Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,2,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.a (trivial) |
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: | yes |
Analytic conductor: | \(1.17380090971\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −0.585786 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.41421 | 0.447214 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | −3.82843 | −1.10517 | ||||||||
\(13\) | −5.41421 | −1.50163 | −0.750816 | − | 0.660511i | \(-0.770340\pi\) | ||||
−0.750816 | + | 0.660511i | \(0.770340\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.585786 | 0.151249 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −6.24264 | −1.51406 | −0.757031 | − | 0.653379i | \(-0.773351\pi\) | ||||
−0.757031 | + | 0.653379i | \(0.773351\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −2.24264 | −0.501470 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.82843 | 1.02942 | ||||||||
\(23\) | 3.65685 | 0.762507 | 0.381253 | − | 0.924471i | \(-0.375493\pi\) | ||||
0.381253 | + | 0.924471i | \(0.375493\pi\) | |||||||
\(24\) | 4.41421 | 0.901048 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 13.0711 | 2.56345 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | −1.41421 | −0.258199 | ||||||||
\(31\) | 6.82843 | 1.22642 | 0.613211 | − | 0.789919i | \(-0.289878\pi\) | ||||
0.613211 | + | 0.789919i | \(0.289878\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 15.0711 | 2.58467 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 6.82843 | 1.10772 | ||||||||
\(39\) | 5.41421 | 0.866968 | ||||||||
\(40\) | 2.58579 | 0.408849 | ||||||||
\(41\) | 2.24264 | 0.350242 | 0.175121 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175121 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.65685 | −0.862662 | −0.431331 | − | 0.902194i | \(-0.641956\pi\) | ||||
−0.431331 | + | 0.902194i | \(0.641956\pi\) | |||||||
\(44\) | −7.65685 | −1.15431 | ||||||||
\(45\) | −0.585786 | −0.0873239 | ||||||||
\(46\) | −8.82843 | −1.30168 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.2426 | 1.58995 | ||||||||
\(51\) | 6.24264 | 0.874145 | ||||||||
\(52\) | −20.7279 | −2.87445 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 2.41421 | 0.328533 | ||||||||
\(55\) | 1.17157 | 0.157975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | 2.82843 | 0.371391 | ||||||||
\(59\) | 6.82843 | 0.888985 | 0.444493 | − | 0.895782i | \(-0.353384\pi\) | ||||
0.444493 | + | 0.895782i | \(0.353384\pi\) | |||||||
\(60\) | 2.24264 | 0.289524 | ||||||||
\(61\) | −3.75736 | −0.481081 | −0.240540 | − | 0.970639i | \(-0.577325\pi\) | ||||
−0.240540 | + | 0.970639i | \(0.577325\pi\) | |||||||
\(62\) | −16.4853 | −2.09363 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 3.17157 | 0.393385 | ||||||||
\(66\) | −4.82843 | −0.594338 | ||||||||
\(67\) | 5.65685 | 0.691095 | 0.345547 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345547 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(68\) | −23.8995 | −2.89824 | ||||||||
\(69\) | −3.65685 | −0.440234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.3137 | −1.58005 | −0.790023 | − | 0.613077i | \(-0.789932\pi\) | ||||
−0.790023 | + | 0.613077i | \(0.789932\pi\) | |||||||
\(72\) | −4.41421 | −0.520220 | ||||||||
\(73\) | 5.89949 | 0.690484 | 0.345242 | − | 0.938514i | \(-0.387797\pi\) | ||||
0.345242 | + | 0.938514i | \(0.387797\pi\) | |||||||
\(74\) | 9.65685 | 1.12259 | ||||||||
\(75\) | 4.65685 | 0.537727 | ||||||||
\(76\) | −10.8284 | −1.24211 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.0711 | −1.48001 | ||||||||
\(79\) | 2.34315 | 0.263624 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(80\) | −1.75736 | −0.196479 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.41421 | −0.597900 | ||||||||
\(83\) | 15.3137 | 1.68090 | 0.840449 | − | 0.541891i | \(-0.182291\pi\) | ||||
0.840449 | + | 0.541891i | \(0.182291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | 0.396642 | ||||||||
\(86\) | 13.6569 | 1.47266 | ||||||||
\(87\) | 1.17157 | 0.125606 | ||||||||
\(88\) | 8.82843 | 0.941113 | ||||||||
\(89\) | 5.75736 | 0.610279 | 0.305139 | − | 0.952308i | \(-0.401297\pi\) | ||||
0.305139 | + | 0.952308i | \(0.401297\pi\) | |||||||
\(90\) | 1.41421 | 0.149071 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.0000 | 1.45960 | ||||||||
\(93\) | −6.82843 | −0.708075 | ||||||||
\(94\) | 6.82843 | 0.704298 | ||||||||
\(95\) | 1.65685 | 0.169990 | ||||||||
\(96\) | −1.58579 | −0.161849 | ||||||||
\(97\) | −5.41421 | −0.549730 | −0.274865 | − | 0.961483i | \(-0.588633\pi\) | ||||
−0.274865 | + | 0.961483i | \(0.588633\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −17.8284 | −1.78284 | ||||||||
\(101\) | −17.0711 | −1.69863 | −0.849317 | − | 0.527883i | \(-0.822986\pi\) | ||||
−0.849317 | + | 0.527883i | \(0.822986\pi\) | |||||||
\(102\) | −15.0711 | −1.49226 | ||||||||
\(103\) | 12.4853 | 1.23021 | 0.615106 | − | 0.788445i | \(-0.289113\pi\) | ||||
0.615106 | + | 0.788445i | \(0.289113\pi\) | |||||||
\(104\) | 23.8995 | 2.34354 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.82843 | 0.468978 | ||||||||
\(107\) | −11.6569 | −1.12691 | −0.563455 | − | 0.826147i | \(-0.690528\pi\) | ||||
−0.563455 | + | 0.826147i | \(0.690528\pi\) | |||||||
\(108\) | −3.82843 | −0.368391 | ||||||||
\(109\) | 5.65685 | 0.541828 | 0.270914 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270914 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(110\) | −2.82843 | −0.269680 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3137 | 1.62874 | 0.814368 | − | 0.580348i | \(-0.197084\pi\) | ||||
0.814368 | + | 0.580348i | \(0.197084\pi\) | |||||||
\(114\) | −6.82843 | −0.639541 | ||||||||
\(115\) | −2.14214 | −0.199755 | ||||||||
\(116\) | −4.48528 | −0.416448 | ||||||||
\(117\) | −5.41421 | −0.500544 | ||||||||
\(118\) | −16.4853 | −1.51759 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.58579 | −0.236049 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 9.07107 | 0.821256 | ||||||||
\(123\) | −2.24264 | −0.202212 | ||||||||
\(124\) | 26.1421 | 2.34763 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.65685 | 0.856907 | 0.428454 | − | 0.903564i | \(-0.359059\pi\) | ||||
0.428454 | + | 0.903564i | \(0.359059\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 5.65685 | 0.498058 | ||||||||
\(130\) | −7.65685 | −0.671551 | ||||||||
\(131\) | −7.31371 | −0.639002 | −0.319501 | − | 0.947586i | \(-0.603515\pi\) | ||||
−0.319501 | + | 0.947586i | \(0.603515\pi\) | |||||||
\(132\) | 7.65685 | 0.666444 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.6569 | −1.17977 | ||||||||
\(135\) | 0.585786 | 0.0504165 | ||||||||
\(136\) | 27.5563 | 2.36294 | ||||||||
\(137\) | −14.1421 | −1.20824 | −0.604122 | − | 0.796892i | \(-0.706476\pi\) | ||||
−0.604122 | + | 0.796892i | \(0.706476\pi\) | |||||||
\(138\) | 8.82843 | 0.751526 | ||||||||
\(139\) | 6.34315 | 0.538019 | 0.269009 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269009 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843 | 0.238197 | ||||||||
\(142\) | 32.1421 | 2.69731 | ||||||||
\(143\) | 10.8284 | 0.905519 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0.686292 | 0.0569934 | ||||||||
\(146\) | −14.2426 | −1.17873 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.3137 | −1.25878 | ||||||||
\(149\) | −5.31371 | −0.435316 | −0.217658 | − | 0.976025i | \(-0.569842\pi\) | ||||
−0.217658 | + | 0.976025i | \(0.569842\pi\) | |||||||
\(150\) | −11.2426 | −0.917958 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 12.4853 | 1.01269 | ||||||||
\(153\) | −6.24264 | −0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 20.7279 | 1.65956 | ||||||||
\(157\) | −20.2426 | −1.61554 | −0.807769 | − | 0.589499i | \(-0.799325\pi\) | ||||
−0.807769 | + | 0.589499i | \(0.799325\pi\) | |||||||
\(158\) | −5.65685 | −0.450035 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | −0.928932 | −0.0734385 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.41421 | −0.189679 | ||||||||
\(163\) | 11.3137 | 0.886158 | 0.443079 | − | 0.896483i | \(-0.353886\pi\) | ||||
0.443079 | + | 0.896483i | \(0.353886\pi\) | |||||||
\(164\) | 8.58579 | 0.670437 | ||||||||
\(165\) | −1.17157 | −0.0912068 | ||||||||
\(166\) | −36.9706 | −2.86947 | ||||||||
\(167\) | −19.7990 | −1.53209 | −0.766046 | − | 0.642786i | \(-0.777779\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.3137 | 1.25490 | ||||||||
\(170\) | −8.82843 | −0.677109 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | −21.6569 | −1.65132 | ||||||||
\(173\) | −6.92893 | −0.526797 | −0.263398 | − | 0.964687i | \(-0.584843\pi\) | ||||
−0.263398 | + | 0.964687i | \(0.584843\pi\) | |||||||
\(174\) | −2.82843 | −0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | −6.82843 | −0.513256 | ||||||||
\(178\) | −13.8995 | −1.04181 | ||||||||
\(179\) | −8.34315 | −0.623596 | −0.311798 | − | 0.950148i | \(-0.600931\pi\) | ||||
−0.311798 | + | 0.950148i | \(0.600931\pi\) | |||||||
\(180\) | −2.24264 | −0.167157 | ||||||||
\(181\) | 5.41421 | 0.402435 | 0.201218 | − | 0.979547i | \(-0.435510\pi\) | ||||
0.201218 | + | 0.979547i | \(0.435510\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.75736 | 0.277752 | ||||||||
\(184\) | −16.1421 | −1.19001 | ||||||||
\(185\) | 2.34315 | 0.172272 | ||||||||
\(186\) | 16.4853 | 1.20876 | ||||||||
\(187\) | 12.4853 | 0.913014 | ||||||||
\(188\) | −10.8284 | −0.789744 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −18.0000 | −1.30243 | −0.651217 | − | 0.758891i | \(-0.725741\pi\) | ||||
−0.651217 | + | 0.758891i | \(0.725741\pi\) | |||||||
\(192\) | 9.82843 | 0.709306 | ||||||||
\(193\) | −17.3137 | −1.24627 | −0.623134 | − | 0.782115i | \(-0.714141\pi\) | ||||
−0.623134 | + | 0.782115i | \(0.714141\pi\) | |||||||
\(194\) | 13.0711 | 0.938448 | ||||||||
\(195\) | −3.17157 | −0.227121 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 4.82843 | 0.343141 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 20.5563 | 1.45355 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | 41.2132 | 2.89975 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 23.8995 | 1.67330 | ||||||||
\(205\) | −1.31371 | −0.0917534 | ||||||||
\(206\) | −30.1421 | −2.10010 | ||||||||
\(207\) | 3.65685 | 0.254169 | ||||||||
\(208\) | −16.2426 | −1.12622 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9706 | −1.44367 | −0.721837 | − | 0.692064i | \(-0.756702\pi\) | ||||
−0.721837 | + | 0.692064i | \(0.756702\pi\) | |||||||
\(212\) | −7.65685 | −0.525875 | ||||||||
\(213\) | 13.3137 | 0.912240 | ||||||||
\(214\) | 28.1421 | 1.92376 | ||||||||
\(215\) | 3.31371 | 0.225993 | ||||||||
\(216\) | 4.41421 | 0.300349 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −13.6569 | −0.924959 | ||||||||
\(219\) | −5.89949 | −0.398651 | ||||||||
\(220\) | 4.48528 | 0.302398 | ||||||||
\(221\) | 33.7990 | 2.27357 | ||||||||
\(222\) | −9.65685 | −0.648126 | ||||||||
\(223\) | 8.97056 | 0.600713 | 0.300357 | − | 0.953827i | \(-0.402894\pi\) | ||||
0.300357 | + | 0.953827i | \(0.402894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | −41.7990 | −2.78043 | ||||||||
\(227\) | 15.7990 | 1.04862 | 0.524308 | − | 0.851529i | \(-0.324324\pi\) | ||||
0.524308 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(228\) | 10.8284 | 0.717130 | ||||||||
\(229\) | −8.24264 | −0.544689 | −0.272345 | − | 0.962200i | \(-0.587799\pi\) | ||||
−0.272345 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(230\) | 5.17157 | 0.341003 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.17157 | 0.339530 | ||||||||
\(233\) | 22.1421 | 1.45058 | 0.725290 | − | 0.688444i | \(-0.241706\pi\) | ||||
0.725290 | + | 0.688444i | \(0.241706\pi\) | |||||||
\(234\) | 13.0711 | 0.854482 | ||||||||
\(235\) | 1.65685 | 0.108081 | ||||||||
\(236\) | 26.1421 | 1.70171 | ||||||||
\(237\) | −2.34315 | −0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.34315 | −0.280935 | −0.140467 | − | 0.990085i | \(-0.544861\pi\) | ||||
−0.140467 | + | 0.990085i | \(0.544861\pi\) | |||||||
\(240\) | 1.75736 | 0.113437 | ||||||||
\(241\) | 7.75736 | 0.499695 | 0.249848 | − | 0.968285i | \(-0.419619\pi\) | ||||
0.249848 | + | 0.968285i | \(0.419619\pi\) | |||||||
\(242\) | 16.8995 | 1.08634 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.3848 | −0.920891 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.41421 | 0.345198 | ||||||||
\(247\) | 15.3137 | 0.974388 | ||||||||
\(248\) | −30.1421 | −1.91403 | ||||||||
\(249\) | −15.3137 | −0.970467 | ||||||||
\(250\) | −13.6569 | −0.863735 | ||||||||
\(251\) | −4.48528 | −0.283108 | −0.141554 | − | 0.989931i | \(-0.545210\pi\) | ||||
−0.141554 | + | 0.989931i | \(0.545210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.31371 | −0.459809 | ||||||||
\(254\) | −23.3137 | −1.46283 | ||||||||
\(255\) | −3.65685 | −0.229001 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 19.2132 | 1.19849 | 0.599243 | − | 0.800567i | \(-0.295468\pi\) | ||||
0.599243 | + | 0.800567i | \(0.295468\pi\) | |||||||
\(258\) | −13.6569 | −0.850239 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.1421 | 0.753023 | ||||||||
\(261\) | −1.17157 | −0.0725185 | ||||||||
\(262\) | 17.6569 | 1.09084 | ||||||||
\(263\) | −17.3137 | −1.06761 | −0.533805 | − | 0.845608i | \(-0.679238\pi\) | ||||
−0.533805 | + | 0.845608i | \(0.679238\pi\) | |||||||
\(264\) | −8.82843 | −0.543352 | ||||||||
\(265\) | 1.17157 | 0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.75736 | −0.352345 | ||||||||
\(268\) | 21.6569 | 1.32290 | ||||||||
\(269\) | −10.7279 | −0.654093 | −0.327046 | − | 0.945008i | \(-0.606053\pi\) | ||||
−0.327046 | + | 0.945008i | \(0.606053\pi\) | |||||||
\(270\) | −1.41421 | −0.0860663 | ||||||||
\(271\) | −18.1421 | −1.10206 | −0.551028 | − | 0.834487i | \(-0.685764\pi\) | ||||
−0.551028 | + | 0.834487i | \(0.685764\pi\) | |||||||
\(272\) | −18.7279 | −1.13555 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 34.1421 | 2.06260 | ||||||||
\(275\) | 9.31371 | 0.561638 | ||||||||
\(276\) | −14.0000 | −0.842701 | ||||||||
\(277\) | 13.3137 | 0.799943 | 0.399972 | − | 0.916528i | \(-0.369020\pi\) | ||||
0.399972 | + | 0.916528i | \(0.369020\pi\) | |||||||
\(278\) | −15.3137 | −0.918455 | ||||||||
\(279\) | 6.82843 | 0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4853 | −0.983429 | −0.491715 | − | 0.870756i | \(-0.663630\pi\) | ||||
−0.491715 | + | 0.870756i | \(0.663630\pi\) | |||||||
\(282\) | −6.82843 | −0.406627 | ||||||||
\(283\) | −8.48528 | −0.504398 | −0.252199 | − | 0.967675i | \(-0.581154\pi\) | ||||
−0.252199 | + | 0.967675i | \(0.581154\pi\) | |||||||
\(284\) | −50.9706 | −3.02455 | ||||||||
\(285\) | −1.65685 | −0.0981436 | ||||||||
\(286\) | −26.1421 | −1.54582 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | 21.9706 | 1.29239 | ||||||||
\(290\) | −1.65685 | −0.0972938 | ||||||||
\(291\) | 5.41421 | 0.317387 | ||||||||
\(292\) | 22.5858 | 1.32173 | ||||||||
\(293\) | −19.4142 | −1.13419 | −0.567095 | − | 0.823652i | \(-0.691933\pi\) | ||||
−0.567095 | + | 0.823652i | \(0.691933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 17.6569 | 1.02628 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 12.8284 | 0.743131 | ||||||||
\(299\) | −19.7990 | −1.14501 | ||||||||
\(300\) | 17.8284 | 1.02932 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −28.9706 | −1.66707 | ||||||||
\(303\) | 17.0711 | 0.980707 | ||||||||
\(304\) | −8.48528 | −0.486664 | ||||||||
\(305\) | 2.20101 | 0.126029 | ||||||||
\(306\) | 15.0711 | 0.861556 | ||||||||
\(307\) | −1.85786 | −0.106034 | −0.0530170 | − | 0.998594i | \(-0.516884\pi\) | ||||
−0.0530170 | + | 0.998594i | \(0.516884\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4853 | −0.710263 | ||||||||
\(310\) | 9.65685 | 0.548472 | ||||||||
\(311\) | 22.1421 | 1.25557 | 0.627783 | − | 0.778389i | \(-0.283963\pi\) | ||||
0.627783 | + | 0.778389i | \(0.283963\pi\) | |||||||
\(312\) | −23.8995 | −1.35304 | ||||||||
\(313\) | 17.8995 | 1.01174 | 0.505870 | − | 0.862610i | \(-0.331172\pi\) | ||||
0.505870 | + | 0.862610i | \(0.331172\pi\) | |||||||
\(314\) | 48.8701 | 2.75790 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.97056 | 0.504634 | ||||||||
\(317\) | 10.0000 | 0.561656 | 0.280828 | − | 0.959758i | \(-0.409391\pi\) | ||||
0.280828 | + | 0.959758i | \(0.409391\pi\) | |||||||
\(318\) | −4.82843 | −0.270765 | ||||||||
\(319\) | 2.34315 | 0.131191 | ||||||||
\(320\) | 5.75736 | 0.321846 | ||||||||
\(321\) | 11.6569 | 0.650622 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.6569 | 0.982454 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 25.2132 | 1.39858 | ||||||||
\(326\) | −27.3137 | −1.51277 | ||||||||
\(327\) | −5.65685 | −0.312825 | ||||||||
\(328\) | −9.89949 | −0.546608 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.82843 | 0.155700 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 58.6274 | 3.21760 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 47.7990 | 2.61544 | ||||||||
\(335\) | −3.31371 | −0.181047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3431 | −0.999215 | −0.499607 | − | 0.866252i | \(-0.666522\pi\) | ||||
−0.499607 | + | 0.866252i | \(0.666522\pi\) | |||||||
\(338\) | −39.3848 | −2.14225 | ||||||||
\(339\) | −17.3137 | −0.940352 | ||||||||
\(340\) | 14.0000 | 0.759257 | ||||||||
\(341\) | −13.6569 | −0.739560 | ||||||||
\(342\) | 6.82843 | 0.369239 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 24.9706 | 1.34632 | ||||||||
\(345\) | 2.14214 | 0.115329 | ||||||||
\(346\) | 16.7279 | 0.899299 | ||||||||
\(347\) | 10.6863 | 0.573670 | 0.286835 | − | 0.957980i | \(-0.407397\pi\) | ||||
0.286835 | + | 0.957980i | \(0.407397\pi\) | |||||||
\(348\) | 4.48528 | 0.240436 | ||||||||
\(349\) | −9.89949 | −0.529908 | −0.264954 | − | 0.964261i | \(-0.585357\pi\) | ||||
−0.264954 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.41421 | 0.288989 | ||||||||
\(352\) | −3.17157 | −0.169045 | ||||||||
\(353\) | −10.7279 | −0.570990 | −0.285495 | − | 0.958380i | \(-0.592158\pi\) | ||||
−0.285495 | + | 0.958380i | \(0.592158\pi\) | |||||||
\(354\) | 16.4853 | 0.876183 | ||||||||
\(355\) | 7.79899 | 0.413927 | ||||||||
\(356\) | 22.0416 | 1.16820 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.1421 | 1.06454 | ||||||||
\(359\) | −11.6569 | −0.615225 | −0.307613 | − | 0.951512i | \(-0.599530\pi\) | ||||
−0.307613 | + | 0.951512i | \(0.599530\pi\) | |||||||
\(360\) | 2.58579 | 0.136283 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −13.0711 | −0.687000 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.45584 | −0.180887 | ||||||||
\(366\) | −9.07107 | −0.474152 | ||||||||
\(367\) | −19.3137 | −1.00817 | −0.504084 | − | 0.863655i | \(-0.668170\pi\) | ||||
−0.504084 | + | 0.863655i | \(0.668170\pi\) | |||||||
\(368\) | 10.9706 | 0.571880 | ||||||||
\(369\) | 2.24264 | 0.116747 | ||||||||
\(370\) | −5.65685 | −0.294086 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.1421 | −1.35541 | ||||||||
\(373\) | −33.3137 | −1.72492 | −0.862459 | − | 0.506127i | \(-0.831077\pi\) | ||||
−0.862459 | + | 0.506127i | \(0.831077\pi\) | |||||||
\(374\) | −30.1421 | −1.55861 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 12.4853 | 0.643879 | ||||||||
\(377\) | 6.34315 | 0.326689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.3137 | 1.60848 | 0.804239 | − | 0.594307i | \(-0.202573\pi\) | ||||
0.804239 | + | 0.594307i | \(0.202573\pi\) | |||||||
\(380\) | 6.34315 | 0.325397 | ||||||||
\(381\) | −9.65685 | −0.494736 | ||||||||
\(382\) | 43.4558 | 2.22339 | ||||||||
\(383\) | 29.6569 | 1.51539 | 0.757697 | − | 0.652606i | \(-0.226324\pi\) | ||||
0.757697 | + | 0.652606i | \(0.226324\pi\) | |||||||
\(384\) | −20.5563 | −1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.7990 | 2.12751 | ||||||||
\(387\) | −5.65685 | −0.287554 | ||||||||
\(388\) | −20.7279 | −1.05230 | ||||||||
\(389\) | 10.1421 | 0.514227 | 0.257113 | − | 0.966381i | \(-0.417229\pi\) | ||||
0.257113 | + | 0.966381i | \(0.417229\pi\) | |||||||
\(390\) | 7.65685 | 0.387720 | ||||||||
\(391\) | −22.8284 | −1.15448 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.31371 | 0.368928 | ||||||||
\(394\) | −4.82843 | −0.243253 | ||||||||
\(395\) | −1.37258 | −0.0690621 | ||||||||
\(396\) | −7.65685 | −0.384771 | ||||||||
\(397\) | −34.3848 | −1.72572 | −0.862861 | − | 0.505441i | \(-0.831330\pi\) | ||||
−0.862861 | + | 0.505441i | \(0.831330\pi\) | |||||||
\(398\) | 24.9706 | 1.25166 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.9706 | −0.698528 | ||||||||
\(401\) | 22.1421 | 1.10573 | 0.552863 | − | 0.833272i | \(-0.313535\pi\) | ||||
0.552863 | + | 0.833272i | \(0.313535\pi\) | |||||||
\(402\) | 13.6569 | 0.681142 | ||||||||
\(403\) | −36.9706 | −1.84163 | ||||||||
\(404\) | −65.3553 | −3.25155 | ||||||||
\(405\) | −0.585786 | −0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | −27.5563 | −1.36424 | ||||||||
\(409\) | 18.5858 | 0.919008 | 0.459504 | − | 0.888176i | \(-0.348027\pi\) | ||||
0.459504 | + | 0.888176i | \(0.348027\pi\) | |||||||
\(410\) | 3.17157 | 0.156633 | ||||||||
\(411\) | 14.1421 | 0.697580 | ||||||||
\(412\) | 47.7990 | 2.35489 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.82843 | −0.433894 | ||||||||
\(415\) | −8.97056 | −0.440348 | ||||||||
\(416\) | −8.58579 | −0.420953 | ||||||||
\(417\) | −6.34315 | −0.310625 | ||||||||
\(418\) | −13.6569 | −0.667979 | ||||||||
\(419\) | −38.8284 | −1.89689 | −0.948446 | − | 0.316938i | \(-0.897345\pi\) | ||||
−0.948446 | + | 0.316938i | \(0.897345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.6274 | −1.39521 | −0.697607 | − | 0.716480i | \(-0.745752\pi\) | ||||
−0.697607 | + | 0.716480i | \(0.745752\pi\) | |||||||
\(422\) | 50.6274 | 2.46450 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 8.82843 | 0.428746 | ||||||||
\(425\) | 29.0711 | 1.41015 | ||||||||
\(426\) | −32.1421 | −1.55729 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −44.6274 | −2.15715 | ||||||||
\(429\) | −10.8284 | −0.522801 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 6.97056 | 0.335760 | 0.167880 | − | 0.985807i | \(-0.446308\pi\) | ||||
0.167880 | + | 0.985807i | \(0.446308\pi\) | |||||||
\(432\) | −3.00000 | −0.144338 | ||||||||
\(433\) | 11.7574 | 0.565023 | 0.282511 | − | 0.959264i | \(-0.408833\pi\) | ||||
0.282511 | + | 0.959264i | \(0.408833\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.686292 | −0.0329052 | ||||||||
\(436\) | 21.6569 | 1.03718 | ||||||||
\(437\) | −10.3431 | −0.494780 | ||||||||
\(438\) | 14.2426 | 0.680540 | ||||||||
\(439\) | −35.3137 | −1.68543 | −0.842716 | − | 0.538359i | \(-0.819044\pi\) | ||||
−0.842716 | + | 0.538359i | \(0.819044\pi\) | |||||||
\(440\) | −5.17157 | −0.246545 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −81.5980 | −3.88122 | ||||||||
\(443\) | 1.02944 | 0.0489100 | 0.0244550 | − | 0.999701i | \(-0.492215\pi\) | ||||
0.0244550 | + | 0.999701i | \(0.492215\pi\) | |||||||
\(444\) | 15.3137 | 0.726756 | ||||||||
\(445\) | −3.37258 | −0.159876 | ||||||||
\(446\) | −21.6569 | −1.02548 | ||||||||
\(447\) | 5.31371 | 0.251330 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.3137 | 0.817084 | 0.408542 | − | 0.912739i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912739i | \(0.366037\pi\) | |||||||
\(450\) | 11.2426 | 0.529983 | ||||||||
\(451\) | −4.48528 | −0.211204 | ||||||||
\(452\) | 66.2843 | 3.11775 | ||||||||
\(453\) | −12.0000 | −0.563809 | ||||||||
\(454\) | −38.1421 | −1.79010 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4853 | −0.584677 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | 19.8995 | 0.929842 | ||||||||
\(459\) | 6.24264 | 0.291382 | ||||||||
\(460\) | −8.20101 | −0.382374 | ||||||||
\(461\) | 19.4142 | 0.904210 | 0.452105 | − | 0.891965i | \(-0.350673\pi\) | ||||
0.452105 | + | 0.891965i | \(0.350673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6274 | 0.865689 | 0.432845 | − | 0.901468i | \(-0.357510\pi\) | ||||
0.432845 | + | 0.901468i | \(0.357510\pi\) | |||||||
\(464\) | −3.51472 | −0.163167 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | −53.4558 | −2.47629 | ||||||||
\(467\) | −39.7990 | −1.84168 | −0.920839 | − | 0.389943i | \(-0.872495\pi\) | ||||
−0.920839 | + | 0.389943i | \(0.872495\pi\) | |||||||
\(468\) | −20.7279 | −0.958149 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.00000 | −0.184506 | ||||||||
\(471\) | 20.2426 | 0.932732 | ||||||||
\(472\) | −30.1421 | −1.38740 | ||||||||
\(473\) | 11.3137 | 0.520205 | ||||||||
\(474\) | 5.65685 | 0.259828 | ||||||||
\(475\) | 13.1716 | 0.604353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 10.4853 | 0.479586 | ||||||||
\(479\) | −30.1421 | −1.37723 | −0.688615 | − | 0.725127i | \(-0.741781\pi\) | ||||
−0.688615 | + | 0.725127i | \(0.741781\pi\) | |||||||
\(480\) | 0.928932 | 0.0423998 | ||||||||
\(481\) | 21.6569 | 0.987468 | ||||||||
\(482\) | −18.7279 | −0.853033 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.7990 | −1.21814 | ||||||||
\(485\) | 3.17157 | 0.144014 | ||||||||
\(486\) | 2.41421 | 0.109511 | ||||||||
\(487\) | −18.6274 | −0.844089 | −0.422044 | − | 0.906575i | \(-0.638687\pi\) | ||||
−0.422044 | + | 0.906575i | \(0.638687\pi\) | |||||||
\(488\) | 16.5858 | 0.750803 | ||||||||
\(489\) | −11.3137 | −0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.9706 | 1.75872 | 0.879358 | − | 0.476160i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476160i | \(0.157972\pi\) | |||||||
\(492\) | −8.58579 | −0.387077 | ||||||||
\(493\) | 7.31371 | 0.329393 | ||||||||
\(494\) | −36.9706 | −1.66338 | ||||||||
\(495\) | 1.17157 | 0.0526583 | ||||||||
\(496\) | 20.4853 | 0.919816 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 36.9706 | 1.65669 | ||||||||
\(499\) | −19.3137 | −0.864600 | −0.432300 | − | 0.901730i | \(-0.642298\pi\) | ||||
−0.432300 | + | 0.901730i | \(0.642298\pi\) | |||||||
\(500\) | 21.6569 | 0.968524 | ||||||||
\(501\) | 19.7990 | 0.884554 | ||||||||
\(502\) | 10.8284 | 0.483296 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 17.6569 | 0.784943 | ||||||||
\(507\) | −16.3137 | −0.724517 | ||||||||
\(508\) | 36.9706 | 1.64030 | ||||||||
\(509\) | 25.5563 | 1.13277 | 0.566383 | − | 0.824142i | \(-0.308342\pi\) | ||||
0.566383 | + | 0.824142i | \(0.308342\pi\) | |||||||
\(510\) | 8.82843 | 0.390929 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 2.82843 | 0.124878 | ||||||||
\(514\) | −46.3848 | −2.04594 | ||||||||
\(515\) | −7.31371 | −0.322281 | ||||||||
\(516\) | 21.6569 | 0.953390 | ||||||||
\(517\) | 5.65685 | 0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.92893 | 0.304146 | ||||||||
\(520\) | −14.0000 | −0.613941 | ||||||||
\(521\) | 32.5858 | 1.42761 | 0.713805 | − | 0.700345i | \(-0.246970\pi\) | ||||
0.713805 | + | 0.700345i | \(0.246970\pi\) | |||||||
\(522\) | 2.82843 | 0.123797 | ||||||||
\(523\) | 14.3431 | 0.627182 | 0.313591 | − | 0.949558i | \(-0.398468\pi\) | ||||
0.313591 | + | 0.949558i | \(0.398468\pi\) | |||||||
\(524\) | −28.0000 | −1.22319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 41.7990 | 1.82252 | ||||||||
\(527\) | −42.6274 | −1.85688 | ||||||||
\(528\) | 6.00000 | 0.261116 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | −2.82843 | −0.122859 | ||||||||
\(531\) | 6.82843 | 0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1421 | −0.525934 | ||||||||
\(534\) | 13.8995 | 0.601490 | ||||||||
\(535\) | 6.82843 | 0.295219 | ||||||||
\(536\) | −24.9706 | −1.07856 | ||||||||
\(537\) | 8.34315 | 0.360033 | ||||||||
\(538\) | 25.8995 | 1.11661 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.24264 | 0.0965079 | ||||||||
\(541\) | −5.31371 | −0.228454 | −0.114227 | − | 0.993455i | \(-0.536439\pi\) | ||||
−0.114227 | + | 0.993455i | \(0.536439\pi\) | |||||||
\(542\) | 43.7990 | 1.88133 | ||||||||
\(543\) | −5.41421 | −0.232346 | ||||||||
\(544\) | −9.89949 | −0.424437 | ||||||||
\(545\) | −3.31371 | −0.141944 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.02944 | −0.129529 | −0.0647647 | − | 0.997901i | \(-0.520630\pi\) | ||||
−0.0647647 | + | 0.997901i | \(0.520630\pi\) | |||||||
\(548\) | −54.1421 | −2.31284 | ||||||||
\(549\) | −3.75736 | −0.160360 | ||||||||
\(550\) | −22.4853 | −0.958776 | ||||||||
\(551\) | 3.31371 | 0.141169 | ||||||||
\(552\) | 16.1421 | 0.687055 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −32.1421 | −1.36559 | ||||||||
\(555\) | −2.34315 | −0.0994610 | ||||||||
\(556\) | 24.2843 | 1.02988 | ||||||||
\(557\) | 26.0000 | 1.10166 | 0.550828 | − | 0.834619i | \(-0.314312\pi\) | ||||
0.550828 | + | 0.834619i | \(0.314312\pi\) | |||||||
\(558\) | −16.4853 | −0.697878 | ||||||||
\(559\) | 30.6274 | 1.29540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.4853 | −0.527129 | ||||||||
\(562\) | 39.7990 | 1.67882 | ||||||||
\(563\) | 6.82843 | 0.287784 | 0.143892 | − | 0.989593i | \(-0.454038\pi\) | ||||
0.143892 | + | 0.989593i | \(0.454038\pi\) | |||||||
\(564\) | 10.8284 | 0.455959 | ||||||||
\(565\) | −10.1421 | −0.426683 | ||||||||
\(566\) | 20.4853 | 0.861061 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 58.7696 | 2.46592 | ||||||||
\(569\) | 0.485281 | 0.0203441 | 0.0101720 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101720 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | 33.6569 | 1.40850 | 0.704248 | − | 0.709954i | \(-0.251284\pi\) | ||||
0.704248 | + | 0.709954i | \(0.251284\pi\) | |||||||
\(572\) | 41.4558 | 1.73336 | ||||||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.0294 | −0.710177 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | 14.1005 | 0.587012 | 0.293506 | − | 0.955957i | \(-0.405178\pi\) | ||||
0.293506 | + | 0.955957i | \(0.405178\pi\) | |||||||
\(578\) | −53.0416 | −2.20624 | ||||||||
\(579\) | 17.3137 | 0.719533 | ||||||||
\(580\) | 2.62742 | 0.109098 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.0711 | −0.541813 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | −26.0416 | −1.07761 | ||||||||
\(585\) | 3.17157 | 0.131128 | ||||||||
\(586\) | 46.8701 | 1.93618 | ||||||||
\(587\) | 17.1716 | 0.708747 | 0.354373 | − | 0.935104i | \(-0.384694\pi\) | ||||
0.354373 | + | 0.935104i | \(0.384694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3137 | −0.795807 | ||||||||
\(590\) | 9.65685 | 0.397566 | ||||||||
\(591\) | −2.00000 | −0.0822690 | ||||||||
\(592\) | −12.0000 | −0.493197 | ||||||||
\(593\) | 21.0711 | 0.865285 | 0.432643 | − | 0.901566i | \(-0.357581\pi\) | ||||
0.432643 | + | 0.901566i | \(0.357581\pi\) | |||||||
\(594\) | −4.82843 | −0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.3431 | −0.833288 | ||||||||
\(597\) | 10.3431 | 0.423317 | ||||||||
\(598\) | 47.7990 | 1.95465 | ||||||||
\(599\) | −2.00000 | −0.0817178 | −0.0408589 | − | 0.999165i | \(-0.513009\pi\) | ||||
−0.0408589 | + | 0.999165i | \(0.513009\pi\) | |||||||
\(600\) | −20.5563 | −0.839209 | ||||||||
\(601\) | 0.928932 | 0.0378919 | 0.0189460 | − | 0.999821i | \(-0.493969\pi\) | ||||
0.0189460 | + | 0.999821i | \(0.493969\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.65685 | 0.230365 | ||||||||
\(604\) | 45.9411 | 1.86932 | ||||||||
\(605\) | 4.10051 | 0.166709 | ||||||||
\(606\) | −41.2132 | −1.67417 | ||||||||
\(607\) | 29.6569 | 1.20373 | 0.601867 | − | 0.798596i | \(-0.294424\pi\) | ||||
0.601867 | + | 0.798596i | \(0.294424\pi\) | |||||||
\(608\) | −4.48528 | −0.181902 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.31371 | −0.215146 | ||||||||
\(611\) | 15.3137 | 0.619526 | ||||||||
\(612\) | −23.8995 | −0.966080 | ||||||||
\(613\) | 27.3137 | 1.10319 | 0.551595 | − | 0.834112i | \(-0.314019\pi\) | ||||
0.551595 | + | 0.834112i | \(0.314019\pi\) | |||||||
\(614\) | 4.48528 | 0.181011 | ||||||||
\(615\) | 1.31371 | 0.0529738 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.51472 | −0.302531 | −0.151266 | − | 0.988493i | \(-0.548335\pi\) | ||||
−0.151266 | + | 0.988493i | \(0.548335\pi\) | |||||||
\(618\) | 30.1421 | 1.21249 | ||||||||
\(619\) | 4.97056 | 0.199784 | 0.0998919 | − | 0.994998i | \(-0.468150\pi\) | ||||
0.0998919 | + | 0.994998i | \(0.468150\pi\) | |||||||
\(620\) | −15.3137 | −0.615013 | ||||||||
\(621\) | −3.65685 | −0.146745 | ||||||||
\(622\) | −53.4558 | −2.14338 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 16.2426 | 0.650226 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | −43.2132 | −1.72715 | ||||||||
\(627\) | −5.65685 | −0.225913 | ||||||||
\(628\) | −77.4975 | −3.09249 | ||||||||
\(629\) | 24.9706 | 0.995642 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.686292 | 0.0273208 | 0.0136604 | − | 0.999907i | \(-0.495652\pi\) | ||||
0.0136604 | + | 0.999907i | \(0.495652\pi\) | |||||||
\(632\) | −10.3431 | −0.411428 | ||||||||
\(633\) | 20.9706 | 0.833505 | ||||||||
\(634\) | −24.1421 | −0.958807 | ||||||||
\(635\) | −5.65685 | −0.224485 | ||||||||
\(636\) | 7.65685 | 0.303614 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.65685 | −0.223957 | ||||||||
\(639\) | −13.3137 | −0.526682 | ||||||||
\(640\) | −12.0416 | −0.475987 | ||||||||
\(641\) | −5.17157 | −0.204265 | −0.102132 | − | 0.994771i | \(-0.532567\pi\) | ||||
−0.102132 | + | 0.994771i | \(0.532567\pi\) | |||||||
\(642\) | −28.1421 | −1.11068 | ||||||||
\(643\) | −50.4264 | −1.98862 | −0.994312 | − | 0.106510i | \(-0.966033\pi\) | ||||
−0.994312 | + | 0.106510i | \(0.966033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.31371 | −0.130477 | ||||||||
\(646\) | −42.6274 | −1.67715 | ||||||||
\(647\) | −21.1716 | −0.832340 | −0.416170 | − | 0.909287i | \(-0.636628\pi\) | ||||
−0.416170 | + | 0.909287i | \(0.636628\pi\) | |||||||
\(648\) | −4.41421 | −0.173407 | ||||||||
\(649\) | −13.6569 | −0.536078 | ||||||||
\(650\) | −60.8701 | −2.38752 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 43.3137 | 1.69630 | ||||||||
\(653\) | 19.5147 | 0.763670 | 0.381835 | − | 0.924231i | \(-0.375292\pi\) | ||||
0.381835 | + | 0.924231i | \(0.375292\pi\) | |||||||
\(654\) | 13.6569 | 0.534025 | ||||||||
\(655\) | 4.28427 | 0.167400 | ||||||||
\(656\) | 6.72792 | 0.262681 | ||||||||
\(657\) | 5.89949 | 0.230161 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3137 | −0.518628 | −0.259314 | − | 0.965793i | \(-0.583497\pi\) | ||||
−0.259314 | + | 0.965793i | \(0.583497\pi\) | |||||||
\(660\) | −4.48528 | −0.174589 | ||||||||
\(661\) | −7.55635 | −0.293908 | −0.146954 | − | 0.989143i | \(-0.546947\pi\) | ||||
−0.146954 | + | 0.989143i | \(0.546947\pi\) | |||||||
\(662\) | 9.65685 | 0.375324 | ||||||||
\(663\) | −33.7990 | −1.31264 | ||||||||
\(664\) | −67.5980 | −2.62331 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.65685 | 0.374196 | ||||||||
\(667\) | −4.28427 | −0.165888 | ||||||||
\(668\) | −75.7990 | −2.93275 | ||||||||
\(669\) | −8.97056 | −0.346822 | ||||||||
\(670\) | 8.00000 | 0.309067 | ||||||||
\(671\) | 7.51472 | 0.290102 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.686292 | 0.0264546 | 0.0132273 | − | 0.999913i | \(-0.495789\pi\) | ||||
0.0132273 | + | 0.999913i | \(0.495789\pi\) | |||||||
\(674\) | 44.2843 | 1.70577 | ||||||||
\(675\) | 4.65685 | 0.179242 | ||||||||
\(676\) | 62.4558 | 2.40215 | ||||||||
\(677\) | −28.5858 | −1.09864 | −0.549321 | − | 0.835612i | \(-0.685113\pi\) | ||||
−0.549321 | + | 0.835612i | \(0.685113\pi\) | |||||||
\(678\) | 41.7990 | 1.60528 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.1421 | −0.619023 | ||||||||
\(681\) | −15.7990 | −0.605419 | ||||||||
\(682\) | 32.9706 | 1.26251 | ||||||||
\(683\) | −8.34315 | −0.319242 | −0.159621 | − | 0.987178i | \(-0.551027\pi\) | ||||
−0.159621 | + | 0.987178i | \(0.551027\pi\) | |||||||
\(684\) | −10.8284 | −0.414035 | ||||||||
\(685\) | 8.28427 | 0.316526 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.24264 | 0.314476 | ||||||||
\(688\) | −16.9706 | −0.646997 | ||||||||
\(689\) | 10.8284 | 0.412530 | ||||||||
\(690\) | −5.17157 | −0.196878 | ||||||||
\(691\) | 23.3137 | 0.886895 | 0.443448 | − | 0.896300i | \(-0.353755\pi\) | ||||
0.443448 | + | 0.896300i | \(0.353755\pi\) | |||||||
\(692\) | −26.5269 | −1.00840 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.7990 | −0.979316 | ||||||||
\(695\) | −3.71573 | −0.140946 | ||||||||
\(696\) | −5.17157 | −0.196028 | ||||||||
\(697\) | −14.0000 | −0.530288 | ||||||||
\(698\) | 23.8995 | 0.904609 | ||||||||
\(699\) | −22.1421 | −0.837492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.8284 | −0.862218 | −0.431109 | − | 0.902300i | \(-0.641878\pi\) | ||||
−0.431109 | + | 0.902300i | \(0.641878\pi\) | |||||||
\(702\) | −13.0711 | −0.493336 | ||||||||
\(703\) | 11.3137 | 0.426705 | ||||||||
\(704\) | 19.6569 | 0.740846 | ||||||||
\(705\) | −1.65685 | −0.0624007 | ||||||||
\(706\) | 25.8995 | 0.974740 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −26.1421 | −0.982482 | ||||||||
\(709\) | 20.2843 | 0.761792 | 0.380896 | − | 0.924618i | \(-0.375616\pi\) | ||||
0.380896 | + | 0.924618i | \(0.375616\pi\) | |||||||
\(710\) | −18.8284 | −0.706618 | ||||||||
\(711\) | 2.34315 | 0.0878748 | ||||||||
\(712\) | −25.4142 | −0.952438 | ||||||||
\(713\) | 24.9706 | 0.935155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.34315 | −0.237220 | ||||||||
\(716\) | −31.9411 | −1.19370 | ||||||||
\(717\) | 4.34315 | 0.162198 | ||||||||
\(718\) | 28.1421 | 1.05026 | ||||||||
\(719\) | 25.9411 | 0.967441 | 0.483720 | − | 0.875223i | \(-0.339285\pi\) | ||||
0.483720 | + | 0.875223i | \(0.339285\pi\) | |||||||
\(720\) | −1.75736 | −0.0654929 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.5563 | 0.988325 | ||||||||
\(723\) | −7.75736 | −0.288499 | ||||||||
\(724\) | 20.7279 | 0.770347 | ||||||||
\(725\) | 5.45584 | 0.202625 | ||||||||
\(726\) | −16.8995 | −0.627199 | ||||||||
\(727\) | 4.48528 | 0.166350 | 0.0831749 | − | 0.996535i | \(-0.473494\pi\) | ||||
0.0831749 | + | 0.996535i | \(0.473494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.34315 | 0.308794 | ||||||||
\(731\) | 35.3137 | 1.30612 | ||||||||
\(732\) | 14.3848 | 0.531677 | ||||||||
\(733\) | 9.69848 | 0.358222 | 0.179111 | − | 0.983829i | \(-0.442678\pi\) | ||||
0.179111 | + | 0.983829i | \(0.442678\pi\) | |||||||
\(734\) | 46.6274 | 1.72105 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.79899 | 0.213754 | ||||||||
\(737\) | −11.3137 | −0.416746 | ||||||||
\(738\) | −5.41421 | −0.199300 | ||||||||
\(739\) | 27.3137 | 1.00475 | 0.502376 | − | 0.864650i | \(-0.332460\pi\) | ||||
0.502376 | + | 0.864650i | \(0.332460\pi\) | |||||||
\(740\) | 8.97056 | 0.329764 | ||||||||
\(741\) | −15.3137 | −0.562563 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.0294 | −0.624749 | −0.312375 | − | 0.949959i | \(-0.601124\pi\) | ||||
−0.312375 | + | 0.949959i | \(0.601124\pi\) | |||||||
\(744\) | 30.1421 | 1.10506 | ||||||||
\(745\) | 3.11270 | 0.114040 | ||||||||
\(746\) | 80.4264 | 2.94462 | ||||||||
\(747\) | 15.3137 | 0.560299 | ||||||||
\(748\) | 47.7990 | 1.74770 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.6569 | 0.498678 | ||||||||
\(751\) | 2.34315 | 0.0855026 | 0.0427513 | − | 0.999086i | \(-0.486388\pi\) | ||||
0.0427513 | + | 0.999086i | \(0.486388\pi\) | |||||||
\(752\) | −8.48528 | −0.309426 | ||||||||
\(753\) | 4.48528 | 0.163453 | ||||||||
\(754\) | −15.3137 | −0.557692 | ||||||||
\(755\) | −7.02944 | −0.255827 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6569 | 1.36866 | 0.684331 | − | 0.729172i | \(-0.260094\pi\) | ||||
0.684331 | + | 0.729172i | \(0.260094\pi\) | |||||||
\(758\) | −75.5980 | −2.74584 | ||||||||
\(759\) | 7.31371 | 0.265471 | ||||||||
\(760\) | −7.31371 | −0.265296 | ||||||||
\(761\) | −46.5269 | −1.68660 | −0.843300 | − | 0.537444i | \(-0.819390\pi\) | ||||
−0.843300 | + | 0.537444i | \(0.819390\pi\) | |||||||
\(762\) | 23.3137 | 0.844567 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −68.9117 | −2.49314 | ||||||||
\(765\) | 3.65685 | 0.132214 | ||||||||
\(766\) | −71.5980 | −2.58694 | ||||||||
\(767\) | −36.9706 | −1.33493 | ||||||||
\(768\) | 29.9706 | 1.08147 | ||||||||
\(769\) | 29.6985 | 1.07095 | 0.535477 | − | 0.844550i | \(-0.320132\pi\) | ||||
0.535477 | + | 0.844550i | \(0.320132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2132 | −0.691947 | ||||||||
\(772\) | −66.2843 | −2.38562 | ||||||||
\(773\) | −21.5563 | −0.775328 | −0.387664 | − | 0.921801i | \(-0.626718\pi\) | ||||
−0.387664 | + | 0.921801i | \(0.626718\pi\) | |||||||
\(774\) | 13.6569 | 0.490885 | ||||||||
\(775\) | −31.7990 | −1.14225 | ||||||||
\(776\) | 23.8995 | 0.857942 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.4853 | −0.877840 | ||||||||
\(779\) | −6.34315 | −0.227267 | ||||||||
\(780\) | −12.1421 | −0.434758 | ||||||||
\(781\) | 26.6274 | 0.952804 | ||||||||
\(782\) | 55.1127 | 1.97083 | ||||||||
\(783\) | 1.17157 | 0.0418686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8579 | 0.423225 | ||||||||
\(786\) | −17.6569 | −0.629799 | ||||||||
\(787\) | −47.3137 | −1.68655 | −0.843276 | − | 0.537481i | \(-0.819376\pi\) | ||||
−0.843276 | + | 0.537481i | \(0.819376\pi\) | |||||||
\(788\) | 7.65685 | 0.272764 | ||||||||
\(789\) | 17.3137 | 0.616384 | ||||||||
\(790\) | 3.31371 | 0.117896 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.82843 | 0.313704 | ||||||||
\(793\) | 20.3431 | 0.722406 | ||||||||
\(794\) | 83.0122 | 2.94599 | ||||||||
\(795\) | −1.17157 | −0.0415514 | ||||||||
\(796\) | −39.5980 | −1.40351 | ||||||||
\(797\) | −28.3848 | −1.00544 | −0.502720 | − | 0.864449i | \(-0.667667\pi\) | ||||
−0.502720 | + | 0.864449i | \(0.667667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.6569 | 0.624655 | ||||||||
\(800\) | −7.38478 | −0.261091 | ||||||||
\(801\) | 5.75736 | 0.203426 | ||||||||
\(802\) | −53.4558 | −1.88759 | ||||||||
\(803\) | −11.7990 | −0.416377 | ||||||||
\(804\) | −21.6569 | −0.763778 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 89.2548 | 3.14387 | ||||||||
\(807\) | 10.7279 | 0.377641 | ||||||||
\(808\) | 75.3553 | 2.65099 | ||||||||
\(809\) | −47.9411 | −1.68552 | −0.842760 | − | 0.538289i | \(-0.819071\pi\) | ||||
−0.842760 | + | 0.538289i | \(0.819071\pi\) | |||||||
\(810\) | 1.41421 | 0.0496904 | ||||||||
\(811\) | 6.34315 | 0.222738 | 0.111369 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111369 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.1421 | 0.636272 | ||||||||
\(814\) | −19.3137 | −0.676945 | ||||||||
\(815\) | −6.62742 | −0.232148 | ||||||||
\(816\) | 18.7279 | 0.655608 | ||||||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | −44.8701 | −1.56884 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.02944 | −0.175636 | ||||||||
\(821\) | −33.3137 | −1.16266 | −0.581328 | − | 0.813669i | \(-0.697467\pi\) | ||||
−0.581328 | + | 0.813669i | \(0.697467\pi\) | |||||||
\(822\) | −34.1421 | −1.19084 | ||||||||
\(823\) | −24.9706 | −0.870419 | −0.435210 | − | 0.900329i | \(-0.643326\pi\) | ||||
−0.435210 | + | 0.900329i | \(0.643326\pi\) | |||||||
\(824\) | −55.1127 | −1.91994 | ||||||||
\(825\) | −9.31371 | −0.324262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.3431 | 1.26378 | 0.631888 | − | 0.775060i | \(-0.282280\pi\) | ||||
0.631888 | + | 0.775060i | \(0.282280\pi\) | |||||||
\(828\) | 14.0000 | 0.486534 | ||||||||
\(829\) | −24.7279 | −0.858836 | −0.429418 | − | 0.903106i | \(-0.641281\pi\) | ||||
−0.429418 | + | 0.903106i | \(0.641281\pi\) | |||||||
\(830\) | 21.6569 | 0.751720 | ||||||||
\(831\) | −13.3137 | −0.461847 | ||||||||
\(832\) | 53.2132 | 1.84484 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.3137 | 0.530270 | ||||||||
\(835\) | 11.5980 | 0.401365 | ||||||||
\(836\) | 21.6569 | 0.749018 | ||||||||
\(837\) | −6.82843 | −0.236025 | ||||||||
\(838\) | 93.7401 | 3.23820 | ||||||||
\(839\) | −45.1716 | −1.55950 | −0.779748 | − | 0.626094i | \(-0.784653\pi\) | ||||
−0.779748 | + | 0.626094i | \(0.784653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | 69.1127 | 2.38178 | ||||||||
\(843\) | 16.4853 | 0.567783 | ||||||||
\(844\) | −80.2843 | −2.76350 | ||||||||
\(845\) | −9.55635 | −0.328748 | ||||||||
\(846\) | 6.82843 | 0.234766 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 8.48528 | 0.291214 | ||||||||
\(850\) | −70.1838 | −2.40728 | ||||||||
\(851\) | −14.6274 | −0.501421 | ||||||||
\(852\) | 50.9706 | 1.74622 | ||||||||
\(853\) | −49.4975 | −1.69476 | −0.847381 | − | 0.530986i | \(-0.821822\pi\) | ||||
−0.847381 | + | 0.530986i | \(0.821822\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.65685 | 0.0566632 | ||||||||
\(856\) | 51.4558 | 1.75872 | ||||||||
\(857\) | −12.5858 | −0.429922 | −0.214961 | − | 0.976623i | \(-0.568962\pi\) | ||||
−0.214961 | + | 0.976623i | \(0.568962\pi\) | |||||||
\(858\) | 26.1421 | 0.892478 | ||||||||
\(859\) | −6.54416 | −0.223284 | −0.111642 | − | 0.993749i | \(-0.535611\pi\) | ||||
−0.111642 | + | 0.993749i | \(0.535611\pi\) | |||||||
\(860\) | 12.6863 | 0.432599 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.8284 | −0.573179 | ||||||||
\(863\) | −5.31371 | −0.180881 | −0.0904404 | − | 0.995902i | \(-0.528827\pi\) | ||||
−0.0904404 | + | 0.995902i | \(0.528827\pi\) | |||||||
\(864\) | −1.58579 | −0.0539496 | ||||||||
\(865\) | 4.05887 | 0.138006 | ||||||||
\(866\) | −28.3848 | −0.964554 | ||||||||
\(867\) | −21.9706 | −0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.68629 | −0.158972 | ||||||||
\(870\) | 1.65685 | 0.0561726 | ||||||||
\(871\) | −30.6274 | −1.03777 | ||||||||
\(872\) | −24.9706 | −0.845610 | ||||||||
\(873\) | −5.41421 | −0.183243 | ||||||||
\(874\) | 24.9706 | 0.844642 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.5858 | −0.763103 | ||||||||
\(877\) | 11.3137 | 0.382037 | 0.191018 | − | 0.981586i | \(-0.438821\pi\) | ||||
0.191018 | + | 0.981586i | \(0.438821\pi\) | |||||||
\(878\) | 85.2548 | 2.87721 | ||||||||
\(879\) | 19.4142 | 0.654825 | ||||||||
\(880\) | 3.51472 | 0.118481 | ||||||||
\(881\) | −30.2426 | −1.01890 | −0.509450 | − | 0.860500i | \(-0.670151\pi\) | ||||
−0.509450 | + | 0.860500i | \(0.670151\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.3137 | −0.919179 | −0.459590 | − | 0.888131i | \(-0.652004\pi\) | ||||
−0.459590 | + | 0.888131i | \(0.652004\pi\) | |||||||
\(884\) | 129.397 | 4.35209 | ||||||||
\(885\) | 4.00000 | 0.134459 | ||||||||
\(886\) | −2.48528 | −0.0834947 | ||||||||
\(887\) | −2.82843 | −0.0949693 | −0.0474846 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474846 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(888\) | −17.6569 | −0.592525 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.14214 | 0.272925 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 34.3431 | 1.14989 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | −12.8284 | −0.429047 | ||||||||
\(895\) | 4.88730 | 0.163364 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.7990 | 0.661069 | ||||||||
\(898\) | −41.7990 | −1.39485 | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | −17.8284 | −0.594281 | ||||||||
\(901\) | 12.4853 | 0.415945 | ||||||||
\(902\) | 10.8284 | 0.360547 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −76.4264 | −2.54190 | ||||||||
\(905\) | −3.17157 | −0.105427 | ||||||||
\(906\) | 28.9706 | 0.962482 | ||||||||
\(907\) | −16.0000 | −0.531271 | −0.265636 | − | 0.964073i | \(-0.585582\pi\) | ||||
−0.265636 | + | 0.964073i | \(0.585582\pi\) | |||||||
\(908\) | 60.4853 | 2.00727 | ||||||||
\(909\) | −17.0711 | −0.566212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.9706 | −1.15863 | −0.579313 | − | 0.815105i | \(-0.696679\pi\) | ||||
−0.579313 | + | 0.815105i | \(0.696679\pi\) | |||||||
\(912\) | 8.48528 | 0.280976 | ||||||||
\(913\) | −30.6274 | −1.01362 | ||||||||
\(914\) | 43.4558 | 1.43739 | ||||||||
\(915\) | −2.20101 | −0.0727632 | ||||||||
\(916\) | −31.5563 | −1.04265 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −15.0711 | −0.497419 | ||||||||
\(919\) | 48.2843 | 1.59275 | 0.796376 | − | 0.604802i | \(-0.206748\pi\) | ||||
0.796376 | + | 0.604802i | \(0.206748\pi\) | |||||||
\(920\) | 9.45584 | 0.311750 | ||||||||
\(921\) | 1.85786 | 0.0612187 | ||||||||
\(922\) | −46.8701 | −1.54358 | ||||||||
\(923\) | 72.0833 | 2.37265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6274 | 0.612466 | ||||||||
\(926\) | −44.9706 | −1.47782 | ||||||||
\(927\) | 12.4853 | 0.410070 | ||||||||
\(928\) | −1.85786 | −0.0609874 | ||||||||
\(929\) | −3.21320 | −0.105422 | −0.0527109 | − | 0.998610i | \(-0.516786\pi\) | ||||
−0.0527109 | + | 0.998610i | \(0.516786\pi\) | |||||||
\(930\) | −9.65685 | −0.316661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 84.7696 | 2.77672 | ||||||||
\(933\) | −22.1421 | −0.724901 | ||||||||
\(934\) | 96.0833 | 3.14394 | ||||||||
\(935\) | −7.31371 | −0.239184 | ||||||||
\(936\) | 23.8995 | 0.781179 | ||||||||
\(937\) | −33.4142 | −1.09159 | −0.545797 | − | 0.837917i | \(-0.683773\pi\) | ||||
−0.545797 | + | 0.837917i | \(0.683773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.8995 | −0.584128 | ||||||||
\(940\) | 6.34315 | 0.206891 | ||||||||
\(941\) | 7.21320 | 0.235144 | 0.117572 | − | 0.993064i | \(-0.462489\pi\) | ||||
0.117572 | + | 0.993064i | \(0.462489\pi\) | |||||||
\(942\) | −48.8701 | −1.59227 | ||||||||
\(943\) | 8.20101 | 0.267062 | ||||||||
\(944\) | 20.4853 | 0.666739 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.3137 | −0.888045 | ||||||||
\(947\) | 53.3137 | 1.73246 | 0.866231 | − | 0.499643i | \(-0.166535\pi\) | ||||
0.866231 | + | 0.499643i | \(0.166535\pi\) | |||||||
\(948\) | −8.97056 | −0.291350 | ||||||||
\(949\) | −31.9411 | −1.03685 | ||||||||
\(950\) | −31.7990 | −1.03170 | ||||||||
\(951\) | −10.0000 | −0.324272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | 4.82843 | 0.156326 | ||||||||
\(955\) | 10.5442 | 0.341201 | ||||||||
\(956\) | −16.6274 | −0.537769 | ||||||||
\(957\) | −2.34315 | −0.0757431 | ||||||||
\(958\) | 72.7696 | 2.35108 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.75736 | −0.185818 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | −52.2843 | −1.68571 | ||||||||
\(963\) | −11.6569 | −0.375637 | ||||||||
\(964\) | 29.6985 | 0.956524 | ||||||||
\(965\) | 10.1421 | 0.326487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.3431 | 0.718507 | 0.359254 | − | 0.933240i | \(-0.383031\pi\) | ||||
0.359254 | + | 0.933240i | \(0.383031\pi\) | |||||||
\(968\) | 30.8995 | 0.993147 | ||||||||
\(969\) | −17.6569 | −0.567220 | ||||||||
\(970\) | −7.65685 | −0.245847 | ||||||||
\(971\) | 5.37258 | 0.172414 | 0.0862072 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862072 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(972\) | −3.82843 | −0.122797 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 44.9706 | 1.44095 | ||||||||
\(975\) | −25.2132 | −0.807469 | ||||||||
\(976\) | −11.2721 | −0.360810 | ||||||||
\(977\) | −26.8284 | −0.858317 | −0.429159 | − | 0.903229i | \(-0.641190\pi\) | ||||
−0.429159 | + | 0.903229i | \(0.641190\pi\) | |||||||
\(978\) | 27.3137 | 0.873396 | ||||||||
\(979\) | −11.5147 | −0.368012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.65685 | 0.180609 | ||||||||
\(982\) | −94.0833 | −3.00232 | ||||||||
\(983\) | −37.2548 | −1.18824 | −0.594122 | − | 0.804375i | \(-0.702501\pi\) | ||||
−0.594122 | + | 0.804375i | \(0.702501\pi\) | |||||||
\(984\) | 9.89949 | 0.315584 | ||||||||
\(985\) | −1.17157 | −0.0373294 | ||||||||
\(986\) | −17.6569 | −0.562309 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 58.6274 | 1.86519 | ||||||||
\(989\) | −20.6863 | −0.657786 | ||||||||
\(990\) | −2.82843 | −0.0898933 | ||||||||
\(991\) | 20.9706 | 0.666152 | 0.333076 | − | 0.942900i | \(-0.391913\pi\) | ||||
0.333076 | + | 0.942900i | \(0.391913\pi\) | |||||||
\(992\) | 10.8284 | 0.343803 | ||||||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.05887 | 0.192079 | ||||||||
\(996\) | −58.6274 | −1.85768 | ||||||||
\(997\) | 10.3848 | 0.328889 | 0.164445 | − | 0.986386i | \(-0.447417\pi\) | ||||
0.164445 | + | 0.986386i | \(0.447417\pi\) | |||||||
\(998\) | 46.6274 | 1.47597 | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 147.2.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 441.2.a.j.1.2 | 2 | |||
4.3 | odd | 2 | 2352.2.a.be.1.2 | 2 | |||
5.4 | even | 2 | 3675.2.a.bf.1.2 | 2 | |||
7.2 | even | 3 | 147.2.e.e.67.2 | 4 | |||
7.3 | odd | 6 | 147.2.e.d.79.2 | 4 | |||
7.4 | even | 3 | 147.2.e.e.79.2 | 4 | |||
7.5 | odd | 6 | 147.2.e.d.67.2 | 4 | |||
7.6 | odd | 2 | 147.2.a.e.1.1 | yes | 2 | ||
8.3 | odd | 2 | 9408.2.a.dq.1.1 | 2 | |||
8.5 | even | 2 | 9408.2.a.ef.1.1 | 2 | |||
12.11 | even | 2 | 7056.2.a.cv.1.1 | 2 | |||
21.2 | odd | 6 | 441.2.e.f.361.1 | 4 | |||
21.5 | even | 6 | 441.2.e.g.361.1 | 4 | |||
21.11 | odd | 6 | 441.2.e.f.226.1 | 4 | |||
21.17 | even | 6 | 441.2.e.g.226.1 | 4 | |||
21.20 | even | 2 | 441.2.a.i.1.2 | 2 | |||
28.3 | even | 6 | 2352.2.q.bd.961.2 | 4 | |||
28.11 | odd | 6 | 2352.2.q.bb.961.1 | 4 | |||
28.19 | even | 6 | 2352.2.q.bd.1537.2 | 4 | |||
28.23 | odd | 6 | 2352.2.q.bb.1537.1 | 4 | |||
28.27 | even | 2 | 2352.2.a.bc.1.1 | 2 | |||
35.34 | odd | 2 | 3675.2.a.bd.1.2 | 2 | |||
56.13 | odd | 2 | 9408.2.a.di.1.2 | 2 | |||
56.27 | even | 2 | 9408.2.a.dt.1.2 | 2 | |||
84.83 | odd | 2 | 7056.2.a.cf.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.2.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
147.2.a.e.1.1 | yes | 2 | 7.6 | odd | 2 | ||
147.2.e.d.67.2 | 4 | 7.5 | odd | 6 | |||
147.2.e.d.79.2 | 4 | 7.3 | odd | 6 | |||
147.2.e.e.67.2 | 4 | 7.2 | even | 3 | |||
147.2.e.e.79.2 | 4 | 7.4 | even | 3 | |||
441.2.a.i.1.2 | 2 | 21.20 | even | 2 | |||
441.2.a.j.1.2 | 2 | 3.2 | odd | 2 | |||
441.2.e.f.226.1 | 4 | 21.11 | odd | 6 | |||
441.2.e.f.361.1 | 4 | 21.2 | odd | 6 | |||
441.2.e.g.226.1 | 4 | 21.17 | even | 6 | |||
441.2.e.g.361.1 | 4 | 21.5 | even | 6 | |||
2352.2.a.bc.1.1 | 2 | 28.27 | even | 2 | |||
2352.2.a.be.1.2 | 2 | 4.3 | odd | 2 | |||
2352.2.q.bb.961.1 | 4 | 28.11 | odd | 6 | |||
2352.2.q.bb.1537.1 | 4 | 28.23 | odd | 6 | |||
2352.2.q.bd.961.2 | 4 | 28.3 | even | 6 | |||
2352.2.q.bd.1537.2 | 4 | 28.19 | even | 6 | |||
3675.2.a.bd.1.2 | 2 | 35.34 | odd | 2 | |||
3675.2.a.bf.1.2 | 2 | 5.4 | even | 2 | |||
7056.2.a.cf.1.2 | 2 | 84.83 | odd | 2 | |||
7056.2.a.cv.1.1 | 2 | 12.11 | even | 2 | |||
9408.2.a.di.1.2 | 2 | 56.13 | odd | 2 | |||
9408.2.a.dq.1.1 | 2 | 8.3 | odd | 2 | |||
9408.2.a.dt.1.2 | 2 | 56.27 | even | 2 | |||
9408.2.a.ef.1.1 | 2 | 8.5 | even | 2 |