Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(124,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.124");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.e (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.1 | ||
Root | \(1.40126 + 1.01807i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.148 |
Dual form | 363.2.e.m.130.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.535233 | − | 1.64728i | −0.378467 | − | 1.16480i | −0.941110 | − | 0.338101i | \(-0.890215\pi\) |
0.562643 | − | 0.826700i | \(-0.309785\pi\) | |||||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −0.927051 | + | 2.85317i | −0.414590 | + | 1.27598i | 0.498027 | + | 0.867161i | \(0.334058\pi\) |
−0.912617 | + | 0.408815i | \(0.865942\pi\) | |||||||
\(6\) | 0.535233 | − | 1.64728i | 0.218508 | − | 0.672499i | ||||
\(7\) | −2.80252 | + | 2.03615i | −1.05925 | + | 0.769592i | −0.973950 | − | 0.226764i | \(-0.927186\pi\) |
−0.0853021 | + | 0.996355i | \(0.527186\pi\) | |||||||
\(8\) | −1.40126 | − | 1.01807i | −0.495420 | − | 0.359943i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 5.19615 | 1.64317 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.535233 | + | 1.64728i | 0.148447 | + | 0.456873i | 0.997438 | − | 0.0715342i | \(-0.0227895\pi\) |
−0.848991 | + | 0.528407i | \(0.822790\pi\) | |||||||
\(14\) | 4.85410 | + | 3.52671i | 1.29731 | + | 0.942553i | ||||
\(15\) | −2.42705 | + | 1.76336i | −0.626662 | + | 0.455296i | ||||
\(16\) | −1.54508 | + | 4.75528i | −0.386271 | + | 1.18882i | ||||
\(17\) | −0.535233 | + | 1.64728i | −0.129813 | + | 0.399524i | −0.994747 | − | 0.102362i | \(-0.967360\pi\) |
0.864934 | + | 0.501885i | \(0.167360\pi\) | |||||||
\(18\) | 1.40126 | − | 1.01807i | 0.330280 | − | 0.239962i | ||||
\(19\) | 5.60503 | + | 4.07230i | 1.28588 | + | 0.934249i | 0.999714 | − | 0.0239303i | \(-0.00761799\pi\) |
0.286169 | + | 0.958179i | \(0.407618\pi\) | |||||||
\(20\) | −0.927051 | − | 2.85317i | −0.207295 | − | 0.637988i | ||||
\(21\) | −3.46410 | −0.755929 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | −0.535233 | − | 1.64728i | −0.109254 | − | 0.336249i | ||||
\(25\) | −3.23607 | − | 2.35114i | −0.647214 | − | 0.470228i | ||||
\(26\) | 2.42705 | − | 1.76336i | 0.475984 | − | 0.345823i | ||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | 1.07047 | − | 3.29456i | 0.202299 | − | 0.622613i | ||||
\(29\) | −1.40126 | + | 1.01807i | −0.260207 | + | 0.189052i | −0.710238 | − | 0.703961i | \(-0.751413\pi\) |
0.450031 | + | 0.893013i | \(0.351413\pi\) | |||||||
\(30\) | 4.20378 | + | 3.05422i | 0.767501 | + | 0.557622i | ||||
\(31\) | 1.23607 | + | 3.80423i | 0.222004 | + | 0.683259i | 0.998582 | + | 0.0532375i | \(0.0169540\pi\) |
−0.776578 | + | 0.630022i | \(0.783046\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | −3.21140 | − | 9.88367i | −0.542825 | − | 1.67065i | ||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | 8.89919 | − | 6.46564i | 1.46302 | − | 1.06294i | 0.480453 | − | 0.877020i | \(-0.340472\pi\) |
0.982564 | − | 0.185924i | \(-0.0595278\pi\) | |||||||
\(38\) | 3.70820 | − | 11.4127i | 0.601550 | − | 1.85138i | ||||
\(39\) | −0.535233 | + | 1.64728i | −0.0857059 | + | 0.263776i | ||||
\(40\) | 4.20378 | − | 3.05422i | 0.664675 | − | 0.482915i | ||||
\(41\) | −1.40126 | − | 1.01807i | −0.218840 | − | 0.158996i | 0.472964 | − | 0.881082i | \(-0.343184\pi\) |
−0.691804 | + | 0.722085i | \(0.743184\pi\) | |||||||
\(42\) | 1.85410 | + | 5.70634i | 0.286094 | + | 0.880507i | ||||
\(43\) | −3.46410 | −0.528271 | −0.264135 | − | 0.964486i | \(-0.585087\pi\) | ||||
−0.264135 | + | 0.964486i | \(0.585087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 3.21140 | + | 9.88367i | 0.473495 | + | 1.45727i | ||||
\(47\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(48\) | −4.04508 | + | 2.93893i | −0.583858 | + | 0.424197i | ||||
\(49\) | 1.54508 | − | 4.75528i | 0.220726 | − | 0.679326i | ||||
\(50\) | −2.14093 | + | 6.58911i | −0.302774 | + | 0.931841i | ||||
\(51\) | −1.40126 | + | 1.01807i | −0.196215 | + | 0.142559i | ||||
\(52\) | −1.40126 | − | 1.01807i | −0.194320 | − | 0.141181i | ||||
\(53\) | −2.78115 | − | 8.55951i | −0.382021 | − | 1.17574i | −0.938619 | − | 0.344957i | \(-0.887894\pi\) |
0.556598 | − | 0.830782i | \(-0.312106\pi\) | |||||||
\(54\) | 1.73205 | 0.235702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.00000 | 0.801784 | ||||||||
\(57\) | 2.14093 | + | 6.58911i | 0.283573 | + | 0.872749i | ||||
\(58\) | 2.42705 | + | 1.76336i | 0.318687 | + | 0.231540i | ||||
\(59\) | 4.85410 | − | 3.52671i | 0.631950 | − | 0.459139i | −0.225125 | − | 0.974330i | \(-0.572279\pi\) |
0.857075 | + | 0.515191i | \(0.172279\pi\) | |||||||
\(60\) | 0.927051 | − | 2.85317i | 0.119682 | − | 0.368343i | ||||
\(61\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(62\) | 5.60503 | − | 4.07230i | 0.711840 | − | 0.517182i | ||||
\(63\) | −2.80252 | − | 2.03615i | −0.353084 | − | 0.256531i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | −5.19615 | −0.644503 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | −0.535233 | − | 1.64728i | −0.0649066 | − | 0.199762i | ||||
\(69\) | −4.85410 | − | 3.52671i | −0.584365 | − | 0.424566i | ||||
\(70\) | −14.5623 | + | 10.5801i | −1.74053 | + | 1.26457i | ||||
\(71\) | −1.85410 | + | 5.70634i | −0.220041 | + | 0.677218i | 0.778716 | + | 0.627377i | \(0.215871\pi\) |
−0.998757 | + | 0.0498409i | \(0.984129\pi\) | |||||||
\(72\) | 0.535233 | − | 1.64728i | 0.0630778 | − | 0.194134i | ||||
\(73\) | 5.60503 | − | 4.07230i | 0.656020 | − | 0.476626i | −0.209297 | − | 0.977852i | \(-0.567117\pi\) |
0.865316 | + | 0.501226i | \(0.167117\pi\) | |||||||
\(74\) | −15.4138 | − | 11.1988i | −1.79182 | − | 1.30184i | ||||
\(75\) | −1.23607 | − | 3.80423i | −0.142729 | − | 0.439274i | ||||
\(76\) | −6.92820 | −0.794719 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(80\) | −12.1353 | − | 8.81678i | −1.35676 | − | 0.985746i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −0.927051 | + | 2.85317i | −0.102376 | + | 0.315080i | ||||
\(83\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(84\) | 2.80252 | − | 2.03615i | 0.305780 | − | 0.222162i | ||||
\(85\) | −4.20378 | − | 3.05422i | −0.455963 | − | 0.331277i | ||||
\(86\) | 1.85410 | + | 5.70634i | 0.199933 | + | 0.615330i | ||||
\(87\) | −1.73205 | −0.185695 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | 1.60570 | + | 4.94183i | 0.169256 | + | 0.520915i | ||||
\(91\) | −4.85410 | − | 3.52671i | −0.508848 | − | 0.369700i | ||||
\(92\) | 4.85410 | − | 3.52671i | 0.506075 | − | 0.367685i | ||||
\(93\) | −1.23607 | + | 3.80423i | −0.128174 | + | 0.394480i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.8151 | + | 12.2169i | −1.72519 | + | 1.25343i | ||||
\(96\) | 4.20378 | + | 3.05422i | 0.429046 | + | 0.311720i | ||||
\(97\) | −2.16312 | − | 6.65740i | −0.219631 | − | 0.675956i | −0.998792 | − | 0.0491321i | \(-0.984354\pi\) |
0.779161 | − | 0.626824i | \(-0.215646\pi\) | |||||||
\(98\) | −8.66025 | −0.874818 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 4.28187 | + | 13.1782i | 0.426061 | + | 1.31128i | 0.901974 | + | 0.431790i | \(0.142118\pi\) |
−0.475913 | + | 0.879493i | \(0.657882\pi\) | |||||||
\(102\) | 2.42705 | + | 1.76336i | 0.240314 | + | 0.174598i | ||||
\(103\) | −11.3262 | + | 8.22899i | −1.11601 | + | 0.810827i | −0.983599 | − | 0.180368i | \(-0.942271\pi\) |
−0.132408 | + | 0.991195i | \(0.542271\pi\) | |||||||
\(104\) | 0.927051 | − | 2.85317i | 0.0909048 | − | 0.279776i | ||||
\(105\) | 3.21140 | − | 9.88367i | 0.313400 | − | 0.964547i | ||||
\(106\) | −12.6113 | + | 9.16267i | −1.22492 | + | 0.889957i | ||||
\(107\) | 2.80252 | + | 2.03615i | 0.270930 | + | 0.196842i | 0.714951 | − | 0.699174i | \(-0.246449\pi\) |
−0.444022 | + | 0.896016i | \(0.646449\pi\) | |||||||
\(108\) | −0.309017 | − | 0.951057i | −0.0297352 | − | 0.0915155i | ||||
\(109\) | −15.5885 | −1.49310 | −0.746552 | − | 0.665327i | \(-0.768292\pi\) | ||||
−0.746552 | + | 0.665327i | \(0.768292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.0000 | 1.04407 | ||||||||
\(112\) | −5.35233 | − | 16.4728i | −0.505748 | − | 1.55653i | ||||
\(113\) | 16.9894 | + | 12.3435i | 1.59822 | + | 1.16118i | 0.890807 | + | 0.454382i | \(0.150140\pi\) |
0.707417 | + | 0.706796i | \(0.249860\pi\) | |||||||
\(114\) | 9.70820 | − | 7.05342i | 0.909257 | − | 0.660614i | ||||
\(115\) | 5.56231 | − | 17.1190i | 0.518688 | − | 1.59636i | ||||
\(116\) | 0.535233 | − | 1.64728i | 0.0496951 | − | 0.152946i | ||||
\(117\) | −1.40126 | + | 1.01807i | −0.129546 | + | 0.0941210i | ||||
\(118\) | −8.40755 | − | 6.10844i | −0.773978 | − | 0.562328i | ||||
\(119\) | −1.85410 | − | 5.70634i | −0.169965 | − | 0.523099i | ||||
\(120\) | 5.19615 | 0.474342 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.535233 | − | 1.64728i | −0.0482603 | − | 0.148530i | ||||
\(124\) | −3.23607 | − | 2.35114i | −0.290607 | − | 0.211139i | ||||
\(125\) | −2.42705 | + | 1.76336i | −0.217082 | + | 0.157719i | ||||
\(126\) | −1.85410 | + | 5.70634i | −0.165177 | + | 0.508361i | ||||
\(127\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(128\) | 9.80881 | − | 7.12652i | 0.866984 | − | 0.629901i | ||||
\(129\) | −2.80252 | − | 2.03615i | −0.246748 | − | 0.179273i | ||||
\(130\) | 2.78115 | + | 8.55951i | 0.243923 | + | 0.750719i | ||||
\(131\) | 17.3205 | 1.51330 | 0.756650 | − | 0.653820i | \(-0.226835\pi\) | ||||
0.756650 | + | 0.653820i | \(0.226835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0000 | −2.08106 | ||||||||
\(134\) | 1.07047 | + | 3.29456i | 0.0924742 | + | 0.284606i | ||||
\(135\) | −2.42705 | − | 1.76336i | −0.208887 | − | 0.151765i | ||||
\(136\) | 2.42705 | − | 1.76336i | 0.208118 | − | 0.151207i | ||||
\(137\) | −1.85410 | + | 5.70634i | −0.158407 | + | 0.487525i | −0.998490 | − | 0.0549317i | \(-0.982506\pi\) |
0.840083 | + | 0.542457i | \(0.182506\pi\) | |||||||
\(138\) | −3.21140 | + | 9.88367i | −0.273372 | + | 0.841354i | ||||
\(139\) | 8.40755 | − | 6.10844i | 0.713119 | − | 0.518111i | −0.171059 | − | 0.985261i | \(-0.554719\pi\) |
0.884178 | + | 0.467149i | \(0.154719\pi\) | |||||||
\(140\) | 8.40755 | + | 6.10844i | 0.710568 | + | 0.516258i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.3923 | 0.872103 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | −1.60570 | − | 4.94183i | −0.133346 | − | 0.410397i | ||||
\(146\) | −9.70820 | − | 7.05342i | −0.803457 | − | 0.583745i | ||||
\(147\) | 4.04508 | − | 2.93893i | 0.333633 | − | 0.242399i | ||||
\(148\) | −3.39919 | + | 10.4616i | −0.279411 | + | 0.859940i | ||||
\(149\) | 3.74663 | − | 11.5309i | 0.306936 | − | 0.944652i | −0.672012 | − | 0.740541i | \(-0.734570\pi\) |
0.978948 | − | 0.204111i | \(-0.0654305\pi\) | |||||||
\(150\) | −5.60503 | + | 4.07230i | −0.457649 | + | 0.332502i | ||||
\(151\) | 11.2101 | + | 8.14459i | 0.912262 | + | 0.662797i | 0.941586 | − | 0.336773i | \(-0.109335\pi\) |
−0.0293236 | + | 0.999570i | \(0.509335\pi\) | |||||||
\(152\) | −3.70820 | − | 11.4127i | −0.300775 | − | 0.925690i | ||||
\(153\) | −1.73205 | −0.140028 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | −0.535233 | − | 1.64728i | −0.0428529 | − | 0.131888i | ||||
\(157\) | 11.3262 | + | 8.22899i | 0.903932 | + | 0.656745i | 0.939473 | − | 0.342623i | \(-0.111315\pi\) |
−0.0355408 | + | 0.999368i | \(0.511315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.78115 | − | 8.55951i | 0.220560 | − | 0.678813i | ||||
\(160\) | −4.81710 | + | 14.8255i | −0.380825 | + | 1.17206i | ||||
\(161\) | 16.8151 | − | 12.2169i | 1.32522 | − | 0.962826i | ||||
\(162\) | 1.40126 | + | 1.01807i | 0.110093 | + | 0.0799874i | ||||
\(163\) | 0.618034 | + | 1.90211i | 0.0484082 | + | 0.148985i | 0.972339 | − | 0.233575i | \(-0.0750425\pi\) |
−0.923931 | + | 0.382560i | \(0.875042\pi\) | |||||||
\(164\) | 1.73205 | 0.135250 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.07047 | + | 3.29456i | 0.0828352 | + | 0.254940i | 0.983893 | − | 0.178759i | \(-0.0572081\pi\) |
−0.901058 | + | 0.433699i | \(0.857208\pi\) | |||||||
\(168\) | 4.85410 | + | 3.52671i | 0.374502 | + | 0.272092i | ||||
\(169\) | 8.09017 | − | 5.87785i | 0.622321 | − | 0.452143i | ||||
\(170\) | −2.78115 | + | 8.55951i | −0.213305 | + | 0.656484i | ||||
\(171\) | −2.14093 | + | 6.58911i | −0.163721 | + | 0.503882i | ||||
\(172\) | 2.80252 | − | 2.03615i | 0.213690 | − | 0.155255i | ||||
\(173\) | 16.8151 | + | 12.2169i | 1.27843 | + | 0.928833i | 0.999504 | − | 0.0314804i | \(-0.0100222\pi\) |
0.278924 | + | 0.960313i | \(0.410022\pi\) | |||||||
\(174\) | 0.927051 | + | 2.85317i | 0.0702796 | + | 0.216298i | ||||
\(175\) | 13.8564 | 1.04745 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | −4.81710 | − | 14.8255i | −0.361057 | − | 1.11122i | ||||
\(179\) | −9.70820 | − | 7.05342i | −0.725625 | − | 0.527198i | 0.162551 | − | 0.986700i | \(-0.448028\pi\) |
−0.888176 | + | 0.459503i | \(0.848028\pi\) | |||||||
\(180\) | 2.42705 | − | 1.76336i | 0.180902 | − | 0.131433i | ||||
\(181\) | −2.16312 | + | 6.65740i | −0.160783 | + | 0.494840i | −0.998701 | − | 0.0509566i | \(-0.983773\pi\) |
0.837918 | + | 0.545797i | \(0.183773\pi\) | |||||||
\(182\) | −3.21140 | + | 9.88367i | −0.238045 | + | 0.732626i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.40755 | + | 6.10844i | 0.619813 | + | 0.450320i | ||||
\(185\) | 10.1976 | + | 31.3849i | 0.749740 | + | 2.30746i | ||||
\(186\) | 6.92820 | 0.508001 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.07047 | − | 3.29456i | −0.0778650 | − | 0.239644i | ||||
\(190\) | 29.1246 | + | 21.1603i | 2.11292 | + | 1.53513i | ||||
\(191\) | −9.70820 | + | 7.05342i | −0.702461 | + | 0.510368i | −0.880733 | − | 0.473614i | \(-0.842949\pi\) |
0.178272 | + | 0.983981i | \(0.442949\pi\) | |||||||
\(192\) | −0.309017 | + | 0.951057i | −0.0223014 | + | 0.0686366i | ||||
\(193\) | 1.60570 | − | 4.94183i | 0.115581 | − | 0.355721i | −0.876487 | − | 0.481426i | \(-0.840119\pi\) |
0.992068 | + | 0.125705i | \(0.0401191\pi\) | |||||||
\(194\) | −9.80881 | + | 7.12652i | −0.704232 | + | 0.511654i | ||||
\(195\) | −4.20378 | − | 3.05422i | −0.301039 | − | 0.218717i | ||||
\(196\) | 1.54508 | + | 4.75528i | 0.110363 | + | 0.339663i | ||||
\(197\) | 19.0526 | 1.35744 | 0.678719 | − | 0.734398i | \(-0.262535\pi\) | ||||
0.678719 | + | 0.734398i | \(0.262535\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | 2.14093 | + | 6.58911i | 0.151387 | + | 0.465921i | ||||
\(201\) | −1.61803 | − | 1.17557i | −0.114127 | − | 0.0829184i | ||||
\(202\) | 19.4164 | − | 14.1068i | 1.36613 | − | 0.992554i | ||||
\(203\) | 1.85410 | − | 5.70634i | 0.130132 | − | 0.400506i | ||||
\(204\) | 0.535233 | − | 1.64728i | 0.0374738 | − | 0.115333i | ||||
\(205\) | 4.20378 | − | 3.05422i | 0.293604 | − | 0.213316i | ||||
\(206\) | 19.6176 | + | 14.2530i | 1.36682 | + | 0.993056i | ||||
\(207\) | −1.85410 | − | 5.70634i | −0.128869 | − | 0.396618i | ||||
\(208\) | −8.66025 | −0.600481 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −18.0000 | −1.24212 | ||||||||
\(211\) | 5.35233 | + | 16.4728i | 0.368470 | + | 1.13403i | 0.947780 | + | 0.318926i | \(0.103322\pi\) |
−0.579310 | + | 0.815107i | \(0.696678\pi\) | |||||||
\(212\) | 7.28115 | + | 5.29007i | 0.500072 | + | 0.363323i | ||||
\(213\) | −4.85410 | + | 3.52671i | −0.332598 | + | 0.241646i | ||||
\(214\) | 1.85410 | − | 5.70634i | 0.126744 | − | 0.390077i | ||||
\(215\) | 3.21140 | − | 9.88367i | 0.219016 | − | 0.674061i | ||||
\(216\) | 1.40126 | − | 1.01807i | 0.0953436 | − | 0.0692712i | ||||
\(217\) | −11.2101 | − | 8.14459i | −0.760989 | − | 0.552891i | ||||
\(218\) | 8.34346 | + | 25.6785i | 0.565090 | + | 1.73917i | ||||
\(219\) | 6.92820 | 0.468165 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | −5.88756 | − | 18.1201i | −0.395147 | − | 1.21614i | ||||
\(223\) | −16.1803 | − | 11.7557i | −1.08352 | − | 0.787220i | −0.105223 | − | 0.994449i | \(-0.533556\pi\) |
−0.978293 | + | 0.207228i | \(0.933556\pi\) | |||||||
\(224\) | −14.5623 | + | 10.5801i | −0.972985 | + | 0.706915i | ||||
\(225\) | 1.23607 | − | 3.80423i | 0.0824045 | − | 0.253615i | ||||
\(226\) | 11.2399 | − | 34.5928i | 0.747667 | − | 2.30108i | ||||
\(227\) | −19.6176 | + | 14.2530i | −1.30207 | + | 0.946007i | −0.999974 | − | 0.00727112i | \(-0.997686\pi\) |
−0.302094 | + | 0.953278i | \(0.597686\pi\) | |||||||
\(228\) | −5.60503 | − | 4.07230i | −0.371202 | − | 0.269694i | ||||
\(229\) | −7.10739 | − | 21.8743i | −0.469670 | − | 1.44549i | −0.853014 | − | 0.521889i | \(-0.825228\pi\) |
0.383344 | − | 0.923606i | \(-0.374772\pi\) | |||||||
\(230\) | −31.1769 | −2.05574 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −9.09896 | − | 28.0037i | −0.596093 | − | 1.83459i | −0.549209 | − | 0.835685i | \(-0.685071\pi\) |
−0.0468838 | − | 0.998900i | \(-0.514929\pi\) | |||||||
\(234\) | 2.42705 | + | 1.76336i | 0.158661 | + | 0.115274i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.85410 | + | 5.70634i | −0.120692 | + | 0.371451i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.40755 | + | 6.10844i | −0.544981 | + | 0.395952i | ||||
\(239\) | −5.60503 | − | 4.07230i | −0.362560 | − | 0.263415i | 0.391559 | − | 0.920153i | \(-0.371936\pi\) |
−0.754119 | + | 0.656738i | \(0.771936\pi\) | |||||||
\(240\) | −4.63525 | − | 14.2658i | −0.299204 | − | 0.920857i | ||||
\(241\) | 20.7846 | 1.33885 | 0.669427 | − | 0.742878i | \(-0.266540\pi\) | ||||
0.669427 | + | 0.742878i | \(0.266540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.1353 | + | 8.81678i | 0.775293 | + | 0.563283i | ||||
\(246\) | −2.42705 | + | 1.76336i | −0.154743 | + | 0.112427i | ||||
\(247\) | −3.70820 | + | 11.4127i | −0.235947 | + | 0.726171i | ||||
\(248\) | 2.14093 | − | 6.58911i | 0.135949 | − | 0.418409i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.20378 | + | 3.05422i | 0.265870 | + | 0.193166i | ||||
\(251\) | −1.85410 | − | 5.70634i | −0.117030 | − | 0.360181i | 0.875335 | − | 0.483517i | \(-0.160641\pi\) |
−0.992365 | + | 0.123336i | \(0.960641\pi\) | |||||||
\(252\) | 3.46410 | 0.218218 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.60570 | − | 4.94183i | −0.100553 | − | 0.309470i | ||||
\(256\) | −15.3713 | − | 11.1679i | −0.960708 | − | 0.697995i | ||||
\(257\) | −7.28115 | + | 5.29007i | −0.454186 | + | 0.329985i | −0.791246 | − | 0.611498i | \(-0.790567\pi\) |
0.337060 | + | 0.941483i | \(0.390567\pi\) | |||||||
\(258\) | −1.85410 | + | 5.70634i | −0.115431 | + | 0.355261i | ||||
\(259\) | −11.7751 | + | 36.2401i | −0.731671 | + | 2.25185i | ||||
\(260\) | 4.20378 | − | 3.05422i | 0.260707 | − | 0.189415i | ||||
\(261\) | −1.40126 | − | 1.01807i | −0.0867357 | − | 0.0630172i | ||||
\(262\) | −9.27051 | − | 28.5317i | −0.572734 | − | 1.76269i | ||||
\(263\) | −13.8564 | −0.854423 | −0.427211 | − | 0.904152i | \(-0.640504\pi\) | ||||
−0.427211 | + | 0.904152i | \(0.640504\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.0000 | 1.65860 | ||||||||
\(266\) | 12.8456 | + | 39.5347i | 0.787614 | + | 2.42403i | ||||
\(267\) | 7.28115 | + | 5.29007i | 0.445599 | + | 0.323747i | ||||
\(268\) | 1.61803 | − | 1.17557i | 0.0988372 | − | 0.0718094i | ||||
\(269\) | −6.48936 | + | 19.9722i | −0.395663 | + | 1.21773i | 0.532781 | + | 0.846253i | \(0.321147\pi\) |
−0.928444 | + | 0.371472i | \(0.878853\pi\) | |||||||
\(270\) | −1.60570 | + | 4.94183i | −0.0977198 | + | 0.300750i | ||||
\(271\) | −2.80252 | + | 2.03615i | −0.170241 | + | 0.123687i | −0.669643 | − | 0.742683i | \(-0.733553\pi\) |
0.499402 | + | 0.866370i | \(0.333553\pi\) | |||||||
\(272\) | −7.00629 | − | 5.09037i | −0.424819 | − | 0.308649i | ||||
\(273\) | −1.85410 | − | 5.70634i | −0.112215 | − | 0.345363i | ||||
\(274\) | 10.3923 | 0.627822 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | 1.60570 | + | 4.94183i | 0.0964771 | + | 0.296926i | 0.987636 | − | 0.156766i | \(-0.0501067\pi\) |
−0.891159 | + | 0.453692i | \(0.850107\pi\) | |||||||
\(278\) | −14.5623 | − | 10.5801i | −0.873389 | − | 0.634554i | ||||
\(279\) | −3.23607 | + | 2.35114i | −0.193738 | + | 0.140759i | ||||
\(280\) | −5.56231 | + | 17.1190i | −0.332411 | + | 1.02306i | ||||
\(281\) | 2.14093 | − | 6.58911i | 0.127717 | − | 0.393074i | −0.866669 | − | 0.498884i | \(-0.833744\pi\) |
0.994386 | + | 0.105810i | \(0.0337435\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.2227 | − | 18.3253i | −1.49933 | − | 1.08933i | −0.970647 | − | 0.240509i | \(-0.922686\pi\) |
−0.528684 | − | 0.848819i | \(-0.677314\pi\) | |||||||
\(284\) | −1.85410 | − | 5.70634i | −0.110021 | − | 0.338609i | ||||
\(285\) | −20.7846 | −1.23117 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 1.60570 | + | 4.94183i | 0.0946167 | + | 0.291200i | ||||
\(289\) | 11.3262 | + | 8.22899i | 0.666249 | + | 0.484058i | ||||
\(290\) | −7.28115 | + | 5.29007i | −0.427564 | + | 0.310643i | ||||
\(291\) | 2.16312 | − | 6.65740i | 0.126804 | − | 0.390263i | ||||
\(292\) | −2.14093 | + | 6.58911i | −0.125289 | + | 0.385599i | ||||
\(293\) | 15.4138 | − | 11.1988i | 0.900486 | − | 0.654242i | −0.0381045 | − | 0.999274i | \(-0.512132\pi\) |
0.938591 | + | 0.345032i | \(0.112132\pi\) | |||||||
\(294\) | −7.00629 | − | 5.09037i | −0.408615 | − | 0.296876i | ||||
\(295\) | 5.56231 | + | 17.1190i | 0.323850 | + | 0.996708i | ||||
\(296\) | −19.0526 | −1.10741 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.0000 | −1.21650 | ||||||||
\(299\) | −3.21140 | − | 9.88367i | −0.185720 | − | 0.571587i | ||||
\(300\) | 3.23607 | + | 2.35114i | 0.186834 | + | 0.135743i | ||||
\(301\) | 9.70820 | − | 7.05342i | 0.559572 | − | 0.406553i | ||||
\(302\) | 7.41641 | − | 22.8254i | 0.426766 | − | 1.31345i | ||||
\(303\) | −4.28187 | + | 13.1782i | −0.245987 | + | 0.757069i | ||||
\(304\) | −28.0252 | + | 20.3615i | −1.60735 | + | 1.16781i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.927051 | + | 2.85317i | 0.0529960 | + | 0.163105i | ||||
\(307\) | −3.46410 | −0.197707 | −0.0988534 | − | 0.995102i | \(-0.531517\pi\) | ||||
−0.0988534 | + | 0.995102i | \(0.531517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.0000 | −0.796432 | ||||||||
\(310\) | 6.42280 | + | 19.7673i | 0.364790 | + | 1.12271i | ||||
\(311\) | −9.70820 | − | 7.05342i | −0.550502 | − | 0.399963i | 0.277469 | − | 0.960735i | \(-0.410505\pi\) |
−0.827970 | + | 0.560772i | \(0.810505\pi\) | |||||||
\(312\) | 2.42705 | − | 1.76336i | 0.137405 | − | 0.0998304i | ||||
\(313\) | 2.16312 | − | 6.65740i | 0.122267 | − | 0.376298i | −0.871126 | − | 0.491059i | \(-0.836610\pi\) |
0.993393 | + | 0.114760i | \(0.0366100\pi\) | |||||||
\(314\) | 7.49326 | − | 23.0619i | 0.422869 | − | 1.30146i | ||||
\(315\) | 8.40755 | − | 6.10844i | 0.473712 | − | 0.344172i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.85410 | + | 5.70634i | 0.104137 | + | 0.320500i | 0.989527 | − | 0.144349i | \(-0.0461087\pi\) |
−0.885390 | + | 0.464849i | \(0.846109\pi\) | |||||||
\(318\) | −15.5885 | −0.874157 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.00000 | −0.167705 | ||||||||
\(321\) | 1.07047 | + | 3.29456i | 0.0597476 | + | 0.183884i | ||||
\(322\) | −29.1246 | − | 21.1603i | −1.62305 | − | 1.17922i | ||||
\(323\) | −9.70820 | + | 7.05342i | −0.540179 | + | 0.392463i | ||||
\(324\) | 0.309017 | − | 0.951057i | 0.0171676 | − | 0.0528365i | ||||
\(325\) | 2.14093 | − | 6.58911i | 0.118758 | − | 0.365498i | ||||
\(326\) | 2.80252 | − | 2.03615i | 0.155217 | − | 0.112772i | ||||
\(327\) | −12.6113 | − | 9.16267i | −0.697408 | − | 0.506697i | ||||
\(328\) | 0.927051 | + | 2.85317i | 0.0511878 | + | 0.157540i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.89919 | + | 6.46564i | 0.487672 | + | 0.354315i | ||||
\(334\) | 4.85410 | − | 3.52671i | 0.265605 | − | 0.192973i | ||||
\(335\) | 1.85410 | − | 5.70634i | 0.101300 | − | 0.311771i | ||||
\(336\) | 5.35233 | − | 16.4728i | 0.291994 | − | 0.898664i | ||||
\(337\) | −9.80881 | + | 7.12652i | −0.534320 | + | 0.388206i | −0.821971 | − | 0.569529i | \(-0.807126\pi\) |
0.287651 | + | 0.957735i | \(0.407126\pi\) | |||||||
\(338\) | −14.0126 | − | 10.1807i | −0.762184 | − | 0.553759i | ||||
\(339\) | 6.48936 | + | 19.9722i | 0.352453 | + | 1.08474i | ||||
\(340\) | 5.19615 | 0.281801 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000 | 0.648886 | ||||||||
\(343\) | −2.14093 | − | 6.58911i | −0.115599 | − | 0.355779i | ||||
\(344\) | 4.85410 | + | 3.52671i | 0.261716 | + | 0.190148i | ||||
\(345\) | 14.5623 | − | 10.5801i | 0.784008 | − | 0.569615i | ||||
\(346\) | 11.1246 | − | 34.2380i | 0.598063 | − | 1.84065i | ||||
\(347\) | −8.56373 | + | 26.3565i | −0.459725 | + | 1.41489i | 0.405772 | + | 0.913974i | \(0.367003\pi\) |
−0.865497 | + | 0.500914i | \(0.832997\pi\) | |||||||
\(348\) | 1.40126 | − | 1.01807i | 0.0751153 | − | 0.0545745i | ||||
\(349\) | −1.40126 | − | 1.01807i | −0.0750076 | − | 0.0544962i | 0.549650 | − | 0.835395i | \(-0.314761\pi\) |
−0.624657 | + | 0.780899i | \(0.714761\pi\) | |||||||
\(350\) | −7.41641 | − | 22.8254i | −0.396424 | − | 1.22007i | ||||
\(351\) | −1.73205 | −0.0924500 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.0000 | 1.11772 | 0.558859 | − | 0.829263i | \(-0.311239\pi\) | ||||
0.558859 | + | 0.829263i | \(0.311239\pi\) | |||||||
\(354\) | −3.21140 | − | 9.88367i | −0.170684 | − | 0.525311i | ||||
\(355\) | −14.5623 | − | 10.5801i | −0.772887 | − | 0.561535i | ||||
\(356\) | −7.28115 | + | 5.29007i | −0.385900 | + | 0.280373i | ||||
\(357\) | 1.85410 | − | 5.70634i | 0.0981295 | − | 0.302011i | ||||
\(358\) | −6.42280 | + | 19.7673i | −0.339455 | + | 1.04474i | ||||
\(359\) | 25.2227 | − | 18.3253i | 1.33120 | − | 0.967174i | 0.331482 | − | 0.943462i | \(-0.392451\pi\) |
0.999719 | − | 0.0237124i | \(-0.00754859\pi\) | |||||||
\(360\) | 4.20378 | + | 3.05422i | 0.221558 | + | 0.160972i | ||||
\(361\) | 8.96149 | + | 27.5806i | 0.471658 | + | 1.45161i | ||||
\(362\) | 12.1244 | 0.637242 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.00000 | 0.314485 | ||||||||
\(365\) | 6.42280 | + | 19.7673i | 0.336185 | + | 1.03467i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.0344 | + | 15.2824i | −1.09799 | + | 0.797736i | −0.980730 | − | 0.195366i | \(-0.937411\pi\) |
−0.117258 | + | 0.993101i | \(0.537411\pi\) | |||||||
\(368\) | 9.27051 | − | 28.5317i | 0.483259 | − | 1.48732i | ||||
\(369\) | 0.535233 | − | 1.64728i | 0.0278631 | − | 0.0857539i | ||||
\(370\) | 46.2415 | − | 33.5964i | 2.40398 | − | 1.74660i | ||||
\(371\) | 25.2227 | + | 18.3253i | 1.30949 | + | 0.951404i | ||||
\(372\) | −1.23607 | − | 3.80423i | −0.0640871 | − | 0.197240i | ||||
\(373\) | −20.7846 | −1.07619 | −0.538093 | − | 0.842885i | \(-0.680855\pi\) | ||||
−0.538093 | + | 0.842885i | \(0.680855\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.00000 | −0.154919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.42705 | − | 1.76336i | −0.124999 | − | 0.0908174i | ||||
\(378\) | −4.85410 | + | 3.52671i | −0.249668 | + | 0.181394i | ||||
\(379\) | 4.32624 | − | 13.3148i | 0.222224 | − | 0.683935i | −0.776338 | − | 0.630317i | \(-0.782925\pi\) |
0.998562 | − | 0.0536176i | \(-0.0170752\pi\) | |||||||
\(380\) | 6.42280 | − | 19.7673i | 0.329483 | − | 1.01404i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.8151 | + | 12.2169i | 0.860335 | + | 0.625070i | ||||
\(383\) | 1.85410 | + | 5.70634i | 0.0947402 | + | 0.291580i | 0.987186 | − | 0.159575i | \(-0.0510122\pi\) |
−0.892446 | + | 0.451155i | \(0.851012\pi\) | |||||||
\(384\) | 12.1244 | 0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.00000 | −0.458088 | ||||||||
\(387\) | −1.07047 | − | 3.29456i | −0.0544149 | − | 0.167472i | ||||
\(388\) | 5.66312 | + | 4.11450i | 0.287501 | + | 0.208882i | ||||
\(389\) | 21.8435 | − | 15.8702i | 1.10751 | − | 0.804651i | 0.125238 | − | 0.992127i | \(-0.460031\pi\) |
0.982269 | + | 0.187476i | \(0.0600305\pi\) | |||||||
\(390\) | −2.78115 | + | 8.55951i | −0.140829 | + | 0.433428i | ||||
\(391\) | 3.21140 | − | 9.88367i | 0.162407 | − | 0.499839i | ||||
\(392\) | −7.00629 | + | 5.09037i | −0.353871 | + | 0.257102i | ||||
\(393\) | 14.0126 | + | 10.1807i | 0.706841 | + | 0.513550i | ||||
\(394\) | −10.1976 | − | 31.3849i | −0.513746 | − | 1.58115i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0000 | 0.552074 | 0.276037 | − | 0.961147i | \(-0.410979\pi\) | ||||
0.276037 | + | 0.961147i | \(0.410979\pi\) | |||||||
\(398\) | −5.35233 | − | 16.4728i | −0.268288 | − | 0.825706i | ||||
\(399\) | −19.4164 | − | 14.1068i | −0.972036 | − | 0.706226i | ||||
\(400\) | 16.1803 | − | 11.7557i | 0.809017 | − | 0.587785i | ||||
\(401\) | 0.927051 | − | 2.85317i | 0.0462947 | − | 0.142480i | −0.925237 | − | 0.379389i | \(-0.876134\pi\) |
0.971532 | + | 0.236909i | \(0.0761342\pi\) | |||||||
\(402\) | −1.07047 | + | 3.29456i | −0.0533900 | + | 0.164318i | ||||
\(403\) | −5.60503 | + | 4.07230i | −0.279207 | + | 0.202855i | ||||
\(404\) | −11.2101 | − | 8.14459i | −0.557722 | − | 0.405209i | ||||
\(405\) | −0.927051 | − | 2.85317i | −0.0460655 | − | 0.141775i | ||||
\(406\) | −10.3923 | −0.515761 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.00000 | 0.148522 | ||||||||
\(409\) | −0.535233 | − | 1.64728i | −0.0264656 | − | 0.0814527i | 0.936951 | − | 0.349460i | \(-0.113635\pi\) |
−0.963417 | + | 0.268007i | \(0.913635\pi\) | |||||||
\(410\) | −7.28115 | − | 5.29007i | −0.359591 | − | 0.261258i | ||||
\(411\) | −4.85410 | + | 3.52671i | −0.239435 | + | 0.173960i | ||||
\(412\) | 4.32624 | − | 13.3148i | 0.213138 | − | 0.655973i | ||||
\(413\) | −6.42280 | + | 19.7673i | −0.316045 | + | 0.972687i | ||||
\(414\) | −8.40755 | + | 6.10844i | −0.413209 | + | 0.300214i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.78115 | + | 8.55951i | 0.136357 | + | 0.419664i | ||||
\(417\) | 10.3923 | 0.508913 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | 3.21140 | + | 9.88367i | 0.156700 | + | 0.482274i | ||||
\(421\) | −5.66312 | − | 4.11450i | −0.276004 | − | 0.200528i | 0.441169 | − | 0.897424i | \(-0.354564\pi\) |
−0.717172 | + | 0.696896i | \(0.754564\pi\) | |||||||
\(422\) | 24.2705 | − | 17.6336i | 1.18147 | − | 0.858388i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.81710 | + | 14.8255i | −0.233939 | + | 0.719990i | ||||
\(425\) | 5.60503 | − | 4.07230i | 0.271884 | − | 0.197535i | ||||
\(426\) | 8.40755 | + | 6.10844i | 0.407347 | + | 0.295955i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.46410 | −0.167444 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.0000 | −0.868037 | ||||||||
\(431\) | 5.35233 | + | 16.4728i | 0.257813 | + | 0.793466i | 0.993262 | + | 0.115887i | \(0.0369709\pi\) |
−0.735450 | + | 0.677579i | \(0.763029\pi\) | |||||||
\(432\) | −4.04508 | − | 2.93893i | −0.194619 | − | 0.141399i | ||||
\(433\) | 15.3713 | − | 11.1679i | 0.738699 | − | 0.536696i | −0.153605 | − | 0.988132i | \(-0.549088\pi\) |
0.892303 | + | 0.451436i | \(0.149088\pi\) | |||||||
\(434\) | −7.41641 | + | 22.8254i | −0.355999 | + | 1.09565i | ||||
\(435\) | 1.60570 | − | 4.94183i | 0.0769874 | − | 0.236943i | ||||
\(436\) | 12.6113 | − | 9.16267i | 0.603973 | − | 0.438812i | ||||
\(437\) | −33.6302 | − | 24.4338i | −1.60875 | − | 1.16883i | ||||
\(438\) | −3.70820 | − | 11.4127i | −0.177185 | − | 0.545319i | ||||
\(439\) | 6.92820 | 0.330665 | 0.165333 | − | 0.986238i | \(-0.447130\pi\) | ||||
0.165333 | + | 0.986238i | \(0.447130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 1.60570 | + | 4.94183i | 0.0763753 | + | 0.235059i | ||||
\(443\) | 14.5623 | + | 10.5801i | 0.691876 | + | 0.502677i | 0.877276 | − | 0.479986i | \(-0.159358\pi\) |
−0.185400 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(444\) | −8.89919 | + | 6.46564i | −0.422337 | + | 0.306846i | ||||
\(445\) | −8.34346 | + | 25.6785i | −0.395518 | + | 1.21728i | ||||
\(446\) | −10.7047 | + | 32.9456i | −0.506880 | + | 1.56002i | ||||
\(447\) | 9.80881 | − | 7.12652i | 0.463941 | − | 0.337073i | ||||
\(448\) | −2.80252 | − | 2.03615i | −0.132406 | − | 0.0961989i | ||||
\(449\) | 6.48936 | + | 19.9722i | 0.306252 | + | 0.942546i | 0.979207 | + | 0.202863i | \(0.0650245\pi\) |
−0.672955 | + | 0.739683i | \(0.734975\pi\) | |||||||
\(450\) | −6.92820 | −0.326599 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −21.0000 | −0.987757 | ||||||||
\(453\) | 4.28187 | + | 13.1782i | 0.201180 | + | 0.619167i | ||||
\(454\) | 33.9787 | + | 24.6870i | 1.59470 | + | 1.15862i | ||||
\(455\) | 14.5623 | − | 10.5801i | 0.682691 | − | 0.496004i | ||||
\(456\) | 3.70820 | − | 11.4127i | 0.173653 | − | 0.534448i | ||||
\(457\) | 9.09896 | − | 28.0037i | 0.425632 | − | 1.30996i | −0.476757 | − | 0.879035i | \(-0.658188\pi\) |
0.902388 | − | 0.430924i | \(-0.141812\pi\) | |||||||
\(458\) | −32.2289 | + | 23.4157i | −1.50596 | + | 1.09414i | ||||
\(459\) | −1.40126 | − | 1.01807i | −0.0654051 | − | 0.0475196i | ||||
\(460\) | 5.56231 | + | 17.1190i | 0.259344 | + | 0.798178i | ||||
\(461\) | 15.5885 | 0.726027 | 0.363013 | − | 0.931784i | \(-0.381748\pi\) | ||||
0.363013 | + | 0.931784i | \(0.381748\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.0000 | −1.58011 | −0.790057 | − | 0.613033i | \(-0.789949\pi\) | ||||
−0.790057 | + | 0.613033i | \(0.789949\pi\) | |||||||
\(464\) | −2.67617 | − | 8.23639i | −0.124238 | − | 0.382365i | ||||
\(465\) | −9.70820 | − | 7.05342i | −0.450207 | − | 0.327095i | ||||
\(466\) | −41.2599 | + | 29.9770i | −1.91133 | + | 1.38866i | ||||
\(467\) | −5.56231 | + | 17.1190i | −0.257393 | + | 0.792174i | 0.735956 | + | 0.677029i | \(0.236733\pi\) |
−0.993349 | + | 0.115144i | \(0.963267\pi\) | |||||||
\(468\) | 0.535233 | − | 1.64728i | 0.0247412 | − | 0.0761455i | ||||
\(469\) | 5.60503 | − | 4.07230i | 0.258816 | − | 0.188041i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.32624 | + | 13.3148i | 0.199343 | + | 0.613513i | ||||
\(472\) | −10.3923 | −0.478345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.56373 | − | 26.3565i | −0.392931 | − | 1.20932i | ||||
\(476\) | 4.85410 | + | 3.52671i | 0.222487 | + | 0.161647i | ||||
\(477\) | 7.28115 | − | 5.29007i | 0.333381 | − | 0.242216i | ||||
\(478\) | −3.70820 | + | 11.4127i | −0.169609 | + | 0.522004i | ||||
\(479\) | −7.49326 | + | 23.0619i | −0.342376 | + | 1.05372i | 0.620598 | + | 0.784129i | \(0.286890\pi\) |
−0.962974 | + | 0.269596i | \(0.913110\pi\) | |||||||
\(480\) | −12.6113 | + | 9.16267i | −0.575626 | + | 0.418217i | ||||
\(481\) | 15.4138 | + | 11.1988i | 0.702811 | + | 0.510622i | ||||
\(482\) | −11.1246 | − | 34.2380i | −0.506712 | − | 1.55950i | ||||
\(483\) | 20.7846 | 0.945732 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0000 | 0.953561 | ||||||||
\(486\) | 0.535233 | + | 1.64728i | 0.0242787 | + | 0.0747221i | ||||
\(487\) | 30.7426 | + | 22.3358i | 1.39308 | + | 1.01213i | 0.995519 | + | 0.0945586i | \(0.0301440\pi\) |
0.397563 | + | 0.917575i | \(0.369856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.618034 | + | 1.90211i | −0.0279485 | + | 0.0860165i | ||||
\(490\) | 8.02850 | − | 24.7092i | 0.362691 | − | 1.11625i | ||||
\(491\) | −16.8151 | + | 12.2169i | −0.758855 | + | 0.551340i | −0.898559 | − | 0.438853i | \(-0.855385\pi\) |
0.139704 | + | 0.990193i | \(0.455385\pi\) | |||||||
\(492\) | 1.40126 | + | 1.01807i | 0.0631736 | + | 0.0458983i | ||||
\(493\) | −0.927051 | − | 2.85317i | −0.0417523 | − | 0.128500i | ||||
\(494\) | 20.7846 | 0.935144 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.0000 | −0.898027 | ||||||||
\(497\) | −6.42280 | − | 19.7673i | −0.288102 | − | 0.886686i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7984 | + | 12.9313i | −0.796765 | + | 0.578883i | −0.909963 | − | 0.414689i | \(-0.863890\pi\) |
0.113199 | + | 0.993572i | \(0.463890\pi\) | |||||||
\(500\) | 0.927051 | − | 2.85317i | 0.0414590 | − | 0.127598i | ||||
\(501\) | −1.07047 | + | 3.29456i | −0.0478249 | + | 0.147190i | ||||
\(502\) | −8.40755 | + | 6.10844i | −0.375247 | + | 0.272633i | ||||
\(503\) | 25.2227 | + | 18.3253i | 1.12462 | + | 0.817086i | 0.984903 | − | 0.173105i | \(-0.0553800\pi\) |
0.139719 | + | 0.990191i | \(0.455380\pi\) | |||||||
\(504\) | 1.85410 | + | 5.70634i | 0.0825883 | + | 0.254181i | ||||
\(505\) | −41.5692 | −1.84981 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0000 | 0.444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.5623 | − | 10.5801i | −0.645463 | − | 0.468956i | 0.216260 | − | 0.976336i | \(-0.430614\pi\) |
−0.861723 | + | 0.507380i | \(0.830614\pi\) | |||||||
\(510\) | −7.28115 | + | 5.29007i | −0.322415 | + | 0.234248i | ||||
\(511\) | −7.41641 | + | 22.8254i | −0.328083 | + | 1.00973i | ||||
\(512\) | −2.67617 | + | 8.23639i | −0.118271 | + | 0.364000i | ||||
\(513\) | −5.60503 | + | 4.07230i | −0.247468 | + | 0.179796i | ||||
\(514\) | 12.6113 | + | 9.16267i | 0.556262 | + | 0.404148i | ||||
\(515\) | −12.9787 | − | 39.9444i | −0.571910 | − | 1.76016i | ||||
\(516\) | 3.46410 | 0.152499 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 66.0000 | 2.89987 | ||||||||
\(519\) | 6.42280 | + | 19.7673i | 0.281930 | + | 0.867690i | ||||
\(520\) | 7.28115 | + | 5.29007i | 0.319300 | + | 0.231985i | ||||
\(521\) | −4.85410 | + | 3.52671i | −0.212662 | + | 0.154508i | −0.689017 | − | 0.724745i | \(-0.741958\pi\) |
0.476355 | + | 0.879253i | \(0.341958\pi\) | |||||||
\(522\) | −0.927051 | + | 2.85317i | −0.0405759 | + | 0.124880i | ||||
\(523\) | 12.8456 | − | 39.5347i | 0.561699 | − | 1.72873i | −0.115863 | − | 0.993265i | \(-0.536963\pi\) |
0.677562 | − | 0.735466i | \(-0.263037\pi\) | |||||||
\(524\) | −14.0126 | + | 10.1807i | −0.612143 | + | 0.444748i | ||||
\(525\) | 11.2101 | + | 8.14459i | 0.489247 | + | 0.355459i | ||||
\(526\) | 7.41641 | + | 22.8254i | 0.323371 | + | 0.995233i | ||||
\(527\) | −6.92820 | −0.301797 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | −14.4513 | − | 44.4765i | −0.627724 | − | 1.93194i | ||||
\(531\) | 4.85410 | + | 3.52671i | 0.210650 | + | 0.153046i | ||||
\(532\) | 19.4164 | − | 14.1068i | 0.841808 | − | 0.611609i | ||||
\(533\) | 0.927051 | − | 2.85317i | 0.0401550 | − | 0.123584i | ||||
\(534\) | 4.81710 | − | 14.8255i | 0.208456 | − | 0.641562i | ||||
\(535\) | −8.40755 | + | 6.10844i | −0.363490 | + | 0.264091i | ||||
\(536\) | 2.80252 | + | 2.03615i | 0.121050 | + | 0.0879482i | ||||
\(537\) | −3.70820 | − | 11.4127i | −0.160021 | − | 0.492493i | ||||
\(538\) | 36.3731 | 1.56815 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.00000 | 0.129099 | ||||||||
\(541\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(542\) | 4.85410 | + | 3.52671i | 0.208502 | + | 0.151485i | ||||
\(543\) | −5.66312 | + | 4.11450i | −0.243028 | + | 0.176570i | ||||
\(544\) | −2.78115 | + | 8.55951i | −0.119241 | + | 0.366986i | ||||
\(545\) | 14.4513 | − | 44.4765i | 0.619025 | − | 1.90516i | ||||
\(546\) | −8.40755 | + | 6.10844i | −0.359810 | + | 0.261417i | ||||
\(547\) | −28.0252 | − | 20.3615i | −1.19827 | − | 0.870594i | −0.204156 | − | 0.978938i | \(-0.565445\pi\) |
−0.994113 | + | 0.108344i | \(0.965445\pi\) | |||||||
\(548\) | −1.85410 | − | 5.70634i | −0.0792033 | − | 0.243763i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 3.21140 | + | 9.88367i | 0.136686 | + | 0.420677i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.28115 | − | 5.29007i | 0.309347 | − | 0.224753i | ||||
\(555\) | −10.1976 | + | 31.3849i | −0.432862 | + | 1.33221i | ||||
\(556\) | −3.21140 | + | 9.88367i | −0.136194 | + | 0.419161i | ||||
\(557\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(558\) | 5.60503 | + | 4.07230i | 0.237280 | + | 0.172394i | ||||
\(559\) | −1.85410 | − | 5.70634i | −0.0784202 | − | 0.241352i | ||||
\(560\) | 51.9615 | 2.19578 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | −5.35233 | − | 16.4728i | −0.225574 | − | 0.694245i | −0.998233 | − | 0.0594237i | \(-0.981074\pi\) |
0.772659 | − | 0.634821i | \(-0.218926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.9681 | + | 37.0305i | −2.14424 | + | 1.55788i | ||||
\(566\) | −16.6869 | + | 51.3571i | −0.701403 | + | 2.15870i | ||||
\(567\) | 1.07047 | − | 3.29456i | 0.0449554 | − | 0.138358i | ||||
\(568\) | 8.40755 | − | 6.10844i | 0.352773 | − | 0.256305i | ||||
\(569\) | −22.4201 | − | 16.2892i | −0.939901 | − | 0.682878i | 0.00849582 | − | 0.999964i | \(-0.497296\pi\) |
−0.948397 | + | 0.317086i | \(0.897296\pi\) | |||||||
\(570\) | 11.1246 | + | 34.2380i | 0.465959 | + | 1.43407i | ||||
\(571\) | −3.46410 | −0.144968 | −0.0724841 | − | 0.997370i | \(-0.523093\pi\) | ||||
−0.0724841 | + | 0.997370i | \(0.523093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | −0.501307 | ||||||||
\(574\) | −3.21140 | − | 9.88367i | −0.134041 | − | 0.412536i | ||||
\(575\) | 19.4164 | + | 14.1068i | 0.809720 | + | 0.588296i | ||||
\(576\) | −0.809017 | + | 0.587785i | −0.0337090 | + | 0.0244911i | ||||
\(577\) | 4.01722 | − | 12.3637i | 0.167239 | − | 0.514709i | −0.831955 | − | 0.554843i | \(-0.812778\pi\) |
0.999194 | + | 0.0401338i | \(0.0127784\pi\) | |||||||
\(578\) | 7.49326 | − | 23.0619i | 0.311679 | − | 0.959248i | ||||
\(579\) | 4.20378 | − | 3.05422i | 0.174703 | − | 0.126929i | ||||
\(580\) | 4.20378 | + | 3.05422i | 0.174552 | + | 0.126820i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.1244 | −0.502571 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | −1.60570 | − | 4.94183i | −0.0663875 | − | 0.204320i | ||||
\(586\) | −26.6976 | − | 19.3969i | −1.10287 | − | 0.801279i | ||||
\(587\) | 9.70820 | − | 7.05342i | 0.400700 | − | 0.291126i | −0.369126 | − | 0.929379i | \(-0.620343\pi\) |
0.769826 | + | 0.638254i | \(0.220343\pi\) | |||||||
\(588\) | −1.54508 | + | 4.75528i | −0.0637182 | + | 0.196105i | ||||
\(589\) | −8.56373 | + | 26.3565i | −0.352862 | + | 1.08600i | ||||
\(590\) | 25.2227 | − | 18.3253i | 1.03840 | − | 0.754442i | ||||
\(591\) | 15.4138 | + | 11.1988i | 0.634041 | + | 0.460658i | ||||
\(592\) | 16.9959 | + | 52.3081i | 0.698529 | + | 2.14985i | ||||
\(593\) | 22.5167 | 0.924648 | 0.462324 | − | 0.886711i | \(-0.347016\pi\) | ||||
0.462324 | + | 0.886711i | \(0.347016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0000 | 0.737928 | ||||||||
\(596\) | 3.74663 | + | 11.5309i | 0.153468 | + | 0.472326i | ||||
\(597\) | 8.09017 | + | 5.87785i | 0.331109 | + | 0.240564i | ||||
\(598\) | −14.5623 | + | 10.5801i | −0.595497 | + | 0.432654i | ||||
\(599\) | 7.41641 | − | 22.8254i | 0.303026 | − | 0.932619i | −0.677380 | − | 0.735633i | \(-0.736885\pi\) |
0.980406 | − | 0.196986i | \(-0.0631152\pi\) | |||||||
\(600\) | −2.14093 | + | 6.58911i | −0.0874032 | + | 0.268999i | ||||
\(601\) | −18.2164 | + | 13.2350i | −0.743061 | + | 0.539865i | −0.893668 | − | 0.448728i | \(-0.851877\pi\) |
0.150607 | + | 0.988594i | \(0.451877\pi\) | |||||||
\(602\) | −16.8151 | − | 12.2169i | −0.685332 | − | 0.497923i | ||||
\(603\) | −0.618034 | − | 1.90211i | −0.0251683 | − | 0.0774600i | ||||
\(604\) | −13.8564 | −0.563809 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24.0000 | 0.974933 | ||||||||
\(607\) | −6.42280 | − | 19.7673i | −0.260693 | − | 0.802332i | −0.992654 | − | 0.120985i | \(-0.961395\pi\) |
0.731961 | − | 0.681347i | \(-0.238605\pi\) | |||||||
\(608\) | 29.1246 | + | 21.1603i | 1.18116 | + | 0.858162i | ||||
\(609\) | 4.85410 | − | 3.52671i | 0.196698 | − | 0.142910i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.40126 | − | 1.01807i | 0.0566425 | − | 0.0411532i | ||||
\(613\) | 15.4138 | + | 11.1988i | 0.622559 | + | 0.452316i | 0.853815 | − | 0.520577i | \(-0.174283\pi\) |
−0.231255 | + | 0.972893i | \(0.574283\pi\) | |||||||
\(614\) | 1.85410 | + | 5.70634i | 0.0748255 | + | 0.230289i | ||||
\(615\) | 5.19615 | 0.209529 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | −0.362326 | −0.181163 | − | 0.983453i | \(-0.557986\pi\) | ||||
−0.181163 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(618\) | 7.49326 | + | 23.0619i | 0.301423 | + | 0.927685i | ||||
\(619\) | 8.09017 | + | 5.87785i | 0.325171 | + | 0.236251i | 0.738379 | − | 0.674386i | \(-0.235592\pi\) |
−0.413208 | + | 0.910637i | \(0.635592\pi\) | |||||||
\(620\) | 9.70820 | − | 7.05342i | 0.389891 | − | 0.283272i | ||||
\(621\) | 1.85410 | − | 5.70634i | 0.0744025 | − | 0.228988i | ||||
\(622\) | −6.42280 | + | 19.7673i | −0.257531 | + | 0.792598i | ||||
\(623\) | −25.2227 | + | 18.3253i | −1.01052 | + | 0.734189i | ||||
\(624\) | −7.00629 | − | 5.09037i | −0.280476 | − | 0.203778i | ||||
\(625\) | −8.96149 | − | 27.5806i | −0.358460 | − | 1.10323i | ||||
\(626\) | −12.1244 | −0.484587 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | 5.88756 | + | 18.1201i | 0.234753 | + | 0.722494i | ||||
\(630\) | −14.5623 | − | 10.5801i | −0.580176 | − | 0.421523i | ||||
\(631\) | 11.3262 | − | 8.22899i | 0.450890 | − | 0.327591i | −0.339057 | − | 0.940766i | \(-0.610108\pi\) |
0.789947 | + | 0.613175i | \(0.210108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.35233 | + | 16.4728i | −0.212736 | + | 0.654734i | ||||
\(634\) | 8.40755 | − | 6.10844i | 0.333907 | − | 0.242597i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.78115 | + | 8.55951i | 0.110280 | + | 0.339407i | ||||
\(637\) | 8.66025 | 0.343132 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 11.2399 | + | 34.5928i | 0.444296 | + | 1.36740i | ||||
\(641\) | 12.1353 | + | 8.81678i | 0.479314 | + | 0.348242i | 0.801060 | − | 0.598584i | \(-0.204270\pi\) |
−0.321746 | + | 0.946826i | \(0.604270\pi\) | |||||||
\(642\) | 4.85410 | − | 3.52671i | 0.191576 | − | 0.139188i | ||||
\(643\) | −4.94427 | + | 15.2169i | −0.194983 | + | 0.600096i | 0.804994 | + | 0.593283i | \(0.202169\pi\) |
−0.999977 | + | 0.00681282i | \(0.997831\pi\) | |||||||
\(644\) | −6.42280 | + | 19.7673i | −0.253094 | + | 0.778942i | ||||
\(645\) | 8.40755 | − | 6.10844i | 0.331047 | − | 0.240520i | ||||
\(646\) | 16.8151 | + | 12.2169i | 0.661581 | + | 0.480667i | ||||
\(647\) | −3.70820 | − | 11.4127i | −0.145785 | − | 0.448679i | 0.851327 | − | 0.524636i | \(-0.175799\pi\) |
−0.997111 | + | 0.0759575i | \(0.975799\pi\) | |||||||
\(648\) | 1.73205 | 0.0680414 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.0000 | −0.470679 | ||||||||
\(651\) | −4.28187 | − | 13.1782i | −0.167820 | − | 0.516495i | ||||
\(652\) | −1.61803 | − | 1.17557i | −0.0633671 | − | 0.0460389i | ||||
\(653\) | 24.2705 | − | 17.6336i | 0.949778 | − | 0.690054i | −0.000976014 | − | 1.00000i | \(-0.500311\pi\) |
0.950754 | + | 0.309945i | \(0.100311\pi\) | |||||||
\(654\) | −8.34346 | + | 25.6785i | −0.326255 | + | 1.00411i | ||||
\(655\) | −16.0570 | + | 49.4183i | −0.627399 | + | 1.93093i | ||||
\(656\) | 7.00629 | − | 5.09037i | 0.273550 | − | 0.198746i | ||||
\(657\) | 5.60503 | + | 4.07230i | 0.218673 | + | 0.158875i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.8564 | −0.539769 | −0.269884 | − | 0.962893i | \(-0.586986\pi\) | ||||
−0.269884 | + | 0.962893i | \(0.586986\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.0000 | −1.59472 | −0.797358 | − | 0.603507i | \(-0.793769\pi\) | ||||
−0.797358 | + | 0.603507i | \(0.793769\pi\) | |||||||
\(662\) | −10.7047 | − | 32.9456i | −0.416049 | − | 1.28047i | ||||
\(663\) | −2.42705 | − | 1.76336i | −0.0942588 | − | 0.0684831i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.2492 | − | 68.4761i | 0.862788 | − | 2.65539i | ||||
\(666\) | 5.88756 | − | 18.1201i | 0.228138 | − | 0.702138i | ||||
\(667\) | 8.40755 | − | 6.10844i | 0.325542 | − | 0.236520i | ||||
\(668\) | −2.80252 | − | 2.03615i | −0.108433 | − | 0.0787809i | ||||
\(669\) | −6.18034 | − | 19.0211i | −0.238946 | − | 0.735399i | ||||
\(670\) | −10.3923 | −0.401490 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −18.0000 | −0.694365 | ||||||||
\(673\) | 6.42280 | + | 19.7673i | 0.247581 | + | 0.761975i | 0.995201 | + | 0.0978489i | \(0.0311962\pi\) |
−0.747621 | + | 0.664126i | \(0.768804\pi\) | |||||||
\(674\) | 16.9894 | + | 12.3435i | 0.654406 | + | 0.475453i | ||||
\(675\) | 3.23607 | − | 2.35114i | 0.124556 | − | 0.0904955i | ||||
\(676\) | −3.09017 | + | 9.51057i | −0.118853 | + | 0.365791i | ||||
\(677\) | −10.1694 | + | 31.2983i | −0.390843 | + | 1.20289i | 0.541309 | + | 0.840824i | \(0.317929\pi\) |
−0.932152 | + | 0.362067i | \(0.882071\pi\) | |||||||
\(678\) | 29.4264 | − | 21.3796i | 1.13012 | − | 0.821077i | ||||
\(679\) | 19.6176 | + | 14.2530i | 0.752855 | + | 0.546981i | ||||
\(680\) | 2.78115 | + | 8.55951i | 0.106652 | + | 0.328242i | ||||
\(681\) | −24.2487 | −0.929213 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | −0.229584 | −0.114792 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114792 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(684\) | −2.14093 | − | 6.58911i | −0.0818606 | − | 0.251941i | ||||
\(685\) | −14.5623 | − | 10.5801i | −0.556397 | − | 0.404246i | ||||
\(686\) | −9.70820 | + | 7.05342i | −0.370661 | + | 0.269301i | ||||
\(687\) | 7.10739 | − | 21.8743i | 0.271164 | − | 0.834557i | ||||
\(688\) | 5.35233 | − | 16.4728i | 0.204056 | − | 0.628019i | ||||
\(689\) | 12.6113 | − | 9.16267i | 0.480453 | − | 0.349070i | ||||
\(690\) | −25.2227 | − | 18.3253i | −0.960210 | − | 0.697633i | ||||
\(691\) | −3.09017 | − | 9.51057i | −0.117556 | − | 0.361799i | 0.874916 | − | 0.484275i | \(-0.160917\pi\) |
−0.992471 | + | 0.122476i | \(0.960917\pi\) | |||||||
\(692\) | −20.7846 | −0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.0000 | 1.82206 | ||||||||
\(695\) | 9.63420 | + | 29.6510i | 0.365446 | + | 1.12473i | ||||
\(696\) | 2.42705 | + | 1.76336i | 0.0919971 | + | 0.0668398i | ||||
\(697\) | 2.42705 | − | 1.76336i | 0.0919311 | − | 0.0667919i | ||||
\(698\) | −0.927051 | + | 2.85317i | −0.0350894 | + | 0.107994i | ||||
\(699\) | 9.09896 | − | 28.0037i | 0.344154 | − | 1.05920i | ||||
\(700\) | −11.2101 | + | 8.14459i | −0.423701 | + | 0.307837i | ||||
\(701\) | −32.2289 | − | 23.4157i | −1.21727 | − | 0.884399i | −0.221400 | − | 0.975183i | \(-0.571063\pi\) |
−0.995871 | + | 0.0907843i | \(0.971063\pi\) | |||||||
\(702\) | 0.927051 | + | 2.85317i | 0.0349893 | + | 0.107686i | ||||
\(703\) | 76.2102 | 2.87432 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.2399 | − | 34.5928i | −0.423019 | − | 1.30192i | ||||
\(707\) | −38.8328 | − | 28.2137i | −1.46046 | − | 1.06109i | ||||
\(708\) | −4.85410 | + | 3.52671i | −0.182428 | + | 0.132542i | ||||
\(709\) | 6.79837 | − | 20.9232i | 0.255318 | − | 0.785789i | −0.738448 | − | 0.674310i | \(-0.764441\pi\) |
0.993767 | − | 0.111479i | \(-0.0355588\pi\) | |||||||
\(710\) | −9.63420 | + | 29.6510i | −0.361565 | + | 1.11278i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.6113 | − | 9.16267i | −0.472629 | − | 0.343385i | ||||
\(713\) | −7.41641 | − | 22.8254i | −0.277747 | − | 0.854816i | ||||
\(714\) | −10.3923 | −0.388922 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | −2.14093 | − | 6.58911i | −0.0799546 | − | 0.246075i | ||||
\(718\) | −43.6869 | − | 31.7404i | −1.63038 | − | 1.18454i | ||||
\(719\) | 24.2705 | − | 17.6336i | 0.905137 | − | 0.657621i | −0.0346431 | − | 0.999400i | \(-0.511029\pi\) |
0.939780 | + | 0.341779i | \(0.111029\pi\) | |||||||
\(720\) | 4.63525 | − | 14.2658i | 0.172746 | − | 0.531657i | ||||
\(721\) | 14.9865 | − | 46.1238i | 0.558127 | − | 1.71774i | ||||
\(722\) | 40.6365 | − | 29.5241i | 1.51233 | − | 1.09877i | ||||
\(723\) | 16.8151 | + | 12.2169i | 0.625360 | + | 0.454351i | ||||
\(724\) | −2.16312 | − | 6.65740i | −0.0803917 | − | 0.247420i | ||||
\(725\) | 6.92820 | 0.257307 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.00000 | −0.0741759 | −0.0370879 | − | 0.999312i | \(-0.511808\pi\) | ||||
−0.0370879 | + | 0.999312i | \(0.511808\pi\) | |||||||
\(728\) | 3.21140 | + | 9.88367i | 0.119022 | + | 0.366313i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 29.1246 | − | 21.1603i | 1.07795 | − | 0.783177i | ||||
\(731\) | 1.85410 | − | 5.70634i | 0.0685764 | − | 0.211057i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.00629 | − | 5.09037i | 0.258783 | − | 0.188017i | −0.450827 | − | 0.892611i | \(-0.648871\pi\) |
0.709610 | + | 0.704594i | \(0.248871\pi\) | |||||||
\(734\) | 36.4327 | + | 26.4699i | 1.34476 | + | 0.977023i | ||||
\(735\) | 4.63525 | + | 14.2658i | 0.170974 | + | 0.526204i | ||||
\(736\) | −31.1769 | −1.14920 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.00000 | −0.110432 | ||||||||
\(739\) | 8.56373 | + | 26.3565i | 0.315022 | + | 0.969538i | 0.975745 | + | 0.218908i | \(0.0702496\pi\) |
−0.660724 | + | 0.750629i | \(0.729750\pi\) | |||||||
\(740\) | −26.6976 | − | 19.3969i | −0.981422 | − | 0.713045i | ||||
\(741\) | −9.70820 | + | 7.05342i | −0.356640 | + | 0.259114i | ||||
\(742\) | 16.6869 | − | 51.3571i | 0.612596 | − | 1.88538i | ||||
\(743\) | 16.0570 | − | 49.4183i | 0.589074 | − | 1.81298i | 0.00681943 | − | 0.999977i | \(-0.497829\pi\) |
0.582255 | − | 0.813007i | \(-0.302171\pi\) | |||||||
\(744\) | 5.60503 | − | 4.07230i | 0.205491 | − | 0.149298i | ||||
\(745\) | 29.4264 | + | 21.3796i | 1.07810 | + | 0.783286i | ||||
\(746\) | 11.1246 | + | 34.2380i | 0.407301 | + | 1.25354i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 1.60570 | + | 4.94183i | 0.0586319 | + | 0.180450i | ||||
\(751\) | 1.61803 | + | 1.17557i | 0.0590429 | + | 0.0428972i | 0.616915 | − | 0.787030i | \(-0.288382\pi\) |
−0.557872 | + | 0.829927i | \(0.688382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.85410 | − | 5.70634i | 0.0675672 | − | 0.207951i | ||||
\(754\) | −1.60570 | + | 4.94183i | −0.0584761 | + | 0.179971i | ||||
\(755\) | −33.6302 | + | 24.4338i | −1.22393 | + | 0.889236i | ||||
\(756\) | 2.80252 | + | 2.03615i | 0.101927 | + | 0.0740540i | ||||
\(757\) | −5.25329 | − | 16.1680i | −0.190934 | − | 0.587635i | 0.809066 | − | 0.587718i | \(-0.199973\pi\) |
−1.00000 | 8.33163e-5i | \(0.999973\pi\) | ||||||||
\(758\) | −24.2487 | −0.880753 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.0000 | 1.30586 | ||||||||
\(761\) | −10.1694 | − | 31.2983i | −0.368642 | − | 1.13456i | −0.947669 | − | 0.319254i | \(-0.896568\pi\) |
0.579028 | − | 0.815308i | \(-0.303432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.6869 | − | 31.7404i | 1.58157 | − | 1.14908i | ||||
\(764\) | 3.70820 | − | 11.4127i | 0.134158 | − | 0.412896i | ||||
\(765\) | 1.60570 | − | 4.94183i | 0.0580542 | − | 0.178672i | ||||
\(766\) | 8.40755 | − | 6.10844i | 0.303777 | − | 0.220707i | ||||
\(767\) | 8.40755 | + | 6.10844i | 0.303579 | + | 0.220563i | ||||
\(768\) | −5.87132 | − | 18.0701i | −0.211863 | − | 0.652048i | ||||
\(769\) | −25.9808 | −0.936890 | −0.468445 | − | 0.883493i | \(-0.655186\pi\) | ||||
−0.468445 | + | 0.883493i | \(0.655186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | −0.324127 | ||||||||
\(772\) | 1.60570 | + | 4.94183i | 0.0577904 | + | 0.177861i | ||||
\(773\) | −14.5623 | − | 10.5801i | −0.523770 | − | 0.380541i | 0.294252 | − | 0.955728i | \(-0.404929\pi\) |
−0.818022 | + | 0.575187i | \(0.804929\pi\) | |||||||
\(774\) | −4.85410 | + | 3.52671i | −0.174477 | + | 0.126765i | ||||
\(775\) | 4.94427 | − | 15.2169i | 0.177603 | − | 0.546607i | ||||
\(776\) | −3.74663 | + | 11.5309i | −0.134496 | + | 0.413937i | ||||
\(777\) | −30.8277 | + | 22.3976i | −1.10594 | + | 0.803510i | ||||
\(778\) | −37.8340 | − | 27.4880i | −1.35641 | − | 0.985492i | ||||
\(779\) | −3.70820 | − | 11.4127i | −0.132860 | − | 0.408902i | ||||
\(780\) | 5.19615 | 0.186052 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | −0.535233 | − | 1.64728i | −0.0191277 | − | 0.0588689i | ||||
\(784\) | 20.2254 | + | 14.6946i | 0.722337 | + | 0.524808i | ||||
\(785\) | −33.9787 | + | 24.6870i | −1.21275 | + | 0.881116i | ||||
\(786\) | 9.27051 | − | 28.5317i | 0.330668 | − | 1.01769i | ||||
\(787\) | 2.14093 | − | 6.58911i | 0.0763160 | − | 0.234877i | −0.905620 | − | 0.424090i | \(-0.860594\pi\) |
0.981936 | + | 0.189214i | \(0.0605939\pi\) | |||||||
\(788\) | −15.4138 | + | 11.1988i | −0.549095 | + | 0.398941i | ||||
\(789\) | −11.2101 | − | 8.14459i | −0.399089 | − | 0.289955i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.7461 | −2.58655 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.88756 | − | 18.1201i | −0.208942 | − | 0.643057i | ||||
\(795\) | 21.8435 | + | 15.8702i | 0.774708 | + | 0.562858i | ||||
\(796\) | −8.09017 | + | 5.87785i | −0.286748 | + | 0.208335i | ||||
\(797\) | −12.9787 | + | 39.9444i | −0.459730 | + | 1.41490i | 0.405762 | + | 0.913979i | \(0.367006\pi\) |
−0.865492 | + | 0.500924i | \(0.832994\pi\) | |||||||
\(798\) | −12.8456 | + | 39.5347i | −0.454729 | + | 1.39951i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −16.8151 | − | 12.2169i | −0.594504 | − | 0.431932i | ||||
\(801\) | 2.78115 | + | 8.55951i | 0.0982672 | + | 0.302435i | ||||
\(802\) | −5.19615 | −0.183483 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 19.2684 | + | 59.3020i | 0.679122 | + | 2.09012i | ||||
\(806\) | 9.70820 | + | 7.05342i | 0.341957 | + | 0.248446i | ||||
\(807\) | −16.9894 | + | 12.3435i | −0.598054 | + | 0.434511i | ||||
\(808\) | 7.41641 | − | 22.8254i | 0.260908 | − | 0.802993i | ||||
\(809\) | −6.42280 | + | 19.7673i | −0.225814 | + | 0.694983i | 0.772394 | + | 0.635143i | \(0.219059\pi\) |
−0.998208 | + | 0.0598395i | \(0.980941\pi\) | |||||||
\(810\) | −4.20378 | + | 3.05422i | −0.147706 | + | 0.107314i | ||||
\(811\) | −22.4201 | − | 16.2892i | −0.787277 | − | 0.571991i | 0.119877 | − | 0.992789i | \(-0.461750\pi\) |
−0.907154 | + | 0.420798i | \(0.861750\pi\) | |||||||
\(812\) | 1.85410 | + | 5.70634i | 0.0650662 | + | 0.200253i | ||||
\(813\) | −3.46410 | −0.121491 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.00000 | −0.210171 | ||||||||
\(816\) | −2.67617 | − | 8.23639i | −0.0936845 | − | 0.288331i | ||||
\(817\) | −19.4164 | − | 14.1068i | −0.679294 | − | 0.493536i | ||||
\(818\) | −2.42705 | + | 1.76336i | −0.0848598 | + | 0.0616543i | ||||
\(819\) | 1.85410 | − | 5.70634i | 0.0647876 | − | 0.199396i | ||||
\(820\) | −1.60570 | + | 4.94183i | −0.0560735 | + | 0.172576i | ||||
\(821\) | 44.8403 | − | 32.5784i | 1.56494 | − | 1.13699i | 0.633125 | − | 0.774049i | \(-0.281772\pi\) |
0.931811 | − | 0.362943i | \(-0.118228\pi\) | |||||||
\(822\) | 8.40755 | + | 6.10844i | 0.293247 | + | 0.213056i | ||||
\(823\) | 4.32624 | + | 13.3148i | 0.150803 | + | 0.464124i | 0.997712 | − | 0.0676144i | \(-0.0215388\pi\) |
−0.846908 | + | 0.531739i | \(0.821539\pi\) | |||||||
\(824\) | 24.2487 | 0.844744 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.0000 | 1.25260 | ||||||||
\(827\) | 11.7751 | + | 36.2401i | 0.409461 | + | 1.26019i | 0.917112 | + | 0.398629i | \(0.130514\pi\) |
−0.507651 | + | 0.861563i | \(0.669486\pi\) | |||||||
\(828\) | 4.85410 | + | 3.52671i | 0.168692 | + | 0.122562i | ||||
\(829\) | −8.89919 | + | 6.46564i | −0.309082 | + | 0.224561i | −0.731502 | − | 0.681839i | \(-0.761180\pi\) |
0.422421 | + | 0.906400i | \(0.361180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.60570 | + | 4.94183i | −0.0557011 | + | 0.171430i | ||||
\(832\) | −1.40126 | + | 1.01807i | −0.0485799 | + | 0.0352954i | ||||
\(833\) | 7.00629 | + | 5.09037i | 0.242754 | + | 0.176371i | ||||
\(834\) | −5.56231 | − | 17.1190i | −0.192607 | − | 0.592783i | ||||
\(835\) | −10.3923 | −0.359641 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 16.0570 | + | 49.4183i | 0.554680 | + | 1.70713i | ||||
\(839\) | −19.4164 | − | 14.1068i | −0.670329 | − | 0.487022i | 0.199806 | − | 0.979835i | \(-0.435969\pi\) |
−0.870135 | + | 0.492813i | \(0.835969\pi\) | |||||||
\(840\) | −14.5623 | + | 10.5801i | −0.502447 | + | 0.365049i | ||||
\(841\) | −8.03444 | + | 24.7275i | −0.277050 | + | 0.852671i | ||||
\(842\) | −3.74663 | + | 11.5309i | −0.129117 | + | 0.397383i | ||||
\(843\) | 5.60503 | − | 4.07230i | 0.193048 | − | 0.140257i | ||||
\(844\) | −14.0126 | − | 10.1807i | −0.482333 | − | 0.350435i | ||||
\(845\) | 9.27051 | + | 28.5317i | 0.318915 | + | 0.981520i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 45.0000 | 1.54531 | ||||||||
\(849\) | −9.63420 | − | 29.6510i | −0.330645 | − | 1.01762i | ||||
\(850\) | −9.70820 | − | 7.05342i | −0.332989 | − | 0.241930i | ||||
\(851\) | −53.3951 | + | 38.7938i | −1.83036 | + | 1.32984i | ||||
\(852\) | 1.85410 | − | 5.70634i | 0.0635205 | − | 0.195496i | ||||
\(853\) | −2.67617 | + | 8.23639i | −0.0916302 | + | 0.282009i | −0.986361 | − | 0.164598i | \(-0.947367\pi\) |
0.894731 | + | 0.446606i | \(0.147367\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.8151 | − | 12.2169i | −0.575064 | − | 0.417809i | ||||
\(856\) | −1.85410 | − | 5.70634i | −0.0633719 | − | 0.195039i | ||||
\(857\) | −41.5692 | −1.41998 | −0.709989 | − | 0.704213i | \(-0.751300\pi\) | ||||
−0.709989 | + | 0.704213i | \(0.751300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | 3.21140 | + | 9.88367i | 0.109508 | + | 0.337030i | ||||
\(861\) | 4.85410 | + | 3.52671i | 0.165427 | + | 0.120190i | ||||
\(862\) | 24.2705 | − | 17.6336i | 0.826657 | − | 0.600601i | ||||
\(863\) | 1.85410 | − | 5.70634i | 0.0631144 | − | 0.194246i | −0.914527 | − | 0.404524i | \(-0.867437\pi\) |
0.977642 | + | 0.210278i | \(0.0674370\pi\) | |||||||
\(864\) | −1.60570 | + | 4.94183i | −0.0546270 | + | 0.168125i | ||||
\(865\) | −50.4453 | + | 36.6507i | −1.71519 | + | 1.24616i | ||||
\(866\) | −26.6239 | − | 19.3434i | −0.904717 | − | 0.657316i | ||||
\(867\) | 4.32624 | + | 13.3148i | 0.146927 | + | 0.452194i | ||||
\(868\) | 13.8564 | 0.470317 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −9.00000 | −0.305129 | ||||||||
\(871\) | −1.07047 | − | 3.29456i | −0.0362714 | − | 0.111632i | ||||
\(872\) | 21.8435 | + | 15.8702i | 0.739713 | + | 0.537433i | ||||
\(873\) | 5.66312 | − | 4.11450i | 0.191668 | − | 0.139255i | ||||
\(874\) | −22.2492 | + | 68.4761i | −0.752591 | + | 2.31624i | ||||
\(875\) | 3.21140 | − | 9.88367i | 0.108565 | − | 0.334129i | ||||
\(876\) | −5.60503 | + | 4.07230i | −0.189377 | + | 0.137590i | ||||
\(877\) | −15.4138 | − | 11.1988i | −0.520489 | − | 0.378157i | 0.296299 | − | 0.955095i | \(-0.404247\pi\) |
−0.816788 | + | 0.576938i | \(0.804247\pi\) | |||||||
\(878\) | −3.70820 | − | 11.4127i | −0.125146 | − | 0.385159i | ||||
\(879\) | 19.0526 | 0.642627 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.00000 | −0.303218 | −0.151609 | − | 0.988441i | \(-0.548445\pi\) | ||||
−0.151609 | + | 0.988441i | \(0.548445\pi\) | |||||||
\(882\) | −2.67617 | − | 8.23639i | −0.0901112 | − | 0.277334i | ||||
\(883\) | −3.23607 | − | 2.35114i | −0.108902 | − | 0.0791222i | 0.532001 | − | 0.846744i | \(-0.321440\pi\) |
−0.640904 | + | 0.767621i | \(0.721440\pi\) | |||||||
\(884\) | 2.42705 | − | 1.76336i | 0.0816306 | − | 0.0593081i | ||||
\(885\) | −5.56231 | + | 17.1190i | −0.186975 | + | 0.575449i | ||||
\(886\) | 9.63420 | − | 29.6510i | 0.323667 | − | 0.996145i | ||||
\(887\) | 25.2227 | − | 18.3253i | 0.846894 | − | 0.615304i | −0.0773940 | − | 0.997001i | \(-0.524660\pi\) |
0.924288 | + | 0.381696i | \(0.124660\pi\) | |||||||
\(888\) | −15.4138 | − | 11.1988i | −0.517255 | − | 0.375808i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 46.7654 | 1.56758 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.0000 | 0.669650 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −16.9894 | − | 12.3435i | −0.568209 | − | 0.412828i | ||||
\(895\) | 29.1246 | − | 21.1603i | 0.973528 | − | 0.707310i | ||||
\(896\) | −12.9787 | + | 39.9444i | −0.433588 | + | 1.33445i | ||||
\(897\) | 3.21140 | − | 9.88367i | 0.107225 | − | 0.330006i | ||||
\(898\) | 29.4264 | − | 21.3796i | 0.981973 | − | 0.713445i | ||||
\(899\) | −5.60503 | − | 4.07230i | −0.186938 | − | 0.135819i | ||||
\(900\) | 1.23607 | + | 3.80423i | 0.0412023 | + | 0.126808i | ||||
\(901\) | 15.5885 | 0.519327 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0000 | 0.399335 | ||||||||
\(904\) | −11.2399 | − | 34.5928i | −0.373833 | − | 1.15054i | ||||
\(905\) | −16.9894 | − | 12.3435i | −0.564745 | − | 0.410312i | ||||
\(906\) | 19.4164 | − | 14.1068i | 0.645067 | − | 0.468669i | ||||
\(907\) | −6.79837 | + | 20.9232i | −0.225736 | + | 0.694745i | 0.772480 | + | 0.635039i | \(0.219016\pi\) |
−0.998216 | + | 0.0597055i | \(0.980984\pi\) | |||||||
\(908\) | 7.49326 | − | 23.0619i | 0.248673 | − | 0.765336i | ||||
\(909\) | −11.2101 | + | 8.14459i | −0.371814 | + | 0.270139i | ||||
\(910\) | −25.2227 | − | 18.3253i | −0.836123 | − | 0.607479i | ||||
\(911\) | −9.27051 | − | 28.5317i | −0.307146 | − | 0.945297i | −0.978868 | − | 0.204494i | \(-0.934445\pi\) |
0.671722 | − | 0.740803i | \(-0.265555\pi\) | |||||||
\(912\) | −34.6410 | −1.14708 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −51.0000 | −1.68693 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.6074 | + | 13.5191i | 0.614805 | + | 0.446682i | ||||
\(917\) | −48.5410 | + | 35.2671i | −1.60297 | + | 1.16462i | ||||
\(918\) | −0.927051 | + | 2.85317i | −0.0305972 | + | 0.0941686i | ||||
\(919\) | 7.49326 | − | 23.0619i | 0.247180 | − | 0.760742i | −0.748090 | − | 0.663597i | \(-0.769029\pi\) |
0.995270 | − | 0.0971448i | \(-0.0309710\pi\) | |||||||
\(920\) | −25.2227 | + | 18.3253i | −0.831566 | + | 0.604168i | ||||
\(921\) | −2.80252 | − | 2.03615i | −0.0923461 | − | 0.0670934i | ||||
\(922\) | −8.34346 | − | 25.6785i | −0.274777 | − | 0.845677i | ||||
\(923\) | −10.3923 | −0.342067 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.0000 | −1.44671 | ||||||||
\(926\) | 18.1979 | + | 56.0075i | 0.598021 | + | 1.84052i | ||||
\(927\) | −11.3262 | − | 8.22899i | −0.372002 | − | 0.270276i | ||||
\(928\) | −7.28115 | + | 5.29007i | −0.239016 | + | 0.173655i | ||||
\(929\) | 12.0517 | − | 37.0912i | 0.395402 | − | 1.21692i | −0.533246 | − | 0.845960i | \(-0.679028\pi\) |
0.928648 | − | 0.370962i | \(-0.120972\pi\) | |||||||
\(930\) | −6.42280 | + | 19.7673i | −0.210612 | + | 0.648197i | ||||
\(931\) | 28.0252 | − | 20.3615i | 0.918488 | − | 0.667321i | ||||
\(932\) | 23.8214 | + | 17.3073i | 0.780296 | + | 0.566918i | ||||
\(933\) | −3.70820 | − | 11.4127i | −0.121401 | − | 0.373634i | ||||
\(934\) | 31.1769 | 1.02014 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.00000 | 0.0980581 | ||||||||
\(937\) | −15.5218 | − | 47.7711i | −0.507074 | − | 1.56061i | −0.797256 | − | 0.603641i | \(-0.793716\pi\) |
0.290182 | − | 0.956971i | \(-0.406284\pi\) | |||||||
\(938\) | −9.70820 | − | 7.05342i | −0.316984 | − | 0.230302i | ||||
\(939\) | 5.66312 | − | 4.11450i | 0.184809 | − | 0.134272i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.09896 | + | 28.0037i | −0.296618 | + | 0.912895i | 0.686056 | + | 0.727549i | \(0.259341\pi\) |
−0.982673 | + | 0.185346i | \(0.940659\pi\) | |||||||
\(942\) | 19.6176 | − | 14.2530i | 0.639177 | − | 0.464389i | ||||
\(943\) | 8.40755 | + | 6.10844i | 0.273788 | + | 0.198918i | ||||
\(944\) | 9.27051 | + | 28.5317i | 0.301729 | + | 0.928628i | ||||
\(945\) | 10.3923 | 0.338062 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.0000 | 1.75476 | 0.877382 | − | 0.479792i | \(-0.159288\pi\) | ||||
0.877382 | + | 0.479792i | \(0.159288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.70820 | + | 7.05342i | 0.315142 | + | 0.228964i | ||||
\(950\) | −38.8328 | + | 28.2137i | −1.25990 | + | 0.915373i | ||||
\(951\) | −1.85410 | + | 5.70634i | −0.0601234 | + | 0.185041i | ||||
\(952\) | −3.21140 | + | 9.88367i | −0.104082 | + | 0.320332i | ||||
\(953\) | −46.2415 | + | 33.5964i | −1.49791 | + | 1.08830i | −0.526706 | + | 0.850048i | \(0.676573\pi\) |
−0.971204 | + | 0.238248i | \(0.923427\pi\) | |||||||
\(954\) | −12.6113 | − | 9.16267i | −0.408307 | − | 0.296652i | ||||
\(955\) | −11.1246 | − | 34.2380i | −0.359984 | − | 1.10792i | ||||
\(956\) | 6.92820 | 0.224074 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 42.0000 | 1.35696 | ||||||||
\(959\) | −6.42280 | − | 19.7673i | −0.207403 | − | 0.638321i | ||||
\(960\) | −2.42705 | − | 1.76336i | −0.0783327 | − | 0.0569121i | ||||
\(961\) | 12.1353 | − | 8.81678i | 0.391460 | − | 0.284412i | ||||
\(962\) | 10.1976 | − | 31.3849i | 0.328783 | − | 1.01189i | ||||
\(963\) | −1.07047 | + | 3.29456i | −0.0344953 | + | 0.106166i | ||||
\(964\) | −16.8151 | + | 12.2169i | −0.541578 | + | 0.393479i | ||||
\(965\) | 12.6113 | + | 9.16267i | 0.405973 | + | 0.294957i | ||||
\(966\) | −11.1246 | − | 34.2380i | −0.357929 | − | 1.10159i | ||||
\(967\) | −10.3923 | −0.334194 | −0.167097 | − | 0.985940i | \(-0.553439\pi\) | ||||
−0.167097 | + | 0.985940i | \(0.553439\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | −0.385496 | ||||||||
\(970\) | −11.2399 | − | 34.5928i | −0.360891 | − | 1.11071i | ||||
\(971\) | 33.9787 | + | 24.6870i | 1.09043 | + | 0.792243i | 0.979472 | − | 0.201582i | \(-0.0646083\pi\) |
0.110957 | + | 0.993825i | \(0.464608\pi\) | |||||||
\(972\) | 0.809017 | − | 0.587785i | 0.0259492 | − | 0.0188532i | ||||
\(973\) | −11.1246 | + | 34.2380i | −0.356639 | + | 1.09762i | ||||
\(974\) | 20.3389 | − | 62.5966i | 0.651699 | − | 2.00572i | ||||
\(975\) | 5.60503 | − | 4.07230i | 0.179505 | − | 0.130418i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.78115 | − | 8.55951i | −0.0889770 | − | 0.273843i | 0.896660 | − | 0.442719i | \(-0.145986\pi\) |
−0.985637 | + | 0.168876i | \(0.945986\pi\) | |||||||
\(978\) | 3.46410 | 0.110770 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −15.0000 | −0.479157 | ||||||||
\(981\) | −4.81710 | − | 14.8255i | −0.153798 | − | 0.473342i | ||||
\(982\) | 29.1246 | + | 21.1603i | 0.929404 | + | 0.675251i | ||||
\(983\) | 29.1246 | − | 21.1603i | 0.928931 | − | 0.674908i | −0.0168000 | − | 0.999859i | \(-0.505348\pi\) |
0.945731 | + | 0.324951i | \(0.105348\pi\) | |||||||
\(984\) | −0.927051 | + | 2.85317i | −0.0295533 | + | 0.0909557i | ||||
\(985\) | −17.6627 | + | 54.3602i | −0.562780 | + | 1.73206i | ||||
\(986\) | −4.20378 | + | 3.05422i | −0.133875 | + | 0.0972662i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.70820 | − | 11.4127i | −0.117974 | − | 0.363086i | ||||
\(989\) | 20.7846 | 0.660912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 6.42280 | + | 19.7673i | 0.203924 | + | 0.627614i | ||||
\(993\) | 16.1803 | + | 11.7557i | 0.513468 | + | 0.373056i | ||||
\(994\) | −29.1246 | + | 21.1603i | −0.923777 | + | 0.671163i | ||||
\(995\) | −9.27051 | + | 28.5317i | −0.293895 | + | 0.904516i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.40126 | + | 1.01807i | −0.0443783 | + | 0.0322427i | −0.609753 | − | 0.792591i | \(-0.708731\pi\) |
0.565375 | + | 0.824834i | \(0.308731\pi\) | |||||||
\(998\) | 30.8277 | + | 22.3976i | 0.975833 | + | 0.708984i | ||||
\(999\) | 3.39919 | + | 10.4616i | 0.107546 | + | 0.330991i |
(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 | 363.2.e.m.148.1 | 8 | ||
11.2 | odd | 10 | inner | 363.2.e.m.130.2 | 8 | ||
11.3 | even | 5 | 363.2.a.f.1.1 | ✓ | 2 | ||
11.4 | even | 5 | inner | 363.2.e.m.124.2 | 8 | ||
11.5 | even | 5 | inner | 363.2.e.m.202.2 | 8 | ||
11.6 | odd | 10 | inner | 363.2.e.m.202.1 | 8 | ||
11.7 | odd | 10 | inner | 363.2.e.m.124.1 | 8 | ||
11.8 | odd | 10 | 363.2.a.f.1.2 | yes | 2 | ||
11.9 | even | 5 | inner | 363.2.e.m.130.1 | 8 | ||
11.10 | odd | 2 | inner | 363.2.e.m.148.2 | 8 | ||
33.8 | even | 10 | 1089.2.a.o.1.1 | 2 | |||
33.14 | odd | 10 | 1089.2.a.o.1.2 | 2 | |||
44.3 | odd | 10 | 5808.2.a.ca.1.1 | 2 | |||
44.19 | even | 10 | 5808.2.a.ca.1.2 | 2 | |||
55.14 | even | 10 | 9075.2.a.bo.1.2 | 2 | |||
55.19 | odd | 10 | 9075.2.a.bo.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.a.f.1.1 | ✓ | 2 | 11.3 | even | 5 | ||
363.2.a.f.1.2 | yes | 2 | 11.8 | odd | 10 | ||
363.2.e.m.124.1 | 8 | 11.7 | odd | 10 | inner | ||
363.2.e.m.124.2 | 8 | 11.4 | even | 5 | inner | ||
363.2.e.m.130.1 | 8 | 11.9 | even | 5 | inner | ||
363.2.e.m.130.2 | 8 | 11.2 | odd | 10 | inner | ||
363.2.e.m.148.1 | 8 | 1.1 | even | 1 | trivial | ||
363.2.e.m.148.2 | 8 | 11.10 | odd | 2 | inner | ||
363.2.e.m.202.1 | 8 | 11.6 | odd | 10 | inner | ||
363.2.e.m.202.2 | 8 | 11.5 | even | 5 | inner | ||
1089.2.a.o.1.1 | 2 | 33.8 | even | 10 | |||
1089.2.a.o.1.2 | 2 | 33.14 | odd | 10 | |||
5808.2.a.ca.1.1 | 2 | 44.3 | odd | 10 | |||
5808.2.a.ca.1.2 | 2 | 44.19 | even | 10 | |||
9075.2.a.bo.1.1 | 2 | 55.19 | odd | 10 | |||
9075.2.a.bo.1.2 | 2 | 55.14 | even | 10 |