Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,3,Mod(307,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.307");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.g (of order \(4\), degree \(2\), 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: | \(12.2616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.343 |
Dual form | 450.3.g.d.307.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.00000 | + | 8.00000i | −1.14286 | + | 1.14286i | −0.154932 | + | 0.987925i | \(0.549516\pi\) |
−0.987925 | + | 0.154932i | \(0.950484\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 0.363636 | 0.181818 | − | 0.983332i | \(-0.441802\pi\) | ||||
0.181818 | + | 0.983332i | \(0.441802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 3.00000i | 0.230769 | + | 0.230769i | 0.813014 | − | 0.582245i | \(-0.197825\pi\) |
−0.582245 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(14\) | 16.0000i | 1.14286i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −19.0000 | + | 19.0000i | −1.11765 | + | 1.11765i | −0.125561 | + | 0.992086i | \(0.540073\pi\) |
−0.992086 | + | 0.125561i | \(0.959927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000i | 0.421053i | 0.977588 | + | 0.210526i | \(0.0675178\pi\) | ||||
−0.977588 | + | 0.210526i | \(0.932482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | − | 4.00000i | 0.181818 | − | 0.181818i | ||||
\(23\) | 20.0000 | + | 20.0000i | 0.869565 | + | 0.869565i | 0.992424 | − | 0.122859i | \(-0.0392063\pi\) |
−0.122859 | + | 0.992424i | \(0.539206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00000 | 0.230769 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.0000 | + | 16.0000i | 0.571429 | + | 0.571429i | ||||
\(29\) | 38.0000i | 1.31034i | 0.755479 | + | 0.655172i | \(0.227404\pi\) | ||||
−0.755479 | + | 0.655172i | \(0.772596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −44.0000 | −1.41935 | −0.709677 | − | 0.704527i | \(-0.751159\pi\) | ||||
−0.709677 | + | 0.704527i | \(0.751159\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 38.0000i | 1.11765i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.0810811 | − | 0.0810811i | −0.665403 | − | 0.746484i | \(-0.731740\pi\) |
0.746484 | + | 0.665403i | \(0.231740\pi\) | |||||||
\(38\) | 8.00000 | + | 8.00000i | 0.210526 | + | 0.210526i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.0000 | 1.70732 | 0.853659 | − | 0.520833i | \(-0.174379\pi\) | ||||
0.853659 | + | 0.520833i | \(0.174379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −36.0000 | − | 36.0000i | −0.837209 | − | 0.837209i | 0.151281 | − | 0.988491i | \(-0.451660\pi\) |
−0.988491 | + | 0.151281i | \(0.951660\pi\) | |||||||
\(44\) | − | 8.00000i | − | 0.181818i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 40.0000 | 0.869565 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 79.0000i | − | 1.61224i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.00000 | − | 6.00000i | 0.115385 | − | 0.115385i | ||||
\(53\) | −17.0000 | − | 17.0000i | −0.320755 | − | 0.320755i | 0.528302 | − | 0.849057i | \(-0.322829\pi\) |
−0.849057 | + | 0.528302i | \(0.822829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 32.0000 | 0.571429 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 38.0000 | + | 38.0000i | 0.655172 | + | 0.655172i | ||||
\(59\) | 92.0000i | 1.55932i | 0.626202 | + | 0.779661i | \(0.284609\pi\) | ||||
−0.626202 | + | 0.779661i | \(0.715391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.0000 | 1.18033 | 0.590164 | − | 0.807283i | \(-0.299063\pi\) | ||||
0.590164 | + | 0.807283i | \(0.299063\pi\) | |||||||
\(62\) | −44.0000 | + | 44.0000i | −0.709677 | + | 0.709677i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44.0000 | + | 44.0000i | −0.656716 | + | 0.656716i | −0.954602 | − | 0.297885i | \(-0.903719\pi\) |
0.297885 | + | 0.954602i | \(0.403719\pi\) | |||||||
\(68\) | 38.0000 | + | 38.0000i | 0.558824 | + | 0.558824i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −88.0000 | −1.23944 | −0.619718 | − | 0.784824i | \(-0.712753\pi\) | ||||
−0.619718 | + | 0.784824i | \(0.712753\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55.0000 | − | 55.0000i | −0.753425 | − | 0.753425i | 0.221692 | − | 0.975117i | \(-0.428842\pi\) |
−0.975117 | + | 0.221692i | \(0.928842\pi\) | |||||||
\(74\) | − | 6.00000i | − | 0.0810811i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.0000 | 0.210526 | ||||||||
\(77\) | −32.0000 | + | 32.0000i | −0.415584 | + | 0.415584i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.0000i | − | 0.151899i | −0.997112 | − | 0.0759494i | \(-0.975801\pi\) | ||
0.997112 | − | 0.0759494i | \(-0.0241987\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 70.0000 | − | 70.0000i | 0.853659 | − | 0.853659i | ||||
\(83\) | 24.0000 | + | 24.0000i | 0.289157 | + | 0.289157i | 0.836747 | − | 0.547590i | \(-0.184455\pi\) |
−0.547590 | + | 0.836747i | \(0.684455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −72.0000 | −0.837209 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.00000 | − | 8.00000i | −0.0909091 | − | 0.0909091i | ||||
\(89\) | − | 26.0000i | − | 0.292135i | −0.989275 | − | 0.146067i | \(-0.953338\pi\) | ||
0.989275 | − | 0.146067i | \(-0.0466616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48.0000 | −0.527473 | ||||||||
\(92\) | 40.0000 | − | 40.0000i | 0.434783 | − | 0.434783i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 57.0000 | − | 57.0000i | 0.587629 | − | 0.587629i | −0.349360 | − | 0.936989i | \(-0.613601\pi\) |
0.936989 | + | 0.349360i | \(0.113601\pi\) | |||||||
\(98\) | −79.0000 | − | 79.0000i | −0.806122 | − | 0.806122i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 56.0000 | 0.554455 | 0.277228 | − | 0.960804i | \(-0.410584\pi\) | ||||
0.277228 | + | 0.960804i | \(0.410584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 4.00000i | −0.0388350 | − | 0.0388350i | 0.687423 | − | 0.726258i | \(-0.258742\pi\) |
−0.726258 | + | 0.687423i | \(0.758742\pi\) | |||||||
\(104\) | − | 12.0000i | − | 0.115385i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −34.0000 | −0.320755 | ||||||||
\(107\) | 68.0000 | − | 68.0000i | 0.635514 | − | 0.635514i | −0.313932 | − | 0.949446i | \(-0.601646\pi\) |
0.949446 | + | 0.313932i | \(0.101646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46.0000i | 0.422018i | 0.977484 | + | 0.211009i | \(0.0676750\pi\) | ||||
−0.977484 | + | 0.211009i | \(0.932325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 32.0000 | − | 32.0000i | 0.285714 | − | 0.285714i | ||||
\(113\) | −53.0000 | − | 53.0000i | −0.469027 | − | 0.469027i | 0.432573 | − | 0.901599i | \(-0.357606\pi\) |
−0.901599 | + | 0.432573i | \(0.857606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 76.0000 | 0.655172 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 92.0000 | + | 92.0000i | 0.779661 | + | 0.779661i | ||||
\(119\) | − | 304.000i | − | 2.55462i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −105.000 | −0.867769 | ||||||||
\(122\) | 72.0000 | − | 72.0000i | 0.590164 | − | 0.590164i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 88.0000i | 0.709677i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −68.0000 | + | 68.0000i | −0.535433 | + | 0.535433i | −0.922184 | − | 0.386751i | \(-0.873597\pi\) |
0.386751 | + | 0.922184i | \(0.373597\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −44.0000 | −0.335878 | −0.167939 | − | 0.985797i | \(-0.553711\pi\) | ||||
−0.167939 | + | 0.985797i | \(0.553711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −64.0000 | − | 64.0000i | −0.481203 | − | 0.481203i | ||||
\(134\) | 88.0000i | 0.656716i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 76.0000 | 0.558824 | ||||||||
\(137\) | 69.0000 | − | 69.0000i | 0.503650 | − | 0.503650i | −0.408920 | − | 0.912570i | \(-0.634095\pi\) |
0.912570 | + | 0.408920i | \(0.134095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 80.0000i | − | 0.575540i | −0.957700 | − | 0.287770i | \(-0.907086\pi\) | ||
0.957700 | − | 0.287770i | \(-0.0929138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −88.0000 | + | 88.0000i | −0.619718 | + | 0.619718i | ||||
\(143\) | 12.0000 | + | 12.0000i | 0.0839161 | + | 0.0839161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −110.000 | −0.753425 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.00000 | − | 6.00000i | −0.0405405 | − | 0.0405405i | ||||
\(149\) | − | 168.000i | − | 1.12752i | −0.825940 | − | 0.563758i | \(-0.809355\pi\) | ||
0.825940 | − | 0.563758i | \(-0.190645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.0264901 | 0.0132450 | − | 0.999912i | \(-0.495784\pi\) | ||||
0.0132450 | + | 0.999912i | \(0.495784\pi\) | |||||||
\(152\) | 16.0000 | − | 16.0000i | 0.105263 | − | 0.105263i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 64.0000i | 0.415584i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −99.0000 | + | 99.0000i | −0.630573 | + | 0.630573i | −0.948212 | − | 0.317639i | \(-0.897110\pi\) |
0.317639 | + | 0.948212i | \(0.397110\pi\) | |||||||
\(158\) | −12.0000 | − | 12.0000i | −0.0759494 | − | 0.0759494i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −320.000 | −1.98758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 160.000 | + | 160.000i | 0.981595 | + | 0.981595i | 0.999834 | − | 0.0182386i | \(-0.00580584\pi\) |
−0.0182386 | + | 0.999834i | \(0.505806\pi\) | |||||||
\(164\) | − | 140.000i | − | 0.853659i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 48.0000 | 0.289157 | ||||||||
\(167\) | −56.0000 | + | 56.0000i | −0.335329 | + | 0.335329i | −0.854606 | − | 0.519277i | \(-0.826201\pi\) |
0.519277 | + | 0.854606i | \(0.326201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 151.000i | − | 0.893491i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −72.0000 | + | 72.0000i | −0.418605 | + | 0.418605i | ||||
\(173\) | 41.0000 | + | 41.0000i | 0.236994 | + | 0.236994i | 0.815604 | − | 0.578610i | \(-0.196405\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.0000 | −0.0909091 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −26.0000 | − | 26.0000i | −0.146067 | − | 0.146067i | ||||
\(179\) | 172.000i | 0.960894i | 0.877024 | + | 0.480447i | \(0.159526\pi\) | ||||
−0.877024 | + | 0.480447i | \(0.840474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 62.0000 | 0.342541 | 0.171271 | − | 0.985224i | \(-0.445213\pi\) | ||||
0.171271 | + | 0.985224i | \(0.445213\pi\) | |||||||
\(182\) | −48.0000 | + | 48.0000i | −0.263736 | + | 0.263736i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 80.0000i | − | 0.434783i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −76.0000 | + | 76.0000i | −0.406417 | + | 0.406417i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 248.000 | 1.29843 | 0.649215 | − | 0.760605i | \(-0.275098\pi\) | ||||
0.649215 | + | 0.760605i | \(0.275098\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −135.000 | − | 135.000i | −0.699482 | − | 0.699482i | 0.264817 | − | 0.964299i | \(-0.414688\pi\) |
−0.964299 | + | 0.264817i | \(0.914688\pi\) | |||||||
\(194\) | − | 114.000i | − | 0.587629i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −158.000 | −0.806122 | ||||||||
\(197\) | 153.000 | − | 153.000i | 0.776650 | − | 0.776650i | −0.202610 | − | 0.979260i | \(-0.564942\pi\) |
0.979260 | + | 0.202610i | \(0.0649423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 252.000i | 1.26633i | 0.774016 | + | 0.633166i | \(0.218245\pi\) | ||||
−0.774016 | + | 0.633166i | \(0.781755\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 56.0000 | − | 56.0000i | 0.277228 | − | 0.277228i | ||||
\(203\) | −304.000 | − | 304.000i | −1.49754 | − | 1.49754i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.0388350 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.0000 | − | 12.0000i | −0.0576923 | − | 0.0576923i | ||||
\(209\) | 32.0000i | 0.153110i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −64.0000 | −0.303318 | −0.151659 | − | 0.988433i | \(-0.548461\pi\) | ||||
−0.151659 | + | 0.988433i | \(0.548461\pi\) | |||||||
\(212\) | −34.0000 | + | 34.0000i | −0.160377 | + | 0.160377i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 136.000i | − | 0.635514i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 352.000 | − | 352.000i | 1.62212 | − | 1.62212i | ||||
\(218\) | 46.0000 | + | 46.0000i | 0.211009 | + | 0.211009i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −114.000 | −0.515837 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 228.000 | + | 228.000i | 1.02242 | + | 1.02242i | 0.999743 | + | 0.0226787i | \(0.00721948\pi\) |
0.0226787 | + | 0.999743i | \(0.492781\pi\) | |||||||
\(224\) | − | 64.0000i | − | 0.285714i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −106.000 | −0.469027 | ||||||||
\(227\) | 100.000 | − | 100.000i | 0.440529 | − | 0.440529i | −0.451661 | − | 0.892190i | \(-0.649168\pi\) |
0.892190 | + | 0.451661i | \(0.149168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 312.000i | 1.36245i | 0.732076 | + | 0.681223i | \(0.238551\pi\) | ||||
−0.732076 | + | 0.681223i | \(0.761449\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 76.0000 | − | 76.0000i | 0.327586 | − | 0.327586i | ||||
\(233\) | 93.0000 | + | 93.0000i | 0.399142 | + | 0.399142i | 0.877930 | − | 0.478789i | \(-0.158924\pi\) |
−0.478789 | + | 0.877930i | \(0.658924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 184.000 | 0.779661 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −304.000 | − | 304.000i | −1.27731 | − | 1.27731i | ||||
\(239\) | 96.0000i | 0.401674i | 0.979625 | + | 0.200837i | \(0.0643661\pi\) | ||||
−0.979625 | + | 0.200837i | \(0.935634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 160.000 | 0.663900 | 0.331950 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331950 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(242\) | −105.000 | + | 105.000i | −0.433884 | + | 0.433884i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 144.000i | − | 0.590164i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | + | 24.0000i | −0.0971660 | + | 0.0971660i | ||||
\(248\) | 88.0000 | + | 88.0000i | 0.354839 | + | 0.354839i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.0478088 | 0.0239044 | − | 0.999714i | \(-0.492390\pi\) | ||||
0.0239044 | + | 0.999714i | \(0.492390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 80.0000 | + | 80.0000i | 0.316206 | + | 0.316206i | ||||
\(254\) | 136.000i | 0.535433i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −101.000 | + | 101.000i | −0.392996 | + | 0.392996i | −0.875754 | − | 0.482758i | \(-0.839635\pi\) |
0.482758 | + | 0.875754i | \(0.339635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48.0000i | 0.185328i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −44.0000 | + | 44.0000i | −0.167939 | + | 0.167939i | ||||
\(263\) | 208.000 | + | 208.000i | 0.790875 | + | 0.790875i | 0.981636 | − | 0.190762i | \(-0.0610958\pi\) |
−0.190762 | + | 0.981636i | \(0.561096\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −128.000 | −0.481203 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 88.0000 | + | 88.0000i | 0.328358 | + | 0.328358i | ||||
\(269\) | 296.000i | 1.10037i | 0.835042 | + | 0.550186i | \(0.185443\pi\) | ||||
−0.835042 | + | 0.550186i | \(0.814557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108.000 | 0.398524 | 0.199262 | − | 0.979946i | \(-0.436146\pi\) | ||||
0.199262 | + | 0.979946i | \(0.436146\pi\) | |||||||
\(272\) | 76.0000 | − | 76.0000i | 0.279412 | − | 0.279412i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 138.000i | − | 0.503650i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 243.000 | − | 243.000i | 0.877256 | − | 0.877256i | −0.115994 | − | 0.993250i | \(-0.537005\pi\) |
0.993250 | + | 0.115994i | \(0.0370052\pi\) | |||||||
\(278\) | −80.0000 | − | 80.0000i | −0.287770 | − | 0.287770i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 378.000 | 1.34520 | 0.672598 | − | 0.740008i | \(-0.265178\pi\) | ||||
0.672598 | + | 0.740008i | \(0.265178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −92.0000 | − | 92.0000i | −0.325088 | − | 0.325088i | 0.525627 | − | 0.850715i | \(-0.323831\pi\) |
−0.850715 | + | 0.525627i | \(0.823831\pi\) | |||||||
\(284\) | 176.000i | 0.619718i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0000 | 0.0839161 | ||||||||
\(287\) | −560.000 | + | 560.000i | −1.95122 | + | 1.95122i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 433.000i | − | 1.49827i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −110.000 | + | 110.000i | −0.376712 | + | 0.376712i | ||||
\(293\) | 279.000 | + | 279.000i | 0.952218 | + | 0.952218i | 0.998909 | − | 0.0466910i | \(-0.0148676\pi\) |
−0.0466910 | + | 0.998909i | \(0.514868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.0000 | −0.0405405 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −168.000 | − | 168.000i | −0.563758 | − | 0.563758i | ||||
\(299\) | 120.000i | 0.401338i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 576.000 | 1.91362 | ||||||||
\(302\) | 4.00000 | − | 4.00000i | 0.0132450 | − | 0.0132450i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 32.0000i | − | 0.105263i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −216.000 | + | 216.000i | −0.703583 | + | 0.703583i | −0.965178 | − | 0.261595i | \(-0.915752\pi\) |
0.261595 | + | 0.965178i | \(0.415752\pi\) | |||||||
\(308\) | 64.0000 | + | 64.0000i | 0.207792 | + | 0.207792i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 272.000 | 0.874598 | 0.437299 | − | 0.899316i | \(-0.355935\pi\) | ||||
0.437299 | + | 0.899316i | \(0.355935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0000 | − | 15.0000i | −0.0479233 | − | 0.0479233i | 0.682739 | − | 0.730662i | \(-0.260789\pi\) |
−0.730662 | + | 0.682739i | \(0.760789\pi\) | |||||||
\(314\) | 198.000i | 0.630573i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.0000 | −0.0759494 | ||||||||
\(317\) | −87.0000 | + | 87.0000i | −0.274448 | + | 0.274448i | −0.830888 | − | 0.556440i | \(-0.812167\pi\) |
0.556440 | + | 0.830888i | \(0.312167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 152.000i | 0.476489i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −320.000 | + | 320.000i | −0.993789 | + | 0.993789i | ||||
\(323\) | −152.000 | − | 152.000i | −0.470588 | − | 0.470588i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 320.000 | 0.981595 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −140.000 | − | 140.000i | −0.426829 | − | 0.426829i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −584.000 | −1.76435 | −0.882175 | − | 0.470921i | \(-0.843922\pi\) | ||||
−0.882175 | + | 0.470921i | \(0.843922\pi\) | |||||||
\(332\) | 48.0000 | − | 48.0000i | 0.144578 | − | 0.144578i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 112.000i | 0.335329i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 129.000 | − | 129.000i | 0.382789 | − | 0.382789i | −0.489317 | − | 0.872106i | \(-0.662754\pi\) |
0.872106 | + | 0.489317i | \(0.162754\pi\) | |||||||
\(338\) | −151.000 | − | 151.000i | −0.446746 | − | 0.446746i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −176.000 | −0.516129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 240.000 | + | 240.000i | 0.699708 | + | 0.699708i | ||||
\(344\) | 144.000i | 0.418605i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 82.0000 | 0.236994 | ||||||||
\(347\) | 260.000 | − | 260.000i | 0.749280 | − | 0.749280i | −0.225064 | − | 0.974344i | \(-0.572259\pi\) |
0.974344 | + | 0.225064i | \(0.0722592\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 136.000i | − | 0.389685i | −0.980835 | − | 0.194842i | \(-0.937580\pi\) | ||
0.980835 | − | 0.194842i | \(-0.0624195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.0000 | + | 16.0000i | −0.0454545 | + | 0.0454545i | ||||
\(353\) | 75.0000 | + | 75.0000i | 0.212465 | + | 0.212465i | 0.805314 | − | 0.592849i | \(-0.201997\pi\) |
−0.592849 | + | 0.805314i | \(0.701997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −52.0000 | −0.146067 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 172.000 | + | 172.000i | 0.480447 | + | 0.480447i | ||||
\(359\) | − | 32.0000i | − | 0.0891365i | −0.999006 | − | 0.0445682i | \(-0.985809\pi\) | ||
0.999006 | − | 0.0445682i | \(-0.0141912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 297.000 | 0.822715 | ||||||||
\(362\) | 62.0000 | − | 62.0000i | 0.171271 | − | 0.171271i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 96.0000i | 0.263736i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | − | 16.0000i | 0.0435967 | − | 0.0435967i | −0.684972 | − | 0.728569i | \(-0.740186\pi\) |
0.728569 | + | 0.684972i | \(0.240186\pi\) | |||||||
\(368\) | −80.0000 | − | 80.0000i | −0.217391 | − | 0.217391i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 272.000 | 0.733154 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 251.000 | + | 251.000i | 0.672922 | + | 0.672922i | 0.958389 | − | 0.285466i | \(-0.0921485\pi\) |
−0.285466 | + | 0.958389i | \(0.592149\pi\) | |||||||
\(374\) | 152.000i | 0.406417i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −114.000 | + | 114.000i | −0.302387 | + | 0.302387i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 560.000i | 1.47757i | 0.673940 | + | 0.738786i | \(0.264601\pi\) | ||||
−0.673940 | + | 0.738786i | \(0.735399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 248.000 | − | 248.000i | 0.649215 | − | 0.649215i | ||||
\(383\) | 300.000 | + | 300.000i | 0.783290 | + | 0.783290i | 0.980384 | − | 0.197095i | \(-0.0631506\pi\) |
−0.197095 | + | 0.980384i | \(0.563151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −270.000 | −0.699482 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −114.000 | − | 114.000i | −0.293814 | − | 0.293814i | ||||
\(389\) | 24.0000i | 0.0616967i | 0.999524 | + | 0.0308483i | \(0.00982089\pi\) | ||||
−0.999524 | + | 0.0308483i | \(0.990179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −760.000 | −1.94373 | ||||||||
\(392\) | −158.000 | + | 158.000i | −0.403061 | + | 0.403061i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 306.000i | − | 0.776650i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 299.000 | − | 299.000i | 0.753149 | − | 0.753149i | −0.221917 | − | 0.975066i | \(-0.571231\pi\) |
0.975066 | + | 0.221917i | \(0.0712314\pi\) | |||||||
\(398\) | 252.000 | + | 252.000i | 0.633166 | + | 0.633166i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −144.000 | −0.359102 | −0.179551 | − | 0.983749i | \(-0.557465\pi\) | ||||
−0.179551 | + | 0.983749i | \(0.557465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −132.000 | − | 132.000i | −0.327543 | − | 0.327543i | ||||
\(404\) | − | 112.000i | − | 0.277228i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −608.000 | −1.49754 | ||||||||
\(407\) | 12.0000 | − | 12.0000i | 0.0294840 | − | 0.0294840i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 354.000i | 0.865526i | 0.901508 | + | 0.432763i | \(0.142461\pi\) | ||||
−0.901508 | + | 0.432763i | \(0.857539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.00000 | + | 8.00000i | −0.0194175 | + | 0.0194175i | ||||
\(413\) | −736.000 | − | 736.000i | −1.78208 | − | 1.78208i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −24.0000 | −0.0576923 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 32.0000 | + | 32.0000i | 0.0765550 | + | 0.0765550i | ||||
\(419\) | 468.000i | 1.11695i | 0.829523 | + | 0.558473i | \(0.188612\pi\) | ||||
−0.829523 | + | 0.558473i | \(0.811388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 104.000 | 0.247031 | 0.123515 | − | 0.992343i | \(-0.460583\pi\) | ||||
0.123515 | + | 0.992343i | \(0.460583\pi\) | |||||||
\(422\) | −64.0000 | + | 64.0000i | −0.151659 | + | 0.151659i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 68.0000i | 0.160377i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −576.000 | + | 576.000i | −1.34895 | + | 1.34895i | ||||
\(428\) | −136.000 | − | 136.000i | −0.317757 | − | 0.317757i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −680.000 | −1.57773 | −0.788863 | − | 0.614569i | \(-0.789330\pi\) | ||||
−0.788863 | + | 0.614569i | \(0.789330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −41.0000 | − | 41.0000i | −0.0946882 | − | 0.0946882i | 0.658176 | − | 0.752864i | \(-0.271328\pi\) |
−0.752864 | + | 0.658176i | \(0.771328\pi\) | |||||||
\(434\) | − | 704.000i | − | 1.62212i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 92.0000 | 0.211009 | ||||||||
\(437\) | −160.000 | + | 160.000i | −0.366133 | + | 0.366133i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 364.000i | 0.829157i | 0.910014 | + | 0.414579i | \(0.136071\pi\) | ||||
−0.910014 | + | 0.414579i | \(0.863929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −114.000 | + | 114.000i | −0.257919 | + | 0.257919i | ||||
\(443\) | 372.000 | + | 372.000i | 0.839729 | + | 0.839729i | 0.988823 | − | 0.149094i | \(-0.0476357\pi\) |
−0.149094 | + | 0.988823i | \(0.547636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 456.000 | 1.02242 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −64.0000 | − | 64.0000i | −0.142857 | − | 0.142857i | ||||
\(449\) | 176.000i | 0.391982i | 0.980606 | + | 0.195991i | \(0.0627924\pi\) | ||||
−0.980606 | + | 0.195991i | \(0.937208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 280.000 | 0.620843 | ||||||||
\(452\) | −106.000 | + | 106.000i | −0.234513 | + | 0.234513i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 200.000i | − | 0.440529i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −129.000 | + | 129.000i | −0.282276 | + | 0.282276i | −0.834016 | − | 0.551740i | \(-0.813964\pi\) |
0.551740 | + | 0.834016i | \(0.313964\pi\) | |||||||
\(458\) | 312.000 | + | 312.000i | 0.681223 | + | 0.681223i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 568.000 | 1.23210 | 0.616052 | − | 0.787705i | \(-0.288731\pi\) | ||||
0.616052 | + | 0.787705i | \(0.288731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 568.000 | + | 568.000i | 1.22678 | + | 1.22678i | 0.965174 | + | 0.261608i | \(0.0842526\pi\) |
0.261608 | + | 0.965174i | \(0.415747\pi\) | |||||||
\(464\) | − | 152.000i | − | 0.327586i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 186.000 | 0.399142 | ||||||||
\(467\) | 272.000 | − | 272.000i | 0.582441 | − | 0.582441i | −0.353132 | − | 0.935573i | \(-0.614883\pi\) |
0.935573 | + | 0.353132i | \(0.114883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 704.000i | − | 1.50107i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 184.000 | − | 184.000i | 0.389831 | − | 0.389831i | ||||
\(473\) | −144.000 | − | 144.000i | −0.304440 | − | 0.304440i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −608.000 | −1.27731 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 96.0000 | + | 96.0000i | 0.200837 | + | 0.200837i | ||||
\(479\) | − | 928.000i | − | 1.93737i | −0.248294 | − | 0.968685i | \(-0.579870\pi\) | ||
0.248294 | − | 0.968685i | \(-0.420130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.0374220 | ||||||||
\(482\) | 160.000 | − | 160.000i | 0.331950 | − | 0.331950i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 210.000i | 0.433884i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −252.000 | + | 252.000i | −0.517454 | + | 0.517454i | −0.916800 | − | 0.399346i | \(-0.869237\pi\) |
0.399346 | + | 0.916800i | \(0.369237\pi\) | |||||||
\(488\) | −144.000 | − | 144.000i | −0.295082 | − | 0.295082i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −844.000 | −1.71894 | −0.859470 | − | 0.511185i | \(-0.829207\pi\) | ||||
−0.859470 | + | 0.511185i | \(0.829207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −722.000 | − | 722.000i | −1.46450 | − | 1.46450i | ||||
\(494\) | 48.0000i | 0.0971660i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 176.000 | 0.354839 | ||||||||
\(497\) | 704.000 | − | 704.000i | 1.41650 | − | 1.41650i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 872.000i | − | 1.74749i | −0.486380 | − | 0.873747i | \(-0.661683\pi\) | ||
0.486380 | − | 0.873747i | \(-0.338317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | − | 12.0000i | 0.0239044 | − | 0.0239044i | ||||
\(503\) | −480.000 | − | 480.000i | −0.954274 | − | 0.954274i | 0.0447250 | − | 0.998999i | \(-0.485759\pi\) |
−0.998999 | + | 0.0447250i | \(0.985759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 160.000 | 0.316206 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 136.000 | + | 136.000i | 0.267717 | + | 0.267717i | ||||
\(509\) | − | 694.000i | − | 1.36346i | −0.731605 | − | 0.681729i | \(-0.761228\pi\) | ||
0.731605 | − | 0.681729i | \(-0.238772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 880.000 | 1.72211 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 202.000i | 0.392996i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 48.0000 | + | 48.0000i | 0.0926641 | + | 0.0926641i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 528.000 | 1.01344 | 0.506718 | − | 0.862112i | \(-0.330859\pi\) | ||||
0.506718 | + | 0.862112i | \(0.330859\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −552.000 | − | 552.000i | −1.05545 | − | 1.05545i | −0.998370 | − | 0.0570797i | \(-0.981821\pi\) |
−0.0570797 | − | 0.998370i | \(-0.518179\pi\) | |||||||
\(524\) | 88.0000i | 0.167939i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 416.000 | 0.790875 | ||||||||
\(527\) | 836.000 | − | 836.000i | 1.58634 | − | 1.58634i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 271.000i | 0.512287i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −128.000 | + | 128.000i | −0.240602 | + | 0.240602i | ||||
\(533\) | 210.000 | + | 210.000i | 0.393996 | + | 0.393996i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 176.000 | 0.328358 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 296.000 | + | 296.000i | 0.550186 | + | 0.550186i | ||||
\(539\) | − | 316.000i | − | 0.586271i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −782.000 | −1.44547 | −0.722736 | − | 0.691125i | \(-0.757116\pi\) | ||||
−0.722736 | + | 0.691125i | \(0.757116\pi\) | |||||||
\(542\) | 108.000 | − | 108.000i | 0.199262 | − | 0.199262i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 152.000i | − | 0.279412i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 420.000 | − | 420.000i | 0.767824 | − | 0.767824i | −0.209899 | − | 0.977723i | \(-0.567313\pi\) |
0.977723 | + | 0.209899i | \(0.0673134\pi\) | |||||||
\(548\) | −138.000 | − | 138.000i | −0.251825 | − | 0.251825i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −304.000 | −0.551724 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 96.0000 | + | 96.0000i | 0.173599 | + | 0.173599i | ||||
\(554\) | − | 486.000i | − | 0.877256i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −160.000 | −0.287770 | ||||||||
\(557\) | −417.000 | + | 417.000i | −0.748654 | + | 0.748654i | −0.974226 | − | 0.225573i | \(-0.927575\pi\) |
0.225573 | + | 0.974226i | \(0.427575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 216.000i | − | 0.386404i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 378.000 | − | 378.000i | 0.672598 | − | 0.672598i | ||||
\(563\) | −228.000 | − | 228.000i | −0.404973 | − | 0.404973i | 0.475008 | − | 0.879981i | \(-0.342445\pi\) |
−0.879981 | + | 0.475008i | \(0.842445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −184.000 | −0.325088 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 176.000 | + | 176.000i | 0.309859 | + | 0.309859i | ||||
\(569\) | − | 368.000i | − | 0.646749i | −0.946271 | − | 0.323374i | \(-0.895183\pi\) | ||
0.946271 | − | 0.323374i | \(-0.104817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −736.000 | −1.28897 | −0.644483 | − | 0.764618i | \(-0.722928\pi\) | ||||
−0.644483 | + | 0.764618i | \(0.722928\pi\) | |||||||
\(572\) | 24.0000 | − | 24.0000i | 0.0419580 | − | 0.0419580i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1120.00i | 1.95122i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 113.000 | − | 113.000i | 0.195841 | − | 0.195841i | −0.602374 | − | 0.798214i | \(-0.705778\pi\) |
0.798214 | + | 0.602374i | \(0.205778\pi\) | |||||||
\(578\) | −433.000 | − | 433.000i | −0.749135 | − | 0.749135i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −384.000 | −0.660929 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −68.0000 | − | 68.0000i | −0.116638 | − | 0.116638i | ||||
\(584\) | 220.000i | 0.376712i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 558.000 | 0.952218 | ||||||||
\(587\) | −684.000 | + | 684.000i | −1.16525 | + | 1.16525i | −0.181937 | + | 0.983310i | \(0.558237\pi\) |
−0.983310 | + | 0.181937i | \(0.941763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 352.000i | − | 0.597623i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | + | 12.0000i | −0.0202703 | + | 0.0202703i | ||||
\(593\) | 149.000 | + | 149.000i | 0.251265 | + | 0.251265i | 0.821489 | − | 0.570224i | \(-0.193144\pi\) |
−0.570224 | + | 0.821489i | \(0.693144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −336.000 | −0.563758 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 120.000 | + | 120.000i | 0.200669 | + | 0.200669i | ||||
\(599\) | 152.000i | 0.253756i | 0.991918 | + | 0.126878i | \(0.0404957\pi\) | ||||
−0.991918 | + | 0.126878i | \(0.959504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 320.000 | 0.532446 | 0.266223 | − | 0.963911i | \(-0.414224\pi\) | ||||
0.266223 | + | 0.963911i | \(0.414224\pi\) | |||||||
\(602\) | 576.000 | − | 576.000i | 0.956811 | − | 0.956811i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 8.00000i | − | 0.0132450i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 528.000 | − | 528.000i | 0.869852 | − | 0.869852i | −0.122604 | − | 0.992456i | \(-0.539124\pi\) |
0.992456 | + | 0.122604i | \(0.0391245\pi\) | |||||||
\(608\) | −32.0000 | − | 32.0000i | −0.0526316 | − | 0.0526316i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −771.000 | − | 771.000i | −1.25775 | − | 1.25775i | −0.952165 | − | 0.305583i | \(-0.901148\pi\) |
−0.305583 | − | 0.952165i | \(-0.598852\pi\) | |||||||
\(614\) | 432.000i | 0.703583i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 128.000 | 0.207792 | ||||||||
\(617\) | −675.000 | + | 675.000i | −1.09400 | + | 1.09400i | −0.0989065 | + | 0.995097i | \(0.531534\pi\) |
−0.995097 | + | 0.0989065i | \(0.968466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 600.000i | − | 0.969305i | −0.874707 | − | 0.484653i | \(-0.838946\pi\) | ||
0.874707 | − | 0.484653i | \(-0.161054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 272.000 | − | 272.000i | 0.437299 | − | 0.437299i | ||||
\(623\) | 208.000 | + | 208.000i | 0.333868 | + | 0.333868i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.0000 | −0.0479233 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 198.000 | + | 198.000i | 0.315287 | + | 0.315287i | ||||
\(629\) | 114.000i | 0.181240i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.0316957 | −0.0158479 | − | 0.999874i | \(-0.505045\pi\) | ||||
−0.0158479 | + | 0.999874i | \(0.505045\pi\) | |||||||
\(632\) | −24.0000 | + | 24.0000i | −0.0379747 | + | 0.0379747i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 174.000i | 0.274448i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 237.000 | − | 237.000i | 0.372057 | − | 0.372057i | ||||
\(638\) | 152.000 | + | 152.000i | 0.238245 | + | 0.238245i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −694.000 | −1.08268 | −0.541342 | − | 0.840803i | \(-0.682083\pi\) | ||||
−0.541342 | + | 0.840803i | \(0.682083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 168.000 | + | 168.000i | 0.261275 | + | 0.261275i | 0.825572 | − | 0.564297i | \(-0.190853\pi\) |
−0.564297 | + | 0.825572i | \(0.690853\pi\) | |||||||
\(644\) | 640.000i | 0.993789i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −304.000 | −0.470588 | ||||||||
\(647\) | 328.000 | − | 328.000i | 0.506955 | − | 0.506955i | −0.406635 | − | 0.913591i | \(-0.633298\pi\) |
0.913591 | + | 0.406635i | \(0.133298\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 368.000i | 0.567026i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 320.000 | − | 320.000i | 0.490798 | − | 0.490798i | ||||
\(653\) | −81.0000 | − | 81.0000i | −0.124043 | − | 0.124043i | 0.642360 | − | 0.766403i | \(-0.277955\pi\) |
−0.766403 | + | 0.642360i | \(0.777955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −280.000 | −0.426829 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 500.000i | − | 0.758725i | −0.925248 | − | 0.379363i | \(-0.876143\pi\) | ||
0.925248 | − | 0.379363i | \(-0.123857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −568.000 | −0.859304 | −0.429652 | − | 0.902995i | \(-0.641364\pi\) | ||||
−0.429652 | + | 0.902995i | \(0.641364\pi\) | |||||||
\(662\) | −584.000 | + | 584.000i | −0.882175 | + | 0.882175i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 96.0000i | − | 0.144578i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −760.000 | + | 760.000i | −1.13943 | + | 1.13943i | ||||
\(668\) | 112.000 | + | 112.000i | 0.167665 | + | 0.167665i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 288.000 | 0.429210 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −73.0000 | − | 73.0000i | −0.108470 | − | 0.108470i | 0.650789 | − | 0.759259i | \(-0.274438\pi\) |
−0.759259 | + | 0.650789i | \(0.774438\pi\) | |||||||
\(674\) | − | 258.000i | − | 0.382789i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −302.000 | −0.446746 | ||||||||
\(677\) | 839.000 | − | 839.000i | 1.23929 | − | 1.23929i | 0.279000 | − | 0.960291i | \(-0.409997\pi\) |
0.960291 | − | 0.279000i | \(-0.0900029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 912.000i | 1.34315i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −176.000 | + | 176.000i | −0.258065 | + | 0.258065i | ||||
\(683\) | 744.000 | + | 744.000i | 1.08931 | + | 1.08931i | 0.995599 | + | 0.0937126i | \(0.0298735\pi\) |
0.0937126 | + | 0.995599i | \(0.470127\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 480.000 | 0.699708 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 144.000 | + | 144.000i | 0.209302 | + | 0.209302i | ||||
\(689\) | − | 102.000i | − | 0.148041i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 504.000 | 0.729378 | 0.364689 | − | 0.931129i | \(-0.381175\pi\) | ||||
0.364689 | + | 0.931129i | \(0.381175\pi\) | |||||||
\(692\) | 82.0000 | − | 82.0000i | 0.118497 | − | 0.118497i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 520.000i | − | 0.749280i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1330.00 | + | 1330.00i | −1.90818 | + | 1.90818i | ||||
\(698\) | −136.000 | − | 136.000i | −0.194842 | − | 0.194842i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 298.000 | 0.425107 | 0.212553 | − | 0.977149i | \(-0.431822\pi\) | ||||
0.212553 | + | 0.977149i | \(0.431822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | + | 24.0000i | 0.0341394 | + | 0.0341394i | ||||
\(704\) | 32.0000i | 0.0454545i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 150.000 | 0.212465 | ||||||||
\(707\) | −448.000 | + | 448.000i | −0.633663 | + | 0.633663i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 472.000i | − | 0.665726i | −0.942975 | − | 0.332863i | \(-0.891985\pi\) | ||
0.942975 | − | 0.332863i | \(-0.108015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −52.0000 | + | 52.0000i | −0.0730337 | + | 0.0730337i | ||||
\(713\) | −880.000 | − | 880.000i | −1.23422 | − | 1.23422i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 344.000 | 0.480447 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.0000 | − | 32.0000i | −0.0445682 | − | 0.0445682i | ||||
\(719\) | 872.000i | 1.21280i | 0.795161 | + | 0.606398i | \(0.207386\pi\) | ||||
−0.795161 | + | 0.606398i | \(0.792614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 64.0000 | 0.0887656 | ||||||||
\(722\) | 297.000 | − | 297.000i | 0.411357 | − | 0.411357i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 124.000i | − | 0.171271i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 60.0000 | − | 60.0000i | 0.0825309 | − | 0.0825309i | −0.664636 | − | 0.747167i | \(-0.731413\pi\) |
0.747167 | + | 0.664636i | \(0.231413\pi\) | |||||||
\(728\) | 96.0000 | + | 96.0000i | 0.131868 | + | 0.131868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1368.00 | 1.87141 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 581.000 | + | 581.000i | 0.792633 | + | 0.792633i | 0.981922 | − | 0.189289i | \(-0.0606181\pi\) |
−0.189289 | + | 0.981922i | \(0.560618\pi\) | |||||||
\(734\) | − | 32.0000i | − | 0.0435967i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −160.000 | −0.217391 | ||||||||
\(737\) | −176.000 | + | 176.000i | −0.238806 | + | 0.238806i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1160.00i | − | 1.56969i | −0.619693 | − | 0.784844i | \(-0.712743\pi\) | ||
0.619693 | − | 0.784844i | \(-0.287257\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 272.000 | − | 272.000i | 0.366577 | − | 0.366577i | ||||
\(743\) | −380.000 | − | 380.000i | −0.511440 | − | 0.511440i | 0.403527 | − | 0.914968i | \(-0.367784\pi\) |
−0.914968 | + | 0.403527i | \(0.867784\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 502.000 | 0.672922 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 152.000 | + | 152.000i | 0.203209 | + | 0.203209i | ||||
\(749\) | 1088.00i | 1.45260i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 780.000 | 1.03862 | 0.519308 | − | 0.854587i | \(-0.326190\pi\) | ||||
0.519308 | + | 0.854587i | \(0.326190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 228.000i | 0.302387i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −285.000 | + | 285.000i | −0.376486 | + | 0.376486i | −0.869833 | − | 0.493347i | \(-0.835773\pi\) |
0.493347 | + | 0.869833i | \(0.335773\pi\) | |||||||
\(758\) | 560.000 | + | 560.000i | 0.738786 | + | 0.738786i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 304.000 | 0.399474 | 0.199737 | − | 0.979850i | \(-0.435991\pi\) | ||||
0.199737 | + | 0.979850i | \(0.435991\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −368.000 | − | 368.000i | −0.482307 | − | 0.482307i | ||||
\(764\) | − | 496.000i | − | 0.649215i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 600.000 | 0.783290 | ||||||||
\(767\) | −276.000 | + | 276.000i | −0.359844 | + | 0.359844i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1072.00i | 1.39402i | 0.717062 | + | 0.697009i | \(0.245486\pi\) | ||||
−0.717062 | + | 0.697009i | \(0.754514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −270.000 | + | 270.000i | −0.349741 | + | 0.349741i | ||||
\(773\) | 897.000 | + | 897.000i | 1.16041 | + | 1.16041i | 0.984385 | + | 0.176029i | \(0.0563252\pi\) |
0.176029 | + | 0.984385i | \(0.443675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −228.000 | −0.293814 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.0000 | + | 24.0000i | 0.0308483 | + | 0.0308483i | ||||
\(779\) | 560.000i | 0.718870i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −352.000 | −0.450704 | ||||||||
\(782\) | −760.000 | + | 760.000i | −0.971867 | + | 0.971867i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 316.000i | 0.403061i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −328.000 | + | 328.000i | −0.416773 | + | 0.416773i | −0.884090 | − | 0.467317i | \(-0.845221\pi\) |
0.467317 | + | 0.884090i | \(0.345221\pi\) | |||||||
\(788\) | −306.000 | − | 306.000i | −0.388325 | − | 0.388325i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 848.000 | 1.07206 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 216.000 | + | 216.000i | 0.272383 | + | 0.272383i | ||||
\(794\) | − | 598.000i | − | 0.753149i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 504.000 | 0.633166 | ||||||||
\(797\) | 87.0000 | − | 87.0000i | 0.109159 | − | 0.109159i | −0.650418 | − | 0.759577i | \(-0.725406\pi\) |
0.759577 | + | 0.650418i | \(0.225406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −144.000 | + | 144.000i | −0.179551 | + | 0.179551i | ||||
\(803\) | −220.000 | − | 220.000i | −0.273973 | − | 0.273973i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −264.000 | −0.327543 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −112.000 | − | 112.000i | −0.138614 | − | 0.138614i | ||||
\(809\) | 922.000i | 1.13968i | 0.821756 | + | 0.569839i | \(0.192995\pi\) | ||||
−0.821756 | + | 0.569839i | \(0.807005\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1312.00 | −1.61776 | −0.808878 | − | 0.587977i | \(-0.799925\pi\) | ||||
−0.808878 | + | 0.587977i | \(0.799925\pi\) | |||||||
\(812\) | −608.000 | + | 608.000i | −0.748768 | + | 0.748768i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 24.0000i | − | 0.0294840i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 288.000 | − | 288.000i | 0.352509 | − | 0.352509i | ||||
\(818\) | 354.000 | + | 354.000i | 0.432763 | + | 0.432763i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −950.000 | −1.15713 | −0.578563 | − | 0.815638i | \(-0.696386\pi\) | ||||
−0.578563 | + | 0.815638i | \(0.696386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −68.0000 | − | 68.0000i | −0.0826245 | − | 0.0826245i | 0.664587 | − | 0.747211i | \(-0.268608\pi\) |
−0.747211 | + | 0.664587i | \(0.768608\pi\) | |||||||
\(824\) | 16.0000i | 0.0194175i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1472.00 | −1.78208 | ||||||||
\(827\) | −264.000 | + | 264.000i | −0.319226 | + | 0.319226i | −0.848470 | − | 0.529244i | \(-0.822476\pi\) |
0.529244 | + | 0.848470i | \(0.322476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 178.000i | 0.214717i | 0.994220 | + | 0.107358i | \(0.0342392\pi\) | ||||
−0.994220 | + | 0.107358i | \(0.965761\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.0000 | + | 24.0000i | −0.0288462 | + | 0.0288462i | ||||
\(833\) | 1501.00 | + | 1501.00i | 1.80192 | + | 1.80192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 64.0000 | 0.0765550 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 468.000 | + | 468.000i | 0.558473 | + | 0.558473i | ||||
\(839\) | 1576.00i | 1.87843i | 0.343334 | + | 0.939213i | \(0.388444\pi\) | ||||
−0.343334 | + | 0.939213i | \(0.611556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −603.000 | −0.717004 | ||||||||
\(842\) | 104.000 | − | 104.000i | 0.123515 | − | 0.123515i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 128.000i | 0.151659i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 840.000 | − | 840.000i | 0.991736 | − | 0.991736i | ||||
\(848\) | 68.0000 | + | 68.0000i | 0.0801887 | + | 0.0801887i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 120.000 | 0.141011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 509.000 | + | 509.000i | 0.596717 | + | 0.596717i | 0.939438 | − | 0.342720i | \(-0.111348\pi\) |
−0.342720 | + | 0.939438i | \(0.611348\pi\) | |||||||
\(854\) | 1152.00i | 1.34895i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −272.000 | −0.317757 | ||||||||
\(857\) | −357.000 | + | 357.000i | −0.416569 | + | 0.416569i | −0.884019 | − | 0.467450i | \(-0.845173\pi\) |
0.467450 | + | 0.884019i | \(0.345173\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 520.000i | 0.605355i | 0.953093 | + | 0.302678i | \(0.0978805\pi\) | ||||
−0.953093 | + | 0.302678i | \(0.902119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −680.000 | + | 680.000i | −0.788863 | + | 0.788863i | ||||
\(863\) | −952.000 | − | 952.000i | −1.10313 | − | 1.10313i | −0.994031 | − | 0.109098i | \(-0.965204\pi\) |
−0.109098 | − | 0.994031i | \(-0.534796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −82.0000 | −0.0946882 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −704.000 | − | 704.000i | −0.811060 | − | 0.811060i | ||||
\(869\) | − | 48.0000i | − | 0.0552359i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −264.000 | −0.303100 | ||||||||
\(872\) | 92.0000 | − | 92.0000i | 0.105505 | − | 0.105505i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 320.000i | 0.366133i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 717.000 | − | 717.000i | 0.817560 | − | 0.817560i | −0.168194 | − | 0.985754i | \(-0.553794\pi\) |
0.985754 | + | 0.168194i | \(0.0537935\pi\) | |||||||
\(878\) | 364.000 | + | 364.000i | 0.414579 | + | 0.414579i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −554.000 | −0.628831 | −0.314415 | − | 0.949285i | \(-0.601808\pi\) | ||||
−0.314415 | + | 0.949285i | \(0.601808\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −952.000 | − | 952.000i | −1.07814 | − | 1.07814i | −0.996676 | − | 0.0814666i | \(-0.974040\pi\) |
−0.0814666 | − | 0.996676i | \(-0.525960\pi\) | |||||||
\(884\) | 228.000i | 0.257919i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 744.000 | 0.839729 | ||||||||
\(887\) | −648.000 | + | 648.000i | −0.730552 | + | 0.730552i | −0.970729 | − | 0.240177i | \(-0.922795\pi\) |
0.240177 | + | 0.970729i | \(0.422795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1088.00i | − | 1.22385i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 456.000 | − | 456.000i | 0.511211 | − | 0.511211i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −128.000 | −0.142857 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 176.000 | + | 176.000i | 0.195991 | + | 0.195991i | ||||
\(899\) | − | 1672.00i | − | 1.85984i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 646.000 | 0.716981 | ||||||||
\(902\) | 280.000 | − | 280.000i | 0.310421 | − | 0.310421i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 212.000i | 0.234513i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 740.000 | − | 740.000i | 0.815877 | − | 0.815877i | −0.169631 | − | 0.985508i | \(-0.554258\pi\) |
0.985508 | + | 0.169631i | \(0.0542576\pi\) | |||||||
\(908\) | −200.000 | − | 200.000i | −0.220264 | − | 0.220264i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −520.000 | −0.570801 | −0.285401 | − | 0.958408i | \(-0.592127\pi\) | ||||
−0.285401 | + | 0.958408i | \(0.592127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 96.0000 | + | 96.0000i | 0.105148 | + | 0.105148i | ||||
\(914\) | 258.000i | 0.282276i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 624.000 | 0.681223 | ||||||||
\(917\) | 352.000 | − | 352.000i | 0.383860 | − | 0.383860i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 844.000i | 0.918390i | 0.888336 | + | 0.459195i | \(0.151862\pi\) | ||||
−0.888336 | + | 0.459195i | \(0.848138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 568.000 | − | 568.000i | 0.616052 | − | 0.616052i | ||||
\(923\) | −264.000 | − | 264.000i | −0.286024 | − | 0.286024i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1136.00 | 1.22678 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −152.000 | − | 152.000i | −0.163793 | − | 0.163793i | ||||
\(929\) | − | 208.000i | − | 0.223897i | −0.993714 | − | 0.111948i | \(-0.964291\pi\) | ||
0.993714 | − | 0.111948i | \(-0.0357091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 632.000 | 0.678840 | ||||||||
\(932\) | 186.000 | − | 186.000i | 0.199571 | − | 0.199571i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 544.000i | − | 0.582441i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.00000 | + | 7.00000i | −0.00747065 | + | 0.00747065i | −0.710832 | − | 0.703362i | \(-0.751681\pi\) |
0.703362 | + | 0.710832i | \(0.251681\pi\) | |||||||
\(938\) | −704.000 | − | 704.000i | −0.750533 | − | 0.750533i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1752.00 | 1.86185 | 0.930925 | − | 0.365212i | \(-0.119003\pi\) | ||||
0.930925 | + | 0.365212i | \(0.119003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1400.00 | + | 1400.00i | 1.48462 | + | 1.48462i | ||||
\(944\) | − | 368.000i | − | 0.389831i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −288.000 | −0.304440 | ||||||||
\(947\) | −224.000 | + | 224.000i | −0.236536 | + | 0.236536i | −0.815414 | − | 0.578878i | \(-0.803491\pi\) |
0.578878 | + | 0.815414i | \(0.303491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 330.000i | − | 0.347734i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −608.000 | + | 608.000i | −0.638655 | + | 0.638655i | ||||
\(953\) | −645.000 | − | 645.000i | −0.676810 | − | 0.676810i | 0.282467 | − | 0.959277i | \(-0.408847\pi\) |
−0.959277 | + | 0.282467i | \(0.908847\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 192.000 | 0.200837 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −928.000 | − | 928.000i | −0.968685 | − | 0.968685i | ||||
\(959\) | 1104.00i | 1.15120i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 975.000 | 1.01457 | ||||||||
\(962\) | 18.0000 | − | 18.0000i | 0.0187110 | − | 0.0187110i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 320.000i | − | 0.331950i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 92.0000 | − | 92.0000i | 0.0951396 | − | 0.0951396i | −0.657935 | − | 0.753075i | \(-0.728570\pi\) |
0.753075 | + | 0.657935i | \(0.228570\pi\) | |||||||
\(968\) | 210.000 | + | 210.000i | 0.216942 | + | 0.216942i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.00000 | −0.00411946 | −0.00205973 | − | 0.999998i | \(-0.500656\pi\) | ||||
−0.00205973 | + | 0.999998i | \(0.500656\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 640.000 | + | 640.000i | 0.657760 | + | 0.657760i | ||||
\(974\) | 504.000i | 0.517454i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −288.000 | −0.295082 | ||||||||
\(977\) | 1011.00 | − | 1011.00i | 1.03480 | − | 1.03480i | 0.0354282 | − | 0.999372i | \(-0.488720\pi\) |
0.999372 | − | 0.0354282i | \(-0.0112795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 104.000i | − | 0.106231i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −844.000 | + | 844.000i | −0.859470 | + | 0.859470i | ||||
\(983\) | 604.000 | + | 604.000i | 0.614446 | + | 0.614446i | 0.944101 | − | 0.329656i | \(-0.106933\pi\) |
−0.329656 | + | 0.944101i | \(0.606933\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1444.00 | −1.46450 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 48.0000 | + | 48.0000i | 0.0485830 | + | 0.0485830i | ||||
\(989\) | − | 1440.00i | − | 1.45602i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 652.000 | 0.657921 | 0.328961 | − | 0.944344i | \(-0.393302\pi\) | ||||
0.328961 | + | 0.944344i | \(0.393302\pi\) | |||||||
\(992\) | 176.000 | − | 176.000i | 0.177419 | − | 0.177419i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 1408.00i | − | 1.41650i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1051.00 | + | 1051.00i | −1.05416 | + | 1.05416i | −0.0557158 | + | 0.998447i | \(0.517744\pi\) |
−0.998447 | + | 0.0557158i | \(0.982256\pi\) | |||||||
\(998\) | −872.000 | − | 872.000i | −0.873747 | − | 0.873747i | ||||
\(999\) | 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 | 450.3.g.d.343.1 | 2 | ||
3.2 | odd | 2 | 450.3.g.a.343.1 | 2 | |||
5.2 | odd | 4 | inner | 450.3.g.d.307.1 | 2 | ||
5.3 | odd | 4 | 90.3.g.a.37.1 | ✓ | 2 | ||
5.4 | even | 2 | 90.3.g.a.73.1 | yes | 2 | ||
15.2 | even | 4 | 450.3.g.a.307.1 | 2 | |||
15.8 | even | 4 | 90.3.g.c.37.1 | yes | 2 | ||
15.14 | odd | 2 | 90.3.g.c.73.1 | yes | 2 | ||
20.3 | even | 4 | 720.3.bh.b.577.1 | 2 | |||
20.19 | odd | 2 | 720.3.bh.b.433.1 | 2 | |||
60.23 | odd | 4 | 720.3.bh.d.577.1 | 2 | |||
60.59 | even | 2 | 720.3.bh.d.433.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.3.g.a.37.1 | ✓ | 2 | 5.3 | odd | 4 | ||
90.3.g.a.73.1 | yes | 2 | 5.4 | even | 2 | ||
90.3.g.c.37.1 | yes | 2 | 15.8 | even | 4 | ||
90.3.g.c.73.1 | yes | 2 | 15.14 | odd | 2 | ||
450.3.g.a.307.1 | 2 | 15.2 | even | 4 | |||
450.3.g.a.343.1 | 2 | 3.2 | odd | 2 | |||
450.3.g.d.307.1 | 2 | 5.2 | odd | 4 | inner | ||
450.3.g.d.343.1 | 2 | 1.1 | even | 1 | trivial | ||
720.3.bh.b.433.1 | 2 | 20.19 | odd | 2 | |||
720.3.bh.b.577.1 | 2 | 20.3 | even | 4 | |||
720.3.bh.d.433.1 | 2 | 60.59 | even | 2 | |||
720.3.bh.d.577.1 | 2 | 60.23 | odd | 4 |