Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2209,1,Mod(67,2209)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2209, base_ring=CyclotomicField(46))
chi = DirichletCharacter(H, H._module([37]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2209.67");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2209 = 47^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2209.d (of order \(46\), degree \(22\), not 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: | \(1.10243461291\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{46})\) |
Coefficient field: | 44.0.3714575655453538975253519356486345582985254755453847127268314361572265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{44} - x^{43} + 2 x^{42} - 3 x^{41} + 5 x^{40} - 8 x^{39} + 13 x^{38} - 21 x^{37} + 34 x^{36} - 55 x^{35} + 89 x^{34} - 144 x^{33} + 233 x^{32} - 377 x^{31} + 610 x^{30} - 987 x^{29} + 1597 x^{28} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 47) |
Projective image: | \(D_{5}\) |
Projective field: | Galois closure of 5.1.2209.1 |
Embedding invariants
Embedding label | 116.2 | ||
Root | \(1.25513 - 1.02112i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2209.116 |
Dual form | 2209.1.d.a.438.2 |
$q$-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 \(\left(\mathbb{Z}/2209\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(e\left(\frac{25}{46}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25513 | − | 1.02112i | 1.25513 | − | 1.02112i | 0.256619 | − | 0.966513i | \(-0.417391\pi\) |
0.998508 | − | 0.0546092i | \(-0.0173913\pi\) | |||||||
\(3\) | −0.566868 | + | 0.246225i | −0.566868 | + | 0.246225i | −0.662336 | − | 0.749207i | \(-0.730435\pi\) |
0.0954681 | + | 0.995432i | \(0.469565\pi\) | |||||||
\(4\) | 0.329199 | − | 1.58419i | 0.329199 | − | 1.58419i | ||||
\(5\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(6\) | −0.460065 | + | 0.887885i | −0.460065 | + | 0.887885i | ||||
\(7\) | 0.541847 | + | 1.52461i | 0.541847 | + | 1.52461i | 0.824770 | + | 0.565468i | \(0.191304\pi\) |
−0.282924 | + | 0.959142i | \(0.591304\pi\) | |||||||
\(8\) | −0.460065 | − | 0.887885i | −0.460065 | − | 0.887885i | ||||
\(9\) | −0.421841 | + | 0.451681i | −0.421841 | + | 0.451681i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(12\) | 0.203456 | + | 0.979084i | 0.203456 | + | 0.979084i | ||||
\(13\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(14\) | 2.23690 | + | 1.36029i | 2.23690 | + | 1.36029i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.356408 | + | 0.504915i | −0.356408 | + | 0.504915i | −0.955189 | − | 0.295998i | \(-0.904348\pi\) |
0.598781 | + | 0.800913i | \(0.295652\pi\) | |||||||
\(18\) | −0.0682424 | + | 0.997669i | −0.0682424 | + | 0.997669i | ||||
\(19\) | 0 | 0 | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.682553 | − | 0.730836i | −0.682553 | − | 0.730836i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(24\) | 0.479416 | + | 0.390034i | 0.479416 | + | 0.390034i | ||||
\(25\) | 0.962917 | + | 0.269797i | 0.962917 | + | 0.269797i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.334880 | − | 0.942261i | 0.334880 | − | 0.942261i | ||||
\(28\) | 2.59365 | − | 0.356489i | 2.59365 | − | 0.356489i | ||||
\(29\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(32\) | 0.962917 | − | 0.269797i | 0.962917 | − | 0.269797i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0682424 | + | 0.997669i | 0.0682424 | + | 0.997669i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.576680 | + | 0.816970i | 0.576680 | + | 0.816970i | ||||
\(37\) | 0.528060 | − | 0.321121i | 0.528060 | − | 0.321121i | −0.230124 | − | 0.973161i | \(-0.573913\pi\) |
0.758184 | + | 0.652041i | \(0.226087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(42\) | −1.60296 | − | 0.220322i | −1.60296 | − | 0.220322i | ||||
\(43\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.25513 | + | 1.02112i | −1.25513 | + | 1.02112i | ||||
\(50\) | 1.48408 | − | 0.644627i | 1.48408 | − | 0.644627i | ||||
\(51\) | 0.0777133 | − | 0.373977i | 0.0777133 | − | 0.373977i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.744401 | + | 1.43663i | −0.744401 | + | 1.43663i | 0.149685 | + | 0.988734i | \(0.452174\pi\) |
−0.894086 | + | 0.447895i | \(0.852174\pi\) | |||||||
\(54\) | −0.541847 | − | 1.52461i | −0.541847 | − | 1.52461i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.10439 | − | 1.18252i | 1.10439 | − | 1.18252i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.329199 | − | 1.58419i | −0.329199 | − | 1.58419i | −0.740091 | − | 0.672507i | \(-0.765217\pi\) |
0.410892 | − | 0.911684i | \(-0.365217\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.38248 | − | 0.840704i | −1.38248 | − | 0.840704i | −0.385836 | − | 0.922567i | \(-0.626087\pi\) |
−0.996644 | + | 0.0818629i | \(0.973913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.917211 | − | 0.398401i | −0.917211 | − | 0.398401i | ||||
\(64\) | 0.933088 | − | 1.32189i | 0.933088 | − | 1.32189i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(68\) | 0.682553 | + | 0.730836i | 0.682553 | + | 0.730836i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.479416 | − | 0.390034i | −0.479416 | − | 0.390034i | 0.360492 | − | 0.932762i | \(-0.382609\pi\) |
−0.839908 | + | 0.542728i | \(0.817391\pi\) | |||||||
\(72\) | 0.595116 | + | 0.166744i | 0.595116 | + | 0.166744i | ||||
\(73\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(74\) | 0.334880 | − | 0.942261i | 0.334880 | − | 0.942261i | ||||
\(75\) | −0.612278 | + | 0.0841556i | −0.612278 | + | 0.0841556i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.595116 | − | 0.166744i | 0.595116 | − | 0.166744i | 0.0409658 | − | 0.999161i | \(-0.486957\pi\) |
0.554150 | + | 0.832417i | \(0.313043\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.15336 | − | 1.63394i | −1.15336 | − | 1.63394i | −0.576680 | − | 0.816970i | \(-0.695652\pi\) |
−0.576680 | − | 0.816970i | \(-0.695652\pi\) | |||||||
\(84\) | −1.38248 | + | 0.840704i | −1.38248 | + | 0.840704i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60296 | + | 0.220322i | 1.60296 | + | 0.220322i | 0.881519 | − | 0.472149i | \(-0.156522\pi\) |
0.721445 | + | 0.692472i | \(0.243478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.479416 | + | 0.390034i | −0.479416 | + | 0.390034i | ||||
\(97\) | 1.48408 | − | 0.644627i | 1.48408 | − | 0.644627i | 0.507865 | − | 0.861437i | \(-0.330435\pi\) |
0.976214 | + | 0.216810i | \(0.0695652\pi\) | |||||||
\(98\) | −0.532655 | + | 2.56328i | −0.532655 | + | 2.56328i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.744401 | − | 1.43663i | 0.744401 | − | 1.43663i | ||||
\(101\) | −0.206967 | − | 0.582349i | −0.206967 | − | 0.582349i | 0.792660 | − | 0.609664i | \(-0.208696\pi\) |
−0.999627 | + | 0.0273148i | \(0.991304\pi\) | |||||||
\(102\) | −0.284336 | − | 0.548743i | −0.284336 | − | 0.548743i | ||||
\(103\) | 0.421841 | − | 0.451681i | 0.421841 | − | 0.451681i | −0.484146 | − | 0.874987i | \(-0.660870\pi\) |
0.905987 | + | 0.423306i | \(0.139130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.532655 | + | 2.56328i | 0.532655 | + | 2.56328i | ||||
\(107\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(108\) | −1.38248 | − | 0.840704i | −1.38248 | − | 0.840704i | ||||
\(109\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.220272 | + | 0.312055i | −0.220272 | + | 0.312055i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.03084 | − | 1.65221i | −2.03084 | − | 1.65221i | ||||
\(119\) | −0.962917 | − | 0.269797i | −0.962917 | − | 0.269797i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.334880 | + | 0.942261i | −0.334880 | + | 0.942261i | ||||
\(122\) | −2.59365 | + | 0.356489i | −2.59365 | + | 0.356489i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.55803 | + | 0.436540i | −1.55803 | + | 0.436540i | ||||
\(127\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(128\) | −0.110419 | − | 1.61426i | −0.110419 | − | 1.61426i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.38248 | + | 0.840704i | −1.38248 | + | 0.840704i | −0.996644 | − | 0.0818629i | \(-0.973913\pi\) |
−0.385836 | + | 0.922567i | \(0.626087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.612278 | + | 0.0841556i | 0.612278 | + | 0.0841556i | ||||
\(137\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.00000 | −1.00000 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.460065 | − | 0.887885i | 0.460065 | − | 0.887885i | ||||
\(148\) | −0.334880 | − | 0.942261i | −0.334880 | − | 0.942261i | ||||
\(149\) | 0.284336 | + | 0.548743i | 0.284336 | + | 0.548743i | 0.986597 | − | 0.163176i | \(-0.0521739\pi\) |
−0.702261 | + | 0.711919i | \(0.747826\pi\) | |||||||
\(150\) | −0.682553 | + | 0.730836i | −0.682553 | + | 0.730836i | ||||
\(151\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0777133 | − | 0.373977i | −0.0777133 | − | 0.373977i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.48408 | + | 0.644627i | 1.48408 | + | 0.644627i | 0.976214 | − | 0.216810i | \(-0.0695652\pi\) |
0.507865 | + | 0.861437i | \(0.330435\pi\) | |||||||
\(158\) | 0.576680 | − | 0.816970i | 0.576680 | − | 0.816970i | ||||
\(159\) | 0.0682424 | − | 0.997669i | 0.0682424 | − | 0.997669i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.11607 | − | 0.873081i | −3.11607 | − | 0.873081i | ||||
\(167\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(168\) | −0.334880 | + | 0.942261i | −0.334880 | + | 0.942261i | ||||
\(169\) | −0.990686 | + | 0.136167i | −0.990686 | + | 0.136167i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.55803 | + | 0.436540i | −1.55803 | + | 0.436540i | −0.937599 | − | 0.347718i | \(-0.886957\pi\) |
−0.620434 | + | 0.784259i | \(0.713043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.110419 | + | 1.61426i | 0.110419 | + | 1.61426i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.576680 | + | 0.816970i | 0.576680 | + | 0.816970i | ||||
\(178\) | 2.23690 | − | 1.36029i | 2.23690 | − | 1.36029i | ||||
\(179\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.990686 | + | 0.136167i | 0.990686 | + | 0.136167i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.61803 | 1.61803 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.83442 | + | 0.796802i | −1.83442 | + | 0.796802i | −0.917211 | + | 0.398401i | \(0.869565\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(192\) | −0.203456 | + | 0.979084i | −0.203456 | + | 0.979084i | ||||
\(193\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(194\) | 1.20447 | − | 2.32451i | 1.20447 | − | 2.32451i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.20447 | + | 2.32451i | 1.20447 | + | 2.32451i | ||||
\(197\) | 1.36511 | − | 1.46167i | 1.36511 | − | 1.46167i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
0.682553 | − | 0.730836i | \(-0.260870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(200\) | −0.203456 | − | 0.979084i | −0.203456 | − | 0.979084i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.854419 | − | 0.519584i | −0.854419 | − | 0.519584i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.566868 | − | 0.246225i | −0.566868 | − | 0.246225i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.0682424 | − | 0.997669i | 0.0682424 | − | 0.997669i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(212\) | 2.03084 | + | 1.65221i | 2.03084 | + | 1.65221i | ||||
\(213\) | 0.367802 | + | 0.103053i | 0.367802 | + | 0.103053i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.990686 | + | 0.136167i | −0.990686 | + | 0.136167i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.0421761 | + | 0.616593i | 0.0421761 | + | 0.616593i | ||||
\(223\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(224\) | 0.933088 | + | 1.32189i | 0.933088 | + | 1.32189i | ||||
\(225\) | −0.528060 | + | 0.321121i | −0.528060 | + | 0.321121i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.61803 | −2.61803 | ||||||||
\(237\) | −0.296295 | + | 0.241054i | −0.296295 | + | 0.241054i | ||||
\(238\) | −1.48408 | + | 0.644627i | −1.48408 | + | 0.644627i | ||||
\(239\) | 0.125743 | − | 0.605107i | 0.125743 | − | 0.605107i | −0.868293 | − | 0.496052i | \(-0.834783\pi\) |
0.994036 | − | 0.109055i | \(-0.0347826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.284336 | − | 0.548743i | 0.284336 | − | 0.548743i | −0.702261 | − | 0.711919i | \(-0.747826\pi\) |
0.986597 | + | 0.163176i | \(0.0521739\pi\) | |||||||
\(242\) | 0.541847 | + | 1.52461i | 0.541847 | + | 1.52461i | ||||
\(243\) | 0.460065 | + | 0.887885i | 0.460065 | + | 0.887885i | ||||
\(244\) | −1.78695 | + | 1.91335i | −1.78695 | + | 1.91335i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.05612 | + | 0.642241i | 1.05612 | + | 0.642241i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.566868 | − | 0.246225i | −0.566868 | − | 0.246225i | 0.0954681 | − | 0.995432i | \(-0.469565\pi\) |
−0.662336 | + | 0.749207i | \(0.730435\pi\) | |||||||
\(252\) | −0.933088 | + | 1.32189i | −0.933088 | + | 1.32189i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.682553 | − | 0.730836i | −0.682553 | − | 0.730836i | ||||
\(257\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.775711 | + | 0.631088i | 0.775711 | + | 0.631088i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.876726 | + | 2.46687i | −0.876726 | + | 2.46687i | ||||
\(263\) | 1.60296 | − | 0.220322i | 1.60296 | − | 0.220322i | 0.721445 | − | 0.692472i | \(-0.243478\pi\) |
0.881519 | + | 0.472149i | \(0.156522\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.962917 | + | 0.269797i | −0.962917 | + | 0.269797i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.136485 | − | 1.99534i | −0.136485 | − | 1.99534i | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) |
−0.0682424 | − | 0.997669i | \(-0.521739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.356408 | − | 0.504915i | −0.356408 | − | 0.504915i | 0.598781 | − | 0.800913i | \(-0.295652\pi\) |
−0.955189 | + | 0.295998i | \(0.904348\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.612278 | − | 0.0841556i | −0.612278 | − | 0.0841556i | −0.176637 | − | 0.984276i | \(-0.556522\pi\) |
−0.435641 | + | 0.900121i | \(0.643478\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(284\) | −0.775711 | + | 0.631088i | −0.775711 | + | 0.631088i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.284336 | + | 0.548743i | −0.284336 | + | 0.548743i | ||||
\(289\) | 0.206967 | + | 0.582349i | 0.206967 | + | 0.582349i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.682553 | + | 0.730836i | −0.682553 | + | 0.730836i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(294\) | −0.329199 | − | 1.58419i | −0.329199 | − | 1.58419i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.528060 | − | 0.321121i | −0.528060 | − | 0.321121i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.917211 | + | 0.398401i | 0.917211 | + | 0.398401i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.0682424 | + | 0.997669i | −0.0682424 | + | 0.997669i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.260712 | + | 0.279154i | 0.260712 | + | 0.279154i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.479416 | − | 0.390034i | −0.479416 | − | 0.390034i | ||||
\(307\) | 0.595116 | + | 0.166744i | 0.595116 | + | 0.166744i | 0.554150 | − | 0.832417i | \(-0.313043\pi\) |
0.0409658 | + | 0.999161i | \(0.486957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.127913 | + | 0.359912i | −0.127913 | + | 0.359912i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(314\) | 2.52095 | − | 0.706337i | 2.52095 | − | 0.706337i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0682424 | − | 0.997669i | −0.0682424 | − | 0.997669i | ||||
\(317\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(318\) | −0.933088 | − | 1.32189i | −0.933088 | − | 1.32189i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.25513 | − | 1.02112i | 1.25513 | − | 1.02112i | 0.256619 | − | 0.966513i | \(-0.417391\pi\) |
0.998508 | − | 0.0546092i | \(-0.0173913\pi\) | |||||||
\(332\) | −2.96816 | + | 1.28925i | −2.96816 | + | 1.28925i | ||||
\(333\) | −0.0777133 | + | 0.373977i | −0.0777133 | + | 0.373977i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.744401 | − | 1.43663i | −0.744401 | − | 1.43663i | −0.894086 | − | 0.447895i | \(-0.852174\pi\) |
0.149685 | − | 0.988734i | \(-0.452174\pi\) | |||||||
\(338\) | −1.10439 | + | 1.18252i | −1.10439 | + | 1.18252i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.854419 | − | 0.519584i | −0.854419 | − | 0.519584i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.50977 | + | 2.13885i | −1.50977 | + | 2.13885i | ||||
\(347\) | −0.0421761 | + | 0.616593i | −0.0421761 | + | 0.616593i | 0.927751 | + | 0.373199i | \(0.121739\pi\) |
−0.969927 | + | 0.243394i | \(0.921739\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(350\) | 1.78695 | + | 1.91335i | 1.78695 | + | 1.91335i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.25513 | + | 1.02112i | 1.25513 | + | 1.02112i | 0.998508 | + | 0.0546092i | \(0.0173913\pi\) |
0.256619 | + | 0.966513i | \(0.417391\pi\) | |||||||
\(354\) | 1.55803 | + | 0.436540i | 1.55803 | + | 0.436540i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.876726 | − | 2.46687i | 0.876726 | − | 2.46687i | ||||
\(357\) | 0.612278 | − | 0.0841556i | 0.612278 | − | 0.0841556i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.962917 | − | 0.269797i | 0.962917 | − | 0.269797i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0421761 | − | 0.616593i | −0.0421761 | − | 0.616593i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.38248 | − | 0.840704i | 1.38248 | − | 0.840704i | ||||
\(367\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.59365 | − | 0.356489i | −2.59365 | − | 0.356489i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.03084 | − | 1.65221i | 2.03084 | − | 1.65221i | ||||
\(379\) | 1.48408 | − | 0.644627i | 1.48408 | − | 0.644627i | 0.507865 | − | 0.861437i | \(-0.330435\pi\) |
0.976214 | + | 0.216810i | \(0.0695652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.48880 | + | 2.87326i | −1.48880 | + | 2.87326i | ||||
\(383\) | −0.206967 | − | 0.582349i | −0.206967 | − | 0.582349i | 0.792660 | − | 0.609664i | \(-0.208696\pi\) |
−0.999627 | + | 0.0273148i | \(0.991304\pi\) | |||||||
\(384\) | 0.460065 | + | 0.887885i | 0.460065 | + | 0.887885i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.532655 | − | 2.56328i | −0.532655 | − | 2.56328i | ||||
\(389\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.48408 | + | 0.644627i | 1.48408 | + | 0.644627i | ||||
\(393\) | 0.576680 | − | 0.816970i | 0.576680 | − | 0.816970i | ||||
\(394\) | 0.220837 | − | 3.22852i | 0.220837 | − | 3.22852i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.421841 | + | 0.451681i | 0.421841 | + | 0.451681i | 0.905987 | − | 0.423306i | \(-0.139130\pi\) |
−0.484146 | + | 0.874987i | \(0.660870\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.595116 | + | 0.166744i | 0.595116 | + | 0.166744i | 0.554150 | − | 0.832417i | \(-0.313043\pi\) |
0.0409658 | + | 0.999161i | \(0.486957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.990686 | + | 0.136167i | −0.990686 | + | 0.136167i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.367802 | + | 0.103053i | −0.367802 | + | 0.103053i | ||||
\(409\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.576680 | − | 0.816970i | −0.576680 | − | 0.816970i | ||||
\(413\) | 2.23690 | − | 1.36029i | 2.23690 | − | 1.36029i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.61803 | 1.61803 | ||||||||
\(425\) | −0.479416 | + | 0.390034i | −0.479416 | + | 0.390034i | ||||
\(426\) | 0.566868 | − | 0.246225i | 0.566868 | − | 0.246225i | ||||
\(427\) | 0.532655 | − | 2.56328i | 0.532655 | − | 2.56328i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.744401 | − | 1.43663i | −0.744401 | − | 1.43663i | −0.894086 | − | 0.447895i | \(-0.852174\pi\) |
0.149685 | − | 0.988734i | \(-0.452174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.83442 | − | 0.796802i | −1.83442 | − | 0.796802i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
−0.917211 | − | 0.398401i | \(-0.869565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0682424 | − | 0.997669i | 0.0682424 | − | 0.997669i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(444\) | 0.421841 | + | 0.451681i | 0.421841 | + | 0.451681i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.296295 | − | 0.241054i | −0.296295 | − | 0.241054i | ||||
\(448\) | 2.52095 | + | 0.706337i | 2.52095 | + | 0.706337i | ||||
\(449\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(450\) | −0.334880 | + | 0.942261i | −0.334880 | + | 0.942261i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0421761 | − | 0.616593i | −0.0421761 | − | 0.616593i | −0.969927 | − | 0.243394i | \(-0.921739\pi\) |
0.927751 | − | 0.373199i | \(-0.121739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.356408 | + | 0.504915i | 0.356408 | + | 0.504915i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00000 | −1.00000 | ||||||||
\(472\) | −1.25513 | + | 1.02112i | −1.25513 | + | 1.02112i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.125743 | + | 0.605107i | −0.125743 | + | 0.605107i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.744401 | + | 1.43663i | −0.744401 | + | 1.43663i | ||||
\(477\) | −0.334880 | − | 0.942261i | −0.334880 | − | 0.942261i | ||||
\(478\) | −0.460065 | − | 0.887885i | −0.460065 | − | 0.887885i | ||||
\(479\) | −1.10439 | + | 1.18252i | −1.10439 | + | 1.18252i | −0.122622 | + | 0.992453i | \(0.539130\pi\) |
−0.981772 | + | 0.190064i | \(0.939130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.203456 | − | 0.979084i | −0.203456 | − | 0.979084i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.38248 | + | 0.840704i | 1.38248 | + | 0.840704i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.48408 | + | 0.644627i | 1.48408 | + | 0.644627i | ||||
\(487\) | −1.15336 | + | 1.63394i | −1.15336 | + | 1.63394i | −0.576680 | + | 0.816970i | \(0.695652\pi\) |
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(488\) | −0.110419 | + | 1.61426i | −0.110419 | + | 1.61426i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.10439 | − | 1.18252i | −1.10439 | − | 1.18252i | −0.981772 | − | 0.190064i | \(-0.939130\pi\) |
−0.122622 | − | 0.992453i | \(-0.539130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.334880 | − | 0.942261i | 0.334880 | − | 0.942261i | ||||
\(498\) | 1.98137 | − | 0.272333i | 1.98137 | − | 0.272333i | ||||
\(499\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.962917 | + | 0.269797i | −0.962917 | + | 0.269797i | ||||
\(503\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(504\) | 0.0682424 | + | 0.997669i | 0.0682424 | + | 0.997669i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.528060 | − | 0.321121i | 0.528060 | − | 0.321121i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.61803 | 1.61803 | ||||||||
\(519\) | 0.775711 | − | 0.631088i | 0.775711 | − | 0.631088i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.329199 | + | 1.58419i | −0.329199 | + | 1.58419i | 0.410892 | + | 0.911684i | \(0.365217\pi\) |
−0.740091 | + | 0.672507i | \(0.765217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.920130 | − | 1.77577i | 0.920130 | − | 1.77577i | 0.460065 | − | 0.887885i | \(-0.347826\pi\) |
0.460065 | − | 0.887885i | \(-0.347826\pi\) | |||||||
\(524\) | 0.876726 | + | 2.46687i | 0.876726 | + | 2.46687i | ||||
\(525\) | −0.460065 | − | 0.887885i | −0.460065 | − | 0.887885i | ||||
\(526\) | 1.78695 | − | 1.91335i | 1.78695 | − | 1.91335i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.203456 | + | 0.979084i | 0.203456 | + | 0.979084i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.854419 | + | 0.519584i | 0.854419 | + | 0.519584i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.933088 | + | 1.32189i | −0.933088 | + | 1.32189i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.20879 | − | 2.36503i | −2.20879 | − | 2.36503i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.25513 | + | 1.02112i | 1.25513 | + | 1.02112i | 0.998508 | + | 0.0546092i | \(0.0173913\pi\) |
0.256619 | + | 0.966513i | \(0.417391\pi\) | |||||||
\(542\) | −0.962917 | − | 0.269797i | −0.962917 | − | 0.269797i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.206967 | + | 0.582349i | −0.206967 | + | 0.582349i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.962917 | − | 0.269797i | 0.962917 | − | 0.269797i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.576680 | + | 0.816970i | 0.576680 | + | 0.816970i | ||||
\(554\) | −0.854419 | + | 0.519584i | −0.854419 | + | 0.519584i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.03084 | + | 1.65221i | −2.03084 | + | 1.65221i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.125743 | + | 0.605107i | −0.125743 | + | 0.605107i | ||||
\(569\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.206967 | − | 0.582349i | −0.206967 | − | 0.582349i | 0.792660 | − | 0.609664i | \(-0.208696\pi\) |
−0.999627 | + | 0.0273148i | \(0.991304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.843682 | − | 0.903363i | 0.843682 | − | 0.903363i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.203456 | + | 0.979084i | 0.203456 | + | 0.979084i | ||||
\(577\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(578\) | 0.854419 | + | 0.519584i | 0.854419 | + | 0.519584i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.86618 | − | 2.64377i | 1.86618 | − | 2.64377i | ||||
\(582\) | −0.110419 | + | 1.61426i | −0.110419 | + | 1.61426i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(588\) | −1.25513 | − | 1.02112i | −1.25513 | − | 1.02112i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.413934 | + | 1.16470i | −0.413934 | + | 1.16470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.962917 | − | 0.269797i | 0.962917 | − | 0.269797i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(600\) | 0.356408 | + | 0.504915i | 0.356408 | + | 0.504915i | ||||
\(601\) | −1.38248 | + | 0.840704i | −1.38248 | + | 0.840704i | −0.996644 | − | 0.0818629i | \(-0.973913\pi\) |
−0.385836 | + | 0.922567i | \(0.626087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.612278 | + | 0.0841556i | 0.612278 | + | 0.0841556i | ||||
\(607\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.618034 | −0.618034 | ||||||||
\(613\) | 1.25513 | − | 1.02112i | 1.25513 | − | 1.02112i | 0.256619 | − | 0.966513i | \(-0.417391\pi\) |
0.998508 | − | 0.0546092i | \(-0.0173913\pi\) | |||||||
\(614\) | 0.917211 | − | 0.398401i | 0.917211 | − | 0.398401i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.284336 | − | 0.548743i | 0.284336 | − | 0.548743i | −0.702261 | − | 0.711919i | \(-0.747826\pi\) |
0.986597 | + | 0.163176i | \(0.0521739\pi\) | |||||||
\(618\) | 0.206967 | + | 0.582349i | 0.206967 | + | 0.582349i | ||||
\(619\) | 0.920130 | + | 1.77577i | 0.920130 | + | 1.77577i | 0.460065 | + | 0.887885i | \(0.347826\pi\) |
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.532655 | + | 2.56328i | 0.532655 | + | 2.56328i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.854419 | + | 0.519584i | 0.854419 | + | 0.519584i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.50977 | − | 2.13885i | 1.50977 | − | 2.13885i | ||||
\(629\) | −0.0260663 | + | 0.381076i | −0.0260663 | + | 0.381076i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(632\) | −0.421841 | − | 0.451681i | −0.421841 | − | 0.451681i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.55803 | − | 0.436540i | −1.55803 | − | 0.436540i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.378408 | − | 0.0520110i | 0.378408 | − | 0.0520110i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.55803 | + | 0.436540i | −1.55803 | + | 0.436540i | −0.937599 | − | 0.347718i | \(-0.886957\pi\) |
−0.620434 | + | 0.784259i | \(0.713043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.933088 | + | 1.32189i | 0.933088 | + | 1.32189i | 0.946747 | + | 0.321978i | \(0.104348\pi\) |
−0.0136587 | + | 0.999907i | \(0.504348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.612278 | − | 0.0841556i | −0.612278 | − | 0.0841556i | −0.176637 | − | 0.984276i | \(-0.556522\pi\) |
−0.435641 | + | 0.900121i | \(0.643478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.566868 | + | 0.246225i | −0.566868 | + | 0.246225i | −0.662336 | − | 0.749207i | \(-0.730435\pi\) |
0.0954681 | + | 0.995432i | \(0.469565\pi\) | |||||||
\(662\) | 0.532655 | − | 2.56328i | 0.532655 | − | 2.56328i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.920130 | + | 1.77577i | −0.920130 | + | 1.77577i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.284336 | + | 0.548743i | 0.284336 | + | 0.548743i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.854419 | − | 0.519584i | −0.854419 | − | 0.519584i | ||||
\(673\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(674\) | −2.40129 | − | 1.04303i | −2.40129 | − | 1.04303i | ||||
\(675\) | 0.576680 | − | 0.816970i | 0.576680 | − | 0.816970i | ||||
\(676\) | −0.110419 | + | 1.61426i | −0.110419 | + | 1.61426i | ||||
\(677\) | 0 | 0 | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.78695 | + | 1.91335i | 1.78695 | + | 1.91335i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.55803 | − | 0.436540i | −1.55803 | − | 0.436540i | −0.620434 | − | 0.784259i | \(-0.713043\pi\) |
−0.937599 | + | 0.347718i | \(0.886957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.60296 | + | 0.220322i | −1.60296 | + | 0.220322i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(692\) | 0.178661 | + | 2.61193i | 0.178661 | + | 2.61193i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.576680 | + | 0.816970i | 0.576680 | + | 0.816970i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.59365 | + | 0.356489i | 2.59365 | + | 0.356489i | ||||
\(701\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.61803 | 2.61803 | ||||||||
\(707\) | 0.775711 | − | 0.631088i | 0.775711 | − | 0.631088i | ||||
\(708\) | 1.48408 | − | 0.644627i | 1.48408 | − | 0.644627i | ||||
\(709\) | −0.329199 | + | 1.58419i | −0.329199 | + | 1.58419i | 0.410892 | + | 0.911684i | \(0.365217\pi\) |
−0.740091 | + | 0.672507i | \(0.765217\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.175729 | + | 0.339142i | −0.175729 | + | 0.339142i | ||||
\(712\) | −0.541847 | − | 1.52461i | −0.541847 | − | 1.52461i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0.682553 | − | 0.730836i | 0.682553 | − | 0.730836i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.0777133 | + | 0.373977i | 0.0777133 | + | 0.373977i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.38248 | − | 0.840704i | −1.38248 | − | 0.840704i | −0.385836 | − | 0.922567i | \(-0.626087\pi\) |
−0.996644 | + | 0.0818629i | \(0.973913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.917211 | + | 0.398401i | 0.917211 | + | 0.398401i | ||||
\(722\) | 0.933088 | − | 1.32189i | 0.933088 | − | 1.32189i | ||||
\(723\) | −0.0260663 | + | 0.381076i | −0.0260663 | + | 0.381076i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.682553 | − | 0.730836i | −0.682553 | − | 0.730836i | ||||
\(727\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.479416 | − | 0.390034i | −0.479416 | − | 0.390034i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.541847 | − | 1.52461i | 0.541847 | − | 1.52461i | ||||
\(733\) | −0.612278 | + | 0.0841556i | −0.612278 | + | 0.0841556i | −0.435641 | − | 0.900121i | \(-0.643478\pi\) |
−0.176637 | + | 0.984276i | \(0.556522\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.110419 | + | 1.61426i | 0.110419 | + | 1.61426i | 0.641624 | + | 0.767019i | \(0.278261\pi\) |
−0.531206 | + | 0.847243i | \(0.678261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.61938 | + | 2.20099i | −3.61938 | + | 2.20099i | ||||
\(743\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.22456 | + | 0.168311i | 1.22456 | + | 0.168311i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.381966 | 0.381966 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.532655 | − | 2.56328i | 0.532655 | − | 2.56328i | ||||
\(757\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(758\) | 1.20447 | − | 2.32451i | 1.20447 | − | 2.32451i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.36511 | − | 1.46167i | 1.36511 | − | 1.46167i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
0.682553 | − | 0.730836i | \(-0.260870\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.658397 | + | 3.16838i | 0.658397 | + | 3.16838i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.854419 | − | 0.519584i | −0.854419 | − | 0.519584i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.566868 | + | 0.246225i | 0.566868 | + | 0.246225i | ||||
\(769\) | −0.356408 | + | 0.504915i | −0.356408 | + | 0.504915i | −0.955189 | − | 0.295998i | \(-0.904348\pi\) |
0.598781 | + | 0.800913i | \(0.295652\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.421841 | + | 0.451681i | 0.421841 | + | 0.451681i | 0.905987 | − | 0.423306i | \(-0.139130\pi\) |
−0.484146 | + | 0.874987i | \(0.660870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.25513 | − | 1.02112i | −1.25513 | − | 1.02112i | ||||
\(777\) | −0.595116 | − | 0.166744i | −0.595116 | − | 0.166744i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.110419 | − | 1.61426i | −0.110419 | − | 1.61426i | ||||
\(787\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(788\) | −1.86618 | − | 2.64377i | −1.86618 | − | 2.64377i | ||||
\(789\) | −0.854419 | + | 0.519584i | −0.854419 | + | 0.519584i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.990686 | + | 0.136167i | 0.990686 | + | 0.136167i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.00000 | 1.00000 | ||||||||
\(801\) | −0.775711 | + | 0.631088i | −0.775711 | + | 0.631088i | ||||
\(802\) | 0.917211 | − | 0.398401i | 0.917211 | − | 0.398401i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.568672 | + | 1.09749i | 0.568672 | + | 1.09749i | ||||
\(808\) | −0.421841 | + | 0.451681i | −0.421841 | + | 0.451681i | ||||
\(809\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.125743 | + | 0.605107i | 0.125743 | + | 0.605107i | 0.994036 | + | 0.109055i | \(0.0347826\pi\) |
−0.868293 | + | 0.496052i | \(0.834783\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.326359 | + | 0.198463i | 0.326359 | + | 0.198463i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.55142 | − | 1.26218i | −1.55142 | − | 1.26218i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) |
−0.775711 | − | 0.631088i | \(-0.782609\pi\) | |||||||
\(824\) | −0.595116 | − | 0.166744i | −0.595116 | − | 0.166744i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.41857 | − | 3.99148i | 1.41857 | − | 3.99148i | ||||
\(827\) | 1.60296 | − | 0.220322i | 1.60296 | − | 0.220322i | 0.721445 | − | 0.692472i | \(-0.243478\pi\) |
0.881519 | + | 0.472149i | \(0.156522\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.367802 | − | 0.103053i | 0.367802 | − | 0.103053i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.0682424 | − | 0.997669i | −0.0682424 | − | 0.997669i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.990686 | − | 0.136167i | −0.990686 | − | 0.136167i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.61803 | −1.61803 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.917211 | − | 0.398401i | 0.917211 | − | 0.398401i | ||||
\(850\) | −0.203456 | + | 0.979084i | −0.203456 | + | 0.979084i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0.284336 | − | 0.548743i | 0.284336 | − | 0.548743i | ||||
\(853\) | −0.206967 | − | 0.582349i | −0.206967 | − | 0.582349i | 0.792660 | − | 0.609664i | \(-0.208696\pi\) |
−0.999627 | + | 0.0273148i | \(0.991304\pi\) | |||||||
\(854\) | −1.94887 | − | 3.76114i | −1.94887 | − | 3.76114i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.40129 | − | 1.04303i | −2.40129 | − | 1.04303i | ||||
\(863\) | −0.356408 | + | 0.504915i | −0.356408 | + | 0.504915i | −0.955189 | − | 0.295998i | \(-0.904348\pi\) |
0.598781 | + | 0.800913i | \(0.295652\pi\) | |||||||
\(864\) | 0.0682424 | − | 0.997669i | 0.0682424 | − | 0.997669i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.260712 | − | 0.279154i | −0.260712 | − | 0.279154i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.334880 | + | 0.942261i | −0.334880 | + | 0.942261i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(878\) | −3.11607 | + | 0.873081i | −3.11607 | + | 0.873081i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(882\) | −0.933088 | − | 1.32189i | −0.933088 | − | 1.32189i | ||||
\(883\) | −1.38248 | + | 0.840704i | −1.38248 | + | 0.840704i | −0.996644 | − | 0.0818629i | \(-0.973913\pi\) |
−0.385836 | + | 0.922567i | \(0.626087\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(888\) | 0.378408 | + | 0.0520110i | 0.378408 | + | 0.0520110i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.618034 | −0.618034 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.40129 | − | 1.04303i | 2.40129 | − | 1.04303i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.334880 | + | 0.942261i | 0.334880 | + | 0.942261i | ||||
\(901\) | −0.460065 | − | 0.887885i | −0.460065 | − | 0.887885i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.70884 | + | 1.03917i | 1.70884 | + | 1.03917i | 0.854419 | + | 0.519584i | \(0.173913\pi\) |
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.350344 | + | 0.152176i | 0.350344 | + | 0.152176i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.110419 | − | 1.61426i | 0.110419 | − | 1.61426i | −0.531206 | − | 0.847243i | \(-0.678261\pi\) |
0.641624 | − | 0.767019i | \(-0.278261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.682553 | − | 0.730836i | −0.682553 | − | 0.730836i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.03084 | − | 1.65221i | −2.03084 | − | 1.65221i | ||||
\(918\) | 0.962917 | + | 0.269797i | 0.962917 | + | 0.269797i | ||||
\(919\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.378408 | + | 0.0520110i | −0.378408 | + | 0.0520110i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.595116 | − | 0.166744i | 0.595116 | − | 0.166744i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0260663 | + | 0.381076i | 0.0260663 | + | 0.381076i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.356408 | − | 0.504915i | −0.356408 | − | 0.504915i | 0.598781 | − | 0.800913i | \(-0.295652\pi\) |
−0.955189 | + | 0.295998i | \(0.904348\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(942\) | −1.25513 | + | 1.02112i | −1.25513 | + | 1.02112i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.669759 | − | 1.88452i | −0.669759 | − | 1.88452i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
−0.334880 | − | 0.942261i | \(-0.608696\pi\) | |||||||
\(948\) | 0.284336 | + | 0.548743i | 0.284336 | + | 0.548743i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.203456 | + | 0.979084i | 0.203456 | + | 0.979084i | ||||
\(953\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(954\) | −1.38248 | − | 0.840704i | −1.38248 | − | 0.840704i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.917211 | − | 0.398401i | −0.917211 | − | 0.398401i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.178661 | + | 2.61193i | −0.178661 | + | 2.61193i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.682553 | + | 0.730836i | 0.682553 | + | 0.730836i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.775711 | − | 0.631088i | −0.775711 | − | 0.631088i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.541847 | − | 1.52461i | 0.541847 | − | 1.52461i | −0.282924 | − | 0.959142i | \(-0.591304\pi\) |
0.824770 | − | 0.565468i | \(-0.191304\pi\) | |||||||
\(968\) | 0.990686 | − | 0.136167i | 0.990686 | − | 0.136167i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(972\) | 1.55803 | − | 0.436540i | 1.55803 | − | 0.436540i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.220837 | + | 3.22852i | 0.220837 | + | 3.22852i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.70884 | − | 1.03917i | 1.70884 | − | 1.03917i | 0.854419 | − | 0.519584i | \(-0.173913\pi\) |
0.854419 | − | 0.519584i | \(-0.173913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.59365 | − | 0.356489i | −2.59365 | − | 0.356489i | ||||
\(983\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.329199 | + | 1.58419i | −0.329199 | + | 1.58419i | 0.410892 | + | 0.911684i | \(0.365217\pi\) |
−0.740091 | + | 0.672507i | \(0.765217\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.460065 | + | 0.887885i | −0.460065 | + | 0.887885i | ||||
\(994\) | −0.541847 | − | 1.52461i | −0.541847 | − | 1.52461i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.36511 | − | 1.46167i | 1.36511 | − | 1.46167i | ||||
\(997\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.125743 | − | 0.605107i | −0.125743 | − | 0.605107i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))