Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), 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: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 897.3 | ||
Root | \(0.639878 + 1.60952i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.897 |
Dual form | 1024.2.g.c.129.3 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.401639 | + | 0.969643i | 0.231887 | + | 0.559824i | 0.996399 | − | 0.0847850i | \(-0.0270204\pi\) |
−0.764513 | + | 0.644609i | \(0.777020\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.49877 | − | 1.44924i | −1.56470 | − | 0.648120i | −0.578801 | − | 0.815469i | \(-0.696479\pi\) |
−0.985898 | + | 0.167349i | \(0.946479\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.21904 | + | 3.21904i | 1.21668 | + | 1.21668i | 0.968786 | + | 0.247897i | \(0.0797394\pi\) |
0.247897 | + | 0.968786i | \(0.420261\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.34243 | − | 1.34243i | 0.447476 | − | 0.447476i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.363728 | + | 0.878116i | −0.109668 | + | 0.264762i | −0.969180 | − | 0.246354i | \(-0.920768\pi\) |
0.859512 | + | 0.511116i | \(0.170768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.37919 | + | 0.985492i | −0.659868 | + | 0.273326i | −0.687383 | − | 0.726295i | \(-0.741241\pi\) |
0.0275150 | + | 0.999621i | \(0.491241\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.97463i | − | 1.02625i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.34416i | 0.326007i | 0.986625 | + | 0.163004i | \(0.0521182\pi\) | ||||
−0.986625 | + | 0.163004i | \(0.947882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.10629 | − | 1.28667i | 0.712632 | − | 0.295182i | 0.00323890 | − | 0.999995i | \(-0.498969\pi\) |
0.709393 | + | 0.704813i | \(0.248969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.82843 | + | 4.41421i | −0.398996 | + | 0.963260i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.30143 | + | 4.30143i | −0.896911 | + | 0.896911i | −0.995162 | − | 0.0982508i | \(-0.968675\pi\) |
0.0982508 | + | 0.995162i | \(0.468675\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.60559 | + | 6.60559i | 1.32112 | + | 1.32112i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.74977 | + | 1.96742i | 0.914095 | + | 0.378630i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.600295 | + | 1.44924i | 0.111472 | + | 0.269117i | 0.969764 | − | 0.244044i | \(-0.0784742\pi\) |
−0.858292 | + | 0.513161i | \(0.828474\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.69552 | −0.663735 | −0.331867 | − | 0.943326i | \(-0.607679\pi\) | ||||
−0.331867 | + | 0.943326i | \(0.607679\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.997546 | −0.173651 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.59753 | − | 15.9279i | −1.11519 | − | 2.69230i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.03257 | + | 1.67035i | 0.662951 | + | 0.274603i | 0.688680 | − | 0.725066i | \(-0.258191\pi\) |
−0.0257289 | + | 0.999669i | \(0.508191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.91115 | − | 1.91115i | −0.306029 | − | 0.306029i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.34171 | + | 5.34171i | −0.834235 | + | 0.834235i | −0.988093 | − | 0.153858i | \(-0.950830\pi\) |
0.153858 | + | 0.988093i | \(0.450830\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.01477 | + | 7.27829i | −0.459747 | + | 1.10993i | 0.508752 | + | 0.860913i | \(0.330107\pi\) |
−0.968500 | + | 0.249015i | \(0.919893\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.64235 | + | 2.75135i | −0.990182 | + | 0.410147i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.02878i | − | 0.150063i | −0.997181 | − | 0.0750313i | \(-0.976094\pi\) | ||
0.997181 | − | 0.0750313i | \(-0.0239057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.7245i | 1.96064i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.30336 | + | 0.539868i | −0.182507 | + | 0.0755967i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.69188 | + | 6.49877i | −0.369758 | + | 0.892675i | 0.624031 | + | 0.781399i | \(0.285494\pi\) |
−0.993790 | + | 0.111276i | \(0.964506\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.54520 | − | 2.54520i | 0.343195 | − | 0.343195i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.49522 | + | 2.49522i | 0.330500 | + | 0.330500i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.90700 | + | 2.44676i | 0.769027 | + | 0.318541i | 0.732478 | − | 0.680791i | \(-0.238364\pi\) |
0.0365485 | + | 0.999332i | \(0.488364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.83444 | + | 4.42872i | 0.234876 | + | 0.567040i | 0.996739 | − | 0.0806985i | \(-0.0257151\pi\) |
−0.761863 | + | 0.647738i | \(0.775715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.64266 | 1.08887 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.75245 | 1.20964 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.58213 | + | 6.23381i | 0.315457 | + | 0.761581i | 0.999484 | + | 0.0321238i | \(0.0102271\pi\) |
−0.684027 | + | 0.729457i | \(0.739773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.89848 | − | 2.44323i | −0.710093 | − | 0.294130i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.75634 | + | 5.75634i | 0.683152 | + | 0.683152i | 0.960709 | − | 0.277557i | \(-0.0895247\pi\) |
−0.277557 | + | 0.960709i | \(0.589525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.94801 | + | 2.94801i | −0.345039 | + | 0.345039i | −0.858258 | − | 0.513219i | \(-0.828453\pi\) |
0.513219 | + | 0.858258i | \(0.328453\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.75200 | + | 9.05812i | −0.433243 | + | 1.04594i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.99755 | + | 1.65584i | −0.455563 | + | 0.188700i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.4357i | − | 1.73665i | −0.495996 | − | 0.868325i | \(-0.665197\pi\) | ||
0.495996 | − | 0.868325i | \(-0.334803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 0.299657i | − | 0.0332952i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2627 | + | 4.66516i | −1.23624 | + | 0.512068i | −0.902538 | − | 0.430610i | \(-0.858298\pi\) |
−0.333703 | + | 0.942678i | \(0.608298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.94801 | − | 4.70292i | 0.211292 | − | 0.510103i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.16414 | + | 1.16414i | −0.124809 | + | 0.124809i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.04708 | − | 9.04708i | −0.958989 | − | 0.958989i | 0.0402029 | − | 0.999192i | \(-0.487200\pi\) |
−0.999192 | + | 0.0402029i | \(0.987200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8310 | − | 4.48636i | −1.13540 | − | 0.470299i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.48427 | − | 3.58333i | −0.153911 | − | 0.371574i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.7329 | −1.30637 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.41176 | 0.854085 | 0.427042 | − | 0.904232i | \(-0.359556\pi\) | ||||
0.427042 | + | 0.904232i | \(0.359556\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.690529 | + | 1.66708i | 0.0694008 | + | 0.167548i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.69188 | − | 3.60029i | −0.864874 | − | 0.358243i | −0.0942625 | − | 0.995547i | \(-0.530049\pi\) |
−0.770612 | + | 0.637305i | \(0.780049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.64927 | + | 6.64927i | 0.655172 | + | 0.655172i | 0.954234 | − | 0.299062i | \(-0.0966736\pi\) |
−0.299062 | + | 0.954234i | \(0.596674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.7945 | − | 12.7945i | 1.24862 | − | 1.24862i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.19970 | − | 7.72475i | 0.309326 | − | 0.746780i | −0.690401 | − | 0.723427i | \(-0.742566\pi\) |
0.999727 | − | 0.0233529i | \(-0.00743413\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.670346 | + | 0.277666i | −0.0642075 | + | 0.0265956i | −0.414556 | − | 0.910024i | \(-0.636063\pi\) |
0.350349 | + | 0.936619i | \(0.386063\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.58103i | 0.434812i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.8960i | − | 1.49537i | −0.664052 | − | 0.747686i | \(-0.731165\pi\) | ||
0.664052 | − | 0.747686i | \(-0.268835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.2835 | − | 8.81593i | 1.98470 | − | 0.822090i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.87094 | + | 4.51684i | −0.172968 | + | 0.417582i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.32691 | + | 4.32691i | −0.396647 | + | 0.396647i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.13938 | + | 7.13938i | 0.649035 | + | 0.649035i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.32499 | − | 3.03411i | −0.660472 | − | 0.273576i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.29217 | − | 15.1907i | −0.562789 | − | 1.35869i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.43664 | 0.304953 | 0.152476 | − | 0.988307i | \(-0.451275\pi\) | ||||
0.152476 | + | 0.988307i | \(0.451275\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.26819 | −0.727973 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.39250 | + | 3.36180i | 0.121664 | + | 0.293722i | 0.972964 | − | 0.230956i | \(-0.0741855\pi\) |
−0.851300 | + | 0.524679i | \(0.824185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.1411 | + | 5.85744i | 1.22619 | + | 0.507905i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.7671 | − | 13.7671i | −1.18489 | − | 1.18489i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.79941 | + | 1.79941i | −0.153734 | + | 0.153734i | −0.779783 | − | 0.626049i | \(-0.784671\pi\) |
0.626049 | + | 0.779783i | \(0.284671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.67049 | − | 16.1040i | 0.565784 | − | 1.36592i | −0.339295 | − | 0.940680i | \(-0.610189\pi\) |
0.905079 | − | 0.425243i | \(-0.139811\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.997546 | − | 0.413197i | 0.0840086 | − | 0.0347975i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.44765i | − | 0.204683i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.94053i | − | 0.493334i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.3078 | + | 5.51228i | −1.09761 | + | 0.454645i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.60029 | − | 15.9345i | 0.540717 | − | 1.30541i | −0.383500 | − | 0.923541i | \(-0.625282\pi\) |
0.924218 | − | 0.381866i | \(-0.124718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.89235 | − | 6.89235i | 0.560892 | − | 0.560892i | −0.368669 | − | 0.929561i | \(-0.620186\pi\) |
0.929561 | + | 0.368669i | \(0.120186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.80444 | + | 1.80444i | 0.145880 | + | 0.145880i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.9298 | + | 5.35569i | 1.03854 | + | 0.430179i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.72090 | + | 6.56882i | 0.217151 | + | 0.524249i | 0.994490 | − | 0.104833i | \(-0.0334308\pi\) |
−0.777339 | + | 0.629082i | \(0.783431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.38265 | −0.585483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.6930 | −2.18251 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.849981 | + | 2.05204i | 0.0665756 | + | 0.160728i | 0.953665 | − | 0.300869i | \(-0.0972767\pi\) |
−0.887090 | + | 0.461597i | \(0.847277\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.49019 | + | 1.44568i | 0.271711 | + | 0.112546i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.05426 | + | 1.05426i | 0.0815808 | + | 0.0815808i | 0.746720 | − | 0.665139i | \(-0.231628\pi\) |
−0.665139 | + | 0.746720i | \(0.731628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.50305 | + | 4.50305i | −0.346388 | + | 0.346388i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.44271 | − | 5.89723i | 0.186799 | − | 0.450972i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.5904 | − | 7.28617i | 1.33737 | − | 0.553957i | 0.404622 | − | 0.914484i | \(-0.367403\pi\) |
0.932749 | + | 0.360527i | \(0.117403\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.5273i | 3.21476i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.71040i | 0.504385i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.2700 | − | 4.25395i | 0.767612 | − | 0.317955i | 0.0357074 | − | 0.999362i | \(-0.488632\pi\) |
0.731905 | + | 0.681407i | \(0.238632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.12805 | + | 2.72335i | −0.0838472 | + | 0.202425i | −0.960242 | − | 0.279168i | \(-0.909941\pi\) |
0.876395 | + | 0.481593i | \(0.159941\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.55750 | + | 3.55750i | −0.262978 | + | 0.262978i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.6883 | − | 11.6883i | −0.859343 | − | 0.859343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.18033 | − | 0.488909i | −0.0863143 | − | 0.0357526i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.95651 | + | 21.6229i | 0.651490 | + | 1.57284i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.2674 | 1.53885 | 0.769426 | − | 0.638736i | \(-0.220542\pi\) | ||||
0.769426 | + | 0.638736i | \(0.220542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.75491 | −0.198302 | −0.0991512 | − | 0.995072i | \(-0.531613\pi\) | ||||
−0.0991512 | + | 0.995072i | \(0.531613\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.91697 | + | 9.45640i | 0.280500 | + | 0.677187i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.05309 | + | 2.09306i | 0.360018 | + | 0.149124i | 0.555358 | − | 0.831611i | \(-0.312581\pi\) |
−0.195340 | + | 0.980735i | \(0.562581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3344 | − | 15.3344i | −1.08702 | − | 1.08702i | −0.995833 | − | 0.0911915i | \(-0.970932\pi\) |
−0.0911915 | − | 0.995833i | \(-0.529068\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.00748 | + | 5.00748i | −0.353201 | + | 0.353201i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.73279 | + | 6.59753i | −0.191804 | + | 0.463056i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.4308 | − | 10.9480i | 1.84601 | − | 0.764642i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.5487i | 0.802692i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.19568i | 0.221050i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3205 | + | 8.83123i | −1.46776 | + | 0.607967i | −0.966347 | − | 0.257240i | \(-0.917187\pi\) |
−0.501414 | + | 0.865207i | \(0.667187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.26962 | + | 7.89357i | −0.224031 | + | 0.540859i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.0960 | − | 21.0960i | 1.43873 | − | 1.43873i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.8960 | − | 11.8960i | −0.807555 | − | 0.807555i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.04256 | − | 1.67448i | −0.273171 | − | 0.113151i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.32466 | − | 3.19801i | −0.0891063 | − | 0.215122i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3493 | 0.826973 | 0.413487 | − | 0.910510i | \(-0.364311\pi\) | ||||
0.413487 | + | 0.910510i | \(0.364311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.7350 | 1.18234 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.77697 | + | 4.28999i | 0.117942 | + | 0.284736i | 0.971815 | − | 0.235744i | \(-0.0757528\pi\) |
−0.853873 | + | 0.520481i | \(0.825753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.32720 | − | 1.79239i | −0.285949 | − | 0.118444i | 0.235098 | − | 0.971972i | \(-0.424459\pi\) |
−0.521048 | + | 0.853527i | \(0.674459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.21114 | − | 3.21114i | −0.211278 | − | 0.211278i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.848945 | + | 0.848945i | −0.0556162 | + | 0.0556162i | −0.734368 | − | 0.678752i | \(-0.762521\pi\) |
0.678752 | + | 0.734368i | \(0.262521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.49094 | + | 3.59946i | −0.0972585 | + | 0.234803i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.9671 | − | 6.19957i | 0.972217 | − | 0.402706i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.40395i | 0.0908141i | 0.998969 | + | 0.0454070i | \(0.0144585\pi\) | ||||
−0.998969 | + | 0.0454070i | \(0.985542\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.3343i | − | 1.11660i | −0.829638 | − | 0.558302i | \(-0.811453\pi\) | ||
0.829638 | − | 0.558302i | \(-0.188547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5399 | − | 6.02262i | 0.932734 | − | 0.386351i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.8900 | − | 48.0187i | 1.27073 | − | 3.06781i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.12245 | + | 6.12245i | −0.389562 | + | 0.389562i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.04708 | − | 9.04708i | −0.573335 | − | 0.573335i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.06378 | + | 1.68327i | 0.256503 | + | 0.106247i | 0.507230 | − | 0.861811i | \(-0.330669\pi\) |
−0.250726 | + | 0.968058i | \(0.580669\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.21261 | − | 5.34171i | −0.139105 | − | 0.335830i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.34255 | 0.334563 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.5843 | −1.53353 | −0.766765 | − | 0.641928i | \(-0.778135\pi\) | ||||
−0.766765 | + | 0.641928i | \(0.778135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.60410 | + | 18.3579i | 0.472496 | + | 1.14071i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.75135 | + | 1.13965i | 0.170304 | + | 0.0705423i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.4858 | + | 13.4858i | 0.831572 | + | 0.831572i | 0.987732 | − | 0.156160i | \(-0.0499114\pi\) |
−0.156160 | + | 0.987732i | \(0.549911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.8366 | − | 18.8366i | 1.15712 | − | 1.15712i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.13877 | − | 12.4061i | 0.314488 | − | 0.759241i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0506 | + | 4.99154i | −0.734740 | + | 0.304339i | −0.718498 | − | 0.695529i | \(-0.755170\pi\) |
−0.0162420 | + | 0.999868i | \(0.505170\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.83168i | − | 0.354250i | −0.984188 | − | 0.177125i | \(-0.943320\pi\) | ||
0.984188 | − | 0.177125i | \(-0.0566796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 12.3041i | − | 0.744681i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.20311 | + | 3.39784i | −0.494666 | + | 0.204897i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.57732 | + | 15.8791i | −0.395193 | + | 0.954080i | 0.593596 | + | 0.804763i | \(0.297708\pi\) |
−0.988789 | + | 0.149317i | \(0.952292\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.96096 | + | 4.96096i | −0.297005 | + | 0.297005i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.49031 | + | 2.49031i | 0.148559 | + | 0.148559i | 0.777474 | − | 0.628915i | \(-0.216501\pi\) |
−0.628915 | + | 0.777474i | \(0.716501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.8218 | − | 9.86733i | −1.41606 | − | 0.586552i | −0.462193 | − | 0.886779i | \(-0.652937\pi\) |
−0.953868 | + | 0.300227i | \(0.902937\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.11403 | − | 12.3464i | −0.302929 | − | 0.731336i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.3904 | −2.03000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.1932 | 0.893719 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.37849 | + | 8.15640i | 0.198051 | + | 0.478137i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.3258 | + | 10.9045i | 1.53797 | + | 0.637047i | 0.981091 | − | 0.193548i | \(-0.0619996\pi\) |
0.556877 | + | 0.830595i | \(0.312000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.1213 | − | 17.1213i | −0.996842 | − | 0.996842i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.45525 | + | 3.45525i | −0.200494 | + | 0.200494i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.99489 | − | 14.4729i | 0.346693 | − | 0.836992i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.1338 | + | 13.7245i | −1.90980 | + | 0.791064i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.87404i | − | 0.567249i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 18.1536i | − | 1.03947i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.50827 | + | 1.03896i | −0.143155 | + | 0.0592967i | −0.453111 | − | 0.891454i | \(-0.649686\pi\) |
0.309956 | + | 0.950751i | \(0.399686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.77681 | + | 9.11803i | −0.214855 | + | 0.518706i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.1737 | − | 15.1737i | 0.860419 | − | 0.860419i | −0.130967 | − | 0.991387i | \(-0.541808\pi\) |
0.991387 | + | 0.130967i | \(0.0418083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.23773 | − | 9.23773i | −0.522148 | − | 0.522148i | 0.396072 | − | 0.918219i | \(-0.370373\pi\) |
−0.918219 | + | 0.396072i | \(0.870373\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.2387 | − | 12.5253i | −1.70376 | − | 0.705719i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.4368 | − | 25.1968i | −0.586192 | − | 1.41519i | −0.887117 | − | 0.461545i | \(-0.847295\pi\) |
0.300925 | − | 0.953648i | \(-0.402705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.49094 | −0.0834769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.77537 | 0.489794 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.72949 | + | 4.17536i | 0.0962314 | + | 0.232323i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.2257 | − | 9.20618i | −1.23286 | − | 0.510667i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.538475 | − | 0.538475i | −0.0297777 | − | 0.0297777i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31168 | − | 3.31168i | 0.182579 | − | 0.182579i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9883 | − | 28.9422i | 0.658935 | − | 1.59081i | −0.140516 | − | 0.990078i | \(-0.544876\pi\) |
0.799451 | − | 0.600731i | \(-0.205124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.65575 | − | 3.17112i | 0.419533 | − | 0.173776i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 25.5528i | − | 1.39610i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.82843i | − | 0.154074i | −0.997028 | − | 0.0770371i | \(-0.975454\pi\) | ||
0.997028 | − | 0.0770371i | \(-0.0245460\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.4135 | − | 6.38447i | 0.837145 | − | 0.346757i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.34416 | − | 3.24509i | 0.0727905 | − | 0.175732i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.6463 | + | 21.6463i | −1.16879 | + | 1.16879i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.0966 | + | 17.0966i | 0.920451 | + | 0.920451i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.7464 | + | 5.69394i | 0.737944 | + | 0.305667i | 0.719812 | − | 0.694169i | \(-0.244228\pi\) |
0.0181324 | + | 0.999836i | \(0.494228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.77043 | − | 4.27420i | −0.0947690 | − | 0.228792i | 0.869385 | − | 0.494135i | \(-0.164515\pi\) |
−0.964154 | + | 0.265342i | \(0.914515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.2395 | −0.706671 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.5598 | −0.828166 | −0.414083 | − | 0.910239i | \(-0.635898\pi\) | ||||
−0.414083 | + | 0.910239i | \(0.635898\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7978 | − | 28.4825i | −0.626163 | − | 1.51169i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.93342 | − | 2.45770i | −0.314030 | − | 0.130075i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.89363 | + | 8.89363i | 0.469388 | + | 0.469388i | 0.901716 | − | 0.432328i | \(-0.142308\pi\) |
−0.432328 | + | 0.901716i | \(0.642308\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.44149 | + | 5.44149i | −0.286394 | + | 0.286394i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.05520 | + | 9.79011i | −0.212843 | + | 0.513848i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.5868 | − | 6.04205i | 0.763508 | − | 0.316255i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.25894i | 0.378914i | 0.981889 | + | 0.189457i | \(0.0606727\pi\) | ||||
−0.981889 | + | 0.189457i | \(0.939327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.3417i | 0.746600i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.5851 | + | 12.2545i | −1.53598 | + | 0.636224i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.57978 | − | 3.81392i | 0.0817978 | − | 0.197477i | −0.877689 | − | 0.479230i | \(-0.840916\pi\) |
0.959487 | + | 0.281753i | \(0.0909159\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.2023 | − | 12.2023i | 0.630125 | − | 0.630125i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.85643 | − | 2.85643i | −0.147113 | − | 0.147113i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0669 | + | 7.48355i | 0.928033 | + | 0.384404i | 0.794932 | − | 0.606698i | \(-0.207506\pi\) |
0.133101 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.38029 | + | 3.33232i | 0.0707144 | + | 0.170720i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.43680 | −0.226710 | −0.113355 | − | 0.993555i | \(-0.536160\pi\) | ||||
−0.113355 | + | 0.993555i | \(0.536160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.3862 | 0.835119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.72347 | + | 13.8177i | 0.290940 | + | 0.702392i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.1002 | + | 7.08312i | 0.867013 | + | 0.359129i | 0.771446 | − | 0.636294i | \(-0.219534\pi\) |
0.0955668 | + | 0.995423i | \(0.469534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.78182 | − | 5.78182i | −0.292399 | − | 0.292399i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.70046 | + | 2.70046i | −0.136220 | + | 0.136220i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.3700 | + | 54.0059i | −1.12556 | + | 2.71733i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.0576 | + | 12.4503i | −1.50855 | + | 0.624860i | −0.975257 | − | 0.221073i | \(-0.929044\pi\) |
−0.533289 | + | 0.845933i | \(0.679044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.0644i | 0.804227i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.1068i | 1.90296i | 0.307708 | + | 0.951481i | \(0.400438\pi\) | ||||
−0.307708 | + | 0.951481i | \(0.599562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.79233 | − | 3.64190i | 0.437977 | − | 0.181416i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.434275 | + | 1.04843i | −0.0215793 | + | 0.0520970i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.93352 | + | 2.93352i | −0.145409 | + | 0.145409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.45034 | − | 4.45034i | −0.220055 | − | 0.220055i | 0.588466 | − | 0.808522i | \(-0.299732\pi\) |
−0.808522 | + | 0.588466i | \(0.799732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.46750 | − | 1.02207i | −0.121713 | − | 0.0504151i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.1387 | + | 26.8911i | 0.548098 | + | 1.32323i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 46.1666 | 2.26623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.2943 | 0.895874 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.82067 | − | 21.2950i | −0.430918 | − | 1.04033i | −0.978992 | − | 0.203899i | \(-0.934639\pi\) |
0.548074 | − | 0.836430i | \(-0.315361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1182 | − | 6.26218i | −0.736818 | − | 0.305200i | −0.0174674 | − | 0.999847i | \(-0.505560\pi\) |
−0.719350 | + | 0.694648i | \(0.755560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.38106 | − | 1.38106i | −0.0671494 | − | 0.0671494i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.87898 | + | 8.87898i | −0.430694 | + | 0.430694i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.35111 | + | 20.1614i | −0.404139 | + | 0.975677i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.37335 | − | 0.983074i | 0.114586 | − | 0.0474633i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.84075i | − | 0.281339i | −0.990057 | − | 0.140670i | \(-0.955074\pi\) | ||
0.990057 | − | 0.140670i | \(-0.0449255\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.77141i | − | 0.0851286i | −0.999094 | − | 0.0425643i | \(-0.986447\pi\) | ||
0.999094 | − | 0.0425643i | \(-0.0135527\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.76019 | − | 2.38595i | 0.276180 | − | 0.114398i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.82699 | + | 18.8960i | −0.374416 | + | 0.903919i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.32755 | − | 5.32755i | 0.254270 | − | 0.254270i | −0.568449 | − | 0.822719i | \(-0.692456\pi\) |
0.822719 | + | 0.568449i | \(0.192456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4241 | + | 18.4241i | 0.877337 | + | 0.877337i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.6293 | + | 14.3439i | 1.64529 | + | 0.681500i | 0.996816 | − | 0.0797396i | \(-0.0254089\pi\) |
0.648471 | + | 0.761240i | \(0.275409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.5423 | + | 44.7651i | 0.878989 | + | 2.12207i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.1017 | 0.856183 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5278 | −0.591225 | −0.295612 | − | 0.955308i | \(-0.595524\pi\) | ||||
−0.295612 | + | 0.955308i | \(0.595524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.74771 | − | 6.63357i | −0.129385 | − | 0.312363i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.45136 | + | 3.91488i | 0.444064 | + | 0.183937i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31.3935 | + | 31.3935i | 1.47175 | + | 1.47175i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.04451 | + | 7.04451i | −0.329528 | + | 0.329528i | −0.852407 | − | 0.522879i | \(-0.824858\pi\) |
0.522879 | + | 0.852407i | \(0.324858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.64453 | + | 6.38447i | −0.123436 | + | 0.298001i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.6991 | − | 13.1302i | 1.47637 | − | 0.611535i | 0.508072 | − | 0.861314i | \(-0.330358\pi\) |
0.968303 | + | 0.249780i | \(0.0803583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.90222i | − | 0.413721i | −0.978370 | − | 0.206861i | \(-0.933675\pi\) | ||
0.978370 | − | 0.206861i | \(-0.0663246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.6883i | 0.681155i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.7108 | − | 9.40713i | 1.05093 | − | 0.435310i | 0.210707 | − | 0.977549i | \(-0.432423\pi\) |
0.840224 | + | 0.542239i | \(0.182423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7549 | + | 28.3789i | −0.542791 | + | 1.31041i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.27660 | + | 5.27660i | −0.243133 | + | 0.243133i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.29463 | − | 5.29463i | −0.243447 | − | 0.243447i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.0181 | + | 12.0197i | 1.33144 | + | 0.551501i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.11048 | + | 12.3378i | 0.233993 | + | 0.564908i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.80923 | −0.402504 | −0.201252 | − | 0.979540i | \(-0.564501\pi\) | ||||
−0.201252 | + | 0.979540i | \(0.564501\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.2404 | −0.512516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.1226 | − | 26.8523i | −0.506095 | − | 1.22182i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.4308 | − | 12.1907i | −1.33639 | − | 0.553549i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.25173 | − | 5.25173i | −0.237979 | − | 0.237979i | 0.578034 | − | 0.816013i | \(-0.303820\pi\) |
−0.816013 | + | 0.578034i | \(0.803820\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.64836 | + | 1.64836i | −0.0745412 | + | 0.0745412i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.18136 | − | 10.0947i | 0.188702 | − | 0.455568i | −0.801008 | − | 0.598654i | \(-0.795703\pi\) |
0.989710 | + | 0.143086i | \(0.0457026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.94801 | + | 0.806893i | −0.0877341 | + | 0.0363406i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 6.83349i | − | 0.307143i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.0598i | 1.66236i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.4331 | + | 10.9489i | −1.18331 | + | 0.490142i | −0.885570 | − | 0.464506i | \(-0.846232\pi\) |
−0.297737 | + | 0.954648i | \(0.596232\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.598822 | + | 1.44568i | −0.0267534 | + | 0.0645884i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.9802 | + | 19.9802i | −0.890873 | + | 0.890873i | −0.994605 | − | 0.103733i | \(-0.966921\pi\) |
0.103733 | + | 0.994605i | \(0.466921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.1932 | + | 25.1932i | 1.12108 | + | 1.12108i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.17495 | − | 2.55775i | −0.274239 | − | 0.113594i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.1351 | − | 34.1252i | −0.626528 | − | 1.51257i | −0.843910 | − | 0.536485i | \(-0.819752\pi\) |
0.217382 | − | 0.976087i | \(-0.430248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.9795 | −0.839606 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.2856 | 0.763178 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.6279 | − | 32.9007i | −0.600517 | − | 1.44978i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.903386 | + | 0.374195i | 0.0397309 | + | 0.0164571i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1300 | + | 14.1300i | 0.620236 | + | 0.620236i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.8690 | + | 28.8690i | −1.26478 | + | 1.26478i | −0.316025 | + | 0.948751i | \(0.602348\pi\) |
−0.948751 | + | 0.316025i | \(0.897652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.01220 | + | 12.1005i | −0.219168 | + | 0.529119i | −0.994774 | − | 0.102098i | \(-0.967444\pi\) |
0.775606 | + | 0.631217i | \(0.217444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −41.2363 | + | 17.0806i | −1.79970 | + | 0.745460i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.96738i | − | 0.216382i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 14.0047i | − | 0.608898i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2143 | − | 4.64512i | 0.486660 | − | 0.201581i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.44472 | − | 17.9731i | 0.322467 | − | 0.778503i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.3900 | + | 22.3900i | −0.968005 | + | 0.968005i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.24963 | + | 8.24963i | 0.355998 | + | 0.355998i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0517 | − | 4.99196i | −0.519102 | − | 0.215019i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.54974 | − | 15.8125i | −0.281596 | − | 0.679832i | 0.718278 | − | 0.695757i | \(-0.244931\pi\) |
−0.999873 | + | 0.0159249i | \(0.994931\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.09375 | −0.132765 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.74779 | 0.117703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.82921 | + | 23.7298i | 0.420267 | + | 1.01461i | 0.982269 | + | 0.187478i | \(0.0600313\pi\) |
−0.562002 | + | 0.827136i | \(0.689969\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.40783 | + | 3.48264i | 0.358838 | + | 0.148635i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.72938 | + | 3.72938i | 0.158877 | + | 0.158877i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 49.6881 | − | 49.6881i | 2.11295 | − | 2.11295i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.63901 | − | 16.0280i | 0.281810 | − | 0.680350i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.0732 | + | 11.2141i | −1.14713 | + | 0.475156i | −0.873569 | − | 0.486700i | \(-0.838201\pi\) |
−0.273558 | + | 0.961855i | \(0.588201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.2874i | − | 0.858067i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1.34086i | − | 0.0566113i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.6272 | − | 11.4436i | 1.16435 | − | 0.482289i | 0.285028 | − | 0.958519i | \(-0.407997\pi\) |
0.879321 | + | 0.476230i | \(0.157997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.0371 | + | 55.6166i | −0.969180 | + | 2.33981i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.964608 | − | 0.964608i | 0.0405097 | − | 0.0405097i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.0917 | + | 28.0917i | 1.17767 | + | 1.17767i | 0.980337 | + | 0.197328i | \(0.0632264\pi\) |
0.197328 | + | 0.980337i | \(0.436774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.99922 | − | 1.65653i | −0.167362 | − | 0.0693237i | 0.297429 | − | 0.954744i | \(-0.403871\pi\) |
−0.464791 | + | 0.885420i | \(0.653871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.54181 | + | 20.6217i | 0.356839 | + | 0.861486i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −56.8270 | −2.36985 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.9445 | −0.538886 | −0.269443 | − | 0.963016i | \(-0.586840\pi\) | ||||
−0.269443 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.10648 | − | 2.67127i | −0.0459837 | − | 0.111014i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −51.2724 | − | 21.2377i | −2.12714 | − | 0.881090i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.72757 | − | 4.72757i | −0.195796 | − | 0.195796i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.0920 | − | 13.0920i | 0.541286 | − | 0.541286i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.82612 | − | 21.3081i | 0.364293 | − | 0.879481i | −0.630369 | − | 0.776295i | \(-0.717097\pi\) |
0.994662 | − | 0.103185i | \(-0.0329035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.4794 | + | 4.75491i | −0.472999 | + | 0.195922i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.74035i | 0.236126i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 34.4804i | − | 1.41594i | −0.706243 | − | 0.707970i | \(-0.749611\pi\) | ||
0.706243 | − | 0.707970i | \(-0.250389\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.4096 | − | 8.86815i | 0.877709 | − | 0.363559i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.70998 | − | 21.0278i | 0.356476 | − | 0.860609i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.59550 | − | 5.59550i | 0.228626 | − | 0.228626i | −0.583493 | − | 0.812118i | \(-0.698314\pi\) |
0.812118 | + | 0.583493i | \(0.198314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.2303 | + | 27.2303i | 1.11075 | + | 1.11075i | 0.993050 | + | 0.117695i | \(0.0375506\pi\) |
0.117695 | + | 0.993050i | \(0.462449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.8347 | + | 4.90211i | 0.481948 | + | 0.199629i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.6324 | − | 35.3258i | −0.594892 | − | 1.43620i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.74369 | 0.151952 | 0.0759758 | − | 0.997110i | \(-0.475793\pi\) | ||||
0.0759758 | + | 0.997110i | \(0.475793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.49485 | −0.303707 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.01385 | + | 2.44765i | 0.0410160 | + | 0.0990215i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.88397 | − | 2.85143i | −0.278041 | − | 0.115168i | 0.239306 | − | 0.970944i | \(-0.423080\pi\) |
−0.517347 | + | 0.855776i | \(0.673080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.2313 | + | 21.2313i | 0.856130 | + | 0.856130i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.08913 | + | 6.08913i | −0.245139 | + | 0.245139i | −0.818972 | − | 0.573833i | \(-0.805456\pi\) |
0.573833 | + | 0.818972i | \(0.305456\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.6058 | + | 30.4332i | −0.506672 | + | 1.22321i | 0.439117 | + | 0.898430i | \(0.355291\pi\) |
−0.945788 | + | 0.324783i | \(0.894709\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.8936 | + | 11.9681i | −1.15946 | + | 0.480264i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 58.2458i | − | 2.33357i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5590i | 0.622359i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.09867 | + | 1.28351i | −0.123749 | + | 0.0512585i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.24522 | + | 5.42043i | −0.0895226 | + | 0.216127i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1982 | − | 12.1982i | 0.485602 | − | 0.485602i | −0.421313 | − | 0.906915i | \(-0.638431\pi\) |
0.906915 | + | 0.421313i | \(0.138431\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.1263 | − | 17.1263i | −0.680708 | − | 0.680708i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0240 | − | 4.98052i | −0.477159 | − | 0.197646i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.5253 | − | 32.6530i | −0.535893 | − | 1.29376i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.4549 | 0.611388 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.7157 | 1.41068 | 0.705342 | − | 0.708867i | \(-0.250794\pi\) | ||||
0.705342 | + | 0.708867i | \(0.250794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.24179 | − | 19.8975i | −0.325025 | − | 0.784679i | −0.998947 | − | 0.0458768i | \(-0.985392\pi\) |
0.673922 | − | 0.738802i | \(-0.264608\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.9285 | + | 11.9826i | 1.13906 | + | 0.471814i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.13152 | + | 6.13152i | 0.241055 | + | 0.241055i | 0.817286 | − | 0.576232i | \(-0.195477\pi\) |
−0.576232 | + | 0.817286i | \(0.695477\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.29708 | + | 4.29708i | −0.168675 | + | 0.168675i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.75699 | − | 16.3128i | 0.264827 | − | 0.639349i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0482 | − | 7.89002i | 0.745413 | − | 0.308760i | 0.0225445 | − | 0.999746i | \(-0.492823\pi\) |
0.722868 | + | 0.690986i | \(0.242823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13.7803i | − | 0.538439i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.91498i | 0.308793i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.7290 | + | 16.4563i | −1.54762 | + | 0.641046i | −0.982884 | − | 0.184225i | \(-0.941022\pi\) |
−0.564737 | + | 0.825271i | \(0.691022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.09412 | − | 17.1267i | 0.275929 | − | 0.666153i | −0.723786 | − | 0.690025i | \(-0.757600\pi\) |
0.999715 | + | 0.0238723i | \(0.00759951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.56890 | − | 2.56890i | 0.0997676 | − | 0.0997676i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −40.9877 | − | 40.9877i | −1.58944 | − | 1.58944i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.81593 | − | 3.65168i | −0.341354 | − | 0.141394i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.95998 | + | 11.9745i | 0.191764 | + | 0.462959i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.55617 | −0.175889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.1192 | 1.27665 | 0.638326 | − | 0.769766i | \(-0.279627\pi\) | ||||
0.638326 | + | 0.769766i | \(0.279627\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.3791 | + | 44.3710i | 0.707411 | + | 1.70784i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.49374 | − | 2.68980i | −0.249575 | − | 0.103377i | 0.254389 | − | 0.967102i | \(-0.418126\pi\) |
−0.503964 | + | 0.863725i | \(0.668126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.0778 | + | 27.0778i | 1.03915 | + | 1.03915i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.44605 | + | 3.44605i | −0.132053 | + | 0.132053i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.44891 | + | 17.9833i | −0.285025 | + | 0.688110i | −0.999938 | − | 0.0111024i | \(-0.996466\pi\) |
0.714914 | + | 0.699213i | \(0.246466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.90351 | − | 3.68795i | 0.340186 | − | 0.140909i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.91573i | − | 0.187547i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 18.1146i | − | 0.690112i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.80634 | + | 2.81928i | −0.258926 | + | 0.107250i | −0.508370 | − | 0.861139i | \(-0.669752\pi\) |
0.249445 | + | 0.968389i | \(0.419752\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.14357 | + | 7.58926i | −0.119414 | + | 0.288292i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.6771 | + | 46.6771i | −1.77056 | + | 1.77056i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.18012 | − | 7.18012i | −0.271967 | − | 0.271967i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.16414 | − | 0.482204i | −0.0440319 | − | 0.0182386i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0726 | + | 41.2169i | 0.644823 | + | 1.55674i | 0.820100 | + | 0.572221i | \(0.193918\pi\) |
−0.175277 | + | 0.984519i | \(0.556082\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.6755 | 0.553498 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.08901 | −0.154001 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.3900 | − | 39.5690i | −0.616410 | − | 1.48815i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.11345 | − | 0.461208i | −0.0418167 | − | 0.0173210i | 0.361677 | − | 0.932303i | \(-0.382204\pi\) |
−0.403494 | + | 0.914982i | \(0.632204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.7213 | − | 20.7213i | −0.777108 | − | 0.777108i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.8960 | − | 15.8960i | 0.595311 | − | 0.595311i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.54724 | + | 8.56379i | −0.132659 | + | 0.320267i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.36133 | + | 0.563882i | −0.0508398 | + | 0.0210586i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.3791i | 1.76694i | 0.468487 | + | 0.883470i | \(0.344799\pi\) | ||||
−0.468487 | + | 0.883470i | \(0.655201\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.8086i | 1.59427i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.8081 | − | 6.96215i | 0.625101 | − | 0.258925i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.60778 | + | 13.5384i | −0.208268 | + | 0.502802i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0891 | − | 32.0891i | 1.19012 | − | 1.19012i | 0.213086 | − | 0.977034i | \(-0.431649\pi\) |
0.977034 | − | 0.213086i | \(-0.0683513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.0439 | + | 11.0439i | 0.409034 | + | 0.409034i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.78320 | − | 4.05233i | −0.361845 | − | 0.149881i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.8815 | + | 38.3414i | 0.586597 | + | 1.41617i | 0.886736 | + | 0.462276i | \(0.152967\pi\) |
−0.300139 | + | 0.953895i | \(0.597033\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 54.5496 | 2.01209 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.41320 | −0.236233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.6166 | + | 42.5302i | 0.648036 | + | 1.56450i | 0.815587 | + | 0.578634i | \(0.196414\pi\) |
−0.167551 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.39561 | − | 3.47757i | −0.308420 | − | 0.127752i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.8955 | − | 21.8955i | −0.803267 | − | 0.803267i | 0.180337 | − | 0.983605i | \(-0.442281\pi\) |
−0.983605 | + | 0.180337i | \(0.942281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.1859 | + | 46.1859i | −1.69212 | + | 1.69212i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.85671 | + | 21.3820i | −0.324050 | + | 0.782326i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.1662 | − | 14.5663i | 1.28495 | − | 0.532242i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9637i | 0.436561i | 0.975886 | + | 0.218281i | \(0.0700448\pi\) | ||||
−0.975886 | + | 0.218281i | \(0.929955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.61648i | 0.168234i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.1034 | + | 14.1261i | −1.24115 | + | 0.514102i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7520 | − | 42.8571i | 0.645207 | − | 1.55767i | −0.174358 | − | 0.984682i | \(-0.555785\pi\) |
0.819565 | − | 0.572986i | \(-0.194215\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.29088 | − | 4.29088i | 0.155749 | − | 0.155749i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.2473 | − | 26.2473i | −0.951464 | − | 0.951464i | 0.0474116 | − | 0.998875i | \(-0.484903\pi\) |
−0.998875 | + | 0.0474116i | \(0.984903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.05169 | − | 1.26405i | −0.110479 | − | 0.0457618i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.69826 | − | 8.92839i | −0.133711 | − | 0.322807i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.4651 | −0.594522 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.5470 | 0.524577 | 0.262288 | − | 0.964990i | \(-0.415523\pi\) | ||||
0.262288 | + | 0.964990i | \(0.415523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.87404 | − | 23.8380i | −0.355605 | − | 0.858506i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.52868 | + | 1.46163i | 0.126918 | + | 0.0525711i | 0.445239 | − | 0.895412i | \(-0.353119\pi\) |
−0.318321 | + | 0.947983i | \(0.603119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.4111 | − | 24.4111i | −0.876871 | − | 0.876871i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.7465 | + | 14.7465i | −0.529029 | + | 0.529029i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.71990 | + | 23.4659i | −0.348252 | + | 0.840754i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.14848 | + | 2.96100i | −0.255793 | + | 0.105953i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.06459i | 0.288205i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 26.9261i | − | 0.961032i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4346 | − | 4.73636i | 0.407599 | − | 0.168833i | −0.169457 | − | 0.985538i | \(-0.554201\pi\) |
0.577056 | + | 0.816705i | \(0.304201\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.66000 | + | 18.4929i | −0.272703 | + | 0.658364i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.1700 | − | 51.1700i | 1.81939 | − | 1.81939i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.72894 | − | 8.72894i | −0.309974 | − | 0.309974i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.8302 | + | 10.6992i | 0.916104 | + | 0.379463i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.560326 | − | 1.35275i | −0.0198478 | − | 0.0479167i | 0.913645 | − | 0.406513i | \(-0.133255\pi\) |
−0.933493 | + | 0.358596i | \(0.883255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.38284 | 0.0489215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.2901 | −0.858248 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.51642 | − | 3.66097i | −0.0535134 | − | 0.129193i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 96.8915 | + | 40.1338i | 3.41498 | + | 1.41453i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.68002 | − | 9.68002i | −0.340753 | − | 0.340753i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.15363 | + | 3.15363i | −0.110876 | + | 0.110876i | −0.760368 | − | 0.649492i | \(-0.774981\pi\) |
0.649492 | + | 0.760368i | \(0.274981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.61166 | − | 20.7904i | 0.302396 | − | 0.730049i | −0.697513 | − | 0.716572i | \(-0.745710\pi\) |
0.999909 | − | 0.0134769i | \(-0.00428995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.65465 | − | 2.34223i | 0.198317 | − | 0.0821457i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 8.41143i | − | 0.294640i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.4875i | 0.926680i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.5625 | + | 8.51727i | −0.718512 | + | 0.297617i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.63781 | − | 3.95402i | 0.0571599 | − | 0.137996i | −0.892719 | − | 0.450613i | \(-0.851205\pi\) |
0.949879 | + | 0.312617i | \(0.101205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.07415 | − | 6.07415i | 0.211731 | − | 0.211731i | −0.593271 | − | 0.805003i | \(-0.702164\pi\) |
0.805003 | + | 0.593271i | \(0.202164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.58938 | − | 6.58938i | −0.229413 | − | 0.229413i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.1075 | + | 10.3999i | 0.873074 | + | 0.361639i | 0.773807 | − | 0.633422i | \(-0.218350\pi\) |
0.0992672 | + | 0.995061i | \(0.468350\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.3361 | − | 24.9536i | −0.358988 | − | 0.866674i | −0.995443 | − | 0.0953602i | \(-0.969600\pi\) |
0.636455 | − | 0.771314i | \(-0.280400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0387 | −0.625757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.4479 | −0.639181 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.16073 | − | 5.21648i | −0.0747753 | − | 0.180524i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.5529 | − | 7.27064i | −0.606716 | − | 0.251310i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.6105 | − | 19.6105i | −0.677028 | − | 0.677028i | 0.282298 | − | 0.959327i | \(-0.408903\pi\) |
−0.959327 | + | 0.282298i | \(0.908903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.7662 | − | 18.7662i | 0.647109 | − | 0.647109i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.41451 | + | 3.41492i | −0.0487181 | + | 0.117616i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.2811 | − | 9.22915i | 0.766494 | − | 0.317492i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 45.9639i | 1.57934i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 27.0618i | − | 0.928758i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.5307 | + | 10.1610i | −0.840902 | + | 0.348313i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.24721 | − | 22.3247i | 0.316619 | − | 0.764385i | −0.682810 | − | 0.730596i | \(-0.739243\pi\) |
0.999429 | − | 0.0337892i | \(-0.0107575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.0930 | + | 17.0930i | −0.584568 | + | 0.584568i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.5074 | + | 21.5074i | 0.734677 | + | 0.734677i | 0.971543 | − | 0.236865i | \(-0.0761200\pi\) |
−0.236865 | + | 0.971543i | \(0.576120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.5057 | − | 12.2217i | −1.00672 | − | 0.416998i | −0.182464 | − | 0.983212i | \(-0.558407\pi\) |
−0.824258 | + | 0.566215i | \(0.808407\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.8125 | − | 33.3464i | −0.470729 | − | 1.13644i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.4436 | 0.900151 | 0.450076 | − | 0.892990i | \(-0.351397\pi\) | ||||
0.450076 | + | 0.892990i | \(0.351397\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.1041 | −2.45161 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.10220 | + | 14.7320i | 0.207241 | + | 0.500325i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.5543 | + | 5.61438i | 0.459799 | + | 0.190455i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.2867 | − | 12.2867i | −0.416320 | − | 0.416320i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.2922 | − | 11.2922i | 0.382182 | − | 0.382182i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.6446 | − | 69.1541i | 0.968363 | − | 2.33784i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.5345 | − | 12.6478i | 1.03108 | − | 0.427086i | 0.197975 | − | 0.980207i | \(-0.436563\pi\) |
0.833101 | + | 0.553121i | \(0.186563\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.9063i | 1.00871i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.9951i | 0.471507i | 0.971813 | + | 0.235753i | \(0.0757557\pi\) | ||||
−0.971813 | + | 0.235753i | \(0.924244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.4774 | − | 18.4231i | 1.49678 | − | 0.619987i | 0.524002 | − | 0.851717i | \(-0.324439\pi\) |
0.972780 | + | 0.231730i | \(0.0744385\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.72498 | − | 23.4782i | 0.326902 | − | 0.789210i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.0611 | + | 11.0611i | −0.371395 | + | 0.371395i | −0.867985 | − | 0.496590i | \(-0.834585\pi\) |
0.496590 | + | 0.867985i | \(0.334585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.0627 | + | 11.0627i | 0.371031 | + | 0.371031i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.263134 | + | 0.108994i | 0.00881531 | + | 0.00365142i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.32369 | − | 3.19568i | −0.0442958 | − | 0.106939i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.0972 | −1.40716 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.4414 | 0.548961 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.21840 | − | 5.35569i | −0.0739878 | − | 0.178622i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.73540 | − | 3.61832i | −0.291019 | − | 0.120544i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.6156 | − | 26.6156i | −0.885713 | − | 0.885713i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.89357 | − | 7.89357i | 0.262391 | − | 0.262391i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.5034 | − | 49.4995i | 0.680803 | − | 1.64360i | −0.0817295 | − | 0.996655i | \(-0.526044\pi\) |
0.762533 | − | 0.646950i | \(-0.223956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.5013 | + | 6.83508i | −0.547315 | + | 0.226705i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.3750i | 1.50334i | 0.659539 | + | 0.751670i | \(0.270752\pi\) | ||||
−0.659539 | + | 0.751670i | \(0.729248\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 11.5868i | − | 0.383467i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.6025 | − | 7.29121i | 0.581922 | − | 0.241040i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.33925 | + | 15.3043i | −0.209341 | + | 0.505393i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.90286 | + | 9.90286i | −0.326665 | + | 0.326665i | −0.851317 | − | 0.524652i | \(-0.824196\pi\) |
0.524652 | + | 0.851317i | \(0.324196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.01484 | − | 2.01484i | −0.0663913 | − | 0.0663913i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.3683 | − | 8.02259i | −0.637514 | − | 0.264067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.6039 | + | 37.6711i | 0.513053 | + | 1.23862i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.8523 | 0.586347 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.64137 | 0.0538515 | 0.0269257 | − | 0.999637i | \(-0.491428\pi\) | ||||
0.0269257 | + | 0.999637i | \(0.491428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.6588 | + | 42.6322i | 0.578744 | + | 1.39721i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.8074 | + | 8.61869i | 0.681203 | + | 0.282163i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.42116 | + | 3.42116i | 0.111884 | + | 0.111884i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.172711 | − | 0.172711i | 0.00564221 | − | 0.00564221i | −0.704280 | − | 0.709922i | \(-0.748730\pi\) |
0.709922 | + | 0.704280i | \(0.248730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.24707 | − | 12.6675i | 0.171232 | − | 0.413389i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.8801 | + | 16.5189i | −1.30005 | + | 0.538500i | −0.921966 | − | 0.387270i | \(-0.873418\pi\) |
−0.378087 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 45.9540i | − | 1.49647i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 88.6339i | − | 2.88326i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.0171 | + | 8.29136i | −0.650469 | + | 0.269433i | −0.683422 | − | 0.730024i | \(-0.739509\pi\) |
0.0329528 | + | 0.999457i | \(0.489509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.10863 | − | 9.91912i | 0.133372 | − | 0.321988i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.2400 | − | 20.2400i | 0.656328 | − | 0.656328i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0721 | − | 35.0721i | −1.13610 | − | 1.13610i | −0.989144 | − | 0.146953i | \(-0.953053\pi\) |
−0.146953 | − | 0.989144i | \(-0.546947\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −74.4097 | − | 30.8215i | −2.40784 | − | 0.997360i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.598822 | − | 1.44568i | −0.0193572 | − | 0.0467323i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.5848 | −0.374091 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3431 | −0.559456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.07456 | − | 14.6653i | −0.195750 | − | 0.472582i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.63879 | + | 3.99252i | 0.310284 | + | 0.128524i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5945 | + | 17.5945i | 0.565802 | + | 0.565802i | 0.930950 | − | 0.365148i | \(-0.118981\pi\) |
−0.365148 | + | 0.930950i | \(0.618981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.35398 | + | 3.35398i | −0.107745 | + | 0.107745i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.858080 | + | 2.07159i | −0.0275371 | + | 0.0664804i | −0.937050 | − | 0.349195i | \(-0.886455\pi\) |
0.909513 | + | 0.415676i | \(0.136455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 73.3120 | − | 30.3668i | 2.35028 | − | 0.973516i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 25.2485i | − | 0.808600i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 39.3535i | − | 1.25903i | −0.776989 | − | 0.629515i | \(-0.783254\pi\) | ||
0.776989 | − | 0.629515i | \(-0.216746\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.2351 | − | 4.65371i | 0.359074 | − | 0.148733i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.527144 | + | 1.27264i | −0.0168304 | + | 0.0406322i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.0511 | + | 30.0511i | −0.958481 | + | 0.958481i | −0.999172 | − | 0.0406903i | \(-0.987044\pi\) |
0.0406903 | + | 0.999172i | \(0.487044\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6463 | − | 14.6463i | −0.466669 | − | 0.466669i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.54124 | + | 1.88104i | 0.144549 | + | 0.0598743i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.3393 | − | 44.2749i | −0.583154 | − | 1.40786i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.5749 | −1.19360 | −0.596802 | − | 0.802388i | \(-0.703562\pi\) | ||||
−0.596802 | + | 0.802388i | \(0.703562\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.8786 | 1.04337 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.4283 | + | 75.8747i | 0.996345 | + | 2.40539i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.6516 | − | 21.8090i | −1.66749 | − | 0.690698i | −0.668881 | − | 0.743369i | \(-0.733227\pi\) |
−0.998612 | + | 0.0526708i | \(0.983227\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.8675 | + | 15.8675i | 0.502027 | + | 0.502027i |
(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 | 1024.2.g.c.897.3 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.c.897.2 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.h.897.3 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.h.897.2 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.e.385.3 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.b.385.3 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.b.385.2 | ✓ | 16 | ||
16.13 | even | 4 | 1024.2.g.e.385.2 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.h.129.3 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.e.641.2 | yes | 16 | ||
32.11 | odd | 8 | 1024.2.g.b.641.2 | yes | 16 | ||
32.13 | even | 8 | inner | 1024.2.g.c.129.3 | yes | 16 | |
32.19 | odd | 8 | inner | 1024.2.g.c.129.2 | yes | 16 | |
32.21 | even | 8 | 1024.2.g.b.641.3 | yes | 16 | ||
32.27 | odd | 8 | 1024.2.g.e.641.3 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.h.129.2 | yes | 16 | ||
64.13 | even | 16 | 4096.2.a.o.1.5 | 8 | |||
64.19 | odd | 16 | 4096.2.a.o.1.6 | 8 | |||
64.45 | even | 16 | 4096.2.a.n.1.4 | 8 | |||
64.51 | odd | 16 | 4096.2.a.n.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.b.385.2 | ✓ | 16 | 16.11 | odd | 4 | ||
1024.2.g.b.385.3 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.b.641.2 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.b.641.3 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.c.129.2 | yes | 16 | 32.19 | odd | 8 | inner | |
1024.2.g.c.129.3 | yes | 16 | 32.13 | even | 8 | inner | |
1024.2.g.c.897.2 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.c.897.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.e.385.2 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.e.385.3 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.e.641.2 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.e.641.3 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.h.129.2 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.h.129.3 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.h.897.2 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.h.897.3 | yes | 16 | 8.3 | odd | 2 | ||
4096.2.a.n.1.3 | 8 | 64.51 | odd | 16 | |||
4096.2.a.n.1.4 | 8 | 64.45 | even | 16 | |||
4096.2.a.o.1.5 | 8 | 64.13 | even | 16 | |||
4096.2.a.o.1.6 | 8 | 64.19 | odd | 16 |