Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3513,1,Mod(20,3513)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3513, base_ring=CyclotomicField(78))
chi = DirichletCharacter(H, H._module([39, 40]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3513.20");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3513 = 3 \cdot 1171 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3513.bc (of order \(78\), degree \(24\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.75321538938\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Coefficient field: | \(\Q(\zeta_{39})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - x^{23} + x^{21} - x^{20} + x^{18} - x^{17} + x^{15} - x^{14} + x^{12} - x^{10} + x^{9} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{39}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{39} - \cdots)\) |
Embedding invariants
Embedding label | 1571.1 | ||
Root | \(0.987050 - 0.160411i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3513.1571 |
Dual form | 3513.1.bc.a.1373.1 |
$q$-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 \(\left(\mathbb{Z}/3513\mathbb{Z}\right)^\times\).
\(n\) | \(1172\) | \(2344\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{39}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) | ||||
0.996757 | + | 0.0804666i | \(0.0256410\pi\) | |||||||
\(3\) | −0.996757 | + | 0.0804666i | −0.996757 | + | 0.0804666i | ||||
\(4\) | 0.987050 | + | 0.160411i | 0.987050 | + | 0.160411i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.854605 | + | 1.80104i | −0.854605 | + | 1.80104i | −0.354605 | + | 0.935016i | \(0.615385\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.987050 | − | 0.160411i | 0.987050 | − | 0.160411i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(12\) | −0.996757 | − | 0.0804666i | −0.996757 | − | 0.0804666i | ||||
\(13\) | −0.850405 | + | 1.23202i | −0.850405 | + | 1.23202i | 0.120537 | + | 0.992709i | \(0.461538\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.948536 | + | 0.316668i | 0.948536 | + | 0.316668i | ||||
\(17\) | 0 | 0 | −0.919979 | − | 0.391967i | \(-0.871795\pi\) | ||||
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.04522 | − | 0.445325i | −1.04522 | − | 0.445325i | −0.200026 | − | 0.979791i | \(-0.564103\pi\) |
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.706910 | − | 1.86397i | 0.706910 | − | 1.86397i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.970942 | + | 0.239316i | −0.970942 | + | 0.239316i | ||||
\(28\) | −1.13245 | + | 1.64063i | −1.13245 | + | 1.64063i | ||||
\(29\) | 0 | 0 | 0.692724 | − | 0.721202i | \(-0.256410\pi\) | ||||
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0557864 | − | 1.38433i | −0.0557864 | − | 1.38433i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.692724 | − | 0.721202i | \(-0.256410\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 1.00000 | ||||||||
\(37\) | −0.171499 | + | 0.840058i | −0.171499 | + | 0.840058i | 0.799443 | + | 0.600742i | \(0.205128\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.748511 | − | 1.29646i | 0.748511 | − | 1.29646i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.171499 | − | 0.840058i | −0.171499 | − | 0.840058i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.799443 | − | 0.600742i | \(-0.205128\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(48\) | −0.970942 | − | 0.239316i | −0.970942 | − | 0.239316i | ||||
\(49\) | −1.88096 | − | 2.30375i | −1.88096 | − | 2.30375i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.03702 | + | 1.07966i | −1.03702 | + | 1.07966i | ||||
\(53\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.07766 | + | 0.359776i | 1.07766 | + | 0.359776i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.379463 | + | 0.126683i | −0.379463 | + | 0.126683i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.554631 | + | 1.91481i | −0.554631 | + | 1.91481i | ||||
\(64\) | 0.885456 | + | 0.464723i | 0.885456 | + | 0.464723i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.69038 | −1.69038 | −0.845190 | − | 0.534466i | \(-0.820513\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.37723 | − | 0.586782i | 1.37723 | − | 0.586782i | 0.428693 | − | 0.903450i | \(-0.358974\pi\) |
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.428693 | − | 0.903450i | 0.428693 | − | 0.903450i | ||||
\(76\) | −0.960245 | − | 0.607222i | −0.960245 | − | 0.607222i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.759177 | + | 1.59993i | 0.759177 | + | 1.59993i | 0.799443 | + | 0.600742i | \(0.205128\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.948536 | − | 0.316668i | 0.948536 | − | 0.316668i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(84\) | 0.996757 | − | 1.72643i | 0.996757 | − | 1.72643i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.49217 | − | 2.58451i | −1.49217 | − | 2.58451i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.166997 | + | 1.37535i | 0.166997 | + | 1.37535i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.599417 | − | 1.58053i | 0.599417 | − | 1.58053i | −0.200026 | − | 0.979791i | \(-0.564103\pi\) |
0.799443 | − | 0.600742i | \(-0.205128\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.632445 | + | 0.774605i | −0.632445 | + | 0.774605i | ||||
\(101\) | 0 | 0 | −0.799443 | − | 0.600742i | \(-0.794872\pi\) | ||||
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.99351 | −1.99351 | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(108\) | −0.996757 | + | 0.0804666i | −0.996757 | + | 0.0804666i | ||||
\(109\) | −0.240292 | + | 1.97898i | −0.240292 | + | 1.97898i | −0.0402659 | + | 0.999189i | \(0.512821\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.103346 | − | 0.851134i | 0.103346 | − | 0.851134i | ||||
\(112\) | −1.38096 | + | 1.43773i | −1.38096 | + | 1.43773i | ||||
\(113\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.641762 | + | 1.35248i | −0.641762 | + | 1.35248i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.568065 | + | 0.822984i | 0.568065 | + | 0.822984i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.166997 | − | 1.37535i | 0.166997 | − | 1.37535i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.385456 | − | 0.401302i | 0.385456 | − | 0.401302i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.238540 | + | 0.823534i | 0.238540 | + | 0.823534i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.919979 | − | 0.391967i | \(-0.871795\pi\) | ||||
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.69530 | − | 1.50190i | 1.69530 | − | 1.50190i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0602790 | + | 1.49581i | 0.0602790 | + | 1.49581i | 0.692724 | + | 0.721202i | \(0.256410\pi\) |
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.987050 | + | 0.160411i | 0.987050 | + | 0.160411i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.06023 | + | 2.14493i | 2.06023 | + | 2.14493i | ||||
\(148\) | −0.304033 | + | 0.801669i | −0.304033 | + | 0.801669i | ||||
\(149\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0680647 | + | 1.68901i | 0.0680647 | + | 1.68901i | 0.568065 | + | 0.822984i | \(0.307692\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.946784 | − | 1.15960i | 0.946784 | − | 1.15960i | ||||
\(157\) | 0.706910 | + | 1.86397i | 0.706910 | + | 1.86397i | 0.428693 | + | 0.903450i | \(0.358974\pi\) |
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.645395 | − | 0.935016i | 0.645395 | − | 0.935016i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
1.00000 | \(0\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.440091 | − | 1.16042i | −0.440091 | − | 1.16042i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.10312 | − | 0.271894i | −1.10312 | − | 0.271894i | ||||
\(172\) | −0.0345234 | − | 0.856690i | −0.0345234 | − | 0.856690i | ||||
\(173\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.13245 | − | 1.64063i | −1.13245 | − | 1.64063i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.228667 | + | 1.88324i | 0.228667 | + | 1.88324i | 0.428693 | + | 0.903450i | \(0.358974\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.368039 | − | 0.156807i | 0.368039 | − | 0.156807i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.398754 | − | 1.95323i | 0.398754 | − | 1.95323i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −0.919979 | − | 0.391967i | −0.919979 | − | 0.391967i | ||||
\(193\) | 0.136945 | − | 0.198399i | 0.136945 | − | 0.198399i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.48705 | − | 2.57565i | −1.48705 | − | 2.57565i | ||||
\(197\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.84195 | + | 0.453999i | −1.84195 | + | 0.453999i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.68490 | − | 0.136019i | 1.68490 | − | 0.136019i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.19678 | + | 0.899324i | −1.19678 | + | 0.899324i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.103346 | + | 0.851134i | 0.103346 | + | 0.851134i | 0.948536 | + | 0.316668i | \(0.102564\pi\) |
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.54090 | + | 1.08258i | 2.54090 | + | 1.08258i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.32555 | + | 0.695701i | −1.32555 | + | 0.695701i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.251489 | + | 0.663123i | 0.251489 | + | 0.663123i | 1.00000 | \(0\) | ||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.354605 | + | 0.935016i | −0.354605 | + | 0.935016i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 1.00599 | + | 0.527986i | 1.00599 | + | 0.527986i | ||||
\(229\) | −0.627974 | − | 1.65583i | −0.627974 | − | 1.65583i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.120537 | − | 0.992709i | \(-0.461538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.885456 | − | 1.53365i | −0.885456 | − | 1.53365i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.724653 | + | 0.458243i | −0.724653 | + | 0.458243i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.919979 | + | 0.391967i | −0.919979 | + | 0.391967i | ||||
\(244\) | −0.394871 | + | 0.0641728i | −0.394871 | + | 0.0641728i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.43751 | − | 0.909025i | 1.43751 | − | 0.909025i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(252\) | −0.854605 | + | 1.80104i | −0.854605 | + | 1.80104i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.799443 | + | 0.600742i | 0.799443 | + | 0.600742i | ||||
\(257\) | 0 | 0 | 0.799443 | − | 0.600742i | \(-0.205128\pi\) | ||||
−0.799443 | + | 0.600742i | \(0.794872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.36642 | − | 1.02679i | −1.36642 | − | 1.02679i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.66849 | − | 0.271156i | −1.66849 | − | 0.271156i | ||||
\(269\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.970942 | − | 1.68172i | 0.970942 | − | 1.68172i | 0.278217 | − | 0.960518i | \(-0.410256\pi\) |
0.692724 | − | 0.721202i | \(-0.256410\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.69530 | + | 2.45606i | 1.69530 | + | 2.45606i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0670708 | − | 0.552378i | 0.0670708 | − | 0.552378i | −0.919979 | − | 0.391967i | \(-0.871795\pi\) |
0.987050 | − | 0.160411i | \(-0.0512821\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.277125 | − | 1.35745i | −0.277125 | − | 1.35745i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.402877 | + | 1.06230i | −0.402877 | + | 1.06230i | 0.568065 | + | 0.822984i | \(0.307692\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.692724 | + | 0.721202i | 0.692724 | + | 0.721202i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.470293 | + | 1.62364i | −0.470293 | + | 1.62364i | ||||
\(292\) | 1.45352 | − | 0.358261i | 1.45352 | − | 0.358261i | ||||
\(293\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.568065 | − | 0.822984i | 0.568065 | − | 0.822984i | ||||
\(301\) | 1.65954 | + | 0.409041i | 1.65954 | + | 0.409041i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.850405 | − | 0.753393i | −0.850405 | − | 0.753393i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.12142 | + | 0.182248i | 1.12142 | + | 0.182248i | 0.692724 | − | 0.721202i | \(-0.256410\pi\) |
0.428693 | + | 0.903450i | \(0.358974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.98705 | − | 0.160411i | 1.98705 | − | 0.160411i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.67977 | − | 0.881614i | 1.67977 | − | 0.881614i | 0.692724 | − | 0.721202i | \(-0.256410\pi\) |
0.987050 | − | 0.160411i | \(-0.0512821\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.492699 | + | 1.70099i | 0.492699 | + | 1.70099i | ||||
\(317\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.987050 | − | 0.160411i | 0.987050 | − | 0.160411i | ||||
\(325\) | −0.641762 | − | 1.35248i | −0.641762 | − | 1.35248i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0802707 | − | 1.99190i | 0.0802707 | − | 1.99190i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.76517 | − | 0.142499i | −1.76517 | − | 0.142499i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0345234 | + | 0.856690i | −0.0345234 | + | 0.856690i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.26079 | − | 1.54419i | 1.26079 | − | 1.54419i | ||||
\(337\) | 0.0740877 | + | 1.83847i | 0.0740877 | + | 1.83847i | 0.428693 | + | 0.903450i | \(0.358974\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.82104 | − | 0.941802i | 3.82104 | − | 0.941802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0161084 | − | 0.0789044i | 0.0161084 | − | 0.0789044i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.530851 | − | 1.39974i | 0.530851 | − | 1.39974i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.200026 | − | 0.979791i | \(-0.564103\pi\) | ||||
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.201437 | + | 0.209719i | 0.201437 | + | 0.209719i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.632445 | − | 0.774605i | −0.632445 | − | 0.774605i | ||||
\(364\) | −1.05826 | − | 2.79040i | −1.05826 | − | 2.79040i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0802707 | + | 0.00648012i | 0.0802707 | + | 0.00648012i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0557864 | + | 1.38433i | −0.0557864 | + | 1.38433i | ||||
\(373\) | −1.03702 | + | 0.918722i | −1.03702 | + | 0.918722i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.338119 | + | 0.213814i | 0.338119 | + | 0.213814i | 0.692724 | − | 0.721202i | \(-0.256410\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.351915 | + | 0.431017i | −0.351915 | + | 0.431017i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.799443 | − | 0.600742i | \(-0.794872\pi\) | ||||
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.304033 | − | 0.801669i | −0.304033 | − | 0.801669i | ||||
\(388\) | 0.845190 | − | 1.46391i | 0.845190 | − | 1.46391i | ||||
\(389\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.549229 | + | 1.89616i | 0.549229 | + | 1.89616i | 0.428693 | + | 0.903450i | \(0.358974\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.56894 | + | 1.63344i | −1.56894 | + | 1.63344i | ||||
\(400\) | −0.748511 | + | 0.663123i | −0.748511 | + | 0.663123i | ||||
\(401\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.75296 | + | 1.10851i | 1.75296 | + | 1.10851i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.593932 | − | 0.618348i | 0.593932 | − | 0.618348i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.96770 | − | 0.319782i | −1.96770 | − | 0.319782i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.180446 | − | 1.48611i | −0.180446 | − | 1.48611i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) | ||||
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.241073 | 0.241073 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0961290 | − | 0.791694i | 0.0961290 | − | 0.791694i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(432\) | −0.996757 | − | 0.0804666i | −0.996757 | − | 0.0804666i | ||||
\(433\) | −0.566973 | − | 0.426052i | −0.566973 | − | 0.426052i | 0.278217 | − | 0.960518i | \(-0.410256\pi\) |
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.554631 | + | 1.91481i | −0.554631 | + | 1.91481i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.45352 | − | 0.358261i | 1.45352 | − | 0.358261i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.22615 | − | 1.97219i | −2.22615 | − | 1.97219i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(444\) | 0.238540 | − | 0.823534i | 0.238540 | − | 0.823534i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.59370 | + | 1.19759i | −1.59370 | + | 1.19759i | ||||
\(449\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.203753 | − | 1.67806i | −0.203753 | − | 1.67806i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.45352 | − | 1.28771i | 1.45352 | − | 1.28771i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.527799 | − | 1.82217i | 0.527799 | − | 1.82217i | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) |
0.568065 | − | 0.822984i | \(-0.307692\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(468\) | −0.850405 | + | 1.23202i | −0.850405 | + | 1.23202i | ||||
\(469\) | 1.44461 | − | 3.04445i | 1.44461 | − | 3.04445i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.854605 | − | 1.80104i | −0.854605 | − | 1.80104i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.908271 | − | 0.682521i | 0.908271 | − | 0.682521i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.889128 | − | 0.925681i | −0.889128 | − | 0.925681i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.428693 | + | 0.903450i | 0.428693 | + | 0.903450i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.368039 | + | 0.156807i | 0.368039 | + | 0.156807i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.568065 | + | 0.983917i | −0.568065 | + | 0.983917i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.385456 | − | 1.33075i | 0.385456 | − | 1.33075i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0557864 | + | 0.0580798i | −0.0557864 | + | 0.0580798i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.692724 | + | 0.721202i | \(0.256410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.200026 | − | 0.979791i | \(-0.564103\pi\) | ||||
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.532039 | + | 1.12125i | 0.532039 | + | 1.12125i | ||||
\(508\) | 0.444838 | − | 0.334274i | 0.444838 | − | 0.334274i | ||||
\(509\) | 0 | 0 | −0.987050 | − | 0.160411i | \(-0.948718\pi\) | ||||
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.120167 | + | 2.98191i | −0.120167 | + | 2.98191i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.12142 | + | 0.182248i | 1.12142 | + | 0.182248i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.103346 | + | 0.851134i | 0.103346 | + | 0.851134i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.93559 | − | 0.156257i | 1.93559 | − | 0.156257i | 0.948536 | − | 0.316668i | \(-0.102564\pi\) |
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.26079 | + | 1.54419i | 1.26079 | + | 1.54419i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.91426 | − | 1.21051i | 1.91426 | − | 1.21051i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.97410 | − | 0.320823i | 1.97410 | − | 0.320823i | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) |
0.987050 | − | 0.160411i | \(-0.0512821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.379463 | − | 1.85873i | −0.379463 | − | 1.85873i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.946784 | − | 0.838778i | 0.946784 | − | 0.838778i | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) |
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.354228 | + | 0.185913i | −0.354228 | + | 0.185913i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.53034 | −3.53034 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.180446 | + | 1.48611i | −0.180446 | + | 1.48611i | ||||
\(557\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.18082 | + | 0.503099i | 1.18082 | + | 0.503099i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.692724 | − | 0.721202i | \(-0.743590\pi\) | ||||
0.692724 | + | 0.721202i | \(0.256410\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.240292 | + | 1.97898i | −0.240292 | + | 1.97898i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||||
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.799974 | − | 0.979791i | 0.799974 | − | 0.979791i | −0.200026 | − | 0.979791i | \(-0.564103\pi\) |
1.00000 | \(0\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.948536 | + | 0.316668i | 0.948536 | + | 0.316668i | ||||
\(577\) | −1.74527 | − | 0.582656i | −1.74527 | − | 0.582656i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.120537 | + | 0.208776i | −0.120537 | + | 0.208776i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(588\) | 1.68948 | + | 2.44764i | 1.68948 | + | 2.44764i | ||||
\(589\) | −0.558166 | + | 1.47176i | −0.558166 | + | 1.47176i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.428693 | + | 0.742517i | −0.428693 | + | 0.742517i | ||||
\(593\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.79944 | − | 0.600742i | 1.79944 | − | 0.600742i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.948536 | − | 0.316668i | \(-0.102564\pi\) | ||||
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.213460 | + | 1.75800i | 0.213460 | + | 1.75800i | 0.568065 | + | 0.822984i | \(0.307692\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.66849 | + | 0.271156i | −1.66849 | + | 0.271156i | ||||
\(604\) | −0.203753 | + | 1.67806i | −0.203753 | + | 1.67806i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.527799 | + | 1.82217i | 0.527799 | + | 1.82217i | 0.568065 | + | 0.822984i | \(0.307692\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | −0.919979 | − | 0.391967i | \(-0.871795\pi\) |
0.799443 | − | 0.600742i | \(-0.205128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.398754 | − | 0.0321908i | 0.398754 | − | 0.0321908i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.12054 | − | 0.992709i | 1.12054 | − | 0.992709i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.398754 | + | 1.95323i | 0.398754 | + | 1.95323i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.316091 | + | 0.457937i | 0.316091 | + | 0.457937i | 0.948536 | − | 0.316668i | \(-0.102564\pi\) |
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.171499 | − | 0.840058i | −0.171499 | − | 0.840058i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.43786 | − | 0.358261i | 4.43786 | − | 0.358261i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.0402659 | − | 0.999189i | \(-0.487179\pi\) | ||||
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.946784 | + | 0.838778i | 0.946784 | + | 0.838778i | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.845190 | − | 0.534466i | \(-0.820513\pi\) | ||||
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.61977 | − | 0.874609i | −2.61977 | − | 0.874609i | ||||
\(652\) | 0.787025 | − | 0.819379i | 0.787025 | − | 0.819379i | ||||
\(653\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.26527 | − | 0.800107i | 1.26527 | − | 0.800107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.203753 | − | 1.67806i | −0.203753 | − | 1.67806i | −0.632445 | − | 0.774605i | \(-0.717949\pi\) |
0.428693 | − | 0.903450i | \(-0.358974\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.304033 | − | 0.640736i | −0.304033 | − | 0.640736i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.01121 | − | 1.23850i | −1.01121 | − | 1.23850i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
−0.0402659 | − | 0.999189i | \(-0.512821\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.278217 | − | 0.960518i | 0.278217 | − | 0.960518i | ||||
\(676\) | −0.248247 | − | 1.21599i | −0.248247 | − | 1.21599i | ||||
\(677\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.33434 | + | 2.43031i | 2.33434 | + | 2.43031i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(684\) | −1.04522 | − | 0.445325i | −1.04522 | − | 0.445325i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.759177 | + | 1.59993i | 0.759177 | + | 1.59993i | ||||
\(688\) | 0.103346 | − | 0.851134i | 0.103346 | − | 0.851134i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.368039 | + | 1.80277i | 0.368039 | + | 1.80277i | 0.568065 | + | 0.822984i | \(0.307692\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.854605 | − | 1.80104i | −0.854605 | − | 1.80104i | ||||
\(701\) | 0 | 0 | 0.692724 | − | 0.721202i | \(-0.256410\pi\) | ||||
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.553352 | − | 0.801669i | 0.553352 | − | 0.801669i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.0643806 | + | 0.0483789i | −0.0643806 | + | 0.0483789i | −0.632445 | − | 0.774605i | \(-0.717949\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00599 | + | 1.45743i | 1.00599 | + | 1.45743i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.70367 | − | 3.59040i | 1.70367 | − | 3.59040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.685430 | − | 0.515067i | 0.685430 | − | 0.515067i | ||||
\(724\) | −0.0763874 | + | 1.89553i | −0.0763874 | + | 1.89553i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.470293 | + | 1.62364i | −0.470293 | + | 1.62364i | 0.278217 | + | 0.960518i | \(0.410256\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.388427 | − | 0.0957386i | 0.388427 | − | 0.0957386i | ||||
\(733\) | −1.74527 | + | 0.743589i | −1.74527 | + | 0.743589i | −0.748511 | + | 0.663123i | \(0.769231\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.76517 | − | 0.142499i | −1.76517 | − | 0.142499i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.35970 | + | 1.02175i | −1.35970 | + | 1.02175i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.948536 | − | 0.316668i | \(-0.102564\pi\) | ||||
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.94188 | −1.94188 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.706910 | − | 1.86397i | 0.706910 | − | 1.86397i | ||||
\(757\) | 1.07766 | − | 0.359776i | 1.07766 | − | 0.359776i | 0.278217 | − | 0.960518i | \(-0.410256\pi\) |
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.278217 | − | 0.960518i | \(-0.410256\pi\) | ||||
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.35887 | − | 2.12402i | −3.35887 | − | 2.12402i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.845190 | − | 0.534466i | −0.845190 | − | 0.534466i | ||||
\(769\) | 1.59889 | 1.59889 | 0.799443 | − | 0.600742i | \(-0.205128\pi\) | ||||
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.166997 | − | 0.173863i | 0.166997 | − | 0.173863i | ||||
\(773\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.22675 | + | 0.643850i | 1.22675 | + | 0.643850i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.44461 | + | 0.913514i | 1.44461 | + | 0.913514i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.05463 | − | 2.78083i | −1.05463 | − | 2.78083i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.62920 | − | 0.855072i | −1.62920 | − | 0.855072i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
−0.632445 | − | 0.774605i | \(-0.717949\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.166620 | − | 0.575240i | 0.166620 | − | 0.575240i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.89092 | + | 0.152651i | −1.89092 | + | 0.152651i | ||||
\(797\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.68490 | + | 0.136019i | 1.68490 | + | 0.136019i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) | ||||
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.685430 | + | 1.44451i | 0.685430 | + | 1.44451i | 0.885456 | + | 0.464723i | \(0.153846\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.832471 | + | 1.75440i | −0.832471 | + | 1.75440i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.194845 | + | 0.954415i | −0.194845 | + | 0.954415i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.88743 | − | 2.31168i | −1.88743 | − | 2.31168i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.12054 | − | 0.992709i | 1.12054 | − | 0.992709i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
1.00000 | \(0\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.0402659 | − | 0.999189i | \(-0.487179\pi\) | ||||
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.74527 | − | 0.582656i | −1.74527 | − | 0.582656i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.0224054 | + | 0.555984i | −0.0224054 | + | 0.555984i | ||||
\(832\) | −1.32555 | + | 0.695701i | −1.32555 | + | 0.695701i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.385456 | + | 1.33075i | 0.385456 | + | 1.33075i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.0402659 | − | 0.999189i | −0.0402659 | − | 0.999189i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.0345234 | + | 0.856690i | −0.0345234 | + | 0.856690i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.96770 | + | 0.319782i | −1.96770 | + | 0.319782i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.316091 | − | 1.09127i | 0.316091 | − | 1.09127i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.213460 | + | 0.112032i | 0.213460 | + | 0.112032i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.38096 | + | 1.43773i | −1.38096 | + | 1.43773i | −0.632445 | + | 0.774605i | \(0.717949\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.748511 | − | 0.663123i | −0.748511 | − | 0.663123i | ||||
\(868\) | 2.33434 | + | 1.47615i | 2.33434 | + | 1.47615i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.43751 | − | 2.08259i | 1.43751 | − | 2.08259i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.338119 | − | 1.65622i | 0.338119 | − | 1.65622i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.41998 | + | 0.474059i | −1.41998 | + | 0.474059i | ||||
\(877\) | 0.0509320 | + | 0.0623804i | 0.0509320 | + | 0.0623804i | 0.799443 | − | 0.600742i | \(-0.205128\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||||
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.388427 | + | 0.0957386i | 0.388427 | + | 0.0957386i | 0.428693 | − | 0.903450i | \(-0.358974\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.393349 | + | 1.03718i | 0.393349 | + | 1.03718i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.141860 | + | 0.694877i | 0.141860 | + | 0.694877i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.68708 | − | 0.274177i | −1.68708 | − | 0.274177i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.444838 | + | 0.334274i | 0.444838 | + | 0.334274i | 0.799443 | − | 0.600742i | \(-0.205128\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(912\) | 0.908271 | + | 0.682521i | 0.908271 | + | 0.682521i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.354228 | − | 1.73512i | −0.354228 | − | 1.73512i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.171499 | + | 0.361427i | −0.171499 | + | 0.361427i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13245 | − | 0.0914204i | −1.13245 | − | 0.0914204i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.641762 | − | 0.568552i | −0.641762 | − | 0.568552i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.96770 | + | 0.319782i | −1.96770 | + | 0.319782i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.940087 | + | 3.24556i | 0.940087 | + | 3.24556i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.987050 | + | 1.70962i | −0.987050 | + | 1.70962i | −0.354605 | + | 0.935016i | \(0.615385\pi\) |
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.60339 | + | 1.01392i | −1.60339 | + | 1.01392i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(948\) | −0.627974 | − | 1.65583i | −0.627974 | − | 1.65583i | ||||
\(949\) | −0.448272 | + | 2.19578i | −0.448272 | + | 2.19578i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.916487 | + | 0.0739864i | −0.916487 | + | 0.0739864i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.788777 | + | 0.336066i | −0.788777 | + | 0.336066i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.12001 | − | 0.587824i | −1.12001 | − | 0.587824i | −0.200026 | − | 0.979791i | \(-0.564103\pi\) |
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.692724 | − | 0.721202i | \(-0.256410\pi\) | ||||
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(972\) | −0.970942 | + | 0.239316i | −0.970942 | + | 0.239316i | ||||
\(973\) | −2.74553 | − | 1.16976i | −2.74553 | − | 1.16976i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.748511 | + | 1.29646i | 0.748511 | + | 1.29646i | ||||
\(976\) | −0.400051 | −0.400051 | ||||||||
\(977\) | 0 | 0 | 0.428693 | − | 0.903450i | \(-0.358974\pi\) | ||||
−0.428693 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0802707 | + | 1.99190i | 0.0802707 | + | 1.99190i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.200026 | − | 0.979791i | \(-0.564103\pi\) | ||||
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.56471 | − | 0.666661i | 1.56471 | − | 0.666661i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.568065 | − | 0.983917i | −0.568065 | − | 0.983917i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
0.428693 | − | 0.903450i | \(-0.358974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.77091 | 1.77091 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.27458 | + | 1.32698i | −1.27458 | + | 1.32698i | −0.354605 | + | 0.935016i | \(0.615385\pi\) |
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0345234 | − | 0.856690i | −0.0345234 | − | 0.856690i |
(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 | 3513.1.bc.a.1571.1 | yes | 24 | |
3.2 | odd | 2 | CM | 3513.1.bc.a.1571.1 | yes | 24 | |
1171.202 | even | 39 | inner | 3513.1.bc.a.1373.1 | ✓ | 24 | |
3513.1373 | odd | 78 | inner | 3513.1.bc.a.1373.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3513.1.bc.a.1373.1 | ✓ | 24 | 1171.202 | even | 39 | inner | |
3513.1.bc.a.1373.1 | ✓ | 24 | 3513.1373 | odd | 78 | inner | |
3513.1.bc.a.1571.1 | yes | 24 | 1.1 | even | 1 | trivial | |
3513.1.bc.a.1571.1 | yes | 24 | 3.2 | odd | 2 | CM |