | − | 5.37945i | − | 0.495219i | ||||||
\(119\) | 3.46410 | 0.317554 | ||||||||
\(120\) | −4.73205 | + | 3.86370i | −0.431975 | + | 0.352706i | ||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | − | 1.51575i | − | 0.137230i | ||||||
\(123\) | − | 9.79796i | − | 0.883452i | ||||||
\(124\) | −15.1244 | −1.35821 | ||||||||
\(125\) | 5.19615 | + | 9.89949i | 0.464758 | + | 0.885438i | ||||
\(126\) | 1.26795 | 0.112958 | ||||||||
\(127\) | − | 4.24264i | − | 0.376473i | −0.982124 | − | 0.188237i | \(-0.939723\pi\) | ||
0.982124 | − | 0.188237i | \(-0.0602772\pi\) | |||||||
\(128\) | − | 11.4524i | − | 1.01226i | ||||||
\(129\) | −12.9282 | −1.13826 | ||||||||
\(130\) | 1.60770 | − | 1.31268i | 0.141004 | − | 0.115129i | ||||
\(131\) | −4.73205 | −0.413441 | −0.206721 | − | 0.978400i | \(-0.566279\pi\) | ||||
−0.206721 | + | 0.978400i | \(0.566279\pi\) | |||||||
\(132\) | − | 3.10583i | − | 0.270328i | ||||||
\(133\) | 8.00481i | 0.694105i | ||||||||
\(134\) | −2.19615 | −0.189719 | ||||||||
\(135\) | −8.00000 | − | 9.79796i | −0.688530 | − | 0.843274i | ||||
\(136\) | −2.73205 | −0.234271 | ||||||||
\(137\) | − | 14.7985i | − | 1.26432i | −0.774838 | − | 0.632159i | \(-0.782169\pi\) | ||
0.774838 | − | 0.632159i | \(-0.217831\pi\) | |||||||
\(138\) | − | 4.62158i | − | 0.393415i | ||||||
\(139\) | 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 | ||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | − | 1.79315i | − | 0.150478i | ||||||
\(143\) | 2.27362i | 0.190130i | ||||||||
\(144\) | 2.46410 | 0.205342 | ||||||||
\(145\) | 1.73205 | − | 1.41421i | 0.143839 | − | 0.117444i | ||||
\(146\) | −3.80385 | −0.314809 | ||||||||
\(147\) | 1.41421i | 0.116642i | ||||||||
\(148\) | − | 15.8338i | − | 1.30153i | ||||||
\(149\) | 0.928203 | 0.0760414 | 0.0380207 | − | 0.999277i | \(-0.487895\pi\) | ||||
0.0380207 | + | 0.999277i | \(0.487895\pi\) | |||||||
\(150\) | 0.732051 | − | 3.58630i | 0.0597717 | − | 0.292820i | ||||
\(151\) | −18.7846 | −1.52867 | −0.764335 | − | 0.644819i | \(-0.776933\pi\) | ||||
−0.764335 | + | 0.644819i | \(0.776933\pi\) | |||||||
\(152\) | − | 6.31319i | − | 0.512068i | ||||||
\(153\) | − | 1.41421i | − | 0.114332i | ||||||
\(154\) | −1.60770 | −0.129552 | ||||||||
\(155\) | 15.1244 | − | 12.3490i | 1.21482 | − | 0.991894i | ||||
\(156\) | 4.39230 | 0.351666 | ||||||||
\(157\) | − | 10.9348i | − | 0.872690i | −0.899780 | − | 0.436345i | \(-0.856273\pi\) | ||
0.899780 | − | 0.436345i | \(-0.143727\pi\) | |||||||
\(158\) | − | 2.17209i | − | 0.172802i | ||||||
\(159\) | −8.39230 | −0.665553 | ||||||||
\(160\) | 7.26795 | + | 8.90138i | 0.574582 | + | 0.703716i | ||||
\(161\) | 15.4641 | 1.21874 | ||||||||
\(162\) | 2.58819i | 0.203347i | ||||||||
\(163\) | 14.0406i | 1.09974i | 0.835249 | + | 0.549872i | \(0.185324\pi\) | ||||
−0.835249 | + | 0.549872i | \(0.814676\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | 2.53590 | + | 3.10583i | 0.197419 | + | 0.241788i | ||||
\(166\) | 5.26795 | 0.408872 | ||||||||
\(167\) | − | 11.2122i | − | 0.867624i | −0.901003 | − | 0.433812i | \(-0.857168\pi\) | ||
0.901003 | − | 0.433812i | \(-0.142832\pi\) | |||||||
\(168\) | 6.69213i | 0.516309i | ||||||||
\(169\) | 9.78461 | 0.752662 | ||||||||
\(170\) | 1.26795 | − | 1.03528i | 0.0972473 | − | 0.0794021i | ||||
\(171\) | 3.26795 | 0.249906 | ||||||||
\(172\) | 15.8338i | 1.20731i | ||||||||
\(173\) | 4.62158i | 0.351372i | 0.984446 | + | 0.175686i | \(0.0562144\pi\) | ||||
−0.984446 | + | 0.175686i | \(0.943786\pi\) | |||||||
\(174\) | −0.732051 | −0.0554966 | ||||||||
\(175\) | 12.0000 | + | 2.44949i | 0.907115 | + | 0.185164i | ||||
\(176\) | −3.12436 | −0.235507 | ||||||||
\(177\) | 14.6969i | 1.10469i | ||||||||
\(178\) | 5.37945i | 0.403207i | ||||||||
\(179\) | −2.53590 | −0.189542 | −0.0947710 | − | 0.995499i | \(-0.530212\pi\) | ||||
−0.0947710 | + | 0.995499i | \(0.530212\pi\) | |||||||
\(180\) | −3.00000 | + | 2.44949i | −0.223607 | + | 0.182574i | ||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | − | 2.27362i | − | 0.168532i | ||||||
\(183\) | 4.14110i | 0.306119i | ||||||||
\(184\) | −12.1962 | −0.899112 | ||||||||
\(185\) | 12.9282 | + | 15.8338i | 0.950500 | + | 1.16412i | ||||
\(186\) | −6.39230 | −0.468707 | ||||||||
\(187\) | 1.79315i | 0.131128i | ||||||||
\(188\) | − | 2.44949i | − | 0.178647i | ||||||
\(189\) | −13.8564 | −1.00791 | ||||||||
\(190\) | 2.39230 | + | 2.92996i | 0.173556 | + | 0.212562i | ||||
\(191\) | 15.1244 | 1.09436 | 0.547180 | − | 0.837015i | \(-0.315701\pi\) | ||||
0.547180 | + | 0.837015i | \(0.315701\pi\) | |||||||
\(192\) | 3.20736i | 0.231472i | ||||||||
\(193\) | − | 0.656339i | − | 0.0472443i | −0.999721 | − | 0.0236222i | \(-0.992480\pi\) | ||
0.999721 | − | 0.0236222i | \(-0.00751986\pi\) | |||||||
\(194\) | 5.66025 | 0.406383 | ||||||||
\(195\) | −4.39230 | + | 3.58630i | −0.314539 | + | 0.256820i | ||||
\(196\) | 1.73205 | 0.123718 | ||||||||
\(197\) | 22.4243i | 1.59767i | 0.601551 | + | 0.798834i | \(0.294550\pi\) | ||||
−0.601551 | + | 0.798834i | \(0.705450\pi\) | |||||||
\(198\) | 0.656339i | 0.0466440i | ||||||||
\(199\) | 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 | ||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 3.10583i | 0.218525i | ||||||||
\(203\) | − | 2.44949i | − | 0.171920i | ||||||
\(204\) | 3.46410 | 0.242536 | ||||||||
\(205\) | 12.0000 | − | 9.79796i | 0.838116 | − | 0.684319i | ||||
\(206\) | 4.73205 | 0.329698 | ||||||||
\(207\) | − | 6.31319i | − | 0.438797i | ||||||
\(208\) | − | 4.41851i | − | 0.306368i | ||||||
\(209\) | −4.14359 | −0.286618 | ||||||||
\(210\) | −2.53590 | − | 3.10583i | −0.174994 | − | 0.214323i | ||||
\(211\) | −14.7321 | −1.01420 | −0.507098 | − | 0.861888i | \(-0.669282\pi\) | ||||
−0.507098 | + | 0.861888i | \(0.669282\pi\) | |||||||
\(212\) | 10.2784i | 0.705926i | ||||||||
\(213\) | 4.89898i | 0.335673i | ||||||||
\(214\) | 9.66025 | 0.660361 | ||||||||
\(215\) | −12.9282 | − | 15.8338i | −0.881696 | − | 1.07985i | ||||
\(216\) | 10.9282 | 0.743570 | ||||||||
\(217\) | − | 21.3891i | − | 1.45198i | ||||||
\(218\) | 9.24316i | 0.626026i | ||||||||
\(219\) | 10.3923 | 0.702247 | ||||||||
\(220\) | 3.80385 | − | 3.10583i | 0.256455 | − | 0.209395i | ||||
\(221\) | −2.53590 | −0.170583 | ||||||||
\(222\) | − | 6.69213i | − | 0.449146i | ||||||
\(223\) | − | 15.3533i | − | 1.02813i | −0.857751 | − | 0.514066i | \(-0.828139\pi\) | ||
0.857751 | − | 0.514066i | \(-0.171861\pi\) | |||||||
\(224\) | 12.5885 | 0.841102 | ||||||||
\(225\) | 1.00000 | − | 4.89898i | 0.0666667 | − | 0.326599i | ||||
\(226\) | −6.73205 | −0.447809 | ||||||||
\(227\) | 20.4553i | 1.35767i | 0.734292 | + | 0.678834i | \(0.237514\pi\) | ||||
−0.734292 | + | 0.678834i | \(0.762486\pi\) | |||||||
\(228\) | 8.00481i | 0.530131i | ||||||||
\(229\) | −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 | ||||
\(231\) | 4.39230 | 0.288992 | ||||||||
\(232\) | 1.93185i | 0.126832i | ||||||||
\(233\) | − | 3.38323i | − | 0.221643i | −0.993840 | − | 0.110821i | \(-0.964652\pi\) | ||
0.993840 | − | 0.110821i | \(-0.0353481\pi\) | |||||||
\(234\) | −0.928203 | −0.0606785 | ||||||||
\(235\) | 2.00000 | + | 2.44949i | 0.130466 | + | 0.159787i | ||||
\(236\) | 18.0000 | 1.17170 | ||||||||
\(237\) | 5.93426i | 0.385471i | ||||||||
\(238\) | − | 1.79315i | − | 0.116233i | ||||||
\(239\) | −10.3923 | −0.672222 | −0.336111 | − | 0.941822i | \(-0.609112\pi\) | ||||
−0.336111 | + | 0.941822i | \(0.609112\pi\) | |||||||
\(240\) | −4.92820 | − | 6.03579i | −0.318114 | − | 0.389609i | ||||
\(241\) | 11.4641 | 0.738468 | 0.369234 | − | 0.929337i | \(-0.379620\pi\) | ||||
0.369234 | + | 0.929337i | \(0.379620\pi\) | |||||||
\(242\) | 4.86181i | 0.312529i | ||||||||
\(243\) | 9.89949i | 0.635053i | ||||||||
\(244\) | 5.07180 | 0.324689 | ||||||||
\(245\) | −1.73205 | + | 1.41421i | −0.110657 | + | 0.0903508i | ||||
\(246\) | −5.07180 | −0.323366 | ||||||||
\(247\) | − | 5.85993i | − | 0.372858i | ||||||
\(248\) | 16.8690i | 1.07118i | ||||||||
\(249\) | −14.3923 | −0.912075 | ||||||||
\(250\) | 5.12436 | − | 2.68973i | 0.324093 | − | 0.170113i | ||||
\(251\) | 15.1244 | 0.954641 | 0.477320 | − | 0.878729i | \(-0.341608\pi\) | ||||
0.477320 | + | 0.878729i | \(0.341608\pi\) | |||||||
\(252\) | 4.24264i | 0.267261i | ||||||||
\(253\) | 8.00481i | 0.503258i | ||||||||
\(254\) | −2.19615 | −0.137799 | ||||||||
\(255\) | −3.46410 | + | 2.82843i | −0.216930 | + | 0.177123i | ||||
\(256\) | −1.39230 | −0.0870191 | ||||||||
\(257\) | 9.52056i | 0.593876i | 0.954897 | + | 0.296938i | \(0.0959655\pi\) | ||||
−0.954897 | + | 0.296938i | \(0.904035\pi\) | |||||||
\(258\) | 6.69213i | 0.416634i | ||||||||
\(259\) | 22.3923 | 1.39139 | ||||||||
\(260\) | 4.39230 | + | 5.37945i | 0.272399 | + | 0.333620i | ||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 2.44949i | 0.151330i | ||||||||
\(263\) | 4.79744i | 0.295823i | 0.989001 | + | 0.147912i | \(0.0472551\pi\) | ||||
−0.989001 | + | 0.147912i | \(0.952745\pi\) | |||||||
\(264\) | −3.46410 | −0.213201 | ||||||||
\(265\) | −8.39230 | − | 10.2784i | −0.515535 | − | 0.631399i | ||||
\(266\) | 4.14359 | 0.254060 | ||||||||
\(267\) | − | 14.6969i | − | 0.899438i | ||||||
\(268\) | − | 7.34847i | − | 0.448879i | ||||||
\(269\) | 12.0000 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(270\) | −5.07180 | + | 4.14110i | −0.308660 | + | 0.252020i | ||||
\(271\) | −26.7321 | −1.62386 | −0.811928 | − | 0.583757i | \(-0.801582\pi\) | ||||
−0.811928 | + | 0.583757i | \(0.801582\pi\) | |||||||
\(272\) | − | 3.48477i | − | 0.211295i | ||||||
\(273\) | 6.21166i | 0.375947i | ||||||||
\(274\) | −7.66025 | −0.462773 | ||||||||
\(275\) | −1.26795 | + | 6.21166i | −0.0764602 | + | 0.374577i | ||||
\(276\) | 15.4641 | 0.930830 | ||||||||
\(277\) | − | 18.7637i | − | 1.12740i | −0.825979 | − | 0.563701i | \(-0.809377\pi\) | ||
0.825979 | − | 0.563701i | \(-0.190623\pi\) | |||||||
\(278\) | − | 4.14110i | − | 0.248367i | ||||||
\(279\) | −8.73205 | −0.522774 | ||||||||
\(280\) | −8.19615 | + | 6.69213i | −0.489814 | + | 0.399931i | ||||
\(281\) | 32.7846 | 1.95577 | 0.977883 | − | 0.209153i | \(-0.0670707\pi\) | ||||
0.977883 | + | 0.209153i | \(0.0670707\pi\) | |||||||
\(282\) | − | 1.03528i | − | 0.0616498i | ||||||
\(283\) | − | 27.4249i | − | 1.63024i | −0.579293 | − | 0.815119i | \(-0.696671\pi\) | ||
0.579293 | − | 0.815119i | \(-0.303329\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | −6.53590 | − | 8.00481i | −0.387153 | − | 0.474164i | ||||
\(286\) | 1.17691 | 0.0695924 | ||||||||
\(287\) | − | 16.9706i | − | 1.00174i | ||||||
\(288\) | − | 5.13922i | − | 0.302831i | ||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | −0.732051 | − | 0.896575i | −0.0429875 | − | 0.0526487i | ||||
\(291\) | −15.4641 | −0.906522 | ||||||||
\(292\) | − | 12.7279i | − | 0.744845i | ||||||
\(293\) | 30.7338i | 1.79549i | 0.440520 | + | 0.897743i | \(0.354794\pi\) | ||||
−0.440520 | + | 0.897743i | \(0.645206\pi\) | |||||||
\(294\) | 0.732051 | 0.0426941 | ||||||||
\(295\) | −18.0000 | + | 14.6969i | −1.04800 | + | 0.855689i | ||||
\(296\) | −17.6603 | −1.02648 | ||||||||
\(297\) | − | 7.17260i | − | 0.416197i | ||||||
\(298\) | − | 0.480473i | − | 0.0278331i | ||||||
\(299\) | −11.3205 | −0.654682 | ||||||||
\(300\) | 12.0000 | + | 2.44949i | 0.692820 | + | 0.141421i | ||||
\(301\) | −22.3923 | −1.29067 | ||||||||
\(302\) | 9.72363i | 0.559532i | ||||||||
\(303\) | − | 8.48528i | − | 0.487467i | ||||||
\(304\) | 8.05256 | 0.461846 | ||||||||
\(305\) | −5.07180 | + | 4.14110i | −0.290410 | + | 0.237119i | ||||
\(306\) | −0.732051 | −0.0418486 | ||||||||
\(307\) | − | 10.4543i | − | 0.596658i | −0.954463 | − | 0.298329i | \(-0.903571\pi\) | ||
0.954463 | − | 0.298329i | \(-0.0964293\pi\) | |||||||
\(308\) | − | 5.37945i | − | 0.306523i | ||||||
\(309\) | −12.9282 | −0.735460 | ||||||||
\(310\) | −6.39230 | − | 7.82894i | −0.363059 | − | 0.444654i | ||||
\(311\) | −6.58846 | −0.373597 | −0.186799 | − | 0.982398i | \(-0.559811\pi\) | ||||
−0.186799 | + | 0.982398i | \(0.559811\pi\) | |||||||
\(312\) | − | 4.89898i | − | 0.277350i | ||||||
\(313\) | − | 23.6627i | − | 1.33749i | −0.743490 | − | 0.668747i | \(-0.766831\pi\) | ||
0.743490 | − | 0.668747i | \(-0.233169\pi\) | |||||||
\(314\) | −5.66025 | −0.319427 | ||||||||
\(315\) | −3.46410 | − | 4.24264i | −0.195180 | − | 0.239046i | ||||
\(316\) | 7.26795 | 0.408854 | ||||||||
\(317\) | 5.75839i | 0.323423i | 0.986838 | + | 0.161712i | \(0.0517015\pi\) | ||||
−0.986838 | + | 0.161712i | \(0.948299\pi\) | |||||||
\(318\) | 4.34418i | 0.243609i | ||||||||
\(319\) | 1.26795 | 0.0709915 | ||||||||
\(320\) | −3.92820 | + | 3.20736i | −0.219593 | + | 0.179297i | ||||
\(321\) | −26.3923 | −1.47307 | ||||||||
\(322\) | − | 8.00481i | − | 0.446091i | ||||||
\(323\) | − | 4.62158i | − | 0.257151i | ||||||
\(324\) | −8.66025 | −0.481125 | ||||||||
\(325\) | −8.78461 | − | 1.79315i | −0.487282 | − | 0.0994661i | ||||
\(326\) | 7.26795 | 0.402534 | ||||||||
\(327\) | − | 25.2528i | − | 1.39648i | ||||||
\(328\) | 13.3843i | 0.739022i | ||||||||
\(329\) | 3.46410 | 0.190982 | ||||||||
\(330\) | 1.60770 | − | 1.31268i | 0.0885007 | − | 0.0722605i | ||||
\(331\) | −18.1962 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(332\) | 17.6269i | 0.967402i | ||||||||
\(333\) | − | 9.14162i | − | 0.500958i | ||||||
\(334\) | −5.80385 | −0.317572 | ||||||||
\(335\) | 6.00000 | + | 7.34847i | 0.327815 | + | 0.401490i | ||||
\(336\) | −8.53590 | −0.465671 | ||||||||
\(337\) | 27.9053i | 1.52010i | 0.649864 | + | 0.760050i | \(0.274826\pi\) | ||||
−0.649864 | + | 0.760050i | \(0.725174\pi\) | |||||||
\(338\) | − | 5.06489i | − | 0.275494i | ||||||
\(339\) | 18.3923 | 0.998933 | ||||||||
\(340\) | 3.46410 | + | 4.24264i | 0.187867 | + | 0.230089i | ||||
\(341\) | 11.0718 | 0.599571 | ||||||||
\(342\) | − | 1.69161i | − | 0.0914721i | ||||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | 17.6603 | 0.952177 | ||||||||
\(345\) | −15.4641 | + | 12.6264i | −0.832559 | + | 0.679782i | ||||
\(346\) | 2.39230 | 0.128611 | ||||||||
\(347\) | − | 21.4906i | − | 1.15368i | −0.816859 | − | 0.576838i | \(-0.804286\pi\) | ||
0.816859 | − | 0.576838i | \(-0.195714\pi\) | |||||||
\(348\) | − | 2.44949i | − | 0.131306i | ||||||
\(349\) | 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 | ||||
\(351\) | 10.1436 | 0.541425 | ||||||||
\(352\) | 6.51626i | 0.347318i | ||||||||
\(353\) | − | 31.9449i | − | 1.70026i | −0.526576 | − | 0.850128i | \(-0.676525\pi\) | ||
0.526576 | − | 0.850128i | \(-0.323475\pi\) | |||||||
\(354\) | 7.60770 | 0.404344 | ||||||||
\(355\) | −6.00000 | + | 4.89898i | −0.318447 | + | 0.260011i | ||||
\(356\) | −18.0000 | −0.953998 | ||||||||
\(357\) | 4.89898i | 0.259281i | ||||||||
\(358\) | 1.31268i | 0.0693772i | ||||||||
\(359\) | 7.26795 | 0.383588 | 0.191794 | − | 0.981435i | \(-0.438570\pi\) | ||||
0.191794 | + | 0.981435i | \(0.438570\pi\) | |||||||
\(360\) | 2.73205 | + | 3.34607i | 0.143992 | + | 0.176353i | ||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | 8.28221i | 0.435303i | ||||||||
\(363\) | − | 13.2827i | − | 0.697162i | ||||||
\(364\) | 7.60770 | 0.398752 | ||||||||
\(365\) | 10.3923 | + | 12.7279i | 0.543958 | + | 0.666210i | ||||
\(366\) | 2.14359 | 0.112047 | ||||||||
\(367\) | 33.6365i | 1.75581i | 0.478833 | + | 0.877906i | \(0.341060\pi\) | ||||
−0.478833 | + | 0.877906i | \(0.658940\pi\) | |||||||
\(368\) | − | 15.5563i | − | 0.810931i | ||||||
\(369\) | −6.92820 | −0.360668 | ||||||||
\(370\) | 8.19615 | − | 6.69213i | 0.426098 | − | 0.347907i | ||||
\(371\) | −14.5359 | −0.754666 | ||||||||
\(372\) | − | 21.3891i | − | 1.10897i | ||||||
\(373\) | − | 19.5959i | − | 1.01464i | −0.861758 | − | 0.507319i | \(-0.830637\pi\) | ||
0.861758 | − | 0.507319i | \(-0.169363\pi\) | |||||||
\(374\) | 0.928203 | 0.0479962 | ||||||||
\(375\) | −14.0000 | + | 7.34847i | −0.722957 | + | 0.379473i | ||||
\(376\) | −2.73205 | −0.140895 | ||||||||
\(377\) | 1.79315i | 0.0923520i | ||||||||
\(378\) | 7.17260i | 0.368919i | ||||||||
\(379\) | 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 | ||||
\(381\) | 6.00000 | 0.307389 | ||||||||
\(382\) | − | 7.82894i | − | 0.400564i | ||||||
\(383\) | − | 0.933740i | − | 0.0477119i | −0.999715 | − | 0.0238559i | \(-0.992406\pi\) | ||
0.999715 | − | 0.0238559i | \(-0.00759430\pi\) | |||||||
\(384\) | 16.1962 | 0.826506 | ||||||||
\(385\) | 4.39230 | + | 5.37945i | 0.223853 | + | 0.274162i | ||||
\(386\) | −0.339746 | −0.0172926 | ||||||||
\(387\) | 9.14162i | 0.464695i | ||||||||
\(388\) | 18.9396i | 0.961511i | ||||||||
\(389\) | 20.7846 | 1.05382 | 0.526911 | − | 0.849921i | \(-0.323350\pi\) | ||||
0.526911 | + | 0.849921i | \(0.323350\pi\) | |||||||
\(390\) | 1.85641 | + | 2.27362i | 0.0940028 | + | 0.115129i | ||||
\(391\) | −8.92820 | −0.451519 | ||||||||
\(392\) | − | 1.93185i | − | 0.0975732i | ||||||
\(393\) | − | 6.69213i | − | 0.337573i | ||||||
\(394\) | 11.6077 | 0.584787 | ||||||||
\(395\) | −7.26795 | + | 5.93426i | −0.365690 | + | 0.298585i | ||||
\(396\) | −2.19615 | −0.110361 | ||||||||
\(397\) | − | 4.89898i | − | 0.245873i | −0.992415 | − | 0.122936i | \(-0.960769\pi\) | ||
0.992415 | − | 0.122936i | \(-0.0392311\pi\) | |||||||
\(398\) | − | 7.24693i | − | 0.363256i | ||||||
\(399\) | −11.3205 | −0.566734 | ||||||||
\(400\) | 2.46410 | − | 12.0716i | 0.123205 | − | 0.603579i | ||||
\(401\) | 37.8564 | 1.89046 | 0.945229 | − | 0.326407i | \(-0.105838\pi\) | ||||
0.945229 | + | 0.326407i | \(0.105838\pi\) | |||||||
\(402\) | − | 3.10583i | − | 0.154905i | ||||||
\(403\) | 15.6579i | 0.779975i | ||||||||
\(404\) | −10.3923 | −0.517036 | ||||||||
\(405\) | 8.66025 | − | 7.07107i | 0.430331 | − | 0.351364i | ||||
\(406\) | −1.26795 | −0.0629273 | ||||||||
\(407\) | 11.5911i | 0.574550i | ||||||||
\(408\) | − | 3.86370i | − | 0.191282i | ||||||
\(409\) | −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 | ||||
\(411\) | 20.9282 | 1.03231 | ||||||||
\(412\) | 15.8338i | 0.780073i | ||||||||
\(413\) | 25.4558i | 1.25260i | ||||||||
\(414\) | −3.26795 | −0.160611 | ||||||||
\(415\) | −14.3923 | − | 17.6269i | −0.706490 | − | 0.865271i | ||||
\(416\) | −9.21539 | −0.451822 | ||||||||
\(417\) | 11.3137i | 0.554035i | ||||||||
\(418\) | 2.14488i | 0.104910i | ||||||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 10.3923 | − | 8.48528i | 0.507093 | − | 0.414039i | ||||
\(421\) | 5.46410 | 0.266304 | 0.133152 | − | 0.991096i | \(-0.457490\pi\) | ||||
0.133152 | + | 0.991096i | \(0.457490\pi\) | |||||||
\(422\) | 7.62587i | 0.371222i | ||||||||
\(423\) | − | 1.41421i | − | 0.0687614i | ||||||
\(424\) | 11.4641 | 0.556746 | ||||||||
\(425\) | −6.92820 | − | 1.41421i | −0.336067 | − | 0.0685994i | ||||
\(426\) | 2.53590 | 0.122865 | ||||||||
\(427\) | 7.17260i | 0.347107i | ||||||||
\(428\) | 32.3238i | 1.56243i | ||||||||
\(429\) | −3.21539 | −0.155241 | ||||||||
\(430\) | −8.19615 | + | 6.69213i | −0.395254 | + | 0.322723i | ||||
\(431\) | −37.1769 | −1.79075 | −0.895374 | − | 0.445314i | \(-0.853092\pi\) | ||||
−0.895374 | + | 0.445314i | \(0.853092\pi\) | |||||||
\(432\) | 13.9391i | 0.670644i | ||||||||
\(433\) | − | 2.92996i | − | 0.140805i | −0.997519 | − | 0.0704025i | \(-0.977572\pi\) | ||
0.997519 | − | 0.0704025i | \(-0.0224284\pi\) | |||||||
\(434\) | −11.0718 | −0.531463 | ||||||||
\(435\) | 2.00000 | + | 2.44949i | 0.0958927 | + | 0.117444i | ||||
\(436\) | −30.9282 | −1.48119 | ||||||||
\(437\) | − | 20.6312i | − | 0.986924i | ||||||
\(438\) | − | 5.37945i | − | 0.257040i | ||||||
\(439\) | 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 | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 1.31268i | 0.0624377i | ||||||||
\(443\) | 18.1817i | 0.863839i | 0.901912 | + | 0.431919i | \(0.142164\pi\) | ||||
−0.901912 | + | 0.431919i | \(0.857836\pi\) | |||||||
\(444\) | 22.3923 | 1.06269 | ||||||||
\(445\) | 18.0000 | − | 14.6969i | 0.853282 | − | 0.696702i | ||||
\(446\) | −7.94744 | −0.376322 | ||||||||
\(447\) | 1.31268i | 0.0620875i | ||||||||
\(448\) | 5.55532i | 0.262464i | ||||||||
\(449\) | 25.8564 | 1.22024 | 0.610120 | − | 0.792309i | \(-0.291121\pi\) | ||||
0.610120 | + | 0.792309i | \(0.291121\pi\) | |||||||
\(450\) | −2.53590 | − | 0.517638i | −0.119543 | − | 0.0244017i | ||||
\(451\) | 8.78461 | 0.413651 | ||||||||
\(452\) | − | 22.5259i | − | 1.05953i | ||||||
\(453\) | − | 26.5654i | − | 1.24815i | ||||||
\(454\) | 10.5885 | 0.496941 | ||||||||
\(455\) | −7.60770 | + | 6.21166i | −0.356654 | + | 0.291207i | ||||
\(456\) | 8.92820 | 0.418101 | ||||||||
\(457\) | 23.6627i | 1.10689i | 0.832884 | + | 0.553447i | \(0.186688\pi\) | ||||
−0.832884 | + | 0.553447i | \(0.813312\pi\) | |||||||
\(458\) | 9.72363i | 0.454355i | ||||||||
\(459\) | 8.00000 | 0.373408 | ||||||||
\(460\) | 15.4641 | + | 18.9396i | 0.721017 | + | 0.883062i | ||||
\(461\) | 24.9282 | 1.16102 | 0.580511 | − | 0.814252i | \(-0.302853\pi\) | ||||
0.580511 | + | 0.814252i | \(0.302853\pi\) | |||||||
\(462\) | − | 2.27362i | − | 0.105779i | ||||||
\(463\) | 6.86800i | 0.319183i | 0.987183 | + | 0.159591i | \(0.0510177\pi\) | ||||
−0.987183 | + | 0.159591i | \(0.948982\pi\) | |||||||
\(464\) | −2.46410 | −0.114393 | ||||||||
\(465\) | 17.4641 | + | 21.3891i | 0.809878 | + | 0.991894i | ||||
\(466\) | −1.75129 | −0.0811269 | ||||||||
\(467\) | − | 21.0101i | − | 0.972233i | −0.873894 | − | 0.486116i | \(-0.838413\pi\) | ||
0.873894 | − | 0.486116i | \(-0.161587\pi\) | |||||||
\(468\) | − | 3.10583i | − | 0.143567i | ||||||
\(469\) | 10.3923 | 0.479872 | ||||||||
\(470\) | 1.26795 | − | 1.03528i | 0.0584861 | − | 0.0477537i | ||||
\(471\) | 15.4641 | 0.712548 | ||||||||
\(472\) | − | 20.0764i | − | 0.924091i | ||||||
\(473\) | − | 11.5911i | − | 0.532960i | ||||||
\(474\) | 3.07180 | 0.141092 | ||||||||
\(475\) | 3.26795 | − | 16.0096i | 0.149944 | − | 0.734572i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | 5.93426i | 0.271711i | ||||||||
\(478\) | 5.37945i | 0.246050i | ||||||||
\(479\) | −5.66025 | −0.258624 | −0.129312 | − | 0.991604i | \(-0.541277\pi\) | ||||
−0.129312 | + | 0.991604i | \(0.541277\pi\) | |||||||
\(480\) | −12.5885 | + | 10.2784i | −0.574582 | + | 0.469144i | ||||
\(481\) | −16.3923 | −0.747425 | ||||||||
\(482\) | − | 5.93426i | − | 0.270298i | ||||||
\(483\) | 21.8695i | 0.995099i | ||||||||
\(484\) | −16.2679 | −0.739452 | ||||||||
\(485\) | −15.4641 | − | 18.9396i | −0.702189 | − | 0.860002i | ||||
\(486\) | 5.12436 | 0.232445 | ||||||||
\(487\) | 10.9348i | 0.495502i | 0.968824 | + | 0.247751i | \(0.0796915\pi\) | ||||
−0.968824 | + | 0.247751i | \(0.920309\pi\) | |||||||
\(488\) | − | 5.65685i | − | 0.256074i | ||||||
\(489\) | −19.8564 | −0.897938 | ||||||||
\(490\) | 0.732051 | + | 0.896575i | 0.0330707 | + | 0.0405032i | ||||
\(491\) | 7.26795 | 0.327998 | 0.163999 | − | 0.986461i | \(-0.447561\pi\) | ||||
0.163999 | + | 0.986461i | \(0.447561\pi\) | |||||||
\(492\) | − | 16.9706i | − | 0.765092i | ||||||
\(493\) | 1.41421i | 0.0636930i | ||||||||
\(494\) | −3.03332 | −0.136476 | ||||||||
\(495\) | 2.19615 | − | 1.79315i | 0.0987097 | − | 0.0805961i | ||||
\(496\) | −21.5167 | −0.966127 | ||||||||
\(497\) | 8.48528i | 0.380617i | ||||||||
\(498\) | 7.45001i | 0.333843i | ||||||||
\(499\) | 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 | ||||
\(501\) | 15.8564 | 0.708412 | ||||||||
\(502\) | − | 7.82894i | − | 0.349423i | ||||||
\(503\) | − | 12.1731i | − | 0.542773i | −0.962471 | − | 0.271386i | \(-0.912518\pi\) | ||
0.962471 | − | 0.271386i | \(-0.0874821\pi\) | |||||||
\(504\) | 4.73205 | 0.210782 | ||||||||
\(505\) | 10.3923 | − | 8.48528i | 0.462451 | − | 0.377590i | ||||
\(506\) | 4.14359 | 0.184205 | ||||||||
\(507\) | 13.8375i | 0.614546i | ||||||||
\(508\) | − | 7.34847i | − | 0.326036i | ||||||
\(509\) | −33.4641 | −1.48327 | −0.741635 | − | 0.670804i | \(-0.765949\pi\) | ||||
−0.741635 | + | 0.670804i | \(0.765949\pi\) | |||||||
\(510\) | 1.46410 | + | 1.79315i | 0.0648315 | + | 0.0794021i | ||||
\(511\) | 18.0000 | 0.796273 | ||||||||
\(512\) | − | 22.1841i | − | 0.980408i | ||||||
\(513\) | 18.4863i | 0.816191i | ||||||||
\(514\) | 4.92820 | 0.217374 | ||||||||
\(515\) | −12.9282 | − | 15.8338i | −0.569685 | − | 0.697718i | ||||
\(516\) | −22.3923 | −0.985766 | ||||||||
\(517\) | 1.79315i | 0.0788627i | ||||||||
\(518\) | − | 11.5911i | − | 0.509284i | ||||||
\(519\) | −6.53590 | −0.286894 | ||||||||
\(520\) | 6.00000 | − | 4.89898i | 0.263117 | − | 0.214834i | ||||
\(521\) | 4.39230 | 0.192430 | 0.0962152 | − | 0.995361i | \(-0.469326\pi\) | ||||
0.0962152 | + | 0.995361i | \(0.469326\pi\) | |||||||
\(522\) | 0.517638i | 0.0226564i | ||||||||
\(523\) | 1.61729i | 0.0707190i | 0.999375 | + | 0.0353595i | \(0.0112576\pi\) | ||||
−0.999375 | + | 0.0353595i | \(0.988742\pi\) | |||||||
\(524\) | −8.19615 | −0.358051 | ||||||||
\(525\) | −3.46410 | + | 16.9706i | −0.151186 | + | 0.740656i | ||||
\(526\) | 2.48334 | 0.108279 | ||||||||
\(527\) | 12.3490i | 0.537930i | ||||||||
\(528\) | − | 4.41851i | − | 0.192291i | ||||||
\(529\) | −16.8564 | −0.732887 | ||||||||
\(530\) | −5.32051 | + | 4.34418i | −0.231108 | + | 0.188699i | ||||
\(531\) | 10.3923 | 0.450988 | ||||||||
\(532\) | 13.8647i | 0.601112i | ||||||||
\(533\) | 12.4233i | 0.538113i | ||||||||
\(534\) | −7.60770 | −0.329217 | ||||||||
\(535\) | −26.3923 | − | 32.3238i | −1.14104 | − | 1.39748i | ||||
\(536\) | −8.19615 | −0.354020 | ||||||||
\(537\) | − | 3.58630i | − | 0.154760i | ||||||
\(538\) | − | 6.21166i | − | 0.267804i | ||||||
\(539\) | −1.26795 | −0.0546144 | ||||||||
\(540\) | −13.8564 | − | 16.9706i | −0.596285 | − | 0.730297i | ||||
\(541\) | 42.3923 | 1.82259 | 0.911294 | − | 0.411757i | \(-0.135085\pi\) | ||||
0.911294 | + | 0.411757i | \(0.135085\pi\) | |||||||
\(542\) | 13.8375i | 0.594373i | ||||||||
\(543\) | − | 22.6274i | − | 0.971035i | ||||||
\(544\) | −7.26795 | −0.311611 | ||||||||
\(545\) | 30.9282 | − | 25.2528i | 1.32482 | − | 1.08171i | ||||
\(546\) | 3.21539 | 0.137606 | ||||||||
\(547\) | 2.44949i | 0.104733i | 0.998628 | + | 0.0523663i | \(0.0166763\pi\) | ||||
−0.998628 | + | 0.0523663i | \(0.983324\pi\) | |||||||
\(548\) | − | 25.6317i | − | 1.09493i | ||||||
\(549\) | 2.92820 | 0.124973 | ||||||||
\(550\) | 3.21539 | + | 0.656339i | 0.137105 | + | 0.0279864i | ||||
\(551\) | −3.26795 | −0.139219 | ||||||||
\(552\) | − | 17.2480i | − | 0.734122i | ||||||
\(553\) | 10.2784i | 0.437083i | ||||||||
\(554\) | −9.71281 | −0.412658 | ||||||||
\(555\) | −22.3923 | + | 18.2832i | −0.950500 | + | 0.776080i | ||||
\(556\) | 13.8564 | 0.587643 | ||||||||
\(557\) | 0.554803i | 0.0235078i | 0.999931 | + | 0.0117539i | \(0.00374146\pi\) | ||||
−0.999931 | + | 0.0117539i | \(0.996259\pi\) | |||||||
\(558\) | 4.52004i | 0.191349i | ||||||||
\(559\) | 16.3923 | 0.693321 | ||||||||
\(560\) | −8.53590 | − | 10.4543i | −0.360708 | − | 0.441775i | ||||
\(561\) | −2.53590 | −0.107066 | ||||||||
\(562\) | − | 16.9706i | − | 0.715860i | ||||||
\(563\) | 13.2827i | 0.559800i | 0.960029 | + | 0.279900i | \(0.0903013\pi\) | ||||
−0.960029 | + | 0.279900i | \(0.909699\pi\) | |||||||
\(564\) | 3.46410 | 0.145865 | ||||||||
\(565\) | 18.3923 | + | 22.5259i | 0.773770 | + | 0.947671i | ||||
\(566\) | −14.1962 | −0.596709 | ||||||||
\(567\) | − | 12.2474i | − | 0.514344i | ||||||
\(568\) | − | 6.69213i | − | 0.280796i | ||||||
\(569\) | −21.4641 | −0.899822 | −0.449911 | − | 0.893073i | \(-0.648544\pi\) | ||||
−0.449911 | + | 0.893073i | \(0.648544\pi\) | |||||||
\(570\) | −4.14359 | + | 3.38323i | −0.173556 | + | 0.141708i | ||||
\(571\) | −39.3205 | −1.64551 | −0.822756 | − | 0.568395i | \(-0.807565\pi\) | ||||
−0.822756 | + | 0.568395i | \(0.807565\pi\) | |||||||
\(572\) | 3.93803i | 0.164657i | ||||||||
\(573\) | 21.3891i | 0.893541i | ||||||||
\(574\) | −8.78461 | −0.366663 | ||||||||
\(575\) | −30.9282 | − | 6.31319i | −1.28980 | − | 0.263278i | ||||
\(576\) | 2.26795 | 0.0944979 | ||||||||
\(577\) | − | 9.14162i | − | 0.380571i | −0.981729 | − | 0.190285i | \(-0.939059\pi\) | ||
0.981729 | − | 0.190285i | \(-0.0609413\pi\) | |||||||
\(578\) | − | 7.76457i | − | 0.322964i | ||||||
\(579\) | 0.928203 | 0.0385748 | ||||||||
\(580\) | 3.00000 | − | 2.44949i | 0.124568 | − | 0.101710i | ||||
\(581\) | −24.9282 | −1.03420 | ||||||||
\(582\) | 8.00481i | 0.331810i | ||||||||
\(583\) | − | 7.52433i | − | 0.311626i | ||||||
\(584\) | −14.1962 | −0.587441 | ||||||||
\(585\) | 2.53590 | + | 3.10583i | 0.104846 | + | 0.128410i | ||||
\(586\) | 15.9090 | 0.657193 | ||||||||
\(587\) | 15.5563i | 0.642079i | 0.947066 | + | 0.321040i | \(0.104032\pi\) | ||||
−0.947066 | + | 0.321040i | \(0.895968\pi\) | |||||||
\(588\) | 2.44949i | 0.101015i | ||||||||
\(589\) | −28.5359 | −1.17580 | ||||||||
\(590\) | 7.60770 | + | 9.31749i | 0.313204 | + | 0.383595i | ||||
\(591\) | −31.7128 | −1.30449 | ||||||||
\(592\) | − | 22.5259i | − | 0.925808i | ||||||
\(593\) | 25.5302i | 1.04840i | 0.851596 | + | 0.524199i | \(0.175635\pi\) | ||||
−0.851596 | + | 0.524199i | \(0.824365\pi\) | |||||||
\(594\) | −3.71281 | −0.152339 | ||||||||
\(595\) | −6.00000 | + | 4.89898i | −0.245976 | + | 0.200839i | ||||
\(596\) | 1.60770 | 0.0658538 | ||||||||
\(597\) | 19.7990i | 0.810319i | ||||||||
\(598\) | 5.85993i | 0.239630i | ||||||||
\(599\) | −1.26795 | −0.0518070 | −0.0259035 | − | 0.999664i | \(-0.508246\pi\) | ||||
−0.0259035 | + | 0.999664i | \(0.508246\pi\) | |||||||
\(600\) | 2.73205 | − | 13.3843i | 0.111536 | − | 0.546410i | ||||
\(601\) | 16.7846 | 0.684659 | 0.342329 | − | 0.939580i | \(-0.388784\pi\) | ||||
0.342329 | + | 0.939580i | \(0.388784\pi\) | |||||||
\(602\) | 11.5911i | 0.472418i | ||||||||
\(603\) | − | 4.24264i | − | 0.172774i | ||||||
\(604\) | −32.5359 | −1.32387 | ||||||||
\(605\) | 16.2679 | − | 13.2827i | 0.661386 | − | 0.540020i | ||||
\(606\) | −4.39230 | −0.178425 | ||||||||
\(607\) | − | 16.3142i | − | 0.662174i | −0.943600 | − | 0.331087i | \(-0.892585\pi\) | ||
0.943600 | − | 0.331087i | \(-0.107415\pi\) | |||||||
\(608\) | − | 16.7947i | − | 0.681115i | ||||||
\(609\) | 3.46410 | 0.140372 | ||||||||
\(610\) | 2.14359 | + | 2.62536i | 0.0867916 | + | 0.106298i | ||||
\(611\) | −2.53590 | −0.102591 | ||||||||
\(612\) | − | 2.44949i | − | 0.0990148i | ||||||
\(613\) | 18.2832i | 0.738453i | 0.929339 | + | 0.369227i | \(0.120377\pi\) | ||||
−0.929339 | + | 0.369227i | \(0.879623\pi\) | |||||||
\(614\) | −5.41154 | −0.218392 | ||||||||
\(615\) | 13.8564 | + | 16.9706i | 0.558744 | + | 0.684319i | ||||
\(616\) | −6.00000 | −0.241747 | ||||||||
\(617\) | 32.0464i | 1.29014i | 0.764123 | + | 0.645071i | \(0.223172\pi\) | ||||
−0.764123 | + | 0.645071i | \(0.776828\pi\) | |||||||
\(618\) | 6.69213i | 0.269197i | ||||||||
\(619\) | 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 | ||||
\(621\) | 35.7128 | 1.43311 | ||||||||
\(622\) | 3.41044i | 0.136746i | ||||||||
\(623\) | − | 25.4558i | − | 1.01987i | ||||||
\(624\) | 6.24871 | 0.250149 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | −12.2487 | −0.489557 | ||||||||
\(627\) | − | 5.85993i | − | 0.234023i | ||||||
\(628\) | − | 18.9396i | − | 0.755771i | ||||||
\(629\) | −12.9282 | −0.515481 | ||||||||
\(630\) | −2.19615 | + | 1.79315i | −0.0874968 | + | 0.0714408i | ||||
\(631\) | 15.6077 | 0.621333 | 0.310666 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310666 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(632\) | − | 8.10634i | − | 0.322453i | ||||||
\(633\) | − | 20.8343i | − | 0.828088i | ||||||
\(634\) | 2.98076 | 0.118381 | ||||||||
\(635\) | 6.00000 | + | 7.34847i | 0.238103 | + | 0.291615i | ||||
\(636\) | −14.5359 | −0.576386 | ||||||||
\(637\) | − | 1.79315i | − | 0.0710472i | ||||||
\(638\) | − | 0.656339i | − | 0.0259847i | ||||||
\(639\) | 3.46410 | 0.137038 | ||||||||
\(640\) | 16.1962 | + | 19.8362i | 0.640209 | + | 0.784093i | ||||
\(641\) | 34.6410 | 1.36824 | 0.684119 | − | 0.729370i | \(-0.260187\pi\) | ||||
0.684119 | + | 0.729370i | \(0.260187\pi\) | |||||||
\(642\) | 13.6617i | 0.539183i | ||||||||
\(643\) | − | 10.4543i | − | 0.412277i | −0.978523 | − | 0.206139i | \(-0.933910\pi\) | ||
0.978523 | − | 0.206139i | \(-0.0660898\pi\) | |||||||
\(644\) | 26.7846 | 1.05546 | ||||||||
\(645\) | 22.3923 | − | 18.2832i | 0.881696 | − | 0.719902i | ||||
\(646\) | −2.39230 | −0.0941240 | ||||||||
\(647\) | − | 14.3180i | − | 0.562899i | −0.959576 | − | 0.281449i | \(-0.909185\pi\) | ||
0.959576 | − | 0.281449i | \(-0.0908151\pi\) | |||||||
\(648\) | 9.65926i | 0.379452i | ||||||||
\(649\) | −13.1769 | −0.517239 | ||||||||
\(650\) | −0.928203 | + | 4.54725i | −0.0364071 | + | 0.178358i | ||||
\(651\) | 30.2487 | 1.18554 | ||||||||
\(652\) | 24.3190i | 0.952407i | ||||||||
\(653\) | − | 13.0053i | − | 0.508938i | −0.967081 | − | 0.254469i | \(-0.918099\pi\) | ||
0.967081 | − | 0.254469i | \(-0.0819006\pi\) | |||||||
\(654\) | −13.0718 | −0.511148 | ||||||||
\(655\) | 8.19615 | − | 6.69213i | 0.320250 | − | 0.261483i | ||||
\(656\) | −17.0718 | −0.666542 | ||||||||
\(657\) | − | 7.34847i | − | 0.286691i | ||||||
\(658\) | − | 1.79315i | − | 0.0699043i | ||||||
\(659\) | −32.4449 | −1.26387 | −0.631936 | − | 0.775020i | \(-0.717740\pi\) | ||||
−0.631936 | + | 0.775020i | \(0.717740\pi\) | |||||||
\(660\) | 4.39230 | + | 5.37945i | 0.170970 | + | 0.209395i | ||||
\(661\) | −0.784610 | −0.0305178 | −0.0152589 | − | 0.999884i | \(-0.504857\pi\) | ||||
−0.0152589 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(662\) | 9.41902i | 0.366081i | ||||||||
\(663\) | − | 3.58630i | − | 0.139280i | ||||||
\(664\) | 19.6603 | 0.762966 | ||||||||
\(665\) | −11.3205 | − | 13.8647i | −0.438990 | − | 0.537651i | ||||
\(666\) | −4.73205 | −0.183363 | ||||||||
\(667\) | 6.31319i | 0.244448i | ||||||||
\(668\) | − | 19.4201i | − | 0.751384i | ||||||
\(669\) | 21.7128 | 0.839466 | ||||||||
\(670\) | 3.80385 | − | 3.10583i | 0.146955 | − | 0.119989i | ||||
\(671\) | −3.71281 | −0.143332 | ||||||||
\(672\) | 17.8028i | 0.686757i | ||||||||
\(673\) | 46.3644i | 1.78722i | 0.448846 | + | 0.893609i | \(0.351835\pi\) | ||||
−0.448846 | + | 0.893609i | \(0.648165\pi\) | |||||||
\(674\) | 14.4449 | 0.556395 | ||||||||
\(675\) | 27.7128 | + | 5.65685i | 1.06667 | + | 0.217732i | ||||
\(676\) | 16.9474 | 0.651825 | ||||||||
\(677\) | − | 32.2495i | − | 1.23945i | −0.784819 | − | 0.619725i | \(-0.787244\pi\) | ||
0.784819 | − | 0.619725i | \(-0.212756\pi\) | |||||||
\(678\) | − | 9.52056i | − | 0.365635i | ||||||
\(679\) | −26.7846 | −1.02790 | ||||||||
\(680\) | 4.73205 | − | 3.86370i | 0.181466 | − | 0.148166i | ||||
\(681\) | −28.9282 | −1.10853 | ||||||||
\(682\) | − | 5.73118i | − | 0.219458i | ||||||
\(683\) | − | 21.9711i | − | 0.840700i | −0.907362 | − | 0.420350i | \(-0.861907\pi\) | ||
0.907362 | − | 0.420350i | \(-0.138093\pi\) | |||||||
\(684\) | 5.66025 | 0.216425 | ||||||||
\(685\) | 20.9282 | + | 25.6317i | 0.799626 | + | 0.979337i | ||||
\(686\) | 10.1436 | 0.387284 | ||||||||
\(687\) | − | 26.5654i | − | 1.01354i | ||||||
\(688\) | 22.5259i | 0.858791i | ||||||||
\(689\) | 10.6410 | 0.405390 | ||||||||
\(690\) | 6.53590 | + | 8.00481i | 0.248817 | + | 0.304738i | ||||
\(691\) | 41.7128 | 1.58683 | 0.793415 | − | 0.608681i | \(-0.208301\pi\) | ||||
0.793415 | + | 0.608681i | \(0.208301\pi\) | |||||||
\(692\) | 8.00481i | 0.304297i | ||||||||
\(693\) | − | 3.10583i | − | 0.117981i | ||||||
\(694\) | −11.1244 | −0.422275 | ||||||||
\(695\) | −13.8564 | + | 11.3137i | −0.525603 | + | 0.429153i | ||||
\(696\) | −2.73205 | −0.103558 | ||||||||
\(697\) | 9.79796i | 0.371124i | ||||||||
\(698\) | − | 11.7942i | − | 0.446416i | ||||||
\(699\) | 4.78461 | 0.180971 | ||||||||
\(700\) | 20.7846 | + | 4.24264i | 0.785584 | + | 0.160357i | ||||
\(701\) | 27.7128 | 1.04670 | 0.523349 | − | 0.852118i | \(-0.324682\pi\) | ||||
0.523349 | + | 0.852118i | \(0.324682\pi\) | |||||||
\(702\) | − | 5.25071i | − | 0.198175i | ||||||
\(703\) | − | 29.8744i | − | 1.12673i | ||||||
\(704\) | −2.87564 | −0.108380 | ||||||||
\(705\) | −3.46410 | + | 2.82843i | −0.130466 | + | 0.106525i | ||||
\(706\) | −16.5359 | −0.622337 | ||||||||
\(707\) | − | 14.6969i | − | 0.552735i | ||||||
\(708\) | 25.4558i | 0.956689i | ||||||||
\(709\) | −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 | ||||
\(711\) | 4.19615 | 0.157368 | ||||||||
\(712\) | 20.0764i | 0.752395i | ||||||||
\(713\) | 55.1271i | 2.06453i | ||||||||
\(714\) | 2.53590 | 0.0949036 | ||||||||
\(715\) | −3.21539 | − | 3.93803i | −0.120249 | − | 0.147274i | ||||
\(716\) | −4.39230 | −0.164148 | ||||||||
\(717\) | − | 14.6969i | − | 0.548867i | ||||||
\(718\) | − | 3.76217i | − | 0.140403i | ||||||
\(719\) | 19.8564 | 0.740519 | 0.370260 | − | 0.928928i | \(-0.379269\pi\) | ||||
0.370260 | + | 0.928928i | \(0.379269\pi\) | |||||||
\(720\) | −4.26795 | + | 3.48477i | −0.159057 | + | 0.129870i | ||||
\(721\) | −22.3923 | −0.833933 | ||||||||
\(722\) | 4.30701i | 0.160290i | ||||||||
\(723\) | 16.2127i | 0.602956i | ||||||||
\(724\) | −27.7128 | −1.02994 | ||||||||
\(725\) | −1.00000 | + | 4.89898i | −0.0371391 | + | 0.181944i | ||||
\(726\) | −6.87564 | −0.255179 | ||||||||
\(727\) | 46.6690i | 1.73086i | 0.501031 | + | 0.865430i | \(0.332954\pi\) | ||||
−0.501031 | + | 0.865430i | \(0.667046\pi\) | |||||||
\(728\) | − | 8.48528i | − | 0.314485i | ||||||
\(729\) | −29.0000 | −1.07407 | ||||||||
\(730\) | 6.58846 | − | 5.37945i | 0.243850 | − | 0.199102i | ||||
\(731\) | 12.9282 | 0.478167 | ||||||||
\(732\) | 7.17260i | 0.265107i | ||||||||
\(733\) | 12.7279i | 0.470117i | 0.971981 | + | 0.235058i | \(0.0755281\pi\) | ||||
−0.971981 | + | 0.235058i | \(0.924472\pi\) | |||||||
\(734\) | 17.4115 | 0.642672 | ||||||||
\(735\) | −2.00000 | − | 2.44949i | −0.0737711 | − | 0.0903508i | ||||
\(736\) | −32.4449 | −1.19593 | ||||||||
\(737\) | 5.37945i | 0.198155i | ||||||||
\(738\) | 3.58630i | 0.132014i | ||||||||
\(739\) | 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 | ||||
\(741\) | 8.28719 | 0.304437 | ||||||||
\(742\) | 7.52433i | 0.276227i | ||||||||
\(743\) | − | 9.89949i | − | 0.363177i | −0.983375 | − | 0.181589i | \(-0.941876\pi\) | ||
0.983375 | − | 0.181589i | \(-0.0581239\pi\) | |||||||
\(744\) | −23.8564 | −0.874618 | ||||||||
\(745\) | −1.60770 | + | 1.31268i | −0.0589014 | + | 0.0480928i | ||||
\(746\) | −10.1436 | −0.371383 | ||||||||
\(747\) | 10.1769i | 0.372353i | ||||||||
\(748\) | 3.10583i | 0.113560i | ||||||||
\(749\) | −45.7128 | −1.67031 | ||||||||
\(750\) | 3.80385 | + | 7.24693i | 0.138897 | + | 0.264621i | ||||
\(751\) | 49.9090 | 1.82120 | 0.910602 | − | 0.413284i | \(-0.135618\pi\) | ||||
0.910602 | + | 0.413284i | \(0.135618\pi\) | |||||||
\(752\) | − | 3.48477i | − | 0.127076i | ||||||
\(753\) | 21.3891i | 0.779461i | ||||||||
\(754\) | 0.928203 | 0.0338032 | ||||||||
\(755\) | 32.5359 | − | 26.5654i | 1.18410 | − | 0.966816i | ||||
\(756\) | −24.0000 | −0.872872 | ||||||||
\(757\) | − | 10.9348i | − | 0.397431i | −0.980057 | − | 0.198716i | \(-0.936323\pi\) | ||
0.980057 | − | 0.198716i | \(-0.0636770\pi\) | |||||||
\(758\) | − | 8.38375i | − | 0.304511i | ||||||
\(759\) | −11.3205 | −0.410908 | ||||||||
\(760\) | 8.92820 | + | 10.9348i | 0.323860 | + | 0.396646i | ||||
\(761\) | −35.5692 | −1.28938 | −0.644692 | − | 0.764443i | \(-0.723014\pi\) | ||||
−0.644692 | + | 0.764443i | \(0.723014\pi\) | |||||||
\(762\) | − | 3.10583i | − | 0.112512i | ||||||
\(763\) | − | 43.7391i | − | 1.58346i | ||||||
\(764\) | 26.1962 | 0.947744 | ||||||||
\(765\) | 2.00000 | + | 2.44949i | 0.0723102 | + | 0.0885615i | ||||
\(766\) | −0.483340 | −0.0174638 | ||||||||
\(767\) | − | 18.6350i | − | 0.672870i | ||||||
\(768\) | − | 1.96902i | − | 0.0710508i | ||||||
\(769\) | 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 | ||||
\(771\) | −13.4641 | −0.484898 | ||||||||
\(772\) | − | 1.13681i | − | 0.0409148i | ||||||
\(773\) | − | 11.2122i | − | 0.403274i | −0.979460 | − | 0.201637i | \(-0.935374\pi\) | ||
0.979460 | − | 0.201637i | \(-0.0646261\pi\) | |||||||
\(774\) | 4.73205 | 0.170090 | ||||||||
\(775\) | −8.73205 | + | 42.7781i | −0.313665 | + | 1.53664i | ||||
\(776\) | 21.1244 | 0.758320 | ||||||||
\(777\) | 31.6675i | 1.13607i | ||||||||
\(778\) | − | 10.7589i | − | 0.385725i | ||||||
\(779\) | −22.6410 | −0.811199 | ||||||||
\(780\) | −7.60770 | + | 6.21166i | −0.272399 | + | 0.222413i | ||||
\(781\) | −4.39230 | −0.157169 | ||||||||
\(782\) | 4.62158i | 0.165267i | ||||||||
\(783\) | − | 5.65685i | − | 0.202159i | ||||||
\(784\) | 2.46410 | 0.0880036 | ||||||||
\(785\) | 15.4641 | + | 18.9396i | 0.551937 | + | 0.675983i | ||||
\(786\) | −3.46410 | −0.123560 | ||||||||
\(787\) | − | 35.0779i | − | 1.25039i | −0.780467 | − | 0.625197i | \(-0.785019\pi\) | ||
0.780467 | − | 0.625197i | \(-0.214981\pi\) | |||||||
\(788\) | 38.8401i | 1.38362i | ||||||||
\(789\) | −6.78461 | −0.241539 | ||||||||
\(790\) | 3.07180 | + | 3.76217i | 0.109290 | + | 0.133852i | ||||
\(791\) | 31.8564 | 1.13268 | ||||||||
\(792\) | 2.44949i | 0.0870388i | ||||||||
\(793\) | − | 5.25071i | − | 0.186458i | ||||||
\(794\) | −2.53590 | −0.0899957 | ||||||||
\(795\) | 14.5359 | − | 11.8685i | 0.515535 | − | 0.420933i | ||||
\(796\) | 24.2487 | 0.859473 | ||||||||
\(797\) | − | 29.0149i | − | 1.02776i | −0.857862 | − | 0.513881i | \(-0.828207\pi\) | ||
0.857862 | − | 0.513881i | \(-0.171793\pi\) | |||||||
\(798\) | 5.85993i | 0.207439i | ||||||||
\(799\) | −2.00000 | −0.0707549 | ||||||||
\(800\) | −25.1769 | − | 5.13922i | −0.890138 | − | 0.181699i | ||||
\(801\) | −10.3923 | −0.367194 | ||||||||
\(802\) | − | 19.5959i | − | 0.691956i | ||||||
\(803\) | 9.31749i | 0.328807i | ||||||||
\(804\) | 10.3923 | 0.366508 | ||||||||
\(805\) | −26.7846 | + | 21.8695i | −0.944033 | + | 0.770800i | ||||
\(806\) | 8.10512 | 0.285491 | ||||||||
\(807\) | 16.9706i | 0.597392i | ||||||||
\(808\) | 11.5911i | 0.407774i | ||||||||
\(809\) | −13.6077 | −0.478421 | −0.239211 | − | 0.970968i | \(-0.576889\pi\) | ||||
−0.239211 | + | 0.970968i | \(0.576889\pi\) | |||||||
\(810\) | −3.66025 | − | 4.48288i | −0.128608 | − | 0.157512i | ||||
\(811\) | −36.7846 | −1.29168 | −0.645841 | − | 0.763472i | \(-0.723493\pi\) | ||||
−0.645841 | + | 0.763472i | \(0.723493\pi\) | |||||||
\(812\) | − | 4.24264i | − | 0.148888i | ||||||
\(813\) | − | 37.8048i | − | 1.32587i | ||||||
\(814\) | 6.00000 | 0.210300 | ||||||||
\(815\) | −19.8564 | − | 24.3190i | −0.695540 | − | 0.851859i | ||||
\(816\) | 4.92820 | 0.172522 | ||||||||
\(817\) | 29.8744i | 1.04517i | ||||||||
\(818\) | 4.69591i | 0.164189i | ||||||||
\(819\) | 4.39230 | 0.153480 | ||||||||
\(820\) | 20.7846 | − | 16.9706i | 0.725830 | − | 0.592638i | ||||
\(821\) | 9.21539 | 0.321619 | 0.160810 | − | 0.986985i | \(-0.448589\pi\) | ||||
0.160810 | + | 0.986985i | \(0.448589\pi\) | |||||||
\(822\) | − | 10.8332i | − | 0.377852i | ||||||
\(823\) | − | 40.8091i | − | 1.42252i | −0.702931 | − | 0.711258i | \(-0.748126\pi\) | ||
0.702931 | − | 0.711258i | \(-0.251874\pi\) | |||||||
\(824\) | 17.6603 | 0.615224 | ||||||||
\(825\) | −8.78461 | − | 1.79315i | −0.305841 | − | 0.0624295i | ||||
\(826\) | 13.1769 | 0.458483 | ||||||||
\(827\) | − | 3.68784i | − | 0.128239i | −0.997942 | − | 0.0641193i | \(-0.979576\pi\) | ||
0.997942 | − | 0.0641193i | \(-0.0204238\pi\) | |||||||
\(828\) | − | 10.9348i | − | 0.380010i | ||||||
\(829\) | 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 | ||||
\(831\) | 26.5359 | 0.920520 | ||||||||
\(832\) | − | 4.06678i | − | 0.140990i | ||||||
\(833\) | − | 1.41421i | − | 0.0489996i | ||||||
\(834\) | 5.85641 | 0.202791 | ||||||||
\(835\) | 15.8564 | + | 19.4201i | 0.548734 | + | 0.672059i | ||||
\(836\) | −7.17691 | −0.248219 | ||||||||
\(837\) | − | 49.3959i | − | 1.70737i | ||||||
\(838\) | − | 3.10583i | − | 0.107289i | ||||||
\(839\) | −40.9808 | −1.41481 | −0.707407 | − | 0.706807i | \(-0.750135\pi\) | ||||
−0.707407 | + | 0.706807i | \(0.750135\pi\) | |||||||
\(840\) | −9.46410 | − | 11.5911i | −0.326543 | − | 0.399931i | ||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − | 2.82843i | − | 0.0974740i | ||||||
\(843\) | 46.3644i | 1.59688i | ||||||||
\(844\) | −25.5167 | −0.878320 | ||||||||
\(845\) | −16.9474 | + | 13.8375i | −0.583010 | + | 0.476025i | ||||
\(846\) | −0.732051 | −0.0251684 | ||||||||
\(847\) | − | 23.0064i | − | 0.790508i | ||||||
\(848\) | 14.6226i | 0.502142i | ||||||||
\(849\) | 38.7846 | 1.33108 | ||||||||
\(850\) | −0.732051 | + | 3.58630i | −0.0251091 | + | 0.123009i | ||||
\(851\) | −57.7128 | −1.97837 | ||||||||
\(852\) | 8.48528i | 0.290701i | ||||||||
\(853\) | 32.3238i | 1.10675i | 0.832933 | + | 0.553374i | \(0.186660\pi\) | ||||
−0.832933 | + | 0.553374i | \(0.813340\pi\) | |||||||
\(854\) | 3.71281 | 0.127050 | ||||||||
\(855\) | −5.66025 | + | 4.62158i | −0.193577 | + | 0.158055i | ||||
\(856\) | 36.0526 | 1.23225 | ||||||||
\(857\) | − | 33.2576i | − | 1.13606i | −0.823009 | − | 0.568029i | \(-0.807706\pi\) | ||
0.823009 | − | 0.568029i | \(-0.192294\pi\) | |||||||
\(858\) | 1.66441i | 0.0568220i | ||||||||
\(859\) | 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 | ||||
\(861\) | 24.0000 | 0.817918 | ||||||||
\(862\) | 19.2442i | 0.655460i | ||||||||
\(863\) | 1.69161i | 0.0575832i | 0.999585 | + | 0.0287916i | \(0.00916592\pi\) | ||||
−0.999585 | + | 0.0287916i | \(0.990834\pi\) | |||||||
\(864\) | 29.0718 | 0.989043 | ||||||||
\(865\) | −6.53590 | − | 8.00481i | −0.222227 | − | 0.272172i | ||||
\(866\) | −1.51666 | −0.0515382 | ||||||||
\(867\) | 21.2132i | 0.720438i | ||||||||
\(868\) | − | 37.0470i | − | 1.25746i | ||||||
\(869\) | −5.32051 | −0.180486 | ||||||||
\(870\) | 1.26795 | − | 1.03528i | 0.0429875 | − | 0.0350991i | ||||
\(871\) | −7.60770 | −0.257777 | ||||||||
\(872\) | 34.4959i | 1.16818i | ||||||||
\(873\) | 10.9348i | 0.370086i | ||||||||
\(874\) | −10.6795 | −0.361239 | ||||||||
\(875\) | −24.2487 | + | 12.7279i | −0.819756 | + | 0.430282i | ||||
\(876\) | 18.0000 | 0.608164 | ||||||||
\(877\) | − | 24.9754i | − | 0.843358i | −0.906745 | − | 0.421679i | \(-0.861441\pi\) | ||
0.906745 | − | 0.421679i | \(-0.138559\pi\) | |||||||
\(878\) | − | 3.66063i | − | 0.123540i | ||||||
\(879\) | −43.4641 | −1.46601 | ||||||||
\(880\) | 5.41154 | − | 4.41851i | 0.182423 | − | 0.148948i | ||||
\(881\) | −50.5359 | −1.70260 | −0.851299 | − | 0.524681i | \(-0.824185\pi\) | ||||
−0.851299 | + | 0.524681i | \(0.824185\pi\) | |||||||
\(882\) | − | 0.517638i | − | 0.0174298i | ||||||
\(883\) | 1.48854i | 0.0500935i | 0.999686 | + | 0.0250467i | \(0.00797346\pi\) | ||||
−0.999686 | + | 0.0250467i | \(0.992027\pi\) | |||||||
\(884\) | −4.39230 | −0.147729 | ||||||||
\(885\) | −20.7846 | − | 25.4558i | −0.698667 | − | 0.855689i | ||||
\(886\) | 9.41154 | 0.316187 | ||||||||
\(887\) | − | 21.0101i | − | 0.705451i | −0.935727 | − | 0.352726i | \(-0.885255\pi\) | ||
0.935727 | − | 0.352726i | \(-0.114745\pi\) | |||||||
\(888\) | − | 24.9754i | − | 0.838119i | ||||||
\(889\) | 10.3923 | 0.348547 | ||||||||
\(890\) | −7.60770 | − | 9.31749i | −0.255011 | − | 0.312323i | ||||
\(891\) | 6.33975 | 0.212389 | ||||||||
\(892\) | − | 26.5927i | − | 0.890388i | ||||||
\(893\) | − | 4.62158i | − | 0.154655i | ||||||
\(894\) | 0.679492 | 0.0227256 | ||||||||
\(895\) | 4.39230 | − | 3.58630i | 0.146819 | − | 0.119877i | ||||
\(896\) | 28.0526 | 0.937170 | ||||||||
\(897\) | − | 16.0096i | − | 0.534546i | ||||||
\(898\) | − | 13.3843i | − | 0.446639i | ||||||
\(899\) | 8.73205 | 0.291230 | ||||||||
\(900\) | 1.73205 | − | 8.48528i | 0.0577350 | − | 0.282843i | ||||
\(901\) | 8.39230 | 0.279588 | ||||||||
\(902\) | − | 4.54725i | − | 0.151407i | ||||||
\(903\) | − | 31.6675i | − | 1.05383i | ||||||
\(904\) | −25.1244 | −0.835624 | ||||||||
\(905\) | 27.7128 | − | 22.6274i | 0.921205 | − | 0.752161i | ||||
\(906\) | −13.7513 | −0.456856 | ||||||||
\(907\) | 45.7081i | 1.51771i | 0.651258 | + | 0.758856i | \(0.274242\pi\) | ||||
−0.651258 | + | 0.758856i | \(0.725758\pi\) | |||||||
\(908\) | 35.4297i | 1.17577i | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 3.21539 | + | 3.93803i | 0.106589 | + | 0.130545i | ||||
\(911\) | −9.80385 | −0.324816 | −0.162408 | − | 0.986724i | \(-0.551926\pi\) | ||||
−0.162408 | + | 0.986724i | \(0.551926\pi\) | |||||||
\(912\) | 11.3880i | 0.377096i | ||||||||
\(913\) | − | 12.9038i | − | 0.427053i | ||||||
\(914\) | 12.2487 | 0.405151 | ||||||||
\(915\) | −5.85641 | − | 7.17260i | −0.193607 | − | 0.237119i | ||||
\(916\) | −32.5359 | −1.07502 | ||||||||
\(917\) | − | 11.5911i | − | 0.382772i | ||||||
\(918\) | − | 4.14110i | − | 0.136677i | ||||||
\(919\) | −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 | ||||
\(921\) | 14.7846 | 0.487169 | ||||||||
\(922\) | − | 12.9038i | − | 0.424964i | ||||||
\(923\) | − | 6.21166i | − | 0.204459i | ||||||
\(924\) | 7.60770 | 0.250275 | ||||||||
\(925\) | −44.7846 | − | 9.14162i | −1.47251 | − | 0.300575i | ||||
\(926\) | 3.55514 | 0.116829 | ||||||||
\(927\) | 9.14162i | 0.300250i | ||||||||
\(928\) | 5.13922i | 0.168703i | ||||||||
\(929\) | −55.8564 | −1.83259 | −0.916295 | − | 0.400505i | \(-0.868835\pi\) | ||||
−0.916295 | + | 0.400505i | \(0.868835\pi\) | |||||||
\(930\) | 11.0718 | − | 9.04008i | 0.363059 | − | 0.296436i | ||||
\(931\) | 3.26795 | 0.107103 | ||||||||
\(932\) | − | 5.85993i | − | 0.191948i | ||||||
\(933\) | − | 9.31749i | − | 0.305041i | ||||||
\(934\) | −10.8756 | −0.355862 | ||||||||
\(935\) | −2.53590 | − | 3.10583i | −0.0829327 | − | 0.101571i | ||||
\(936\) | −3.46410 | −0.113228 | ||||||||
\(937\) | − | 2.75410i | − | 0.0899724i | −0.998988 | − | 0.0449862i | \(-0.985676\pi\) | ||
0.998988 | − | 0.0449862i | \(-0.0143244\pi\) | |||||||
\(938\) | − | 5.37945i | − | 0.175645i | ||||||
\(939\) | 33.4641 | 1.09206 | ||||||||
\(940\) | 3.46410 | + | 4.24264i | 0.112987 | + | 0.138380i | ||||
\(941\) | −7.85641 | −0.256112 | −0.128056 | − | 0.991767i | \(-0.540874\pi\) | ||||
−0.128056 | + | 0.991767i | \(0.540874\pi\) | |||||||
\(942\) | − | 8.00481i | − | 0.260811i | ||||||
\(943\) | 43.7391i | 1.42434i | ||||||||
\(944\) | 25.6077 | 0.833459 | ||||||||
\(945\) | 24.0000 | − | 19.5959i | 0.780720 | − | 0.637455i | ||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | 27.9797i | 0.909217i | 0.890691 | + | 0.454608i | \(0.150221\pi\) | ||||
−0.890691 | + | 0.454608i | \(0.849779\pi\) | |||||||
\(948\) | 10.2784i | 0.333828i | ||||||||
\(949\) | −13.1769 | −0.427741 | ||||||||
\(950\) | −8.28719 | − | 1.69161i | −0.268872 | − | 0.0548832i | ||||
\(951\) | −8.14359 | −0.264074 | ||||||||
\(952\) | − | 6.69213i | − | 0.216893i | ||||||
\(953\) | − | 5.65685i | − | 0.183243i | −0.995794 | − | 0.0916217i | \(-0.970795\pi\) | ||
0.995794 | − | 0.0916217i | \(-0.0292051\pi\) | |||||||
\(954\) | 3.07180 | 0.0994531 | ||||||||
\(955\) | −26.1962 | + | 21.3891i | −0.847688 | + | 0.692134i | ||||
\(956\) | −18.0000 | −0.582162 | ||||||||
\(957\) | 1.79315i | 0.0579643i | ||||||||
\(958\) | 2.92996i | 0.0946628i | ||||||||
\(959\) | 36.2487 | 1.17053 | ||||||||
\(960\) | −4.53590 | − | 5.55532i | −0.146395 | − | 0.179297i | ||||
\(961\) | 45.2487 | 1.45964 | ||||||||
\(962\) | 8.48528i | 0.273576i | ||||||||
\(963\) | 18.6622i | 0.601380i | ||||||||
\(964\) | 19.8564 | 0.639532 | ||||||||
\(965\) | 0.928203 | + | 1.13681i | 0.0298799 | + | 0.0365953i | ||||
\(966\) | 11.3205 | 0.364231 | ||||||||
\(967\) | 1.96902i | 0.0633193i | 0.999499 | + | 0.0316596i | \(0.0100793\pi\) | ||||
−0.999499 | + | 0.0316596i | \(0.989921\pi\) | |||||||
\(968\) | 18.1445i | 0.583188i | ||||||||
\(969\) | 6.53590 | 0.209963 | ||||||||
\(970\) | −9.80385 | + | 8.00481i | −0.314783 | + | 0.257019i | ||||
\(971\) | −49.5167 | −1.58907 | −0.794533 | − | 0.607221i | \(-0.792284\pi\) | ||||
−0.794533 | + | 0.607221i | \(0.792284\pi\) | |||||||
\(972\) | 17.1464i | 0.549972i | ||||||||
\(973\) | 19.5959i | 0.628216i | ||||||||
\(974\) | 5.66025 | 0.181366 | ||||||||
\(975\) | 2.53590 | − | 12.4233i | 0.0812137 | − | 0.397864i | ||||
\(976\) | 7.21539 | 0.230959 | ||||||||
\(977\) | 22.9048i | 0.732790i | 0.930459 | + | 0.366395i | \(0.119408\pi\) | ||||
−0.930459 | + | 0.366395i | \(0.880592\pi\) | |||||||
\(978\) | 10.2784i | 0.328668i | ||||||||
\(979\) | 13.1769 | 0.421136 | ||||||||
\(980\) | −3.00000 | + | 2.44949i | −0.0958315 | + | 0.0782461i | ||||
\(981\) | −17.8564 | −0.570111 | ||||||||
\(982\) | − | 3.76217i | − | 0.120056i | ||||||
\(983\) | 30.2533i | 0.964930i | 0.875915 | + | 0.482465i | \(0.160258\pi\) | ||||
−0.875915 | + | 0.482465i | \(0.839742\pi\) | |||||||
\(984\) | −18.9282 | −0.603409 | ||||||||
\(985\) | −31.7128 | − | 38.8401i | −1.01045 | − | 1.23755i | ||||
\(986\) | 0.732051 | 0.0233132 | ||||||||
\(987\) | 4.89898i | 0.155936i | ||||||||
\(988\) | − | 10.1497i | − | 0.322905i | ||||||
\(989\) | 57.7128 | 1.83516 | ||||||||
\(990\) | −0.928203 | − | 1.13681i | −0.0295002 | − | 0.0361303i | ||||
\(991\) | 34.7846 | 1.10497 | 0.552485 | − | 0.833523i | \(-0.313680\pi\) | ||||
0.552485 | + | 0.833523i | \(0.313680\pi\) | |||||||
\(992\) | 44.8759i | 1.42481i | ||||||||
\(993\) | − | 25.7332i | − | 0.816620i | ||||||
\(994\) | 4.39230 | 0.139315 | ||||||||
\(995\) | −24.2487 | + | 19.7990i | −0.768736 | + | 0.627670i | ||||
\(996\) | −24.9282 | −0.789880 | ||||||||
\(997\) | − | 26.5927i | − | 0.842198i | −0.907015 | − | 0.421099i | \(-0.861645\pi\) | ||
0.907015 | − | 0.421099i | \(-0.138355\pi\) | |||||||
\(998\) | − | 0.554803i | − | 0.0175620i | ||||||
\(999\) | 51.7128 | 1.63612 |
(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 | 145.2.b.b.59.2 | ✓ | 4 | |
3.2 | odd | 2 | 1305.2.c.f.784.3 | 4 | |||
4.3 | odd | 2 | 2320.2.d.f.929.1 | 4 | |||
5.2 | odd | 4 | 725.2.a.f.1.3 | 4 | |||
5.3 | odd | 4 | 725.2.a.f.1.2 | 4 | |||
5.4 | even | 2 | inner | 145.2.b.b.59.3 | yes | 4 | |
15.2 | even | 4 | 6525.2.a.bj.1.2 | 4 | |||
15.8 | even | 4 | 6525.2.a.bj.1.3 | 4 | |||
15.14 | odd | 2 | 1305.2.c.f.784.2 | 4 | |||
20.19 | odd | 2 | 2320.2.d.f.929.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.b.b.59.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
145.2.b.b.59.3 | yes | 4 | 5.4 | even | 2 | inner | |
725.2.a.f.1.2 | 4 | 5.3 | odd | 4 | |||
725.2.a.f.1.3 | 4 | 5.2 | odd | 4 | |||
1305.2.c.f.784.2 | 4 | 15.14 | odd | 2 | |||
1305.2.c.f.784.3 | 4 | 3.2 | odd | 2 | |||
2320.2.d.f.929.1 | 4 | 4.3 | odd | 2 | |||
2320.2.d.f.929.3 | 4 | 20.19 | odd | 2 | |||
6525.2.a.bj.1.2 | 4 | 15.2 | even | 4 | |||
6525.2.a.bj.1.3 | 4 | 15.8 | even | 4 |