Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,1,Mod(107,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(92))
chi = DirichletCharacter(H, H._module([46, 23, 22]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3525.107");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.bg (of order \(92\), degree \(44\), 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: | \(1.75920416953\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{92})\) |
Coefficient field: | \(\Q(\zeta_{184})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{88} - x^{84} + x^{80} - x^{76} + x^{72} - x^{68} + x^{64} - x^{60} + x^{56} - x^{52} + x^{48} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{46}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{46} - \cdots)\) |
Embedding invariants
Embedding label | 293.2 | ||
Root | \(-0.999417 + 0.0341411i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.293 |
Dual form | 3525.1.bg.a.782.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times\).
\(n\) | \(1552\) | \(2026\) | \(2351\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.919594 | − | 0.0314143i | 0.919594 | − | 0.0314143i | 0.429483 | − | 0.903075i | \(-0.358696\pi\) |
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(3\) | −0.796805 | + | 0.604236i | −0.796805 | + | 0.604236i | ||||
\(4\) | −0.153003 | + | 0.0104657i | −0.153003 | + | 0.0104657i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.713755 | + | 0.580683i | −0.713755 | + | 0.580683i | ||||
\(7\) | 0 | 0 | −0.930278 | − | 0.366854i | \(-0.880435\pi\) | ||||
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(8\) | −1.05568 | + | 0.108527i | −1.05568 | + | 0.108527i | ||||
\(9\) | 0.269797 | − | 0.962917i | 0.269797 | − | 0.962917i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(12\) | 0.115590 | − | 0.100789i | 0.115590 | − | 0.100789i | ||||
\(13\) | 0 | 0 | −0.236764 | − | 0.971567i | \(-0.576087\pi\) | ||||
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.815453 | + | 0.112081i | −0.815453 | + | 0.112081i | ||||
\(17\) | 1.00609 | − | 1.53391i | 1.00609 | − | 1.53391i | 0.169910 | − | 0.985460i | \(-0.445652\pi\) |
0.836182 | − | 0.548452i | \(-0.184783\pi\) | |||||||
\(18\) | 0.217854 | − | 0.893968i | 0.217854 | − | 0.893968i | ||||
\(19\) | 0.917985 | + | 1.77163i | 0.917985 | + | 1.77163i | 0.519584 | + | 0.854419i | \(0.326087\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0499031 | − | 1.46082i | 0.0499031 | − | 1.46082i | −0.657204 | − | 0.753713i | \(-0.728261\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(24\) | 0.775594 | − | 0.724354i | 0.775594 | − | 0.724354i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.366854 | + | 0.930278i | 0.366854 | + | 0.930278i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.266637 | + | 1.93993i | 0.266637 | + | 1.93993i | 0.334880 | + | 0.942261i | \(0.391304\pi\) |
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(32\) | 0.299446 | − | 0.0516297i | 0.299446 | − | 0.0516297i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.877010 | − | 1.44218i | 0.877010 | − | 1.44218i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0312021 | + | 0.150153i | −0.0312021 | + | 0.150153i | ||||
\(37\) | 0 | 0 | 0.429483 | − | 0.903075i | \(-0.358696\pi\) | ||||
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(38\) | 0.899828 | + | 1.60034i | 0.899828 | + | 1.60034i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.631088 | − | 0.775711i | \(-0.717391\pi\) | ||||
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.657204 | − | 0.753713i | \(-0.271739\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 1.34493i | − | 1.34493i | ||||||
\(47\) | 0.903075 | − | 0.429483i | 0.903075 | − | 0.429483i | ||||
\(48\) | 0.582034 | − | 0.582034i | 0.582034 | − | 0.582034i | ||||
\(49\) | 0.730836 | + | 0.682553i | 0.730836 | + | 0.682553i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.125185 | + | 1.83015i | 0.125185 | + | 1.83015i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.196944 | + | 1.91574i | −0.196944 | + | 1.91574i | 0.169910 | + | 0.985460i | \(0.445652\pi\) |
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(54\) | 0.366581 | + | 0.843954i | 0.366581 | + | 0.843954i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.80194 | − | 0.856964i | −1.80194 | − | 0.856964i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.572255 | − | 1.61017i | 0.572255 | − | 1.61017i | −0.203456 | − | 0.979084i | \(-0.565217\pi\) |
0.775711 | − | 0.631088i | \(-0.217391\pi\) | |||||||
\(62\) | 0.306139 | + | 1.77557i | 0.306139 | + | 1.77557i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.07965 | − | 0.224354i | 1.07965 | − | 0.224354i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(68\) | −0.137882 | + | 0.245223i | −0.137882 | + | 0.245223i | ||||
\(69\) | 0.842917 | + | 1.19414i | 0.842917 | + | 1.19414i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(72\) | −0.180316 | + | 1.04581i | −0.180316 | + | 1.04581i | ||||
\(73\) | 0 | 0 | −0.871660 | − | 0.490110i | \(-0.836957\pi\) | ||||
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.158996 | − | 0.261458i | −0.158996 | − | 0.261458i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.332435 | + | 0.234658i | 0.332435 | + | 0.234658i | 0.730836 | − | 0.682553i | \(-0.239130\pi\) |
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.854419 | − | 0.519584i | −0.854419 | − | 0.519584i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.850881 | + | 1.29727i | 0.850881 | + | 1.29727i | 0.953145 | + | 0.302515i | \(0.0978261\pi\) |
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.00765317 | + | 0.224032i | 0.00765317 | + | 0.224032i | ||||
\(93\) | −1.38463 | − | 1.38463i | −1.38463 | − | 1.38463i | ||||
\(94\) | 0.816970 | − | 0.423320i | 0.816970 | − | 0.423320i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.207404 | + | 0.222075i | −0.207404 | + | 0.222075i | ||||
\(97\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(98\) | 0.693514 | + | 0.604713i | 0.693514 | + | 0.604713i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(102\) | 0.172612 | + | 1.67906i | 0.172612 | + | 1.67906i | ||||
\(103\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.120927 | + | 1.76789i | −0.120927 | + | 1.76789i | ||||
\(107\) | −0.264590 | + | 0.0644788i | −0.264590 | + | 0.0644788i | −0.366854 | − | 0.930278i | \(-0.619565\pi\) |
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(108\) | −0.0658659 | − | 0.138496i | −0.0658659 | − | 0.138496i | ||||
\(109\) | −0.727872 | + | 1.03116i | −0.727872 | + | 1.03116i | 0.269797 | + | 0.962917i | \(0.413043\pi\) |
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.570095 | − | 1.79622i | 0.570095 | − | 1.79622i | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) |
0.604236 | − | 0.796805i | \(-0.293478\pi\) | |||||||
\(114\) | −1.68397 | − | 0.731452i | −1.68397 | − | 0.731452i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.917211 | + | 0.398401i | 0.917211 | + | 0.398401i | ||||
\(122\) | 0.475660 | − | 1.49868i | 0.475660 | − | 1.49868i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0610990 | − | 0.294025i | −0.0610990 | − | 0.294025i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.429483 | − | 0.903075i | \(-0.641304\pi\) | ||||
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(128\) | 0.690567 | − | 0.168287i | 0.690567 | − | 0.168287i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.895639 | + | 1.72850i | −0.895639 | + | 1.72850i | ||||
\(137\) | −0.951318 | − | 0.829507i | −0.951318 | − | 0.829507i | 0.0341411 | − | 0.999417i | \(-0.489130\pi\) |
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(138\) | 0.812655 | + | 1.07165i | 0.812655 | + | 1.07165i | ||||
\(139\) | 1.11525 | − | 1.19414i | 1.11525 | − | 1.19414i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
0.979084 | − | 0.203456i | \(-0.0652174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.460065 | + | 0.887885i | −0.460065 | + | 0.887885i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.112081 | + | 0.815453i | −0.112081 | + | 0.815453i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.994757 | − | 0.102264i | −0.994757 | − | 0.102264i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.979167 | − | 0.347996i | 0.979167 | − | 0.347996i | 0.203456 | − | 0.979084i | \(-0.434783\pi\) |
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(152\) | −1.16137 | − | 1.77065i | −1.16137 | − | 1.77065i | ||||
\(153\) | −1.20559 | − | 1.38263i | −1.20559 | − | 1.38263i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.796805 | − | 0.604236i | \(-0.793478\pi\) | ||||
0.796805 | + | 0.604236i | \(0.206522\pi\) | |||||||
\(158\) | 0.313077 | + | 0.205347i | 0.313077 | + | 0.205347i | ||||
\(159\) | −1.00063 | − | 1.64547i | −1.00063 | − | 1.64547i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.802041 | − | 0.450965i | −0.802041 | − | 0.450965i | ||||
\(163\) | 0 | 0 | 0.169910 | − | 0.985460i | \(-0.445652\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.823217 | + | 1.16623i | 0.823217 | + | 1.16623i | ||||
\(167\) | −0.264460 | + | 0.470342i | −0.264460 | + | 0.470342i | −0.971567 | − | 0.236764i | \(-0.923913\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.887885 | + | 0.460065i | −0.887885 | + | 0.460065i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.95360 | − | 0.405963i | 1.95360 | − | 0.405963i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.113799 | − | 0.660021i | −0.113799 | − | 0.660021i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
0.871660 | − | 0.490110i | \(-0.163043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.750796 | − | 1.72850i | −0.750796 | − | 1.72850i | −0.682553 | − | 0.730836i | \(-0.739130\pi\) |
−0.0682424 | − | 0.997669i | \(-0.521739\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.516949 | + | 1.62877i | 0.516949 | + | 1.62877i | ||||
\(184\) | 0.105857 | + | 1.54757i | 0.105857 | + | 1.54757i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.31680 | − | 1.22980i | −1.31680 | − | 1.22980i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.133678 | + | 0.0751636i | −0.133678 | + | 0.0751636i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(192\) | −0.724708 | + | 0.831130i | −0.724708 | + | 0.831130i | ||||
\(193\) | 0 | 0 | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) | ||||
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.118964 | − | 0.0967841i | −0.118964 | − | 0.0967841i | ||||
\(197\) | 0.837519 | + | 1.48953i | 0.837519 | + | 1.48953i | 0.871660 | + | 0.490110i | \(0.163043\pi\) |
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.109784 | − | 0.528307i | 0.109784 | − | 0.528307i | −0.887885 | − | 0.460065i | \(-0.847826\pi\) |
0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0383075 | − | 0.278708i | −0.0383075 | − | 0.278708i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.39318 | − | 0.442177i | −1.39318 | − | 0.442177i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.199031 | + | 0.185882i | −0.199031 | + | 0.185882i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) |
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(212\) | 0.0100835 | − | 0.295175i | 0.0100835 | − | 0.295175i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.241290 | + | 0.0676062i | −0.241290 | + | 0.0676062i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.488240 | − | 0.942261i | −0.488240 | − | 0.942261i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.636953 | + | 0.971113i | −0.636953 | + | 0.971113i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.753713 | − | 0.657204i | \(-0.228261\pi\) | ||||
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.467829 | − | 1.66970i | 0.467829 | − | 1.66970i | ||||
\(227\) | −1.03372 | + | 0.106270i | −1.03372 | + | 0.106270i | −0.604236 | − | 0.796805i | \(-0.706522\pi\) |
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(228\) | 0.284671 | + | 0.112260i | 0.284671 | + | 0.112260i | ||||
\(229\) | −0.806094 | + | 0.655806i | −0.806094 | + | 0.655806i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) |
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.539279 | − | 0.0184223i | 0.539279 | − | 0.0184223i | 0.236764 | − | 0.971567i | \(-0.423913\pi\) |
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.406675 | + | 0.0138924i | −0.406675 | + | 0.0138924i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.49389 | − | 1.21537i | 1.49389 | − | 1.21537i | 0.576680 | − | 0.816970i | \(-0.304348\pi\) |
0.917211 | − | 0.398401i | \(-0.130435\pi\) | |||||||
\(242\) | 0.855977 | + | 0.337554i | 0.855977 | + | 0.337554i | ||||
\(243\) | 0.994757 | − | 0.102264i | 0.994757 | − | 0.102264i | ||||
\(244\) | −0.0707053 | + | 0.252350i | −0.0707053 | + | 0.252350i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.492018 | − | 2.01900i | −0.492018 | − | 2.01900i | ||||
\(249\) | −1.46184 | − | 0.519540i | −1.46184 | − | 0.519540i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.432069 | + | 0.121060i | −0.432069 | + | 0.121060i | ||||
\(257\) | 0.785216 | + | 0.135385i | 0.785216 | + | 0.135385i | 0.548452 | − | 0.836182i | \(-0.315217\pi\) |
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.30114 | − | 0.412965i | −1.30114 | − | 0.412965i | −0.429483 | − | 0.903075i | \(-0.641304\pi\) |
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0277687 | − | 0.133630i | 0.0277687 | − | 0.133630i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(272\) | −0.648498 | + | 1.36360i | −0.648498 | + | 1.36360i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.900885 | − | 0.732924i | −0.900885 | − | 0.732924i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.141467 | − | 0.173886i | −0.141467 | − | 0.173886i | ||||
\(277\) | 0 | 0 | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) | ||||
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(278\) | 0.988064 | − | 1.13316i | 0.988064 | − | 1.13316i | ||||
\(279\) | 1.93993 | + | 0.266637i | 1.93993 | + | 0.266637i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −0.395181 | + | 0.830946i | −0.395181 | + | 0.830946i | ||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0310744 | − | 0.302271i | 0.0310744 | − | 0.302271i | ||||
\(289\) | −0.942261 | − | 2.16930i | −0.942261 | − | 2.16930i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.48487 | + | 0.973925i | −1.48487 | + | 0.973925i | −0.490110 | + | 0.871660i | \(0.663043\pi\) |
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(294\) | −0.917985 | − | 0.0627919i | −0.917985 | − | 0.0627919i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.889504 | − | 0.350775i | 0.889504 | − | 0.350775i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.947141 | − | 1.34179i | −0.947141 | − | 1.34179i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.15209 | − | 1.23358i | −1.15209 | − | 1.23358i | ||||
\(307\) | 0 | 0 | 0.169910 | − | 0.985460i | \(-0.445652\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.796805 | − | 0.604236i | \(-0.793478\pi\) | ||||
0.796805 | + | 0.604236i | \(0.206522\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0533194 | − | 0.0324243i | −0.0533194 | − | 0.0324243i | ||||
\(317\) | −0.178978 | − | 0.205261i | −0.178978 | − | 0.205261i | 0.657204 | − | 0.753713i | \(-0.271739\pi\) |
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(318\) | −0.971867 | − | 1.48173i | −0.971867 | − | 1.48173i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.171866 | − | 0.211252i | 0.171866 | − | 0.211252i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.64110 | + | 0.374317i | 3.64110 | + | 0.374317i | ||||
\(324\) | 0.136167 | + | 0.0705559i | 0.136167 | + | 0.0705559i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.0430921 | − | 1.26144i | −0.0430921 | − | 1.26144i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.05893 | − | 1.13384i | 1.05893 | − | 1.13384i | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) |
0.990686 | − | 0.136167i | \(-0.0434783\pi\) | |||||||
\(332\) | −0.143764 | − | 0.189582i | −0.143764 | − | 0.189582i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.228421 | + | 0.440832i | −0.228421 | + | 0.440832i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.102264 | − | 0.994757i | \(-0.532609\pi\) | ||||
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(338\) | −0.802041 | + | 0.450965i | −0.802041 | + | 0.450965i | ||||
\(339\) | 0.631088 | + | 1.77571i | 0.631088 | + | 1.77571i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.78377 | − | 0.434692i | 1.78377 | − | 0.434692i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.125383 | − | 0.603376i | −0.125383 | − | 0.603376i | ||||
\(347\) | −0.650716 | − | 0.158575i | −0.650716 | − | 0.158575i | −0.102264 | − | 0.994757i | \(-0.532609\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.49867 | − | 0.650963i | −1.49867 | − | 0.650963i | −0.519584 | − | 0.854419i | \(-0.673913\pi\) |
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.136405 | + | 0.00465974i | 0.136405 | + | 0.00465974i | 0.102264 | − | 0.994757i | \(-0.467391\pi\) |
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.71930 | + | 2.43569i | −1.71930 | + | 2.43569i | ||||
\(362\) | −0.744727 | − | 1.56594i | −0.744727 | − | 1.56594i | ||||
\(363\) | −0.971567 | + | 0.236764i | −0.971567 | + | 0.236764i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.526549 | + | 1.48157i | 0.526549 | + | 1.48157i | ||||
\(367\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(368\) | 0.123037 | + | 1.19682i | 0.123037 | + | 1.19682i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.226344 | + | 0.197362i | 0.226344 | + | 0.197362i | ||||
\(373\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.906746 | + | 0.551404i | −0.906746 | + | 0.551404i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.269797 | + | 1.96292i | −0.269797 | + | 1.96292i | 1.00000i | \(0.5\pi\) | ||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.245704 | − | 0.623063i | 0.245704 | − | 0.623063i | −0.753713 | − | 0.657204i | \(-0.771739\pi\) |
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(384\) | −0.448562 | + | 0.551357i | −0.448562 | + | 0.551357i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.19056 | − | 1.54627i | −2.19056 | − | 1.54627i | ||||
\(392\) | −0.845603 | − | 0.641241i | −0.845603 | − | 0.641241i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.816970 | + | 1.34345i | 0.816970 | + | 1.34345i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.871660 | − | 0.490110i | \(-0.836957\pi\) | ||||
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(398\) | 0.0843599 | − | 0.489277i | 0.0843599 | − | 0.489277i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.330776 | − | 1.91846i | −0.330776 | − | 1.91846i | ||||
\(409\) | −0.547173 | + | 1.53960i | −0.547173 | + | 1.53960i | 0.269797 | + | 0.962917i | \(0.413043\pi\) |
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.25923 | + | 0.0861339i | 1.25923 | + | 0.0861339i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.29505 | − | 0.362857i | −1.29505 | − | 0.362857i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.167093 | + | 1.62537i | −0.167093 | + | 1.62537i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.199031 | − | 0.185882i | −0.199031 | − | 0.185882i | 0.576680 | − | 0.816970i | \(-0.304348\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(422\) | −0.177188 | + | 0.177188i | −0.177188 | + | 0.177188i | ||||
\(423\) | −0.169910 | − | 0.985460i | −0.169910 | − | 0.985460i | ||||
\(424\) | − | 2.04378i | − | 2.04378i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0398083 | − | 0.0126346i | 0.0398083 | − | 0.0126346i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(432\) | −0.403419 | − | 0.717481i | −0.403419 | − | 0.717481i | ||||
\(433\) | 0 | 0 | 0.429483 | − | 0.903075i | \(-0.358696\pi\) | ||||
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.100575 | − | 0.165388i | 0.100575 | − | 0.165388i | ||||
\(437\) | 2.63384 | − | 1.25260i | 2.63384 | − | 1.25260i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.211252 | − | 1.53697i | −0.211252 | − | 1.53697i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
0.519584 | − | 0.854419i | \(-0.326087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.854419 | − | 0.519584i | 0.854419 | − | 0.519584i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.463035 | − | 1.17418i | −0.463035 | − | 1.17418i | −0.953145 | − | 0.302515i | \(-0.902174\pi\) |
0.490110 | − | 0.871660i | \(-0.336957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.0684276 | + | 0.280794i | −0.0684276 | + | 0.280794i | ||||
\(453\) | −0.569934 | + | 0.868934i | −0.569934 | + | 0.868934i | ||||
\(454\) | −0.947264 | + | 0.130198i | −0.947264 | + | 0.130198i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.99527 | + | 0.709120i | 1.99527 | + | 0.709120i | ||||
\(457\) | 0 | 0 | −0.236764 | − | 0.971567i | \(-0.576087\pi\) | ||||
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(458\) | −0.720678 | + | 0.628398i | −0.720678 | + | 0.628398i | ||||
\(459\) | 1.79605 | + | 0.373224i | 1.79605 | + | 0.373224i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.930278 | − | 0.366854i | \(-0.880435\pi\) | ||||
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.495339 | − | 0.0338821i | 0.495339 | − | 0.0338821i | ||||
\(467\) | −1.30193 | + | 0.987286i | −1.30193 | + | 0.987286i | −0.302515 | + | 0.953145i | \(0.597826\pi\) |
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.373539 | + | 0.0255508i | −0.373539 | + | 0.0255508i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.79156 | + | 0.706501i | 1.79156 | + | 0.706501i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.33559 | − | 1.16458i | 1.33559 | − | 1.16458i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.144506 | − | 0.0513574i | −0.144506 | − | 0.0513574i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.911560 | − | 0.125291i | 0.911560 | − | 0.125291i | ||||
\(487\) | 0 | 0 | 0.548452 | − | 0.836182i | \(-0.315217\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(488\) | −0.429370 | + | 1.76193i | −0.429370 | + | 1.76193i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.434860 | − | 1.55204i | −0.434860 | − | 1.55204i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.36062 | − | 0.431843i | −1.36062 | − | 0.431843i | ||||
\(499\) | −1.24888 | + | 0.759461i | −1.24888 | + | 0.759461i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0734746 | − | 0.534568i | −0.0734746 | − | 0.534568i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.60365 | + | 0.762664i | −1.60365 | + | 0.762664i | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) |
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.429483 | − | 0.903075i | 0.429483 | − | 0.903075i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.07100 | + | 0.339919i | −1.07100 | + | 0.339919i | ||||
\(513\) | −1.31134 | + | 1.50391i | −1.31134 | + | 1.50391i | ||||
\(514\) | 0.726333 | + | 0.0998322i | 0.726333 | + | 0.0998322i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.489484 | + | 0.457146i | 0.489484 | + | 0.457146i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.102264 | − | 0.994757i | \(-0.467391\pi\) | ||||
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.20950 | − | 0.338885i | −1.20950 | − | 0.338885i | ||||
\(527\) | 3.24394 | + | 1.54275i | 3.24394 | + | 1.54275i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.13384 | − | 0.0775565i | −1.13384 | − | 0.0775565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.277739 | + | 0.297386i | 0.277739 | + | 0.297386i | 0.854419 | − | 0.519584i | \(-0.173913\pi\) |
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(542\) | 0.0213380 | − | 0.123758i | 0.0213380 | − | 0.123758i | ||||
\(543\) | 1.64266 | + | 0.923623i | 1.64266 | + | 0.923623i | ||||
\(544\) | 0.222075 | − | 0.511268i | 0.222075 | − | 0.511268i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.836182 | − | 0.548452i | \(-0.815217\pi\) | ||||
0.836182 | + | 0.548452i | \(0.184783\pi\) | |||||||
\(548\) | 0.154236 | + | 0.116961i | 0.154236 | + | 0.116961i | ||||
\(549\) | −1.39607 | − | 0.985454i | −1.39607 | − | 0.985454i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.01945 | − | 1.16915i | −1.01945 | − | 1.16915i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.158139 | + | 0.194379i | −0.158139 | + | 0.194379i | ||||
\(557\) | 0.292310 | − | 0.741248i | 0.292310 | − | 0.741248i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | |||||||
\(558\) | 1.79232 | + | 0.184256i | 1.79232 | + | 0.184256i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.563424 | − | 0.563424i | −0.563424 | − | 0.563424i | 0.366854 | − | 0.930278i | \(-0.380435\pi\) |
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(564\) | 0.0610990 | − | 0.140664i | 0.0610990 | − | 0.140664i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.125185 | − | 0.0543757i | 0.125185 | − | 0.0543757i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0752519 | − | 1.10014i | 0.0752519 | − | 1.10014i | ||||
\(577\) | 0 | 0 | 0.971567 | − | 0.236764i | \(-0.0760870\pi\) | ||||
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(578\) | −0.934644 | − | 1.96528i | −0.934644 | − | 1.96528i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.33488 | + | 0.942261i | −1.33488 | + | 0.942261i | ||||
\(587\) | 1.99417 | + | 0.0681230i | 1.99417 | + | 0.0681230i | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) |
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(588\) | 0.153271 | + | 0.00523590i | 0.153271 | + | 0.00523590i | ||||
\(589\) | −3.19207 | + | 2.25321i | −3.19207 | + | 2.25321i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.56737 | − | 0.680803i | −1.56737 | − | 0.680803i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.72528 | − | 0.420439i | −1.72528 | − | 0.420439i | −0.753713 | − | 0.657204i | \(-0.771739\pi\) |
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.231746 | + | 0.487293i | 0.231746 | + | 0.487293i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.224289 | − | 0.631088i | −0.224289 | − | 0.631088i | 0.775711 | − | 0.631088i | \(-0.217391\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.146174 | + | 0.0634922i | −0.146174 | + | 0.0634922i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.753713 | − | 0.657204i | \(-0.771739\pi\) | ||||
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(608\) | 0.366356 | + | 0.483113i | 0.366356 | + | 0.483113i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.198929 | + | 0.198929i | 0.198929 | + | 0.198929i | ||||
\(613\) | 0 | 0 | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) | ||||
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.404779 | − | 0.0416125i | −0.404779 | − | 0.0416125i | −0.102264 | − | 0.994757i | \(-0.532609\pi\) |
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.07843 | − | 1.32557i | 1.07843 | − | 1.32557i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
0.942261 | − | 0.334880i | \(-0.108696\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.37728 | − | 0.489484i | 1.37728 | − | 0.489484i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.582332 | + | 1.34066i | −0.582332 | + | 1.34066i | 0.334880 | + | 0.942261i | \(0.391304\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(632\) | −0.376411 | − | 0.211645i | −0.376411 | − | 0.211645i | ||||
\(633\) | 0.0462723 | − | 0.268373i | 0.0462723 | − | 0.268373i | ||||
\(634\) | −0.171036 | − | 0.183134i | −0.171036 | − | 0.183134i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.170321 | + | 0.241290i | 0.170321 | + | 0.241290i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) | ||||
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(642\) | 0.151411 | − | 0.199665i | 0.151411 | − | 0.199665i | ||||
\(643\) | 0 | 0 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.36009 | + | 0.229837i | 3.36009 | + | 0.229837i | ||||
\(647\) | −1.61035 | + | 1.05623i | −1.61035 | + | 1.05623i | −0.657204 | + | 0.753713i | \(0.728261\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(648\) | 0.958381 | + | 0.455786i | 0.958381 | + | 0.455786i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.0412886 | + | 0.130090i | 0.0412886 | + | 0.130090i | 0.971567 | − | 0.236764i | \(-0.0760870\pi\) |
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(654\) | −0.0792544 | − | 1.15866i | −0.0792544 | − | 1.15866i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.81734 | − | 0.249787i | −1.81734 | − | 0.249787i | −0.854419 | − | 0.519584i | \(-0.826087\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(662\) | 0.938165 | − | 1.07593i | 0.938165 | − | 1.07593i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.03904 | − | 1.27716i | −1.03904 | − | 1.27716i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.0355408 | − | 0.0747316i | 0.0355408 | − | 0.0747316i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) | ||||
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.131034 | − | 0.0796837i | 0.131034 | − | 0.0796837i | ||||
\(677\) | 1.55738 | + | 0.494291i | 1.55738 | + | 0.494291i | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) |
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(678\) | 0.636127 | + | 1.61311i | 0.636127 | + | 1.61311i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.759461 | − | 0.709287i | 0.759461 | − | 0.709287i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.34526 | + | 0.231946i | 1.34526 | + | 0.231946i | 0.796805 | − | 0.604236i | \(-0.206522\pi\) |
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(684\) | −0.294659 | + | 0.0825595i | −0.294659 | + | 0.0825595i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.246038 | − | 1.00962i | 0.246038 | − | 1.00962i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.750796 | + | 0.266833i | 0.750796 | + | 0.266833i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(692\) | 0.0243192 | + | 0.0997942i | 0.0243192 | + | 0.0997942i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.603376 | − | 0.125383i | −0.603376 | − | 0.125383i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.39862 | − | 0.551542i | −1.39862 | − | 0.551542i | ||||
\(699\) | −0.418569 | + | 0.340531i | −0.418569 | + | 0.340531i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.125584 | 0.125584 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.36192 | − | 0.0931581i | 1.36192 | − | 0.0931581i | 0.631088 | − | 0.775711i | \(-0.282609\pi\) |
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.315646 | − | 0.256797i | 0.315646 | − | 0.256797i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.84719 | − | 0.292700i | 2.84719 | − | 0.292700i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.50454 | + | 2.29386i | −1.50454 | + | 2.29386i | ||||
\(723\) | −0.455969 | + | 1.87108i | −0.455969 | + | 1.87108i | ||||
\(724\) | 0.132964 | + | 0.256609i | 0.132964 | + | 0.256609i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.886009 | + | 0.248248i | −0.886009 | + | 0.248248i | ||||
\(727\) | 0 | 0 | −0.985460 | − | 0.169910i | \(-0.945652\pi\) | ||||
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.730836 | + | 0.682553i | −0.730836 | + | 0.682553i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.0961410 | − | 0.243797i | −0.0961410 | − | 0.243797i | ||||
\(733\) | 0 | 0 | −0.953145 | − | 0.302515i | \(-0.902174\pi\) | ||||
0.953145 | + | 0.302515i | \(0.0978261\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0604784 | − | 0.440013i | −0.0604784 | − | 0.440013i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.347996 | + | 0.572255i | −0.347996 | + | 0.572255i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.977935 | + | 1.73926i | 0.977935 | + | 1.73926i | 0.548452 | + | 0.836182i | \(0.315217\pi\) |
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(744\) | 1.61200 | + | 1.31146i | 1.61200 | + | 1.31146i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.47873 | − | 0.469328i | 1.47873 | − | 0.469328i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.272333i | 0.272333i | 0.990686 | + | 0.136167i | \(0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(752\) | −0.688278 | + | 0.451442i | −0.688278 | + | 0.451442i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(758\) | −0.186440 | + | 1.81356i | −0.186440 | + | 1.81356i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.206375 | − | 0.580683i | 0.206375 | − | 0.580683i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.271126 | − | 0.357533i | 0.271126 | − | 0.357533i | ||||
\(769\) | 1.79605 | − | 0.373224i | 1.79605 | − | 0.373224i | 0.816970 | − | 0.576680i | \(-0.195652\pi\) |
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.707469 | + | 0.366581i | −0.707469 | + | 0.366581i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.565274 | − | 1.00534i | 0.565274 | − | 1.00534i | −0.429483 | − | 0.903075i | \(-0.641304\pi\) |
0.994757 | − | 0.102264i | \(-0.0326087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.06300 | − | 1.35312i | −2.06300 | − | 1.35312i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.672464 | − | 0.474677i | −0.672464 | − | 0.474677i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.657204 | − | 0.753713i | \(-0.728261\pi\) | ||||
0.657204 | + | 0.753713i | \(0.271739\pi\) | |||||||
\(788\) | −0.143732 | − | 0.219137i | −0.143732 | − | 0.219137i | ||||
\(789\) | 1.28629 | − | 0.457146i | 1.28629 | − | 0.457146i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0112681 | + | 0.0819817i | −0.0112681 | + | 0.0819817i | ||||
\(797\) | 0.0557845 | + | 1.63299i | 0.0557845 | + | 1.63299i | 0.604236 | + | 0.796805i | \(0.293478\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.249787 | − | 1.81734i | 0.249787 | − | 1.81734i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0457060 | − | 0.668198i | 0.0457060 | − | 0.668198i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
0.962917 | − | 0.269797i | \(-0.0869565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0586180 | + | 0.123256i | 0.0586180 | + | 0.123256i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.307208 | − | 1.47837i | −0.307208 | − | 1.47837i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.454812 | + | 1.43299i | −0.454812 | + | 1.43299i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.816970 | − | 0.576680i | \(-0.195652\pi\) | ||||
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(822\) | 1.16069 | + | 0.0396503i | 1.16069 | + | 0.0396503i | ||||
\(823\) | 0 | 0 | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) | ||||
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.348908 | + | 1.09932i | −0.348908 | + | 1.09932i | 0.604236 | + | 0.796805i | \(0.293478\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(828\) | 0.217789 | + | 0.0530738i | 0.217789 | + | 0.0530738i | ||||
\(829\) | −0.361291 | − | 1.73863i | −0.361291 | − | 1.73863i | −0.631088 | − | 0.775711i | \(-0.717391\pi\) |
0.269797 | − | 0.962917i | \(-0.413043\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.78226 | − | 0.434326i | 1.78226 | − | 0.434326i | ||||
\(834\) | −0.102598 | + | 1.49993i | −0.102598 | + | 1.49993i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.70686 | + | 0.959718i | −1.70686 | + | 0.959718i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.460065 | − | 0.887885i | 0.460065 | − | 0.887885i | ||||
\(842\) | −0.188867 | − | 0.164683i | −0.188867 | − | 0.164683i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0285070 | − | 0.0305235i | 0.0285070 | − | 0.0305235i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.187206 | − | 0.900885i | −0.187206 | − | 0.900885i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.0541202 | − | 1.58427i | −0.0541202 | − | 1.58427i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.366854 | − | 0.930278i | \(-0.380435\pi\) | ||||
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.272324 | − | 0.0967841i | 0.272324 | − | 0.0967841i | ||||
\(857\) | −0.149362 | − | 0.227720i | −0.149362 | − | 0.227720i | 0.753713 | − | 0.657204i | \(-0.228261\pi\) |
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.51725 | + | 0.922662i | 1.51725 | + | 0.922662i | 0.997669 | + | 0.0682424i | \(0.0217391\pi\) |
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.340253 | − | 0.223172i | −0.340253 | − | 0.223172i | 0.366854 | − | 0.930278i | \(-0.380435\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0.157883 | + | 0.259628i | 0.157883 | + | 0.259628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.06157 | + | 1.15916i | 2.06157 | + | 1.15916i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.656490 | − | 1.16757i | 0.656490 | − | 1.16757i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.38272 | − | 1.23462i | 2.38272 | − | 1.23462i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.604236 | − | 0.796805i | \(-0.293478\pi\) | ||||
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(878\) | −0.242549 | − | 1.40675i | −0.242549 | − | 1.40675i | ||||
\(879\) | 0.594669 | − | 1.67324i | 0.594669 | − | 1.67324i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(882\) | 0.769396 | − | 0.504647i | 0.769396 | − | 0.504647i | ||||
\(883\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.462689 | − | 1.06522i | −0.462689 | − | 1.06522i | ||||
\(887\) | −0.204051 | + | 1.98488i | −0.204051 | + | 1.98488i | −0.0341411 | + | 0.999417i | \(0.510870\pi\) |
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.58990 | + | 1.20566i | 1.58990 | + | 1.20566i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.74043 | + | 2.22950i | 2.74043 | + | 2.22950i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.406898 | + | 1.95810i | −0.406898 | + | 1.95810i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.496810 | + | 0.816970i | −0.496810 | + | 0.816970i | ||||
\(907\) | 0 | 0 | 0.903075 | − | 0.429483i | \(-0.141304\pi\) | ||||
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(908\) | 0.157050 | − | 0.0270782i | 0.157050 | − | 0.0270782i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(912\) | 1.56545 | + | 0.496850i | 1.56545 | + | 0.496850i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.116471 | − | 0.108777i | 0.116471 | − | 0.108777i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.66336 | + | 0.286793i | 1.66336 | + | 0.286793i | ||||
\(919\) | −1.40747 | + | 0.394354i | −1.40747 | + | 0.394354i | −0.887885 | − | 0.460065i | \(-0.847826\pi\) |
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.538336 | + | 1.92135i | −0.538336 | + | 1.92135i | ||||
\(932\) | −0.0823186 | + | 0.00846261i | −0.0823186 | + | 0.00846261i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.16623 | + | 0.948801i | −1.16623 | + | 0.948801i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.07295 | − | 0.423115i | −1.07295 | − | 0.423115i | −0.236764 | − | 0.971567i | \(-0.576087\pi\) |
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(948\) | 0.0620771 | − | 0.00638172i | 0.0620771 | − | 0.00638172i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.266637 | + | 0.0554078i | 0.266637 | + | 0.0554078i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.420439 | + | 1.72528i | 0.420439 | + | 1.72528i | 0.657204 | + | 0.753713i | \(0.271739\pi\) |
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(954\) | 1.66970 | + | 0.593413i | 1.66970 | + | 0.593413i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72931 | + | 0.764718i | −2.72931 | + | 0.764718i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.00929776 | + | 0.272175i | −0.00929776 | + | 0.272175i | ||||
\(964\) | −0.215850 | + | 0.201590i | −0.215850 | + | 0.201590i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.366854 | − | 0.930278i | \(-0.619565\pi\) | ||||
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(968\) | −1.01152 | − | 0.321041i | −1.01152 | − | 0.321041i | ||||
\(969\) | −3.12742 | + | 1.90183i | −3.12742 | + | 1.90183i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(972\) | −0.151131 | + | 0.0260576i | −0.151131 | + | 0.0260576i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.286177 | + | 1.37716i | −0.286177 | + | 1.37716i | ||||
\(977\) | −0.287650 | + | 0.604843i | −0.287650 | + | 0.604843i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.796544 | + | 0.979084i | 0.796544 | + | 0.979084i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.682945 | + | 0.783234i | −0.682945 | + | 0.783234i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.135214 | + | 1.97675i | 0.135214 | + | 1.97675i | 0.203456 | + | 0.979084i | \(0.434783\pi\) |
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(992\) | 0.180002 | + | 0.567138i | 0.180002 | + | 0.567138i | ||||
\(993\) | −0.158655 | + | 1.54329i | −0.158655 | + | 1.54329i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.229104 | + | 0.0641920i | 0.229104 | + | 0.0641920i | ||||
\(997\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(998\) | −1.12461 | + | 0.737628i | −1.12461 | + | 0.737628i | ||||
\(999\) | 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 | 3525.1.bg.a.293.2 | yes | 88 | |
3.2 | odd | 2 | inner | 3525.1.bg.a.293.1 | yes | 88 | |
5.2 | odd | 4 | inner | 3525.1.bg.a.857.2 | yes | 88 | |
5.3 | odd | 4 | inner | 3525.1.bg.a.857.1 | yes | 88 | |
5.4 | even | 2 | inner | 3525.1.bg.a.293.1 | yes | 88 | |
15.2 | even | 4 | inner | 3525.1.bg.a.857.1 | yes | 88 | |
15.8 | even | 4 | inner | 3525.1.bg.a.857.2 | yes | 88 | |
15.14 | odd | 2 | CM | 3525.1.bg.a.293.2 | yes | 88 | |
47.30 | odd | 46 | inner | 3525.1.bg.a.218.1 | ✓ | 88 | |
141.77 | even | 46 | inner | 3525.1.bg.a.218.2 | yes | 88 | |
235.77 | even | 92 | inner | 3525.1.bg.a.782.1 | yes | 88 | |
235.124 | odd | 46 | inner | 3525.1.bg.a.218.2 | yes | 88 | |
235.218 | even | 92 | inner | 3525.1.bg.a.782.2 | yes | 88 | |
705.77 | odd | 92 | inner | 3525.1.bg.a.782.2 | yes | 88 | |
705.218 | odd | 92 | inner | 3525.1.bg.a.782.1 | yes | 88 | |
705.359 | even | 46 | inner | 3525.1.bg.a.218.1 | ✓ | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.1.bg.a.218.1 | ✓ | 88 | 47.30 | odd | 46 | inner | |
3525.1.bg.a.218.1 | ✓ | 88 | 705.359 | even | 46 | inner | |
3525.1.bg.a.218.2 | yes | 88 | 141.77 | even | 46 | inner | |
3525.1.bg.a.218.2 | yes | 88 | 235.124 | odd | 46 | inner | |
3525.1.bg.a.293.1 | yes | 88 | 3.2 | odd | 2 | inner | |
3525.1.bg.a.293.1 | yes | 88 | 5.4 | even | 2 | inner | |
3525.1.bg.a.293.2 | yes | 88 | 1.1 | even | 1 | trivial | |
3525.1.bg.a.293.2 | yes | 88 | 15.14 | odd | 2 | CM | |
3525.1.bg.a.782.1 | yes | 88 | 235.77 | even | 92 | inner | |
3525.1.bg.a.782.1 | yes | 88 | 705.218 | odd | 92 | inner | |
3525.1.bg.a.782.2 | yes | 88 | 235.218 | even | 92 | inner | |
3525.1.bg.a.782.2 | yes | 88 | 705.77 | odd | 92 | inner | |
3525.1.bg.a.857.1 | yes | 88 | 5.3 | odd | 4 | inner | |
3525.1.bg.a.857.1 | yes | 88 | 15.2 | even | 4 | inner | |
3525.1.bg.a.857.2 | yes | 88 | 5.2 | odd | 4 | inner | |
3525.1.bg.a.857.2 | yes | 88 | 15.8 | even | 4 | inner |