Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(107,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.23123460096.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} + 6x^{4} + 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.5 | ||
Root | \(-0.563016 - 1.29731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.107 |
Dual form | 216.2.f.a.107.6 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.563016 | − | 1.29731i | 0.398113 | − | 0.917337i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.36603 | − | 1.46081i | −0.683013 | − | 0.730406i | ||||
\(5\) | −3.07638 | −1.37580 | −0.687899 | − | 0.725806i | \(-0.741467\pi\) | ||||
−0.687899 | + | 0.725806i | \(0.741467\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.99102i | − | 1.50846i | −0.656609 | − | 0.754231i | \(-0.728010\pi\) | ||
0.656609 | − | 0.754231i | \(-0.271990\pi\) | |||||||
\(8\) | −2.66422 | + | 0.949697i | −0.941945 | + | 0.335768i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.73205 | + | 3.99102i | −0.547723 | + | 1.26207i | ||||
\(11\) | 1.89939i | 0.572689i | 0.958127 | + | 0.286344i | \(0.0924401\pi\) | ||||
−0.958127 | + | 0.286344i | \(0.907560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.06939i | − | 0.296595i | −0.988943 | − | 0.148298i | \(-0.952621\pi\) | ||
0.988943 | − | 0.148298i | \(-0.0473794\pi\) | |||||||
\(14\) | −5.17758 | − | 2.24701i | −1.38377 | − | 0.600538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.267949 | + | 3.99102i | −0.0669873 | + | 0.997754i | ||||
\(17\) | − | 7.08863i | − | 1.71925i | −0.510929 | − | 0.859623i | \(-0.670698\pi\) | ||
0.510929 | − | 0.859623i | \(-0.329302\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.73205 | 0.856191 | 0.428096 | − | 0.903733i | \(-0.359185\pi\) | ||||
0.428096 | + | 0.903733i | \(0.359185\pi\) | |||||||
\(20\) | 4.20241 | + | 4.49401i | 0.939688 | + | 1.00489i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.46410 | + | 1.06939i | 0.525348 | + | 0.227995i | ||||
\(23\) | 0.824313 | 0.171881 | 0.0859406 | − | 0.996300i | \(-0.472610\pi\) | ||||
0.0859406 | + | 0.996300i | \(0.472610\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | 0.892820 | ||||||||
\(26\) | −1.38733 | − | 0.602084i | −0.272078 | − | 0.118078i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.83013 | + | 5.45183i | −1.10179 | + | 1.03030i | ||||
\(29\) | 4.50413 | 0.836396 | 0.418198 | − | 0.908356i | \(-0.362662\pi\) | ||||
0.418198 | + | 0.908356i | \(0.362662\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.84325i | 1.04948i | 0.851263 | + | 0.524740i | \(0.175837\pi\) | ||||
−0.851263 | + | 0.524740i | \(0.824163\pi\) | |||||||
\(32\) | 5.02672 | + | 2.59462i | 0.888608 | + | 0.458668i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.19615 | − | 3.99102i | −1.57713 | − | 0.684453i | ||||
\(35\) | 12.2779i | 2.07534i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.91264i | − | 1.13643i | −0.822880 | − | 0.568216i | \(-0.807634\pi\) | ||
0.822880 | − | 0.568216i | \(-0.192366\pi\) | |||||||
\(38\) | 2.10121 | − | 4.84163i | 0.340861 | − | 0.785415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.19615 | − | 2.92163i | 1.29593 | − | 0.461950i | ||||
\(41\) | − | 3.79879i | − | 0.593271i | −0.954991 | − | 0.296635i | \(-0.904135\pi\) | ||
0.954991 | − | 0.296635i | \(-0.0958646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 2.77466 | − | 2.59462i | 0.418296 | − | 0.391154i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.464102 | − | 1.06939i | 0.0684280 | − | 0.157673i | ||||
\(47\) | 6.97707 | 1.01771 | 0.508855 | − | 0.860852i | \(-0.330069\pi\) | ||||
0.508855 | + | 0.860852i | \(0.330069\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.92820 | −1.27546 | ||||||||
\(50\) | 2.51336 | − | 5.79132i | 0.355443 | − | 0.819017i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.56218 | + | 1.46081i | −0.216635 | + | 0.202578i | ||||
\(53\) | −10.6569 | −1.46384 | −0.731918 | − | 0.681393i | \(-0.761375\pi\) | ||||
−0.731918 | + | 0.681393i | \(0.761375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.84325i | − | 0.787904i | ||||||
\(56\) | 3.79025 | + | 10.6329i | 0.506494 | + | 1.42089i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.53590 | − | 5.84325i | 0.332980 | − | 0.767257i | ||||
\(59\) | 1.89939i | 0.247280i | 0.992327 | + | 0.123640i | \(0.0394568\pi\) | ||||
−0.992327 | + | 0.123640i | \(0.960543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.06939i | 0.136921i | 0.997654 | + | 0.0684606i | \(0.0218088\pi\) | ||||
−0.997654 | + | 0.0684606i | \(0.978191\pi\) | |||||||
\(62\) | 7.58051 | + | 3.28985i | 0.962725 | + | 0.417811i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.19615 | − | 5.06040i | 0.774519 | − | 0.632551i | ||||
\(65\) | 3.28985i | 0.408055i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.19615 | −1.12349 | −0.561744 | − | 0.827311i | \(-0.689870\pi\) | ||||
−0.561744 | + | 0.827311i | \(0.689870\pi\) | |||||||
\(68\) | −10.3552 | + | 9.68325i | −1.25575 | + | 1.17427i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.9282 | + | 6.91264i | 1.90378 | + | 0.826219i | ||||
\(71\) | 10.6569 | 1.26474 | 0.632370 | − | 0.774667i | \(-0.282082\pi\) | ||||
0.632370 | + | 0.774667i | \(0.282082\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.92820 | 0.693844 | 0.346922 | − | 0.937894i | \(-0.387227\pi\) | ||||
0.346922 | + | 0.937894i | \(0.387227\pi\) | |||||||
\(74\) | −8.96784 | − | 3.89193i | −1.04249 | − | 0.452428i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.09808 | − | 5.45183i | −0.584789 | − | 0.625368i | ||||
\(77\) | 7.58051 | 0.863879 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.12979i | 0.689656i | 0.938666 | + | 0.344828i | \(0.112063\pi\) | ||||
−0.938666 | + | 0.344828i | \(0.887937\pi\) | |||||||
\(80\) | 0.824313 | − | 12.2779i | 0.0921610 | − | 1.37271i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.92820 | − | 2.13878i | −0.544229 | − | 0.236189i | ||||
\(83\) | − | 10.3785i | − | 1.13919i | −0.821927 | − | 0.569593i | \(-0.807101\pi\) | ||
0.821927 | − | 0.569593i | \(-0.192899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.8073i | 2.36534i | ||||||||
\(86\) | 1.12603 | − | 2.59462i | 0.121423 | − | 0.279785i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.80385 | − | 5.06040i | −0.192291 | − | 0.539441i | ||||
\(89\) | − | 13.6683i | − | 1.44884i | −0.689359 | − | 0.724420i | \(-0.742108\pi\) | ||
0.689359 | − | 0.724420i | \(-0.257892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.26795 | −0.447403 | ||||||||
\(92\) | −1.12603 | − | 1.20417i | −0.117397 | − | 0.125543i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.92820 | − | 9.05142i | 0.405163 | − | 0.933583i | ||||
\(95\) | −11.4812 | −1.17795 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3923 | −1.15671 | −0.578357 | − | 0.815784i | \(-0.696306\pi\) | ||||
−0.578357 | + | 0.815784i | \(0.696306\pi\) | |||||||
\(98\) | −5.02672 | + | 11.5826i | −0.507776 | + | 1.17002i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.09808 | − | 6.52122i | −0.609808 | − | 0.652122i | ||||
\(101\) | −6.15276 | −0.612222 | −0.306111 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306111 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.99102i | 0.393246i | 0.980479 | + | 0.196623i | \(0.0629976\pi\) | ||||
−0.980479 | + | 0.196623i | \(0.937002\pi\) | |||||||
\(104\) | 1.01560 | + | 2.84909i | 0.0995873 | + | 0.279376i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | + | 13.8253i | −0.582772 | + | 1.34283i | ||||
\(107\) | 8.47908i | 0.819704i | 0.912152 | + | 0.409852i | \(0.134420\pi\) | ||||
−0.912152 | + | 0.409852i | \(0.865580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1208i | 0.969398i | 0.874681 | + | 0.484699i | \(0.161071\pi\) | ||||
−0.874681 | + | 0.484699i | \(0.838929\pi\) | |||||||
\(110\) | −7.58051 | − | 3.28985i | −0.722773 | − | 0.313674i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.9282 | + | 1.06939i | 1.50507 | + | 0.101048i | ||||
\(113\) | 10.8874i | 1.02420i | 0.858925 | + | 0.512101i | \(0.171133\pi\) | ||||
−0.858925 | + | 0.512101i | \(0.828867\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.53590 | −0.236474 | ||||||||
\(116\) | −6.15276 | − | 6.57969i | −0.571269 | − | 0.610909i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.46410 | + | 1.06939i | 0.226839 | + | 0.0984453i | ||||
\(119\) | −28.2908 | −2.59342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.39230 | 0.672028 | ||||||||
\(122\) | 1.38733 | + | 0.602084i | 0.125603 | + | 0.0545101i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.53590 | − | 7.98203i | 0.766546 | − | 0.716808i | ||||
\(125\) | 1.64863 | 0.147458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −3.07638 | − | 10.8874i | −0.271916 | − | 0.962321i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.26795 | + | 1.85224i | 0.374324 | + | 0.162452i | ||||
\(131\) | − | 10.3785i | − | 0.906772i | −0.891314 | − | 0.453386i | \(-0.850216\pi\) | ||
0.891314 | − | 0.453386i | \(-0.149784\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 14.8947i | − | 1.29153i | ||||||
\(134\) | −5.17758 | + | 11.9303i | −0.447275 | + | 1.03062i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.73205 | + | 18.8857i | 0.577269 | + | 1.61943i | ||||
\(137\) | 17.4671i | 1.49232i | 0.665769 | + | 0.746158i | \(0.268104\pi\) | ||||
−0.665769 | + | 0.746158i | \(0.731896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.19615 | −0.271094 | −0.135547 | − | 0.990771i | \(-0.543279\pi\) | ||||
−0.135547 | + | 0.990771i | \(0.543279\pi\) | |||||||
\(140\) | 17.9357 | − | 16.7719i | 1.51584 | − | 1.41748i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | − | 13.8253i | 0.503509 | − | 1.16019i | ||||
\(143\) | 2.03119 | 0.169857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.8564 | −1.15071 | ||||||||
\(146\) | 3.33767 | − | 7.69072i | 0.276228 | − | 0.636488i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0981 | + | 9.44284i | −0.830057 | + | 0.776197i | ||||
\(149\) | 6.15276 | 0.504053 | 0.252027 | − | 0.967720i | \(-0.418903\pi\) | ||||
0.252027 | + | 0.967720i | \(0.418903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.83427i | 0.800301i | 0.916449 | + | 0.400151i | \(0.131042\pi\) | ||||
−0.916449 | + | 0.400151i | \(0.868958\pi\) | |||||||
\(152\) | −9.94301 | + | 3.54432i | −0.806485 | + | 0.287482i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.26795 | − | 9.83427i | 0.343921 | − | 0.792468i | ||||
\(155\) | − | 17.9761i | − | 1.44387i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 21.8073i | − | 1.74041i | −0.492687 | − | 0.870207i | \(-0.663985\pi\) | ||
0.492687 | − | 0.870207i | \(-0.336015\pi\) | |||||||
\(158\) | 7.95224 | + | 3.45117i | 0.632646 | + | 0.274561i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.4641 | − | 7.98203i | −1.22254 | − | 0.631035i | ||||
\(161\) | − | 3.28985i | − | 0.259276i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.80385 | 0.689571 | 0.344785 | − | 0.938682i | \(-0.387952\pi\) | ||||
0.344785 | + | 0.938682i | \(0.387952\pi\) | |||||||
\(164\) | −5.54932 | + | 5.18924i | −0.433329 | + | 0.405212i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.4641 | − | 5.84325i | −1.04502 | − | 0.453524i | ||||
\(167\) | 22.1381 | 1.71310 | 0.856548 | − | 0.516067i | \(-0.172604\pi\) | ||||
0.856548 | + | 0.516067i | \(0.172604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8564 | 0.912031 | ||||||||
\(170\) | 28.2908 | + | 12.2779i | 2.16981 | + | 0.941670i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.73205 | − | 2.92163i | −0.208317 | − | 0.222772i | ||||
\(173\) | 1.64863 | 0.125343 | 0.0626714 | − | 0.998034i | \(-0.480038\pi\) | ||||
0.0626714 | + | 0.998034i | \(0.480038\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 17.8163i | − | 1.34679i | ||||||
\(176\) | −7.58051 | − | 0.508941i | −0.571402 | − | 0.0383629i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.7321 | − | 7.69549i | −1.32907 | − | 0.576801i | ||||
\(179\) | − | 3.79879i | − | 0.283935i | −0.989871 | − | 0.141967i | \(-0.954657\pi\) | ||
0.989871 | − | 0.141967i | \(-0.0453428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.20817i | − | 0.238461i | −0.992867 | − | 0.119231i | \(-0.961957\pi\) | ||
0.992867 | − | 0.119231i | \(-0.0380428\pi\) | |||||||
\(182\) | −2.40292 | + | 5.53685i | −0.178117 | + | 0.410419i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.19615 | + | 0.782847i | −0.161903 | + | 0.0577123i | ||||
\(185\) | 21.2659i | 1.56350i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4641 | 0.984593 | ||||||||
\(188\) | −9.53085 | − | 10.1922i | −0.695109 | − | 0.743342i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.46410 | + | 14.8947i | −0.468955 | + | 1.08057i | ||||
\(191\) | 6.97707 | 0.504843 | 0.252421 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252421 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.39230 | −0.388147 | −0.194073 | − | 0.980987i | \(-0.562170\pi\) | ||||
−0.194073 | + | 0.980987i | \(0.562170\pi\) | |||||||
\(194\) | −6.41405 | + | 14.7793i | −0.460502 | + | 1.06110i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.1962 | + | 13.0424i | 0.871154 | + | 0.931603i | ||||
\(197\) | 17.0305 | 1.21337 | 0.606687 | − | 0.794941i | \(-0.292498\pi\) | ||||
0.606687 | + | 0.794941i | \(0.292498\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.6775i | 1.11135i | 0.831400 | + | 0.555675i | \(0.187540\pi\) | ||||
−0.831400 | + | 0.555675i | \(0.812460\pi\) | |||||||
\(200\) | −11.8934 | + | 4.23954i | −0.840987 | + | 0.299781i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.46410 | + | 7.98203i | −0.243733 | + | 0.561614i | ||||
\(203\) | − | 17.9761i | − | 1.26167i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6865i | 0.816221i | ||||||||
\(206\) | 5.17758 | + | 2.24701i | 0.360739 | + | 0.156556i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.26795 | + | 0.286542i | 0.295929 | + | 0.0198681i | ||||
\(209\) | 7.08863i | 0.490331i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.0526 | 1.44932 | 0.724659 | − | 0.689108i | \(-0.241997\pi\) | ||||
0.724659 | + | 0.689108i | \(0.241997\pi\) | |||||||
\(212\) | 14.5576 | + | 15.5677i | 0.999818 | + | 1.06920i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.0000 | + | 4.77386i | 0.751945 | + | 0.326335i | ||||
\(215\) | −6.15276 | −0.419614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.3205 | 1.58310 | ||||||||
\(218\) | 13.1298 | + | 5.69818i | 0.889264 | + | 0.385929i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.53590 | + | 7.98203i | −0.575490 | + | 0.538148i | ||||
\(221\) | −7.58051 | −0.509920 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.0849i | − | 1.74677i | −0.487029 | − | 0.873386i | \(-0.661919\pi\) | ||
0.487029 | − | 0.873386i | \(-0.338081\pi\) | |||||||
\(224\) | 10.3552 | − | 20.0617i | 0.691884 | − | 1.34043i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1244 | + | 6.12979i | 0.939538 | + | 0.407748i | ||||
\(227\) | − | 3.79879i | − | 0.252134i | −0.992022 | − | 0.126067i | \(-0.959765\pi\) | ||
0.992022 | − | 0.126067i | \(-0.0402355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.6865i | − | 0.772266i | −0.922443 | − | 0.386133i | \(-0.873811\pi\) | ||
0.922443 | − | 0.386133i | \(-0.126189\pi\) | |||||||
\(230\) | −1.42775 | + | 3.28985i | −0.0941432 | + | 0.216926i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0000 | + | 4.27756i | −0.787839 | + | 0.280835i | ||||
\(233\) | 14.1773i | 0.928784i | 0.885630 | + | 0.464392i | \(0.153727\pi\) | ||||
−0.885630 | + | 0.464392i | \(0.846273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.4641 | −1.40016 | ||||||||
\(236\) | 2.77466 | − | 2.59462i | 0.180615 | − | 0.168895i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.9282 | + | 36.7020i | −1.03247 | + | 2.37904i | ||||
\(239\) | −12.3055 | −0.795977 | −0.397989 | − | 0.917390i | \(-0.630292\pi\) | ||||
−0.397989 | + | 0.917390i | \(0.630292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.39230 | −0.347349 | −0.173674 | − | 0.984803i | \(-0.555564\pi\) | ||||
−0.173674 | + | 0.984803i | \(0.555564\pi\) | |||||||
\(242\) | 4.16199 | − | 9.59011i | 0.267543 | − | 0.616476i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.56218 | − | 1.46081i | 0.100008 | − | 0.0935190i | ||||
\(245\) | 27.4665 | 1.75477 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.99102i | − | 0.253942i | ||||||
\(248\) | −5.54932 | − | 15.5677i | −0.352382 | − | 0.988551i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.928203 | − | 2.13878i | 0.0587047 | − | 0.135268i | ||||
\(251\) | 14.1773i | 0.894861i | 0.894319 | + | 0.447431i | \(0.147661\pi\) | ||||
−0.894319 | + | 0.447431i | \(0.852339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.56569i | 0.0984344i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.8564 | − | 2.13878i | −0.991025 | − | 0.133674i | ||||
\(257\) | − | 3.79879i | − | 0.236962i | −0.992956 | − | 0.118481i | \(-0.962198\pi\) | ||
0.992956 | − | 0.118481i | \(-0.0378024\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.5885 | −1.71426 | ||||||||
\(260\) | 4.80585 | − | 4.49401i | 0.298046 | − | 0.278707i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.4641 | − | 5.84325i | −0.831815 | − | 0.360997i | ||||
\(263\) | −3.29725 | −0.203317 | −0.101659 | − | 0.994819i | \(-0.532415\pi\) | ||||
−0.101659 | + | 0.994819i | \(0.532415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.7846 | 2.01394 | ||||||||
\(266\) | −19.3230 | − | 8.38594i | −1.18477 | − | 0.514175i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.5622 | + | 13.4339i | 0.767357 | + | 0.820604i | ||||
\(269\) | −19.8860 | −1.21247 | −0.606236 | − | 0.795285i | \(-0.707321\pi\) | ||||
−0.606236 | + | 0.795285i | \(0.707321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.9730i | − | 0.727311i | −0.931534 | − | 0.363655i | \(-0.881529\pi\) | ||
0.931534 | − | 0.363655i | \(-0.118471\pi\) | |||||||
\(272\) | 28.2908 | + | 1.89939i | 1.71538 | + | 0.115168i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.6603 | + | 9.83427i | 1.36896 | + | 0.594110i | ||||
\(275\) | 8.47908i | 0.511308i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.8073i | 1.31027i | 0.755510 | + | 0.655137i | \(0.227389\pi\) | ||||
−0.755510 | + | 0.655137i | \(0.772611\pi\) | |||||||
\(278\) | −1.79949 | + | 4.14640i | −0.107926 | + | 0.248685i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.6603 | − | 32.7110i | −0.696833 | − | 1.95485i | ||||
\(281\) | − | 10.3785i | − | 0.619128i | −0.950879 | − | 0.309564i | \(-0.899817\pi\) | ||
0.950879 | − | 0.309564i | \(-0.100183\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.8564 | 1.65589 | 0.827946 | − | 0.560808i | \(-0.189509\pi\) | ||||
0.827946 | + | 0.560808i | \(0.189509\pi\) | |||||||
\(284\) | −14.5576 | − | 15.5677i | −0.863833 | − | 0.923774i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.14359 | − | 2.63508i | 0.0676221 | − | 0.155816i | ||||
\(287\) | −15.1610 | −0.894926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.2487 | −1.95581 | ||||||||
\(290\) | −7.80138 | + | 17.9761i | −0.458113 | + | 1.05559i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.09808 | − | 8.66000i | −0.473904 | − | 0.506788i | ||||
\(293\) | 7.58051 | 0.442858 | 0.221429 | − | 0.975176i | \(-0.428928\pi\) | ||||
0.221429 | + | 0.975176i | \(0.428928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.84325i | − | 0.340207i | ||||||
\(296\) | 6.56491 | + | 18.4168i | 0.381578 | + | 1.07046i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.46410 | − | 7.98203i | 0.200670 | − | 0.462387i | ||||
\(299\) | − | 0.881512i | − | 0.0509791i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 7.98203i | − | 0.460077i | ||||||
\(302\) | 12.7581 | + | 5.53685i | 0.734146 | + | 0.318610i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | + | 14.8947i | −0.0573539 | + | 0.854268i | ||||
\(305\) | − | 3.28985i | − | 0.188376i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9282 | 1.19444 | 0.597218 | − | 0.802079i | \(-0.296273\pi\) | ||||
0.597218 | + | 0.802079i | \(0.296273\pi\) | |||||||
\(308\) | −10.3552 | − | 11.0737i | −0.590040 | − | 0.630983i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −23.3205 | − | 10.1208i | −1.32452 | − | 0.574823i | ||||
\(311\) | −20.4895 | −1.16185 | −0.580925 | − | 0.813957i | \(-0.697309\pi\) | ||||
−0.580925 | + | 0.813957i | \(0.697309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.39230 | 0.530884 | 0.265442 | − | 0.964127i | \(-0.414482\pi\) | ||||
0.265442 | + | 0.964127i | \(0.414482\pi\) | |||||||
\(314\) | −28.2908 | − | 12.2779i | −1.59654 | − | 0.692880i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.95448 | − | 8.37345i | 0.503729 | − | 0.471044i | ||||
\(317\) | −16.8096 | −0.944124 | −0.472062 | − | 0.881565i | \(-0.656490\pi\) | ||||
−0.472062 | + | 0.881565i | \(0.656490\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.55511i | 0.478994i | ||||||||
\(320\) | −19.0617 | + | 15.5677i | −1.06558 | + | 0.870262i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.26795 | − | 1.85224i | −0.237844 | − | 0.103221i | ||||
\(323\) | − | 26.4551i | − | 1.47200i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.77386i | − | 0.264806i | ||||||
\(326\) | 4.95671 | − | 11.4213i | 0.274527 | − | 0.632568i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.60770 | + | 10.1208i | 0.199202 | + | 0.558828i | ||||
\(329\) | − | 27.8456i | − | 1.53518i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.87564 | 0.103095 | 0.0515474 | − | 0.998671i | \(-0.483585\pi\) | ||||
0.0515474 | + | 0.998671i | \(0.483585\pi\) | |||||||
\(332\) | −15.1610 | + | 14.1773i | −0.832069 | + | 0.778079i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4641 | − | 28.7200i | 0.682005 | − | 1.57149i | ||||
\(335\) | 28.2908 | 1.54569 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3923 | −0.620578 | −0.310289 | − | 0.950642i | \(-0.600426\pi\) | ||||
−0.310289 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(338\) | 6.67535 | − | 15.3814i | 0.363091 | − | 0.836640i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 31.8564 | − | 29.7893i | 1.72766 | − | 1.61555i | ||||
\(341\) | −11.0986 | −0.601025 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.69549i | 0.415517i | ||||||||
\(344\) | −5.32844 | + | 1.89939i | −0.287290 | + | 0.102408i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.928203 | − | 2.13878i | 0.0499005 | − | 0.114981i | ||||
\(347\) | 7.59757i | 0.407859i | 0.978986 | + | 0.203930i | \(0.0653714\pi\) | ||||
−0.978986 | + | 0.203930i | \(0.934629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.63508i | − | 0.141053i | −0.997510 | − | 0.0705264i | \(-0.977532\pi\) | ||
0.997510 | − | 0.0705264i | \(-0.0224679\pi\) | |||||||
\(350\) | −23.1133 | − | 10.0309i | −1.23546 | − | 0.536172i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.92820 | + | 9.54773i | −0.262674 | + | 0.508895i | ||||
\(353\) | 7.59757i | 0.404378i | 0.979347 | + | 0.202189i | \(0.0648055\pi\) | ||||
−0.979347 | + | 0.202189i | \(0.935194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.7846 | −1.74003 | ||||||||
\(356\) | −19.9669 | + | 18.6713i | −1.05824 | + | 0.989576i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.92820 | − | 2.13878i | −0.260464 | − | 0.113038i | ||||
\(359\) | 23.7867 | 1.25541 | 0.627707 | − | 0.778449i | \(-0.283993\pi\) | ||||
0.627707 | + | 0.778449i | \(0.283993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.07180 | −0.266937 | ||||||||
\(362\) | −4.16199 | − | 1.80625i | −0.218749 | − | 0.0949344i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.83013 | + | 6.23468i | 0.305582 | + | 0.326786i | ||||
\(365\) | −18.2374 | −0.954589 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 37.4848i | 1.95669i | 0.206975 | + | 0.978346i | \(0.433638\pi\) | ||||
−0.206975 | + | 0.978346i | \(0.566362\pi\) | |||||||
\(368\) | −0.220874 | + | 3.28985i | −0.0115139 | + | 0.171495i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 27.5885 | + | 11.9730i | 1.43426 | + | 0.622449i | ||||
\(371\) | 42.5318i | 2.20814i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.5991i | − | 0.963027i | −0.876439 | − | 0.481514i | \(-0.840087\pi\) | ||
0.876439 | − | 0.481514i | \(-0.159913\pi\) | |||||||
\(374\) | 7.58051 | − | 17.4671i | 0.391979 | − | 0.903203i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.5885 | + | 6.62610i | −0.958626 | + | 0.341715i | ||||
\(377\) | − | 4.81667i | − | 0.248071i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2679 | −1.34929 | −0.674647 | − | 0.738141i | \(-0.735704\pi\) | ||||
−0.674647 | + | 0.738141i | \(0.735704\pi\) | |||||||
\(380\) | 15.6836 | + | 16.7719i | 0.804552 | + | 0.860380i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.92820 | − | 9.05142i | 0.200984 | − | 0.463111i | ||||
\(383\) | −1.64863 | −0.0842409 | −0.0421204 | − | 0.999113i | \(-0.513411\pi\) | ||||
−0.0421204 | + | 0.999113i | \(0.513411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.3205 | −1.18852 | ||||||||
\(386\) | −3.03596 | + | 6.99549i | −0.154526 | + | 0.356061i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.5622 | + | 16.6420i | 0.790050 | + | 0.844871i | ||||
\(389\) | −15.3819 | −0.779893 | −0.389946 | − | 0.920838i | \(-0.627506\pi\) | ||||
−0.389946 | + | 0.920838i | \(0.627506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.84325i | − | 0.295506i | ||||||
\(392\) | 23.7867 | − | 8.47908i | 1.20141 | − | 0.428258i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.58846 | − | 22.0939i | 0.483059 | − | 1.11307i | ||||
\(395\) | − | 18.8576i | − | 0.948827i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1208i | 0.507949i | 0.967211 | + | 0.253974i | \(0.0817379\pi\) | ||||
−0.967211 | + | 0.253974i | \(0.918262\pi\) | |||||||
\(398\) | 20.3386 | + | 8.82670i | 1.01948 | + | 0.442442i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.19615 | + | 17.8163i | −0.0598076 | + | 0.890815i | ||||
\(401\) | − | 15.1951i | − | 0.758809i | −0.925231 | − | 0.379405i | \(-0.876129\pi\) | ||
0.925231 | − | 0.379405i | \(-0.123871\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.24871 | 0.311270 | ||||||||
\(404\) | 8.40482 | + | 8.98803i | 0.418155 | + | 0.447171i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.3205 | − | 10.1208i | −1.15738 | − | 0.502287i | ||||
\(407\) | 13.1298 | 0.650821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.60770 | −0.425623 | −0.212812 | − | 0.977093i | \(-0.568262\pi\) | ||||
−0.212812 | + | 0.977093i | \(0.568262\pi\) | |||||||
\(410\) | 15.1610 | + | 6.57969i | 0.748749 | + | 0.324948i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.83013 | − | 5.45183i | 0.287230 | − | 0.268592i | ||||
\(413\) | 7.58051 | 0.373012 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.9281i | 1.56729i | ||||||||
\(416\) | 2.77466 | − | 5.37552i | 0.136039 | − | 0.263557i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.19615 | + | 3.99102i | 0.449799 | + | 0.195207i | ||||
\(419\) | 26.4551i | 1.29242i | 0.763160 | + | 0.646209i | \(0.223647\pi\) | ||||
−0.763160 | + | 0.646209i | \(0.776353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.77386i | 0.232664i | 0.993210 | + | 0.116332i | \(0.0371136\pi\) | ||||
−0.993210 | + | 0.116332i | \(0.962886\pi\) | |||||||
\(422\) | 11.8529 | − | 27.3117i | 0.576992 | − | 1.32951i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.3923 | − | 10.1208i | 1.37885 | − | 0.491510i | ||||
\(425\) | − | 31.6444i | − | 1.53498i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.26795 | 0.206541 | ||||||||
\(428\) | 12.3864 | − | 11.5826i | 0.598717 | − | 0.559868i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.46410 | + | 7.98203i | −0.167054 | + | 0.384928i | ||||
\(431\) | −0.382565 | −0.0184275 | −0.00921375 | − | 0.999958i | \(-0.502933\pi\) | ||||
−0.00921375 | + | 0.999958i | \(0.502933\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.53590 | 0.217981 | 0.108991 | − | 0.994043i | \(-0.465238\pi\) | ||||
0.108991 | + | 0.994043i | \(0.465238\pi\) | |||||||
\(434\) | 13.1298 | − | 30.2539i | 0.630252 | − | 1.45223i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.7846 | − | 13.8253i | 0.708054 | − | 0.662111i | ||||
\(437\) | 3.07638 | 0.147163 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3984i | 0.687197i | 0.939117 | + | 0.343598i | \(0.111646\pi\) | ||||
−0.939117 | + | 0.343598i | \(0.888354\pi\) | |||||||
\(440\) | 5.54932 | + | 15.5677i | 0.264553 | + | 0.742162i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.26795 | + | 9.83427i | −0.203006 | + | 0.467768i | ||||
\(443\) | 27.3366i | 1.29880i | 0.760446 | + | 0.649402i | \(0.224981\pi\) | ||||
−0.760446 | + | 0.649402i | \(0.775019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.0489i | 1.99331i | ||||||||
\(446\) | −33.8402 | − | 14.6862i | −1.60238 | − | 0.695412i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.1962 | − | 24.7289i | −0.954179 | − | 1.16833i | ||||
\(449\) | 24.0468i | 1.13484i | 0.823429 | + | 0.567419i | \(0.192058\pi\) | ||||
−0.823429 | + | 0.567419i | \(0.807942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.21539 | 0.339759 | ||||||||
\(452\) | 15.9045 | − | 14.8725i | 0.748084 | − | 0.699543i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.92820 | − | 2.13878i | −0.231292 | − | 0.100378i | ||||
\(455\) | 13.1298 | 0.615536 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.39230 | 0.299019 | 0.149510 | − | 0.988760i | \(-0.452230\pi\) | ||||
0.149510 | + | 0.988760i | \(0.452230\pi\) | |||||||
\(458\) | −15.1610 | − | 6.57969i | −0.708428 | − | 0.307449i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.46410 | + | 3.70447i | 0.161515 | + | 0.172722i | ||||
\(461\) | 5.93188 | 0.276275 | 0.138138 | − | 0.990413i | \(-0.455888\pi\) | ||||
0.138138 | + | 0.990413i | \(0.455888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.42532i | − | 0.112714i | −0.998411 | − | 0.0563571i | \(-0.982051\pi\) | ||
0.998411 | − | 0.0563571i | \(-0.0179485\pi\) | |||||||
\(464\) | −1.20688 | + | 17.9761i | −0.0560279 | + | 0.834517i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.3923 | + | 7.98203i | 0.852007 | + | 0.369760i | ||||
\(467\) | 19.8754i | 0.919726i | 0.887990 | + | 0.459863i | \(0.152101\pi\) | ||||
−0.887990 | + | 0.459863i | \(0.847899\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.7020i | 1.69474i | ||||||||
\(470\) | −12.0846 | + | 27.8456i | −0.557423 | + | 1.28442i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.80385 | − | 5.06040i | −0.0830288 | − | 0.232924i | ||||
\(473\) | 3.79879i | 0.174668i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.6603 | 0.764425 | ||||||||
\(476\) | 38.6460 | + | 41.3276i | 1.77134 | + | 1.89425i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.92820 | + | 15.9641i | −0.316889 | + | 0.730179i | ||||
\(479\) | −6.15276 | −0.281127 | −0.140563 | − | 0.990072i | \(-0.544891\pi\) | ||||
−0.140563 | + | 0.990072i | \(0.544891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.39230 | −0.337060 | ||||||||
\(482\) | −3.03596 | + | 6.99549i | −0.138284 | + | 0.318636i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0981 | − | 10.7988i | −0.459003 | − | 0.490853i | ||||
\(485\) | 35.0470 | 1.59140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 33.2073i | − | 1.50477i | −0.658726 | − | 0.752383i | \(-0.728904\pi\) | ||
0.658726 | − | 0.752383i | \(-0.271096\pi\) | |||||||
\(488\) | −1.01560 | − | 2.84909i | −0.0459738 | − | 0.128972i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.4641 | − | 35.6326i | 0.698597 | − | 1.60972i | ||||
\(491\) | 33.0348i | 1.49084i | 0.666595 | + | 0.745420i | \(0.267751\pi\) | ||||
−0.666595 | + | 0.745420i | \(0.732249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 31.9281i | − | 1.43797i | ||||||
\(494\) | −5.17758 | − | 2.24701i | −0.232950 | − | 0.101098i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.3205 | − | 1.56569i | −1.04712 | − | 0.0703018i | ||||
\(497\) | − | 42.5318i | − | 1.90781i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.60770 | −0.251035 | −0.125517 | − | 0.992091i | \(-0.540059\pi\) | ||||
−0.125517 | + | 0.992091i | \(0.540059\pi\) | |||||||
\(500\) | −2.25207 | − | 2.40833i | −0.100715 | − | 0.107704i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.3923 | + | 7.98203i | 0.820889 | + | 0.356255i | ||||
\(503\) | −29.4977 | −1.31524 | −0.657619 | − | 0.753351i | \(-0.728436\pi\) | ||||
−0.657619 | + | 0.753351i | \(0.728436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9282 | 0.842294 | ||||||||
\(506\) | 2.03119 | + | 0.881512i | 0.0902975 | + | 0.0391880i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.220874 | −0.00979007 | −0.00489503 | − | 0.999988i | \(-0.501558\pi\) | ||||
−0.00489503 | + | 0.999988i | \(0.501558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 23.6595i | − | 1.04664i | ||||||
\(512\) | −11.7021 | + | 19.3665i | −0.517163 | + | 0.855887i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.92820 | − | 2.13878i | −0.217374 | − | 0.0943375i | ||||
\(515\) | − | 12.2779i | − | 0.541028i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2522i | 0.582831i | ||||||||
\(518\) | −15.5327 | + | 35.7908i | −0.682470 | + | 1.57256i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.12436 | − | 8.76488i | −0.137012 | − | 0.384365i | ||||
\(521\) | − | 7.08863i | − | 0.310559i | −0.987871 | − | 0.155279i | \(-0.950372\pi\) | ||
0.987871 | − | 0.155279i | \(-0.0496278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.5885 | −1.64363 | −0.821814 | − | 0.569756i | \(-0.807038\pi\) | ||||
−0.821814 | + | 0.569756i | \(0.807038\pi\) | |||||||
\(524\) | −15.1610 | + | 14.1773i | −0.662312 | + | 0.619337i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.85641 | + | 4.27756i | −0.0809432 | + | 0.186510i | ||||
\(527\) | 41.4207 | 1.80431 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3205 | −0.970457 | ||||||||
\(530\) | 18.4583 | − | 42.5318i | 0.801776 | − | 1.84746i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.7583 | + | 20.3465i | −0.943343 | + | 0.882133i | ||||
\(533\) | −4.06238 | −0.175961 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 26.0849i | − | 1.12775i | ||||||
\(536\) | 24.5006 | − | 8.73356i | 1.05826 | − | 0.377232i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.1962 | + | 25.7983i | −0.482700 | + | 1.11224i | ||||
\(539\) | − | 16.9582i | − | 0.730440i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 34.5632i | − | 1.48599i | −0.669298 | − | 0.742994i | \(-0.733405\pi\) | ||
0.669298 | − | 0.742994i | \(-0.266595\pi\) | |||||||
\(542\) | −15.5327 | − | 6.74102i | −0.667189 | − | 0.289552i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.3923 | − | 35.6326i | 0.788564 | − | 1.52773i | ||||
\(545\) | − | 31.1354i | − | 1.33370i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.5885 | −1.35062 | −0.675312 | − | 0.737532i | \(-0.735991\pi\) | ||||
−0.675312 | + | 0.737532i | \(0.735991\pi\) | |||||||
\(548\) | 25.5162 | − | 23.8605i | 1.09000 | − | 1.01927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.0000 | + | 4.77386i | 0.469042 | + | 0.203558i | ||||
\(551\) | 16.8096 | 0.716115 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.4641 | 1.04032 | ||||||||
\(554\) | 28.2908 | + | 12.2779i | 1.20196 | + | 0.521637i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.36603 | + | 4.66898i | 0.185161 | + | 0.198009i | ||||
\(557\) | 14.9401 | 0.633034 | 0.316517 | − | 0.948587i | \(-0.397487\pi\) | ||||
0.316517 | + | 0.948587i | \(0.397487\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.13878i | − | 0.0904607i | ||||||
\(560\) | −49.0012 | − | 3.28985i | −2.07068 | − | 0.139021i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.4641 | − | 5.84325i | −0.567949 | − | 0.246483i | ||||
\(563\) | − | 34.9342i | − | 1.47230i | −0.676817 | − | 0.736151i | \(-0.736641\pi\) | ||
0.676817 | − | 0.736151i | \(-0.263359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 33.4938i | − | 1.40910i | ||||||
\(566\) | 15.6836 | − | 36.1384i | 0.659231 | − | 1.51901i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.3923 | + | 10.1208i | −1.19131 | + | 0.424660i | ||||
\(569\) | 6.07075i | 0.254499i | 0.991871 | + | 0.127250i | \(0.0406149\pi\) | ||||
−0.991871 | + | 0.127250i | \(0.959385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.19615 | −0.133755 | −0.0668774 | − | 0.997761i | \(-0.521304\pi\) | ||||
−0.0668774 | + | 0.997761i | \(0.521304\pi\) | |||||||
\(572\) | −2.77466 | − | 2.96719i | −0.116014 | − | 0.124064i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.53590 | + | 19.6685i | −0.356282 | + | 0.820949i | ||||
\(575\) | 3.67982 | 0.153459 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9282 | 0.496578 | 0.248289 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248289 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(578\) | −18.7196 | + | 43.1339i | −0.778631 | + | 1.79413i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 18.9282 | + | 20.2416i | 0.785951 | + | 0.840487i | ||||
\(581\) | −41.4207 | −1.71842 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 20.2416i | − | 0.838322i | ||||||
\(584\) | −15.7940 | + | 5.62999i | −0.653562 | + | 0.232971i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.26795 | − | 9.83427i | 0.176307 | − | 0.406250i | ||||
\(587\) | 33.0348i | 1.36349i | 0.731588 | + | 0.681747i | \(0.238779\pi\) | ||||
−0.731588 | + | 0.681747i | \(0.761221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.8073i | 0.898555i | ||||||||
\(590\) | −7.58051 | − | 3.28985i | −0.312085 | − | 0.135441i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.5885 | + | 1.85224i | 1.13388 | + | 0.0761265i | ||||
\(593\) | 38.7330i | 1.59057i | 0.606233 | + | 0.795287i | \(0.292680\pi\) | ||||
−0.606233 | + | 0.795287i | \(0.707320\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 87.0333 | 3.56802 | ||||||||
\(596\) | −8.40482 | − | 8.98803i | −0.344275 | − | 0.368164i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.14359 | − | 0.496305i | −0.0467650 | − | 0.0202954i | ||||
\(599\) | 22.5207 | 0.920169 | 0.460084 | − | 0.887875i | \(-0.347819\pi\) | ||||
0.460084 | + | 0.887875i | \(0.347819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.3923 | 1.23973 | 0.619864 | − | 0.784709i | \(-0.287188\pi\) | ||||
0.619864 | + | 0.784709i | \(0.287188\pi\) | |||||||
\(602\) | −10.3552 | − | 4.49401i | −0.422045 | − | 0.183162i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.3660 | − | 13.4339i | 0.584545 | − | 0.546616i | ||||
\(605\) | −22.7415 | −0.924574 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.3461i | 1.43465i | 0.696738 | + | 0.717326i | \(0.254634\pi\) | ||||
−0.696738 | + | 0.717326i | \(0.745366\pi\) | |||||||
\(608\) | 18.7600 | + | 9.68325i | 0.760818 | + | 0.392708i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.26795 | − | 1.85224i | −0.172804 | − | 0.0749949i | ||||
\(611\) | − | 7.46120i | − | 0.301848i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.91264i | 0.279199i | 0.990208 | + | 0.139599i | \(0.0445815\pi\) | ||||
−0.990208 | + | 0.139599i | \(0.955418\pi\) | |||||||
\(614\) | 11.7829 | − | 27.1504i | 0.475520 | − | 1.09570i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.1962 | + | 7.19918i | −0.813726 | + | 0.290063i | ||||
\(617\) | 28.8635i | 1.16200i | 0.813904 | + | 0.581000i | \(0.197338\pi\) | ||||
−0.813904 | + | 0.581000i | \(0.802662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.1962 | 1.49504 | 0.747520 | − | 0.664240i | \(-0.231245\pi\) | ||||
0.747520 | + | 0.664240i | \(0.231245\pi\) | |||||||
\(620\) | −26.2597 | + | 24.5557i | −1.05461 | + | 0.986182i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.5359 | + | 26.5812i | −0.462547 | + | 1.06581i | ||||
\(623\) | −54.5505 | −2.18552 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.3923 | −1.09569 | ||||||||
\(626\) | 5.28802 | − | 12.1847i | 0.211352 | − | 0.487000i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31.8564 | + | 29.7893i | −1.27121 | + | 1.18872i | ||||
\(629\) | −49.0012 | −1.95380 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.0939i | − | 0.879542i | −0.898110 | − | 0.439771i | \(-0.855060\pi\) | ||
0.898110 | − | 0.439771i | \(-0.144940\pi\) | |||||||
\(632\) | −5.82145 | − | 16.3311i | −0.231565 | − | 0.649617i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.46410 | + | 21.8073i | −0.375867 | + | 0.866079i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.54773i | 0.378295i | ||||||||
\(638\) | 11.0986 | + | 4.81667i | 0.439399 | + | 0.190694i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.46410 | + | 33.4938i | 0.374101 | + | 1.32396i | ||||
\(641\) | − | 34.9342i | − | 1.37982i | −0.723896 | − | 0.689909i | \(-0.757650\pi\) | ||
0.723896 | − | 0.689909i | \(-0.242350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.7846 | −0.740793 | −0.370396 | − | 0.928874i | \(-0.620778\pi\) | ||||
−0.370396 | + | 0.928874i | \(0.620778\pi\) | |||||||
\(644\) | −4.80585 | + | 4.49401i | −0.189377 | + | 0.177089i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −34.3205 | − | 14.8947i | −1.35032 | − | 0.586023i | ||||
\(647\) | −39.7720 | −1.56360 | −0.781800 | − | 0.623529i | \(-0.785698\pi\) | ||||
−0.781800 | + | 0.623529i | \(0.785698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.60770 | −0.141614 | ||||||||
\(650\) | −6.19318 | − | 2.68776i | −0.242916 | − | 0.105423i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0263 | − | 12.8608i | −0.470985 | − | 0.503667i | ||||
\(653\) | 32.4124 | 1.26840 | 0.634198 | − | 0.773171i | \(-0.281331\pi\) | ||||
0.634198 | + | 0.773171i | \(0.281331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.9281i | 1.24753i | ||||||||
\(656\) | 15.1610 | + | 1.01788i | 0.591938 | + | 0.0397416i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −36.1244 | − | 15.6775i | −1.40827 | − | 0.611173i | ||||
\(659\) | − | 21.7748i | − | 0.848227i | −0.905609 | − | 0.424114i | \(-0.860586\pi\) | ||
0.905609 | − | 0.424114i | \(-0.139414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 45.2571i | − | 1.76030i | −0.474698 | − | 0.880149i | \(-0.657443\pi\) | ||
0.474698 | − | 0.880149i | \(-0.342557\pi\) | |||||||
\(662\) | 1.05602 | − | 2.43329i | 0.0410433 | − | 0.0945726i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.85641 | + | 27.6506i | 0.382503 | + | 1.07305i | ||||
\(665\) | 45.8216i | 1.77689i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.71281 | 0.143761 | ||||||||
\(668\) | −30.2412 | − | 32.3396i | −1.17007 | − | 1.25126i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.9282 | − | 36.7020i | 0.615360 | − | 1.41792i | ||||
\(671\) | −2.03119 | −0.0784133 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2487 | 1.35874 | 0.679369 | − | 0.733797i | \(-0.262254\pi\) | ||||
0.679369 | + | 0.733797i | \(0.262254\pi\) | |||||||
\(674\) | −6.41405 | + | 14.7793i | −0.247060 | + | 0.569279i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.1962 | − | 17.3200i | −0.622929 | − | 0.666154i | ||||
\(677\) | −44.4970 | −1.71016 | −0.855080 | − | 0.518496i | \(-0.826492\pi\) | ||||
−0.855080 | + | 0.518496i | \(0.826492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.4669i | 1.74486i | ||||||||
\(680\) | −20.7103 | − | 58.0995i | −0.794205 | − | 2.22801i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.24871 | + | 14.3984i | −0.239276 | + | 0.551342i | ||||
\(683\) | − | 39.7509i | − | 1.52103i | −0.649323 | − | 0.760513i | \(-0.724948\pi\) | ||
0.649323 | − | 0.760513i | \(-0.275052\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 53.7354i | − | 2.05313i | ||||||
\(686\) | 9.98343 | + | 4.33269i | 0.381169 | + | 0.165423i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.535898 | + | 7.98203i | −0.0204309 | + | 0.304312i | ||||
\(689\) | 11.3964i | 0.434167i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.85641 | 0.146705 | 0.0733523 | − | 0.997306i | \(-0.476630\pi\) | ||||
0.0733523 | + | 0.997306i | \(0.476630\pi\) | |||||||
\(692\) | −2.25207 | − | 2.40833i | −0.0856107 | − | 0.0915511i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.85641 | + | 4.27756i | 0.374144 | + | 0.162374i | ||||
\(695\) | 9.83257 | 0.372971 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.9282 | −1.01998 | ||||||||
\(698\) | −3.41852 | − | 1.48360i | −0.129393 | − | 0.0561549i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −26.0263 | + | 24.3375i | −0.983701 | + | 0.919872i | ||||
\(701\) | 51.8567 | 1.95860 | 0.979300 | − | 0.202415i | \(-0.0648790\pi\) | ||||
0.979300 | + | 0.202415i | \(0.0648790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 25.7983i | − | 0.973002i | ||||||
\(704\) | 9.61170 | + | 11.7689i | 0.362255 | + | 0.443558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.85641 | + | 4.27756i | 0.370951 | + | 0.160988i | ||||
\(707\) | 24.5557i | 0.923514i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.1363i | 1.31957i | 0.751454 | + | 0.659786i | \(0.229353\pi\) | ||||
−0.751454 | + | 0.659786i | \(0.770647\pi\) | |||||||
\(710\) | −18.4583 | + | 42.5318i | −0.692726 | + | 1.59619i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.9808 | + | 36.4154i | 0.486475 | + | 1.36473i | ||||
\(713\) | 4.81667i | 0.180386i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24871 | −0.233689 | ||||||||
\(716\) | −5.54932 | + | 5.18924i | −0.207388 | + | 0.193931i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.3923 | − | 30.8587i | 0.499796 | − | 1.15164i | ||||
\(719\) | 7.80138 | 0.290942 | 0.145471 | − | 0.989362i | \(-0.453530\pi\) | ||||
0.145471 | + | 0.989362i | \(0.453530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9282 | 0.593197 | ||||||||
\(722\) | −2.85550 | + | 6.57969i | −0.106271 | + | 0.244871i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.68653 | + | 4.38244i | −0.174174 | + | 0.162872i | ||||
\(725\) | 20.1069 | 0.746751 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.0849i | − | 0.967434i | −0.875224 | − | 0.483717i | \(-0.839286\pi\) | ||
0.875224 | − | 0.483717i | \(-0.160714\pi\) | |||||||
\(728\) | 11.3708 | − | 4.05326i | 0.421428 | − | 0.150224i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.2679 | + | 23.6595i | −0.380034 | + | 0.875679i | ||||
\(731\) | − | 14.1773i | − | 0.524365i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2522i | 0.489481i | 0.969589 | + | 0.244741i | \(0.0787028\pi\) | ||||
−0.969589 | + | 0.244741i | \(0.921297\pi\) | |||||||
\(734\) | 48.6294 | + | 21.1046i | 1.79495 | + | 0.778984i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.14359 | + | 2.13878i | 0.152735 | + | 0.0788364i | ||||
\(737\) | − | 17.4671i | − | 0.643409i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.6410 | −0.759292 | −0.379646 | − | 0.925132i | \(-0.623954\pi\) | ||||
−0.379646 | + | 0.925132i | \(0.623954\pi\) | |||||||
\(740\) | 31.0655 | − | 29.0498i | 1.14199 | − | 1.06789i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 55.1769 | + | 23.9461i | 2.02561 | + | 0.879089i | ||||
\(743\) | −51.6950 | −1.89651 | −0.948253 | − | 0.317517i | \(-0.897151\pi\) | ||||
−0.948253 | + | 0.317517i | \(0.897151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.9282 | −0.693476 | ||||||||
\(746\) | −24.1289 | − | 10.4716i | −0.883420 | − | 0.383393i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18.3923 | − | 19.6685i | −0.672489 | − | 0.719153i | ||||
\(749\) | 33.8402 | 1.23649 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 19.9551i | − | 0.728171i | −0.931366 | − | 0.364086i | \(-0.881382\pi\) | ||
0.931366 | − | 0.364086i | \(-0.118618\pi\) | |||||||
\(752\) | −1.86950 | + | 27.8456i | −0.0681737 | + | 1.01542i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.24871 | − | 2.71186i | −0.227565 | − | 0.0987602i | ||||
\(755\) | − | 30.2539i | − | 1.10105i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 52.0930i | − | 1.89335i | −0.322189 | − | 0.946675i | \(-0.604419\pi\) | ||
0.322189 | − | 0.946675i | \(-0.395581\pi\) | |||||||
\(758\) | −14.7893 | + | 34.0777i | −0.537171 | + | 1.23776i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 30.5885 | − | 10.9037i | 1.10956 | − | 0.395517i | ||||
\(761\) | − | 43.0407i | − | 1.56023i | −0.625639 | − | 0.780113i | \(-0.715162\pi\) | ||
0.625639 | − | 0.780113i | \(-0.284838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.3923 | 1.46230 | ||||||||
\(764\) | −9.53085 | − | 10.1922i | −0.344814 | − | 0.368741i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.928203 | + | 2.13878i | −0.0335373 | + | 0.0772772i | ||||
\(767\) | 2.03119 | 0.0733421 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.07180 | 0.146833 | 0.0734164 | − | 0.997301i | \(-0.476610\pi\) | ||||
0.0734164 | + | 0.997301i | \(0.476610\pi\) | |||||||
\(770\) | −13.1298 | + | 30.2539i | −0.473166 | + | 1.09028i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.36603 | + | 7.87715i | 0.265109 | + | 0.283505i | ||||
\(773\) | 44.7179 | 1.60839 | 0.804196 | − | 0.594364i | \(-0.202596\pi\) | ||||
0.804196 | + | 0.594364i | \(0.202596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.0849i | 0.936996i | ||||||||
\(776\) | 30.3516 | − | 10.8192i | 1.08956 | − | 0.388388i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.66025 | + | 19.9551i | −0.310485 | + | 0.715424i | ||||
\(779\) | − | 14.1773i | − | 0.507953i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.2416i | 0.724302i | ||||||||
\(782\) | −7.58051 | − | 3.28985i | −0.271078 | − | 0.117645i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.39230 | − | 35.6326i | 0.0854395 | − | 1.27259i | ||||
\(785\) | 67.0875i | 2.39446i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.44486 | 0.265381 | 0.132690 | − | 0.991158i | \(-0.457638\pi\) | ||||
0.132690 | + | 0.991158i | \(0.457638\pi\) | |||||||
\(788\) | −23.2641 | − | 24.8784i | −0.828750 | − | 0.886256i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.4641 | − | 10.6171i | −0.870394 | − | 0.377740i | ||||
\(791\) | 43.4519 | 1.54497 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14359 | 0.0406102 | ||||||||
\(794\) | 13.1298 | + | 5.69818i | 0.465960 | + | 0.202221i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.9019 | − | 21.4159i | 0.811737 | − | 0.759066i | ||||
\(797\) | 27.4665 | 0.972914 | 0.486457 | − | 0.873704i | \(-0.338289\pi\) | ||||
0.486457 | + | 0.873704i | \(0.338289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49.4579i | − | 1.74969i | ||||||
\(800\) | 22.4398 | + | 11.5826i | 0.793367 | + | 0.409508i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.7128 | − | 8.55511i | −0.696084 | − | 0.302092i | ||||
\(803\) | 11.2600i | 0.397356i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1208i | 0.356712i | ||||||||
\(806\) | 3.51813 | − | 8.10651i | 0.123921 | − | 0.285540i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.3923 | − | 5.84325i | 0.576679 | − | 0.205565i | ||||
\(809\) | 14.1773i | 0.498446i | 0.968446 | + | 0.249223i | \(0.0801752\pi\) | ||||
−0.968446 | + | 0.249223i | \(0.919825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0718 | −0.950619 | −0.475310 | − | 0.879819i | \(-0.657664\pi\) | ||||
−0.475310 | + | 0.879819i | \(0.657664\pi\) | |||||||
\(812\) | −26.2597 | + | 24.5557i | −0.921533 | + | 0.861738i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.39230 | − | 17.0335i | 0.259100 | − | 0.597022i | ||||
\(815\) | −27.0840 | −0.948710 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.46410 | 0.261136 | ||||||||
\(818\) | −4.84627 | + | 11.1668i | −0.169446 | + | 0.390440i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.0718 | − | 15.9641i | 0.596173 | − | 0.557489i | ||||
\(821\) | 10.8778 | 0.379636 | 0.189818 | − | 0.981819i | \(-0.439210\pi\) | ||||
0.189818 | + | 0.981819i | \(0.439210\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.2326i | 0.844697i | 0.906434 | + | 0.422348i | \(0.138794\pi\) | ||||
−0.906434 | + | 0.422348i | \(0.861206\pi\) | |||||||
\(824\) | −3.79025 | − | 10.6329i | −0.132040 | − | 0.370416i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.26795 | − | 9.83427i | 0.148501 | − | 0.342178i | ||||
\(827\) | − | 40.6324i | − | 1.41293i | −0.707749 | − | 0.706464i | \(-0.750289\pi\) | ||
0.707749 | − | 0.706464i | \(-0.249711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5632i | 1.20043i | 0.799839 | + | 0.600215i | \(0.204918\pi\) | ||||
−0.799839 | + | 0.600215i | \(0.795082\pi\) | |||||||
\(830\) | 41.4207 | + | 17.9761i | 1.43773 | + | 0.623958i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.41154 | − | 6.62610i | −0.187611 | − | 0.229719i | ||||
\(833\) | 63.2888i | 2.19283i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −68.1051 | −2.35687 | ||||||||
\(836\) | 10.3552 | − | 9.68325i | 0.358141 | − | 0.334902i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.3205 | + | 14.8947i | 1.18558 | + | 0.514528i | ||||
\(839\) | 25.0528 | 0.864918 | 0.432459 | − | 0.901654i | \(-0.357646\pi\) | ||||
0.432459 | + | 0.901654i | \(0.357646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.71281 | −0.300442 | ||||||||
\(842\) | 6.19318 | + | 2.68776i | 0.213431 | + | 0.0926264i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.7583 | − | 30.7539i | −0.989903 | − | 1.05859i | ||||
\(845\) | −36.4748 | −1.25477 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 29.5028i | − | 1.01373i | ||||||
\(848\) | 2.85550 | − | 42.5318i | 0.0980584 | − | 1.46055i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −41.0526 | − | 17.8163i | −1.40809 | − | 0.611094i | ||||
\(851\) | − | 5.69818i | − | 0.195331i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.8947i | 0.509984i | 0.966943 | + | 0.254992i | \(0.0820728\pi\) | ||||
−0.966943 | + | 0.254992i | \(0.917927\pi\) | |||||||
\(854\) | 2.40292 | − | 5.53685i | 0.0822264 | − | 0.189467i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.05256 | − | 22.5902i | −0.275231 | − | 0.772116i | ||||
\(857\) | 1.01788i | 0.0347702i | 0.999849 | + | 0.0173851i | \(0.00553413\pi\) | ||||
−0.999849 | + | 0.0173851i | \(0.994466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5885 | 0.395393 | 0.197697 | − | 0.980263i | \(-0.436654\pi\) | ||||
0.197697 | + | 0.980263i | \(0.436654\pi\) | |||||||
\(860\) | 8.40482 | + | 8.98803i | 0.286602 | + | 0.306489i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.215390 | + | 0.496305i | −0.00733622 | + | 0.0169042i | ||||
\(863\) | 15.9853 | 0.544147 | 0.272073 | − | 0.962276i | \(-0.412291\pi\) | ||||
0.272073 | + | 0.962276i | \(0.412291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07180 | −0.172446 | ||||||||
\(866\) | 2.55378 | − | 5.88447i | 0.0867811 | − | 0.199962i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −31.8564 | − | 34.0669i | −1.08128 | − | 1.15631i | ||||
\(869\) | −11.6429 | −0.394958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.83427i | 0.333221i | ||||||||
\(872\) | −9.61170 | − | 26.9641i | −0.325493 | − | 0.913119i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.73205 | − | 3.99102i | 0.0585875 | − | 0.134998i | ||||
\(875\) | − | 6.57969i | − | 0.222434i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.1722i | 0.647400i | 0.946160 | + | 0.323700i | \(0.104927\pi\) | ||||
−0.946160 | + | 0.323700i | \(0.895073\pi\) | |||||||
\(878\) | 18.6791 | + | 8.10651i | 0.630391 | + | 0.273582i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.3205 | + | 1.56569i | 0.786134 | + | 0.0527796i | ||||
\(881\) | 6.07075i | 0.204529i | 0.994757 | + | 0.102264i | \(0.0326088\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.1244 | 1.48490 | 0.742451 | − | 0.669900i | \(-0.233663\pi\) | ||||
0.742451 | + | 0.669900i | \(0.233663\pi\) | |||||||
\(884\) | 10.3552 | + | 11.0737i | 0.348282 | + | 0.372449i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.4641 | + | 15.3910i | 1.19144 | + | 0.517070i | ||||
\(887\) | −25.8179 | −0.866880 | −0.433440 | − | 0.901182i | \(-0.642700\pi\) | ||||
−0.433440 | + | 0.901182i | \(0.642700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 54.5505 | + | 23.6742i | 1.82854 | + | 0.793562i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −38.1051 | + | 35.6326i | −1.27585 | + | 1.19307i | ||||
\(893\) | 26.0388 | 0.871354 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.6865i | 0.390637i | ||||||||
\(896\) | −43.4519 | + | 12.2779i | −1.45162 | + | 0.410175i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.1962 | + | 13.5387i | 1.04103 | + | 0.451794i | ||||
\(899\) | 26.3188i | 0.877780i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75.5427i | 2.51669i | ||||||||
\(902\) | 4.06238 | − | 9.36060i | 0.135263 | − | 0.311674i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.3397 | − | 29.0065i | −0.343895 | − | 0.964742i | ||||
\(905\) | 9.86954i | 0.328075i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.3731 | −1.53979 | −0.769896 | − | 0.638169i | \(-0.779692\pi\) | ||||
−0.769896 | + | 0.638169i | \(0.779692\pi\) | |||||||
\(908\) | −5.54932 | + | 5.18924i | −0.184161 | + | 0.172211i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.39230 | − | 17.0335i | 0.245053 | − | 0.564653i | ||||
\(911\) | −0.441748 | −0.0146358 | −0.00731788 | − | 0.999973i | \(-0.502329\pi\) | ||||
−0.00731788 | + | 0.999973i | \(0.502329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.7128 | 0.652399 | ||||||||
\(914\) | 3.59897 | − | 8.29280i | 0.119043 | − | 0.274301i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.0718 | + | 15.9641i | −0.564068 | + | 0.527467i | ||||
\(917\) | −41.4207 | −1.36783 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.0130i | 1.91367i | 0.290628 | + | 0.956836i | \(0.406136\pi\) | ||||
−0.290628 | + | 0.956836i | \(0.593864\pi\) | |||||||
\(920\) | 6.75620 | − | 2.40833i | 0.222745 | − | 0.0794004i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.33975 | − | 7.69549i | 0.109989 | − | 0.253437i | ||||
\(923\) | − | 11.3964i | − | 0.375116i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 30.8587i | − | 1.01463i | ||||||
\(926\) | −3.14639 | − | 1.36549i | −0.103397 | − | 0.0448729i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.6410 | + | 11.6865i | 0.743228 | + | 0.383628i | ||||
\(929\) | 20.7570i | 0.681014i | 0.940242 | + | 0.340507i | \(0.110599\pi\) | ||||
−0.940242 | + | 0.340507i | \(0.889401\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.3205 | −1.09204 | ||||||||
\(932\) | 20.7103 | − | 19.3665i | 0.678390 | − | 0.634371i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.7846 | + | 11.1902i | 0.843698 | + | 0.366154i | ||||
\(935\) | −41.4207 | −1.35460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3923 | −0.764193 | −0.382097 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382097 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(938\) | 47.6138 | + | 20.6638i | 1.55465 | + | 0.674697i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.3205 | + | 31.3550i | 0.956330 | + | 1.02269i | ||||
\(941\) | −18.6791 | −0.608923 | −0.304461 | − | 0.952525i | \(-0.598476\pi\) | ||||
−0.304461 | + | 0.952525i | \(0.598476\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.13139i | − | 0.101972i | ||||||
\(944\) | −7.58051 | − | 0.508941i | −0.246725 | − | 0.0165646i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.92820 | + | 2.13878i | 0.160230 | + | 0.0695377i | ||||
\(947\) | − | 29.2360i | − | 0.950044i | −0.879974 | − | 0.475022i | \(-0.842440\pi\) | ||
0.879974 | − | 0.475022i | \(-0.157560\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.33956i | − | 0.205791i | ||||||
\(950\) | 9.37999 | − | 21.6135i | 0.304327 | − | 0.701235i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 75.3731 | − | 26.8677i | 2.44286 | − | 0.870788i | ||||
\(953\) | 15.7041i | 0.508705i | 0.967112 | + | 0.254353i | \(0.0818624\pi\) | ||||
−0.967112 | + | 0.254353i | \(0.918138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.4641 | −0.694562 | ||||||||
\(956\) | 16.8096 | + | 17.9761i | 0.543663 | + | 0.581387i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.46410 | + | 7.98203i | −0.111920 | + | 0.257888i | ||||
\(959\) | 69.7115 | 2.25110 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.14359 | −0.101406 | ||||||||
\(962\) | −4.16199 | + | 9.59011i | −0.134188 | + | 0.309198i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.36603 | + | 7.87715i | 0.237244 | + | 0.253706i | ||||
\(965\) | 16.5888 | 0.534011 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.83427i | − | 0.316249i | −0.987419 | − | 0.158124i | \(-0.949455\pi\) | ||
0.987419 | − | 0.158124i | \(-0.0505447\pi\) | |||||||
\(968\) | −19.6947 | + | 7.02045i | −0.633013 | + | 0.225646i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.7321 | − | 45.4669i | 0.633558 | − | 1.45985i | ||||
\(971\) | 55.8275i | 1.79159i | 0.444466 | + | 0.895796i | \(0.353393\pi\) | ||||
−0.444466 | + | 0.895796i | \(0.646607\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.7559i | 0.408935i | ||||||||
\(974\) | −43.0801 | − | 18.6962i | −1.38038 | − | 0.599066i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.26795 | − | 0.286542i | −0.136614 | − | 0.00917199i | ||||
\(977\) | − | 23.5379i | − | 0.753043i | −0.926408 | − | 0.376521i | \(-0.877120\pi\) | ||
0.926408 | − | 0.376521i | \(-0.122880\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.9615 | 0.829734 | ||||||||
\(980\) | −37.5200 | − | 40.1235i | −1.19853 | − | 1.28170i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42.8564 | + | 18.5991i | 1.36760 | + | 0.593523i | ||||
\(983\) | 55.3156 | 1.76429 | 0.882147 | − | 0.470974i | \(-0.156097\pi\) | ||||
0.882147 | + | 0.470974i | \(0.156097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.3923 | −1.66936 | ||||||||
\(986\) | −41.4207 | − | 17.9761i | −1.31910 | − | 0.572474i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.83013 | + | 5.45183i | −0.185481 | + | 0.173446i | ||||
\(989\) | 1.64863 | 0.0524233 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.7983i | 0.819511i | 0.912195 | + | 0.409755i | \(0.134386\pi\) | ||||
−0.912195 | + | 0.409755i | \(0.865614\pi\) | |||||||
\(992\) | −15.1610 | + | 29.3724i | −0.481363 | + | 0.932575i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −55.1769 | − | 23.9461i | −1.75011 | − | 0.759524i | ||||
\(995\) | − | 48.2300i | − | 1.52899i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.56569i | 0.0495860i | 0.999693 | + | 0.0247930i | \(0.00789267\pi\) | ||||
−0.999693 | + | 0.0247930i | \(0.992107\pi\) | |||||||
\(998\) | −3.15722 | + | 7.27492i | −0.0999402 | + | 0.230284i | ||||
\(999\) | 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 | 216.2.f.a.107.5 | yes | 8 | |
3.2 | odd | 2 | inner | 216.2.f.a.107.4 | yes | 8 | |
4.3 | odd | 2 | 864.2.f.a.431.2 | 8 | |||
8.3 | odd | 2 | inner | 216.2.f.a.107.3 | ✓ | 8 | |
8.5 | even | 2 | 864.2.f.a.431.7 | 8 | |||
9.2 | odd | 6 | 648.2.l.f.539.8 | 16 | |||
9.4 | even | 3 | 648.2.l.f.107.6 | 16 | |||
9.5 | odd | 6 | 648.2.l.f.107.3 | 16 | |||
9.7 | even | 3 | 648.2.l.f.539.1 | 16 | |||
12.11 | even | 2 | 864.2.f.a.431.8 | 8 | |||
24.5 | odd | 2 | 864.2.f.a.431.1 | 8 | |||
24.11 | even | 2 | inner | 216.2.f.a.107.6 | yes | 8 | |
36.7 | odd | 6 | 2592.2.p.f.2159.8 | 16 | |||
36.11 | even | 6 | 2592.2.p.f.2159.2 | 16 | |||
36.23 | even | 6 | 2592.2.p.f.431.1 | 16 | |||
36.31 | odd | 6 | 2592.2.p.f.431.7 | 16 | |||
72.5 | odd | 6 | 2592.2.p.f.431.8 | 16 | |||
72.11 | even | 6 | 648.2.l.f.539.6 | 16 | |||
72.13 | even | 6 | 2592.2.p.f.431.2 | 16 | |||
72.29 | odd | 6 | 2592.2.p.f.2159.7 | 16 | |||
72.43 | odd | 6 | 648.2.l.f.539.3 | 16 | |||
72.59 | even | 6 | 648.2.l.f.107.1 | 16 | |||
72.61 | even | 6 | 2592.2.p.f.2159.1 | 16 | |||
72.67 | odd | 6 | 648.2.l.f.107.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.f.a.107.3 | ✓ | 8 | 8.3 | odd | 2 | inner | |
216.2.f.a.107.4 | yes | 8 | 3.2 | odd | 2 | inner | |
216.2.f.a.107.5 | yes | 8 | 1.1 | even | 1 | trivial | |
216.2.f.a.107.6 | yes | 8 | 24.11 | even | 2 | inner | |
648.2.l.f.107.1 | 16 | 72.59 | even | 6 | |||
648.2.l.f.107.3 | 16 | 9.5 | odd | 6 | |||
648.2.l.f.107.6 | 16 | 9.4 | even | 3 | |||
648.2.l.f.107.8 | 16 | 72.67 | odd | 6 | |||
648.2.l.f.539.1 | 16 | 9.7 | even | 3 | |||
648.2.l.f.539.3 | 16 | 72.43 | odd | 6 | |||
648.2.l.f.539.6 | 16 | 72.11 | even | 6 | |||
648.2.l.f.539.8 | 16 | 9.2 | odd | 6 | |||
864.2.f.a.431.1 | 8 | 24.5 | odd | 2 | |||
864.2.f.a.431.2 | 8 | 4.3 | odd | 2 | |||
864.2.f.a.431.7 | 8 | 8.5 | even | 2 | |||
864.2.f.a.431.8 | 8 | 12.11 | even | 2 | |||
2592.2.p.f.431.1 | 16 | 36.23 | even | 6 | |||
2592.2.p.f.431.2 | 16 | 72.13 | even | 6 | |||
2592.2.p.f.431.7 | 16 | 36.31 | odd | 6 | |||
2592.2.p.f.431.8 | 16 | 72.5 | odd | 6 | |||
2592.2.p.f.2159.1 | 16 | 72.61 | even | 6 | |||
2592.2.p.f.2159.2 | 16 | 36.11 | even | 6 | |||
2592.2.p.f.2159.7 | 16 | 72.29 | odd | 6 | |||
2592.2.p.f.2159.8 | 16 | 36.7 | odd | 6 |