Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [943,1,Mod(367,943)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(943, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("943.367");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 943 = 23 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 943.n (of order \(20\), 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: | \(0.470618306913\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{20})\) |
Coefficient field: | \(\Q(\zeta_{60})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{60}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{60} - \cdots)\) |
Embedding invariants
Embedding label | 459.1 | ||
Root | \(0.207912 + 0.978148i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 943.459 |
Dual form | 943.1.n.b.528.1 |
$q$-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 \(\left(\mathbb{Z}/943\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(534\) |
\(\chi(n)\) | \(e\left(\frac{19}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.122881 | + | 0.169131i | −0.122881 | + | 0.169131i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(3\) | 1.18606 | + | 1.18606i | 1.18606 | + | 1.18606i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(4\) | 0.295511 | + | 0.909491i | 0.295511 | + | 0.909491i | ||||
\(5\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(6\) | −0.346343 | + | 0.0548553i | −0.346343 | + | 0.0548553i | ||||
\(7\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(8\) | −0.388960 | − | 0.126381i | −0.388960 | − | 0.126381i | ||||
\(9\) | 1.81347i | 1.81347i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(12\) | −0.728216 | + | 1.42920i | −0.728216 | + | 1.42920i | ||||
\(13\) | −0.312440 | − | 1.97267i | −0.312440 | − | 1.97267i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.704489 | + | 0.511841i | −0.704489 | + | 0.511841i | ||||
\(17\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(18\) | −0.306714 | − | 0.222841i | −0.306714 | − | 0.222841i | ||||
\(19\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(24\) | −0.311435 | − | 0.611225i | −0.311435 | − | 0.611225i | ||||
\(25\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(26\) | 0.372032 | + | 0.189560i | 0.372032 | + | 0.189560i | ||||
\(27\) | −0.964828 | + | 0.964828i | −0.964828 | + | 0.964828i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.494522 | − | 0.970554i | 0.494522 | − | 0.970554i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.128496 | + | 0.395472i | −0.128496 | + | 0.395472i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | − | 0.591023i | − | 0.591023i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.64934 | + | 0.535902i | −1.64934 | + | 0.535902i | ||||
\(37\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.96913 | − | 2.71028i | 1.96913 | − | 2.71028i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.198825 | − | 0.0646021i | 0.198825 | − | 0.0646021i | ||||
\(47\) | −1.84417 | + | 0.292088i | −1.84417 | + | 0.292088i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | −1.44264 | − | 0.228492i | −1.44264 | − | 0.228492i | ||||
\(49\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(50\) | 0.209057i | 0.209057i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.70180 | − | 0.867108i | 1.70180 | − | 0.867108i | ||||
\(53\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(54\) | −0.0446233 | − | 0.281740i | −0.0446233 | − | 0.281740i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.103383 | + | 0.202901i | 0.103383 | + | 0.202901i | ||||
\(59\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(62\) | −0.0510966 | − | 0.0703285i | −0.0510966 | − | 0.0703285i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.604528 | − | 0.439216i | −0.604528 | − | 0.439216i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.262394 | − | 1.65669i | −0.262394 | − | 1.65669i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.12146 | + | 0.571411i | −1.12146 | + | 0.571411i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(72\) | 0.229188 | − | 0.705369i | 0.229188 | − | 0.705369i | ||||
\(73\) | 1.48629i | 1.48629i | 0.669131 | + | 0.743145i | \(0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.65669 | + | 0.262394i | 1.65669 | + | 0.262394i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.216423 | + | 0.666080i | 0.216423 | + | 0.666080i | ||||
\(79\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.475212 | −0.475212 | ||||||||
\(82\) | −0.155360 | − | 0.139886i | −0.155360 | − | 0.139886i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.73767 | − | 0.564602i | 1.73767 | − | 0.564602i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.295511 | − | 0.909491i | 0.295511 | − | 0.909491i | ||||
\(93\) | −0.621457 | + | 0.316648i | −0.621457 | + | 0.316648i | ||||
\(94\) | 0.177212 | − | 0.347798i | 0.177212 | − | 0.347798i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.700988 | − | 0.700988i | 0.700988 | − | 0.700988i | ||||
\(97\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(98\) | −0.169131 | + | 0.122881i | −0.169131 | + | 0.122881i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.773659 | + | 0.562096i | 0.773659 | + | 0.562096i | ||||
\(101\) | −0.278768 | + | 1.76007i | −0.278768 | + | 1.76007i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(104\) | −0.127781 | + | 0.806777i | −0.127781 | + | 0.806777i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(108\) | −1.16262 | − | 0.592384i | −1.16262 | − | 0.592384i | ||||
\(109\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.02885 | + | 0.162953i | 1.02885 | + | 0.162953i | ||||
\(117\) | 3.57738 | − | 0.566602i | 3.57738 | − | 0.566602i | ||||
\(118\) | 0.122881 | − | 0.0399263i | 0.122881 | − | 0.0399263i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.30354 | + | 1.05558i | −1.30354 | + | 1.05558i | ||||
\(124\) | −0.397650 | −0.397650 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(128\) | 0.710666 | − | 0.230909i | 0.710666 | − | 0.230909i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.27276 | + | 0.413545i | 1.27276 | + | 0.413545i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | 0.312440 | + | 0.159196i | 0.312440 | + | 0.159196i | ||||
\(139\) | 1.60917 | − | 1.16913i | 1.60917 | − | 1.16913i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.53373 | − | 1.84086i | −2.53373 | − | 1.84086i | ||||
\(142\) | 0.0411622 | − | 0.259888i | 0.0411622 | − | 0.259888i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.928210 | − | 1.27757i | −0.928210 | − | 1.27757i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.251377 | − | 0.182636i | −0.251377 | − | 0.182636i | ||||
\(147\) | 0.761497 | + | 1.49452i | 0.761497 | + | 1.49452i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(150\) | −0.247954 | + | 0.247954i | −0.247954 | + | 0.247954i | ||||
\(151\) | −0.0163743 | − | 0.103383i | −0.0163743 | − | 0.103383i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.04687 | + | 0.989988i | 3.04687 | + | 0.989988i | ||||
\(157\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.0583943 | − | 0.0803729i | 0.0583943 | − | 0.0803729i | ||||
\(163\) | −1.48629 | −1.48629 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(164\) | −0.935398 | + | 0.198825i | −0.935398 | + | 0.198825i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.84275 | + | 0.923665i | −2.84275 | + | 0.923665i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(174\) | −0.118034 | + | 0.363271i | −0.118034 | + | 0.363271i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.162168 | − | 1.02389i | −0.162168 | − | 1.02389i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.72129 | − | 0.877042i | −1.72129 | − | 0.877042i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.743145 | − | 0.669131i | \(-0.766667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.240391 | + | 0.330869i | 0.240391 | + | 0.330869i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0228101 | − | 0.144017i | 0.0228101 | − | 0.144017i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.810626 | − | 1.59094i | −0.810626 | − | 1.59094i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | −0.196071 | − | 1.23794i | −0.196071 | − | 1.23794i | ||||
\(193\) | 0.906737 | − | 1.77957i | 0.906737 | − | 1.77957i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.956295i | 0.956295i | ||||||||
\(197\) | 0.773659 | + | 0.251377i | 0.773659 | + | 0.251377i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(200\) | −0.388960 | + | 0.126381i | −0.388960 | + | 0.126381i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.263427 | − | 0.263427i | −0.263427 | − | 0.263427i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.06593 | − | 1.46713i | 1.06593 | − | 1.46713i | ||||
\(208\) | 1.22980 | + | 1.22980i | 1.22980 | + | 1.22980i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.95106 | + | 0.309017i | −1.95106 | + | 0.309017i | −0.951057 | + | 0.309017i | \(0.900000\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.00784 | − | 0.652387i | −2.00784 | − | 0.652387i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.497215 | − | 0.253344i | 0.497215 | − | 0.253344i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.76283 | + | 1.76283i | −1.76283 | + | 1.76283i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.53884 | + | 1.11803i | 1.53884 | + | 1.11803i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.06593 | + | 1.46713i | 1.06593 | + | 1.46713i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.315009 | + | 0.315009i | −0.315009 | + | 0.315009i | ||||
\(233\) | −0.302208 | − | 1.90807i | −0.302208 | − | 1.90807i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(234\) | −0.343761 | + | 0.674669i | −0.343761 | + | 0.674669i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.182636 | − | 0.562096i | 0.182636 | − | 0.562096i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.07587 | + | 0.170401i | 1.07587 | + | 0.170401i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(242\) | 0.0646021 | + | 0.198825i | 0.0646021 | + | 0.198825i | ||||
\(243\) | 0.401198 | + | 0.401198i | 0.401198 | + | 0.401198i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0183521 | − | 0.350179i | −0.0183521 | − | 0.350179i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.0999601 | − | 0.137583i | 0.0999601 | − | 0.137583i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.198825 | − | 0.0646021i | −0.198825 | − | 0.0646021i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.182636 | − | 0.562096i | 0.182636 | − | 0.562096i | ||||
\(257\) | 0.0932634 | − | 0.0475201i | 0.0932634 | − | 0.0475201i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.76007 | + | 0.896802i | 1.76007 | + | 0.896802i | ||||
\(262\) | −0.226341 | + | 0.164446i | −0.226341 | + | 0.164446i | ||||
\(263\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.20243 | + | 0.873619i | 1.20243 | + | 0.873619i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.951057 | + | 0.690983i | −0.951057 | + | 0.690983i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.42920 | − | 0.728216i | 1.42920 | − | 0.728216i | ||||
\(277\) | 0.128496 | − | 0.395472i | 0.128496 | − | 0.395472i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(278\) | 0.415823i | 0.415823i | ||||||||
\(279\) | −0.717177 | − | 0.233025i | −0.717177 | − | 0.233025i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(282\) | 0.622693 | − | 0.202325i | 0.622693 | − | 0.202325i | ||||
\(283\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(284\) | −0.851096 | − | 0.851096i | −0.851096 | − | 0.851096i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.07180 | 1.07180 | ||||||||
\(289\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.35177 | + | 0.439216i | −1.35177 | + | 0.439216i | ||||
\(293\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(294\) | −0.346343 | − | 0.0548553i | −0.346343 | − | 0.0548553i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.906737 | + | 1.77957i | −0.906737 | + | 1.77957i | ||||
\(300\) | 0.250926 | + | 1.58428i | 0.250926 | + | 1.58428i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.0194974 | + | 0.00993440i | 0.0194974 | + | 0.00993440i | ||||
\(303\) | −2.41819 | + | 1.75692i | −2.41819 | + | 1.75692i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.690983 | + | 0.951057i | 0.690983 | + | 0.951057i | 1.00000 | \(0\) | ||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.705634 | + | 1.38488i | 0.705634 | + | 1.38488i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(312\) | −1.10844 | + | 0.805329i | −1.10844 | + | 0.805329i | ||||
\(313\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.76007 | − | 0.896802i | 1.76007 | − | 0.896802i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.140431 | − | 0.432201i | −0.140431 | − | 0.432201i | ||||
\(325\) | −1.41228 | − | 1.41228i | −1.41228 | − | 1.41228i | ||||
\(326\) | 0.182636 | − | 0.251377i | 0.182636 | − | 0.251377i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.166346 | − | 0.373619i | 0.166346 | − | 0.373619i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.506809 | + | 0.506809i | 0.506809 | + | 0.506809i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.367956 | − | 0.0582784i | 0.367956 | − | 0.0582784i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0.193099 | − | 0.594296i | 0.193099 | − | 0.594296i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.273659 | + | 0.198825i | 0.273659 | + | 0.198825i | ||||
\(347\) | −0.142040 | + | 0.896802i | −0.142040 | + | 0.896802i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(348\) | 1.02700 | + | 1.41355i | 1.02700 | + | 1.41355i | ||||
\(349\) | −0.786610 | − | 1.08268i | −0.786610 | − | 1.08268i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
0.207912 | − | 0.978148i | \(-0.433333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.20474 | + | 1.60184i | 2.20474 | + | 1.60184i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.60917 | + | 1.16913i | −1.60917 | + | 1.16913i | −0.743145 | + | 0.669131i | \(0.766667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0.193099 | + | 0.0983887i | 0.193099 | + | 0.0983887i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.359848 | − | 0.183352i | 0.359848 | − | 0.183352i | ||||
\(359\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.65669 | − | 0.262394i | 1.65669 | − | 0.262394i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(368\) | 0.870796 | 0.870796 | ||||||||
\(369\) | −1.80354 | − | 0.189560i | −1.80354 | − | 0.189560i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.471636 | − | 0.471636i | −0.471636 | − | 0.471636i | ||||
\(373\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.754224 | + | 0.119457i | 0.754224 | + | 0.119457i | ||||
\(377\) | −2.06909 | − | 0.672288i | −2.06909 | − | 0.672288i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.761497 | + | 1.49452i | −0.761497 | + | 1.49452i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 1.11676 | + | 0.569020i | 1.11676 | + | 0.569020i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.189560 | + | 0.372032i | 0.189560 | + | 0.372032i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.330869 | − | 0.240391i | −0.330869 | − | 0.240391i | ||||
\(393\) | 1.01908 | + | 2.00006i | 1.01908 | + | 2.00006i | ||||
\(394\) | −0.137583 | + | 0.0999601i | −0.137583 | + | 0.0999601i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.302208 | + | 1.90807i | 0.302208 | + | 1.90807i | 0.406737 | + | 0.913545i | \(0.366667\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.269091 | + | 0.828176i | −0.269091 | + | 0.828176i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.820282 | + | 0.129920i | 0.820282 | + | 0.129920i | ||||
\(404\) | −1.68315 | + | 0.266585i | −1.68315 | + | 0.266585i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.117154 | + | 0.360564i | 0.117154 | + | 0.360564i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.16589 | + | 0.184659i | −1.16589 | + | 0.184659i | ||||
\(417\) | 3.29523 | + | 0.521913i | 3.29523 | + | 0.521913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(422\) | 0.187483 | − | 0.367956i | 0.187483 | − | 0.367956i | ||||
\(423\) | −0.529694 | − | 3.34436i | −0.529694 | − | 3.34436i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.357063 | − | 0.259422i | 0.357063 | − | 0.259422i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(432\) | 0.185872 | − | 1.17355i | 0.185872 | − | 1.17355i | ||||
\(433\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.0815308 | − | 0.514765i | −0.0815308 | − | 0.514765i | ||||
\(439\) | 0.705634 | − | 1.38488i | 0.705634 | − | 1.38488i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.560394 | + | 1.72472i | −0.560394 | + | 1.72472i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.198825 | + | 0.0646021i | 0.198825 | + | 0.0646021i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.378188 | + | 0.122881i | −0.378188 | + | 0.122881i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(450\) | −0.379119 | −0.379119 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.103198 | − | 0.142040i | 0.103198 | − | 0.142040i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.564602 | + | 1.73767i | −0.564602 | + | 1.73767i | 0.104528 | + | 0.994522i | \(0.466667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.809017 | − | 1.58779i | 0.809017 | − | 1.58779i | − | 1.00000i | \(-0.5\pi\) | |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(464\) | 0.148384 | + | 0.936861i | 0.148384 | + | 0.936861i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.359848 | + | 0.183352i | 0.359848 | + | 0.183352i | ||||
\(467\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(468\) | 1.57248 | + | 3.08616i | 1.57248 | + | 3.08616i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.148570 | + | 0.204489i | 0.148570 | + | 0.204489i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.161023 | + | 0.161023i | −0.161023 | + | 0.161023i | ||||
\(479\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.909491 | + | 0.295511i | 0.909491 | + | 0.295511i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.117154 | + | 0.0185554i | −0.117154 | + | 0.0185554i | ||||
\(487\) | −1.27276 | + | 0.413545i | −1.27276 | + | 0.413545i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.76283 | − | 1.76283i | −1.76283 | − | 1.76283i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.415823 | 0.415823 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(492\) | −1.34526 | − | 0.873619i | −1.34526 | − | 0.873619i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.111894 | − | 0.344375i | −0.111894 | − | 0.344375i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.707912 | + | 0.112122i | 0.707912 | + | 0.112122i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 2.98904i | − | 2.98904i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.46719 | − | 2.27615i | −4.46719 | − | 2.27615i | ||||
\(508\) | −0.773659 | + | 0.562096i | −0.773659 | + | 0.562096i | ||||
\(509\) | −0.235003 | − | 0.461219i | −0.235003 | − | 0.461219i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.511841 | + | 0.704489i | 0.511841 | + | 0.704489i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.00342316 | + | 0.0216130i | −0.00342316 | + | 0.0216130i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.91908 | − | 1.91908i | 1.91908 | − | 1.91908i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(522\) | −0.367956 | + | 0.187483i | −0.367956 | + | 0.187483i | ||||
\(523\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(524\) | 1.27977i | 1.27977i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.658783 | − | 0.906737i | 0.658783 | − | 0.906737i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.99452 | − | 0.104528i | 1.99452 | − | 0.104528i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.00133 | − | 3.08178i | −1.00133 | − | 3.08178i | ||||
\(538\) | −0.295511 | + | 0.0960175i | −0.295511 | + | 0.0960175i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.64728 | − | 0.535233i | −1.64728 | − | 0.535233i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(542\) | − | 0.245761i | − | 0.245761i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0740142 | − | 0.0740142i | 0.0740142 | − | 0.0740142i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.107313 | + | 0.677548i | −0.107313 | + | 0.677548i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.0510966 | + | 0.0703285i | 0.0510966 | + | 0.0703285i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.53884 | + | 1.11803i | 1.53884 | + | 1.11803i | ||||
\(557\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(558\) | 0.127539 | − | 0.0926624i | 0.127539 | − | 0.0926624i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(564\) | 0.925502 | − | 2.84840i | 0.925502 | − | 2.84840i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.508418 | − | 0.0805255i | 0.508418 | − | 0.0805255i | ||||
\(569\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −1.00000 | ||||||||
\(576\) | 0.796506 | − | 1.09630i | 0.796506 | − | 1.09630i | ||||
\(577\) | −0.889993 | − | 0.889993i | −0.889993 | − | 0.889993i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(578\) | −0.0646021 | − | 0.198825i | −0.0646021 | − | 0.198825i | ||||
\(579\) | 3.18612 | − | 1.03523i | 3.18612 | − | 1.03523i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.187839 | − | 0.578108i | 0.187839 | − | 0.578108i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.243145 | + | 1.53516i | 0.243145 | + | 1.53516i | 0.743145 | + | 0.669131i | \(0.233333\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | −1.13422 | + | 1.13422i | −1.13422 | + | 1.13422i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.619457 | + | 1.21575i | 0.619457 | + | 1.21575i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.309017 | − | 1.95106i | 0.309017 | − | 1.95106i | − | 1.00000i | \(-0.5\pi\) | |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.189560 | − | 0.372032i | −0.189560 | − | 0.372032i | ||||
\(599\) | 0.951057 | − | 0.690983i | 0.951057 | − | 0.690983i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(600\) | −0.611225 | − | 0.311435i | −0.611225 | − | 0.311435i | ||||
\(601\) | −0.770236 | + | 0.770236i | −0.770236 | + | 0.770236i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0891873 | − | 0.0454432i | 0.0891873 | − | 0.0454432i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 0.624880i | − | 0.624880i | ||||||
\(607\) | −1.80902 | − | 0.587785i | −1.80902 | − | 0.587785i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.15239 | + | 3.54668i | 1.15239 | + | 3.54668i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(614\) | −0.245761 | −0.245761 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.34767 | − | 0.213450i | 1.34767 | − | 0.213450i | ||||
\(622\) | −0.320935 | − | 0.0508311i | −0.320935 | − | 0.0508311i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.91724i | 2.91724i | ||||||||
\(625\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.68058 | − | 1.94756i | −2.68058 | − | 1.94756i | ||||
\(634\) | −0.0646021 | + | 0.407882i | −0.0646021 | + | 0.407882i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.312440 | − | 1.97267i | 0.312440 | − | 1.97267i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.03624 | − | 2.03373i | −1.03624 | − | 2.03373i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.73205i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0.184839 | + | 0.0600577i | 0.184839 | + | 0.0600577i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.412400 | − | 0.0653178i | 0.412400 | − | 0.0653178i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.439216 | − | 1.35177i | −0.439216 | − | 1.35177i | ||||
\(653\) | 1.09905 | + | 1.09905i | 1.09905 | + | 1.09905i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.435398 | − | 0.754131i | −0.435398 | − | 0.754131i | ||||
\(657\) | −2.69535 | −2.69535 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(662\) | −0.147994 | + | 0.0234399i | −0.147994 | + | 0.0234399i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.970554 | + | 0.494522i | −0.970554 | + | 0.494522i | ||||
\(668\) | 0.773659 | − | 1.51839i | 0.773659 | − | 1.51839i | ||||
\(669\) | 0.499103 | + | 3.15121i | 0.499103 | + | 3.15121i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0475201 | − | 0.0932634i | −0.0475201 | − | 0.0932634i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.213450 | + | 1.34767i | −0.213450 | + | 1.34767i | ||||
\(676\) | −1.68013 | − | 2.31250i | −1.68013 | − | 2.31250i | ||||
\(677\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.18606 | − | 1.18606i | 1.18606 | − | 1.18606i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.39680 | − | 0.221232i | 1.39680 | − | 0.221232i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(692\) | 1.47159 | − | 0.478148i | 1.47159 | − | 0.478148i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.134223 | − | 0.134223i | −0.134223 | − | 0.134223i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.747238 | −0.747238 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.279773 | 0.279773 | ||||||||
\(699\) | 1.90464 | − | 2.62152i | 1.90464 | − | 2.62152i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(702\) | −0.541839 | + | 0.176054i | −0.541839 | + | 0.176054i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 0.415823i | − | 0.415823i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.883297 | − | 0.450062i | 0.883297 | − | 0.450062i | ||||
\(709\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.336408 | − | 0.244415i | 0.336408 | − | 0.244415i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.289000 | − | 1.82468i | 0.289000 | − | 1.82468i | ||||
\(717\) | 1.07394 | + | 1.47815i | 1.07394 | + | 1.47815i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.309017 | + | 1.95106i | −0.309017 | + | 1.95106i | 1.00000i | \(0.5\pi\) | ||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.169131 | − | 0.122881i | 0.169131 | − | 0.122881i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.170401 | − | 1.07587i | −0.170401 | − | 1.07587i | ||||
\(726\) | −0.159196 | + | 0.312440i | −0.159196 | + | 0.312440i | ||||
\(727\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.42690i | 1.42690i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.347395 | + | 0.478148i | −0.347395 | + | 0.478148i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.253680 | − | 0.281740i | 0.253680 | − | 0.281740i | ||||
\(739\) | 1.95630 | 1.95630 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(744\) | 0.281740 | − | 0.0446233i | 0.281740 | − | 0.0446233i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(752\) | 1.14970 | − | 1.14970i | 1.14970 | − | 1.14970i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.367956 | − | 0.267335i | 0.367956 | − | 0.267335i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.40126 | − | 1.01807i | −1.40126 | − | 1.01807i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
−0.406737 | − | 0.913545i | \(-0.633333\pi\) | |||||||
\(762\) | −0.159196 | − | 0.312440i | −0.159196 | − | 0.312440i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.560394 | + | 1.09984i | −0.560394 | + | 1.09984i | ||||
\(768\) | 0.883297 | − | 0.450062i | 0.883297 | − | 0.450062i | ||||
\(769\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.166977 | + | 0.0542543i | 0.166977 | + | 0.0542543i | ||||
\(772\) | 1.88645 | + | 0.298785i | 1.88645 | + | 0.298785i | ||||
\(773\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.128496 | + | 0.395472i | 0.128496 | + | 0.395472i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.459289 | + | 1.41355i | 0.459289 | + | 1.41355i | ||||
\(784\) | −0.828176 | + | 0.269091i | −0.828176 | + | 0.269091i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.463497 | − | 0.0734107i | −0.463497 | − | 0.0734107i | ||||
\(787\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(788\) | 0.777921i | 0.777921i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.359848 | − | 0.183352i | −0.359848 | − | 0.183352i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.347395 | − | 0.478148i | −0.347395 | − | 0.478148i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.122770 | + | 0.122770i | −0.122770 | + | 0.122770i | ||||
\(807\) | 0.389993 | + | 2.46232i | 0.389993 | + | 2.46232i | ||||
\(808\) | 0.330869 | − | 0.649368i | 0.330869 | − | 0.649368i | ||||
\(809\) | −1.26007 | + | 0.642040i | −1.26007 | + | 0.642040i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.813473i | 0.813473i | 0.913545 | + | 0.406737i | \(0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.94756 | − | 0.308463i | −1.94756 | − | 0.308463i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.122881 | − | 0.169131i | 0.122881 | − | 0.169131i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.90211 | 1.90211 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.32028 | − | 1.32028i | −1.32028 | − | 1.32028i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.406737 | − | 0.913545i | \(-0.633333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(828\) | 1.64934 | + | 0.535902i | 1.64934 | + | 0.535902i | ||||
\(829\) | 1.90211i | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.621457 | − | 0.316648i | 0.621457 | − | 0.316648i | ||||
\(832\) | −0.677548 | + | 1.32976i | −0.677548 | + | 1.32976i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.493191 | + | 0.493191i | −0.493191 | + | 0.493191i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.257585 | − | 0.505539i | −0.257585 | − | 0.505539i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.109638 | − | 0.150903i | −0.109638 | − | 0.150903i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.857608 | − | 1.68315i | −0.857608 | − | 1.68315i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.630723 | + | 0.321369i | 0.630723 | + | 0.321369i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − | 2.01890i | − | 2.01890i | ||||||
\(853\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.0646021 | − | 0.198825i | −0.0646021 | − | 0.198825i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.873619 | − | 1.20243i | 0.873619 | − | 1.20243i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(864\) | 0.570235 | + | 0.570235i | 0.570235 | + | 0.570235i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.65669 | + | 0.262394i | −1.65669 | + | 0.262394i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.12421 | − | 1.08234i | −2.12421 | − | 1.08234i | ||||
\(877\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(878\) | 0.147518 | + | 0.289520i | 0.147518 | + | 0.289520i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(882\) | −0.222841 | − | 0.306714i | −0.222841 | − | 0.306714i | ||||
\(883\) | −0.221232 | + | 1.39680i | −0.221232 | + | 1.39680i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0353579 | + | 0.0256890i | −0.0353579 | + | 0.0256890i | ||||
\(887\) | −0.461219 | − | 0.235003i | −0.461219 | − | 0.235003i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.562096 | + | 1.72995i | −0.562096 | + | 1.72995i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.18612 | + | 1.03523i | −3.18612 | + | 1.03523i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.320282 | + | 0.320282i | 0.320282 | + | 0.320282i | ||||
\(900\) | −1.01935 | + | 1.40301i | −1.01935 | + | 1.40301i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.0113422 | + | 0.0349078i | 0.0113422 | + | 0.0349078i | ||||
\(907\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.19185 | − | 0.505539i | −3.19185 | − | 0.505539i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.308463 | + | 1.94756i | −0.308463 | + | 1.94756i | ||||
\(922\) | −0.224514 | − | 0.309017i | −0.224514 | − | 0.309017i | ||||
\(923\) | 1.47759 | + | 2.03373i | 1.47759 | + | 2.03373i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.169131 | + | 0.331938i | 0.169131 | + | 0.331938i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.573620 | − | 0.292274i | −0.573620 | − | 0.292274i | ||||
\(929\) | 1.32028 | − | 1.32028i | 1.32028 | − | 1.32028i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.64606 | − | 0.838711i | 1.64606 | − | 0.838711i | ||||
\(933\) | −0.805631 | + | 2.47948i | −0.805631 | + | 2.47948i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.46307 | − | 0.231727i | −1.46307 | − | 0.231727i | ||||
\(937\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(944\) | 0.538181 | 0.538181 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.604528 | − | 1.86055i | −0.604528 | − | 1.86055i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.93196 | − | 0.464377i | 2.93196 | − | 0.464377i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.15121 | + | 1.02389i | 3.15121 | + | 1.02389i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.162953 | + | 1.02885i | 0.162953 | + | 1.02885i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.669131 | + | 0.486152i | 0.669131 | + | 0.486152i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.235003 | − | 0.461219i | −0.235003 | − | 0.461219i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(968\) | −0.330869 | + | 0.240391i | −0.330869 | + | 0.240391i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(972\) | −0.246327 | + | 0.483444i | −0.246327 | + | 0.483444i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.0864545 | − | 0.266080i | 0.0864545 | − | 0.266080i | ||||
\(975\) | − | 3.35008i | − | 3.35008i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(978\) | 0.514765 | − | 0.0815308i | 0.514765 | − | 0.0815308i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.0510966 | + | 0.0703285i | −0.0510966 | + | 0.0703285i | ||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | 0.640431 | − | 0.245838i | 0.640431 | − | 0.245838i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.896802 | − | 0.142040i | −0.896802 | − | 0.142040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(992\) | 0.233733 | + | 0.0759444i | 0.233733 | + | 0.0759444i | ||||
\(993\) | 1.20221i | 1.20221i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0489435 | − | 0.309017i | −0.0489435 | − | 0.309017i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(998\) | −0.105952 | + | 0.105952i | −0.105952 | + | 0.105952i | ||||
\(999\) | 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 | 943.1.n.b.459.1 | ✓ | 16 | |
23.22 | odd | 2 | CM | 943.1.n.b.459.1 | ✓ | 16 | |
41.36 | even | 20 | inner | 943.1.n.b.528.1 | yes | 16 | |
943.528 | odd | 20 | inner | 943.1.n.b.528.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
943.1.n.b.459.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
943.1.n.b.459.1 | ✓ | 16 | 23.22 | odd | 2 | CM | |
943.1.n.b.528.1 | yes | 16 | 41.36 | even | 20 | inner | |
943.1.n.b.528.1 | yes | 16 | 943.528 | odd | 20 | inner |