Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,2,Mod(335,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("608.335");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.85490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 559.13 | ||
Character | \(\chi\) | \(=\) | 608.559 |
Dual form | 608.2.s.c.335.13 |
$q$-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 \(\left(\mathbb{Z}/608\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.65547 | + | 1.53314i | 1.53314 | + | 0.885156i | 0.999215 | + | 0.0396221i | \(0.0126154\pi\) |
0.533921 | + | 0.845534i | \(0.320718\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.25688 | − | 1.30301i | −1.00931 | − | 0.582723i | −0.0983176 | − | 0.995155i | \(-0.531346\pi\) |
−0.910988 | + | 0.412432i | \(0.864679\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.30088i | 1.62558i | 0.582556 | + | 0.812791i | \(0.302053\pi\) | ||||
−0.582556 | + | 0.812791i | \(0.697947\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.20101 | + | 5.54431i | 1.06700 | + | 1.84810i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.349633 | 0.105418 | 0.0527092 | − | 0.998610i | \(-0.483214\pi\) | ||||
0.0527092 | + | 0.998610i | \(0.483214\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.839767 | + | 1.45452i | 0.232910 | + | 0.403411i | 0.958663 | − | 0.284544i | \(-0.0918421\pi\) |
−0.725754 | + | 0.687955i | \(0.758509\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.99538 | − | 6.92020i | −1.03160 | − | 1.78679i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.357047 | − | 0.618424i | 0.0865967 | − | 0.149990i | −0.819474 | − | 0.573117i | \(-0.805734\pi\) |
0.906070 | + | 0.423127i | \(0.139068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.35063 | − | 0.268300i | −0.998104 | − | 0.0615522i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.59384 | + | 11.4209i | −1.43889 | + | 2.49224i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.38083 | − | 0.797223i | 0.287923 | − | 0.166233i | −0.349082 | − | 0.937092i | \(-0.613506\pi\) |
0.637005 | + | 0.770860i | \(0.280173\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.895662 | + | 1.55133i | 0.179132 | + | 0.310266i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.4315i | 2.00755i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.463655 | + | 0.803074i | 0.0860985 | + | 0.149127i | 0.905859 | − | 0.423580i | \(-0.139227\pi\) |
−0.819760 | + | 0.572707i | \(0.805893\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.80517 | 0.503824 | 0.251912 | − | 0.967750i | \(-0.418941\pi\) | ||||
0.251912 | + | 0.967750i | \(0.418941\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.928441 | + | 0.536035i | 0.161621 | + | 0.0933118i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.60409 | − | 9.70656i | 0.947264 | − | 1.64071i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2099 | 1.67849 | 0.839245 | − | 0.543753i | \(-0.182997\pi\) | ||||
0.839245 | + | 0.543753i | \(0.182997\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.14991i | 0.824645i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.87850 | + | 2.81660i | 0.761893 | + | 0.439879i | 0.829975 | − | 0.557801i | \(-0.188355\pi\) |
−0.0680819 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.32286 | + | 7.48741i | −0.659230 | + | 1.14182i | 0.321586 | + | 0.946880i | \(0.395784\pi\) |
−0.980815 | + | 0.194939i | \(0.937549\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 16.6838i | − | 2.48707i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.26395 | − | 3.61649i | 0.913691 | − | 0.527520i | 0.0320740 | − | 0.999485i | \(-0.489789\pi\) |
0.881617 | + | 0.471966i | \(0.156455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.4976 | −1.64251 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.89626 | − | 1.09480i | 0.265529 | − | 0.153303i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.73541 | − | 8.20196i | −0.650458 | − | 1.12663i | −0.983012 | − | 0.183542i | \(-0.941244\pi\) |
0.332554 | − | 0.943084i | \(-0.392090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.789079 | − | 0.455575i | −0.106399 | − | 0.0614297i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.1416 | − | 7.38258i | −1.47575 | − | 0.977846i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.62664 | − | 3.82589i | −0.862715 | − | 0.498089i | 0.00220531 | − | 0.999998i | \(-0.499298\pi\) |
−0.864921 | + | 0.501909i | \(0.832631\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.46531 | + | 2.00070i | −0.443687 | + | 0.256163i | −0.705160 | − | 0.709048i | \(-0.749125\pi\) |
0.261473 | + | 0.965211i | \(0.415792\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −23.8454 | + | 13.7672i | −3.00424 | + | 1.73450i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.37690i | − | 0.542887i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6067 | − | 6.12378i | 1.29581 | − | 0.748139i | 0.316136 | − | 0.948714i | \(-0.397614\pi\) |
0.979678 | + | 0.200575i | \(0.0642810\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.88901 | 0.588567 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.09365 | − | 8.82246i | 0.604505 | − | 1.04703i | −0.387624 | − | 0.921817i | \(-0.626704\pi\) |
0.992129 | − | 0.125216i | \(-0.0399625\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.54260 | − | 4.40392i | 0.297589 | − | 0.515439i | −0.677995 | − | 0.735067i | \(-0.737151\pi\) |
0.975584 | + | 0.219627i | \(0.0704842\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.49268i | 0.634241i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.50373i | 0.171366i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.31170 | − | 2.27193i | 0.147578 | − | 0.255612i | −0.782754 | − | 0.622331i | \(-0.786186\pi\) |
0.930332 | + | 0.366719i | \(0.119519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.38991 | + | 11.0677i | −0.709990 | + | 1.22974i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.69293 | 0.515116 | 0.257558 | − | 0.966263i | \(-0.417082\pi\) | ||||
0.257558 | + | 0.966263i | \(0.417082\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.61162 | + | 0.930471i | −0.174805 | + | 0.100924i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.84338i | 0.304843i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.37293 | − | 4.25676i | 0.781529 | − | 0.451216i | −0.0554428 | − | 0.998462i | \(-0.517657\pi\) |
0.836972 | + | 0.547246i | \(0.184324\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.25572 | + | 3.61174i | −0.655778 | + | 0.378613i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.44905 | + | 4.30071i | 0.772430 | + | 0.445963i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.46925 | + | 6.27443i | 0.971524 | + | 0.643743i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.30190 | + | 3.63841i | 0.639861 | + | 0.369424i | 0.784561 | − | 0.620051i | \(-0.212888\pi\) |
−0.144700 | + | 0.989476i | \(0.546222\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.11918 | + | 1.93848i | 0.112482 | + | 0.194824i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.66074 | + | 2.11353i | −0.364257 | + | 0.210304i | −0.670947 | − | 0.741506i | \(-0.734112\pi\) |
0.306689 | + | 0.951810i | \(0.400779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.3567 | −1.80874 | −0.904370 | − | 0.426750i | \(-0.859659\pi\) | ||||
−0.904370 | + | 0.426750i | \(0.859659\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 29.7630 | − | 17.1837i | 2.90457 | − | 1.67695i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.6010i | − | 1.12151i | −0.827982 | − | 0.560754i | \(-0.810511\pi\) | ||
0.827982 | − | 0.560754i | \(-0.189489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.253698 | + | 0.439417i | −0.0242998 | + | 0.0420886i | −0.877920 | − | 0.478808i | \(-0.841069\pi\) |
0.853620 | + | 0.520897i | \(0.174402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.1120 | + | 15.6531i | 2.57335 | + | 1.48573i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.70645i | 0.724961i | 0.931991 | + | 0.362481i | \(0.118070\pi\) | ||||
−0.931991 | + | 0.362481i | \(0.881930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.15515 | −0.387470 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.37621 | + | 9.31187i | −0.497031 | + | 0.860882i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.65977 | + | 1.53562i | 0.243821 | + | 0.140770i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8778 | −0.988887 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.63647 | + | 14.9588i | 0.778724 | + | 1.34879i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.36186i | 0.747908i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.90707 | − | 11.9634i | −0.612903 | − | 1.06158i | −0.990749 | − | 0.135710i | \(-0.956668\pi\) |
0.377846 | − | 0.925869i | \(-0.376665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.9584 | + | 13.2551i | −2.02138 | + | 1.16704i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.66432 | − | 13.2750i | 0.669635 | − | 1.15984i | −0.308372 | − | 0.951266i | \(-0.599784\pi\) |
0.978006 | − | 0.208575i | \(-0.0668826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.15393 | − | 18.7116i | 0.100058 | − | 1.62250i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.5924 | − | 23.5427i | 1.16984 | − | 2.02623i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.73230 | − | 8.19659i | −0.404308 | − | 0.700282i | 0.589933 | − | 0.807452i | \(-0.299154\pi\) |
−0.994241 | + | 0.107171i | \(0.965821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.16855 | + | 3.75604i | 0.183934 | + | 0.318583i | 0.943217 | − | 0.332178i | \(-0.107783\pi\) |
−0.759283 | + | 0.650761i | \(0.774450\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.1783 | 1.86775 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.293611 | + | 0.508549i | 0.0245530 | + | 0.0425270i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.41658i | − | 0.200686i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −30.5315 | − | 17.6274i | −2.51820 | − | 1.45388i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50515 | + | 2.60105i | 0.369076 | + | 0.213086i | 0.673055 | − | 0.739592i | \(-0.264982\pi\) |
−0.303978 | + | 0.952679i | \(0.598315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.14034 | 0.336936 | 0.168468 | − | 0.985707i | \(-0.446118\pi\) | ||||
0.168468 | + | 0.985707i | \(0.446118\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.57165 | 0.369596 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.33093 | − | 3.65516i | −0.508512 | − | 0.293590i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.57943 | + | 1.48923i | 0.205861 | + | 0.118854i | 0.599386 | − | 0.800460i | \(-0.295411\pi\) |
−0.393525 | + | 0.919314i | \(0.628745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 29.0401i | − | 2.30303i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.42876 | + | 5.93879i | 0.270224 | + | 0.468042i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.299245 | 0.0234387 | 0.0117194 | − | 0.999931i | \(-0.496270\pi\) | ||||
0.0117194 | + | 0.999931i | \(0.496270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.39692 | − | 2.41953i | −0.108750 | − | 0.188360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.94944 | + | 6.84063i | 0.305617 | + | 0.529344i | 0.977398 | − | 0.211405i | \(-0.0678040\pi\) |
−0.671782 | + | 0.740749i | \(0.734471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.08958 | − | 8.81541i | 0.391506 | − | 0.678109i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4389 | − | 24.9801i | −0.951226 | − | 1.91028i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.01754 | + | 13.8868i | −0.609562 | + | 1.05579i | 0.381751 | + | 0.924265i | \(0.375321\pi\) |
−0.991313 | + | 0.131527i | \(0.958012\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.67210 | + | 3.85214i | −0.504363 | + | 0.291194i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7312 | − | 20.3191i | −0.881773 | − | 1.52728i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.5488i | 1.16218i | 0.813841 | + | 0.581088i | \(0.197373\pi\) | ||||
−0.813841 | + | 0.581088i | \(0.802627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.129430 | − | 0.224180i | −0.00962046 | − | 0.0166631i | 0.861175 | − | 0.508308i | \(-0.169729\pi\) |
−0.870796 | + | 0.491645i | \(0.836396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2694 | −0.906977 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.0424 | − | 13.3035i | −1.69411 | − | 0.978095i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.124836 | − | 0.216222i | 0.00912889 | − | 0.0158117i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −44.8648 | −3.26343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00136i | 0.434244i | 0.976145 | + | 0.217122i | \(0.0696669\pi\) | ||||
−0.976145 | + | 0.217122i | \(0.930333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.63936 | − | 3.83324i | −0.477912 | − | 0.275922i | 0.241634 | − | 0.970367i | \(-0.422317\pi\) |
−0.719546 | + | 0.694445i | \(0.755650\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.71037 | − | 11.6227i | 0.480540 | − | 0.832320i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.38374i | − | 0.383576i | −0.981436 | − | 0.191788i | \(-0.938571\pi\) | ||
0.981436 | − | 0.191788i | \(-0.0614286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.1469 | + | 9.32240i | −1.14462 | + | 0.660847i | −0.947571 | − | 0.319546i | \(-0.896470\pi\) |
−0.197050 | + | 0.980393i | \(0.563136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37.5544 | 2.64888 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.45393 | + | 1.99413i | −0.242418 | + | 0.139960i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.34011 | − | 12.7134i | −0.512656 | − | 0.887945i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.84011 | + | 5.10384i | 0.614430 | + | 0.354741i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.52113 | − | 0.0938066i | −0.105219 | − | 0.00648874i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.807263 | − | 0.466073i | −0.0555743 | − | 0.0320858i | 0.471955 | − | 0.881622i | \(-0.343548\pi\) |
−0.527530 | + | 0.849537i | \(0.676882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 27.0521 | − | 15.6185i | 1.85358 | − | 1.07016i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.5123 | − | 11.2654i | 1.33073 | − | 0.768297i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0647i | 0.819006i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.5036 | − | 7.79631i | 0.912489 | − | 0.526826i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.19935 | 0.0806768 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.62648 | − | 13.2095i | 0.510707 | − | 0.884571i | −0.489216 | − | 0.872163i | \(-0.662717\pi\) |
0.999923 | − | 0.0124080i | \(-0.00394968\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.73405 | + | 9.93166i | −0.382270 | + | 0.662111i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.51895i | 0.366306i | 0.983084 | + | 0.183153i | \(0.0586303\pi\) | ||||
−0.983084 | + | 0.183153i | \(0.941370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8139i | 0.846768i | 0.905950 | + | 0.423384i | \(0.139158\pi\) | ||||
−0.905950 | + | 0.423384i | \(0.860842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.30543 | + | 3.99311i | −0.151686 | + | 0.262728i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.958205 | − | 1.65966i | 0.0627741 | − | 0.108728i | −0.832930 | − | 0.553378i | \(-0.813339\pi\) |
0.895704 | + | 0.444650i | \(0.146672\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.8493 | −1.22959 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.96636 | − | 4.02203i | 0.452514 | − | 0.261259i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1872i | 1.69391i | 0.531665 | + | 0.846955i | \(0.321566\pi\) | ||||
−0.531665 | + | 0.846955i | \(0.678434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2053 | + | 7.62406i | −0.850625 | + | 0.491109i | −0.860862 | − | 0.508839i | \(-0.830075\pi\) |
0.0102365 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.83453 | + | 3.94592i | −0.438435 | + | 0.253131i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.9487 | + | 14.9815i | 1.65780 | + | 0.957131i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.26327 | − | 6.55339i | −0.207637 | − | 0.416982i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.4619 | + | 7.19490i | 0.789743 | + | 0.455958i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.40850 | + | 5.90370i | 0.215143 | + | 0.372638i | 0.953317 | − | 0.301972i | \(-0.0976450\pi\) |
−0.738174 | + | 0.674610i | \(0.764312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.482785 | − | 0.278736i | 0.0303524 | − | 0.0175240i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.70616 | −0.357333 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.99669 | − | 5.77159i | 0.623576 | − | 0.360022i | −0.154684 | − | 0.987964i | \(-0.549436\pi\) |
0.778260 | + | 0.627942i | \(0.216103\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 43.9114i | 2.72852i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.96833 | + | 5.14130i | −0.183735 | + | 0.318238i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.8061 | − | 6.81625i | −0.727994 | − | 0.420308i | 0.0896937 | − | 0.995969i | \(-0.471411\pi\) |
−0.817688 | + | 0.575662i | \(0.804745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.6811i | 1.51615i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.1048 | 1.59759 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0715 | − | 24.3725i | 0.857953 | − | 1.48602i | −0.0159257 | − | 0.999873i | \(-0.505070\pi\) |
0.873878 | − | 0.486144i | \(-0.161597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.45517 | − | 1.99485i | −0.209887 | − | 0.121178i | 0.391372 | − | 0.920233i | \(-0.372001\pi\) |
−0.601259 | + | 0.799054i | \(0.705334\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.1492 | −1.34053 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.313153 | + | 0.542397i | 0.0188838 | + | 0.0327078i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.1974i | − | 0.732869i | −0.930444 | − | 0.366435i | \(-0.880578\pi\) | ||
0.930444 | − | 0.366435i | \(-0.119422\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.97939 | + | 15.5528i | 0.537582 | + | 0.931119i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.459532 | + | 0.265311i | −0.0274134 | + | 0.0158271i | −0.513644 | − | 0.858003i | \(-0.671705\pi\) |
0.486231 | + | 0.873830i | \(0.338371\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.48484 | + | 2.57181i | −0.0882644 | + | 0.152878i | −0.906778 | − | 0.421609i | \(-0.861465\pi\) |
0.818513 | + | 0.574488i | \(0.194799\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.5257 | + | 31.1792i | 0.919665 | + | 1.84690i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.1139 | + | 20.9818i | −0.715059 | + | 1.23852i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.24503 | + | 14.2808i | 0.485002 | + | 0.840048i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1563 | + | 19.3233i | 0.653996 | + | 1.13275i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.8714 | −0.927216 | −0.463608 | − | 0.886040i | \(-0.653445\pi\) | ||||
−0.463608 | + | 0.886040i | \(0.653445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.97034 | + | 17.2691i | 0.580496 | + | 1.00545i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.64721i | 0.211633i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.31915 | + | 1.33896i | 0.134120 | + | 0.0774343i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.2025 | − | 18.5921i | −1.85612 | − | 1.07163i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9613 | −0.744608 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.4277 | 0.597088 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.5928 | + | 11.3119i | 1.11822 | + | 0.645605i | 0.940946 | − | 0.338557i | \(-0.109939\pi\) |
0.177274 | + | 0.984161i | \(0.443272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.7457 | − | 28.1433i | −2.77304 | − | 1.60102i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.1802i | 0.860792i | 0.902640 | + | 0.430396i | \(0.141626\pi\) | ||||
−0.902640 | + | 0.430396i | \(0.858374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.14838 | + | 3.72111i | 0.121434 | + | 0.210330i | 0.920333 | − | 0.391135i | \(-0.127917\pi\) |
−0.798899 | + | 0.601465i | \(0.794584\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 71.7550 | 4.04294 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.160202 | + | 0.277479i | 0.00899787 | + | 0.0155848i | 0.870489 | − | 0.492187i | \(-0.163803\pi\) |
−0.861491 | + | 0.507772i | \(0.830469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.162109 | + | 0.280781i | 0.00907637 | + | 0.0157207i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.7859 | − | 30.8060i | 0.992710 | − | 1.71942i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.71931 | + | 2.59474i | −0.0956647 | + | 0.144375i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.50429 | + | 2.60552i | −0.0834433 | + | 0.144528i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.34737 | + | 0.777906i | −0.0745099 | + | 0.0430183i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.5541 | + | 26.9405i | 0.857526 | + | 1.48528i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 15.7503i | − | 0.865713i | −0.901463 | − | 0.432856i | \(-0.857506\pi\) | ||
0.901463 | − | 0.432856i | \(-0.142494\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.6819 | + | 56.6067i | 1.79096 | + | 3.10203i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.9174 | −1.74383 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.84020 | − | 2.21714i | −0.209189 | − | 0.120775i | 0.391746 | − | 0.920074i | \(-0.371871\pi\) |
−0.600934 | + | 0.799298i | \(0.705205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.8150 | + | 20.4642i | −0.641704 | + | 1.11146i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.980782 | 0.0531123 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.3436i | − | 1.04446i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.0339 | − | 6.37042i | −0.594044 | − | 0.342972i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.37820 | − | 7.58327i | 0.235034 | − | 0.407091i | −0.724248 | − | 0.689539i | \(-0.757813\pi\) |
0.959283 | + | 0.282448i | \(0.0911465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.3794i | 1.67970i | 0.542819 | + | 0.839850i | \(0.317357\pi\) | ||||
−0.542819 | + | 0.839850i | \(0.682643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.1729 | + | 8.76005i | −0.809867 | + | 0.467577i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.85737 | −0.205307 | −0.102653 | − | 0.994717i | \(-0.532733\pi\) | ||||
−0.102653 | + | 0.994717i | \(0.532733\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.9915 | + | 13.2741i | −1.22026 | + | 0.704518i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.70862 | + | 8.15558i | 0.249207 | + | 0.431639i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.0177 | − | 14.4440i | −1.32039 | − | 0.762325i | −0.336596 | − | 0.941649i | \(-0.609276\pi\) |
−0.983790 | + | 0.179324i | \(0.942609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8560 | + | 2.33455i | 0.992423 | + | 0.122871i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28.8855 | − | 16.6771i | −1.51610 | − | 0.875320i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.4767 | + | 6.62606i | −0.600717 | + | 0.346824i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.0071 | − | 17.3246i | 1.56636 | − | 0.904336i | 0.569767 | − | 0.821806i | \(-0.307034\pi\) |
0.996589 | − | 0.0825294i | \(-0.0262998\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 36.0639i | 1.87741i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.2757 | − | 20.3664i | 1.83142 | − | 1.05737i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.50847 | −0.336996 | −0.168498 | − | 0.985702i | \(-0.553892\pi\) | ||||
−0.168498 | + | 0.985702i | \(0.553892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.8199 | + | 22.2047i | −0.662015 | + | 1.14664i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.778724 | + | 1.34879i | −0.0401063 | + | 0.0694662i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.8576i | 1.17412i | 0.809544 | + | 0.587059i | \(0.199714\pi\) | ||||
−0.809544 | + | 0.587059i | \(0.800286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 42.3579i | − | 2.17006i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.86012 | − | 6.68592i | 0.197243 | − | 0.341634i | −0.750391 | − | 0.660995i | \(-0.770135\pi\) |
0.947633 | + | 0.319360i | \(0.103468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.95938 | − | 3.39374i | 0.0998590 | − | 0.172961i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −55.3501 | −2.81360 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.5074 | + | 7.79852i | −0.684854 | + | 0.395401i | −0.801681 | − | 0.597752i | \(-0.796061\pi\) |
0.116827 | + | 0.993152i | \(0.462728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.13859i | − | 0.0575807i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 40.7047 | − | 23.5009i | 2.05328 | − | 1.18546i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.92069 | + | 3.41831i | −0.297902 | + | 0.171994i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.5633 | − | 10.1402i | −0.881478 | − | 0.508922i | −0.0103327 | − | 0.999947i | \(-0.503289\pi\) |
−0.871146 | + | 0.491025i | \(0.836622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.7516 | − | 47.9189i | 1.58957 | − | 2.39894i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.7743 | − | 10.2620i | −0.887608 | − | 0.512461i | −0.0144489 | − | 0.999896i | \(-0.504599\pi\) |
−0.873159 | + | 0.487435i | \(0.837933\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.35569 | + | 4.08018i | 0.117345 | + | 0.203248i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 28.8425 | − | 16.6522i | 1.43319 | − | 0.827455i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.56971 | 0.176944 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.46841 | + | 5.46659i | −0.468183 | + | 0.270306i | −0.715479 | − | 0.698634i | \(-0.753791\pi\) |
0.247296 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 29.0210i | − | 1.43150i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.4547 | − | 28.5004i | 0.809684 | − | 1.40241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.5914 | − | 6.11493i | −0.519910 | − | 0.300170i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2987i | 0.651242i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.2865 | −1.23532 | −0.617662 | − | 0.786443i | \(-0.711920\pi\) | ||||
−0.617662 | + | 0.786443i | \(0.711920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.89762 | + | 13.6791i | −0.384906 | + | 0.666677i | −0.991756 | − | 0.128139i | \(-0.959100\pi\) |
0.606850 | + | 0.794816i | \(0.292433\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 40.1019 | + | 23.1529i | 1.94982 | + | 1.12573i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.27917 | 0.0620491 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.60476 | − | 14.9039i | −0.416414 | − | 0.721249i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.80058i | 0.0869328i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.9346 | − | 32.7957i | −0.912048 | − | 1.57971i | −0.811166 | − | 0.584816i | \(-0.801167\pi\) |
−0.100882 | − | 0.994898i | \(-0.532166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.1519 | + | 18.5629i | −1.54512 | + | 0.892077i | −0.546620 | + | 0.837381i | \(0.684086\pi\) |
−0.998503 | + | 0.0546959i | \(0.982581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.70495 | − | 6.41717i | 0.177639 | − | 0.307680i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.22138 | + | 3.09795i | −0.297609 | + | 0.148195i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.17633 | − | 14.1618i | 0.390235 | − | 0.675907i | −0.602245 | − | 0.798311i | \(-0.705727\pi\) |
0.992480 | + | 0.122404i | \(0.0390604\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.8039 | − | 63.7463i | −1.75257 | − | 3.03554i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.30941 | − | 2.26796i | −0.0622119 | − | 0.107754i | 0.833242 | − | 0.552909i | \(-0.186482\pi\) |
−0.895454 | + | 0.445154i | \(0.853149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.1864 | −1.05174 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.97553 | + | 13.8140i | 0.377230 | + | 0.653381i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.9548i | 0.847342i | 0.905816 | + | 0.423671i | \(0.139259\pi\) | ||||
−0.905816 | + | 0.423671i | \(0.860741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.70569 | + | 0.984778i | 0.0803176 | + | 0.0463714i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.9945 | + | 6.34770i | 0.516569 | + | 0.298241i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.8245 | 0.882507 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.9102 | −0.744246 | −0.372123 | − | 0.928183i | \(-0.621370\pi\) | ||||
−0.372123 | + | 0.928183i | \(0.621370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.45111 | + | 3.72455i | 0.301112 | + | 0.173847i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.3144 | + | 8.84177i | 0.713262 | + | 0.411802i | 0.812268 | − | 0.583285i | \(-0.198233\pi\) |
−0.0990055 | + | 0.995087i | \(0.531566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4205i | 1.04197i | 0.853566 | + | 0.520985i | \(0.174435\pi\) | ||||
−0.853566 | + | 0.520985i | \(0.825565\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.2077 | − | 19.4123i | −0.519746 | − | 0.900226i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.8007 | −1.70293 | −0.851467 | − | 0.524408i | \(-0.824287\pi\) | ||||
−0.851467 | + | 0.524408i | \(0.824287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.3377 | + | 45.6182i | 1.21616 | + | 2.10645i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.56639 | + | 7.90923i | 0.210408 | + | 0.364438i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.51142 | + | 2.61785i | −0.0694949 | + | 0.120369i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.48047 | − | 6.98958i | −0.159695 | − | 0.320704i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.3162 | − | 52.5091i | 1.38808 | − | 2.40423i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.17380 | + | 0.677696i | −0.0536324 | + | 0.0309647i | −0.526576 | − | 0.850128i | \(-0.676525\pi\) |
0.472944 | + | 0.881092i | \(0.343191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.57390 | + | 14.8504i | 0.390936 | + | 0.677122i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.0270i | 0.956764i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.48175 | − | 16.4229i | −0.430544 | − | 0.745724i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1529 | 0.731957 | 0.365979 | − | 0.930623i | \(-0.380734\pi\) | ||||
0.365979 | + | 0.930623i | \(0.380734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.794637 | + | 0.458784i | 0.0359347 | + | 0.0207469i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.839069 | − | 1.45331i | 0.0378666 | − | 0.0655870i | −0.846471 | − | 0.532435i | \(-0.821277\pi\) |
0.884338 | + | 0.466848i | \(0.154610\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.662187 | 0.0298234 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5.83321i | − | 0.262183i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.9444 | + | 21.9072i | 1.70204 | + | 0.982672i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.6119 | − | 20.1124i | 0.519819 | − | 0.900354i | −0.479915 | − | 0.877315i | \(-0.659333\pi\) |
0.999735 | − | 0.0230387i | \(-0.00733410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.2201i | 1.08207i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.5941 | − | 14.7768i | 1.14118 | − | 0.658863i | 0.194460 | − | 0.980910i | \(-0.437704\pi\) |
0.946724 | + | 0.322047i | \(0.104371\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.0158 | 0.490196 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.0305 | − | 15.6060i | 1.20046 | − | 0.693089i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.27450 | − | 2.20750i | −0.0564913 | − | 0.0978459i | 0.836397 | − | 0.548124i | \(-0.184658\pi\) |
−0.892888 | + | 0.450279i | \(0.851325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.9407 | + | 10.9354i | 0.837888 | + | 0.483755i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.79878 | − | 45.3837i | 0.123569 | − | 2.00374i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 41.4288 | + | 23.9189i | 1.82557 | + | 1.05399i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.19009 | − | 1.26445i | 0.0963199 | − | 0.0556103i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −42.5806 | + | 24.5839i | −1.86908 | + | 1.07912i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 36.4489i | − | 1.59686i | −0.602091 | − | 0.798428i | \(-0.705665\pi\) | ||
0.602091 | − | 0.798428i | \(-0.294335\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.0155 | + | 12.7107i | −0.962673 | + | 0.555799i | −0.896995 | − | 0.442041i | \(-0.854254\pi\) |
−0.0656782 | + | 0.997841i | \(0.520921\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.6234 | −1.03101 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.00158 | − | 1.73479i | 0.0436295 | − | 0.0755685i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2289 | + | 17.7169i | −0.444734 | + | 0.770301i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 48.9869i | − | 2.12585i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.46116i | 0.409808i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.1162 | + | 26.1820i | −0.653529 | + | 1.13194i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.8385 | + | 41.2895i | −1.02871 | + | 1.78177i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.01994 | −0.173151 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1779 | − | 11.0724i | 0.824524 | − | 0.476039i | −0.0274503 | − | 0.999623i | \(-0.508739\pi\) |
0.851974 | + | 0.523584i | \(0.175405\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 0.793736i | − | 0.0340625i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.14513 | − | 0.661141i | 0.0490519 | − | 0.0283202i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.87144 | − | 4.54458i | 0.336559 | − | 0.194312i | −0.322191 | − | 0.946675i | \(-0.604419\pi\) |
0.658749 | + | 0.752363i | \(0.271086\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.1850 | − | 12.8085i | −0.946832 | − | 0.546654i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.80173 | − | 3.61828i | −0.0767562 | − | 0.154144i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.77132 | + | 5.64147i | 0.415519 | + | 0.239900i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −40.7922 | − | 70.6542i | −1.73153 | − | 2.99911i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.28385 | + | 4.78268i | −0.350998 | + | 0.202649i | −0.665125 | − | 0.746732i | \(-0.731622\pi\) |
0.314127 | + | 0.949381i | \(0.398288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.5208 | −0.614163 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.662994 | − | 0.382780i | 0.0279916 | − | 0.0161610i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.0350i | 1.18153i | 0.806842 | + | 0.590767i | \(0.201175\pi\) | ||||
−0.806842 | + | 0.590767i | \(0.798825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0416 | − | 17.3925i | 0.422452 | − | 0.731708i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −47.6007 | − | 27.4823i | −1.99904 | − | 1.15415i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 37.1158i | − | 1.55597i | −0.628280 | − | 0.777987i | \(-0.716241\pi\) | ||
0.628280 | − | 0.777987i | \(-0.283759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.10876 | −0.297492 | −0.148746 | − | 0.988875i | \(-0.547524\pi\) | ||||
−0.148746 | + | 0.988875i | \(0.547524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.20091 | + | 15.9364i | −0.384373 | + | 0.665754i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.47351 | + | 1.42808i | 0.103153 | + | 0.0595552i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.48963 | −0.270167 | −0.135083 | − | 0.990834i | \(-0.543130\pi\) | ||||
−0.135083 | + | 0.990834i | \(0.543130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.7537 | − | 20.3581i | −0.488469 | − | 0.846053i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.1838i | 0.837363i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.65566 | − | 2.86768i | −0.0685702 | − | 0.118767i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.2669 | − | 14.0105i | 1.00331 | − | 0.579262i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.8311 | + | 30.8843i | −0.735966 | + | 1.27473i | 0.218332 | + | 0.975875i | \(0.429939\pi\) |
−0.954298 | + | 0.298856i | \(0.903395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.2043 | − | 0.752628i | −0.502868 | − | 0.0310115i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.25401 | − | 14.2964i | 0.339525 | − | 0.588074i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0443 | − | 19.1293i | −0.453536 | − | 0.785547i | 0.545067 | − | 0.838393i | \(-0.316504\pi\) |
−0.998603 | + | 0.0528454i | \(0.983171\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00185 | − | 6.93140i | −0.164060 | − | 0.284160i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −57.1700 | −2.33981 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.63842 | − | 8.03398i | −0.189521 | − | 0.328260i | 0.755570 | − | 0.655068i | \(-0.227360\pi\) |
−0.945091 | + | 0.326809i | \(0.894027\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5743i | 0.839245i | 0.907699 | + | 0.419622i | \(0.137837\pi\) | ||||
−0.907699 | + | 0.419622i | \(0.862163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 67.9043 | + | 39.2046i | 2.76528 | + | 1.59653i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.5498 | + | 14.1738i | 0.998090 | + | 0.576247i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.329758 | −0.0133845 | −0.00669223 | − | 0.999978i | \(-0.502130\pi\) | ||||
−0.00669223 | + | 0.999978i | \(0.502130\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.2291 | −0.495546 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.5205 | + | 6.07402i | 0.425615 | + | 0.245729i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.6430 | + | 13.0730i | 0.914544 | + | 0.528012i | 0.881890 | − | 0.471455i | \(-0.156271\pi\) |
0.0326533 | + | 0.999467i | \(0.489604\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 45.0135i | − | 1.81512i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.8159 | − | 30.8580i | −0.717240 | − | 1.24230i | −0.962089 | − | 0.272735i | \(-0.912072\pi\) |
0.244849 | − | 0.969561i | \(-0.421262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.09549 | −0.365579 | −0.182789 | − | 0.983152i | \(-0.558513\pi\) | ||||
−0.182789 | + | 0.983152i | \(0.558513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.31625 | + | 14.4042i | 0.333720 | + | 0.578020i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.3078 | + | 31.7101i | 0.733488 | + | 1.27044i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3739 | − | 26.6284i | 0.614956 | − | 1.06513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.89549 | − | 2.58119i | −0.155571 | − | 0.103083i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.64540 | − | 6.31402i | 0.145352 | − | 0.251757i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.9863 | − | 20.1993i | 1.39278 | − | 0.804123i | 0.399160 | − | 0.916881i | \(-0.369302\pi\) |
0.993622 | + | 0.112758i | \(0.0359684\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.42911 | − | 2.47529i | −0.0568019 | − | 0.0983838i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.9999i | 1.42861i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.65530 | − | 16.7235i | −0.382557 | − | 0.662608i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 65.2193 | 2.58004 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.3374 | + | 24.4435i | 1.67223 | + | 0.965461i | 0.966388 | + | 0.257088i | \(0.0827630\pi\) |
0.705839 | + | 0.708373i | \(0.250570\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.70125 | − | 15.0710i | 0.343144 | − | 0.594343i | −0.641871 | − | 0.766813i | \(-0.721842\pi\) |
0.985015 | + | 0.172470i | \(0.0551748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 69.0858 | 2.72025 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 17.5279i | − | 0.689094i | −0.938769 | − | 0.344547i | \(-0.888033\pi\) | ||
0.938769 | − | 0.344547i | \(-0.111967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.31690 | − | 1.33766i | −0.0909461 | − | 0.0525077i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.4969 | + | 32.0375i | −0.724949 | + | 1.25565i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 43.4983i | − | 1.70222i | −0.524987 | − | 0.851111i | \(-0.675930\pi\) | ||
0.524987 | − | 0.851111i | \(-0.324070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.5948 | + | 19.9733i | −1.35173 | + | 0.780423i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.5556 | 1.27011 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.1331 | − | 20.8615i | 1.40755 | − | 0.812648i | 0.412396 | − | 0.911005i | \(-0.364692\pi\) |
0.995151 | + | 0.0983571i | \(0.0313587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.52479 | − | 16.4974i | −0.370471 | − | 0.641675i | 0.619167 | − | 0.785259i | \(-0.287470\pi\) |
−0.989638 | + | 0.143584i | \(0.954137\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.18483 | + | 1.83876i | 0.123688 | + | 0.0714116i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.9856 | + | 40.7261i | −1.04646 | + | 1.57929i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.28046 | + | 0.739273i | 0.0495795 | + | 0.0286248i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.5038 | − | 23.3849i | 1.56597 | − | 0.904111i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.21159 | + | 0.699510i | −0.0467728 | + | 0.0270043i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.4291i | 1.82826i | 0.405424 | + | 0.914129i | \(0.367124\pi\) | ||||
−0.405424 | + | 0.914129i | \(0.632876\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.1828 | + | 9.34312i | −0.622875 | + | 0.359617i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.6229 | −1.10007 | −0.550034 | − | 0.835142i | \(-0.685385\pi\) | ||||
−0.550034 | + | 0.835142i | \(0.685385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.6484 | + | 27.1038i | −0.600529 | + | 1.04015i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.46131 | + | 14.6554i | −0.324238 | + | 0.561597i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 31.8971i | − | 1.22051i | −0.792206 | − | 0.610254i | \(-0.791067\pi\) | ||
0.792206 | − | 0.610254i | \(-0.208933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.6649i | 0.942398i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.6455 | + | 34.0270i | −0.749522 | + | 1.29821i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.95328 | − | 13.7755i | 0.302996 | − | 0.524804i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.7829 | 1.43733 | 0.718664 | − | 0.695358i | \(-0.244754\pi\) | ||||
0.718664 | + | 0.695358i | \(0.244754\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.33716 | + | 4.81346i | −0.316703 | + | 0.182848i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 11.3026i | − | 0.428731i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.48371 | − | 2.01132i | 0.131955 | − | 0.0761842i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.08897 | − | 2.93812i | 0.192483 | − | 0.111130i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.5119 | + | 15.8840i | 1.03911 | + | 0.599930i | 0.919581 | − | 0.392900i | \(-0.128528\pi\) |
0.119529 | + | 0.992831i | \(0.461862\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.4194 | − | 2.73931i | −1.67531 | − | 0.103315i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −50.0537 | − | 28.8985i | −1.88513 | − | 1.08838i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.09004 | − | 15.7444i | −0.341866 | − | 0.592130i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.9172 | − | 11.4992i | 0.748007 | − | 0.431862i | −0.0769660 | − | 0.997034i | \(-0.524523\pi\) |
0.824974 | + | 0.565171i | \(0.191190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.7951 | 0.629865 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.87347 | − | 2.23635i | 0.145063 | − | 0.0837519i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.53031i | − | 0.0572303i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.1485 | + | 69.5393i | −1.49937 | + | 2.59699i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.7769 | − | 12.5729i | −0.812142 | − | 0.468890i | 0.0355572 | − | 0.999368i | \(-0.488679\pi\) |
−0.847699 | + | 0.530477i | \(0.822013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 78.9500i | − | 2.94025i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.7549 | −1.73883 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.830556 | + | 1.43856i | −0.0308461 | + | 0.0534270i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.5628 | − | 21.1095i | −1.35604 | − | 0.782909i | −0.366951 | − | 0.930240i | \(-0.619598\pi\) |
−0.989087 | + | 0.147331i | \(0.952932\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1410 | 0.523739 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.08693 | + | 5.34672i | 0.114174 | + | 0.197756i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.5644i | − | 1.46134i | −0.682729 | − | 0.730671i | \(-0.739207\pi\) | ||
0.682729 | − | 0.730671i | \(-0.260793\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 45.9372 | + | 79.5656i | 1.69442 | + | 2.93482i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.70846 | − | 2.14108i | 0.136603 | − | 0.0788676i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.0534 | − | 36.4655i | 0.774461 | − | 1.34141i | −0.160636 | − | 0.987014i | \(-0.551355\pi\) |
0.935097 | − | 0.354392i | \(-0.115312\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.38172 | − | 22.4054i | 0.0507588 | − | 0.823082i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.26746 | + | 14.3197i | −0.303304 | + | 0.525338i | −0.976882 | − | 0.213778i | \(-0.931423\pi\) |
0.673578 | + | 0.739116i | \(0.264756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.77838 | − | 11.7405i | −0.248341 | − | 0.430139i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.0221 | + | 26.0191i | 0.549631 | + | 0.951989i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.8944 | 1.82310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.7472 | + | 46.3274i | 0.976018 | + | 1.69051i | 0.676535 | + | 0.736411i | \(0.263481\pi\) |
0.299483 | + | 0.954102i | \(0.403186\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.9028i | 0.761740i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.34424 | − | 5.39490i | −0.340072 | − | 0.196340i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.9142 | − | 15.5389i | −0.978212 | − | 0.564771i | −0.0764821 | − | 0.997071i | \(-0.524369\pi\) |
−0.901730 | + | 0.432300i | \(0.857702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.70936 | 0.0620458 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1446 | −0.875242 | −0.437621 | − | 0.899160i | \(-0.644179\pi\) | ||||
−0.437621 | + | 0.899160i | \(0.644179\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.88988 | − | 1.09112i | −0.0684184 | − | 0.0395014i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.3177 | − | 5.95690i | −0.373035 | − | 0.215372i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12.8514i | − | 0.464039i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.1275 | − | 46.9862i | −0.978242 | − | 1.69437i | −0.668792 | − | 0.743450i | \(-0.733188\pi\) |
−0.309450 | − | 0.950916i | \(-0.600145\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.3945 | 1.27470 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2153 | − | 21.1576i | −0.439356 | − | 0.760986i | 0.558284 | − | 0.829650i | \(-0.311460\pi\) |
−0.997640 | + | 0.0686636i | \(0.978126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.51249 | + | 4.35175i | 0.0902511 | + | 0.156320i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −67.3222 | + | 116.605i | −2.41517 | + | 4.18320i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.4689 | − | 13.5629i | −0.733373 | − | 0.485941i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.78091 | − | 3.08463i | 0.0637260 | − | 0.110377i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.37728 | + | 4.83663i | −0.299380 | + | 0.172847i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.88097 | − | 6.72203i | −0.138518 | − | 0.239920i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.34461i | 0.261807i | 0.991395 | + | 0.130903i | \(0.0417878\pi\) | ||||
−0.991395 | + | 0.130903i | \(0.958212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9005 | − | 36.2007i | −0.744076 | − | 1.28878i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.1445 | −1.17848 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.82010 | − | 3.36024i | −0.206678 | − | 0.119326i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −37.8395 | + | 65.5399i | −1.34203 | + | 2.32446i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.5903 | −1.11899 | −0.559493 | − | 0.828835i | \(-0.689004\pi\) | ||||
−0.559493 | + | 0.828835i | \(0.689004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.16504i | − | 0.182726i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 47.2017 | + | 27.2519i | 1.66779 | + | 0.962898i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.888978 | − | 1.53976i | 0.0313714 | − | 0.0543368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 17.8708i | − | 0.629864i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 74.7327 | − | 43.1470i | 2.63072 | − | 1.51884i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.1923 | −1.76467 | −0.882334 | − | 0.470624i | \(-0.844029\pi\) | ||||
−0.882334 | + | 0.470624i | \(0.844029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.2290 | + | 11.1018i | −0.675220 | + | 0.389838i | −0.798052 | − | 0.602589i | \(-0.794136\pi\) |
0.122832 | + | 0.992428i | \(0.460802\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.11674 | − | 10.5945i | −0.214523 | − | 0.371565i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.675360 | − | 0.389919i | −0.0236568 | − | 0.0136583i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.8160 | − | 31.4152i | 0.728261 | − | 1.09908i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −40.0493 | − | 23.1224i | −1.39943 | − | 0.807964i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.6691 | − | 24.6350i | 1.48916 | − | 0.859769i | 0.489239 | − | 0.872150i | \(-0.337274\pi\) |
0.999923 | + | 0.0123810i | \(0.00394108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.331446 | − | 0.191360i | 0.0115535 | − | 0.00667040i | −0.494212 | − | 0.869341i | \(-0.664543\pi\) |
0.505766 | + | 0.862671i | \(0.331210\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.92043i | 0.0668606i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.33960 | + | 0.773418i | −0.0465824 | + | 0.0268944i | −0.523110 | − | 0.852265i | \(-0.675228\pi\) |
0.476528 | + | 0.879159i | \(0.341895\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.7078 | 1.13599 | 0.567994 | − | 0.823033i | \(-0.307720\pi\) | ||||
0.567994 | + | 0.823033i | \(0.307720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.7002 | − | 32.3898i | 0.648704 | − | 1.12359i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.10519 | + | 7.11039i | −0.142236 | + | 0.246360i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 20.5846i | − | 0.712360i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.2622i | 1.01145i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.97923 | + | 6.89223i | −0.137378 | + | 0.237946i | −0.926504 | − | 0.376286i | \(-0.877201\pi\) |
0.789125 | + | 0.614233i | \(0.210534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0700 | − | 24.3700i | 0.485174 | − | 0.840346i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.62703 | −0.0560379 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.9731 | + | 13.2635i | −0.790299 | + | 0.456280i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 46.7840i | − | 1.60752i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.88588 | + | 4.55291i | −0.270643 | + | 0.156256i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.0981 | − | 8.13954i | 0.483276 | − | 0.279020i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.06060 | + | 2.92174i | 0.173272 | + | 0.100039i | 0.584128 | − | 0.811662i | \(-0.301437\pi\) |
−0.410856 | + | 0.911700i | \(0.634770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.47626 | + | 72.5850i | −0.153085 | + | 2.48235i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.6433 | + | 15.3825i | 0.910118 | + | 0.525457i | 0.880469 | − | 0.474103i | \(-0.157228\pi\) |
0.0296491 | + | 0.999560i | \(0.490561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.27545 | − | 7.40529i | −0.145876 | − | 0.252665i | 0.783823 | − | 0.620984i | \(-0.213267\pi\) |
−0.929700 | + | 0.368319i | \(0.879933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −64.3360 | + | 37.1444i | −2.19257 | + | 1.26588i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.5152 | 0.494103 | 0.247052 | − | 0.969002i | \(-0.420538\pi\) | ||||
0.247052 | + | 0.969002i | \(0.420538\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.1892 | − | 20.8938i | 1.23047 | − | 0.710412i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 50.5630i | 1.71721i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.458614 | − | 0.794343i | 0.0155574 | − | 0.0269463i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.8143 | + | 10.2851i | 0.603615 | + | 0.348497i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.5863i | 1.57671i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.9634 | −1.21578 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.8262 | + | 18.7515i | −0.365575 | + | 0.633194i | −0.988868 | − | 0.148794i | \(-0.952461\pi\) |
0.623294 | + | 0.781988i | \(0.285794\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42.1460 | − | 24.3330i | −1.42155 | − | 0.820731i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.75645 | 0.193940 | 0.0969698 | − | 0.995287i | \(-0.469085\pi\) | ||||
0.0969698 | + | 0.995287i | \(0.469085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.9840 | − | 32.8813i | −0.638863 | − | 1.10654i | −0.985683 | − | 0.168612i | \(-0.946072\pi\) |
0.346819 | − | 0.937932i | \(-0.387262\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 61.1436i | 2.05532i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.8432 | + | 18.7809i | 0.364078 | + | 0.630602i | 0.988628 | − | 0.150383i | \(-0.0480507\pi\) |
−0.624550 | + | 0.780985i | \(0.714717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 51.4531 | − | 29.7065i | 1.72568 | − | 0.996323i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.23413 | + | 3.86962i | −0.0748460 | + | 0.129637i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.2225 | + | 14.0534i | −0.944428 | + | 0.470280i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.2603 | − | 35.0918i | 0.677226 | − | 1.17299i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.10563 | + | 7.11115i | 0.137083 | + | 0.237435i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.30063 | + | 2.25276i | 0.0433785 | + | 0.0751337i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.76305 | −0.225310 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −57.0085 | − | 98.7415i | −1.89712 | − | 3.28591i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.674594i | 0.0224243i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7864 | + | 16.0425i | 0.922633 | + | 0.532683i | 0.884474 | − | 0.466589i | \(-0.154517\pi\) |
0.0381590 | + | 0.999272i | \(0.487851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.4361 | − | 13.5309i | −0.777328 | − | 0.448790i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.7962 | −1.28538 | −0.642688 | − | 0.766128i | \(-0.722181\pi\) | ||||
−0.642688 | + | 0.766128i | \(0.722181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.64081 | 0.0543027 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.6904 | + | 15.9871i | 0.915417 | + | 0.528516i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 57.0942 | + | 32.9633i | 1.88542 | + | 1.08855i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.09055i | − | 0.134935i | −0.997721 | − | 0.0674674i | \(-0.978508\pi\) | ||
0.997721 | − | 0.0674674i | \(-0.0214919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.6854 | + | 60.0769i | 1.14292 | + | 1.97960i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.1099 | 0.563180 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.14458 | + | 15.8389i | 0.300672 | + | 0.520779i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −58.7600 | − | 101.775i | −1.92993 | − | 3.34274i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0628 | − | 24.3575i | 0.461385 | − | 0.799143i | −0.537645 | − | 0.843171i | \(-0.680686\pi\) |
0.999030 | + | 0.0440285i | \(0.0140192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.0218 | + | 3.08481i | 1.63940 | + | 0.101100i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.2734 | + | 40.3107i | −0.761936 | + | 1.31971i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.563477 | + | 0.325324i | −0.0184277 | + | 0.0106392i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.2150 | + | 35.0135i | 0.660397 | + | 1.14384i | 0.980511 | + | 0.196462i | \(0.0629452\pi\) |
−0.320115 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.1751i | 0.429952i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.0744 | + | 22.6456i | 0.426215 | + | 0.738226i | 0.996533 | − | 0.0831981i | \(-0.0265134\pi\) |
−0.570318 | + | 0.821424i | \(0.693180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.98184 | 0.292489 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 101.254 | + | 58.4592i | 3.29380 | + | 1.90168i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.0421 | + | 27.7858i | −0.521299 | + | 0.902917i | 0.478394 | + | 0.878145i | \(0.341219\pi\) |
−0.999693 | + | 0.0247713i | \(0.992114\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.54077 | 0.277245 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.982449i | 0.0318581i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.9593 | − | 8.05939i | −0.452185 | − | 0.261069i | 0.256567 | − | 0.966526i | \(-0.417408\pi\) |
−0.708753 | + | 0.705457i | \(0.750742\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.81983 | − | 13.5443i | 0.253044 | − | 0.438285i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.994142i | 0.0321360i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.2526 | − | 20.3531i | 1.13836 | − | 0.657235i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.1310 | −0.746162 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 64.3194 | − | 37.1348i | 2.07266 | − | 1.19665i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.98948 | + | 17.3023i | 0.321573 | + | 0.556980i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.9035 | + | 19.5742i | 1.09026 | + | 0.629464i | 0.933647 | − | 0.358195i | \(-0.116608\pi\) |
0.156617 | + | 0.987659i | \(0.449941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.54365 | + | 4.25433i | −0.274462 | + | 0.136669i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3501 | − | 6.55297i | −0.364241 | − | 0.210295i | 0.306698 | − | 0.951807i | \(-0.400776\pi\) |
−0.670940 | + | 0.741512i | \(0.734109\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.1543 | + | 9.32669i | −0.517883 | + | 0.299000i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.98922 | + | 4.61258i | −0.255860 | + | 0.147721i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.1689i | 1.15715i | 0.815631 | + | 0.578573i | \(0.196390\pi\) | ||||
−0.815631 | + | 0.578573i | \(0.803610\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.57782 | − | 1.48831i | 0.0823876 | − | 0.0475665i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.24836 | −0.103712 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.9126 | + | 22.3653i | −0.411849 | + | 0.713343i | −0.995092 | − | 0.0989546i | \(-0.968450\pi\) |
0.583243 | + | 0.812298i | \(0.301783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.01506 | + | 12.1504i | −0.223519 | + | 0.387145i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 95.3863i | 3.03618i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.7851i | 0.438342i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0397 | + | 22.5855i | −0.414221 | + | 0.717452i | −0.995346 | − | 0.0963621i | \(-0.969279\pi\) |
0.581125 | + | 0.813814i | \(0.302613\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.1473 | − | 41.8243i | 0.766291 | − | 1.32726i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.5886 | 1.54036 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.5744 | − | 16.4974i | 0.904961 | − | 0.522479i | 0.0261544 | − | 0.999658i | \(-0.491674\pi\) |
0.878806 | + | 0.477179i | \(0.158341\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 106.504i | 3.36965i |
(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 | 608.2.s.c.559.13 | 28 | ||
4.3 | odd | 2 | 152.2.o.c.27.14 | yes | 28 | ||
8.3 | odd | 2 | inner | 608.2.s.c.559.14 | 28 | ||
8.5 | even | 2 | 152.2.o.c.27.11 | ✓ | 28 | ||
19.12 | odd | 6 | inner | 608.2.s.c.335.14 | 28 | ||
76.31 | even | 6 | 152.2.o.c.107.11 | yes | 28 | ||
152.69 | odd | 6 | 152.2.o.c.107.14 | yes | 28 | ||
152.107 | even | 6 | inner | 608.2.s.c.335.13 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.o.c.27.11 | ✓ | 28 | 8.5 | even | 2 | ||
152.2.o.c.27.14 | yes | 28 | 4.3 | odd | 2 | ||
152.2.o.c.107.11 | yes | 28 | 76.31 | even | 6 | ||
152.2.o.c.107.14 | yes | 28 | 152.69 | odd | 6 | ||
608.2.s.c.335.13 | 28 | 152.107 | even | 6 | inner | ||
608.2.s.c.335.14 | 28 | 19.12 | odd | 6 | inner | ||
608.2.s.c.559.13 | 28 | 1.1 | even | 1 | trivial | ||
608.2.s.c.559.14 | 28 | 8.3 | odd | 2 | inner |