Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,2,Mod(23,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.31753163335\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 23.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.23 |
Dual form | 165.2.k.b.122.2 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70711 | + | 1.70711i | 1.20711 | + | 1.20711i | 0.971960 | + | 0.235147i | \(0.0755571\pi\) |
0.235147 | + | 0.971960i | \(0.424443\pi\) | |||||||
\(3\) | −1.41421 | − | 1.00000i | −0.816497 | − | 0.577350i | ||||
\(4\) | 3.82843i | 1.91421i | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | −0.707107 | − | 4.12132i | −0.288675 | − | 1.68252i | ||||
\(7\) | −0.585786 | + | 0.585786i | −0.221406 | + | 0.221406i | −0.809091 | − | 0.587684i | \(-0.800040\pi\) |
0.587684 | + | 0.809091i | \(0.300040\pi\) | |||||||
\(8\) | −3.12132 | + | 3.12132i | −1.10355 | + | 1.10355i | ||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 1.70711 | + | 5.12132i | 0.539835 | + | 1.61950i | ||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 3.82843 | − | 5.41421i | 1.10517 | − | 1.56295i | ||||
\(13\) | −2.00000 | − | 2.00000i | −0.554700 | − | 0.554700i | 0.373094 | − | 0.927794i | \(-0.378297\pi\) |
−0.927794 | + | 0.373094i | \(0.878297\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | −1.82843 | − | 3.41421i | −0.472098 | − | 0.881546i | ||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | −2.82843 | − | 2.82843i | −0.685994 | − | 0.685994i | 0.275350 | − | 0.961344i | \(-0.411206\pi\) |
−0.961344 | + | 0.275350i | \(0.911206\pi\) | |||||||
\(18\) | −3.12132 | + | 6.53553i | −0.735702 | + | 1.54044i | ||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | −3.82843 | + | 7.65685i | −0.856062 | + | 1.71212i | ||||
\(21\) | 1.41421 | − | 0.242641i | 0.308607 | − | 0.0529485i | ||||
\(22\) | 1.70711 | − | 1.70711i | 0.363956 | − | 0.363956i | ||||
\(23\) | 5.24264 | − | 5.24264i | 1.09317 | − | 1.09317i | 0.0979775 | − | 0.995189i | \(-0.468763\pi\) |
0.995189 | − | 0.0979775i | \(-0.0312373\pi\) | |||||||
\(24\) | 7.53553 | − | 1.29289i | 1.53818 | − | 0.263911i | ||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | − | 6.82843i | − | 1.33916i | ||||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | −2.24264 | − | 2.24264i | −0.423819 | − | 0.423819i | ||||
\(29\) | 4.82843 | 0.896616 | 0.448308 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448308 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(30\) | 2.70711 | − | 8.94975i | 0.494248 | − | 1.63399i | ||||
\(31\) | −8.82843 | −1.58563 | −0.792816 | − | 0.609461i | \(-0.791386\pi\) | ||||
−0.792816 | + | 0.609461i | \(0.791386\pi\) | |||||||
\(32\) | 1.12132 | + | 1.12132i | 0.198223 | + | 0.198223i | ||||
\(33\) | −1.00000 | + | 1.41421i | −0.174078 | + | 0.246183i | ||||
\(34\) | − | 9.65685i | − | 1.65614i | ||||||
\(35\) | −1.75736 | + | 0.585786i | −0.297048 | + | 0.0990160i | ||||
\(36\) | −10.8284 | + | 3.82843i | −1.80474 | + | 0.638071i | ||||
\(37\) | −5.82843 | + | 5.82843i | −0.958188 | + | 0.958188i | −0.999160 | − | 0.0409727i | \(-0.986954\pi\) |
0.0409727 | + | 0.999160i | \(0.486954\pi\) | |||||||
\(38\) | 4.82843 | − | 4.82843i | 0.783274 | − | 0.783274i | ||||
\(39\) | 0.828427 | + | 4.82843i | 0.132655 | + | 0.773167i | ||||
\(40\) | −9.36396 | + | 3.12132i | −1.48057 | + | 0.493524i | ||||
\(41\) | 3.65685i | 0.571105i | 0.958363 | + | 0.285552i | \(0.0921770\pi\) | ||||
−0.958363 | + | 0.285552i | \(0.907823\pi\) | |||||||
\(42\) | 2.82843 | + | 2.00000i | 0.436436 | + | 0.308607i | ||||
\(43\) | −8.24264 | − | 8.24264i | −1.25699 | − | 1.25699i | −0.952522 | − | 0.304469i | \(-0.901521\pi\) |
−0.304469 | − | 0.952522i | \(-0.598479\pi\) | |||||||
\(44\) | 3.82843 | 0.577157 | ||||||||
\(45\) | −0.828427 | + | 6.65685i | −0.123495 | + | 0.992345i | ||||
\(46\) | 17.8995 | 2.63914 | ||||||||
\(47\) | −1.24264 | − | 1.24264i | −0.181258 | − | 0.181258i | 0.610646 | − | 0.791904i | \(-0.290910\pi\) |
−0.791904 | + | 0.610646i | \(0.790910\pi\) | |||||||
\(48\) | 4.24264 | + | 3.00000i | 0.612372 | + | 0.433013i | ||||
\(49\) | 6.31371i | 0.901958i | ||||||||
\(50\) | −1.70711 | + | 11.9497i | −0.241421 | + | 1.68995i | ||||
\(51\) | 1.17157 | + | 6.82843i | 0.164053 | + | 0.956171i | ||||
\(52\) | 7.65685 | − | 7.65685i | 1.06181 | − | 1.06181i | ||||
\(53\) | −1.00000 | + | 1.00000i | −0.137361 | + | 0.137361i | −0.772444 | − | 0.635083i | \(-0.780966\pi\) |
0.635083 | + | 0.772444i | \(0.280966\pi\) | |||||||
\(54\) | 10.9497 | − | 6.12132i | 1.49007 | − | 0.833006i | ||||
\(55\) | 1.00000 | − | 2.00000i | 0.134840 | − | 0.269680i | ||||
\(56\) | − | 3.65685i | − | 0.488668i | ||||||
\(57\) | −2.82843 | + | 4.00000i | −0.374634 | + | 0.529813i | ||||
\(58\) | 8.24264 | + | 8.24264i | 1.08231 | + | 1.08231i | ||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 13.0711 | − | 7.00000i | 1.68747 | − | 0.903696i | ||||
\(61\) | 10.4853 | 1.34250 | 0.671251 | − | 0.741230i | \(-0.265757\pi\) | ||||
0.671251 | + | 0.741230i | \(0.265757\pi\) | |||||||
\(62\) | −15.0711 | − | 15.0711i | −1.91403 | − | 1.91403i | ||||
\(63\) | −2.24264 | − | 1.07107i | −0.282546 | − | 0.134942i | ||||
\(64\) | 9.82843i | 1.22855i | ||||||||
\(65\) | −2.00000 | − | 6.00000i | −0.248069 | − | 0.744208i | ||||
\(66\) | −4.12132 | + | 0.707107i | −0.507299 | + | 0.0870388i | ||||
\(67\) | −3.58579 | + | 3.58579i | −0.438074 | + | 0.438074i | −0.891363 | − | 0.453290i | \(-0.850250\pi\) |
0.453290 | + | 0.891363i | \(0.350250\pi\) | |||||||
\(68\) | 10.8284 | − | 10.8284i | 1.31314 | − | 1.31314i | ||||
\(69\) | −12.6569 | + | 2.17157i | −1.52371 | + | 0.261427i | ||||
\(70\) | −4.00000 | − | 2.00000i | −0.478091 | − | 0.239046i | ||||
\(71\) | 14.4853i | 1.71909i | 0.511063 | + | 0.859543i | \(0.329252\pi\) | ||||
−0.511063 | + | 0.859543i | \(0.670748\pi\) | |||||||
\(72\) | −11.9497 | − | 5.70711i | −1.40829 | − | 0.672589i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | −19.8995 | −2.31327 | ||||||||
\(75\) | −0.242641 | − | 8.65685i | −0.0280177 | − | 0.999607i | ||||
\(76\) | 10.8284 | 1.24211 | ||||||||
\(77\) | 0.585786 | + | 0.585786i | 0.0667566 | + | 0.0667566i | ||||
\(78\) | −6.82843 | + | 9.65685i | −0.773167 | + | 1.09342i | ||||
\(79\) | − | 5.17157i | − | 0.581847i | −0.956746 | − | 0.290924i | \(-0.906037\pi\) | ||
0.956746 | − | 0.290924i | \(-0.0939626\pi\) | |||||||
\(80\) | −6.00000 | − | 3.00000i | −0.670820 | − | 0.335410i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | −6.24264 | + | 6.24264i | −0.689384 | + | 0.689384i | ||||
\(83\) | −5.07107 | + | 5.07107i | −0.556622 | + | 0.556622i | −0.928344 | − | 0.371722i | \(-0.878767\pi\) |
0.371722 | + | 0.928344i | \(0.378767\pi\) | |||||||
\(84\) | 0.928932 | + | 5.41421i | 0.101355 | + | 0.590739i | ||||
\(85\) | −2.82843 | − | 8.48528i | −0.306786 | − | 0.920358i | ||||
\(86\) | − | 28.1421i | − | 3.03464i | ||||||
\(87\) | −6.82843 | − | 4.82843i | −0.732084 | − | 0.517662i | ||||
\(88\) | 3.12132 | + | 3.12132i | 0.332734 | + | 0.332734i | ||||
\(89\) | −1.65685 | −0.175626 | −0.0878131 | − | 0.996137i | \(-0.527988\pi\) | ||||
−0.0878131 | + | 0.996137i | \(0.527988\pi\) | |||||||
\(90\) | −12.7782 | + | 9.94975i | −1.34694 | + | 1.04880i | ||||
\(91\) | 2.34315 | 0.245628 | ||||||||
\(92\) | 20.0711 | + | 20.0711i | 2.09255 | + | 2.09255i | ||||
\(93\) | 12.4853 | + | 8.82843i | 1.29466 | + | 0.915465i | ||||
\(94\) | − | 4.24264i | − | 0.437595i | ||||||
\(95\) | 2.82843 | − | 5.65685i | 0.290191 | − | 0.580381i | ||||
\(96\) | −0.464466 | − | 2.70711i | −0.0474044 | − | 0.276293i | ||||
\(97\) | −0.656854 | + | 0.656854i | −0.0666934 | + | 0.0666934i | −0.739667 | − | 0.672973i | \(-0.765017\pi\) |
0.672973 | + | 0.739667i | \(0.265017\pi\) | |||||||
\(98\) | −10.7782 | + | 10.7782i | −1.08876 | + | 1.08876i | ||||
\(99\) | 2.82843 | − | 1.00000i | 0.284268 | − | 0.100504i | ||||
\(100\) | −15.3137 | + | 11.4853i | −1.53137 | + | 1.14853i | ||||
\(101\) | − | 12.8284i | − | 1.27648i | −0.769839 | − | 0.638238i | \(-0.779664\pi\) | ||
0.769839 | − | 0.638238i | \(-0.220336\pi\) | |||||||
\(102\) | −9.65685 | + | 13.6569i | −0.956171 | + | 1.35223i | ||||
\(103\) | −3.58579 | − | 3.58579i | −0.353318 | − | 0.353318i | 0.508025 | − | 0.861343i | \(-0.330376\pi\) |
−0.861343 | + | 0.508025i | \(0.830376\pi\) | |||||||
\(104\) | 12.4853 | 1.22428 | ||||||||
\(105\) | 3.07107 | + | 0.928932i | 0.299706 | + | 0.0906545i | ||||
\(106\) | −3.41421 | −0.331618 | ||||||||
\(107\) | 8.24264 | + | 8.24264i | 0.796846 | + | 0.796846i | 0.982597 | − | 0.185751i | \(-0.0594717\pi\) |
−0.185751 | + | 0.982597i | \(0.559472\pi\) | |||||||
\(108\) | 19.1421 | + | 5.41421i | 1.84195 | + | 0.520983i | ||||
\(109\) | − | 8.82843i | − | 0.845610i | −0.906221 | − | 0.422805i | \(-0.861046\pi\) | ||
0.906221 | − | 0.422805i | \(-0.138954\pi\) | |||||||
\(110\) | 5.12132 | − | 1.70711i | 0.488299 | − | 0.162766i | ||||
\(111\) | 14.0711 | − | 2.41421i | 1.33557 | − | 0.229147i | ||||
\(112\) | 1.75736 | − | 1.75736i | 0.166055 | − | 0.166055i | ||||
\(113\) | 0.171573 | − | 0.171573i | 0.0161402 | − | 0.0161402i | −0.698991 | − | 0.715131i | \(-0.746367\pi\) |
0.715131 | + | 0.698991i | \(0.246367\pi\) | |||||||
\(114\) | −11.6569 | + | 2.00000i | −1.09176 | + | 0.187317i | ||||
\(115\) | 15.7279 | − | 5.24264i | 1.46664 | − | 0.488879i | ||||
\(116\) | 18.4853i | 1.71632i | ||||||||
\(117\) | 3.65685 | − | 7.65685i | 0.338076 | − | 0.707876i | ||||
\(118\) | 6.82843 | + | 6.82843i | 0.628608 | + | 0.628608i | ||||
\(119\) | 3.31371 | 0.303767 | ||||||||
\(120\) | 16.3640 | + | 4.94975i | 1.49382 | + | 0.451848i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 17.8995 | + | 17.8995i | 1.62054 | + | 1.62054i | ||||
\(123\) | 3.65685 | − | 5.17157i | 0.329727 | − | 0.466305i | ||||
\(124\) | − | 33.7990i | − | 3.03524i | ||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | −2.00000 | − | 5.65685i | −0.178174 | − | 0.503953i | ||||
\(127\) | −1.41421 | + | 1.41421i | −0.125491 | + | 0.125491i | −0.767063 | − | 0.641572i | \(-0.778283\pi\) |
0.641572 | + | 0.767063i | \(0.278283\pi\) | |||||||
\(128\) | −14.5355 | + | 14.5355i | −1.28477 | + | 1.28477i | ||||
\(129\) | 3.41421 | + | 19.8995i | 0.300605 | + | 1.75205i | ||||
\(130\) | 6.82843 | − | 13.6569i | 0.598893 | − | 1.19779i | ||||
\(131\) | 1.17157i | 0.102361i | 0.998689 | + | 0.0511804i | \(0.0162983\pi\) | ||||
−0.998689 | + | 0.0511804i | \(0.983702\pi\) | |||||||
\(132\) | −5.41421 | − | 3.82843i | −0.471247 | − | 0.333222i | ||||
\(133\) | 1.65685 | + | 1.65685i | 0.143667 | + | 0.143667i | ||||
\(134\) | −12.2426 | −1.05760 | ||||||||
\(135\) | 7.82843 | − | 8.58579i | 0.673764 | − | 0.738947i | ||||
\(136\) | 17.6569 | 1.51406 | ||||||||
\(137\) | −5.82843 | − | 5.82843i | −0.497956 | − | 0.497956i | 0.412845 | − | 0.910801i | \(-0.364535\pi\) |
−0.910801 | + | 0.412845i | \(0.864535\pi\) | |||||||
\(138\) | −25.3137 | − | 17.8995i | −2.15485 | − | 1.52371i | ||||
\(139\) | 6.34315i | 0.538019i | 0.963138 | + | 0.269009i | \(0.0866962\pi\) | ||||
−0.963138 | + | 0.269009i | \(0.913304\pi\) | |||||||
\(140\) | −2.24264 | − | 6.72792i | −0.189538 | − | 0.568613i | ||||
\(141\) | 0.514719 | + | 3.00000i | 0.0433471 | + | 0.252646i | ||||
\(142\) | −24.7279 | + | 24.7279i | −2.07512 | + | 2.07512i | ||||
\(143\) | −2.00000 | + | 2.00000i | −0.167248 | + | 0.167248i | ||||
\(144\) | −3.00000 | − | 8.48528i | −0.250000 | − | 0.707107i | ||||
\(145\) | 9.65685 | + | 4.82843i | 0.801958 | + | 0.400979i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.31371 | − | 8.92893i | 0.520746 | − | 0.736446i | ||||
\(148\) | −22.3137 | − | 22.3137i | −1.83418 | − | 1.83418i | ||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | 14.3640 | − | 15.1924i | 1.17281 | − | 1.24045i | ||||
\(151\) | −18.1421 | −1.47639 | −0.738193 | − | 0.674590i | \(-0.764321\pi\) | ||||
−0.738193 | + | 0.674590i | \(0.764321\pi\) | |||||||
\(152\) | 8.82843 | + | 8.82843i | 0.716080 | + | 0.716080i | ||||
\(153\) | 5.17157 | − | 10.8284i | 0.418097 | − | 0.875426i | ||||
\(154\) | 2.00000i | 0.161165i | ||||||||
\(155\) | −17.6569 | − | 8.82843i | −1.41823 | − | 0.709116i | ||||
\(156\) | −18.4853 | + | 3.17157i | −1.48001 | + | 0.253929i | ||||
\(157\) | 7.48528 | − | 7.48528i | 0.597390 | − | 0.597390i | −0.342227 | − | 0.939617i | \(-0.611181\pi\) |
0.939617 | + | 0.342227i | \(0.111181\pi\) | |||||||
\(158\) | 8.82843 | − | 8.82843i | 0.702352 | − | 0.702352i | ||||
\(159\) | 2.41421 | − | 0.414214i | 0.191460 | − | 0.0328493i | ||||
\(160\) | 1.12132 | + | 3.36396i | 0.0886482 | + | 0.265944i | ||||
\(161\) | 6.14214i | 0.484068i | ||||||||
\(162\) | −21.6066 | − | 2.29289i | −1.69757 | − | 0.180147i | ||||
\(163\) | 6.41421 | + | 6.41421i | 0.502400 | + | 0.502400i | 0.912183 | − | 0.409783i | \(-0.134396\pi\) |
−0.409783 | + | 0.912183i | \(0.634396\pi\) | |||||||
\(164\) | −14.0000 | −1.09322 | ||||||||
\(165\) | −3.41421 | + | 1.82843i | −0.265796 | + | 0.142343i | ||||
\(166\) | −17.3137 | −1.34380 | ||||||||
\(167\) | 10.7279 | + | 10.7279i | 0.830152 | + | 0.830152i | 0.987537 | − | 0.157386i | \(-0.0503066\pi\) |
−0.157386 | + | 0.987537i | \(0.550307\pi\) | |||||||
\(168\) | −3.65685 | + | 5.17157i | −0.282132 | + | 0.398996i | ||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 9.65685 | − | 19.3137i | 0.740647 | − | 1.48129i | ||||
\(171\) | 8.00000 | − | 2.82843i | 0.611775 | − | 0.216295i | ||||
\(172\) | 31.5563 | − | 31.5563i | 2.40615 | − | 2.40615i | ||||
\(173\) | 8.48528 | − | 8.48528i | 0.645124 | − | 0.645124i | −0.306687 | − | 0.951811i | \(-0.599220\pi\) |
0.951811 | + | 0.306687i | \(0.0992203\pi\) | |||||||
\(174\) | −3.41421 | − | 19.8995i | −0.258831 | − | 1.50858i | ||||
\(175\) | −4.10051 | − | 0.585786i | −0.309969 | − | 0.0442813i | ||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | −5.65685 | − | 4.00000i | −0.425195 | − | 0.300658i | ||||
\(178\) | −2.82843 | − | 2.82843i | −0.212000 | − | 0.212000i | ||||
\(179\) | 4.14214 | 0.309598 | 0.154799 | − | 0.987946i | \(-0.450527\pi\) | ||||
0.154799 | + | 0.987946i | \(0.450527\pi\) | |||||||
\(180\) | −25.4853 | − | 3.17157i | −1.89956 | − | 0.236395i | ||||
\(181\) | −5.65685 | −0.420471 | −0.210235 | − | 0.977651i | \(-0.567423\pi\) | ||||
−0.210235 | + | 0.977651i | \(0.567423\pi\) | |||||||
\(182\) | 4.00000 | + | 4.00000i | 0.296500 | + | 0.296500i | ||||
\(183\) | −14.8284 | − | 10.4853i | −1.09615 | − | 0.775094i | ||||
\(184\) | 32.7279i | 2.41273i | ||||||||
\(185\) | −17.4853 | + | 5.82843i | −1.28554 | + | 0.428514i | ||||
\(186\) | 6.24264 | + | 36.3848i | 0.457733 | + | 2.66786i | ||||
\(187\) | −2.82843 | + | 2.82843i | −0.206835 | + | 0.206835i | ||||
\(188\) | 4.75736 | − | 4.75736i | 0.346966 | − | 0.346966i | ||||
\(189\) | 2.10051 | + | 3.75736i | 0.152789 | + | 0.273308i | ||||
\(190\) | 14.4853 | − | 4.82843i | 1.05087 | − | 0.350291i | ||||
\(191\) | − | 11.3137i | − | 0.818631i | −0.912393 | − | 0.409316i | \(-0.865768\pi\) | ||
0.912393 | − | 0.409316i | \(-0.134232\pi\) | |||||||
\(192\) | 9.82843 | − | 13.8995i | 0.709306 | − | 1.00311i | ||||
\(193\) | 8.00000 | + | 8.00000i | 0.575853 | + | 0.575853i | 0.933758 | − | 0.357905i | \(-0.116509\pi\) |
−0.357905 | + | 0.933758i | \(0.616509\pi\) | |||||||
\(194\) | −2.24264 | −0.161012 | ||||||||
\(195\) | −3.17157 | + | 10.4853i | −0.227121 | + | 0.750867i | ||||
\(196\) | −24.1716 | −1.72654 | ||||||||
\(197\) | −14.1421 | − | 14.1421i | −1.00759 | − | 1.00759i | −0.999971 | − | 0.00761443i | \(-0.997576\pi\) |
−0.00761443 | − | 0.999971i | \(-0.502424\pi\) | |||||||
\(198\) | 6.53553 | + | 3.12132i | 0.464460 | + | 0.221823i | ||||
\(199\) | − | 2.48528i | − | 0.176177i | −0.996113 | − | 0.0880885i | \(-0.971924\pi\) | ||
0.996113 | − | 0.0880885i | \(-0.0280758\pi\) | |||||||
\(200\) | −21.8492 | − | 3.12132i | −1.54497 | − | 0.220711i | ||||
\(201\) | 8.65685 | − | 1.48528i | 0.610607 | − | 0.104764i | ||||
\(202\) | 21.8995 | − | 21.8995i | 1.54084 | − | 1.54084i | ||||
\(203\) | −2.82843 | + | 2.82843i | −0.198517 | + | 0.198517i | ||||
\(204\) | −26.1421 | + | 4.48528i | −1.83032 | + | 0.314033i | ||||
\(205\) | −3.65685 | + | 7.31371i | −0.255406 | + | 0.510812i | ||||
\(206\) | − | 12.2426i | − | 0.852985i | ||||||
\(207\) | 20.0711 | + | 9.58579i | 1.39504 | + | 0.666258i | ||||
\(208\) | 6.00000 | + | 6.00000i | 0.416025 | + | 0.416025i | ||||
\(209\) | −2.82843 | −0.195646 | ||||||||
\(210\) | 3.65685 | + | 6.82843i | 0.252347 | + | 0.471206i | ||||
\(211\) | 12.4853 | 0.859522 | 0.429761 | − | 0.902943i | \(-0.358598\pi\) | ||||
0.429761 | + | 0.902943i | \(0.358598\pi\) | |||||||
\(212\) | −3.82843 | − | 3.82843i | −0.262937 | − | 0.262937i | ||||
\(213\) | 14.4853 | − | 20.4853i | 0.992515 | − | 1.40363i | ||||
\(214\) | 28.1421i | 1.92376i | ||||||||
\(215\) | −8.24264 | − | 24.7279i | −0.562143 | − | 1.68643i | ||||
\(216\) | 11.1924 | + | 20.0208i | 0.761546 | + | 1.36224i | ||||
\(217\) | 5.17157 | − | 5.17157i | 0.351069 | − | 0.351069i | ||||
\(218\) | 15.0711 | − | 15.0711i | 1.02074 | − | 1.02074i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.65685 | + | 3.82843i | 0.516225 | + | 0.258113i | ||||
\(221\) | 11.3137i | 0.761042i | ||||||||
\(222\) | 28.1421 | + | 19.8995i | 1.88878 | + | 1.33557i | ||||
\(223\) | 14.5563 | + | 14.5563i | 0.974765 | + | 0.974765i | 0.999689 | − | 0.0249241i | \(-0.00793441\pi\) |
−0.0249241 | + | 0.999689i | \(0.507934\pi\) | |||||||
\(224\) | −1.31371 | −0.0877758 | ||||||||
\(225\) | −8.31371 | + | 12.4853i | −0.554247 | + | 0.832352i | ||||
\(226\) | 0.585786 | 0.0389659 | ||||||||
\(227\) | −1.75736 | − | 1.75736i | −0.116640 | − | 0.116640i | 0.646378 | − | 0.763018i | \(-0.276283\pi\) |
−0.763018 | + | 0.646378i | \(0.776283\pi\) | |||||||
\(228\) | −15.3137 | − | 10.8284i | −1.01418 | − | 0.717130i | ||||
\(229\) | − | 1.65685i | − | 0.109488i | −0.998500 | − | 0.0547440i | \(-0.982566\pi\) | ||
0.998500 | − | 0.0547440i | \(-0.0174343\pi\) | |||||||
\(230\) | 35.7990 | + | 17.8995i | 2.36052 | + | 1.18026i | ||||
\(231\) | −0.242641 | − | 1.41421i | −0.0159646 | − | 0.0930484i | ||||
\(232\) | −15.0711 | + | 15.0711i | −0.989464 | + | 0.989464i | ||||
\(233\) | −8.34315 | + | 8.34315i | −0.546578 | + | 0.546578i | −0.925449 | − | 0.378872i | \(-0.876312\pi\) |
0.378872 | + | 0.925449i | \(0.376312\pi\) | |||||||
\(234\) | 19.3137 | − | 6.82843i | 1.26258 | − | 0.446388i | ||||
\(235\) | −1.24264 | − | 3.72792i | −0.0810609 | − | 0.243183i | ||||
\(236\) | 15.3137i | 0.996838i | ||||||||
\(237\) | −5.17157 | + | 7.31371i | −0.335930 | + | 0.475076i | ||||
\(238\) | 5.65685 | + | 5.65685i | 0.366679 | + | 0.366679i | ||||
\(239\) | −15.7990 | −1.02195 | −0.510976 | − | 0.859595i | \(-0.670716\pi\) | ||||
−0.510976 | + | 0.859595i | \(0.670716\pi\) | |||||||
\(240\) | 5.48528 | + | 10.2426i | 0.354073 | + | 0.661160i | ||||
\(241\) | −28.1421 | −1.81279 | −0.906397 | − | 0.422427i | \(-0.861178\pi\) | ||||
−0.906397 | + | 0.422427i | \(0.861178\pi\) | |||||||
\(242\) | −1.70711 | − | 1.70711i | −0.109737 | − | 0.109737i | ||||
\(243\) | 15.5563 | − | 1.00000i | 0.997940 | − | 0.0641500i | ||||
\(244\) | 40.1421i | 2.56984i | ||||||||
\(245\) | −6.31371 | + | 12.6274i | −0.403368 | + | 0.806736i | ||||
\(246\) | 15.0711 | − | 2.58579i | 0.960896 | − | 0.164864i | ||||
\(247\) | −5.65685 | + | 5.65685i | −0.359937 | + | 0.359937i | ||||
\(248\) | 27.5563 | − | 27.5563i | 1.74983 | − | 1.74983i | ||||
\(249\) | 12.2426 | − | 2.10051i | 0.775846 | − | 0.133114i | ||||
\(250\) | −15.3640 | + | 22.1924i | −0.971702 | + | 1.40357i | ||||
\(251\) | 12.1421i | 0.766405i | 0.923664 | + | 0.383202i | \(0.125179\pi\) | ||||
−0.923664 | + | 0.383202i | \(0.874821\pi\) | |||||||
\(252\) | 4.10051 | − | 8.58579i | 0.258308 | − | 0.540854i | ||||
\(253\) | −5.24264 | − | 5.24264i | −0.329602 | − | 0.329602i | ||||
\(254\) | −4.82843 | −0.302962 | ||||||||
\(255\) | −4.48528 | + | 14.8284i | −0.280879 | + | 0.928592i | ||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −3.82843 | − | 3.82843i | −0.238811 | − | 0.238811i | 0.577547 | − | 0.816358i | \(-0.304010\pi\) |
−0.816358 | + | 0.577547i | \(0.804010\pi\) | |||||||
\(258\) | −28.1421 | + | 39.7990i | −1.75205 | + | 2.47778i | ||||
\(259\) | − | 6.82843i | − | 0.424298i | ||||||
\(260\) | 22.9706 | − | 7.65685i | 1.42457 | − | 0.474858i | ||||
\(261\) | 4.82843 | + | 13.6569i | 0.298872 | + | 0.845338i | ||||
\(262\) | −2.00000 | + | 2.00000i | −0.123560 | + | 0.123560i | ||||
\(263\) | 10.2426 | − | 10.2426i | 0.631588 | − | 0.631588i | −0.316878 | − | 0.948466i | \(-0.602635\pi\) |
0.948466 | + | 0.316878i | \(0.102635\pi\) | |||||||
\(264\) | −1.29289 | − | 7.53553i | −0.0795721 | − | 0.463780i | ||||
\(265\) | −3.00000 | + | 1.00000i | −0.184289 | + | 0.0614295i | ||||
\(266\) | 5.65685i | 0.346844i | ||||||||
\(267\) | 2.34315 | + | 1.65685i | 0.143398 | + | 0.101398i | ||||
\(268\) | −13.7279 | − | 13.7279i | −0.838566 | − | 0.838566i | ||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 28.0208 | − | 1.29289i | 1.70529 | − | 0.0786830i | ||||
\(271\) | −8.48528 | −0.515444 | −0.257722 | − | 0.966219i | \(-0.582972\pi\) | ||||
−0.257722 | + | 0.966219i | \(0.582972\pi\) | |||||||
\(272\) | 8.48528 | + | 8.48528i | 0.514496 | + | 0.514496i | ||||
\(273\) | −3.31371 | − | 2.34315i | −0.200555 | − | 0.141814i | ||||
\(274\) | − | 19.8995i | − | 1.20217i | ||||||
\(275\) | 4.00000 | − | 3.00000i | 0.241209 | − | 0.180907i | ||||
\(276\) | −8.31371 | − | 48.4558i | −0.500426 | − | 2.91670i | ||||
\(277\) | −1.51472 | + | 1.51472i | −0.0910106 | + | 0.0910106i | −0.751146 | − | 0.660136i | \(-0.770499\pi\) |
0.660136 | + | 0.751146i | \(0.270499\pi\) | |||||||
\(278\) | −10.8284 | + | 10.8284i | −0.649446 | + | 0.649446i | ||||
\(279\) | −8.82843 | − | 24.9706i | −0.528544 | − | 1.49495i | ||||
\(280\) | 3.65685 | − | 7.31371i | 0.218539 | − | 0.437078i | ||||
\(281\) | − | 16.6274i | − | 0.991909i | −0.868349 | − | 0.495954i | \(-0.834818\pi\) | ||
0.868349 | − | 0.495954i | \(-0.165182\pi\) | |||||||
\(282\) | −4.24264 | + | 6.00000i | −0.252646 | + | 0.357295i | ||||
\(283\) | −0.928932 | − | 0.928932i | −0.0552193 | − | 0.0552193i | 0.678958 | − | 0.734177i | \(-0.262432\pi\) |
−0.734177 | + | 0.678958i | \(0.762432\pi\) | |||||||
\(284\) | −55.4558 | −3.29070 | ||||||||
\(285\) | −9.65685 | + | 5.17157i | −0.572023 | + | 0.306338i | ||||
\(286\) | −6.82843 | −0.403773 | ||||||||
\(287\) | −2.14214 | − | 2.14214i | −0.126446 | − | 0.126446i | ||||
\(288\) | −2.05025 | + | 4.29289i | −0.120812 | + | 0.252961i | ||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 8.24264 | + | 24.7279i | 0.484025 | + | 1.45207i | ||||
\(291\) | 1.58579 | − | 0.272078i | 0.0929604 | − | 0.0159495i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.65685 | + | 7.65685i | −0.447318 | + | 0.447318i | −0.894462 | − | 0.447144i | \(-0.852441\pi\) |
0.447144 | + | 0.894462i | \(0.352441\pi\) | |||||||
\(294\) | 26.0208 | − | 4.46447i | 1.51756 | − | 0.260373i | ||||
\(295\) | 8.00000 | + | 4.00000i | 0.465778 | + | 0.232889i | ||||
\(296\) | − | 36.3848i | − | 2.11482i | ||||||
\(297\) | −5.00000 | − | 1.41421i | −0.290129 | − | 0.0820610i | ||||
\(298\) | 17.0711 | + | 17.0711i | 0.988900 | + | 0.988900i | ||||
\(299\) | −20.9706 | −1.21276 | ||||||||
\(300\) | 33.1421 | − | 0.928932i | 1.91346 | − | 0.0536319i | ||||
\(301\) | 9.65685 | 0.556612 | ||||||||
\(302\) | −30.9706 | − | 30.9706i | −1.78216 | − | 1.78216i | ||||
\(303\) | −12.8284 | + | 18.1421i | −0.736974 | + | 1.04224i | ||||
\(304\) | 8.48528i | 0.486664i | ||||||||
\(305\) | 20.9706 | + | 10.4853i | 1.20077 | + | 0.600385i | ||||
\(306\) | 27.3137 | − | 9.65685i | 1.56142 | − | 0.552046i | ||||
\(307\) | 7.89949 | − | 7.89949i | 0.450848 | − | 0.450848i | −0.444788 | − | 0.895636i | \(-0.646721\pi\) |
0.895636 | + | 0.444788i | \(0.146721\pi\) | |||||||
\(308\) | −2.24264 | + | 2.24264i | −0.127786 | + | 0.127786i | ||||
\(309\) | 1.48528 | + | 8.65685i | 0.0844947 | + | 0.492471i | ||||
\(310\) | −15.0711 | − | 45.2132i | −0.855979 | − | 2.56794i | ||||
\(311\) | − | 0.142136i | − | 0.00805977i | −0.999992 | − | 0.00402989i | \(-0.998717\pi\) | ||
0.999992 | − | 0.00402989i | \(-0.00128276\pi\) | |||||||
\(312\) | −17.6569 | − | 12.4853i | −0.999623 | − | 0.706840i | ||||
\(313\) | 1.34315 | + | 1.34315i | 0.0759191 | + | 0.0759191i | 0.744047 | − | 0.668128i | \(-0.232904\pi\) |
−0.668128 | + | 0.744047i | \(0.732904\pi\) | |||||||
\(314\) | 25.5563 | 1.44223 | ||||||||
\(315\) | −3.41421 | − | 4.38478i | −0.192369 | − | 0.247054i | ||||
\(316\) | 19.7990 | 1.11378 | ||||||||
\(317\) | 20.3137 | + | 20.3137i | 1.14093 | + | 1.14093i | 0.988280 | + | 0.152651i | \(0.0487812\pi\) |
0.152651 | + | 0.988280i | \(0.451219\pi\) | |||||||
\(318\) | 4.82843 | + | 3.41421i | 0.270765 | + | 0.191460i | ||||
\(319\) | − | 4.82843i | − | 0.270340i | ||||||
\(320\) | −9.82843 | + | 19.6569i | −0.549426 | + | 1.09885i | ||||
\(321\) | −3.41421 | − | 19.8995i | −0.190563 | − | 1.11068i | ||||
\(322\) | −10.4853 | + | 10.4853i | −0.584322 | + | 0.584322i | ||||
\(323\) | −8.00000 | + | 8.00000i | −0.445132 | + | 0.445132i | ||||
\(324\) | −21.6569 | − | 26.7990i | −1.20316 | − | 1.48883i | ||||
\(325\) | 2.00000 | − | 14.0000i | 0.110940 | − | 0.776580i | ||||
\(326\) | 21.8995i | 1.21290i | ||||||||
\(327\) | −8.82843 | + | 12.4853i | −0.488213 | + | 0.690438i | ||||
\(328\) | −11.4142 | − | 11.4142i | −0.630245 | − | 0.630245i | ||||
\(329\) | 1.45584 | 0.0802633 | ||||||||
\(330\) | −8.94975 | − | 2.70711i | −0.492667 | − | 0.149021i | ||||
\(331\) | 10.4853 | 0.576323 | 0.288162 | − | 0.957582i | \(-0.406956\pi\) | ||||
0.288162 | + | 0.957582i | \(0.406956\pi\) | |||||||
\(332\) | −19.4142 | − | 19.4142i | −1.06549 | − | 1.06549i | ||||
\(333\) | −22.3137 | − | 10.6569i | −1.22278 | − | 0.583992i | ||||
\(334\) | 36.6274i | 2.00416i | ||||||||
\(335\) | −10.7574 | + | 3.58579i | −0.587737 | + | 0.195912i | ||||
\(336\) | −4.24264 | + | 0.727922i | −0.231455 | + | 0.0397114i | ||||
\(337\) | −5.17157 | + | 5.17157i | −0.281714 | + | 0.281714i | −0.833792 | − | 0.552079i | \(-0.813835\pi\) |
0.552079 | + | 0.833792i | \(0.313835\pi\) | |||||||
\(338\) | 8.53553 | − | 8.53553i | 0.464272 | − | 0.464272i | ||||
\(339\) | −0.414214 | + | 0.0710678i | −0.0224970 | + | 0.00385987i | ||||
\(340\) | 32.4853 | − | 10.8284i | 1.76176 | − | 0.587254i | ||||
\(341\) | 8.82843i | 0.478086i | ||||||||
\(342\) | 18.4853 | + | 8.82843i | 0.999570 | + | 0.477387i | ||||
\(343\) | −7.79899 | − | 7.79899i | −0.421106 | − | 0.421106i | ||||
\(344\) | 51.4558 | 2.77431 | ||||||||
\(345\) | −27.4853 | − | 8.31371i | −1.47976 | − | 0.447595i | ||||
\(346\) | 28.9706 | 1.55747 | ||||||||
\(347\) | 17.8995 | + | 17.8995i | 0.960895 | + | 0.960895i | 0.999264 | − | 0.0383684i | \(-0.0122160\pi\) |
−0.0383684 | + | 0.999264i | \(0.512216\pi\) | |||||||
\(348\) | 18.4853 | − | 26.1421i | 0.990915 | − | 1.40137i | ||||
\(349\) | − | 30.0000i | − | 1.60586i | −0.596071 | − | 0.802932i | \(-0.703272\pi\) | ||
0.596071 | − | 0.802932i | \(-0.296728\pi\) | |||||||
\(350\) | −6.00000 | − | 8.00000i | −0.320713 | − | 0.427618i | ||||
\(351\) | −12.8284 | + | 7.17157i | −0.684731 | + | 0.382790i | ||||
\(352\) | 1.12132 | − | 1.12132i | 0.0597666 | − | 0.0597666i | ||||
\(353\) | −2.17157 | + | 2.17157i | −0.115581 | + | 0.115581i | −0.762532 | − | 0.646951i | \(-0.776044\pi\) |
0.646951 | + | 0.762532i | \(0.276044\pi\) | |||||||
\(354\) | −2.82843 | − | 16.4853i | −0.150329 | − | 0.876183i | ||||
\(355\) | −14.4853 | + | 28.9706i | −0.768799 | + | 1.53760i | ||||
\(356\) | − | 6.34315i | − | 0.336186i | ||||||
\(357\) | −4.68629 | − | 3.31371i | −0.248025 | − | 0.175380i | ||||
\(358\) | 7.07107 | + | 7.07107i | 0.373718 | + | 0.373718i | ||||
\(359\) | −6.14214 | −0.324170 | −0.162085 | − | 0.986777i | \(-0.551822\pi\) | ||||
−0.162085 | + | 0.986777i | \(0.551822\pi\) | |||||||
\(360\) | −18.1924 | − | 23.3640i | −0.958823 | − | 1.23139i | ||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | −9.65685 | − | 9.65685i | −0.507553 | − | 0.507553i | ||||
\(363\) | 1.41421 | + | 1.00000i | 0.0742270 | + | 0.0524864i | ||||
\(364\) | 8.97056i | 0.470185i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.41421 | − | 43.2132i | −0.387547 | − | 2.25879i | ||||
\(367\) | −20.8995 | + | 20.8995i | −1.09094 | + | 1.09094i | −0.0955170 | + | 0.995428i | \(0.530450\pi\) |
−0.995428 | + | 0.0955170i | \(0.969550\pi\) | |||||||
\(368\) | −15.7279 | + | 15.7279i | −0.819875 | + | 0.819875i | ||||
\(369\) | −10.3431 | + | 3.65685i | −0.538443 | + | 0.190368i | ||||
\(370\) | −39.7990 | − | 19.8995i | −2.06905 | − | 1.03453i | ||||
\(371\) | − | 1.17157i | − | 0.0608250i | ||||||
\(372\) | −33.7990 | + | 47.7990i | −1.75240 | + | 2.47826i | ||||
\(373\) | 20.4853 | + | 20.4853i | 1.06069 | + | 1.06069i | 0.998035 | + | 0.0626522i | \(0.0199559\pi\) |
0.0626522 | + | 0.998035i | \(0.480044\pi\) | |||||||
\(374\) | −9.65685 | −0.499344 | ||||||||
\(375\) | 8.17157 | − | 17.5563i | 0.421978 | − | 0.906606i | ||||
\(376\) | 7.75736 | 0.400055 | ||||||||
\(377\) | −9.65685 | − | 9.65685i | −0.497353 | − | 0.497353i | ||||
\(378\) | −2.82843 | + | 10.0000i | −0.145479 | + | 0.514344i | ||||
\(379\) | − | 0.142136i | − | 0.00730102i | −0.999993 | − | 0.00365051i | \(-0.998838\pi\) | ||
0.999993 | − | 0.00365051i | \(-0.00116200\pi\) | |||||||
\(380\) | 21.6569 | + | 10.8284i | 1.11097 | + | 0.555487i | ||||
\(381\) | 3.41421 | − | 0.585786i | 0.174915 | − | 0.0300107i | ||||
\(382\) | 19.3137 | − | 19.3137i | 0.988175 | − | 0.988175i | ||||
\(383\) | −8.07107 | + | 8.07107i | −0.412412 | + | 0.412412i | −0.882578 | − | 0.470166i | \(-0.844194\pi\) |
0.470166 | + | 0.882578i | \(0.344194\pi\) | |||||||
\(384\) | 35.0919 | − | 6.02082i | 1.79078 | − | 0.307248i | ||||
\(385\) | 0.585786 | + | 1.75736i | 0.0298544 | + | 0.0895633i | ||||
\(386\) | 27.3137i | 1.39023i | ||||||||
\(387\) | 15.0711 | − | 31.5563i | 0.766105 | − | 1.60410i | ||||
\(388\) | −2.51472 | − | 2.51472i | −0.127665 | − | 0.127665i | ||||
\(389\) | −5.31371 | −0.269416 | −0.134708 | − | 0.990885i | \(-0.543010\pi\) | ||||
−0.134708 | + | 0.990885i | \(0.543010\pi\) | |||||||
\(390\) | −23.3137 | + | 12.4853i | −1.18054 | + | 0.632217i | ||||
\(391\) | −29.6569 | −1.49981 | ||||||||
\(392\) | −19.7071 | − | 19.7071i | −0.995359 | − | 0.995359i | ||||
\(393\) | 1.17157 | − | 1.65685i | 0.0590980 | − | 0.0835772i | ||||
\(394\) | − | 48.2843i | − | 2.43253i | ||||||
\(395\) | 5.17157 | − | 10.3431i | 0.260210 | − | 0.520420i | ||||
\(396\) | 3.82843 | + | 10.8284i | 0.192386 | + | 0.544149i | ||||
\(397\) | 11.8284 | − | 11.8284i | 0.593652 | − | 0.593652i | −0.344964 | − | 0.938616i | \(-0.612109\pi\) |
0.938616 | + | 0.344964i | \(0.112109\pi\) | |||||||
\(398\) | 4.24264 | − | 4.24264i | 0.212664 | − | 0.212664i | ||||
\(399\) | −0.686292 | − | 4.00000i | −0.0343575 | − | 0.200250i | ||||
\(400\) | −9.00000 | − | 12.0000i | −0.450000 | − | 0.600000i | ||||
\(401\) | 24.3431i | 1.21564i | 0.794075 | + | 0.607819i | \(0.207956\pi\) | ||||
−0.794075 | + | 0.607819i | \(0.792044\pi\) | |||||||
\(402\) | 17.3137 | + | 12.2426i | 0.863529 | + | 0.610607i | ||||
\(403\) | 17.6569 | + | 17.6569i | 0.879551 | + | 0.879551i | ||||
\(404\) | 49.1127 | 2.44345 | ||||||||
\(405\) | −19.6569 | + | 4.31371i | −0.976757 | + | 0.214350i | ||||
\(406\) | −9.65685 | −0.479262 | ||||||||
\(407\) | 5.82843 | + | 5.82843i | 0.288904 | + | 0.288904i | ||||
\(408\) | −24.9706 | − | 17.6569i | −1.23623 | − | 0.874145i | ||||
\(409\) | − | 1.51472i | − | 0.0748980i | −0.999299 | − | 0.0374490i | \(-0.988077\pi\) | ||
0.999299 | − | 0.0374490i | \(-0.0119232\pi\) | |||||||
\(410\) | −18.7279 | + | 6.24264i | −0.924906 | + | 0.308302i | ||||
\(411\) | 2.41421 | + | 14.0711i | 0.119084 | + | 0.694075i | ||||
\(412\) | 13.7279 | − | 13.7279i | 0.676326 | − | 0.676326i | ||||
\(413\) | −2.34315 | + | 2.34315i | −0.115299 | + | 0.115299i | ||||
\(414\) | 17.8995 | + | 50.6274i | 0.879712 | + | 2.48820i | ||||
\(415\) | −15.2132 | + | 5.07107i | −0.746787 | + | 0.248929i | ||||
\(416\) | − | 4.48528i | − | 0.219909i | ||||||
\(417\) | 6.34315 | − | 8.97056i | 0.310625 | − | 0.439290i | ||||
\(418\) | −4.82843 | − | 4.82843i | −0.236166 | − | 0.236166i | ||||
\(419\) | 35.4558 | 1.73213 | 0.866066 | − | 0.499930i | \(-0.166641\pi\) | ||||
0.866066 | + | 0.499930i | \(0.166641\pi\) | |||||||
\(420\) | −3.55635 | + | 11.7574i | −0.173532 | + | 0.573700i | ||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 21.3137 | + | 21.3137i | 1.03754 | + | 1.03754i | ||||
\(423\) | 2.27208 | − | 4.75736i | 0.110472 | − | 0.231311i | ||||
\(424\) | − | 6.24264i | − | 0.303169i | ||||||
\(425\) | 2.82843 | − | 19.7990i | 0.137199 | − | 0.960392i | ||||
\(426\) | 59.6985 | − | 10.2426i | 2.89240 | − | 0.496258i | ||||
\(427\) | −6.14214 | + | 6.14214i | −0.297239 | + | 0.297239i | ||||
\(428\) | −31.5563 | + | 31.5563i | −1.52533 | + | 1.52533i | ||||
\(429\) | 4.82843 | − | 0.828427i | 0.233119 | − | 0.0399968i | ||||
\(430\) | 28.1421 | − | 56.2843i | 1.35713 | − | 2.71427i | ||||
\(431\) | − | 17.6569i | − | 0.850501i | −0.905076 | − | 0.425250i | \(-0.860186\pi\) | ||
0.905076 | − | 0.425250i | \(-0.139814\pi\) | |||||||
\(432\) | −4.24264 | + | 15.0000i | −0.204124 | + | 0.721688i | ||||
\(433\) | 22.3137 | + | 22.3137i | 1.07233 | + | 1.07233i | 0.997172 | + | 0.0751567i | \(0.0239457\pi\) |
0.0751567 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(434\) | 17.6569 | 0.847556 | ||||||||
\(435\) | −8.82843 | − | 16.4853i | −0.423291 | − | 0.790409i | ||||
\(436\) | 33.7990 | 1.61868 | ||||||||
\(437\) | −14.8284 | − | 14.8284i | −0.709340 | − | 0.709340i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3137i | 0.730883i | 0.930834 | + | 0.365442i | \(0.119082\pi\) | ||||
−0.930834 | + | 0.365442i | \(0.880918\pi\) | |||||||
\(440\) | 3.12132 | + | 9.36396i | 0.148803 | + | 0.446409i | ||||
\(441\) | −17.8579 | + | 6.31371i | −0.850374 | + | 0.300653i | ||||
\(442\) | −19.3137 | + | 19.3137i | −0.918659 | + | 0.918659i | ||||
\(443\) | 29.2426 | − | 29.2426i | 1.38936 | − | 1.38936i | 0.562696 | − | 0.826664i | \(-0.309764\pi\) |
0.826664 | − | 0.562696i | \(-0.190236\pi\) | |||||||
\(444\) | 9.24264 | + | 53.8701i | 0.438636 | + | 2.55656i | ||||
\(445\) | −3.31371 | − | 1.65685i | −0.157085 | − | 0.0785424i | ||||
\(446\) | 49.6985i | 2.35329i | ||||||||
\(447\) | −14.1421 | − | 10.0000i | −0.668900 | − | 0.472984i | ||||
\(448\) | −5.75736 | − | 5.75736i | −0.272010 | − | 0.272010i | ||||
\(449\) | 36.9706 | 1.74475 | 0.872374 | − | 0.488838i | \(-0.162579\pi\) | ||||
0.872374 | + | 0.488838i | \(0.162579\pi\) | |||||||
\(450\) | −35.5061 | + | 7.12132i | −1.67377 | + | 0.335702i | ||||
\(451\) | 3.65685 | 0.172195 | ||||||||
\(452\) | 0.656854 | + | 0.656854i | 0.0308958 | + | 0.0308958i | ||||
\(453\) | 25.6569 | + | 18.1421i | 1.20546 | + | 0.852392i | ||||
\(454\) | − | 6.00000i | − | 0.281594i | ||||||
\(455\) | 4.68629 | + | 2.34315i | 0.219697 | + | 0.109848i | ||||
\(456\) | −3.65685 | − | 21.3137i | −0.171248 | − | 0.998106i | ||||
\(457\) | 10.4853 | − | 10.4853i | 0.490481 | − | 0.490481i | −0.417977 | − | 0.908458i | \(-0.637261\pi\) |
0.908458 | + | 0.417977i | \(0.137261\pi\) | |||||||
\(458\) | 2.82843 | − | 2.82843i | 0.132164 | − | 0.132164i | ||||
\(459\) | −18.1421 | + | 10.1421i | −0.846802 | + | 0.473394i | ||||
\(460\) | 20.0711 | + | 60.2132i | 0.935818 | + | 2.80746i | ||||
\(461\) | − | 30.4853i | − | 1.41984i | −0.704282 | − | 0.709921i | \(-0.748731\pi\) | ||
0.704282 | − | 0.709921i | \(-0.251269\pi\) | |||||||
\(462\) | 2.00000 | − | 2.82843i | 0.0930484 | − | 0.131590i | ||||
\(463\) | −13.7279 | − | 13.7279i | −0.637991 | − | 0.637991i | 0.312069 | − | 0.950059i | \(-0.398978\pi\) |
−0.950059 | + | 0.312069i | \(0.898978\pi\) | |||||||
\(464\) | −14.4853 | −0.672462 | ||||||||
\(465\) | 16.1421 | + | 30.1421i | 0.748574 | + | 1.39781i | ||||
\(466\) | −28.4853 | −1.31956 | ||||||||
\(467\) | −2.41421 | − | 2.41421i | −0.111716 | − | 0.111716i | 0.649039 | − | 0.760755i | \(-0.275171\pi\) |
−0.760755 | + | 0.649039i | \(0.775171\pi\) | |||||||
\(468\) | 29.3137 | + | 14.0000i | 1.35503 | + | 0.647150i | ||||
\(469\) | − | 4.20101i | − | 0.193985i | ||||||
\(470\) | 4.24264 | − | 8.48528i | 0.195698 | − | 0.391397i | ||||
\(471\) | −18.0711 | + | 3.10051i | −0.832671 | + | 0.142864i | ||||
\(472\) | −12.4853 | + | 12.4853i | −0.574682 | + | 0.574682i | ||||
\(473\) | −8.24264 | + | 8.24264i | −0.378997 | + | 0.378997i | ||||
\(474\) | −21.3137 | + | 3.65685i | −0.978971 | + | 0.167965i | ||||
\(475\) | 11.3137 | − | 8.48528i | 0.519109 | − | 0.389331i | ||||
\(476\) | 12.6863i | 0.581475i | ||||||||
\(477\) | −3.82843 | − | 1.82843i | −0.175292 | − | 0.0837179i | ||||
\(478\) | −26.9706 | − | 26.9706i | −1.23360 | − | 1.23360i | ||||
\(479\) | 1.85786 | 0.0848880 | 0.0424440 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424440 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(480\) | 1.77817 | − | 5.87868i | 0.0811622 | − | 0.268324i | ||||
\(481\) | 23.3137 | 1.06301 | ||||||||
\(482\) | −48.0416 | − | 48.0416i | −2.18824 | − | 2.18824i | ||||
\(483\) | 6.14214 | − | 8.68629i | 0.279477 | − | 0.395240i | ||||
\(484\) | − | 3.82843i | − | 0.174019i | ||||||
\(485\) | −1.97056 | + | 0.656854i | −0.0894786 | + | 0.0298262i | ||||
\(486\) | 28.2635 | + | 24.8492i | 1.28206 | + | 1.12718i | ||||
\(487\) | −13.7279 | + | 13.7279i | −0.622072 | + | 0.622072i | −0.946061 | − | 0.323989i | \(-0.894976\pi\) |
0.323989 | + | 0.946061i | \(0.394976\pi\) | |||||||
\(488\) | −32.7279 | + | 32.7279i | −1.48152 | + | 1.48152i | ||||
\(489\) | −2.65685 | − | 15.4853i | −0.120147 | − | 0.700269i | ||||
\(490\) | −32.3345 | + | 10.7782i | −1.46072 | + | 0.486908i | ||||
\(491\) | − | 20.0000i | − | 0.902587i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) | ||
0.892375 | − | 0.451294i | \(-0.149037\pi\) | |||||||
\(492\) | 19.7990 | + | 14.0000i | 0.892607 | + | 0.631169i | ||||
\(493\) | −13.6569 | − | 13.6569i | −0.615074 | − | 0.615074i | ||||
\(494\) | −19.3137 | −0.868965 | ||||||||
\(495\) | 6.65685 | + | 0.828427i | 0.299203 | + | 0.0372350i | ||||
\(496\) | 26.4853 | 1.18922 | ||||||||
\(497\) | −8.48528 | − | 8.48528i | −0.380617 | − | 0.380617i | ||||
\(498\) | 24.4853 | + | 17.3137i | 1.09721 | + | 0.775846i | ||||
\(499\) | 19.1716i | 0.858237i | 0.903248 | + | 0.429119i | \(0.141176\pi\) | ||||
−0.903248 | + | 0.429119i | \(0.858824\pi\) | |||||||
\(500\) | −42.1127 | + | 7.65685i | −1.88334 | + | 0.342425i | ||||
\(501\) | −4.44365 | − | 25.8995i | −0.198528 | − | 1.15710i | ||||
\(502\) | −20.7279 | + | 20.7279i | −0.925132 | + | 0.925132i | ||||
\(503\) | −15.0711 | + | 15.0711i | −0.671986 | + | 0.671986i | −0.958174 | − | 0.286188i | \(-0.907612\pi\) |
0.286188 | + | 0.958174i | \(0.407612\pi\) | |||||||
\(504\) | 10.3431 | − | 3.65685i | 0.460720 | − | 0.162889i | ||||
\(505\) | 12.8284 | − | 25.6569i | 0.570858 | − | 1.14172i | ||||
\(506\) | − | 17.8995i | − | 0.795730i | ||||||
\(507\) | −5.00000 | + | 7.07107i | −0.222058 | + | 0.314037i | ||||
\(508\) | −5.41421 | − | 5.41421i | −0.240217 | − | 0.240217i | ||||
\(509\) | −24.3431 | −1.07899 | −0.539495 | − | 0.841988i | \(-0.681385\pi\) | ||||
−0.539495 | + | 0.841988i | \(0.681385\pi\) | |||||||
\(510\) | −32.9706 | + | 17.6569i | −1.45996 | + | 0.781859i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.0919 | − | 22.0919i | −0.976333 | − | 0.976333i | ||||
\(513\) | −14.1421 | − | 4.00000i | −0.624391 | − | 0.176604i | ||||
\(514\) | − | 13.0711i | − | 0.576540i | ||||||
\(515\) | −3.58579 | − | 10.7574i | −0.158009 | − | 0.474026i | ||||
\(516\) | −76.1838 | + | 13.0711i | −3.35380 | + | 0.575422i | ||||
\(517\) | −1.24264 | + | 1.24264i | −0.0546513 | + | 0.0546513i | ||||
\(518\) | 11.6569 | − | 11.6569i | 0.512173 | − | 0.512173i | ||||
\(519\) | −20.4853 | + | 3.51472i | −0.899204 | + | 0.154279i | ||||
\(520\) | 24.9706 | + | 12.4853i | 1.09503 | + | 0.547516i | ||||
\(521\) | − | 16.3431i | − | 0.716006i | −0.933720 | − | 0.358003i | \(-0.883458\pi\) | ||
0.933720 | − | 0.358003i | \(-0.116542\pi\) | |||||||
\(522\) | −15.0711 | + | 31.5563i | −0.659643 | + | 1.38118i | ||||
\(523\) | 15.2132 | + | 15.2132i | 0.665227 | + | 0.665227i | 0.956607 | − | 0.291380i | \(-0.0941145\pi\) |
−0.291380 | + | 0.956607i | \(0.594115\pi\) | |||||||
\(524\) | −4.48528 | −0.195940 | ||||||||
\(525\) | 5.21320 | + | 4.92893i | 0.227523 | + | 0.215116i | ||||
\(526\) | 34.9706 | 1.52479 | ||||||||
\(527\) | 24.9706 | + | 24.9706i | 1.08773 | + | 1.08773i | ||||
\(528\) | 3.00000 | − | 4.24264i | 0.130558 | − | 0.184637i | ||||
\(529\) | − | 31.9706i | − | 1.39002i | ||||||
\(530\) | −6.82843 | − | 3.41421i | −0.296608 | − | 0.148304i | ||||
\(531\) | 4.00000 | + | 11.3137i | 0.173585 | + | 0.490973i | ||||
\(532\) | −6.34315 | + | 6.34315i | −0.275010 | + | 0.275010i | ||||
\(533\) | 7.31371 | − | 7.31371i | 0.316792 | − | 0.316792i | ||||
\(534\) | 1.17157 | + | 6.82843i | 0.0506989 | + | 0.295495i | ||||
\(535\) | 8.24264 | + | 24.7279i | 0.356360 | + | 1.06908i | ||||
\(536\) | − | 22.3848i | − | 0.966875i | ||||||
\(537\) | −5.85786 | − | 4.14214i | −0.252786 | − | 0.178746i | ||||
\(538\) | 23.8995 | + | 23.8995i | 1.03038 | + | 1.03038i | ||||
\(539\) | 6.31371 | 0.271951 | ||||||||
\(540\) | 32.8701 | + | 29.9706i | 1.41450 | + | 1.28973i | ||||
\(541\) | −33.3137 | −1.43227 | −0.716134 | − | 0.697963i | \(-0.754090\pi\) | ||||
−0.716134 | + | 0.697963i | \(0.754090\pi\) | |||||||
\(542\) | −14.4853 | − | 14.4853i | −0.622196 | − | 0.622196i | ||||
\(543\) | 8.00000 | + | 5.65685i | 0.343313 | + | 0.242759i | ||||
\(544\) | − | 6.34315i | − | 0.271960i | ||||||
\(545\) | 8.82843 | − | 17.6569i | 0.378168 | − | 0.756337i | ||||
\(546\) | −1.65685 | − | 9.65685i | −0.0709068 | − | 0.413275i | ||||
\(547\) | 21.8995 | − | 21.8995i | 0.936355 | − | 0.936355i | −0.0617376 | − | 0.998092i | \(-0.519664\pi\) |
0.998092 | + | 0.0617376i | \(0.0196642\pi\) | |||||||
\(548\) | 22.3137 | − | 22.3137i | 0.953194 | − | 0.953194i | ||||
\(549\) | 10.4853 | + | 29.6569i | 0.447501 | + | 1.26572i | ||||
\(550\) | 11.9497 | + | 1.70711i | 0.509539 | + | 0.0727913i | ||||
\(551\) | − | 13.6569i | − | 0.581802i | ||||||
\(552\) | 32.7279 | − | 46.2843i | 1.39299 | − | 1.96999i | ||||
\(553\) | 3.02944 | + | 3.02944i | 0.128825 | + | 0.128825i | ||||
\(554\) | −5.17157 | −0.219719 | ||||||||
\(555\) | 30.5563 | + | 9.24264i | 1.29704 | + | 0.392328i | ||||
\(556\) | −24.2843 | −1.02988 | ||||||||
\(557\) | 24.9706 | + | 24.9706i | 1.05804 | + | 1.05804i | 0.998209 | + | 0.0598280i | \(0.0190552\pi\) |
0.0598280 | + | 0.998209i | \(0.480945\pi\) | |||||||
\(558\) | 27.5563 | − | 57.6985i | 1.16655 | − | 2.44257i | ||||
\(559\) | 32.9706i | 1.39451i | ||||||||
\(560\) | 5.27208 | − | 1.75736i | 0.222786 | − | 0.0742620i | ||||
\(561\) | 6.82843 | − | 1.17157i | 0.288296 | − | 0.0494638i | ||||
\(562\) | 28.3848 | − | 28.3848i | 1.19734 | − | 1.19734i | ||||
\(563\) | −9.89949 | + | 9.89949i | −0.417214 | + | 0.417214i | −0.884242 | − | 0.467028i | \(-0.845325\pi\) |
0.467028 | + | 0.884242i | \(0.345325\pi\) | |||||||
\(564\) | −11.4853 | + | 1.97056i | −0.483618 | + | 0.0829757i | ||||
\(565\) | 0.514719 | − | 0.171573i | 0.0216544 | − | 0.00721813i | ||||
\(566\) | − | 3.17157i | − | 0.133311i | ||||||
\(567\) | 0.786797 | − | 7.41421i | 0.0330423 | − | 0.311368i | ||||
\(568\) | −45.2132 | − | 45.2132i | −1.89710 | − | 1.89710i | ||||
\(569\) | 39.6569 | 1.66250 | 0.831251 | − | 0.555897i | \(-0.187625\pi\) | ||||
0.831251 | + | 0.555897i | \(0.187625\pi\) | |||||||
\(570\) | −25.3137 | − | 7.65685i | −1.06027 | − | 0.320710i | ||||
\(571\) | 18.3431 | 0.767637 | 0.383818 | − | 0.923409i | \(-0.374609\pi\) | ||||
0.383818 | + | 0.923409i | \(0.374609\pi\) | |||||||
\(572\) | −7.65685 | − | 7.65685i | −0.320149 | − | 0.320149i | ||||
\(573\) | −11.3137 | + | 16.0000i | −0.472637 | + | 0.668410i | ||||
\(574\) | − | 7.31371i | − | 0.305268i | ||||||
\(575\) | 36.6985 | + | 5.24264i | 1.53043 | + | 0.218633i | ||||
\(576\) | −27.7990 | + | 9.82843i | −1.15829 | + | 0.409518i | ||||
\(577\) | 17.0000 | − | 17.0000i | 0.707719 | − | 0.707719i | −0.258336 | − | 0.966055i | \(-0.583174\pi\) |
0.966055 | + | 0.258336i | \(0.0831741\pi\) | |||||||
\(578\) | 1.70711 | − | 1.70711i | 0.0710063 | − | 0.0710063i | ||||
\(579\) | −3.31371 | − | 19.3137i | −0.137713 | − | 0.802650i | ||||
\(580\) | −18.4853 | + | 36.9706i | −0.767560 | + | 1.53512i | ||||
\(581\) | − | 5.94113i | − | 0.246479i | ||||||
\(582\) | 3.17157 | + | 2.24264i | 0.131466 | + | 0.0929604i | ||||
\(583\) | 1.00000 | + | 1.00000i | 0.0414158 | + | 0.0414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.9706 | − | 11.6569i | 0.618957 | − | 0.481952i | ||||
\(586\) | −26.1421 | −1.07992 | ||||||||
\(587\) | −2.41421 | − | 2.41421i | −0.0996453 | − | 0.0996453i | 0.655527 | − | 0.755172i | \(-0.272447\pi\) |
−0.755172 | + | 0.655527i | \(0.772447\pi\) | |||||||
\(588\) | 34.1838 | + | 24.1716i | 1.40971 | + | 0.996819i | ||||
\(589\) | 24.9706i | 1.02889i | ||||||||
\(590\) | 6.82843 | + | 20.4853i | 0.281122 | + | 0.843366i | ||||
\(591\) | 5.85786 | + | 34.1421i | 0.240960 | + | 1.40442i | ||||
\(592\) | 17.4853 | − | 17.4853i | 0.718641 | − | 0.718641i | ||||
\(593\) | −34.1421 | + | 34.1421i | −1.40205 | + | 1.40205i | −0.608481 | + | 0.793568i | \(0.708221\pi\) |
−0.793568 | + | 0.608481i | \(0.791779\pi\) | |||||||
\(594\) | −6.12132 | − | 10.9497i | −0.251161 | − | 0.449274i | ||||
\(595\) | 6.62742 | + | 3.31371i | 0.271698 | + | 0.135849i | ||||
\(596\) | 38.2843i | 1.56818i | ||||||||
\(597\) | −2.48528 | + | 3.51472i | −0.101716 | + | 0.143848i | ||||
\(598\) | −35.7990 | − | 35.7990i | −1.46393 | − | 1.46393i | ||||
\(599\) | −47.4558 | −1.93899 | −0.969497 | − | 0.245105i | \(-0.921178\pi\) | ||||
−0.969497 | + | 0.245105i | \(0.921178\pi\) | |||||||
\(600\) | 27.7782 | + | 26.2635i | 1.13404 | + | 1.07220i | ||||
\(601\) | 23.4558 | 0.956784 | 0.478392 | − | 0.878146i | \(-0.341220\pi\) | ||||
0.478392 | + | 0.878146i | \(0.341220\pi\) | |||||||
\(602\) | 16.4853 | + | 16.4853i | 0.671890 | + | 0.671890i | ||||
\(603\) | −13.7279 | − | 6.55635i | −0.559044 | − | 0.266995i | ||||
\(604\) | − | 69.4558i | − | 2.82612i | ||||||
\(605\) | −2.00000 | − | 1.00000i | −0.0813116 | − | 0.0406558i | ||||
\(606\) | −52.8701 | + | 9.07107i | −2.14770 | + | 0.368487i | ||||
\(607\) | −2.10051 | + | 2.10051i | −0.0852569 | + | 0.0852569i | −0.748449 | − | 0.663192i | \(-0.769201\pi\) |
0.663192 | + | 0.748449i | \(0.269201\pi\) | |||||||
\(608\) | 3.17157 | − | 3.17157i | 0.128624 | − | 0.128624i | ||||
\(609\) | 6.82843 | − | 1.17157i | 0.276702 | − | 0.0474745i | ||||
\(610\) | 17.8995 | + | 53.6985i | 0.724729 | + | 2.17419i | ||||
\(611\) | 4.97056i | 0.201087i | ||||||||
\(612\) | 41.4558 | + | 19.7990i | 1.67575 | + | 0.800327i | ||||
\(613\) | −16.0000 | − | 16.0000i | −0.646234 | − | 0.646234i | 0.305847 | − | 0.952081i | \(-0.401060\pi\) |
−0.952081 | + | 0.305847i | \(0.901060\pi\) | |||||||
\(614\) | 26.9706 | 1.08844 | ||||||||
\(615\) | 12.4853 | − | 6.68629i | 0.503455 | − | 0.269617i | ||||
\(616\) | −3.65685 | −0.147339 | ||||||||
\(617\) | −24.1716 | − | 24.1716i | −0.973111 | − | 0.973111i | 0.0265370 | − | 0.999648i | \(-0.491552\pi\) |
−0.999648 | + | 0.0265370i | \(0.991552\pi\) | |||||||
\(618\) | −12.2426 | + | 17.3137i | −0.492471 | + | 0.696459i | ||||
\(619\) | − | 23.3137i | − | 0.937057i | −0.883448 | − | 0.468529i | \(-0.844784\pi\) | ||
0.883448 | − | 0.468529i | \(-0.155216\pi\) | |||||||
\(620\) | 33.7990 | − | 67.5980i | 1.35740 | − | 2.71480i | ||||
\(621\) | −18.7990 | − | 33.6274i | −0.754377 | − | 1.34942i | ||||
\(622\) | 0.242641 | − | 0.242641i | 0.00972901 | − | 0.00972901i | ||||
\(623\) | 0.970563 | − | 0.970563i | 0.0388848 | − | 0.0388848i | ||||
\(624\) | −2.48528 | − | 14.4853i | −0.0994909 | − | 0.579875i | ||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 4.58579i | 0.183285i | ||||||||
\(627\) | 4.00000 | + | 2.82843i | 0.159745 | + | 0.112956i | ||||
\(628\) | 28.6569 | + | 28.6569i | 1.14353 | + | 1.14353i | ||||
\(629\) | 32.9706 | 1.31462 | ||||||||
\(630\) | 1.65685 | − | 13.3137i | 0.0660107 | − | 0.530431i | ||||
\(631\) | 16.9706 | 0.675587 | 0.337794 | − | 0.941220i | \(-0.390319\pi\) | ||||
0.337794 | + | 0.941220i | \(0.390319\pi\) | |||||||
\(632\) | 16.1421 | + | 16.1421i | 0.642100 | + | 0.642100i | ||||
\(633\) | −17.6569 | − | 12.4853i | −0.701797 | − | 0.496245i | ||||
\(634\) | 69.3553i | 2.75445i | ||||||||
\(635\) | −4.24264 | + | 1.41421i | −0.168364 | + | 0.0561214i | ||||
\(636\) | 1.58579 | + | 9.24264i | 0.0628805 | + | 0.366495i | ||||
\(637\) | 12.6274 | − | 12.6274i | 0.500316 | − | 0.500316i | ||||
\(638\) | 8.24264 | − | 8.24264i | 0.326329 | − | 0.326329i | ||||
\(639\) | −40.9706 | + | 14.4853i | −1.62077 | + | 0.573029i | ||||
\(640\) | −43.6066 | + | 14.5355i | −1.72370 | + | 0.574567i | ||||
\(641\) | 12.6274i | 0.498753i | 0.968407 | + | 0.249376i | \(0.0802257\pi\) | ||||
−0.968407 | + | 0.249376i | \(0.919774\pi\) | |||||||
\(642\) | 28.1421 | − | 39.7990i | 1.11068 | − | 1.57074i | ||||
\(643\) | −0.757359 | − | 0.757359i | −0.0298673 | − | 0.0298673i | 0.692015 | − | 0.721883i | \(-0.256723\pi\) |
−0.721883 | + | 0.692015i | \(0.756723\pi\) | |||||||
\(644\) | −23.5147 | −0.926610 | ||||||||
\(645\) | −13.0711 | + | 43.2132i | −0.514673 | + | 1.70152i | ||||
\(646\) | −27.3137 | −1.07464 | ||||||||
\(647\) | 13.7279 | + | 13.7279i | 0.539700 | + | 0.539700i | 0.923441 | − | 0.383741i | \(-0.125364\pi\) |
−0.383741 | + | 0.923441i | \(0.625364\pi\) | |||||||
\(648\) | 4.19239 | − | 39.5061i | 0.164693 | − | 1.55195i | ||||
\(649\) | − | 4.00000i | − | 0.157014i | ||||||
\(650\) | 27.3137 | − | 20.4853i | 1.07133 | − | 0.803499i | ||||
\(651\) | −12.4853 | + | 2.14214i | −0.489337 | + | 0.0839569i | ||||
\(652\) | −24.5563 | + | 24.5563i | −0.961701 | + | 0.961701i | ||||
\(653\) | 2.65685 | − | 2.65685i | 0.103971 | − | 0.103971i | −0.653208 | − | 0.757179i | \(-0.726577\pi\) |
0.757179 | + | 0.653208i | \(0.226577\pi\) | |||||||
\(654\) | −36.3848 | + | 6.24264i | −1.42276 | + | 0.244107i | ||||
\(655\) | −1.17157 | + | 2.34315i | −0.0457771 | + | 0.0915543i | ||||
\(656\) | − | 10.9706i | − | 0.428329i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.48528 | + | 2.48528i | 0.0968864 | + | 0.0968864i | ||||
\(659\) | −8.97056 | −0.349444 | −0.174722 | − | 0.984618i | \(-0.555903\pi\) | ||||
−0.174722 | + | 0.984618i | \(0.555903\pi\) | |||||||
\(660\) | −7.00000 | − | 13.0711i | −0.272475 | − | 0.508791i | ||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 17.8995 | + | 17.8995i | 0.695684 | + | 0.695684i | ||||
\(663\) | 11.3137 | − | 16.0000i | 0.439388 | − | 0.621389i | ||||
\(664\) | − | 31.6569i | − | 1.22852i | ||||||
\(665\) | 1.65685 | + | 4.97056i | 0.0642501 | + | 0.192750i | ||||
\(666\) | −19.8995 | − | 56.2843i | −0.771090 | − | 2.18097i | ||||
\(667\) | 25.3137 | − | 25.3137i | 0.980151 | − | 0.980151i | ||||
\(668\) | −41.0711 | + | 41.0711i | −1.58909 | + | 1.58909i | ||||
\(669\) | −6.02944 | − | 35.1421i | −0.233112 | − | 1.35867i | ||||
\(670\) | −24.4853 | − | 12.2426i | −0.945949 | − | 0.472974i | ||||
\(671\) | − | 10.4853i | − | 0.404780i | ||||||
\(672\) | 1.85786 | + | 1.31371i | 0.0716687 | + | 0.0506774i | ||||
\(673\) | −33.6569 | − | 33.6569i | −1.29738 | − | 1.29738i | −0.930120 | − | 0.367257i | \(-0.880297\pi\) |
−0.367257 | − | 0.930120i | \(-0.619703\pi\) | |||||||
\(674\) | −17.6569 | −0.680117 | ||||||||
\(675\) | 24.2426 | − | 9.34315i | 0.933100 | − | 0.359618i | ||||
\(676\) | 19.1421 | 0.736236 | ||||||||
\(677\) | −8.34315 | − | 8.34315i | −0.320653 | − | 0.320653i | 0.528365 | − | 0.849018i | \(-0.322805\pi\) |
−0.849018 | + | 0.528365i | \(0.822805\pi\) | |||||||
\(678\) | −0.828427 | − | 0.585786i | −0.0318156 | − | 0.0224970i | ||||
\(679\) | − | 0.769553i | − | 0.0295327i | ||||||
\(680\) | 35.3137 | + | 17.6569i | 1.35422 | + | 0.677109i | ||||
\(681\) | 0.727922 | + | 4.24264i | 0.0278940 | + | 0.162578i | ||||
\(682\) | −15.0711 | + | 15.0711i | −0.577101 | + | 0.577101i | ||||
\(683\) | 17.7279 | − | 17.7279i | 0.678340 | − | 0.678340i | −0.281284 | − | 0.959624i | \(-0.590760\pi\) |
0.959624 | + | 0.281284i | \(0.0907604\pi\) | |||||||
\(684\) | 10.8284 | + | 30.6274i | 0.414035 | + | 1.17107i | ||||
\(685\) | −5.82843 | − | 17.4853i | −0.222693 | − | 0.668078i | ||||
\(686\) | − | 26.6274i | − | 1.01664i | ||||||
\(687\) | −1.65685 | + | 2.34315i | −0.0632129 | + | 0.0893966i | ||||
\(688\) | 24.7279 | + | 24.7279i | 0.942743 | + | 0.942743i | ||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | −32.7279 | − | 61.1127i | −1.24593 | − | 2.32652i | ||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 32.4853 | + | 32.4853i | 1.23491 | + | 1.23491i | ||||
\(693\) | −1.07107 | + | 2.24264i | −0.0406865 | + | 0.0851909i | ||||
\(694\) | 61.1127i | 2.31981i | ||||||||
\(695\) | −6.34315 | + | 12.6863i | −0.240609 | + | 0.481218i | ||||
\(696\) | 36.3848 | − | 6.24264i | 1.37916 | − | 0.236627i | ||||
\(697\) | 10.3431 | − | 10.3431i | 0.391775 | − | 0.391775i | ||||
\(698\) | 51.2132 | − | 51.2132i | 1.93845 | − | 1.93845i | ||||
\(699\) | 20.1421 | − | 3.45584i | 0.761846 | − | 0.130712i | ||||
\(700\) | 2.24264 | − | 15.6985i | 0.0847639 | − | 0.593347i | ||||
\(701\) | − | 21.3137i | − | 0.805008i | −0.915418 | − | 0.402504i | \(-0.868140\pi\) | ||
0.915418 | − | 0.402504i | \(-0.131860\pi\) | |||||||
\(702\) | −34.1421 | − | 9.65685i | −1.28861 | − | 0.364474i | ||||
\(703\) | 16.4853 | + | 16.4853i | 0.621754 | + | 0.621754i | ||||
\(704\) | 9.82843 | 0.370423 | ||||||||
\(705\) | −1.97056 | + | 6.51472i | −0.0742157 | + | 0.245358i | ||||
\(706\) | −7.41421 | −0.279038 | ||||||||
\(707\) | 7.51472 | + | 7.51472i | 0.282620 | + | 0.282620i | ||||
\(708\) | 15.3137 | − | 21.6569i | 0.575524 | − | 0.813914i | ||||
\(709\) | 6.68629i | 0.251109i | 0.992087 | + | 0.125554i | \(0.0400710\pi\) | ||||
−0.992087 | + | 0.125554i | \(0.959929\pi\) | |||||||
\(710\) | −74.1838 | + | 24.7279i | −2.78407 | + | 0.928022i | ||||
\(711\) | 14.6274 | − | 5.17157i | 0.548571 | − | 0.193949i | ||||
\(712\) | 5.17157 | − | 5.17157i | 0.193813 | − | 0.193813i | ||||
\(713\) | −46.2843 | + | 46.2843i | −1.73336 | + | 1.73336i | ||||
\(714\) | −2.34315 | − | 13.6569i | −0.0876900 | − | 0.511095i | ||||
\(715\) | −6.00000 | + | 2.00000i | −0.224387 | + | 0.0747958i | ||||
\(716\) | 15.8579i | 0.592636i | ||||||||
\(717\) | 22.3431 | + | 15.7990i | 0.834420 | + | 0.590024i | ||||
\(718\) | −10.4853 | − | 10.4853i | −0.391307 | − | 0.391307i | ||||
\(719\) | −50.7696 | −1.89338 | −0.946692 | − | 0.322139i | \(-0.895598\pi\) | ||||
−0.946692 | + | 0.322139i | \(0.895598\pi\) | |||||||
\(720\) | 2.48528 | − | 19.9706i | 0.0926210 | − | 0.744259i | ||||
\(721\) | 4.20101 | 0.156454 | ||||||||
\(722\) | 18.7782 | + | 18.7782i | 0.698851 | + | 0.698851i | ||||
\(723\) | 39.7990 | + | 28.1421i | 1.48014 | + | 1.04662i | ||||
\(724\) | − | 21.6569i | − | 0.804871i | ||||||
\(725\) | 14.4853 | + | 19.3137i | 0.537970 | + | 0.717293i | ||||
\(726\) | 0.707107 | + | 4.12132i | 0.0262432 | + | 0.152957i | ||||
\(727\) | −22.2132 | + | 22.2132i | −0.823842 | + | 0.823842i | −0.986657 | − | 0.162815i | \(-0.947943\pi\) |
0.162815 | + | 0.986657i | \(0.447943\pi\) | |||||||
\(728\) | −7.31371 | + | 7.31371i | −0.271064 | + | 0.271064i | ||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.6274i | 1.72458i | ||||||||
\(732\) | 40.1421 | − | 56.7696i | 1.48370 | − | 2.09826i | ||||
\(733\) | −35.7990 | − | 35.7990i | −1.32227 | − | 1.32227i | −0.911938 | − | 0.410328i | \(-0.865414\pi\) |
−0.410328 | − | 0.911938i | \(-0.634586\pi\) | |||||||
\(734\) | −71.3553 | −2.63377 | ||||||||
\(735\) | 21.5563 | − | 11.5442i | 0.795118 | − | 0.425813i | ||||
\(736\) | 11.7574 | 0.433382 | ||||||||
\(737\) | 3.58579 | + | 3.58579i | 0.132084 | + | 0.132084i | ||||
\(738\) | −23.8995 | − | 11.4142i | −0.879753 | − | 0.420163i | ||||
\(739\) | 30.6274i | 1.12665i | 0.826236 | + | 0.563324i | \(0.190478\pi\) | ||||
−0.826236 | + | 0.563324i | \(0.809522\pi\) | |||||||
\(740\) | −22.3137 | − | 66.9411i | −0.820268 | − | 2.46080i | ||||
\(741\) | 13.6569 | − | 2.34315i | 0.501697 | − | 0.0860776i | ||||
\(742\) | 2.00000 | − | 2.00000i | 0.0734223 | − | 0.0734223i | ||||
\(743\) | −22.0416 | + | 22.0416i | −0.808629 | + | 0.808629i | −0.984426 | − | 0.175797i | \(-0.943750\pi\) |
0.175797 | + | 0.984426i | \(0.443750\pi\) | |||||||
\(744\) | −66.5269 | + | 11.4142i | −2.43899 | + | 0.418465i | ||||
\(745\) | 20.0000 | + | 10.0000i | 0.732743 | + | 0.366372i | ||||
\(746\) | 69.9411i | 2.56073i | ||||||||
\(747\) | −19.4142 | − | 9.27208i | −0.710329 | − | 0.339248i | ||||
\(748\) | −10.8284 | − | 10.8284i | −0.395927 | − | 0.395927i | ||||
\(749\) | −9.65685 | −0.352854 | ||||||||
\(750\) | 43.9203 | − | 16.0208i | 1.60374 | − | 0.584997i | ||||
\(751\) | −1.37258 | −0.0500863 | −0.0250431 | − | 0.999686i | \(-0.507972\pi\) | ||||
−0.0250431 | + | 0.999686i | \(0.507972\pi\) | |||||||
\(752\) | 3.72792 | + | 3.72792i | 0.135943 | + | 0.135943i | ||||
\(753\) | 12.1421 | − | 17.1716i | 0.442484 | − | 0.625767i | ||||
\(754\) | − | 32.9706i | − | 1.20072i | ||||||
\(755\) | −36.2843 | − | 18.1421i | −1.32052 | − | 0.660260i | ||||
\(756\) | −14.3848 | + | 8.04163i | −0.523169 | + | 0.292471i | ||||
\(757\) | 5.82843 | − | 5.82843i | 0.211838 | − | 0.211838i | −0.593210 | − | 0.805048i | \(-0.702140\pi\) |
0.805048 | + | 0.593210i | \(0.202140\pi\) | |||||||
\(758\) | 0.242641 | − | 0.242641i | 0.00881311 | − | 0.00881311i | ||||
\(759\) | 2.17157 | + | 12.6569i | 0.0788231 | + | 0.459415i | ||||
\(760\) | 8.82843 | + | 26.4853i | 0.320241 | + | 0.960722i | ||||
\(761\) | 18.4853i | 0.670091i | 0.942202 | + | 0.335045i | \(0.108752\pi\) | ||||
−0.942202 | + | 0.335045i | \(0.891248\pi\) | |||||||
\(762\) | 6.82843 | + | 4.82843i | 0.247368 | + | 0.174915i | ||||
\(763\) | 5.17157 | + | 5.17157i | 0.187224 | + | 0.187224i | ||||
\(764\) | 43.3137 | 1.56703 | ||||||||
\(765\) | 21.1716 | − | 16.4853i | 0.765460 | − | 0.596027i | ||||
\(766\) | −27.5563 | −0.995651 | ||||||||
\(767\) | −8.00000 | − | 8.00000i | −0.288863 | − | 0.288863i | ||||
\(768\) | 42.3848 | + | 29.9706i | 1.52943 | + | 1.08147i | ||||
\(769\) | 7.37258i | 0.265862i | 0.991125 | + | 0.132931i | \(0.0424389\pi\) | ||||
−0.991125 | + | 0.132931i | \(0.957561\pi\) | |||||||
\(770\) | −2.00000 | + | 4.00000i | −0.0720750 | + | 0.144150i | ||||
\(771\) | 1.58579 | + | 9.24264i | 0.0571107 | + | 0.332866i | ||||
\(772\) | −30.6274 | + | 30.6274i | −1.10230 | + | 1.10230i | ||||
\(773\) | 0.656854 | − | 0.656854i | 0.0236254 | − | 0.0236254i | −0.695195 | − | 0.718821i | \(-0.744682\pi\) |
0.718821 | + | 0.695195i | \(0.244682\pi\) | |||||||
\(774\) | 79.5980 | − | 28.1421i | 2.86109 | − | 1.01155i | ||||
\(775\) | −26.4853 | − | 35.3137i | −0.951379 | − | 1.26851i | ||||
\(776\) | − | 4.10051i | − | 0.147200i | ||||||
\(777\) | −6.82843 | + | 9.65685i | −0.244968 | + | 0.346438i | ||||
\(778\) | −9.07107 | − | 9.07107i | −0.325214 | − | 0.325214i | ||||
\(779\) | 10.3431 | 0.370582 | ||||||||
\(780\) | −40.1421 | − | 12.1421i | −1.43732 | − | 0.434758i | ||||
\(781\) | 14.4853 | 0.518324 | ||||||||
\(782\) | −50.6274 | − | 50.6274i | −1.81043 | − | 1.81043i | ||||
\(783\) | 6.82843 | − | 24.1421i | 0.244028 | − | 0.862770i | ||||
\(784\) | − | 18.9411i | − | 0.676469i | ||||||
\(785\) | 22.4558 | − | 7.48528i | 0.801483 | − | 0.267161i | ||||
\(786\) | 4.82843 | − | 0.828427i | 0.172224 | − | 0.0295490i | ||||
\(787\) | −31.4142 | + | 31.4142i | −1.11980 | + | 1.11980i | −0.128025 | + | 0.991771i | \(0.540864\pi\) |
−0.991771 | + | 0.128025i | \(0.959136\pi\) | |||||||
\(788\) | 54.1421 | − | 54.1421i | 1.92873 | − | 1.92873i | ||||
\(789\) | −24.7279 | + | 4.24264i | −0.880337 | + | 0.151042i | ||||
\(790\) | 26.4853 | − | 8.82843i | 0.942304 | − | 0.314101i | ||||
\(791\) | 0.201010i | 0.00714710i | ||||||||
\(792\) | −5.70711 | + | 11.9497i | −0.202793 | + | 0.424616i | ||||
\(793\) | −20.9706 | − | 20.9706i | −0.744687 | − | 0.744687i | ||||
\(794\) | 40.3848 | 1.43320 | ||||||||
\(795\) | 5.24264 | + | 1.58579i | 0.185937 | + | 0.0562420i | ||||
\(796\) | 9.51472 | 0.337240 | ||||||||
\(797\) | 7.97056 | + | 7.97056i | 0.282332 | + | 0.282332i | 0.834038 | − | 0.551707i | \(-0.186023\pi\) |
−0.551707 | + | 0.834038i | \(0.686023\pi\) | |||||||
\(798\) | 5.65685 | − | 8.00000i | 0.200250 | − | 0.283197i | ||||
\(799\) | 7.02944i | 0.248684i | ||||||||
\(800\) | −1.12132 | + | 7.84924i | −0.0396447 | + | 0.277513i | ||||
\(801\) | −1.65685 | − | 4.68629i | −0.0585421 | − | 0.165582i | ||||
\(802\) | −41.5563 | + | 41.5563i | −1.46741 | + | 1.46741i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.68629 | + | 33.1421i | 0.200540 | + | 1.16883i | ||||
\(805\) | −6.14214 | + | 12.2843i | −0.216482 | + | 0.432964i | ||||
\(806\) | 60.2843i | 2.12342i | ||||||||
\(807\) | −19.7990 | − | 14.0000i | −0.696957 | − | 0.492823i | ||||
\(808\) | 40.0416 | + | 40.0416i | 1.40866 | + | 1.40866i | ||||
\(809\) | 44.1421 | 1.55195 | 0.775977 | − | 0.630761i | \(-0.217257\pi\) | ||||
0.775977 | + | 0.630761i | \(0.217257\pi\) | |||||||
\(810\) | −40.9203 | − | 26.1924i | −1.43779 | − | 0.920307i | ||||
\(811\) | −30.3431 | −1.06549 | −0.532746 | − | 0.846275i | \(-0.678840\pi\) | ||||
−0.532746 | + | 0.846275i | \(0.678840\pi\) | |||||||
\(812\) | −10.8284 | − | 10.8284i | −0.380003 | − | 0.380003i | ||||
\(813\) | 12.0000 | + | 8.48528i | 0.420858 | + | 0.297592i | ||||
\(814\) | 19.8995i | 0.697477i | ||||||||
\(815\) | 6.41421 | + | 19.2426i | 0.224680 | + | 0.674040i | ||||
\(816\) | −3.51472 | − | 20.4853i | −0.123040 | − | 0.717128i | ||||
\(817\) | −23.3137 | + | 23.3137i | −0.815643 | + | 0.815643i | ||||
\(818\) | 2.58579 | − | 2.58579i | 0.0904099 | − | 0.0904099i | ||||
\(819\) | 2.34315 | + | 6.62742i | 0.0818761 | + | 0.231581i | ||||
\(820\) | −28.0000 | − | 14.0000i | −0.977802 | − | 0.488901i | ||||
\(821\) | − | 11.6569i | − | 0.406827i | −0.979093 | − | 0.203414i | \(-0.934796\pi\) | ||
0.979093 | − | 0.203414i | \(-0.0652036\pi\) | |||||||
\(822\) | −19.8995 | + | 28.1421i | −0.694075 | + | 0.981570i | ||||
\(823\) | −15.5858 | − | 15.5858i | −0.543286 | − | 0.543286i | 0.381204 | − | 0.924491i | \(-0.375509\pi\) |
−0.924491 | + | 0.381204i | \(0.875509\pi\) | |||||||
\(824\) | 22.3848 | 0.779811 | ||||||||
\(825\) | −8.65685 | + | 0.242641i | −0.301393 | + | 0.00844766i | ||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | −20.0416 | − | 20.0416i | −0.696916 | − | 0.696916i | 0.266828 | − | 0.963744i | \(-0.414024\pi\) |
−0.963744 | + | 0.266828i | \(0.914024\pi\) | |||||||
\(828\) | −36.6985 | + | 76.8406i | −1.27536 | + | 2.67040i | ||||
\(829\) | 22.9706i | 0.797801i | 0.916994 | + | 0.398900i | \(0.130608\pi\) | ||||
−0.916994 | + | 0.398900i | \(0.869392\pi\) | |||||||
\(830\) | −34.6274 | − | 17.3137i | −1.20194 | − | 0.600968i | ||||
\(831\) | 3.65685 | − | 0.627417i | 0.126855 | − | 0.0217649i | ||||
\(832\) | 19.6569 | − | 19.6569i | 0.681479 | − | 0.681479i | ||||
\(833\) | 17.8579 | − | 17.8579i | 0.618738 | − | 0.618738i | ||||
\(834\) | 26.1421 | − | 4.48528i | 0.905228 | − | 0.155313i | ||||
\(835\) | 10.7279 | + | 32.1838i | 0.371255 | + | 1.11377i | ||||
\(836\) | − | 10.8284i | − | 0.374509i | ||||||
\(837\) | −12.4853 | + | 44.1421i | −0.431554 | + | 1.52578i | ||||
\(838\) | 60.5269 | + | 60.5269i | 2.09087 | + | 2.09087i | ||||
\(839\) | 10.3431 | 0.357085 | 0.178543 | − | 0.983932i | \(-0.442862\pi\) | ||||
0.178543 | + | 0.983932i | \(0.442862\pi\) | |||||||
\(840\) | −12.4853 | + | 6.68629i | −0.430783 | + | 0.230699i | ||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | −6.82843 | − | 6.82843i | −0.235323 | − | 0.235323i | ||||
\(843\) | −16.6274 | + | 23.5147i | −0.572679 | + | 0.809890i | ||||
\(844\) | 47.7990i | 1.64531i | ||||||||
\(845\) | 5.00000 | − | 10.0000i | 0.172005 | − | 0.344010i | ||||
\(846\) | 12.0000 | − | 4.24264i | 0.412568 | − | 0.145865i | ||||
\(847\) | 0.585786 | − | 0.585786i | 0.0201279 | − | 0.0201279i | ||||
\(848\) | 3.00000 | − | 3.00000i | 0.103020 | − | 0.103020i | ||||
\(849\) | 0.384776 | + | 2.24264i | 0.0132055 | + | 0.0769672i | ||||
\(850\) | 38.6274 | − | 28.9706i | 1.32491 | − | 0.993682i | ||||
\(851\) | 61.1127i | 2.09492i | ||||||||
\(852\) | 78.4264 | + | 55.4558i | 2.68684 | + | 1.89989i | ||||
\(853\) | −10.1421 | − | 10.1421i | −0.347260 | − | 0.347260i | 0.511828 | − | 0.859088i | \(-0.328969\pi\) |
−0.859088 | + | 0.511828i | \(0.828969\pi\) | |||||||
\(854\) | −20.9706 | −0.717598 | ||||||||
\(855\) | 18.8284 | + | 2.34315i | 0.643919 | + | 0.0801339i | ||||
\(856\) | −51.4558 | −1.75872 | ||||||||
\(857\) | −0.485281 | − | 0.485281i | −0.0165769 | − | 0.0165769i | 0.698770 | − | 0.715347i | \(-0.253731\pi\) |
−0.715347 | + | 0.698770i | \(0.753731\pi\) | |||||||
\(858\) | 9.65685 | + | 6.82843i | 0.329680 | + | 0.233119i | ||||
\(859\) | − | 36.0000i | − | 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | 94.6690 | − | 31.5563i | 3.22819 | − | 1.07606i | ||||
\(861\) | 0.887302 | + | 5.17157i | 0.0302392 | + | 0.176247i | ||||
\(862\) | 30.1421 | − | 30.1421i | 1.02665 | − | 1.02665i | ||||
\(863\) | 18.5563 | − | 18.5563i | 0.631665 | − | 0.631665i | −0.316820 | − | 0.948486i | \(-0.602615\pi\) |
0.948486 | + | 0.316820i | \(0.102615\pi\) | |||||||
\(864\) | 7.19239 | − | 4.02082i | 0.244690 | − | 0.136791i | ||||
\(865\) | 25.4558 | − | 8.48528i | 0.865525 | − | 0.288508i | ||||
\(866\) | 76.1838i | 2.58883i | ||||||||
\(867\) | −1.00000 | + | 1.41421i | −0.0339618 | + | 0.0480292i | ||||
\(868\) | 19.7990 | + | 19.7990i | 0.672022 | + | 0.672022i | ||||
\(869\) | −5.17157 | −0.175434 | ||||||||
\(870\) | 13.0711 | − | 43.2132i | 0.443151 | − | 1.46506i | ||||
\(871\) | 14.3431 | 0.485999 | ||||||||
\(872\) | 27.5563 | + | 27.5563i | 0.933176 | + | 0.933176i | ||||
\(873\) | −2.51472 | − | 1.20101i | −0.0851103 | − | 0.0406480i | ||||
\(874\) | − | 50.6274i | − | 1.71250i | ||||||
\(875\) | −7.61522 | − | 5.27208i | −0.257442 | − | 0.178229i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.6274 | + | 38.6274i | −1.30436 | + | 1.30436i | −0.378930 | + | 0.925425i | \(0.623708\pi\) |
−0.925425 | + | 0.378930i | \(0.876292\pi\) | |||||||
\(878\) | −26.1421 | + | 26.1421i | −0.882254 | + | 0.882254i | ||||
\(879\) | 18.4853 | − | 3.17157i | 0.623493 | − | 0.106974i | ||||
\(880\) | −3.00000 | + | 6.00000i | −0.101130 | + | 0.202260i | ||||
\(881\) | − | 20.9706i | − | 0.706516i | −0.935526 | − | 0.353258i | \(-0.885074\pi\) | ||
0.935526 | − | 0.353258i | \(-0.114926\pi\) | |||||||
\(882\) | −41.2635 | − | 19.7071i | −1.38941 | − | 0.663573i | ||||
\(883\) | −6.41421 | − | 6.41421i | −0.215855 | − | 0.215855i | 0.590894 | − | 0.806749i | \(-0.298775\pi\) |
−0.806749 | + | 0.590894i | \(0.798775\pi\) | |||||||
\(884\) | −43.3137 | −1.45680 | ||||||||
\(885\) | −7.31371 | − | 13.6569i | −0.245848 | − | 0.459070i | ||||
\(886\) | 99.8406 | 3.35421 | ||||||||
\(887\) | 18.2426 | + | 18.2426i | 0.612528 | + | 0.612528i | 0.943604 | − | 0.331076i | \(-0.107412\pi\) |
−0.331076 | + | 0.943604i | \(0.607412\pi\) | |||||||
\(888\) | −36.3848 | + | 51.4558i | −1.22099 | + | 1.72675i | ||||
\(889\) | − | 1.65685i | − | 0.0555691i | ||||||
\(890\) | −2.82843 | − | 8.48528i | −0.0948091 | − | 0.284427i | ||||
\(891\) | 5.65685 | + | 7.00000i | 0.189512 | + | 0.234509i | ||||
\(892\) | −55.7279 | + | 55.7279i | −1.86591 | + | 1.86591i | ||||
\(893\) | −3.51472 | + | 3.51472i | −0.117616 | + | 0.117616i | ||||
\(894\) | −7.07107 | − | 41.2132i | −0.236492 | − | 1.37838i | ||||
\(895\) | 8.28427 | + | 4.14214i | 0.276913 | + | 0.138456i | ||||
\(896\) | − | 17.0294i | − | 0.568914i | ||||||
\(897\) | 29.6569 | + | 20.9706i | 0.990214 | + | 0.700187i | ||||
\(898\) | 63.1127 | + | 63.1127i | 2.10610 | + | 2.10610i | ||||
\(899\) | −42.6274 | −1.42170 | ||||||||
\(900\) | −47.7990 | − | 31.8284i | −1.59330 | − | 1.06095i | ||||
\(901\) | 5.65685 | 0.188457 | ||||||||
\(902\) | 6.24264 | + | 6.24264i | 0.207857 | + | 0.207857i | ||||
\(903\) | −13.6569 | − | 9.65685i | −0.454472 | − | 0.321360i | ||||
\(904\) | 1.07107i | 0.0356232i | ||||||||
\(905\) | −11.3137 | − | 5.65685i | −0.376080 | − | 0.188040i | ||||
\(906\) | 12.8284 | + | 74.7696i | 0.426196 | + | 2.48405i | ||||
\(907\) | −19.0416 | + | 19.0416i | −0.632267 | + | 0.632267i | −0.948636 | − | 0.316369i | \(-0.897536\pi\) |
0.316369 | + | 0.948636i | \(0.397536\pi\) | |||||||
\(908\) | 6.72792 | − | 6.72792i | 0.223274 | − | 0.223274i | ||||
\(909\) | 36.2843 | − | 12.8284i | 1.20347 | − | 0.425492i | ||||
\(910\) | 4.00000 | + | 12.0000i | 0.132599 | + | 0.397796i | ||||
\(911\) | − | 56.0000i | − | 1.85536i | −0.373373 | − | 0.927681i | \(-0.621799\pi\) | ||
0.373373 | − | 0.927681i | \(-0.378201\pi\) | |||||||
\(912\) | 8.48528 | − | 12.0000i | 0.280976 | − | 0.397360i | ||||
\(913\) | 5.07107 | + | 5.07107i | 0.167828 | + | 0.167828i | ||||
\(914\) | 35.7990 | 1.18413 | ||||||||
\(915\) | −19.1716 | − | 35.7990i | −0.633793 | − | 1.18348i | ||||
\(916\) | 6.34315 | 0.209583 | ||||||||
\(917\) | −0.686292 | − | 0.686292i | −0.0226633 | − | 0.0226633i | ||||
\(918\) | −48.2843 | − | 13.6569i | −1.59362 | − | 0.450743i | ||||
\(919\) | − | 30.6274i | − | 1.01031i | −0.863030 | − | 0.505153i | \(-0.831436\pi\) | ||
0.863030 | − | 0.505153i | \(-0.168564\pi\) | |||||||
\(920\) | −32.7279 | + | 65.4558i | −1.07901 | + | 2.15802i | ||||
\(921\) | −19.0711 | + | 3.27208i | −0.628413 | + | 0.107819i | ||||
\(922\) | 52.0416 | − | 52.0416i | 1.71390 | − | 1.71390i | ||||
\(923\) | 28.9706 | − | 28.9706i | 0.953578 | − | 0.953578i | ||||
\(924\) | 5.41421 | − | 0.928932i | 0.178115 | − | 0.0305596i | ||||
\(925\) | −40.7990 | − | 5.82843i | −1.34146 | − | 0.191638i | ||||
\(926\) | − | 46.8701i | − | 1.54025i | ||||||
\(927\) | 6.55635 | − | 13.7279i | 0.215339 | − | 0.450884i | ||||
\(928\) | 5.41421 | + | 5.41421i | 0.177730 | + | 0.177730i | ||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | −23.8995 | + | 79.0122i | −0.783695 | + | 2.59091i | ||||
\(931\) | 17.8579 | 0.585268 | ||||||||
\(932\) | −31.9411 | − | 31.9411i | −1.04627 | − | 1.04627i | ||||
\(933\) | −0.142136 | + | 0.201010i | −0.00465331 | + | 0.00658078i | ||||
\(934\) | − | 8.24264i | − | 0.269707i | ||||||
\(935\) | −8.48528 | + | 2.82843i | −0.277498 | + | 0.0924995i | ||||
\(936\) | 12.4853 | + | 35.3137i | 0.408094 | + | 1.15426i | ||||
\(937\) | 22.9706 | − | 22.9706i | 0.750416 | − | 0.750416i | −0.224141 | − | 0.974557i | \(-0.571958\pi\) |
0.974557 | + | 0.224141i | \(0.0719577\pi\) | |||||||
\(938\) | 7.17157 | − | 7.17157i | 0.234160 | − | 0.234160i | ||||
\(939\) | −0.556349 | − | 3.24264i | −0.0181558 | − | 0.105820i | ||||
\(940\) | 14.2721 | − | 4.75736i | 0.465504 | − | 0.155168i | ||||
\(941\) | − | 25.1127i | − | 0.818651i | −0.912389 | − | 0.409325i | \(-0.865764\pi\) | ||
0.912389 | − | 0.409325i | \(-0.134236\pi\) | |||||||
\(942\) | −36.1421 | − | 25.5563i | −1.17757 | − | 0.832671i | ||||
\(943\) | 19.1716 | + | 19.1716i | 0.624312 | + | 0.624312i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0.443651 | + | 9.61522i | 0.0144320 | + | 0.312783i | ||||
\(946\) | −28.1421 | −0.914980 | ||||||||
\(947\) | 8.75736 | + | 8.75736i | 0.284576 | + | 0.284576i | 0.834931 | − | 0.550355i | \(-0.185508\pi\) |
−0.550355 | + | 0.834931i | \(0.685508\pi\) | |||||||
\(948\) | −28.0000 | − | 19.7990i | −0.909398 | − | 0.643041i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 33.7990 | + | 4.82843i | 1.09658 | + | 0.156655i | ||||
\(951\) | −8.41421 | − | 49.0416i | −0.272850 | − | 1.59028i | ||||
\(952\) | −10.3431 | + | 10.3431i | −0.335223 | + | 0.335223i | ||||
\(953\) | 33.7990 | − | 33.7990i | 1.09486 | − | 1.09486i | 0.0998546 | − | 0.995002i | \(-0.468162\pi\) |
0.995002 | − | 0.0998546i | \(-0.0318378\pi\) | |||||||
\(954\) | −3.41421 | − | 9.65685i | −0.110539 | − | 0.312652i | ||||
\(955\) | 11.3137 | − | 22.6274i | 0.366103 | − | 0.732206i | ||||
\(956\) | − | 60.4853i | − | 1.95623i | ||||||
\(957\) | −4.82843 | + | 6.82843i | −0.156081 | + | 0.220732i | ||||
\(958\) | 3.17157 | + | 3.17157i | 0.102469 | + | 0.102469i | ||||
\(959\) | 6.82843 | 0.220501 | ||||||||
\(960\) | 33.5563 | − | 17.9706i | 1.08303 | − | 0.579997i | ||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | 39.7990 | + | 39.7990i | 1.28317 | + | 1.28317i | ||||
\(963\) | −15.0711 | + | 31.5563i | −0.485658 | + | 1.01689i | ||||
\(964\) | − | 107.740i | − | 3.47008i | ||||||
\(965\) | 8.00000 | + | 24.0000i | 0.257529 | + | 0.772587i | ||||
\(966\) | 25.3137 | − | 4.34315i | 0.814455 | − | 0.139738i | ||||
\(967\) | 1.61522 | − | 1.61522i | 0.0519421 | − | 0.0519421i | −0.680659 | − | 0.732601i | \(-0.738306\pi\) |
0.732601 | + | 0.680659i | \(0.238306\pi\) | |||||||
\(968\) | 3.12132 | − | 3.12132i | 0.100323 | − | 0.100323i | ||||
\(969\) | 19.3137 | − | 3.31371i | 0.620446 | − | 0.106452i | ||||
\(970\) | −4.48528 | − | 2.24264i | −0.144014 | − | 0.0720069i | ||||
\(971\) | − | 20.0000i | − | 0.641831i | −0.947108 | − | 0.320915i | \(-0.896010\pi\) | ||
0.947108 | − | 0.320915i | \(-0.103990\pi\) | |||||||
\(972\) | 3.82843 | + | 59.5563i | 0.122797 | + | 1.91027i | ||||
\(973\) | −3.71573 | − | 3.71573i | −0.119121 | − | 0.119121i | ||||
\(974\) | −46.8701 | −1.50181 | ||||||||
\(975\) | −16.8284 | + | 17.7990i | −0.538941 | + | 0.570024i | ||||
\(976\) | −31.4558 | −1.00688 | ||||||||
\(977\) | −24.1127 | − | 24.1127i | −0.771434 | − | 0.771434i | 0.206924 | − | 0.978357i | \(-0.433655\pi\) |
−0.978357 | + | 0.206924i | \(0.933655\pi\) | |||||||
\(978\) | 21.8995 | − | 30.9706i | 0.700269 | − | 0.990329i | ||||
\(979\) | 1.65685i | 0.0529533i | ||||||||
\(980\) | −48.3431 | − | 24.1716i | −1.54427 | − | 0.772133i | ||||
\(981\) | 24.9706 | − | 8.82843i | 0.797249 | − | 0.281870i | ||||
\(982\) | 34.1421 | − | 34.1421i | 1.08952 | − | 1.08952i | ||||
\(983\) | 1.72792 | − | 1.72792i | 0.0551122 | − | 0.0551122i | −0.679014 | − | 0.734126i | \(-0.737592\pi\) |
0.734126 | + | 0.679014i | \(0.237592\pi\) | |||||||
\(984\) | 4.72792 | + | 27.5563i | 0.150721 | + | 0.878464i | ||||
\(985\) | −14.1421 | − | 42.4264i | −0.450606 | − | 1.35182i | ||||
\(986\) | − | 46.6274i | − | 1.48492i | ||||||
\(987\) | −2.05887 | − | 1.45584i | −0.0655347 | − | 0.0463400i | ||||
\(988\) | −21.6569 | − | 21.6569i | −0.688996 | − | 0.688996i | ||||
\(989\) | −86.4264 | −2.74820 | ||||||||
\(990\) | 9.94975 | + | 12.7782i | 0.316224 | + | 0.406117i | ||||
\(991\) | 19.1716 | 0.609005 | 0.304503 | − | 0.952512i | \(-0.401510\pi\) | ||||
0.304503 | + | 0.952512i | \(0.401510\pi\) | |||||||
\(992\) | −9.89949 | − | 9.89949i | −0.314309 | − | 0.314309i | ||||
\(993\) | −14.8284 | − | 10.4853i | −0.470566 | − | 0.332740i | ||||
\(994\) | − | 28.9706i | − | 0.918890i | ||||||
\(995\) | 2.48528 | − | 4.97056i | 0.0787887 | − | 0.157577i | ||||
\(996\) | 8.04163 | + | 46.8701i | 0.254809 | + | 1.48513i | ||||
\(997\) | −36.7696 | + | 36.7696i | −1.16450 | + | 1.16450i | −0.181025 | + | 0.983479i | \(0.557941\pi\) |
−0.983479 | + | 0.181025i | \(0.942059\pi\) | |||||||
\(998\) | −32.7279 | + | 32.7279i | −1.03598 | + | 1.03598i | ||||
\(999\) | 20.8995 | + | 37.3848i | 0.661231 | + | 1.18280i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 165.2.k.b.23.2 | yes | 4 | |
3.2 | odd | 2 | 165.2.k.a.23.1 | ✓ | 4 | ||
5.2 | odd | 4 | 165.2.k.a.122.1 | yes | 4 | ||
5.3 | odd | 4 | 825.2.k.f.782.2 | 4 | |||
5.4 | even | 2 | 825.2.k.c.518.1 | 4 | |||
15.2 | even | 4 | inner | 165.2.k.b.122.2 | yes | 4 | |
15.8 | even | 4 | 825.2.k.c.782.1 | 4 | |||
15.14 | odd | 2 | 825.2.k.f.518.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.k.a.23.1 | ✓ | 4 | 3.2 | odd | 2 | ||
165.2.k.a.122.1 | yes | 4 | 5.2 | odd | 4 | ||
165.2.k.b.23.2 | yes | 4 | 1.1 | even | 1 | trivial | |
165.2.k.b.122.2 | yes | 4 | 15.2 | even | 4 | inner | |
825.2.k.c.518.1 | 4 | 5.4 | even | 2 | |||
825.2.k.c.782.1 | 4 | 15.8 | even | 4 | |||
825.2.k.f.518.2 | 4 | 15.14 | odd | 2 | |||
825.2.k.f.782.2 | 4 | 5.3 | odd | 4 |