Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [799,1,Mod(93,799)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(799, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([5, 4]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("799.93");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 799 = 17 \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 799.h (of order \(8\), degree \(4\), 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: | \(0.398752945094\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{40}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{40} + \cdots)\) |
Embedding invariants
Embedding label | 281.3 | ||
Root | \(0.987688 - 0.156434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 799.281 |
Dual form | 799.1.h.b.563.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(377\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.831254 | − | 0.831254i | 0.831254 | − | 0.831254i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(3\) | −0.144974 | − | 0.0600500i | −0.144974 | − | 0.0600500i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(4\) | − | 0.381966i | − | 0.381966i | ||||||
\(5\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(6\) | −0.170427 | + | 0.0705930i | −0.170427 | + | 0.0705930i | ||||
\(7\) | 0.744220 | + | 1.79671i | 0.744220 | + | 1.79671i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(8\) | 0.513743 | + | 0.513743i | 0.513743 | + | 0.513743i | ||||
\(9\) | −0.689695 | − | 0.689695i | −0.689695 | − | 0.689695i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(12\) | −0.0229371 | + | 0.0553750i | −0.0229371 | + | 0.0553750i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 2.11215 | + | 0.874883i | 2.11215 | + | 0.874883i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | 1.23607 | ||||||||
\(17\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(18\) | −1.14662 | −1.14662 | ||||||||
\(19\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.305165i | − | 0.305165i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(24\) | −0.0436289 | − | 0.105329i | −0.0436289 | − | 0.105329i | ||||
\(25\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.118621 | + | 0.286377i | 0.118621 | + | 0.286377i | ||||
\(28\) | 0.686280 | − | 0.284267i | 0.686280 | − | 0.284267i | ||||
\(29\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(32\) | 0.513743 | − | 0.513743i | 0.513743 | − | 0.513743i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.04744 | − | 0.533698i | −1.04744 | − | 0.533698i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.263440 | + | 0.263440i | −0.263440 | + | 0.263440i | ||||
\(37\) | −1.84206 | − | 0.763007i | −1.84206 | − | 0.763007i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.891007 | − | 0.453990i | \(-0.850000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(42\) | −0.253670 | − | 0.253670i | −0.253670 | − | 0.253670i | ||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.00000i | − | 1.00000i | ||||||
\(48\) | −0.179197 | − | 0.0742259i | −0.179197 | − | 0.0742259i | ||||
\(49\) | −1.96718 | + | 1.96718i | −1.96718 | + | 1.96718i | ||||
\(50\) | −1.17557 | −1.17557 | ||||||||
\(51\) | −0.0123117 | + | 0.156434i | −0.0123117 | + | 0.156434i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(54\) | 0.336657 | + | 0.139448i | 0.336657 | + | 0.139448i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.540707 | + | 1.30538i | −0.540707 | + | 1.30538i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.14412 | − | 1.14412i | −1.14412 | − | 1.14412i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.652583 | + | 1.57547i | 0.652583 | + | 1.57547i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.725895 | − | 1.75246i | 0.725895 | − | 1.75246i | ||||
\(64\) | 0.381966i | 0.381966i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | −0.363271 | + | 0.118034i | −0.363271 | + | 0.118034i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.20002 | + | 0.497066i | 1.20002 | + | 0.497066i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(72\) | − | 0.708653i | − | 0.708653i | ||||||
\(73\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(74\) | −2.16547 | + | 0.896969i | −2.16547 | + | 0.896969i | ||||
\(75\) | 0.0600500 | + | 0.144974i | 0.0600500 | + | 0.144974i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.20002 | − | 0.497066i | 1.20002 | − | 0.497066i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.926736i | 0.926736i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −0.116563 | −0.116563 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.17557i | 1.17557i | 0.809017 | + | 0.587785i | \(0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.831254 | − | 0.831254i | −0.831254 | − | 0.831254i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.105329 | + | 0.0436289i | −0.105329 | + | 0.0436289i | ||||
\(97\) | −0.399903 | + | 0.965451i | −0.399903 | + | 0.965451i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(98\) | 3.27045i | 3.27045i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.270091 | + | 0.270091i | −0.270091 | + | 0.270091i | ||||
\(101\) | −0.907981 | −0.907981 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(102\) | 0.119803 | + | 0.140271i | 0.119803 | + | 0.140271i | ||||
\(103\) | −1.78201 | −1.78201 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 2.32219i | − | 2.32219i | ||||||
\(107\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(108\) | 0.109386 | − | 0.0453093i | 0.109386 | − | 0.0453093i | ||||
\(109\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.221232 | + | 0.221232i | 0.221232 | + | 0.221232i | ||||
\(112\) | 0.919906 | + | 2.22085i | 0.919906 | + | 2.22085i | ||||
\(113\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.90211 | −1.90211 | ||||||||
\(119\) | 1.47879 | − | 1.26301i | 1.47879 | − | 1.26301i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(122\) | 1.85208 | + | 0.767157i | 1.85208 | + | 0.767157i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.853340 | − | 2.06015i | −0.853340 | − | 2.06015i | ||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | 0.831254 | + | 0.831254i | 0.831254 | + | 0.831254i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.399903 | − | 0.965451i | 0.399903 | − | 0.965451i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.329843 | − | 0.647354i | 0.329843 | − | 0.647354i | ||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0600500 | + | 0.144974i | −0.0600500 | + | 0.144974i | ||||
\(142\) | 1.41071 | − | 0.584336i | 1.41071 | − | 0.584336i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.852510 | − | 0.852510i | −0.852510 | − | 0.852510i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.403318 | − | 0.167060i | 0.403318 | − | 0.167060i | ||||
\(148\) | −0.291443 | + | 0.703605i | −0.291443 | + | 0.703605i | ||||
\(149\) | − | 1.78201i | − | 1.78201i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(150\) | 0.170427 | + | 0.0705930i | 0.170427 | + | 0.0705930i | ||||
\(151\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.442812 | + | 0.869067i | −0.442812 | + | 0.869067i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.312869i | − | 0.312869i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(158\) | 0.584336 | − | 1.41071i | 0.584336 | − | 1.41071i | ||||
\(159\) | −0.286377 | + | 0.118621i | −0.286377 | + | 0.118621i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.770353 | + | 0.770353i | 0.770353 | + | 0.770353i | ||||
\(163\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.66251i | 1.66251i | ||||||||
\(167\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(168\) | 0.156776 | − | 0.156776i | 0.156776 | − | 0.156776i | ||||
\(169\) | −1.00000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.431351 | − | 0.178671i | −0.431351 | − | 0.178671i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.744220 | − | 1.79671i | 0.744220 | − | 1.79671i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0971629 | + | 0.234572i | 0.0971629 | + | 0.234572i | ||||
\(178\) | 0.977198 | + | 0.977198i | 0.977198 | + | 0.977198i | ||||
\(179\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.267590i | − | 0.267590i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.381966 | −0.381966 | ||||||||
\(189\) | −0.426255 | + | 0.426255i | −0.426255 | + | 0.426255i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | 0.0229371 | − | 0.0553750i | 0.0229371 | − | 0.0553750i | ||||
\(193\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(194\) | 0.470114 | + | 1.13496i | 0.470114 | + | 1.13496i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.751396 | + | 0.751396i | 0.751396 | + | 0.751396i | ||||
\(197\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | 1.00000 | \(0\) | ||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(200\) | − | 0.726543i | − | 0.726543i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.754763 | + | 0.754763i | −0.754763 | + | 0.754763i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.0597526 | + | 0.00470264i | 0.0597526 | + | 0.00470264i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.48131 | + | 1.48131i | −1.48131 | + | 1.48131i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(212\) | −0.533531 | − | 0.533531i | −0.533531 | − | 0.533531i | ||||
\(213\) | −0.144123 | − | 0.144123i | −0.144123 | − | 0.144123i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.0861835 | + | 0.208065i | −0.0861835 | + | 0.208065i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.367799 | 0.367799 | ||||||||
\(223\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(224\) | 1.30538 | + | 0.540707i | 1.30538 | + | 0.540707i | ||||
\(225\) | 0.975377i | 0.975377i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.437016 | + | 0.437016i | −0.437016 | + | 0.437016i | ||||
\(237\) | −0.203820 | −0.203820 | ||||||||
\(238\) | 0.179372 | − | 2.27913i | 0.179372 | − | 2.27913i | ||||
\(239\) | 1.90211 | 1.90211 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.84206 | + | 0.763007i | 1.84206 | + | 0.763007i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(242\) | − | 1.17557i | − | 1.17557i | ||||||
\(243\) | 0.174272 | − | 0.420729i | 0.174272 | − | 0.420729i | ||||
\(244\) | 0.601777 | − | 0.249264i | 0.601777 | − | 0.249264i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.205023 | − | 0.0849235i | 0.205023 | − | 0.0849235i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.907981i | − | 0.907981i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(252\) | −0.669382 | − | 0.277267i | −0.669382 | − | 0.277267i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.87749i | − | 3.87749i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.470114 | − | 1.13496i | −0.470114 | − | 1.13496i | ||||
\(263\) | 1.14412 | + | 1.14412i | 1.14412 | + | 1.14412i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0705930 | − | 0.170427i | 0.0705930 | − | 0.170427i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.907981 | 0.907981 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(272\) | −0.381966 | − | 1.17557i | −0.381966 | − | 1.17557i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.497066 | + | 1.20002i | −0.497066 | + | 1.20002i | 0.453990 | + | 0.891007i | \(0.350000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(282\) | 0.0705930 | + | 0.170427i | 0.0705930 | + | 0.170427i | ||||
\(283\) | −1.79671 | + | 0.744220i | −1.79671 | + | 0.744220i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(284\) | 0.189862 | − | 0.458368i | 0.189862 | − | 0.458368i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.708653 | −0.708653 | ||||||||
\(289\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.115951 | − | 0.115951i | 0.115951 | − | 0.115951i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0.196391 | − | 0.474129i | 0.196391 | − | 0.474129i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.554357 | − | 1.33834i | −0.554357 | − | 1.33834i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.48131 | − | 1.48131i | −1.48131 | − | 1.48131i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.0553750 | − | 0.0229371i | 0.0553750 | − | 0.0229371i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.131633 | + | 0.0545243i | 0.131633 | + | 0.0545243i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.354326 | + | 1.09050i | 0.354326 | + | 1.09050i | ||||
\(307\) | 0.907981 | 0.907981 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.258345 | + | 0.107010i | 0.258345 | + | 0.107010i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(314\) | −0.260074 | − | 0.260074i | −0.260074 | − | 0.260074i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.189862 | − | 0.458368i | −0.189862 | − | 0.458368i | ||||
\(317\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(318\) | −0.139448 | + | 0.336657i | −0.139448 | + | 0.336657i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.353982 | 0.353982 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.79671 | − | 0.744220i | 1.79671 | − | 0.744220i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.831254 | + | 0.831254i | 0.831254 | + | 0.831254i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(332\) | 0.381966 | + | 0.381966i | 0.381966 | + | 0.381966i | ||||
\(333\) | 0.744220 | + | 1.79671i | 0.744220 | + | 1.79671i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 0.377205i | − | 0.377205i | ||||||
\(337\) | 0.431351 | + | 0.178671i | 0.431351 | + | 0.178671i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(338\) | −0.831254 | + | 0.831254i | −0.831254 | + | 0.831254i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.20175 | − | 1.32621i | −3.20175 | − | 1.32621i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.507083 | + | 0.210041i | −0.507083 | + | 0.210041i | ||||
\(347\) | −0.0600500 | − | 0.144974i | −0.0600500 | − | 0.144974i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(350\) | −0.874883 | − | 2.11215i | −0.874883 | − | 2.11215i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.312869i | 0.312869i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(354\) | 0.275756 | + | 0.114222i | 0.275756 | + | 0.114222i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.449028 | 0.449028 | ||||||||
\(357\) | −0.290229 | + | 0.0943012i | −0.290229 | + | 0.0943012i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 1.00000i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.144974 | + | 0.0600500i | −0.144974 | + | 0.0600500i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.222435 | − | 0.222435i | −0.222435 | − | 0.222435i | ||||
\(367\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.54917 | + | 1.47011i | 3.54917 | + | 1.47011i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.513743 | − | 0.513743i | 0.513743 | − | 0.513743i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.708653i | 0.708653i | ||||||||
\(379\) | 0.178671 | − | 0.431351i | 0.178671 | − | 0.431351i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.17557 | + | 1.17557i | 1.17557 | + | 1.17557i | ||||
\(383\) | 1.26007 | + | 1.26007i | 1.26007 | + | 1.26007i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(384\) | −0.0705930 | − | 0.170427i | −0.0705930 | − | 0.170427i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.368770 | + | 0.152749i | 0.368770 | + | 0.152749i | ||||
\(389\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.02125 | −2.02125 | ||||||||
\(393\) | −0.115951 | + | 0.115951i | −0.115951 | + | 0.115951i | ||||
\(394\) | 0.831254 | + | 0.344317i | 0.831254 | + | 0.344317i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.40505 | + | 0.581990i | −1.40505 | + | 0.581990i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.874032 | − | 0.874032i | −0.874032 | − | 0.874032i | ||||
\(401\) | 0.0600500 | + | 0.144974i | 0.0600500 | + | 0.144974i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.346818i | 0.346818i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.0866922 | + | 0.0740421i | −0.0866922 | + | 0.0740421i | ||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.680668i | 0.680668i | ||||||||
\(413\) | 1.20417 | − | 2.90713i | 1.20417 | − | 2.90713i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.689695 | + | 0.689695i | −0.689695 | + | 0.689695i | ||||
\(424\) | 1.43520 | 1.43520 | ||||||||
\(425\) | −0.453990 | + | 0.891007i | −0.453990 | + | 0.891007i | ||||
\(426\) | −0.239605 | −0.239605 | ||||||||
\(427\) | −2.34500 | + | 2.34500i | −2.34500 | + | 2.34500i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.965451 | + | 0.399903i | −0.965451 | + | 0.399903i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(432\) | 0.146624 | + | 0.353982i | 0.146624 | + | 0.353982i | ||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | − | 1.00000i | \(-0.5\pi\) | |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.71351 | 2.71351 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0.0845030 | − | 0.0845030i | 0.0845030 | − | 0.0845030i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.107010 | + | 0.258345i | −0.107010 | + | 0.258345i | ||||
\(448\) | −0.686280 | + | 0.284267i | −0.686280 | + | 0.284267i | ||||
\(449\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(450\) | 0.810786 | + | 0.810786i | 0.810786 | + | 0.810786i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.642040 | − | 0.642040i | 0.642040 | − | 0.642040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.235705 | − | 0.201311i | 0.235705 | − | 0.201311i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0187878 | + | 0.0453577i | −0.0187878 | + | 0.0453577i | ||||
\(472\) | − | 1.17557i | − | 1.17557i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.169427 | + | 0.169427i | −0.169427 | + | 0.169427i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.482426 | − | 0.564848i | −0.482426 | − | 0.564848i | ||||
\(477\) | −1.92674 | −1.92674 | ||||||||
\(478\) | 1.58114 | − | 1.58114i | 1.58114 | − | 1.58114i | ||||
\(479\) | 1.79671 | + | 0.744220i | 1.79671 | + | 0.744220i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.16547 | − | 0.896969i | 2.16547 | − | 0.896969i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.270091 | − | 0.270091i | −0.270091 | − | 0.270091i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.204869 | − | 0.494597i | −0.204869 | − | 0.494597i | ||||
\(487\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | − | 1.00000i | \(-0.5\pi\) | |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(488\) | −0.474129 | + | 1.14465i | −0.474129 | + | 1.14465i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.221232 | + | 0.221232i | −0.221232 | + | 0.221232i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.52601i | 2.52601i | ||||||||
\(498\) | 0.0998336 | − | 0.241020i | 0.0998336 | − | 0.241020i | ||||
\(499\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.754763 | − | 0.754763i | −0.754763 | − | 0.754763i | ||||
\(503\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(504\) | 1.27324 | − | 0.527393i | 1.27324 | − | 0.527393i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.144974 | + | 0.0600500i | 0.144974 | + | 0.0600500i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.22318 | − | 3.22318i | −3.22318 | − | 3.22318i | ||||
\(519\) | 0.0518052 | + | 0.0518052i | 0.0518052 | + | 0.0518052i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.431351 | + | 0.178671i | −0.431351 | + | 0.178671i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | −0.368770 | − | 0.152749i | −0.368770 | − | 0.152749i | ||||
\(525\) | −0.215784 | + | 0.215784i | −0.215784 | + | 0.215784i | ||||
\(526\) | 1.90211 | 1.90211 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.57819i | 1.57819i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0829870 | − | 0.200348i | −0.0829870 | − | 0.200348i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.00682 | + | 0.831254i | −2.00682 | + | 0.831254i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.431351 | − | 0.178671i | −0.431351 | − | 0.178671i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(542\) | 0.754763 | − | 0.754763i | 0.754763 | − | 0.754763i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.647354 | − | 0.329843i | −0.647354 | − | 0.329843i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.636514 | − | 1.53668i | 0.636514 | − | 1.53668i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.78616 | + | 1.78616i | 1.78616 | + | 1.78616i | ||||
\(554\) | 0.584336 | + | 1.41071i | 0.584336 | + | 1.41071i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 0.0553750 | + | 0.0229371i | 0.0553750 | + | 0.0229371i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.874883 | + | 2.11215i | −0.874883 | + | 2.11215i | ||||
\(567\) | −1.66507 | + | 0.689695i | −1.66507 | + | 0.689695i | ||||
\(568\) | 0.361140 | + | 0.871868i | 0.361140 | + | 0.871868i | ||||
\(569\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.581990 | + | 1.40505i | 0.581990 | + | 1.40505i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0849235 | − | 0.205023i | 0.0849235 | − | 0.205023i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.263440 | − | 0.263440i | 0.263440 | − | 0.263440i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −0.183900 | + | 1.16110i | −0.183900 | + | 1.16110i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.54093 | − | 1.05249i | −2.54093 | − | 1.05249i | ||||
\(582\) | − | 0.192769i | − | 0.192769i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | −0.0638112 | − | 0.154054i | −0.0638112 | − | 0.154054i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 0.120100i | − | 0.120100i | ||||||
\(592\) | −2.27692 | − | 0.943129i | −2.27692 | − | 0.943129i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.680668 | −0.680668 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −0.0436289 | + | 0.105329i | −0.0436289 | + | 0.105329i | ||||
\(601\) | −1.57547 | + | 0.652583i | −1.57547 | + | 0.652583i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.154744 | − | 0.0640971i | 0.154744 | − | 0.0640971i | ||||
\(607\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.331954 | + | 0.169139i | 0.331954 | + | 0.169139i | ||||
\(613\) | −1.17557 | −1.17557 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(614\) | 0.754763 | − | 0.754763i | 0.754763 | − | 0.754763i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.581990 | + | 1.40505i | −0.581990 | + | 1.40505i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(618\) | 0.303702 | − | 0.125798i | 0.303702 | − | 0.125798i | ||||
\(619\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.11215 | + | 0.874883i | −2.11215 | + | 0.874883i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000i | 1.00000i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.119505 | −0.119505 | ||||||||
\(629\) | −0.156434 | + | 1.98769i | −0.156434 | + | 1.98769i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(632\) | 0.871868 | + | 0.361140i | 0.871868 | + | 0.361140i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0453093 | + | 0.109386i | 0.0453093 | + | 0.109386i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.484827 | − | 1.17047i | −0.484827 | − | 1.17047i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.57547 | + | 0.652583i | 1.57547 | + | 0.652583i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.312869 | −0.312869 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(648\) | −0.476104 | + | 0.476104i | −0.476104 | + | 0.476104i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.763007 | − | 1.84206i | −0.763007 | − | 1.84206i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.874883 | − | 2.11215i | 0.874883 | − | 2.11215i | ||||
\(659\) | 0.618034i | 0.618034i | 0.951057 | + | 0.309017i | \(0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.34500 | − | 1.34500i | 1.34500 | − | 1.34500i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(662\) | 1.38197 | 1.38197 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.02749 | −1.02749 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.11215 | + | 0.874883i | 2.11215 | + | 0.874883i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.156776 | − | 0.156776i | −0.156776 | − | 0.156776i | ||||
\(673\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(674\) | 0.507083 | − | 0.210041i | 0.507083 | − | 0.210041i | ||||
\(675\) | 0.118621 | − | 0.286377i | 0.118621 | − | 0.286377i | ||||
\(676\) | 0.381966i | 0.381966i | ||||||||
\(677\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.03225 | −2.03225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.57547 | − | 0.652583i | −1.57547 | − | 0.652583i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.76389 | + | 1.55905i | −3.76389 | + | 1.55905i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(692\) | −0.0682464 | + | 0.164761i | −0.0682464 | + | 0.164761i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.170427 | − | 0.0705930i | −0.170427 | − | 0.0705930i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.686280 | − | 0.284267i | −0.686280 | − | 0.284267i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.260074 | + | 0.260074i | 0.260074 | + | 0.260074i | ||||
\(707\) | −0.675737 | − | 1.63137i | −0.675737 | − | 1.63137i | ||||
\(708\) | 0.0895986 | − | 0.0371129i | 0.0895986 | − | 0.0371129i | ||||
\(709\) | 0.744220 | − | 1.79671i | 0.744220 | − | 1.79671i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.17047 | − | 0.484827i | −1.17047 | − | 0.484827i | ||||
\(712\) | −0.603941 | + | 0.603941i | −0.603941 | + | 0.603941i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −0.162866 | + | 0.319642i | −0.162866 | + | 0.319642i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.275756 | − | 0.114222i | −0.275756 | − | 0.114222i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.652583 | + | 1.57547i | −0.652583 | + | 1.57547i | 0.156434 | + | 0.987688i | \(0.450000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.32621 | − | 3.20175i | −1.32621 | − | 3.20175i | ||||
\(722\) | −0.831254 | − | 0.831254i | −0.831254 | − | 0.831254i | ||||
\(723\) | −0.221232 | − | 0.221232i | −0.221232 | − | 0.221232i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.0705930 | + | 0.170427i | −0.0705930 | + | 0.170427i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.604772 | − | 0.604772i | 0.604772 | − | 0.604772i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.102210 | −0.102210 | ||||||||
\(733\) | 1.34500 | − | 1.34500i | 1.34500 | − | 1.34500i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.221232 | + | 0.221232i | 0.221232 | + | 0.221232i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.17230 | − | 1.72822i | 4.17230 | − | 1.72822i | ||||
\(743\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.37939 | 1.37939 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(752\) | − | 1.23607i | − | 1.23607i | ||||||
\(753\) | −0.0545243 | + | 0.131633i | −0.0545243 | + | 0.131633i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.162815 | + | 0.162815i | 0.162815 | + | 0.162815i | ||||
\(757\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(758\) | −0.210041 | − | 0.507083i | −0.210041 | − | 0.507083i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.540182 | 0.540182 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.09488 | 2.09488 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.144974 | − | 0.0600500i | −0.144974 | − | 0.0600500i | ||||
\(769\) | 1.90211i | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.34500 | − | 1.34500i | −1.34500 | − | 1.34500i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.453990 | − | 0.891007i | \(-0.650000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.701442 | + | 0.290547i | −0.701442 | + | 0.290547i | ||||
\(777\) | −0.232843 | + | 0.562133i | −0.232843 | + | 0.562133i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.43157 | + | 2.43157i | −2.43157 | + | 2.43157i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.192769i | 0.192769i | ||||||||
\(787\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(788\) | 0.270091 | − | 0.111875i | 0.270091 | − | 0.111875i | ||||
\(789\) | −0.0971629 | − | 0.234572i | −0.0971629 | − | 0.234572i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.684170 | + | 1.65173i | −0.684170 | + | 1.65173i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(800\) | −0.726543 | −0.726543 | ||||||||
\(801\) | 0.810786 | − | 0.810786i | 0.810786 | − | 0.810786i | ||||
\(802\) | 0.170427 | + | 0.0705930i | 0.170427 | + | 0.0705930i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.205023 | + | 0.205023i | 0.205023 | + | 0.205023i | ||||
\(808\) | −0.466469 | − | 0.466469i | −0.466469 | − | 0.466469i | ||||
\(809\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.497066 | − | 1.20002i | 0.497066 | − | 1.20002i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.131633 | − | 0.0545243i | −0.131633 | − | 0.0545243i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.0152180 | + | 0.193364i | −0.0152180 | + | 0.193364i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | −0.915497 | − | 0.915497i | −0.915497 | − | 0.915497i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.41559 | − | 3.41754i | −1.41559 | − | 3.41754i | ||||
\(827\) | −1.57547 | + | 0.652583i | −1.57547 | + | 0.652583i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.144123 | − | 0.144123i | 0.144123 | − | 0.144123i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.47879 | + | 1.26301i | 2.47879 | + | 1.26301i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.14662i | 1.14662i | ||||||||
\(847\) | 1.79671 | + | 0.744220i | 1.79671 | + | 0.744220i | ||||
\(848\) | 1.72654 | − | 1.72654i | 1.72654 | − | 1.72654i | ||||
\(849\) | 0.305165 | 0.305165 | ||||||||
\(850\) | 0.363271 | + | 1.11803i | 0.363271 | + | 1.11803i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.0550500 | + | 0.0550500i | −0.0550500 | + | 0.0550500i | ||||
\(853\) | 1.40505 | + | 0.581990i | 1.40505 | + | 0.581990i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(854\) | 3.89858i | 3.89858i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.470114 | + | 1.13496i | −0.470114 | + | 1.13496i | ||||
\(863\) | − | 0.618034i | − | 0.618034i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(864\) | 0.208065 | + | 0.0861835i | 0.208065 | + | 0.0861835i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.152583 | − | 0.0366318i | 0.152583 | − | 0.0366318i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.941679 | − | 0.390056i | 0.941679 | − | 0.390056i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(878\) | −0.831254 | + | 0.344317i | −0.831254 | + | 0.344317i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(882\) | 2.25562 | − | 2.25562i | 2.25562 | − | 2.25562i | ||||
\(883\) | −0.312869 | −0.312869 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(888\) | 0.227313i | 0.227313i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.125798 | + | 0.303702i | 0.125798 | + | 0.303702i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.874883 | + | 2.11215i | −0.874883 | + | 2.11215i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.372561 | 0.372561 | ||||||||
\(901\) | −1.76007 | − | 0.896802i | −1.76007 | − | 0.896802i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.70711 | − | 0.707107i | 1.70711 | − | 0.707107i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
1.00000 | \(0\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.626230 | + | 0.626230i | 0.626230 | + | 0.626230i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.652583 | − | 1.57547i | −0.652583 | − | 1.57547i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.156434 | − | 0.987688i | \(-0.450000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 1.06740i | − | 1.06740i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.03225 | 2.03225 | ||||||||
\(918\) | 0.0285901 | − | 0.363271i | 0.0285901 | − | 0.363271i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.131633 | − | 0.0545243i | −0.131633 | − | 0.0545243i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.763007 | + | 1.84206i | 0.763007 | + | 1.84206i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.22905 | + | 1.22905i | 1.22905 | + | 1.22905i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.84206 | + | 0.763007i | −1.84206 | + | 0.763007i | −0.891007 | + | 0.453990i | \(0.850000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.965451 | − | 0.399903i | 0.965451 | − | 0.399903i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(942\) | 0.0220864 | + | 0.0533212i | 0.0220864 | + | 0.0533212i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.707107 | − | 1.70711i | 0.707107 | − | 1.70711i | − | 1.00000i | \(-0.5\pi\) | |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(948\) | 0.0778525i | 0.0778525i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.40858 | + | 0.110858i | 1.40858 | + | 0.110858i | ||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | −1.60161 | + | 1.60161i | −1.60161 | + | 1.60161i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 0.726543i | − | 0.726543i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.11215 | − | 0.874883i | 2.11215 | − | 0.874883i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.291443 | − | 0.703605i | 0.291443 | − | 0.703605i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.221232 | − | 0.221232i | 0.221232 | − | 0.221232i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(968\) | 0.726543 | 0.726543 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(972\) | −0.160704 | − | 0.0665659i | −0.160704 | − | 0.0665659i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.344317 | − | 0.831254i | 0.344317 | − | 0.831254i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.806636 | + | 1.94739i | 0.806636 | + | 1.94739i | ||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.367799i | 0.367799i | ||||||||
\(983\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.305165 | −0.305165 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.652583 | − | 1.57547i | 0.652583 | − | 1.57547i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.0705930 | − | 0.170427i | −0.0705930 | − | 0.170427i | ||||
\(994\) | 2.09976 | + | 2.09976i | 2.09976 | + | 2.09976i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0324379 | − | 0.0783120i | −0.0324379 | − | 0.0783120i | ||||
\(997\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 0.618034i | − | 0.618034i |
(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 | 799.1.h.b.281.3 | ✓ | 16 | |
17.2 | even | 8 | inner | 799.1.h.b.563.3 | yes | 16 | |
47.46 | odd | 2 | CM | 799.1.h.b.281.3 | ✓ | 16 | |
799.563 | odd | 8 | inner | 799.1.h.b.563.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
799.1.h.b.281.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
799.1.h.b.281.3 | ✓ | 16 | 47.46 | odd | 2 | CM | |
799.1.h.b.563.3 | yes | 16 | 17.2 | even | 8 | inner | |
799.1.h.b.563.3 | yes | 16 | 799.563 | odd | 8 | inner |