Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [536,1,Mod(19,536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(536, 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("536.19");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 536 = 2^{3} \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 536.ba (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: | \(0.267498846771\) |
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 | 291.1 | ||
Root | \(0.723734 - 0.690079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 536.291 |
Dual form | 536.1.ba.a.35.1 |
$q$-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 \(\left(\mathbb{Z}/536\mathbb{Z}\right)^\times\).
\(n\) | \(135\) | \(269\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{14}{33}\right)\) |
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 | ||||
\(3\) | −0.279486 | + | 1.94387i | −0.279486 | + | 1.94387i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(4\) | −0.888835 | + | 0.458227i | −0.888835 | + | 0.458227i | ||||
\(5\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(6\) | −1.95496 | + | 0.186677i | −1.95496 | + | 0.186677i | ||||
\(7\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(8\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(9\) | −2.74102 | − | 0.804835i | −2.74102 | − | 0.804835i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30379 | + | 0.124497i | 1.30379 | + | 0.124497i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(12\) | −0.642315 | − | 1.85585i | −0.642315 | − | 1.85585i | ||||
\(13\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.580057 | − | 0.814576i | 0.580057 | − | 0.814576i | ||||
\(17\) | −0.0845850 | − | 0.0436066i | −0.0845850 | − | 0.0436066i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0.135929 | − | 2.85350i | 0.135929 | − | 2.85350i | ||||
\(19\) | 0.839614 | + | 0.800570i | 0.839614 | + | 0.800570i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(23\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(24\) | 1.65210 | − | 1.06174i | 1.65210 | − | 1.06174i | ||||
\(25\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.51475 | − | 3.31685i | 1.51475 | − | 3.31685i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(32\) | 0.928368 | + | 0.371662i | 0.928368 | + | 0.371662i | ||||
\(33\) | −0.606397 | + | 2.49960i | −0.606397 | + | 2.49960i | ||||
\(34\) | 0.0224357 | − | 0.0924813i | 0.0224357 | − | 0.0924813i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.80511 | − | 0.540641i | 2.80511 | − | 0.540641i | ||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | −0.580057 | + | 1.00469i | −0.580057 | + | 1.00469i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0913090 | − | 1.91681i | −0.0913090 | − | 1.91681i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.67489 | + | 1.07639i | −1.67489 | + | 1.07639i | −0.786053 | + | 0.618159i | \(0.787879\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(44\) | −1.21590 | + | 0.486774i | −1.21590 | + | 0.486774i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(48\) | 1.42131 | + | 1.35522i | 1.42131 | + | 1.35522i | ||||
\(49\) | 0.0475819 | − | 0.998867i | 0.0475819 | − | 0.998867i | ||||
\(50\) | −0.888835 | − | 0.458227i | −0.888835 | − | 0.458227i | ||||
\(51\) | 0.108406 | − | 0.152235i | 0.108406 | − | 0.152235i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(54\) | 3.58047 | + | 0.690079i | 3.58047 | + | 0.690079i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.79086 | + | 1.40835i | −1.79086 | + | 1.40835i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.428368 | + | 0.494363i | 0.428368 | + | 0.494363i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.57211 | −2.57211 | ||||||||
\(67\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(68\) | 0.0951638 | 0.0951638 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(72\) | 1.18673 | + | 2.59858i | 1.18673 | + | 2.59858i | ||||
\(73\) | 1.76962 | − | 0.168978i | 1.76962 | − | 0.168978i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.28605 | − | 1.48418i | −1.28605 | − | 1.48418i | ||||
\(76\) | −1.11312 | − | 0.326842i | −1.11312 | − | 0.326842i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.62093 | + | 2.32703i | 3.62093 | + | 2.32703i | ||||
\(82\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(83\) | 0.481929 | − | 0.676774i | 0.481929 | − | 0.676774i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.44091 | − | 1.37391i | −1.44091 | − | 1.37391i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.759713 | − | 1.06687i | −0.759713 | − | 1.06687i | ||||
\(89\) | −0.0671040 | − | 0.466718i | −0.0671040 | − | 0.466718i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | ||||
\(97\) | 0.888835 | + | 1.53951i | 0.888835 | + | 1.53951i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(98\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(99\) | −3.47351 | − | 1.39059i | −3.47351 | − | 1.39059i | ||||
\(100\) | 0.235759 | − | 0.971812i | 0.235759 | − | 0.971812i | ||||
\(101\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(102\) | 0.173501 | + | 0.0694593i | 0.173501 | + | 0.0694593i | ||||
\(103\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(108\) | 0.173501 | + | 3.64223i | 0.173501 | + | 3.64223i | ||||
\(109\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.379436 | − | 0.532843i | −0.379436 | − | 0.532843i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(114\) | −1.79086 | − | 1.40835i | −1.79086 | − | 1.40835i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.379436 | + | 0.532843i | −0.379436 | + | 0.532843i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.702443 | + | 0.135385i | 0.702443 | + | 0.135385i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.75155 | + | 0.358230i | 3.75155 | + | 0.358230i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(128\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(129\) | −1.62424 | − | 3.55660i | −1.62424 | − | 3.55660i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(132\) | −0.606397 | − | 2.49960i | −0.606397 | − | 2.49960i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.786053 | + | 0.618159i | −0.786053 | + | 0.618159i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.0224357 | + | 0.0924813i | 0.0224357 | + | 0.0924813i | ||||
\(137\) | 0.223734 | − | 1.55610i | 0.223734 | − | 1.55610i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.24555 | + | 1.76592i | −2.24555 | + | 1.76592i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.581419 | + | 1.67990i | 0.581419 | + | 1.67990i | ||||
\(147\) | 1.92837 | + | 0.371662i | 1.92837 | + | 0.371662i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(150\) | 1.13915 | − | 1.59971i | 1.13915 | − | 1.59971i | ||||
\(151\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(152\) | 0.0552004 | − | 1.15880i | 0.0552004 | − | 1.15880i | ||||
\(153\) | 0.196753 | + | 0.187603i | 0.196753 | + | 0.187603i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.40777 | + | 4.06748i | −1.40777 | + | 4.06748i | ||||
\(163\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(164\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.771316 | + | 0.308788i | 0.771316 | + | 0.308788i | ||||
\(167\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.928368 | + | 0.371662i | 0.928368 | + | 0.371662i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.65707 | − | 2.87013i | −1.65707 | − | 2.87013i | ||||
\(172\) | 0.995472 | − | 1.72421i | 0.995472 | − | 1.72421i | ||||
\(173\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(177\) | −1.08070 | + | 0.694523i | −1.08070 | + | 0.694523i | ||||
\(178\) | 0.437742 | − | 0.175245i | 0.437742 | − | 0.175245i | ||||
\(179\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.104852 | − | 0.0673845i | −0.104852 | − | 0.0673845i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(192\) | −1.88431 | − | 0.553283i | −1.88431 | − | 0.553283i | ||||
\(193\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(194\) | −1.28656 | + | 1.22673i | −1.28656 | + | 1.22673i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(197\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(198\) | 0.532475 | − | 3.70344i | 0.532475 | − | 3.70344i | ||||
\(199\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(200\) | 1.00000 | 1.00000 | ||||||||
\(201\) | −1.88431 | + | 0.553283i | −1.88431 | + | 0.553283i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0265970 | + | 0.184986i | −0.0265970 | + | 0.184986i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.995012 | + | 1.14831i | 0.995012 | + | 1.14831i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.370638 | + | 0.291473i | −0.370638 | + | 0.291473i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.279486 | − | 0.0538665i | −0.279486 | − | 0.0538665i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.49866 | + | 1.02730i | −3.49866 | + | 1.02730i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.166113 | + | 3.48714i | −0.166113 | + | 3.48714i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.40324 | − | 1.54447i | 2.40324 | − | 1.54447i | ||||
\(226\) | 0.428368 | − | 0.494363i | 0.428368 | − | 0.494363i | ||||
\(227\) | 0.0688733 | + | 1.44583i | 0.0688733 | + | 1.44583i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(228\) | 0.946439 | − | 2.07241i | 0.946439 | − | 2.07241i | ||||
\(229\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.928368 | − | 0.371662i | −0.928368 | − | 0.371662i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.607279 | − | 0.243118i | −0.607279 | − | 0.243118i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
1.00000 | \(0\) | |||||||||
\(242\) | 0.0340387 | + | 0.714560i | 0.0340387 | + | 0.714560i | ||||
\(243\) | −3.14757 | + | 3.63249i | −3.14757 | + | 3.63249i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.536330 | + | 3.73026i | 0.536330 | + | 3.73026i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.18087 | + | 1.12595i | 1.18087 | + | 1.12595i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.28656 | − | 0.663268i | −1.28656 | − | 0.663268i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.327068 | − | 0.945001i | −0.327068 | − | 0.945001i | ||||
\(257\) | −1.67489 | − | 0.159932i | −1.67489 | − | 0.159932i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(258\) | 3.07341 | − | 2.41696i | 3.07341 | − | 2.41696i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.91030 | − | 0.182411i | 1.91030 | − | 0.182411i | ||||
\(263\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(264\) | 2.28618 | − | 1.17861i | 2.28618 | − | 1.17861i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.925994 | 0.925994 | ||||||||
\(268\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(272\) | −0.0845850 | + | 0.0436066i | −0.0845850 | + | 0.0436066i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.56499 | − | 0.149438i | 1.56499 | − | 0.149438i | ||||
\(275\) | −0.947890 | + | 0.903811i | −0.947890 | + | 0.903811i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(278\) | 0.786053 | − | 0.618159i | 0.786053 | − | 0.618159i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0934441 | + | 0.0180099i | 0.0934441 | + | 0.0180099i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.24555 | − | 1.76592i | −2.24555 | − | 1.76592i | ||||
\(289\) | −0.574804 | − | 0.807199i | −0.574804 | − | 0.807199i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.24102 | + | 1.29751i | −3.24102 | + | 1.29751i | ||||
\(292\) | −1.49547 | + | 0.961081i | −1.49547 | + | 0.961081i | ||||
\(293\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(294\) | 0.0934441 | + | 1.96163i | 0.0934441 | + | 1.96163i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.38786 | − | 4.13590i | 2.38786 | − | 4.13590i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.82318 | + | 0.729892i | 1.82318 | + | 0.729892i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.13915 | − | 0.219553i | 1.13915 | − | 0.219553i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.135929 | + | 0.235436i | −0.135929 | + | 0.235436i | ||||
\(307\) | 0.651174 | − | 1.88144i | 0.651174 | − | 1.88144i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.165101 | − | 1.14831i | −0.165101 | − | 1.14831i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.470237 | − | 0.302203i | −0.470237 | − | 0.302203i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0361086 | − | 0.104329i | −0.0361086 | − | 0.104329i | ||||
\(324\) | −4.28471 | − | 0.409141i | −4.28471 | − | 0.409141i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.38884 | − | 0.407799i | −1.38884 | − | 0.407799i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.38884 | + | 1.32425i | −1.38884 | + | 1.32425i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.03115 | + | 0.531595i | −1.03115 | + | 0.531595i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(332\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.396666 | + | 1.63508i | 0.396666 | + | 1.63508i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(338\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(339\) | 1.14182 | − | 0.588651i | 1.14182 | − | 0.588651i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.39856 | − | 2.28702i | 2.39856 | − | 2.28702i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.91030 | + | 0.560914i | 1.91030 | + | 0.560914i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.327068 | + | 0.945001i | 0.327068 | + | 0.945001i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.16413 | + | 0.600149i | 1.16413 | + | 0.600149i | ||||
\(353\) | −0.0135432 | + | 0.284307i | −0.0135432 | + | 0.284307i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(354\) | −0.929730 | − | 0.886496i | −0.929730 | − | 0.886496i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.273507 | + | 0.384087i | 0.273507 | + | 0.384087i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.771316 | − | 0.308788i | 0.771316 | − | 0.308788i | ||||
\(359\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.0164569 | + | 0.345472i | 0.0164569 | + | 0.345472i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.459493 | + | 1.32762i | −0.459493 | + | 1.32762i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.29244 | + | 5.32751i | −1.29244 | + | 5.32751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0.0407651 | − | 0.117783i | 0.0407651 | − | 0.117783i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.78153 | + | 0.713215i | −1.78153 | + | 0.713215i | −0.786053 | + | 0.618159i | \(0.787879\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(384\) | 0.0934441 | − | 1.96163i | 0.0934441 | − | 1.96163i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.975950 | − | 1.37053i | 0.975950 | − | 1.37053i | ||||
\(387\) | 5.45721 | − | 1.60238i | 5.45721 | − | 1.60238i | ||||
\(388\) | −1.49547 | − | 0.961081i | −1.49547 | − | 0.961081i | ||||
\(389\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.786053 | + | 0.618159i | −0.786053 | + | 0.618159i | ||||
\(393\) | 3.61596 | + | 1.06174i | 3.61596 | + | 1.06174i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.72459 | − | 0.355655i | 3.72459 | − | 0.355655i | ||||
\(397\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.235759 | + | 0.971812i | 0.235759 | + | 0.971812i | ||||
\(401\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(402\) | −0.981929 | − | 1.70075i | −0.981929 | − | 1.70075i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.186042 | + | 0.0177649i | −0.186042 | + | 0.0177649i | ||||
\(409\) | −0.205996 | + | 0.196417i | −0.205996 | + | 0.196417i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.96233 | + | 0.869819i | 2.96233 | + | 0.869819i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.88431 | − | 0.553283i | 1.88431 | − | 0.553283i | ||||
\(418\) | −0.881354 | + | 1.23769i | −0.881354 | + | 1.23769i | ||||
\(419\) | 1.58006 | + | 0.814576i | 1.58006 | + | 0.814576i | 1.00000 | \(0\) | ||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(422\) | −0.370638 | − | 0.291473i | −0.370638 | − | 0.291473i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0883470 | − | 0.0353688i | 0.0883470 | − | 0.0353688i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.0135432 | − | 0.284307i | −0.0135432 | − | 0.284307i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | −1.82318 | − | 3.15784i | −1.82318 | − | 3.15784i | ||||
\(433\) | −1.54370 | + | 0.297523i | −1.54370 | + | 0.297523i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.42800 | + | 0.660694i | −3.42800 | + | 0.660694i | ||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.934347 | + | 2.69962i | −0.934347 | + | 2.69962i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.00452808 | + | 0.0950560i | 0.00452808 | + | 0.0950560i | 1.00000 | \(0\) | ||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.02951 | + | 0.809616i | 1.02951 | + | 0.809616i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(450\) | 2.06752 | + | 1.97137i | 2.06752 | + | 1.97137i | ||||
\(451\) | 0.119589 | − | 2.51049i | 0.119589 | − | 2.51049i | ||||
\(452\) | 0.581419 | + | 0.299742i | 0.581419 | + | 0.299742i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.38884 | + | 0.407799i | −1.38884 | + | 0.407799i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23713 | + | 0.431171i | 2.23713 | + | 0.431171i | ||||
\(457\) | −0.154218 | − | 0.445585i | −0.154218 | − | 0.445585i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.272762 | + | 0.214502i | −0.272762 | + | 0.214502i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(467\) | −0.308779 | − | 1.27280i | −0.308779 | − | 1.27280i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0930932 | − | 0.647478i | 0.0930932 | − | 0.647478i | ||||
\(473\) | −2.31771 | + | 1.19486i | −2.31771 | + | 1.19486i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.15486 | + | 0.110276i | −1.15486 | + | 0.110276i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.815816 | + | 0.157236i | 0.815816 | + | 0.157236i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.686393 | + | 0.201543i | −0.686393 | + | 0.201543i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.27217 | − | 2.20246i | −4.27217 | − | 2.20246i | ||||
\(487\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.23445 | − | 1.75719i | −2.23445 | − | 1.75719i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(492\) | −3.49866 | + | 1.40065i | −3.49866 | + | 1.40065i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.815816 | + | 1.41303i | −0.815816 | + | 1.41303i | ||||
\(499\) | −0.928368 | − | 1.60798i | −0.928368 | − | 1.60798i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.341254 | − | 1.40667i | 0.341254 | − | 1.40667i | ||||
\(503\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.981929 | + | 1.70075i | −0.981929 | + | 1.70075i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(513\) | 3.92718 | − | 1.57221i | 3.92718 | − | 1.57221i | ||||
\(514\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.07341 | + | 2.41696i | 3.07341 | + | 2.41696i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.78153 | + | 0.523103i | −1.78153 | + | 0.523103i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.54370 | − | 0.297523i | −1.54370 | − | 0.297523i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(524\) | 0.627639 | + | 1.81344i | 0.627639 | + | 1.81344i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.68437 | + | 1.94387i | 1.68437 | + | 1.94387i | ||||
\(529\) | 0.723734 | − | 0.690079i | 0.723734 | − | 0.690079i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.776283 | − | 1.69982i | −0.776283 | − | 1.69982i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.218311 | + | 0.899892i | 0.218311 | + | 0.899892i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(537\) | 1.63163 | 1.63163 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.0623191 | − | 0.0719200i | −0.0623191 | − | 0.0719200i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.827068 | − | 0.0789754i | −0.827068 | − | 0.0789754i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(548\) | 0.514186 | + | 1.48564i | 0.514186 | + | 1.48564i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.786053 | + | 0.618159i | 0.786053 | + | 0.618159i | ||||
\(557\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.160291 | − | 0.184986i | 0.160291 | − | 0.184986i | ||||
\(562\) | 0.00452808 | + | 0.0950560i | 0.00452808 | + | 0.0950560i | ||||
\(563\) | 0.771316 | − | 1.68895i | 0.771316 | − | 1.68895i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.419102 | + | 1.72756i | −0.419102 | + | 1.72756i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0883470 | + | 0.0353688i | 0.0883470 | + | 0.0353688i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.18673 | − | 2.59858i | 1.18673 | − | 2.59858i | ||||
\(577\) | 0.0224357 | + | 0.470984i | 0.0224357 | + | 0.470984i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(578\) | 0.648930 | − | 0.748905i | 0.648930 | − | 0.748905i | ||||
\(579\) | 2.77967 | − | 1.78639i | 2.77967 | − | 1.78639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.02503 | − | 2.84376i | −2.02503 | − | 2.84376i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.28656 | − | 1.22673i | −1.28656 | − | 1.22673i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.03115 | + | 1.44805i | −1.03115 | + | 1.44805i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(588\) | −1.88431 | + | 0.553283i | −1.88431 | + | 0.553283i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.39734 | − | 1.09888i | 1.39734 | − | 1.09888i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(594\) | 4.58227 | + | 1.34548i | 4.58227 | + | 1.34548i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(600\) | −0.279486 | + | 1.94387i | −0.279486 | + | 1.94387i | ||||
\(601\) | 0.341254 | + | 1.40667i | 0.341254 | + | 1.40667i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.406556 | − | 2.82766i | −0.406556 | − | 2.82766i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(608\) | 0.481929 | + | 1.05528i | 0.481929 | + | 1.05528i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.260846 | − | 0.0765912i | −0.260846 | − | 0.0765912i | ||||
\(613\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(614\) | 1.98193 | + | 0.189251i | 1.98193 | + | 0.189251i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.911911 | + | 1.28060i | −0.911911 | + | 1.28060i | 0.0475819 | + | 0.998867i | \(0.484848\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(626\) | 1.07701 | − | 0.431171i | 1.07701 | − | 0.431171i | ||||
\(627\) | −2.51025 | + | 1.61324i | −2.51025 | + | 1.61324i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.462997 | − | 0.801934i | −0.462997 | − | 0.801934i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.723734 | + | 1.25354i | −0.723734 | + | 1.25354i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(642\) | 0.182822 | − | 0.528229i | 0.182822 | − | 0.528229i | ||||
\(643\) | −0.271738 | + | 0.595023i | −0.271738 | + | 0.595023i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.0928751 | − | 0.0596872i | 0.0928751 | − | 0.0596872i | ||||
\(647\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(648\) | −0.612552 | − | 4.26039i | −0.612552 | − | 4.26039i | ||||
\(649\) | 0.496956 | + | 0.697876i | 0.496956 | + | 0.697876i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.0688733 | − | 1.44583i | 0.0688733 | − | 1.44583i | ||||
\(653\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(657\) | −4.98656 | − | 0.961081i | −4.98656 | − | 0.961081i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.995472 | + | 0.0950560i | 0.995472 | + | 0.0950560i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(662\) | −0.759713 | − | 0.876756i | −0.759713 | − | 0.876756i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.827068 | + | 0.0789754i | −0.827068 | + | 0.0789754i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.264241 | + | 1.83784i | −0.264241 | + | 1.83784i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | −1.49547 | + | 0.770969i | −1.49547 | + | 0.770969i | ||||
\(675\) | 1.51475 | + | 3.31685i | 1.51475 | + | 3.31685i | ||||
\(676\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(677\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(678\) | 0.841254 | + | 0.970858i | 0.841254 | + | 0.970858i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.82975 | − | 0.270208i | −2.82975 | − | 0.270208i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.54370 | − | 0.297523i | −1.54370 | − | 0.297523i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(684\) | 2.78803 | + | 1.79176i | 2.78803 | + | 1.79176i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0947329 | + | 1.98869i | −0.0947329 | + | 1.98869i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.165101 | − | 0.231852i | −0.165101 | − | 0.231852i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.841254 | + | 0.540641i | −0.841254 | + | 0.540641i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0758623 | + | 0.166115i | −0.0758623 | + | 0.166115i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.981929 | − | 1.70075i | 0.981929 | − | 1.70075i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.308779 | + | 1.27280i | −0.308779 | + | 1.27280i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.279486 | + | 0.0538665i | −0.279486 | + | 0.0538665i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.642315 | − | 1.11252i | 0.642315 | − | 1.11252i | ||||
\(709\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.308779 | + | 0.356349i | −0.308779 | + | 0.356349i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.481929 | + | 0.676774i | 0.481929 | + | 0.676774i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.331854 | + | 0.0974412i | −0.331854 | + | 0.0974412i | ||||
\(723\) | 1.37262 | + | 0.882127i | 1.37262 | + | 0.882127i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.39852 | − | 0.133543i | −1.39852 | − | 0.133543i | ||||
\(727\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.36273 | − | 3.88080i | −3.36273 | − | 3.88080i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.188608 | − | 0.0180099i | 0.188608 | − | 0.0180099i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.428368 | + | 1.23769i | 0.428368 | + | 1.23769i | ||||
\(738\) | −5.48204 | −5.48204 | ||||||||
\(739\) | −0.154218 | − | 0.635697i | −0.154218 | − | 0.635697i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.86567 | + | 1.46718i | −1.86567 | + | 1.46718i | ||||
\(748\) | 0.124074 | + | 0.0118476i | 0.124074 | + | 0.0118476i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.64888 | − | 2.31553i | 1.64888 | − | 2.31553i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(758\) | −1.11312 | − | 1.56316i | −1.11312 | − | 1.56316i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.92837 | − | 0.371662i | 1.92837 | − | 0.371662i | ||||
\(769\) | 1.34378 | + | 0.537970i | 1.34378 | + | 0.537970i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.778996 | − | 3.21106i | 0.778996 | − | 3.21106i | ||||
\(772\) | 1.56199 | + | 0.625325i | 1.56199 | + | 0.625325i | ||||
\(773\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(774\) | 2.84380 | + | 4.92561i | 2.84380 | + | 4.92561i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.581419 | − | 1.67990i | 0.581419 | − | 1.67990i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.45788 | − | 1.68248i | 1.45788 | − | 1.68248i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.786053 | − | 0.618159i | −0.786053 | − | 0.618159i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.179318 | + | 3.76435i | −0.179318 | + | 3.76435i | ||||
\(787\) | 0.252989 | + | 0.130425i | 0.252989 | + | 0.130425i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.22373 | + | 3.53575i | 1.22373 | + | 3.53575i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.888835 | + | 0.458227i | −0.888835 | + | 0.458227i | ||||
\(801\) | −0.191698 | + | 1.33329i | −0.191698 | + | 1.33329i | ||||
\(802\) | 0.396666 | + | 1.63508i | 0.396666 | + | 1.63508i | ||||
\(803\) | 2.32825 | 2.32825 | ||||||||
\(804\) | 1.42131 | − | 1.35522i | 1.42131 | − | 1.35522i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | 1.00000 | \(0\) | ||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.601300 | − | 0.573338i | 0.601300 | − | 0.573338i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.0611251 | − | 0.176609i | −0.0611251 | − | 0.176609i | ||||
\(817\) | −2.26798 | − | 0.437118i | −2.26798 | − | 0.437118i | ||||
\(818\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(822\) | −0.146904 | + | 3.08390i | −0.146904 | + | 3.08390i | ||||
\(823\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.49197 | − | 2.09518i | −1.49197 | − | 2.09518i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.21590 | + | 0.486774i | −1.21590 | + | 0.486774i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.0475819 | + | 0.0824143i | −0.0475819 | + | 0.0824143i | ||||
\(834\) | 0.981929 | + | 1.70075i | 0.981929 | + | 1.70075i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.41059 | − | 0.564714i | −1.41059 | − | 0.564714i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.419102 | + | 1.72756i | −0.419102 | + | 1.72756i | ||||
\(839\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0611251 | + | 0.176609i | −0.0611251 | + | 0.176609i | ||||
\(844\) | 0.195876 | − | 0.428908i | 0.195876 | − | 0.428908i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.279486 | + | 1.94387i | 0.279486 | + | 1.94387i | ||||
\(850\) | 0.0552004 | + | 0.0775182i | 0.0552004 | + | 0.0775182i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(857\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | 1.00000 | \(0\) | ||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0311250 | − | 0.0899299i | −0.0311250 | − | 0.0899299i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(864\) | 2.63900 | − | 2.51628i | 2.63900 | − | 2.51628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.653077 | − | 1.43004i | −0.653077 | − | 1.43004i | ||||
\(867\) | 1.72974 | − | 0.891742i | 1.72974 | − | 0.891742i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.19726 | − | 4.93519i | −1.19726 | − | 4.93519i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.45025 | − | 3.17561i | −1.45025 | − | 3.17561i | ||||
\(877\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.02951 | − | 0.809616i | 1.02951 | − | 0.809616i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(882\) | −2.84380 | − | 0.271550i | −2.84380 | − | 0.271550i | ||||
\(883\) | 0.627639 | + | 1.81344i | 0.627639 | + | 1.81344i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0913090 | + | 0.0268107i | −0.0913090 | + | 0.0268107i | ||||
\(887\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.43122 | + | 3.48475i | 4.43122 | + | 3.48475i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.42837 | + | 2.47401i | −1.42837 | + | 2.47401i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.46792 | − | 0.475652i | 2.46792 | − | 0.475652i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.154218 | + | 0.635697i | −0.154218 | + | 0.635697i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.65210 | − | 0.318417i | 1.65210 | − | 0.318417i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(908\) | −0.723734 | − | 1.25354i | −0.723734 | − | 1.25354i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(912\) | 0.108406 | + | 2.27572i | 0.108406 | + | 2.27572i | ||||
\(913\) | 0.712591 | − | 0.822373i | 0.712591 | − | 0.822373i | ||||
\(914\) | 0.396666 | − | 0.254922i | 0.396666 | − | 0.254922i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.272762 | − | 0.214502i | −0.272762 | − | 0.214502i | ||||
\(919\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.47528 | + | 1.79163i | 3.47528 | + | 1.79163i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.78153 | − | 0.523103i | −1.78153 | − | 0.523103i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.839614 | − | 0.800570i | 0.839614 | − | 0.800570i | ||||
\(932\) | 0.995472 | − | 0.0950560i | 0.995472 | − | 0.0950560i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.16413 | − | 0.600149i | 1.16413 | − | 0.600149i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.27830 | 2.27830 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.651174 | − | 0.0621796i | 0.651174 | − | 0.0621796i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.70760 | − | 1.97068i | −1.70760 | − | 1.97068i | ||||
\(947\) | −0.452418 | − | 0.132842i | −0.452418 | − | 0.132842i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.379436 | − | 1.09631i | −0.379436 | − | 1.09631i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.91030 | − | 0.560914i | 1.91030 | − | 0.560914i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.928368 | − | 0.371662i | 0.928368 | − | 0.371662i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.532475 | − | 0.614509i | 0.532475 | − | 0.614509i | ||||
\(964\) | 0.0395325 | + | 0.829889i | 0.0395325 | + | 0.829889i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(968\) | −0.357685 | − | 0.619529i | −0.357685 | − | 0.619529i | ||||
\(969\) | 0.212894 | − | 0.0410319i | 0.212894 | − | 0.0410319i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.469383 | + | 1.93482i | −0.469383 | + | 1.93482i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(972\) | 1.13317 | − | 4.67099i | 1.13317 | − | 4.67099i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.271738 | + | 0.785135i | −0.271738 | + | 0.785135i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(978\) | 1.18087 | − | 2.58574i | 1.18087 | − | 2.58574i | ||||
\(979\) | −0.0293845 | − | 0.616858i | −0.0293845 | − | 0.616858i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.928368 | + | 0.371662i | −0.928368 | + | 0.371662i | ||||
\(983\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(984\) | −2.18601 | − | 3.06982i | −2.18601 | − | 3.06982i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.745158 | − | 2.15299i | −0.745158 | − | 2.15299i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.56554 | − | 0.459684i | −1.56554 | − | 0.459684i | ||||
\(997\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(998\) | 1.34378 | − | 1.28129i | 1.34378 | − | 1.28129i | ||||
\(999\) | 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 | 536.1.ba.a.291.1 | yes | 20 | |
4.3 | odd | 2 | 2144.1.bu.a.559.1 | 20 | |||
8.3 | odd | 2 | CM | 536.1.ba.a.291.1 | yes | 20 | |
8.5 | even | 2 | 2144.1.bu.a.559.1 | 20 | |||
67.35 | even | 33 | inner | 536.1.ba.a.35.1 | ✓ | 20 | |
268.35 | odd | 66 | 2144.1.bu.a.303.1 | 20 | |||
536.35 | odd | 66 | inner | 536.1.ba.a.35.1 | ✓ | 20 | |
536.437 | even | 66 | 2144.1.bu.a.303.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
536.1.ba.a.35.1 | ✓ | 20 | 67.35 | even | 33 | inner | |
536.1.ba.a.35.1 | ✓ | 20 | 536.35 | odd | 66 | inner | |
536.1.ba.a.291.1 | yes | 20 | 1.1 | even | 1 | trivial | |
536.1.ba.a.291.1 | yes | 20 | 8.3 | odd | 2 | CM | |
2144.1.bu.a.303.1 | 20 | 268.35 | odd | 66 | |||
2144.1.bu.a.303.1 | 20 | 536.437 | even | 66 | |||
2144.1.bu.a.559.1 | 20 | 4.3 | odd | 2 | |||
2144.1.bu.a.559.1 | 20 | 8.5 | even | 2 |