Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (of order \(6\), degree \(2\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 28x^{14} + 542x^{12} + 5488x^{10} + 40451x^{8} + 151312x^{6} + 395134x^{4} + 52164x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1855.5 | ||
Root | \(-1.51646 - 2.62659i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1855 |
Dual form | 2736.2.bm.t.559.6 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.767178 | + | 1.32879i | 0.343092 | + | 0.594254i | 0.985005 | − | 0.172524i | \(-0.0551922\pi\) |
−0.641913 | + | 0.766778i | \(0.721859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.31392i | − | 0.874581i | −0.899320 | − | 0.437291i | \(-0.855938\pi\) | ||
0.899320 | − | 0.437291i | \(-0.144062\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.49807i | 1.65773i | 0.559449 | + | 0.828865i | \(0.311013\pi\) | ||||
−0.559449 | + | 0.828865i | \(0.688987\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.96863 | − | 2.29129i | −1.10070 | − | 0.635489i | −0.164295 | − | 0.986411i | \(-0.552535\pi\) |
−0.936405 | + | 0.350922i | \(0.885868\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.79694 | + | 4.84444i | 0.678358 | + | 1.17495i | 0.975475 | + | 0.220109i | \(0.0706413\pi\) |
−0.297118 | + | 0.954841i | \(0.596025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.09932 | + | 4.21800i | −0.252201 | + | 0.967675i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.07472 | − | 1.77519i | −0.641124 | − | 0.370153i | 0.143923 | − | 0.989589i | \(-0.454028\pi\) |
−0.785047 | + | 0.619436i | \(0.787361\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.32288 | − | 2.29129i | 0.264575 | − | 0.458258i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.12824 | − | 4.11549i | −1.32368 | − | 0.764227i | −0.339367 | − | 0.940654i | \(-0.610213\pi\) |
−0.984314 | + | 0.176427i | \(0.943546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.20647 | −1.11471 | −0.557357 | − | 0.830273i | \(-0.688185\pi\) | ||||
−0.557357 | + | 0.830273i | \(0.688185\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.07472 | − | 1.77519i | 0.519723 | − | 0.300062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.73205i | − | 0.284747i | −0.989813 | − | 0.142374i | \(-0.954527\pi\) | ||
0.989813 | − | 0.142374i | \(-0.0454735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.86565 | − | 3.38654i | 0.916061 | − | 0.528888i | 0.0336847 | − | 0.999433i | \(-0.489276\pi\) |
0.882376 | + | 0.470544i | \(0.155942\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.30970 | + | 5.37496i | −1.41972 | + | 0.819674i | −0.996274 | − | 0.0862491i | \(-0.972512\pi\) |
−0.423443 | + | 0.905923i | \(0.639179\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.68674 | + | 0.973842i | 0.246037 | + | 0.142049i | 0.617948 | − | 0.786219i | \(-0.287964\pi\) |
−0.371911 | + | 0.928268i | \(0.621297\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.64575 | 0.235107 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.16719 | − | 4.71533i | −1.12185 | − | 0.647700i | −0.179977 | − | 0.983671i | \(-0.557602\pi\) |
−0.941872 | + | 0.335971i | \(0.890936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.30579 | + | 4.21800i | −0.985112 | + | 0.568755i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.76147 | − | 8.24710i | −0.619890 | − | 1.07368i | −0.989505 | − | 0.144496i | \(-0.953844\pi\) |
0.369615 | − | 0.929185i | \(-0.379490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.32288 | + | 4.02334i | −0.297414 | + | 0.515136i | −0.975543 | − | 0.219806i | \(-0.929457\pi\) |
0.678130 | + | 0.734942i | \(0.262791\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.03130i | − | 0.872126i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.20255 | + | 7.27903i | −0.513423 | + | 0.889275i | 0.486455 | + | 0.873705i | \(0.338290\pi\) |
−0.999879 | + | 0.0155700i | \(0.995044\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.83619 | + | 13.5727i | 0.929985 | + | 1.61078i | 0.783342 | + | 0.621591i | \(0.213514\pi\) |
0.146643 | + | 0.989189i | \(0.453153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.79150 | + | 11.7632i | 0.794885 | + | 1.37678i | 0.922912 | + | 0.385011i | \(0.125802\pi\) |
−0.128027 | + | 0.991771i | \(0.540864\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.7221 | 1.44982 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.11107 | − | 12.3167i | −0.800058 | − | 1.38574i | −0.919577 | − | 0.392909i | \(-0.871469\pi\) |
0.119519 | − | 0.992832i | \(-0.461865\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.94768i | − | 0.213786i | −0.994271 | − | 0.106893i | \(-0.965910\pi\) | ||
0.994271 | − | 0.106893i | \(-0.0340902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.29150 | + | 7.43310i | −0.465479 | + | 0.806233i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.82670 | − | 2.78670i | −0.511629 | − | 0.295389i | 0.221874 | − | 0.975075i | \(-0.428783\pi\) |
−0.733503 | + | 0.679686i | \(0.762116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.30187 | + | 9.18310i | −0.555787 | + | 0.962651i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.44821 | + | 1.77519i | −0.661572 | + | 0.182131i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.40588 | − | 4.27579i | 0.751953 | − | 0.434140i | −0.0744460 | − | 0.997225i | \(-0.523719\pi\) |
0.826399 | + | 0.563085i | \(0.190385\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.92518 | + | 17.1909i | −0.987592 | + | 1.71056i | −0.357794 | + | 0.933800i | \(0.616471\pi\) |
−0.629798 | + | 0.776759i | \(0.716862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.389432 | −0.0383718 | −0.0191859 | − | 0.999816i | \(-0.506107\pi\) | ||||
−0.0191859 | + | 0.999816i | \(0.506107\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.0459 | −1.84123 | −0.920617 | − | 0.390467i | \(-0.872313\pi\) | ||||
−0.920617 | + | 0.390467i | \(0.872313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.46863 | − | 3.15731i | 0.523799 | − | 0.302416i | −0.214688 | − | 0.976683i | \(-0.568874\pi\) |
0.738488 | + | 0.674267i | \(0.235540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.2623i | 1.43575i | 0.696170 | + | 0.717877i | \(0.254886\pi\) | ||||
−0.696170 | + | 0.717877i | \(0.745114\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.44755i | − | 0.507987i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.2097 | − | 6.47191i | 1.02759 | − | 0.593279i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.2288 | −1.74807 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7313 | 1.04928 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.20647 | + | 10.7499i | −0.550735 | + | 0.953901i | 0.447487 | + | 0.894291i | \(0.352319\pi\) |
−0.998222 | + | 0.0596105i | \(0.981014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3591 | − | 10.0223i | 1.51667 | − | 0.875652i | 0.516866 | − | 0.856067i | \(-0.327099\pi\) |
0.999808 | − | 0.0195854i | \(-0.00623463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.76013 | + | 2.54374i | 0.846311 | + | 0.220570i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.06871 | − | 5.31517i | 0.262178 | − | 0.454105i | −0.704643 | − | 0.709562i | \(-0.748893\pi\) |
0.966820 | + | 0.255457i | \(0.0822260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.3254 | − | 10.0028i | −1.46952 | − | 0.848427i | −0.470104 | − | 0.882611i | \(-0.655783\pi\) |
−0.999416 | + | 0.0341840i | \(0.989117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5977 | − | 21.8198i | 1.05347 | − | 1.82466i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 12.6293i | − | 1.04880i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.495406 | − | 0.858069i | −0.0405853 | − | 0.0702957i | 0.845019 | − | 0.534736i | \(-0.179589\pi\) |
−0.885604 | + | 0.464440i | \(0.846256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.39727 | −0.357845 | −0.178922 | − | 0.983863i | \(-0.557261\pi\) | ||||
−0.178922 | + | 0.983863i | \(0.557261\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.76147 | − | 8.24710i | −0.382450 | − | 0.662423i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.79150 | − | 8.29913i | −0.382404 | − | 0.662342i | 0.609002 | − | 0.793169i | \(-0.291570\pi\) |
−0.991405 | + | 0.130827i | \(0.958237\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.10766 | + | 7.11468i | −0.323729 | + | 0.560715i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.1859i | 1.50276i | 0.659872 | + | 0.751378i | \(0.270611\pi\) | ||||
−0.659872 | + | 0.751378i | \(0.729389\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.07472 | + | 5.32558i | −0.237929 | + | 0.412106i | −0.960120 | − | 0.279588i | \(-0.909802\pi\) |
0.722191 | + | 0.691694i | \(0.243135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | + | 6.92820i | 0.307692 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.05034 | − | 2.91581i | 0.383970 | − | 0.221685i | −0.295574 | − | 0.955320i | \(-0.595511\pi\) |
0.679544 | + | 0.733635i | \(0.262178\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.30187 | − | 3.06103i | −0.400784 | − | 0.231392i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.52293 | −0.711777 | −0.355889 | − | 0.934528i | \(-0.615822\pi\) | ||||
−0.355889 | + | 0.934528i | \(0.615822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4059 | − | 9.47194i | −1.21944 | − | 0.704044i | −0.254641 | − | 0.967036i | \(-0.581957\pi\) |
−0.964798 | + | 0.262992i | \(0.915291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.30153 | − | 1.32879i | 0.169212 | − | 0.0976947i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.6351 | + | 15.3778i | −1.94775 | + | 1.12453i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4419i | 1.33441i | 0.744875 | + | 0.667204i | \(0.232509\pi\) | ||||
−0.744875 | + | 0.667204i | \(0.767491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.03137 | − | 2.90486i | 0.362166 | − | 0.209097i | −0.307864 | − | 0.951430i | \(-0.599614\pi\) |
0.670031 | + | 0.742334i | \(0.266281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.7405 | 0.765228 | 0.382614 | − | 0.923908i | \(-0.375024\pi\) | ||||
0.382614 | + | 0.923908i | \(0.375024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.30970 | − | 5.37496i | −0.659947 | − | 0.381021i | 0.132310 | − | 0.991208i | \(-0.457761\pi\) |
−0.792257 | + | 0.610188i | \(0.791094\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.52293 | + | 16.4942i | −0.668379 | + | 1.15767i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 5.19615i | 0.628587 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.1908 | − | 6.04412i | −1.60414 | − | 0.418080i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.10323 | + | 5.37496i | 0.213635 | + | 0.370028i | 0.952850 | − | 0.303443i | \(-0.0981362\pi\) |
−0.739214 | + | 0.673470i | \(0.764803\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.2844 | − | 8.24710i | −0.974188 | − | 0.562448i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.3613i | 0.974909i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 25.6344i | − | 1.72436i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.91244 | + | 8.50859i | 0.328961 | + | 0.569777i | 0.982306 | − | 0.187283i | \(-0.0599682\pi\) |
−0.653345 | + | 0.757060i | \(0.726635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8964 | 0.855966 | 0.427983 | − | 0.903787i | \(-0.359224\pi\) | ||||
0.427983 | + | 0.903787i | \(0.359224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.35425 | 0.0894913 | 0.0447456 | − | 0.998998i | \(-0.485752\pi\) | ||||
0.0447456 | + | 0.998998i | \(0.485752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.40001 | − | 12.8172i | −0.484791 | − | 0.839682i | 0.515057 | − | 0.857156i | \(-0.327771\pi\) |
−0.999847 | + | 0.0174740i | \(0.994438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.98844i | 0.194944i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.4903i | 1.77820i | 0.457711 | + | 0.889101i | \(0.348670\pi\) | ||||
−0.457711 | + | 0.889101i | \(0.651330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3745 | − | 8.29913i | −0.925943 | − | 0.534594i | −0.0404171 | − | 0.999183i | \(-0.512869\pi\) |
−0.885526 | + | 0.464589i | \(0.846202\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.26258 | + | 2.18686i | 0.0806636 | + | 0.139713i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0274 | − | 14.2208i | 0.892544 | − | 0.904848i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.14945 | + | 3.55038i | 0.388150 | + | 0.224098i | 0.681358 | − | 0.731950i | \(-0.261390\pi\) |
−0.293208 | + | 0.956049i | \(0.594723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.76013 | − | 16.9050i | 0.613614 | − | 1.06281i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.08929 | − | 3.51565i | −0.379839 | − | 0.219300i | 0.297909 | − | 0.954594i | \(-0.403711\pi\) |
−0.677748 | + | 0.735294i | \(0.737044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00784 | −0.249035 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.68674 | − | 0.973842i | 0.104009 | − | 0.0600497i | −0.447093 | − | 0.894487i | \(-0.647541\pi\) |
0.551102 | + | 0.834438i | \(0.314207\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 14.4700i | − | 0.888884i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.08929 | + | 3.51565i | −0.371270 | + | 0.214353i | −0.674013 | − | 0.738719i | \(-0.735431\pi\) |
0.302743 | + | 0.953072i | \(0.402098\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0235 | + | 6.94177i | −0.730376 | + | 0.421683i | −0.818560 | − | 0.574421i | \(-0.805227\pi\) |
0.0881837 | + | 0.996104i | \(0.471894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.5977 | + | 7.27326i | 0.759667 | + | 0.438594i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.22876 | 0.133913 | 0.0669565 | − | 0.997756i | \(-0.478671\pi\) | ||||
0.0669565 | + | 0.997756i | \(0.478671\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.87704 | + | 5.70251i | 0.589215 | + | 0.340183i | 0.764787 | − | 0.644283i | \(-0.222844\pi\) |
−0.175572 | + | 0.984467i | \(0.556178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.83619 | − | 13.5727i | −0.462556 | − | 0.801170i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.14575 | + | 12.3768i | −0.420338 | + | 0.728047i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.1765i | 1.41240i | 0.708010 | + | 0.706202i | \(0.249593\pi\) | ||||
−0.708010 | + | 0.706202i | \(0.750407\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.30579 | − | 12.6540i | 0.425359 | − | 0.736744i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.13495 | + | 14.0902i | 0.470457 | + | 0.814855i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.4373 | + | 21.5420i | 0.716871 | + | 1.24166i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.12824 | −0.408162 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.49658 | + | 9.52036i | 0.313707 | + | 0.543356i | 0.979162 | − | 0.203082i | \(-0.0650958\pi\) |
−0.665455 | + | 0.746438i | \(0.731762\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 21.6473i | − | 1.22751i | −0.789498 | − | 0.613753i | \(-0.789659\pi\) | ||
0.789498 | − | 0.613753i | \(-0.210341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.822876 | + | 1.42526i | −0.0465117 | + | 0.0805606i | −0.888344 | − | 0.459179i | \(-0.848144\pi\) |
0.841832 | + | 0.539739i | \(0.181477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.2954 | + | 8.83082i | 0.859077 | + | 0.495988i | 0.863703 | − | 0.504001i | \(-0.168139\pi\) |
−0.00462637 | + | 0.999989i | \(0.501473\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.6272 | − | 39.1915i | 1.26688 | − | 2.19430i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.5086 | + | 6.47191i | −1.30805 | + | 0.360107i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5000 | + | 6.06218i | −0.582435 | + | 0.336269i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.25340 | − | 3.90300i | 0.124234 | − | 0.215179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.2378 | 1.22230 | 0.611150 | − | 0.791515i | \(-0.290707\pi\) | ||||
0.611150 | + | 0.791515i | \(0.290707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8964 | −0.704607 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9059 | − | 10.3380i | 0.975395 | − | 0.563145i | 0.0745186 | − | 0.997220i | \(-0.476258\pi\) |
0.900877 | + | 0.434075i | \(0.142925\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 34.1236i | − | 1.84790i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0056i | − | 1.08020i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.4338 | − | 11.7975i | 1.09695 | − | 0.633322i | 0.161529 | − | 0.986868i | \(-0.448357\pi\) |
0.935417 | + | 0.353546i | \(0.115024\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0627 | −0.752762 | −0.376381 | − | 0.926465i | \(-0.622832\pi\) | ||||
−0.376381 | + | 0.926465i | \(0.622832\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.4718 | 1.19605 | 0.598027 | − | 0.801476i | \(-0.295952\pi\) | ||||
0.598027 | + | 0.801476i | \(0.295952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0235 | + | 20.8253i | −0.638141 | + | 1.10529i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.14945 | + | 3.55038i | −0.324555 | + | 0.187382i | −0.653421 | − | 0.756995i | \(-0.726667\pi\) |
0.328866 | + | 0.944377i | \(0.393334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5830 | − | 9.27383i | −0.872790 | − | 0.488096i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.4206 | + | 18.0490i | −0.545438 | + | 0.944727i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.30970 | + | 5.37496i | 0.485963 | + | 0.280571i | 0.722898 | − | 0.690955i | \(-0.242810\pi\) |
−0.236935 | + | 0.971525i | \(0.576143\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.9109 | + | 18.8983i | −0.566466 | + | 0.981149i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.31463i | 0.326959i | 0.986547 | + | 0.163479i | \(0.0522718\pi\) | ||||
−0.986547 | + | 0.163479i | \(0.947728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.8595 | + | 32.6657i | 0.971316 | + | 1.68237i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.80920 | −0.0929325 | −0.0464662 | − | 0.998920i | \(-0.514796\pi\) | ||||
−0.0464662 | + | 0.998920i | \(0.514796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.07472 | + | 5.32558i | 0.157111 | + | 0.272124i | 0.933826 | − | 0.357728i | \(-0.116449\pi\) |
−0.776715 | + | 0.629853i | \(0.783115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.76013 | + | 16.9050i | 0.497422 | + | 0.861561i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.83589 | + | 6.64396i | −0.194487 | + | 0.336862i | −0.946732 | − | 0.322022i | \(-0.895638\pi\) |
0.752245 | + | 0.658884i | \(0.228971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.8604i | − | 1.00439i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9109 | − | 18.8983i | 0.548988 | − | 0.950875i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.6144 | + | 32.2410i | 0.934229 | + | 1.61813i | 0.776003 | + | 0.630729i | \(0.217244\pi\) |
0.158226 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.0832 | + | 11.0177i | −0.952968 | + | 0.550197i | −0.894002 | − | 0.448063i | \(-0.852114\pi\) |
−0.0589666 | + | 0.998260i | \(0.518781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.6312 | + | 14.2208i | 1.22697 | + | 0.708389i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.52293 | 0.472034 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.53137 | − | 2.03884i | −0.174615 | − | 0.100814i | 0.410145 | − | 0.912020i | \(-0.365478\pi\) |
−0.584760 | + | 0.811206i | \(0.698811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.0832 | + | 11.0177i | −0.939022 | + | 0.542144i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.58807 | − | 1.49422i | 0.127043 | − | 0.0733484i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.4419i | − | 0.900945i | −0.892790 | − | 0.450473i | \(-0.851255\pi\) | ||
0.892790 | − | 0.450473i | \(-0.148745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.59412 | − | 0.920365i | 0.0776926 | − | 0.0448558i | −0.460650 | − | 0.887582i | \(-0.652384\pi\) |
0.538343 | + | 0.842726i | \(0.319050\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.8000 | 0.717906 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.30970 | + | 5.37496i | 0.450528 | + | 0.260113i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.68674 | − | 2.92153i | 0.0812476 | − | 0.140725i | −0.822538 | − | 0.568709i | \(-0.807443\pi\) |
0.903786 | + | 0.427985i | \(0.140776\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.03137 | + | 2.90486i | 0.241792 | + | 0.139599i | 0.616000 | − | 0.787746i | \(-0.288752\pi\) |
−0.374208 | + | 0.927345i | \(0.622085\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.8679 | − | 11.0177i | 0.519880 | − | 0.527047i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.39335 | − | 4.14540i | −0.114228 | − | 0.197849i | 0.803243 | − | 0.595652i | \(-0.203106\pi\) |
−0.917471 | + | 0.397803i | \(0.869773\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0459 | + | 10.9961i | 0.904896 | + | 0.522442i | 0.878786 | − | 0.477217i | \(-0.158354\pi\) |
0.0261109 | + | 0.999659i | \(0.491688\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.55157i | − | 0.405384i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.83163i | 0.275211i | 0.990487 | + | 0.137606i | \(0.0439407\pi\) | ||||
−0.990487 | + | 0.137606i | \(0.956059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.6194 | + | 32.2498i | 0.876754 | + | 1.51858i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.2699 | −0.762745 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9373 | 0.839069 | 0.419535 | − | 0.907739i | \(-0.362193\pi\) | ||||
0.419535 | + | 0.907739i | \(0.362193\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.10766 | + | 7.11468i | 0.191313 | + | 0.331364i | 0.945686 | − | 0.325083i | \(-0.105392\pi\) |
−0.754373 | + | 0.656446i | \(0.772059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.1744i | − | 1.03053i | −0.857031 | − | 0.515265i | \(-0.827694\pi\) | ||
0.857031 | − | 0.515265i | \(-0.172306\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.94768i | − | 0.0901280i | −0.998984 | − | 0.0450640i | \(-0.985651\pi\) | ||
0.998984 | − | 0.0450640i | \(-0.0143492\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.8431 | + | 9.72439i | 0.777744 | + | 0.449031i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −29.5519 | − | 51.1854i | −1.35880 | − | 2.35351i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.21039 | + | 8.09874i | 0.376718 | + | 0.371596i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.2097 | − | 6.47191i | −0.512183 | − | 0.295709i | 0.221547 | − | 0.975150i | \(-0.428889\pi\) |
−0.733731 | + | 0.679440i | \(0.762223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.96863 | + | 6.87386i | −0.180954 | + | 0.313421i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.3633 | + | 6.56058i | 0.515979 | + | 0.297901i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.61840 | −0.163966 | −0.0819828 | − | 0.996634i | \(-0.526125\pi\) | ||||
−0.0819828 | + | 0.996634i | \(0.526125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.9856 | + | 8.07461i | −0.631163 | + | 0.364402i | −0.781202 | − | 0.624278i | \(-0.785393\pi\) |
0.150039 | + | 0.988680i | \(0.452060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 46.0431i | − | 2.07368i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.4062 | − | 18.1324i | 1.40876 | − | 0.813347i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.2192 | − | 15.7150i | 1.21850 | − | 0.703501i | 0.253903 | − | 0.967230i | \(-0.418286\pi\) |
0.964597 | + | 0.263728i | \(0.0849523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.8218 | + | 12.5988i | 0.972987 | + | 0.561754i | 0.900146 | − | 0.435589i | \(-0.143460\pi\) |
0.0728416 | + | 0.997344i | \(0.476793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.4575 | −1.35534 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.6687 | − | 18.8613i | −1.44802 | − | 0.836013i | −0.449653 | − | 0.893203i | \(-0.648453\pi\) |
−0.998363 | + | 0.0571902i | \(0.981786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.2192 | − | 15.7150i | 1.20411 | − | 0.695192i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.298763 | − | 0.517473i | −0.0131651 | − | 0.0228026i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.35425 | + | 9.27383i | −0.235480 | + | 0.407863i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.9768i | 1.00663i | 0.864102 | + | 0.503316i | \(0.167887\pi\) | ||||
−0.864102 | + | 0.503316i | \(0.832113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.21039 | + | 14.2208i | −0.359015 | + | 0.621832i | −0.987797 | − | 0.155750i | \(-0.950221\pi\) |
0.628781 | + | 0.777582i | \(0.283554\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.3591 | − | 30.0669i | −0.756175 | − | 1.30973i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.19738 | − | 9.00213i | −0.225973 | − | 0.391397i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.0381 | −1.34441 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6116 | − | 25.3080i | −0.631713 | − | 1.09416i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.04845i | 0.389744i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7915 | − | 27.3517i | 0.678930 | − | 1.17594i | −0.296374 | − | 0.955072i | \(-0.595777\pi\) |
0.975304 | − | 0.220869i | \(-0.0708892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.39082 | + | 4.84444i | 0.359423 | + | 0.207513i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1189 | + | 19.2585i | −0.475410 | + | 0.823434i | −0.999603 | − | 0.0281650i | \(-0.991034\pi\) |
0.524193 | + | 0.851599i | \(0.324367\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.1953 | − | 25.5427i | 1.07336 | − | 1.08815i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.5000 | + | 16.4545i | −1.21194 | + | 0.699716i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.7221 | − | 22.0354i | 0.539053 | − | 0.933668i | −0.459902 | − | 0.887970i | \(-0.652115\pi\) |
0.998955 | − | 0.0456982i | \(-0.0145512\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49.2623 | 2.08357 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.74697 | 0.284351 | 0.142176 | − | 0.989841i | \(-0.454590\pi\) | ||||
0.142176 | + | 0.989841i | \(0.454590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.2804 | + | 11.7089i | −0.853202 | + | 0.492597i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.68889i | − | 0.406179i | −0.979160 | − | 0.203090i | \(-0.934902\pi\) | ||
0.979160 | − | 0.203090i | \(-0.0650983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 28.4416i | − | 1.19024i | −0.803635 | − | 0.595122i | \(-0.797104\pi\) | ||
0.803635 | − | 0.595122i | \(-0.202896\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.13495 | + | 4.69672i | −0.339251 | + | 0.195867i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.3542 | −0.930620 | −0.465310 | − | 0.885148i | \(-0.654057\pi\) | ||||
−0.465310 | + | 0.885148i | \(0.654057\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.50679 | −0.186973 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.9252 | − | 44.9038i | 1.07371 | − | 1.85972i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.07472 | + | 1.77519i | −0.126907 | + | 0.0732700i | −0.562110 | − | 0.827063i | \(-0.690010\pi\) |
0.435202 | + | 0.900333i | \(0.356677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.82288 | − | 26.1789i | 0.281132 | − | 1.07868i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.0145 | − | 27.7379i | 0.657635 | − | 1.13906i | −0.323591 | − | 0.946197i | \(-0.604890\pi\) |
0.981226 | − | 0.192861i | \(-0.0617765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.1996 | + | 9.93022i | 0.705116 | + | 0.407099i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.44821 | − | 11.1686i | 0.263467 | − | 0.456338i | −0.703694 | − | 0.710503i | \(-0.748467\pi\) |
0.967161 | + | 0.254165i | \(0.0818007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 31.0682i | − | 1.26730i | −0.773620 | − | 0.633650i | \(-0.781556\pi\) | ||
0.773620 | − | 0.633650i | \(-0.218444\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.7519 | − | 25.5510i | −0.599749 | − | 1.03880i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.0637 | 1.91026 | 0.955128 | − | 0.296193i | \(-0.0957172\pi\) | ||||
0.955128 | + | 0.296193i | \(0.0957172\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.46270 | − | 7.72963i | −0.180542 | − | 0.312707i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.76013 | − | 15.1730i | −0.353818 | − | 0.612831i | 0.633097 | − | 0.774073i | \(-0.281784\pi\) |
−0.986915 | + | 0.161241i | \(0.948450\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8298 | + | 29.1500i | −0.677541 | + | 1.17354i | 0.298178 | + | 0.954510i | \(0.403621\pi\) |
−0.975719 | + | 0.219026i | \(0.929712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.1859i | − | 0.771147i | −0.922677 | − | 0.385574i | \(-0.874004\pi\) | ||
0.922677 | − | 0.385574i | \(-0.125996\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.44821 | + | 11.1686i | −0.258342 | + | 0.447462i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.38562 | + | 4.13202i | 0.0954249 | + | 0.165281i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.39082 | − | 4.84444i | 0.334564 | − | 0.193161i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0196 | − | 5.78481i | −0.398874 | − | 0.230290i | 0.287124 | − | 0.957893i | \(-0.407301\pi\) |
−0.685998 | + | 0.727604i | \(0.740634\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.0459 | −0.755812 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.53137 | − | 3.77089i | −0.258782 | − | 0.149408i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.31292 | − | 3.64477i | 0.249345 | − | 0.143960i | −0.370119 | − | 0.928984i | \(-0.620683\pi\) |
0.619464 | + | 0.785025i | \(0.287350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.2036 | − | 11.0872i | 0.757314 | − | 0.437236i | −0.0710164 | − | 0.997475i | \(-0.522624\pi\) |
0.828331 | + | 0.560240i | \(0.189291\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.1977i | 0.990623i | 0.868715 | + | 0.495311i | \(0.164946\pi\) | ||||
−0.868715 | + | 0.495311i | \(0.835054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.3431 | − | 26.1789i | 1.77987 | − | 1.02761i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.61226 | 0.141358 | 0.0706792 | − | 0.997499i | \(-0.477483\pi\) | ||||
0.0706792 | + | 0.997499i | \(0.477483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.6351 | + | 15.3778i | 1.04072 | + | 0.600859i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.4338 | − | 35.3925i | 0.795990 | − | 1.37869i | −0.126219 | − | 0.992002i | \(-0.540284\pi\) |
0.922209 | − | 0.386692i | \(-0.126382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0000 | + | 15.5885i | 1.05018 | + | 0.606321i | 0.922699 | − | 0.385521i | \(-0.125978\pi\) |
0.127479 | + | 0.991841i | \(0.459311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.10766 | + | 14.9207i | 0.159288 | + | 0.578599i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6116 | + | 25.3080i | 0.565762 | + | 0.979929i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.1206 | − | 12.7713i | −0.853956 | − | 0.493032i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.2334i | 1.55088i | 0.631419 | + | 0.775442i | \(0.282473\pi\) | ||||
−0.631419 | + | 0.775442i | \(0.717527\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.0626i | 0.540470i | 0.962794 | + | 0.270235i | \(0.0871014\pi\) | ||||
−0.962794 | + | 0.270235i | \(0.912899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.89385 | − | 17.1367i | −0.379691 | − | 0.657644i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.1953 | 0.964072 | 0.482036 | − | 0.876151i | \(-0.339897\pi\) | ||||
0.482036 | + | 0.876151i | \(0.339897\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.41699 | 0.359805 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.6083 | + | 37.4268i | 0.823212 | + | 1.42585i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13.8835i | − | 0.528155i | −0.964501 | − | 0.264078i | \(-0.914933\pi\) | ||
0.964501 | − | 0.264078i | \(-0.0850675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 30.6957i | − | 1.16436i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.8118 | + | 18.9439i | 1.24283 | + | 0.717551i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.5672 | + | 26.9632i | 0.587965 | + | 1.01839i | 0.994499 | + | 0.104749i | \(0.0334040\pi\) |
−0.406534 | + | 0.913636i | \(0.633263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.30579 | + | 1.90407i | 0.275543 | + | 0.0718135i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.7785 | + | 22.9661i | 1.49602 | + | 0.863730i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5516 | + | 20.0080i | −0.433831 | + | 0.751417i | −0.997199 | − | 0.0747888i | \(-0.976172\pi\) |
0.563369 | + | 0.826206i | \(0.309505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.0832 | + | 11.0177i | 0.714671 | + | 0.412615i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.6586 | 1.44575 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.76147 | + | 2.74903i | −0.177573 | + | 0.102522i | −0.586152 | − | 0.810201i | \(-0.699358\pi\) |
0.408579 | + | 0.912723i | \(0.366024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.901115i | 0.0335593i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.8595 | + | 10.8886i | −0.700426 | + | 0.404391i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.71380 | + | 1.56681i | −0.100649 | + | 0.0581099i | −0.549480 | − | 0.835507i | \(-0.685174\pi\) |
0.448830 | + | 0.893617i | \(0.351841\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −52.0774 | − | 30.0669i | −1.92615 | − | 1.11206i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.6458 | −1.31661 | −0.658303 | − | 0.752753i | \(-0.728725\pi\) | ||||
−0.658303 | + | 0.752753i | \(0.728725\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.0206 | − | 23.1059i | −1.47418 | − | 0.851117i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0196 | + | 5.78481i | −0.368577 | + | 0.212798i | −0.672836 | − | 0.739791i | \(-0.734924\pi\) |
0.304260 | + | 0.952589i | \(0.401591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.4941 | + | 44.1570i | 0.935287 | + | 1.61996i | 0.774121 | + | 0.633037i | \(0.218192\pi\) |
0.161166 | + | 0.986927i | \(0.448475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.760130 | − | 1.31658i | 0.0278490 | − | 0.0482359i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 44.0707i | 1.61031i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.8063 | − | 25.6452i | 0.540289 | − | 0.935808i | −0.458598 | − | 0.888644i | \(-0.651648\pi\) |
0.998887 | − | 0.0471644i | \(-0.0150185\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.37349 | − | 5.84305i | −0.122774 | − | 0.212650i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.38562 | + | 5.86407i | 0.123053 | + | 0.213133i | 0.920970 | − | 0.389633i | \(-0.127398\pi\) |
−0.797917 | + | 0.602767i | \(0.794065\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.21532 | 0.297805 | 0.148903 | − | 0.988852i | \(-0.452426\pi\) | ||||
0.148903 | + | 0.988852i | \(0.452426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.30579 | − | 12.6540i | −0.264487 | − | 0.458105i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.6396i | 1.57573i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0203 | − | 27.7479i | 0.577705 | − | 1.00061i | −0.418037 | − | 0.908430i | \(-0.637282\pi\) |
0.995742 | − | 0.0921848i | \(-0.0293850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.5466 | + | 7.24379i | 0.451271 | + | 0.260541i | 0.708367 | − | 0.705845i | \(-0.249432\pi\) |
−0.257096 | + | 0.966386i | \(0.582766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.21039 | + | 14.2208i | −0.294926 | + | 0.510826i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.83619 | + | 28.4642i | 0.280761 | + | 1.01984i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −74.6235 | + | 43.0839i | −2.67024 | + | 1.54166i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.35187 | − | 12.7338i | 0.262400 | − | 0.454489i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.6419 | −0.557574 | −0.278787 | − | 0.960353i | \(-0.589932\pi\) | ||||
−0.278787 | + | 0.960353i | \(0.589932\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.3158 | 1.25568 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.4373 | − | 10.6448i | 0.654726 | − | 0.378006i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.77307i | 0.239915i | 0.992779 | + | 0.119957i | \(0.0382758\pi\) | ||||
−0.992779 | + | 0.119957i | \(0.961724\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8951i | 0.385441i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −64.6750 | + | 37.3401i | −2.28233 | + | 1.31771i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.6052 | −0.444276 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.7725 | −0.624846 | −0.312423 | − | 0.949943i | \(-0.601141\pi\) | ||||
−0.312423 | + | 0.949943i | \(0.601141\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.4208 | + | 28.4416i | −0.576611 | + | 0.998720i | 0.419253 | + | 0.907869i | \(0.362292\pi\) |
−0.995865 | + | 0.0908508i | \(0.971041\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.4941 | + | 14.7190i | −0.893019 | + | 0.515585i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.4373 | − | 45.1771i | −0.435124 | − | 1.58055i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.9970 | − | 43.2960i | 0.872400 | − | 1.51104i | 0.0128935 | − | 0.999917i | \(-0.495896\pi\) |
0.859507 | − | 0.511125i | \(-0.170771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.1996 | − | 9.93022i | −0.599542 | − | 0.346146i | 0.169320 | − | 0.985561i | \(-0.445843\pi\) |
−0.768861 | + | 0.639416i | \(0.779176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.4194 | + | 38.8315i | −0.779597 | + | 1.35030i | 0.152577 | + | 0.988292i | \(0.451243\pi\) |
−0.932174 | + | 0.362011i | \(0.882090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.3150i | 1.19181i | 0.803056 | + | 0.595904i | \(0.203206\pi\) | ||||
−0.803056 | + | 0.595904i | \(0.796794\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.60307 | + | 7.97275i | 0.159487 | + | 0.276239i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.43544 | −0.326527 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.07472 | + | 5.32558i | 0.106151 | + | 0.183859i | 0.914208 | − | 0.405245i | \(-0.132814\pi\) |
−0.808057 | + | 0.589105i | \(0.799481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.3745 | + | 33.5576i | 0.668086 | + | 1.15716i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.13742 | + | 10.6303i | −0.211134 | + | 0.365695i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.4939i | 1.52883i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.07472 | + | 5.32558i | −0.105400 | + | 0.182558i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.1458 | + | 33.1614i | 0.655538 | + | 1.13543i | 0.981759 | + | 0.190132i | \(0.0608914\pi\) |
−0.326221 | + | 0.945294i | \(0.605775\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.8473 | + | 25.8926i | −1.53196 | + | 0.884475i | −0.532684 | + | 0.846314i | \(0.678816\pi\) |
−0.999272 | + | 0.0381604i | \(0.987850\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.43152 | + | 4.29059i | 0.253560 | + | 0.146393i | 0.621393 | − | 0.783499i | \(-0.286567\pi\) |
−0.367833 | + | 0.929892i | \(0.619900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.4652 | 1.41149 | 0.705746 | − | 0.708465i | \(-0.250612\pi\) | ||||
0.705746 | + | 0.708465i | \(0.250612\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.74902 | + | 4.47390i | 0.263474 | + | 0.152117i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 67.7183 | − | 39.0972i | 2.29718 | − | 1.32628i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3567 | − | 19.2585i | 1.13025 | − | 0.652550i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 27.1454i | − | 0.917681i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.3745 | − | 18.6914i | 1.09321 | − | 0.631165i | 0.158780 | − | 0.987314i | \(-0.449244\pi\) |
0.934429 | + | 0.356149i | \(0.115911\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0473 | −1.01232 | −0.506160 | − | 0.862440i | \(-0.668935\pi\) | ||||
−0.506160 | + | 0.862440i | \(0.668935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.9134 | + | 11.4970i | 0.670141 | + | 0.386906i | 0.796130 | − | 0.605126i | \(-0.206877\pi\) |
−0.125989 | + | 0.992032i | \(0.540211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.13495 | + | 14.0902i | −0.273145 | + | 0.473101i | −0.969665 | − | 0.244436i | \(-0.921397\pi\) |
0.696520 | + | 0.717537i | \(0.254731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.8745 | + | 14.3613i | 0.834264 | + | 0.481663i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.96193 | + | 6.04412i | −0.199508 | + | 0.202259i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.30579 | − | 12.6540i | −0.244205 | − | 0.422976i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.2412 | + | 25.5427i | 1.47553 | + | 0.851895i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 52.7540i | − | 1.75749i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 29.0667i | − | 0.966208i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.2378 | − | 38.5170i | −0.738394 | − | 1.27894i | −0.953218 | − | 0.302284i | \(-0.902251\pi\) |
0.214824 | − | 0.976653i | \(-0.431082\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.6724 | −0.519249 | −0.259625 | − | 0.965710i | \(-0.583599\pi\) | ||||
−0.259625 | + | 0.965710i | \(0.583599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.7085 | 0.354400 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.1908 | − | 40.1677i | −0.765829 | − | 1.32645i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.1975i | 0.534305i | 0.963654 | + | 0.267153i | \(0.0860828\pi\) | ||||
−0.963654 | + | 0.267153i | \(0.913917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 71.8199i | − | 2.36398i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.96863 | − | 2.29129i | −0.130488 | − | 0.0753371i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.81752 | + | 10.0762i | 0.190866 | + | 0.330590i | 0.945538 | − | 0.325513i | \(-0.105537\pi\) |
−0.754671 | + | 0.656103i | \(0.772204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.80920 | + | 6.94177i | −0.0592942 | + | 0.227507i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.8677 | − | 23.5950i | −1.33652 | − | 0.771638i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.9059 | + | 32.7459i | −0.617628 | + | 1.06976i | 0.372289 | + | 0.928117i | \(0.378573\pi\) |
−0.989917 | + | 0.141647i | \(0.954760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0470 | −0.783079 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.1351 | − | 11.6250i | 0.654302 | − | 0.377762i | −0.135800 | − | 0.990736i | \(-0.543361\pi\) |
0.790103 | + | 0.612975i | \(0.210027\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 62.2451i | − | 2.02056i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.5580 | − | 9.55977i | 0.536366 | − | 0.309671i | −0.207239 | − | 0.978290i | \(-0.566448\pi\) |
0.743605 | + | 0.668619i | \(0.233114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.5054 | + | 14.1482i | −0.792977 | + | 0.457825i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.2989 | − | 7.10077i | −0.397152 | − | 0.229296i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.52026 | 0.242589 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.71992 | + | 4.45710i | 0.248513 | + | 0.143479i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.72164 | − | 3.88074i | 0.216153 | − | 0.124796i | −0.388015 | − | 0.921653i | \(-0.626839\pi\) |
0.604168 | + | 0.796857i | \(0.293506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.06023 | + | 8.76458i | 0.162391 | + | 0.281269i | 0.935726 | − | 0.352729i | \(-0.114746\pi\) |
−0.773335 | + | 0.633998i | \(0.781413\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.1458 | + | 40.0896i | −0.742019 | + | 1.28521i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 47.9280i | − | 1.53335i | −0.642034 | − | 0.766676i | \(-0.721909\pi\) | ||
0.642034 | − | 0.766676i | \(-0.278091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.3215 | − | 26.5375i | 0.489676 | − | 0.848144i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.2844 | − | 24.7413i | −0.455602 | − | 0.789125i | 0.543121 | − | 0.839654i | \(-0.317243\pi\) |
−0.998723 | + | 0.0505293i | \(0.983909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.23987 | + | 14.2719i | 0.262544 | + | 0.454740i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.1664 | 1.21362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7148 | + | 30.6829i | 0.562729 | + | 0.974676i | 0.997257 | + | 0.0740173i | \(0.0235820\pi\) |
−0.434528 | + | 0.900659i | \(0.643085\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 16.4942i | − | 0.522901i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.20850 | − | 12.4855i | 0.228295 | − | 0.395419i | −0.729008 | − | 0.684506i | \(-0.760018\pi\) |
0.957303 | + | 0.289086i | \(0.0933515\pi\) | |||||||
\(998\) | 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 | 2736.2.bm.t.1855.5 | yes | 16 | |
3.2 | odd | 2 | inner | 2736.2.bm.t.1855.3 | yes | 16 | |
4.3 | odd | 2 | inner | 2736.2.bm.t.1855.6 | yes | 16 | |
12.11 | even | 2 | inner | 2736.2.bm.t.1855.4 | yes | 16 | |
19.8 | odd | 6 | inner | 2736.2.bm.t.559.5 | yes | 16 | |
57.8 | even | 6 | inner | 2736.2.bm.t.559.3 | ✓ | 16 | |
76.27 | even | 6 | inner | 2736.2.bm.t.559.6 | yes | 16 | |
228.179 | odd | 6 | inner | 2736.2.bm.t.559.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.bm.t.559.3 | ✓ | 16 | 57.8 | even | 6 | inner | |
2736.2.bm.t.559.4 | yes | 16 | 228.179 | odd | 6 | inner | |
2736.2.bm.t.559.5 | yes | 16 | 19.8 | odd | 6 | inner | |
2736.2.bm.t.559.6 | yes | 16 | 76.27 | even | 6 | inner | |
2736.2.bm.t.1855.3 | yes | 16 | 3.2 | odd | 2 | inner | |
2736.2.bm.t.1855.4 | yes | 16 | 12.11 | even | 2 | inner | |
2736.2.bm.t.1855.5 | yes | 16 | 1.1 | even | 1 | trivial | |
2736.2.bm.t.1855.6 | yes | 16 | 4.3 | odd | 2 | inner |