Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(193,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.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: | \(4.59938315643\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.193 |
Dual form | 576.2.i.m.385.1 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.724745 | − | 1.25529i | −0.273928 | − | 0.474457i | 0.695936 | − | 0.718104i | \(-0.254990\pi\) |
−0.969864 | + | 0.243647i | \(0.921656\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.72474 | + | 2.98735i | 0.520030 | + | 0.900719i | 0.999729 | + | 0.0232854i | \(0.00741263\pi\) |
−0.479699 | + | 0.877433i | \(0.659254\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.94949 | + | 3.37662i | −0.540691 | + | 0.936505i | 0.458173 | + | 0.888863i | \(0.348504\pi\) |
−0.998864 | + | 0.0476417i | \(0.984829\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.72474 | + | 0.158919i | −0.445327 | + | 0.0410326i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.89898 | −1.18818 | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.05051 | − | 2.28024i | 0.229240 | − | 0.497589i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.275255 | + | 0.476756i | −0.0573947 | + | 0.0994105i | −0.893295 | − | 0.449471i | \(-0.851613\pi\) |
0.835900 | + | 0.548881i | \(0.184946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.94949 | + | 8.57277i | 0.919097 | + | 1.59192i | 0.800789 | + | 0.598946i | \(0.204414\pi\) |
0.118308 | + | 0.992977i | \(0.462253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.72474 | − | 6.45145i | 0.668984 | − | 1.15871i | −0.309205 | − | 0.950996i | \(-0.600063\pi\) |
0.978189 | − | 0.207719i | \(-0.0666038\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.50000 | + | 5.42650i | −0.435194 | + | 0.944633i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.44949 | 0.245008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.89898 | −1.46298 | −0.731492 | − | 0.681850i | \(-0.761175\pi\) | ||||
−0.731492 | + | 0.681850i | \(0.761175\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.72474 | + | 0.619620i | −1.07682 | + | 0.0992187i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.05051 | − | 1.81954i | 0.164062 | − | 0.284164i | −0.772260 | − | 0.635307i | \(-0.780874\pi\) |
0.936322 | + | 0.351143i | \(0.114207\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.17423 | − | 10.6941i | −0.941562 | − | 1.63083i | −0.762493 | − | 0.646997i | \(-0.776025\pi\) |
−0.179069 | − | 0.983836i | \(-0.557309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.94949 | − | 2.28024i | −0.290613 | − | 0.339918i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.17423 | + | 7.22999i | 0.608875 | + | 1.05460i | 0.991426 | + | 0.130668i | \(0.0417121\pi\) |
−0.382552 | + | 0.923934i | \(0.624955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.44949 | − | 4.24264i | 0.349927 | − | 0.606092i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.89898 | − | 6.92820i | −0.685994 | − | 0.970143i | ||||
\(52\) | 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 | ||||||||
\(57\) | 4.00000 | + | 5.65685i | 0.529813 | + | 0.749269i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.174235 | − | 0.301783i | 0.0226834 | − | 0.0392888i | −0.854461 | − | 0.519516i | \(-0.826112\pi\) |
0.877144 | + | 0.480227i | \(0.159446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.949490 | + | 1.64456i | 0.121570 | + | 0.210565i | 0.920387 | − | 0.391009i | \(-0.127874\pi\) |
−0.798817 | + | 0.601574i | \(0.794541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.27526 | − | 0.794593i | 0.538632 | − | 0.100109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.94949 | − | 3.37662i | −0.241804 | − | 0.418818i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.17423 | − | 2.03383i | 0.143456 | − | 0.248472i | −0.785340 | − | 0.619065i | \(-0.787512\pi\) |
0.928796 | + | 0.370592i | \(0.120845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.949490 | + | 0.0874863i | −0.114305 | + | 0.0105321i | ||||
\(70\) | 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 | ||||||||
\(75\) | −2.89898 | + | 6.29253i | −0.334745 | + | 0.726599i | ||||
\(76\) | 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 | \(-0.00693899\pi\) |
−0.518759 | + | 0.854921i | \(0.673606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.72474 | + | 4.71940i | 0.299080 | + | 0.518021i | 0.975926 | − | 0.218104i | \(-0.0699871\pi\) |
−0.676846 | + | 0.736125i | \(0.736654\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.44949 | − | 4.24264i | 0.265684 | − | 0.460179i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.17423 | + | 15.5724i | −0.769159 | + | 1.66954i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.10102 | −0.328708 | −0.164354 | − | 0.986401i | \(-0.552554\pi\) | ||||
−0.164354 | + | 0.986401i | \(0.552554\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65153 | 0.592441 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.8485 | − | 1.18386i | 1.33232 | − | 0.122761i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | + | 3.46410i | −0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.94949 | − | 5.10867i | −0.299475 | − | 0.518706i | 0.676541 | − | 0.736405i | \(-0.263478\pi\) |
−0.976016 | + | 0.217699i | \(0.930145\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.1742 | + | 1.89097i | −1.02255 | + | 0.190050i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.39898 | − | 5.88721i | −0.338211 | − | 0.585799i | 0.645885 | − | 0.763435i | \(-0.276488\pi\) |
−0.984096 | + | 0.177636i | \(0.943155\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.72474 | − | 15.1117i | 0.859675 | − | 1.48900i | −0.0125648 | − | 0.999921i | \(-0.504000\pi\) |
0.872239 | − | 0.489079i | \(-0.162667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.44949 | + | 2.04989i | 0.141456 | + | 0.200049i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7980 | 1.33390 | 0.666950 | − | 0.745103i | \(-0.267600\pi\) | ||||
0.666950 | + | 0.745103i | \(0.267600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.89898 | 0.852368 | 0.426184 | − | 0.904637i | \(-0.359858\pi\) | ||||
0.426184 | + | 0.904637i | \(0.359858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.89898 | − | 12.5851i | −0.844654 | − | 1.19452i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.39898 | − | 9.35131i | 0.507893 | − | 0.879697i | −0.492065 | − | 0.870558i | \(-0.663758\pi\) |
0.999958 | − | 0.00913847i | \(-0.00290891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.275255 | − | 0.476756i | −0.0256677 | − | 0.0444577i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.60102 | − | 8.89060i | −0.702715 | − | 0.821937i | ||||
\(118\) | 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 | ||||||||
\(123\) | 3.62372 | − | 0.333891i | 0.326740 | − | 0.0301060i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.94949 | − | 19.4258i | 0.787959 | − | 1.71034i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.62372 | + | 9.74058i | −0.491347 | + | 0.851038i | −0.999950 | − | 0.00996288i | \(-0.996829\pi\) |
0.508603 | + | 0.861001i | \(0.330162\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89898 | − | 5.02118i | −0.251373 | − | 0.435392i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.27526 | − | 5.03723i | 0.109756 | − | 0.433536i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.94949 | + | 17.2330i | 0.850042 | + | 1.47232i | 0.881169 | + | 0.472801i | \(0.156757\pi\) |
−0.0311270 | + | 0.999515i | \(0.509910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.724745 | + | 1.25529i | −0.0614721 | + | 0.106473i | −0.895124 | − | 0.445818i | \(-0.852913\pi\) |
0.833652 | + | 0.552291i | \(0.186246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.05051 | + | 13.1332i | −0.509545 | + | 1.10602i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.4495 | −1.12470 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.89898 | −0.822066 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.44949 | − | 0.778539i | 0.696902 | − | 0.0642128i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.94949 | − | 12.0369i | 0.569324 | − | 0.986099i | −0.427309 | − | 0.904106i | \(-0.640538\pi\) |
0.996633 | − | 0.0819929i | \(-0.0261285\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.62372 | − | 8.00853i | −0.376273 | − | 0.651725i | 0.614243 | − | 0.789117i | \(-0.289461\pi\) |
−0.990517 | + | 0.137392i | \(0.956128\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.89898 | − | 13.8564i | 0.396059 | − | 1.12022i | ||||
\(154\) | 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 | \(-0.719149\pi\) |
0.986438 | + | 0.164132i | \(0.0524823\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.898979 | + | 1.27135i | 0.0712937 | + | 0.100825i | ||||
\(160\) | 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 | ||||||||
\(165\) | −3.44949 | − | 4.87832i | −0.268542 | − | 0.379776i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.72474 | − | 8.18350i | 0.365612 | − | 0.633258i | −0.623262 | − | 0.782013i | \(-0.714193\pi\) |
0.988874 | + | 0.148755i | \(0.0475265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.10102 | − | 1.90702i | −0.0846939 | − | 0.146694i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | + | 11.3137i | −0.305888 | + | 0.865181i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | \(-0.130287\pi\) |
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.89898 | − | 5.02118i | 0.219142 | − | 0.379566i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.601021 | − | 0.0553782i | 0.0451755 | − | 0.00416248i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6969 | 1.38973 | 0.694866 | − | 0.719139i | \(-0.255464\pi\) | ||||
0.694866 | + | 0.719139i | \(0.255464\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.37628 | + | 2.98735i | −0.101737 | + | 0.220831i | ||||
\(184\) | 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 | ||||||||
\(189\) | 5.39898 | + | 5.25153i | 0.392718 | + | 0.381993i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.72474 | − | 15.1117i | −0.631300 | − | 1.09344i | −0.987286 | − | 0.158953i | \(-0.949188\pi\) |
0.355986 | − | 0.934491i | \(-0.384145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.94949 | + | 12.0369i | −0.500235 | + | 0.866433i | 0.499765 | + | 0.866161i | \(0.333420\pi\) |
−1.00000 | 0.000271627i | \(0.999914\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.82577 | − | 6.13361i | 0.202357 | − | 0.439237i | ||||
\(196\) | 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 | \(-0.637328\pi\) | ||||
−0.418168 | + | 0.908370i | \(0.637328\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.05051 | − | 0.373215i | 0.285701 | − | 0.0263246i | ||||
\(202\) | 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 | ||||||||
\(207\) | −1.07321 | − | 1.25529i | −0.0745935 | − | 0.0872490i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.89898 | + | 11.9494i | 0.477212 | + | 0.826556i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.72474 | + | 13.3797i | −0.531793 | + | 0.921093i | 0.467518 | + | 0.883984i | \(0.345148\pi\) |
−0.999311 | + | 0.0371095i | \(0.988185\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.7980 | + | 16.6848i | 0.808383 | + | 1.14323i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.3485 | 0.842159 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7980 | −0.733013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.89898 | + | 6.92820i | 0.331042 | + | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.55051 | − | 16.5420i | 0.642437 | − | 1.11273i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.07321 | + | 15.7153i | 0.607587 | + | 1.05237i | 0.991637 | + | 0.129060i | \(0.0411959\pi\) |
−0.384049 | + | 0.923313i | \(0.625471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.7980 | + | 2.19275i | −0.786531 | + | 0.146184i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1742 | − | 19.3543i | −0.741660 | − | 1.28459i | −0.951739 | − | 0.306908i | \(-0.900705\pi\) |
0.210079 | − | 0.977684i | \(-0.432628\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | + | 0.866025i | −0.0330409 | + | 0.0572286i | −0.882073 | − | 0.471113i | \(-0.843853\pi\) |
0.849032 | + | 0.528341i | \(0.177186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.62372 | − | 0.794593i | 0.567399 | − | 0.0522804i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.34847 | −0.544594 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.19694 | + | 13.4511i | −0.402534 | + | 0.873742i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0732 | + | 17.4473i | −0.651582 | + | 1.12857i | 0.331157 | + | 0.943576i | \(0.392561\pi\) |
−0.982739 | + | 0.184998i | \(0.940772\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 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 | ||||||||
\(249\) | −3.94949 | + | 8.57277i | −0.250289 | + | 0.543277i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.20204 | 0.138992 | 0.0694958 | − | 0.997582i | \(-0.477861\pi\) | ||||
0.0694958 | + | 0.997582i | \(0.477861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.89898 | −0.119388 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.44949 | − | 0.778539i | 0.529128 | − | 0.0487540i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.39898 | + | 7.61926i | −0.274401 | + | 0.475276i | −0.969984 | − | 0.243170i | \(-0.921813\pi\) |
0.695583 | + | 0.718446i | \(0.255146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.44949 | + | 11.1708i | 0.400752 | + | 0.694122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.1969 | + | 5.42650i | −1.80725 | + | 0.335892i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.275255 | + | 0.476756i | 0.0169730 | + | 0.0293980i | 0.874387 | − | 0.485229i | \(-0.161264\pi\) |
−0.857414 | + | 0.514627i | \(0.827930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.449490 | + | 0.778539i | −0.0276119 | + | 0.0478253i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.10102 | − | 4.38551i | −0.189779 | − | 0.268389i | ||||
\(268\) | 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 | \(-0.148755\pi\) | ||||
0.892775 | + | 0.450502i | \(0.148755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.65153 | + | 7.99247i | 0.342046 | + | 0.483726i | ||||
\(274\) | 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 | \(-0.120625\pi\) |
−0.784911 | + | 0.619608i | \(0.787292\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5227 | + | 16.9866i | 0.869452 | + | 1.01696i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.94949 | + | 17.2330i | 0.593537 | + | 1.02804i | 0.993752 | + | 0.111615i | \(0.0356022\pi\) |
−0.400215 | + | 0.916421i | \(0.631064\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.724745 | + | 1.25529i | −0.0430816 | + | 0.0746195i | −0.886762 | − | 0.462226i | \(-0.847051\pi\) |
0.843681 | + | 0.536846i | \(0.180384\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.89898 | + | 0.635674i | −0.408660 | + | 0.0376541i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.04541 | −0.179765 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.27526 | − | 9.27987i | 0.250620 | − | 0.543996i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.39898 | + | 16.2795i | −0.549094 | + | 0.951059i | 0.449243 | + | 0.893410i | \(0.351694\pi\) |
−0.998337 | + | 0.0576493i | \(0.981639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.174235 | + | 0.301783i | 0.0101443 | + | 0.0175705i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.8485 | − | 12.4976i | −0.745544 | − | 0.725183i | ||||
\(298\) | 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 | ||||||||
\(303\) | 4.92679 | − | 10.6941i | 0.283036 | − | 0.614359i | ||||
\(304\) | 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 | ||||||||
\(309\) | 30.0959 | − | 2.77305i | 1.71210 | − | 0.157753i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.62372 | − | 8.00853i | 0.262187 | − | 0.454122i | −0.704636 | − | 0.709569i | \(-0.748889\pi\) |
0.966823 | + | 0.255448i | \(0.0822228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.44949 | + | 4.09978i | −0.0816695 | + | 0.230996i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.05051 | + | 13.9439i | 0.452162 | + | 0.783167i | 0.998520 | − | 0.0543845i | \(-0.0173197\pi\) |
−0.546358 | + | 0.837552i | \(0.683986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.0732 | + | 29.5717i | −0.955916 | + | 1.65570i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.7980 | + | 19.5133i | 0.770127 | + | 1.08912i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5959 | −1.09035 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.5959 | −0.865106 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.89898 | + | 12.5851i | 0.492115 | + | 0.695955i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.05051 | − | 10.4798i | 0.333575 | − | 0.577770i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.62372 | + | 11.4726i | 0.364073 | + | 0.630593i | 0.988627 | − | 0.150389i | \(-0.0480526\pi\) |
−0.624554 | + | 0.780982i | \(0.714719\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.89898 | − | 25.1701i | 0.487661 | − | 1.37931i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.17423 | + | 2.03383i | 0.0641553 | + | 0.111120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.39898 | + | 7.61926i | −0.239628 | + | 0.415047i | −0.960607 | − | 0.277909i | \(-0.910359\pi\) |
0.720980 | + | 0.692956i | \(0.243692\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6237 | − | 1.71600i | 1.01150 | − | 0.0932002i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.6969 | 1.39157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2474 | −0.931275 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.398979 | − | 0.866025i | 0.0214803 | − | 0.0466252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0732 | − | 24.3755i | 0.755490 | − | 1.30855i | −0.189641 | − | 0.981854i | \(-0.560732\pi\) |
0.945130 | − | 0.326693i | \(-0.105934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.39898 | + | 4.15515i | 0.128414 | + | 0.222420i | 0.923062 | − | 0.384650i | \(-0.125678\pi\) |
−0.794648 | + | 0.607070i | \(0.792345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.97219 | − | 19.6401i | 0.265396 | − | 1.04831i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.84847 | − | 13.5939i | −0.417732 | − | 0.723533i | 0.577979 | − | 0.816052i | \(-0.303842\pi\) |
−0.995711 | + | 0.0925188i | \(0.970508\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.89898 | + | 10.2173i | −0.313085 | + | 0.542280i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.14643 | + | 11.1708i | −0.272378 | + | 0.591224i | ||||
\(358\) | 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 | ||||||||
\(363\) | −1.55051 | + | 0.142865i | −0.0813807 | + | 0.00749845i | ||||
\(364\) | 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 | \(-0.0796123\pi\) |
−0.698793 | + | 0.715324i | \(0.746279\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.09592 | + | 4.79083i | 0.213225 | + | 0.249401i | ||||
\(370\) | 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 | \(-0.814343\pi\) |
0.894297 | + | 0.447475i | \(0.147676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.00000 | − | 12.7279i | −0.464758 | − | 0.657267i | ||||
\(376\) | 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 | ||||||||
\(381\) | −8.00000 | − | 11.3137i | −0.409852 | − | 0.579619i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.7247 | − | 28.9681i | 0.854595 | − | 1.48020i | −0.0224261 | − | 0.999749i | \(-0.507139\pi\) |
0.877021 | − | 0.480453i | \(-0.159528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.50000 | + | 4.33013i | 0.127412 | + | 0.220684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 36.4217 | − | 6.76928i | 1.85142 | − | 0.344102i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.39898 | + | 11.0834i | 0.324441 | + | 0.561949i | 0.981399 | − | 0.191979i | \(-0.0614904\pi\) |
−0.656958 | + | 0.753927i | \(0.728157\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.34847 | − | 2.33562i | 0.0681950 | − | 0.118117i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.3990 | + | 1.78743i | −0.978549 | + | 0.0901639i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.55051 | −0.430223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.6969 | −0.938372 | −0.469186 | − | 0.883099i | \(-0.655453\pi\) | ||||
−0.469186 | + | 0.883099i | \(0.655453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.20204 | − | 9.12096i | 0.210365 | − | 0.456619i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.84847 | + | 13.5939i | −0.391934 | + | 0.678849i | −0.992705 | − | 0.120572i | \(-0.961527\pi\) |
0.600771 | + | 0.799421i | \(0.294860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.5227 | + | 25.1541i | 0.723427 | + | 1.25301i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.39898 | − | 3.23375i | 0.417349 | − | 0.160686i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.3485 | − | 26.5843i | −0.760795 | − | 1.31774i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.29796 | − | 10.9084i | 0.311414 | − | 0.539385i | −0.667255 | − | 0.744830i | \(-0.732531\pi\) |
0.978669 | + | 0.205445i | \(0.0658641\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4217 | + | 31.3037i | −0.711369 | + | 1.54410i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.505103 | −0.0248545 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.44949 | −0.267505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.50000 | + | 0.230351i | −0.122426 | + | 0.0112803i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.37628 | − | 5.84788i | 0.164942 | − | 0.285688i | −0.771693 | − | 0.635995i | \(-0.780590\pi\) |
0.936635 | + | 0.350308i | \(0.113923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.94949 | + | 8.57277i | 0.241223 | + | 0.417811i | 0.961063 | − | 0.276329i | \(-0.0891180\pi\) |
−0.719840 | + | 0.694140i | \(0.755785\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.6237 | + | 4.57653i | −1.19725 | + | 0.222519i | ||||
\(424\) | 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 | ||||||||
\(429\) | −13.4495 | − | 19.0205i | −0.649347 | − | 0.918316i | ||||
\(430\) | 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 | ||||||||
\(435\) | −9.89898 | − | 13.9993i | −0.474620 | − | 0.671214i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.10102 | + | 1.90702i | −0.0526690 | + | 0.0912253i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8258 | − | 18.7508i | −0.516686 | − | 0.894926i | −0.999812 | − | 0.0193752i | \(-0.993832\pi\) |
0.483127 | − | 0.875550i | \(-0.339501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.55051 | + | 11.1708i | 0.454786 | + | 0.531945i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.27526 | − | 16.0652i | −0.440681 | − | 0.763281i | 0.557059 | − | 0.830473i | \(-0.311930\pi\) |
−0.997740 | + | 0.0671913i | \(0.978596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55051 | − | 2.68556i | 0.0735012 | − | 0.127308i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.9722 | − | 2.20881i | 1.13385 | − | 0.104473i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.8990 | 0.986284 | 0.493142 | − | 0.869949i | \(-0.335848\pi\) | ||||
0.493142 | + | 0.869949i | \(0.335848\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.24745 | 0.341269 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.70204 | − | 14.5475i | 0.314889 | − | 0.683499i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.82577 | + | 4.89437i | −0.132474 | + | 0.229452i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.74745 | − | 15.1510i | −0.409188 | − | 0.708735i | 0.585611 | − | 0.810593i | \(-0.300855\pi\) |
−0.994799 | + | 0.101857i | \(0.967521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.4949 | − | 6.92820i | 1.14332 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.15153 | + | 5.45861i | 0.146781 | + | 0.254233i | 0.930036 | − | 0.367468i | \(-0.119775\pi\) |
−0.783255 | + | 0.621701i | \(0.786442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.37628 | + | 5.84788i | −0.156909 | + | 0.271774i | −0.933752 | − | 0.357920i | \(-0.883486\pi\) |
0.776844 | + | 0.629694i | \(0.216820\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.39898 | + | 11.7190i | −0.250372 | + | 0.543457i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.404082 | 0.0186987 | 0.00934934 | − | 0.999956i | \(-0.497024\pi\) | ||||
0.00934934 | + | 0.999956i | \(0.497024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.40408 | −0.157186 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.1742 | − | 1.39816i | 0.699192 | − | 0.0644238i | ||||
\(472\) | 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 | ||||||||
\(477\) | −0.898979 | + | 2.54270i | −0.0411614 | + | 0.116422i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.52270 | − | 16.4938i | −0.435103 | − | 0.753621i | 0.562201 | − | 0.827001i | \(-0.309955\pi\) |
−0.997304 | + | 0.0733796i | \(0.976622\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.3485 | − | 30.0484i | 0.791022 | − | 1.37009i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.797959 | + | 1.12848i | 0.0363084 | + | 0.0513478i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.89898 | 0.267859 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.79796 | −0.0814733 | −0.0407366 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407366 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.7980 | + | 19.5133i | 0.623965 | + | 0.882420i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6237 | + | 30.5252i | −0.795348 | + | 1.37758i | 0.127271 | + | 0.991868i | \(0.459378\pi\) |
−0.922618 | + | 0.385714i | \(0.873955\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.2474 | − | 41.9978i | −1.09205 | − | 1.89149i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.44949 | − | 9.75663i | 0.155043 | − | 0.438528i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.55051 | − | 14.8099i | −0.383543 | − | 0.664316i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.17423 | − | 14.1582i | 0.365929 | − | 0.633808i | −0.622996 | − | 0.782225i | \(-0.714085\pi\) |
0.988925 | + | 0.148418i | \(0.0474180\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.2980 | − | 1.50170i | 0.728139 | − | 0.0670910i | ||||
\(502\) | 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 | ||||||||
\(507\) | 1.59592 | − | 3.46410i | 0.0708772 | − | 0.153846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7474 | − | 29.0074i | 0.742318 | − | 1.28573i | −0.209120 | − | 0.977890i | \(-0.567060\pi\) |
0.951438 | − | 0.307842i | \(-0.0996068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.55051 | − | 6.14966i | −0.157065 | − | 0.272045i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0000 | + | 5.65685i | −0.883022 | + | 0.249756i | ||||
\(514\) | 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 | ||||||||
\(519\) | −2.17423 | + | 4.71940i | −0.0954383 | + | 0.207159i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5959 | −1.11923 | −0.559616 | − | 0.828752i | \(-0.689051\pi\) | ||||
−0.559616 | + | 0.828752i | \(0.689051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.0000 | − | 0.921404i | 0.436436 | − | 0.0402134i | ||||
\(526\) | 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 | ||||||||
\(531\) | 0.679337 | + | 0.794593i | 0.0294807 | + | 0.0344824i | ||||
\(532\) | 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 | ||||||||
\(537\) | −12.0000 | − | 16.9706i | −0.517838 | − | 0.732334i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.8990 | 0.727891 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.59592 | 0.412561 | 0.206280 | − | 0.978493i | \(-0.433864\pi\) | ||||
0.206280 | + | 0.978493i | \(0.433864\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.6969 | + | 26.4415i | 0.802362 | + | 1.13471i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.44949 | + | 7.70674i | −0.190595 | + | 0.330121i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.72474 | + | 9.91555i | 0.244772 | + | 0.423958i | 0.962068 | − | 0.272811i | \(-0.0879534\pi\) |
−0.717295 | + | 0.696769i | \(0.754620\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.60102 | + | 1.04100i | −0.239046 | + | 0.0444287i | ||||
\(550\) | 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 | ||||||||
\(555\) | 15.3485 | − | 1.41421i | 0.651506 | − | 0.0600300i | ||||
\(556\) | 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 | ||||||||
\(561\) | 12.2474 | − | 26.5843i | 0.517088 | − | 1.12239i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.17423 | − | 8.96204i | 0.218068 | − | 0.377705i | −0.736149 | − | 0.676819i | \(-0.763358\pi\) |
0.954217 | + | 0.299114i | \(0.0966912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.39898 | + | 9.35131i | 0.227137 | + | 0.393412i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.02781 | + | 12.8868i | −0.0851599 | + | 0.541196i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.500000 | + | 0.866025i | 0.0209611 | + | 0.0363057i | 0.876316 | − | 0.481737i | \(-0.159994\pi\) |
−0.855355 | + | 0.518043i | \(0.826661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.17423 | − | 15.8902i | 0.383930 | − | 0.664986i | −0.607690 | − | 0.794174i | \(-0.707904\pi\) |
0.991620 | + | 0.129188i | \(0.0412371\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.6464 | − | 27.4504i | 0.528312 | − | 1.14675i | ||||
\(574\) | 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 | ||||||||
\(579\) | −23.9722 | + | 2.20881i | −0.996250 | + | 0.0917949i | ||||
\(580\) | 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 | ||||||||
\(585\) | 11.5000 | − | 2.13737i | 0.475466 | − | 0.0883696i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9722 | − | 20.7364i | −0.494145 | − | 0.855885i | 0.505832 | − | 0.862632i | \(-0.331186\pi\) |
−0.999977 | + | 0.00674727i | \(0.997852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8990 | − | 25.8058i | 0.613902 | − | 1.06331i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.5959 | − | 30.5412i | −0.888337 | − | 1.25630i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1010 | 0.784385 | 0.392192 | − | 0.919883i | \(-0.371717\pi\) | ||||
0.392192 | + | 0.919883i | \(0.371717\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.10102 | −0.291113 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.7980 | − | 16.6848i | −0.482858 | − | 0.682865i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.7247 | − | 28.9681i | 0.683355 | − | 1.18360i | −0.290596 | − | 0.956846i | \(-0.593854\pi\) |
0.973951 | − | 0.226759i | \(-0.0728130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8485 | − | 34.3786i | −0.809636 | − | 1.40233i | −0.913116 | − | 0.407699i | \(-0.866331\pi\) |
0.103480 | − | 0.994631i | \(-0.467002\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.57832 | + | 5.35507i | 0.186443 | + | 0.218075i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.449490 | − | 0.778539i | −0.0182744 | − | 0.0316521i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.9722 | + | 24.2005i | −0.567114 | + | 0.982270i | 0.429736 | + | 0.902955i | \(0.358607\pi\) |
−0.996850 | + | 0.0793153i | \(0.974727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.7474 | − | 2.28024i | 1.00282 | − | 0.0923999i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.5505 | −1.31685 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.69694 | −0.108928 | −0.0544642 | − | 0.998516i | \(-0.517345\pi\) | ||||
−0.0544642 | + | 0.998516i | \(0.517345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.52270 | + | 3.30518i | −0.0614013 | + | 0.133278i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.84847 | − | 4.93369i | 0.114675 | − | 0.198623i | −0.802975 | − | 0.596013i | \(-0.796751\pi\) |
0.917650 | + | 0.397390i | \(0.130084\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.07321 | − | 7.05501i | −0.163716 | − | 0.283565i | 0.772482 | − | 0.635036i | \(-0.219015\pi\) |
−0.936199 | + | 0.351471i | \(0.885681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.702041 | − | 2.77305i | 0.0281719 | − | 0.111279i | ||||
\(622\) | 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 | ||||||||
\(627\) | −10.0000 | + | 21.7060i | −0.399362 | + | 0.866855i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.5959 | 1.73828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.7980 | 1.02700 | 0.513500 | − | 0.858089i | \(-0.328349\pi\) | ||||
0.513500 | + | 0.858089i | \(0.328349\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.6464 | + | 2.45521i | −1.05910 | + | 0.0975859i | ||||
\(634\) | 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 | ||||||||
\(639\) | −11.7980 | + | 33.3697i | −0.466720 | + | 1.32008i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.29796 | + | 10.9084i | 0.248754 | + | 0.430855i | 0.963180 | − | 0.268856i | \(-0.0866455\pi\) |
−0.714426 | + | 0.699711i | \(0.753312\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.17423 | − | 8.96204i | 0.204052 | − | 0.353428i | −0.745778 | − | 0.666194i | \(-0.767922\pi\) |
0.949830 | + | 0.312766i | \(0.101256\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.3485 | + | 17.4634i | 0.486221 | + | 0.687620i | ||||
\(646\) | 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 | ||||||||
\(651\) | −10.7980 | − | 15.2706i | −0.423205 | − | 0.598503i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.50000 | + | 14.7224i | −0.332631 | + | 0.576133i | −0.983027 | − | 0.183462i | \(-0.941270\pi\) |
0.650396 | + | 0.759595i | \(0.274603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.62372 | − | 9.74058i | −0.219737 | − | 0.380596i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.89898 | + | 13.8564i | −0.191127 | + | 0.540590i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.1742 | − | 19.3543i | −0.435286 | − | 0.753938i | 0.562033 | − | 0.827115i | \(-0.310020\pi\) |
−0.997319 | + | 0.0731770i | \(0.976686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.1969 | − | 24.5898i | 0.552197 | − | 0.956433i | −0.445919 | − | 0.895073i | \(-0.647123\pi\) |
0.998116 | − | 0.0613597i | \(-0.0195437\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 32.9444 | − | 3.03551i | 1.27945 | − | 0.117889i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.79796 | 0.224835 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.44949 | −0.211005 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.1515 | + | 28.5467i | −0.508468 | + | 1.10368i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.27526 | + | 5.67291i | −0.126440 | + | 0.219000i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6464 | + | 35.7607i | 0.795861 | + | 1.37847i | 0.922291 | + | 0.386497i | \(0.126315\pi\) |
−0.126429 | + | 0.991976i | \(0.540352\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.8990 | − | 14.4921i | −0.573462 | − | 0.557800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.1969 | − | 29.7860i | −0.660932 | − | 1.14477i | −0.980371 | − | 0.197161i | \(-0.936828\pi\) |
0.319439 | − | 0.947607i | \(-0.396506\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.27526 | + | 7.40496i | −0.164069 | + | 0.284176i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.1969 | − | 35.1571i | 0.620668 | − | 1.34722i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.3939 | 1.58389 | 0.791946 | − | 0.610591i | \(-0.209068\pi\) | ||||
0.791946 | + | 0.610591i | \(0.209068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.8990 | −0.760301 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.72474 | + | 0.158919i | −0.0658031 | + | 0.00606312i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.75255 | + | 3.03551i | −0.0667669 | + | 0.115644i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.97219 | − | 13.8082i | −0.303277 | − | 0.525290i | 0.673600 | − | 0.739096i | \(-0.264747\pi\) |
−0.976876 | + | 0.213806i | \(0.931414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.74745 | + | 11.4012i | 0.370275 | + | 0.433096i | ||||
\(694\) | 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 | ||||||||
\(699\) | −6.00000 | − | 8.48528i | −0.226941 | − | 0.320943i | ||||
\(700\) | 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 | ||||||||
\(705\) | −8.34847 | − | 11.8065i | −0.314422 | − | 0.444659i | ||||
\(706\) | 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 | \(-0.196597\pi\) |
−0.909145 | + | 0.416481i | \(0.863263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.2196 | + | 4.68729i | −0.945810 | + | 0.175787i | ||||
\(712\) | 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 | ||||||||
\(717\) | −34.7474 | + | 3.20164i | −1.29767 | + | 0.119568i | ||||
\(718\) | 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 | ||||||||
\(723\) | 5.07321 | − | 11.0119i | 0.188675 | − | 0.409538i | ||||
\(724\) | 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 | \(-0.309864\pi\) |
−0.997283 | + | 0.0736639i | \(0.976531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 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 | \(-0.845687\pi\) |
0.845972 | + | 0.533227i | \(0.179021\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.55051 | + | 7.70674i | −0.130963 | + | 0.284267i | ||||
\(736\) | 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 | ||||||||
\(741\) | −26.8990 | + | 2.47848i | −0.988159 | + | 0.0910493i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2753 | + | 26.4575i | −0.560395 | + | 0.970632i | 0.437067 | + | 0.899429i | \(0.356017\pi\) |
−0.997462 | + | 0.0712033i | \(0.977316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.94949 | + | 12.0369i | 0.254610 | + | 0.440997i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.0732 | + | 2.98735i | −0.588088 | + | 0.109301i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.0000 | − | 17.3205i | −0.365392 | − | 0.632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.3207 | − | 35.1964i | 0.741512 | − | 1.28434i | −0.210295 | − | 0.977638i | \(-0.567443\pi\) |
0.951807 | − | 0.306698i | \(-0.0992241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.20204 | + | 3.11416i | 0.0802468 | + | 0.113486i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.24745 | 0.336549 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.89898 | − | 2.68556i | −0.0689286 | − | 0.0974797i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.6464 | + | 37.4927i | −0.784682 | + | 1.35911i | 0.144506 | + | 0.989504i | \(0.453841\pi\) |
−0.929189 | + | 0.369606i | \(0.879493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.44949 | − | 11.1708i | −0.233487 | − | 0.404412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.55051 | + | 11.1708i | 0.345299 | + | 0.403883i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.679337 | + | 1.17665i | 0.0245294 | + | 0.0424862i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.29796 | + | 2.24813i | −0.0468056 | + | 0.0810697i | −0.888479 | − | 0.458917i | \(-0.848237\pi\) |
0.841673 | + | 0.539987i | \(0.181571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.1742 | + | 1.39816i | −0.546487 | + | 0.0503535i | ||||
\(772\) | 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 | ||||||||
\(777\) | −9.34847 | + | 20.2918i | −0.335374 | + | 0.727964i | ||||
\(778\) | 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 | ||||||||
\(783\) | −36.8712 | − | 35.8642i | −1.31767 | − | 1.28168i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.39898 | + | 7.61926i | 0.157006 | + | 0.271943i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.62372 | + | 2.81237i | −0.0578795 | + | 0.100250i | −0.893513 | − | 0.449037i | \(-0.851767\pi\) |
0.835634 | + | 0.549287i | \(0.185101\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.398979 | + | 0.866025i | −0.0142040 | + | 0.0308313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.6515 | −0.556504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.40408 | −0.262927 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.55051 | + | 0.142865i | −0.0549909 | + | 0.00506688i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.15153 | − | 15.8509i | 0.324164 | − | 0.561468i | −0.657179 | − | 0.753735i | \(-0.728250\pi\) |
0.981343 | + | 0.192266i | \(0.0615838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.4495 | − | 35.4196i | −0.723451 | − | 1.25305i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.10102 | − | 8.77101i | 0.109569 | − | 0.309908i | ||||
\(802\) | 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 | ||||||||
\(807\) | −16.8990 | − | 23.8988i | −0.594872 | − | 0.841276i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4949 | 0.579930 | 0.289965 | − | 0.957037i | \(-0.406356\pi\) | ||||
0.289965 | + | 0.957037i | \(0.406356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.5959 | 1.67132 | 0.835659 | − | 0.549248i | \(-0.185086\pi\) | ||||
0.835659 | + | 0.549248i | \(0.185086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.3939 | + | 41.5692i | 1.03089 | + | 1.45790i | ||||
\(814\) | 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 | ||||||||
\(819\) | −5.65153 | + | 15.9849i | −0.197480 | + | 0.558559i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6464 | − | 46.1530i | −0.929967 | − | 1.61075i | −0.783372 | − | 0.621553i | \(-0.786502\pi\) |
−0.146595 | − | 0.989197i | \(-0.546831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.72474 | − | 13.3797i | 0.269268 | − | 0.466385i | −0.699405 | − | 0.714725i | \(-0.746552\pi\) |
0.968673 | + | 0.248340i | \(0.0798850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.7980 | + | 2.19275i | −0.828539 | + | 0.0763418i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.0000 | −0.973655 | −0.486828 | − | 0.873498i | \(-0.661846\pi\) | ||||
−0.486828 | + | 0.873498i | \(0.661846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.8990 | 1.14263 | 0.571314 | − | 0.820731i | \(-0.306434\pi\) | ||||
0.571314 | + | 0.820731i | \(0.306434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.47730 | + | 7.54782i | −0.120626 | + | 0.261831i | ||||
\(832\) | 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 | ||||||||
\(837\) | −9.50000 | + | 37.5248i | −0.328368 | + | 1.29705i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.82577 | − | 13.5546i | −0.270175 | − | 0.467958i | 0.698731 | − | 0.715384i | \(-0.253748\pi\) |
−0.968907 | + | 0.247427i | \(0.920415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.4949 | + | 59.7469i | −1.18948 | + | 2.06024i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4217 | + | 31.3037i | −0.496709 | + | 1.07816i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.20204 | 0.0757525 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.30306 | 0.0447737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.50000 | + | 0.230351i | −0.0857998 | + | 0.00790562i | ||||
\(850\) | 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 | \(-0.156317\pi\) |
−0.849313 | + | 0.527890i | \(0.822983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.79796 | − | 9.12096i | −0.266685 | − | 0.311930i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.05051 | + | 15.6759i | 0.309160 | + | 0.535480i | 0.978179 | − | 0.207765i | \(-0.0666190\pi\) |
−0.669019 | + | 0.743245i | \(0.733286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.27526 | − | 14.3332i | 0.282348 | − | 0.489041i | −0.689615 | − | 0.724177i | \(-0.742220\pi\) |
0.971963 | + | 0.235135i | \(0.0755534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.04541 | − | 4.30686i | −0.103787 | − | 0.146777i | ||||
\(862\) | 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 | ||||||||
\(867\) | 7.00000 | + | 9.89949i | 0.237732 | + | 0.336204i | ||||
\(868\) | 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 | ||||||||
\(873\) | 17.3990 | − | 3.23375i | 0.588866 | − | 0.109446i | ||||
\(874\) | 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 | \(-0.932195\pi\) |
0.671784 | + | 0.740747i | \(0.265528\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.4217 | + | 2.98735i | −1.09356 | + | 0.100761i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.4949 | 0.825254 | 0.412627 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412627 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.404082 | 0.0135984 | 0.00679922 | − | 0.999977i | \(-0.497836\pi\) | ||||
0.00679922 | + | 0.999977i | \(0.497836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.252551 | + | 0.548188i | −0.00848942 | + | 0.0184271i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.4217 | − | 24.9791i | 0.484233 | − | 0.838716i | −0.515603 | − | 0.856827i | \(-0.672432\pi\) |
0.999836 | + | 0.0181118i | \(0.00576547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.79796 | + | 10.0424i | 0.194457 | + | 0.336810i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.82577 | − | 30.6681i | 0.161669 | − | 1.02742i | ||||
\(892\) | 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 | ||||||||
\(897\) | 1.55561 | − | 3.37662i | 0.0519404 | − | 0.112742i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 73.7423 | 2.45944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.40408 | −0.146721 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.8712 | + | 2.84448i | −1.02733 | + | 0.0946584i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.34847 | + | 16.1920i | −0.310754 | + | 0.538241i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.376276 | − | 0.651729i | −0.0124940 | − | 0.0216403i | 0.859711 | − | 0.510781i | \(-0.170644\pi\) |
−0.872205 | + | 0.489141i | \(0.837310\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.0505 | − | 3.72656i | 0.665033 | − | 0.123602i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7702 | + | 42.9032i | 0.820672 | + | 1.42145i | 0.905183 | + | 0.425023i | \(0.139734\pi\) |
−0.0845109 | + | 0.996423i | \(0.526933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.39898 | + | 16.2795i | −0.311061 | + | 0.538773i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.89898 | − | 2.68556i | −0.0627783 | − | 0.0887820i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.3031 | 0.538375 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.79796 | −0.323205 | −0.161602 | − | 0.986856i | \(-0.551666\pi\) | ||||
−0.161602 | + | 0.986856i | \(0.551666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.20204 | − | 3.11416i | −0.0725597 | − | 0.102615i | ||||
\(922\) | 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 | ||||||||
\(927\) | 34.0176 | + | 39.7890i | 1.11728 | + | 1.30684i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.15153 | − | 15.8509i | −0.300252 | − | 0.520052i | 0.675941 | − | 0.736956i | \(-0.263737\pi\) |
−0.976193 | + | 0.216904i | \(0.930404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.79796 | − | 16.9706i | 0.321115 | − | 0.556188i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.9495 | − | 1.46959i | 0.522163 | − | 0.0481123i | ||||
\(934\) | 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 | ||||||||
\(939\) | −12.3207 | + | 26.7432i | −0.402070 | + | 0.872733i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.50000 | − | 6.06218i | 0.114097 | − | 0.197621i | −0.803322 | − | 0.595545i | \(-0.796936\pi\) |
0.917418 | + | 0.397924i | \(0.130269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.578317 | + | 1.00167i | 0.0188326 | + | 0.0326190i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.24745 | + | 2.04989i | −0.235760 | + | 0.0666829i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6237 | + | 39.1854i | 0.735172 | + | 1.27336i | 0.954648 | + | 0.297738i | \(0.0962321\pi\) |
−0.219475 | + | 0.975618i | \(0.570435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.55051 | + | 16.5420i | −0.310023 | + | 0.536975i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.6691 | + | 25.3290i | −0.378398 | + | 0.821350i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.8990 | 1.71357 | 0.856783 | − | 0.515677i | \(-0.172460\pi\) | ||||
0.856783 | + | 0.515677i | \(0.172460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.4495 | 0.564652 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −58.8939 | + | 5.42650i | −1.90377 | + | 0.175414i | ||||
\(958\) | 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 | ||||||||
\(963\) | −13.7980 | + | 39.0265i | −0.444633 | + | 1.25761i | ||||
\(964\) | 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 | \(-0.785828\pi\) |
0.930743 | + | 0.365674i | \(0.119161\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.5959 | − | 27.7128i | −0.629512 | − | 0.890264i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0000 | −0.320915 | −0.160458 | − | 0.987043i | \(-0.551297\pi\) | ||||
−0.160458 | + | 0.987043i | \(0.551297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.10102 | 0.0673556 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.5959 | − | 22.0560i | −0.499469 | − | 0.706356i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.3990 | + | 28.4039i | −0.524650 | + | 0.908720i | 0.474938 | + | 0.880019i | \(0.342470\pi\) |
−0.999588 | + | 0.0287010i | \(0.990863\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.34847 | − | 9.26382i | −0.170938 | − | 0.296073i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.89898 | + | 25.1701i | −0.284123 | + | 0.803620i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.1742 | + | 29.7466i | 0.547773 | + | 0.948771i | 0.998427 | + | 0.0560718i | \(0.0178576\pi\) |
−0.450654 | + | 0.892699i | \(0.648809\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7980 | − | 18.7026i | 0.344052 | − | 0.595915i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.8712 | − | 1.92308i | 0.664337 | − | 0.0612122i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.79796 | 0.216163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.3939 | −1.18786 | −0.593928 | − | 0.804518i | \(-0.702424\pi\) | ||||
−0.593928 | + | 0.804518i | \(0.702424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.60102 | + | 20.8400i | −0.304679 | + | 0.661337i | ||||
\(994\) | 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 | \(-0.303918\pi\) |
−0.995733 | + | 0.0922783i | \(0.970585\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.4949 | − | 12.5851i | 1.40776 | − | 0.398174i |
(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 | 576.2.i.m.193.2 | 4 | ||
3.2 | odd | 2 | 1728.2.i.m.577.1 | 4 | |||
4.3 | odd | 2 | 576.2.i.i.193.1 | 4 | |||
8.3 | odd | 2 | 288.2.i.e.193.2 | yes | 4 | ||
8.5 | even | 2 | 288.2.i.c.193.1 | yes | 4 | ||
9.2 | odd | 6 | 1728.2.i.m.1153.1 | 4 | |||
9.4 | even | 3 | 5184.2.a.bu.1.2 | 2 | |||
9.5 | odd | 6 | 5184.2.a.bj.1.2 | 2 | |||
9.7 | even | 3 | inner | 576.2.i.m.385.1 | 4 | ||
12.11 | even | 2 | 1728.2.i.k.577.2 | 4 | |||
24.5 | odd | 2 | 864.2.i.e.577.1 | 4 | |||
24.11 | even | 2 | 864.2.i.c.577.2 | 4 | |||
36.7 | odd | 6 | 576.2.i.i.385.2 | 4 | |||
36.11 | even | 6 | 1728.2.i.k.1153.2 | 4 | |||
36.23 | even | 6 | 5184.2.a.bn.1.1 | 2 | |||
36.31 | odd | 6 | 5184.2.a.by.1.1 | 2 | |||
72.5 | odd | 6 | 2592.2.a.o.1.2 | 2 | |||
72.11 | even | 6 | 864.2.i.c.289.2 | 4 | |||
72.13 | even | 6 | 2592.2.a.j.1.2 | 2 | |||
72.29 | odd | 6 | 864.2.i.e.289.1 | 4 | |||
72.43 | odd | 6 | 288.2.i.e.97.1 | yes | 4 | ||
72.59 | even | 6 | 2592.2.a.s.1.1 | 2 | |||
72.61 | even | 6 | 288.2.i.c.97.2 | ✓ | 4 | ||
72.67 | odd | 6 | 2592.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.c.97.2 | ✓ | 4 | 72.61 | even | 6 | ||
288.2.i.c.193.1 | yes | 4 | 8.5 | even | 2 | ||
288.2.i.e.97.1 | yes | 4 | 72.43 | odd | 6 | ||
288.2.i.e.193.2 | yes | 4 | 8.3 | odd | 2 | ||
576.2.i.i.193.1 | 4 | 4.3 | odd | 2 | |||
576.2.i.i.385.2 | 4 | 36.7 | odd | 6 | |||
576.2.i.m.193.2 | 4 | 1.1 | even | 1 | trivial | ||
576.2.i.m.385.1 | 4 | 9.7 | even | 3 | inner | ||
864.2.i.c.289.2 | 4 | 72.11 | even | 6 | |||
864.2.i.c.577.2 | 4 | 24.11 | even | 2 | |||
864.2.i.e.289.1 | 4 | 72.29 | odd | 6 | |||
864.2.i.e.577.1 | 4 | 24.5 | odd | 2 | |||
1728.2.i.k.577.2 | 4 | 12.11 | even | 2 | |||
1728.2.i.k.1153.2 | 4 | 36.11 | even | 6 | |||
1728.2.i.m.577.1 | 4 | 3.2 | odd | 2 | |||
1728.2.i.m.1153.1 | 4 | 9.2 | odd | 6 | |||
2592.2.a.j.1.2 | 2 | 72.13 | even | 6 | |||
2592.2.a.n.1.1 | 2 | 72.67 | odd | 6 | |||
2592.2.a.o.1.2 | 2 | 72.5 | odd | 6 | |||
2592.2.a.s.1.1 | 2 | 72.59 | even | 6 | |||
5184.2.a.bj.1.2 | 2 | 9.5 | odd | 6 | |||
5184.2.a.bn.1.1 | 2 | 36.23 | even | 6 | |||
5184.2.a.bu.1.2 | 2 | 9.4 | even | 3 | |||
5184.2.a.by.1.1 | 2 | 36.31 | odd | 6 |