Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [55,2,Mod(34,55)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(55, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("55.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.b (of order \(2\), degree \(1\), 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: | \(0.439177211117\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.4 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 55.34 |
Dual form | 55.2.b.a.34.1 |
$q$-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 \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).
\(n\) | \(12\) | \(46\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.52434i | 1.78498i | 0.451071 | + | 0.892488i | \(0.351042\pi\) | ||||
−0.451071 | + | 0.892488i | \(0.648958\pi\) | |||||||
\(3\) | − | 0.792287i | − | 0.457427i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) | ||
0.973494 | − | 0.228714i | \(-0.0734519\pi\) | |||||||
\(4\) | −4.37228 | −2.18614 | ||||||||
\(5\) | 0.686141 | + | 2.12819i | 0.306851 | + | 0.951757i | ||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | − | 3.46410i | − | 1.30931i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||
0.755929 | − | 0.654654i | \(-0.227186\pi\) | |||||||
\(8\) | − | 5.98844i | − | 2.11723i | ||||||
\(9\) | 2.37228 | 0.790760 | ||||||||
\(10\) | −5.37228 | + | 1.73205i | −1.69886 | + | 0.547723i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.46410i | 1.00000i | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 8.74456 | 2.33708 | ||||||||
\(15\) | 1.68614 | − | 0.543620i | 0.435360 | − | 0.140362i | ||||
\(16\) | 6.37228 | 1.59307 | ||||||||
\(17\) | − | 1.58457i | − | 0.384316i | −0.981364 | − | 0.192158i | \(-0.938451\pi\) | ||
0.981364 | − | 0.192158i | \(-0.0615486\pi\) | |||||||
\(18\) | 5.98844i | 1.41149i | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | −3.00000 | − | 9.30506i | −0.670820 | − | 2.08068i | ||||
\(21\) | −2.74456 | −0.598913 | ||||||||
\(22\) | − | 2.52434i | − | 0.538191i | ||||||
\(23\) | 0.792287i | 0.165203i | 0.996583 | + | 0.0826016i | \(0.0263229\pi\) | ||||
−0.996583 | + | 0.0826016i | \(0.973677\pi\) | |||||||
\(24\) | −4.74456 | −0.968480 | ||||||||
\(25\) | −4.05842 | + | 2.92048i | −0.811684 | + | 0.584096i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.25639i | − | 0.819142i | ||||||
\(28\) | 15.1460i | 2.86233i | ||||||||
\(29\) | −8.74456 | −1.62382 | −0.811912 | − | 0.583779i | \(-0.801573\pi\) | ||||
−0.811912 | + | 0.583779i | \(0.801573\pi\) | |||||||
\(30\) | 1.37228 | + | 4.25639i | 0.250543 | + | 0.777107i | ||||
\(31\) | 3.37228 | 0.605680 | 0.302840 | − | 0.953041i | \(-0.402065\pi\) | ||||
0.302840 | + | 0.953041i | \(0.402065\pi\) | |||||||
\(32\) | 4.10891i | 0.726360i | ||||||||
\(33\) | 0.792287i | 0.137919i | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 7.37228 | − | 2.37686i | 1.24614 | − | 0.401763i | ||||
\(36\) | −10.3723 | −1.72871 | ||||||||
\(37\) | 1.08724i | 0.178741i | 0.995998 | + | 0.0893706i | \(0.0284856\pi\) | ||||
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | − | 10.0974i | − | 1.63801i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.7446 | − | 4.10891i | 2.01509 | − | 0.649676i | ||||
\(41\) | 8.74456 | 1.36567 | 0.682836 | − | 0.730572i | \(-0.260747\pi\) | ||||
0.682836 | + | 0.730572i | \(0.260747\pi\) | |||||||
\(42\) | − | 6.92820i | − | 1.06904i | ||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | 4.37228 | 0.659146 | ||||||||
\(45\) | 1.62772 | + | 5.04868i | 0.242646 | + | 0.752612i | ||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 6.63325i | 0.967559i | 0.875190 | + | 0.483779i | \(0.160736\pi\) | ||||
−0.875190 | + | 0.483779i | \(0.839264\pi\) | |||||||
\(48\) | − | 5.04868i | − | 0.728714i | ||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | −7.37228 | − | 10.2448i | −1.04260 | − | 1.44884i | ||||
\(51\) | −1.25544 | −0.175796 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0974i | 1.38698i | 0.720467 | + | 0.693489i | \(0.243927\pi\) | ||||
−0.720467 | + | 0.693489i | \(0.756073\pi\) | |||||||
\(54\) | 10.7446 | 1.46215 | ||||||||
\(55\) | −0.686141 | − | 2.12819i | −0.0925192 | − | 0.286966i | ||||
\(56\) | −20.7446 | −2.77211 | ||||||||
\(57\) | 3.16915i | 0.419764i | ||||||||
\(58\) | − | 22.0742i | − | 2.89849i | ||||||
\(59\) | 7.37228 | 0.959789 | 0.479895 | − | 0.877326i | \(-0.340675\pi\) | ||||
0.479895 | + | 0.877326i | \(0.340675\pi\) | |||||||
\(60\) | −7.37228 | + | 2.37686i | −0.951757 | + | 0.306851i | ||||
\(61\) | −0.744563 | −0.0953315 | −0.0476657 | − | 0.998863i | \(-0.515178\pi\) | ||||
−0.0476657 | + | 0.998863i | \(0.515178\pi\) | |||||||
\(62\) | 8.51278i | 1.08112i | ||||||||
\(63\) | − | 8.21782i | − | 1.03535i | ||||||
\(64\) | 2.37228 | 0.296535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.00000 | −0.246183 | ||||||||
\(67\) | − | 9.30506i | − | 1.13679i | −0.822754 | − | 0.568397i | \(-0.807564\pi\) | ||
0.822754 | − | 0.568397i | \(-0.192436\pi\) | |||||||
\(68\) | 6.92820i | 0.840168i | ||||||||
\(69\) | 0.627719 | 0.0755684 | ||||||||
\(70\) | 6.00000 | + | 18.6101i | 0.717137 | + | 2.22434i | ||||
\(71\) | −10.1168 | −1.20065 | −0.600324 | − | 0.799757i | \(-0.704962\pi\) | ||||
−0.600324 | + | 0.799757i | \(0.704962\pi\) | |||||||
\(72\) | − | 14.2063i | − | 1.67422i | ||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | −2.74456 | −0.319049 | ||||||||
\(75\) | 2.31386 | + | 3.21543i | 0.267181 | + | 0.371286i | ||||
\(76\) | 17.4891 | 2.00614 | ||||||||
\(77\) | 3.46410i | 0.394771i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.25544 | −0.141248 | −0.0706239 | − | 0.997503i | \(-0.522499\pi\) | ||||
−0.0706239 | + | 0.997503i | \(0.522499\pi\) | |||||||
\(80\) | 4.37228 | + | 13.5615i | 0.488836 | + | 1.51622i | ||||
\(81\) | 3.74456 | 0.416063 | ||||||||
\(82\) | 22.0742i | 2.43769i | ||||||||
\(83\) | 6.63325i | 0.728094i | 0.931381 | + | 0.364047i | \(0.118605\pi\) | ||||
−0.931381 | + | 0.364047i | \(0.881395\pi\) | |||||||
\(84\) | 12.0000 | 1.30931 | ||||||||
\(85\) | 3.37228 | − | 1.08724i | 0.365775 | − | 0.117928i | ||||
\(86\) | −8.74456 | −0.942950 | ||||||||
\(87\) | 6.92820i | 0.742781i | ||||||||
\(88\) | 5.98844i | 0.638370i | ||||||||
\(89\) | −1.37228 | −0.145462 | −0.0727308 | − | 0.997352i | \(-0.523171\pi\) | ||||
−0.0727308 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(90\) | −12.7446 | + | 4.10891i | −1.34339 | + | 0.433117i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 3.46410i | − | 0.361158i | ||||||
\(93\) | − | 2.67181i | − | 0.277054i | ||||||
\(94\) | −16.7446 | −1.72707 | ||||||||
\(95\) | −2.74456 | − | 8.51278i | −0.281586 | − | 0.873393i | ||||
\(96\) | 3.25544 | 0.332257 | ||||||||
\(97\) | − | 5.84096i | − | 0.593060i | −0.955024 | − | 0.296530i | \(-0.904171\pi\) | ||
0.955024 | − | 0.296530i | \(-0.0958295\pi\) | |||||||
\(98\) | − | 12.6217i | − | 1.27498i | ||||||
\(99\) | −2.37228 | −0.238423 | ||||||||
\(100\) | 17.7446 | − | 12.7692i | 1.77446 | − | 1.27692i | ||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | − | 3.16915i | − | 0.313792i | ||||||
\(103\) | − | 10.3923i | − | 1.02398i | −0.858990 | − | 0.511992i | \(-0.828908\pi\) | ||
0.858990 | − | 0.511992i | \(-0.171092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.88316 | − | 5.84096i | −0.183777 | − | 0.570020i | ||||
\(106\) | −25.4891 | −2.47572 | ||||||||
\(107\) | 6.63325i | 0.641260i | 0.947204 | + | 0.320630i | \(0.103895\pi\) | ||||
−0.947204 | + | 0.320630i | \(0.896105\pi\) | |||||||
\(108\) | 18.6101i | 1.79076i | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 5.37228 | − | 1.73205i | 0.512227 | − | 0.165145i | ||||
\(111\) | 0.861407 | 0.0817611 | ||||||||
\(112\) | − | 22.0742i | − | 2.08582i | ||||||
\(113\) | − | 0.497333i | − | 0.0467852i | −0.999726 | − | 0.0233926i | \(-0.992553\pi\) | ||
0.999726 | − | 0.0233926i | \(-0.00744677\pi\) | |||||||
\(114\) | −8.00000 | −0.749269 | ||||||||
\(115\) | −1.68614 | + | 0.543620i | −0.157233 | + | 0.0506929i | ||||
\(116\) | 38.2337 | 3.54991 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.6101i | 1.71320i | ||||||||
\(119\) | −5.48913 | −0.503187 | ||||||||
\(120\) | −3.25544 | − | 10.0974i | −0.297179 | − | 0.921758i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 1.87953i | − | 0.170164i | ||||||
\(123\) | − | 6.92820i | − | 0.624695i | ||||||
\(124\) | −14.7446 | −1.32410 | ||||||||
\(125\) | −9.00000 | − | 6.63325i | −0.804984 | − | 0.593296i | ||||
\(126\) | 20.7446 | 1.84807 | ||||||||
\(127\) | 8.21782i | 0.729214i | 0.931162 | + | 0.364607i | \(0.118797\pi\) | ||||
−0.931162 | + | 0.364607i | \(0.881203\pi\) | |||||||
\(128\) | 14.2063i | 1.25567i | ||||||||
\(129\) | 2.74456 | 0.241645 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.74456 | −0.239794 | −0.119897 | − | 0.992786i | \(-0.538256\pi\) | ||||
−0.119897 | + | 0.992786i | \(0.538256\pi\) | |||||||
\(132\) | − | 3.46410i | − | 0.301511i | ||||||
\(133\) | 13.8564i | 1.20150i | ||||||||
\(134\) | 23.4891 | 2.02915 | ||||||||
\(135\) | 9.05842 | − | 2.92048i | 0.779625 | − | 0.251355i | ||||
\(136\) | −9.48913 | −0.813686 | ||||||||
\(137\) | − | 14.3537i | − | 1.22632i | −0.789958 | − | 0.613161i | \(-0.789898\pi\) | ||
0.789958 | − | 0.613161i | \(-0.210102\pi\) | |||||||
\(138\) | 1.58457i | 0.134888i | ||||||||
\(139\) | 16.2337 | 1.37692 | 0.688462 | − | 0.725273i | \(-0.258286\pi\) | ||||
0.688462 | + | 0.725273i | \(0.258286\pi\) | |||||||
\(140\) | −32.2337 | + | 10.3923i | −2.72424 | + | 0.878310i | ||||
\(141\) | 5.25544 | 0.442588 | ||||||||
\(142\) | − | 25.5383i | − | 2.14313i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 15.1168 | 1.25974 | ||||||||
\(145\) | −6.00000 | − | 18.6101i | −0.498273 | − | 1.54549i | ||||
\(146\) | 17.4891 | 1.44741 | ||||||||
\(147\) | 3.96143i | 0.326734i | ||||||||
\(148\) | − | 4.75372i | − | 0.390754i | ||||||
\(149\) | 11.4891 | 0.941226 | 0.470613 | − | 0.882340i | \(-0.344033\pi\) | ||||
0.470613 | + | 0.882340i | \(0.344033\pi\) | |||||||
\(150\) | −8.11684 | + | 5.84096i | −0.662738 | + | 0.476913i | ||||
\(151\) | −12.2337 | −0.995563 | −0.497782 | − | 0.867302i | \(-0.665852\pi\) | ||||
−0.497782 | + | 0.867302i | \(0.665852\pi\) | |||||||
\(152\) | 23.9538i | 1.94291i | ||||||||
\(153\) | − | 3.75906i | − | 0.303902i | ||||||
\(154\) | −8.74456 | −0.704657 | ||||||||
\(155\) | 2.31386 | + | 7.17687i | 0.185854 | + | 0.576460i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.4511i | 1.95141i | 0.219090 | + | 0.975705i | \(0.429691\pi\) | ||||
−0.219090 | + | 0.975705i | \(0.570309\pi\) | |||||||
\(158\) | − | 3.16915i | − | 0.252124i | ||||||
\(159\) | 8.00000 | 0.634441 | ||||||||
\(160\) | −8.74456 | + | 2.81929i | −0.691318 | + | 0.222885i | ||||
\(161\) | 2.74456 | 0.216302 | ||||||||
\(162\) | 9.45254i | 0.742662i | ||||||||
\(163\) | − | 3.46410i | − | 0.271329i | −0.990755 | − | 0.135665i | \(-0.956683\pi\) | ||
0.990755 | − | 0.135665i | \(-0.0433170\pi\) | |||||||
\(164\) | −38.2337 | −2.98555 | ||||||||
\(165\) | −1.68614 | + | 0.543620i | −0.131266 | + | 0.0423208i | ||||
\(166\) | −16.7446 | −1.29963 | ||||||||
\(167\) | 15.7359i | 1.21768i | 0.793292 | + | 0.608842i | \(0.208365\pi\) | ||||
−0.793292 | + | 0.608842i | \(0.791635\pi\) | |||||||
\(168\) | 16.4356i | 1.26804i | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 2.74456 | + | 8.51278i | 0.210498 | + | 0.652900i | ||||
\(171\) | −9.48913 | −0.725652 | ||||||||
\(172\) | − | 15.1460i | − | 1.15487i | ||||||
\(173\) | − | 8.51278i | − | 0.647214i | −0.946192 | − | 0.323607i | \(-0.895104\pi\) | ||
0.946192 | − | 0.323607i | \(-0.104896\pi\) | |||||||
\(174\) | −17.4891 | −1.32585 | ||||||||
\(175\) | 10.1168 | + | 14.0588i | 0.764762 | + | 1.06274i | ||||
\(176\) | −6.37228 | −0.480329 | ||||||||
\(177\) | − | 5.84096i | − | 0.439034i | ||||||
\(178\) | − | 3.46410i | − | 0.259645i | ||||||
\(179\) | −12.8614 | −0.961307 | −0.480653 | − | 0.876911i | \(-0.659600\pi\) | ||||
−0.480653 | + | 0.876911i | \(0.659600\pi\) | |||||||
\(180\) | −7.11684 | − | 22.0742i | −0.530458 | − | 1.64532i | ||||
\(181\) | 24.1168 | 1.79259 | 0.896295 | − | 0.443457i | \(-0.146248\pi\) | ||||
0.896295 | + | 0.443457i | \(0.146248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.589907i | 0.0436072i | ||||||||
\(184\) | 4.74456 | 0.349774 | ||||||||
\(185\) | −2.31386 | + | 0.746000i | −0.170118 | + | 0.0548470i | ||||
\(186\) | 6.74456 | 0.494535 | ||||||||
\(187\) | 1.58457i | 0.115876i | ||||||||
\(188\) | − | 29.0024i | − | 2.11522i | ||||||
\(189\) | −14.7446 | −1.07251 | ||||||||
\(190\) | 21.4891 | − | 6.92820i | 1.55899 | − | 0.502625i | ||||
\(191\) | −19.3723 | −1.40173 | −0.700865 | − | 0.713294i | \(-0.747202\pi\) | ||||
−0.700865 | + | 0.713294i | \(0.747202\pi\) | |||||||
\(192\) | − | 1.87953i | − | 0.135643i | ||||||
\(193\) | − | 16.4356i | − | 1.18306i | −0.806282 | − | 0.591532i | \(-0.798523\pi\) | ||
0.806282 | − | 0.591532i | \(-0.201477\pi\) | |||||||
\(194\) | 14.7446 | 1.05860 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 21.8614 | 1.56153 | ||||||||
\(197\) | − | 8.51278i | − | 0.606510i | −0.952909 | − | 0.303255i | \(-0.901927\pi\) | ||
0.952909 | − | 0.303255i | \(-0.0980734\pi\) | |||||||
\(198\) | − | 5.98844i | − | 0.425580i | ||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 17.4891 | + | 24.3036i | 1.23667 | + | 1.71853i | ||||
\(201\) | −7.37228 | −0.520001 | ||||||||
\(202\) | 15.1460i | 1.06567i | ||||||||
\(203\) | 30.2921i | 2.12609i | ||||||||
\(204\) | 5.48913 | 0.384316 | ||||||||
\(205\) | 6.00000 | + | 18.6101i | 0.419058 | + | 1.29979i | ||||
\(206\) | 26.2337 | 1.82779 | ||||||||
\(207\) | 1.87953i | 0.130636i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 14.7446 | − | 4.75372i | 1.01747 | − | 0.328038i | ||||
\(211\) | 1.48913 | 0.102516 | 0.0512578 | − | 0.998685i | \(-0.483677\pi\) | ||||
0.0512578 | + | 0.998685i | \(0.483677\pi\) | |||||||
\(212\) | − | 44.1485i | − | 3.03213i | ||||||
\(213\) | 8.01544i | 0.549209i | ||||||||
\(214\) | −16.7446 | −1.14463 | ||||||||
\(215\) | −7.37228 | + | 2.37686i | −0.502785 | + | 0.162101i | ||||
\(216\) | −25.4891 | −1.73432 | ||||||||
\(217\) | − | 11.6819i | − | 0.793021i | ||||||
\(218\) | − | 25.2434i | − | 1.70970i | ||||||
\(219\) | −5.48913 | −0.370921 | ||||||||
\(220\) | 3.00000 | + | 9.30506i | 0.202260 | + | 0.627347i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.17448i | 0.145942i | ||||||||
\(223\) | − | 2.37686i | − | 0.159166i | −0.996828 | − | 0.0795832i | \(-0.974641\pi\) | ||
0.996828 | − | 0.0795832i | \(-0.0253589\pi\) | |||||||
\(224\) | 14.2337 | 0.951028 | ||||||||
\(225\) | −9.62772 | + | 6.92820i | −0.641848 | + | 0.461880i | ||||
\(226\) | 1.25544 | 0.0835105 | ||||||||
\(227\) | − | 16.7306i | − | 1.11045i | −0.831701 | − | 0.555224i | \(-0.812632\pi\) | ||
0.831701 | − | 0.555224i | \(-0.187368\pi\) | |||||||
\(228\) | − | 13.8564i | − | 0.917663i | ||||||
\(229\) | −14.6277 | −0.966627 | −0.483313 | − | 0.875447i | \(-0.660567\pi\) | ||||
−0.483313 | + | 0.875447i | \(0.660567\pi\) | |||||||
\(230\) | −1.37228 | − | 4.25639i | −0.0904856 | − | 0.280658i | ||||
\(231\) | 2.74456 | 0.180579 | ||||||||
\(232\) | 52.3663i | 3.43801i | ||||||||
\(233\) | − | 3.75906i | − | 0.246264i | −0.992390 | − | 0.123132i | \(-0.960706\pi\) | ||
0.992390 | − | 0.123132i | \(-0.0392938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.1168 | + | 4.55134i | −0.920881 | + | 0.296897i | ||||
\(236\) | −32.2337 | −2.09823 | ||||||||
\(237\) | 0.994667i | 0.0646105i | ||||||||
\(238\) | − | 13.8564i | − | 0.898177i | ||||||
\(239\) | 14.7446 | 0.953746 | 0.476873 | − | 0.878972i | \(-0.341770\pi\) | ||||
0.476873 | + | 0.878972i | \(0.341770\pi\) | |||||||
\(240\) | 10.7446 | − | 3.46410i | 0.693559 | − | 0.223607i | ||||
\(241\) | 16.7446 | 1.07861 | 0.539306 | − | 0.842110i | \(-0.318687\pi\) | ||||
0.539306 | + | 0.842110i | \(0.318687\pi\) | |||||||
\(242\) | 2.52434i | 0.162271i | ||||||||
\(243\) | − | 15.7359i | − | 1.00946i | ||||||
\(244\) | 3.25544 | 0.208408 | ||||||||
\(245\) | −3.43070 | − | 10.6410i | −0.219180 | − | 0.679827i | ||||
\(246\) | 17.4891 | 1.11507 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 20.1947i | − | 1.28236i | ||||||
\(249\) | 5.25544 | 0.333050 | ||||||||
\(250\) | 16.7446 | − | 22.7190i | 1.05902 | − | 1.43688i | ||||
\(251\) | −22.1168 | −1.39600 | −0.698001 | − | 0.716096i | \(-0.745927\pi\) | ||||
−0.698001 | + | 0.716096i | \(0.745927\pi\) | |||||||
\(252\) | 35.9306i | 2.26342i | ||||||||
\(253\) | − | 0.792287i | − | 0.0498107i | ||||||
\(254\) | −20.7446 | −1.30163 | ||||||||
\(255\) | −0.861407 | − | 2.67181i | −0.0539434 | − | 0.167316i | ||||
\(256\) | −31.1168 | −1.94480 | ||||||||
\(257\) | − | 10.6873i | − | 0.666653i | −0.942811 | − | 0.333326i | \(-0.891829\pi\) | ||
0.942811 | − | 0.333326i | \(-0.108171\pi\) | |||||||
\(258\) | 6.92820i | 0.431331i | ||||||||
\(259\) | 3.76631 | 0.234027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.7446 | −1.28406 | ||||||||
\(262\) | − | 6.92820i | − | 0.428026i | ||||||
\(263\) | 27.4179i | 1.69066i | 0.534246 | + | 0.845329i | \(0.320595\pi\) | ||||
−0.534246 | + | 0.845329i | \(0.679405\pi\) | |||||||
\(264\) | 4.74456 | 0.292008 | ||||||||
\(265\) | −21.4891 | + | 6.92820i | −1.32007 | + | 0.425596i | ||||
\(266\) | −34.9783 | −2.14465 | ||||||||
\(267\) | 1.08724i | 0.0665380i | ||||||||
\(268\) | 40.6844i | 2.48519i | ||||||||
\(269\) | 11.4891 | 0.700504 | 0.350252 | − | 0.936655i | \(-0.386096\pi\) | ||||
0.350252 | + | 0.936655i | \(0.386096\pi\) | |||||||
\(270\) | 7.37228 | + | 22.8665i | 0.448663 | + | 1.39161i | ||||
\(271\) | 13.4891 | 0.819406 | 0.409703 | − | 0.912219i | \(-0.365632\pi\) | ||||
0.409703 | + | 0.912219i | \(0.365632\pi\) | |||||||
\(272\) | − | 10.0974i | − | 0.612242i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 36.2337 | 2.18896 | ||||||||
\(275\) | 4.05842 | − | 2.92048i | 0.244732 | − | 0.176112i | ||||
\(276\) | −2.74456 | −0.165203 | ||||||||
\(277\) | 11.6819i | 0.701899i | 0.936394 | + | 0.350949i | \(0.114141\pi\) | ||||
−0.936394 | + | 0.350949i | \(0.885859\pi\) | |||||||
\(278\) | 40.9793i | 2.45778i | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | −14.2337 | − | 44.1485i | −0.850626 | − | 2.63838i | ||||
\(281\) | −0.510875 | −0.0304762 | −0.0152381 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152381 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(282\) | 13.2665i | 0.790009i | ||||||||
\(283\) | 15.1460i | 0.900338i | 0.892943 | + | 0.450169i | \(0.148636\pi\) | ||||
−0.892943 | + | 0.450169i | \(0.851364\pi\) | |||||||
\(284\) | 44.2337 | 2.62479 | ||||||||
\(285\) | −6.74456 | + | 2.17448i | −0.399513 | + | 0.128805i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 30.2921i | − | 1.78808i | ||||||
\(288\) | 9.74749i | 0.574377i | ||||||||
\(289\) | 14.4891 | 0.852301 | ||||||||
\(290\) | 46.9783 | − | 15.1460i | 2.75866 | − | 0.889405i | ||||
\(291\) | −4.62772 | −0.271282 | ||||||||
\(292\) | 30.2921i | 1.77271i | ||||||||
\(293\) | 3.16915i | 0.185144i | 0.995706 | + | 0.0925718i | \(0.0295088\pi\) | ||||
−0.995706 | + | 0.0925718i | \(0.970491\pi\) | |||||||
\(294\) | −10.0000 | −0.583212 | ||||||||
\(295\) | 5.05842 | + | 15.6896i | 0.294513 | + | 0.913487i | ||||
\(296\) | 6.51087 | 0.378437 | ||||||||
\(297\) | 4.25639i | 0.246981i | ||||||||
\(298\) | 29.0024i | 1.68007i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.1168 | − | 14.0588i | −0.584096 | − | 0.811684i | ||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | − | 30.8820i | − | 1.77706i | ||||||
\(303\) | − | 4.75372i | − | 0.273094i | ||||||
\(304\) | −25.4891 | −1.46190 | ||||||||
\(305\) | −0.510875 | − | 1.58457i | −0.0292526 | − | 0.0907324i | ||||
\(306\) | 9.48913 | 0.542457 | ||||||||
\(307\) | − | 31.5817i | − | 1.80246i | −0.433340 | − | 0.901231i | \(-0.642665\pi\) | ||
0.433340 | − | 0.901231i | \(-0.357335\pi\) | |||||||
\(308\) | − | 15.1460i | − | 0.863025i | ||||||
\(309\) | −8.23369 | −0.468398 | ||||||||
\(310\) | −18.1168 | + | 5.84096i | −1.02897 | + | 0.331744i | ||||
\(311\) | 5.48913 | 0.311260 | 0.155630 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155630 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.8719i | − | 1.23627i | −0.786072 | − | 0.618135i | \(-0.787888\pi\) | ||
0.786072 | − | 0.618135i | \(-0.212112\pi\) | |||||||
\(314\) | −61.7228 | −3.48322 | ||||||||
\(315\) | 17.4891 | − | 5.63858i | 0.985401 | − | 0.317698i | ||||
\(316\) | 5.48913 | 0.308787 | ||||||||
\(317\) | − | 32.9639i | − | 1.85144i | −0.378215 | − | 0.925718i | \(-0.623462\pi\) | ||
0.378215 | − | 0.925718i | \(-0.376538\pi\) | |||||||
\(318\) | 20.1947i | 1.13246i | ||||||||
\(319\) | 8.74456 | 0.489602 | ||||||||
\(320\) | 1.62772 | + | 5.04868i | 0.0909922 | + | 0.282230i | ||||
\(321\) | 5.25544 | 0.293330 | ||||||||
\(322\) | 6.92820i | 0.386094i | ||||||||
\(323\) | 6.33830i | 0.352672i | ||||||||
\(324\) | −16.3723 | −0.909571 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.74456 | 0.484317 | ||||||||
\(327\) | 7.92287i | 0.438136i | ||||||||
\(328\) | − | 52.3663i | − | 2.89144i | ||||||
\(329\) | 22.9783 | 1.26683 | ||||||||
\(330\) | −1.37228 | − | 4.25639i | −0.0755416 | − | 0.234306i | ||||
\(331\) | −14.1168 | −0.775932 | −0.387966 | − | 0.921674i | \(-0.626822\pi\) | ||||
−0.387966 | + | 0.921674i | \(0.626822\pi\) | |||||||
\(332\) | − | 29.0024i | − | 1.59172i | ||||||
\(333\) | 2.57924i | 0.141342i | ||||||||
\(334\) | −39.7228 | −2.17354 | ||||||||
\(335\) | 19.8030 | − | 6.38458i | 1.08195 | − | 0.348827i | ||||
\(336\) | −17.4891 | −0.954110 | ||||||||
\(337\) | 32.4665i | 1.76856i | 0.466952 | + | 0.884282i | \(0.345352\pi\) | ||||
−0.466952 | + | 0.884282i | \(0.654648\pi\) | |||||||
\(338\) | 32.8164i | 1.78498i | ||||||||
\(339\) | −0.394031 | −0.0214008 | ||||||||
\(340\) | −14.7446 | + | 4.75372i | −0.799636 | + | 0.257807i | ||||
\(341\) | −3.37228 | −0.182619 | ||||||||
\(342\) | − | 23.9538i | − | 1.29527i | ||||||
\(343\) | − | 6.92820i | − | 0.374088i | ||||||
\(344\) | 20.7446 | 1.11847 | ||||||||
\(345\) | 0.430703 | + | 1.33591i | 0.0231883 | + | 0.0719228i | ||||
\(346\) | 21.4891 | 1.15526 | ||||||||
\(347\) | 22.6641i | 1.21667i | 0.793679 | + | 0.608337i | \(0.208163\pi\) | ||||
−0.793679 | + | 0.608337i | \(0.791837\pi\) | |||||||
\(348\) | − | 30.2921i | − | 1.62382i | ||||||
\(349\) | −15.4891 | −0.829114 | −0.414557 | − | 0.910023i | \(-0.636063\pi\) | ||||
−0.414557 | + | 0.910023i | \(0.636063\pi\) | |||||||
\(350\) | −35.4891 | + | 25.5383i | −1.89697 | + | 1.36508i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.10891i | − | 0.219006i | ||||||
\(353\) | 25.0410i | 1.33280i | 0.745595 | + | 0.666399i | \(0.232165\pi\) | ||||
−0.745595 | + | 0.666399i | \(0.767835\pi\) | |||||||
\(354\) | 14.7446 | 0.783665 | ||||||||
\(355\) | −6.94158 | − | 21.5306i | −0.368421 | − | 1.14273i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 4.34896i | 0.230172i | ||||||||
\(358\) | − | 32.4665i | − | 1.71591i | ||||||
\(359\) | −29.4891 | −1.55638 | −0.778188 | − | 0.628031i | \(-0.783861\pi\) | ||||
−0.778188 | + | 0.628031i | \(0.783861\pi\) | |||||||
\(360\) | 30.2337 | − | 9.74749i | 1.59346 | − | 0.513738i | ||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 60.8791i | 3.19973i | ||||||||
\(363\) | − | 0.792287i | − | 0.0415843i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7446 | − | 4.75372i | 0.771766 | − | 0.248821i | ||||
\(366\) | −1.48913 | −0.0778378 | ||||||||
\(367\) | − | 25.7407i | − | 1.34365i | −0.740708 | − | 0.671827i | \(-0.765510\pi\) | ||
0.740708 | − | 0.671827i | \(-0.234490\pi\) | |||||||
\(368\) | 5.04868i | 0.263180i | ||||||||
\(369\) | 20.7446 | 1.07992 | ||||||||
\(370\) | −1.88316 | − | 5.84096i | −0.0979006 | − | 0.303657i | ||||
\(371\) | 34.9783 | 1.81598 | ||||||||
\(372\) | 11.6819i | 0.605680i | ||||||||
\(373\) | − | 11.6819i | − | 0.604867i | −0.953170 | − | 0.302434i | \(-0.902201\pi\) | ||
0.953170 | − | 0.302434i | \(-0.0977990\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | −5.25544 | + | 7.13058i | −0.271390 | + | 0.368222i | ||||
\(376\) | 39.7228 | 2.04855 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | − | 37.2203i | − | 1.91440i | ||||||
\(379\) | 0.627719 | 0.0322437 | 0.0161219 | − | 0.999870i | \(-0.494868\pi\) | ||||
0.0161219 | + | 0.999870i | \(0.494868\pi\) | |||||||
\(380\) | 12.0000 | + | 37.2203i | 0.615587 | + | 1.90936i | ||||
\(381\) | 6.51087 | 0.333562 | ||||||||
\(382\) | − | 48.9022i | − | 2.50205i | ||||||
\(383\) | − | 10.8896i | − | 0.556435i | −0.960518 | − | 0.278217i | \(-0.910256\pi\) | ||
0.960518 | − | 0.278217i | \(-0.0897435\pi\) | |||||||
\(384\) | 11.2554 | 0.574377 | ||||||||
\(385\) | −7.37228 | + | 2.37686i | −0.375726 | + | 0.121136i | ||||
\(386\) | 41.4891 | 2.11174 | ||||||||
\(387\) | 8.21782i | 0.417735i | ||||||||
\(388\) | 25.5383i | 1.29651i | ||||||||
\(389\) | −18.8614 | −0.956311 | −0.478156 | − | 0.878275i | \(-0.658695\pi\) | ||||
−0.478156 | + | 0.878275i | \(0.658695\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25544 | 0.0634902 | ||||||||
\(392\) | 29.9422i | 1.51231i | ||||||||
\(393\) | 2.17448i | 0.109688i | ||||||||
\(394\) | 21.4891 | 1.08261 | ||||||||
\(395\) | −0.861407 | − | 2.67181i | −0.0433421 | − | 0.134434i | ||||
\(396\) | 10.3723 | 0.521227 | ||||||||
\(397\) | 16.4356i | 0.824881i | 0.910984 | + | 0.412441i | \(0.135324\pi\) | ||||
−0.910984 | + | 0.412441i | \(0.864676\pi\) | |||||||
\(398\) | 20.1947i | 1.01227i | ||||||||
\(399\) | 10.9783 | 0.549600 | ||||||||
\(400\) | −25.8614 | + | 18.6101i | −1.29307 | + | 0.930506i | ||||
\(401\) | −11.4891 | −0.573740 | −0.286870 | − | 0.957970i | \(-0.592615\pi\) | ||||
−0.286870 | + | 0.957970i | \(0.592615\pi\) | |||||||
\(402\) | − | 18.6101i | − | 0.928189i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −26.2337 | −1.30517 | ||||||||
\(405\) | 2.56930 | + | 7.96916i | 0.127669 | + | 0.395991i | ||||
\(406\) | −76.4674 | −3.79501 | ||||||||
\(407\) | − | 1.08724i | − | 0.0538925i | ||||||
\(408\) | 7.51811i | 0.372202i | ||||||||
\(409\) | −27.4891 | −1.35925 | −0.679625 | − | 0.733560i | \(-0.737857\pi\) | ||||
−0.679625 | + | 0.733560i | \(0.737857\pi\) | |||||||
\(410\) | −46.9783 | + | 15.1460i | −2.32009 | + | 0.748009i | ||||
\(411\) | −11.3723 | −0.560953 | ||||||||
\(412\) | 45.4381i | 2.23857i | ||||||||
\(413\) | − | 25.5383i | − | 1.25666i | ||||||
\(414\) | −4.74456 | −0.233183 | ||||||||
\(415\) | −14.1168 | + | 4.55134i | −0.692969 | + | 0.223417i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12.8617i | − | 0.629842i | ||||||
\(418\) | 10.0974i | 0.493878i | ||||||||
\(419\) | 22.9783 | 1.12256 | 0.561280 | − | 0.827626i | \(-0.310309\pi\) | ||||
0.561280 | + | 0.827626i | \(0.310309\pi\) | |||||||
\(420\) | 8.23369 | + | 25.5383i | 0.401763 | + | 1.24614i | ||||
\(421\) | 8.51087 | 0.414795 | 0.207397 | − | 0.978257i | \(-0.433501\pi\) | ||||
0.207397 | + | 0.978257i | \(0.433501\pi\) | |||||||
\(422\) | 3.75906i | 0.182988i | ||||||||
\(423\) | 15.7359i | 0.765107i | ||||||||
\(424\) | 60.4674 | 2.93656 | ||||||||
\(425\) | 4.62772 | + | 6.43087i | 0.224477 | + | 0.311943i | ||||
\(426\) | −20.2337 | −0.980325 | ||||||||
\(427\) | 2.57924i | 0.124818i | ||||||||
\(428\) | − | 29.0024i | − | 1.40189i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00000 | − | 18.6101i | −0.289346 | − | 0.897460i | ||||
\(431\) | −25.7228 | −1.23902 | −0.619512 | − | 0.784987i | \(-0.712670\pi\) | ||||
−0.619512 | + | 0.784987i | \(0.712670\pi\) | |||||||
\(432\) | − | 27.1229i | − | 1.30495i | ||||||
\(433\) | 29.2048i | 1.40349i | 0.712426 | + | 0.701747i | \(0.247596\pi\) | ||||
−0.712426 | + | 0.701747i | \(0.752404\pi\) | |||||||
\(434\) | 29.4891 | 1.41552 | ||||||||
\(435\) | −14.7446 | + | 4.75372i | −0.706948 | + | 0.227924i | ||||
\(436\) | 43.7228 | 2.09394 | ||||||||
\(437\) | − | 3.16915i | − | 0.151601i | ||||||
\(438\) | − | 13.8564i | − | 0.662085i | ||||||
\(439\) | −21.4891 | −1.02562 | −0.512810 | − | 0.858502i | \(-0.671395\pi\) | ||||
−0.512810 | + | 0.858502i | \(0.671395\pi\) | |||||||
\(440\) | −12.7446 | + | 4.10891i | −0.607573 | + | 0.195885i | ||||
\(441\) | −11.8614 | −0.564829 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 31.6742i | − | 1.50489i | −0.658656 | − | 0.752444i | \(-0.728875\pi\) | ||
0.658656 | − | 0.752444i | \(-0.271125\pi\) | |||||||
\(444\) | −3.76631 | −0.178741 | ||||||||
\(445\) | −0.941578 | − | 2.92048i | −0.0446351 | − | 0.138444i | ||||
\(446\) | 6.00000 | 0.284108 | ||||||||
\(447\) | − | 9.10268i | − | 0.430542i | ||||||
\(448\) | − | 8.21782i | − | 0.388256i | ||||||
\(449\) | −6.86141 | −0.323810 | −0.161905 | − | 0.986806i | \(-0.551764\pi\) | ||||
−0.161905 | + | 0.986806i | \(0.551764\pi\) | |||||||
\(450\) | −17.4891 | − | 24.3036i | −0.824445 | − | 1.14568i | ||||
\(451\) | −8.74456 | −0.411765 | ||||||||
\(452\) | 2.17448i | 0.102279i | ||||||||
\(453\) | 9.69259i | 0.455398i | ||||||||
\(454\) | 42.2337 | 1.98213 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.9783 | 0.888738 | ||||||||
\(457\) | 20.7846i | 0.972263i | 0.873886 | + | 0.486132i | \(0.161592\pi\) | ||||
−0.873886 | + | 0.486132i | \(0.838408\pi\) | |||||||
\(458\) | − | 36.9253i | − | 1.72541i | ||||||
\(459\) | −6.74456 | −0.314809 | ||||||||
\(460\) | 7.37228 | − | 2.37686i | 0.343734 | − | 0.110822i | ||||
\(461\) | 2.23369 | 0.104033 | 0.0520166 | − | 0.998646i | \(-0.483435\pi\) | ||||
0.0520166 | + | 0.998646i | \(0.483435\pi\) | |||||||
\(462\) | 6.92820i | 0.322329i | ||||||||
\(463\) | − | 30.0897i | − | 1.39839i | −0.714933 | − | 0.699193i | \(-0.753543\pi\) | ||
0.714933 | − | 0.699193i | \(-0.246457\pi\) | |||||||
\(464\) | −55.7228 | −2.58687 | ||||||||
\(465\) | 5.68614 | − | 1.83324i | 0.263688 | − | 0.0850145i | ||||
\(466\) | 9.48913 | 0.439575 | ||||||||
\(467\) | 7.72049i | 0.357262i | 0.983916 | + | 0.178631i | \(0.0571668\pi\) | ||||
−0.983916 | + | 0.178631i | \(0.942833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.2337 | −1.48841 | ||||||||
\(470\) | −11.4891 | − | 35.6357i | −0.529954 | − | 1.64375i | ||||
\(471\) | 19.3723 | 0.892628 | ||||||||
\(472\) | − | 44.1485i | − | 2.03210i | ||||||
\(473\) | − | 3.46410i | − | 0.159280i | ||||||
\(474\) | −2.51087 | −0.115328 | ||||||||
\(475\) | 16.2337 | − | 11.6819i | 0.744853 | − | 0.536003i | ||||
\(476\) | 24.0000 | 1.10004 | ||||||||
\(477\) | 23.9538i | 1.09677i | ||||||||
\(478\) | 37.2203i | 1.70241i | ||||||||
\(479\) | 5.48913 | 0.250805 | 0.125402 | − | 0.992106i | \(-0.459978\pi\) | ||||
0.125402 | + | 0.992106i | \(0.459978\pi\) | |||||||
\(480\) | 2.23369 | + | 6.92820i | 0.101953 | + | 0.316228i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 42.2689i | 1.92530i | ||||||||
\(483\) | − | 2.17448i | − | 0.0989423i | ||||||
\(484\) | −4.37228 | −0.198740 | ||||||||
\(485\) | 12.4307 | − | 4.00772i | 0.564449 | − | 0.181981i | ||||
\(486\) | 39.7228 | 1.80186 | ||||||||
\(487\) | 7.13058i | 0.323118i | 0.986863 | + | 0.161559i | \(0.0516521\pi\) | ||||
−0.986863 | + | 0.161559i | \(0.948348\pi\) | |||||||
\(488\) | 4.45877i | 0.201839i | ||||||||
\(489\) | −2.74456 | −0.124113 | ||||||||
\(490\) | 26.8614 | − | 8.66025i | 1.21347 | − | 0.391230i | ||||
\(491\) | 6.51087 | 0.293832 | 0.146916 | − | 0.989149i | \(-0.453065\pi\) | ||||
0.146916 | + | 0.989149i | \(0.453065\pi\) | |||||||
\(492\) | 30.2921i | 1.36567i | ||||||||
\(493\) | 13.8564i | 0.624061i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.62772 | − | 5.04868i | −0.0731605 | − | 0.226921i | ||||
\(496\) | 21.4891 | 0.964890 | ||||||||
\(497\) | 35.0458i | 1.57202i | ||||||||
\(498\) | 13.2665i | 0.594486i | ||||||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 39.3505 | + | 29.0024i | 1.75981 | + | 1.29703i | ||||
\(501\) | 12.4674 | 0.557001 | ||||||||
\(502\) | − | 55.8304i | − | 2.49183i | ||||||
\(503\) | 13.5615i | 0.604675i | 0.953201 | + | 0.302338i | \(0.0977670\pi\) | ||||
−0.953201 | + | 0.302338i | \(0.902233\pi\) | |||||||
\(504\) | −49.2119 | −2.19207 | ||||||||
\(505\) | 4.11684 | + | 12.7692i | 0.183197 | + | 0.568220i | ||||
\(506\) | 2.00000 | 0.0889108 | ||||||||
\(507\) | − | 10.2997i | − | 0.457427i | ||||||
\(508\) | − | 35.9306i | − | 1.59416i | ||||||
\(509\) | −22.6277 | −1.00296 | −0.501478 | − | 0.865170i | \(-0.667210\pi\) | ||||
−0.501478 | + | 0.865170i | \(0.667210\pi\) | |||||||
\(510\) | 6.74456 | − | 2.17448i | 0.298654 | − | 0.0962876i | ||||
\(511\) | −24.0000 | −1.06170 | ||||||||
\(512\) | − | 50.1369i | − | 2.21576i | ||||||
\(513\) | 17.0256i | 0.751697i | ||||||||
\(514\) | 26.9783 | 1.18996 | ||||||||
\(515\) | 22.1168 | − | 7.13058i | 0.974585 | − | 0.314211i | ||||
\(516\) | −12.0000 | −0.528271 | ||||||||
\(517\) | − | 6.63325i | − | 0.291730i | ||||||
\(518\) | 9.50744i | 0.417733i | ||||||||
\(519\) | −6.74456 | −0.296053 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.6060 | −0.946575 | −0.473287 | − | 0.880908i | \(-0.656933\pi\) | ||||
−0.473287 | + | 0.880908i | \(0.656933\pi\) | |||||||
\(522\) | − | 52.3663i | − | 2.29201i | ||||||
\(523\) | 29.0024i | 1.26819i | 0.773256 | + | 0.634094i | \(0.218627\pi\) | ||||
−0.773256 | + | 0.634094i | \(0.781373\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | 11.1386 | − | 8.01544i | 0.486128 | − | 0.349823i | ||||
\(526\) | −69.2119 | −3.01778 | ||||||||
\(527\) | − | 5.34363i | − | 0.232772i | ||||||
\(528\) | 5.04868i | 0.219715i | ||||||||
\(529\) | 22.3723 | 0.972708 | ||||||||
\(530\) | −17.4891 | − | 54.2458i | −0.759679 | − | 2.35629i | ||||
\(531\) | 17.4891 | 0.758963 | ||||||||
\(532\) | − | 60.5841i | − | 2.62665i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.74456 | −0.118769 | ||||||||
\(535\) | −14.1168 | + | 4.55134i | −0.610324 | + | 0.196772i | ||||
\(536\) | −55.7228 | −2.40686 | ||||||||
\(537\) | 10.1899i | 0.439728i | ||||||||
\(538\) | 29.0024i | 1.25038i | ||||||||
\(539\) | 5.00000 | 0.215365 | ||||||||
\(540\) | −39.6060 | + | 12.7692i | −1.70437 | + | 0.549497i | ||||
\(541\) | 34.2337 | 1.47182 | 0.735911 | − | 0.677079i | \(-0.236754\pi\) | ||||
0.735911 | + | 0.677079i | \(0.236754\pi\) | |||||||
\(542\) | 34.0511i | 1.46262i | ||||||||
\(543\) | − | 19.1075i | − | 0.819980i | ||||||
\(544\) | 6.51087 | 0.279151 | ||||||||
\(545\) | −6.86141 | − | 21.2819i | −0.293910 | − | 0.911618i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0024i | 1.24005i | 0.784580 | + | 0.620027i | \(0.212878\pi\) | ||||
−0.784580 | + | 0.620027i | \(0.787122\pi\) | |||||||
\(548\) | 62.7586i | 2.68091i | ||||||||
\(549\) | −1.76631 | −0.0753844 | ||||||||
\(550\) | 7.37228 | + | 10.2448i | 0.314355 | + | 0.436841i | ||||
\(551\) | 34.9783 | 1.49012 | ||||||||
\(552\) | − | 3.75906i | − | 0.159996i | ||||||
\(553\) | 4.34896i | 0.184937i | ||||||||
\(554\) | −29.4891 | −1.25287 | ||||||||
\(555\) | 0.591046 | + | 1.83324i | 0.0250885 | + | 0.0778167i | ||||
\(556\) | −70.9783 | −3.01015 | ||||||||
\(557\) | 0.994667i | 0.0421454i | 0.999778 | + | 0.0210727i | \(0.00670814\pi\) | ||||
−0.999778 | + | 0.0210727i | \(0.993292\pi\) | |||||||
\(558\) | 20.1947i | 0.854910i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 46.9783 | − | 15.1460i | 1.98519 | − | 0.640036i | ||||
\(561\) | 1.25544 | 0.0530046 | ||||||||
\(562\) | − | 1.28962i | − | 0.0543994i | ||||||
\(563\) | − | 18.9051i | − | 0.796754i | −0.917222 | − | 0.398377i | \(-0.869574\pi\) | ||
0.917222 | − | 0.398377i | \(-0.130426\pi\) | |||||||
\(564\) | −22.9783 | −0.967559 | ||||||||
\(565\) | 1.05842 | − | 0.341241i | 0.0445281 | − | 0.0143561i | ||||
\(566\) | −38.2337 | −1.60708 | ||||||||
\(567\) | − | 12.9715i | − | 0.544754i | ||||||
\(568\) | 60.5841i | 2.54205i | ||||||||
\(569\) | 27.2554 | 1.14261 | 0.571304 | − | 0.820739i | \(-0.306438\pi\) | ||||
0.571304 | + | 0.820739i | \(0.306438\pi\) | |||||||
\(570\) | −5.48913 | − | 17.0256i | −0.229914 | − | 0.713122i | ||||
\(571\) | 1.48913 | 0.0623180 | 0.0311590 | − | 0.999514i | \(-0.490080\pi\) | ||||
0.0311590 | + | 0.999514i | \(0.490080\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.3484i | 0.641189i | ||||||||
\(574\) | 76.4674 | 3.19169 | ||||||||
\(575\) | −2.31386 | − | 3.21543i | −0.0964946 | − | 0.134093i | ||||
\(576\) | 5.62772 | 0.234488 | ||||||||
\(577\) | − | 21.8719i | − | 0.910537i | −0.890354 | − | 0.455269i | \(-0.849543\pi\) | ||
0.890354 | − | 0.455269i | \(-0.150457\pi\) | |||||||
\(578\) | 36.5754i | 1.52134i | ||||||||
\(579\) | −13.0217 | −0.541165 | ||||||||
\(580\) | 26.2337 | + | 81.3687i | 1.08929 | + | 3.37865i | ||||
\(581\) | 22.9783 | 0.953298 | ||||||||
\(582\) | − | 11.6819i | − | 0.484231i | ||||||
\(583\) | − | 10.0974i | − | 0.418190i | ||||||
\(584\) | −41.4891 | −1.71683 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.00000 | −0.330477 | ||||||||
\(587\) | 41.2743i | 1.70357i | 0.523890 | + | 0.851786i | \(0.324480\pi\) | ||||
−0.523890 | + | 0.851786i | \(0.675520\pi\) | |||||||
\(588\) | − | 17.3205i | − | 0.714286i | ||||||
\(589\) | −13.4891 | −0.555810 | ||||||||
\(590\) | −39.6060 | + | 12.7692i | −1.63055 | + | 0.525698i | ||||
\(591\) | −6.74456 | −0.277434 | ||||||||
\(592\) | 6.92820i | 0.284747i | ||||||||
\(593\) | − | 22.7739i | − | 0.935214i | −0.883937 | − | 0.467607i | \(-0.845116\pi\) | ||
0.883937 | − | 0.467607i | \(-0.154884\pi\) | |||||||
\(594\) | −10.7446 | −0.440855 | ||||||||
\(595\) | −3.76631 | − | 11.6819i | −0.154404 | − | 0.478912i | ||||
\(596\) | −50.2337 | −2.05765 | ||||||||
\(597\) | − | 6.33830i | − | 0.259409i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9783 | −0.448559 | −0.224280 | − | 0.974525i | \(-0.572003\pi\) | ||||
−0.224280 | + | 0.974525i | \(0.572003\pi\) | |||||||
\(600\) | 19.2554 | − | 13.8564i | 0.786100 | − | 0.565685i | ||||
\(601\) | −38.4674 | −1.56912 | −0.784558 | − | 0.620055i | \(-0.787110\pi\) | ||||
−0.784558 | + | 0.620055i | \(0.787110\pi\) | |||||||
\(602\) | 30.2921i | 1.23461i | ||||||||
\(603\) | − | 22.0742i | − | 0.898932i | ||||||
\(604\) | 53.4891 | 2.17644 | ||||||||
\(605\) | 0.686141 | + | 2.12819i | 0.0278956 | + | 0.0865234i | ||||
\(606\) | 12.0000 | 0.487467 | ||||||||
\(607\) | − | 3.46410i | − | 0.140604i | −0.997526 | − | 0.0703018i | \(-0.977604\pi\) | ||
0.997526 | − | 0.0703018i | \(-0.0223962\pi\) | |||||||
\(608\) | − | 16.4356i | − | 0.666554i | ||||||
\(609\) | 24.0000 | 0.972529 | ||||||||
\(610\) | 4.00000 | − | 1.28962i | 0.161955 | − | 0.0522152i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 16.4356i | 0.664372i | ||||||||
\(613\) | − | 4.34896i | − | 0.175653i | −0.996136 | − | 0.0878265i | \(-0.972008\pi\) | ||
0.996136 | − | 0.0878265i | \(-0.0279921\pi\) | |||||||
\(614\) | 79.7228 | 3.21735 | ||||||||
\(615\) | 14.7446 | − | 4.75372i | 0.594558 | − | 0.191689i | ||||
\(616\) | 20.7446 | 0.835822 | ||||||||
\(617\) | 17.0256i | 0.685423i | 0.939441 | + | 0.342712i | \(0.111345\pi\) | ||||
−0.939441 | + | 0.342712i | \(0.888655\pi\) | |||||||
\(618\) | − | 20.7846i | − | 0.836080i | ||||||
\(619\) | −14.1168 | −0.567404 | −0.283702 | − | 0.958913i | \(-0.591563\pi\) | ||||
−0.283702 | + | 0.958913i | \(0.591563\pi\) | |||||||
\(620\) | −10.1168 | − | 31.3793i | −0.406302 | − | 1.26022i | ||||
\(621\) | 3.37228 | 0.135325 | ||||||||
\(622\) | 13.8564i | 0.555591i | ||||||||
\(623\) | 4.75372i | 0.190454i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.94158 | − | 23.7051i | 0.317663 | − | 0.948204i | ||||
\(626\) | 55.2119 | 2.20671 | ||||||||
\(627\) | − | 3.16915i | − | 0.126564i | ||||||
\(628\) | − | 106.907i | − | 4.26606i | ||||||
\(629\) | 1.72281 | 0.0686931 | ||||||||
\(630\) | 14.2337 | + | 44.1485i | 0.567084 | + | 1.75892i | ||||
\(631\) | 23.6060 | 0.939739 | 0.469869 | − | 0.882736i | \(-0.344301\pi\) | ||||
0.469869 | + | 0.882736i | \(0.344301\pi\) | |||||||
\(632\) | 7.51811i | 0.299054i | ||||||||
\(633\) | − | 1.17981i | − | 0.0468934i | ||||||
\(634\) | 83.2119 | 3.30477 | ||||||||
\(635\) | −17.4891 | + | 5.63858i | −0.694035 | + | 0.223760i | ||||
\(636\) | −34.9783 | −1.38698 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.0742i | 0.873927i | ||||||||
\(639\) | −24.0000 | −0.949425 | ||||||||
\(640\) | −30.2337 | + | 9.74749i | −1.19509 | + | 0.385304i | ||||
\(641\) | −25.3723 | −1.00214 | −0.501072 | − | 0.865405i | \(-0.667061\pi\) | ||||
−0.501072 | + | 0.865405i | \(0.667061\pi\) | |||||||
\(642\) | 13.2665i | 0.523587i | ||||||||
\(643\) | − | 30.4944i | − | 1.20258i | −0.799030 | − | 0.601292i | \(-0.794653\pi\) | ||
0.799030 | − | 0.601292i | \(-0.205347\pi\) | |||||||
\(644\) | −12.0000 | −0.472866 | ||||||||
\(645\) | 1.88316 | + | 5.84096i | 0.0741492 | + | 0.229988i | ||||
\(646\) | −16.0000 | −0.629512 | ||||||||
\(647\) | 21.9817i | 0.864188i | 0.901829 | + | 0.432094i | \(0.142225\pi\) | ||||
−0.901829 | + | 0.432094i | \(0.857775\pi\) | |||||||
\(648\) | − | 22.4241i | − | 0.880901i | ||||||
\(649\) | −7.37228 | −0.289387 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.25544 | −0.362749 | ||||||||
\(652\) | 15.1460i | 0.593164i | ||||||||
\(653\) | − | 30.7894i | − | 1.20488i | −0.798163 | − | 0.602441i | \(-0.794195\pi\) | ||
0.798163 | − | 0.602441i | \(-0.205805\pi\) | |||||||
\(654\) | −20.0000 | −0.782062 | ||||||||
\(655\) | −1.88316 | − | 5.84096i | −0.0735810 | − | 0.228225i | ||||
\(656\) | 55.7228 | 2.17561 | ||||||||
\(657\) | − | 16.4356i | − | 0.641216i | ||||||
\(658\) | 58.0049i | 2.26127i | ||||||||
\(659\) | −21.2554 | −0.827994 | −0.413997 | − | 0.910278i | \(-0.635868\pi\) | ||||
−0.413997 | + | 0.910278i | \(0.635868\pi\) | |||||||
\(660\) | 7.37228 | − | 2.37686i | 0.286966 | − | 0.0925192i | ||||
\(661\) | −16.3505 | −0.635962 | −0.317981 | − | 0.948097i | \(-0.603005\pi\) | ||||
−0.317981 | + | 0.948097i | \(0.603005\pi\) | |||||||
\(662\) | − | 35.6357i | − | 1.38502i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 39.7228 | 1.54154 | ||||||||
\(665\) | −29.4891 | + | 9.50744i | −1.14354 | + | 0.368683i | ||||
\(666\) | −6.51087 | −0.252291 | ||||||||
\(667\) | − | 6.92820i | − | 0.268261i | ||||||
\(668\) | − | 68.8019i | − | 2.66203i | ||||||
\(669\) | −1.88316 | −0.0728070 | ||||||||
\(670\) | 16.1168 | + | 49.9894i | 0.622648 | + | 1.93126i | ||||
\(671\) | 0.744563 | 0.0287435 | ||||||||
\(672\) | − | 11.2772i | − | 0.435026i | ||||||
\(673\) | 18.6101i | 0.717368i | 0.933459 | + | 0.358684i | \(0.116774\pi\) | ||||
−0.933459 | + | 0.358684i | \(0.883226\pi\) | |||||||
\(674\) | −81.9565 | −3.15685 | ||||||||
\(675\) | 12.4307 | + | 17.2742i | 0.478458 | + | 0.664885i | ||||
\(676\) | −56.8397 | −2.18614 | ||||||||
\(677\) | − | 50.0820i | − | 1.92481i | −0.271623 | − | 0.962404i | \(-0.587560\pi\) | ||
0.271623 | − | 0.962404i | \(-0.412440\pi\) | |||||||
\(678\) | − | 0.994667i | − | 0.0381999i | ||||||
\(679\) | −20.2337 | −0.776498 | ||||||||
\(680\) | −6.51087 | − | 20.1947i | −0.249681 | − | 0.774431i | ||||
\(681\) | −13.2554 | −0.507949 | ||||||||
\(682\) | − | 8.51278i | − | 0.325971i | ||||||
\(683\) | 17.9104i | 0.685323i | 0.939459 | + | 0.342661i | \(0.111328\pi\) | ||||
−0.939459 | + | 0.342661i | \(0.888672\pi\) | |||||||
\(684\) | 41.4891 | 1.58638 | ||||||||
\(685\) | 30.5475 | − | 9.84868i | 1.16716 | − | 0.376299i | ||||
\(686\) | 17.4891 | 0.667738 | ||||||||
\(687\) | 11.5894i | 0.442161i | ||||||||
\(688\) | 22.0742i | 0.841572i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.37228 | + | 1.08724i | −0.128381 | + | 0.0413905i | ||||
\(691\) | 44.8614 | 1.70661 | 0.853304 | − | 0.521413i | \(-0.174595\pi\) | ||||
0.853304 | + | 0.521413i | \(0.174595\pi\) | |||||||
\(692\) | 37.2203i | 1.41490i | ||||||||
\(693\) | 8.21782i | 0.312169i | ||||||||
\(694\) | −57.2119 | −2.17174 | ||||||||
\(695\) | 11.1386 | + | 34.5484i | 0.422511 | + | 1.31050i | ||||
\(696\) | 41.4891 | 1.57264 | ||||||||
\(697\) | − | 13.8564i | − | 0.524849i | ||||||
\(698\) | − | 39.0998i | − | 1.47995i | ||||||
\(699\) | −2.97825 | −0.112648 | ||||||||
\(700\) | −44.2337 | − | 61.4690i | −1.67188 | − | 2.32331i | ||||
\(701\) | −12.5109 | −0.472529 | −0.236265 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236265 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.34896i | − | 0.164024i | ||||||
\(704\) | −2.37228 | −0.0894087 | ||||||||
\(705\) | 3.60597 | + | 11.1846i | 0.135809 | + | 0.421236i | ||||
\(706\) | −63.2119 | −2.37901 | ||||||||
\(707\) | − | 20.7846i | − | 0.781686i | ||||||
\(708\) | 25.5383i | 0.959789i | ||||||||
\(709\) | −23.8832 | −0.896951 | −0.448475 | − | 0.893795i | \(-0.648033\pi\) | ||||
−0.448475 | + | 0.893795i | \(0.648033\pi\) | |||||||
\(710\) | 54.3505 | − | 17.5229i | 2.03974 | − | 0.657622i | ||||
\(711\) | −2.97825 | −0.111693 | ||||||||
\(712\) | 8.21782i | 0.307976i | ||||||||
\(713\) | 2.67181i | 0.100060i | ||||||||
\(714\) | −10.9783 | −0.410851 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 56.2337 | 2.10155 | ||||||||
\(717\) | − | 11.6819i | − | 0.436269i | ||||||
\(718\) | − | 74.4405i | − | 2.77810i | ||||||
\(719\) | 30.3505 | 1.13188 | 0.565942 | − | 0.824445i | \(-0.308513\pi\) | ||||
0.565942 | + | 0.824445i | \(0.308513\pi\) | |||||||
\(720\) | 10.3723 | + | 32.1716i | 0.386552 | + | 1.19896i | ||||
\(721\) | −36.0000 | −1.34071 | ||||||||
\(722\) | − | 7.57301i | − | 0.281838i | ||||||
\(723\) | − | 13.2665i | − | 0.493386i | ||||||
\(724\) | −105.446 | −3.91886 | ||||||||
\(725\) | 35.4891 | − | 25.5383i | 1.31803 | − | 0.948470i | ||||
\(726\) | 2.00000 | 0.0742270 | ||||||||
\(727\) | − | 14.0588i | − | 0.521412i | −0.965418 | − | 0.260706i | \(-0.916045\pi\) | ||
0.965418 | − | 0.260706i | \(-0.0839552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.23369 | −0.0456921 | ||||||||
\(730\) | 12.0000 | + | 37.2203i | 0.444140 | + | 1.37758i | ||||
\(731\) | 5.48913 | 0.203023 | ||||||||
\(732\) | − | 2.57924i | − | 0.0953315i | ||||||
\(733\) | − | 9.50744i | − | 0.351165i | −0.984465 | − | 0.175583i | \(-0.943819\pi\) | ||
0.984465 | − | 0.175583i | \(-0.0561809\pi\) | |||||||
\(734\) | 64.9783 | 2.39839 | ||||||||
\(735\) | −8.43070 | + | 2.71810i | −0.310971 | + | 0.100259i | ||||
\(736\) | −3.25544 | −0.119997 | ||||||||
\(737\) | 9.30506i | 0.342756i | ||||||||
\(738\) | 52.3663i | 1.92763i | ||||||||
\(739\) | 10.7446 | 0.395245 | 0.197623 | − | 0.980278i | \(-0.436678\pi\) | ||||
0.197623 | + | 0.980278i | \(0.436678\pi\) | |||||||
\(740\) | 10.1168 | − | 3.26172i | 0.371903 | − | 0.119903i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 88.2969i | 3.24148i | ||||||||
\(743\) | 11.3870i | 0.417747i | 0.977943 | + | 0.208874i | \(0.0669798\pi\) | ||||
−0.977943 | + | 0.208874i | \(0.933020\pi\) | |||||||
\(744\) | −16.0000 | −0.586588 | ||||||||
\(745\) | 7.88316 | + | 24.4511i | 0.288816 | + | 0.895819i | ||||
\(746\) | 29.4891 | 1.07967 | ||||||||
\(747\) | 15.7359i | 0.575748i | ||||||||
\(748\) | − | 6.92820i | − | 0.253320i | ||||||
\(749\) | 22.9783 | 0.839607 | ||||||||
\(750\) | −18.0000 | − | 13.2665i | −0.657267 | − | 0.484424i | ||||
\(751\) | 27.3723 | 0.998829 | 0.499414 | − | 0.866363i | \(-0.333549\pi\) | ||||
0.499414 | + | 0.866363i | \(0.333549\pi\) | |||||||
\(752\) | 42.2689i | 1.54139i | ||||||||
\(753\) | 17.5229i | 0.638570i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.39403 | − | 26.0357i | −0.305490 | − | 0.947535i | ||||
\(756\) | 64.4674 | 2.34466 | ||||||||
\(757\) | − | 39.7995i | − | 1.44654i | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||
0.690567 | − | 0.723269i | \(-0.257361\pi\) | |||||||
\(758\) | 1.58457i | 0.0575543i | ||||||||
\(759\) | −0.627719 | −0.0227847 | ||||||||
\(760\) | −50.9783 | + | 16.4356i | −1.84918 | + | 0.596184i | ||||
\(761\) | 32.7446 | 1.18699 | 0.593495 | − | 0.804838i | \(-0.297748\pi\) | ||||
0.593495 | + | 0.804838i | \(0.297748\pi\) | |||||||
\(762\) | 16.4356i | 0.595401i | ||||||||
\(763\) | 34.6410i | 1.25409i | ||||||||
\(764\) | 84.7011 | 3.06438 | ||||||||
\(765\) | 8.00000 | − | 2.57924i | 0.289241 | − | 0.0932526i | ||||
\(766\) | 27.4891 | 0.993222 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 24.6535i | 0.889605i | ||||||||
\(769\) | −29.2119 | −1.05341 | −0.526705 | − | 0.850048i | \(-0.676573\pi\) | ||||
−0.526705 | + | 0.850048i | \(0.676573\pi\) | |||||||
\(770\) | −6.00000 | − | 18.6101i | −0.216225 | − | 0.670662i | ||||
\(771\) | −8.46738 | −0.304945 | ||||||||
\(772\) | 71.8613i | 2.58634i | ||||||||
\(773\) | − | 17.6155i | − | 0.633584i | −0.948495 | − | 0.316792i | \(-0.897394\pi\) | ||
0.948495 | − | 0.316792i | \(-0.102606\pi\) | |||||||
\(774\) | −20.7446 | −0.745648 | ||||||||
\(775\) | −13.6861 | + | 9.84868i | −0.491621 | + | 0.353775i | ||||
\(776\) | −34.9783 | −1.25565 | ||||||||
\(777\) | − | 2.98400i | − | 0.107050i | ||||||
\(778\) | − | 47.6126i | − | 1.70699i | ||||||
\(779\) | −34.9783 | −1.25323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.1168 | 0.362009 | ||||||||
\(782\) | 3.16915i | 0.113328i | ||||||||
\(783\) | 37.2203i | 1.33014i | ||||||||
\(784\) | −31.8614 | −1.13791 | ||||||||
\(785\) | −52.0367 | + | 16.7769i | −1.85727 | + | 0.598793i | ||||
\(786\) | −5.48913 | −0.195791 | ||||||||
\(787\) | 15.1460i | 0.539898i | 0.962875 | + | 0.269949i | \(0.0870068\pi\) | ||||
−0.962875 | + | 0.269949i | \(0.912993\pi\) | |||||||
\(788\) | 37.2203i | 1.32592i | ||||||||
\(789\) | 21.7228 | 0.773353 | ||||||||
\(790\) | 6.74456 | − | 2.17448i | 0.239961 | − | 0.0773646i | ||||
\(791\) | −1.72281 | −0.0612562 | ||||||||
\(792\) | 14.2063i | 0.504798i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −41.4891 | −1.47239 | ||||||||
\(795\) | 5.48913 | + | 17.0256i | 0.194679 | + | 0.603834i | ||||
\(796\) | −34.9783 | −1.23977 | ||||||||
\(797\) | − | 5.25106i | − | 0.186002i | −0.995666 | − | 0.0930010i | \(-0.970354\pi\) | ||
0.995666 | − | 0.0930010i | \(-0.0296460\pi\) | |||||||
\(798\) | 27.7128i | 0.981023i | ||||||||
\(799\) | 10.5109 | 0.371848 | ||||||||
\(800\) | −12.0000 | − | 16.6757i | −0.424264 | − | 0.589575i | ||||
\(801\) | −3.25544 | −0.115025 | ||||||||
\(802\) | − | 29.0024i | − | 1.02411i | ||||||
\(803\) | 6.92820i | 0.244491i | ||||||||
\(804\) | 32.2337 | 1.13679 | ||||||||
\(805\) | 1.88316 | + | 5.84096i | 0.0663725 | + | 0.205867i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.10268i | − | 0.320430i | ||||||
\(808\) | − | 35.9306i | − | 1.26404i | ||||||
\(809\) | 32.7446 | 1.15124 | 0.575619 | − | 0.817718i | \(-0.304761\pi\) | ||||
0.575619 | + | 0.817718i | \(0.304761\pi\) | |||||||
\(810\) | −20.1168 | + | 6.48577i | −0.706834 | + | 0.227887i | ||||
\(811\) | −0.233688 | −0.00820589 | −0.00410295 | − | 0.999992i | \(-0.501306\pi\) | ||||
−0.00410295 | + | 0.999992i | \(0.501306\pi\) | |||||||
\(812\) | − | 132.445i | − | 4.64792i | ||||||
\(813\) | − | 10.6873i | − | 0.374819i | ||||||
\(814\) | 2.74456 | 0.0961969 | ||||||||
\(815\) | 7.37228 | − | 2.37686i | 0.258240 | − | 0.0832578i | ||||
\(816\) | −8.00000 | −0.280056 | ||||||||
\(817\) | − | 13.8564i | − | 0.484774i | ||||||
\(818\) | − | 69.3918i | − | 2.42623i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.2337 | − | 81.3687i | −0.916120 | − | 2.84152i | ||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | − | 28.7075i | − | 1.00129i | ||||||
\(823\) | 56.0328i | 1.95318i | 0.215111 | + | 0.976590i | \(0.430989\pi\) | ||||
−0.215111 | + | 0.976590i | \(0.569011\pi\) | |||||||
\(824\) | −62.2337 | −2.16801 | ||||||||
\(825\) | −2.31386 | − | 3.21543i | −0.0805582 | − | 0.111947i | ||||
\(826\) | 64.4674 | 2.24311 | ||||||||
\(827\) | − | 28.4125i | − | 0.988000i | −0.869462 | − | 0.494000i | \(-0.835534\pi\) | ||
0.869462 | − | 0.494000i | \(-0.164466\pi\) | |||||||
\(828\) | − | 8.21782i | − | 0.285589i | ||||||
\(829\) | 20.3505 | 0.706803 | 0.353402 | − | 0.935472i | \(-0.385025\pi\) | ||||
0.353402 | + | 0.935472i | \(0.385025\pi\) | |||||||
\(830\) | −11.4891 | − | 35.6357i | −0.398793 | − | 1.23693i | ||||
\(831\) | 9.25544 | 0.321068 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.92287i | 0.274511i | ||||||||
\(834\) | 32.4674 | 1.12425 | ||||||||
\(835\) | −33.4891 | + | 10.7971i | −1.15894 | + | 0.373648i | ||||
\(836\) | −17.4891 | −0.604874 | ||||||||
\(837\) | − | 14.3537i | − | 0.496138i | ||||||
\(838\) | 58.0049i | 2.00374i | ||||||||
\(839\) | 10.1168 | 0.349272 | 0.174636 | − | 0.984633i | \(-0.444125\pi\) | ||||
0.174636 | + | 0.984633i | \(0.444125\pi\) | |||||||
\(840\) | −34.9783 | + | 11.2772i | −1.20686 | + | 0.389099i | ||||
\(841\) | 47.4674 | 1.63681 | ||||||||
\(842\) | 21.4843i | 0.740399i | ||||||||
\(843\) | 0.404759i | 0.0139407i | ||||||||
\(844\) | −6.51087 | −0.224114 | ||||||||
\(845\) | 8.91983 | + | 27.6665i | 0.306851 | + | 0.951757i | ||||
\(846\) | −39.7228 | −1.36570 | ||||||||
\(847\) | − | 3.46410i | − | 0.119028i | ||||||
\(848\) | 64.3432i | 2.20955i | ||||||||
\(849\) | 12.0000 | 0.411839 | ||||||||
\(850\) | −16.2337 | + | 11.6819i | −0.556811 | + | 0.400687i | ||||
\(851\) | −0.861407 | −0.0295286 | ||||||||
\(852\) | − | 35.0458i | − | 1.20065i | ||||||
\(853\) | 35.0458i | 1.19994i | 0.800021 | + | 0.599972i | \(0.204822\pi\) | ||||
−0.800021 | + | 0.599972i | \(0.795178\pi\) | |||||||
\(854\) | −6.51087 | −0.222798 | ||||||||
\(855\) | −6.51087 | − | 20.1947i | −0.222667 | − | 0.690644i | ||||
\(856\) | 39.7228 | 1.35770 | ||||||||
\(857\) | 23.9538i | 0.818245i | 0.912480 | + | 0.409122i | \(0.134165\pi\) | ||||
−0.912480 | + | 0.409122i | \(0.865835\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.11684 | 0.208704 | 0.104352 | − | 0.994540i | \(-0.466723\pi\) | ||||
0.104352 | + | 0.994540i | \(0.466723\pi\) | |||||||
\(860\) | 32.2337 | − | 10.3923i | 1.09916 | − | 0.354375i | ||||
\(861\) | −24.0000 | −0.817918 | ||||||||
\(862\) | − | 64.9331i | − | 2.21163i | ||||||
\(863\) | − | 2.87419i | − | 0.0978387i | −0.998803 | − | 0.0489194i | \(-0.984422\pi\) | ||
0.998803 | − | 0.0489194i | \(-0.0155777\pi\) | |||||||
\(864\) | 17.4891 | 0.594992 | ||||||||
\(865\) | 18.1168 | − | 5.84096i | 0.615991 | − | 0.198599i | ||||
\(866\) | −73.7228 | −2.50520 | ||||||||
\(867\) | − | 11.4795i | − | 0.389866i | ||||||
\(868\) | 51.0767i | 1.73365i | ||||||||
\(869\) | 1.25544 | 0.0425878 | ||||||||
\(870\) | −12.0000 | − | 37.2203i | −0.406838 | − | 1.26188i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 59.8844i | 2.02794i | ||||||||
\(873\) | − | 13.8564i | − | 0.468968i | ||||||
\(874\) | 8.00000 | 0.270604 | ||||||||
\(875\) | −22.9783 | + | 31.1769i | −0.776807 | + | 1.05397i | ||||
\(876\) | 24.0000 | 0.810885 | ||||||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | − | 54.2458i | − | 1.83071i | ||||||
\(879\) | 2.51087 | 0.0846897 | ||||||||
\(880\) | −4.37228 | − | 13.5615i | −0.147390 | − | 0.457156i | ||||
\(881\) | −6.86141 | −0.231167 | −0.115583 | − | 0.993298i | \(-0.536874\pi\) | ||||
−0.115583 | + | 0.993298i | \(0.536874\pi\) | |||||||
\(882\) | − | 29.9422i | − | 1.00821i | ||||||
\(883\) | 24.2487i | 0.816034i | 0.912974 | + | 0.408017i | \(0.133780\pi\) | ||||
−0.912974 | + | 0.408017i | \(0.866220\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.4307 | − | 4.00772i | 0.417854 | − | 0.134718i | ||||
\(886\) | 79.9565 | 2.68619 | ||||||||
\(887\) | 27.4179i | 0.920602i | 0.887763 | + | 0.460301i | \(0.152258\pi\) | ||||
−0.887763 | + | 0.460301i | \(0.847742\pi\) | |||||||
\(888\) | − | 5.15848i | − | 0.173107i | ||||||
\(889\) | 28.4674 | 0.954765 | ||||||||
\(890\) | 7.37228 | − | 2.37686i | 0.247119 | − | 0.0796726i | ||||
\(891\) | −3.74456 | −0.125448 | ||||||||
\(892\) | 10.3923i | 0.347960i | ||||||||
\(893\) | − | 26.5330i | − | 0.887893i | ||||||
\(894\) | 22.9783 | 0.768508 | ||||||||
\(895\) | −8.82473 | − | 27.3716i | −0.294978 | − | 0.914931i | ||||
\(896\) | 49.2119 | 1.64406 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 17.3205i | − | 0.577993i | ||||||
\(899\) | −29.4891 | −0.983517 | ||||||||
\(900\) | 42.0951 | − | 30.2921i | 1.40317 | − | 1.00974i | ||||
\(901\) | 16.0000 | 0.533037 | ||||||||
\(902\) | − | 22.0742i | − | 0.734991i | ||||||
\(903\) | − | 9.50744i | − | 0.316388i | ||||||
\(904\) | −2.97825 | −0.0990551 | ||||||||
\(905\) | 16.5475 | + | 51.3253i | 0.550059 | + | 1.70611i | ||||
\(906\) | −24.4674 | −0.812874 | ||||||||
\(907\) | 19.8997i | 0.660760i | 0.943848 | + | 0.330380i | \(0.107177\pi\) | ||||
−0.943848 | + | 0.330380i | \(0.892823\pi\) | |||||||
\(908\) | 73.1509i | 2.42760i | ||||||||
\(909\) | 14.2337 | 0.472102 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.4891 | −1.77217 | −0.886087 | − | 0.463519i | \(-0.846587\pi\) | ||||
−0.886087 | + | 0.463519i | \(0.846587\pi\) | |||||||
\(912\) | 20.1947i | 0.668713i | ||||||||
\(913\) | − | 6.63325i | − | 0.219529i | ||||||
\(914\) | −52.4674 | −1.73547 | ||||||||
\(915\) | −1.25544 | + | 0.404759i | −0.0415035 | + | 0.0133809i | ||||
\(916\) | 63.9565 | 2.11318 | ||||||||
\(917\) | 9.50744i | 0.313963i | ||||||||
\(918\) | − | 17.0256i | − | 0.561927i | ||||||
\(919\) | 28.2337 | 0.931343 | 0.465672 | − | 0.884958i | \(-0.345813\pi\) | ||||
0.465672 | + | 0.884958i | \(0.345813\pi\) | |||||||
\(920\) | 3.25544 | + | 10.0974i | 0.107329 | + | 0.332900i | ||||
\(921\) | −25.0217 | −0.824495 | ||||||||
\(922\) | 5.63858i | 0.185697i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12.0000 | −0.394771 | ||||||||
\(925\) | −3.17527 | − | 4.41248i | −0.104402 | − | 0.145081i | ||||
\(926\) | 75.9565 | 2.49609 | ||||||||
\(927\) | − | 24.6535i | − | 0.809726i | ||||||
\(928\) | − | 35.9306i | − | 1.17948i | ||||||
\(929\) | 7.02175 | 0.230376 | 0.115188 | − | 0.993344i | \(-0.463253\pi\) | ||||
0.115188 | + | 0.993344i | \(0.463253\pi\) | |||||||
\(930\) | 4.62772 | + | 14.3537i | 0.151749 | + | 0.470678i | ||||
\(931\) | 20.0000 | 0.655474 | ||||||||
\(932\) | 16.4356i | 0.538368i | ||||||||
\(933\) | − | 4.34896i | − | 0.142379i | ||||||
\(934\) | −19.4891 | −0.637704 | ||||||||
\(935\) | −3.37228 | + | 1.08724i | −0.110285 | + | 0.0355566i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53.6559i | − | 1.75286i | −0.481527 | − | 0.876431i | \(-0.659918\pi\) | ||
0.481527 | − | 0.876431i | \(-0.340082\pi\) | |||||||
\(938\) | − | 81.3687i | − | 2.65678i | ||||||
\(939\) | −17.3288 | −0.565503 | ||||||||
\(940\) | 61.7228 | − | 19.8997i | 2.01318 | − | 0.649058i | ||||
\(941\) | −58.4674 | −1.90598 | −0.952991 | − | 0.302999i | \(-0.902012\pi\) | ||||
−0.952991 | + | 0.302999i | \(0.902012\pi\) | |||||||
\(942\) | 48.9022i | 1.59332i | ||||||||
\(943\) | 6.92820i | 0.225613i | ||||||||
\(944\) | 46.9783 | 1.52901 | ||||||||
\(945\) | −10.1168 | − | 31.3793i | −0.329101 | − | 1.02077i | ||||
\(946\) | 8.74456 | 0.284310 | ||||||||
\(947\) | 26.7354i | 0.868783i | 0.900724 | + | 0.434392i | \(0.143037\pi\) | ||||
−0.900724 | + | 0.434392i | \(0.856963\pi\) | |||||||
\(948\) | − | 4.34896i | − | 0.141248i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 29.4891 | + | 40.9793i | 0.956754 | + | 1.32954i | ||||
\(951\) | −26.1168 | −0.846897 | ||||||||
\(952\) | 32.8713i | 1.06536i | ||||||||
\(953\) | 31.2867i | 1.01348i | 0.862100 | + | 0.506738i | \(0.169149\pi\) | ||||
−0.862100 | + | 0.506738i | \(0.830851\pi\) | |||||||
\(954\) | −60.4674 | −1.95770 | ||||||||
\(955\) | −13.2921 | − | 41.2280i | −0.430123 | − | 1.33411i | ||||
\(956\) | −64.4674 | −2.08502 | ||||||||
\(957\) | − | 6.92820i | − | 0.223957i | ||||||
\(958\) | 13.8564i | 0.447680i | ||||||||
\(959\) | −49.7228 | −1.60563 | ||||||||
\(960\) | 4.00000 | − | 1.28962i | 0.129099 | − | 0.0416223i | ||||
\(961\) | −19.6277 | −0.633152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.7359i | 0.507083i | ||||||||
\(964\) | −73.2119 | −2.35800 | ||||||||
\(965\) | 34.9783 | − | 11.2772i | 1.12599 | − | 0.363025i | ||||
\(966\) | 5.48913 | 0.176610 | ||||||||
\(967\) | 26.4232i | 0.849713i | 0.905261 | + | 0.424856i | \(0.139675\pi\) | ||||
−0.905261 | + | 0.424856i | \(0.860325\pi\) | |||||||
\(968\) | − | 5.98844i | − | 0.192476i | ||||||
\(969\) | 5.02175 | 0.161322 | ||||||||
\(970\) | 10.1168 | + | 31.3793i | 0.324832 | + | 1.00753i | ||||
\(971\) | −9.09509 | −0.291875 | −0.145938 | − | 0.989294i | \(-0.546620\pi\) | ||||
−0.145938 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(972\) | 68.8019i | 2.20682i | ||||||||
\(973\) | − | 56.2351i | − | 1.80282i | ||||||
\(974\) | −18.0000 | −0.576757 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.74456 | −0.151870 | ||||||||
\(977\) | 50.5793i | 1.61818i | 0.587687 | + | 0.809088i | \(0.300038\pi\) | ||||
−0.587687 | + | 0.809088i | \(0.699962\pi\) | |||||||
\(978\) | − | 6.92820i | − | 0.221540i | ||||||
\(979\) | 1.37228 | 0.0438583 | ||||||||
\(980\) | 15.0000 | + | 46.5253i | 0.479157 | + | 1.48620i | ||||
\(981\) | −23.7228 | −0.757411 | ||||||||
\(982\) | 16.4356i | 0.524483i | ||||||||
\(983\) | − | 24.7460i | − | 0.789276i | −0.918837 | − | 0.394638i | \(-0.870870\pi\) | ||
0.918837 | − | 0.394638i | \(-0.129130\pi\) | |||||||
\(984\) | −41.4891 | −1.32263 | ||||||||
\(985\) | 18.1168 | − | 5.84096i | 0.577251 | − | 0.186109i | ||||
\(986\) | −34.9783 | −1.11393 | ||||||||
\(987\) | − | 18.2054i | − | 0.579483i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.74456 | −0.0872720 | ||||||||
\(990\) | 12.7446 | − | 4.10891i | 0.405049 | − | 0.130590i | ||||
\(991\) | 18.9783 | 0.602864 | 0.301432 | − | 0.953488i | \(-0.402535\pi\) | ||||
0.301432 | + | 0.953488i | \(0.402535\pi\) | |||||||
\(992\) | 13.8564i | 0.439941i | ||||||||
\(993\) | 11.1846i | 0.354932i | ||||||||
\(994\) | −88.4674 | −2.80601 | ||||||||
\(995\) | 5.48913 | + | 17.0256i | 0.174017 | + | 0.539746i | ||||
\(996\) | −22.9783 | −0.728094 | ||||||||
\(997\) | − | 2.17448i | − | 0.0688665i | −0.999407 | − | 0.0344333i | \(-0.989037\pi\) | ||
0.999407 | − | 0.0344333i | \(-0.0109626\pi\) | |||||||
\(998\) | 50.4868i | 1.59813i | ||||||||
\(999\) | 4.62772 | 0.146415 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))