Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), not 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 719.3 | ||
Character | \(\chi\) | \(=\) | 1152.719 |
Dual form | 1152.2.w.b.431.3 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.64859 | − | 0.682869i | −0.737273 | − | 0.305388i | −0.0177359 | − | 0.999843i | \(-0.505646\pi\) |
−0.719537 | + | 0.694454i | \(0.755646\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51270 | + | 2.51270i | −0.949711 | + | 0.949711i | −0.998795 | − | 0.0490835i | \(-0.984370\pi\) |
0.0490835 | + | 0.998795i | \(0.484370\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.69097 | + | 1.11464i | 0.811357 | + | 0.336075i | 0.749495 | − | 0.662010i | \(-0.230296\pi\) |
0.0618618 | + | 0.998085i | \(0.480296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.76057 | − | 4.25040i | −0.488295 | − | 1.17885i | −0.955577 | − | 0.294740i | \(-0.904767\pi\) |
0.467283 | − | 0.884108i | \(-0.345233\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.10169 | 1.47988 | 0.739939 | − | 0.672674i | \(-0.234854\pi\) | ||||
0.739939 | + | 0.672674i | \(0.234854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.43292 | + | 1.42196i | −0.787567 | + | 0.326221i | −0.739965 | − | 0.672645i | \(-0.765158\pi\) |
−0.0476020 | + | 0.998866i | \(0.515158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.525502 | − | 0.525502i | 0.109575 | − | 0.109575i | −0.650194 | − | 0.759768i | \(-0.725312\pi\) |
0.759768 | + | 0.650194i | \(0.225312\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.28399 | − | 1.28399i | −0.256798 | − | 0.256798i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.46544 | − | 3.53788i | −0.272125 | − | 0.656967i | 0.727449 | − | 0.686162i | \(-0.240706\pi\) |
−0.999574 | + | 0.0291945i | \(0.990706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.55322i | − | 1.35660i | −0.734786 | − | 0.678299i | \(-0.762717\pi\) | ||
0.734786 | − | 0.678299i | \(-0.237283\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.85826 | − | 2.42657i | 0.990227 | − | 0.410165i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.30333 | − | 5.56073i | 0.378665 | − | 0.914178i | −0.613552 | − | 0.789655i | \(-0.710260\pi\) |
0.992217 | − | 0.124523i | \(-0.0397402\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.04402 | − | 3.04402i | −0.475396 | − | 0.475396i | 0.428260 | − | 0.903656i | \(-0.359127\pi\) |
−0.903656 | + | 0.428260i | \(0.859127\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.31422 | − | 8.00123i | 0.505414 | − | 1.22018i | −0.441084 | − | 0.897466i | \(-0.645406\pi\) |
0.946498 | − | 0.322711i | \(-0.104594\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.59875i | 1.25426i | 0.778916 | + | 0.627128i | \(0.215770\pi\) | ||||
−0.778916 | + | 0.627128i | \(0.784230\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.62732i | − | 0.803903i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.78946 | − | 9.14856i | 0.520522 | − | 1.25665i | −0.417058 | − | 0.908880i | \(-0.636939\pi\) |
0.937580 | − | 0.347771i | \(-0.113061\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.67516 | − | 3.67516i | −0.495558 | − | 0.495558i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.73387 | − | 9.01437i | 0.486109 | − | 1.17357i | −0.470553 | − | 0.882372i | \(-0.655946\pi\) |
0.956662 | − | 0.291199i | \(-0.0940543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.41173 | − | 1.41318i | 0.436827 | − | 0.180940i | −0.153422 | − | 0.988161i | \(-0.549030\pi\) |
0.590249 | + | 0.807221i | \(0.299030\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.20941i | 1.01825i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0538792 | − | 0.130076i | −0.00658239 | − | 0.0158913i | 0.920554 | − | 0.390615i | \(-0.127738\pi\) |
−0.927137 | + | 0.374724i | \(0.877738\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.31641 | + | 1.31641i | 0.156229 | + | 0.156229i | 0.780893 | − | 0.624664i | \(-0.214764\pi\) |
−0.624664 | + | 0.780893i | \(0.714764\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9226 | + | 10.9226i | −1.27839 | + | 1.27839i | −0.336829 | + | 0.941566i | \(0.609354\pi\) |
−0.941566 | + | 0.336829i | \(0.890646\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.56234 | + | 3.96085i | −1.08973 | + | 0.451381i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8735 | −1.33588 | −0.667939 | − | 0.744216i | \(-0.732823\pi\) | ||||
−0.667939 | + | 0.744216i | \(0.732823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.38490 | − | 10.5861i | −0.481305 | − | 1.16197i | −0.958989 | − | 0.283442i | \(-0.908524\pi\) |
0.477684 | − | 0.878532i | \(-0.341476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0592 | − | 4.16666i | −1.09107 | − | 0.451937i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.97566 | − | 5.97566i | 0.633418 | − | 0.633418i | −0.315506 | − | 0.948924i | \(-0.602174\pi\) |
0.948924 | + | 0.315506i | \(0.102174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.1038 | + | 6.25618i | 1.58330 | + | 0.655826i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.63051 | 0.680276 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.21530 | −0.326464 | −0.163232 | − | 0.986588i | \(-0.552192\pi\) | ||||
−0.163232 | + | 0.986588i | \(0.552192\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.62739 | − | 0.674085i | −0.161931 | − | 0.0670740i | 0.300246 | − | 0.953862i | \(-0.402931\pi\) |
−0.462177 | + | 0.886788i | \(0.652931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.111372 | + | 0.111372i | −0.0109738 | + | 0.0109738i | −0.712572 | − | 0.701599i | \(-0.752470\pi\) |
0.701599 | + | 0.712572i | \(0.252470\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.59142 | − | 1.48762i | −0.347196 | − | 0.143813i | 0.202269 | − | 0.979330i | \(-0.435168\pi\) |
−0.549465 | + | 0.835517i | \(0.685168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.90637 | + | 14.2592i | 0.565727 | + | 1.36579i | 0.905126 | + | 0.425144i | \(0.139777\pi\) |
−0.339398 | + | 0.940643i | \(0.610223\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.6022 | 1.56180 | 0.780902 | − | 0.624653i | \(-0.214760\pi\) | ||||
0.780902 | + | 0.624653i | \(0.214760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.22519 | + | 0.507489i | −0.114249 | + | 0.0473236i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.3317 | + | 15.3317i | −1.40546 | + | 1.40546i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.77928 | − | 1.77928i | −0.161753 | − | 0.161753i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.65432 | + | 11.2365i | 0.416295 | + | 1.00503i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.5462i | − | 1.73444i | −0.497923 | − | 0.867221i | \(-0.665904\pi\) | ||
0.497923 | − | 0.867221i | \(-0.334096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.97269 | − | 2.47397i | 0.521837 | − | 0.216152i | −0.106187 | − | 0.994346i | \(-0.533864\pi\) |
0.628023 | + | 0.778194i | \(0.283864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.05294 | − | 12.1989i | 0.438145 | − | 1.05778i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.9438 | + | 13.9438i | 1.19130 | + | 1.19130i | 0.976703 | + | 0.214594i | \(0.0688429\pi\) |
0.214594 | + | 0.976703i | \(0.431157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.10923 | + | 12.3348i | −0.433359 | + | 1.04622i | 0.544838 | + | 0.838542i | \(0.316591\pi\) |
−0.978197 | + | 0.207680i | \(0.933409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 13.4001i | − | 1.12057i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.83322i | 0.567468i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.29028 | − | 3.11502i | 0.105704 | − | 0.255192i | −0.862174 | − | 0.506612i | \(-0.830898\pi\) |
0.967878 | + | 0.251420i | \(0.0808975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0537 | + | 10.0537i | 0.818159 | + | 0.818159i | 0.985841 | − | 0.167682i | \(-0.0536281\pi\) |
−0.167682 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.15786 | + | 12.4522i | −0.414289 | + | 1.00018i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3765 | − | 6.36916i | 1.22718 | − | 0.508315i | 0.327494 | − | 0.944853i | \(-0.393796\pi\) |
0.899686 | + | 0.436539i | \(0.143796\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.64086i | 0.208129i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.22080 | − | 10.1899i | −0.330599 | − | 0.798136i | −0.998545 | − | 0.0539266i | \(-0.982826\pi\) |
0.667946 | − | 0.744210i | \(-0.267174\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.1209 | − | 11.1209i | −0.860562 | − | 0.860562i | 0.130842 | − | 0.991403i | \(-0.458232\pi\) |
−0.991403 | + | 0.130842i | \(0.958232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.77387 | + | 5.77387i | −0.444144 | + | 0.444144i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.66463 | + | 4.00322i | −0.734788 | + | 0.304359i | −0.718518 | − | 0.695509i | \(-0.755179\pi\) |
−0.0162700 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.45256 | 0.487768 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.65549 | − | 16.0678i | −0.497455 | − | 1.20096i | −0.950850 | − | 0.309652i | \(-0.899787\pi\) |
0.453395 | − | 0.891310i | \(-0.350213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5604 | − | 6.85953i | −1.23092 | − | 0.509865i | −0.330056 | − | 0.943961i | \(-0.607068\pi\) |
−0.900867 | + | 0.434096i | \(0.857068\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.59450 | + | 7.59450i | −0.558359 | + | 0.558359i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.4195 | + | 6.80116i | 1.20071 | + | 0.497350i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.545506 | −0.0394715 | −0.0197357 | − | 0.999805i | \(-0.506282\pi\) | ||||
−0.0197357 | + | 0.999805i | \(0.506282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7484 | 0.989632 | 0.494816 | − | 0.868998i | \(-0.335235\pi\) | ||||
0.494816 | + | 0.868998i | \(0.335235\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.74434 | − | 1.55095i | −0.266773 | − | 0.110501i | 0.245288 | − | 0.969450i | \(-0.421118\pi\) |
−0.512060 | + | 0.858949i | \(0.671118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.72904 | + | 9.72904i | −0.689673 | + | 0.689673i | −0.962160 | − | 0.272486i | \(-0.912154\pi\) |
0.272486 | + | 0.962160i | \(0.412154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.5718 | + | 5.20742i | 0.882369 | + | 0.365489i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.93968 | + | 7.09701i | 0.205316 | + | 0.495677i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.8229 | −0.748633 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.8221 | + | 5.31108i | −0.882708 | + | 0.365630i | −0.777546 | − | 0.628826i | \(-0.783536\pi\) |
−0.105162 | + | 0.994455i | \(0.533536\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.9276 | + | 10.9276i | −0.745255 | + | 0.745255i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9790 | + | 18.9790i | 1.28838 | + | 1.28838i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.7425 | − | 25.9346i | −0.722616 | − | 1.74455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9519i | 0.800361i | 0.916436 | + | 0.400180i | \(0.131053\pi\) | ||||
−0.916436 | + | 0.400180i | \(0.868947\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.57146 | − | 3.13620i | 0.502536 | − | 0.208157i | −0.116991 | − | 0.993133i | \(-0.537325\pi\) |
0.619526 | + | 0.784976i | \(0.287325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.36683 | + | 10.5425i | −0.288568 | + | 0.696665i | −0.999981 | − | 0.00610879i | \(-0.998055\pi\) |
0.711413 | + | 0.702774i | \(0.248055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.6048 | − | 16.6048i | −1.08782 | − | 1.08782i | −0.995753 | − | 0.0920662i | \(-0.970653\pi\) |
−0.0920662 | − | 0.995753i | \(-0.529347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.87182 | − | 14.1758i | 0.383035 | − | 0.924729i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8212i | 1.28213i | 0.767488 | + | 0.641063i | \(0.221506\pi\) | ||||
−0.767488 | + | 0.641063i | \(0.778494\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7.78762i | − | 0.501645i | −0.968033 | − | 0.250823i | \(-0.919299\pi\) | ||
0.968033 | − | 0.250823i | \(-0.0807011\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.84272 | + | 9.27715i | −0.245503 | + | 0.592695i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0878 | + | 12.0878i | 0.769130 | + | 0.769130i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.1471 | + | 26.9114i | −0.703597 | + | 1.69863i | 0.0118144 | + | 0.999930i | \(0.496239\pi\) |
−0.715412 | + | 0.698703i | \(0.753761\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.99985 | − | 0.828365i | 0.125729 | − | 0.0520789i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.18232i | 0.385643i | 0.981234 | + | 0.192821i | \(0.0617638\pi\) | ||||
−0.981234 | + | 0.192821i | \(0.938236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.18487 | + | 19.7600i | 0.508583 | + | 1.22783i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.98771 | + | 2.98771i | 0.184230 | + | 0.184230i | 0.793196 | − | 0.608966i | \(-0.208416\pi\) |
−0.608966 | + | 0.793196i | \(0.708416\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.4945 | + | 12.4945i | −0.767533 | + | 0.767533i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.2963 | + | 5.92170i | −0.871658 | + | 0.361053i | −0.773256 | − | 0.634094i | \(-0.781373\pi\) |
−0.0984022 | + | 0.995147i | \(0.531373\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.23625 | 0.257334 | 0.128667 | − | 0.991688i | \(-0.458930\pi\) | ||||
0.128667 | + | 0.991688i | \(0.458930\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.02399 | − | 4.88635i | −0.122051 | − | 0.294658i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.63206 | + | 0.676023i | 0.0980612 | + | 0.0406183i | 0.431175 | − | 0.902268i | \(-0.358099\pi\) |
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.648281 | − | 0.648281i | 0.0386732 | − | 0.0386732i | −0.687506 | − | 0.726179i | \(-0.741294\pi\) |
0.726179 | + | 0.687506i | \(0.241294\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.905971 | + | 0.375265i | 0.0538544 | + | 0.0223072i | 0.409448 | − | 0.912333i | \(-0.365721\pi\) |
−0.355594 | + | 0.934641i | \(0.615721\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.2974 | 0.902978 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.2306 | 1.19004 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.85498 | + | 1.59678i | 0.225210 | + | 0.0932851i | 0.492435 | − | 0.870349i | \(-0.336107\pi\) |
−0.267225 | + | 0.963634i | \(0.586107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.3113 | + | 12.3113i | −0.716790 | + | 0.716790i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.15877 | − | 1.30841i | −0.182677 | − | 0.0756671i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7771 | + | 28.4323i | 0.678818 | + | 1.63881i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.58956 | −0.377317 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.77567 | − | 1.97815i | 0.272562 | − | 0.112899i | −0.242216 | − | 0.970222i | \(-0.577874\pi\) |
0.514778 | + | 0.857323i | \(0.327874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.85083 | − | 5.85083i | 0.331770 | − | 0.331770i | −0.521488 | − | 0.853258i | \(-0.674623\pi\) |
0.853258 | + | 0.521488i | \(0.174623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.37980 | − | 9.37980i | −0.530178 | − | 0.530178i | 0.390448 | − | 0.920625i | \(-0.372320\pi\) |
−0.920625 | + | 0.390448i | \(0.872320\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.45951 | + | 18.0089i | 0.418968 | + | 1.01148i | 0.982647 | + | 0.185484i | \(0.0593853\pi\) |
−0.563679 | + | 0.825994i | \(0.690615\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11.1537i | − | 0.624490i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.9466 | + | 8.67638i | −1.16550 | + | 0.482767i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.19691 | + | 7.71802i | −0.177333 | + | 0.428119i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.6061 | − | 21.6061i | −1.19118 | − | 1.19118i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.04504 | − | 4.93715i | 0.112405 | − | 0.271370i | −0.857659 | − | 0.514219i | \(-0.828082\pi\) |
0.970064 | + | 0.242849i | \(0.0780818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.251234i | 0.0137264i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 32.7329i | − | 1.78308i | −0.452946 | − | 0.891538i | \(-0.649627\pi\) | ||
0.452946 | − | 0.891538i | \(-0.350373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.41908 | − | 20.3255i | 0.455919 | − | 1.10069i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.44913 | − | 3.44913i | −0.186236 | − | 0.186236i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0545 | − | 24.2737i | 0.539755 | − | 1.30308i | −0.385140 | − | 0.922858i | \(-0.625847\pi\) |
0.924894 | − | 0.380225i | \(-0.124153\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.53157 | + | 3.11968i | −0.403156 | + | 0.166993i | −0.575041 | − | 0.818124i | \(-0.695014\pi\) |
0.171886 | + | 0.985117i | \(0.445014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.4403i | 0.768579i | 0.923213 | + | 0.384290i | \(0.125554\pi\) | ||||
−0.923213 | + | 0.384290i | \(0.874446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.27128 | − | 3.06915i | −0.0674728 | − | 0.162894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.26776 | + | 1.26776i | 0.0669099 | + | 0.0669099i | 0.739770 | − | 0.672860i | \(-0.234934\pi\) |
−0.672860 | + | 0.739770i | \(0.734934\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.67204 | + | 3.67204i | −0.193265 | + | 0.193265i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.4656 | − | 10.5482i | 1.33293 | − | 0.552119i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.516344 | 0.0269529 | 0.0134765 | − | 0.999909i | \(-0.495710\pi\) | ||||
0.0134765 | + | 0.999909i | \(0.495710\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.4658 | + | 32.5093i | 0.699110 | + | 1.68780i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.7829 | + | 6.53747i | 0.817205 | + | 0.338498i | 0.751825 | − | 0.659363i | \(-0.229174\pi\) |
0.0653805 | + | 0.997860i | \(0.479174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.4574 | + | 12.4574i | −0.641587 | + | 0.641587i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1190 | − | 4.19144i | −0.519780 | − | 0.215300i | 0.107340 | − | 0.994222i | \(-0.465767\pi\) |
−0.627120 | + | 0.778922i | \(0.715767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5915 | 0.541201 | 0.270601 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270601 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.4691 | 0.941274 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.74428 | + | 4.03621i | 0.494054 | + | 0.204644i | 0.615778 | − | 0.787920i | \(-0.288842\pi\) |
−0.121723 | + | 0.992564i | \(0.538842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.20645 | − | 3.20645i | 0.162157 | − | 0.162157i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.5746 | + | 8.10808i | 0.984906 | + | 0.407962i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.26413 | − | 15.1230i | −0.314388 | − | 0.759000i | −0.999532 | − | 0.0305919i | \(-0.990261\pi\) |
0.685144 | − | 0.728408i | \(-0.259739\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.54016 | 0.476413 | 0.238207 | − | 0.971215i | \(-0.423440\pi\) | ||||
0.238207 | + | 0.971215i | \(0.423440\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.1042 | + | 13.2980i | −1.59922 | + | 0.662420i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.3964 | − | 12.3964i | 0.614465 | − | 0.614465i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.43887 | − | 9.43887i | −0.466722 | − | 0.466722i | 0.434129 | − | 0.900851i | \(-0.357056\pi\) |
−0.900851 | + | 0.434129i | \(0.857056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.2683 | + | 32.0325i | 0.652890 | + | 1.57622i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.4464i | 1.00368i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.2081 | + | 7.54205i | −0.889525 | + | 0.368453i | −0.780183 | − | 0.625551i | \(-0.784874\pi\) |
−0.109342 | + | 0.994004i | \(0.534874\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.63758 | − | 18.4387i | 0.372233 | − | 0.898649i | −0.621139 | − | 0.783701i | \(-0.713330\pi\) |
0.993371 | − | 0.114949i | \(-0.0366704\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.83451 | − | 7.83451i | −0.380029 | − | 0.380029i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.02174 | + | 12.1235i | −0.243019 | + | 0.586700i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.7171i | − | 0.757067i | −0.925588 | − | 0.378534i | \(-0.876428\pi\) | ||
0.925588 | − | 0.378534i | \(-0.123572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.04349i | 0.0982041i | 0.998794 | + | 0.0491020i | \(0.0156360\pi\) | ||||
−0.998794 | + | 0.0491020i | \(0.984364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.05676 | + | 2.55125i | −0.0505518 | + | 0.122043i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.47375 | + | 8.47375i | 0.404430 | + | 0.404430i | 0.879791 | − | 0.475361i | \(-0.157682\pi\) |
−0.475361 | + | 0.879791i | \(0.657682\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8153 | + | 30.9388i | −0.608873 | + | 1.46995i | 0.255355 | + | 0.966847i | \(0.417808\pi\) |
−0.864228 | + | 0.503101i | \(0.832192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.9320 | + | 5.77083i | −0.660440 | + | 0.273563i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.7880i | − | 0.933851i | −0.884297 | − | 0.466926i | \(-0.845362\pi\) | ||
0.884297 | − | 0.466926i | \(-0.154638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.79839 | − | 11.5843i | −0.225947 | − | 0.545485i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.6278 | − | 20.6278i | −0.967045 | − | 0.967045i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.46165 | − | 9.46165i | 0.442597 | − | 0.442597i | −0.450287 | − | 0.892884i | \(-0.648678\pi\) |
0.892884 | + | 0.450287i | \(0.148678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.16779 | + | 3.38321i | −0.380412 | + | 0.157572i | −0.564691 | − | 0.825302i | \(-0.691005\pi\) |
0.184280 | + | 0.982874i | \(0.441005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.2301 | 1.82318 | 0.911590 | − | 0.411101i | \(-0.134856\pi\) | ||||
0.911590 | + | 0.411101i | \(0.134856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.94459 | − | 16.7657i | −0.321357 | − | 0.775825i | −0.999176 | − | 0.0405959i | \(-0.987074\pi\) |
0.677818 | − | 0.735230i | \(-0.262926\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.462224 | + | 0.191459i | 0.0213435 | + | 0.00884078i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.8369 | − | 17.8369i | 0.820142 | − | 0.820142i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.23363 | + | 2.58205i | 0.286018 | + | 0.118473i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.6817 | −0.488058 | −0.244029 | − | 0.969768i | \(-0.578469\pi\) | ||||
−0.244029 | + | 0.969768i | \(0.578469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.6905 | −1.26258 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.30071 | + | 2.19563i | 0.240693 | + | 0.0996983i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.67417 | − | 7.67417i | 0.347750 | − | 0.347750i | −0.511521 | − | 0.859271i | \(-0.670918\pi\) |
0.859271 | + | 0.511521i | \(0.170918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.6885 | − | 16.0253i | −1.74599 | − | 0.723212i | −0.998245 | − | 0.0592250i | \(-0.981137\pi\) |
−0.747744 | − | 0.663987i | \(-0.768863\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.94164 | − | 21.5870i | −0.402711 | − | 0.972231i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.61547 | −0.296745 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1565 | + | 7.52067i | −0.812797 | + | 0.336671i | −0.750069 | − | 0.661359i | \(-0.769980\pi\) |
−0.0627275 | + | 0.998031i | \(0.519980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.9341 | − | 20.9341i | 0.933405 | − | 0.933405i | −0.0645124 | − | 0.997917i | \(-0.520549\pi\) |
0.997917 | + | 0.0645124i | \(0.0205492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.22258 | + | 2.22258i | 0.0989036 | + | 0.0989036i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.399075 | + | 0.963453i | 0.0176887 | + | 0.0427043i | 0.932477 | − | 0.361229i | \(-0.117643\pi\) |
−0.914788 | + | 0.403933i | \(0.867643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 54.8905i | − | 2.42821i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.259658 | − | 0.107554i | 0.0114419 | − | 0.00473940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.58447 | + | 23.1390i | −0.421525 | + | 1.01765i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.86359 | + | 3.86359i | 0.169267 | + | 0.169267i | 0.786657 | − | 0.617390i | \(-0.211810\pi\) |
−0.617390 | + | 0.786657i | \(0.711810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.40221 | − | 20.2847i | 0.367403 | − | 0.886989i | −0.626771 | − | 0.779203i | \(-0.715624\pi\) |
0.994174 | − | 0.107786i | \(-0.0343761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 46.0874i | − | 2.00760i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4477i | 0.975987i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.57908 | + | 18.2975i | −0.328286 | + | 0.792553i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.90494 | + | 4.90494i | 0.212059 | + | 0.212059i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.27241 | − | 15.1429i | 0.270172 | − | 0.652252i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.504857 | − | 0.209119i | 0.0217055 | − | 0.00899071i | −0.371804 | − | 0.928311i | \(-0.621261\pi\) |
0.393510 | + | 0.919320i | \(0.371261\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 27.5409i | − | 1.17972i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9972 | − | 28.9639i | −0.512964 | − | 1.23841i | −0.942151 | − | 0.335190i | \(-0.891200\pi\) |
0.429186 | − | 0.903216i | \(-0.358800\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.0615 | + | 10.0615i | 0.428633 | + | 0.428633i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.8347 | − | 29.8347i | 1.26870 | − | 1.26870i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.31995 | − | 1.37517i | 0.140671 | − | 0.0582677i | −0.311238 | − | 0.950332i | \(-0.600743\pi\) |
0.451908 | + | 0.892064i | \(0.350743\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.8433 | −1.68519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.47196 | + | 8.38204i | 0.146325 | + | 0.353261i | 0.980001 | − | 0.198994i | \(-0.0637675\pi\) |
−0.833675 | + | 0.552255i | \(0.813767\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.3703 | − | 11.3371i | −1.15148 | − | 0.476957i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.72691 | + | 2.72691i | −0.114318 | + | 0.114318i | −0.761952 | − | 0.647634i | \(-0.775759\pi\) |
0.647634 | + | 0.761952i | \(0.275759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.8517 | − | 12.7792i | −1.29110 | − | 0.534792i | −0.371789 | − | 0.928317i | \(-0.621255\pi\) |
−0.919314 | + | 0.393525i | \(0.871255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.34948 | −0.0562771 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.9313 | −1.91214 | −0.956072 | − | 0.293131i | \(-0.905303\pi\) | ||||
−0.956072 | + | 0.293131i | \(0.905303\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.6176 | + | 15.5817i | 1.56064 | + | 0.646438i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.3946 | − | 20.3946i | 0.844658 | − | 0.844658i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.3774 | − | 4.71269i | −0.469597 | − | 0.194514i | 0.135320 | − | 0.990802i | \(-0.456794\pi\) |
−0.604917 | + | 0.796288i | \(0.706794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7404 | + | 25.9296i | 0.442551 | + | 1.06841i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.4266 | 0.592431 | 0.296216 | − | 0.955121i | \(-0.404275\pi\) | ||||
0.296216 | + | 0.955121i | \(0.404275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.7453 | − | 14.8062i | 1.46541 | − | 0.606994i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.4738 | − | 11.4738i | 0.468808 | − | 0.468808i | −0.432720 | − | 0.901528i | \(-0.642446\pi\) |
0.901528 | + | 0.432720i | \(0.142446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.94470 | − | 5.94470i | −0.242489 | − | 0.242489i | 0.575390 | − | 0.817879i | \(-0.304850\pi\) |
−0.817879 | + | 0.575390i | \(0.804850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.71829 | + | 4.14832i | 0.0698585 | + | 0.168653i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.8701i | 0.928269i | 0.885765 | + | 0.464135i | \(0.153635\pi\) | ||||
−0.885765 | + | 0.464135i | \(0.846365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.5481 | − | 15.1387i | 1.47858 | − | 0.612447i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.36341 | + | 12.9484i | −0.216626 | + | 0.522982i | −0.994415 | − | 0.105544i | \(-0.966342\pi\) |
0.777788 | + | 0.628526i | \(0.216342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.5540 | + | 20.5540i | 0.827474 | + | 0.827474i | 0.987167 | − | 0.159693i | \(-0.0510505\pi\) |
−0.159693 | + | 0.987167i | \(0.551050\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.42844 | − | 10.6912i | 0.177994 | − | 0.429716i | −0.809551 | − | 0.587049i | \(-0.800290\pi\) |
0.987546 | + | 0.157333i | \(0.0502896\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0301i | 1.20313i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 12.6236i | − | 0.504943i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.0542 | − | 33.9298i | 0.560378 | − | 1.35287i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.402845 | − | 0.402845i | −0.0160370 | − | 0.0160370i | 0.699043 | − | 0.715080i | \(-0.253610\pi\) |
−0.715080 | + | 0.699043i | \(0.753610\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.3475 | + | 32.2237i | −0.529678 | + | 1.27876i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.9183 | + | 9.90730i | −0.947679 | + | 0.392542i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.0551i | 0.436649i | 0.975876 | + | 0.218324i | \(0.0700591\pi\) | ||||
−0.975876 | + | 0.218324i | \(0.929941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.8771 | − | 26.2596i | −0.428950 | − | 1.03558i | −0.979621 | − | 0.200854i | \(-0.935628\pi\) |
0.550671 | − | 0.834722i | \(-0.314372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.60517 | + | 3.60517i | 0.141734 | + | 0.141734i | 0.774414 | − | 0.632680i | \(-0.218045\pi\) |
−0.632680 | + | 0.774414i | \(0.718045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.0955 | − | 20.0955i | 0.788816 | − | 0.788816i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.1322 | − | 14.1380i | 1.33570 | − | 0.553264i | 0.403423 | − | 0.915014i | \(-0.367820\pi\) |
0.932275 | + | 0.361749i | \(0.117820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.5359 | −0.450746 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.8965 | + | 43.2060i | 0.697150 | + | 1.68307i | 0.729854 | + | 0.683603i | \(0.239588\pi\) |
−0.0327038 | + | 0.999465i | \(0.510412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.26994 | − | 1.35446i | −0.127186 | − | 0.0526822i | 0.318183 | − | 0.948029i | \(-0.396927\pi\) |
−0.445369 | + | 0.895347i | \(0.646927\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.6605 | + | 16.6605i | −0.646065 | + | 0.646065i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.62925 | − | 1.08907i | −0.101805 | − | 0.0421690i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.7560 | 0.415232 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8698 | 1.22849 | 0.614245 | − | 0.789115i | \(-0.289461\pi\) | ||||
0.614245 | + | 0.789115i | \(0.289461\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.6153 | + | 5.63965i | 0.523279 | + | 0.216749i | 0.628657 | − | 0.777683i | \(-0.283605\pi\) |
−0.105378 | + | 0.994432i | \(0.533605\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.07908 | − | 8.07908i | 0.310047 | − | 0.310047i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0468 | + | 9.96050i | 0.920124 | + | 0.381128i | 0.791923 | − | 0.610621i | \(-0.209080\pi\) |
0.128200 | + | 0.991748i | \(0.459080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.4658 | − | 32.5094i | −0.514503 | − | 1.24212i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45.5566 | −1.73557 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.6111 | − | 15.5790i | 1.43079 | − | 0.592653i | 0.473245 | − | 0.880931i | \(-0.343083\pi\) |
0.957547 | + | 0.288278i | \(0.0930826\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.8461 | − | 16.8461i | 0.639008 | − | 0.639008i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5737 | − | 18.5737i | −0.703528 | − | 0.703528i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.53278 | − | 23.0142i | −0.360048 | − | 0.869233i | −0.995292 | − | 0.0969216i | \(-0.969100\pi\) |
0.635244 | − | 0.772312i | \(-0.280900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.3648i | 0.843505i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.78290 | − | 2.39536i | 0.217488 | − | 0.0900867i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.93081 | + | 4.66140i | −0.0725132 | + | 0.175062i | −0.955980 | − | 0.293431i | \(-0.905203\pi\) |
0.883467 | + | 0.468493i | \(0.155203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.96923 | − | 3.96923i | −0.148649 | − | 0.148649i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.15050 | + | 22.0913i | −0.342209 | + | 0.826166i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 39.1090i | − | 1.45852i | −0.684237 | − | 0.729260i | \(-0.739865\pi\) | ||
0.684237 | − | 0.729260i | \(-0.260135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 0.559686i | − | 0.0208438i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.66099 | + | 6.42420i | −0.0988268 | + | 0.238589i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.8274 | − | 17.8274i | −0.661183 | − | 0.661183i | 0.294476 | − | 0.955659i | \(-0.404855\pi\) |
−0.955659 | + | 0.294476i | \(0.904855\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.2223 | − | 48.8210i | 0.747950 | − | 1.80571i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.09283 | − | 1.28109i | 0.114236 | − | 0.0473182i | −0.324833 | − | 0.945771i | \(-0.605308\pi\) |
0.439070 | + | 0.898453i | \(0.355308\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.410086i | − | 0.0151057i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.57114 | + | 20.6926i | 0.315295 | + | 0.761188i | 0.999491 | + | 0.0318910i | \(0.0101529\pi\) |
−0.684197 | + | 0.729297i | \(0.739847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.6030 | + | 30.6030i | 1.12272 | + | 1.12272i | 0.991332 | + | 0.131384i | \(0.0419421\pi\) |
0.131384 | + | 0.991332i | \(0.458058\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.25430 | + | 4.25430i | −0.155866 | + | 0.155866i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.7621 | − | 5.28623i | 0.466317 | − | 0.193155i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.79523 | 0.357433 | 0.178716 | − | 0.983901i | \(-0.442806\pi\) | ||||
0.178716 | + | 0.983901i | \(0.442806\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.70910 | − | 23.4398i | −0.353350 | − | 0.853063i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1531 | + | 4.20556i | 0.369021 | + | 0.152854i | 0.559485 | − | 0.828841i | \(-0.310999\pi\) |
−0.190463 | + | 0.981694i | \(0.560999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.7195 | − | 19.7195i | 0.714832 | − | 0.714832i | −0.252710 | − | 0.967542i | \(-0.581322\pi\) |
0.967542 | + | 0.252710i | \(0.0813219\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −50.6701 | − | 20.9882i | −1.83438 | − | 0.759825i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44.8884 | −1.62083 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.6440 | −0.419894 | −0.209947 | − | 0.977713i | \(-0.567329\pi\) | ||||
−0.209947 | + | 0.977713i | \(0.567329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.6494 | − | 13.5238i | −1.17432 | − | 0.486418i | −0.291700 | − | 0.956510i | \(-0.594221\pi\) |
−0.882617 | + | 0.470092i | \(0.844221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.69825 | + | 9.69825i | −0.348372 | + | 0.348372i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.7784 | + | 6.12140i | 0.529490 | + | 0.219322i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.07510 | + | 5.00972i | 0.0742528 | + | 0.179262i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.6989 | −1.06000 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.72873 | + | 1.95870i | −0.168561 | + | 0.0698203i | −0.465368 | − | 0.885117i | \(-0.654078\pi\) |
0.296807 | + | 0.954937i | \(0.404078\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.7164 | + | 41.7164i | −1.48326 | + | 1.48326i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0132 | − | 12.0132i | −0.426600 | − | 0.426600i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.47493 | + | 3.56079i | 0.0522447 | + | 0.126130i | 0.947847 | − | 0.318726i | \(-0.103255\pi\) |
−0.895602 | + | 0.444856i | \(0.853255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.4669i | 1.85615i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.5671 | + | 17.2177i | −1.46687 | + | 0.607598i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.80336 | − | 4.35369i | 0.0635600 | − | 0.153447i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.851642 | − | 0.851642i | −0.0299421 | − | 0.0299421i | 0.691977 | − | 0.721919i | \(-0.256740\pi\) |
−0.721919 | + | 0.691977i | \(0.756740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.0808 | + | 26.7515i | −0.389100 | + | 0.939371i | 0.601031 | + | 0.799226i | \(0.294757\pi\) |
−0.990131 | + | 0.140145i | \(0.955243\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.6813i | 0.689405i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.1803i | 1.12585i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.6802 | + | 35.4411i | −0.512342 | + | 1.23690i | 0.430176 | + | 0.902745i | \(0.358452\pi\) |
−0.942517 | + | 0.334157i | \(0.891548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.7916 | − | 23.7916i | −0.829322 | − | 0.829322i | 0.158101 | − | 0.987423i | \(-0.449463\pi\) |
−0.987423 | + | 0.158101i | \(0.949463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.95203 | − | 16.7837i | 0.241746 | − | 0.583626i | −0.755711 | − | 0.654906i | \(-0.772708\pi\) |
0.997456 | + | 0.0712800i | \(0.0227084\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6000 | − | 7.29015i | 0.611272 | − | 0.253197i | −0.0555001 | − | 0.998459i | \(-0.517675\pi\) |
0.666772 | + | 0.745261i | \(0.267675\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 34.3362i | − | 1.18968i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.7397 | + | 25.9280i | 0.371663 | + | 0.897274i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.74463 | + | 4.74463i | 0.163803 | + | 0.163803i | 0.784249 | − | 0.620446i | \(-0.213048\pi\) |
−0.620446 | + | 0.784249i | \(0.713048\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.1370 | − | 10.1370i | 0.349553 | − | 0.349553i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.4616 | − | 5.57596i | 0.463092 | − | 0.191819i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.94160 | 0.307237 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.71177 | − | 4.13257i | −0.0586787 | − | 0.141663i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3984 | + | 8.86349i | 0.732666 | + | 0.303480i | 0.717647 | − | 0.696407i | \(-0.245219\pi\) |
0.0150190 | + | 0.999887i | \(0.495219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.9755 | + | 14.9755i | −0.511554 | + | 0.511554i | −0.915003 | − | 0.403448i | \(-0.867812\pi\) |
0.403448 | + | 0.915003i | \(0.367812\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.68023 | + | 1.52440i | 0.125568 | + | 0.0520119i | 0.444583 | − | 0.895738i | \(-0.353352\pi\) |
−0.319015 | + | 0.947750i | \(0.603352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.6581 | 1.79250 | 0.896252 | − | 0.443545i | \(-0.146279\pi\) | ||||
0.896252 | + | 0.443545i | \(0.146279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.6667 | 0.634687 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.9513 | − | 13.2347i | −1.08387 | − | 0.448955i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.458016 | + | 0.458016i | −0.0155193 | + | 0.0155193i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.9289 | − | 16.5391i | −1.34984 | − | 0.559124i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.99743 | − | 12.0649i | −0.168751 | − | 0.407401i | 0.816768 | − | 0.576966i | \(-0.195764\pi\) |
−0.985519 | + | 0.169565i | \(0.945764\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.6516 | 1.30221 | 0.651103 | − | 0.758989i | \(-0.274306\pi\) | ||||
0.651103 | + | 0.758989i | \(0.274306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8231 | − | 4.48306i | 0.364226 | − | 0.150867i | −0.193062 | − | 0.981186i | \(-0.561842\pi\) |
0.557288 | + | 0.830319i | \(0.311842\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.30593 | − | 3.30593i | 0.111002 | − | 0.111002i | −0.649424 | − | 0.760426i | \(-0.724990\pi\) |
0.760426 | + | 0.649424i | \(0.224990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.1137 | + | 49.1137i | 1.64722 | + | 1.64722i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.2271 | − | 29.5189i | −0.409165 | − | 0.987811i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.0340i | 1.03735i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.7224 | + | 11.0688i | −0.891241 | + | 0.369164i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.1221 | − | 55.8217i | 0.770309 | − | 1.85969i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.6171 | + | 22.6171i | 0.751819 | + | 0.751819i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0586 | + | 33.9405i | −0.466809 | + | 1.12698i | 0.498739 | + | 0.866752i | \(0.333797\pi\) |
−0.965548 | + | 0.260225i | \(0.916203\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5526i | 0.945990i | 0.881065 | + | 0.472995i | \(0.156827\pi\) | ||||
−0.881065 | + | 0.472995i | \(0.843173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 33.3744i | − | 1.10453i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.79124 | + | 21.2239i | −0.290312 | + | 0.700876i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.1101 | − | 14.1101i | −0.465448 | − | 0.465448i | 0.434988 | − | 0.900436i | \(-0.356753\pi\) |
−0.900436 | + | 0.434988i | \(0.856753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.27762 | − | 7.91289i | 0.107884 | − | 0.260456i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0974 | + | 4.18247i | −0.331999 | + | 0.137519i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.88348i | − | 0.0617951i | −0.999523 | − | 0.0308975i | \(-0.990163\pi\) | ||
0.999523 | − | 0.0308975i | \(-0.00983656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00185 | + | 19.3182i | 0.262250 | + | 0.633127i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.4247 | − | 22.4247i | −0.733365 | − | 0.733365i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2871 | + | 15.2871i | −0.499409 | + | 0.499409i | −0.911254 | − | 0.411845i | \(-0.864885\pi\) |
0.411845 | + | 0.911254i | \(0.364885\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.4271 | + | 14.6744i | −1.15489 | + | 0.478372i | −0.876171 | − | 0.482000i | \(-0.839910\pi\) |
−0.278721 | + | 0.960372i | \(0.589910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.19927 | −0.104183 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.28542 | + | 20.0028i | 0.269240 | + | 0.650003i | 0.999448 | − | 0.0332221i | \(-0.0105769\pi\) |
−0.730208 | + | 0.683225i | \(0.760577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 65.6555 | + | 27.1954i | 2.13127 | + | 0.882800i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.6252 | − | 27.6252i | 0.894867 | − | 0.894867i | −0.100110 | − | 0.994976i | \(-0.531919\pi\) |
0.994976 | + | 0.100110i | \(0.0319194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.899317 | + | 0.372509i | 0.0291012 | + | 0.0120541i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −70.0731 | −2.26278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.0511 | −0.840358 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.6655 | − | 9.38836i | −0.729629 | − | 0.302222i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.5133 | − | 32.5133i | 1.04556 | − | 1.04556i | 0.0466463 | − | 0.998911i | \(-0.485147\pi\) |
0.998911 | − | 0.0466463i | \(-0.0148534\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.5609 | + | 20.5288i | 1.59048 | + | 0.658800i | 0.990030 | − | 0.140859i | \(-0.0449863\pi\) |
0.600455 | + | 0.799659i | \(0.294986\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.1556 | − | 43.8315i | −0.582042 | − | 1.40517i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.2129 | −0.934603 | −0.467301 | − | 0.884098i | \(-0.654774\pi\) | ||||
−0.467301 | + | 0.884098i | \(0.654774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.7410 | − | 9.41962i | 0.726805 | − | 0.301052i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.7320 | − | 33.7320i | 1.07588 | − | 1.07588i | 0.0790094 | − | 0.996874i | \(-0.474824\pi\) |
0.996874 | − | 0.0790094i | \(-0.0251757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.11378 | + | 5.11378i | 0.162939 | + | 0.162939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.46303 | − | 5.94629i | −0.0783199 | − | 0.189081i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.34392i | − | 0.0744571i | −0.999307 | − | 0.0372285i | \(-0.988147\pi\) | ||
0.999307 | − | 0.0372285i | \(-0.0118530\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.6829 | − | 9.39555i | 0.719095 | − | 0.297859i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.7502 | + | 35.6102i | −0.467145 | + | 1.12779i | 0.498259 | + | 0.867028i | \(0.333973\pi\) |
−0.965404 | + | 0.260759i | \(0.916027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1152.2.w.b.719.3 | 32 | ||
3.2 | odd | 2 | 1152.2.w.a.719.6 | 32 | |||
4.3 | odd | 2 | 288.2.w.a.107.4 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.b.107.5 | yes | 32 | ||
32.3 | odd | 8 | 1152.2.w.a.431.6 | 32 | |||
32.29 | even | 8 | 288.2.w.b.35.5 | yes | 32 | ||
96.29 | odd | 8 | 288.2.w.a.35.4 | ✓ | 32 | ||
96.35 | even | 8 | inner | 1152.2.w.b.431.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.35.4 | ✓ | 32 | 96.29 | odd | 8 | ||
288.2.w.a.107.4 | yes | 32 | 4.3 | odd | 2 | ||
288.2.w.b.35.5 | yes | 32 | 32.29 | even | 8 | ||
288.2.w.b.107.5 | yes | 32 | 12.11 | even | 2 | ||
1152.2.w.a.431.6 | 32 | 32.3 | odd | 8 | |||
1152.2.w.a.719.6 | 32 | 3.2 | odd | 2 | |||
1152.2.w.b.431.3 | 32 | 96.35 | even | 8 | inner | ||
1152.2.w.b.719.3 | 32 | 1.1 | even | 1 | trivial |