Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(169,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bh (of order \(6\), degree \(2\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 169.8 | ||
Character | \(\chi\) | \(=\) | 315.169 |
Dual form | 315.2.bh.c.274.8 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39315 | − | 0.804334i | −0.985105 | − | 0.568750i | −0.0812972 | − | 0.996690i | \(-0.525906\pi\) |
−0.903807 | + | 0.427940i | \(0.859240\pi\) | |||||||
\(3\) | 1.72917 | + | 0.0997919i | 0.998339 | + | 0.0576149i | ||||
\(4\) | 0.293908 | + | 0.509063i | 0.146954 | + | 0.254532i | ||||
\(5\) | −2.18712 | + | 0.465298i | −0.978110 | + | 0.208088i | ||||
\(6\) | −2.32873 | − | 1.52986i | −0.950700 | − | 0.624562i | ||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | 2.27174i | 0.803180i | ||||||||
\(9\) | 2.98008 | + | 0.345115i | 0.993361 | + | 0.115038i | ||||
\(10\) | 3.42124 | + | 1.11095i | 1.08189 | + | 0.351312i | ||||
\(11\) | 2.56920 | − | 4.44998i | 0.774642 | − | 1.34172i | −0.160354 | − | 0.987060i | \(-0.551264\pi\) |
0.934996 | − | 0.354659i | \(-0.115403\pi\) | |||||||
\(12\) | 0.457417 | + | 0.909589i | 0.132045 | + | 0.262576i | ||||
\(13\) | 2.41638 | − | 1.39510i | 0.670183 | − | 0.386930i | −0.125963 | − | 0.992035i | \(-0.540202\pi\) |
0.796146 | + | 0.605105i | \(0.206869\pi\) | |||||||
\(14\) | −0.804334 | − | 1.39315i | −0.214967 | − | 0.372335i | ||||
\(15\) | −3.82834 | + | 0.586324i | −0.988474 | + | 0.151388i | ||||
\(16\) | 2.41505 | − | 4.18299i | 0.603763 | − | 1.04575i | ||||
\(17\) | − | 5.02287i | − | 1.21822i | −0.793084 | − | 0.609112i | \(-0.791526\pi\) | ||
0.793084 | − | 0.609112i | \(-0.208474\pi\) | |||||||
\(18\) | −3.87411 | − | 2.87778i | −0.913136 | − | 0.678299i | ||||
\(19\) | 3.95491 | 0.907318 | 0.453659 | − | 0.891175i | \(-0.350118\pi\) | ||||
0.453659 | + | 0.891175i | \(0.350118\pi\) | |||||||
\(20\) | −0.879678 | − | 0.976628i | −0.196702 | − | 0.218381i | ||||
\(21\) | 1.44761 | + | 0.951009i | 0.315895 | + | 0.207527i | ||||
\(22\) | −7.15854 | + | 4.13299i | −1.52621 | + | 0.881155i | ||||
\(23\) | −2.87747 | + | 1.66131i | −0.599994 | + | 0.346407i | −0.769039 | − | 0.639201i | \(-0.779265\pi\) |
0.169045 | + | 0.985608i | \(0.445932\pi\) | |||||||
\(24\) | −0.226701 | + | 3.92823i | −0.0462751 | + | 0.801846i | ||||
\(25\) | 4.56700 | − | 2.03533i | 0.913399 | − | 0.407065i | ||||
\(26\) | −4.48850 | −0.880267 | ||||||||
\(27\) | 5.11864 | + | 0.894152i | 0.985083 | + | 0.172080i | ||||
\(28\) | 0.587816i | 0.111087i | ||||||||
\(29\) | −3.53526 | + | 6.12325i | −0.656481 | + | 1.13706i | 0.325039 | + | 0.945701i | \(0.394622\pi\) |
−0.981520 | + | 0.191358i | \(0.938711\pi\) | |||||||
\(30\) | 5.80505 | + | 2.26243i | 1.05985 | + | 0.413062i | ||||
\(31\) | −1.26129 | − | 2.18461i | −0.226534 | − | 0.392368i | 0.730245 | − | 0.683186i | \(-0.239406\pi\) |
−0.956778 | + | 0.290818i | \(0.906073\pi\) | |||||||
\(32\) | −2.79429 | + | 1.61328i | −0.493965 | + | 0.285191i | ||||
\(33\) | 4.88666 | − | 7.43840i | 0.850658 | − | 1.29486i | ||||
\(34\) | −4.04006 | + | 6.99760i | −0.692865 | + | 1.20008i | ||||
\(35\) | −2.12675 | − | 0.690600i | −0.359487 | − | 0.116733i | ||||
\(36\) | 0.700185 | + | 1.61848i | 0.116697 | + | 0.269747i | ||||
\(37\) | − | 0.847715i | − | 0.139364i | −0.997569 | − | 0.0696818i | \(-0.977802\pi\) | ||
0.997569 | − | 0.0696818i | \(-0.0221984\pi\) | |||||||
\(38\) | −5.50977 | − | 3.18107i | −0.893803 | − | 0.516037i | ||||
\(39\) | 4.31756 | − | 2.17123i | 0.691363 | − | 0.347675i | ||||
\(40\) | −1.05704 | − | 4.96856i | −0.167132 | − | 0.785599i | ||||
\(41\) | −0.533089 | − | 0.923337i | −0.0832545 | − | 0.144201i | 0.821392 | − | 0.570365i | \(-0.193198\pi\) |
−0.904646 | + | 0.426164i | \(0.859865\pi\) | |||||||
\(42\) | −1.25181 | − | 2.48926i | −0.193158 | − | 0.384101i | ||||
\(43\) | −1.32058 | − | 0.762435i | −0.201386 | − | 0.116270i | 0.395916 | − | 0.918287i | \(-0.370427\pi\) |
−0.597302 | + | 0.802017i | \(0.703761\pi\) | |||||||
\(44\) | 3.02043 | 0.455347 | ||||||||
\(45\) | −6.67838 | + | 0.631819i | −0.995555 | + | 0.0941860i | ||||
\(46\) | 5.34499 | 0.788076 | ||||||||
\(47\) | 6.74570 | + | 3.89463i | 0.983962 | + | 0.568091i | 0.903464 | − | 0.428664i | \(-0.141016\pi\) |
0.0804981 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(48\) | 4.59347 | − | 6.99212i | 0.663011 | − | 1.00923i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | −7.99958 | − | 0.837880i | −1.13131 | − | 0.118494i | ||||
\(51\) | 0.501241 | − | 8.68541i | 0.0701878 | − | 1.21620i | ||||
\(52\) | 1.42039 | + | 0.820060i | 0.196972 | + | 0.113722i | ||||
\(53\) | − | 13.6197i | − | 1.87081i | −0.353581 | − | 0.935404i | \(-0.615036\pi\) | ||
0.353581 | − | 0.935404i | \(-0.384964\pi\) | |||||||
\(54\) | −6.41183 | − | 5.36279i | −0.872539 | − | 0.729783i | ||||
\(55\) | −3.54858 | + | 10.9281i | −0.478490 | + | 1.47354i | ||||
\(56\) | −1.13587 | + | 1.96738i | −0.151787 | + | 0.262902i | ||||
\(57\) | 6.83872 | + | 0.394668i | 0.905810 | + | 0.0522750i | ||||
\(58\) | 9.85028 | − | 5.68706i | 1.29340 | − | 0.746748i | ||||
\(59\) | 6.59761 | + | 11.4274i | 0.858935 | + | 1.48772i | 0.872946 | + | 0.487817i | \(0.162207\pi\) |
−0.0140106 | + | 0.999902i | \(0.504460\pi\) | |||||||
\(60\) | −1.42366 | − | 1.77654i | −0.183793 | − | 0.229351i | ||||
\(61\) | −2.62959 | + | 4.55458i | −0.336684 | + | 0.583154i | −0.983807 | − | 0.179232i | \(-0.942639\pi\) |
0.647123 | + | 0.762386i | \(0.275972\pi\) | |||||||
\(62\) | 4.05798i | 0.515364i | ||||||||
\(63\) | 2.40827 | + | 1.78892i | 0.303414 | + | 0.225383i | ||||
\(64\) | −4.46973 | −0.558717 | ||||||||
\(65\) | −4.63578 | + | 4.17558i | −0.574997 | + | 0.517917i | ||||
\(66\) | −12.7908 | + | 6.43229i | −1.57444 | + | 0.791760i | ||||
\(67\) | −8.26580 | + | 4.77226i | −1.00983 | + | 0.583024i | −0.911141 | − | 0.412094i | \(-0.864797\pi\) |
−0.0986866 | + | 0.995119i | \(0.531464\pi\) | |||||||
\(68\) | 2.55696 | − | 1.47626i | 0.310077 | − | 0.179023i | ||||
\(69\) | −5.14143 | + | 2.58554i | −0.618956 | + | 0.311263i | ||||
\(70\) | 2.40741 | + | 2.67273i | 0.287740 | + | 0.319452i | ||||
\(71\) | 0.967909 | 0.114870 | 0.0574349 | − | 0.998349i | \(-0.481708\pi\) | ||||
0.0574349 | + | 0.998349i | \(0.481708\pi\) | |||||||
\(72\) | −0.784011 | + | 6.76996i | −0.0923965 | + | 0.797848i | ||||
\(73\) | 4.82868i | 0.565155i | 0.959245 | + | 0.282577i | \(0.0911894\pi\) | ||||
−0.959245 | + | 0.282577i | \(0.908811\pi\) | |||||||
\(74\) | −0.681846 | + | 1.18099i | −0.0792630 | + | 0.137288i | ||||
\(75\) | 8.10024 | − | 3.06368i | 0.935335 | − | 0.353764i | ||||
\(76\) | 1.16238 | + | 2.01330i | 0.133334 | + | 0.230941i | ||||
\(77\) | 4.44998 | − | 2.56920i | 0.507122 | − | 0.292787i | ||||
\(78\) | −7.76139 | − | 0.447916i | −0.878805 | − | 0.0507165i | ||||
\(79\) | −3.00027 | + | 5.19662i | −0.337556 | + | 0.584665i | −0.983973 | − | 0.178320i | \(-0.942934\pi\) |
0.646416 | + | 0.762985i | \(0.276267\pi\) | |||||||
\(80\) | −3.33567 | + | 10.2724i | −0.372939 | + | 1.14849i | ||||
\(81\) | 8.76179 | + | 2.05694i | 0.973532 | + | 0.228549i | ||||
\(82\) | 1.71513i | 0.189404i | ||||||||
\(83\) | 2.17078 | + | 1.25330i | 0.238275 | + | 0.137568i | 0.614383 | − | 0.789008i | \(-0.289405\pi\) |
−0.376109 | + | 0.926575i | \(0.622738\pi\) | |||||||
\(84\) | −0.0586592 | + | 1.01644i | −0.00640025 | + | 0.110902i | ||||
\(85\) | 2.33713 | + | 10.9856i | 0.253497 | + | 1.19156i | ||||
\(86\) | 1.22651 | + | 2.12437i | 0.132258 | + | 0.229077i | ||||
\(87\) | −6.72413 | + | 10.2354i | −0.720902 | + | 1.09735i | ||||
\(88\) | 10.1092 | + | 5.83654i | 1.07764 | + | 0.622177i | ||||
\(89\) | 7.34250 | 0.778303 | 0.389152 | − | 0.921174i | \(-0.372768\pi\) | ||||
0.389152 | + | 0.921174i | \(0.372768\pi\) | |||||||
\(90\) | 9.81217 | + | 4.49144i | 1.03429 | + | 0.473439i | ||||
\(91\) | 2.79019 | 0.292492 | ||||||||
\(92\) | −1.69142 | − | 0.976544i | −0.176343 | − | 0.101812i | ||||
\(93\) | −1.96298 | − | 3.90344i | −0.203551 | − | 0.404768i | ||||
\(94\) | −6.26518 | − | 10.8516i | −0.646204 | − | 1.11926i | ||||
\(95\) | −8.64986 | + | 1.84021i | −0.887457 | + | 0.188802i | ||||
\(96\) | −4.99280 | + | 2.51080i | −0.509576 | + | 0.256257i | ||||
\(97\) | −2.22850 | − | 1.28662i | −0.226270 | − | 0.130637i | 0.382580 | − | 0.923922i | \(-0.375036\pi\) |
−0.608850 | + | 0.793285i | \(0.708369\pi\) | |||||||
\(98\) | − | 1.60867i | − | 0.162500i | ||||||
\(99\) | 9.19217 | − | 12.3746i | 0.923848 | − | 1.24370i | ||||
\(100\) | 2.37839 | + | 1.72669i | 0.237839 | + | 0.172669i | ||||
\(101\) | −2.50533 | + | 4.33935i | −0.249289 | + | 0.431782i | −0.963329 | − | 0.268324i | \(-0.913530\pi\) |
0.714039 | + | 0.700105i | \(0.246864\pi\) | |||||||
\(102\) | −7.68428 | + | 11.6969i | −0.760857 | + | 1.15817i | ||||
\(103\) | −13.8168 | + | 7.97712i | −1.36141 | + | 0.786009i | −0.989811 | − | 0.142386i | \(-0.954523\pi\) |
−0.371596 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(104\) | 3.16929 | + | 5.48938i | 0.310775 | + | 0.538278i | ||||
\(105\) | −3.60861 | − | 1.40640i | −0.352164 | − | 0.137251i | ||||
\(106\) | −10.9548 | + | 18.9742i | −1.06402 | + | 1.84294i | ||||
\(107\) | − | 14.8227i | − | 1.43296i | −0.697606 | − | 0.716481i | \(-0.745752\pi\) | ||
0.697606 | − | 0.716481i | \(-0.254248\pi\) | |||||||
\(108\) | 1.04923 | + | 2.86851i | 0.100962 | + | 0.276023i | ||||
\(109\) | −5.14661 | −0.492956 | −0.246478 | − | 0.969148i | \(-0.579273\pi\) | ||||
−0.246478 | + | 0.969148i | \(0.579273\pi\) | |||||||
\(110\) | 13.7335 | − | 12.3702i | 1.30944 | − | 1.17945i | ||||
\(111\) | 0.0845951 | − | 1.46585i | 0.00802941 | − | 0.139132i | ||||
\(112\) | 4.18299 | − | 2.41505i | 0.395256 | − | 0.228201i | ||||
\(113\) | −16.2597 | + | 9.38755i | −1.52958 | + | 0.883106i | −0.530206 | + | 0.847869i | \(0.677885\pi\) |
−0.999379 | + | 0.0352374i | \(0.988781\pi\) | |||||||
\(114\) | −9.20990 | − | 6.05045i | −0.862587 | − | 0.566676i | ||||
\(115\) | 5.52037 | − | 4.97237i | 0.514778 | − | 0.463676i | ||||
\(116\) | −4.15616 | −0.385890 | ||||||||
\(117\) | 7.68248 | − | 3.32358i | 0.710246 | − | 0.307265i | ||||
\(118\) | − | 21.2267i | − | 1.95408i | ||||||
\(119\) | 2.51143 | − | 4.34993i | 0.230223 | − | 0.398757i | ||||
\(120\) | −1.33197 | − | 8.69699i | −0.121592 | − | 0.793923i | ||||
\(121\) | −7.70153 | − | 13.3394i | −0.700139 | − | 1.21268i | ||||
\(122\) | 7.32681 | − | 4.23014i | 0.663338 | − | 0.382979i | ||||
\(123\) | −0.829662 | − | 1.64981i | −0.0748081 | − | 0.148758i | ||||
\(124\) | 0.741404 | − | 1.28415i | 0.0665800 | − | 0.115320i | ||||
\(125\) | −9.04154 | + | 6.57652i | −0.808700 | + | 0.588222i | ||||
\(126\) | −1.91619 | − | 4.42929i | −0.170708 | − | 0.394592i | ||||
\(127\) | − | 10.0154i | − | 0.888724i | −0.895847 | − | 0.444362i | \(-0.853430\pi\) | ||
0.895847 | − | 0.444362i | \(-0.146570\pi\) | |||||||
\(128\) | 11.8156 | + | 6.82173i | 1.04436 | + | 0.602961i | ||||
\(129\) | −2.20742 | − | 1.45017i | −0.194353 | − | 0.127680i | ||||
\(130\) | 9.81689 | − | 2.08849i | 0.860998 | − | 0.183173i | ||||
\(131\) | 7.33474 | + | 12.7041i | 0.640840 | + | 1.10997i | 0.985246 | + | 0.171146i | \(0.0547470\pi\) |
−0.344406 | + | 0.938821i | \(0.611920\pi\) | |||||||
\(132\) | 5.22284 | + | 0.301414i | 0.454590 | + | 0.0262347i | ||||
\(133\) | 3.42505 | + | 1.97745i | 0.296989 | + | 0.171467i | ||||
\(134\) | 15.3540 | 1.32638 | ||||||||
\(135\) | −11.6111 | + | 0.426076i | −0.999327 | + | 0.0366708i | ||||
\(136\) | 11.4106 | 0.978453 | ||||||||
\(137\) | −6.19298 | − | 3.57552i | −0.529102 | − | 0.305477i | 0.211549 | − | 0.977367i | \(-0.432149\pi\) |
−0.740651 | + | 0.671890i | \(0.765483\pi\) | |||||||
\(138\) | 9.24242 | + | 0.533387i | 0.786767 | + | 0.0454049i | ||||
\(139\) | −9.20239 | − | 15.9390i | −0.780536 | − | 1.35193i | −0.931630 | − | 0.363409i | \(-0.881613\pi\) |
0.151093 | − | 0.988519i | \(-0.451721\pi\) | |||||||
\(140\) | −0.273510 | − | 1.28562i | −0.0231158 | − | 0.108655i | ||||
\(141\) | 11.2758 | + | 7.40767i | 0.949597 | + | 0.623838i | ||||
\(142\) | −1.34844 | − | 0.778523i | −0.113159 | − | 0.0653322i | ||||
\(143\) | − | 14.3371i | − | 1.19893i | ||||||
\(144\) | 8.64067 | − | 11.6322i | 0.720056 | − | 0.969350i | ||||
\(145\) | 4.88290 | − | 15.0372i | 0.405503 | − | 1.24877i | ||||
\(146\) | 3.88388 | − | 6.72707i | 0.321432 | − | 0.556736i | ||||
\(147\) | 0.778165 | + | 1.54740i | 0.0641819 | + | 0.127628i | ||||
\(148\) | 0.431541 | − | 0.249150i | 0.0354724 | − | 0.0204800i | ||||
\(149\) | 3.50121 | + | 6.06427i | 0.286830 | + | 0.496804i | 0.973051 | − | 0.230589i | \(-0.0740651\pi\) |
−0.686221 | + | 0.727393i | \(0.740732\pi\) | |||||||
\(150\) | −13.7491 | − | 2.24713i | −1.12261 | − | 0.183478i | ||||
\(151\) | −3.63064 | + | 6.28846i | −0.295458 | + | 0.511747i | −0.975091 | − | 0.221804i | \(-0.928805\pi\) |
0.679634 | + | 0.733552i | \(0.262139\pi\) | |||||||
\(152\) | 8.98450i | 0.728740i | ||||||||
\(153\) | 1.73347 | − | 14.9686i | 0.140142 | − | 1.21014i | ||||
\(154\) | −8.26597 | −0.666091 | ||||||||
\(155\) | 3.77508 | + | 4.19114i | 0.303222 | + | 0.336640i | ||||
\(156\) | 2.37426 | + | 1.55977i | 0.190093 | + | 0.124881i | ||||
\(157\) | −8.03571 | + | 4.63942i | −0.641320 | + | 0.370266i | −0.785123 | − | 0.619340i | \(-0.787400\pi\) |
0.143803 | + | 0.989606i | \(0.454067\pi\) | |||||||
\(158\) | 8.35963 | − | 4.82644i | 0.665057 | − | 0.383971i | ||||
\(159\) | 1.35913 | − | 23.5508i | 0.107786 | − | 1.86770i | ||||
\(160\) | 5.36079 | − | 4.82862i | 0.423807 | − | 0.381736i | ||||
\(161\) | −3.32262 | −0.261859 | ||||||||
\(162\) | −10.5520 | − | 9.91304i | −0.829044 | − | 0.778842i | ||||
\(163\) | 9.61624i | 0.753202i | 0.926376 | + | 0.376601i | \(0.122907\pi\) | ||||
−0.926376 | + | 0.376601i | \(0.877093\pi\) | |||||||
\(164\) | 0.313358 | − | 0.542752i | 0.0244692 | − | 0.0423818i | ||||
\(165\) | −7.22664 | + | 18.5424i | −0.562593 | + | 1.44353i | ||||
\(166\) | −2.01615 | − | 3.49207i | −0.156484 | − | 0.271038i | ||||
\(167\) | 20.1797 | − | 11.6508i | 1.56155 | − | 0.901563i | 0.564452 | − | 0.825466i | \(-0.309088\pi\) |
0.997100 | − | 0.0760968i | \(-0.0242458\pi\) | |||||||
\(168\) | −2.16044 | + | 3.28859i | −0.166682 | + | 0.253721i | ||||
\(169\) | −2.60741 | + | 4.51616i | −0.200570 | + | 0.347397i | ||||
\(170\) | 5.58014 | − | 17.1844i | 0.427977 | − | 1.31799i | ||||
\(171\) | 11.7859 | + | 1.36490i | 0.901294 | + | 0.104376i | ||||
\(172\) | − | 0.896343i | − | 0.0683455i | ||||||
\(173\) | 9.10571 | + | 5.25719i | 0.692295 | + | 0.399696i | 0.804471 | − | 0.593992i | \(-0.202449\pi\) |
−0.112176 | + | 0.993688i | \(0.535782\pi\) | |||||||
\(174\) | 17.6004 | − | 8.85094i | 1.33428 | − | 0.670988i | ||||
\(175\) | 4.97280 | + | 0.520853i | 0.375908 | + | 0.0393728i | ||||
\(176\) | −12.4095 | − | 21.4939i | −0.935400 | − | 1.62016i | ||||
\(177\) | 10.2680 | + | 20.4183i | 0.771794 | + | 1.53474i | ||||
\(178\) | −10.2292 | − | 5.90582i | −0.766710 | − | 0.442660i | ||||
\(179\) | −23.5829 | −1.76267 | −0.881333 | − | 0.472496i | \(-0.843353\pi\) | ||||
−0.881333 | + | 0.472496i | \(0.843353\pi\) | |||||||
\(180\) | −2.28447 | − | 3.21402i | −0.170274 | − | 0.239559i | ||||
\(181\) | 13.9662 | 1.03810 | 0.519050 | − | 0.854744i | \(-0.326286\pi\) | ||||
0.519050 | + | 0.854744i | \(0.326286\pi\) | |||||||
\(182\) | −3.88715 | − | 2.24425i | −0.288135 | − | 0.166355i | ||||
\(183\) | −5.00153 | + | 7.61325i | −0.369723 | + | 0.562788i | ||||
\(184\) | −3.77406 | − | 6.53686i | −0.278227 | − | 0.481904i | ||||
\(185\) | 0.394440 | + | 1.85406i | 0.0289998 | + | 0.136313i | ||||
\(186\) | −0.404954 | + | 7.01696i | −0.0296927 | + | 0.514508i | ||||
\(187\) | −22.3516 | − | 12.9047i | −1.63451 | − | 0.943687i | ||||
\(188\) | 4.57866i | 0.333933i | ||||||||
\(189\) | 3.98580 | + | 3.33368i | 0.289924 | + | 0.242489i | ||||
\(190\) | 13.5307 | + | 4.39369i | 0.981618 | + | 0.318752i | ||||
\(191\) | 2.67604 | − | 4.63504i | 0.193631 | − | 0.335380i | −0.752820 | − | 0.658227i | \(-0.771307\pi\) |
0.946451 | + | 0.322847i | \(0.104640\pi\) | |||||||
\(192\) | −7.72895 | − | 0.446043i | −0.557789 | − | 0.0321904i | ||||
\(193\) | 6.16954 | − | 3.56199i | 0.444093 | − | 0.256397i | −0.261239 | − | 0.965274i | \(-0.584131\pi\) |
0.705332 | + | 0.708877i | \(0.250798\pi\) | |||||||
\(194\) | 2.06975 | + | 3.58492i | 0.148600 | + | 0.257382i | ||||
\(195\) | −8.43275 | + | 6.75770i | −0.603882 | + | 0.483929i | ||||
\(196\) | −0.293908 | + | 0.509063i | −0.0209934 | + | 0.0363617i | ||||
\(197\) | 13.5208i | 0.963320i | 0.876358 | + | 0.481660i | \(0.159966\pi\) | ||||
−0.876358 | + | 0.481660i | \(0.840034\pi\) | |||||||
\(198\) | −22.7594 | + | 9.84612i | −1.61744 | + | 0.699733i | ||||
\(199\) | −6.61711 | −0.469074 | −0.234537 | − | 0.972107i | \(-0.575357\pi\) | ||||
−0.234537 | + | 0.972107i | \(0.575357\pi\) | |||||||
\(200\) | 4.62373 | + | 10.3750i | 0.326947 | + | 0.733624i | ||||
\(201\) | −14.7692 | + | 7.42721i | −1.04174 | + | 0.523875i | ||||
\(202\) | 6.98058 | − | 4.03024i | 0.491152 | − | 0.283567i | ||||
\(203\) | −6.12325 | + | 3.53526i | −0.429768 | + | 0.248127i | ||||
\(204\) | 4.56874 | − | 2.29755i | 0.319876 | − | 0.160860i | ||||
\(205\) | 1.59556 | + | 1.77140i | 0.111439 | + | 0.123720i | ||||
\(206\) | 25.6651 | 1.78817 | ||||||||
\(207\) | −9.14845 | + | 3.95778i | −0.635861 | + | 0.275085i | ||||
\(208\) | − | 13.4769i | − | 0.934457i | ||||||
\(209\) | 10.1609 | − | 17.5992i | 0.702846 | − | 1.21736i | ||||
\(210\) | 3.89611 | + | 4.86185i | 0.268857 | + | 0.335500i | ||||
\(211\) | −4.11043 | − | 7.11948i | −0.282974 | − | 0.490125i | 0.689142 | − | 0.724626i | \(-0.257988\pi\) |
−0.972116 | + | 0.234501i | \(0.924654\pi\) | |||||||
\(212\) | 6.93328 | − | 4.00293i | 0.476180 | − | 0.274923i | ||||
\(213\) | 1.67368 | + | 0.0965895i | 0.114679 | + | 0.00661820i | ||||
\(214\) | −11.9224 | + | 20.6502i | −0.814998 | + | 1.41162i | ||||
\(215\) | 3.24302 | + | 1.05308i | 0.221172 | + | 0.0718192i | ||||
\(216\) | −2.03128 | + | 11.6282i | −0.138211 | + | 0.791199i | ||||
\(217\) | − | 2.52257i | − | 0.171243i | ||||||
\(218\) | 7.17000 | + | 4.13960i | 0.485613 | + | 0.280369i | ||||
\(219\) | −0.481864 | + | 8.34963i | −0.0325613 | + | 0.564216i | ||||
\(220\) | −6.60604 | + | 1.40540i | −0.445379 | + | 0.0947520i | ||||
\(221\) | −7.00739 | − | 12.1371i | −0.471368 | − | 0.816433i | ||||
\(222\) | −1.29688 | + | 1.97410i | −0.0870412 | + | 0.132493i | ||||
\(223\) | −2.57291 | − | 1.48547i | −0.172295 | − | 0.0994745i | 0.411373 | − | 0.911467i | \(-0.365049\pi\) |
−0.583667 | + | 0.811993i | \(0.698383\pi\) | |||||||
\(224\) | −3.22656 | −0.215584 | ||||||||
\(225\) | 14.3124 | − | 4.48930i | 0.954163 | − | 0.299287i | ||||
\(226\) | 30.2029 | 2.00907 | ||||||||
\(227\) | 9.15036 | + | 5.28296i | 0.607331 | + | 0.350643i | 0.771920 | − | 0.635720i | \(-0.219297\pi\) |
−0.164589 | + | 0.986362i | \(0.552630\pi\) | |||||||
\(228\) | 1.80904 | + | 3.59734i | 0.119807 | + | 0.238239i | ||||
\(229\) | 5.94717 | + | 10.3008i | 0.393000 | + | 0.680696i | 0.992844 | − | 0.119421i | \(-0.0381039\pi\) |
−0.599844 | + | 0.800117i | \(0.704771\pi\) | |||||||
\(230\) | −11.6901 | + | 2.48702i | −0.770825 | + | 0.163989i | ||||
\(231\) | 7.95117 | − | 3.99851i | 0.523148 | − | 0.263083i | ||||
\(232\) | −13.9104 | − | 8.03118i | −0.913263 | − | 0.527273i | ||||
\(233\) | 18.9856i | 1.24379i | 0.783103 | + | 0.621893i | \(0.213636\pi\) | ||||
−0.783103 | + | 0.621893i | \(0.786364\pi\) | |||||||
\(234\) | −13.3761 | − | 1.54905i | −0.874423 | − | 0.101264i | ||||
\(235\) | −16.5658 | − | 5.37927i | −1.08064 | − | 0.350905i | ||||
\(236\) | −3.87818 | + | 6.71720i | −0.252448 | + | 0.437252i | ||||
\(237\) | −5.70656 | + | 8.68645i | −0.370681 | + | 0.564245i | ||||
\(238\) | −6.99760 | + | 4.04006i | −0.453587 | + | 0.261878i | ||||
\(239\) | −9.59908 | − | 16.6261i | −0.620913 | − | 1.07545i | −0.989316 | − | 0.145786i | \(-0.953429\pi\) |
0.368404 | − | 0.929666i | \(-0.379904\pi\) | |||||||
\(240\) | −6.79306 | + | 17.4299i | −0.438490 | + | 1.12510i | ||||
\(241\) | 12.5787 | − | 21.7869i | 0.810263 | − | 1.40342i | −0.102418 | − | 0.994741i | \(-0.532658\pi\) |
0.912680 | − | 0.408674i | \(-0.134009\pi\) | |||||||
\(242\) | 24.7784i | 1.59282i | ||||||||
\(243\) | 14.9454 | + | 4.43117i | 0.958747 | + | 0.284260i | ||||
\(244\) | −3.09143 | −0.197908 | ||||||||
\(245\) | −1.49652 | − | 1.66145i | −0.0956092 | − | 0.106146i | ||||
\(246\) | −0.171156 | + | 2.96575i | −0.0109125 | + | 0.189090i | ||||
\(247\) | 9.55655 | − | 5.51748i | 0.608069 | − | 0.351069i | ||||
\(248\) | 4.96286 | − | 2.86531i | 0.315142 | − | 0.181947i | ||||
\(249\) | 3.62859 | + | 2.38381i | 0.229953 | + | 0.151068i | ||||
\(250\) | 17.8859 | − | 1.88965i | 1.13121 | − | 0.119512i | ||||
\(251\) | −29.8394 | −1.88344 | −0.941722 | − | 0.336391i | \(-0.890794\pi\) | ||||
−0.941722 | + | 0.336391i | \(0.890794\pi\) | |||||||
\(252\) | −0.202864 | + | 1.75174i | −0.0127792 | + | 0.110349i | ||||
\(253\) | 17.0729i | 1.07336i | ||||||||
\(254\) | −8.05574 | + | 13.9529i | −0.505462 | + | 0.875486i | ||||
\(255\) | 2.94503 | + | 19.2293i | 0.184425 | + | 1.20418i | ||||
\(256\) | −6.50416 | − | 11.2655i | −0.406510 | − | 0.704096i | ||||
\(257\) | 5.13224 | − | 2.96310i | 0.320140 | − | 0.184833i | −0.331315 | − | 0.943520i | \(-0.607492\pi\) |
0.651455 | + | 0.758687i | \(0.274159\pi\) | |||||||
\(258\) | 1.90885 | + | 3.79580i | 0.118840 | + | 0.236316i | ||||
\(259\) | 0.423858 | − | 0.734143i | 0.0263372 | − | 0.0456174i | ||||
\(260\) | −3.48813 | − | 1.13267i | −0.216325 | − | 0.0702451i | ||||
\(261\) | −12.6486 | + | 17.0277i | −0.782928 | + | 1.05399i | ||||
\(262\) | − | 23.5984i | − | 1.45791i | ||||||
\(263\) | −17.8685 | − | 10.3164i | −1.10182 | − | 0.636136i | −0.165121 | − | 0.986273i | \(-0.552801\pi\) |
−0.936698 | + | 0.350138i | \(0.886135\pi\) | |||||||
\(264\) | 16.8981 | + | 11.1012i | 1.04001 | + | 0.683232i | ||||
\(265\) | 6.33722 | + | 29.7879i | 0.389292 | + | 1.82986i | ||||
\(266\) | −3.18107 | − | 5.50977i | −0.195044 | − | 0.337826i | ||||
\(267\) | 12.6965 | + | 0.732722i | 0.777010 | + | 0.0448418i | ||||
\(268\) | −4.85877 | − | 2.80521i | −0.296796 | − | 0.171355i | ||||
\(269\) | 27.8389 | 1.69737 | 0.848683 | − | 0.528902i | \(-0.177396\pi\) | ||||
0.848683 | + | 0.528902i | \(0.177396\pi\) | |||||||
\(270\) | 16.5187 | + | 8.74565i | 1.00530 | + | 0.532243i | ||||
\(271\) | −1.10302 | −0.0670039 | −0.0335020 | − | 0.999439i | \(-0.510666\pi\) | ||||
−0.0335020 | + | 0.999439i | \(0.510666\pi\) | |||||||
\(272\) | −21.0106 | − | 12.1305i | −1.27396 | − | 0.735519i | ||||
\(273\) | 4.82473 | + | 0.278439i | 0.292006 | + | 0.0168519i | ||||
\(274\) | 5.75183 | + | 9.96246i | 0.347481 | + | 0.601854i | ||||
\(275\) | 2.67635 | − | 25.5522i | 0.161390 | − | 1.54085i | ||||
\(276\) | −2.82731 | − | 1.85740i | −0.170184 | − | 0.111803i | ||||
\(277\) | 21.9744 | + | 12.6869i | 1.32031 | + | 0.762283i | 0.983778 | − | 0.179388i | \(-0.0574119\pi\) |
0.336534 | + | 0.941671i | \(0.390745\pi\) | |||||||
\(278\) | 29.6072i | 1.77572i | ||||||||
\(279\) | −3.00479 | − | 6.94561i | −0.179892 | − | 0.415823i | ||||
\(280\) | 1.56886 | − | 4.83142i | 0.0937575 | − | 0.288733i | ||||
\(281\) | −7.19700 | + | 12.4656i | −0.429337 | + | 0.743634i | −0.996814 | − | 0.0797551i | \(-0.974586\pi\) |
0.567477 | + | 0.823389i | \(0.307920\pi\) | |||||||
\(282\) | −9.75068 | − | 19.3895i | −0.580644 | − | 1.15463i | ||||
\(283\) | 7.06326 | − | 4.07798i | 0.419867 | − | 0.242411i | −0.275153 | − | 0.961400i | \(-0.588729\pi\) |
0.695021 | + | 0.718990i | \(0.255395\pi\) | |||||||
\(284\) | 0.284476 | + | 0.492727i | 0.0168806 | + | 0.0292380i | ||||
\(285\) | −15.1407 | + | 2.31886i | −0.896860 | + | 0.137357i | ||||
\(286\) | −11.5318 | + | 19.9737i | −0.681892 | + | 1.18107i | ||||
\(287\) | − | 1.06618i | − | 0.0629345i | ||||||
\(288\) | −8.88398 | + | 3.84337i | −0.523493 | + | 0.226472i | ||||
\(289\) | −8.22918 | −0.484069 | ||||||||
\(290\) | −18.8976 | + | 17.0216i | −1.10970 | + | 0.999543i | ||||
\(291\) | −3.72507 | − | 2.44718i | −0.218367 | − | 0.143456i | ||||
\(292\) | −2.45811 | + | 1.41919i | −0.143850 | + | 0.0830517i | ||||
\(293\) | 1.79534 | − | 1.03654i | 0.104885 | − | 0.0605552i | −0.446640 | − | 0.894714i | \(-0.647380\pi\) |
0.551525 | + | 0.834159i | \(0.314046\pi\) | |||||||
\(294\) | 0.160532 | − | 2.78167i | 0.00936242 | − | 0.162230i | ||||
\(295\) | −19.7469 | − | 21.9232i | −1.14971 | − | 1.27642i | ||||
\(296\) | 1.92579 | 0.111934 | ||||||||
\(297\) | 17.1297 | − | 20.4806i | 0.993969 | − | 1.18840i | ||||
\(298\) | − | 11.2646i | − | 0.652539i | ||||||
\(299\) | −4.63537 | + | 8.02870i | −0.268071 | + | 0.464312i | ||||
\(300\) | 3.94033 | + | 3.22309i | 0.227495 | + | 0.186085i | ||||
\(301\) | −0.762435 | − | 1.32058i | −0.0439460 | − | 0.0761168i | ||||
\(302\) | 10.1160 | − | 5.84050i | 0.582113 | − | 0.336083i | ||||
\(303\) | −4.76518 | + | 7.25349i | −0.273752 | + | 0.416702i | ||||
\(304\) | 9.55130 | − | 16.5433i | 0.547805 | − | 0.948826i | ||||
\(305\) | 3.63199 | − | 11.1850i | 0.207967 | − | 0.640449i | ||||
\(306\) | −14.4547 | + | 19.4591i | −0.826320 | + | 1.11240i | ||||
\(307\) | 21.5818i | 1.23174i | 0.787849 | + | 0.615869i | \(0.211195\pi\) | ||||
−0.787849 | + | 0.615869i | \(0.788805\pi\) | |||||||
\(308\) | 2.61577 | + | 1.51021i | 0.149047 | + | 0.0860524i | ||||
\(309\) | −24.6876 | + | 12.4150i | −1.40443 | + | 0.706266i | ||||
\(310\) | −1.88817 | − | 8.87530i | −0.107241 | − | 0.504083i | ||||
\(311\) | −3.87305 | − | 6.70832i | −0.219621 | − | 0.380394i | 0.735071 | − | 0.677990i | \(-0.237149\pi\) |
−0.954692 | + | 0.297596i | \(0.903815\pi\) | |||||||
\(312\) | 4.93246 | + | 9.80836i | 0.279246 | + | 0.555289i | ||||
\(313\) | −1.39842 | − | 0.807378i | −0.0790434 | − | 0.0456357i | 0.459957 | − | 0.887941i | \(-0.347865\pi\) |
−0.539001 | + | 0.842305i | \(0.681198\pi\) | |||||||
\(314\) | 14.9266 | 0.842356 | ||||||||
\(315\) | −6.09956 | − | 2.79202i | −0.343671 | − | 0.157313i | ||||
\(316\) | −3.52721 | −0.198421 | ||||||||
\(317\) | −11.0720 | − | 6.39243i | −0.621867 | − | 0.359035i | 0.155729 | − | 0.987800i | \(-0.450227\pi\) |
−0.777595 | + | 0.628765i | \(0.783561\pi\) | |||||||
\(318\) | −20.8362 | + | 31.7166i | −1.16844 | + | 1.77858i | ||||
\(319\) | 18.1655 | + | 31.4636i | 1.01708 | + | 1.76163i | ||||
\(320\) | 9.77585 | − | 2.07976i | 0.546487 | − | 0.116262i | ||||
\(321\) | 1.47918 | − | 25.6310i | 0.0825600 | − | 1.43058i | ||||
\(322\) | 4.62890 | + | 2.67250i | 0.257958 | + | 0.148932i | ||||
\(323\) | − | 19.8650i | − | 1.10532i | ||||||
\(324\) | 1.52805 | + | 5.06486i | 0.0848914 | + | 0.281381i | ||||
\(325\) | 8.19611 | − | 11.2895i | 0.454639 | − | 0.626230i | ||||
\(326\) | 7.73468 | − | 13.3969i | 0.428384 | − | 0.741983i | ||||
\(327\) | −8.89939 | − | 0.513590i | −0.492137 | − | 0.0284016i | ||||
\(328\) | 2.09758 | − | 1.21104i | 0.115819 | − | 0.0668684i | ||||
\(329\) | 3.89463 | + | 6.74570i | 0.214718 | + | 0.371903i | ||||
\(330\) | 24.9821 | − | 20.0197i | 1.37522 | − | 1.10205i | ||||
\(331\) | 5.62073 | − | 9.73540i | 0.308943 | − | 0.535106i | −0.669188 | − | 0.743093i | \(-0.733358\pi\) |
0.978132 | + | 0.207987i | \(0.0666913\pi\) | |||||||
\(332\) | 1.47342i | 0.0808646i | ||||||||
\(333\) | 0.292559 | − | 2.52626i | 0.0160321 | − | 0.138438i | ||||
\(334\) | −37.4844 | −2.05106 | ||||||||
\(335\) | 15.8578 | − | 14.2836i | 0.866403 | − | 0.780395i | ||||
\(336\) | 7.47412 | − | 3.75862i | 0.407747 | − | 0.205049i | ||||
\(337\) | 26.5384 | − | 15.3219i | 1.44564 | − | 0.834639i | 0.447420 | − | 0.894324i | \(-0.352343\pi\) |
0.998217 | + | 0.0596846i | \(0.0190095\pi\) | |||||||
\(338\) | 7.26501 | − | 4.19446i | 0.395165 | − | 0.228148i | ||||
\(339\) | −29.0527 | + | 14.6101i | −1.57792 | + | 0.793512i | ||||
\(340\) | −4.90547 | + | 4.41851i | −0.266037 | + | 0.239627i | ||||
\(341\) | −12.9620 | −0.701930 | ||||||||
\(342\) | −15.3217 | − | 11.3813i | −0.828505 | − | 0.615433i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 1.73205 | − | 3.00000i | 0.0933860 | − | 0.161749i | ||||
\(345\) | 10.0419 | − | 8.04720i | 0.540637 | − | 0.433246i | ||||
\(346\) | −8.45707 | − | 14.6481i | −0.454655 | − | 0.787486i | ||||
\(347\) | 14.3293 | − | 8.27302i | 0.769236 | − | 0.444119i | −0.0633658 | − | 0.997990i | \(-0.520183\pi\) |
0.832602 | + | 0.553872i | \(0.186850\pi\) | |||||||
\(348\) | −7.18673 | − | 0.414751i | −0.385249 | − | 0.0222330i | ||||
\(349\) | −7.08905 | + | 12.2786i | −0.379468 | + | 0.657258i | −0.990985 | − | 0.133973i | \(-0.957226\pi\) |
0.611517 | + | 0.791231i | \(0.290560\pi\) | |||||||
\(350\) | −6.50890 | − | 4.72542i | −0.347916 | − | 0.252584i | ||||
\(351\) | 13.6160 | − | 4.98039i | 0.726769 | − | 0.265834i | ||||
\(352\) | 16.5794i | 0.883682i | ||||||||
\(353\) | 4.67333 | + | 2.69815i | 0.248736 | + | 0.143608i | 0.619185 | − | 0.785245i | \(-0.287463\pi\) |
−0.370449 | + | 0.928853i | \(0.620796\pi\) | |||||||
\(354\) | 2.11826 | − | 36.7047i | 0.112584 | − | 1.95083i | ||||
\(355\) | −2.11693 | + | 0.450366i | −0.112355 | + | 0.0239030i | ||||
\(356\) | 2.15802 | + | 3.73780i | 0.114375 | + | 0.198103i | ||||
\(357\) | 4.77679 | − | 7.27116i | 0.252815 | − | 0.384831i | ||||
\(358\) | 32.8544 | + | 18.9685i | 1.73641 | + | 1.00252i | ||||
\(359\) | −7.90118 | −0.417008 | −0.208504 | − | 0.978021i | \(-0.566859\pi\) | ||||
−0.208504 | + | 0.978021i | \(0.566859\pi\) | |||||||
\(360\) | −1.43533 | − | 15.1715i | −0.0756484 | − | 0.799610i | ||||
\(361\) | −3.35872 | −0.176775 | ||||||||
\(362\) | −19.4570 | − | 11.2335i | −1.02264 | − | 0.590420i | ||||
\(363\) | −11.9861 | − | 23.8348i | −0.629108 | − | 1.25100i | ||||
\(364\) | 0.820060 | + | 1.42039i | 0.0429828 | + | 0.0744484i | ||||
\(365\) | −2.24678 | − | 10.5609i | −0.117602 | − | 0.552784i | ||||
\(366\) | 13.0915 | − | 6.58349i | 0.684302 | − | 0.344124i | ||||
\(367\) | 9.46994 | + | 5.46747i | 0.494327 | + | 0.285400i | 0.726368 | − | 0.687306i | \(-0.241207\pi\) |
−0.232041 | + | 0.972706i | \(0.574540\pi\) | |||||||
\(368\) | 16.0486i | 0.836591i | ||||||||
\(369\) | −1.26999 | − | 2.93560i | −0.0661131 | − | 0.152821i | ||||
\(370\) | 0.941767 | − | 2.90024i | 0.0489601 | − | 0.150776i | ||||
\(371\) | 6.80984 | − | 11.7950i | 0.353549 | − | 0.612366i | ||||
\(372\) | 1.41016 | − | 2.14653i | 0.0731136 | − | 0.111292i | ||||
\(373\) | −13.5989 | + | 7.85130i | −0.704122 | + | 0.406525i | −0.808881 | − | 0.587973i | \(-0.799926\pi\) |
0.104759 | + | 0.994498i | \(0.466593\pi\) | |||||||
\(374\) | 20.7594 | + | 35.9564i | 1.07344 | + | 1.85926i | ||||
\(375\) | −16.2907 | + | 10.4697i | −0.841247 | + | 0.540652i | ||||
\(376\) | −8.84758 | + | 15.3245i | −0.456279 | + | 0.790299i | ||||
\(377\) | 19.7281i | 1.01605i | ||||||||
\(378\) | −2.87141 | − | 7.85022i | −0.147690 | − | 0.403772i | ||||
\(379\) | −19.3313 | −0.992981 | −0.496491 | − | 0.868042i | \(-0.665378\pi\) | ||||
−0.496491 | + | 0.868042i | \(0.665378\pi\) | |||||||
\(380\) | −3.47904 | − | 3.86247i | −0.178471 | − | 0.198141i | ||||
\(381\) | 0.999456 | − | 17.3184i | 0.0512037 | − | 0.887247i | ||||
\(382\) | −7.45624 | + | 4.30486i | −0.381495 | + | 0.220256i | ||||
\(383\) | −19.2876 | + | 11.1357i | −0.985551 | + | 0.569008i | −0.903941 | − | 0.427657i | \(-0.859339\pi\) |
−0.0816093 | + | 0.996664i | \(0.526006\pi\) | |||||||
\(384\) | 19.7504 | + | 12.9750i | 1.00788 | + | 0.662130i | ||||
\(385\) | −8.53720 | + | 7.68971i | −0.435096 | + | 0.391904i | ||||
\(386\) | −11.4601 | −0.583305 | ||||||||
\(387\) | −3.67230 | − | 2.72787i | −0.186673 | − | 0.138665i | ||||
\(388\) | − | 1.51260i | − | 0.0767905i | ||||||
\(389\) | −17.1650 | + | 29.7307i | −0.870301 | + | 1.50741i | −0.00861633 | + | 0.999963i | \(0.502743\pi\) |
−0.861685 | + | 0.507443i | \(0.830591\pi\) | |||||||
\(390\) | 17.1835 | − | 2.63172i | 0.870121 | − | 0.133262i | ||||
\(391\) | 8.34453 | + | 14.4532i | 0.422001 | + | 0.730927i | ||||
\(392\) | −1.96738 | + | 1.13587i | −0.0993678 | + | 0.0573700i | ||||
\(393\) | 11.4153 | + | 22.6996i | 0.575824 | + | 1.14504i | ||||
\(394\) | 10.8753 | − | 18.8365i | 0.547888 | − | 0.948971i | ||||
\(395\) | 4.14397 | − | 12.7616i | 0.208506 | − | 0.642108i | ||||
\(396\) | 9.00113 | + | 1.04239i | 0.452324 | + | 0.0523823i | ||||
\(397\) | 7.97072i | 0.400039i | 0.979792 | + | 0.200019i | \(0.0641005\pi\) | ||||
−0.979792 | + | 0.200019i | \(0.935899\pi\) | |||||||
\(398\) | 9.21861 | + | 5.32237i | 0.462087 | + | 0.266786i | ||||
\(399\) | 5.72517 | + | 3.76115i | 0.286617 | + | 0.188293i | ||||
\(400\) | 2.51577 | − | 24.0191i | 0.125789 | − | 1.20096i | ||||
\(401\) | 10.4149 | + | 18.0392i | 0.520096 | + | 0.900832i | 0.999727 | + | 0.0233622i | \(0.00743709\pi\) |
−0.479631 | + | 0.877470i | \(0.659230\pi\) | |||||||
\(402\) | 26.5497 | + | 1.53220i | 1.32418 | + | 0.0764193i | ||||
\(403\) | −6.09549 | − | 3.51923i | −0.303638 | − | 0.175305i | ||||
\(404\) | −2.94534 | −0.146536 | ||||||||
\(405\) | −20.1202 | − | 0.421937i | −0.999780 | − | 0.0209662i | ||||
\(406\) | 11.3741 | 0.564488 | ||||||||
\(407\) | −3.77231 | − | 2.17795i | −0.186987 | − | 0.107957i | ||||
\(408\) | 19.7310 | + | 1.13869i | 0.976828 | + | 0.0563735i | ||||
\(409\) | −8.72032 | − | 15.1040i | −0.431192 | − | 0.746847i | 0.565784 | − | 0.824553i | \(-0.308574\pi\) |
−0.996976 | + | 0.0777066i | \(0.975240\pi\) | |||||||
\(410\) | −0.798046 | − | 3.75119i | −0.0394127 | − | 0.185258i | ||||
\(411\) | −10.3519 | − | 6.80070i | −0.510623 | − | 0.335454i | ||||
\(412\) | −8.12172 | − | 4.68907i | −0.400128 | − | 0.231014i | ||||
\(413\) | 13.1952i | 0.649294i | ||||||||
\(414\) | 15.9285 | + | 1.84464i | 0.782844 | + | 0.0906590i | ||||
\(415\) | −5.33093 | − | 1.73106i | −0.261685 | − | 0.0849746i | ||||
\(416\) | −4.50137 | + | 7.79660i | −0.220698 | + | 0.382260i | ||||
\(417\) | −14.3219 | − | 28.4796i | −0.701348 | − | 1.39465i | ||||
\(418\) | −28.3114 | + | 16.3456i | −1.38475 | + | 0.799488i | ||||
\(419\) | 2.45387 | + | 4.25022i | 0.119879 | + | 0.207637i | 0.919720 | − | 0.392576i | \(-0.128416\pi\) |
−0.799840 | + | 0.600213i | \(0.795083\pi\) | |||||||
\(420\) | −0.344651 | − | 2.25036i | −0.0168172 | − | 0.109806i | ||||
\(421\) | −9.61276 | + | 16.6498i | −0.468497 | + | 0.811461i | −0.999352 | − | 0.0360017i | \(-0.988538\pi\) |
0.530854 | + | 0.847463i | \(0.321871\pi\) | |||||||
\(422\) | 13.2247i | 0.643766i | ||||||||
\(423\) | 18.7587 | + | 13.9344i | 0.912077 | + | 0.677513i | ||||
\(424\) | 30.9403 | 1.50260 | ||||||||
\(425\) | −10.2232 | − | 22.9394i | −0.495897 | − | 1.11272i | ||||
\(426\) | −2.25400 | − | 1.48076i | −0.109207 | − | 0.0717433i | ||||
\(427\) | −4.55458 | + | 2.62959i | −0.220412 | + | 0.127255i | ||||
\(428\) | 7.54568 | − | 4.35650i | 0.364734 | − | 0.210580i | ||||
\(429\) | 1.43073 | − | 24.7914i | 0.0690762 | − | 1.19694i | ||||
\(430\) | −3.67098 | − | 4.07556i | −0.177030 | − | 0.196541i | ||||
\(431\) | 40.8153 | 1.96600 | 0.983001 | − | 0.183601i | \(-0.0587753\pi\) | ||||
0.983001 | + | 0.183601i | \(0.0587753\pi\) | |||||||
\(432\) | 16.1020 | − | 19.2518i | 0.774709 | − | 0.926254i | ||||
\(433\) | 33.9312i | 1.63063i | 0.579019 | + | 0.815314i | \(0.303436\pi\) | ||||
−0.579019 | + | 0.815314i | \(0.696564\pi\) | |||||||
\(434\) | −2.02899 | + | 3.51432i | −0.0973947 | + | 0.168693i | ||||
\(435\) | 9.94398 | − | 25.5147i | 0.476777 | − | 1.22334i | ||||
\(436\) | −1.51263 | − | 2.61995i | −0.0724419 | − | 0.125473i | ||||
\(437\) | −11.3801 | + | 6.57032i | −0.544385 | + | 0.314301i | ||||
\(438\) | 7.38721 | − | 11.2447i | 0.352974 | − | 0.537292i | ||||
\(439\) | 9.57454 | − | 16.5836i | 0.456968 | − | 0.791492i | −0.541831 | − | 0.840487i | \(-0.682269\pi\) |
0.998799 | + | 0.0489957i | \(0.0156021\pi\) | |||||||
\(440\) | −24.8257 | − | 8.06143i | −1.18352 | − | 0.384314i | ||||
\(441\) | 1.19116 | + | 2.75339i | 0.0567221 | + | 0.131114i | ||||
\(442\) | 22.5451i | 1.07236i | ||||||||
\(443\) | −18.9074 | − | 10.9162i | −0.898317 | − | 0.518644i | −0.0216634 | − | 0.999765i | \(-0.506896\pi\) |
−0.876654 | + | 0.481122i | \(0.840230\pi\) | |||||||
\(444\) | 0.771072 | − | 0.387760i | 0.0365935 | − | 0.0184023i | ||||
\(445\) | −16.0589 | + | 3.41645i | −0.761266 | + | 0.161955i | ||||
\(446\) | 2.38963 | + | 4.13896i | 0.113152 | + | 0.195985i | ||||
\(447\) | 5.44903 | + | 10.8356i | 0.257730 | + | 0.512505i | ||||
\(448\) | −3.87090 | − | 2.23487i | −0.182883 | − | 0.105588i | ||||
\(449\) | 33.8190 | 1.59601 | 0.798007 | − | 0.602648i | \(-0.205887\pi\) | ||||
0.798007 | + | 0.602648i | \(0.205887\pi\) | |||||||
\(450\) | −23.5503 | − | 5.25773i | −1.11017 | − | 0.247852i | ||||
\(451\) | −5.47844 | −0.257970 | ||||||||
\(452\) | −9.55771 | − | 5.51815i | −0.449557 | − | 0.259552i | ||||
\(453\) | −6.90555 | + | 10.5115i | −0.324451 | + | 0.493875i | ||||
\(454\) | −8.49854 | − | 14.7199i | −0.398856 | − | 0.690839i | ||||
\(455\) | −6.10249 | + | 1.29827i | −0.286089 | + | 0.0608639i | ||||
\(456\) | −0.896581 | + | 15.5358i | −0.0419862 | + | 0.727529i | ||||
\(457\) | −10.2735 | − | 5.93139i | −0.480573 | − | 0.277459i | 0.240082 | − | 0.970753i | \(-0.422826\pi\) |
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(458\) | − | 19.1341i | − | 0.894076i | ||||||
\(459\) | 4.49121 | − | 25.7102i | 0.209631 | − | 1.20005i | ||||
\(460\) | 4.15373 | + | 1.34880i | 0.193669 | + | 0.0628883i | ||||
\(461\) | −10.5461 | + | 18.2664i | −0.491182 | + | 0.850753i | −0.999948 | − | 0.0101519i | \(-0.996769\pi\) |
0.508766 | + | 0.860905i | \(0.330102\pi\) | |||||||
\(462\) | −14.2933 | − | 0.824877i | −0.664984 | − | 0.0383767i | ||||
\(463\) | 7.80262 | − | 4.50485i | 0.362619 | − | 0.209358i | −0.307610 | − | 0.951512i | \(-0.599529\pi\) |
0.670229 | + | 0.742155i | \(0.266196\pi\) | |||||||
\(464\) | 17.0757 | + | 29.5759i | 0.792718 | + | 1.37303i | ||||
\(465\) | 6.10953 | + | 7.62392i | 0.283323 | + | 0.353551i | ||||
\(466\) | 15.2707 | − | 26.4497i | 0.707403 | − | 1.22526i | ||||
\(467\) | − | 2.76614i | − | 0.128002i | −0.997950 | − | 0.0640008i | \(-0.979614\pi\) | ||
0.997950 | − | 0.0640008i | \(-0.0203860\pi\) | |||||||
\(468\) | 3.94985 | + | 2.93404i | 0.182582 | + | 0.135626i | ||||
\(469\) | −9.54452 | −0.440725 | ||||||||
\(470\) | 18.7519 | + | 20.8186i | 0.864962 | + | 0.960290i | ||||
\(471\) | −14.3581 | + | 7.22047i | −0.661587 | + | 0.332701i | ||||
\(472\) | −25.9600 | + | 14.9880i | −1.19491 | + | 0.689880i | ||||
\(473\) | −6.78564 | + | 3.91769i | −0.312004 | + | 0.180136i | ||||
\(474\) | 14.9369 | − | 7.51152i | 0.686074 | − | 0.345016i | ||||
\(475\) | 18.0620 | − | 8.04952i | 0.828743 | − | 0.369338i | ||||
\(476\) | 2.95252 | 0.135329 | ||||||||
\(477\) | 4.70036 | − | 40.5878i | 0.215215 | − | 1.85839i | ||||
\(478\) | 30.8835i | 1.41258i | ||||||||
\(479\) | 3.77488 | − | 6.53828i | 0.172479 | − | 0.298742i | −0.766807 | − | 0.641878i | \(-0.778156\pi\) |
0.939286 | + | 0.343136i | \(0.111489\pi\) | |||||||
\(480\) | 9.75159 | − | 7.81456i | 0.445097 | − | 0.356684i | ||||
\(481\) | −1.18264 | − | 2.04840i | −0.0539240 | − | 0.0933991i | ||||
\(482\) | −35.0479 | + | 20.2349i | −1.59639 | + | 0.921674i | ||||
\(483\) | −5.74538 | − | 0.331570i | −0.261424 | − | 0.0150870i | ||||
\(484\) | 4.52708 | − | 7.84114i | 0.205776 | − | 0.356415i | ||||
\(485\) | 5.47266 | + | 1.77709i | 0.248501 | + | 0.0806934i | ||||
\(486\) | −17.2570 | − | 18.1944i | −0.782794 | − | 0.825313i | ||||
\(487\) | − | 6.91178i | − | 0.313203i | −0.987662 | − | 0.156601i | \(-0.949946\pi\) | ||
0.987662 | − | 0.156601i | \(-0.0500538\pi\) | |||||||
\(488\) | −10.3468 | − | 5.97373i | −0.468378 | − | 0.270418i | ||||
\(489\) | −0.959623 | + | 16.6282i | −0.0433957 | + | 0.751951i | ||||
\(490\) | 0.748511 | + | 3.51835i | 0.0338143 | + | 0.158943i | ||||
\(491\) | 1.20549 | + | 2.08798i | 0.0544032 | + | 0.0942290i | 0.891944 | − | 0.452145i | \(-0.149341\pi\) |
−0.837541 | + | 0.546374i | \(0.816008\pi\) | |||||||
\(492\) | 0.596013 | − | 0.907242i | 0.0268703 | − | 0.0409016i | ||||
\(493\) | 30.7562 | + | 17.7571i | 1.38519 | + | 0.799741i | ||||
\(494\) | −17.7516 | −0.798682 | ||||||||
\(495\) | −14.3465 | + | 31.3419i | −0.644827 | + | 1.40871i | ||||
\(496\) | −12.1843 | −0.547091 | ||||||||
\(497\) | 0.838234 | + | 0.483955i | 0.0375999 | + | 0.0217083i | ||||
\(498\) | −3.13779 | − | 6.23960i | −0.140608 | − | 0.279603i | ||||
\(499\) | 15.6623 | + | 27.1278i | 0.701139 | + | 1.21441i | 0.968067 | + | 0.250692i | \(0.0806581\pi\) |
−0.266928 | + | 0.963716i | \(0.586009\pi\) | |||||||
\(500\) | −6.00524 | − | 2.66982i | −0.268563 | − | 0.119398i | ||||
\(501\) | 36.0569 | − | 18.1324i | 1.61090 | − | 0.810096i | ||||
\(502\) | 41.5707 | + | 24.0008i | 1.85539 | + | 1.07121i | ||||
\(503\) | − | 26.5245i | − | 1.18267i | −0.806427 | − | 0.591333i | \(-0.798602\pi\) | ||
0.806427 | − | 0.591333i | \(-0.201398\pi\) | |||||||
\(504\) | −4.06396 | + | 5.47096i | −0.181023 | + | 0.243696i | ||||
\(505\) | 3.46036 | − | 10.6564i | 0.153984 | − | 0.474204i | ||||
\(506\) | 13.7323 | − | 23.7851i | 0.610477 | − | 1.05738i | ||||
\(507\) | −4.95934 | + | 7.54903i | −0.220252 | + | 0.335264i | ||||
\(508\) | 5.09848 | − | 2.94361i | 0.226208 | − | 0.130601i | ||||
\(509\) | 4.22519 | + | 7.31825i | 0.187278 | + | 0.324376i | 0.944342 | − | 0.328966i | \(-0.106700\pi\) |
−0.757064 | + | 0.653341i | \(0.773367\pi\) | |||||||
\(510\) | 11.3639 | − | 29.1580i | 0.503202 | − | 1.29114i | ||||
\(511\) | −2.41434 | + | 4.18176i | −0.106804 | + | 0.184990i | ||||
\(512\) | − | 6.36081i | − | 0.281111i | ||||||
\(513\) | 20.2437 | + | 3.53629i | 0.893783 | + | 0.156131i | ||||
\(514\) | −9.53329 | −0.420495 | ||||||||
\(515\) | 26.5072 | − | 23.8758i | 1.16805 | − | 1.05209i | ||||
\(516\) | 0.0894477 | − | 1.54993i | 0.00393772 | − | 0.0682320i | ||||
\(517\) | 34.6621 | − | 20.0122i | 1.52444 | − | 0.880134i | ||||
\(518\) | −1.18099 | + | 0.681846i | −0.0518898 | + | 0.0299586i | ||||
\(519\) | 15.2207 | + | 9.99926i | 0.668116 | + | 0.438919i | ||||
\(520\) | −9.48583 | − | 10.5313i | −0.415981 | − | 0.461827i | ||||
\(521\) | −2.93428 | −0.128553 | −0.0642767 | − | 0.997932i | \(-0.520474\pi\) | ||||
−0.0642767 | + | 0.997932i | \(0.520474\pi\) | |||||||
\(522\) | 31.3173 | − | 13.5484i | 1.37072 | − | 0.592999i | ||||
\(523\) | − | 6.38846i | − | 0.279348i | −0.990198 | − | 0.139674i | \(-0.955395\pi\) | ||
0.990198 | − | 0.139674i | \(-0.0446055\pi\) | |||||||
\(524\) | −4.31148 | + | 7.46770i | −0.188348 | + | 0.326228i | ||||
\(525\) | 8.54685 | + | 1.39689i | 0.373015 | + | 0.0609653i | ||||
\(526\) | 16.5957 | + | 28.7445i | 0.723605 | + | 1.25332i | ||||
\(527\) | −10.9730 | + | 6.33527i | −0.477992 | + | 0.275969i | ||||
\(528\) | −19.3132 | − | 38.4050i | −0.840501 | − | 1.67136i | ||||
\(529\) | −5.98010 | + | 10.3578i | −0.260005 | + | 0.450341i | ||||
\(530\) | 15.1308 | − | 46.5962i | 0.657238 | − | 2.02401i | ||||
\(531\) | 15.7177 | + | 36.3315i | 0.682088 | + | 1.57665i | ||||
\(532\) | 2.32476i | 0.100791i | ||||||||
\(533\) | −2.57629 | − | 1.48742i | −0.111592 | − | 0.0644274i | ||||
\(534\) | −17.0987 | − | 11.2330i | −0.739932 | − | 0.486099i | ||||
\(535\) | 6.89697 | + | 32.4190i | 0.298182 | + | 1.40160i | ||||
\(536\) | −10.8413 | − | 18.7777i | −0.468274 | − | 0.811074i | ||||
\(537\) | −40.7789 | − | 2.35338i | −1.75974 | − | 0.101556i | ||||
\(538\) | −38.7837 | − | 22.3918i | −1.67208 | − | 0.965378i | ||||
\(539\) | 5.13839 | 0.221326 | ||||||||
\(540\) | −3.62950 | − | 5.78558i | −0.156189 | − | 0.248972i | ||||
\(541\) | −14.9483 | −0.642678 | −0.321339 | − | 0.946964i | \(-0.604133\pi\) | ||||
−0.321339 | + | 0.946964i | \(0.604133\pi\) | |||||||
\(542\) | 1.53668 | + | 0.887200i | 0.0660059 | + | 0.0381085i | ||||
\(543\) | 24.1500 | + | 1.39371i | 1.03638 | + | 0.0598100i | ||||
\(544\) | 8.10330 | + | 14.0353i | 0.347426 | + | 0.601760i | ||||
\(545\) | 11.2563 | − | 2.39471i | 0.482166 | − | 0.102578i | ||||
\(546\) | −6.49761 | − | 4.26860i | −0.278072 | − | 0.182679i | ||||
\(547\) | 25.5542 | + | 14.7537i | 1.09262 | + | 0.630824i | 0.934273 | − | 0.356559i | \(-0.116050\pi\) |
0.158347 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(548\) | − | 4.20349i | − | 0.179564i | ||||||
\(549\) | −9.40825 | + | 12.6655i | −0.401534 | + | 0.540551i | ||||
\(550\) | −24.2810 | + | 33.4453i | −1.03535 | + | 1.42611i | ||||
\(551\) | −13.9816 | + | 24.2169i | −0.595637 | + | 1.03167i | ||||
\(552\) | −5.87367 | − | 11.6800i | −0.250000 | − | 0.497133i | ||||
\(553\) | −5.19662 | + | 3.00027i | −0.220983 | + | 0.127584i | ||||
\(554\) | −20.4090 | − | 35.3495i | −0.867097 | − | 1.50186i | ||||
\(555\) | 0.497036 | + | 3.24535i | 0.0210980 | + | 0.137757i | ||||
\(556\) | 5.40931 | − | 9.36920i | 0.229406 | − | 0.397342i | ||||
\(557\) | − | 10.5465i | − | 0.446868i | −0.974719 | − | 0.223434i | \(-0.928273\pi\) | ||
0.974719 | − | 0.223434i | \(-0.0717267\pi\) | |||||||
\(558\) | −1.40047 | + | 12.0931i | −0.0592867 | + | 0.511943i | ||||
\(559\) | −4.25468 | −0.179954 | ||||||||
\(560\) | −8.02499 | + | 7.22835i | −0.339118 | + | 0.305454i | ||||
\(561\) | −37.3621 | − | 24.5450i | −1.57743 | − | 1.03629i | ||||
\(562\) | 20.0530 | − | 11.5776i | 0.845884 | − | 0.488371i | ||||
\(563\) | 4.86466 | − | 2.80861i | 0.205021 | − | 0.118369i | −0.393974 | − | 0.919121i | \(-0.628900\pi\) |
0.598995 | + | 0.800752i | \(0.295567\pi\) | |||||||
\(564\) | −0.456913 | + | 7.91729i | −0.0192395 | + | 0.333378i | ||||
\(565\) | 31.1939 | − | 28.0973i | 1.31234 | − | 1.18206i | ||||
\(566\) | −13.1202 | −0.551484 | ||||||||
\(567\) | 6.55946 | + | 6.16226i | 0.275472 | + | 0.258791i | ||||
\(568\) | 2.19884i | 0.0922611i | ||||||||
\(569\) | 15.4294 | − | 26.7245i | 0.646834 | − | 1.12035i | −0.337041 | − | 0.941490i | \(-0.609426\pi\) |
0.983875 | − | 0.178859i | \(-0.0572406\pi\) | |||||||
\(570\) | 22.9584 | + | 8.94771i | 0.961623 | + | 0.374778i | ||||
\(571\) | −4.11966 | − | 7.13545i | −0.172402 | − | 0.298609i | 0.766857 | − | 0.641818i | \(-0.221820\pi\) |
−0.939259 | + | 0.343209i | \(0.888486\pi\) | |||||||
\(572\) | 7.29850 | − | 4.21379i | 0.305166 | − | 0.176187i | ||||
\(573\) | 5.08988 | − | 7.74774i | 0.212633 | − | 0.323666i | ||||
\(574\) | −0.857564 | + | 1.48534i | −0.0357940 | + | 0.0619971i | ||||
\(575\) | −9.76009 | + | 13.4438i | −0.407024 | + | 0.560645i | ||||
\(576\) | −13.3202 | − | 1.54257i | −0.555007 | − | 0.0642738i | ||||
\(577\) | − | 7.25745i | − | 0.302132i | −0.988524 | − | 0.151066i | \(-0.951729\pi\) | ||
0.988524 | − | 0.151066i | \(-0.0482705\pi\) | |||||||
\(578\) | 11.4645 | + | 6.61901i | 0.476859 | + | 0.275315i | ||||
\(579\) | 11.0237 | − | 5.54363i | 0.458128 | − | 0.230385i | ||||
\(580\) | 9.09003 | − | 1.93385i | 0.377443 | − | 0.0802989i | ||||
\(581\) | 1.25330 | + | 2.17078i | 0.0519958 | + | 0.0900593i | ||||
\(582\) | 3.22122 | + | 6.40549i | 0.133524 | + | 0.265516i | ||||
\(583\) | −60.6073 | − | 34.9916i | −2.51010 | − | 1.44921i | ||||
\(584\) | −10.9695 | −0.453921 | ||||||||
\(585\) | −15.2561 | + | 10.8437i | −0.630760 | + | 0.448332i | ||||
\(586\) | −3.33489 | −0.137763 | ||||||||
\(587\) | −6.79751 | − | 3.92455i | −0.280563 | − | 0.161983i | 0.353115 | − | 0.935580i | \(-0.385122\pi\) |
−0.633678 | + | 0.773597i | \(0.718456\pi\) | |||||||
\(588\) | −0.559018 | + | 0.850929i | −0.0230535 | + | 0.0350917i | ||||
\(589\) | −4.98827 | − | 8.63993i | −0.205538 | − | 0.356002i | ||||
\(590\) | 9.87676 | + | 46.4254i | 0.406620 | + | 1.91130i | ||||
\(591\) | −1.34927 | + | 23.3799i | −0.0555015 | + | 0.961720i | ||||
\(592\) | −3.54599 | − | 2.04728i | −0.145739 | − | 0.0841425i | ||||
\(593\) | − | 9.64578i | − | 0.396105i | −0.980191 | − | 0.198052i | \(-0.936538\pi\) | ||
0.980191 | − | 0.198052i | \(-0.0634616\pi\) | |||||||
\(594\) | −40.3375 | + | 14.7544i | −1.65507 | + | 0.605382i | ||||
\(595\) | −3.46879 | + | 10.6824i | −0.142207 | + | 0.437935i | ||||
\(596\) | −2.05807 | + | 3.56467i | −0.0843016 | + | 0.146015i | ||||
\(597\) | −11.4421 | − | 0.660333i | −0.468295 | − | 0.0270256i | ||||
\(598\) | 12.9155 | − | 7.45678i | 0.528155 | − | 0.304931i | ||||
\(599\) | −22.5812 | − | 39.1118i | −0.922643 | − | 1.59806i | −0.795309 | − | 0.606204i | \(-0.792692\pi\) |
−0.127333 | − | 0.991860i | \(-0.540642\pi\) | |||||||
\(600\) | 6.95988 | + | 18.4016i | 0.284136 | + | 0.751242i | ||||
\(601\) | 6.56530 | − | 11.3714i | 0.267804 | − | 0.463850i | −0.700490 | − | 0.713662i | \(-0.747035\pi\) |
0.968294 | + | 0.249811i | \(0.0803687\pi\) | |||||||
\(602\) | 2.45301i | 0.0999773i | ||||||||
\(603\) | −26.2797 | + | 11.3691i | −1.07019 | + | 0.462985i | ||||
\(604\) | −4.26830 | −0.173675 | ||||||||
\(605\) | 23.0510 | + | 25.5915i | 0.937157 | + | 1.04044i | ||||
\(606\) | 12.4728 | − | 6.27238i | 0.506674 | − | 0.254798i | ||||
\(607\) | 18.9487 | − | 10.9400i | 0.769105 | − | 0.444043i | −0.0634504 | − | 0.997985i | \(-0.520210\pi\) |
0.832555 | + | 0.553942i | \(0.186877\pi\) | |||||||
\(608\) | −11.0511 | + | 6.38038i | −0.448183 | + | 0.258759i | ||||
\(609\) | −10.9409 | + | 5.50203i | −0.443350 | + | 0.222953i | ||||
\(610\) | −14.0564 | + | 12.6610i | −0.569125 | + | 0.512628i | ||||
\(611\) | 21.7336 | 0.879246 | ||||||||
\(612\) | 8.12942 | − | 3.51693i | 0.328613 | − | 0.142164i | ||||
\(613\) | − | 7.96920i | − | 0.321873i | −0.986965 | − | 0.160937i | \(-0.948549\pi\) | ||
0.986965 | − | 0.160937i | \(-0.0514515\pi\) | |||||||
\(614\) | 17.3590 | − | 30.0666i | 0.700551 | − | 1.21339i | ||||
\(615\) | 2.58222 | + | 3.22229i | 0.104125 | + | 0.129935i | ||||
\(616\) | 5.83654 | + | 10.1092i | 0.235161 | + | 0.407310i | ||||
\(617\) | −14.9784 | + | 8.64777i | −0.603007 | + | 0.348146i | −0.770223 | − | 0.637774i | \(-0.779855\pi\) |
0.167217 | + | 0.985920i | \(0.446522\pi\) | |||||||
\(618\) | 44.3794 | + | 2.56117i | 1.78520 | + | 0.103025i | ||||
\(619\) | 7.76411 | − | 13.4478i | 0.312066 | − | 0.540514i | −0.666743 | − | 0.745287i | \(-0.732312\pi\) |
0.978809 | + | 0.204773i | \(0.0656457\pi\) | |||||||
\(620\) | −1.02403 | + | 3.15356i | −0.0411259 | + | 0.126650i | ||||
\(621\) | −16.2142 | + | 5.93075i | −0.650654 | + | 0.237993i | ||||
\(622\) | 12.4609i | 0.499637i | ||||||||
\(623\) | 6.35879 | + | 3.67125i | 0.254759 | + | 0.147085i | ||||
\(624\) | 1.34489 | − | 23.3040i | 0.0538386 | − | 0.932905i | ||||
\(625\) | 16.7149 | − | 18.5907i | 0.668596 | − | 0.743626i | ||||
\(626\) | 1.29880 | + | 2.24960i | 0.0519107 | + | 0.0899119i | ||||
\(627\) | 19.3263 | − | 29.4182i | 0.771817 | − | 1.17485i | ||||
\(628\) | −4.72352 | − | 2.72712i | −0.188489 | − | 0.108824i | ||||
\(629\) | −4.25796 | −0.169776 | ||||||||
\(630\) | 6.25187 | + | 8.79578i | 0.249081 | + | 0.350432i | ||||
\(631\) | 7.88432 | 0.313870 | 0.156935 | − | 0.987609i | \(-0.449839\pi\) | ||||
0.156935 | + | 0.987609i | \(0.449839\pi\) | |||||||
\(632\) | −11.8053 | − | 6.81582i | −0.469591 | − | 0.271119i | ||||
\(633\) | −6.39719 | − | 12.7210i | −0.254265 | − | 0.505615i | ||||
\(634\) | 10.2833 | + | 17.8112i | 0.408402 | + | 0.707374i | ||||
\(635\) | 4.66015 | + | 21.9049i | 0.184932 | + | 0.869270i | ||||
\(636\) | 12.3883 | − | 6.22988i | 0.491229 | − | 0.247031i | ||||
\(637\) | 2.41638 | + | 1.39510i | 0.0957404 | + | 0.0552758i | ||||
\(638\) | − | 58.4447i | − | 2.31385i | ||||||
\(639\) | 2.88445 | + | 0.334040i | 0.114107 | + | 0.0132144i | ||||
\(640\) | −29.0162 | − | 9.42217i | −1.14697 | − | 0.372444i | ||||
\(641\) | −0.192272 | + | 0.333025i | −0.00759428 | + | 0.0131537i | −0.869798 | − | 0.493409i | \(-0.835751\pi\) |
0.862203 | + | 0.506562i | \(0.169084\pi\) | |||||||
\(642\) | −22.6766 | + | 34.5180i | −0.894974 | + | 1.36232i | ||||
\(643\) | −15.0953 | + | 8.71526i | −0.595299 | + | 0.343696i | −0.767190 | − | 0.641420i | \(-0.778346\pi\) |
0.171891 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(644\) | −0.976544 | − | 1.69142i | −0.0384812 | − | 0.0666514i | ||||
\(645\) | 5.50266 | + | 2.14458i | 0.216667 | + | 0.0844427i | ||||
\(646\) | −15.9781 | + | 27.6748i | −0.628649 | + | 1.08885i | ||||
\(647\) | 38.8775i | 1.52843i | 0.644961 | + | 0.764215i | \(0.276874\pi\) | ||||
−0.644961 | + | 0.764215i | \(0.723126\pi\) | |||||||
\(648\) | −4.67283 | + | 19.9045i | −0.183566 | + | 0.781922i | ||||
\(649\) | 67.8022 | 2.66147 | ||||||||
\(650\) | −20.4990 | + | 9.13556i | −0.804035 | + | 0.358326i | ||||
\(651\) | 0.251732 | − | 4.36197i | 0.00986616 | − | 0.170959i | ||||
\(652\) | −4.89528 | + | 2.82629i | −0.191714 | + | 0.110686i | ||||
\(653\) | −23.1331 | + | 13.3559i | −0.905269 | + | 0.522657i | −0.878906 | − | 0.476995i | \(-0.841726\pi\) |
−0.0263633 | + | 0.999652i | \(0.508393\pi\) | |||||||
\(654\) | 11.9851 | + | 7.87359i | 0.468653 | + | 0.307882i | ||||
\(655\) | −21.9532 | − | 24.3727i | −0.857782 | − | 0.952319i | ||||
\(656\) | −5.14975 | −0.201064 | ||||||||
\(657\) | −1.66645 | + | 14.3899i | −0.0650145 | + | 0.561403i | ||||
\(658\) | − | 12.5304i | − | 0.488484i | ||||||
\(659\) | −10.3342 | + | 17.8993i | −0.402562 | + | 0.697258i | −0.994034 | − | 0.109068i | \(-0.965214\pi\) |
0.591472 | + | 0.806325i | \(0.298547\pi\) | |||||||
\(660\) | −11.5632 | + | 1.77095i | −0.450098 | + | 0.0689342i | ||||
\(661\) | 7.59618 | + | 13.1570i | 0.295457 | + | 0.511747i | 0.975091 | − | 0.221804i | \(-0.0711947\pi\) |
−0.679634 | + | 0.733551i | \(0.737861\pi\) | |||||||
\(662\) | −15.6610 | + | 9.04190i | −0.608683 | + | 0.351423i | ||||
\(663\) | −10.9058 | − | 21.6865i | −0.423546 | − | 0.842235i | ||||
\(664\) | −2.84718 | + | 4.93145i | −0.110492 | + | 0.191377i | ||||
\(665\) | −8.41110 | − | 2.73126i | −0.326168 | − | 0.105914i | ||||
\(666\) | −2.43954 | + | 3.28414i | −0.0945302 | + | 0.127258i | ||||
\(667\) | − | 23.4926i | − | 0.909638i | ||||||
\(668\) | 11.8619 | + | 6.84850i | 0.458953 | + | 0.264976i | ||||
\(669\) | −4.30077 | − | 2.82539i | −0.166277 | − | 0.109236i | ||||
\(670\) | −33.5810 | + | 7.14418i | −1.29735 | + | 0.276004i | ||||
\(671\) | 13.5119 | + | 23.4032i | 0.521619 | + | 0.903471i | ||||
\(672\) | −5.57929 | − | 0.321985i | −0.215226 | − | 0.0124208i | ||||
\(673\) | 34.6344 | + | 19.9962i | 1.33506 | + | 0.770796i | 0.986070 | − | 0.166332i | \(-0.0531922\pi\) |
0.348988 | + | 0.937127i | \(0.386526\pi\) | |||||||
\(674\) | −49.2959 | −1.89881 | ||||||||
\(675\) | 25.1967 | − | 6.33452i | 0.969822 | − | 0.243816i | ||||
\(676\) | −3.06535 | −0.117898 | ||||||||
\(677\) | −23.0021 | − | 13.2803i | −0.884043 | − | 0.510402i | −0.0120534 | − | 0.999927i | \(-0.503837\pi\) |
−0.871989 | + | 0.489525i | \(0.837170\pi\) | |||||||
\(678\) | 52.2261 | + | 3.01401i | 2.00573 | + | 0.115752i | ||||
\(679\) | −1.28662 | − | 2.22850i | −0.0493761 | − | 0.0855220i | ||||
\(680\) | −24.9564 | + | 5.30935i | −0.957035 | + | 0.203604i | ||||
\(681\) | 15.2954 | + | 10.0483i | 0.586120 | + | 0.385051i | ||||
\(682\) | 18.0579 | + | 10.4258i | 0.691474 | + | 0.399223i | ||||
\(683\) | 10.3626i | 0.396512i | 0.980150 | + | 0.198256i | \(0.0635277\pi\) | ||||
−0.980150 | + | 0.198256i | \(0.936472\pi\) | |||||||
\(684\) | 2.76916 | + | 6.40095i | 0.105882 | + | 0.244746i | ||||
\(685\) | 15.2085 | + | 4.93851i | 0.581086 | + | 0.188691i | ||||
\(686\) | 0.804334 | − | 1.39315i | 0.0307096 | − | 0.0531906i | ||||
\(687\) | 9.25576 | + | 18.4054i | 0.353129 | + | 0.702208i | ||||
\(688\) | −6.37852 | + | 3.68264i | −0.243179 | + | 0.140399i | ||||
\(689\) | −19.0008 | − | 32.9103i | −0.723872 | − | 1.25378i | ||||
\(690\) | −20.4625 | + | 3.13390i | −0.778993 | + | 0.119306i | ||||
\(691\) | −0.423942 | + | 0.734290i | −0.0161275 | + | 0.0279337i | −0.873977 | − | 0.485968i | \(-0.838467\pi\) |
0.857849 | + | 0.513902i | \(0.171800\pi\) | |||||||
\(692\) | 6.18051i | 0.234948i | ||||||||
\(693\) | 14.1480 | − | 6.12066i | 0.537437 | − | 0.232505i | ||||
\(694\) | −26.6171 | −1.01037 | ||||||||
\(695\) | 27.5431 | + | 30.5787i | 1.04477 | + | 1.15991i | ||||
\(696\) | −23.2521 | − | 15.2754i | −0.881367 | − | 0.579014i | ||||
\(697\) | −4.63780 | + | 2.67763i | −0.175669 | + | 0.101423i | ||||
\(698\) | 19.7522 | − | 11.4039i | 0.747632 | − | 0.431645i | ||||
\(699\) | −1.89460 | + | 32.8293i | −0.0716605 | + | 1.24172i | ||||
\(700\) | 1.19640 | + | 2.68455i | 0.0452196 | + | 0.101467i | ||||
\(701\) | −21.6568 | −0.817968 | −0.408984 | − | 0.912542i | \(-0.634117\pi\) | ||||
−0.408984 | + | 0.912542i | \(0.634117\pi\) | |||||||
\(702\) | −22.9750 | − | 4.01340i | −0.867136 | − | 0.151476i | ||||
\(703\) | − | 3.35263i | − | 0.126447i | ||||||
\(704\) | −11.4836 | + | 19.8902i | −0.432805 | + | 0.749641i | ||||
\(705\) | −28.1084 | − | 10.9548i | −1.05862 | − | 0.412583i | ||||
\(706\) | −4.34043 | − | 7.51784i | −0.163354 | − | 0.282938i | ||||
\(707\) | −4.33935 | + | 2.50533i | −0.163198 | + | 0.0942225i | ||||
\(708\) | −7.37636 | + | 11.2282i | −0.277221 | + | 0.421981i | ||||
\(709\) | 1.22418 | − | 2.12035i | 0.0459751 | − | 0.0796313i | −0.842122 | − | 0.539287i | \(-0.818694\pi\) |
0.888097 | + | 0.459656i | \(0.152027\pi\) | |||||||
\(710\) | 3.31145 | + | 1.07530i | 0.124276 | + | 0.0403552i | ||||
\(711\) | −10.7345 | + | 14.4509i | −0.402574 | + | 0.541951i | ||||
\(712\) | 16.6802i | 0.625118i | ||||||||
\(713\) | 7.25863 | + | 4.19077i | 0.271838 | + | 0.156946i | ||||
\(714\) | −12.5032 | + | 6.28767i | −0.467921 | + | 0.235310i | ||||
\(715\) | 6.67103 | + | 31.3570i | 0.249482 | + | 1.17269i | ||||
\(716\) | −6.93119 | − | 12.0052i | −0.259031 | − | 0.448654i | ||||
\(717\) | −14.9393 | − | 29.7073i | −0.557919 | − | 1.10944i | ||||
\(718\) | 11.0075 | + | 6.35519i | 0.410797 | + | 0.237174i | ||||
\(719\) | −36.6105 | −1.36534 | −0.682671 | − | 0.730726i | \(-0.739182\pi\) | ||||
−0.682671 | + | 0.730726i | \(0.739182\pi\) | |||||||
\(720\) | −13.4857 | + | 29.4615i | −0.502584 | + | 1.09797i | ||||
\(721\) | −15.9542 | −0.594167 | ||||||||
\(722\) | 4.67920 | + | 2.70154i | 0.174142 | + | 0.100541i | ||||
\(723\) | 23.9248 | − | 36.4180i | 0.889774 | − | 1.35440i | ||||
\(724\) | 4.10478 | + | 7.10968i | 0.152553 | + | 0.264229i | ||||
\(725\) | −3.68270 | + | 35.1602i | −0.136772 | + | 1.30582i | ||||
\(726\) | −2.47269 | + | 42.8462i | −0.0917700 | + | 1.59017i | ||||
\(727\) | 3.87756 | + | 2.23871i | 0.143811 | + | 0.0830292i | 0.570179 | − | 0.821521i | \(-0.306874\pi\) |
−0.426368 | + | 0.904550i | \(0.640207\pi\) | |||||||
\(728\) | 6.33859i | 0.234924i | ||||||||
\(729\) | 25.4010 | + | 9.15369i | 0.940777 | + | 0.339025i | ||||
\(730\) | −5.36441 | + | 16.5201i | −0.198546 | + | 0.611436i | ||||
\(731\) | −3.82961 | + | 6.63308i | −0.141643 | + | 0.245333i | ||||
\(732\) | −5.34561 | − | 0.308499i | −0.197580 | − | 0.0114025i | ||||
\(733\) | 40.6147 | − | 23.4489i | 1.50014 | − | 0.866106i | 0.500139 | − | 0.865945i | \(-0.333282\pi\) |
1.00000 | 0.000160408i | \(-5.10595e-5\pi\) | ||||||||
\(734\) | −8.79535 | − | 15.2340i | −0.324642 | − | 0.562297i | ||||
\(735\) | −2.42194 | − | 3.02228i | −0.0893348 | − | 0.111479i | ||||
\(736\) | 5.36032 | − | 9.28435i | 0.197584 | − | 0.342226i | ||||
\(737\) | 49.0435i | 1.80654i | ||||||||
\(738\) | −0.591916 | + | 5.11122i | −0.0217887 | + | 0.188147i | ||||
\(739\) | 8.33703 | 0.306683 | 0.153341 | − | 0.988173i | \(-0.450997\pi\) | ||||
0.153341 | + | 0.988173i | \(0.450997\pi\) | |||||||
\(740\) | −0.827903 | + | 0.745717i | −0.0304343 | + | 0.0274131i | ||||
\(741\) | 17.0755 | − | 8.58701i | 0.627286 | − | 0.315452i | ||||
\(742\) | −18.9742 | + | 10.9548i | −0.696566 | + | 0.402163i | ||||
\(743\) | 26.4585 | − | 15.2758i | 0.970668 | − | 0.560415i | 0.0712280 | − | 0.997460i | \(-0.477308\pi\) |
0.899440 | + | 0.437045i | \(0.143975\pi\) | |||||||
\(744\) | 8.86759 | − | 4.45937i | 0.325101 | − | 0.163488i | ||||
\(745\) | −10.4793 | − | 11.6342i | −0.383930 | − | 0.426244i | ||||
\(746\) | 25.2603 | 0.924845 | ||||||||
\(747\) | 6.03659 | + | 4.48412i | 0.220867 | + | 0.164065i | ||||
\(748\) | − | 15.1712i | − | 0.554714i | ||||||
\(749\) | 7.41134 | − | 12.8368i | 0.270804 | − | 0.469047i | ||||
\(750\) | 31.1164 | − | 1.48266i | 1.13621 | − | 0.0541390i | ||||
\(751\) | −11.5992 | − | 20.0904i | −0.423260 | − | 0.733109i | 0.572996 | − | 0.819558i | \(-0.305781\pi\) |
−0.996256 | + | 0.0864497i | \(0.972448\pi\) | |||||||
\(752\) | 32.5825 | − | 18.8115i | 1.18816 | − | 0.685984i | ||||
\(753\) | −51.5975 | − | 2.97773i | −1.88032 | − | 0.108514i | ||||
\(754\) | 15.8680 | − | 27.4842i | 0.577879 | − | 1.00092i | ||||
\(755\) | 5.01465 | − | 15.4429i | 0.182502 | − | 0.562026i | ||||
\(756\) | −0.525597 | + | 3.00882i | −0.0191158 | + | 0.109430i | ||||
\(757\) | − | 7.34831i | − | 0.267079i | −0.991044 | − | 0.133539i | \(-0.957366\pi\) | ||
0.991044 | − | 0.133539i | \(-0.0426343\pi\) | |||||||
\(758\) | 26.9313 | + | 15.5488i | 0.978190 | + | 0.564759i | ||||
\(759\) | −1.70374 | + | 29.5220i | −0.0618418 | + | 1.07158i | ||||
\(760\) | −4.18047 | − | 19.6502i | −0.151642 | − | 0.712788i | ||||
\(761\) | 4.42586 | + | 7.66582i | 0.160437 | + | 0.277886i | 0.935026 | − | 0.354580i | \(-0.115376\pi\) |
−0.774588 | + | 0.632466i | \(0.782043\pi\) | |||||||
\(762\) | −15.3222 | + | 23.3232i | −0.555063 | + | 0.844909i | ||||
\(763\) | −4.45710 | − | 2.57331i | −0.161358 | − | 0.0931600i | ||||
\(764\) | 3.14604 | 0.113820 | ||||||||
\(765\) | 3.17354 | + | 33.5446i | 0.114740 | + | 1.21281i | ||||
\(766\) | 35.8273 | 1.29449 | ||||||||
\(767\) | 31.8846 | + | 18.4086i | 1.15129 | + | 0.664696i | ||||
\(768\) | −10.1226 | − | 20.1291i | −0.365269 | − | 0.726348i | ||||
\(769\) | −7.42151 | − | 12.8544i | −0.267627 | − | 0.463543i | 0.700622 | − | 0.713533i | \(-0.252906\pi\) |
−0.968248 | + | 0.249990i | \(0.919573\pi\) | |||||||
\(770\) | 18.0787 | − | 3.84614i | 0.651510 | − | 0.138605i | ||||
\(771\) | 9.17022 | − | 4.61156i | 0.330257 | − | 0.166081i | ||||
\(772\) | 3.62656 | + | 2.09379i | 0.130523 | + | 0.0753572i | ||||
\(773\) | − | 13.6071i | − | 0.489415i | −0.969597 | − | 0.244707i | \(-0.921308\pi\) | ||
0.969597 | − | 0.244707i | \(-0.0786919\pi\) | |||||||
\(774\) | 2.92194 | + | 6.75409i | 0.105027 | + | 0.242771i | ||||
\(775\) | −10.2067 | − | 7.40998i | −0.366635 | − | 0.266174i | ||||
\(776\) | 2.92287 | − | 5.06256i | 0.104925 | − | 0.181735i | ||||
\(777\) | 0.806185 | − | 1.22716i | 0.0289217 | − | 0.0440242i | ||||
\(778\) | 47.8269 | − | 27.6128i | 1.71468 | − | 0.989968i | ||||
\(779\) | −2.10832 | − | 3.65171i | −0.0755383 | − | 0.130836i | ||||
\(780\) | −5.91855 | − | 2.30667i | −0.211918 | − | 0.0825919i | ||||
\(781\) | 2.48675 | − | 4.30718i | 0.0889829 | − | 0.154123i | ||||
\(782\) | − | 26.8472i | − | 0.960053i | ||||||
\(783\) | −23.5708 | + | 28.1817i | −0.842353 | + | 1.00713i | ||||
\(784\) | 4.83010 | 0.172504 | ||||||||
\(785\) | 15.4164 | − | 13.8860i | 0.550233 | − | 0.495612i | ||||
\(786\) | 2.35492 | − | 40.8056i | 0.0839974 | − | 1.45549i | ||||
\(787\) | −43.6762 | + | 25.2164i | −1.55689 | + | 0.898869i | −0.559335 | + | 0.828942i | \(0.688944\pi\) |
−0.997552 | + | 0.0699278i | \(0.977723\pi\) | |||||||
\(788\) | −6.88296 | + | 3.97388i | −0.245195 | + | 0.141564i | ||||
\(789\) | −29.8683 | − | 19.6220i | −1.06334 | − | 0.698560i | ||||
\(790\) | −16.0378 | + | 14.4457i | −0.570599 | + | 0.513956i | ||||
\(791\) | −18.7751 | −0.667566 | ||||||||
\(792\) | 28.1119 | + | 20.8822i | 0.998913 | + | 0.742016i | ||||
\(793\) | 14.6741i | 0.521093i | ||||||||
\(794\) | 6.41112 | − | 11.1044i | 0.227522 | − | 0.394080i | ||||
\(795\) | 7.98556 | + | 52.1409i | 0.283218 | + | 1.84925i | ||||
\(796\) | −1.94482 | − | 3.36853i | −0.0689323 | − | 0.119394i | ||||
\(797\) | 18.1215 | − | 10.4625i | 0.641897 | − | 0.370599i | −0.143448 | − | 0.989658i | \(-0.545819\pi\) |
0.785345 | + | 0.619058i | \(0.212486\pi\) | |||||||
\(798\) | −4.95079 | − | 9.84479i | −0.175256 | − | 0.348502i | ||||
\(799\) | 19.5622 | − | 33.8828i | 0.692062 | − | 1.19869i | ||||
\(800\) | −9.47794 | + | 13.0551i | −0.335096 | + | 0.461569i | ||||
\(801\) | 21.8812 | + | 2.53401i | 0.773136 | + | 0.0895347i | ||||
\(802\) | − | 33.5083i | − | 1.18322i | ||||||
\(803\) | 21.4875 | + | 12.4058i | 0.758279 | + | 0.437792i | ||||
\(804\) | −8.12171 | − | 5.33556i | −0.286431 | − | 0.188171i | ||||
\(805\) | 7.26697 | − | 1.54601i | 0.256127 | − | 0.0544896i | ||||
\(806\) | 5.66128 | + | 9.80563i | 0.199410 | + | 0.345388i | ||||
\(807\) | 48.1383 | + | 2.77809i | 1.69455 | + | 0.0977935i | ||||
\(808\) | −9.85787 | − | 5.69144i | −0.346799 | − | 0.200224i | ||||
\(809\) | −18.1877 | −0.639445 | −0.319722 | − | 0.947511i | \(-0.603590\pi\) | ||||
−0.319722 | + | 0.947511i | \(0.603590\pi\) | |||||||
\(810\) | 27.6910 | + | 16.7712i | 0.972963 | + | 0.589279i | ||||
\(811\) | −24.5937 | −0.863600 | −0.431800 | − | 0.901969i | \(-0.642121\pi\) | ||||
−0.431800 | + | 0.901969i | \(0.642121\pi\) | |||||||
\(812\) | −3.59934 | − | 2.07808i | −0.126312 | − | 0.0729263i | ||||
\(813\) | −1.90732 | − | 0.110073i | −0.0668926 | − | 0.00386042i | ||||
\(814\) | 3.50359 | + | 6.06840i | 0.122801 | + | 0.212697i | ||||
\(815\) | −4.47442 | − | 21.0319i | −0.156732 | − | 0.736715i | ||||
\(816\) | −35.1205 | − | 23.0724i | −1.22946 | − | 0.807696i | ||||
\(817\) | −5.22276 | − | 3.01536i | −0.182721 | − | 0.105494i | ||||
\(818\) | 28.0562i | 0.980963i | ||||||||
\(819\) | 8.31501 | + | 0.962938i | 0.290550 | + | 0.0336478i | ||||
\(820\) | −0.432811 | + | 1.33287i | −0.0151144 | + | 0.0465458i | ||||
\(821\) | 5.06771 | − | 8.77753i | 0.176864 | − | 0.306338i | −0.763941 | − | 0.645287i | \(-0.776738\pi\) |
0.940805 | + | 0.338949i | \(0.110071\pi\) | |||||||
\(822\) | 8.95174 | + | 17.8008i | 0.312228 | + | 0.620874i | ||||
\(823\) | −17.4650 | + | 10.0834i | −0.608793 | + | 0.351487i | −0.772493 | − | 0.635024i | \(-0.780990\pi\) |
0.163700 | + | 0.986510i | \(0.447657\pi\) | |||||||
\(824\) | −18.1219 | − | 31.3881i | −0.631307 | − | 1.09346i | ||||
\(825\) | 7.17777 | − | 43.9171i | 0.249898 | − | 1.52900i | ||||
\(826\) | 10.6134 | − | 18.3829i | 0.369286 | − | 0.639622i | ||||
\(827\) | 42.4406i | 1.47581i | 0.674907 | + | 0.737903i | \(0.264184\pi\) | ||||
−0.674907 | + | 0.737903i | \(0.735816\pi\) | |||||||
\(828\) | −4.70356 | − | 3.49392i | −0.163460 | − | 0.121422i | ||||
\(829\) | −37.3130 | −1.29593 | −0.647967 | − | 0.761668i | \(-0.724381\pi\) | ||||
−0.647967 | + | 0.761668i | \(0.724381\pi\) | |||||||
\(830\) | 6.03442 | + | 6.69948i | 0.209458 | + | 0.232542i | ||||
\(831\) | 36.7315 | + | 24.1307i | 1.27420 | + | 0.837086i | ||||
\(832\) | −10.8006 | + | 6.23571i | −0.374442 | + | 0.216184i | ||||
\(833\) | 4.34993 | − | 2.51143i | 0.150716 | − | 0.0870160i | ||||
\(834\) | −2.95456 | + | 51.1960i | −0.102308 | + | 1.77277i | ||||
\(835\) | −38.7144 | + | 34.8712i | −1.33977 | + | 1.20677i | ||||
\(836\) | 11.9455 | 0.413144 | ||||||||
\(837\) | −4.50270 | − | 12.3100i | −0.155636 | − | 0.425497i | ||||
\(838\) | − | 7.89491i | − | 0.272725i | ||||||
\(839\) | 20.9567 | − | 36.2981i | 0.723505 | − | 1.25315i | −0.236081 | − | 0.971733i | \(-0.575863\pi\) |
0.959586 | − | 0.281415i | \(-0.0908036\pi\) | |||||||
\(840\) | 3.19497 | − | 8.19780i | 0.110237 | − | 0.282851i | ||||
\(841\) | −10.4961 | − | 18.1798i | −0.361935 | − | 0.626889i | ||||
\(842\) | 26.7840 | − | 15.4638i | 0.923038 | − | 0.532916i | ||||
\(843\) | −13.6888 | + | 20.8369i | −0.471469 | + | 0.717663i | ||||
\(844\) | 2.41618 | − | 4.18494i | 0.0831683 | − | 0.144052i | ||||
\(845\) | 3.60135 | − | 11.0906i | 0.123890 | − | 0.381529i | ||||
\(846\) | −14.9257 | − | 34.5009i | −0.513156 | − | 1.18617i | ||||
\(847\) | − | 15.4031i | − | 0.529256i | ||||||
\(848\) | −56.9711 | − | 32.8923i | −1.95639 | − | 1.12952i | ||||
\(849\) | 12.6206 | − | 6.34667i | 0.433136 | − | 0.217817i | ||||
\(850\) | −4.20856 | + | 40.1808i | −0.144352 | + | 1.37819i | ||||
\(851\) | 1.40832 | + | 2.43928i | 0.0482765 | + | 0.0836173i | ||||
\(852\) | 0.442739 | + | 0.880399i | 0.0151680 | + | 0.0301620i | ||||
\(853\) | 7.52505 | + | 4.34459i | 0.257653 | + | 0.148756i | 0.623263 | − | 0.782012i | \(-0.285806\pi\) |
−0.365611 | + | 0.930768i | \(0.619140\pi\) | |||||||
\(854\) | 8.46027 | 0.289505 | ||||||||
\(855\) | −26.4124 | + | 2.49878i | −0.903284 | + | 0.0854566i | ||||
\(856\) | 33.6732 | 1.15093 | ||||||||
\(857\) | −33.2805 | − | 19.2145i | −1.13684 | − | 0.656355i | −0.191194 | − | 0.981552i | \(-0.561236\pi\) |
−0.945646 | + | 0.325197i | \(0.894569\pi\) | |||||||
\(858\) | −21.9338 | + | 33.3872i | −0.748806 | + | 1.13982i | ||||
\(859\) | 6.59880 | + | 11.4295i | 0.225148 | + | 0.389968i | 0.956364 | − | 0.292178i | \(-0.0943800\pi\) |
−0.731216 | + | 0.682146i | \(0.761047\pi\) | |||||||
\(860\) | 0.417067 | + | 1.96041i | 0.0142219 | + | 0.0668494i | ||||
\(861\) | 0.106396 | − | 1.84361i | 0.00362596 | − | 0.0628300i | ||||
\(862\) | −56.8617 | − | 32.8291i | −1.93672 | − | 1.11816i | ||||
\(863\) | − | 10.5429i | − | 0.358885i | −0.983768 | − | 0.179443i | \(-0.942571\pi\) | ||
0.983768 | − | 0.179443i | \(-0.0574294\pi\) | |||||||
\(864\) | −15.7455 | + | 5.75930i | −0.535672 | + | 0.195935i | ||||
\(865\) | −22.3615 | − | 7.26123i | −0.760312 | − | 0.246889i | ||||
\(866\) | 27.2920 | − | 47.2711i | 0.927420 | − | 1.60634i | ||||
\(867\) | −14.2297 | − | 0.821205i | −0.483265 | − | 0.0278896i | ||||
\(868\) | 1.28415 | − | 0.741404i | 0.0435869 | − | 0.0251649i | ||||
\(869\) | 15.4165 | + | 26.7022i | 0.522971 | + | 0.905812i | ||||
\(870\) | −34.3758 | + | 27.5475i | −1.16545 | + | 0.933947i | ||||
\(871\) | −13.3155 | + | 23.0632i | −0.451180 | + | 0.781466i | ||||
\(872\) | − | 11.6918i | − | 0.395933i | ||||||
\(873\) | −6.19708 | − | 4.60334i | −0.209739 | − | 0.155799i | ||||
\(874\) | 21.1389 | 0.715035 | ||||||||
\(875\) | −11.1185 | + | 1.17467i | −0.375873 | + | 0.0397109i | ||||
\(876\) | −4.39212 | + | 2.20872i | −0.148396 | + | 0.0746259i | ||||
\(877\) | −0.289820 | + | 0.167328i | −0.00978654 | + | 0.00565026i | −0.504885 | − | 0.863186i | \(-0.668465\pi\) |
0.495099 | + | 0.868837i | \(0.335132\pi\) | |||||||
\(878\) | −26.6775 | + | 15.4023i | −0.900322 | + | 0.519801i | ||||
\(879\) | 3.20789 | − | 1.61319i | 0.108199 | − | 0.0544117i | ||||
\(880\) | 37.1421 | + | 41.2355i | 1.25206 | + | 1.39005i | ||||
\(881\) | 36.2414 | 1.22100 | 0.610501 | − | 0.792015i | \(-0.290968\pi\) | ||||
0.610501 | + | 0.792015i | \(0.290968\pi\) | |||||||
\(882\) | 0.555176 | − | 4.79397i | 0.0186937 | − | 0.161421i | ||||
\(883\) | − | 42.7261i | − | 1.43785i | −0.695089 | − | 0.718924i | \(-0.744635\pi\) | ||
0.695089 | − | 0.718924i | \(-0.255365\pi\) | |||||||
\(884\) | 4.11905 | − | 7.13441i | 0.138539 | − | 0.239956i | ||||
\(885\) | −31.9581 | − | 39.8796i | −1.07426 | − | 1.34054i | ||||
\(886\) | 17.5605 | + | 30.4157i | 0.589958 | + | 1.02184i | ||||
\(887\) | 42.5235 | − | 24.5509i | 1.42780 | − | 0.824340i | 0.430852 | − | 0.902423i | \(-0.358213\pi\) |
0.996947 | + | 0.0780826i | \(0.0248798\pi\) | |||||||
\(888\) | 3.33002 | + | 0.192178i | 0.111748 | + | 0.00644906i | ||||
\(889\) | 5.00770 | − | 8.67360i | 0.167953 | − | 0.290903i | ||||
\(890\) | 25.1204 | + | 8.15713i | 0.842039 | + | 0.273428i | ||||
\(891\) | 31.6641 | − | 33.7051i | 1.06079 | − | 1.12916i | ||||
\(892\) | − | 1.74637i | − | 0.0584727i | ||||||
\(893\) | 26.6786 | + | 15.4029i | 0.892766 | + | 0.515439i | ||||
\(894\) | 1.12411 | − | 19.4784i | 0.0375960 | − | 0.651455i | ||||
\(895\) | 51.5786 | − | 10.9731i | 1.72408 | − | 0.366789i | ||||
\(896\) | 6.82173 | + | 11.8156i | 0.227898 | + | 0.394731i | ||||
\(897\) | −8.81657 | + | 13.4205i | −0.294377 | + | 0.448096i | ||||
\(898\) | −47.1148 | − | 27.2017i | −1.57224 | − | 0.907734i | ||||
\(899\) | 17.8359 | 0.594860 | ||||||||
\(900\) | 6.49188 | + | 5.96650i | 0.216396 | + | 0.198883i | ||||
\(901\) | −68.4099 | −2.27906 | ||||||||
\(902\) | 7.63228 | + | 4.40650i | 0.254127 | + | 0.146720i | ||||
\(903\) | −1.18660 | − | 2.35959i | −0.0394876 | − | 0.0785223i | ||||
\(904\) | −21.3260 | − | 36.9378i | −0.709294 | − | 1.22853i | ||||
\(905\) | −30.5458 | + | 6.49845i | −1.01538 | + | 0.216016i | ||||
\(906\) | 18.0752 | − | 9.08974i | 0.600509 | − | 0.301986i | ||||
\(907\) | −9.31713 | − | 5.37925i | −0.309370 | − | 0.178615i | 0.337274 | − | 0.941406i | \(-0.390495\pi\) |
−0.646645 | + | 0.762791i | \(0.723828\pi\) | |||||||
\(908\) | 6.21082i | 0.206113i | ||||||||
\(909\) | −8.96366 | + | 12.0670i | −0.297306 | + | 0.400238i | ||||
\(910\) | 9.54592 | + | 3.09976i | 0.316444 | + | 0.102756i | ||||
\(911\) | −11.5054 | + | 19.9280i | −0.381191 | + | 0.660243i | −0.991233 | − | 0.132127i | \(-0.957819\pi\) |
0.610041 | + | 0.792369i | \(0.291153\pi\) | |||||||
\(912\) | 18.1668 | − | 27.6532i | 0.601561 | − | 0.915688i | ||||
\(913\) | 11.1543 | − | 6.43996i | 0.369155 | − | 0.213132i | ||||
\(914\) | 9.54165 | + | 16.5266i | 0.315610 | + | 0.546652i | ||||
\(915\) | 7.39651 | − | 18.9783i | 0.244521 | − | 0.627403i | ||||
\(916\) | −3.49584 | + | 6.05497i | −0.115506 | + | 0.200062i | ||||
\(917\) | 14.6695i | 0.484429i | ||||||||
\(918\) | −26.9366 | + | 32.2058i | −0.889039 | + | 1.06295i | ||||
\(919\) | 15.3731 | 0.507110 | 0.253555 | − | 0.967321i | \(-0.418400\pi\) | ||||
0.253555 | + | 0.967321i | \(0.418400\pi\) | |||||||
\(920\) | 11.2959 | + | 12.5408i | 0.372415 | + | 0.413459i | ||||
\(921\) | −2.15369 | + | 37.3187i | −0.0709664 | + | 1.22969i | ||||
\(922\) | 29.3847 | − | 16.9652i | 0.967732 | − | 0.558720i | ||||
\(923\) | 2.33884 | − | 1.35033i | 0.0769837 | − | 0.0444466i | ||||
\(924\) | 4.37241 | + | 2.87245i | 0.143842 | + | 0.0944968i | ||||
\(925\) | −1.72538 | − | 3.87151i | −0.0567301 | − | 0.127294i | ||||
\(926\) | −14.4936 | −0.476290 | ||||||||
\(927\) | −43.9281 | + | 19.0041i | −1.44279 | + | 0.624176i | ||||
\(928\) | − | 22.8135i | − | 0.748889i | ||||||
\(929\) | −13.5022 | + | 23.3866i | −0.442994 | + | 0.767288i | −0.997910 | − | 0.0646182i | \(-0.979417\pi\) |
0.554916 | + | 0.831906i | \(0.312750\pi\) | |||||||
\(930\) | −2.37929 | − | 15.5354i | −0.0780201 | − | 0.509424i | ||||
\(931\) | 1.97745 | + | 3.42505i | 0.0648084 | + | 0.112251i | ||||
\(932\) | −9.66485 | + | 5.58001i | −0.316583 | + | 0.182779i | ||||
\(933\) | −6.02774 | − | 11.9864i | −0.197339 | − | 0.392416i | ||||
\(934\) | −2.22490 | + | 3.85364i | −0.0728010 | + | 0.126095i | ||||
\(935\) | 54.8903 | + | 17.8240i | 1.79510 | + | 0.582908i | ||||
\(936\) | 7.55029 | + | 17.4526i | 0.246789 | + | 0.570455i | ||||
\(937\) | 7.70105i | 0.251582i | 0.992057 | + | 0.125791i | \(0.0401469\pi\) | ||||
−0.992057 | + | 0.125791i | \(0.959853\pi\) | |||||||
\(938\) | 13.2969 | + | 7.67699i | 0.434160 | + | 0.250663i | ||||
\(939\) | −2.33754 | − | 1.53565i | −0.0762828 | − | 0.0501140i | ||||
\(940\) | −2.13044 | − | 10.0141i | −0.0694873 | − | 0.326623i | ||||
\(941\) | −2.03358 | − | 3.52227i | −0.0662929 | − | 0.114823i | 0.830974 | − | 0.556311i | \(-0.187784\pi\) |
−0.897267 | + | 0.441489i | \(0.854450\pi\) | |||||||
\(942\) | 25.8107 | + | 1.48955i | 0.840957 | + | 0.0485322i | ||||
\(943\) | 3.06790 | + | 1.77125i | 0.0999045 | + | 0.0576799i | ||||
\(944\) | 63.7342 | 2.07437 | ||||||||
\(945\) | −10.2686 | − | 5.43657i | −0.334037 | − | 0.176852i | ||||
\(946\) | 12.6045 | 0.409809 | ||||||||
\(947\) | −0.656686 | − | 0.379138i | −0.0213394 | − | 0.0123203i | 0.489292 | − | 0.872120i | \(-0.337255\pi\) |
−0.510632 | + | 0.859800i | \(0.670588\pi\) | |||||||
\(948\) | −6.09916 | − | 0.351987i | −0.198091 | − | 0.0114320i | ||||
\(949\) | 6.73648 | + | 11.6679i | 0.218676 | + | 0.378757i | ||||
\(950\) | −31.6376 | − | 3.31374i | −1.02646 | − | 0.107512i | ||||
\(951\) | −18.5075 | − | 12.1585i | −0.600148 | − | 0.394267i | ||||
\(952\) | 9.88189 | + | 5.70531i | 0.320274 | + | 0.184910i | ||||
\(953\) | − | 36.3529i | − | 1.17759i | −0.808284 | − | 0.588793i | \(-0.799603\pi\) | ||
0.808284 | − | 0.588793i | \(-0.200397\pi\) | |||||||
\(954\) | −39.1945 | + | 52.7642i | −1.26897 | + | 1.70830i | ||||
\(955\) | −3.69615 | + | 11.3825i | −0.119605 | + | 0.368331i | ||||
\(956\) | 5.64249 | − | 9.77308i | 0.182491 | − | 0.316084i | ||||
\(957\) | 28.2716 | + | 56.2189i | 0.913890 | + | 1.81730i | ||||
\(958\) | −10.5179 | + | 6.07253i | −0.339819 | + | 0.196195i | ||||
\(959\) | −3.57552 | − | 6.19298i | −0.115460 | − | 0.199982i | ||||
\(960\) | 17.1117 | − | 2.62071i | 0.552277 | − | 0.0845832i | ||||
\(961\) | 12.3183 | − | 21.3359i | 0.397365 | − | 0.688256i | ||||
\(962\) | 3.80497i | 0.122677i | ||||||||
\(963\) | 5.11553 | − | 44.1728i | 0.164846 | − | 1.42345i | ||||
\(964\) | 14.7879 | 0.476285 | ||||||||
\(965\) | −11.8362 | + | 10.6612i | −0.381019 | + | 0.343195i | ||||
\(966\) | 7.73748 | + | 5.08314i | 0.248949 | + | 0.163547i | ||||
\(967\) | −9.30540 | + | 5.37247i | −0.299241 | + | 0.172767i | −0.642102 | − | 0.766619i | \(-0.721937\pi\) |
0.342861 | + | 0.939386i | \(0.388604\pi\) | |||||||
\(968\) | 30.3037 | − | 17.4959i | 0.973998 | − | 0.562338i | ||||
\(969\) | 1.98236 | − | 34.3500i | 0.0636826 | − | 1.10348i | ||||
\(970\) | −6.19486 | − | 6.87760i | −0.198905 | − | 0.220826i | ||||
\(971\) | −30.5229 | −0.979528 | −0.489764 | − | 0.871855i | \(-0.662917\pi\) | ||||
−0.489764 | + | 0.871855i | \(0.662917\pi\) | |||||||
\(972\) | 2.13682 | + | 8.91051i | 0.0685387 | + | 0.285805i | ||||
\(973\) | − | 18.4048i | − | 0.590030i | ||||||
\(974\) | −5.55938 | + | 9.62914i | −0.178134 | + | 0.308537i | ||||
\(975\) | 15.2991 | − | 18.7036i | 0.489964 | − | 0.598996i | ||||
\(976\) | 12.7012 | + | 21.9991i | 0.406555 | + | 0.704174i | ||||
\(977\) | 13.6399 | − | 7.87497i | 0.436378 | − | 0.251943i | −0.265682 | − | 0.964061i | \(-0.585597\pi\) |
0.702060 | + | 0.712118i | \(0.252264\pi\) | |||||||
\(978\) | 14.7115 | − | 22.3936i | 0.470422 | − | 0.716069i | ||||
\(979\) | 18.8643 | − | 32.6739i | 0.602906 | − | 1.04426i | ||||
\(980\) | 0.405946 | − | 1.25014i | 0.0129675 | − | 0.0399342i | ||||
\(981\) | −15.3373 | − | 1.77617i | −0.489684 | − | 0.0567089i | ||||
\(982\) | − | 3.87848i | − | 0.123767i | ||||||
\(983\) | 18.0937 | + | 10.4464i | 0.577099 | + | 0.333188i | 0.759980 | − | 0.649947i | \(-0.225209\pi\) |
−0.182881 | + | 0.983135i | \(0.558542\pi\) | |||||||
\(984\) | 3.74793 | − | 1.88477i | 0.119480 | − | 0.0600844i | ||||
\(985\) | −6.29122 | − | 29.5717i | −0.200455 | − | 0.942233i | ||||
\(986\) | −28.5653 | − | 49.4766i | −0.909706 | − | 1.57566i | ||||
\(987\) | 6.06133 | + | 12.0531i | 0.192934 | + | 0.383656i | ||||
\(988\) | 5.61749 | + | 3.24326i | 0.178716 | + | 0.103182i | ||||
\(989\) | 5.06656 | 0.161107 | ||||||||
\(990\) | 45.1962 | − | 32.1246i | 1.43643 | − | 1.02099i | ||||
\(991\) | −54.0076 | −1.71561 | −0.857803 | − | 0.513978i | \(-0.828171\pi\) | ||||
−0.857803 | + | 0.513978i | \(0.828171\pi\) | |||||||
\(992\) | 7.04879 | + | 4.06962i | 0.223799 | + | 0.129211i | ||||
\(993\) | 10.6907 | − | 16.2733i | 0.339260 | − | 0.516417i | ||||
\(994\) | −0.778523 | − | 1.34844i | −0.0246932 | − | 0.0427700i | ||||
\(995\) | 14.4724 | − | 3.07893i | 0.458806 | − | 0.0976086i | ||||
\(996\) | −0.147036 | + | 2.54780i | −0.00465900 | + | 0.0807303i | ||||
\(997\) | −20.2659 | − | 11.7005i | −0.641827 | − | 0.370559i | 0.143491 | − | 0.989652i | \(-0.454167\pi\) |
−0.785318 | + | 0.619093i | \(0.787500\pi\) | |||||||
\(998\) | − | 50.3908i | − | 1.59509i | ||||||
\(999\) | 0.757986 | − | 4.33915i | 0.0239816 | − | 0.137285i |
(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 | 315.2.bh.c.169.8 | ✓ | 64 | |
3.2 | odd | 2 | 945.2.bh.c.694.25 | 64 | |||
5.4 | even | 2 | inner | 315.2.bh.c.169.25 | yes | 64 | |
9.4 | even | 3 | inner | 315.2.bh.c.274.25 | yes | 64 | |
9.5 | odd | 6 | 945.2.bh.c.64.8 | 64 | |||
15.14 | odd | 2 | 945.2.bh.c.694.8 | 64 | |||
45.4 | even | 6 | inner | 315.2.bh.c.274.8 | yes | 64 | |
45.14 | odd | 6 | 945.2.bh.c.64.25 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bh.c.169.8 | ✓ | 64 | 1.1 | even | 1 | trivial | |
315.2.bh.c.169.25 | yes | 64 | 5.4 | even | 2 | inner | |
315.2.bh.c.274.8 | yes | 64 | 45.4 | even | 6 | inner | |
315.2.bh.c.274.25 | yes | 64 | 9.4 | even | 3 | inner | |
945.2.bh.c.64.8 | 64 | 9.5 | odd | 6 | |||
945.2.bh.c.64.25 | 64 | 45.14 | odd | 6 | |||
945.2.bh.c.694.8 | 64 | 15.14 | odd | 2 | |||
945.2.bh.c.694.25 | 64 | 3.2 | odd | 2 |