Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [935,1,Mod(219,935)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(935, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 4, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("935.219");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 935 = 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 935.y (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: | \(0.466625786812\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{32})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{16}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
Embedding invariants
Embedding label | 219.4 | ||
Root | \(-0.195090 + 0.980785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 935.219 |
Dual form | 935.1.y.a.824.4 |
$q$-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 \(\left(\mathbb{Z}/935\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(562\) | \(596\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38704 | + | 1.38704i | 1.38704 | + | 1.38704i | 0.831470 | + | 0.555570i | \(0.187500\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(3\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(4\) | 2.84776i | 2.84776i | ||||||||
\(5\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.360480 | − | 0.149316i | −0.360480 | − | 0.149316i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(8\) | −2.56292 | + | 2.56292i | −2.56292 | + | 2.56292i | ||||
\(9\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(10\) | 1.81225 | + | 0.750661i | 1.81225 | + | 0.750661i | ||||
\(11\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.11114i | − | 1.11114i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(14\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.26197 | −4.26197 | ||||||||
\(17\) | −0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | ||||
\(18\) | −1.96157 | −1.96157 | ||||||||
\(19\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | 1.08979 | + | 2.63099i | 1.08979 | + | 2.63099i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.81225 | − | 0.750661i | 1.81225 | − | 0.750661i | ||||
\(23\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(26\) | 1.54120 | − | 1.54120i | 1.54120 | − | 1.54120i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.425215 | − | 1.02656i | 0.425215 | − | 1.02656i | ||||
\(29\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.541196 | + | 1.30656i | 0.541196 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(32\) | −3.34861 | − | 3.34861i | −3.34861 | − | 3.34861i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.382683 | − | 1.92388i | 0.382683 | − | 1.92388i | ||||
\(35\) | −0.390181 | −0.390181 | ||||||||
\(36\) | −2.01367 | − | 2.01367i | −2.01367 | − | 2.01367i | ||||
\(37\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.38704 | + | 3.34861i | −1.38704 | + | 3.34861i | ||||
\(41\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.38704 | + | 1.38704i | −1.38704 | + | 1.38704i | −0.555570 | + | 0.831470i | \(0.687500\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(44\) | 2.63099 | + | 1.08979i | 2.63099 | + | 1.08979i | ||||
\(45\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.599456 | − | 0.599456i | −0.599456 | − | 0.599456i | ||||
\(50\) | 1.96157 | 1.96157 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.16426 | 3.16426 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.00000i | − | 1.00000i | ||||||
\(56\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(62\) | −1.06159 | + | 2.56292i | −1.06159 | + | 2.56292i | ||||
\(63\) | 0.360480 | − | 0.149316i | 0.360480 | − | 0.149316i | ||||
\(64\) | − | 5.02734i | − | 5.02734i | ||||||
\(65\) | −0.425215 | − | 1.02656i | −0.425215 | − | 1.02656i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 2.36783 | − | 1.58213i | 2.36783 | − | 1.58213i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | ||||
\(71\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(72\) | − | 3.62451i | − | 3.62451i | ||||||
\(73\) | 1.53636 | − | 0.636379i | 1.53636 | − | 0.636379i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.275899 | + | 0.275899i | −0.275899 | + | 0.275899i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(80\) | −3.93755 | + | 1.63099i | −3.93755 | + | 1.63099i | ||||
\(81\) | − | 1.00000i | − | 1.00000i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.17588 | + | 1.17588i | 1.17588 | + | 1.17588i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(86\) | −3.84776 | −3.84776 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.38704 | + | 3.34861i | 1.38704 | + | 3.34861i | ||||
\(89\) | 0.765367i | 0.765367i | 0.923880 | + | 0.382683i | \(0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(90\) | −1.81225 | + | 0.750661i | −1.81225 | + | 0.750661i | ||||
\(91\) | −0.165911 | + | 0.400544i | −0.165911 | + | 0.400544i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(98\) | − | 1.66294i | − | 1.66294i | ||||||
\(99\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(100\) | 2.01367 | + | 2.01367i | 2.01367 | + | 2.01367i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 2.84776 | + | 2.84776i | 2.84776 | + | 2.84776i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.53636 | + | 0.636379i | −1.53636 | + | 0.636379i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(110\) | 1.38704 | − | 1.38704i | 1.38704 | − | 1.38704i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.53636 | + | 0.636379i | 1.53636 | + | 0.636379i | ||||
\(113\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.785695 | + | 0.785695i | 0.785695 | + | 0.785695i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0761205 | + | 0.382683i | 0.0761205 | + | 0.382683i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.72078 | + | 1.54120i | −3.72078 | + | 1.54120i | ||||
\(125\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(126\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(127\) | −0.785695 | + | 0.785695i | −0.785695 | + | 0.785695i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(128\) | 3.62451 | − | 3.62451i | 3.62451 | − | 3.62451i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.834089 | − | 2.01367i | 0.834089 | − | 2.01367i | ||||
\(131\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.55487 | + | 0.707107i | 3.55487 | + | 0.707107i | ||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(140\) | − | 1.11114i | − | 1.11114i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.574531 | − | 1.38704i | 0.574531 | − | 1.38704i | ||||
\(143\) | −1.02656 | − | 0.425215i | −1.02656 | − | 0.425215i | ||||
\(144\) | 3.01367 | − | 3.01367i | 3.01367 | − | 3.01367i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.01367 | + | 1.24830i | 3.01367 | + | 1.24830i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.980785 | + | 0.195090i | 0.980785 | + | 0.195090i | ||||
\(154\) | −0.765367 | −0.765367 | ||||||||
\(155\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.37517 | − | 1.81225i | −4.37517 | − | 1.81225i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.38704 | − | 1.38704i | 1.38704 | − | 1.38704i | ||||
\(163\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.26197i | 3.26197i | ||||||||
\(167\) | −0.149316 | − | 0.360480i | −0.149316 | − | 0.360480i | 0.831470 | − | 0.555570i | \(-0.187500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.234633 | −0.234633 | ||||||||
\(170\) | −0.382683 | − | 1.92388i | −0.382683 | − | 1.92388i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.94996 | − | 3.94996i | −3.94996 | − | 3.94996i | ||||
\(173\) | 0.149316 | + | 0.360480i | 0.149316 | + | 0.360480i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.360480 | + | 0.149316i | −0.360480 | + | 0.149316i | ||||
\(176\) | −1.63099 | + | 3.93755i | −1.63099 | + | 3.93755i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.06159 | + | 1.06159i | −1.06159 | + | 1.06159i | ||||
\(179\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(180\) | −2.63099 | − | 1.08979i | −2.63099 | − | 1.08979i | ||||
\(181\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | 0.382683 | + | 0.923880i | \(0.375000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(182\) | −0.785695 | + | 0.325446i | −0.785695 | + | 0.325446i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.765367i | − | 0.765367i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.750661 | − | 1.81225i | 0.750661 | − | 1.81225i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.555570 | − | 0.831470i | \(-0.312500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.70711 | − | 1.70711i | 1.70711 | − | 1.70711i | ||||
\(197\) | 1.53636 | + | 0.636379i | 1.53636 | + | 0.636379i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(198\) | −0.750661 | + | 1.81225i | −0.750661 | + | 1.81225i | ||||
\(199\) | −1.70711 | + | 0.707107i | −1.70711 | + | 0.707107i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(200\) | 3.62451i | 3.62451i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.73565i | 4.73565i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.01367 | − | 1.24830i | −3.01367 | − | 1.24830i | ||||
\(215\) | −0.750661 | + | 1.81225i | −0.750661 | + | 1.81225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.551799i | − | 0.551799i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.84776 | 2.84776 | ||||||||
\(221\) | −0.923880 | + | 0.617317i | −0.923880 | + | 0.617317i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(225\) | 1.00000i | 1.00000i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.636379 | − | 1.53636i | 0.636379 | − | 1.53636i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.02656 | − | 0.425215i | 1.02656 | − | 0.425215i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(234\) | 2.17958i | 2.17958i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.425215 | + | 0.636379i | −0.425215 | + | 0.636379i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(242\) | − | 1.96157i | − | 1.96157i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.783227 | − | 0.324423i | −0.783227 | − | 0.324423i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.73565 | − | 1.96157i | −4.73565 | − | 1.96157i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.81225 | − | 0.750661i | 1.81225 | − | 0.750661i | ||||
\(251\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(252\) | 0.425215 | + | 1.02656i | 0.425215 | + | 1.02656i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.17958 | −2.17958 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.02734 | 5.02734 | ||||||||
\(257\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.92340 | − | 1.21091i | 2.92340 | − | 1.21091i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.275899 | − | 0.275899i | 0.275899 | − | 0.275899i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 2.36783 | + | 3.54370i | 2.36783 | + | 3.54370i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.02656 | + | 0.425215i | −1.02656 | + | 0.425215i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.30656 | − | 0.541196i | −1.30656 | − | 0.541196i | ||||
\(280\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | ||||
\(281\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.425215 | + | 1.02656i | −0.425215 | + | 1.02656i | 0.555570 | + | 0.831470i | \(0.312500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(284\) | 2.01367 | − | 0.834089i | 2.01367 | − | 0.834089i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.834089 | − | 2.01367i | −0.834089 | − | 2.01367i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.73565 | 4.73565 | ||||||||
\(289\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.81225 | + | 4.37517i | 1.81225 | + | 4.37517i | ||||
\(293\) | − | 1.11114i | − | 1.11114i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.08979 | + | 1.63099i | 1.08979 | + | 1.63099i | ||||
\(307\) | 0.390181 | 0.390181 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(308\) | −0.785695 | − | 0.785695i | −0.785695 | − | 0.785695i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.77408i | 2.77408i | ||||||||
\(311\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | − | 1.00000i | \(-0.5\pi\) | |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.275899 | − | 0.275899i | 0.275899 | − | 0.275899i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.92388 | − | 4.64466i | −1.92388 | − | 4.64466i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.84776 | 2.84776 | ||||||||
\(325\) | −0.785695 | − | 0.785695i | −0.785695 | − | 0.785695i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | −0.382683 | + | 0.923880i | \(0.625000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(332\) | −3.34861 | + | 3.34861i | −3.34861 | + | 3.34861i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.636379 | + | 1.53636i | 0.636379 | + | 1.53636i | 0.831470 | + | 0.555570i | \(0.187500\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(338\) | −0.325446 | − | 0.325446i | −0.325446 | − | 0.325446i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.58213 | − | 2.36783i | 1.58213 | − | 2.36783i | ||||
\(341\) | 1.41421 | 1.41421 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.275899 | + | 0.666080i | 0.275899 | + | 0.666080i | ||||
\(344\) | − | 7.10973i | − | 7.10973i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(347\) | 1.81225 | + | 0.750661i | 1.81225 | + | 0.750661i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(350\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.37517 | + | 1.81225i | −4.37517 | + | 1.81225i | ||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | ||||
\(356\) | −2.17958 | −2.17958 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.50132 | −1.50132 | ||||||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | −1.38704 | − | 3.34861i | −1.38704 | − | 3.34861i | ||||
\(361\) | 1.00000i | 1.00000i | ||||||||
\(362\) | −2.56292 | + | 1.06159i | −2.56292 | + | 1.06159i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.14065 | − | 0.472474i | −1.14065 | − | 0.472474i | ||||
\(365\) | 1.17588 | − | 1.17588i | 1.17588 | − | 1.17588i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.96157 | −1.96157 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(374\) | −1.63099 | − | 1.08979i | −1.63099 | − | 1.08979i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | − | 1.00000i | \(-0.5\pi\) | |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.06159 | − | 1.06159i | 1.06159 | − | 1.06159i | ||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.149316 | + | 0.360480i | −0.149316 | + | 0.360480i | ||||
\(386\) | 3.55487 | − | 1.47247i | 3.55487 | − | 1.47247i | ||||
\(387\) | − | 1.96157i | − | 1.96157i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.07271 | 3.07271 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.24830 | + | 3.01367i | 1.24830 | + | 3.01367i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.63099 | + | 1.08979i | −2.63099 | + | 1.08979i | ||||
\(397\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(398\) | −3.34861 | − | 1.38704i | −3.34861 | − | 1.38704i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.01367 | + | 3.01367i | −3.01367 | + | 3.01367i | ||||
\(401\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.45177 | − | 0.601345i | 1.45177 | − | 0.601345i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.53636 | + | 0.636379i | 1.53636 | + | 0.636379i | ||||
\(416\) | −3.72078 | + | 3.72078i | −3.72078 | + | 3.72078i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.765367i | 0.765367i | 0.923880 | + | 0.382683i | \(0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.81225 | − | 4.37517i | −1.81225 | − | 4.37517i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.55487 | + | 1.47247i | −3.55487 | + | 1.47247i | ||||
\(431\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(434\) | 0.765367 | − | 0.765367i | 0.765367 | − | 0.765367i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(440\) | 2.56292 | + | 2.56292i | 2.56292 | + | 2.56292i | ||||
\(441\) | 0.847759 | 0.847759 | ||||||||
\(442\) | −2.13770 | − | 0.425215i | −2.13770 | − | 0.425215i | ||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.750661 | + | 1.81225i | −0.750661 | + | 1.81225i | ||||
\(449\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(450\) | −1.38704 | + | 1.38704i | −1.38704 | + | 1.38704i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.01367 | − | 1.24830i | 3.01367 | − | 1.24830i | ||||
\(455\) | 0.433546i | 0.433546i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.275899 | − | 0.275899i | −0.275899 | − | 0.275899i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(458\) | −2.77408 | −2.77408 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.01367 | + | 0.834089i | 2.01367 | + | 0.834089i | ||||
\(467\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(468\) | −2.23747 | + | 2.23747i | −2.23747 | + | 2.23747i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.750661 | + | 1.81225i | 0.750661 | + | 1.81225i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.08979 | + | 0.216773i | −1.08979 | + | 0.216773i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.01367 | − | 2.01367i | 2.01367 | − | 2.01367i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.636379 | − | 1.53636i | −0.636379 | − | 1.53636i | ||||
\(491\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(496\) | −2.30656 | − | 5.56854i | −2.30656 | − | 5.56854i | ||||
\(497\) | 0.298631i | 0.298631i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.707107 | − | 1.70711i | 0.707107 | − | 1.70711i | − | 1.00000i | \(-0.5\pi\) | |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(500\) | 2.63099 | + | 1.08979i | 2.63099 | + | 1.08979i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.96157 | − | 1.96157i | 1.96157 | − | 1.96157i | ||||
\(503\) | 1.81225 | + | 0.750661i | 1.81225 | + | 0.750661i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(504\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.23747 | − | 2.23747i | −2.23747 | − | 2.23747i | ||||
\(509\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.648847 | −0.648847 | ||||||||
\(512\) | 3.34861 | + | 3.34861i | 3.34861 | + | 3.34861i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.72078 | + | 1.54120i | 3.72078 | + | 1.54120i | ||||
\(521\) | 0.541196 | − | 1.30656i | 0.541196 | − | 1.30656i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.66294i | 1.66294i | 0.555570 | + | 0.831470i | \(0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.765367 | 0.765367 | ||||||||
\(527\) | 0.785695 | − | 1.17588i | 0.785695 | − | 1.17588i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.17588 | + | 1.17588i | −1.17588 | + | 1.17588i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.38704 | − | 3.34861i | 1.38704 | − | 3.34861i | ||||
\(539\) | −0.783227 | + | 0.324423i | −0.783227 | + | 0.324423i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.923880 | + | 4.64466i | −0.923880 | + | 4.64466i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.425215 | − | 1.02656i | −0.425215 | − | 1.02656i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.555570 | − | 0.831470i | \(-0.312500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.750661 | − | 1.81225i | 0.750661 | − | 1.81225i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.01367 | − | 0.834089i | −2.01367 | − | 0.834089i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.390181i | 0.390181i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(558\) | −1.06159 | − | 2.56292i | −1.06159 | − | 2.56292i | ||||
\(559\) | 1.54120 | + | 1.54120i | 1.54120 | + | 1.54120i | ||||
\(560\) | 1.66294 | 1.66294 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.785695 | + | 0.785695i | 0.785695 | + | 0.785695i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.01367 | + | 0.834089i | −2.01367 | + | 0.834089i | ||||
\(567\) | −0.149316 | + | 0.360480i | −0.149316 | + | 0.360480i | ||||
\(568\) | 2.56292 | + | 1.06159i | 2.56292 | + | 1.06159i | ||||
\(569\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(572\) | 1.21091 | − | 2.92340i | 1.21091 | − | 2.92340i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.55487 | + | 3.55487i | 3.55487 | + | 3.55487i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −1.81225 | + | 0.750661i | −1.81225 | + | 0.750661i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.248303 | − | 0.599456i | −0.248303 | − | 0.599456i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.30656 | + | 5.56854i | −2.30656 | + | 5.56854i | ||||
\(585\) | 1.02656 | + | 0.425215i | 1.02656 | + | 0.425215i | ||||
\(586\) | 1.54120 | − | 1.54120i | 1.54120 | − | 1.54120i | ||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.38704 | + | 1.38704i | 1.38704 | + | 1.38704i | 0.831470 | + | 0.555570i | \(0.187500\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.216773 | + | 0.324423i | 0.216773 | + | 0.324423i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.84776i | − | 1.84776i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(602\) | 1.38704 | + | 0.574531i | 1.38704 | + | 0.574531i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.53636 | − | 0.636379i | 1.53636 | − | 0.636379i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.555570 | + | 2.79304i | −0.555570 | + | 2.79304i | ||||
\(613\) | −1.66294 | −1.66294 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(614\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.41421i | − | 1.41421i | ||||||
\(617\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(620\) | −2.84776 | + | 2.84776i | −2.84776 | + | 2.84776i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.38704 | + | 0.574531i | 1.38704 | + | 0.574531i | ||||
\(623\) | 0.114281 | − | 0.275899i | 0.114281 | − | 0.275899i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 1.00000i | − | 1.00000i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.765367 | 0.765367 | ||||||||
\(631\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.425215 | + | 1.02656i | −0.425215 | + | 1.02656i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.666080 | + | 0.666080i | −0.666080 | + | 0.666080i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(640\) | 1.96157 | − | 4.73565i | 1.96157 | − | 4.73565i | ||||
\(641\) | −1.30656 | + | 0.541196i | −1.30656 | + | 0.541196i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 2.56292 | + | 2.56292i | 2.56292 | + | 2.56292i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 2.17958i | − | 2.17958i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.636379 | + | 1.53636i | −0.636379 | + | 1.53636i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(662\) | −3.62451 | −3.62451 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.02734 | −6.02734 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.02656 | − | 0.425215i | 1.02656 | − | 0.425215i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.81225 | + | 0.750661i | 1.81225 | + | 0.750661i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(674\) | −1.24830 | + | 3.01367i | −1.24830 | + | 3.01367i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 0.668179i | − | 0.668179i | ||||||
\(677\) | −0.750661 | − | 1.81225i | −0.750661 | − | 1.81225i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
−0.195090 | − | 0.980785i | \(-0.562500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.55487 | − | 0.707107i | 3.55487 | − | 0.707107i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.96157 | + | 1.96157i | 1.96157 | + | 1.96157i | ||||
\(683\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.91153 | − | 5.91153i | 5.91153 | − | 5.91153i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(692\) | −1.02656 | + | 0.425215i | −1.02656 | + | 0.425215i | ||||
\(693\) | − | 0.390181i | − | 0.390181i | ||||||
\(694\) | 1.47247 | + | 3.55487i | 1.47247 | + | 3.55487i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.425215 | − | 1.02656i | −0.425215 | − | 1.02656i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.64466 | − | 1.92388i | −4.64466 | − | 1.92388i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(710\) | − | 1.50132i | − | 1.50132i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.96157 | − | 1.96157i | −1.96157 | − | 1.96157i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.11114 | −1.11114 | ||||||||
\(716\) | −1.54120 | − | 1.54120i | −1.54120 | − | 1.54120i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(720\) | 1.63099 | − | 3.93755i | 1.63099 | − | 3.93755i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.38704 | + | 1.38704i | −1.38704 | + | 1.38704i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.72078 | − | 1.54120i | −3.72078 | − | 1.54120i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | −0.601345 | − | 1.45177i | −0.601345 | − | 1.45177i | ||||
\(729\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(730\) | 3.26197 | 3.26197 | ||||||||
\(731\) | 1.92388 | + | 0.382683i | 1.92388 | + | 0.382683i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.17588 | − | 1.17588i | −1.17588 | − | 1.17588i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.195090 | − | 0.980785i | \(-0.562500\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.02656 | + | 0.425215i | −1.02656 | + | 0.425215i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.72078 | − | 2.72078i | −2.72078 | − | 2.72078i | ||||
\(747\) | −1.66294 | −1.66294 | ||||||||
\(748\) | −0.555570 | − | 2.79304i | −0.555570 | − | 2.79304i | ||||
\(749\) | 0.648847 | 0.648847 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | 1.38704 | + | 0.574531i | 1.38704 | + | 0.574531i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.17958 | 2.17958 | ||||||||
\(765\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | −0.707107 | + | 0.292893i | −0.707107 | + | 0.292893i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.16087 | + | 2.13770i | 5.16087 | + | 2.13770i | ||||
\(773\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(774\) | 2.72078 | − | 2.72078i | 2.72078 | − | 2.72078i | ||||
\(775\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.765367 | −0.765367 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.55487 | + | 2.55487i | 2.55487 | + | 2.55487i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.81225 | − | 0.750661i | 1.81225 | − | 0.750661i | 0.831470 | − | 0.555570i | \(-0.187500\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(788\) | −1.81225 | + | 4.37517i | −1.81225 | + | 4.37517i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.34861 | − | 1.38704i | −3.34861 | − | 1.38704i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.01367 | − | 4.86143i | −2.01367 | − | 4.86143i | ||||
\(797\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.73565 | −4.73565 | ||||||||
\(801\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.66294i | − | 1.66294i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.84776 | + | 1.17958i | 2.84776 | + | 1.17958i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(810\) | 0.750661 | − | 1.81225i | 0.750661 | − | 1.81225i | ||||
\(811\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.165911 | − | 0.400544i | −0.165911 | − | 0.400544i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.149316 | + | 0.360480i | −0.149316 | + | 0.360480i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.765367i | − | 0.765367i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(830\) | 1.24830 | + | 3.01367i | 1.24830 | + | 3.01367i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.58608 | −5.58608 | ||||||||
\(833\) | −0.165390 | + | 0.831470i | −0.165390 | + | 0.831470i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.275899 | − | 0.275899i | −0.275899 | − | 0.275899i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | 1.00000i | \(0.5\pi\) | ||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(842\) | −1.06159 | + | 1.06159i | −1.06159 | + | 1.06159i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.216773 | + | 0.0897902i | −0.216773 | + | 0.0897902i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.149316 | + | 0.360480i | 0.149316 | + | 0.360480i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.08979 | − | 1.63099i | −1.08979 | − | 1.63099i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.750661 | − | 1.81225i | −0.750661 | − | 1.81225i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
−0.195090 | − | 0.980785i | \(-0.562500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.30656 | − | 5.56854i | 2.30656 | − | 5.56854i | ||||
\(857\) | 0.360480 | + | 0.149316i | 0.360480 | + | 0.149316i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(860\) | −5.16087 | − | 2.13770i | −5.16087 | − | 2.13770i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.275899 | + | 0.275899i | 0.275899 | + | 0.275899i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.57139 | 1.57139 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.275899 | + | 0.275899i | −0.275899 | + | 0.275899i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.53636 | − | 0.636379i | −1.53636 | − | 0.636379i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.26197i | 4.26197i | ||||||||
\(881\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | 1.00000 | \(0\) | ||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(882\) | 1.17588 | + | 1.17588i | 1.17588 | + | 1.17588i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | −1.75797 | − | 2.63099i | −1.75797 | − | 2.63099i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.636379 | − | 1.53636i | −0.636379 | − | 1.53636i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.195090 | − | 0.980785i | \(-0.437500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.400544 | − | 0.165911i | 0.400544 | − | 0.165911i | ||||
\(890\) | −0.574531 | + | 1.38704i | −0.574531 | + | 1.38704i | ||||
\(891\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(896\) | −1.84776 | + | 0.765367i | −1.84776 | + | 0.765367i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.06159 | + | 2.56292i | 1.06159 | + | 2.56292i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.84776 | −2.84776 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.41421i | 1.41421i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(908\) | 4.37517 | + | 1.81225i | 4.37517 | + | 1.81225i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.601345 | + | 0.601345i | −0.601345 | + | 0.601345i | ||||
\(911\) | −1.30656 | − | 0.541196i | −1.30656 | − | 0.541196i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.53636 | − | 0.636379i | 1.53636 | − | 0.636379i | ||||
\(914\) | − | 0.765367i | − | 0.765367i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.84776 | − | 2.84776i | −2.84776 | − | 2.84776i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.785695 | + | 0.325446i | −0.785695 | + | 0.325446i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.707107 | − | 1.70711i | 0.707107 | − | 1.70711i | − | 1.00000i | \(-0.5\pi\) | |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.21091 | + | 2.92340i | 1.21091 | + | 2.92340i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.831470 | + | 0.555570i | −0.831470 | + | 0.555570i | ||||
\(936\) | −4.02734 | −4.02734 | ||||||||
\(937\) | 0.275899 | + | 0.275899i | 0.275899 | + | 0.275899i | 0.831470 | − | 0.555570i | \(-0.187500\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.47247 | + | 3.55487i | −1.47247 | + | 3.55487i | ||||
\(947\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.17588 | − | 0.785695i | −1.17588 | − | 0.785695i | ||||
\(953\) | 0.390181 | 0.390181 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.636379 | − | 1.53636i | 0.636379 | − | 1.53636i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.96157i | − | 1.96157i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.275899 | + | 0.275899i | 0.275899 | + | 0.275899i | 0.831470 | − | 0.555570i | \(-0.187500\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(968\) | 3.62451 | 3.62451 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(980\) | 0.923880 | − | 2.23044i | 0.923880 | − | 2.23044i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.66294 | 1.66294 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1.96157i | 1.96157i | ||||||||
\(991\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(992\) | 2.56292 | − | 6.18743i | 2.56292 | − | 6.18743i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.414214 | + | 0.414214i | −0.414214 | + | 0.414214i | ||||
\(995\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.425215 | + | 1.02656i | −0.425215 | + | 1.02656i | 0.555570 | + | 0.831470i | \(0.312500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(998\) | 3.34861 | − | 1.38704i | 3.34861 | − | 1.38704i | ||||
\(999\) | 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 | 935.1.y.a.219.4 | yes | 16 | |
5.4 | even | 2 | inner | 935.1.y.a.219.1 | ✓ | 16 | |
11.10 | odd | 2 | inner | 935.1.y.a.219.1 | ✓ | 16 | |
17.8 | even | 8 | inner | 935.1.y.a.824.4 | yes | 16 | |
55.54 | odd | 2 | CM | 935.1.y.a.219.4 | yes | 16 | |
85.59 | even | 8 | inner | 935.1.y.a.824.1 | yes | 16 | |
187.76 | odd | 8 | inner | 935.1.y.a.824.1 | yes | 16 | |
935.824 | odd | 8 | inner | 935.1.y.a.824.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
935.1.y.a.219.1 | ✓ | 16 | 5.4 | even | 2 | inner | |
935.1.y.a.219.1 | ✓ | 16 | 11.10 | odd | 2 | inner | |
935.1.y.a.219.4 | yes | 16 | 1.1 | even | 1 | trivial | |
935.1.y.a.219.4 | yes | 16 | 55.54 | odd | 2 | CM | |
935.1.y.a.824.1 | yes | 16 | 85.59 | even | 8 | inner | |
935.1.y.a.824.1 | yes | 16 | 187.76 | odd | 8 | inner | |
935.1.y.a.824.4 | yes | 16 | 17.8 | even | 8 | inner | |
935.1.y.a.824.4 | yes | 16 | 935.824 | odd | 8 | inner |