Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(127,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (of order \(2\), degree \(1\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.127 |
Dual form | 384.3.g.b.127.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.63567 | 0.527135 | 0.263567 | − | 0.964641i | \(-0.415101\pi\) | ||||
0.263567 | + | 0.964641i | \(0.415101\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.5558i | 1.79369i | 0.442344 | + | 0.896845i | \(0.354147\pi\) | ||||
−0.442344 | + | 0.896845i | \(0.645853\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.79796i | 0.527087i | 0.964647 | + | 0.263544i | \(0.0848913\pi\) | ||||
−0.964647 | + | 0.263544i | \(0.915109\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.78710 | −0.675931 | −0.337965 | − | 0.941159i | \(-0.609739\pi\) | ||||
−0.337965 | + | 0.941159i | \(0.609739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 4.56512i | − 0.304341i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.1810 | −1.77535 | −0.887676 | − | 0.460469i | \(-0.847681\pi\) | ||||
−0.887676 | + | 0.460469i | \(0.847681\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.4125i | 0.916445i | 0.888838 | + | 0.458222i | \(0.151514\pi\) | ||||
−0.888838 | + | 0.458222i | \(0.848486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.7473 | 1.03559 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.48425i | 0.108011i | 0.998541 | + | 0.0540054i | \(0.0171988\pi\) | ||||
−0.998541 | + | 0.0540054i | \(0.982801\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.0532 | −0.722129 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.4175 | 0.910950 | 0.455475 | − | 0.890249i | \(-0.349469\pi\) | ||||
0.455475 | + | 0.890249i | \(0.349469\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.0082i | 1.22607i | 0.790056 | + | 0.613035i | \(0.210051\pi\) | ||||
−0.790056 | + | 0.613035i | \(0.789949\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.0424 | 0.304314 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 33.0931i | 0.945517i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 47.7930 | 1.29170 | 0.645851 | − | 0.763463i | \(-0.276503\pi\) | ||||
0.645851 | + | 0.763463i | \(0.276503\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.2197i | 0.390249i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.3294 | 1.30072 | 0.650358 | − | 0.759628i | \(-0.274619\pi\) | ||||
0.650358 | + | 0.759628i | \(0.274619\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 30.7044i | − 0.714057i | −0.934094 | − | 0.357028i | \(-0.883790\pi\) | ||||
0.934094 | − | 0.357028i | \(-0.116210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.90702 | −0.175712 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.2238i | 0.345186i | 0.984993 | + | 0.172593i | \(0.0552146\pi\) | ||||
−0.984993 | + | 0.172593i | \(0.944785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −108.649 | −2.21733 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.2750i | 1.02500i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 49.8432 | 0.940437 | 0.470219 | − | 0.882550i | \(-0.344175\pi\) | ||||
0.470219 | + | 0.882550i | \(0.344175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.2815i | 0.277846i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.1593 | 0.529110 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 107.412i | 1.82054i | 0.414012 | + | 0.910271i | \(0.364127\pi\) | ||||
−0.414012 | + | 0.910271i | \(0.635873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −62.6220 | −1.02659 | −0.513295 | − | 0.858212i | \(-0.671575\pi\) | ||||
−0.513295 | + | 0.858212i | \(0.671575\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 37.6675i | − 0.597897i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −23.1599 | −0.356307 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 60.9540i | − 0.909762i | −0.890552 | − | 0.454881i | \(-0.849682\pi\) | ||||
0.890552 | − | 0.454881i | \(-0.150318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.30285 | 0.0623601 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 19.9465i | − 0.280937i | −0.990085 | − | 0.140469i | \(-0.955139\pi\) | ||||
0.990085 | − | 0.140469i | \(-0.0448609\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.13929 | 0.0704013 | 0.0352006 | − | 0.999380i | \(-0.488793\pi\) | ||||
0.0352006 | + | 0.999380i | \(0.488793\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 31.2691i | 0.416921i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −72.7982 | −0.945431 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6.83349i | − 0.0864999i | −0.999064 | − | 0.0432500i | \(-0.986229\pi\) | ||||
0.999064 | − | 0.0432500i | \(-0.0137712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 159.213i | − 1.91823i | −0.283016 | − | 0.959115i | \(-0.591335\pi\) | ||||
0.283016 | − | 0.959115i | \(-0.408665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −79.5472 | −0.935850 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 45.7565i | − 0.525937i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 39.4473 | 0.443229 | 0.221614 | − | 0.975134i | \(-0.428867\pi\) | ||||
0.221614 | + | 0.975134i | \(0.428867\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 110.329i | − 1.21241i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 65.8321 | 0.707872 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 45.8936i | 0.483090i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −60.5944 | −0.624684 | −0.312342 | − | 0.949970i | \(-0.601114\pi\) | ||||
−0.312342 | + | 0.949970i | \(0.601114\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 17.3939i | − 0.175696i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 169.076 | 1.67402 | 0.837011 | − | 0.547186i | \(-0.184301\pi\) | ||||
0.837011 | + | 0.547186i | \(0.184301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 163.390i | 1.58631i | 0.609020 | + | 0.793155i | \(0.291563\pi\) | ||||
−0.609020 | + | 0.793155i | \(0.708437\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 57.3189 | 0.545894 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 37.4288i | − 0.349802i | −0.984586 | − | 0.174901i | \(-0.944040\pi\) | ||||
0.984586 | − | 0.174901i | \(-0.0559605\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −210.117 | −1.92768 | −0.963838 | − | 0.266489i | \(-0.914137\pi\) | ||||
−0.963838 | + | 0.266489i | \(0.914137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 82.7799i | − 0.745765i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 190.809 | 1.68857 | 0.844286 | − | 0.535893i | \(-0.180025\pi\) | ||||
0.844286 | + | 0.535893i | \(0.180025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.54768i | 0.0569363i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.3613 | 0.225310 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 378.947i | − 3.18443i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 87.3837 | 0.722179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 92.3692i | − 0.750969i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −113.474 | −0.907794 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 34.4377i | 0.271163i | 0.990766 | + | 0.135581i | \(0.0432902\pi\) | ||||
−0.990766 | + | 0.135581i | \(0.956710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −53.1817 | −0.412261 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 92.5491i | 0.706482i | 0.935532 | + | 0.353241i | \(0.114920\pi\) | ||||
−0.935532 | + | 0.353241i | \(0.885080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −218.628 | −1.64382 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.6954i | 0.101447i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.0745 | −0.146529 | −0.0732647 | − | 0.997313i | \(-0.523342\pi\) | ||||
−0.0732647 | + | 0.997313i | \(0.523342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 70.0557i | − 0.503998i | −0.967728 | − | 0.251999i | \(-0.918912\pi\) | ||||
0.967728 | − | 0.251999i | \(-0.0810879\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 28.1004 | 0.199293 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 50.9472i | − 0.356274i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 69.6281 | 0.480193 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 188.186i | 1.28017i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −165.919 | −1.11355 | −0.556774 | − | 0.830664i | \(-0.687961\pi\) | ||||
−0.556774 | + | 0.830664i | \(0.687961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 59.7106i | − 0.395434i | −0.980259 | − | 0.197717i | \(-0.936647\pi\) | ||||
0.980259 | − | 0.197717i | \(-0.0633528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 90.5429 | 0.591784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 100.177i | 0.646304i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 138.133 | 0.879829 | 0.439915 | − | 0.898040i | \(-0.355009\pi\) | ||||
0.439915 | + | 0.898040i | \(0.355009\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 86.3309i | − 0.542962i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31.1918 | −0.193738 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 178.296i | − 1.09384i | −0.837185 | − | 0.546920i | \(-0.815800\pi\) | ||||
0.837185 | − | 0.546920i | \(-0.184200\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26.4684 | 0.160414 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 98.6284i | 0.590589i | 0.955406 | + | 0.295295i | \(0.0954178\pi\) | ||||
−0.955406 | + | 0.295295i | \(0.904582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −91.7869 | −0.543118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 52.2374i | − 0.305482i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 166.380 | 0.961733 | 0.480867 | − | 0.876794i | \(-0.340322\pi\) | ||||
0.480867 | + | 0.876794i | \(0.340322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 226.673i | − 1.29528i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 186.043 | 1.05109 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 206.496i | − 1.15361i | −0.816882 | − | 0.576805i | \(-0.804299\pi\) | ||||
0.816882 | − | 0.576805i | \(-0.195701\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 181.330 | 1.00182 | 0.500911 | − | 0.865499i | \(-0.332998\pi\) | ||||
0.500911 | + | 0.865499i | \(0.332998\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 108.465i | 0.592702i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 125.967 | 0.680901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 174.988i | − 0.935765i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −65.2420 | −0.345196 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 185.390i | 0.970627i | 0.874340 | + | 0.485314i | \(0.161295\pi\) | ||||
−0.874340 | + | 0.485314i | \(0.838705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.5439 | 0.0805382 | 0.0402691 | − | 0.999189i | \(-0.487178\pi\) | ||||
0.0402691 | + | 0.999189i | \(0.487178\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 40.1142i | 0.205714i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −114.464 | −0.581034 | −0.290517 | − | 0.956870i | \(-0.593827\pi\) | ||||
−0.290517 | + | 0.956870i | \(0.593827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 299.009i | 1.50256i | 0.659984 | + | 0.751280i | \(0.270563\pi\) | ||||
−0.659984 | + | 0.751280i | \(0.729437\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −105.576 | −0.525251 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 331.694i | 1.63396i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 140.559 | 0.685653 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 7.45275i | − 0.0360036i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −100.957 | −0.483046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 139.706i | 0.662111i | 0.943611 | + | 0.331056i | \(0.107405\pi\) | ||||
−0.943611 | + | 0.331056i | \(0.892595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −34.5484 | −0.162199 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 80.9269i | − 0.376404i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −477.224 | −2.19919 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 8.90152i | − 0.0406462i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 265.203 | 1.20001 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 66.1141i | − 0.296476i | −0.988952 | − | 0.148238i | \(-0.952640\pi\) | ||||
0.988952 | − | 0.148238i | \(-0.0473601\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 54.1597 | 0.240710 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 49.9611i | − 0.220093i | −0.993926 | − | 0.110046i | \(-0.964900\pi\) | ||||
0.993926 | − | 0.110046i | \(-0.0351000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −129.255 | −0.564431 | −0.282215 | − | 0.959351i | \(-0.591069\pi\) | ||||
−0.282215 | + | 0.959351i | \(0.591069\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 126.090i | 0.545845i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −196.318 | −0.842567 | −0.421284 | − | 0.906929i | \(-0.638420\pi\) | ||||
−0.421284 | + | 0.906929i | \(0.638420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 42.7606i | 0.181960i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.8360 | −0.0499407 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 153.654i | 0.642905i | 0.946926 | + | 0.321452i | \(0.104171\pi\) | ||||
−0.946926 | + | 0.321452i | \(0.895829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −41.3543 | −0.171595 | −0.0857974 | − | 0.996313i | \(-0.527344\pi\) | ||||
−0.0857974 | + | 0.996313i | \(0.527344\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −286.363 | −1.16883 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 153.005i | − 0.619453i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −275.765 | −1.10749 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 35.4495i | 0.141233i | 0.997504 | + | 0.0706165i | \(0.0224967\pi\) | ||||
−0.997504 | + | 0.0706165i | \(0.977503\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.4036 | −0.0569312 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 137.780i | 0.540313i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 66.0626 | 0.257053 | 0.128527 | − | 0.991706i | \(-0.458975\pi\) | ||||
0.128527 | + | 0.991706i | \(0.458975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 600.081i | 2.31691i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −79.2526 | −0.303650 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 93.5910i | 0.355859i | 0.984043 | + | 0.177930i | \(0.0569400\pi\) | ||||
−0.984043 | + | 0.177930i | \(0.943060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 131.370 | 0.495737 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 68.3248i | − 0.255898i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 305.548 | 1.13587 | 0.567933 | − | 0.823074i | \(-0.307743\pi\) | ||||
0.567933 | + | 0.823074i | \(0.307743\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 191.602i | 0.707017i | 0.935431 | + | 0.353509i | \(0.115012\pi\) | ||||
−0.935431 | + | 0.353509i | \(0.884988\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −191.096 | −0.699985 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 104.672i | − 0.380625i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 188.436 | 0.680276 | 0.340138 | − | 0.940376i | \(-0.389526\pi\) | ||||
0.340138 | + | 0.940376i | \(0.389526\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 114.024i | − 0.408690i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −296.087 | −1.05369 | −0.526844 | − | 0.849962i | \(-0.676625\pi\) | ||||
−0.526844 | + | 0.849962i | \(0.676625\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 260.681i | 0.921136i | 0.887625 | + | 0.460568i | \(0.152354\pi\) | ||||
−0.887625 | + | 0.460568i | \(0.847646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 79.4900 | 0.278912 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 669.595i | 2.33308i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 621.891 | 2.15187 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 104.953i | 0.360662i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 314.756 | 1.07425 | 0.537127 | − | 0.843501i | \(-0.319510\pi\) | ||||
0.537127 | + | 0.843501i | \(0.319510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 283.103i | 0.959672i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.1271 | −0.101438 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 21.8294i | − 0.0730079i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 385.520 | 1.28080 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 292.849i | − 0.966497i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −165.051 | −0.541152 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 168.120i | 0.547621i | 0.961784 | + | 0.273811i | \(0.0882841\pi\) | ||||
−0.961784 | + | 0.273811i | \(0.911716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 283.000 | 0.915856 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 468.033i | − 1.50493i | −0.658633 | − | 0.752464i | \(-0.728865\pi\) | ||||
0.658633 | − | 0.752464i | \(-0.271135\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 225.370 | 0.720033 | 0.360017 | − | 0.932946i | \(-0.382771\pi\) | ||||
0.360017 | + | 0.932946i | \(0.382771\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 99.2793i | − 0.315172i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −162.613 | −0.512976 | −0.256488 | − | 0.966547i | \(-0.582565\pi\) | ||||
−0.256488 | + | 0.966547i | \(0.582565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 153.168i | 0.480150i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −64.8285 | −0.201958 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 525.525i | − 1.62701i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 158.635 | 0.488109 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 363.933i | 1.11294i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −203.703 | −0.619158 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 254.527i | 0.768964i | 0.923133 | + | 0.384482i | \(0.125620\pi\) | ||||
−0.923133 | + | 0.384482i | \(0.874380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −143.379 | −0.430567 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 160.655i | − 0.479567i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −94.7347 | −0.281112 | −0.140556 | − | 0.990073i | \(-0.544889\pi\) | ||||
−0.140556 | + | 0.990073i | \(0.544889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 330.490i | − 0.974897i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −220.370 | −0.646246 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 748.942i | − 2.18351i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.3409 | 0.0328722 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 173.315i | 0.499467i | 0.968315 | + | 0.249734i | \(0.0803431\pi\) | ||||
−0.968315 | + | 0.249734i | \(0.919657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 195.247 | 0.559448 | 0.279724 | − | 0.960081i | \(-0.409757\pi\) | ||||
0.279724 | + | 0.960081i | \(0.409757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 45.6591i | − 0.130083i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 296.107 | 0.838830 | 0.419415 | − | 0.907795i | \(-0.362235\pi\) | ||||
0.419415 | + | 0.907795i | \(0.362235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 52.5726i | − 0.148092i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −656.356 | −1.83853 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 448.964i | 1.25060i | 0.780386 | + | 0.625298i | \(0.215023\pi\) | ||||
−0.780386 | + | 0.625298i | \(0.784977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 57.8065 | 0.160129 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 151.353i | − 0.416950i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.5455 | 0.0371110 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 623.564i | − 1.69908i | −0.527521 | − | 0.849542i | \(-0.676878\pi\) | ||||
0.527521 | − | 0.849542i | \(-0.323122\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −159.988 | −0.433572 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 625.823i | 1.68685i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −297.116 | −0.796558 | −0.398279 | − | 0.917264i | \(-0.630392\pi\) | ||||
−0.398279 | + | 0.917264i | \(0.630392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 196.543i | 0.524115i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −232.134 | −0.615739 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 224.021i | 0.591084i | 0.955330 | + | 0.295542i | \(0.0955003\pi\) | ||||
−0.955330 | + | 0.295542i | \(0.904500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 59.6478 | 0.156556 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 573.847i | − 1.49830i | −0.662403 | − | 0.749148i | \(-0.730463\pi\) | ||||
0.662403 | − | 0.749148i | \(-0.269537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −191.872 | −0.498370 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 92.1133i | 0.238019i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 148.849 | 0.382646 | 0.191323 | − | 0.981527i | \(-0.438722\pi\) | ||||
0.191323 | + | 0.981527i | \(0.438722\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 74.9771i | − 0.191757i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 160.300 | 0.407887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 18.0109i | − 0.0455971i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 245.952 | 0.619526 | 0.309763 | − | 0.950814i | \(-0.399750\pi\) | ||||
0.309763 | + | 0.950814i | \(0.399750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 378.675i | 0.949059i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 64.0509 | 0.159728 | 0.0798640 | − | 0.996806i | \(-0.474551\pi\) | ||||
0.0798640 | + | 0.996806i | \(0.474551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 333.981i | − 0.828738i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.7211 | 0.0585705 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 277.102i | 0.680840i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 555.403 | 1.35795 | 0.678977 | − | 0.734160i | \(-0.262424\pi\) | ||||
0.678977 | + | 0.734160i | \(0.262424\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.7701i | 0.0845988i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1348.65 | −3.26549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 419.634i | − 1.01117i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −121.340 | −0.290983 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 793.486i | − 1.89376i | −0.321583 | − | 0.946881i | \(-0.604215\pi\) | ||||
0.321583 | − | 0.946881i | \(-0.395785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 87.1175 | 0.206930 | 0.103465 | − | 0.994633i | \(-0.467007\pi\) | ||||
0.103465 | + | 0.994633i | \(0.467007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 48.6713i | − 0.115062i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 544.864 | 1.28203 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 786.272i | − 1.84139i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −88.2432 | −0.205695 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 432.932i | 1.00448i | 0.864727 | + | 0.502242i | \(0.167491\pi\) | ||||
−0.864727 | + | 0.502242i | \(0.832509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 391.344 | 0.903798 | 0.451899 | − | 0.892069i | \(-0.350747\pi\) | ||||
0.451899 | + | 0.892069i | \(0.350747\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 120.599i | − 0.277240i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −43.2569 | −0.0989860 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3066i | 0.0280332i | 0.999902 | + | 0.0140166i | \(0.00446177\pi\) | ||||
−0.999902 | + | 0.0140166i | \(0.995538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 325.947 | 0.739109 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 567.554i | − 1.28116i | −0.767892 | − | 0.640580i | \(-0.778694\pi\) | ||||
0.767892 | − | 0.640580i | \(-0.221306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 103.970 | 0.233641 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 287.380i | 0.642908i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −407.897 | −0.908457 | −0.454229 | − | 0.890885i | \(-0.650085\pi\) | ||||
−0.454229 | + | 0.890885i | \(0.650085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 309.201i | 0.685591i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −103.422 | −0.228304 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 290.792i | − 0.639104i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 231.789 | 0.507197 | 0.253598 | − | 0.967310i | \(-0.418386\pi\) | ||||
0.253598 | + | 0.967310i | \(0.418386\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 156.825i | − 0.341667i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −438.217 | −0.950578 | −0.475289 | − | 0.879830i | \(-0.657657\pi\) | ||||
−0.475289 | + | 0.879830i | \(0.657657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 185.141i | − 0.399873i | −0.979809 | − | 0.199936i | \(-0.935926\pi\) | ||||
0.979809 | − | 0.199936i | \(-0.0640735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 173.512 | 0.373144 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 82.9765i | 0.177680i | 0.996046 | + | 0.0888399i | \(0.0283159\pi\) | ||||
−0.996046 | + | 0.0888399i | \(0.971684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 765.329 | 1.63183 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 239.254i | − 0.507970i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 178.023 | 0.376370 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 314.351i | − 0.661791i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −149.530 | −0.313479 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 173.847i | 0.362936i | 0.983397 | + | 0.181468i | \(0.0580849\pi\) | ||||
−0.983397 | + | 0.181468i | \(0.941915\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −419.962 | −0.873101 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 54.0258i | 0.111855i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −159.707 | −0.329293 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 250.667i | − 0.514716i | −0.966316 | − | 0.257358i | \(-0.917148\pi\) | ||||
0.966316 | − | 0.257358i | \(-0.0828520\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −308.817 | −0.631529 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 283.478i | − 0.577349i | −0.957427 | − | 0.288674i | \(-0.906786\pi\) | ||||
0.957427 | − | 0.288674i | \(-0.0932145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −797.307 | −1.61726 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 45.8446i | − 0.0926153i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 250.445 | 0.503914 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 192.802i | 0.386377i | 0.981162 | + | 0.193188i | \(0.0618829\pi\) | ||||
−0.981162 | + | 0.193188i | \(0.938117\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 170.829 | 0.340977 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 398.251i | − 0.791752i | −0.918304 | − | 0.395876i | \(-0.870441\pi\) | ||||
0.918304 | − | 0.395876i | \(-0.129559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 445.630 | 0.882436 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 158.980i | 0.313569i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 550.212 | 1.08097 | 0.540483 | − | 0.841355i | \(-0.318242\pi\) | ||||
0.540483 | + | 0.841355i | \(0.318242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 64.5281i | 0.126278i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −90.4778 | −0.176370 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 430.643i | 0.836199i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −94.0647 | −0.181943 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 288.178i | − 0.555257i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −164.181 | −0.315126 | −0.157563 | − | 0.987509i | \(-0.550364\pi\) | ||||
−0.157563 | + | 0.987509i | \(0.550364\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 643.556i | 1.23051i | 0.788328 | + | 0.615255i | \(0.210947\pi\) | ||||
−0.788328 | + | 0.615255i | \(0.789053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −392.610 | −0.747828 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1147.12i | − 2.17670i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 522.828 | 0.988334 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 322.236i | − 0.606848i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −468.610 | −0.879194 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 98.6501i | − 0.184393i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −357.662 | −0.666037 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 629.942i | − 1.16872i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −727.713 | −1.34513 | −0.672563 | − | 0.740040i | \(-0.734807\pi\) | ||||
−0.672563 | + | 0.740040i | \(0.734807\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 314.072i | − 0.578402i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −553.799 | −1.01615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 97.2958i | − 0.177872i | −0.996037 | − | 0.0889359i | \(-0.971653\pi\) | ||||
0.996037 | − | 0.0889359i | \(-0.0283466\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 187.866 | 0.342197 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 459.994i | 0.834835i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 85.8002 | 0.155154 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 218.181i | − 0.393119i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 520.548 | 0.934556 | 0.467278 | − | 0.884110i | \(-0.345235\pi\) | ||||
0.467278 | + | 0.884110i | \(0.345235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 269.803i | 0.482653i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −303.088 | −0.540264 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 525.371i | 0.933163i | 0.884478 | + | 0.466581i | \(0.154515\pi\) | ||||
−0.884478 | + | 0.466581i | \(0.845485\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 502.909 | 0.890105 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 113.003i | 0.199299i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 824.774 | 1.44951 | 0.724757 | − | 0.689004i | \(-0.241952\pi\) | ||||
0.724757 | + | 0.689004i | \(0.241952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1088.90i | 1.90701i | 0.301381 | + | 0.953504i | \(0.402552\pi\) | ||||
−0.301381 | + | 0.953504i | \(0.597448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 321.105 | 0.560392 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 44.8487i | − 0.0779978i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −688.463 | −1.19318 | −0.596589 | − | 0.802547i | \(-0.703478\pi\) | ||||
−0.596589 | + | 0.802547i | \(0.703478\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 26.9228i | − 0.0464988i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1999.05 | 3.44071 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 288.989i | 0.495692i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 69.4798 | 0.118769 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 441.108i | 0.751462i | 0.926729 | + | 0.375731i | \(0.122608\pi\) | ||||
−0.926729 | + | 0.375731i | \(0.877392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −661.815 | −1.12363 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 198.257i | 0.335460i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −481.317 | −0.811664 | −0.405832 | − | 0.913948i | \(-0.633018\pi\) | ||||
−0.405832 | + | 0.913948i | \(0.633018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 998.782i | − 1.67862i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 517.899 | 0.867503 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 541.322i | 0.903709i | 0.892092 | + | 0.451854i | \(0.149237\pi\) | ||||
−0.892092 | + | 0.451854i | \(0.850763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 64.7772 | 0.107782 | 0.0538912 | − | 0.998547i | \(-0.482838\pi\) | ||||
0.0538912 | + | 0.998547i | \(0.482838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 182.862i | 0.303254i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 230.315 | 0.380686 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 608.260i | 1.00208i | 0.865426 | + | 0.501038i | \(0.167048\pi\) | ||||
−0.865426 | + | 0.501038i | \(0.832952\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 574.511 | 0.943368 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 142.560i | − 0.233322i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −924.407 | −1.50800 | −0.754002 | − | 0.656872i | \(-0.771879\pi\) | ||||
−0.754002 | + | 0.656872i | \(0.771879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 243.455i | − 0.395862i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 652.781 | 1.05799 | 0.528996 | − | 0.848624i | \(-0.322569\pi\) | ||||
0.528996 | + | 0.848624i | \(0.322569\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 246.098i | 0.397574i | 0.980043 | + | 0.198787i | \(0.0637001\pi\) | ||||
−0.980043 | + | 0.198787i | \(0.936300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.9085 | −0.0207867 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 495.294i | 0.795015i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 152.249 | 0.243599 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 174.862i | 0.278887i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1442.44 | −2.29323 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 563.715i | 0.893368i | 0.894692 | + | 0.446684i | \(0.147395\pi\) | ||||
−0.894692 | + | 0.446684i | \(0.852605\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 241.977 | 0.382270 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 90.7665i | 0.142939i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 954.709 | 1.49876 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 59.8396i | 0.0936457i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −163.485 | −0.255046 | −0.127523 | − | 0.991836i | \(-0.540703\pi\) | ||||
−0.127523 | + | 0.991836i | \(0.540703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 307.908i | − 0.478862i | −0.970913 | − | 0.239431i | \(-0.923039\pi\) | ||||
0.970913 | − | 0.239431i | \(-0.0769609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −140.170 | −0.217317 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 909.931i | 1.40638i | 0.711000 | + | 0.703192i | \(0.248243\pi\) | ||||
−0.711000 | + | 0.703192i | \(0.751757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −622.771 | −0.959585 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 826.576i | 1.26970i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 299.487 | 0.458632 | 0.229316 | − | 0.973352i | \(-0.426351\pi\) | ||||
0.229316 | + | 0.973352i | \(0.426351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 243.929i | 0.372411i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.4179 | −0.0234671 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 141.105i | 0.214120i | 0.994253 | + | 0.107060i | \(0.0341437\pi\) | ||||
−0.994253 | + | 0.107060i | \(0.965856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1176.74 | 1.78024 | 0.890121 | − | 0.455725i | \(-0.150620\pi\) | ||||
0.890121 | + | 0.455725i | \(0.150620\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 459.345i | − 0.692829i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −576.232 | −0.866514 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 65.6278i | 0.0983925i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −114.513 | −0.171170 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 363.080i | − 0.541103i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −230.780 | −0.342912 | −0.171456 | − | 0.985192i | \(-0.554847\pi\) | ||||
−0.171456 | + | 0.985192i | \(0.554847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 93.8073i | − 0.138974i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 768.499 | 1.13515 | 0.567577 | − | 0.823320i | \(-0.307881\pi\) | ||||
0.567577 | + | 0.823320i | \(0.307881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 760.813i | − 1.12049i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −86.5352 | −0.127071 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 963.083i | − 1.41008i | −0.709169 | − | 0.705039i | \(-0.750930\pi\) | ||||
0.709169 | − | 0.705039i | \(-0.249070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −52.9099 | −0.0772408 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 223.876i | 0.325874i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −437.977 | −0.635670 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 376.440i | 0.544776i | 0.962188 | + | 0.272388i | \(0.0878134\pi\) | ||||
−0.962188 | + | 0.272388i | \(0.912187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 218.395 | 0.315144 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 184.644i | − 0.265675i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1609.53 | −2.30923 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 340.033i | 0.486456i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −543.266 | −0.774988 | −0.387494 | − | 0.921872i | \(-0.626659\pi\) | ||||
−0.387494 | + | 0.921872i | \(0.626659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 832.193i | 1.18377i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 74.0635 | 0.105055 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2122.89i | 3.00268i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −403.852 | −0.569608 | −0.284804 | − | 0.958586i | \(-0.591929\pi\) | ||||
−0.284804 | + | 0.958586i | \(0.591929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.5005i | 0.0288333i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −94.4218 | −0.132429 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 134.280i | − 0.187805i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 266.137 | 0.371181 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 183.791i | 0.255620i | 0.991799 | + | 0.127810i | \(0.0407948\pi\) | ||||
−0.991799 | + | 0.127810i | \(0.959205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2051.50 | −2.84535 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 71.6278i | 0.0990703i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −476.922 | −0.657823 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 843.226i | 1.15987i | 0.814663 | + | 0.579935i | \(0.196922\pi\) | ||||
−0.814663 | + | 0.579935i | \(0.803078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 926.690i | 1.26770i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 286.176 | 0.390418 | 0.195209 | − | 0.980762i | \(-0.437461\pi\) | ||||
0.195209 | + | 0.980762i | \(0.437461\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 495.996i | 0.674824i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 353.409 | 0.479524 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 821.243i | − 1.11129i | −0.831420 | − | 0.555645i | \(-0.812471\pi\) | ||||
0.831420 | − | 0.555645i | \(-0.187529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −265.012 | −0.357641 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1227.08i | − 1.65153i | −0.564018 | − | 0.825763i | \(-0.690745\pi\) | ||||
0.564018 | − | 0.825763i | \(-0.309255\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −437.308 | −0.586990 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 477.639i | 0.639410i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 469.949 | 0.627436 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 966.507i | 1.28696i | 0.765463 | + | 0.643480i | \(0.222510\pi\) | ||||
−0.765463 | + | 0.643480i | \(0.777490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 61.4003 | 0.0815409 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 157.378i | − 0.208447i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −876.359 | −1.15767 | −0.578837 | − | 0.815443i | \(-0.696493\pi\) | ||||
−0.578837 | + | 0.815443i | \(0.696493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.9477i | 0.0328692i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 217.575 | 0.285907 | 0.142953 | − | 0.989729i | \(-0.454340\pi\) | ||||
0.142953 | + | 0.989729i | \(0.454340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2638.19i | − 3.45765i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 238.642 | 0.311950 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 943.840i | − 1.23056i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 497.583 | 0.647053 | 0.323526 | − | 0.946219i | \(-0.395132\pi\) | ||||
0.323526 | + | 0.946219i | \(0.395132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 114.424i | − 0.148410i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 664.490 | 0.859624 | 0.429812 | − | 0.902918i | \(-0.358580\pi\) | ||||
0.429812 | + | 0.902918i | \(0.358580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 686.170i | − 0.885380i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1039.37 | 1.33767 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 928.595i | 1.19203i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 115.649 | 0.148078 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 137.270i | 0.175312i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 364.074 | 0.463789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 214.321i | 0.272326i | 0.990686 | + | 0.136163i | \(0.0434772\pi\) | ||||
−0.990686 | + | 0.136163i | \(0.956523\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 162.104 | 0.205456 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2395.76i | 3.02878i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 550.266 | 0.693904 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 227.540i | − 0.286214i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 487.535 | 0.611713 | 0.305857 | − | 0.952078i | \(-0.401057\pi\) | ||||
0.305857 | + | 0.952078i | \(0.401057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 489.649i | − 0.612827i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −118.342 | −0.147743 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.7974i | 0.0371076i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −82.2115 | −0.102126 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 529.225i | − 0.655793i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1232.31 | −1.52325 | −0.761623 | − | 0.648021i | \(-0.775597\pi\) | ||||
−0.761623 | + | 0.648021i | \(0.775597\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.1721i | 0.0470679i | 0.999723 | + | 0.0235340i | \(0.00749178\pi\) | ||||
−0.999723 | + | 0.0235340i | \(0.992508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 331.864 | 0.408197 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 469.930i | − 0.576601i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 534.640 | 0.654394 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 330.988i | 0.404137i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 490.147 | 0.597012 | 0.298506 | − | 0.954408i | \(-0.403512\pi\) | ||||
0.298506 | + | 0.954408i | \(0.403512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 582.258i | 0.707482i | 0.935343 | + | 0.353741i | \(0.115091\pi\) | ||||
−0.935343 | + | 0.353741i | \(0.884909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −181.297 | −0.219754 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 852.873i | − 1.03128i | −0.856804 | − | 0.515642i | \(-0.827553\pi\) | ||||
0.856804 | − | 0.515642i | \(-0.172447\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 692.476 | 0.835315 | 0.417657 | − | 0.908605i | \(-0.362851\pi\) | ||||
0.417657 | + | 0.908605i | \(0.362851\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 326.381i | − 0.392757i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3279.13 | 3.93653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 259.952i | 0.311320i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −197.496 | −0.235957 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 761.022i | − 0.907059i | −0.891241 | − | 0.453529i | \(-0.850165\pi\) | ||||
0.891241 | − | 0.453529i | \(-0.149835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −143.113 | −0.170170 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 512.837i | 0.608347i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −241.920 | −0.286296 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1097.17i | 1.29537i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 451.513 | 0.531818 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 118.730i | 0.139518i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1245.38 | −1.46000 | −0.729999 | − | 0.683448i | \(-0.760480\pi\) | ||||
−0.729999 | + | 0.683448i | \(0.760480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 137.681i | − 0.161030i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1517.00 | −1.77013 | −0.885064 | − | 0.465469i | \(-0.845886\pi\) | ||||
−0.885064 | + | 0.465469i | \(0.845886\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1311.75i | 1.52706i | 0.645770 | + | 0.763532i | \(0.276537\pi\) | ||||
−0.645770 | + | 0.763532i | \(0.723463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1159.77 | 1.34701 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1304.34i | − 1.51140i | −0.654920 | − | 0.755698i | \(-0.727298\pi\) | ||||
0.654920 | − | 0.755698i | \(-0.272702\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 438.523 | 0.506963 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1077.15i | − 1.24238i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.6203 | 0.0455930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 535.609i | 0.614936i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 181.783 | 0.208228 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1424.76i | − 1.62830i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1207.07 | −1.37637 | −0.688183 | − | 0.725537i | \(-0.741591\pi\) | ||||
−0.688183 | + | 0.725537i | \(0.741591\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 545.174i | − 0.620221i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −375.974 | −0.426758 | −0.213379 | − | 0.976970i | \(-0.568447\pi\) | ||||
−0.213379 | + | 0.976970i | \(0.568447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 395.955i | − 0.448420i | −0.974541 | − | 0.224210i | \(-0.928020\pi\) | ||||
0.974541 | − | 0.224210i | \(-0.0719802\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 490.349 | 0.554067 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 960.050i | 1.08236i | 0.840908 | + | 0.541178i | \(0.182021\pi\) | ||||
−0.840908 | + | 0.541178i | \(0.817979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −432.394 | −0.486382 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52.1816i | 0.0585652i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −282.496 | −0.316344 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 544.256i | − 0.608108i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.8095 | −0.0421511 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1004.08i | 1.11689i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1504.32 | −1.66961 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 667.740i | − 0.739468i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 477.926 | 0.528095 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1301.18i | 1.43460i | 0.696766 | + | 0.717298i | \(0.254622\pi\) | ||||
−0.696766 | + | 0.717298i | \(0.745378\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −507.229 | −0.558008 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1274.60i | − 1.39912i | −0.714573 | − | 0.699561i | \(-0.753379\pi\) | ||||
0.714573 | − | 0.699561i | \(-0.246621\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 923.111 | 1.01107 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 285.877i | 0.312434i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1162.03 | −1.26721 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 957.109i | − 1.04147i | −0.853719 | − | 0.520734i | \(-0.825658\pi\) | ||||
0.853719 | − | 0.520734i | \(-0.174342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 291.192 | 0.316169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 175.272i | 0.189894i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −862.817 | −0.932775 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 490.170i | − 0.528770i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −912.989 | −0.982765 | −0.491383 | − | 0.870944i | \(-0.663508\pi\) | ||||
−0.491383 | + | 0.870944i | \(0.663508\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1891.84i | − 2.03206i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −810.657 | −0.868871 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 461.212i | − 0.493274i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 751.958 | 0.802516 | 0.401258 | − | 0.915965i | \(-0.368573\pi\) | ||||
0.401258 | + | 0.915965i | \(0.368573\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 390.353i | − 0.415711i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 417.550 | 0.443730 | 0.221865 | − | 0.975077i | \(-0.428786\pi\) | ||||
0.221865 | + | 0.975077i | \(0.428786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 132.484i | 0.140492i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −171.957 | −0.181965 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 928.909i | − 0.980897i | −0.871470 | − | 0.490448i | \(-0.836833\pi\) | ||||
0.871470 | − | 0.490448i | \(-0.163167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.1595 | −0.0475864 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 281.655i | 0.296167i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 676.685 | 0.710058 | 0.355029 | − | 0.934855i | \(-0.384471\pi\) | ||||
0.355029 | + | 0.934855i | \(0.384471\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 488.627i | 0.511652i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 265.294 | 0.277215 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 252.053i | − 0.262828i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −483.620 | −0.503247 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 112.286i | 0.116601i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 40.9686 | 0.0424545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 208.530i | − 0.215646i | −0.994170 | − | 0.107823i | \(-0.965612\pi\) | ||||
0.994170 | − | 0.107823i | \(-0.0343880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −910.236 | −0.939356 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 932.159i | − 0.959999i | −0.877269 | − | 0.480000i | \(-0.840637\pi\) | ||||
0.877269 | − | 0.480000i | \(-0.159363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 879.608 | 0.904016 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 274.765i | − 0.281810i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1567.22 | 1.60412 | 0.802059 | − | 0.597245i | \(-0.203738\pi\) | ||||
0.802059 | + | 0.597245i | \(0.203738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 228.714i | 0.233620i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 630.350 | 0.642559 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1201.11i | − 1.22188i | −0.791676 | − | 0.610941i | \(-0.790791\pi\) | ||||
0.791676 | − | 0.610941i | \(-0.209209\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −301.689 | −0.306283 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 352.824i | 0.357471i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 76.2775 | 0.0771259 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 568.813i | 0.573979i | 0.957934 | + | 0.286989i | \(0.0926545\pi\) | ||||
−0.957934 | + | 0.286989i | \(0.907346\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 440.854 | 0.443961 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 788.091i | 0.792052i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 66.4659 | 0.0666659 | 0.0333330 | − | 0.999444i | \(-0.489388\pi\) | ||||
0.0333330 | + | 0.999444i | \(0.489388\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 248.340i | 0.248588i |
(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 | 384.3.g.b.127.3 | yes | 8 | |
3.2 | odd | 2 | 1152.3.g.c.127.4 | 8 | |||
4.3 | odd | 2 | inner | 384.3.g.b.127.7 | yes | 8 | |
8.3 | odd | 2 | 384.3.g.a.127.2 | ✓ | 8 | ||
8.5 | even | 2 | 384.3.g.a.127.6 | yes | 8 | ||
12.11 | even | 2 | 1152.3.g.c.127.3 | 8 | |||
16.3 | odd | 4 | 768.3.b.f.127.2 | 8 | |||
16.5 | even | 4 | 768.3.b.f.127.3 | 8 | |||
16.11 | odd | 4 | 768.3.b.e.127.7 | 8 | |||
16.13 | even | 4 | 768.3.b.e.127.6 | 8 | |||
24.5 | odd | 2 | 1152.3.g.f.127.6 | 8 | |||
24.11 | even | 2 | 1152.3.g.f.127.5 | 8 | |||
48.5 | odd | 4 | 2304.3.b.q.127.3 | 8 | |||
48.11 | even | 4 | 2304.3.b.t.127.3 | 8 | |||
48.29 | odd | 4 | 2304.3.b.t.127.6 | 8 | |||
48.35 | even | 4 | 2304.3.b.q.127.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.g.a.127.2 | ✓ | 8 | 8.3 | odd | 2 | ||
384.3.g.a.127.6 | yes | 8 | 8.5 | even | 2 | ||
384.3.g.b.127.3 | yes | 8 | 1.1 | even | 1 | trivial | |
384.3.g.b.127.7 | yes | 8 | 4.3 | odd | 2 | inner | |
768.3.b.e.127.6 | 8 | 16.13 | even | 4 | |||
768.3.b.e.127.7 | 8 | 16.11 | odd | 4 | |||
768.3.b.f.127.2 | 8 | 16.3 | odd | 4 | |||
768.3.b.f.127.3 | 8 | 16.5 | even | 4 | |||
1152.3.g.c.127.3 | 8 | 12.11 | even | 2 | |||
1152.3.g.c.127.4 | 8 | 3.2 | odd | 2 | |||
1152.3.g.f.127.5 | 8 | 24.11 | even | 2 | |||
1152.3.g.f.127.6 | 8 | 24.5 | odd | 2 | |||
2304.3.b.q.127.3 | 8 | 48.5 | odd | 4 | |||
2304.3.b.q.127.6 | 8 | 48.35 | even | 4 | |||
2304.3.b.t.127.3 | 8 | 48.11 | even | 4 | |||
2304.3.b.t.127.6 | 8 | 48.29 | odd | 4 |