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: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.31726512.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 10x^{4} + 3x^{3} + 84x^{2} - 27x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 304) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 559.3 | ||
Root | \(1.69617 - 2.93786i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.559 |
Dual form | 2736.2.bm.l.1855.3 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.19617 | − | 2.07183i | 0.534944 | − | 0.926551i | −0.464222 | − | 0.885719i | \(-0.653666\pi\) |
0.999166 | − | 0.0408319i | \(-0.0130008\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.22147i | 0.461674i | 0.972992 | + | 0.230837i | \(0.0741464\pi\) | ||||
−0.972992 | + | 0.230837i | \(0.925854\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.95353i | − | 0.890521i | −0.895401 | − | 0.445261i | \(-0.853111\pi\) | ||
0.895401 | − | 0.445261i | \(-0.146889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 1.73205i | 0.832050 | − | 0.480384i | −0.0225039 | − | 0.999747i | \(-0.507164\pi\) |
0.854554 | + | 0.519362i | \(0.173830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.138344 | + | 0.239619i | −0.0335534 | + | 0.0581162i | −0.882314 | − | 0.470660i | \(-0.844016\pi\) |
0.848761 | + | 0.528777i | \(0.177349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.30383 | − | 4.15933i | −0.299119 | − | 0.954216i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.05783 | − | 0.610737i | 0.220572 | − | 0.127348i | −0.385643 | − | 0.922648i | \(-0.626020\pi\) |
0.606215 | + | 0.795301i | \(0.292687\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.361656 | − | 0.626406i | −0.0723311 | − | 0.125281i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.58852 | − | 3.80388i | 1.22346 | − | 0.706363i | 0.257804 | − | 0.966197i | \(-0.417001\pi\) |
0.965653 | + | 0.259834i | \(0.0836679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.90034 | −1.59855 | −0.799275 | − | 0.600966i | \(-0.794783\pi\) | ||||
−0.799275 | + | 0.600966i | \(0.794783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53069 | + | 1.46109i | 0.427764 | + | 0.246970i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.60776i | 1.25071i | 0.780341 | + | 0.625354i | \(0.215046\pi\) | ||||
−0.780341 | + | 0.625354i | \(0.784954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.26200 | − | 4.77007i | −1.29031 | − | 0.744959i | −0.311599 | − | 0.950214i | \(-0.600865\pi\) |
−0.978709 | + | 0.205254i | \(0.934198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 1.73205i | −0.457496 | − | 0.264135i | 0.253495 | − | 0.967337i | \(-0.418420\pi\) |
−0.710991 | + | 0.703201i | \(0.751753\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.05783 | + | 2.34279i | −0.591895 | + | 0.341731i | −0.765846 | − | 0.643023i | \(-0.777680\pi\) |
0.173951 | + | 0.984754i | \(0.444346\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50800 | 0.786857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 3.46410i | 0.824163 | − | 0.475831i | −0.0276867 | − | 0.999617i | \(-0.508814\pi\) |
0.851850 | + | 0.523786i | \(0.175481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.11921 | − | 3.53292i | −0.825113 | − | 0.476379i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.44217 | − | 5.96202i | 0.448133 | − | 0.776188i | −0.550132 | − | 0.835078i | \(-0.685423\pi\) |
0.998265 | + | 0.0588893i | \(0.0187559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.19617 | − | 5.53593i | −0.409228 | − | 0.708804i | 0.585576 | − | 0.810618i | \(-0.300869\pi\) |
−0.994803 | + | 0.101814i | \(0.967535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 8.28732i | − | 1.02792i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.83452 | + | 6.64158i | 0.468461 | + | 0.811398i | 0.999350 | − | 0.0360433i | \(-0.0114754\pi\) |
−0.530889 | + | 0.847441i | \(0.678142\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.75400 | − | 3.03802i | 0.205290 | − | 0.355573i | −0.744935 | − | 0.667137i | \(-0.767520\pi\) |
0.950225 | + | 0.311564i | \(0.100853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.60766 | 0.411131 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.392344 | + | 0.679560i | −0.0441422 | + | 0.0764565i | −0.887252 | − | 0.461284i | \(-0.847389\pi\) |
0.843110 | + | 0.537741i | \(0.180722\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.31866i | 0.913092i | 0.889700 | + | 0.456546i | \(0.150914\pi\) | ||||
−0.889700 | + | 0.456546i | \(0.849086\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.330967 | + | 0.573252i | 0.0358984 | + | 0.0621779i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.58497 | − | 1.49243i | 0.274006 | − | 0.158197i | −0.356701 | − | 0.934219i | \(-0.616098\pi\) |
0.630707 | + | 0.776021i | \(0.282765\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.11566 | + | 3.66442i | 0.221781 | + | 0.384136i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.1770 | − | 2.27396i | −1.04414 | − | 0.233304i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.67703 | − | 3.27764i | −0.576415 | − | 0.332794i | 0.183292 | − | 0.983058i | \(-0.441325\pi\) |
−0.759708 | + | 0.650265i | \(0.774658\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.09652 | − | 14.0236i | −0.805634 | − | 1.39540i | −0.915863 | − | 0.401492i | \(-0.868492\pi\) |
0.110229 | − | 0.993906i | \(-0.464842\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.55338 | 0.251592 | 0.125796 | − | 0.992056i | \(-0.459852\pi\) | ||||
0.125796 | + | 0.992056i | \(0.459852\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.23131 | −0.409056 | −0.204528 | − | 0.978861i | \(-0.565566\pi\) | ||||
−0.204528 | + | 0.978861i | \(0.565566\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.17703 | − | 4.14366i | −0.687435 | − | 0.396891i | 0.115215 | − | 0.993341i | \(-0.463244\pi\) |
−0.802650 | + | 0.596450i | \(0.796578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.73205i | − | 0.162938i | −0.996676 | − | 0.0814688i | \(-0.974039\pi\) | ||
0.996676 | − | 0.0814688i | \(-0.0259611\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.92219i | − | 0.272495i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.292689 | − | 0.168984i | −0.0268307 | − | 0.0154907i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.27669 | 0.206972 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2313 | 0.915116 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.27669 | + | 7.40744i | 0.379495 | + | 0.657304i | 0.990989 | − | 0.133945i | \(-0.0427645\pi\) |
−0.611494 | + | 0.791249i | \(0.709431\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.97286 | − | 3.44843i | −0.521851 | − | 0.301291i | 0.215840 | − | 0.976429i | \(-0.430751\pi\) |
−0.737692 | + | 0.675138i | \(0.764084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.08052 | − | 1.59259i | 0.440537 | − | 0.138095i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.10766 | + | 3.65057i | 0.180069 | + | 0.311889i | 0.941904 | − | 0.335882i | \(-0.109035\pi\) |
−0.761835 | + | 0.647771i | \(0.775701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.44217 | − | 1.98734i | 0.291961 | − | 0.168564i | −0.346865 | − | 0.937915i | \(-0.612754\pi\) |
0.638826 | + | 0.769351i | \(0.279420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.11566 | − | 8.86058i | −0.427793 | − | 0.740959i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 18.2004i | − | 1.51146i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.31183 | − | 5.73625i | 0.271316 | − | 0.469932i | −0.697883 | − | 0.716211i | \(-0.745875\pi\) |
0.969199 | + | 0.246279i | \(0.0792080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.22241 | −0.587751 | −0.293876 | − | 0.955844i | \(-0.594945\pi\) | ||||
−0.293876 | + | 0.955844i | \(0.594945\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.6463 | + | 18.4400i | −0.855135 | + | 1.48114i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.50800 | − | 9.54014i | 0.439586 | − | 0.761386i | −0.558071 | − | 0.829793i | \(-0.688458\pi\) |
0.997657 | + | 0.0684073i | \(0.0217917\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.746000 | + | 1.29211i | 0.0587930 | + | 0.101833i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.61556i | − | 0.204866i | −0.994740 | − | 0.102433i | \(-0.967337\pi\) | ||
0.994740 | − | 0.102433i | \(-0.0326628\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.29269 | − | 10.8993i | −0.486943 | − | 0.843410i | 0.512944 | − | 0.858422i | \(-0.328555\pi\) |
−0.999887 | + | 0.0150120i | \(0.995221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.0000 | − | 8.66025i | −1.14043 | − | 0.658427i | −0.193892 | − | 0.981023i | \(-0.562111\pi\) |
−0.946537 | + | 0.322596i | \(0.895445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.765139 | − | 0.441753i | 0.0578391 | − | 0.0333934i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.40834 | 0.180008 | 0.0900041 | − | 0.995941i | \(-0.471312\pi\) | ||||
0.0900041 | + | 0.995941i | \(0.471312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.9355 | + | 9.20036i | −1.18448 | + | 0.683857i | −0.957046 | − | 0.289937i | \(-0.906365\pi\) |
−0.227430 | + | 0.973795i | \(0.573032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.7620 | + | 9.10020i | 1.15885 | + | 0.669060i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.707722 | + | 0.408603i | 0.0517537 | + | 0.0298800i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.04231i | − | 0.147776i | −0.997267 | − | 0.0738880i | \(-0.976459\pi\) | ||
0.997267 | − | 0.0738880i | \(-0.0235407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.41503 | + | 5.43577i | 0.677709 | + | 0.391275i | 0.798991 | − | 0.601343i | \(-0.205367\pi\) |
−0.121282 | + | 0.992618i | \(0.538701\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.16103 | 0.296461 | 0.148231 | − | 0.988953i | \(-0.452642\pi\) | ||||
0.148231 | + | 0.988953i | \(0.452642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3541 | − | 8.28732i | 1.01753 | − | 0.587473i | 0.104144 | − | 0.994562i | \(-0.466790\pi\) |
0.913388 | + | 0.407089i | \(0.133456\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.64634 | + | 8.04770i | 0.326109 | + | 0.564838i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.7655 | + | 11.4116i | −1.38049 | + | 0.797024i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.2847 | + | 3.85089i | −0.849750 | + | 0.266372i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.03869 | − | 8.72726i | 0.346878 | − | 0.600810i | −0.638815 | − | 0.769360i | \(-0.720575\pi\) |
0.985693 | + | 0.168550i | \(0.0539086\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.17703 | + | 4.14366i | −0.489470 | + | 0.282595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.8715i | − | 0.738008i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.958477i | 0.0644742i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.78114 | − | 4.81707i | 0.186239 | − | 0.322575i | −0.757754 | − | 0.652540i | \(-0.773704\pi\) |
0.943993 | + | 0.329965i | \(0.107037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.1770 | −1.07371 | −0.536854 | − | 0.843675i | \(-0.680387\pi\) | ||||
−0.536854 | + | 0.843675i | \(0.680387\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.78469 | 0.448345 | 0.224172 | − | 0.974549i | \(-0.428032\pi\) | ||||
0.224172 | + | 0.974549i | \(0.428032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.53869 | + | 9.59329i | −0.362852 | + | 0.628477i | −0.988429 | − | 0.151685i | \(-0.951530\pi\) |
0.625577 | + | 0.780162i | \(0.284863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.2095i | 0.731228i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.38027i | 0.153967i | 0.997032 | + | 0.0769835i | \(0.0245289\pi\) | ||||
−0.997032 | + | 0.0769835i | \(0.975471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.4390 | − | 10.6458i | 1.18776 | − | 0.685755i | 0.229965 | − | 0.973199i | \(-0.426139\pi\) |
0.957797 | + | 0.287444i | \(0.0928055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.58852 | − | 11.4116i | 0.420925 | − | 0.729063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1157 | − | 10.2197i | −0.707272 | − | 0.650264i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.85720 | + | 2.22696i | −0.243465 | + | 0.140564i | −0.616768 | − | 0.787145i | \(-0.711558\pi\) |
0.373303 | + | 0.927709i | \(0.378225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80383 | − | 3.12432i | −0.113406 | − | 0.196424i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.08497 | − | 2.35846i | 0.254813 | − | 0.147117i | −0.367153 | − | 0.930161i | \(-0.619667\pi\) |
0.621966 | + | 0.783044i | \(0.286334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.29269 | −0.577420 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.7589 | − | 14.2945i | −1.52670 | − | 0.881439i | −0.999498 | − | 0.0316971i | \(-0.989909\pi\) |
−0.527199 | − | 0.849742i | \(-0.676758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 16.5746i | − | 1.01817i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.83007 | + | 5.67539i | 0.599350 | + | 0.346035i | 0.768786 | − | 0.639506i | \(-0.220861\pi\) |
−0.169436 | + | 0.985541i | \(0.554195\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.35052 | + | 2.51177i | 0.264275 | + | 0.152579i | 0.626283 | − | 0.779596i | \(-0.284575\pi\) |
−0.362008 | + | 0.932175i | \(0.617909\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.85011 | + | 1.06816i | −0.111566 | + | 0.0644124i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.4243 | 1.70785 | 0.853927 | − | 0.520393i | \(-0.174215\pi\) | ||||
0.853927 | + | 0.520393i | \(0.174215\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9150 | − | 8.03385i | 0.830101 | − | 0.479259i | −0.0237861 | − | 0.999717i | \(-0.507572\pi\) |
0.853887 | + | 0.520458i | \(0.174239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0885 | + | 9.86606i | 1.01581 | + | 0.586476i | 0.912887 | − | 0.408213i | \(-0.133848\pi\) |
0.102920 | + | 0.994690i | \(0.467181\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.82652 | − | 10.0918i | 0.343928 | − | 0.595701i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.46172 | + | 14.6561i | 0.497748 | + | 0.862125i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9366i | 0.872606i | 0.899800 | + | 0.436303i | \(0.143712\pi\) | ||||
−0.899800 | + | 0.436303i | \(0.856288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.23486 | − | 14.2632i | −0.479452 | − | 0.830435i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.11566 | − | 3.66442i | 0.122352 | − | 0.211919i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.11566 | − | 3.66442i | 0.121944 | − | 0.211214i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.2927 | −0.875657 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0658 | + | 19.1666i | −0.631560 | + | 1.09389i | 0.355673 | + | 0.934611i | \(0.384252\pi\) |
−0.987233 | + | 0.159284i | \(0.949082\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 26.8293i | − | 1.52135i | −0.649133 | − | 0.760675i | \(-0.724868\pi\) | ||
0.649133 | − | 0.760675i | \(-0.275132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.246000 | + | 0.426084i | 0.0139047 | + | 0.0240837i | 0.872894 | − | 0.487910i | \(-0.162241\pi\) |
−0.858989 | + | 0.511994i | \(0.828907\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.5240 | − | 7.80809i | 0.759584 | − | 0.438546i | −0.0695627 | − | 0.997578i | \(-0.522160\pi\) |
0.829146 | + | 0.559032i | \(0.188827\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.2349 | − | 19.4593i | −0.629031 | − | 1.08951i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.17703 | + | 0.262997i | 0.0654919 | + | 0.0146336i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.16993 | − | 1.25281i | −0.120366 | − | 0.0694935i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.86166 | − | 4.95653i | −0.157768 | − | 0.273263i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.1930 | 1.49466 | 0.747332 | − | 0.664451i | \(-0.231334\pi\) | ||||
0.747332 | + | 0.664451i | \(0.231334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.3470 | 1.00240 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0240 | + | 10.4062i | 0.981830 | + | 0.566860i | 0.902822 | − | 0.430014i | \(-0.141491\pi\) |
0.0790078 | + | 0.996874i | \(0.474825\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.2874i | 1.42354i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.2782i | 0.824945i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.5649 | + | 13.0279i | 1.21135 | + | 0.699373i | 0.963053 | − | 0.269312i | \(-0.0867962\pi\) |
0.248296 | + | 0.968684i | \(0.420130\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.3541 | −1.30364 | −0.651822 | − | 0.758372i | \(-0.725995\pi\) | ||||
−0.651822 | + | 0.758372i | \(0.725995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0160 | −0.958895 | −0.479447 | − | 0.877571i | \(-0.659163\pi\) | ||||
−0.479447 | + | 0.877571i | \(0.659163\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.17703 | − | 12.4310i | −0.380917 | − | 0.659768i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.1192 | + | 13.9252i | 1.27296 | + | 0.734946i | 0.975545 | − | 0.219802i | \(-0.0705410\pi\) |
0.297418 | + | 0.954747i | \(0.403874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6001 | + | 10.8461i | −0.821056 | + | 0.570848i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.19617 | − | 7.26798i | −0.219638 | − | 0.380424i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.1806 | − | 15.1154i | 1.36662 | − | 0.789016i | 0.376121 | − | 0.926571i | \(-0.377258\pi\) |
0.990494 | + | 0.137555i | \(0.0439243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.23131 | + | 7.32885i | 0.219679 | + | 0.380495i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10.7929i | − | 0.558838i | −0.960169 | − | 0.279419i | \(-0.909858\pi\) | ||
0.960169 | − | 0.279419i | \(-0.0901418\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.1770 | − | 22.8233i | 0.678652 | − | 1.17546i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5080 | −1.05343 | −0.526713 | − | 0.850043i | \(-0.676576\pi\) | ||||
−0.526713 | + | 0.850043i | \(0.676576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.05783 | + | 12.2245i | −0.360638 | + | 0.624644i | −0.988066 | − | 0.154031i | \(-0.950774\pi\) |
0.627428 | + | 0.778675i | \(0.284108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.31538 | − | 7.47445i | 0.219932 | − | 0.380933i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.27669 | − | 5.67539i | −0.166135 | − | 0.287754i | 0.770923 | − | 0.636928i | \(-0.219795\pi\) |
−0.937058 | + | 0.349175i | \(0.886462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.337968i | 0.0170918i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.938623 | + | 1.62574i | 0.0472272 | + | 0.0818000i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.6045 | + | 18.3676i | −0.532225 | + | 0.921842i | 0.467067 | + | 0.884222i | \(0.345311\pi\) |
−0.999292 | + | 0.0376194i | \(0.988023\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.33007 | − | 3.07731i | −0.266171 | − | 0.153674i | 0.360975 | − | 0.932575i | \(-0.382444\pi\) |
−0.627146 | + | 0.778902i | \(0.715777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.7010 | + | 15.4158i | −1.33007 | + | 0.767918i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.4697 | 1.11378 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.09207 | + | 5.24931i | −0.449574 | + | 0.259562i | −0.707650 | − | 0.706563i | \(-0.750245\pi\) |
0.258076 | + | 0.966125i | \(0.416911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.28245 | + | 4.20453i | 0.358346 | + | 0.206891i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2349 | + | 9.95055i | 0.846026 | + | 0.488453i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.3381i | 1.77523i | 0.460584 | + | 0.887616i | \(0.347640\pi\) | ||||
−0.460584 | + | 0.887616i | \(0.652360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2896 | + | 10.5595i | 0.891378 | + | 0.514637i | 0.874393 | − | 0.485218i | \(-0.161260\pi\) |
0.0169851 | + | 0.999856i | \(0.494593\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.200132 | 0.00970783 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.76200 | − | 3.90404i | 0.327236 | − | 0.188930i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.23131 | − | 12.5250i | −0.348320 | − | 0.603308i | 0.637631 | − | 0.770342i | \(-0.279914\pi\) |
−0.985951 | + | 0.167034i | \(0.946581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.2931 | + | 18.0671i | −1.50385 | + | 0.868248i | −0.503860 | + | 0.863785i | \(0.668087\pi\) |
−0.999990 | + | 0.00446329i | \(0.998579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.91948 | − | 3.60356i | −0.187494 | − | 0.172382i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.84252 | − | 13.5836i | 0.374303 | − | 0.648312i | −0.615920 | − | 0.787809i | \(-0.711215\pi\) |
0.990222 | + | 0.139497i | \(0.0445487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.6739 | − | 8.47198i | 0.697178 | − | 0.402516i | −0.109118 | − | 0.994029i | \(-0.534803\pi\) |
0.806295 | + | 0.591513i | \(0.201469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 7.14082i | − | 0.338507i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.8275i | 0.841330i | 0.907216 | + | 0.420665i | \(0.138203\pi\) | ||||
−0.907216 | + | 0.420665i | \(0.861797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0885 | + | 24.4020i | −0.663402 | + | 1.14905i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.1228 | 0.474562 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8301 | 0.927611 | 0.463806 | − | 0.885937i | \(-0.346484\pi\) | ||||
0.463806 | + | 0.885937i | \(0.346484\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.4537 | + | 28.4987i | −0.766326 | + | 1.32732i | 0.173216 | + | 0.984884i | \(0.444584\pi\) |
−0.939543 | + | 0.342432i | \(0.888749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.3979i | 0.994443i | 0.867624 | + | 0.497222i | \(0.165646\pi\) | ||||
−0.867624 | + | 0.497222i | \(0.834354\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.79790i | 0.407118i | 0.979063 | + | 0.203559i | \(0.0652509\pi\) | ||||
−0.979063 | + | 0.203559i | \(0.934749\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.11252 | + | 4.68376i | −0.374601 | + | 0.216276i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.11566 | + | 8.86058i | −0.235218 | + | 0.407410i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.13389 | + | 2.32097i | −0.0979097 | + | 0.106493i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.11566 | − | 1.22147i | 0.0966668 | − | 0.0558106i | −0.450887 | − | 0.892581i | \(-0.648892\pi\) |
0.547554 | + | 0.836770i | \(0.315559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1770 | + | 22.8233i | 0.600821 | + | 1.04065i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.5814 | + | 7.84124i | −0.616700 | + | 0.356052i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0231 | −1.13390 | −0.566952 | − | 0.823751i | \(-0.691878\pi\) | ||||
−0.566952 | + | 0.823751i | \(0.691878\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.6397 | + | 21.1539i | 1.65352 | + | 0.954663i | 0.975607 | + | 0.219525i | \(0.0704508\pi\) |
0.677918 | + | 0.735138i | \(0.262883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.10498i | 0.0948036i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.34697 | + | 3.66442i | 0.284700 | + | 0.164372i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.2113 | − | 12.2463i | −0.949547 | − | 0.548221i | −0.0566067 | − | 0.998397i | \(-0.518028\pi\) |
−0.892940 | + | 0.450175i | \(0.851361\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.9288 | − | 19.0114i | 1.46822 | − | 0.847679i | 0.468856 | − | 0.883275i | \(-0.344666\pi\) |
0.999366 | + | 0.0355959i | \(0.0113329\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.7393 | −1.72388 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.34697 | + | 5.39647i | −0.414297 | + | 0.239195i | −0.692634 | − | 0.721289i | \(-0.743550\pi\) |
0.278337 | + | 0.960483i | \(0.410217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.71086 | + | 2.14247i | 0.164159 | + | 0.0947771i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.05428 | − | 5.29017i | 0.134588 | − | 0.233113i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.91948 | + | 11.9849i | 0.304319 | + | 0.527095i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.4835i | 0.590722i | 0.955386 | + | 0.295361i | \(0.0954399\pi\) | ||||
−0.955386 | + | 0.295361i | \(0.904560\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7393 | + | 22.0651i | 0.557051 | + | 0.964841i | 0.997741 | + | 0.0671814i | \(0.0214006\pi\) |
−0.440690 | + | 0.897660i | \(0.645266\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.23131 | − | 2.13269i | 0.0536368 | − | 0.0929016i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7540 | + | 18.6265i | −0.467565 | + | 0.809847i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.0480 | −1.43147 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.06138 | + | 8.76656i | −0.218822 | + | 0.379012i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 16.2680i | − | 0.700713i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5080 | − | 26.8606i | −0.666741 | − | 1.15483i | −0.978810 | − | 0.204770i | \(-0.934355\pi\) |
0.312069 | − | 0.950059i | \(-0.398978\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.1699 | + | 9.91307i | −0.735479 | + | 0.424629i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.83897 | + | 17.0416i | 0.420684 | + | 0.728646i | 0.996007 | − | 0.0892807i | \(-0.0284568\pi\) |
−0.575323 | + | 0.817927i | \(0.695123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.4119 | − | 22.4442i | −1.03998 | − | 0.956156i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.830066 | − | 0.479239i | −0.0352980 | − | 0.0203793i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.56938 | − | 16.5746i | −0.405468 | − | 0.702290i | 0.588908 | − | 0.808200i | \(-0.299558\pi\) |
−0.994376 | + | 0.105910i | \(0.966225\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.4083 | −1.61872 | −0.809359 | − | 0.587314i | \(-0.800185\pi\) | ||||
−0.809359 | + | 0.587314i | \(0.800185\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.58852 | − | 2.07183i | −0.150970 | − | 0.0871626i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.7750i | 1.45785i | 0.684596 | + | 0.728923i | \(0.259979\pi\) | ||||
−0.684596 | + | 0.728923i | \(0.740021\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 30.9257i | − | 1.29420i | −0.762405 | − | 0.647100i | \(-0.775981\pi\) | ||
0.762405 | − | 0.647100i | \(-0.224019\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.765139 | − | 0.441753i | −0.0319085 | − | 0.0184224i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.7847 | −1.15669 | −0.578346 | − | 0.815792i | \(-0.696302\pi\) | ||||
−0.578346 | + | 0.815792i | \(0.696302\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.1610 | −0.421551 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.2313 | − | 17.7212i | −0.423738 | − | 0.733935i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0614 | + | 8.11834i | 0.580375 | + | 0.335080i | 0.761282 | − | 0.648420i | \(-0.224570\pi\) |
−0.180907 | + | 0.983500i | \(0.557903\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6045 | + | 37.0195i | 0.478156 | + | 1.52536i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.57697 | − | 9.65959i | −0.229019 | − | 0.396672i | 0.728499 | − | 0.685047i | \(-0.240218\pi\) |
−0.957518 | + | 0.288375i | \(0.906885\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.700213 | + | 0.404268i | −0.0287059 | + | 0.0165734i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.00355 | − | 12.1305i | −0.286157 | − | 0.495639i | 0.686732 | − | 0.726911i | \(-0.259045\pi\) |
−0.972889 | + | 0.231272i | \(0.925711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.5486i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.72331 | − | 4.71691i | 0.110718 | − | 0.191770i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.13166 | −0.289465 | −0.144732 | − | 0.989471i | \(-0.546232\pi\) | ||||
−0.144732 | + | 0.989471i | \(0.546232\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.11566 | + | 14.0567i | −0.328324 | + | 0.568674i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.90034 | + | 15.4158i | −0.359482 | + | 0.622640i | −0.987874 | − | 0.155256i | \(-0.950380\pi\) |
0.628393 | + | 0.777896i | \(0.283713\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.2847 | + | 21.2777i | 0.494563 | + | 0.856608i | 0.999980 | − | 0.00626683i | \(-0.00199481\pi\) |
−0.505417 | + | 0.862875i | \(0.668661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.6804i | 0.871409i | 0.900090 | + | 0.435705i | \(0.143501\pi\) | ||||
−0.900090 | + | 0.435705i | \(0.856499\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.82297 | + | 3.15747i | 0.0730356 | + | 0.126501i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0467 | − | 24.3296i | 0.561868 | − | 0.973183i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.82297 | − | 1.05249i | −0.0726865 | − | 0.0419655i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.7589 | − | 21.2227i | 1.46335 | − | 0.844864i | 0.464183 | − | 0.885739i | \(-0.346348\pi\) |
0.999164 | + | 0.0408755i | \(0.0130147\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.4626 | 0.812034 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.5240 | − | 9.54014i | 0.654705 | − | 0.377994i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.7451 | + | 6.78104i | 0.463903 | + | 0.267835i | 0.713684 | − | 0.700468i | \(-0.247025\pi\) |
−0.249781 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4355 | + | 15.2625i | 1.04251 | + | 0.601896i | 0.920544 | − | 0.390638i | \(-0.127746\pi\) |
0.121969 | + | 0.992534i | \(0.461079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7219i | 0.814663i | 0.913280 | + | 0.407332i | \(0.133541\pi\) | ||||
−0.913280 | + | 0.407332i | \(0.866459\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6090 | − | 10.1665i | −0.691212 | − | 0.399072i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.9234 | 1.40579 | 0.702896 | − | 0.711292i | \(-0.251890\pi\) | ||||
0.702896 | + | 0.711292i | \(0.251890\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.2891 | + | 8.24984i | −0.558323 | + | 0.322348i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.5854 | + | 32.1908i | 0.723984 | + | 1.25398i | 0.959391 | + | 0.282079i | \(0.0910242\pi\) |
−0.235408 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1054 | − | 6.98907i | 0.470846 | − | 0.271843i | −0.245748 | − | 0.969334i | \(-0.579033\pi\) |
0.716594 | + | 0.697491i | \(0.245700\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.77759 | − | 12.4310i | 0.107710 | − | 0.482053i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.64634 | − | 8.04770i | 0.179907 | − | 0.311608i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.3505 | + | 9.43998i | −0.631205 | + | 0.364426i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.62574i | − | 0.0626678i | −0.999509 | − | 0.0313339i | \(-0.990024\pi\) | ||
0.999509 | − | 0.0313339i | \(-0.00997552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.6881i | 1.71750i | 0.512392 | + | 0.858752i | \(0.328759\pi\) | ||||
−0.512392 | + | 0.858752i | \(0.671241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00355 | − | 6.93435i | 0.153642 | − | 0.266116i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.5374 | −0.594521 | −0.297261 | − | 0.954796i | \(-0.596073\pi\) | ||||
−0.297261 | + | 0.954796i | \(0.596073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0845 | 0.385308 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.18234i | 0.235187i | 0.993062 | + | 0.117594i | \(0.0375180\pi\) | ||||
−0.993062 | + | 0.117594i | \(0.962482\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 9.50880i | − | 0.360689i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.28600 | − | 1.31982i | 0.0865885 | − | 0.0499919i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.60452 | + | 11.4394i | −0.249449 | + | 0.432059i | −0.963373 | − | 0.268165i | \(-0.913583\pi\) |
0.713924 | + | 0.700223i | \(0.246916\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.6432 | − | 9.91921i | 1.19345 | − | 0.374110i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.1294 | − | 9.88969i | 0.644219 | − | 0.371940i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.42748 | + | 11.1327i | 0.241389 | + | 0.418098i | 0.961110 | − | 0.276165i | \(-0.0890636\pi\) |
−0.719721 | + | 0.694263i | \(0.755730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.41503 | + | 5.43577i | −0.352596 | + | 0.203571i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.4768 | −0.915381 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.2998 | + | 22.1124i | 1.42834 | + | 0.824653i | 0.996990 | − | 0.0775310i | \(-0.0247037\pi\) |
0.431351 | + | 0.902184i | \(0.358037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.11888i | 0.116153i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.76555 | − | 2.75139i | −0.176988 | − | 0.102184i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.47600 | + | 4.31627i | 0.277269 | + | 0.160082i | 0.632187 | − | 0.774816i | \(-0.282158\pi\) |
−0.354917 | + | 0.934898i | \(0.615491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.830066 | − | 0.479239i | 0.0307011 | − | 0.0177253i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.8532 | 1.25040 | 0.625198 | − | 0.780467i | \(-0.285018\pi\) | ||||
0.625198 | + | 0.780467i | \(0.285018\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.6161 | − | 11.3253i | 0.722567 | − | 0.417174i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.26514 | − | 1.30778i | −0.0833245 | − | 0.0481074i | 0.457759 | − | 0.889076i | \(-0.348652\pi\) |
−0.541083 | + | 0.840969i | \(0.681986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.4119 | − | 31.8903i | 0.675467 | − | 1.16994i | −0.300865 | − | 0.953667i | \(-0.597275\pi\) |
0.976332 | − | 0.216276i | \(-0.0693912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.92303 | − | 13.7231i | −0.290277 | − | 0.502775i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.16844i | − | 0.188851i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.3923 | − | 26.6603i | −0.561675 | − | 0.972849i | −0.997351 | − | 0.0727454i | \(-0.976824\pi\) |
0.435676 | − | 0.900104i | \(-0.356509\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.63925 | + | 14.9636i | −0.314414 | + | 0.544582i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.37634 | − | 12.7762i | 0.268098 | − | 0.464359i | −0.700273 | − | 0.713875i | \(-0.746938\pi\) |
0.968371 | + | 0.249516i | \(0.0802716\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.80069 | 0.174025 | 0.0870124 | − | 0.996207i | \(-0.472268\pi\) | ||||
0.0870124 | + | 0.996207i | \(0.472268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.06138 | − | 8.76656i | 0.183234 | − | 0.317371i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 23.8481i | − | 0.861104i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.86166 | + | 6.68858i | 0.139255 | + | 0.241197i | 0.927215 | − | 0.374530i | \(-0.122196\pi\) |
−0.787960 | + | 0.615727i | \(0.788863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.2966 | + | 25.5747i | −1.59324 | + | 0.919857i | −0.600493 | + | 0.799630i | \(0.705029\pi\) |
−0.992746 | + | 0.120228i | \(0.961638\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.21886 | + | 5.57523i | 0.115625 | + | 0.200268i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.06807 | + | 40.5837i | −0.324897 | + | 1.45406i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.3470 | − | 8.86058i | −0.549158 | − | 0.317056i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.1770 | − | 22.8233i | −0.470308 | − | 0.814598i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.2090 | 1.14813 | 0.574064 | − | 0.818810i | \(-0.305366\pi\) | ||||
0.574064 | + | 0.818810i | \(0.305366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.11566 | 0.0752241 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.1770 | − | 11.0719i | −0.680996 | − | 0.393173i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.5142i | 1.64762i | 0.566869 | + | 0.823808i | \(0.308155\pi\) | ||||
−0.566869 | + | 0.823808i | \(0.691845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.29645i | − | 0.0458649i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.97286 | − | 5.18048i | −0.316645 | − | 0.182815i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.56938 | 0.125804 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.36925 | −0.223931 | −0.111965 | − | 0.993712i | \(-0.535715\pi\) | ||||
−0.111965 | + | 0.993712i | \(0.535715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.3087 | + | 45.5680i | 0.923823 | + | 1.60011i | 0.793443 | + | 0.608644i | \(0.208286\pi\) |
0.130380 | + | 0.991464i | \(0.458380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.41899 | − | 3.12866i | −0.189819 | − | 0.109592i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.29269 | + | 14.7363i | −0.115197 | + | 0.515557i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.73931 | + | 4.74463i | 0.0956026 | + | 0.165589i | 0.909860 | − | 0.414915i | \(-0.136189\pi\) |
−0.814257 | + | 0.580504i | \(0.802856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.7553 | − | 17.1792i | 1.03720 | − | 0.598831i | 0.118165 | − | 0.992994i | \(-0.462299\pi\) |
0.919040 | + | 0.394163i | \(0.128966\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.3812 | − | 35.3013i | −0.708724 | − | 1.22755i | −0.965331 | − | 0.261030i | \(-0.915938\pi\) |
0.256607 | − | 0.966516i | \(-0.417395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 12.3093i | − | 0.427518i | −0.976886 | − | 0.213759i | \(-0.931429\pi\) | ||
0.976886 | − | 0.213759i | \(-0.0685708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.762000 | + | 1.31982i | −0.0264017 | + | 0.0457292i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.1086 | −1.04195 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.28914 | − | 3.96491i | 0.0790299 | − | 0.136884i | −0.823802 | − | 0.566878i | \(-0.808151\pi\) |
0.902832 | + | 0.429994i | \(0.141484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4390 | − | 25.0091i | 0.497898 | − | 0.862384i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.19617 | + | 2.07183i | 0.0411496 | + | 0.0712732i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.78092i | 0.0955534i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.64634 | + | 8.04770i | 0.159275 | + | 0.275872i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5080 | − | 26.8606i | 0.530984 | − | 0.919691i | −0.468362 | − | 0.883536i | \(-0.655156\pi\) |
0.999346 | − | 0.0361545i | \(-0.0115108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.8541 | + | 19.5457i | 1.15643 | + | 0.667667i | 0.950447 | − | 0.310888i | \(-0.100626\pi\) |
0.205986 | + | 0.978555i | \(0.433960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.3269 | − | 18.6640i | 1.10298 | − | 0.636806i | 0.165978 | − | 0.986129i | \(-0.446922\pi\) |
0.937002 | + | 0.349323i | \(0.113589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.70103 | −0.0919443 | −0.0459721 | − | 0.998943i | \(-0.514639\pi\) | ||||
−0.0459721 | + | 0.998943i | \(0.514639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.8852 | + | 20.7183i | −1.22013 | + | 0.704444i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.00710 | + | 1.15880i | 0.0680862 | + | 0.0393096i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.0071 | + | 13.2832i | 0.779566 | + | 0.450083i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.4973i | 0.422485i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.5956 | + | 8.42678i | 0.492859 | + | 0.284552i | 0.725760 | − | 0.687948i | \(-0.241488\pi\) |
−0.232901 | + | 0.972500i | \(0.574822\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0454 | −0.776418 | −0.388209 | − | 0.921571i | \(-0.626906\pi\) | ||||
−0.388209 | + | 0.921571i | \(0.626906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5582 | − | 10.7146i | 0.624534 | − | 0.360575i | −0.154098 | − | 0.988056i | \(-0.549247\pi\) |
0.778632 | + | 0.627480i | \(0.215914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.29269 | − | 5.70310i | −0.110558 | − | 0.191492i | 0.805438 | − | 0.592681i | \(-0.201930\pi\) |
−0.915995 | + | 0.401189i | \(0.868597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.04800 | + | 5.22387i | −0.303460 | + | 0.175203i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.0351 | + | 13.8233i | 0.503132 | + | 0.462578i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.88079 | − | 4.98968i | 0.0962944 | − | 0.166787i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.6401 | + | 33.8559i | −1.95576 | + | 1.12916i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.91695i | 0.0638630i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44.0208i | 1.46330i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.342517 | + | 0.593256i | −0.0113731 | + | 0.0196987i | −0.871656 | − | 0.490118i | \(-0.836954\pi\) |
0.860283 | + | 0.509817i | \(0.170287\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.3470 | −1.20423 | −0.602114 | − | 0.798410i | \(-0.705675\pi\) | ||||
−0.602114 | + | 0.798410i | \(0.705675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.5694 | 0.813128 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.21217 | − | 7.29570i | 0.139098 | − | 0.240925i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.97963i | − | 0.0653020i | −0.999467 | − | 0.0326510i | \(-0.989605\pi\) | ||
0.999467 | − | 0.0326510i | \(-0.0103950\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 20.7846i | − | 0.684134i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.76555 | − | 2.75139i | 0.156690 | − | 0.0904652i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.3390 | − | 21.3717i | 0.404828 | − | 0.701183i | −0.589473 | − | 0.807788i | \(-0.700665\pi\) |
0.994301 | + | 0.106605i | \(0.0339979\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.18148 | − | 22.9096i | −0.235364 | − | 0.750832i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.69311 | − | 0.977520i | 0.0553707 | − | 0.0319683i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.0921 | + | 34.8005i | 0.656379 | + | 1.13688i | 0.981546 | + | 0.191225i | \(0.0612462\pi\) |
−0.325167 | + | 0.945657i | \(0.605421\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.65303 | + | 1.53173i | −0.0864864 | + | 0.0499329i | −0.542619 | − | 0.839979i | \(-0.682567\pi\) |
0.456133 | + | 0.889912i | \(0.349234\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.6530 | −0.379475 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.93862 | + | 5.73807i | 0.322962 | + | 0.186462i | 0.652712 | − | 0.757606i | \(-0.273631\pi\) |
−0.329750 | + | 0.944068i | \(0.606965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.1521i | − | 0.394473i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.91503 | − | 1.10564i | −0.0620340 | − | 0.0358153i | 0.468662 | − | 0.883377i | \(-0.344736\pi\) |
−0.530696 | + | 0.847562i | \(0.678069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.23131 | − | 2.44295i | −0.136922 | − | 0.0790520i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.45907 | + | 2.57445i | −0.143991 | + | 0.0831332i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.2161 | 1.55536 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.5240 | − | 13.0042i | 0.725073 | − | 0.418621i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.7624 | − | 14.8739i | −0.828463 | − | 0.478313i | 0.0248629 | − | 0.999691i | \(-0.492085\pi\) |
−0.853326 | + | 0.521377i | \(0.825418\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.85052 | − | 10.1334i | 0.187752 | − | 0.325196i | −0.756748 | − | 0.653706i | \(-0.773213\pi\) |
0.944500 | + | 0.328510i | \(0.106547\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.42748 | + | 4.20453i | 0.0778216 | + | 0.134791i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 30.4588i | − | 0.974462i | −0.873273 | − | 0.487231i | \(-0.838007\pi\) | ||
0.873273 | − | 0.487231i | \(-0.161993\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.40793 | − | 7.63477i | −0.140878 | − | 0.244008i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.3470 | + | 26.5817i | −0.489492 | + | 0.847825i | −0.999927 | − | 0.0120911i | \(-0.996151\pi\) |
0.510435 | + | 0.859917i | \(0.329485\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.97731 | − | 8.62096i | 0.158590 | − | 0.274687i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.23131 | −0.134548 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.6690 | + | 39.2639i | −0.720106 | + | 1.24726i | 0.240852 | + | 0.970562i | \(0.422573\pi\) |
−0.960957 | + | 0.276697i | \(0.910760\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 39.6523i | − | 1.25706i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.8972 | − | 51.7835i | −0.946854 | − | 1.64000i | −0.751996 | − | 0.659168i | \(-0.770909\pi\) |
−0.194858 | − | 0.980831i | \(-0.562425\pi\) | |||||||
\(998\) | 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.l.559.3 | 6 | ||
3.2 | odd | 2 | 304.2.n.d.255.1 | yes | 6 | ||
4.3 | odd | 2 | 2736.2.bm.m.559.3 | 6 | |||
12.11 | even | 2 | 304.2.n.e.255.3 | yes | 6 | ||
19.12 | odd | 6 | 2736.2.bm.m.1855.3 | 6 | |||
24.5 | odd | 2 | 1216.2.n.e.255.3 | 6 | |||
24.11 | even | 2 | 1216.2.n.d.255.1 | 6 | |||
57.50 | even | 6 | 304.2.n.e.31.3 | yes | 6 | ||
76.31 | even | 6 | inner | 2736.2.bm.l.1855.3 | 6 | ||
228.107 | odd | 6 | 304.2.n.d.31.1 | ✓ | 6 | ||
456.107 | odd | 6 | 1216.2.n.e.639.3 | 6 | |||
456.221 | even | 6 | 1216.2.n.d.639.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.n.d.31.1 | ✓ | 6 | 228.107 | odd | 6 | ||
304.2.n.d.255.1 | yes | 6 | 3.2 | odd | 2 | ||
304.2.n.e.31.3 | yes | 6 | 57.50 | even | 6 | ||
304.2.n.e.255.3 | yes | 6 | 12.11 | even | 2 | ||
1216.2.n.d.255.1 | 6 | 24.11 | even | 2 | |||
1216.2.n.d.639.1 | 6 | 456.221 | even | 6 | |||
1216.2.n.e.255.3 | 6 | 24.5 | odd | 2 | |||
1216.2.n.e.639.3 | 6 | 456.107 | odd | 6 | |||
2736.2.bm.l.559.3 | 6 | 1.1 | even | 1 | trivial | ||
2736.2.bm.l.1855.3 | 6 | 76.31 | even | 6 | inner | ||
2736.2.bm.m.559.3 | 6 | 4.3 | odd | 2 | |||
2736.2.bm.m.1855.3 | 6 | 19.12 | odd | 6 |