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 | 641.3 | ||
Root | \(0.639878 - 1.60952i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.641 |
Dual form | 1024.2.g.e.385.3 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.969643 | + | 0.401639i | 0.559824 | + | 0.231887i | 0.644609 | − | 0.764513i | \(-0.277020\pi\) |
−0.0847850 | + | 0.996399i | \(0.527020\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.44924 | − | 3.49877i | −0.648120 | − | 1.56470i | −0.815469 | − | 0.578801i | \(-0.803521\pi\) |
0.167349 | − | 0.985898i | \(-0.446479\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.21904 | − | 3.21904i | 1.21668 | − | 1.21668i | 0.247897 | − | 0.968786i | \(-0.420261\pi\) |
0.968786 | − | 0.247897i | \(-0.0797394\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.34243 | − | 1.34243i | −0.447476 | − | 0.447476i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.878116 | + | 0.363728i | −0.264762 | + | 0.109668i | −0.511116 | − | 0.859512i | \(-0.670768\pi\) |
0.246354 | + | 0.969180i | \(0.420768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.985492 | + | 2.37919i | −0.273326 | + | 0.659868i | −0.999621 | − | 0.0275150i | \(-0.991241\pi\) |
0.726295 | + | 0.687383i | \(0.241241\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.97463i | − | 1.02625i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.34416i | − | 0.326007i | −0.986625 | − | 0.163004i | \(-0.947882\pi\) | ||
0.986625 | − | 0.163004i | \(-0.0521182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.28667 | + | 3.10629i | −0.295182 | + | 0.712632i | 0.704813 | + | 0.709393i | \(0.251031\pi\) |
−0.999995 | + | 0.00323890i | \(0.998969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.41421 | − | 1.82843i | 0.963260 | − | 0.398996i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.30143 | − | 4.30143i | −0.896911 | − | 0.896911i | 0.0982508 | − | 0.995162i | \(-0.468675\pi\) |
−0.995162 | + | 0.0982508i | \(0.968675\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.60559 | + | 6.60559i | −1.32112 | + | 1.32112i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.96742 | − | 4.74977i | −0.378630 | − | 0.914095i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.44924 | − | 0.600295i | −0.269117 | − | 0.111472i | 0.244044 | − | 0.969764i | \(-0.421526\pi\) |
−0.513161 | + | 0.858292i | \(0.671526\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69552 | 0.663735 | 0.331867 | − | 0.943326i | \(-0.392321\pi\) | ||||
0.331867 | + | 0.943326i | \(0.392321\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.997546 | −0.173651 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.9279 | − | 6.59753i | −2.69230 | − | 1.11519i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.67035 | + | 4.03257i | 0.274603 | + | 0.662951i | 0.999669 | − | 0.0257289i | \(-0.00819066\pi\) |
−0.725066 | + | 0.688680i | \(0.758191\pi\) | |||||||
\(38\) | 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 | \(-0.0491699\pi\) |
−0.153858 | + | 0.988093i | \(0.549170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.27829 | + | 3.01477i | −1.10993 | + | 0.459747i | −0.860913 | − | 0.508752i | \(-0.830107\pi\) |
−0.249015 | + | 0.968500i | \(0.580107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.75135 | + | 6.64235i | −0.410147 | + | 0.990182i | ||||
\(46\) | 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 | ||||||||
\(51\) | 0.539868 | − | 1.30336i | 0.0755967 | − | 0.182507i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.49877 | − | 2.69188i | 0.892675 | − | 0.369758i | 0.111276 | − | 0.993790i | \(-0.464506\pi\) |
0.781399 | + | 0.624031i | \(0.214506\pi\) | |||||||
\(54\) | 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 | ||||||||
\(59\) | −2.44676 | − | 5.90700i | −0.318541 | − | 0.769027i | −0.999332 | − | 0.0365485i | \(-0.988364\pi\) |
0.680791 | − | 0.732478i | \(-0.261636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.42872 | − | 1.83444i | −0.567040 | − | 0.234876i | 0.0806985 | − | 0.996739i | \(-0.474285\pi\) |
−0.647738 | + | 0.761863i | \(0.724285\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.64266 | −1.08887 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.75245 | 1.20964 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.23381 | + | 2.58213i | 0.761581 | + | 0.315457i | 0.729457 | − | 0.684027i | \(-0.239773\pi\) |
0.0321238 | + | 0.999484i | \(0.489773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.44323 | − | 5.89848i | −0.294130 | − | 0.710093i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.75634 | − | 5.75634i | 0.683152 | − | 0.683152i | −0.277557 | − | 0.960709i | \(-0.589525\pi\) |
0.960709 | + | 0.277557i | \(0.0895247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94801 | + | 2.94801i | 0.345039 | + | 0.345039i | 0.858258 | − | 0.513219i | \(-0.171547\pi\) |
−0.513219 | + | 0.858258i | \(0.671547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.05812 | + | 3.75200i | −1.04594 | + | 0.433243i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.65584 | + | 3.99755i | −0.188700 | + | 0.455563i | ||||
\(78\) | 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 | ||||||||
\(83\) | 4.66516 | − | 11.2627i | 0.512068 | − | 1.23624i | −0.430610 | − | 0.902538i | \(-0.641702\pi\) |
0.942678 | − | 0.333703i | \(-0.108298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.70292 | + | 1.94801i | −0.510103 | + | 0.211292i | ||||
\(86\) | 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 | \(-0.512800\pi\) |
0.999192 | + | 0.0402029i | \(0.0128004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.48636 | + | 10.8310i | 0.470299 | + | 1.13540i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.58333 | + | 1.48427i | 0.371574 | + | 0.153911i | ||||
\(94\) | 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 | ||||||||
\(99\) | 1.66708 | + | 0.690529i | 0.167548 | + | 0.0694008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.60029 | − | 8.69188i | −0.358243 | − | 0.864874i | −0.995547 | − | 0.0942625i | \(-0.969951\pi\) |
0.637305 | − | 0.770612i | \(-0.280049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.64927 | − | 6.64927i | 0.655172 | − | 0.655172i | −0.299062 | − | 0.954234i | \(-0.596674\pi\) |
0.954234 | + | 0.299062i | \(0.0966736\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.7945 | − | 12.7945i | −1.24862 | − | 1.24862i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.72475 | − | 3.19970i | 0.746780 | − | 0.309326i | 0.0233529 | − | 0.999727i | \(-0.492566\pi\) |
0.723427 | + | 0.690401i | \(0.242566\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.277666 | + | 0.670346i | −0.0265956 | + | 0.0642075i | −0.936619 | − | 0.350349i | \(-0.886063\pi\) |
0.910024 | + | 0.414556i | \(0.136063\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.58103i | 0.434812i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.8960i | 1.49537i | 0.664052 | + | 0.747686i | \(0.268835\pi\) | ||||
−0.664052 | + | 0.747686i | \(0.731165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.81593 | + | 21.2835i | −0.822090 | + | 1.98470i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.51684 | − | 1.87094i | 0.417582 | − | 0.172968i | ||||
\(118\) | 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 | ||||||||
\(123\) | 3.03411 | + | 7.32499i | 0.273576 | + | 0.660472i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15.1907 | + | 6.29217i | 1.35869 | + | 0.562789i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.43664 | −0.304953 | −0.152476 | − | 0.988307i | \(-0.548725\pi\) | ||||
−0.152476 | + | 0.988307i | \(0.548725\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.26819 | −0.727973 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.36180 | + | 1.39250i | 0.293722 | + | 0.121664i | 0.524679 | − | 0.851300i | \(-0.324185\pi\) |
−0.230956 | + | 0.972964i | \(0.574185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.85744 | + | 14.1411i | 0.507905 | + | 1.22619i | ||||
\(134\) | 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 | \(-0.215329\pi\) |
−0.626049 | + | 0.779783i | \(0.715329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1040 | − | 6.67049i | 1.36592 | − | 0.565784i | 0.425243 | − | 0.905079i | \(-0.360189\pi\) |
0.940680 | + | 0.339295i | \(0.110189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.413197 | − | 0.997546i | 0.0347975 | − | 0.0840086i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.44765i | − | 0.204683i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.94053i | 0.493334i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.51228 | − | 13.3078i | 0.454645 | − | 1.09761i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.9345 | + | 6.60029i | −1.30541 | + | 0.540717i | −0.923541 | − | 0.383500i | \(-0.874718\pi\) |
−0.381866 | + | 0.924218i | \(0.624718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.89235 | + | 6.89235i | 0.560892 | + | 0.560892i | 0.929561 | − | 0.368669i | \(-0.120186\pi\) |
−0.368669 | + | 0.929561i | \(0.620186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.80444 | + | 1.80444i | −0.145880 | + | 0.145880i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.35569 | − | 12.9298i | −0.430179 | − | 1.03854i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.56882 | − | 2.72090i | −0.524249 | − | 0.217151i | 0.104833 | − | 0.994490i | \(-0.466569\pi\) |
−0.629082 | + | 0.777339i | \(0.716569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.38265 | 0.585483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.6930 | −2.18251 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.05204 | + | 0.849981i | 0.160728 | + | 0.0665756i | 0.461597 | − | 0.887090i | \(-0.347277\pi\) |
−0.300869 | + | 0.953665i | \(0.597277\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.44568 | + | 3.49019i | 0.112546 | + | 0.271711i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.05426 | − | 1.05426i | 0.0815808 | − | 0.0815808i | −0.665139 | − | 0.746720i | \(-0.731628\pi\) |
0.746720 | + | 0.665139i | \(0.231628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50305 | + | 4.50305i | 0.346388 | + | 0.346388i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.89723 | − | 2.44271i | 0.450972 | − | 0.186799i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.28617 | − | 17.5904i | 0.553957 | − | 1.33737i | −0.360527 | − | 0.932749i | \(-0.617403\pi\) |
0.914484 | − | 0.404622i | \(-0.132597\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.5273i | 3.21476i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.71040i | − | 0.504385i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.25395 | + | 10.2700i | −0.317955 | + | 0.767612i | 0.681407 | + | 0.731905i | \(0.261368\pi\) |
−0.999362 | + | 0.0357074i | \(0.988632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.72335 | − | 1.12805i | 0.202425 | − | 0.0838472i | −0.279168 | − | 0.960242i | \(-0.590059\pi\) |
0.481593 | + | 0.876395i | \(0.340059\pi\) | |||||||
\(182\) | 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 | ||||||||
\(187\) | 0.488909 | + | 1.18033i | 0.0357526 | + | 0.0863143i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.6229 | − | 8.95651i | −1.57284 | − | 0.651490i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2674 | −1.53885 | −0.769426 | − | 0.638736i | \(-0.779458\pi\) | ||||
−0.769426 | + | 0.638736i | \(0.779458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.75491 | −0.198302 | −0.0991512 | − | 0.995072i | \(-0.531613\pi\) | ||||
−0.0991512 | + | 0.995072i | \(0.531613\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.45640 | + | 3.91697i | 0.677187 | + | 0.280500i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.09306 | + | 5.05309i | 0.149124 | + | 0.360018i | 0.980735 | − | 0.195340i | \(-0.0625812\pi\) |
−0.831611 | + | 0.555358i | \(0.812581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3344 | + | 15.3344i | −1.08702 | + | 1.08702i | −0.0911915 | + | 0.995833i | \(0.529068\pi\) |
−0.995833 | + | 0.0911915i | \(0.970932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.00748 | + | 5.00748i | 0.353201 | + | 0.353201i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.59753 | + | 2.73279i | −0.463056 | + | 0.191804i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.9480 | − | 26.4308i | 0.764642 | − | 1.84601i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.5487i | 0.802692i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.19568i | − | 0.221050i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.83123 | − | 21.3205i | 0.607967 | − | 1.46776i | −0.257240 | − | 0.966347i | \(-0.582813\pi\) |
0.865207 | − | 0.501414i | \(-0.167187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.89357 | − | 3.26962i | 0.540859 | − | 0.224031i | ||||
\(214\) | 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 | ||||||||
\(219\) | 1.67448 | + | 4.04256i | 0.113151 | + | 0.273171i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.19801 | + | 1.32466i | 0.215122 | + | 0.0891063i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3493 | −0.826973 | −0.413487 | − | 0.910510i | \(-0.635689\pi\) | ||||
−0.413487 | + | 0.910510i | \(0.635689\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.7350 | 1.18234 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.28999 | + | 1.77697i | 0.284736 | + | 0.117942i | 0.520481 | − | 0.853873i | \(-0.325753\pi\) |
−0.235744 | + | 0.971815i | \(0.575753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.79239 | − | 4.32720i | −0.118444 | − | 0.285949i | 0.853527 | − | 0.521048i | \(-0.174459\pi\) |
−0.971972 | + | 0.235098i | \(0.924459\pi\) | |||||||
\(230\) | 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 | \(-0.237479\pi\) |
−0.678752 | + | 0.734368i | \(0.737479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.59946 | + | 1.49094i | −0.234803 | + | 0.0972585i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.19957 | − | 14.9671i | 0.402706 | − | 0.972217i | ||||
\(238\) | 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 | \(0.188547\pi\) | ||||
−0.829638 | + | 0.558302i | \(0.811453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.02262 | + | 14.5399i | −0.386351 | + | 0.932734i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −48.0187 | + | 19.8900i | −3.06781 | + | 1.27073i | ||||
\(246\) | 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 | ||||||||
\(251\) | −1.68327 | − | 4.06378i | −0.106247 | − | 0.256503i | 0.861811 | − | 0.507230i | \(-0.169331\pi\) |
−0.968058 | + | 0.250726i | \(0.919331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.34171 | + | 2.21261i | 0.335830 | + | 0.139105i | ||||
\(254\) | 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 | ||||||||
\(259\) | 18.3579 | + | 7.60410i | 1.14071 | + | 0.472496i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.13965 | + | 2.75135i | 0.0705423 | + | 0.170304i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.4858 | − | 13.4858i | 0.831572 | − | 0.831572i | −0.156160 | − | 0.987732i | \(-0.549911\pi\) |
0.987732 | + | 0.156160i | \(0.0499114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.8366 | − | 18.8366i | −1.15712 | − | 1.15712i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4061 | − | 5.13877i | 0.759241 | − | 0.314488i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.99154 | + | 12.0506i | −0.304339 | + | 0.734740i | 0.695529 | + | 0.718498i | \(0.255170\pi\) |
−0.999868 | + | 0.0162420i | \(0.994830\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 3.39784 | − | 8.20311i | 0.204897 | − | 0.494666i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8791 | − | 6.57732i | 0.954080 | − | 0.395193i | 0.149317 | − | 0.988789i | \(-0.452292\pi\) |
0.804763 | + | 0.593596i | \(0.202292\pi\) | |||||||
\(278\) | 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 | \(-0.783499\pi\) |
0.628915 | + | 0.777474i | \(0.283499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.86733 | + | 23.8218i | 0.586552 | + | 1.41606i | 0.886779 | + | 0.462193i | \(0.152937\pi\) |
−0.300227 | + | 0.953868i | \(0.597063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.3464 | + | 5.11403i | 0.731336 | + | 0.302929i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.3904 | 2.03000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.1932 | 0.893719 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.15640 | + | 3.37849i | 0.478137 | + | 0.198051i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.9045 | + | 26.3258i | 0.637047 | + | 1.53797i | 0.830595 | + | 0.556877i | \(0.188000\pi\) |
−0.193548 | + | 0.981091i | \(0.562000\pi\) | |||||||
\(294\) | 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 | ||||||||
\(299\) | 14.4729 | − | 5.99489i | 0.836992 | − | 0.346693i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.7245 | + | 33.1338i | −0.791064 | + | 1.90980i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.87404i | − | 0.567249i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.1536i | 1.03947i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.03896 | − | 2.50827i | 0.0592967 | − | 0.143155i | −0.891454 | − | 0.453111i | \(-0.850314\pi\) |
0.950751 | + | 0.309956i | \(0.100314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.11803 | − | 3.77681i | 0.518706 | − | 0.214855i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.1737 | + | 15.1737i | 0.860419 | + | 0.860419i | 0.991387 | − | 0.130967i | \(-0.0418083\pi\) |
−0.130967 | + | 0.991387i | \(0.541808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.23773 | − | 9.23773i | 0.522148 | − | 0.522148i | −0.396072 | − | 0.918219i | \(-0.629627\pi\) |
0.918219 | + | 0.396072i | \(0.129627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.5253 | + | 30.2387i | 0.705719 | + | 1.70376i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.1968 | + | 10.4368i | 1.41519 | + | 0.586192i | 0.953648 | − | 0.300925i | \(-0.0972954\pi\) |
0.461545 | + | 0.887117i | \(0.347295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.49094 | 0.0834769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.77537 | 0.489794 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.17536 | + | 1.72949i | 0.232323 | + | 0.0962314i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.20618 | − | 22.2257i | −0.510667 | − | 1.23286i | ||||
\(326\) | 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 | ||||||||
\(331\) | 28.9422 | − | 11.9883i | 1.59081 | − | 0.658935i | 0.600731 | − | 0.799451i | \(-0.294876\pi\) |
0.990078 | + | 0.140516i | \(0.0448761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.17112 | − | 7.65575i | 0.173776 | − | 0.419533i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 25.5528i | − | 1.39610i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.82843i | 0.154074i | 0.997028 | + | 0.0770371i | \(0.0245460\pi\) | ||||
−0.997028 | + | 0.0770371i | \(0.975454\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.38447 | + | 15.4135i | −0.346757 | + | 0.837145i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.24509 | + | 1.34416i | −0.175732 | + | 0.0727905i | ||||
\(342\) | 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 | ||||||||
\(347\) | −5.69394 | − | 13.7464i | −0.305667 | − | 0.737944i | −0.999836 | − | 0.0181324i | \(-0.994228\pi\) |
0.694169 | − | 0.719812i | \(-0.255772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.27420 | + | 1.77043i | 0.228792 | + | 0.0947690i | 0.494135 | − | 0.869385i | \(-0.335485\pi\) |
−0.265342 | + | 0.964154i | \(0.585485\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −28.4825 | − | 11.7978i | −1.51169 | − | 0.626163i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.45770 | − | 5.93342i | −0.130075 | − | 0.314030i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.89363 | − | 8.89363i | 0.469388 | − | 0.469388i | −0.432328 | − | 0.901716i | \(-0.642308\pi\) |
0.901716 | + | 0.432328i | \(0.142308\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.44149 | + | 5.44149i | 0.286394 | + | 0.286394i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.79011 | + | 4.05520i | −0.513848 | + | 0.212843i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.04205 | − | 14.5868i | 0.316255 | − | 0.763508i | ||||
\(366\) | 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 | ||||||||
\(371\) | 12.2545 | − | 29.5851i | 0.636224 | − | 1.53598i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.81392 | + | 1.57978i | −0.197477 | + | 0.0817978i | −0.479230 | − | 0.877689i | \(-0.659084\pi\) |
0.281753 | + | 0.959487i | \(0.409084\pi\) | |||||||
\(374\) | 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 | ||||||||
\(379\) | −7.48355 | − | 18.0669i | −0.384404 | − | 0.928033i | −0.991102 | − | 0.133101i | \(-0.957506\pi\) |
0.606698 | − | 0.794932i | \(-0.292494\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.33232 | − | 1.38029i | −0.170720 | − | 0.0707144i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.43680 | 0.226710 | 0.113355 | − | 0.993555i | \(-0.463840\pi\) | ||||
0.113355 | + | 0.993555i | \(0.463840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.3862 | 0.835119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.8177 | + | 5.72347i | 0.702392 | + | 0.290940i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.08312 | + | 17.1002i | 0.359129 | + | 0.867013i | 0.995423 | + | 0.0955668i | \(0.0304663\pi\) |
−0.636294 | + | 0.771446i | \(0.719534\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | −54.0059 | + | 22.3700i | −2.71733 | + | 1.12556i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.4503 | + | 30.0576i | −0.624860 | + | 1.50855i | 0.221073 | + | 0.975257i | \(0.429044\pi\) |
−0.845933 | + | 0.533289i | \(0.820956\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.0644i | 0.804227i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 38.1068i | − | 1.90296i | −0.307708 | − | 0.951481i | \(-0.599562\pi\) | ||
0.307708 | − | 0.951481i | \(-0.400438\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.64190 | + | 8.79233i | −0.181416 | + | 0.437977i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.04843 | − | 0.434275i | 0.0520970 | − | 0.0215793i | ||||
\(406\) | 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 | \(-0.700268\pi\) |
0.808522 | + | 0.588466i | \(0.200268\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.02207 | + | 2.46750i | 0.0504151 | + | 0.121713i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.8911 | − | 11.1387i | −1.32323 | − | 0.548098i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −46.1666 | −2.26623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.2943 | 0.895874 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.2950 | − | 8.82067i | −1.04033 | − | 0.430918i | −0.203899 | − | 0.978992i | \(-0.565361\pi\) |
−0.836430 | + | 0.548074i | \(0.815361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.26218 | − | 15.1182i | −0.305200 | − | 0.736818i | −0.999847 | − | 0.0174674i | \(-0.994440\pi\) |
0.694648 | − | 0.719350i | \(-0.255560\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | −20.1614 | + | 8.35111i | −0.975677 | + | 0.404139i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.983074 | − | 2.37335i | 0.0474633 | − | 0.114586i | ||||
\(430\) | 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 | \(0.0135527\pi\) | ||||
−0.999094 | + | 0.0425643i | \(0.986447\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.38595 | + | 5.76019i | −0.114398 | + | 0.276180i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.8960 | − | 7.82699i | 0.903919 | − | 0.374416i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.32755 | + | 5.32755i | 0.254270 | + | 0.254270i | 0.822719 | − | 0.568449i | \(-0.192456\pi\) |
−0.568449 | + | 0.822719i | \(0.692456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.4241 | + | 18.4241i | −0.877337 | + | 0.877337i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.3439 | − | 34.6293i | −0.681500 | − | 1.64529i | −0.761240 | − | 0.648471i | \(-0.775409\pi\) |
0.0797396 | − | 0.996816i | \(-0.474591\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −44.7651 | − | 18.5423i | −2.12207 | − | 0.878989i | ||||
\(446\) | 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 | ||||||||
\(451\) | −6.63357 | − | 2.74771i | −0.312363 | − | 0.129385i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.91488 | + | 9.45136i | 0.183937 | + | 0.444064i | ||||
\(454\) | 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 | \(-0.175142\pi\) |
−0.522879 | + | 0.852407i | \(0.675142\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.38447 | + | 2.64453i | −0.298001 | + | 0.123436i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.1302 | − | 31.6991i | 0.611535 | − | 1.47637i | −0.249780 | − | 0.968303i | \(-0.580358\pi\) |
0.861314 | − | 0.508072i | \(-0.169642\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | −9.40713 | + | 22.7108i | −0.435310 | + | 1.05093i | 0.542239 | + | 0.840224i | \(0.317577\pi\) |
−0.977549 | + | 0.210707i | \(0.932423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.3789 | − | 11.7549i | 1.31041 | − | 0.542791i | ||||
\(470\) | 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 | ||||||||
\(475\) | −12.0197 | − | 29.0181i | −0.551501 | − | 1.33144i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.3378 | − | 5.11048i | −0.564908 | − | 0.233993i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.80923 | 0.402504 | 0.201252 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201252 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.2404 | −0.512516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.8523 | − | 11.1226i | −1.22182 | − | 0.506095i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.1907 | − | 29.4308i | −0.553549 | − | 1.33639i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.25173 | + | 5.25173i | −0.237979 | + | 0.237979i | −0.816013 | − | 0.578034i | \(-0.803820\pi\) |
0.578034 | + | 0.816013i | \(0.303820\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.64836 | + | 1.64836i | 0.0745412 | + | 0.0745412i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0947 | − | 4.18136i | 0.455568 | − | 0.188702i | −0.143086 | − | 0.989710i | \(-0.545703\pi\) |
0.598654 | + | 0.801008i | \(0.295703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.806893 | + | 1.94801i | −0.0363406 | + | 0.0877341i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 6.83349i | − | 0.307143i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 37.0598i | − | 1.66236i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9489 | − | 26.4331i | 0.490142 | − | 1.18331i | −0.464506 | − | 0.885570i | \(-0.653768\pi\) |
0.954648 | − | 0.297737i | \(-0.0962319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.44568 | − | 0.598822i | 0.0645884 | − | 0.0267534i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.9802 | − | 19.9802i | −0.890873 | − | 0.890873i | 0.103733 | − | 0.994605i | \(-0.466921\pi\) |
−0.994605 | + | 0.103733i | \(0.966921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.1932 | + | 25.1932i | −1.12108 | + | 1.12108i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.55775 | + | 6.17495i | 0.113594 | + | 0.274239i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.1252 | + | 14.1351i | 1.51257 | + | 0.626528i | 0.976087 | − | 0.217382i | \(-0.0697517\pi\) |
0.536485 | + | 0.843910i | \(0.319752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.9795 | 0.839606 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.2856 | 0.763178 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.9007 | − | 13.6279i | −1.44978 | − | 0.600517i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.374195 | + | 0.903386i | 0.0164571 | + | 0.0397309i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1300 | − | 14.1300i | 0.620236 | − | 0.620236i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8690 | + | 28.8690i | 1.26478 | + | 1.26478i | 0.948751 | + | 0.316025i | \(0.102348\pi\) |
0.316025 | + | 0.948751i | \(0.397652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.1005 | + | 5.01220i | −0.529119 | + | 0.219168i | −0.631217 | − | 0.775606i | \(-0.717444\pi\) |
0.102098 | + | 0.994774i | \(0.467444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.0806 | + | 41.2363i | −0.745460 | + | 1.79970i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.96738i | − | 0.216382i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0047i | 0.608898i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.64512 | + | 11.2143i | −0.201581 | + | 0.486660i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.9731 | + | 7.44472i | −0.778503 | + | 0.322467i | ||||
\(534\) | 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 | ||||||||
\(539\) | 4.99196 | + | 12.0517i | 0.215019 | + | 0.519102i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8125 | + | 6.54974i | 0.679832 | + | 0.281596i | 0.695757 | − | 0.718278i | \(-0.255069\pi\) |
−0.0159249 | + | 0.999873i | \(0.505069\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.09375 | 0.132765 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.74779 | 0.117703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.7298 | + | 9.82921i | 1.01461 | + | 0.420267i | 0.827136 | − | 0.562002i | \(-0.189969\pi\) |
0.187478 | + | 0.982269i | \(0.439969\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.48264 | + | 8.40783i | 0.148635 | + | 0.358838i | ||||
\(550\) | 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 | ||||||||
\(555\) | 16.0280 | − | 6.63901i | 0.680350 | − | 0.281810i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.2141 | + | 27.0732i | −0.475156 | + | 1.14713i | 0.486700 | + | 0.873569i | \(0.338201\pi\) |
−0.961855 | + | 0.273558i | \(0.911799\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.2874i | − | 0.858067i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.34086i | 0.0566113i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.4436 | + | 27.6272i | −0.482289 | + | 1.16435i | 0.476230 | + | 0.879321i | \(0.342003\pi\) |
−0.958519 | + | 0.285028i | \(0.907997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 55.6166 | − | 23.0371i | 2.33981 | − | 0.969180i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.964608 | + | 0.964608i | 0.0405097 | + | 0.0405097i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.0917 | + | 28.0917i | −1.17767 | + | 1.17767i | −0.197328 | + | 0.980337i | \(0.563226\pi\) |
−0.980337 | + | 0.197328i | \(0.936774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.65653 | + | 3.99922i | 0.0693237 | + | 0.167362i | 0.954744 | − | 0.297429i | \(-0.0961293\pi\) |
−0.885420 | + | 0.464791i | \(0.846129\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.6217 | − | 8.54181i | −0.861486 | − | 0.356839i | ||||
\(574\) | 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 | ||||||||
\(579\) | −2.67127 | − | 1.10648i | −0.111014 | − | 0.0459837i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.2377 | − | 51.2724i | −0.881090 | − | 2.12714i | ||||
\(582\) | 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 | ||||||||
\(587\) | 21.3081 | − | 8.82612i | 0.879481 | − | 0.364293i | 0.103185 | − | 0.994662i | \(-0.467097\pi\) |
0.776295 | + | 0.630369i | \(0.217097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.75491 | + | 11.4794i | −0.195922 | + | 0.472999i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.74035i | 0.236126i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.4804i | 1.41594i | 0.706243 | + | 0.707970i | \(0.250389\pi\) | ||||
−0.706243 | + | 0.707970i | \(0.749611\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.86815 | + | 21.4096i | −0.363559 | + | 0.877709i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0278 | + | 8.70998i | −0.860609 | + | 0.356476i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.59550 | + | 5.59550i | 0.228626 | + | 0.228626i | 0.812118 | − | 0.583493i | \(-0.198314\pi\) |
−0.583493 | + | 0.812118i | \(0.698314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.2303 | + | 27.2303i | −1.11075 | + | 1.11075i | −0.117695 | + | 0.993050i | \(0.537551\pi\) |
−0.993050 | + | 0.117695i | \(0.962449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.90211 | − | 11.8347i | −0.199629 | − | 0.481948i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35.3258 | + | 14.6324i | 1.43620 | + | 0.594892i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.74369 | −0.151952 | −0.0759758 | − | 0.997110i | \(-0.524207\pi\) | ||||
−0.0759758 | + | 0.997110i | \(0.524207\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.49485 | −0.303707 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.44765 | + | 1.01385i | 0.0990215 | + | 0.0410160i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.85143 | − | 6.88397i | −0.115168 | − | 0.278041i | 0.855776 | − | 0.517347i | \(-0.173080\pi\) |
−0.970944 | + | 0.239306i | \(0.923080\pi\) | |||||||
\(614\) | 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 | \(-0.194544\pi\) |
−0.573833 | + | 0.818972i | \(0.694544\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.4332 | + | 12.6058i | −1.22321 | + | 0.506672i | −0.898430 | − | 0.439117i | \(-0.855291\pi\) |
−0.324783 | + | 0.945788i | \(0.605291\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.9681 | + | 28.8936i | −0.480264 | + | 1.15946i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 58.2458i | − | 2.33357i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 15.5590i | − | 0.622359i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.28351 | − | 3.09867i | 0.0512585 | − | 0.123749i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.42043 | − | 2.24522i | 0.216127 | − | 0.0895226i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1982 | + | 12.1982i | 0.485602 | + | 0.485602i | 0.906915 | − | 0.421313i | \(-0.138431\pi\) |
−0.421313 | + | 0.906915i | \(0.638431\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.1263 | − | 17.1263i | 0.680708 | − | 0.680708i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.98052 | + | 12.0240i | 0.197646 | + | 0.477159i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.6530 | + | 13.5253i | 1.29376 | + | 0.535893i | ||||
\(638\) | 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 | ||||||||
\(643\) | −19.8975 | − | 8.24179i | −0.784679 | − | 0.325025i | −0.0458768 | − | 0.998947i | \(-0.514608\pi\) |
−0.738802 | + | 0.673922i | \(0.764608\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.9826 | + | 28.9285i | 0.471814 | + | 1.13906i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.13152 | − | 6.13152i | 0.241055 | − | 0.241055i | −0.576232 | − | 0.817286i | \(-0.695477\pi\) |
0.817286 | + | 0.576232i | \(0.195477\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.29708 | + | 4.29708i | 0.168675 | + | 0.168675i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.3128 | − | 6.75699i | 0.639349 | − | 0.264827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.89002 | − | 19.0482i | 0.308760 | − | 0.745413i | −0.690986 | − | 0.722868i | \(-0.742823\pi\) |
0.999746 | − | 0.0225445i | \(-0.00717676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13.7803i | − | 0.538439i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7.91498i | − | 0.308793i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.4563 | − | 39.7290i | 0.641046 | − | 1.54762i | −0.184225 | − | 0.982884i | \(-0.558978\pi\) |
0.825271 | − | 0.564737i | \(-0.191022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1267 | + | 7.09412i | −0.666153 | + | 0.275929i | −0.690025 | − | 0.723786i | \(-0.742400\pi\) |
0.0238723 | + | 0.999715i | \(0.492400\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | 3.65168 | + | 8.81593i | 0.141394 | + | 0.341354i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.9745 | − | 4.95998i | −0.462959 | − | 0.191764i | ||||
\(670\) | 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 | ||||||||
\(675\) | 44.3710 | + | 18.3791i | 1.70784 | + | 0.707411i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.68980 | − | 6.49374i | −0.103377 | − | 0.249575i | 0.863725 | − | 0.503964i | \(-0.168126\pi\) |
−0.967102 | + | 0.254389i | \(0.918126\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | −17.9833 | + | 7.44891i | −0.688110 | + | 0.285025i | −0.699213 | − | 0.714914i | \(-0.746466\pi\) |
0.0111024 | + | 0.999938i | \(0.496466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.68795 | − | 8.90351i | 0.140909 | − | 0.340186i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.91573i | − | 0.187547i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.1146i | 0.690112i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.81928 | − | 6.80634i | 0.107250 | − | 0.258926i | −0.861139 | − | 0.508370i | \(-0.830248\pi\) |
0.968389 | + | 0.249445i | \(0.0802481\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.58926 | − | 3.14357i | 0.288292 | − | 0.119414i | ||||
\(694\) | 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 | ||||||||
\(699\) | 0.482204 | + | 1.16414i | 0.0182386 | + | 0.0440319i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2169 | − | 17.0726i | −1.55674 | − | 0.644823i | −0.572221 | − | 0.820100i | \(-0.693918\pi\) |
−0.984519 | + | 0.175277i | \(0.943918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.6755 | −0.553498 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.08901 | −0.154001 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.5690 | − | 16.3900i | −1.48815 | − | 0.616410i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.461208 | − | 1.11345i | −0.0173210 | − | 0.0418167i | 0.914982 | − | 0.403494i | \(-0.132204\pi\) |
−0.932303 | + | 0.361677i | \(0.882204\pi\) | |||||||
\(710\) | 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 | ||||||||
\(715\) | −8.56379 | + | 3.54724i | −0.320267 | + | 0.132659i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.563882 | + | 1.36133i | −0.0210586 | + | 0.0508398i | ||||
\(718\) | 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 | ||||||||
\(723\) | −6.96215 | + | 16.8081i | −0.258925 | + | 0.625101i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.5384 | − | 5.60778i | 0.502802 | − | 0.208268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0891 | + | 32.0891i | 1.19012 | + | 1.19012i | 0.977034 | + | 0.213086i | \(0.0683513\pi\) |
0.213086 | + | 0.977034i | \(0.431649\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.0439 | + | 11.0439i | −0.409034 | + | 0.409034i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.05233 | + | 9.78320i | 0.149881 | + | 0.361845i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.3414 | − | 15.8815i | −1.41617 | − | 0.586597i | −0.462276 | − | 0.886736i | \(-0.652967\pi\) |
−0.953895 | + | 0.300139i | \(0.902967\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −54.5496 | −2.01209 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.41320 | −0.236233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.5302 | + | 17.6166i | 1.56450 | + | 0.648036i | 0.985863 | − | 0.167551i | \(-0.0535860\pi\) |
0.578634 | + | 0.815587i | \(0.303586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.47757 | − | 8.39561i | −0.127752 | − | 0.308420i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.8955 | + | 21.8955i | −0.803267 | + | 0.803267i | −0.983605 | − | 0.180337i | \(-0.942281\pi\) |
0.180337 | + | 0.983605i | \(0.442281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.1859 | + | 46.1859i | 1.69212 | + | 1.69212i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.3820 | + | 8.85671i | −0.782326 | + | 0.324050i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.5663 | − | 35.1662i | 0.532242 | − | 1.28495i | ||||
\(750\) | 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 | ||||||||
\(755\) | 14.1261 | − | 34.1034i | 0.514102 | − | 1.24115i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.8571 | + | 17.7520i | −1.55767 | + | 0.645207i | −0.984682 | − | 0.174358i | \(-0.944215\pi\) |
−0.572986 | + | 0.819565i | \(0.694215\pi\) | |||||||
\(758\) | 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 | \(-0.515097\pi\) |
0.998875 | + | 0.0474116i | \(0.0150972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.26405 | + | 3.05169i | 0.0457618 | + | 0.110479i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.92839 | + | 3.69826i | 0.322807 | + | 0.133711i | ||||
\(766\) | 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 | ||||||||
\(771\) | −23.8380 | − | 9.87404i | −0.858506 | − | 0.355605i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.46163 | + | 3.52868i | 0.0525711 | + | 0.126918i | 0.947983 | − | 0.318321i | \(-0.103119\pi\) |
−0.895412 | + | 0.445239i | \(0.853119\pi\) | |||||||
\(774\) | 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 | ||||||||
\(779\) | −23.4659 | + | 9.71990i | −0.840754 | + | 0.348252i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.96100 | + | 7.14848i | −0.105953 | + | 0.255793i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.06459i | 0.288205i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.9261i | 0.961032i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.73636 | + | 11.4346i | −0.168833 | + | 0.407599i | −0.985538 | − | 0.169457i | \(-0.945799\pi\) |
0.816705 | + | 0.577056i | \(0.195799\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.4929 | − | 7.66000i | 0.658364 | − | 0.272703i | ||||
\(790\) | 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 | ||||||||
\(795\) | −10.6992 | − | 25.8302i | −0.379463 | − | 0.916104i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.35275 | + | 0.560326i | 0.0479167 | + | 0.0198478i | 0.406513 | − | 0.913645i | \(-0.366745\pi\) |
−0.358596 | + | 0.933493i | \(0.616745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.38284 | −0.0489215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.2901 | −0.858248 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.66097 | − | 1.51642i | −0.129193 | − | 0.0535134i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.1338 | + | 96.8915i | 1.41453 | + | 3.41498i | ||||
\(806\) | 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 | \(-0.225019\pi\) |
−0.649492 | + | 0.760368i | \(0.725019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7904 | − | 8.61166i | 0.730049 | − | 0.302396i | 0.0134769 | − | 0.999909i | \(-0.495710\pi\) |
0.716572 | + | 0.697513i | \(0.245710\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.34223 | − | 5.65465i | 0.0821457 | − | 0.198317i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 8.41143i | − | 0.294640i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 26.4875i | − | 0.926680i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.51727 | − | 20.5625i | 0.297617 | − | 0.718512i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.95402 | + | 1.63781i | −0.137996 | + | 0.0571599i | −0.450613 | − | 0.892719i | \(-0.648795\pi\) |
0.312617 | + | 0.949879i | \(0.398795\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.07415 | + | 6.07415i | 0.211731 | + | 0.211731i | 0.805003 | − | 0.593271i | \(-0.202164\pi\) |
−0.593271 | + | 0.805003i | \(0.702164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.58938 | − | 6.58938i | 0.229413 | − | 0.229413i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.3999 | − | 25.1075i | −0.361639 | − | 0.873074i | −0.995061 | − | 0.0992672i | \(-0.968350\pi\) |
0.633422 | − | 0.773807i | \(-0.281650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.9536 | + | 10.3361i | 0.866674 | + | 0.358988i | 0.771314 | − | 0.636455i | \(-0.219600\pi\) |
0.0953602 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.0387 | 0.625757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.4479 | −0.639181 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.21648 | − | 2.16073i | −0.180524 | − | 0.0747753i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.27064 | − | 17.5529i | −0.251310 | − | 0.606716i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.6105 | + | 19.6105i | −0.677028 | + | 0.677028i | −0.959327 | − | 0.282298i | \(-0.908903\pi\) |
0.282298 | + | 0.959327i | \(0.408903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.7662 | − | 18.7662i | −0.647109 | − | 0.647109i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.41492 | + | 1.41451i | −0.117616 | + | 0.0487181i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.22915 | − | 22.2811i | 0.317492 | − | 0.766494i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 45.9639i | 1.57934i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.0618i | 0.928758i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1610 | − | 24.5307i | 0.348313 | − | 0.840902i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.3247 | + | 9.24721i | −0.764385 | + | 0.316619i | −0.730596 | − | 0.682810i | \(-0.760757\pi\) |
−0.0337892 | + | 0.999429i | \(0.510757\pi\) | |||||||
\(854\) | 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 | \(-0.923880\pi\) |
0.236865 | + | 0.971543i | \(0.423880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.2217 | + | 29.5057i | 0.416998 | + | 1.00672i | 0.983212 | + | 0.182464i | \(0.0584074\pi\) |
−0.566215 | + | 0.824258i | \(0.691593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 33.3464 | + | 13.8125i | 1.13644 | + | 0.470729i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.4436 | −0.900151 | −0.450076 | − | 0.892990i | \(-0.648603\pi\) | ||||
−0.450076 | + | 0.892990i | \(0.648603\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.1041 | −2.45161 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7320 | + | 6.10220i | 0.500325 | + | 0.207241i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.61438 | + | 13.5543i | 0.190455 | + | 0.459799i | ||||
\(870\) | 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 | ||||||||
\(875\) | 69.1541 | − | 28.6446i | 2.33784 | − | 0.968363i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6478 | − | 30.5345i | 0.427086 | − | 1.03108i | −0.553121 | − | 0.833101i | \(-0.686563\pi\) |
0.980207 | − | 0.197975i | \(-0.0634366\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.9063i | 1.00871i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.9951i | − | 0.471507i | −0.971813 | − | 0.235753i | \(-0.924244\pi\) | ||
0.971813 | − | 0.235753i | \(-0.0757557\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.4231 | + | 44.4774i | −0.619987 | + | 1.49678i | 0.231730 | + | 0.972780i | \(0.425561\pi\) |
−0.851717 | + | 0.524002i | \(0.824439\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.4782 | + | 9.72498i | −0.789210 | + | 0.326902i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.0611 | − | 11.0611i | −0.371395 | − | 0.371395i | 0.496590 | − | 0.867985i | \(-0.334585\pi\) |
−0.867985 | + | 0.496590i | \(0.834585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.0627 | + | 11.0627i | −0.371031 | + | 0.371031i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.108994 | − | 0.263134i | −0.00365142 | − | 0.00881531i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.19568 | + | 1.32369i | 0.106939 | + | 0.0442958i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.0972 | 1.40716 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.4414 | 0.548961 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.35569 | − | 2.21840i | −0.178622 | − | 0.0739878i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.61832 | − | 8.73540i | −0.120544 | − | 0.291019i | ||||
\(902\) | 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 | ||||||||
\(907\) | 49.4995 | − | 20.5034i | 1.64360 | − | 0.680803i | 0.646950 | − | 0.762533i | \(-0.276044\pi\) |
0.996655 | + | 0.0817295i | \(0.0260444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.83508 | + | 16.5013i | −0.226705 | + | 0.547315i | ||||
\(910\) | 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 | ||||||||
\(915\) | −7.29121 | + | 17.6025i | −0.241040 | + | 0.581922i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.3043 | − | 6.33925i | 0.505393 | − | 0.209341i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.90286 | − | 9.90286i | −0.326665 | − | 0.326665i | 0.524652 | − | 0.851317i | \(-0.324196\pi\) |
−0.851317 | + | 0.524652i | \(0.824196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.01484 | − | 2.01484i | 0.0663913 | − | 0.0663913i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.02259 | + | 19.3683i | 0.264067 | + | 0.637514i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.6711 | − | 15.6039i | −1.23862 | − | 0.513053i | ||||
\(926\) | 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 | ||||||||
\(931\) | 42.6322 | + | 17.6588i | 1.39721 | + | 0.578744i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.61869 | + | 20.8074i | 0.282163 | + | 0.681203i | ||||
\(934\) | 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 | \(-0.251270\pi\) |
−0.709922 | + | 0.704280i | \(0.751270\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.6675 | − | 5.24707i | 0.413389 | − | 0.171232i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.5189 | + | 39.8801i | −0.538500 | + | 1.30005i | 0.387270 | + | 0.921966i | \(0.373418\pi\) |
−0.925770 | + | 0.378087i | \(0.876582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 45.9540i | − | 1.49647i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 88.6339i | 2.88326i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.29136 | − | 20.0171i | 0.269433 | − | 0.650469i | −0.730024 | − | 0.683422i | \(-0.760491\pi\) |
0.999457 | + | 0.0329528i | \(0.0104911\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.91912 | + | 4.10863i | −0.321988 | + | 0.133372i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.2400 | + | 20.2400i | 0.656328 | + | 0.656328i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.0721 | − | 35.0721i | 1.13610 | − | 1.13610i | 0.146953 | − | 0.989144i | \(-0.453053\pi\) |
0.989144 | − | 0.146953i | \(-0.0469465\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.8215 | + | 74.4097i | 0.997360 | + | 2.40784i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.44568 | + | 0.598822i | 0.0467323 | + | 0.0193572i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.5848 | 0.374091 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3431 | −0.559456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6653 | − | 6.07456i | −0.472582 | − | 0.195750i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.99252 | + | 9.63879i | 0.128524 | + | 0.310284i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5945 | − | 17.5945i | 0.565802 | − | 0.565802i | −0.365148 | − | 0.930950i | \(-0.618981\pi\) |
0.930950 | + | 0.365148i | \(0.118981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.35398 | + | 3.35398i | 0.107745 | + | 0.107745i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.07159 | + | 0.858080i | −0.0664804 | + | 0.0275371i | −0.415676 | − | 0.909513i | \(-0.636455\pi\) |
0.349195 | + | 0.937050i | \(0.386455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.3668 | − | 73.3120i | 0.973516 | − | 2.35028i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 25.2485i | − | 0.808600i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.3535i | 1.25903i | 0.776989 | + | 0.629515i | \(0.216746\pi\) | ||||
−0.776989 | + | 0.629515i | \(0.783254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.65371 | + | 11.2351i | −0.148733 | + | 0.359074i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.27264 | − | 0.527144i | 0.0406322 | − | 0.0168304i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.0511 | − | 30.0511i | −0.958481 | − | 0.958481i | 0.0406903 | − | 0.999172i | \(-0.487044\pi\) |
−0.999172 | + | 0.0406903i | \(0.987044\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.6463 | − | 14.6463i | 0.466669 | − | 0.466669i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.88104 | − | 4.54124i | −0.0598743 | − | 0.144549i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.2749 | + | 18.3393i | 1.40786 | + | 0.583154i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.5749 | 1.19360 | 0.596802 | − | 0.802388i | \(-0.296438\pi\) | ||||
0.596802 | + | 0.802388i | \(0.296438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.8786 | 1.04337 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 75.8747 | + | 31.4283i | 2.40539 | + | 0.996345i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.8090 | − | 52.6516i | −0.690698 | − | 1.66749i | −0.743369 | − | 0.668881i | \(-0.766773\pi\) |
0.0526708 | − | 0.998612i | \(-0.483227\pi\) | |||||||
\(998\) | 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.e.641.3 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.e.641.2 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.b.641.3 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.b.641.2 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.c.129.3 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.h.129.3 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.h.129.2 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.c.129.2 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.h.897.2 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.b.385.2 | ✓ | 16 | ||
32.11 | odd | 8 | inner | 1024.2.g.e.385.2 | yes | 16 | |
32.13 | even | 8 | 1024.2.g.c.897.2 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.c.897.3 | yes | 16 | ||
32.21 | even | 8 | inner | 1024.2.g.e.385.3 | yes | 16 | |
32.27 | odd | 8 | 1024.2.g.b.385.3 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.h.897.3 | yes | 16 | ||
64.11 | odd | 16 | 4096.2.a.n.1.4 | 8 | |||
64.21 | even | 16 | 4096.2.a.n.1.3 | 8 | |||
64.43 | odd | 16 | 4096.2.a.o.1.5 | 8 | |||
64.53 | even | 16 | 4096.2.a.o.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.b.385.2 | ✓ | 16 | 32.5 | even | 8 | ||
1024.2.g.b.385.3 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.b.641.2 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.b.641.3 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.c.129.2 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.c.129.3 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.c.897.2 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.c.897.3 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.e.385.2 | yes | 16 | 32.11 | odd | 8 | inner | |
1024.2.g.e.385.3 | yes | 16 | 32.21 | even | 8 | inner | |
1024.2.g.e.641.2 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.e.641.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.h.129.2 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.h.129.3 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.h.897.2 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.h.897.3 | yes | 16 | 32.29 | even | 8 | ||
4096.2.a.n.1.3 | 8 | 64.21 | even | 16 | |||
4096.2.a.n.1.4 | 8 | 64.11 | odd | 16 | |||
4096.2.a.o.1.5 | 8 | 64.43 | odd | 16 | |||
4096.2.a.o.1.6 | 8 | 64.53 | even | 16 |