Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,1,Mod(95,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(78))
chi = DirichletCharacter(H, H._module([39, 52, 37]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.95");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.da (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: | \(1.77118172983\) |
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: | \( x^{24} - x^{23} + x^{21} - x^{20} + x^{18} - x^{17} + x^{15} - x^{14} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{78}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{78} - \cdots)\) |
Embedding invariants
Embedding label | 2480.1 | ||
Root | \(-0.632445 + 0.774605i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.2480 |
Dual form | 3549.1.da.a.1733.1 |
$q$-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 \(\left(\mathbb{Z}/3549\mathbb{Z}\right)^\times\).
\(n\) | \(1184\) | \(1522\) | \(3382\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{78}\right)\) |
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 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(3\) | −0.428693 | − | 0.903450i | −0.428693 | − | 0.903450i | ||||
\(4\) | 0.748511 | − | 0.663123i | 0.748511 | − | 0.663123i | ||||
\(5\) | 0 | 0 | 0.391967 | − | 0.919979i | \(-0.371795\pi\) | ||||
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.919979 | + | 0.391967i | 0.919979 | + | 0.391967i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.632445 | + | 0.774605i | −0.632445 | + | 0.774605i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.774605 | − | 0.632445i | \(-0.217949\pi\) | ||||
−0.774605 | + | 0.632445i | \(0.782051\pi\) | |||||||
\(12\) | −0.919979 | − | 0.391967i | −0.919979 | − | 0.391967i | ||||
\(13\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.120537 | − | 0.992709i | 0.120537 | − | 0.992709i | ||||
\(17\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.277840 | + | 0.160411i | −0.277840 | + | 0.160411i | −0.632445 | − | 0.774605i | \(-0.717949\pi\) |
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0402659 | − | 0.999189i | −0.0402659 | − | 0.999189i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.692724 | − | 0.721202i | −0.692724 | − | 0.721202i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.970942 | + | 0.239316i | 0.970942 | + | 0.239316i | ||||
\(28\) | 0.948536 | − | 0.316668i | 0.948536 | − | 0.316668i | ||||
\(29\) | 0 | 0 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.27388 | − | 0.368985i | 1.27388 | − | 0.368985i | 0.428693 | − | 0.903450i | \(-0.358974\pi\) |
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0402659 | + | 0.999189i | 0.0402659 | + | 0.999189i | ||||
\(37\) | 0.478243 | − | 1.94031i | 0.478243 | − | 1.94031i | 0.200026 | − | 0.979791i | \(-0.435897\pi\) |
0.278217 | − | 0.960518i | \(-0.410256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.568065 | − | 0.822984i | 0.568065 | − | 0.822984i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.0804666 | − | 0.996757i | \(-0.474359\pi\) | ||||
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0224054 | + | 0.0773523i | −0.0224054 | + | 0.0773523i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(48\) | −0.948536 | + | 0.316668i | −0.948536 | + | 0.316668i | ||||
\(49\) | 0.692724 | + | 0.721202i | 0.692724 | + | 0.721202i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.948536 | + | 0.316668i | 0.948536 | + | 0.316668i | ||||
\(53\) | 0 | 0 | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) | ||||
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.264032 | + | 0.182248i | 0.264032 | + | 0.182248i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.60339 | + | 1.01392i | 1.60339 | + | 1.01392i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.885456 | + | 0.464723i | −0.885456 | + | 0.464723i | ||||
\(64\) | −0.568065 | − | 0.822984i | −0.568065 | − | 0.822984i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.151567 | − | 0.453999i | −0.151567 | − | 0.453999i | 0.845190 | − | 0.534466i | \(-0.179487\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.903450 | − | 0.428693i | \(-0.141026\pi\) | ||||
−0.903450 | + | 0.428693i | \(0.858974\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.192732 | − | 1.18593i | −0.192732 | − | 1.18593i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
0.692724 | − | 0.721202i | \(-0.256410\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.354605 | + | 0.935016i | −0.354605 | + | 0.935016i | ||||
\(76\) | −0.101594 | + | 0.304312i | −0.101594 | + | 0.304312i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.07766 | + | 0.359776i | −1.07766 | + | 0.359776i | −0.799443 | − | 0.600742i | \(-0.794872\pi\) |
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.200026 | − | 0.979791i | −0.200026 | − | 0.979791i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.822984 | − | 0.568065i | \(-0.192308\pi\) | ||||
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(84\) | −0.692724 | − | 0.721202i | −0.692724 | − | 0.721202i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.120537 | + | 0.992709i | 0.120537 | + | 0.992709i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.879463 | − | 0.992709i | −0.879463 | − | 0.992709i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.04052 | + | 1.38468i | −1.04052 | + | 1.38468i | −0.120537 | + | 0.992709i | \(0.538462\pi\) |
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.996757 | − | 0.0804666i | −0.996757 | − | 0.0804666i | ||||
\(101\) | 0 | 0 | 0.278217 | − | 0.960518i | \(-0.410256\pi\) | ||||
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.685430 | + | 1.44451i | 0.685430 | + | 1.44451i | 0.885456 | + | 0.464723i | \(0.153846\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(108\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(109\) | 0.565375 | − | 0.543050i | 0.565375 | − | 0.543050i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.95799 | + | 0.399727i | −1.95799 | + | 0.399727i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(113\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.987050 | − | 0.160411i | −0.987050 | − | 0.160411i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.200026 | − | 0.979791i | 0.200026 | − | 0.979791i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.708833 | − | 1.12093i | 0.708833 | − | 1.12093i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.368039 | + | 1.80277i | −0.368039 | + | 1.80277i | 0.200026 | + | 0.979791i | \(0.435897\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0794890 | − | 0.0129182i | 0.0794890 | − | 0.0129182i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.987050 | − | 0.160411i | \(-0.948718\pi\) | ||||
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.318483 | + | 0.0386709i | −0.318483 | + | 0.0386709i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.55242 | − | 1.16657i | −1.55242 | − | 1.16657i | −0.919979 | − | 0.391967i | \(-0.871795\pi\) |
−0.632445 | − | 0.774605i | \(-0.717949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.692724 | + | 0.721202i | 0.692724 | + | 0.721202i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.354605 | − | 0.935016i | 0.354605 | − | 0.935016i | ||||
\(148\) | −0.928693 | − | 1.76948i | −0.928693 | − | 1.76948i | ||||
\(149\) | 0 | 0 | −0.979791 | − | 0.200026i | \(-0.935897\pi\) | ||||
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.151567 | − | 0.453999i | 0.151567 | − | 0.453999i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
0.996757 | + | 0.0804666i | \(0.0256410\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | ||||
\(157\) | −0.319818 | + | 0.240328i | −0.319818 | + | 0.240328i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.428693 | + | 0.903450i | \(0.358974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.84519 | + | 0.534466i | −1.84519 | + | 0.534466i | −0.845190 | + | 0.534466i | \(0.820513\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.774605 | − | 0.632445i | \(-0.782051\pi\) | ||||
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0514636 | − | 0.316668i | 0.0514636 | − | 0.316668i | ||||
\(172\) | 0.0345234 | + | 0.0727566i | 0.0345234 | + | 0.0727566i | ||||
\(173\) | 0 | 0 | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||||
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.354605 | − | 0.935016i | −0.354605 | − | 0.935016i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.0402659 | − | 0.999189i | \(-0.487179\pi\) | ||||
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0670708 | + | 0.552378i | 0.0670708 | + | 0.552378i | 0.987050 | + | 0.160411i | \(0.0512821\pi\) |
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.228667 | − | 1.88324i | 0.228667 | − | 1.88324i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.799443 | + | 0.600742i | 0.799443 | + | 0.600742i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(193\) | −1.06806 | − | 0.0430415i | −1.06806 | − | 0.0430415i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.996757 | + | 0.0804666i | 0.996757 | + | 0.0804666i | ||||
\(197\) | 0 | 0 | 0.721202 | − | 0.692724i | \(-0.243590\pi\) | ||||
−0.721202 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.237952 | + | 1.95971i | −0.237952 | + | 1.95971i | 0.0402659 | + | 0.999189i | \(0.487179\pi\) |
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.345190 | + | 0.331560i | −0.345190 | + | 0.331560i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.919979 | − | 0.391967i | 0.919979 | − | 0.391967i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.111301 | − | 0.545190i | 0.111301 | − | 0.545190i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.31658 | + | 0.159861i | 1.31658 | + | 0.159861i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.988802 | + | 0.682521i | −0.988802 | + | 0.682521i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.799443 | − | 0.600742i | \(-0.205128\pi\) | ||||
−0.799443 | + | 0.600742i | \(0.794872\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.996757 | − | 0.0804666i | 0.996757 | − | 0.0804666i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(228\) | 0.318483 | − | 0.0386709i | 0.318483 | − | 0.0386709i | ||||
\(229\) | 0.752982 | + | 0.218104i | 0.752982 | + | 0.218104i | 0.632445 | − | 0.774605i | \(-0.282051\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.787025 | + | 0.819379i | 0.787025 | + | 0.819379i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31658 | − | 0.159861i | −1.31658 | − | 0.159861i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.799443 | + | 0.600742i | −0.799443 | + | 0.600742i | ||||
\(244\) | 1.87251 | − | 0.304312i | 1.87251 | − | 0.304312i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.277840 | − | 0.160411i | −0.277840 | − | 0.160411i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.692724 | − | 0.721202i | \(-0.256410\pi\) | ||||
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(252\) | −0.354605 | + | 0.935016i | −0.354605 | + | 0.935016i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.970942 | − | 0.239316i | −0.970942 | − | 0.239316i | ||||
\(257\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.20051 | − | 1.59759i | 1.20051 | − | 1.59759i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.414507 | − | 0.239316i | −0.414507 | − | 0.239316i | ||||
\(269\) | 0 | 0 | 0.568065 | − | 0.822984i | \(-0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.29944 | − | 1.46677i | 1.29944 | − | 1.46677i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.799443 | − | 0.600742i | \(-0.205128\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.845190 | − | 0.534466i | 0.845190 | − | 0.534466i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.759177 | − | 0.398447i | 0.759177 | − | 0.398447i | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) |
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.519844 | + | 1.22012i | −0.519844 | + | 1.22012i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.10759 | + | 1.15312i | −1.10759 | + | 1.15312i | −0.120537 | + | 0.992709i | \(0.538462\pi\) |
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.568065 | + | 0.822984i | 0.568065 | + | 0.822984i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.69705 | + | 0.346455i | 1.69705 | + | 0.346455i | ||||
\(292\) | −0.930676 | − | 0.759873i | −0.930676 | − | 0.759873i | ||||
\(293\) | 0 | 0 | −0.999189 | − | 0.0402659i | \(-0.987179\pi\) | ||||
0.999189 | + | 0.0402659i | \(0.0128205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.354605 | + | 0.935016i | 0.354605 | + | 0.935016i | ||||
\(301\) | −0.0509320 | + | 0.0623804i | −0.0509320 | + | 0.0623804i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.125752 | + | 0.295150i | 0.125752 | + | 0.295150i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.222431 | − | 0.902438i | 0.222431 | − | 0.902438i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.01121 | − | 1.23850i | 1.01121 | − | 1.23850i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.238540 | + | 0.823534i | −0.238540 | + | 0.823534i | 0.748511 | + | 0.663123i | \(0.230769\pi\) |
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.568065 | + | 0.983917i | −0.568065 | + | 0.983917i | ||||
\(317\) | 0 | 0 | −0.999189 | − | 0.0402659i | \(-0.987179\pi\) | ||||
0.999189 | + | 0.0402659i | \(0.0128205\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.799443 | − | 0.600742i | −0.799443 | − | 0.600742i | ||||
\(325\) | 0.278217 | − | 0.960518i | 0.278217 | − | 0.960518i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.732990 | − | 0.277987i | −0.732990 | − | 0.277987i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.44124 | + | 0.0580798i | −1.44124 | + | 0.0580798i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.20051 | + | 1.59759i | 1.20051 | + | 1.59759i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.996757 | − | 0.0804666i | −0.996757 | − | 0.0804666i | ||||
\(337\) | 1.69038 | 1.69038 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.354605 | + | 0.935016i | 0.354605 | + | 0.935016i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.277840 | + | 1.70962i | 0.277840 | + | 1.70962i | 0.632445 | + | 0.774605i | \(0.282051\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.278217 | + | 0.960518i | 0.278217 | + | 0.960518i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.534466 | − | 0.845190i | \(-0.679487\pi\) | ||||
0.534466 | + | 0.845190i | \(0.320513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.999189 | − | 0.0402659i | \(-0.987179\pi\) | ||||
0.999189 | + | 0.0402659i | \(0.0128205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.448536 | + | 0.776888i | −0.448536 | + | 0.776888i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.970942 | + | 0.239316i | −0.970942 | + | 0.239316i | ||||
\(364\) | 0.748511 | + | 0.663123i | 0.748511 | + | 0.663123i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.96770 | − | 0.319782i | −1.96770 | − | 0.319782i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
−0.970942 | − | 0.239316i | \(-0.923077\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.31658 | − | 0.159861i | −1.31658 | − | 0.159861i | ||||
\(373\) | 1.47764 | − | 0.240139i | 1.47764 | − | 0.240139i | 0.632445 | − | 0.774605i | \(-0.282051\pi\) |
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.150475 | + | 1.86397i | −0.150475 | + | 1.86397i | 0.278217 | + | 0.960518i | \(0.410256\pi\) |
−0.428693 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.78649 | − | 0.440331i | 1.78649 | − | 0.440331i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.534466 | − | 0.845190i | \(-0.320513\pi\) | ||||
−0.534466 | + | 0.845190i | \(0.679487\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.0457473 | − | 0.0662764i | −0.0457473 | − | 0.0662764i | ||||
\(388\) | 0.139372 | + | 1.72643i | 0.139372 | + | 1.72643i | ||||
\(389\) | 0 | 0 | −0.845190 | − | 0.534466i | \(-0.820513\pi\) | ||||
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.380472 | − | 0.506316i | −0.380472 | − | 0.506316i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.171469 | + | 0.271156i | 0.171469 | + | 0.271156i | ||||
\(400\) | −0.799443 | + | 0.600742i | −0.799443 | + | 0.600742i | ||||
\(401\) | 0 | 0 | −0.992709 | − | 0.120537i | \(-0.961538\pi\) | ||||
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.956491 | + | 0.918722i | 0.956491 | + | 0.918722i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.27497 | + | 0.880052i | 1.27497 | + | 0.880052i | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) |
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.47094 | + | 0.626710i | 1.47094 | + | 0.626710i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.388427 | + | 1.90264i | −0.388427 | + | 1.90264i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||||
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.63397 | − | 1.12785i | 1.63397 | − | 1.12785i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.07766 | + | 1.56126i | 1.07766 | + | 1.56126i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(432\) | 0.354605 | − | 0.935016i | 0.354605 | − | 0.935016i | ||||
\(433\) | −0.652458 | − | 0.277987i | −0.652458 | − | 0.277987i | 0.0402659 | − | 0.999189i | \(-0.487179\pi\) |
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.0630804 | − | 0.781391i | 0.0630804 | − | 0.781391i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.91674 | + | 0.472433i | −1.91674 | + | 0.472433i | −0.919979 | + | 0.391967i | \(0.871795\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.996757 | + | 0.0804666i | −0.996757 | + | 0.0804666i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(444\) | −1.20051 | + | 1.59759i | −1.20051 | + | 1.59759i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.200026 | − | 0.979791i | −0.200026 | − | 0.979791i | ||||
\(449\) | 0 | 0 | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.475142 | + | 0.0576926i | −0.475142 | + | 0.0576926i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.63397 | + | 1.12785i | −1.63397 | + | 1.12785i | −0.748511 | + | 0.663123i | \(0.769231\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44854 | + | 0.549357i | −1.44854 | + | 0.549357i | −0.948536 | − | 0.316668i | \(-0.897436\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(468\) | −0.845190 | + | 0.534466i | −0.845190 | + | 0.534466i | ||||
\(469\) | 0.0385138 | − | 0.477079i | 0.0385138 | − | 0.477079i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.354228 | + | 0.185913i | 0.354228 | + | 0.185913i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.308156 | + | 0.0892584i | 0.308156 | + | 0.0892584i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.960518 | − | 0.278217i | \(-0.910256\pi\) | ||||
0.960518 | + | 0.278217i | \(0.0897436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.91948 | − | 0.555984i | 1.91948 | − | 0.555984i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.29944 | + | 1.46677i | −1.29944 | + | 1.46677i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.799443 | + | 0.600742i | \(0.794872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.27388 | + | 1.43792i | 1.27388 | + | 1.43792i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.212745 | − | 1.30907i | −0.212745 | − | 1.30907i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.642152 | − | 1.01548i | −0.642152 | − | 1.01548i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
0.354605 | − | 0.935016i | \(-0.384615\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | 0.996757 | + | 0.0804666i | 0.996757 | + | 0.0804666i | ||||
\(508\) | 0.919979 | + | 1.59345i | 0.919979 | + | 1.59345i | ||||
\(509\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.287534 | − | 1.16657i | 0.287534 | − | 1.16657i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.308156 | + | 0.0892584i | −0.308156 | + | 0.0892584i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0509320 | − | 0.0623804i | 0.0509320 | − | 0.0623804i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.152466 | + | 1.25567i | −0.152466 | + | 1.25567i | 0.692724 | + | 0.721202i | \(0.256410\pi\) |
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.692724 | + | 0.721202i | −0.692724 | + | 0.721202i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.212745 | + | 0.240139i | −0.212745 | + | 0.240139i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.866514 | − | 1.15312i | 0.866514 | − | 1.15312i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.987050 | − | 0.160411i | \(-0.0512821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.470293 | − | 0.297395i | 0.470293 | − | 0.297395i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.141860 | − | 0.374055i | 0.141860 | − | 0.374055i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.79944 | + | 0.600742i | −1.79944 | + | 0.600742i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.13245 | − | 0.0914204i | −1.13245 | − | 0.0914204i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.93559 | + | 0.156257i | −1.93559 | + | 0.156257i | ||||
\(557\) | 0 | 0 | −0.0804666 | − | 0.996757i | \(-0.525641\pi\) | ||||
0.0804666 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0781918 | + | 0.0192725i | −0.0781918 | + | 0.0192725i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.200026 | − | 0.979791i | 0.200026 | − | 0.979791i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.854605 | − | 1.80104i | 0.854605 | − | 1.80104i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.996757 | + | 0.0804666i | 0.996757 | + | 0.0804666i | ||||
\(577\) | −1.66367 | + | 0.960518i | −1.66367 | + | 0.960518i | −0.692724 | + | 0.721202i | \(0.743590\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.418986 | + | 0.983395i | 0.418986 | + | 0.983395i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(588\) | −0.354605 | − | 0.935016i | −0.354605 | − | 0.935016i | ||||
\(589\) | −0.294747 | + | 0.306864i | −0.294747 | + | 0.306864i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.86852 | − | 0.708635i | −1.86852 | − | 0.708635i | ||||
\(593\) | 0 | 0 | −0.0804666 | − | 0.996757i | \(-0.525641\pi\) | ||||
0.0804666 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.87251 | − | 0.625134i | 1.87251 | − | 0.625134i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||||
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0794890 | − | 0.0129182i | 0.0794890 | − | 0.0129182i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.447528 | + | 0.169725i | 0.447528 | + | 0.169725i | ||||
\(604\) | −0.187607 | − | 0.440331i | −0.187607 | − | 0.440331i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.68490 | + | 0.136019i | 1.68490 | + | 0.136019i | 0.885456 | − | 0.464723i | \(-0.153846\pi\) |
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.642152 | + | 0.854550i | −0.642152 | + | 0.854550i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.391967 | − | 0.919979i | \(-0.371795\pi\) | ||||
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.160803 | − | 1.99190i | 0.160803 | − | 1.99190i | 0.0402659 | − | 0.999189i | \(-0.487179\pi\) |
0.120537 | − | 0.992709i | \(-0.461538\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.748511 | − | 0.663123i | −0.748511 | − | 0.663123i | ||||
\(625\) | −0.0402659 | + | 0.999189i | −0.0402659 | + | 0.999189i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0800206 | + | 0.391967i | −0.0800206 | + | 0.391967i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.99676 | + | 0.0804666i | 1.99676 | + | 0.0804666i | 1.00000 | \(0\) | ||
0.996757 | + | 0.0804666i | \(0.0256410\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.540266 | + | 0.133164i | −0.540266 | + | 0.133164i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.278217 | + | 0.960518i | −0.278217 | + | 0.960518i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0860133 | + | 1.06547i | 0.0860133 | + | 1.06547i | 0.885456 | + | 0.464723i | \(0.153846\pi\) |
−0.799443 | + | 0.600742i | \(0.794872\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.987050 | − | 0.160411i | \(-0.948718\pi\) | ||||
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.419979 | − | 1.25799i | −0.419979 | − | 1.25799i | ||||
\(652\) | −1.02673 | + | 1.62364i | −1.02673 | + | 1.62364i | ||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.04052 | + | 0.600742i | 1.04052 | + | 0.600742i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.999468 | − | 1.58053i | −0.999468 | − | 1.58053i | −0.799443 | − | 0.600742i | \(-0.794872\pi\) |
−0.200026 | − | 0.979791i | \(-0.564103\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26079 | + | 0.101781i | 1.26079 | + | 0.101781i | 0.692724 | − | 0.721202i | \(-0.256410\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(676\) | 0.200026 | + | 0.979791i | 0.200026 | + | 0.979791i | ||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(684\) | −0.171469 | − | 0.271156i | −0.171469 | − | 0.271156i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.125752 | − | 0.773781i | −0.125752 | − | 0.773781i | ||||
\(688\) | 0.0740877 | + | 0.0315658i | 0.0740877 | + | 0.0315658i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.294326 | − | 0.560791i | 0.294326 | − | 0.560791i | −0.692724 | − | 0.721202i | \(-0.743590\pi\) |
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.885456 | − | 0.464723i | −0.885456 | − | 0.464723i | ||||
\(701\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.178372 | + | 0.615812i | 0.178372 | + | 0.615812i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.73556 | − | 0.823534i | −1.73556 | − | 0.823534i | −0.987050 | − | 0.160411i | \(-0.948718\pi\) |
−0.748511 | − | 0.663123i | \(-0.769231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.402877 | − | 1.06230i | 0.402877 | − | 1.06230i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.692724 | − | 0.721202i | \(-0.743590\pi\) | ||||
0.692724 | + | 0.721202i | \(0.256410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0643806 | + | 1.59759i | 0.0643806 | + | 1.59759i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.419979 | + | 1.25799i | 0.419979 | + | 1.25799i | ||||
\(724\) | 0.416498 | + | 0.368985i | 0.416498 | + | 0.368985i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.56806 | + | 0.822984i | −1.56806 | + | 0.822984i | −0.568065 | + | 0.822984i | \(0.692308\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.885456 | + | 0.464723i | 0.885456 | + | 0.464723i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.07766 | − | 1.56126i | −1.07766 | − | 1.56126i | ||||
\(733\) | −0.839709 | + | 0.398447i | −0.839709 | + | 0.398447i | −0.799443 | − | 0.600742i | \(-0.794872\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.380472 | − | 0.506316i | 0.380472 | − | 0.506316i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0258155 | + | 0.319782i | −0.0258155 | + | 0.319782i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.979791 | − | 0.200026i | \(-0.935897\pi\) | ||||
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.652458 | − | 1.72039i | 0.652458 | − | 1.72039i | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) |
0.692724 | − | 0.721202i | \(-0.256410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.996757 | − | 0.0804666i | 0.996757 | − | 0.0804666i | ||||
\(757\) | −1.67977 | − | 0.560791i | −1.67977 | − | 0.560791i | −0.692724 | − | 0.721202i | \(-0.743590\pi\) |
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.732990 | − | 0.277987i | 0.732990 | − | 0.277987i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.200026 | + | 0.979791i | 0.200026 | + | 0.979791i | ||||
\(769\) | 0.456763 | − | 1.36817i | 0.456763 | − | 1.36817i | −0.428693 | − | 0.903450i | \(-0.641026\pi\) |
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.828000 | + | 0.676041i | −0.828000 | + | 0.676041i | ||||
\(773\) | 0 | 0 | −0.992709 | − | 0.120537i | \(-0.961538\pi\) | ||||
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.14856 | − | 0.663123i | −1.14856 | − | 0.663123i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.95799 | − | 0.399727i | −1.95799 | − | 0.399727i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.799443 | − | 0.600742i | 0.799443 | − | 0.600742i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.796732 | − | 0.899324i | −0.796732 | − | 0.899324i | 0.200026 | − | 0.979791i | \(-0.435897\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0763874 | + | 1.89553i | −0.0763874 | + | 1.89553i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.12142 | + | 1.62465i | 1.12142 | + | 1.62465i | ||||
\(797\) | 0 | 0 | 0.948536 | − | 0.316668i | \(-0.102564\pi\) | ||||
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.0385138 | + | 0.477079i | −0.0385138 | + | 0.477079i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.318483 | + | 0.0386709i | 0.318483 | + | 0.0386709i | 0.278217 | − | 0.960518i | \(-0.410256\pi\) |
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.88221 | − | 0.545190i | −1.88221 | − | 0.545190i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.00618307 | − | 0.0250857i | −0.00618307 | − | 0.0250857i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.845190 | − | 0.534466i | −0.845190 | − | 0.534466i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.709210 | −0.709210 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.47094 | + | 1.10534i | 1.47094 | + | 1.10534i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.685430 | − | 0.515067i | −0.685430 | − | 0.515067i | ||||
\(832\) | 0.428693 | − | 0.903450i | 0.428693 | − | 0.903450i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.32517 | − | 0.0534025i | 1.32517 | − | 0.0534025i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.721202 | − | 0.692724i | \(-0.756410\pi\) | ||||
0.721202 | + | 0.692724i | \(0.243590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.200026 | − | 0.979791i | −0.200026 | − | 0.979791i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.278217 | − | 0.481887i | −0.278217 | − | 0.481887i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.568065 | − | 0.822984i | 0.568065 | − | 0.822984i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.51660 | + | 0.506316i | 1.51660 | + | 0.506316i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.922670 | − | 1.75800i | 0.922670 | − | 1.75800i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
0.568065 | − | 0.822984i | \(-0.307692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.799443 | − | 0.600742i | \(-0.205128\pi\) | ||||
−0.799443 | + | 0.600742i | \(0.794872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.59370 | + | 1.19759i | 1.59370 | + | 1.19759i | 0.845190 | + | 0.534466i | \(0.179487\pi\) |
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(868\) | 1.09148 | − | 0.753393i | 1.09148 | − | 0.753393i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.317391 | − | 0.358261i | 0.317391 | − | 0.358261i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.414507 | − | 1.68172i | −0.414507 | − | 1.68172i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.287534 | + | 1.16657i | −0.287534 | + | 1.16657i | ||||
\(877\) | 0.670319 | − | 0.643850i | 0.670319 | − | 0.643850i | −0.278217 | − | 0.960518i | \(-0.589744\pi\) |
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) | ||||
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.0285570 | − | 0.0752986i | −0.0285570 | − | 0.0752986i | 0.919979 | − | 0.391967i | \(-0.128205\pi\) |
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.04522 | + | 1.51426i | −1.04522 | + | 1.51426i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.692724 | − | 0.721202i | 0.692724 | − | 0.721202i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0781918 | + | 0.0192725i | 0.0781918 | + | 0.0192725i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.27458 | + | 0.543050i | 1.27458 | + | 0.543050i | 0.919979 | − | 0.391967i | \(-0.128205\pi\) |
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.568065 | − | 0.822984i | \(-0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(912\) | 0.212745 | − | 0.240139i | 0.212745 | − | 0.240139i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.708245 | − | 0.336066i | 0.708245 | − | 0.336066i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.10759 | + | 0.832298i | −1.10759 | + | 0.832298i | −0.987050 | − | 0.160411i | \(-0.948718\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.910663 | + | 0.185913i | −0.910663 | + | 0.185913i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.73065 | + | 0.999189i | −1.73065 | + | 0.999189i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.55242 | − | 0.382638i | −1.55242 | − | 0.382638i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.308156 | − | 0.0892584i | −0.308156 | − | 0.0892584i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.946784 | + | 0.838778i | −0.946784 | + | 0.838778i | −0.987050 | − | 0.160411i | \(-0.948718\pi\) |
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.846282 | − | 0.137534i | 0.846282 | − | 0.137534i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(948\) | 1.13245 | + | 0.0914204i | 1.13245 | + | 0.0914204i | ||||
\(949\) | 0.930676 | − | 0.759873i | 0.930676 | − | 0.759873i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.0402659 | − | 0.999189i | \(-0.487179\pi\) | ||||
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.641437 | − | 0.405620i | 0.641437 | − | 0.405620i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.09148 | + | 0.753393i | −1.09148 | + | 0.753393i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.419979 | + | 0.474059i | −0.419979 | + | 0.474059i | −0.919979 | − | 0.391967i | \(-0.871795\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.692724 | − | 0.721202i | \(-0.743590\pi\) | ||||
0.692724 | + | 0.721202i | \(0.256410\pi\) | |||||||
\(972\) | −0.200026 | + | 0.979791i | −0.200026 | + | 0.979791i | ||||
\(973\) | −0.970942 | − | 1.68172i | −0.970942 | − | 1.68172i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.987050 | + | 0.160411i | −0.987050 | + | 0.160411i | ||||
\(976\) | 1.19979 | − | 1.46948i | 1.19979 | − | 1.46948i | ||||
\(977\) | 0 | 0 | −0.721202 | − | 0.692724i | \(-0.756410\pi\) | ||||
0.721202 | + | 0.692724i | \(0.243590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0630804 | + | 0.781391i | 0.0630804 | + | 0.781391i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.960518 | − | 0.278217i | \(-0.0897436\pi\) | ||||
−0.960518 | + | 0.278217i | \(0.910256\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.314339 | + | 0.0641728i | −0.314339 | + | 0.0641728i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.987050 | + | 1.70962i | −0.987050 | + | 1.70962i | −0.354605 | + | 0.935016i | \(0.615385\pi\) |
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.670319 | + | 1.27719i | 0.670319 | + | 1.27719i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.22675 | + | 0.643850i | 1.22675 | + | 0.643850i | 0.948536 | − | 0.316668i | \(-0.102564\pi\) |
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.928693 | − | 1.76948i | 0.928693 | − | 1.76948i |
(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 | 3549.1.da.a.2480.1 | yes | 24 | |
3.2 | odd | 2 | CM | 3549.1.da.a.2480.1 | yes | 24 | |
7.4 | even | 3 | 3549.1.ds.a.452.1 | yes | 24 | ||
21.11 | odd | 6 | 3549.1.ds.a.452.1 | yes | 24 | ||
169.43 | even | 78 | 3549.1.ds.a.212.1 | yes | 24 | ||
507.212 | odd | 78 | 3549.1.ds.a.212.1 | yes | 24 | ||
1183.550 | even | 78 | inner | 3549.1.da.a.1733.1 | ✓ | 24 | |
3549.1733 | odd | 78 | inner | 3549.1.da.a.1733.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.1.da.a.1733.1 | ✓ | 24 | 1183.550 | even | 78 | inner | |
3549.1.da.a.1733.1 | ✓ | 24 | 3549.1733 | odd | 78 | inner | |
3549.1.da.a.2480.1 | yes | 24 | 1.1 | even | 1 | trivial | |
3549.1.da.a.2480.1 | yes | 24 | 3.2 | odd | 2 | CM | |
3549.1.ds.a.212.1 | yes | 24 | 169.43 | even | 78 | ||
3549.1.ds.a.212.1 | yes | 24 | 507.212 | odd | 78 | ||
3549.1.ds.a.452.1 | yes | 24 | 7.4 | even | 3 | ||
3549.1.ds.a.452.1 | yes | 24 | 21.11 | odd | 6 |