Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(65,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bn (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
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: | \( x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} - 18 x^{7} - 846 x^{6} - 108 x^{5} + 1701 x^{4} + 1215 x^{3} - 4374 x^{2} - 2187 x + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(-1.72340 + 0.172852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.449 |
Dual form | 912.2.bn.n.65.4 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.712008 | + | 1.57894i | −0.411078 | + | 0.911600i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.02997 | − | 0.594652i | 0.460615 | − | 0.265936i | −0.251688 | − | 0.967808i | \(-0.580986\pi\) |
0.712303 | + | 0.701872i | \(0.247652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.04533 | −0.395096 | −0.197548 | − | 0.980293i | \(-0.563298\pi\) | ||||
−0.197548 | + | 0.980293i | \(0.563298\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.98609 | − | 2.24843i | −0.662029 | − | 0.749478i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41364i | 1.02925i | 0.857415 | + | 0.514626i | \(0.172069\pi\) | ||||
−0.857415 | + | 0.514626i | \(0.827931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.793296 | + | 0.458009i | 0.220021 | + | 0.127029i | 0.605960 | − | 0.795495i | \(-0.292789\pi\) |
−0.385939 | + | 0.922524i | \(0.626123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.205573 | + | 2.04965i | 0.0530787 | + | 0.529217i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.59249 | + | 1.49677i | −0.628771 | + | 0.363021i | −0.780276 | − | 0.625436i | \(-0.784921\pi\) |
0.151505 | + | 0.988456i | \(0.451588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.30418 | + | 0.688533i | −0.987445 | + | 0.157960i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.744282 | − | 1.65051i | 0.162416 | − | 0.360170i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.62874 | − | 0.940355i | −0.339616 | − | 0.196077i | 0.320486 | − | 0.947253i | \(-0.396154\pi\) |
−0.660102 | + | 0.751176i | \(0.729487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79278 | + | 3.10518i | −0.358556 | + | 0.621037i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.96425 | − | 1.53501i | 0.955370 | − | 0.295412i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.797081 | − | 1.38058i | 0.148014 | − | 0.256368i | −0.782479 | − | 0.622677i | \(-0.786045\pi\) |
0.930493 | + | 0.366309i | \(0.119379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.98511i | 1.61377i | 0.590706 | + | 0.806887i | \(0.298849\pi\) | ||||
−0.590706 | + | 0.806887i | \(0.701151\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.38993 | − | 2.43054i | −0.938266 | − | 0.423103i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.07665 | + | 0.621605i | −0.181987 | + | 0.105070i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.54422i | 0.747066i | 0.927617 | + | 0.373533i | \(0.121854\pi\) | ||||
−0.927617 | + | 0.373533i | \(0.878146\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.28800 | + | 0.926458i | −0.206245 | + | 0.148352i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.469860 | − | 0.813822i | −0.0733798 | − | 0.127098i | 0.827001 | − | 0.562201i | \(-0.190045\pi\) |
−0.900381 | + | 0.435103i | \(0.856712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.73567 | + | 4.73832i | 0.417185 | + | 0.722586i | 0.995655 | − | 0.0931175i | \(-0.0296832\pi\) |
−0.578470 | + | 0.815704i | \(0.696350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.38264 | − | 1.13478i | −0.504254 | − | 0.169163i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.82414 | − | 4.51727i | −1.14127 | − | 0.658911i | −0.194524 | − | 0.980898i | \(-0.562316\pi\) |
−0.946744 | + | 0.321986i | \(0.895649\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.90729 | −0.843899 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.517439 | − | 5.15909i | −0.0724560 | − | 0.722417i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0418792 | − | 0.0725369i | 0.00575255 | − | 0.00996371i | −0.863135 | − | 0.504974i | \(-0.831502\pi\) |
0.868887 | + | 0.495010i | \(0.164836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.02993 | + | 3.51594i | 0.273715 | + | 0.474089i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.97746 | − | 7.28627i | 0.261921 | − | 0.965089i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.12477 | − | 8.87636i | −0.667188 | − | 1.15560i | −0.978687 | − | 0.205358i | \(-0.934164\pi\) |
0.311499 | − | 0.950247i | \(-0.399169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.766777 | + | 1.32810i | −0.0981757 | + | 0.170045i | −0.910930 | − | 0.412562i | \(-0.864634\pi\) |
0.812754 | + | 0.582607i | \(0.197967\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.07611 | + | 2.35035i | 0.261565 | + | 0.296116i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.08942 | 0.135126 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.67930 | − | 5.01100i | −1.06035 | − | 0.612191i | −0.134817 | − | 0.990870i | \(-0.543045\pi\) |
−0.925528 | + | 0.378680i | \(0.876378\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.64444 | − | 1.90214i | 0.318353 | − | 0.228991i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.80899 | − | 3.13327i | −0.214688 | − | 0.371851i | 0.738488 | − | 0.674267i | \(-0.235540\pi\) |
−0.953176 | + | 0.302416i | \(0.902207\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.38049 | + | 7.58723i | 0.512698 | + | 0.888018i | 0.999892 | + | 0.0147244i | \(0.00468709\pi\) |
−0.487194 | + | 0.873294i | \(0.661980\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.62642 | − | 5.04160i | −0.418743 | − | 0.582154i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.56837i | − | 0.406654i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.95719 | − | 1.70734i | 0.332710 | − | 0.192090i | −0.324334 | − | 0.945943i | \(-0.605140\pi\) |
0.657044 | + | 0.753853i | \(0.271807\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.11091 | + | 8.93117i | −0.123434 | + | 0.992353i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.04823i | − | 0.773644i | −0.922154 | − | 0.386822i | \(-0.873573\pi\) | ||
0.922154 | − | 0.386822i | \(-0.126427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.78012 | + | 3.08325i | −0.193081 | + | 0.334426i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.61233 | + | 2.24153i | 0.172860 | + | 0.240317i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.48869 | + | 4.31053i | −0.263800 | + | 0.456916i | −0.967249 | − | 0.253831i | \(-0.918309\pi\) |
0.703448 | + | 0.710746i | \(0.251643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.829253 | − | 0.478770i | −0.0869294 | − | 0.0501887i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.1869 | − | 6.39747i | −1.47112 | − | 0.663387i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.02372 | + | 3.26865i | −0.412825 | + | 0.335356i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.48961 | + | 4.32413i | −0.760455 | + | 0.439049i | −0.829459 | − | 0.558568i | \(-0.811351\pi\) |
0.0690043 | + | 0.997616i | \(0.478018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.67534 | − | 6.77979i | 0.771401 | − | 0.681395i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4238 | + | 8.90495i | 1.53473 | + | 0.886076i | 0.999134 | + | 0.0416008i | \(0.0132458\pi\) |
0.535595 | + | 0.844475i | \(0.320088\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3812i | 1.31849i | 0.751929 | + | 0.659244i | \(0.229123\pi\) | ||||
−0.751929 | + | 0.659244i | \(0.770877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.214891 | − | 2.14255i | −0.0209712 | − | 0.209092i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.74732 | −0.652288 | −0.326144 | − | 0.945320i | \(-0.605749\pi\) | ||||
−0.326144 | + | 0.945320i | \(0.605749\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.56805 | + | 0.905316i | −0.150192 | + | 0.0867135i | −0.573213 | − | 0.819407i | \(-0.694303\pi\) |
0.423021 | + | 0.906120i | \(0.360970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.17504 | − | 3.23552i | −0.681025 | − | 0.307102i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.00792875 | −0.000745874 | −0.000372937 | − | 1.00000i | \(-0.500119\pi\) | ||||
−0.000372937 | 1.00000i | \(0.500119\pi\) | ||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.23673 | −0.208576 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.545751 | − | 2.69332i | −0.0504547 | − | 0.248997i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.71000 | − | 1.56462i | 0.248425 | − | 0.143428i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.652944 | −0.0593585 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.61952 | − | 0.162432i | 0.146027 | − | 0.0146460i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2108i | 0.913284i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4312 | + | 7.75450i | 1.19182 | + | 0.688100i | 0.958720 | − | 0.284351i | \(-0.0917782\pi\) |
0.233105 | + | 0.972452i | \(0.425111\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.42932 | + | 0.945729i | −0.830206 | + | 0.0832668i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0950 | − | 8.71513i | 1.31886 | − | 0.761444i | 0.335315 | − | 0.942106i | \(-0.391157\pi\) |
0.983545 | + | 0.180662i | \(0.0578241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.49927 | − | 0.719742i | 0.390136 | − | 0.0624095i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.20022 | − | 4.53300i | 0.361497 | − | 0.390139i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6485 | + | 7.30262i | 1.08064 | + | 0.623905i | 0.931068 | − | 0.364846i | \(-0.118878\pi\) |
0.149568 | + | 0.988751i | \(0.452212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.42559 | − | 14.5936i | 0.714649 | − | 1.23781i | −0.248445 | − | 0.968646i | \(-0.579920\pi\) |
0.963095 | − | 0.269163i | \(-0.0867471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.7033 | − | 9.13750i | 1.06981 | − | 0.769516i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.56348 | + | 2.70803i | −0.130745 | + | 0.226457i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.89594i | − | 0.157449i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.20604 | − | 9.32724i | 0.346908 | − | 0.769298i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.37577 | − | 1.37165i | 0.194631 | − | 0.112370i | −0.399518 | − | 0.916725i | \(-0.630822\pi\) |
0.594149 | + | 0.804355i | \(0.297489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.29062i | 0.186408i | 0.995647 | + | 0.0932038i | \(0.0297108\pi\) | ||||
−0.995647 | + | 0.0932038i | \(0.970289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.51431 | + | 2.85631i | 0.688341 | + | 0.230919i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.34301 | + | 9.25436i | 0.429161 | + | 0.743328i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.60941 | + | 11.4478i | 0.527488 | + | 0.913637i | 0.999487 | + | 0.0320372i | \(0.0101995\pi\) |
−0.471998 | + | 0.881599i | \(0.656467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0847129 | + | 0.117772i | 0.00671817 | + | 0.00933989i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.70257 | + | 0.982978i | 0.134181 | + | 0.0774695i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.23577 | 0.0967932 | 0.0483966 | − | 0.998828i | \(-0.484589\pi\) | ||||
0.0483966 | + | 0.998828i | \(0.484589\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.99677 | + | 0.701752i | −0.544698 | + | 0.0546313i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.40067 | + | 7.62219i | −0.340534 | + | 0.589823i | −0.984532 | − | 0.175205i | \(-0.943941\pi\) |
0.643998 | + | 0.765027i | \(0.277275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.08045 | − | 10.5317i | −0.467727 | − | 0.810127i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.0966 | + | 8.31016i | 0.772106 | + | 0.635494i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0208 | − | 22.5527i | −0.989952 | − | 1.71465i | −0.617433 | − | 0.786623i | \(-0.711827\pi\) |
−0.372519 | − | 0.928024i | \(-0.621506\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.87404 | − | 3.24593i | 0.141664 | − | 0.245369i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.6641 | − | 1.77165i | 1.32772 | − | 0.133165i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.7770 | 1.70243 | 0.851217 | − | 0.524815i | \(-0.175865\pi\) | ||||
0.851217 | + | 0.524815i | \(0.175865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.61211 | + | 3.24015i | 0.417145 | + | 0.240839i | 0.693855 | − | 0.720115i | \(-0.255911\pi\) |
−0.276710 | + | 0.960953i | \(0.589244\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.55103 | − | 2.15631i | −0.114655 | − | 0.159399i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.70223 | + | 4.68040i | 0.198672 | + | 0.344110i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.10945 | − | 8.84982i | −0.373640 | − | 0.647163i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.18926 | + | 1.60458i | −0.377463 | + | 0.116716i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.8390i | 1.21843i | 0.793007 | + | 0.609213i | \(0.208514\pi\) | ||||
−0.793007 | + | 0.609213i | \(0.791486\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8046 | − | 7.39275i | 0.921696 | − | 0.532142i | 0.0375205 | − | 0.999296i | \(-0.488054\pi\) |
0.884176 | + | 0.467154i | \(0.154721\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.775679 | + | 1.72013i | −0.0555475 | + | 0.123181i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.97140i | 0.639186i | 0.947555 | + | 0.319593i | \(0.103546\pi\) | ||||
−0.947555 | + | 0.319593i | \(0.896454\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.73567 | − | 3.00627i | 0.123038 | − | 0.213108i | −0.797926 | − | 0.602755i | \(-0.794070\pi\) |
0.920964 | + | 0.389647i | \(0.127403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0918 | − | 10.1362i | 0.993958 | − | 0.714953i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.833210 | + | 1.44316i | −0.0584799 | + | 0.101290i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.967881 | − | 0.558806i | −0.0675997 | − | 0.0390287i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.12050 | + | 5.52975i | 0.0778802 | + | 0.384344i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.35040 | − | 14.6929i | −0.162581 | − | 1.01633i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.14092 | − | 1.81341i | 0.216230 | − | 0.124840i | −0.387973 | − | 0.921671i | \(-0.626825\pi\) |
0.604203 | + | 0.796830i | \(0.293491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.23525 | − | 0.625375i | 0.427233 | − | 0.0428500i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.63529 | + | 3.25354i | 0.384324 | + | 0.221889i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.39238i | − | 0.637596i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.0987 | + | 1.51435i | −1.02028 | + | 0.102330i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.74215 | −0.184457 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1524 | + | 8.17089i | −0.947714 | + | 0.547163i | −0.892370 | − | 0.451304i | \(-0.850959\pi\) |
−0.0553443 | + | 0.998467i | \(0.517626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.5424 | − | 2.13623i | 0.702828 | − | 0.142415i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.0153826 | 0.00102098 | 0.000510491 | − | 1.00000i | \(-0.499838\pi\) | ||||
0.000510491 | 1.00000i | \(0.499838\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.3381 | 1.80655 | 0.903275 | − | 0.429062i | \(-0.141156\pi\) | ||||
0.903275 | + | 0.429062i | \(0.141156\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.63424 | + | 2.54071i | 0.370705 | + | 0.167166i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.6729 | + | 10.7808i | −1.22330 | + | 0.706273i | −0.965620 | − | 0.259957i | \(-0.916292\pi\) |
−0.257681 | + | 0.966230i | \(0.582958\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7448 | −0.700914 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.590231 | + | 5.88486i | 0.0383396 | + | 0.382263i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0836i | 0.781626i | 0.920470 | + | 0.390813i | \(0.127806\pi\) | ||||
−0.920470 | + | 0.390813i | \(0.872194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6746 | − | 10.2044i | −1.13852 | − | 0.657325i | −0.192457 | − | 0.981305i | \(-0.561646\pi\) |
−0.946064 | + | 0.323980i | \(0.894979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.3108 | − | 8.11312i | −0.853888 | − | 0.520457i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.08431 | + | 3.51278i | −0.388713 | + | 0.224423i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.72984 | − | 1.42514i | −0.237324 | − | 0.0906797i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1287 | + | 5.01840i | 0.705254 | + | 0.318028i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9785 | + | 13.8440i | 1.51351 | + | 0.873824i | 0.999875 | + | 0.0158130i | \(0.00503365\pi\) |
0.513632 | + | 0.858011i | \(0.328300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.21003 | − | 5.55994i | 0.201813 | − | 0.349550i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.60081 | − | 5.00600i | −0.225491 | − | 0.313488i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7065 | − | 25.4724i | 0.917367 | − | 1.58893i | 0.113969 | − | 0.993484i | \(-0.463644\pi\) |
0.803398 | − | 0.595442i | \(-0.203023\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.75020i | − | 0.295163i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.68723 | + | 0.949780i | −0.290132 | + | 0.0587899i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.78482 | + | 5.07192i | −0.541695 | + | 0.312748i | −0.745766 | − | 0.666208i | \(-0.767916\pi\) |
0.204071 | + | 0.978956i | \(0.434583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.0996141i | − | 0.00611925i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.03410 | − | 6.99862i | −0.308082 | − | 0.428309i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2191 | − | 17.6999i | −0.623067 | − | 1.07918i | −0.988911 | − | 0.148507i | \(-0.952553\pi\) |
0.365845 | − | 0.930676i | \(-0.380780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.39147 | + | 11.0703i | 0.388254 | + | 0.672476i | 0.992215 | − | 0.124538i | \(-0.0397450\pi\) |
−0.603961 | + | 0.797014i | \(0.706412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.34638 | − | 0.968451i | 0.0814868 | − | 0.0586133i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.6000 | − | 6.11990i | −0.639203 | − | 0.369044i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.32291 | 0.560159 | 0.280080 | − | 0.959977i | \(-0.409639\pi\) | ||||
0.280080 | + | 0.959977i | \(0.409639\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.2024 | − | 17.8452i | 1.20949 | − | 1.06837i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.29185 | − | 3.96959i | 0.136720 | − | 0.236806i | −0.789533 | − | 0.613708i | \(-0.789677\pi\) |
0.926253 | + | 0.376902i | \(0.123011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.95495 | + | 17.2425i | 0.591761 | + | 1.02496i | 0.993995 | + | 0.109423i | \(0.0349002\pi\) |
−0.402235 | + | 0.915537i | \(0.631766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.29607 | − | 8.68051i | −0.136008 | − | 0.514189i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.491158 | + | 0.850710i | 0.0289921 | + | 0.0502158i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.01934 | + | 6.96170i | −0.236432 | + | 0.409512i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.49486 | − | 14.9044i | −0.0876305 | − | 0.873714i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.0913 | −1.52427 | −0.762136 | − | 0.647417i | \(-0.775849\pi\) | ||||
−0.762136 | + | 0.647417i | \(0.775849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.5567 | − | 6.09491i | −0.614634 | − | 0.354859i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.23996 | + | 16.9462i | 0.304053 | + | 0.983316i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.861383 | − | 1.49196i | −0.0498150 | − | 0.0862822i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.85967 | − | 4.95309i | −0.164829 | − | 0.285491i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.0423 | + | 18.0129i | −1.43864 | + | 1.03481i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.82386i | 0.104434i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.94327 | + | 2.27665i | −0.225054 | + | 0.129935i | −0.608288 | − | 0.793716i | \(-0.708144\pi\) |
0.383234 | + | 0.923651i | \(0.374810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.1281 | − | 9.52751i | −1.20193 | − | 0.542001i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 18.2836i | − | 1.03677i | −0.855147 | − | 0.518385i | \(-0.826533\pi\) | ||
0.855147 | − | 0.518385i | \(-0.173467\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.796717 | − | 1.37995i | 0.0450331 | − | 0.0779997i | −0.842630 | − | 0.538493i | \(-0.818994\pi\) |
0.887663 | + | 0.460493i | \(0.152327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.53596 | + | 1.18622i | 0.199229 | + | 0.0668358i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.67389 | − | 6.36336i | 0.206346 | − | 0.357402i | −0.744215 | − | 0.667940i | \(-0.767176\pi\) |
0.950561 | + | 0.310539i | \(0.100509\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.71282 | + | 2.72095i | 0.263867 | + | 0.152344i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.80415 | − | 10.6536i | 0.268141 | − | 0.594625i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1279 | − | 8.22739i | 0.563534 | − | 0.457784i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.84441 | + | 1.64222i | −0.157779 | + | 0.0910939i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.312970 | − | 3.12045i | −0.0173073 | − | 0.172561i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.17878 | + | 4.72202i | 0.450911 | + | 0.260334i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.27646i | − | 0.399950i | −0.979801 | − | 0.199975i | \(-0.935914\pi\) | ||
0.979801 | − | 0.199975i | \(-0.0640862\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2174 | − | 9.02523i | 0.559909 | − | 0.494579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.9192 | −0.651215 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5410 | + | 8.97260i | −0.846572 | + | 0.488768i | −0.859493 | − | 0.511148i | \(-0.829220\pi\) |
0.0129208 | + | 0.999917i | \(0.495887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.00564533 | − | 0.0125190i | 0.000306612 | − | 0.000679939i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.6719 | −1.66098 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4923 | 0.728518 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.59257 | − | 3.53166i | 0.0857412 | − | 0.190138i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.8410 | + | 12.6099i | −1.17249 | + | 0.676936i | −0.954265 | − | 0.298962i | \(-0.903359\pi\) |
−0.218223 | + | 0.975899i | \(0.570026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.0609 | −1.82324 | −0.911620 | − | 0.411035i | \(-0.865167\pi\) | ||||
−0.911620 | + | 0.411035i | \(0.865167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.64116 | + | 1.05596i | 0.247727 | + | 0.0563629i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2144i | 0.596884i | 0.954428 | + | 0.298442i | \(0.0964670\pi\) | ||||
−0.954428 | + | 0.298442i | \(0.903533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.72641 | − | 2.15144i | −0.197777 | − | 0.114187i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.540893 | + | 5.39294i | 0.0286271 | + | 0.285425i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.0882 | − | 17.9488i | 1.64077 | − | 0.947300i | 0.660212 | − | 0.751079i | \(-0.270466\pi\) |
0.980560 | − | 0.196221i | \(-0.0628670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0518 | − | 5.92713i | 0.950097 | − | 0.311954i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.464901 | − | 1.03096i | 0.0244010 | − | 0.0541112i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.02352 | + | 5.20973i | 0.472312 | + | 0.272690i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7083 | − | 23.7434i | 0.715566 | − | 1.23940i | −0.247175 | − | 0.968971i | \(-0.579502\pi\) |
0.962741 | − | 0.270425i | \(-0.0871643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.896640 | + | 2.67277i | −0.0466772 | + | 0.139139i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0437775 | + | 0.0758248i | −0.00227281 | + | 0.00393663i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.4573i | 1.93946i | 0.244173 | + | 0.969732i | \(0.421483\pi\) | ||||
−0.244173 | + | 0.969732i | \(0.578517\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.1223 | − | 7.27020i | −0.832550 | − | 0.375431i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.26464 | − | 0.730141i | 0.0651324 | − | 0.0376042i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.41500i | 0.0726837i | 0.999339 | + | 0.0363419i | \(0.0115705\pi\) | ||||
−0.999339 | + | 0.0363419i | \(0.988429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.8070 | + | 15.6857i | −1.11721 | + | 0.803605i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5830 | + | 28.7225i | 0.847349 | + | 1.46765i | 0.883565 | + | 0.468308i | \(0.155136\pi\) |
−0.0362158 | + | 0.999344i | \(0.511530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.12194 | − | 3.67530i | −0.108144 | − | 0.187311i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.22051 | − | 15.5617i | 0.265373 | − | 0.791045i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.7534 | + | 14.8687i | 1.30575 | + | 0.753875i | 0.981384 | − | 0.192057i | \(-0.0615158\pi\) |
0.324366 | + | 0.945932i | \(0.394849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.62999 | 0.284721 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.01285 | + | 30.0394i | 0.151978 | + | 1.51529i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.03054 | − | 3.51700i | 0.102168 | − | 0.176959i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.46894 | + | 11.2045i | 0.324667 | + | 0.562339i | 0.981445 | − | 0.191745i | \(-0.0614146\pi\) |
−0.656778 | + | 0.754084i | \(0.728081\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.06709 | + | 7.61653i | −0.103484 | + | 0.381303i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.87324 | − | 4.97659i | −0.143483 | − | 0.248519i | 0.785323 | − | 0.619086i | \(-0.212497\pi\) |
−0.928806 | + | 0.370567i | \(0.879163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.11526 | + | 7.12785i | −0.204996 | + | 0.355063i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.16674 | + | 9.85942i | 0.207047 | + | 0.489918i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.5123 | −0.768918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.6583 | − | 7.30828i | −0.625913 | − | 0.361371i | 0.153254 | − | 0.988187i | \(-0.451025\pi\) |
−0.779168 | + | 0.626815i | \(0.784358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.5362 | + | 14.7717i | −1.01298 | + | 0.728634i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.35706 | + | 9.27870i | 0.263604 | + | 0.456575i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.19124 | − | 7.25944i | −0.205740 | − | 0.356352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.0432 | + | 23.6942i | 0.834610 | + | 1.16031i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.03348i | 0.0993419i | 0.998766 | + | 0.0496709i | \(0.0158173\pi\) | ||||
−0.998766 | + | 0.0496709i | \(0.984183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.2813 | − | 15.1735i | 1.28087 | − | 0.739512i | 0.303865 | − | 0.952715i | \(-0.401723\pi\) |
0.977008 | + | 0.213203i | \(0.0683895\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.38265 | + | 26.5638i | 0.261714 | + | 1.29157i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 10.7335i | − | 0.520653i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.801532 | − | 1.38829i | 0.0387889 | − | 0.0671843i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.16259 | − | 4.39677i | −0.152691 | − | 0.212278i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1542 | − | 26.2478i | 0.729950 | − | 1.26431i | −0.226954 | − | 0.973905i | \(-0.572877\pi\) |
0.956904 | − | 0.290405i | \(-0.0937899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0370 | − | 11.5684i | −0.962917 | − | 0.555941i | −0.0658477 | − | 0.997830i | \(-0.520975\pi\) |
−0.897070 | + | 0.441889i | \(0.854308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.99357 | + | 1.34993i | 0.143531 | + | 0.0647240i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.65786 | + | 2.92601i | 0.366325 | + | 0.139970i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.5058 | + | 19.9219i | −1.64687 | + | 0.950822i | −0.668566 | + | 0.743653i | \(0.733092\pi\) |
−0.978305 | + | 0.207169i | \(0.933575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.7324 | + | 13.2822i | 0.558686 | + | 0.632483i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7959 | − | 10.2744i | −0.845507 | − | 0.488154i | 0.0136253 | − | 0.999907i | \(-0.495663\pi\) |
−0.859132 | + | 0.511753i | \(0.828996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.91961i | 0.280616i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.474184 | + | 4.72782i | 0.0224281 | + | 0.223618i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.29168 | −0.344116 | −0.172058 | − | 0.985087i | \(-0.555042\pi\) | ||||
−0.172058 | + | 0.985087i | \(0.555042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.77810 | − | 1.60393i | 0.130815 | − | 0.0755263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.61674 | − | 1.63094i | −0.169929 | − | 0.0766281i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.13880 | −0.0533880 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3652 | −0.718754 | −0.359377 | − | 0.933193i | \(-0.617011\pi\) | ||||
−0.359377 | + | 0.933193i | \(0.617011\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.5722 | + | 11.4098i | −0.493468 | + | 0.532566i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.41846 | + | 1.39630i | −0.112639 | + | 0.0650322i | −0.555261 | − | 0.831676i | \(-0.687382\pi\) |
0.442622 | + | 0.896708i | \(0.354048\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.11119 | 0.284011 | 0.142006 | − | 0.989866i | \(-0.454645\pi\) | ||||
0.142006 | + | 0.989866i | \(0.454645\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.4163 | + | 1.84709i | −0.854037 | + | 0.0856569i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.17320i | 0.193113i | 0.995328 | + | 0.0965564i | \(0.0307828\pi\) | ||||
−0.995328 | + | 0.0965564i | \(0.969217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.07271 | + | 5.23813i | 0.418939 | + | 0.241874i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.7814 | + | 2.28489i | −1.04971 | + | 0.105282i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.1749 | + | 9.33859i | −0.743723 | + | 0.429389i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.57841 | − | 14.5996i | 0.255955 | − | 0.669878i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.246270 | + | 0.0499021i | −0.0112759 | + | 0.00228486i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.06865 | + | 1.77169i | 0.140210 | + | 0.0809504i | 0.568464 | − | 0.822708i | \(-0.307538\pi\) |
−0.428254 | + | 0.903658i | \(0.640871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.08130 | + | 3.60491i | −0.0948990 | + | 0.164370i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.76430 | + | 1.98836i | −0.125780 | + | 0.0904735i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.14270 | + | 8.90742i | −0.233518 | + | 0.404465i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.1819i | − | 0.823900i | −0.911207 | − | 0.411950i | \(-0.864848\pi\) | ||
0.911207 | − | 0.411950i | \(-0.135152\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.879880 | + | 1.95121i | −0.0397896 | + | 0.0882367i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4107 | + | 6.58799i | −0.514959 | + | 0.297312i | −0.734870 | − | 0.678208i | \(-0.762757\pi\) |
0.219911 | + | 0.975520i | \(0.429423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.77220i | 0.214929i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.87374 | − | 11.5471i | 0.174111 | − | 0.519004i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.89099 | + | 3.27529i | 0.0848225 | + | 0.146917i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.34894 | + | 16.1928i | 0.418516 | + | 0.724891i | 0.995790 | − | 0.0916594i | \(-0.0292171\pi\) |
−0.577275 | + | 0.816550i | \(0.695884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.90165 | − | 12.3755i | −0.397696 | − | 0.552894i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5448 | − | 17.6351i | −1.36193 | − | 0.786309i | −0.372046 | − | 0.928214i | \(-0.621344\pi\) |
−0.989880 | + | 0.141906i | \(0.954677\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.1814 | 0.942559 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.9582 | − | 2.10203i | 0.930785 | − | 0.0933545i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.9499 | − | 34.5542i | 0.884262 | − | 1.53159i | 0.0377043 | − | 0.999289i | \(-0.487996\pi\) |
0.846557 | − | 0.532297i | \(-0.178671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.57904 | − | 7.93114i | −0.202565 | − | 0.350853i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.3101 | + | 10.0250i | −0.896712 | + | 0.442614i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.95714 | + | 13.7822i | 0.350634 | + | 0.607315i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.4203 | − | 26.7088i | 0.678186 | − | 1.17465i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44.8802 | − | 4.50133i | 1.97002 | − | 0.197586i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.2560 | −0.712188 | −0.356094 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356094 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.37315 | + | 3.10219i | 0.234952 | + | 0.135649i | 0.612854 | − | 0.790196i | \(-0.290021\pi\) |
−0.377903 | + | 0.925845i | \(0.623355\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.79079 | + | 5.27012i | 0.165444 | + | 0.230007i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.4487 | − | 23.2938i | −0.585833 | − | 1.01469i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.73147 | − | 16.8554i | −0.423107 | − | 0.732843i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.77967 | + | 29.1519i | −0.424401 | + | 1.26509i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.860802i | − | 0.0372855i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.94951 | + | 4.01230i | −0.300454 | + | 0.173467i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.2174 | + | 35.9635i | −0.699833 | + | 1.55194i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 20.1654i | − | 0.868584i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9064 | + | 31.0147i | −0.769855 | + | 1.33343i | 0.167786 | + | 0.985823i | \(0.446338\pi\) |
−0.937641 | + | 0.347605i | \(0.886995\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.11187 | + | 6.55415i | −0.391028 | + | 0.281266i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.07669 | + | 1.86489i | −0.0461205 | + | 0.0798831i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7443 | − | 13.7088i | −1.01523 | − | 0.586144i | −0.102512 | − | 0.994732i | \(-0.532688\pi\) |
−0.912719 | + | 0.408587i | \(0.866021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.50902 | − | 0.913670i | 0.192440 | − | 0.0389945i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.48020 | + | 6.49110i | −0.105660 | + | 0.276530i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.09123 | + | 1.78472i | −0.131453 | + | 0.0758942i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.31407 | + | 0.934169i | −0.395360 | + | 0.0396533i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.5249 | + | 17.0462i | 1.25101 | + | 0.722271i | 0.971310 | − | 0.237816i | \(-0.0764315\pi\) |
0.279700 | + | 0.960087i | \(0.409765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.01185i | 0.211979i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.6113 | − | 1.76635i | 0.743549 | − | 0.0745754i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.5649 | −0.908854 | −0.454427 | − | 0.890784i | \(-0.650156\pi\) | ||||
−0.454427 | + | 0.890784i | \(0.650156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.00816634 | + | 0.00471484i | −0.000343561 | + | 0.000198355i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.16126 | − | 9.33600i | 0.0487684 | − | 0.392075i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.8187 | −0.579311 | −0.289656 | − | 0.957131i | \(-0.593541\pi\) | ||||
−0.289656 | + | 0.957131i | \(0.593541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.0772 | 1.13314 | 0.566572 | − | 0.824012i | \(-0.308269\pi\) | ||||
0.566572 | + | 0.824012i | \(0.308269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.5877 | − | 11.9895i | −1.11072 | − | 0.500868i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.83995 | − | 3.37170i | 0.243543 | − | 0.140609i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.4381 | −1.60020 | −0.800099 | − | 0.599868i | \(-0.795220\pi\) | ||||
−0.800099 | + | 0.599868i | \(0.795220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.55570 | + | 25.4814i | 0.106211 | + | 1.05897i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.36771i | 0.305664i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.247615 | + | 0.142961i | 0.0102552 | + | 0.00592082i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.16369 | − | 2.44950i | −0.0894577 | − | 0.101274i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.18916 | + | 3.57331i | −0.255454 | + | 0.147486i | −0.622259 | − | 0.782811i | \(-0.713785\pi\) |
0.366805 | + | 0.930298i | \(0.380452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.18654 | − | 38.6735i | −0.254912 | − | 1.59351i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.1653 | − | 6.38771i | −0.582682 | − | 0.262755i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.1089 | − | 16.8060i | −1.19536 | − | 0.690141i | −0.235843 | − | 0.971791i | \(-0.575785\pi\) |
−0.959517 | + | 0.281650i | \(0.909118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.86080 | − | 3.22301i | 0.0762856 | − | 0.132130i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.51090 | + | 4.88100i | 0.143691 | + | 0.199766i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.75537 | − | 11.7006i | 0.276017 | − | 0.478076i | −0.694374 | − | 0.719614i | \(-0.744319\pi\) |
0.970391 | + | 0.241539i | \(0.0776520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3030i | 0.501850i | 0.968007 | + | 0.250925i | \(0.0807347\pi\) | ||||
−0.968007 | + | 0.250925i | \(0.919265\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.97096 | + | 29.4671i | 0.243156 | + | 1.19999i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.672510 | + | 0.388274i | −0.0273414 | + | 0.0157856i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 11.7542i | − | 0.477087i | −0.971132 | − | 0.238543i | \(-0.923330\pi\) | ||
0.971132 | − | 0.238543i | \(-0.0766699\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.68541 | − | 2.34313i | −0.0682963 | − | 0.0949485i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.13790 | − | 7.16706i | −0.167402 | − | 0.289948i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.26759 | − | 14.3199i | −0.333925 | − | 0.578375i | 0.649353 | − | 0.760487i | \(-0.275040\pi\) |
−0.983278 | + | 0.182112i | \(0.941707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.57146 | − | 1.13035i | 0.0633674 | − | 0.0455801i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.7140 | + | 15.4233i | 1.07546 | + | 0.620920i | 0.929669 | − | 0.368395i | \(-0.120093\pi\) |
0.145795 | + | 0.989315i | \(0.453426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.7056 | −0.631260 | −0.315630 | − | 0.948882i | \(-0.602216\pi\) | ||||
−0.315630 | + | 0.948882i | \(0.602216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.52893 | − | 2.16802i | −0.382383 | − | 0.0869998i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.60149 | − | 4.50592i | 0.104227 | − | 0.180526i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.89201 | − | 5.00911i | −0.115680 | − | 0.200364i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.8727 | + | 6.75033i | 0.993320 | + | 0.269582i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.80167 | − | 11.7808i | −0.271200 | − | 0.469733i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.14864 | + | 7.18566i | −0.165155 | + | 0.286056i | −0.936710 | − | 0.350106i | \(-0.886146\pi\) |
0.771555 | + | 0.636162i | \(0.219479\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.626902 | + | 6.25049i | 0.0249171 | + | 0.248434i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.4449 | 0.731963 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.68623 | − | 2.70560i | −0.185675 | − | 0.107200i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.45213 | + | 10.2904i | −0.136564 | + | 0.407080i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8249 | − | 18.7493i | −0.427559 | − | 0.740553i | 0.569097 | − | 0.822270i | \(-0.307293\pi\) |
−0.996656 | + | 0.0817172i | \(0.973960\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0677 | + | 26.0980i | 0.594211 | + | 1.02920i | 0.993658 | + | 0.112447i | \(0.0358689\pi\) |
−0.399447 | + | 0.916756i | \(0.630798\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.14951 | + | 6.58123i | −0.360262 | + | 0.259136i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.9584i | 1.49230i | 0.665778 | + | 0.746150i | \(0.268100\pi\) | ||||
−0.665778 | + | 0.746150i | \(0.731900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.3007 | − | 17.4941i | 1.18941 | − | 0.686705i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.8300 | + | 6.68745i | 0.581233 | + | 0.262102i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.08483i | 0.120719i | 0.998177 | + | 0.0603593i | \(0.0192246\pi\) | ||||
−0.998177 | + | 0.0603593i | \(0.980775\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3649 | − | 17.9526i | 0.404991 | − | 0.701465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.35934 | − | 24.9181i | 0.326129 | − | 0.972150i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4544 | + | 33.6961i | −0.757837 | + | 1.31261i | 0.186114 | + | 0.982528i | \(0.440411\pi\) |
−0.943951 | + | 0.330084i | \(0.892923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.5116 | + | 14.1518i | 0.953392 | + | 0.550441i | 0.894133 | − | 0.447801i | \(-0.147793\pi\) |
0.0592592 | + | 0.998243i | \(0.481126\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.95243 | − | 4.32968i | 0.0758261 | − | 0.168151i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.20610 | − | 3.41681i | 0.163106 | − | 0.132498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.59648 | + | 1.49908i | −0.100536 | + | 0.0580445i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.82470 | − | 28.1635i | −0.109209 | − | 1.08886i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.53364 | − | 2.61750i | −0.175019 | − | 0.101047i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.62600i | 0.371055i | 0.982639 | + | 0.185528i | \(0.0593994\pi\) | ||||
−0.982639 | + | 0.185528i | \(0.940601\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.13332 | + | 18.1668i | −0.159092 | + | 0.699242i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.0999 | 1.31056 | 0.655282 | − | 0.755384i | \(-0.272550\pi\) | ||||
0.655282 | + | 0.755384i | \(0.272550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.82909 | − | 4.52013i | 0.300453 | − | 0.173467i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0109526 | + | 0.0242882i | −0.000419703 | + | 0.000930727i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.12003 | 0.119385 | 0.0596924 | − | 0.998217i | \(-0.480988\pi\) | ||||
0.0596924 | + | 0.998217i | \(0.480988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3701 | 0.663676 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.4649 | + | 43.1651i | −0.742633 | + | 1.64685i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0664452 | − | 0.0383621i | 0.00253136 | − | 0.00146148i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.4071 | −1.08066 | −0.540328 | − | 0.841454i | \(-0.681700\pi\) | ||||
−0.540328 | + | 0.841454i | \(0.681700\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.02325 | + | 7.08710i | −0.304778 | + | 0.269217i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 20.0412i | − | 0.760205i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.43621 | + | 1.40655i | 0.0922782 | + | 0.0532768i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.72695 | − | 37.1593i | −0.140966 | − | 1.40550i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.6634 | + | 7.88854i | −0.516058 | + | 0.297946i | −0.735320 | − | 0.677720i | \(-0.762968\pi\) |
0.219262 | + | 0.975666i | \(0.429635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.12885 | − | 19.5591i | −0.118007 | − | 0.737687i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.65039 | − | 16.9654i | 0.288130 | − | 0.638953i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.1230 | − | 9.30859i | −0.606366 | − | 0.350086i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.4121 | − | 44.0150i | 0.954371 | − | 1.65302i | 0.218569 | − | 0.975822i | \(-0.429861\pi\) |
0.735802 | − | 0.677197i | \(-0.236805\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.71207 | − | 3.25813i | −0.364231 | − | 0.122189i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.44919 | − | 14.6344i | 0.316425 | − | 0.548063i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.71890i | 0.139079i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.0793 | − | 8.60365i | −0.712530 | − | 0.321309i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.3153 | − | 20.3893i | 1.31704 | − | 0.760393i | 0.333788 | − | 0.942648i | \(-0.391673\pi\) |
0.983251 | + | 0.182255i | \(0.0583396\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13.9877i | − | 0.520930i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.6966 | − | 20.6414i | 1.06724 | − | 0.767664i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.85798 | + | 4.95017i | 0.106143 | + | 0.183845i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9402 | − | 20.6811i | −0.442839 | − | 0.767020i | 0.555060 | − | 0.831810i | \(-0.312695\pi\) |
−0.997899 | + | 0.0647907i | \(0.979362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.2875 | − | 15.2403i | 0.825463 | − | 0.564456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.1844 | − | 8.18935i | −0.524628 | − | 0.302894i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.85130 | 0.142251 | 0.0711255 | − | 0.997467i | \(-0.477341\pi\) | ||||
0.0711255 | + | 0.997467i | \(0.477341\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.21438 | − | 12.1079i | −0.0447930 | − | 0.446606i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.1057 | − | 29.6280i | 0.630098 | − | 1.09136i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.89096 | + | 6.73933i | 0.143131 | + | 0.247910i | 0.928674 | − | 0.370897i | \(-0.120950\pi\) |
−0.785543 | + | 0.618807i | \(0.787616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.90589 | − | 4.87447i | 0.180222 | − | 0.179068i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.6890 | + | 28.9062i | 0.612260 | + | 1.06046i | 0.990859 | + | 0.134904i | \(0.0430726\pi\) |
−0.378599 | + | 0.925561i | \(0.623594\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.63131 | − | 2.82551i | 0.0597666 | − | 0.103519i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.8475 | + | 13.9984i | −0.579829 | + | 0.512175i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.05315 | 0.257717 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.3286 | − | 19.2423i | −1.21618 | − | 0.702161i | −0.252081 | − | 0.967706i | \(-0.581115\pi\) |
−0.964099 | + | 0.265545i | \(0.914448\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −38.9316 | + | 28.0035i | −1.41875 | + | 1.02050i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.36212 | + | 2.35926i | 0.0495726 | + | 0.0858622i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.74237 | + | 9.94608i | 0.208710 | + | 0.361497i | 0.951308 | − | 0.308240i | \(-0.0997401\pi\) |
−0.742598 | + | 0.669737i | \(0.766407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.49323 | + | 9.02717i | 0.235689 | + | 0.327665i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.17421i | − | 0.0425651i | −0.999774 | − | 0.0212825i | \(-0.993225\pi\) | ||
0.999774 | − | 0.0212825i | \(-0.00677496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.63913 | − | 0.946351i | 0.0593404 | − | 0.0342602i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.4680 | − | 2.12114i | 0.378470 | − | 0.0766899i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.38877i | − | 0.339009i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.8688 | − | 22.2895i | 0.464062 | − | 0.803779i | −0.535097 | − | 0.844791i | \(-0.679725\pi\) |
0.999159 | + | 0.0410120i | \(0.0130582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.7482 | + | 41.3572i | 1.07136 | + | 1.48944i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.919746 | + | 1.59305i | −0.0330810 | + | 0.0572979i | −0.882092 | − | 0.471077i | \(-0.843865\pi\) |
0.849011 | + | 0.528375i | \(0.177199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.9004 | − | 16.1083i | −1.00221 | − | 0.578628i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.50027 | + | 3.38218i | 0.269071 | + | 0.121335i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.58270 | + | 3.17932i | 0.0925350 | + | 0.113911i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6959 | − | 6.17525i | 0.382728 | − | 0.220968i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.83770 | − | 8.07709i | 0.0656741 | − | 0.288652i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.6149 | + | 7.86059i | 0.485938 | + | 0.280557i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.20260i | 0.221099i | 0.993871 | + | 0.110549i | \(0.0352610\pi\) | ||||
−0.993871 | + | 0.110549i | \(0.964739\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.75338 | − | 17.4819i | −0.0624219 | − | 0.622373i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.00828813 | 0.000294692 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.21656 | + | 0.702382i | −0.0432014 | + | 0.0249423i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.157284 | + | 0.0709261i | 0.00557831 | + | 0.00251549i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.63497 | −0.270444 | −0.135222 | − | 0.990815i | \(-0.543175\pi\) | ||||
−0.135222 | + | 0.990815i | \(0.543175\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.0453 | 0.956795 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.6347 | − | 2.96545i | 0.517092 | − | 0.104779i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.9001 | + | 14.9534i | −0.913994 | + | 0.527695i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.33812 | 0.0824078 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.2231 | − | 3.53276i | 1.23991 | − | 0.124359i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.3075i | 1.20619i | 0.797670 | + | 0.603094i | \(0.206066\pi\) | ||||
−0.797670 | + | 0.603094i | \(0.793934\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5409 | + | 19.3649i | 1.17778 | + | 0.679993i | 0.955500 | − | 0.294990i | \(-0.0953163\pi\) |
0.222281 | + | 0.974983i | \(0.428650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.0302 | + | 2.20955i | −0.772632 | + | 0.0774923i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.27280 | − | 0.734854i | 0.0445844 | − | 0.0257408i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.0373 | − | 18.5109i | −0.526088 | − | 0.647616i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.570489 | + | 2.81540i | 0.0199345 | + | 0.0983780i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9969 | + | 6.34907i | 0.383795 | + | 0.221584i | 0.679468 | − | 0.733705i | \(-0.262211\pi\) |
−0.295673 | + | 0.955289i | \(0.595544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3998 | − | 21.4770i | 0.432228 | − | 0.748641i | −0.564837 | − | 0.825203i | \(-0.691061\pi\) |
0.997065 | + | 0.0765614i | \(0.0243941\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.2102 | − | 12.3793i | 0.599183 | − | 0.430992i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.2728 | − | 17.7929i | 0.357219 | − | 0.618721i | −0.630276 | − | 0.776371i | \(-0.717058\pi\) |
0.987495 | + | 0.157650i | \(0.0503917\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.70009i | 0.336898i | 0.985710 | + | 0.168449i | \(0.0538758\pi\) | ||||
−0.985710 | + | 0.168449i | \(0.946124\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.63799 | + | 14.7203i | −0.230269 | + | 0.510641i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.3146 | − | 8.84188i | 0.530619 | − | 0.306353i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.4675i | 0.362242i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.7922 | + | 44.6043i | 0.476728 | + | 1.54175i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.3395 | + | 31.7649i | 0.633149 | + | 1.09665i | 0.986904 | + | 0.161309i | \(0.0515715\pi\) |
−0.353755 | + | 0.935338i | \(0.615095\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.2293 | + | 22.9139i | 0.456184 | + | 0.790133i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.63593 | + | 6.44506i | 0.159670 | + | 0.221980i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.5253 | − | 7.23150i | −0.430885 | − | 0.248771i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.682540 | 0.0234523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.3128 | + | 3.44146i | −1.17761 | + | 0.118111i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.27318 | − | 7.40137i | 0.146483 | − | 0.253716i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7924 | + | 20.4251i | 0.403765 | + | 0.699341i | 0.994177 | − | 0.107761i | \(-0.0343682\pi\) |
−0.590412 | + | 0.807102i | \(0.701035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.3408 | + | 2.55524i | 0.524644 | + | 0.0873873i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.5699 | + | 23.5038i | 0.463539 | + | 0.802874i | 0.999134 | − | 0.0416012i | \(-0.0132459\pi\) |
−0.535595 | + | 0.844475i | \(0.679913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4649 | − | 18.1257i | 0.357058 | − | 0.618442i | −0.630410 | − | 0.776262i | \(-0.717113\pi\) |
0.987468 | + | 0.157820i | \(0.0504466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.69293 | + | 0.169795i | −0.0576948 | + | 0.00578659i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.52529 | 0.324245 | 0.162122 | − | 0.986771i | \(-0.448166\pi\) | ||||
0.162122 | + | 0.986771i | \(0.448166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.8220 | − | 15.4857i | −0.911974 | − | 0.526528i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.13028 | − | 11.3031i | −0.276119 | − | 0.383872i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.82823 | + | 10.0948i | 0.197709 | + | 0.342442i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.59017 | − | 7.95040i | −0.155532 | − | 0.269389i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.5975 | + | 8.25179i | 0.832501 | + | 0.279281i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 10.6737i | − | 0.360835i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.96965 | + | 5.75598i | −0.336651 | + | 0.194366i | −0.658790 | − | 0.752327i | \(-0.728931\pi\) |
0.322139 | + | 0.946692i | \(0.395598\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.5772 | − | 41.1966i | 0.626595 | − | 1.38953i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0306i | 1.41605i | 0.706189 | + | 0.708024i | \(0.250413\pi\) | ||||
−0.706189 | + | 0.708024i | \(0.749587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.6448 | − | 18.4374i | 0.358227 | − | 0.620468i | −0.629438 | − | 0.777051i | \(-0.716715\pi\) |
0.987665 | + | 0.156583i | \(0.0500480\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.1399 | − | 12.3287i | 0.576152 | − | 0.414426i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.6484 | + | 40.9603i | −0.794036 | + | 1.37531i | 0.129413 | + | 0.991591i | \(0.458691\pi\) |
−0.923449 | + | 0.383720i | \(0.874643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.0400 | − | 8.10599i | −0.470886 | − | 0.271866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.4878 | − | 3.79224i | −1.02138 | − | 0.127045i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.7868 | + | 14.0559i | 1.23102 | + | 0.470364i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.4596 | − | 13.5444i | 0.784166 | − | 0.452739i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.96902 | − | 0.297783i | 0.0991327 | − | 0.00994267i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.4047 | + | 7.16186i | 0.413720 | + | 0.238861i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.250735i | 0.00835318i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.85673 | − | 0.988596i | 0.328011 | − | 0.0328984i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.70705 | 0.256191 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.37924 | − | 5.41511i | 0.311433 | − | 0.179806i | −0.336135 | − | 0.941814i | \(-0.609120\pi\) |
0.647567 | + | 0.762008i | \(0.275786\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.6109 | − | 52.3655i | −0.351941 | − | 1.73685i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.1178 | 0.534008 | 0.267004 | − | 0.963695i | \(-0.413966\pi\) | ||||
0.267004 | + | 0.963695i | \(0.413966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0601 | 0.796274 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.87976 | − | 1.29860i | −0.0952020 | − | 0.0429305i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.7793 | + | 9.11016i | −0.521077 | + | 0.300844i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.9311 | −0.888376 | −0.444188 | − | 0.895934i | \(-0.646508\pi\) | ||||
−0.444188 | + | 0.895934i | \(0.646508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.787044 | − | 7.84717i | −0.0259340 | − | 0.258573i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 3.31414i | − | 0.109086i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.1107 | − | 8.14679i | −0.463955 | − | 0.267865i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.0867 | − | 26.5762i | 0.988177 | − | 0.872877i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.8822 | + | 17.2525i | −0.980405 | + | 0.566037i | −0.902392 | − | 0.430915i | \(-0.858191\pi\) |
−0.0780125 | + | 0.996952i | \(0.524857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.4260 | − | 4.06736i | 0.833304 | − | 0.133302i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.8687 | + | 13.0181i | 0.945120 | + | 0.426194i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.5251 | − | 6.07668i | −0.344208 | − | 0.198729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1803 | − | 28.0252i | 0.528588 | − | 0.915542i | −0.470856 | − | 0.882210i | \(-0.656055\pi\) |
0.999444 | − | 0.0333319i | \(-0.0106118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.61159 | + | 2.24051i | 0.0525924 | + | 0.0731162i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.0330 | + | 29.5020i | −0.555260 | + | 0.961738i | 0.442624 | + | 0.896708i | \(0.354048\pi\) |
−0.997883 | + | 0.0650306i | \(0.979286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.76734i | 0.0575525i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.39060 | + | 4.73847i | −0.142826 | + | 0.154142i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.8522 | + | 14.3484i | −0.807589 | + | 0.466262i | −0.846118 | − | 0.532996i | \(-0.821066\pi\) |
0.0385292 | + | 0.999257i | \(0.487733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.02522i | 0.260510i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.43151 | + | 10.3316i | 0.240983 | + | 0.335025i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.8722 | + | 39.6159i | 0.740905 | + | 1.28328i | 0.952084 | + | 0.305837i | \(0.0989364\pi\) |
−0.211179 | + | 0.977447i | \(0.567730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0133 | + | 17.3436i | 0.324023 | + | 0.561225i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.65178 | + | 5.50391i | −0.247347 | + | 0.177916i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.2218 | − | 7.63363i | −0.426955 | − | 0.246503i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −49.7322 | −1.60426 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.4008 | + | 15.1709i | 0.431834 | + | 0.488875i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.79222 | − | 15.2286i | 0.283031 | − | 0.490225i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.59096 | + | 16.6120i | 0.308424 | + | 0.534207i | 0.978018 | − | 0.208521i | \(-0.0668650\pi\) |
−0.669593 | + | 0.742728i | \(0.733532\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.77935 | + | 21.8494i | 0.185660 | + | 0.701903i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.55749 | + | 6.16176i | 0.114165 | + | 0.197740i | 0.917446 | − | 0.397861i | \(-0.130247\pi\) |
−0.803280 | + | 0.595601i | \(0.796914\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.80750 | + | 15.2550i | −0.282355 | + | 0.489054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.567720 | − | 5.66042i | −0.0181816 | − | 0.181278i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4357 | 0.525823 | 0.262912 | − | 0.964820i | \(-0.415317\pi\) | ||||
0.262912 | + | 0.964820i | \(0.415317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.7146 | − | 8.49549i | −0.470281 | − | 0.271517i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.14983 | + | 1.72763i | 0.164422 | + | 0.0551588i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.2278 | − | 52.3560i | −0.964116 | − | 1.66990i | −0.711972 | − | 0.702207i | \(-0.752198\pi\) |
−0.252143 | − | 0.967690i | \(-0.581135\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.33486 | + | 9.24025i | 0.169983 | + | 0.294419i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.2791 | + | 9.55167i | −0.422680 | + | 0.304033i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.2900i | − | 0.327203i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.8229 | − | 27.0332i | 1.48738 | − | 0.858738i | 0.487482 | − | 0.873133i | \(-0.337916\pi\) |
0.999896 | + | 0.0143949i | \(0.00458218\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.4891 | + | 5.18090i | 0.364595 | + | 0.164411i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.12847i | − | 0.130881i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.2536 | + | 21.2238i | −0.388074 | + | 0.672164i | −0.992190 | − | 0.124732i | \(-0.960193\pi\) |
0.604116 | + | 0.796896i | \(0.293526\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.97541 | + | 22.5586i | 0.220692 | + | 0.713724i |
(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 | 912.2.bn.n.449.4 | 16 | ||
3.2 | odd | 2 | 912.2.bn.o.449.1 | 16 | |||
4.3 | odd | 2 | 456.2.bf.d.449.5 | yes | 16 | ||
12.11 | even | 2 | 456.2.bf.c.449.8 | yes | 16 | ||
19.8 | odd | 6 | 912.2.bn.o.65.1 | 16 | |||
57.8 | even | 6 | inner | 912.2.bn.n.65.4 | 16 | ||
76.27 | even | 6 | 456.2.bf.c.65.8 | ✓ | 16 | ||
228.179 | odd | 6 | 456.2.bf.d.65.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.bf.c.65.8 | ✓ | 16 | 76.27 | even | 6 | ||
456.2.bf.c.449.8 | yes | 16 | 12.11 | even | 2 | ||
456.2.bf.d.65.5 | yes | 16 | 228.179 | odd | 6 | ||
456.2.bf.d.449.5 | yes | 16 | 4.3 | odd | 2 | ||
912.2.bn.n.65.4 | 16 | 57.8 | even | 6 | inner | ||
912.2.bn.n.449.4 | 16 | 1.1 | even | 1 | trivial | ||
912.2.bn.o.65.1 | 16 | 19.8 | odd | 6 | |||
912.2.bn.o.449.1 | 16 | 3.2 | odd | 2 |