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: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 122.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.122 |
Dual form | 165.2.k.a.23.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | −0.235147 | + | 0.971960i | \(0.575557\pi\) |
−0.971960 | + | 0.235147i | \(0.924443\pi\) | |||||||
\(3\) | −1.00000 | + | 1.41421i | −0.577350 | + | 0.816497i | ||||
\(4\) | − | 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 | 0.587684 | − | 0.809091i | \(-0.300040\pi\) |
−0.809091 | + | 0.587684i | \(0.800040\pi\) | |||||||
\(8\) | 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 | ||||||
\(12\) | 5.41421 | + | 3.82843i | 1.56295 | + | 1.10517i | ||||
\(13\) | −2.00000 | + | 2.00000i | −0.554700 | + | 0.554700i | −0.927794 | − | 0.373094i | \(-0.878297\pi\) |
0.373094 | + | 0.927794i | \(0.378297\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0.585786 | − | 3.82843i | 0.151249 | − | 0.988496i | ||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 2.82843 | − | 2.82843i | 0.685994 | − | 0.685994i | −0.275350 | − | 0.961344i | \(-0.588794\pi\) |
0.961344 | + | 0.275350i | \(0.0887937\pi\) | |||||||
\(18\) | 6.53553 | + | 3.12132i | 1.54044 | + | 0.735702i | ||||
\(19\) | 2.82843i | 0.648886i | 0.945905 | + | 0.324443i | \(0.105177\pi\) | ||||
−0.945905 | + | 0.324443i | \(0.894823\pi\) | |||||||
\(20\) | 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 | −0.995189 | − | 0.0979775i | \(-0.968763\pi\) |
−0.0979775 | − | 0.995189i | \(-0.531237\pi\) | |||||||
\(24\) | −7.53553 | + | 1.29289i | −1.53818 | + | 0.263911i | ||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | − | 6.82843i | − | 1.33916i | ||||||
\(27\) | 5.00000 | + | 1.41421i | 0.962250 | + | 0.272166i | ||||
\(28\) | −2.24264 | + | 2.24264i | −0.423819 | + | 0.423819i | ||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | 5.53553 | + | 7.53553i | 1.01065 | + | 1.37579i | ||||
\(31\) | −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 | ||||
\(33\) | 1.41421 | + | 1.00000i | 0.246183 | + | 0.174078i | ||||
\(34\) | 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 | 0.0409727 | − | 0.999160i | \(-0.486954\pi\) |
−0.999160 | + | 0.0409727i | \(0.986954\pi\) | |||||||
\(38\) | −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 | \(0.907823\pi\) | |||||||
\(42\) | −2.00000 | + | 2.82843i | −0.308607 | + | 0.436436i | ||||
\(43\) | −8.24264 | + | 8.24264i | −1.25699 | + | 1.25699i | −0.304469 | + | 0.952522i | \(0.598479\pi\) |
−0.952522 | + | 0.304469i | \(0.901521\pi\) | |||||||
\(44\) | −3.82843 | −0.577157 | ||||||||
\(45\) | 4.82843 | + | 4.65685i | 0.719779 | + | 0.694203i | ||||
\(46\) | 17.8995 | 2.63914 | ||||||||
\(47\) | 1.24264 | − | 1.24264i | 0.181258 | − | 0.181258i | −0.610646 | − | 0.791904i | \(-0.709090\pi\) |
0.791904 | + | 0.610646i | \(0.209090\pi\) | |||||||
\(48\) | 3.00000 | − | 4.24264i | 0.433013 | − | 0.612372i | ||||
\(49\) | − | 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 | \(-0.219034\pi\) |
−0.635083 | + | 0.772444i | \(0.719034\pi\) | |||||||
\(54\) | −10.9497 | + | 6.12132i | −1.49007 | + | 0.833006i | ||||
\(55\) | 1.00000 | + | 2.00000i | 0.134840 | + | 0.269680i | ||||
\(56\) | − | 3.65685i | − | 0.488668i | ||||||
\(57\) | −4.00000 | − | 2.82843i | −0.529813 | − | 0.374634i | ||||
\(58\) | 8.24264 | − | 8.24264i | 1.08231 | − | 1.08231i | ||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | −14.6569 | − | 2.24264i | −1.89219 | − | 0.289524i | ||||
\(61\) | 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 | ||||
\(63\) | −1.07107 | + | 2.24264i | −0.134942 | + | 0.282546i | ||||
\(64\) | − | 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 | 0.453290 | − | 0.891363i | \(-0.350250\pi\) |
−0.891363 | + | 0.453290i | \(0.850250\pi\) | |||||||
\(68\) | −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 | \(0.670748\pi\) | |||||||
\(72\) | 5.70711 | − | 11.9497i | 0.672589 | − | 1.40829i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 19.8995 | 2.31327 | ||||||||
\(75\) | 2.65685 | + | 8.24264i | 0.306787 | + | 0.951778i | ||||
\(76\) | 10.8284 | 1.24211 | ||||||||
\(77\) | −0.585786 | + | 0.585786i | −0.0667566 | + | 0.0667566i | ||||
\(78\) | 9.65685 | + | 6.82843i | 1.09342 | + | 0.773167i | ||||
\(79\) | 5.17157i | 0.581847i | 0.956746 | + | 0.290924i | \(0.0939626\pi\) | ||||
−0.956746 | + | 0.290924i | \(0.906037\pi\) | |||||||
\(80\) | 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 | \(-0.121233\pi\) |
−0.371722 | + | 0.928344i | \(0.621233\pi\) | |||||||
\(84\) | −0.928932 | − | 5.41421i | −0.101355 | − | 0.590739i | ||||
\(85\) | −2.82843 | + | 8.48528i | −0.306786 | + | 0.920358i | ||||
\(86\) | − | 28.1421i | − | 3.03464i | ||||||
\(87\) | 4.82843 | − | 6.82843i | 0.517662 | − | 0.732084i | ||||
\(88\) | 3.12132 | − | 3.12132i | 0.332734 | − | 0.332734i | ||||
\(89\) | 1.65685 | 0.175626 | 0.0878131 | − | 0.996137i | \(-0.472012\pi\) | ||||
0.0878131 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(90\) | −16.1924 | + | 0.292893i | −1.70683 | + | 0.0308737i | ||||
\(91\) | 2.34315 | 0.245628 | ||||||||
\(92\) | −20.0711 | + | 20.0711i | −2.09255 | + | 2.09255i | ||||
\(93\) | 8.82843 | − | 12.4853i | 0.915465 | − | 1.29466i | ||||
\(94\) | 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 | 0.672973 | − | 0.739667i | \(-0.265017\pi\) |
−0.739667 | + | 0.672973i | \(0.765017\pi\) | |||||||
\(98\) | 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 | \(-0.220336\pi\) | |||||||
\(102\) | −13.6569 | − | 9.65685i | −1.35223 | − | 0.956171i | ||||
\(103\) | −3.58579 | + | 3.58579i | −0.353318 | + | 0.353318i | −0.861343 | − | 0.508025i | \(-0.830376\pi\) |
0.508025 | + | 0.861343i | \(0.330376\pi\) | |||||||
\(104\) | −12.4853 | −1.22428 | ||||||||
\(105\) | −2.58579 | + | 1.89949i | −0.252347 | + | 0.185372i | ||||
\(106\) | −3.41421 | −0.331618 | ||||||||
\(107\) | −8.24264 | + | 8.24264i | −0.796846 | + | 0.796846i | −0.982597 | − | 0.185751i | \(-0.940528\pi\) |
0.185751 | + | 0.982597i | \(0.440528\pi\) | |||||||
\(108\) | 5.41421 | − | 19.1421i | 0.520983 | − | 1.84195i | ||||
\(109\) | 8.82843i | 0.845610i | 0.906221 | + | 0.422805i | \(0.138954\pi\) | ||||
−0.906221 | + | 0.422805i | \(0.861046\pi\) | |||||||
\(110\) | −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 | \(-0.253633\pi\) |
−0.715131 | + | 0.698991i | \(0.753633\pi\) | |||||||
\(114\) | 11.6569 | − | 2.00000i | 1.09176 | − | 0.187317i | ||||
\(115\) | 15.7279 | + | 5.24264i | 1.46664 | + | 0.488879i | ||||
\(116\) | 18.4853i | 1.71632i | ||||||||
\(117\) | 7.65685 | + | 3.65685i | 0.707876 | + | 0.338076i | ||||
\(118\) | 6.82843 | − | 6.82843i | 0.628608 | − | 0.628608i | ||||
\(119\) | −3.31371 | −0.303767 | ||||||||
\(120\) | 13.7782 | − | 10.1213i | 1.25777 | − | 0.923946i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −17.8995 | + | 17.8995i | −1.62054 | + | 1.62054i | ||||
\(123\) | −5.17157 | − | 3.65685i | −0.466305 | − | 0.329727i | ||||
\(124\) | 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 | 0.641572 | − | 0.767063i | \(-0.278283\pi\) |
−0.767063 | + | 0.641572i | \(0.778283\pi\) | |||||||
\(128\) | 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 | \(0.983702\pi\) | |||||||
\(132\) | 3.82843 | − | 5.41421i | 0.333222 | − | 0.471247i | ||||
\(133\) | 1.65685 | − | 1.65685i | 0.143667 | − | 0.143667i | ||||
\(134\) | 12.2426 | 1.05760 | ||||||||
\(135\) | −11.4142 | + | 2.17157i | −0.982379 | + | 0.186899i | ||||
\(136\) | 17.6569 | 1.51406 | ||||||||
\(137\) | 5.82843 | − | 5.82843i | 0.497956 | − | 0.497956i | −0.412845 | − | 0.910801i | \(-0.635465\pi\) |
0.910801 | + | 0.412845i | \(0.135465\pi\) | |||||||
\(138\) | −17.8995 | + | 25.3137i | −1.52371 | + | 2.15485i | ||||
\(139\) | − | 6.34315i | − | 0.538019i | −0.963138 | − | 0.269009i | \(-0.913304\pi\) | ||
0.963138 | − | 0.269009i | \(-0.0866962\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 8.92893 | + | 6.31371i | 0.736446 | + | 0.520746i | ||||
\(148\) | −22.3137 | + | 22.3137i | −1.83418 | + | 1.83418i | ||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −18.6066 | − | 9.53553i | −1.51922 | − | 0.778573i | ||||
\(151\) | −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 | ||||
\(153\) | −10.8284 | − | 5.17157i | −0.875426 | − | 0.418097i | ||||
\(154\) | − | 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 | 0.939617 | − | 0.342227i | \(-0.111181\pi\) |
−0.342227 | + | 0.939617i | \(0.611181\pi\) | |||||||
\(158\) | −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 | ||||||||
\(162\) | 2.29289 | − | 21.6066i | 0.180147 | − | 1.69757i | ||||
\(163\) | 6.41421 | − | 6.41421i | 0.502400 | − | 0.502400i | −0.409783 | − | 0.912183i | \(-0.634396\pi\) |
0.912183 | + | 0.409783i | \(0.134396\pi\) | |||||||
\(164\) | 14.0000 | 1.09322 | ||||||||
\(165\) | −3.82843 | − | 0.585786i | −0.298043 | − | 0.0456034i | ||||
\(166\) | −17.3137 | −1.34380 | ||||||||
\(167\) | −10.7279 | + | 10.7279i | −0.830152 | + | 0.830152i | −0.987537 | − | 0.157386i | \(-0.949693\pi\) |
0.157386 | + | 0.987537i | \(0.449693\pi\) | |||||||
\(168\) | 5.17157 | + | 3.65685i | 0.398996 | + | 0.282132i | ||||
\(169\) | 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 | \(-0.400780\pi\) |
−0.951811 | + | 0.306687i | \(0.900780\pi\) | |||||||
\(174\) | 3.41421 | + | 19.8995i | 0.258831 | + | 1.50858i | ||||
\(175\) | −4.10051 | + | 0.585786i | −0.309969 | + | 0.0442813i | ||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | 4.00000 | − | 5.65685i | 0.300658 | − | 0.425195i | ||||
\(178\) | −2.82843 | + | 2.82843i | −0.212000 | + | 0.212000i | ||||
\(179\) | −4.14214 | −0.309598 | −0.154799 | − | 0.987946i | \(-0.549473\pi\) | ||||
−0.154799 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(180\) | 17.8284 | − | 18.4853i | 1.32885 | − | 1.37781i | ||||
\(181\) | −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 | ||||
\(183\) | −10.4853 | + | 14.8284i | −0.775094 | + | 1.09615i | ||||
\(184\) | − | 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 | \(-0.134232\pi\) | |||||||
\(192\) | 13.8995 | + | 9.82843i | 1.00311 | + | 0.709306i | ||||
\(193\) | 8.00000 | − | 8.00000i | 0.575853 | − | 0.575853i | −0.357905 | − | 0.933758i | \(-0.616509\pi\) |
0.933758 | + | 0.357905i | \(0.116509\pi\) | |||||||
\(194\) | 2.24264 | 0.161012 | ||||||||
\(195\) | 6.48528 | + | 8.82843i | 0.464421 | + | 0.632217i | ||||
\(196\) | −24.1716 | −1.72654 | ||||||||
\(197\) | 14.1421 | − | 14.1421i | 1.00759 | − | 1.00759i | 0.00761443 | − | 0.999971i | \(-0.497576\pi\) |
0.999971 | − | 0.00761443i | \(-0.00242377\pi\) | |||||||
\(198\) | 3.12132 | − | 6.53553i | 0.221823 | − | 0.464460i | ||||
\(199\) | 2.48528i | 0.176177i | 0.996113 | + | 0.0880885i | \(0.0280758\pi\) | ||||
−0.996113 | + | 0.0880885i | \(0.971924\pi\) | |||||||
\(200\) | 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 | ||||||
\(207\) | −9.58579 | + | 20.0711i | −0.666258 | + | 1.39504i | ||||
\(208\) | 6.00000 | − | 6.00000i | 0.416025 | − | 0.416025i | ||||
\(209\) | 2.82843 | 0.195646 | ||||||||
\(210\) | 1.17157 | − | 7.65685i | 0.0808462 | − | 0.528373i | ||||
\(211\) | 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 | ||||
\(213\) | −20.4853 | − | 14.4853i | −1.40363 | − | 0.992515i | ||||
\(214\) | − | 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 | ||||||||
\(222\) | −19.8995 | + | 28.1421i | −1.33557 | + | 1.88878i | ||||
\(223\) | 14.5563 | − | 14.5563i | 0.974765 | − | 0.974765i | −0.0249241 | − | 0.999689i | \(-0.507934\pi\) |
0.999689 | + | 0.0249241i | \(0.00793441\pi\) | |||||||
\(224\) | 1.31371 | 0.0877758 | ||||||||
\(225\) | −14.3137 | − | 4.48528i | −0.954247 | − | 0.299019i | ||||
\(226\) | 0.585786 | 0.0389659 | ||||||||
\(227\) | 1.75736 | − | 1.75736i | 0.116640 | − | 0.116640i | −0.646378 | − | 0.763018i | \(-0.723717\pi\) |
0.763018 | + | 0.646378i | \(0.223717\pi\) | |||||||
\(228\) | −10.8284 | + | 15.3137i | −0.717130 | + | 1.01418i | ||||
\(229\) | 1.65685i | 0.109488i | 0.998500 | + | 0.0547440i | \(0.0174343\pi\) | ||||
−0.998500 | + | 0.0547440i | \(0.982566\pi\) | |||||||
\(230\) | −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 | \(-0.123688\pi\) |
−0.378872 | + | 0.925449i | \(0.623688\pi\) | |||||||
\(234\) | −19.3137 | + | 6.82843i | −1.26258 | + | 0.446388i | ||||
\(235\) | −1.24264 | + | 3.72792i | −0.0810609 | + | 0.243183i | ||||
\(236\) | 15.3137i | 0.996838i | ||||||||
\(237\) | −7.31371 | − | 5.17157i | −0.475076 | − | 0.335930i | ||||
\(238\) | 5.65685 | − | 5.65685i | 0.366679 | − | 0.366679i | ||||
\(239\) | 15.7990 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(240\) | −1.75736 | + | 11.4853i | −0.113437 | + | 0.741372i | ||||
\(241\) | −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 | ||||
\(243\) | −1.00000 | − | 15.5563i | −0.0641500 | − | 0.997940i | ||||
\(244\) | − | 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 | \(0.874821\pi\) | |||||||
\(252\) | 8.58579 | + | 4.10051i | 0.540854 | + | 0.258308i | ||||
\(253\) | −5.24264 | + | 5.24264i | −0.329602 | + | 0.329602i | ||||
\(254\) | 4.82843 | 0.302962 | ||||||||
\(255\) | −9.17157 | − | 12.4853i | −0.574346 | − | 0.781859i | ||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 3.82843 | − | 3.82843i | 0.238811 | − | 0.238811i | −0.577547 | − | 0.816358i | \(-0.695990\pi\) |
0.816358 | + | 0.577547i | \(0.195990\pi\) | |||||||
\(258\) | 39.7990 | + | 28.1421i | 2.47778 | + | 1.75205i | ||||
\(259\) | 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 | \(-0.397365\pi\) |
−0.948466 | + | 0.316878i | \(0.897365\pi\) | |||||||
\(264\) | 1.29289 | + | 7.53553i | 0.0795721 | + | 0.463780i | ||||
\(265\) | −3.00000 | − | 1.00000i | −0.184289 | − | 0.0614295i | ||||
\(266\) | 5.65685i | 0.346844i | ||||||||
\(267\) | −1.65685 | + | 2.34315i | −0.101398 | + | 0.143398i | ||||
\(268\) | −13.7279 | + | 13.7279i | −0.838566 | + | 0.838566i | ||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 15.7782 | − | 23.1924i | 0.960229 | − | 1.41144i | ||||
\(271\) | −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 | ||||
\(273\) | −2.34315 | + | 3.31371i | −0.141814 | + | 0.200555i | ||||
\(274\) | 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 | 0.660136 | − | 0.751146i | \(-0.270499\pi\) |
−0.751146 | + | 0.660136i | \(0.770499\pi\) | |||||||
\(278\) | 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 | \(-0.165182\pi\) | |||||||
\(282\) | −6.00000 | − | 4.24264i | −0.357295 | − | 0.252646i | ||||
\(283\) | −0.928932 | + | 0.928932i | −0.0552193 | + | 0.0552193i | −0.734177 | − | 0.678958i | \(-0.762432\pi\) |
0.678958 | + | 0.734177i | \(0.262432\pi\) | |||||||
\(284\) | 55.4558 | 3.29070 | ||||||||
\(285\) | 10.8284 | + | 1.65685i | 0.641421 | + | 0.0981436i | ||||
\(286\) | −6.82843 | −0.403773 | ||||||||
\(287\) | 2.14214 | − | 2.14214i | 0.126446 | − | 0.126446i | ||||
\(288\) | 4.29289 | + | 2.05025i | 0.252961 | + | 0.120812i | ||||
\(289\) | 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 | \(-0.147559\pi\) |
−0.447144 | + | 0.894462i | \(0.647559\pi\) | |||||||
\(294\) | −26.0208 | + | 4.46447i | −1.51756 | + | 0.260373i | ||||
\(295\) | 8.00000 | − | 4.00000i | 0.465778 | − | 0.232889i | ||||
\(296\) | − | 36.3848i | − | 2.11482i | ||||||
\(297\) | 1.41421 | − | 5.00000i | 0.0820610 | − | 0.290129i | ||||
\(298\) | 17.0711 | − | 17.0711i | 0.988900 | − | 0.988900i | ||||
\(299\) | 20.9706 | 1.21276 | ||||||||
\(300\) | 31.5563 | − | 10.1716i | 1.82191 | − | 0.587256i | ||||
\(301\) | 9.65685 | 0.556612 | ||||||||
\(302\) | 30.9706 | − | 30.9706i | 1.78216 | − | 1.78216i | ||||
\(303\) | 18.1421 | + | 12.8284i | 1.04224 | + | 0.736974i | ||||
\(304\) | − | 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 | 0.895636 | − | 0.444788i | \(-0.146721\pi\) |
−0.444788 | + | 0.895636i | \(0.646721\pi\) | |||||||
\(308\) | 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 | \(-0.00128276\pi\) | |||||||
\(312\) | 12.4853 | − | 17.6569i | 0.706840 | − | 0.999623i | ||||
\(313\) | 1.34315 | − | 1.34315i | 0.0759191 | − | 0.0759191i | −0.668128 | − | 0.744047i | \(-0.732904\pi\) |
0.744047 | + | 0.668128i | \(0.232904\pi\) | |||||||
\(314\) | −25.5563 | −1.44223 | ||||||||
\(315\) | −0.100505 | − | 5.55635i | −0.00566282 | − | 0.313065i | ||||
\(316\) | 19.7990 | 1.11378 | ||||||||
\(317\) | −20.3137 | + | 20.3137i | −1.14093 | + | 1.14093i | −0.152651 | + | 0.988280i | \(0.548781\pi\) |
−0.988280 | + | 0.152651i | \(0.951219\pi\) | |||||||
\(318\) | 3.41421 | − | 4.82843i | 0.191460 | − | 0.270765i | ||||
\(319\) | 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 | ||||||||
\(327\) | −12.4853 | − | 8.82843i | −0.690438 | − | 0.488213i | ||||
\(328\) | −11.4142 | + | 11.4142i | −0.630245 | + | 0.630245i | ||||
\(329\) | −1.45584 | −0.0802633 | ||||||||
\(330\) | 7.53553 | − | 5.53553i | 0.414817 | − | 0.304721i | ||||
\(331\) | 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 | ||||
\(333\) | −10.6569 | + | 22.3137i | −0.583992 | + | 1.22278i | ||||
\(334\) | − | 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 | 0.552079 | − | 0.833792i | \(-0.313835\pi\) |
−0.833792 | + | 0.552079i | \(0.813835\pi\) | |||||||
\(338\) | −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 | ||||||||
\(342\) | −8.82843 | + | 18.4853i | −0.477387 | + | 0.999570i | ||||
\(343\) | −7.79899 | + | 7.79899i | −0.421106 | + | 0.421106i | ||||
\(344\) | −51.4558 | −2.77431 | ||||||||
\(345\) | −23.1421 | + | 17.0000i | −1.24593 | + | 0.915249i | ||||
\(346\) | 28.9706 | 1.55747 | ||||||||
\(347\) | −17.8995 | + | 17.8995i | −0.960895 | + | 0.960895i | −0.999264 | − | 0.0383684i | \(-0.987784\pi\) |
0.0383684 | + | 0.999264i | \(0.487784\pi\) | |||||||
\(348\) | −26.1421 | − | 18.4853i | −1.40137 | − | 0.990915i | ||||
\(349\) | 30.0000i | 1.60586i | 0.596071 | + | 0.802932i | \(0.296728\pi\) | ||||
−0.596071 | + | 0.802932i | \(0.703272\pi\) | |||||||
\(350\) | 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 | \(-0.223956\pi\) |
−0.646951 | + | 0.762532i | \(0.723956\pi\) | |||||||
\(354\) | 2.82843 | + | 16.4853i | 0.150329 | + | 0.876183i | ||||
\(355\) | −14.4853 | − | 28.9706i | −0.768799 | − | 1.53760i | ||||
\(356\) | − | 6.34315i | − | 0.336186i | ||||||
\(357\) | 3.31371 | − | 4.68629i | 0.175380 | − | 0.248025i | ||||
\(358\) | 7.07107 | − | 7.07107i | 0.373718 | − | 0.373718i | ||||
\(359\) | 6.14214 | 0.324170 | 0.162085 | − | 0.986777i | \(-0.448178\pi\) | ||||
0.162085 | + | 0.986777i | \(0.448178\pi\) | |||||||
\(360\) | 0.535534 | + | 29.6066i | 0.0282251 | + | 1.56040i | ||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 9.65685 | − | 9.65685i | 0.507553 | − | 0.507553i | ||||
\(363\) | 1.00000 | − | 1.41421i | 0.0524864 | − | 0.0742270i | ||||
\(364\) | − | 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 | −0.995428 | − | 0.0955170i | \(-0.969550\pi\) |
−0.0955170 | − | 0.995428i | \(-0.530450\pi\) | |||||||
\(368\) | 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 | ||||||
\(372\) | −47.7990 | − | 33.7990i | −2.47826 | − | 1.75240i | ||||
\(373\) | 20.4853 | − | 20.4853i | 1.06069 | − | 1.06069i | 0.0626522 | − | 0.998035i | \(-0.480044\pi\) |
0.998035 | − | 0.0626522i | \(-0.0199559\pi\) | |||||||
\(374\) | 9.65685 | 0.499344 | ||||||||
\(375\) | −13.5563 | − | 13.8284i | −0.700047 | − | 0.714097i | ||||
\(376\) | 7.75736 | 0.400055 | ||||||||
\(377\) | 9.65685 | − | 9.65685i | 0.497353 | − | 0.497353i | ||||
\(378\) | 10.0000 | + | 2.82843i | 0.514344 | + | 0.145479i | ||||
\(379\) | 0.142136i | 0.00730102i | 0.999993 | + | 0.00365051i | \(0.00116200\pi\) | ||||
−0.999993 | + | 0.00365051i | \(0.998838\pi\) | |||||||
\(380\) | −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 | \(-0.155806\pi\) |
−0.470166 | + | 0.882578i | \(0.655806\pi\) | |||||||
\(384\) | −35.0919 | + | 6.02082i | −1.79078 | + | 0.307248i | ||||
\(385\) | 0.585786 | − | 1.75736i | 0.0298544 | − | 0.0895633i | ||||
\(386\) | 27.3137i | 1.39023i | ||||||||
\(387\) | 31.5563 | + | 15.0711i | 1.60410 | + | 0.766105i | ||||
\(388\) | −2.51472 | + | 2.51472i | −0.127665 | + | 0.127665i | ||||
\(389\) | 5.31371 | 0.269416 | 0.134708 | − | 0.990885i | \(-0.456990\pi\) | ||||
0.134708 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(390\) | −26.1421 | − | 4.00000i | −1.32376 | − | 0.202548i | ||||
\(391\) | −29.6569 | −1.49981 | ||||||||
\(392\) | 19.7071 | − | 19.7071i | 0.995359 | − | 0.995359i | ||||
\(393\) | −1.65685 | − | 1.17157i | −0.0835772 | − | 0.0590980i | ||||
\(394\) | 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 | 0.938616 | − | 0.344964i | \(-0.112109\pi\) |
−0.344964 | + | 0.938616i | \(0.612109\pi\) | |||||||
\(398\) | −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 | \(0.792044\pi\) | |||||||
\(402\) | −12.2426 | + | 17.3137i | −0.610607 | + | 0.863529i | ||||
\(403\) | 17.6569 | − | 17.6569i | 0.879551 | − | 0.879551i | ||||
\(404\) | −49.1127 | −2.44345 | ||||||||
\(405\) | 8.34315 | − | 18.3137i | 0.414574 | − | 0.910015i | ||||
\(406\) | −9.65685 | −0.479262 | ||||||||
\(407\) | −5.82843 | + | 5.82843i | −0.288904 | + | 0.288904i | ||||
\(408\) | −17.6569 | + | 24.9706i | −0.874145 | + | 1.23623i | ||||
\(409\) | 1.51472i | 0.0748980i | 0.999299 | + | 0.0374490i | \(0.0119232\pi\) | ||||
−0.999299 | + | 0.0374490i | \(0.988077\pi\) | |||||||
\(410\) | 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 | ||||||
\(417\) | 8.97056 | + | 6.34315i | 0.439290 | + | 0.310625i | ||||
\(418\) | −4.82843 | + | 4.82843i | −0.236166 | + | 0.236166i | ||||
\(419\) | −35.4558 | −1.73213 | −0.866066 | − | 0.499930i | \(-0.833359\pi\) | ||||
−0.866066 | + | 0.499930i | \(0.833359\pi\) | |||||||
\(420\) | 7.27208 | + | 9.89949i | 0.354841 | + | 0.483046i | ||||
\(421\) | −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 | ||||
\(423\) | −4.75736 | − | 2.27208i | −0.231311 | − | 0.110472i | ||||
\(424\) | 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 | \(-0.139814\pi\) | |||||||
\(432\) | −15.0000 | − | 4.24264i | −0.721688 | − | 0.204124i | ||||
\(433\) | 22.3137 | − | 22.3137i | 1.07233 | − | 1.07233i | 0.0751567 | − | 0.997172i | \(-0.476054\pi\) |
0.997172 | − | 0.0751567i | \(-0.0239457\pi\) | |||||||
\(434\) | −17.6569 | −0.847556 | ||||||||
\(435\) | −2.82843 | + | 18.4853i | −0.135613 | + | 0.886301i | ||||
\(436\) | 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 | \(-0.880918\pi\) | ||
0.930834 | − | 0.365442i | \(-0.119082\pi\) | |||||||
\(440\) | −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 | −0.826664 | − | 0.562696i | \(-0.809764\pi\) |
−0.562696 | − | 0.826664i | \(-0.690236\pi\) | |||||||
\(444\) | −9.24264 | − | 53.8701i | −0.438636 | − | 2.55656i | ||||
\(445\) | −3.31371 | + | 1.65685i | −0.157085 | + | 0.0785424i | ||||
\(446\) | 49.6985i | 2.35329i | ||||||||
\(447\) | 10.0000 | − | 14.1421i | 0.472984 | − | 0.668900i | ||||
\(448\) | −5.75736 | + | 5.75736i | −0.272010 | + | 0.272010i | ||||
\(449\) | −36.9706 | −1.74475 | −0.872374 | − | 0.488838i | \(-0.837421\pi\) | ||||
−0.872374 | + | 0.488838i | \(0.837421\pi\) | |||||||
\(450\) | 32.0919 | − | 16.7782i | 1.51283 | − | 0.790931i | ||||
\(451\) | 3.65685 | 0.172195 | ||||||||
\(452\) | −0.656854 | + | 0.656854i | −0.0308958 | + | 0.0308958i | ||||
\(453\) | 18.1421 | − | 25.6569i | 0.852392 | − | 1.20546i | ||||
\(454\) | 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 | 0.908458 | − | 0.417977i | \(-0.137261\pi\) |
−0.417977 | + | 0.908458i | \(0.637261\pi\) | |||||||
\(458\) | −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 | \(-0.251269\pi\) | |||||||
\(462\) | 2.82843 | + | 2.00000i | 0.131590 | + | 0.0930484i | ||||
\(463\) | −13.7279 | + | 13.7279i | −0.637991 | + | 0.637991i | −0.950059 | − | 0.312069i | \(-0.898978\pi\) |
0.312069 | + | 0.950059i | \(0.398978\pi\) | |||||||
\(464\) | 14.4853 | 0.672462 | ||||||||
\(465\) | −5.17157 | + | 33.7990i | −0.239826 | + | 1.56739i | ||||
\(466\) | −28.4853 | −1.31956 | ||||||||
\(467\) | 2.41421 | − | 2.41421i | 0.111716 | − | 0.111716i | −0.649039 | − | 0.760755i | \(-0.724829\pi\) |
0.760755 | + | 0.649039i | \(0.224829\pi\) | |||||||
\(468\) | 14.0000 | − | 29.3137i | 0.647150 | − | 1.35503i | ||||
\(469\) | 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 | ||||||||
\(477\) | 1.82843 | − | 3.82843i | 0.0837179 | − | 0.175292i | ||||
\(478\) | −26.9706 | + | 26.9706i | −1.23360 | + | 1.23360i | ||||
\(479\) | −1.85786 | −0.0848880 | −0.0424440 | − | 0.999099i | \(-0.513514\pi\) | ||||
−0.0424440 | + | 0.999099i | \(0.513514\pi\) | |||||||
\(480\) | 3.63604 | + | 4.94975i | 0.165962 | + | 0.225924i | ||||
\(481\) | 23.3137 | 1.06301 | ||||||||
\(482\) | 48.0416 | − | 48.0416i | 2.18824 | − | 2.18824i | ||||
\(483\) | −8.68629 | − | 6.14214i | −0.395240 | − | 0.279477i | ||||
\(484\) | 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 | 0.323989 | − | 0.946061i | \(-0.394976\pi\) |
−0.946061 | + | 0.323989i | \(0.894976\pi\) | |||||||
\(488\) | 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 | \(-0.149037\pi\) | |||||||
\(492\) | −14.0000 | + | 19.7990i | −0.631169 | + | 0.892607i | ||||
\(493\) | −13.6569 | + | 13.6569i | −0.615074 | + | 0.615074i | ||||
\(494\) | 19.3137 | 0.868965 | ||||||||
\(495\) | 4.65685 | − | 4.82843i | 0.209310 | − | 0.217022i | ||||
\(496\) | 26.4853 | 1.18922 | ||||||||
\(497\) | 8.48528 | − | 8.48528i | 0.380617 | − | 0.380617i | ||||
\(498\) | 17.3137 | − | 24.4853i | 0.775846 | − | 1.09721i | ||||
\(499\) | − | 19.1716i | − | 0.858237i | −0.903248 | − | 0.429119i | \(-0.858824\pi\) | ||
0.903248 | − | 0.429119i | \(-0.141176\pi\) | |||||||
\(500\) | 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 | \(-0.0923881\pi\) |
−0.286188 | + | 0.958174i | \(0.592388\pi\) | |||||||
\(504\) | −10.3431 | + | 3.65685i | −0.460720 | + | 0.162889i | ||||
\(505\) | 12.8284 | + | 25.6569i | 0.570858 | + | 1.14172i | ||||
\(506\) | − | 17.8995i | − | 0.795730i | ||||||
\(507\) | −7.07107 | − | 5.00000i | −0.314037 | − | 0.222058i | ||||
\(508\) | −5.41421 | + | 5.41421i | −0.240217 | + | 0.240217i | ||||
\(509\) | 24.3431 | 1.07899 | 0.539495 | − | 0.841988i | \(-0.318615\pi\) | ||||
0.539495 | + | 0.841988i | \(0.318615\pi\) | |||||||
\(510\) | 36.9706 | + | 5.65685i | 1.63708 | + | 0.250490i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.0919 | − | 22.0919i | 0.976333 | − | 0.976333i | ||||
\(513\) | −4.00000 | + | 14.1421i | −0.176604 | + | 0.624391i | ||||
\(514\) | 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 | \(-0.116542\pi\) | |||||||
\(522\) | −31.5563 | − | 15.0711i | −1.38118 | − | 0.659643i | ||||
\(523\) | 15.2132 | − | 15.2132i | 0.665227 | − | 0.665227i | −0.291380 | − | 0.956607i | \(-0.594115\pi\) |
0.956607 | + | 0.291380i | \(0.0941145\pi\) | |||||||
\(524\) | 4.48528 | 0.195940 | ||||||||
\(525\) | 3.27208 | − | 6.38478i | 0.142805 | − | 0.278654i | ||||
\(526\) | 34.9706 | 1.52479 | ||||||||
\(527\) | −24.9706 | + | 24.9706i | −1.08773 | + | 1.08773i | ||||
\(528\) | −4.24264 | − | 3.00000i | −0.184637 | − | 0.130558i | ||||
\(529\) | 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 | ||||||
\(537\) | 4.14214 | − | 5.85786i | 0.178746 | − | 0.252786i | ||||
\(538\) | 23.8995 | − | 23.8995i | 1.03038 | − | 1.03038i | ||||
\(539\) | −6.31371 | −0.271951 | ||||||||
\(540\) | 8.31371 | + | 43.6985i | 0.357765 | + | 1.88048i | ||||
\(541\) | −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 | ||||
\(543\) | 5.65685 | − | 8.00000i | 0.242759 | − | 0.343313i | ||||
\(544\) | 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 | 0.998092 | − | 0.0617376i | \(-0.0196642\pi\) |
−0.0617376 | + | 0.998092i | \(0.519664\pi\) | |||||||
\(548\) | −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 | ||||||
\(552\) | 46.2843 | + | 32.7279i | 1.96999 | + | 1.39299i | ||||
\(553\) | 3.02944 | − | 3.02944i | 0.128825 | − | 0.128825i | ||||
\(554\) | 5.17157 | 0.219719 | ||||||||
\(555\) | −25.7279 | + | 18.8995i | −1.09209 | + | 0.802239i | ||||
\(556\) | −24.2843 | −1.02988 | ||||||||
\(557\) | −24.9706 | + | 24.9706i | −1.05804 | + | 1.05804i | −0.0598280 | + | 0.998209i | \(0.519055\pi\) |
−0.998209 | + | 0.0598280i | \(0.980945\pi\) | |||||||
\(558\) | −57.6985 | − | 27.5563i | −2.44257 | − | 1.16655i | ||||
\(559\) | − | 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 | \(-0.154675\pi\) |
−0.467028 | + | 0.884242i | \(0.654675\pi\) | |||||||
\(564\) | 11.4853 | − | 1.97056i | 0.483618 | − | 0.0829757i | ||||
\(565\) | 0.514719 | + | 0.171573i | 0.0216544 | + | 0.00721813i | ||||
\(566\) | − | 3.17157i | − | 0.133311i | ||||||
\(567\) | 7.41421 | + | 0.786797i | 0.311368 | + | 0.0330423i | ||||
\(568\) | −45.2132 | + | 45.2132i | −1.89710 | + | 1.89710i | ||||
\(569\) | −39.6569 | −1.66250 | −0.831251 | − | 0.555897i | \(-0.812375\pi\) | ||||
−0.831251 | + | 0.555897i | \(0.812375\pi\) | |||||||
\(570\) | −21.3137 | + | 15.6569i | −0.892733 | + | 0.655793i | ||||
\(571\) | 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 | ||||
\(573\) | 16.0000 | + | 11.3137i | 0.668410 | + | 0.472637i | ||||
\(574\) | 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 | 0.966055 | − | 0.258336i | \(-0.0831741\pi\) |
−0.258336 | + | 0.966055i | \(0.583174\pi\) | |||||||
\(578\) | −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 | ||||||
\(582\) | −2.24264 | + | 3.17157i | −0.0929604 | + | 0.131466i | ||||
\(583\) | 1.00000 | − | 1.00000i | 0.0414158 | − | 0.0414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.9706 | + | 0.343146i | −0.784336 | + | 0.0141873i | ||||
\(586\) | −26.1421 | −1.07992 | ||||||||
\(587\) | 2.41421 | − | 2.41421i | 0.0996453 | − | 0.0996453i | −0.655527 | − | 0.755172i | \(-0.727553\pi\) |
0.755172 | + | 0.655527i | \(0.227553\pi\) | |||||||
\(588\) | 24.1716 | − | 34.1838i | 0.996819 | − | 1.40971i | ||||
\(589\) | − | 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 | 0.793568 | + | 0.608481i | \(0.208221\pi\) |
0.608481 | + | 0.793568i | \(0.291779\pi\) | |||||||
\(594\) | 6.12132 | + | 10.9497i | 0.251161 | + | 0.449274i | ||||
\(595\) | 6.62742 | − | 3.31371i | 0.271698 | − | 0.135849i | ||||
\(596\) | 38.2843i | 1.56818i | ||||||||
\(597\) | −3.51472 | − | 2.48528i | −0.143848 | − | 0.101716i | ||||
\(598\) | −35.7990 | + | 35.7990i | −1.46393 | + | 1.46393i | ||||
\(599\) | 47.4558 | 1.93899 | 0.969497 | − | 0.245105i | \(-0.0788223\pi\) | ||||
0.969497 | + | 0.245105i | \(0.0788223\pi\) | |||||||
\(600\) | −17.4350 | + | 34.0208i | −0.711782 | + | 1.38889i | ||||
\(601\) | 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 | ||||
\(603\) | −6.55635 | + | 13.7279i | −0.266995 | + | 0.559044i | ||||
\(604\) | 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 | 0.663192 | − | 0.748449i | \(-0.269201\pi\) |
−0.748449 | + | 0.663192i | \(0.769201\pi\) | |||||||
\(608\) | −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 | ||||||||
\(612\) | −19.7990 | + | 41.4558i | −0.800327 | + | 1.67575i | ||||
\(613\) | −16.0000 | + | 16.0000i | −0.646234 | + | 0.646234i | −0.952081 | − | 0.305847i | \(-0.901060\pi\) |
0.305847 | + | 0.952081i | \(0.401060\pi\) | |||||||
\(614\) | −26.9706 | −1.08844 | ||||||||
\(615\) | 14.0000 | + | 2.14214i | 0.564534 | + | 0.0863792i | ||||
\(616\) | −3.65685 | −0.147339 | ||||||||
\(617\) | 24.1716 | − | 24.1716i | 0.973111 | − | 0.973111i | −0.0265370 | − | 0.999648i | \(-0.508448\pi\) |
0.999648 | + | 0.0265370i | \(0.00844797\pi\) | |||||||
\(618\) | 17.3137 | + | 12.2426i | 0.696459 | + | 0.492471i | ||||
\(619\) | 23.3137i | 0.937057i | 0.883448 | + | 0.468529i | \(0.155216\pi\) | ||||
−0.883448 | + | 0.468529i | \(0.844784\pi\) | |||||||
\(620\) | −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 | ||||||||
\(627\) | −2.82843 | + | 4.00000i | −0.112956 | + | 0.159745i | ||||
\(628\) | 28.6569 | − | 28.6569i | 1.14353 | − | 1.14353i | ||||
\(629\) | −32.9706 | −1.31462 | ||||||||
\(630\) | 9.65685 | + | 9.31371i | 0.384738 | + | 0.371067i | ||||
\(631\) | 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 | ||||
\(633\) | −12.4853 | + | 17.6569i | −0.496245 | + | 0.701797i | ||||
\(634\) | − | 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 | \(0.919774\pi\) | |||||||
\(642\) | 39.7990 | + | 28.1421i | 1.57074 | + | 1.11068i | ||||
\(643\) | −0.757359 | + | 0.757359i | −0.0298673 | + | 0.0298673i | −0.721883 | − | 0.692015i | \(-0.756723\pi\) |
0.692015 | + | 0.721883i | \(0.256723\pi\) | |||||||
\(644\) | 23.5147 | 0.926610 | ||||||||
\(645\) | 26.7279 | + | 36.3848i | 1.05241 | + | 1.43265i | ||||
\(646\) | −27.3137 | −1.07464 | ||||||||
\(647\) | −13.7279 | + | 13.7279i | −0.539700 | + | 0.539700i | −0.923441 | − | 0.383741i | \(-0.874636\pi\) |
0.383741 | + | 0.923441i | \(0.374636\pi\) | |||||||
\(648\) | −39.5061 | − | 4.19239i | −1.55195 | − | 0.164693i | ||||
\(649\) | 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 | \(-0.273423\pi\) |
−0.757179 | + | 0.653208i | \(0.773423\pi\) | |||||||
\(654\) | 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 | \(-0.444097\pi\) | ||||
0.174722 | + | 0.984618i | \(0.444097\pi\) | |||||||
\(660\) | −2.24264 | + | 14.6569i | −0.0872947 | + | 0.570517i | ||||
\(661\) | 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 | ||||
\(663\) | −16.0000 | − | 11.3137i | −0.621389 | − | 0.439388i | ||||
\(664\) | 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 | ||||||
\(672\) | −1.31371 | + | 1.85786i | −0.0506774 | + | 0.0716687i | ||||
\(673\) | −33.6569 | + | 33.6569i | −1.29738 | + | 1.29738i | −0.367257 | + | 0.930120i | \(0.619703\pi\) |
−0.930120 | + | 0.367257i | \(0.880297\pi\) | |||||||
\(674\) | 17.6569 | 0.680117 | ||||||||
\(675\) | 20.6569 | − | 15.7574i | 0.795083 | − | 0.606501i | ||||
\(676\) | 19.1421 | 0.736236 | ||||||||
\(677\) | 8.34315 | − | 8.34315i | 0.320653 | − | 0.320653i | −0.528365 | − | 0.849018i | \(-0.677195\pi\) |
0.849018 | + | 0.528365i | \(0.177195\pi\) | |||||||
\(678\) | −0.585786 | + | 0.828427i | −0.0224970 | + | 0.0318156i | ||||
\(679\) | 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 | \(-0.409240\pi\) |
−0.959624 | + | 0.281284i | \(0.909240\pi\) | |||||||
\(684\) | −10.8284 | − | 30.6274i | −0.414035 | − | 1.17107i | ||||
\(685\) | −5.82843 | + | 17.4853i | −0.222693 | + | 0.668078i | ||||
\(686\) | − | 26.6274i | − | 1.01664i | ||||||
\(687\) | −2.34315 | − | 1.65685i | −0.0893966 | − | 0.0632129i | ||||
\(688\) | 24.7279 | − | 24.7279i | 0.942743 | − | 0.942743i | ||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 10.4853 | − | 68.5269i | 0.399168 | − | 2.60877i | ||||
\(691\) | 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 | ||||
\(693\) | 2.24264 | + | 1.07107i | 0.0851909 | + | 0.0406865i | ||||
\(694\) | − | 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 | \(-0.131860\pi\) | |||||||
\(702\) | 9.65685 | − | 34.1421i | 0.364474 | − | 1.28861i | ||||
\(703\) | 16.4853 | − | 16.4853i | 0.621754 | − | 0.621754i | ||||
\(704\) | −9.82843 | −0.370423 | ||||||||
\(705\) | −4.02944 | − | 5.48528i | −0.151757 | − | 0.206588i | ||||
\(706\) | −7.41421 | −0.279038 | ||||||||
\(707\) | −7.51472 | + | 7.51472i | −0.282620 | + | 0.282620i | ||||
\(708\) | −21.6569 | − | 15.3137i | −0.813914 | − | 0.575524i | ||||
\(709\) | − | 6.68629i | − | 0.251109i | −0.992087 | − | 0.125554i | \(-0.959929\pi\) | ||
0.992087 | − | 0.125554i | \(-0.0400710\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | −15.7990 | + | 22.3431i | −0.590024 | + | 0.834420i | ||||
\(718\) | −10.4853 | + | 10.4853i | −0.391307 | + | 0.391307i | ||||
\(719\) | 50.7696 | 1.89338 | 0.946692 | − | 0.322139i | \(-0.104402\pi\) | ||||
0.946692 | + | 0.322139i | \(0.104402\pi\) | |||||||
\(720\) | −14.4853 | − | 13.9706i | −0.539835 | − | 0.520652i | ||||
\(721\) | 4.20101 | 0.156454 | ||||||||
\(722\) | −18.7782 | + | 18.7782i | −0.698851 | + | 0.698851i | ||||
\(723\) | 28.1421 | − | 39.7990i | 1.04662 | − | 1.48014i | ||||
\(724\) | 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 | 0.162815 | − | 0.986657i | \(-0.447943\pi\) |
−0.986657 | + | 0.162815i | \(0.947943\pi\) | |||||||
\(728\) | 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 | ||||||||
\(732\) | 56.7696 | + | 40.1421i | 2.09826 | + | 1.48370i | ||||
\(733\) | −35.7990 | + | 35.7990i | −1.32227 | + | 1.32227i | −0.410328 | + | 0.911938i | \(0.634586\pi\) |
−0.911938 | + | 0.410328i | \(0.865414\pi\) | |||||||
\(734\) | 71.3553 | 2.63377 | ||||||||
\(735\) | −24.1716 | − | 3.69848i | −0.891582 | − | 0.136421i | ||||
\(736\) | 11.7574 | 0.433382 | ||||||||
\(737\) | −3.58579 | + | 3.58579i | −0.132084 | + | 0.132084i | ||||
\(738\) | −11.4142 | + | 23.8995i | −0.420163 | + | 0.879753i | ||||
\(739\) | − | 30.6274i | − | 1.12665i | −0.826236 | − | 0.563324i | \(-0.809522\pi\) | ||
0.826236 | − | 0.563324i | \(-0.190478\pi\) | |||||||
\(740\) | 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 | \(-0.0562504\pi\) |
−0.175797 | + | 0.984426i | \(0.556250\pi\) | |||||||
\(744\) | 66.5269 | − | 11.4142i | 2.43899 | − | 0.418465i | ||||
\(745\) | 20.0000 | − | 10.0000i | 0.732743 | − | 0.366372i | ||||
\(746\) | 69.9411i | 2.56073i | ||||||||
\(747\) | 9.27208 | − | 19.4142i | 0.339248 | − | 0.710329i | ||||
\(748\) | −10.8284 | + | 10.8284i | −0.395927 | + | 0.395927i | ||||
\(749\) | 9.65685 | 0.352854 | ||||||||
\(750\) | 46.7487 | + | 0.464466i | 1.70702 | + | 0.0169599i | ||||
\(751\) | −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 | ||||
\(753\) | −17.1716 | − | 12.1421i | −0.625767 | − | 0.442484i | ||||
\(754\) | 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 | 0.805048 | − | 0.593210i | \(-0.202140\pi\) |
−0.593210 | + | 0.805048i | \(0.702140\pi\) | |||||||
\(758\) | −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 | \(0.891248\pi\) | |||||||
\(762\) | −4.82843 | + | 6.82843i | −0.174915 | + | 0.247368i | ||||
\(763\) | 5.17157 | − | 5.17157i | 0.187224 | − | 0.187224i | ||||
\(764\) | −43.3137 | −1.56703 | ||||||||
\(765\) | 26.8284 | − | 0.485281i | 0.969984 | − | 0.0175454i | ||||
\(766\) | −27.5563 | −0.995651 | ||||||||
\(767\) | 8.00000 | − | 8.00000i | 0.288863 | − | 0.288863i | ||||
\(768\) | 29.9706 | − | 42.3848i | 1.08147 | − | 1.52943i | ||||
\(769\) | − | 7.37258i | − | 0.265862i | −0.991125 | − | 0.132931i | \(-0.957561\pi\) | ||
0.991125 | − | 0.132931i | \(-0.0424389\pi\) | |||||||
\(770\) | 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 | \(-0.255318\pi\) |
−0.718821 | + | 0.695195i | \(0.755318\pi\) | |||||||
\(774\) | −79.5980 | + | 28.1421i | −2.86109 | + | 1.01155i | ||||
\(775\) | −26.4853 | + | 35.3137i | −0.951379 | + | 1.26851i | ||||
\(776\) | − | 4.10051i | − | 0.147200i | ||||||
\(777\) | −9.65685 | − | 6.82843i | −0.346438 | − | 0.244968i | ||||
\(778\) | −9.07107 | + | 9.07107i | −0.325214 | + | 0.325214i | ||||
\(779\) | −10.3431 | −0.370582 | ||||||||
\(780\) | 33.7990 | − | 24.8284i | 1.21020 | − | 0.889000i | ||||
\(781\) | 14.4853 | 0.518324 | ||||||||
\(782\) | 50.6274 | − | 50.6274i | 1.81043 | − | 1.81043i | ||||
\(783\) | −24.1421 | − | 6.82843i | −0.862770 | − | 0.244028i | ||||
\(784\) | 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 | −0.991771 | − | 0.128025i | \(-0.959136\pi\) |
−0.128025 | − | 0.991771i | \(-0.540864\pi\) | |||||||
\(788\) | −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 | ||||||||
\(792\) | −11.9497 | − | 5.70711i | −0.424616 | − | 0.202793i | ||||
\(793\) | −20.9706 | + | 20.9706i | −0.744687 | + | 0.744687i | ||||
\(794\) | −40.3848 | −1.43320 | ||||||||
\(795\) | 4.41421 | − | 3.24264i | 0.156556 | − | 0.115005i | ||||
\(796\) | 9.51472 | 0.337240 | ||||||||
\(797\) | −7.97056 | + | 7.97056i | −0.282332 | + | 0.282332i | −0.834038 | − | 0.551707i | \(-0.813977\pi\) |
0.551707 | + | 0.834038i | \(0.313977\pi\) | |||||||
\(798\) | −8.00000 | − | 5.65685i | −0.283197 | − | 0.200250i | ||||
\(799\) | − | 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 | ||||||||
\(807\) | 14.0000 | − | 19.7990i | 0.492823 | − | 0.696957i | ||||
\(808\) | 40.0416 | − | 40.0416i | 1.40866 | − | 1.40866i | ||||
\(809\) | −44.1421 | −1.55195 | −0.775977 | − | 0.630761i | \(-0.782743\pi\) | ||||
−0.775977 | + | 0.630761i | \(0.782743\pi\) | |||||||
\(810\) | 17.0208 | + | 45.5061i | 0.598050 | + | 1.59892i | ||||
\(811\) | −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 | ||||
\(813\) | 8.48528 | − | 12.0000i | 0.297592 | − | 0.420858i | ||||
\(814\) | − | 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 | \(-0.0652036\pi\) | |||||||
\(822\) | −28.1421 | − | 19.8995i | −0.981570 | − | 0.694075i | ||||
\(823\) | −15.5858 | + | 15.5858i | −0.543286 | + | 0.543286i | −0.924491 | − | 0.381204i | \(-0.875509\pi\) |
0.381204 | + | 0.924491i | \(0.375509\pi\) | |||||||
\(824\) | −22.3848 | −0.779811 | ||||||||
\(825\) | 8.24264 | − | 2.65685i | 0.286972 | − | 0.0924998i | ||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 20.0416 | − | 20.0416i | 0.696916 | − | 0.696916i | −0.266828 | − | 0.963744i | \(-0.585976\pi\) |
0.963744 | + | 0.266828i | \(0.0859757\pi\) | |||||||
\(828\) | 76.8406 | + | 36.6985i | 2.67040 | + | 1.27536i | ||||
\(829\) | − | 22.9706i | − | 0.797801i | −0.916994 | − | 0.398900i | \(-0.869392\pi\) | ||
0.916994 | − | 0.398900i | \(-0.130608\pi\) | |||||||
\(830\) | 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 | ||||||
\(837\) | −44.1421 | − | 12.4853i | −1.52578 | − | 0.431554i | ||||
\(838\) | 60.5269 | − | 60.5269i | 2.09087 | − | 2.09087i | ||||
\(839\) | −10.3431 | −0.357085 | −0.178543 | − | 0.983932i | \(-0.557138\pi\) | ||||
−0.178543 | + | 0.983932i | \(0.557138\pi\) | |||||||
\(840\) | −14.0000 | − | 2.14214i | −0.483046 | − | 0.0739107i | ||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 6.82843 | − | 6.82843i | 0.235323 | − | 0.235323i | ||||
\(843\) | 23.5147 | + | 16.6274i | 0.809890 | + | 0.572679i | ||||
\(844\) | − | 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 | ||||||||
\(852\) | −55.4558 | + | 78.4264i | −1.89989 | + | 2.68684i | ||||
\(853\) | −10.1421 | + | 10.1421i | −0.347260 | + | 0.347260i | −0.859088 | − | 0.511828i | \(-0.828969\pi\) |
0.511828 | + | 0.859088i | \(0.328969\pi\) | |||||||
\(854\) | 20.9706 | 0.717598 | ||||||||
\(855\) | −13.1716 | + | 13.6569i | −0.450458 | + | 0.467055i | ||||
\(856\) | −51.4558 | −1.75872 | ||||||||
\(857\) | 0.485281 | − | 0.485281i | 0.0165769 | − | 0.0165769i | −0.698770 | − | 0.715347i | \(-0.746269\pi\) |
0.715347 | + | 0.698770i | \(0.246269\pi\) | |||||||
\(858\) | 6.82843 | − | 9.65685i | 0.233119 | − | 0.329680i | ||||
\(859\) | 36.0000i | 1.22830i | 0.789188 | + | 0.614152i | \(0.210502\pi\) | ||||
−0.789188 | + | 0.614152i | \(0.789498\pi\) | |||||||
\(860\) | −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 | \(-0.397385\pi\) |
−0.948486 | + | 0.316820i | \(0.897385\pi\) | |||||||
\(864\) | −7.19239 | + | 4.02082i | −0.244690 | + | 0.136791i | ||||
\(865\) | 25.4558 | + | 8.48528i | 0.865525 | + | 0.288508i | ||||
\(866\) | 76.1838i | 2.58883i | ||||||||
\(867\) | −1.41421 | − | 1.00000i | −0.0480292 | − | 0.0339618i | ||||
\(868\) | 19.7990 | − | 19.7990i | 0.672022 | − | 0.672022i | ||||
\(869\) | 5.17157 | 0.175434 | ||||||||
\(870\) | −26.7279 | − | 36.3848i | −0.906161 | − | 1.23356i | ||||
\(871\) | 14.3431 | 0.485999 | ||||||||
\(872\) | −27.5563 | + | 27.5563i | −0.933176 | + | 0.933176i | ||||
\(873\) | −1.20101 | + | 2.51472i | −0.0406480 | + | 0.0851103i | ||||
\(874\) | 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 | −0.925425 | − | 0.378930i | \(-0.876292\pi\) |
−0.378930 | − | 0.925425i | \(-0.623708\pi\) | |||||||
\(878\) | 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 | \(-0.114926\pi\) | |||||||
\(882\) | 19.7071 | − | 41.2635i | 0.663573 | − | 1.38941i | ||||
\(883\) | −6.41421 | + | 6.41421i | −0.215855 | + | 0.215855i | −0.806749 | − | 0.590894i | \(-0.798775\pi\) |
0.590894 | + | 0.806749i | \(0.298775\pi\) | |||||||
\(884\) | 43.3137 | 1.45680 | ||||||||
\(885\) | −2.34315 | + | 15.3137i | −0.0787640 | + | 0.514765i | ||||
\(886\) | 99.8406 | 3.35421 | ||||||||
\(887\) | −18.2426 | + | 18.2426i | −0.612528 | + | 0.612528i | −0.943604 | − | 0.331076i | \(-0.892588\pi\) |
0.331076 | + | 0.943604i | \(0.392588\pi\) | |||||||
\(888\) | 51.4558 | + | 36.3848i | 1.72675 | + | 1.22099i | ||||
\(889\) | 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 | ||||||
\(897\) | −20.9706 | + | 29.6569i | −0.700187 | + | 0.990214i | ||||
\(898\) | 63.1127 | − | 63.1127i | 2.10610 | − | 2.10610i | ||||
\(899\) | 42.6274 | 1.42170 | ||||||||
\(900\) | −17.1716 | + | 54.7990i | −0.572386 | + | 1.82663i | ||||
\(901\) | 5.65685 | 0.188457 | ||||||||
\(902\) | −6.24264 | + | 6.24264i | −0.207857 | + | 0.207857i | ||||
\(903\) | −9.65685 | + | 13.6569i | −0.321360 | + | 0.454472i | ||||
\(904\) | − | 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 | 0.316369 | − | 0.948636i | \(-0.397536\pi\) |
−0.948636 | + | 0.316369i | \(0.897536\pi\) | |||||||
\(908\) | −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 | \(-0.378201\pi\) | |||||||
\(912\) | 12.0000 | + | 8.48528i | 0.397360 | + | 0.280976i | ||||
\(913\) | 5.07107 | − | 5.07107i | 0.167828 | − | 0.167828i | ||||
\(914\) | −35.7990 | −1.18413 | ||||||||
\(915\) | 6.14214 | − | 40.1421i | 0.203053 | − | 1.32706i | ||||
\(916\) | 6.34315 | 0.209583 | ||||||||
\(917\) | 0.686292 | − | 0.686292i | 0.0226633 | − | 0.0226633i | ||||
\(918\) | −13.6569 | + | 48.2843i | −0.450743 | + | 1.59362i | ||||
\(919\) | 30.6274i | 1.01031i | 0.863030 | + | 0.505153i | \(0.168564\pi\) | ||||
−0.863030 | + | 0.505153i | \(0.831436\pi\) | |||||||
\(920\) | 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 | ||||||
\(927\) | 13.7279 | + | 6.55635i | 0.450884 | + | 0.215339i | ||||
\(928\) | 5.41421 | − | 5.41421i | 0.177730 | − | 0.177730i | ||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | −48.8701 | − | 66.5269i | −1.60251 | − | 2.18150i | ||||
\(931\) | 17.8579 | 0.585268 | ||||||||
\(932\) | 31.9411 | − | 31.9411i | 1.04627 | − | 1.04627i | ||||
\(933\) | 0.201010 | + | 0.142136i | 0.00658078 | + | 0.00465331i | ||||
\(934\) | 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 | 0.974557 | − | 0.224141i | \(-0.0719577\pi\) |
−0.224141 | + | 0.974557i | \(0.571958\pi\) | |||||||
\(938\) | −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 | \(-0.134236\pi\) | |||||||
\(942\) | 25.5563 | − | 36.1421i | 0.832671 | − | 1.17757i | ||||
\(943\) | 19.1716 | − | 19.1716i | 0.624312 | − | 0.624312i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 7.95837 | + | 5.41421i | 0.258886 | + | 0.176124i | ||||
\(946\) | −28.1421 | −0.914980 | ||||||||
\(947\) | −8.75736 | + | 8.75736i | −0.284576 | + | 0.284576i | −0.834931 | − | 0.550355i | \(-0.814492\pi\) |
0.550355 | + | 0.834931i | \(0.314492\pi\) | |||||||
\(948\) | −19.7990 | + | 28.0000i | −0.643041 | + | 0.909398i | ||||
\(949\) | 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 | −0.995002 | − | 0.0998546i | \(-0.968162\pi\) |
−0.0998546 | − | 0.995002i | \(-0.531838\pi\) | |||||||
\(954\) | 3.41421 | + | 9.65685i | 0.110539 | + | 0.312652i | ||||
\(955\) | 11.3137 | + | 22.6274i | 0.366103 | + | 0.732206i | ||||
\(956\) | − | 60.4853i | − | 1.95623i | ||||||
\(957\) | −6.82843 | − | 4.82843i | −0.220732 | − | 0.156081i | ||||
\(958\) | 3.17157 | − | 3.17157i | 0.102469 | − | 0.102469i | ||||
\(959\) | −6.82843 | −0.220501 | ||||||||
\(960\) | −37.6274 | − | 5.75736i | −1.21442 | − | 0.185818i | ||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | −39.7990 | + | 39.7990i | −1.28317 | + | 1.28317i | ||||
\(963\) | 31.5563 | + | 15.0711i | 1.01689 | + | 0.485658i | ||||
\(964\) | 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 | 0.732601 | − | 0.680659i | \(-0.238306\pi\) |
−0.680659 | + | 0.732601i | \(0.738306\pi\) | |||||||
\(968\) | −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 | \(-0.103990\pi\) | |||||||
\(972\) | −59.5563 | + | 3.82843i | −1.91027 | + | 0.122797i | ||||
\(973\) | −3.71573 | + | 3.71573i | −0.119121 | + | 0.119121i | ||||
\(974\) | 46.8701 | 1.50181 | ||||||||
\(975\) | −21.7990 | − | 11.1716i | −0.698126 | − | 0.357777i | ||||
\(976\) | −31.4558 | −1.00688 | ||||||||
\(977\) | 24.1127 | − | 24.1127i | 0.771434 | − | 0.771434i | −0.206924 | − | 0.978357i | \(-0.566345\pi\) |
0.978357 | + | 0.206924i | \(0.0663451\pi\) | |||||||
\(978\) | −30.9706 | − | 21.8995i | −0.990329 | − | 0.700269i | ||||
\(979\) | − | 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 | \(-0.262408\pi\) |
−0.734126 | + | 0.679014i | \(0.762408\pi\) | |||||||
\(984\) | −4.72792 | − | 27.5563i | −0.150721 | − | 0.878464i | ||||
\(985\) | −14.1421 | + | 42.4264i | −0.450606 | + | 1.35182i | ||||
\(986\) | − | 46.6274i | − | 1.48492i | ||||||
\(987\) | 1.45584 | − | 2.05887i | 0.0463400 | − | 0.0655347i | ||||
\(988\) | −21.6569 | + | 21.6569i | −0.688996 | + | 0.688996i | ||||
\(989\) | 86.4264 | 2.74820 | ||||||||
\(990\) | 0.292893 | + | 16.1924i | 0.00930876 | + | 0.514628i | ||||
\(991\) | 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 | ||||
\(993\) | −10.4853 | + | 14.8284i | −0.332740 | + | 0.470566i | ||||
\(994\) | 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 | −0.983479 | − | 0.181025i | \(-0.942059\pi\) |
−0.181025 | − | 0.983479i | \(-0.557941\pi\) | |||||||
\(998\) | 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.a.122.1 | yes | 4 | |
3.2 | odd | 2 | 165.2.k.b.122.2 | yes | 4 | ||
5.2 | odd | 4 | 825.2.k.c.518.1 | 4 | |||
5.3 | odd | 4 | 165.2.k.b.23.2 | yes | 4 | ||
5.4 | even | 2 | 825.2.k.f.782.2 | 4 | |||
15.2 | even | 4 | 825.2.k.f.518.2 | 4 | |||
15.8 | even | 4 | inner | 165.2.k.a.23.1 | ✓ | 4 | |
15.14 | odd | 2 | 825.2.k.c.782.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.k.a.23.1 | ✓ | 4 | 15.8 | even | 4 | inner | |
165.2.k.a.122.1 | yes | 4 | 1.1 | even | 1 | trivial | |
165.2.k.b.23.2 | yes | 4 | 5.3 | odd | 4 | ||
165.2.k.b.122.2 | yes | 4 | 3.2 | odd | 2 | ||
825.2.k.c.518.1 | 4 | 5.2 | odd | 4 | |||
825.2.k.c.782.1 | 4 | 15.14 | odd | 2 | |||
825.2.k.f.518.2 | 4 | 15.2 | even | 4 | |||
825.2.k.f.782.2 | 4 | 5.4 | even | 2 |