Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(209,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1040.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.30444181021\) |
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 | 209.5 | ||
Root | \(1.45161 + 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.209 |
Dual form | 1040.2.d.c.209.2 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.31111i | 0.756968i | 0.925608 | + | 0.378484i | \(0.123555\pi\) | ||||
−0.925608 | + | 0.378484i | \(0.876445\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.21432 | + | 0.311108i | −0.990274 | + | 0.139132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.90321i | − | 1.09731i | −0.836049 | − | 0.548655i | \(-0.815140\pi\) | ||
0.836049 | − | 0.548655i | \(-0.184860\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.28100 | 0.426999 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −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 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.407896 | − | 2.90321i | −0.105318 | − | 0.749606i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.42864i | 1.55917i | 0.626294 | + | 0.779587i | \(0.284571\pi\) | ||||
−0.626294 | + | 0.779587i | \(0.715429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.21432 | 0.508000 | 0.254000 | − | 0.967204i | \(-0.418254\pi\) | ||||
0.254000 | + | 0.967204i | \(0.418254\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.80642 | 0.830630 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 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 | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61285i | 1.08019i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.70964 | −1.61734 | −0.808669 | − | 0.588263i | \(-0.799812\pi\) | ||||
−0.808669 | + | 0.588263i | \(0.799812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.59210 | 1.00437 | 0.502186 | − | 0.864760i | \(-0.332529\pi\) | ||||
0.502186 | + | 0.864760i | \(0.332529\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.280996i | − | 0.0489152i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 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 | \(0.939963\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.31111 | −0.209945 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.05086 | 0.476464 | 0.238232 | − | 0.971208i | \(-0.423432\pi\) | ||||
0.238232 | + | 0.971208i | \(0.423432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.36196i | 0.970190i | 0.874461 | + | 0.485095i | \(0.161215\pi\) | ||||
−0.874461 | + | 0.485095i | \(0.838785\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.83654 | + | 0.398528i | −0.422846 | + | 0.0594090i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 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 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.42864 | −1.18025 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.23506i | 0.856452i | 0.903672 | + | 0.428226i | \(0.140861\pi\) | ||||
−0.903672 | + | 0.428226i | \(0.859139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.474572 | − | 0.0666765i | 0.0639913 | − | 0.00899066i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.90321i | 0.384540i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −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 | \(0.505726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.71900i | − | 0.468550i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.311108 | − | 2.21432i | −0.0385882 | − | 0.274653i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.76049i | 0.948095i | 0.880499 | + | 0.474047i | \(0.157207\pi\) | ||||
−0.880499 | + | 0.474047i | \(0.842793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.14764 | −0.740089 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(0.794510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.80642 | + | 6.30174i | 0.208588 | + | 0.727662i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.622216i | 0.0709081i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2351 | −1.60157 | −0.800785 | − | 0.598952i | \(-0.795584\pi\) | ||||
−0.800785 | + | 0.598952i | \(0.795584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.51606 | −0.390673 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 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 | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 11.4193i | − | 1.22427i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.61285 | 0.594961 | 0.297480 | − | 0.954728i | \(-0.403854\pi\) | ||||
0.297480 | + | 0.954728i | \(0.403854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.90321 | 0.304339 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.33185i | 0.760278i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −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 | \(-0.368536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.274543 | −0.0275926 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.93978 | 0.392022 | 0.196011 | − | 0.980602i | \(-0.437201\pi\) | ||||
0.196011 | + | 0.980602i | \(0.437201\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.82225i | 0.278084i | 0.990286 | + | 0.139042i | \(0.0444023\pi\) | ||||
−0.990286 | + | 0.139042i | \(0.955598\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.42864 | + | 1.18421i | −0.822551 | + | 0.115567i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 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 | 0 | ||||||||
\(111\) | −2.99063 | −0.283858 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.18421i | − | 0.111401i | −0.998448 | − | 0.0557005i | \(-0.982261\pi\) | ||
0.998448 | − | 0.0557005i | \(-0.0177392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.45875 | − | 10.3827i | −0.136029 | − | 0.968192i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.28100i | 0.118428i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.6637 | 1.71090 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9541 | −0.995824 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.00000i | 0.360668i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2143 | + | 4.54617i | −0.913597 | + | 0.406622i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.30174i | − | 0.204246i | −0.994772 | − | 0.102123i | \(-0.967436\pi\) | ||
0.994772 | − | 0.102123i | \(-0.0325636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.34122 | −0.734403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 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 | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.74620 | − | 12.4286i | −0.150289 | − | 1.06969i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.1526i | 1.63631i | 0.574995 | + | 0.818157i | \(0.305004\pi\) | ||||
−0.574995 | + | 0.818157i | \(0.694996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0923 | 1.61939 | 0.809696 | − | 0.586850i | \(-0.199632\pi\) | ||||
0.809696 | + | 0.586850i | \(0.199632\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.43801 | 0.121102 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.214320i | − | 0.0179223i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.2859 | − | 2.70964i | 1.60161 | − | 0.225023i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.87310i | − | 0.154491i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.57136 | 0.292577 | 0.146289 | − | 0.989242i | \(-0.453267\pi\) | ||||
0.146289 | + | 0.989242i | \(0.453267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.26517 | 0.102958 | 0.0514792 | − | 0.998674i | \(-0.483606\pi\) | ||||
0.0514792 | + | 0.998674i | \(0.483606\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.23506i | 0.665765i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −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 | \(-0.0719041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.17484 | −0.648307 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.6128 | 1.07284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.71900i | 0.291295i | 0.989337 | + | 0.145647i | \(0.0465265\pi\) | ||||
−0.989337 | + | 0.145647i | \(0.953473\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0874201 | + | 0.622216i | 0.00680565 | + | 0.0484394i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.83654 | 0.216915 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 0.723926i | − | 0.0550391i | −0.999621 | − | 0.0275195i | \(-0.991239\pi\) | ||
0.999621 | − | 0.0275195i | \(-0.00876085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | − | 13.9541i | −0.302372 | − | 1.05483i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.1476i | − | 0.913073i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −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 | \(0.472269\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.368416i | − | 0.0272341i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.709636 | − | 5.05086i | −0.0521735 | − | 0.371346i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.37778i | − | 0.100754i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.2953 | 1.18531 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(-0.161774\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.90321 | − | 0.407896i | 0.207903 | − | 0.0292100i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.1432 | 1.56969 | 0.784845 | − | 0.619692i | \(-0.212743\pi\) | ||||
0.784845 | + | 0.619692i | \(0.212743\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.1748 | −0.717678 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.2859i | 1.77472i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.75557 | + | 0.949145i | −0.471829 | + | 0.0662912i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00645i | 0.417477i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.474572 | −0.0328269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.6543 | −1.35306 | −0.676530 | − | 0.736415i | \(-0.736517\pi\) | ||||
−0.676530 | + | 0.736415i | \(0.736517\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.97280i | 0.546287i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.97926 | − | 14.0874i | −0.134984 | − | 0.960754i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.2351i | − | 1.10211i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.4795 | −0.910860 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.42864 | −0.432437 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.6686i | − | 1.31711i | −0.752533 | − | 0.658554i | \(-0.771168\pi\) | ||
0.752533 | − | 0.658554i | \(-0.228832\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.15701 | − | 1.76494i | 0.410467 | − | 0.117662i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 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 | \(0.474430\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.815792 | −0.0536752 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1748i | 1.05965i | 0.848107 | + | 0.529825i | \(0.177742\pi\) | ||||
−0.848107 | + | 0.529825i | \(0.822258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.341219 | + | 2.42864i | 0.0222587 | + | 0.158427i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 18.6637i | − | 1.21234i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(0.560839\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.2286i | 0.784466i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.16346 | − | 0.444461i | 0.202106 | − | 0.0283956i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.21432i | 0.140894i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.4889 | −0.791450 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.6637 | − | 2.62222i | 1.16877 | − | 0.164210i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.3970i | − | 1.14757i | −0.819005 | − | 0.573787i | \(-0.805474\pi\) | ||
0.819005 | − | 0.573787i | \(-0.194526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.62222 | 0.411484 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.1570 | −0.690602 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 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 | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.35905i | 0.450366i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.1432 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0114 | −0.790385 | −0.395192 | − | 0.918598i | \(-0.629322\pi\) | ||||
−0.395192 | + | 0.918598i | \(0.629322\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.80642i | 0.230375i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −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 | \(-0.0730419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.16346 | 0.428865 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.75557 | 0.403003 | 0.201502 | − | 0.979488i | \(-0.435418\pi\) | ||||
0.201502 | + | 0.979488i | \(0.435418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 19.0859i | − | 1.13454i | −0.823532 | − | 0.567269i | \(-0.808000\pi\) | ||
0.823532 | − | 0.567269i | \(-0.192000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.903212 | − | 6.42864i | −0.0535017 | − | 0.380800i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.85728i | − | 0.522829i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.3274 | −1.43102 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.6543 | 1.38664 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.08742i | − | 0.472472i | −0.971696 | − | 0.236236i | \(-0.924086\pi\) | ||
0.971696 | − | 0.236236i | \(-0.0759139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.5161 | − | 2.88247i | 1.19449 | − | 0.167824i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.20294i | − | 0.0698019i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.68889 | −0.271166 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.4701 | 1.06460 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.16547i | 0.296749i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.622216 | − | 0.0874201i | 0.0356280 | − | 0.00500566i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.4336i | − | 0.766694i | −0.923604 | − | 0.383347i | \(-0.874771\pi\) | ||
0.923604 | − | 0.383347i | \(-0.125229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.70027 | −0.210501 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(0.859548\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.15701 | + | 8.23506i | 0.0651902 | + | 0.463993i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 22.2810i | − | 1.25143i | −0.780054 | − | 0.625713i | \(-0.784808\pi\) | ||
0.780054 | − | 0.625713i | \(-0.215192\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.86665 | 0.104512 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.4429 | 1.25264 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.2351i | 0.792060i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.37778 | + | 4.80642i | 0.0764257 | + | 0.266612i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.9269i | 1.21256i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.18421 | −0.175551 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.25581 | −0.453780 | −0.226890 | − | 0.973920i | \(-0.572856\pi\) | ||||
−0.226890 | + | 0.973920i | \(0.572856\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.92195i | 0.160122i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −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 | \(0.877848\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.55262 | 0.0843270 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.19850 | −0.0649023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.1748i | − | 0.873359i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.6128 | − | 1.91258i | 0.732891 | − | 0.102970i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 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 | \(0.705832\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.61285 | −0.299592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 14.2810i | − | 0.760101i | −0.924966 | − | 0.380050i | \(-0.875907\pi\) | ||
0.924966 | − | 0.380050i | \(-0.124093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.4652 | + | 1.89184i | −0.714659 | + | 0.100408i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.4701i | 1.29510i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 14.3620i | − | 0.753808i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.19850 | − | 22.7654i | −0.167417 | − | 1.19160i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.65725i | − | 0.243106i | −0.992585 | − | 0.121553i | \(-0.961212\pi\) | ||
0.992585 | − | 0.121553i | \(-0.0387875\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.90813 | 0.203449 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.1017 | 0.939794 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.9403i | 1.80914i | 0.426328 | + | 0.904569i | \(0.359807\pi\) | ||||
−0.426328 | + | 0.904569i | \(0.640193\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.96052 | − | 13.3921i | −0.307800 | − | 0.691564i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.70964i | − | 0.448569i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.4717 | −0.897459 | −0.448729 | − | 0.893668i | \(-0.648123\pi\) | ||||
−0.448729 | + | 0.893668i | \(0.648123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.01783 | 0.154608 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 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 | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.14965i | 0.414270i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.61285 | −0.0817746 | −0.0408873 | − | 0.999164i | \(-0.513018\pi\) | ||||
−0.0408873 | + | 0.999164i | \(0.513018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.1432 | −1.52441 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.5941i | 0.887506i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 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 | \(-0.0527712\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.42864 | 0.421960 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.9081 | −1.09404 | −0.547020 | − | 0.837120i | \(-0.684238\pi\) | ||||
−0.547020 | + | 0.837120i | \(0.684238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.59210i | 0.278563i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.78568 | − | 1.09387i | 0.386874 | − | 0.0543550i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.488863i | − | 0.0242320i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1936 | 0.504040 | 0.252020 | − | 0.967722i | \(-0.418905\pi\) | ||||
0.252020 | + | 0.967722i | \(0.418905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.1111 | −1.23864 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.8988i | 1.32360i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.96343 | − | 21.0923i | −0.145469 | − | 1.03538i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.0321i | 1.22583i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 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 | \(0.561400\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.40498i | − | 0.0683125i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.85728 | + | 30.8988i | 0.429641 | + | 1.49881i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.815792i | 0.0394789i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.280996 | 0.0135666 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(-0.161347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.55262 | + | 25.2859i | 0.170335 | + | 1.21237i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.3827i | 0.496672i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8889 | 0.519700 | 0.259850 | − | 0.965649i | \(-0.416327\pi\) | ||||
0.259850 | + | 0.965649i | \(0.416327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.83008 | −0.0871468 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 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 | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.68244i | 0.221472i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.9304 | 0.515838 | 0.257919 | − | 0.966167i | \(-0.416963\pi\) | ||||
0.257919 | + | 0.966167i | \(0.416963\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.653858 | −0.0307890 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.65878i | 0.0779363i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −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 | \(0.914039\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −36.0830 | −1.68421 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.1334 | −1.21715 | −0.608576 | − | 0.793496i | \(-0.708259\pi\) | ||||
−0.608576 | + | 0.793496i | \(0.708259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.92242i | 0.368186i | 0.982909 | + | 0.184093i | \(0.0589348\pi\) | ||||
−0.982909 | + | 0.184093i | \(0.941065\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.28100 | − | 16.2351i | −0.105779 | − | 0.752883i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.35905 | 0.339087 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.36349i | − | 0.0626935i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.6430 | − | 3.05086i | 0.488332 | − | 0.139983i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.98709i | 0.365704i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.8479i | 0.812108i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.61285 | + | 39.9496i | 0.254866 | + | 1.81402i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.1891i | − | 0.733600i | −0.930300 | − | 0.366800i | \(-0.880453\pi\) | ||
0.930300 | − | 0.366800i | \(-0.119547\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.87601 | −0.220501 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −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 | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.607926 | − | 0.0854124i | 0.0273242 | − | 0.00383900i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 17.6543i | − | 0.791905i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.0306 | 1.34435 | 0.672177 | − | 0.740391i | \(-0.265359\pi\) | ||||
0.672177 | + | 0.740391i | \(0.265359\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.22570 | −0.412174 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 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 | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.31111i | − | 0.0582283i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.9684 | 0.530488 | 0.265244 | − | 0.964181i | \(-0.414547\pi\) | ||||
0.265244 | + | 0.964181i | \(0.414547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.8479 | 1.32039 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.4286i | 0.548738i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.878023 | − | 6.24935i | −0.0386903 | − | 0.275379i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.235063i | 0.0103381i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.949145 | 0.0416628 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.75065 | 0.251940 | 0.125970 | − | 0.992034i | \(-0.459796\pi\) | ||||
0.125970 | + | 0.992034i | \(0.459796\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8035i | 0.909674i | 0.890575 | + | 0.454837i | \(0.150302\pi\) | ||||
−0.890575 | + | 0.454837i | \(0.849698\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.2953 | − | 5.24443i | 0.798472 | − | 0.228886i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.9496i | 1.56599i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.01429 | 0.0440996 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.8687 | −0.515056 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.05086i | 0.132147i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.32540 | + | 37.9037i | 0.230237 | + | 1.63872i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.29883i | − | 0.228661i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.306186 | 0.0131883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.6222 | 0.714645 | 0.357322 | − | 0.933981i | \(-0.383690\pi\) | ||||
0.357322 | + | 0.933981i | \(0.383690\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.06959i | 0.131729i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37.0321 | + | 5.20294i | −1.58628 | + | 0.222870i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 29.9748i | − | 1.28163i | −0.767695 | − | 0.640815i | \(-0.778596\pi\) | ||
0.767695 | − | 0.640815i | \(-0.221404\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.359955 | −0.0153625 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.2859 | −0.821608 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 41.3274i | 1.75742i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.62222 | − | 0.930409i | 0.281097 | − | 0.0394937i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.03657i | 0.213406i | 0.994291 | + | 0.106703i | \(0.0340294\pi\) | ||||
−0.994291 | + | 0.106703i | \(0.965971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.36196 | −0.269082 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.80642 | 0.0762673 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 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 | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.2079i | 0.428690i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.37286 | 0.183320 | 0.0916600 | − | 0.995790i | \(-0.470783\pi\) | ||||
0.0916600 | + | 0.995790i | \(0.470783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.58120 | 0.0661714 | 0.0330857 | − | 0.999453i | \(-0.489467\pi\) | ||||
0.0330857 | + | 0.999453i | \(0.489467\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.75557i | 0.115116i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 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 | \(0.949316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.7275 | 0.736728 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.6543 | 1.14730 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.33630i | − | 0.0553438i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.398528 | − | 2.83654i | −0.0164771 | − | 0.117276i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.62222 | −0.107864 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.9398i | − | 0.654568i | −0.944926 | − | 0.327284i | \(-0.893867\pi\) | ||
0.944926 | − | 0.327284i | \(-0.106133\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −41.3274 | + | 5.80642i | −1.69426 | + | 0.238040i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.0321i | 1.18821i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 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 | \(0.360865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.94116i | 0.404835i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.2558 | − | 3.40790i | 0.986139 | − | 0.138551i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0765i | 1.46430i | 0.681143 | + | 0.732150i | \(0.261483\pi\) | ||||
−0.681143 | + | 0.732150i | \(0.738517\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.1526 | −1.34341 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.09679 | 0.0443713 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.94962i | 0.401861i | 0.979605 | + | 0.200931i | \(0.0643966\pi\) | ||||
−0.979605 | + | 0.200931i | \(0.935603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.24443 | − | 8.85728i | −0.0501803 | − | 0.357160i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.09187i | − | 0.0842154i | −0.999113 | − | 0.0421077i | \(-0.986593\pi\) | ||
0.999113 | − | 0.0421077i | \(-0.0134073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4681 | 0.742296 | 0.371148 | − | 0.928574i | \(-0.378964\pi\) | ||||
0.371148 | + | 0.928574i | \(0.378964\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.3180 | −1.05611 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 16.2953i | − | 0.652857i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | − | 13.2444i | 0.848137 | − | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.622216i | − | 0.0248489i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.6637 | −0.584680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.6657 | 1.53926 | 0.769629 | − | 0.638492i | \(-0.220441\pi\) | ||||
0.769629 | + | 0.638492i | \(0.220441\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 25.7690i | − | 1.02422i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.716089 | + | 5.09679i | 0.0284171 | + | 0.202260i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.42864i | − | 0.0566048i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.78970 | 0.308156 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.5718 | 0.970529 | 0.485265 | − | 0.874367i | \(-0.338723\pi\) | ||||
0.485265 | + | 0.874367i | \(0.338723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.4938i | − | 1.08425i | −0.840298 | − | 0.542125i | \(-0.817620\pi\) | ||
0.840298 | − | 0.542125i | \(-0.182380\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.4701 | − | 2.59502i | 0.727261 | − | 0.102179i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.2859 | 0.834261 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.12045i | − | 0.0829795i | −0.999139 | − | 0.0414897i | \(-0.986790\pi\) | ||
0.999139 | − | 0.0414897i | \(-0.0132104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.7146 | + | 4.17484i | −1.16104 | + | 0.163125i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.1699i | 0.513807i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(0.758966\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 8.42864i | − | 0.327341i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | + | 14.2351i | 0.0775567 | + | 0.552012i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 40.8385i | − | 1.58127i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.7877 | 0.997010 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0602231 | 0.00232489 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 35.4608i | − | 1.36691i | −0.729992 | − | 0.683456i | \(-0.760476\pi\) | ||
0.729992 | − | 0.683456i | \(-0.239524\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.73329 | + | 26.9777i | 0.297655 | + | 1.03837i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 15.3047i | − | 0.588206i | −0.955774 | − | 0.294103i | \(-0.904979\pi\) | ||
0.955774 | − | 0.294103i | \(-0.0950208\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52.3783 | −2.01009 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4005 | 0.666790 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 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 | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.18421i | 0.121485i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.23506 | −0.237537 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.4079 | 0.700269 | 0.350135 | − | 0.936699i | \(-0.386136\pi\) | ||||
0.350135 | + | 0.936699i | \(0.386136\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.797056i | 0.0302777i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42.2766 | + | 5.93978i | −1.60364 | + | 0.225309i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.6128i | 0.742890i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.2070 | −0.802121 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.3689 | −1.18479 | −0.592393 | − | 0.805649i | \(-0.701817\pi\) | ||||
−0.592393 | + | 0.805649i | \(0.701817\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.05086i | 0.190497i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.18421 | + | 0.447375i | −0.119924 | + | 0.0168491i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 11.4380i | − | 0.430171i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.47949 | −0.356010 | −0.178005 | − | 0.984030i | \(-0.556964\pi\) | ||||
−0.178005 | + | 0.984030i | \(0.556964\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.2351 | −0.683868 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.2208i | 0.981976i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0666765 | + | 0.474572i | 0.00249356 | + | 0.0177480i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 16.7511i | − | 0.625582i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7.73329i | − | 0.287604i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −41.8622 | + | 12.0000i | −1.55472 | + | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.6702i | 1.58255i | 0.611461 | + | 0.791274i | \(0.290582\pi\) | ||||
−0.611461 | + | 0.791274i | \(0.709418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5812 | −0.984489 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.8988 | −1.51270 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0830i | 0.963397i | 0.876337 | + | 0.481698i | \(0.159980\pi\) | ||||
−0.876337 | + | 0.481698i | \(0.840020\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.582736 | + | 4.14764i | 0.0214945 | + | 0.152988i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.66323i | − | 0.0612657i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.2687 | −1.03988 | −0.519941 | − | 0.854202i | \(-0.674046\pi\) | ||||
−0.519941 | + | 0.854202i | \(0.674046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.90321 | −0.106652 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 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 | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2020i | 0.446449i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.6958 | −1.81585 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.46028 | −0.0897770 | −0.0448885 | − | 0.998992i | \(-0.514293\pi\) | ||||
−0.0448885 | + | 0.998992i | \(0.514293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.71810i | 0.0990530i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −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 | \(0.655342\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.31756 | 0.0478244 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.8252 | −0.501162 | −0.250581 | − | 0.968096i | \(-0.580622\pi\) | ||||
−0.250581 | + | 0.968096i | \(0.580622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 48.5531i | − | 1.75774i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.56199 | − | 18.2351i | −0.0926290 | − | 0.659290i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.26517i | − | 0.334546i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.9688 | 1.40525 | 0.702626 | − | 0.711559i | \(-0.252011\pi\) | ||||
0.702626 | + | 0.711559i | \(0.252011\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1204 | 0.868677 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 0.445992i | − | 0.0160412i | −0.999968 | − | 0.00802061i | \(-0.997447\pi\) | ||
0.999968 | − | 0.00802061i | \(-0.00255307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.8780 | − | 7.70471i | 0.965487 | − | 0.276761i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.68244i | 0.311481i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.75557 | 0.242043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30327 | −0.0466347 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 48.8859i | − | 1.74704i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.74620 | + | 12.4286i | 0.0623246 | + | 0.443597i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33.9037i | − | 1.20854i | −0.796781 | − | 0.604268i | \(-0.793466\pi\) | ||
0.796781 | − | 0.604268i | \(-0.206534\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.4558 | 0.514641 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.43801 | −0.122241 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.280996i | − | 0.00997847i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.1017 | − | 2.54326i | 0.642002 | − | 0.0902000i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 10.2953i | − | 0.364678i | −0.983236 | − | 0.182339i | \(-0.941633\pi\) | ||
0.983236 | − | 0.182339i | \(-0.0583668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.05086 | 0.249441 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.19004 | 0.254047 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.20342i | − | 0.0777570i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.1432 | + | 4.23506i | −1.06241 | + | 0.149266i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.1655i | 0.745060i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.94422 | −0.279304 | −0.139652 | − | 0.990201i | \(-0.544598\pi\) | ||||
−0.139652 | + | 0.990201i | \(0.544598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.12245 | 0.285218 | 0.142609 | − | 0.989779i | \(-0.454451\pi\) | ||||
0.142609 | + | 0.989779i | \(0.454451\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 17.0593i | − | 0.598296i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.15701 | − | 8.23506i | −0.0405283 | − | 0.288462i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0874i | 0.492856i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.71900 | 0.129953 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.2065 | −0.775012 | −0.387506 | − | 0.921867i | \(-0.626663\pi\) | ||||
−0.387506 | + | 0.921867i | \(0.626663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.1175i | 0.387533i | 0.981048 | + | 0.193766i | \(0.0620704\pi\) | ||||
−0.981048 | + | 0.193766i | \(0.937930\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.387152 | − | 1.35059i | −0.0134789 | − | 0.0470214i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 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 | \(0.343911\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.92687 | 0.344359 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 9.18421i | − | 0.318214i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.18913 | − | 15.5812i | −0.0757580 | − | 0.539210i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.3876i | 1.08492i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.85728i | 0.305061i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.21432 | − | 0.311108i | 0.0761749 | − | 0.0107024i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.8020i | 1.09273i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.0237 | 0.858810 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −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 | 0 | ||||||||
\(855\) | −6.28100 | + | 0.882468i | −0.214806 | + | 0.0301798i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.61285i | 0.260050i | 0.991511 | + | 0.130025i | \(0.0415057\pi\) | ||||
−0.991511 | + | 0.130025i | \(0.958494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.1432 | 1.43791 | 0.718954 | − | 0.695058i | \(-0.244621\pi\) | ||||
0.718954 | + | 0.695058i | \(0.244621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6128 | 0.395765 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 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 | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 31.8959i | − | 1.08324i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.05086 | 0.103493 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.76049 | −0.262954 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 23.1111i | − | 0.782191i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 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 | \(-0.195088\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.6035 | 0.357646 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.71900 | 0.125296 | 0.0626482 | − | 0.998036i | \(-0.480045\pi\) | ||||
0.0626482 | + | 0.998036i | \(0.480045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 42.0163i | − | 1.41396i | −0.707233 | − | 0.706981i | \(-0.750057\pi\) | ||
0.707233 | − | 0.706981i | \(-0.249943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.77923 | + | 26.8988i | 0.127037 | + | 0.904192i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 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 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.753561 | 0.0252452 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.42864i | − | 0.0812713i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.94914 | − | 1.25734i | 0.299137 | − | 0.0420282i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.14764i | − | 0.205264i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.7052 | −1.62441 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.0830 | −1.33536 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.2163i | 0.805869i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.18421 | + | 0.728372i | −0.172329 | + | 0.0242119i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 34.8419i | − | 1.15691i | −0.815715 | − | 0.578454i | \(-0.803656\pi\) | ||
0.815715 | − | 0.578454i | \(-0.196344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.04684 | 0.167393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.114617 | + | 0.815792i | 0.00378913 | + | 0.0269692i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 38.9590i | − | 1.28654i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.22570 | −0.106406 | −0.0532029 | − | 0.998584i | \(-0.516943\pi\) | ||||
−0.0532029 | + | 0.998584i | \(0.516943\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.6128 | 0.580363 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.08097i | 0.200157i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.14272 | + | 10.9634i | 0.103332 | + | 0.360476i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.61529i | 0.118742i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.3461 | 1.29091 | 0.645453 | − | 0.763800i | \(-0.276669\pi\) | ||||
0.645453 | + | 0.763800i | \(0.276669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.16346 | −0.103678 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 26.4889i | − | 0.867206i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 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 | \(-0.319162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.8123 | −0.646548 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.5081 | 1.22273 | 0.611364 | − | 0.791349i | \(-0.290621\pi\) | ||||
0.611364 | + | 0.791349i | \(0.290621\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.3051i | 0.465839i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −36.0830 | + | 5.06959i | −1.17378 | + | 0.164914i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.2128 | 0.947290 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 28.7368i | − | 0.930877i | −0.885080 | − | 0.465439i | \(-0.845897\pi\) | ||
0.885080 | − | 0.465439i | \(-0.154103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.65386 | + | 0.653858i | −0.150595 | + | 0.0211584i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.44738i | 0.0791124i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 55.6040 | 1.79555 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.271628 | 0.00876221 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 21.9275i | − | 0.706604i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.20648 | + | 29.9398i | 0.135411 | + | 0.963796i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.0593i | 0.934485i | 0.884129 | + | 0.467242i | \(0.154752\pi\) | ||||
−0.884129 | + | 0.467242i | \(0.845248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.6637 | −0.599565 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.30174 | + | 1.80642i | −0.201817 | + | 0.0578519i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.8617i | 0.411483i | 0.978606 | + | 0.205742i | \(0.0659606\pi\) | ||||
−0.978606 | + | 0.205742i | \(0.934039\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.20294 | −0.0384463 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.4233 | 0.683993 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 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 | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.17484i | − | 0.132887i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.8306 | −0.948557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.07007 | −0.256354 | −0.128177 | − | 0.991751i | \(-0.540913\pi\) | ||||
−0.128177 | + | 0.991751i | \(0.540913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 10.8243i | − | 0.343497i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −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 | \(0.826065\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.8029 | −0.405065 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))