Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(49,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.z (of order \(6\), degree \(2\), 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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.5 | ||
Root | \(-1.72890 - 0.104392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.69 |
Dual form | 260.2.z.a.49.5 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.180812 | + | 0.104392i | 0.104392 | + | 0.0602706i | 0.551287 | − | 0.834316i | \(-0.314137\pi\) |
−0.446895 | + | 0.894586i | \(0.647470\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.60081 | − | 1.56122i | −0.715906 | − | 0.698197i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.72890 | − | 2.99455i | −0.653464 | − | 1.13183i | −0.982277 | − | 0.187437i | \(-0.939982\pi\) |
0.328813 | − | 0.944395i | \(-0.393351\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.47820 | − | 2.56033i | −0.492735 | − | 0.853442i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.625212 | + | 0.360966i | 0.188509 | + | 0.108835i | 0.591284 | − | 0.806463i | \(-0.298621\pi\) |
−0.402776 | + | 0.915299i | \(0.631955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.18457 | + | 1.69071i | −0.883241 | + | 0.468919i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.126468 | − | 0.449398i | −0.0326539 | − | 0.116034i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.10921 | − | 1.79510i | 0.754094 | − | 0.435376i | −0.0730774 | − | 0.997326i | \(-0.523282\pi\) |
0.827171 | + | 0.561950i | \(0.189949\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.51351 | − | 3.76057i | 1.49430 | − | 0.862735i | 0.494322 | − | 0.869279i | \(-0.335416\pi\) |
0.999979 | + | 0.00654367i | \(0.00208293\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.721933i | − | 0.157539i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.05486 | − | 1.18637i | −0.428468 | − | 0.247376i | 0.270226 | − | 0.962797i | \(-0.412902\pi\) |
−0.698694 | + | 0.715421i | \(0.746235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.125212 | + | 4.99843i | 0.0250424 | + | 0.999686i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.24360i | − | 0.239331i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.68231 | + | 6.37795i | −0.683788 | + | 1.18435i | 0.290028 | + | 0.957018i | \(0.406335\pi\) |
−0.973816 | + | 0.227337i | \(0.926998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.668447i | − | 0.120057i | −0.998197 | − | 0.0600284i | \(-0.980881\pi\) | ||
0.998197 | − | 0.0600284i | \(-0.0191191\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0753639 | + | 0.130534i | 0.0131192 | + | 0.0227231i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.90748 | + | 7.49290i | −0.322423 | + | 1.26653i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.36538 | − | 5.82902i | 0.553266 | − | 0.958284i | −0.444771 | − | 0.895645i | \(-0.646715\pi\) |
0.998036 | − | 0.0626397i | \(-0.0199519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.752305 | − | 0.0267426i | −0.120465 | − | 0.00428225i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.32932 | − | 3.65423i | −0.988473 | − | 0.570695i | −0.0836556 | − | 0.996495i | \(-0.526660\pi\) |
−0.904818 | + | 0.425799i | \(0.859993\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.06075 | − | 4.07653i | 1.07675 | − | 0.621665i | 0.146736 | − | 0.989176i | \(-0.453123\pi\) |
0.930019 | + | 0.367511i | \(0.119790\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.63089 | + | 6.40640i | −0.243119 | + | 0.955010i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.40326 | 0.934011 | 0.467005 | − | 0.884254i | \(-0.345333\pi\) | ||||
0.467005 | + | 0.884254i | \(0.345333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.47820 | + | 4.29238i | −0.354029 | + | 0.613197i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.749576 | 0.104962 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.7433i | 1.61306i | 0.591193 | + | 0.806530i | \(0.298657\pi\) | ||||
−0.591193 | + | 0.806530i | \(0.701343\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.437302 | − | 1.55393i | −0.0589658 | − | 0.209532i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.57029 | 0.207990 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.20410 | + | 2.42724i | −0.547328 | + | 0.316000i | −0.748044 | − | 0.663650i | \(-0.769007\pi\) |
0.200716 | + | 0.979650i | \(0.435673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.68231 | + | 4.64590i | 0.343435 | + | 0.594846i | 0.985068 | − | 0.172165i | \(-0.0550763\pi\) |
−0.641634 | + | 0.767011i | \(0.721743\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.11134 | + | 8.85310i | −0.643969 | + | 1.11539i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.73747 | + | 2.26529i | 0.959715 | + | 0.280975i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.80620 | − | 13.5207i | 0.953679 | − | 1.65182i | 0.216318 | − | 0.976323i | \(-0.430595\pi\) |
0.737362 | − | 0.675498i | \(-0.236071\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.247695 | − | 0.429021i | −0.0298190 | − | 0.0516480i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.10530 | + | 2.37019i | −0.487209 | + | 0.281290i | −0.723416 | − | 0.690412i | \(-0.757429\pi\) |
0.236207 | + | 0.971703i | \(0.424096\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.36914 | −0.745452 | −0.372726 | − | 0.927941i | \(-0.621577\pi\) | ||||
−0.372726 | + | 0.927941i | \(0.621577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.499155 | + | 0.916847i | −0.0576375 | + | 0.105868i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.49630i | − | 0.284480i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.20683 | 0.585815 | 0.292907 | − | 0.956141i | \(-0.405377\pi\) | ||||
0.292907 | + | 0.956141i | \(0.405377\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.30479 | + | 7.45612i | −0.478310 | + | 0.828458i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.3902 | 1.46977 | 0.734883 | − | 0.678194i | \(-0.237237\pi\) | ||||
0.734883 | + | 0.678194i | \(0.237237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.77981 | − | 1.98052i | −0.843838 | − | 0.214817i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.33161 | + | 0.768806i | −0.142764 | + | 0.0824246i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.20410 | + | 2.42724i | 0.445634 | + | 0.257287i | 0.705985 | − | 0.708227i | \(-0.250505\pi\) |
−0.260350 | + | 0.965514i | \(0.583838\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5687 | + | 6.61328i | 1.10790 | + | 0.693260i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0697804 | − | 0.120863i | 0.00723589 | − | 0.0125329i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.2980 | − | 4.14901i | −1.67214 | − | 0.425679i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.83435 | + | 3.17719i | 0.186250 | + | 0.322595i | 0.943997 | − | 0.329954i | \(-0.107033\pi\) |
−0.757747 | + | 0.652548i | \(0.773700\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.13433i | − | 0.214508i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.85299 | − | 8.40563i | 0.482891 | − | 0.836391i | −0.516916 | − | 0.856036i | \(-0.672920\pi\) |
0.999807 | + | 0.0196446i | \(0.00625347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.36274i | − | 0.528407i | −0.964467 | − | 0.264203i | \(-0.914891\pi\) | ||
0.964467 | − | 0.264203i | \(-0.0851090\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.12709 | + | 1.15568i | −0.109993 | + | 0.112783i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6408 | − | 7.87552i | −1.31871 | − | 0.761355i | −0.335185 | − | 0.942152i | \(-0.608799\pi\) |
−0.983520 | + | 0.180798i | \(0.942132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.4879i | − | 1.38769i | −0.720123 | − | 0.693847i | \(-0.755915\pi\) | ||
0.720123 | − | 0.693847i | \(-0.244085\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.21700 | − | 0.702637i | 0.115513 | − | 0.0666913i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.74758 | + | 1.58632i | −0.258471 | + | 0.149228i | −0.623637 | − | 0.781714i | \(-0.714346\pi\) |
0.365166 | + | 0.930942i | \(0.381012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.43726 | + | 5.10724i | 0.134025 | + | 0.476253i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.03622 | + | 5.65433i | 0.835399 | + | 0.522743i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.7510 | − | 6.20711i | −0.985546 | − | 0.569005i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.23941 | − | 9.07492i | −0.476310 | − | 0.824993i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.762944 | − | 1.32146i | −0.0687923 | − | 0.119152i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.60319 | − | 8.19704i | 0.680050 | − | 0.733166i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.33161 | − | 0.768806i | −0.118161 | − | 0.0682205i | 0.439754 | − | 0.898118i | \(-0.355065\pi\) |
−0.557916 | + | 0.829898i | \(0.688399\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.70222 | 0.149872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.45180 | 0.563696 | 0.281848 | − | 0.959459i | \(-0.409053\pi\) | ||||
0.281848 | + | 0.959459i | \(0.409053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.5224 | − | 13.0033i | −1.95294 | − | 1.12753i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.94153 | + | 1.99077i | −0.167100 | + | 0.171338i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.62163 | − | 8.00490i | −0.394853 | − | 0.683905i | 0.598230 | − | 0.801325i | \(-0.295871\pi\) |
−0.993082 | + | 0.117420i | \(0.962538\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.38641 | + | 14.5257i | 0.711326 | + | 1.23205i | 0.964359 | + | 0.264596i | \(0.0852385\pi\) |
−0.253033 | + | 0.967458i | \(0.581428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.15778 | + | 0.668447i | 0.0975031 | + | 0.0562934i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.60132 | − | 0.0924708i | −0.217534 | − | 0.00773280i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.8520 | − | 4.46103i | 1.31644 | − | 0.370468i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.896178 | + | 0.517408i | −0.0739155 | + | 0.0426751i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.17153 | − | 1.25373i | 0.177899 | − | 0.102710i | −0.408406 | − | 0.912800i | \(-0.633915\pi\) |
0.586305 | + | 0.810090i | \(0.300582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.0238i | − | 0.897108i | −0.893756 | − | 0.448554i | \(-0.851939\pi\) | ||
0.893756 | − | 0.448554i | \(-0.148061\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.19209 | − | 5.30706i | −0.743137 | − | 0.429050i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.04359 | + | 1.07006i | −0.0838232 | + | 0.0859493i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.946504i | − | 0.0755392i | −0.999286 | − | 0.0377696i | \(-0.987975\pi\) | ||
0.999286 | − | 0.0377696i | \(-0.0120253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.22590 | + | 2.12332i | −0.0972202 | + | 0.168390i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.20449i | 0.646604i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.20187 | + | 12.4740i | 0.564094 | + | 0.977039i | 0.997133 | + | 0.0756643i | \(0.0241077\pi\) |
−0.433039 | + | 0.901375i | \(0.642559\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0831482 | − | 0.326620i | 0.00647308 | − | 0.0254273i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.35429 | + | 16.2021i | −0.723857 | + | 1.25376i | 0.235586 | + | 0.971854i | \(0.424299\pi\) |
−0.959443 | + | 0.281903i | \(0.909034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.28300 | − | 10.7684i | 0.560231 | − | 0.828337i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.2566 | − | 11.1178i | −1.47259 | − | 0.850199i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.3261 | − | 8.84855i | 1.16523 | − | 0.672743i | 0.212675 | − | 0.977123i | \(-0.431783\pi\) |
0.952551 | + | 0.304380i | \(0.0984493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.7516 | − | 9.01675i | 1.11511 | − | 0.681602i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.01354 | −0.0761820 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.20410 | + | 7.28172i | −0.314230 | + | 0.544262i | −0.979273 | − | 0.202543i | \(-0.935079\pi\) |
0.665044 | + | 0.746804i | \(0.268413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6150 | 1.23499 | 0.617493 | − | 0.786576i | \(-0.288148\pi\) | ||||
0.617493 | + | 0.786576i | \(0.288148\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.12004i | 0.0827961i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.4877 | + | 4.07708i | −1.06516 | + | 0.299753i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.59189 | 0.189537 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.72402 | + | 2.15006i | −0.270883 | + | 0.156394i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.93461 | − | 15.4752i | −0.646486 | − | 1.11975i | −0.983956 | − | 0.178410i | \(-0.942905\pi\) |
0.337470 | − | 0.941336i | \(-0.390429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.62156 | + | 6.27273i | −0.260686 | + | 0.451521i | −0.966424 | − | 0.256952i | \(-0.917282\pi\) |
0.705739 | + | 0.708472i | \(0.250615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.16255 | + | 1.21732i | 0.0832519 | + | 0.0871741i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.36349 | + | 9.28984i | −0.382133 | + | 0.661873i | −0.991367 | − | 0.131117i | \(-0.958144\pi\) |
0.609234 | + | 0.792990i | \(0.291477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.62521 | − | 2.81495i | −0.115208 | − | 0.199547i | 0.802655 | − | 0.596444i | \(-0.203420\pi\) |
−0.917863 | + | 0.396897i | \(0.870087\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.82291 | − | 1.62981i | 0.199113 | − | 0.114958i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.4654 | 1.78732 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.42702 | + | 15.7312i | 0.309196 | + | 1.09871i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.01481i | 0.487563i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.42976 | 0.375585 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7639 | + | 20.3757i | −0.809862 | + | 1.40272i | 0.103097 | + | 0.994671i | \(0.467125\pi\) |
−0.912959 | + | 0.408051i | \(0.866208\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.989715 | −0.0678142 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.6673 | − | 4.49759i | −1.20490 | − | 0.306733i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00170 | + | 1.15568i | −0.135884 | + | 0.0784527i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.15162 | − | 0.664886i | −0.0778191 | − | 0.0449289i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.86650 | + | 10.9734i | −0.461891 | + | 0.738151i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.29378 | − | 10.9011i | 0.421463 | − | 0.729995i | −0.574620 | − | 0.818420i | \(-0.694850\pi\) |
0.996083 | + | 0.0884255i | \(0.0281835\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.6125 | − | 7.70929i | 0.840835 | − | 0.513953i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.22075 | + | 7.31055i | 0.280141 | + | 0.485218i | 0.971419 | − | 0.237370i | \(-0.0762855\pi\) |
−0.691278 | + | 0.722589i | \(0.742952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.26510i | 0.546173i | 0.961989 | + | 0.273087i | \(0.0880445\pi\) | ||||
−0.961989 | + | 0.273087i | \(0.911955\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.260593 | − | 0.451361i | 0.0171458 | − | 0.0296974i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.31046i | 0.347900i | 0.984755 | + | 0.173950i | \(0.0556531\pi\) | ||||
−0.984755 | + | 0.173950i | \(0.944347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2504 | − | 9.99686i | −0.668664 | − | 0.652123i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.941457 | + | 0.543551i | 0.0611542 | + | 0.0353074i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.14744i | − | 0.268276i | −0.990963 | − | 0.134138i | \(-0.957173\pi\) | ||
0.990963 | − | 0.134138i | \(-0.0428265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.46804 | + | 0.847571i | −0.0945645 | + | 0.0545968i | −0.546536 | − | 0.837435i | \(-0.684054\pi\) |
0.451972 | + | 0.892032i | \(0.350721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.78768 | + | 2.76417i | −0.307130 | + | 0.177322i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.6685 | − | 3.00229i | 0.681584 | − | 0.191809i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.3847 | + | 22.9883i | −0.915276 | + | 1.46271i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.42111 | + | 1.39783i | 0.153431 | + | 0.0885837i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.86650 | + | 17.0893i | 0.622768 | + | 1.07867i | 0.988968 | + | 0.148130i | \(0.0473252\pi\) |
−0.366200 | + | 0.930536i | \(0.619341\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.856482 | − | 1.48347i | −0.0538465 | − | 0.0932649i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.19993 | − | 1.17025i | −0.0751426 | − | 0.0732839i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.2231 | + | 5.90232i | 0.637701 | + | 0.368177i | 0.783728 | − | 0.621104i | \(-0.213315\pi\) |
−0.146027 | + | 0.989281i | \(0.546649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.2737 | −1.44616 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.7728 | 1.34770 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3013 | + | 7.10216i | 0.758531 | + | 0.437938i | 0.828768 | − | 0.559592i | \(-0.189042\pi\) |
−0.0702373 | + | 0.997530i | \(0.522376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.3338 | − | 18.7988i | 1.12623 | − | 1.15480i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.506768 | + | 0.877748i | 0.0310137 | + | 0.0537173i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.33120 | + | 7.50185i | 0.264078 | + | 0.457396i | 0.967322 | − | 0.253553i | \(-0.0815991\pi\) |
−0.703244 | + | 0.710949i | \(0.748266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.51351 | + | 2.02852i | 0.213430 | + | 0.123224i | 0.602905 | − | 0.797813i | \(-0.294010\pi\) |
−0.389474 | + | 0.921037i | \(0.627343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.22058 | + | 2.29905i | 0.0738728 | + | 0.139145i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.72598 | + | 3.17028i | −0.104081 | + | 0.191175i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.17344 | + | 0.677485i | −0.0705051 | + | 0.0407061i | −0.534838 | − | 0.844955i | \(-0.679627\pi\) |
0.464333 | + | 0.885661i | \(0.346294\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.71144 | + | 0.988102i | −0.102461 | + | 0.0591561i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3840i | 1.21601i | 0.793934 | + | 0.608004i | \(0.208030\pi\) | ||||
−0.793934 | + | 0.608004i | \(0.791970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.22779 | + | 1.28621i | 0.132428 | + | 0.0764575i | 0.564751 | − | 0.825262i | \(-0.308972\pi\) |
−0.432322 | + | 0.901719i | \(0.642306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.51375 | − | 2.45157i | −0.148902 | − | 0.145218i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.2712i | 1.49171i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.05522 | + | 3.55974i | −0.120895 | + | 0.209396i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.765964i | 0.0449016i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.38481 | − | 16.2550i | −0.548267 | − | 0.949626i | −0.998393 | − | 0.0566611i | \(-0.981955\pi\) |
0.450127 | − | 0.892965i | \(-0.351379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5194 | + | 2.67795i | 0.612465 | + | 0.155916i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.448898 | − | 0.777514i | 0.0260477 | − | 0.0451159i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.54966 | + | 0.303920i | 0.494439 | + | 0.0175761i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.4147 | − | 14.0958i | −1.40724 | − | 0.812470i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.75496 | − | 1.01323i | 0.100820 | − | 0.0582083i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.95937 | − | 11.6249i | 0.169453 | − | 0.665639i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.93740 | −0.167646 | −0.0838230 | − | 0.996481i | \(-0.526713\pi\) | ||||
−0.0838230 | + | 0.996481i | \(0.526713\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.559826 | − | 0.969647i | 0.0318474 | − | 0.0551613i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.13623 | 0.234544 | 0.117272 | − | 0.993100i | \(-0.462585\pi\) | ||||
0.117272 | + | 0.993100i | \(0.462585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.2199i | − | 0.690710i | −0.938472 | − | 0.345355i | \(-0.887758\pi\) | ||
0.938472 | − | 0.345355i | \(-0.112242\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22.0039 | − | 6.19227i | 1.23978 | − | 0.348895i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.6351 | −0.653490 | −0.326745 | − | 0.945112i | \(-0.605952\pi\) | ||||
−0.326745 | + | 0.945112i | \(0.605952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.60445 | + | 2.65838i | −0.257800 | + | 0.148841i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.64428 | − | 2.84797i | −0.0917747 | − | 0.158958i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.5012 | − | 23.3848i | 0.751229 | − | 1.30117i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.84965 | − | 15.7062i | −0.490890 | − | 0.871221i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.51242 | − | 2.61959i | 0.0836372 | − | 0.144864i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.0706 | − | 19.1748i | −0.610342 | − | 1.05714i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9346 | + | 6.89045i | −0.655986 | + | 0.378734i | −0.790746 | − | 0.612145i | \(-0.790307\pi\) |
0.134760 | + | 0.990878i | \(0.456974\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.8989 | −1.09045 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.6051 | + | 9.45703i | −1.83604 | + | 0.516693i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.6710i | 0.962599i | 0.876556 | + | 0.481299i | \(0.159835\pi\) | ||||
−0.876556 | + | 0.481299i | \(0.840165\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.662395 | −0.0359763 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.241287 | − | 0.417921i | 0.0130664 | − | 0.0226317i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.06634 | −0.381546 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.273280 | + | 1.07349i | −0.0147129 | + | 0.0577947i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.3190 | + | 15.7726i | −1.46656 | + | 0.846719i | −0.999300 | − | 0.0374015i | \(-0.988092\pi\) |
−0.467260 | + | 0.884120i | \(0.654759\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.19794 | + | 0.691629i | 0.0641241 | + | 0.0370221i | 0.531719 | − | 0.846921i | \(-0.321546\pi\) |
−0.467595 | + | 0.883943i | \(0.654879\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.10257 | + | 3.96034i | 0.112227 | + | 0.211387i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.84369 | − | 8.38952i | 0.257804 | − | 0.446529i | −0.707849 | − | 0.706363i | \(-0.750335\pi\) |
0.965653 | + | 0.259834i | \(0.0836678\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.2722 | + | 2.61501i | 0.545192 | + | 0.138790i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.29594 | − | 2.24464i | −0.0685886 | − | 0.118799i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 33.1233i | − | 1.74818i | −0.485762 | − | 0.874091i | \(-0.661458\pi\) | ||
0.485762 | − | 0.874091i | \(-0.338542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7838 | − | 32.5346i | 0.988623 | − | 1.71235i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.18780i | − | 0.114830i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1958 | + | 9.94361i | 0.533673 | + | 0.520472i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.20396 | − | 0.695107i | −0.0628462 | − | 0.0362843i | 0.468248 | − | 0.883597i | \(-0.344886\pi\) |
−0.531094 | + | 0.847313i | \(0.678219\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.6068i | 1.12481i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.1657 | − | 20.3029i | 1.82571 | − | 1.05408i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.67280 | + | 5.58460i | −0.500839 | + | 0.289159i | −0.729060 | − | 0.684450i | \(-0.760042\pi\) |
0.228221 | + | 0.973609i | \(0.426709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.23045 | − | 0.688413i | 0.115180 | − | 0.0355495i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.943318 | − | 26.5367i | 0.0485834 | − | 1.36671i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.3827 | + | 17.5415i | 1.56066 | + | 0.901045i | 0.997191 | + | 0.0749058i | \(0.0238656\pi\) |
0.563466 | + | 0.826139i | \(0.309468\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.160514 | − | 0.278018i | −0.00822338 | − | 0.0142433i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.27327 | + | 14.3297i | 0.422745 | + | 0.732215i | 0.996207 | − | 0.0870169i | \(-0.0277334\pi\) |
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.89727 | + | 3.99612i | −0.198623 | + | 0.203661i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.8745 | − | 12.0519i | −1.06111 | − | 0.612632i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.6856 | 1.30231 | 0.651157 | − | 0.758943i | \(-0.274284\pi\) | ||||
0.651157 | + | 0.758943i | \(0.274284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.51864 | −0.430806 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.16656 | + | 0.673515i | 0.0588453 | + | 0.0339743i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.33517 | − | 8.12899i | −0.419388 | − | 0.409014i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.90231 | + | 17.1513i | 0.496983 | + | 0.860799i | 0.999994 | − | 0.00348048i | \(-0.00110787\pi\) |
−0.503011 | + | 0.864280i | \(0.667775\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.71488 | − | 4.70231i | −0.135914 | − | 0.235410i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.8364 | − | 14.9167i | −1.29021 | − | 0.744903i | −0.311518 | − | 0.950240i | \(-0.600837\pi\) |
−0.978691 | + | 0.205338i | \(0.934171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.13015 | + | 2.12872i | 0.0562968 | + | 0.106039i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.5318 | − | 5.21515i | 0.920852 | − | 0.259143i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.20816 | − | 2.42958i | 0.208591 | − | 0.120430i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.36923 | + | 0.790524i | −0.0677040 | + | 0.0390889i | −0.533470 | − | 0.845819i | \(-0.679112\pi\) |
0.465766 | + | 0.884908i | \(0.345779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.92984i | − | 0.0951921i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.5370 | + | 8.39292i | 0.715318 | + | 0.412989i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.4352 | − | 20.9050i | −1.05221 | − | 1.02619i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.50189i | 0.171488i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.8627 | − | 18.8148i | 0.530679 | − | 0.919164i | −0.468680 | − | 0.883368i | \(-0.655270\pi\) |
0.999359 | − | 0.0357956i | \(-0.0113965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.356564i | 0.0173779i | 0.999962 | + | 0.00868894i | \(0.00276581\pi\) | ||||
−0.999962 | + | 0.00868894i | \(0.997234\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.46532 | − | 16.3944i | −0.460220 | − | 0.797124i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.36201 | + | 15.3164i | 0.454124 | + | 0.742954i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.27490 | − | 16.0646i | 0.448844 | − | 0.777420i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.460697 | − | 0.288277i | −0.0222427 | − | 0.0139181i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.7959 | − | 11.4292i | −0.953535 | − | 0.550524i | −0.0593575 | − | 0.998237i | \(-0.518905\pi\) |
−0.894177 | + | 0.447713i | \(0.852239\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.0555 | + | 18.5073i | −1.54049 | + | 0.889402i | −0.541681 | + | 0.840584i | \(0.682212\pi\) |
−0.998808 | + | 0.0488177i | \(0.984455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.33193 | + | 0.848216i | 0.159754 | + | 0.0406688i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.8458 | −0.853679 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.04632 | + | 1.81228i | −0.0499381 | + | 0.0864953i | −0.889914 | − | 0.456128i | \(-0.849236\pi\) |
0.839976 | + | 0.542624i | \(0.182569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.6532 | 0.697770 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 3.10367i | − | 0.147460i | −0.997278 | − | 0.0737298i | \(-0.976510\pi\) | ||
0.997278 | − | 0.0737298i | \(-0.0234902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.94054 | − | 10.4491i | −0.139395 | − | 0.495334i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.523518 | 0.0247616 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.0733 | + | 9.27994i | −0.758547 | + | 0.437948i | −0.828774 | − | 0.559583i | \(-0.810961\pi\) |
0.0702265 | + | 0.997531i | \(0.477628\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.63811 | − | 4.56934i | −0.124224 | − | 0.215162i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.15080 | − | 1.99324i | 0.0540692 | − | 0.0936507i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.59381 | − | 27.0867i | −0.309123 | − | 1.26984i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.2853 | + | 26.4750i | −0.715018 | + | 1.23845i | 0.247935 | + | 0.968777i | \(0.420248\pi\) |
−0.962953 | + | 0.269670i | \(0.913085\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.23239 | − | 3.86661i | −0.104199 | − | 0.180478i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.8953 | + | 14.3733i | −1.15949 | + | 0.669432i | −0.951182 | − | 0.308631i | \(-0.900129\pi\) |
−0.208308 | + | 0.978063i | \(0.566796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.47784 | −0.393999 | −0.196999 | − | 0.980404i | \(-0.563120\pi\) | ||||
−0.196999 | + | 0.980404i | \(0.563120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.300399 | + | 0.0845373i | −0.0139307 | + | 0.00392032i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 37.8996i | − | 1.75379i | −0.480686 | − | 0.876893i | \(-0.659612\pi\) | ||
0.480686 | − | 0.876893i | \(-0.340388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −53.9846 | −2.49278 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0988073 | − | 0.171139i | 0.00455280 | − | 0.00788568i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.88596 | 0.270637 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.6125 | + | 32.0864i | 0.899885 | + | 1.47223i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.0666 | − | 17.3589i | 1.37665 | − | 0.794811i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.6522 | + | 9.61417i | 0.760860 | + | 0.439282i | 0.829604 | − | 0.558352i | \(-0.188566\pi\) |
−0.0687447 | + | 0.997634i | \(0.521899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.862130 | + | 24.2528i | −0.0393097 | + | 1.10583i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.856482 | + | 1.48347i | −0.0389713 | + | 0.0675002i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.02382 | − | 7.94990i | 0.0918970 | − | 0.360986i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.32952 | + | 12.6951i | 0.332132 | + | 0.575270i | 0.982930 | − | 0.183982i | \(-0.0588987\pi\) |
−0.650798 | + | 0.759251i | \(0.725565\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.00726i | 0.135993i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.2876 | − | 26.4789i | 0.689920 | − | 1.19498i | −0.281943 | − | 0.959431i | \(-0.590979\pi\) |
0.971863 | − | 0.235545i | \(-0.0756877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.4405i | 1.19082i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.33215 | + | 3.41666i | −0.149769 | + | 0.153568i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.1953 | + | 8.19567i | 0.636747 | + | 0.367626i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.440262i | 0.0197088i | 0.999951 | + | 0.00985441i | \(0.00313681\pi\) | ||||
−0.999951 | + | 0.00985441i | \(0.996863\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.38273 | + | 1.95302i | −0.151129 | + | 0.0872546i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.6208 | − | 20.5657i | 1.58825 | − | 0.916978i | 0.594657 | − | 0.803979i | \(-0.297288\pi\) |
0.993595 | − | 0.112999i | \(-0.0360456\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.8917 | + | 5.87928i | −0.929670 | + | 0.261625i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.44098 | − | 1.18677i | 0.108408 | − | 0.0527061i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.3434 | + | 12.9000i | 0.990355 | + | 0.571782i | 0.905380 | − | 0.424601i | \(-0.139586\pi\) |
0.0849747 | + | 0.996383i | \(0.472919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0116 | + | 19.0727i | 0.487126 | + | 0.843726i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.67665 | − | 8.10020i | −0.206479 | − | 0.357633i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.37240 | + | 8.58475i | −0.368932 | + | 0.378289i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00339 | + | 2.31136i | 0.176069 | + | 0.101654i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.69487 | 0.162187 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.1632 | 1.14623 | 0.573116 | − | 0.819474i | \(-0.305734\pi\) | ||||
0.573116 | + | 0.819474i | \(0.305734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.3510 | + | 10.5949i | 0.802433 | + | 0.463285i | 0.844321 | − | 0.535838i | \(-0.180004\pi\) |
−0.0418883 | + | 0.999122i | \(0.513337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.60853 | − | 0.0903947i | 0.157489 | − | 0.00394515i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.19993 | − | 2.07834i | −0.0522698 | − | 0.0905340i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.68504 | − | 15.0429i | −0.377610 | − | 0.654040i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.4291 | + | 7.17592i | 0.539375 | + | 0.311408i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.3344 | + | 0.936126i | 1.14067 | + | 0.0405481i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.54100 | + | 33.9035i | 0.412493 | + | 1.46577i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.52030 | + | 0.877748i | −0.0656060 | + | 0.0378776i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.09881 | + | 1.78910i | −0.133475 | + | 0.0770619i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.1921i | 1.08309i | 0.840670 | + | 0.541547i | \(0.182161\pi\) | ||||
−0.840670 | + | 0.541547i | \(0.817839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.00420 | + | 1.73447i | 0.128922 | + | 0.0744334i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.6188 | + | 23.1925i | −0.968883 | + | 0.993458i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 22.4525i | − | 0.959999i | −0.877269 | − | 0.479999i | \(-0.840637\pi\) | ||
0.877269 | − | 0.479999i | \(-0.159363\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.93000 | − | 13.7352i | 0.338444 | − | 0.586203i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 55.3904i | 2.35971i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.00211 | − | 15.5921i | −0.382808 | − | 0.663044i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.04516 | − | 0.775213i | −0.129260 | − | 0.0329059i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.72965 | + | 11.6561i | −0.285144 | + | 0.493885i | −0.972644 | − | 0.232300i | \(-0.925375\pi\) |
0.687500 | + | 0.726185i | \(0.258708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.5932 | + | 24.9197i | −0.659524 | + | 1.05399i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.468644 | + | 0.270572i | 0.0197862 | + | 0.0114235i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.8796 | + | 22.4472i | −1.63858 | + | 0.946035i | −0.657257 | + | 0.753666i | \(0.728283\pi\) |
−0.981323 | + | 0.192368i | \(0.938383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.87496 | + | 1.75017i | 0.289232 | + | 0.0736302i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.7703 | 1.25023 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.39931 | + | 16.2801i | −0.394040 | + | 0.682497i | −0.992978 | − | 0.118298i | \(-0.962256\pi\) |
0.598938 | + | 0.800795i | \(0.295589\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.79062 | −0.367876 | −0.183938 | − | 0.982938i | \(-0.558885\pi\) | ||||
−0.183938 | + | 0.982938i | \(0.558885\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.73080i | − | 0.155856i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.67271 | − | 10.4196i | 0.236568 | − | 0.434528i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.2751 | 1.01059 | 0.505293 | − | 0.862948i | \(-0.331385\pi\) | ||||
0.505293 | + | 0.862948i | \(0.331385\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.30964 | + | 0.756122i | −0.0544269 | + | 0.0314234i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.1503 | − | 40.0976i | −0.960438 | − | 1.66353i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.23892 | + | 7.34203i | −0.175558 | + | 0.304076i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.63769 | − | 23.1590i | −0.233090 | − | 0.957507i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.5202 | − | 19.9535i | 0.475489 | − | 0.823571i | −0.524117 | − | 0.851646i | \(-0.675605\pi\) |
0.999606 | + | 0.0280755i | \(0.00893788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.51375 | − | 4.35394i | −0.103577 | − | 0.179401i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.93957 | + | 1.11981i | −0.0797831 | + | 0.0460628i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.4174 | 1.12590 | 0.562949 | − | 0.826491i | \(-0.309667\pi\) | ||||
0.562949 | + | 0.826491i | \(0.309667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.51977 | + | 26.7211i | 0.308280 | + | 1.09546i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 0.678635i | − | 0.0277747i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.02325 | −0.327821 | −0.163911 | − | 0.986475i | \(-0.552411\pi\) | ||||
−0.163911 | + | 0.986475i | \(0.552411\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.18146 | + | 8.97455i | −0.211356 | + | 0.366080i | −0.952139 | − | 0.305665i | \(-0.901121\pi\) |
0.740783 | + | 0.671744i | \(0.234455\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −46.1567 | −1.87964 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.78059 | + | 22.7071i | −0.235014 | + | 0.923175i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.1239 | − | 16.2374i | 1.14151 | − | 0.659054i | 0.194710 | − | 0.980861i | \(-0.437624\pi\) |
0.946805 | + | 0.321807i | \(0.104290\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.60445 | + | 2.65838i | 0.186582 | + | 0.107723i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.3916 | + | 10.8261i | −0.824957 | + | 0.437975i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.8135 | + | 30.8539i | −0.719482 | + | 1.24618i | 0.241724 | + | 0.970345i | \(0.422287\pi\) |
−0.961205 | + | 0.275833i | \(0.911046\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.841749 | + | 3.30653i | −0.0339426 | + | 0.133332i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.3902 | − | 37.0490i | −0.861139 | − | 1.49154i | −0.870831 | − | 0.491583i | \(-0.836418\pi\) |
0.00969198 | − | 0.999953i | \(-0.496915\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.85102i | − | 0.275366i | −0.990476 | − | 0.137683i | \(-0.956035\pi\) | ||
0.990476 | − | 0.137683i | \(-0.0439655\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.47537 | + | 2.55542i | −0.0592047 | + | 0.102546i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 16.7858i | − | 0.672511i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9686 | + | 1.25173i | −0.998746 | + | 0.0500691i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.981766 | + | 0.566823i | 0.0392080 | + | 0.0226367i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 24.1648i | − | 0.963515i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.3170 | − | 22.1223i | 1.52538 | − | 0.880677i | 0.525829 | − | 0.850590i | \(-0.323755\pi\) |
0.999547 | − | 0.0300867i | \(-0.00957833\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.25412 | + | 2.45612i | −0.169086 | + | 0.0976218i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.931390 | + | 3.30965i | 0.0369611 | + | 0.131339i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.634856 | − | 17.8593i | 0.0251539 | − | 0.707612i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.1369 | + | 7.00727i | 0.480130 | + | 0.277203i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5706 | + | 26.9691i | 0.615002 | + | 1.06521i | 0.990384 | + | 0.138344i | \(0.0441781\pi\) |
−0.375382 | + | 0.926870i | \(0.622489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.83855 | + | 8.38061i | 0.190814 | + | 0.330499i | 0.945520 | − | 0.325564i | \(-0.105554\pi\) |
−0.754706 | + | 0.656063i | \(0.772221\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.72494 | − | 2.65754i | −0.107295 | − | 0.104640i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.6951 | + | 11.3710i | 0.774296 | + | 0.447040i | 0.834405 | − | 0.551152i | \(-0.185811\pi\) |
−0.0601089 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.50461 | −0.137568 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.482574 | −0.0189136 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.5155 | + | 8.95789i | 0.607169 | + | 0.350549i | 0.771857 | − | 0.635796i | \(-0.219328\pi\) |
−0.164688 | + | 0.986346i | \(0.552662\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3281 | − | 10.0727i | −0.403554 | − | 0.393571i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.41490 | + | 16.3071i | 0.367310 | + | 0.636200i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.2041 | + | 17.6740i | 0.397495 | + | 0.688482i | 0.993416 | − | 0.114561i | \(-0.0365461\pi\) |
−0.595921 | + | 0.803043i | \(0.703213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.0818 | − | 20.2545i | −1.36452 | − | 0.787808i | −0.374302 | − | 0.927307i | \(-0.622118\pi\) |
−0.990222 | + | 0.139499i | \(0.955451\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.38708 | + | 1.26732i | −0.0927064 | + | 0.0492185i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.7532 | + | 55.9783i | 0.610884 | + | 2.17074i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.1332 | − | 8.73718i | 0.585962 | − | 0.338305i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.27598 | − | 1.31404i | 0.0879945 | − | 0.0508036i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.87289i | 0.149511i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6979 | + | 10.7952i | 0.720749 | + | 0.416125i | 0.815028 | − | 0.579421i | \(-0.196721\pi\) |
−0.0942791 | + | 0.995546i | \(0.530055\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.21605 | − | 0.155714i | 0.239256 | − | 0.00599343i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.7466i | − | 1.41229i | −0.708068 | − | 0.706144i | \(-0.750433\pi\) | ||
0.708068 | − | 0.706144i | \(-0.249567\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.34282 | − | 10.9861i | 0.243415 | − | 0.421608i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.76245i | 0.0675371i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9494 | + | 29.3573i | 0.648552 | + | 1.12332i | 0.983469 | + | 0.181077i | \(0.0579583\pi\) |
−0.334917 | + | 0.942248i | \(0.608708\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.09900 | + | 20.0297i | −0.194823 | + | 0.765296i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.862808 | + | 1.49443i | −0.0329182 | + | 0.0570160i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.8544 | − | 37.3973i | −0.756394 | − | 1.42472i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.6461 | − | 23.4670i | −1.54625 | − | 0.892727i | −0.998423 | − | 0.0561347i | \(-0.982122\pi\) |
−0.547826 | − | 0.836593i | \(-0.684544\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.39135 | + | 3.69005i | −0.242787 | + | 0.140173i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.25265 | − | 36.3459i | 0.350973 | − | 1.37868i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.2389 | −0.993869 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.554368 | + | 0.960194i | −0.0209681 | + | 0.0363179i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.1412 | 1.06288 | 0.531439 | − | 0.847096i | \(-0.321651\pi\) | ||||
0.531439 | + | 0.847096i | \(0.321651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 50.6231i | − | 1.90929i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.809808 | − | 2.87761i | −0.0304991 | − | 0.108377i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.5614 | −1.26221 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.5939 | − | 15.3540i | 0.998753 | − | 0.576630i | 0.0908741 | − | 0.995862i | \(-0.471034\pi\) |
0.907879 | + | 0.419232i | \(0.137701\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.69677 | − | 13.3312i | −0.288651 | − | 0.499959i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.793028 | + | 1.37356i | −0.0296991 | + | 0.0514404i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.01987 | + | 4.20925i | 0.150335 | + | 0.157417i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.432959 | − | 0.749907i | 0.0161692 | − | 0.0280058i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.4815 | + | 42.4033i | 0.913007 | + | 1.58138i | 0.809793 | + | 0.586716i | \(0.199580\pi\) |
0.103215 | + | 0.994659i | \(0.467087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0590 | + | 9.27166i | −0.598068 | + | 0.345294i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.353918 | −0.0131623 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32.3408 | − | 17.6072i | −1.20111 | − | 0.653914i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 17.7593i | − | 0.658655i | −0.944216 | − | 0.329328i | \(-0.893178\pi\) | ||
0.944216 | − | 0.329328i | \(-0.106822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.6745 | 0.913871 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.6356 | − | 25.3495i | 0.541316 | − | 0.937587i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4924 | 0.424481 | 0.212241 | − | 0.977217i | \(-0.431924\pi\) | ||||
0.212241 | + | 0.977217i | \(0.431924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.24240 | + | 0.570852i | 0.0827122 | + | 0.0210562i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.76107 | − | 5.63555i | 0.359553 | − | 0.207588i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.6663 | − | 25.7881i | −1.64308 | − | 0.948631i | −0.979731 | − | 0.200320i | \(-0.935802\pi\) |
−0.663347 | − | 0.748312i | \(-0.730865\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.00071 | + | 2.65491i | −0.183706 | + | 0.0975306i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.69913 | + | 11.6032i | −0.245767 | + | 0.425681i | −0.962347 | − | 0.271824i | \(-0.912373\pi\) |
0.716580 | + | 0.697505i | \(0.245707\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.43357 | − | 1.38323i | −0.199071 | − | 0.0506777i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.7935 | − | 34.2833i | −0.724205 | − | 1.25436i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.4640i | 1.99007i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.7548 | − | 41.1445i | 0.866825 | − | 1.50138i | 0.00160088 | − | 0.999999i | \(-0.499490\pi\) |
0.865224 | − | 0.501386i | \(-0.167176\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.11993i | 0.150138i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.2106 | + | 17.6471i | −0.626358 | + | 0.642245i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.27646 | + | 5.35576i | 0.337158 | + | 0.194659i | 0.659015 | − | 0.752130i | \(-0.270973\pi\) |
−0.321856 | + | 0.946789i | \(0.604307\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 0.357639i | − | 0.0129815i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.4754 | − | 15.8629i | 0.995982 | − | 0.575030i | 0.0889247 | − | 0.996038i | \(-0.471657\pi\) |
0.907057 | + | 0.421008i | \(0.138324\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.3848 | + | 25.0482i | −1.57064 | + | 0.906807i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.42937 | + | 22.8464i | 0.232454 | + | 0.826015i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.28451 | − | 14.8376i | 0.335244 | − | 0.535756i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0143 | + | 5.78174i | 0.361124 | + | 0.208495i | 0.669574 | − | 0.742746i | \(-0.266477\pi\) |
−0.308450 | + | 0.951241i | \(0.599810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.23231 | + | 2.13442i | 0.0443805 | + | 0.0768693i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5093 | − | 23.3988i | −0.485895 | − | 0.841595i | 0.513973 | − | 0.857806i | \(-0.328173\pi\) |
−0.999869 | + | 0.0162108i | \(0.994840\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.34119 | − | 0.0836977i | 0.120019 | − | 0.00300651i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.20816 | − | 2.42958i | −0.150967 | − | 0.0871607i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −54.9681 | −1.96944 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.42224 | −0.122457 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.93162 | + | 4.57932i | 0.283453 | + | 0.163652i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.47770 | + | 1.51518i | −0.0527413 | + | 0.0540790i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.20573 | + | 7.28453i | 0.149918 | + | 0.259666i | 0.931197 | − | 0.364516i | \(-0.118766\pi\) |
−0.781279 | + | 0.624182i | \(0.785432\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.48281 | + | 2.56831i | 0.0527896 | + | 0.0914342i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.50061 | + | 5.48518i | 0.337803 | + | 0.195031i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.3969 | − | 10.2602i | −0.582270 | − | 0.364350i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.27740 | − | 1.48515i | 0.187170 | − | 0.0526728i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.59259 | + | 2.07418i | −0.127256 | + | 0.0734714i | −0.562277 | − | 0.826949i | \(-0.690074\pi\) |
0.435021 | + | 0.900421i | \(0.356741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.9091 | − | 11.4945i | 0.704332 | − | 0.406646i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 14.3518i | − | 0.507097i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.98207 | − | 2.29905i | −0.140524 | − | 0.0811316i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8090 | − | 13.1339i | 0.451457 | − | 0.462908i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.80857i | 0.0636645i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.9082 | − | 27.5538i | 0.559303 | − | 0.968741i | −0.438252 | − | 0.898852i | \(-0.644402\pi\) |
0.997555 | − | 0.0698888i | \(-0.0222644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.23592i | 0.113628i | 0.998385 | + | 0.0568142i | \(0.0180943\pi\) | ||||
−0.998385 | + | 0.0568142i | \(0.981906\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.423523 | + | 0.733563i | 0.0148536 | + | 0.0257272i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.94575 | − | 31.2122i | 0.278328 | − | 1.09332i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.6602 | − | 53.1050i | 1.07266 | − | 1.85791i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.30940 | − | 36.8351i | 0.0457542 | − | 1.28712i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.48771 | + | 2.01363i | 0.121722 | + | 0.0702762i | 0.559625 | − | 0.828746i | \(-0.310945\pi\) |
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0214 | + | 6.94054i | −0.419039 | + | 0.241932i | −0.694666 | − | 0.719333i | \(-0.744448\pi\) |
0.275627 | + | 0.961265i | \(0.411114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.643029 | + | 0.393046i | −0.0223874 | + | 0.0136841i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.60853 | −0.125481 | −0.0627405 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627405 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.47420 | − | 11.2136i | 0.224858 | − | 0.389466i | −0.731419 | − | 0.681929i | \(-0.761141\pi\) |
0.956277 | + | 0.292463i | \(0.0944747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.282896 | −0.00981354 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.7945i | 0.616544i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.2695 | − | 11.3325i | 1.39358 | − | 0.392177i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.831282 | −0.0287333 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.01931 | + | 2.89790i | −0.173286 | + | 0.100047i | −0.584134 | − | 0.811657i | \(-0.698566\pi\) |
0.410849 | + | 0.911704i | \(0.365233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6188 | − | 21.8564i | −0.435131 | − | 0.753669i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.12792 | + | 3.68567i | −0.0732896 | + | 0.126941i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.4705 | + | 5.86784i | −0.979414 | + | 0.201860i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.1168 | + | 31.3793i | −0.622502 | + | 1.07821i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.268540 | + | 0.465126i | 0.00921628 | + | 0.0159631i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8308 | + | 7.98520i | −0.474113 | + | 0.273729i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.7950 | −1.02016 | −0.510080 | − | 0.860127i | \(-0.670384\pi\) | ||||
−0.510080 | + | 0.860127i | \(0.670384\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.4689 | + | 47.8612i | 0.460628 | + | 1.63682i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5362i | 0.564865i | 0.959287 | + | 0.282433i | \(0.0911413\pi\) | ||||
−0.959287 | + | 0.282433i | \(0.908859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1978 | 0.825618 | 0.412809 | − | 0.910818i | \(-0.364548\pi\) | ||||
0.412809 | + | 0.910818i | \(0.364548\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.63811 | + | 4.56934i | −0.0899066 | + | 0.155723i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.2651 | −0.723874 | −0.361937 | − | 0.932203i | \(-0.617884\pi\) | ||||
−0.361937 | + | 0.932203i | \(0.617884\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.3488 | − | 9.76253i | −1.30390 | − | 0.331936i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.743215 | + | 0.429096i | −0.0252409 | + | 0.0145728i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.25538 | + | 1.87949i | 0.110431 | + | 0.0637574i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.99976 | + | 56.2558i | −0.0677593 | + | 1.90615i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.42309 | − | 9.39307i | 0.183544 | − | 0.317907i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.6916 | − | 8.59621i | −1.27421 | − | 0.290605i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.38433 | + | 2.39774i | 0.0467457 | + | 0.0809659i | 0.888452 | − | 0.458970i | \(-0.151782\pi\) |
−0.841706 | + | 0.539936i | \(0.818448\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.91879i | − | 0.132178i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2986 | − | 24.7659i | 0.481733 | − | 0.834386i | −0.518047 | − | 0.855352i | \(-0.673341\pi\) |
0.999780 | + | 0.0209661i | \(0.00667421\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.0580i | − | 0.742310i | −0.928571 | − | 0.371155i | \(-0.878962\pi\) | ||
0.928571 | − | 0.371155i | \(-0.121038\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.62248 | + | 1.58235i | 0.0545392 | + | 0.0531901i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.3455 | + | 20.4067i | 1.18679 | + | 0.685191i | 0.957575 | − | 0.288185i | \(-0.0930519\pi\) |
0.229212 | + | 0.973377i | \(0.426385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.31676i | 0.178318i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.38282 | + | 3.10777i | −0.180331 | + | 0.104114i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.7077 | − | 24.0799i | 1.39569 | − | 0.805804i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0983 | − | 5.09317i | 0.604960 | − | 0.170246i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.51415 | + | 0.947466i | 0.0505561 | + | 0.0316350i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.26332 | + | 2.46143i | 0.142190 | + | 0.0820933i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.0803 | + | 36.5122i | 0.702288 | + | 1.21640i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.94298 | − | 5.09739i | −0.0979362 | − | 0.169630i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.5976 | − | 25.9397i | −0.884134 | − | 0.862264i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.6530 | − | 11.9240i | −0.685773 | − | 0.395931i | 0.116253 | − | 0.993220i | \(-0.462912\pi\) |
−0.802027 | + | 0.597288i | \(0.796245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.6949 | −0.951749 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.2559 | −0.372924 | −0.186462 | − | 0.982462i | \(-0.559702\pi\) | ||||
−0.186462 | + | 0.982462i | \(0.559702\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.37172 | + | 4.83341i | 0.277063 | + | 0.159963i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.74863 | − | 1.79298i | 0.0578079 | − | 0.0592742i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1545 | − | 19.3202i | −0.368355 | − | 0.638010i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.81128 | + | 11.7975i | 0.224683 | + | 0.389163i | 0.956224 | − | 0.292634i | \(-0.0945319\pi\) |
−0.731541 | + | 0.681798i | \(0.761199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.531116 | − | 0.306640i | −0.0175009 | − | 0.0101041i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.06630 | − | 14.4889i | 0.298421 | − | 0.476909i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.5573 | + | 16.0918i | 0.971839 | + | 0.529094i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.7304 | + | 7.92723i | −0.450964 | + | 0.260364i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.4152 | + | 8.89998i | −0.505757 | + | 0.291999i | −0.731088 | − | 0.682283i | \(-0.760987\pi\) |
0.225331 | + | 0.974282i | \(0.427654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.2779i | 1.22173i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.747880 | + | 0.431788i | 0.0244845 | + | 0.0141361i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.14913 | − | 4.04649i | −0.135691 | − | 0.132334i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.06467i | − | 0.0347814i | −0.999849 | − | 0.0173907i | \(-0.994464\pi\) | ||
0.999849 | − | 0.0173907i | \(-0.00553591\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.27566 | − | 2.20951i | 0.0416295 | − | 0.0721045i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.2630i | 1.05174i | 0.850564 | + | 0.525871i | \(0.176261\pi\) | ||||
−0.850564 | + | 0.525871i | \(0.823739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.67057 | + | 15.0179i | 0.282352 | + | 0.489049i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.31818 | + | 2.37214i | 0.303120 | + | 0.0771659i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.0866 | + | 27.8628i | −0.522745 | + | 0.905420i | 0.476905 | + | 0.878955i | \(0.341759\pi\) |
−0.999650 | + | 0.0264656i | \(0.991575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.2830 | − | 10.7684i | 0.658414 | − | 0.349556i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.10376 | − | 1.21461i | −0.0682190 | − | 0.0393863i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.0839 | − | 28.9160i | 1.62238 | − | 0.936681i | 0.636097 | − | 0.771609i | \(-0.280548\pi\) |
0.986282 | − | 0.165071i | \(-0.0527853\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.85747 | + | 38.7218i | −0.318980 | + | 1.25301i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.11005 | −0.0358829 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.9807 | + | 27.6794i | −0.516044 | + | 0.893814i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.5532 | 0.985586 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.5665i | 1.50058i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.5905 | − | 4.38743i | 0.501877 | − | 0.141236i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.8280 | 1.34510 | 0.672549 | − | 0.740053i | \(-0.265200\pi\) | ||||
0.672549 | + | 0.740053i | \(0.265200\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.88237 | − | 2.81884i | 0.156844 | − | 0.0905540i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.83949 | − | 4.91813i | −0.0911234 | − | 0.157830i | 0.816861 | − | 0.576835i | \(-0.195712\pi\) |
−0.907984 | + | 0.419005i | \(0.862379\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9986 | − | 50.2270i | 0.929652 | − | 1.61020i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0394736 | − | 3.76369i | 0.00126417 | − | 0.120535i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.14109 | − | 12.3687i | 0.228464 | − | 0.395711i | −0.728889 | − | 0.684632i | \(-0.759963\pi\) |
0.957353 | + | 0.288921i | \(0.0932965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.75230 | + | 3.03508i | 0.0560039 | + | 0.0970016i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.0939 | + | 21.4161i | −1.18432 | + | 0.683765i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.7988 | −0.599588 | −0.299794 | − | 0.954004i | \(-0.596918\pi\) | ||||
−0.299794 | + | 0.954004i | \(0.596918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.0894 | − | 6.49774i | 0.735689 | − | 0.207035i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.62272i | − | 0.147143i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.3451 | −0.615139 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.14513 | + | 1.98342i | −0.0363762 | + | 0.0630053i | −0.883640 | − | 0.468166i | \(-0.844915\pi\) |
0.847264 | + | 0.531172i | \(0.178248\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.87723 | −0.0913060 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.79308 | + | 7.04352i | −0.0568445 | + | 0.223295i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.3308 | + | 20.3982i | −1.11894 | + | 0.646018i | −0.941129 | − | 0.338047i | \(-0.890234\pi\) |
−0.177807 | + | 0.984065i | \(0.556900\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.24897 | − | 4.18519i | −0.229347 | − | 0.132414i |
(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 | 260.2.z.a.69.5 | yes | 16 | |
3.2 | odd | 2 | 2340.2.cr.a.1369.7 | 16 | |||
4.3 | odd | 2 | 1040.2.df.d.849.4 | 16 | |||
5.2 | odd | 4 | 1300.2.y.e.901.5 | 16 | |||
5.3 | odd | 4 | 1300.2.y.e.901.4 | 16 | |||
5.4 | even | 2 | inner | 260.2.z.a.69.4 | yes | 16 | |
13.4 | even | 6 | 3380.2.d.d.1689.8 | 16 | |||
13.6 | odd | 12 | 3380.2.c.e.2029.7 | 16 | |||
13.7 | odd | 12 | 3380.2.c.e.2029.8 | 16 | |||
13.9 | even | 3 | 3380.2.d.d.1689.7 | 16 | |||
13.10 | even | 6 | inner | 260.2.z.a.49.4 | ✓ | 16 | |
15.14 | odd | 2 | 2340.2.cr.a.1369.2 | 16 | |||
20.19 | odd | 2 | 1040.2.df.d.849.5 | 16 | |||
39.23 | odd | 6 | 2340.2.cr.a.829.2 | 16 | |||
52.23 | odd | 6 | 1040.2.df.d.49.5 | 16 | |||
65.4 | even | 6 | 3380.2.d.d.1689.9 | 16 | |||
65.9 | even | 6 | 3380.2.d.d.1689.10 | 16 | |||
65.19 | odd | 12 | 3380.2.c.e.2029.9 | 16 | |||
65.23 | odd | 12 | 1300.2.y.e.101.4 | 16 | |||
65.49 | even | 6 | inner | 260.2.z.a.49.5 | yes | 16 | |
65.59 | odd | 12 | 3380.2.c.e.2029.10 | 16 | |||
65.62 | odd | 12 | 1300.2.y.e.101.5 | 16 | |||
195.179 | odd | 6 | 2340.2.cr.a.829.7 | 16 | |||
260.179 | odd | 6 | 1040.2.df.d.49.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.z.a.49.4 | ✓ | 16 | 13.10 | even | 6 | inner | |
260.2.z.a.49.5 | yes | 16 | 65.49 | even | 6 | inner | |
260.2.z.a.69.4 | yes | 16 | 5.4 | even | 2 | inner | |
260.2.z.a.69.5 | yes | 16 | 1.1 | even | 1 | trivial | |
1040.2.df.d.49.4 | 16 | 260.179 | odd | 6 | |||
1040.2.df.d.49.5 | 16 | 52.23 | odd | 6 | |||
1040.2.df.d.849.4 | 16 | 4.3 | odd | 2 | |||
1040.2.df.d.849.5 | 16 | 20.19 | odd | 2 | |||
1300.2.y.e.101.4 | 16 | 65.23 | odd | 12 | |||
1300.2.y.e.101.5 | 16 | 65.62 | odd | 12 | |||
1300.2.y.e.901.4 | 16 | 5.3 | odd | 4 | |||
1300.2.y.e.901.5 | 16 | 5.2 | odd | 4 | |||
2340.2.cr.a.829.2 | 16 | 39.23 | odd | 6 | |||
2340.2.cr.a.829.7 | 16 | 195.179 | odd | 6 | |||
2340.2.cr.a.1369.2 | 16 | 15.14 | odd | 2 | |||
2340.2.cr.a.1369.7 | 16 | 3.2 | odd | 2 | |||
3380.2.c.e.2029.7 | 16 | 13.6 | odd | 12 | |||
3380.2.c.e.2029.8 | 16 | 13.7 | odd | 12 | |||
3380.2.c.e.2029.9 | 16 | 65.19 | odd | 12 | |||
3380.2.c.e.2029.10 | 16 | 65.59 | odd | 12 | |||
3380.2.d.d.1689.7 | 16 | 13.9 | even | 3 | |||
3380.2.d.d.1689.8 | 16 | 13.4 | even | 6 | |||
3380.2.d.d.1689.9 | 16 | 65.4 | even | 6 | |||
3380.2.d.d.1689.10 | 16 | 65.9 | even | 6 |