Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(469,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("585.469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.c (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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 469.4 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.469 |
Dual form | 585.2.c.b.469.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21432i | 0.858654i | 0.903149 | + | 0.429327i | \(0.141249\pi\) | ||||
−0.903149 | + | 0.429327i | \(0.858751\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.525428 | 0.262714 | ||||||||
\(5\) | 2.21432 | − | 0.311108i | 0.990274 | − | 0.139132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.90321i | 1.09731i | 0.836049 | + | 0.548655i | \(0.184860\pi\) | ||||
−0.836049 | + | 0.548655i | \(0.815140\pi\) | |||||||
\(8\) | 3.06668i | 1.08423i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.377784 | + | 2.68889i | 0.119466 | + | 0.850302i | ||||
\(11\) | −0.214320 | −0.0646198 | −0.0323099 | − | 0.999478i | \(-0.510286\pi\) | ||||
−0.0323099 | + | 0.999478i | \(0.510286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | −3.52543 | −0.942210 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.67307 | −0.668268 | ||||||||
\(17\) | − | 6.42864i | − | 1.55917i | −0.626294 | − | 0.779587i | \(-0.715429\pi\) | ||
0.626294 | − | 0.779587i | \(-0.284571\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.21432 | −0.508000 | −0.254000 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.254000 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(20\) | 1.16346 | − | 0.163465i | 0.260159 | − | 0.0365518i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.260253i | − | 0.0554861i | ||||||
\(23\) | 4.68889i | 0.977702i | 0.872367 | + | 0.488851i | \(0.162584\pi\) | ||||
−0.872367 | + | 0.488851i | \(0.837416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.80642 | − | 1.37778i | 0.961285 | − | 0.275557i | ||||
\(26\) | −1.21432 | −0.238148 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.52543i | 0.288279i | ||||||||
\(29\) | 8.70964 | 1.61734 | 0.808669 | − | 0.588263i | \(-0.200188\pi\) | ||||
0.808669 | + | 0.588263i | \(0.200188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.59210 | −1.00437 | −0.502186 | − | 0.864760i | \(-0.667471\pi\) | ||||
−0.502186 | + | 0.864760i | \(0.667471\pi\) | |||||||
\(32\) | 2.88739i | 0.510423i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.80642 | 1.33879 | ||||||||
\(35\) | 0.903212 | + | 6.42864i | 0.152671 | + | 1.08664i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.28100i | 0.374993i | 0.982265 | + | 0.187497i | \(0.0600374\pi\) | ||||
−0.982265 | + | 0.187497i | \(0.939963\pi\) | |||||||
\(38\) | − | 2.68889i | − | 0.436196i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.954067 | + | 6.79060i | 0.150851 | + | 1.07369i | ||||
\(41\) | −3.05086 | −0.476464 | −0.238232 | − | 0.971208i | \(-0.576568\pi\) | ||||
−0.238232 | + | 0.971208i | \(0.576568\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.36196i | − | 0.970190i | −0.874461 | − | 0.485095i | \(-0.838785\pi\) | ||
0.874461 | − | 0.485095i | \(-0.161215\pi\) | |||||||
\(44\) | −0.112610 | −0.0169765 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.69381 | −0.839507 | ||||||||
\(47\) | − | 1.09679i | − | 0.159983i | −0.996796 | − | 0.0799915i | \(-0.974511\pi\) | ||
0.996796 | − | 0.0799915i | \(-0.0254893\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.42864 | −0.204091 | ||||||||
\(50\) | 1.67307 | + | 5.83654i | 0.236608 | + | 0.825411i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.525428i | 0.0728637i | ||||||||
\(53\) | − | 6.23506i | − | 0.856452i | −0.903672 | − | 0.428226i | \(-0.859139\pi\) | ||
0.903672 | − | 0.428226i | \(-0.140861\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.474572 | + | 0.0666765i | −0.0639913 | + | 0.00899066i | ||||
\(56\) | −8.90321 | −1.18974 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.5763i | 1.38873i | ||||||||
\(59\) | −9.26517 | −1.20622 | −0.603112 | − | 0.797657i | \(-0.706073\pi\) | ||||
−0.603112 | + | 0.797657i | \(0.706073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.280996 | −0.0359779 | −0.0179889 | − | 0.999838i | \(-0.505726\pi\) | ||||
−0.0179889 | + | 0.999838i | \(0.505726\pi\) | |||||||
\(62\) | − | 6.79060i | − | 0.862407i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.85236 | −1.10654 | ||||||||
\(65\) | 0.311108 | + | 2.21432i | 0.0385882 | + | 0.274653i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.76049i | − | 0.948095i | −0.880499 | − | 0.474047i | \(-0.842793\pi\) | ||
0.880499 | − | 0.474047i | \(-0.157207\pi\) | |||||||
\(68\) | − | 3.37778i | − | 0.409617i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.80642 | + | 1.09679i | −0.933046 | + | 0.131091i | ||||
\(71\) | 6.08097 | 0.721678 | 0.360839 | − | 0.932628i | \(-0.382490\pi\) | ||||
0.360839 | + | 0.932628i | \(0.382490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2810i | 1.20330i | 0.798760 | + | 0.601650i | \(0.205490\pi\) | ||||
−0.798760 | + | 0.601650i | \(0.794510\pi\) | |||||||
\(74\) | −2.76986 | −0.321990 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.16346 | −0.133459 | ||||||||
\(77\) | − | 0.622216i | − | 0.0709081i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.2351 | 1.60157 | 0.800785 | − | 0.598952i | \(-0.204416\pi\) | ||||
0.800785 | + | 0.598952i | \(0.204416\pi\) | |||||||
\(80\) | −5.91903 | + | 0.831613i | −0.661768 | + | 0.0929772i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.70471i | − | 0.409117i | ||||||
\(83\) | 9.52543i | 1.04555i | 0.852470 | + | 0.522776i | \(0.175103\pi\) | ||||
−0.852470 | + | 0.522776i | \(0.824897\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | − | 14.2351i | −0.216930 | − | 1.54401i | ||||
\(86\) | 7.72546 | 0.833057 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 0.657249i | − | 0.0700630i | ||||||
\(89\) | −5.61285 | −0.594961 | −0.297480 | − | 0.954728i | \(-0.596146\pi\) | ||||
−0.297480 | + | 0.954728i | \(0.596146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.90321 | −0.304339 | ||||||||
\(92\) | 2.46367i | 0.256856i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.33185 | 0.137370 | ||||||||
\(95\) | −4.90321 | + | 0.688892i | −0.503059 | + | 0.0706788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.0415i | − | 1.83184i | −0.401366 | − | 0.915918i | \(-0.631464\pi\) | ||
0.401366 | − | 0.915918i | \(-0.368536\pi\) | |||||||
\(98\) | − | 1.73483i | − | 0.175244i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.52543 | − | 0.723926i | 0.252543 | − | 0.0723926i | ||||
\(101\) | −3.93978 | −0.392022 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.82225i | − | 0.278084i | −0.990286 | − | 0.139042i | \(-0.955598\pi\) | ||
0.990286 | − | 0.139042i | \(-0.0444023\pi\) | |||||||
\(104\) | −3.06668 | −0.300712 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.57136 | 0.735396 | ||||||||
\(107\) | − | 17.1175i | − | 1.65481i | −0.561603 | − | 0.827407i | \(-0.689815\pi\) | ||
0.561603 | − | 0.827407i | \(-0.310185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.7239 | 1.60186 | 0.800931 | − | 0.598757i | \(-0.204338\pi\) | ||||
0.800931 | + | 0.598757i | \(0.204338\pi\) | |||||||
\(110\) | −0.0809666 | − | 0.576283i | −0.00771987 | − | 0.0549464i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 7.76049i | − | 0.733297i | ||||||
\(113\) | 1.18421i | 0.111401i | 0.998448 | + | 0.0557005i | \(0.0177392\pi\) | ||||
−0.998448 | + | 0.0557005i | \(0.982261\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.45875 | + | 10.3827i | 0.136029 | + | 0.968192i | ||||
\(116\) | 4.57628 | 0.424897 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 11.2509i | − | 1.03573i | ||||||
\(119\) | 18.6637 | 1.71090 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9541 | −0.995824 | ||||||||
\(122\) | − | 0.341219i | − | 0.0308925i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.93825 | −0.263862 | ||||||||
\(125\) | 10.2143 | − | 4.54617i | 0.913597 | − | 0.406622i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.30174i | 0.204246i | 0.994772 | + | 0.102123i | \(0.0325636\pi\) | ||||
−0.994772 | + | 0.102123i | \(0.967436\pi\) | |||||||
\(128\) | − | 4.97481i | − | 0.439715i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.68889 | + | 0.377784i | −0.235831 | + | 0.0331339i | ||||
\(131\) | 13.4193 | 1.17245 | 0.586224 | − | 0.810149i | \(-0.300614\pi\) | ||||
0.586224 | + | 0.810149i | \(0.300614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.42864i | − | 0.557434i | ||||||
\(134\) | 9.42372 | 0.814085 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.7146 | 1.69051 | ||||||||
\(137\) | − | 19.1526i | − | 1.63631i | −0.574995 | − | 0.818157i | \(-0.694996\pi\) | ||
0.574995 | − | 0.818157i | \(-0.305004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.0923 | −1.61939 | −0.809696 | − | 0.586850i | \(-0.800368\pi\) | ||||
−0.809696 | + | 0.586850i | \(0.800368\pi\) | |||||||
\(140\) | 0.474572 | + | 3.37778i | 0.0401087 | + | 0.285475i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.38424i | 0.619671i | ||||||||
\(143\) | − | 0.214320i | − | 0.0179223i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.2859 | − | 2.70964i | 1.60161 | − | 0.225023i | ||||
\(146\) | −12.4844 | −1.03322 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.19850i | 0.0985160i | ||||||||
\(149\) | −3.57136 | −0.292577 | −0.146289 | − | 0.989242i | \(-0.546733\pi\) | ||||
−0.146289 | + | 0.989242i | \(0.546733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.26517 | −0.102958 | −0.0514792 | − | 0.998674i | \(-0.516394\pi\) | ||||
−0.0514792 | + | 0.998674i | \(0.516394\pi\) | |||||||
\(152\) | − | 6.79060i | − | 0.550791i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.755569 | 0.0608855 | ||||||||
\(155\) | −12.3827 | + | 1.73975i | −0.994603 | + | 0.139740i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.61285i | − | 0.447954i | −0.974594 | − | 0.223977i | \(-0.928096\pi\) | ||
0.974594 | − | 0.223977i | \(-0.0719041\pi\) | |||||||
\(158\) | 17.2859i | 1.37519i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.898290 | + | 6.39361i | 0.0710160 | + | 0.505459i | ||||
\(161\) | −13.6128 | −1.07284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.71900i | − | 0.291295i | −0.989337 | − | 0.145647i | \(-0.953473\pi\) | ||
0.989337 | − | 0.145647i | \(-0.0465265\pi\) | |||||||
\(164\) | −1.60300 | −0.125174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.5669 | −0.897767 | ||||||||
\(167\) | 7.03657i | 0.544506i | 0.962226 | + | 0.272253i | \(0.0877687\pi\) | ||||
−0.962226 | + | 0.272253i | \(0.912231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 17.2859 | − | 2.42864i | 1.32577 | − | 0.186268i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 3.34275i | − | 0.254882i | ||||||
\(173\) | 0.723926i | 0.0550391i | 0.999621 | + | 0.0275195i | \(0.00876085\pi\) | ||||
−0.999621 | + | 0.0275195i | \(0.991239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | + | 13.9541i | 0.302372 | + | 1.05483i | ||||
\(176\) | 0.572892 | 0.0431833 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 6.81579i | − | 0.510865i | ||||||
\(179\) | −4.04149 | −0.302075 | −0.151037 | − | 0.988528i | \(-0.548261\pi\) | ||||
−0.151037 | + | 0.988528i | \(0.548261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34122 | 0.174021 | 0.0870107 | − | 0.996207i | \(-0.472269\pi\) | ||||
0.0870107 | + | 0.996207i | \(0.472269\pi\) | |||||||
\(182\) | − | 3.52543i | − | 0.261322i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.3793 | −1.06006 | ||||||||
\(185\) | 0.709636 | + | 5.05086i | 0.0521735 | + | 0.371346i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.37778i | 0.100754i | ||||||||
\(188\) | − | 0.576283i | − | 0.0420297i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.836535 | − | 5.95407i | −0.0606887 | − | 0.431953i | ||||
\(191\) | 2.10171 | 0.152074 | 0.0760372 | − | 0.997105i | \(-0.475773\pi\) | ||||
0.0760372 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.5210i | − | 0.973262i | −0.873608 | − | 0.486631i | \(-0.838226\pi\) | ||
0.873608 | − | 0.486631i | \(-0.161774\pi\) | |||||||
\(194\) | 21.9081 | 1.57291 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.750647 | −0.0536176 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.1432 | −1.56969 | −0.784845 | − | 0.619692i | \(-0.787257\pi\) | ||||
−0.784845 | + | 0.619692i | \(0.787257\pi\) | |||||||
\(200\) | 4.22522 | + | 14.7397i | 0.298768 | + | 1.04226i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.78415i | − | 0.336612i | ||||||
\(203\) | 25.2859i | 1.77472i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.75557 | + | 0.949145i | −0.471829 | + | 0.0662912i | ||||
\(206\) | 3.42711 | 0.238778 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.67307i | − | 0.185344i | ||||||
\(209\) | 0.474572 | 0.0328269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.6543 | 1.35306 | 0.676530 | − | 0.736415i | \(-0.263483\pi\) | ||||
0.676530 | + | 0.736415i | \(0.263483\pi\) | |||||||
\(212\) | − | 3.27607i | − | 0.225002i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.7862 | 1.42091 | ||||||||
\(215\) | −1.97926 | − | 14.0874i | −0.134984 | − | 0.960754i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.2351i | − | 1.10211i | ||||||
\(218\) | 20.3082i | 1.37544i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.249353 | + | 0.0350337i | −0.0168114 | + | 0.00236197i | ||||
\(221\) | 6.42864 | 0.432437 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.6686i | 1.31711i | 0.752533 | + | 0.658554i | \(0.228832\pi\) | ||||
−0.752533 | + | 0.658554i | \(0.771168\pi\) | |||||||
\(224\) | −8.38271 | −0.560093 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.43801 | −0.0956548 | ||||||||
\(227\) | − | 13.2716i | − | 0.880869i | −0.897785 | − | 0.440434i | \(-0.854824\pi\) | ||
0.897785 | − | 0.440434i | \(-0.145176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.42864 | 0.160489 | 0.0802445 | − | 0.996775i | \(-0.474430\pi\) | ||||
0.0802445 | + | 0.996775i | \(0.474430\pi\) | |||||||
\(230\) | −12.6079 | + | 1.77139i | −0.831342 | + | 0.116802i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.7096i | 1.75357i | ||||||||
\(233\) | − | 16.1748i | − | 1.05965i | −0.848107 | − | 0.529825i | \(-0.822258\pi\) | ||
0.848107 | − | 0.529825i | \(-0.177742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.341219 | − | 2.42864i | −0.0222587 | − | 0.158427i | ||||
\(236\) | −4.86818 | −0.316891 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.6637i | 1.46907i | ||||||||
\(239\) | −12.7763 | −0.826431 | −0.413215 | − | 0.910633i | \(-0.635594\pi\) | ||||
−0.413215 | + | 0.910633i | \(0.635594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.89829 | −0.379942 | −0.189971 | − | 0.981790i | \(-0.560839\pi\) | ||||
−0.189971 | + | 0.981790i | \(0.560839\pi\) | |||||||
\(242\) | − | 13.3017i | − | 0.855068i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.147643 | −0.00945189 | ||||||||
\(245\) | −3.16346 | + | 0.444461i | −0.202106 | + | 0.0283956i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.21432i | − | 0.140894i | ||||||
\(248\) | − | 17.1492i | − | 1.08897i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.52051 | + | 12.4035i | 0.349147 | + | 0.784463i | ||||
\(251\) | 2.07313 | 0.130855 | 0.0654274 | − | 0.997857i | \(-0.479159\pi\) | ||||
0.0654274 | + | 0.997857i | \(0.479159\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.00492i | − | 0.0631789i | ||||||
\(254\) | −2.79505 | −0.175377 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.6637 | −0.728981 | ||||||||
\(257\) | 18.3970i | 1.14757i | 0.819005 | + | 0.573787i | \(0.194526\pi\) | ||||
−0.819005 | + | 0.573787i | \(0.805474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.62222 | −0.411484 | ||||||||
\(260\) | 0.163465 | + | 1.16346i | 0.0101376 | + | 0.0721550i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.2953i | 1.00673i | ||||||||
\(263\) | − | 11.0257i | − | 0.679872i | −0.940449 | − | 0.339936i | \(-0.889595\pi\) | ||
0.940449 | − | 0.339936i | \(-0.110405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.93978 | − | 13.8064i | −0.119160 | − | 0.848122i | ||||
\(266\) | 7.80642 | 0.478643 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.07758i | − | 0.249078i | ||||||
\(269\) | −16.1432 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0114 | 0.790385 | 0.395192 | − | 0.918598i | \(-0.370678\pi\) | ||||
0.395192 | + | 0.918598i | \(0.370678\pi\) | |||||||
\(272\) | 17.1842i | 1.04195i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.2573 | 1.40503 | ||||||||
\(275\) | −1.03011 | + | 0.295286i | −0.0621181 | + | 0.0178064i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7.57136i | − | 0.454919i | −0.973788 | − | 0.227459i | \(-0.926958\pi\) | ||
0.973788 | − | 0.227459i | \(-0.0730419\pi\) | |||||||
\(278\) | − | 23.1842i | − | 1.39050i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.7146 | + | 2.76986i | −1.17817 | + | 0.165531i | ||||
\(281\) | −6.75557 | −0.403003 | −0.201502 | − | 0.979488i | \(-0.564582\pi\) | ||||
−0.201502 | + | 0.979488i | \(0.564582\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0859i | 1.13454i | 0.823532 | + | 0.567269i | \(0.192000\pi\) | ||||
−0.823532 | + | 0.567269i | \(0.808000\pi\) | |||||||
\(284\) | 3.19511 | 0.189595 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.260253 | 0.0153891 | ||||||||
\(287\) | − | 8.85728i | − | 0.522829i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.3274 | −1.43102 | ||||||||
\(290\) | 3.29036 | + | 23.4193i | 0.193217 | + | 1.37523i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.40192i | 0.316123i | ||||||||
\(293\) | 8.08742i | 0.472472i | 0.971696 | + | 0.236236i | \(0.0759139\pi\) | ||||
−0.971696 | + | 0.236236i | \(0.924086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.5161 | + | 2.88247i | −1.19449 | + | 0.167824i | ||||
\(296\) | −6.99508 | −0.406581 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 4.33677i | − | 0.251223i | ||||||
\(299\) | −4.68889 | −0.271166 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.4701 | 1.06460 | ||||||||
\(302\) | − | 1.53633i | − | 0.0884057i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.91903 | 0.339480 | ||||||||
\(305\) | −0.622216 | + | 0.0874201i | −0.0356280 | + | 0.00500566i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.4336i | 0.766694i | 0.923604 | + | 0.383347i | \(0.125229\pi\) | ||||
−0.923604 | + | 0.383347i | \(0.874771\pi\) | |||||||
\(308\) | − | 0.326929i | − | 0.0186285i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.11261 | − | 15.0366i | −0.119988 | − | 0.854020i | ||||
\(311\) | −20.2034 | −1.14563 | −0.572815 | − | 0.819684i | \(-0.694149\pi\) | ||||
−0.572815 | + | 0.819684i | \(0.694149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1111i | 0.854129i | 0.904221 | + | 0.427064i | \(0.140452\pi\) | ||||
−0.904221 | + | 0.427064i | \(0.859548\pi\) | |||||||
\(314\) | 6.81579 | 0.384637 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.47949 | 0.420754 | ||||||||
\(317\) | 22.2810i | 1.25143i | 0.780054 | + | 0.625713i | \(0.215192\pi\) | ||||
−0.780054 | + | 0.625713i | \(0.784808\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.86665 | −0.104512 | ||||||||
\(320\) | −19.6019 | + | 2.75404i | −1.09578 | + | 0.153955i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 16.5303i | − | 0.921200i | ||||||
\(323\) | 14.2351i | 0.792060i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.37778 | + | 4.80642i | 0.0764257 | + | 0.266612i | ||||
\(326\) | 4.51606 | 0.250121 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 9.35599i | − | 0.516598i | ||||||
\(329\) | 3.18421 | 0.175551 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.25581 | 0.453780 | 0.226890 | − | 0.973920i | \(-0.427144\pi\) | ||||
0.226890 | + | 0.973920i | \(0.427144\pi\) | |||||||
\(332\) | 5.00492i | 0.274681i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.54464 | −0.467542 | ||||||||
\(335\) | −2.41435 | − | 17.1842i | −0.131910 | − | 0.938874i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7462i | 0.748803i | 0.927267 | + | 0.374402i | \(0.122152\pi\) | ||||
−0.927267 | + | 0.374402i | \(0.877848\pi\) | |||||||
\(338\) | − | 1.21432i | − | 0.0660503i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.05086 | − | 7.47949i | −0.0569906 | − | 0.405633i | ||||
\(341\) | 1.19850 | 0.0649023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1748i | 0.873359i | ||||||||
\(344\) | 19.5101 | 1.05191 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.879077 | −0.0472595 | ||||||||
\(347\) | 1.21924i | 0.0654523i | 0.999464 | + | 0.0327262i | \(0.0104189\pi\) | ||||
−0.999464 | + | 0.0327262i | \(0.989581\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.5116 | −1.20502 | −0.602510 | − | 0.798112i | \(-0.705832\pi\) | ||||
−0.602510 | + | 0.798112i | \(0.705832\pi\) | |||||||
\(350\) | −16.9447 | + | 4.85728i | −0.905732 | + | 0.259632i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 0.618825i | − | 0.0329835i | ||||||
\(353\) | 14.2810i | 0.760101i | 0.924966 | + | 0.380050i | \(0.124093\pi\) | ||||
−0.924966 | + | 0.380050i | \(0.875907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.4652 | − | 1.89184i | 0.714659 | − | 0.100408i | ||||
\(356\) | −2.94914 | −0.156304 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 4.90766i | − | 0.259378i | ||||||
\(359\) | −12.1541 | −0.641469 | −0.320734 | − | 0.947169i | \(-0.603930\pi\) | ||||
−0.320734 | + | 0.947169i | \(0.603930\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0968 | −0.741936 | ||||||||
\(362\) | 2.84299i | 0.149424i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.52543 | −0.0799541 | ||||||||
\(365\) | 3.19850 | + | 22.7654i | 0.167417 | + | 1.19160i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.65725i | 0.243106i | 0.992585 | + | 0.121553i | \(0.0387875\pi\) | ||||
−0.992585 | + | 0.121553i | \(0.961212\pi\) | |||||||
\(368\) | − | 12.5337i | − | 0.653366i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.13335 | + | 0.861725i | −0.318858 | + | 0.0447989i | ||||
\(371\) | 18.1017 | 0.939794 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.9403i | 1.80914i | 0.426328 | + | 0.904569i | \(0.359807\pi\) | ||||
−0.426328 | + | 0.904569i | \(0.640193\pi\) | |||||||
\(374\) | −1.67307 | −0.0865124 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.36349 | 0.173459 | ||||||||
\(377\) | 8.70964i | 0.448569i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.4717 | 0.897459 | 0.448729 | − | 0.893668i | \(-0.351877\pi\) | ||||
0.448729 | + | 0.893668i | \(0.351877\pi\) | |||||||
\(380\) | −2.57628 | + | 0.361963i | −0.132161 | + | 0.0185683i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.55215i | 0.130579i | ||||||||
\(383\) | 18.6780i | 0.954401i | 0.878794 | + | 0.477200i | \(0.158348\pi\) | ||||
−0.878794 | + | 0.477200i | \(0.841652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.193576 | − | 1.37778i | −0.00986555 | − | 0.0702184i | ||||
\(386\) | 16.4188 | 0.835695 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 9.47949i | − | 0.481248i | ||||||
\(389\) | 1.61285 | 0.0817746 | 0.0408873 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408873 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.1432 | 1.52441 | ||||||||
\(392\) | − | 4.38118i | − | 0.221283i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.42864 | 0.122353 | ||||||||
\(395\) | 31.5210 | − | 4.42864i | 1.58599 | − | 0.222829i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6.57628i | − | 0.330054i | −0.986289 | − | 0.165027i | \(-0.947229\pi\) | ||
0.986289 | − | 0.165027i | \(-0.0527712\pi\) | |||||||
\(398\) | − | 26.8889i | − | 1.34782i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.8479 | + | 3.68292i | −0.642396 | + | 0.184146i | ||||
\(401\) | 21.9081 | 1.09404 | 0.547020 | − | 0.837120i | \(-0.315762\pi\) | ||||
0.547020 | + | 0.837120i | \(0.315762\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.59210i | − | 0.278563i | ||||||
\(404\) | −2.07007 | −0.102990 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30.7052 | −1.52387 | ||||||||
\(407\) | − | 0.488863i | − | 0.0242320i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1936 | 0.504040 | 0.252020 | − | 0.967722i | \(-0.418905\pi\) | ||||
0.252020 | + | 0.967722i | \(0.418905\pi\) | |||||||
\(410\) | −1.15257 | − | 8.20342i | −0.0569211 | − | 0.405138i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.48289i | − | 0.0730565i | ||||||
\(413\) | − | 26.8988i | − | 1.32360i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.96343 | + | 21.0923i | 0.145469 | + | 1.03538i | ||||
\(416\) | −2.88739 | −0.141566 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.576283i | 0.0281869i | ||||||||
\(419\) | 7.31756 | 0.357486 | 0.178743 | − | 0.983896i | \(-0.442797\pi\) | ||||
0.178743 | + | 0.983896i | \(0.442797\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.86665 | −0.383397 | −0.191698 | − | 0.981454i | \(-0.561400\pi\) | ||||
−0.191698 | + | 0.981454i | \(0.561400\pi\) | |||||||
\(422\) | 23.8666i | 1.16181i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.1209 | 0.928594 | ||||||||
\(425\) | −8.85728 | − | 30.8988i | −0.429641 | − | 1.49881i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.815792i | − | 0.0394789i | ||||||
\(428\) | − | 8.99402i | − | 0.434743i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.1066 | − | 2.40345i | 0.824955 | − | 0.115905i | ||||
\(431\) | 38.9195 | 1.87469 | 0.937343 | − | 0.348407i | \(-0.113277\pi\) | ||||
0.937343 | + | 0.348407i | \(0.113277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.2034i | − | 0.970914i | −0.874260 | − | 0.485457i | \(-0.838653\pi\) | ||
0.874260 | − | 0.485457i | \(-0.161347\pi\) | |||||||
\(434\) | 19.7146 | 0.946329 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.78721 | 0.420831 | ||||||||
\(437\) | − | 10.3827i | − | 0.496672i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8889 | −0.519700 | −0.259850 | − | 0.965649i | \(-0.583673\pi\) | ||||
−0.259850 | + | 0.965649i | \(0.583673\pi\) | |||||||
\(440\) | −0.204475 | − | 1.45536i | −0.00974798 | − | 0.0693816i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.80642i | 0.371314i | ||||||||
\(443\) | 28.6287i | 1.36019i | 0.733124 | + | 0.680095i | \(0.238061\pi\) | ||||
−0.733124 | + | 0.680095i | \(0.761939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.4286 | + | 1.74620i | −0.589174 | + | 0.0827779i | ||||
\(446\) | −23.8840 | −1.13094 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 25.7003i | − | 1.21422i | ||||||
\(449\) | −10.9304 | −0.515838 | −0.257919 | − | 0.966167i | \(-0.583037\pi\) | ||||
−0.257919 | + | 0.966167i | \(0.583037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.653858 | 0.0307890 | ||||||||
\(452\) | 0.622216i | 0.0292666i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.1160 | 0.756361 | ||||||||
\(455\) | −6.42864 | + | 0.903212i | −0.301379 | + | 0.0423432i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.4064i | 0.533567i | 0.963756 | + | 0.266784i | \(0.0859609\pi\) | ||||
−0.963756 | + | 0.266784i | \(0.914039\pi\) | |||||||
\(458\) | 2.94914i | 0.137804i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.766468 | + | 5.45536i | 0.0357368 | + | 0.254357i | ||||
\(461\) | 26.1334 | 1.21715 | 0.608576 | − | 0.793496i | \(-0.291741\pi\) | ||||
0.608576 | + | 0.793496i | \(0.291741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.92242i | − | 0.368186i | −0.982909 | − | 0.184093i | \(-0.941065\pi\) | ||
0.982909 | − | 0.184093i | \(-0.0589348\pi\) | |||||||
\(464\) | −23.2815 | −1.08082 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.6414 | 0.909872 | ||||||||
\(467\) | 10.8923i | 0.504036i | 0.967723 | + | 0.252018i | \(0.0810942\pi\) | ||||
−0.967723 | + | 0.252018i | \(0.918906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.5303 | 1.04035 | ||||||||
\(470\) | 2.94914 | − | 0.414349i | 0.136034 | − | 0.0191125i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 28.4133i | − | 1.30783i | ||||||
\(473\) | 1.36349i | 0.0626935i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.6430 | + | 3.05086i | −0.488332 | + | 0.139983i | ||||
\(476\) | 9.80642 | 0.449477 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 15.5145i | − | 0.709618i | ||||||
\(479\) | −9.13182 | −0.417244 | −0.208622 | − | 0.977996i | \(-0.566898\pi\) | ||||
−0.208622 | + | 0.977996i | \(0.566898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.28100 | −0.104004 | ||||||||
\(482\) | − | 7.16241i | − | 0.326239i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.75557 | −0.261617 | ||||||||
\(485\) | −5.61285 | − | 39.9496i | −0.254866 | − | 1.81402i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1891i | 0.733600i | 0.930300 | + | 0.366800i | \(0.119547\pi\) | ||||
−0.930300 | + | 0.366800i | \(0.880453\pi\) | |||||||
\(488\) | − | 0.861725i | − | 0.0390084i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.539718 | − | 3.84146i | −0.0243820 | − | 0.173539i | ||||
\(491\) | −26.2636 | −1.18526 | −0.592631 | − | 0.805474i | \(-0.701911\pi\) | ||||
−0.592631 | + | 0.805474i | \(0.701911\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 55.9911i | − | 2.52171i | ||||||
\(494\) | 2.68889 | 0.120979 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.9481 | 0.671189 | ||||||||
\(497\) | 17.6543i | 0.791905i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.0306 | −1.34435 | −0.672177 | − | 0.740391i | \(-0.734641\pi\) | ||||
−0.672177 | + | 0.740391i | \(0.734641\pi\) | |||||||
\(500\) | 5.36689 | − | 2.38868i | 0.240014 | − | 0.106825i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.51744i | 0.112359i | ||||||||
\(503\) | 16.7304i | 0.745971i | 0.927837 | + | 0.372985i | \(0.121666\pi\) | ||||
−0.927837 | + | 0.372985i | \(0.878334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.72393 | + | 1.22570i | −0.388210 | + | 0.0545427i | ||||
\(506\) | 1.22030 | 0.0542488 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.20940i | 0.0536583i | ||||||||
\(509\) | −11.9684 | −0.530488 | −0.265244 | − | 0.964181i | \(-0.585453\pi\) | ||||
−0.265244 | + | 0.964181i | \(0.585453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.8479 | −1.32039 | ||||||||
\(512\) | − | 24.1131i | − | 1.06566i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.3398 | −0.985368 | ||||||||
\(515\) | −0.878023 | − | 6.24935i | −0.0386903 | − | 0.275379i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.235063i | 0.0103381i | ||||||||
\(518\) | − | 8.04149i | − | 0.353323i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.79060 | + | 0.954067i | −0.297788 | + | 0.0418386i | ||||
\(521\) | −5.75065 | −0.251940 | −0.125970 | − | 0.992034i | \(-0.540204\pi\) | ||||
−0.125970 | + | 0.992034i | \(0.540204\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.8035i | − | 0.909674i | −0.890575 | − | 0.454837i | \(-0.849698\pi\) | ||
0.890575 | − | 0.454837i | \(-0.150302\pi\) | |||||||
\(524\) | 7.05086 | 0.308018 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.3887 | 0.583774 | ||||||||
\(527\) | 35.9496i | 1.56599i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.01429 | 0.0440996 | ||||||||
\(530\) | 16.7654 | − | 2.35551i | 0.728243 | − | 0.102317i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 3.37778i | − | 0.146446i | ||||||
\(533\) | − | 3.05086i | − | 0.132147i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.32540 | − | 37.9037i | −0.230237 | − | 1.63872i | ||||
\(536\) | 23.7989 | 1.02796 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 19.6030i | − | 0.845145i | ||||||
\(539\) | 0.306186 | 0.0131883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.6222 | 0.714645 | 0.357322 | − | 0.933981i | \(-0.383690\pi\) | ||||
0.357322 | + | 0.933981i | \(0.383690\pi\) | |||||||
\(542\) | 15.8000i | 0.678667i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.5620 | 0.795839 | ||||||||
\(545\) | 37.0321 | − | 5.20294i | 1.58628 | − | 0.222870i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.9748i | 1.28163i | 0.767695 | + | 0.640815i | \(0.221404\pi\) | ||||
−0.767695 | + | 0.640815i | \(0.778596\pi\) | |||||||
\(548\) | − | 10.0633i | − | 0.429882i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.358572 | − | 1.25088i | −0.0152896 | − | 0.0533379i | ||||
\(551\) | −19.2859 | −0.821608 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 41.3274i | 1.75742i | ||||||||
\(554\) | 9.19405 | 0.390618 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0316 | −0.425436 | ||||||||
\(557\) | − | 5.03657i | − | 0.213406i | −0.994291 | − | 0.106703i | \(-0.965971\pi\) | ||
0.994291 | − | 0.106703i | \(-0.0340294\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.36196 | 0.269082 | ||||||||
\(560\) | −2.41435 | − | 17.1842i | −0.102025 | − | 0.726165i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 8.20342i | − | 0.346040i | ||||||
\(563\) | − | 2.88247i | − | 0.121482i | −0.998154 | − | 0.0607408i | \(-0.980654\pi\) | ||
0.998154 | − | 0.0607408i | \(-0.0193463\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.368416 | + | 2.62222i | 0.0154994 | + | 0.110317i | ||||
\(566\) | −23.1764 | −0.974176 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.6484i | 0.782468i | ||||||||
\(569\) | −4.37286 | −0.183320 | −0.0916600 | − | 0.995790i | \(-0.529217\pi\) | ||||
−0.0916600 | + | 0.995790i | \(0.529217\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.58120 | −0.0661714 | −0.0330857 | − | 0.999453i | \(-0.510533\pi\) | ||||
−0.0330857 | + | 0.999453i | \(0.510533\pi\) | |||||||
\(572\) | − | 0.112610i | − | 0.00470844i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.7556 | 0.448929 | ||||||||
\(575\) | 6.46028 | + | 22.5368i | 0.269412 | + | 0.939850i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.61729i | 0.317112i | 0.987350 | + | 0.158556i | \(0.0506839\pi\) | ||||
−0.987350 | + | 0.158556i | \(0.949316\pi\) | |||||||
\(578\) | − | 29.5412i | − | 1.22875i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.1334 | − | 1.42372i | 0.420765 | − | 0.0591166i | ||||
\(581\) | −27.6543 | −1.14730 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.33630i | 0.0553438i | ||||||||
\(584\) | −31.5285 | −1.30466 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.82071 | −0.405690 | ||||||||
\(587\) | − | 46.8243i | − | 1.93264i | −0.257336 | − | 0.966322i | \(-0.582845\pi\) | ||
0.257336 | − | 0.966322i | \(-0.417155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3827 | 0.510221 | ||||||||
\(590\) | −3.50024 | − | 24.9131i | −0.144103 | − | 1.02565i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 6.09726i | − | 0.250596i | ||||||
\(593\) | 15.9398i | 0.654568i | 0.944926 | + | 0.327284i | \(0.106133\pi\) | ||||
−0.944926 | + | 0.327284i | \(0.893867\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.3274 | − | 5.80642i | 1.69426 | − | 0.238040i | ||||
\(596\) | −1.87649 | −0.0768641 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 5.69381i | − | 0.232837i | ||||||
\(599\) | 18.4889 | 0.755434 | 0.377717 | − | 0.925921i | \(-0.376709\pi\) | ||||
0.377717 | + | 0.925921i | \(0.376709\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7556 | 0.846637 | 0.423319 | − | 0.905981i | \(-0.360865\pi\) | ||||
0.423319 | + | 0.905981i | \(0.360865\pi\) | |||||||
\(602\) | 22.4286i | 0.914123i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.664758 | −0.0270486 | ||||||||
\(605\) | −24.2558 | + | 3.40790i | −0.986139 | + | 0.138551i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 36.0765i | − | 1.46430i | −0.681143 | − | 0.732150i | \(-0.738517\pi\) | ||
0.681143 | − | 0.732150i | \(-0.261483\pi\) | |||||||
\(608\) | − | 6.39361i | − | 0.259295i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.106156 | − | 0.755569i | −0.00429813 | − | 0.0305921i | ||||
\(611\) | 1.09679 | 0.0443713 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.94962i | 0.401861i | 0.979605 | + | 0.200931i | \(0.0643966\pi\) | ||||
−0.979605 | + | 0.200931i | \(0.935603\pi\) | |||||||
\(614\) | −16.3126 | −0.658325 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.90813 | 0.0768809 | ||||||||
\(617\) | 2.09187i | 0.0842154i | 0.999113 | + | 0.0421077i | \(0.0134073\pi\) | ||||
−0.999113 | + | 0.0421077i | \(0.986593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.4681 | −0.742296 | −0.371148 | − | 0.928574i | \(-0.621036\pi\) | ||||
−0.371148 | + | 0.928574i | \(0.621036\pi\) | |||||||
\(620\) | −6.50622 | + | 0.914111i | −0.261296 | + | 0.0367116i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 24.5334i | − | 0.983700i | ||||||
\(623\) | − | 16.2953i | − | 0.652857i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | − | 13.2444i | 0.848137 | − | 0.529777i | ||||
\(626\) | −18.3497 | −0.733401 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 2.94914i | − | 0.117684i | ||||||
\(629\) | 14.6637 | 0.584680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.6657 | −1.53926 | −0.769629 | − | 0.638492i | \(-0.779559\pi\) | ||||
−0.769629 | + | 0.638492i | \(0.779559\pi\) | |||||||
\(632\) | 43.6543i | 1.73648i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.0563 | −1.07454 | ||||||||
\(635\) | 0.716089 | + | 5.09679i | 0.0284171 | + | 0.202260i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.42864i | − | 0.0566048i | ||||||
\(638\) | − | 2.26671i | − | 0.0897398i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.54770 | − | 11.0158i | −0.0611783 | − | 0.435439i | ||||
\(641\) | −24.5718 | −0.970529 | −0.485265 | − | 0.874367i | \(-0.661277\pi\) | ||||
−0.485265 | + | 0.874367i | \(0.661277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.4938i | 1.08425i | 0.840298 | + | 0.542125i | \(0.182380\pi\) | ||||
−0.840298 | + | 0.542125i | \(0.817620\pi\) | |||||||
\(644\) | −7.15257 | −0.281851 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.2859 | −0.680105 | ||||||||
\(647\) | 13.7812i | 0.541796i | 0.962608 | + | 0.270898i | \(0.0873207\pi\) | ||||
−0.962608 | + | 0.270898i | \(0.912679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.98571 | 0.0779459 | ||||||||
\(650\) | −5.83654 | + | 1.67307i | −0.228928 | + | 0.0656232i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 1.95407i | − | 0.0765272i | ||||||
\(653\) | 2.12045i | 0.0829795i | 0.999139 | + | 0.0414897i | \(0.0132104\pi\) | ||||
−0.999139 | + | 0.0414897i | \(0.986790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.7146 | − | 4.17484i | 1.16104 | − | 0.163125i | ||||
\(656\) | 8.15515 | 0.318405 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.86665i | 0.150738i | ||||||||
\(659\) | 33.8894 | 1.32014 | 0.660072 | − | 0.751203i | \(-0.270526\pi\) | ||||
0.660072 | + | 0.751203i | \(0.270526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.3689 | −1.45348 | −0.726741 | − | 0.686912i | \(-0.758966\pi\) | ||||
−0.726741 | + | 0.686912i | \(0.758966\pi\) | |||||||
\(662\) | 10.0252i | 0.389640i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.2114 | −1.13362 | ||||||||
\(665\) | −2.00000 | − | 14.2351i | −0.0775567 | − | 0.552012i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.8385i | 1.58127i | ||||||||
\(668\) | 3.69721i | 0.143049i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.8671 | − | 2.93179i | 0.806167 | − | 0.113265i | ||||
\(671\) | 0.0602231 | 0.00232489 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 35.4608i | − | 1.36691i | −0.729992 | − | 0.683456i | \(-0.760476\pi\) | ||
0.729992 | − | 0.683456i | \(-0.239524\pi\) | |||||||
\(674\) | −16.6923 | −0.642963 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.525428 | −0.0202088 | ||||||||
\(677\) | 15.3047i | 0.588206i | 0.955774 | + | 0.294103i | \(0.0950208\pi\) | ||||
−0.955774 | + | 0.294103i | \(0.904979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 52.3783 | 2.01009 | ||||||||
\(680\) | 43.6543 | − | 6.13335i | 1.67407 | − | 0.235203i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.45536i | 0.0557286i | ||||||||
\(683\) | 13.0968i | 0.501135i | 0.968099 | + | 0.250567i | \(0.0806171\pi\) | ||||
−0.968099 | + | 0.250567i | \(0.919383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.95851 | − | 42.4099i | −0.227663 | − | 1.62040i | ||||
\(686\) | −19.6414 | −0.749913 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.0060i | 0.648347i | ||||||||
\(689\) | 6.23506 | 0.237537 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4079 | −0.700269 | −0.350135 | − | 0.936699i | \(-0.613864\pi\) | ||||
−0.350135 | + | 0.936699i | \(0.613864\pi\) | |||||||
\(692\) | 0.380371i | 0.0144595i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.48055 | −0.0562009 | ||||||||
\(695\) | −42.2766 | + | 5.93978i | −1.60364 | + | 0.225309i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.6128i | 0.742890i | ||||||||
\(698\) | − | 27.3363i | − | 1.03469i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.10171 | + | 7.33185i | 0.0794372 | + | 0.277118i | ||||
\(701\) | 31.3689 | 1.18479 | 0.592393 | − | 0.805649i | \(-0.298183\pi\) | ||||
0.592393 | + | 0.805649i | \(0.298183\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.05086i | − | 0.190497i | ||||||
\(704\) | 1.89723 | 0.0715047 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.3417 | −0.652663 | ||||||||
\(707\) | − | 11.4380i | − | 0.430171i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.47949 | −0.356010 | −0.178005 | − | 0.984030i | \(-0.556964\pi\) | ||||
−0.178005 | + | 0.984030i | \(0.556964\pi\) | |||||||
\(710\) | 2.29729 | + | 16.3511i | 0.0862159 | + | 0.613644i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 17.2128i | − | 0.645077i | ||||||
\(713\) | − | 26.2208i | − | 0.981976i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0666765 | − | 0.474572i | −0.00249356 | − | 0.0177480i | ||||
\(716\) | −2.12351 | −0.0793592 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 14.7590i | − | 0.550799i | ||||||
\(719\) | −29.6227 | −1.10474 | −0.552370 | − | 0.833599i | \(-0.686276\pi\) | ||||
−0.552370 | + | 0.833599i | \(0.686276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.19358 | 0.305145 | ||||||||
\(722\) | − | 17.1180i | − | 0.637066i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.23014 | 0.0457178 | ||||||||
\(725\) | 41.8622 | − | 12.0000i | 1.55472 | − | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 42.6702i | − | 1.58255i | −0.611461 | − | 0.791274i | \(-0.709418\pi\) | ||
0.611461 | − | 0.791274i | \(-0.290582\pi\) | |||||||
\(728\) | − | 8.90321i | − | 0.329975i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −27.6445 | + | 3.88400i | −1.02317 | + | 0.143753i | ||||
\(731\) | −40.8988 | −1.51270 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0830i | 0.963397i | 0.876337 | + | 0.481698i | \(0.159980\pi\) | ||||
−0.876337 | + | 0.481698i | \(0.840020\pi\) | |||||||
\(734\) | −5.65539 | −0.208744 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.5387 | −0.499042 | ||||||||
\(737\) | 1.66323i | 0.0612657i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.2687 | 1.03988 | 0.519941 | − | 0.854202i | \(-0.325954\pi\) | ||||
0.519941 | + | 0.854202i | \(0.325954\pi\) | |||||||
\(740\) | 0.372862 | + | 2.65386i | 0.0137067 | + | 0.0975578i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.9813i | 0.806958i | ||||||||
\(743\) | − | 20.6681i | − | 0.758241i | −0.925347 | − | 0.379120i | \(-0.876227\pi\) | ||
0.925347 | − | 0.379120i | \(-0.123773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.90813 | + | 1.11108i | −0.289732 | + | 0.0407068i | ||||
\(746\) | −42.4286 | −1.55342 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.723926i | 0.0264694i | ||||||||
\(749\) | 49.6958 | 1.81585 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.46028 | 0.0897770 | 0.0448885 | − | 0.998992i | \(-0.485707\pi\) | ||||
0.0448885 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(752\) | 2.93179i | 0.106911i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.5763 | −0.385165 | ||||||||
\(755\) | −2.80150 | + | 0.393606i | −0.101957 | + | 0.0143248i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.6035i | 1.76652i | 0.468880 | + | 0.883262i | \(0.344658\pi\) | ||||
−0.468880 | + | 0.883262i | \(0.655342\pi\) | |||||||
\(758\) | 21.2162i | 0.770606i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.11261 | − | 15.0366i | −0.0766324 | − | 0.545434i | ||||
\(761\) | 13.8252 | 0.501162 | 0.250581 | − | 0.968096i | \(-0.419378\pi\) | ||||
0.250581 | + | 0.968096i | \(0.419378\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.5531i | 1.75774i | ||||||||
\(764\) | 1.10430 | 0.0399520 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.6811 | −0.819500 | ||||||||
\(767\) | − | 9.26517i | − | 0.334546i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.9688 | 1.40525 | 0.702626 | − | 0.711559i | \(-0.252011\pi\) | ||||
0.702626 | + | 0.711559i | \(0.252011\pi\) | |||||||
\(770\) | 1.67307 | − | 0.235063i | 0.0602933 | − | 0.00847109i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 7.10430i | − | 0.255689i | ||||||
\(773\) | 0.445992i | 0.0160412i | 0.999968 | + | 0.00802061i | \(0.00255307\pi\) | ||||
−0.999968 | + | 0.00802061i | \(0.997447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.8780 | + | 7.70471i | −0.965487 | + | 0.276761i | ||||
\(776\) | 55.3274 | 1.98614 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.95851i | 0.0702161i | ||||||||
\(779\) | 6.75557 | 0.242043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30327 | −0.0466347 | ||||||||
\(782\) | 36.6035i | 1.30894i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.81885 | 0.136388 | ||||||||
\(785\) | −1.74620 | − | 12.4286i | −0.0623246 | − | 0.443597i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9037i | 1.20854i | 0.796781 | + | 0.604268i | \(0.206534\pi\) | ||||
−0.796781 | + | 0.604268i | \(0.793466\pi\) | |||||||
\(788\) | − | 1.05086i | − | 0.0374352i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.37778 | + | 38.2766i | 0.191333 | + | 1.36182i | ||||
\(791\) | −3.43801 | −0.122241 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.280996i | − | 0.00997847i | ||||||
\(794\) | 7.98571 | 0.283402 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.6346 | −0.412379 | ||||||||
\(797\) | 10.2953i | 0.364678i | 0.983236 | + | 0.182339i | \(0.0583668\pi\) | ||||
−0.983236 | + | 0.182339i | \(0.941633\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.05086 | −0.249441 | ||||||||
\(800\) | 3.97820 | + | 13.8780i | 0.140651 | + | 0.490662i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.6035i | 0.939402i | ||||||||
\(803\) | − | 2.20342i | − | 0.0777570i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.1432 | + | 4.23506i | −1.06241 | + | 0.149266i | ||||
\(806\) | 6.79060 | 0.239189 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 12.0820i | − | 0.425044i | ||||||
\(809\) | 7.94422 | 0.279304 | 0.139652 | − | 0.990201i | \(-0.455402\pi\) | ||||
0.139652 | + | 0.990201i | \(0.455402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.12245 | −0.285218 | −0.142609 | − | 0.989779i | \(-0.545549\pi\) | ||||
−0.142609 | + | 0.989779i | \(0.545549\pi\) | |||||||
\(812\) | 13.2859i | 0.466244i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.593635 | 0.0208069 | ||||||||
\(815\) | −1.15701 | − | 8.23506i | −0.0405283 | − | 0.288462i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0874i | 0.492856i | ||||||||
\(818\) | 12.3783i | 0.432796i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.54956 | + | 0.498707i | −0.123956 | + | 0.0174156i | ||||
\(821\) | 22.2065 | 0.775012 | 0.387506 | − | 0.921867i | \(-0.373337\pi\) | ||||
0.387506 | + | 0.921867i | \(0.373337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 11.1175i | − | 0.387533i | −0.981048 | − | 0.193766i | \(-0.937930\pi\) | ||
0.981048 | − | 0.193766i | \(-0.0620704\pi\) | |||||||
\(824\) | 8.65491 | 0.301508 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 32.6637 | 1.13652 | ||||||||
\(827\) | − | 23.1570i | − | 0.805248i | −0.915365 | − | 0.402624i | \(-0.868098\pi\) | ||
0.915365 | − | 0.402624i | \(-0.131902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.1195 | 0.941901 | 0.470950 | − | 0.882160i | \(-0.343911\pi\) | ||||
0.470950 | + | 0.882160i | \(0.343911\pi\) | |||||||
\(830\) | −25.6128 | + | 3.59856i | −0.889035 | + | 0.124908i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 8.85236i | − | 0.306900i | ||||||
\(833\) | 9.18421i | 0.318214i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.18913 | + | 15.5812i | 0.0757580 | + | 0.539210i | ||||
\(836\) | 0.249353 | 0.00862407 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.88586i | 0.306957i | ||||||||
\(839\) | 25.3955 | 0.876749 | 0.438374 | − | 0.898792i | \(-0.355554\pi\) | ||||
0.438374 | + | 0.898792i | \(0.355554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.8578 | 1.61578 | ||||||||
\(842\) | − | 9.55262i | − | 0.329205i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.3269 | 0.355468 | ||||||||
\(845\) | −2.21432 | + | 0.311108i | −0.0761749 | + | 0.0107024i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 31.8020i | − | 1.09273i | ||||||
\(848\) | 16.6668i | 0.572339i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 37.5210 | − | 10.7556i | 1.28696 | − | 0.368913i | ||||
\(851\) | −10.6953 | −0.366632 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.0651i | − | 0.858214i | −0.903254 | − | 0.429107i | \(-0.858828\pi\) | ||
0.903254 | − | 0.429107i | \(-0.141172\pi\) | |||||||
\(854\) | 0.990632 | 0.0338987 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 52.4939 | 1.79421 | ||||||||
\(857\) | − | 7.61285i | − | 0.260050i | −0.991511 | − | 0.130025i | \(-0.958494\pi\) | ||
0.991511 | − | 0.130025i | \(-0.0415057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.1432 | −1.43791 | −0.718954 | − | 0.695058i | \(-0.755379\pi\) | ||||
−0.718954 | + | 0.695058i | \(0.755379\pi\) | |||||||
\(860\) | −1.03996 | − | 7.40192i | −0.0354622 | − | 0.252403i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 47.2607i | 1.60971i | ||||||||
\(863\) | 51.5768i | 1.75569i | 0.478942 | + | 0.877847i | \(0.341020\pi\) | ||||
−0.478942 | + | 0.877847i | \(0.658980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.225219 | + | 1.60300i | 0.00765768 | + | 0.0545037i | ||||
\(866\) | 24.5334 | 0.833679 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 8.53035i | − | 0.289539i | ||||||
\(869\) | −3.05086 | −0.103493 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.76049 | 0.262954 | ||||||||
\(872\) | 51.2869i | 1.73679i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.6079 | 0.426469 | ||||||||
\(875\) | 13.1985 | + | 29.6543i | 0.446191 | + | 1.00250i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 34.0701i | − | 1.15046i | −0.817990 | − | 0.575232i | \(-0.804912\pi\) | ||
0.817990 | − | 0.575232i | \(-0.195088\pi\) | |||||||
\(878\) | − | 13.2226i | − | 0.446242i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.26857 | − | 0.178231i | 0.0427633 | − | 0.00600817i | ||||
\(881\) | −3.71900 | −0.125296 | −0.0626482 | − | 0.998036i | \(-0.519955\pi\) | ||||
−0.0626482 | + | 0.998036i | \(0.519955\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.0163i | 1.41396i | 0.707233 | + | 0.706981i | \(0.249943\pi\) | ||||
−0.707233 | + | 0.706981i | \(0.750057\pi\) | |||||||
\(884\) | 3.37778 | 0.113607 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.7644 | −1.16793 | ||||||||
\(887\) | 40.3116i | 1.35353i | 0.736199 | + | 0.676765i | \(0.236619\pi\) | ||||
−0.736199 | + | 0.676765i | \(0.763381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.68244 | −0.224122 | ||||||||
\(890\) | −2.12045 | − | 15.0923i | −0.0710775 | − | 0.505896i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3344i | 0.346023i | ||||||||
\(893\) | 2.42864i | 0.0812713i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.94914 | + | 1.25734i | −0.299137 | + | 0.0420282i | ||||
\(896\) | 14.4429 | 0.482504 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 13.2730i | − | 0.442926i | ||||||
\(899\) | −48.7052 | −1.62441 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.0830 | −1.33536 | ||||||||
\(902\) | 0.793993i | 0.0264371i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.63158 | −0.120785 | ||||||||
\(905\) | 5.18421 | − | 0.728372i | 0.172329 | − | 0.0242119i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.8419i | 1.15691i | 0.815715 | + | 0.578454i | \(0.196344\pi\) | ||||
−0.815715 | + | 0.578454i | \(0.803656\pi\) | |||||||
\(908\) | − | 6.97328i | − | 0.231416i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.09679 | − | 7.80642i | −0.0363582 | − | 0.258780i | ||||
\(911\) | −23.2672 | −0.770876 | −0.385438 | − | 0.922734i | \(-0.625950\pi\) | ||||
−0.385438 | + | 0.922734i | \(0.625950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.04149i | − | 0.0675634i | ||||||
\(914\) | −13.8510 | −0.458149 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.27607 | 0.0421627 | ||||||||
\(917\) | 38.9590i | 1.28654i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.22570 | 0.106406 | 0.0532029 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532029 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(920\) | −31.8404 | + | 4.47352i | −1.04975 | + | 0.147488i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.7342i | 1.04511i | ||||||||
\(923\) | 6.08097i | 0.200157i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.14272 | + | 10.9634i | 0.103332 | + | 0.360476i | ||||
\(926\) | 9.62036 | 0.316145 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25.1481i | 0.825527i | ||||||||
\(929\) | −39.3461 | −1.29091 | −0.645453 | − | 0.763800i | \(-0.723331\pi\) | ||||
−0.645453 | + | 0.763800i | \(0.723331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.16346 | 0.103678 | ||||||||
\(932\) | − | 8.49871i | − | 0.278384i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.2268 | −0.432792 | ||||||||
\(935\) | 0.428639 | + | 3.05086i | 0.0140180 | + | 0.0997736i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 51.6040i | − | 1.68583i | −0.538048 | − | 0.842914i | \(-0.680838\pi\) | ||
0.538048 | − | 0.842914i | \(-0.319162\pi\) | |||||||
\(938\) | 27.3590i | 0.893305i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.179286 | − | 1.27607i | −0.00584767 | − | 0.0416209i | ||||
\(941\) | −37.5081 | −1.22273 | −0.611364 | − | 0.791349i | \(-0.709379\pi\) | ||||
−0.611364 | + | 0.791349i | \(0.709379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.3051i | − | 0.465839i | ||||||
\(944\) | 24.7665 | 0.806080 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.65572 | −0.0538320 | ||||||||
\(947\) | − | 38.1160i | − | 1.23860i | −0.785153 | − | 0.619302i | \(-0.787416\pi\) | ||
0.785153 | − | 0.619302i | \(-0.212584\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.2810 | −0.333735 | ||||||||
\(950\) | −3.70471 | − | 12.9240i | −0.120197 | − | 0.419308i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 57.2355i | 1.85501i | ||||||||
\(953\) | 28.7368i | 0.930877i | 0.885080 | + | 0.465439i | \(0.154103\pi\) | ||||
−0.885080 | + | 0.465439i | \(0.845897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.65386 | − | 0.653858i | 0.150595 | − | 0.0211584i | ||||
\(956\) | −6.71303 | −0.217115 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 11.0890i | − | 0.358268i | ||||||
\(959\) | 55.6040 | 1.79555 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.271628 | 0.00876221 | ||||||||
\(962\) | − | 2.76986i | − | 0.0893038i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.09912 | −0.0998161 | ||||||||
\(965\) | −4.20648 | − | 29.9398i | −0.135411 | − | 0.963796i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29.0593i | − | 0.934485i | −0.884129 | − | 0.467242i | \(-0.845248\pi\) | ||
0.884129 | − | 0.467242i | \(-0.154752\pi\) | |||||||
\(968\) | − | 33.5926i | − | 1.07971i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48.5116 | − | 6.81579i | 1.55761 | − | 0.218842i | ||||
\(971\) | 39.8578 | 1.27910 | 0.639548 | − | 0.768751i | \(-0.279121\pi\) | ||||
0.639548 | + | 0.768751i | \(0.279121\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 55.4291i | − | 1.77698i | ||||||
\(974\) | −19.6588 | −0.629908 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.751123 | 0.0240429 | ||||||||
\(977\) | − | 12.8617i | − | 0.411483i | −0.978606 | − | 0.205742i | \(-0.934039\pi\) | ||
0.978606 | − | 0.205742i | \(-0.0659606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.20294 | 0.0384463 | ||||||||
\(980\) | −1.66217 | + | 0.233532i | −0.0530961 | + | 0.00745991i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 31.8925i | − | 1.01773i | ||||||
\(983\) | − | 45.4880i | − | 1.45084i | −0.688306 | − | 0.725420i | \(-0.741645\pi\) | ||
0.688306 | − | 0.725420i | \(-0.258355\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.622216 | − | 4.42864i | −0.0198254 | − | 0.141108i | ||||
\(986\) | 67.9911 | 2.16528 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.16346i | − | 0.0370147i | ||||||
\(989\) | 29.8306 | 0.948557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.07007 | 0.256354 | 0.128177 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128177 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(992\) | − | 16.1466i | − | 0.512655i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.4380 | −0.679972 | ||||||||
\(995\) | −49.0321 | + | 6.88892i | −1.55442 | + | 0.218394i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.8158i | 1.03929i | 0.854383 | + | 0.519643i | \(0.173935\pi\) | ||||
−0.854383 | + | 0.519643i | \(0.826065\pi\) | |||||||
\(998\) | − | 36.4667i | − | 1.15433i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))