Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(197,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1386.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.c (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 4x^{10} - 8x^{9} + 17x^{8} - 16x^{7} + 88x^{6} - 48x^{5} + 153x^{4} - 216x^{3} + 324x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.5 | ||
Root | \(-0.833477 + 1.51833i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.197 |
Dual form | 1386.2.c.b.197.8 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 0.968524i | − | 0.433137i | −0.976267 | − | 0.216568i | \(-0.930514\pi\) | ||
0.976267 | − | 0.216568i | \(-0.0694865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 0.968524i | − | 0.306274i | ||||||
\(11\) | −3.27778 | − | 0.506135i | −0.988287 | − | 0.152606i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.36261i | 1.76467i | 0.470622 | + | 0.882335i | \(0.344029\pi\) | ||||
−0.470622 | + | 0.882335i | \(0.655971\pi\) | |||||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.67213 | 1.86077 | 0.930383 | − | 0.366590i | \(-0.119475\pi\) | ||||
0.930383 | + | 0.366590i | \(0.119475\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.690475i | 0.158406i | 0.996859 | + | 0.0792029i | \(0.0252375\pi\) | ||||
−0.996859 | + | 0.0792029i | \(0.974762\pi\) | |||||||
\(20\) | − | 0.968524i | − | 0.216568i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.27778 | − | 0.506135i | −0.698825 | − | 0.107908i | ||||
\(23\) | 3.04461i | 0.634845i | 0.948284 | + | 0.317422i | \(0.102817\pi\) | ||||
−0.948284 | + | 0.317422i | \(0.897183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.06196 | 0.812392 | ||||||||
\(26\) | 6.36261i | 1.24781i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 9.36769 | 1.73954 | 0.869768 | − | 0.493461i | \(-0.164268\pi\) | ||||
0.869768 | + | 0.493461i | \(0.164268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20608 | 0.755435 | 0.377717 | − | 0.925921i | \(-0.376709\pi\) | ||||
0.377717 | + | 0.925921i | \(0.376709\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.67213 | 1.31576 | ||||||||
\(35\) | 0.968524 | 0.163710 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.16234 | −0.684284 | −0.342142 | − | 0.939648i | \(-0.611152\pi\) | ||||
−0.342142 | + | 0.939648i | \(0.611152\pi\) | |||||||
\(38\) | 0.690475i | 0.112010i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 0.968524i | − | 0.153137i | ||||||
\(41\) | −0.349474 | −0.0545786 | −0.0272893 | − | 0.999628i | \(-0.508688\pi\) | ||||
−0.0272893 | + | 0.999628i | \(0.508688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.794780i | − | 0.121203i | −0.998162 | − | 0.0606014i | \(-0.980698\pi\) | ||
0.998162 | − | 0.0606014i | \(-0.0193019\pi\) | |||||||
\(44\) | −3.27778 | − | 0.506135i | −0.494144 | − | 0.0763028i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.04461i | 0.448903i | ||||||||
\(47\) | − | 8.19535i | − | 1.19541i | −0.801714 | − | 0.597707i | \(-0.796079\pi\) | ||
0.801714 | − | 0.597707i | \(-0.203921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.06196 | 0.574448 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.36261i | 0.882335i | ||||||||
\(53\) | 7.24488i | 0.995161i | 0.867418 | + | 0.497580i | \(0.165778\pi\) | ||||
−0.867418 | + | 0.497580i | \(0.834222\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.490204 | + | 3.17461i | −0.0660991 | + | 0.428064i | ||||
\(56\) | 1.00000i | 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.36769 | 1.23004 | ||||||||
\(59\) | − | 12.0994i | − | 1.57521i | −0.616183 | − | 0.787603i | \(-0.711322\pi\) | ||
0.616183 | − | 0.787603i | \(-0.288678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.29965i | − | 1.06266i | −0.847164 | − | 0.531331i | \(-0.821692\pi\) | ||
0.847164 | − | 0.531331i | \(-0.178308\pi\) | |||||||
\(62\) | 4.20608 | 0.534173 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.16234 | 0.764344 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2823 | −1.50052 | −0.750261 | − | 0.661142i | \(-0.770072\pi\) | ||||
−0.750261 | + | 0.661142i | \(0.770072\pi\) | |||||||
\(68\) | 7.67213 | 0.930383 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.968524 | 0.115761 | ||||||||
\(71\) | 4.98166i | 0.591214i | 0.955310 | + | 0.295607i | \(0.0955219\pi\) | ||||
−0.955310 | + | 0.295607i | \(0.904478\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.97054i | 1.16696i | 0.812126 | + | 0.583482i | \(0.198310\pi\) | ||||
−0.812126 | + | 0.583482i | \(0.801690\pi\) | |||||||
\(74\) | −4.16234 | −0.483862 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.690475i | 0.0792029i | ||||||||
\(77\) | 0.506135 | − | 3.27778i | 0.0576795 | − | 0.373537i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.37996i | 0.267766i | 0.990997 | + | 0.133883i | \(0.0427447\pi\) | ||||
−0.990997 | + | 0.133883i | \(0.957255\pi\) | |||||||
\(80\) | − | 0.968524i | − | 0.108284i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.349474 | −0.0385929 | ||||||||
\(83\) | 4.79593 | 0.526422 | 0.263211 | − | 0.964738i | \(-0.415218\pi\) | ||||
0.263211 | + | 0.964738i | \(0.415218\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.43064i | − | 0.805966i | ||||||
\(86\) | − | 0.794780i | − | 0.0857034i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.27778 | − | 0.506135i | −0.349412 | − | 0.0539542i | ||||
\(89\) | − | 7.23148i | − | 0.766536i | −0.923637 | − | 0.383268i | \(-0.874799\pi\) | ||
0.923637 | − | 0.383268i | \(-0.125201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.36261 | −0.666982 | ||||||||
\(92\) | 3.04461i | 0.317422i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 8.19535i | − | 0.845286i | ||||||
\(95\) | 0.668741 | 0.0686114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.78871 | −0.283150 | −0.141575 | − | 0.989928i | \(-0.545217\pi\) | ||||
−0.141575 | + | 0.989928i | \(0.545217\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.06196 | 0.406196 | ||||||||
\(101\) | −15.9272 | −1.58482 | −0.792408 | − | 0.609992i | \(-0.791173\pi\) | ||||
−0.792408 | + | 0.609992i | \(0.791173\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.44969 | −0.734039 | −0.367020 | − | 0.930213i | \(-0.619622\pi\) | ||||
−0.367020 | + | 0.930213i | \(0.619622\pi\) | |||||||
\(104\) | 6.36261i | 0.623905i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.24488i | 0.703685i | ||||||||
\(107\) | 3.91251 | 0.378236 | 0.189118 | − | 0.981954i | \(-0.439437\pi\) | ||||
0.189118 | + | 0.981954i | \(0.439437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5606i | 1.49044i | 0.666819 | + | 0.745219i | \(0.267655\pi\) | ||||
−0.666819 | + | 0.745219i | \(0.732345\pi\) | |||||||
\(110\) | −0.490204 | + | 3.17461i | −0.0467391 | + | 0.302687i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 14.2751i | 1.34289i | 0.741055 | + | 0.671445i | \(0.234326\pi\) | ||||
−0.741055 | + | 0.671445i | \(0.765674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.94878 | 0.274975 | ||||||||
\(116\) | 9.36769 | 0.869768 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 12.0994i | − | 1.11384i | ||||||
\(119\) | 7.67213i | 0.703303i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4877 | + | 3.31800i | 0.953423 | + | 0.301636i | ||||
\(122\) | − | 8.29965i | − | 0.751415i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.20608 | 0.377717 | ||||||||
\(125\) | − | 8.77673i | − | 0.785014i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2658i | 1.70956i | 0.518989 | + | 0.854781i | \(0.326309\pi\) | ||||
−0.518989 | + | 0.854781i | \(0.673691\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.16234 | 0.540473 | ||||||||
\(131\) | 18.7832 | 1.64110 | 0.820550 | − | 0.571575i | \(-0.193667\pi\) | ||||
0.820550 | + | 0.571575i | \(0.193667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.690475 | −0.0598718 | ||||||||
\(134\) | −12.2823 | −1.06103 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.67213 | 0.657880 | ||||||||
\(137\) | − | 12.8552i | − | 1.09829i | −0.835726 | − | 0.549147i | \(-0.814953\pi\) | ||
0.835726 | − | 0.549147i | \(-0.185047\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.8642i | − | 1.09113i | −0.838068 | − | 0.545566i | \(-0.816315\pi\) | ||
0.838068 | − | 0.545566i | \(-0.183685\pi\) | |||||||
\(140\) | 0.968524 | 0.0818552 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.98166i | 0.418051i | ||||||||
\(143\) | 3.22034 | − | 20.8552i | 0.269298 | − | 1.74400i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.07283i | − | 0.753457i | ||||||
\(146\) | 9.97054i | 0.825167i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.16234 | −0.342142 | ||||||||
\(149\) | −9.48765 | −0.777259 | −0.388629 | − | 0.921394i | \(-0.627051\pi\) | ||||
−0.388629 | + | 0.921394i | \(0.627051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8618i | 0.883923i | 0.897034 | + | 0.441961i | \(0.145717\pi\) | ||||
−0.897034 | + | 0.441961i | \(0.854283\pi\) | |||||||
\(152\) | 0.690475i | 0.0560049i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.506135 | − | 3.27778i | 0.0407855 | − | 0.264131i | ||||
\(155\) | − | 4.07369i | − | 0.327207i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.89046 | −0.310492 | −0.155246 | − | 0.987876i | \(-0.549617\pi\) | ||||
−0.155246 | + | 0.987876i | \(0.549617\pi\) | |||||||
\(158\) | 2.37996i | 0.189339i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 0.968524i | − | 0.0765685i | ||||||
\(161\) | −3.04461 | −0.239949 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.8831 | −1.24406 | −0.622032 | − | 0.782992i | \(-0.713693\pi\) | ||||
−0.622032 | + | 0.782992i | \(0.713693\pi\) | |||||||
\(164\) | −0.349474 | −0.0272893 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.79593 | 0.372236 | ||||||||
\(167\) | −3.23024 | −0.249963 | −0.124982 | − | 0.992159i | \(-0.539887\pi\) | ||||
−0.124982 | + | 0.992159i | \(0.539887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.4828 | −2.11406 | ||||||||
\(170\) | − | 7.43064i | − | 0.569904i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 0.794780i | − | 0.0606014i | ||||||
\(173\) | 6.30573 | 0.479416 | 0.239708 | − | 0.970845i | \(-0.422948\pi\) | ||||
0.239708 | + | 0.970845i | \(0.422948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.06196i | 0.307055i | ||||||||
\(176\) | −3.27778 | − | 0.506135i | −0.247072 | − | 0.0381514i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 7.23148i | − | 0.542023i | ||||||
\(179\) | − | 14.7744i | − | 1.10429i | −0.833749 | − | 0.552144i | \(-0.813810\pi\) | ||
0.833749 | − | 0.552144i | \(-0.186190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.51181 | −0.484019 | −0.242009 | − | 0.970274i | \(-0.577807\pi\) | ||||
−0.242009 | + | 0.970274i | \(0.577807\pi\) | |||||||
\(182\) | −6.36261 | −0.471628 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.04461i | 0.224452i | ||||||||
\(185\) | 4.03132i | 0.296389i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.1475 | − | 3.88314i | −1.83897 | − | 0.283963i | ||||
\(188\) | − | 8.19535i | − | 0.597707i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.668741 | 0.0485156 | ||||||||
\(191\) | − | 18.2020i | − | 1.31705i | −0.752559 | − | 0.658525i | \(-0.771181\pi\) | ||
0.752559 | − | 0.658525i | \(-0.228819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.63864i | 0.405878i | 0.979191 | + | 0.202939i | \(0.0650494\pi\) | ||||
−0.979191 | + | 0.202939i | \(0.934951\pi\) | |||||||
\(194\) | −2.78871 | −0.200217 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −10.6097 | −0.755912 | −0.377956 | − | 0.925824i | \(-0.623373\pi\) | ||||
−0.377956 | + | 0.925824i | \(0.623373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4026 | 1.16275 | 0.581374 | − | 0.813636i | \(-0.302515\pi\) | ||||
0.581374 | + | 0.813636i | \(0.302515\pi\) | |||||||
\(200\) | 4.06196 | 0.287224 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.9272 | −1.12063 | ||||||||
\(203\) | 9.36769i | 0.657483i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.338474i | 0.0236400i | ||||||||
\(206\) | −7.44969 | −0.519044 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.36261i | 0.441167i | ||||||||
\(209\) | 0.349474 | − | 2.26322i | 0.0241736 | − | 0.156550i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 27.0878i | − | 1.86480i | −0.361425 | − | 0.932401i | \(-0.617710\pi\) | ||
0.361425 | − | 0.932401i | \(-0.382290\pi\) | |||||||
\(212\) | 7.24488i | 0.497580i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.91251 | 0.267453 | ||||||||
\(215\) | −0.769764 | −0.0524974 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.20608i | 0.285527i | ||||||||
\(218\) | 15.5606i | 1.05390i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.490204 | + | 3.17461i | −0.0330495 | + | 0.214032i | ||||
\(221\) | 48.8147i | 3.28364i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.796023 | −0.0533057 | −0.0266528 | − | 0.999645i | \(-0.508485\pi\) | ||||
−0.0266528 | + | 0.999645i | \(0.508485\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.2751i | 0.949566i | ||||||||
\(227\) | −22.1143 | −1.46778 | −0.733890 | − | 0.679268i | \(-0.762297\pi\) | ||||
−0.733890 | + | 0.679268i | \(0.762297\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.8581 | 1.77483 | 0.887416 | − | 0.460969i | \(-0.152498\pi\) | ||||
0.887416 | + | 0.460969i | \(0.152498\pi\) | |||||||
\(230\) | 2.94878 | 0.194437 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.36769 | 0.615019 | ||||||||
\(233\) | −12.4954 | −0.818604 | −0.409302 | − | 0.912399i | \(-0.634228\pi\) | ||||
−0.409302 | + | 0.912399i | \(0.634228\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.93739 | −0.517778 | ||||||||
\(236\) | − | 12.0994i | − | 0.787603i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.67213i | 0.497310i | ||||||||
\(239\) | 11.4659 | 0.741669 | 0.370834 | − | 0.928699i | \(-0.379072\pi\) | ||||
0.370834 | + | 0.928699i | \(0.379072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.26479i | − | 0.532382i | −0.963920 | − | 0.266191i | \(-0.914235\pi\) | ||
0.963920 | − | 0.266191i | \(-0.0857651\pi\) | |||||||
\(242\) | 10.4877 | + | 3.31800i | 0.674172 | + | 0.213289i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.29965i | − | 0.531331i | ||||||
\(245\) | 0.968524i | 0.0618767i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.39322 | −0.279534 | ||||||||
\(248\) | 4.20608 | 0.267086 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 8.77673i | − | 0.555089i | ||||||
\(251\) | − | 1.83153i | − | 0.115605i | −0.998328 | − | 0.0578024i | \(-0.981591\pi\) | ||
0.998328 | − | 0.0578024i | \(-0.0184093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.54098 | − | 9.97955i | 0.0968808 | − | 0.627409i | ||||
\(254\) | 19.2658i | 1.20884i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.02981i | 0.500886i | 0.968131 | + | 0.250443i | \(0.0805763\pi\) | ||||
−0.968131 | + | 0.250443i | \(0.919424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.16234i | − | 0.258635i | ||||||
\(260\) | 6.16234 | 0.382172 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.7832 | 1.16043 | ||||||||
\(263\) | −17.5901 | −1.08465 | −0.542327 | − | 0.840167i | \(-0.682457\pi\) | ||||
−0.542327 | + | 0.840167i | \(0.682457\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.01684 | 0.431041 | ||||||||
\(266\) | −0.690475 | −0.0423357 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.2823 | −0.750261 | ||||||||
\(269\) | − | 7.84431i | − | 0.478276i | −0.970986 | − | 0.239138i | \(-0.923135\pi\) | ||
0.970986 | − | 0.239138i | \(-0.0768649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.4223i | − | 1.11908i | −0.828804 | − | 0.559538i | \(-0.810978\pi\) | ||
0.828804 | − | 0.559538i | \(-0.189022\pi\) | |||||||
\(272\) | 7.67213 | 0.465191 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 12.8552i | − | 0.776612i | ||||||
\(275\) | −13.3142 | − | 2.05590i | −0.802877 | − | 0.123976i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.2859i | − | 1.69953i | −0.527160 | − | 0.849766i | \(-0.676743\pi\) | ||
0.527160 | − | 0.849766i | \(-0.323257\pi\) | |||||||
\(278\) | − | 12.8642i | − | 0.771546i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.968524 | 0.0578804 | ||||||||
\(281\) | 8.83955 | 0.527323 | 0.263662 | − | 0.964615i | \(-0.415070\pi\) | ||||
0.263662 | + | 0.964615i | \(0.415070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.9517i | − | 0.769901i | −0.922937 | − | 0.384951i | \(-0.874218\pi\) | ||
0.922937 | − | 0.384951i | \(-0.125782\pi\) | |||||||
\(284\) | 4.98166i | 0.295607i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.22034 | − | 20.8552i | 0.190423 | − | 1.23319i | ||||
\(287\) | − | 0.349474i | − | 0.0206288i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.8616 | 2.46245 | ||||||||
\(290\) | − | 9.07283i | − | 0.532775i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.97054i | 0.583482i | ||||||||
\(293\) | −19.8507 | −1.15969 | −0.579846 | − | 0.814726i | \(-0.696887\pi\) | ||||
−0.579846 | + | 0.814726i | \(0.696887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7185 | −0.682280 | ||||||||
\(296\) | −4.16234 | −0.241931 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.48765 | −0.549605 | ||||||||
\(299\) | −19.3716 | −1.12029 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.794780 | 0.0458104 | ||||||||
\(302\) | 10.8618i | 0.625028i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.690475i | 0.0396015i | ||||||||
\(305\) | −8.03841 | −0.460278 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.9138i | 1.53605i | 0.640419 | + | 0.768025i | \(0.278761\pi\) | ||||
−0.640419 | + | 0.768025i | \(0.721239\pi\) | |||||||
\(308\) | 0.506135 | − | 3.27778i | 0.0288397 | − | 0.186769i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 4.07369i | − | 0.231370i | ||||||
\(311\) | − | 13.4037i | − | 0.760052i | −0.924976 | − | 0.380026i | \(-0.875915\pi\) | ||
0.924976 | − | 0.380026i | \(-0.124085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.88512 | 0.332647 | 0.166323 | − | 0.986071i | \(-0.446810\pi\) | ||||
0.166323 | + | 0.986071i | \(0.446810\pi\) | |||||||
\(314\) | −3.89046 | −0.219551 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.37996i | 0.133883i | ||||||||
\(317\) | − | 19.3875i | − | 1.08891i | −0.838790 | − | 0.544454i | \(-0.816737\pi\) | ||
0.838790 | − | 0.544454i | \(-0.183263\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.7052 | − | 4.74132i | −1.71916 | − | 0.265463i | ||||
\(320\) | − | 0.968524i | − | 0.0541421i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.04461 | −0.169669 | ||||||||
\(323\) | 5.29741i | 0.294756i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.8447i | 1.43360i | ||||||||
\(326\) | −15.8831 | −0.879686 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.349474 | −0.0192965 | ||||||||
\(329\) | 8.19535 | 0.451824 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.2283 | 1.27674 | 0.638372 | − | 0.769728i | \(-0.279608\pi\) | ||||
0.638372 | + | 0.769728i | \(0.279608\pi\) | |||||||
\(332\) | 4.79593 | 0.263211 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.23024 | −0.176751 | ||||||||
\(335\) | 11.8957i | 0.649932i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.5217i | − | 1.22684i | −0.789758 | − | 0.613418i | \(-0.789794\pi\) | ||
0.789758 | − | 0.613418i | \(-0.210206\pi\) | |||||||
\(338\) | −27.4828 | −1.49486 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 7.43064i | − | 0.402983i | ||||||
\(341\) | −13.7866 | − | 2.12885i | −0.746586 | − | 0.115283i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 0.794780i | − | 0.0428517i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.30573 | 0.338998 | ||||||||
\(347\) | −5.02864 | −0.269951 | −0.134976 | − | 0.990849i | \(-0.543096\pi\) | ||||
−0.134976 | + | 0.990849i | \(0.543096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.62260i | − | 0.354500i | −0.984166 | − | 0.177250i | \(-0.943280\pi\) | ||
0.984166 | − | 0.177250i | \(-0.0567201\pi\) | |||||||
\(350\) | 4.06196i | 0.217121i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.27778 | − | 0.506135i | −0.174706 | − | 0.0269771i | ||||
\(353\) | − | 26.9128i | − | 1.43243i | −0.697882 | − | 0.716213i | \(-0.745874\pi\) | ||
0.697882 | − | 0.716213i | \(-0.254126\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.82485 | 0.256077 | ||||||||
\(356\) | − | 7.23148i | − | 0.383268i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 14.7744i | − | 0.780849i | ||||||
\(359\) | 0.126745 | 0.00668936 | 0.00334468 | − | 0.999994i | \(-0.498935\pi\) | ||||
0.00334468 | + | 0.999994i | \(0.498935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5232 | 0.974908 | ||||||||
\(362\) | −6.51181 | −0.342253 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.36261 | −0.333491 | ||||||||
\(365\) | 9.65670 | 0.505455 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.5235 | 1.17572 | 0.587859 | − | 0.808963i | \(-0.299971\pi\) | ||||
0.587859 | + | 0.808963i | \(0.299971\pi\) | |||||||
\(368\) | 3.04461i | 0.158711i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.03132i | 0.209578i | ||||||||
\(371\) | −7.24488 | −0.376135 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.0593i | − | 0.676185i | −0.941113 | − | 0.338093i | \(-0.890218\pi\) | ||
0.941113 | − | 0.338093i | \(-0.109782\pi\) | |||||||
\(374\) | −25.1475 | − | 3.88314i | −1.30035 | − | 0.200792i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 8.19535i | − | 0.422643i | ||||||
\(377\) | 59.6029i | 3.06971i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.8782 | −1.58611 | −0.793054 | − | 0.609151i | \(-0.791510\pi\) | ||||
−0.793054 | + | 0.609151i | \(0.791510\pi\) | |||||||
\(380\) | 0.668741 | 0.0343057 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 18.2020i | − | 0.931295i | ||||||
\(383\) | 14.8598i | 0.759299i | 0.925130 | + | 0.379649i | \(0.123955\pi\) | ||||
−0.925130 | + | 0.379649i | \(0.876045\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.17461 | − | 0.490204i | −0.161793 | − | 0.0249831i | ||||
\(386\) | 5.63864i | 0.286999i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.78871 | −0.141575 | ||||||||
\(389\) | 27.6308i | 1.40094i | 0.713684 | + | 0.700468i | \(0.247025\pi\) | ||||
−0.713684 | + | 0.700468i | \(0.752975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.3586i | 1.18130i | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.6097 | −0.534510 | ||||||||
\(395\) | 2.30505 | 0.115980 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9319 | 0.799597 | 0.399798 | − | 0.916603i | \(-0.369080\pi\) | ||||
0.399798 | + | 0.916603i | \(0.369080\pi\) | |||||||
\(398\) | 16.4026 | 0.822187 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.06196 | 0.203098 | ||||||||
\(401\) | − | 17.3215i | − | 0.864995i | −0.901635 | − | 0.432498i | \(-0.857632\pi\) | ||
0.901635 | − | 0.432498i | \(-0.142368\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.7616i | 1.33309i | ||||||||
\(404\) | −15.9272 | −0.792408 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.36769i | 0.464911i | ||||||||
\(407\) | 13.6432 | + | 2.10670i | 0.676269 | + | 0.104425i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.23472i | 0.258840i | 0.991590 | + | 0.129420i | \(0.0413116\pi\) | ||||
−0.991590 | + | 0.129420i | \(0.958688\pi\) | |||||||
\(410\) | 0.338474i | 0.0167160i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.44969 | −0.367020 | ||||||||
\(413\) | 12.0994 | 0.595372 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.64497i | − | 0.228013i | ||||||
\(416\) | 6.36261i | 0.311952i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.349474 | − | 2.26322i | 0.0170933 | − | 0.110698i | ||||
\(419\) | 22.0977i | 1.07954i | 0.841812 | + | 0.539771i | \(0.181489\pi\) | ||||
−0.841812 | + | 0.539771i | \(0.818511\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.16019 | −0.154018 | −0.0770092 | − | 0.997030i | \(-0.524537\pi\) | ||||
−0.0770092 | + | 0.997030i | \(0.524537\pi\) | |||||||
\(422\) | − | 27.0878i | − | 1.31861i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.24488i | 0.351842i | ||||||||
\(425\) | 31.1639 | 1.51167 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.29965 | 0.401648 | ||||||||
\(428\) | 3.91251 | 0.189118 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.769764 | −0.0371213 | ||||||||
\(431\) | −30.7860 | −1.48291 | −0.741454 | − | 0.671003i | \(-0.765864\pi\) | ||||
−0.741454 | + | 0.671003i | \(0.765864\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6539 | −0.800333 | −0.400167 | − | 0.916442i | \(-0.631048\pi\) | ||||
−0.400167 | + | 0.916442i | \(0.631048\pi\) | |||||||
\(434\) | 4.20608i | 0.201898i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.5606i | 0.745219i | ||||||||
\(437\) | −2.10223 | −0.100563 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 31.6856i | − | 1.51227i | −0.654415 | − | 0.756136i | \(-0.727085\pi\) | ||
0.654415 | − | 0.756136i | \(-0.272915\pi\) | |||||||
\(440\) | −0.490204 | + | 3.17461i | −0.0233696 | + | 0.151343i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 48.8147i | 2.32188i | ||||||||
\(443\) | − | 11.0473i | − | 0.524874i | −0.964949 | − | 0.262437i | \(-0.915474\pi\) | ||
0.964949 | − | 0.262437i | \(-0.0845262\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.00386 | −0.332015 | ||||||||
\(446\) | −0.796023 | −0.0376928 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | 22.1346i | 1.04459i | 0.852763 | + | 0.522297i | \(0.174925\pi\) | ||||
−0.852763 | + | 0.522297i | \(0.825075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.14550 | + | 0.176881i | 0.0539394 | + | 0.00832900i | ||||
\(452\) | 14.2751i | 0.671445i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.1143 | −1.03788 | ||||||||
\(455\) | 6.16234i | 0.288895i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.2665i | − | 1.22870i | −0.789035 | − | 0.614348i | \(-0.789419\pi\) | ||
0.789035 | − | 0.614348i | \(-0.210581\pi\) | |||||||
\(458\) | 26.8581 | 1.25500 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.94878 | 0.137487 | ||||||||
\(461\) | 17.7454 | 0.826486 | 0.413243 | − | 0.910621i | \(-0.364396\pi\) | ||||
0.413243 | + | 0.910621i | \(0.364396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8222 | 1.10711 | 0.553556 | − | 0.832812i | \(-0.313270\pi\) | ||||
0.553556 | + | 0.832812i | \(0.313270\pi\) | |||||||
\(464\) | 9.36769 | 0.434884 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.4954 | −0.578840 | ||||||||
\(467\) | − | 11.2649i | − | 0.521279i | −0.965436 | − | 0.260640i | \(-0.916067\pi\) | ||
0.965436 | − | 0.260640i | \(-0.0839335\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12.2823i | − | 0.567144i | ||||||
\(470\) | −7.93739 | −0.366124 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 12.0994i | − | 0.556919i | ||||||
\(473\) | −0.402266 | + | 2.60511i | −0.0184962 | + | 0.119783i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.80468i | 0.128688i | ||||||||
\(476\) | 7.67213i | 0.351652i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.4659 | 0.524439 | ||||||||
\(479\) | −9.58585 | −0.437989 | −0.218994 | − | 0.975726i | \(-0.570278\pi\) | ||||
−0.218994 | + | 0.975726i | \(0.570278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 26.4833i | − | 1.20753i | ||||||
\(482\) | − | 8.26479i | − | 0.376451i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.4877 | + | 3.31800i | 0.476712 | + | 0.150818i | ||||
\(485\) | 2.70093i | 0.122643i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.21142 | 0.281466 | 0.140733 | − | 0.990048i | \(-0.455054\pi\) | ||||
0.140733 | + | 0.990048i | \(0.455054\pi\) | |||||||
\(488\) | − | 8.29965i | − | 0.375708i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.968524i | 0.0437534i | ||||||||
\(491\) | −9.06426 | −0.409064 | −0.204532 | − | 0.978860i | \(-0.565567\pi\) | ||||
−0.204532 | + | 0.978860i | \(0.565567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 71.8701 | 3.23687 | ||||||||
\(494\) | −4.39322 | −0.197660 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.20608 | 0.188859 | ||||||||
\(497\) | −4.98166 | −0.223458 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.7758 | −1.82537 | −0.912687 | − | 0.408659i | \(-0.865996\pi\) | ||||
−0.912687 | + | 0.408659i | \(0.865996\pi\) | |||||||
\(500\) | − | 8.77673i | − | 0.392507i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 1.83153i | − | 0.0817450i | ||||||
\(503\) | −36.2530 | −1.61644 | −0.808220 | − | 0.588881i | \(-0.799569\pi\) | ||||
−0.808220 | + | 0.588881i | \(0.799569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4259i | 0.686442i | ||||||||
\(506\) | 1.54098 | − | 9.97955i | 0.0685051 | − | 0.443645i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.2658i | 0.854781i | ||||||||
\(509\) | − | 11.3348i | − | 0.502407i | −0.967934 | − | 0.251203i | \(-0.919174\pi\) | ||
0.967934 | − | 0.251203i | \(-0.0808263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.97054 | −0.441071 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.02981i | 0.354180i | ||||||||
\(515\) | 7.21520i | 0.317940i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.14795 | + | 26.8625i | −0.182427 | + | 1.18141i | ||||
\(518\) | − | 4.16234i | − | 0.182883i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.16234 | 0.270236 | ||||||||
\(521\) | − | 21.7715i | − | 0.953826i | −0.878951 | − | 0.476913i | \(-0.841756\pi\) | ||
0.878951 | − | 0.476913i | \(-0.158244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.49377i | 0.327680i | 0.986487 | + | 0.163840i | \(0.0523881\pi\) | ||||
−0.986487 | + | 0.163840i | \(0.947612\pi\) | |||||||
\(524\) | 18.7832 | 0.820550 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.5901 | −0.766966 | ||||||||
\(527\) | 32.2696 | 1.40569 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.7304 | 0.596972 | ||||||||
\(530\) | 7.01684 | 0.304792 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.690475 | −0.0299359 | ||||||||
\(533\) | − | 2.22356i | − | 0.0963132i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.78936i | − | 0.163828i | ||||||
\(536\) | −12.2823 | −0.530515 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 7.84431i | − | 0.338192i | ||||||
\(539\) | 3.27778 | + | 0.506135i | 0.141184 | + | 0.0218008i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 9.33253i | − | 0.401237i | −0.979669 | − | 0.200618i | \(-0.935705\pi\) | ||
0.979669 | − | 0.200618i | \(-0.0642951\pi\) | |||||||
\(542\) | − | 18.4223i | − | 0.791307i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.67213 | 0.328940 | ||||||||
\(545\) | 15.0708 | 0.645564 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7544i | 0.972907i | 0.873706 | + | 0.486454i | \(0.161710\pi\) | ||||
−0.873706 | + | 0.486454i | \(0.838290\pi\) | |||||||
\(548\) | − | 12.8552i | − | 0.549147i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.3142 | − | 2.05590i | −0.567720 | − | 0.0876639i | ||||
\(551\) | 6.46815i | 0.275553i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.37996 | −0.101206 | ||||||||
\(554\) | − | 28.2859i | − | 1.20175i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 12.8642i | − | 0.545566i | ||||||
\(557\) | 25.3558 | 1.07436 | 0.537180 | − | 0.843468i | \(-0.319490\pi\) | ||||
0.537180 | + | 0.843468i | \(0.319490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.05687 | 0.213883 | ||||||||
\(560\) | 0.968524 | 0.0409276 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.83955 | 0.372874 | ||||||||
\(563\) | 22.1493 | 0.933483 | 0.466742 | − | 0.884394i | \(-0.345428\pi\) | ||||
0.466742 | + | 0.884394i | \(0.345428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.8258 | 0.581655 | ||||||||
\(566\) | − | 12.9517i | − | 0.544402i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.98166i | 0.209026i | ||||||||
\(569\) | −14.6605 | −0.614602 | −0.307301 | − | 0.951612i | \(-0.599426\pi\) | ||||
−0.307301 | + | 0.951612i | \(0.599426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.4233i | 0.603597i | 0.953372 | + | 0.301798i | \(0.0975869\pi\) | ||||
−0.953372 | + | 0.301798i | \(0.902413\pi\) | |||||||
\(572\) | 3.22034 | − | 20.8552i | 0.134649 | − | 0.872000i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 0.349474i | − | 0.0145867i | ||||||
\(575\) | 12.3671i | 0.515743i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.249866 | −0.0104020 | −0.00520102 | − | 0.999986i | \(-0.501656\pi\) | ||||
−0.00520102 | + | 0.999986i | \(0.501656\pi\) | |||||||
\(578\) | 41.8616 | 1.74121 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 9.07283i | − | 0.376729i | ||||||
\(581\) | 4.79593i | 0.198969i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.66689 | − | 23.7471i | 0.151867 | − | 0.983505i | ||||
\(584\) | 9.97054i | 0.412584i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.8507 | −0.820026 | ||||||||
\(587\) | − | 41.6743i | − | 1.72008i | −0.510224 | − | 0.860041i | \(-0.670438\pi\) | ||
0.510224 | − | 0.860041i | \(-0.329562\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.90419i | 0.119665i | ||||||||
\(590\) | −11.7185 | −0.482445 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.16234 | −0.171071 | ||||||||
\(593\) | 25.5097 | 1.04756 | 0.523778 | − | 0.851855i | \(-0.324522\pi\) | ||||
0.523778 | + | 0.851855i | \(0.324522\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.43064 | 0.304627 | ||||||||
\(596\) | −9.48765 | −0.388629 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.3716 | −0.792166 | ||||||||
\(599\) | 8.01287i | 0.327397i | 0.986510 | + | 0.163698i | \(0.0523424\pi\) | ||||
−0.986510 | + | 0.163698i | \(0.947658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.16202i | 0.332936i | 0.986047 | + | 0.166468i | \(0.0532362\pi\) | ||||
−0.986047 | + | 0.166468i | \(0.946764\pi\) | |||||||
\(602\) | 0.794780 | 0.0323928 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.8618i | 0.441961i | ||||||||
\(605\) | 3.21356 | − | 10.1575i | 0.130650 | − | 0.412963i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6663i | 1.00117i | 0.865686 | + | 0.500587i | \(0.166882\pi\) | ||||
−0.865686 | + | 0.500587i | \(0.833118\pi\) | |||||||
\(608\) | 0.690475i | 0.0280025i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.03841 | −0.325466 | ||||||||
\(611\) | 52.1438 | 2.10951 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.4293i | 1.79448i | 0.441541 | + | 0.897241i | \(0.354432\pi\) | ||||
−0.441541 | + | 0.897241i | \(0.645568\pi\) | |||||||
\(614\) | 26.9138i | 1.08615i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.506135 | − | 3.27778i | 0.0203928 | − | 0.132065i | ||||
\(617\) | 28.8338i | 1.16080i | 0.814330 | + | 0.580402i | \(0.197104\pi\) | ||||
−0.814330 | + | 0.580402i | \(0.802896\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.6095 | −1.23030 | −0.615149 | − | 0.788411i | \(-0.710904\pi\) | ||||
−0.615149 | + | 0.788411i | \(0.710904\pi\) | |||||||
\(620\) | − | 4.07369i | − | 0.163603i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 13.4037i | − | 0.537438i | ||||||
\(623\) | 7.23148 | 0.289723 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8093 | 0.472374 | ||||||||
\(626\) | 5.88512 | 0.235217 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.89046 | −0.155246 | ||||||||
\(629\) | −31.9340 | −1.27329 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.7730 | −0.667722 | −0.333861 | − | 0.942622i | \(-0.608352\pi\) | ||||
−0.333861 | + | 0.942622i | \(0.608352\pi\) | |||||||
\(632\) | 2.37996i | 0.0946697i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 19.3875i | − | 0.769975i | ||||||
\(635\) | 18.6594 | 0.740474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.36261i | − | 0.252096i | ||||||
\(638\) | −30.7052 | − | 4.74132i | −1.21563 | − | 0.187711i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 0.968524i | − | 0.0382843i | ||||||
\(641\) | 8.74257i | 0.345311i | 0.984982 | + | 0.172655i | \(0.0552347\pi\) | ||||
−0.984982 | + | 0.172655i | \(0.944765\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.1706 | −0.716577 | −0.358289 | − | 0.933611i | \(-0.616640\pi\) | ||||
−0.358289 | + | 0.933611i | \(0.616640\pi\) | |||||||
\(644\) | −3.04461 | −0.119974 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.29741i | 0.208424i | ||||||||
\(647\) | − | 20.7346i | − | 0.815163i | −0.913169 | − | 0.407581i | \(-0.866372\pi\) | ||
0.913169 | − | 0.407581i | \(-0.133628\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.12392 | + | 39.6591i | −0.240385 | + | 1.55676i | ||||
\(650\) | 25.8447i | 1.01371i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.8831 | −0.622032 | ||||||||
\(653\) | 3.99386i | 0.156292i | 0.996942 | + | 0.0781459i | \(0.0249000\pi\) | ||||
−0.996942 | + | 0.0781459i | \(0.975100\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 18.1920i | − | 0.710821i | ||||||
\(656\) | −0.349474 | −0.0136447 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.19535 | 0.319488 | ||||||||
\(659\) | −5.75013 | −0.223993 | −0.111997 | − | 0.993709i | \(-0.535725\pi\) | ||||
−0.111997 | + | 0.993709i | \(0.535725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.5089 | 1.65341 | 0.826703 | − | 0.562639i | \(-0.190214\pi\) | ||||
0.826703 | + | 0.562639i | \(0.190214\pi\) | |||||||
\(662\) | 23.2283 | 0.902794 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.79593 | 0.186118 | ||||||||
\(665\) | 0.668741i | 0.0259327i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.5209i | 1.10434i | ||||||||
\(668\) | −3.23024 | −0.124982 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.8957i | 0.459571i | ||||||||
\(671\) | −4.20075 | + | 27.2044i | −0.162168 | + | 1.05022i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.45886i | − | 0.0562348i | −0.999605 | − | 0.0281174i | \(-0.991049\pi\) | ||
0.999605 | − | 0.0281174i | \(-0.00895123\pi\) | |||||||
\(674\) | − | 22.5217i | − | 0.867504i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27.4828 | −1.05703 | ||||||||
\(677\) | −3.94184 | −0.151497 | −0.0757485 | − | 0.997127i | \(-0.524135\pi\) | ||||
−0.0757485 | + | 0.997127i | \(0.524135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.78871i | − | 0.107021i | ||||||
\(680\) | − | 7.43064i | − | 0.284952i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.7866 | − | 2.12885i | −0.527916 | − | 0.0815177i | ||||
\(683\) | 2.11146i | 0.0807928i | 0.999184 | + | 0.0403964i | \(0.0128621\pi\) | ||||
−0.999184 | + | 0.0403964i | \(0.987138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.4506 | −0.475712 | ||||||||
\(686\) | − | 1.00000i | − | 0.0381802i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 0.794780i | − | 0.0303007i | ||||||
\(689\) | −46.0963 | −1.75613 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1455 | −0.576162 | −0.288081 | − | 0.957606i | \(-0.593017\pi\) | ||||
−0.288081 | + | 0.957606i | \(0.593017\pi\) | |||||||
\(692\) | 6.30573 | 0.239708 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.02864 | −0.190884 | ||||||||
\(695\) | −12.4593 | −0.472609 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.68121 | −0.101558 | ||||||||
\(698\) | − | 6.62260i | − | 0.250669i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.06196i | 0.153528i | ||||||||
\(701\) | 37.1475 | 1.40304 | 0.701521 | − | 0.712649i | \(-0.252505\pi\) | ||||
0.701521 | + | 0.712649i | \(0.252505\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.87399i | − | 0.108395i | ||||||
\(704\) | −3.27778 | − | 0.506135i | −0.123536 | − | 0.0190757i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 26.9128i | − | 1.01288i | ||||||
\(707\) | − | 15.9272i | − | 0.599004i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.2497 | −1.32383 | −0.661916 | − | 0.749578i | \(-0.730256\pi\) | ||||
−0.661916 | + | 0.749578i | \(0.730256\pi\) | |||||||
\(710\) | 4.82485 | 0.181073 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 7.23148i | − | 0.271011i | ||||||
\(713\) | 12.8059i | 0.479584i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.1988 | − | 3.11897i | −0.755391 | − | 0.116643i | ||||
\(716\) | − | 14.7744i | − | 0.552144i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.126745 | 0.00473009 | ||||||||
\(719\) | − | 43.0144i | − | 1.60417i | −0.597211 | − | 0.802084i | \(-0.703725\pi\) | ||
0.597211 | − | 0.802084i | \(-0.296275\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 7.44969i | − | 0.277441i | ||||||
\(722\) | 18.5232 | 0.689364 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.51181 | −0.242009 | ||||||||
\(725\) | 38.0512 | 1.41319 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.2866 | 0.678211 | 0.339106 | − | 0.940748i | \(-0.389876\pi\) | ||||
0.339106 | + | 0.940748i | \(0.389876\pi\) | |||||||
\(728\) | −6.36261 | −0.235814 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.65670 | 0.357411 | ||||||||
\(731\) | − | 6.09766i | − | 0.225530i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.08135i | − | 0.261556i | −0.991412 | − | 0.130778i | \(-0.958253\pi\) | ||
0.991412 | − | 0.130778i | \(-0.0417474\pi\) | |||||||
\(734\) | 22.5235 | 0.831358 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.04461i | 0.112226i | ||||||||
\(737\) | 40.2587 | + | 6.21650i | 1.48295 | + | 0.228988i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.2950i | 1.29835i | 0.760640 | + | 0.649174i | \(0.224885\pi\) | ||||
−0.760640 | + | 0.649174i | \(0.775115\pi\) | |||||||
\(740\) | 4.03132i | 0.148194i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.24488 | −0.265968 | ||||||||
\(743\) | 1.16019 | 0.0425633 | 0.0212817 | − | 0.999774i | \(-0.493225\pi\) | ||||
0.0212817 | + | 0.999774i | \(0.493225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.18902i | 0.336660i | ||||||||
\(746\) | − | 13.0593i | − | 0.478135i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25.1475 | − | 3.88314i | −0.919485 | − | 0.141982i | ||||
\(749\) | 3.91251i | 0.142960i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2096 | 0.773950 | 0.386975 | − | 0.922090i | \(-0.373520\pi\) | ||||
0.386975 | + | 0.922090i | \(0.373520\pi\) | |||||||
\(752\) | − | 8.19535i | − | 0.298854i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 59.6029i | 2.17061i | ||||||||
\(755\) | 10.5199 | 0.382860 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.5045 | 0.817938 | 0.408969 | − | 0.912548i | \(-0.365888\pi\) | ||||
0.408969 | + | 0.912548i | \(0.365888\pi\) | |||||||
\(758\) | −30.8782 | −1.12155 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.668741 | 0.0242578 | ||||||||
\(761\) | −46.3962 | −1.68186 | −0.840930 | − | 0.541144i | \(-0.817992\pi\) | ||||
−0.840930 | + | 0.541144i | \(0.817992\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.5606 | −0.563333 | ||||||||
\(764\) | − | 18.2020i | − | 0.658525i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.8598i | 0.536905i | ||||||||
\(767\) | 76.9836 | 2.77972 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7.34810i | − | 0.264979i | −0.991184 | − | 0.132490i | \(-0.957703\pi\) | ||
0.991184 | − | 0.132490i | \(-0.0422971\pi\) | |||||||
\(770\) | −3.17461 | − | 0.490204i | −0.114405 | − | 0.0176657i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.63864i | 0.202939i | ||||||||
\(773\) | 4.73217i | 0.170204i | 0.996372 | + | 0.0851021i | \(0.0271217\pi\) | ||||
−0.996372 | + | 0.0851021i | \(0.972878\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.0849 | 0.613709 | ||||||||
\(776\) | −2.78871 | −0.100109 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.6308i | 0.990612i | ||||||||
\(779\) | − | 0.241303i | − | 0.00864557i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.52139 | − | 16.3288i | 0.0902225 | − | 0.584289i | ||||
\(782\) | 23.3586i | 0.835303i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 3.76800i | 0.134486i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.64274i | 0.165496i | 0.996571 | + | 0.0827480i | \(0.0263696\pi\) | ||||
−0.996571 | + | 0.0827480i | \(0.973630\pi\) | |||||||
\(788\) | −10.6097 | −0.377956 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.30505 | 0.0820099 | ||||||||
\(791\) | −14.2751 | −0.507565 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.8074 | 1.87525 | ||||||||
\(794\) | 15.9319 | 0.565400 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.4026 | 0.581374 | ||||||||
\(797\) | − | 10.2652i | − | 0.363613i | −0.983334 | − | 0.181807i | \(-0.941805\pi\) | ||
0.983334 | − | 0.181807i | \(-0.0581945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 62.8758i | − | 2.22439i | ||||||
\(800\) | 4.06196 | 0.143612 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 17.3215i | − | 0.611644i | ||||||
\(803\) | 5.04644 | − | 32.6812i | 0.178085 | − | 1.15329i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.94878i | 0.103931i | ||||||||
\(806\) | 26.7616i | 0.942639i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.9272 | −0.560317 | ||||||||
\(809\) | −18.8569 | −0.662972 | −0.331486 | − | 0.943460i | \(-0.607550\pi\) | ||||
−0.331486 | + | 0.943460i | \(0.607550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0613i | 1.65255i | 0.563270 | + | 0.826273i | \(0.309543\pi\) | ||||
−0.563270 | + | 0.826273i | \(0.690457\pi\) | |||||||
\(812\) | 9.36769i | 0.328741i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.6432 | + | 2.10670i | 0.478194 | + | 0.0738399i | ||||
\(815\) | 15.3832i | 0.538850i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.548776 | 0.0191992 | ||||||||
\(818\) | 5.23472i | 0.183028i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.338474i | 0.0118200i | ||||||||
\(821\) | −22.6115 | −0.789145 | −0.394573 | − | 0.918865i | \(-0.629107\pi\) | ||||
−0.394573 | + | 0.918865i | \(0.629107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1001 | 0.596073 | 0.298036 | − | 0.954555i | \(-0.403668\pi\) | ||||
0.298036 | + | 0.954555i | \(0.403668\pi\) | |||||||
\(824\) | −7.44969 | −0.259522 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0994 | 0.420991 | ||||||||
\(827\) | −0.366688 | −0.0127510 | −0.00637549 | − | 0.999980i | \(-0.502029\pi\) | ||||
−0.00637549 | + | 0.999980i | \(0.502029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.24917 | −0.251774 | −0.125887 | − | 0.992045i | \(-0.540178\pi\) | ||||
−0.125887 | + | 0.992045i | \(0.540178\pi\) | |||||||
\(830\) | − | 4.64497i | − | 0.161229i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.36261i | 0.220584i | ||||||||
\(833\) | −7.67213 | −0.265824 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.12856i | 0.108268i | ||||||||
\(836\) | 0.349474 | − | 2.26322i | 0.0120868 | − | 0.0782752i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.0977i | 0.763351i | ||||||||
\(839\) | − | 16.1924i | − | 0.559022i | −0.960142 | − | 0.279511i | \(-0.909828\pi\) | ||
0.960142 | − | 0.279511i | \(-0.0901724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.7536 | 2.02599 | ||||||||
\(842\) | −3.16019 | −0.108907 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 27.0878i | − | 0.932401i | ||||||
\(845\) | 26.6177i | 0.915677i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.31800 | + | 10.4877i | −0.114008 | + | 0.360360i | ||||
\(848\) | 7.24488i | 0.248790i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 31.1639 | 1.06891 | ||||||||
\(851\) | − | 12.6727i | − | 0.434414i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.4113i | − | 0.664629i | −0.943169 | − | 0.332315i | \(-0.892170\pi\) | ||
0.943169 | − | 0.332315i | \(-0.107830\pi\) | |||||||
\(854\) | 8.29965 | 0.284008 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.91251 | 0.133727 | ||||||||
\(857\) | 15.2405 | 0.520607 | 0.260303 | − | 0.965527i | \(-0.416177\pi\) | ||||
0.260303 | + | 0.965527i | \(0.416177\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0502 | 0.513506 | 0.256753 | − | 0.966477i | \(-0.417347\pi\) | ||||
0.256753 | + | 0.966477i | \(0.417347\pi\) | |||||||
\(860\) | −0.769764 | −0.0262487 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.7860 | −1.04857 | ||||||||
\(863\) | − | 10.3687i | − | 0.352956i | −0.984305 | − | 0.176478i | \(-0.943530\pi\) | ||
0.984305 | − | 0.176478i | \(-0.0564705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 6.10725i | − | 0.207653i | ||||||
\(866\) | −16.6539 | −0.565921 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.20608i | 0.142764i | ||||||||
\(869\) | 1.20458 | − | 7.80098i | 0.0408626 | − | 0.264630i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 78.1474i | − | 2.64793i | ||||||
\(872\) | 15.5606i | 0.526950i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.10223 | −0.0711089 | ||||||||
\(875\) | 8.77673 | 0.296707 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.8867i | 1.21181i | 0.795538 | + | 0.605904i | \(0.207189\pi\) | ||||
−0.795538 | + | 0.605904i | \(0.792811\pi\) | |||||||
\(878\) | − | 31.6856i | − | 1.06934i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.490204 | + | 3.17461i | −0.0165248 | + | 0.107016i | ||||
\(881\) | 47.2646i | 1.59238i | 0.605044 | + | 0.796192i | \(0.293156\pi\) | ||||
−0.605044 | + | 0.796192i | \(0.706844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7187 | 0.831849 | 0.415925 | − | 0.909399i | \(-0.363458\pi\) | ||||
0.415925 | + | 0.909399i | \(0.363458\pi\) | |||||||
\(884\) | 48.8147i | 1.64182i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 11.0473i | − | 0.371142i | ||||||
\(887\) | 20.2723 | 0.680678 | 0.340339 | − | 0.940303i | \(-0.389458\pi\) | ||||
0.340339 | + | 0.940303i | \(0.389458\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2658 | −0.646154 | ||||||||
\(890\) | −7.00386 | −0.234770 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.796023 | −0.0266528 | ||||||||
\(893\) | 5.65868 | 0.189361 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.3093 | −0.478308 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.1346i | 0.738640i | ||||||||
\(899\) | 39.4013 | 1.31411 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.5837i | 1.85176i | ||||||||
\(902\) | 1.14550 | + | 0.176881i | 0.0381409 | + | 0.00588949i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.2751i | 0.474783i | ||||||||
\(905\) | 6.30684i | 0.209647i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.0305 | −0.665102 | −0.332551 | − | 0.943085i | \(-0.607909\pi\) | ||||
−0.332551 | + | 0.943085i | \(0.607909\pi\) | |||||||
\(908\) | −22.1143 | −0.733890 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.16234i | 0.204279i | ||||||||
\(911\) | 41.4786i | 1.37425i | 0.726541 | + | 0.687123i | \(0.241127\pi\) | ||||
−0.726541 | + | 0.687123i | \(0.758873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.7200 | − | 2.42739i | −0.520256 | − | 0.0803349i | ||||
\(914\) | − | 26.2665i | − | 0.868819i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.8581 | 0.887416 | ||||||||
\(917\) | 18.7832i | 0.620277i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 19.1193i | − | 0.630688i | −0.948977 | − | 0.315344i | \(-0.897880\pi\) | ||
0.948977 | − | 0.315344i | \(-0.102120\pi\) | |||||||
\(920\) | 2.94878 | 0.0972183 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.7454 | 0.584414 | ||||||||
\(923\) | −31.6963 | −1.04330 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.9072 | −0.555907 | ||||||||
\(926\) | 23.8222 | 0.782847 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.36769 | 0.307509 | ||||||||
\(929\) | − | 33.3761i | − | 1.09503i | −0.836795 | − | 0.547516i | \(-0.815573\pi\) | ||
0.836795 | − | 0.547516i | \(-0.184427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.690475i | − | 0.0226294i | ||||||
\(932\) | −12.4954 | −0.409302 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 11.2649i | − | 0.368600i | ||||||
\(935\) | −3.76091 | + | 24.3560i | −0.122995 | + | 0.796526i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6228i | 1.09841i | 0.835688 | + | 0.549204i | \(0.185069\pi\) | ||||
−0.835688 | + | 0.549204i | \(0.814931\pi\) | |||||||
\(938\) | − | 12.2823i | − | 0.401031i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.93739 | −0.258889 | ||||||||
\(941\) | −2.54376 | −0.0829241 | −0.0414620 | − | 0.999140i | \(-0.513202\pi\) | ||||
−0.0414620 | + | 0.999140i | \(0.513202\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.06401i | − | 0.0346490i | ||||||
\(944\) | − | 12.0994i | − | 0.393801i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.402266 | + | 2.60511i | −0.0130788 | + | 0.0846995i | ||||
\(947\) | − | 14.4954i | − | 0.471039i | −0.971870 | − | 0.235519i | \(-0.924321\pi\) | ||
0.971870 | − | 0.235519i | \(-0.0756791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.4386 | −2.05930 | ||||||||
\(950\) | 2.80468i | 0.0909959i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.67213i | 0.248655i | ||||||||
\(953\) | −20.0850 | −0.650616 | −0.325308 | − | 0.945608i | \(-0.605468\pi\) | ||||
−0.325308 | + | 0.945608i | \(0.605468\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.6291 | −0.570463 | ||||||||
\(956\) | 11.4659 | 0.370834 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.58585 | −0.309705 | ||||||||
\(959\) | 12.8552 | 0.415116 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.3089 | −0.429319 | ||||||||
\(962\) | − | 26.4833i | − | 0.853856i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 8.26479i | − | 0.266191i | ||||||
\(965\) | 5.46116 | 0.175801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.8984i | 1.12226i | 0.827729 | + | 0.561128i | \(0.189632\pi\) | ||||
−0.827729 | + | 0.561128i | \(0.810368\pi\) | |||||||
\(968\) | 10.4877 | + | 3.31800i | 0.337086 | + | 0.106644i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.70093i | 0.0867216i | ||||||||
\(971\) | 15.1574i | 0.486424i | 0.969973 | + | 0.243212i | \(0.0782010\pi\) | ||||
−0.969973 | + | 0.243212i | \(0.921799\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.8642 | 0.412409 | ||||||||
\(974\) | 6.21142 | 0.199027 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 8.29965i | − | 0.265665i | ||||||
\(977\) | − | 37.3885i | − | 1.19616i | −0.801435 | − | 0.598081i | \(-0.795930\pi\) | ||
0.801435 | − | 0.598081i | \(-0.204070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.66011 | + | 23.7032i | −0.116978 | + | 0.757558i | ||||
\(980\) | 0.968524i | 0.0309384i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.06426 | −0.289252 | ||||||||
\(983\) | − | 1.12437i | − | 0.0358619i | −0.999839 | − | 0.0179310i | \(-0.994292\pi\) | ||
0.999839 | − | 0.0179310i | \(-0.00570791\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.2758i | 0.327413i | ||||||||
\(986\) | 71.8701 | 2.28881 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.39322 | −0.139767 | ||||||||
\(989\) | 2.41979 | 0.0769450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3347 | 0.677719 | 0.338859 | − | 0.940837i | \(-0.389959\pi\) | ||||
0.338859 | + | 0.940837i | \(0.389959\pi\) | |||||||
\(992\) | 4.20608 | 0.133543 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.98166 | −0.158009 | ||||||||
\(995\) | − | 15.8863i | − | 0.503629i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.9595i | 0.917156i | 0.888654 | + | 0.458578i | \(0.151641\pi\) | ||||
−0.888654 | + | 0.458578i | \(0.848359\pi\) | |||||||
\(998\) | −40.7758 | −1.29073 | ||||||||
\(999\) | 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 | 1386.2.c.b.197.5 | yes | 12 | |
3.2 | odd | 2 | 1386.2.c.a.197.8 | yes | 12 | ||
11.10 | odd | 2 | 1386.2.c.a.197.5 | ✓ | 12 | ||
33.32 | even | 2 | inner | 1386.2.c.b.197.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.c.a.197.5 | ✓ | 12 | 11.10 | odd | 2 | ||
1386.2.c.a.197.8 | yes | 12 | 3.2 | odd | 2 | ||
1386.2.c.b.197.5 | yes | 12 | 1.1 | even | 1 | trivial | |
1386.2.c.b.197.8 | yes | 12 | 33.32 | even | 2 | inner |