Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(319,384)]
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, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (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: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.3.b.b.319.4 |
$q$-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 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 6.92820i | − 1.38564i | −0.721110 | − | 0.692820i | \(-0.756368\pi\) | ||||
0.721110 | − | 0.692820i | \(-0.243632\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0000i | 1.71429i | 0.515079 | + | 0.857143i | \(0.327763\pi\) | ||||
−0.515079 | + | 0.857143i | \(0.672237\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.92820 | 0.629837 | 0.314918 | − | 0.949119i | \(-0.398023\pi\) | ||||
0.314918 | + | 0.949119i | \(0.398023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.8564i | 1.06588i | 0.846154 | + | 0.532939i | \(0.178912\pi\) | ||||
−0.846154 | + | 0.532939i | \(0.821088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 12.0000i | − 0.800000i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.0000 | 0.823529 | 0.411765 | − | 0.911290i | \(-0.364913\pi\) | ||||
0.411765 | + | 0.911290i | \(0.364913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34.6410 | 1.82321 | 0.911606 | − | 0.411066i | \(-0.134843\pi\) | ||||
0.911606 | + | 0.411066i | \(0.134843\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 20.7846i | 0.989743i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 24.0000i | − 1.04348i | −0.853105 | − | 0.521739i | \(-0.825283\pi\) | ||||
0.853105 | − | 0.521739i | \(-0.174717\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.0000 | −0.920000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 34.6410i | − 1.19452i | −0.802049 | − | 0.597259i | \(-0.796256\pi\) | ||||
0.802049 | − | 0.597259i | \(-0.203744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 12.0000i | − 0.387097i | −0.981091 | − | 0.193548i | \(-0.938000\pi\) | ||||
0.981091 | − | 0.193548i | \(-0.0619996\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000 | 0.363636 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 83.1384 | 2.37538 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 27.7128i | − 0.748995i | −0.927228 | − | 0.374497i | \(-0.877815\pi\) | ||||
0.927228 | − | 0.374497i | \(-0.122185\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.0000i | 0.615385i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14.0000 | −0.341463 | −0.170732 | − | 0.985318i | \(-0.554613\pi\) | ||||
−0.170732 | + | 0.985318i | \(0.554613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.92820 | 0.161121 | 0.0805605 | − | 0.996750i | \(-0.474329\pi\) | ||||
0.0805605 | + | 0.996750i | \(0.474329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 20.7846i | − 0.461880i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.0000i | 1.53191i | 0.642891 | + | 0.765957i | \(0.277735\pi\) | ||||
−0.642891 | + | 0.765957i | \(0.722265\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −95.0000 | −1.93878 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24.2487 | 0.475465 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 62.3538i | 1.17649i | 0.808684 | + | 0.588244i | \(0.200180\pi\) | ||||
−0.808684 | + | 0.588244i | \(0.799820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 48.0000i | − 0.872727i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60.0000 | 1.05263 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −48.4974 | −0.821990 | −0.410995 | − | 0.911638i | \(-0.634819\pi\) | ||||
−0.410995 | + | 0.911638i | \(0.634819\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 55.4256i | 0.908617i | 0.890844 | + | 0.454308i | \(0.150114\pi\) | ||||
−0.890844 | + | 0.454308i | \(0.849886\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 36.0000i | 0.571429i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 96.0000 | 1.47692 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 90.0666 | 1.34428 | 0.672139 | − | 0.740425i | \(-0.265376\pi\) | ||||
0.672139 | + | 0.740425i | \(0.265376\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 41.5692i | − 0.602452i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 24.0000i | 0.338028i | 0.985614 | + | 0.169014i | \(0.0540583\pi\) | ||||
−0.985614 | + | 0.169014i | \(0.945942\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −50.0000 | −0.684932 | −0.342466 | − | 0.939530i | \(-0.611262\pi\) | ||||
−0.342466 | + | 0.939530i | \(0.611262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −39.8372 | −0.531162 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 83.1384i | 1.07972i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 12.0000i | − 0.151899i | −0.997112 | − | 0.0759494i | \(-0.975801\pi\) | ||||
0.997112 | − | 0.0759494i | \(-0.0241987\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −20.7846 | −0.250417 | −0.125208 | − | 0.992130i | \(-0.539960\pi\) | ||||
−0.125208 | + | 0.992130i | \(0.539960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 96.9948i | − 1.14112i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 60.0000i | − 0.689655i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 62.0000 | 0.696629 | 0.348315 | − | 0.937378i | \(-0.386754\pi\) | ||||
0.348315 | + | 0.937378i | \(0.386754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −166.277 | −1.82722 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 20.7846i | − 0.223490i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 240.000i | − 2.52632i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −146.000 | −1.50515 | −0.752577 | − | 0.658504i | \(-0.771190\pi\) | ||||
−0.752577 | + | 0.658504i | \(0.771190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.7846 | 0.209946 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 20.7846i | − 0.205788i | −0.994692 | − | 0.102894i | \(-0.967190\pi\) | ||||
0.994692 | − | 0.102894i | \(-0.0328103\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 84.0000i | 0.815534i | 0.913086 | + | 0.407767i | \(0.133692\pi\) | ||||
−0.913086 | + | 0.407767i | \(0.866308\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 144.000 | 1.37143 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −131.636 | −1.23024 | −0.615121 | − | 0.788433i | \(-0.710893\pi\) | ||||
−0.615121 | + | 0.788433i | \(0.710893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 180.133i | − 1.65260i | −0.563231 | − | 0.826299i | \(-0.690442\pi\) | ||||
0.563231 | − | 0.826299i | \(-0.309558\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 48.0000i | − 0.432432i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 130.000 | 1.15044 | 0.575221 | − | 0.817998i | \(-0.304916\pi\) | ||||
0.575221 | + | 0.817998i | \(0.304916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −166.277 | −1.44589 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 41.5692i | 0.355292i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 168.000i | 1.41176i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −73.0000 | −0.603306 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.2487 | −0.197144 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 13.8564i | − 0.110851i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 204.000i | 1.60630i | 0.595777 | + | 0.803150i | \(0.296844\pi\) | ||||
−0.595777 | + | 0.803150i | \(0.703156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | 0.0930233 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.7846 | −0.158661 | −0.0793306 | − | 0.996848i | \(-0.525278\pi\) | ||||
−0.0793306 | + | 0.996848i | \(0.525278\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 415.692i | 3.12551i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 36.0000i | − 0.266667i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −206.000 | −1.50365 | −0.751825 | − | 0.659363i | \(-0.770826\pi\) | ||||
−0.751825 | + | 0.659363i | \(0.770826\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −48.4974 | −0.348902 | −0.174451 | − | 0.984666i | \(-0.555815\pi\) | ||||
−0.174451 | + | 0.984666i | \(0.555815\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 124.708i | 0.884451i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 96.0000i | 0.671329i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −240.000 | −1.65517 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −164.545 | −1.11935 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 200.918i | − 1.34844i | −0.738530 | − | 0.674221i | \(-0.764479\pi\) | ||||
0.738530 | − | 0.674221i | \(-0.235521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 36.0000i | − 0.238411i | −0.992870 | − | 0.119205i | \(-0.961965\pi\) | ||||
0.992870 | − | 0.119205i | \(-0.0380347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 42.0000 | 0.274510 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −83.1384 | −0.536377 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 27.7128i | 0.176515i | 0.996098 | + | 0.0882574i | \(0.0281298\pi\) | ||||
−0.996098 | + | 0.0882574i | \(0.971870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 108.000i | 0.679245i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 288.000 | 1.78882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 62.3538 | 0.382539 | 0.191269 | − | 0.981538i | \(-0.438740\pi\) | ||||
0.191269 | + | 0.981538i | \(0.438740\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 83.1384i | − 0.503869i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 240.000i | − 1.43713i | −0.695462 | − | 0.718563i | \(-0.744800\pi\) | ||||
0.695462 | − | 0.718563i | \(-0.255200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 103.923 | 0.607737 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 131.636i | − 0.760901i | −0.924801 | − | 0.380450i | \(-0.875769\pi\) | ||||
0.924801 | − | 0.380450i | \(-0.124231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 276.000i | − 1.57714i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −84.0000 | −0.474576 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −270.200 | −1.50950 | −0.754748 | − | 0.656014i | \(-0.772241\pi\) | ||||
−0.754748 | + | 0.656014i | \(0.772241\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 207.846i | − 1.14832i | −0.818743 | − | 0.574160i | \(-0.805329\pi\) | ||||
0.818743 | − | 0.574160i | \(-0.194671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 96.0000i | 0.524590i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −192.000 | −1.03784 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 96.9948 | 0.518689 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 62.3538i | 0.329914i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 240.000i | 1.25654i | 0.777994 | + | 0.628272i | \(0.216238\pi\) | ||||
−0.777994 | + | 0.628272i | \(0.783762\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.0103627 | −0.00518135 | − | 0.999987i | \(-0.501649\pi\) | ||||
−0.00518135 | + | 0.999987i | \(0.501649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 166.277 | 0.852702 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 131.636i | − 0.668202i | −0.942537 | − | 0.334101i | \(-0.891567\pi\) | ||||
0.942537 | − | 0.334101i | \(-0.108433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 300.000i | − 1.50754i | −0.657140 | − | 0.753769i | \(-0.728234\pi\) | ||||
0.657140 | − | 0.753769i | \(-0.271766\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 156.000 | 0.776119 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 415.692 | 2.04774 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 96.9948i | 0.473146i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 72.0000i | − 0.347826i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 240.000 | 1.14833 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −270.200 | −1.28057 | −0.640284 | − | 0.768138i | \(-0.721183\pi\) | ||||
−0.640284 | + | 0.768138i | \(0.721183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.5692i | 0.195161i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 48.0000i | − 0.223256i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 144.000 | 0.663594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −86.6025 | −0.395445 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 193.990i | 0.877781i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 132.000i | − 0.591928i | −0.955199 | − | 0.295964i | \(-0.904359\pi\) | ||||
0.955199 | − | 0.295964i | \(-0.0956409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −69.0000 | −0.306667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 200.918 | 0.885101 | 0.442550 | − | 0.896744i | \(-0.354074\pi\) | ||||
0.442550 | + | 0.896744i | \(0.354074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 69.2820i | − 0.302542i | −0.988492 | − | 0.151271i | \(-0.951663\pi\) | ||||
0.988492 | − | 0.151271i | \(-0.0483366\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 144.000i | 0.623377i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −130.000 | −0.557940 | −0.278970 | − | 0.960300i | \(-0.589993\pi\) | ||||
−0.278970 | + | 0.960300i | \(0.589993\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 498.831 | 2.12268 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 20.7846i | − 0.0876988i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 96.0000i | 0.401674i | 0.979625 | + | 0.200837i | \(0.0643661\pi\) | ||||
−0.979625 | + | 0.200837i | \(0.935634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 190.000 | 0.788382 | 0.394191 | − | 0.919029i | \(-0.371025\pi\) | ||||
0.394191 | + | 0.919029i | \(0.371025\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 658.179i | 2.68645i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 480.000i | 1.94332i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −36.0000 | −0.144578 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 256.344 | 1.02129 | 0.510644 | − | 0.859792i | \(-0.329407\pi\) | ||||
0.510644 | + | 0.859792i | \(0.329407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 166.277i | − 0.657221i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 168.000i | − 0.658824i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −254.000 | −0.988327 | −0.494163 | − | 0.869369i | \(-0.664526\pi\) | ||||
−0.494163 | + | 0.869369i | \(0.664526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 332.554 | 1.28399 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 103.923i | − 0.398173i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 432.000 | 1.63019 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 107.387 | 0.402199 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6.92820i | − 0.0257554i | −0.999917 | − | 0.0128777i | \(-0.995901\pi\) | ||||
0.999917 | − | 0.0128777i | \(-0.00409921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 348.000i | 1.28413i | 0.766649 | + | 0.642066i | \(0.221923\pi\) | ||||
−0.766649 | + | 0.642066i | \(0.778077\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −288.000 | −1.05495 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −159.349 | −0.579450 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 41.5692i | − 0.150069i | −0.997181 | − | 0.0750347i | \(-0.976093\pi\) | ||||
0.997181 | − | 0.0750347i | \(-0.0239068\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 36.0000i | − 0.129032i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −34.0000 | −0.120996 | −0.0604982 | − | 0.998168i | \(-0.519269\pi\) | ||||
−0.0604982 | + | 0.998168i | \(0.519269\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 311.769 | 1.10166 | 0.550829 | − | 0.834618i | \(-0.314312\pi\) | ||||
0.550829 | + | 0.834618i | \(0.314312\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 415.692i | − 1.45857i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 168.000i | − 0.585366i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −93.0000 | −0.321799 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −252.879 | −0.869001 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 159.349i | − 0.543852i | −0.962318 | − | 0.271926i | \(-0.912339\pi\) | ||||
0.962318 | − | 0.271926i | \(-0.0876606\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 336.000i | 1.13898i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 36.0000 | 0.121212 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 332.554 | 1.11222 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 83.1384i | 0.276207i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 36.0000i | − 0.118812i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 384.000 | 1.25902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −408.764 | −1.33148 | −0.665739 | − | 0.746184i | \(-0.731884\pi\) | ||||
−0.665739 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 145.492i | 0.470849i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 48.0000i | − 0.154341i | −0.997018 | − | 0.0771704i | \(-0.975411\pi\) | ||||
0.997018 | − | 0.0771704i | \(-0.0245886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 98.0000 | 0.313099 | 0.156550 | − | 0.987670i | \(-0.449963\pi\) | ||||
0.156550 | + | 0.987670i | \(0.449963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 249.415 | 0.791795 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 173.205i | − 0.546388i | −0.961959 | − | 0.273194i | \(-0.911920\pi\) | ||||
0.961959 | − | 0.273194i | \(-0.0880801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 240.000i | − 0.752351i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −228.000 | −0.710280 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 484.974 | 1.50147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 318.697i | − 0.980607i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 312.000i | − 0.954128i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −864.000 | −2.62614 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7846 | −0.0627934 | −0.0313967 | − | 0.999507i | \(-0.509996\pi\) | ||||
−0.0313967 | + | 0.999507i | \(0.509996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 83.1384i | − 0.249665i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 624.000i | − 1.86269i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 50.0000 | 0.148368 | 0.0741840 | − | 0.997245i | \(-0.476365\pi\) | ||||
0.0741840 | + | 0.997245i | \(0.476365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 225.167 | 0.664208 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 83.1384i | − 0.243808i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 552.000i | − 1.60933i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −288.000 | −0.834783 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −408.764 | −1.17799 | −0.588997 | − | 0.808135i | \(-0.700477\pi\) | ||||
−0.588997 | + | 0.808135i | \(0.700477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 498.831i | 1.42931i | 0.699475 | + | 0.714657i | \(0.253417\pi\) | ||||
−0.699475 | + | 0.714657i | \(0.746583\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 72.0000i | 0.205128i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −542.000 | −1.53541 | −0.767705 | − | 0.640803i | \(-0.778602\pi\) | ||||
−0.767705 | + | 0.640803i | \(0.778602\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 166.277 | 0.468386 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 290.985i | 0.815083i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 312.000i | 0.869081i | 0.900652 | + | 0.434540i | \(0.143089\pi\) | ||||
−0.900652 | + | 0.434540i | \(0.856911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 839.000 | 2.32410 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −126.440 | −0.348319 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 346.410i | 0.949069i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 276.000i | 0.752044i | 0.926611 | + | 0.376022i | \(0.122708\pi\) | ||||
−0.926611 | + | 0.376022i | \(0.877292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −42.0000 | −0.113821 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −748.246 | −2.01684 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 24.0000i | − 0.0640000i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 480.000 | 1.27321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −325.626 | −0.859170 | −0.429585 | − | 0.903026i | \(-0.641340\pi\) | ||||
−0.429585 | + | 0.903026i | \(0.641340\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 353.338i | 0.927397i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 720.000i | 1.87990i | 0.341318 | + | 0.939948i | \(0.389127\pi\) | ||||
−0.341318 | + | 0.939948i | \(0.610873\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 576.000 | 1.49610 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.7846 | 0.0537070 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.7846i | 0.0534309i | 0.999643 | + | 0.0267154i | \(0.00850480\pi\) | ||||
−0.999643 | + | 0.0267154i | \(0.991495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 336.000i | − 0.859335i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −36.0000 | −0.0916031 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −83.1384 | −0.210477 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 221.703i | 0.558445i | 0.960226 | + | 0.279222i | \(0.0900766\pi\) | ||||
−0.960226 | + | 0.279222i | \(0.909923\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 720.000i | 1.80451i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −178.000 | −0.443890 | −0.221945 | − | 0.975059i | \(-0.571241\pi\) | ||||
−0.221945 | + | 0.975059i | \(0.571241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 166.277 | 0.412598 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 62.3538i | − 0.153960i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 192.000i | − 0.471744i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −142.000 | −0.347188 | −0.173594 | − | 0.984817i | \(-0.555538\pi\) | ||||
−0.173594 | + | 0.984817i | \(0.555538\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −356.802 | −0.868133 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 581.969i | − 1.40913i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 144.000i | 0.346988i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −84.0000 | −0.201439 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −103.923 | −0.248026 | −0.124013 | − | 0.992281i | \(-0.539577\pi\) | ||||
−0.124013 | + | 0.992281i | \(0.539577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 263.272i | − 0.625349i | −0.949860 | − | 0.312674i | \(-0.898775\pi\) | ||||
0.949860 | − | 0.312674i | \(-0.101225\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 216.000i | 0.510638i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −322.000 | −0.757647 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −665.108 | −1.55763 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 166.277i | 0.387592i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 168.000i | − 0.389791i | −0.980824 | − | 0.194896i | \(-0.937563\pi\) | ||||
0.980824 | − | 0.194896i | \(-0.0624368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 526.000 | 1.21478 | 0.607390 | − | 0.794404i | \(-0.292216\pi\) | ||||
0.607390 | + | 0.794404i | \(0.292216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −415.692 | −0.955614 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 831.384i | − 1.90248i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 444.000i | − 1.01139i | −0.862712 | − | 0.505695i | \(-0.831236\pi\) | ||||
0.862712 | − | 0.505695i | \(-0.168764\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −285.000 | −0.646259 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −214.774 | −0.484818 | −0.242409 | − | 0.970174i | \(-0.577938\pi\) | ||||
−0.242409 | + | 0.970174i | \(0.577938\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 429.549i | − 0.965278i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 348.000i | − 0.778523i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 494.000 | 1.10022 | 0.550111 | − | 0.835091i | \(-0.314585\pi\) | ||||
0.550111 | + | 0.835091i | \(0.314585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −96.9948 | −0.215066 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 62.3538i | − 0.137646i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1152.00i | 2.53187i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −46.0000 | −0.100656 | −0.0503282 | − | 0.998733i | \(-0.516027\pi\) | ||||
−0.0503282 | + | 0.998733i | \(0.516027\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 72.7461 | 0.158488 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 769.031i | − 1.66818i | −0.551629 | − | 0.834090i | \(-0.685994\pi\) | ||||
0.551629 | − | 0.834090i | \(-0.314006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 132.000i | − 0.285097i | −0.989788 | − | 0.142549i | \(-0.954470\pi\) | ||||
0.989788 | − | 0.142549i | \(-0.0455297\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −144.000 | −0.309677 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 117.779 | 0.252204 | 0.126102 | − | 0.992017i | \(-0.459753\pi\) | ||||
0.126102 | + | 0.992017i | \(0.459753\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1080.80i | 2.30448i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.0000i | 0.101911i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 48.0000 | 0.101480 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −796.743 | −1.67735 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 187.061i | 0.392162i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 408.000i | − 0.851775i | −0.904776 | − | 0.425887i | \(-0.859962\pi\) | ||||
0.904776 | − | 0.425887i | \(-0.140038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 384.000 | 0.798337 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 498.831 | 1.03278 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1011.52i | 2.08560i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 444.000i | 0.911704i | 0.890056 | + | 0.455852i | \(0.150665\pi\) | ||||
−0.890056 | + | 0.455852i | \(0.849335\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 108.000 | 0.220859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −824.456 | −1.67914 | −0.839568 | − | 0.543254i | \(-0.817192\pi\) | ||||
−0.839568 | + | 0.543254i | \(0.817192\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 484.974i | − 0.983721i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 144.000i | − 0.290909i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −288.000 | −0.579477 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −381.051 | −0.763630 | −0.381815 | − | 0.924239i | \(-0.624701\pi\) | ||||
−0.381815 | + | 0.924239i | \(0.624701\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 415.692i | − 0.829725i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 744.000i | − 1.47913i | −0.673088 | − | 0.739563i | \(-0.735032\pi\) | ||||
0.673088 | − | 0.739563i | \(-0.264968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −144.000 | −0.285149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.8372 | −0.0785743 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 852.169i | 1.67420i | 0.547048 | + | 0.837101i | \(0.315751\pi\) | ||||
−0.547048 | + | 0.837101i | \(0.684249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 600.000i | − 1.17417i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 180.000 | 0.350877 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 581.969 | 1.13004 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 498.831i | 0.964856i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 228.000i | − 0.439306i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 82.0000 | 0.157390 | 0.0786948 | − | 0.996899i | \(-0.474925\pi\) | ||||
0.0786948 | + | 0.996899i | \(0.474925\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 311.769 | 0.596117 | 0.298058 | − | 0.954548i | \(-0.403661\pi\) | ||||
0.298058 | + | 0.954548i | \(0.403661\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 478.046i | − 0.910564i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 168.000i | − 0.318786i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −47.0000 | −0.0888469 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −145.492 | −0.273997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 193.990i | − 0.363958i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 912.000i | 1.70467i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −468.000 | −0.871508 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −658.179 | −1.22111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 96.9948i | 0.179288i | 0.995974 | + | 0.0896440i | \(0.0285729\pi\) | ||||
−0.995974 | + | 0.0896440i | \(0.971427\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 360.000i | − 0.662983i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1248.00 | −2.28991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6410 | 0.0633291 | 0.0316645 | − | 0.999499i | \(-0.489919\pi\) | ||||
0.0316645 | + | 0.999499i | \(0.489919\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 166.277i | 0.302872i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1200.00i | − 2.17786i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 144.000 | 0.260398 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −332.554 | −0.599196 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 949.164i | 1.70406i | 0.523489 | + | 0.852032i | \(0.324630\pi\) | ||||
−0.523489 | + | 0.852032i | \(0.675370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 96.0000i | 0.171735i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 168.000 | 0.299465 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 949.164 | 1.68590 | 0.842952 | − | 0.537989i | \(-0.180816\pi\) | ||||
0.842952 | + | 0.537989i | \(0.180816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 900.666i | − 1.59410i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 108.000i | 0.190476i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 658.000 | 1.15641 | 0.578207 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578207 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 256.344 | 0.448938 | 0.224469 | − | 0.974481i | \(-0.427935\pi\) | ||||
0.224469 | + | 0.974481i | \(0.427935\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 415.692i | 0.725466i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 552.000i | 0.960000i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −526.000 | −0.911612 | −0.455806 | − | 0.890079i | \(-0.650649\pi\) | ||||
−0.455806 | + | 0.890079i | \(0.650649\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.46410 | −0.00598290 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 249.415i | − 0.429286i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 432.000i | 0.740995i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 288.000 | 0.492308 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −464.190 | −0.790783 | −0.395391 | − | 0.918513i | \(-0.629391\pi\) | ||||
−0.395391 | + | 0.918513i | \(0.629391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 415.692i | − 0.705759i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 228.000i | − 0.385787i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 514.000 | 0.866779 | 0.433390 | − | 0.901207i | \(-0.357317\pi\) | ||||
0.433390 | + | 0.901207i | \(0.357317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1163.94 | 1.95620 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 519.615i | − 0.870377i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 408.000i | 0.681135i | 0.940220 | + | 0.340568i | \(0.110619\pi\) | ||||
−0.940220 | + | 0.340568i | \(0.889381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −818.000 | −1.36106 | −0.680532 | − | 0.732718i | \(-0.738251\pi\) | ||||
−0.680532 | + | 0.732718i | \(0.738251\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 270.200 | 0.448093 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 505.759i | 0.835965i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 684.000i | 1.12685i | 0.826166 | + | 0.563427i | \(0.190517\pi\) | ||||
−0.826166 | + | 0.563427i | \(0.809483\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 720.000 | 1.18227 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −997.661 | −1.63283 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 498.831i | − 0.813753i | −0.913483 | − | 0.406877i | \(-0.866618\pi\) | ||||
0.913483 | − | 0.406877i | \(-0.133382\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 168.000i | 0.273171i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −322.000 | −0.521880 | −0.260940 | − | 0.965355i | \(-0.584032\pi\) | ||||
−0.260940 | + | 0.965355i | \(0.584032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 90.0666 | 0.145503 | 0.0727517 | − | 0.997350i | \(-0.476822\pi\) | ||||
0.0727517 | + | 0.997350i | \(0.476822\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 124.708i | − 0.200817i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 744.000i | 1.19422i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −671.000 | −1.07360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 415.692 | 0.662986 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 387.979i | − 0.616819i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 252.000i | 0.399366i | 0.979861 | + | 0.199683i | \(0.0639912\pi\) | ||||
−0.979861 | + | 0.199683i | \(0.936009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −468.000 | −0.739336 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1413.35 | 2.22575 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1316.36i | − 2.06650i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 72.0000i | 0.112676i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −370.000 | −0.577223 | −0.288612 | − | 0.957446i | \(-0.593194\pi\) | ||||
−0.288612 | + | 0.957446i | \(0.593194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1032.30 | 1.60545 | 0.802723 | − | 0.596352i | \(-0.203384\pi\) | ||||
0.802723 | + | 0.596352i | \(0.203384\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 83.1384i | − 0.128897i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 216.000i | − 0.333849i | −0.985970 | − | 0.166924i | \(-0.946616\pi\) | ||||
0.985970 | − | 0.166924i | \(-0.0533835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −336.000 | −0.517720 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 249.415 | 0.383126 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 145.492i | 0.222806i | 0.993775 | + | 0.111403i | \(0.0355344\pi\) | ||||
−0.993775 | + | 0.111403i | \(0.964466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 144.000i | 0.219847i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −150.000 | −0.228311 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1060.02 | 1.60852 | 0.804260 | − | 0.594277i | \(-0.202562\pi\) | ||||
0.804260 | + | 0.594277i | \(0.202562\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1302.50i | 1.97050i | 0.171114 | + | 0.985251i | \(0.445263\pi\) | ||||
−0.171114 | + | 0.985251i | \(0.554737\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 336.000i | 0.506787i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2880.00 | 4.33083 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −831.384 | −1.24645 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 228.631i | − 0.341750i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 384.000i | 0.572280i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1006.00 | 1.49480 | 0.747400 | − | 0.664375i | \(-0.231302\pi\) | ||||
0.747400 | + | 0.664375i | \(0.231302\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −119.512 | −0.177054 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 270.200i | 0.399114i | 0.979886 | + | 0.199557i | \(0.0639502\pi\) | ||||
−0.979886 | + | 0.199557i | \(0.936050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1752.00i | − 2.58027i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 348.000 | 0.511013 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1198.58 | 1.75487 | 0.877437 | − | 0.479692i | \(-0.159251\pi\) | ||||
0.877437 | + | 0.479692i | \(0.159251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1427.21i | 2.08352i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 120.000i | − 0.174672i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −864.000 | −1.25399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −436.477 | −0.631660 | −0.315830 | − | 0.948816i | \(-0.602283\pi\) | ||||
−0.315830 | + | 0.948816i | \(0.602283\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 249.415i | 0.359907i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 336.000i | 0.483453i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −196.000 | −0.281205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −225.167 | −0.322127 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 588.897i | − 0.840082i | −0.907505 | − | 0.420041i | \(-0.862016\pi\) | ||||
0.907505 | − | 0.420041i | \(-0.137984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 960.000i | − 1.36558i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 864.000 | 1.22553 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 249.415 | 0.352780 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 568.113i | − 0.801287i | −0.916234 | − | 0.400644i | \(-0.868787\pi\) | ||||
0.916234 | − | 0.400644i | \(-0.131213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 36.0000i | − 0.0506329i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −288.000 | −0.403927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 665.108 | 0.930220 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 166.277i | 0.231906i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 360.000i | − 0.500695i | −0.968156 | − | 0.250348i | \(-0.919455\pi\) | ||||
0.968156 | − | 0.250348i | \(-0.0805449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1008.00 | −1.39806 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 329.090 | 0.455172 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 796.743i | 1.09896i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 660.000i | − 0.907840i | −0.891042 | − | 0.453920i | \(-0.850025\pi\) | ||||
0.891042 | − | 0.453920i | \(-0.149975\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 96.9948 | 0.132688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 956.092i | 1.30435i | 0.758066 | + | 0.652177i | \(0.226144\pi\) | ||||
−0.758066 | + | 0.652177i | \(0.773856\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1140.00i | 1.55102i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 624.000 | 0.846676 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −547.328 | −0.740633 | −0.370317 | − | 0.928906i | \(-0.620751\pi\) | ||||
−0.370317 | + | 0.928906i | \(0.620751\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 831.384i | 1.12198i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 864.000i | − 1.16285i | −0.813599 | − | 0.581427i | \(-0.802495\pi\) | ||||
0.813599 | − | 0.581427i | \(-0.197505\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1392.00 | −1.86846 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62.3538 | −0.0834723 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1579.63i | − 2.10899i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 444.000i | − 0.591212i | −0.955310 | − | 0.295606i | \(-0.904478\pi\) | ||||
0.955310 | − | 0.295606i | \(-0.0955215\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 444.000 | 0.589641 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −249.415 | −0.330351 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 872.954i | 1.15318i | 0.817035 | + | 0.576588i | \(0.195616\pi\) | ||||
−0.817035 | + | 0.576588i | \(0.804384\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 288.000i | − 0.379447i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.0000 | −0.0183968 | −0.00919842 | − | 0.999958i | \(-0.502928\pi\) | ||||
−0.00919842 | + | 0.999958i | \(0.502928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2161.60 | 2.83303 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 290.985i | − 0.380372i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 672.000i | − 0.876141i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −194.000 | −0.252276 | −0.126138 | − | 0.992013i | \(-0.540258\pi\) | ||||
−0.126138 | + | 0.992013i | \(0.540258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −439.941 | −0.570611 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 713.605i | − 0.923163i | −0.887098 | − | 0.461581i | \(-0.847282\pi\) | ||||
0.887098 | − | 0.461581i | \(-0.152718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 276.000i | 0.356129i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 576.000 | 0.741313 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −484.974 | −0.622560 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 166.277i | 0.212903i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 180.000i | − 0.229885i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 192.000 | 0.244586 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1060.02 | 1.34691 | 0.673453 | − | 0.739230i | \(-0.264810\pi\) | ||||
0.673453 | + | 0.739230i | \(0.264810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1560.00i | 1.97219i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −768.000 | −0.968474 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 748.246 | 0.941190 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1461.85i | − 1.83419i | −0.398667 | − | 0.917096i | \(-0.630527\pi\) | ||||
0.398667 | − | 0.917096i | \(-0.369473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1008.00i | 1.26158i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 186.000 | 0.232210 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −346.410 | −0.431395 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1995.32i | − 2.47866i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 12.0000i | − 0.0148699i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1138.00 | 1.40667 | 0.703337 | − | 0.710856i | \(-0.251692\pi\) | ||||
0.703337 | + | 0.710856i | \(0.251692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −630.466 | −0.777394 | −0.388697 | − | 0.921366i | \(-0.627075\pi\) | ||||
−0.388697 | + | 0.921366i | \(0.627075\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 602.754i | 0.741394i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 432.000i | − 0.530061i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 240.000 | 0.293758 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −498.831 | −0.609073 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 256.344i | 0.312233i | 0.987739 | + | 0.156117i | \(0.0498976\pi\) | ||||
−0.987739 | + | 0.156117i | \(0.950102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 396.000i | 0.481166i | 0.970629 | + | 0.240583i | \(0.0773387\pi\) | ||||
−0.970629 | + | 0.240583i | \(0.922661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −276.000 | −0.334545 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 145.492 | 0.175928 | 0.0879639 | − | 0.996124i | \(-0.471964\pi\) | ||||
0.0879639 | + | 0.996124i | \(0.471964\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.5692i | 0.0501438i | 0.999686 | + | 0.0250719i | \(0.00798147\pi\) | ||||
−0.999686 | + | 0.0250719i | \(0.992019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 72.0000i | − 0.0866426i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1330.00 | −1.59664 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1662.77 | −1.99134 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 62.3538i | − 0.0744968i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1512.00i | 1.80215i | 0.433668 | + | 0.901073i | \(0.357219\pi\) | ||||
−0.433668 | + | 0.901073i | \(0.642781\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −359.000 | −0.426873 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −58.8897 | −0.0698573 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 159.349i | 0.188578i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 876.000i | − 1.03424i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 540.000 | 0.636042 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −665.108 | −0.781560 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 748.246i | − 0.877193i | −0.898684 | − | 0.438597i | \(-0.855476\pi\) | ||||
0.898684 | − | 0.438597i | \(-0.144524\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 720.000i | − 0.842105i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1042.00 | 1.21587 | 0.607935 | − | 0.793987i | \(-0.291998\pi\) | ||||
0.607935 | + | 0.793987i | \(0.291998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −159.349 | −0.185505 | −0.0927524 | − | 0.995689i | \(-0.529567\pi\) | ||||
−0.0927524 | + | 0.995689i | \(0.529567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 290.985i | − 0.337961i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1104.00i | − 1.27926i | −0.768684 | − | 0.639629i | \(-0.779088\pi\) | ||||
0.768684 | − | 0.639629i | \(-0.220912\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −912.000 | −1.05434 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −161.081 | −0.185791 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 83.1384i | − 0.0956714i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1248.00i | 1.43284i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −438.000 | −0.501718 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 166.277 | 0.190031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 554.256i | 0.631991i | 0.948761 | + | 0.315996i | \(0.102338\pi\) | ||||
−0.948761 | + | 0.315996i | \(0.897662\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 276.000i | − 0.313993i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 610.000 | 0.692395 | 0.346198 | − | 0.938162i | \(-0.387473\pi\) | ||||
0.346198 | + | 0.938162i | \(0.387473\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −76.2102 | −0.0863083 | −0.0431542 | − | 0.999068i | \(-0.513741\pi\) | ||||
−0.0431542 | + | 0.999068i | \(0.513741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 581.969i | 0.657592i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 384.000i | − 0.432920i | −0.976291 | − | 0.216460i | \(-0.930549\pi\) | ||||
0.976291 | − | 0.216460i | \(-0.0694511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2448.00 | −2.75366 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 62.3538 | 0.0699819 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2494.15i | 2.79300i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1872.00i | 2.09162i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 576.000 | 0.642140 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −415.692 | −0.462394 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 872.954i | 0.968872i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 144.000i | 0.159468i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1440.00 | −1.59116 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −713.605 | −0.786775 | −0.393388 | − | 0.919373i | \(-0.628697\pi\) | ||||
−0.393388 | + | 0.919373i | \(0.628697\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 62.3538i | − 0.0685961i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 864.000i | 0.948408i | 0.880415 | + | 0.474204i | \(0.157264\pi\) | ||||
−0.880415 | + | 0.474204i | \(0.842736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −144.000 | −0.157722 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 665.108 | 0.726893 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 249.415i | − 0.271991i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1068.00i | 1.16213i | 0.813856 | + | 0.581066i | \(0.197364\pi\) | ||||
−0.813856 | + | 0.581066i | \(0.802636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −708.000 | −0.768730 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −332.554 | −0.360297 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 637.395i | 0.689075i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 252.000i | 0.271845i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 110.000 | 0.118407 | 0.0592034 | − | 0.998246i | \(-0.481144\pi\) | ||||
0.0592034 | + | 0.998246i | \(0.481144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3290.90 | −3.53480 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 83.1384i | − 0.0891087i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 672.000i | − 0.718717i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1630.00 | 1.73959 | 0.869797 | − | 0.493409i | \(-0.164250\pi\) | ||||
0.869797 | + | 0.493409i | \(0.164250\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 169.741 | 0.180768 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 48.4974i | − 0.0515382i | −0.999668 | − | 0.0257691i | \(-0.991797\pi\) | ||||
0.999668 | − | 0.0257691i | \(-0.00820346\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 336.000i | 0.356310i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 432.000 | 0.457143 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1738.98 | −1.83630 | −0.918152 | − | 0.396229i | \(-0.870318\pi\) | ||||
−0.918152 | + | 0.396229i | \(0.870318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 692.820i | − 0.730053i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 300.000i | − 0.315457i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1714.00 | 1.79853 | 0.899265 | − | 0.437403i | \(-0.144102\pi\) | ||||
0.899265 | + | 0.437403i | \(0.144102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1662.77 | 1.74112 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 415.692i | − 0.434370i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2472.00i | − 2.57769i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 817.000 | 0.850156 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −394.908 | −0.410081 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.8564i | 0.0143590i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1212.00i | − 1.25336i | −0.779276 | − | 0.626680i | \(-0.784413\pi\) | ||||
0.779276 | − | 0.626680i | \(-0.215587\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 840.000 | 0.866873 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 311.769 | 0.321080 | 0.160540 | − | 0.987029i | \(-0.448676\pi\) | ||||
0.160540 | + | 0.987029i | \(0.448676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 581.969i | − 0.598118i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 552.000i | − 0.566154i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.0000 | 0.0143296 | 0.00716479 | − | 0.999974i | \(-0.497719\pi\) | ||||
0.00716479 | + | 0.999974i | \(0.497719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 429.549 | 0.438763 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 540.400i | − 0.550866i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 384.000i | − 0.390641i | −0.980739 | − | 0.195320i | \(-0.937425\pi\) | ||||
0.980739 | − | 0.195320i | \(-0.0625747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −912.000 | −0.925888 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1496.49 | −1.51620 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 166.277i | − 0.168126i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 636.000i | − 0.641776i | −0.947117 | − | 0.320888i | \(-0.896019\pi\) | ||||
0.947117 | − | 0.320888i | \(-0.103981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.0000 | −0.0362538 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2078.46 | −2.08891 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1441.07i | 1.44540i | 0.691161 | + | 0.722701i | \(0.257100\pi\) | ||||
−0.691161 | + | 0.722701i | \(0.742900\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 144.000i | − 0.144144i |
(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.b.b.319.3 | yes | 4 | |
3.2 | odd | 2 | 1152.3.b.e.703.4 | 4 | |||
4.3 | odd | 2 | inner | 384.3.b.b.319.1 | ✓ | 4 | |
8.3 | odd | 2 | inner | 384.3.b.b.319.4 | yes | 4 | |
8.5 | even | 2 | inner | 384.3.b.b.319.2 | yes | 4 | |
12.11 | even | 2 | 1152.3.b.e.703.3 | 4 | |||
16.3 | odd | 4 | 768.3.g.e.511.1 | 4 | |||
16.5 | even | 4 | 768.3.g.e.511.2 | 4 | |||
16.11 | odd | 4 | 768.3.g.e.511.4 | 4 | |||
16.13 | even | 4 | 768.3.g.e.511.3 | 4 | |||
24.5 | odd | 2 | 1152.3.b.e.703.2 | 4 | |||
24.11 | even | 2 | 1152.3.b.e.703.1 | 4 | |||
48.5 | odd | 4 | 2304.3.g.r.1279.1 | 4 | |||
48.11 | even | 4 | 2304.3.g.r.1279.2 | 4 | |||
48.29 | odd | 4 | 2304.3.g.r.1279.3 | 4 | |||
48.35 | even | 4 | 2304.3.g.r.1279.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.b.b.319.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
384.3.b.b.319.2 | yes | 4 | 8.5 | even | 2 | inner | |
384.3.b.b.319.3 | yes | 4 | 1.1 | even | 1 | trivial | |
384.3.b.b.319.4 | yes | 4 | 8.3 | odd | 2 | inner | |
768.3.g.e.511.1 | 4 | 16.3 | odd | 4 | |||
768.3.g.e.511.2 | 4 | 16.5 | even | 4 | |||
768.3.g.e.511.3 | 4 | 16.13 | even | 4 | |||
768.3.g.e.511.4 | 4 | 16.11 | odd | 4 | |||
1152.3.b.e.703.1 | 4 | 24.11 | even | 2 | |||
1152.3.b.e.703.2 | 4 | 24.5 | odd | 2 | |||
1152.3.b.e.703.3 | 4 | 12.11 | even | 2 | |||
1152.3.b.e.703.4 | 4 | 3.2 | odd | 2 | |||
2304.3.g.r.1279.1 | 4 | 48.5 | odd | 4 | |||
2304.3.g.r.1279.2 | 4 | 48.11 | even | 4 | |||
2304.3.g.r.1279.3 | 4 | 48.29 | odd | 4 | |||
2304.3.g.r.1279.4 | 4 | 48.35 | even | 4 |