Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(1549,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.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: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.214798336.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.8 | ||
Root | \(-0.565036 + 1.29643i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1549 |
Dual form | 1800.2.d.s.1549.7 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.796431 | + | 1.16863i | 0.563162 | + | 0.826347i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.731395 | + | 1.86147i | −0.365697 | + | 0.930734i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.72294i | 1.78510i | 0.450947 | + | 0.892551i | \(0.351086\pi\) | ||||
−0.450947 | + | 0.892551i | \(0.648914\pi\) | |||||||
\(8\) | −2.75787 | + | 0.627801i | −0.975056 | + | 0.221961i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.93012i | 1.18498i | 0.805579 | + | 0.592488i | \(0.201854\pi\) | ||||
−0.805579 | + | 0.592488i | \(0.798146\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46733 | −0.961665 | −0.480833 | − | 0.876812i | \(-0.659666\pi\) | ||||
−0.480833 | + | 0.876812i | \(0.659666\pi\) | |||||||
\(14\) | −5.51937 | + | 3.76149i | −1.47511 | + | 1.00530i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.93012 | − | 2.72294i | −0.732531 | − | 0.680734i | ||||
\(17\) | − | 3.51575i | − | 0.852694i | −0.904560 | − | 0.426347i | \(-0.859800\pi\) | ||
0.904560 | − | 0.426347i | \(-0.140200\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.44133i | 1.24833i | 0.781294 | + | 0.624163i | \(0.214560\pi\) | ||||
−0.781294 | + | 0.624163i | \(0.785440\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.59286 | + | 3.13007i | −0.979202 | + | 0.667334i | ||||
\(23\) | − | 7.11585i | − | 1.48376i | −0.670534 | − | 0.741878i | \(-0.733935\pi\) | ||
0.670534 | − | 0.741878i | \(-0.266065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.76149 | − | 4.05203i | −0.541573 | − | 0.794669i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.79159 | − | 3.45433i | −1.66145 | − | 0.652807i | ||||
\(29\) | − | 3.66998i | − | 0.681498i | −0.940154 | − | 0.340749i | \(-0.889319\pi\) | ||
0.940154 | − | 0.340749i | \(-0.110681\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.23414 | 0.940079 | 0.470039 | − | 0.882645i | \(-0.344240\pi\) | ||||
0.470039 | + | 0.882645i | \(0.344240\pi\) | |||||||
\(32\) | 0.848464 | − | 5.59286i | 0.149989 | − | 0.988688i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.10861 | − | 2.80005i | 0.704621 | − | 0.480205i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.414376 | 0.0681231 | 0.0340615 | − | 0.999420i | \(-0.489156\pi\) | ||||
0.0340615 | + | 0.999420i | \(0.489156\pi\) | |||||||
\(38\) | −6.35890 | + | 4.33364i | −1.03155 | + | 0.703010i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00454 | −0.469231 | −0.234616 | − | 0.972088i | \(-0.575383\pi\) | ||||
−0.234616 | + | 0.972088i | \(0.575383\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.34450 | 0.815029 | 0.407514 | − | 0.913199i | \(-0.366396\pi\) | ||||
0.407514 | + | 0.913199i | \(0.366396\pi\) | |||||||
\(44\) | −7.31580 | − | 2.87447i | −1.10290 | − | 0.433343i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.31580 | − | 5.66728i | 1.22610 | − | 0.835595i | ||||
\(47\) | 0.925579i | 0.135010i | 0.997719 | + | 0.0675048i | \(0.0215038\pi\) | ||||
−0.997719 | + | 0.0675048i | \(0.978496\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.3061 | −2.18659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.53599 | − | 6.45433i | 0.351679 | − | 0.895055i | ||||
\(53\) | 0.233196 | 0.0320320 | 0.0160160 | − | 0.999872i | \(-0.494902\pi\) | ||||
0.0160160 | + | 0.999872i | \(0.494902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.96506 | − | 13.0253i | −0.396223 | − | 1.74057i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.28885 | − | 2.92288i | 0.563153 | − | 0.383794i | ||||
\(59\) | 14.3805i | 1.87219i | 0.351752 | + | 0.936093i | \(0.385586\pi\) | ||||
−0.351752 | + | 0.936093i | \(0.614414\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.118290i | − | 0.0151454i | −0.999971 | − | 0.00757271i | \(-0.997590\pi\) | ||
0.999971 | − | 0.00757271i | \(-0.00241049\pi\) | |||||||
\(62\) | 4.16863 | + | 6.11677i | 0.529417 | + | 0.776831i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.21173 | − | 3.46279i | 0.901467 | − | 0.432849i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.4504 | −1.64323 | −0.821615 | − | 0.570043i | \(-0.806927\pi\) | ||||
−0.821615 | + | 0.570043i | \(0.806927\pi\) | |||||||
\(68\) | 6.54445 | + | 2.57140i | 0.793631 | + | 0.311828i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.19027 | −0.259937 | −0.129969 | − | 0.991518i | \(-0.541488\pi\) | ||||
−0.129969 | + | 0.991518i | \(0.541488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.563219i | 0.0659197i | 0.999457 | + | 0.0329599i | \(0.0104934\pi\) | ||||
−0.999457 | + | 0.0329599i | \(0.989507\pi\) | |||||||
\(74\) | 0.330022 | + | 0.484253i | 0.0383643 | + | 0.0562933i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.1289 | − | 3.97976i | −1.16186 | − | 0.456509i | ||||
\(77\) | −18.5617 | −2.11530 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2746 | 1.15599 | 0.577993 | − | 0.816042i | \(-0.303836\pi\) | ||||
0.577993 | + | 0.816042i | \(0.303836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.39291 | − | 3.51120i | −0.264253 | − | 0.387747i | ||||
\(83\) | −11.3490 | −1.24572 | −0.622860 | − | 0.782334i | \(-0.714029\pi\) | ||||
−0.622860 | + | 0.782334i | \(0.714029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.25653 | + | 6.24575i | 0.458993 | + | 0.673496i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.46733 | − | 10.8388i | −0.263019 | − | 1.15542i | ||||
\(89\) | 8.88265 | 0.941559 | 0.470780 | − | 0.882251i | \(-0.343973\pi\) | ||||
0.470780 | + | 0.882251i | \(0.343973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 16.3760i | − | 1.71667i | ||||||
\(92\) | 13.2459 | + | 5.20449i | 1.38098 | + | 0.542606i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.08166 | + | 0.737160i | −0.111565 | + | 0.0760322i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.27462i | 0.738626i | 0.929305 | + | 0.369313i | \(0.120407\pi\) | ||||
−0.929305 | + | 0.369313i | \(0.879593\pi\) | |||||||
\(98\) | −12.1903 | − | 17.8872i | −1.23140 | − | 1.80688i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.23320i | − | 0.421219i | −0.977570 | − | 0.210609i | \(-0.932455\pi\) | ||
0.977570 | − | 0.210609i | \(-0.0675448\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.0429270i | − | 0.00422972i | −0.999998 | − | 0.00211486i | \(-0.999327\pi\) | ||
0.999998 | − | 0.00211486i | \(-0.000673181\pi\) | |||||||
\(104\) | 9.56247 | − | 2.17679i | 0.937677 | − | 0.213452i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.185725 | + | 0.272520i | 0.0180392 | + | 0.0264695i | ||||
\(107\) | −15.4728 | −1.49581 | −0.747907 | − | 0.663804i | \(-0.768941\pi\) | ||||
−0.747907 | + | 0.663804i | \(0.768941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9561i | 1.24097i | 0.784217 | + | 0.620486i | \(0.213065\pi\) | ||||
−0.784217 | + | 0.620486i | \(0.786935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.8602 | − | 13.8388i | 1.21518 | − | 1.30764i | ||||
\(113\) | 3.86025i | 0.363141i | 0.983378 | + | 0.181571i | \(0.0581181\pi\) | ||||
−0.983378 | + | 0.181571i | \(0.941882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.83154 | + | 2.68420i | 0.634293 | + | 0.249222i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.8055 | + | 11.4531i | −1.54708 | + | 1.05434i | ||||
\(119\) | 16.6046 | 1.52215 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.44587 | −0.404170 | ||||||||
\(122\) | 0.138237 | − | 0.0942095i | 0.0125154 | − | 0.00852933i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.82822 | + | 9.74318i | −0.343784 | + | 0.874963i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.3805i | − | 1.63101i | −0.578751 | − | 0.815505i | \(-0.696460\pi\) | ||
0.578751 | − | 0.815505i | \(-0.303540\pi\) | |||||||
\(128\) | 9.79037 | + | 5.66998i | 0.865355 | + | 0.501160i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.41892i | 0.298713i | 0.988783 | + | 0.149356i | \(0.0477201\pi\) | ||||
−0.988783 | + | 0.149356i | \(0.952280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.6990 | −2.22839 | ||||||||
\(134\) | −10.7123 | − | 15.7186i | −0.925404 | − | 1.35788i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.20719 | + | 9.69599i | 0.189265 | + | 0.831424i | ||||
\(137\) | 16.3714i | 1.39871i | 0.714776 | + | 0.699354i | \(0.246529\pi\) | ||||
−0.714776 | + | 0.699354i | \(0.753471\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.95707i | 0.165997i | 0.996550 | + | 0.0829984i | \(0.0264496\pi\) | ||||
−0.996550 | + | 0.0829984i | \(0.973550\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.74440 | − | 2.55962i | −0.146387 | − | 0.214798i | ||||
\(143\) | − | 13.6271i | − | 1.13955i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.658194 | + | 0.448565i | −0.0544726 | + | 0.0371235i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.303073 | + | 0.771348i | −0.0249124 | + | 0.0634044i | ||||
\(149\) | 12.0968i | 0.991011i | 0.868605 | + | 0.495505i | \(0.165017\pi\) | ||||
−0.868605 | + | 0.495505i | \(0.834983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.87178 | −0.396460 | −0.198230 | − | 0.980156i | \(-0.563519\pi\) | ||||
−0.198230 | + | 0.980156i | \(0.563519\pi\) | |||||||
\(152\) | −3.41607 | − | 15.0065i | −0.277080 | − | 1.21719i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.7831 | − | 21.6918i | −1.19126 | − | 1.74797i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.6561 | −1.72835 | −0.864173 | − | 0.503195i | \(-0.832158\pi\) | ||||
−0.864173 | + | 0.503195i | \(0.832158\pi\) | |||||||
\(158\) | 8.18303 | + | 12.0072i | 0.651007 | + | 0.955245i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 33.6077 | 2.64866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2362 | 1.27172 | 0.635860 | − | 0.771804i | \(-0.280645\pi\) | ||||
0.635860 | + | 0.771804i | \(0.280645\pi\) | |||||||
\(164\) | 2.19751 | − | 5.59286i | 0.171597 | − | 0.436729i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.03873 | − | 13.2628i | −0.701542 | − | 1.02940i | ||||
\(167\) | 6.69238i | 0.517872i | 0.965894 | + | 0.258936i | \(0.0833719\pi\) | ||||
−0.965894 | + | 0.258936i | \(0.916628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.977595 | −0.0751996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.90894 | + | 9.94861i | −0.298054 | + | 0.758575i | ||||
\(173\) | 22.4220 | 1.70471 | 0.852355 | − | 0.522963i | \(-0.175173\pi\) | ||||
0.852355 | + | 0.522963i | \(0.175173\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.7015 | − | 11.5157i | 0.806654 | − | 0.868032i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.07442 | + | 10.3805i | 0.530250 | + | 0.778054i | ||||
\(179\) | − | 0.148842i | − | 0.0111250i | −0.999985 | − | 0.00556249i | \(-0.998229\pi\) | ||
0.999985 | − | 0.00556249i | \(-0.00177060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3929i | 0.772499i | 0.922394 | + | 0.386250i | \(0.126230\pi\) | ||||
−0.922394 | + | 0.386250i | \(0.873770\pi\) | |||||||
\(182\) | 19.1375 | − | 13.0424i | 1.41856 | − | 0.966763i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.46733 | + | 19.6246i | 0.329336 | + | 1.44675i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8173 | 1.01042 | ||||||||
\(188\) | −1.72294 | − | 0.676964i | −0.125658 | − | 0.0493726i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.23320 | −0.451018 | −0.225509 | − | 0.974241i | \(-0.572405\pi\) | ||||
−0.225509 | + | 0.974241i | \(0.572405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.391971i | 0.0282147i | 0.999900 | + | 0.0141074i | \(0.00449066\pi\) | ||||
−0.999900 | + | 0.0141074i | \(0.995509\pi\) | |||||||
\(194\) | −8.50135 | + | 5.79374i | −0.610361 | + | 0.415966i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.1948 | − | 28.4918i | 0.799630 | − | 2.03513i | ||||
\(197\) | −5.96616 | −0.425071 | −0.212536 | − | 0.977153i | \(-0.568172\pi\) | ||||
−0.212536 | + | 0.977153i | \(0.568172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.9322 | 1.27118 | 0.635591 | − | 0.772026i | \(-0.280757\pi\) | ||||
0.635591 | + | 0.772026i | \(0.280757\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.94704 | − | 3.37145i | 0.348073 | − | 0.237214i | ||||
\(203\) | 17.3331 | 1.21654 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.0501658 | − | 0.0341884i | 0.00349521 | − | 0.00238202i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.1597 | + | 9.44133i | 0.704450 | + | 0.654638i | ||||
\(209\) | −21.3851 | −1.47924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.51575i | 0.448563i | 0.974524 | + | 0.224281i | \(0.0720034\pi\) | ||||
−0.974524 | + | 0.224281i | \(0.927997\pi\) | |||||||
\(212\) | −0.170558 | + | 0.434087i | −0.0117140 | + | 0.0298132i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.3230 | − | 18.0820i | −0.842385 | − | 1.23606i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.7205i | 1.67814i | ||||||||
\(218\) | −15.1409 | + | 10.3187i | −1.02547 | + | 0.698868i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.1903i | 0.820006i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.14640i | − | 0.210699i | −0.994435 | − | 0.105349i | \(-0.966404\pi\) | ||
0.994435 | − | 0.105349i | \(-0.0335961\pi\) | |||||||
\(224\) | 26.4147 | + | 4.00724i | 1.76491 | + | 0.267745i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.51120 | + | 3.07442i | −0.300081 | + | 0.204507i | ||||
\(227\) | 3.92103 | 0.260248 | 0.130124 | − | 0.991498i | \(-0.458462\pi\) | ||||
0.130124 | + | 0.991498i | \(0.458462\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.6899i | − | 1.69764i | −0.528683 | − | 0.848820i | \(-0.677314\pi\) | ||
0.528683 | − | 0.848820i | \(-0.322686\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.30401 | + | 10.1213i | 0.151266 | + | 0.664498i | ||||
\(233\) | 25.7565i | 1.68737i | 0.536841 | + | 0.843683i | \(0.319617\pi\) | ||||
−0.536841 | + | 0.843683i | \(0.680383\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −26.7689 | − | 10.5179i | −1.74251 | − | 0.684654i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.2245 | + | 19.4047i | 0.857214 | + | 1.25782i | ||||
\(239\) | −15.8727 | −1.02672 | −0.513360 | − | 0.858173i | \(-0.671600\pi\) | ||||
−0.513360 | + | 0.858173i | \(0.671600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1664 | 1.81436 | 0.907178 | − | 0.420748i | \(-0.138232\pi\) | ||||
0.907178 | + | 0.420748i | \(0.138232\pi\) | |||||||
\(242\) | −3.54083 | − | 5.19558i | −0.227613 | − | 0.333985i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.220192 | + | 0.0865164i | 0.0140964 | + | 0.00553864i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.8669i | − | 1.20047i | ||||||
\(248\) | −14.4351 | + | 3.28600i | −0.916629 | + | 0.208661i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.66004i | 0.294139i | 0.989126 | + | 0.147070i | \(0.0469842\pi\) | ||||
−0.989126 | + | 0.147070i | \(0.953016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.9662 | 1.75822 | ||||||||
\(254\) | 21.4801 | − | 14.6388i | 1.34778 | − | 0.918522i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.17125 | + | 15.9571i | 0.0732029 | + | 0.997317i | ||||
\(257\) | 3.33996i | 0.208341i | 0.994559 | + | 0.104170i | \(0.0332187\pi\) | ||||
−0.994559 | + | 0.104170i | \(0.966781\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.95707i | 0.121607i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.99546 | + | 2.72294i | −0.246840 | + | 0.168224i | ||||
\(263\) | 27.5932i | 1.70147i | 0.525595 | + | 0.850735i | \(0.323843\pi\) | ||||
−0.525595 | + | 0.850735i | \(0.676157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −20.4675 | − | 30.0327i | −1.25494 | − | 1.84142i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.83756 | − | 25.0375i | 0.600925 | − | 1.52941i | ||||
\(269\) | − | 21.8727i | − | 1.33360i | −0.745235 | − | 0.666802i | \(-0.767663\pi\) | ||
0.745235 | − | 0.666802i | \(-0.232337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.78583 | −0.533701 | −0.266850 | − | 0.963738i | \(-0.585983\pi\) | ||||
−0.266850 | + | 0.963738i | \(0.585983\pi\) | |||||||
\(272\) | −9.57315 | + | 10.3016i | −0.580458 | + | 0.624625i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.1322 | + | 13.0387i | −1.15582 | + | 0.787699i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3838 | −0.623904 | −0.311952 | − | 0.950098i | \(-0.600983\pi\) | ||||
−0.311952 | + | 0.950098i | \(0.600983\pi\) | |||||||
\(278\) | −2.28710 | + | 1.55867i | −0.137171 | + | 0.0934831i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.0584 | −1.01762 | −0.508811 | − | 0.860878i | \(-0.669915\pi\) | ||||
−0.508811 | + | 0.860878i | \(0.669915\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.54724 | 0.210862 | 0.105431 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105431 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(284\) | 1.60195 | − | 4.07712i | 0.0950583 | − | 0.241932i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.9250 | − | 10.8530i | 0.941664 | − | 0.641752i | ||||
\(287\) | − | 14.1903i | − | 0.837625i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.63952 | 0.272913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.04841 | − | 0.411935i | −0.0613537 | − | 0.0241067i | ||||
\(293\) | 5.72538 | 0.334480 | 0.167240 | − | 0.985916i | \(-0.446515\pi\) | ||||
0.167240 | + | 0.985916i | \(0.446515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.14280 | + | 0.260146i | −0.0664238 | + | 0.0151207i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.1367 | + | 9.63429i | −0.818918 | + | 0.558099i | ||||
\(299\) | 24.6730i | 1.42688i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.2417i | 1.45491i | ||||||||
\(302\) | −3.88004 | − | 5.69331i | −0.223271 | − | 0.327613i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.8164 | − | 15.9438i | 0.849778 | − | 0.914437i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3760 | 0.706335 | 0.353168 | − | 0.935560i | \(-0.385105\pi\) | ||||
0.353168 | + | 0.935560i | \(0.385105\pi\) | |||||||
\(308\) | 13.5759 | − | 34.5520i | 0.773561 | − | 1.96879i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.2746 | 1.03626 | 0.518129 | − | 0.855302i | \(-0.326629\pi\) | ||||
0.518129 | + | 0.855302i | \(0.326629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7114i | 0.718491i | 0.933243 | + | 0.359246i | \(0.116966\pi\) | ||||
−0.933243 | + | 0.359246i | \(0.883034\pi\) | |||||||
\(314\) | −17.2476 | − | 25.3080i | −0.973338 | − | 1.42821i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.51481 | + | 19.1259i | −0.422741 | + | 1.07591i | ||||
\(317\) | −15.8602 | −0.890800 | −0.445400 | − | 0.895332i | \(-0.646939\pi\) | ||||
−0.445400 | + | 0.895332i | \(0.646939\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.4235 | 0.807559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 26.7662 | + | 39.2750i | 1.49162 | + | 2.18871i | ||||
\(323\) | 19.1303 | 1.06444 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.9310 | + | 18.9742i | 0.716185 | + | 1.05088i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.28615 | − | 1.88625i | 0.457526 | − | 0.104151i | ||||
\(329\) | −4.37145 | −0.241006 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.0315i | 1.26593i | 0.774182 | + | 0.632963i | \(0.218161\pi\) | ||||
−0.774182 | + | 0.632963i | \(0.781839\pi\) | |||||||
\(332\) | 8.30063 | − | 21.1259i | 0.455556 | − | 1.15943i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.82092 | + | 5.33002i | −0.427942 | + | 0.291646i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.860247i | − | 0.0468606i | −0.999725 | − | 0.0234303i | \(-0.992541\pi\) | ||
0.999725 | − | 0.0234303i | \(-0.00745878\pi\) | |||||||
\(338\) | −0.778587 | − | 1.14245i | −0.0423496 | − | 0.0621409i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.5708i | 1.11397i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 39.2293i | − | 2.11818i | ||||||
\(344\) | −14.7395 | + | 3.35528i | −0.794698 | + | 0.180905i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.8576 | + | 26.2030i | 0.960028 | + | 1.40868i | ||||
\(347\) | 32.2856 | 1.73318 | 0.866591 | − | 0.499019i | \(-0.166306\pi\) | ||||
0.866591 | + | 0.499019i | \(0.166306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.742899i | − | 0.0397665i | −0.999802 | − | 0.0198832i | \(-0.993671\pi\) | ||
0.999802 | − | 0.0198832i | \(-0.00632945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.9806 | + | 3.33457i | 1.17157 | + | 0.177733i | ||||
\(353\) | − | 32.6392i | − | 1.73721i | −0.495506 | − | 0.868604i | \(-0.665018\pi\) | ||
0.495506 | − | 0.868604i | \(-0.334982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.49672 | + | 16.5348i | −0.344326 | + | 0.876341i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.173941 | − | 0.118542i | 0.00919309 | − | 0.00626517i | ||||
\(359\) | −2.71056 | −0.143058 | −0.0715290 | − | 0.997439i | \(-0.522788\pi\) | ||||
−0.0715290 | + | 0.997439i | \(0.522788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.6080 | −0.558317 | ||||||||
\(362\) | −12.1455 | + | 8.27724i | −0.638352 | + | 0.435042i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 30.4834 | + | 11.9773i | 1.59776 | + | 0.627782i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.680008i | 0.0354961i | 0.999842 | + | 0.0177481i | \(0.00564968\pi\) | ||||
−0.999842 | + | 0.0177481i | \(0.994350\pi\) | |||||||
\(368\) | −19.3760 | + | 20.8503i | −1.01004 | + | 1.08690i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.10137i | 0.0571803i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.47642 | 0.180002 | 0.0900012 | − | 0.995942i | \(-0.471313\pi\) | ||||
0.0900012 | + | 0.995942i | \(0.471313\pi\) | |||||||
\(374\) | 11.0045 | + | 16.1473i | 0.569031 | + | 0.834959i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.581079 | − | 2.55263i | −0.0299669 | − | 0.131642i | ||||
\(377\) | 12.7250i | 0.655373i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0650i | 1.18477i | 0.805655 | + | 0.592385i | \(0.201813\pi\) | ||||
−0.805655 | + | 0.592385i | \(0.798187\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.96431 | − | 7.28430i | −0.253996 | − | 0.372697i | ||||
\(383\) | − | 9.81544i | − | 0.501545i | −0.968046 | − | 0.250773i | \(-0.919315\pi\) | ||
0.968046 | − | 0.250773i | \(-0.0806847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.458070 | + | 0.312178i | −0.0233151 | + | 0.0158895i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.5415 | − | 5.32062i | −0.687464 | − | 0.270114i | ||||
\(389\) | 9.86175i | 0.500010i | 0.968244 | + | 0.250005i | \(0.0804323\pi\) | ||||
−0.968244 | + | 0.250005i | \(0.919568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.0175 | −1.26519 | ||||||||
\(392\) | 42.2123 | − | 9.60919i | 2.13204 | − | 0.485337i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.75164 | − | 6.97224i | −0.239384 | − | 0.351256i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7783 | 0.641326 | 0.320663 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320663 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(398\) | 14.2818 | + | 20.9561i | 0.715881 | + | 1.05044i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.17325 | −0.158465 | −0.0792323 | − | 0.996856i | \(-0.525247\pi\) | ||||
−0.0792323 | + | 0.996856i | \(0.525247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.1485 | −0.904041 | ||||||||
\(404\) | 7.87996 | + | 3.09614i | 0.392043 | + | 0.154039i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.8046 | + | 20.2560i | 0.685111 | + | 1.00529i | ||||
\(407\) | 1.62855i | 0.0807243i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.1125 | −0.598923 | −0.299461 | − | 0.954108i | \(-0.596807\pi\) | ||||
−0.299461 | + | 0.954108i | \(0.596807\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.0799071 | + | 0.0313965i | 0.00393674 | + | 0.00154680i | ||||
\(413\) | −67.9184 | −3.34204 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.94191 | + | 19.3923i | −0.144239 | + | 0.950787i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.0317 | − | 24.9913i | −0.833050 | − | 1.22236i | ||||
\(419\) | − | 4.24767i | − | 0.207512i | −0.994603 | − | 0.103756i | \(-0.966914\pi\) | ||
0.994603 | − | 0.103756i | \(-0.0330862\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.77928i | 0.184191i | 0.995750 | + | 0.0920953i | \(0.0293564\pi\) | ||||
−0.995750 | + | 0.0920953i | \(0.970644\pi\) | |||||||
\(422\) | −7.61450 | + | 5.18934i | −0.370668 | + | 0.252613i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.643126 | + | 0.146401i | −0.0312329 | + | 0.00710985i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.558674 | 0.0270361 | ||||||||
\(428\) | 11.3167 | − | 28.8022i | 0.547015 | − | 1.39220i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6271 | −1.23441 | −0.617206 | − | 0.786802i | \(-0.711735\pi\) | ||||
−0.617206 | + | 0.786802i | \(0.711735\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.03149i | 0.0976274i | 0.998808 | + | 0.0488137i | \(0.0155441\pi\) | ||||
−0.998808 | + | 0.0488137i | \(0.984456\pi\) | |||||||
\(434\) | −28.8891 | + | 19.6882i | −1.38672 | + | 0.945063i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.1174 | − | 9.47605i | −1.15501 | − | 0.453820i | ||||
\(437\) | 38.7196 | 1.85221 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.4864 | 1.07322 | 0.536608 | − | 0.843832i | \(-0.319706\pi\) | ||||
0.536608 | + | 0.843832i | \(0.319706\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.2459 | + | 9.70871i | −0.677609 | + | 0.461796i | ||||
\(443\) | −3.39385 | −0.161247 | −0.0806234 | − | 0.996745i | \(-0.525691\pi\) | ||||
−0.0806234 | + | 0.996745i | \(0.525691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.67698 | − | 2.50589i | 0.174110 | − | 0.118657i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.3545 | + | 34.0605i | 0.772679 | + | 1.60921i | ||||
\(449\) | −2.17780 | −0.102777 | −0.0513883 | − | 0.998679i | \(-0.516365\pi\) | ||||
−0.0513883 | + | 0.998679i | \(0.516365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11.8082i | − | 0.556028i | ||||||
\(452\) | −7.18572 | − | 2.82336i | −0.337988 | − | 0.132800i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.12283 | + | 4.58224i | 0.146562 | + | 0.215055i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.57653i | − | 0.167303i | −0.996495 | − | 0.0836516i | \(-0.973342\pi\) | ||
0.996495 | − | 0.0836516i | \(-0.0266583\pi\) | |||||||
\(458\) | 30.0221 | − | 20.4603i | 1.40284 | − | 0.956046i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.1158i | 0.610866i | 0.952214 | + | 0.305433i | \(0.0988012\pi\) | ||||
−0.952214 | + | 0.305433i | \(0.901199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.21417i | 0.149375i | 0.997207 | + | 0.0746877i | \(0.0237960\pi\) | ||||
−0.997207 | + | 0.0746877i | \(0.976204\pi\) | |||||||
\(464\) | −9.99311 | + | 10.7535i | −0.463919 | + | 0.499218i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.0999 | + | 20.5133i | −1.39435 | + | 0.950261i | ||||
\(467\) | −30.3016 | −1.40219 | −0.701095 | − | 0.713068i | \(-0.747305\pi\) | ||||
−0.701095 | + | 0.713068i | \(0.747305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 63.5254i | − | 2.93333i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.02811 | − | 39.6597i | −0.415552 | − | 1.82549i | ||||
\(473\) | 21.0045i | 0.965790i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.1446 | + | 30.9090i | −0.556645 | + | 1.41671i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.6415 | − | 18.5493i | −0.578210 | − | 0.848427i | ||||
\(479\) | 35.0896 | 1.60328 | 0.801642 | − | 0.597804i | \(-0.203960\pi\) | ||||
0.801642 | + | 0.597804i | \(0.203960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.43678 | −0.0655116 | ||||||||
\(482\) | 22.4326 | + | 32.9161i | 1.02178 | + | 1.49929i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.25169 | − | 8.27584i | 0.147804 | − | 0.376175i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.9117i | 1.67263i | 0.548250 | + | 0.836315i | \(0.315294\pi\) | ||||
−0.548250 | + | 0.836315i | \(0.684706\pi\) | |||||||
\(488\) | 0.0742623 | + | 0.326228i | 0.00336169 | + | 0.0147676i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.9867i | − | 0.947116i | −0.880763 | − | 0.473558i | \(-0.842969\pi\) | ||
0.880763 | − | 0.473558i | \(-0.157031\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.9027 | −0.581109 | ||||||||
\(494\) | 22.0484 | − | 15.0262i | 0.992006 | − | 0.676060i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.3367 | − | 14.2522i | −0.688637 | − | 0.639943i | ||||
\(497\) | − | 10.3445i | − | 0.464014i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.9906i | 0.715836i | 0.933753 | + | 0.357918i | \(0.116513\pi\) | ||||
−0.933753 | + | 0.357918i | \(0.883487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.44587 | + | 3.71140i | −0.243061 | + | 0.165648i | ||||
\(503\) | − | 37.6023i | − | 1.67660i | −0.545206 | − | 0.838302i | \(-0.683549\pi\) | ||
0.545206 | − | 0.838302i | \(-0.316451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.2731 | + | 32.6821i | 0.990161 | + | 1.45290i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 34.2148 | + | 13.4434i | 1.51804 | + | 0.596456i | ||||
\(509\) | 12.8579i | 0.569917i | 0.958540 | + | 0.284958i | \(0.0919797\pi\) | ||||
−0.958540 | + | 0.284958i | \(0.908020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.66004 | −0.117673 | ||||||||
\(512\) | −17.7151 | + | 14.0775i | −0.782904 | + | 0.622142i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.90317 | + | 2.66004i | −0.172162 | + | 0.117330i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.63764 | −0.159983 | ||||||||
\(518\) | −2.28710 | + | 1.55867i | −0.100489 | + | 0.0684842i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.0015 | −1.62107 | −0.810534 | − | 0.585692i | \(-0.800823\pi\) | ||||
−0.810534 | + | 0.585692i | \(0.800823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.4952 | 0.765013 | 0.382506 | − | 0.923953i | \(-0.375061\pi\) | ||||
0.382506 | + | 0.923953i | \(0.375061\pi\) | |||||||
\(524\) | −6.36421 | − | 2.50058i | −0.278022 | − | 0.109238i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −32.2463 | + | 21.9761i | −1.40600 | + | 0.958203i | ||||
\(527\) | − | 18.4019i | − | 0.801600i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.6353 | −1.20153 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.7961 | − | 47.8379i | 0.814916 | − | 2.07404i | ||||
\(533\) | 10.4178 | 0.451243 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 37.0945 | − | 8.44418i | 1.60224 | − | 0.364733i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.5611 | − | 17.4201i | 1.10202 | − | 0.751035i | ||||
\(539\) | − | 60.1549i | − | 2.59106i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 38.1225i | − | 1.63901i | −0.573069 | − | 0.819507i | \(-0.694247\pi\) | ||
0.573069 | − | 0.819507i | \(-0.305753\pi\) | |||||||
\(542\) | −6.99731 | − | 10.2674i | −0.300560 | − | 0.441022i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.6631 | − | 2.98298i | −0.843048 | − | 0.127894i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.7406 | 1.52816 | 0.764078 | − | 0.645124i | \(-0.223194\pi\) | ||||
0.764078 | + | 0.645124i | \(0.223194\pi\) | |||||||
\(548\) | −30.4749 | − | 11.9740i | −1.30182 | − | 0.511504i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.9695 | 0.850731 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 48.5264i | 2.06355i | ||||||||
\(554\) | −8.27000 | − | 12.1349i | −0.351359 | − | 0.515561i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.64303 | − | 1.43139i | −0.154499 | − | 0.0607046i | ||||
\(557\) | 2.65516 | 0.112503 | 0.0562514 | − | 0.998417i | \(-0.482085\pi\) | ||||
0.0562514 | + | 0.998417i | \(0.482085\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.5312 | −0.783785 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5859 | − | 19.9350i | −0.573086 | − | 0.840908i | ||||
\(563\) | 20.3107 | 0.855992 | 0.427996 | − | 0.903781i | \(-0.359220\pi\) | ||||
0.427996 | + | 0.903781i | \(0.359220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.82513 | + | 4.14541i | 0.118749 | + | 0.174245i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.04049 | − | 1.37505i | 0.253453 | − | 0.0576959i | ||||
\(569\) | −28.4274 | −1.19174 | −0.595868 | − | 0.803082i | \(-0.703192\pi\) | ||||
−0.595868 | + | 0.803082i | \(0.703192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.1485i | 0.675794i | 0.941183 | + | 0.337897i | \(0.109716\pi\) | ||||
−0.941183 | + | 0.337897i | \(0.890284\pi\) | |||||||
\(572\) | 25.3663 | + | 9.96675i | 1.06062 | + | 0.416731i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.5832 | − | 11.3016i | 0.692169 | − | 0.471719i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 30.3600i | − | 1.26390i | −0.775008 | − | 0.631952i | \(-0.782254\pi\) | ||
0.775008 | − | 0.631952i | \(-0.217746\pi\) | |||||||
\(578\) | 3.69506 | + | 5.42189i | 0.153694 | + | 0.225521i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 53.6008i | − | 2.22374i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.916490i | 0.0379571i | ||||||||
\(584\) | −0.353589 | − | 1.55329i | −0.0146316 | − | 0.0642754i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.55987 | + | 6.69085i | 0.188366 | + | 0.276396i | ||||
\(587\) | −2.74070 | −0.113121 | −0.0565604 | − | 0.998399i | \(-0.518013\pi\) | ||||
−0.0565604 | + | 0.998399i | \(0.518013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.4807i | 1.17352i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.21417 | − | 1.12832i | −0.0499022 | − | 0.0463737i | ||||
\(593\) | − | 22.2586i | − | 0.914053i | −0.889453 | − | 0.457027i | \(-0.848914\pi\) | ||
0.889453 | − | 0.457027i | \(-0.151086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.5179 | − | 8.84755i | −0.922367 | − | 0.362410i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28.8336 | + | 19.6504i | −1.17910 | + | 0.803563i | ||||
\(599\) | 48.4526 | 1.97972 | 0.989860 | − | 0.142046i | \(-0.0453680\pi\) | ||||
0.989860 | + | 0.142046i | \(0.0453680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.26553 | 0.214786 | 0.107393 | − | 0.994217i | \(-0.465750\pi\) | ||||
0.107393 | + | 0.994217i | \(0.465750\pi\) | |||||||
\(602\) | −29.4983 | + | 20.1033i | −1.20226 | + | 0.819349i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.56319 | − | 9.06866i | 0.144984 | − | 0.368998i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.38288i | − | 0.299662i | −0.988712 | − | 0.149831i | \(-0.952127\pi\) | ||
0.988712 | − | 0.149831i | \(-0.0478730\pi\) | |||||||
\(608\) | 30.4326 | + | 4.61677i | 1.23420 | + | 0.187235i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.20929i | − | 0.129834i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.64607 | 0.106874 | 0.0534369 | − | 0.998571i | \(-0.482982\pi\) | ||||
0.0534369 | + | 0.998571i | \(0.482982\pi\) | |||||||
\(614\) | 9.85663 | + | 14.4630i | 0.397781 | + | 0.583678i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 51.1909 | − | 11.6531i | 2.06254 | − | 0.469515i | ||||
\(617\) | 21.0136i | 0.845977i | 0.906135 | + | 0.422989i | \(0.139019\pi\) | ||||
−0.906135 | + | 0.422989i | \(0.860981\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0874i | 0.968154i | 0.875025 | + | 0.484077i | \(0.160845\pi\) | ||||
−0.875025 | + | 0.484077i | \(0.839155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.5545 | + | 21.3563i | 0.583581 | + | 0.856309i | ||||
\(623\) | 41.9522i | 1.68078i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.8549 | + | 10.1238i | −0.593723 | + | 0.404627i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.8392 | − | 40.3121i | 0.632051 | − | 1.60863i | ||||
\(629\) | − | 1.45684i | − | 0.0580881i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.2094 | 1.00357 | 0.501785 | − | 0.864992i | \(-0.332677\pi\) | ||||
0.501785 | + | 0.864992i | \(0.332677\pi\) | |||||||
\(632\) | −28.3361 | + | 6.45042i | −1.12715 | + | 0.256584i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.6316 | − | 18.5348i | −0.501665 | − | 0.736110i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 53.0714 | 2.10277 | ||||||||
\(638\) | 11.4873 | + | 16.8557i | 0.454786 | + | 0.667324i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.4755 | 0.729738 | 0.364869 | − | 0.931059i | \(-0.381114\pi\) | ||||
0.364869 | + | 0.931059i | \(0.381114\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.636984 | 0.0251202 | 0.0125601 | − | 0.999921i | \(-0.496002\pi\) | ||||
0.0125601 | + | 0.999921i | \(0.496002\pi\) | |||||||
\(644\) | −24.5805 | + | 62.5596i | −0.968607 | + | 2.46519i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.2360 | + | 22.3563i | 0.599452 | + | 0.879596i | ||||
\(647\) | 32.0182i | 1.25876i | 0.777096 | + | 0.629382i | \(0.216692\pi\) | ||||
−0.777096 | + | 0.629382i | \(0.783308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −56.5173 | −2.21850 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.8751 | + | 30.2232i | −0.465065 | + | 1.18363i | ||||
\(653\) | −25.9769 | −1.01656 | −0.508278 | − | 0.861193i | \(-0.669718\pi\) | ||||
−0.508278 | + | 0.861193i | \(0.669718\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.80369 | + | 8.18118i | 0.343726 | + | 0.319421i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.48156 | − | 5.10861i | −0.135725 | − | 0.199154i | ||||
\(659\) | 21.3422i | 0.831372i | 0.909508 | + | 0.415686i | \(0.136459\pi\) | ||||
−0.909508 | + | 0.415686i | \(0.863541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 14.8397i | − | 0.577198i | −0.957450 | − | 0.288599i | \(-0.906810\pi\) | ||
0.957450 | − | 0.288599i | \(-0.0931895\pi\) | |||||||
\(662\) | −26.9153 | + | 18.3430i | −1.04609 | + | 0.712921i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.2992 | − | 7.12494i | 1.21465 | − | 0.276501i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.1150 | −1.01118 | ||||||||
\(668\) | −12.4577 | − | 4.89477i | −0.482001 | − | 0.189384i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.464893 | 0.0179470 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1167i | 0.698347i | 0.937058 | + | 0.349174i | \(0.113538\pi\) | ||||
−0.937058 | + | 0.349174i | \(0.886462\pi\) | |||||||
\(674\) | 1.00531 | − | 0.685127i | 0.0387231 | − | 0.0263901i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.715008 | − | 1.81976i | 0.0275003 | − | 0.0699908i | ||||
\(677\) | 30.5617 | 1.17458 | 0.587291 | − | 0.809376i | \(-0.300194\pi\) | ||||
0.587291 | + | 0.809376i | \(0.300194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.3576 | −1.31852 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.0397 | + | 16.3832i | −0.920527 | + | 0.627346i | ||||
\(683\) | −22.2027 | −0.849564 | −0.424782 | − | 0.905296i | \(-0.639649\pi\) | ||||
−0.424782 | + | 0.905296i | \(0.639649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 45.8445 | − | 31.2434i | 1.75035 | − | 1.19288i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.6600 | − | 14.5527i | −0.597034 | − | 0.554818i | ||||
\(689\) | −0.808569 | −0.0308040 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6890i | 0.482712i | 0.970437 | + | 0.241356i | \(0.0775922\pi\) | ||||
−0.970437 | + | 0.241356i | \(0.922408\pi\) | |||||||
\(692\) | −16.3993 | + | 41.7378i | −0.623408 | + | 1.58663i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.7133 | + | 37.7299i | 0.976062 | + | 1.43221i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.5632i | 0.400110i | ||||||||
\(698\) | 0.868174 | − | 0.591668i | 0.0328609 | − | 0.0223950i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9241i | 1.31906i | 0.751676 | + | 0.659532i | \(0.229246\pi\) | ||||
−0.751676 | + | 0.659532i | \(0.770754\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.25476i | 0.0850398i | ||||||||
\(704\) | 13.6092 | + | 28.3430i | 0.512916 | + | 1.06822i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 38.1431 | − | 25.9949i | 1.43554 | − | 0.978330i | ||||
\(707\) | 19.9931 | 0.751918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.65610i | 0.212419i | 0.994344 | + | 0.106210i | \(0.0338715\pi\) | ||||
−0.994344 | + | 0.106210i | \(0.966129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −24.4972 | + | 5.57653i | −0.918073 | + | 0.208989i | ||||
\(713\) | − | 37.2453i | − | 1.39485i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.277065 | + | 0.108862i | 0.0103544 | + | 0.00406838i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.15878 | − | 3.16764i | −0.0805648 | − | 0.118215i | ||||
\(719\) | −20.0844 | −0.749020 | −0.374510 | − | 0.927223i | \(-0.622189\pi\) | ||||
−0.374510 | + | 0.927223i | \(0.622189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.202741 | 0.00755048 | ||||||||
\(722\) | −8.44856 | − | 12.3969i | −0.314423 | − | 0.461364i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.3461 | − | 7.60132i | −0.718991 | − | 0.282501i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 13.0424i | − | 0.483715i | −0.970312 | − | 0.241857i | \(-0.922243\pi\) | ||
0.970312 | − | 0.241857i | \(-0.0777566\pi\) | |||||||
\(728\) | 10.2809 | + | 45.1629i | 0.381034 | + | 1.67385i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 18.7899i | − | 0.694970i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.8917 | 1.28876 | 0.644378 | − | 0.764707i | \(-0.277116\pi\) | ||||
0.644378 | + | 0.764707i | \(0.277116\pi\) | |||||||
\(734\) | −0.794678 | + | 0.541580i | −0.0293321 | + | 0.0199901i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −39.7980 | − | 6.03754i | −1.46697 | − | 0.222547i | ||||
\(737\) | − | 52.8618i | − | 1.94719i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 41.5040i | − | 1.52675i | −0.645957 | − | 0.763374i | \(-0.723541\pi\) | ||
0.645957 | − | 0.763374i | \(-0.276459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.28710 | + | 0.877166i | −0.0472508 | + | 0.0322018i | ||||
\(743\) | − | 7.63764i | − | 0.280198i | −0.990138 | − | 0.140099i | \(-0.955258\pi\) | ||
0.990138 | − | 0.140099i | \(-0.0447421\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.76873 | + | 4.06265i | 0.101370 | + | 0.148744i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.1059 | + | 25.7205i | −0.369509 | + | 0.940434i | ||||
\(749\) | − | 73.0771i | − | 2.67018i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.4029 | −0.708023 | −0.354012 | − | 0.935241i | \(-0.615183\pi\) | ||||
−0.354012 | + | 0.935241i | \(0.615183\pi\) | |||||||
\(752\) | 2.52029 | − | 2.71206i | 0.0919056 | − | 0.0988987i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.8709 | + | 10.1346i | −0.541565 | + | 0.369081i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.7959 | −1.59179 | −0.795894 | − | 0.605436i | \(-0.792999\pi\) | ||||
−0.795894 | + | 0.605436i | \(0.792999\pi\) | |||||||
\(758\) | −26.9545 | + | 18.3697i | −0.979030 | + | 0.667217i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.95519 | −0.360875 | −0.180438 | − | 0.983586i | \(-0.557751\pi\) | ||||
−0.180438 | + | 0.983586i | \(0.557751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −61.1910 | −2.21526 | ||||||||
\(764\) | 4.55893 | − | 11.6029i | 0.164936 | − | 0.419778i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.4706 | − | 7.81732i | 0.414450 | − | 0.282451i | ||||
\(767\) | − | 49.8621i | − | 1.80042i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9008 | 0.645520 | 0.322760 | − | 0.946481i | \(-0.395389\pi\) | ||||
0.322760 | + | 0.946481i | \(0.395389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.729642 | − | 0.286686i | −0.0262604 | − | 0.0103180i | ||||
\(773\) | 20.8182 | 0.748777 | 0.374389 | − | 0.927272i | \(-0.377853\pi\) | ||||
0.374389 | + | 0.927272i | \(0.377853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.56701 | − | 20.0625i | −0.163946 | − | 0.720201i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.5247 | + | 7.85420i | −0.413182 | + | 0.281587i | ||||
\(779\) | − | 16.3487i | − | 0.585753i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 8.60803i | − | 0.308019i | ||||||
\(782\) | −19.9247 | − | 29.2362i | −0.712507 | − | 1.04549i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 44.8488 | + | 41.6776i | 1.60174 | + | 1.48848i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.2047 | 0.969744 | 0.484872 | − | 0.874585i | \(-0.338866\pi\) | ||||
0.484872 | + | 0.874585i | \(0.338866\pi\) | |||||||
\(788\) | 4.36362 | − | 11.1058i | 0.155448 | − | 0.395628i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.2317 | −0.648244 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.410149i | 0.0145648i | ||||||||
\(794\) | 10.1771 | + | 14.9332i | 0.361170 | + | 0.529958i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.1155 | + | 33.3803i | −0.464868 | + | 1.18313i | ||||
\(797\) | 16.4344 | 0.582138 | 0.291069 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291069 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.25410 | 0.115122 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.52728 | − | 3.70836i | −0.0892413 | − | 0.130947i | ||||
\(803\) | −2.21352 | −0.0781134 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.4540 | − | 21.2089i | −0.509122 | − | 0.747052i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.65760 | + | 11.6746i | 0.0934942 | + | 0.410712i | ||||
\(809\) | 28.7698 | 1.01149 | 0.505747 | − | 0.862682i | \(-0.331217\pi\) | ||||
0.505747 | + | 0.862682i | \(0.331217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14.3512i | − | 0.503940i | −0.967735 | − | 0.251970i | \(-0.918922\pi\) | ||
0.967735 | − | 0.251970i | \(-0.0810785\pi\) | |||||||
\(812\) | −12.6773 | + | 32.2649i | −0.444887 | + | 1.13228i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.90317 | + | 1.29703i | −0.0667062 | + | 0.0454608i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.0812i | 1.01742i | ||||||||
\(818\) | −9.64675 | − | 14.1550i | −0.337291 | − | 0.494918i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.97271i | 0.173549i | 0.996228 | + | 0.0867744i | \(0.0276559\pi\) | ||||
−0.996228 | + | 0.0867744i | \(0.972344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 20.3625i | − | 0.709791i | −0.934906 | − | 0.354895i | \(-0.884517\pi\) | ||
0.934906 | − | 0.354895i | \(-0.115483\pi\) | |||||||
\(824\) | 0.0269496 | + | 0.118387i | 0.000938833 | + | 0.00412421i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −54.0923 | − | 79.3715i | −1.88211 | − | 2.76169i | ||||
\(827\) | 36.0039 | 1.25198 | 0.625989 | − | 0.779832i | \(-0.284696\pi\) | ||||
0.625989 | + | 0.779832i | \(0.284696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7.68666i | − | 0.266969i | −0.991051 | − | 0.133484i | \(-0.957383\pi\) | ||
0.991051 | − | 0.133484i | \(-0.0426166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25.0055 | + | 12.0066i | −0.866909 | + | 0.416256i | ||||
\(833\) | 53.8124i | 1.86449i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.6409 | − | 39.8076i | 0.540953 | − | 1.37678i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.96396 | − | 3.38298i | 0.171477 | − | 0.116863i | ||||
\(839\) | −25.3725 | −0.875956 | −0.437978 | − | 0.898986i | \(-0.644305\pi\) | ||||
−0.437978 | + | 0.898986i | \(0.644305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.5313 | 0.535561 | ||||||||
\(842\) | −4.41658 | + | 3.00993i | −0.152205 | + | 0.103729i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.1289 | − | 4.76558i | −0.417492 | − | 0.164038i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.9976i | − | 0.721485i | ||||||
\(848\) | −0.683294 | − | 0.634978i | −0.0234644 | − | 0.0218052i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.94864i | − | 0.101078i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.1365 | −0.689460 | −0.344730 | − | 0.938702i | \(-0.612029\pi\) | ||||
−0.344730 | + | 0.938702i | \(0.612029\pi\) | |||||||
\(854\) | 0.444945 | + | 0.652884i | 0.0152257 | + | 0.0223412i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.6721 | − | 9.71385i | 1.45850 | − | 0.332012i | ||||
\(857\) | − | 42.0380i | − | 1.43599i | −0.696047 | − | 0.717996i | \(-0.745060\pi\) | ||
0.696047 | − | 0.717996i | \(-0.254940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.4095i | − | 0.423406i | −0.977334 | − | 0.211703i | \(-0.932099\pi\) | ||
0.977334 | − | 0.211703i | \(-0.0679010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.4102 | − | 29.9486i | −0.695174 | − | 1.02005i | ||||
\(863\) | 21.8154i | 0.742606i | 0.928512 | + | 0.371303i | \(0.121089\pi\) | ||||
−0.928512 | + | 0.371303i | \(0.878911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.37407 | + | 1.61795i | −0.0806740 | + | 0.0549800i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −46.0164 | − | 18.0804i | −1.56190 | − | 0.613690i | ||||
\(869\) | 40.3805i | 1.36982i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.6371 | 1.58024 | ||||||||
\(872\) | −8.13387 | − | 35.7314i | −0.275448 | − | 1.21002i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.8375 | + | 45.2490i | 1.04310 | + | 1.53057i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.83690 | 0.197098 | 0.0985491 | − | 0.995132i | \(-0.468580\pi\) | ||||
0.0985491 | + | 0.995132i | \(0.468580\pi\) | |||||||
\(878\) | 17.9088 | + | 26.2782i | 0.604394 | + | 0.886848i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.9613 | 0.402986 | 0.201493 | − | 0.979490i | \(-0.435421\pi\) | ||||
0.201493 | + | 0.979490i | \(0.435421\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.74810 | 0.126134 | 0.0630668 | − | 0.998009i | \(-0.479912\pi\) | ||||
0.0630668 | + | 0.998009i | \(0.479912\pi\) | |||||||
\(884\) | −22.6918 | − | 8.91590i | −0.763208 | − | 0.299874i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.70297 | − | 3.96616i | −0.0908081 | − | 0.133246i | ||||
\(887\) | − | 42.8101i | − | 1.43742i | −0.695309 | − | 0.718711i | \(-0.744732\pi\) | ||
0.695309 | − | 0.718711i | \(-0.255268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 86.8101 | 2.91152 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.85692 | + | 2.30126i | 0.196104 | + | 0.0770519i | ||||
\(893\) | −5.03638 | −0.168536 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −26.7789 | + | 46.2393i | −0.894622 | + | 1.54475i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.73447 | − | 2.54504i | −0.0578799 | − | 0.0849291i | ||||
\(899\) | − | 19.2092i | − | 0.640662i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.819859i | − | 0.0273135i | ||||||
\(902\) | 13.7995 | − | 9.40444i | 0.459472 | − | 0.313134i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.42347 | − | 10.6461i | −0.0806033 | − | 0.354083i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.97759 | 0.231687 | 0.115844 | − | 0.993267i | \(-0.463043\pi\) | ||||
0.115844 | + | 0.993267i | \(0.463043\pi\) | |||||||
\(908\) | −2.86782 | + | 7.29888i | −0.0951721 | + | 0.242222i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2837 | −0.804555 | −0.402278 | − | 0.915518i | \(-0.631781\pi\) | ||||
−0.402278 | + | 0.915518i | \(0.631781\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 44.6031i | − | 1.47615i | ||||||
\(914\) | 4.17965 | − | 2.84846i | 0.138250 | − | 0.0942188i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 47.8210 | + | 18.7895i | 1.58005 | + | 0.620822i | ||||
\(917\) | −16.1473 | −0.533232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.25720 | 0.0414712 | 0.0207356 | − | 0.999785i | \(-0.493399\pi\) | ||||
0.0207356 | + | 0.999785i | \(0.493399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.3276 | + | 10.4459i | −0.504787 | + | 0.344016i | ||||
\(923\) | 7.59440 | 0.249973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.75618 | + | 2.55987i | −0.123436 | + | 0.0841225i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.5257 | − | 3.11384i | −0.673788 | − | 0.102217i | ||||
\(929\) | 10.4933 | 0.344275 | 0.172138 | − | 0.985073i | \(-0.444933\pi\) | ||||
0.172138 | + | 0.985073i | \(0.444933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 83.2856i | − | 2.72957i | ||||||
\(932\) | −47.9450 | − | 18.8382i | −1.57049 | − | 0.617066i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.1331 | − | 35.4113i | −0.789660 | − | 1.15869i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.9680i | 0.423648i | 0.977308 | + | 0.211824i | \(0.0679403\pi\) | ||||
−0.977308 | + | 0.211824i | \(0.932060\pi\) | |||||||
\(938\) | 74.2378 | − | 50.5936i | 2.42395 | − | 1.65194i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 44.9947i | − | 1.46678i | −0.679806 | − | 0.733392i | \(-0.737936\pi\) | ||
0.679806 | − | 0.733392i | \(-0.262064\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.3799i | 0.696225i | ||||||||
\(944\) | 39.1573 | − | 42.1368i | 1.27446 | − | 1.37143i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.5466 | + | 16.7287i | −0.798077 | + | 0.543896i | ||||
\(947\) | 30.6282 | 0.995283 | 0.497642 | − | 0.867383i | \(-0.334199\pi\) | ||||
0.497642 | + | 0.867383i | \(0.334199\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.95287i | − | 0.0633927i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −45.7935 | + | 10.4244i | −1.48418 | + | 0.337857i | ||||
\(953\) | 17.5717i | 0.569202i | 0.958646 | + | 0.284601i | \(0.0918610\pi\) | ||||
−0.958646 | + | 0.284601i | \(0.908139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.6092 | − | 29.5466i | 0.375469 | − | 0.955604i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.9465 | + | 41.0068i | 0.902909 | + | 1.32487i | ||||
\(959\) | −77.3213 | −2.49683 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.60380 | −0.116252 | ||||||||
\(962\) | −1.14430 | − | 1.67907i | −0.0368936 | − | 0.0541353i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.6007 | + | 52.4308i | −0.663505 | + | 1.68868i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.50932i | 0.145010i | 0.997368 | + | 0.0725050i | \(0.0230993\pi\) | ||||
−0.997368 | + | 0.0725050i | \(0.976901\pi\) | |||||||
\(968\) | 12.2611 | − | 2.79112i | 0.394088 | − | 0.0897100i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 35.8512i | − | 1.15052i | −0.817971 | − | 0.575259i | \(-0.804901\pi\) | ||
0.817971 | − | 0.575259i | \(-0.195099\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.24313 | −0.296321 | ||||||||
\(974\) | −43.1361 | + | 29.3976i | −1.38217 | + | 0.941961i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.322095 | + | 0.346603i | −0.0103100 | + | 0.0110945i | ||||
\(977\) | 43.9704i | 1.40674i | 0.710826 | + | 0.703368i | \(0.248322\pi\) | ||||
−0.710826 | + | 0.703368i | \(0.751678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.9099i | 1.11573i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.5257 | − | 16.7144i | 0.782646 | − | 0.533380i | ||||
\(983\) | − | 4.64187i | − | 0.148053i | −0.997256 | − | 0.0740263i | \(-0.976415\pi\) | ||
0.997256 | − | 0.0740263i | \(-0.0235849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.2761 | − | 15.0785i | −0.327258 | − | 0.480197i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 35.1201 | + | 13.7991i | 1.11732 | + | 0.439009i | ||||
\(989\) | − | 38.0307i | − | 1.20930i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.9117 | −1.68080 | −0.840398 | − | 0.541970i | \(-0.817679\pi\) | ||||
−0.840398 | + | 0.541970i | \(0.817679\pi\) | |||||||
\(992\) | 4.44098 | − | 29.2738i | 0.141001 | − | 0.929444i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0889 | − | 8.23868i | 0.383437 | − | 0.261315i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.4228 | −1.24853 | −0.624266 | − | 0.781211i | \(-0.714602\pi\) | ||||
−0.624266 | + | 0.781211i | \(0.714602\pi\) | |||||||
\(998\) | −18.6871 | + | 12.7354i | −0.591529 | + | 0.403132i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))