Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(289,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.i (of order \(3\), degree \(2\), not 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.289 |
Dual form | 864.2.i.c.577.2 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.724745 | − | 1.25529i | 0.273928 | − | 0.474457i | −0.695936 | − | 0.718104i | \(-0.745010\pi\) |
0.969864 | + | 0.243647i | \(0.0783437\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.72474 | + | 2.98735i | −0.520030 | + | 0.900719i | 0.479699 | + | 0.877433i | \(0.340746\pi\) |
−0.999729 | + | 0.0232854i | \(0.992587\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.94949 | + | 3.37662i | 0.540691 | + | 0.936505i | 0.998864 | + | 0.0476417i | \(0.0151706\pi\) |
−0.458173 | + | 0.888863i | \(0.651496\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89898 | 1.18818 | 0.594089 | − | 0.804400i | \(-0.297513\pi\) | ||||
0.594089 | + | 0.804400i | \(0.297513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.275255 | − | 0.476756i | −0.0573947 | − | 0.0994105i | 0.835900 | − | 0.548881i | \(-0.184946\pi\) |
−0.893295 | + | 0.449471i | \(0.851613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.94949 | − | 8.57277i | 0.919097 | − | 1.59192i | 0.118308 | − | 0.992977i | \(-0.462253\pi\) |
0.800789 | − | 0.598946i | \(-0.204414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.72474 | − | 6.45145i | −0.668984 | − | 1.15871i | −0.978189 | − | 0.207719i | \(-0.933396\pi\) |
0.309205 | − | 0.950996i | \(-0.399937\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.44949 | −0.245008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.89898 | 1.46298 | 0.731492 | − | 0.681850i | \(-0.238825\pi\) | ||||
0.731492 | + | 0.681850i | \(0.238825\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.05051 | − | 1.81954i | −0.164062 | − | 0.284164i | 0.772260 | − | 0.635307i | \(-0.219126\pi\) |
−0.936322 | + | 0.351143i | \(0.885793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.17423 | + | 10.6941i | −0.941562 | + | 1.63083i | −0.179069 | + | 0.983836i | \(0.557309\pi\) |
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.17423 | − | 7.22999i | 0.608875 | − | 1.05460i | −0.382552 | − | 0.923934i | \(-0.624955\pi\) |
0.991426 | − | 0.130668i | \(-0.0417121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.44949 | + | 4.24264i | 0.349927 | + | 0.606092i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.898979 | 0.123484 | 0.0617422 | − | 0.998092i | \(-0.480334\pi\) | ||||
0.0617422 | + | 0.998092i | \(0.480334\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.44949 | 0.465129 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.174235 | − | 0.301783i | −0.0226834 | − | 0.0392888i | 0.854461 | − | 0.519516i | \(-0.173888\pi\) |
−0.877144 | + | 0.480227i | \(0.840554\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.949490 | + | 1.64456i | −0.121570 | + | 0.210565i | −0.920387 | − | 0.391009i | \(-0.872126\pi\) |
0.798817 | + | 0.601574i | \(0.205459\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.94949 | − | 3.37662i | 0.241804 | − | 0.418818i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.17423 | + | 2.03383i | 0.143456 | + | 0.248472i | 0.928796 | − | 0.370592i | \(-0.120845\pi\) |
−0.785340 | + | 0.619065i | \(0.787512\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.7980 | 1.40016 | 0.700080 | − | 0.714064i | \(-0.253148\pi\) | ||||
0.700080 | + | 0.714064i | \(0.253148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.89898 | 0.573382 | 0.286691 | − | 0.958023i | \(-0.407445\pi\) | ||||
0.286691 | + | 0.958023i | \(0.407445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.50000 | + | 4.33013i | 0.284901 | + | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.27526 | + | 7.40496i | −0.481004 | + | 0.833123i | −0.999762 | − | 0.0217978i | \(-0.993061\pi\) |
0.518759 | + | 0.854921i | \(0.326394\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.72474 | + | 4.71940i | −0.299080 | + | 0.518021i | −0.975926 | − | 0.218104i | \(-0.930013\pi\) |
0.676846 | + | 0.736125i | \(0.263346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.44949 | − | 4.24264i | −0.265684 | − | 0.460179i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.10102 | 0.328708 | 0.164354 | − | 0.986401i | \(-0.447446\pi\) | ||||
0.164354 | + | 0.986401i | \(0.447446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65153 | 0.592441 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | − | 3.46410i | −0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.94949 | + | 5.10867i | −0.299475 | + | 0.518706i | −0.976016 | − | 0.217699i | \(-0.930145\pi\) |
0.676541 | + | 0.736405i | \(0.263478\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.39898 | + | 5.88721i | −0.338211 | + | 0.585799i | −0.984096 | − | 0.177636i | \(-0.943155\pi\) |
0.645885 | + | 0.763435i | \(0.276488\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.72474 | − | 15.1117i | −0.859675 | − | 1.48900i | −0.872239 | − | 0.489079i | \(-0.837333\pi\) |
0.0125648 | − | 0.999921i | \(-0.496000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.7980 | −1.33390 | −0.666950 | − | 0.745103i | \(-0.732400\pi\) | ||||
−0.666950 | + | 0.745103i | \(0.732400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.89898 | −0.852368 | −0.426184 | − | 0.904637i | \(-0.640142\pi\) | ||||
−0.426184 | + | 0.904637i | \(0.640142\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.39898 | − | 9.35131i | −0.507893 | − | 0.879697i | −0.999958 | − | 0.00913847i | \(-0.997091\pi\) |
0.492065 | − | 0.870558i | \(-0.336242\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.275255 | + | 0.476756i | −0.0256677 | + | 0.0444577i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.55051 | − | 6.14966i | 0.325475 | − | 0.563739i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.449490 | − | 0.778539i | −0.0408627 | − | 0.0707763i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.62372 | + | 9.74058i | 0.491347 | + | 0.851038i | 0.999950 | − | 0.00996288i | \(-0.00317134\pi\) |
−0.508603 | + | 0.861001i | \(0.669838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.89898 | − | 5.02118i | 0.251373 | − | 0.435392i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.94949 | + | 17.2330i | −0.850042 | + | 1.47232i | 0.0311270 | + | 0.999515i | \(0.490090\pi\) |
−0.881169 | + | 0.472801i | \(0.843243\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.724745 | − | 1.25529i | −0.0614721 | − | 0.106473i | 0.833652 | − | 0.552291i | \(-0.186246\pi\) |
−0.895124 | + | 0.445818i | \(0.852913\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.4495 | −1.12470 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.89898 | −0.822066 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.94949 | + | 12.0369i | 0.569324 | + | 0.986099i | 0.996633 | + | 0.0819929i | \(0.0261285\pi\) |
−0.427309 | + | 0.904106i | \(0.640538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.62372 | − | 8.00853i | 0.376273 | − | 0.651725i | −0.614243 | − | 0.789117i | \(-0.710539\pi\) |
0.990517 | + | 0.137392i | \(0.0438720\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.72474 | + | 6.45145i | −0.299179 | + | 0.518193i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.39898 | − | 7.61926i | −0.351077 | − | 0.608083i | 0.635362 | − | 0.772215i | \(-0.280851\pi\) |
−0.986438 | + | 0.164132i | \(0.947518\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.797959 | −0.0628880 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7980 | 1.08074 | 0.540370 | − | 0.841428i | \(-0.318284\pi\) | ||||
0.540370 | + | 0.841428i | \(0.318284\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.72474 | + | 8.18350i | 0.365612 | + | 0.633258i | 0.988874 | − | 0.148755i | \(-0.0475265\pi\) |
−0.623262 | + | 0.782013i | \(0.714193\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.10102 | + | 1.90702i | −0.0846939 | + | 0.146694i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.50000 | − | 2.59808i | 0.114043 | − | 0.197528i | −0.803354 | − | 0.595502i | \(-0.796953\pi\) |
0.917397 | + | 0.397974i | \(0.130287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.89898 | − | 5.02118i | −0.219142 | − | 0.379566i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.6969 | −1.38973 | −0.694866 | − | 0.719139i | \(-0.744536\pi\) | ||||
−0.694866 | + | 0.719139i | \(0.744536\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.44949 | − | 7.70674i | −0.327133 | − | 0.566611i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.44949 | + | 14.6349i | −0.617888 | + | 1.07021i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.72474 | + | 15.1117i | −0.631300 | + | 1.09344i | 0.355986 | + | 0.934491i | \(0.384145\pi\) |
−0.987286 | + | 0.158953i | \(0.949188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.94949 | − | 12.0369i | −0.500235 | − | 0.866433i | −1.00000 | 0.000271627i | \(-0.999914\pi\) | |
0.499765 | − | 0.866161i | \(-0.333420\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.5959 | −1.53865 | −0.769323 | − | 0.638860i | \(-0.779406\pi\) | ||||
−0.769323 | + | 0.638860i | \(0.779406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7980 | 0.836335 | 0.418168 | − | 0.908370i | \(-0.362672\pi\) | ||||
0.418168 | + | 0.908370i | \(0.362672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.17423 | − | 12.4261i | −0.503533 | − | 0.872144i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.05051 | + | 1.81954i | −0.0733708 | + | 0.127082i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.89898 | + | 11.9494i | −0.477212 | + | 0.826556i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.72474 | − | 13.3797i | −0.531793 | − | 0.921093i | −0.999311 | − | 0.0371095i | \(-0.988185\pi\) |
0.467518 | − | 0.883984i | \(-0.345148\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.3485 | 0.842159 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7980 | −0.733013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.55051 | + | 16.5420i | 0.642437 | + | 1.11273i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.07321 | + | 15.7153i | −0.607587 | + | 1.05237i | 0.384049 | + | 0.923313i | \(0.374529\pi\) |
−0.991637 | + | 0.129060i | \(0.958804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.1742 | − | 19.3543i | 0.741660 | − | 1.28459i | −0.210079 | − | 0.977684i | \(-0.567372\pi\) |
0.951739 | − | 0.306908i | \(-0.0992945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | + | 0.866025i | 0.0330409 | + | 0.0572286i | 0.882073 | − | 0.471113i | \(-0.156147\pi\) |
−0.849032 | + | 0.528341i | \(0.822814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.34847 | −0.544594 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0732 | − | 17.4473i | −0.651582 | − | 1.12857i | −0.982739 | − | 0.184998i | \(-0.940772\pi\) |
0.331157 | − | 0.943576i | \(-0.392561\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | + | 6.06218i | −0.225455 | + | 0.390499i | −0.956456 | − | 0.291877i | \(-0.905720\pi\) |
0.731001 | + | 0.682376i | \(0.239053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.44949 | − | 4.24264i | 0.156492 | − | 0.271052i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.79796 | + | 13.5065i | 0.496172 | + | 0.859396i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.20204 | −0.138992 | −0.0694958 | − | 0.997582i | \(-0.522139\pi\) | ||||
−0.0694958 | + | 0.997582i | \(0.522139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.89898 | 0.119388 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.39898 | + | 7.61926i | 0.274401 | + | 0.475276i | 0.969984 | − | 0.243170i | \(-0.0781872\pi\) |
−0.695583 | + | 0.718446i | \(0.744854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.44949 | − | 11.1708i | 0.400752 | − | 0.694122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.275255 | − | 0.476756i | 0.0169730 | − | 0.0293980i | −0.857414 | − | 0.514627i | \(-0.827930\pi\) |
0.874387 | + | 0.485229i | \(0.161264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.449490 | − | 0.778539i | −0.0276119 | − | 0.0478253i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.8990 | −1.03035 | −0.515174 | − | 0.857085i | \(-0.672273\pi\) | ||||
−0.515174 | + | 0.857085i | \(0.672273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.3939 | −1.78555 | −0.892775 | − | 0.450502i | \(-0.851245\pi\) | ||||
−0.892775 | + | 0.450502i | \(0.851245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.89898 | + | 11.9494i | 0.416024 | + | 0.720575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.39898 | + | 4.15515i | −0.144141 | + | 0.249659i | −0.929052 | − | 0.369949i | \(-0.879375\pi\) |
0.784911 | + | 0.619608i | \(0.212708\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.94949 | + | 17.2330i | −0.593537 | + | 1.02804i | 0.400215 | + | 0.916421i | \(0.368936\pi\) |
−0.993752 | + | 0.111615i | \(0.964398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.724745 | − | 1.25529i | −0.0430816 | − | 0.0746195i | 0.843681 | − | 0.536846i | \(-0.180384\pi\) |
−0.886762 | + | 0.462226i | \(0.847051\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.04541 | −0.179765 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.39898 | − | 16.2795i | −0.549094 | − | 0.951059i | −0.998337 | − | 0.0576493i | \(-0.981639\pi\) |
0.449243 | − | 0.893410i | \(-0.351694\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.174235 | + | 0.301783i | −0.0101443 | + | 0.0175705i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.07321 | − | 1.85886i | 0.0620656 | − | 0.107501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.94949 | + | 15.5010i | 0.515840 | + | 0.893461i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.89898 | 0.108735 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.20204 | −0.125677 | −0.0628386 | − | 0.998024i | \(-0.520015\pi\) | ||||
−0.0628386 | + | 0.998024i | \(0.520015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.62372 | + | 8.00853i | 0.262187 | + | 0.454122i | 0.966823 | − | 0.255448i | \(-0.0822228\pi\) |
−0.704636 | + | 0.709569i | \(0.748889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | − | 14.7224i | 0.480448 | − | 0.832161i | −0.519300 | − | 0.854592i | \(-0.673807\pi\) |
0.999748 | + | 0.0224310i | \(0.00714060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.05051 | − | 13.9439i | 0.452162 | − | 0.783167i | −0.546358 | − | 0.837552i | \(-0.683986\pi\) |
0.998520 | + | 0.0543845i | \(0.0173197\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.0732 | + | 29.5717i | 0.955916 | + | 1.65570i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.5959 | 1.09035 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.5959 | 0.865106 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.05051 | − | 10.4798i | −0.333575 | − | 0.577770i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.62372 | − | 11.4726i | 0.364073 | − | 0.630593i | −0.624554 | − | 0.780982i | \(-0.714719\pi\) |
0.988627 | + | 0.150389i | \(0.0480526\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.17423 | − | 2.03383i | 0.0641553 | − | 0.111120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.39898 | − | 7.61926i | −0.239628 | − | 0.415047i | 0.720980 | − | 0.692956i | \(-0.243692\pi\) |
−0.960607 | + | 0.277909i | \(0.910359\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.6969 | 1.39157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2474 | 0.931275 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0732 | − | 24.3755i | −0.755490 | − | 1.30855i | −0.945130 | − | 0.326693i | \(-0.894066\pi\) |
0.189641 | − | 0.981854i | \(-0.439268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.39898 | + | 4.15515i | −0.128414 | + | 0.222420i | −0.923062 | − | 0.384650i | \(-0.874322\pi\) |
0.794648 | + | 0.607070i | \(0.207655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.84847 | − | 13.5939i | 0.417732 | − | 0.723533i | −0.577979 | − | 0.816052i | \(-0.696158\pi\) |
0.995711 | + | 0.0925188i | \(0.0294918\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.89898 | − | 10.2173i | −0.313085 | − | 0.542280i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.7980 | −0.939340 | −0.469670 | − | 0.882842i | \(-0.655627\pi\) | ||||
−0.469670 | + | 0.882842i | \(0.655627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.44949 | − | 4.24264i | −0.128212 | − | 0.222070i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.17423 | + | 8.96204i | −0.270093 | + | 0.467815i | −0.968885 | − | 0.247510i | \(-0.920388\pi\) |
0.698793 | + | 0.715324i | \(0.253721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.651531 | − | 1.12848i | 0.0338258 | − | 0.0585880i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.15153 | − | 1.99451i | −0.0596240 | − | 0.103272i | 0.834673 | − | 0.550746i | \(-0.185657\pi\) |
−0.894297 | + | 0.447475i | \(0.852324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.5959 | 1.98779 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.7247 | + | 28.9681i | 0.854595 | + | 1.48020i | 0.877021 | + | 0.480453i | \(0.159528\pi\) |
−0.0224261 | + | 0.999749i | \(0.507139\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.50000 | − | 4.33013i | 0.127412 | − | 0.220684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.39898 | − | 11.0834i | 0.324441 | − | 0.561949i | −0.656958 | − | 0.753927i | \(-0.728157\pi\) |
0.981399 | + | 0.191979i | \(0.0614904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.34847 | − | 2.33562i | −0.0681950 | − | 0.118117i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.55051 | 0.430223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.6969 | 0.938372 | 0.469186 | − | 0.883099i | \(-0.344547\pi\) | ||||
0.469186 | + | 0.883099i | \(0.344547\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.84847 | + | 13.5939i | 0.391934 | + | 0.678849i | 0.992705 | − | 0.120572i | \(-0.0384729\pi\) |
−0.600771 | + | 0.799421i | \(0.705140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.5227 | − | 25.1541i | 0.723427 | − | 1.25301i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.3485 | + | 26.5843i | −0.760795 | + | 1.31774i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.29796 | + | 10.9084i | 0.311414 | + | 0.539385i | 0.978669 | − | 0.205445i | \(-0.0658641\pi\) |
−0.667255 | + | 0.744830i | \(0.732531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.505103 | −0.0248545 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.44949 | 0.267505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.37628 | − | 5.84788i | −0.164942 | − | 0.285688i | 0.771693 | − | 0.635995i | \(-0.219410\pi\) |
−0.936635 | + | 0.350308i | \(0.886077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.94949 | + | 8.57277i | −0.241223 | + | 0.417811i | −0.961063 | − | 0.276329i | \(-0.910882\pi\) |
0.719840 | + | 0.694140i | \(0.244215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.79796 | − | 16.9706i | 0.475271 | − | 0.823193i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.37628 | + | 2.38378i | 0.0666026 | + | 0.115359i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7980 | −1.62799 | −0.813995 | − | 0.580872i | \(-0.802712\pi\) | ||||
−0.813995 | + | 0.580872i | \(0.802712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.4949 | 1.94606 | 0.973030 | − | 0.230677i | \(-0.0740942\pi\) | ||||
0.973030 | + | 0.230677i | \(0.0740942\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.10102 | − | 1.90702i | −0.0526690 | − | 0.0912253i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8258 | − | 18.7508i | 0.516686 | − | 0.894926i | −0.483127 | − | 0.875550i | \(-0.660499\pi\) |
0.999812 | − | 0.0193752i | \(-0.00616772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.27526 | − | 16.0652i | 0.440681 | − | 0.763281i | −0.557059 | − | 0.830473i | \(-0.688070\pi\) |
0.997740 | + | 0.0671913i | \(0.0214038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.55051 | − | 2.68556i | −0.0735012 | − | 0.127308i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.8990 | −0.986284 | −0.493142 | − | 0.869949i | \(-0.664152\pi\) | ||||
−0.493142 | + | 0.869949i | \(0.664152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.24745 | 0.341269 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.82577 | − | 4.89437i | −0.132474 | − | 0.229452i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.74745 | + | 15.1510i | −0.409188 | + | 0.708735i | −0.994799 | − | 0.101857i | \(-0.967521\pi\) |
0.585611 | + | 0.810593i | \(0.300855\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.15153 | − | 5.45861i | 0.146781 | − | 0.254233i | −0.783255 | − | 0.621701i | \(-0.786442\pi\) |
0.930036 | + | 0.367468i | \(0.119775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.37628 | + | 5.84788i | 0.156909 | + | 0.271774i | 0.933752 | − | 0.357920i | \(-0.116514\pi\) |
−0.776844 | + | 0.629694i | \(0.783180\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.404082 | −0.0186987 | −0.00934934 | − | 0.999956i | \(-0.502976\pi\) | ||||
−0.00934934 | + | 0.999956i | \(0.502976\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.40408 | 0.157186 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.2980 | − | 36.8891i | −0.979281 | − | 1.69616i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | − | 13.8564i | 0.367065 | − | 0.635776i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.52270 | + | 16.4938i | −0.435103 | + | 0.753621i | −0.997304 | − | 0.0733796i | \(-0.976622\pi\) |
0.562201 | + | 0.827001i | \(0.309955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.3485 | + | 30.0484i | 0.791022 | + | 1.37009i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.89898 | 0.267859 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.79796 | 0.0814733 | 0.0407366 | − | 0.999170i | \(-0.487030\pi\) | ||||
0.0407366 | + | 0.999170i | \(0.487030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6237 | + | 30.5252i | 0.795348 | + | 1.37758i | 0.922618 | + | 0.385714i | \(0.126045\pi\) |
−0.127271 | + | 0.991868i | \(0.540622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.2474 | − | 41.9978i | 1.09205 | − | 1.89149i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.55051 | − | 14.8099i | 0.383543 | − | 0.664316i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.17423 | + | 14.1582i | 0.365929 | + | 0.633808i | 0.988925 | − | 0.148418i | \(-0.0474180\pi\) |
−0.622996 | + | 0.782225i | \(0.714085\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.2020 | 0.900764 | 0.450382 | − | 0.892836i | \(-0.351288\pi\) | ||||
0.450382 | + | 0.892836i | \(0.351288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.79796 | 0.302505 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7474 | + | 29.0074i | 0.742318 | + | 1.28573i | 0.951438 | + | 0.307842i | \(0.0996068\pi\) |
−0.209120 | + | 0.977890i | \(0.567060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.55051 | − | 6.14966i | 0.157065 | − | 0.272045i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.72474 | + | 15.1117i | −0.384458 | + | 0.665901i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3990 | + | 24.9398i | 0.633266 | + | 1.09685i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5959 | −1.11923 | −0.559616 | − | 0.828752i | \(-0.689051\pi\) | ||||
−0.559616 | + | 0.828752i | \(0.689051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.2474 | − | 31.6055i | −0.794871 | − | 1.37676i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3485 | − | 19.6561i | 0.493412 | − | 0.854614i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.09592 | − | 7.09434i | 0.177414 | − | 0.307290i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.89898 | + | 11.9494i | 0.298269 | + | 0.516617i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.8990 | −0.727891 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.59592 | −0.412561 | −0.206280 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206280 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.44949 | + | 7.70674i | 0.190595 | + | 0.330121i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.72474 | − | 9.91555i | 0.244772 | − | 0.423958i | −0.717295 | − | 0.696769i | \(-0.754620\pi\) |
0.962068 | + | 0.272811i | \(0.0879534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.7980 | − | 34.2911i | 0.843421 | − | 1.46085i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.19694 | + | 10.7334i | 0.263521 | + | 0.456431i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.6969 | −0.453244 | −0.226622 | − | 0.973983i | \(-0.572768\pi\) | ||||
−0.226622 | + | 0.973983i | \(0.572768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.1464 | −2.03638 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.17423 | − | 8.96204i | −0.218068 | − | 0.377705i | 0.736149 | − | 0.676819i | \(-0.236642\pi\) |
−0.954217 | + | 0.299114i | \(0.903309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.39898 | + | 9.35131i | −0.227137 | + | 0.393412i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.500000 | + | 0.866025i | −0.0209611 | + | 0.0363057i | −0.876316 | − | 0.481737i | \(-0.840006\pi\) |
0.855355 | + | 0.518043i | \(0.173339\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.17423 | + | 15.8902i | 0.383930 | + | 0.664986i | 0.991620 | − | 0.129188i | \(-0.0412371\pi\) |
−0.607690 | + | 0.794174i | \(0.707904\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.20204 | −0.0918315 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.8990 | −1.20308 | −0.601540 | − | 0.798843i | \(-0.705446\pi\) | ||||
−0.601540 | + | 0.798843i | \(0.705446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.94949 | + | 6.84072i | 0.163852 | + | 0.283801i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.55051 | + | 2.68556i | −0.0642156 | + | 0.111225i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.9722 | − | 20.7364i | 0.494145 | − | 0.855885i | −0.505832 | − | 0.862632i | \(-0.668814\pi\) |
0.999977 | + | 0.00674727i | \(0.00214774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.8990 | − | 25.8058i | −0.613902 | − | 1.06331i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.1010 | −0.784385 | −0.392192 | − | 0.919883i | \(-0.628283\pi\) | ||||
−0.392192 | + | 0.919883i | \(0.628283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.10102 | −0.291113 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.7247 | + | 28.9681i | 0.683355 | + | 1.18360i | 0.973951 | + | 0.226759i | \(0.0728130\pi\) |
−0.290596 | + | 0.956846i | \(0.593854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8485 | + | 34.3786i | −0.809636 | + | 1.40233i | 0.103480 | + | 0.994631i | \(0.467002\pi\) |
−0.913116 | + | 0.407699i | \(0.866331\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.449490 | + | 0.778539i | −0.0182744 | + | 0.0316521i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.9722 | + | 24.2005i | 0.567114 | + | 0.982270i | 0.996850 | + | 0.0793153i | \(0.0252734\pi\) |
−0.429736 | + | 0.902955i | \(0.641393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.5505 | 1.31685 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.69694 | 0.108928 | 0.0544642 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544642 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.84847 | − | 4.93369i | −0.114675 | − | 0.198623i | 0.802975 | − | 0.596013i | \(-0.203249\pi\) |
−0.917650 | + | 0.397390i | \(0.869916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.07321 | + | 7.05501i | −0.163716 | + | 0.283565i | −0.936199 | − | 0.351471i | \(-0.885681\pi\) |
0.772482 | + | 0.635036i | \(0.219015\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.24745 | − | 3.89270i | 0.0900421 | − | 0.155958i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.5959 | 1.73828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.7980 | −1.02700 | −0.513500 | − | 0.858089i | \(-0.671651\pi\) | ||||
−0.513500 | + | 0.858089i | \(0.671651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | − | 6.92820i | −0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.55051 | + | 16.5420i | −0.378405 | + | 0.655417i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.29796 | + | 10.9084i | −0.248754 | + | 0.430855i | −0.963180 | − | 0.268856i | \(-0.913355\pi\) |
0.714426 | + | 0.699711i | \(0.246688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.17423 | + | 8.96204i | 0.204052 | + | 0.353428i | 0.949830 | − | 0.312766i | \(-0.101256\pi\) |
−0.745778 | + | 0.666194i | \(0.767922\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.79796 | 0.385198 | 0.192599 | − | 0.981278i | \(-0.438308\pi\) | ||||
0.192599 | + | 0.981278i | \(0.438308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.20204 | 0.0471842 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.50000 | − | 14.7224i | −0.332631 | − | 0.576133i | 0.650396 | − | 0.759595i | \(-0.274603\pi\) |
−0.983027 | + | 0.183462i | \(0.941270\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.62372 | − | 9.74058i | 0.219737 | − | 0.380596i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.1742 | − | 19.3543i | 0.435286 | − | 0.753938i | −0.562033 | − | 0.827115i | \(-0.689980\pi\) |
0.997319 | + | 0.0731770i | \(0.0233138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.1969 | − | 24.5898i | −0.552197 | − | 0.956433i | −0.998116 | − | 0.0613597i | \(-0.980456\pi\) |
0.445919 | − | 0.895073i | \(-0.352877\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.79796 | −0.224835 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.44949 | −0.211005 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.27526 | − | 5.67291i | −0.126440 | − | 0.219000i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6464 | − | 35.7607i | 0.795861 | − | 1.37847i | −0.126429 | − | 0.991976i | \(-0.540352\pi\) |
0.922291 | − | 0.386497i | \(-0.126315\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.1969 | + | 29.7860i | −0.660932 | + | 1.14477i | 0.319439 | + | 0.947607i | \(0.396506\pi\) |
−0.980371 | + | 0.197161i | \(0.936828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.27526 | + | 7.40496i | 0.164069 | + | 0.284176i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.3939 | −1.58389 | −0.791946 | − | 0.610591i | \(-0.790932\pi\) | ||||
−0.791946 | + | 0.610591i | \(0.790932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.8990 | 0.760301 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.75255 | + | 3.03551i | 0.0667669 | + | 0.115644i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.97219 | + | 13.8082i | −0.303277 | + | 0.525290i | −0.976876 | − | 0.213806i | \(-0.931414\pi\) |
0.673600 | + | 0.739096i | \(0.264747\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.724745 | + | 1.25529i | −0.0274911 | + | 0.0476161i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.14643 | − | 8.91388i | −0.194935 | − | 0.337637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.4949 | −1.37839 | −0.689197 | − | 0.724574i | \(-0.742036\pi\) | ||||
−0.689197 | + | 0.724574i | \(0.742036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.5959 | 1.34253 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.92679 | + | 8.53344i | 0.185291 | + | 0.320933i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.50000 | − | 4.33013i | 0.0938895 | − | 0.162621i | −0.815255 | − | 0.579102i | \(-0.803403\pi\) |
0.909145 | + | 0.416481i | \(0.136737\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.05051 | + | 3.55159i | −0.0767922 | + | 0.133008i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.72474 | + | 11.6476i | 0.251491 | + | 0.435596i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.1918 | 1.75996 | 0.879979 | − | 0.475012i | \(-0.157556\pi\) | ||||
0.879979 | + | 0.475012i | \(0.157556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.2929 | −0.941955 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.7980 | − | 34.2911i | −0.735278 | − | 1.27354i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.7247 | − | 20.3079i | 0.434847 | − | 0.753177i | −0.562436 | − | 0.826841i | \(-0.690136\pi\) |
0.997283 | + | 0.0736639i | \(0.0234692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.2474 | + | 52.3901i | −1.11874 | + | 1.93772i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.05051 | + | 1.81954i | 0.0388015 | + | 0.0672061i | 0.884774 | − | 0.466020i | \(-0.154313\pi\) |
−0.845972 | + | 0.533227i | \(0.820979\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.10102 | −0.298405 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0000 | −0.514998 | −0.257499 | − | 0.966279i | \(-0.582898\pi\) | ||||
−0.257499 | + | 0.966279i | \(0.582898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2753 | − | 26.4575i | −0.560395 | − | 0.970632i | −0.997462 | − | 0.0712033i | \(-0.977316\pi\) |
0.437067 | − | 0.899429i | \(-0.356017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.94949 | − | 12.0369i | 0.254610 | − | 0.440997i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.0000 | + | 17.3205i | −0.365392 | + | 0.632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3207 | − | 35.1964i | −0.741512 | − | 1.28434i | −0.951807 | − | 0.306698i | \(-0.900776\pi\) |
0.210295 | − | 0.977638i | \(-0.432557\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.24745 | −0.336549 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.0000 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.6464 | + | 37.4927i | 0.784682 | + | 1.35911i | 0.929189 | + | 0.369606i | \(0.120507\pi\) |
−0.144506 | + | 0.989504i | \(0.546159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.44949 | + | 11.1708i | −0.233487 | + | 0.404412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.679337 | − | 1.17665i | 0.0245294 | − | 0.0424862i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.29796 | − | 2.24813i | −0.0468056 | − | 0.0810697i | 0.841673 | − | 0.539987i | \(-0.181571\pi\) |
−0.888479 | + | 0.458917i | \(0.848237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.4949 | −0.449410 | −0.224705 | − | 0.974427i | \(-0.572142\pi\) | ||||
−0.224705 | + | 0.974427i | \(0.572142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.7980 | −1.07037 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.20204 | − | 7.27815i | −0.150554 | − | 0.260767i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.3485 | + | 35.2446i | −0.728125 | + | 1.26115i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.39898 | + | 7.61926i | −0.157006 | + | 0.271943i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.62372 | − | 2.81237i | −0.0578795 | − | 0.100250i | 0.835634 | − | 0.549287i | \(-0.185101\pi\) |
−0.893513 | + | 0.449037i | \(0.851767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.6515 | −0.556504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.40408 | −0.262927 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.15153 | + | 15.8509i | 0.324164 | + | 0.561468i | 0.981343 | − | 0.192266i | \(-0.0615838\pi\) |
−0.657179 | + | 0.753735i | \(0.728250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.4495 | − | 35.4196i | 0.723451 | − | 1.25305i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.44949 | + | 14.6349i | −0.298176 | + | 0.516456i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.398979 | + | 0.691053i | 0.0140622 | + | 0.0243564i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4949 | −0.579930 | −0.289965 | − | 0.957037i | \(-0.593644\pi\) | ||||
−0.289965 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.5959 | 1.67132 | 0.835659 | − | 0.549248i | \(-0.185086\pi\) | ||||
0.835659 | + | 0.549248i | \(0.185086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.89898 | − | 11.9494i | −0.241661 | − | 0.418569i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.6969 | + | 42.7764i | −0.864037 | + | 1.49656i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6464 | + | 46.1530i | −0.929967 | + | 1.61075i | −0.146595 | + | 0.989197i | \(0.546831\pi\) |
−0.783372 | + | 0.621553i | \(0.786502\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.72474 | − | 13.3797i | −0.269268 | − | 0.466385i | 0.699405 | − | 0.714725i | \(-0.253448\pi\) |
−0.968673 | + | 0.248340i | \(0.920115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.8990 | −1.14263 | −0.571314 | − | 0.820731i | \(-0.693566\pi\) | ||||
−0.571314 | + | 0.820731i | \(0.693566\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0000 | + | 20.7846i | 0.415775 | + | 0.720144i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.72474 | − | 8.18350i | 0.163507 | − | 0.283202i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.82577 | + | 13.5546i | −0.270175 | + | 0.467958i | −0.968907 | − | 0.247427i | \(-0.920415\pi\) |
0.698731 | + | 0.715384i | \(0.253748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.4949 | − | 59.7469i | −1.18948 | − | 2.06024i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.20204 | 0.0757525 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.30306 | −0.0447737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.44949 | − | 4.24264i | −0.0839674 | − | 0.145436i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.949490 | + | 1.64456i | −0.0325099 | + | 0.0563088i | −0.881823 | − | 0.471581i | \(-0.843683\pi\) |
0.849313 | + | 0.527890i | \(0.177017\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.05051 | + | 15.6759i | −0.309160 | + | 0.535480i | −0.978179 | − | 0.207765i | \(-0.933381\pi\) |
0.669019 | + | 0.743245i | \(0.266714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.27526 | + | 14.3332i | 0.282348 | + | 0.489041i | 0.971963 | − | 0.235135i | \(-0.0755534\pi\) |
−0.689615 | + | 0.724177i | \(0.742220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.79796 | −0.0612032 | −0.0306016 | − | 0.999532i | \(-0.509742\pi\) | ||||
−0.0306016 | + | 0.999532i | \(0.509742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | −0.102003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.7474 | − | 25.5433i | −0.500273 | − | 0.866498i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.57832 | + | 7.92988i | −0.155130 | + | 0.268694i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.52270 | + | 11.2977i | −0.220508 | + | 0.381930i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.05051 | + | 15.6759i | 0.305614 | + | 0.529339i | 0.977398 | − | 0.211408i | \(-0.0678050\pi\) |
−0.671784 | + | 0.740747i | \(0.734472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4949 | −0.825254 | −0.412627 | − | 0.910900i | \(-0.635389\pi\) | ||||
−0.412627 | + | 0.910900i | \(0.635389\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.404082 | 0.0135984 | 0.00679922 | − | 0.999977i | \(-0.497836\pi\) | ||||
0.00679922 | + | 0.999977i | \(0.497836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.4217 | + | 24.9791i | 0.484233 | + | 0.838716i | 0.999836 | − | 0.0181118i | \(-0.00576547\pi\) |
−0.515603 | + | 0.856827i | \(0.672432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.79796 | − | 10.0424i | 0.194457 | − | 0.336810i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6969 | − | 28.9199i | 0.558742 | − | 0.967769i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | − | 10.3923i | −0.200558 | − | 0.347376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −73.7423 | −2.45944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.40408 | 0.146721 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.34847 | + | 16.1920i | 0.310754 | + | 0.538241i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.376276 | + | 0.651729i | −0.0124940 | + | 0.0216403i | −0.872205 | − | 0.489141i | \(-0.837310\pi\) |
0.859711 | + | 0.510781i | \(0.170644\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7702 | − | 42.9032i | 0.820672 | − | 1.42145i | −0.0845109 | − | 0.996423i | \(-0.526933\pi\) |
0.905183 | − | 0.425023i | \(-0.139734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.39898 | − | 16.2795i | −0.311061 | − | 0.538773i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.3031 | 0.538375 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.79796 | 0.323205 | 0.161602 | − | 0.986856i | \(-0.448334\pi\) | ||||
0.161602 | + | 0.986856i | \(0.448334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.0000 | + | 39.8372i | 0.757054 | + | 1.31126i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.7980 | − | 30.8270i | 0.585193 | − | 1.01358i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.15153 | − | 15.8509i | 0.300252 | − | 0.520052i | −0.675941 | − | 0.736956i | \(-0.736263\pi\) |
0.976193 | + | 0.216904i | \(0.0695959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.79796 | + | 16.9706i | 0.321115 | + | 0.556188i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.8990 | 0.552656 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.50510 | 0.245181 | 0.122591 | − | 0.992457i | \(-0.460880\pi\) | ||||
0.122591 | + | 0.992457i | \(0.460880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.50000 | + | 6.06218i | 0.114097 | + | 0.197621i | 0.917418 | − | 0.397924i | \(-0.130269\pi\) |
−0.803322 | + | 0.595545i | \(0.796936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.578317 | + | 1.00167i | −0.0188326 | + | 0.0326190i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.6237 | + | 39.1854i | −0.735172 | + | 1.27336i | 0.219475 | + | 0.975618i | \(0.429565\pi\) |
−0.954648 | + | 0.297738i | \(0.903768\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.55051 | + | 16.5420i | 0.310023 | + | 0.536975i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.8990 | −1.71357 | −0.856783 | − | 0.515677i | \(-0.827540\pi\) | ||||
−0.856783 | + | 0.515677i | \(0.827540\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.4495 | 0.564652 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.4217 | + | 24.9791i | 0.465700 | + | 0.806617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.2474 | + | 21.2132i | −0.395079 | + | 0.684297i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.94949 | + | 12.0369i | −0.223712 | + | 0.387481i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.62372 | − | 8.00853i | −0.148689 | − | 0.257537i | 0.782054 | − | 0.623210i | \(-0.214172\pi\) |
−0.930743 | + | 0.365674i | \(0.880839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.0000 | 0.320915 | 0.160458 | − | 0.987043i | \(-0.448703\pi\) | ||||
0.160458 | + | 0.987043i | \(0.448703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.10102 | −0.0673556 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.3990 | + | 28.4039i | 0.524650 | + | 0.908720i | 0.999588 | + | 0.0287010i | \(0.00913707\pi\) |
−0.474938 | + | 0.880019i | \(0.657530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.34847 | + | 9.26382i | −0.170938 | + | 0.296073i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.1742 | − | 29.7466i | 0.547773 | − | 0.948771i | −0.450654 | − | 0.892699i | \(-0.648809\pi\) |
0.998427 | − | 0.0560718i | \(-0.0178576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7980 | + | 18.7026i | 0.344052 | + | 0.595915i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.79796 | 0.216163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.3939 | 1.18786 | 0.593928 | − | 0.804518i | \(-0.297576\pi\) | ||||
0.593928 | + | 0.804518i | \(0.297576\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.89898 | − | 10.2173i | −0.187010 | − | 0.323911i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.1969 | − | 22.8578i | 0.417951 | − | 0.723913i | −0.577782 | − | 0.816191i | \(-0.696082\pi\) |
0.995733 | + | 0.0922783i | \(0.0294150\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.i.c.289.2 | 4 | ||
3.2 | odd | 2 | 288.2.i.e.97.1 | yes | 4 | ||
4.3 | odd | 2 | 864.2.i.e.289.1 | 4 | |||
8.3 | odd | 2 | 1728.2.i.m.1153.1 | 4 | |||
8.5 | even | 2 | 1728.2.i.k.1153.2 | 4 | |||
9.2 | odd | 6 | 2592.2.a.n.1.1 | 2 | |||
9.4 | even | 3 | inner | 864.2.i.c.577.2 | 4 | ||
9.5 | odd | 6 | 288.2.i.e.193.2 | yes | 4 | ||
9.7 | even | 3 | 2592.2.a.s.1.1 | 2 | |||
12.11 | even | 2 | 288.2.i.c.97.2 | ✓ | 4 | ||
24.5 | odd | 2 | 576.2.i.i.385.2 | 4 | |||
24.11 | even | 2 | 576.2.i.m.385.1 | 4 | |||
36.7 | odd | 6 | 2592.2.a.o.1.2 | 2 | |||
36.11 | even | 6 | 2592.2.a.j.1.2 | 2 | |||
36.23 | even | 6 | 288.2.i.c.193.1 | yes | 4 | ||
36.31 | odd | 6 | 864.2.i.e.577.1 | 4 | |||
72.5 | odd | 6 | 576.2.i.i.193.1 | 4 | |||
72.11 | even | 6 | 5184.2.a.bu.1.2 | 2 | |||
72.13 | even | 6 | 1728.2.i.k.577.2 | 4 | |||
72.29 | odd | 6 | 5184.2.a.by.1.1 | 2 | |||
72.43 | odd | 6 | 5184.2.a.bj.1.2 | 2 | |||
72.59 | even | 6 | 576.2.i.m.193.2 | 4 | |||
72.61 | even | 6 | 5184.2.a.bn.1.1 | 2 | |||
72.67 | odd | 6 | 1728.2.i.m.577.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.c.97.2 | ✓ | 4 | 12.11 | even | 2 | ||
288.2.i.c.193.1 | yes | 4 | 36.23 | even | 6 | ||
288.2.i.e.97.1 | yes | 4 | 3.2 | odd | 2 | ||
288.2.i.e.193.2 | yes | 4 | 9.5 | odd | 6 | ||
576.2.i.i.193.1 | 4 | 72.5 | odd | 6 | |||
576.2.i.i.385.2 | 4 | 24.5 | odd | 2 | |||
576.2.i.m.193.2 | 4 | 72.59 | even | 6 | |||
576.2.i.m.385.1 | 4 | 24.11 | even | 2 | |||
864.2.i.c.289.2 | 4 | 1.1 | even | 1 | trivial | ||
864.2.i.c.577.2 | 4 | 9.4 | even | 3 | inner | ||
864.2.i.e.289.1 | 4 | 4.3 | odd | 2 | |||
864.2.i.e.577.1 | 4 | 36.31 | odd | 6 | |||
1728.2.i.k.577.2 | 4 | 72.13 | even | 6 | |||
1728.2.i.k.1153.2 | 4 | 8.5 | even | 2 | |||
1728.2.i.m.577.1 | 4 | 72.67 | odd | 6 | |||
1728.2.i.m.1153.1 | 4 | 8.3 | odd | 2 | |||
2592.2.a.j.1.2 | 2 | 36.11 | even | 6 | |||
2592.2.a.n.1.1 | 2 | 9.2 | odd | 6 | |||
2592.2.a.o.1.2 | 2 | 36.7 | odd | 6 | |||
2592.2.a.s.1.1 | 2 | 9.7 | even | 3 | |||
5184.2.a.bj.1.2 | 2 | 72.43 | odd | 6 | |||
5184.2.a.bn.1.1 | 2 | 72.61 | even | 6 | |||
5184.2.a.bu.1.2 | 2 | 72.11 | even | 6 | |||
5184.2.a.by.1.1 | 2 | 72.29 | odd | 6 |