Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(961,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(2.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.961 |
Dual form | 1110.2.h.e.961.1 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −2.37228 | −0.896638 | −0.448319 | − | 0.893874i | \(-0.647977\pi\) | ||||
−0.448319 | + | 0.893874i | \(0.647977\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 6.37228 | 1.92132 | 0.960658 | − | 0.277736i | \(-0.0895839\pi\) | ||||
0.960658 | + | 0.277736i | \(0.0895839\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.74456i | 1.31590i | 0.753059 | + | 0.657952i | \(0.228577\pi\) | ||||
−0.753059 | + | 0.657952i | \(0.771423\pi\) | |||||||
\(14\) | − | 2.37228i | − | 0.634019i | ||||||
\(15\) | − | 1.00000i | − | 0.258199i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.372281i | − | 0.0902915i | −0.998980 | − | 0.0451457i | \(-0.985625\pi\) | ||
0.998980 | − | 0.0451457i | \(-0.0143752\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 2.37228 | 0.517674 | ||||||||
\(22\) | 6.37228i | 1.35857i | ||||||||
\(23\) | 8.74456i | 1.82337i | 0.410893 | + | 0.911684i | \(0.365217\pi\) | ||||
−0.410893 | + | 0.911684i | \(0.634783\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −4.74456 | −0.930485 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.37228 | 0.448319 | ||||||||
\(29\) | − | 3.62772i | − | 0.673650i | −0.941567 | − | 0.336825i | \(-0.890647\pi\) | ||
0.941567 | − | 0.336825i | \(-0.109353\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 8.37228i | 1.50371i | 0.659331 | + | 0.751853i | \(0.270840\pi\) | ||||
−0.659331 | + | 0.751853i | \(0.729160\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −6.37228 | −1.10927 | ||||||||
\(34\) | 0.372281 | 0.0638457 | ||||||||
\(35\) | − | 2.37228i | − | 0.400989i | ||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −5.74456 | − | 2.00000i | −0.944400 | − | 0.328798i | ||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | − | 4.74456i | − | 0.759738i | ||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −9.11684 | −1.42381 | −0.711906 | − | 0.702275i | \(-0.752168\pi\) | ||||
−0.711906 | + | 0.702275i | \(0.752168\pi\) | |||||||
\(42\) | 2.37228i | 0.366051i | ||||||||
\(43\) | 4.37228i | 0.666767i | 0.942791 | + | 0.333383i | \(0.108190\pi\) | ||||
−0.942791 | + | 0.333383i | \(0.891810\pi\) | |||||||
\(44\) | −6.37228 | −0.960658 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | −8.74456 | −1.28932 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0.372281i | 0.0521298i | ||||||||
\(52\) | − | 4.74456i | − | 0.657952i | ||||||
\(53\) | −8.37228 | −1.15002 | −0.575011 | − | 0.818146i | \(-0.695002\pi\) | ||||
−0.575011 | + | 0.818146i | \(0.695002\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 6.37228i | 0.859238i | ||||||||
\(56\) | 2.37228i | 0.317009i | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 3.62772 | 0.476343 | ||||||||
\(59\) | 8.00000i | 1.04151i | 0.853706 | + | 0.520756i | \(0.174350\pi\) | ||||
−0.853706 | + | 0.520756i | \(0.825650\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 5.62772i | 0.720556i | 0.932845 | + | 0.360278i | \(0.117318\pi\) | ||||
−0.932845 | + | 0.360278i | \(0.882682\pi\) | |||||||
\(62\) | −8.37228 | −1.06328 | ||||||||
\(63\) | −2.37228 | −0.298879 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.74456 | −0.588491 | ||||||||
\(66\) | − | 6.37228i | − | 0.784374i | ||||||
\(67\) | 8.74456 | 1.06832 | 0.534159 | − | 0.845384i | \(-0.320628\pi\) | ||||
0.534159 | + | 0.845384i | \(0.320628\pi\) | |||||||
\(68\) | 0.372281i | 0.0451457i | ||||||||
\(69\) | − | 8.74456i | − | 1.05272i | ||||||
\(70\) | 2.37228 | 0.283542 | ||||||||
\(71\) | −8.74456 | −1.03779 | −0.518894 | − | 0.854838i | \(-0.673656\pi\) | ||||
−0.518894 | + | 0.854838i | \(0.673656\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 2.00000 | − | 5.74456i | 0.232495 | − | 0.667792i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 6.00000i | 0.688247i | ||||||||
\(77\) | −15.1168 | −1.72272 | ||||||||
\(78\) | 4.74456 | 0.537216 | ||||||||
\(79\) | 6.74456i | 0.758823i | 0.925228 | + | 0.379411i | \(0.123873\pi\) | ||||
−0.925228 | + | 0.379411i | \(0.876127\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 9.11684i | − | 1.00679i | ||||||
\(83\) | −5.48913 | −0.602510 | −0.301255 | − | 0.953544i | \(-0.597406\pi\) | ||||
−0.301255 | + | 0.953544i | \(0.597406\pi\) | |||||||
\(84\) | −2.37228 | −0.258837 | ||||||||
\(85\) | 0.372281 | 0.0403796 | ||||||||
\(86\) | −4.37228 | −0.471475 | ||||||||
\(87\) | 3.62772i | 0.388932i | ||||||||
\(88\) | − | 6.37228i | − | 0.679287i | ||||||
\(89\) | − | 2.74456i | − | 0.290923i | −0.989364 | − | 0.145462i | \(-0.953533\pi\) | ||
0.989364 | − | 0.145462i | \(-0.0464667\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | − | 11.2554i | − | 1.17989i | ||||||
\(92\) | − | 8.74456i | − | 0.911684i | ||||||
\(93\) | − | 8.37228i | − | 0.868165i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 7.11684i | 0.722606i | 0.932448 | + | 0.361303i | \(0.117668\pi\) | ||||
−0.932448 | + | 0.361303i | \(0.882332\pi\) | |||||||
\(98\) | − | 1.37228i | − | 0.138621i | ||||||
\(99\) | 6.37228 | 0.640438 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.25544 | −0.522936 | −0.261468 | − | 0.965212i | \(-0.584207\pi\) | ||||
−0.261468 | + | 0.965212i | \(0.584207\pi\) | |||||||
\(102\) | −0.372281 | −0.0368613 | ||||||||
\(103\) | 7.48913i | 0.737925i | 0.929444 | + | 0.368963i | \(0.120287\pi\) | ||||
−0.929444 | + | 0.368963i | \(0.879713\pi\) | |||||||
\(104\) | 4.74456 | 0.465243 | ||||||||
\(105\) | 2.37228i | 0.231511i | ||||||||
\(106\) | − | 8.37228i | − | 0.813188i | ||||||
\(107\) | 3.25544 | 0.314715 | 0.157358 | − | 0.987542i | \(-0.449703\pi\) | ||||
0.157358 | + | 0.987542i | \(0.449703\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − | 3.11684i | − | 0.298540i | −0.988797 | − | 0.149270i | \(-0.952308\pi\) | ||
0.988797 | − | 0.149270i | \(-0.0476923\pi\) | |||||||
\(110\) | −6.37228 | −0.607573 | ||||||||
\(111\) | 5.74456 | + | 2.00000i | 0.545250 | + | 0.189832i | ||||
\(112\) | −2.37228 | −0.224160 | ||||||||
\(113\) | − | 9.86141i | − | 0.927683i | −0.885918 | − | 0.463842i | \(-0.846471\pi\) | ||
0.885918 | − | 0.463842i | \(-0.153529\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | −8.74456 | −0.815435 | ||||||||
\(116\) | 3.62772i | 0.336825i | ||||||||
\(117\) | 4.74456i | 0.438635i | ||||||||
\(118\) | −8.00000 | −0.736460 | ||||||||
\(119\) | 0.883156i | 0.0809588i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 29.6060 | 2.69145 | ||||||||
\(122\) | −5.62772 | −0.509510 | ||||||||
\(123\) | 9.11684 | 0.822038 | ||||||||
\(124\) | − | 8.37228i | − | 0.751853i | ||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | − | 2.37228i | − | 0.211340i | ||||||
\(127\) | −9.48913 | −0.842024 | −0.421012 | − | 0.907055i | \(-0.638325\pi\) | ||||
−0.421012 | + | 0.907055i | \(0.638325\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | − | 4.37228i | − | 0.384958i | ||||||
\(130\) | − | 4.74456i | − | 0.416126i | ||||||
\(131\) | 9.48913i | 0.829069i | 0.910034 | + | 0.414534i | \(0.136056\pi\) | ||||
−0.910034 | + | 0.414534i | \(0.863944\pi\) | |||||||
\(132\) | 6.37228 | 0.554636 | ||||||||
\(133\) | 14.2337i | 1.23422i | ||||||||
\(134\) | 8.74456i | 0.755415i | ||||||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | −0.372281 | −0.0319229 | ||||||||
\(137\) | −2.74456 | −0.234484 | −0.117242 | − | 0.993103i | \(-0.537405\pi\) | ||||
−0.117242 | + | 0.993103i | \(0.537405\pi\) | |||||||
\(138\) | 8.74456 | 0.744387 | ||||||||
\(139\) | −1.62772 | −0.138061 | −0.0690306 | − | 0.997615i | \(-0.521991\pi\) | ||||
−0.0690306 | + | 0.997615i | \(0.521991\pi\) | |||||||
\(140\) | 2.37228i | 0.200494i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 8.74456i | − | 0.733827i | ||||||
\(143\) | 30.2337i | 2.52827i | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.62772 | 0.301266 | ||||||||
\(146\) | 14.0000i | 1.15865i | ||||||||
\(147\) | 1.37228 | 0.113184 | ||||||||
\(148\) | 5.74456 | + | 2.00000i | 0.472200 | + | 0.164399i | ||||
\(149\) | 11.4891 | 0.941226 | 0.470613 | − | 0.882340i | \(-0.344033\pi\) | ||||
0.470613 | + | 0.882340i | \(0.344033\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | −11.2554 | −0.915955 | −0.457977 | − | 0.888964i | \(-0.651426\pi\) | ||||
−0.457977 | + | 0.888964i | \(0.651426\pi\) | |||||||
\(152\) | −6.00000 | −0.486664 | ||||||||
\(153\) | − | 0.372281i | − | 0.0300972i | ||||||
\(154\) | − | 15.1168i | − | 1.21815i | ||||||
\(155\) | −8.37228 | −0.672478 | ||||||||
\(156\) | 4.74456i | 0.379869i | ||||||||
\(157\) | −16.3723 | −1.30665 | −0.653325 | − | 0.757077i | \(-0.726627\pi\) | ||||
−0.653325 | + | 0.757077i | \(0.726627\pi\) | |||||||
\(158\) | −6.74456 | −0.536569 | ||||||||
\(159\) | 8.37228 | 0.663965 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | − | 20.7446i | − | 1.63490i | ||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 9.11684i | 0.714086i | 0.934088 | + | 0.357043i | \(0.116215\pi\) | ||||
−0.934088 | + | 0.357043i | \(0.883785\pi\) | |||||||
\(164\) | 9.11684 | 0.711906 | ||||||||
\(165\) | − | 6.37228i | − | 0.496081i | ||||||
\(166\) | − | 5.48913i | − | 0.426039i | ||||||
\(167\) | − | 3.25544i | − | 0.251913i | −0.992036 | − | 0.125957i | \(-0.959800\pi\) | ||
0.992036 | − | 0.125957i | \(-0.0402000\pi\) | |||||||
\(168\) | − | 2.37228i | − | 0.183025i | ||||||
\(169\) | −9.51087 | −0.731606 | ||||||||
\(170\) | 0.372281i | 0.0285527i | ||||||||
\(171\) | − | 6.00000i | − | 0.458831i | ||||||
\(172\) | − | 4.37228i | − | 0.333383i | ||||||
\(173\) | −7.62772 | −0.579925 | −0.289962 | − | 0.957038i | \(-0.593643\pi\) | ||||
−0.289962 | + | 0.957038i | \(0.593643\pi\) | |||||||
\(174\) | −3.62772 | −0.275017 | ||||||||
\(175\) | 2.37228 | 0.179328 | ||||||||
\(176\) | 6.37228 | 0.480329 | ||||||||
\(177\) | − | 8.00000i | − | 0.601317i | ||||||
\(178\) | 2.74456 | 0.205714 | ||||||||
\(179\) | − | 8.74456i | − | 0.653599i | −0.945094 | − | 0.326800i | \(-0.894030\pi\) | ||
0.945094 | − | 0.326800i | \(-0.105970\pi\) | |||||||
\(180\) | − | 1.00000i | − | 0.0745356i | ||||||
\(181\) | 22.7446 | 1.69059 | 0.845295 | − | 0.534300i | \(-0.179425\pi\) | ||||
0.845295 | + | 0.534300i | \(0.179425\pi\) | |||||||
\(182\) | 11.2554 | 0.834309 | ||||||||
\(183\) | − | 5.62772i | − | 0.416013i | ||||||
\(184\) | 8.74456 | 0.644658 | ||||||||
\(185\) | 2.00000 | − | 5.74456i | 0.147043 | − | 0.422349i | ||||
\(186\) | 8.37228 | 0.613885 | ||||||||
\(187\) | − | 2.37228i | − | 0.173478i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.37228 | 0.172558 | ||||||||
\(190\) | 6.00000i | 0.435286i | ||||||||
\(191\) | 7.11684i | 0.514957i | 0.966284 | + | 0.257478i | \(0.0828916\pi\) | ||||
−0.966284 | + | 0.257478i | \(0.917108\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − | 18.2337i | − | 1.31249i | −0.754548 | − | 0.656245i | \(-0.772144\pi\) | ||
0.754548 | − | 0.656245i | \(-0.227856\pi\) | |||||||
\(194\) | −7.11684 | −0.510960 | ||||||||
\(195\) | 4.74456 | 0.339765 | ||||||||
\(196\) | 1.37228 | 0.0980201 | ||||||||
\(197\) | 15.4891 | 1.10355 | 0.551777 | − | 0.833992i | \(-0.313950\pi\) | ||||
0.551777 | + | 0.833992i | \(0.313950\pi\) | |||||||
\(198\) | 6.37228i | 0.452858i | ||||||||
\(199\) | 10.7446i | 0.761662i | 0.924645 | + | 0.380831i | \(0.124362\pi\) | ||||
−0.924645 | + | 0.380831i | \(0.875638\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −8.74456 | −0.616794 | ||||||||
\(202\) | − | 5.25544i | − | 0.369771i | ||||||
\(203\) | 8.60597i | 0.604021i | ||||||||
\(204\) | − | 0.372281i | − | 0.0260649i | ||||||
\(205\) | − | 9.11684i | − | 0.636748i | ||||||
\(206\) | −7.48913 | −0.521792 | ||||||||
\(207\) | 8.74456i | 0.607789i | ||||||||
\(208\) | 4.74456i | 0.328976i | ||||||||
\(209\) | − | 38.2337i | − | 2.64468i | ||||||
\(210\) | −2.37228 | −0.163703 | ||||||||
\(211\) | 23.8614 | 1.64269 | 0.821343 | − | 0.570434i | \(-0.193225\pi\) | ||||
0.821343 | + | 0.570434i | \(0.193225\pi\) | |||||||
\(212\) | 8.37228 | 0.575011 | ||||||||
\(213\) | 8.74456 | 0.599168 | ||||||||
\(214\) | 3.25544i | 0.222537i | ||||||||
\(215\) | −4.37228 | −0.298187 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | − | 19.8614i | − | 1.34828i | ||||||
\(218\) | 3.11684 | 0.211099 | ||||||||
\(219\) | −14.0000 | −0.946032 | ||||||||
\(220\) | − | 6.37228i | − | 0.429619i | ||||||
\(221\) | 1.76631 | 0.118815 | ||||||||
\(222\) | −2.00000 | + | 5.74456i | −0.134231 | + | 0.385550i | ||||
\(223\) | 18.3723 | 1.23030 | 0.615149 | − | 0.788411i | \(-0.289096\pi\) | ||||
0.615149 | + | 0.788411i | \(0.289096\pi\) | |||||||
\(224\) | − | 2.37228i | − | 0.158505i | ||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 9.86141 | 0.655971 | ||||||||
\(227\) | 6.37228i | 0.422943i | 0.977384 | + | 0.211472i | \(0.0678256\pi\) | ||||
−0.977384 | + | 0.211472i | \(0.932174\pi\) | |||||||
\(228\) | − | 6.00000i | − | 0.397360i | ||||||
\(229\) | 4.51087 | 0.298087 | 0.149043 | − | 0.988831i | \(-0.452381\pi\) | ||||
0.149043 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(230\) | − | 8.74456i | − | 0.576599i | ||||||
\(231\) | 15.1168 | 0.994615 | ||||||||
\(232\) | −3.62772 | −0.238171 | ||||||||
\(233\) | 14.7446 | 0.965948 | 0.482974 | − | 0.875635i | \(-0.339556\pi\) | ||||
0.482974 | + | 0.875635i | \(0.339556\pi\) | |||||||
\(234\) | −4.74456 | −0.310162 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 8.00000i | − | 0.520756i | ||||||
\(237\) | − | 6.74456i | − | 0.438106i | ||||||
\(238\) | −0.883156 | −0.0572465 | ||||||||
\(239\) | − | 7.86141i | − | 0.508512i | −0.967137 | − | 0.254256i | \(-0.918169\pi\) | ||
0.967137 | − | 0.254256i | \(-0.0818306\pi\) | |||||||
\(240\) | − | 1.00000i | − | 0.0645497i | ||||||
\(241\) | 21.4891i | 1.38424i | 0.721784 | + | 0.692118i | \(0.243322\pi\) | ||||
−0.721784 | + | 0.692118i | \(0.756678\pi\) | |||||||
\(242\) | 29.6060i | 1.90314i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | − | 5.62772i | − | 0.360278i | ||||||
\(245\) | − | 1.37228i | − | 0.0876718i | ||||||
\(246\) | 9.11684i | 0.581269i | ||||||||
\(247\) | 28.4674 | 1.81134 | ||||||||
\(248\) | 8.37228 | 0.531640 | ||||||||
\(249\) | 5.48913 | 0.347859 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 4.00000i | 0.252478i | 0.992000 | + | 0.126239i | \(0.0402906\pi\) | ||||
−0.992000 | + | 0.126239i | \(0.959709\pi\) | |||||||
\(252\) | 2.37228 | 0.149440 | ||||||||
\(253\) | 55.7228i | 3.50326i | ||||||||
\(254\) | − | 9.48913i | − | 0.595401i | ||||||
\(255\) | −0.372281 | −0.0233132 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.4891i | 1.46521i | 0.680653 | + | 0.732606i | \(0.261696\pi\) | ||||
−0.680653 | + | 0.732606i | \(0.738304\pi\) | |||||||
\(258\) | 4.37228 | 0.272206 | ||||||||
\(259\) | 13.6277 | + | 4.74456i | 0.846785 | + | 0.294813i | ||||
\(260\) | 4.74456 | 0.294245 | ||||||||
\(261\) | − | 3.62772i | − | 0.224550i | ||||||
\(262\) | −9.48913 | −0.586240 | ||||||||
\(263\) | 16.6060 | 1.02397 | 0.511984 | − | 0.858995i | \(-0.328911\pi\) | ||||
0.511984 | + | 0.858995i | \(0.328911\pi\) | |||||||
\(264\) | 6.37228i | 0.392187i | ||||||||
\(265\) | − | 8.37228i | − | 0.514305i | ||||||
\(266\) | −14.2337 | −0.872723 | ||||||||
\(267\) | 2.74456i | 0.167965i | ||||||||
\(268\) | −8.74456 | −0.534159 | ||||||||
\(269\) | −28.2337 | −1.72144 | −0.860719 | − | 0.509080i | \(-0.829986\pi\) | ||||
−0.860719 | + | 0.509080i | \(0.829986\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 1.48913 | 0.0904579 | 0.0452290 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452290 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(272\) | − | 0.372281i | − | 0.0225729i | ||||||
\(273\) | 11.2554i | 0.681210i | ||||||||
\(274\) | − | 2.74456i | − | 0.165805i | ||||||
\(275\) | −6.37228 | −0.384263 | ||||||||
\(276\) | 8.74456i | 0.526361i | ||||||||
\(277\) | − | 9.48913i | − | 0.570146i | −0.958506 | − | 0.285073i | \(-0.907982\pi\) | ||
0.958506 | − | 0.285073i | \(-0.0920179\pi\) | |||||||
\(278\) | − | 1.62772i | − | 0.0976241i | ||||||
\(279\) | 8.37228i | 0.501235i | ||||||||
\(280\) | −2.37228 | −0.141771 | ||||||||
\(281\) | − | 20.9783i | − | 1.25146i | −0.780041 | − | 0.625729i | \(-0.784802\pi\) | ||
0.780041 | − | 0.625729i | \(-0.215198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 30.7446i | − | 1.82757i | −0.406193 | − | 0.913787i | \(-0.633144\pi\) | ||
0.406193 | − | 0.913787i | \(-0.366856\pi\) | |||||||
\(284\) | 8.74456 | 0.518894 | ||||||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | −30.2337 | −1.78776 | ||||||||
\(287\) | 21.6277 | 1.27664 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 16.8614 | 0.991847 | ||||||||
\(290\) | 3.62772i | 0.213027i | ||||||||
\(291\) | − | 7.11684i | − | 0.417197i | ||||||
\(292\) | −14.0000 | −0.819288 | ||||||||
\(293\) | −13.1168 | −0.766294 | −0.383147 | − | 0.923687i | \(-0.625160\pi\) | ||||
−0.383147 | + | 0.923687i | \(0.625160\pi\) | |||||||
\(294\) | 1.37228i | 0.0800331i | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | −2.00000 | + | 5.74456i | −0.116248 | + | 0.333896i | ||||
\(297\) | −6.37228 | −0.369757 | ||||||||
\(298\) | 11.4891i | 0.665547i | ||||||||
\(299\) | −41.4891 | −2.39938 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | − | 10.3723i | − | 0.597848i | ||||||
\(302\) | − | 11.2554i | − | 0.647678i | ||||||
\(303\) | 5.25544 | 0.301917 | ||||||||
\(304\) | − | 6.00000i | − | 0.344124i | ||||||
\(305\) | −5.62772 | −0.322242 | ||||||||
\(306\) | 0.372281 | 0.0212819 | ||||||||
\(307\) | 2.51087 | 0.143303 | 0.0716516 | − | 0.997430i | \(-0.477173\pi\) | ||||
0.0716516 | + | 0.997430i | \(0.477173\pi\) | |||||||
\(308\) | 15.1168 | 0.861362 | ||||||||
\(309\) | − | 7.48913i | − | 0.426041i | ||||||
\(310\) | − | 8.37228i | − | 0.475514i | ||||||
\(311\) | 19.8614i | 1.12624i | 0.826376 | + | 0.563119i | \(0.190399\pi\) | ||||
−0.826376 | + | 0.563119i | \(0.809601\pi\) | |||||||
\(312\) | −4.74456 | −0.268608 | ||||||||
\(313\) | 18.2337i | 1.03063i | 0.857001 | + | 0.515314i | \(0.172325\pi\) | ||||
−0.857001 | + | 0.515314i | \(0.827675\pi\) | |||||||
\(314\) | − | 16.3723i | − | 0.923941i | ||||||
\(315\) | − | 2.37228i | − | 0.133663i | ||||||
\(316\) | − | 6.74456i | − | 0.379411i | ||||||
\(317\) | 16.3723 | 0.919559 | 0.459779 | − | 0.888033i | \(-0.347928\pi\) | ||||
0.459779 | + | 0.888033i | \(0.347928\pi\) | |||||||
\(318\) | 8.37228i | 0.469494i | ||||||||
\(319\) | − | 23.1168i | − | 1.29429i | ||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | −3.25544 | −0.181701 | ||||||||
\(322\) | 20.7446 | 1.15605 | ||||||||
\(323\) | −2.23369 | −0.124286 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − | 4.74456i | − | 0.263181i | ||||||
\(326\) | −9.11684 | −0.504935 | ||||||||
\(327\) | 3.11684i | 0.172362i | ||||||||
\(328\) | 9.11684i | 0.503393i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.37228 | 0.350783 | ||||||||
\(331\) | 3.48913i | 0.191780i | 0.995392 | + | 0.0958898i | \(0.0305697\pi\) | ||||
−0.995392 | + | 0.0958898i | \(0.969430\pi\) | |||||||
\(332\) | 5.48913 | 0.301255 | ||||||||
\(333\) | −5.74456 | − | 2.00000i | −0.314800 | − | 0.109599i | ||||
\(334\) | 3.25544 | 0.178130 | ||||||||
\(335\) | 8.74456i | 0.477766i | ||||||||
\(336\) | 2.37228 | 0.129419 | ||||||||
\(337\) | −34.7446 | −1.89266 | −0.946328 | − | 0.323206i | \(-0.895239\pi\) | ||||
−0.946328 | + | 0.323206i | \(0.895239\pi\) | |||||||
\(338\) | − | 9.51087i | − | 0.517323i | ||||||
\(339\) | 9.86141i | 0.535598i | ||||||||
\(340\) | −0.372281 | −0.0201898 | ||||||||
\(341\) | 53.3505i | 2.88909i | ||||||||
\(342\) | 6.00000 | 0.324443 | ||||||||
\(343\) | 19.8614 | 1.07242 | ||||||||
\(344\) | 4.37228 | 0.235738 | ||||||||
\(345\) | 8.74456 | 0.470791 | ||||||||
\(346\) | − | 7.62772i | − | 0.410069i | ||||||
\(347\) | 30.9783i | 1.66300i | 0.555525 | + | 0.831500i | \(0.312517\pi\) | ||||
−0.555525 | + | 0.831500i | \(0.687483\pi\) | |||||||
\(348\) | − | 3.62772i | − | 0.194466i | ||||||
\(349\) | 11.4891 | 0.614999 | 0.307499 | − | 0.951548i | \(-0.400508\pi\) | ||||
0.307499 | + | 0.951548i | \(0.400508\pi\) | |||||||
\(350\) | 2.37228i | 0.126804i | ||||||||
\(351\) | − | 4.74456i | − | 0.253246i | ||||||
\(352\) | 6.37228i | 0.339644i | ||||||||
\(353\) | − | 5.11684i | − | 0.272342i | −0.990685 | − | 0.136171i | \(-0.956520\pi\) | ||
0.990685 | − | 0.136171i | \(-0.0434797\pi\) | |||||||
\(354\) | 8.00000 | 0.425195 | ||||||||
\(355\) | − | 8.74456i | − | 0.464113i | ||||||
\(356\) | 2.74456i | 0.145462i | ||||||||
\(357\) | − | 0.883156i | − | 0.0467416i | ||||||
\(358\) | 8.74456 | 0.462164 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 22.7446i | 1.19543i | ||||||||
\(363\) | −29.6060 | −1.55391 | ||||||||
\(364\) | 11.2554i | 0.589945i | ||||||||
\(365\) | 14.0000i | 0.732793i | ||||||||
\(366\) | 5.62772 | 0.294166 | ||||||||
\(367\) | 13.6277 | 0.711361 | 0.355681 | − | 0.934608i | \(-0.384249\pi\) | ||||
0.355681 | + | 0.934608i | \(0.384249\pi\) | |||||||
\(368\) | 8.74456i | 0.455842i | ||||||||
\(369\) | −9.11684 | −0.474604 | ||||||||
\(370\) | 5.74456 | + | 2.00000i | 0.298646 | + | 0.103975i | ||||
\(371\) | 19.8614 | 1.03115 | ||||||||
\(372\) | 8.37228i | 0.434083i | ||||||||
\(373\) | −23.4891 | −1.21622 | −0.608110 | − | 0.793852i | \(-0.708072\pi\) | ||||
−0.608110 | + | 0.793852i | \(0.708072\pi\) | |||||||
\(374\) | 2.37228 | 0.122668 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.2119 | 0.886460 | ||||||||
\(378\) | 2.37228i | 0.122017i | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | −6.00000 | −0.307794 | ||||||||
\(381\) | 9.48913 | 0.486143 | ||||||||
\(382\) | −7.11684 | −0.364129 | ||||||||
\(383\) | − | 35.7228i | − | 1.82535i | −0.408686 | − | 0.912675i | \(-0.634013\pi\) | ||
0.408686 | − | 0.912675i | \(-0.365987\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − | 15.1168i | − | 0.770426i | ||||||
\(386\) | 18.2337 | 0.928070 | ||||||||
\(387\) | 4.37228i | 0.222256i | ||||||||
\(388\) | − | 7.11684i | − | 0.361303i | ||||||
\(389\) | 5.86141i | 0.297185i | 0.988899 | + | 0.148593i | \(0.0474743\pi\) | ||||
−0.988899 | + | 0.148593i | \(0.952526\pi\) | |||||||
\(390\) | 4.74456i | 0.240250i | ||||||||
\(391\) | 3.25544 | 0.164635 | ||||||||
\(392\) | 1.37228i | 0.0693107i | ||||||||
\(393\) | − | 9.48913i | − | 0.478663i | ||||||
\(394\) | 15.4891i | 0.780331i | ||||||||
\(395\) | −6.74456 | −0.339356 | ||||||||
\(396\) | −6.37228 | −0.320219 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | −10.7446 | −0.538576 | ||||||||
\(399\) | − | 14.2337i | − | 0.712576i | ||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − | 28.9783i | − | 1.44710i | −0.690269 | − | 0.723552i | \(-0.742508\pi\) | ||
0.690269 | − | 0.723552i | \(-0.257492\pi\) | |||||||
\(402\) | − | 8.74456i | − | 0.436139i | ||||||
\(403\) | −39.7228 | −1.97873 | ||||||||
\(404\) | 5.25544 | 0.261468 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −8.60597 | −0.427107 | ||||||||
\(407\) | −36.6060 | − | 12.7446i | −1.81449 | − | 0.631725i | ||||
\(408\) | 0.372281 | 0.0184307 | ||||||||
\(409\) | 21.4891i | 1.06257i | 0.847194 | + | 0.531284i | \(0.178290\pi\) | ||||
−0.847194 | + | 0.531284i | \(0.821710\pi\) | |||||||
\(410\) | 9.11684 | 0.450249 | ||||||||
\(411\) | 2.74456 | 0.135379 | ||||||||
\(412\) | − | 7.48913i | − | 0.368963i | ||||||
\(413\) | − | 18.9783i | − | 0.933859i | ||||||
\(414\) | −8.74456 | −0.429772 | ||||||||
\(415\) | − | 5.48913i | − | 0.269451i | ||||||
\(416\) | −4.74456 | −0.232621 | ||||||||
\(417\) | 1.62772 | 0.0797097 | ||||||||
\(418\) | 38.2337 | 1.87007 | ||||||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | − | 2.37228i | − | 0.115755i | ||||||
\(421\) | 8.74456i | 0.426184i | 0.977032 | + | 0.213092i | \(0.0683534\pi\) | ||||
−0.977032 | + | 0.213092i | \(0.931647\pi\) | |||||||
\(422\) | 23.8614i | 1.16156i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.37228i | 0.406594i | ||||||||
\(425\) | 0.372281i | 0.0180583i | ||||||||
\(426\) | 8.74456i | 0.423675i | ||||||||
\(427\) | − | 13.3505i | − | 0.646078i | ||||||
\(428\) | −3.25544 | −0.157358 | ||||||||
\(429\) | − | 30.2337i | − | 1.45970i | ||||||
\(430\) | − | 4.37228i | − | 0.210850i | ||||||
\(431\) | − | 13.6277i | − | 0.656424i | −0.944604 | − | 0.328212i | \(-0.893554\pi\) | ||
0.944604 | − | 0.328212i | \(-0.106446\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −11.4891 | −0.552132 | −0.276066 | − | 0.961139i | \(-0.589031\pi\) | ||||
−0.276066 | + | 0.961139i | \(0.589031\pi\) | |||||||
\(434\) | 19.8614 | 0.953378 | ||||||||
\(435\) | −3.62772 | −0.173936 | ||||||||
\(436\) | 3.11684i | 0.149270i | ||||||||
\(437\) | 52.4674 | 2.50985 | ||||||||
\(438\) | − | 14.0000i | − | 0.668946i | ||||||
\(439\) | − | 12.3723i | − | 0.590497i | −0.955421 | − | 0.295248i | \(-0.904598\pi\) | ||
0.955421 | − | 0.295248i | \(-0.0954024\pi\) | |||||||
\(440\) | 6.37228 | 0.303787 | ||||||||
\(441\) | −1.37228 | −0.0653467 | ||||||||
\(442\) | 1.76631i | 0.0840149i | ||||||||
\(443\) | 4.00000 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(444\) | −5.74456 | − | 2.00000i | −0.272625 | − | 0.0949158i | ||||
\(445\) | 2.74456 | 0.130105 | ||||||||
\(446\) | 18.3723i | 0.869953i | ||||||||
\(447\) | −11.4891 | −0.543417 | ||||||||
\(448\) | 2.37228 | 0.112080 | ||||||||
\(449\) | − | 36.9783i | − | 1.74511i | −0.488515 | − | 0.872556i | \(-0.662461\pi\) | ||
0.488515 | − | 0.872556i | \(-0.337539\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | −58.0951 | −2.73559 | ||||||||
\(452\) | 9.86141i | 0.463842i | ||||||||
\(453\) | 11.2554 | 0.528827 | ||||||||
\(454\) | −6.37228 | −0.299066 | ||||||||
\(455\) | 11.2554 | 0.527663 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | 5.62772i | 0.263254i | 0.991299 | + | 0.131627i | \(0.0420200\pi\) | ||||
−0.991299 | + | 0.131627i | \(0.957980\pi\) | |||||||
\(458\) | 4.51087i | 0.210779i | ||||||||
\(459\) | 0.372281i | 0.0173766i | ||||||||
\(460\) | 8.74456 | 0.407717 | ||||||||
\(461\) | − | 14.6060i | − | 0.680268i | −0.940377 | − | 0.340134i | \(-0.889528\pi\) | ||
0.940377 | − | 0.340134i | \(-0.110472\pi\) | |||||||
\(462\) | 15.1168i | 0.703299i | ||||||||
\(463\) | − | 12.2337i | − | 0.568548i | −0.958743 | − | 0.284274i | \(-0.908248\pi\) | ||
0.958743 | − | 0.284274i | \(-0.0917525\pi\) | |||||||
\(464\) | − | 3.62772i | − | 0.168413i | ||||||
\(465\) | 8.37228 | 0.388255 | ||||||||
\(466\) | 14.7446i | 0.683029i | ||||||||
\(467\) | − | 26.3723i | − | 1.22036i | −0.792261 | − | 0.610182i | \(-0.791096\pi\) | ||
0.792261 | − | 0.610182i | \(-0.208904\pi\) | |||||||
\(468\) | − | 4.74456i | − | 0.219317i | ||||||
\(469\) | −20.7446 | −0.957895 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.3723 | 0.754395 | ||||||||
\(472\) | 8.00000 | 0.368230 | ||||||||
\(473\) | 27.8614i | 1.28107i | ||||||||
\(474\) | 6.74456 | 0.309788 | ||||||||
\(475\) | 6.00000i | 0.275299i | ||||||||
\(476\) | − | 0.883156i | − | 0.0404794i | ||||||
\(477\) | −8.37228 | −0.383340 | ||||||||
\(478\) | 7.86141 | 0.359572 | ||||||||
\(479\) | − | 10.9783i | − | 0.501609i | −0.968038 | − | 0.250805i | \(-0.919305\pi\) | ||
0.968038 | − | 0.250805i | \(-0.0806951\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 9.48913 | − | 27.2554i | 0.432667 | − | 1.24274i | ||||
\(482\) | −21.4891 | −0.978803 | ||||||||
\(483\) | 20.7446i | 0.943910i | ||||||||
\(484\) | −29.6060 | −1.34573 | ||||||||
\(485\) | −7.11684 | −0.323159 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 18.7446i | 0.849397i | 0.905335 | + | 0.424699i | \(0.139620\pi\) | ||||
−0.905335 | + | 0.424699i | \(0.860380\pi\) | |||||||
\(488\) | 5.62772 | 0.254755 | ||||||||
\(489\) | − | 9.11684i | − | 0.412278i | ||||||
\(490\) | 1.37228 | 0.0619934 | ||||||||
\(491\) | 36.4674 | 1.64575 | 0.822875 | − | 0.568223i | \(-0.192369\pi\) | ||||
0.822875 | + | 0.568223i | \(0.192369\pi\) | |||||||
\(492\) | −9.11684 | −0.411019 | ||||||||
\(493\) | −1.35053 | −0.0608249 | ||||||||
\(494\) | 28.4674i | 1.28081i | ||||||||
\(495\) | 6.37228i | 0.286413i | ||||||||
\(496\) | 8.37228i | 0.375927i | ||||||||
\(497\) | 20.7446 | 0.930521 | ||||||||
\(498\) | 5.48913i | 0.245974i | ||||||||
\(499\) | 24.9783i | 1.11818i | 0.829107 | + | 0.559090i | \(0.188849\pi\) | ||||
−0.829107 | + | 0.559090i | \(0.811151\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 3.25544i | 0.145442i | ||||||||
\(502\) | −4.00000 | −0.178529 | ||||||||
\(503\) | − | 21.4891i | − | 0.958153i | −0.877773 | − | 0.479076i | \(-0.840972\pi\) | ||
0.877773 | − | 0.479076i | \(-0.159028\pi\) | |||||||
\(504\) | 2.37228i | 0.105670i | ||||||||
\(505\) | − | 5.25544i | − | 0.233864i | ||||||
\(506\) | −55.7228 | −2.47718 | ||||||||
\(507\) | 9.51087 | 0.422393 | ||||||||
\(508\) | 9.48913 | 0.421012 | ||||||||
\(509\) | −18.7446 | −0.830838 | −0.415419 | − | 0.909630i | \(-0.636365\pi\) | ||||
−0.415419 | + | 0.909630i | \(0.636365\pi\) | |||||||
\(510\) | − | 0.372281i | − | 0.0164849i | ||||||
\(511\) | −33.2119 | −1.46921 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 6.00000i | 0.264906i | ||||||||
\(514\) | −23.4891 | −1.03606 | ||||||||
\(515\) | −7.48913 | −0.330010 | ||||||||
\(516\) | 4.37228i | 0.192479i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.74456 | + | 13.6277i | −0.208464 | + | 0.598768i | ||||
\(519\) | 7.62772 | 0.334820 | ||||||||
\(520\) | 4.74456i | 0.208063i | ||||||||
\(521\) | 5.11684 | 0.224173 | 0.112087 | − | 0.993698i | \(-0.464247\pi\) | ||||
0.112087 | + | 0.993698i | \(0.464247\pi\) | |||||||
\(522\) | 3.62772 | 0.158781 | ||||||||
\(523\) | 29.2554i | 1.27925i | 0.768687 | + | 0.639625i | \(0.220911\pi\) | ||||
−0.768687 | + | 0.639625i | \(0.779089\pi\) | |||||||
\(524\) | − | 9.48913i | − | 0.414534i | ||||||
\(525\) | −2.37228 | −0.103535 | ||||||||
\(526\) | 16.6060i | 0.724055i | ||||||||
\(527\) | 3.11684 | 0.135772 | ||||||||
\(528\) | −6.37228 | −0.277318 | ||||||||
\(529\) | −53.4674 | −2.32467 | ||||||||
\(530\) | 8.37228 | 0.363669 | ||||||||
\(531\) | 8.00000i | 0.347170i | ||||||||
\(532\) | − | 14.2337i | − | 0.617109i | ||||||
\(533\) | − | 43.2554i | − | 1.87360i | ||||||
\(534\) | −2.74456 | −0.118769 | ||||||||
\(535\) | 3.25544i | 0.140745i | ||||||||
\(536\) | − | 8.74456i | − | 0.377708i | ||||||
\(537\) | 8.74456i | 0.377356i | ||||||||
\(538\) | − | 28.2337i | − | 1.21724i | ||||||
\(539\) | −8.74456 | −0.376655 | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | − | 27.7228i | − | 1.19190i | −0.803023 | − | 0.595948i | \(-0.796776\pi\) | ||
0.803023 | − | 0.595948i | \(-0.203224\pi\) | |||||||
\(542\) | 1.48913i | 0.0639634i | ||||||||
\(543\) | −22.7446 | −0.976063 | ||||||||
\(544\) | 0.372281 | 0.0159614 | ||||||||
\(545\) | 3.11684 | 0.133511 | ||||||||
\(546\) | −11.2554 | −0.481688 | ||||||||
\(547\) | − | 11.3505i | − | 0.485314i | −0.970112 | − | 0.242657i | \(-0.921981\pi\) | ||
0.970112 | − | 0.242657i | \(-0.0780189\pi\) | |||||||
\(548\) | 2.74456 | 0.117242 | ||||||||
\(549\) | 5.62772i | 0.240185i | ||||||||
\(550\) | − | 6.37228i | − | 0.271715i | ||||||
\(551\) | −21.7663 | −0.927276 | ||||||||
\(552\) | −8.74456 | −0.372193 | ||||||||
\(553\) | − | 16.0000i | − | 0.680389i | ||||||
\(554\) | 9.48913 | 0.403154 | ||||||||
\(555\) | −2.00000 | + | 5.74456i | −0.0848953 | + | 0.243843i | ||||
\(556\) | 1.62772 | 0.0690306 | ||||||||
\(557\) | − | 24.2337i | − | 1.02681i | −0.858145 | − | 0.513407i | \(-0.828383\pi\) | ||
0.858145 | − | 0.513407i | \(-0.171617\pi\) | |||||||
\(558\) | −8.37228 | −0.354427 | ||||||||
\(559\) | −20.7446 | −0.877402 | ||||||||
\(560\) | − | 2.37228i | − | 0.100247i | ||||||
\(561\) | 2.37228i | 0.100158i | ||||||||
\(562\) | 20.9783 | 0.884914 | ||||||||
\(563\) | 3.86141i | 0.162739i | 0.996684 | + | 0.0813694i | \(0.0259294\pi\) | ||||
−0.996684 | + | 0.0813694i | \(0.974071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.86141 | 0.414872 | ||||||||
\(566\) | 30.7446 | 1.29229 | ||||||||
\(567\) | −2.37228 | −0.0996265 | ||||||||
\(568\) | 8.74456i | 0.366914i | ||||||||
\(569\) | 21.2554i | 0.891074i | 0.895263 | + | 0.445537i | \(0.146987\pi\) | ||||
−0.895263 | + | 0.445537i | \(0.853013\pi\) | |||||||
\(570\) | − | 6.00000i | − | 0.251312i | ||||||
\(571\) | 41.3505 | 1.73047 | 0.865233 | − | 0.501370i | \(-0.167170\pi\) | ||||
0.865233 | + | 0.501370i | \(0.167170\pi\) | |||||||
\(572\) | − | 30.2337i | − | 1.26413i | ||||||
\(573\) | − | 7.11684i | − | 0.297310i | ||||||
\(574\) | 21.6277i | 0.902724i | ||||||||
\(575\) | − | 8.74456i | − | 0.364673i | ||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − | 35.7228i | − | 1.48716i | −0.668647 | − | 0.743580i | \(-0.733126\pi\) | ||
0.668647 | − | 0.743580i | \(-0.266874\pi\) | |||||||
\(578\) | 16.8614i | 0.701342i | ||||||||
\(579\) | 18.2337i | 0.757766i | ||||||||
\(580\) | −3.62772 | −0.150633 | ||||||||
\(581\) | 13.0217 | 0.540233 | ||||||||
\(582\) | 7.11684 | 0.295003 | ||||||||
\(583\) | −53.3505 | −2.20955 | ||||||||
\(584\) | − | 14.0000i | − | 0.579324i | ||||||
\(585\) | −4.74456 | −0.196164 | ||||||||
\(586\) | − | 13.1168i | − | 0.541852i | ||||||
\(587\) | − | 1.62772i | − | 0.0671831i | −0.999436 | − | 0.0335916i | \(-0.989305\pi\) | ||
0.999436 | − | 0.0335916i | \(-0.0106945\pi\) | |||||||
\(588\) | −1.37228 | −0.0565919 | ||||||||
\(589\) | 50.2337 | 2.06984 | ||||||||
\(590\) | − | 8.00000i | − | 0.329355i | ||||||
\(591\) | −15.4891 | −0.637137 | ||||||||
\(592\) | −5.74456 | − | 2.00000i | −0.236100 | − | 0.0821995i | ||||
\(593\) | −40.2337 | −1.65220 | −0.826100 | − | 0.563524i | \(-0.809445\pi\) | ||||
−0.826100 | + | 0.563524i | \(0.809445\pi\) | |||||||
\(594\) | − | 6.37228i | − | 0.261458i | ||||||
\(595\) | −0.883156 | −0.0362059 | ||||||||
\(596\) | −11.4891 | −0.470613 | ||||||||
\(597\) | − | 10.7446i | − | 0.439746i | ||||||
\(598\) | − | 41.4891i | − | 1.69662i | ||||||
\(599\) | 0.744563 | 0.0304220 | 0.0152110 | − | 0.999884i | \(-0.495158\pi\) | ||||
0.0152110 | + | 0.999884i | \(0.495158\pi\) | |||||||
\(600\) | − | 1.00000i | − | 0.0408248i | ||||||
\(601\) | 40.3723 | 1.64682 | 0.823410 | − | 0.567447i | \(-0.192069\pi\) | ||||
0.823410 | + | 0.567447i | \(0.192069\pi\) | |||||||
\(602\) | 10.3723 | 0.422743 | ||||||||
\(603\) | 8.74456 | 0.356106 | ||||||||
\(604\) | 11.2554 | 0.457977 | ||||||||
\(605\) | 29.6060i | 1.20365i | ||||||||
\(606\) | 5.25544i | 0.213488i | ||||||||
\(607\) | − | 3.76631i | − | 0.152870i | −0.997075 | − | 0.0764349i | \(-0.975646\pi\) | ||
0.997075 | − | 0.0764349i | \(-0.0243538\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | − | 8.60597i | − | 0.348731i | ||||||
\(610\) | − | 5.62772i | − | 0.227860i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.372281i | 0.0150486i | ||||||||
\(613\) | −31.3505 | −1.26624 | −0.633118 | − | 0.774055i | \(-0.718225\pi\) | ||||
−0.633118 | + | 0.774055i | \(0.718225\pi\) | |||||||
\(614\) | 2.51087i | 0.101331i | ||||||||
\(615\) | 9.11684i | 0.367627i | ||||||||
\(616\) | 15.1168i | 0.609075i | ||||||||
\(617\) | −37.2554 | −1.49985 | −0.749924 | − | 0.661524i | \(-0.769910\pi\) | ||||
−0.749924 | + | 0.661524i | \(0.769910\pi\) | |||||||
\(618\) | 7.48913 | 0.301257 | ||||||||
\(619\) | −9.62772 | −0.386971 | −0.193485 | − | 0.981103i | \(-0.561979\pi\) | ||||
−0.193485 | + | 0.981103i | \(0.561979\pi\) | |||||||
\(620\) | 8.37228 | 0.336239 | ||||||||
\(621\) | − | 8.74456i | − | 0.350907i | ||||||
\(622\) | −19.8614 | −0.796370 | ||||||||
\(623\) | 6.51087i | 0.260853i | ||||||||
\(624\) | − | 4.74456i | − | 0.189935i | ||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.2337 | −0.728765 | ||||||||
\(627\) | 38.2337i | 1.52691i | ||||||||
\(628\) | 16.3723 | 0.653325 | ||||||||
\(629\) | −0.744563 | + | 2.13859i | −0.0296877 | + | 0.0852713i | ||||
\(630\) | 2.37228 | 0.0945140 | ||||||||
\(631\) | 2.88316i | 0.114777i | 0.998352 | + | 0.0573883i | \(0.0182773\pi\) | ||||
−0.998352 | + | 0.0573883i | \(0.981723\pi\) | |||||||
\(632\) | 6.74456 | 0.268284 | ||||||||
\(633\) | −23.8614 | −0.948406 | ||||||||
\(634\) | 16.3723i | 0.650226i | ||||||||
\(635\) | − | 9.48913i | − | 0.376564i | ||||||
\(636\) | −8.37228 | −0.331983 | ||||||||
\(637\) | − | 6.51087i | − | 0.257970i | ||||||
\(638\) | 23.1168 | 0.915205 | ||||||||
\(639\) | −8.74456 | −0.345930 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −25.8614 | −1.02146 | −0.510732 | − | 0.859740i | \(-0.670626\pi\) | ||||
−0.510732 | + | 0.859740i | \(0.670626\pi\) | |||||||
\(642\) | − | 3.25544i | − | 0.128482i | ||||||
\(643\) | 29.1168i | 1.14826i | 0.818765 | + | 0.574128i | \(0.194659\pi\) | ||||
−0.818765 | + | 0.574128i | \(0.805341\pi\) | |||||||
\(644\) | 20.7446i | 0.817450i | ||||||||
\(645\) | 4.37228 | 0.172158 | ||||||||
\(646\) | − | 2.23369i | − | 0.0878833i | ||||||
\(647\) | − | 9.76631i | − | 0.383953i | −0.981399 | − | 0.191977i | \(-0.938510\pi\) | ||
0.981399 | − | 0.191977i | \(-0.0614898\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 50.9783i | 2.00107i | ||||||||
\(650\) | 4.74456 | 0.186097 | ||||||||
\(651\) | 19.8614i | 0.778430i | ||||||||
\(652\) | − | 9.11684i | − | 0.357043i | ||||||
\(653\) | 15.4891i | 0.606136i | 0.952969 | + | 0.303068i | \(0.0980110\pi\) | ||||
−0.952969 | + | 0.303068i | \(0.901989\pi\) | |||||||
\(654\) | −3.11684 | −0.121878 | ||||||||
\(655\) | −9.48913 | −0.370771 | ||||||||
\(656\) | −9.11684 | −0.355953 | ||||||||
\(657\) | 14.0000 | 0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.9783 | 1.83001 | 0.915006 | − | 0.403439i | \(-0.132185\pi\) | ||||
0.915006 | + | 0.403439i | \(0.132185\pi\) | |||||||
\(660\) | 6.37228i | 0.248041i | ||||||||
\(661\) | 29.3505i | 1.14160i | 0.821088 | + | 0.570802i | \(0.193367\pi\) | ||||
−0.821088 | + | 0.570802i | \(0.806633\pi\) | |||||||
\(662\) | −3.48913 | −0.135609 | ||||||||
\(663\) | −1.76631 | −0.0685979 | ||||||||
\(664\) | 5.48913i | 0.213019i | ||||||||
\(665\) | −14.2337 | −0.551959 | ||||||||
\(666\) | 2.00000 | − | 5.74456i | 0.0774984 | − | 0.222597i | ||||
\(667\) | 31.7228 | 1.22831 | ||||||||
\(668\) | 3.25544i | 0.125957i | ||||||||
\(669\) | −18.3723 | −0.710313 | ||||||||
\(670\) | −8.74456 | −0.337832 | ||||||||
\(671\) | 35.8614i | 1.38441i | ||||||||
\(672\) | 2.37228i | 0.0915127i | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | − | 34.7446i | − | 1.33831i | ||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 9.51087 | 0.365803 | ||||||||
\(677\) | 32.9783 | 1.26746 | 0.633729 | − | 0.773555i | \(-0.281524\pi\) | ||||
0.633729 | + | 0.773555i | \(0.281524\pi\) | |||||||
\(678\) | −9.86141 | −0.378725 | ||||||||
\(679\) | − | 16.8832i | − | 0.647916i | ||||||
\(680\) | − | 0.372281i | − | 0.0142763i | ||||||
\(681\) | − | 6.37228i | − | 0.244186i | ||||||
\(682\) | −53.3505 | −2.04290 | ||||||||
\(683\) | 18.3723i | 0.702996i | 0.936189 | + | 0.351498i | \(0.114328\pi\) | ||||
−0.936189 | + | 0.351498i | \(0.885672\pi\) | |||||||
\(684\) | 6.00000i | 0.229416i | ||||||||
\(685\) | − | 2.74456i | − | 0.104864i | ||||||
\(686\) | 19.8614i | 0.758312i | ||||||||
\(687\) | −4.51087 | −0.172101 | ||||||||
\(688\) | 4.37228i | 0.166692i | ||||||||
\(689\) | − | 39.7228i | − | 1.51332i | ||||||
\(690\) | 8.74456i | 0.332900i | ||||||||
\(691\) | 33.6277 | 1.27926 | 0.639629 | − | 0.768683i | \(-0.279088\pi\) | ||||
0.639629 | + | 0.768683i | \(0.279088\pi\) | |||||||
\(692\) | 7.62772 | 0.289962 | ||||||||
\(693\) | −15.1168 | −0.574241 | ||||||||
\(694\) | −30.9783 | −1.17592 | ||||||||
\(695\) | − | 1.62772i | − | 0.0617429i | ||||||
\(696\) | 3.62772 | 0.137508 | ||||||||
\(697\) | 3.39403i | 0.128558i | ||||||||
\(698\) | 11.4891i | 0.434870i | ||||||||
\(699\) | −14.7446 | −0.557691 | ||||||||
\(700\) | −2.37228 | −0.0896638 | ||||||||
\(701\) | 28.9783i | 1.09449i | 0.836971 | + | 0.547247i | \(0.184324\pi\) | ||||
−0.836971 | + | 0.547247i | \(0.815676\pi\) | |||||||
\(702\) | 4.74456 | 0.179072 | ||||||||
\(703\) | −12.0000 | + | 34.4674i | −0.452589 | + | 1.29996i | ||||
\(704\) | −6.37228 | −0.240164 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.11684 | 0.192575 | ||||||||
\(707\) | 12.4674 | 0.468884 | ||||||||
\(708\) | 8.00000i | 0.300658i | ||||||||
\(709\) | 39.8614i | 1.49703i | 0.663120 | + | 0.748513i | \(0.269232\pi\) | ||||
−0.663120 | + | 0.748513i | \(0.730768\pi\) | |||||||
\(710\) | 8.74456 | 0.328178 | ||||||||
\(711\) | 6.74456i | 0.252941i | ||||||||
\(712\) | −2.74456 | −0.102857 | ||||||||
\(713\) | −73.2119 | −2.74181 | ||||||||
\(714\) | 0.883156 | 0.0330513 | ||||||||
\(715\) | −30.2337 | −1.13068 | ||||||||
\(716\) | 8.74456i | 0.326800i | ||||||||
\(717\) | 7.86141i | 0.293590i | ||||||||
\(718\) | − | 8.00000i | − | 0.298557i | ||||||
\(719\) | 48.0000 | 1.79010 | 0.895049 | − | 0.445968i | \(-0.147140\pi\) | ||||
0.895049 | + | 0.445968i | \(0.147140\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | − | 17.7663i | − | 0.661652i | ||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | − | 21.4891i | − | 0.799189i | ||||||
\(724\) | −22.7446 | −0.845295 | ||||||||
\(725\) | 3.62772i | 0.134730i | ||||||||
\(726\) | − | 29.6060i | − | 1.09878i | ||||||
\(727\) | − | 18.4674i | − | 0.684917i | −0.939533 | − | 0.342459i | \(-0.888740\pi\) | ||
0.939533 | − | 0.342459i | \(-0.111260\pi\) | |||||||
\(728\) | −11.2554 | −0.417154 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.0000 | −0.518163 | ||||||||
\(731\) | 1.62772 | 0.0602034 | ||||||||
\(732\) | 5.62772i | 0.208006i | ||||||||
\(733\) | 38.6060 | 1.42594 | 0.712972 | − | 0.701192i | \(-0.247349\pi\) | ||||
0.712972 | + | 0.701192i | \(0.247349\pi\) | |||||||
\(734\) | 13.6277i | 0.503008i | ||||||||
\(735\) | 1.37228i | 0.0506174i | ||||||||
\(736\) | −8.74456 | −0.322329 | ||||||||
\(737\) | 55.7228 | 2.05258 | ||||||||
\(738\) | − | 9.11684i | − | 0.335596i | ||||||
\(739\) | 25.3505 | 0.932534 | 0.466267 | − | 0.884644i | \(-0.345599\pi\) | ||||
0.466267 | + | 0.884644i | \(0.345599\pi\) | |||||||
\(740\) | −2.00000 | + | 5.74456i | −0.0735215 | + | 0.211174i | ||||
\(741\) | −28.4674 | −1.04578 | ||||||||
\(742\) | 19.8614i | 0.729135i | ||||||||
\(743\) | 8.60597 | 0.315722 | 0.157861 | − | 0.987461i | \(-0.449540\pi\) | ||||
0.157861 | + | 0.987461i | \(0.449540\pi\) | |||||||
\(744\) | −8.37228 | −0.306943 | ||||||||
\(745\) | 11.4891i | 0.420929i | ||||||||
\(746\) | − | 23.4891i | − | 0.859998i | ||||||
\(747\) | −5.48913 | −0.200837 | ||||||||
\(748\) | 2.37228i | 0.0867392i | ||||||||
\(749\) | −7.72281 | −0.282185 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −3.25544 | −0.118793 | −0.0593963 | − | 0.998234i | \(-0.518918\pi\) | ||||
−0.0593963 | + | 0.998234i | \(0.518918\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.00000i | − | 0.145768i | ||||||
\(754\) | 17.2119i | 0.626822i | ||||||||
\(755\) | − | 11.2554i | − | 0.409627i | ||||||
\(756\) | −2.37228 | −0.0862790 | ||||||||
\(757\) | − | 22.5109i | − | 0.818172i | −0.912496 | − | 0.409086i | \(-0.865848\pi\) | ||
0.912496 | − | 0.409086i | \(-0.134152\pi\) | |||||||
\(758\) | 28.0000i | 1.01701i | ||||||||
\(759\) | − | 55.7228i | − | 2.02261i | ||||||
\(760\) | − | 6.00000i | − | 0.217643i | ||||||
\(761\) | 10.8832 | 0.394514 | 0.197257 | − | 0.980352i | \(-0.436797\pi\) | ||||
0.197257 | + | 0.980352i | \(0.436797\pi\) | |||||||
\(762\) | 9.48913i | 0.343755i | ||||||||
\(763\) | 7.39403i | 0.267682i | ||||||||
\(764\) | − | 7.11684i | − | 0.257478i | ||||||
\(765\) | 0.372281 | 0.0134599 | ||||||||
\(766\) | 35.7228 | 1.29072 | ||||||||
\(767\) | −37.9565 | −1.37053 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | − | 32.0000i | − | 1.15395i | −0.816762 | − | 0.576975i | \(-0.804233\pi\) | ||
0.816762 | − | 0.576975i | \(-0.195767\pi\) | |||||||
\(770\) | 15.1168 | 0.544773 | ||||||||
\(771\) | − | 23.4891i | − | 0.845940i | ||||||
\(772\) | 18.2337i | 0.656245i | ||||||||
\(773\) | 35.3505 | 1.27147 | 0.635735 | − | 0.771907i | \(-0.280697\pi\) | ||||
0.635735 | + | 0.771907i | \(0.280697\pi\) | |||||||
\(774\) | −4.37228 | −0.157158 | ||||||||
\(775\) | − | 8.37228i | − | 0.300741i | ||||||
\(776\) | 7.11684 | 0.255480 | ||||||||
\(777\) | −13.6277 | − | 4.74456i | −0.488892 | − | 0.170210i | ||||
\(778\) | −5.86141 | −0.210142 | ||||||||
\(779\) | 54.7011i | 1.95987i | ||||||||
\(780\) | −4.74456 | −0.169883 | ||||||||
\(781\) | −55.7228 | −1.99392 | ||||||||
\(782\) | 3.25544i | 0.116414i | ||||||||
\(783\) | 3.62772i | 0.129644i | ||||||||
\(784\) | −1.37228 | −0.0490100 | ||||||||
\(785\) | − | 16.3723i | − | 0.584352i | ||||||
\(786\) | 9.48913 | 0.338466 | ||||||||
\(787\) | −45.2119 | −1.61163 | −0.805816 | − | 0.592166i | \(-0.798273\pi\) | ||||
−0.805816 | + | 0.592166i | \(0.798273\pi\) | |||||||
\(788\) | −15.4891 | −0.551777 | ||||||||
\(789\) | −16.6060 | −0.591188 | ||||||||
\(790\) | − | 6.74456i | − | 0.239961i | ||||||
\(791\) | 23.3940i | 0.831796i | ||||||||
\(792\) | − | 6.37228i | − | 0.226429i | ||||||
\(793\) | −26.7011 | −0.948183 | ||||||||
\(794\) | − | 14.0000i | − | 0.496841i | ||||||
\(795\) | 8.37228i | 0.296934i | ||||||||
\(796\) | − | 10.7446i | − | 0.380831i | ||||||
\(797\) | − | 10.7446i | − | 0.380592i | −0.981727 | − | 0.190296i | \(-0.939055\pi\) | ||
0.981727 | − | 0.190296i | \(-0.0609448\pi\) | |||||||
\(798\) | 14.2337 | 0.503867 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | − | 2.74456i | − | 0.0969744i | ||||||
\(802\) | 28.9783 | 1.02326 | ||||||||
\(803\) | 89.2119 | 3.14822 | ||||||||
\(804\) | 8.74456 | 0.308397 | ||||||||
\(805\) | 20.7446 | 0.731150 | ||||||||
\(806\) | − | 39.7228i | − | 1.39918i | ||||||
\(807\) | 28.2337 | 0.993873 | ||||||||
\(808\) | 5.25544i | 0.184886i | ||||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 13.4891 | 0.473667 | 0.236834 | − | 0.971550i | \(-0.423890\pi\) | ||||
0.236834 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(812\) | − | 8.60597i | − | 0.302010i | ||||||
\(813\) | −1.48913 | −0.0522259 | ||||||||
\(814\) | 12.7446 | − | 36.6060i | 0.446697 | − | 1.28304i | ||||
\(815\) | −9.11684 | −0.319349 | ||||||||
\(816\) | 0.372281i | 0.0130325i | ||||||||
\(817\) | 26.2337 | 0.917801 | ||||||||
\(818\) | −21.4891 | −0.751350 | ||||||||
\(819\) | − | 11.2554i | − | 0.393297i | ||||||
\(820\) | 9.11684i | 0.318374i | ||||||||
\(821\) | 13.7228 | 0.478929 | 0.239465 | − | 0.970905i | \(-0.423028\pi\) | ||||
0.239465 | + | 0.970905i | \(0.423028\pi\) | |||||||
\(822\) | 2.74456i | 0.0957276i | ||||||||
\(823\) | 42.9783 | 1.49813 | 0.749064 | − | 0.662498i | \(-0.230504\pi\) | ||||
0.749064 | + | 0.662498i | \(0.230504\pi\) | |||||||
\(824\) | 7.48913 | 0.260896 | ||||||||
\(825\) | 6.37228 | 0.221854 | ||||||||
\(826\) | 18.9783 | 0.660338 | ||||||||
\(827\) | 3.86141i | 0.134274i | 0.997744 | + | 0.0671371i | \(0.0213865\pi\) | ||||
−0.997744 | + | 0.0671371i | \(0.978614\pi\) | |||||||
\(828\) | − | 8.74456i | − | 0.303895i | ||||||
\(829\) | − | 23.8614i | − | 0.828741i | −0.910108 | − | 0.414370i | \(-0.864002\pi\) | ||
0.910108 | − | 0.414370i | \(-0.135998\pi\) | |||||||
\(830\) | 5.48913 | 0.190530 | ||||||||
\(831\) | 9.48913i | 0.329174i | ||||||||
\(832\) | − | 4.74456i | − | 0.164488i | ||||||
\(833\) | 0.510875i | 0.0177008i | ||||||||
\(834\) | 1.62772i | 0.0563633i | ||||||||
\(835\) | 3.25544 | 0.112659 | ||||||||
\(836\) | 38.2337i | 1.32234i | ||||||||
\(837\) | − | 8.37228i | − | 0.289388i | ||||||
\(838\) | − | 8.00000i | − | 0.276355i | ||||||
\(839\) | −43.7228 | −1.50948 | −0.754740 | − | 0.656025i | \(-0.772237\pi\) | ||||
−0.754740 | + | 0.656025i | \(0.772237\pi\) | |||||||
\(840\) | 2.37228 | 0.0818515 | ||||||||
\(841\) | 15.8397 | 0.546195 | ||||||||
\(842\) | −8.74456 | −0.301358 | ||||||||
\(843\) | 20.9783i | 0.722529i | ||||||||
\(844\) | −23.8614 | −0.821343 | ||||||||
\(845\) | − | 9.51087i | − | 0.327184i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −70.2337 | −2.41326 | ||||||||
\(848\) | −8.37228 | −0.287505 | ||||||||
\(849\) | 30.7446i | 1.05515i | ||||||||
\(850\) | −0.372281 | −0.0127691 | ||||||||
\(851\) | 17.4891 | − | 50.2337i | 0.599519 | − | 1.72199i | ||||
\(852\) | −8.74456 | −0.299584 | ||||||||
\(853\) | 32.7446i | 1.12115i | 0.828103 | + | 0.560576i | \(0.189420\pi\) | ||||
−0.828103 | + | 0.560576i | \(0.810580\pi\) | |||||||
\(854\) | 13.3505 | 0.456846 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | − | 3.25544i | − | 0.111269i | ||||||
\(857\) | − | 18.6060i | − | 0.635568i | −0.948163 | − | 0.317784i | \(-0.897061\pi\) | ||
0.948163 | − | 0.317784i | \(-0.102939\pi\) | |||||||
\(858\) | 30.2337 | 1.03216 | ||||||||
\(859\) | 30.0000i | 1.02359i | 0.859109 | + | 0.511793i | \(0.171019\pi\) | ||||
−0.859109 | + | 0.511793i | \(0.828981\pi\) | |||||||
\(860\) | 4.37228 | 0.149094 | ||||||||
\(861\) | −21.6277 | −0.737071 | ||||||||
\(862\) | 13.6277 | 0.464162 | ||||||||
\(863\) | 47.5842 | 1.61979 | 0.809893 | − | 0.586578i | \(-0.199525\pi\) | ||||
0.809893 | + | 0.586578i | \(0.199525\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | − | 7.62772i | − | 0.259350i | ||||||
\(866\) | − | 11.4891i | − | 0.390416i | ||||||
\(867\) | −16.8614 | −0.572643 | ||||||||
\(868\) | 19.8614i | 0.674140i | ||||||||
\(869\) | 42.9783i | 1.45794i | ||||||||
\(870\) | − | 3.62772i | − | 0.122991i | ||||||
\(871\) | 41.4891i | 1.40581i | ||||||||
\(872\) | −3.11684 | −0.105550 | ||||||||
\(873\) | 7.11684i | 0.240869i | ||||||||
\(874\) | 52.4674i | 1.77474i | ||||||||
\(875\) | 2.37228i | 0.0801977i | ||||||||
\(876\) | 14.0000 | 0.473016 | ||||||||
\(877\) | 41.1168 | 1.38842 | 0.694209 | − | 0.719774i | \(-0.255755\pi\) | ||||
0.694209 | + | 0.719774i | \(0.255755\pi\) | |||||||
\(878\) | 12.3723 | 0.417544 | ||||||||
\(879\) | 13.1168 | 0.442420 | ||||||||
\(880\) | 6.37228i | 0.214810i | ||||||||
\(881\) | −43.6277 | −1.46986 | −0.734928 | − | 0.678146i | \(-0.762784\pi\) | ||||
−0.734928 | + | 0.678146i | \(0.762784\pi\) | |||||||
\(882\) | − | 1.37228i | − | 0.0462071i | ||||||
\(883\) | 33.8614i | 1.13953i | 0.821809 | + | 0.569764i | \(0.192965\pi\) | ||||
−0.821809 | + | 0.569764i | \(0.807035\pi\) | |||||||
\(884\) | −1.76631 | −0.0594075 | ||||||||
\(885\) | 8.00000 | 0.268917 | ||||||||
\(886\) | 4.00000i | 0.134383i | ||||||||
\(887\) | −10.3723 | −0.348267 | −0.174134 | − | 0.984722i | \(-0.555712\pi\) | ||||
−0.174134 | + | 0.984722i | \(0.555712\pi\) | |||||||
\(888\) | 2.00000 | − | 5.74456i | 0.0671156 | − | 0.192775i | ||||
\(889\) | 22.5109 | 0.754991 | ||||||||
\(890\) | 2.74456i | 0.0919979i | ||||||||
\(891\) | 6.37228 | 0.213479 | ||||||||
\(892\) | −18.3723 | −0.615149 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 11.4891i | − | 0.384254i | ||||||
\(895\) | 8.74456 | 0.292298 | ||||||||
\(896\) | 2.37228i | 0.0792524i | ||||||||
\(897\) | 41.4891 | 1.38528 | ||||||||
\(898\) | 36.9783 | 1.23398 | ||||||||
\(899\) | 30.3723 | 1.01297 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 3.11684i | 0.103837i | ||||||||
\(902\) | − | 58.0951i | − | 1.93436i | ||||||
\(903\) | 10.3723i | 0.345168i | ||||||||
\(904\) | −9.86141 | −0.327986 | ||||||||
\(905\) | 22.7446i | 0.756055i | ||||||||
\(906\) | 11.2554i | 0.373937i | ||||||||
\(907\) | − | 29.7228i | − | 0.986930i | −0.869766 | − | 0.493465i | \(-0.835730\pi\) | ||
0.869766 | − | 0.493465i | \(-0.164270\pi\) | |||||||
\(908\) | − | 6.37228i | − | 0.211472i | ||||||
\(909\) | −5.25544 | −0.174312 | ||||||||
\(910\) | 11.2554i | 0.373114i | ||||||||
\(911\) | − | 53.4891i | − | 1.77217i | −0.463519 | − | 0.886087i | \(-0.653413\pi\) | ||
0.463519 | − | 0.886087i | \(-0.346587\pi\) | |||||||
\(912\) | 6.00000i | 0.198680i | ||||||||
\(913\) | −34.9783 | −1.15761 | ||||||||
\(914\) | −5.62772 | −0.186148 | ||||||||
\(915\) | 5.62772 | 0.186047 | ||||||||
\(916\) | −4.51087 | −0.149043 | ||||||||
\(917\) | − | 22.5109i | − | 0.743375i | ||||||
\(918\) | −0.372281 | −0.0122871 | ||||||||
\(919\) | 33.7228i | 1.11241i | 0.831044 | + | 0.556206i | \(0.187744\pi\) | ||||
−0.831044 | + | 0.556206i | \(0.812256\pi\) | |||||||
\(920\) | 8.74456i | 0.288300i | ||||||||
\(921\) | −2.51087 | −0.0827361 | ||||||||
\(922\) | 14.6060 | 0.481022 | ||||||||
\(923\) | − | 41.4891i | − | 1.36563i | ||||||
\(924\) | −15.1168 | −0.497308 | ||||||||
\(925\) | 5.74456 | + | 2.00000i | 0.188880 | + | 0.0657596i | ||||
\(926\) | 12.2337 | 0.402024 | ||||||||
\(927\) | 7.48913i | 0.245975i | ||||||||
\(928\) | 3.62772 | 0.119086 | ||||||||
\(929\) | 22.6060 | 0.741678 | 0.370839 | − | 0.928697i | \(-0.379070\pi\) | ||||
0.370839 | + | 0.928697i | \(0.379070\pi\) | |||||||
\(930\) | 8.37228i | 0.274538i | ||||||||
\(931\) | 8.23369i | 0.269848i | ||||||||
\(932\) | −14.7446 | −0.482974 | ||||||||
\(933\) | − | 19.8614i | − | 0.650233i | ||||||
\(934\) | 26.3723 | 0.862927 | ||||||||
\(935\) | 2.37228 | 0.0775819 | ||||||||
\(936\) | 4.74456 | 0.155081 | ||||||||
\(937\) | 5.25544 | 0.171688 | 0.0858438 | − | 0.996309i | \(-0.472641\pi\) | ||||
0.0858438 | + | 0.996309i | \(0.472641\pi\) | |||||||
\(938\) | − | 20.7446i | − | 0.677334i | ||||||
\(939\) | − | 18.2337i | − | 0.595034i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.7228 | 0.447351 | 0.223675 | − | 0.974664i | \(-0.428194\pi\) | ||||
0.223675 | + | 0.974664i | \(0.428194\pi\) | |||||||
\(942\) | 16.3723i | 0.533438i | ||||||||
\(943\) | − | 79.7228i | − | 2.59613i | ||||||
\(944\) | 8.00000i | 0.260378i | ||||||||
\(945\) | 2.37228i | 0.0771703i | ||||||||
\(946\) | −27.8614 | −0.905852 | ||||||||
\(947\) | 51.8614i | 1.68527i | 0.538486 | + | 0.842635i | \(0.318997\pi\) | ||||
−0.538486 | + | 0.842635i | \(0.681003\pi\) | |||||||
\(948\) | 6.74456i | 0.219053i | ||||||||
\(949\) | 66.4239i | 2.15621i | ||||||||
\(950\) | −6.00000 | −0.194666 | ||||||||
\(951\) | −16.3723 | −0.530908 | ||||||||
\(952\) | 0.883156 | 0.0286233 | ||||||||
\(953\) | 43.9565 | 1.42389 | 0.711945 | − | 0.702235i | \(-0.247814\pi\) | ||||
0.711945 | + | 0.702235i | \(0.247814\pi\) | |||||||
\(954\) | − | 8.37228i | − | 0.271063i | ||||||
\(955\) | −7.11684 | −0.230296 | ||||||||
\(956\) | 7.86141i | 0.254256i | ||||||||
\(957\) | 23.1168i | 0.747261i | ||||||||
\(958\) | 10.9783 | 0.354691 | ||||||||
\(959\) | 6.51087 | 0.210247 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | −39.0951 | −1.26113 | ||||||||
\(962\) | 27.2554 | + | 9.48913i | 0.878751 | + | 0.305942i | ||||
\(963\) | 3.25544 | 0.104905 | ||||||||
\(964\) | − | 21.4891i | − | 0.692118i | ||||||
\(965\) | 18.2337 | 0.586963 | ||||||||
\(966\) | −20.7446 | −0.667445 | ||||||||
\(967\) | 19.4891i | 0.626728i | 0.949633 | + | 0.313364i | \(0.101456\pi\) | ||||
−0.949633 | + | 0.313364i | \(0.898544\pi\) | |||||||
\(968\) | − | 29.6060i | − | 0.951572i | ||||||
\(969\) | 2.23369 | 0.0717564 | ||||||||
\(970\) | − | 7.11684i | − | 0.228508i | ||||||
\(971\) | 5.35053 | 0.171707 | 0.0858534 | − | 0.996308i | \(-0.472638\pi\) | ||||
0.0858534 | + | 0.996308i | \(0.472638\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 3.86141 | 0.123791 | ||||||||
\(974\) | −18.7446 | −0.600615 | ||||||||
\(975\) | 4.74456i | 0.151948i | ||||||||
\(976\) | 5.62772i | 0.180139i | ||||||||
\(977\) | − | 42.6060i | − | 1.36309i | −0.731778 | − | 0.681543i | \(-0.761309\pi\) | ||
0.731778 | − | 0.681543i | \(-0.238691\pi\) | |||||||
\(978\) | 9.11684 | 0.291525 | ||||||||
\(979\) | − | 17.4891i | − | 0.558955i | ||||||
\(980\) | 1.37228i | 0.0438359i | ||||||||
\(981\) | − | 3.11684i | − | 0.0995132i | ||||||
\(982\) | 36.4674i | 1.16372i | ||||||||
\(983\) | −0.605969 | −0.0193274 | −0.00966371 | − | 0.999953i | \(-0.503076\pi\) | ||||
−0.00966371 | + | 0.999953i | \(0.503076\pi\) | |||||||
\(984\) | − | 9.11684i | − | 0.290634i | ||||||
\(985\) | 15.4891i | 0.493525i | ||||||||
\(986\) | − | 1.35053i | − | 0.0430097i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −28.4674 | −0.905668 | ||||||||
\(989\) | −38.2337 | −1.21576 | ||||||||
\(990\) | −6.37228 | −0.202524 | ||||||||
\(991\) | − | 29.8614i | − | 0.948579i | −0.880369 | − | 0.474289i | \(-0.842705\pi\) | ||
0.880369 | − | 0.474289i | \(-0.157295\pi\) | |||||||
\(992\) | −8.37228 | −0.265820 | ||||||||
\(993\) | − | 3.48913i | − | 0.110724i | ||||||
\(994\) | 20.7446i | 0.657978i | ||||||||
\(995\) | −10.7446 | −0.340626 | ||||||||
\(996\) | −5.48913 | −0.173930 | ||||||||
\(997\) | 48.4674i | 1.53498i | 0.641063 | + | 0.767489i | \(0.278494\pi\) | ||||
−0.641063 | + | 0.767489i | \(0.721506\pi\) | |||||||
\(998\) | −24.9783 | −0.790673 | ||||||||
\(999\) | 5.74456 | + | 2.00000i | 0.181750 | + | 0.0632772i |
(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 | 1110.2.h.e.961.3 | yes | 4 | |
3.2 | odd | 2 | 3330.2.h.k.2071.1 | 4 | |||
37.36 | even | 2 | inner | 1110.2.h.e.961.1 | ✓ | 4 | |
111.110 | odd | 2 | 3330.2.h.k.2071.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.h.e.961.1 | ✓ | 4 | 37.36 | even | 2 | inner | |
1110.2.h.e.961.3 | yes | 4 | 1.1 | even | 1 | trivial | |
3330.2.h.k.2071.1 | 4 | 3.2 | odd | 2 | |||
3330.2.h.k.2071.3 | 4 | 111.110 | odd | 2 |