Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 157.3 | ||
Character | \(\chi\) | \(=\) | 429.157 |
Dual form | 429.2.n.c.235.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35790 | + | 0.986569i | −0.960177 | + | 0.697609i | −0.953192 | − | 0.302366i | \(-0.902223\pi\) |
−0.00698512 | + | 0.999976i | \(0.502223\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | 0.252528 | − | 0.777201i | 0.126264 | − | 0.388600i | ||||
\(5\) | 0.627776 | + | 0.456106i | 0.280750 | + | 0.203977i | 0.719244 | − | 0.694757i | \(-0.244488\pi\) |
−0.438494 | + | 0.898734i | \(0.644488\pi\) | |||||||
\(6\) | 1.35790 | + | 0.986569i | 0.554358 | + | 0.402765i | ||||
\(7\) | 0.0948896 | − | 0.292040i | 0.0358649 | − | 0.110381i | −0.931521 | − | 0.363687i | \(-0.881518\pi\) |
0.967386 | + | 0.253306i | \(0.0815179\pi\) | |||||||
\(8\) | −0.613484 | − | 1.88811i | −0.216899 | − | 0.667548i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −1.30243 | −0.411866 | ||||||||
\(11\) | −1.11510 | − | 3.12355i | −0.336215 | − | 0.941785i | ||||
\(12\) | −0.817197 | −0.235905 | ||||||||
\(13\) | −0.809017 | + | 0.587785i | −0.224381 | + | 0.163022i | ||||
\(14\) | 0.159267 | + | 0.490175i | 0.0425660 | + | 0.131005i | ||||
\(15\) | 0.239789 | − | 0.737995i | 0.0619133 | − | 0.190550i | ||||
\(16\) | 4.01805 | + | 2.91928i | 1.00451 | + | 0.729821i | ||||
\(17\) | −2.88671 | − | 2.09732i | −0.700130 | − | 0.508674i | 0.179844 | − | 0.983695i | \(-0.442441\pi\) |
−0.879975 | + | 0.475021i | \(0.842441\pi\) | |||||||
\(18\) | 0.518670 | − | 1.59630i | 0.122252 | − | 0.376252i | ||||
\(19\) | 0.616165 | + | 1.89636i | 0.141358 | + | 0.435055i | 0.996525 | − | 0.0832981i | \(-0.0265454\pi\) |
−0.855167 | + | 0.518353i | \(0.826545\pi\) | |||||||
\(20\) | 0.513017 | − | 0.372729i | 0.114714 | − | 0.0833447i | ||||
\(21\) | −0.307069 | −0.0670080 | ||||||||
\(22\) | 4.59578 | + | 3.14133i | 0.979824 | + | 0.669734i | ||||
\(23\) | −4.18140 | −0.871882 | −0.435941 | − | 0.899975i | \(-0.643584\pi\) | ||||
−0.435941 | + | 0.899975i | \(0.643584\pi\) | |||||||
\(24\) | −1.60612 | + | 1.16692i | −0.327848 | + | 0.238196i | ||||
\(25\) | −1.35901 | − | 4.18262i | −0.271803 | − | 0.836524i | ||||
\(26\) | 0.518670 | − | 1.59630i | 0.101720 | − | 0.313061i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | −0.203012 | − | 0.147497i | −0.0383656 | − | 0.0278742i | ||||
\(29\) | 2.46290 | − | 7.58001i | 0.457348 | − | 1.40757i | −0.411008 | − | 0.911632i | \(-0.634823\pi\) |
0.868356 | − | 0.495941i | \(-0.165177\pi\) | |||||||
\(30\) | 0.402474 | + | 1.23869i | 0.0734814 | + | 0.226153i | ||||
\(31\) | 2.78484 | − | 2.02330i | 0.500171 | − | 0.363396i | −0.308911 | − | 0.951091i | \(-0.599965\pi\) |
0.809082 | + | 0.587695i | \(0.199965\pi\) | |||||||
\(32\) | −4.36561 | −0.771739 | ||||||||
\(33\) | −2.62609 | + | 2.02575i | −0.457143 | + | 0.352638i | ||||
\(34\) | 5.98900 | 1.02711 | ||||||||
\(35\) | 0.192771 | − | 0.140056i | 0.0325842 | − | 0.0236738i | ||||
\(36\) | 0.252528 | + | 0.777201i | 0.0420880 | + | 0.129533i | ||||
\(37\) | 3.20487 | − | 9.86359i | 0.526878 | − | 1.62156i | −0.233694 | − | 0.972310i | \(-0.575081\pi\) |
0.760572 | − | 0.649254i | \(-0.224919\pi\) | |||||||
\(38\) | −2.70758 | − | 1.96717i | −0.439227 | − | 0.319117i | ||||
\(39\) | 0.809017 | + | 0.587785i | 0.129546 | + | 0.0941210i | ||||
\(40\) | 0.476048 | − | 1.46512i | 0.0752698 | − | 0.231656i | ||||
\(41\) | −3.95358 | − | 12.1679i | −0.617446 | − | 1.90030i | −0.350193 | − | 0.936678i | \(-0.613884\pi\) |
−0.267254 | − | 0.963626i | \(-0.586116\pi\) | |||||||
\(42\) | 0.416968 | − | 0.302945i | 0.0643395 | − | 0.0467454i | ||||
\(43\) | −0.426420 | −0.0650284 | −0.0325142 | − | 0.999471i | \(-0.510351\pi\) | ||||
−0.0325142 | + | 0.999471i | \(0.510351\pi\) | |||||||
\(44\) | −2.70922 | + | 0.0778729i | −0.408430 | + | 0.0117398i | ||||
\(45\) | −0.775974 | −0.115675 | ||||||||
\(46\) | 5.67790 | − | 4.12524i | 0.837161 | − | 0.608233i | ||||
\(47\) | 2.23136 | + | 6.86741i | 0.325477 | + | 1.00171i | 0.971225 | + | 0.238164i | \(0.0765456\pi\) |
−0.645748 | + | 0.763550i | \(0.723454\pi\) | |||||||
\(48\) | 1.53476 | − | 4.72350i | 0.221523 | − | 0.681779i | ||||
\(49\) | 5.58684 | + | 4.05907i | 0.798119 | + | 0.579868i | ||||
\(50\) | 5.97184 | + | 4.33880i | 0.844546 | + | 0.613598i | ||||
\(51\) | −1.10263 | + | 3.39353i | −0.154398 | + | 0.475190i | ||||
\(52\) | 0.252528 | + | 0.777201i | 0.0350193 | + | 0.107778i | ||||
\(53\) | −4.35227 | + | 3.16211i | −0.597831 | + | 0.434349i | −0.845108 | − | 0.534595i | \(-0.820464\pi\) |
0.247278 | + | 0.968945i | \(0.420464\pi\) | |||||||
\(54\) | −1.67845 | −0.228408 | ||||||||
\(55\) | 0.724637 | − | 2.46949i | 0.0977100 | − | 0.332986i | ||||
\(56\) | −0.609617 | −0.0814635 | ||||||||
\(57\) | 1.61314 | − | 1.17201i | 0.213666 | − | 0.155237i | ||||
\(58\) | 4.13385 | + | 12.7227i | 0.542801 | + | 1.67057i | ||||
\(59\) | 1.35726 | − | 4.17722i | 0.176700 | − | 0.543827i | −0.823007 | − | 0.568031i | \(-0.807705\pi\) |
0.999707 | + | 0.0242042i | \(0.00770517\pi\) | |||||||
\(60\) | −0.513017 | − | 0.372729i | −0.0662302 | − | 0.0481191i | ||||
\(61\) | −3.23644 | − | 2.35141i | −0.414384 | − | 0.301067i | 0.360990 | − | 0.932569i | \(-0.382439\pi\) |
−0.775374 | + | 0.631502i | \(0.782439\pi\) | |||||||
\(62\) | −1.78539 | + | 5.49486i | −0.226745 | + | 0.697848i | ||||
\(63\) | 0.0948896 | + | 0.292040i | 0.0119550 | + | 0.0367936i | ||||
\(64\) | −2.10805 | + | 1.53159i | −0.263507 | + | 0.191449i | ||||
\(65\) | −0.775974 | −0.0962477 | ||||||||
\(66\) | 1.56741 | − | 5.34157i | 0.192935 | − | 0.657502i | ||||
\(67\) | 0.00770561 | 0.000941390 | 0.000470695 | − | 1.00000i | \(-0.499850\pi\) | ||||
0.000470695 | 1.00000i | \(0.499850\pi\) | ||||||||
\(68\) | −2.35901 | + | 1.71392i | −0.286072 | + | 0.207844i | ||||
\(69\) | 1.29212 | + | 3.97675i | 0.155553 | + | 0.478744i | ||||
\(70\) | −0.123587 | + | 0.380363i | −0.0147715 | + | 0.0454621i | ||||
\(71\) | 9.42803 | + | 6.84986i | 1.11890 | + | 0.812929i | 0.984042 | − | 0.177936i | \(-0.0569419\pi\) |
0.134859 | + | 0.990865i | \(0.456942\pi\) | |||||||
\(72\) | 1.60612 | + | 1.16692i | 0.189283 | + | 0.137522i | ||||
\(73\) | 2.33300 | − | 7.18023i | 0.273057 | − | 0.840383i | −0.716670 | − | 0.697412i | \(-0.754335\pi\) |
0.989727 | − | 0.142970i | \(-0.0456653\pi\) | |||||||
\(74\) | 5.37922 | + | 16.5556i | 0.625322 | + | 1.92454i | ||||
\(75\) | −3.55795 | + | 2.58500i | −0.410836 | + | 0.298490i | ||||
\(76\) | 1.62945 | 0.186911 | ||||||||
\(77\) | −1.01801 | + | 0.0292614i | −0.116013 | + | 0.00333465i | ||||
\(78\) | −1.67845 | −0.190047 | ||||||||
\(79\) | −9.13869 | + | 6.63965i | −1.02818 | + | 0.747018i | −0.967944 | − | 0.251166i | \(-0.919186\pi\) |
−0.0602386 | + | 0.998184i | \(0.519186\pi\) | |||||||
\(80\) | 1.19093 | + | 3.66531i | 0.133150 | + | 0.409795i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 17.3730 | + | 12.6222i | 1.91853 | + | 1.39389i | ||||
\(83\) | −13.9770 | − | 10.1549i | −1.53418 | − | 1.11465i | −0.953858 | − | 0.300257i | \(-0.902928\pi\) |
−0.580320 | − | 0.814389i | \(-0.697072\pi\) | |||||||
\(84\) | −0.0775435 | + | 0.238654i | −0.00846069 | + | 0.0260393i | ||||
\(85\) | −0.855609 | − | 2.63329i | −0.0928038 | − | 0.285621i | ||||
\(86\) | 0.579033 | − | 0.420692i | 0.0624388 | − | 0.0453644i | ||||
\(87\) | −7.97010 | −0.854484 | ||||||||
\(88\) | −5.21351 | + | 4.02168i | −0.555762 | + | 0.428712i | ||||
\(89\) | 5.89819 | 0.625207 | 0.312604 | − | 0.949884i | \(-0.398799\pi\) | ||||
0.312604 | + | 0.949884i | \(0.398799\pi\) | |||||||
\(90\) | 1.05369 | − | 0.765552i | 0.111069 | − | 0.0806962i | ||||
\(91\) | 0.0948896 | + | 0.292040i | 0.00994713 | + | 0.0306141i | ||||
\(92\) | −1.05592 | + | 3.24979i | −0.110087 | + | 0.338814i | ||||
\(93\) | −2.78484 | − | 2.02330i | −0.288774 | − | 0.209807i | ||||
\(94\) | −9.80512 | − | 7.12384i | −1.01132 | − | 0.734767i | ||||
\(95\) | −0.478128 | + | 1.47153i | −0.0490549 | + | 0.150975i | ||||
\(96\) | 1.34905 | + | 4.15195i | 0.137687 | + | 0.423756i | ||||
\(97\) | −6.91981 | + | 5.02754i | −0.702601 | + | 0.510469i | −0.880778 | − | 0.473529i | \(-0.842980\pi\) |
0.178178 | + | 0.983998i | \(0.442980\pi\) | |||||||
\(98\) | −11.5909 | −1.17086 | ||||||||
\(99\) | 2.73811 | + | 1.87156i | 0.275190 | + | 0.188099i | ||||
\(100\) | −3.59392 | −0.359392 | ||||||||
\(101\) | −10.0738 | + | 7.31905i | −1.00238 | + | 0.728273i | −0.962598 | − | 0.270935i | \(-0.912667\pi\) |
−0.0397843 | + | 0.999208i | \(0.512667\pi\) | |||||||
\(102\) | −1.85070 | − | 5.69588i | −0.183247 | − | 0.563976i | ||||
\(103\) | −1.41848 | + | 4.36565i | −0.139767 | + | 0.430160i | −0.996301 | − | 0.0859313i | \(-0.972613\pi\) |
0.856534 | + | 0.516091i | \(0.172613\pi\) | |||||||
\(104\) | 1.60612 | + | 1.16692i | 0.157493 | + | 0.114426i | ||||
\(105\) | −0.192771 | − | 0.140056i | −0.0188125 | − | 0.0136681i | ||||
\(106\) | 2.79029 | − | 8.58763i | 0.271017 | − | 0.834104i | ||||
\(107\) | 1.39246 | + | 4.28555i | 0.134614 | + | 0.414300i | 0.995530 | − | 0.0944477i | \(-0.0301085\pi\) |
−0.860916 | + | 0.508748i | \(0.830109\pi\) | |||||||
\(108\) | 0.661127 | − | 0.480337i | 0.0636169 | − | 0.0462204i | ||||
\(109\) | 14.1424 | 1.35460 | 0.677299 | − | 0.735708i | \(-0.263150\pi\) | ||||
0.677299 | + | 0.735708i | \(0.263150\pi\) | |||||||
\(110\) | 1.45234 | + | 4.06822i | 0.138475 | + | 0.387889i | ||||
\(111\) | −10.3712 | −0.984390 | ||||||||
\(112\) | 1.23382 | − | 0.896422i | 0.116585 | − | 0.0847039i | ||||
\(113\) | 3.50841 | + | 10.7978i | 0.330043 | + | 1.01577i | 0.969112 | + | 0.246620i | \(0.0793198\pi\) |
−0.639069 | + | 0.769149i | \(0.720680\pi\) | |||||||
\(114\) | −1.03420 | + | 3.18295i | −0.0968619 | + | 0.298110i | ||||
\(115\) | −2.62498 | − | 1.90716i | −0.244781 | − | 0.177844i | ||||
\(116\) | −5.26924 | − | 3.82833i | −0.489237 | − | 0.355451i | ||||
\(117\) | 0.309017 | − | 0.951057i | 0.0285686 | − | 0.0879252i | ||||
\(118\) | 2.27809 | + | 7.01125i | 0.209716 | + | 0.645438i | ||||
\(119\) | −0.886420 | + | 0.644022i | −0.0812580 | + | 0.0590374i | ||||
\(120\) | −1.54052 | −0.140630 | ||||||||
\(121\) | −8.51311 | + | 6.96613i | −0.773919 | + | 0.633285i | ||||
\(122\) | 6.71457 | 0.607909 | ||||||||
\(123\) | −10.3506 | + | 7.52016i | −0.933284 | + | 0.678070i | ||||
\(124\) | −0.869263 | − | 2.67532i | −0.0780621 | − | 0.240250i | ||||
\(125\) | 2.25351 | − | 6.93558i | 0.201560 | − | 0.620337i | ||||
\(126\) | −0.416968 | − | 0.302945i | −0.0371464 | − | 0.0269885i | ||||
\(127\) | −9.59180 | − | 6.96885i | −0.851134 | − | 0.618385i | 0.0743243 | − | 0.997234i | \(-0.476320\pi\) |
−0.925459 | + | 0.378849i | \(0.876320\pi\) | |||||||
\(128\) | 4.04959 | − | 12.4634i | 0.357937 | − | 1.10162i | ||||
\(129\) | 0.131771 | + | 0.405549i | 0.0116018 | + | 0.0357066i | ||||
\(130\) | 1.05369 | − | 0.765552i | 0.0924149 | − | 0.0671433i | ||||
\(131\) | −2.68464 | −0.234558 | −0.117279 | − | 0.993099i | \(-0.537417\pi\) | ||||
−0.117279 | + | 0.993099i | \(0.537417\pi\) | |||||||
\(132\) | 0.911256 | + | 2.55256i | 0.0793146 | + | 0.222171i | ||||
\(133\) | 0.612281 | 0.0530915 | ||||||||
\(134\) | −0.0104634 | + | 0.00760211i | −0.000903901 | + | 0.000656723i | ||||
\(135\) | 0.239789 | + | 0.737995i | 0.0206378 | + | 0.0635165i | ||||
\(136\) | −2.18902 | + | 6.73710i | −0.187707 | + | 0.577702i | ||||
\(137\) | −1.67185 | − | 1.21467i | −0.142836 | − | 0.103776i | 0.514073 | − | 0.857747i | \(-0.328136\pi\) |
−0.656908 | + | 0.753970i | \(0.728136\pi\) | |||||||
\(138\) | −5.67790 | − | 4.12524i | −0.483335 | − | 0.351164i | ||||
\(139\) | −4.69117 | + | 14.4380i | −0.397900 | + | 1.22461i | 0.528780 | + | 0.848759i | \(0.322650\pi\) |
−0.926680 | + | 0.375852i | \(0.877350\pi\) | |||||||
\(140\) | −0.0601717 | − | 0.185190i | −0.00508544 | − | 0.0156514i | ||||
\(141\) | 5.84177 | − | 4.24429i | 0.491965 | − | 0.357434i | ||||
\(142\) | −19.5601 | −1.64145 | ||||||||
\(143\) | 2.73811 | + | 1.87156i | 0.228972 | + | 0.156508i | ||||
\(144\) | −4.96658 | −0.413882 | ||||||||
\(145\) | 5.00344 | − | 3.63521i | 0.415513 | − | 0.301888i | ||||
\(146\) | 3.91582 | + | 12.0517i | 0.324076 | + | 0.997403i | ||||
\(147\) | 2.13398 | − | 6.56772i | 0.176008 | − | 0.541696i | ||||
\(148\) | −6.85667 | − | 4.98166i | −0.563615 | − | 0.409490i | ||||
\(149\) | 14.7373 | + | 10.7073i | 1.20732 | + | 0.877172i | 0.994985 | − | 0.100024i | \(-0.0318918\pi\) |
0.212339 | + | 0.977196i | \(0.431892\pi\) | |||||||
\(150\) | 2.28104 | − | 7.02032i | 0.186246 | − | 0.573207i | ||||
\(151\) | −0.704145 | − | 2.16714i | −0.0573025 | − | 0.176359i | 0.918309 | − | 0.395865i | \(-0.129555\pi\) |
−0.975611 | + | 0.219506i | \(0.929555\pi\) | |||||||
\(152\) | 3.20253 | − | 2.32677i | 0.259759 | − | 0.188726i | ||||
\(153\) | 3.56817 | 0.288470 | ||||||||
\(154\) | 1.35349 | − | 1.04407i | 0.109067 | − | 0.0841338i | ||||
\(155\) | 2.67109 | 0.214547 | ||||||||
\(156\) | 0.661127 | − | 0.480337i | 0.0529325 | − | 0.0384577i | ||||
\(157\) | −3.99344 | − | 12.2905i | −0.318711 | − | 0.980892i | −0.974200 | − | 0.225687i | \(-0.927537\pi\) |
0.655489 | − | 0.755205i | \(-0.272463\pi\) | |||||||
\(158\) | 5.85892 | − | 18.0319i | 0.466110 | − | 1.43454i | ||||
\(159\) | 4.35227 | + | 3.16211i | 0.345158 | + | 0.250772i | ||||
\(160\) | −2.74063 | − | 1.99118i | −0.216666 | − | 0.157417i | ||||
\(161\) | −0.396771 | + | 1.22114i | −0.0312699 | + | 0.0962390i | ||||
\(162\) | 0.518670 | + | 1.59630i | 0.0407506 | + | 0.125417i | ||||
\(163\) | 1.14958 | − | 0.835219i | 0.0900421 | − | 0.0654194i | −0.541853 | − | 0.840473i | \(-0.682277\pi\) |
0.631895 | + | 0.775054i | \(0.282277\pi\) | |||||||
\(164\) | −10.4553 | −0.816420 | ||||||||
\(165\) | −2.57255 | + | 0.0739446i | −0.200273 | + | 0.00575658i | ||||
\(166\) | 28.9979 | 2.25067 | ||||||||
\(167\) | 2.63525 | − | 1.91462i | 0.203922 | − | 0.148158i | −0.481138 | − | 0.876645i | \(-0.659776\pi\) |
0.685059 | + | 0.728487i | \(0.259776\pi\) | |||||||
\(168\) | 0.188382 | + | 0.579780i | 0.0145340 | + | 0.0447310i | ||||
\(169\) | 0.309017 | − | 0.951057i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | 3.75975 | + | 2.73162i | 0.288360 | + | 0.209506i | ||||
\(171\) | −1.61314 | − | 1.17201i | −0.123360 | − | 0.0896262i | ||||
\(172\) | −0.107683 | + | 0.331414i | −0.00821074 | + | 0.0252701i | ||||
\(173\) | 3.79288 | + | 11.6733i | 0.288368 | + | 0.887504i | 0.985369 | + | 0.170434i | \(0.0545171\pi\) |
−0.697002 | + | 0.717070i | \(0.745483\pi\) | |||||||
\(174\) | 10.8226 | − | 7.86305i | 0.820456 | − | 0.596096i | ||||
\(175\) | −1.35045 | −0.102084 | ||||||||
\(176\) | 4.63800 | − | 15.8059i | 0.349603 | − | 1.19141i | ||||
\(177\) | −4.39219 | −0.330137 | ||||||||
\(178\) | −8.00913 | + | 5.81897i | −0.600310 | + | 0.436150i | ||||
\(179\) | 5.37319 | + | 16.5370i | 0.401611 | + | 1.23603i | 0.923692 | + | 0.383136i | \(0.125156\pi\) |
−0.522081 | + | 0.852896i | \(0.674844\pi\) | |||||||
\(180\) | −0.195955 | + | 0.603088i | −0.0146056 | + | 0.0449515i | ||||
\(181\) | 5.93533 | + | 4.31227i | 0.441170 | + | 0.320529i | 0.786100 | − | 0.618100i | \(-0.212097\pi\) |
−0.344930 | + | 0.938628i | \(0.612097\pi\) | |||||||
\(182\) | −0.416968 | − | 0.302945i | −0.0309077 | − | 0.0224558i | ||||
\(183\) | −1.23621 | + | 3.80466i | −0.0913833 | + | 0.281249i | ||||
\(184\) | 2.56522 | + | 7.89494i | 0.189111 | + | 0.582023i | ||||
\(185\) | 6.51079 | − | 4.73036i | 0.478683 | − | 0.347783i | ||||
\(186\) | 5.77764 | 0.423637 | ||||||||
\(187\) | −3.33211 | + | 11.3555i | −0.243668 | + | 0.830396i | ||||
\(188\) | 5.90083 | 0.430363 | ||||||||
\(189\) | 0.248424 | − | 0.180491i | 0.0180702 | − | 0.0131288i | ||||
\(190\) | −0.802514 | − | 2.46988i | −0.0582205 | − | 0.179184i | ||||
\(191\) | 7.18952 | − | 22.1271i | 0.520216 | − | 1.60106i | −0.253371 | − | 0.967369i | \(-0.581539\pi\) |
0.773587 | − | 0.633690i | \(-0.218461\pi\) | |||||||
\(192\) | 2.10805 | + | 1.53159i | 0.152136 | + | 0.110533i | ||||
\(193\) | −19.8691 | − | 14.4357i | −1.43021 | − | 1.03911i | −0.989978 | − | 0.141221i | \(-0.954897\pi\) |
−0.440230 | − | 0.897885i | \(-0.645103\pi\) | |||||||
\(194\) | 4.43637 | − | 13.6537i | 0.318513 | − | 0.980281i | ||||
\(195\) | 0.239789 | + | 0.737995i | 0.0171717 | + | 0.0528489i | ||||
\(196\) | 4.56555 | − | 3.31706i | 0.326111 | − | 0.236933i | ||||
\(197\) | 17.0488 | 1.21468 | 0.607338 | − | 0.794444i | \(-0.292238\pi\) | ||||
0.607338 | + | 0.794444i | \(0.292238\pi\) | |||||||
\(198\) | −5.56449 | + | 0.159944i | −0.395451 | + | 0.0113667i | ||||
\(199\) | 13.4899 | 0.956274 | 0.478137 | − | 0.878285i | \(-0.341312\pi\) | ||||
0.478137 | + | 0.878285i | \(0.341312\pi\) | |||||||
\(200\) | −7.06351 | + | 5.13194i | −0.499465 | + | 0.362883i | ||||
\(201\) | −0.00238116 | − | 0.00732847i | −0.000167954 | − | 0.000516910i | ||||
\(202\) | 6.45843 | − | 19.8770i | 0.454414 | − | 1.39854i | ||||
\(203\) | −1.97996 | − | 1.43853i | −0.138966 | − | 0.100965i | ||||
\(204\) | 2.35901 | + | 1.71392i | 0.165164 | + | 0.119999i | ||||
\(205\) | 3.06788 | − | 9.44196i | 0.214270 | − | 0.659455i | ||||
\(206\) | −2.38086 | − | 7.32752i | −0.165882 | − | 0.510533i | ||||
\(207\) | 3.38282 | − | 2.45776i | 0.235122 | − | 0.170826i | ||||
\(208\) | −4.96658 | −0.344371 | ||||||||
\(209\) | 5.23629 | − | 4.03925i | 0.362202 | − | 0.279401i | ||||
\(210\) | 0.399937 | 0.0275983 | ||||||||
\(211\) | 18.5782 | − | 13.4978i | 1.27897 | − | 0.929229i | 0.279453 | − | 0.960159i | \(-0.409847\pi\) |
0.999522 | + | 0.0309299i | \(0.00984686\pi\) | |||||||
\(212\) | 1.35853 | + | 4.18111i | 0.0933039 | + | 0.287160i | ||||
\(213\) | 3.60119 | − | 11.0833i | 0.246749 | − | 0.759416i | ||||
\(214\) | −6.11881 | − | 4.44558i | −0.418273 | − | 0.303893i | ||||
\(215\) | −0.267696 | − | 0.194493i | −0.0182567 | − | 0.0132643i | ||||
\(216\) | 0.613484 | − | 1.88811i | 0.0417423 | − | 0.128470i | ||||
\(217\) | −0.326633 | − | 1.00527i | −0.0221733 | − | 0.0682424i | ||||
\(218\) | −19.2039 | + | 13.9525i | −1.30065 | + | 0.944981i | ||||
\(219\) | −7.54974 | −0.510164 | ||||||||
\(220\) | −1.73630 | − | 1.18680i | −0.117061 | − | 0.0800143i | ||||
\(221\) | 3.56817 | 0.240021 | ||||||||
\(222\) | 14.0830 | − | 10.2319i | 0.945189 | − | 0.686720i | ||||
\(223\) | −3.10519 | − | 9.55678i | −0.207939 | − | 0.639969i | −0.999580 | − | 0.0289832i | \(-0.990773\pi\) |
0.791641 | − | 0.610986i | \(-0.209227\pi\) | |||||||
\(224\) | −0.414251 | + | 1.27493i | −0.0276783 | + | 0.0851851i | ||||
\(225\) | 3.55795 | + | 2.58500i | 0.237196 | + | 0.172333i | ||||
\(226\) | −15.4168 | − | 11.2010i | −1.02551 | − | 0.745077i | ||||
\(227\) | −6.10872 | + | 18.8007i | −0.405450 | + | 1.24785i | 0.515069 | + | 0.857149i | \(0.327766\pi\) |
−0.920519 | + | 0.390698i | \(0.872234\pi\) | |||||||
\(228\) | −0.503528 | − | 1.54970i | −0.0333470 | − | 0.102631i | ||||
\(229\) | 4.00661 | − | 2.91097i | 0.264764 | − | 0.192363i | −0.447480 | − | 0.894294i | \(-0.647679\pi\) |
0.712245 | + | 0.701931i | \(0.247679\pi\) | |||||||
\(230\) | 5.44600 | 0.359098 | ||||||||
\(231\) | 0.342412 | + | 0.959145i | 0.0225291 | + | 0.0631071i | ||||
\(232\) | −15.8228 | −1.03882 | ||||||||
\(233\) | 10.4559 | − | 7.59667i | 0.684990 | − | 0.497674i | −0.190019 | − | 0.981780i | \(-0.560855\pi\) |
0.875009 | + | 0.484106i | \(0.160855\pi\) | |||||||
\(234\) | 0.518670 | + | 1.59630i | 0.0339065 | + | 0.104354i | ||||
\(235\) | −1.73147 | + | 5.32893i | −0.112949 | + | 0.347621i | ||||
\(236\) | −2.90379 | − | 2.10973i | −0.189021 | − | 0.137332i | ||||
\(237\) | 9.13869 | + | 6.63965i | 0.593622 | + | 0.431291i | ||||
\(238\) | 0.568294 | − | 1.74903i | 0.0368370 | − | 0.113373i | ||||
\(239\) | −2.67482 | − | 8.23224i | −0.173020 | − | 0.532499i | 0.826518 | − | 0.562910i | \(-0.190318\pi\) |
−0.999537 | + | 0.0304111i | \(0.990318\pi\) | |||||||
\(240\) | 3.11790 | − | 2.26529i | 0.201260 | − | 0.146224i | ||||
\(241\) | −8.92483 | −0.574899 | −0.287449 | − | 0.957796i | \(-0.592807\pi\) | ||||
−0.287449 | + | 0.957796i | \(0.592807\pi\) | |||||||
\(242\) | 4.68734 | − | 17.8580i | 0.301314 | − | 1.14796i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.64481 | + | 1.92157i | −0.169317 | + | 0.123016i | ||||
\(245\) | 1.65591 | + | 5.09638i | 0.105792 | + | 0.325596i | ||||
\(246\) | 6.63590 | − | 20.4232i | 0.423089 | − | 1.30214i | ||||
\(247\) | −1.61314 | − | 1.17201i | −0.102642 | − | 0.0745735i | ||||
\(248\) | −5.52867 | − | 4.01681i | −0.351071 | − | 0.255068i | ||||
\(249\) | −5.33875 | + | 16.4310i | −0.338330 | + | 1.04127i | ||||
\(250\) | 3.78240 | + | 11.6410i | 0.239220 | + | 0.736243i | ||||
\(251\) | −9.12966 | + | 6.63309i | −0.576259 | + | 0.418677i | −0.837373 | − | 0.546631i | \(-0.815910\pi\) |
0.261115 | + | 0.965308i | \(0.415910\pi\) | |||||||
\(252\) | 0.250936 | 0.0158075 | ||||||||
\(253\) | 4.66267 | + | 13.0608i | 0.293140 | + | 0.821126i | ||||
\(254\) | 19.8999 | 1.24863 | ||||||||
\(255\) | −2.24001 | + | 1.62746i | −0.140275 | + | 0.101916i | ||||
\(256\) | 5.18664 | + | 15.9628i | 0.324165 | + | 0.997676i | ||||
\(257\) | 3.10711 | − | 9.56271i | 0.193816 | − | 0.596506i | −0.806172 | − | 0.591681i | \(-0.798464\pi\) |
0.999988 | − | 0.00482422i | \(-0.00153560\pi\) | |||||||
\(258\) | −0.579033 | − | 0.420692i | −0.0360490 | − | 0.0261912i | ||||
\(259\) | −2.57645 | − | 1.87190i | −0.160093 | − | 0.116314i | ||||
\(260\) | −0.195955 | + | 0.603088i | −0.0121526 | + | 0.0374019i | ||||
\(261\) | 2.46290 | + | 7.58001i | 0.152449 | + | 0.469191i | ||||
\(262\) | 3.64546 | − | 2.64858i | 0.225217 | − | 0.163630i | ||||
\(263\) | −7.99294 | −0.492866 | −0.246433 | − | 0.969160i | \(-0.579258\pi\) | ||||
−0.246433 | + | 0.969160i | \(0.579258\pi\) | |||||||
\(264\) | 5.43590 | + | 3.71557i | 0.334557 | + | 0.228678i | ||||
\(265\) | −4.17451 | −0.256438 | ||||||||
\(266\) | −0.831413 | + | 0.604057i | −0.0509772 | + | 0.0370371i | ||||
\(267\) | −1.82264 | − | 5.60952i | −0.111544 | − | 0.343297i | ||||
\(268\) | 0.00194588 | − | 0.00598881i | 0.000118864 | − | 0.000365825i | ||||
\(269\) | −5.95850 | − | 4.32911i | −0.363296 | − | 0.263950i | 0.391129 | − | 0.920336i | \(-0.372085\pi\) |
−0.754426 | + | 0.656385i | \(0.772085\pi\) | |||||||
\(270\) | −1.05369 | − | 0.765552i | −0.0641256 | − | 0.0465900i | ||||
\(271\) | 1.99183 | − | 6.13021i | 0.120995 | − | 0.372384i | −0.872155 | − | 0.489229i | \(-0.837278\pi\) |
0.993150 | + | 0.116845i | \(0.0372782\pi\) | |||||||
\(272\) | −5.47628 | − | 16.8543i | −0.332048 | − | 1.02194i | ||||
\(273\) | 0.248424 | − | 0.180491i | 0.0150353 | − | 0.0109238i | ||||
\(274\) | 3.46855 | 0.209543 | ||||||||
\(275\) | −11.5492 | + | 8.90898i | −0.696441 | + | 0.537232i | ||||
\(276\) | 3.41703 | 0.205681 | ||||||||
\(277\) | 7.28194 | − | 5.29064i | 0.437530 | − | 0.317884i | −0.347123 | − | 0.937820i | \(-0.612841\pi\) |
0.784653 | + | 0.619936i | \(0.212841\pi\) | |||||||
\(278\) | −7.87391 | − | 24.2334i | −0.472246 | − | 1.45342i | ||||
\(279\) | −1.06371 | + | 3.27377i | −0.0636828 | + | 0.195995i | ||||
\(280\) | −0.382703 | − | 0.278050i | −0.0228709 | − | 0.0166167i | ||||
\(281\) | 9.44855 | + | 6.86477i | 0.563653 | + | 0.409518i | 0.832794 | − | 0.553583i | \(-0.186740\pi\) |
−0.269141 | + | 0.963101i | \(0.586740\pi\) | |||||||
\(282\) | −3.74522 | + | 11.5266i | −0.223025 | + | 0.686399i | ||||
\(283\) | 3.55419 | + | 10.9387i | 0.211275 | + | 0.650237i | 0.999397 | + | 0.0347181i | \(0.0110533\pi\) |
−0.788122 | + | 0.615518i | \(0.788947\pi\) | |||||||
\(284\) | 7.70456 | − | 5.59769i | 0.457181 | − | 0.332162i | ||||
\(285\) | 1.54725 | 0.0916514 | ||||||||
\(286\) | −5.56449 | + | 0.159944i | −0.329035 | + | 0.00945769i | ||||
\(287\) | −3.92866 | −0.231902 | ||||||||
\(288\) | 3.53186 | − | 2.56604i | 0.208117 | − | 0.151206i | ||||
\(289\) | −1.31893 | − | 4.05925i | −0.0775842 | − | 0.238780i | ||||
\(290\) | −3.20776 | + | 9.87247i | −0.188366 | + | 0.579731i | ||||
\(291\) | 6.91981 | + | 5.02754i | 0.405647 | + | 0.294720i | ||||
\(292\) | −4.99133 | − | 3.62642i | −0.292096 | − | 0.212220i | ||||
\(293\) | 2.16500 | − | 6.66318i | 0.126481 | − | 0.389267i | −0.867687 | − | 0.497110i | \(-0.834394\pi\) |
0.994168 | + | 0.107843i | \(0.0343944\pi\) | |||||||
\(294\) | 3.58178 | + | 11.0236i | 0.208894 | + | 0.642909i | ||||
\(295\) | 2.75731 | − | 2.00330i | 0.160537 | − | 0.116637i | ||||
\(296\) | −20.5897 | −1.19675 | ||||||||
\(297\) | 0.933842 | − | 3.18244i | 0.0541870 | − | 0.184664i | ||||
\(298\) | −30.5751 | −1.77117 | ||||||||
\(299\) | 3.38282 | − | 2.45776i | 0.195634 | − | 0.142136i | ||||
\(300\) | 1.11058 | + | 3.41802i | 0.0641196 | + | 0.197340i | ||||
\(301\) | −0.0404628 | + | 0.124532i | −0.00233224 | + | 0.00717789i | ||||
\(302\) | 3.09418 | + | 2.24806i | 0.178050 | + | 0.129361i | ||||
\(303\) | 10.0738 | + | 7.31905i | 0.578725 | + | 0.420469i | ||||
\(304\) | −3.06023 | + | 9.41843i | −0.175516 | + | 0.540184i | ||||
\(305\) | −0.959267 | − | 2.95232i | −0.0549275 | − | 0.169049i | ||||
\(306\) | −4.84520 | + | 3.52025i | −0.276982 | + | 0.201239i | ||||
\(307\) | 27.3102 | 1.55868 | 0.779339 | − | 0.626603i | \(-0.215555\pi\) | ||||
0.779339 | + | 0.626603i | \(0.215555\pi\) | |||||||
\(308\) | −0.234335 | + | 0.798590i | −0.0133524 | + | 0.0455039i | ||||
\(309\) | 4.59031 | 0.261134 | ||||||||
\(310\) | −3.62706 | + | 2.63522i | −0.206003 | + | 0.149670i | ||||
\(311\) | 4.09766 | + | 12.6113i | 0.232357 | + | 0.715121i | 0.997461 | + | 0.0712144i | \(0.0226874\pi\) |
−0.765104 | + | 0.643907i | \(0.777313\pi\) | |||||||
\(312\) | 0.613484 | − | 1.88811i | 0.0347317 | − | 0.106893i | ||||
\(313\) | −11.0861 | − | 8.05450i | −0.626622 | − | 0.455267i | 0.228607 | − | 0.973519i | \(-0.426583\pi\) |
−0.855228 | + | 0.518252i | \(0.826583\pi\) | |||||||
\(314\) | 17.5481 | + | 12.7495i | 0.990298 | + | 0.719494i | ||||
\(315\) | −0.0736318 | + | 0.226616i | −0.00414868 | + | 0.0127683i | ||||
\(316\) | 2.85256 | + | 8.77929i | 0.160469 | + | 0.493874i | ||||
\(317\) | −21.2833 | + | 15.4632i | −1.19539 | + | 0.868501i | −0.993823 | − | 0.110973i | \(-0.964603\pi\) |
−0.201566 | + | 0.979475i | \(0.564603\pi\) | |||||||
\(318\) | −9.02957 | −0.506353 | ||||||||
\(319\) | −26.4229 | + | 0.759492i | −1.47940 | + | 0.0425234i | ||||
\(320\) | −2.02195 | −0.113031 | ||||||||
\(321\) | 3.64551 | − | 2.64862i | 0.203473 | − | 0.147831i | ||||
\(322\) | −0.665961 | − | 2.04962i | −0.0371125 | − | 0.114221i | ||||
\(323\) | 2.19858 | − | 6.76654i | 0.122332 | − | 0.376500i | ||||
\(324\) | −0.661127 | − | 0.480337i | −0.0367293 | − | 0.0266854i | ||||
\(325\) | 3.55795 | + | 2.58500i | 0.197359 | + | 0.143390i | ||||
\(326\) | −0.737009 | + | 2.26828i | −0.0408191 | + | 0.125628i | ||||
\(327\) | −4.37025 | − | 13.4502i | −0.241675 | − | 0.743800i | ||||
\(328\) | −20.5488 | + | 14.9296i | −1.13462 | + | 0.824349i | ||||
\(329\) | 2.21729 | 0.122243 | ||||||||
\(330\) | 3.42031 | − | 2.63841i | 0.188282 | − | 0.145240i | ||||
\(331\) | −11.7249 | −0.644461 | −0.322231 | − | 0.946661i | \(-0.604433\pi\) | ||||
−0.322231 | + | 0.946661i | \(0.604433\pi\) | |||||||
\(332\) | −11.4220 | + | 8.29856i | −0.626863 | + | 0.455443i | ||||
\(333\) | 3.20487 | + | 9.86359i | 0.175626 | + | 0.540521i | ||||
\(334\) | −1.68949 | + | 5.19971i | −0.0924447 | + | 0.284515i | ||||
\(335\) | 0.00483740 | + | 0.00351458i | 0.000264295 | + | 0.000192022i | ||||
\(336\) | −1.23382 | − | 0.896422i | −0.0673104 | − | 0.0489038i | ||||
\(337\) | −0.188128 | + | 0.578999i | −0.0102480 | + | 0.0315401i | −0.956050 | − | 0.293204i | \(-0.905278\pi\) |
0.945802 | + | 0.324745i | \(0.105278\pi\) | |||||||
\(338\) | 0.518670 | + | 1.59630i | 0.0282119 | + | 0.0868274i | ||||
\(339\) | 9.18513 | − | 6.67339i | 0.498868 | − | 0.362449i | ||||
\(340\) | −2.26266 | −0.122710 | ||||||||
\(341\) | −9.42525 | − | 6.44239i | −0.510406 | − | 0.348875i | ||||
\(342\) | 3.34675 | 0.180971 | ||||||||
\(343\) | 3.45451 | − | 2.50985i | 0.186526 | − | 0.135519i | ||||
\(344\) | 0.261602 | + | 0.805127i | 0.0141046 | + | 0.0434096i | ||||
\(345\) | −1.00265 | + | 3.08585i | −0.0539811 | + | 0.166137i | ||||
\(346\) | −16.6668 | − | 12.1092i | −0.896015 | − | 0.650993i | ||||
\(347\) | 6.34083 | + | 4.60688i | 0.340394 | + | 0.247310i | 0.744828 | − | 0.667257i | \(-0.232532\pi\) |
−0.404434 | + | 0.914567i | \(0.632532\pi\) | |||||||
\(348\) | −2.01267 | + | 6.19437i | −0.107891 | + | 0.332053i | ||||
\(349\) | −3.52953 | − | 10.8628i | −0.188931 | − | 0.581471i | 0.811063 | − | 0.584959i | \(-0.198890\pi\) |
−0.999994 | + | 0.00348870i | \(0.998890\pi\) | |||||||
\(350\) | 1.83377 | − | 1.33231i | 0.0980190 | − | 0.0712150i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 4.86809 | + | 13.6362i | 0.259470 | + | 0.726812i | ||||
\(353\) | −16.0778 | −0.855732 | −0.427866 | − | 0.903842i | \(-0.640735\pi\) | ||||
−0.427866 | + | 0.903842i | \(0.640735\pi\) | |||||||
\(354\) | 5.96413 | − | 4.33319i | 0.316990 | − | 0.230307i | ||||
\(355\) | 2.79443 | + | 8.60036i | 0.148313 | + | 0.456460i | ||||
\(356\) | 1.48946 | − | 4.58408i | 0.0789411 | − | 0.242956i | ||||
\(357\) | 0.886420 | + | 0.644022i | 0.0469143 | + | 0.0340852i | ||||
\(358\) | −23.6111 | − | 17.1545i | −1.24788 | − | 0.906641i | ||||
\(359\) | −9.30077 | + | 28.6248i | −0.490876 | + | 1.51076i | 0.332411 | + | 0.943135i | \(0.392138\pi\) |
−0.823287 | + | 0.567625i | \(0.807862\pi\) | |||||||
\(360\) | 0.476048 | + | 1.46512i | 0.0250899 | + | 0.0772188i | ||||
\(361\) | 12.1548 | − | 8.83098i | 0.639726 | − | 0.464788i | ||||
\(362\) | −12.3139 | −0.647205 | ||||||||
\(363\) | 9.25588 | + | 5.94379i | 0.485808 | + | 0.311968i | ||||
\(364\) | 0.250936 | 0.0131526 | ||||||||
\(365\) | 4.73955 | − | 3.44348i | 0.248079 | − | 0.180240i | ||||
\(366\) | −2.07492 | − | 6.38594i | −0.108458 | − | 0.333798i | ||||
\(367\) | −9.12405 | + | 28.0809i | −0.476271 | + | 1.46581i | 0.367964 | + | 0.929840i | \(0.380055\pi\) |
−0.844235 | + | 0.535973i | \(0.819945\pi\) | |||||||
\(368\) | −16.8011 | − | 12.2067i | −0.875816 | − | 0.636318i | ||||
\(369\) | 10.3506 | + | 7.52016i | 0.538832 | + | 0.391484i | ||||
\(370\) | −4.17414 | + | 12.8467i | −0.217003 | + | 0.667867i | ||||
\(371\) | 0.510478 | + | 1.57109i | 0.0265027 | + | 0.0815669i | ||||
\(372\) | −2.27576 | + | 1.65344i | −0.117993 | + | 0.0857267i | ||||
\(373\) | −15.2700 | −0.790650 | −0.395325 | − | 0.918541i | \(-0.629368\pi\) | ||||
−0.395325 | + | 0.918541i | \(0.629368\pi\) | |||||||
\(374\) | −6.67833 | − | 18.7069i | −0.345328 | − | 0.967312i | ||||
\(375\) | −7.29250 | −0.376583 | ||||||||
\(376\) | 11.5975 | − | 8.42609i | 0.598096 | − | 0.434542i | ||||
\(377\) | 2.46290 | + | 7.58001i | 0.126846 | + | 0.390391i | ||||
\(378\) | −0.159267 | + | 0.490175i | −0.00819184 | + | 0.0252119i | ||||
\(379\) | 4.70246 | + | 3.41654i | 0.241549 | + | 0.175496i | 0.701973 | − | 0.712203i | \(-0.252303\pi\) |
−0.460424 | + | 0.887699i | \(0.652303\pi\) | |||||||
\(380\) | 1.02293 | + | 0.743203i | 0.0524752 | + | 0.0381255i | ||||
\(381\) | −3.66374 | + | 11.2758i | −0.187699 | + | 0.577678i | ||||
\(382\) | 12.0673 | + | 37.1392i | 0.617415 | + | 1.90021i | ||||
\(383\) | 16.7336 | − | 12.1576i | 0.855045 | − | 0.621227i | −0.0714874 | − | 0.997442i | \(-0.522775\pi\) |
0.926532 | + | 0.376215i | \(0.122775\pi\) | |||||||
\(384\) | −13.1048 | −0.668750 | ||||||||
\(385\) | −0.652430 | − | 0.445952i | −0.0332509 | − | 0.0227278i | ||||
\(386\) | 41.2220 | 2.09814 | ||||||||
\(387\) | 0.344981 | − | 0.250643i | 0.0175364 | − | 0.0127409i | ||||
\(388\) | 2.15996 | + | 6.64768i | 0.109655 | + | 0.337485i | ||||
\(389\) | 9.01746 | − | 27.7529i | 0.457204 | − | 1.40713i | −0.411325 | − | 0.911489i | \(-0.634934\pi\) |
0.868529 | − | 0.495639i | \(-0.165066\pi\) | |||||||
\(390\) | −1.05369 | − | 0.765552i | −0.0533557 | − | 0.0387652i | ||||
\(391\) | 12.0705 | + | 8.76973i | 0.610431 | + | 0.443504i | ||||
\(392\) | 4.23654 | − | 13.0387i | 0.213978 | − | 0.658556i | ||||
\(393\) | 0.829599 | + | 2.55324i | 0.0418477 | + | 0.128794i | ||||
\(394\) | −23.1505 | + | 16.8198i | −1.16630 | + | 0.847369i | ||||
\(395\) | −8.76543 | −0.441037 | ||||||||
\(396\) | 2.14603 | − | 1.65544i | 0.107842 | − | 0.0831889i | ||||
\(397\) | 38.0612 | 1.91024 | 0.955118 | − | 0.296226i | \(-0.0957281\pi\) | ||||
0.955118 | + | 0.296226i | \(0.0957281\pi\) | |||||||
\(398\) | −18.3179 | + | 13.3087i | −0.918192 | + | 0.667106i | ||||
\(399\) | −0.189205 | − | 0.582314i | −0.00947210 | − | 0.0291521i | ||||
\(400\) | 6.74966 | − | 20.7733i | 0.337483 | − | 1.03867i | ||||
\(401\) | 1.38434 | + | 1.00578i | 0.0691308 | + | 0.0502264i | 0.621814 | − | 0.783165i | \(-0.286396\pi\) |
−0.552683 | + | 0.833391i | \(0.686396\pi\) | |||||||
\(402\) | 0.0104634 | + | 0.00760211i | 0.000521867 | + | 0.000379159i | ||||
\(403\) | −1.06371 | + | 3.27377i | −0.0529873 | + | 0.163078i | ||||
\(404\) | 3.14446 | + | 9.67764i | 0.156443 | + | 0.481481i | ||||
\(405\) | 0.627776 | − | 0.456106i | 0.0311944 | − | 0.0226641i | ||||
\(406\) | 4.10779 | 0.203866 | ||||||||
\(407\) | −34.3832 | + | 0.988298i | −1.70431 | + | 0.0489881i | ||||
\(408\) | 7.08381 | 0.350701 | ||||||||
\(409\) | 19.3054 | − | 14.0262i | 0.954589 | − | 0.693550i | 0.00270130 | − | 0.999996i | \(-0.499140\pi\) |
0.951888 | + | 0.306447i | \(0.0991401\pi\) | |||||||
\(410\) | 5.14928 | + | 15.8479i | 0.254305 | + | 0.782670i | ||||
\(411\) | −0.638589 | + | 1.96537i | −0.0314993 | + | 0.0969448i | ||||
\(412\) | 3.03478 | + | 2.20489i | 0.149513 | + | 0.108627i | ||||
\(413\) | −1.09112 | − | 0.792749i | −0.0536907 | − | 0.0390086i | ||||
\(414\) | −2.16877 | + | 6.67477i | −0.106589 | + | 0.328047i | ||||
\(415\) | −4.14273 | − | 12.7500i | −0.203359 | − | 0.625874i | ||||
\(416\) | 3.53186 | − | 2.56604i | 0.173163 | − | 0.125811i | ||||
\(417\) | 15.1810 | 0.743415 | ||||||||
\(418\) | −3.12533 | + | 10.6508i | −0.152865 | + | 0.520949i | ||||
\(419\) | 15.7851 | 0.771154 | 0.385577 | − | 0.922676i | \(-0.374002\pi\) | ||||
0.385577 | + | 0.922676i | \(0.374002\pi\) | |||||||
\(420\) | −0.157532 | + | 0.114453i | −0.00768676 | + | 0.00558476i | ||||
\(421\) | 0.227790 | + | 0.701065i | 0.0111018 | + | 0.0341678i | 0.956454 | − | 0.291883i | \(-0.0942819\pi\) |
−0.945352 | + | 0.326051i | \(0.894282\pi\) | |||||||
\(422\) | −11.9107 | + | 36.6573i | −0.579803 | + | 1.78445i | ||||
\(423\) | −5.84177 | − | 4.24429i | −0.284036 | − | 0.206365i | ||||
\(424\) | 8.64046 | + | 6.27766i | 0.419618 | + | 0.304870i | ||||
\(425\) | −4.84920 | + | 14.9243i | −0.235221 | + | 0.723935i | ||||
\(426\) | 6.04441 | + | 18.6028i | 0.292853 | + | 0.901308i | ||||
\(427\) | −0.993811 | + | 0.722046i | −0.0480939 | + | 0.0349422i | ||||
\(428\) | 3.68237 | 0.177994 | ||||||||
\(429\) | 0.933842 | − | 3.18244i | 0.0450863 | − | 0.153650i | ||||
\(430\) | 0.555384 | 0.0267830 | ||||||||
\(431\) | −23.4928 | + | 17.0685i | −1.13161 | + | 0.822163i | −0.985928 | − | 0.167168i | \(-0.946538\pi\) |
−0.145682 | + | 0.989331i | \(0.546538\pi\) | |||||||
\(432\) | 1.53476 | + | 4.72350i | 0.0738411 | + | 0.227260i | ||||
\(433\) | 1.78898 | − | 5.50592i | 0.0859730 | − | 0.264598i | −0.898823 | − | 0.438311i | \(-0.855577\pi\) |
0.984796 | + | 0.173714i | \(0.0555767\pi\) | |||||||
\(434\) | 1.43531 | + | 1.04281i | 0.0688969 | + | 0.0500565i | ||||
\(435\) | −5.00344 | − | 3.63521i | −0.239896 | − | 0.174295i | ||||
\(436\) | 3.57136 | − | 10.9915i | 0.171037 | − | 0.526398i | ||||
\(437\) | −2.57643 | − | 7.92944i | −0.123247 | − | 0.379316i | ||||
\(438\) | 10.2518 | − | 7.44834i | 0.489848 | − | 0.355895i | ||||
\(439\) | 24.3031 | 1.15992 | 0.579961 | − | 0.814644i | \(-0.303068\pi\) | ||||
0.579961 | + | 0.814644i | \(0.303068\pi\) | |||||||
\(440\) | −5.10723 | + | 0.146800i | −0.243477 | + | 0.00699844i | ||||
\(441\) | −6.90571 | −0.328843 | ||||||||
\(442\) | −4.84520 | + | 3.52025i | −0.230463 | + | 0.167441i | ||||
\(443\) | −9.82575 | − | 30.2405i | −0.466835 | − | 1.43677i | −0.856660 | − | 0.515882i | \(-0.827464\pi\) |
0.389824 | − | 0.920889i | \(-0.372536\pi\) | |||||||
\(444\) | −2.61901 | + | 8.06050i | −0.124293 | + | 0.382534i | ||||
\(445\) | 3.70275 | + | 2.69020i | 0.175527 | + | 0.127528i | ||||
\(446\) | 13.6449 | + | 9.91363i | 0.646107 | + | 0.469424i | ||||
\(447\) | 5.62914 | − | 17.3247i | 0.266249 | − | 0.819430i | ||||
\(448\) | 0.247254 | + | 0.760968i | 0.0116816 | + | 0.0359524i | ||||
\(449\) | 9.11348 | − | 6.62133i | 0.430092 | − | 0.312480i | −0.351594 | − | 0.936153i | \(-0.614360\pi\) |
0.781686 | + | 0.623673i | \(0.214360\pi\) | |||||||
\(450\) | −7.38160 | −0.347972 | ||||||||
\(451\) | −33.5983 | + | 25.9176i | −1.58208 | + | 1.22041i | ||||
\(452\) | 9.27801 | 0.436401 | ||||||||
\(453\) | −1.84348 | + | 1.33936i | −0.0866141 | + | 0.0629288i | ||||
\(454\) | −10.2532 | − | 31.5561i | −0.481206 | − | 1.48100i | ||||
\(455\) | −0.0736318 | + | 0.226616i | −0.00345191 | + | 0.0106239i | ||||
\(456\) | −3.20253 | − | 2.32677i | −0.149972 | − | 0.108961i | ||||
\(457\) | 6.86402 | + | 4.98700i | 0.321085 | + | 0.233282i | 0.736638 | − | 0.676287i | \(-0.236412\pi\) |
−0.415553 | + | 0.909569i | \(0.636412\pi\) | |||||||
\(458\) | −2.56868 | + | 7.90560i | −0.120027 | + | 0.369404i | ||||
\(459\) | −1.10263 | − | 3.39353i | −0.0514662 | − | 0.158397i | ||||
\(460\) | −2.14513 | + | 1.55853i | −0.100017 | + | 0.0726667i | ||||
\(461\) | 29.5182 | 1.37480 | 0.687399 | − | 0.726280i | \(-0.258752\pi\) | ||||
0.687399 | + | 0.726280i | \(0.258752\pi\) | |||||||
\(462\) | −1.41122 | − | 0.964605i | −0.0656560 | − | 0.0448775i | ||||
\(463\) | 15.2387 | 0.708201 | 0.354100 | − | 0.935207i | \(-0.384787\pi\) | ||||
0.354100 | + | 0.935207i | \(0.384787\pi\) | |||||||
\(464\) | 32.0243 | − | 23.2670i | 1.48669 | − | 1.08014i | ||||
\(465\) | −0.825413 | − | 2.54036i | −0.0382776 | − | 0.117806i | ||||
\(466\) | −6.70341 | + | 20.6310i | −0.310529 | + | 0.955711i | ||||
\(467\) | 10.7222 | + | 7.79013i | 0.496164 | + | 0.360484i | 0.807550 | − | 0.589799i | \(-0.200793\pi\) |
−0.311386 | + | 0.950284i | \(0.600793\pi\) | |||||||
\(468\) | −0.661127 | − | 0.480337i | −0.0305606 | − | 0.0222036i | ||||
\(469\) | 0.000731182 | − | 0.00225035i | 3.37628e−5 | − | 0.000103911i | ||||
\(470\) | −2.90619 | − | 8.94435i | −0.134053 | − | 0.412572i | ||||
\(471\) | −10.4550 | + | 7.59597i | −0.481739 | + | 0.350004i | ||||
\(472\) | −8.71970 | −0.401357 | ||||||||
\(473\) | 0.475500 | + | 1.33194i | 0.0218635 | + | 0.0612428i | ||||
\(474\) | −18.9598 | −0.870855 | ||||||||
\(475\) | 7.09437 | − | 5.15436i | 0.325512 | − | 0.236498i | ||||
\(476\) | 0.276689 | + | 0.851560i | 0.0126820 | + | 0.0390312i | ||||
\(477\) | 1.66242 | − | 5.11640i | 0.0761170 | − | 0.234264i | ||||
\(478\) | 11.7538 | + | 8.53963i | 0.537606 | + | 0.390594i | ||||
\(479\) | 1.94025 | + | 1.40967i | 0.0886521 | + | 0.0644096i | 0.631228 | − | 0.775597i | \(-0.282551\pi\) |
−0.542576 | + | 0.840007i | \(0.682551\pi\) | |||||||
\(480\) | −1.04683 | + | 3.22180i | −0.0477809 | + | 0.147054i | ||||
\(481\) | 3.20487 | + | 9.86359i | 0.146130 | + | 0.449741i | ||||
\(482\) | 12.1190 | − | 8.80496i | 0.552005 | − | 0.401055i | ||||
\(483\) | 1.28398 | 0.0584230 | ||||||||
\(484\) | 3.26429 | + | 8.37554i | 0.148377 | + | 0.380706i | ||||
\(485\) | −6.63718 | −0.301379 | ||||||||
\(486\) | 1.35790 | − | 0.986569i | 0.0615954 | − | 0.0447517i | ||||
\(487\) | −12.0231 | − | 37.0033i | −0.544819 | − | 1.67678i | −0.721421 | − | 0.692497i | \(-0.756511\pi\) |
0.176602 | − | 0.984282i | \(-0.443489\pi\) | |||||||
\(488\) | −2.45422 | + | 7.55331i | −0.111097 | + | 0.341922i | ||||
\(489\) | −1.14958 | − | 0.835219i | −0.0519858 | − | 0.0377699i | ||||
\(490\) | −7.27649 | − | 5.28668i | −0.328718 | − | 0.238828i | ||||
\(491\) | 1.13313 | − | 3.48742i | 0.0511376 | − | 0.157385i | −0.922227 | − | 0.386650i | \(-0.873632\pi\) |
0.973364 | + | 0.229265i | \(0.0736322\pi\) | |||||||
\(492\) | 3.23086 | + | 9.94356i | 0.145658 | + | 0.448290i | ||||
\(493\) | −23.0074 | + | 16.7158i | −1.03620 | + | 0.752843i | ||||
\(494\) | 3.34675 | 0.150577 | ||||||||
\(495\) | 0.865288 | + | 2.42379i | 0.0388918 | + | 0.108941i | ||||
\(496\) | 17.0962 | 0.767642 | ||||||||
\(497\) | 2.89506 | − | 2.10338i | 0.129861 | − | 0.0943495i | ||||
\(498\) | −8.96083 | − | 27.5786i | −0.401544 | − | 1.23583i | ||||
\(499\) | 5.66147 | − | 17.4242i | 0.253442 | − | 0.780014i | −0.740691 | − | 0.671846i | \(-0.765502\pi\) |
0.994133 | − | 0.108168i | \(-0.0344984\pi\) | |||||||
\(500\) | −4.82126 | − | 3.50285i | −0.215613 | − | 0.156652i | ||||
\(501\) | −2.63525 | − | 1.91462i | −0.117734 | − | 0.0855389i | ||||
\(502\) | 5.85313 | − | 18.0141i | 0.261238 | − | 0.804007i | ||||
\(503\) | −8.98571 | − | 27.6552i | −0.400653 | − | 1.23308i | −0.924471 | − | 0.381253i | \(-0.875493\pi\) |
0.523818 | − | 0.851830i | \(-0.324507\pi\) | |||||||
\(504\) | 0.493191 | − | 0.358324i | 0.0219685 | − | 0.0159610i | ||||
\(505\) | −9.66236 | −0.429970 | ||||||||
\(506\) | −19.2168 | − | 13.1352i | −0.854291 | − | 0.583929i | ||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −7.83839 | + | 5.69492i | −0.347772 | + | 0.252671i | ||||
\(509\) | 7.09219 | + | 21.8275i | 0.314356 | + | 0.967488i | 0.976019 | + | 0.217686i | \(0.0698510\pi\) |
−0.661663 | + | 0.749801i | \(0.730149\pi\) | |||||||
\(510\) | 1.43610 | − | 4.41985i | 0.0635915 | − | 0.195714i | ||||
\(511\) | −1.87554 | − | 1.36266i | −0.0829689 | − | 0.0602804i | ||||
\(512\) | −1.58738 | − | 1.15330i | −0.0701527 | − | 0.0509690i | ||||
\(513\) | −0.616165 | + | 1.89636i | −0.0272043 | + | 0.0837263i | ||||
\(514\) | 5.21514 | + | 16.0505i | 0.230030 | + | 0.707959i | ||||
\(515\) | −2.88169 | + | 2.09367i | −0.126982 | + | 0.0922581i | ||||
\(516\) | 0.348469 | 0.0153405 | ||||||||
\(517\) | 18.9625 | − | 14.6276i | 0.833970 | − | 0.643321i | ||||
\(518\) | 5.34532 | 0.234860 | ||||||||
\(519\) | 9.92990 | − | 7.21449i | 0.435874 | − | 0.316681i | ||||
\(520\) | 0.476048 | + | 1.46512i | 0.0208761 | + | 0.0642499i | ||||
\(521\) | −9.00598 | + | 27.7176i | −0.394559 | + | 1.21433i | 0.534745 | + | 0.845013i | \(0.320408\pi\) |
−0.929304 | + | 0.369315i | \(0.879592\pi\) | |||||||
\(522\) | −10.8226 | − | 7.86305i | −0.473691 | − | 0.344156i | ||||
\(523\) | 14.8720 | + | 10.8052i | 0.650309 | + | 0.472477i | 0.863376 | − | 0.504561i | \(-0.168345\pi\) |
−0.213068 | + | 0.977037i | \(0.568345\pi\) | |||||||
\(524\) | −0.677946 | + | 2.08650i | −0.0296162 | + | 0.0911493i | ||||
\(525\) | 0.417311 | + | 1.28435i | 0.0182130 | + | 0.0560537i | ||||
\(526\) | 10.8536 | − | 7.88558i | 0.473238 | − | 0.343828i | ||||
\(527\) | −12.2825 | −0.535035 | ||||||||
\(528\) | −16.4655 | + | 0.473279i | −0.716569 | + | 0.0205968i | ||||
\(529\) | −5.51590 | −0.239822 | ||||||||
\(530\) | 5.66855 | − | 4.11844i | 0.246226 | − | 0.178894i | ||||
\(531\) | 1.35726 | + | 4.17722i | 0.0589001 | + | 0.181276i | ||||
\(532\) | 0.154618 | − | 0.475865i | 0.00670354 | − | 0.0206314i | ||||
\(533\) | 10.3506 | + | 7.52016i | 0.448335 | + | 0.325734i | ||||
\(534\) | 8.00913 | + | 5.81897i | 0.346589 | + | 0.251812i | ||||
\(535\) | −1.08051 | + | 3.32548i | −0.0467147 | + | 0.143773i | ||||
\(536\) | −0.00472727 | − | 0.0145490i | −0.000204187 | − | 0.000628423i | ||||
\(537\) | 14.0672 | − | 10.2204i | 0.607044 | − | 0.441043i | ||||
\(538\) | 12.3620 | 0.532963 | ||||||||
\(539\) | 6.44884 | − | 21.9770i | 0.277771 | − | 0.946617i | ||||
\(540\) | 0.634124 | 0.0272883 | ||||||||
\(541\) | 5.83059 | − | 4.23617i | 0.250677 | − | 0.182127i | −0.455350 | − | 0.890313i | \(-0.650486\pi\) |
0.706027 | + | 0.708185i | \(0.250486\pi\) | |||||||
\(542\) | 3.34318 | + | 10.2893i | 0.143602 | + | 0.441961i | ||||
\(543\) | 2.26710 | − | 6.97740i | 0.0972904 | − | 0.299429i | ||||
\(544\) | 12.6023 | + | 9.15608i | 0.540318 | + | 0.392564i | ||||
\(545\) | 8.87828 | + | 6.45045i | 0.380304 | + | 0.276307i | ||||
\(546\) | −0.159267 | + | 0.490175i | −0.00681602 | + | 0.0209776i | ||||
\(547\) | −3.81000 | − | 11.7260i | −0.162904 | − | 0.501366i | 0.835972 | − | 0.548772i | \(-0.184905\pi\) |
−0.998876 | + | 0.0474058i | \(0.984905\pi\) | |||||||
\(548\) | −1.36623 | + | 0.992624i | −0.0583624 | + | 0.0424028i | ||||
\(549\) | 4.00046 | 0.170735 | ||||||||
\(550\) | 6.89324 | − | 23.4915i | 0.293929 | − | 1.00168i | ||||
\(551\) | 15.8920 | 0.677021 | ||||||||
\(552\) | 6.71584 | − | 4.87934i | 0.285845 | − | 0.207679i | ||||
\(553\) | 1.07188 | + | 3.29890i | 0.0455808 | + | 0.140283i | ||||
\(554\) | −4.66854 | + | 14.3683i | −0.198347 | + | 0.610450i | ||||
\(555\) | −6.51079 | − | 4.73036i | −0.276368 | − | 0.200793i | ||||
\(556\) | 10.0365 | + | 7.29197i | 0.425644 | + | 0.309248i | ||||
\(557\) | 1.13082 | − | 3.48032i | 0.0479145 | − | 0.147466i | −0.924237 | − | 0.381820i | \(-0.875298\pi\) |
0.972151 | + | 0.234354i | \(0.0752975\pi\) | |||||||
\(558\) | −1.78539 | − | 5.49486i | −0.0755815 | − | 0.232616i | ||||
\(559\) | 0.344981 | − | 0.250643i | 0.0145911 | − | 0.0106011i | ||||
\(560\) | 1.18343 | 0.0500089 | ||||||||
\(561\) | 11.8294 | − | 0.340020i | 0.499438 | − | 0.0143557i | ||||
\(562\) | −19.6027 | −0.826890 | ||||||||
\(563\) | −10.6729 | + | 7.75435i | −0.449811 | + | 0.326807i | −0.789521 | − | 0.613723i | \(-0.789671\pi\) |
0.339710 | + | 0.940530i | \(0.389671\pi\) | |||||||
\(564\) | −1.82346 | − | 5.61203i | −0.0767814 | − | 0.236309i | ||||
\(565\) | −2.72243 | + | 8.37879i | −0.114534 | + | 0.352498i | ||||
\(566\) | −15.6180 | − | 11.3471i | −0.656472 | − | 0.476955i | ||||
\(567\) | −0.248424 | − | 0.180491i | −0.0104328 | − | 0.00757990i | ||||
\(568\) | 7.14935 | − | 22.0034i | 0.299980 | − | 0.923243i | ||||
\(569\) | −3.15811 | − | 9.71966i | −0.132395 | − | 0.407469i | 0.862781 | − | 0.505578i | \(-0.168721\pi\) |
−0.995176 | + | 0.0981088i | \(0.968721\pi\) | |||||||
\(570\) | −2.10101 | + | 1.52647i | −0.0880016 | + | 0.0639369i | ||||
\(571\) | 15.2983 | 0.640215 | 0.320107 | − | 0.947381i | \(-0.396281\pi\) | ||||
0.320107 | + | 0.947381i | \(0.396281\pi\) | |||||||
\(572\) | 2.14603 | − | 1.65544i | 0.0897301 | − | 0.0692174i | ||||
\(573\) | −23.2658 | −0.971942 | ||||||||
\(574\) | 5.33471 | − | 3.87590i | 0.222667 | − | 0.161777i | ||||
\(575\) | 5.68258 | + | 17.4892i | 0.236980 | + | 0.729350i | ||||
\(576\) | 0.805205 | − | 2.47817i | 0.0335502 | − | 0.103257i | ||||
\(577\) | −30.6847 | − | 22.2937i | −1.27742 | − | 0.928101i | −0.277949 | − | 0.960596i | \(-0.589655\pi\) |
−0.999472 | + | 0.0324953i | \(0.989655\pi\) | |||||||
\(578\) | 5.79570 | + | 4.21083i | 0.241070 | + | 0.175147i | ||||
\(579\) | −7.58931 | + | 23.3575i | −0.315401 | + | 0.970705i | ||||
\(580\) | −1.56178 | − | 4.80667i | −0.0648494 | − | 0.199586i | ||||
\(581\) | −4.29191 | + | 3.11826i | −0.178059 | + | 0.129367i | ||||
\(582\) | −14.3564 | −0.595092 | ||||||||
\(583\) | 14.7302 | + | 10.0685i | 0.610063 | + | 0.416993i | ||||
\(584\) | −14.9883 | −0.620221 | ||||||||
\(585\) | 0.627776 | − | 0.456106i | 0.0259554 | − | 0.0188577i | ||||
\(586\) | 3.63384 | + | 11.1838i | 0.150113 | + | 0.461999i | ||||
\(587\) | −11.8736 | + | 36.5432i | −0.490076 | + | 1.50830i | 0.334416 | + | 0.942426i | \(0.391461\pi\) |
−0.824492 | + | 0.565874i | \(0.808539\pi\) | |||||||
\(588\) | −4.56555 | − | 3.31706i | −0.188280 | − | 0.136793i | ||||
\(589\) | 5.55282 | + | 4.03436i | 0.228800 | + | 0.166233i | ||||
\(590\) | −1.76774 | + | 5.44055i | −0.0727768 | + | 0.223984i | ||||
\(591\) | −5.26836 | − | 16.2144i | −0.216711 | − | 0.666969i | ||||
\(592\) | 41.6720 | − | 30.2765i | 1.71271 | − | 1.24435i | ||||
\(593\) | −11.7601 | −0.482927 | −0.241464 | − | 0.970410i | \(-0.577627\pi\) | ||||
−0.241464 | + | 0.970410i | \(0.577627\pi\) | |||||||
\(594\) | 1.87164 | + | 5.24272i | 0.0767943 | + | 0.215112i | ||||
\(595\) | −0.850216 | −0.0348554 | ||||||||
\(596\) | 12.0433 | − | 8.74994i | 0.493311 | − | 0.358412i | ||||
\(597\) | −4.16861 | − | 12.8297i | −0.170610 | − | 0.525083i | ||||
\(598\) | −2.16877 | + | 6.67477i | −0.0886874 | + | 0.272952i | ||||
\(599\) | −36.5496 | − | 26.5548i | −1.49338 | − | 1.08500i | −0.972928 | − | 0.231108i | \(-0.925765\pi\) |
−0.520448 | − | 0.853893i | \(-0.674235\pi\) | |||||||
\(600\) | 7.06351 | + | 5.13194i | 0.288366 | + | 0.209511i | ||||
\(601\) | −4.94125 | + | 15.2076i | −0.201558 | + | 0.620331i | 0.798280 | + | 0.602287i | \(0.205744\pi\) |
−0.999837 | + | 0.0180435i | \(0.994256\pi\) | |||||||
\(602\) | −0.0679148 | − | 0.209020i | −0.00276800 | − | 0.00851903i | ||||
\(603\) | −0.00623397 | + | 0.00452924i | −0.000253867 | + | 0.000184445i | ||||
\(604\) | −1.86212 | −0.0757684 | ||||||||
\(605\) | −8.52162 | + | 0.490290i | −0.346453 | + | 0.0199331i | ||||
\(606\) | −20.8999 | −0.849002 | ||||||||
\(607\) | 3.47157 | − | 2.52224i | 0.140907 | − | 0.102375i | −0.515099 | − | 0.857131i | \(-0.672245\pi\) |
0.656005 | + | 0.754756i | \(0.272245\pi\) | |||||||
\(608\) | −2.68994 | − | 8.27877i | −0.109091 | − | 0.335749i | ||||
\(609\) | −0.756279 | + | 2.32759i | −0.0306460 | + | 0.0943186i | ||||
\(610\) | 4.21525 | + | 3.06256i | 0.170670 | + | 0.123999i | ||||
\(611\) | −5.84177 | − | 4.24429i | −0.236333 | − | 0.171706i | ||||
\(612\) | 0.901063 | − | 2.77319i | 0.0364233 | − | 0.112099i | ||||
\(613\) | −13.6062 | − | 41.8757i | −0.549551 | − | 1.69134i | −0.709916 | − | 0.704286i | \(-0.751267\pi\) |
0.160365 | − | 0.987058i | \(-0.448733\pi\) | |||||||
\(614\) | −37.0844 | + | 26.9434i | −1.49661 | + | 1.08735i | ||||
\(615\) | −9.92786 | −0.400330 | ||||||||
\(616\) | 0.679783 | + | 1.90417i | 0.0273892 | + | 0.0767211i | ||||
\(617\) | 45.4122 | 1.82823 | 0.914113 | − | 0.405460i | \(-0.132889\pi\) | ||||
0.914113 | + | 0.405460i | \(0.132889\pi\) | |||||||
\(618\) | −6.23316 | + | 4.52866i | −0.250735 | + | 0.182169i | ||||
\(619\) | 2.43194 | + | 7.48473i | 0.0977478 | + | 0.300837i | 0.987960 | − | 0.154709i | \(-0.0494440\pi\) |
−0.890212 | + | 0.455546i | \(0.849444\pi\) | |||||||
\(620\) | 0.674525 | − | 2.07598i | 0.0270896 | − | 0.0833732i | ||||
\(621\) | −3.38282 | − | 2.45776i | −0.135748 | − | 0.0986267i | ||||
\(622\) | −18.0061 | − | 13.0822i | −0.721979 | − | 0.524548i | ||||
\(623\) | 0.559677 | − | 1.72251i | 0.0224230 | − | 0.0690109i | ||||
\(624\) | 1.53476 | + | 4.72350i | 0.0614395 | + | 0.189091i | ||||
\(625\) | −13.2117 | + | 9.59885i | −0.528467 | + | 0.383954i | ||||
\(626\) | 23.0000 | 0.919266 | ||||||||
\(627\) | −5.45966 | − | 3.73181i | −0.218038 | − | 0.149034i | ||||
\(628\) | −10.5607 | −0.421417 | ||||||||
\(629\) | −29.9386 | + | 21.7517i | −1.19373 | + | 0.867297i | ||||
\(630\) | −0.123587 | − | 0.380363i | −0.00492384 | − | 0.0151540i | ||||
\(631\) | 1.95698 | − | 6.02296i | 0.0779061 | − | 0.239770i | −0.904517 | − | 0.426437i | \(-0.859769\pi\) |
0.982423 | + | 0.186667i | \(0.0597685\pi\) | |||||||
\(632\) | 18.1428 | + | 13.1815i | 0.721683 | + | 0.524333i | ||||
\(633\) | −18.5782 | − | 13.4978i | −0.738416 | − | 0.536491i | ||||
\(634\) | 13.6450 | − | 41.9949i | 0.541911 | − | 1.66783i | ||||
\(635\) | −2.84297 | − | 8.74975i | −0.112820 | − | 0.347223i | ||||
\(636\) | 3.55667 | − | 2.58407i | 0.141031 | − | 0.102465i | ||||
\(637\) | −6.90571 | −0.273614 | ||||||||
\(638\) | 35.1303 | − | 27.0993i | 1.39082 | − | 1.07287i | ||||
\(639\) | −11.6537 | −0.461013 | ||||||||
\(640\) | 8.22686 | − | 5.97716i | 0.325195 | − | 0.236268i | ||||
\(641\) | −2.06303 | − | 6.34935i | −0.0814848 | − | 0.250784i | 0.902012 | − | 0.431712i | \(-0.142090\pi\) |
−0.983496 | + | 0.180927i | \(0.942090\pi\) | |||||||
\(642\) | −2.33718 | + | 7.19309i | −0.0922410 | + | 0.283889i | ||||
\(643\) | 0.298516 | + | 0.216884i | 0.0117723 | + | 0.00855308i | 0.593656 | − | 0.804719i | \(-0.297684\pi\) |
−0.581884 | + | 0.813272i | \(0.697684\pi\) | |||||||
\(644\) | 0.848872 | + | 0.616742i | 0.0334503 | + | 0.0243030i | ||||
\(645\) | −0.102251 | + | 0.314696i | −0.00402612 | + | 0.0123911i | ||||
\(646\) | 3.69021 | + | 11.3573i | 0.145189 | + | 0.446847i | ||||
\(647\) | −16.9325 | + | 12.3022i | −0.665684 | + | 0.483648i | −0.868578 | − | 0.495553i | \(-0.834965\pi\) |
0.202894 | + | 0.979201i | \(0.434965\pi\) | |||||||
\(648\) | −1.98528 | −0.0779890 | ||||||||
\(649\) | −14.5612 | + | 0.418543i | −0.571578 | + | 0.0164292i | ||||
\(650\) | −7.38160 | −0.289530 | ||||||||
\(651\) | −0.855137 | + | 0.621293i | −0.0335155 | + | 0.0243504i | ||||
\(652\) | −0.358832 | − | 1.10437i | −0.0140529 | − | 0.0432505i | ||||
\(653\) | 1.50895 | − | 4.64406i | 0.0590496 | − | 0.181736i | −0.917181 | − | 0.398471i | \(-0.869541\pi\) |
0.976230 | + | 0.216735i | \(0.0695409\pi\) | |||||||
\(654\) | 19.2039 | + | 13.9525i | 0.750933 | + | 0.545585i | ||||
\(655\) | −1.68535 | − | 1.22448i | −0.0658521 | − | 0.0478444i | ||||
\(656\) | 19.6358 | − | 60.4328i | 0.766649 | − | 2.35950i | ||||
\(657\) | 2.33300 | + | 7.18023i | 0.0910189 | + | 0.280128i | ||||
\(658\) | −3.01085 | + | 2.18751i | −0.117375 | + | 0.0852780i | ||||
\(659\) | −23.2054 | −0.903956 | −0.451978 | − | 0.892029i | \(-0.649281\pi\) | ||||
−0.451978 | + | 0.892029i | \(0.649281\pi\) | |||||||
\(660\) | −0.592171 | + | 2.01806i | −0.0230502 | + | 0.0785530i | ||||
\(661\) | 4.13915 | 0.160994 | 0.0804971 | − | 0.996755i | \(-0.474349\pi\) | ||||
0.0804971 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(662\) | 15.9213 | − | 11.5675i | 0.618797 | − | 0.449582i | ||||
\(663\) | −1.10263 | − | 3.39353i | −0.0428224 | − | 0.131794i | ||||
\(664\) | −10.5989 | + | 32.6200i | −0.411317 | + | 1.26590i | ||||
\(665\) | 0.384375 | + | 0.279265i | 0.0149054 | + | 0.0108294i | ||||
\(666\) | −14.0830 | − | 10.2319i | −0.545705 | − | 0.396478i | ||||
\(667\) | −10.2983 | + | 31.6951i | −0.398754 | + | 1.22724i | ||||
\(668\) | −0.822571 | − | 2.53161i | −0.0318262 | − | 0.0979510i | ||||
\(669\) | −8.12948 | + | 5.90642i | −0.314304 | + | 0.228355i | ||||
\(670\) | −0.0100360 | −0.000387726 | ||||||||
\(671\) | −3.73580 | + | 12.7312i | −0.144219 | + | 0.491484i | ||||
\(672\) | 1.34055 | 0.0517126 | ||||||||
\(673\) | 25.9585 | − | 18.8600i | 1.00063 | − | 0.726999i | 0.0384050 | − | 0.999262i | \(-0.487772\pi\) |
0.962223 | + | 0.272264i | \(0.0877723\pi\) | |||||||
\(674\) | −0.315764 | − | 0.971822i | −0.0121628 | − | 0.0374332i | ||||
\(675\) | 1.35901 | − | 4.18262i | 0.0523085 | − | 0.160989i | ||||
\(676\) | −0.661127 | − | 0.480337i | −0.0254279 | − | 0.0184745i | ||||
\(677\) | 31.5825 | + | 22.9461i | 1.21382 | + | 0.881889i | 0.995572 | − | 0.0940058i | \(-0.0299672\pi\) |
0.218244 | + | 0.975894i | \(0.429967\pi\) | |||||||
\(678\) | −5.88869 | + | 18.1235i | −0.226154 | + | 0.696030i | ||||
\(679\) | 0.811625 | + | 2.49792i | 0.0311473 | + | 0.0958615i | ||||
\(680\) | −4.44704 | + | 3.23097i | −0.170536 | + | 0.123902i | ||||
\(681\) | 19.7682 | 0.757521 | ||||||||
\(682\) | 19.1544 | − | 0.550566i | 0.733458 | − | 0.0210823i | ||||
\(683\) | 32.1749 | 1.23114 | 0.615570 | − | 0.788082i | \(-0.288926\pi\) | ||||
0.615570 | + | 0.788082i | \(0.288926\pi\) | |||||||
\(684\) | −1.31825 | + | 0.957767i | −0.0504047 | + | 0.0366211i | ||||
\(685\) | −0.495528 | − | 1.52508i | −0.0189332 | − | 0.0582703i | ||||
\(686\) | −2.21473 | + | 6.81623i | −0.0845587 | + | 0.260245i | ||||
\(687\) | −4.00661 | − | 2.91097i | −0.152862 | − | 0.111061i | ||||
\(688\) | −1.71338 | − | 1.24484i | −0.0653218 | − | 0.0474591i | ||||
\(689\) | 1.66242 | − | 5.11640i | 0.0633332 | − | 0.194919i | ||||
\(690\) | −1.68291 | − | 5.17945i | −0.0640671 | − | 0.197178i | ||||
\(691\) | −15.1197 | + | 10.9851i | −0.575182 | + | 0.417894i | −0.836984 | − | 0.547227i | \(-0.815683\pi\) |
0.261802 | + | 0.965122i | \(0.415683\pi\) | |||||||
\(692\) | 10.0303 | 0.381295 | ||||||||
\(693\) | 0.806390 | − | 0.622046i | 0.0306322 | − | 0.0236296i | ||||
\(694\) | −13.1552 | −0.499364 | ||||||||
\(695\) | −9.53025 | + | 6.92413i | −0.361503 | + | 0.262647i | ||||
\(696\) | 4.88953 | + | 15.0484i | 0.185337 | + | 0.570409i | ||||
\(697\) | −14.1071 | + | 43.4171i | −0.534343 | + | 1.64454i | ||||
\(698\) | 15.5096 | + | 11.2684i | 0.587047 | + | 0.426514i | ||||
\(699\) | −10.4559 | − | 7.59667i | −0.395479 | − | 0.287332i | ||||
\(700\) | −0.341026 | + | 1.04957i | −0.0128896 | + | 0.0396700i | ||||
\(701\) | 5.47164 | + | 16.8400i | 0.206661 | + | 0.636037i | 0.999641 | + | 0.0267897i | \(0.00852845\pi\) |
−0.792980 | + | 0.609248i | \(0.791472\pi\) | |||||||
\(702\) | 1.35790 | − | 0.986569i | 0.0512505 | − | 0.0372356i | ||||
\(703\) | 20.6796 | 0.779948 | ||||||||
\(704\) | 7.13469 | + | 4.87673i | 0.268899 | + | 0.183799i | ||||
\(705\) | 5.60317 | 0.211028 | ||||||||
\(706\) | 21.8319 | − | 15.8618i | 0.821654 | − | 0.596967i | ||||
\(707\) | 1.18156 | + | 3.63646i | 0.0444370 | + | 0.136763i | ||||
\(708\) | −1.10915 | + | 3.41361i | −0.0416844 | + | 0.128291i | ||||
\(709\) | −32.5437 | − | 23.6443i | −1.22220 | − | 0.887982i | −0.225921 | − | 0.974146i | \(-0.572539\pi\) |
−0.996281 | + | 0.0861635i | \(0.972539\pi\) | |||||||
\(710\) | −12.2794 | − | 8.92149i | −0.460837 | − | 0.334818i | ||||
\(711\) | 3.49067 | − | 10.7432i | 0.130910 | − | 0.402900i | ||||
\(712\) | −3.61845 | − | 11.1364i | −0.135607 | − | 0.417356i | ||||
\(713\) | −11.6445 | + | 8.46023i | −0.436090 | + | 0.316838i | ||||
\(714\) | −1.83904 | −0.0688242 | ||||||||
\(715\) | 0.865288 | + | 2.42379i | 0.0323599 | + | 0.0906447i | ||||
\(716\) | 14.2094 | 0.531031 | ||||||||
\(717\) | −7.00276 | + | 5.08780i | −0.261523 | + | 0.190008i | ||||
\(718\) | −15.6109 | − | 48.0453i | −0.582593 | − | 1.79304i | ||||
\(719\) | 14.6708 | − | 45.1520i | 0.547127 | − | 1.68388i | −0.168751 | − | 0.985659i | \(-0.553973\pi\) |
0.715878 | − | 0.698225i | \(-0.246027\pi\) | |||||||
\(720\) | −3.11790 | − | 2.26529i | −0.116197 | − | 0.0844223i | ||||
\(721\) | 1.14034 | + | 0.828509i | 0.0424686 | + | 0.0308553i | ||||
\(722\) | −7.79258 | + | 23.9831i | −0.290010 | + | 0.892558i | ||||
\(723\) | 2.75792 | + | 8.48802i | 0.102568 | + | 0.315673i | ||||
\(724\) | 4.85034 | − | 3.52398i | 0.180261 | − | 0.130968i | ||||
\(725\) | −35.0514 | −1.30178 | ||||||||
\(726\) | −18.4325 | + | 1.06051i | −0.684093 | + | 0.0393592i | ||||
\(727\) | 34.2838 | 1.27152 | 0.635758 | − | 0.771889i | \(-0.280688\pi\) | ||||
0.635758 | + | 0.771889i | \(0.280688\pi\) | |||||||
\(728\) | 0.493191 | − | 0.358324i | 0.0182789 | − | 0.0132804i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −3.03858 | + | 9.35178i | −0.112463 | + | 0.346125i | ||||
\(731\) | 1.23095 | + | 0.894338i | 0.0455284 | + | 0.0330783i | ||||
\(732\) | 2.64481 | + | 1.92157i | 0.0977550 | + | 0.0710232i | ||||
\(733\) | −4.62571 | + | 14.2365i | −0.170855 | + | 0.525837i | −0.999420 | − | 0.0340559i | \(-0.989158\pi\) |
0.828565 | + | 0.559893i | \(0.189158\pi\) | |||||||
\(734\) | −15.3143 | − | 47.1325i | −0.565260 | − | 1.73969i | ||||
\(735\) | 4.33524 | − | 3.14974i | 0.159908 | − | 0.116180i | ||||
\(736\) | 18.2544 | 0.672865 | ||||||||
\(737\) | −0.00859252 | − | 0.0240688i | −0.000316509 | − | 0.000886587i | ||||
\(738\) | −21.4742 | −0.790477 | ||||||||
\(739\) | 12.2801 | − | 8.92201i | 0.451731 | − | 0.328201i | −0.338548 | − | 0.940949i | \(-0.609936\pi\) |
0.790279 | + | 0.612748i | \(0.209936\pi\) | |||||||
\(740\) | −2.03229 | − | 6.25474i | −0.0747084 | − | 0.229929i | ||||
\(741\) | −0.616165 | + | 1.89636i | −0.0226354 | + | 0.0696645i | ||||
\(742\) | −2.24316 | − | 1.62975i | −0.0823491 | − | 0.0598301i | ||||
\(743\) | −0.382040 | − | 0.277569i | −0.0140157 | − | 0.0101830i | 0.580755 | − | 0.814078i | \(-0.302757\pi\) |
−0.594771 | + | 0.803895i | \(0.702757\pi\) | |||||||
\(744\) | −2.11176 | + | 6.49934i | −0.0774210 | + | 0.238277i | ||||
\(745\) | 4.36806 | + | 13.4435i | 0.160033 | + | 0.492532i | ||||
\(746\) | 20.7350 | − | 15.0649i | 0.759164 | − | 0.551565i | ||||
\(747\) | 17.2766 | 0.632116 | ||||||||
\(748\) | 7.98405 | + | 5.45730i | 0.291926 | + | 0.199539i | ||||
\(749\) | 1.38368 | 0.0505587 | ||||||||
\(750\) | 9.90245 | − | 7.19455i | 0.361586 | − | 0.262708i | ||||
\(751\) | −8.46110 | − | 26.0406i | −0.308750 | − | 0.950234i | −0.978251 | − | 0.207424i | \(-0.933492\pi\) |
0.669501 | − | 0.742811i | \(-0.266508\pi\) | |||||||
\(752\) | −11.0822 | + | 34.1076i | −0.404127 | + | 1.24377i | ||||
\(753\) | 9.12966 | + | 6.63309i | 0.332703 | + | 0.241723i | ||||
\(754\) | −10.8226 | − | 7.86305i | −0.394134 | − | 0.286355i | ||||
\(755\) | 0.546398 | − | 1.68164i | 0.0198855 | − | 0.0612012i | ||||
\(756\) | −0.0775435 | − | 0.238654i | −0.00282023 | − | 0.00867978i | ||||
\(757\) | 32.6314 | − | 23.7081i | 1.18601 | − | 0.861685i | 0.193171 | − | 0.981165i | \(-0.438123\pi\) |
0.992837 | + | 0.119480i | \(0.0381228\pi\) | |||||||
\(758\) | −9.75610 | −0.354358 | ||||||||
\(759\) | 10.9807 | − | 8.47048i | 0.398575 | − | 0.307459i | ||||
\(760\) | 3.07173 | 0.111423 | ||||||||
\(761\) | 27.5431 | − | 20.0112i | 0.998436 | − | 0.725406i | 0.0366837 | − | 0.999327i | \(-0.488321\pi\) |
0.961752 | + | 0.273921i | \(0.0883206\pi\) | |||||||
\(762\) | −6.14941 | − | 18.9259i | −0.222770 | − | 0.685614i | ||||
\(763\) | 1.34197 | − | 4.13016i | 0.0485825 | − | 0.149522i | ||||
\(764\) | −15.3816 | − | 11.1754i | −0.556488 | − | 0.404312i | ||||
\(765\) | 2.24001 | + | 1.62746i | 0.0809878 | + | 0.0588411i | ||||
\(766\) | −10.7281 | + | 33.0176i | −0.387621 | + | 1.19297i | ||||
\(767\) | 1.35726 | + | 4.17722i | 0.0490078 | + | 0.150831i | ||||
\(768\) | 13.5788 | − | 9.86557i | 0.489982 | − | 0.355993i | ||||
\(769\) | 5.84163 | 0.210654 | 0.105327 | − | 0.994438i | \(-0.466411\pi\) | ||||
0.105327 | + | 0.994438i | \(0.466411\pi\) | |||||||
\(770\) | 1.32589 | − | 0.0381111i | 0.0477819 | − | 0.00137343i | ||||
\(771\) | −10.0548 | −0.362116 | ||||||||
\(772\) | −16.2370 | + | 11.7968i | −0.584381 | + | 0.424578i | ||||
\(773\) | −3.21738 | − | 9.90207i | −0.115721 | − | 0.356153i | 0.876376 | − | 0.481628i | \(-0.159954\pi\) |
−0.992097 | + | 0.125475i | \(0.959954\pi\) | |||||||
\(774\) | −0.221171 | + | 0.680695i | −0.00794983 | + | 0.0244671i | ||||
\(775\) | −12.2473 | − | 8.89820i | −0.439937 | − | 0.319633i | ||||
\(776\) | 13.7377 | + | 9.98105i | 0.493156 | + | 0.358299i | ||||
\(777\) | −0.984118 | + | 3.02880i | −0.0353050 | + | 0.108658i | ||||
\(778\) | 15.1354 | + | 46.5819i | 0.542629 | + | 1.67004i | ||||
\(779\) | 20.6386 | − | 14.9948i | 0.739455 | − | 0.537246i | ||||
\(780\) | 0.634124 | 0.0227053 | ||||||||
\(781\) | 10.8827 | − | 37.0872i | 0.389413 | − | 1.32708i | ||||
\(782\) | −25.0424 | −0.895514 | ||||||||
\(783\) | 6.44795 | − | 4.68471i | 0.230431 | − | 0.167418i | ||||
\(784\) | 10.5986 | + | 32.6191i | 0.378521 | + | 1.16497i | ||||
\(785\) | 3.09880 | − | 9.53714i | 0.110601 | − | 0.340395i | ||||
\(786\) | −3.64546 | − | 2.64858i | −0.130029 | − | 0.0944717i | ||||
\(787\) | 31.9300 | + | 23.1985i | 1.13818 | + | 0.826936i | 0.986865 | − | 0.161549i | \(-0.0516491\pi\) |
0.151315 | + | 0.988486i | \(0.451649\pi\) | |||||||
\(788\) | 4.30529 | − | 13.2503i | 0.153370 | − | 0.472023i | ||||
\(789\) | 2.46995 | + | 7.60174i | 0.0879327 | + | 0.270629i | ||||
\(790\) | 11.9025 | − | 8.64770i | 0.423473 | − | 0.307671i | ||||
\(791\) | 3.48629 | 0.123958 | ||||||||
\(792\) | 1.85393 | − | 6.31803i | 0.0658767 | − | 0.224501i | ||||
\(793\) | 4.00046 | 0.142060 | ||||||||
\(794\) | −51.6831 | + | 37.5500i | −1.83416 | + | 1.33260i | ||||
\(795\) | 1.28999 | + | 3.97020i | 0.0457514 | + | 0.140808i | ||||
\(796\) | 3.40658 | − | 10.4844i | 0.120743 | − | 0.371608i | ||||
\(797\) | 20.5407 | + | 14.9237i | 0.727589 | + | 0.528624i | 0.888800 | − | 0.458296i | \(-0.151540\pi\) |
−0.161211 | + | 0.986920i | \(0.551540\pi\) | |||||||
\(798\) | 0.831413 | + | 0.604057i | 0.0294317 | + | 0.0213834i | ||||
\(799\) | 7.96186 | − | 24.5041i | 0.281670 | − | 0.866892i | ||||
\(800\) | 5.93293 | + | 18.2597i | 0.209761 | + | 0.645578i | ||||
\(801\) | −4.77174 | + | 3.46687i | −0.168601 | + | 0.122496i | ||||
\(802\) | −2.87207 | −0.101416 | ||||||||
\(803\) | −25.0293 | + | 0.719435i | −0.883266 | + | 0.0253883i | ||||
\(804\) | −0.00629700 | −0.000222078 | ||||||||
\(805\) | −0.806051 | + | 0.585630i | −0.0284096 | + | 0.0206408i | ||||
\(806\) | −1.78539 | − | 5.49486i | −0.0628876 | − | 0.193548i | ||||
\(807\) | −2.27595 | + | 7.00464i | −0.0801171 | + | 0.246575i | ||||
\(808\) | 19.9993 | + | 14.5303i | 0.703573 | + | 0.511176i | ||||
\(809\) | 9.97535 | + | 7.24751i | 0.350715 | + | 0.254809i | 0.749169 | − | 0.662379i | \(-0.230453\pi\) |
−0.398454 | + | 0.917188i | \(0.630453\pi\) | |||||||
\(810\) | −0.402474 | + | 1.23869i | −0.0141415 | + | 0.0435231i | ||||
\(811\) | 15.4332 | + | 47.4984i | 0.541932 | + | 1.66789i | 0.728176 | + | 0.685390i | \(0.240368\pi\) |
−0.186244 | + | 0.982503i | \(0.559632\pi\) | |||||||
\(812\) | −1.61802 | + | 1.17556i | −0.0567814 | + | 0.0412541i | ||||
\(813\) | −6.44568 | −0.226060 | ||||||||
\(814\) | 45.7137 | − | 35.2633i | 1.60226 | − | 1.23598i | ||||
\(815\) | 1.10263 | 0.0386234 | ||||||||
\(816\) | −14.3371 | + | 10.4165i | −0.501899 | + | 0.364651i | ||||
\(817\) | −0.262745 | − | 0.808645i | −0.00919228 | − | 0.0282909i | ||||
\(818\) | −12.3769 | + | 38.0921i | −0.432748 | + | 1.33186i | ||||
\(819\) | −0.248424 | − | 0.180491i | −0.00868064 | − | 0.00630686i | ||||
\(820\) | −6.56357 | − | 4.76872i | −0.229210 | − | 0.166531i | ||||
\(821\) | 2.95508 | − | 9.09479i | 0.103133 | − | 0.317410i | −0.886155 | − | 0.463389i | \(-0.846633\pi\) |
0.989288 | + | 0.145979i | \(0.0466332\pi\) | |||||||
\(822\) | −1.07184 | − | 3.29878i | −0.0373847 | − | 0.115058i | ||||
\(823\) | 6.30685 | − | 4.58220i | 0.219843 | − | 0.159725i | −0.472413 | − | 0.881377i | \(-0.656617\pi\) |
0.692256 | + | 0.721652i | \(0.256617\pi\) | |||||||
\(824\) | 9.11304 | 0.317468 | ||||||||
\(825\) | 12.0418 | + | 8.23089i | 0.419243 | + | 0.286563i | ||||
\(826\) | 2.26373 | 0.0787654 | ||||||||
\(827\) | −29.1094 | + | 21.1492i | −1.01223 | + | 0.735430i | −0.964676 | − | 0.263438i | \(-0.915143\pi\) |
−0.0475565 | + | 0.998869i | \(0.515143\pi\) | |||||||
\(828\) | −1.05592 | − | 3.24979i | −0.0366957 | − | 0.112938i | ||||
\(829\) | 7.95549 | − | 24.4845i | 0.276306 | − | 0.850381i | −0.712565 | − | 0.701606i | \(-0.752467\pi\) |
0.988871 | − | 0.148776i | \(-0.0475332\pi\) | |||||||
\(830\) | 18.2042 | + | 13.2261i | 0.631876 | + | 0.459085i | ||||
\(831\) | −7.28194 | − | 5.29064i | −0.252608 | − | 0.183530i | ||||
\(832\) | 0.805205 | − | 2.47817i | 0.0279155 | − | 0.0859150i | ||||
\(833\) | −7.61441 | − | 23.4347i | −0.263824 | − | 0.811966i | ||||
\(834\) | −20.6142 | + | 14.9771i | −0.713810 | + | 0.518613i | ||||
\(835\) | 2.52762 | 0.0874718 | ||||||||
\(836\) | −1.81700 | − | 5.08967i | −0.0628422 | − | 0.176030i | ||||
\(837\) | 3.44225 | 0.118981 | ||||||||
\(838\) | −21.4345 | + | 15.5731i | −0.740444 | + | 0.537964i | ||||
\(839\) | −4.49487 | − | 13.8338i | −0.155180 | − | 0.477595i | 0.842999 | − | 0.537915i | \(-0.180788\pi\) |
−0.998179 | + | 0.0603199i | \(0.980788\pi\) | |||||||
\(840\) | −0.146180 | + | 0.449894i | −0.00504367 | + | 0.0155228i | ||||
\(841\) | −27.9293 | − | 20.2918i | −0.963078 | − | 0.699717i | ||||
\(842\) | −1.00096 | − | 0.727243i | −0.0344955 | − | 0.0250624i | ||||
\(843\) | 3.60902 | − | 11.1074i | 0.124301 | − | 0.382560i | ||||
\(844\) | −5.79902 | − | 17.8476i | −0.199611 | − | 0.614338i | ||||
\(845\) | 0.627776 | − | 0.456106i | 0.0215962 | − | 0.0156905i | ||||
\(846\) | 12.1198 | 0.416687 | ||||||||
\(847\) | 1.22658 | + | 3.14718i | 0.0421459 | + | 0.108138i | ||||
\(848\) | −26.7188 | −0.917526 | ||||||||
\(849\) | 9.30499 | − | 6.76047i | 0.319346 | − | 0.232019i | ||||
\(850\) | −8.13914 | − | 25.0497i | −0.279170 | − | 0.859198i | ||||
\(851\) | −13.4009 | + | 41.2436i | −0.459376 | + | 1.41381i | ||||
\(852\) | −7.70456 | − | 5.59769i | −0.263954 | − | 0.191774i | ||||
\(853\) | 3.17471 | + | 2.30656i | 0.108700 | + | 0.0789751i | 0.640807 | − | 0.767702i | \(-0.278600\pi\) |
−0.532107 | + | 0.846677i | \(0.678600\pi\) | |||||||
\(854\) | 0.637143 | − | 1.96092i | 0.0218026 | − | 0.0671015i | ||||
\(855\) | −0.478128 | − | 1.47153i | −0.0163516 | − | 0.0503251i | ||||
\(856\) | 7.23735 | − | 5.25824i | 0.247367 | − | 0.179723i | ||||
\(857\) | 22.1704 | 0.757327 | 0.378663 | − | 0.925534i | \(-0.376384\pi\) | ||||
0.378663 | + | 0.925534i | \(0.376384\pi\) | |||||||
\(858\) | 1.87164 | + | 5.24272i | 0.0638967 | + | 0.178984i | ||||
\(859\) | −41.2926 | −1.40888 | −0.704442 | − | 0.709762i | \(-0.748803\pi\) | ||||
−0.704442 | + | 0.709762i | \(0.748803\pi\) | |||||||
\(860\) | −0.218761 | + | 0.158939i | −0.00745967 | + | 0.00541977i | ||||
\(861\) | 1.21402 | + | 3.73638i | 0.0413738 | + | 0.127336i | ||||
\(862\) | 15.0615 | − | 46.3546i | 0.512998 | − | 1.57884i | ||||
\(863\) | −3.09399 | − | 2.24791i | −0.105321 | − | 0.0765199i | 0.533878 | − | 0.845561i | \(-0.320734\pi\) |
−0.639199 | + | 0.769041i | \(0.720734\pi\) | |||||||
\(864\) | −3.53186 | − | 2.56604i | −0.120156 | − | 0.0872986i | ||||
\(865\) | −2.94318 | + | 9.05817i | −0.100071 | + | 0.307987i | ||||
\(866\) | 3.00272 | + | 9.24142i | 0.102037 | + | 0.314036i | ||||
\(867\) | −3.45301 | + | 2.50876i | −0.117270 | + | 0.0852019i | ||||
\(868\) | −0.863784 | −0.0293187 | ||||||||
\(869\) | 30.9298 | + | 21.1413i | 1.04922 | + | 0.717169i | ||||
\(870\) | 10.3805 | 0.351933 | ||||||||
\(871\) | −0.00623397 | + | 0.00452924i | −0.000211230 | + | 0.000153468i | ||||
\(872\) | −8.67615 | − | 26.7025i | −0.293812 | − | 0.904259i | ||||
\(873\) | 2.64313 | − | 8.13473i | 0.0894565 | − | 0.275319i | ||||
\(874\) | 11.3215 | + | 8.22552i | 0.382954 | + | 0.278232i | ||||
\(875\) | −1.81163 | − | 1.31623i | −0.0612444 | − | 0.0444966i | ||||
\(876\) | −1.90652 | + | 5.86767i | −0.0644153 | + | 0.198250i | ||||
\(877\) | −9.37478 | − | 28.8526i | −0.316564 | − | 0.974284i | −0.975106 | − | 0.221740i | \(-0.928827\pi\) |
0.658542 | − | 0.752544i | \(-0.271173\pi\) | |||||||
\(878\) | −33.0010 | + | 23.9766i | −1.11373 | + | 0.809173i | ||||
\(879\) | −7.00608 | −0.236309 | ||||||||
\(880\) | 10.1208 | − | 7.80712i | 0.341171 | − | 0.263178i | ||||
\(881\) | −0.995648 | −0.0335442 | −0.0167721 | − | 0.999859i | \(-0.505339\pi\) | ||||
−0.0167721 | + | 0.999859i | \(0.505339\pi\) | |||||||
\(882\) | 9.37723 | − | 6.81296i | 0.315748 | − | 0.229404i | ||||
\(883\) | 13.8362 | + | 42.5833i | 0.465624 | + | 1.43304i | 0.858196 | + | 0.513322i | \(0.171585\pi\) |
−0.392572 | + | 0.919721i | \(0.628415\pi\) | |||||||
\(884\) | 0.901063 | − | 2.77319i | 0.0303060 | − | 0.0932723i | ||||
\(885\) | −2.75731 | − | 2.00330i | −0.0926859 | − | 0.0673403i | ||||
\(886\) | 43.1767 | + | 31.3697i | 1.45055 | + | 1.05389i | ||||
\(887\) | 12.3998 | − | 38.1626i | 0.416343 | − | 1.28137i | −0.494700 | − | 0.869064i | \(-0.664722\pi\) |
0.911044 | − | 0.412310i | \(-0.135278\pi\) | |||||||
\(888\) | 6.36256 | + | 19.5819i | 0.213514 | + | 0.657127i | ||||
\(889\) | −2.94534 | + | 2.13992i | −0.0987837 | + | 0.0717705i | ||||
\(890\) | −7.68201 | −0.257502 | ||||||||
\(891\) | −3.31526 | + | 0.0952926i | −0.111065 | + | 0.00319242i | ||||
\(892\) | −8.21169 | −0.274948 | ||||||||
\(893\) | −11.6482 | + | 8.46291i | −0.389792 | + | 0.283200i | ||||
\(894\) | 9.44823 | + | 29.0787i | 0.315996 | + | 0.972536i | ||||
\(895\) | −4.16946 | + | 12.8323i | −0.139370 | + | 0.428935i | ||||
\(896\) | −3.25554 | − | 2.36529i | −0.108760 | − | 0.0790187i | ||||
\(897\) | −3.38282 | − | 2.45776i | −0.112949 | − | 0.0820624i | ||||
\(898\) | −5.84275 | + | 17.9821i | −0.194975 | + | 0.600072i | ||||
\(899\) | −8.47789 | − | 26.0923i | −0.282754 | − | 0.870226i | ||||
\(900\) | 2.90754 | − | 2.11245i | 0.0969182 | − | 0.0704152i | ||||
\(901\) | 19.1957 | 0.639502 | ||||||||
\(902\) | 20.0535 | − | 68.3405i | 0.667709 | − | 2.27549i | ||||
\(903\) | 0.130940 | 0.00435742 | ||||||||
\(904\) | 18.2350 | − | 13.2485i | 0.606488 | − | 0.440639i | ||||
\(905\) | 1.75921 | + | 5.41428i | 0.0584780 | + | 0.179977i | ||||
\(906\) | 1.18187 | − | 3.63743i | 0.0392651 | − | 0.120846i | ||||
\(907\) | 46.2080 | + | 33.5721i | 1.53431 | + | 1.11474i | 0.953780 | + | 0.300505i | \(0.0971553\pi\) |
0.580532 | + | 0.814238i | \(0.302845\pi\) | |||||||
\(908\) | 13.0693 | + | 9.49541i | 0.433720 | + | 0.315116i | ||||
\(909\) | 3.84785 | − | 11.8425i | 0.127625 | − | 0.392790i | ||||
\(910\) | −0.123587 | − | 0.380363i | −0.00409688 | − | 0.0126089i | ||||
\(911\) | 17.3726 | − | 12.6220i | 0.575582 | − | 0.418184i | −0.261547 | − | 0.965191i | \(-0.584233\pi\) |
0.837128 | + | 0.547006i | \(0.184233\pi\) | |||||||
\(912\) | 9.90312 | 0.327925 | ||||||||
\(913\) | −16.1336 | + | 54.9816i | −0.533943 | + | 1.81963i | ||||
\(914\) | −14.2406 | −0.471038 | ||||||||
\(915\) | −2.51139 | + | 1.82463i | −0.0830241 | + | 0.0603205i | ||||
\(916\) | −1.25063 | − | 3.84904i | −0.0413220 | − | 0.127176i | ||||
\(917\) | −0.254744 | + | 0.784022i | −0.00841239 | + | 0.0258907i | ||||
\(918\) | 4.84520 | + | 3.52025i | 0.159916 | + | 0.116185i | ||||
\(919\) | −31.0248 | − | 22.5408i | −1.02341 | − | 0.743553i | −0.0564332 | − | 0.998406i | \(-0.517973\pi\) |
−0.966980 | + | 0.254853i | \(0.917973\pi\) | |||||||
\(920\) | −1.99055 | + | 6.12627i | −0.0656263 | + | 0.201977i | ||||
\(921\) | −8.43933 | − | 25.9736i | −0.278085 | − | 0.855859i | ||||
\(922\) | −40.0826 | + | 29.1217i | −1.32005 | + | 0.959072i | ||||
\(923\) | −11.6537 | −0.383586 | ||||||||
\(924\) | 0.831917 | − | 0.0239124i | 0.0273681 | − | 0.000786659i | ||||
\(925\) | −45.6111 | −1.49968 | ||||||||
\(926\) | −20.6925 | + | 15.0340i | −0.679998 | + | 0.494047i | ||||
\(927\) | −1.41848 | − | 4.36565i | −0.0465891 | − | 0.143387i | ||||
\(928\) | −10.7521 | + | 33.0914i | −0.352953 | + | 1.08628i | ||||
\(929\) | −47.9260 | − | 34.8203i | −1.57240 | − | 1.14242i | −0.924809 | − | 0.380431i | \(-0.875776\pi\) |
−0.647593 | − | 0.761986i | \(-0.724224\pi\) | |||||||
\(930\) | 3.62706 | + | 2.63522i | 0.118936 | + | 0.0864122i | ||||
\(931\) | −4.25505 | + | 13.0957i | −0.139454 | + | 0.429194i | ||||
\(932\) | −3.26373 | − | 10.0447i | −0.106907 | − | 0.329026i | ||||
\(933\) | 10.7278 | − | 7.79421i | 0.351213 | − | 0.255171i | ||||
\(934\) | −22.2451 | −0.727882 | ||||||||
\(935\) | −7.27113 | + | 5.60892i | −0.237791 | + | 0.183431i | ||||
\(936\) | −1.98528 | −0.0648908 | ||||||||
\(937\) | −32.3622 | + | 23.5125i | −1.05723 | + | 0.768121i | −0.973573 | − | 0.228374i | \(-0.926659\pi\) |
−0.0836539 | + | 0.996495i | \(0.526659\pi\) | |||||||
\(938\) | 0.00122725 | + | 0.00377710i | 4.00712e−5 | + | 0.000123327i | ||||
\(939\) | −4.23450 | + | 13.0325i | −0.138188 | + | 0.425298i | ||||
\(940\) | 3.70440 | + | 2.69141i | 0.120824 | + | 0.0877840i | ||||
\(941\) | 1.11870 | + | 0.812785i | 0.0364687 | + | 0.0264960i | 0.605870 | − | 0.795563i | \(-0.292825\pi\) |
−0.569402 | + | 0.822059i | \(0.692825\pi\) | |||||||
\(942\) | 6.70279 | − | 20.6291i | 0.218389 | − | 0.672131i | ||||
\(943\) | 16.5315 | + | 50.8788i | 0.538340 | + | 1.65684i | ||||
\(944\) | 17.6480 | − | 12.8220i | 0.574394 | − | 0.417322i | ||||
\(945\) | 0.238278 | 0.00775117 | ||||||||
\(946\) | −1.95973 | − | 1.33953i | −0.0637164 | − | 0.0435517i | ||||
\(947\) | −7.84116 | −0.254803 | −0.127402 | − | 0.991851i | \(-0.540664\pi\) | ||||
−0.127402 | + | 0.991851i | \(0.540664\pi\) | |||||||
\(948\) | 7.46811 | − | 5.42590i | 0.242553 | − | 0.176225i | ||||
\(949\) | 2.33300 | + | 7.18023i | 0.0757323 | + | 0.233080i | ||||
\(950\) | −4.54828 | + | 13.9982i | −0.147566 | + | 0.454161i | ||||
\(951\) | 21.2833 | + | 15.4632i | 0.690159 | + | 0.501430i | ||||
\(952\) | 1.75979 | + | 1.27856i | 0.0570351 | + | 0.0414384i | ||||
\(953\) | 2.93875 | − | 9.04455i | 0.0951955 | − | 0.292982i | −0.892109 | − | 0.451820i | \(-0.850775\pi\) |
0.987305 | + | 0.158838i | \(0.0507749\pi\) | |||||||
\(954\) | 2.79029 | + | 8.58763i | 0.0903390 | + | 0.278035i | ||||
\(955\) | 14.6057 | − | 10.6117i | 0.472630 | − | 0.343386i | ||||
\(956\) | −7.07357 | −0.228776 | ||||||||
\(957\) | 8.88745 | + | 24.8950i | 0.287290 | + | 0.804741i | ||||
\(958\) | −4.02539 | −0.130054 | ||||||||
\(959\) | −0.513373 | + | 0.372987i | −0.0165777 | + | 0.0120444i | ||||
\(960\) | 0.624818 | + | 1.92299i | 0.0201659 | + | 0.0620643i | ||||
\(961\) | −5.91797 | + | 18.2136i | −0.190902 | + | 0.587536i | ||||
\(962\) | −14.0830 | − | 10.2319i | −0.454054 | − | 0.329889i | ||||
\(963\) | −3.64551 | − | 2.64862i | −0.117475 | − | 0.0853505i | ||||
\(964\) | −2.25377 | + | 6.93639i | −0.0725890 | + | 0.223406i | ||||
\(965\) | −5.88911 | − | 18.1248i | −0.189577 | − | 0.583458i | ||||
\(966\) | −1.74351 | + | 1.26673i | −0.0560965 | + | 0.0407565i | ||||
\(967\) | −29.1462 | −0.937277 | −0.468639 | − | 0.883390i | \(-0.655255\pi\) | ||||
−0.468639 | + | 0.883390i | \(0.655255\pi\) | |||||||
\(968\) | 18.3755 | + | 11.8001i | 0.590610 | + | 0.379269i | ||||
\(969\) | −7.11476 | −0.228559 | ||||||||
\(970\) | 9.01260 | − | 6.54804i | 0.289377 | − | 0.210245i | ||||
\(971\) | 5.81365 | + | 17.8926i | 0.186569 | + | 0.574200i | 0.999972 | − | 0.00750047i | \(-0.00238750\pi\) |
−0.813403 | + | 0.581701i | \(0.802387\pi\) | |||||||
\(972\) | −0.252528 | + | 0.777201i | −0.00809983 | + | 0.0249287i | ||||
\(973\) | 3.77132 | + | 2.74002i | 0.120903 | + | 0.0878411i | ||||
\(974\) | 52.8324 | + | 38.3850i | 1.69286 | + | 1.22993i | ||||
\(975\) | 1.35901 | − | 4.18262i | 0.0435233 | − | 0.133951i | ||||
\(976\) | −6.13974 | − | 18.8962i | −0.196528 | − | 0.604852i | ||||
\(977\) | −31.8476 | + | 23.1387i | −1.01890 | + | 0.740271i | −0.966056 | − | 0.258332i | \(-0.916827\pi\) |
−0.0528396 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(978\) | 2.38501 | 0.0762642 | ||||||||
\(979\) | −6.57707 | − | 18.4233i | −0.210204 | − | 0.588811i | ||||
\(980\) | 4.37907 | 0.139884 | ||||||||
\(981\) | −11.4415 | + | 8.31271i | −0.365298 | + | 0.265404i | ||||
\(982\) | 1.90191 | + | 5.85347i | 0.0606923 | + | 0.186792i | ||||
\(983\) | −1.02851 | + | 3.16542i | −0.0328043 | + | 0.100961i | −0.966118 | − | 0.258101i | \(-0.916903\pi\) |
0.933314 | + | 0.359062i | \(0.116903\pi\) | |||||||
\(984\) | 20.5488 | + | 14.9296i | 0.655073 | + | 0.475938i | ||||
\(985\) | 10.7028 | + | 7.77605i | 0.341020 | + | 0.247766i | ||||
\(986\) | 14.7503 | − | 45.3967i | 0.469745 | − | 1.44573i | ||||
\(987\) | −0.685181 | − | 2.10877i | −0.0218095 | − | 0.0671229i | ||||
\(988\) | −1.31825 | + | 0.957767i | −0.0419392 | + | 0.0304706i | ||||
\(989\) | 1.78303 | 0.0566971 | ||||||||
\(990\) | −3.56621 | − | 2.43759i | −0.113342 | − | 0.0774717i | ||||
\(991\) | −15.7573 | −0.500546 | −0.250273 | − | 0.968175i | \(-0.580520\pi\) | ||||
−0.250273 | + | 0.968175i | \(0.580520\pi\) | |||||||
\(992\) | −12.1575 | + | 8.83295i | −0.386001 | + | 0.280446i | ||||
\(993\) | 3.62321 | + | 11.1511i | 0.114979 | + | 0.353869i | ||||
\(994\) | −1.85605 | + | 5.71234i | −0.0588704 | + | 0.181184i | ||||
\(995\) | 8.46864 | + | 6.15283i | 0.268474 | + | 0.195058i | ||||
\(996\) | 11.4220 | + | 8.29856i | 0.361920 | + | 0.262950i | ||||
\(997\) | −2.94253 | + | 9.05617i | −0.0931908 | + | 0.286812i | −0.986778 | − | 0.162078i | \(-0.948180\pi\) |
0.893587 | + | 0.448890i | \(0.148180\pi\) | |||||||
\(998\) | 9.50249 | + | 29.2457i | 0.300796 | + | 0.925755i | ||||
\(999\) | 8.39047 | − | 6.09603i | 0.265463 | − | 0.192870i |
(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 | 429.2.n.c.157.3 | ✓ | 28 | |
11.2 | odd | 10 | 4719.2.a.bo.1.5 | 14 | |||
11.4 | even | 5 | inner | 429.2.n.c.235.3 | yes | 28 | |
11.9 | even | 5 | 4719.2.a.bp.1.10 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.c.157.3 | ✓ | 28 | 1.1 | even | 1 | trivial | |
429.2.n.c.235.3 | yes | 28 | 11.4 | even | 5 | inner | |
4719.2.a.bo.1.5 | 14 | 11.2 | odd | 10 | |||
4719.2.a.bp.1.10 | 14 | 11.9 | even | 5 |