Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,3,Mod(3,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.3");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.435968422976\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(1.40680 + 0.144584i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.3 |
Dual form | 16.3.f.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.55139 | − | 1.26222i | −0.775694 | − | 0.631109i | ||||
\(3\) | 2.10278 | − | 2.10278i | 0.700925 | − | 0.700925i | −0.263684 | − | 0.964609i | \(-0.584938\pi\) |
0.964609 | + | 0.263684i | \(0.0849376\pi\) | |||||||
\(4\) | 0.813607 | + | 3.91638i | 0.203402 | + | 0.979095i | ||||
\(5\) | −4.62721 | + | 4.62721i | −0.925443 | + | 0.925443i | −0.997407 | − | 0.0719646i | \(-0.977073\pi\) |
0.0719646 | + | 0.997407i | \(0.477073\pi\) | |||||||
\(6\) | −5.91638 | + | 0.608056i | −0.986064 | + | 0.101343i | ||||
\(7\) | 3.04888 | 0.435554 | 0.217777 | − | 0.975999i | \(-0.430119\pi\) | ||||
0.217777 | + | 0.975999i | \(0.430119\pi\) | |||||||
\(8\) | 3.68111 | − | 7.10278i | 0.460139 | − | 0.887847i | ||||
\(9\) | 0.156674i | 0.0174082i | ||||||||
\(10\) | 13.0192 | − | 1.33804i | 1.30192 | − | 0.133804i | ||||
\(11\) | −9.15165 | − | 9.15165i | −0.831968 | − | 0.831968i | 0.155818 | − | 0.987786i | \(-0.450199\pi\) |
−0.987786 | + | 0.155818i | \(0.950199\pi\) | |||||||
\(12\) | 9.94610 | + | 6.52444i | 0.828842 | + | 0.543703i | ||||
\(13\) | −5.78389 | − | 5.78389i | −0.444914 | − | 0.444914i | 0.448745 | − | 0.893660i | \(-0.351871\pi\) |
−0.893660 | + | 0.448745i | \(0.851871\pi\) | |||||||
\(14\) | −4.72999 | − | 3.84835i | −0.337856 | − | 0.274882i | ||||
\(15\) | 19.4600i | 1.29733i | ||||||||
\(16\) | −14.6761 | + | 6.37279i | −0.917256 | + | 0.398299i | ||||
\(17\) | 17.6655 | 1.03915 | 0.519574 | − | 0.854425i | \(-0.326091\pi\) | ||||
0.519574 | + | 0.854425i | \(0.326091\pi\) | |||||||
\(18\) | 0.197757 | − | 0.243062i | 0.0109865 | − | 0.0135035i | ||||
\(19\) | −1.15165 | + | 1.15165i | −0.0606132 | + | 0.0606132i | −0.736764 | − | 0.676150i | \(-0.763647\pi\) |
0.676150 | + | 0.736764i | \(0.263647\pi\) | |||||||
\(20\) | −21.8867 | − | 14.3572i | −1.09433 | − | 0.717860i | ||||
\(21\) | 6.41110 | − | 6.41110i | 0.305290 | − | 0.305290i | ||||
\(22\) | 2.64637 | + | 25.7491i | 0.120290 | + | 1.17042i | ||||
\(23\) | −3.45998 | −0.150434 | −0.0752169 | − | 0.997167i | \(-0.523965\pi\) | ||||
−0.0752169 | + | 0.997167i | \(0.523965\pi\) | |||||||
\(24\) | −7.19499 | − | 22.6761i | −0.299791 | − | 0.944837i | ||||
\(25\) | − | 17.8222i | − | 0.712888i | ||||||
\(26\) | 1.67252 | + | 16.2736i | 0.0643276 | + | 0.625907i | ||||
\(27\) | 19.2544 | + | 19.2544i | 0.713127 | + | 0.713127i | ||||
\(28\) | 2.48059 | + | 11.9406i | 0.0885923 | + | 0.426449i | ||||
\(29\) | 12.1950 | + | 12.1950i | 0.420517 | + | 0.420517i | 0.885382 | − | 0.464865i | \(-0.153897\pi\) |
−0.464865 | + | 0.885382i | \(0.653897\pi\) | |||||||
\(30\) | 24.5628 | − | 30.1900i | 0.818758 | − | 1.00633i | ||||
\(31\) | − | 38.5089i | − | 1.24222i | −0.783723 | − | 0.621111i | \(-0.786682\pi\) | ||
0.783723 | − | 0.621111i | \(-0.213318\pi\) | |||||||
\(32\) | 30.8122 | + | 8.63778i | 0.962880 | + | 0.269930i | ||||
\(33\) | −38.4877 | −1.16629 | ||||||||
\(34\) | −27.4061 | − | 22.2978i | −0.806061 | − | 0.655817i | ||||
\(35\) | −14.1078 | + | 14.1078i | −0.403080 | + | 0.403080i | ||||
\(36\) | −0.613596 | + | 0.127471i | −0.0170443 | + | 0.00354086i | ||||
\(37\) | −0.0972356 | + | 0.0972356i | −0.00262799 | + | 0.00262799i | −0.708420 | − | 0.705792i | \(-0.750592\pi\) |
0.705792 | + | 0.708420i | \(0.250592\pi\) | |||||||
\(38\) | 3.24029 | − | 0.333021i | 0.0852709 | − | 0.00876372i | ||||
\(39\) | −24.3244 | −0.623703 | ||||||||
\(40\) | 15.8328 | + | 49.8993i | 0.395819 | + | 1.24748i | ||||
\(41\) | 51.5266i | 1.25675i | 0.777912 | + | 0.628373i | \(0.216279\pi\) | ||||
−0.777912 | + | 0.628373i | \(0.783721\pi\) | |||||||
\(42\) | −18.0383 | + | 1.85389i | −0.429484 | + | 0.0441402i | ||||
\(43\) | −1.70172 | − | 1.70172i | −0.0395749 | − | 0.0395749i | 0.687042 | − | 0.726617i | \(-0.258909\pi\) |
−0.726617 | + | 0.687042i | \(0.758909\pi\) | |||||||
\(44\) | 28.3955 | − | 43.2872i | 0.645353 | − | 0.983800i | ||||
\(45\) | −0.724965 | − | 0.724965i | −0.0161103 | − | 0.0161103i | ||||
\(46\) | 5.36776 | + | 4.36725i | 0.116691 | + | 0.0949402i | ||||
\(47\) | − | 24.1533i | − | 0.513899i | −0.966425 | − | 0.256949i | \(-0.917283\pi\) | ||
0.966425 | − | 0.256949i | \(-0.0827174\pi\) | |||||||
\(48\) | −17.4600 | + | 44.2611i | −0.363750 | + | 0.922105i | ||||
\(49\) | −39.7044 | −0.810293 | ||||||||
\(50\) | −22.4955 | + | 27.6491i | −0.449910 | + | 0.552983i | ||||
\(51\) | 37.1466 | − | 37.1466i | 0.728365 | − | 0.728365i | ||||
\(52\) | 17.9461 | − | 27.3577i | 0.345117 | − | 0.526110i | ||||
\(53\) | 27.0383 | − | 27.0383i | 0.510157 | − | 0.510157i | −0.404418 | − | 0.914574i | \(-0.632526\pi\) |
0.914574 | + | 0.404418i | \(0.132526\pi\) | |||||||
\(54\) | −5.56777 | − | 54.1744i | −0.103107 | − | 1.00323i | ||||
\(55\) | 84.6933 | 1.53988 | ||||||||
\(56\) | 11.2233 | − | 21.6555i | 0.200415 | − | 0.386705i | ||||
\(57\) | 4.84333i | 0.0849706i | ||||||||
\(58\) | −3.52641 | − | 34.3119i | −0.0608001 | − | 0.591584i | ||||
\(59\) | 19.5939 | + | 19.5939i | 0.332100 | + | 0.332100i | 0.853384 | − | 0.521283i | \(-0.174547\pi\) |
−0.521283 | + | 0.853384i | \(0.674547\pi\) | |||||||
\(60\) | −76.2127 | + | 15.8328i | −1.27021 | + | 0.263879i | ||||
\(61\) | 16.7250 | + | 16.7250i | 0.274180 | + | 0.274180i | 0.830780 | − | 0.556601i | \(-0.187895\pi\) |
−0.556601 | + | 0.830780i | \(0.687895\pi\) | |||||||
\(62\) | −48.6066 | + | 59.7422i | −0.783977 | + | 0.963583i | ||||
\(63\) | 0.477680i | 0.00758222i | ||||||||
\(64\) | −36.8988 | − | 52.2922i | −0.576544 | − | 0.817066i | ||||
\(65\) | 53.5266 | 0.823485 | ||||||||
\(66\) | 59.7094 | + | 48.5799i | 0.904688 | + | 0.736060i | ||||
\(67\) | −75.8560 | + | 75.8560i | −1.13218 | + | 1.13218i | −0.142365 | + | 0.989814i | \(0.545471\pi\) |
−0.989814 | + | 0.142365i | \(0.954529\pi\) | |||||||
\(68\) | 14.3728 | + | 69.1849i | 0.211365 | + | 1.01743i | ||||
\(69\) | −7.27555 | + | 7.27555i | −0.105443 | + | 0.105443i | ||||
\(70\) | 39.6938 | − | 4.07953i | 0.567054 | − | 0.0582790i | ||||
\(71\) | −134.749 | −1.89787 | −0.948935 | − | 0.315471i | \(-0.897837\pi\) | ||||
−0.948935 | + | 0.315471i | \(0.897837\pi\) | |||||||
\(72\) | 1.11282 | + | 0.576735i | 0.0154559 | + | 0.00801021i | ||||
\(73\) | − | 112.210i | − | 1.53712i | −0.639777 | − | 0.768560i | \(-0.720974\pi\) | ||
0.639777 | − | 0.768560i | \(-0.279026\pi\) | |||||||
\(74\) | 0.273583 | − | 0.0281175i | 0.00369706 | − | 0.000379966i | ||||
\(75\) | −37.4761 | − | 37.4761i | −0.499681 | − | 0.499681i | ||||
\(76\) | −5.44730 | − | 3.57331i | −0.0716749 | − | 0.0470173i | ||||
\(77\) | −27.9022 | − | 27.9022i | −0.362367 | − | 0.362367i | ||||
\(78\) | 37.7366 | + | 30.7028i | 0.483803 | + | 0.393625i | ||||
\(79\) | 135.915i | 1.72045i | 0.509915 | + | 0.860225i | \(0.329677\pi\) | ||||
−0.509915 | + | 0.860225i | \(0.670323\pi\) | |||||||
\(80\) | 38.4211 | − | 97.3976i | 0.480264 | − | 1.21747i | ||||
\(81\) | 79.5654 | 0.982289 | ||||||||
\(82\) | 65.0378 | − | 79.9377i | 0.793144 | − | 0.974849i | ||||
\(83\) | 74.9250 | − | 74.9250i | 0.902711 | − | 0.902711i | −0.0929594 | − | 0.995670i | \(-0.529633\pi\) |
0.995670 | + | 0.0929594i | \(0.0296327\pi\) | |||||||
\(84\) | 30.3244 | + | 19.8922i | 0.361005 | + | 0.236812i | ||||
\(85\) | −81.7422 | + | 81.7422i | −0.961672 | + | 0.961672i | ||||
\(86\) | 0.492084 | + | 4.78797i | 0.00572191 | + | 0.0556741i | ||||
\(87\) | 51.2866 | 0.589501 | ||||||||
\(88\) | −98.6904 | + | 31.3139i | −1.12148 | + | 0.355839i | ||||
\(89\) | 31.4278i | 0.353121i | 0.984290 | + | 0.176561i | \(0.0564971\pi\) | ||||
−0.984290 | + | 0.176561i | \(0.943503\pi\) | |||||||
\(90\) | 0.209637 | + | 2.03977i | 0.00232930 | + | 0.0226641i | ||||
\(91\) | −17.6344 | − | 17.6344i | −0.193784 | − | 0.193784i | ||||
\(92\) | −2.81506 | − | 13.5506i | −0.0305985 | − | 0.147289i | ||||
\(93\) | −80.9755 | − | 80.9755i | −0.870704 | − | 0.870704i | ||||
\(94\) | −30.4867 | + | 37.4711i | −0.324327 | + | 0.398628i | ||||
\(95\) | − | 10.6579i | − | 0.112188i | ||||||
\(96\) | 82.9543 | − | 46.6277i | 0.864108 | − | 0.485706i | ||||
\(97\) | 31.5456 | 0.325213 | 0.162606 | − | 0.986691i | \(-0.448010\pi\) | ||||
0.162606 | + | 0.986691i | \(0.448010\pi\) | |||||||
\(98\) | 61.5968 | + | 50.1156i | 0.628539 | + | 0.511384i | ||||
\(99\) | 1.43383 | − | 1.43383i | 0.0144831 | − | 0.0144831i | ||||
\(100\) | 69.7985 | − | 14.5003i | 0.697985 | − | 0.145003i | ||||
\(101\) | 27.4695 | − | 27.4695i | 0.271975 | − | 0.271975i | −0.557920 | − | 0.829895i | \(-0.688400\pi\) |
0.829895 | + | 0.557920i | \(0.188400\pi\) | |||||||
\(102\) | −104.516 | + | 10.7416i | −1.02467 | + | 0.105310i | ||||
\(103\) | 102.882 | 0.998854 | 0.499427 | − | 0.866356i | \(-0.333544\pi\) | ||||
0.499427 | + | 0.866356i | \(0.333544\pi\) | |||||||
\(104\) | −62.3728 | + | 19.7905i | −0.599738 | + | 0.190293i | ||||
\(105\) | 59.3311i | 0.565058i | ||||||||
\(106\) | −76.0752 | + | 7.81863i | −0.717690 | + | 0.0737607i | ||||
\(107\) | −79.6605 | − | 79.6605i | −0.744491 | − | 0.744491i | 0.228948 | − | 0.973439i | \(-0.426471\pi\) |
−0.973439 | + | 0.228948i | \(0.926471\pi\) | |||||||
\(108\) | −59.7422 | + | 91.0732i | −0.553168 | + | 0.843270i | ||||
\(109\) | 125.408 | + | 125.408i | 1.15053 | + | 1.15053i | 0.986446 | + | 0.164088i | \(0.0524682\pi\) |
0.164088 | + | 0.986446i | \(0.447532\pi\) | |||||||
\(110\) | −131.392 | − | 106.901i | −1.19447 | − | 0.971831i | ||||
\(111\) | 0.408929i | 0.00368405i | ||||||||
\(112\) | −44.7456 | + | 19.4298i | −0.399514 | + | 0.173481i | ||||
\(113\) | −96.6199 | −0.855043 | −0.427521 | − | 0.904005i | \(-0.640613\pi\) | ||||
−0.427521 | + | 0.904005i | \(0.640613\pi\) | |||||||
\(114\) | 6.11334 | − | 7.51388i | 0.0536258 | − | 0.0659112i | ||||
\(115\) | 16.0100 | − | 16.0100i | 0.139218 | − | 0.139218i | ||||
\(116\) | −37.8383 | + | 57.6821i | −0.326192 | + | 0.497260i | ||||
\(117\) | 0.906186 | − | 0.906186i | 0.00774518 | − | 0.00774518i | ||||
\(118\) | −5.66595 | − | 55.1296i | −0.0480165 | − | 0.467200i | ||||
\(119\) | 53.8600 | 0.452605 | ||||||||
\(120\) | 138.220 | + | 71.6344i | 1.15183 | + | 0.596953i | ||||
\(121\) | 46.5054i | 0.384342i | ||||||||
\(122\) | −4.83633 | − | 47.0575i | −0.0396421 | − | 0.385717i | ||||
\(123\) | 108.349 | + | 108.349i | 0.880884 | + | 0.880884i | ||||
\(124\) | 150.815 | − | 31.3311i | 1.21625 | − | 0.252670i | ||||
\(125\) | −33.2132 | − | 33.2132i | −0.265706 | − | 0.265706i | ||||
\(126\) | 0.602937 | − | 0.741067i | 0.00478521 | − | 0.00588148i | ||||
\(127\) | − | 196.309i | − | 1.54574i | −0.634566 | − | 0.772868i | \(-0.718821\pi\) | ||
0.634566 | − | 0.772868i | \(-0.281179\pi\) | |||||||
\(128\) | −8.75986 | + | 127.700i | −0.0684364 | + | 0.997655i | ||||
\(129\) | −7.15667 | −0.0554781 | ||||||||
\(130\) | −83.0404 | − | 67.5622i | −0.638773 | − | 0.519709i | ||||
\(131\) | 17.9437 | − | 17.9437i | 0.136975 | − | 0.136975i | −0.635295 | − | 0.772270i | \(-0.719121\pi\) |
0.772270 | + | 0.635295i | \(0.219121\pi\) | |||||||
\(132\) | −31.3139 | − | 150.733i | −0.237226 | − | 1.14191i | ||||
\(133\) | −3.51124 | + | 3.51124i | −0.0264003 | + | 0.0264003i | ||||
\(134\) | 213.429 | − | 21.9352i | 1.59275 | − | 0.163695i | ||||
\(135\) | −178.189 | −1.31992 | ||||||||
\(136\) | 65.0288 | − | 125.474i | 0.478153 | − | 0.922605i | ||||
\(137\) | − | 51.7200i | − | 0.377518i | −0.982023 | − | 0.188759i | \(-0.939553\pi\) | ||
0.982023 | − | 0.188759i | \(-0.0604465\pi\) | |||||||
\(138\) | 20.4705 | − | 2.10386i | 0.148337 | − | 0.0152454i | ||||
\(139\) | −17.4640 | − | 17.4640i | −0.125640 | − | 0.125640i | 0.641491 | − | 0.767131i | \(-0.278316\pi\) |
−0.767131 | + | 0.641491i | \(0.778316\pi\) | |||||||
\(140\) | −66.7297 | − | 43.7733i | −0.476641 | − | 0.312667i | ||||
\(141\) | −50.7889 | − | 50.7889i | −0.360205 | − | 0.360205i | ||||
\(142\) | 209.048 | + | 170.082i | 1.47217 | + | 1.19776i | ||||
\(143\) | 105.864i | 0.740309i | ||||||||
\(144\) | −0.998451 | − | 2.29936i | −0.00693369 | − | 0.0159678i | ||||
\(145\) | −112.858 | −0.778328 | ||||||||
\(146\) | −141.633 | + | 174.081i | −0.970091 | + | 1.19233i | ||||
\(147\) | −83.4893 | + | 83.4893i | −0.567955 | + | 0.567955i | ||||
\(148\) | −0.459923 | − | 0.301700i | −0.00310759 | − | 0.00203851i | ||||
\(149\) | 11.9170 | − | 11.9170i | 0.0799802 | − | 0.0799802i | −0.665985 | − | 0.745965i | \(-0.731989\pi\) |
0.745965 | + | 0.665985i | \(0.231989\pi\) | |||||||
\(150\) | 10.8369 | + | 105.443i | 0.0722460 | + | 0.702953i | ||||
\(151\) | −132.548 | −0.877805 | −0.438902 | − | 0.898535i | \(-0.644633\pi\) | ||||
−0.438902 | + | 0.898535i | \(0.644633\pi\) | |||||||
\(152\) | 3.94056 | + | 12.4193i | 0.0259247 | + | 0.0817058i | ||||
\(153\) | 2.76773i | 0.0180898i | ||||||||
\(154\) | 8.06845 | + | 78.5059i | 0.0523925 | + | 0.509779i | ||||
\(155\) | 178.189 | + | 178.189i | 1.14960 | + | 1.14960i | ||||
\(156\) | −19.7905 | − | 95.2637i | −0.126862 | − | 0.610665i | ||||
\(157\) | 106.091 | + | 106.091i | 0.675742 | + | 0.675742i | 0.959034 | − | 0.283292i | \(-0.0914266\pi\) |
−0.283292 | + | 0.959034i | \(0.591427\pi\) | |||||||
\(158\) | 171.555 | − | 210.858i | 1.08579 | − | 1.33454i | ||||
\(159\) | − | 113.711i | − | 0.715163i | ||||||
\(160\) | −182.543 | + | 102.606i | −1.14090 | + | 0.641285i | ||||
\(161\) | −10.5490 | −0.0655220 | ||||||||
\(162\) | −123.437 | − | 100.429i | −0.761955 | − | 0.619932i | ||||
\(163\) | −105.577 | + | 105.577i | −0.647712 | + | 0.647712i | −0.952440 | − | 0.304728i | \(-0.901435\pi\) |
0.304728 | + | 0.952440i | \(0.401435\pi\) | |||||||
\(164\) | −201.798 | + | 41.9223i | −1.23047 | + | 0.255624i | ||||
\(165\) | 178.091 | − | 178.091i | 1.07934 | − | 1.07934i | ||||
\(166\) | −210.809 | + | 21.6659i | −1.26994 | + | 0.130518i | ||||
\(167\) | 111.591 | 0.668210 | 0.334105 | − | 0.942536i | \(-0.391566\pi\) | ||||
0.334105 | + | 0.942536i | \(0.391566\pi\) | |||||||
\(168\) | −21.9366 | − | 69.1366i | −0.130575 | − | 0.411527i | ||||
\(169\) | − | 102.093i | − | 0.604102i | ||||||
\(170\) | 229.990 | − | 23.6373i | 1.35288 | − | 0.139043i | ||||
\(171\) | −0.180434 | − | 0.180434i | −0.00105517 | − | 0.00105517i | ||||
\(172\) | 5.28006 | − | 8.04912i | 0.0306980 | − | 0.0467972i | ||||
\(173\) | 14.5363 | + | 14.5363i | 0.0840249 | + | 0.0840249i | 0.747870 | − | 0.663845i | \(-0.231077\pi\) |
−0.663845 | + | 0.747870i | \(0.731077\pi\) | |||||||
\(174\) | −79.5654 | − | 64.7350i | −0.457273 | − | 0.372040i | ||||
\(175\) | − | 54.3377i | − | 0.310501i | ||||||
\(176\) | 192.632 | + | 75.9889i | 1.09450 | + | 0.431755i | ||||
\(177\) | 82.4032 | 0.465555 | ||||||||
\(178\) | 39.6687 | − | 48.7567i | 0.222858 | − | 0.273914i | ||||
\(179\) | −19.7371 | + | 19.7371i | −0.110263 | + | 0.110263i | −0.760086 | − | 0.649823i | \(-0.774843\pi\) |
0.649823 | + | 0.760086i | \(0.274843\pi\) | |||||||
\(180\) | 2.24940 | − | 3.42907i | 0.0124967 | − | 0.0190504i | ||||
\(181\) | 168.153 | − | 168.153i | 0.929021 | − | 0.929021i | −0.0686221 | − | 0.997643i | \(-0.521860\pi\) |
0.997643 | + | 0.0686221i | \(0.0218603\pi\) | |||||||
\(182\) | 5.09930 | + | 49.6161i | 0.0280181 | + | 0.272616i | ||||
\(183\) | 70.3377 | 0.384359 | ||||||||
\(184\) | −12.7366 | + | 24.5754i | −0.0692204 | + | 0.133562i | ||||
\(185\) | − | 0.899859i | − | 0.00486410i | ||||||
\(186\) | 23.4156 | + | 227.833i | 0.125890 | + | 1.22491i | ||||
\(187\) | −161.669 | − | 161.669i | −0.864539 | − | 0.864539i | ||||
\(188\) | 94.5934 | − | 19.6512i | 0.503156 | − | 0.104528i | ||||
\(189\) | 58.7044 | + | 58.7044i | 0.310605 | + | 0.310605i | ||||
\(190\) | −13.4526 | + | 16.5345i | −0.0708030 | + | 0.0870236i | ||||
\(191\) | 196.309i | 1.02779i | 0.857852 | + | 0.513897i | \(0.171799\pi\) | ||||
−0.857852 | + | 0.513897i | \(0.828201\pi\) | |||||||
\(192\) | −187.549 | − | 32.3688i | −0.976816 | − | 0.168588i | ||||
\(193\) | −40.3699 | −0.209170 | −0.104585 | − | 0.994516i | \(-0.533351\pi\) | ||||
−0.104585 | + | 0.994516i | \(0.533351\pi\) | |||||||
\(194\) | −48.9395 | − | 39.8175i | −0.252265 | − | 0.205245i | ||||
\(195\) | 112.554 | − | 112.554i | 0.577202 | − | 0.577202i | ||||
\(196\) | −32.3037 | − | 155.497i | −0.164815 | − | 0.793354i | ||||
\(197\) | −230.578 | + | 230.578i | −1.17045 | + | 1.17045i | −0.188344 | + | 0.982103i | \(0.560312\pi\) |
−0.982103 | + | 0.188344i | \(0.939688\pi\) | |||||||
\(198\) | −4.03423 | + | 0.414618i | −0.0203749 | + | 0.00209403i | ||||
\(199\) | 61.5598 | 0.309346 | 0.154673 | − | 0.987966i | \(-0.450568\pi\) | ||||
0.154673 | + | 0.987966i | \(0.450568\pi\) | |||||||
\(200\) | −126.587 | − | 65.6055i | −0.632935 | − | 0.328028i | ||||
\(201\) | 319.016i | 1.58715i | ||||||||
\(202\) | −77.2884 | + | 7.94332i | −0.382616 | + | 0.0393234i | ||||
\(203\) | 37.1810 | + | 37.1810i | 0.183158 | + | 0.183158i | ||||
\(204\) | 175.703 | + | 115.258i | 0.861290 | + | 0.564988i | ||||
\(205\) | −238.424 | − | 238.424i | −1.16305 | − | 1.16305i | ||||
\(206\) | −159.610 | − | 129.860i | −0.774805 | − | 0.630386i | ||||
\(207\) | − | 0.542089i | − | 0.00261879i | ||||||
\(208\) | 121.744 | + | 48.0254i | 0.585309 | + | 0.230891i | ||||
\(209\) | 21.0790 | 0.100857 | ||||||||
\(210\) | 74.8888 | − | 92.0455i | 0.356613 | − | 0.438312i | ||||
\(211\) | 151.149 | − | 151.149i | 0.716346 | − | 0.716346i | −0.251509 | − | 0.967855i | \(-0.580927\pi\) |
0.967855 | + | 0.251509i | \(0.0809267\pi\) | |||||||
\(212\) | 127.891 | + | 83.8938i | 0.603259 | + | 0.395725i | ||||
\(213\) | −283.346 | + | 283.346i | −1.33026 | + | 1.33026i | ||||
\(214\) | 23.0353 | + | 224.133i | 0.107642 | + | 1.04735i | ||||
\(215\) | 15.7485 | 0.0732486 | ||||||||
\(216\) | 207.638 | − | 65.8822i | 0.961285 | − | 0.305010i | ||||
\(217\) | − | 117.409i | − | 0.541054i | ||||||
\(218\) | −36.2641 | − | 352.849i | −0.166349 | − | 1.61857i | ||||
\(219\) | −235.952 | − | 235.952i | −1.07741 | − | 1.07741i | ||||
\(220\) | 68.9070 | + | 331.691i | 0.313214 | + | 1.50769i | ||||
\(221\) | −102.175 | − | 102.175i | −0.462332 | − | 0.462332i | ||||
\(222\) | 0.516158 | − | 0.634407i | 0.00232504 | − | 0.00285769i | ||||
\(223\) | 115.527i | 0.518056i | 0.965870 | + | 0.259028i | \(0.0834022\pi\) | ||||
−0.965870 | + | 0.259028i | \(0.916598\pi\) | |||||||
\(224\) | 93.9424 | + | 26.3355i | 0.419386 | + | 0.117569i | ||||
\(225\) | 2.79228 | 0.0124101 | ||||||||
\(226\) | 149.895 | + | 121.955i | 0.663251 | + | 0.539626i | ||||
\(227\) | 25.2363 | − | 25.2363i | 0.111173 | − | 0.111173i | −0.649332 | − | 0.760505i | \(-0.724951\pi\) |
0.760505 | + | 0.649332i | \(0.224951\pi\) | |||||||
\(228\) | −18.9683 | + | 3.94056i | −0.0831944 | + | 0.0172832i | ||||
\(229\) | −155.318 | + | 155.318i | −0.678244 | + | 0.678244i | −0.959603 | − | 0.281359i | \(-0.909215\pi\) |
0.281359 | + | 0.959603i | \(0.409215\pi\) | |||||||
\(230\) | −45.0460 | + | 4.62960i | −0.195852 | + | 0.0201287i | ||||
\(231\) | −117.344 | −0.507984 | ||||||||
\(232\) | 131.509 | − | 41.7271i | 0.566851 | − | 0.179858i | ||||
\(233\) | − | 119.738i | − | 0.513899i | −0.966425 | − | 0.256949i | \(-0.917283\pi\) | ||
0.966425 | − | 0.256949i | \(-0.0827174\pi\) | |||||||
\(234\) | −2.54965 | + | 0.262040i | −0.0108959 | + | 0.00111983i | ||||
\(235\) | 111.762 | + | 111.762i | 0.475584 | + | 0.475584i | ||||
\(236\) | −60.7955 | + | 92.6790i | −0.257608 | + | 0.392708i | ||||
\(237\) | 285.800 | + | 285.800i | 1.20591 | + | 1.20591i | ||||
\(238\) | −83.5577 | − | 67.9831i | −0.351083 | − | 0.285643i | ||||
\(239\) | − | 245.409i | − | 1.02681i | −0.858145 | − | 0.513407i | \(-0.828383\pi\) | ||
0.858145 | − | 0.513407i | \(-0.171617\pi\) | |||||||
\(240\) | −124.014 | − | 285.596i | −0.516726 | − | 1.18998i | ||||
\(241\) | 431.216 | 1.78928 | 0.894639 | − | 0.446790i | \(-0.147433\pi\) | ||||
0.894639 | + | 0.446790i | \(0.147433\pi\) | |||||||
\(242\) | 58.7000 | − | 72.1479i | 0.242562 | − | 0.298132i | ||||
\(243\) | −5.98173 | + | 5.98173i | −0.0246162 | + | 0.0246162i | ||||
\(244\) | −51.8938 | + | 79.1089i | −0.212680 | + | 0.324217i | ||||
\(245\) | 183.721 | − | 183.721i | 0.749880 | − | 0.749880i | ||||
\(246\) | −31.3311 | − | 304.851i | −0.127362 | − | 1.23923i | ||||
\(247\) | 13.3220 | 0.0539354 | ||||||||
\(248\) | −273.520 | − | 141.755i | −1.10290 | − | 0.571594i | ||||
\(249\) | − | 315.101i | − | 1.26546i | ||||||
\(250\) | 9.60421 | + | 93.4489i | 0.0384169 | + | 0.373796i | ||||
\(251\) | −24.0171 | − | 24.0171i | −0.0956858 | − | 0.0956858i | 0.657643 | − | 0.753329i | \(-0.271553\pi\) |
−0.753329 | + | 0.657643i | \(0.771553\pi\) | |||||||
\(252\) | −1.87078 | + | 0.388644i | −0.00742372 | + | 0.00154224i | ||||
\(253\) | 31.6645 | + | 31.6645i | 0.125156 | + | 0.125156i | ||||
\(254\) | −247.784 | + | 304.551i | −0.975529 | + | 1.19902i | ||||
\(255\) | 343.771i | 1.34812i | ||||||||
\(256\) | 174.775 | − | 187.055i | 0.682716 | − | 0.730684i | ||||
\(257\) | −100.860 | −0.392450 | −0.196225 | − | 0.980559i | \(-0.562868\pi\) | ||||
−0.196225 | + | 0.980559i | \(0.562868\pi\) | |||||||
\(258\) | 11.1028 | + | 9.03329i | 0.0430340 | + | 0.0350128i | ||||
\(259\) | −0.296459 | + | 0.296459i | −0.00114463 | + | 0.00114463i | ||||
\(260\) | 43.5496 | + | 209.630i | 0.167498 | + | 0.806271i | ||||
\(261\) | −1.91064 | + | 1.91064i | −0.00732046 | + | 0.00732046i | ||||
\(262\) | −50.4865 | + | 5.18876i | −0.192697 | + | 0.0198044i | ||||
\(263\) | 216.776 | 0.824242 | 0.412121 | − | 0.911129i | \(-0.364788\pi\) | ||||
0.412121 | + | 0.911129i | \(0.364788\pi\) | |||||||
\(264\) | −141.678 | + | 273.370i | −0.536658 | + | 1.03549i | ||||
\(265\) | 250.224i | 0.944242i | ||||||||
\(266\) | 9.87925 | − | 1.01534i | 0.0371400 | − | 0.00381707i | ||||
\(267\) | 66.0855 | + | 66.0855i | 0.247511 | + | 0.247511i | ||||
\(268\) | −358.798 | − | 235.364i | −1.33880 | − | 0.878224i | ||||
\(269\) | −256.778 | − | 256.778i | −0.954567 | − | 0.954567i | 0.0444453 | − | 0.999012i | \(-0.485848\pi\) |
−0.999012 | + | 0.0444453i | \(0.985848\pi\) | |||||||
\(270\) | 276.440 | + | 224.913i | 1.02385 | + | 0.833012i | ||||
\(271\) | − | 12.8603i | − | 0.0474551i | −0.999718 | − | 0.0237275i | \(-0.992447\pi\) | ||
0.999718 | − | 0.0237275i | \(-0.00755342\pi\) | |||||||
\(272\) | −259.261 | + | 112.579i | −0.953165 | + | 0.413892i | ||||
\(273\) | −74.1622 | −0.271656 | ||||||||
\(274\) | −65.2820 | + | 80.2378i | −0.238255 | + | 0.292839i | ||||
\(275\) | −163.103 | + | 163.103i | −0.593100 | + | 0.593100i | ||||
\(276\) | −34.4133 | − | 22.5744i | −0.124686 | − | 0.0817913i | ||||
\(277\) | 77.1023 | − | 77.1023i | 0.278348 | − | 0.278348i | −0.554102 | − | 0.832449i | \(-0.686938\pi\) |
0.832449 | + | 0.554102i | \(0.186938\pi\) | |||||||
\(278\) | 5.05003 | + | 49.1367i | 0.0181656 | + | 0.176751i | ||||
\(279\) | 6.03334 | 0.0216249 | ||||||||
\(280\) | 48.2721 | + | 152.137i | 0.172400 | + | 0.543346i | ||||
\(281\) | 189.034i | 0.672719i | 0.941734 | + | 0.336360i | \(0.109196\pi\) | ||||
−0.941734 | + | 0.336360i | \(0.890804\pi\) | |||||||
\(282\) | 14.6865 | + | 142.900i | 0.0520799 | + | 0.506737i | ||||
\(283\) | −69.4317 | − | 69.4317i | −0.245342 | − | 0.245342i | 0.573714 | − | 0.819056i | \(-0.305502\pi\) |
−0.819056 | + | 0.573714i | \(0.805502\pi\) | |||||||
\(284\) | −109.632 | − | 527.728i | −0.386030 | − | 1.85820i | ||||
\(285\) | −22.4111 | − | 22.4111i | −0.0786354 | − | 0.0786354i | ||||
\(286\) | 133.624 | − | 164.236i | 0.467216 | − | 0.574253i | ||||
\(287\) | 157.098i | 0.547380i | ||||||||
\(288\) | −1.35332 | + | 4.82747i | −0.00469902 | + | 0.0167620i | ||||
\(289\) | 23.0708 | 0.0798298 | ||||||||
\(290\) | 175.086 | + | 142.451i | 0.603744 | + | 0.491210i | ||||
\(291\) | 66.3333 | − | 66.3333i | 0.227950 | − | 0.227950i | ||||
\(292\) | 439.456 | − | 91.2946i | 1.50499 | − | 0.312653i | ||||
\(293\) | 239.919 | − | 239.919i | 0.818837 | − | 0.818837i | −0.167103 | − | 0.985939i | \(-0.553441\pi\) |
0.985939 | + | 0.167103i | \(0.0534412\pi\) | |||||||
\(294\) | 234.906 | − | 24.1425i | 0.799000 | − | 0.0821173i | ||||
\(295\) | −181.331 | −0.614680 | ||||||||
\(296\) | 0.332707 | + | 1.04858i | 0.00112401 | + | 0.00354249i | ||||
\(297\) | − | 352.420i | − | 1.18660i | ||||||
\(298\) | −33.5299 | + | 3.44604i | −0.112516 | + | 0.0115639i | ||||
\(299\) | 20.0121 | + | 20.0121i | 0.0669301 | + | 0.0669301i | ||||
\(300\) | 116.280 | − | 177.261i | 0.387599 | − | 0.590871i | ||||
\(301\) | −5.18834 | − | 5.18834i | −0.0172370 | − | 0.0172370i | ||||
\(302\) | 205.634 | + | 167.305i | 0.680908 | + | 0.553991i | ||||
\(303\) | − | 115.524i | − | 0.381269i | ||||||
\(304\) | 9.56251 | − | 24.2410i | 0.0314556 | − | 0.0797400i | ||||
\(305\) | −154.780 | −0.507475 | ||||||||
\(306\) | 3.49348 | − | 4.29382i | 0.0114166 | − | 0.0140321i | ||||
\(307\) | −231.185 | + | 231.185i | −0.753046 | + | 0.753046i | −0.975046 | − | 0.222001i | \(-0.928741\pi\) |
0.222001 | + | 0.975046i | \(0.428741\pi\) | |||||||
\(308\) | 86.5744 | − | 131.977i | 0.281086 | − | 0.428498i | ||||
\(309\) | 216.338 | − | 216.338i | 0.700122 | − | 0.700122i | ||||
\(310\) | −51.5266 | − | 501.353i | −0.166215 | − | 1.61727i | ||||
\(311\) | −513.328 | −1.65057 | −0.825287 | − | 0.564714i | \(-0.808987\pi\) | ||||
−0.825287 | + | 0.564714i | \(0.808987\pi\) | |||||||
\(312\) | −89.5409 | + | 172.771i | −0.286990 | + | 0.553753i | ||||
\(313\) | 345.242i | 1.10301i | 0.834172 | + | 0.551504i | \(0.185946\pi\) | ||||
−0.834172 | + | 0.551504i | \(0.814054\pi\) | |||||||
\(314\) | −30.6783 | − | 298.500i | −0.0977016 | − | 0.950635i | ||||
\(315\) | −2.21033 | − | 2.21033i | −0.00701691 | − | 0.00701691i | ||||
\(316\) | −532.297 | + | 110.582i | −1.68448 | + | 0.349942i | ||||
\(317\) | 345.632 | + | 345.632i | 1.09032 | + | 1.09032i | 0.995494 | + | 0.0948290i | \(0.0302304\pi\) |
0.0948290 | + | 0.995494i | \(0.469770\pi\) | |||||||
\(318\) | −143.528 | + | 176.410i | −0.451346 | + | 0.554748i | ||||
\(319\) | − | 223.209i | − | 0.699713i | ||||||
\(320\) | 412.706 | + | 71.2285i | 1.28971 | + | 0.222589i | ||||
\(321\) | −335.016 | −1.04366 | ||||||||
\(322\) | 16.3656 | + | 13.3152i | 0.0508250 | + | 0.0413515i | ||||
\(323\) | −20.3445 | + | 20.3445i | −0.0629861 | + | 0.0629861i | ||||
\(324\) | 64.7349 | + | 311.608i | 0.199799 | + | 0.961754i | ||||
\(325\) | −103.082 | + | 103.082i | −0.317174 | + | 0.317174i | ||||
\(326\) | 297.052 | − | 30.5296i | 0.911203 | − | 0.0936489i | ||||
\(327\) | 527.410 | 1.61288 | ||||||||
\(328\) | 365.982 | + | 189.675i | 1.11580 | + | 0.578278i | ||||
\(329\) | − | 73.6403i | − | 0.223831i | ||||||
\(330\) | −501.078 | + | 51.4983i | −1.51842 | + | 0.156055i | ||||
\(331\) | 425.968 | + | 425.968i | 1.28691 | + | 1.28691i | 0.936652 | + | 0.350261i | \(0.113907\pi\) |
0.350261 | + | 0.936652i | \(0.386093\pi\) | |||||||
\(332\) | 354.394 | + | 232.475i | 1.06745 | + | 0.700227i | ||||
\(333\) | −0.0152343 | − | 0.0152343i | −4.57487e−5 | − | 4.57487e-5i | ||||
\(334\) | −173.121 | − | 140.852i | −0.518326 | − | 0.421714i | ||||
\(335\) | − | 702.004i | − | 2.09553i | ||||||
\(336\) | −53.2333 | + | 134.946i | −0.158432 | + | 0.401626i | ||||
\(337\) | −467.297 | −1.38664 | −0.693319 | − | 0.720631i | \(-0.743852\pi\) | ||||
−0.693319 | + | 0.720631i | \(0.743852\pi\) | |||||||
\(338\) | −128.864 | + | 158.386i | −0.381255 | + | 0.468598i | ||||
\(339\) | −203.170 | + | 203.170i | −0.599321 | + | 0.599321i | ||||
\(340\) | −386.639 | − | 253.628i | −1.13717 | − | 0.745963i | ||||
\(341\) | −352.420 | + | 352.420i | −1.03349 | + | 1.03349i | ||||
\(342\) | 0.0521758 | + | 0.507670i | 0.000152561 | + | 0.00148442i | ||||
\(343\) | −270.449 | −0.788480 | ||||||||
\(344\) | −18.3512 | + | 5.82272i | −0.0533464 | + | 0.0169265i | ||||
\(345\) | − | 67.3311i | − | 0.195162i | ||||||
\(346\) | −4.20344 | − | 40.8994i | −0.0121487 | − | 0.118206i | ||||
\(347\) | −22.0463 | − | 22.0463i | −0.0635341 | − | 0.0635341i | 0.674626 | − | 0.738160i | \(-0.264305\pi\) |
−0.738160 | + | 0.674626i | \(0.764305\pi\) | |||||||
\(348\) | 41.7271 | + | 200.858i | 0.119906 | + | 0.577178i | ||||
\(349\) | −158.622 | − | 158.622i | −0.454506 | − | 0.454506i | 0.442341 | − | 0.896847i | \(-0.354148\pi\) |
−0.896847 | + | 0.442341i | \(0.854148\pi\) | |||||||
\(350\) | −68.5860 | + | 84.2988i | −0.195960 | + | 0.240854i | ||||
\(351\) | − | 222.731i | − | 0.634561i | ||||||
\(352\) | −202.932 | − | 361.032i | −0.576512 | − | 1.02566i | ||||
\(353\) | 404.451 | 1.14575 | 0.572877 | − | 0.819642i | \(-0.305827\pi\) | ||||
0.572877 | + | 0.819642i | \(0.305827\pi\) | |||||||
\(354\) | −127.839 | − | 104.011i | −0.361128 | − | 0.293816i | ||||
\(355\) | 623.511 | − | 623.511i | 1.75637 | − | 1.75637i | ||||
\(356\) | −123.083 | + | 25.5698i | −0.345739 | + | 0.0718254i | ||||
\(357\) | 113.255 | − | 113.255i | 0.317242 | − | 0.317242i | ||||
\(358\) | 55.5325 | − | 5.70736i | 0.155119 | − | 0.0159423i | ||||
\(359\) | 423.833 | 1.18059 | 0.590297 | − | 0.807186i | \(-0.299011\pi\) | ||||
0.590297 | + | 0.807186i | \(0.299011\pi\) | |||||||
\(360\) | −7.81794 | + | 2.48059i | −0.0217165 | + | 0.00689051i | ||||
\(361\) | 358.347i | 0.992652i | ||||||||
\(362\) | −473.116 | + | 48.6245i | −1.30695 | + | 0.134322i | ||||
\(363\) | 97.7905 | + | 97.7905i | 0.269395 | + | 0.269395i | ||||
\(364\) | 54.7154 | − | 83.4103i | 0.150317 | − | 0.229149i | ||||
\(365\) | 519.219 | + | 519.219i | 1.42252 | + | 1.42252i | ||||
\(366\) | −109.121 | − | 88.7816i | −0.298145 | − | 0.242573i | ||||
\(367\) | 477.144i | 1.30012i | 0.759883 | + | 0.650059i | \(0.225256\pi\) | ||||
−0.759883 | + | 0.650059i | \(0.774744\pi\) | |||||||
\(368\) | 50.7789 | − | 22.0497i | 0.137986 | − | 0.0599176i | ||||
\(369\) | −8.07288 | −0.0218777 | ||||||||
\(370\) | −1.13582 | + | 1.39603i | −0.00306978 | + | 0.00377306i | ||||
\(371\) | 82.4365 | − | 82.4365i | 0.222201 | − | 0.222201i | ||||
\(372\) | 251.249 | − | 383.013i | 0.675400 | − | 1.02960i | ||||
\(373\) | 112.221 | − | 112.221i | 0.300860 | − | 0.300860i | −0.540490 | − | 0.841350i | \(-0.681761\pi\) |
0.841350 | + | 0.540490i | \(0.181761\pi\) | |||||||
\(374\) | 46.7495 | + | 454.872i | 0.124999 | + | 1.21624i | ||||
\(375\) | −139.680 | −0.372479 | ||||||||
\(376\) | −171.555 | − | 88.9108i | −0.456264 | − | 0.236465i | ||||
\(377\) | − | 141.069i | − | 0.374188i | ||||||
\(378\) | −16.9755 | − | 165.171i | −0.0449086 | − | 0.436960i | ||||
\(379\) | 52.2069 | + | 52.2069i | 0.137749 | + | 0.137749i | 0.772619 | − | 0.634870i | \(-0.218946\pi\) |
−0.634870 | + | 0.772619i | \(0.718946\pi\) | |||||||
\(380\) | 41.7403 | − | 8.67131i | 0.109843 | − | 0.0228192i | ||||
\(381\) | −412.793 | − | 412.793i | −1.08345 | − | 1.08345i | ||||
\(382\) | 247.784 | − | 304.551i | 0.648650 | − | 0.797253i | ||||
\(383\) | 74.8407i | 0.195406i | 0.995216 | + | 0.0977032i | \(0.0311496\pi\) | ||||
−0.995216 | + | 0.0977032i | \(0.968850\pi\) | |||||||
\(384\) | 250.104 | + | 286.944i | 0.651313 | + | 0.747250i | ||||
\(385\) | 258.219 | 0.670699 | ||||||||
\(386\) | 62.6293 | + | 50.9556i | 0.162252 | + | 0.132009i | ||||
\(387\) | 0.266616 | − | 0.266616i | 0.000688930 | − | 0.000688930i | ||||
\(388\) | 25.6657 | + | 123.545i | 0.0661488 | + | 0.318414i | ||||
\(389\) | −57.0441 | + | 57.0441i | −0.146643 | + | 0.146643i | −0.776617 | − | 0.629974i | \(-0.783066\pi\) |
0.629974 | + | 0.776617i | \(0.283066\pi\) | |||||||
\(390\) | −316.684 | + | 32.5472i | −0.812009 | + | 0.0834543i | ||||
\(391\) | −61.1223 | −0.156323 | ||||||||
\(392\) | −146.156 | + | 282.011i | −0.372847 | + | 0.719416i | ||||
\(393\) | − | 75.4632i | − | 0.192018i | ||||||
\(394\) | 648.756 | − | 66.6759i | 1.64659 | − | 0.169228i | ||||
\(395\) | −628.910 | − | 628.910i | −1.59218 | − | 1.59218i | ||||
\(396\) | 6.78199 | + | 4.44884i | 0.0171262 | + | 0.0112345i | ||||
\(397\) | −355.874 | − | 355.874i | −0.896407 | − | 0.896407i | 0.0987089 | − | 0.995116i | \(-0.468529\pi\) |
−0.995116 | + | 0.0987089i | \(0.968529\pi\) | |||||||
\(398\) | −95.5031 | − | 77.7019i | −0.239958 | − | 0.195231i | ||||
\(399\) | 14.7667i | 0.0370093i | ||||||||
\(400\) | 113.577 | + | 261.560i | 0.283943 | + | 0.653900i | ||||
\(401\) | 113.892 | 0.284019 | 0.142010 | − | 0.989865i | \(-0.454644\pi\) | ||||
0.142010 | + | 0.989865i | \(0.454644\pi\) | |||||||
\(402\) | 402.668 | − | 494.918i | 1.00166 | − | 1.23114i | ||||
\(403\) | −222.731 | + | 222.731i | −0.552682 | + | 0.552682i | ||||
\(404\) | 129.930 | + | 85.2317i | 0.321610 | + | 0.210970i | ||||
\(405\) | −368.166 | + | 368.166i | −0.909052 | + | 0.909052i | ||||
\(406\) | −10.7516 | − | 104.613i | −0.0264817 | − | 0.257667i | ||||
\(407\) | 1.77973 | 0.00437281 | ||||||||
\(408\) | −127.103 | − | 400.585i | −0.311528 | − | 0.981826i | ||||
\(409\) | 139.909i | 0.342077i | 0.985264 | + | 0.171038i | \(0.0547122\pi\) | ||||
−0.985264 | + | 0.171038i | \(0.945288\pi\) | |||||||
\(410\) | 68.9448 | + | 670.832i | 0.168158 | + | 1.63618i | ||||
\(411\) | −108.756 | − | 108.756i | −0.264612 | − | 0.264612i | ||||
\(412\) | 83.7054 | + | 402.925i | 0.203168 | + | 0.977973i | ||||
\(413\) | 59.7394 | + | 59.7394i | 0.144648 | + | 0.144648i | ||||
\(414\) | −0.684235 | + | 0.840990i | −0.00165274 | + | 0.00203138i | ||||
\(415\) | 693.388i | 1.67081i | ||||||||
\(416\) | −128.254 | − | 228.174i | −0.308303 | − | 0.548495i | ||||
\(417\) | −73.4456 | −0.176129 | ||||||||
\(418\) | −32.7017 | − | 26.6063i | −0.0782338 | − | 0.0636515i | ||||
\(419\) | −370.978 | + | 370.978i | −0.885389 | + | 0.885389i | −0.994076 | − | 0.108687i | \(-0.965335\pi\) |
0.108687 | + | 0.994076i | \(0.465335\pi\) | |||||||
\(420\) | −232.363 | + | 48.2721i | −0.553245 | + | 0.114934i | ||||
\(421\) | 465.112 | − | 465.112i | 1.10478 | − | 1.10478i | 0.110955 | − | 0.993825i | \(-0.464609\pi\) |
0.993825 | − | 0.110955i | \(-0.0353908\pi\) | |||||||
\(422\) | −425.274 | + | 43.7075i | −1.00776 | + | 0.103572i | ||||
\(423\) | 3.78419 | 0.00894608 | ||||||||
\(424\) | −92.5160 | − | 291.578i | −0.218198 | − | 0.687684i | ||||
\(425\) | − | 314.839i | − | 0.740797i | ||||||
\(426\) | 797.225 | − | 81.9349i | 1.87142 | − | 0.192335i | ||||
\(427\) | 50.9923 | + | 50.9923i | 0.119420 | + | 0.119420i | ||||
\(428\) | 247.169 | − | 376.793i | 0.577497 | − | 0.880358i | ||||
\(429\) | 222.609 | + | 222.609i | 0.518901 | + | 0.518901i | ||||
\(430\) | −24.4320 | − | 19.8780i | −0.0568185 | − | 0.0462279i | ||||
\(431\) | 409.924i | 0.951099i | 0.879689 | + | 0.475549i | \(0.157751\pi\) | ||||
−0.879689 | + | 0.475549i | \(0.842249\pi\) | |||||||
\(432\) | −405.284 | − | 159.875i | −0.938157 | − | 0.370082i | ||||
\(433\) | −20.6859 | −0.0477735 | −0.0238868 | − | 0.999715i | \(-0.507604\pi\) | ||||
−0.0238868 | + | 0.999715i | \(0.507604\pi\) | |||||||
\(434\) | −148.196 | + | 182.146i | −0.341464 | + | 0.419692i | ||||
\(435\) | −237.314 | + | 237.314i | −0.545550 | + | 0.545550i | ||||
\(436\) | −389.113 | + | 593.179i | −0.892462 | + | 1.36050i | ||||
\(437\) | 3.98468 | − | 3.98468i | 0.00911827 | − | 0.00911827i | ||||
\(438\) | 68.2299 | + | 663.876i | 0.155776 | + | 1.51570i | ||||
\(439\) | −63.2889 | −0.144166 | −0.0720830 | − | 0.997399i | \(-0.522965\pi\) | ||||
−0.0720830 | + | 0.997399i | \(0.522965\pi\) | |||||||
\(440\) | 311.765 | − | 601.557i | 0.708558 | − | 1.36718i | ||||
\(441\) | − | 6.22065i | − | 0.0141058i | ||||||
\(442\) | 29.5459 | + | 287.481i | 0.0668460 | + | 0.650410i | ||||
\(443\) | −297.084 | − | 297.084i | −0.670619 | − | 0.670619i | 0.287240 | − | 0.957859i | \(-0.407262\pi\) |
−0.957859 | + | 0.287240i | \(0.907262\pi\) | |||||||
\(444\) | −1.60152 | + | 0.332707i | −0.00360703 | + | 0.000749341i | ||||
\(445\) | −145.423 | − | 145.423i | −0.326793 | − | 0.326793i | ||||
\(446\) | 145.820 | − | 179.226i | 0.326950 | − | 0.401853i | ||||
\(447\) | − | 50.1177i | − | 0.112120i | ||||||
\(448\) | −112.500 | − | 159.432i | −0.251116 | − | 0.355876i | ||||
\(449\) | 364.701 | 0.812251 | 0.406126 | − | 0.913817i | \(-0.366880\pi\) | ||||
0.406126 | + | 0.913817i | \(0.366880\pi\) | |||||||
\(450\) | −4.33191 | − | 3.52447i | −0.00962646 | − | 0.00783215i | ||||
\(451\) | 471.553 | − | 471.553i | 1.04557 | − | 1.04557i | ||||
\(452\) | −78.6105 | − | 378.400i | −0.173917 | − | 0.837169i | ||||
\(453\) | −278.720 | + | 278.720i | −0.615275 | + | 0.615275i | ||||
\(454\) | −71.0049 | + | 7.29753i | −0.156398 | + | 0.0160739i | ||||
\(455\) | 163.196 | 0.358672 | ||||||||
\(456\) | 34.4011 | + | 17.8288i | 0.0754409 | + | 0.0390983i | ||||
\(457\) | − | 640.046i | − | 1.40054i | −0.713879 | − | 0.700269i | \(-0.753064\pi\) | ||
0.713879 | − | 0.700269i | \(-0.246936\pi\) | |||||||
\(458\) | 437.003 | − | 44.9130i | 0.954156 | − | 0.0980634i | ||||
\(459\) | 340.140 | + | 340.140i | 0.741045 | + | 0.741045i | ||||
\(460\) | 75.7273 | + | 49.6756i | 0.164625 | + | 0.107990i | ||||
\(461\) | −239.416 | − | 239.416i | −0.519341 | − | 0.519341i | 0.398031 | − | 0.917372i | \(-0.369694\pi\) |
−0.917372 | + | 0.398031i | \(0.869694\pi\) | |||||||
\(462\) | 182.046 | + | 148.114i | 0.394040 | + | 0.320594i | ||||
\(463\) | − | 479.413i | − | 1.03545i | −0.855548 | − | 0.517724i | \(-0.826779\pi\) | ||
0.855548 | − | 0.517724i | \(-0.173221\pi\) | |||||||
\(464\) | −256.691 | − | 101.259i | −0.553213 | − | 0.218230i | ||||
\(465\) | 749.381 | 1.61157 | ||||||||
\(466\) | −151.136 | + | 185.761i | −0.324326 | + | 0.398628i | ||||
\(467\) | 403.375 | − | 403.375i | 0.863758 | − | 0.863758i | −0.128015 | − | 0.991772i | \(-0.540860\pi\) |
0.991772 | + | 0.128015i | \(0.0408605\pi\) | |||||||
\(468\) | 4.28625 | + | 2.81169i | 0.00915865 | + | 0.00600789i | ||||
\(469\) | −231.276 | + | 231.276i | −0.493125 | + | 0.493125i | ||||
\(470\) | −32.3181 | − | 314.455i | −0.0687620 | − | 0.669053i | ||||
\(471\) | 446.173 | 0.947288 | ||||||||
\(472\) | 211.299 | − | 67.0438i | 0.447667 | − | 0.142042i | ||||
\(473\) | 31.1471i | 0.0658501i | ||||||||
\(474\) | −82.6443 | − | 804.128i | −0.174355 | − | 1.69647i | ||||
\(475\) | 20.5250 | + | 20.5250i | 0.0432104 | + | 0.0432104i | ||||
\(476\) | 43.8208 | + | 210.936i | 0.0920606 | + | 0.443143i | ||||
\(477\) | 4.23621 | + | 4.23621i | 0.00888093 | + | 0.00888093i | ||||
\(478\) | −309.760 | + | 380.724i | −0.648032 | + | 0.796494i | ||||
\(479\) | 460.611i | 0.961609i | 0.876828 | + | 0.480805i | \(0.159655\pi\) | ||||
−0.876828 | + | 0.480805i | \(0.840345\pi\) | |||||||
\(480\) | −168.091 | + | 599.604i | −0.350189 | + | 1.24917i | ||||
\(481\) | 1.12480 | 0.00233846 | ||||||||
\(482\) | −668.983 | − | 544.289i | −1.38793 | − | 1.12923i | ||||
\(483\) | −22.1823 | + | 22.1823i | −0.0459260 | + | 0.0459260i | ||||
\(484\) | −182.133 | + | 37.8371i | −0.376308 | + | 0.0781759i | ||||
\(485\) | −145.968 | + | 145.968i | −0.300966 | + | 0.300966i | ||||
\(486\) | 16.8302 | − | 1.72973i | 0.0346301 | − | 0.00355911i | ||||
\(487\) | −575.128 | −1.18096 | −0.590481 | − | 0.807052i | \(-0.701062\pi\) | ||||
−0.590481 | + | 0.807052i | \(0.701062\pi\) | |||||||
\(488\) | 180.360 | − | 57.2272i | 0.369590 | − | 0.117269i | ||||
\(489\) | 444.010i | 0.907995i | ||||||||
\(490\) | −516.917 | + | 53.1262i | −1.05493 | + | 0.108421i | ||||
\(491\) | 271.375 | + | 271.375i | 0.552699 | + | 0.552699i | 0.927219 | − | 0.374520i | \(-0.122192\pi\) |
−0.374520 | + | 0.927219i | \(0.622192\pi\) | |||||||
\(492\) | −336.182 | + | 512.488i | −0.683296 | + | 1.04164i | ||||
\(493\) | 215.431 | + | 215.431i | 0.436979 | + | 0.436979i | ||||
\(494\) | −20.6676 | − | 16.8153i | −0.0418373 | − | 0.0340391i | ||||
\(495\) | 13.2693i | 0.0268066i | ||||||||
\(496\) | 245.409 | + | 565.159i | 0.494776 | + | 1.13943i | ||||
\(497\) | −410.832 | −0.826624 | ||||||||
\(498\) | −397.726 | + | 488.843i | −0.798647 | + | 0.981613i | ||||
\(499\) | 268.082 | − | 268.082i | 0.537239 | − | 0.537239i | −0.385478 | − | 0.922717i | \(-0.625963\pi\) |
0.922717 | + | 0.385478i | \(0.125963\pi\) | |||||||
\(500\) | 103.053 | − | 157.098i | 0.206106 | − | 0.314196i | ||||
\(501\) | 234.651 | − | 234.651i | 0.468365 | − | 0.468365i | ||||
\(502\) | 6.94500 | + | 67.5748i | 0.0138347 | + | 0.134611i | ||||
\(503\) | −368.002 | −0.731615 | −0.365807 | − | 0.930691i | \(-0.619207\pi\) | ||||
−0.365807 | + | 0.930691i | \(0.619207\pi\) | |||||||
\(504\) | 3.39285 | + | 1.75839i | 0.00673185 | + | 0.00348888i | ||||
\(505\) | 254.215i | 0.503395i | ||||||||
\(506\) | −9.15638 | − | 89.0914i | −0.0180956 | − | 0.176070i | ||||
\(507\) | −214.679 | − | 214.679i | −0.423430 | − | 0.423430i | ||||
\(508\) | 768.819 | − | 159.718i | 1.51342 | − | 0.314405i | ||||
\(509\) | 297.809 | + | 297.809i | 0.585087 | + | 0.585087i | 0.936297 | − | 0.351210i | \(-0.114230\pi\) |
−0.351210 | + | 0.936297i | \(0.614230\pi\) | |||||||
\(510\) | 433.914 | − | 533.322i | 0.850812 | − | 1.04573i | ||||
\(511\) | − | 342.114i | − | 0.669498i | ||||||
\(512\) | −507.249 | + | 69.5905i | −0.990720 | + | 0.135919i | ||||
\(513\) | −44.3488 | −0.0864498 | ||||||||
\(514\) | 156.472 | + | 127.307i | 0.304421 | + | 0.247679i | ||||
\(515\) | −476.057 | + | 476.057i | −0.924382 | + | 0.924382i | ||||
\(516\) | −5.82272 | − | 28.0283i | −0.0112843 | − | 0.0543183i | ||||
\(517\) | −221.042 | + | 221.042i | −0.427548 | + | 0.427548i | ||||
\(518\) | 0.834119 | − | 0.0857267i | 0.00161027 | − | 0.000165495i | ||||
\(519\) | 61.1332 | 0.117790 | ||||||||
\(520\) | 197.037 | − | 380.187i | 0.378918 | − | 0.731129i | ||||
\(521\) | 95.5605i | 0.183418i | 0.995786 | + | 0.0917088i | \(0.0292329\pi\) | ||||
−0.995786 | + | 0.0917088i | \(0.970767\pi\) | |||||||
\(522\) | 5.37579 | − | 0.552497i | 0.0102984 | − | 0.00105842i | ||||
\(523\) | −250.389 | − | 250.389i | −0.478756 | − | 0.478756i | 0.425978 | − | 0.904734i | \(-0.359930\pi\) |
−0.904734 | + | 0.425978i | \(0.859930\pi\) | |||||||
\(524\) | 84.8735 | + | 55.6753i | 0.161972 | + | 0.106251i | ||||
\(525\) | −114.260 | − | 114.260i | −0.217638 | − | 0.217638i | ||||
\(526\) | −336.303 | − | 273.618i | −0.639360 | − | 0.520187i | ||||
\(527\) | − | 680.279i | − | 1.29085i | ||||||
\(528\) | 564.849 | − | 245.274i | 1.06979 | − | 0.464534i | ||||
\(529\) | −517.029 | −0.977370 | ||||||||
\(530\) | 315.838 | − | 388.194i | 0.595920 | − | 0.732442i | ||||
\(531\) | −3.06986 | + | 3.06986i | −0.00578128 | + | 0.00578128i | ||||
\(532\) | −16.6081 | − | 10.8946i | −0.0312183 | − | 0.0204786i | ||||
\(533\) | 298.024 | − | 298.024i | 0.559144 | − | 0.559144i | ||||
\(534\) | −19.1099 | − | 185.939i | −0.0357863 | − | 0.348200i | ||||
\(535\) | 737.212 | 1.37797 | ||||||||
\(536\) | 259.554 | + | 818.023i | 0.484242 | + | 1.52616i | ||||
\(537\) | 83.0055i | 0.154573i | ||||||||
\(538\) | 74.2522 | + | 722.473i | 0.138015 | + | 1.34289i | ||||
\(539\) | 363.360 | + | 363.360i | 0.674138 | + | 0.674138i | ||||
\(540\) | −144.975 | − | 697.855i | −0.268473 | − | 1.29232i | ||||
\(541\) | −81.7015 | − | 81.7015i | −0.151019 | − | 0.151019i | 0.627554 | − | 0.778573i | \(-0.284056\pi\) |
−0.778573 | + | 0.627554i | \(0.784056\pi\) | |||||||
\(542\) | −16.2325 | + | 19.9513i | −0.0299493 | + | 0.0368106i | ||||
\(543\) | − | 707.175i | − | 1.30235i | ||||||
\(544\) | 544.313 | + | 152.591i | 1.00058 | + | 0.280498i | ||||
\(545\) | −1160.58 | −2.12951 | ||||||||
\(546\) | 115.054 | + | 93.6089i | 0.210722 | + | 0.171445i | ||||
\(547\) | −381.162 | + | 381.162i | −0.696823 | + | 0.696823i | −0.963724 | − | 0.266901i | \(-0.914000\pi\) |
0.266901 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(548\) | 202.555 | − | 42.0797i | 0.369626 | − | 0.0767878i | ||||
\(549\) | −2.62037 | + | 2.62037i | −0.00477299 | + | 0.00477299i | ||||
\(550\) | 458.906 | − | 47.1641i | 0.834375 | − | 0.0857530i | ||||
\(551\) | −28.0887 | −0.0509777 | ||||||||
\(552\) | 24.8945 | + | 78.4587i | 0.0450987 | + | 0.142135i | ||||
\(553\) | 414.389i | 0.749348i | ||||||||
\(554\) | −216.935 | + | 22.2956i | −0.391580 | + | 0.0402447i | ||||
\(555\) | −1.89220 | − | 1.89220i | −0.00340937 | − | 0.00340937i | ||||
\(556\) | 54.1868 | − | 82.6044i | 0.0974582 | − | 0.148569i | ||||
\(557\) | −63.7634 | − | 63.7634i | −0.114476 | − | 0.114476i | 0.647548 | − | 0.762025i | \(-0.275794\pi\) |
−0.762025 | + | 0.647548i | \(0.775794\pi\) | |||||||
\(558\) | −9.36005 | − | 7.61540i | −0.0167743 | − | 0.0136477i | ||||
\(559\) | 19.6851i | 0.0352149i | ||||||||
\(560\) | 117.141 | − | 296.953i | 0.209181 | − | 0.530274i | ||||
\(561\) | −679.906 | −1.21195 | ||||||||
\(562\) | 238.602 | − | 293.265i | 0.424559 | − | 0.521824i | ||||
\(563\) | 333.679 | − | 333.679i | 0.592681 | − | 0.592681i | −0.345674 | − | 0.938355i | \(-0.612350\pi\) |
0.938355 | + | 0.345674i | \(0.112350\pi\) | |||||||
\(564\) | 157.586 | − | 240.231i | 0.279409 | − | 0.425941i | ||||
\(565\) | 447.081 | − | 447.081i | 0.791293 | − | 0.791293i | ||||
\(566\) | 20.0775 | + | 195.353i | 0.0354725 | + | 0.345147i | ||||
\(567\) | 242.585 | 0.427839 | ||||||||
\(568\) | −496.025 | + | 957.090i | −0.873284 | + | 1.68502i | ||||
\(569\) | 93.3114i | 0.163992i | 0.996633 | + | 0.0819960i | \(0.0261295\pi\) | ||||
−0.996633 | + | 0.0819960i | \(0.973871\pi\) | |||||||
\(570\) | 6.48059 | + | 63.0560i | 0.0113694 | + | 0.110625i | ||||
\(571\) | 196.999 | + | 196.999i | 0.345007 | + | 0.345007i | 0.858246 | − | 0.513239i | \(-0.171555\pi\) |
−0.513239 | + | 0.858246i | \(0.671555\pi\) | |||||||
\(572\) | −414.605 | + | 86.1318i | −0.724833 | + | 0.150580i | ||||
\(573\) | 412.793 | + | 412.793i | 0.720406 | + | 0.720406i | ||||
\(574\) | 198.292 | − | 243.720i | 0.345457 | − | 0.424599i | ||||
\(575\) | 61.6644i | 0.107242i | ||||||||
\(576\) | 8.19284 | − | 5.78109i | 0.0142237 | − | 0.0100366i | ||||
\(577\) | 370.057 | 0.641347 | 0.320673 | − | 0.947190i | \(-0.396091\pi\) | ||||
0.320673 | + | 0.947190i | \(0.396091\pi\) | |||||||
\(578\) | −35.7918 | − | 29.1204i | −0.0619235 | − | 0.0503814i | ||||
\(579\) | −84.8888 | + | 84.8888i | −0.146613 | + | 0.146613i | ||||
\(580\) | −91.8217 | − | 441.993i | −0.158313 | − | 0.762058i | ||||
\(581\) | 228.437 | − | 228.437i | 0.393179 | − | 0.393179i | ||||
\(582\) | −186.636 | + | 19.1815i | −0.320680 | + | 0.0329579i | ||||
\(583\) | −494.890 | −0.848869 | ||||||||
\(584\) | −797.001 | − | 413.057i | −1.36473 | − | 0.707289i | ||||
\(585\) | 8.38623i | 0.0143354i | ||||||||
\(586\) | −675.038 | + | 69.3771i | −1.15194 | + | 0.118391i | ||||
\(587\) | 328.063 | + | 328.063i | 0.558880 | + | 0.558880i | 0.928989 | − | 0.370108i | \(-0.120679\pi\) |
−0.370108 | + | 0.928989i | \(0.620679\pi\) | |||||||
\(588\) | −394.904 | − | 259.049i | −0.671605 | − | 0.440559i | ||||
\(589\) | 44.3488 | + | 44.3488i | 0.0752950 | + | 0.0752950i | ||||
\(590\) | 281.314 | + | 228.879i | 0.476803 | + | 0.387930i | ||||
\(591\) | 969.708i | 1.64079i | ||||||||
\(592\) | 0.807376 | − | 2.04670i | 0.00136381 | − | 0.00345726i | ||||
\(593\) | 1088.78 | 1.83605 | 0.918024 | − | 0.396525i | \(-0.129784\pi\) | ||||
0.918024 | + | 0.396525i | \(0.129784\pi\) | |||||||
\(594\) | −444.831 | + | 546.739i | −0.748873 | + | 0.920437i | ||||
\(595\) | −249.222 | + | 249.222i | −0.418860 | + | 0.418860i | ||||
\(596\) | 56.3675 | + | 36.9759i | 0.0945763 | + | 0.0620401i | ||||
\(597\) | 129.446 | − | 129.446i | 0.216828 | − | 0.216828i | ||||
\(598\) | −5.78687 | − | 56.3062i | −0.00967705 | − | 0.0941575i | ||||
\(599\) | −350.354 | −0.584899 | −0.292449 | − | 0.956281i | \(-0.594470\pi\) | ||||
−0.292449 | + | 0.956281i | \(0.594470\pi\) | |||||||
\(600\) | −404.138 | + | 128.231i | −0.673563 | + | 0.213718i | ||||
\(601\) | − | 1021.45i | − | 1.69958i | −0.527123 | − | 0.849789i | \(-0.676729\pi\) | ||
0.527123 | − | 0.849789i | \(-0.323271\pi\) | |||||||
\(602\) | 1.50030 | + | 14.5979i | 0.00249220 | + | 0.0242491i | ||||
\(603\) | −11.8847 | − | 11.8847i | −0.0197093 | − | 0.0197093i | ||||
\(604\) | −107.842 | − | 519.110i | −0.178547 | − | 0.859454i | ||||
\(605\) | −215.191 | − | 215.191i | −0.355687 | − | 0.355687i | ||||
\(606\) | −145.817 | + | 179.223i | −0.240622 | + | 0.295748i | ||||
\(607\) | − | 394.204i | − | 0.649431i | −0.945812 | − | 0.324715i | \(-0.894732\pi\) | ||
0.945812 | − | 0.324715i | \(-0.105268\pi\) | |||||||
\(608\) | −45.4325 | + | 25.5371i | −0.0747246 | + | 0.0420019i | ||||
\(609\) | 156.367 | 0.256760 | ||||||||
\(610\) | 240.124 | + | 195.366i | 0.393645 | + | 0.320272i | ||||
\(611\) | −139.700 | + | 139.700i | −0.228641 | + | 0.228641i | ||||
\(612\) | −10.8395 | + | 2.25184i | −0.0177116 | + | 0.00367948i | ||||
\(613\) | 157.606 | − | 157.606i | 0.257106 | − | 0.257106i | −0.566770 | − | 0.823876i | \(-0.691807\pi\) |
0.823876 | + | 0.566770i | \(0.191807\pi\) | |||||||
\(614\) | 650.464 | − | 66.8514i | 1.05939 | − | 0.108879i | ||||
\(615\) | −1002.71 | −1.63042 | ||||||||
\(616\) | −300.895 | + | 95.4721i | −0.488465 | + | 0.154987i | ||||
\(617\) | 609.080i | 0.987164i | 0.869699 | + | 0.493582i | \(0.164313\pi\) | ||||
−0.869699 | + | 0.493582i | \(0.835687\pi\) | |||||||
\(618\) | −608.689 | + | 62.5580i | −0.984933 | + | 0.101227i | ||||
\(619\) | −497.519 | − | 497.519i | −0.803747 | − | 0.803747i | 0.179932 | − | 0.983679i | \(-0.442412\pi\) |
−0.983679 | + | 0.179932i | \(0.942412\pi\) | |||||||
\(620\) | −552.879 | + | 842.830i | −0.891741 | + | 1.35940i | ||||
\(621\) | −66.6199 | − | 66.6199i | −0.107278 | − | 0.107278i | ||||
\(622\) | 796.371 | + | 647.933i | 1.28034 | + | 1.04169i | ||||
\(623\) | 95.8194i | 0.153803i | ||||||||
\(624\) | 356.987 | − | 155.014i | 0.572095 | − | 0.248421i | ||||
\(625\) | 752.924 | 1.20468 | ||||||||
\(626\) | 435.771 | − | 535.604i | 0.696119 | − | 0.855597i | ||||
\(627\) | 44.3244 | − | 44.3244i | 0.0706929 | − | 0.0706929i | ||||
\(628\) | −329.178 | + | 501.811i | −0.524169 | + | 0.799062i | ||||
\(629\) | −1.71772 | + | 1.71772i | −0.00273087 | + | 0.00273087i | ||||
\(630\) | 0.639157 | + | 6.21899i | 0.00101454 | + | 0.00987142i | ||||
\(631\) | 668.065 | 1.05874 | 0.529370 | − | 0.848391i | \(-0.322428\pi\) | ||||
0.529370 | + | 0.848391i | \(0.322428\pi\) | |||||||
\(632\) | 965.377 | + | 500.320i | 1.52750 | + | 0.791646i | ||||
\(633\) | − | 635.665i | − | 1.00421i | ||||||
\(634\) | −99.9460 | − | 972.473i | −0.157644 | − | 1.53387i | ||||
\(635\) | 908.362 | + | 908.362i | 1.43049 | + | 1.43049i | ||||
\(636\) | 445.336 | − | 92.5160i | 0.700213 | − | 0.145465i | ||||
\(637\) | 229.646 | + | 229.646i | 0.360511 | + | 0.360511i | ||||
\(638\) | −281.738 | + | 346.283i | −0.441596 | + | 0.542763i | ||||
\(639\) | − | 21.1117i | − | 0.0330386i | ||||||
\(640\) | −550.361 | − | 631.428i | −0.859939 | − | 0.986607i | ||||
\(641\) | −419.792 | −0.654902 | −0.327451 | − | 0.944868i | \(-0.606190\pi\) | ||||
−0.327451 | + | 0.944868i | \(0.606190\pi\) | |||||||
\(642\) | 519.740 | + | 422.864i | 0.809564 | + | 0.658666i | ||||
\(643\) | −138.767 | + | 138.767i | −0.215813 | + | 0.215813i | −0.806731 | − | 0.590919i | \(-0.798765\pi\) |
0.590919 | + | 0.806731i | \(0.298765\pi\) | |||||||
\(644\) | −8.58277 | − | 41.3141i | −0.0133273 | − | 0.0641523i | ||||
\(645\) | 33.1155 | − | 33.1155i | 0.0513418 | − | 0.0513418i | ||||
\(646\) | 57.2415 | − | 5.88300i | 0.0886091 | − | 0.00910680i | ||||
\(647\) | 647.036 | 1.00006 | 0.500028 | − | 0.866009i | \(-0.333323\pi\) | ||||
0.500028 | + | 0.866009i | \(0.333323\pi\) | |||||||
\(648\) | 292.889 | − | 565.135i | 0.451989 | − | 0.872122i | ||||
\(649\) | − | 358.633i | − | 0.552594i | ||||||
\(650\) | 290.031 | − | 29.8080i | 0.446202 | − | 0.0458584i | ||||
\(651\) | −246.884 | − | 246.884i | −0.379238 | − | 0.379238i | ||||
\(652\) | −499.378 | − | 327.582i | −0.765917 | − | 0.502426i | ||||
\(653\) | −452.293 | − | 452.293i | −0.692639 | − | 0.692639i | 0.270173 | − | 0.962812i | \(-0.412919\pi\) |
−0.962812 | + | 0.270173i | \(0.912919\pi\) | |||||||
\(654\) | −818.218 | − | 665.707i | −1.25110 | − | 1.01790i | ||||
\(655\) | 166.059i | 0.253525i | ||||||||
\(656\) | −328.368 | − | 756.208i | −0.500561 | − | 1.15276i | ||||
\(657\) | 17.5804 | 0.0267586 | ||||||||
\(658\) | −92.9501 | + | 114.245i | −0.141262 | + | 0.173624i | ||||
\(659\) | 382.858 | − | 382.858i | 0.580969 | − | 0.580969i | −0.354201 | − | 0.935169i | \(-0.615247\pi\) |
0.935169 | + | 0.354201i | \(0.115247\pi\) | |||||||
\(660\) | 842.368 | + | 552.576i | 1.27631 | + | 0.837236i | ||||
\(661\) | −841.606 | + | 841.606i | −1.27323 | + | 1.27323i | −0.328849 | + | 0.944383i | \(0.606661\pi\) |
−0.944383 | + | 0.328849i | \(0.893339\pi\) | |||||||
\(662\) | −123.177 | − | 1198.51i | −0.186067 | − | 1.81043i | ||||
\(663\) | −429.704 | −0.648120 | ||||||||
\(664\) | −256.368 | − | 807.982i | −0.386096 | − | 1.21684i | ||||
\(665\) | − | 32.4945i | − | 0.0488639i | ||||||
\(666\) | 0.00440528 | + | 0.0428633i | 6.61454e−6 | + | 6.43594e-5i | ||||
\(667\) | −42.1944 | − | 42.1944i | −0.0632599 | − | 0.0632599i | ||||
\(668\) | 90.7912 | + | 437.033i | 0.135915 | + | 0.654241i | ||||
\(669\) | 242.926 | + | 242.926i | 0.363119 | + | 0.363119i | ||||
\(670\) | −886.083 | + | 1089.08i | −1.32251 | + | 1.62549i | ||||
\(671\) | − | 306.122i | − | 0.456218i | ||||||
\(672\) | 252.917 | − | 142.162i | 0.376365 | − | 0.211551i | ||||
\(673\) | −506.103 | −0.752010 | −0.376005 | − | 0.926618i | \(-0.622703\pi\) | ||||
−0.376005 | + | 0.926618i | \(0.622703\pi\) | |||||||
\(674\) | 724.958 | + | 589.831i | 1.07561 | + | 0.875120i | ||||
\(675\) | 343.156 | − | 343.156i | 0.508380 | − | 0.508380i | ||||
\(676\) | 399.836 | − | 83.0638i | 0.591474 | − | 0.122875i | ||||
\(677\) | −430.816 | + | 430.816i | −0.636361 | + | 0.636361i | −0.949656 | − | 0.313295i | \(-0.898567\pi\) |
0.313295 | + | 0.949656i | \(0.398567\pi\) | |||||||
\(678\) | 571.640 | − | 58.7503i | 0.843127 | − | 0.0866524i | ||||
\(679\) | 96.1787 | 0.141648 | ||||||||
\(680\) | 279.694 | + | 881.498i | 0.411315 | + | 1.29632i | ||||
\(681\) | − | 106.132i | − | 0.155848i | ||||||
\(682\) | 991.570 | − | 101.909i | 1.45391 | − | 0.149426i | ||||
\(683\) | −910.083 | − | 910.083i | −1.33248 | − | 1.33248i | −0.903146 | − | 0.429333i | \(-0.858749\pi\) |
−0.429333 | − | 0.903146i | \(-0.641251\pi\) | |||||||
\(684\) | 0.559846 | − | 0.853451i | 0.000818488 | − | 0.00124773i | ||||
\(685\) | 239.319 | + | 239.319i | 0.349371 | + | 0.349371i | ||||
\(686\) | 419.571 | + | 341.365i | 0.611619 | + | 0.497617i | ||||
\(687\) | 653.197i | 0.950796i | ||||||||
\(688\) | 35.8193 | + | 14.1299i | 0.0520630 | + | 0.0205377i | ||||
\(689\) | −312.773 | −0.453952 | ||||||||
\(690\) | −84.9865 | + | 104.457i | −0.123169 | + | 0.151386i | ||||
\(691\) | −601.836 | + | 601.836i | −0.870964 | + | 0.870964i | −0.992577 | − | 0.121614i | \(-0.961193\pi\) |
0.121614 | + | 0.992577i | \(0.461193\pi\) | |||||||
\(692\) | −45.1029 | + | 68.7565i | −0.0651776 | + | 0.0993592i | ||||
\(693\) | 4.37156 | − | 4.37156i | 0.00630817 | − | 0.00630817i | ||||
\(694\) | 6.37511 | + | 62.0297i | 0.00918604 | + | 0.0893800i | ||||
\(695\) | 161.619 | 0.232545 | ||||||||
\(696\) | 188.792 | − | 364.277i | 0.271253 | − | 0.523387i | ||||
\(697\) | 910.244i | 1.30595i | ||||||||
\(698\) | 45.8686 | + | 446.301i | 0.0657144 | + | 0.639400i | ||||
\(699\) | −251.783 | − | 251.783i | −0.360204 | − | 0.360204i | ||||
\(700\) | 212.807 | − | 44.2095i | 0.304010 | − | 0.0631564i | ||||
\(701\) | −555.343 | − | 555.343i | −0.792215 | − | 0.792215i | 0.189639 | − | 0.981854i | \(-0.439268\pi\) |
−0.981854 | + | 0.189639i | \(0.939268\pi\) | |||||||
\(702\) | −281.135 | + | 345.542i | −0.400477 | + | 0.492225i | ||||
\(703\) | − | 0.223963i | − | 0.000318582i | ||||||
\(704\) | −140.875 | + | 816.245i | −0.200107 | + | 1.15944i | ||||
\(705\) | 470.022 | 0.666697 | ||||||||
\(706\) | −627.460 | − | 510.506i | −0.888754 | − | 0.723096i | ||||
\(707\) | 83.7511 | − | 83.7511i | 0.118460 | − | 0.118460i | ||||
\(708\) | 67.0438 | + | 322.722i | 0.0946946 | + | 0.455823i | ||||
\(709\) | −412.979 | + | 412.979i | −0.582480 | + | 0.582480i | −0.935584 | − | 0.353104i | \(-0.885126\pi\) |
0.353104 | + | 0.935584i | \(0.385126\pi\) | |||||||
\(710\) | −1754.32 | + | 180.300i | −2.47087 | + | 0.253943i | ||||
\(711\) | −21.2945 | −0.0299500 | ||||||||
\(712\) | 223.224 | + | 115.689i | 0.313517 | + | 0.162485i | ||||
\(713\) | 133.240i | 0.186872i | ||||||||
\(714\) | −318.656 | + | 32.7499i | −0.446297 | + | 0.0458682i | ||||
\(715\) | −489.856 | − | 489.856i | −0.685114 | − | 0.685114i | ||||
\(716\) | −93.3564 | − | 61.2399i | −0.130386 | − | 0.0855305i | ||||
\(717\) | −516.039 | − | 516.039i | −0.719720 | − | 0.719720i | ||||
\(718\) | −657.529 | − | 534.970i | −0.915779 | − | 0.745084i | ||||
\(719\) | 1173.98i | 1.63279i | 0.577495 | + | 0.816394i | \(0.304030\pi\) | ||||
−0.577495 | + | 0.816394i | \(0.695970\pi\) | |||||||
\(720\) | 15.2597 | + | 6.01960i | 0.0211940 | + | 0.00836056i | ||||
\(721\) | 313.674 | 0.435054 | ||||||||
\(722\) | 452.313 | − | 555.936i | 0.626472 | − | 0.769994i | ||||
\(723\) | 906.750 | − | 906.750i | 1.25415 | − | 1.25415i | ||||
\(724\) | 795.360 | + | 521.740i | 1.09856 | + | 0.720636i | ||||
\(725\) | 217.342 | − | 217.342i | 0.299781 | − | 0.299781i | ||||
\(726\) | −28.2779 | − | 275.144i | −0.0389503 | − | 0.378986i | ||||
\(727\) | 678.813 | 0.933718 | 0.466859 | − | 0.884332i | \(-0.345386\pi\) | ||||
0.466859 | + | 0.884332i | \(0.345386\pi\) | |||||||
\(728\) | −190.167 | + | 60.3388i | −0.261218 | + | 0.0828830i | ||||
\(729\) | 741.245i | 1.01680i | ||||||||
\(730\) | −150.142 | − | 1460.88i | −0.205674 | − | 2.00120i | ||||
\(731\) | −30.0618 | − | 30.0618i | −0.0411242 | − | 0.0411242i | ||||
\(732\) | 57.2272 | + | 275.469i | 0.0781792 | + | 0.376324i | ||||
\(733\) | 336.854 | + | 336.854i | 0.459556 | + | 0.459556i | 0.898510 | − | 0.438954i | \(-0.144651\pi\) |
−0.438954 | + | 0.898510i | \(0.644651\pi\) | |||||||
\(734\) | 602.260 | − | 740.235i | 0.820517 | − | 1.00849i | ||||
\(735\) | − | 772.646i | − | 1.05122i | ||||||
\(736\) | −106.609 | − | 29.8865i | −0.144850 | − | 0.0406067i | ||||
\(737\) | 1388.42 | 1.88387 | ||||||||
\(738\) | 12.5242 | + | 10.1897i | 0.0169704 | + | 0.0138072i | ||||
\(739\) | 178.478 | − | 178.478i | 0.241513 | − | 0.241513i | −0.575963 | − | 0.817476i | \(-0.695373\pi\) |
0.817476 | + | 0.575963i | \(0.195373\pi\) | |||||||
\(740\) | 3.52419 | − | 0.732131i | 0.00476242 | − | 0.000989367i | ||||
\(741\) | 28.0133 | − | 28.0133i | 0.0378047 | − | 0.0378047i | ||||
\(742\) | −231.944 | + | 23.8380i | −0.312593 | + | 0.0321267i | ||||
\(743\) | 795.320 | 1.07042 | 0.535208 | − | 0.844720i | \(-0.320233\pi\) | ||||
0.535208 | + | 0.844720i | \(0.320233\pi\) | |||||||
\(744\) | −873.230 | + | 277.071i | −1.17370 | + | 0.372407i | ||||
\(745\) | 110.285i | 0.148034i | ||||||||
\(746\) | −315.745 | + | 32.4508i | −0.423251 | + | 0.0434997i | ||||
\(747\) | 11.7388 | + | 11.7388i | 0.0157146 | + | 0.0157146i | ||||
\(748\) | 501.622 | − | 764.691i | 0.670617 | − | 1.02231i | ||||
\(749\) | −242.875 | − | 242.875i | −0.324266 | − | 0.324266i | ||||
\(750\) | 216.698 | + | 176.307i | 0.288930 | + | 0.235075i | ||||
\(751\) | 102.850i | 0.136951i | 0.997653 | + | 0.0684755i | \(0.0218135\pi\) | ||||
−0.997653 | + | 0.0684755i | \(0.978186\pi\) | |||||||
\(752\) | 153.924 | + | 354.475i | 0.204686 | + | 0.471377i | ||||
\(753\) | −101.005 | −0.134137 | ||||||||
\(754\) | −178.060 | + | 218.852i | −0.236154 | + | 0.290255i | ||||
\(755\) | 613.330 | − | 613.330i | 0.812358 | − | 0.812358i | ||||
\(756\) | −182.146 | + | 277.671i | −0.240934 | + | 0.367290i | ||||
\(757\) | 48.6324 | − | 48.6324i | 0.0642436 | − | 0.0642436i | −0.674255 | − | 0.738499i | \(-0.735535\pi\) |
0.738499 | + | 0.674255i | \(0.235535\pi\) | |||||||
\(758\) | −15.0966 | − | 146.890i | −0.0199164 | − | 0.193786i | ||||
\(759\) | 133.167 | 0.175450 | ||||||||
\(760\) | −75.7004 | − | 39.2328i | −0.0996058 | − | 0.0516221i | ||||
\(761\) | − | 947.802i | − | 1.24547i | −0.782433 | − | 0.622734i | \(-0.786022\pi\) | ||
0.782433 | − | 0.622734i | \(-0.213978\pi\) | |||||||
\(762\) | 119.367 | + | 1161.44i | 0.156649 | + | 1.52419i | ||||
\(763\) | 382.354 | + | 382.354i | 0.501119 | + | 0.501119i | ||||
\(764\) | −768.819 | + | 159.718i | −1.00631 | + | 0.209055i | ||||
\(765\) | −12.8069 | − | 12.8069i | −0.0167410 | − | 0.0167410i | ||||
\(766\) | 94.4653 | − | 116.107i | 0.123323 | − | 0.151576i | ||||
\(767\) | − | 226.658i | − | 0.295512i | ||||||
\(768\) | −25.8221 | − | 760.848i | −0.0336225 | − | 0.990687i | ||||
\(769\) | −183.427 | −0.238527 | −0.119263 | − | 0.992863i | \(-0.538053\pi\) | ||||
−0.119263 | + | 0.992863i | \(0.538053\pi\) | |||||||
\(770\) | −400.598 | − | 325.929i | −0.520257 | − | 0.423285i | ||||
\(771\) | −212.085 | + | 212.085i | −0.275078 | + | 0.275078i | ||||
\(772\) | −32.8452 | − | 158.104i | −0.0425456 | − | 0.204798i | ||||
\(773\) | −178.338 | + | 178.338i | −0.230710 | + | 0.230710i | −0.812989 | − | 0.582279i | \(-0.802161\pi\) |
0.582279 | + | 0.812989i | \(0.302161\pi\) | |||||||
\(774\) | −0.750152 | + | 0.0770969i | −0.000969189 | + | 9.96084e-5i | ||||
\(775\) | −686.312 | −0.885564 | ||||||||
\(776\) | 116.123 | − | 224.061i | 0.149643 | − | 0.288739i | ||||
\(777\) | 1.24677i | 0.00160460i | ||||||||
\(778\) | 160.500 | − | 16.4954i | 0.206298 | − | 0.0212023i | ||||
\(779\) | −59.3406 | − | 59.3406i | −0.0761754 | − | 0.0761754i | ||||
\(780\) | 532.381 | + | 349.231i | 0.682539 | + | 0.447732i | ||||
\(781\) | 1233.17 | + | 1233.17i | 1.57897 | + | 1.57897i | ||||
\(782\) | 94.8244 | + | 77.1497i | 0.121259 | + | 0.0986569i | ||||
\(783\) | 469.615i | 0.599764i | ||||||||
\(784\) | 582.705 | − | 253.027i | 0.743246 | − | 0.322739i | ||||
\(785\) | −981.815 | −1.25072 | ||||||||
\(786\) | −95.2511 | + | 117.073i | −0.121185 | + | 0.148947i | ||||
\(787\) | −480.981 | + | 480.981i | −0.611158 | + | 0.611158i | −0.943248 | − | 0.332090i | \(-0.892246\pi\) |
0.332090 | + | 0.943248i | \(0.392246\pi\) | |||||||
\(788\) | −1090.63 | − | 715.432i | −1.38405 | − | 0.907909i | ||||
\(789\) | 455.831 | − | 455.831i | 0.577732 | − | 0.577732i | ||||
\(790\) | 181.861 | + | 1769.51i | 0.230204 | + | 2.23988i | ||||
\(791\) | −294.582 | −0.372417 | ||||||||
\(792\) | −4.90607 | − | 15.4622i | −0.00619454 | − | 0.0195230i | ||||
\(793\) | − | 193.471i | − | 0.243973i | ||||||
\(794\) | 102.907 | + | 1001.29i | 0.129606 | + | 1.26107i | ||||
\(795\) | 526.165 | + | 526.165i | 0.661843 | + | 0.661843i | ||||
\(796\) | 50.0854 | + | 241.092i | 0.0629214 | + | 0.302879i | ||||
\(797\) | −558.478 | − | 558.478i | −0.700725 | − | 0.700725i | 0.263841 | − | 0.964566i | \(-0.415011\pi\) |
−0.964566 | + | 0.263841i | \(0.915011\pi\) | |||||||
\(798\) | 18.6388 | − | 22.9089i | 0.0233569 | − | 0.0287079i | ||||
\(799\) | − | 426.680i | − | 0.534017i | ||||||
\(800\) | 153.944 | − | 549.140i | 0.192430 | − | 0.686425i | ||||
\(801\) | −4.92392 | −0.00614722 | ||||||||
\(802\) | −176.690 | − | 143.756i | −0.220312 | − | 0.179247i | ||||
\(803\) | −1026.90 | + | 1026.90i | −1.27884 | + | 1.27884i | ||||
\(804\) | −1249.39 | + | 259.554i | −1.55397 | + | 0.322828i | ||||
\(805\) | 48.8126 | − | 48.8126i | 0.0606368 | − | 0.0606368i | ||||
\(806\) | 626.677 | − | 64.4068i | 0.777515 | − | 0.0799091i | ||||
\(807\) | −1079.89 | −1.33816 | ||||||||
\(808\) | −93.9914 | − | 296.228i | −0.116326 | − | 0.366619i | ||||
\(809\) | − | 1152.43i | − | 1.42451i | −0.701918 | − | 0.712257i | \(-0.747673\pi\) | ||
0.701918 | − | 0.712257i | \(-0.252327\pi\) | |||||||
\(810\) | 1035.87 | − | 106.462i | 1.27886 | − | 0.131435i | ||||
\(811\) | 364.890 | + | 364.890i | 0.449926 | + | 0.449926i | 0.895330 | − | 0.445404i | \(-0.146940\pi\) |
−0.445404 | + | 0.895330i | \(0.646940\pi\) | |||||||
\(812\) | −115.364 | + | 175.866i | −0.142074 | + | 0.216583i | ||||
\(813\) | −27.0424 | − | 27.0424i | −0.0332624 | − | 0.0332624i | ||||
\(814\) | −2.76105 | − | 2.24641i | −0.00339196 | − | 0.00275972i | ||||
\(815\) | − | 977.055i | − | 1.19884i | ||||||
\(816\) | −308.440 | + | 781.895i | −0.377990 | + | 0.958204i | ||||
\(817\) | 3.91958 | 0.00479753 | ||||||||
\(818\) | 176.596 | − | 217.054i | 0.215888 | − | 0.265347i | ||||
\(819\) | 2.76285 | − | 2.76285i | 0.00337344 | − | 0.00337344i | ||||
\(820\) | 739.777 | − | 1127.74i | 0.902167 | − | 1.37530i | ||||
\(821\) | −618.975 | + | 618.975i | −0.753928 | + | 0.753928i | −0.975210 | − | 0.221282i | \(-0.928976\pi\) |
0.221282 | + | 0.975210i | \(0.428976\pi\) | |||||||
\(822\) | 31.4487 | + | 305.995i | 0.0382587 | + | 0.372257i | ||||
\(823\) | 626.066 | 0.760712 | 0.380356 | − | 0.924840i | \(-0.375801\pi\) | ||||
0.380356 | + | 0.924840i | \(0.375801\pi\) | |||||||
\(824\) | 378.720 | − | 730.747i | 0.459612 | − | 0.886829i | ||||
\(825\) | 685.936i | 0.831438i | ||||||||
\(826\) | −17.2748 | − | 168.083i | −0.0209138 | − | 0.203491i | ||||
\(827\) | 375.666 | + | 375.666i | 0.454252 | + | 0.454252i | 0.896763 | − | 0.442511i | \(-0.145912\pi\) |
−0.442511 | + | 0.896763i | \(0.645912\pi\) | |||||||
\(828\) | 2.12303 | − | 0.441047i | 0.00256404 | − | 0.000532666i | ||||
\(829\) | −299.648 | − | 299.648i | −0.361457 | − | 0.361457i | 0.502892 | − | 0.864349i | \(-0.332269\pi\) |
−0.864349 | + | 0.502892i | \(0.832269\pi\) | |||||||
\(830\) | 875.207 | − | 1075.71i | 1.05447 | − | 1.29604i | ||||
\(831\) | − | 324.258i | − | 0.390202i | ||||||
\(832\) | −89.0337 | + | 515.871i | −0.107012 | + | 0.620037i | ||||
\(833\) | −701.398 | −0.842015 | ||||||||
\(834\) | 113.943 | + | 92.7044i | 0.136622 | + | 0.111156i | ||||
\(835\) | −516.356 | + | 516.356i | −0.618390 | + | 0.618390i | ||||
\(836\) | 17.1500 | + | 82.5535i | 0.0205144 | + | 0.0987482i | ||||
\(837\) | 741.466 | − | 741.466i | 0.885861 | − | 0.885861i | ||||
\(838\) | 1043.79 | − | 107.275i | 1.24557 | − | 0.128013i | ||||
\(839\) | −1477.80 | −1.76138 | −0.880689 | − | 0.473694i | \(-0.842920\pi\) | ||||
−0.880689 | + | 0.473694i | \(0.842920\pi\) | |||||||
\(840\) | 421.415 | + | 218.404i | 0.501685 | + | 0.260005i | ||||
\(841\) | − | 543.565i | − | 0.646331i | ||||||
\(842\) | −1308.64 | + | 134.496i | −1.55421 | + | 0.159734i | ||||
\(843\) | 397.496 | + | 397.496i | 0.471526 | + | 0.471526i | ||||
\(844\) | 714.933 | + | 468.981i | 0.847077 | + | 0.555665i | ||||
\(845\) | 472.407 | + | 472.407i | 0.559062 | + | 0.559062i | ||||
\(846\) | −5.87075 | − | 4.77648i | −0.00693942 | − | 0.00564596i | ||||
\(847\) | 141.789i | 0.167402i | ||||||||
\(848\) | −224.507 | + | 569.126i | −0.264749 | + | 0.671139i | ||||
\(849\) | −291.998 | −0.343932 | ||||||||
\(850\) | −397.395 | + | 488.437i | −0.467524 | + | 0.574631i | ||||
\(851\) | 0.336433 | − | 0.336433i | 0.000395338 | − | 0.000395338i | ||||
\(852\) | −1340.22 | − | 879.160i | −1.57303 | − | 1.03188i | ||||
\(853\) | 404.051 | − | 404.051i | 0.473682 | − | 0.473682i | −0.429422 | − | 0.903104i | \(-0.641283\pi\) |
0.903104 | + | 0.429422i | \(0.141283\pi\) | |||||||
\(854\) | −14.7454 | − | 143.472i | −0.0172663 | − | 0.168000i | ||||
\(855\) | 1.66981 | 0.00195300 | ||||||||
\(856\) | −859.050 | + | 272.571i | −1.00356 | + | 0.318425i | ||||
\(857\) | 892.363i | 1.04126i | 0.853781 | + | 0.520632i | \(0.174304\pi\) | ||||
−0.853781 | + | 0.520632i | \(0.825696\pi\) | |||||||
\(858\) | −64.3714 | − | 626.333i | −0.0750250 | − | 0.729992i | ||||
\(859\) | −378.424 | − | 378.424i | −0.440540 | − | 0.440540i | 0.451654 | − | 0.892193i | \(-0.350834\pi\) |
−0.892193 | + | 0.451654i | \(0.850834\pi\) | |||||||
\(860\) | 12.8130 | + | 61.6770i | 0.0148989 | + | 0.0717174i | ||||
\(861\) | 330.342 | + | 330.342i | 0.383672 | + | 0.383672i | ||||
\(862\) | 517.413 | − | 635.950i | 0.600247 | − | 0.737761i | ||||
\(863\) | 1457.30i | 1.68865i | 0.535833 | + | 0.844324i | \(0.319998\pi\) | ||||
−0.535833 | + | 0.844324i | \(0.680002\pi\) | |||||||
\(864\) | 426.955 | + | 759.586i | 0.494161 | + | 0.879150i | ||||
\(865\) | −134.525 | −0.155520 | ||||||||
\(866\) | 32.0919 | + | 26.1102i | 0.0370576 | + | 0.0301503i | ||||
\(867\) | 48.5127 | − | 48.5127i | 0.0559547 | − | 0.0559547i | ||||
\(868\) | 459.817 | − | 95.5245i | 0.529743 | − | 0.110051i | ||||
\(869\) | 1243.85 | − | 1243.85i | 1.43136 | − | 1.43136i | ||||
\(870\) | 667.709 | − | 68.6238i | 0.767481 | − | 0.0788779i | ||||
\(871\) | 877.485 | 1.00745 | ||||||||
\(872\) | 1352.39 | − | 429.105i | 1.55090 | − | 0.492092i | ||||
\(873\) | 4.94238i | 0.00566138i | ||||||||
\(874\) | −11.2113 | + | 1.15225i | −0.0128276 | + | 0.00131836i | ||||
\(875\) | −101.263 | − | 101.263i | −0.115729 | − | 0.115729i | ||||
\(876\) | 732.106 | − | 1116.05i | 0.835737 | − | 1.27403i | ||||
\(877\) | −571.322 | − | 571.322i | −0.651450 | − | 0.651450i | 0.301892 | − | 0.953342i | \(-0.402382\pi\) |
−0.953342 | + | 0.301892i | \(0.902382\pi\) | |||||||
\(878\) | 98.1856 | + | 79.8845i | 0.111829 | + | 0.0909846i | ||||
\(879\) | − | 1008.99i | − | 1.14789i | ||||||
\(880\) | −1242.97 | + | 539.732i | −1.41246 | + | 0.613332i | ||||
\(881\) | 994.662 | 1.12901 | 0.564507 | − | 0.825428i | \(-0.309066\pi\) | ||||
0.564507 | + | 0.825428i | \(0.309066\pi\) | |||||||
\(882\) | −7.85182 | + | 9.65064i | −0.00890229 | + | 0.0109418i | ||||
\(883\) | 74.0725 | − | 74.0725i | 0.0838873 | − | 0.0838873i | −0.663918 | − | 0.747805i | \(-0.731108\pi\) |
0.747805 | + | 0.663918i | \(0.231108\pi\) | |||||||
\(884\) | 317.027 | − | 483.288i | 0.358628 | − | 0.546706i | ||||
\(885\) | −381.297 | + | 381.297i | −0.430844 | + | 0.430844i | ||||
\(886\) | 85.9074 | + | 835.878i | 0.0969609 | + | 0.943429i | ||||
\(887\) | −522.759 | −0.589356 | −0.294678 | − | 0.955597i | \(-0.595212\pi\) | ||||
−0.294678 | + | 0.955597i | \(0.595212\pi\) | |||||||
\(888\) | 2.90453 | + | 1.50531i | 0.00327087 | + | 0.00169517i | ||||
\(889\) | − | 598.520i | − | 0.673251i | ||||||
\(890\) | 42.0518 | + | 409.163i | 0.0472492 | + | 0.459734i | ||||
\(891\) | −728.155 | − | 728.155i | −0.817233 | − | 0.817233i | ||||
\(892\) | −452.446 | + | 93.9932i | −0.507227 | + | 0.105373i | ||||
\(893\) | 27.8161 | + | 27.8161i | 0.0311491 | + | 0.0311491i | ||||
\(894\) | −63.2596 | + | 77.7520i | −0.0707601 | + | 0.0869710i | ||||
\(895\) | − | 182.656i | − | 0.204085i | ||||||
\(896\) | −26.7077 | + | 389.341i | −0.0298077 | + | 0.434533i | ||||
\(897\) | 84.1619 | 0.0938260 | ||||||||
\(898\) | −565.792 | − | 460.332i | −0.630058 | − | 0.512619i | ||||
\(899\) | 469.615 | − | 469.615i | 0.522375 | − | 0.522375i | ||||
\(900\) | 2.27182 | + | 10.9356i | 0.00252424 | + | 0.0121507i | ||||
\(901\) | 477.646 | − | 477.646i | 0.530129 | − | 0.530129i | ||||
\(902\) | −1326.76 | + | 136.358i | −1.47091 | + | 0.151173i | ||||
\(903\) | −21.8198 | −0.0241637 | ||||||||
\(904\) | −355.669 | + | 686.269i | −0.393439 | + | 0.759147i | ||||
\(905\) | 1556.16i | 1.71951i | ||||||||
\(906\) | 784.207 | − | 80.5970i | 0.865571 | − | 0.0889591i | ||||
\(907\) | 442.760 | + | 442.760i | 0.488159 | + | 0.488159i | 0.907725 | − | 0.419566i | \(-0.137818\pi\) |
−0.419566 | + | 0.907725i | \(0.637818\pi\) | |||||||
\(908\) | 119.367 | + | 78.3024i | 0.131462 | + | 0.0862362i | ||||
\(909\) | 4.30376 | + | 4.30376i | 0.00473461 | + | 0.00473461i | ||||
\(910\) | −253.180 | − | 205.989i | −0.278220 | − | 0.226361i | ||||
\(911\) | − | 835.738i | − | 0.917385i | −0.888595 | − | 0.458692i | \(-0.848318\pi\) | ||
0.888595 | − | 0.458692i | \(-0.151682\pi\) | |||||||
\(912\) | −30.8655 | − | 71.0811i | −0.0338437 | − | 0.0779398i | ||||
\(913\) | −1371.37 | −1.50205 | ||||||||
\(914\) | −807.878 | + | 992.959i | −0.883892 | + | 1.08639i | ||||
\(915\) | −325.467 | + | 325.467i | −0.355702 | + | 0.355702i | ||||
\(916\) | −734.652 | − | 481.916i | −0.802022 | − | 0.526110i | ||||
\(917\) | 54.7082 | − | 54.7082i | 0.0596599 | − | 0.0596599i | ||||
\(918\) | −98.3577 | − | 957.019i | −0.107143 | − | 1.04250i | ||||
\(919\) | 776.423 | 0.844856 | 0.422428 | − | 0.906396i | \(-0.361178\pi\) | ||||
0.422428 | + | 0.906396i | \(0.361178\pi\) | |||||||
\(920\) | −54.7810 | − | 172.651i | −0.0595445 | − | 0.187664i | ||||
\(921\) | 972.260i | 1.05566i | ||||||||
\(922\) | 69.2316 | + | 673.623i | 0.0750885 | + | 0.730610i | ||||
\(923\) | 779.372 | + | 779.372i | 0.844390 | + | 0.844390i | ||||
\(924\) | −95.4721 | − | 459.565i | −0.103325 | − | 0.497365i | ||||
\(925\) | 1.73295 | + | 1.73295i | 0.00187346 | + | 0.00187346i | ||||
\(926\) | −605.124 | + | 743.755i | −0.653481 | + | 0.803191i | ||||
\(927\) | 16.1189i | 0.0173883i | ||||||||
\(928\) | 270.416 | + | 481.091i | 0.291397 | + | 0.518417i | ||||
\(929\) | −144.945 | −0.156022 | −0.0780112 | − | 0.996952i | \(-0.524857\pi\) | ||||
−0.0780112 | + | 0.996952i | \(0.524857\pi\) | |||||||
\(930\) | −1162.58 | − | 945.883i | −1.25009 | − | 1.01708i | ||||
\(931\) | 45.7256 | − | 45.7256i | 0.0491145 | − | 0.0491145i | ||||
\(932\) | 468.941 | − | 97.4199i | 0.503156 | − | 0.104528i | ||||
\(933\) | −1079.41 | + | 1079.41i | −1.15693 | + | 1.15693i | ||||
\(934\) | −1134.94 | + | 116.643i | −1.21514 | + | 0.124886i | ||||
\(935\) | 1496.15 | 1.60016 | ||||||||
\(936\) | −3.10066 | − | 9.77221i | −0.00331267 | − | 0.0104404i | ||||
\(937\) | − | 851.499i | − | 0.908750i | −0.890811 | − | 0.454375i | \(-0.849863\pi\) | ||
0.890811 | − | 0.454375i | \(-0.150137\pi\) | |||||||
\(938\) | 650.718 | − | 66.8776i | 0.693730 | − | 0.0712981i | ||||
\(939\) | 725.966 | + | 725.966i | 0.773127 | + | 0.773127i | ||||
\(940\) | −346.773 | + | 528.634i | −0.368908 | + | 0.562377i | ||||
\(941\) | 1251.60 | + | 1251.60i | 1.33008 | + | 1.33008i | 0.905297 | + | 0.424778i | \(0.139648\pi\) |
0.424778 | + | 0.905297i | \(0.360352\pi\) | |||||||
\(942\) | −692.187 | − | 563.168i | −0.734806 | − | 0.597843i | ||||
\(943\) | − | 178.281i | − | 0.189057i | ||||||
\(944\) | −412.430 | − | 162.694i | −0.436896 | − | 0.172346i | ||||
\(945\) | −543.275 | −0.574894 | ||||||||
\(946\) | 39.3145 | − | 48.3213i | 0.0415587 | − | 0.0510795i | ||||
\(947\) | 919.818 | − | 919.818i | 0.971296 | − | 0.971296i | −0.0283032 | − | 0.999599i | \(-0.509010\pi\) |
0.999599 | + | 0.0283032i | \(0.00901039\pi\) | |||||||
\(948\) | −886.772 | + | 1351.83i | −0.935414 | + | 1.42598i | ||||
\(949\) | −649.009 | + | 649.009i | −0.683887 | + | 0.683887i | ||||
\(950\) | −5.93517 | − | 57.7491i | −0.00624755 | − | 0.0607886i | ||||
\(951\) | 1453.57 | 1.52847 | ||||||||
\(952\) | 198.265 | − | 382.555i | 0.208261 | − | 0.401844i | ||||
\(953\) | 489.450i | 0.513589i | 0.966466 | + | 0.256794i | \(0.0826663\pi\) | ||||
−0.966466 | + | 0.256794i | \(0.917334\pi\) | |||||||
\(954\) | −1.22498 | − | 11.9190i | −0.00128404 | − | 0.0124937i | ||||
\(955\) | −908.362 | − | 908.362i | −0.951164 | − | 0.951164i | ||||
\(956\) | 961.114 | − | 199.666i | 1.00535 | − | 0.208856i | ||||
\(957\) | −469.357 | − | 469.357i | −0.490447 | − | 0.490447i | ||||
\(958\) | 581.392 | − | 714.586i | 0.606881 | − | 0.745914i | ||||
\(959\) | − | 157.688i | − | 0.164429i | ||||||
\(960\) | 1017.61 | − | 718.050i | 1.06001 | − | 0.747969i | ||||
\(961\) | −521.932 | −0.543113 | ||||||||
\(962\) | −1.74500 | − | 1.41974i | −0.00181393 | − | 0.00147582i | ||||
\(963\) | 12.4807 | − | 12.4807i | 0.0129603 | − | 0.0129603i | ||||
\(964\) | 350.840 | + | 1688.81i | 0.363942 | + | 1.75187i | ||||
\(965\) | 186.800 | − | 186.800i | 0.193575 | − | 0.193575i | ||||
\(966\) | 62.4121 | − | 6.41441i | 0.0646088 | − | 0.00664018i | ||||
\(967\) | −1368.49 | −1.41519 | −0.707594 | − | 0.706619i | \(-0.750220\pi\) | ||||
−0.707594 | + | 0.706619i | \(0.750220\pi\) | |||||||
\(968\) | 330.318 | + | 171.192i | 0.341237 | + | 0.176851i | ||||
\(969\) | 85.5599i | 0.0882971i | ||||||||
\(970\) | 410.697 | − | 42.2094i | 0.423399 | − | 0.0435149i | ||||
\(971\) | −1013.79 | − | 1013.79i | −1.04407 | − | 1.04407i | −0.998983 | − | 0.0450900i | \(-0.985643\pi\) |
−0.0450900 | − | 0.998983i | \(-0.514357\pi\) | |||||||
\(972\) | −28.2935 | − | 18.5600i | −0.0291085 | − | 0.0190946i | ||||
\(973\) | −53.2455 | − | 53.2455i | −0.0547230 | − | 0.0547230i | ||||
\(974\) | 892.247 | + | 725.938i | 0.916064 | + | 0.745316i | ||||
\(975\) | 433.515i | 0.444631i | ||||||||
\(976\) | −352.042 | − | 138.872i | −0.360698 | − | 0.142287i | ||||
\(977\) | −5.19534 | −0.00531765 | −0.00265882 | − | 0.999996i | \(-0.500846\pi\) | ||||
−0.00265882 | + | 0.999996i | \(0.500846\pi\) | |||||||
\(978\) | 560.437 | − | 688.831i | 0.573044 | − | 0.704326i | ||||
\(979\) | 287.616 | − | 287.616i | 0.293785 | − | 0.293785i | ||||
\(980\) | 868.996 | + | 570.043i | 0.886730 | + | 0.581677i | ||||
\(981\) | −19.6482 | + | 19.6482i | −0.0200288 | + | 0.0200288i | ||||
\(982\) | −78.4732 | − | 763.543i | −0.0799116 | − | 0.777539i | ||||
\(983\) | −1591.90 | −1.61943 | −0.809714 | − | 0.586825i | \(-0.800378\pi\) | ||||
−0.809714 | + | 0.586825i | \(0.800378\pi\) | |||||||
\(984\) | 1168.42 | − | 370.733i | 1.18742 | − | 0.376761i | ||||
\(985\) | − | 2133.87i | − | 2.16636i | ||||||
\(986\) | −62.2958 | − | 606.138i | −0.0631804 | − | 0.614744i | ||||
\(987\) | −154.849 | − | 154.849i | −0.156888 | − | 0.156888i | ||||
\(988\) | 10.8389 | + | 52.1742i | 0.0109705 | + | 0.0528079i | ||||
\(989\) | 5.88792 | + | 5.88792i | 0.00595340 | + | 0.00595340i | ||||
\(990\) | 16.7487 | − | 20.5857i | 0.0169179 | − | 0.0207937i | ||||
\(991\) | − | 622.896i | − | 0.628553i | −0.949331 | − | 0.314277i | \(-0.898238\pi\) | ||
0.949331 | − | 0.314277i | \(-0.101762\pi\) | |||||||
\(992\) | 332.631 | − | 1186.54i | 0.335313 | − | 1.19611i | ||||
\(993\) | 1791.43 | 1.80406 | ||||||||
\(994\) | 637.360 | + | 518.560i | 0.641207 | + | 0.521690i | ||||
\(995\) | −284.850 | + | 284.850i | −0.286282 | + | 0.286282i | ||||
\(996\) | 1234.05 | − | 256.368i | 1.23901 | − | 0.257398i | ||||
\(997\) | −635.503 | + | 635.503i | −0.637415 | + | 0.637415i | −0.949917 | − | 0.312502i | \(-0.898833\pi\) |
0.312502 | + | 0.949917i | \(0.398833\pi\) | |||||||
\(998\) | −754.278 | + | 77.5210i | −0.755790 | + | 0.0776763i | ||||
\(999\) | −3.74443 | −0.00374818 |
(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 | 16.3.f.a.3.1 | ✓ | 6 | |
3.2 | odd | 2 | 144.3.m.a.19.3 | 6 | |||
4.3 | odd | 2 | 64.3.f.a.47.1 | 6 | |||
5.2 | odd | 4 | 400.3.k.d.99.2 | 6 | |||
5.3 | odd | 4 | 400.3.k.c.99.2 | 6 | |||
5.4 | even | 2 | 400.3.r.c.51.3 | 6 | |||
8.3 | odd | 2 | 128.3.f.a.95.3 | 6 | |||
8.5 | even | 2 | 128.3.f.b.95.1 | 6 | |||
12.11 | even | 2 | 576.3.m.a.559.3 | 6 | |||
16.3 | odd | 4 | 128.3.f.b.31.1 | 6 | |||
16.5 | even | 4 | 64.3.f.a.15.1 | 6 | |||
16.11 | odd | 4 | inner | 16.3.f.a.11.1 | yes | 6 | |
16.13 | even | 4 | 128.3.f.a.31.3 | 6 | |||
24.5 | odd | 2 | 1152.3.m.a.991.1 | 6 | |||
24.11 | even | 2 | 1152.3.m.b.991.1 | 6 | |||
32.3 | odd | 8 | 1024.3.d.k.511.3 | 12 | |||
32.5 | even | 8 | 1024.3.c.j.1023.9 | 12 | |||
32.11 | odd | 8 | 1024.3.c.j.1023.10 | 12 | |||
32.13 | even | 8 | 1024.3.d.k.511.4 | 12 | |||
32.19 | odd | 8 | 1024.3.d.k.511.10 | 12 | |||
32.21 | even | 8 | 1024.3.c.j.1023.4 | 12 | |||
32.27 | odd | 8 | 1024.3.c.j.1023.3 | 12 | |||
32.29 | even | 8 | 1024.3.d.k.511.9 | 12 | |||
48.5 | odd | 4 | 576.3.m.a.271.3 | 6 | |||
48.11 | even | 4 | 144.3.m.a.91.3 | 6 | |||
48.29 | odd | 4 | 1152.3.m.b.415.1 | 6 | |||
48.35 | even | 4 | 1152.3.m.a.415.1 | 6 | |||
80.27 | even | 4 | 400.3.k.c.299.2 | 6 | |||
80.43 | even | 4 | 400.3.k.d.299.2 | 6 | |||
80.59 | odd | 4 | 400.3.r.c.251.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.3.f.a.3.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
16.3.f.a.11.1 | yes | 6 | 16.11 | odd | 4 | inner | |
64.3.f.a.15.1 | 6 | 16.5 | even | 4 | |||
64.3.f.a.47.1 | 6 | 4.3 | odd | 2 | |||
128.3.f.a.31.3 | 6 | 16.13 | even | 4 | |||
128.3.f.a.95.3 | 6 | 8.3 | odd | 2 | |||
128.3.f.b.31.1 | 6 | 16.3 | odd | 4 | |||
128.3.f.b.95.1 | 6 | 8.5 | even | 2 | |||
144.3.m.a.19.3 | 6 | 3.2 | odd | 2 | |||
144.3.m.a.91.3 | 6 | 48.11 | even | 4 | |||
400.3.k.c.99.2 | 6 | 5.3 | odd | 4 | |||
400.3.k.c.299.2 | 6 | 80.27 | even | 4 | |||
400.3.k.d.99.2 | 6 | 5.2 | odd | 4 | |||
400.3.k.d.299.2 | 6 | 80.43 | even | 4 | |||
400.3.r.c.51.3 | 6 | 5.4 | even | 2 | |||
400.3.r.c.251.3 | 6 | 80.59 | odd | 4 | |||
576.3.m.a.271.3 | 6 | 48.5 | odd | 4 | |||
576.3.m.a.559.3 | 6 | 12.11 | even | 2 | |||
1024.3.c.j.1023.3 | 12 | 32.27 | odd | 8 | |||
1024.3.c.j.1023.4 | 12 | 32.21 | even | 8 | |||
1024.3.c.j.1023.9 | 12 | 32.5 | even | 8 | |||
1024.3.c.j.1023.10 | 12 | 32.11 | odd | 8 | |||
1024.3.d.k.511.3 | 12 | 32.3 | odd | 8 | |||
1024.3.d.k.511.4 | 12 | 32.13 | even | 8 | |||
1024.3.d.k.511.9 | 12 | 32.29 | even | 8 | |||
1024.3.d.k.511.10 | 12 | 32.19 | odd | 8 | |||
1152.3.m.a.415.1 | 6 | 48.35 | even | 4 | |||
1152.3.m.a.991.1 | 6 | 24.5 | odd | 2 | |||
1152.3.m.b.415.1 | 6 | 48.29 | odd | 4 | |||
1152.3.m.b.991.1 | 6 | 24.11 | even | 2 |