Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3459,1,Mod(176,3459)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3459, base_ring=CyclotomicField(192))
chi = DirichletCharacter(H, H._module([96, 25]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3459.176");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3459 = 3 \cdot 1153 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3459.bm (of order \(192\), degree \(64\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.72626587870\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Coefficient field: | \(\Q(\zeta_{192})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{64} - x^{32} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{192}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{192} - \cdots)\) |
Embedding invariants
Embedding label | 707.1 | ||
Root | \(-0.0327191 - 0.999465i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3459.707 |
Dual form | 3459.1.bm.a.1502.1 |
$q$-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 \(\left(\mathbb{Z}/3459\mathbb{Z}\right)^\times\).
\(n\) | \(1154\) | \(2311\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{67}{192}\right)\) |
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 | −0.659346 | − | 0.751840i | \(-0.729167\pi\) | ||||
0.659346 | + | 0.751840i | \(0.270833\pi\) | |||||||
\(3\) | −0.986643 | − | 0.162895i | −0.986643 | − | 0.162895i | ||||
\(4\) | −0.130526 | + | 0.991445i | −0.130526 | + | 0.991445i | ||||
\(5\) | 0 | 0 | −0.456904 | − | 0.889516i | \(-0.651042\pi\) | ||||
0.456904 | + | 0.889516i | \(0.348958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.142243 | − | 0.397542i | 0.142243 | − | 0.397542i | −0.849202 | − | 0.528068i | \(-0.822917\pi\) |
0.991445 | + | 0.130526i | \(0.0416667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.946930 | + | 0.321439i | 0.946930 | + | 0.321439i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.683592 | − | 0.729864i | \(-0.739583\pi\) | ||||
0.683592 | + | 0.729864i | \(0.260417\pi\) | |||||||
\(12\) | 0.290285 | − | 0.956940i | 0.290285 | − | 0.956940i | ||||
\(13\) | −1.61787 | − | 0.159346i | −1.61787 | − | 0.159346i | −0.751840 | − | 0.659346i | \(-0.770833\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(17\) | 0 | 0 | 0.718582 | − | 0.695443i | \(-0.244792\pi\) | ||||
−0.718582 | + | 0.695443i | \(0.755208\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.19553 | + | 0.341402i | 1.19553 | + | 0.341402i | 0.812847 | − | 0.582478i | \(-0.197917\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.205101 | + | 0.369061i | −0.205101 | + | 0.369061i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.582478 | + | 0.812847i | −0.582478 | + | 0.812847i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.881921 | − | 0.471397i | −0.881921 | − | 0.471397i | ||||
\(28\) | 0.375574 | + | 0.192915i | 0.375574 | + | 0.192915i | ||||
\(29\) | 0 | 0 | −0.162895 | − | 0.986643i | \(-0.552083\pi\) | ||||
0.162895 | + | 0.986643i | \(0.447917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.740816 | + | 1.33304i | 0.740816 | + | 1.33304i | 0.935906 | + | 0.352250i | \(0.114583\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.442289 | + | 0.896873i | −0.442289 | + | 0.896873i | ||||
\(37\) | −0.293107 | + | 0.0143994i | −0.293107 | + | 0.0143994i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.57030 | + | 0.420760i | 1.57030 | + | 0.420760i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.812847 | − | 0.582478i | \(-0.802083\pi\) | ||||
0.812847 | + | 0.582478i | \(0.197917\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.783904 | + | 1.46658i | −0.783904 | + | 1.46658i | 0.0980171 | + | 0.995185i | \(0.468750\pi\) |
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0.910864 | + | 0.412707i | 0.910864 | + | 0.412707i | ||||
\(49\) | 0.635204 | + | 0.521299i | 0.635204 | + | 0.521299i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.369156 | − | 1.58323i | 0.369156 | − | 1.58323i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.12395 | − | 0.531588i | −1.12395 | − | 0.531588i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.671559 | − | 0.740951i | \(-0.734375\pi\) | ||||
0.671559 | + | 0.740951i | \(0.265625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.16075 | − | 1.05205i | −1.16075 | − | 1.05205i | −0.997859 | − | 0.0654031i | \(-0.979167\pi\) |
−0.162895 | − | 0.986643i | \(-0.552083\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.262479 | − | 0.330722i | 0.262479 | − | 0.330722i | ||||
\(64\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.514103 | − | 0.857729i | \(-0.328125\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.123862 | + | 0.192105i | 0.123862 | + | 0.192105i | 0.896873 | − | 0.442289i | \(-0.145833\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(76\) | −0.494529 | + | 1.14074i | −0.494529 | + | 1.14074i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.62674 | + | 0.241304i | −1.62674 | + | 0.241304i | −0.896873 | − | 0.442289i | \(-0.854167\pi\) |
−0.729864 | + | 0.683592i | \(0.760417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.793353 | + | 0.608761i | 0.793353 | + | 0.608761i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.762527 | − | 0.646956i | \(-0.776042\pi\) | ||||
0.762527 | + | 0.646956i | \(0.223958\pi\) | |||||||
\(84\) | −0.339133 | − | 0.251518i | −0.339133 | − | 0.251518i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.0327191 | − | 0.999465i | \(-0.489583\pi\) | ||||
−0.0327191 | + | 0.999465i | \(0.510417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.293476 | + | 0.620503i | −0.293476 | + | 0.620503i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.513775 | − | 1.43591i | −0.513775 | − | 1.43591i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.582478 | + | 1.00888i | −0.582478 | + | 1.00888i | 0.412707 | + | 0.910864i | \(0.364583\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.729864 | − | 0.683592i | −0.729864 | − | 0.683592i | ||||
\(101\) | 0 | 0 | 0.514103 | − | 0.857729i | \(-0.328125\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.668574 | + | 1.54221i | −0.668574 | + | 1.54221i | 0.162895 | + | 0.986643i | \(0.447917\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.321439 | − | 0.946930i | \(-0.395833\pi\) | ||||
−0.321439 | + | 0.946930i | \(0.604167\pi\) | |||||||
\(108\) | 0.582478 | − | 0.812847i | 0.582478 | − | 0.812847i | ||||
\(109\) | 1.68789 | + | 0.512016i | 1.68789 | + | 0.512016i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.291538 | + | 0.0335388i | 0.291538 | + | 0.0335388i | ||||
\(112\) | −0.240287 | + | 0.347181i | −0.240287 | + | 0.347181i | ||||
\(113\) | 0 | 0 | −0.114287 | − | 0.993448i | \(-0.536458\pi\) | ||||
0.114287 | + | 0.993448i | \(0.463542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.48079 | − | 0.670935i | −1.48079 | − | 0.670935i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0654031 | + | 0.997859i | −0.0654031 | + | 0.997859i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.41833 | + | 0.560482i | −1.41833 | + | 0.560482i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0951944 | + | 1.93773i | −0.0951944 | + | 1.93773i | 0.195090 | + | 0.980785i | \(0.437500\pi\) |
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.01233 | − | 1.31930i | 1.01233 | − | 1.31930i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.812847 | − | 0.582478i | \(-0.802083\pi\) | ||||
0.812847 | + | 0.582478i | \(0.197917\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.305777 | − | 0.426711i | 0.305777 | − | 0.426711i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.464509 | − | 1.23417i | −0.464509 | − | 1.23417i | −0.935906 | − | 0.352250i | \(-0.885417\pi\) |
0.471397 | − | 0.881921i | \(-0.343750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.541803 | − | 0.617808i | −0.541803 | − | 0.617808i | ||||
\(148\) | 0.0239819 | − | 0.292479i | 0.0239819 | − | 0.292479i | ||||
\(149\) | 0 | 0 | −0.659346 | − | 0.751840i | \(-0.729167\pi\) | ||||
0.659346 | + | 0.751840i | \(0.270833\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.57021 | + | 1.16455i | −1.57021 | + | 1.16455i | −0.659346 | + | 0.751840i | \(0.729167\pi\) |
−0.910864 | + | 0.412707i | \(0.864583\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.622126 | + | 1.50194i | −0.622126 | + | 1.50194i | ||||
\(157\) | 1.51951 | − | 0.979728i | 1.51951 | − | 0.979728i | 0.528068 | − | 0.849202i | \(-0.322917\pi\) |
0.991445 | − | 0.130526i | \(-0.0416667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.96532 | + | 0.0965501i | −1.96532 | + | 0.0965501i | −0.991445 | − | 0.130526i | \(-0.958333\pi\) |
−0.973877 | + | 0.227076i | \(0.927083\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.0817211 | − | 0.996655i | \(-0.526042\pi\) | ||||
0.0817211 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.61131 | + | 0.320510i | 1.61131 | + | 0.320510i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.02234 | + | 0.707574i | 1.02234 | + | 0.707574i | ||||
\(172\) | −1.35171 | − | 0.968625i | −1.35171 | − | 0.968625i | ||||
\(173\) | 0 | 0 | −0.941544 | − | 0.336890i | \(-0.890625\pi\) | ||||
0.941544 | + | 0.336890i | \(0.109375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.240287 | + | 0.347181i | 0.240287 | + | 0.347181i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.397748 | − | 0.917494i | \(-0.369792\pi\) | ||||
−0.397748 | + | 0.917494i | \(0.630208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.317157 | − | 0.227272i | 0.317157 | − | 0.227272i | −0.412707 | − | 0.910864i | \(-0.635417\pi\) |
0.729864 | + | 0.683592i | \(0.239583\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.973877 | + | 1.22708i | 0.973877 | + | 1.22708i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.312847 | + | 0.283548i | −0.312847 | + | 0.283548i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.621661 | − | 0.783287i | \(-0.713542\pi\) | ||||
0.621661 | + | 0.783287i | \(0.286458\pi\) | |||||||
\(192\) | −0.528068 | + | 0.849202i | −0.528068 | + | 0.849202i | ||||
\(193\) | −1.08016 | − | 0.0885679i | −1.08016 | − | 0.0885679i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) |
−0.608761 | + | 0.793353i | \(0.708333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.599749 | + | 0.561727i | −0.599749 | + | 0.561727i | ||||
\(197\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.78480 | + | 0.739288i | −1.78480 | + | 0.739288i | −0.793353 | + | 0.608761i | \(0.791667\pi\) |
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.56912 | + | 0.975742i | 1.56912 | + | 0.975742i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.52150 | + | 0.572651i | 1.52150 | + | 0.572651i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.78841 | + | 0.845855i | 1.78841 | + | 0.845855i | 0.956940 | + | 0.290285i | \(0.0937500\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.635313 | − | 0.104891i | 0.635313 | − | 0.104891i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0909149 | − | 0.209715i | −0.0909149 | − | 0.209715i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.260913 | − | 0.00854139i | −0.260913 | − | 0.00854139i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
−0.162895 | + | 0.986643i | \(0.552083\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.812847 | + | 0.582478i | −0.812847 | + | 0.582478i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.996655 | − | 0.0817211i | \(-0.973958\pi\) | ||||
0.996655 | + | 0.0817211i | \(0.0260417\pi\) | |||||||
\(228\) | 0.673745 | − | 1.04495i | 0.673745 | − | 1.04495i | ||||
\(229\) | −0.215212 | − | 1.87075i | −0.215212 | − | 1.87075i | −0.442289 | − | 0.896873i | \(-0.645833\pi\) |
0.227076 | − | 0.973877i | \(-0.427083\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.718582 | − | 0.695443i | \(-0.755208\pi\) | ||||
0.718582 | + | 0.695443i | \(0.244792\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.64432 | + | 0.0269075i | 1.64432 | + | 0.0269075i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0249525 | + | 0.0211706i | 0.0249525 | + | 0.0211706i | 0.659346 | − | 0.751840i | \(-0.270833\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.683592 | − | 0.729864i | −0.683592 | − | 0.729864i | ||||
\(244\) | 1.19455 | − | 1.01350i | 1.19455 | − | 1.01350i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.87981 | − | 0.742845i | −1.87981 | − | 0.742845i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.659346 | − | 0.751840i | \(-0.270833\pi\) | ||||
−0.659346 | + | 0.751840i | \(0.729167\pi\) | |||||||
\(252\) | 0.293632 | + | 0.303402i | 0.293632 | + | 0.303402i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(257\) | 0 | 0 | 0.0163617 | − | 0.999866i | \(-0.494792\pi\) | ||||
−0.0163617 | + | 0.999866i | \(0.505208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0359680 | + | 0.118571i | −0.0359680 | + | 0.118571i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.917494 | − | 0.397748i | \(-0.869792\pi\) | ||||
0.917494 | + | 0.397748i | \(0.130208\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.923880 | − | 1.60021i | 0.923880 | − | 1.60021i | ||||
\(269\) | 0 | 0 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.555570 | − | 1.83147i | 0.555570 | − | 1.83147i | − | 1.00000i | \(-0.5\pi\) | |
0.555570 | − | 0.831470i | \(-0.312500\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.390633 | − | 0.564409i | 0.390633 | − | 0.564409i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.588289 | + | 0.167995i | −0.588289 | + | 0.167995i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
−0.0327191 | + | 0.999465i | \(0.510417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.273010 | + | 1.50042i | 0.273010 | + | 1.50042i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) | ||||
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.59540 | + | 0.630458i | 1.59540 | + | 0.630458i | 0.986643 | − | 0.162895i | \(-0.0520833\pi\) |
0.608761 | + | 0.793353i | \(0.291667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0327191 | − | 0.999465i | 0.0327191 | − | 0.999465i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.739040 | − | 0.900523i | 0.739040 | − | 0.900523i | ||||
\(292\) | −0.206628 | + | 0.0977279i | −0.206628 | + | 0.0977279i | ||||
\(293\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.608761 | + | 0.793353i | 0.608761 | + | 0.793353i | ||||
\(301\) | 0.471523 | + | 0.520245i | 0.471523 | + | 0.520245i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.06643 | − | 0.639195i | −1.06643 | − | 0.639195i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.34743 | + | 1.03392i | 1.34743 | + | 1.03392i | 0.995185 | + | 0.0980171i | \(0.0312500\pi\) |
0.352250 | + | 0.935906i | \(0.385417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.910864 | − | 1.41271i | 0.910864 | − | 1.41271i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.952063 | − | 0.305903i | \(-0.901042\pi\) | ||||
0.952063 | + | 0.305903i | \(0.0989583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.68387 | − | 1.04710i | 1.68387 | − | 1.04710i | 0.773010 | − | 0.634393i | \(-0.218750\pi\) |
0.910864 | − | 0.412707i | \(-0.135417\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0269075 | − | 1.64432i | −0.0269075 | − | 1.64432i | ||||
\(317\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(325\) | 1.07189 | − | 1.22226i | 1.07189 | − | 1.22226i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.58194 | − | 0.780128i | −1.58194 | − | 0.780128i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.907820 | + | 1.76738i | −0.907820 | + | 1.76738i | −0.352250 | + | 0.935906i | \(0.614583\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.282181 | − | 0.0805810i | −0.282181 | − | 0.0805810i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.293632 | − | 0.303402i | 0.293632 | − | 0.303402i | ||||
\(337\) | 0.968101 | − | 0.346392i | 0.968101 | − | 0.346392i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.659744 | − | 0.395435i | 0.659744 | − | 0.395435i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.427555 | − | 0.903989i | \(-0.359375\pi\) | ||||
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.953924 | − | 1.16236i | 0.953924 | − | 1.16236i | −0.0327191 | − | 0.999465i | \(-0.510417\pi\) |
0.986643 | − | 0.162895i | \(-0.0520833\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.35171 | + | 0.903187i | 1.35171 | + | 0.903187i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.986643 | − | 0.162895i | \(-0.947917\pi\) | ||||
0.986643 | + | 0.162895i | \(0.0520833\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.242980 | − | 0.970031i | \(-0.421875\pi\) | ||||
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.463535 | + | 0.288245i | 0.463535 | + | 0.288245i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.227076 | − | 0.973877i | 0.227076 | − | 0.973877i | ||||
\(364\) | −0.576888 | − | 0.371957i | −0.576888 | − | 0.371957i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0726721 | − | 1.10876i | 0.0726721 | − | 1.10876i | −0.793353 | − | 0.608761i | \(-0.791667\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.49068 | − | 0.321957i | 1.49068 | − | 0.321957i | ||||
\(373\) | 1.77308 | − | 0.145384i | 1.77308 | − | 0.145384i | 0.849202 | − | 0.528068i | \(-0.177083\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.21166 | + | 0.119338i | 1.21166 | + | 0.119338i | 0.683592 | − | 0.729864i | \(-0.260417\pi\) |
0.528068 | + | 0.849202i | \(0.322917\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.409570 | − | 1.89634i | 0.409570 | − | 1.89634i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.0327191 | − | 0.999465i | \(-0.510417\pi\) | ||||
0.0327191 | + | 0.999465i | \(0.489583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.21372 | + | 1.13677i | −1.21372 | + | 1.13677i | ||||
\(388\) | −0.924221 | − | 0.709180i | −0.924221 | − | 0.709180i | ||||
\(389\) | 0 | 0 | 0.857729 | − | 0.514103i | \(-0.171875\pi\) | ||||
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.13805 | + | 1.64432i | 1.13805 | + | 1.64432i | 0.582478 | + | 0.812847i | \(0.302083\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.371202 | + | 0.371202i | −0.371202 | + | 0.371202i | ||||
\(400\) | 0.773010 | − | 0.634393i | 0.773010 | − | 0.634393i | ||||
\(401\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.986126 | − | 2.27472i | −0.986126 | − | 2.27472i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.131278 | + | 0.0973624i | 0.131278 | + | 0.0973624i | 0.659346 | − | 0.751840i | \(-0.270833\pi\) |
−0.528068 | + | 0.849202i | \(0.677083\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.44175 | − | 0.864154i | −1.44175 | − | 0.864154i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.257264 | + | 1.29335i | 0.257264 | + | 1.29335i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.793353 | − | 0.608761i | \(-0.208333\pi\) | ||||
−0.793353 | + | 0.608761i | \(0.791667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49946 | + | 0.898744i | −1.49946 | + | 0.898744i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.999465 | + | 0.0327191i | \(0.989583\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.583341 | + | 0.311802i | −0.583341 | + | 0.311802i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.162895 | − | 0.986643i | \(-0.552083\pi\) | ||||
0.162895 | + | 0.986643i | \(0.447917\pi\) | |||||||
\(432\) | 0.729864 | + | 0.683592i | 0.729864 | + | 0.683592i | ||||
\(433\) | −0.183592 | + | 1.59589i | −0.183592 | + | 1.59589i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.683592 | + | 0.729864i | \(0.739583\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.727950 | + | 1.60662i | −0.727950 | + | 1.60662i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.458575 | − | 0.686307i | 0.458575 | − | 0.686307i | −0.528068 | − | 0.849202i | \(-0.677083\pi\) |
0.986643 | + | 0.162895i | \(0.0520833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.433928 | + | 0.697813i | 0.433928 | + | 0.697813i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.608761 | − | 0.793353i | \(-0.708333\pi\) | ||||
0.608761 | + | 0.793353i | \(0.291667\pi\) | |||||||
\(444\) | −0.0713052 | + | 0.284666i | −0.0713052 | + | 0.284666i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.312847 | − | 0.283548i | −0.312847 | − | 0.283548i | ||||
\(449\) | 0 | 0 | 0.935906 | − | 0.352250i | \(-0.114583\pi\) | ||||
−0.935906 | + | 0.352250i | \(0.885417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.73894 | − | 0.893212i | 1.73894 | − | 0.893212i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.322547 | + | 0.482726i | 0.322547 | + | 0.482726i | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.456904 | − | 0.889516i | \(-0.348958\pi\) | ||||
−0.456904 | + | 0.889516i | \(0.651042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.929782 | − | 0.899842i | 0.929782 | − | 0.899842i | −0.0654031 | − | 0.997859i | \(-0.520833\pi\) |
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.952063 | − | 0.305903i | \(-0.901042\pi\) | ||||
0.952063 | + | 0.305903i | \(0.0989583\pi\) | |||||||
\(468\) | 0.858476 | − | 1.38054i | 0.858476 | − | 1.38054i | ||||
\(469\) | −0.523928 | + | 0.578065i | −0.523928 | + | 0.578065i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.65881 | + | 0.719121i | −1.65881 | + | 0.719121i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.973877 | + | 0.772924i | −0.973877 | + | 0.772924i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.874090 | − | 0.485763i | \(-0.838542\pi\) | ||||
0.874090 | + | 0.485763i | \(0.161458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.476503 | + | 0.0234091i | 0.476503 | + | 0.0234091i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.288078 | + | 0.609090i | 0.288078 | + | 0.609090i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.95480 | + | 0.224882i | 1.95480 | + | 0.224882i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) | ||||
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.370558 | − | 1.47935i | −0.370558 | − | 1.47935i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.0843209 | + | 0.314690i | 0.0843209 | + | 0.314690i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
−0.910864 | + | 0.412707i | \(0.864583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.53758 | − | 0.578704i | −1.53758 | − | 0.578704i | ||||
\(508\) | −1.90872 | − | 0.347304i | −1.90872 | − | 0.347304i | ||||
\(509\) | 0 | 0 | −0.740951 | − | 0.671559i | \(-0.765625\pi\) | ||||
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0939881 | − | 0.0219149i | 0.0939881 | − | 0.0219149i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.893428 | − | 0.864659i | −0.893428 | − | 0.864659i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.17588 | + | 1.17588i | 1.17588 | + | 1.17588i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.683592 | + | 1.18402i | 0.683592 | + | 1.18402i | 0.973877 | + | 0.227076i | \(0.0729167\pi\) |
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.180524 | − | 0.381685i | −0.180524 | − | 0.381685i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.383149 | + | 0.358858i | 0.383149 | + | 0.358858i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.611069 | − | 1.90183i | −0.611069 | − | 1.90183i | −0.352250 | − | 0.935906i | \(-0.614583\pi\) |
−0.258819 | − | 0.965926i | \(-0.583333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.349942 | + | 0.172572i | −0.349942 | + | 0.172572i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.971397 | + | 0.0158959i | −0.971397 | + | 0.0158959i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.760984 | − | 1.36933i | −0.760984 | − | 1.36933i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.135463 | + | 0.681019i | −0.135463 | + | 0.681019i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.28424 | − | 0.299444i | 1.28424 | − | 0.299444i | ||||
\(557\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.50194 | − | 2.24782i | 1.50194 | − | 2.24782i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.935906 | − | 0.352250i | \(-0.114583\pi\) | ||||
−0.935906 | + | 0.352250i | \(0.885417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.354857 | − | 0.228799i | 0.354857 | − | 0.228799i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.917494 | − | 0.397748i | \(-0.869792\pi\) | ||||
0.917494 | + | 0.397748i | \(0.130208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.517361 | + | 0.0169366i | −0.517361 | + | 0.0169366i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
−0.227076 | + | 0.973877i | \(0.572917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.659346 | − | 0.751840i | 0.659346 | − | 0.751840i | ||||
\(577\) | −0.129254 | + | 0.147386i | −0.129254 | + | 0.147386i | −0.812847 | − | 0.582478i | \(-0.802083\pi\) |
0.683592 | + | 0.729864i | \(0.260417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.05130 | + | 0.263338i | 1.05130 | + | 0.263338i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(588\) | 0.683242 | − | 0.456527i | 0.683242 | − | 0.456527i | ||||
\(589\) | 0.430567 | + | 1.84660i | 0.430567 | + | 1.84660i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.286847 | + | 0.0619530i | 0.286847 | + | 0.0619530i | ||||
\(593\) | 0 | 0 | −0.991445 | − | 0.130526i | \(-0.958333\pi\) | ||||
0.991445 | + | 0.130526i | \(0.0416667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.88139 | − | 0.438678i | 1.88139 | − | 0.438678i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.840448 | − | 0.541892i | \(-0.817708\pi\) | ||||
0.840448 | + | 0.541892i | \(0.182292\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.44023 | − | 0.237783i | 1.44023 | − | 0.237783i | 0.608761 | − | 0.793353i | \(-0.291667\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.38922 | − | 1.21831i | −1.38922 | − | 1.21831i | ||||
\(604\) | −0.949630 | − | 1.70878i | −0.949630 | − | 1.70878i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.89165 | − | 0.217617i | 1.89165 | − | 0.217617i | 0.910864 | − | 0.412707i | \(-0.135417\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.83990 | − | 0.272924i | −1.83990 | − | 0.272924i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.973877 | + | 0.227076i | \(0.927083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.73112 | − | 0.999465i | 1.73112 | − | 0.999465i | 0.849202 | − | 0.528068i | \(-0.177083\pi\) |
0.881921 | − | 0.471397i | \(-0.156250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.40789 | − | 0.812847i | −1.40789 | − | 0.812847i | ||||
\(625\) | −0.321439 | − | 0.946930i | −0.321439 | − | 0.946930i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.773010 | + | 1.63439i | 0.773010 | + | 1.63439i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.67572 | + | 1.04203i | −1.67572 | + | 1.04203i | −0.751840 | + | 0.659346i | \(0.770833\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.62674 | − | 1.12588i | −1.62674 | − | 1.12588i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.944608 | − | 0.944608i | −0.944608 | − | 0.944608i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.239823 | − | 1.02855i | −0.239823 | − | 1.02855i | −0.946930 | − | 0.321439i | \(-0.895833\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.352250 | − | 0.935906i | \(-0.385417\pi\) | ||||
−0.352250 | + | 0.935906i | \(0.614583\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.643913 | −0.643913 | ||||||||
\(652\) | 0.160802 | − | 1.96111i | 0.160802 | − | 1.96111i | ||||
\(653\) | 0 | 0 | 0.274589 | − | 0.961562i | \(-0.411458\pi\) | ||||
−0.274589 | + | 0.961562i | \(0.588542\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.0555389 | + | 0.221724i | 0.0555389 | + | 0.221724i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.57907 | + | 1.21166i | −1.57907 | + | 1.21166i | −0.729864 | + | 0.683592i | \(0.760417\pi\) |
−0.849202 | + | 0.528068i | \(0.822917\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.256036 | + | 0.0509288i | 0.256036 | + | 0.0509288i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.33659 | − | 1.29355i | 1.33659 | − | 1.29355i | 0.412707 | − | 0.910864i | \(-0.364583\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.896873 | − | 0.442289i | 0.896873 | − | 0.442289i | ||||
\(676\) | −0.528086 | + | 1.55569i | −0.528086 | + | 1.55569i | ||||
\(677\) | 0 | 0 | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) | ||||
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.318219 | + | 0.375065i | 0.318219 | + | 0.375065i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(684\) | −0.834963 | + | 0.921240i | −0.834963 | + | 0.921240i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0923988 | + | 1.88082i | −0.0923988 | + | 1.88082i | ||||
\(688\) | 1.13677 | − | 1.21372i | 1.13677 | − | 1.21372i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.14368 | − | 0.791553i | −1.14368 | − | 0.791553i | −0.162895 | − | 0.986643i | \(-0.552083\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.375574 | + | 0.192915i | −0.375574 | + | 0.192915i | ||||
\(701\) | 0 | 0 | −0.999866 | − | 0.0163617i | \(-0.994792\pi\) | ||||
0.999866 | + | 0.0163617i | \(0.00520833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.355335 | − | 0.0828525i | −0.355335 | − | 0.0828525i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0869951 | − | 0.347304i | 0.0869951 | − | 0.347304i | −0.910864 | − | 0.412707i | \(-0.864583\pi\) |
0.997859 | + | 0.0654031i | \(0.0208333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.61797 | − | 0.294400i | −1.61797 | − | 0.294400i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.517994 | + | 0.485155i | 0.517994 | + | 0.485155i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.0211706 | − | 0.0249525i | −0.0211706 | − | 0.0249525i | ||||
\(724\) | 0.183930 | + | 0.344109i | 0.183930 | + | 0.344109i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.854996 | − | 0.0139911i | 0.854996 | − | 0.0139911i | 0.412707 | − | 0.910864i | \(-0.364583\pi\) |
0.442289 | + | 0.896873i | \(0.354167\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.34369 | + | 0.805380i | −1.34369 | + | 0.805380i | ||||
\(733\) | −0.0843209 | + | 0.510724i | −0.0843209 | + | 0.510724i | 0.910864 | + | 0.412707i | \(0.135417\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.184592 | + | 1.40211i | 0.184592 | + | 1.40211i | 0.793353 | + | 0.608761i | \(0.208333\pi\) |
−0.608761 | + | 0.793353i | \(0.708333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.73369 | + | 1.03913i | 1.73369 | + | 1.03913i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.840448 | − | 0.541892i | \(-0.182292\pi\) | ||||
−0.840448 | + | 0.541892i | \(0.817708\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.317280 | − | 1.92174i | −0.317280 | − | 1.92174i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.0654031 | − | 0.997859i | \(-0.479167\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.240287 | − | 0.347181i | −0.240287 | − | 0.347181i | ||||
\(757\) | 0.956940 | − | 0.290285i | 0.956940 | − | 0.290285i | 0.227076 | − | 0.973877i | \(-0.427083\pi\) |
0.729864 | + | 0.683592i | \(0.239583\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.443638 | − | 0.598177i | 0.443638 | − | 0.598177i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.773010 | − | 0.634393i | −0.773010 | − | 0.634393i | ||||
\(769\) | −0.129059 | + | 0.0213077i | −0.129059 | + | 0.0213077i | −0.227076 | − | 0.973877i | \(-0.572917\pi\) |
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.228799 | − | 1.05936i | 0.228799 | − | 1.05936i | ||||
\(773\) | 0 | 0 | 0.997859 | − | 0.0654031i | \(-0.0208333\pi\) | ||||
−0.997859 | + | 0.0654031i | \(0.979167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.51506 | − | 0.174294i | −1.51506 | − | 0.174294i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0548022 | − | 0.111128i | 0.0548022 | − | 0.111128i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.478638 | − | 0.667939i | −0.478638 | − | 0.667939i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.328494 | + | 1.80535i | −0.328494 | + | 1.80535i | 0.227076 | + | 0.973877i | \(0.427083\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.71030 | + | 1.88703i | 1.71030 | + | 1.88703i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.500000 | − | 1.86603i | −0.500000 | − | 1.86603i | ||||
\(797\) | 0 | 0 | −0.986643 | − | 0.162895i | \(-0.947917\pi\) | ||||
0.986643 | + | 0.162895i | \(0.0520833\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.17221 | + | 1.42834i | −1.17221 | + | 1.42834i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) | ||||
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.130081 | + | 1.13074i | 0.130081 | + | 1.13074i | 0.881921 | + | 0.471397i | \(0.156250\pi\) |
−0.751840 | + | 0.659346i | \(0.770833\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.846488 | + | 1.71651i | −0.846488 | + | 1.71651i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.43787 | + | 1.48572i | −1.43787 | + | 1.48572i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.477356 | + | 0.493238i | −0.477356 | + | 0.493238i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.893212 | + | 0.192915i | −0.893212 | + | 0.192915i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.695443 | − | 0.718582i | \(-0.744792\pi\) | ||||
0.695443 | + | 0.718582i | \(0.255208\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.410525 | + | 0.410525i | −0.410525 | + | 0.410525i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.607797 | − | 0.0699215i | 0.607797 | − | 0.0699215i | ||||
\(832\) | −0.766347 | + | 1.43373i | −0.766347 | + | 1.43373i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.0249525 | − | 1.52485i | −0.0249525 | − | 1.52485i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.961562 | − | 0.274589i | \(-0.911458\pi\) | ||||
0.961562 | + | 0.274589i | \(0.0885417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.946930 | + | 0.321439i | −0.946930 | + | 0.321439i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.07205 | + | 1.66270i | −1.07205 | + | 1.66270i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.387387 | + | 0.167939i | 0.387387 | + | 0.167939i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.47140 | − | 0.881921i | −1.47140 | − | 0.881921i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.05441 | − | 1.37413i | −1.05441 | − | 1.37413i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.130526 | − | 0.991445i | \(-0.541667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.803208 | − | 0.595699i | \(-0.203125\pi\) | ||||
−0.803208 | + | 0.595699i | \(0.796875\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.247198 | + | 1.87766i | −0.247198 | + | 1.87766i | 0.195090 | + | 0.980785i | \(0.437500\pi\) |
−0.442289 | + | 0.896873i | \(0.645833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.977462 | − | 0.211112i | \(-0.932292\pi\) | ||||
0.977462 | + | 0.211112i | \(0.0677083\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | ||||
\(868\) | 0.0210682 | + | 0.643568i | 0.0210682 | + | 0.643568i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.64919 | + | 1.41602i | 2.64919 | + | 1.41602i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.875860 | + | 0.768108i | −0.875860 | + | 0.768108i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.219788 | − | 0.0627638i | 0.219788 | − | 0.0627638i | ||||
\(877\) | 0.816404 | − | 1.31288i | 0.816404 | − | 1.31288i | −0.130526 | − | 0.991445i | \(-0.541667\pi\) |
0.946930 | − | 0.321439i | \(-0.104167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.874090 | − | 0.485763i | \(-0.161458\pi\) | ||||
−0.874090 | + | 0.485763i | \(0.838542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.51995 | − | 1.28958i | 1.51995 | − | 1.28958i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.812847 | − | 0.582478i | \(-0.197917\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.756786 | + | 0.313471i | 0.756786 | + | 0.313471i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.0425243 | − | 0.257566i | 0.0425243 | − | 0.257566i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.380479 | − | 0.590105i | −0.380479 | − | 0.590105i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0500574 | + | 0.763728i | −0.0500574 | + | 0.763728i | 0.896873 | + | 0.442289i | \(0.145833\pi\) |
−0.946930 | + | 0.321439i | \(0.895833\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.793353 | − | 0.608761i | \(-0.208333\pi\) | ||||
−0.793353 | + | 0.608761i | \(0.791667\pi\) | |||||||
\(912\) | 0.948066 | + | 0.804374i | 0.948066 | + | 0.804374i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.88284 | + | 0.0308106i | 1.88284 | + | 0.0308106i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.322547 | − | 1.06330i | −0.322547 | − | 1.06330i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
0.634393 | − | 0.773010i | \(-0.281250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.16102 | − | 1.23960i | −1.16102 | − | 1.23960i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.159024 | − | 0.246639i | 0.159024 | − | 0.246639i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.12882 | + | 1.24546i | −1.12882 | + | 1.24546i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.993448 | − | 0.114287i | \(-0.0364583\pi\) | ||||
−0.993448 | + | 0.114287i | \(0.963542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.581433 | + | 0.840088i | 0.581433 | + | 0.840088i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.195090 | − | 0.0192147i | 0.195090 | − | 0.0192147i | − | 1.00000i | \(-0.5\pi\) | |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.83195 | + | 0.758819i | −1.83195 | + | 0.758819i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.991445 | − | 0.130526i | \(-0.958333\pi\) | ||||
0.991445 | + | 0.130526i | \(0.0416667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.952063 | − | 0.305903i | \(-0.0989583\pi\) | ||||
−0.952063 | + | 0.305903i | \(0.901042\pi\) | |||||||
\(948\) | −0.241304 | + | 1.62674i | −0.241304 | + | 1.62674i | ||||
\(949\) | −0.169781 | − | 0.330536i | −0.169781 | − | 0.330536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.0327191 | − | 0.999465i | \(-0.489583\pi\) | ||||
−0.0327191 | + | 0.999465i | \(0.510417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.700108 | + | 1.12586i | −0.700108 | + | 1.12586i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.0242465 | + | 0.0219757i | −0.0242465 | + | 0.0219757i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.415381 | + | 0.747444i | −0.415381 | + | 0.747444i | −0.997859 | − | 0.0654031i | \(-0.979167\pi\) |
0.582478 | + | 0.812847i | \(0.302083\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.961562 | − | 0.274589i | \(-0.0885417\pi\) | ||||
−0.961562 | + | 0.274589i | \(0.911458\pi\) | |||||||
\(972\) | 0.812847 | − | 0.582478i | 0.812847 | − | 0.582478i | ||||
\(973\) | −0.556708 | + | 0.00910992i | −0.556708 | + | 0.00910992i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.25668 | + | 1.03133i | −1.25668 | + | 1.03133i | ||||
\(976\) | 0.848913 | + | 1.31662i | 0.848913 | + | 1.31662i | ||||
\(977\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.43373 | + | 1.02740i | 1.43373 | + | 1.02740i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.981854 | − | 1.76676i | 0.981854 | − | 1.76676i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.129059 | + | 1.96906i | 0.129059 | + | 1.96906i | 0.227076 | + | 0.973877i | \(0.427083\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.18359 | − | 1.59589i | 1.18359 | − | 1.59589i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0500574 | − | 0.120849i | 0.0500574 | − | 0.120849i | −0.896873 | − | 0.442289i | \(-0.854167\pi\) |
0.946930 | + | 0.321439i | \(0.104167\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.265286 | + | 0.125471i | 0.265286 | + | 0.125471i |
(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 | 3459.1.bm.a.707.1 | ✓ | 64 | |
3.2 | odd | 2 | CM | 3459.1.bm.a.707.1 | ✓ | 64 | |
1153.349 | even | 192 | inner | 3459.1.bm.a.1502.1 | yes | 64 | |
3459.1502 | odd | 192 | inner | 3459.1.bm.a.1502.1 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3459.1.bm.a.707.1 | ✓ | 64 | 1.1 | even | 1 | trivial | |
3459.1.bm.a.707.1 | ✓ | 64 | 3.2 | odd | 2 | CM | |
3459.1.bm.a.1502.1 | yes | 64 | 1153.349 | even | 192 | inner | |
3459.1.bm.a.1502.1 | yes | 64 | 3459.1502 | odd | 192 | inner |