Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1340,1,Mod(19,1340)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1340, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 33, 10]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1340.19");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1340 = 2^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1340.bl (of order \(66\), degree \(20\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.668747116928\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{33}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{33} - \cdots)\) |
Embedding invariants
Embedding label | 839.1 | ||
Root | \(-0.786053 - 0.618159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1340.839 |
Dual form | 1340.1.bl.a.559.1 |
$q$-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 \(\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times\).
\(n\) | \(537\) | \(671\) | \(1141\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{19}{33}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.235759 | + | 0.971812i | −0.235759 | + | 0.971812i | ||||
\(3\) | −0.252989 | − | 1.75958i | −0.252989 | − | 1.75958i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.327068 | − | 0.945001i | \(-0.393939\pi\) | |||||||
\(4\) | −0.888835 | − | 0.458227i | −0.888835 | − | 0.458227i | ||||
\(5\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(6\) | 1.76962 | + | 0.168978i | 1.76962 | + | 0.168978i | ||||
\(7\) | −1.34378 | − | 1.28129i | −1.34378 | − | 1.28129i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(8\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(9\) | −2.07261 | + | 0.608574i | −2.07261 | + | 0.608574i | ||||
\(10\) | 0.786053 | + | 0.618159i | 0.786053 | + | 0.618159i | ||||
\(11\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(12\) | −0.581419 | + | 1.67990i | −0.581419 | + | 1.67990i | ||||
\(13\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(14\) | 1.56199 | − | 1.00383i | 1.56199 | − | 1.00383i | ||||
\(15\) | −1.70566 | − | 0.500828i | −1.70566 | − | 0.500828i | ||||
\(16\) | 0.580057 | + | 0.814576i | 0.580057 | + | 0.814576i | ||||
\(17\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(18\) | −0.102782 | − | 2.15767i | −0.102782 | − | 2.15767i | ||||
\(19\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(20\) | −0.786053 | + | 0.618159i | −0.786053 | + | 0.618159i | ||||
\(21\) | −1.91457 | + | 2.68864i | −1.91457 | + | 2.68864i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.928368 | + | 0.371662i | 0.928368 | + | 0.371662i | 0.786053 | − | 0.618159i | \(-0.212121\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(24\) | −1.49547 | − | 0.961081i | −1.49547 | − | 0.961081i | ||||
\(25\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.856711 | + | 1.87593i | 0.856711 | + | 1.87593i | ||||
\(28\) | 0.607279 | + | 1.75462i | 0.607279 | + | 1.75462i | ||||
\(29\) | 0.786053 | + | 1.36148i | 0.786053 | + | 1.36148i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(30\) | 0.888835 | − | 1.53951i | 0.888835 | − | 1.53951i | ||||
\(31\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(32\) | −0.928368 | + | 0.371662i | −0.928368 | + | 0.371662i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.72373 | + | 0.690079i | −1.72373 | + | 0.690079i | ||||
\(36\) | 2.12108 | + | 0.408804i | 2.12108 | + | 0.408804i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(41\) | 0.0934441 | − | 1.96163i | 0.0934441 | − | 1.96163i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(42\) | −2.16148 | − | 2.49448i | −2.16148 | − | 2.49448i | ||||
\(43\) | −0.0800569 | − | 0.0514495i | −0.0800569 | − | 0.0514495i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.307416 | + | 2.13813i | −0.307416 | + | 2.13813i | ||||
\(46\) | −0.580057 | + | 0.814576i | −0.580057 | + | 0.814576i | ||||
\(47\) | −0.514186 | + | 0.404360i | −0.514186 | + | 0.404360i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(48\) | 1.28656 | − | 1.22673i | 1.28656 | − | 1.22673i | ||||
\(49\) | 0.116455 | + | 2.44470i | 0.116455 | + | 2.44470i | ||||
\(50\) | 0.888835 | − | 0.458227i | 0.888835 | − | 0.458227i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(54\) | −2.02503 | + | 0.390293i | −2.02503 | + | 0.390293i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.84833 | + | 0.176494i | −1.84833 | + | 0.176494i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.50842 | + | 0.442913i | −1.50842 | + | 0.442913i | ||||
\(59\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(60\) | 1.28656 | + | 1.22673i | 1.28656 | + | 1.22673i | ||||
\(61\) | −0.827068 | − | 0.0789754i | −0.827068 | − | 0.0789754i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.56491 | + | 1.83784i | 3.56491 | + | 1.83784i | ||||
\(64\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0475819 | − | 0.998867i | −0.0475819 | − | 0.998867i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.419102 | − | 1.72756i | 0.419102 | − | 1.72756i | ||||
\(70\) | −0.264241 | − | 1.83784i | −0.264241 | − | 1.83784i | ||||
\(71\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(72\) | −0.897344 | + | 1.96491i | −0.897344 | + | 1.96491i | ||||
\(73\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.16413 | + | 1.34347i | −1.16413 | + | 1.34347i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(80\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(81\) | 1.26691 | − | 0.814193i | 1.26691 | − | 0.814193i | ||||
\(82\) | 1.88431 | + | 0.553283i | 1.88431 | + | 0.553283i | ||||
\(83\) | −0.839614 | − | 1.17907i | −0.839614 | − | 1.17907i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(84\) | 2.93375 | − | 1.51245i | 2.93375 | − | 1.51245i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0688733 | − | 0.0656706i | 0.0688733 | − | 0.0656706i | ||||
\(87\) | 2.19677 | − | 1.72756i | 2.19677 | − | 1.72756i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(90\) | −2.00538 | − | 0.802833i | −2.00538 | − | 0.802833i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.271738 | − | 0.595023i | −0.271738 | − | 0.595023i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | ||||
\(97\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(98\) | −2.40324 | − | 0.463186i | −2.40324 | − | 0.463186i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.235759 | + | 0.971812i | 0.235759 | + | 0.971812i | ||||
\(101\) | −0.452418 | − | 1.86489i | −0.452418 | − | 1.86489i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.462997 | − | 0.0892353i | −0.462997 | − | 0.0892353i | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.65033 | + | 2.85846i | 1.65033 | + | 2.85846i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(108\) | 0.0981282 | − | 2.05996i | 0.0981282 | − | 2.05996i | ||||
\(109\) | −0.308779 | − | 0.356349i | −0.308779 | − | 0.356349i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.264241 | − | 1.83784i | 0.264241 | − | 1.83784i | ||||
\(113\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.723734 | − | 0.690079i | 0.723734 | − | 0.690079i | ||||
\(116\) | −0.0748038 | − | 1.57033i | −0.0748038 | − | 1.57033i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.49547 | + | 0.961081i | −1.49547 | + | 0.961081i | ||||
\(121\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(122\) | 0.271738 | − | 0.785135i | 0.271738 | − | 0.785135i | ||||
\(123\) | −3.47528 | + | 0.331849i | −3.47528 | + | 0.331849i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(126\) | −2.62649 | + | 3.03113i | −2.62649 | + | 3.03113i | ||||
\(127\) | 1.44091 | + | 1.37391i | 1.44091 | + | 1.37391i | 0.786053 | + | 0.618159i | \(0.212121\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(128\) | 0.995472 | + | 0.0950560i | 0.995472 | + | 0.0950560i | ||||
\(129\) | −0.0702757 | + | 0.153882i | −0.0702757 | + | 0.153882i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.981929 | + | 0.189251i | 0.981929 | + | 0.189251i | ||||
\(135\) | 2.06230 | 2.06230 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(138\) | 1.58006 | + | 0.814576i | 1.58006 | + | 0.814576i | ||||
\(139\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(140\) | 1.84833 | + | 0.176494i | 1.84833 | + | 0.176494i | ||||
\(141\) | 0.841586 | + | 0.802450i | 0.841586 | + | 0.802450i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.69796 | − | 1.33529i | −1.69796 | − | 1.33529i | ||||
\(145\) | 1.56499 | − | 0.149438i | 1.56499 | − | 0.149438i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.27217 | − | 0.823393i | 4.27217 | − | 0.823393i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.88431 | − | 0.553283i | −1.88431 | − | 0.553283i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
−0.888835 | − | 0.458227i | \(-0.848485\pi\) | |||||||
\(150\) | −1.03115 | − | 1.44805i | −1.03115 | − | 1.44805i | ||||
\(151\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.0475819 | + | 0.998867i | −0.0475819 | + | 0.998867i | ||||
\(161\) | −0.771316 | − | 1.68895i | −0.771316 | − | 1.68895i | ||||
\(162\) | 0.492557 | + | 1.42315i | 0.492557 | + | 1.42315i | ||||
\(163\) | 0.841254 | + | 1.45709i | 0.841254 | + | 1.45709i | 0.888835 | + | 0.458227i | \(0.151515\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(164\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.34378 | − | 0.537970i | 1.34378 | − | 0.537970i | ||||
\(167\) | 0.0671040 | + | 0.276606i | 0.0671040 | + | 0.276606i | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(168\) | 0.778161 | + | 3.20762i | 0.778161 | + | 3.20762i | ||||
\(169\) | 0.928368 | − | 0.371662i | 0.928368 | − | 0.371662i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0475819 | + | 0.0824143i | 0.0475819 | + | 0.0824143i | ||||
\(173\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(174\) | 1.16096 | + | 2.54214i | 1.16096 | + | 2.54214i | ||||
\(175\) | −0.0883470 | + | 1.85463i | −0.0883470 | + | 1.85463i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.78153 | + | 0.713215i | 1.78153 | + | 0.713215i | ||||
\(179\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(180\) | 1.25299 | − | 1.75958i | 1.25299 | − | 1.75958i | ||||
\(181\) | −1.32254 | + | 1.04006i | −1.32254 | + | 1.04006i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0702757 | + | 1.47527i | 0.0702757 | + | 1.47527i | ||||
\(184\) | 0.888835 | − | 0.458227i | 0.888835 | − | 0.458227i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.642315 | − | 0.123796i | 0.642315 | − | 0.123796i | ||||
\(189\) | 1.25239 | − | 3.61855i | 1.25239 | − | 3.61855i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(192\) | −1.70566 | + | 0.500828i | −1.70566 | + | 0.500828i | ||||
\(193\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.01671 | − | 2.22630i | 1.01671 | − | 2.22630i | ||||
\(197\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(200\) | −1.00000 | −1.00000 | ||||||||
\(201\) | −1.74555 | + | 0.336426i | −1.74555 | + | 0.336426i | ||||
\(202\) | 1.91899 | 1.91899 | ||||||||
\(203\) | 0.688177 | − | 2.83670i | 0.688177 | − | 2.83670i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.74555 | − | 0.899892i | −1.74555 | − | 0.899892i | ||||
\(206\) | 0.195876 | − | 0.428908i | 0.195876 | − | 0.428908i | ||||
\(207\) | −2.15033 | − | 0.205332i | −2.15033 | − | 0.205332i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.16697 | + | 0.929905i | −3.16697 | + | 0.929905i | ||||
\(211\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.28605 | + | 0.247866i | −1.28605 | + | 0.247866i | ||||
\(215\) | −0.0800569 | + | 0.0514495i | −0.0800569 | + | 0.0514495i | ||||
\(216\) | 1.97876 | + | 0.581017i | 1.97876 | + | 0.581017i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.419102 | − | 0.216062i | 0.419102 | − | 0.216062i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(224\) | 1.72373 | + | 0.690079i | 1.72373 | + | 0.690079i | ||||
\(225\) | 1.81720 | + | 1.16785i | 1.81720 | + | 1.16785i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.0913090 | − | 1.91681i | 0.0913090 | − | 1.91681i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.327068 | − | 0.945001i | \(-0.393939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.651174 | + | 1.88144i | 0.651174 | + | 1.88144i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(230\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.54370 | + | 0.297523i | 1.54370 | + | 0.297523i | ||||
\(233\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.154218 | + | 0.635697i | 0.154218 | + | 0.635697i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | −0.581419 | − | 1.67990i | −0.581419 | − | 1.67990i | ||||
\(241\) | 0.195876 | + | 0.428908i | 0.195876 | + | 0.428908i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(242\) | −0.0475819 | + | 0.998867i | −0.0475819 | + | 0.998867i | ||||
\(243\) | −0.402630 | − | 0.464659i | −0.402630 | − | 0.464659i | ||||
\(244\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(245\) | 2.27215 | + | 0.909632i | 2.27215 | + | 0.909632i | ||||
\(246\) | 0.496834 | − | 3.45556i | 0.496834 | − | 3.45556i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.86226 | + | 1.77566i | −1.86226 | + | 1.77566i | ||||
\(250\) | −0.0475819 | − | 0.998867i | −0.0475819 | − | 0.998867i | ||||
\(251\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(252\) | −2.32647 | − | 3.26707i | −2.32647 | − | 3.26707i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.67489 | + | 1.07639i | −1.67489 | + | 1.07639i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.327068 | + | 0.945001i | −0.327068 | + | 0.945001i | ||||
\(257\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(258\) | −0.132977 | − | 0.104574i | −0.132977 | − | 0.104574i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.45775 | − | 2.34346i | −2.45775 | − | 2.34346i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.481929 | + | 1.05528i | −0.481929 | + | 1.05528i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.41133 | −3.41133 | ||||||||
\(268\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(269\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(270\) | −0.486206 | + | 2.00417i | −0.486206 | + | 2.00417i | ||||
\(271\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.16413 | + | 1.34347i | −1.16413 | + | 1.34347i | ||||
\(277\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.607279 | + | 1.75462i | −0.607279 | + | 1.75462i | ||||
\(281\) | −0.642315 | + | 0.123796i | −0.642315 | + | 0.123796i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(282\) | −0.978242 | + | 0.628678i | −0.978242 | + | 0.628678i | ||||
\(283\) | 1.11312 | + | 0.326842i | 1.11312 | + | 0.326842i | 0.786053 | − | 0.618159i | \(-0.212121\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.63900 | + | 2.51628i | −2.63900 | + | 2.51628i | ||||
\(288\) | 1.69796 | − | 1.33529i | 1.69796 | − | 1.33529i | ||||
\(289\) | 0.580057 | − | 0.814576i | 0.580057 | − | 0.814576i | ||||
\(290\) | −0.223734 | + | 1.55610i | −0.223734 | + | 1.55610i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(294\) | −0.207019 | + | 4.34586i | −0.207019 | + | 4.34586i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.981929 | − | 1.70075i | 0.981929 | − | 1.70075i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.65033 | − | 0.660694i | 1.65033 | − | 0.660694i | ||||
\(301\) | 0.0416572 | + | 0.171713i | 0.0416572 | + | 0.171713i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.16697 | + | 1.26786i | −3.16697 | + | 1.26786i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.415415 | + | 0.719520i | −0.415415 | + | 0.719520i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.428368 | − | 1.23769i | −0.428368 | − | 1.23769i | −0.928368 | − | 0.371662i | \(-0.878788\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0398833 | + | 0.837254i | −0.0398833 | + | 0.837254i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.15267 | − | 2.47929i | 3.15267 | − | 2.47929i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(321\) | 1.95865 | − | 1.25875i | 1.95865 | − | 1.25875i | ||||
\(322\) | 1.82318 | − | 0.351390i | 1.82318 | − | 0.351390i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.49916 | + | 0.143152i | −1.49916 | + | 0.143152i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(327\) | −0.548907 | + | 0.633472i | −0.548907 | + | 0.633472i | ||||
\(328\) | −1.42131 | − | 1.35522i | −1.42131 | − | 1.35522i | ||||
\(329\) | 1.20906 | + | 0.115451i | 1.20906 | + | 0.115451i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(332\) | 0.205996 | + | 1.43273i | 0.205996 | + | 1.43273i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.284630 | −0.284630 | ||||||||
\(335\) | −0.928368 | − | 0.371662i | −0.928368 | − | 0.371662i | ||||
\(336\) | −3.30067 | −3.30067 | ||||||||
\(337\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(338\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.75998 | − | 2.03113i | 1.75998 | − | 2.03113i | ||||
\(344\) | −0.0913090 | + | 0.0268107i | −0.0913090 | + | 0.0268107i | ||||
\(345\) | −1.39734 | − | 1.09888i | −1.39734 | − | 1.09888i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.271738 | − | 0.785135i | 0.271738 | − | 0.785135i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | |||||||
\(348\) | −2.74418 | + | 0.528898i | −2.74418 | + | 0.528898i | ||||
\(349\) | 0.0800569 | − | 0.0514495i | 0.0800569 | − | 0.0514495i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(350\) | −1.78153 | − | 0.523103i | −1.78153 | − | 0.523103i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.11312 | + | 1.56316i | −1.11312 | + | 1.56316i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(360\) | 1.41457 | + | 1.63251i | 1.41457 | + | 1.63251i | ||||
\(361\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | ||||
\(362\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | ||||
\(363\) | −0.581419 | − | 1.67990i | −0.581419 | − | 1.67990i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.45025 | − | 0.279513i | −1.45025 | − | 0.279513i | ||||
\(367\) | −0.437742 | + | 0.175245i | −0.437742 | + | 0.175245i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(368\) | 0.235759 | + | 0.971812i | 0.235759 | + | 0.971812i | ||||
\(369\) | 1.00013 | + | 4.12258i | 1.00013 | + | 4.12258i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.738471 | + | 1.61703i | 0.738471 | + | 1.61703i | ||||
\(376\) | −0.0311250 | + | 0.653395i | −0.0311250 | + | 0.653395i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.22128 | + | 2.07019i | 3.22128 | + | 2.07019i | ||||
\(379\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.05296 | − | 2.88298i | 2.05296 | − | 2.88298i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.473420 | − | 0.451405i | 0.473420 | − | 0.451405i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(384\) | −0.0845850 | − | 1.77566i | −0.0845850 | − | 1.77566i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.197238 | + | 0.0579143i | 0.197238 | + | 0.0579143i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.462997 | − | 0.0892353i | 0.462997 | − | 0.0892353i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.92384 | + | 1.51292i | 1.92384 | + | 1.51292i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | ||||
\(401\) | 1.85674 | 1.85674 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(402\) | 0.0845850 | − | 1.77566i | 0.0845850 | − | 1.77566i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.452418 | + | 1.86489i | −0.452418 | + | 1.86489i | ||||
\(405\) | −0.214323 | − | 1.49065i | −0.214323 | − | 1.49065i | ||||
\(406\) | 2.59450 | + | 1.33756i | 2.59450 | + | 1.33756i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.21769 | + | 1.16106i | 1.21769 | + | 1.16106i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(410\) | 1.28605 | − | 1.48418i | 1.28605 | − | 1.48418i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.370638 | + | 0.291473i | 0.370638 | + | 0.291473i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.706504 | − | 2.04131i | 0.706504 | − | 2.04131i | ||||
\(415\) | −1.42131 | + | 0.273935i | −1.42131 | + | 0.273935i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(420\) | −0.157052 | − | 3.29693i | −0.157052 | − | 3.29693i | ||||
\(421\) | −0.205996 | + | 0.196417i | −0.205996 | + | 0.196417i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.819625 | − | 1.15100i | 0.819625 | − | 1.15100i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.01021 | + | 1.16584i | 1.01021 | + | 1.16584i | ||||
\(428\) | 0.0623191 | − | 1.30824i | 0.0623191 | − | 1.30824i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0311250 | − | 0.0899299i | −0.0311250 | − | 0.0899299i | ||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −1.03115 | + | 1.78600i | −1.03115 | + | 1.78600i | ||||
\(433\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.658873 | − | 2.71591i | −0.658873 | − | 2.71591i | ||||
\(436\) | 0.111165 | + | 0.458227i | 0.111165 | + | 0.458227i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.72915 | − | 4.99604i | −1.72915 | − | 4.99604i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0748038 | − | 1.57033i | 0.0748038 | − | 1.57033i | −0.580057 | − | 0.814576i | \(-0.696970\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(446\) | 0.771316 | + | 0.308788i | 0.771316 | + | 0.308788i | ||||
\(447\) | −0.496834 | + | 3.45556i | −0.496834 | + | 3.45556i | ||||
\(448\) | −1.07701 | + | 1.51245i | −1.07701 | + | 1.51245i | ||||
\(449\) | 0.514186 | − | 0.404360i | 0.514186 | − | 0.404360i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(450\) | −1.56335 | + | 1.49065i | −1.56335 | + | 1.49065i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(458\) | −1.98193 | + | 0.189251i | −1.98193 | + | 0.189251i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(461\) | −0.947890 | + | 1.09392i | −0.947890 | + | 1.09392i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.67489 | + | 0.159932i | 1.67489 | + | 0.159932i | 0.888835 | − | 0.458227i | \(-0.151515\pi\) |
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(464\) | −0.653077 | + | 1.43004i | −0.653077 | + | 1.43004i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.469383 | − | 1.93482i | 0.469383 | − | 1.93482i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.327068 | − | 0.945001i | \(-0.393939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21590 | + | 1.40323i | −1.21590 | + | 1.40323i | ||||
\(470\) | −0.654136 | −0.654136 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(480\) | 1.76962 | − | 0.168978i | 1.76962 | − | 0.168978i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.462997 | + | 0.0892353i | −0.462997 | + | 0.0892353i | ||||
\(483\) | −2.77670 | + | 1.78447i | −2.77670 | + | 1.78447i | ||||
\(484\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.546485 | − | 0.281733i | 0.546485 | − | 0.281733i | ||||
\(487\) | −0.0688733 | − | 1.44583i | −0.0688733 | − | 1.44583i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(488\) | −0.601300 | + | 0.573338i | −0.601300 | + | 0.573338i | ||||
\(489\) | 2.35104 | − | 1.84888i | 2.35104 | − | 1.84888i | ||||
\(490\) | −1.41967 | + | 1.99365i | −1.41967 | + | 1.99365i | ||||
\(491\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(492\) | 3.24102 | + | 1.29751i | 3.24102 | + | 1.29751i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.28656 | − | 2.22839i | −1.28656 | − | 2.22839i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0.981929 | + | 0.189251i | 0.981929 | + | 0.189251i | ||||
\(501\) | 0.469734 | − | 0.188053i | 0.469734 | − | 0.188053i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.462997 | − | 1.90850i | −0.462997 | − | 1.90850i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−0.0475819 | − | 0.998867i | \(-0.515152\pi\) | |||||||
\(504\) | 3.72346 | − | 1.49065i | 3.72346 | − | 1.49065i | ||||
\(505\) | −1.88431 | − | 0.363170i | −1.88431 | − | 0.363170i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.888835 | − | 1.53951i | −0.888835 | − | 1.53951i | ||||
\(508\) | −0.651174 | − | 1.88144i | −0.651174 | − | 1.88144i | ||||
\(509\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.273507 | + | 0.384087i | −0.273507 | + | 0.384087i | ||||
\(516\) | 0.132977 | − | 0.104574i | 0.132977 | − | 0.104574i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(522\) | 2.85684 | − | 1.83598i | 2.85684 | − | 1.83598i | ||||
\(523\) | −0.0934441 | + | 0.0180099i | −0.0934441 | + | 0.0180099i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.28572 | − | 0.313748i | 3.28572 | − | 0.313748i | ||||
\(526\) | −0.911911 | − | 0.717135i | −0.911911 | − | 0.717135i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.804250 | − | 3.31517i | 0.804250 | − | 3.31517i | ||||
\(535\) | 1.30972 | 1.30972 | ||||||||
\(536\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.396666 | + | 1.63508i | −0.396666 | + | 1.63508i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.83305 | − | 0.945001i | −1.83305 | − | 0.945001i | ||||
\(541\) | 0.0395325 | − | 0.0865641i | 0.0395325 | − | 0.0865641i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.16465 | + | 2.06399i | 2.16465 | + | 2.06399i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.452418 | + | 0.132842i | −0.452418 | + | 0.132842i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.98193 | + | 0.189251i | −1.98193 | + | 0.189251i | −0.981929 | + | 0.189251i | \(0.939394\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.76226 | − | 0.339647i | 1.76226 | − | 0.339647i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.03115 | − | 1.44805i | −1.03115 | − | 1.44805i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.56199 | − | 1.00383i | −1.56199 | − | 1.00383i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.0311250 | − | 0.653395i | 0.0311250 | − | 0.653395i | ||||
\(563\) | −0.0395325 | − | 0.0865641i | −0.0395325 | − | 0.0865641i | 0.888835 | − | 0.458227i | \(-0.151515\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(564\) | −0.380327 | − | 1.09888i | −0.380327 | − | 1.09888i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | ||||
\(567\) | −2.74567 | − | 0.529185i | −2.74567 | − | 0.529185i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.0671040 | − | 0.276606i | −0.0671040 | − | 0.276606i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.82318 | − | 3.15784i | −1.82318 | − | 3.15784i | ||||
\(575\) | −0.327068 | − | 0.945001i | −0.327068 | − | 0.945001i | ||||
\(576\) | 0.897344 | + | 1.96491i | 0.897344 | + | 1.96491i | ||||
\(577\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(578\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.45949 | − | 0.584293i | −1.45949 | − | 0.584293i | ||||
\(581\) | −0.382481 | + | 2.66021i | −0.382481 | + | 2.66021i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.759713 | + | 1.06687i | 0.759713 | + | 1.06687i | 0.995472 | + | 0.0950560i | \(0.0303030\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(588\) | −4.17456 | − | 1.22576i | −4.17456 | − | 1.22576i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.42131 | + | 1.35522i | 1.42131 | + | 1.35522i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(600\) | 0.252989 | + | 1.75958i | 0.252989 | + | 1.75958i | ||||
\(601\) | 0.0224357 | − | 0.0924813i | 0.0224357 | − | 0.0924813i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(602\) | −0.176694 | −0.176694 | ||||||||
\(603\) | 0.706504 | + | 2.04131i | 0.706504 | + | 2.04131i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | ||||
\(606\) | −0.485482 | − | 3.37660i | −0.485482 | − | 3.37660i | ||||
\(607\) | −0.581419 | − | 0.299742i | −0.581419 | − | 0.299742i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.16550 | − | 0.493245i | −5.16550 | − | 0.493245i | ||||
\(610\) | −0.601300 | − | 0.573338i | −0.601300 | − | 0.573338i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(614\) | 1.30379 | − | 0.124497i | 1.30379 | − | 0.124497i | ||||
\(615\) | −1.14182 | + | 3.29908i | −1.14182 | + | 3.29908i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(618\) | −0.804250 | − | 0.236149i | −0.804250 | − | 0.236149i | ||||
\(619\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.0981282 | + | 2.05996i | 0.0981282 | + | 2.05996i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.80075 | + | 2.20253i | −2.80075 | + | 2.20253i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.66613 | + | 3.64832i | 1.66613 | + | 3.64832i | ||||
\(631\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.84833 | − | 0.739959i | 1.84833 | − | 0.739959i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(641\) | −0.580057 | − | 1.00469i | −0.580057 | − | 1.00469i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(642\) | 0.761497 | + | 2.20020i | 0.761497 | + | 2.20020i | ||||
\(643\) | 0.653077 | + | 1.43004i | 0.653077 | + | 1.43004i | 0.888835 | + | 0.458227i | \(0.151515\pi\) |
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(644\) | −0.0883470 | + | 1.85463i | −0.0883470 | + | 1.85463i | ||||
\(645\) | 0.110783 | + | 0.127850i | 0.110783 | + | 0.127850i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.607279 | + | 0.243118i | 0.607279 | + | 0.243118i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(648\) | 0.214323 | − | 1.49065i | 0.214323 | − | 1.49065i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0800569 | − | 1.68060i | −0.0800569 | − | 1.68060i | ||||
\(653\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(654\) | −0.486206 | − | 0.682780i | −0.486206 | − | 0.682780i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.65210 | − | 1.06174i | 1.65210 | − | 1.06174i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.397243 | + | 1.14776i | −0.397243 | + | 1.14776i | ||||
\(659\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.44091 | − | 0.137591i | −1.44091 | − | 0.137591i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.223734 | + | 1.55610i | 0.223734 | + | 1.55610i | ||||
\(668\) | 0.0671040 | − | 0.276606i | 0.0671040 | − | 0.276606i | ||||
\(669\) | −1.47694 | −1.47694 | ||||||||
\(670\) | 0.580057 | − | 0.814576i | 0.580057 | − | 0.814576i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.778161 | − | 3.20762i | 0.778161 | − | 3.20762i | ||||
\(673\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.856711 | − | 1.87593i | 0.856711 | − | 1.87593i | ||||
\(676\) | −0.995472 | − | 0.0950560i | −0.995472 | − | 0.0950560i | ||||
\(677\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.39588 | + | 0.324267i | −3.39588 | + | 0.324267i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.28605 | − | 0.247866i | 1.28605 | − | 0.247866i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.55894 | + | 2.18923i | 1.55894 | + | 2.18923i | ||||
\(687\) | 3.14580 | − | 1.62177i | 3.14580 | − | 1.62177i | ||||
\(688\) | −0.00452808 | − | 0.0950560i | −0.00452808 | − | 0.0950560i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.39734 | − | 1.09888i | 1.39734 | − | 1.09888i | ||||
\(691\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.132977 | − | 2.79152i | 0.132977 | − | 2.79152i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.0311250 | + | 0.0899299i | 0.0311250 | + | 0.0899299i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.928368 | − | 1.60798i | 0.928368 | − | 1.60798i | ||||
\(701\) | −0.981929 | − | 0.189251i | −0.981929 | − | 0.189251i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.07954 | − | 0.432183i | 1.07954 | − | 0.432183i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.78153 | + | 3.08569i | −1.78153 | + | 3.08569i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.327068 | + | 0.945001i | 0.327068 | + | 0.945001i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(720\) | −1.91999 | + | 0.989821i | −1.91999 | + | 0.989821i | ||||
\(721\) | 0.507831 | + | 0.713148i | 0.507831 | + | 0.713148i | ||||
\(722\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(723\) | 0.705142 | − | 0.453167i | 0.705142 | − | 0.453167i | ||||
\(724\) | 1.65210 | − | 0.318417i | 1.65210 | − | 0.318417i | ||||
\(725\) | 0.514186 | − | 1.48564i | 0.514186 | − | 1.48564i | ||||
\(726\) | 1.76962 | − | 0.168978i | 1.76962 | − | 0.168978i | ||||
\(727\) | 1.54370 | + | 1.21398i | 1.54370 | + | 1.21398i | 0.888835 | + | 0.458227i | \(0.151515\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.270463 | − | 0.312131i | 0.270463 | − | 0.312131i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.613544 | − | 1.34347i | 0.613544 | − | 1.34347i | ||||
\(733\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(734\) | −0.0671040 | − | 0.466718i | −0.0671040 | − | 0.466718i | ||||
\(735\) | 1.02574 | − | 4.22815i | 1.02574 | − | 4.22815i | ||||
\(736\) | −1.00000 | −1.00000 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.24216 | −4.24216 | ||||||||
\(739\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.67489 | + | 0.159932i | 1.67489 | + | 0.159932i | 0.888835 | − | 0.458227i | \(-0.151515\pi\) |
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.28605 | + | 1.48418i | −1.28605 | + | 1.48418i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.45775 | + | 1.93280i | 2.45775 | + | 1.93280i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.795366 | − | 2.29806i | 0.795366 | − | 2.29806i | ||||
\(750\) | −1.74555 | + | 0.336426i | −1.74555 | + | 0.336426i | ||||
\(751\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(752\) | −0.627639 | − | 0.184291i | −0.627639 | − | 0.184291i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.77128 | + | 2.64241i | −2.77128 | + | 2.64241i | ||||
\(757\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | 1.00000 | \(0\) | ||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(762\) | 2.31771 | + | 2.67478i | 2.31771 | + | 2.67478i | ||||
\(763\) | −0.0416572 | + | 0.874493i | −0.0416572 | + | 0.874493i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.327068 | + | 0.566498i | 0.327068 | + | 0.566498i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.74555 | + | 0.336426i | 1.74555 | + | 0.336426i | ||||
\(769\) | −1.65033 | + | 0.660694i | −1.65033 | + | 0.660694i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(774\) | −0.102782 | + | 0.178024i | −0.102782 | + | 0.178024i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0224357 | + | 0.470984i | −0.0224357 | + | 0.470984i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.88063 | + | 2.64098i | −1.88063 | + | 2.64098i | ||||
\(784\) | −1.92384 | + | 1.51292i | −1.92384 | + | 1.51292i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.76962 | + | 0.912303i | −1.76962 | + | 0.912303i | −0.841254 | + | 0.540641i | \(0.818182\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.97876 | + | 0.581017i | 1.97876 | + | 0.581017i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.888835 | + | 0.458227i | 0.888835 | + | 0.458227i | ||||
\(801\) | 0.589927 | + | 4.10304i | 0.589927 | + | 4.10304i | ||||
\(802\) | −0.437742 | + | 1.80440i | −0.437742 | + | 1.80440i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.70566 | + | 0.500828i | 1.70566 | + | 0.500828i | ||||
\(805\) | −1.85674 | −1.85674 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.425656 | − | 2.96050i | −0.425656 | − | 2.96050i | ||||
\(808\) | −1.70566 | − | 0.879330i | −1.70566 | − | 0.879330i | ||||
\(809\) | −0.827068 | + | 1.81103i | −0.827068 | + | 1.81103i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 1.49916 | + | 0.143152i | 1.49916 | + | 0.143152i | ||||
\(811\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(812\) | −1.91153 | + | 2.20602i | −1.91153 | + | 2.20602i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.67489 | − | 0.159932i | 1.67489 | − | 0.159932i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.13915 | + | 1.59971i | 1.13915 | + | 1.59971i | ||||
\(821\) | −0.738471 | + | 0.380708i | −0.738471 | + | 0.380708i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.13779 | − | 1.08488i | 1.13779 | − | 1.08488i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | |||||||
\(824\) | −0.370638 | + | 0.291473i | −0.370638 | + | 0.291473i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.82318 | − | 0.729892i | −1.82318 | − | 0.729892i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
−0.841254 | − | 0.540641i | \(-0.818182\pi\) | |||||||
\(828\) | 1.81720 | + | 1.16785i | 1.81720 | + | 1.16785i | ||||
\(829\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(830\) | 0.0688733 | − | 1.44583i | 0.0688733 | − | 1.44583i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.279486 | + | 0.0538665i | 0.279486 | + | 0.0538665i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(840\) | 3.24102 | + | 0.624655i | 3.24102 | + | 0.624655i | ||||
\(841\) | −0.735759 | + | 1.27437i | −0.735759 | + | 1.27437i | ||||
\(842\) | −0.142315 | − | 0.246497i | −0.142315 | − | 0.246497i | ||||
\(843\) | 0.380327 | + | 1.09888i | 0.380327 | + | 1.09888i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | ||||
\(846\) | 0.925323 | + | 1.06788i | 0.925323 | + | 1.06788i | ||||
\(847\) | −1.56199 | − | 1.00383i | −1.56199 | − | 1.00383i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.293496 | − | 2.04131i | 0.293496 | − | 2.04131i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(854\) | −1.37115 | + | 0.706875i | −1.37115 | + | 0.706875i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(857\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(860\) | 0.0947329 | − | 0.00904590i | 0.0947329 | − | 0.00904590i | ||||
\(861\) | 5.09522 | + | 4.00693i | 5.09522 | + | 4.00693i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.759713 | − | 0.876756i | 0.759713 | − | 0.876756i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(864\) | −1.49256 | − | 1.42315i | −1.49256 | − | 1.42315i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.58006 | − | 0.814576i | −1.58006 | − | 0.814576i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.79469 | 2.79469 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.471518 | −0.471518 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.65033 | + | 0.850806i | 1.65033 | + | 0.850806i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.786053 | + | 0.618159i | 0.786053 | + | 0.618159i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(882\) | 5.26287 | − | 0.502543i | 5.26287 | − | 0.502543i | ||||
\(883\) | −0.428368 | + | 1.23769i | −0.428368 | + | 1.23769i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.50842 | + | 0.442913i | 1.50842 | + | 0.442913i | ||||
\(887\) | 0.911911 | + | 1.28060i | 0.911911 | + | 1.28060i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.175894 | − | 3.69247i | −0.175894 | − | 3.69247i | ||||
\(890\) | 1.38884 | − | 1.32425i | 1.38884 | − | 1.32425i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.481929 | + | 0.676774i | −0.481929 | + | 0.676774i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −3.24102 | − | 1.29751i | −3.24102 | − | 1.29751i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.21590 | − | 1.40323i | −1.21590 | − | 1.40323i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.271738 | + | 0.595023i | 0.271738 | + | 0.595023i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.08006 | − | 1.87071i | −1.08006 | − | 1.87071i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.291604 | − | 0.116741i | 0.291604 | − | 0.116741i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.396666 | + | 1.63508i | 0.396666 | + | 1.63508i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.815816 | − | 0.157236i | −0.815816 | − | 0.157236i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(908\) | −0.959493 | + | 1.66189i | −0.959493 | + | 1.66189i | ||||
\(909\) | 2.07261 | + | 3.58987i | 2.07261 | + | 3.58987i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.37115 | + | 0.548924i | 1.37115 | + | 0.548924i | ||||
\(916\) | 0.283341 | − | 1.97068i | 0.283341 | − | 1.97068i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(920\) | −0.0475819 | − | 0.998867i | −0.0475819 | − | 0.998867i | ||||
\(921\) | −2.06943 | + | 1.06687i | −2.06943 | + | 1.06687i | ||||
\(922\) | −0.839614 | − | 1.17907i | −0.839614 | − | 1.17907i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.550294 | + | 1.58997i | −0.550294 | + | 1.58997i | ||||
\(927\) | 1.01392 | − | 0.0968176i | 1.01392 | − | 0.0968176i | ||||
\(928\) | −1.23576 | − | 0.971812i | −1.23576 | − | 0.971812i | ||||
\(929\) | −1.38884 | + | 0.407799i | −1.38884 | + | 0.407799i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.76962 | + | 0.912303i | 1.76962 | + | 0.912303i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | −1.07701 | − | 1.51245i | −1.07701 | − | 1.51245i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.154218 | − | 0.635697i | 0.154218 | − | 0.635697i | ||||
\(941\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.815816 | − | 1.78639i | 0.815816 | − | 1.78639i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.77128 | − | 2.64241i | −2.77128 | − | 2.64241i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.0913090 | − | 0.0268107i | 0.0913090 | − | 0.0268107i | −0.235759 | − | 0.971812i | \(-0.575758\pi\) |
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.252989 | + | 1.75958i | −0.252989 | + | 1.75958i | ||||
\(961\) | 0.928368 | + | 0.371662i | 0.928368 | + | 0.371662i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.85270 | − | 2.13813i | −1.85270 | − | 2.13813i | ||||
\(964\) | 0.0224357 | − | 0.470984i | 0.0224357 | − | 0.470984i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.07954 | − | 3.11913i | −1.07954 | − | 3.11913i | ||||
\(967\) | −0.654861 | − | 1.13425i | −0.654861 | − | 1.13425i | −0.981929 | − | 0.189251i | \(-0.939394\pi\) |
0.327068 | − | 0.945001i | \(-0.393939\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(972\) | 0.144952 | + | 0.597501i | 0.144952 | + | 0.597501i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.42131 | + | 0.273935i | 1.42131 | + | 0.273935i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.415415 | − | 0.719520i | −0.415415 | − | 0.719520i | ||||
\(977\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(978\) | 1.24248 | + | 2.72066i | 1.24248 | + | 2.72066i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.60275 | − | 1.84967i | −1.60275 | − | 1.84967i | ||||
\(981\) | 0.856844 | + | 0.550660i | 0.856844 | + | 0.550660i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(984\) | −2.02503 | + | 2.84376i | −2.02503 | + | 2.84376i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.102733 | − | 2.15664i | −0.102733 | − | 2.15664i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.0552004 | − | 0.0775182i | −0.0552004 | − | 0.0775182i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.46889 | − | 0.724932i | 2.46889 | − | 0.724932i | ||||
\(997\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1340.1.bl.a.839.1 | yes | 20 | |
4.3 | odd | 2 | 1340.1.bl.b.839.1 | yes | 20 | ||
5.4 | even | 2 | 1340.1.bl.b.839.1 | yes | 20 | ||
20.19 | odd | 2 | CM | 1340.1.bl.a.839.1 | yes | 20 | |
67.23 | even | 33 | inner | 1340.1.bl.a.559.1 | ✓ | 20 | |
268.23 | odd | 66 | 1340.1.bl.b.559.1 | yes | 20 | ||
335.224 | even | 66 | 1340.1.bl.b.559.1 | yes | 20 | ||
1340.559 | odd | 66 | inner | 1340.1.bl.a.559.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1340.1.bl.a.559.1 | ✓ | 20 | 67.23 | even | 33 | inner | |
1340.1.bl.a.559.1 | ✓ | 20 | 1340.559 | odd | 66 | inner | |
1340.1.bl.a.839.1 | yes | 20 | 1.1 | even | 1 | trivial | |
1340.1.bl.a.839.1 | yes | 20 | 20.19 | odd | 2 | CM | |
1340.1.bl.b.559.1 | yes | 20 | 268.23 | odd | 66 | ||
1340.1.bl.b.559.1 | yes | 20 | 335.224 | even | 66 | ||
1340.1.bl.b.839.1 | yes | 20 | 4.3 | odd | 2 | ||
1340.1.bl.b.839.1 | yes | 20 | 5.4 | even | 2 |