Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(47,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.ch (of order \(18\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 815.1 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.815 |
Dual form | 912.2.ch.c.47.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{9}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.11334 | − | 1.32683i | 0.642788 | − | 0.766044i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0714517 | − | 0.0412527i | 0.0270062 | − | 0.0155920i | −0.486436 | − | 0.873716i | \(-0.661703\pi\) |
0.513442 | + | 0.858124i | \(0.328370\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.520945 | − | 2.95442i | −0.173648 | − | 0.984808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.25490 | − | 2.73119i | 0.902747 | − | 0.757495i | −0.0679785 | − | 0.997687i | \(-0.521655\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 2.59808i | −0.802955 | − | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0248149 | − | 0.140732i | 0.00541506 | − | 0.0307103i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.83022 | − | 3.21394i | 0.766044 | − | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | − | 2.59808i | −0.866025 | − | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.84864 | − | 1.06731i | 0.332026 | − | 0.191695i | −0.324714 | − | 0.945812i | \(-0.605268\pi\) |
0.656740 | + | 0.754117i | \(0.271935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.08647 | 0.836210 | 0.418105 | − | 0.908399i | \(-0.362694\pi\) | ||||
0.418105 | + | 0.908399i | \(0.362694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 7.35943i | − | 1.17845i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.31180 | − | 9.09911i | −0.505045 | − | 1.38760i | −0.886292 | − | 0.463127i | \(-0.846727\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.49660 | + | 6.05628i | −0.499514 | + | 0.865183i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.34389 | + | 1.75135i | −0.972722 | + | 0.231972i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5890 | + | 5.30996i | 1.86793 | + | 0.679871i | 0.971671 | + | 0.236338i | \(0.0759472\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.159100 | − | 0.189608i | −0.0200447 | − | 0.0238884i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.51501 | + | 1.32510i | −0.918105 | + | 0.161887i | −0.612682 | − | 0.790330i | \(-0.709909\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.56805 | − | 2.99395i | −0.417608 | − | 0.350415i | 0.409644 | − | 0.912245i | \(-0.365653\pi\) |
−0.827252 | + | 0.561830i | \(0.810097\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 1.00000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.87598 | + | 8.19448i | −0.773608 | + | 0.921951i | −0.998626 | − | 0.0524041i | \(-0.983312\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.45723 | + | 3.07818i | −0.939693 | + | 0.342020i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.119900 | − | 0.329421i | 0.0125689 | − | 0.0345327i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.642026 | − | 3.64111i | 0.0665750 | − | 0.377566i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.868241 | + | 4.92404i | −0.0881565 | + | 0.499960i | 0.908474 | + | 0.417941i | \(0.137248\pi\) |
−0.996631 | + | 0.0820195i | \(0.973863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.10488 | − | 1.79261i | −0.305933 | − | 0.176631i | 0.339172 | − | 0.940724i | \(-0.389853\pi\) |
−0.645105 | + | 0.764094i | \(0.723187\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9748 | − | 5.81434i | 1.53011 | − | 0.556913i | 0.566458 | − | 0.824090i | \(-0.308313\pi\) |
0.963647 | + | 0.267177i | \(0.0860909\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.66297 | − | 6.74887i | 0.537505 | − | 0.640574i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.76470 | − | 8.19356i | −0.902747 | − | 0.757495i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.4734 | + | 17.2488i | 1.28431 | + | 1.53058i | 0.676142 | + | 0.736771i | \(0.263650\pi\) |
0.608167 | + | 0.793809i | \(0.291905\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.7601 | − | 5.73621i | −1.38760 | − | 0.505045i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.357259 | − | 0.0412527i | −0.0309783 | − | 0.00357706i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.94444 | + | 8.27606i | 0.589020 | + | 0.701966i | 0.975417 | − | 0.220366i | \(-0.0707252\pi\) |
−0.386398 | + | 0.922332i | \(0.626281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.14274 | + | 11.3821i | 0.341688 | + | 0.938779i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.66025i | 0.704761i | 0.935857 | + | 0.352381i | \(0.114628\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.47653 | − | 0.901383i | 0.197649 | − | 0.0719382i | −0.241299 | − | 0.970451i | \(-0.577574\pi\) |
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.1031 | + | 12.7612i | 1.73125 | + | 0.999538i | 0.880821 | + | 0.473450i | \(0.156991\pi\) |
0.850430 | + | 0.526088i | \(0.176342\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.877574 | − | 4.97697i | 0.0675057 | − | 0.382844i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.85251 | + | 11.6939i | −0.447553 | + | 0.894258i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.141092 | − | 0.387648i | 0.0106656 | − | 0.0293035i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.21554 | + | 6.89365i | 0.0903502 | + | 0.512401i | 0.996073 | + | 0.0885316i | \(0.0282174\pi\) |
−0.905723 | + | 0.423870i | \(0.860671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.2879 | − | 13.4453i | 1.72149 | − | 0.993904i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.428710 | −0.0311841 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6407 | − | 17.3196i | −1.48575 | − | 1.24669i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
−0.585979 | − | 0.810326i | \(-0.699290\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.7481 | + | 4.89274i | −1.96701 | + | 0.346837i | −0.974576 | + | 0.224055i | \(0.928070\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.60859 | + | 11.4464i | −0.466134 | + | 0.807368i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.6643 | + | 3.46735i | 1.35375 | + | 0.238702i | 0.803005 | − | 0.595973i | \(-0.203233\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0880590 | − | 0.152523i | 0.00597784 | − | 0.0103539i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.94491 | + | 1.40090i | −0.536867 | + | 0.0946642i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.87851 | + | 24.3935i | 0.594549 | + | 1.63351i | 0.761961 | + | 0.647623i | \(0.224237\pi\) |
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4907 | − | 9.64181i | −0.766044 | − | 0.642788i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.2891 | 1.60507 | 0.802535 | − | 0.596606i | \(-0.203484\pi\) | ||||
0.802535 | + | 0.596606i | \(0.203484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.21735 | + | 18.2465i | 0.208989 | + | 1.18524i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8614 | + | 18.3439i | −1.40822 | + | 1.18164i | −0.450910 | + | 0.892570i | \(0.648900\pi\) |
−0.957309 | + | 0.289066i | \(0.906655\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.33157 | + | 14.6484i | −0.342020 | + | 0.939693i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.4880 | + | 1.10267i | −1.17636 | + | 0.0701613i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.363437 | − | 0.209830i | 0.0225829 | − | 0.0130382i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.33157 | − | 14.6484i | −0.323870 | − | 0.889824i | −0.989628 | − | 0.143657i | \(-0.954114\pi\) |
0.665758 | − | 0.746168i | \(-0.268108\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.303596 | − | 0.525844i | −0.0183745 | − | 0.0318255i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5000 | + | 26.8468i | −0.931305 | + | 1.61307i | −0.150210 | + | 0.988654i | \(0.547995\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.11633 | − | 4.90566i | −0.246438 | − | 0.293694i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.1746 | + | 3.90998i | 1.31814 | + | 0.232424i | 0.788100 | − | 0.615547i | \(-0.211065\pi\) |
0.530042 | + | 0.847971i | \(0.322176\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9748 | − | 5.81434i | −0.939693 | − | 0.342020i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.56670 | + | 6.63414i | 0.326326 | + | 0.388900i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.611997 | − | 0.513526i | −0.0352749 | − | 0.0295992i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.11334 | + | 1.32683i | −0.0635417 | + | 0.0757261i | −0.796879 | − | 0.604139i | \(-0.793517\pi\) |
0.733337 | + | 0.679865i | \(0.237962\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.83527 | + | 2.12387i | −0.331957 | + | 0.120823i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.07769 | + | 34.4683i | 0.343531 | + | 1.94826i | 0.316387 | + | 0.948630i | \(0.397530\pi\) |
0.0271446 | + | 0.999632i | \(0.491359\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.68913 | − | 20.9221i | 0.204636 | − | 1.16055i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0707 | − | 27.6691i | 0.556913 | − | 1.53011i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6871 | − | 14.2531i | −1.35692 | − | 0.783420i | −0.367716 | − | 0.929938i | \(-0.619860\pi\) |
−0.989208 | + | 0.146518i | \(0.953193\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.64977 | − | 15.0276i | −0.145206 | − | 0.823506i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.5694 | − | 9.30650i | 1.39285 | − | 0.506957i | 0.466805 | − | 0.884361i | \(-0.345405\pi\) |
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.15451i | 0.0623379i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8418 | + | 27.4389i | 0.847994 | + | 1.46877i | 0.882996 | + | 0.469381i | \(0.155523\pi\) |
−0.0350017 | + | 0.999387i | \(0.511144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.7429 | + | 3.83386i | −1.16055 | + | 0.204636i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.7631 | + | 3.30844i | 0.984808 | + | 0.173648i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.78534 | − | 8.08645i | −0.354192 | − | 0.422109i | 0.559301 | − | 0.828965i | \(-0.311070\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | − | 32.9090i | −0.983783 | − | 1.70396i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
−0.336557 | − | 0.941663i | \(-0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 38.5433i | − | 1.97983i | −0.141648 | − | 0.989917i | \(-0.545240\pi\) | ||
0.141648 | − | 0.989917i | \(-0.454760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.0000 | 1.99803 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.1573 | + | 14.5246i | −1.27882 | + | 0.738327i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.31356 | − | 24.4634i | 0.216491 | − | 1.22778i | −0.661809 | − | 0.749673i | \(-0.730211\pi\) |
0.878300 | − | 0.478110i | \(-0.158678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.452486 | + | 0.428092i | −0.0226526 | + | 0.0214314i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.10211 | − | 8.52298i | 0.154527 | − | 0.424560i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.59863 | − | 37.4227i | −0.326281 | − | 1.85043i | −0.500514 | − | 0.865729i | \(-0.666856\pi\) |
0.174232 | − | 0.984705i | \(-0.444256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.7124 | 0.916352 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.4078 | − | 26.3543i | −1.53072 | − | 1.28443i | −0.792492 | − | 0.609882i | \(-0.791217\pi\) |
−0.738231 | − | 0.674548i | \(-0.764339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.26146 | − | 0.222429i | 0.0610463 | − | 0.0107641i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.5484 | − | 9.66284i | −1.27584 | − | 0.464367i | −0.386784 | − | 0.922170i | \(-0.626414\pi\) |
−0.889053 | + | 0.457804i | \(0.848636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4206 | − | 3.42437i | −0.926893 | − | 0.163436i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
−0.616665 | + | 0.787226i | \(0.711517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.7144 | + | 7.17544i | 0.938779 | + | 0.341688i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.4907 | + | 9.64181i | 0.539879 | + | 0.453012i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.3806 | 1.60826 | 0.804129 | − | 0.594455i | \(-0.202632\pi\) | ||||
0.804129 | + | 0.594455i | \(0.202632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.0859 | − | 14.4833i | 1.16584 | − | 0.673098i | 0.213144 | − | 0.977021i | \(-0.431630\pi\) |
0.952697 | + | 0.303923i | \(0.0982964\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.482297 | + | 0.404695i | −0.0222704 | + | 0.0186871i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.56124 | − | 4.28947i | 0.0719382 | − | 0.197649i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.7558 | + | 1.29757i | −0.998226 | + | 0.0595368i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.5559 | − | 13.8921i | 0.754886 | − | 0.633424i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.5000 | − | 18.1865i | 1.42740 | − | 0.824110i | 0.430486 | − | 0.902597i | \(-0.358342\pi\) |
0.996915 | + | 0.0784867i | \(0.0250088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.5403 | − | 15.1194i | 1.87852 | − | 0.683724i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7634 | − | 37.8145i | −0.616132 | − | 1.69281i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.100126 | − | 0.994975i | \(-0.468075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.62654 | − | 6.70545i | −0.249884 | − | 0.297800i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.378452 | − | 0.0667312i | −0.0167417 | − | 0.00295202i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.00000 | + | 20.7846i | 0.397360 | + | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4599 | − | 2.72600i | 0.676015 | − | 0.119200i | 0.174908 | − | 0.984585i | \(-0.444037\pi\) |
0.501107 | + | 0.865385i | \(0.332926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.357259 | − | 0.618790i | −0.0155920 | − | 0.0270062i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6190 | − | 14.7841i | −0.766044 | − | 0.642788i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.89234 | + | 39.0884i | 0.296325 | + | 1.68054i | 0.661768 | + | 0.749708i | \(0.269806\pi\) |
−0.365444 | + | 0.930834i | \(0.619083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5000 | + | 6.06218i | 0.450598 | + | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.1471 | − | 41.6163i | 0.647642 | − | 1.77938i | 0.0213785 | − | 0.999771i | \(-0.493195\pi\) |
0.626264 | − | 0.779611i | \(-0.284583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.08781 | − | 45.8683i | 0.345179 | − | 1.95761i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.153257 | + | 0.869162i | −0.00651714 | + | 0.0369605i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.6309 | − | 20.5715i | −1.50703 | − | 0.870083i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.477301 | + | 0.568825i | −0.0200447 | + | 0.0238884i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.93697i | 0.332152i | 0.986113 | + | 0.166076i | \(0.0531097\pi\) | ||||
−0.986113 | + | 0.166076i | \(0.946890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.50000 | − | 9.52628i | −0.228968 | − | 0.396584i | 0.728535 | − | 0.685009i | \(-0.240202\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −45.9602 | + | 8.10403i | −1.91004 | + | 0.336792i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.24320 | − | 1.06731i | −0.380860 | − | 0.0439779i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.4013 | + | 42.2642i | −0.998677 | + | 1.72976i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.10725 | + | 8.84601i | 0.208329 | + | 0.360836i | 0.951188 | − | 0.308611i | \(-0.0998642\pi\) |
−0.742859 | + | 0.669448i | \(0.766531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.82981 | + | 21.5122i | 0.318855 | + | 0.876046i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.3533i | 1.92201i | 0.276531 | + | 0.961005i | \(0.410815\pi\) | ||||
−0.276531 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.1656 | + | 16.0749i | −1.78383 | + | 0.649261i | −0.784245 | + | 0.620451i | \(0.786949\pi\) |
−0.999585 | + | 0.0288097i | \(0.990828\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.0929 | − | 24.8797i | −1.73205 | − | 1.00000i | −0.866226 | − | 0.499653i | \(-0.833461\pi\) |
−0.865825 | − | 0.500347i | \(-0.833206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.34120 | − | 24.6202i | 0.173648 | − | 0.984808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.2604 | + | 44.6751i | −0.647317 | + | 1.77849i | −0.0199047 | + | 0.999802i | \(0.506336\pi\) |
−0.627412 | + | 0.778687i | \(0.715886\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.4937 | − | 22.2308i | 1.05303 | − | 0.883596i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.15976 | + | 29.2624i | 0.204437 | + | 1.15942i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.8787 | − | 37.9915i | 1.25717 | − | 1.49824i | 0.468449 | − | 0.883491i | \(-0.344813\pi\) |
0.788723 | − | 0.614749i | \(-0.210743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.104332 | − | 0.286649i | −0.00408908 | − | 0.0112347i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.98663 | + | 12.1012i | −0.272575 | + | 0.472113i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7083 | − | 12.9968i | −1.38889 | − | 0.505516i | −0.464031 | − | 0.885819i | \(-0.653597\pi\) |
−0.924862 | + | 0.380303i | \(0.875820\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.2508 | + | 15.3780i | 1.63351 | + | 0.594549i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6977 | + | 25.4572i | −0.566557 | + | 0.981305i | 0.430346 | + | 0.902664i | \(0.358391\pi\) |
−0.996903 | + | 0.0786409i | \(0.974942\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.5861 | + | 4.51151i | −0.984808 | + | 0.173648i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.141092 | + | 0.387648i | 0.00541463 | + | 0.0148766i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.0421 | − | 32.2275i | 1.03172 | − | 1.22955i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5000 | + | 9.52628i | −0.627690 | + | 0.362397i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) |
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.8026 | − | 13.2150i | −0.671439 | − | 0.498414i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.5431 | + | 23.9505i | −1.07196 | + | 0.899479i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
−0.0767291 | + | 0.997052i | \(0.524448\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.7920 | + | 16.0457i | 1.04228 | + | 0.601760i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.295799 | −0.0110161 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 49.4294i | 1.83830i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.87304 | + | 13.3886i | 0.180731 | + | 0.496555i | 0.996666 | − | 0.0815889i | \(-0.0259995\pi\) |
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | + | 23.3827i | 0.500000 | + | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.50000 | + | 6.06218i | −0.129275 | + | 0.223912i | −0.923396 | − | 0.383849i | \(-0.874598\pi\) |
0.794121 | + | 0.607760i | \(0.207932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.3285 | + | 8.69794i | 1.81458 | + | 0.319959i | 0.974818 | − | 0.223001i | \(-0.0715853\pi\) |
0.839759 | + | 0.542960i | \(0.182696\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.1204 | + | 25.7580i | −0.702404 | + | 0.946244i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.5435 | − | 5.91463i | 1.22402 | − | 0.215828i | 0.475965 | − | 0.879464i | \(-0.342099\pi\) |
0.748056 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.0453 | − | 33.6020i | −1.45547 | − | 1.22129i | −0.928461 | − | 0.371429i | \(-0.878868\pi\) |
−0.527011 | − | 0.849858i | \(-0.676688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.901568 | − | 1.07445i | 0.0326390 | − | 0.0388976i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.96544 | + | 16.8179i | 0.106937 | + | 0.606467i | 0.990429 | + | 0.138022i | \(0.0440745\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.65043 | − | 10.0295i | 0.131127 | − | 0.360269i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.126220 | − | 0.715831i | 0.00452813 | − | 0.0256803i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4062 | − | 11.2042i | −0.691755 | − | 0.399385i | 0.112514 | − | 0.993650i | \(-0.464110\pi\) |
−0.804269 | + | 0.594265i | \(0.797443\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.9882 | − | 22.5619i | 2.20127 | − | 0.801195i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.8335 | + | 33.1707i | 0.977367 | + | 1.16478i | 0.986324 | + | 0.164821i | \(0.0527046\pi\) |
−0.00895645 | + | 0.999960i | \(0.502851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.3717 | − | 9.23454i | −0.889824 | − | 0.323870i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0489 | + | 40.4512i | −0.421536 | + | 1.41521i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.03571 | − | 0.182624i | −0.0361907 | − | 0.00638139i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.7402 | + | 43.7853i | 1.28068 | + | 1.52626i | 0.707099 | + | 0.707115i | \(0.250004\pi\) |
0.573586 | + | 0.819146i | \(0.305552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.7524 | − | 49.8007i | −0.998613 | − | 1.72965i | −0.544900 | − | 0.838501i | \(-0.683433\pi\) |
−0.453713 | − | 0.891148i | \(-0.649901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.3643 | + | 50.4555i | 0.637050 | + | 1.75028i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.0918 | −0.383390 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2511 | + | 9.91858i | −0.939693 | + | 0.342020i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.785969 | + | 0.453779i | 0.0270062 | + | 0.0155920i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.8757 | − | 25.0687i | 1.02533 | − | 0.860356i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.93371 | + | 16.6379i | −0.100448 | + | 0.569670i | 0.892493 | + | 0.451061i | \(0.148954\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8494 | + | 46.2934i | −0.574895 | + | 1.57951i | 0.221777 | + | 0.975097i | \(0.428814\pi\) |
−0.796672 | + | 0.604412i | \(0.793408\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.5000 | + | 14.7224i | −0.866025 | + | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.8415 | + | 24.8380i | −0.706188 | + | 0.841602i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0000 | 0.507673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.8323 | − | 36.7797i | −1.48011 | − | 1.24196i | −0.906064 | − | 0.423141i | \(-0.860927\pi\) |
−0.574049 | − | 0.818821i | \(-0.694628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.4910 | − | 8.72659i | 1.66550 | − | 0.293673i | 0.740055 | − | 0.672546i | \(-0.234799\pi\) |
0.925449 | + | 0.378873i | \(0.123688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.74571 | + | 0.635386i | 0.0585492 | + | 0.0213102i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.36272 | + | 0.240285i | −0.0453485 | + | 0.00799617i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.14677 | + | 11.3932i | 0.137691 | + | 0.378304i | 0.989304 | − | 0.145868i | \(-0.0465973\pi\) |
−0.851613 | + | 0.524171i | \(0.824375\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.6607 | + | 22.8981i | −1.30828 | + | 0.755338i | −0.981810 | − | 0.189867i | \(-0.939194\pi\) |
−0.326475 | + | 0.945206i | \(0.605861\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.520945 | + | 2.95442i | 0.0171657 | + | 0.0973516i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.4823 | − | 16.3476i | 0.640574 | − | 0.537505i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.67864 | + | 10.1070i | −0.120823 | + | 0.331957i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.9728 | − | 12.1126i | 0.916771 | − | 0.396973i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.5492 | − | 35.7030i | 1.39002 | − | 1.16637i | 0.424691 | − | 0.905338i | \(-0.360383\pi\) |
0.965331 | − | 0.261029i | \(-0.0840619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.5000 | + | 30.3109i | 1.71327 | + | 0.989158i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.7907 | −0.642432 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2217 | + | 22.9006i | −0.426506 | + | 0.738730i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.4677 | + | 5.19594i | 0.947616 | + | 0.167090i | 0.626038 | − | 0.779793i | \(-0.284676\pi\) |
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.837602 | + | 0.304862i | 0.0268523 | + | 0.00977343i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.6528 | − | 28.1883i | −0.757495 | − | 0.902747i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5000 | − | 44.1673i | −0.814152 | − | 1.41015i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.8744 | − | 43.9452i | 1.17135 | − | 1.39596i | 0.270011 | − | 0.962857i | \(-0.412973\pi\) |
0.901342 | − | 0.433108i | \(-0.142583\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −46.3965 | + | 16.8870i | −1.47235 | + | 0.535891i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3616 | + | 58.7635i | 0.328155 | + | 1.86106i | 0.486507 | + | 0.873677i | \(0.338271\pi\) |
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.8891 | − | 13.2150i | −0.724179 | − | 0.418105i |
(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 | 912.2.ch.c.815.1 | yes | 6 | |
3.2 | odd | 2 | CM | 912.2.ch.c.815.1 | yes | 6 | |
4.3 | odd | 2 | 912.2.ch.d.815.1 | yes | 6 | ||
12.11 | even | 2 | 912.2.ch.d.815.1 | yes | 6 | ||
19.9 | even | 9 | 912.2.ch.d.47.1 | yes | 6 | ||
57.47 | odd | 18 | 912.2.ch.d.47.1 | yes | 6 | ||
76.47 | odd | 18 | inner | 912.2.ch.c.47.1 | ✓ | 6 | |
228.47 | even | 18 | inner | 912.2.ch.c.47.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.ch.c.47.1 | ✓ | 6 | 76.47 | odd | 18 | inner | |
912.2.ch.c.47.1 | ✓ | 6 | 228.47 | even | 18 | inner | |
912.2.ch.c.815.1 | yes | 6 | 1.1 | even | 1 | trivial | |
912.2.ch.c.815.1 | yes | 6 | 3.2 | odd | 2 | CM | |
912.2.ch.d.47.1 | yes | 6 | 19.9 | even | 9 | ||
912.2.ch.d.47.1 | yes | 6 | 57.47 | odd | 18 | ||
912.2.ch.d.815.1 | yes | 6 | 4.3 | odd | 2 | ||
912.2.ch.d.815.1 | yes | 6 | 12.11 | even | 2 |