Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(214,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.s (of order \(16\), degree \(8\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{16})\) |
Coefficient field: | 16.0.3289935900927224469054816256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10319x^{8} + 214358881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{16}]$ |
Embedding invariants
Embedding label | 343.2 | ||
Root | \(2.83780 - 1.71665i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.343 |
Dual form | 731.2.s.a.601.2 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{1}{16}\right)\) | \(-1\) |
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 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(3\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(4\) | 1.41421 | − | 1.41421i | 0.707107 | − | 0.707107i | ||||
\(5\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.77164 | + | 1.14805i | 0.923880 | + | 0.382683i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17208 | + | 5.89244i | 0.353395 | + | 1.77664i | 0.592425 | + | 0.805626i | \(0.298171\pi\) |
−0.239030 | + | 0.971012i | \(0.576829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.77872 | + | 1.77872i | 0.493328 | + | 0.493328i | 0.909353 | − | 0.416025i | \(-0.136577\pi\) |
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 4.00000i | − | 1.00000i | ||||||
\(17\) | −3.98585 | + | 1.05499i | −0.966711 | + | 0.255872i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.98829 | − | 1.58897i | 1.66567 | − | 0.331323i | 0.729800 | − | 0.683660i | \(-0.239613\pi\) |
0.935873 | + | 0.352337i | \(0.114613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.91342 | + | 4.61940i | −0.382683 | + | 0.923880i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.17064 | − | 10.9126i | 0.389859 | − | 1.95995i | 0.155103 | − | 0.987898i | \(-0.450429\pi\) |
0.234756 | − | 0.972054i | \(-0.424571\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.54328 | − | 2.29610i | 0.923880 | − | 0.382683i | ||||
\(37\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.76537 | − | 7.13187i | 0.744225 | − | 1.11381i | −0.245299 | − | 0.969447i | \(-0.578886\pi\) |
0.989525 | − | 0.144364i | \(-0.0461137\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.05828 | − | 2.50942i | −0.923880 | − | 0.382683i | ||||
\(44\) | 9.99074 | + | 6.67560i | 1.50616 | + | 1.00638i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.935734 | + | 0.935734i | 0.136491 | + | 0.136491i | 0.772051 | − | 0.635560i | \(-0.219231\pi\) |
−0.635560 | + | 0.772051i | \(0.719231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.67878 | − | 6.46716i | −0.382683 | − | 0.923880i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.03098 | 0.697671 | ||||||||
\(53\) | −1.00093 | + | 0.414599i | −0.137488 | + | 0.0569495i | −0.450367 | − | 0.892844i | \(-0.648707\pi\) |
0.312878 | + | 0.949793i | \(0.398707\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.80838 | + | 14.0227i | −0.756187 | + | 1.82560i | −0.235431 | + | 0.971891i | \(0.575650\pi\) |
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.65685 | − | 5.65685i | −0.707107 | − | 0.707107i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.3676i | 1.99962i | 0.0194269 | + | 0.999811i | \(0.493816\pi\) | ||||
−0.0194269 | + | 0.999811i | \(0.506184\pi\) | |||||||
\(68\) | −4.14487 | + | 7.12882i | −0.502639 | + | 0.864496i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.05270 | − | 10.3196i | −0.230947 | − | 1.16105i | −0.906000 | − | 0.423279i | \(-0.860879\pi\) |
0.675053 | − | 0.737769i | \(-0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.36396 | + | 6.36396i | 0.707107 | + | 0.707107i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.50942 | − | 6.05828i | −0.275445 | − | 0.664983i | 0.724254 | − | 0.689534i | \(-0.242184\pi\) |
−0.999699 | + | 0.0245507i | \(0.992184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.05001 | − | 13.5443i | 0.943528 | − | 1.41209i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8804 | − | 10.6110i | 1.61241 | − | 1.07738i | 0.670297 | − | 0.742093i | \(-0.266167\pi\) |
0.942116 | − | 0.335287i | \(-0.108833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.51624 | + | 17.6773i | −0.353395 | + | 1.77664i | ||||
\(100\) | 3.82683 | + | 9.23880i | 0.382683 | + | 0.923880i | ||||
\(101\) | − | 15.0443i | − | 1.49696i | −0.663156 | − | 0.748481i | \(-0.730783\pi\) | ||
0.663156 | − | 0.748481i | \(-0.269217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.2614 | −1.60229 | −0.801143 | − | 0.598473i | \(-0.795775\pi\) | ||||
−0.801143 | + | 0.598473i | \(0.795775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.34302 | + | 5.00318i | 0.323182 | + | 0.483676i | 0.957114 | − | 0.289713i | \(-0.0935599\pi\) |
−0.633932 | + | 0.773389i | \(0.718560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.83844 | − | 4.24803i | 0.271874 | − | 0.406888i | −0.670259 | − | 0.742127i | \(-0.733817\pi\) |
0.942133 | + | 0.335239i | \(0.108817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.88791 | + | 6.97203i | 0.266987 | + | 0.644564i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.1844 | + | 9.60330i | −2.10767 | + | 0.873027i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.3629 | − | 18.5024i | −1.11022 | − | 1.66157i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.77003 | + | 16.3443i | −0.600743 | + | 1.45032i | 0.272075 | + | 0.962276i | \(0.412290\pi\) |
−0.872818 | + | 0.488046i | \(0.837710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.74108 | − | 1.73871i | −0.741409 | − | 0.147475i | −0.190086 | − | 0.981767i | \(-0.560877\pi\) |
−0.551323 | + | 0.834292i | \(0.685877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.39620 | + | 12.5658i | −0.702125 | + | 1.05080i | ||||
\(144\) | 4.59220 | − | 11.0866i | 0.382683 | − | 0.923880i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.2585 | − | 1.65191i | −0.991042 | − | 0.133549i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(164\) | −3.34675 | − | 16.8252i | −0.261337 | − | 1.31383i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.34455 | + | 16.8142i | −0.258809 | + | 1.30112i | 0.604564 | + | 0.796557i | \(0.293347\pi\) |
−0.863373 | + | 0.504566i | \(0.831653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.67232i | − | 0.513255i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.1166 | + | 5.01885i | −0.923880 | + | 0.382683i | ||||
\(173\) | −15.9235 | − | 3.16737i | −1.21064 | − | 0.240811i | −0.451817 | − | 0.892111i | \(-0.649224\pi\) |
−0.758820 | + | 0.651300i | \(0.774224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.5698 | − | 4.68832i | 1.77664 | − | 0.353395i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.149740 | + | 0.752792i | 0.0111301 | + | 0.0559546i | 0.985951 | − | 0.167034i | \(-0.0534188\pi\) |
−0.974821 | + | 0.222988i | \(0.928419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8882 | − | 22.2499i | −0.796223 | − | 1.62707i | ||||
\(188\) | 2.64666 | 0.193027 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.7177 | + | 4.91665i | −1.77922 | + | 0.353908i | −0.971751 | − | 0.236007i | \(-0.924161\pi\) |
−0.807465 | + | 0.589915i | \(0.799161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.9343 | − | 5.35757i | −0.923880 | − | 0.382683i | ||||
\(197\) | −23.0123 | − | 15.3763i | −1.63956 | − | 1.09552i | −0.912614 | − | 0.408822i | \(-0.865940\pi\) |
−0.726944 | − | 0.686696i | \(-0.759060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.9649 | + | 4.76691i | 1.66567 | + | 0.331323i | ||||
\(208\) | 7.11488 | − | 7.11488i | 0.493328 | − | 0.493328i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(212\) | −0.829197 | + | 2.00186i | −0.0569495 | + | 0.137488i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.96623 | − | 5.21318i | −0.603134 | − | 0.350677i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.6066 | + | 10.6066i | −0.707107 | + | 0.707107i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.25078 | − | 12.6765i | 0.346982 | − | 0.837688i | −0.649992 | − | 0.759941i | \(-0.725228\pi\) |
0.996973 | − | 0.0777462i | \(-0.0247724\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.6168 | + | 28.0453i | 0.756187 | + | 1.82560i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.0726 | 1.88055 | 0.940275 | − | 0.340415i | \(-0.110568\pi\) | ||||
0.940275 | + | 0.340415i | \(0.110568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7787 | + | 18.7787i | 1.18530 | + | 1.18530i | 0.978351 | + | 0.206951i | \(0.0663540\pi\) |
0.206951 | + | 0.978351i | \(0.433646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.7258 | + | 45.2081i | 1.17728 | + | 2.84221i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.0000 | −1.00000 | ||||||||
\(257\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.1473 | + | 23.1473i | 1.41395 | + | 1.41395i | ||||
\(269\) | −1.43923 | + | 7.23550i | −0.0877514 | + | 0.441156i | 0.911784 | + | 0.410671i | \(0.134705\pi\) |
−0.999535 | + | 0.0304855i | \(0.990295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31.4395i | − | 1.90981i | −0.296909 | − | 0.954906i | \(-0.595956\pi\) | ||
0.296909 | − | 0.954906i | \(-0.404044\pi\) | |||||||
\(272\) | 4.21995 | + | 15.9434i | 0.255872 | + | 0.966711i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29.4622 | − | 5.86040i | −1.77664 | − | 0.353395i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.5444 | − | 27.7537i | 1.11022 | − | 1.66157i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.5669 | − | 7.27645i | −1.04795 | − | 0.434076i | −0.208792 | − | 0.977960i | \(-0.566953\pi\) |
−0.839161 | + | 0.543884i | \(0.816953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.51306 | − | 12.6340i | −0.149386 | − | 0.751013i | −0.980747 | − | 0.195281i | \(-0.937438\pi\) |
0.831362 | − | 0.555732i | \(-0.187562\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7740 | − | 8.41004i | 0.869059 | − | 0.494708i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.1149 | − | 24.1149i | 1.40881 | − | 1.40881i | 0.642627 | − | 0.766179i | \(-0.277845\pi\) |
0.766179 | − | 0.642627i | \(-0.222155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.0353 | + | 11.3826i | 0.985174 | + | 0.658272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.2727 | −1.67068 | −0.835340 | − | 0.549734i | \(-0.814729\pi\) | ||||
−0.835340 | + | 0.549734i | \(0.814729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.4566 | + | 24.6290i | 0.933166 | + | 1.39658i | 0.917950 | + | 0.396697i | \(0.129844\pi\) |
0.0152162 | + | 0.999884i | \(0.495156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.4971 | − | 11.6912i | −0.984289 | − | 0.657681i | ||||
\(317\) | 4.85722 | + | 24.4189i | 0.272808 | + | 1.37150i | 0.837608 | + | 0.546272i | \(0.183954\pi\) |
−0.564799 | + | 0.825228i | \(0.691046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0000 | 1.00000 | ||||||||
\(325\) | −11.6200 | + | 4.81318i | −0.644564 | + | 0.266987i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(332\) | −12.1166 | − | 5.01885i | −0.664983 | − | 0.275445i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.168898 | − | 0.849110i | 0.00920048 | − | 0.0462539i | −0.975912 | − | 0.218163i | \(-0.929994\pi\) |
0.985113 | + | 0.171909i | \(0.0549935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 66.8458 | 3.61990 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.2213 | − | 15.2213i | −0.810147 | − | 0.810147i | 0.174509 | − | 0.984656i | \(-0.444166\pi\) |
−0.984656 | + | 0.174509i | \(0.944166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.8316 | + | 14.0135i | −1.78556 | + | 0.739605i | −0.794330 | + | 0.607486i | \(0.792178\pi\) |
−0.991234 | + | 0.132119i | \(0.957822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.4350 | − | 13.4350i | 0.707107 | − | 0.707107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.6967 | + | 17.1700i | 1.34136 | + | 0.896266i | 0.999061 | − | 0.0433266i | \(-0.0137956\pi\) |
0.342296 | + | 0.939592i | \(0.388796\pi\) | |||||||
\(368\) | −6.35588 | − | 31.9532i | −0.331323 | − | 1.66567i | ||||
\(369\) | 21.3956 | − | 14.2961i | 1.11381 | − | 0.744225i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.1417 | + | 30.1442i | 1.03461 | + | 1.54840i | 0.820544 | + | 0.571583i | \(0.193670\pi\) |
0.214065 | + | 0.976819i | \(0.431330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.9104 | − | 13.9104i | −0.707107 | − | 0.707107i | ||||
\(388\) | 7.45215 | − | 37.4645i | 0.378326 | − | 1.90197i | ||||
\(389\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.1638 | + | 14.7609i | −1.52545 | + | 0.746493i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 20.0268 | + | 29.9722i | 1.00638 | + | 1.50616i | ||||
\(397\) | 5.04333 | − | 1.00318i | 0.253118 | − | 0.0503482i | −0.0669005 | − | 0.997760i | \(-0.521311\pi\) |
0.320018 | + | 0.947411i | \(0.396311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.4776 | + | 7.65367i | 0.923880 | + | 0.382683i | ||||
\(401\) | −0.755151 | − | 0.504576i | −0.0377105 | − | 0.0251973i | 0.536572 | − | 0.843854i | \(-0.319719\pi\) |
−0.574283 | + | 0.818657i | \(0.694719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.2713 | − | 15.5494i | 1.15923 | − | 0.774571i | ||||
\(404\) | −21.2758 | − | 21.2758i | −1.05851 | − | 1.05851i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.9971 | + | 22.9971i | −1.13299 | + | 1.13299i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.51925 | + | 3.66779i | 0.0738683 | + | 0.178334i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.75319 | − | 20.4309i | 0.133549 | − | 0.991042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.8033 | + | 2.34783i | 0.570535 | + | 0.113486i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.6942 | − | 8.09459i | 1.96017 | − | 0.389903i | 0.972722 | − | 0.231972i | \(-0.0745179\pi\) |
0.987450 | − | 0.157930i | \(-0.0504821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.99346 | − | 10.0218i | −0.0954693 | − | 0.479957i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.20138 | + | 36.2038i | −0.343703 | + | 1.72791i | 0.292391 | + | 0.956299i | \(0.405549\pi\) |
−0.636093 | + | 0.771612i | \(0.719451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 21.0000i | − | 1.00000i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.0107 | −0.903223 | −0.451612 | − | 0.892215i | \(-0.649151\pi\) | ||||
−0.451612 | + | 0.892215i | \(0.649151\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.6095 | + | 19.7205i | 2.24185 | + | 0.928603i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.2331 | + | 10.0377i | −1.12865 | + | 0.467502i | −0.867322 | − | 0.497748i | \(-0.834160\pi\) |
−0.261328 | + | 0.965250i | \(0.584160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(468\) | 13.9441 | + | 5.77582i | 0.644564 | + | 0.266987i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.68584 | − | 38.6393i | 0.353395 | − | 1.77664i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.25020 | −0.148816 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.9358 | − | 2.17526i | −0.499668 | − | 0.0993902i | −0.0611793 | − | 0.998127i | \(-0.519486\pi\) |
−0.438489 | + | 0.898737i | \(0.644486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.2066 | + | 46.3688i | −0.873027 | + | 2.10767i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.50866 | − | 37.7486i | −0.340250 | − | 1.71055i | −0.650171 | − | 0.759788i | \(-0.725303\pi\) |
0.309921 | − | 0.950762i | \(-0.399697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −43.6502 | − | 8.68257i | −1.95995 | − | 0.389859i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.5401 | + | 32.6886i | 0.600743 | + | 1.45032i | ||||
\(509\) | − | 18.4282i | − | 0.816817i | −0.912799 | − | 0.408408i | \(-0.866084\pi\) | ||
0.912799 | − | 0.408408i | \(-0.133916\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.41700 | + | 6.61051i | −0.194260 | + | 0.290730i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.86075 | + | 45.7858i | 0.124616 | + | 1.99446i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.0387 | − | 16.5846i | 1.74081 | − | 0.721069i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.1975 | + | 32.1975i | −1.39725 | + | 1.39725i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.1619 | − | 4.20935i | 0.916622 | − | 0.182327i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.9676 | − | 23.3646i | 1.50616 | − | 1.00638i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.06639 | − | 25.4705i | 0.217821 | − | 1.09506i | −0.704816 | − | 0.709390i | \(-0.748970\pi\) |
0.922637 | − | 0.385670i | \(-0.126030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.8771 | − | 9.12552i | −1.96156 | − | 0.390179i | −0.981315 | − | 0.192406i | \(-0.938371\pi\) |
−0.980248 | − | 0.197773i | \(-0.936629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.8207 | + | 9.90285i | −0.628536 | + | 0.419974i | ||||
\(557\) | 32.9636 | + | 32.9636i | 1.39671 | + | 1.39671i | 0.809260 | + | 0.587450i | \(0.199868\pi\) |
0.587450 | + | 0.809260i | \(0.300132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.31243 | − | 15.2395i | −0.266987 | − | 0.644564i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.0199 | − | 4.56459i | 0.464433 | − | 0.192374i | −0.138182 | − | 0.990407i | \(-0.544126\pi\) |
0.602614 | + | 0.798033i | \(0.294126\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.9388 | − | 38.4796i | 0.668189 | − | 1.61315i | −0.116450 | − | 0.993197i | \(-0.537151\pi\) |
0.784639 | − | 0.619953i | \(-0.212849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(572\) | 5.89671 | + | 29.6447i | 0.246554 | + | 1.23951i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.94485 | + | 39.9414i | −0.331323 | + | 1.66567i | ||||
\(576\) | −9.18440 | − | 22.1731i | −0.382683 | − | 0.923880i | ||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.61617 | − | 5.41198i | −0.149766 | − | 0.224141i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.4577 | + | 32.4577i | −1.32618 | + | 1.32618i | −0.417514 | + | 0.908671i | \(0.637098\pi\) |
−0.908671 | + | 0.417514i | \(0.862902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.7908 | + | 45.3651i | −0.765222 | + | 1.84741i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.32882i | 0.134670i | ||||||||
\(612\) | −19.6723 | + | 15.0000i | −0.795206 | + | 0.606339i | ||||
\(613\) | −28.7652 | −1.16182 | −0.580909 | − | 0.813969i | \(-0.697303\pi\) | ||||
−0.580909 | + | 0.813969i | \(0.697303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.37785 | + | 8.04852i | 0.216504 | + | 0.324021i | 0.923785 | − | 0.382911i | \(-0.125078\pi\) |
−0.707281 | + | 0.706932i | \(0.750078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.5764 | − | 41.2711i | 1.10839 | − | 1.65882i | 0.495735 | − | 0.868474i | \(-0.334899\pi\) |
0.612655 | − | 0.790350i | \(-0.290101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.6777 | − | 17.6777i | −0.707107 | − | 0.707107i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.73845 | − | 16.2681i | 0.266987 | − | 0.644564i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.74620 | − | 43.9701i | 0.344916 | − | 1.73401i | −0.286062 | − | 0.958211i | \(-0.592346\pi\) |
0.630978 | − | 0.775800i | \(-0.282654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −89.4357 | − | 17.7899i | −3.51066 | − | 0.698313i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −28.5275 | − | 19.0615i | −1.11381 | − | 0.744225i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.7632 | + | 23.7632i | 0.925684 | + | 0.925684i | 0.997423 | − | 0.0717399i | \(-0.0228551\pi\) |
−0.0717399 | + | 0.997423i | \(0.522855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.50942 | − | 6.05828i | −0.0976052 | − | 0.235640i | 0.867533 | − | 0.497379i | \(-0.165704\pi\) |
−0.965139 | + | 0.261739i | \(0.915704\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 19.0490 | + | 28.5088i | 0.737027 | + | 1.10304i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.43608 | − | 9.43608i | −0.362926 | − | 0.362926i | ||||
\(677\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.3715 | − | 7.83147i | −1.50651 | − | 0.299663i | −0.628311 | − | 0.777962i | \(-0.716253\pi\) |
−0.878197 | + | 0.478299i | \(0.841253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.0377 | + | 24.2331i | −0.382683 | + | 0.923880i | ||||
\(689\) | −2.51783 | − | 1.04292i | −0.0959216 | − | 0.0397320i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(692\) | −26.9985 | + | 18.0398i | −1.02633 | + | 0.685771i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.4700 | + | 33.4540i | −0.434457 | + | 1.26716i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.88512 | + | 9.88512i | −0.373356 | + | 0.373356i | −0.868698 | − | 0.495342i | \(-0.835043\pi\) |
0.495342 | + | 0.868698i | \(0.335043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 26.7024 | − | 39.9630i | 1.00638 | − | 1.50616i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.2616 | − | 12.8702i | 0.723386 | − | 0.483351i | −0.138558 | − | 0.990354i | \(-0.544247\pi\) |
0.861944 | + | 0.507003i | \(0.169247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.15810 | − | 30.9589i | 0.230947 | − | 1.16105i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 90.6217i | − | 3.39381i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0689 | − | 42.0081i | −1.04679 | − | 1.56664i | −0.802242 | − | 0.597000i | \(-0.796359\pi\) |
−0.244551 | − | 0.969636i | \(-0.578641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.27637 | + | 0.852845i | 0.0474360 | + | 0.0316957i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.3325 | + | 24.9447i | 0.382683 | + | 0.923880i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.7948 | + | 3.61077i | 0.991042 | + | 0.133549i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −96.4452 | + | 19.1841i | −3.55261 | + | 0.706657i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.6723i | − | 0.719772i | ||||||
\(748\) | −46.8643 | − | 16.0678i | −1.71353 | − | 0.587498i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(752\) | 3.74294 | − | 3.74294i | 0.136491 | − | 0.136491i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.2739 | + | 14.6109i | −1.27367 | + | 0.527570i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.9545 | − | 25.9545i | 0.935943 | − | 0.935943i | −0.0621249 | − | 0.998068i | \(-0.519788\pi\) |
0.998068 | + | 0.0621249i | \(0.0197877\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −28.0029 | + | 41.9092i | −1.00785 | + | 1.50835i | ||||
\(773\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 46.2561 | + | 30.9073i | 1.66157 | + | 1.11022i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.8686 | + | 10.7151i | −0.923880 | + | 0.382683i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.5212 | + | 45.6782i | 1.08796 | + | 1.62825i | 0.712923 | + | 0.701242i | \(0.247371\pi\) |
0.375040 | + | 0.927009i | \(0.377629\pi\) | |||||||
\(788\) | −54.2897 | + | 10.7989i | −1.93399 | + | 0.384695i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5959 | + | 40.0662i | 0.587859 | + | 1.41922i | 0.885545 | + | 0.464553i | \(0.153785\pi\) |
−0.297687 | + | 0.954664i | \(0.596215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.71688 | − | 2.74251i | −0.166871 | − | 0.0970230i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.4504 | − | 17.6736i | −0.929946 | − | 0.621370i | −0.00439415 | − | 0.999990i | \(-0.501399\pi\) |
−0.925552 | + | 0.378620i | \(0.876399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.7714 | + | 19.1138i | 0.445726 | + | 0.667076i | 0.984502 | − | 0.175373i | \(-0.0561132\pi\) |
−0.538776 | + | 0.842449i | \(0.681113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.60491 | + | 3.89852i | −0.0908014 | + | 0.135894i | −0.874089 | − | 0.485765i | \(-0.838541\pi\) |
0.783288 | + | 0.621659i | \(0.213541\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.64080 | − | 23.3309i | −0.161376 | − | 0.811293i | −0.973655 | − | 0.228024i | \(-0.926773\pi\) |
0.812279 | − | 0.583269i | \(-0.198227\pi\) | |||||||
\(828\) | 40.6329 | − | 27.1500i | 1.41209 | − | 0.943528i | ||||
\(829\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 20.1239i | − | 0.697671i | ||||||
\(833\) | 17.5000 | + | 22.9510i | 0.606339 | + | 0.795206i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0978 | − | 26.7925i | 0.382683 | − | 0.923880i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.65839 | + | 4.00372i | 0.0569495 | + | 0.137488i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.6708 | + | 11.2725i | 1.94037 | + | 0.385964i | 0.998790 | + | 0.0491804i | \(0.0156609\pi\) |
0.941582 | + | 0.336784i | \(0.109339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.2080 | − | 24.2570i | 0.553655 | − | 0.828604i | −0.444072 | − | 0.895991i | \(-0.646466\pi\) |
0.997727 | + | 0.0673876i | \(0.0214664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 58.4018 | − | 24.1908i | 1.98115 | − | 0.820618i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.1134 | + | 29.1134i | −0.986470 | + | 0.986470i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 56.1967 | − | 11.1782i | 1.90197 | − | 0.378326i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.49577 | + | 3.67216i | 0.185579 | + | 0.124000i | 0.644889 | − | 0.764276i | \(-0.276903\pi\) |
−0.459310 | + | 0.888276i | \(0.651903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.85975 | + | 44.5410i | −0.298493 | + | 1.50062i | 0.482396 | + | 0.875953i | \(0.339767\pi\) |
−0.780889 | + | 0.624670i | \(0.785233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.6810i | 1.57094i | 0.618899 | + | 0.785471i | \(0.287579\pi\) | ||||
−0.618899 | + | 0.785471i | \(0.712421\pi\) | |||||||
\(884\) | −20.0527 | + | 5.30762i | −0.674446 | + | 0.178514i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.0402 | + | 44.9583i | −1.00638 | + | 1.50616i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 30.0000i | 1.00000i | ||||||||
\(901\) | 3.55216 | − | 2.70850i | 0.118340 | − | 0.0902331i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.79242 | − | 1.35110i | 0.225539 | − | 0.0448624i | −0.0810272 | − | 0.996712i | \(-0.525820\pi\) |
0.306566 | + | 0.951849i | \(0.400820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.2716 | − | 41.6973i | 0.572863 | − | 1.38301i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.7568 | − | 21.8874i | 1.08409 | − | 0.724368i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.5016 | − | 25.3530i | −0.346982 | − | 0.837688i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.7872 | 1.08155 | 0.540775 | − | 0.841167i | \(-0.318131\pi\) | ||||
0.540775 | + | 0.841167i | \(0.318131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.0708 | − | 18.6689i | −1.48032 | − | 0.613169i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.4236 | + | 11.4223i | −1.87196 | + | 0.372355i | −0.994272 | − | 0.106883i | \(-0.965913\pi\) |
−0.877685 | + | 0.479238i | \(0.840913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.7348 | − | 64.5435i | 0.870605 | − | 2.10183i | ||||
\(944\) | 56.0907 | + | 23.2335i | 1.82560 | + | 0.756187i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.6735 | − | 33.8590i | 1.64667 | − | 1.10027i | 0.745808 | − | 0.666160i | \(-0.232063\pi\) |
0.900861 | − | 0.434109i | \(-0.142937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 41.1149 | − | 41.1149i | 1.32975 | − | 1.32975i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −85.7319 | − | 35.5113i | −2.76554 | − | 1.14553i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.52174 | + | 17.7050i | 0.113486 | + | 0.570535i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2886 | + | 51.3952i | 0.684594 | + | 1.65276i | 0.755397 | + | 0.655267i | \(0.227444\pi\) |
−0.0708031 | + | 0.997490i | \(0.522556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.0432 | + | 23.2138i | −1.79851 | + | 0.744968i | −0.811493 | + | 0.584363i | \(0.801345\pi\) |
−0.987019 | + | 0.160605i | \(0.948655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.0754 | + | 48.4663i | −0.642268 | + | 1.55057i | 0.181344 | + | 0.983420i | \(0.441955\pi\) |
−0.823612 | + | 0.567153i | \(0.808045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7441 | − | 8.51533i | 0.406888 | − | 0.271874i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.3827 | − | 10.4196i | −1.66567 | − | 0.331323i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(998\) | 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 | 731.2.s.a.343.2 | ✓ | 16 | |
17.6 | odd | 16 | inner | 731.2.s.a.601.2 | yes | 16 | |
43.42 | odd | 2 | CM | 731.2.s.a.343.2 | ✓ | 16 | |
731.601 | even | 16 | inner | 731.2.s.a.601.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.s.a.343.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
731.2.s.a.343.2 | ✓ | 16 | 43.42 | odd | 2 | CM | |
731.2.s.a.601.2 | yes | 16 | 17.6 | odd | 16 | inner | |
731.2.s.a.601.2 | yes | 16 | 731.601 | even | 16 | inner |