Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,2,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, 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("256.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.04417029174\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(0.500000 - 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.97 |
Dual form | 256.2.g.d.161.2 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 2.27882 | − | 0.943920i | 1.31568 | − | 0.544972i | 0.389143 | − | 0.921177i | \(-0.372771\pi\) |
0.926536 | + | 0.376205i | \(0.122771\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | − | 1.70711i | 0.316228 | − | 0.763441i | −0.683220 | − | 0.730213i | \(-0.739421\pi\) |
0.999448 | − | 0.0332288i | \(-0.0105790\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.665096 | − | 0.665096i | −0.251383 | − | 0.251383i | 0.570155 | − | 0.821537i | \(-0.306883\pi\) |
−0.821537 | + | 0.570155i | \(0.806883\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.18073 | − | 2.18073i | 0.726911 | − | 0.726911i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.69304 | − | 1.52971i | −1.11349 | − | 0.461224i | −0.251353 | − | 0.967895i | \(-0.580876\pi\) |
−0.862139 | + | 0.506672i | \(0.830876\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.76652 | + | 4.26475i | 0.489944 | + | 1.18283i | 0.954748 | + | 0.297416i | \(0.0961249\pi\) |
−0.464804 | + | 0.885414i | \(0.653875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.55765i | − | 1.17678i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.61706i | 0.877266i | 0.898666 | + | 0.438633i | \(0.144537\pi\) | ||||
−0.898666 | + | 0.438633i | \(0.855463\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.194802 | − | 0.470294i | −0.0446907 | − | 0.107893i | 0.899958 | − | 0.435977i | \(-0.143597\pi\) |
−0.944649 | + | 0.328084i | \(0.893597\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.14343 | − | 0.887839i | −0.467736 | − | 0.193742i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.33490 | + | 1.33490i | −0.278347 | + | 0.278347i | −0.832449 | − | 0.554102i | \(-0.813062\pi\) |
0.554102 | + | 0.832449i | \(0.313062\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.12132 | + | 1.12132i | 0.224264 | + | 0.224264i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.0793096 | − | 0.191470i | 0.0152631 | − | 0.0368485i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.73838 | − | 2.37691i | 1.06559 | − | 0.441382i | 0.220158 | − | 0.975464i | \(-0.429343\pi\) |
0.845433 | + | 0.534082i | \(0.179343\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17157 | 0.210421 | 0.105210 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105210 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.85970 | −1.71635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.60568 | + | 0.665096i | −0.271410 | + | 0.112422i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.510925 | + | 1.23348i | −0.0839955 | + | 0.202783i | −0.960297 | − | 0.278980i | \(-0.910004\pi\) |
0.876301 | + | 0.481763i | \(0.160004\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.05117 | + | 8.05117i | 1.28922 | + | 1.28922i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.66981 | − | 1.66981i | 0.260780 | − | 0.260780i | −0.564591 | − | 0.825371i | \(-0.690966\pi\) |
0.825371 | + | 0.564591i | \(0.190966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.54960 | + | 1.05608i | 0.388811 | + | 0.161051i | 0.568521 | − | 0.822669i | \(-0.307516\pi\) |
−0.179710 | + | 0.983720i | \(0.557516\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.18073 | − | 5.26475i | −0.325084 | − | 0.784823i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.49824i | − | 0.218540i | −0.994012 | − | 0.109270i | \(-0.965149\pi\) | ||
0.994012 | − | 0.109270i | \(-0.0348513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.11529i | − | 0.873614i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.41421 | + | 8.24264i | 0.478086 | + | 1.15420i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.59495 | − | 1.90329i | −0.631164 | − | 0.261437i | 0.0440833 | − | 0.999028i | \(-0.485963\pi\) |
−0.675248 | + | 0.737591i | \(0.735963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.22274 | + | 5.22274i | −0.704235 | + | 0.704235i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.887839 | − | 0.887839i | −0.117597 | − | 0.117597i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.04784 | + | 4.94392i | −0.266606 | + | 0.643644i | −0.999319 | − | 0.0368939i | \(-0.988254\pi\) |
0.732713 | + | 0.680537i | \(0.238254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.7102 | + | 5.67897i | −1.75542 | + | 0.727117i | −0.758244 | + | 0.651971i | \(0.773942\pi\) |
−0.997173 | + | 0.0751463i | \(0.976058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.90079 | −0.365466 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.52951 | 1.05796 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.40617 | − | 1.41088i | 0.416130 | − | 0.172367i | −0.164788 | − | 0.986329i | \(-0.552694\pi\) |
0.580918 | + | 0.813962i | \(0.302694\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.78197 | + | 4.30205i | −0.214524 | + | 0.517906i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.66157 | − | 9.66157i | −1.14662 | − | 1.14662i | −0.987214 | − | 0.159403i | \(-0.949043\pi\) |
−0.159403 | − | 0.987214i | \(-0.550957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.55765 | + | 7.55765i | −0.884556 | + | 0.884556i | −0.993994 | − | 0.109438i | \(-0.965095\pi\) |
0.109438 | + | 0.993994i | \(0.465095\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.61373 | + | 1.49685i | 0.417277 | + | 0.172842i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.43882 | + | 3.47363i | 0.163969 | + | 0.395856i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.2176i | 1.93714i | 0.248750 | + | 0.968568i | \(0.419980\pi\) | ||||
−0.248750 | + | 0.968568i | \(0.580020\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.74088i | 0.971208i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.82981 | − | 11.6602i | −0.530140 | − | 1.27987i | −0.931430 | − | 0.363921i | \(-0.881438\pi\) |
0.401290 | − | 0.915951i | \(-0.368562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.17471 | + | 2.55765i | 0.669741 | + | 0.277416i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.8331 | − | 10.8331i | 1.16143 | − | 1.16143i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.43882 | − | 5.43882i | −0.576514 | − | 0.576514i | 0.357427 | − | 0.933941i | \(-0.383654\pi\) |
−0.933941 | + | 0.357427i | \(0.883654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.66157 | − | 4.01138i | 0.174179 | − | 0.420506i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.66981 | − | 1.10587i | 0.276846 | − | 0.114673i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.940588 | −0.0965023 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.15862 | 0.625313 | 0.312657 | − | 0.949866i | \(-0.398781\pi\) | ||||
0.312657 | + | 0.949866i | \(0.398781\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.3894 | + | 4.71765i | −1.14468 | + | 0.474141i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.09671 | − | 7.47612i | 0.308134 | − | 0.743902i | −0.691631 | − | 0.722251i | \(-0.743108\pi\) |
0.999766 | − | 0.0216512i | \(-0.00689233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.72764 | − | 4.72764i | −0.465828 | − | 0.465828i | 0.434732 | − | 0.900560i | \(-0.356843\pi\) |
−0.900560 | + | 0.434732i | \(0.856843\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.03127 | + | 3.03127i | −0.295822 | + | 0.295822i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.57774 | − | 1.06774i | −0.249200 | − | 0.103222i | 0.254587 | − | 0.967050i | \(-0.418060\pi\) |
−0.503787 | + | 0.863828i | \(0.668060\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.46094 | − | 8.35544i | −0.331498 | − | 0.800306i | −0.998474 | − | 0.0552270i | \(-0.982412\pi\) |
0.666976 | − | 0.745079i | \(-0.267588\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.29316i | 0.312573i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.7757i | − | 1.10776i | −0.832596 | − | 0.553881i | \(-0.813146\pi\) | ||
0.832596 | − | 0.553881i | \(-0.186854\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.33490 | + | 3.22274i | 0.124480 | + | 0.300522i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.1526 | + | 5.44798i | 1.21596 | + | 0.503666i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.40569 | − | 2.40569i | 0.220529 | − | 0.220529i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.52035 | + | 3.52035i | 0.320032 | + | 0.320032i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.22903 | − | 5.38136i | 0.200985 | − | 0.485221i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2426 | − | 4.65685i | 1.00557 | − | 0.416522i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0590 | 1.15880 | 0.579400 | − | 0.815043i | \(-0.303287\pi\) | ||||
0.579400 | + | 0.815043i | \(0.303287\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.80695 | 0.599319 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.52146 | − | 2.70128i | 0.569783 | − | 0.236012i | −0.0791431 | − | 0.996863i | \(-0.525218\pi\) |
0.648926 | + | 0.760851i | \(0.275218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.183228 | + | 0.442353i | −0.0158879 | + | 0.0383568i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.270780 | − | 0.270780i | −0.0233050 | − | 0.0233050i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.88118 | − | 4.88118i | 0.417027 | − | 0.417027i | −0.467151 | − | 0.884178i | \(-0.654719\pi\) |
0.884178 | + | 0.467151i | \(0.154719\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7837 | + | 4.88098i | 0.999482 | + | 0.413999i | 0.821607 | − | 0.570054i | \(-0.193078\pi\) |
0.177875 | + | 0.984053i | \(0.443078\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.41421 | − | 3.41421i | −0.119098 | − | 0.287529i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 18.4522i | − | 1.54305i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 11.4768i | − | 0.953093i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.77235 | − | 13.9357i | −0.476095 | − | 1.14940i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.73838 | + | 2.37691i | 0.470106 | + | 0.194724i | 0.605144 | − | 0.796116i | \(-0.293116\pi\) |
−0.135038 | + | 0.990840i | \(0.543116\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1504 | − | 11.1504i | 0.907405 | − | 0.907405i | −0.0886573 | − | 0.996062i | \(-0.528258\pi\) |
0.996062 | + | 0.0886573i | \(0.0282576\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.88784 | + | 7.88784i | 0.637694 | + | 0.637694i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.828427 | − | 2.00000i | 0.0665409 | − | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.22496 | + | 0.507395i | −0.0977624 | + | 0.0404945i | −0.431029 | − | 0.902338i | \(-0.641849\pi\) |
0.333266 | + | 0.942833i | \(0.391849\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.2676 | −0.972886 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.77568 | 0.139943 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.3218 | + | 8.83176i | −1.67005 | + | 0.691757i | −0.998776 | − | 0.0494542i | \(-0.984252\pi\) |
−0.671272 | + | 0.741211i | \(0.734252\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.97186 | + | 16.8316i | −0.542759 | + | 1.31034i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.8863 | + | 10.8863i | 0.842404 | + | 0.842404i | 0.989171 | − | 0.146767i | \(-0.0468867\pi\) |
−0.146767 | + | 0.989171i | \(0.546887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.87515 | + | 5.87515i | −0.451935 | + | 0.451935i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.45040 | − | 0.600774i | −0.110915 | − | 0.0459423i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.735246 | − | 1.77504i | −0.0558997 | − | 0.134954i | 0.893462 | − | 0.449138i | \(-0.148269\pi\) |
−0.949362 | + | 0.314184i | \(0.898269\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.49157i | − | 0.112752i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.1993i | 0.992121i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.87980 | + | 4.53823i | 0.140503 | + | 0.339203i | 0.978430 | − | 0.206578i | \(-0.0662329\pi\) |
−0.837928 | + | 0.545782i | \(0.816233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.87868 | − | 0.778175i | −0.139641 | − | 0.0578413i | 0.311768 | − | 0.950158i | \(-0.399079\pi\) |
−0.451410 | + | 0.892317i | \(0.649079\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.8827 | + | 25.8827i | −1.91331 | + | 1.91331i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.74441 | + | 1.74441i | 0.128251 | + | 0.128251i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.53304 | − | 13.3579i | 0.404616 | − | 0.976829i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.180095 | + | 0.0745976i | −0.0131000 | + | 0.00542618i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.4022 | −1.40389 | −0.701946 | − | 0.712231i | \(-0.747685\pi\) | ||||
−0.701946 | + | 0.712231i | \(0.747685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0461 | −1.29898 | −0.649492 | − | 0.760368i | \(-0.725018\pi\) | ||||
−0.649492 | + | 0.760368i | \(0.725018\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 19.4372 | − | 8.05117i | 1.39193 | − | 0.576556i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0865175 | − | 0.208872i | 0.00616412 | − | 0.0148815i | −0.920768 | − | 0.390112i | \(-0.872436\pi\) |
0.926932 | + | 0.375230i | \(0.122436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8992 | − | 11.8992i | −0.843513 | − | 0.843513i | 0.145801 | − | 0.989314i | \(-0.453424\pi\) |
−0.989314 | + | 0.145801i | \(0.953424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.43030 | − | 6.43030i | 0.453558 | − | 0.453558i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.39745 | − | 2.23570i | −0.378827 | − | 0.156915i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.66981 | − | 4.03127i | −0.116624 | − | 0.281556i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.82214i | 0.404667i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.03480i | 0.140750i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.73060 | + | 9.00647i | 0.256825 | + | 0.620031i | 0.998725 | − | 0.0504799i | \(-0.0160751\pi\) |
−0.741900 | + | 0.670511i | \(0.766075\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.1367 | − | 12.8973i | −2.13345 | − | 0.883706i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.60568 | − | 3.60568i | 0.245906 | − | 0.245906i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.779208 | − | 0.779208i | −0.0528961 | − | 0.0528961i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0887 | + | 24.3564i | −0.681733 | + | 1.64585i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.4259 | + | 6.38960i | −1.03766 | + | 0.429811i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.6174 | 1.51458 | 0.757288 | − | 0.653081i | \(-0.226524\pi\) | ||||
0.757288 | + | 0.653081i | \(0.226524\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.89060 | 0.326040 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.51294 | − | 3.94039i | 0.631396 | − | 0.261533i | −0.0439500 | − | 0.999034i | \(-0.513994\pi\) |
0.675346 | + | 0.737501i | \(0.263994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.53200 | − | 15.7697i | 0.431647 | − | 1.04209i | −0.547109 | − | 0.837061i | \(-0.684272\pi\) |
0.978756 | − | 0.205027i | \(-0.0657282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.55765 | + | 6.55765i | 0.431462 | + | 0.431462i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.4486 | − | 10.4486i | 0.684512 | − | 0.684512i | −0.276502 | − | 0.961013i | \(-0.589175\pi\) |
0.961013 | + | 0.276502i | \(0.0891751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.55765 | − | 1.05941i | −0.166843 | − | 0.0691084i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.2521 | + | 39.2360i | 1.05569 | + | 2.54865i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6733i | 0.755085i | 0.925992 | + | 0.377543i | \(0.123231\pi\) | ||||
−0.925992 | + | 0.377543i | \(0.876769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8288i | 0.890791i | 0.895334 | + | 0.445396i | \(0.146937\pi\) | ||||
−0.895334 | + | 0.445396i | \(0.853063\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.48861 | + | 20.4933i | 0.544545 | + | 1.31465i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.4395 | − | 4.32417i | −0.666953 | − | 0.276261i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.66157 | − | 1.66157i | 0.105723 | − | 0.105723i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.0126 | − | 22.0126i | −1.39499 | − | 1.39499i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.38745 | + | 13.0065i | −0.340053 | + | 0.820961i | 0.657656 | + | 0.753318i | \(0.271548\pi\) |
−0.997710 | + | 0.0676429i | \(0.978452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.97186 | − | 2.88784i | 0.438317 | − | 0.181557i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.4853 | 1.03235 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.9043 | −1.17922 | −0.589609 | − | 0.807689i | \(-0.700718\pi\) | ||||
−0.589609 | + | 0.807689i | \(0.700718\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.16020 | − | 0.480569i | 0.0720911 | − | 0.0298611i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.33046 | − | 17.6973i | 0.453744 | − | 1.09543i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.9086 | + | 13.9086i | 0.857643 | + | 0.857643i | 0.991060 | − | 0.133417i | \(-0.0425948\pi\) |
−0.133417 | + | 0.991060i | \(0.542595\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.49824 | + | 6.49824i | −0.399183 | + | 0.399183i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.5279 | − | 7.26031i | −1.07269 | − | 0.444324i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.05209 | − | 12.1968i | −0.308031 | − | 0.743653i | −0.999769 | − | 0.0215042i | \(-0.993154\pi\) |
0.691737 | − | 0.722149i | \(-0.256846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.41512i | − | 0.268199i | −0.990968 | − | 0.134100i | \(-0.957186\pi\) | ||
0.990968 | − | 0.134100i | \(-0.0428142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10.7096i | − | 0.648175i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.42579 | − | 5.85637i | −0.146280 | − | 0.353152i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0454 | + | 9.54573i | 1.38467 | + | 0.573547i | 0.945725 | − | 0.324969i | \(-0.105354\pi\) |
0.438941 | + | 0.898516i | \(0.355354\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.55489 | − | 2.55489i | 0.152957 | − | 0.152957i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.83509 | − | 5.83509i | −0.348092 | − | 0.348092i | 0.511306 | − | 0.859399i | \(-0.329162\pi\) |
−0.859399 | + | 0.511306i | \(0.829162\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.31992 | + | 3.18656i | −0.0784609 | + | 0.189421i | −0.958243 | − | 0.285957i | \(-0.907689\pi\) |
0.879782 | + | 0.475378i | \(0.157689\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.14343 | + | 0.887839i | −0.126966 | + | 0.0525911i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.22117 | −0.131111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.91688 | 0.230405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0344 | − | 5.81324i | 0.822712 | − | 0.340778i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.89663 | + | 6.99307i | −0.169223 | + | 0.408540i | −0.985626 | − | 0.168943i | \(-0.945965\pi\) |
0.816403 | + | 0.577482i | \(0.195965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.99176 | + | 6.99176i | 0.407076 | + | 0.407076i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.585786 | + | 0.585786i | −0.0339908 | + | 0.0339908i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.05117 | − | 3.33490i | −0.465611 | − | 0.192862i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.993336 | − | 2.39813i | −0.0572550 | − | 0.138226i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 19.9598i | − | 1.14666i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.4205i | 1.57009i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.14481 | + | 7.59225i | 0.179484 | + | 0.433313i | 0.987859 | − | 0.155356i | \(-0.0496524\pi\) |
−0.808375 | + | 0.588668i | \(0.799652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.2360 | − | 6.31095i | −0.866744 | − | 0.359017i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0543 | + | 15.0543i | −0.853651 | + | 0.853651i | −0.990581 | − | 0.136930i | \(-0.956277\pi\) |
0.136930 | + | 0.990581i | \(0.456277\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.3365 | + | 18.3365i | 1.03644 | + | 1.03644i | 0.999311 | + | 0.0371274i | \(0.0118208\pi\) |
0.0371274 | + | 0.999311i | \(0.488179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.05117 | + | 4.95196i | −0.115570 | + | 0.279012i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.52348 | − | 3.94476i | 0.534892 | − | 0.221560i | −0.0988523 | − | 0.995102i | \(-0.531517\pi\) |
0.633744 | + | 0.773543i | \(0.281517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.8280 | −1.39010 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.88208 | −0.384120 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.70108 | − | 0.704611i | 0.0946507 | − | 0.0392056i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.80132 | + | 6.76299i | −0.155389 | + | 0.375143i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.7737 | − | 15.7737i | −0.872289 | − | 0.872289i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.996470 | + | 0.996470i | −0.0549372 | + | 0.0549372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.57421 | − | 3.13734i | −0.416316 | − | 0.172444i | 0.164685 | − | 0.986346i | \(-0.447339\pi\) |
−0.581002 | + | 0.813902i | \(0.697339\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.57570 | + | 3.80408i | 0.0863480 | + | 0.208462i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 6.81234i | − | 0.372198i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.8910i | − | 0.920110i | −0.887890 | − | 0.460055i | \(-0.847830\pi\) | ||
0.887890 | − | 0.460055i | \(-0.152170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.1153 | − | 26.8347i | −0.603700 | − | 1.45746i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.32666 | − | 1.79216i | −0.234302 | − | 0.0970510i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.72293 | + | 8.72293i | −0.470994 | + | 0.470994i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.08402 | + | 6.08402i | 0.327553 | + | 0.327553i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6582 | − | 28.1455i | 0.625847 | − | 1.51093i | −0.218892 | − | 0.975749i | \(-0.570244\pi\) |
0.844739 | − | 0.535179i | \(-0.179756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.99044 | + | 4.13818i | −0.534776 | + | 0.221512i | −0.633694 | − | 0.773584i | \(-0.718462\pi\) |
0.0989174 | + | 0.995096i | \(0.468462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.956675 | 0.0510636 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.673711 | 0.0358580 | 0.0179290 | − | 0.999839i | \(-0.494293\pi\) | ||||
0.0179290 | + | 0.999839i | \(0.494293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.3251 | + | 9.66157i | −1.23797 | + | 0.512783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.21137 | − | 7.75293i | 0.169964 | − | 0.410328i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.92568 | + | 3.92568i | 0.207190 | + | 0.207190i | 0.803072 | − | 0.595882i | \(-0.203198\pi\) |
−0.595882 | + | 0.803072i | \(0.703198\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.2518 | − | 13.2518i | 0.697463 | − | 0.697463i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.3452 | + | 4.69933i | 0.595467 | + | 0.246651i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.55765 | + | 18.2458i | 0.395585 | + | 0.955027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.4759i | − | 0.860033i | −0.902821 | − | 0.430016i | \(-0.858508\pi\) | ||
0.902821 | − | 0.430016i | \(-0.141492\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.28281i | − | 0.379128i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.79021 | + | 4.32195i | 0.0929431 | + | 0.224384i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6790 | + | 5.25180i | 0.656492 | + | 0.271928i | 0.685962 | − | 0.727638i | \(-0.259382\pi\) |
−0.0294695 | + | 0.999566i | \(0.509382\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.2243 | − | 21.2243i | 1.09602 | − | 1.09602i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.2739 | + | 20.2739i | 1.04416 | + | 1.04416i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.06746 | − | 12.2339i | 0.260298 | − | 0.628414i | −0.738659 | − | 0.674079i | \(-0.764541\pi\) |
0.998957 | + | 0.0456649i | \(0.0145406\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.7592 | − | 12.3267i | 1.52461 | − | 0.631514i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.5667 | 0.744322 | 0.372161 | − | 0.928168i | \(-0.378617\pi\) | ||||
0.372161 | + | 0.928168i | \(0.378617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.94725 | 0.354065 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.86303 | − | 3.25697i | 0.399700 | − | 0.165561i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.2795 | + | 34.4739i | −0.724002 | + | 1.74789i | −0.0623850 | + | 0.998052i | \(0.519871\pi\) |
−0.661617 | + | 0.749842i | \(0.730129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.82843 | − | 4.82843i | −0.244184 | − | 0.244184i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.3115 | − | 12.3115i | 0.621032 | − | 0.621032i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.3923 | + | 12.1747i | 1.47889 | + | 0.612576i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.88405 | − | 21.4480i | −0.445877 | − | 1.07644i | −0.973852 | − | 0.227183i | \(-0.927048\pi\) |
0.527975 | − | 0.849260i | \(-0.322952\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.18100i | 0.0591238i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.51509i | − | 0.125598i | −0.998026 | − | 0.0627989i | \(-0.979997\pi\) | ||
0.998026 | − | 0.0627989i | \(-0.0200027\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.06961 | + | 4.99647i | 0.103094 | + | 0.248892i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.9216 | + | 6.18073i | 0.741461 | + | 0.307123i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.77373 | − | 3.77373i | 0.187057 | − | 0.187057i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.32666 | − | 5.32666i | −0.263386 | − | 0.263386i | 0.563042 | − | 0.826428i | \(-0.309631\pi\) |
−0.826428 | + | 0.563042i | \(0.809631\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.51590 | − | 15.7308i | 0.321406 | − | 0.775942i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.65019 | − | 1.92617i | 0.228821 | − | 0.0947807i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.3204 | −1.14475 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.4603 | 1.54062 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5509 | + | 4.37032i | −0.515444 | + | 0.213504i | −0.625214 | − | 0.780453i | \(-0.714988\pi\) |
0.109770 | + | 0.993957i | \(0.464988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.72505 | + | 4.16464i | −0.0840739 | + | 0.202972i | −0.960326 | − | 0.278881i | \(-0.910036\pi\) |
0.876252 | + | 0.481854i | \(0.160036\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.26725 | − | 3.26725i | −0.158859 | − | 0.158859i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.05588 | + | 4.05588i | −0.196739 | + | 0.196739i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.8957 | + | 5.34157i | 0.624066 | + | 0.258497i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.4173 | − | 42.0492i | −0.840917 | − | 2.03015i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9800i | 0.817897i | 0.912557 | + | 0.408949i | \(0.134104\pi\) | ||||
−0.912557 | + | 0.408949i | \(0.865896\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 16.9567i | − | 0.814886i | −0.913231 | − | 0.407443i | \(-0.866421\pi\) | ||
0.913231 | − | 0.407443i | \(-0.133579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.8331 | − | 26.1535i | −0.519409 | − | 1.25396i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.887839 | + | 0.367755i | 0.0424711 | + | 0.0175921i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5596 | − | 10.5596i | 0.503982 | − | 0.503982i | −0.408691 | − | 0.912673i | \(-0.634015\pi\) |
0.912673 | + | 0.408691i | \(0.134015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.3358 | − | 13.3358i | −0.635039 | − | 0.635039i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.31087 | + | 15.2358i | −0.299838 | + | 0.723874i | 0.700113 | + | 0.714032i | \(0.253133\pi\) |
−0.999952 | + | 0.00984190i | \(0.996867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.1305 | + | 5.43882i | −0.622444 | + | 0.257825i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.3204 | 0.724629 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.07197 | 0.380940 | 0.190470 | − | 0.981693i | \(-0.438999\pi\) | ||||
0.190470 | + | 0.981693i | \(0.438999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.72098 | + | 3.61235i | −0.410655 | + | 0.170099i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.8847 | − | 35.9348i | 0.699343 | − | 1.68836i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.67294 | − | 5.67294i | −0.265952 | − | 0.265952i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.68314 | + | 7.68314i | −0.359402 | + | 0.359402i | −0.863592 | − | 0.504191i | \(-0.831791\pi\) |
0.504191 | + | 0.863592i | \(0.331791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.692559 | + | 0.286867i | 0.0323259 | + | 0.0133898i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.90199 | + | 14.2487i | 0.274883 | + | 0.663627i | 0.999679 | − | 0.0253371i | \(-0.00806593\pi\) |
−0.724796 | + | 0.688964i | \(0.758066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.3231i | 1.26981i | 0.772589 | + | 0.634907i | \(0.218962\pi\) | ||||
−0.772589 | + | 0.634907i | \(0.781038\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 5.33962i | − | 0.247619i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.40577 | + | 22.7075i | 0.435247 | + | 1.05078i | 0.977570 | + | 0.210610i | \(0.0675449\pi\) |
−0.542323 | + | 0.840170i | \(0.682455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.20380 | − | 1.32706i | −0.147938 | − | 0.0612779i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.31253 | + | 2.31253i | −0.106556 | + | 0.106556i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.80029 | − | 7.80029i | −0.358658 | − | 0.358658i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.308915 | − | 0.745786i | 0.0141740 | − | 0.0342190i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.1709 | + | 5.86978i | −0.648842 | + | 0.268759i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.91155 | 0.178723 | 0.0893616 | − | 0.995999i | \(-0.471517\pi\) | ||||
0.0893616 | + | 0.995999i | \(0.471517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.16305 | −0.281011 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.04646 | − | 1.67610i | 0.184120 | − | 0.0762651i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.35480 | − | 10.5134i | 0.197741 | − | 0.477390i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.14685 | − | 8.14685i | −0.369169 | − | 0.369169i | 0.498005 | − | 0.867174i | \(-0.334066\pi\) |
−0.867174 | + | 0.498005i | \(0.834066\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −40.2520 | + | 40.2520i | −1.82026 | + | 1.82026i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2886 | − | 4.67590i | −0.509448 | − | 0.211020i | 0.113127 | − | 0.993581i | \(-0.463913\pi\) |
−0.622575 | + | 0.782560i | \(0.713913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.59744 | + | 20.7561i | 0.387209 | + | 0.934806i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.7788i | 1.02383i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8517i | 0.576479i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4071 | − | 29.9533i | −0.555417 | − | 1.34089i | −0.913361 | − | 0.407152i | \(-0.866522\pi\) |
0.357944 | − | 0.933743i | \(-0.383478\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.0836 | + | 14.5321i | 1.56742 | + | 0.649247i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.77059 | − | 8.77059i | 0.391061 | − | 0.391061i | −0.484004 | − | 0.875066i | \(-0.660818\pi\) |
0.875066 | + | 0.484004i | \(0.160818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5728 | − | 10.5728i | −0.470485 | − | 0.470485i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.84276 | + | 18.9341i | −0.348309 | + | 0.840893i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.0994 | + | 8.32546i | −0.890892 | + | 0.369020i | −0.780711 | − | 0.624892i | \(-0.785143\pi\) |
−0.110181 | + | 0.993912i | \(0.535143\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0531 | 0.444724 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.105497 | −0.00465780 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4135 | + | 4.72764i | −0.502941 | + | 0.208325i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.29186 | + | 5.53304i | −0.100796 | + | 0.243343i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.35099 | − | 3.35099i | −0.147092 | − | 0.147092i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.8910 | + | 29.8910i | −1.30955 | + | 1.30955i | −0.387807 | + | 0.921741i | \(0.626767\pi\) |
−0.921741 | + | 0.387807i | \(0.873233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.7654 | − | 13.5719i | −1.43273 | − | 0.593456i | −0.474706 | − | 0.880144i | \(-0.657446\pi\) |
−0.958024 | + | 0.286688i | \(0.907446\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.40792 | − | 3.39903i | −0.0614468 | − | 0.148346i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.23765i | 0.184595i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4361i | 0.845046i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.31558 | + | 15.2472i | 0.274073 | + | 0.661670i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.0711 | + | 4.17157i | 0.436226 | + | 0.180691i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.64548 | + | 3.64548i | −0.157608 | + | 0.157608i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.56744 | + | 8.56744i | 0.369713 | + | 0.369713i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.35460 | + | 22.5840i | −0.402931 | + | 0.972762i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2925 | − | 4.67751i | 0.485502 | − | 0.201102i | −0.126486 | − | 0.991968i | \(-0.540370\pi\) |
0.611988 | + | 0.790867i | \(0.290370\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.01571 | −0.215245 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.7109 | −0.715815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1256 | − | 7.92207i | 0.817750 | − | 0.338723i | 0.0657087 | − | 0.997839i | \(-0.479069\pi\) |
0.752042 | + | 0.659116i | \(0.229069\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.5141 | + | 42.2827i | −0.747482 | + | 1.80458i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.23570 | − | 2.23570i | −0.0952439 | − | 0.0952439i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4514 | − | 11.4514i | 0.486962 | − | 0.486962i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.62177 | + | 2.32861i | 0.238631 | + | 0.0988442i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.3617 | − | 29.8439i | −0.523783 | − | 1.26452i | −0.935537 | − | 0.353229i | \(-0.885084\pi\) |
0.411753 | − | 0.911295i | \(-0.364916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.7390i | 0.538803i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 35.6631i | − | 1.50570i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5540 | + | 25.4797i | 0.444800 | + | 1.07384i | 0.974244 | + | 0.225497i | \(0.0724004\pi\) |
−0.529444 | + | 0.848345i | \(0.677600\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1023 | − | 8.32666i | −0.845712 | − | 0.350305i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.81352 | − | 5.81352i | 0.244145 | − | 0.244145i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.7855 | − | 23.7855i | −0.997139 | − | 0.997139i | 0.00285688 | − | 0.999996i | \(-0.499091\pi\) |
−0.999996 | + | 0.00285688i | \(0.999091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.904405 | − | 2.18343i | 0.0378482 | − | 0.0913736i | −0.903825 | − | 0.427902i | \(-0.859253\pi\) |
0.941673 | + | 0.336528i | \(0.109253\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.2141 | + | 18.3141i | −1.84707 | + | 0.765082i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.99371 | −0.124846 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.8839 | 1.03593 | 0.517965 | − | 0.855402i | \(-0.326690\pi\) | ||||
0.517965 | + | 0.855402i | \(0.326690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.1238 | + | 17.0340i | −1.70905 | + | 0.707910i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.54286 | + | 10.9674i | −0.188469 | + | 0.455006i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.0578 | + | 14.0578i | 0.582216 | + | 0.582216i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.6006 | − | 18.6006i | 0.769039 | − | 0.769039i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.1685 | + | 16.6383i | 1.65793 | + | 0.686738i | 0.997917 | − | 0.0645151i | \(-0.0205501\pi\) |
0.660015 | + | 0.751253i | \(0.270550\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.228225 | − | 0.550984i | −0.00940384 | − | 0.0227029i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 0.557647i | − | 0.0229385i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.10197i | 0.373773i | 0.982382 | + | 0.186886i | \(0.0598397\pi\) | ||||
−0.982382 | + | 0.186886i | \(0.940160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.40569 | − | 5.80785i | −0.0986238 | − | 0.238099i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −38.3481 | − | 15.8843i | −1.56948 | − | 0.650102i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.04488 | − | 3.04488i | 0.124410 | − | 0.124410i | −0.642160 | − | 0.766571i | \(-0.721962\pi\) |
0.766571 | + | 0.642160i | \(0.221962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.53880 | + | 9.53880i | 0.389096 | + | 0.389096i | 0.874365 | − | 0.485269i | \(-0.161278\pi\) |
−0.485269 | + | 0.874365i | \(0.661278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.35119 | − | 10.5047i | 0.177194 | − | 0.427784i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.49887 | − | 3.52035i | 0.345528 | − | 0.143123i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.66391 | −0.148714 | −0.0743568 | − | 0.997232i | \(-0.523690\pi\) | ||||
−0.0743568 | + | 0.997232i | \(0.523690\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.4102 | −0.583929 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.38960 | − | 2.64666i | 0.258496 | − | 0.107072i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6012 | − | 28.0079i | 0.468570 | − | 1.13123i | −0.496218 | − | 0.868198i | \(-0.665278\pi\) |
0.964788 | − | 0.263029i | \(-0.0847215\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.61040 | − | 7.61040i | −0.306881 | − | 0.306881i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.86100 | − | 5.86100i | 0.235955 | − | 0.235955i | −0.579218 | − | 0.815173i | \(-0.696642\pi\) |
0.815173 | + | 0.579218i | \(0.196642\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.9173 | + | 15.2917i | 1.48383 | + | 0.614624i | 0.969965 | − | 0.243245i | \(-0.0782120\pi\) |
0.513868 | + | 0.857869i | \(0.328212\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.149724 | + | 0.361465i | 0.00600821 | + | 0.0145051i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.23468i | 0.289851i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 14.5563i | − | 0.582254i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.92069 | + | 4.63696i | 0.0767050 | + | 0.185182i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.46157 | − | 1.84804i | −0.177895 | − | 0.0736864i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0543 | + | 21.0543i | −0.838159 | + | 0.838159i | −0.988616 | − | 0.150458i | \(-0.951925\pi\) |
0.150458 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.0028 | + | 17.0028i | 0.675799 | + | 0.675799i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.23412 | − | 22.2931i | 0.366445 | − | 0.884676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.0802 | − | 10.8028i | 1.03334 | − | 0.428022i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −42.1386 | −1.66698 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.57429 | −0.259669 | −0.129835 | − | 0.991536i | \(-0.541445\pi\) | ||||
−0.129835 | + | 0.991536i | \(0.541445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.1050 | − | 9.98462i | 0.950608 | − | 0.393755i | 0.147149 | − | 0.989114i | \(-0.452990\pi\) |
0.803459 | + | 0.595360i | \(0.202990\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.81324 | − | 11.6202i | 0.189521 | − | 0.457545i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.1598 | + | 19.1598i | 0.753250 | + | 0.753250i | 0.975084 | − | 0.221835i | \(-0.0712046\pi\) |
−0.221835 | + | 0.975084i | \(0.571205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.1255 | − | 15.1255i | 0.593727 | − | 0.593727i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.51119 | − | 1.04017i | −0.0984212 | − | 0.0407674i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.73339 | + | 13.8416i | 0.224365 | + | 0.541665i | 0.995474 | − | 0.0950389i | \(-0.0302975\pi\) |
−0.771109 | + | 0.636703i | \(0.780298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13.0429i | − | 0.509629i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.9624i | 1.28599i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.202554 | + | 0.489009i | 0.00789039 | + | 0.0190491i | 0.927776 | − | 0.373139i | \(-0.121718\pi\) |
−0.919885 | + | 0.392188i | \(0.871718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.45241 | − | 2.67268i | −0.250970 | − | 0.103955i | 0.253652 | − | 0.967295i | \(-0.418368\pi\) |
−0.504622 | + | 0.863340i | \(0.668368\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29.1216 | + | 29.1216i | −1.13099 | + | 1.13099i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.625581 | + | 0.625581i | 0.0242590 | + | 0.0242590i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.48723 | + | 10.8331i | −0.173746 | + | 0.419461i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 51.5411 | − | 21.3490i | 1.99270 | − | 0.825402i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59.3196 | 2.29001 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.3285 | −0.937793 | −0.468897 | − | 0.883253i | \(-0.655348\pi\) | ||||
−0.468897 | + | 0.883253i | \(0.655348\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.303631 | − | 0.125768i | 0.0116868 | − | 0.00484081i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.60737 | + | 3.88054i | −0.0617763 | + | 0.149141i | −0.951753 | − | 0.306864i | \(-0.900720\pi\) |
0.889977 | + | 0.456005i | \(0.150720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.09607 | − | 4.09607i | −0.157193 | − | 0.157193i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.9589 | − | 17.9589i | 0.688187 | − | 0.688187i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.8133 | − | 10.2780i | −0.949455 | − | 0.393277i | −0.146429 | − | 0.989221i | \(-0.546778\pi\) |
−0.803026 | + | 0.595944i | \(0.796778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.88118 | − | 11.7842i | −0.186500 | − | 0.450251i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 42.1019i | − | 1.60629i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 22.9585i | − | 0.874650i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.56885 | − | 20.6870i | −0.325974 | − | 0.786972i | −0.998883 | − | 0.0472463i | \(-0.984955\pi\) |
0.672909 | − | 0.739725i | \(-0.265045\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.7127 | + | 4.43736i | 0.406943 | + | 0.168561i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.6647 | − | 16.6647i | 0.632128 | − | 0.632128i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.03979 | + | 6.03979i | 0.228774 | + | 0.228774i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.9479 | − | 33.6732i | 0.527558 | − | 1.27364i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.1557 | + | 11.6625i | −1.06343 | + | 0.440486i | −0.844667 | − | 0.535293i | \(-0.820201\pi\) |
−0.218760 | + | 0.975779i | \(0.570201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.679628 | 0.0256326 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.82843 | −0.257173 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.03195 | + | 2.91273i | −0.264464 | + | 0.109544i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4408 | + | 30.0346i | −0.467223 | + | 1.12797i | 0.498148 | + | 0.867092i | \(0.334014\pi\) |
−0.965370 | + | 0.260883i | \(0.915986\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.5471 | + | 37.5471i | 1.40812 | + | 1.40812i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.56394 | + | 1.56394i | −0.0585699 | + | 0.0585699i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.4998 | − | 13.0476i | −1.17803 | − | 0.487954i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.0187 | + | 26.6015i | 0.411501 | + | 0.993450i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 33.6333i | − | 1.25431i | −0.778894 | − | 0.627155i | \(-0.784219\pi\) | ||
0.778894 | − | 0.627155i | \(-0.215781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.28867i | 0.234202i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.0533 | + | 31.5134i | 0.485457 | + | 1.17200i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.09984 | + | 3.76928i | 0.337960 | + | 0.139988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.43334 | + | 7.43334i | −0.275687 | + | 0.275687i | −0.831385 | − | 0.555697i | \(-0.812451\pi\) |
0.555697 | + | 0.831385i | \(0.312451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1459 | + | 20.1459i | 0.746145 | + | 0.746145i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.81991 | + | 9.22207i | −0.141284 | + | 0.341090i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.328598 | − | 0.136110i | 0.0121371 | − | 0.00502733i | −0.376607 | − | 0.926373i | \(-0.622909\pi\) |
0.388744 | + | 0.921346i | \(0.372909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −27.8714 | −1.02805 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.7373 | −0.542857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.8857 | − | 18.1780i | 1.61436 | − | 0.668690i | 0.621008 | − | 0.783804i | \(-0.286723\pi\) |
0.993352 | + | 0.115114i | \(0.0367234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.21803 | − | 5.35480i | 0.0814814 | − | 0.196714i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.3220 | − | 30.3220i | −1.11240 | − | 1.11240i | −0.992825 | − | 0.119580i | \(-0.961845\pi\) |
−0.119580 | − | 0.992825i | \(-0.538155\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.11529 | − | 8.11529i | 0.297321 | − | 0.297321i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.9603 | − | 14.8952i | −1.31572 | − | 0.544988i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.00430 | + | 2.42459i | 0.0366963 | + | 0.0885927i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 51.3686i | − | 1.87447i | −0.348701 | − | 0.937234i | \(-0.613377\pi\) | ||
0.348701 | − | 0.937234i | \(-0.386623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.7248i | 1.26544i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.1504 | − | 26.9194i | −0.405804 | − | 0.979697i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2644 | − | 6.32270i | −0.554793 | − | 0.229803i | 0.0876302 | − | 0.996153i | \(-0.472071\pi\) |
−0.642423 | + | 0.766350i | \(0.722071\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.1618 | − | 13.1618i | 0.477741 | − | 0.477741i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.6859 | + | 26.6859i | 0.967362 | + | 0.967362i | 0.999484 | − | 0.0321218i | \(-0.0102264\pi\) |
−0.0321218 | + | 0.999484i | \(0.510226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.25531 | + | 7.85902i | −0.117850 | + | 0.284516i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.0429 | − | 7.88784i | 0.688499 | − | 0.285185i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.7021 | −0.891943 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0390 | 1.58809 | 0.794044 | − | 0.607861i | \(-0.207972\pi\) | ||||
0.794044 | + | 0.607861i | \(0.207972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.0796 | + | 17.8441i | −1.55147 | + | 0.642641i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.4001 | − | 37.1790i | 0.553902 | − | 1.33724i | −0.360625 | − | 0.932711i | \(-0.617436\pi\) |
0.914526 | − | 0.404526i | \(-0.132564\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.31371 | + | 1.31371i | 0.0471898 | + | 0.0471898i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.19027 | − | 2.19027i | 0.0785754 | − | 0.0785754i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.11058 | − | 0.460018i | −0.0397908 | − | 0.0164819i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.9012 | + | 50.4599i | 0.747903 | + | 1.80560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.28724i | − | 0.0460022i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.44992i | 0.0874413i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.948632 | − | 2.29020i | −0.0338151 | − | 0.0816368i | 0.906070 | − | 0.423128i | \(-0.139068\pi\) |
−0.939885 | + | 0.341491i | \(0.889068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44.8240 | + | 18.5667i | 1.59578 | + | 0.660992i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.83196 | + | 7.83196i | −0.278472 | + | 0.278472i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.4388 | − | 48.4388i | −1.72011 | − | 1.72011i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.67452 | + | 20.9421i | −0.307654 | + | 0.742741i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.76562 | − | 1.14556i | 0.0979632 | − | 0.0405777i | −0.333164 | − | 0.942869i | \(-0.608116\pi\) |
0.431127 | + | 0.902291i | \(0.358116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.41921 | 0.191718 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.7212 | −0.838149 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.4717 | − | 16.3497i | 1.39292 | − | 0.576968i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.25559 | − | 3.03127i | 0.0442539 | − | 0.106838i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.0256 | − | 23.0256i | −0.810541 | − | 0.810541i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.12825 | + | 7.12825i | −0.250616 | + | 0.250616i | −0.821223 | − | 0.570607i | \(-0.806708\pi\) |
0.570607 | + | 0.821223i | \(0.306708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.4750 | − | 11.3805i | −0.964777 | − | 0.399624i | −0.156012 | − | 0.987755i | \(-0.549864\pi\) |
−0.808765 | + | 0.588131i | \(0.799864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.16751 | − | 10.0613i | −0.146161 | − | 0.352864i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42.6435i | 1.49374i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.40479i | − | 0.0491474i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.12431 | − | 12.3712i | −0.179058 | − | 0.432284i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.1861 | − | 14.1603i | −1.19310 | − | 0.494199i | −0.304339 | − | 0.952564i | \(-0.598435\pi\) |
−0.888764 | + | 0.458364i | \(0.848435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.3810 | − | 27.3810i | 0.954440 | − | 0.954440i | −0.0445659 | − | 0.999006i | \(-0.514190\pi\) |
0.999006 | + | 0.0445659i | \(0.0141905\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.0559 | − | 11.0559i | −0.384916 | − | 0.384916i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.98030 | + | 19.2661i | −0.277502 | + | 0.669950i | −0.999765 | − | 0.0216689i | \(-0.993102\pi\) |
0.722263 | + | 0.691619i | \(0.243102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.59585 | − | 1.48945i | 0.124889 | − | 0.0517307i | −0.319364 | − | 0.947632i | \(-0.603469\pi\) |
0.444253 | + | 0.895901i | \(0.353469\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 61.5269 | 2.13434 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.1194 | 0.766391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2818 | − | 10.8863i | 0.909518 | − | 0.376735i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.0929169 | − | 0.224321i | 0.00321168 | − | 0.00775368i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.8461 | + | 13.8461i | 0.478020 | + | 0.478020i | 0.904498 | − | 0.426478i | \(-0.140246\pi\) |
−0.426478 | + | 0.904498i | \(0.640246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.77318 | − | 6.77318i | 0.233558 | − | 0.233558i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.8050 | − | 7.78929i | −0.647679 | − | 0.268277i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.87515 | + | 14.1839i | 0.202111 | + | 0.487940i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.68274i | − | 0.160901i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.50750i | 0.291977i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.964543 | − | 2.32861i | −0.0330641 | − | 0.0798239i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.0597 | − | 7.48055i | −0.618351 | − | 0.256129i | 0.0514436 | − | 0.998676i | \(-0.483618\pi\) |
−0.669794 | + | 0.742547i | \(0.733618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.05117 | + | 2.05117i | −0.0701485 | + | 0.0701485i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.35294 | − | 6.35294i | −0.217012 | − | 0.217012i | 0.590226 | − | 0.807238i | \(-0.299039\pi\) |
−0.807238 | + | 0.590226i | \(0.799039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.72800 | + | 23.4855i | −0.331915 | + | 0.801314i | 0.666525 | + | 0.745483i | \(0.267781\pi\) |
−0.998440 | + | 0.0558315i | \(0.982219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.06164 | + | 2.09660i | −0.172500 | + | 0.0714520i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.0884535 | −0.00301099 | −0.00150550 | − | 0.999999i | \(-0.500479\pi\) | ||||
−0.00150550 | + | 0.999999i | \(0.500479\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.55008 | −0.120706 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.92588 | − | 3.69722i | 0.303139 | − | 0.125564i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.3379 | − | 63.5854i | 0.893453 | − | 2.15699i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0341 | + | 12.0341i | 0.407761 | + | 0.407761i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.4303 | − | 13.4303i | 0.454547 | − | 0.454547i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5747 | − | 4.38018i | −0.357490 | − | 0.148077i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.24514 | + | 10.2487i | 0.143348 | + | 0.346073i | 0.979205 | − | 0.202875i | \(-0.0650285\pi\) |
−0.835857 | + | 0.548948i | \(0.815029\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.6702i | 0.629729i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.9859i | − | 0.808105i | −0.914736 | − | 0.404052i | \(-0.867601\pi\) | ||
0.914736 | − | 0.404052i | \(-0.132399\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.74892 | + | 18.7075i | 0.260772 | + | 0.629559i | 0.998987 | − | 0.0450067i | \(-0.0143309\pi\) |
−0.738215 | + | 0.674566i | \(0.764331\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.5326 | + | 9.33333i | 0.757426 | + | 0.313736i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.4494 | + | 36.4494i | −1.22385 | + | 1.22385i | −0.257600 | + | 0.966252i | \(0.582932\pi\) |
−0.966252 | + | 0.257600i | \(0.917068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.68550 | − | 8.68550i | −0.291302 | − | 0.291302i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.3710 | − | 32.2804i | 0.447944 | − | 1.08143i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.704611 | + | 0.291859i | −0.0235789 | + | 0.00976670i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.07646 | 0.303392 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4951 | −0.717700 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.72293 | − | 2.78473i | 0.224222 | − | 0.0928759i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.88431 | − | 16.6202i | 0.229350 | − | 0.553699i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.52728 | − | 4.52728i | −0.150658 | − | 0.150658i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.65685 | + | 2.65685i | −0.0883168 | + | 0.0883168i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.2753 | + | 15.8541i | 1.27091 | + | 0.526428i | 0.913241 | − | 0.407421i | \(-0.133572\pi\) |
0.357669 | + | 0.933848i | \(0.383572\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.55032 | − | 23.0565i | −0.316764 | − | 0.764737i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5214i | 0.414851i | 0.978251 | + | 0.207426i | \(0.0665085\pi\) | ||||
−0.978251 | + | 0.207426i | \(0.933492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.4497i | 1.66964i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.8827 | + | 62.4864i | 0.855657 | + | 2.06574i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.13401 | − | 2.54079i | −0.202563 | − | 0.0839043i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.19513 | − | 1.19513i | 0.0394238 | − | 0.0394238i | −0.687120 | − | 0.726544i | \(-0.741125\pi\) |
0.726544 | + | 0.687120i | \(0.241125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.3330 | + | 14.3330i | 0.472287 | + | 0.472287i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.1369 | − | 58.2715i | 0.794475 | − | 1.91803i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.95604 | + | 0.810217i | −0.0643141 | + | 0.0266398i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.6194 | −0.677231 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.1410 | 1.48103 | 0.740514 | − | 0.672041i | \(-0.234582\pi\) | ||||
0.740514 | + | 0.672041i | \(0.234582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.87599 | + | 1.19127i | −0.0942566 | + | 0.0390424i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.0961 | + | 48.5162i | −0.657915 | + | 1.58835i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.8910 | − | 18.8910i | −0.617801 | − | 0.617801i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.58002 | − | 2.58002i | 0.0842857 | − | 0.0842857i | −0.663707 | − | 0.747993i | \(-0.731018\pi\) |
0.747993 | + | 0.663707i | \(0.231018\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.0937 | + | 24.4774i | 1.92845 | + | 0.798790i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.24720 | − | 5.42523i | −0.0732568 | − | 0.176857i | 0.883009 | − | 0.469355i | \(-0.155514\pi\) |
−0.956266 | + | 0.292498i | \(0.905514\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.45807i | 0.145175i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.360189i | 0.0117170i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.5640 | − | 42.4032i | −0.570753 | − | 1.37792i | −0.900915 | − | 0.433996i | \(-0.857103\pi\) |
0.330162 | − | 0.943924i | \(-0.392897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.5822 | − | 18.8808i | −1.47966 | − | 0.612896i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.9788 | − | 17.9788i | 0.583003 | − | 0.583003i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.8079 | + | 14.8079i | 0.479673 | + | 0.479673i | 0.905027 | − | 0.425354i | \(-0.139850\pi\) |
−0.425354 | + | 0.905027i | \(0.639850\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.7194 | + | 33.1216i | −0.443949 | + | 1.07179i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −56.5787 | + | 23.4357i | −1.82893 | + | 0.757568i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.49290 | −0.209667 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.94981 | + | 3.29292i | −0.256179 | + | 0.106113i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.7605 | + | 30.8066i | −0.410775 | + | 0.991698i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.8604 | + | 24.8604i | 0.799455 | + | 0.799455i | 0.983010 | − | 0.183554i | \(-0.0587604\pi\) |
−0.183554 | + | 0.983010i | \(0.558760\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.21137 | − | 3.21137i | 0.103164 | − | 0.103164i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.3388 | + | 9.66725i | 0.748978 | + | 0.310237i | 0.724324 | − | 0.689459i | \(-0.242152\pi\) |
0.0246533 | + | 0.999696i | \(0.492152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.59099 | − | 11.0836i | −0.147180 | − | 0.355325i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.0559i | 0.578251i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 54.7057i | − | 1.75019i | −0.483952 | − | 0.875094i | \(-0.660799\pi\) | ||
0.483952 | − | 0.875094i | \(-0.339201\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.7660 | + | 28.4056i | 0.376042 | + | 0.907846i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.7684 | − | 10.6736i | −0.822720 | − | 0.340782i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.85315 | + | 7.85315i | −0.250477 | + | 0.250477i | −0.821166 | − | 0.570689i | \(-0.806676\pi\) |
0.570689 | + | 0.821166i | \(0.306676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.295389 | − | 0.295389i | −0.00941188 | − | 0.00941188i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.33019 | + | 3.21137i | −0.0423405 | + | 0.102219i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.81324 | + | 1.99371i | −0.153052 | + | 0.0633963i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.4878 | −1.66733 | −0.833665 | − | 0.552270i | \(-0.813762\pi\) | ||||
−0.833665 | + | 0.552270i | \(0.813762\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.2217 | −0.641716 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.7272 | + | 11.8992i | −0.910715 | + | 0.377230i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.8431 | + | 31.0060i | −0.406745 | + | 0.981970i | 0.579243 | + | 0.815155i | \(0.303348\pi\) |
−0.985988 | + | 0.166815i | \(0.946652\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.195654 | + | 0.195654i | 0.00619021 | + | 0.00619021i |
(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 | 256.2.g.d.97.2 | 8 | ||
4.3 | odd | 2 | 256.2.g.c.97.1 | 8 | |||
8.3 | odd | 2 | 128.2.g.b.49.2 | 8 | |||
8.5 | even | 2 | 32.2.g.b.21.2 | ✓ | 8 | ||
16.3 | odd | 4 | 512.2.g.g.449.1 | 8 | |||
16.5 | even | 4 | 512.2.g.h.449.1 | 8 | |||
16.11 | odd | 4 | 512.2.g.f.449.2 | 8 | |||
16.13 | even | 4 | 512.2.g.e.449.2 | 8 | |||
24.5 | odd | 2 | 288.2.v.b.181.1 | 8 | |||
24.11 | even | 2 | 1152.2.v.b.433.1 | 8 | |||
32.3 | odd | 8 | 256.2.g.c.161.1 | 8 | |||
32.5 | even | 8 | 512.2.g.h.65.1 | 8 | |||
32.11 | odd | 8 | 512.2.g.g.65.1 | 8 | |||
32.13 | even | 8 | 32.2.g.b.29.2 | yes | 8 | ||
32.19 | odd | 8 | 128.2.g.b.81.2 | 8 | |||
32.21 | even | 8 | 512.2.g.e.65.2 | 8 | |||
32.27 | odd | 8 | 512.2.g.f.65.2 | 8 | |||
32.29 | even | 8 | inner | 256.2.g.d.161.2 | 8 | ||
40.13 | odd | 4 | 800.2.ba.d.149.1 | 8 | |||
40.29 | even | 2 | 800.2.y.b.501.1 | 8 | |||
40.37 | odd | 4 | 800.2.ba.c.149.2 | 8 | |||
64.3 | odd | 16 | 4096.2.a.q.1.7 | 8 | |||
64.29 | even | 16 | 4096.2.a.k.1.7 | 8 | |||
64.35 | odd | 16 | 4096.2.a.q.1.2 | 8 | |||
64.61 | even | 16 | 4096.2.a.k.1.2 | 8 | |||
96.77 | odd | 8 | 288.2.v.b.253.1 | 8 | |||
96.83 | even | 8 | 1152.2.v.b.721.1 | 8 | |||
160.13 | odd | 8 | 800.2.ba.c.349.2 | 8 | |||
160.77 | odd | 8 | 800.2.ba.d.349.1 | 8 | |||
160.109 | even | 8 | 800.2.y.b.701.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.2.g.b.21.2 | ✓ | 8 | 8.5 | even | 2 | ||
32.2.g.b.29.2 | yes | 8 | 32.13 | even | 8 | ||
128.2.g.b.49.2 | 8 | 8.3 | odd | 2 | |||
128.2.g.b.81.2 | 8 | 32.19 | odd | 8 | |||
256.2.g.c.97.1 | 8 | 4.3 | odd | 2 | |||
256.2.g.c.161.1 | 8 | 32.3 | odd | 8 | |||
256.2.g.d.97.2 | 8 | 1.1 | even | 1 | trivial | ||
256.2.g.d.161.2 | 8 | 32.29 | even | 8 | inner | ||
288.2.v.b.181.1 | 8 | 24.5 | odd | 2 | |||
288.2.v.b.253.1 | 8 | 96.77 | odd | 8 | |||
512.2.g.e.65.2 | 8 | 32.21 | even | 8 | |||
512.2.g.e.449.2 | 8 | 16.13 | even | 4 | |||
512.2.g.f.65.2 | 8 | 32.27 | odd | 8 | |||
512.2.g.f.449.2 | 8 | 16.11 | odd | 4 | |||
512.2.g.g.65.1 | 8 | 32.11 | odd | 8 | |||
512.2.g.g.449.1 | 8 | 16.3 | odd | 4 | |||
512.2.g.h.65.1 | 8 | 32.5 | even | 8 | |||
512.2.g.h.449.1 | 8 | 16.5 | even | 4 | |||
800.2.y.b.501.1 | 8 | 40.29 | even | 2 | |||
800.2.y.b.701.1 | 8 | 160.109 | even | 8 | |||
800.2.ba.c.149.2 | 8 | 40.37 | odd | 4 | |||
800.2.ba.c.349.2 | 8 | 160.13 | odd | 8 | |||
800.2.ba.d.149.1 | 8 | 40.13 | odd | 4 | |||
800.2.ba.d.349.1 | 8 | 160.77 | odd | 8 | |||
1152.2.v.b.433.1 | 8 | 24.11 | even | 2 | |||
1152.2.v.b.721.1 | 8 | 96.83 | even | 8 | |||
4096.2.a.k.1.2 | 8 | 64.61 | even | 16 | |||
4096.2.a.k.1.7 | 8 | 64.29 | even | 16 | |||
4096.2.a.q.1.2 | 8 | 64.35 | odd | 16 | |||
4096.2.a.q.1.7 | 8 | 64.3 | odd | 16 |